LMFDB - Embedded newform 546.2.q.e.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	546.251
Dual form			546.2.q.e.335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.52434i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.52434i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +(-2.18614 - 1.26217i) q^{10} +(0.686141 - 1.18843i) q^{11} +(1.18614 + 1.26217i) q^{12} +(3.50000 - 0.866025i) q^{13} +(2.00000 + 1.73205i) q^{14} +(-1.00000 - 4.25639i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-0.186141 + 2.99422i) q^{18} +(1.68614 + 2.92048i) q^{19} +(2.18614 - 1.26217i) q^{20} +(0.186141 + 4.57879i) q^{21} +(0.686141 + 1.18843i) q^{22} +(-0.813859 - 0.469882i) q^{23} +(-1.68614 + 0.396143i) q^{24} -1.37228 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-2.50000 + 0.866025i) q^{28} +(0.686141 + 0.396143i) q^{29} +(4.18614 + 1.26217i) q^{30} -4.74456 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.686141 + 2.27567i) q^{33} -1.37228 q^{34} +(6.55842 + 1.26217i) q^{35} +(-2.50000 - 1.65831i) q^{36} +(7.11684 + 4.10891i) q^{37} -3.37228 q^{38} +(-5.55842 + 2.84674i) q^{39} +2.52434i q^{40} +(5.31386 + 3.06796i) q^{41} +(-4.05842 - 2.12819i) q^{42} +(2.00000 + 3.46410i) q^{43} -1.37228 q^{44} +(3.37228 + 6.78073i) q^{45} +(0.813859 - 0.469882i) q^{46} +4.25639i q^{47} +(0.500000 - 1.65831i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(0.686141 - 1.18843i) q^{50} +(-1.62772 - 1.73205i) q^{51} +(-2.50000 - 2.59808i) q^{52} +14.3537i q^{53} +(-0.872281 - 5.12241i) q^{54} +(3.00000 + 1.73205i) q^{55} +(0.500000 - 2.59808i) q^{56} +(-4.00000 - 4.25639i) q^{57} +(-0.686141 + 0.396143i) q^{58} +(8.18614 - 4.72627i) q^{59} +(-3.18614 + 2.99422i) q^{60} +(4.50000 - 2.59808i) q^{61} +(2.37228 - 4.10891i) q^{62} +(-2.12772 - 7.64675i) q^{63} +1.00000 q^{64} +(2.18614 + 8.83518i) q^{65} +(-1.62772 - 1.73205i) q^{66} +(-7.11684 - 4.10891i) q^{67} +(0.686141 - 1.18843i) q^{68} +(1.55842 + 0.469882i) q^{69} +(-4.37228 + 5.04868i) q^{70} +(-0.558422 - 0.967215i) q^{71} +(2.68614 - 1.33591i) q^{72} +0.744563 q^{73} +(-7.11684 + 4.10891i) q^{74} +(2.31386 - 0.543620i) q^{75} +(1.68614 - 2.92048i) q^{76} +(-2.74456 - 2.37686i) q^{77} +(0.313859 - 6.23711i) q^{78} +15.3723 q^{79} +(-2.18614 - 1.26217i) q^{80} +(5.43070 - 7.17687i) q^{81} +(-5.31386 + 3.06796i) q^{82} -5.04868i q^{83} +(3.87228 - 2.45060i) q^{84} +(-3.00000 + 1.73205i) q^{85} -4.00000 q^{86} +(-1.31386 - 0.396143i) q^{87} +(0.686141 - 1.18843i) q^{88} +(-10.8030 - 6.23711i) q^{89} +(-7.55842 - 0.469882i) q^{90} +(-0.500000 - 9.52628i) q^{91} +0.939764i q^{92} +(8.00000 - 1.87953i) q^{93} +(-3.68614 - 2.12819i) q^{94} +(-7.37228 + 4.25639i) q^{95} +(1.18614 + 1.26217i) q^{96} +(5.37228 + 9.30506i) q^{97} +(5.50000 - 4.33013i) q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 14 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 3 q^{17} + 5 q^{18} + q^{19} + 3 q^{20} - 5 q^{21} - 3 q^{22} - 9 q^{23} - q^{24} + 6 q^{25} - 4 q^{26} - 16 q^{27} - 10 q^{28} - 3 q^{29} + 11 q^{30} + 4 q^{31} - 2 q^{32} + 3 q^{33} + 6 q^{34} + 9 q^{35} - 10 q^{36} - 6 q^{37} - 2 q^{38} - 5 q^{39} + 27 q^{41} + q^{42} + 8 q^{43} + 6 q^{44} + 2 q^{45} + 9 q^{46} + 2 q^{48} - 26 q^{49} - 3 q^{50} - 18 q^{51} - 10 q^{52} + 8 q^{54} + 12 q^{55} + 2 q^{56} - 16 q^{57} + 3 q^{58} + 27 q^{59} - 7 q^{60} + 18 q^{61} - 2 q^{62} - 20 q^{63} + 4 q^{64} + 3 q^{65} - 18 q^{66} + 6 q^{67} - 3 q^{68} - 11 q^{69} - 6 q^{70} + 15 q^{71} + 5 q^{72} - 20 q^{73} + 6 q^{74} + 15 q^{75} + q^{76} + 12 q^{77} + 7 q^{78} + 50 q^{79} - 3 q^{80} - 7 q^{81} - 27 q^{82} + 4 q^{84} - 12 q^{85} - 16 q^{86} - 11 q^{87} - 3 q^{88} - 3 q^{89} - 13 q^{90} - 2 q^{91} + 32 q^{93} - 9 q^{94} - 18 q^{95} - q^{96} + 10 q^{97} + 22 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 - q^12 + 14 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 - 3 * q^17 + 5 * q^18 + q^19 + 3 * q^20 - 5 * q^21 - 3 * q^22 - 9 * q^23 - q^24 + 6 * q^25 - 4 * q^26 - 16 * q^27 - 10 * q^28 - 3 * q^29 + 11 * q^30 + 4 * q^31 - 2 * q^32 + 3 * q^33 + 6 * q^34 + 9 * q^35 - 10 * q^36 - 6 * q^37 - 2 * q^38 - 5 * q^39 + 27 * q^41 + q^42 + 8 * q^43 + 6 * q^44 + 2 * q^45 + 9 * q^46 + 2 * q^48 - 26 * q^49 - 3 * q^50 - 18 * q^51 - 10 * q^52 + 8 * q^54 + 12 * q^55 + 2 * q^56 - 16 * q^57 + 3 * q^58 + 27 * q^59 - 7 * q^60 + 18 * q^61 - 2 * q^62 - 20 * q^63 + 4 * q^64 + 3 * q^65 - 18 * q^66 + 6 * q^67 - 3 * q^68 - 11 * q^69 - 6 * q^70 + 15 * q^71 + 5 * q^72 - 20 * q^73 + 6 * q^74 + 15 * q^75 + q^76 + 12 * q^77 + 7 * q^78 + 50 * q^79 - 3 * q^80 - 7 * q^81 - 27 * q^82 + 4 * q^84 - 12 * q^85 - 16 * q^86 - 11 * q^87 - 3 * q^88 - 3 * q^89 - 13 * q^90 - 2 * q^91 + 32 * q^93 - 9 * q^94 - 18 * q^95 - q^96 + 10 * q^97 + 22 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$			2.52434i			1.12892i	0.825461	+	0.564459i	$0.190915\pi$
$5$			2.52434i			1.12892i	−0.825461	+	0.564459i	$0.809085\pi$
$6$	0.500000	−	1.65831i	0.204124	−	0.677003i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	1.00000			0.353553
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$	−2.18614	−	1.26217i	−0.691318	−	0.399133i
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	−0.743851	−	0.668346i	$-0.767003\pi$
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	0.950730	+	0.310021i	$0.100336\pi$
$12$	1.18614	+	1.26217i	0.342409	+	0.364357i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$	−1.00000	−	4.25639i	−0.258199	−	1.09899i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.686141	+	1.18843i	0.166414	+	0.288237i	0.937156	−	0.348910i	$-0.113448\pi$
$17$	0.686141	+	1.18843i	0.166414	+	0.288237i	−0.770743	+	0.637146i	$0.780115\pi$
$18$	−0.186141	+	2.99422i	−0.0438738	+	0.705744i
$19$	1.68614	+	2.92048i	0.386827	+	0.670004i	0.992021	−	0.126074i	$-0.0402377\pi$
$19$	1.68614	+	2.92048i	0.386827	+	0.670004i	−0.605194	+	0.796078i	$0.706904\pi$
$20$	2.18614	−	1.26217i	0.488836	−	0.282230i
$21$	0.186141	+	4.57879i	0.0406192	+	0.999175i
$22$	0.686141	+	1.18843i	0.146286	+	0.253374i
$23$	−0.813859	−	0.469882i	−0.169701	−	0.0979772i	0.412744	−	0.910847i	$-0.364571\pi$
$23$	−0.813859	−	0.469882i	−0.169701	−	0.0979772i	−0.582445	+	0.812870i	$0.697904\pi$
$24$	−1.68614	+	0.396143i	−0.344182	+	0.0808625i
$25$	−1.37228			−0.274456
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	0.686141	+	0.396143i	0.127413	+	0.0735620i	0.562352	−	0.826898i	$-0.309897\pi$
$29$	0.686141	+	0.396143i	0.127413	+	0.0735620i	−0.434939	+	0.900460i	$0.643230\pi$
$30$	4.18614	+	1.26217i	0.764281	+	0.230439i
$31$	−4.74456			−0.852149			−0.426074	−	0.904688i	$-0.640104\pi$
$31$	−4.74456			−0.852149			−0.426074	+	0.904688i	$0.640104\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.686141	+	2.27567i	−0.119442	+	0.396143i
$34$	−1.37228			−0.235344
$35$	6.55842	+	1.26217i	1.10858	+	0.213345i
$36$	−2.50000	−	1.65831i	−0.416667	−	0.276385i
$37$	7.11684	+	4.10891i	1.17000	+	0.675501i	0.953681	−	0.300821i	$-0.0972608\pi$
$37$	7.11684	+	4.10891i	1.17000	+	0.675501i	0.216321	+	0.976322i	$0.430594\pi$
$38$	−3.37228			−0.547056
$39$	−5.55842	+	2.84674i	−0.890060	+	0.455844i
$40$			2.52434i			0.399133i
$41$	5.31386	+	3.06796i	0.829885	+	0.479135i	0.853813	−	0.520579i	$-0.174284\pi$
$41$	5.31386	+	3.06796i	0.829885	+	0.479135i	−0.0239280	+	0.999714i	$0.507617\pi$
$42$	−4.05842	−	2.12819i	−0.626228	−	0.328388i
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−1.37228			−0.206879
$45$	3.37228	+	6.78073i	0.502710	+	1.01081i
$46$	0.813859	−	0.469882i	0.119997	−	0.0692803i
$47$			4.25639i			0.620858i	0.950597	+	0.310429i	$0.100473\pi$
$47$			4.25639i			0.620858i	−0.950597	+	0.310429i	$0.899527\pi$
$48$	0.500000	−	1.65831i	0.0721688	−	0.239357i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	0.686141	−	1.18843i	0.0970349	−	0.168069i
$51$	−1.62772	−	1.73205i	−0.227926	−	0.242536i
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$			14.3537i			1.97164i	0.167813	+	0.985819i	$0.446330\pi$
$53$			14.3537i			1.97164i	−0.167813	+	0.985819i	$0.553670\pi$
$54$	−0.872281	−	5.12241i	−0.118702	−	0.697072i
$55$	3.00000	+	1.73205i	0.404520	+	0.233550i
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$	−4.00000	−	4.25639i	−0.529813	−	0.563772i
$58$	−0.686141	+	0.396143i	−0.0900947	+	0.0520162i
$59$	8.18614	−	4.72627i	1.06574	−	0.615308i	0.138729	−	0.990330i	$-0.455698\pi$
$59$	8.18614	−	4.72627i	1.06574	−	0.615308i	0.927016	+	0.375022i	$0.122365\pi$
$60$	−3.18614	+	2.99422i	−0.411329	+	0.386552i
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	−0.183442	−	0.983030i	$-0.558724\pi$
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	0.759608	+	0.650381i	$0.225391\pi$
$62$	2.37228	−	4.10891i	0.301280	−	0.521832i
$63$	−2.12772	−	7.64675i	−0.268067	−	0.963400i
$64$	1.00000			0.125000
$65$	2.18614	+	8.83518i	0.271157	+	1.09587i
$66$	−1.62772	−	1.73205i	−0.200358	−	0.213201i
$67$	−7.11684	−	4.10891i	−0.869461	−	0.501983i	−0.00229183	−	0.999997i	$-0.500730\pi$
$67$	−7.11684	−	4.10891i	−0.869461	−	0.501983i	−0.867169	+	0.498014i	$0.834063\pi$
