LMFDB - Embedded newform 546.2.l.i.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.i.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.280776 + 0.486319i) q^{10} +(0.780776 - 1.35234i) q^{11} +1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.280776 + 0.486319i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(2.34233 + 4.05703i) q^{19} +(-0.280776 - 0.486319i) q^{20} -1.00000 q^{21} +(0.780776 + 1.35234i) q^{22} +(0.438447 - 0.759413i) q^{23} +(-0.500000 + 0.866025i) q^{24} -4.68466 q^{25} +(-2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.280776 - 0.486319i) q^{30} -3.12311 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.780776 + 1.35234i) q^{33} -5.00000 q^{34} +(0.280776 + 0.486319i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.40388 + 9.35980i) q^{37} -4.68466 q^{38} +(-2.84233 - 2.21837i) q^{39} +0.561553 q^{40} +(2.06155 - 3.57071i) q^{41} +(0.500000 - 0.866025i) q^{42} +(5.56155 + 9.63289i) q^{43} -1.56155 q^{44} +(-0.280776 - 0.486319i) q^{45} +(0.438447 + 0.759413i) q^{46} +4.68466 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.34233 - 4.05703i) q^{50} -5.00000 q^{51} +(3.34233 - 1.35234i) q^{52} -12.1231 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.438447 - 0.759413i) q^{55} +(0.500000 + 0.866025i) q^{56} -4.68466 q^{57} +(0.500000 + 0.866025i) q^{58} +(-2.43845 - 4.22351i) q^{59} +0.561553 q^{60} +(0.500000 + 0.866025i) q^{61} +(1.56155 - 2.70469i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-0.280776 + 2.00514i) q^{65} -1.56155 q^{66} +(3.56155 - 6.16879i) q^{67} +(2.50000 - 4.33013i) q^{68} +(0.438447 + 0.759413i) q^{69} -0.561553 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.56155 q^{73} +(-5.40388 - 9.35980i) q^{74} +(2.34233 - 4.05703i) q^{75} +(2.34233 - 4.05703i) q^{76} +1.56155 q^{77} +(3.34233 - 1.35234i) q^{78} +5.56155 q^{79} +(-0.280776 + 0.486319i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.06155 + 3.57071i) q^{82} +6.24621 q^{83} +(0.500000 + 0.866025i) q^{84} +(1.40388 + 2.43160i) q^{85} -11.1231 q^{86} +(0.500000 + 0.866025i) q^{87} +(0.780776 - 1.35234i) q^{88} +(-1.34233 + 2.32498i) q^{89} +0.561553 q^{90} +(-3.34233 + 1.35234i) q^{91} -0.876894 q^{92} +(1.56155 - 2.70469i) q^{93} +(-2.34233 + 4.05703i) q^{94} +(1.31534 + 2.27824i) q^{95} +1.00000 q^{96} +(2.12311 + 3.67733i) q^{97} +(-0.500000 - 0.866025i) q^{98} -1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 3 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 4 q^{14} + 3 q^{15} - 2 q^{16} + 10 q^{17} + 4 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} - q^{22} + 10 q^{23} - 2 q^{24} + 6 q^{25} + q^{26} + 4 q^{27} + 2 q^{28} + 2 q^{29} + 3 q^{30} + 4 q^{31} - 2 q^{32} - q^{33} - 20 q^{34} - 3 q^{35} - 2 q^{36} - q^{37} + 6 q^{38} + q^{39} - 6 q^{40} + 2 q^{42} + 14 q^{43} + 2 q^{44} + 3 q^{45} + 10 q^{46} - 6 q^{47} - 2 q^{48} - 2 q^{49} - 3 q^{50} - 20 q^{51} + q^{52} - 32 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 6 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 2 q^{61} - 2 q^{62} + 2 q^{63} + 4 q^{64} + 3 q^{65} + 2 q^{66} + 6 q^{67} + 10 q^{68} + 10 q^{69} + 6 q^{70} + 8 q^{71} - 2 q^{72} - 18 q^{73} - q^{74} - 3 q^{75} - 3 q^{76} - 2 q^{77} + q^{78} + 14 q^{79} + 3 q^{80} - 2 q^{81} - 8 q^{83} + 2 q^{84} - 15 q^{85} - 28 q^{86} + 2 q^{87} - q^{88} + 7 q^{89} - 6 q^{90} - q^{91} - 20 q^{92} - 2 q^{93} + 3 q^{94} + 30 q^{95} + 4 q^{96} - 8 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 3 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 3 * q^15 - 2 * q^16 + 10 * q^17 + 4 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 - q^22 + 10 * q^23 - 2 * q^24 + 6 * q^25 + q^26 + 4 * q^27 + 2 * q^28 + 2 * q^29 + 3 * q^30 + 4 * q^31 - 2 * q^32 - q^33 - 20 * q^34 - 3 * q^35 - 2 * q^36 - q^37 + 6 * q^38 + q^39 - 6 * q^40 + 2 * q^42 + 14 * q^43 + 2 * q^44 + 3 * q^45 + 10 * q^46 - 6 * q^47 - 2 * q^48 - 2 * q^49 - 3 * q^50 - 20 * q^51 + q^52 - 32 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 6 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 2 * q^61 - 2 * q^62 + 2 * q^63 + 4 * q^64 + 3 * q^65 + 2 * q^66 + 6 * q^67 + 10 * q^68 + 10 * q^69 + 6 * q^70 + 8 * q^71 - 2 * q^72 - 18 * q^73 - q^74 - 3 * q^75 - 3 * q^76 - 2 * q^77 + q^78 + 14 * q^79 + 3 * q^80 - 2 * q^81 - 8 * q^83 + 2 * q^84 - 15 * q^85 - 28 * q^86 + 2 * q^87 - q^88 + 7 * q^89 - 6 * q^90 - q^91 - 20 * q^92 - 2 * q^93 + 3 * q^94 + 30 * q^95 + 4 * q^96 - 8 * q^97 - 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.561553			0.251134			0.125567	−	0.992085i	$-0.459925\pi$
$5$	0.561553			0.251134			0.125567	+	0.992085i	$0.459925\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.280776	+	0.486319i	−0.0887893	+	0.153788i
$11$	0.780776	−	1.35234i	0.235413	−	0.407747i	−0.723980	−	0.689821i	$-0.757689\pi$
$11$	0.780776	−	1.35234i	0.235413	−	0.407747i	0.959393	+	0.282074i	$0.0910224\pi$
$12$	1.00000			0.288675
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$14$	−1.00000			−0.267261
$15$	−0.280776	+	0.486319i	−0.0724962	+	0.125567i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$	1.00000			0.235702
$19$	2.34233	+	4.05703i	0.537367	+	0.930747i	0.999045	+	0.0436994i	$0.0139144\pi$
$19$	2.34233	+	4.05703i	0.537367	+	0.930747i	−0.461678	+	0.887048i	$0.652752\pi$
$20$	−0.280776	−	0.486319i	−0.0627835	−	0.108744i
$21$	−1.00000			−0.218218
$22$	0.780776	+	1.35234i	0.166462	+	0.288321i
$23$	0.438447	−	0.759413i	0.0914226	−	0.158349i	−0.816687	−	0.577080i	$-0.804192\pi$
$23$	0.438447	−	0.759413i	0.0914226	−	0.158349i	0.908110	+	0.418732i	$0.137525\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.68466			−0.936932
$26$	−2.84233	−	2.21837i	−0.557427	−	0.435058i
$27$	1.00000			0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	−0.280776	−	0.486319i	−0.0512625	−	0.0887893i
$31$	−3.12311			−0.560926			−0.280463	−	0.959865i	$-0.590488\pi$
$31$	−3.12311			−0.560926			−0.280463	+	0.959865i	$0.590488\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.780776	+	1.35234i	0.135916	+	0.235413i
$34$	−5.00000			−0.857493
$35$	0.280776	+	0.486319i	0.0474599	+	0.0822029i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.40388	+	9.35980i	−0.888393	+	1.53874i	−0.0466177	+	0.998913i	$0.514844\pi$
$37$	−5.40388	+	9.35980i	−0.888393	+	1.53874i	−0.841775	+	0.539829i	$0.818489\pi$
$38$	−4.68466			−0.759952
$39$	−2.84233	−	2.21837i	−0.455137	−	0.355223i
$40$	0.561553			0.0887893
$41$	2.06155	−	3.57071i	0.321960	−	0.557652i	−0.658932	−	0.752202i	$-0.728992\pi$
$41$	2.06155	−	3.57071i	0.321960	−	0.557652i	0.980892	+	0.194551i	$0.0623249\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	5.56155	+	9.63289i	0.848129	+	1.46900i	0.882876	+	0.469606i	$0.155604\pi$
$43$	5.56155	+	9.63289i	0.848129	+	1.46900i	−0.0347472	+	0.999396i	$0.511063\pi$
$44$	−1.56155			−0.235413
$45$	−0.280776	−	0.486319i	−0.0418557	−	0.0724962i
$46$	0.438447	+	0.759413i	0.0646455	+	0.111969i
$47$	4.68466			0.683328			0.341664	−	0.939822i	$-0.389010\pi$
$47$	4.68466			0.683328			0.341664	+	0.939822i	$0.389010\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.34233	−	4.05703i	0.331255	−	0.573751i
$51$	−5.00000			−0.700140
$52$	3.34233	−	1.35234i	0.463498	−	0.187536i
$53$	−12.1231			−1.66524			−0.832618	−	0.553847i	$-0.813159\pi$
$53$	−12.1231			−1.66524			−0.832618	+	0.553847i	$0.813159\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.438447	−	0.759413i	0.0591202	−	0.102399i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−4.68466			−0.620498
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	−2.43845	−	4.22351i	−0.317459	−	0.549855i	0.662498	−	0.749063i	$-0.269496\pi$
