LMFDB - Embedded newform 546.2.bx.a.349.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			349.10
Character	$\chi$	$=$	546.349
Dual form			546.2.bx.a.97.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.46294 - 2.46294i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.38574 - 2.25383i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.46294 - 2.46294i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.38574 - 2.25383i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.74156 - 3.01647i) q^{10} +(-5.73180 - 1.53583i) q^{11} +1.00000 q^{12} +(2.00189 + 2.99874i) q^{13} +(-2.53568 + 0.755188i) q^{14} +(-0.901498 + 3.36444i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.681755 - 1.18083i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-0.203136 - 0.758114i) q^{19} +(-3.36444 + 0.901498i) q^{20} +(2.32700 + 1.25900i) q^{21} +(-2.96700 + 5.13899i) q^{22} +(-0.338051 + 0.195174i) q^{23} +(0.258819 - 0.965926i) q^{24} -7.13213i q^{25} +(3.41469 - 1.15755i) q^{26} +1.00000i q^{27} +(0.0731721 + 2.64474i) q^{28} +(-3.44143 - 5.96073i) q^{29} +(3.01647 + 1.74156i) q^{30} +(-0.211182 + 0.211182i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.73180 - 1.53583i) q^{33} +(-0.964147 - 0.964147i) q^{34} +(-8.96402 - 2.13804i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-5.84975 - 1.56744i) q^{37} -0.784857 q^{38} +(-3.23306 - 1.59604i) q^{39} +3.48312i q^{40} +(3.49404 + 0.936225i) q^{41} +(1.81837 - 1.92185i) q^{42} +(2.10364 + 1.21454i) q^{43} +(4.19597 + 4.19597i) q^{44} +(-0.901498 - 3.36444i) q^{45} +(0.101029 + 0.377047i) q^{46} +(-6.84615 - 6.84615i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.15946 + 6.24643i) q^{49} +(-6.88911 - 1.84593i) q^{50} +1.36351i q^{51} +(-0.234317 - 3.59793i) q^{52} +9.73688 q^{53} +(0.965926 + 0.258819i) q^{54} +(-17.8997 + 10.3344i) q^{55} +(2.57356 + 0.613830i) q^{56} +(0.554978 + 0.554978i) q^{57} +(-6.64833 + 1.78141i) q^{58} +(5.37683 - 1.44072i) q^{59} +(2.46294 - 2.46294i) q^{60} +(-8.38542 - 4.84132i) q^{61} +(0.149328 + 0.258644i) q^{62} +(-2.64474 + 0.0731721i) q^{63} -1.00000i q^{64} +(12.3162 + 2.45518i) q^{65} -5.93400i q^{66} +(1.38874 - 5.18284i) q^{67} +(-1.18083 + 0.681755i) q^{68} +(0.195174 - 0.338051i) q^{69} +(-4.38525 + 8.10521i) q^{70} +(12.8877 - 3.45324i) q^{71} +(0.258819 + 0.965926i) q^{72} +(5.09775 + 5.09775i) q^{73} +(-3.02805 + 5.24474i) q^{74} +(3.56607 + 6.17661i) q^{75} +(-0.203136 + 0.758114i) q^{76} +(4.48128 + 15.0467i) q^{77} +(-2.37843 + 2.70981i) q^{78} +9.25714 q^{79} +(3.36444 + 0.901498i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.80865 - 3.13267i) q^{82} +(9.33819 - 9.33819i) q^{83} +(-1.38574 - 2.25383i) q^{84} +(-1.22920 - 4.58744i) q^{85} +(1.71762 - 1.71762i) q^{86} +(5.96073 + 3.44143i) q^{87} +(5.13899 - 2.96700i) q^{88} +(1.44141 - 5.37940i) q^{89} -3.48312 q^{90} +(3.98454 - 8.66738i) q^{91} +0.390347 q^{92} +(0.0772979 - 0.288480i) q^{93} +(-8.38479 + 4.84096i) q^{94} +(-2.36750 - 1.36688i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(3.44763 + 12.8667i) q^{97} +(5.21586 + 4.66850i) q^{98} +(-4.19597 + 4.19597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 + 20 * q^9	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.46294	−	2.46294i	1.10146	−	1.10146i	0.107225	−	0.994235i	$-0.465804\pi$
$5$	2.46294	−	2.46294i	1.10146	−	1.10146i	0.994235	−	0.107225i	$-0.0341965\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	−1.38574	−	2.25383i	−0.523760	−	0.851866i
$7$	−1.38574	−	2.25383i	−0.523760	−	0.851866i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.74156	−	3.01647i	−0.550730	−	0.953892i
$11$	−5.73180	−	1.53583i	−1.72820	−	0.463071i	−0.748435	−	0.663208i	$-0.769194\pi$
$11$	−5.73180	−	1.53583i	−1.72820	−	0.463071i	−0.979768	+	0.200137i	$0.935861\pi$
$12$	1.00000			0.288675
$13$	2.00189	+	2.99874i	0.555224	+	0.831701i
$13$	2.00189	+	2.99874i	0.555224	+	0.831701i
$14$	−2.53568	+	0.755188i	−0.677690	+	0.201832i
$15$	−0.901498	+	3.36444i	−0.232766	+	0.868694i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.681755	−	1.18083i	0.165350	−	0.286394i	−0.771430	−	0.636315i	$-0.780458\pi$
$17$	0.681755	−	1.18083i	0.165350	−	0.286394i	0.936779	+	0.349920i	$0.113791\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−0.203136	−	0.758114i	−0.0466026	−	0.173923i	0.938702	−	0.344730i	$-0.112029\pi$
$19$	−0.203136	−	0.758114i	−0.0466026	−	0.173923i	−0.985305	+	0.170806i	$0.945363\pi$
$20$	−3.36444	+	0.901498i	−0.752311	+	0.201581i
$21$	2.32700	+	1.25900i	0.507792	+	0.274736i
$22$	−2.96700	+	5.13899i	−0.632566	+	1.09564i
$23$	−0.338051	+	0.195174i	−0.0704884	+	0.0406965i	−0.534830	−	0.844960i	$-0.679624\pi$
$23$	−0.338051	+	0.195174i	−0.0704884	+	0.0406965i	0.464342	+	0.885656i	$0.346291\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$		−	7.13213i		−	1.42643i
$26$	3.41469	−	1.15755i	0.669675	−	0.227013i
$27$			1.00000i			0.192450i
$28$	0.0731721	+	2.64474i	0.0138282	+	0.499809i
$29$	−3.44143	−	5.96073i	−0.639057	−	1.10688i	−0.985640	−	0.168860i	$-0.945991\pi$
$29$	−3.44143	−	5.96073i	−0.639057	−	1.10688i	0.346583	−	0.938019i	$-0.387342\pi$
$30$	3.01647	+	1.74156i	0.550730	+	0.317964i
$31$	−0.211182	+	0.211182i	−0.0379294	+	0.0379294i	−0.725817	−	0.687888i	$-0.758538\pi$
$31$	−0.211182	+	0.211182i	−0.0379294	+	0.0379294i	0.687888	+	0.725817i	$0.258538\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	5.73180	−	1.53583i	0.997778	−	0.267354i
$34$	−0.964147	−	0.964147i	−0.165350	−	0.165350i
$35$	−8.96402	−	2.13804i	−1.51520	−	0.361395i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−5.84975	−	1.56744i	−0.961693	−	0.257685i	−0.256376	−	0.966577i	$-0.582528\pi$
$37$	−5.84975	−	1.56744i	−0.961693	−	0.257685i	−0.705317	+	0.708892i	$0.749195\pi$
$38$	−0.784857			−0.127321
$39$	−3.23306	−	1.59604i	−0.517703	−	0.255571i
$40$			3.48312i			0.550730i
$41$	3.49404	+	0.936225i	0.545677	+	0.146214i	0.521118	−	0.853485i	$-0.325515\pi$
$41$	3.49404	+	0.936225i	0.545677	+	0.146214i	0.0245592	+	0.999698i	$0.492182\pi$
$42$	1.81837	−	1.92185i	0.280581	−	0.296548i
$43$	2.10364	+	1.21454i	0.320803	+	0.185216i	0.651750	−	0.758434i	$-0.274035\pi$
$43$	2.10364	+	1.21454i	0.320803	+	0.185216i	−0.330948	+	0.943649i	$0.607368\pi$
$44$	4.19597	+	4.19597i	0.632566	+	0.632566i
$45$	−0.901498	−	3.36444i	−0.134387	−	0.501541i
$46$	0.101029	+	0.377047i	0.0148960	+	0.0555925i
$47$	−6.84615	−	6.84615i	−0.998614	−	0.998614i	0.00138548	−	0.999999i	$-0.499559\pi$
$47$	−6.84615	−	6.84615i	−0.998614	−	0.998614i	−0.999999	+	0.00138548i	$0.999559\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−3.15946	+	6.24643i	−0.451351	+	0.892346i
$50$	−6.88911	−	1.84593i	−0.974267	−	0.261054i
$51$			1.36351i			0.190930i
$52$	−0.234317	−	3.59793i	−0.0324940	−	0.498943i
$53$	9.73688			1.33746			0.668732	−	0.743504i	$-0.266837\pi$
$53$	9.73688			1.33746			0.668732	+	0.743504i	$0.266837\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	−17.8997	+	10.3344i	−2.41360	+	1.39349i
$56$	2.57356	+	0.613830i	0.343906	+	0.0820265i
$57$	0.554978	+	0.554978i	0.0735086	+	0.0735086i
$58$	−6.64833	+	1.78141i	−0.872969	+	0.233911i
$59$	5.37683	−	1.44072i	0.700004	−	0.187566i	0.108772	−	0.994067i	$-0.465308\pi$
$59$	5.37683	−	1.44072i	0.700004	−	0.187566i	0.591232	+	0.806501i	$0.298642\pi$
$60$	2.46294	−	2.46294i	0.317964	−	0.317964i
$61$	−8.38542	−	4.84132i	−1.07364	−	0.619868i	−0.144468	−	0.989509i	$-0.546147\pi$
$61$	−8.38542	−	4.84132i	−1.07364	−	0.619868i	−0.929174	+	0.369642i	$0.879480\pi$
$62$	0.149328	+	0.258644i	0.0189647	+	0.0328478i
$63$	−2.64474	+	0.0731721i	−0.333206	+	0.00921882i
$64$		−	1.00000i		−	0.125000i
$65$	12.3162	+	2.45518i	1.52764	+	0.304528i
$66$		−	5.93400i		−	0.730425i
$67$	1.38874	−	5.18284i	0.169661	−	0.633185i	−0.827738	−	0.561114i	$-0.810373\pi$
$67$	1.38874	−	5.18284i	0.169661	−	0.633185i	0.997400	−	0.0720702i	$-0.0229606\pi$
$68$	−1.18083	+	0.681755i	−0.143197	+	0.0826749i
$69$	0.195174	−	0.338051i	0.0234961	−	0.0406965i
$70$	−4.38525	+	8.10521i	−0.524138	+	0.968758i
$71$	12.8877	−	3.45324i	1.52948	−	0.409824i	0.606633	−	0.794982i	$-0.292520\pi$
$71$	12.8877	−	3.45324i	1.52948	−	0.409824i	0.922850	+	0.385158i	$0.125853\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	5.09775	+	5.09775i	0.596647	+	0.596647i	0.939419	−	0.342772i	$-0.111366\pi$
$73$	5.09775	+	5.09775i	0.596647	+	0.596647i	−0.342772	+	0.939419i	$0.611366\pi$
$74$	−3.02805	+	5.24474i	−0.352004	+	0.609689i
$75$	3.56607	+	6.17661i	0.411774	+	0.713213i
$76$	−0.203136	+	0.758114i	−0.0233013	+	0.0869616i
$77$	4.48128	+	15.0467i	0.510689	+	1.71474i
$78$	−2.37843	+	2.70981i	−0.269304	+	0.306825i
$79$	9.25714			1.04151			0.520755	−	0.853706i	$-0.325651\pi$
$79$	9.25714			1.04151			0.520755	+	0.853706i	$0.325651\pi$
$80$	3.36444	+	0.901498i	0.376155	+	0.100791i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.80865	−	3.13267i	0.199732	−	0.345946i
