LMFDB - Embedded newform 546.2.bd.b.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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([0, 2, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$0.508531i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.440400 + 0.254265i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.39031 + 1.13420i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.440400 + 0.254265i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.39031 + 1.13420i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +0.508531 q^{10} +3.86324i q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.12559 - 1.79742i) q^{13} +(2.63717 + 0.212907i) q^{14} +(-0.440400 + 0.254265i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.89376 + 6.74420i) q^{17} +(-0.866025 - 0.500000i) q^{18} -0.115446i q^{19} +(-0.440400 - 0.254265i) q^{20} +(-2.39031 + 1.13420i) q^{21} +(1.93162 - 3.34566i) q^{22} +(-0.614785 + 1.06484i) q^{23} -1.00000i q^{24} +(-2.37070 + 4.10617i) q^{25} +(1.80813 + 3.11940i) q^{26} +1.00000 q^{27} +(-2.17740 - 1.50297i) q^{28} +(1.86905 + 3.23729i) q^{29} +0.508531 q^{30} +(-3.83229 - 2.21258i) q^{31} +(0.866025 - 0.500000i) q^{32} +3.86324i q^{33} -7.78753i q^{34} +(0.764305 - 1.10728i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.50367 + 0.868142i) q^{37} +(-0.0577229 + 0.0999790i) q^{38} +(-3.12559 - 1.79742i) q^{39} +(0.254265 + 0.440400i) q^{40} +(0.138041 - 0.0796979i) q^{41} +(2.63717 + 0.212907i) q^{42} +(-0.153620 + 0.266078i) q^{43} +(-3.34566 + 1.93162i) q^{44} +(-0.440400 + 0.254265i) q^{45} +(1.06484 - 0.614785i) q^{46} +(-6.61173 + 3.81729i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(4.42717 - 5.42219i) q^{49} +(4.10617 - 2.37070i) q^{50} +(3.89376 + 6.74420i) q^{51} +(-0.00618631 - 3.60555i) q^{52} +(-2.08305 + 3.60794i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.982287 - 1.70137i) q^{55} +(1.13420 + 2.39031i) q^{56} -0.115446i q^{57} -3.73810i q^{58} +(7.24338 - 4.18197i) q^{59} +(-0.440400 - 0.254265i) q^{60} +6.14619 q^{61} +(2.21258 + 3.83229i) q^{62} +(-2.39031 + 1.13420i) q^{63} -1.00000 q^{64} +(1.83353 - 0.00314593i) q^{65} +(1.93162 - 3.34566i) q^{66} +1.54044i q^{67} +(-3.89376 + 6.74420i) q^{68} +(-0.614785 + 1.06484i) q^{69} +(-1.21555 + 0.576777i) q^{70} +(-0.505964 - 0.292119i) q^{71} -1.00000i q^{72} +(4.78934 + 2.76512i) q^{73} +(-0.868142 - 1.50367i) q^{74} +(-2.37070 + 4.10617i) q^{75} +(0.0999790 - 0.0577229i) q^{76} +(-4.38169 - 9.23433i) q^{77} +(1.80813 + 3.11940i) q^{78} +(2.16963 + 3.75790i) q^{79} -0.508531i q^{80} +1.00000 q^{81} -0.159396 q^{82} +3.96800i q^{83} +(-2.17740 - 1.50297i) q^{84} +(-3.42963 - 1.98010i) q^{85} +(0.266078 - 0.153620i) q^{86} +(1.86905 + 3.23729i) q^{87} +3.86324 q^{88} +(3.92640 + 2.26691i) q^{89} +0.508531 q^{90} +(9.50976 + 0.751331i) q^{91} -1.22957 q^{92} +(-3.83229 - 2.21258i) q^{93} +7.63457 q^{94} +(0.0293539 + 0.0508424i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-13.4014 - 7.73733i) q^{97} +(-6.54514 + 2.48217i) q^{98} +3.86324i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	$ 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.440400	+	0.254265i	−0.196953	+	0.113711i	−0.595233	−	0.803553i	$-0.702940\pi$
$5$	−0.440400	+	0.254265i	−0.196953	+	0.113711i	0.398280	+	0.917264i	$0.369607\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−2.39031	+	1.13420i	−0.903452	+	0.428688i
$7$	−2.39031	+	1.13420i	−0.903452	+	0.428688i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	0.508531			0.160812
$11$			3.86324i			1.16481i	0.812899	+	0.582405i	$0.197888\pi$
$11$			3.86324i			1.16481i	−0.812899	+	0.582405i	$0.802112\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.12559	−	1.79742i	−0.866882	−	0.498513i
$13$	−3.12559	−	1.79742i	−0.866882	−	0.498513i
$14$	2.63717	+	0.212907i	0.704814	+	0.0569018i
$15$	−0.440400	+	0.254265i	−0.113711	+	0.0656510i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.89376	+	6.74420i	0.944377	+	1.63571i	0.756994	+	0.653421i	$0.226667\pi$
$17$	3.89376	+	6.74420i	0.944377	+	1.63571i	0.187382	+	0.982287i	$0.440000\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$		−	0.115446i		−	0.0264851i	−0.999912	−	0.0132425i	$-0.995785\pi$
$19$		−	0.115446i		−	0.0264851i	0.999912	−	0.0132425i	$-0.00421535\pi$
$20$	−0.440400	−	0.254265i	−0.0984765	−	0.0568555i
$21$	−2.39031	+	1.13420i	−0.521609	+	0.247503i
$22$	1.93162	−	3.34566i	0.411822	−	0.713297i
$23$	−0.614785	+	1.06484i	−0.128192	+	0.222034i	−0.922976	−	0.384858i	$-0.874251\pi$
$23$	−0.614785	+	1.06484i	−0.128192	+	0.222034i	0.794784	+	0.606892i	$0.207584\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−2.37070	+	4.10617i	−0.474140	+	0.821234i
$26$	1.80813	+	3.11940i	0.354604	+	0.611765i
$27$	1.00000			0.192450
$28$	−2.17740	−	1.50297i	−0.411491	−	0.284034i
$29$	1.86905	+	3.23729i	0.347074	+	0.601150i	0.985728	−	0.168344i	$-0.0538420\pi$
$29$	1.86905	+	3.23729i	0.347074	+	0.601150i	−0.638654	+	0.769494i	$0.720509\pi$
$30$	0.508531			0.0928446
$31$	−3.83229	−	2.21258i	−0.688300	−	0.397390i	0.114675	−	0.993403i	$-0.463417\pi$
$31$	−3.83229	−	2.21258i	−0.688300	−	0.397390i	−0.802975	+	0.596013i	$0.796751\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$			3.86324i			0.672503i
$34$		−	7.78753i		−	1.33555i
$35$	0.764305	−	1.10728i	0.129191	−	0.187164i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	1.50367	+	0.868142i	0.247201	+	0.142722i	0.618482	−	0.785799i	$-0.287748\pi$
$37$	1.50367	+	0.868142i	0.247201	+	0.142722i	−0.371281	+	0.928521i	$0.621081\pi$
$38$	−0.0577229	+	0.0999790i	−0.00936389	+	0.0162187i
$39$	−3.12559	−	1.79742i	−0.500495	−	0.287817i
$40$	0.254265	+	0.440400i	0.0402029	+	0.0696334i
$41$	0.138041	−	0.0796979i	0.0215583	−	0.0124467i	−0.489182	−	0.872182i	$-0.662705\pi$
$41$	0.138041	−	0.0796979i	0.0215583	−	0.0124467i	0.510740	+	0.859735i	$0.329371\pi$
$42$	2.63717	+	0.212907i	0.406924	+	0.0328522i
$43$	−0.153620	+	0.266078i	−0.0234269	+	0.0405766i	−0.877501	−	0.479575i	$-0.840791\pi$
$43$	−0.153620	+	0.266078i	−0.0234269	+	0.0405766i	0.854074	+	0.520151i	$0.174124\pi$
$44$	−3.34566	+	1.93162i	−0.504377	+	0.291202i
$45$	−0.440400	+	0.254265i	−0.0656510	+	0.0379036i
$46$	1.06484	−	0.614785i	0.157002	−	0.0906451i
$47$	−6.61173	+	3.81729i	−0.964420	+	0.556808i	−0.897531	−	0.440952i	$-0.854641\pi$
$47$	−6.61173	+	3.81729i	−0.964420	+	0.556808i	−0.0668896	+	0.997760i	$0.521308\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	4.42717	−	5.42219i	0.632453	−	0.774599i
$50$	4.10617	−	2.37070i	0.580700	−	0.335267i
$51$	3.89376	+	6.74420i	0.545236	+	0.944377i
$52$	−0.00618631	−	3.60555i	−0.000857886	−	0.499999i
$53$	−2.08305	+	3.60794i	−0.286128	+	0.495589i	−0.972882	−	0.231301i	$-0.925702\pi$
$53$	−2.08305	+	3.60794i	−0.286128	+	0.495589i	0.686754	+	0.726890i	$0.259035\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−0.982287	−	1.70137i	−0.132452	−	0.229413i
$56$	1.13420	+	2.39031i	0.151564	+	0.319419i
$57$		−	0.115446i		−	0.0152912i
$58$		−	3.73810i		−	0.490837i
$59$	7.24338	−	4.18197i	0.943008	−	0.544446i	0.0521061	−	0.998642i	$-0.483407\pi$
$59$	7.24338	−	4.18197i	0.943008	−	0.544446i	0.890902	+	0.454196i	$0.150073\pi$
$60$	−0.440400	−	0.254265i	−0.0568555	−	0.0328255i
$61$	6.14619			0.786939			0.393470	−	0.919338i	$-0.371275\pi$
$61$	6.14619			0.786939			0.393470	+	0.919338i	$0.371275\pi$
$62$	2.21258	+	3.83229i	0.280997	+	0.486702i
$63$	−2.39031	+	1.13420i	−0.301151	+	0.142896i
$64$	−1.00000			−0.125000
$65$	1.83353	−	0.00314593i	0.227421	−	0.000390204i
$66$	1.93162	−	3.34566i	0.237766	−	0.411822i
$67$			1.54044i			0.188195i	0.995563	+	0.0940975i	$0.0299965\pi$
$67$			1.54044i			0.188195i	−0.995563	+	0.0940975i	$0.970003\pi$
$68$	−3.89376	+	6.74420i	−0.472188	+	0.817854i
$69$	−0.614785	+	1.06484i	−0.0740114	+	0.128192i
$70$	−1.21555	+	0.576777i	−0.145286	+	0.0689380i
$71$	−0.505964	−	0.292119i	−0.0600469	−	0.0346681i	0.469676	−	0.882839i	$-0.344371\pi$
$71$	−0.505964	−	0.292119i	−0.0600469	−	0.0346681i	−0.529723	+	0.848171i	$0.677704\pi$
$72$		−	1.00000i		−	0.117851i
$73$	4.78934	+	2.76512i	0.560549	+	0.323633i	0.753366	−	0.657601i	$-0.228429\pi$
$73$	4.78934	+	2.76512i	0.560549	+	0.323633i	−0.192817	+	0.981235i	$0.561762\pi$
$74$	−0.868142	−	1.50367i	−0.100919	−	0.174798i
$75$	−2.37070	+	4.10617i	−0.273745	+	0.474140i
$76$	0.0999790	−	0.0577229i	0.0114684	−	0.00662127i
$77$	−4.38169	−	9.23433i	−0.499340	−	1.05235i
$78$	1.80813	+	3.11940i	0.204730	+	0.353203i
$79$	2.16963	+	3.75790i	0.244102	+	0.422797i	0.961879	−	0.273476i	$-0.0881735\pi$
$79$	2.16963	+	3.75790i	0.244102	+	0.422797i	−0.717777	+	0.696273i	$0.754840\pi$
$80$		−	0.508531i		−	0.0568555i
$81$	1.00000			0.111111
$82$	−0.159396			−0.0176023
$83$			3.96800i			0.435545i	0.976000	+	0.217772i	$0.0698791\pi$
$83$			3.96800i			0.435545i	−0.976000	+	0.217772i	$0.930121\pi$