$59$	−2.43845	−	4.22351i	−0.317459	−	0.549855i	−0.979957	+	0.199209i	$0.936163\pi$
$60$	0.561553			0.0724962
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	1.56155	−	2.70469i	0.198317	−	0.343496i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	−0.280776	+	2.00514i	−0.0348260	+	0.248708i
$66$	−1.56155			−0.192214
$67$	3.56155	−	6.16879i	0.435113	−	0.753638i	−0.562192	−	0.827007i	$-0.690042\pi$
$67$	3.56155	−	6.16879i	0.435113	−	0.753638i	0.997305	+	0.0733691i	$0.0233751\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$	0.438447	+	0.759413i	0.0527828	+	0.0914226i
$70$	−0.561553			−0.0671184
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	0.959955	−	0.280155i	$-0.0903858\pi$
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	−0.722599	+	0.691268i	$0.757052\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−6.56155			−0.767972			−0.383986	−	0.923339i	$-0.625449\pi$
$73$	−6.56155			−0.767972			−0.383986	+	0.923339i	$0.625449\pi$
$74$	−5.40388	−	9.35980i	−0.628189	−	1.08805i
$75$	2.34233	−	4.05703i	0.270469	−	0.468466i
$76$	2.34233	−	4.05703i	0.268684	−	0.465374i
$77$	1.56155			0.177955
$78$	3.34233	−	1.35234i	0.378444	−	0.153123i
$79$	5.56155			0.625724			0.312862	−	0.949799i	$-0.398712\pi$
$79$	5.56155			0.625724			0.312862	+	0.949799i	$0.398712\pi$
$80$	−0.280776	+	0.486319i	−0.0313918	+	0.0543721i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.06155	+	3.57071i	0.227660	+	0.394319i
$83$	6.24621			0.685611			0.342805	−	0.939406i	$-0.388623\pi$
$83$	6.24621			0.685611			0.342805	+	0.939406i	$0.388623\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	1.40388	+	2.43160i	0.152272	+	0.263744i
$86$	−11.1231			−1.19944
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	0.780776	−	1.35234i	0.0832310	−	0.144160i
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	−0.928357	−	0.371689i	$-0.878779\pi$
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	0.786071	+	0.618137i	$0.212112\pi$
$90$	0.561553			0.0591929
$91$	−3.34233	+	1.35234i	−0.350371	+	0.141764i
$92$	−0.876894			−0.0914226
$93$	1.56155	−	2.70469i	0.161925	−	0.280463i
$94$	−2.34233	+	4.05703i	−0.241593	+	0.418451i
$95$	1.31534	+	2.27824i	0.134951	+	0.233742i
$96$	1.00000			0.102062
$97$	2.12311	+	3.67733i	0.215569	+	0.373376i	0.953448	−	0.301556i	$-0.0975061\pi$
$97$	2.12311	+	3.67733i	0.215569	+	0.373376i	−0.737880	+	0.674932i	$0.764173\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	−1.56155			−0.156942
$100$	2.34233	+	4.05703i	0.234233	+	0.405703i
$101$	7.71922	−	13.3701i	0.768091	−	1.33037i	−0.170505	−	0.985357i	$-0.554540\pi$
$101$	7.71922	−	13.3701i	0.768091	−	1.33037i	0.938597	−	0.345017i	$-0.112127\pi$
$102$	2.50000	−	4.33013i	0.247537	−	0.428746i
$103$	13.3693			1.31732			0.658659	−	0.752442i	$-0.271124\pi$
$103$	13.3693			1.31732			0.658659	+	0.752442i	$0.271124\pi$
$104$	−0.500000	+	3.57071i	−0.0490290	+	0.350137i
$105$	−0.561553			−0.0548019
$106$	6.06155	−	10.4989i	0.588750	−	1.01975i
$107$	6.78078	−	11.7446i	0.655522	−	1.13540i	−0.326240	−	0.945287i	$-0.605782\pi$
$107$	6.78078	−	11.7446i	0.655522	−	1.13540i	0.981763	−	0.190111i	$-0.0608848\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.12311			0.873835			0.436918	−	0.899502i	$-0.356070\pi$
$109$	9.12311			0.873835			0.436918	+	0.899502i	$0.356070\pi$
$110$	0.438447	+	0.759413i	0.0418043	+	0.0724072i
$111$	−5.40388	−	9.35980i	−0.512914	−	0.888393i
$112$	−1.00000			−0.0944911
$113$	5.96543	+	10.3324i	0.561181	+	0.971994i	0.997394	+	0.0721503i	$0.0229861\pi$
$113$	5.96543	+	10.3324i	0.561181	+	0.971994i	−0.436213	+	0.899844i	$0.643681\pi$
$114$	2.34233	−	4.05703i	0.219379	−	0.379976i
$115$	0.246211	−	0.426450i	0.0229593	−	0.0397667i
$116$	−1.00000			−0.0928477
$117$	3.34233	−	1.35234i	0.308998	−	0.125024i
$118$	4.87689			0.448955
$119$	−2.50000	+	4.33013i	−0.229175	+	0.396942i
$120$	−0.280776	+	0.486319i	−0.0256313	+	0.0443946i
$121$	4.28078	+	7.41452i	0.389161	+	0.674047i
$122$	−1.00000			−0.0905357
$123$	2.06155	+	3.57071i	0.185884	+	0.321960i
$124$	1.56155	+	2.70469i	0.140232	+	0.242888i
$125$	−5.43845			−0.486430
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	7.12311	−	12.3376i	0.632073	−	1.09478i	−0.355054	−	0.934846i	$-0.615537\pi$
$127$	7.12311	−	12.3376i	0.632073	−	1.09478i	0.987127	−	0.159937i	$-0.0511292\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−11.1231			−0.979335
$130$	−1.59612	−	1.24573i	−0.139989	−	0.109258i
$131$	16.4924			1.44095			0.720475	−	0.693481i	$-0.243924\pi$
$131$	16.4924			1.44095			0.720475	+	0.693481i	$0.243924\pi$
$132$	0.780776	−	1.35234i	0.0679579	−	0.117706i
$133$	−2.34233	+	4.05703i	−0.203106	+	0.351789i
$134$	3.56155	+	6.16879i	0.307671	+	0.532902i
$135$	0.561553			0.0483308
$136$	2.50000	+	4.33013i	0.214373	+	0.371305i
$137$	−7.40388	−	12.8239i	−0.632556	−	1.09562i	−0.987027	−	0.160553i	$-0.948672\pi$
$137$	−7.40388	−	12.8239i	−0.632556	−	1.09562i	0.354471	−	0.935067i	$-0.384661\pi$
$138$	−0.876894			−0.0746462
$139$	−2.34233	−	4.05703i	−0.198674	−	0.344113i	0.749425	−	0.662089i	$-0.230330\pi$
$139$	−2.34233	−	4.05703i	−0.198674	−	0.344113i	−0.948099	+	0.317976i	$0.896997\pi$
$140$	0.280776	−	0.486319i	0.0237299	−	0.0411015i
$141$	−2.34233	+	4.05703i	−0.197260	+	0.341664i
$142$	−4.00000			−0.335673
$143$	4.43845	+	3.46410i	0.371162	+	0.289683i
$144$	1.00000			0.0833333
$145$	0.280776	−	0.486319i	0.0233172	−	0.0403866i
$146$	3.28078	−	5.68247i	0.271519	−	0.470285i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	10.8078			0.888393
$149$	−1.40388	−	2.43160i	−0.115010	−	0.199204i	0.802773	−	0.596284i	$-0.203357\pi$
$149$	−1.40388	−	2.43160i	−0.115010	−	0.199204i	−0.917784	+	0.397080i	$0.870024\pi$
$150$	2.34233	+	4.05703i	0.191250	+	0.331255i
$151$	−21.5616			−1.75465			−0.877327	−	0.479893i	$-0.840676\pi$
$151$	−21.5616			−1.75465			−0.877327	+	0.479893i	$0.840676\pi$
$152$	2.34233	+	4.05703i	0.189988	+	0.329069i
$153$	2.50000	−	4.33013i	0.202113	−	0.350070i
$154$	−0.780776	+	1.35234i	−0.0629168	+	0.108975i
$155$	−1.75379			−0.140868
$156$	−0.500000	+	3.57071i	−0.0400320	+	0.285886i
$157$	14.8078			1.18179			0.590894	−	0.806749i	$-0.298775\pi$
$157$	14.8078			1.18179			0.590894	+	0.806749i	$0.298775\pi$
$158$	−2.78078	+	4.81645i	−0.221227	+	0.383176i
$159$	6.06155	−	10.4989i	0.480712	−	0.832618i
$160$	−0.280776	−	0.486319i	−0.0221973	−	0.0384469i
$161$	0.876894			0.0691090
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−3.56155	−	6.16879i	−0.278962	−	0.483177i	0.692165	−	0.721739i	$-0.256657\pi$
$163$	−3.56155	−	6.16879i	−0.278962	−	0.483177i	−0.971127	+	0.238563i	$0.923324\pi$
$164$	−4.12311			−0.321960
$165$	0.438447	+	0.759413i	0.0341331	+	0.0591202i
$166$	−3.12311	+	5.40938i	−0.242400	+	0.419849i
$167$	6.24621	−	10.8188i	0.483346	−	0.837180i	−0.516471	−	0.856305i	$-0.672755\pi$
$167$	6.24621	−	10.8188i	0.483346	−	0.837180i	0.999817	+	0.0191244i	$0.00608786\pi$
$168$	−1.00000			−0.0771517
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	−2.80776			−0.215346
$171$	2.34233	−	4.05703i	0.179122	−	0.310249i
$172$	5.56155	−	9.63289i	0.424064	−	0.734501i
$173$	6.56155	+	11.3649i	0.498866	+	0.864061i	0.999999	−	0.00130937i	$-0.000416786\pi$
$173$	6.56155	+	11.3649i	0.498866	+	0.864061i	−0.501134	+	0.865370i	$0.667083\pi$
$174$	−1.00000			−0.0758098
$175$	−2.34233	−	4.05703i	−0.177063	−	0.306683i
$176$	0.780776	+	1.35234i	0.0588532	+	0.101937i
$177$	4.87689			0.366570
$178$	−1.34233	−	2.32498i	−0.100612	−	0.174265i
$179$	−8.24621	+	14.2829i	−0.616351	+	1.06755i	0.373795	+	0.927511i	$0.378056\pi$
$179$	−8.24621	+	14.2829i	−0.616351	+	1.06755i	−0.990146	+	0.140040i	$0.955277\pi$