$83$	9.33819	−	9.33819i	1.02500	−	1.02500i	0.0253199	−	0.999679i	$-0.491940\pi$
$83$	9.33819	−	9.33819i	1.02500	−	1.02500i	0.999679	−	0.0253199i	$-0.00806045\pi$
$84$	−1.38574	−	2.25383i	−0.151196	−	0.245913i
$85$	−1.22920	−	4.58744i	−0.133326	−	0.497578i
$86$	1.71762	−	1.71762i	0.185216	−	0.185216i
$87$	5.96073	+	3.44143i	0.639057	+	0.368960i
$88$	5.13899	−	2.96700i	0.547818	−	0.316283i
$89$	1.44141	−	5.37940i	0.152789	−	0.570215i	−0.846496	−	0.532395i	$-0.821292\pi$
$89$	1.44141	−	5.37940i	0.152789	−	0.570215i	0.999285	−	0.0378199i	$-0.0120413\pi$
$90$	−3.48312			−0.367153
$91$	3.98454	−	8.66738i	0.417693	−	0.908588i
$92$	0.390347			0.0406965
$93$	0.0772979	−	0.288480i	0.00801542	−	0.0299139i
$94$	−8.38479	+	4.84096i	−0.864825	+	0.499307i
$95$	−2.36750	−	1.36688i	−0.242900	−	0.140239i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	3.44763	+	12.8667i	0.350054	+	1.30642i	0.886595	+	0.462546i	$0.153064\pi$
$97$	3.44763	+	12.8667i	0.350054	+	1.30642i	−0.536541	+	0.843874i	$0.680269\pi$
$98$	5.21586	+	4.66850i	0.526881	+	0.471589i
$99$	−4.19597	+	4.19597i	−0.421711	+	0.421711i
$100$	−3.56607	+	6.17661i	−0.356607	+	0.617661i
$101$	8.86523	+	15.3550i	0.882123	+	1.52788i	0.848976	+	0.528431i	$0.177220\pi$
$101$	8.86523	+	15.3550i	0.882123	+	1.52788i	0.0331469	+	0.999450i	$0.489447\pi$
$102$	1.31705	+	0.352902i	0.130407	+	0.0349425i
$103$	−2.94833			−0.290508			−0.145254	−	0.989394i	$-0.546400\pi$
$103$	−2.94833			−0.290508			−0.145254	+	0.989394i	$0.546400\pi$
$104$	−3.53598	−	0.704879i	−0.346731	−	0.0691191i
$105$	8.83209	−	2.63041i	0.861924	−	0.256702i
$106$	2.52009	−	9.40511i	0.244773	−	0.913505i
$107$	−1.37037	−	2.37355i	−0.132479	−	0.229460i	0.792153	−	0.610323i	$-0.208960\pi$
$107$	−1.37037	−	2.37355i	−0.132479	−	0.229460i	−0.924631	+	0.380863i	$0.875627\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−5.77402	−	5.77402i	−0.553051	−	0.553051i	0.374269	−	0.927320i	$-0.377894\pi$
$109$	−5.77402	−	5.77402i	−0.553051	−	0.553051i	−0.927320	+	0.374269i	$0.877894\pi$
$110$	5.34949	+	19.9646i	0.510054	+	1.90355i
$111$	5.84975	−	1.56744i	0.555233	−	0.148774i
$112$	1.25900	−	2.32700i	0.118964	−	0.219881i
$113$	3.17554	−	5.50020i	0.298730	−	0.517415i	−0.677116	−	0.735876i	$-0.736770\pi$
$113$	3.17554	−	5.50020i	0.298730	−	0.517415i	0.975846	+	0.218461i	$0.0701037\pi$
$114$	0.679706	−	0.392429i	0.0636603	−	0.0367543i
$115$	−0.351897	+	1.31330i	−0.0328146	+	0.122466i
$116$			6.88286i			0.639057i
$117$	3.59793	−	0.234317i	0.332629	−	0.0216626i
$118$		−	5.56651i		−	0.512439i
$119$	−3.60613	+	0.0997709i	−0.330573	+	0.00914599i
$120$	−1.74156	−	3.01647i	−0.158982	−	0.275365i
$121$	20.9685	+	12.1062i	1.90623	+	1.10056i
$122$	−6.84666	+	6.84666i	−0.619868	+	0.619868i
$123$	−3.49404	+	0.936225i	−0.315047	+	0.0844166i
$124$	0.288480	−	0.0772979i	0.0259062	−	0.00694155i
$125$	−5.25131	−	5.25131i	−0.469692	−	0.469692i
$126$	−0.613830	+	2.57356i	−0.0546843	+	0.229271i
$127$	−11.2797	+	6.51235i	−1.00091	+	0.577877i	−0.908518	−	0.417845i	$-0.862785\pi$
$127$	−11.2797	+	6.51235i	−1.00091	+	0.577877i	−0.0923947	+	0.995722i	$0.529452\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−2.42908			−0.213868
$130$	5.55920	−	11.2611i	0.487574	−	0.987666i
$131$			22.5136i			1.96702i	0.180841	+	0.983512i	$0.442118\pi$
$131$			22.5136i			1.96702i	−0.180841	+	0.983512i	$0.557882\pi$
$132$	−5.73180	−	1.53583i	−0.498889	−	0.133677i
$133$	−1.42716	+	1.50838i	−0.123751	+	0.130793i
$134$	−4.64681	−	2.68284i	−0.401423	−	0.231762i
$135$	2.46294	+	2.46294i	0.211976	+	0.211976i
$136$	0.352902	+	1.31705i	0.0302611	+	0.112936i
$137$	−5.53036	−	20.6396i	−0.472491	−	1.76336i	−0.630774	−	0.775966i	$-0.717263\pi$
$137$	−5.53036	−	20.6396i	−0.472491	−	1.76336i	0.158283	−	0.987394i	$-0.449404\pi$
$138$	−0.276017	−	0.276017i	−0.0234961	−	0.0234961i
$139$	13.2381	+	7.64304i	1.12284	+	0.648274i	0.942125	−	0.335261i	$-0.108824\pi$
$139$	13.2381	+	7.64304i	1.12284	+	0.648274i	0.180718	+	0.983535i	$0.442158\pi$
$140$	6.69405	+	6.33361i	0.565750	+	0.535288i
$141$	9.35201	+	2.50586i	0.787582	+	0.211032i
$142$		−	13.3423i		−	1.11966i
$143$	−6.86887	−	20.2627i	−0.574404	−	1.69446i
$144$	1.00000			0.0833333
$145$	−23.1569	−	6.20488i	−1.92308	−	0.515288i
$146$	6.24345	−	3.60466i	0.516711	−	0.298323i
$147$	−0.387042	−	6.98929i	−0.0319227	−	0.576467i
$148$	4.28231	+	4.28231i	0.352004	+	0.352004i
$149$	1.20776	−	0.323617i	0.0989433	−	0.0265118i	−0.209008	−	0.977914i	$-0.567023\pi$
$149$	1.20776	−	0.323617i	0.0989433	−	0.0265118i	0.307951	+	0.951402i	$0.400357\pi$
$150$	6.88911	−	1.84593i	0.562494	−	0.150720i
$151$	10.7007	−	10.7007i	0.870812	−	0.870812i	−0.121749	−	0.992561i	$-0.538850\pi$
$151$	10.7007	−	10.7007i	0.870812	−	0.870812i	0.992561	+	0.121749i	$0.0388504\pi$
$152$	0.679706	+	0.392429i	0.0551315	+	0.0318302i
$153$	−0.681755	−	1.18083i	−0.0551166	−	0.0954648i
$154$	15.6939	−	0.434203i	1.26465	−	0.0349891i
$155$			1.04026i			0.0835553i
$156$	2.00189	+	2.99874i	0.160279	+	0.240091i
$157$		−	14.5407i		−	1.16048i	−0.814447	−	0.580238i	$-0.802959\pi$
$157$		−	14.5407i		−	1.16048i	0.814447	−	0.580238i	$-0.197041\pi$
$158$	2.39592	−	8.94171i	0.190609	−	0.711364i
$159$	−8.43239	+	4.86844i	−0.668732	+	0.386093i
$160$	1.74156	−	3.01647i	0.137682	−	0.238473i
$161$	0.908337	+	0.491447i	0.0715870	+	0.0387315i
$162$	−0.965926	+	0.258819i	−0.0758903	+	0.0203347i
$163$	4.75964	+	17.7632i	0.372804	+	1.39132i	0.856527	+	0.516102i	$0.172617\pi$
$163$	4.75964	+	17.7632i	0.372804	+	1.39132i	−0.483723	+	0.875221i	$0.660716\pi$
$164$	−2.55781	−	2.55781i	−0.199732	−	0.199732i
$165$	10.3344	−	17.8997i	0.804533	−	1.39349i
$166$	−6.60310	−	11.4369i	−0.512500	−	0.887675i
$167$	5.97631	−	22.3039i	0.462460	−	1.72593i	−0.202714	−	0.979238i	$-0.564976\pi$
$167$	5.97631	−	22.3039i	0.462460	−	1.72593i	0.665174	−	0.746688i	$-0.268357\pi$
$168$	−2.53568	+	0.755188i	−0.195632	+	0.0582640i
$169$	−4.98488	+	12.0063i	−0.383452	+	0.923561i
$170$	−4.74927			−0.364252
$171$	−0.758114	−	0.203136i	−0.0579744	−	0.0155342i
$172$	−1.21454	−	2.10364i	−0.0926078	−	0.160401i
$173$	3.62516	−	6.27896i	0.275616	−	0.477380i	−0.694675	−	0.719324i	$-0.744452\pi$
$173$	3.62516	−	6.27896i	0.275616	−	0.477380i	0.970290	+	0.241944i	$0.0777850\pi$
$174$	4.86692	−	4.86692i	0.368960	−	0.368960i
$175$	−16.0746	+	9.88327i	−1.21512	+	0.747105i
$176$	−1.53583	−	5.73180i	−0.115768	−	0.432051i
$177$	−3.93612	+	3.93612i	−0.295857	+	0.295857i
$178$	−4.82304	−	2.78458i	−0.361502	−	0.208713i
$179$	−13.0221	+	7.51831i	−0.973317	+	0.561945i	−0.900246	−	0.435382i	$-0.856613\pi$
$179$	−13.0221	+	7.51831i	−0.973317	+	0.561945i	−0.0730713	+	0.997327i	$0.523280\pi$
$180$	−0.901498	+	3.36444i	−0.0671937	+	0.250770i
$181$	−7.96888			−0.592322			−0.296161	−	0.955138i	$-0.595707\pi$
$181$	−7.96888			−0.592322			−0.296161	+	0.955138i	$0.595707\pi$
$182$	−7.34077	−	6.09205i	−0.544134	−	0.451573i
$183$	9.68265			0.715762
$184$	0.101029	−	0.377047i	0.00744798	−	0.0277962i
$185$	−18.2681	+	10.5471i	−1.34309	+	0.775436i
$186$	−0.258644	−	0.149328i	−0.0189647	−	0.0109493i
$187$	−5.72125	+	5.72125i	−0.418379	+	0.418379i
$188$	2.50586	+	9.35201i	0.182759	+	0.682066i
$189$	2.25383	−	1.38574i	0.163942	−	0.100798i
$190$	−1.93306	+	1.93306i	−0.140239	+	0.140239i
$191$	−4.43523	+	7.68204i	−0.320922	+	0.555853i	−0.980679	−	0.195626i	$-0.937326\pi$
$191$	−4.43523	+	7.68204i	−0.320922	+	0.555853i	0.659757	+	0.751479i	$0.270659\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	3.54651	+	0.950284i	0.255283	+	0.0684030i	0.384191	−	0.923254i	$-0.374480\pi$
$193$	3.54651	+	0.950284i	0.255283	+	0.0684030i	−0.128908	+	0.991657i	$0.541147\pi$
$194$	13.3206			0.956366
$195$	−11.8938	+	4.03187i	−0.851730	+	0.288728i
$196$	5.85938	−	3.82983i	0.418527	−	0.273560i
$197$	3.90018	−	14.5557i	0.277877	−	1.03705i	−0.676013	−	0.736890i	$-0.736294\pi$
$197$	3.90018	−	14.5557i	0.277877	−	1.03705i	0.953889	−	0.300159i	$-0.0970398\pi$
$198$	2.96700	+	5.13899i	0.210855	+	0.365212i
$199$	−4.30556	+	7.45745i	−0.305213	+	0.528645i	−0.977309	−	0.211820i	$-0.932061\pi$
$199$	−4.30556	+	7.45745i	−0.305213	+	0.528645i	0.672095	+	0.740464i	$0.265394\pi$
$200$	5.04318	+	5.04318i	0.356607	+	0.356607i
$201$	1.38874	+	5.18284i	0.0979540	+	0.365569i
$202$	17.1263	−	4.58898i	1.20500	−	0.322879i
$203$	−8.66552	+	16.0164i	−0.608201	+	1.12413i
$204$	0.681755	−	1.18083i	0.0477324	−	0.0826749i
$205$	10.9115	−	6.29974i	0.762090	−	0.439993i
$206$	−0.763084	+	2.84787i	−0.0531666	+	0.198420i
$207$			0.390347i			0.0271310i
$208$	−1.59604	+	3.23306i	−0.110665	+	0.224172i
$209$			4.65734i			0.322155i
$210$	−0.254867	−	9.21195i	−0.0175875	−	0.635685i
$211$	−2.46370	−	4.26725i	−0.169608	−	0.293769i	0.768674	−	0.639641i	$-0.220917\pi$
$211$	−2.46370	−	4.26725i	−0.169608	−	0.293769i	−0.938282	+	0.345871i	$0.887583\pi$
$212$	−8.43239	−	4.86844i	−0.579139	−	0.334366i
$213$	−9.43442	+	9.43442i	−0.646436	+	0.646436i
$214$	−2.64735	+	0.709356i	−0.180969	+	0.0484905i
