LMFDB - Embedded newform 342.2.p.b.227.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(113,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("342.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{18} + 3 x^{17} - 15 x^{16} + 33 x^{15} - 42 x^{14} + 72 x^{12} - 243 x^{11} + \cdots + 59049 $ x^20 - x^19 + x^18 + 3x^17 - 15x^16 + 33x^15 - 42x^14 + 72x^12 - 243x^11 + 675x^10 - 729x^9 + 648x^8 - 3402x^6 + 8019x^5 - 10935x^4 + 6561x^3 + 6561x^2 - 19683*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.5
Root			$1.01548 + 1.40314i$ of defining polynomial
Character	$\chi$	$=$	342.227
Dual form			342.2.p.b.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.707416 + 1.58100i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.77331 + 1.60117i) q^{5} +(1.01548 + 1.40314i) q^{6} +(0.760344 - 1.31695i) q^{7} -1.00000 q^{8} +(-1.99912 - 2.23685i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.707416 + 1.58100i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.77331 + 1.60117i) q^{5} +(1.01548 + 1.40314i) q^{6} +(0.760344 - 1.31695i) q^{7} -1.00000 q^{8} +(-1.99912 - 2.23685i) q^{9} +3.20235i q^{10} +(-3.69166 - 2.13138i) q^{11} +(1.72289 - 0.177860i) q^{12} +(-2.19748 + 1.26872i) q^{13} +(-0.760344 - 1.31695i) q^{14} +(-0.569568 - 5.51730i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.67109i q^{17} +(-2.93673 + 0.612867i) q^{18} +(-2.68816 + 3.43130i) q^{19} +(2.77331 + 1.60117i) q^{20} +(1.54422 + 2.13374i) q^{21} +(-3.69166 + 2.13138i) q^{22} +(-5.53874 + 3.19780i) q^{23} +(0.707416 - 1.58100i) q^{24} +(2.62751 - 4.55098i) q^{25} +2.53743i q^{26} +(4.95068 - 1.57823i) q^{27} -1.52069 q^{28} +(-3.08137 + 5.33710i) q^{29} +(-5.06291 - 2.26539i) q^{30} +(4.80457 - 2.77392i) q^{31} +(0.500000 + 0.866025i) q^{32} +(5.98126 - 4.32875i) q^{33} +(-4.04528 - 2.33554i) q^{34} +4.86977i q^{35} +(-0.937608 + 2.84972i) q^{36} +0.247975i q^{37} +(1.62751 + 4.04366i) q^{38} +(-0.451307 - 4.37173i) q^{39} +(2.77331 - 1.60117i) q^{40} +(-0.107795 - 0.186707i) q^{41} +(2.61998 - 0.270469i) q^{42} +(1.40210 - 2.42852i) q^{43} +4.26277i q^{44} +(9.12578 + 3.00254i) q^{45} +6.39559i q^{46} +(7.45554 + 4.30446i) q^{47} +(-1.01548 - 1.40314i) q^{48} +(2.34375 + 4.05950i) q^{49} +(-2.62751 - 4.55098i) q^{50} +(7.38499 + 3.30441i) q^{51} +(2.19748 + 1.26872i) q^{52} -13.5109 q^{53} +(1.10855 - 5.07653i) q^{54} +13.6508 q^{55} +(-0.760344 + 1.31695i) q^{56} +(-3.52323 - 6.67734i) q^{57} +(3.08137 + 5.33710i) q^{58} +(0.290473 + 0.503113i) q^{59} +(-4.49334 + 3.25191i) q^{60} +(3.86921 - 6.70166i) q^{61} -5.54784i q^{62} +(-4.46585 + 0.931978i) q^{63} +1.00000 q^{64} +(4.06287 - 7.03710i) q^{65} +(-0.758173 - 7.34430i) q^{66} +(-5.60803 + 3.23780i) q^{67} +(-4.04528 + 2.33554i) q^{68} +(-1.13752 - 11.0189i) q^{69} +(4.21734 + 2.43488i) q^{70} +9.99801 q^{71} +(1.99912 + 2.23685i) q^{72} -13.3133 q^{73} +(0.214753 + 0.123988i) q^{74} +(5.33635 + 7.37353i) q^{75} +(4.31567 + 0.612369i) q^{76} +(-5.61387 + 3.24117i) q^{77} +(-4.01169 - 1.79502i) q^{78} +(-3.36054 - 1.94021i) q^{79} -3.20235i q^{80} +(-1.00701 + 8.94349i) q^{81} -0.215591 q^{82} +(5.32565 + 3.07477i) q^{83} +(1.07576 - 2.40421i) q^{84} +(7.47922 + 12.9544i) q^{85} +(-1.40210 - 2.42852i) q^{86} +(-6.25814 - 8.64720i) q^{87} +(3.69166 + 2.13138i) q^{88} -12.4040 q^{89} +(7.16317 - 6.40189i) q^{90} +3.85865i q^{91} +(5.53874 + 3.19780i) q^{92} +(0.986737 + 9.55835i) q^{93} +(7.45554 - 4.30446i) q^{94} +(1.96102 - 13.8203i) q^{95} +(-1.72289 + 0.177860i) q^{96} +(-2.24692 - 1.29726i) q^{97} +4.68751 q^{98} +(2.61251 + 12.5186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} - q^{3} - 10 q^{4} + q^{6} + 2 q^{7} - 20 q^{8} - q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 - q^3 - 10 * q^4 + q^6 + 2 * q^7 - 20 * q^8 - q^9	$ 20 q + 10 q^{2} - q^{3} - 10 q^{4} + q^{6} + 2 q^{7} - 20 q^{8} - q^{9} - 3 q^{11} + 2 q^{12} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{18} + q^{19} - 11 q^{21} - 3 q^{22} - 12 q^{23} + q^{24} + 10 q^{25} + 11 q^{27} - 4 q^{28} + 2 q^{30} - 18 q^{31} + 10 q^{32} + q^{33} + 15 q^{34} - q^{36} - 10 q^{38} + 9 q^{39} + 3 q^{41} - 13 q^{42} - 5 q^{43} - 14 q^{45} + 39 q^{47} - q^{48} - 12 q^{49} - 10 q^{50} + q^{51} - 17 q^{54} - 2 q^{56} - q^{57} - 3 q^{59} - 14 q^{60} + 14 q^{61} - 2 q^{63} + 20 q^{64} - 12 q^{65} - 22 q^{66} - 27 q^{67} + 15 q^{68} + 4 q^{69} - 24 q^{71} + q^{72} + 34 q^{73} + 33 q^{74} + 27 q^{75} - 11 q^{76} - 24 q^{77} + 27 q^{78} + 18 q^{79} - q^{81} + 6 q^{82} + 30 q^{83} - 2 q^{84} + 5 q^{86} - 69 q^{87} + 3 q^{88} - 36 q^{89} + 8 q^{90} + 12 q^{92} + 54 q^{93} + 39 q^{94} + 36 q^{95} - 2 q^{96} - 27 q^{97} - 24 q^{98} + 52 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 - q^3 - 10 * q^4 + q^6 + 2 * q^7 - 20 * q^8 - q^9 - 3 * q^11 + 2 * q^12 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^18 + q^19 - 11 * q^21 - 3 * q^22 - 12 * q^23 + q^24 + 10 * q^25 + 11 * q^27 - 4 * q^28 + 2 * q^30 - 18 * q^31 + 10 * q^32 + q^33 + 15 * q^34 - q^36 - 10 * q^38 + 9 * q^39 + 3 * q^41 - 13 * q^42 - 5 * q^43 - 14 * q^45 + 39 * q^47 - q^48 - 12 * q^49 - 10 * q^50 + q^51 - 17 * q^54 - 2 * q^56 - q^57 - 3 * q^59 - 14 * q^60 + 14 * q^61 - 2 * q^63 + 20 * q^64 - 12 * q^65 - 22 * q^66 - 27 * q^67 + 15 * q^68 + 4 * q^69 - 24 * q^71 + q^72 + 34 * q^73 + 33 * q^74 + 27 * q^75 - 11 * q^76 - 24 * q^77 + 27 * q^78 + 18 * q^79 - q^81 + 6 * q^82 + 30 * q^83 - 2 * q^84 + 5 * q^86 - 69 * q^87 + 3 * q^88 - 36 * q^89 + 8 * q^90 + 12 * q^92 + 54 * q^93 + 39 * q^94 + 36 * q^95 - 2 * q^96 - 27 * q^97 - 24 * q^98 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.707416	+	1.58100i	−0.408427	+	0.912791i
$3$	−0.707416	+	1.58100i	−0.408427	+	0.912791i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.77331	+	1.60117i	−1.24026	+	0.716066i	−0.969148	−	0.246481i	$-0.920726\pi$
$5$	−2.77331	+	1.60117i	−1.24026	+	0.716066i	−0.271115	+	0.962547i	$0.587392\pi$
$6$	1.01548	+	1.40314i	0.414567	+	0.572830i
$7$	0.760344	−	1.31695i	0.287383	−	0.497762i	−0.685801	−	0.727789i	$-0.740548\pi$
$7$	0.760344	−	1.31695i	0.287383	−	0.497762i	0.973184	+	0.230027i	$0.0738814\pi$
$8$	−1.00000			−0.353553
$9$	−1.99912	−	2.23685i	−0.666375	−	0.745617i
$10$			3.20235i			1.01267i
$11$	−3.69166	−	2.13138i	−1.11308	−	0.642636i	−0.173453	−	0.984842i	$-0.555493\pi$
$11$	−3.69166	−	2.13138i	−1.11308	−	0.642636i	−0.939625	+	0.342206i	$0.888826\pi$
$12$	1.72289	−	0.177860i	0.497357	−	0.0513436i
$13$	−2.19748	+	1.26872i	−0.609472	+	0.351879i	−0.772759	−	0.634700i	$-0.781124\pi$
$13$	−2.19748	+	1.26872i	−0.609472	+	0.351879i	0.163287	+	0.986579i	$0.447790\pi$
$14$	−0.760344	−	1.31695i	−0.203210	−	0.351971i
$15$	−0.569568	−	5.51730i	−0.147062	−	1.42456i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	4.67109i		−	1.13291i	−0.824094	−	0.566453i	$-0.808315\pi$
$17$		−	4.67109i		−	1.13291i	0.824094	−	0.566453i	$-0.191685\pi$
$18$	−2.93673	+	0.612867i	−0.692194	+	0.144454i
$19$	−2.68816	+	3.43130i	−0.616707	+	0.787193i
$19$	−2.68816	+	3.43130i	−0.616707	+	0.787193i
$20$	2.77331	+	1.60117i	0.620132	+	0.358033i
$21$	1.54422	+	2.13374i	0.336978	+	0.465620i
$22$	−3.69166	+	2.13138i	−0.787065	+	0.454412i
$23$	−5.53874	+	3.19780i	−1.15491	+	0.666787i	−0.950078	−	0.312011i	$-0.898997\pi$
$23$	−5.53874	+	3.19780i	−1.15491	+	0.666787i	−0.204830	+	0.978798i	$0.565664\pi$
$24$	0.707416	−	1.58100i	0.144401	−	0.322720i
$25$	2.62751	−	4.55098i	0.525502	−	0.910195i
$26$			2.53743i			0.497632i
$27$	4.95068	−	1.57823i	0.952758	−	0.303731i
$28$	−1.52069			−0.287383
$29$	−3.08137	+	5.33710i	−0.572197	+	0.991074i	0.424143	+	0.905595i	$0.360575\pi$
$29$	−3.08137	+	5.33710i	−0.572197	+	0.991074i	−0.996340	+	0.0854788i	$0.972758\pi$
$30$	−5.06291	−	2.26539i	−0.924356	−	0.413602i
$31$	4.80457	−	2.77392i	0.862926	−	0.498211i	−0.00206471	−	0.999998i	$-0.500657\pi$
$31$	4.80457	−	2.77392i	0.862926	−	0.498211i	0.864991	+	0.501787i	$0.167324\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	5.98126	−	4.32875i	1.04120	−	0.753538i
$34$	−4.04528	−	2.33554i	−0.693760	−	0.400543i
$35$			4.86977i			0.823141i
$36$	−0.937608	+	2.84972i	−0.156268	+	0.474953i
$37$			0.247975i			0.0407669i	0.999792	+	0.0203834i	$0.00648870\pi$
$37$			0.247975i			0.0407669i	−0.999792	+	0.0203834i	$0.993511\pi$
$38$	1.62751	+	4.04366i	0.264017	+	0.655969i
$39$	−0.451307	−	4.37173i	−0.0722670	−	0.700038i
$40$	2.77331	−	1.60117i	0.438499	−	0.253168i
$41$	−0.107795	−	0.186707i	−0.0168348	−	0.0291588i	0.857485	−	0.514509i	$-0.172026\pi$
$41$	−0.107795	−	0.186707i	−0.0168348	−	0.0291588i	−0.874320	+	0.485350i	$0.838692\pi$
$42$	2.61998	−	0.270469i	0.404272	−	0.0417342i
$43$	1.40210	−	2.42852i	0.213819	−	0.370345i	−0.739088	−	0.673609i	$-0.764743\pi$
$43$	1.40210	−	2.42852i	0.213819	−	0.370345i	0.952907	+	0.303264i	$0.0980764\pi$
$44$			4.26277i			0.642636i
$45$	9.12578	+	3.00254i	1.36039	+	0.447593i
$46$			6.39559i			0.942979i
$47$	7.45554	+	4.30446i	1.08750	+	0.627869i	0.932910	−	0.360109i	$-0.117261\pi$
$47$	7.45554	+	4.30446i	1.08750	+	0.627869i	0.154591	+	0.987978i	$0.450594\pi$
$48$	−1.01548	−	1.40314i	−0.146572	−	0.202526i
$49$	2.34375	+	4.05950i	0.334822	+	0.579929i
$50$	−2.62751	−	4.55098i	−0.371586	−	0.643605i
$51$	7.38499	+	3.30441i	1.03411	+	0.462709i
$52$	2.19748	+	1.26872i	0.304736	+	0.175939i