$84$	−2.17740	−	1.50297i	−0.237574	−	0.163987i
$85$	−3.42963	−	1.98010i	−0.371996	−	0.214772i
$86$	0.266078	−	0.153620i	0.0286920	−	0.0165653i
$87$	1.86905	+	3.23729i	0.200383	+	0.347074i
$88$	3.86324			0.411822
$89$	3.92640	+	2.26691i	0.416198	+	0.240292i	0.693449	−	0.720505i	$-0.256090\pi$
$89$	3.92640	+	2.26691i	0.416198	+	0.240292i	−0.277251	+	0.960797i	$0.589423\pi$
$90$	0.508531			0.0536038
$91$	9.50976	+	0.751331i	0.996894	+	0.0787609i
$92$	−1.22957			−0.128192
$93$	−3.83229	−	2.21258i	−0.397390	−	0.229433i
$94$	7.63457			0.787446
$95$	0.0293539	+	0.0508424i	0.00301164	+	0.00521632i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−13.4014	−	7.73733i	−1.36071	−	0.785606i	−0.370992	−	0.928636i	$-0.620982\pi$
$97$	−13.4014	−	7.73733i	−1.36071	−	0.785606i	−0.989718	+	0.143030i	$0.954316\pi$
$98$	−6.54514	+	2.48217i	−0.661159	+	0.250737i
$99$			3.86324i			0.388270i
$100$	−4.74140			−0.474140
$101$	18.0901			1.80003			0.900014	−	0.435860i	$-0.143556\pi$
$101$	18.0901			1.80003			0.900014	+	0.435860i	$0.143556\pi$
$102$		−	7.78753i		−	0.771080i
$103$	−2.96384	−	5.13353i	−0.292036	−	0.505822i	0.682255	−	0.731114i	$-0.260999\pi$
$103$	−2.96384	−	5.13353i	−0.292036	−	0.505822i	−0.974291	+	0.225293i	$0.927666\pi$
$104$	−1.79742	+	3.12559i	−0.176251	+	0.306489i
$105$	0.764305	−	1.10728i	0.0745886	−	0.108059i
$106$	3.60794	−	2.08305i	0.350434	−	0.202323i
$107$	−4.00023	+	6.92860i	−0.386717	+	0.669813i	−0.992006	−	0.126193i	$-0.959724\pi$
$107$	−4.00023	+	6.92860i	−0.386717	+	0.669813i	0.605289	+	0.796006i	$0.293058\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−13.6094	−	7.85741i	−1.30355	−	0.752604i	−0.322537	−	0.946557i	$-0.604536\pi$
$109$	−13.6094	−	7.85741i	−1.30355	−	0.752604i	−0.981011	+	0.193953i	$0.937869\pi$
$110$			1.96457i			0.187315i
$111$	1.50367	+	0.868142i	0.142722	+	0.0824004i
$112$	0.212907	−	2.63717i	0.0201178	−	0.249189i
$113$	8.26440	−	14.3144i	0.777449	−	1.34658i	−0.155958	−	0.987764i	$-0.549846\pi$
$113$	8.26440	−	14.3144i	0.777449	−	1.34658i	0.933407	−	0.358818i	$-0.116820\pi$
$114$	−0.0577229	+	0.0999790i	−0.00540624	+	0.00936389i
$115$		−	0.625274i		−	0.0583071i
$116$	−1.86905	+	3.23729i	−0.173537	+	0.300575i
$117$	−3.12559	−	1.79742i	−0.288961	−	0.166171i
$118$	−8.36394			−0.769963
$119$	−16.9566	−	11.7044i	−1.55441	−	1.07294i
$120$	0.254265	+	0.440400i	0.0232111	+	0.0402029i
$121$	−3.92460			−0.356781
$122$	−5.32276	−	3.07310i	−0.481900	−	0.278225i
$123$	0.138041	−	0.0796979i	0.0124467	−	0.00718611i
$124$		−	4.42515i		−	0.397390i
$125$		−	4.95380i		−	0.443081i
$126$	2.63717	+	0.212907i	0.234938	+	0.0189673i
$127$	−9.27963	−	16.0728i	−0.823434	−	1.42623i	−0.903110	−	0.429409i	$-0.858722\pi$
$127$	−9.27963	−	16.0728i	−0.823434	−	1.42623i	0.0796759	−	0.996821i	$-0.474611\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.153620	+	0.266078i	−0.0135255	+	0.0234269i
$130$	−1.58946	−	0.914041i	−0.139405	−	0.0801667i
$131$	−6.73686	−	11.6686i	−0.588602	−	1.01949i	−0.994416	−	0.105533i	$-0.966345\pi$
$131$	−6.73686	−	11.6686i	−0.588602	−	1.01949i	0.405814	−	0.913956i	$-0.366988\pi$
$132$	−3.34566	+	1.93162i	−0.291202	+	0.168126i
$133$	0.130939	+	0.275951i	0.0113538	+	0.0239280i
$134$	0.770221	−	1.33406i	0.0665370	−	0.115245i
$135$	−0.440400	+	0.254265i	−0.0379036	+	0.0218837i
$136$	6.74420	−	3.89376i	0.578310	−	0.333888i
$137$	0.686424	−	0.396307i	0.0586452	−	0.0338588i	−0.470391	−	0.882458i	$-0.655887\pi$
$137$	0.686424	−	0.396307i	0.0586452	−	0.0338588i	0.529036	+	0.848599i	$0.322554\pi$
$138$	1.06484	−	0.614785i	0.0906451	−	0.0523340i
$139$	3.02179	−	5.23390i	0.256305	−	0.443933i	−0.708944	−	0.705265i	$-0.750828\pi$
$139$	3.02179	−	5.23390i	0.256305	−	0.443933i	0.965249	+	0.261331i	$0.0841615\pi$
$140$	1.34108	+	0.108270i	0.113342	+	0.00915046i
$141$	−6.61173	+	3.81729i	−0.556808	+	0.321473i
$142$	0.292119	+	0.505964i	0.0245141	+	0.0424596i
$143$	6.94384	−	12.0749i	0.580673	−	1.00975i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.64626	−	0.950469i	−0.136715	−	0.0789322i
$146$	−2.76512	−	4.78934i	−0.228843	−	0.396368i
$147$	4.42717	−	5.42219i	0.365147	−	0.447215i
$148$			1.73628i			0.142722i
$149$		−	8.64689i		−	0.708381i	−0.935173	−	0.354190i	$-0.884756\pi$
$149$		−	8.64689i		−	0.708381i	0.935173	−	0.354190i	$-0.115244\pi$
$150$	4.10617	−	2.37070i	0.335267	−	0.193567i
$151$	12.5995	+	7.27434i	1.02534	+	0.591978i	0.915645	−	0.401988i	$-0.131681\pi$
$151$	12.5995	+	7.27434i	1.02534	+	0.591978i	0.109690	+	0.993966i	$0.465014\pi$
$152$	−0.115446			−0.00936389
$153$	3.89376	+	6.74420i	0.314792	+	0.545236i
$154$	−0.822510	+	10.1880i	−0.0662797	+	0.820974i
$155$	2.25032			0.180750
$156$	−0.00618631	−	3.60555i	−0.000495301	−	0.288675i
$157$	3.80558	−	6.59146i	0.303718	−	0.526056i	−0.673257	−	0.739409i	$-0.735105\pi$
$157$	3.80558	−	6.59146i	0.303718	−	0.526056i	0.976975	+	0.213353i	$0.0684385\pi$
$158$		−	4.33925i		−	0.345213i
$159$	−2.08305	+	3.60794i	−0.165196	+	0.286128i
$160$	−0.254265	+	0.440400i	−0.0201014	+	0.0348167i
$161$	0.261784	−	3.24259i	0.0206315	−	0.255552i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$			10.5153i			0.823620i	0.911270	+	0.411810i	$0.135103\pi$
$163$			10.5153i			0.823620i	−0.911270	+	0.411810i	$0.864897\pi$
$164$	0.138041	+	0.0796979i	0.0107792	+	0.00622336i
$165$	−0.982287	−	1.70137i	−0.0764709	−	0.132452i
$166$	1.98400	−	3.43639i	0.153988	−	0.266716i
$167$	−14.4942	+	8.36826i	−1.12160	+	0.647555i	−0.941809	−	0.336150i	$-0.890875\pi$
$167$	−14.4942	+	8.36826i	−1.12160	+	0.647555i	−0.179790	+	0.983705i	$0.557542\pi$
$168$	1.13420	+	2.39031i	0.0875056	+	0.184416i
$169$	6.53860	+	11.2360i	0.502969	+	0.864305i
$170$	1.98010	+	3.42963i	0.151867	+	0.263041i
$171$		−	0.115446i		−	0.00882836i
$172$	−0.307241			−0.0234269
$173$	15.1229			1.14977			0.574887	−	0.818233i	$-0.305046\pi$
$173$	15.1229			1.14977			0.574887	+	0.818233i	$0.305046\pi$
$174$		−	3.73810i		−	0.283385i
$175$	1.00948	−	12.5039i	0.0763092	−	0.945204i
$176$	−3.34566	−	1.93162i	−0.252189	−	0.145601i
$177$	7.24338	−	4.18197i	0.544446	−	0.314336i
$178$	−2.26691	−	3.92640i	−0.169912	−	0.294296i
$179$	−24.2973			−1.81607			−0.908034	−	0.418896i	$-0.862417\pi$
$179$	−24.2973			−1.81607			−0.908034	+	0.418896i	$0.862417\pi$
$180$	−0.440400	−	0.254265i	−0.0328255	−	0.0189518i
$181$	4.37128			0.324915			0.162457	−	0.986716i	$-0.448058\pi$
$181$	4.37128			0.324915			0.162457	+	0.986716i	$0.448058\pi$
$182$	−7.86003	−	5.40555i	−0.582624	−	0.400686i
$183$	6.14619			0.454340
$184$	1.06484	+	0.614785i	0.0785010	+	0.0453226i
$185$	−0.882953			−0.0649160
$186$	2.21258	+	3.83229i	0.162234	+	0.280997i
$187$	−26.0544	+	15.0425i	−1.90529	+	1.10002i
$188$	−6.61173	−	3.81729i	−0.482210	−	0.278404i
$189$	−2.39031	+	1.13420i	−0.173870	+	0.0825011i
$190$		−	0.0587077i		−	0.00425911i
$191$	12.6832			0.917724			0.458862	−	0.888508i	$-0.348257\pi$
$191$	12.6832			0.917724			0.458862	+	0.888508i	$0.348257\pi$
$192$	−1.00000			−0.0721688
$193$			18.0250i			1.29747i	0.761016	+	0.648733i	$0.224701\pi$
$193$			18.0250i			1.29747i	−0.761016	+	0.648733i	$0.775299\pi$
$194$	7.73733	+	13.4014i	0.555508	+	0.962167i
$195$	1.83353	−	0.00314593i	0.131302	−	0.000225284i
$196$	6.90934	+	1.12294i	0.493524	+	0.0802103i
$197$	−3.30735	+	1.90950i	−0.235639	+	0.136046i	−0.613171	−	0.789950i	$-0.710106\pi$
$197$	−3.30735	+	1.90950i	−0.235639	+	0.136046i	0.377532	+	0.925997i	$0.376773\pi$
$198$	1.93162	−	3.34566i	0.137274	−	0.237766i
$199$	−8.40616	−	14.5599i	−0.595897	−	1.03212i	−0.993420	−	0.114531i	$-0.963463\pi$
$199$	−8.40616	−	14.5599i	−0.595897	−	1.03212i	0.397523	−	0.917592i	$-0.369870\pi$
$200$	4.10617	+	2.37070i	0.290350	+	0.167634i
$201$			1.54044i			0.108654i
$202$	−15.6665	−	9.04503i	−1.10229	−	0.636406i
$203$	−8.13935	−	5.61825i	−0.571271	−	0.394324i
$204$	−3.89376	+	6.74420i	−0.272618	+	0.472188i
$205$	−0.0405288	+	0.0701979i	−0.00283065	+	0.00490284i
$206$			5.92769i			0.413002i
$207$	−0.614785	+	1.06484i	−0.0427305	+	0.0740114i
$208$	3.11940	−	1.80813i	0.216292	−	0.125371i
$209$	0.445994			0.0308501
$210$	−1.21555	+	0.576777i	−0.0838806	+	0.0398014i
$211$	9.39942	+	16.2803i	0.647083	+	1.12078i	0.983816	+	0.179180i	$0.0573445\pi$
$211$	9.39942	+	16.2803i	0.647083	+	1.12078i	−0.336733	+	0.941600i	$0.609322\pi$
$212$	−4.16609			−0.286128
$213$	−0.505964	−	0.292119i	−0.0346681	−	0.0200156i
$214$	6.92860	−	4.00023i	0.473629	−	0.273450i
$215$		−	0.156241i		−	0.0106556i
$216$		−	1.00000i		−	0.0680414i
$217$	11.6699	+	0.942145i	0.792203	+	0.0639570i
$218$	7.85741	+	13.6094i	0.532171	+	0.921748i
$219$	4.78934	+	2.76512i	0.323633	+	0.186850i
$220$	0.982287	−	1.70137i	0.0662258	−	0.114706i
$221$	−0.0481761	−	28.0783i	−0.00324067	−	1.88875i
$222$	−0.868142	−	1.50367i	−0.0582659	−	0.100919i
$223$	20.5537	−	11.8667i	1.37638	−	0.794653i	0.384658	−	0.923059i	$-0.374319\pi$