$215$	8.17248	−	2.18981i	0.557359	−	0.149344i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	0.768609	+	0.183324i	0.0521766	+	0.0124448i
$218$	−7.07171	+	4.08285i	−0.478956	+	0.276526i
$219$	−6.96366	−	1.86591i	−0.470560	−	0.126086i
$220$	20.6688			1.39349
$221$	4.90581	−	0.319494i	0.330001	−	0.0214915i
$222$		−	6.05610i		−	0.406459i
$223$	11.3141	+	3.03159i	0.757646	+	0.203011i	0.616907	−	0.787036i	$-0.288386\pi$
$223$	11.3141	+	3.03159i	0.757646	+	0.203011i	0.140739	+	0.990047i	$0.455052\pi$
$224$	−1.92185	−	1.81837i	−0.128409	−	0.121495i
$225$	−6.17661	−	3.56607i	−0.411774	−	0.237738i
$226$	−4.49089	−	4.49089i	−0.298730	−	0.298730i
$227$	1.79513	+	6.69952i	0.119147	+	0.444662i	0.999564	−	0.0295384i	$-0.00940372\pi$
$227$	1.79513	+	6.69952i	0.119147	+	0.444662i	−0.880417	+	0.474201i	$0.842737\pi$
$228$	−0.203136	−	0.758114i	−0.0134530	−	0.0502073i
$229$	0.832759	+	0.832759i	0.0550302	+	0.0550302i	0.734086	−	0.679056i	$-0.237611\pi$
$229$	0.832759	+	0.832759i	0.0550302	+	0.0550302i	−0.679056	+	0.734086i	$0.737611\pi$
$230$	1.17747	+	0.679813i	0.0776402	+	0.0448256i
$231$	−11.4043	−	10.7902i	−0.750346	−	0.709944i
$232$	6.64833	+	1.78141i	0.436484	+	0.116956i
$233$		−	6.83577i		−	0.447826i	−0.974609	−	0.223913i	$-0.928117\pi$
$233$		−	6.83577i		−	0.447826i	0.974609	−	0.223913i	$-0.0718832\pi$
$234$	0.704879	−	3.53598i	0.0460794	−	0.231154i
$235$	−33.7233			−2.19986
$236$	−5.37683	−	1.44072i	−0.350002	−	0.0937828i
$237$	−8.01692	+	4.62857i	−0.520755	+	0.300658i
$238$	−0.836963	+	3.50907i	−0.0542523	+	0.227460i
$239$	6.87053	+	6.87053i	0.444418	+	0.444418i	0.893494	−	0.449076i	$-0.148247\pi$
$239$	6.87053	+	6.87053i	0.444418	+	0.444418i	−0.449076	+	0.893494i	$0.648247\pi$
$240$	−3.36444	+	0.901498i	−0.217173	+	0.0581915i
$241$	3.78785	−	1.01495i	0.243997	−	0.0653787i	−0.134748	−	0.990880i	$-0.543022\pi$
$241$	3.78785	−	1.01495i	0.243997	−	0.0653787i	0.378745	+	0.925501i	$0.376356\pi$
$242$	17.1207	−	17.1207i	1.10056	−	1.10056i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.84132	+	8.38542i	0.309934	+	0.536821i
$245$	7.60301	+	23.1661i	0.485739	+	1.48003i
$246$			3.61730i			0.230630i
$247$	1.86673	−	2.12681i	0.118777	−	0.135326i
$248$		−	0.298656i		−	0.0189647i
$249$	−3.41801	+	12.7562i	−0.216608	+	0.808391i
$250$	−6.43152	+	3.71324i	−0.406765	+	0.234846i
$251$	9.97113	−	17.2705i	0.629372	−	1.09010i	−0.358306	−	0.933604i	$-0.616645\pi$
$251$	9.97113	−	17.2705i	0.629372	−	1.09010i	0.987678	−	0.156500i	$-0.0500213\pi$
$252$	2.32700	+	1.25900i	0.146587	+	0.0793096i
$253$	2.23739	−	0.599508i	0.140664	−	0.0376907i
$254$	3.37104	+	12.5809i	0.211518	+	0.789395i
$255$	3.35824	+	3.35824i	0.210301	+	0.210301i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.32794	+	12.6924i	0.457105	+	0.791728i	0.998807	−	0.0488423i	$-0.0155532\pi$
$257$	7.32794	+	12.6924i	0.457105	+	0.791728i	−0.541702	+	0.840571i	$0.682220\pi$
$258$	−0.628692	+	2.34631i	−0.0391406	+	0.146075i
$259$	4.57350	+	15.3564i	0.284183	+	0.954198i
$260$	−9.43859	−	8.28437i	−0.585356	−	0.513775i
$261$	−6.88286			−0.426038
$262$	21.7465	+	5.82696i	1.34350	+	0.359991i
$263$	6.28232	+	10.8813i	0.387384	+	0.670969i	0.992097	−	0.125474i	$-0.0400453\pi$
$263$	6.28232	+	10.8813i	0.387384	+	0.670969i	−0.604713	+	0.796444i	$0.706712\pi$
$264$	−2.96700	+	5.13899i	−0.182606	+	0.316283i
$265$	23.9813	−	23.9813i	1.47316	−	1.47316i
$266$	1.08761	+	1.76893i	0.0666855	+	0.108460i
$267$	1.44141	+	5.37940i	0.0882126	+	0.329214i
$268$	−3.79410	+	3.79410i	−0.231762	+	0.231762i
$269$	−18.6795	−	10.7846i	−1.13891	−	0.657550i	−0.192750	−	0.981248i	$-0.561741\pi$
$269$	−18.6795	−	10.7846i	−1.13891	−	0.657550i	−0.946161	+	0.323698i	$0.895074\pi$
$270$	3.01647	−	1.74156i	0.183577	−	0.105988i
$271$	−1.23435	+	4.60664i	−0.0749811	+	0.279833i	−0.993229	−	0.116173i	$-0.962937\pi$
$271$	−1.23435	+	4.60664i	−0.0749811	+	0.279833i	0.918248	+	0.396006i	$0.129604\pi$
$272$	1.36351			0.0826749
$273$	0.882976	+	9.49844i	0.0534402	+	0.574872i
$274$	−21.3677			−1.29087
$275$	−10.9538	+	40.8800i	−0.660536	+	2.46515i
$276$	−0.338051	+	0.195174i	−0.0203483	+	0.0117481i
$277$	−23.5013	−	13.5685i	−1.41206	−	0.815251i	−0.416474	−	0.909147i	$-0.636734\pi$
$277$	−23.5013	−	13.5685i	−1.41206	−	0.815251i	−0.995582	+	0.0938963i	$0.970068\pi$
$278$	10.8089	−	10.8089i	0.648274	−	0.648274i
$279$	0.0772979	+	0.288480i	0.00462770	+	0.0172708i
$280$	7.85035	−	4.82670i	0.469148	−	0.288450i
$281$	−12.1315	+	12.1315i	−0.723704	+	0.723704i	−0.969358	−	0.245653i	$-0.920997\pi$
$281$	−12.1315	+	12.1315i	−0.723704	+	0.723704i	0.245653	+	0.969358i	$0.420997\pi$
$282$	4.84096	−	8.38479i	0.288275	−	0.499307i
$283$	−3.51788	−	6.09314i	−0.209116	−	0.362200i	0.742320	−	0.670045i	$-0.233725\pi$
$283$	−3.51788	−	6.09314i	−0.209116	−	0.362200i	−0.951436	+	0.307846i	$0.900392\pi$
$284$	−12.8877	−	3.45324i	−0.764742	−	0.204912i
$285$	2.73375			0.161934
$286$	−21.3501	+	1.39044i	−1.26246	+	0.0822183i
$287$	−2.73174	−	9.17232i	−0.161249	−	0.541425i
$288$	0.258819	−	0.965926i	0.0152511	−	0.0569177i
$289$	7.57042	+	13.1124i	0.445319	+	0.771315i
$290$	−11.9869	+	20.7619i	−0.703896	+	1.21918i
$291$	−9.41911	−	9.41911i	−0.552158	−	0.552158i
$292$	−1.86591	−	6.96366i	−0.109194	−	0.407517i
$293$	−17.9193	+	4.80147i	−1.04686	+	0.280505i	−0.740953	−	0.671557i	$-0.765626\pi$
$293$	−17.9193	+	4.80147i	−1.04686	+	0.280505i	−0.305906	+	0.952062i	$0.598959\pi$
$294$	−6.85131	−	1.43511i	−0.399577	−	0.0836972i
$295$	9.69441	−	16.7912i	0.564430	−	0.977622i
$296$	5.24474	−	3.02805i	0.304844	−	0.176002i
$297$	1.53583	−	5.73180i	0.0891180	−	0.332593i
$298$		−	1.25036i		−	0.0724315i
$299$	−1.26201	−	0.623010i	−0.0729842	−	0.0360296i
$300$		−	7.13213i		−	0.411774i
$301$	−0.177741	−	6.42428i	−0.0102448	−	0.370289i
$302$	−7.56655	−	13.1056i	−0.435406	−	0.754145i
$303$	−15.3550	−	8.86523i	−0.882123	−	0.509294i
$304$	0.554978	−	0.554978i	0.0318302	−	0.0318302i
$305$	−32.5766	+	8.72889i	−1.86533	+	0.499815i
$306$	−1.31705	+	0.352902i	−0.0752907	+	0.0201741i
$307$	2.41349	+	2.41349i	0.137745	+	0.137745i	0.772617	−	0.634872i	$-0.218947\pi$
$307$	2.41349	+	2.41349i	0.137745	+	0.137745i	−0.634872	+	0.772617i	$0.718947\pi$
$308$	3.64247	−	15.2715i	0.207549	−	0.870174i
$309$	2.55333	−	1.47417i	0.145254	−	0.0838624i
$310$	1.00481	+	0.269238i	0.0570693	+	0.0152917i
$311$	3.90589			0.221483			0.110741	−	0.993849i	$-0.464677\pi$
$311$	3.90589			0.221483			0.110741	+	0.993849i	$0.464677\pi$
$312$	3.41469	−	1.15755i	0.193319	−	0.0655331i
$313$		−	30.2872i		−	1.71193i	−0.517033	−	0.855966i	$-0.672963\pi$
$313$		−	30.2872i		−	1.71193i	0.517033	−	0.855966i	$-0.327037\pi$
$314$	−14.0453	−	3.76342i	−0.792620	−	0.212382i
$315$	−6.33361	+	6.69405i	−0.356859	+	0.377167i
$316$	−8.01692	−	4.62857i	−0.450987	−	0.260377i
$317$	−16.4263	−	16.4263i	−0.922590	−	0.922590i	0.0746216	−	0.997212i	$-0.476225\pi$
$317$	−16.4263	−	16.4263i	−0.922590	−	0.922590i	−0.997212	+	0.0746216i	$0.976225\pi$
$318$	2.52009	+	9.40511i	0.141320	+	0.527412i
$319$	10.5709	+	39.4512i	0.591857	+	2.20884i
$320$	−2.46294	−	2.46294i	−0.137682	−	0.137682i
$321$	2.37355	+	1.37037i	0.132479	+	0.0764866i
$322$	0.709797	−	0.750190i	0.0395554	−	0.0418065i
$323$	−1.03370	−	0.276978i	−0.0575164	−	0.0154115i
$324$			1.00000i			0.0555556i
$325$	21.3874	−	14.2777i	1.18636	−	0.791987i
$326$	18.3898			1.01852
$327$	7.88746	+	2.11344i	0.436178	+	0.116873i
$328$	−3.13267	+	1.80865i	−0.172973	+	0.0998659i
$329$	−5.94305	+	24.9170i	−0.327651	+	1.37372i
$330$	−14.6151	−	14.6151i	−0.804533	−	0.804533i
$331$	−28.9021	+	7.74430i	−1.58860	+	0.425665i	−0.941576	−	0.336800i	$-0.890655\pi$
$331$	−28.9021	+	7.74430i	−1.58860	+	0.425665i	−0.647029	+	0.762466i	$0.723989\pi$
$332$	−12.7562	+	3.41801i	−0.700088	+	0.187588i
$333$	−4.28231	+	4.28231i	−0.234669	+	0.234669i
$334$	−19.9971	−	11.5453i	−1.09419	−	0.631733i
$335$	−9.34464	−	16.1854i	−0.510552	−	0.884302i
$336$	0.0731721	+	2.64474i	0.00399187	+	0.144282i
$337$		−	21.7225i		−	1.18330i	−0.806195	−	0.591650i	$-0.798477\pi$
$337$		−	21.7225i		−	1.18330i	0.806195	−	0.591650i	$-0.201523\pi$
$338$	10.3070	+	7.92248i	0.560627	+	0.430926i
$339$			6.35108i			0.344943i
$340$	−1.22920	+	4.58744i	−0.0666628	+	0.248789i
$341$	1.53479	−	0.886112i	0.0831136	−	0.0479857i
$342$	−0.392429	+	0.679706i	−0.0212201	+	0.0367543i
$343$	18.4565	−	1.53505i	0.996559	−	0.0828848i
$344$	−2.34631	+	0.628692i	−0.126505	+	0.0338968i
$345$	−0.351897	−	1.31330i	−0.0189455	−	0.0707056i
$346$	−5.12675	−	5.12675i	−0.275616	−	0.275616i
$347$	13.7048	−	23.7374i	0.735712	−	1.27429i	−0.218698	−	0.975793i	$-0.570181\pi$
$347$	13.7048	−	23.7374i	0.735712	−	1.27429i	0.954410	−	0.298498i	$-0.0964856\pi$
$348$	−3.44143	−	5.96073i	−0.184480	−	0.319529i
$349$	−2.01381	+	7.51566i	−0.107797	+	0.402304i	−0.998647	−	0.0519928i	$-0.983443\pi$
$349$	−2.01381	+	7.51566i	−0.107797	+	0.402304i	0.890850	+	0.454297i	$0.150109\pi$
$350$	5.38610	+	18.0848i	0.287899	+	0.966675i