$68$	0.686141	−	1.18843i	0.0832068	−	0.144118i
$69$	1.55842	+	0.469882i	0.187612	+	0.0565671i
$70$	−4.37228	+	5.04868i	−0.522588	+	0.603432i
$71$	−0.558422	−	0.967215i	−0.0662725	−	0.114787i	0.830985	−	0.556294i	$-0.187777\pi$
$71$	−0.558422	−	0.967215i	−0.0662725	−	0.114787i	−0.897258	+	0.441507i	$0.854444\pi$
$72$	2.68614	−	1.33591i	0.316565	−	0.157438i
$73$	0.744563			0.0871445			0.0435722	−	0.999050i	$-0.486126\pi$
$73$	0.744563			0.0871445			0.0435722	+	0.999050i	$0.486126\pi$
$74$	−7.11684	+	4.10891i	−0.827316	+	0.477651i
$75$	2.31386	−	0.543620i	0.267181	−	0.0627719i
$76$	1.68614	−	2.92048i	0.193414	−	0.335002i
$77$	−2.74456	−	2.37686i	−0.312772	−	0.270868i
$78$	0.313859	−	6.23711i	0.0355376	−	0.706213i
$79$	15.3723			1.72952			0.864758	−	0.502188i	$-0.167472\pi$
$79$	15.3723			1.72952			0.864758	+	0.502188i	$0.167472\pi$
$80$	−2.18614	−	1.26217i	−0.244418	−	0.141115i
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$	−5.31386	+	3.06796i	−0.586818	+	0.338799i
$83$		−	5.04868i		−	0.554164i	−0.960846	−	0.277082i	$-0.910633\pi$
$83$		−	5.04868i		−	0.554164i	0.960846	−	0.277082i	$-0.0893674\pi$
$84$	3.87228	−	2.45060i	0.422501	−	0.267382i
$85$	−3.00000	+	1.73205i	−0.325396	+	0.187867i
$86$	−4.00000			−0.431331
$87$	−1.31386	−	0.396143i	−0.140861	−	0.0424710i
$88$	0.686141	−	1.18843i	0.0731428	−	0.126687i
$89$	−10.8030	−	6.23711i	−1.14511	−	0.661132i	−0.197422	−	0.980319i	$-0.563257\pi$
$89$	−10.8030	−	6.23711i	−1.14511	−	0.661132i	−0.947692	+	0.319187i	$0.896590\pi$
$90$	−7.55842	−	0.469882i	−0.796728	−	0.0495299i
$91$	−0.500000	−	9.52628i	−0.0524142	−	0.998625i
$92$			0.939764i			0.0979772i
$93$	8.00000	−	1.87953i	0.829561	−	0.194898i
$94$	−3.68614	−	2.12819i	−0.380196	−	0.219506i
$95$	−7.37228	+	4.25639i	−0.756380	+	0.436696i
$96$	1.18614	+	1.26217i	0.121060	+	0.128820i
$97$	5.37228	+	9.30506i	0.545473	+	0.944786i	0.998577	+	0.0533287i	$0.0169831\pi$
$97$	5.37228	+	9.30506i	0.545473	+	0.944786i	−0.453104	+	0.891457i	$0.649684\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$	0.255437	−	4.10891i	0.0256724	−	0.412961i
$100$	0.686141	+	1.18843i	0.0686141	+	0.118843i
$101$	1.62772	−	2.81929i	0.161964	−	0.280530i	−0.773609	−	0.633663i	$-0.781550\pi$
$101$	1.62772	−	2.81929i	0.161964	−	0.280530i	0.935573	+	0.353133i	$0.114884\pi$
$102$	2.31386	−	0.543620i	0.229106	−	0.0538264i
$103$		−	11.6819i		−	1.15105i	−0.817783	−	0.575527i	$-0.804797\pi$
$103$		−	11.6819i		−	1.15105i	0.817783	−	0.575527i	$-0.195203\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	−11.5584	+	0.469882i	−1.12799	+	0.0458558i
$106$	−12.4307	−	7.17687i	−1.20738	−	0.697079i
$107$	3.68614	+	2.12819i	0.356353	+	0.205740i	0.667480	−	0.744628i	$-0.267373\pi$
$107$	3.68614	+	2.12819i	0.356353	+	0.205740i	−0.311127	+	0.950368i	$0.600706\pi$
$108$	4.87228	+	1.80579i	0.468835	+	0.173762i
$109$		−	19.8997i		−	1.90605i	−0.302891	−	0.953025i	$-0.597952\pi$
$109$		−	19.8997i		−	1.90605i	0.302891	−	0.953025i	$-0.402048\pi$
$110$	−3.00000	+	1.73205i	−0.286039	+	0.165145i
$111$	−13.6277	−	4.10891i	−1.29349	−	0.390001i
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	−14.7446	+	8.51278i	−1.38705	+	0.800815i	−0.992982	−	0.118266i	$-0.962267\pi$
$113$	−14.7446	+	8.51278i	−1.38705	+	0.800815i	−0.394070	+	0.919081i	$0.628933\pi$
$114$	5.68614	−	1.33591i	0.532556	−	0.125119i
$115$	1.18614	−	2.05446i	0.110608	−	0.191579i
$116$		−	0.792287i		−	0.0735620i
$117$	8.24456	−	7.00194i	0.762210	−	0.647330i
$118$			9.45254i			0.870177i
$119$	3.43070	−	1.18843i	0.314492	−	0.108943i
$120$	−1.00000	−	4.25639i	−0.0912871	−	0.388553i
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$			5.19615i			0.470438i
$123$	−10.1753	−	3.06796i	−0.917473	−	0.276628i
$124$	2.37228	+	4.10891i	0.213037	+	0.368991i
$125$			9.15759i			0.819080i
$126$	7.68614	+	1.98072i	0.684736	+	0.176456i
$127$	−7.55842	+	13.0916i	−0.670701	+	1.16169i	0.307004	+	0.951708i	$0.400673\pi$
$127$	−7.55842	+	13.0916i	−0.670701	+	1.16169i	−0.977706	+	0.209981i	$0.932660\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.74456	−	5.04868i	−0.417735	−	0.444511i
$130$	−8.74456	−	2.52434i	−0.766949	−	0.221399i
$131$	18.6060			1.62561			0.812806	−	0.582535i	$-0.197939\pi$
$131$	18.6060			1.62561			0.812806	+	0.582535i	$0.197939\pi$
$132$	2.31386	−	0.543620i	0.201396	−	0.0473161i
$133$	8.43070	−	2.92048i	0.731035	−	0.253238i
$134$	7.11684	−	4.10891i	0.614802	−	0.354956i
$135$	−8.37228	−	10.0974i	−0.720571	−	0.869042i
$136$	0.686141	+	1.18843i	0.0588361	+	0.101907i
$137$	−0.813859	−	1.40965i	−0.0695327	−	0.120434i	0.829163	−	0.559007i	$-0.188817\pi$
$137$	−0.813859	−	1.40965i	−0.0695327	−	0.120434i	−0.898696	+	0.438573i	$0.855484\pi$
$138$	−1.18614	+	1.11469i	−0.100971	+	0.0948889i
$139$	18.1753	−	10.4935i	1.54161	−	0.890047i	0.542868	−	0.839818i	$-0.317338\pi$
$139$	18.1753	−	10.4935i	1.54161	−	0.890047i	0.998738	−	0.0502287i	$-0.0159950\pi$
$140$	−2.18614	−	6.31084i	−0.184763	−	0.533364i
$141$	−1.68614	−	7.17687i	−0.141999	−	0.604401i
$142$	1.11684			0.0937235
$143$	1.37228	−	4.75372i	0.114756	−	0.397526i
$144$	−0.186141	+	2.99422i	−0.0155117	+	0.249518i
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$	−0.372281	+	0.644810i	−0.0308102	+	0.0533649i
$147$	11.9891	+	1.80579i	0.988846	+	0.148939i
$148$		−	8.21782i		−	0.675501i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	−0.686141	+	2.27567i	−0.0560232	+	0.185808i
$151$		−	3.02167i		−	0.245900i	−0.992413	−	0.122950i	$-0.960765\pi$
$151$		−	3.02167i		−	0.245900i	0.992413	−	0.122950i	$-0.0392355\pi$
$152$	1.68614	+	2.92048i	0.136764	+	0.236882i
$153$	3.43070	+	2.27567i	0.277356	+	0.183977i
$154$	3.43070	−	1.18843i	0.276454	−	0.0957665i
$155$		−	11.9769i		−	0.962006i
$156$	5.24456	+	3.39036i	0.419901	+	0.271446i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	−7.68614	+	13.3128i	−0.611477	+	1.05911i
$159$	−5.68614	−	24.2024i	−0.450940	−	1.91938i
$160$	2.18614	−	1.26217i	0.172830	−	0.0997832i
$161$	−1.62772	+	1.87953i	−0.128282	+	0.148128i
$162$	3.50000	+	8.29156i	0.274986	+	0.651447i
$163$	−9.00000	+	5.19615i	−0.704934	+	0.406994i	−0.809183	−	0.587557i	$-0.800090\pi$
$163$	−9.00000	+	5.19615i	−0.704934	+	0.406994i	0.104248	+	0.994551i	$0.466756\pi$
$164$		−	6.13592i		−	0.479135i
$165$	−5.74456	−	1.73205i	−0.447214	−	0.134840i
$166$	4.37228	+	2.52434i	0.339355	+	0.195927i
$167$	−5.74456	−	3.31662i	−0.444528	−	0.256648i	0.260989	−	0.965342i	$-0.415951\pi$
$167$	−5.74456	−	3.31662i	−0.444528	−	0.256648i	−0.705516	+	0.708694i	$0.749285\pi$
$168$	0.186141	+	4.57879i	0.0143611	+	0.353262i
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		−	3.46410i		−	0.265684i
$171$	8.43070	+	5.59230i	0.644712	+	0.427654i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−9.55842	−	16.5557i	−0.726713	−	1.25870i	−0.958265	−	0.285882i	$-0.907714\pi$
$173$	−9.55842	−	16.5557i	−0.726713	−	1.25870i	0.231552	−	0.972823i	$-0.425620\pi$
$174$	1.00000	−	0.939764i	0.0758098	−	0.0712433i
$175$	−0.686141	+	3.56529i	−0.0518674	+	0.269511i
$176$	0.686141	+	1.18843i	0.0517198	+	0.0895813i
$177$	−11.9307	+	11.2120i	−0.896767	+	0.842749i
$178$	10.8030	−	6.23711i	0.809718	−	0.467491i
$179$	−1.37228	−	0.792287i	−0.102569	−	0.0592183i	0.447838	−	0.894115i	$-0.352194\pi$
$179$	−1.37228	−	0.792287i	−0.102569	−	0.0592183i	−0.550407	+	0.834896i	$0.685527\pi$
$180$	4.18614	−	6.31084i	0.312017	−	0.470383i
$181$			12.1244i			0.901196i	0.892727	+	0.450598i	$0.148789\pi$
$181$			12.1244i			0.901196i	−0.892727	+	0.450598i	$0.851211\pi$
$182$	8.50000	+	4.33013i	0.630062	+	0.320970i
$183$	−6.55842	+	6.16337i	−0.484813	+	0.455609i
$184$	−0.813859	−	0.469882i	−0.0599985	−	0.0346402i
$185$	−10.3723	+	17.9653i	−0.762585	+	1.32084i
$186$	−2.37228	+	7.86797i	−0.173944	+	0.576907i
$187$	1.88316			0.137710
$188$	3.68614	−	2.12819i	0.268839	−	0.155215i
$189$	6.61684	+	12.0506i	0.481305	+	0.876553i
$190$		−	8.51278i		−	0.617582i
$191$	16.3723	−	9.45254i	1.18466	−	0.683962i	0.227569	−	0.973762i	$-0.426922\pi$
$191$	16.3723	−	9.45254i	1.18466	−	0.683962i	0.957087	+	0.289800i	$0.0935888\pi$
$192$	−1.68614	+	0.396143i	−0.121687	+	0.0285892i
$193$	−5.61684	−	3.24289i	−0.404309	−	0.233428i	0.284032	−	0.958815i	$-0.408328\pi$
$193$	−5.61684	−	3.24289i	−0.404309	−	0.233428i	−0.688342	+	0.725387i	$0.741661\pi$
$194$	−10.7446			−0.771415
$195$	−7.18614	−	14.0313i	−0.514610	−	1.00480i
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−7.80298	+	13.5152i	−0.555940	+	0.962916i	0.441890	+	0.897069i	$0.354308\pi$
$197$	−7.80298	+	13.5152i	−0.555940	+	0.962916i	−0.997830	+	0.0658465i	$0.979025\pi$
$198$	3.43070	+	2.27567i	0.243809	+	0.161725i
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	0.389885	+	0.920864i	$0.372515\pi$
$200$	−1.37228			−0.0970349
$201$	13.6277	+	4.10891i	0.961225	+	0.289820i
$202$	1.62772	+	2.81929i	0.114526	+	0.198365i
$203$	1.37228	−	1.58457i	0.0963153	−	0.111215i
$204$	−0.686141	+	2.27567i	−0.0480395	+	0.159329i
$205$	−7.74456	+	13.4140i	−0.540904	+	0.936873i
$206$	10.1168	+	5.84096i	0.704874	+	0.406959i
$207$	−2.81386	−	0.174928i	−0.195577	−	0.0121584i