$180$	−0.280776	+	0.486319i	−0.0209278	+	0.0362481i
$181$	−3.24621			−0.241289			−0.120644	−	0.992696i	$-0.538496\pi$
$181$	−3.24621			−0.241289			−0.120644	+	0.992696i	$0.538496\pi$
$182$	0.500000	−	3.57071i	0.0370625	−	0.264679i
$183$	−1.00000			−0.0739221
$184$	0.438447	−	0.759413i	0.0323228	−	0.0559847i
$185$	−3.03457	+	5.25602i	−0.223106	+	0.386430i
$186$	1.56155	+	2.70469i	0.114499	+	0.198317i
$187$	7.80776			0.570960
$188$	−2.34233	−	4.05703i	−0.170832	−	0.295890i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−2.63068			−0.190850
$191$	−11.1231	−	19.2658i	−0.804840	−	1.39402i	−0.916399	−	0.400265i	$-0.868918\pi$
$191$	−11.1231	−	19.2658i	−0.804840	−	1.39402i	0.111560	−	0.993758i	$-0.464415\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.18466	+	3.78394i	−0.157255	+	0.272374i	−0.933878	−	0.357592i	$-0.883598\pi$
$193$	−2.18466	+	3.78394i	−0.157255	+	0.272374i	0.776623	+	0.629966i	$0.216931\pi$
$194$	−4.24621			−0.304860
$195$	−1.59612	−	1.24573i	−0.114300	−	0.0892087i
$196$	1.00000			0.0714286
$197$	−1.78078	+	3.08440i	−0.126875	+	0.219754i	−0.922464	−	0.386082i	$-0.873828\pi$
$197$	−1.78078	+	3.08440i	−0.126875	+	0.219754i	0.795589	+	0.605836i	$0.207161\pi$
$198$	0.780776	−	1.35234i	0.0554874	−	0.0961069i
$199$	−11.8078	−	20.4516i	−0.837030	−	1.44978i	−0.892367	−	0.451311i	$-0.850956\pi$
$199$	−11.8078	−	20.4516i	−0.837030	−	1.44978i	0.0553365	−	0.998468i	$-0.482377\pi$
$200$	−4.68466			−0.331255
$201$	3.56155	+	6.16879i	0.251213	+	0.435113i
$202$	7.71922	+	13.3701i	0.543123	+	0.940716i
$203$	1.00000			0.0701862
$204$	2.50000	+	4.33013i	0.175035	+	0.303170i
$205$	1.15767	−	2.00514i	0.0808552	−	0.140045i
$206$	−6.68466	+	11.5782i	−0.465742	+	0.806689i
$207$	−0.876894			−0.0609484
$208$	−2.84233	−	2.21837i	−0.197080	−	0.153816i
$209$	7.31534			0.506013
$210$	0.280776	−	0.486319i	0.0193754	−	0.0335592i
$211$	5.56155	−	9.63289i	0.382873	−	0.663156i	−0.608599	−	0.793478i	$-0.708268\pi$
$211$	5.56155	−	9.63289i	0.382873	−	0.663156i	0.991472	+	0.130323i	$0.0416013\pi$
$212$	6.06155	+	10.4989i	0.416309	+	0.721069i
$213$	−4.00000			−0.274075
$214$	6.78078	+	11.7446i	0.463524	+	0.802848i
$215$	3.12311	+	5.40938i	0.212994	+	0.368916i
$216$	1.00000			0.0680414
$217$	−1.56155	−	2.70469i	−0.106005	−	0.183606i
$218$	−4.56155	+	7.90084i	−0.308947	+	0.535112i
$219$	3.28078	−	5.68247i	0.221694	−	0.383986i
$220$	−0.876894			−0.0591202
$221$	−16.7116	+	6.76172i	−1.12415	+	0.454843i
$222$	10.8078			0.725370
$223$	−8.24621	+	14.2829i	−0.552207	+	0.956451i	0.445908	+	0.895079i	$0.352881\pi$
$223$	−8.24621	+	14.2829i	−0.552207	+	0.956451i	−0.998115	+	0.0613719i	$0.980452\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	2.34233	+	4.05703i	0.156155	+	0.270469i
$226$	−11.9309			−0.793630
$227$	−2.43845	−	4.22351i	−0.161845	−	0.280324i	0.773685	−	0.633570i	$-0.218411\pi$
$227$	−2.43845	−	4.22351i	−0.161845	−	0.280324i	−0.935531	+	0.353246i	$0.885078\pi$
$228$	2.34233	+	4.05703i	0.155125	+	0.268684i
$229$	2.19224			0.144867			0.0724335	−	0.997373i	$-0.476923\pi$
$229$	2.19224			0.144867			0.0724335	+	0.997373i	$0.476923\pi$
$230$	0.246211	+	0.426450i	0.0162347	+	0.0281193i
$231$	−0.780776	+	1.35234i	−0.0513713	+	0.0889777i
$232$	0.500000	−	0.866025i	0.0328266	−	0.0568574i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	−0.500000	+	3.57071i	−0.0326860	+	0.233425i
$235$	2.63068			0.171607
$236$	−2.43845	+	4.22351i	−0.158729	+	0.274927i
$237$	−2.78078	+	4.81645i	−0.180631	+	0.312862i
$238$	−2.50000	−	4.33013i	−0.162051	−	0.280680i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	−0.280776	−	0.486319i	−0.0181240	−	0.0313918i
$241$	−11.8423	−	20.5115i	−0.762831	−	1.32126i	−0.941385	−	0.337333i	$-0.890475\pi$
$241$	−11.8423	−	20.5115i	−0.762831	−	1.32126i	0.178554	−	0.983930i	$-0.442858\pi$
$242$	−8.56155			−0.550357
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	−0.280776	+	0.486319i	−0.0179381	+	0.0310698i
$246$	−4.12311			−0.262880
$247$	−15.6577	+	6.33527i	−0.996274	+	0.403104i
$248$	−3.12311			−0.198317
$249$	−3.12311	+	5.40938i	−0.197919	+	0.342805i
$250$	2.71922	−	4.70983i	0.171979	−	0.297876i
$251$	12.2462	+	21.2111i	0.772974	+	1.33883i	0.935926	+	0.352196i	$0.114565\pi$
$251$	12.2462	+	21.2111i	0.772974	+	1.33883i	−0.162952	+	0.986634i	$0.552102\pi$
$252$	−1.00000			−0.0629941
$253$	−0.684658	−	1.18586i	−0.0430441	−	0.0745546i
$254$	7.12311	+	12.3376i	0.446943	+	0.774129i
$255$	−2.80776			−0.175829
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.6231	−	27.0600i	0.974543	−	1.68796i	0.293106	−	0.956080i	$-0.405311\pi$
$257$	15.6231	−	27.0600i	0.974543	−	1.68796i	0.681436	−	0.731877i	$-0.261356\pi$
$258$	5.56155	−	9.63289i	0.346247	−	0.599718i
$259$	−10.8078			−0.671562
$260$	1.87689	−	0.759413i	0.116400	−	0.0470968i
$261$	−1.00000			−0.0618984
$262$	−8.24621	+	14.2829i	−0.509453	+	0.882398i
$263$	−6.24621	+	10.8188i	−0.385158	+	0.667113i	−0.991791	−	0.127869i	$-0.959186\pi$
$263$	−6.24621	+	10.8188i	−0.385158	+	0.667113i	0.606633	+	0.794982i	$0.292520\pi$
$264$	0.780776	+	1.35234i	0.0480535	+	0.0832310i
$265$	−6.80776			−0.418198
$266$	−2.34233	−	4.05703i	−0.143617	−	0.248753i
$267$	−1.34233	−	2.32498i	−0.0821492	−	0.142287i
$268$	−7.12311			−0.435113
$269$	6.56155	+	11.3649i	0.400065	+	0.692933i	0.993733	−	0.111777i	$-0.0356542\pi$
$269$	6.56155	+	11.3649i	0.400065	+	0.692933i	−0.593668	+	0.804710i	$0.702321\pi$
$270$	−0.280776	+	0.486319i	−0.0170875	+	0.0295964i
$271$	−2.43845	+	4.22351i	−0.148125	+	0.256560i	−0.930535	−	0.366204i	$-0.880657\pi$
$271$	−2.43845	+	4.22351i	−0.148125	+	0.256560i	0.782409	+	0.622764i	$0.213990\pi$
$272$	−5.00000			−0.303170
$273$	0.500000	−	3.57071i	0.0302614	−	0.216109i
$274$	14.8078			0.894570
$275$	−3.65767	+	6.33527i	−0.220566	+	0.382031i
$276$	0.438447	−	0.759413i	0.0263914	−	0.0457113i
$277$	−0.280776	−	0.486319i	−0.0168702	−	0.0292201i	0.857467	−	0.514539i	$-0.172037\pi$
$277$	−0.280776	−	0.486319i	−0.0168702	−	0.0292201i	−0.874337	+	0.485319i	$0.838704\pi$
$278$	4.68466			0.280967
$279$	1.56155	+	2.70469i	0.0934877	+	0.161925i
$280$	0.280776	+	0.486319i	0.0167796	+	0.0290631i
$281$	−12.8078			−0.764047			−0.382024	−	0.924153i	$-0.624773\pi$
$281$	−12.8078			−0.764047			−0.382024	+	0.924153i	$0.624773\pi$
$282$	−2.34233	−	4.05703i	−0.139484	−	0.241593i
$283$	12.2462	−	21.2111i	0.727962	−	1.26087i	−0.229782	−	0.973242i	$-0.573801\pi$
$283$	12.2462	−	21.2111i	0.727962	−	1.26087i	0.957743	−	0.287624i	$-0.0928655\pi$
$284$	2.00000	−	3.46410i	0.118678	−	0.205557i
$285$	−2.63068			−0.155828
$286$	−5.21922	+	2.11176i	−0.308619	+	0.124871i
$287$	4.12311			0.243379
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	0.280776	+	0.486319i	0.0164878	+	0.0285576i
$291$	−4.24621			−0.248917
$292$	3.28078	+	5.68247i	0.191993	+	0.332541i
$293$	−3.84233	−	6.65511i	−0.224471	−	0.388796i	0.731689	−	0.681638i	$-0.238732\pi$
$293$	−3.84233	−	6.65511i	−0.224471	−	0.388796i	−0.956161	+	0.292843i	$0.905399\pi$
$294$	1.00000			0.0583212
$295$	−1.36932	−	2.37173i	−0.0797247	−	0.138087i
$296$	−5.40388	+	9.35980i	−0.314094	+	0.544027i
$297$	0.780776	−	1.35234i	0.0453052	−	0.0784710i
$298$	2.80776			0.162649
$299$	2.49242	+	1.94528i	0.144141	+	0.112498i
$300$	−4.68466			−0.270469
$301$	−5.56155	+	9.63289i	−0.320563	+	0.555231i
$302$	10.7808	−	18.6729i	0.620364	−	1.07450i
$303$	7.71922	+	13.3701i	0.443458	+	0.768091i
$304$	−4.68466			−0.268684
$305$	0.280776	+	0.486319i	0.0160772	+	0.0278465i
$306$	2.50000	+	4.33013i	0.142915	+	0.247537i
$307$	−5.06913			−0.289311			−0.144655	−	0.989482i	$-0.546207\pi$
$307$	−5.06913			−0.289311			−0.144655	+	0.989482i	$0.546207\pi$