$351$	−2.99874	+	2.00189i	−0.160061	+	0.106853i
$352$	−5.93400			−0.316283
$353$	2.29704	+	0.615489i	0.122259	+	0.0327592i	0.319430	−	0.947610i	$-0.396509\pi$
$353$	2.29704	+	0.615489i	0.122259	+	0.0327592i	−0.197171	+	0.980369i	$0.563175\pi$
$354$	2.78325	+	4.82074i	0.147928	+	0.256219i
$355$	23.2364	−	40.2466i	1.23326	−	2.13607i
$356$	−3.93799	+	3.93799i	−0.208713	+	0.208713i
$357$	3.07311	−	1.88947i	0.162646	−	0.100001i
$358$	3.89176	+	14.5243i	0.205686	+	0.767631i
$359$	12.2708	−	12.2708i	0.647629	−	0.647629i	−0.304790	−	0.952419i	$-0.598586\pi$
$359$	12.2708	−	12.2708i	0.647629	−	0.647629i	0.952419	+	0.304790i	$0.0985864\pi$
$360$	3.01647	+	1.74156i	0.158982	+	0.0917883i
$361$	15.9210	−	9.19200i	0.837948	−	0.483789i
$362$	−2.06250	+	7.69735i	−0.108402	+	0.404564i
$363$	−24.2123			−1.27082
$364$	−7.78440	+	5.51390i	−0.408014	+	0.289007i
$365$	25.1109			1.31436
$366$	2.50605	−	9.35272i	0.130993	−	0.488874i
$367$	−27.1547	+	15.6778i	−1.41747	+	0.818374i	−0.996076	−	0.0885060i	$-0.971791\pi$
$367$	−27.1547	+	15.6778i	−1.41747	+	0.818374i	−0.421389	+	0.906880i	$0.638457\pi$
$368$	−0.338051	−	0.195174i	−0.0176221	−	0.0101741i
$369$	2.55781	−	2.55781i	0.133154	−	0.133154i
$370$	5.45957	+	20.3754i	0.283829	+	1.05927i
$371$	−13.4928	−	21.9452i	−0.700510	−	1.13934i
$372$	−0.211182	+	0.211182i	−0.0109493	+	0.0109493i
$373$	−12.3546	+	21.3987i	−0.639695	+	1.10798i	0.345805	+	0.938306i	$0.387606\pi$
$373$	−12.3546	+	21.3987i	−0.639695	+	1.10798i	−0.985500	+	0.169677i	$0.945727\pi$
$374$	4.04553	+	7.00707i	0.209189	+	0.362327i
$375$	7.17343	+	1.92211i	0.370434	+	0.0992575i
$376$	9.68192			0.499307
$377$	10.9853	−	22.2527i	0.565773	−	1.14607i
$378$	−0.755188	−	2.53568i	−0.0388427	−	0.130421i
$379$	4.75813	−	17.7576i	0.244409	−	0.912145i	−0.729271	−	0.684225i	$-0.760141\pi$
$379$	4.75813	−	17.7576i	0.244409	−	0.912145i	0.973680	−	0.227921i	$-0.0731927\pi$
$380$	1.36688	+	2.36750i	0.0701193	+	0.121450i
$381$	6.51235	−	11.2797i	0.333638	−	0.577877i
$382$	6.27236	+	6.27236i	0.320922	+	0.320922i
$383$	2.50600	+	9.35251i	0.128051	+	0.477891i	0.999930	−	0.0118294i	$-0.00376551\pi$
$383$	2.50600	+	9.35251i	0.128051	+	0.477891i	−0.871880	+	0.489720i	$0.837099\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	48.0963	+	26.0221i	2.45122	+	1.32621i
$386$	1.83581	−	3.17971i	0.0934402	−	0.161843i
$387$	2.10364	−	1.21454i	0.106934	−	0.0617385i
$388$	3.44763	−	12.8667i	0.175027	−	0.653210i
$389$		−	13.3041i		−	0.674545i	−0.941407	−	0.337272i	$-0.890496\pi$
$389$		−	13.3041i		−	0.674545i	0.941407	−	0.337272i	$-0.109504\pi$
$390$	0.816156	+	12.5320i	0.0413276	+	0.634584i
$391$			0.532242i			0.0269167i
$392$	−2.18282	−	6.65096i	−0.110249	−	0.335924i
$393$	−11.2568	−	19.4974i	−0.567831	−	0.983512i
$394$	−13.0503	−	7.53457i	−0.657463	−	0.379586i
$395$	22.7998	−	22.7998i	1.14718	−	1.14718i
$396$	5.73180	−	1.53583i	0.288034	−	0.0771784i
$397$	20.2162	−	5.41692i	1.01462	−	0.271868i	0.287064	−	0.957912i	$-0.407321\pi$
$397$	20.2162	−	5.41692i	1.01462	−	0.271868i	0.727560	+	0.686044i	$0.240654\pi$
$398$	6.08899	+	6.08899i	0.305213	+	0.305213i
$399$	0.481769	−	2.01988i	0.0241186	−	0.101120i
$400$	6.17661	−	3.56607i	0.308830	−	0.178303i
$401$	−11.8638	−	3.17888i	−0.592448	−	0.158746i	−0.0498760	−	0.998755i	$-0.515883\pi$
$401$	−11.8638	−	3.17888i	−0.592448	−	0.158746i	−0.542572	+	0.840010i	$0.682549\pi$
$402$	5.36567			0.267615
$403$	−1.05604	−	0.210517i	−0.0526052	−	0.0104866i
$404$		−	17.7305i		−	0.882123i
$405$	−3.36444	−	0.901498i	−0.167180	−	0.0447958i
$406$	13.2278	+	12.5156i	0.656487	+	0.621139i
$407$	31.1223	+	17.9685i	1.54267	+	0.890663i
$408$	−0.964147	−	0.964147i	−0.0477324	−	0.0477324i
$409$	1.07120	+	3.99778i	0.0529675	+	0.197677i	0.987339	−	0.158622i	$-0.0507051\pi$
$409$	1.07120	+	3.99778i	0.0529675	+	0.197677i	−0.934372	+	0.356299i	$0.884038\pi$
$410$	−3.26098	−	12.1702i	−0.161049	−	0.601041i
$411$	15.1092	+	15.1092i	0.745284	+	0.745284i
$412$	2.55333	+	1.47417i	0.125794	+	0.0726269i
$413$	−10.6980	−	10.1220i	−0.526415	−	0.498070i
$414$	0.377047	+	0.101029i	0.0185308	+	0.00496532i
$415$		−	45.9988i		−	2.25799i
$416$	2.70981	+	2.37843i	0.132859	+	0.116612i
$417$	−15.2861			−0.748562
$418$	4.49865	+	1.20541i	0.220036	+	0.0589584i
$419$	−26.8922	+	15.5262i	−1.31377	+	0.758504i	−0.982718	−	0.185109i	$-0.940736\pi$
$419$	−26.8922	+	15.5262i	−1.31377	+	0.758504i	−0.331050	+	0.943613i	$0.607403\pi$
$420$	−8.96402	−	2.13804i	−0.437399	−	0.104326i
$421$	23.7904	+	23.7904i	1.15947	+	1.15947i	0.984589	+	0.174882i	$0.0559545\pi$
$421$	23.7904	+	23.7904i	1.15947	+	1.15947i	0.174882	+	0.984589i	$0.444046\pi$
$422$	−4.75950	+	1.27530i	−0.231689	+	0.0620808i
$423$	−9.35201	+	2.50586i	−0.454710	+	0.121839i
$424$	−6.88502	+	6.88502i	−0.334366	+	0.334366i
$425$	−8.42187	−	4.86237i	−0.408520	−	0.235859i
$426$	6.67114	+	11.5548i	0.323218	+	0.559830i
$427$	0.708500	+	25.6081i	0.0342867	+	1.23926i
$428$			2.74074i			0.132479i
$429$	16.0800	+	14.1136i	0.776349	+	0.681412i
$430$		−	8.46077i		−	0.408015i
$431$	2.38619	−	8.90540i	0.114939	−	0.428958i	−0.884343	−	0.466837i	$-0.845393\pi$
$431$	2.38619	−	8.90540i	0.114939	−	0.428958i	0.999282	+	0.0378790i	$0.0120601\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−9.06647	+	15.7036i	−0.435707	+	0.754666i	−0.997353	−	0.0727111i	$-0.976835\pi$
$433$	−9.06647	+	15.7036i	−0.435707	+	0.754666i	0.561646	+	0.827378i	$0.310168\pi$
$434$	0.376008	−	0.694972i	0.0180490	−	0.0333597i
$435$	23.1569	−	6.20488i	1.11029	−	0.297501i
$436$	2.11344	+	7.88746i	0.101215	+	0.377741i
$437$	0.216634	+	0.216634i	0.0103630	+	0.0103630i
$438$	−3.60466	+	6.24345i	−0.172237	+	0.298323i
$439$	17.0376	+	29.5100i	0.813160	+	1.40844i	0.910641	+	0.413198i	$0.135588\pi$
$439$	17.0376	+	29.5100i	0.813160	+	1.40844i	−0.0974810	+	0.995237i	$0.531079\pi$
$440$	5.34949	−	19.9646i	0.255027	−	0.951773i
$441$	3.82983	+	5.85938i	0.182373	+	0.279018i
$442$	0.961110	−	4.82134i	0.0457153	−	0.229328i
$443$	−37.1553			−1.76530			−0.882650	−	0.470030i	$-0.844243\pi$
$443$	−37.1553			−1.76530			−0.882650	+	0.470030i	$0.844243\pi$
$444$	−5.84975	−	1.56744i	−0.277617	−	0.0743872i
$445$	−9.69904	−	16.7992i	−0.459778	−	0.796360i
$446$	5.85659	−	10.1439i	0.277318	−	0.480328i
$447$	−0.884139	+	0.884139i	−0.0418183	+	0.0418183i
$448$	−2.25383	+	1.38574i	−0.106483	+	0.0654700i
$449$	3.12913	+	11.6781i	0.147673	+	0.551122i	0.999622	+	0.0274976i	$0.00875387\pi$
$449$	3.12913	+	11.6781i	0.147673	+	0.551122i	−0.851949	+	0.523625i	$0.824579\pi$
$450$	−5.04318	+	5.04318i	−0.237738	+	0.237738i
$451$	−18.5893	−	10.7325i	−0.875334	−	0.505374i
$452$	−5.50020	+	3.17554i	−0.258708	+	0.149365i
$453$	−3.91673	+	14.6174i	−0.184024	+	0.686787i
$454$	6.93585			0.325516
$455$	−11.5335	−	31.1609i	−0.540701	−	1.46085i
$456$	−0.784857			−0.0367543
$457$	−1.71247	+	6.39104i	−0.0801061	+	0.298960i	−0.994343	−	0.106221i	$-0.966125\pi$
$457$	−1.71247	+	6.39104i	−0.0801061	+	0.298960i	0.914236	+	0.405181i	$0.132792\pi$
$458$	1.01992	−	0.588849i	0.0476576	−	0.0275151i
$459$	1.18083	+	0.681755i	0.0551166	+	0.0318216i
$460$	0.961401	−	0.961401i	0.0448256	−	0.0448256i
$461$	6.00819	+	22.4229i	0.279829	+	1.04434i	0.952536	+	0.304427i	$0.0984650\pi$
$461$	6.00819	+	22.4229i	0.279829	+	1.04434i	−0.672706	+	0.739909i	$0.734868\pi$
$462$	−13.3742	+	8.22297i	−0.622224	+	0.382567i
$463$	−4.55758	+	4.55758i	−0.211809	+	0.211809i	−0.805035	−	0.593227i	$-0.797854\pi$
$463$	−4.55758	+	4.55758i	−0.211809	+	0.211809i	0.593227	+	0.805035i	$0.297854\pi$
$464$	3.44143	−	5.96073i	0.159764	−	0.276720i
$465$	−0.520128	−	0.900888i	−0.0241203	−	0.0417777i
$466$	−6.60285	−	1.76923i	−0.305871	−	0.0819579i
$467$	−11.0261			−0.510228			−0.255114	−	0.966911i	$-0.582113\pi$
$467$	−11.0261			−0.510228			−0.255114	+	0.966911i	$0.582113\pi$
$468$	−3.23306	−	1.59604i	−0.149448	−	0.0737770i
$469$	−13.6056	+	4.05209i	−0.628250	+	0.187108i
$470$	−8.72823	+	32.5742i	−0.402603	+	1.50254i
$471$	7.27036	+	12.5926i	0.335001	+	0.580238i
$472$	−2.78325	+	4.82074i	−0.128110	+	0.221892i
$473$	−10.1923	−	10.1923i	−0.468644	−	0.468644i
$474$	2.39592	+	8.94171i	0.110048	+	0.410706i
$475$	−5.40697	+	1.44879i	−0.248089	+	0.0664752i
$476$	3.17288	+	1.71666i	0.145429	+	0.0786830i
$477$	4.86844	−	8.43239i	0.222911	−	0.386093i
$478$	8.41465	−	4.85820i	0.384877	−	0.222209i
$479$	1.58884	−	5.92965i	0.0725961	−	0.270932i	−0.920081	−	0.391727i	$-0.871878\pi$
$479$	1.58884	−	5.92965i	0.0725961	−	0.270932i	0.992677	+	0.120795i	$0.0385443\pi$
$480$			3.48312i			0.158982i
$481$	−7.01022	−	20.6797i	−0.319638	−	0.942913i
$482$		−	3.92147i		−	0.178618i
$483$	−1.03237	+	0.0285625i	−0.0469743	+	0.00129964i
$484$	−12.1062	−	20.9685i	−0.550280	−	0.953113i
$485$	40.1813	+	23.1987i	1.82454	+	1.05340i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	10.5482	−	2.82637i	0.477983	−	0.128075i	−0.0117801	−	0.999931i	$-0.503750\pi$
$487$	10.5482	−	2.82637i	0.477983	−	0.128075i	0.489763	+	0.871855i	$0.337083\pi$