$53$	−13.5109			−1.85586			−0.927932	−	0.372749i	$-0.878415\pi$
$53$	−13.5109			−1.85586			−0.927932	+	0.372749i	$0.878415\pi$
$54$	1.10855	−	5.07653i	0.150855	−	0.690828i
$55$	13.6508			1.84068
$56$	−0.760344	+	1.31695i	−0.101605	+	0.175985i
$57$	−3.52323	−	6.67734i	−0.466663	−	0.884435i
$58$	3.08137	+	5.33710i	0.404604	+	0.700795i
$59$	0.290473	+	0.503113i	0.0378163	+	0.0654998i	0.884314	−	0.466892i	$-0.154626\pi$
$59$	0.290473	+	0.503113i	0.0378163	+	0.0654998i	−0.846498	+	0.532392i	$0.821293\pi$
$60$	−4.49334	+	3.25191i	−0.580088	+	0.419820i
$61$	3.86921	−	6.70166i	0.495401	−	0.858060i	−0.504585	−	0.863362i	$-0.668354\pi$
$61$	3.86921	−	6.70166i	0.495401	−	0.858060i	0.999986	+	0.00530199i	$0.00168768\pi$
$62$		−	5.54784i		−	0.704577i
$63$	−4.46585	+	0.931978i	−0.562644	+	0.117418i
$64$	1.00000			0.125000
$65$	4.06287	−	7.03710i	0.503937	−	0.872845i
$66$	−0.758173	−	7.34430i	−0.0933247	−	0.904020i
$67$	−5.60803	+	3.23780i	−0.685130	+	0.395560i	−0.801785	−	0.597613i	$-0.796116\pi$
$67$	−5.60803	+	3.23780i	−0.685130	+	0.395560i	0.116655	+	0.993172i	$0.462783\pi$
$68$	−4.04528	+	2.33554i	−0.490563	+	0.283226i
$69$	−1.13752	−	11.0189i	−0.136941	−	1.32652i
$70$	4.21734	+	2.43488i	0.504069	+	0.291024i
$71$	9.99801			1.18654			0.593272	−	0.805002i	$-0.297836\pi$
$71$	9.99801			1.18654			0.593272	+	0.805002i	$0.297836\pi$
$72$	1.99912	+	2.23685i	0.235599	+	0.263615i
$73$	−13.3133			−1.55820			−0.779101	−	0.626899i	$-0.784324\pi$
$73$	−13.3133			−1.55820			−0.779101	+	0.626899i	$0.784324\pi$
$74$	0.214753	+	0.123988i	0.0249645	+	0.0144133i
$75$	5.33635	+	7.37353i	0.616189	+	0.851422i
$76$	4.31567	+	0.612369i	0.495041	+	0.0702435i
$77$	−5.61387	+	3.24117i	−0.639759	+	0.369365i
$78$	−4.01169	−	1.79502i	−0.454234	−	0.203246i
$79$	−3.36054	−	1.94021i	−0.378091	−	0.218291i	0.298897	−	0.954286i	$-0.403381\pi$
$79$	−3.36054	−	1.94021i	−0.378091	−	0.218291i	−0.676987	+	0.735995i	$0.736715\pi$
$80$		−	3.20235i		−	0.358033i
$81$	−1.00701	+	8.94349i	−0.111890	+	0.993721i
$82$	−0.215591			−0.0238080
$83$	5.32565	+	3.07477i	0.584566	+	0.337499i	0.762946	−	0.646462i	$-0.223752\pi$
$83$	5.32565	+	3.07477i	0.584566	+	0.337499i	−0.178380	+	0.983962i	$0.557086\pi$
$84$	1.07576	−	2.40421i	0.117375	−	0.262321i
$85$	7.47922	+	12.9544i	0.811235	+	1.40510i
$86$	−1.40210	−	2.42852i	−0.151193	−	0.261874i
$87$	−6.25814	−	8.64720i	−0.670943	−	0.927078i
$88$	3.69166	+	2.13138i	0.393533	+	0.227206i
$89$	−12.4040			−1.31482			−0.657410	−	0.753533i	$-0.728348\pi$
$89$	−12.4040			−1.31482			−0.657410	+	0.753533i	$0.728348\pi$
$90$	7.16317	−	6.40189i	0.755064	−	0.674818i
$91$			3.85865i			0.404496i
$92$	5.53874	+	3.19780i	0.577454	+	0.333393i
$93$	0.986737	+	9.55835i	0.102320	+	0.991154i
$94$	7.45554	−	4.30446i	0.768980	−	0.443971i
$95$	1.96102	−	13.8203i	0.201196	−	1.41793i
$96$	−1.72289	+	0.177860i	−0.175842	+	0.0181527i
$97$	−2.24692	−	1.29726i	−0.228140	−	0.131717i	0.381574	−	0.924338i	$-0.375382\pi$
$97$	−2.24692	−	1.29726i	−0.228140	−	0.131717i	−0.609714	+	0.792622i	$0.708716\pi$
$98$	4.68751			0.473510
$99$	2.61251	+	12.5186i	0.262567	+	1.25817i
$100$	−5.25502			−0.525502
$101$	−10.0450	−	5.79949i	−0.999515	−	0.577070i	−0.0914103	−	0.995813i	$-0.529137\pi$
$101$	−10.0450	−	5.79949i	−0.999515	−	0.577070i	−0.908105	+	0.418743i	$0.862471\pi$
$102$	6.55420	−	4.74339i	0.648962	−	0.469666i
$103$	8.78440	−	5.07167i	0.865552	−	0.499727i	−0.000315413	−	1.00000i	$-0.500100\pi$
$103$	8.78440	−	5.07167i	0.865552	−	0.499727i	0.865868	+	0.500273i	$0.166767\pi$
$104$	2.19748	−	1.26872i	0.215481	−	0.124408i
$105$	−7.69910	−	3.44495i	−0.751355	−	0.336193i
$106$	−6.75545	+	11.7008i	−0.656147	+	1.13648i
$107$	9.34489			0.903404			0.451702	−	0.892169i	$-0.350817\pi$
$107$	9.34489			0.903404			0.451702	+	0.892169i	$0.350817\pi$
$108$	−3.84213	−	3.49830i	−0.369709	−	0.336624i
$109$		−	4.86226i		−	0.465720i	−0.972510	−	0.232860i	$-0.925192\pi$
$109$		−	4.86226i		−	0.465720i	0.972510	−	0.232860i	$-0.0748084\pi$
$110$	6.82542	−	11.8220i	0.650779	−	1.12718i
$111$	−0.392049	−	0.175422i	−0.0372116	−	0.0166503i
$112$	0.760344	+	1.31695i	0.0718457	+	0.124440i
$113$	−2.59521	−	4.49503i	−0.244137	−	0.422857i	0.717752	−	0.696299i	$-0.245171\pi$
$113$	−2.59521	−	4.49503i	−0.244137	−	0.422857i	−0.961889	+	0.273442i	$0.911838\pi$
$114$	−7.54436	−	0.287464i	−0.706594	−	0.0269234i
$115$	10.2404	−	17.7370i	0.954927	−	1.65398i
$116$	6.16275			0.572197
$117$	7.23097	+	2.37912i	0.668504	+	0.219950i
$118$	0.580945			0.0534803
$119$	−6.15161	−	3.55163i	−0.563917	−	0.325578i
$120$	0.569568	+	5.51730i	0.0519942	+	0.503659i
$121$	3.58558	+	6.21041i	0.325962	+	0.564583i
$122$	−3.86921	−	6.70166i	−0.350302	−	0.606740i
$123$	0.371441	−	0.0383449i	0.0334917	−	0.00345744i
$124$	−4.80457	−	2.77392i	−0.431463	−	0.249105i
$125$			0.816649i			0.0730433i
$126$	−1.42581	+	4.33353i	−0.127021	+	0.386062i
$127$			19.0260i			1.68829i	0.536117	+	0.844144i	$0.319891\pi$
$127$			19.0260i			1.68829i	−0.536117	+	0.844144i	$0.680109\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.84761	+	3.93470i	0.250718	+	0.346431i
$130$	−4.06287	−	7.03710i	−0.356337	−	0.617194i
$131$	6.24932	−	3.60805i	0.546005	−	0.315236i	−0.201504	−	0.979488i	$-0.564583\pi$
$131$	6.24932	−	3.60805i	0.546005	−	0.315236i	0.747509	+	0.664251i	$0.231250\pi$
$132$	−6.73943	−	3.01555i	−0.586592	−	0.262470i
$133$	2.47493	+	6.14915i	0.214604	+	0.533199i
$134$			6.47560i			0.559406i
$135$	−11.2028	+	12.3038i	−0.964179	+	1.05894i
$136$			4.67109i			0.400543i
$137$	−16.9726	−	9.79911i	−1.45006	−	0.837195i	−0.451579	−	0.892231i	$-0.649139\pi$
$137$	−16.9726	−	9.79911i	−1.45006	−	0.837195i	−0.998484	+	0.0550362i	$0.982473\pi$
$138$	−10.1114	−	4.52435i	−0.860742	−	0.385138i
$139$	−5.31583	−	9.20729i	−0.450883	−	0.780953i	0.547558	−	0.836768i	$-0.315558\pi$
$139$	−5.31583	−	9.20729i	−0.450883	−	0.780953i	−0.998441	+	0.0558152i	$0.982224\pi$
$140$	4.21734	−	2.43488i	0.356430	−	0.205785i
$141$	−12.0795	+	8.74216i	−1.01728	+	0.736223i
$142$	4.99900	−	8.65853i	0.419507	−	0.726607i
$143$	10.8165			0.904520
$144$	2.93673	−	0.612867i	0.244728	−	0.0510722i
$145$		−	19.7352i		−	1.63892i
$146$	−6.65664	+	11.5296i	−0.550907	+	0.954200i
$147$	−8.07609	+	0.833718i	−0.666104	+	0.0687639i
$148$	0.214753	−	0.123988i	0.0176526	−	0.0101917i
$149$	16.5766	−	9.57051i	1.35801	−	0.784047i	0.368653	−	0.929567i	$-0.379819\pi$
$149$	16.5766	−	9.57051i	1.35801	−	0.784047i	0.989355	+	0.145520i	$0.0464856\pi$
$150$	9.05384	−	0.934655i	0.739243	−	0.0763142i
$151$	−13.5513	−	7.82382i	−1.10279	−	0.636693i	−0.165834	−	0.986154i	$-0.553032\pi$
$151$	−13.5513	−	7.82382i	−1.10279	−	0.636693i	−0.936951	+	0.349460i	$0.886365\pi$
$152$	2.68816	−	3.43130i	0.218039	−	0.278315i
$153$	−10.4485	+	9.33809i	−0.844714	+	0.754940i
$154$			6.48233i			0.522361i
$155$	−8.88305	+	15.3859i	−0.713504	+	1.23582i
$156$	−3.56038	+	2.57671i	−0.285058	+	0.206302i
$157$	5.68649	+	9.84929i	0.453831	+	0.786059i	0.998620	−	0.0525143i	$-0.0167235\pi$
$157$	5.68649	+	9.84929i	0.453831	+	0.786059i	−0.544789	+	0.838573i	$0.683390\pi$
$158$	−3.36054	+	1.94021i	−0.267350	+	0.154355i
$159$	9.55783	−	21.3607i	0.757985	−	1.69402i
$160$	−2.77331	−	1.60117i	−0.219250	−	0.126584i
$161$			9.72570i			0.766492i
$162$	7.24178	+	5.34384i	0.568968	+	0.419851i
$163$	−21.1943			−1.66007			−0.830034	−	0.557713i	$-0.811679\pi$
$163$	−21.1943			−1.66007			−0.830034	+	0.557713i	$0.811679\pi$
$164$	−0.107795	+	0.186707i	−0.00841741	+	0.0145794i
$165$	−9.65683	+	21.5820i	−0.751783	+	1.68016i
$166$	5.32565	−	3.07477i	0.413351	−	0.238648i
$167$	12.0669	+	20.9004i	0.933762	+	1.61732i	0.776826	+	0.629715i	$0.216828\pi$
$167$	12.0669	+	20.9004i	0.933762	+	1.61732i	0.156936	+	0.987609i	$0.449838\pi$
$168$	−1.54422	−	2.13374i	−0.119140	−	0.164621i
$169$	−3.28071	+	5.68236i	−0.252362	+	0.437105i
$170$	14.9584			1.14726
$171$	13.0493	−	0.846567i	0.997902	−	0.0647386i
$172$	−2.80421			−0.213819
$173$	−11.0711	+	19.1757i	−0.841720	+	1.45790i	0.0467193	+	0.998908i	$0.485123\pi$
$173$	−11.0711	+	19.1757i	−0.841720	+	1.45790i	−0.888439	+	0.458994i	$0.848210\pi$
$174$	−10.6178	+	1.09610i	−0.804931	+	0.0830954i
$175$	−3.99562	−	6.92061i	−0.302040	−	0.523149i
$176$	3.69166	−	2.13138i	0.278270	−	0.160659i
$177$	−1.00091	+	0.103327i	−0.0752328	+	0.00776651i
$178$	−6.20199	+	10.7422i	−0.464859	+	0.805159i
$179$	−16.7184			−1.24959			−0.624796	−	0.780788i	$-0.714818\pi$
$179$	−16.7184			−1.24959			−0.624796	+	0.780788i	$0.714818\pi$
$180$	−1.96261	−	9.40443i	−0.146284	−	0.700965i
$181$		−	1.92544i		−	0.143116i	−0.997436	−	0.0715582i	$-0.977203\pi$
$181$		−	1.92544i		−	0.143116i	0.997436	−	0.0715582i	$-0.0227972\pi$
$182$	3.34168	+	1.92932i	0.247702	+	0.143011i
$183$	7.85819	+	10.8581i	0.580894	+	0.802653i
$184$	5.53874	−	3.19780i	0.408322	−	0.235745i
$185$	−0.397051	−	0.687713i	−0.0291918	−	0.0505617i
$186$	8.77114	+	3.92463i	0.643131	+	0.287768i
$187$	−9.95588	+	17.2441i	−0.728046	+	1.26101i
$188$		−	8.60891i		−	0.627869i
$189$	1.68576	−	7.71981i	0.122621	−	0.561533i
$190$	−10.9882	−	8.60842i	−0.797167	−	0.624521i
$191$	0.637900	+	0.368292i	0.0461568	+	0.0266487i	0.522901	−	0.852394i	$-0.324850\pi$
$191$	0.637900	+	0.368292i	0.0461568	+	0.0266487i	−0.476744	+	0.879042i	$0.658183\pi$
$192$	−0.707416	+	1.58100i	−0.0510534	+	0.114099i