$223$	20.5537	−	11.8667i	1.37638	−	0.794653i	0.991722	+	0.128406i	$0.0409862\pi$
$224$	−1.50297	+	2.17740i	−0.100421	+	0.145484i
$225$	−2.37070	+	4.10617i	−0.158047	+	0.273745i
$226$	−14.3144	+	8.26440i	−0.952177	+	0.549740i
$227$	4.31918	−	2.49368i	0.286674	−	0.165511i	−0.349767	−	0.936837i	$-0.613739\pi$
$227$	4.31918	−	2.49368i	0.286674	−	0.165511i	0.636441	+	0.771326i	$0.280406\pi$
$228$	0.0999790	−	0.0577229i	0.00662127	−	0.00382279i
$229$	−4.42876	+	2.55695i	−0.292661	+	0.168968i	−0.639141	−	0.769089i	$-0.720710\pi$
$229$	−4.42876	+	2.55695i	−0.292661	+	0.168968i	0.346480	+	0.938057i	$0.387377\pi$
$230$	−0.312637	+	0.541503i	−0.0206147	+	0.0357057i
$231$	−4.38169	−	9.23433i	−0.288294	−	0.607575i
$232$	3.23729	−	1.86905i	0.212539	−	0.122709i
$233$	14.4275	+	24.9892i	0.945178	+	1.63710i	0.755394	+	0.655271i	$0.227445\pi$
$233$	14.4275	+	24.9892i	0.945178	+	1.63710i	0.189784	+	0.981826i	$0.439221\pi$
$234$	1.80813	+	3.11940i	0.118201	+	0.203922i
$235$	1.94121	−	3.36227i	0.126630	−	0.219330i
$236$	7.24338	+	4.18197i	0.471504	+	0.272223i
$237$	2.16963	+	3.75790i	0.140932	+	0.244102i
$238$	8.83264	+	18.6146i	0.572535	+	1.20661i
$239$			16.0044i			1.03524i	0.855612	+	0.517618i	$0.173181\pi$
$239$			16.0044i			1.03524i	−0.855612	+	0.517618i	$0.826819\pi$
$240$		−	0.508531i		−	0.0328255i
$241$	22.2788	−	12.8627i	1.43511	−	0.828558i	0.437601	−	0.899169i	$-0.355828\pi$
$241$	22.2788	−	12.8627i	1.43511	−	0.828558i	0.997504	+	0.0706107i	$0.0224948\pi$
$242$	3.39880	+	1.96230i	0.218483	+	0.126141i
$243$	1.00000			0.0641500
$244$	3.07310	+	5.32276i	0.196735	+	0.340755i
$245$	−0.571051	+	3.51361i	−0.0364831	+	0.224476i
$246$	−0.159396			−0.0101627
$247$	−0.207504	+	0.360836i	−0.0132032	+	0.0229594i
$248$	−2.21258	+	3.83229i	−0.140499	+	0.243351i
$249$			3.96800i			0.251462i
$250$	−2.47690	+	4.29012i	−0.156653	+	0.271331i
$251$	3.62300	−	6.27522i	0.228682	−	0.396088i	−0.728736	−	0.684795i	$-0.759892\pi$
$251$	3.62300	−	6.27522i	0.228682	−	0.396088i	0.957418	+	0.288706i	$0.0932252\pi$
$252$	−2.17740	−	1.50297i	−0.137164	−	0.0946781i
$253$	−4.11372	−	2.37506i	−0.258628	−	0.149319i
$254$			18.5593i			1.16451i
$255$	−3.42963	−	1.98010i	−0.214772	−	0.123999i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.52008	−	13.0252i	0.469090	−	0.812487i	−0.530286	−	0.847819i	$-0.677915\pi$
$257$	7.52008	−	13.0252i	0.469090	−	0.812487i	0.999376	+	0.0353315i	$0.0112487\pi$
$258$	0.266078	−	0.153620i	0.0165653	−	0.00956398i
$259$	−4.57888	−	0.369667i	−0.284517	−	0.0229700i
$260$	0.919490	+	1.58631i	0.0570243	+	0.0983788i
$261$	1.86905	+	3.23729i	0.115691	+	0.200383i
$262$			13.4737i			0.832409i
$263$	−22.3615			−1.37887			−0.689436	−	0.724347i	$-0.742142\pi$
$263$	−22.3615			−1.37887			−0.689436	+	0.724347i	$0.742142\pi$
$264$	3.86324			0.237766
$265$		−	2.11859i		−	0.130144i
$266$	0.0245792	−	0.304450i	0.00150705	−	0.0186670i
$267$	3.92640	+	2.26691i	0.240292	+	0.138733i
$268$	−1.33406	+	0.770221i	−0.0814908	+	0.0470487i
$269$	9.24986	+	16.0212i	0.563974	+	0.976831i	0.997144	+	0.0755193i	$0.0240615\pi$
$269$	9.24986	+	16.0212i	0.563974	+	0.976831i	−0.433171	+	0.901312i	$0.642605\pi$
$270$	0.508531			0.0309482
$271$	23.3112	+	13.4587i	1.41605	+	0.817559i	0.995949	−	0.0899170i	$-0.0286602\pi$
$271$	23.3112	+	13.4587i	1.41605	+	0.817559i	0.420104	+	0.907476i	$0.361993\pi$
$272$	−7.78753			−0.472188
$273$	9.50976	+	0.751331i	0.575557	+	0.0454726i
$274$	−0.792615			−0.0478836
$275$	−15.8631	−	9.15857i	−0.956581	−	0.552282i
$276$	−1.22957			−0.0740114
$277$	11.5439	+	19.9946i	0.693605	+	1.20136i	0.970649	+	0.240502i	$0.0773122\pi$
$277$	11.5439	+	19.9946i	0.693605	+	1.20136i	−0.277043	+	0.960857i	$0.589354\pi$
$278$	−5.23390	+	3.02179i	−0.313908	+	0.181235i
$279$	−3.83229	−	2.21258i	−0.229433	−	0.132463i
$280$	−1.10728	−	0.764305i	−0.0661724	−	0.0456760i
$281$		−	12.8790i		−	0.768294i	−0.923272	−	0.384147i	$-0.874496\pi$
$281$		−	12.8790i		−	0.768294i	0.923272	−	0.384147i	$-0.125504\pi$
$282$	7.63457			0.454632
$283$	−22.8100			−1.35591			−0.677957	−	0.735102i	$-0.737134\pi$
$283$	−22.8100			−1.35591			−0.677957	+	0.735102i	$0.737134\pi$
$284$		−	0.584237i		−	0.0346681i
$285$	0.0293539	+	0.0508424i	0.00173877	+	0.00301164i
$286$	−12.0510	+	6.98524i	−0.712590	+	0.413046i
$287$	−0.239567	+	0.347069i	−0.0141412	+	0.0204868i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−21.8228	+	37.7982i	−1.28369	+	2.22342i
$290$	0.950469	+	1.64626i	0.0558135	+	0.0966718i
$291$	−13.4014	−	7.73733i	−0.785606	−	0.453570i
$292$			5.53025i			0.323633i
$293$	25.3580	+	14.6405i	1.48143	+	0.855305i	0.999778	−	0.0210567i	$-0.00670305\pi$
$293$	25.3580	+	14.6405i	1.48143	+	0.855305i	0.481654	+	0.876362i	$0.340036\pi$
$294$	−6.54514	+	2.48217i	−0.381720	+	0.144763i
$295$	−2.12666	+	3.68348i	−0.123819	+	0.214461i
$296$	0.868142	−	1.50367i	0.0504597	−	0.0873988i
$297$			3.86324i			0.224168i
$298$	−4.32345	+	7.48843i	−0.250450	+	0.433793i
$299$	3.83552	−	2.22322i	0.221814	−	0.128572i
$300$	−4.74140			−0.273745
$301$	0.0654137	−	0.810246i	0.00377038	−	0.0467018i
$302$	−7.27434	−	12.5995i	−0.418591	−	0.725021i
$303$	18.0901			1.03925
$304$	0.0999790	+	0.0577229i	0.00573419	+	0.00331064i
$305$	−2.70679	+	1.56276i	−0.154990	+	0.0894836i
$306$		−	7.78753i		−	0.445183i
$307$			13.4520i			0.767745i	0.923386	+	0.383873i	$0.125410\pi$
$307$			13.4520i			0.767745i	−0.923386	+	0.383873i	$0.874590\pi$
$308$	5.80632	−	8.41182i	0.330846	−	0.479308i
$309$	−2.96384	−	5.13353i	−0.168607	−	0.292036i
$310$	−1.94884	−	1.12516i	−0.110687	−	0.0639049i
$311$	−10.6425	+	18.4334i	−0.603482	+	1.04526i	0.388807	+	0.921319i	$0.372887\pi$
$311$	−10.6425	+	18.4334i	−0.603482	+	1.04526i	−0.992289	+	0.123942i	$0.960446\pi$
$312$	−1.79742	+	3.12559i	−0.101759	+	0.176952i
$313$	−5.24307	−	9.08127i	−0.296356	−	0.513304i	0.678943	−	0.734191i	$-0.262438\pi$
$313$	−5.24307	−	9.08127i	−0.296356	−	0.513304i	−0.975299	+	0.220887i	$0.929105\pi$
$314$	−6.59146	+	3.80558i	−0.371978	+	0.214761i
$315$	0.764305	−	1.10728i	0.0430637	−	0.0623880i
$316$	−2.16963	+	3.75790i	−0.122051	+	0.211399i
$317$	7.22692	−	4.17247i	0.405904	−	0.234349i	−0.283124	−	0.959083i	$-0.591371\pi$
$317$	7.22692	−	4.17247i	0.405904	−	0.234349i	0.689029	+	0.724734i	$0.258037\pi$
$318$	3.60794	−	2.08305i	0.202323	−	0.116811i
$319$	−12.5064	+	7.22058i	−0.700225	+	0.404275i
$320$	0.440400	−	0.254265i	0.0246191	−	0.0142139i
$321$	−4.00023	+	6.92860i	−0.223271	+	0.386717i
$322$	−1.84800	+	2.67727i	−0.102985	+	0.149198i
$323$	0.778589	−	0.449519i	0.0433219	−	0.0250119i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	14.7903	−	8.57306i	0.820419	−	0.475548i
$326$	5.25764	−	9.10650i	0.291194	−	0.504362i
$327$	−13.6094	−	7.85741i	−0.752604	−	0.434516i
$328$	−0.0796979	−	0.138041i	−0.00440058	−	0.00762202i
$329$	11.4745	−	16.6235i	0.632611	−	0.916485i
$330$			1.96457i			0.108146i
$331$			34.3963i			1.89059i	0.326217	+	0.945295i	$0.394226\pi$
$331$			34.3963i			1.89059i	−0.326217	+	0.945295i	$0.605774\pi$
$332$	−3.43639	+	1.98400i	−0.188597	+	0.108886i
$333$	1.50367	+	0.868142i	0.0824004	+	0.0475739i
$334$	16.7365			0.915782
$335$	−0.391681	−	0.678411i	−0.0213998	−	0.0370656i
$336$	0.212907	−	2.63717i	0.0116150	−	0.143869i
$337$	−11.3697			−0.619350			−0.309675	−	0.950843i	$-0.600220\pi$
$337$	−11.3697			−0.619350			−0.309675	+	0.950843i	$0.600220\pi$
$338$	−0.0446100	−	12.9999i	−0.00242647	−	0.707103i
$339$	8.26440	−	14.3144i	0.448861	−	0.777449i
$340$		−	3.96020i		−	0.214772i
$341$	8.54770	−	14.8051i	0.462884	−	0.801739i
$342$	−0.0577229	+	0.0999790i	−0.00312130	+	0.00540624i
$343$	−4.43244	+	17.9820i	−0.239329	+	0.970938i
$344$	0.266078	+	0.153620i	0.0143460	+	0.00828265i
$345$		−	0.625274i		−	0.0336636i
$346$	−13.0968	−	7.56146i	−0.704090	−	0.406506i
$347$	14.9697	+	25.9282i	0.803613	+	1.39190i	0.917223	+	0.398373i	$0.130425\pi$
$347$	14.9697	+	25.9282i	0.803613	+	1.39190i	−0.113610	+	0.993525i	$0.536242\pi$
$348$	−1.86905	+	3.23729i	−0.100192	+	0.173537i
$349$	26.1367	−	15.0900i	1.39906	−	0.807750i	0.404770	−	0.914419i	$-0.367352\pi$
$349$	26.1367	−	15.0900i	1.39906	−	0.807750i	0.994295	+	0.106668i	$0.0340183\pi$
$350$	−7.12617	+	10.3239i	−0.380910	+	0.551837i
$351$	−3.12559	−	1.79742i	−0.166832	−	0.0959389i
$352$	1.93162	+	3.34566i	0.102956	+	0.178324i
$353$		−	0.437459i		−	0.0232836i	−0.999932	−	0.0116418i	$-0.996294\pi$
$353$		−	0.437459i		−	0.0232836i	0.999932	−	0.0116418i	$-0.00370578\pi$
$354$	−8.36394			−0.444538
$355$	0.297103			0.0157686
$356$			4.53382i			0.240292i
$357$	−16.9566	−	11.7044i	−0.897438	−	0.619463i
$358$	21.0421	+	12.1487i	1.11211	+	0.642077i
$359$	−0.990143	+	0.571659i	−0.0522577	+	0.0301710i	−0.525901	−	0.850546i	$-0.676272\pi$
$359$	−0.990143	+	0.571659i	−0.0522577	+	0.0301710i	0.473644	+	0.880717i	$0.342939\pi$
$360$	0.254265	+	0.440400i	0.0134010	+	0.0232111i