$488$	9.35272	−	2.50605i	0.423378	−	0.113444i
$489$	−13.0036	−	13.0036i	−0.588042	−	0.588042i
$490$	24.3445	−	1.34812i	1.09977	−	0.0609017i
$491$	−7.10942	+	4.10463i	−0.320844	+	0.185239i	−0.651769	−	0.758418i	$-0.725973\pi$
$491$	−7.10942	+	4.10463i	−0.320844	+	0.185239i	0.330925	+	0.943657i	$0.392639\pi$
$492$	3.49404	+	0.936225i	0.157523	+	0.0422083i
$493$	−9.38485			−0.422672
$494$	−1.57120	−	2.35358i	−0.0706915	−	0.105893i
$495$			20.6688i			0.928995i
$496$	−0.288480	−	0.0772979i	−0.0129531	−	0.00347078i
$497$	−25.6419	−	24.2612i	−1.15020	−	1.08827i
$498$	11.4369	+	6.60310i	0.512500	+	0.295892i
$499$	24.2077	+	24.2077i	1.08369	+	1.08369i	0.996162	+	0.0875246i	$0.0278957\pi$
$499$	24.2077	+	24.2077i	1.08369	+	1.08369i	0.0875246	+	0.996162i	$0.472104\pi$
$500$	1.92211	+	7.17343i	0.0859595	+	0.320805i
$501$	5.97631	+	22.3039i	0.267002	+	0.996464i
$502$	−14.1013	−	14.1013i	−0.629372	−	0.629372i
$503$	8.94037	+	5.16172i	0.398631	+	0.230150i	0.685893	−	0.727702i	$-0.259412\pi$
$503$	8.94037	+	5.16172i	0.398631	+	0.230150i	−0.287262	+	0.957852i	$0.592745\pi$
$504$	1.81837	−	1.92185i	0.0809968	−	0.0856062i
$505$	59.6530	+	15.9840i	2.65452	+	0.711277i
$506$		−	2.31632i		−	0.102973i
$507$	−1.68611	−	12.8902i	−0.0748830	−	0.572473i
$508$	13.0247			0.577877
$509$	−18.5789	−	4.97820i	−0.823495	−	0.220655i	−0.177621	−	0.984099i	$-0.556840\pi$
$509$	−18.5789	−	4.97820i	−0.823495	−	0.220655i	−0.645874	+	0.763444i	$0.723507\pi$
$510$	4.11299	−	2.37463i	0.182126	−	0.105151i
$511$	4.42529	−	18.5536i	0.195763	−	0.820763i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.758114	−	0.203136i	0.0334715	−	0.00896867i
$514$	14.1565	−	3.79322i	0.624416	−	0.167312i
$515$	−7.26156	+	7.26156i	−0.319983	+	0.319983i
$516$	2.10364	+	1.21454i	0.0926078	+	0.0534671i
$517$	28.7262	+	49.7553i	1.26338	+	2.18824i
$518$	16.0168	−	0.443138i	0.703739	−	0.0194704i
$519$			7.25031i			0.318253i
$520$	−10.4450	+	6.97282i	−0.458042	+	0.305779i
$521$			39.9065i			1.74833i	0.485625	+	0.874167i	$0.338592\pi$
$521$			39.9065i			1.74833i	−0.485625	+	0.874167i	$0.661408\pi$
$522$	−1.78141	+	6.64833i	−0.0779704	+	0.290990i
$523$	8.17412	−	4.71933i	0.357429	−	0.206362i	−0.310523	−	0.950566i	$-0.600504\pi$
$523$	8.17412	−	4.71933i	0.357429	−	0.206362i	0.667953	+	0.744204i	$0.267171\pi$
$524$	11.2568	−	19.4974i	0.491756	−	0.851747i
$525$	8.97936	−	16.5965i	0.391891	−	0.724329i
$526$	12.1365	−	3.25197i	0.529177	−	0.141793i
$527$	0.105396	+	0.393345i	0.00459114	+	0.0171344i
$528$	4.19597	+	4.19597i	0.182606	+	0.182606i
$529$	−11.4238	+	19.7866i	−0.496688	+	0.860288i
$530$	−16.9574	−	29.3710i	−0.736581	−	1.27580i
$531$	1.44072	−	5.37683i	0.0625219	−	0.233335i
$532$	1.99015	−	0.592715i	0.0862839	−	0.0256974i
$533$	4.18719	+	12.3519i	0.181367	+	0.535022i
$534$	5.56916			0.241001
$535$	−9.22104	−	2.47077i	−0.398661	−	0.106821i
$536$	2.68284	+	4.64681i	0.115881	+	0.200712i
$537$	7.51831	−	13.0221i	0.324439	−	0.561945i
$538$	−15.2518	+	15.2518i	−0.657550	+	0.657550i
$539$	27.7028	−	30.9509i	1.19325	−	1.33315i
$540$	−0.901498	−	3.36444i	−0.0387943	−	0.144782i
$541$	11.1738	−	11.1738i	0.480397	−	0.480397i	−0.424861	−	0.905259i	$-0.639677\pi$
$541$	11.1738	−	11.1738i	0.480397	−	0.480397i	0.905259	+	0.424861i	$0.139677\pi$
$542$	4.13020	+	2.38457i	0.177407	+	0.102426i
$543$	6.90125	−	3.98444i	0.296161	−	0.170989i
$544$	0.352902	−	1.31705i	0.0151306	−	0.0564680i
$545$	−28.4421			−1.21833
$546$	9.40332	+	1.60549i	0.402425	+	0.0687085i
$547$	3.67435			0.157104			0.0785519	−	0.996910i	$-0.474970\pi$
$547$	3.67435			0.157104			0.0785519	+	0.996910i	$0.474970\pi$
$548$	−5.53036	+	20.6396i	−0.236245	+	0.881680i
$549$	−8.38542	+	4.84132i	−0.357881	+	0.206623i
$550$	36.6520	+	21.1610i	1.56285	+	0.902309i
$551$	−3.81983	+	3.81983i	−0.162730	+	0.162730i
$552$	0.101029	+	0.377047i	0.00430009	+	0.0160482i
$553$	−12.8280	−	20.8640i	−0.545501	−	0.887226i
$554$	−19.1887	+	19.1887i	−0.815251	+	0.815251i
$555$	10.5471	−	18.2681i	0.447698	−	0.775436i
$556$	−7.64304	−	13.2381i	−0.324137	−	0.561422i
$557$	−1.80798	−	0.484446i	−0.0766065	−	0.0205267i	0.220312	−	0.975429i	$-0.429292\pi$
$557$	−1.80798	−	0.484446i	−0.0766065	−	0.0205267i	−0.296919	+	0.954903i	$0.595959\pi$
$558$	0.298656			0.0126431
$559$	0.569175	+	8.73965i	0.0240735	+	0.369648i
$560$	−2.63041	−	8.83209i	−0.111155	−	0.373224i
$561$	2.09412	−	7.81537i	0.0884139	−	0.329965i
$562$	8.57826	+	14.8580i	0.361852	+	0.626746i
$563$	0.329848	−	0.571314i	0.0139014	−	0.0240780i	−0.858991	−	0.511991i	$-0.828908\pi$
$563$	0.329848	−	0.571314i	0.0139014	−	0.0240780i	0.872892	+	0.487913i	$0.162242\pi$
$564$	−6.84615	−	6.84615i	−0.288275	−	0.288275i
$565$	−5.72549	−	21.3678i	−0.240873	−	0.898951i
$566$	−6.79602	+	1.82099i	−0.285658	+	0.0765418i
$567$	−1.25900	+	2.32700i	−0.0528731	+	0.0977247i
$568$	−6.67114	+	11.5548i	−0.279915	+	0.484827i
$569$	19.3083	−	11.1477i	0.809446	−	0.467334i	−0.0373172	−	0.999303i	$-0.511881\pi$
$569$	19.3083	−	11.1477i	0.809446	−	0.467334i	0.846764	+	0.531969i	$0.178548\pi$
$570$	0.707547	−	2.64060i	0.0296359	−	0.110603i
$571$		−	5.98049i		−	0.250276i	−0.992139	−	0.125138i	$-0.960063\pi$
$571$		−	5.98049i		−	0.250276i	0.992139	−	0.125138i	$-0.0399373\pi$
$572$	−4.18275	+	20.9825i	−0.174890	+	0.877322i
$573$		−	8.87046i		−	0.370569i
$574$	−9.56680	+	0.264685i	−0.399311	+	0.0110477i
$575$	1.39200	+	2.41102i	0.0580506	+	0.100547i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	7.43677	−	7.43677i	0.309597	−	0.309597i	−0.535156	−	0.844753i	$-0.679747\pi$
$577$	7.43677	−	7.43677i	0.309597	−	0.309597i	0.844753	+	0.535156i	$0.179747\pi$
$578$	14.6249	−	3.91874i	0.608317	−	0.162998i
$579$	−3.54651	+	0.950284i	−0.147388	+	0.0394925i
$580$	16.9521	+	16.9521i	0.703896	+	0.703896i
$581$	−33.9869	−	8.10636i	−1.41002	−	0.336308i
$582$	−11.5360	+	6.66032i	−0.478183	+	0.276079i
$583$	−55.8099	−	14.9542i	−2.31141	−	0.619340i
$584$	−7.20931			−0.298323
$585$	8.28437	−	9.43859i	0.342517	−	0.390238i
$586$			18.5515i			0.766354i
$587$	21.0591	+	5.64276i	0.869201	+	0.232902i	0.665742	−	0.746182i	$-0.268115\pi$
$587$	21.0591	+	5.64276i	0.869201	+	0.232902i	0.203459	+	0.979083i	$0.434782\pi$
$588$	−3.15946	+	6.24643i	−0.130294	+	0.257598i
$589$	0.202998	+	0.117201i	0.00836440	+	0.00482919i
$590$	−13.7100	−	13.7100i	−0.564430	−	0.564430i
$591$	3.90018	+	14.5557i	0.160432	+	0.598741i
$592$	−1.56744	−	5.84975i	−0.0644212	−	0.240423i
$593$	31.6701	+	31.6701i	1.30054	+	1.30054i	0.928029	+	0.372508i	$0.121502\pi$
$593$	31.6701	+	31.6701i	1.30054	+	1.30054i	0.372508	+	0.928029i	$0.378498\pi$
$594$	−5.13899	−	2.96700i	−0.210855	−	0.121737i
$595$	−8.63594	+	9.12740i	−0.354039	+	0.374187i
$596$	−1.20776	−	0.323617i	−0.0494716	−	0.0132559i
$597$		−	8.61113i		−	0.352430i
$598$	−0.928415	+	1.05777i	−0.0379657	+	0.0432553i
$599$	23.5065			0.960451			0.480226	−	0.877145i	$-0.340555\pi$
$599$	23.5065			0.960451			0.480226	+	0.877145i	$0.340555\pi$
$600$	−6.88911	−	1.84593i	−0.281247	−	0.0753598i
$601$	41.2432	−	23.8118i	1.68234	−	0.971302i	0.722247	−	0.691636i	$-0.243110\pi$
$601$	41.2432	−	23.8118i	1.68234	−	0.971302i	0.960097	−	0.279666i	$-0.0902238\pi$
$602$	−6.25138	−	1.49104i	−0.254787	−	0.0607703i
$603$	−3.79410	−	3.79410i	−0.154508	−	0.154508i
$604$	−14.6174	+	3.91673i	−0.594775	+	0.159370i
$605$	81.4608	−	21.8274i	3.31185	−	0.887408i
$606$	−12.5373	+	12.5373i	−0.509294	+	0.509294i
$607$	−1.65889	−	0.957758i	−0.0673321	−	0.0388742i	0.465956	−	0.884808i	$-0.345710\pi$
$607$	−1.65889	−	0.957758i	−0.0673321	−	0.0388742i	−0.533288	+	0.845934i	$0.679044\pi$
$608$	−0.392429	−	0.679706i	−0.0159151	−	0.0275657i
$609$	−0.503633	−	18.2034i	−0.0204083	−	0.737638i
$610$			33.7258i			1.36552i
$611$	6.82458	−	34.2351i	0.276093	−	1.38500i
$612$			1.36351i			0.0551166i
$613$	−0.684906	+	2.55611i	−0.0276631	+	0.103240i	−0.978377	−	0.206829i	$-0.933686\pi$
$613$	−0.684906	+	2.55611i	−0.0276631	+	0.103240i	0.950714	+	0.310069i	$0.100352\pi$
$614$	2.95591	−	1.70659i	0.119291	−	0.0688725i
$615$	−6.29974	+	10.9115i	−0.254030	+	0.439993i
$616$	−13.8084	−	7.47091i	−0.556356	−	0.301011i
$617$	−3.04305	+	0.815383i	−0.122509	+	0.0328261i	−0.319552	−	0.947569i	$-0.603533\pi$
$617$	−3.04305	+	0.815383i	−0.122509	+	0.0328261i	0.197044	+	0.980395i	$0.436866\pi$
$618$	−0.763084	−	2.84787i	−0.0306958	−	0.114558i
$619$	−23.7062	−	23.7062i	−0.952831	−	0.952831i	0.0461053	−	0.998937i	$-0.485319\pi$
$619$	−23.7062	−	23.7062i	−0.952831	−	0.952831i	−0.998937	+	0.0461053i	$0.985319\pi$
$620$	0.520128	−	0.900888i	0.0208888	−	0.0361805i
$621$	−0.195174	−	0.338051i	−0.00783205	−	0.0135655i
$622$	1.01092	−	3.77280i	0.0405342	−	0.151276i
$623$	−14.1216	+	4.20576i	−0.565772	+	0.168500i
$624$	−0.234317	−	3.59793i	−0.00938020	−	0.144032i
$625$	9.79335			0.391734
$626$	−29.2551	−	7.83889i	−1.16927	−	0.313305i
$627$	−2.32867	−	4.03337i	−0.0929981	−	0.161077i
$628$	−7.27036	+	12.5926i	−0.290119	+	0.502501i
$629$	−5.83897	+	5.83897i	−0.232815	+	0.232815i