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	4.62772			0.320106
$210$	5.37228	−	10.2448i	0.370723	−	0.706960i
$211$	−11.3723	+	19.6974i	−0.782900	+	1.35602i	0.147345	+	0.989085i	$0.452927\pi$
$211$	−11.3723	+	19.6974i	−0.782900	+	1.35602i	−0.930246	+	0.366938i	$0.880406\pi$
$212$	12.4307	−	7.17687i	0.853744	−	0.492909i
$213$	1.32473	+	1.40965i	0.0907693	+	0.0965873i
$214$	−3.68614	+	2.12819i	−0.251979	+	0.145480i
$215$	−8.74456	+	5.04868i	−0.596374	+	0.344317i
$216$	−4.00000	+	3.31662i	−0.272166	+	0.225668i
$217$	−2.37228	+	12.3267i	−0.161041	+	0.836793i
$218$	17.2337	+	9.94987i	1.16721	+	0.673891i
$219$	−1.25544	+	0.294954i	−0.0848346	+	0.0199311i
$220$		−	3.46410i		−	0.233550i
$221$	3.43070	+	3.56529i	0.230774	+	0.239827i
$222$	10.3723	−	9.74749i	0.696142	−	0.654209i
$223$	−3.11684	+	5.39853i	−0.208719	+	0.361512i	−0.951311	−	0.308232i	$-0.900263\pi$
$223$	−3.11684	+	5.39853i	−0.208719	+	0.361512i	0.742592	+	0.669744i	$0.233596\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$	−3.68614	+	1.83324i	−0.245743	+	0.122216i
$226$		−	17.0256i		−	1.13252i
$227$	3.30298	−	1.90698i	0.219227	−	0.126571i	−0.386365	−	0.922346i	$-0.626270\pi$
$227$	3.30298	−	1.90698i	0.219227	−	0.126571i	0.605592	+	0.795775i	$0.292936\pi$
$228$	−1.68614	+	5.59230i	−0.111667	+	0.370359i
$229$	−12.1168			−0.800704			−0.400352	−	0.916362i	$-0.631112\pi$
$229$	−12.1168			−0.800704			−0.400352	+	0.916362i	$0.631112\pi$
$230$	1.18614	+	2.05446i	0.0782118	+	0.135467i
$231$	5.56930	+	2.92048i	0.366433	+	0.192154i
$232$	0.686141	+	0.396143i	0.0450473	+	0.0260081i
$233$		−	28.0627i		−	1.83845i	−0.393737	−	0.919223i	$-0.628818\pi$
$233$		−	28.0627i		−	1.83845i	0.393737	−	0.919223i	$-0.371182\pi$
$234$	1.94158	+	10.6410i	0.126925	+	0.695622i
$235$	−10.7446			−0.700898
$236$	−8.18614	−	4.72627i	−0.532872	−	0.307654i
$237$	−25.9198	+	6.08963i	−1.68367	+	0.395564i
$238$	−0.686141	+	3.56529i	−0.0444759	+	0.231104i
$239$	−24.6060			−1.59163			−0.795814	−	0.605541i	$-0.792957\pi$
$239$	−24.6060			−1.59163			−0.795814	+	0.605541i	$0.792957\pi$
$240$	4.18614	+	1.26217i	0.270214	+	0.0814727i
$241$	−0.627719	−	1.08724i	−0.0404349	−	0.0700353i	0.845100	−	0.534609i	$-0.179541\pi$
$241$	−0.627719	−	1.08724i	−0.0404349	−	0.0700353i	−0.885535	+	0.464573i	$0.846208\pi$
$242$	−9.11684			−0.586053
$243$	−6.31386	+	14.2525i	−0.405034	+	0.914302i
$244$	−4.50000	−	2.59808i	−0.288083	−	0.166325i
$245$	6.55842	−	16.4082i	0.419002	−	1.04828i
$246$	7.74456	−	7.27806i	0.493775	−	0.464032i
$247$	8.43070	+	8.76144i	0.536433	+	0.557477i
$248$	−4.74456			−0.301280
$249$	2.00000	+	8.51278i	0.126745	+	0.539475i
$250$	−7.93070	−	4.57879i	−0.501582	−	0.289588i
$251$	0.558422	+	0.967215i	0.0352473	+	0.0610501i	0.883111	−	0.469164i	$-0.155445\pi$
$251$	0.558422	+	0.967215i	0.0352473	+	0.0610501i	−0.847864	+	0.530214i	$0.822111\pi$
$252$	−5.55842	+	5.66603i	−0.350148	+	0.356927i
$253$	−1.11684	+	0.644810i	−0.0702154	+	0.0405389i
$254$	−7.55842	−	13.0916i	−0.474258	−	0.821438i
$255$	4.37228	−	4.10891i	0.273803	−	0.257310i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.0584	+	19.1537i	−0.689805	+	1.19478i	0.282095	+	0.959386i	$0.408971\pi$
$257$	−11.0584	+	19.1537i	−0.689805	+	1.19478i	−0.971901	+	0.235392i	$0.924363\pi$
$258$	6.74456	−	1.58457i	0.419898	−	0.0986513i
$259$	14.2337	−	16.4356i	0.884438	−	1.02126i
$260$	6.55842	−	6.31084i	0.406736	−	0.391382i
$261$	2.37228	+	0.147477i	0.146841	+	0.00912859i
$262$	−9.30298	+	16.1132i	−0.574740	+	0.995479i
$263$	−12.0475	−	6.95565i	−0.742884	−	0.428904i	0.0802332	−	0.996776i	$-0.474433\pi$
$263$	−12.0475	−	6.95565i	−0.742884	−	0.428904i	−0.823117	+	0.567872i	$0.807767\pi$
$264$	−0.686141	+	2.27567i	−0.0422290	+	0.140058i
$265$	−36.2337			−2.22582
$266$	−1.68614	+	8.76144i	−0.103384	+	0.537199i
$267$	20.6861	+	6.23711i	1.26597	+	0.381705i
$268$			8.21782i			0.501983i
$269$	−13.9307	−	24.1287i	−0.849370	−	1.47115i	−0.881771	−	0.471677i	$-0.843649\pi$
$269$	−13.9307	−	24.1287i	−0.849370	−	1.47115i	0.0324014	−	0.999475i	$-0.489684\pi$
$270$	12.9307	−	2.20193i	0.786938	−	0.134005i
$271$	−2.00000	+	3.46410i	−0.121491	+	0.210429i	−0.920356	−	0.391082i	$-0.872101\pi$
$271$	−2.00000	+	3.46410i	−0.121491	+	0.210429i	0.798865	+	0.601511i	$0.205434\pi$
$272$	−1.37228			−0.0832068
$273$	4.61684	+	15.8646i	0.279424	+	0.960168i
$274$	1.62772			0.0983341
$275$	−0.941578	+	1.63086i	−0.0567793	+	0.0983446i
$276$	−0.372281	−	1.58457i	−0.0224087	−	0.0953801i
$277$	4.74456	+	8.21782i	0.285073	+	0.493761i	0.972627	−	0.232372i	$-0.0746488\pi$
$277$	4.74456	+	8.21782i	0.285073	+	0.493761i	−0.687554	+	0.726133i	$0.741315\pi$
$278$			20.9870i			1.25872i
$279$	−12.7446	+	6.33830i	−0.762997	+	0.379464i
$280$	6.55842	+	1.26217i	0.391941	+	0.0754290i
$281$	3.25544			0.194203			0.0971016	−	0.995274i	$-0.469043\pi$
$281$	3.25544			0.194203			0.0971016	+	0.995274i	$0.469043\pi$
$282$	7.05842	+	2.12819i	0.420323	+	0.126732i
$283$	6.55842	+	3.78651i	0.389858	+	0.225084i	0.682098	−	0.731260i	$-0.261068\pi$
$283$	6.55842	+	3.78651i	0.389858	+	0.225084i	−0.292241	+	0.956345i	$0.594401\pi$
$284$	−0.558422	+	0.967215i	−0.0331362	+	0.0573937i
$285$	10.7446	−	10.0974i	0.636453	−	0.598115i
$286$	3.43070	+	3.56529i	0.202862	+	0.210820i
$287$	10.6277	−	12.2718i	0.627334	−	0.724383i
$288$	−2.50000	−	1.65831i	−0.147314	−	0.0977170i
$289$	7.55842	−	13.0916i	0.444613	−	0.770092i
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$	−12.7446	−	13.5615i	−0.747099	−	0.794986i
$292$	−0.372281	−	0.644810i	−0.0217861	−	0.0377347i
$293$	14.7446	−	8.51278i	0.861387	−	0.497322i	−0.00308982	−	0.999995i	$-0.500984\pi$
$293$	14.7446	−	8.51278i	0.861387	−	0.497322i	0.864476	+	0.502673i	$0.167650\pi$
$294$	−7.55842	+	9.47999i	−0.440816	+	0.552884i
$295$	11.9307	+	20.6646i	0.694632	+	1.20314i
$296$	7.11684	+	4.10891i	0.413658	+	0.238826i
$297$	1.19702	+	7.02939i	0.0694579	+	0.407887i
$298$	−6.00000			−0.347571
$299$	−3.25544	−	0.939764i	−0.188267	−	0.0543479i
$300$	−1.62772	−	1.73205i	−0.0939764	−	0.100000i
$301$	10.0000	−	3.46410i	0.576390	−	0.199667i
$302$	2.61684	+	1.51084i	0.150582	+	0.0869388i
$303$	−1.62772	+	5.39853i	−0.0935100	+	0.310138i
$304$	−3.37228			−0.193414
$305$	6.55842	+	11.3595i	0.375534	+	0.650444i
$306$	−3.68614	+	1.83324i	−0.210723	+	0.104799i
$307$	−13.2337			−0.755286			−0.377643	−	0.925951i	$-0.623265\pi$
$307$	−13.2337			−0.755286			−0.377643	+	0.925951i	$0.623265\pi$
$308$	−0.686141	+	3.56529i	−0.0390965	+	0.203151i
$309$	4.62772	+	19.6974i	0.263262	+	1.12054i
$310$	10.3723	+	5.98844i	0.589106	+	0.340121i
$311$	4.62772			0.262414			0.131207	−	0.991355i	$-0.458115\pi$
$311$	4.62772			0.262414			0.131207	+	0.991355i	$0.458115\pi$
$312$	−5.55842	+	2.84674i	−0.314684	+	0.161165i
$313$		−	13.8564i		−	0.783210i	−0.920133	−	0.391605i	$-0.871920\pi$
$313$		−	13.8564i		−	0.783210i	0.920133	−	0.391605i	$-0.128080\pi$
$314$		0			0
$315$	19.3030	−	5.37108i	1.08760	−	0.302626i
$316$	−7.68614	−	13.3128i	−0.432379	−	0.748903i
$317$	26.7446			1.50212			0.751062	−	0.660232i	$-0.229542\pi$
$317$	26.7446			1.50212			0.751062	+	0.660232i	$0.229542\pi$
$318$	23.8030	+	7.17687i	1.33481	+	0.402459i
$319$	0.941578	−	0.543620i	0.0527182	−	0.0304369i
$320$			2.52434i			0.141115i
$321$	−7.05842	−	2.12819i	−0.393963	−	0.118784i
$322$	−0.813859	−	2.34941i	−0.0453546	−	0.130927i
$323$	−2.31386	+	4.00772i	−0.128747	+	0.222996i
$324$	−8.93070	−	1.11469i	−0.496150	−	0.0619273i
$325$	−4.80298	+	1.18843i	−0.266422	+	0.0659223i
$326$		−	10.3923i		−	0.575577i
$327$	7.88316	+	33.5538i	0.435940	+	1.85553i
$328$	5.31386	+	3.06796i	0.293409	+	0.169400i
$329$	11.0584	+	2.12819i	0.609671	+	0.117331i
$330$	4.37228	−	4.10891i	0.240686	−	0.226188i
$331$	−19.1168	+	11.0371i	−1.05076	+	0.606655i	−0.922861	−	0.385133i	$-0.874156\pi$
$331$	−19.1168	+	11.0371i	−1.05076	+	0.606655i	−0.127896	+	0.991788i	$0.540822\pi$
$332$	−4.37228	+	2.52434i	−0.239960	+	0.138541i
$333$	24.6060	+	1.52967i	1.34840	+	0.0838255i
$334$	5.74456	−	3.31662i	0.314328	−	0.181478i
$335$	10.3723	−	17.9653i	0.566698	−	0.981550i
$336$	−4.05842	−	2.12819i	−0.221405	−	0.116103i
$337$	29.6060			1.61274			0.806370	−	0.591411i	$-0.201429\pi$
$337$	29.6060			1.61274			0.806370	+	0.591411i	$0.201429\pi$
$338$	−0.500000	+	12.9904i	−0.0271964	+	0.706584i
$339$	21.4891	−	20.1947i	1.16713	−	1.09683i
$340$	3.00000	+	1.73205i	0.162698	+	0.0939336i
$341$	−3.25544	+	5.63858i	−0.176292	+	0.305346i
$342$	−9.05842	+	4.50506i	−0.489823	+	0.243605i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	2.00000	+	3.46410i	0.107833	+	0.186772i
$345$	−1.18614	+	3.93398i	−0.0638597	+	0.211799i
$346$	19.1168			1.02773
$347$	13.5475	−	7.82168i	0.727270	−	0.419890i	−0.0901523	−	0.995928i	$-0.528735\pi$
$347$	13.5475	−	7.82168i	0.727270	−	0.419890i	0.817423	+	0.576038i	$0.195402\pi$
$348$	0.313859	+	1.33591i	0.0168246	+	0.0716121i
$349$	−1.44158	+	2.49689i	−0.0771659	+	0.133655i	−0.902026	−	0.431682i	$-0.857920\pi$
$349$	−1.44158	+	2.49689i	−0.0771659	+	0.133655i	0.824860	+	0.565337i	$0.191254\pi$
$350$	−2.74456	−	2.37686i	−0.146703	−	0.127049i