$193$	−7.89658	+	4.55909i	−0.568408	+	0.328171i	−0.756513	−	0.653978i	$-0.773099\pi$
$193$	−7.89658	+	4.55909i	−0.568408	+	0.328171i	0.188105	+	0.982149i	$0.439765\pi$
$194$	−2.24692	+	1.29726i	−0.161319	+	0.0931377i
$195$	8.25151	+	11.4016i	0.590903	+	0.816483i
$196$	2.34375	−	4.05950i	0.167411	−	0.289964i
$197$		−	8.47801i		−	0.604033i	−0.953303	−	0.302017i	$-0.902340\pi$
$197$		−	8.47801i		−	0.604033i	0.953303	−	0.302017i	$-0.0976598\pi$
$198$	12.1477	+	3.99680i	0.863298	+	0.284040i
$199$	16.4335			1.16494			0.582470	−	0.812852i	$-0.302086\pi$
$199$	16.4335			1.16494			0.582470	+	0.812852i	$0.302086\pi$
$200$	−2.62751	+	4.55098i	−0.185793	+	0.321803i
$201$	−1.15175	−	11.1568i	−0.0812379	−	0.786938i
$202$	−10.0450	+	5.79949i	−0.706764	+	0.408050i
$203$	4.68581	+	8.11606i	0.328879	+	0.569635i
$204$	−0.830798	−	8.04780i	−0.0581675	−	0.563458i
$205$	0.597901	+	0.345198i	0.0417592	+	0.0241097i
$206$		−	10.1433i		−	0.706720i
$207$	18.2256	+	5.99656i	1.26677	+	0.416790i
$208$		−	2.53743i		−	0.175939i
$209$	17.2372	−	6.93768i	1.19232	−	0.479890i
$210$	−6.83297	+	4.94514i	−0.471520	+	0.341247i
$211$	−0.803576	+	0.463945i	−0.0553204	+	0.0319393i	−0.527405	−	0.849614i	$-0.676835\pi$
$211$	−0.803576	+	0.463945i	−0.0553204	+	0.0319393i	0.472085	+	0.881553i	$0.343502\pi$
$212$	6.75545	+	11.7008i	0.463966	+	0.803613i
$213$	−7.07275	+	15.8068i	−0.484617	+	1.08307i
$214$	4.67244	−	8.09291i	0.319402	−	0.553220i
$215$			8.98004i			0.612434i
$216$	−4.95068	+	1.57823i	−0.336851	+	0.107385i
$217$		−	8.43653i		−	0.572709i
$218$	−4.21084	−	2.43113i	−0.285194	−	0.164657i
$219$	9.41803	−	21.0483i	0.636412	−	1.42231i
$220$	−6.82542	−	11.8220i	−0.460170	−	0.797038i
$221$	5.92629	+	10.2646i	0.398646	+	0.690474i
$222$	−0.347944	+	0.251814i	−0.0233525	+	0.0169006i
$223$	−16.6727	−	9.62600i	−1.11649	−	0.644605i	−0.175986	−	0.984393i	$-0.556311\pi$
$223$	−16.6727	−	9.62600i	−1.11649	−	0.644605i	−0.940502	+	0.339788i	$0.889645\pi$
$224$	1.52069			0.101605
$225$	−15.4326	+	3.22062i	−1.02884	+	0.214708i
$226$	−5.19041			−0.345261
$227$	10.5610	−	18.2921i	0.700955	−	1.21409i	−0.267176	−	0.963648i	$-0.586091\pi$
$227$	10.5610	−	18.2921i	0.700955	−	1.21409i	0.968131	−	0.250443i	$-0.0805761\pi$
$228$	−4.02113	+	6.38988i	−0.266306	+	0.423180i
$229$	−0.512954	−	0.888462i	−0.0338970	−	0.0587113i	0.848579	−	0.529068i	$-0.177458\pi$
$229$	−0.512954	−	0.888462i	−0.0338970	−	0.0587113i	−0.882476	+	0.470357i	$0.844125\pi$
$230$	−10.2404	−	17.7370i	−0.675235	−	1.16954i
$231$	−1.15294	−	11.1684i	−0.0758582	−	0.734825i
$232$	3.08137	−	5.33710i	0.202302	−	0.350398i
$233$		−	5.08018i		−	0.332814i	−0.986057	−	0.166407i	$-0.946784\pi$
$233$		−	5.08018i		−	0.332814i	0.986057	−	0.166407i	$-0.0532165\pi$
$234$	5.67586	−	5.07265i	0.371043	−	0.331609i
$235$	−27.5687			−1.79838
$236$	0.290473	−	0.503113i	0.0189082	−	0.0327499i
$237$	5.44478	−	3.94048i	0.353676	−	0.255962i
$238$	−6.15161	+	3.55163i	−0.398750	+	0.230218i
$239$	−9.65331	+	5.57334i	−0.624421	+	0.360510i	−0.778588	−	0.627535i	$-0.784064\pi$
$239$	−9.65331	+	5.57334i	−0.624421	+	0.360510i	0.154167	+	0.988045i	$0.450731\pi$
$240$	5.06291	+	2.26539i	0.326809	+	0.146230i
$241$	−9.53797	−	5.50675i	−0.614394	−	0.354721i	0.160289	−	0.987070i	$-0.448757\pi$
$241$	−9.53797	−	5.50675i	−0.614394	−	0.354721i	−0.774683	+	0.632349i	$0.782091\pi$
$242$	7.17117			0.460980
$243$	−13.4273	−	7.91885i	−0.861360	−	0.507994i
$244$	−7.73842			−0.495401
$245$	−12.9999	−	7.50551i	−0.830535	−	0.479510i
$246$	0.152513	−	0.340849i	0.00972385	−	0.0217318i
$247$	1.55385	−	10.9507i	0.0988688	−	0.696778i
$248$	−4.80457	+	2.77392i	−0.305091	+	0.176144i
$249$	−8.62866	+	6.24472i	−0.546819	+	0.395743i
$250$	0.707239	+	0.408325i	0.0447297	+	0.0258247i
$251$		−	19.9197i		−	1.25732i	−0.777679	−	0.628661i	$-0.783603\pi$
$251$		−	19.9197i		−	1.25732i	0.777679	−	0.628661i	$-0.216397\pi$
$252$	3.04004	+	3.40155i	0.191505	+	0.214278i
$253$	27.2629			1.71400
$254$	16.4770	+	9.51301i	1.03386	+	0.596900i
$255$	−25.7718	+	2.66050i	−1.61389	+	0.166607i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.90480	+	15.4236i	0.555466	+	0.962096i	0.997867	+	0.0652783i	$0.0207935\pi$
$257$	8.90480	+	15.4236i	0.555466	+	0.962096i	−0.442401	+	0.896817i	$0.645873\pi$
$258$	4.83135	−	0.498755i	0.300787	−	0.0310511i
$259$	0.326572	+	0.188546i	0.0202922	+	0.0117157i
$260$	−8.12574			−0.503937
$261$	18.0983	−	3.77694i	1.12026	−	0.233787i
$262$		−	7.21609i		−	0.445812i
$263$	5.26192	+	3.03797i	0.324464	+	0.187329i	0.653381	−	0.757030i	$-0.273350\pi$
$263$	5.26192	+	3.03797i	0.324464	+	0.187329i	−0.328917	+	0.944359i	$0.606684\pi$
$264$	−5.98126	+	4.32875i	−0.368121	+	0.266416i
$265$	37.4699	−	21.6333i	2.30176	−	1.32892i
$266$	6.56278	+	0.931221i	0.402390	+	0.0570968i
$267$	8.77478	−	19.6107i	0.537008	−	1.20016i
$268$	5.60803	+	3.23780i	0.342565	+	0.197780i
$269$	1.92957			0.117648			0.0588240	−	0.998268i	$-0.481265\pi$
$269$	1.92957			0.117648			0.0588240	+	0.998268i	$0.481265\pi$
$270$	5.05404	+	15.8538i	0.307579	+	0.964830i
$271$	−11.8324			−0.718767			−0.359384	−	0.933190i	$-0.617013\pi$
$271$	−11.8324			−0.718767			−0.359384	+	0.933190i	$0.617013\pi$
$272$	4.04528	+	2.33554i	0.245281	+	0.141613i
$273$	−6.10052	−	2.72967i	−0.369220	−	0.165207i
$274$	−16.9726	+	9.79911i	−1.02535	+	0.591986i
$275$	−19.3997	+	11.2004i	−1.16985	+	0.675412i
$276$	−8.97392	+	6.49458i	−0.540166	+	0.390928i
$277$	1.50712	−	2.61040i	0.0905538	−	0.156844i	−0.817191	−	0.576368i	$-0.804470\pi$
$277$	1.50712	−	2.61040i	0.0905538	−	0.156844i	0.907744	+	0.419524i	$0.137803\pi$
$278$	−10.6317			−0.637645
$279$	−15.8098	−	5.20170i	−0.946507	−	0.311418i
$280$		−	4.86977i		−	0.291024i
$281$	8.20762	−	14.2160i	0.489625	−	0.848056i	−0.510303	−	0.859995i	$-0.670467\pi$
$281$	8.20762	−	14.2160i	0.489625	−	0.848056i	0.999929	+	0.0119384i	$0.00380019\pi$
$282$	1.53118	+	14.8322i	0.0911803	+	0.883247i
$283$	−7.70989	−	13.3539i	−0.458305	−	0.793808i	0.540566	−	0.841302i	$-0.318210\pi$
$283$	−7.70989	−	13.3539i	−0.458305	−	0.793808i	−0.998872	+	0.0474933i	$0.984877\pi$
$284$	−4.99900	−	8.65853i	−0.296636	−	0.513789i
$285$	20.4626	+	12.8770i	1.21210	+	0.762771i
$286$	5.40824	−	9.36735i	0.319796	−	0.553903i
$287$	−0.327846			−0.0193522
$288$	0.937608	−	2.84972i	0.0552491	−	0.167921i
$289$	−4.81908			−0.283475
$290$	−17.0912	−	9.86762i	−1.00363	−	0.579447i
$291$	3.64047	−	2.63467i	0.213408	−	0.154447i
$292$	6.65664	+	11.5296i	0.389550	+	0.674721i
$293$	12.3284	+	21.3534i	0.720231	+	1.24748i	0.960907	+	0.276871i	$0.0892976\pi$
$293$	12.3284	+	21.3534i	0.720231	+	1.24748i	−0.240676	+	0.970606i	$0.577369\pi$
$294$	−3.31602	+	7.41095i	−0.193394	+	0.432216i
$295$	−1.61114	−	0.930194i	−0.0938044	−	0.0541580i
$296$		−	0.247975i		−	0.0144133i
$297$	−21.6400	−	4.72549i	−1.25568	−	0.274201i
$298$		−	19.1410i		−	1.10881i
$299$	8.11420	−	14.0542i	0.469256	−	0.812776i
$300$	3.71748	−	8.30818i	0.214629	−	0.479673i
$301$	−2.13216	−	3.69301i	−0.122896	−	0.212862i
$302$	−13.5513	+	7.82382i	−0.779787	+	0.450210i
$303$	16.2750	−	11.7785i	0.934974	−	0.676657i
$304$	−1.62751	−	4.04366i	−0.0933440	−	0.231920i
$305$			24.7811i			1.41896i
$306$	2.86275	+	13.7177i	0.163653	+	0.784191i
$307$			18.4337i			1.05207i	0.850464	+	0.526033i	$0.176321\pi$
$307$			18.4337i			1.05207i	−0.850464	+	0.526033i	$0.823679\pi$
$308$	5.61387	+	3.24117i	0.319880	+	0.184683i
$309$	1.80409	+	17.4759i	0.102631	+	0.994170i
$310$	8.88305	+	15.3859i	0.504523	+	0.873860i
$311$	15.5953	−	9.00392i	0.884326	−	0.510566i	0.0122435	−	0.999925i	$-0.496103\pi$
$311$	15.5953	−	9.00392i	0.884326	−	0.510566i	0.872082	+	0.489359i	$0.162769\pi$
$312$	0.451307	+	4.37173i	0.0255502	+	0.247501i
$313$	5.69972	−	9.87221i	0.322167	−	0.558010i	−0.658768	−	0.752346i	$-0.728922\pi$
$313$	5.69972	−	9.87221i	0.322167	−	0.558010i	0.980935	+	0.194336i	$0.0622553\pi$
$314$	11.3730			0.641814
$315$	10.8929	−	9.73527i	0.613748	−	0.548520i
$316$			3.88042i			0.218291i
$317$	15.1713	−	26.2774i	0.852102	−	1.47588i	−0.0272048	−	0.999630i	$-0.508661\pi$
$317$	15.1713	−	26.2774i	0.852102	−	1.47588i	0.879307	−	0.476255i	$-0.158006\pi$
$318$	−13.7200	−	18.9577i	−0.769381	−	1.06309i
$319$	22.7508	−	13.1352i	1.27380	−	0.735429i
$320$	−2.77331	+	1.60117i	−0.155033	+	0.0895083i
$321$	−6.61073	+	14.7743i	−0.368975	+	0.824619i
$322$	8.42270	+	4.86285i	0.469379	+	0.270996i
$323$	16.0279	+	12.5566i	0.891816	+	0.698670i
$324$	8.24879	−	3.59965i	0.458266	−	0.199981i
$325$			13.3343i			0.739652i
$326$	−10.5972	+	18.3548i	−0.586923	+	1.01658i
$327$	7.68724	+	3.43964i	0.425105	+	0.190213i
$328$	0.107795	+	0.186707i	0.00595201	+	0.0103092i
$329$	11.3375	−	6.54573i	0.625059	−	0.360878i
$330$	13.8621	+	19.1541i	0.763086	+	1.05440i
$331$	23.7021	+	13.6844i	1.30279	+	0.752165i	0.980881	−	0.194606i	$-0.0623430\pi$
$331$	23.7021	+	13.6844i	1.30279	+	0.752165i	0.321907	+	0.946771i	$0.395676\pi$
$332$		−	6.14953i		−	0.337499i
$333$	0.554684	−	0.495733i	0.0303965	−	0.0271660i
$334$	24.1337			1.32054
$335$	10.3685	−	17.9588i	0.566494	−	0.981197i
$336$	−2.61998	+	0.270469i	−0.142932	+	0.0147553i
$337$	−9.18024	+	5.30022i	−0.500080	+	0.288721i	−0.728746	−	0.684784i	$-0.759897\pi$
$337$	−9.18024	+	5.30022i	−0.500080	+	0.288721i	0.228667	+	0.973505i	$0.426563\pi$
$338$	3.28071	+	5.68236i	0.178447	+	0.309080i