$308$	−0.780776	−	1.35234i	−0.0444889	−	0.0770570i
$309$	−6.68466	+	11.5782i	−0.380277	+	0.658659i
$310$	0.876894	−	1.51883i	0.0498043	−	0.0862635i
$311$	18.4384			1.04555			0.522774	−	0.852471i	$-0.324897\pi$
$311$	18.4384			1.04555			0.522774	+	0.852471i	$0.324897\pi$
$312$	−2.84233	−	2.21837i	−0.160915	−	0.125590i
$313$	−13.6155			−0.769595			−0.384798	−	0.923001i	$-0.625729\pi$
$313$	−13.6155			−0.769595			−0.384798	+	0.923001i	$0.625729\pi$
$314$	−7.40388	+	12.8239i	−0.417825	+	0.723695i
$315$	0.280776	−	0.486319i	0.0158200	−	0.0274010i
$316$	−2.78078	−	4.81645i	−0.156431	−	0.270946i
$317$	−7.43845			−0.417785			−0.208892	−	0.977939i	$-0.566986\pi$
$317$	−7.43845			−0.417785			−0.208892	+	0.977939i	$0.566986\pi$
$318$	6.06155	+	10.4989i	0.339915	+	0.588750i
$319$	−0.780776	−	1.35234i	−0.0437151	−	0.0757168i
$320$	0.561553			0.0313918
$321$	6.78078	+	11.7446i	0.378466	+	0.655522i
$322$	−0.438447	+	0.759413i	−0.0244337	+	0.0423204i
$323$	−11.7116	+	20.2852i	−0.651653	+	1.12870i
$324$	1.00000			0.0555556
$325$	2.34233	−	16.7276i	0.129929	−	0.927879i
$326$	7.12311			0.394512
$327$	−4.56155	+	7.90084i	−0.252254	+	0.436918i
$328$	2.06155	−	3.57071i	0.113830	−	0.197160i
$329$	2.34233	+	4.05703i	0.129137	+	0.223671i
$330$	−0.876894			−0.0482714
$331$	5.31534	+	9.20644i	0.292158	+	0.506032i	0.974320	−	0.225169i	$-0.0722935\pi$
$331$	5.31534	+	9.20644i	0.292158	+	0.506032i	−0.682162	+	0.731201i	$0.738960\pi$
$332$	−3.12311	−	5.40938i	−0.171403	−	0.296878i
$333$	10.8078			0.592262
$334$	6.24621	+	10.8188i	0.341777	+	0.591976i
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	3.49242			0.190244			0.0951222	−	0.995466i	$-0.469676\pi$
$337$	3.49242			0.190244			0.0951222	+	0.995466i	$0.469676\pi$
$338$	9.34233	−	9.03996i	0.508156	−	0.491709i
$339$	−11.9309			−0.647996
$340$	1.40388	−	2.43160i	0.0761362	−	0.131872i
$341$	−2.43845	+	4.22351i	−0.132049	+	0.228716i
$342$	2.34233	+	4.05703i	0.126659	+	0.219379i
$343$	−1.00000			−0.0539949
$344$	5.56155	+	9.63289i	0.299859	+	0.519371i
$345$	0.246211	+	0.426450i	0.0132556	+	0.0229593i
$346$	−13.1231			−0.705503
$347$	6.34233	+	10.9852i	0.340474	+	0.589718i	0.984521	−	0.175268i	$-0.0560791\pi$
$347$	6.34233	+	10.9852i	0.340474	+	0.589718i	−0.644047	+	0.764986i	$0.722746\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	−13.2462	+	22.9431i	−0.709053	+	1.22812i	0.256155	+	0.966636i	$0.417544\pi$
$349$	−13.2462	+	22.9431i	−0.709053	+	1.22812i	−0.965209	+	0.261481i	$0.915789\pi$
$350$	4.68466			0.250406
$351$	−0.500000	+	3.57071i	−0.0266880	+	0.190591i
$352$	−1.56155			−0.0832310
$353$	−5.40388	+	9.35980i	−0.287620	+	0.498172i	−0.973241	−	0.229786i	$-0.926197\pi$
$353$	−5.40388	+	9.35980i	−0.287620	+	0.498172i	0.685621	+	0.727958i	$0.259531\pi$
$354$	−2.43845	+	4.22351i	−0.129602	+	0.224477i
$355$	1.12311	+	1.94528i	0.0596083	+	0.103245i
$356$	2.68466			0.142287
$357$	−2.50000	−	4.33013i	−0.132314	−	0.229175i
$358$	−8.24621	−	14.2829i	−0.435826	−	0.754872i
$359$	−29.3693			−1.55005			−0.775027	−	0.631929i	$-0.782264\pi$
$359$	−29.3693			−1.55005			−0.775027	+	0.631929i	$0.782264\pi$
$360$	−0.280776	−	0.486319i	−0.0147982	−	0.0256313i
$361$	−1.47301	+	2.55133i	−0.0775270	+	0.134281i
$362$	1.62311	−	2.81130i	0.0853085	−	0.147759i
$363$	−8.56155			−0.449365
$364$	2.84233	+	2.21837i	0.148979	+	0.116274i
$365$	−3.68466			−0.192864
$366$	0.500000	−	0.866025i	0.0261354	−	0.0452679i
$367$	6.68466	−	11.5782i	0.348936	−	0.604375i	−0.637124	−	0.770761i	$-0.719876\pi$
$367$	6.68466	−	11.5782i	0.348936	−	0.604375i	0.986061	+	0.166385i	$0.0532096\pi$
$368$	0.438447	+	0.759413i	0.0228556	+	0.0395871i
$369$	−4.12311			−0.214640
$370$	−3.03457	−	5.25602i	−0.157760	−	0.273248i
$371$	−6.06155	−	10.4989i	−0.314700	−	0.545077i
$372$	−3.12311			−0.161925
$373$	−8.71922	−	15.1021i	−0.451464	−	0.781959i	0.547013	−	0.837124i	$-0.315765\pi$
$373$	−8.71922	−	15.1021i	−0.451464	−	0.781959i	−0.998477	+	0.0551651i	$0.982431\pi$
$374$	−3.90388	+	6.76172i	−0.201865	+	0.349640i
$375$	2.71922	−	4.70983i	0.140420	−	0.243215i
$376$	4.68466			0.241593
$377$	2.84233	+	2.21837i	0.146387	+	0.114252i
$378$	−1.00000			−0.0514344
$379$	16.2462	−	28.1393i	0.834512	−	1.44542i	−0.0599155	−	0.998203i	$-0.519083\pi$
$379$	16.2462	−	28.1393i	0.834512	−	1.44542i	0.894427	−	0.447213i	$-0.147584\pi$
$380$	1.31534	−	2.27824i	0.0674756	−	0.116871i
$381$	7.12311	+	12.3376i	0.364928	+	0.632073i
$382$	22.2462			1.13822
$383$	−10.3423	−	17.9134i	−0.528468	−	0.915334i	−0.999449	−	0.0331905i	$-0.989433\pi$
$383$	−10.3423	−	17.9134i	−0.528468	−	0.915334i	0.470981	−	0.882144i	$-0.343900\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	0.876894			0.0446907
$386$	−2.18466	−	3.78394i	−0.111196	−	0.192597i
$387$	5.56155	−	9.63289i	0.282710	−	0.489667i
$388$	2.12311	−	3.67733i	0.107784	−	0.186688i
$389$	6.31534			0.320201			0.160100	−	0.987101i	$-0.448818\pi$
$389$	6.31534			0.320201			0.160100	+	0.987101i	$0.448818\pi$
$390$	1.87689	−	0.759413i	0.0950402	−	0.0384544i
$391$	4.38447			0.221732
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−8.24621	+	14.2829i	−0.415966	+	0.720475i
$394$	−1.78078	−	3.08440i	−0.0897142	−	0.155390i
$395$	3.12311			0.157140
$396$	0.780776	+	1.35234i	0.0392355	+	0.0679579i
$397$	5.34233	+	9.25319i	0.268124	+	0.464404i	0.968377	−	0.249490i	$-0.0802630\pi$
$397$	5.34233	+	9.25319i	0.268124	+	0.464404i	−0.700254	+	0.713894i	$0.746930\pi$
$398$	23.6155			1.18374
$399$	−2.34233	−	4.05703i	−0.117263	−	0.203106i
$400$	2.34233	−	4.05703i	0.117116	−	0.202852i
$401$	15.0885	−	26.1341i	0.753486	−	1.30508i	−0.192638	−	0.981270i	$-0.561704\pi$
$401$	15.0885	−	26.1341i	0.753486	−	1.30508i	0.946124	−	0.323806i	$-0.104962\pi$
$402$	−7.12311			−0.355268
$403$	1.56155	−	11.1517i	0.0777865	−	0.555507i
$404$	−15.4384			−0.768091
$405$	−0.280776	+	0.486319i	−0.0139519	+	0.0241654i
$406$	−0.500000	+	0.866025i	−0.0248146	+	0.0429801i
$407$	8.43845	+	14.6158i	0.418278	+	0.724479i
$408$	−5.00000			−0.247537
$409$	17.2808	+	29.9312i	0.854479	+	1.48000i	0.877127	+	0.480258i	$0.159457\pi$
$409$	17.2808	+	29.9312i	0.854479	+	1.48000i	−0.0226477	+	0.999744i	$0.507210\pi$
$410$	1.15767	+	2.00514i	0.0571733	+	0.0990270i
$411$	14.8078			0.730413
$412$	−6.68466	−	11.5782i	−0.329329	−	0.570415i
$413$	2.43845	−	4.22351i	0.119988	−	0.207826i
$414$	0.438447	−	0.759413i	0.0215485	−	0.0373231i
$415$	3.50758			0.172180
$416$	3.34233	−	1.35234i	0.163871	−	0.0663041i
$417$	4.68466			0.229409
$418$	−3.65767	+	6.33527i	−0.178903	+	0.309868i
$419$	13.3693	−	23.1563i	0.653134	−	1.13126i	−0.329224	−	0.944252i	$-0.606787\pi$
$419$	13.3693	−	23.1563i	0.653134	−	1.13126i	0.982358	−	0.187009i	$-0.0598795\pi$
$420$	0.280776	+	0.486319i	0.0137005	+	0.0237299i
$421$	12.5616			0.612213			0.306106	−	0.951997i	$-0.400974\pi$
$421$	12.5616			0.612213			0.306106	+	0.951997i	$0.400974\pi$
$422$	5.56155	+	9.63289i	0.270732	+	0.468922i
$423$	−2.34233	−	4.05703i	−0.113888	−	0.197260i
$424$	−12.1231			−0.588750
$425$	−11.7116	−	20.2852i	−0.568098	−	0.983975i
$426$	2.00000	−	3.46410i	0.0969003	−	0.167836i
$427$	−0.500000	+	0.866025i	−0.0241967	+	0.0419099i
$428$	−13.5616			−0.655522
$429$	−5.21922	+	2.11176i	−0.251986	+	0.101957i
$430$	−6.24621			−0.301219
$431$	−15.3693	+	26.6204i	−0.740314	+	1.28226i	0.212038	+	0.977261i	$0.431990\pi$
$431$	−15.3693	+	26.6204i	−0.740314	+	1.28226i	−0.952352	+	0.305000i	$0.901344\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	8.84233	+	15.3154i	0.424935	+	0.736009i	0.996414	−	0.0846072i	$-0.0269635\pi$
$433$	8.84233	+	15.3154i	0.424935	+	0.736009i	−0.571479	+	0.820617i	$0.693630\pi$