$351$	−11.1277	+	15.0723i	−0.593954	+	0.804499i
$352$	−1.37228			−0.0731428
$353$	−19.6277	−	11.3321i	−1.04468	−	0.603145i	−0.123523	−	0.992342i	$-0.539419\pi$
$353$	−19.6277	−	11.3321i	−1.04468	−	0.603145i	−0.921155	+	0.389197i	$0.872753\pi$
$354$	−3.74456	−	15.9383i	−0.199021	−	0.847112i
$355$	2.44158	−	1.40965i	0.129586	−	0.0748162i
$356$			12.4742i			0.661132i
$357$	−5.31386	+	3.36291i	−0.281239	+	0.177984i
$358$	1.37228	−	0.792287i	0.0725273	−	0.0418737i
$359$	−22.3723			−1.18076			−0.590382	−	0.807124i	$-0.701023\pi$
$359$	−22.3723			−1.18076			−0.590382	+	0.807124i	$0.701023\pi$
$360$	3.37228	+	6.78073i	0.177735	+	0.357376i
$361$	3.81386	−	6.60580i	0.200729	−	0.347674i
$362$	−10.5000	−	6.06218i	−0.551868	−	0.318621i
$363$	−10.8139	−	11.5070i	−0.567580	−	0.603961i
$364$	−8.00000	+	5.19615i	−0.419314	+	0.272352i
$365$			1.87953i			0.0983790i
$366$	−2.05842	−	8.76144i	−0.107595	−	0.457968i
$367$	−8.23369	−	4.75372i	−0.429795	−	0.248142i	0.269464	−	0.963010i	$-0.413153\pi$
$367$	−8.23369	−	4.75372i	−0.429795	−	0.248142i	−0.699259	+	0.714868i	$0.746487\pi$
$368$	0.813859	−	0.469882i	0.0424254	−	0.0244943i
$369$	18.3723	+	1.14214i	0.956423	+	0.0594576i
$370$	−10.3723	−	17.9653i	−0.539229	−	0.933972i
$371$	37.2921	+	7.17687i	1.93611	+	0.372605i
$372$	−5.62772	−	5.98844i	−0.291784	−	0.310486i
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$	−0.941578	+	1.63086i	−0.0486878	+	0.0843298i
$375$	−3.62772	−	15.4410i	−0.187335	−	0.797369i
$376$			4.25639i			0.219506i
$377$	2.74456	+	0.792287i	0.141352	+	0.0408049i
$378$	−13.7446	−	0.294954i	−0.706944	−	0.0151708i
$379$	−22.1168	−	12.7692i	−1.13607	−	0.655908i	−0.190613	−	0.981665i	$-0.561047\pi$
$379$	−22.1168	−	12.7692i	−1.13607	−	0.655908i	−0.945453	+	0.325757i	$0.894381\pi$
$380$	7.37228	+	4.25639i	0.378190	+	0.218348i
$381$	7.55842	−	25.0684i	0.387230	−	1.28430i
$382$			18.9051i			0.967268i
$383$	−27.4307	+	15.8371i	−1.40164	+	0.809239i	−0.994561	−	0.104152i	$-0.966787\pi$
$383$	−27.4307	+	15.8371i	−1.40164	+	0.809239i	−0.407082	+	0.913392i	$0.633454\pi$
$384$	0.500000	−	1.65831i	0.0255155	−	0.0846254i
$385$	6.00000	−	6.92820i	0.305788	−	0.353094i
$386$	5.61684	−	3.24289i	0.285890	−	0.165059i
$387$	10.0000	+	6.63325i	0.508329	+	0.337187i
$388$	5.37228	−	9.30506i	0.272736	−	0.472393i
$389$		−	22.6641i		−	1.14912i	−0.818463	−	0.574559i	$-0.805174\pi$
$389$		−	22.6641i		−	1.14912i	0.818463	−	0.574559i	$-0.194826\pi$
$390$	15.7446	+	0.792287i	0.797257	+	0.0401190i
$391$		−	1.28962i		−	0.0652189i
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	−31.3723	+	7.37063i	−1.58252	+	0.371799i
$394$	−7.80298	−	13.5152i	−0.393109	−	0.680884i
$395$			38.8048i			1.95248i
$396$	−3.68614	+	1.83324i	−0.185236	+	0.0921238i
$397$	6.87228	+	11.9031i	0.344910	+	0.597401i	0.985337	−	0.170617i	$-0.0545761\pi$
$397$	6.87228	+	11.9031i	0.344910	+	0.597401i	−0.640427	+	0.768019i	$0.721243\pi$
$398$		−	3.46410i		−	0.173640i
$399$	−13.0584	+	8.26411i	−0.653739	+	0.413723i
$400$	0.686141	−	1.18843i	0.0343070	−	0.0594215i
$401$	5.74456	−	9.94987i	0.286870	−	0.496873i	−0.686191	−	0.727421i	$-0.740719\pi$
$401$	5.74456	−	9.94987i	0.286870	−	0.496873i	0.973061	+	0.230548i	$0.0740520\pi$
$402$	−10.3723	+	9.74749i	−0.517322	+	0.486161i
$403$	−16.6060	+	4.10891i	−0.827202	+	0.204679i
$404$	−3.25544			−0.161964
$405$	18.1168	+	13.7089i	0.900233	+	0.681202i
$406$	0.686141	+	1.98072i	0.0340526	+	0.0983014i
$407$	9.76631	−	5.63858i	0.484098	−	0.279494i
$408$	−1.62772	−	1.73205i	−0.0805841	−	0.0857493i
$409$	0.744563	+	1.28962i	0.0368163	+	0.0637676i	0.883846	−	0.467777i	$-0.154945\pi$
$409$	0.744563	+	1.28962i	0.0368163	+	0.0637676i	−0.847030	+	0.531545i	$0.821612\pi$
$410$	−7.74456	−	13.4140i	−0.382477	−	0.662469i
$411$	1.93070	+	2.05446i	0.0952346	+	0.101339i
$412$	−10.1168	+	5.84096i	−0.498421	+	0.287764i
$413$	−8.18614	−	23.6314i	−0.402814	−	1.16282i
$414$	1.55842	−	2.34941i	0.0765923	−	0.115467i
$415$	12.7446			0.625606
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	−26.4891	+	24.8935i	−1.29718	+	1.21904i
$418$	−2.31386	+	4.00772i	−0.113175	+	0.196024i
$419$	−8.74456	+	15.1460i	−0.427200	+	0.739932i	−0.996623	−	0.0821127i	$-0.973833\pi$
$419$	−8.74456	+	15.1460i	−0.427200	+	0.739932i	0.569423	+	0.822045i	$0.307167\pi$
$420$	6.18614	+	9.77495i	0.301853	+	0.476969i
$421$		−	12.9715i		−	0.632194i	−0.948727	−	0.316097i	$-0.897627\pi$
$421$		−	12.9715i		−	0.632194i	0.948727	−	0.316097i	$-0.102373\pi$
$422$	−11.3723	−	19.6974i	−0.553594	−	0.958853i
$423$	5.68614	+	11.4333i	0.276470	+	0.555904i
$424$			14.3537i			0.697079i
$425$	−0.941578	−	1.63086i	−0.0456732	−	0.0791084i
$426$	−1.88316	+	0.442430i	−0.0912392	+	0.0214358i
$427$	−4.50000	−	12.9904i	−0.217770	−	0.628649i
$428$		−	4.25639i		−	0.205740i
$429$	−0.430703	+	8.55906i	−0.0207946	+	0.413236i
$430$		−	10.0974i		−	0.486938i
$431$	−9.81386	+	16.9981i	−0.472717	+	0.818770i	−0.999512	−	0.0312223i	$-0.990060\pi$
$431$	−9.81386	+	16.9981i	−0.472717	+	0.818770i	0.526795	+	0.849992i	$0.323393\pi$
$432$	−0.872281	−	5.12241i	−0.0419677	−	0.246452i
$433$	30.3505	−	17.5229i	1.45855	−	0.842096i	0.459613	−	0.888119i	$-0.347988\pi$
$433$	30.3505	−	17.5229i	1.45855	−	0.842096i	0.998940	+	0.0460230i	$0.0146548\pi$
$434$	−9.48913	−	8.21782i	−0.455493	−	0.394468i
$435$	1.00000	−	3.31662i	0.0479463	−	0.159020i
$436$	−17.2337	+	9.94987i	−0.825344	+	0.476513i
$437$		−	3.16915i		−	0.151601i
$438$	0.372281	−	1.23472i	0.0177883	−	0.0589971i
$439$	30.3505	+	17.5229i	1.44855	+	0.836322i	0.998395	−	0.0566279i	$-0.0180349\pi$
$439$	30.3505	+	17.5229i	1.44855	+	0.836322i	0.450157	+	0.892950i	$0.351368\pi$
$440$	3.00000	+	1.73205i	0.143019	+	0.0825723i
$441$	−20.9307	+	1.70460i	−0.996700	+	0.0811714i
$442$	−4.80298	+	1.18843i	−0.228455	+	0.0565279i
$443$		−	11.1846i		−	0.531396i	−0.964056	−	0.265698i	$-0.914398\pi$
$443$		−	11.1846i		−	0.531396i	0.964056	−	0.265698i	$-0.0856024\pi$
$444$	3.25544	+	13.8564i	0.154496	+	0.657596i
$445$	15.7446	−	27.2704i	0.746364	−	1.29274i
$446$	−3.11684	−	5.39853i	−0.147587	−	0.255628i
$447$	−7.11684	−	7.57301i	−0.336615	−	0.358191i
$448$	0.500000	−	2.59808i	0.0236228	−	0.122748i
$449$	0.302985	+	0.524785i	0.0142987	+	0.0247661i	0.873086	−	0.487566i	$-0.162115\pi$
$449$	0.302985	+	0.524785i	0.0142987	+	0.0247661i	−0.858788	+	0.512332i	$0.828782\pi$
$450$	0.255437	−	4.10891i	0.0120414	−	0.193696i
$451$	7.29211	−	4.21010i	0.343372	−	0.198246i
$452$	14.7446	+	8.51278i	0.693526	+	0.400407i
$453$	1.19702	+	5.09496i	0.0562407	+	0.239382i
$454$			3.81396i			0.178998i
$455$	24.0475	−	1.26217i	1.12737	−	0.0591714i
$456$	−4.00000	−	4.25639i	−0.187317	−	0.199324i
$457$	−16.6753	−	9.62747i	−0.780036	−	0.450354i	0.0564070	−	0.998408i	$-0.482036\pi$
$457$	−16.6753	−	9.62747i	−0.780036	−	0.450354i	−0.836443	+	0.548054i	$0.815369\pi$
$458$	6.05842	−	10.4935i	0.283091	−	0.490329i
$459$	−6.68614	−	2.47805i	−0.312082	−	0.115666i
$460$	−2.37228			−0.110608
$461$	13.0693	−	7.54556i	0.608698	−	0.351432i	−0.163758	−	0.986501i	$-0.552362\pi$
$461$	13.0693	−	7.54556i	0.608698	−	0.351432i	0.772456	+	0.635069i	$0.219028\pi$
$462$	−5.31386	+	3.36291i	−0.247223	+	0.156457i
$463$		−	30.7345i		−	1.42835i	−0.699966	−	0.714176i	$-0.746801\pi$
$463$		−	30.7345i		−	1.42835i	0.699966	−	0.714176i	$-0.253199\pi$
$464$	−0.686141	+	0.396143i	−0.0318533	+	0.0183905i
$465$	4.74456	+	20.1947i	0.220024	+	0.936507i
$466$	24.3030	+	14.0313i	1.12581	+	0.649989i
$467$	−19.6277			−0.908263			−0.454131	−	0.890935i	$-0.650050\pi$
$467$	−19.6277			−0.908263			−0.454131	+	0.890935i	$0.650050\pi$
$468$	−10.1861	−	3.63903i	−0.470855	−	0.168214i
$469$	−14.2337	+	16.4356i	−0.657251	+	0.758928i
$470$	5.37228	−	9.30506i	0.247805	−	0.429211i
$471$		0			0
$472$	8.18614	−	4.72627i	0.376798	−	0.217544i
$473$	5.48913			0.252390
$474$	7.68614	−	25.4920i	0.353036	−	1.17089i
$475$	−2.31386	−	4.00772i	−0.106167	−	0.183887i
$476$	−2.74456	−	2.37686i	−0.125797	−	0.108943i
$477$	19.1753	+	38.5562i	0.877975	+	1.76537i
$478$	12.3030	−	21.3094i	0.562725	−	0.974669i
$479$	−22.8030	−	13.1653i	−1.04189	−	0.601538i	−0.121526	−	0.992588i	$-0.538779\pi$
$479$	−22.8030	−	13.1653i	−1.04189	−	0.601538i	−0.920369	+	0.391050i	$0.872112\pi$
$480$	−3.18614	+	2.99422i	−0.145427	+	0.136667i
$481$	28.4674	+	8.21782i	1.29800	+	0.374701i
$482$	1.25544			0.0571836
$483$	2.00000	−	3.81396i	0.0910032	−	0.173541i
$484$	4.55842	−	7.89542i	0.207201	−	0.358883i
$485$	−23.4891	+	13.5615i	−1.06659	+	0.615794i
$486$	−9.18614	−	12.5942i	−0.416692	−	0.571286i
$487$	−9.38316	+	5.41737i	−0.425191	+	0.245484i	−0.697296	−	0.716783i	$-0.745614\pi$
$487$	−9.38316	+	5.41737i	−0.425191	+	0.245484i	0.272105	+	0.962268i	$0.412280\pi$
$488$	4.50000	−	2.59808i	0.203705	−	0.117609i
$489$	13.1168	−	12.3267i	0.593164	−	0.557434i
$490$	10.9307	+	13.8839i	0.493799	+	0.627209i
$491$	−33.6060	−	19.4024i	−1.51662	−	0.875619i	−0.999810	−	0.0195166i	$-0.993787\pi$
$491$	−33.6060	−	19.4024i	−1.51662	−	0.875619i	−0.516807	−	0.856102i	$-0.672879\pi$
$492$	2.43070	+	10.3460i	0.109585	+	0.466435i