$339$	8.94254	−	0.923165i	0.485692	−	0.0501394i
$340$	7.47922	−	12.9544i	0.405618	−	0.702550i
$341$	−23.6491			−1.28067
$342$	5.79148	−	11.7243i	0.313168	−	0.633976i
$343$	17.7730			0.959654
$344$	−1.40210	+	2.42852i	−0.0755964	+	0.130937i
$345$	20.7979	+	28.7376i	1.11972	+	1.54718i
$346$	11.0711	+	19.1757i	0.595186	+	1.03089i
$347$	−5.19012	+	2.99652i	−0.278620	+	0.160861i	−0.632799	−	0.774316i	$-0.718094\pi$
$347$	−5.19012	+	2.99652i	−0.278620	+	0.160861i	0.354178	+	0.935178i	$0.384761\pi$
$348$	−4.35963	+	9.74331i	−0.233701	+	0.522296i
$349$	−0.670429	+	1.16122i	−0.0358872	+	0.0621585i	−0.883411	−	0.468599i	$-0.844759\pi$
$349$	−0.670429	+	1.16122i	−0.0358872	+	0.0621585i	0.847524	+	0.530757i	$0.178092\pi$
$350$	−7.99124			−0.427150
$351$	−8.87670	+	9.74914i	−0.473803	+	0.520371i
$352$		−	4.26277i		−	0.227206i
$353$	9.93618	+	5.73666i	0.528850	+	0.305332i	0.740548	−	0.672004i	$-0.234566\pi$
$353$	9.93618	+	5.73666i	0.528850	+	0.305332i	−0.211698	+	0.977335i	$0.567899\pi$
$354$	−0.410970	+	0.918475i	−0.0218428	+	0.0488164i
$355$	−27.7276	+	16.0085i	−1.47163	+	0.849645i
$356$	6.20199	+	10.7422i	0.328705	+	0.569334i
$357$	9.96688	−	7.21321i	0.527503	−	0.381764i
$358$	−8.35919	+	14.4785i	−0.441797	+	0.765215i
$359$		−	2.97199i		−	0.156856i	−0.996920	−	0.0784278i	$-0.975010\pi$
$359$		−	2.97199i		−	0.156856i	0.996920	−	0.0784278i	$-0.0249900\pi$
$360$	−9.12578	−	3.00254i	−0.480971	−	0.158248i
$361$	−4.54757	−	18.4478i	−0.239346	−	0.970934i
$362$	−1.66748	−	0.962718i	−0.0876406	−	0.0505993i
$363$	−12.3552	+	1.27546i	−0.648478	+	0.0669443i
$364$	3.34168	−	1.92932i	0.175152	−	0.101124i
$365$	36.9219	−	21.3169i	1.93258	−	1.11578i
$366$	13.3325	−	1.37635i	0.696900	−	0.0719430i
$367$	−6.86377	+	11.8884i	−0.358286	+	0.620569i	−0.987675	−	0.156522i	$-0.949972\pi$
$367$	−6.86377	+	11.8884i	−0.358286	+	0.620569i	0.629389	+	0.777090i	$0.283305\pi$
$368$		−	6.39559i		−	0.333393i
$369$	−0.202140	+	0.614373i	−0.0105230	+	0.0319830i
$370$	−0.794103			−0.0412834
$371$	−10.2729	+	17.7932i	−0.533344	+	0.923778i
$372$	7.78440	−	5.63371i	0.403602	−	0.292094i
$373$	−13.0698	+	7.54587i	−0.676730	+	0.390711i	−0.798622	−	0.601833i	$-0.794437\pi$
$373$	−13.0698	+	7.54587i	−0.676730	+	0.390711i	0.121892	+	0.992543i	$0.461104\pi$
$374$	9.95588	+	17.2441i	0.514806	+	0.891671i
$375$	−1.29112	−	0.577711i	−0.0666733	−	0.0298329i
$376$	−7.45554	−	4.30446i	−0.384490	−	0.221985i
$377$		−	15.6376i		−	0.805376i
$378$	−5.84267	−	5.31981i	−0.300515	−	0.273622i
$379$			1.29330i			0.0664322i	0.999448	+	0.0332161i	$0.0105750\pi$
$379$			1.29330i			0.0664322i	−0.999448	+	0.0332161i	$0.989425\pi$
$380$	−12.9492	+	5.21184i	−0.664280	+	0.267362i
$381$	−30.0802	−	13.4593i	−1.54105	−	0.689542i
$382$	0.637900	−	0.368292i	0.0326378	−	0.0188435i
$383$	1.02925	+	1.78271i	0.0525923	+	0.0910925i	0.891123	−	0.453762i	$-0.149918\pi$
$383$	1.02925	+	1.78271i	0.0525923	+	0.0910925i	−0.838531	+	0.544854i	$0.816585\pi$
$384$	1.01548	+	1.40314i	0.0518209	+	0.0716037i
$385$	10.3793	−	17.9775i	0.528980	−	0.916220i
$386$			9.11819i			0.464103i
$387$	−8.23521	+	1.71861i	−0.418619	+	0.0873616i
$388$			2.59452i			0.131717i
$389$	19.5718	+	11.2998i	0.992331	+	0.572923i	0.905970	−	0.423341i	$-0.139143\pi$
$389$	19.5718	+	11.2998i	0.992331	+	0.572923i	0.0863610	+	0.996264i	$0.472476\pi$
$390$	13.9998	−	1.44524i	0.708907	−	0.0731826i
$391$	14.9372	+	25.8720i	0.755406	+	1.30840i
$392$	−2.34375	−	4.05950i	−0.118377	−	0.205036i
$393$	1.28345	+	12.4326i	0.0647415	+	0.627140i
$394$	−7.34217	−	4.23901i	−0.369893	−	0.213558i
$395$	12.4264			0.625242
$396$	9.53517	−	8.52180i	0.479160	−	0.428236i
$397$	−21.6329			−1.08572			−0.542862	−	0.839822i	$-0.682659\pi$
$397$	−21.6329			−1.08572			−0.542862	+	0.839822i	$0.682659\pi$
$398$	8.21675	−	14.2318i	0.411868	−	0.713377i
$399$	−11.4726	−	0.437142i	−0.574349	−	0.0218845i
$400$	2.62751	+	4.55098i	0.131375	+	0.227549i
$401$	−17.2674	−	29.9080i	−0.862291	−	1.49353i	−0.869712	−	0.493560i	$-0.835695\pi$
$401$	−17.2674	−	29.9080i	−0.862291	−	1.49353i	0.00742022	−	0.999972i	$-0.497638\pi$
$402$	−10.2379	−	4.58094i	−0.510621	−	0.228477i
$403$	−7.03864	+	12.1913i	−0.350620	+	0.607291i
$404$			11.5990i			0.577070i
$405$	−11.5273	−	26.4155i	−0.572797	−	1.31260i
$406$	9.37161			0.465105
$407$	0.528530	−	0.915441i	0.0261983	−	0.0453767i
$408$	−7.38499	−	3.30441i	−0.365612	−	0.163592i
$409$	−15.7230	+	9.07768i	−0.777452	+	0.448862i	−0.835527	−	0.549450i	$-0.814837\pi$
$409$	−15.7230	+	9.07768i	−0.777452	+	0.448862i	0.0580743	+	0.998312i	$0.481504\pi$
$410$	0.597901	−	0.345198i	0.0295282	−	0.0170481i
$411$	27.4991	−	19.9016i	1.35643	−	0.981672i
$412$	−8.78440	−	5.07167i	−0.432776	−	0.249863i
$413$	0.883436			0.0434711
$414$	14.3060	−	12.7856i	0.703101	−	0.628377i
$415$	−19.6929			−0.966688
$416$	−2.19748	−	1.26872i	−0.107740	−	0.0622040i
$417$	18.3172	−	1.89094i	0.896999	−	0.0925999i
$418$	2.61038	−	18.3967i	0.127678	−	0.899811i
$419$	−13.0631	+	7.54199i	−0.638175	+	0.368450i	−0.783911	−	0.620873i	$-0.786778\pi$
$419$	−13.0631	+	7.54199i	−0.638175	+	0.368450i	0.145736	+	0.989323i	$0.453445\pi$
$420$	0.866134	+	8.39009i	0.0422630	+	0.409395i
$421$	−22.3704	−	12.9156i	−1.09027	−	0.629466i	−0.156620	−	0.987659i	$-0.550060\pi$
$421$	−22.3704	−	12.9156i	−1.09027	−	0.629466i	−0.933648	+	0.358193i	$0.883393\pi$
$422$			0.927889i			0.0451689i
$423$	−5.27611	−	25.2821i	−0.256533	−	1.22926i
$424$	13.5109			0.656147
$425$	−21.2580	−	12.2733i	−1.03117	−	0.595344i
$426$	10.1528	+	14.0286i	0.491903	+	0.679688i
$427$	−5.88386	−	10.1911i	−0.284740	−	0.493184i
$428$	−4.67244	−	8.09291i	−0.225851	−	0.391185i
$429$	−7.65176	+	17.1009i	−0.369431	+	0.825638i
$430$	7.77694	+	4.49002i	0.375038	+	0.216528i
$431$	−18.7560			−0.903444			−0.451722	−	0.892159i	$-0.649190\pi$
$431$	−18.7560			−0.903444			−0.451722	+	0.892159i	$0.649190\pi$
$432$	−1.10855	+	5.07653i	−0.0533352	+	0.244244i
$433$			21.8593i			1.05049i	0.850951	+	0.525245i	$0.176026\pi$
$433$			21.8593i			1.05049i	−0.850951	+	0.525245i	$0.823974\pi$
$434$	−7.30625	−	4.21827i	−0.350711	−	0.202483i
$435$	31.2014	+	13.9610i	1.49599	+	0.669381i
$436$	−4.21084	+	2.43113i	−0.201663	+	0.116430i
$437$	3.91646	−	27.6013i	0.187350	−	1.32035i
$438$	−13.5193	−	18.6804i	−0.645979	−	0.892584i
$439$	19.6150	+	11.3247i	0.936172	+	0.540499i	0.888758	−	0.458376i	$-0.151569\pi$
$439$	19.6150	+	11.3247i	0.936172	+	0.540499i	0.0474134	+	0.998875i	$0.484902\pi$
$440$	−13.6508			−0.650779
$441$	4.39505	−	13.3581i	0.209288	−	0.636099i
$442$	11.8526			0.563770
$443$	−7.04532	−	4.06762i	−0.334733	−	0.193258i	0.323207	−	0.946328i	$-0.395239\pi$
$443$	−7.04532	−	4.06762i	−0.334733	−	0.193258i	−0.657941	+	0.753070i	$0.728572\pi$
$444$	0.0441048	+	0.427235i	0.00209312	+	0.0202757i
$445$	34.4001	−	19.8609i	1.63072	−	0.941498i
$446$	−16.6727	+	9.62600i	−0.789477	+	0.455805i
$447$	3.40441	+	32.9780i	0.161023	+	1.55980i
$448$	0.760344	−	1.31695i	0.0359229	−	0.0622202i
$449$	−34.4488			−1.62574			−0.812870	−	0.582445i	$-0.802096\pi$
$449$	−34.4488			−1.62574			−0.812870	+	0.582445i	$0.802096\pi$
$450$	−4.92715	+	14.9753i	−0.232268	+	0.705943i
$451$			0.919014i			0.0432747i
$452$	−2.59521	+	4.49503i	−0.122068	+	0.211428i
$453$	21.9558	−	15.8898i	1.03158	−	0.746570i
$454$	−10.5610	−	18.2921i	−0.495650	−	0.858491i
$455$	−6.17836	−	10.7012i	−0.289646	−	0.501681i
$456$	3.52323	+	6.67734i	0.164990	+	0.312695i
$457$	−14.3739	+	24.8964i	−0.672385	+	1.16460i	0.304841	+	0.952403i	$0.401397\pi$
$457$	−14.3739	+	24.8964i	−0.672385	+	1.16460i	−0.977226	+	0.212201i	$0.931937\pi$
$458$	−1.02591			−0.0479375
$459$	−7.37206	−	23.1250i	−0.344098	−	1.07938i
$460$	−20.4809			−0.954927
$461$	−6.60586	−	3.81390i	−0.307666	−	0.177631i	0.338216	−	0.941069i	$-0.390177\pi$
$461$	−6.60586	−	3.81390i	−0.307666	−	0.177631i	−0.645881	+	0.763438i	$0.723510\pi$
$462$	−10.2486	−	4.58571i	−0.476807	−	0.213346i
$463$	−1.92246	−	3.32979i	−0.0893441	−	0.154748i	0.817890	−	0.575375i	$-0.195144\pi$
$463$	−1.92246	−	3.32979i	−0.0893441	−	0.154748i	−0.907234	+	0.420626i	$0.861810\pi$
$464$	−3.08137	−	5.33710i	−0.143049	−	0.247768i
$465$	−18.0411	−	24.9283i	−0.836636	−	1.15602i
$466$	−4.39956	−	2.54009i	−0.203806	−	0.117667i
$467$			17.3946i			0.804926i	0.915436	+	0.402463i	$0.131846\pi$
$467$			17.3946i			0.804926i	−0.915436	+	0.402463i	$0.868154\pi$
$468$	−1.55511	−	7.45177i	−0.0718849	−	0.344458i
$469$			9.84736i			0.454709i
$470$	−13.7844	+	23.8752i	−0.635825	+	1.10128i
$471$	−19.5944	+	2.02279i	−0.902865	+	0.0932054i
$472$	−0.290473	−	0.503113i	−0.0133701	−	0.0231577i
$473$	−10.3522	+	5.97684i	−0.475994	+	0.274815i
$474$	−0.690170	−	6.68556i	−0.0317005	−	0.307078i
$475$	8.55258	+	21.2495i	0.392419	+	0.974995i
$476$			7.10327i			0.325578i
$477$	27.0100	+	30.2219i	1.23670	+	1.38376i
$478$			11.1467i			0.509838i
$479$	25.5750	+	14.7657i	1.16855	+	0.674664i	0.953339	−	0.301903i	$-0.0976218\pi$
$479$	25.5750	+	14.7657i	1.16855	+	0.674664i	0.215214	+	0.976567i	$0.430955\pi$
$480$	4.49334	−	3.25191i	0.205092	−	0.148429i
$481$	−0.314611	−	0.544922i	−0.0143450	−	0.0248463i
$482$	−9.53797	+	5.50675i	−0.434442	+	0.250825i
$483$	−15.3763	−	6.88012i	−0.699647	−	0.313056i
$484$	3.58558	−	6.21041i	0.162981	−	0.282291i
$485$	8.30854			0.377271
$486$	−13.5716	+	7.66894i	−0.615619	+	0.347870i