$361$	18.9867			0.999299
$362$	−3.78564	−	2.18564i	−0.198969	−	0.114875i
$363$	−3.92460			−0.205988
$364$	4.10421	+	8.61136i	0.215119	+	0.451358i
$365$	−2.81230			−0.147203
$366$	−5.32276	−	3.07310i	−0.278225	−	0.160633i
$367$	−31.9146			−1.66593			−0.832965	−	0.553325i	$-0.813359\pi$
$367$	−31.9146			−1.66593			−0.832965	+	0.553325i	$0.813359\pi$
$368$	−0.614785	−	1.06484i	−0.0320479	−	0.0555086i
$369$	0.138041	−	0.0796979i	0.00718611	−	0.00414890i
$370$	0.764660	+	0.441477i	0.0397528	+	0.0229513i
$371$	0.886990	−	10.9867i	0.0460502	−	0.570401i
$372$		−	4.42515i		−	0.229433i
$373$	−6.41597			−0.332206			−0.166103	−	0.986108i	$-0.553118\pi$
$373$	−6.41597			−0.332206			−0.166103	+	0.986108i	$0.553118\pi$
$374$	30.0851			1.55566
$375$		−	4.95380i		−	0.255813i
$376$	3.81729	+	6.61173i	0.196861	+	0.340974i
$377$	−0.0231250	−	13.4779i	−0.00119100	−	0.694147i
$378$	2.63717	+	0.212907i	0.135641	+	0.0109507i
$379$	20.5865	−	11.8856i	1.05746	−	0.610524i	0.132731	−	0.991152i	$-0.457626\pi$
$379$	20.5865	−	11.8856i	1.05746	−	0.610524i	0.924728	+	0.380628i	$0.124292\pi$
$380$	−0.0293539	+	0.0508424i	−0.00150582	+	0.00260816i
$381$	−9.27963	−	16.0728i	−0.475410	−	0.823434i
$382$	−10.9840	−	6.34160i	−0.561989	−	0.324464i
$383$		−	29.9936i		−	1.53260i	−0.642481	−	0.766302i	$-0.722095\pi$
$383$		−	29.9936i		−	1.53260i	0.642481	−	0.766302i	$-0.277905\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	4.27767	+	2.95269i	0.218010	+	0.150483i
$386$	9.01248	−	15.6101i	0.458723	−	0.794532i
$387$	−0.153620	+	0.266078i	−0.00780896	+	0.0135255i
$388$		−	15.4747i		−	0.785606i
$389$	1.03997	−	1.80127i	0.0527283	−	0.0913282i	−0.838457	−	0.544969i	$-0.816542\pi$
$389$	1.03997	−	1.80127i	0.0527283	−	0.0913282i	0.891185	+	0.453640i	$0.149875\pi$
$390$	−1.58946	−	0.914041i	−0.0804853	−	0.0462843i
$391$	−9.57531			−0.484244
$392$	−5.42219	−	4.42717i	−0.273862	−	0.223606i
$393$	−6.73686	−	11.6686i	−0.339830	−	0.588602i
$394$	3.81900			0.192399
$395$	−1.91101	−	1.10332i	−0.0961533	−	0.0555141i
$396$	−3.34566	+	1.93162i	−0.168126	+	0.0970675i
$397$		−	33.8811i		−	1.70044i	−0.526425	−	0.850222i	$-0.676468\pi$
$397$		−	33.8811i		−	1.70044i	0.526425	−	0.850222i	$-0.323532\pi$
$398$			16.8123i			0.842725i
$399$	0.130939	+	0.275951i	0.00655515	+	0.0138148i
$400$	−2.37070	−	4.10617i	−0.118535	−	0.205308i
$401$	−0.541568	−	0.312674i	−0.0270446	−	0.0156142i	0.486417	−	0.873727i	$-0.338304\pi$
$401$	−0.541568	−	0.312674i	−0.0270446	−	0.0156142i	−0.513461	+	0.858113i	$0.671637\pi$
$402$	0.770221	−	1.33406i	0.0384151	−	0.0665370i
$403$	8.00125	+	13.8038i	0.398571	+	0.687617i
$404$	9.04503	+	15.6665i	0.450007	+	0.779435i
$405$	−0.440400	+	0.254265i	−0.0218837	+	0.0126345i
$406$	4.23976	+	8.93522i	0.210416	+	0.443448i
$407$	−3.35384	+	5.80901i	−0.166243	+	0.287942i
$408$	6.74420	−	3.89376i	0.333888	−	0.192770i
$409$	0.472414	−	0.272748i	0.0233594	−	0.0134865i	−0.488275	−	0.872690i	$-0.662374\pi$
$409$	0.472414	−	0.272748i	0.0233594	−	0.0134865i	0.511634	+	0.859203i	$0.329040\pi$
$410$	0.0701979	−	0.0405288i	0.00346683	−	0.00200157i
$411$	0.686424	−	0.396307i	0.0338588	−	0.0195484i
$412$	2.96384	−	5.13353i	0.146018	−	0.252911i
$413$	−12.5707	+	18.2117i	−0.618565	+	0.896138i
$414$	1.06484	−	0.614785i	0.0523340	−	0.0302150i
$415$	−1.00893	−	1.74751i	−0.0495262	−	0.0857819i
$416$	−3.60555	+	0.00618631i	−0.176776	+	0.000303309i
$417$	3.02179	−	5.23390i	0.147978	−	0.256305i
$418$	−0.386242	−	0.222997i	−0.0188917	−	0.0109071i
$419$	−8.81282	−	15.2642i	−0.430534	−	0.745707i	0.566385	−	0.824141i	$-0.308342\pi$
$419$	−8.81282	−	15.2642i	−0.430534	−	0.745707i	−0.996919	+	0.0784334i	$0.975008\pi$
$420$	1.34108	+	0.108270i	0.0654381	+	0.00528302i
$421$			31.1725i			1.51925i	0.650360	+	0.759627i	$0.274618\pi$
$421$			31.1725i			1.51925i	−0.650360	+	0.759627i	$0.725382\pi$
$422$		−	18.7988i		−	0.915113i
$423$	−6.61173	+	3.81729i	−0.321473	+	0.185603i
$424$	3.60794	+	2.08305i	0.175217	+	0.101162i
$425$	−36.9238			−1.79107
$426$	0.292119	+	0.505964i	0.0141532	+	0.0245141i
$427$	−14.6913	+	6.97103i	−0.710962	+	0.337352i
$428$	−8.00046			−0.386717
$429$	6.94384	−	12.0749i	0.335252	−	0.582981i
$430$	−0.0781206	+	0.135309i	−0.00376731	+	0.00652518i
$431$			3.01273i			0.145118i	0.997364	+	0.0725589i	$0.0231165\pi$
$431$			3.01273i			0.145118i	−0.997364	+	0.0725589i	$0.976883\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	9.91519	−	17.1736i	0.476494	−	0.825312i	−0.523143	−	0.852245i	$-0.675241\pi$
$433$	9.91519	−	17.1736i	0.476494	−	0.825312i	0.999637	+	0.0269331i	$0.00857412\pi$
$434$	−9.63534	−	6.65086i	−0.462511	−	0.319252i
$435$	−1.64626	−	0.950469i	−0.0789322	−	0.0455715i
$436$		−	15.7148i		−	0.752604i
$437$	0.122931	+	0.0709743i	0.00588060	+	0.00339516i
$438$	−2.76512	−	4.78934i	−0.132123	−	0.228843i
$439$	4.02441	−	6.97048i	0.192075	−	0.332683i	−0.753863	−	0.657032i	$-0.771812\pi$
$439$	4.02441	−	6.97048i	0.192075	−	0.332683i	0.945938	+	0.324349i	$0.105145\pi$
$440$	−1.70137	+	0.982287i	−0.0811097	+	0.0468287i
$441$	4.42717	−	5.42219i	0.210818	−	0.258200i
$442$	−13.9974	+	24.3406i	−0.665790	+	1.15776i
$443$	−8.69495	−	15.0601i	−0.413109	−	0.715527i	0.582118	−	0.813104i	$-0.302224\pi$
$443$	−8.69495	−	15.0601i	−0.413109	−	0.715527i	−0.995228	+	0.0975774i	$0.968891\pi$
$444$			1.73628i			0.0824004i
$445$	−2.30559			−0.109295
$446$	−23.7334			−1.12381
$447$		−	8.64689i		−	0.408984i
$448$	2.39031	−	1.13420i	0.112932	−	0.0535860i
$449$	13.2655	+	7.65886i	0.626039	+	0.361444i	0.779217	−	0.626755i	$-0.215617\pi$
$449$	13.2655	+	7.65886i	0.626039	+	0.361444i	−0.153177	+	0.988199i	$0.548951\pi$
$450$	4.10617	−	2.37070i	0.193567	−	0.111756i
$451$	0.307892	+	0.533284i	0.0144981	+	0.0251114i
$452$	16.5288			0.777449
$453$	12.5995	+	7.27434i	0.591978	+	0.341778i
$454$	−4.98735			−0.234068
$455$	−4.37914	+	2.08712i	−0.205297	+	0.0978455i
$456$	−0.115446			−0.00540624
$457$	−10.8222	−	6.24822i	−0.506243	−	0.292279i	0.225045	−	0.974348i	$-0.427747\pi$
$457$	−10.8222	−	6.24822i	−0.506243	−	0.292279i	−0.731288	+	0.682069i	$0.761080\pi$
$458$	5.11389			0.238956
$459$	3.89376	+	6.74420i	0.181745	+	0.314792i
$460$	0.541503	−	0.312637i	0.0252477	−	0.0145768i
$461$	4.88568	+	2.82075i	0.227549	+	0.131375i	0.609441	−	0.792832i	$-0.291394\pi$
$461$	4.88568	+	2.82075i	0.227549	+	0.131375i	−0.381892	+	0.924207i	$0.624727\pi$
$462$	−0.822510	+	10.1880i	−0.0382666	+	0.473989i
$463$		−	9.74426i		−	0.452854i	−0.974028	−	0.226427i	$-0.927296\pi$
$463$		−	9.74426i		−	0.452854i	0.974028	−	0.226427i	$-0.0727045\pi$
$464$	−3.73810			−0.173537
$465$	2.25032			0.104356
$466$		−	28.8550i		−	1.33668i
$467$	13.6713	+	23.6794i	0.632633	+	1.09575i	0.987011	+	0.160650i	$0.0513590\pi$
$467$	13.6713	+	23.6794i	0.632633	+	1.09575i	−0.354379	+	0.935102i	$0.615308\pi$
$468$	−0.00618631	−	3.60555i	−0.000285962	−	0.166666i
$469$	−1.74717	−	3.68214i	−0.0806770	−	0.170025i
$470$	−3.36227	+	1.94121i	−0.155090	+	0.0895412i
$471$	3.80558	−	6.59146i	0.175352	−	0.303718i
$472$	−4.18197	−	7.24338i	−0.192491	−	0.333404i
$473$	−1.02792	−	0.593472i	−0.0472640	−	0.0272879i
$474$		−	4.33925i		−	0.199309i
$475$	0.474040	+	0.273687i	0.0217504	+	0.0125576i
$476$	1.65802	−	20.5370i	0.0759952	−	0.941314i
$477$	−2.08305	+	3.60794i	−0.0953761	+	0.165196i
$478$	8.00218	−	13.8602i	0.366011	−	0.633950i
$479$		−	16.4453i		−	0.751407i	−0.926740	−	0.375703i	$-0.877401\pi$
$479$		−	16.4453i		−	0.751407i	0.926740	−	0.375703i	$-0.122599\pi$
$480$	−0.254265	+	0.440400i	−0.0116056	+	0.0201014i
$481$	−3.13943	−	5.41616i	−0.143146	−	0.246956i
$482$	−25.7254			−1.17176
$483$	0.261784	−	3.24259i	0.0119116	−	0.147543i
$484$	−1.96230	−	3.39880i	−0.0891953	−	0.154491i
$485$	7.86933			0.357328
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	25.5410	−	14.7461i	1.15737	−	0.668208i	0.206698	−	0.978405i	$-0.433728\pi$
$487$	25.5410	−	14.7461i	1.15737	−	0.668208i	0.950673	+	0.310196i	$0.100395\pi$
$488$		−	6.14619i		−	0.278225i
$489$			10.5153i			0.475517i
$490$	2.25135	−	2.75735i	0.101706	−	0.124564i
$491$	11.9162	+	20.6395i	0.537772	+	0.931448i	0.999024	+	0.0441790i	$0.0140672\pi$
$491$	11.9162	+	20.6395i	0.537772	+	0.931448i	−0.461252	+	0.887269i	$0.652599\pi$
$492$	0.138041	+	0.0796979i	0.00622336	+	0.00359306i
$493$	−14.5553	+	25.2105i	−0.655537	+	1.13542i
$494$	0.360122	−	0.208741i	0.0162026	−	0.00939170i
$495$	−0.982287	−	1.70137i	−0.0441505	−	0.0764709i
$496$	3.83229	−	2.21258i	0.172075	−	0.0993476i
$497$	1.54073	+	0.124388i	0.0691113	+	0.00557957i
$498$	1.98400	−	3.43639i	0.0889052	−	0.153988i
$499$	1.33802	−	0.772506i	0.0598980	−	0.0345821i	−0.469752	−	0.882798i	$-0.655657\pi$
$499$	1.33802	−	0.772506i	0.0598980	−	0.0345821i	0.529650	+	0.848216i	$0.322323\pi$
$500$	4.29012	−	2.47690i	0.191860	−	0.110770i
$501$	−14.4942	+	8.36826i	−0.647555	+	0.373866i
$502$	−6.27522	+	3.62300i	−0.280077	+	0.161702i