$434$	3.12311			0.149914
$435$	0.280776	+	0.486319i	0.0134622	+	0.0233172i
$436$	−4.56155	−	7.90084i	−0.218459	−	0.378382i
$437$	4.10795			0.196510
$438$	3.28078	+	5.68247i	0.156762	+	0.271519i
$439$	−2.24621	+	3.89055i	−0.107206	+	0.185686i	−0.914637	−	0.404275i	$-0.867524\pi$
$439$	−2.24621	+	3.89055i	−0.107206	+	0.185686i	0.807431	+	0.589961i	$0.200857\pi$
$440$	0.438447	−	0.759413i	0.0209021	−	0.0362036i
$441$	1.00000			0.0476190
$442$	2.50000	−	17.8536i	0.118913	−	0.849208i
$443$	27.4233			1.30292			0.651460	−	0.758683i	$-0.274157\pi$
$443$	27.4233			1.30292			0.651460	+	0.758683i	$0.274157\pi$
$444$	−5.40388	+	9.35980i	−0.256457	+	0.444196i
$445$	−0.753789	+	1.30560i	−0.0357330	+	0.0618914i
$446$	−8.24621	−	14.2829i	−0.390469	−	0.676313i
$447$	2.80776			0.132803
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	0.571660	−	0.820491i	$-0.306300\pi$
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	−0.996396	+	0.0848262i	$0.972967\pi$
$450$	−4.68466			−0.220837
$451$	−3.21922	−	5.57586i	−0.151587	−	0.262557i
$452$	5.96543	−	10.3324i	0.280590	−	0.485997i
$453$	10.7808	−	18.6729i	0.506525	−	0.877327i
$454$	4.87689			0.228884
$455$	−1.87689	+	0.759413i	−0.0879902	+	0.0356018i
$456$	−4.68466			−0.219379
$457$	12.8423	−	22.2436i	0.600739	−	1.04051i	−0.391971	−	0.919978i	$-0.628206\pi$
$457$	12.8423	−	22.2436i	0.600739	−	1.04051i	0.992709	−	0.120532i	$-0.0384602\pi$
$458$	−1.09612	+	1.89853i	−0.0512182	+	0.0887126i
$459$	2.50000	+	4.33013i	0.116690	+	0.202113i
$460$	−0.492423			−0.0229593
$461$	3.52699	+	6.10892i	0.164268	+	0.284521i	0.936395	−	0.350947i	$-0.114140\pi$
$461$	3.52699	+	6.10892i	0.164268	+	0.284521i	−0.772127	+	0.635468i	$0.780807\pi$
$462$	−0.780776	−	1.35234i	−0.0363250	−	0.0629168i
$463$	0.684658			0.0318188			0.0159094	−	0.999873i	$-0.494936\pi$
$463$	0.684658			0.0318188			0.0159094	+	0.999873i	$0.494936\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	0.876894	−	1.51883i	0.0406650	−	0.0704339i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$	−2.84233	−	2.21837i	−0.131387	−	0.102544i
$469$	7.12311			0.328914
$470$	−1.31534	+	2.27824i	−0.0606722	+	0.105087i
$471$	−7.40388	+	12.8239i	−0.341153	+	0.590894i
$472$	−2.43845	−	4.22351i	−0.112239	−	0.194403i
$473$	17.3693			0.798642
$474$	−2.78078	−	4.81645i	−0.127725	−	0.221227i
$475$	−10.9730	−	19.0058i	−0.503476	−	0.872047i
$476$	5.00000			0.229175
$477$	6.06155	+	10.4989i	0.277539	+	0.480712i
$478$	−2.00000	+	3.46410i	−0.0914779	+	0.158444i
$479$	−0.780776	+	1.35234i	−0.0356746	+	0.0617902i	−0.883311	−	0.468787i	$-0.844691\pi$
$479$	−0.780776	+	1.35234i	−0.0356746	+	0.0617902i	0.847637	+	0.530577i	$0.178025\pi$
$480$	0.561553			0.0256313
$481$	−30.7192	−	23.9756i	−1.40068	−	1.09319i
$482$	23.6847			1.07881
$483$	−0.438447	+	0.759413i	−0.0199500	+	0.0345545i
$484$	4.28078	−	7.41452i	0.194581	−	0.337024i
$485$	1.19224	+	2.06501i	0.0541366	+	0.0937674i
$486$	1.00000			0.0453609
$487$	−5.65767	−	9.79937i	−0.256374	−	0.444052i	0.708894	−	0.705315i	$-0.249194\pi$
$487$	−5.65767	−	9.79937i	−0.256374	−	0.444052i	−0.965268	+	0.261263i	$0.915861\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$	7.12311			0.322118
$490$	−0.280776	−	0.486319i	−0.0126842	−	0.0219697i
$491$	9.12311	−	15.8017i	0.411720	−	0.713120i	−0.583358	−	0.812215i	$-0.698262\pi$
$491$	9.12311	−	15.8017i	0.411720	−	0.713120i	0.995078	+	0.0990952i	$0.0315948\pi$
$492$	2.06155	−	3.57071i	0.0929420	−	0.160980i
$493$	5.00000			0.225189
$494$	2.34233	−	16.7276i	0.105386	−	0.752609i
$495$	−0.876894			−0.0394135
$496$	1.56155	−	2.70469i	0.0701158	−	0.121444i
$497$	−2.00000	+	3.46410i	−0.0897123	+	0.155386i
$498$	−3.12311	−	5.40938i	−0.139950	−	0.242400i
$499$	−2.63068			−0.117766			−0.0588828	−	0.998265i	$-0.518754\pi$
$499$	−2.63068			−0.117766			−0.0588828	+	0.998265i	$0.518754\pi$
$500$	2.71922	+	4.70983i	0.121607	+	0.210630i
$501$	6.24621	+	10.8188i	0.279060	+	0.483346i
$502$	−24.4924			−1.09315
$503$	6.24621	+	10.8188i	0.278505	+	0.482384i	0.971013	−	0.239025i	$-0.0768279\pi$
$503$	6.24621	+	10.8188i	0.278505	+	0.482384i	−0.692509	+	0.721410i	$0.743495\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	4.33475	−	7.50801i	0.192894	−	0.334102i
$506$	1.36932			0.0608736
$507$	9.34233	−	9.03996i	0.414907	−	0.401479i
$508$	−14.2462			−0.632073
$509$	−19.8423	+	34.3679i	−0.879496	+	1.52333i	−0.0276006	+	0.999619i	$0.508787\pi$
$509$	−19.8423	+	34.3679i	−0.879496	+	1.52333i	−0.851895	+	0.523712i	$0.824547\pi$
$510$	1.40388	−	2.43160i	0.0621649	−	0.107673i
$511$	−3.28078	−	5.68247i	−0.145133	−	0.251378i
$512$	1.00000			0.0441942
$513$	2.34233	+	4.05703i	0.103416	+	0.179122i
$514$	15.6231	+	27.0600i	0.689106	+	1.19357i
$515$	7.50758			0.330823
$516$	5.56155	+	9.63289i	0.244834	+	0.424064i
$517$	3.65767	−	6.33527i	0.160864	−	0.278625i
$518$	5.40388	−	9.35980i	0.237433	−	0.411246i
$519$	−13.1231			−0.576040
$520$	−0.280776	+	2.00514i	−0.0123129	+	0.0879314i
$521$	−17.0000			−0.744784			−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000			−0.744784			−0.372392	+	0.928076i	$0.621462\pi$
$522$	0.500000	−	0.866025i	0.0218844	−	0.0379049i
$523$	−17.9039	+	31.0104i	−0.782882	+	1.35599i	0.147374	+	0.989081i	$0.452918\pi$
$523$	−17.9039	+	31.0104i	−0.782882	+	1.35599i	−0.930256	+	0.366911i	$0.880415\pi$
$524$	−8.24621	−	14.2829i	−0.360237	−	0.623949i
$525$	4.68466			0.204455
$526$	−6.24621	−	10.8188i	−0.272348	−	0.471720i
$527$	−7.80776	−	13.5234i	−0.340112	−	0.589090i
$528$	−1.56155			−0.0679579
$529$	11.1155	+	19.2527i	0.483284	+	0.837072i
$530$	3.40388	−	5.89570i	0.147855	−	0.256093i
$531$	−2.43845	+	4.22351i	−0.105820	+	0.183285i
$532$	4.68466			0.203106
$533$	11.7192	+	9.14657i	0.507616	+	0.396182i
$534$	2.68466			0.116177
$535$	3.80776	−	6.59524i	0.164624	−	0.285137i
$536$	3.56155	−	6.16879i	0.153836	−	0.266451i
$537$	−8.24621	−	14.2829i	−0.355850	−	0.616351i
$538$	−13.1231			−0.565777
$539$	0.780776	+	1.35234i	0.0336304	+	0.0582496i
$540$	−0.280776	−	0.486319i	−0.0120827	−	0.0209278i
$541$	−2.56155			−0.110130			−0.0550649	−	0.998483i	$-0.517537\pi$
$541$	−2.56155			−0.110130			−0.0550649	+	0.998483i	$0.517537\pi$
$542$	−2.43845	−	4.22351i	−0.104740	−	0.181415i
$543$	1.62311	−	2.81130i	0.0696541	−	0.120644i
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	5.12311			0.219450
$546$	2.84233	+	2.21837i	0.121640	+	0.0949375i
$547$	26.7386			1.14326			0.571631	−	0.820511i	$-0.306311\pi$
$547$	26.7386			1.14326			0.571631	+	0.820511i	$0.306311\pi$
$548$	−7.40388	+	12.8239i	−0.316278	+	0.547810i
$549$	0.500000	−	0.866025i	0.0213395	−	0.0369611i
$550$	−3.65767	−	6.33527i	−0.155964	−	0.270137i
$551$	4.68466			0.199573
$552$	0.438447	+	0.759413i	0.0186616	+	0.0323228i
$553$	2.78078	+	4.81645i	0.118251	+	0.204816i
$554$	0.561553			0.0238581
$555$	−3.03457	−	5.25602i	−0.128810	−	0.223106i
$556$	−2.34233	+	4.05703i	−0.0993369	+	0.172057i
$557$	13.8693	−	24.0224i	0.587662	−	1.01786i	−0.406876	−	0.913483i	$-0.633382\pi$
$557$	13.8693	−	24.0224i	0.587662	−	1.01786i	0.994538	−	0.104377i	$-0.0332848\pi$
$558$	−3.12311			−0.132212
$559$	−37.1771	+	15.0423i	−1.57242	+	0.636220i
$560$	−0.561553			−0.0237299
$561$	−3.90388	+	6.76172i	−0.164822	+	0.285480i
$562$	6.40388	−	11.0918i	0.270131	−	0.467881i
$563$	12.6847	+	21.9705i	0.534595	+	0.925945i	0.999183	+	0.0404182i	$0.0128690\pi$
$563$	12.6847	+	21.9705i	0.534595	+	0.925945i	−0.464588	+	0.885527i	$0.653798\pi$
$564$	4.68466			0.197260
$565$	3.34991	+	5.80221i	0.140932	+	0.244101i
$566$	12.2462	+	21.2111i	0.514747	+	0.891567i
$567$	−1.00000			−0.0419961
$568$	2.00000	+	3.46410i	0.0839181	+	0.145350i