$630$	4.82670	+	7.85035i	0.192300	+	0.312765i
$631$	0.430633	+	1.60714i	0.0171432	+	0.0639794i	0.973968	−	0.226687i	$-0.0727896\pi$
$631$	0.430633	+	1.60714i	0.0171432	+	0.0639794i	−0.956824	+	0.290667i	$0.906123\pi$
$632$	−6.54579	+	6.54579i	−0.260377	+	0.260377i
$633$	4.26725	+	2.46370i	0.169608	+	0.0979231i
$634$	−20.1180	+	11.6151i	−0.798987	+	0.461295i
$635$	−11.7417	+	43.8208i	−0.465957	+	1.73897i
$636$	9.73688			0.386093
$637$	−25.0563	+	3.03026i	−0.992766	+	0.120063i
$638$	40.8429			1.61698
$639$	3.45324	−	12.8877i	0.136608	−	0.509828i
$640$	−3.01647	+	1.74156i	−0.119237	+	0.0688412i
$641$	−10.3277	−	5.96272i	−0.407921	−	0.235513i	0.281975	−	0.959422i	$-0.409010\pi$
$641$	−10.3277	−	5.96272i	−0.407921	−	0.235513i	−0.689896	+	0.723908i	$0.742344\pi$
$642$	1.93800	−	1.93800i	0.0764866	−	0.0764866i
$643$	−6.28890	−	23.4705i	−0.248010	−	0.925585i	−0.971847	−	0.235614i	$-0.924290\pi$
$643$	−6.28890	−	23.4705i	−0.248010	−	0.925585i	0.723837	−	0.689971i	$-0.242377\pi$
$644$	−0.540919	−	0.879775i	−0.0213152	−	0.0346680i
$645$	−5.98267	+	5.98267i	−0.235567	+	0.235567i
$646$	−0.535080	+	0.926786i	−0.0210525	+	0.0364639i
$647$	22.1120	+	38.2991i	0.869312	+	1.50569i	0.862701	+	0.505714i	$0.168771\pi$
$647$	22.1120	+	38.2991i	0.869312	+	1.50569i	0.00661029	+	0.999978i	$0.497896\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−33.0316			−1.29661
$650$	−8.25577	−	24.3540i	−0.323818	−	0.955243i
$651$	−0.757297	+	0.225541i	−0.0296808	+	0.00883967i
$652$	4.75964	−	17.7632i	0.186402	−	0.695662i
$653$	−8.80949	−	15.2585i	−0.344742	−	0.597111i	0.640565	−	0.767904i	$-0.278700\pi$
$653$	−8.80949	−	15.2585i	−0.344742	−	0.597111i	−0.985307	+	0.170793i	$0.945367\pi$
$654$	4.08285	−	7.07171i	0.159652	−	0.276526i
$655$	55.4497	+	55.4497i	2.16660	+	2.16660i
$656$	0.936225	+	3.49404i	0.0365534	+	0.136419i
$657$	6.96366	−	1.86591i	0.271678	−	0.0727960i
$658$	22.5298	+	12.1895i	0.878303	+	0.475198i
$659$	−19.7135	+	34.1447i	−0.767928	+	1.33009i	0.170757	+	0.985313i	$0.445379\pi$
$659$	−19.7135	+	34.1447i	−0.767928	+	1.33009i	−0.938685	+	0.344777i	$0.887955\pi$
$660$	−17.8997	+	10.3344i	−0.696746	+	0.402267i
$661$	−2.09098	+	7.80365i	−0.0813297	+	0.303527i	−0.994594	−	0.103841i	$-0.966887\pi$
$661$	−2.09098	+	7.80365i	−0.0813297	+	0.303527i	0.913264	+	0.407368i	$0.133553\pi$
$662$			29.9217i			1.16294i
$663$	−4.08881	+	2.72960i	−0.158796	+	0.106009i
$664$			13.2062i			0.512500i
$665$	0.200035	+	7.23006i	0.00775701	+	0.280370i
$666$	3.02805	+	5.24474i	0.117335	+	0.203230i
$667$	2.32675	+	1.34335i	0.0900923	+	0.0520148i
$668$	−16.3276	+	16.3276i	−0.631733	+	0.631733i
$669$	−11.3141	+	3.03159i	−0.437427	+	0.117208i
$670$	−18.0525	+	4.83714i	−0.697427	+	0.186875i
$671$	40.6281	+	40.6281i	1.56843	+	1.56843i
$672$	2.57356	+	0.613830i	0.0992772	+	0.0236790i
$673$	20.2298	−	11.6797i	0.779803	−	0.450219i	−0.0565577	−	0.998399i	$-0.518012\pi$
$673$	20.2298	−	11.6797i	0.779803	−	0.450219i	0.836360	+	0.548180i	$0.184679\pi$
$674$	−20.9823	−	5.62220i	−0.808209	−	0.216559i
$675$	7.13213			0.274516
$676$	10.3202	−	7.90531i	0.396930	−	0.304051i
$677$			42.4364i			1.63097i	0.578782	+	0.815483i	$0.303528\pi$
$677$			42.4364i			1.63097i	−0.578782	+	0.815483i	$0.696472\pi$
$678$	6.13467	+	1.64378i	0.235601	+	0.0631290i
$679$	24.2219	−	25.6003i	0.929551	−	0.982450i
$680$	4.11299	+	2.37463i	0.157726	+	0.0910631i
$681$	−4.90439	−	4.90439i	−0.187936	−	0.187936i
$682$	−0.458685	−	1.71184i	−0.0175640	−	0.0655496i
$683$	3.84079	+	14.3340i	0.146964	+	0.548476i	0.999660	+	0.0260692i	$0.00829902\pi$
$683$	3.84079	+	14.3340i	0.146964	+	0.548476i	−0.852696	+	0.522407i	$0.825034\pi$
$684$	0.554978	+	0.554978i	0.0212201	+	0.0212201i
$685$	−64.4550	−	37.2131i	−2.46270	−	1.42184i
$686$	3.29416	−	18.2249i	0.125772	−	0.695832i
$687$	−1.13757	−	0.304811i	−0.0434010	−	0.0116293i
$688$			2.42908i			0.0926078i
$689$	19.4922	+	29.1984i	0.742592	+	1.11237i
$690$	−1.35963			−0.0517601
$691$	−41.4261	−	11.1001i	−1.57592	−	0.422267i	−0.638261	−	0.769820i	$-0.720346\pi$
$691$	−41.4261	−	11.1001i	−1.57592	−	0.422267i	−0.937660	+	0.347553i	$0.887013\pi$
$692$	−6.27896	+	3.62516i	−0.238690	+	0.137808i
$693$	15.2715	+	3.64247i	0.580116	+	0.138366i
$694$	−19.3815	−	19.3815i	−0.735712	−	0.735712i
$695$	51.4290	−	13.7804i	1.95081	−	0.522719i
$696$	−6.64833	+	1.78141i	−0.252004	+	0.0675244i
$697$	3.48760	−	3.48760i	0.132102	−	0.132102i
$698$	6.73835	+	3.89039i	0.255050	+	0.147253i
$699$	3.41788	+	5.91995i	0.129276	+	0.223913i
$700$	18.8626	−	0.521873i	0.712940	−	0.0197250i
$701$			21.6520i			0.817783i	0.912583	+	0.408892i	$0.134085\pi$
$701$			21.6520i			0.817783i	−0.912583	+	0.408892i	$0.865915\pi$
$702$	1.15755	+	3.41469i	0.0436888	+	0.128879i
$703$			4.75318i			0.179269i
$704$	−1.53583	+	5.73180i	−0.0578838	+	0.216025i
$705$	29.2052	−	16.8616i	1.09993	−	0.635046i
$706$	1.18903	−	2.05947i	0.0447499	−	0.0775091i
$707$	22.3227	−	41.2587i	0.839530	−	1.55169i
$708$	5.37683	−	1.44072i	0.202074	−	0.0541455i
$709$	−3.84427	−	14.3470i	−0.144375	−	0.538813i	−0.999782	−	0.0208583i	$-0.993360\pi$
$709$	−3.84427	−	14.3470i	−0.144375	−	0.538813i	0.855408	−	0.517955i	$-0.173307\pi$
$710$	−32.8612	−	32.8612i	−1.23326	−	1.23326i
$711$	4.62857	−	8.01692i	0.173585	−	0.300658i
$712$	2.78458	+	4.82304i	0.104357	+	0.180751i
$713$	0.0301730	−	0.112607i	0.00112999	−	0.00421717i
$714$	−1.02971	−	3.45743i	−0.0385358	−	0.129391i
$715$	−66.8235	−	32.9883i	−2.49906	−	1.23369i
$716$	15.0366			0.561945
$717$	−9.38532	−	2.51479i	−0.350501	−	0.0939165i
$718$	−8.67678	−	15.0286i	−0.323814	−	0.560863i
$719$	19.3705	−	33.5507i	0.722399	−	1.25123i	−0.237637	−	0.971354i	$-0.576373\pi$
$719$	19.3705	−	33.5507i	0.722399	−	1.25123i	0.960036	−	0.279877i	$-0.0902938\pi$
$720$	2.46294	−	2.46294i	0.0917883	−	0.0917883i
$721$	4.08562	+	6.64502i	0.152156	+	0.247474i
$722$	−4.75813	−	17.7576i	−0.177079	−	0.660869i
$723$	−2.77290	+	2.77290i	−0.103125	+	0.103125i
$724$	6.90125	+	3.98444i	0.256483	+	0.148081i
$725$	−42.5127	+	24.5447i	−1.57888	+	0.911568i
$726$	−6.26661	+	23.3873i	−0.232576	+	0.867984i
$727$	9.19936			0.341186			0.170593	−	0.985342i	$-0.445432\pi$
$727$	9.19936			0.341186			0.170593	+	0.985342i	$0.445432\pi$
$728$	3.31127	+	8.94626i	0.122724	+	0.331570i
$729$	−1.00000			−0.0370370
$730$	6.49918	−	24.2553i	0.240545	−	0.897728i
$731$	2.86834	−	1.65604i	0.106089	−	0.0612507i
$732$	−8.38542	−	4.84132i	−0.309934	−	0.178940i
$733$	−26.3545	+	26.3545i	−0.973426	+	0.973426i	−0.999656	−	0.0262295i	$-0.991650\pi$
$733$	−26.3545	+	26.3545i	−0.973426	+	0.973426i	0.0262295	+	0.999656i	$0.491650\pi$
$734$	8.11542	+	30.2872i	0.299546	+	1.11792i
$735$	−18.1675	−	16.2609i	−0.670117	−	0.599794i
$736$	−0.276017	+	0.276017i	−0.0101741	+	0.0101741i
$737$	−15.9199	+	27.5741i	−0.586418	+	1.01571i
$738$	−1.80865	−	3.13267i	−0.0665772	−	0.115315i
$739$	10.3275	+	2.76726i	0.379905	+	0.101795i	0.443718	−	0.896167i	$-0.353659\pi$
$739$	10.3275	+	2.76726i	0.379905	+	0.101795i	−0.0638126	+	0.997962i	$0.520326\pi$
$740$	21.0941			0.775436
$741$	−0.553230	+	2.77524i	−0.0203234	+	0.101951i
$742$	−24.6897	+	7.35317i	−0.906386	+	0.269944i
$743$	7.78997	−	29.0726i	0.285786	−	1.06657i	−0.662477	−	0.749083i	$-0.730495\pi$
$743$	7.78997	−	29.0726i	0.285786	−	1.06657i	0.948263	−	0.317486i	$-0.102839\pi$
$744$	0.149328	+	0.258644i	0.00547463	+	0.00948234i
$745$	2.17758	−	3.77168i	0.0797804	−	0.138184i
$746$	17.4720	+	17.4720i	0.639695	+	0.639695i
$747$	−3.41801	−	12.7562i	−0.125059	−	0.466725i
$748$	7.81537	−	2.09412i	0.285758	−	0.0765687i
$749$	−3.45059	+	6.37769i	−0.126082	+	0.233036i
$750$	3.71324	−	6.43152i	0.135588	−	0.234846i
$751$	25.9043	−	14.9559i	0.945263	−	0.545748i	0.0536565	−	0.998559i	$-0.482912\pi$
$751$	25.9043	−	14.9559i	0.945263	−	0.545748i	0.891606	+	0.452812i	$0.149579\pi$
$752$	2.50586	−	9.35201i	0.0913795	−	0.341033i
$753$			19.9423i			0.726737i
$754$	−18.6512	−	16.3704i	−0.679237	−	0.596175i
$755$		−	52.7104i		−	1.91833i
$756$	−2.64474	+	0.0731721i	−0.0961882	+	0.00266124i
$757$	0.589796	+	1.02156i	0.0214365	+	0.0371291i	0.876545	−	0.481321i	$-0.159843\pi$
$757$	0.589796	+	1.02156i	0.0214365	+	0.0371291i	−0.855108	+	0.518450i	$0.826509\pi$
$758$	−15.9210	−	9.19200i	−0.578277	−	0.333868i
$759$	−1.63789	+	1.63789i	−0.0594515	+	0.0594515i
$760$	2.64060	−	0.707547i	0.0957847	−	0.0256654i
$761$	−33.8587	+	9.07242i	−1.22738	+	0.328875i	−0.813558	−	0.581484i	$-0.802472\pi$
$761$	−33.8587	+	9.07242i	−1.22738	+	0.328875i	−0.413820	+	0.910359i	$0.635806\pi$
$762$	−9.20985	−	9.20985i	−0.333638	−	0.333638i
$763$	−5.01235	+	21.0149i	−0.181459	+	0.760791i
$764$	7.68204	−	4.43523i	0.277927	−	0.160461i
$765$	−4.58744	−	1.22920i	−0.165859	−	0.0444419i
$766$	9.68243			0.349841
$767$	15.0842	+	13.2396i	0.544658	+	0.478053i
$768$		−	1.00000i		−	0.0360844i
$769$	31.5481	+	8.45328i	1.13765	+	0.304833i	0.778007	−	0.628256i	$-0.216231\pi$
$769$	31.5481	+	8.45328i	1.13765	+	0.304833i	0.359646	+	0.933089i	$0.382898\pi$