$503$	−15.7896	+	27.3484i	−0.704025	+	1.21941i	0.263017	+	0.964791i	$0.415282\pi$
$503$	−15.7896	+	27.3484i	−0.704025	+	1.21941i	−0.967042	+	0.254616i	$0.918051\pi$
$504$	1.13420	+	2.39031i	0.0505214	+	0.106473i
$505$	−7.96687	+	4.59968i	−0.354521	+	0.204683i
$506$	2.37506	+	4.11372i	0.105584	+	0.182877i
$507$	6.53860	+	11.2360i	0.290389	+	0.499006i
$508$	9.27963	−	16.0728i	0.411717	−	0.713115i
$509$	−8.91061	−	5.14454i	−0.394956	−	0.228028i	0.289349	−	0.957224i	$-0.406561\pi$
$509$	−8.91061	−	5.14454i	−0.394956	−	0.228028i	−0.684305	+	0.729196i	$0.739894\pi$
$510$	1.98010	+	3.42963i	0.0876802	+	0.151867i
$511$	−14.5842	−	1.17743i	−0.645168	−	0.0520864i
$512$			1.00000i			0.0441942i
$513$		−	0.115446i		−	0.00509706i
$514$	−13.0252	+	7.52008i	−0.574515	+	0.331697i
$515$	2.61056	+	1.50721i	0.115035	+	0.0664154i
$516$	−0.307241			−0.0135255
$517$	−14.7471	−	25.5427i	−0.648576	−	1.12337i
$518$	3.78059	+	2.60958i	0.166110	+	0.114658i
$519$	15.1229			0.663822
$520$	−0.00314593	−	1.83353i	−0.000137958	−	0.0804056i
$521$	−11.8525	+	20.5291i	−0.519266	+	0.899395i	0.480483	+	0.877004i	$0.340461\pi$
$521$	−11.8525	+	20.5291i	−0.519266	+	0.899395i	−0.999749	+	0.0223914i	$0.992872\pi$
$522$		−	3.73810i		−	0.163612i
$523$	13.0321	−	22.5722i	0.569853	−	0.987014i	−0.426727	−	0.904380i	$-0.640334\pi$
$523$	13.0321	−	22.5722i	0.569853	−	0.987014i	0.996580	−	0.0826335i	$-0.0263331\pi$
$524$	6.73686	−	11.6686i	0.294301	−	0.509744i
$525$	1.00948	−	12.5039i	0.0440571	−	0.545714i
$526$	19.3657	+	11.1808i	0.844383	+	0.487505i
$527$		−	34.4610i		−	1.50114i
$528$	−3.34566	−	1.93162i	−0.145601	−	0.0840629i
$529$	10.7441	+	18.6093i	0.467134	+	0.809100i
$530$	−1.05929	+	1.83475i	−0.0460127	+	0.0796964i
$531$	7.24338	−	4.18197i	0.314336	−	0.181482i
$532$	−0.173511	+	0.251372i	−0.00752267	+	0.0108984i
$533$	−0.574709		0.000986071i	−0.0248934		4.27115e-5i
$534$	−2.26691	−	3.92640i	−0.0980988	−	0.169912i
$535$		−	4.06848i		−	0.175896i
$536$	1.54044			0.0665370
$537$	−24.2973			−1.04851
$538$		−	18.4997i		−	0.797579i
$539$	20.9472	+	17.1032i	0.902260	+	0.736687i
$540$	−0.440400	−	0.254265i	−0.0189518	−	0.0109418i
$541$	−33.7140	+	19.4648i	−1.44948	+	0.836857i	−0.998450	−	0.0556533i	$-0.982276\pi$
$541$	−33.7140	+	19.4648i	−1.44948	+	0.836857i	−0.451028	+	0.892510i	$0.648943\pi$
$542$	−13.4587	−	23.3112i	−0.578101	−	1.00130i
$543$	4.37128			0.187589
$544$	6.74420	+	3.89376i	0.289155	+	0.166944i
$545$	7.99147			0.342317
$546$	−7.86003	−	5.40555i	−0.336378	−	0.231336i
$547$	7.20402			0.308021			0.154011	−	0.988069i	$-0.450781\pi$
$547$	7.20402			0.308021			0.154011	+	0.988069i	$0.450781\pi$
$548$	0.686424	+	0.396307i	0.0293226	+	0.0169294i
$549$	6.14619			0.262313
$550$	9.15857	+	15.8631i	0.390523	+	0.676405i
$551$	0.373732	−	0.215774i	0.0159215	−	0.00919228i
$552$	1.06484	+	0.614785i	0.0453226	+	0.0261670i
$553$	−9.44831	−	6.52176i	−0.401783	−	0.277334i
$554$		−	23.0878i		−	0.980906i
$555$	−0.882953			−0.0374793
$556$	6.04359			0.256305
$557$			43.9252i			1.86117i	0.366076	+	0.930585i	$0.380701\pi$
$557$			43.9252i			1.86117i	−0.366076	+	0.930585i	$0.619299\pi$
$558$	2.21258	+	3.83229i	0.0936658	+	0.162234i
$559$	0.958407	−	0.555531i	0.0405363	−	0.0234965i
$560$	0.576777	+	1.21555i	0.0243733	+	0.0513662i
$561$	−26.0544	+	15.0425i	−1.10002	+	0.635096i
$562$	−6.43948	+	11.1535i	−0.271633	+	0.470482i
$563$	7.52677	+	13.0368i	0.317216	+	0.549434i	0.979906	−	0.199460i	$-0.0639187\pi$
$563$	7.52677	+	13.0368i	0.317216	+	0.549434i	−0.662690	+	0.748894i	$0.730585\pi$
$564$	−6.61173	−	3.81729i	−0.278404	−	0.160737i
$565$			8.40540i			0.353618i
$566$	19.7540	+	11.4050i	0.830324	+	0.479388i
$567$	−2.39031	+	1.13420i	−0.100384	+	0.0476320i
$568$	−0.292119	+	0.505964i	−0.0122570	+	0.0212298i
$569$	5.23871	−	9.07371i	0.219618	−	0.380390i	−0.735073	−	0.677988i	$-0.762852\pi$
$569$	5.23871	−	9.07371i	0.219618	−	0.380390i	0.954691	+	0.297598i	$0.0961855\pi$
$570$		−	0.0587077i		−	0.00245900i
$571$	21.0300	−	36.4250i	0.880078	−	1.52434i	0.0288250	−	0.999584i	$-0.490823\pi$
$571$	21.0300	−	36.4250i	0.880078	−	1.52434i	0.851253	−	0.524755i	$-0.175843\pi$
$572$	13.9291	−	0.0238992i	0.582404	−	0.000999274i
$573$	12.6832			0.529848
$574$	0.381005	−	0.180787i	0.0159029	−	0.00754591i
$575$	−2.91494	−	5.04882i	−0.121561	−	0.210551i
$576$	−1.00000			−0.0416667
$577$	−8.52701	−	4.92307i	−0.354984	−	0.204950i	0.311894	−	0.950117i	$-0.399037\pi$
$577$	−8.52701	−	4.92307i	−0.354984	−	0.204950i	−0.666878	+	0.745167i	$0.732370\pi$
$578$	37.7982	−	21.8228i	1.57220	−	0.907709i
$579$			18.0250i			0.749092i
$580$		−	1.90094i		−	0.0789322i
$581$	−4.50052	−	9.48476i	−0.186713	−	0.393494i
$582$	7.73733	+	13.4014i	0.320722	+	0.555508i
$583$	−13.9383	−	8.04730i	−0.577267	−	0.333285i
$584$	2.76512	−	4.78934i	0.114422	−	0.198184i
$585$	1.83353	−	0.00314593i	0.0758072	−	0.000130068i
$586$	−14.6405	−	25.3580i	−0.604792	−	1.04753i
$587$	−0.286591	+	0.165464i	−0.0118289	+	0.00682942i	−0.505903	−	0.862590i	$-0.668841\pi$
$587$	−0.286591	+	0.165464i	−0.0118289	+	0.00682942i	0.494074	+	0.869420i	$0.335507\pi$
$588$	6.90934	+	1.12294i	0.284936	+	0.0463094i
$589$	−0.255433	+	0.442422i	−0.0105249	+	0.0182297i
$590$	3.68348	−	2.12666i	0.151647	−	0.0875532i
$591$	−3.30735	+	1.90950i	−0.136046	+	0.0785464i
$592$	−1.50367	+	0.868142i	−0.0618003	+	0.0356804i
$593$	−5.37756	+	3.10474i	−0.220830	+	0.127496i	−0.606335	−	0.795210i	$-0.707361\pi$
$593$	−5.37756	+	3.10474i	−0.220830	+	0.127496i	0.385505	+	0.922706i	$0.374027\pi$
$594$	1.93162	−	3.34566i	0.0792553	−	0.137274i
$595$	10.4437	+	0.843153i	0.428151	+	0.0345659i
$596$	7.48843	−	4.32345i	0.306738	−	0.177095i
$597$	−8.40616	−	14.5599i	−0.344041	−	0.595897i
$598$	−4.43327	+	0.00760650i	−0.181290	+	0.000311053i
$599$	−2.62691	+	4.54995i	−0.107333	+	0.185906i	−0.914689	−	0.404159i	$-0.867564\pi$
$599$	−2.62691	+	4.54995i	−0.107333	+	0.185906i	0.807356	+	0.590064i	$0.200898\pi$
$600$	4.10617	+	2.37070i	0.167634	+	0.0967834i
$601$	10.2061	+	17.6775i	0.416315	+	0.721079i	0.995566	−	0.0940708i	$-0.0299880\pi$
$601$	10.2061	+	17.6775i	0.416315	+	0.721079i	−0.579250	+	0.815150i	$0.696655\pi$
$602$	−0.461773	+	0.668987i	−0.0188205	+	0.0272659i
$603$			1.54044i			0.0627317i
$604$			14.5487i			0.591978i
$605$	1.72839	−	0.997888i	0.0702692	−	0.0405699i
$606$	−15.6665	−	9.04503i	−0.636406	−	0.367429i
$607$	4.13185			0.167707			0.0838534	−	0.996478i	$-0.473277\pi$
$607$	4.13185			0.167707			0.0838534	+	0.996478i	$0.473277\pi$
$608$	−0.0577229	−	0.0999790i	−0.00234097	−	0.00405468i
$609$	−8.13935	−	5.61825i	−0.329823	−	0.227663i
$610$	3.12553			0.126549
$611$	27.5268	−	0.0472298i	1.11361	−	0.00191071i
$612$	−3.89376	+	6.74420i	−0.157396	+	0.272618i
$613$		−	5.56078i		−	0.224598i	−0.993674	−	0.112299i	$-0.964179\pi$
$613$		−	5.56078i		−	0.224598i	0.993674	−	0.112299i	$-0.0358214\pi$
$614$	6.72599	−	11.6498i	0.271439	−	0.470146i
$615$	−0.0405288	+	0.0701979i	−0.00163428	+	0.00283065i
$616$	−9.23433	+	4.38169i	−0.372062	+	0.176543i
$617$	−19.9539	−	11.5204i	−0.803314	−	0.463794i	0.0413145	−	0.999146i	$-0.486845\pi$
$617$	−19.9539	−	11.5204i	−0.803314	−	0.463794i	−0.844629	+	0.535353i	$0.820179\pi$
$618$			5.92769i			0.238447i
$619$	−4.57139	−	2.63929i	−0.183740	−	0.106082i	0.405309	−	0.914180i	$-0.367164\pi$
$619$	−4.57139	−	2.63929i	−0.183740	−	0.106082i	−0.589048	+	0.808098i	$0.700497\pi$
$620$	1.12516	+	1.94884i	0.0451876	+	0.0782672i
$621$	−0.614785	+	1.06484i	−0.0246705	+	0.0427305i
$622$	18.4334	−	10.6425i	0.739111	−	0.426726i
$623$	−11.9565	−	0.965281i	−0.479025	−	0.0386732i
$624$	3.11940	−	1.80813i	0.124876	−	0.0723831i
$625$	−10.5939	−	18.3492i	−0.423756	−	0.733968i
$626$			10.4861i			0.419111i
$627$	0.445994			0.0178113
$628$	7.61116			0.303718
$629$			13.5214i			0.539132i
$630$	−1.21555	+	0.576777i	−0.0484285	+	0.0229793i
$631$	−28.4149	−	16.4054i	−1.13118	−	0.653087i	−0.186949	−	0.982370i	$-0.559860\pi$
$631$	−28.4149	−	16.4054i	−1.13118	−	0.653087i	−0.944232	+	0.329282i	$0.893193\pi$
$632$	3.75790	−	2.16963i	0.149481	−	0.0863031i
$633$	9.39942	+	16.2803i	0.373593	+	0.647083i
$634$	−8.34493			−0.331420
$635$	8.17351	+	4.71898i	0.324356	+	0.187267i
$636$	−4.16609			−0.165196
$637$	−23.5834	+	8.99008i	−0.934410	+	0.356200i
$638$	14.4412			0.571731
$639$	−0.505964	−	0.292119i	−0.0200156	−	0.0115560i
$640$	−0.508531			−0.0201014
$641$	−12.0390	−	20.8521i	−0.475510	−	0.823608i	0.524096	−	0.851659i	$-0.324403\pi$
$641$	−12.0390	−	20.8521i	−0.475510	−	0.823608i	−0.999606	+	0.0280513i	$0.991070\pi$
$642$	6.92860	−	4.00023i	0.273450	−	0.157876i
$643$	38.9271	+	22.4746i	1.53513	+	0.886310i	0.999113	+	0.0421060i	$0.0134067\pi$
$643$	38.9271	+	22.4746i	1.53513	+	0.886310i	0.536021	+	0.844204i	$0.319927\pi$
$644$	2.93905	−	1.39458i	0.115815	−	0.0549542i
$645$		−	0.156241i		−	0.00615200i
$646$	−0.899038			−0.0353722