$569$	14.8078	−	25.6478i	0.620774	−	1.07521i	−0.368568	−	0.929601i	$-0.620152\pi$
$569$	14.8078	−	25.6478i	0.620774	−	1.07521i	0.989342	−	0.145611i	$-0.0465148\pi$
$570$	1.31534	−	2.27824i	0.0550936	−	0.0954249i
$571$	30.2462			1.26576			0.632882	−	0.774248i	$-0.281872\pi$
$571$	30.2462			1.26576			0.632882	+	0.774248i	$0.281872\pi$
$572$	0.780776	−	5.57586i	0.0326459	−	0.233138i
$573$	22.2462			0.929349
$574$	−2.06155	+	3.57071i	−0.0860476	+	0.149039i
$575$	−2.05398	+	3.55759i	−0.0856567	+	0.148362i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	43.6847			1.81862			0.909308	−	0.416124i	$-0.136612\pi$
$577$	43.6847			1.81862			0.909308	+	0.416124i	$0.136612\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−2.18466	−	3.78394i	−0.0907913	−	0.157255i
$580$	−0.561553			−0.0233172
$581$	3.12311	+	5.40938i	0.129568	+	0.224419i
$582$	2.12311	−	3.67733i	0.0880056	−	0.152430i
$583$	−9.46543	+	16.3946i	−0.392018	+	0.678996i
$584$	−6.56155			−0.271519
$585$	1.87689	−	0.759413i	0.0776000	−	0.0313979i
$586$	7.68466			0.317450
$587$	−3.31534	+	5.74234i	−0.136839	+	0.237012i	−0.926298	−	0.376791i	$-0.877028\pi$
$587$	−3.31534	+	5.74234i	−0.136839	+	0.237012i	0.789460	+	0.613803i	$0.210361\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	−7.31534	−	12.6705i	−0.301423	−	0.522081i
$590$	2.73863			0.112748
$591$	−1.78078	−	3.08440i	−0.0732514	−	0.126875i
$592$	−5.40388	−	9.35980i	−0.222098	−	0.384685i
$593$	−8.61553			−0.353797			−0.176899	−	0.984229i	$-0.556606\pi$
$593$	−8.61553			−0.353797			−0.176899	+	0.984229i	$0.556606\pi$
$594$	0.780776	+	1.35234i	0.0320356	+	0.0554874i
$595$	−1.40388	+	2.43160i	−0.0575536	+	0.0996857i
$596$	−1.40388	+	2.43160i	−0.0575052	+	0.0996020i
$597$	23.6155			0.966519
$598$	−2.93087	+	1.18586i	−0.119852	+	0.0484936i
$599$	−31.1231			−1.27166			−0.635828	−	0.771831i	$-0.719341\pi$
$599$	−31.1231			−1.27166			−0.635828	+	0.771831i	$0.719341\pi$
$600$	2.34233	−	4.05703i	0.0956252	−	0.165628i
$601$	−4.03457	+	6.98807i	−0.164573	+	0.285049i	−0.936504	−	0.350658i	$-0.885958\pi$
$601$	−4.03457	+	6.98807i	−0.164573	+	0.285049i	0.771930	+	0.635707i	$0.219291\pi$
$602$	−5.56155	−	9.63289i	−0.226672	−	0.392607i
$603$	−7.12311			−0.290075
$604$	10.7808	+	18.6729i	0.438664	+	0.759788i
$605$	2.40388	+	4.16365i	0.0977317	+	0.169276i
$606$	−15.4384			−0.627144
$607$	−6.43845	−	11.1517i	−0.261329	−	0.452634i	0.705267	−	0.708942i	$-0.250827\pi$
$607$	−6.43845	−	11.1517i	−0.261329	−	0.452634i	−0.966595	+	0.256308i	$0.917494\pi$
$608$	2.34233	−	4.05703i	0.0949940	−	0.164534i
$609$	−0.500000	+	0.866025i	−0.0202610	+	0.0350931i
$610$	−0.561553			−0.0227366
$611$	−2.34233	+	16.7276i	−0.0947605	+	0.676725i
$612$	−5.00000			−0.202113
$613$	8.65009	−	14.9824i	0.349374	−	0.605133i	−0.636764	−	0.771058i	$-0.719728\pi$
$613$	8.65009	−	14.9824i	0.349374	−	0.605133i	0.986138	+	0.165925i	$0.0530609\pi$
$614$	2.53457	−	4.39000i	0.102287	−	0.177166i
$615$	1.15767	+	2.00514i	0.0466818	+	0.0808552i
$616$	1.56155			0.0629168
$617$	−17.2116	−	29.8114i	−0.692915	−	1.20016i	−0.970879	−	0.239572i	$-0.922993\pi$
$617$	−17.2116	−	29.8114i	−0.692915	−	1.20016i	0.277964	−	0.960592i	$-0.410340\pi$
$618$	−6.68466	−	11.5782i	−0.268896	−	0.465742i
$619$	16.6847			0.670613			0.335307	−	0.942109i	$-0.391160\pi$
$619$	16.6847			0.670613			0.335307	+	0.942109i	$0.391160\pi$
$620$	0.876894	+	1.51883i	0.0352169	+	0.0609975i
$621$	0.438447	−	0.759413i	0.0175943	−	0.0304742i
$622$	−9.21922	+	15.9682i	−0.369657	+	0.640265i
$623$	−2.68466			−0.107559
$624$	3.34233	−	1.35234i	0.133800	−	0.0541371i
$625$	20.3693			0.814773
$626$	6.80776	−	11.7914i	0.272093	−	0.471279i
$627$	−3.65767	+	6.33527i	−0.146073	+	0.253006i
$628$	−7.40388	−	12.8239i	−0.295447	−	0.511729i
$629$	−54.0388			−2.15467
$630$	0.280776	+	0.486319i	0.0111864	+	0.0193754i
$631$	−21.9039	−	37.9386i	−0.871980	−	1.51031i	−0.859946	−	0.510386i	$-0.829503\pi$
$631$	−21.9039	−	37.9386i	−0.871980	−	1.51031i	−0.0120342	−	0.999928i	$-0.503831\pi$
$632$	5.56155			0.221227
$633$	5.56155	+	9.63289i	0.221052	+	0.382873i
$634$	3.71922	−	6.44188i	0.147709	−	0.255840i
$635$	4.00000	−	6.92820i	0.158735	−	0.274937i
$636$	−12.1231			−0.480712
$637$	−2.84233	−	2.21837i	−0.112617	−	0.0878950i
$638$	1.56155			0.0618225
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$	−0.280776	+	0.486319i	−0.0110987	+	0.0192234i
$641$	−4.03457	−	6.98807i	−0.159356	−	0.276012i	0.775281	−	0.631617i	$-0.217608\pi$
$641$	−4.03457	−	6.98807i	−0.159356	−	0.276012i	−0.934637	+	0.355604i	$0.884275\pi$
$642$	−13.5616			−0.535232
$643$	11.2192	+	19.4323i	0.442443	+	0.766334i	0.997870	−	0.0652314i	$-0.0207786\pi$
$643$	11.2192	+	19.4323i	0.442443	+	0.766334i	−0.555427	+	0.831565i	$0.687445\pi$
$644$	−0.438447	−	0.759413i	−0.0172772	−	0.0299251i
$645$	−6.24621			−0.245944
$646$	−11.7116	−	20.2852i	−0.460789	−	0.798109i
$647$	0.0961180	−	0.166481i	0.00377879	−	0.00654505i	−0.864130	−	0.503269i	$-0.832131\pi$
$647$	0.0961180	−	0.166481i	0.00377879	−	0.00654505i	0.867909	+	0.496724i	$0.165464\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−7.61553			−0.298936
$650$	13.3153	+	10.3923i	0.522271	+	0.407620i
$651$	3.12311			0.122404
$652$	−3.56155	+	6.16879i	−0.139481	+	0.241588i
$653$	−0.903882	+	1.56557i	−0.0353716	+	0.0612655i	−0.883169	−	0.469054i	$-0.844595\pi$
$653$	−0.903882	+	1.56557i	−0.0353716	+	0.0612655i	0.847798	+	0.530320i	$0.177928\pi$
$654$	−4.56155	−	7.90084i	−0.178371	−	0.308947i
$655$	9.26137			0.361872
$656$	2.06155	+	3.57071i	0.0804901	+	0.139413i
$657$	3.28078	+	5.68247i	0.127995	+	0.221694i
$658$	−4.68466			−0.182627
$659$	20.3423	+	35.2339i	0.792425	+	1.37252i	0.924462	+	0.381275i	$0.124515\pi$
$659$	20.3423	+	35.2339i	0.792425	+	1.37252i	−0.132037	+	0.991245i	$0.542152\pi$
$660$	0.438447	−	0.759413i	0.0170665	−	0.0295601i
$661$	−5.40388	+	9.35980i	−0.210187	+	0.364054i	−0.951773	−	0.306804i	$-0.900741\pi$
$661$	−5.40388	+	9.35980i	−0.210187	+	0.364054i	0.741586	+	0.670858i	$0.234074\pi$
$662$	−10.6307			−0.413173
$663$	2.50000	−	17.8536i	0.0970920	−	0.693375i
$664$	6.24621			0.242400
$665$	−1.31534	+	2.27824i	−0.0510068	+	0.0883463i
$666$	−5.40388	+	9.35980i	−0.209396	+	0.362685i
$667$	−0.438447	−	0.759413i	−0.0169767	−	0.0294046i
$668$	−12.4924			−0.483346
$669$	−8.24621	−	14.2829i	−0.318817	−	0.552207i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$	1.56155			0.0602831
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	−12.6231	+	21.8639i	−0.486585	+	0.842790i	−0.999881	−	0.0154217i	$-0.995091\pi$
$673$	−12.6231	+	21.8639i	−0.486585	+	0.842790i	0.513296	+	0.858212i	$0.328424\pi$
$674$	−1.74621	+	3.02453i	−0.0672615	+	0.116500i
$675$	−4.68466			−0.180313
$676$	3.15767	+	12.6107i	0.121449	+	0.485026i
$677$	−49.6155			−1.90688			−0.953440	−	0.301583i	$-0.902485\pi$
$677$	−49.6155			−1.90688			−0.953440	+	0.301583i	$0.902485\pi$
$678$	5.96543	−	10.3324i	0.229101	−	0.396815i
$679$	−2.12311	+	3.67733i	−0.0814773	+	0.141123i
$680$	1.40388	+	2.43160i	0.0538364	+	0.0932474i
$681$	4.87689			0.186883
$682$	−2.43845	−	4.22351i	−0.0933730	−	0.161727i
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$	−4.68466			−0.179122
$685$	−4.15767	−	7.20130i	−0.158856	−	0.275147i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−1.09612	+	1.89853i	−0.0418195	+	0.0724335i
$688$	−11.1231			−0.424064
$689$	6.06155	−	43.2881i	0.230927	−	1.64915i
$690$	−0.492423			−0.0187462
$691$	−2.24621	+	3.89055i	−0.0854499	+	0.148004i	−0.905583	−	0.424169i	$-0.860566\pi$
$691$	−2.24621	+	3.89055i	−0.0854499	+	0.148004i	0.820133	+	0.572173i	$0.193899\pi$
$692$	6.56155	−	11.3649i	0.249433	−	0.432030i
$693$	−0.780776	−	1.35234i	−0.0296592	−	0.0513713i