$770$	37.5836	−	39.7225i	1.35442	−	1.43150i
$771$	−12.6924	−	7.32794i	−0.457105	−	0.263909i
$772$	−2.59622	−	2.59622i	−0.0934402	−	0.0934402i
$773$	−10.6566	−	39.7711i	−0.383292	−	1.43047i	−0.840841	−	0.541282i	$-0.817939\pi$
$773$	−10.6566	−	39.7711i	−0.383292	−	1.43047i	0.457549	−	0.889184i	$-0.348727\pi$
$774$	−0.628692	−	2.34631i	−0.0225979	−	0.0843364i
$775$	1.50618	+	1.50618i	0.0541034	+	0.0541034i
$776$	−11.5360	−	6.66032i	−0.414119	−	0.239092i
$777$	−11.6389	−	11.0123i	−0.417545	−	0.395062i
$778$	−12.8508	−	3.44335i	−0.460722	−	0.123450i
$779$		−	2.83906i		−	0.101720i
$780$	12.3162	+	2.45518i	0.440992	+	0.0879096i
$781$	−79.1731			−2.83303
$782$	0.514107	+	0.137754i	0.0183844	+	0.00492609i
$783$	5.96073	−	3.44143i	0.213019	−	0.122987i
$784$	−6.98929	+	0.387042i	−0.249618	+	0.0138229i
$785$	−35.8129	−	35.8129i	−1.27822	−	1.27822i
$786$	−21.7465	+	5.82696i	−0.775672	+	0.207841i
$787$	−26.8450	+	7.19309i	−0.956920	+	0.256406i	−0.703296	−	0.710897i	$-0.748289\pi$
$787$	−26.8450	+	7.19309i	−0.956920	+	0.256406i	−0.253624	+	0.967303i	$0.581623\pi$
$788$	−10.6555	+	10.6555i	−0.379586	+	0.379586i
$789$	−10.8813	−	6.28232i	−0.387384	−	0.223656i
$790$	−16.1219	−	27.9239i	−0.573590	−	0.993488i
$791$	−16.7970	+	0.464722i	−0.597231	+	0.0165236i
$792$		−	5.93400i		−	0.210855i
$793$	−2.26881	−	34.8375i	−0.0805679	−	1.23712i
$794$		−	20.9294i		−	0.742756i
$795$	−8.77778	+	32.7591i	−0.311316	+	1.16185i
$796$	7.45745	−	4.30556i	0.264322	−	0.152607i
$797$	−2.40148	+	4.15948i	−0.0850646	+	0.147336i	−0.905419	−	0.424520i	$-0.860443\pi$
$797$	−2.40148	+	4.15948i	−0.0850646	+	0.147336i	0.820354	+	0.571856i	$0.193776\pi$
$798$	−1.82636	−	0.988136i	−0.0646525	−	0.0349796i
$799$	−12.7516	+	3.41677i	−0.451118	+	0.120877i
$800$	−1.84593	−	6.88911i	−0.0652635	−	0.243567i
$801$	−3.93799	−	3.93799i	−0.139142	−	0.139142i
$802$	−6.14113	+	10.6367i	−0.216851	+	0.375597i
$803$	−21.3900	−	37.0486i	−0.754837	−	1.30742i
$804$	1.38874	−	5.18284i	0.0489770	−	0.182785i
$805$	3.44758	−	1.02677i	0.121511	−	0.0361890i
$806$	−0.476667	+	0.965572i	−0.0167899	+	0.0340108i
$807$	21.5692			0.759273
$808$	−17.1263	−	4.58898i	−0.602501	−	0.161440i
$809$	25.3509	+	43.9090i	0.891290	+	1.54376i	0.838330	+	0.545163i	$0.183532\pi$
$809$	25.3509	+	43.9090i	0.891290	+	1.54376i	0.0529601	+	0.998597i	$0.483134\pi$
$810$	−1.74156	+	3.01647i	−0.0611922	+	0.105988i
$811$	−10.8776	+	10.8776i	−0.381963	+	0.381963i	−0.871809	−	0.489846i	$-0.837053\pi$
$811$	−10.8776	+	10.8776i	−0.381963	+	0.381963i	0.489846	+	0.871809i	$0.337053\pi$
$812$	15.5128	−	9.53784i	0.544391	−	0.334713i
$813$	−1.23435	−	4.60664i	−0.0432904	−	0.161562i
$814$	25.4112	−	25.4112i	0.890663	−	0.890663i
$815$	55.4724	+	32.0270i	1.94311	+	1.12186i
$816$	−1.18083	+	0.681755i	−0.0413375	+	0.0238662i
$817$	0.493433	−	1.84152i	0.0172630	−	0.0644266i
$818$	4.13880			0.144710
$819$	−5.51390	−	7.78440i	−0.192671	−	0.272009i
$820$	−12.5995			−0.439993
$821$	−2.20982	+	8.24715i	−0.0771231	+	0.287828i	−0.993706	−	0.112017i	$-0.964269\pi$
$821$	−2.20982	+	8.24715i	−0.0771231	+	0.287828i	0.916583	+	0.399844i	$0.130936\pi$
$822$	18.5050	−	10.6838i	0.645435	−	0.372642i
$823$	17.0903	+	9.86707i	0.595729	+	0.343944i	0.767360	−	0.641217i	$-0.221570\pi$
$823$	17.0903	+	9.86707i	0.595729	+	0.343944i	−0.171630	+	0.985161i	$0.554903\pi$
$824$	2.08479	−	2.08479i	0.0726269	−	0.0726269i
$825$	−10.9538	−	40.8800i	−0.381361	−	1.42326i
$826$	−12.5459	+	7.71373i	−0.436529	+	0.268395i
$827$	8.80285	−	8.80285i	0.306105	−	0.306105i	−0.537292	−	0.843397i	$-0.680553\pi$
$827$	8.80285	−	8.80285i	0.306105	−	0.306105i	0.843397	+	0.537292i	$0.180553\pi$
$828$	0.195174	−	0.338051i	0.00678275	−	0.0117481i
$829$	−11.2622	−	19.5067i	−0.391152	−	0.677495i	0.601450	−	0.798910i	$-0.294590\pi$
$829$	−11.2622	−	19.5067i	−0.391152	−	0.677495i	−0.992602	+	0.121416i	$0.961257\pi$
$830$	−44.4314	−	11.9054i	−1.54224	−	0.413241i
$831$	27.1370			0.941371
$832$	2.99874	−	2.00189i	0.103963	−	0.0694030i
$833$	5.22202	+	7.98933i	0.180932	+	0.276814i
$834$	−3.95633	+	14.7652i	−0.136996	+	0.511278i
$835$	−40.2138	−	69.6524i	−1.39166	−	2.41042i
$836$	2.32867	−	4.03337i	0.0805387	−	0.139497i
$837$	−0.211182	−	0.211182i	−0.00729951	−	0.00729951i
$838$	8.03695	+	29.9943i	0.277632	+	1.03614i
$839$	−18.1332	+	4.85878i	−0.626029	+	0.167744i	−0.557867	−	0.829930i	$-0.688380\pi$
$839$	−18.1332	+	4.85878i	−0.626029	+	0.167744i	−0.0681618	+	0.997674i	$0.521713\pi$
$840$	−4.38525	+	8.10521i	−0.151306	+	0.279656i
$841$	−9.18687	+	15.9121i	−0.316789	+	0.548694i
$842$	29.1371	−	16.8223i	1.00413	−	0.579736i
$843$	4.44043	−	16.5719i	0.152937	−	0.570768i
$844$			4.92739i			0.169608i
$845$	17.2933	+	41.8482i	0.594908	+	1.43962i
$846$			9.68192i			0.332871i
$847$	−1.77167	−	64.0353i	−0.0608752	−	2.20028i
$848$	4.86844	+	8.43239i	0.167183	+	0.289569i
$849$	6.09314	+	3.51788i	0.209116	+	0.120733i
$850$	−6.87642	+	6.87642i	−0.235859	+	0.235859i
$851$	2.28343	−	0.611844i	0.0782751	−	0.0209737i
$852$	12.8877	−	3.45324i	0.441524	−	0.118306i
$853$	0.958043	+	0.958043i	0.0328028	+	0.0328028i	0.723318	−	0.690515i	$-0.242616\pi$
$853$	0.958043	+	0.958043i	0.0328028	+	0.0328028i	−0.690515	+	0.723318i	$0.742616\pi$
$854$	24.9189	+	5.94350i	0.852706	+	0.203382i
$855$	−2.36750	+	1.36688i	−0.0809668	+	0.0467462i
$856$	2.64735	+	0.709356i	0.0904846	+	0.0242453i
$857$	−23.9274			−0.817346			−0.408673	−	0.912681i	$-0.634008\pi$
$857$	−23.9274			−0.817346			−0.408673	+	0.912681i	$0.634008\pi$
$858$	17.7945	−	11.8792i	0.607495	−	0.405549i
$859$			9.89523i			0.337621i	0.985649	+	0.168810i	$0.0539926\pi$
$859$			9.89523i			0.337621i	−0.985649	+	0.168810i	$0.946007\pi$
$860$	−8.17248	−	2.18981i	−0.278679	−	0.0746719i
$861$	6.95191	+	6.57759i	0.236921	+	0.224164i
$862$	−7.98436	−	4.60977i	−0.271948	−	0.157010i
$863$	−24.3259	−	24.3259i	−0.828065	−	0.828065i	0.159184	−	0.987249i	$-0.449114\pi$
$863$	−24.3259	−	24.3259i	−0.828065	−	0.828065i	−0.987249	+	0.159184i	$0.949114\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	−6.53614	−	24.3932i	−0.222236	−	0.829395i
$866$	12.8219	+	12.8219i	0.435707	+	0.435707i
$867$	−13.1124	−	7.57042i	−0.445319	−	0.257105i
$868$	−0.573973	−	0.543068i	−0.0194819	−	0.0184329i
$869$	−53.0601	−	14.2174i	−1.79994	−	0.482292i
$870$		−	23.9738i		−	0.812789i
$871$	18.3221	−	6.21101i	0.620820	−	0.210452i
$872$	8.16570			0.276526
$873$	12.8667	+	3.44763i	0.435473	+	0.116685i
$874$	0.265321	−	0.153183i	0.00897463	−	0.00518151i
$875$	−4.55859	+	19.1125i	−0.154109	+	0.646120i
$876$	5.09775	+	5.09775i	0.172237	+	0.172237i
$877$	5.13739	−	1.37656i	0.173477	−	0.0464831i	−0.171035	−	0.985265i	$-0.554711\pi$
$877$	5.13739	−	1.37656i	0.173477	−	0.0464831i	0.344512	+	0.938782i	$0.388044\pi$
$878$	32.9141	−	8.81931i	1.11080	−	0.297637i
$879$	13.1179	−	13.1179i	0.442455	−	0.442455i
$880$	−17.8997	−	10.3344i	−0.603400	−	0.348373i
$881$	−26.3870	−	45.7036i	−0.889001	−	1.53979i	−0.841058	−	0.540945i	$-0.818067\pi$
$881$	−26.3870	−	45.7036i	−0.889001	−	1.53979i	−0.0479427	−	0.998850i	$-0.515266\pi$
$882$	6.65096	−	2.18282i	0.223950	−	0.0734992i
$883$		−	5.02529i		−	0.169115i	−0.996419	−	0.0845573i	$-0.973052\pi$
$883$		−	5.02529i		−	0.169115i	0.996419	−	0.0845573i	$-0.0269476\pi$
$884$	−4.40830	−	2.17622i	−0.148267	−	0.0731941i
$885$			19.3888i			0.651748i
$886$	−9.61649	+	35.8892i	−0.323072	+	1.20572i
$887$	−0.688294	+	0.397387i	−0.0231107	+	0.0133429i	−0.511511	−	0.859277i	$-0.670914\pi$
$887$	−0.688294	+	0.397387i	−0.0231107	+	0.0133429i	0.488400	+	0.872620i	$0.337581\pi$
$888$	−3.02805	+	5.24474i	−0.101615	+	0.176002i
$889$	30.3084	+	16.3981i	1.01651	+	0.549975i
$890$	−18.7371	+	5.02059i	−0.628069	+	0.168291i
$891$	1.53583	+	5.73180i	0.0514523	+	0.192023i
$892$	−8.28247	−	8.28247i	−0.277318	−	0.277318i
$893$	−3.79946	+	6.58086i	−0.127144	+	0.220220i
$894$	0.625181	+	1.08284i	0.0209092	+	0.0362158i
$895$	−13.5555	+	50.5898i	−0.453110	+	1.69103i
$896$	0.755188	+	2.53568i	0.0252291	+	0.0847112i
$897$	1.40444	−	0.0914651i	0.0468929	−	0.00305393i
$898$	12.0900			0.403449
$899$	1.98556	+	0.532030i	0.0662223	+	0.0177442i
$900$	3.56607	+	6.17661i	0.118869	+	0.205887i
$901$	6.63817	−	11.4976i	0.221149	−	0.383042i
$902$	−15.1781	+	15.1781i	−0.505374	+	0.505374i
$903$	3.36607	+	5.47472i	0.112016	+	0.182187i
$904$	1.64378	+	6.13467i	0.0546713	+	0.204036i
$905$	−19.6269	+	19.6269i	−0.652419	+	0.652419i
$906$	13.1056	+	7.56655i	0.435406	+	0.251382i
$907$	7.86742	−	4.54226i	0.261233	−	0.150823i	−0.363664	−	0.931530i	$-0.618474\pi$
$907$	7.86742	−	4.54226i	0.261233	−	0.150823i	0.624897	+	0.780707i	$0.285141\pi$
$908$	1.79513	−	6.69952i	0.0595735	−	0.222331i
$909$	17.7305			0.588082
$910$	−33.0842	+	3.07551i	−1.09673	+	0.101952i
$911$	21.6692			0.717933			0.358967	−	0.933350i	$-0.383129\pi$
$911$	21.6692			0.717933			0.358967	+	0.933350i	$0.383129\pi$
$912$	−0.203136	+	0.758114i	−0.00672650	+	0.0251037i