$647$	−26.1420			−1.02775			−0.513875	−	0.857865i	$-0.671790\pi$
$647$	−26.1420			−1.02775			−0.513875	+	0.857865i	$0.671790\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	16.1559	+	27.9829i	0.634176	+	1.09842i
$650$	−17.0953	+	0.0293317i	−0.670534	+	0.00115049i
$651$	11.6699	+	0.942145i	0.457379	+	0.0369256i
$652$	−9.10650	+	5.25764i	−0.356638	+	0.205905i
$653$	−17.1871	+	29.7690i	−0.672584	+	1.16495i	0.304585	+	0.952485i	$0.401482\pi$
$653$	−17.1871	+	29.7690i	−0.672584	+	1.16495i	−0.977169	+	0.212464i	$0.931851\pi$
$654$	7.85741	+	13.6094i	0.307249	+	0.532171i
$655$	5.93383	+	3.42590i	0.231854	+	0.133861i
$656$			0.159396i			0.00622336i
$657$	4.78934	+	2.76512i	0.186850	+	0.107878i
$658$	−18.2490	+	8.65915i	−0.711420	+	0.337569i
$659$	5.35630	−	9.27739i	0.208652	−	0.361396i	−0.742638	−	0.669693i	$-0.766426\pi$
$659$	5.35630	−	9.27739i	0.208652	−	0.361396i	0.951290	+	0.308297i	$0.0997591\pi$
$660$	0.982287	−	1.70137i	0.0382355	−	0.0662258i
$661$			47.6873i			1.85482i	0.374046	+	0.927410i	$0.377970\pi$
$661$			47.6873i			1.85482i	−0.374046	+	0.927410i	$0.622030\pi$
$662$	17.1981	−	29.7880i	0.668424	−	1.15775i
$663$	−0.0481761	−	28.0783i	−0.00187100	−	1.09047i
$664$	3.96800			0.153988
$665$	−0.127830	−	0.0882358i	−0.00495705	−	0.00342164i
$666$	−0.868142	−	1.50367i	−0.0336398	−	0.0582659i
$667$	−4.59626			−0.177968
$668$	−14.4942	−	8.36826i	−0.560799	−	0.323778i
$669$	20.5537	−	11.8667i	0.794653	−	0.458793i
$670$			0.783362i			0.0302639i
$671$			23.7442i			0.916634i
$672$	−1.50297	+	2.17740i	−0.0579783	+	0.0839952i
$673$	−19.9249	−	34.5109i	−0.768047	−	1.33030i	−0.938621	−	0.344951i	$-0.887895\pi$
$673$	−19.9249	−	34.5109i	−0.768047	−	1.33030i	0.170574	−	0.985345i	$-0.445438\pi$
$674$	9.84649	+	5.68487i	0.379273	+	0.218973i
$675$	−2.37070	+	4.10617i	−0.0912482	+	0.158047i
$676$	−6.46133	+	11.2806i	−0.248513	+	0.433868i
$677$	13.5454	+	23.4614i	0.520593	+	0.901693i	0.999713	+	0.0239439i	$0.00762230\pi$
$677$	13.5454	+	23.4614i	0.520593	+	0.901693i	−0.479121	+	0.877749i	$0.659044\pi$
$678$	−14.3144	+	8.26440i	−0.549740	+	0.317392i
$679$	40.8093	+	3.29466i	1.56612	+	0.126437i
$680$	−1.98010	+	3.42963i	−0.0759333	+	0.131520i
$681$	4.31918	−	2.49368i	0.165511	−	0.0955579i
$682$	−14.8051	+	8.54770i	−0.566915	+	0.327308i
$683$	−21.2787	+	12.2853i	−0.814207	+	0.470083i	−0.848415	−	0.529332i	$-0.822443\pi$
$683$	−21.2787	+	12.2853i	−0.814207	+	0.470083i	0.0342078	+	0.999415i	$0.489109\pi$
$684$	0.0999790	−	0.0577229i	0.00382279	−	0.00220709i
$685$	−0.201534	+	0.349068i	−0.00770023	+	0.0133372i
$686$	12.8296	−	13.3567i	0.489837	−	0.509960i
$687$	−4.42876	+	2.55695i	−0.168968	+	0.0975536i
$688$	−0.153620	−	0.266078i	−0.00585672	−	0.0101441i
$689$	12.9957	−	7.53284i	0.495097	−	0.286978i
$690$	−0.312637	+	0.541503i	−0.0119019	+	0.0206147i
$691$	30.0437	+	17.3457i	1.14292	+	0.659863i	0.947151	−	0.320787i	$-0.103947\pi$
$691$	30.0437	+	17.3457i	1.14292	+	0.659863i	0.195766	+	0.980651i	$0.437281\pi$
$692$	7.56146	+	13.0968i	0.287444	+	0.497867i
$693$	−4.38169	−	9.23433i	−0.166447	−	0.350783i
$694$		−	29.9393i		−	1.13648i
$695$			3.07335i			0.116579i
$696$	3.23729	−	1.86905i	0.122709	−	0.0708462i
$697$	1.07500	+	0.620649i	0.0407184	+	0.0235088i
$698$	−30.1800			−1.14233
$699$	14.4275	+	24.9892i	0.545699	+	0.945178i
$700$	11.3334	−	5.37770i	0.428363	−	0.203258i
$701$	33.8723			1.27934			0.639669	−	0.768651i	$-0.279072\pi$
$701$	33.8723			1.27934			0.639669	+	0.768651i	$0.279072\pi$
$702$	1.80813	+	3.11940i	0.0682435	+	0.117734i
$703$	0.100223	−	0.173592i	0.00377999	−	0.00654714i
$704$		−	3.86324i		−	0.145601i
$705$	1.94121	−	3.36227i	0.0731101	−	0.126630i
$706$	−0.218730	+	0.378851i	−0.00823199	+	0.0142582i
$707$	−43.2409	+	20.5178i	−1.62624	+	0.771651i
$708$	7.24338	+	4.18197i	0.272223	+	0.157168i
$709$		−	17.4907i		−	0.656876i	−0.944526	−	0.328438i	$-0.893478\pi$
$709$		−	17.4907i		−	0.656876i	0.944526	−	0.328438i	$-0.106522\pi$
$710$	−0.257298	−	0.148551i	−0.00965624	−	0.00557503i
$711$	2.16963	+	3.75790i	0.0813674	+	0.140932i
$712$	2.26691	−	3.92640i	0.0849560	−	0.147148i
$713$	4.71207	−	2.72052i	0.176469	−	0.101884i
$714$	8.83264	+	18.6146i	0.330553	+	0.696634i
$715$	0.0121535	+	7.08336i	0.000454514	+	0.264903i
$716$	−12.1487	−	21.0421i	−0.454017	−	0.786381i
$717$			16.0044i			0.597694i
$718$	1.14332			0.0426683
$719$	8.53975			0.318479			0.159239	−	0.987240i	$-0.449096\pi$
$719$	8.53975			0.318479			0.159239	+	0.987240i	$0.449096\pi$
$720$		−	0.508531i		−	0.0189518i
$721$	12.9070	+	8.90913i	0.480681	+	0.331793i
$722$	−16.4429	−	9.49334i	−0.611943	−	0.353305i
$723$	22.2788	−	12.8627i	0.828558	−	0.478368i
$724$	2.18564	+	3.78564i	0.0812286	+	0.140692i
$725$	−17.7238			−0.658246
$726$	3.39880	+	1.96230i	0.126141	+	0.0728277i
$727$	−46.3540			−1.71918			−0.859588	−	0.510989i	$-0.829279\pi$
$727$	−46.3540			−1.71918			−0.859588	+	0.510989i	$0.829279\pi$
$728$	0.751331	−	9.50976i	0.0278462	−	0.352455i
$729$	1.00000			0.0370370
$730$	2.43552	+	1.40615i	0.0901428	+	0.0520440i
$731$	−2.39265			−0.0884952
$732$	3.07310	+	5.32276i	0.113585	+	0.196735i
$733$	−1.96686	+	1.13557i	−0.0726477	+	0.0419431i	−0.535884	−	0.844292i	$-0.680022\pi$
$733$	−1.96686	+	1.13557i	−0.0726477	+	0.0419431i	0.463236	+	0.886235i	$0.346688\pi$
$734$	27.6389	+	15.9573i	1.02017	+	0.588995i
$735$	−0.571051	+	3.51361i	−0.0210635	+	0.129602i
$736$			1.22957i			0.0453226i
$737$	−5.95109			−0.219211
$738$	−0.159396			−0.00586744
$739$		−	7.27095i		−	0.267466i	−0.991017	−	0.133733i	$-0.957304\pi$
$739$		−	7.27095i		−	0.267466i	0.991017	−	0.133733i	$-0.0426965\pi$
$740$	−0.441477	−	0.764660i	−0.0162290	−	0.0281095i
$741$	−0.207504	+	0.360836i	−0.00762285	+	0.0132556i
$742$	−6.26150	+	9.07126i	−0.229867	+	0.333017i
$743$	1.42103	−	0.820430i	0.0521324	−	0.0300986i	−0.473707	−	0.880682i	$-0.657085\pi$
$743$	1.42103	−	0.820430i	0.0521324	−	0.0300986i	0.525840	+	0.850584i	$0.323751\pi$
$744$	−2.21258	+	3.83229i	−0.0811170	+	0.140499i
$745$	2.19860	+	3.80809i	0.0805506	+	0.139518i
$746$	5.55639	+	3.20799i	0.203434	+	0.117453i
$747$			3.96800i			0.145182i
$748$	−26.0544	−	15.0425i	−0.952644	−	0.550010i
$749$	1.70335	−	21.0986i	0.0622391	−	0.770925i
$750$	−2.47690	+	4.29012i	−0.0904436	+	0.156653i
$751$	18.8995	−	32.7348i	0.689651	−	1.19451i	−0.282300	−	0.959326i	$-0.591097\pi$
$751$	18.8995	−	32.7348i	0.689651	−	1.19451i	0.971951	−	0.235185i	$-0.0755695\pi$
$752$		−	7.63457i		−	0.278404i
$753$	3.62300	−	6.27522i	0.132029	−	0.228682i
$754$	−6.71892	+	11.6838i	−0.244689	+	0.425497i
$755$	−7.39845			−0.269257
$756$	−2.17740	−	1.50297i	−0.0791914	−	0.0546624i
$757$	−16.5417	−	28.6511i	−0.601219	−	1.04134i	−0.992637	−	0.121129i	$-0.961349\pi$
$757$	−16.5417	−	28.6511i	−0.601219	−	1.04134i	0.391418	−	0.920213i	$-0.371985\pi$
$758$	−23.7713			−0.863411
$759$	−4.11372	−	2.37506i	−0.149319	−	0.0862092i
$760$	0.0508424	−	0.0293539i	0.00184425	−	0.00106478i
$761$		−	30.3135i		−	1.09886i	−0.835539	−	0.549431i	$-0.814844\pi$
$761$		−	30.3135i		−	1.09886i	0.835539	−	0.549431i	$-0.185156\pi$
$762$			18.5593i			0.672331i
$763$	41.4427	+	3.34580i	1.50033	+	0.121126i
$764$	6.34160	+	10.9840i	0.229431	+	0.397386i
$765$	−3.42963	−	1.98010i	−0.123999	−	0.0715906i
$766$	−14.9968	+	25.9753i	−0.541857	+	0.938524i
$767$	−30.1566	+	0.0517419i	−1.08889	+	0.00186829i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	40.8561	−	23.5883i	1.47331	−	0.850615i	0.473760	−	0.880654i	$-0.342896\pi$
$769$	40.8561	−	23.5883i	1.47331	−	0.850615i	0.999549	+	0.0300384i	$0.00956295\pi$
$770$	−2.22823	−	4.69594i	−0.0802997	−	0.169230i
$771$	7.52008	−	13.0252i	0.270829	−	0.469090i
$772$	−15.6101	+	9.01248i	−0.561819	+	0.324366i
$773$	−31.9687	+	18.4571i	−1.14983	+	0.663857i	−0.948847	−	0.315737i	$-0.897748\pi$
$773$	−31.9687	+	18.4571i	−1.14983	+	0.663857i	−0.200987	+	0.979594i	$0.564415\pi$
$774$	0.266078	−	0.153620i	0.00956398	−	0.00552177i
$775$	18.1704	−	10.4907i	0.652701	−	0.376837i
$776$	−7.73733	+	13.4014i	−0.277754	+	0.481084i
$777$	−4.57888	−	0.369667i	−0.164266	−	0.0132617i
$778$	−1.80127	+	1.03997i	−0.0645788	+	0.0372846i
$779$	−0.00920078	−	0.0159362i	−0.000329652	−	0.000570974i
$780$	0.919490	+	1.58631i	0.0329230	+	0.0567990i
$781$	1.12852	−	1.95466i	0.0403817	−	0.0699432i
$782$	8.29246	+	4.78766i	0.296538	+	0.171206i
$783$	1.86905	+	3.23729i	0.0667944	+	0.115691i
$784$	2.48217	+	6.54514i	0.0886490	+	0.233755i
$785$			3.87051i			0.138144i
$786$			13.4737i			0.480592i
$787$	−7.09167	+	4.09438i	−0.252791	+	0.145949i	−0.621041	−	0.783778i	$-0.713290\pi$
$787$	−7.09167	+	4.09438i	−0.252791	+	0.145949i	0.368251	+	0.929727i	$0.379957\pi$
$788$	−3.30735	−	1.90950i	−0.117820	−	0.0680232i
$789$	−22.3615			−0.796092
$790$	1.10332	+	1.91101i	0.0392544	+	0.0679907i
$791$	−3.51910	+	43.5893i	−0.125125	+	1.54986i
$792$	3.86324			0.137274
$793$	−19.2105	−	11.0473i	−0.682183	−	0.392300i