$493$			1.08724i			0.0489669i
$494$	−11.8030	+	2.92048i	−0.531041	+	0.131399i
$495$	10.3723	+	0.644810i	0.466199	+	0.0289821i
$496$	2.37228	−	4.10891i	0.106519	−	0.184496i
$497$	−2.79211	+	0.967215i	−0.125243	+	0.0433855i
$498$	−8.37228	−	2.52434i	−0.375171	−	0.113118i
$499$		−	23.3639i		−	1.04591i	−0.852360	−	0.522955i	$-0.824830\pi$
$499$		−	23.3639i		−	1.04591i	0.852360	−	0.522955i	$-0.175170\pi$
$500$	7.93070	−	4.57879i	0.354672	−	0.204770i
$501$	11.0000	+	3.31662i	0.491444	+	0.148176i
$502$	−1.11684			−0.0498472
$503$	−11.4891	−	19.8997i	−0.512275	−	0.887286i	−0.999899	−	0.0142322i	$-0.995470\pi$
$503$	−11.4891	−	19.8997i	−0.512275	−	0.887286i	0.487624	−	0.873054i	$-0.337864\pi$
$504$	−2.12772	−	7.64675i	−0.0947761	−	0.340613i
$505$	7.11684	+	4.10891i	0.316695	+	0.182844i
$506$		−	1.28962i		−	0.0573306i
$507$	−16.9891	+	14.7773i	−0.754514	+	0.656284i
$508$	15.1168			0.670701
$509$	−23.1861	−	13.3865i	−1.02771	−	0.593347i	−0.111381	−	0.993778i	$-0.535527\pi$
$509$	−23.1861	−	13.3865i	−1.02771	−	0.593347i	−0.916327	+	0.400431i	$0.868861\pi$
$510$	1.37228	+	5.84096i	0.0607656	+	0.258642i
$511$	0.372281	−	1.93443i	0.0164688	−	0.0855742i
$512$	1.00000			0.0441942
$513$	−16.4307	−	6.08963i	−0.725433	−	0.268864i
$514$	−11.0584	−	19.1537i	−0.487766	−	0.844836i
$515$	29.4891			1.29945
$516$	−2.00000	+	6.63325i	−0.0880451	+	0.292013i
$517$	5.05842	+	2.92048i	0.222469	+	0.128443i
$518$	7.11684	+	20.5446i	0.312696	+	0.902676i
$519$	22.6753	+	24.1287i	0.995334	+	1.05913i
$520$	2.18614	+	8.83518i	0.0958686	+	0.387448i
$521$	−16.1168			−0.706092			−0.353046	−	0.935606i	$-0.614854\pi$
$521$	−16.1168			−0.706092			−0.353046	+	0.935606i	$0.614854\pi$
$522$	−1.31386	+	1.98072i	−0.0575061	+	0.0866936i
$523$	−7.50000	−	4.33013i	−0.327952	−	0.189343i	0.326979	−	0.945031i	$-0.393969\pi$
$523$	−7.50000	−	4.33013i	−0.327952	−	0.189343i	−0.654932	+	0.755688i	$0.727303\pi$
$524$	−9.30298	−	16.1132i	−0.406403	−	0.703910i
$525$	−0.255437	−	6.28339i	−0.0111482	−	0.274230i
$526$	12.0475	−	6.95565i	0.525298	−	0.303281i
$527$	−3.25544	−	5.63858i	−0.141809	−	0.245621i
$528$	−1.62772	−	1.73205i	−0.0708374	−	0.0753778i
$529$	−11.0584	−	19.1537i	−0.480801	−	0.832772i
$530$	18.1168	−	31.3793i	0.786945	−	1.36303i
$531$	15.6753	−	23.6314i	0.680249	−	1.02551i
$532$	−6.74456	−	5.84096i	−0.292414	−	0.253238i
$533$	21.2554	+	6.13592i	0.920675	+	0.265776i
$534$	−15.7446	+	14.7962i	−0.681334	+	0.640293i
$535$	−5.37228	+	9.30506i	−0.232264	+	0.402293i
$536$	−7.11684	−	4.10891i	−0.307401	−	0.177478i
$537$	2.62772	+	0.792287i	0.113394	+	0.0341897i
$538$	27.8614			1.20119
$539$	−7.54755	+	5.94215i	−0.325096	+	0.255947i
$540$	−4.55842	+	12.2993i	−0.196163	+	0.529277i
$541$		−	18.6101i		−	0.800112i	−0.916491	−	0.400056i	$-0.868991\pi$
$541$		−	18.6101i		−	0.800112i	0.916491	−	0.400056i	$-0.131009\pi$
$542$	−2.00000	−	3.46410i	−0.0859074	−	0.148796i
$543$	−4.80298	−	20.4434i	−0.206116	−	0.877309i
$544$	0.686141	−	1.18843i	0.0294180	−	0.0509535i
$545$	50.2337			2.15177
$546$	−16.0475	−	3.93398i	−0.686772	−	0.168359i
$547$	31.4891			1.34638			0.673189	−	0.739471i	$-0.264924\pi$
$547$	31.4891			1.34638			0.673189	+	0.739471i	$0.264924\pi$
$548$	−0.813859	+	1.40965i	−0.0347663	+	0.0602171i
$549$	8.61684	−	12.9904i	0.367758	−	0.554416i
$550$	−0.941578	−	1.63086i	−0.0401490	−	0.0695401i
$551$			2.67181i			0.113823i
$552$	1.55842	+	0.469882i	0.0663308	+	0.0199995i
$553$	7.68614	−	39.9384i	0.326848	−	1.69835i
$554$	−9.48913			−0.403154
$555$	10.3723	−	34.4010i	0.440279	−	1.46024i
$556$	−18.1753	−	10.4935i	−0.770803	−	0.445023i
$557$	7.80298	−	13.5152i	0.330623	−	0.572656i	−0.652011	−	0.758209i	$-0.726074\pi$
$557$	7.80298	−	13.5152i	0.330623	−	0.572656i	0.982634	+	0.185553i	$0.0594078\pi$
$558$	0.883156	−	14.2063i	0.0373870	−	0.601399i
$559$	10.0000	+	10.3923i	0.422955	+	0.439548i
$560$	−4.37228	+	5.04868i	−0.184763	+	0.213345i
$561$	−3.17527	+	0.746000i	−0.134060	+	0.0314961i
$562$	−1.62772	+	2.81929i	−0.0686612	+	0.118925i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−5.37228	+	5.04868i	−0.226214	+	0.212588i
$565$	−21.4891	−	37.2203i	−0.904054	−	1.56587i
$566$	−6.55842	+	3.78651i	−0.275671	+	0.159159i
$567$	−15.9307	−	17.6978i	−0.669027	−	0.743238i
$568$	−0.558422	−	0.967215i	−0.0234309	−	0.0405835i
$569$	−19.1644	−	11.0646i	−0.803413	−	0.463851i	0.0412501	−	0.999149i	$-0.486866\pi$
$569$	−19.1644	−	11.0646i	−0.803413	−	0.463851i	−0.844663	+	0.535298i	$0.820199\pi$
$570$	3.37228	+	14.3537i	0.141249	+	0.601212i
$571$	13.4891			0.564502			0.282251	−	0.959341i	$-0.408919\pi$
$571$	13.4891			0.564502			0.282251	+	0.959341i	$0.408919\pi$
$572$	−4.80298	+	1.18843i	−0.200823	+	0.0496908i
$573$	−23.8614	+	22.4241i	−0.996825	+	0.936780i
$574$	5.31386	+	15.3398i	0.221796	+	0.640270i
$575$	1.11684	+	0.644810i	0.0465756	+	0.0268904i
$576$	2.68614	−	1.33591i	0.111923	−	0.0556628i
$577$	−40.2337			−1.67495			−0.837475	−	0.546475i	$-0.815969\pi$
$577$	−40.2337			−1.67495			−0.837475	+	0.546475i	$0.815969\pi$
$578$	7.55842	+	13.0916i	0.314389	+	0.544538i
$579$	10.7554	+	3.24289i	0.446981	+	0.134770i
$580$	2.00000			0.0830455
$581$	−13.1168	−	2.52434i	−0.544178	−	0.104727i
$582$	18.1168	−	4.25639i	0.750967	−	0.176433i
$583$	17.0584	+	9.84868i	0.706488	+	0.407891i
$584$	0.744563			0.0308102
$585$	17.6753	+	20.8121i	0.730782	+	0.860473i
$586$			17.0256i			0.703319i
$587$	−5.95245	−	3.43665i	−0.245684	−	0.141846i	0.372102	−	0.928192i	$-0.378637\pi$
$587$	−5.95245	−	3.43665i	−0.245684	−	0.141846i	−0.617786	+	0.786346i	$0.711970\pi$
$588$	−4.43070	−	11.2858i	−0.182719	−	0.465418i
$589$	−8.00000	−	13.8564i	−0.329634	−	0.570943i
$590$	−23.8614			−0.982359
$591$	7.80298	−	25.8796i	0.320972	−	1.06454i
$592$	−7.11684	+	4.10891i	−0.292500	+	0.168875i
$593$			26.3306i			1.08127i	0.841258	+	0.540634i	$0.181816\pi$
$593$			26.3306i			1.08127i	−0.841258	+	0.540634i	$0.818184\pi$
$594$	−6.68614	−	2.47805i	−0.274336	−	0.101676i
$595$	3.00000	+	8.66025i	0.122988	+	0.355036i
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	4.37228	−	4.10891i	0.178946	−	0.168167i
$598$	2.44158	−	2.34941i	0.0998435	−	0.0960745i
$599$			13.9113i			0.568401i	0.958765	+	0.284200i	$0.0917281\pi$
$599$			13.9113i			0.568401i	−0.958765	+	0.284200i	$0.908272\pi$
$600$	2.31386	−	0.543620i	0.0944629	−	0.0221932i
$601$	19.8832	+	11.4795i	0.811051	+	0.468260i	0.847321	−	0.531082i	$-0.178214\pi$
$601$	19.8832	+	11.4795i	0.811051	+	0.468260i	−0.0362698	+	0.999342i	$0.511548\pi$
$602$	−2.00000	+	10.3923i	−0.0815139	+	0.423559i
$603$	−24.6060	−	1.52967i	−1.00203	−	0.0622930i
$604$	−2.61684	+	1.51084i	−0.106478	+	0.0614750i
$605$	−19.9307	+	11.5070i	−0.810298	+	0.467826i
$606$	−3.86141	−	4.10891i	−0.156859	−	0.166913i
$607$	−21.3505	+	12.3267i	−0.866591	+	0.500327i	−0.866214	−	0.499673i	$-0.833453\pi$
$607$	−21.3505	+	12.3267i	−0.866591	+	0.500327i	−0.000377344		1.00000i	$0.500120\pi$
$608$	1.68614	−	2.92048i	0.0683820	−	0.118441i
$609$	−1.68614	+	3.21543i	−0.0683259	+	0.130296i
$610$	−13.1168			−0.531085
$611$	3.68614	+	14.8974i	0.149125	+	0.602683i
$612$	0.255437	−	4.10891i	0.0103254	−	0.166093i
$613$	26.2337	+	15.1460i	1.05957	+	0.611742i	0.925313	−	0.379204i	$-0.123802\pi$
$613$	26.2337	+	15.1460i	1.05957	+	0.611742i	0.134256	+	0.990947i	$0.457136\pi$
$614$	6.61684	−	11.4607i	0.267034	−	0.462517i
$615$	7.74456	−	25.6858i	0.312291	−	1.03575i
$616$	−2.74456	−	2.37686i	−0.110582	−	0.0957665i
$617$	3.30298	+	5.72094i	0.132973	+	0.230316i	0.924821	−	0.380402i	$-0.124214\pi$
$617$	3.30298	+	5.72094i	0.132973	+	0.230316i	−0.791848	+	0.610718i	$0.790881\pi$
$618$	−19.3723	−	5.84096i	−0.779267	−	0.234958i
$619$	35.4674			1.42555			0.712777	−	0.701391i	$-0.247437\pi$
$619$	35.4674			1.42555			0.712777	+	0.701391i	$0.247437\pi$
$620$	−10.3723	+	5.98844i	−0.416561	+	0.240502i
$621$	4.81386	−	0.819738i	0.193174	−	0.0328950i
$622$	−2.31386	+	4.00772i	−0.0927773	+	0.160695i
$623$	−21.6060	+	24.9484i	−0.865625	+	0.999538i
$624$	0.313859	−	6.23711i	0.0125644	−	0.249684i
$625$	−29.9783			−1.19913
$626$	12.0000	+	6.92820i	0.479616	+	0.276907i
$627$	−7.80298	+	1.83324i	−0.311621	+	0.0732126i
$628$		0			0
$629$			11.2772i			0.449650i
$630$	−5.00000	+	19.4024i	−0.199205	+	0.773011i
$631$	−28.5000	+	16.4545i	−1.13457	+	0.655043i	−0.945080	−	0.326841i	$-0.894016\pi$
$631$	−28.5000	+	16.4545i	−1.13457	+	0.655043i	−0.189488	+	0.981883i	$0.560683\pi$
$632$	15.3723			0.611477
$633$	11.3723	−	37.7176i	0.452008	−	1.49914i
$634$	−13.3723	+	23.1615i	−0.531081	+	0.919860i
$635$	−33.0475	−	19.0800i	−1.31145	−	0.757167i
$636$	−18.1168	+	17.0256i	−0.718380	+	0.675107i
$637$	−25.0000	−	3.46410i	−0.990536	−	0.137253i
$638$			1.08724i			0.0430443i
$639$	−2.79211	−	1.85208i	−0.110454	−	0.0732670i
$640$	−2.18614	−	1.26217i	−0.0864148	−	0.0498916i
$641$	25.1644	−	14.5287i	0.993934	−	0.573848i	0.0874859	−	0.996166i	$-0.472117\pi$
$641$	25.1644	−	14.5287i	0.993934	−	0.573848i	0.906448	+	0.422318i	$0.138783\pi$
$642$	5.37228	−	5.04868i	0.212027	−	0.199255i
$643$	15.6168	+	27.0492i	0.615868	+	1.06672i	0.990232	+	0.139433i	$0.0445280\pi$