$487$		−	15.8426i		−	0.717895i	−0.933358	−	0.358948i	$-0.883136\pi$
$487$		−	15.8426i		−	0.717895i	0.933358	−	0.358948i	$-0.116864\pi$
$488$	−3.86921	+	6.70166i	−0.175151	+	0.303370i
$489$	14.9932	−	33.5082i	0.678017	−	1.51530i
$490$	−12.9999	+	7.50551i	−0.587277	+	0.339065i
$491$	3.78518	−	2.18537i	0.170823	−	0.0986245i	−0.412151	−	0.911116i	$-0.635222\pi$
$491$	3.78518	−	2.18537i	0.170823	−	0.0986245i	0.582974	+	0.812491i	$0.301889\pi$
$492$	−0.218928	−	0.302504i	−0.00987003	−	0.0136380i
$493$	24.9301	+	14.3934i	1.12279	+	0.648245i
$494$	−8.70669	−	6.82104i	−0.391732	−	0.306893i
$495$	−27.2897	−	30.5349i	−1.22658	−	1.37244i
$496$			5.54784i			0.249105i
$497$	7.60192	−	13.1669i	0.340993	−	0.590617i
$498$	1.09375	+	10.5950i	0.0490123	+	0.474773i
$499$	10.2440	+	17.7430i	0.458582	+	0.794288i	0.998886	−	0.0471820i	$-0.0150241\pi$
$499$	10.2440	+	17.7430i	0.458582	+	0.794288i	−0.540304	+	0.841470i	$0.681691\pi$
$500$	0.707239	−	0.408325i	0.0316287	−	0.0182608i
$501$	−41.5799	+	4.29241i	−1.85765	+	0.191771i
$502$	−17.2510	−	9.95987i	−0.769950	−	0.444531i
$503$			37.5977i			1.67640i	0.545366	+	0.838198i	$0.316391\pi$
$503$			37.5977i			1.67640i	−0.545366	+	0.838198i	$0.683609\pi$
$504$	4.46585	−	0.931978i	0.198925	−	0.0415136i
$505$	37.1439			1.65288
$506$	13.6315	−	23.6104i	0.605992	−	1.04961i
$507$	−6.66298	−	9.20660i	−0.295913	−	0.408880i
$508$	16.4770	−	9.51301i	0.731050	−	0.422072i
$509$	−1.84925	−	3.20300i	−0.0819666	−	0.141970i	0.822128	−	0.569303i	$-0.192787\pi$
$509$	−1.84925	−	3.20300i	−0.0819666	−	0.141970i	−0.904095	+	0.427332i	$0.859453\pi$
$510$	−10.5818	+	23.6493i	−0.468572	+	1.04721i
$511$	−10.1227	+	17.5330i	−0.447800	+	0.775613i
$512$	−1.00000			−0.0441942
$513$	−7.89284	+	21.2298i	−0.348478	+	0.937317i
$514$	17.8096			0.785548
$515$	−16.2412	+	28.1307i	−0.715675	+	1.23959i
$516$	1.98374	−	4.43345i	0.0873294	−	0.195172i
$517$	−18.3489	−	31.7812i	−0.806983	−	1.39774i
$518$	0.326572	−	0.188546i	0.0143488	−	0.00828426i
$519$	−22.4849	−	31.0686i	−0.986978	−	1.36376i
$520$	−4.06287	+	7.03710i	−0.178169	+	0.308597i
$521$	13.3408			0.584472			0.292236	−	0.956346i	$-0.405601\pi$
$521$	13.3408			0.584472			0.292236	+	0.956346i	$0.405601\pi$
$522$	5.77824	−	17.5621i	0.252907	−	0.768672i
$523$			16.5133i			0.722078i	0.932551	+	0.361039i	$0.117578\pi$
$523$			16.5133i			0.722078i	−0.932551	+	0.361039i	$0.882422\pi$
$524$	−6.24932	−	3.60805i	−0.273003	−	0.157618i
$525$	13.7681	−	1.42132i	0.600887	−	0.0620314i
$526$	5.26192	−	3.03797i	0.229431	−	0.132462i
$527$	−12.9572	−	22.4426i	−0.564426	−	0.977614i
$528$	0.758173	+	7.34430i	0.0329953	+	0.319619i
$529$	8.95180	−	15.5050i	0.389209	−	0.674129i
$530$		−	43.2666i		−	1.87938i
$531$	0.544699	−	1.65553i	0.0236379	−	0.0718439i
$532$	4.08785	−	5.21793i	0.177231	−	0.226226i
$533$	0.473758	+	0.273524i	0.0205207	+	0.0118476i
$534$	−12.5960	−	17.4045i	−0.545081	−	0.753168i
$535$	−25.9163	+	14.9628i	−1.12046	+	0.646897i
$536$	5.60803	−	3.23780i	0.242230	−	0.139852i
$537$	11.8269	−	26.4318i	0.510367	−	1.14062i
$538$	0.964785	−	1.67106i	0.0415949	−	0.0720444i
$539$		−	19.9818i		−	0.860675i
$540$	16.2568	+	3.54996i	0.699581	+	0.152766i
$541$	33.5888			1.44410			0.722049	−	0.691842i	$-0.243201\pi$
$541$	33.5888			1.44410			0.722049	+	0.691842i	$0.243201\pi$
$542$	−5.91620	+	10.2472i	−0.254123	+	0.440153i
$543$	3.04411	+	1.36208i	0.130635	+	0.0584526i
$544$	4.04528	−	2.33554i	0.173440	−	0.100136i
$545$	7.78532	+	13.4846i	0.333486	+	0.577615i
$546$	−5.41422	+	3.91837i	−0.231707	+	0.167691i
$547$	−27.2760	−	15.7478i	−1.16624	−	0.673328i	−0.213447	−	0.976955i	$-0.568469\pi$
$547$	−27.2760	−	15.7478i	−1.16624	−	0.673328i	−0.952791	+	0.303626i	$0.901803\pi$
$548$			19.5982i			0.837195i
$549$	−22.7257	+	4.74262i	−0.969907	+	0.202410i
$550$			22.4009i			0.955178i
$551$	−10.0299	−	24.9201i	−0.427289	−	1.06163i
$552$	1.13752	+	11.0189i	0.0484159	+	0.468997i
$553$	−5.11033	+	2.95045i	−0.217314	+	0.125466i
$554$	−1.50712	−	2.61040i	−0.0640312	−	0.110905i
$555$	1.36816	−	0.141239i	0.0580749	−	0.00599525i
$556$	−5.31583	+	9.20729i	−0.225442	+	0.390476i
$557$			28.7677i			1.21893i	0.792814	+	0.609464i	$0.208615\pi$
$557$			28.7677i			1.21893i	−0.792814	+	0.609464i	$0.791385\pi$
$558$	−12.4097	+	11.0908i	−0.525344	+	0.469512i
$559$			7.11549i			0.300953i
$560$	−4.21734	−	2.43488i	−0.178215	−	0.102893i
$561$	−20.2200	−	27.9390i	−0.853687	−	1.17959i
$562$	−8.20762	−	14.2160i	−0.346217	−	0.599666i
$563$	14.3247	+	24.8112i	0.603716	+	1.04567i	0.992253	+	0.124234i	$0.0396472\pi$
$563$	14.3247	+	24.8112i	0.603716	+	1.04567i	−0.388537	+	0.921433i	$0.627019\pi$
$564$	13.6107	+	6.09008i	0.573113	+	0.256439i
$565$	14.3946	+	8.31075i	0.605587	+	0.349636i
$566$	−15.4198			−0.648142
$567$	11.0125	+	8.12630i	0.462481	+	0.341273i
$568$	−9.99801			−0.419507
$569$	−13.3791	+	23.1734i	−0.560883	+	0.971478i	0.436537	+	0.899686i	$0.356205\pi$
$569$	−13.3791	+	23.1734i	−0.560883	+	0.971478i	−0.997420	+	0.0717913i	$0.977128\pi$
$570$	21.3831	−	11.2826i	0.895641	−	0.472576i
$571$	4.08381	+	7.07336i	0.170902	+	0.296011i	0.938735	−	0.344638i	$-0.111999\pi$
$571$	4.08381	+	7.07336i	0.170902	+	0.296011i	−0.767833	+	0.640650i	$0.778665\pi$
$572$	−5.40824	−	9.36735i	−0.226130	−	0.391669i
$573$	−1.03353	+	0.747985i	−0.0431764	+	0.0312475i
$574$	−0.163923	+	0.283923i	−0.00684202	+	0.0118507i
$575$			33.6089i			1.40159i
$576$	−1.99912	−	2.23685i	−0.0832968	−	0.0932021i
$577$	−19.9431			−0.830242			−0.415121	−	0.909766i	$-0.636261\pi$
$577$	−19.9431			−0.830242			−0.415121	+	0.909766i	$0.636261\pi$
$578$	−2.40954	+	4.17344i	−0.100224	+	0.173592i
$579$	−1.62176	−	15.7097i	−0.0673979	−	0.652872i
$580$	−17.0912	+	9.86762i	−0.709675	+	0.409731i
$581$	8.09865	−	4.67576i	0.335989	−	0.193983i
$582$	−0.461459	−	4.47008i	−0.0191281	−	0.185291i
$583$	49.8777	+	28.7969i	2.06572	+	1.19265i
$584$	13.3133			0.550907
$585$	−23.8631	+	4.98000i	−0.986619	+	0.205897i
$586$	24.6567			1.01856
$587$	21.2874	+	12.2903i	0.878625	+	0.507274i	0.870205	−	0.492690i	$-0.163986\pi$
$587$	21.2874	+	12.2903i	0.878625	+	0.507274i	0.00842005	+	0.999965i	$0.497320\pi$
$588$	4.76006	+	6.57724i	0.196302	+	0.271241i
$589$	−3.39732	+	23.9426i	−0.139984	+	0.986540i
$590$	−1.61114	+	0.930194i	−0.0663297	+	0.0382955i
$591$	13.4037	+	5.99749i	0.551356	+	0.246704i
$592$	−0.214753	−	0.123988i	−0.00882629	−	0.00509586i
$593$		−	35.9084i		−	1.47458i	−0.675575	−	0.737292i	$-0.736104\pi$
$593$		−	35.9084i		−	1.47458i	0.675575	−	0.737292i	$-0.263896\pi$
$594$	−14.9124	+	16.3781i	−0.611864	+	0.672001i
$595$	22.7471			0.932541
$596$	−16.5766	−	9.57051i	−0.679004	−	0.392023i
$597$	−11.6253	+	25.9814i	−0.475793	+	1.06335i
$598$	−8.11420	−	14.0542i	−0.331814	−	0.574719i
$599$	−2.70632	−	4.68749i	−0.110577	−	0.191526i	0.805426	−	0.592697i	$-0.201937\pi$
$599$	−2.70632	−	4.68749i	−0.110577	−	0.191526i	−0.916003	+	0.401171i	$0.868603\pi$
$600$	−5.33635	−	7.37353i	−0.217856	−	0.301023i
$601$	38.4757	+	22.2139i	1.56946	+	0.906125i	0.996232	+	0.0867257i	$0.0276404\pi$
$601$	38.4757	+	22.2139i	1.56946	+	0.906125i	0.573223	+	0.819400i	$0.305693\pi$
$602$	−4.26432			−0.173801
$603$	18.4536	+	6.07157i	0.751489	+	0.247253i
$604$			15.6476i			0.636693i
$605$	−19.8879	−	11.4823i	−0.808557	−	0.466821i
$606$	−2.06299	−	19.9838i	−0.0838031	−	0.811787i
$607$	−33.5481	+	19.3690i	−1.36167	+	0.786163i	−0.989847	−	0.142139i	$-0.954602\pi$
$607$	−33.5481	+	19.3690i	−1.36167	+	0.786163i	−0.371827	+	0.928302i	$0.621269\pi$
$608$	−4.31567	−	0.612369i	−0.175024	−	0.0248348i
$609$	−16.1463	+	1.66683i	−0.654281	+	0.0675434i
$610$	21.4610	+	12.3905i	0.868932	+	0.501678i
$611$	−21.8446			−0.883736
$612$	13.3113	+	4.37965i	0.538077	+	0.177037i
$613$	12.7971			0.516870			0.258435	−	0.966029i	$-0.416793\pi$
$613$	12.7971			0.516870			0.258435	+	0.966029i	$0.416793\pi$
$614$	15.9640	+	9.21685i	0.644257	+	0.371962i
$615$	−0.968724	+	0.701083i	−0.0390627	+	0.0282704i
$616$	5.61387	−	3.24117i	0.226189	−	0.130590i
$617$	−20.0513	+	11.5766i	−0.807235	+	0.466057i	−0.845995	−	0.533191i	$-0.820993\pi$
$617$	−20.0513	+	11.5766i	−0.807235	+	0.466057i	0.0387598	+	0.999249i	$0.487659\pi$
$618$	16.0366	+	7.17557i	0.645088	+	0.288644i
$619$	18.3125	−	31.7182i	0.736042	−	1.27486i	−0.218223	−	0.975899i	$-0.570026\pi$
$619$	18.3125	−	31.7182i	0.736042	−	1.27486i	0.954265	−	0.298963i	$-0.0966408\pi$
$620$	17.7661			0.713504
$621$	−22.3737	+	24.5727i	−0.897824	+	0.986067i
$622$		−	18.0078i		−	0.722049i
$623$	−9.43129	+	16.3355i	−0.377857	+	0.654467i
$624$	4.01169	+	1.79502i	0.160596	+	0.0718584i
$625$	11.8299	+	20.4901i	0.473198	+	0.819603i
$626$	−5.69972	−	9.87221i	−0.227807	−	0.394573i
$627$	−1.22539	+	32.1598i	−0.0489374	+	1.28434i
$628$	5.68649	−	9.84929i	0.226916	−	0.393029i
$629$	1.15831			0.0461850
$630$	−2.98452	−	14.3012i	−0.118906	−	0.569773i
$631$	−34.7571			−1.38366			−0.691830	−	0.722060i	$-0.743195\pi$
$631$	−34.7571			−1.38366			−0.691830	+	0.722060i	$0.743195\pi$
$632$	3.36054	+	1.94021i	0.133675	+	0.0771774i
$633$	−0.165034	−	1.59866i	−0.00655951	−	0.0635409i
$634$	−15.1713	−	26.2774i	−0.602527	−	1.04361i
$635$	−30.4640	−	52.7651i	−1.20893	−	2.09392i
$636$	−23.2779	+	2.40304i	−0.923027	+	0.0952868i
$637$	−10.3007	−	5.94713i	−0.408130	−	0.235634i
$638$		−	26.2703i		−	1.04005i