$794$	−16.9405	+	29.3419i	−0.601197	+	1.04130i
$795$		−	2.11859i		−	0.0751385i
$796$	8.40616	−	14.5599i	0.297948	−	0.516062i
$797$	19.2227	−	33.2948i	0.680904	−	1.17936i	−0.293801	−	0.955867i	$-0.594920\pi$
$797$	19.2227	−	33.2948i	0.680904	−	1.17936i	0.974705	−	0.223494i	$-0.0717464\pi$
$798$	0.0245792	−	0.304450i	0.000870094	−	0.0107774i
$799$	−51.4891	−	29.7272i	−1.82155	−	1.05167i
$800$			4.74140i			0.167634i
$801$	3.92640	+	2.26691i	0.138733	+	0.0800973i
$802$	0.312674	+	0.541568i	0.0110409	+	0.0191234i
$803$	−10.6823	+	18.5023i	−0.376971	+	0.652933i
$804$	−1.33406	+	0.770221i	−0.0470487	+	0.0271636i
$805$	0.709188	+	1.49460i	0.0249956	+	0.0526777i
$806$	−0.0273753	−	15.9551i	−0.000964255	−	0.561994i
$807$	9.24986	+	16.0212i	0.325610	+	0.563974i
$808$		−	18.0901i		−	0.636406i
$809$	−40.8252			−1.43534			−0.717669	−	0.696384i	$-0.754791\pi$
$809$	−40.8252			−1.43534			−0.717669	+	0.696384i	$0.754791\pi$
$810$	0.508531			0.0178679
$811$		−	35.7805i		−	1.25642i	−0.778043	−	0.628211i	$-0.783787\pi$
$811$		−	35.7805i		−	1.25642i	0.778043	−	0.628211i	$-0.216213\pi$
$812$	0.795867	−	9.85801i	0.0279295	−	0.345948i
$813$	23.3112	+	13.4587i	0.817559	+	0.472018i
$814$	5.80901	−	3.35384i	0.203606	−	0.117552i
$815$	−2.67367	−	4.63093i	−0.0936546	−	0.162215i
$816$	−7.78753			−0.272618
$817$	0.0307176	+	0.0177348i	0.00107467	+	0.000620463i
$818$	−0.545496			−0.0190728
$819$	9.50976	+	0.751331i	0.332298	+	0.0262536i
$820$	−0.0810576			−0.00283065
$821$	15.9820	+	9.22720i	0.557775	+	0.322032i	0.752252	−	0.658876i	$-0.228968\pi$
$821$	15.9820	+	9.22720i	0.557775	+	0.322032i	−0.194477	+	0.980907i	$0.562301\pi$
$822$	−0.792615			−0.0276456
$823$	16.7044	+	28.9329i	0.582279	+	1.00854i	0.995209	+	0.0977741i	$0.0311723\pi$
$823$	16.7044	+	28.9329i	0.582279	+	1.00854i	−0.412929	+	0.910763i	$0.635494\pi$
$824$	−5.13353	+	2.96384i	−0.178835	+	0.103250i
$825$	−15.8631	−	9.15857i	−0.552282	−	0.318860i
$826$	19.9924	−	9.48640i	0.695625	−	0.330074i
$827$			32.1212i			1.11696i	0.829517	+	0.558481i	$0.188616\pi$
$827$			32.1212i			1.11696i	−0.829517	+	0.558481i	$0.811384\pi$
$828$	−1.22957			−0.0427305
$829$	−41.9006			−1.45527			−0.727634	−	0.685965i	$-0.759380\pi$
$829$	−41.9006			−1.45527			−0.727634	+	0.685965i	$0.759380\pi$
$830$			2.01785i			0.0700406i
$831$	11.5439	+	19.9946i	0.400453	+	0.693605i
$832$	3.12559	+	1.79742i	0.108360	+	0.0623142i
$833$	53.8067	+	8.74496i	1.86429	+	0.302995i
$834$	−5.23390	+	3.02179i	−0.181235	+	0.104636i
$835$	4.25552	−	7.37077i	0.147268	−	0.255076i
$836$	0.222997	+	0.386242i	0.00771252	+	0.0133585i
$837$	−3.83229	−	2.21258i	−0.132463	−	0.0764778i
$838$			17.6256i			0.608867i
$839$	31.8058	+	18.3631i	1.09806	+	0.633965i	0.935711	−	0.352769i	$-0.114760\pi$
$839$	31.8058	+	18.3631i	1.09806	+	0.633965i	0.162349	+	0.986733i	$0.448093\pi$
$840$	−1.10728	−	0.764305i	−0.0382047	−	0.0263710i
$841$	7.51330	−	13.0134i	0.259079	−	0.448739i
$842$	15.5862	−	26.9961i	0.537137	−	0.930349i
$843$		−	12.8790i		−	0.443575i
$844$	−9.39942	+	16.2803i	−0.323541	+	0.560390i
$845$	−5.73651	−	3.28578i	−0.197342	−	0.113034i
$846$	7.63457			0.262482
$847$	9.38100	−	4.45129i	0.322335	−	0.152948i
$848$	−2.08305	−	3.60794i	−0.0715321	−	0.123897i
$849$	−22.8100			−0.782837
$850$	31.9769	+	18.4619i	1.09680	+	0.633237i
$851$	−1.84886	+	1.06744i	−0.0633782	+	0.0365914i
$852$		−	0.584237i		−	0.0200156i
$853$			17.4622i			0.597893i	0.954270	+	0.298947i	$0.0966353\pi$
$853$			17.4622i			0.597893i	−0.954270	+	0.298947i	$0.903365\pi$
$854$	16.2086	+	1.30857i	0.554645	+	0.0447782i
$855$	0.0293539	+	0.0508424i	0.00100388	+	0.00173877i
$856$	6.92860	+	4.00023i	0.236815	+	0.136725i
$857$	−11.7151	+	20.2912i	−0.400181	+	0.693134i	−0.993747	−	0.111651i	$-0.964386\pi$
$857$	−11.7151	+	20.2912i	−0.400181	+	0.693134i	0.593566	+	0.804785i	$0.297719\pi$
$858$	−12.0510	+	6.98524i	−0.411414	+	0.238472i
$859$	−14.7681	−	25.5791i	−0.503882	−	0.872748i	−0.999990	−	0.00448784i	$-0.998571\pi$
$859$	−14.7681	−	25.5791i	−0.503882	−	0.872748i	0.496108	−	0.868261i	$-0.334762\pi$
$860$	0.135309	−	0.0781206i	0.00461400	−	0.00266389i
$861$	−0.239567	+	0.347069i	−0.00816441	+	0.0118281i
$862$	1.50636	−	2.60910i	0.0513069	−	0.0888662i
$863$	44.4171	−	25.6442i	1.51198	−	0.872939i	0.512073	−	0.858942i	$-0.328878\pi$
$863$	44.4171	−	25.6442i	1.51198	−	0.872939i	0.999902	−	0.0139978i	$-0.00445579\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−6.66014	+	3.84523i	−0.226452	+	0.130742i
$866$	−17.1736	+	9.91519i	−0.583583	+	0.336932i
$867$	−21.8228	+	37.7982i	−0.741141	+	1.28369i
$868$	5.01902	+	10.5775i	0.170357	+	0.359023i
$869$	−14.5177	+	8.38178i	−0.492478	+	0.284333i
$870$	0.950469	+	1.64626i	0.0322239	+	0.0558135i
$871$	2.76881	−	4.81479i	0.0938177	−	0.163143i
$872$	−7.85741	+	13.6094i	−0.266086	+	0.460874i
$873$	−13.4014	−	7.73733i	−0.453570	−	0.261869i
$874$	−0.0709743	−	0.122931i	−0.00240074	−	0.00415821i
$875$	5.61861	+	11.8411i	0.189944	+	0.400303i
$876$			5.53025i			0.186850i
$877$		−	8.76614i		−	0.296012i	−0.988986	−	0.148006i	$-0.952715\pi$
$877$		−	8.76614i		−	0.296012i	0.988986	−	0.148006i	$-0.0472854\pi$
$878$	−6.97048	+	4.02441i	−0.235242	+	0.135817i
$879$	25.3580	+	14.6405i	0.855305	+	0.493811i
$880$	1.96457			0.0662258
$881$	−6.59533	−	11.4234i	−0.222202	−	0.384865i	0.733274	−	0.679933i	$-0.237991\pi$
$881$	−6.59533	−	11.4234i	−0.222202	−	0.384865i	−0.955476	+	0.295068i	$0.904658\pi$
$882$	−6.54514	+	2.48217i	−0.220386	+	0.0835791i
$883$	43.6636			1.46940			0.734698	−	0.678394i	$-0.237324\pi$
$883$	43.6636			1.46940			0.734698	+	0.678394i	$0.237324\pi$
$884$	24.2924	−	14.0809i	0.817043	−	0.473591i
$885$	−2.12666	+	3.68348i	−0.0714869	+	0.123819i
$886$			17.3899i			0.584225i
$887$	12.8273	−	22.2176i	0.430699	−	0.745993i	−0.566235	−	0.824244i	$-0.691600\pi$
$887$	12.8273	−	22.2176i	0.430699	−	0.745993i	0.996934	+	0.0782514i	$0.0249337\pi$
$888$	0.868142	−	1.50367i	0.0291329	−	0.0504597i
$889$	40.4110	+	27.8940i	1.35534	+	0.935534i
$890$	1.99670	+	1.15279i	0.0669294	+	0.0386417i
$891$			3.86324i			0.129423i
$892$	20.5537	+	11.8667i	0.688190	+	0.397326i
$893$	0.440689	+	0.763297i	0.0147471	+	0.0255427i
$894$	−4.32345	+	7.48843i	−0.144598	+	0.250450i
$895$	10.7006	−	6.17797i	0.357680	−	0.206507i
$896$	−2.63717	−	0.212907i	−0.0881017	−	0.00711272i
$897$	3.83552	−	2.22322i	0.128064	−	0.0742313i
$898$	−7.65886	−	13.2655i	−0.255579	−	0.442677i
$899$		−	16.5417i		−	0.551695i
$900$	−4.74140			−0.158047
$901$	−32.4436			−1.08085
$902$		−	0.615783i		−	0.0205033i
$903$	0.0654137	−	0.810246i	0.00217683	−	0.0269633i
$904$	−14.3144	−	8.26440i	−0.476089	−	0.274870i
$905$	−1.92511	+	1.11146i	−0.0639929	+	0.0369463i
$906$	−7.27434	−	12.5995i	−0.241674	−	0.418591i
$907$	−34.8100			−1.15585			−0.577924	−	0.816090i	$-0.696137\pi$
$907$	−34.8100			−1.15585			−0.577924	+	0.816090i	$0.696137\pi$
$908$	4.31918	+	2.49368i	0.143337	+	0.0827556i
$909$	18.0901			0.600010
$910$	4.83600	+	0.382075i	0.160312	+	0.0126657i
$911$	−39.6014			−1.31205			−0.656026	−	0.754738i	$-0.727764\pi$
$911$	−39.6014			−1.31205			−0.656026	+	0.754738i	$0.727764\pi$
$912$	0.0999790	+	0.0577229i	0.00331064	+	0.00191140i
$913$	−15.3293			−0.507327
$914$	6.24822	+	10.8222i	0.206673	+	0.357968i
$915$	−2.70679	+	1.56276i	−0.0894836	+	0.0516634i
$916$	−4.42876	−	2.55695i	−0.146330	−	0.0844839i
$917$	29.3377	+	20.2506i	0.968817	+	0.668733i
$918$		−	7.78753i		−	0.257027i
$919$	−1.13570			−0.0374633			−0.0187316	−	0.999825i	$-0.505963\pi$
$919$	−1.13570			−0.0374633			−0.0187316	+	0.999825i	$0.505963\pi$
$920$	−0.625274			−0.0206147
$921$			13.4520i			0.443258i
$922$	−2.82075	−	4.88568i	−0.0928964	−	0.160901i
$923$	1.05638	+	1.82247i	0.0347711	+	0.0599873i
$924$	5.80632	−	8.41182i	0.191014	−	0.276729i
$925$	−7.12947	+	4.11620i	−0.234416	+	0.135340i
$926$	−4.87213	+	8.43877i	−0.160108	+	0.277315i
$927$	−2.96384	−	5.13353i	−0.0973454	−	0.168607i
$928$	3.23729	+	1.86905i	0.106269	+	0.0613546i
$929$			48.2009i			1.58142i	0.612192	+	0.790709i	$0.290288\pi$
$929$			48.2009i			1.58142i	−0.612192	+	0.790709i	$0.709712\pi$
$930$	−1.94884	−	1.12516i	−0.0639049	−	0.0368955i
$931$	−0.625969	−	0.511098i	−0.0205153	−	0.0167506i
$932$	−14.4275	+	24.9892i	−0.472589	+	0.818548i
$933$	−10.6425	+	18.4334i	−0.348420	+	0.603482i
$934$		−	27.3426i		−	0.894678i
$935$	7.64959	−	13.2495i	0.250168	−	0.433304i
$936$	−1.79742	+	3.12559i	−0.0587504	+	0.102163i
$937$	−26.6391			−0.870262			−0.435131	−	0.900367i	$-0.643298\pi$
$937$	−26.6391			−0.870262			−0.435131	+	0.900367i	$0.643298\pi$
$938$	−0.327971	+	4.06241i	−0.0107086	+	0.132642i
$939$	−5.24307	−	9.08127i	−0.171101	−	0.296356i
$940$	3.88241			0.126630
$941$	21.9380	+	12.6659i	0.715159	+	0.412897i	0.812968	−	0.582308i	$-0.197850\pi$
$941$	21.9380	+	12.6659i	0.715159	+	0.412897i	−0.0978091	+	0.995205i	$0.531183\pi$