$643$	15.6168	+	27.0492i	0.615868	+	1.06672i	−0.374363	+	0.927282i	$0.622139\pi$
$644$	2.44158	+	0.469882i	0.0962117	+	0.0185159i
$645$	12.7446	−	11.9769i	0.501817	−	0.471589i
$646$	−2.31386	−	4.00772i	−0.0910376	−	0.157682i
$647$	5.56930	−	9.64630i	0.218952	−	0.379235i	−0.735536	−	0.677486i	$-0.763070\pi$
$647$	5.56930	−	9.64630i	0.218952	−	0.379235i	0.954488	+	0.298250i	$0.0964030\pi$
$648$	5.43070	−	7.17687i	0.213338	−	0.281934i
$649$		−	12.9715i		−	0.509178i
$650$	1.37228	−	4.75372i	0.0538253	−	0.186456i
$651$	−0.883156	−	21.7244i	−0.0346136	−	0.851445i
$652$	9.00000	+	5.19615i	0.352467	+	0.203497i
$653$	−22.5475	−	13.0178i	−0.882354	−	0.509427i	−0.0109200	−	0.999940i	$-0.503476\pi$
$653$	−22.5475	−	13.0178i	−0.882354	−	0.509427i	−0.871434	+	0.490513i	$0.836809\pi$
$654$	−33.0000	−	9.94987i	−1.29040	−	0.389071i
$655$			46.9678i			1.83518i
$656$	−5.31386	+	3.06796i	−0.207471	+	0.119784i
$657$	2.00000	−	0.994667i	0.0780274	−	0.0388056i
$658$	−7.37228	+	8.51278i	−0.287401	+	0.331863i
$659$	11.6644	−	6.73444i	0.454380	−	0.262337i	−0.255298	−	0.966862i	$-0.582174\pi$
$659$	11.6644	−	6.73444i	0.454380	−	0.262337i	0.709678	+	0.704526i	$0.248840\pi$
$660$	1.37228	+	5.84096i	0.0534160	+	0.227359i
$661$	−24.9307	+	43.1812i	−0.969692	+	1.67956i	−0.273249	+	0.961943i	$0.588098\pi$
$661$	−24.9307	+	43.1812i	−0.969692	+	1.67956i	−0.696443	+	0.717613i	$0.745235\pi$
$662$		−	22.0742i		−	0.857939i
$663$	−7.19702	−	4.65253i	−0.279509	−	0.180689i
$664$		−	5.04868i		−	0.195927i
$665$	7.37228	+	21.2819i	0.285885	+	0.825278i
$666$	−13.6277	+	20.5446i	−0.528063	+	0.796085i
$667$	−0.372281	−	0.644810i	−0.0144148	−	0.0249671i
$668$			6.63325i			0.256648i
$669$	3.11684	−	10.3374i	0.120504	−	0.399667i
$670$	10.3723	+	17.9653i	0.400716	+	0.694061i
$671$		−	7.13058i		−	0.275273i
$672$	3.87228	−	2.45060i	0.149376	−	0.0945339i
$673$	1.31386	−	2.27567i	0.0506456	−	0.0877207i	−0.839591	−	0.543219i	$-0.817205\pi$
$673$	1.31386	−	2.27567i	0.0506456	−	0.0877207i	0.890237	+	0.455498i	$0.150539\pi$
$674$	−14.8030	+	25.6395i	−0.570190	+	0.987597i
$675$	5.48913	−	4.55134i	0.211277	−	0.175181i
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−4.37228			−0.168040			−0.0840202	−	0.996464i	$-0.526776\pi$
$677$	−4.37228			−0.168040			−0.0840202	+	0.996464i	$0.526776\pi$
$678$	6.74456	+	28.7075i	0.259023	+	1.10250i
$679$	26.8614	−	9.30506i	1.03085	−	0.357096i
$680$	−3.00000	+	1.73205i	−0.115045	+	0.0664211i
$681$	−4.81386	+	4.52389i	−0.184467	+	0.173356i
$682$	−3.25544	−	5.63858i	−0.124657	−	0.215912i
$683$	−21.8614	−	37.8651i	−0.836503	−	1.44887i	−0.892800	−	0.450452i	$-0.851263\pi$
$683$	−21.8614	−	37.8651i	−0.836503	−	1.44887i	0.0562969	−	0.998414i	$-0.482071\pi$
$684$	0.627719	−	10.0974i	0.0240014	−	0.386082i
$685$	3.55842	−	2.05446i	0.135960	−	0.0784967i
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	20.4307	−	4.80001i	0.779480	−	0.183132i
$688$	−4.00000			−0.152499
$689$	12.4307	+	50.2381i	0.473572	+	1.91392i
$690$	−2.81386	−	2.99422i	−0.107122	−	0.113988i
$691$	19.5584	−	33.8762i	0.744037	−	1.28871i	−0.206606	−	0.978424i	$-0.566242\pi$
$691$	19.5584	−	33.8762i	0.744037	−	1.28871i	0.950643	−	0.310286i	$-0.100425\pi$
$692$	−9.55842	+	16.5557i	−0.363357	+	0.629352i
$693$	−10.5475	−	2.71810i	−0.400668	−	0.103252i
$694$			15.6434i			0.593814i
$695$	26.4891	+	45.8805i	1.00479	+	1.74035i
$696$	−1.31386	−	0.396143i	−0.0498017	−	0.0150158i
$697$			8.42020i			0.318938i
$698$	−1.44158	−	2.49689i	−0.0545645	−	0.0945085i
$699$	11.1168	+	47.3176i	0.420478	+	1.78972i
$700$	3.43070	−	1.18843i	0.129668	−	0.0449185i
$701$			22.1668i			0.837229i	0.908164	+	0.418614i	$0.137484\pi$
$701$			22.1668i			0.837229i	−0.908164	+	0.418614i	$0.862516\pi$
$702$	−7.48913	−	17.1730i	−0.282659	−	0.648154i
$703$			27.7128i			1.04521i
$704$	0.686141	−	1.18843i	0.0258599	−	0.0447907i
$705$	18.1168	−	4.25639i	0.682320	−	0.160305i
$706$	19.6277	−	11.3321i	0.738699	−	0.426488i
$707$	−6.51087	−	5.63858i	−0.244867	−	0.212061i
$708$	15.6753	+	4.72627i	0.589113	+	0.177624i
$709$	−40.1168	+	23.1615i	−1.50662	+	0.869847i	−0.506649	+	0.862152i	$0.669116\pi$
$709$	−40.1168	+	23.1615i	−1.50662	+	0.869847i	−0.999970	+	0.00769505i	$0.997551\pi$
$710$			2.81929i			0.105806i
$711$	41.2921	−	20.5359i	1.54858	−	0.770158i
$712$	−10.8030	−	6.23711i	−0.404859	−	0.233745i
$713$	3.86141	+	2.22938i	0.144611	+	0.0834911i
$714$	−0.255437	−	6.28339i	−0.00955950	−	0.235150i
$715$	12.0000	+	3.46410i	0.448775	+	0.129550i
$716$			1.58457i			0.0592183i
$717$	41.4891	−	9.74749i	1.54944	−	0.364027i
$718$	11.1861	−	19.3750i	0.417463	−	0.723067i
$719$	3.94158	+	6.82701i	0.146996	+	0.254605i	0.930116	−	0.367266i	$-0.119706\pi$
$719$	3.94158	+	6.82701i	0.146996	+	0.254605i	−0.783120	+	0.621871i	$0.786373\pi$
$720$	−7.55842	−	0.469882i	−0.281686	−	0.0175115i
$721$	−30.3505	−	5.84096i	−1.13031	−	0.217529i
$722$	3.81386	+	6.60580i	0.141937	+	0.245842i
$723$	1.48913	+	1.58457i	0.0553812	+	0.0589309i
$724$	10.5000	−	6.06218i	0.390229	−	0.225299i
$725$	−0.941578	−	0.543620i	−0.0349693	−	0.0201896i
$726$	15.3723	−	3.61158i	0.570519	−	0.134038i
$727$			31.5817i			1.17130i	0.810564	+	0.585650i	$0.199161\pi$
$727$			31.5817i			1.17130i	−0.810564	+	0.585650i	$0.800839\pi$
$728$	−0.500000	−	9.52628i	−0.0185312	−	0.353067i
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−1.62772	−	0.939764i	−0.0602446	−	0.0347822i
$731$	−2.74456	+	4.75372i	−0.101511	+	0.175823i
$732$	8.61684	+	2.59808i	0.318488	+	0.0960277i
$733$	−32.2554			−1.19138			−0.595691	−	0.803214i	$-0.703122\pi$
$733$	−32.2554			−1.19138			−0.595691	+	0.803214i	$0.703122\pi$
$734$	8.23369	−	4.75372i	0.303911	−	0.175463i
$735$	−4.55842	+	30.2646i	−0.168140	+	1.11633i
$736$			0.939764i			0.0346402i
$737$	−9.76631	+	5.63858i	−0.359747	+	0.207700i
$738$	−10.1753	+	15.3398i	−0.374557	+	0.564665i
$739$	−16.8832	−	9.74749i	−0.621057	−	0.358567i	0.156223	−	0.987722i	$-0.450068\pi$
$739$	−16.8832	−	9.74749i	−0.621057	−	0.358567i	−0.777280	+	0.629154i	$0.783401\pi$
$740$	20.7446			0.762585
$741$	−17.6861	−	11.4333i	−0.649717	−	0.420011i
$742$	−24.8614	+	28.7075i	−0.912691	+	1.05388i
$743$	−7.37228	+	12.7692i	−0.270463	+	0.468455i	−0.968980	−	0.247138i	$-0.920510\pi$
$743$	−7.37228	+	12.7692i	−0.270463	+	0.468455i	0.698518	+	0.715593i	$0.253843\pi$
$744$	8.00000	−	1.87953i	0.293294	−	0.0689068i
$745$	−13.1168	+	7.57301i	−0.480564	+	0.277454i
$746$	8.00000			0.292901
$747$	−6.74456	−	13.5615i	−0.246771	−	0.496188i
$748$	−0.941578	−	1.63086i	−0.0344275	−	0.0596302i
$749$	7.37228	−	8.51278i	0.269377	−	0.311050i
$750$	15.1861	+	4.57879i	0.554519	+	0.167194i
$751$	0.500000	−	0.866025i	0.0182453	−	0.0316017i	−0.856759	−	0.515718i	$-0.827525\pi$
$751$	0.500000	−	0.866025i	0.0182453	−	0.0316017i	0.875004	+	0.484116i	$0.160859\pi$
$752$	−3.68614	−	2.12819i	−0.134420	−	0.0776073i
$753$	−1.32473	−	1.40965i	−0.0482760	−	0.0513703i
$754$	−2.05842	+	1.98072i	−0.0749633	+	0.0721335i
$755$	7.62772			0.277601
$756$	7.12772	−	11.7557i	0.259233	−	0.427549i
$757$	−19.8614	+	34.4010i	−0.721875	+	1.25032i	0.238372	+	0.971174i	$0.423386\pi$
$757$	−19.8614	+	34.4010i	−0.721875	+	1.25032i	−0.960247	+	0.279150i	$0.909947\pi$
$758$	22.1168	−	12.7692i	0.803320	−	0.463797i
$759$	1.62772	−	1.52967i	0.0590824	−	0.0555235i
$760$	−7.37228	+	4.25639i	−0.267421	+	0.154395i
$761$	14.7446	−	8.51278i	0.534490	−	0.308588i	−0.208353	−	0.978054i	$-0.566810\pi$
$761$	14.7446	−	8.51278i	0.534490	−	0.308588i	0.742843	+	0.669466i	$0.233477\pi$
$762$	17.9307	+	19.0800i	0.649561	+	0.691196i
$763$	−51.7011	−	9.94987i	−1.87170	−	0.360210i
$764$	−16.3723	−	9.45254i	−0.592328	−	0.341981i
$765$	−5.74456	+	8.66025i	−0.207695	+	0.313112i
$766$		−	31.6742i		−	1.14444i
$767$	24.5584	−	23.6314i	0.886753	−	0.853279i
$768$	1.18614	+	1.26217i	0.0428012	+	0.0455446i
$769$	5.11684	−	8.86263i	0.184518	−	0.319595i	−0.758896	−	0.651212i	$-0.774261\pi$
$769$	5.11684	−	8.86263i	0.184518	−	0.319595i	0.943414	+	0.331617i	$0.107594\pi$
$770$	3.00000	+	8.66025i	0.108112	+	0.312094i
$771$	11.0584	−	36.6766i	0.398259	−	1.32088i
$772$			6.48577i			0.233428i
$773$	45.0951	−	26.0357i	1.62196	−	0.936438i	0.635562	−	0.772050i	$-0.280768\pi$
$773$	45.0951	−	26.0357i	1.62196	−	0.936438i	0.986396	−	0.164388i	$-0.0525649\pi$
$774$	−10.7446	+	5.34363i	−0.386205	+	0.192073i
$775$	6.51087			0.233878
$776$	5.37228	+	9.30506i	0.192854	+	0.334032i
$777$	−17.4891	+	33.3514i	−0.627419	+	1.19647i
$778$	19.6277	+	11.3321i	0.703688	+	0.406274i
$779$			20.6920i			0.741369i
$780$	−8.55842	+	13.2390i	−0.306441	+	0.474034i
$781$	−1.53262			−0.0548416
$782$	1.11684	+	0.644810i	0.0399383	+	0.0230584i
$783$	−4.05842	+	0.691097i	−0.145036	+	0.0246978i
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$		0			0
$786$	9.30298	−	30.8545i	0.331826	−	1.10054i
$787$	−7.36141	−	12.7503i	−0.262406	−	0.454500i	0.704475	−	0.709729i	$-0.251183\pi$
$787$	−7.36141	−	12.7503i	−0.262406	−	0.454500i	−0.966881	+	0.255229i	$0.917849\pi$
$788$	15.6060			0.555940
$789$	23.0693	+	6.95565i	0.821289	+	0.247628i
$790$	−33.6060	−	19.4024i	−1.19565	−	0.690307i