$639$	−19.9873	−	22.3641i	−0.790683	−	0.884708i
$640$			3.20235i			0.126584i
$641$	−5.32969	+	9.23129i	−0.210510	+	0.364614i	−0.951874	−	0.306489i	$-0.900846\pi$
$641$	−5.32969	+	9.23129i	−0.210510	+	0.364614i	0.741364	+	0.671103i	$0.234179\pi$
$642$	9.48953	+	13.1122i	0.374522	+	0.517497i
$643$	−12.3485	−	21.3882i	−0.486976	−	0.843467i	0.512912	−	0.858441i	$-0.328567\pi$
$643$	−12.3485	−	21.3882i	−0.486976	−	0.843467i	−0.999888	+	0.0149744i	$0.995233\pi$
$644$	8.42270	−	4.86285i	0.331901	−	0.191623i
$645$	−14.1974	−	6.35263i	−0.559024	−	0.250135i
$646$	18.8883	−	7.60224i	0.743151	−	0.299106i
$647$			6.34810i			0.249569i	0.992184	+	0.124785i	$0.0398240\pi$
$647$			6.34810i			0.249569i	−0.992184	+	0.124785i	$0.960176\pi$
$648$	1.00701	−	8.94349i	0.0395590	−	0.351333i
$649$		−	2.47643i		−	0.0972085i
$650$	11.5478	+	6.66713i	0.452942	+	0.261506i
$651$	13.3382	+	5.96814i	0.522764	+	0.233910i
$652$	10.5972	+	18.3548i	0.415017	+	0.718831i
$653$	−19.5859	+	11.3079i	−0.766457	+	0.442514i	−0.831609	−	0.555361i	$-0.812580\pi$
$653$	−19.5859	+	11.3079i	−0.766457	+	0.442514i	0.0651524	+	0.997875i	$0.479247\pi$
$654$	6.82244	−	4.93752i	0.266778	−	0.193072i
$655$	−11.5542	+	20.0125i	−0.451460	+	0.781952i
$656$	0.215591			0.00841741
$657$	26.6149	+	29.7798i	1.03835	+	1.16182i
$658$		−	13.0915i		−	0.510358i
$659$	13.3617	−	23.1431i	0.520497	−	0.901527i	−0.479219	−	0.877695i	$-0.659080\pi$
$659$	13.3617	−	23.1431i	0.520497	−	0.901527i	0.999716	−	0.0238320i	$-0.00758668\pi$
$660$	23.5190	−	2.42793i	0.915475	−	0.0945072i
$661$	−4.37986	+	2.52871i	−0.170357	+	0.0983556i	−0.582754	−	0.812649i	$-0.698025\pi$
$661$	−4.37986	+	2.52871i	−0.170357	+	0.0983556i	0.412397	+	0.911004i	$0.364692\pi$
$662$	23.7021	−	13.6844i	0.921210	−	0.531861i
$663$	−20.4208	+	2.10810i	−0.793076	+	0.0818716i
$664$	−5.32565	−	3.07477i	−0.206675	−	0.119324i
$665$	−16.7096	−	13.0907i	−0.647971	−	0.507636i
$666$	−0.151976	−	0.728237i	−0.00588894	−	0.0282186i
$667$		−	39.4144i		−	1.52613i
$668$	12.0669	−	20.9004i	0.466881	−	0.808662i
$669$	27.0133	−	19.5500i	1.04439	−	0.755846i
$670$	−10.3685	−	17.9588i	−0.400572	−	0.693811i
$671$	−28.5676	+	16.4935i	−1.10284	+	0.636725i
$672$	−1.07576	+	2.40421i	−0.0414983	+	0.0927443i
$673$	15.2820	+	8.82309i	0.589079	+	0.340105i	0.764733	−	0.644347i	$-0.222871\pi$
$673$	15.2820	+	8.82309i	0.589079	+	0.340105i	−0.175654	+	0.984452i	$0.556204\pi$
$674$			10.6004i			0.408313i
$675$	5.82545	−	26.6772i	0.224222	−	1.02681i
$676$	6.56142			0.252362
$677$	4.87808	−	8.44908i	0.187480	−	0.324725i	−0.756930	−	0.653497i	$-0.773301\pi$
$677$	4.87808	−	8.44908i	0.187480	−	0.324725i	0.944409	+	0.328772i	$0.106635\pi$
$678$	3.67178	−	8.20605i	0.141014	−	0.315151i
$679$	−3.41686	+	1.97272i	−0.131127	+	0.0757062i
$680$	−7.47922	−	12.9544i	−0.286815	−	0.496778i
$681$	21.4488	+	29.6370i	0.821921	+	1.13569i
$682$	−11.8246	+	20.4808i	−0.452786	+	0.784249i
$683$	8.11524			0.310521			0.155261	−	0.987874i	$-0.450378\pi$
$683$	8.11524			0.310521			0.155261	+	0.987874i	$0.450378\pi$
$684$	−7.25778	−	10.8777i	−0.277508	−	0.415920i
$685$	62.7603			2.39795
$686$	8.88652	−	15.3919i	0.339289	−	0.587666i
$687$	1.76753	−	0.182468i	0.0674355	−	0.00696157i
$688$	1.40210	+	2.42852i	0.0534547	+	0.0925863i
$689$	29.6900	−	17.1415i	1.13110	−	0.653039i
$690$	35.2864	−	3.64272i	1.34333	−	0.138676i
$691$	10.7977	−	18.7022i	0.410766	−	0.711467i	−0.584208	−	0.811604i	$-0.698595\pi$
$691$	10.7977	−	18.7022i	0.410766	−	0.711467i	0.994974	+	0.100137i	$0.0319281\pi$
$692$	22.1422			0.841720
$693$	18.4728	+	6.07789i	0.701724	+	0.230880i
$694$			5.99303i			0.227492i
$695$	29.4849	+	17.0231i	1.11843	+	0.645724i
$696$	6.25814	+	8.64720i	0.237214	+	0.327771i
$697$	−0.872126	+	0.503522i	−0.0330341	+	0.0190723i
$698$	0.670429	+	1.16122i	0.0253761	+	0.0439527i
$699$	8.03176	+	3.59380i	0.303789	+	0.135930i
$700$	−3.99562	+	6.92061i	−0.151020	+	0.261575i
$701$			32.3415i			1.22152i	0.791815	+	0.610761i	$0.209137\pi$
$701$			32.3415i			1.22152i	−0.791815	+	0.610761i	$0.790863\pi$
$702$	4.00466	+	12.5620i	0.151146	+	0.474123i
$703$	−0.850876	−	0.666598i	−0.0320914	−	0.0251412i
$704$	−3.69166	−	2.13138i	−0.139135	−	0.0803295i
$705$	19.5026	−	43.5861i	0.734509	−	1.64155i
$706$	9.93618	−	5.73666i	0.373953	−	0.215902i
$707$	−15.2753	+	8.81920i	−0.574487	+	0.331680i
$708$	0.589937	+	0.815148i	0.0221712	+	0.0306351i
$709$	4.85264	−	8.40503i	0.182245	−	0.315657i	−0.760400	−	0.649455i	$-0.774997\pi$
$709$	4.85264	−	8.40503i	0.182245	−	0.315657i	0.942645	+	0.333798i	$0.108330\pi$
$710$			32.0171i			1.20158i
$711$	2.37818	+	11.3958i	0.0891887	+	0.427374i
$712$	12.4040			0.464859
$713$	−17.7409	+	30.7281i	−0.664401	+	1.15078i
$714$	−1.26338	−	12.2382i	−0.0472810	−	0.458002i
$715$	−29.9975	+	17.3191i	−1.12184	+	0.647696i
$716$	8.35919	+	14.4785i	0.312398	+	0.541089i
$717$	−1.98254	−	19.2046i	−0.0740395	−	0.717208i
$718$	−2.57382	−	1.48599i	−0.0960540	−	0.0554568i
$719$		−	33.3349i		−	1.24318i	−0.783342	−	0.621591i	$-0.786487\pi$
$719$		−	33.3349i		−	1.24318i	0.783342	−	0.621591i	$-0.213513\pi$
$720$	−7.16317	+	6.40189i	−0.266956	+	0.238584i
$721$		−	15.4249i		−	0.574452i
$722$	−18.2500	−	5.28556i	−0.679195	−	0.196708i
$723$	15.4535	−	11.1840i	0.574721	−	0.415936i
$724$	−1.66748	+	0.962718i	−0.0619712	+	0.0357791i
$725$	16.1927	+	28.0465i	0.601381	+	1.04162i
$726$	−5.07300	+	11.3376i	−0.188277	+	0.420778i
$727$	−18.9445	+	32.8128i	−0.702611	+	1.21696i	0.264935	+	0.964266i	$0.414649\pi$
$727$	−18.9445	+	32.8128i	−0.702611	+	1.21696i	−0.967547	+	0.252692i	$0.918684\pi$
$728$		−	3.85865i		−	0.143011i
$729$	22.0184	−	15.6266i	0.815495	−	0.578763i
$730$		−	42.6337i		−	1.57794i
$731$	−11.3438	−	6.54935i	−0.419566	−	0.242237i
$732$	5.47428	−	12.2344i	0.202335	−	0.452198i
$733$	−0.361335	−	0.625850i	−0.0133462	−	0.0231163i	0.859275	−	0.511514i	$-0.170915\pi$
$733$	−0.361335	−	0.625850i	−0.0133462	−	0.0231163i	−0.872621	+	0.488397i	$0.837582\pi$
$734$	6.86377	+	11.8884i	0.253346	+	0.438809i
$735$	21.0626	−	15.2434i	0.776905	−	0.562260i
$736$	−5.53874	−	3.19780i	−0.204161	−	0.117872i
$737$	27.6039			1.01680
$738$	0.430993	+	0.482245i	0.0158651	+	0.0177517i
$739$	−18.6408			−0.685713			−0.342856	−	0.939388i	$-0.611394\pi$
$739$	−18.6408			−0.685713			−0.342856	+	0.939388i	$0.611394\pi$
$740$	−0.397051	+	0.687713i	−0.0145959	+	0.0252808i
$741$	16.2139	+	10.2034i	0.595632	+	0.374830i
$742$	10.2729	+	17.7932i	0.377131	+	0.653210i
$743$	−4.20109	−	7.27650i	−0.154123	−	0.266949i	0.778616	−	0.627500i	$-0.215922\pi$
$743$	−4.20109	−	7.27650i	−0.154123	−	0.266949i	−0.932739	+	0.360551i	$0.882589\pi$
$744$	−0.986737	−	9.55835i	−0.0361755	−	0.350426i
$745$	−30.6481	+	53.0840i	−1.12286	+	1.94485i
$746$			15.0917i			0.552548i
$747$	−3.76884	−	18.0595i	−0.137895	−	0.660764i
$748$	19.9118			0.728046
$749$	7.10532	−	12.3068i	0.259623	−	0.449680i
$750$	−1.14587	+	0.829289i	−0.0418414	+	0.0302814i
$751$	8.99054	−	5.19069i	0.328069	−	0.189411i	−0.326914	−	0.945054i	$-0.606009\pi$
$751$	8.99054	−	5.19069i	0.328069	−	0.189411i	0.654984	+	0.755643i	$0.272676\pi$
$752$	−7.45554	+	4.30446i	−0.271875	+	0.156967i
$753$	31.4931	+	14.0915i	1.14767	+	0.513525i
$754$	−13.5425	−	7.81879i	−0.493190	−	0.284743i
$755$	50.1091			1.82366
$756$	−7.52843	+	2.39999i	−0.273806	+	0.0872870i
$757$	−6.21886			−0.226028			−0.113014	−	0.993593i	$-0.536051\pi$
$757$	−6.21886			−0.226028			−0.113014	+	0.993593i	$0.536051\pi$
$758$	1.12003	+	0.646649i	0.0406813	+	0.0234873i
$759$	−19.2862	+	43.1027i	−0.700046	+	1.56453i
$760$	−1.96102	+	13.8203i	−0.0711335	+	0.501314i
$761$	−35.2962	+	20.3783i	−1.27949	+	0.738711i	−0.976754	−	0.214365i	$-0.931232\pi$
$761$	−35.2962	+	20.3783i	−1.27949	+	0.738711i	−0.302732	+	0.953076i	$0.597899\pi$
$762$	−26.6962	+	19.3205i	−0.967101	+	0.699909i
$763$	−6.40337	−	3.69699i	−0.231818	−	0.133840i
$764$		−	0.736584i		−	0.0266487i
$765$	14.0252	−	42.6273i	0.507081	−	1.54119i
$766$	2.05850			0.0743767
$767$	−1.27662	−	0.737055i	−0.0460960	−	0.0266135i
$768$	1.72289	−	0.177860i	0.0621696	−	0.00641795i
$769$	0.306158	+	0.530282i	0.0110404	+	0.0191225i	0.871493	−	0.490408i	$-0.163152\pi$
$769$	0.306158	+	0.530282i	0.0110404	+	0.0191225i	−0.860452	+	0.509531i	$0.829819\pi$
$770$	−10.3793	−	17.9775i	−0.374045	−	0.647865i
$771$	−30.6841	+	3.16761i	−1.10506	+	0.114079i
$772$	7.89658	+	4.55909i	0.284204	+	0.164085i
$773$	−23.8826			−0.858998			−0.429499	−	0.903067i	$-0.641310\pi$
$773$	−23.8826			−0.858998			−0.429499	+	0.903067i	$0.641310\pi$
$774$	−2.62925	+	7.99120i	−0.0945064	+	0.287238i
$775$		−	29.1540i		−	1.04724i
$776$	2.24692	+	1.29726i	0.0806596	+	0.0465688i
$777$	−0.529114	+	0.382930i	−0.0189819	+	0.0137375i
$778$	19.5718	−	11.2998i	0.701684	−	0.405118i
$779$	0.930419	+	0.132021i	0.0333357	+	0.00473015i
$780$	5.74828	−	12.8468i	0.205822	−	0.459989i
$781$	−36.9093	−	21.3096i	−1.32072	−	0.762517i
$782$	29.8744			1.06831
$783$	−6.83172	+	31.2854i	−0.244146	+	1.11805i
$784$	−4.68751			−0.167411
$785$	−31.5408	−	18.2101i	−1.12574	−	0.649947i
$786$	11.4086	+	5.10478i	0.406933	+	0.182082i
$787$	−20.6429	+	11.9182i	−0.735840	+	0.424838i	−0.820555	−	0.571568i	$-0.806335\pi$
$787$	−20.6429	+	11.9182i	−0.735840	+	0.424838i	0.0847146	+	0.996405i	$0.473002\pi$
$788$	−7.34217	+	4.23901i	−0.261554	+	0.151008i