$942$	−6.59146	+	3.80558i	−0.214761	+	0.123993i
$943$			0.195988i			0.00638225i
$944$			8.36394i			0.272223i
$945$	0.764305	−	1.10728i	0.0248629	−	0.0360197i
$946$	0.593472	+	1.02792i	0.0192954	+	0.0334207i
$947$	−30.8415	−	17.8063i	−1.00221	−	0.578628i	−0.0933111	−	0.995637i	$-0.529745\pi$
$947$	−30.8415	−	17.8063i	−1.00221	−	0.578628i	−0.908902	+	0.417009i	$0.863078\pi$
$948$	−2.16963	+	3.75790i	−0.0704662	+	0.122051i
$949$	−9.99941	−	17.2511i	−0.324595	−	0.559993i
$950$	−0.273687	−	0.474040i	−0.00887958	−	0.0153799i
$951$	7.22692	−	4.17247i	0.234349	−	0.135301i
$952$	−11.7044	+	16.9566i	−0.379342	+	0.549566i
$953$	−1.15225	+	1.99576i	−0.0373252	+	0.0646491i	−0.884085	−	0.467327i	$-0.845217\pi$
$953$	−1.15225	+	1.99576i	−0.0373252	+	0.0646491i	0.846759	+	0.531976i	$0.178550\pi$
$954$	3.60794	−	2.08305i	0.116811	−	0.0674411i
$955$	−5.58569	+	3.22490i	−0.180749	+	0.104355i
$956$	−13.8602	+	8.00218i	−0.448270	+	0.258809i
$957$	−12.5064	+	7.22058i	−0.404275	+	0.233408i
$958$	−8.22267	+	14.2421i	−0.265662	+	0.460141i
$959$	−1.19127	+	1.72584i	−0.0384683	+	0.0557303i
$960$	0.440400	−	0.254265i	0.0142139	−	0.00820638i
$961$	−5.70902	−	9.88831i	−0.184162	−	0.318978i
$962$	0.0107412	+	6.26025i	0.000346310	+	0.201839i
$963$	−4.00023	+	6.92860i	−0.128906	+	0.223271i
$964$	22.2788	+	12.8627i	0.717553	+	0.414279i
$965$	−4.58312	−	7.93820i	−0.147536	−	0.255540i
$966$	−1.84800	+	2.67727i	−0.0594586	+	0.0861398i
$967$		−	19.3406i		−	0.621952i	−0.950418	−	0.310976i	$-0.899344\pi$
$967$		−	19.3406i		−	0.621952i	0.950418	−	0.310976i	$-0.100656\pi$
$968$			3.92460i			0.126141i
$969$	0.778589	−	0.449519i	0.0250119	−	0.0144406i
$970$	−6.81504	−	3.93467i	−0.218818	−	0.126335i
$971$	−20.0658			−0.643942			−0.321971	−	0.946749i	$-0.604345\pi$
$971$	−20.0658			−0.643942			−0.321971	+	0.946749i	$0.604345\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−1.28672	+	15.9380i	−0.0412504	+	0.510948i
$974$	−29.4922			−0.944989
$975$	14.7903	−	8.57306i	0.473669	−	0.274558i
$976$	−3.07310	+	5.32276i	−0.0983674	+	0.170377i
$977$		−	57.9308i		−	1.85337i	−0.375837	−	0.926686i	$-0.622645\pi$
$977$		−	57.9308i		−	1.85337i	0.375837	−	0.926686i	$-0.377355\pi$
$978$	5.25764	−	9.10650i	0.168121	−	0.291194i
$979$	−8.75761	+	15.1686i	−0.279894	+	0.484791i
$980$	−3.32840	+	1.26226i	−0.106322	+	0.0403214i
$981$	−13.6094	−	7.85741i	−0.434516	−	0.250868i
$982$		−	23.8325i		−	0.760524i
$983$	−6.75412	−	3.89949i	−0.215423	−	0.124374i	0.388406	−	0.921488i	$-0.373026\pi$
$983$	−6.75412	−	3.89949i	−0.215423	−	0.124374i	−0.603829	+	0.797114i	$0.706359\pi$
$984$	−0.0796979	−	0.138041i	−0.00254067	−	0.00440058i
$985$	0.971040	−	1.68189i	0.0309399	−	0.0535895i
$986$	25.2105	−	14.5553i	0.802866	−	0.463535i
$987$	11.4745	−	16.6235i	0.365238	−	0.529133i
$988$	−0.416245		0.000714183i	−0.0132425		2.27212e-5i
$989$	−0.188887	−	0.327162i	−0.00600626	−	0.0104031i
$990$			1.96457i			0.0624383i
$991$	28.0486			0.890993			0.445496	−	0.895284i	$-0.353027\pi$
$991$	28.0486			0.890993			0.445496	+	0.895284i	$0.353027\pi$
$992$	−4.42515			−0.140499
$993$			34.3963i			1.09153i
$994$	−1.27212	−	0.878090i	−0.0403492	−	0.0278513i
$995$	7.40415	+	4.27479i	0.234727	+	0.135520i
$996$	−3.43639	+	1.98400i	−0.108886	+	0.0628655i
$997$	−5.41183	−	9.37357i	−0.171394	−	0.296864i	0.767513	−	0.641033i	$-0.221494\pi$
$997$	−5.41183	−	9.37357i	−0.171394	−	0.296864i	−0.938908	+	0.344169i	$0.888161\pi$
$998$	−1.54501			−0.0489065
$999$	1.50367	+	0.868142i	0.0475739	+	0.0274668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.b.361.2	yes	20
3.2	odd	2		1638.2.cr.b.361.9		20
7.2	even	3		546.2.bm.b.205.9	yes	20
13.4	even	6		546.2.bm.b.277.4	yes	20
21.2	odd	6		1638.2.dt.b.1297.2		20
39.17	odd	6		1638.2.dt.b.1369.7		20
91.30	even	6	inner	546.2.bd.b.121.2	✓	20
273.212	odd	6		1638.2.cr.b.667.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.2	✓	20	91.30	even	6	inner
546.2.bd.b.361.2	yes	20	1.1	even	1	trivial
546.2.bm.b.205.9	yes	20	7.2	even	3
546.2.bm.b.277.4	yes	20	13.4	even	6
1638.2.cr.b.361.9		20	3.2	odd	2
1638.2.cr.b.667.9		20	273.212	odd	6
1638.2.dt.b.1297.2		20	21.2	odd	6
1638.2.dt.b.1369.7		20	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.440400 + 0.254265i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.39031 + 1.13420i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.440400 + 0.254265i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.39031 + 1.13420i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +0.508531 q^{10} +3.86324i q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.12559 - 1.79742i) q^{13} +(2.63717 + 0.212907i) q^{14} +(-0.440400 + 0.254265i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.89376 + 6.74420i) q^{17} +(-0.866025 - 0.500000i) q^{18} -0.115446i q^{19} +(-0.440400 - 0.254265i) q^{20} +(-2.39031 + 1.13420i) q^{21} +(1.93162 - 3.34566i) q^{22} +(-0.614785 + 1.06484i) q^{23} -1.00000i q^{24} +(-2.37070 + 4.10617i) q^{25} +(1.80813 + 3.11940i) q^{26} +1.00000 q^{27} +(-2.17740 - 1.50297i) q^{28} +(1.86905 + 3.23729i) q^{29} +0.508531 q^{30} +(-3.83229 - 2.21258i) q^{31} +(0.866025 - 0.500000i) q^{32} +3.86324i q^{33} -7.78753i q^{34} +(0.764305 - 1.10728i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.50367 + 0.868142i) q^{37} +(-0.0577229 + 0.0999790i) q^{38} +(-3.12559 - 1.79742i) q^{39} +(0.254265 + 0.440400i) q^{40} +(0.138041 - 0.0796979i) q^{41} +(2.63717 + 0.212907i) q^{42} +(-0.153620 + 0.266078i) q^{43} +(-3.34566 + 1.93162i) q^{44} +(-0.440400 + 0.254265i) q^{45} +(1.06484 - 0.614785i) q^{46} +(-6.61173 + 3.81729i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(4.42717 - 5.42219i) q^{49} +(4.10617 - 2.37070i) q^{50} +(3.89376 + 6.74420i) q^{51} +(-0.00618631 - 3.60555i) q^{52} +(-2.08305 + 3.60794i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.982287 - 1.70137i) q^{55} +(1.13420 + 2.39031i) q^{56} -0.115446i q^{57} -3.73810i q^{58} +(7.24338 - 4.18197i) q^{59} +(-0.440400 - 0.254265i) q^{60} +6.14619 q^{61} +(2.21258 + 3.83229i) q^{62} +(-2.39031 + 1.13420i) q^{63} -1.00000 q^{64} +(1.83353 - 0.00314593i) q^{65} +(1.93162 - 3.34566i) q^{66} +1.54044i q^{67} +(-3.89376 + 6.74420i) q^{68} +(-0.614785 + 1.06484i) q^{69} +(-1.21555 + 0.576777i) q^{70} +(-0.505964 - 0.292119i) q^{71} -1.00000i q^{72} +(4.78934 + 2.76512i) q^{73} +(-0.868142 - 1.50367i) q^{74} +(-2.37070 + 4.10617i) q^{75} +(0.0999790 - 0.0577229i) q^{76} +(-4.38169 - 9.23433i) q^{77} +(1.80813 + 3.11940i) q^{78} +(2.16963 + 3.75790i) q^{79} -0.508531i q^{80} +1.00000 q^{81} -0.159396 q^{82} +3.96800i q^{83} +(-2.17740 - 1.50297i) q^{84} +(-3.42963 - 1.98010i) q^{85} +(0.266078 - 0.153620i) q^{86} +(1.86905 + 3.23729i) q^{87} +3.86324 q^{88} +(3.92640 + 2.26691i) q^{89} +0.508531 q^{90} +(9.50976 + 0.751331i) q^{91} -1.22957 q^{92} +(-3.83229 - 2.21258i) q^{93} +7.63457 q^{94} +(0.0293539 + 0.0508424i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-13.4014 - 7.73733i) q^{97} +(-6.54514 + 2.48217i) q^{98} +3.86324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9	\( 20 q + 20 q^{3} + 10 q^{4} - 6 q^{7} + 20 q^{9} - 8 q^{10} + 10 q^{12} + 8 q^{13} + 4 q^{14} - 10 q^{16} + 4 q^{17} - 6 q^{21} - 10 q^{22} + 8 q^{23} + 6 q^{25} + 2 q^{26} + 20 q^{27} - 6 q^{28} + 8 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{35} + 10 q^{36} + 6 q^{38} + 8 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} + 18 q^{43} + 6 q^{44} - 24 q^{46} + 6 q^{47} - 10 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} - 2 q^{52} + 18 q^{53} - 12 q^{55} + 2 q^{56} + 36 q^{59} + 12 q^{61} - 6 q^{63} - 20 q^{64} - 10 q^{66} - 4 q^{68} + 8 q^{69} - 42 q^{70} - 6 q^{71} - 24 q^{73} - 18 q^{74} + 6 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} + 20 q^{81} - 36 q^{82} - 6 q^{84} + 36 q^{86} + 8 q^{87} - 20 q^{88} + 18 q^{89} - 8 q^{90} - 94 q^{91} + 16 q^{92} - 12 q^{93} + 32 q^{94} + 40 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q + 20 * q^3 + 10 * q^4 - 6 * q^7 + 20 * q^9 - 8 * q^10 + 10 * q^12 + 8 * q^13 + 4 * q^14 - 10 * q^16 + 4 * q^17 - 6 * q^21 - 10 * q^22 + 8 * q^23 + 6 * q^25 + 2 * q^26 + 20 * q^27 - 6 * q^28 + 8 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^35 + 10 * q^36 + 6 * q^38 + 8 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 + 18 * q^43 + 6 * q^44 - 24 * q^46 + 6 * q^47 - 10 * q^48 + 4 * q^49 + 12 * q^50 + 4 * q^51 - 2 * q^52 + 18 * q^53 - 12 * q^55 + 2 * q^56 + 36 * q^59 + 12 * q^61 - 6 * q^63 - 20 * q^64 - 10 * q^66 - 4 * q^68 + 8 * q^69 - 42 * q^70 - 6 * q^71 - 24 * q^73 - 18 * q^74 + 6 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 + 20 * q^81 - 36 * q^82 - 6 * q^84 + 36 * q^86 + 8 * q^87 - 20 * q^88 + 18 * q^89 - 8 * q^90 - 94 * q^91 + 16 * q^92 - 12 * q^93 + 32 * q^94 + 40 * q^95 - 96 * q^97 - 12 * q^98

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