$791$	14.7446	+	42.5639i	0.524256	+	1.51340i
$792$	0.255437	−	4.10891i	0.00907657	−	0.146004i
$793$	13.5000	−	12.9904i	0.479399	−	0.461302i
$794$	−13.7446			−0.487776
$795$	61.0951	−	14.3537i	2.16682	−	0.509075i
$796$	3.00000	+	1.73205i	0.106332	+	0.0613909i
$797$	25.9307	+	44.9133i	0.918513	+	1.59091i	0.801676	+	0.597759i	$0.203942\pi$
$797$	25.9307	+	44.9133i	0.918513	+	1.59091i	0.116837	+	0.993151i	$0.462724\pi$
$798$	−0.627719	−	15.4410i	−0.0222210	−	0.546605i
$799$	−5.05842	+	2.92048i	−0.178954	+	0.103319i
$800$	0.686141	+	1.18843i	0.0242587	+	0.0420174i
$801$	−37.3505	−	2.32196i	−1.31972	−	0.0820424i
$802$	5.74456	+	9.94987i	0.202848	+	0.351342i
$803$	0.510875	−	0.884861i	0.0180284	−	0.0312261i
$804$	−3.25544	−	13.8564i	−0.114810	−	0.488678i
$805$	−4.74456	−	4.10891i	−0.167224	−	0.144820i
$806$	4.74456	−	16.4356i	0.167120	−	0.578921i
$807$	33.0475	+	35.1658i	1.16333	+	1.23789i
$808$	1.62772	−	2.81929i	0.0572629	−	0.0991823i
$809$	32.7446	+	18.9051i	1.15124	+	0.664667i	0.949188	−	0.314708i	$-0.101907\pi$
$809$	32.7446	+	18.9051i	1.15124	+	0.664667i	0.202049	+	0.979375i	$0.435240\pi$
$810$	−20.9307	+	8.83518i	−0.735430	+	0.310437i
$811$	−3.11684			−0.109447			−0.0547236	−	0.998502i	$-0.517428\pi$
$811$	−3.11684			−0.109447			−0.0547236	+	0.998502i	$0.517428\pi$
$812$	−2.05842	−	0.396143i	−0.0722365	−	0.0139019i
$813$	2.00000	−	6.63325i	0.0701431	−	0.232638i
$814$			11.2772i			0.395264i
$815$	−13.1168	−	22.7190i	−0.459463	−	0.795813i
$816$	2.31386	−	0.543620i	0.0810013	−	0.0190305i
$817$	−6.74456	+	11.6819i	−0.235962	+	0.408699i
$818$	−1.48913			−0.0520660
$819$	−14.0693	−	24.9210i	−0.491621	−	0.870809i
$820$	15.4891			0.540904
$821$	−26.9198	+	46.6265i	−0.939508	+	1.62728i	−0.173118	+	0.984901i	$0.555384\pi$
$821$	−26.9198	+	46.6265i	−0.939508	+	1.62728i	−0.766390	+	0.642375i	$0.777949\pi$
$822$	−2.74456	+	0.644810i	−0.0957276	+	0.0224903i
$823$	25.7921	+	44.6732i	0.899056	+	1.55721i	0.828703	+	0.559689i	$0.189080\pi$
$823$	25.7921	+	44.6732i	0.899056	+	1.55721i	0.0703539	+	0.997522i	$0.477587\pi$
$824$		−	11.6819i		−	0.406959i
$825$	0.941578	−	3.12286i	0.0327815	−	0.108724i
$826$	24.5584	+	4.72627i	0.854497	+	0.164448i
$827$	26.2337			0.912235			0.456117	−	0.889920i	$-0.349240\pi$
$827$	26.2337			0.912235			0.456117	+	0.889920i	$0.349240\pi$
$828$	1.25544	+	2.52434i	0.0436295	+	0.0877268i
$829$	13.5000	+	7.79423i	0.468874	+	0.270705i	0.715768	−	0.698338i	$-0.246077\pi$
$829$	13.5000	+	7.79423i	0.468874	+	0.270705i	−0.246894	+	0.969042i	$0.579410\pi$
$830$	−6.37228	+	11.0371i	−0.221185	+	0.383104i
$831$	−11.2554	−	11.9769i	−0.390447	−	0.415473i
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−1.37228	−	9.50744i	−0.0475467	−	0.329413i
$834$	−8.31386	−	35.3870i	−0.287885	−	1.22535i
$835$	8.37228	−	14.5012i	0.289735	−	0.501835i
$836$	−2.31386	−	4.00772i	−0.0800265	−	0.138610i
$837$	18.9783	−	15.7359i	0.655984	−	0.543913i
$838$	−8.74456	−	15.1460i	−0.302076	−	0.523211i
$839$	2.39403	−	1.38219i	0.0826511	−	0.0477186i	−0.458105	−	0.888898i	$-0.651472\pi$
$839$	2.39403	−	1.38219i	0.0826511	−	0.0477186i	0.540756	+	0.841180i	$0.318138\pi$
$840$	−11.5584	+	0.469882i	−0.398803	+	0.0162125i
$841$	−14.1861	−	24.5711i	−0.489177	−	0.847280i
$842$	11.2337	+	6.48577i	0.387138	+	0.223514i
$843$	−5.48913	+	1.28962i	−0.189056	+	0.0444169i
$844$	22.7446			0.782900
$845$	15.3030	+	29.0299i	0.526439	+	0.998658i
$846$	−12.7446	−	0.792287i	−0.438167	−	0.0272394i
$847$	22.7921	−	7.89542i	0.783146	−	0.271290i
$848$	−12.4307	−	7.17687i	−0.426872	−	0.246455i
$849$	−12.5584	−	3.78651i	−0.431004	−	0.129953i
$850$	1.88316			0.0645917
$851$	−3.86141	−	6.68815i	−0.132367	−	0.229267i
$852$	0.558422	−	1.85208i	0.0191312	−	0.0634511i
$853$	−42.7228			−1.46280			−0.731401	−	0.681948i	$-0.761133\pi$
$853$	−42.7228			−1.46280			−0.731401	+	0.681948i	$0.761133\pi$
$854$	13.5000	+	2.59808i	0.461960	+	0.0889043i
$855$	−14.1168	+	21.2819i	−0.482786	+	0.727827i
$856$	3.68614	+	2.12819i	0.125990	+	0.0727402i
$857$	37.7228			1.28859			0.644293	−	0.764778i	$-0.277152\pi$
$857$	37.7228			1.28859			0.644293	+	0.764778i	$0.277152\pi$
$858$	−7.19702	−	4.65253i	−0.245702	−	0.158835i
$859$			16.2333i			0.553872i	0.960888	+	0.276936i	$0.0893190\pi$
$859$			16.2333i			0.553872i	−0.960888	+	0.276936i	$0.910681\pi$
$860$	8.74456	+	5.04868i	0.298187	+	0.172158i
$861$	−13.0584	+	24.9021i	−0.445030	+	0.848663i
$862$	−9.81386	−	16.9981i	−0.334261	−	0.578958i
$863$	37.6277			1.28086			0.640431	−	0.768016i	$-0.278756\pi$
$863$	37.6277			1.28086			0.640431	+	0.768016i	$0.278756\pi$
$864$	4.87228	+	1.80579i	0.165758	+	0.0614342i
$865$	41.7921	−	24.1287i	1.42097	−	0.820400i
$866$			35.0458i			1.19090i
$867$	−7.55842	+	25.0684i	−0.256697	+	0.851369i
$868$	11.8614	−	4.10891i	0.402602	−	0.139466i
$869$	10.5475	−	18.2689i	0.357801	−	0.619730i
$870$	2.37228	+	2.52434i	0.0804279	+	0.0855831i
$871$	−28.4674	−	8.21782i	−0.964580	−	0.278450i
$872$		−	19.8997i		−	0.673891i
$873$	26.8614	+	17.8178i	0.909121	+	0.603043i
$874$	2.74456	+	1.58457i	0.0928362	+	0.0535990i
$875$	23.7921	+	4.57879i	0.804320	+	0.154791i
$876$	0.883156	+	0.939764i	0.0298391	+	0.0317517i
$877$	15.0000	−	8.66025i	0.506514	−	0.292436i	−0.224886	−	0.974385i	$-0.572201\pi$
$877$	15.0000	−	8.66025i	0.506514	−	0.292436i	0.731400	+	0.681949i	$0.238867\pi$
$878$	−30.3505	+	17.5229i	−1.02428	+	0.591369i
$879$	−21.4891	+	20.1947i	−0.724810	+	0.681150i
$880$	−3.00000	+	1.73205i	−0.101130	+	0.0583874i
$881$	12.2554	−	21.2270i	0.412896	−	0.715157i	−0.582309	−	0.812968i	$-0.697851\pi$
$881$	12.2554	−	21.2270i	0.412896	−	0.715157i	0.995205	+	0.0978105i	$0.0311839\pi$
$882$	8.98913	−	18.9788i	0.302680	−	0.639050i
$883$	−10.0000			−0.336527			−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000			−0.336527			−0.168263	+	0.985742i	$0.553816\pi$
$884$	1.37228	−	4.75372i	0.0461548	−	0.159885i
$885$	−28.3030	−	30.1171i	−0.951394	−	1.01238i
$886$	9.68614	+	5.59230i	0.325412	+	0.187877i
$887$	−3.94158	+	6.82701i	−0.132345	+	0.229229i	−0.924580	−	0.380988i	$-0.875584\pi$
$887$	−3.94158	+	6.82701i	−0.132345	+	0.229229i	0.792235	+	0.610216i	$0.208917\pi$
$888$	−13.6277	−	4.10891i	−0.457316	−	0.137886i
$889$	30.2337	+	26.1831i	1.01401	+	0.878154i
$890$	15.7446	+	27.2704i	0.527759	+	0.914105i
$891$	−4.80298	−	11.3784i	−0.160906	−	0.381189i
$892$	6.23369			0.208719
$893$	−12.4307	+	7.17687i	−0.415978	+	0.240165i
$894$	10.1168	−	2.37686i	0.338358	−	0.0794941i
$895$	2.00000	−	3.46410i	0.0668526	−	0.115792i
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	5.86141	+	0.294954i	0.195707	+	0.00984822i
$898$	−0.605969			−0.0202215
$899$	−3.25544	−	1.87953i	−0.108575	−	0.0626858i
$900$	3.43070	+	2.27567i	0.114357	+	0.0758557i
$901$	−17.0584	+	9.84868i	−0.568298	+	0.328107i
$902$			8.42020i			0.280362i
$903$	−15.4891	+	9.80240i	−0.515446	+	0.326203i
$904$	−14.7446	+	8.51278i	−0.490397	+	0.283131i
$905$	−30.6060			−1.01738
$906$	−5.01087	−	1.51084i	−0.166475	−	0.0501941i
$907$	−12.4891	+	21.6318i	−0.414695	+	0.718272i	−0.995396	−	0.0958443i	$-0.969445\pi$
$907$	−12.4891	+	21.6318i	−0.414695	+	0.718272i	0.580702	+	0.814116i	$0.302778\pi$
$908$	−3.30298	−	1.90698i	−0.109613	−	0.0632853i
$909$	0.605969	−	9.74749i	0.0200987	−	0.323304i
$910$	−10.9307	+	21.4569i	−0.362349	+	0.711288i
$911$			7.86797i			0.260677i	0.991470	+	0.130339i	$0.0416065\pi$
$911$			7.86797i			0.260677i	−0.991470	+	0.130339i	$0.958394\pi$
$912$	5.68614	−	1.33591i	0.188287	−	0.0442363i
$913$	−6.00000	−	3.46410i	−0.198571	−	0.114645i
$914$	16.6753	−	9.62747i	0.551569	−	0.318448i
$915$	−15.5584	−	16.5557i	−0.514346	−	0.547314i
$916$	6.05842	+	10.4935i	0.200176	+	0.346715i
$917$	9.30298	−	48.3397i	0.307212	−	1.59632i
$918$	5.48913	−	4.55134i	0.181168	−	0.150217i
$919$	−16.7337	−	28.9836i	−0.551993	−	0.956081i	−0.998131	−	0.0611161i	$-0.980534\pi$
$919$	−16.7337	−	28.9836i	−0.551993	−	0.956081i	0.446137	−	0.894965i	$-0.352799\pi$
$920$	1.18614	−	2.05446i	0.0391059	−	0.0677334i
$921$	22.3139	−	5.24244i	0.735267	−	0.172744i
$922$			15.0911i			0.497000i
$923$	−2.79211	−	2.90165i	−0.0919034	−	0.0955088i
$924$	−0.255437	−	6.28339i	−0.00840327	−	0.206708i
$925$	−9.76631	−	5.63858i	−0.321114	−	0.185395i
$926$	26.6168	+	15.3672i	0.874684	+	0.504999i
$927$	−15.6060	−	31.3793i	−0.512567	−	1.03063i
$928$		−	0.792287i		−	0.0260081i
$929$	2.91983	−	1.68576i	0.0957965	−	0.0553081i	−0.451336	−	0.892354i	$-0.649053\pi$
$929$	2.91983	−	1.68576i	0.0957965	−	0.0553081i	0.547133	+	0.837046i	$0.315719\pi$
$930$	−19.8614	−	5.98844i	−0.651281	−	0.196369i
$931$	−3.37228	−	23.3639i	−0.110522	−	0.765719i
$932$	−24.3030	+	14.0313i	−0.796071	+	0.459612i
$933$	−7.80298	+	1.83324i	−0.255458	+	0.0600176i
$934$	9.81386	−	16.9981i	0.321119	−	0.556195i
$935$			4.75372i			0.155463i
$936$	8.24456	−	7.00194i	0.269482	−	0.228866i
$937$		−	16.0309i		−	0.523706i	−0.965108	−	0.261853i	$-0.915666\pi$
$937$		−	16.0309i		−	0.523706i	0.965108	−	0.261853i	$-0.0843336\pi$
$938$	−7.11684	−	20.5446i	−0.232373	−	0.670804i
$939$	5.48913	+	23.3639i	0.179131	+	0.762450i