$913$	−67.8665	+	39.1828i	−2.24605	+	1.29676i
$914$	5.73005	+	3.30824i	0.189533	+	0.109427i
$915$	23.8478	−	23.8478i	0.788383	−	0.788383i
$916$	−0.304811	−	1.13757i	−0.0100712	−	0.0375863i
$917$	50.7418	−	31.1980i	1.67564	−	1.03025i
$918$	0.964147	−	0.964147i	0.0318216	−	0.0318216i
$919$	−14.5126	+	25.1366i	−0.478727	+	0.829180i	−0.999702	−	0.0243920i	$-0.992235\pi$
$919$	−14.5126	+	25.1366i	−0.478727	+	0.829180i	0.520975	+	0.853572i	$0.325568\pi$
$920$	−0.679813	−	1.17747i	−0.0224128	−	0.0388201i
$921$	−3.29688	−	0.883398i	−0.108636	−	0.0291089i
$922$	23.2139			0.764507
$923$	36.1550	+	31.7337i	1.19006	+	1.04453i
$924$	4.48128	+	15.0467i	0.147423	+	0.495001i
$925$	−11.1792	+	41.7212i	−0.367568	+	1.37178i
$926$	3.22270	+	5.58187i	0.105904	+	0.183432i
$927$	−1.47417	+	2.55333i	−0.0484180	+	0.0838624i
$928$	−4.86692	−	4.86692i	−0.159764	−	0.159764i
$929$	2.84426	+	10.6149i	0.0933173	+	0.348265i	0.996759	−	0.0804463i	$-0.0256345\pi$
$929$	2.84426	+	10.6149i	0.0933173	+	0.348265i	−0.903442	+	0.428711i	$0.858968\pi$
$930$	−1.00481	+	0.269238i	−0.0329490	+	0.00882866i
$931$	5.37730	+	1.12635i	0.176234	+	0.0369148i
$932$	−3.41788	+	5.91995i	−0.111957	+	0.193914i
$933$	−3.38260	+	1.95295i	−0.110741	+	0.0639366i
$934$	−2.85377	+	10.6504i	−0.0933783	+	0.348492i
$935$			28.1822i			0.921655i
$936$	−2.37843	+	2.70981i	−0.0777415	+	0.0885728i
$937$			1.49801i			0.0489378i	0.999701	+	0.0244689i	$0.00778947\pi$
$937$			1.49801i			0.0489378i	−0.999701	+	0.0244689i	$0.992211\pi$
$938$	0.392618	+	14.1908i	0.0128194	+	0.463346i
$939$	15.1436	+	26.2294i	0.494192	+	0.855966i
$940$	29.2052	+	16.8616i	0.952569	+	0.549966i
$941$	−12.8482	+	12.8482i	−0.418841	+	0.418841i	−0.884804	−	0.465963i	$-0.845708\pi$
$941$	−12.8482	+	12.8482i	−0.418841	+	0.418841i	0.465963	+	0.884804i	$0.345708\pi$
$942$	14.0453	−	3.76342i	0.457619	−	0.122619i
$943$	−1.36389	+	0.365453i	−0.0444143	+	0.0119008i
$944$	3.93612	+	3.93612i	0.128110	+	0.128110i
$945$	2.13804	−	8.96402i	0.0695506	−	0.291600i
$946$	−12.4830	+	7.20707i	−0.405858	+	0.234322i
$947$	−18.3580	−	4.91900i	−0.596554	−	0.159846i	−0.0521072	−	0.998641i	$-0.516594\pi$
$947$	−18.3580	−	4.91900i	−0.596554	−	0.159846i	−0.544447	+	0.838795i	$0.683260\pi$
$948$	9.25714			0.300658
$949$	−5.08169	+	25.4920i	−0.164959	+	0.827504i
$950$			5.59771i			0.181614i
$951$	22.4387	+	6.01243i	0.727624	+	0.194966i
$952$	2.47937	−	2.62047i	0.0803568	−	0.0849298i
$953$	−31.5430	−	18.2114i	−1.02178	−	0.589924i	−0.107160	−	0.994242i	$-0.534176\pi$
$953$	−31.5430	−	18.2114i	−1.02178	−	0.589924i	−0.914619	+	0.404318i	$0.867509\pi$
$954$	−6.88502	−	6.88502i	−0.222911	−	0.222911i
$955$	7.99670	+	29.8441i	0.258767	+	0.965732i
$956$	−2.51479	−	9.38532i	−0.0813341	−	0.303543i
$957$	−28.8803	−	28.8803i	−0.933566	−	0.933566i
$958$	−5.31637	−	3.06941i	−0.171764	−	0.0991682i
$959$	−38.8544	+	41.0656i	−1.25467	+	1.32608i
$960$	3.36444	+	0.901498i	0.108587	+	0.0290957i
$961$			30.9108i			0.997123i
$962$	−21.7894	+	1.41905i	−0.702520	+	0.0457520i
$963$	−2.74074			−0.0883191
$964$	−3.78785	−	1.01495i	−0.121998	−	0.0326894i
$965$	11.0753	−	6.39434i	0.356527	−	0.205841i
$966$	−0.239607	+	1.00458i	−0.00770922	+	0.0323219i
$967$	12.1331	+	12.1331i	0.390174	+	0.390174i	0.874750	−	0.484575i	$-0.161026\pi$
$967$	12.1331	+	12.1331i	0.390174	+	0.390174i	−0.484575	+	0.874750i	$0.661026\pi$
$968$	−23.3873	+	6.26661i	−0.751696	+	0.201416i
$969$	1.03370	−	0.276978i	0.0332071	−	0.00889781i
$970$	32.8079	−	32.8079i	1.05340	−	1.05340i
$971$	−12.5245	−	7.23103i	−0.401930	−	0.232055i	0.285386	−	0.958413i	$-0.407878\pi$
$971$	−12.5245	−	7.23103i	−0.401930	−	0.232055i	−0.687317	+	0.726358i	$0.741211\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−1.11851	−	40.4277i	−0.0358579	−	1.29605i
$974$		−	10.9203i		−	0.349908i
$975$	−11.3832	+	23.0586i	−0.364553	+	0.738466i
$976$		−	9.68265i		−	0.309934i
$977$	10.5148	−	39.2419i	0.336400	−	1.25546i	−0.565944	−	0.824443i	$-0.691488\pi$
$977$	10.5148	−	39.2419i	0.336400	−	1.25546i	0.902344	−	0.431017i	$-0.141845\pi$
$978$	−15.9261	+	9.19492i	−0.509260	+	0.294021i
$979$	−16.5237	+	28.6199i	−0.528100	+	0.914696i
$980$	4.99865	−	23.8639i	0.159676	−	0.762306i
$981$	−7.88746	+	2.11344i	−0.251827	+	0.0674769i
$982$	2.12471	+	7.92953i	0.0678023	+	0.253041i
$983$	−31.4962	−	31.4962i	−1.00457	−	1.00457i	−0.999989	−	0.00458449i	$-0.998541\pi$
$983$	−31.4962	−	31.4962i	−1.00457	−	1.00457i	−0.00458449	−	0.999989i	$-0.501459\pi$
$984$	1.80865	−	3.13267i	0.0576576	−	0.0998659i
$985$	−26.2438	−	45.4557i	−0.836198	−	1.44834i
$986$	−2.42898	+	9.06506i	−0.0773544	+	0.288690i
$987$	−7.31167	−	24.5503i	−0.232733	−	0.781444i
$988$	−2.68004	+	0.908508i	−0.0852635	+	0.0289035i
$989$	−0.948184			−0.0301505
$990$	19.9646	+	5.34949i	0.634515	+	0.170018i
$991$	26.2447	+	45.4571i	0.833690	+	1.44399i	0.895093	+	0.445880i	$0.147109\pi$
$991$	26.2447	+	45.4571i	0.833690	+	1.44399i	−0.0614024	+	0.998113i	$0.519557\pi$
$992$	−0.149328	+	0.258644i	−0.00474117	+	0.00821195i
$993$	21.1578	−	21.1578i	0.671423	−	0.671423i
$994$	−30.0712	+	18.4889i	−0.953800	+	0.586433i
$995$	7.76291	+	28.9716i	0.246101	+	0.918461i
$996$	9.33819	−	9.33819i	0.295892	−	0.295892i
$997$	32.9828	+	19.0426i	1.04458	+	0.603086i	0.921126	−	0.389265i	$-0.127271\pi$
$997$	32.9828	+	19.0426i	1.04458	+	0.603086i	0.123449	+	0.992351i	$0.460604\pi$
$998$	29.6483	−	17.1175i	0.938500	−	0.541843i
$999$	1.56744	−	5.84975i	0.0495915	−	0.185078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.349.10	yes	40
7.6	odd	2		546.2.bx.b.349.6	yes	40
13.6	odd	12		546.2.bx.b.97.6	yes	40
91.6	even	12	inner	546.2.bx.a.97.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.10	✓	40	91.6	even	12	inner
546.2.bx.a.349.10	yes	40	1.1	even	1	trivial
546.2.bx.b.97.6	yes	40	13.6	odd	12
546.2.bx.b.349.6	yes	40	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.46294 - 2.46294i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.38574 - 2.25383i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.46294 - 2.46294i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.38574 - 2.25383i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.74156 - 3.01647i) q^{10} +(-5.73180 - 1.53583i) q^{11} +1.00000 q^{12} +(2.00189 + 2.99874i) q^{13} +(-2.53568 + 0.755188i) q^{14} +(-0.901498 + 3.36444i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.681755 - 1.18083i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-0.203136 - 0.758114i) q^{19} +(-3.36444 + 0.901498i) q^{20} +(2.32700 + 1.25900i) q^{21} +(-2.96700 + 5.13899i) q^{22} +(-0.338051 + 0.195174i) q^{23} +(0.258819 - 0.965926i) q^{24} -7.13213i q^{25} +(3.41469 - 1.15755i) q^{26} +1.00000i q^{27} +(0.0731721 + 2.64474i) q^{28} +(-3.44143 - 5.96073i) q^{29} +(3.01647 + 1.74156i) q^{30} +(-0.211182 + 0.211182i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.73180 - 1.53583i) q^{33} +(-0.964147 - 0.964147i) q^{34} +(-8.96402 - 2.13804i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-5.84975 - 1.56744i) q^{37} -0.784857 q^{38} +(-3.23306 - 1.59604i) q^{39} +3.48312i q^{40} +(3.49404 + 0.936225i) q^{41} +(1.81837 - 1.92185i) q^{42} +(2.10364 + 1.21454i) q^{43} +(4.19597 + 4.19597i) q^{44} +(-0.901498 - 3.36444i) q^{45} +(0.101029 + 0.377047i) q^{46} +(-6.84615 - 6.84615i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.15946 + 6.24643i) q^{49} +(-6.88911 - 1.84593i) q^{50} +1.36351i q^{51} +(-0.234317 - 3.59793i) q^{52} +9.73688 q^{53} +(0.965926 + 0.258819i) q^{54} +(-17.8997 + 10.3344i) q^{55} +(2.57356 + 0.613830i) q^{56} +(0.554978 + 0.554978i) q^{57} +(-6.64833 + 1.78141i) q^{58} +(5.37683 - 1.44072i) q^{59} +(2.46294 - 2.46294i) q^{60} +(-8.38542 - 4.84132i) q^{61} +(0.149328 + 0.258644i) q^{62} +(-2.64474 + 0.0731721i) q^{63} -1.00000i q^{64} +(12.3162 + 2.45518i) q^{65} -5.93400i q^{66} +(1.38874 - 5.18284i) q^{67} +(-1.18083 + 0.681755i) q^{68} +(0.195174 - 0.338051i) q^{69} +(-4.38525 + 8.10521i) q^{70} +(12.8877 - 3.45324i) q^{71} +(0.258819 + 0.965926i) q^{72} +(5.09775 + 5.09775i) q^{73} +(-3.02805 + 5.24474i) q^{74} +(3.56607 + 6.17661i) q^{75} +(-0.203136 + 0.758114i) q^{76} +(4.48128 + 15.0467i) q^{77} +(-2.37843 + 2.70981i) q^{78} +9.25714 q^{79} +(3.36444 + 0.901498i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.80865 - 3.13267i) q^{82} +(9.33819 - 9.33819i) q^{83} +(-1.38574 - 2.25383i) q^{84} +(-1.22920 - 4.58744i) q^{85} +(1.71762 - 1.71762i) q^{86} +(5.96073 + 3.44143i) q^{87} +(5.13899 - 2.96700i) q^{88} +(1.44141 - 5.37940i) q^{89} -3.48312 q^{90} +(3.98454 - 8.66738i) q^{91} +0.390347 q^{92} +(0.0772979 - 0.288480i) q^{93} +(-8.38479 + 4.84096i) q^{94} +(-2.36750 - 1.36688i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(3.44763 + 12.8667i) q^{97} +(5.21586 + 4.66850i) q^{98} +(-4.19597 + 4.19597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 + 20 * q^9	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

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