$694$	−12.6847			−0.481503
$695$	−1.31534	−	2.27824i	−0.0498937	−	0.0864185i
$696$	0.500000	+	0.866025i	0.0189525	+	0.0328266i
$697$	20.6155			0.780869
$698$	−13.2462	−	22.9431i	−0.501376	−	0.868410i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	−2.34233	+	4.05703i	−0.0885317	+	0.153341i
$701$	−28.0540			−1.05958			−0.529792	−	0.848128i	$-0.677730\pi$
$701$	−28.0540			−1.05958			−0.529792	+	0.848128i	$0.677730\pi$
$702$	−2.84233	−	2.21837i	−0.107277	−	0.0837270i
$703$	−50.6307			−1.90957
$704$	0.780776	−	1.35234i	0.0294266	−	0.0509684i
$705$	−1.31534	+	2.27824i	−0.0495386	+	0.0858034i
$706$	−5.40388	−	9.35980i	−0.203378	−	0.352261i
$707$	15.4384			0.580623
$708$	−2.43845	−	4.22351i	−0.0916425	−	0.158729i
$709$	16.6501	+	28.8388i	0.625307	+	1.08306i	0.988481	+	0.151343i	$0.0483597\pi$
$709$	16.6501	+	28.8388i	0.625307	+	1.08306i	−0.363174	+	0.931721i	$0.618307\pi$
$710$	−2.24621			−0.0842988
$711$	−2.78078	−	4.81645i	−0.104287	−	0.180631i
$712$	−1.34233	+	2.32498i	−0.0503059	+	0.0871324i
$713$	−1.36932	+	2.37173i	−0.0512813	+	0.0888219i
$714$	5.00000			0.187120
$715$	2.49242	+	1.94528i	0.0932113	+	0.0727492i
$716$	16.4924			0.616351
$717$	−2.00000	+	3.46410i	−0.0746914	+	0.129369i
$718$	14.6847	−	25.4346i	0.548027	−	0.949210i
$719$	3.46543	+	6.00231i	0.129239	+	0.223848i	0.923382	−	0.383883i	$-0.125413\pi$
$719$	3.46543	+	6.00231i	0.129239	+	0.223848i	−0.794143	+	0.607731i	$0.792080\pi$
$720$	0.561553			0.0209278
$721$	6.68466	+	11.5782i	0.248950	+	0.431194i
$722$	−1.47301	−	2.55133i	−0.0548198	−	0.0949508i
$723$	23.6847			0.880842
$724$	1.62311	+	2.81130i	0.0603222	+	0.104481i
$725$	−2.34233	+	4.05703i	−0.0869919	+	0.150674i
$726$	4.28078	−	7.41452i	0.158875	−	0.275179i
$727$	33.7538			1.25186			0.625929	−	0.779880i	$-0.284720\pi$
$727$	33.7538			1.25186			0.625929	+	0.779880i	$0.284720\pi$
$728$	−3.34233	+	1.35234i	−0.123875	+	0.0501212i
$729$	1.00000			0.0370370
$730$	1.84233	−	3.19101i	0.0681877	−	0.118104i
$731$	−27.8078	+	48.1645i	−1.02851	+	1.78143i
$732$	0.500000	+	0.866025i	0.0184805	+	0.0320092i
$733$	−8.61553			−0.318222			−0.159111	−	0.987261i	$-0.550863\pi$
$733$	−8.61553			−0.318222			−0.159111	+	0.987261i	$0.550863\pi$
$734$	6.68466	+	11.5782i	0.246735	+	0.427358i
$735$	−0.280776	−	0.486319i	−0.0103566	−	0.0179381i
$736$	−0.876894			−0.0323228
$737$	−5.56155	−	9.63289i	−0.204862	−	0.354832i
$738$	2.06155	−	3.57071i	0.0758868	−	0.131440i
$739$	−11.3153	+	19.5987i	−0.416242	+	0.720952i	−0.995558	−	0.0941513i	$-0.969986\pi$
$739$	−11.3153	+	19.5987i	−0.416242	+	0.720952i	0.579316	+	0.815103i	$0.303320\pi$
$740$	6.06913			0.223106
$741$	2.34233	−	16.7276i	0.0860476	−	0.614503i
$742$	12.1231			0.445053
$743$	−16.6847	+	28.8987i	−0.612101	+	1.06019i	0.378785	+	0.925485i	$0.376342\pi$
$743$	−16.6847	+	28.8987i	−0.612101	+	1.06019i	−0.990886	+	0.134705i	$0.956991\pi$
$744$	1.56155	−	2.70469i	0.0572493	−	0.0991587i
$745$	−0.788354	−	1.36547i	−0.0288831	−	0.0500269i
$746$	17.4384			0.638467
$747$	−3.12311	−	5.40938i	−0.114268	−	0.197919i
$748$	−3.90388	−	6.76172i	−0.142740	−	0.247233i
$749$	13.5616			0.495528
$750$	2.71922	+	4.70983i	0.0992920	+	0.171979i
$751$	−9.90388	+	17.1540i	−0.361398	+	0.625959i	−0.988191	−	0.153226i	$-0.951034\pi$
$751$	−9.90388	+	17.1540i	−0.361398	+	0.625959i	0.626793	+	0.779186i	$0.284367\pi$
$752$	−2.34233	+	4.05703i	−0.0854160	+	0.147945i
$753$	−24.4924			−0.892553
$754$	−3.34233	+	1.35234i	−0.121720	+	0.0492495i
$755$	−12.1080			−0.440653
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	−0.561553	+	0.972638i	−0.0204100	+	0.0353511i	−0.876050	−	0.482220i	$-0.839830\pi$
$757$	−0.561553	+	0.972638i	−0.0204100	+	0.0353511i	0.855640	+	0.517571i	$0.173164\pi$
$758$	16.2462	+	28.1393i	0.590089	+	1.02206i
$759$	1.36932			0.0497031
$760$	1.31534	+	2.27824i	0.0477125	+	0.0826404i
$761$	4.75379	+	8.23380i	0.172325	+	0.298475i	0.939232	−	0.343283i	$-0.111539\pi$
$761$	4.75379	+	8.23380i	0.172325	+	0.298475i	−0.766907	+	0.641758i	$0.778205\pi$
$762$	−14.2462			−0.516086
$763$	4.56155	+	7.90084i	0.165139	+	0.286030i
$764$	−11.1231	+	19.2658i	−0.402420	+	0.697012i
$765$	1.40388	−	2.43160i	0.0507575	−	0.0879145i
$766$	20.6847			0.747367
$767$	16.3002	−	6.59524i	0.588566	−	0.238140i
$768$	1.00000			0.0360844
$769$	−21.4924	+	37.2260i	−0.775037	+	1.34240i	0.159737	+	0.987160i	$0.448935\pi$
$769$	−21.4924	+	37.2260i	−0.775037	+	1.34240i	−0.934774	+	0.355243i	$0.884398\pi$
$770$	−0.438447	+	0.759413i	−0.0158005	+	0.0273673i
$771$	15.6231	+	27.0600i	0.562652	+	0.974543i
$772$	4.36932			0.157255
$773$	3.24621	+	5.62260i	0.116758	+	0.202231i	0.918481	−	0.395465i	$-0.129416\pi$
$773$	3.24621	+	5.62260i	0.116758	+	0.202231i	−0.801723	+	0.597696i	$0.796083\pi$
$774$	5.56155	+	9.63289i	0.199906	+	0.346247i
$775$	14.6307			0.525550
$776$	2.12311	+	3.67733i	0.0762151	+	0.132008i
$777$	5.40388	−	9.35980i	0.193863	−	0.335781i
$778$	−3.15767	+	5.46925i	−0.113208	+	0.196082i
$779$	19.3153			0.692044
$780$	−0.280776	+	2.00514i	−0.0100534	+	0.0717957i
$781$	6.24621			0.223507
$782$	−2.19224	+	3.79706i	−0.0783942	+	0.135783i
$783$	0.500000	−	0.866025i	0.0178685	−	0.0309492i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	8.31534			0.296787
$786$	−8.24621	−	14.2829i	−0.294133	−	0.509453i
$787$	9.90388	+	17.1540i	0.353035	+	0.611475i	0.986780	−	0.162067i	$-0.0518162\pi$
$787$	9.90388	+	17.1540i	0.353035	+	0.611475i	−0.633744	+	0.773543i	$0.718483\pi$
$788$	3.56155			0.126875
$789$	−6.24621	−	10.8188i	−0.222371	−	0.385158i
$790$	−1.56155	+	2.70469i	−0.0555576	+	0.0962285i
$791$	−5.96543	+	10.3324i	−0.212106	+	0.367379i
$792$	−1.56155			−0.0554874
$793$	−3.34233	+	1.35234i	−0.118690	+	0.0480232i
$794$	−10.6847			−0.379184
$795$	3.40388	−	5.89570i	0.120723	−	0.209099i
$796$	−11.8078	+	20.4516i	−0.418515	+	0.724889i
$797$	−25.0540	−	43.3948i	−0.887457	−	1.53712i	−0.842871	−	0.538116i	$-0.819136\pi$
$797$	−25.0540	−	43.3948i	−0.887457	−	1.53712i	−0.0445863	−	0.999006i	$-0.514197\pi$
$798$	4.68466			0.165835
$799$	11.7116	+	20.2852i	0.414328	+	0.717638i
$800$	2.34233	+	4.05703i	0.0828138	+	0.143438i
$801$	2.68466			0.0948577
$802$	15.0885	+	26.1341i	0.532795	+	0.922828i
$803$	−5.12311	+	8.87348i	−0.180790	+	0.313138i
$804$	3.56155	−	6.16879i	0.125606	−	0.217556i
$805$	0.492423			0.0173556
$806$	8.87689	+	6.92820i	0.312675	+	0.244036i
$807$	−13.1231			−0.461955
$808$	7.71922	−	13.3701i	0.271561	−	0.470358i
$809$	−8.96543	+	15.5286i	−0.315208	+	0.545956i	−0.979482	−	0.201533i	$-0.935408\pi$
$809$	−8.96543	+	15.5286i	−0.315208	+	0.545956i	0.664274	+	0.747489i	$0.268741\pi$
$810$	−0.280776	−	0.486319i	−0.00986548	−	0.0170875i
$811$	22.2462			0.781170			0.390585	−	0.920567i	$-0.372273\pi$
$811$	22.2462			0.781170			0.390585	+	0.920567i	$0.372273\pi$
$812$	−0.500000	−	0.866025i	−0.0175466	−	0.0303915i
$813$	−2.43845	−	4.22351i	−0.0855201	−	0.148125i
$814$	−16.8769			−0.591535
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	2.50000	−	4.33013i	0.0875175	−	0.151585i
$817$	−26.0540	+	45.1268i	−0.911513	+	1.57879i
$818$	−34.5616			−1.20842
$819$	2.84233	+	2.21837i	0.0993190	+	0.0775161i
$820$	−2.31534			−0.0808552
$821$	20.4654	−	35.4472i	0.714249	−	1.23711i	−0.249000	−	0.968503i	$-0.580102\pi$
$821$	20.4654	−	35.4472i	0.714249	−	1.23711i	0.963249	−	0.268611i	$-0.0865647\pi$
$822$	−7.40388	+	12.8239i	−0.258240	+	0.447285i
$823$	1.12311	+	1.94528i	0.0391490	+	0.0678081i	0.884936	−	0.465713i	$-0.154202\pi$
$823$	1.12311	+	1.94528i	0.0391490	+	0.0678081i	−0.845787	+	0.533521i	$0.820869\pi$
$824$	13.3693			0.465742
$825$	−3.65767	−	6.33527i	−0.127344	−	0.220566i
$826$	2.43845	+	4.22351i	0.0848444	+	0.146955i