$940$	5.37228	+	9.30506i	0.175224	+	0.303498i
$941$			16.3807i			0.533997i	0.963697	+	0.266999i	$0.0860319\pi$
$941$			16.3807i			0.533997i	−0.963697	+	0.266999i	$0.913968\pi$
$942$		0			0
$943$	−2.88316	−	4.99377i	−0.0938885	−	0.162620i
$944$			9.45254i			0.307654i
$945$	−30.4198	+	16.7031i	−0.989557	+	0.543353i
$946$	−2.74456	+	4.75372i	−0.0892334	+	0.154557i
$947$	2.56930	−	4.45015i	0.0834909	−	0.144611i	−0.821256	−	0.570560i	$-0.806726\pi$
$947$	2.56930	−	4.45015i	0.0834909	−	0.144611i	0.904747	+	0.425949i	$0.140060\pi$
$948$	18.2337	+	19.4024i	0.592203	+	0.630161i
$949$	2.60597	−	0.644810i	0.0845933	−	0.0209314i
$950$	4.62772			0.150143
$951$	−45.0951	+	10.5947i	−1.46231	+	0.343556i
$952$	3.43070	−	1.18843i	0.111190	−	0.0385173i
$953$	−4.41983	+	2.55179i	−0.143172	+	0.0826606i	−0.569875	−	0.821731i	$-0.693008\pi$
$953$	−4.41983	+	2.55179i	−0.143172	+	0.0826606i	0.426703	+	0.904392i	$0.359675\pi$
$954$	−42.9783	−	2.67181i	−1.39147	−	0.0865032i
$955$	23.8614	+	41.3292i	0.772137	+	1.33738i
$956$	12.3030	+	21.3094i	0.397907	+	0.689195i
$957$	−1.37228	+	1.28962i	−0.0443596	+	0.0416875i
$958$	22.8030	−	13.1653i	0.736731	−	0.425352i
$959$	−4.06930	+	1.40965i	−0.131404	+	0.0455198i
$960$	−1.00000	−	4.25639i	−0.0322749	−	0.137374i
$961$	−8.48913			−0.273843
$962$	−21.3505	+	20.5446i	−0.688369	+	0.662383i
$963$	12.7446	+	0.792287i	0.410688	+	0.0255311i
$964$	−0.627719	+	1.08724i	−0.0202175	+	0.0350177i
$965$	8.18614	−	14.1788i	0.263521	−	0.456432i
$966$	2.30298	+	3.63903i	0.0740973	+	0.117084i
$967$		−	0.884861i		−	0.0284552i	−0.999899	−	0.0142276i	$-0.995471\pi$
$967$		−	0.884861i		−	0.0284552i	0.999899	−	0.0142276i	$-0.00452894\pi$
$968$	4.55842	+	7.89542i	0.146513	+	0.253768i
$969$	2.31386	−	7.67420i	0.0743319	−	0.246531i
$970$		−	27.1229i		−	0.870864i
$971$	15.5584	+	26.9480i	0.499294	+	0.864802i	1.00000		0.000815578i	$-0.000259607\pi$
$971$	15.5584	+	26.9480i	0.499294	+	0.864802i	−0.500706	+	0.865617i	$0.666926\pi$
$972$	15.5000	−	1.65831i	0.497163	−	0.0531904i
$973$	−18.1753	−	52.4675i	−0.582672	−	1.68203i
$974$		−	10.8347i		−	0.347167i
$975$	7.62772	−	3.90653i	0.244283	−	0.125109i
$976$			5.19615i			0.166325i
$977$	4.93070	−	8.54023i	0.157747	−	0.273226i	−0.776309	−	0.630353i	$-0.782910\pi$
$977$	4.93070	−	8.54023i	0.157747	−	0.273226i	0.934056	+	0.357127i	$0.116244\pi$
$978$	4.11684	+	17.5229i	0.131642	+	0.560320i
$979$	−14.8247	+	8.55906i	−0.473801	+	0.273549i
$980$	−17.4891	+	2.52434i	−0.558670	+	0.0806370i
$981$	−26.5842	−	53.4535i	−0.848769	−	1.70664i
$982$	33.6060	−	19.4024i	1.07241	−	0.619156i
$983$		−	48.3123i		−	1.54092i	−0.637487	−	0.770461i	$-0.720026\pi$
$983$		−	48.3123i		−	1.54092i	0.637487	−	0.770461i	$-0.279974\pi$
$984$	−10.1753	−	3.06796i	−0.324376	−	0.0978029i
$985$	−34.1168	−	19.6974i	−1.08705	−	0.627610i
$986$	−0.941578	−	0.543620i	−0.0299860	−	0.0173124i
$987$	−19.4891	+	0.792287i	−0.620346	+	0.0252188i
$988$	3.37228	−	11.6819i	0.107287	−	0.371652i
$989$		−	3.75906i		−	0.119531i
$990$	−5.74456	+	8.66025i	−0.182574	+	0.275241i
$991$	−6.61684	+	11.4607i	−0.210191	+	0.364061i	−0.951774	−	0.306799i	$-0.900742\pi$
$991$	−6.61684	+	11.4607i	−0.210191	+	0.364061i	0.741583	+	0.670861i	$0.234075\pi$
$992$	2.37228	+	4.10891i	0.0753200	+	0.130458i
$993$	27.8614	−	26.1831i	0.884155	−	0.830897i
$994$	0.558422	−	2.90165i	0.0177121	−	0.0920346i
$995$	−4.37228	−	7.57301i	−0.138611	−	0.240081i
$996$	6.37228	−	5.98844i	0.201913	−	0.189751i
$997$	−5.26631	+	3.04051i	−0.166786	+	0.0962938i	−0.581069	−	0.813854i	$-0.697366\pi$
$997$	−5.26631	+	3.04051i	−0.166786	+	0.0962938i	0.414284	+	0.910148i	$0.364032\pi$
$998$	20.2337	+	11.6819i	0.640486	+	0.369785i
$999$	−42.0951	+	7.16825i	−1.33183	+	0.226794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.e.251.1	✓	4
3.2	odd	2		546.2.q.g.251.1	yes	4
7.6	odd	2		546.2.q.f.251.2	yes	4
13.10	even	6		546.2.q.h.335.1	yes	4
21.20	even	2		546.2.q.h.251.2	yes	4
39.23	odd	6		546.2.q.f.335.2	yes	4
91.62	odd	6		546.2.q.g.335.2	yes	4
273.62	even	6	inner	546.2.q.e.335.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.e.251.1	✓	4	1.1	even	1	trivial
546.2.q.e.335.1	yes	4	273.62	even	6	inner
546.2.q.f.251.2	yes	4	7.6	odd	2
546.2.q.f.335.2	yes	4	39.23	odd	6
546.2.q.g.251.1	yes	4	3.2	odd	2
546.2.q.g.335.2	yes	4	91.62	odd	6
546.2.q.h.251.2	yes	4	21.20	even	2
546.2.q.h.335.1	yes	4	13.10	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.52434i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.52434i q^{5} +(0.500000 - 1.65831i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +(-2.18614 - 1.26217i) q^{10} +(0.686141 - 1.18843i) q^{11} +(1.18614 + 1.26217i) q^{12} +(3.50000 - 0.866025i) q^{13} +(2.00000 + 1.73205i) q^{14} +(-1.00000 - 4.25639i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-0.186141 + 2.99422i) q^{18} +(1.68614 + 2.92048i) q^{19} +(2.18614 - 1.26217i) q^{20} +(0.186141 + 4.57879i) q^{21} +(0.686141 + 1.18843i) q^{22} +(-0.813859 - 0.469882i) q^{23} +(-1.68614 + 0.396143i) q^{24} -1.37228 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-2.50000 + 0.866025i) q^{28} +(0.686141 + 0.396143i) q^{29} +(4.18614 + 1.26217i) q^{30} -4.74456 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.686141 + 2.27567i) q^{33} -1.37228 q^{34} +(6.55842 + 1.26217i) q^{35} +(-2.50000 - 1.65831i) q^{36} +(7.11684 + 4.10891i) q^{37} -3.37228 q^{38} +(-5.55842 + 2.84674i) q^{39} +2.52434i q^{40} +(5.31386 + 3.06796i) q^{41} +(-4.05842 - 2.12819i) q^{42} +(2.00000 + 3.46410i) q^{43} -1.37228 q^{44} +(3.37228 + 6.78073i) q^{45} +(0.813859 - 0.469882i) q^{46} +4.25639i q^{47} +(0.500000 - 1.65831i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(0.686141 - 1.18843i) q^{50} +(-1.62772 - 1.73205i) q^{51} +(-2.50000 - 2.59808i) q^{52} +14.3537i q^{53} +(-0.872281 - 5.12241i) q^{54} +(3.00000 + 1.73205i) q^{55} +(0.500000 - 2.59808i) q^{56} +(-4.00000 - 4.25639i) q^{57} +(-0.686141 + 0.396143i) q^{58} +(8.18614 - 4.72627i) q^{59} +(-3.18614 + 2.99422i) q^{60} +(4.50000 - 2.59808i) q^{61} +(2.37228 - 4.10891i) q^{62} +(-2.12772 - 7.64675i) q^{63} +1.00000 q^{64} +(2.18614 + 8.83518i) q^{65} +(-1.62772 - 1.73205i) q^{66} +(-7.11684 - 4.10891i) q^{67} +(0.686141 - 1.18843i) q^{68} +(1.55842 + 0.469882i) q^{69} +(-4.37228 + 5.04868i) q^{70} +(-0.558422 - 0.967215i) q^{71} +(2.68614 - 1.33591i) q^{72} +0.744563 q^{73} +(-7.11684 + 4.10891i) q^{74} +(2.31386 - 0.543620i) q^{75} +(1.68614 - 2.92048i) q^{76} +(-2.74456 - 2.37686i) q^{77} +(0.313859 - 6.23711i) q^{78} +15.3723 q^{79} +(-2.18614 - 1.26217i) q^{80} +(5.43070 - 7.17687i) q^{81} +(-5.31386 + 3.06796i) q^{82} -5.04868i q^{83} +(3.87228 - 2.45060i) q^{84} +(-3.00000 + 1.73205i) q^{85} -4.00000 q^{86} +(-1.31386 - 0.396143i) q^{87} +(0.686141 - 1.18843i) q^{88} +(-10.8030 - 6.23711i) q^{89} +(-7.55842 - 0.469882i) q^{90} +(-0.500000 - 9.52628i) q^{91} +0.939764i q^{92} +(8.00000 - 1.87953i) q^{93} +(-3.68614 - 2.12819i) q^{94} +(-7.37228 + 4.25639i) q^{95} +(1.18614 + 1.26217i) q^{96} +(5.37228 + 9.30506i) q^{97} +(5.50000 - 4.33013i) q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 14 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 3 q^{17} + 5 q^{18} + q^{19} + 3 q^{20} - 5 q^{21} - 3 q^{22} - 9 q^{23} - q^{24} + 6 q^{25} - 4 q^{26} - 16 q^{27} - 10 q^{28} - 3 q^{29} + 11 q^{30} + 4 q^{31} - 2 q^{32} + 3 q^{33} + 6 q^{34} + 9 q^{35} - 10 q^{36} - 6 q^{37} - 2 q^{38} - 5 q^{39} + 27 q^{41} + q^{42} + 8 q^{43} + 6 q^{44} + 2 q^{45} + 9 q^{46} + 2 q^{48} - 26 q^{49} - 3 q^{50} - 18 q^{51} - 10 q^{52} + 8 q^{54} + 12 q^{55} + 2 q^{56} - 16 q^{57} + 3 q^{58} + 27 q^{59} - 7 q^{60} + 18 q^{61} - 2 q^{62} - 20 q^{63} + 4 q^{64} + 3 q^{65} - 18 q^{66} + 6 q^{67} - 3 q^{68} - 11 q^{69} - 6 q^{70} + 15 q^{71} + 5 q^{72} - 20 q^{73} + 6 q^{74} + 15 q^{75} + q^{76} + 12 q^{77} + 7 q^{78} + 50 q^{79} - 3 q^{80} - 7 q^{81} - 27 q^{82} + 4 q^{84} - 12 q^{85} - 16 q^{86} - 11 q^{87} - 3 q^{88} - 3 q^{89} - 13 q^{90} - 2 q^{91} + 32 q^{93} - 9 q^{94} - 18 q^{95} - q^{96} + 10 q^{97} + 22 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 - q^12 + 14 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 - 3 * q^17 + 5 * q^18 + q^19 + 3 * q^20 - 5 * q^21 - 3 * q^22 - 9 * q^23 - q^24 + 6 * q^25 - 4 * q^26 - 16 * q^27 - 10 * q^28 - 3 * q^29 + 11 * q^30 + 4 * q^31 - 2 * q^32 + 3 * q^33 + 6 * q^34 + 9 * q^35 - 10 * q^36 - 6 * q^37 - 2 * q^38 - 5 * q^39 + 27 * q^41 + q^42 + 8 * q^43 + 6 * q^44 + 2 * q^45 + 9 * q^46 + 2 * q^48 - 26 * q^49 - 3 * q^50 - 18 * q^51 - 10 * q^52 + 8 * q^54 + 12 * q^55 + 2 * q^56 - 16 * q^57 + 3 * q^58 + 27 * q^59 - 7 * q^60 + 18 * q^61 - 2 * q^62 - 20 * q^63 + 4 * q^64 + 3 * q^65 - 18 * q^66 + 6 * q^67 - 3 * q^68 - 11 * q^69 - 6 * q^70 + 15 * q^71 + 5 * q^72 - 20 * q^73 + 6 * q^74 + 15 * q^75 + q^76 + 12 * q^77 + 7 * q^78 + 50 * q^79 - 3 * q^80 - 7 * q^81 - 27 * q^82 + 4 * q^84 - 12 * q^85 - 16 * q^86 - 11 * q^87 - 3 * q^88 - 3 * q^89 - 13 * q^90 - 2 * q^91 + 32 * q^93 - 9 * q^94 - 18 * q^95 - q^96 + 10 * q^97 + 22 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more