$789$	−8.52540	+	6.16999i	−0.303512	+	0.219657i
$790$	6.21322	−	10.7616i	0.221057	−	0.382881i
$791$	−7.89300			−0.280643
$792$	−2.61251	−	12.5186i	−0.0928314	−	0.444829i
$793$			19.6357i			0.697285i
$794$	−10.8165	+	18.7347i	−0.383862	+	0.664868i
$795$	7.69537	+	74.5437i	0.272927	+	2.64379i
$796$	−8.21675	−	14.2318i	−0.291235	−	0.504434i
$797$	21.2612	+	36.8254i	0.753109	+	1.30442i	0.946309	+	0.323264i	$0.104780\pi$
$797$	21.2612	+	36.8254i	0.753109	+	1.30442i	−0.193200	+	0.981159i	$0.561887\pi$
$798$	−6.11488	+	9.71700i	−0.216465	+	0.343978i
$799$	20.1065	−	34.8255i	0.711317	−	1.23204i
$800$	5.25502			0.185793
$801$	24.7971	+	27.7459i	0.876163	+	0.980352i
$802$	−34.5347			−1.21946
$803$	49.1481	+	28.3757i	1.73440	+	1.00136i
$804$	−9.08617	+	6.57583i	−0.320445	+	0.231912i
$805$	−15.5725	−	26.9724i	−0.548859	−	0.950652i
$806$	7.03864	+	12.1913i	0.247926	+	0.429420i
$807$	−1.36501	+	3.05065i	−0.0480506	+	0.107388i
$808$	10.0450	+	5.79949i	0.353382	+	0.204025i
$809$			7.46870i			0.262585i	0.991344	+	0.131293i	$0.0419128\pi$
$809$			7.46870i			0.262585i	−0.991344	+	0.131293i	$0.958087\pi$
$810$	−28.6401	−	3.22478i	−1.00631	−	0.113307i
$811$		−	12.1478i		−	0.426568i	−0.976990	−	0.213284i	$-0.931584\pi$
$811$		−	12.1478i		−	0.426568i	0.976990	−	0.213284i	$-0.0684160\pi$
$812$	4.68581	−	8.11606i	0.164440	−	0.284818i
$813$	8.37044	−	18.7070i	0.293564	−	0.656084i
$814$	−0.528530	−	0.915441i	−0.0185250	−	0.0320862i
$815$	58.7785	−	33.9358i	2.05892	−	1.18872i
$816$	−6.55420	+	4.74339i	−0.229443	+	0.166052i
$817$	4.56387	+	11.3393i	0.159670	+	0.396711i
$818$			18.1554i			0.634787i
$819$	8.63122	−	7.71391i	0.301599	−	0.269546i
$820$		−	0.690397i		−	0.0241097i
$821$	28.1872	+	16.2739i	0.983739	+	0.567962i	0.903397	−	0.428805i	$-0.141065\pi$
$821$	28.1872	+	16.2739i	0.983739	+	0.567962i	0.0803423	+	0.996767i	$0.474399\pi$
$822$	−3.48573	−	33.7657i	−0.121579	−	1.17771i
$823$	−6.06015	−	10.4965i	−0.211243	−	0.365884i	0.740860	−	0.671659i	$-0.234418\pi$
$823$	−6.06015	−	10.4965i	−0.211243	−	0.365884i	−0.952104	+	0.305774i	$0.901085\pi$
$824$	−8.78440	+	5.07167i	−0.306019	+	0.176680i
$825$	−3.98421	−	38.5944i	−0.138713	−	1.34368i
$826$	0.441718	−	0.765078i	0.0153693	−	0.0266205i
$827$	9.56163			0.332490			0.166245	−	0.986084i	$-0.446836\pi$
$827$	9.56163			0.332490			0.166245	+	0.986084i	$0.446836\pi$
$828$	−3.91964	−	18.7821i	−0.136217	−	0.652724i
$829$		−	26.0509i		−	0.904786i	−0.891819	−	0.452393i	$-0.850570\pi$
$829$		−	26.0509i		−	0.904786i	0.891819	−	0.452393i	$-0.149430\pi$
$830$	−9.84646	+	17.0546i	−0.341776	+	0.591973i
$831$	3.06089	+	4.22939i	0.106181	+	0.146716i
$832$	−2.19748	+	1.26872i	−0.0761840	+	0.0439849i
$833$	18.9623	−	10.9479i	0.657005	−	0.379322i
$834$	7.52102	−	16.8087i	0.260432	−	0.582037i
$835$	−66.9304	−	38.6423i	−2.31622	−	1.33727i
$836$	−14.6268	−	11.4590i	−0.505879	−	0.396318i
$837$	19.4080	−	21.3155i	0.670838	−	0.736771i
$838$			15.0840i			0.521067i
$839$	−16.5981	+	28.7487i	−0.573029	+	0.992515i	0.423224	+	0.906025i	$0.360898\pi$
$839$	−16.5981	+	28.7487i	−0.573029	+	0.992515i	−0.996253	+	0.0864896i	$0.972435\pi$
$840$	7.69910	+	3.44495i	0.265644	+	0.118862i
$841$	−4.48973	−	7.77645i	−0.154818	−	0.268153i
$842$	−22.3704	+	12.9156i	−0.770936	+	0.445100i
$843$	16.6693	+	23.0329i	0.574122	+	0.793295i
$844$	0.803576	+	0.463945i	0.0276602	+	0.0159696i
$845$		−	21.0119i		−	0.722833i
$846$	−24.5330	−	8.07178i	−0.843461	−	0.277514i
$847$	10.9051			0.374704
$848$	6.75545	−	11.7008i	0.231983	−	0.401806i
$849$	26.5667	−	2.74256i	0.911765	−	0.0941242i
$850$	−21.2580	+	12.2733i	−0.729144	+	0.420972i
$851$	−0.792974	−	1.37347i	−0.0271828	−	0.0470820i
$852$	17.2255	−	1.77824i	0.590136	−	0.0609215i
$853$	−20.6887	+	35.8339i	−0.708369	+	1.22693i	0.257093	+	0.966387i	$0.417235\pi$
$853$	−20.6887	+	35.8339i	−0.708369	+	1.22693i	−0.965462	+	0.260544i	$0.916098\pi$
$854$	−11.7677			−0.402683
$855$	−34.8342	+	23.2419i	−1.19130	+	0.794857i
$856$	−9.34489			−0.319402
$857$	8.81466	−	15.2674i	0.301103	−	0.521526i	−0.675283	−	0.737559i	$-0.735979\pi$
$857$	8.81466	−	15.2674i	0.301103	−	0.521526i	0.976386	+	0.216033i	$0.0693119\pi$
$858$	10.9839	+	15.1771i	0.374984	+	0.518136i
$859$	−22.7487	−	39.4019i	−0.776176	−	1.34438i	−0.934131	−	0.356931i	$-0.883823\pi$
$859$	−22.7487	−	39.4019i	−0.776176	−	1.34438i	0.157954	−	0.987446i	$-0.449510\pi$
$860$	7.77694	−	4.49002i	0.265192	−	0.153108i
$861$	0.231924	−	0.518325i	0.00790395	−	0.0176645i
$862$	−9.37800	+	16.2432i	−0.319416	+	0.553244i
$863$	19.9241			0.678223			0.339111	−	0.940746i	$-0.389874\pi$
$863$	19.9241			0.678223			0.339111	+	0.940746i	$0.389874\pi$
$864$	3.84213	+	3.49830i	0.130712	+	0.119014i
$865$		−	70.9070i		−	2.41091i
$866$	18.9307	+	10.9296i	0.643291	+	0.371404i
$867$	3.40910	−	7.61896i	0.115779	−	0.258754i
$868$	−7.30625	+	4.21827i	−0.247990	+	0.143177i
$869$	8.27066	+	14.3252i	0.280563	+	0.485949i
$870$	27.6913	−	20.0407i	0.938824	−	0.679444i
$871$	8.21570	−	14.2300i	0.278378	−	0.482166i
$872$			4.86226i			0.164657i
$873$	1.59009	+	7.61940i	0.0538165	+	0.257878i
$874$	−21.9452	−	17.1924i	−0.742306	−	0.581541i
$875$	1.07549	+	0.620934i	0.0363582	+	0.0209914i
$876$	−22.9374	+	2.36789i	−0.774982	+	0.0800037i
$877$	24.0657	−	13.8943i	0.812639	−	0.469178i	−0.0352322	−	0.999379i	$-0.511217\pi$
$877$	24.0657	−	13.8943i	0.812639	−	0.469178i	0.847872	+	0.530202i	$0.177884\pi$
$878$	19.6150	−	11.3247i	0.661973	−	0.382190i
$879$	−42.4810	+	4.38544i	−1.43285	+	0.147917i
$880$	−6.82542	+	11.8220i	−0.230085	+	0.398519i
$881$		−	52.4731i		−	1.76786i	−0.467615	−	0.883932i	$-0.654887\pi$
$881$		−	52.4731i		−	1.76786i	0.467615	−	0.883932i	$-0.345113\pi$
$882$	−9.37091	−	10.4853i	−0.315535	−	0.353057i
$883$	38.6910			1.30206			0.651028	−	0.759054i	$-0.274338\pi$
$883$	38.6910			1.30206			0.651028	+	0.759054i	$0.274338\pi$
$884$	5.92629	−	10.2646i	0.199323	−	0.345237i
$885$	2.61039	−	1.88918i	0.0877471	−	0.0635042i
$886$	−7.04532	+	4.06762i	−0.236692	+	0.136654i
$887$	−7.24759	−	12.5532i	−0.243350	−	0.421495i	0.718316	−	0.695717i	$-0.244913\pi$
$887$	−7.24759	−	12.5532i	−0.243350	−	0.421495i	−0.961666	+	0.274222i	$0.911580\pi$
$888$	0.392049	+	0.175422i	0.0131563	+	0.00588677i
$889$	25.0564	+	14.4663i	0.840365	+	0.485185i
$890$		−	39.7218i		−	1.33148i
$891$	22.7795	−	30.8700i	0.763143	−	1.03418i
$892$			19.2520i			0.644605i
$893$	−34.8115	+	14.0111i	−1.16492	+	0.468863i
$894$	30.2620	+	13.5407i	1.01211	+	0.452868i
$895$	46.3653	−	26.7690i	1.54982	−	0.894790i
$896$	−0.760344	−	1.31695i	−0.0254013	−	0.0439963i
$897$	16.4796	+	22.7707i	0.550237	+	0.760292i
$898$	−17.2244	+	29.8336i	−0.574786	+	0.995559i
$899$			34.1899i			1.14030i
$900$	10.5054	+	11.7547i	0.350181	+	0.391823i
$901$			63.1106i			2.10252i
$902$	0.795889	+	0.459507i	0.0265002	+	0.0152999i
$903$	7.34698	−	0.758451i	0.244492	−	0.0252397i
$904$	2.59521	+	4.49503i	0.0863153	+	0.149503i
$905$	3.08295	+	5.33983i	0.102481	+	0.177502i
$906$	−2.78308	−	26.9592i	−0.0924617	−	0.895660i
$907$	−38.5812	−	22.2749i	−1.28107	−	0.739625i	−0.304024	−	0.952664i	$-0.598330\pi$
$907$	−38.5812	−	22.2749i	−1.28107	−	0.739625i	−0.977044	+	0.213039i	$0.931664\pi$
$908$	−21.1219			−0.700955
$909$	7.10862	+	34.0631i	0.235778	+	1.12980i
$910$	−12.3567			−0.409621
$911$	9.46719	−	16.3977i	0.313662	−	0.543279i	−0.665490	−	0.746407i	$-0.731777\pi$
$911$	9.46719	−	16.3977i	0.313662	−	0.543279i	0.979152	+	0.203128i	$0.0651108\pi$
$912$	7.54436	+	0.287464i	0.249819	+	0.00951887i
$913$	−13.1070	−	22.7020i	−0.433779	−	0.751327i
$914$	14.3739	+	24.8964i	0.475448	+	0.823500i
$915$	−39.1789	−	17.5305i	−1.29521	−	0.579542i
$916$	−0.512954	+	0.888462i	−0.0169485	+	0.0293556i
$917$		−	10.9734i		−	0.362374i
$918$	−23.7129	−	5.17814i	−0.782643	−	0.170904i
$919$	11.7145			0.386424			0.193212	−	0.981157i	$-0.438109\pi$
$919$	11.7145			0.386424			0.193212	+	0.981157i	$0.438109\pi$
$920$	−10.2404	+	17.7370i	−0.337618	+	0.584771i
$921$	−29.1437	−	13.0403i	−0.960317	−	0.429693i
$922$	−6.60586	+	3.81390i	−0.217553	+	0.125604i
$923$	−21.9704	+	12.6846i	−0.723166	+	0.417520i
$924$	−9.09563	+	6.58267i	−0.299224	+	0.216554i
$925$	1.12853	+	0.651557i	0.0371058	+	0.0214231i
$926$	−3.84491			−0.126352
$927$	−28.9057	−	9.51048i	−0.949387	−	0.312365i
$928$	−6.16275			−0.202302
$929$	16.0303	+	9.25507i	0.525936	+	0.303649i	0.739360	−	0.673311i	$-0.235128\pi$
$929$	16.0303	+	9.25507i	0.525936	+	0.303649i	−0.213424	+	0.976960i	$0.568462\pi$
$930$	−30.6091	+	3.15987i	−1.00371	+	0.103616i
$931$	−20.2297	−	2.87048i	−0.663003	−	0.0940763i
$932$	−4.39956	+	2.54009i	−0.144113	+	0.0832034i
$933$	3.20287	+	31.0256i	0.104857	+	1.01573i
$934$	15.0642	+	8.69730i	0.492915	+	0.284584i
$935$		−	63.7643i		−	2.08532i
$936$	−7.23097	−	2.37912i	−0.236352	−	0.0777639i
$937$	−28.6238			−0.935100			−0.467550	−	0.883967i	$-0.654863\pi$
$937$	−28.6238			−0.935100			−0.467550	+	0.883967i	$0.654863\pi$
$938$	8.52806	+	4.92368i	0.278451	+	0.160764i
$939$	11.5759	+	15.9950i	0.377765	+	0.521978i
$940$	13.7844	+	23.8752i	0.449596	+	0.778723i
$941$	4.76089	+	8.24611i	0.155201	+	0.268815i	0.933132	−	0.359534i	$-0.117064\pi$
$941$	4.76089	+	8.24611i	0.155201	+	0.268815i	−0.777931	+	0.628349i	$0.783731\pi$
$942$	−8.04543	+	17.9807i	−0.262134	+	0.585842i
$943$	1.19410	+	0.689416i	0.0388854	+	0.0224505i
$944$	−0.580945			−0.0189082
$945$	7.68561	+	24.1086i	0.250013	+	0.784254i
$946$			11.9537i			0.388648i
$947$	−36.2830	−	20.9480i	−1.17904	−	0.680719i	−0.223247	−	0.974762i	$-0.571666\pi$
$947$	−36.2830	−	20.9480i	−1.17904	−	0.680719i	−0.955792	+	0.294043i	$0.904999\pi$
$948$	−6.13495	−	2.74507i	−0.199254	−	0.0891558i
$949$	29.2557	−	16.8908i	0.949680	−	0.548298i
$950$	22.6789	+	3.21801i	0.735801	+	0.104406i
$951$	30.8122	+	42.5748i	0.999153	+	1.38058i
$952$	6.15161	+	3.55163i	0.199375	+	0.115109i
$953$	29.1035			0.942755			0.471378	−	0.881932i	$-0.343757\pi$
$953$	29.1035			0.942755			0.471378	+	0.881932i	$0.343757\pi$
$954$	39.6779	−	8.28038i	1.28462	−	0.268087i
$955$	−2.35880			−0.0763288
$956$	9.65331	+	5.57334i	0.312210	+	0.180255i
$957$	4.67243	+	45.2610i	0.151038	+	1.46308i
$958$	25.5750	−	14.7657i	0.826291	−	0.477060i
$959$	−25.8100	+	14.9014i	−0.833447	+	0.481191i
$960$	−0.569568	−	5.51730i	−0.0183827	−	0.178070i
$961$	−0.110729	+	0.191788i	−0.00357191	+	0.00618673i
$962$	−0.629221			−0.0202869
$963$	−18.6816	−	20.9031i	−0.602006	−	0.673594i
$964$			11.0135i			0.354721i
$965$	14.5998	−	25.2876i	0.469984	−	0.814036i
$966$	−13.6465	+	9.87623i	−0.439070	+	0.317763i
$967$	−1.66790	−	2.88888i	−0.0536359	−	0.0929001i	0.837961	−	0.545730i	$-0.183748\pi$
$967$	−1.66790	−	2.88888i	−0.0536359	−	0.0929001i	−0.891597	+	0.452830i	$0.850414\pi$
$968$	−3.58558	−	6.21041i	−0.115245	−	0.199610i
$969$	−31.1904	+	16.4573i	−1.00198	+	0.528685i
$970$	4.15427	−	7.19540i	0.133386	−	0.231030i
$971$	−7.01147			−0.225009			−0.112504	−	0.993651i	$-0.535887\pi$
$971$	−7.01147			−0.225009			−0.112504	+	0.993651i	$0.535887\pi$
$972$	−0.144282	+	15.5878i	−0.00462786	+	0.499979i
$973$	−16.1674			−0.518304
$974$	−13.7201	−	7.92129i	−0.439619	−	0.253814i
$975$	−21.0815	−	9.43288i	−0.675147	−	0.302094i
$976$	3.86921	+	6.70166i	0.123850	+	0.214515i
$977$	−17.5963	−	30.4777i	−0.562957	−	0.975069i	−0.997237	−	0.0742914i	$-0.976331\pi$
$977$	−17.5963	−	30.4777i	−0.562957	−	0.975069i	0.434280	−	0.900778i	$-0.357003\pi$
$978$	−21.5224	−	29.7386i	−0.688210	−	0.950937i
$979$	45.7913	+	26.4376i	1.46350	+	0.844951i
$980$			15.0110i			0.479510i
$981$	−10.8762	+	9.72026i	−0.347249	+	0.310344i
$982$		−	4.37074i		−	0.139476i
$983$	1.24877	−	2.16293i	0.0398296	−	0.0689868i	−0.845423	−	0.534097i	$-0.820652\pi$
$983$	1.24877	−	2.16293i	0.0398296	−	0.0689868i	0.885253	+	0.465110i	$0.153985\pi$
$984$	−0.371441	+	0.0383449i	−0.0118411	+	0.00122239i
$985$	13.5748	+	23.5122i	0.432528	+	0.749160i
$986$	24.9301	−	14.3934i	0.793935	−	0.458378i
$987$	2.32844	+	22.5552i	0.0741151	+	0.717940i
$988$	−10.2605	+	4.12970i	−0.326431	+	0.131383i
$989$			17.9346i			0.570286i
$990$	−40.0889	+	8.36615i	−1.27411	+	0.265894i
$991$			1.66534i			0.0529012i	0.999650	+	0.0264506i	$0.00842047\pi$
$991$			1.66534i			0.0529012i	−0.999650	+	0.0264506i	$0.991580\pi$
$992$	4.80457	+	2.77392i	0.152545	+	0.0880721i
$993$	−38.4024	+	27.7925i	−1.21866	+	0.881969i
$994$	−7.60192	−	13.1669i	−0.241118	−	0.417629i
$995$	−45.5752	+	26.3129i	−1.44483	+	0.834174i
$996$	9.72241	+	4.35028i	0.308066	+	0.137844i
$997$	14.3062	−	24.7790i	0.453081	−	0.784760i	−0.545494	−	0.838115i	$-0.683658\pi$
$997$	14.3062	−	24.7790i	0.453081	−	0.784760i	0.998576	+	0.0533546i	$0.0169914\pi$
$998$	20.4879			0.648533
$999$	0.391362	+	1.22765i	0.0123821	+	0.0388410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.p.b.227.5	yes	20
3.2	odd	2		1026.2.p.a.683.10		20
9.2	odd	6		3078.2.b.c.3077.19		20
9.4	even	3		1026.2.p.b.341.10		20
9.5	odd	6		342.2.p.a.113.6	✓	20
9.7	even	3		3078.2.b.a.3077.2		20
19.18	odd	2		342.2.p.a.227.6	yes	20
57.56	even	2		1026.2.p.b.683.10		20
171.56	even	6		3078.2.b.a.3077.19		20
171.94	odd	6		1026.2.p.a.341.10		20
171.113	even	6	inner	342.2.p.b.113.5	yes	20
171.151	odd	6		3078.2.b.c.3077.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.p.a.113.6	✓	20	9.5	odd	6
342.2.p.a.227.6	yes	20	19.18	odd	2
342.2.p.b.113.5	yes	20	171.113	even	6	inner
342.2.p.b.227.5	yes	20	1.1	even	1	trivial
1026.2.p.a.341.10		20	171.94	odd	6
1026.2.p.a.683.10		20	3.2	odd	2
1026.2.p.b.341.10		20	9.4	even	3
1026.2.p.b.683.10		20	57.56	even	2
3078.2.b.a.3077.2		20	9.7	even	3
3078.2.b.a.3077.19		20	171.56	even	6
3078.2.b.c.3077.2		20	171.151	odd	6
3078.2.b.c.3077.19		20	9.2	odd	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.707416 + 1.58100i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.77331 + 1.60117i) q^{5} +(1.01548 + 1.40314i) q^{6} +(0.760344 - 1.31695i) q^{7} -1.00000 q^{8} +(-1.99912 - 2.23685i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.707416 + 1.58100i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.77331 + 1.60117i) q^{5} +(1.01548 + 1.40314i) q^{6} +(0.760344 - 1.31695i) q^{7} -1.00000 q^{8} +(-1.99912 - 2.23685i) q^{9} +3.20235i q^{10} +(-3.69166 - 2.13138i) q^{11} +(1.72289 - 0.177860i) q^{12} +(-2.19748 + 1.26872i) q^{13} +(-0.760344 - 1.31695i) q^{14} +(-0.569568 - 5.51730i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.67109i q^{17} +(-2.93673 + 0.612867i) q^{18} +(-2.68816 + 3.43130i) q^{19} +(2.77331 + 1.60117i) q^{20} +(1.54422 + 2.13374i) q^{21} +(-3.69166 + 2.13138i) q^{22} +(-5.53874 + 3.19780i) q^{23} +(0.707416 - 1.58100i) q^{24} +(2.62751 - 4.55098i) q^{25} +2.53743i q^{26} +(4.95068 - 1.57823i) q^{27} -1.52069 q^{28} +(-3.08137 + 5.33710i) q^{29} +(-5.06291 - 2.26539i) q^{30} +(4.80457 - 2.77392i) q^{31} +(0.500000 + 0.866025i) q^{32} +(5.98126 - 4.32875i) q^{33} +(-4.04528 - 2.33554i) q^{34} +4.86977i q^{35} +(-0.937608 + 2.84972i) q^{36} +0.247975i q^{37} +(1.62751 + 4.04366i) q^{38} +(-0.451307 - 4.37173i) q^{39} +(2.77331 - 1.60117i) q^{40} +(-0.107795 - 0.186707i) q^{41} +(2.61998 - 0.270469i) q^{42} +(1.40210 - 2.42852i) q^{43} +4.26277i q^{44} +(9.12578 + 3.00254i) q^{45} +6.39559i q^{46} +(7.45554 + 4.30446i) q^{47} +(-1.01548 - 1.40314i) q^{48} +(2.34375 + 4.05950i) q^{49} +(-2.62751 - 4.55098i) q^{50} +(7.38499 + 3.30441i) q^{51} +(2.19748 + 1.26872i) q^{52} -13.5109 q^{53} +(1.10855 - 5.07653i) q^{54} +13.6508 q^{55} +(-0.760344 + 1.31695i) q^{56} +(-3.52323 - 6.67734i) q^{57} +(3.08137 + 5.33710i) q^{58} +(0.290473 + 0.503113i) q^{59} +(-4.49334 + 3.25191i) q^{60} +(3.86921 - 6.70166i) q^{61} -5.54784i q^{62} +(-4.46585 + 0.931978i) q^{63} +1.00000 q^{64} +(4.06287 - 7.03710i) q^{65} +(-0.758173 - 7.34430i) q^{66} +(-5.60803 + 3.23780i) q^{67} +(-4.04528 + 2.33554i) q^{68} +(-1.13752 - 11.0189i) q^{69} +(4.21734 + 2.43488i) q^{70} +9.99801 q^{71} +(1.99912 + 2.23685i) q^{72} -13.3133 q^{73} +(0.214753 + 0.123988i) q^{74} +(5.33635 + 7.37353i) q^{75} +(4.31567 + 0.612369i) q^{76} +(-5.61387 + 3.24117i) q^{77} +(-4.01169 - 1.79502i) q^{78} +(-3.36054 - 1.94021i) q^{79} -3.20235i q^{80} +(-1.00701 + 8.94349i) q^{81} -0.215591 q^{82} +(5.32565 + 3.07477i) q^{83} +(1.07576 - 2.40421i) q^{84} +(7.47922 + 12.9544i) q^{85} +(-1.40210 - 2.42852i) q^{86} +(-6.25814 - 8.64720i) q^{87} +(3.69166 + 2.13138i) q^{88} -12.4040 q^{89} +(7.16317 - 6.40189i) q^{90} +3.85865i q^{91} +(5.53874 + 3.19780i) q^{92} +(0.986737 + 9.55835i) q^{93} +(7.45554 - 4.30446i) q^{94} +(1.96102 - 13.8203i) q^{95} +(-1.72289 + 0.177860i) q^{96} +(-2.24692 - 1.29726i) q^{97} +4.68751 q^{98} +(2.61251 + 12.5186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} - q^{3} - 10 q^{4} + q^{6} + 2 q^{7} - 20 q^{8} - q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 - q^3 - 10 * q^4 + q^6 + 2 * q^7 - 20 * q^8 - q^9	\( 20 q + 10 q^{2} - q^{3} - 10 q^{4} + q^{6} + 2 q^{7} - 20 q^{8} - q^{9} - 3 q^{11} + 2 q^{12} - 2 q^{14} + 16 q^{15} - 10 q^{16} - 2 q^{18} + q^{19} - 11 q^{21} - 3 q^{22} - 12 q^{23} + q^{24} + 10 q^{25} + 11 q^{27} - 4 q^{28} + 2 q^{30} - 18 q^{31} + 10 q^{32} + q^{33} + 15 q^{34} - q^{36} - 10 q^{38} + 9 q^{39} + 3 q^{41} - 13 q^{42} - 5 q^{43} - 14 q^{45} + 39 q^{47} - q^{48} - 12 q^{49} - 10 q^{50} + q^{51} - 17 q^{54} - 2 q^{56} - q^{57} - 3 q^{59} - 14 q^{60} + 14 q^{61} - 2 q^{63} + 20 q^{64} - 12 q^{65} - 22 q^{66} - 27 q^{67} + 15 q^{68} + 4 q^{69} - 24 q^{71} + q^{72} + 34 q^{73} + 33 q^{74} + 27 q^{75} - 11 q^{76} - 24 q^{77} + 27 q^{78} + 18 q^{79} - q^{81} + 6 q^{82} + 30 q^{83} - 2 q^{84} + 5 q^{86} - 69 q^{87} + 3 q^{88} - 36 q^{89} + 8 q^{90} + 12 q^{92} + 54 q^{93} + 39 q^{94} + 36 q^{95} - 2 q^{96} - 27 q^{97} - 24 q^{98} + 52 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 - q^3 - 10 * q^4 + q^6 + 2 * q^7 - 20 * q^8 - q^9 - 3 * q^11 + 2 * q^12 - 2 * q^14 + 16 * q^15 - 10 * q^16 - 2 * q^18 + q^19 - 11 * q^21 - 3 * q^22 - 12 * q^23 + q^24 + 10 * q^25 + 11 * q^27 - 4 * q^28 + 2 * q^30 - 18 * q^31 + 10 * q^32 + q^33 + 15 * q^34 - q^36 - 10 * q^38 + 9 * q^39 + 3 * q^41 - 13 * q^42 - 5 * q^43 - 14 * q^45 + 39 * q^47 - q^48 - 12 * q^49 - 10 * q^50 + q^51 - 17 * q^54 - 2 * q^56 - q^57 - 3 * q^59 - 14 * q^60 + 14 * q^61 - 2 * q^63 + 20 * q^64 - 12 * q^65 - 22 * q^66 - 27 * q^67 + 15 * q^68 + 4 * q^69 - 24 * q^71 + q^72 + 34 * q^73 + 33 * q^74 + 27 * q^75 - 11 * q^76 - 24 * q^77 + 27 * q^78 + 18 * q^79 - q^81 + 6 * q^82 + 30 * q^83 - 2 * q^84 + 5 * q^86 - 69 * q^87 + 3 * q^88 - 36 * q^89 + 8 * q^90 + 12 * q^92 + 54 * q^93 + 39 * q^94 + 36 * q^95 - 2 * q^96 - 27 * q^97 - 24 * q^98 + 52 * q^99

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