$827$	−44.4924			−1.54715			−0.773577	−	0.633703i	$-0.781534\pi$
$827$	−44.4924			−1.54715			−0.773577	+	0.633703i	$0.781534\pi$
$828$	0.438447	+	0.759413i	0.0152371	+	0.0263914i
$829$	22.5540	−	39.0646i	0.783332	−	1.35677i	−0.146659	−	0.989187i	$-0.546852\pi$
$829$	22.5540	−	39.0646i	0.783332	−	1.35677i	0.929991	−	0.367584i	$-0.119815\pi$
$830$	−1.75379	+	3.03765i	−0.0608749	+	0.105438i
$831$	0.561553			0.0194801
$832$	−0.500000	+	3.57071i	−0.0173344	+	0.123792i
$833$	−5.00000			−0.173240
$834$	−2.34233	+	4.05703i	−0.0811082	+	0.140484i
$835$	3.50758	−	6.07530i	0.121385	−	0.210245i
$836$	−3.65767	−	6.33527i	−0.126503	−	0.219110i
$837$	−3.12311			−0.107950
$838$	13.3693	+	23.1563i	0.461835	+	0.799922i
$839$	−4.00000	−	6.92820i	−0.138095	−	0.239188i	0.788680	−	0.614804i	$-0.210765\pi$
$839$	−4.00000	−	6.92820i	−0.138095	−	0.239188i	−0.926776	+	0.375615i	$0.877431\pi$
$840$	−0.561553			−0.0193754
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−6.28078	+	10.8786i	−0.216450	+	0.374902i
$843$	6.40388	−	11.0918i	0.220561	−	0.382024i
$844$	−11.1231			−0.382873
$845$	−7.01941	−	2.00514i	−0.241475	−	0.0689791i
$846$	4.68466			0.161062
$847$	−4.28078	+	7.41452i	−0.147089	+	0.254766i
$848$	6.06155	−	10.4989i	0.208155	−	0.360534i
$849$	12.2462	+	21.2111i	0.420289	+	0.727962i
$850$	23.4233			0.803412
$851$	4.73863	+	8.20755i	0.162438	+	0.281351i
$852$	2.00000	+	3.46410i	0.0685189	+	0.118678i
$853$	24.3693			0.834390			0.417195	−	0.908817i	$-0.363013\pi$
$853$	24.3693			0.834390			0.417195	+	0.908817i	$0.363013\pi$
$854$	−0.500000	−	0.866025i	−0.0171096	−	0.0296348i
$855$	1.31534	−	2.27824i	0.0449837	−	0.0779141i
$856$	6.78078	−	11.7446i	0.231762	−	0.401424i
$857$	31.3002			1.06919			0.534597	−	0.845107i	$-0.320463\pi$
$857$	31.3002			1.06919			0.534597	+	0.845107i	$0.320463\pi$
$858$	0.780776	−	5.57586i	0.0266553	−	0.190357i
$859$	−16.1922			−0.552472			−0.276236	−	0.961090i	$-0.589087\pi$
$859$	−16.1922			−0.552472			−0.276236	+	0.961090i	$0.589087\pi$
$860$	3.12311	−	5.40938i	0.106497	−	0.184458i
$861$	−2.06155	+	3.57071i	−0.0702575	+	0.121690i
$862$	−15.3693	−	26.6204i	−0.523481	−	0.906696i
$863$	−48.1080			−1.63761			−0.818807	−	0.574069i	$-0.805364\pi$
$863$	−48.1080			−1.63761			−0.818807	+	0.574069i	$0.805364\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	3.68466	+	6.38202i	0.125282	+	0.216995i
$866$	−17.6847			−0.600949
$867$	−4.00000	−	6.92820i	−0.135847	−	0.235294i
$868$	−1.56155	+	2.70469i	−0.0530026	+	0.0918031i
$869$	4.34233	−	7.52113i	0.147303	−	0.255137i
$870$	−0.561553			−0.0190384
$871$	20.2462	+	15.8017i	0.686017	+	0.535420i
$872$	9.12311			0.308947
$873$	2.12311	−	3.67733i	0.0718562	−	0.124459i
$874$	−2.05398	+	3.55759i	−0.0694768	+	0.120337i
$875$	−2.71922	−	4.70983i	−0.0919265	−	0.159221i
$876$	−6.56155			−0.221694
$877$	22.6501	+	39.2311i	0.764839	+	1.32474i	0.940331	+	0.340260i	$0.110515\pi$
$877$	22.6501	+	39.2311i	0.764839	+	1.32474i	−0.175492	+	0.984481i	$0.556152\pi$
$878$	−2.24621	−	3.89055i	−0.0758060	−	0.131300i
$879$	7.68466			0.259197
$880$	0.438447	+	0.759413i	0.0147801	+	0.0255998i
$881$	−0.911460	+	1.57869i	−0.0307079	+	0.0531876i	−0.880971	−	0.473170i	$-0.843109\pi$
$881$	−0.911460	+	1.57869i	−0.0307079	+	0.0531876i	0.850263	+	0.526358i	$0.176443\pi$
$882$	−0.500000	+	0.866025i	−0.0168359	+	0.0291606i
$883$	8.87689			0.298731			0.149366	−	0.988782i	$-0.452277\pi$
$883$	8.87689			0.298731			0.149366	+	0.988782i	$0.452277\pi$
$884$	14.2116	+	11.0918i	0.477989	+	0.373059i
$885$	2.73863			0.0920582
$886$	−13.7116	+	23.7493i	−0.460652	+	0.797872i
$887$	−4.78078	+	8.28055i	−0.160523	+	0.278034i	−0.935056	−	0.354499i	$-0.884651\pi$
$887$	−4.78078	+	8.28055i	−0.160523	+	0.278034i	0.774534	+	0.632533i	$0.217985\pi$
$888$	−5.40388	−	9.35980i	−0.181342	−	0.314094i
$889$	14.2462			0.477803
$890$	−0.753789	−	1.30560i	−0.0252671	−	0.0437638i
$891$	0.780776	+	1.35234i	0.0261570	+	0.0453052i
$892$	16.4924			0.552207
$893$	10.9730	+	19.0058i	0.367198	+	0.636005i
$894$	−1.40388	+	2.43160i	−0.0469528	+	0.0813247i
$895$	−4.63068	+	8.02058i	−0.154787	+	0.268098i
$896$	−1.00000			−0.0334077
$897$	−2.93087	+	1.18586i	−0.0978589	+	0.0395948i
$898$	18.0000			0.600668
$899$	−1.56155	+	2.70469i	−0.0520807	+	0.0902064i
$900$	2.34233	−	4.05703i	0.0780776	−	0.135234i
$901$	−30.3078	−	52.4946i	−1.00970	−	1.74885i
$902$	6.43845			0.214377
$903$	−5.56155	−	9.63289i	−0.185077	−	0.320563i
$904$	5.96543	+	10.3324i	0.198407	+	0.343652i
$905$	−1.82292			−0.0605959
$906$	10.7808	+	18.6729i	0.358167	+	0.620364i
$907$	−15.5616	+	26.9534i	−0.516713	+	0.894973i	0.483099	+	0.875566i	$0.339511\pi$
$907$	−15.5616	+	26.9534i	−0.516713	+	0.894973i	−0.999812	+	0.0194071i	$0.993822\pi$
$908$	−2.43845	+	4.22351i	−0.0809227	+	0.140162i
$909$	−15.4384			−0.512061
$910$	0.280776	−	2.00514i	0.00930765	−	0.0664699i
$911$	−54.7386			−1.81357			−0.906786	−	0.421591i	$-0.861472\pi$
$911$	−54.7386			−1.81357			−0.906786	+	0.421591i	$0.861472\pi$
$912$	2.34233	−	4.05703i	0.0775623	−	0.134342i
$913$	4.87689	−	8.44703i	0.161402	−	0.279556i
$914$	12.8423	+	22.2436i	0.424786	+	0.735752i
$915$	−0.561553			−0.0185644
$916$	−1.09612	−	1.89853i	−0.0362168	−	0.0627293i
$917$	8.24621	+	14.2829i	0.272314	+	0.471661i
$918$	−5.00000			−0.165025
$919$	−1.21922	−	2.11176i	−0.0402185	−	0.0696604i	0.845215	−	0.534426i	$-0.179472\pi$
$919$	−1.21922	−	2.11176i	−0.0402185	−	0.0696604i	−0.885434	+	0.464765i	$0.846139\pi$
$920$	0.246211	−	0.426450i	0.00811734	−	0.0140597i
$921$	2.53457	−	4.39000i	0.0835168	−	0.144655i
$922$	−7.05398			−0.232310
$923$	−13.3693	+	5.40938i	−0.440056	+	0.178052i
$924$	1.56155			0.0513713
$925$	25.3153	−	43.8475i	0.832363	−	1.44170i
$926$	−0.342329	+	0.592932i	−0.0112496	+	0.0194849i
$927$	−6.68466	−	11.5782i	−0.219553	−	0.380277i
$928$	−1.00000			−0.0328266
$929$	−17.3078	−	29.9779i	−0.567849	−	0.983544i	−0.996778	−	0.0802057i	$-0.974442\pi$
$929$	−17.3078	−	29.9779i	−0.567849	−	0.983544i	0.428929	−	0.903338i	$-0.358891\pi$
$930$	0.876894	+	1.51883i	0.0287545	+	0.0498043i
$931$	−4.68466			−0.153533
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	−9.21922	+	15.9682i	−0.301824	+	0.522774i
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	4.38447			0.143388
$936$	3.34233	−	1.35234i	0.109247	−	0.0442028i
$937$	9.43845			0.308341			0.154170	−	0.988044i	$-0.450730\pi$
$937$	9.43845			0.308341			0.154170	+	0.988044i	$0.450730\pi$
$938$	−3.56155	+	6.16879i	−0.116289	+	0.201418i
$939$	6.80776	−	11.7914i	0.222163	−	0.384798i
$940$	−1.31534	−	2.27824i	−0.0429017	−	0.0743079i
$941$	28.6307			0.933334			0.466667	−	0.884433i	$-0.345455\pi$
$941$	28.6307			0.933334			0.466667	+	0.884433i	$0.345455\pi$
$942$	−7.40388	−	12.8239i	−0.241232	−	0.417825i
$943$	−1.80776	−	3.13114i	−0.0588689	−	0.101964i
$944$	4.87689			0.158729
$945$	0.280776	+	0.486319i	0.00913366	+	0.0158200i
$946$	−8.68466	+	15.0423i	−0.282363	+	0.489066i
$947$	6.34233	−	10.9852i	0.206098	−	0.356972i	−0.744384	−	0.667752i	$-0.767257\pi$
$947$	6.34233	−	10.9852i	0.206098	−	0.356972i	0.950482	+	0.310780i	$0.100590\pi$
$948$	5.56155			0.180631
$949$	3.28078	−	23.4294i	0.106499	−	0.760551i
$950$	21.9460			0.712023
$951$	3.71922	−	6.44188i	0.120604	−	0.208892i
$952$	−2.50000	+	4.33013i	−0.0810255	+	0.140340i
$953$	1.63068	+	2.82443i	0.0528230	+	0.0914921i	0.891228	−	0.453556i	$-0.149845\pi$
$953$	1.63068	+	2.82443i	0.0528230	+	0.0914921i	−0.838405	+	0.545048i	$0.816511\pi$
$954$	−12.1231			−0.392500
$955$	−6.24621	−	10.8188i	−0.202123	−	0.350087i
$956$	−2.00000	−	3.46410i	−0.0646846	−	0.112037i
$957$	1.56155			0.0504778
$958$	−0.780776	−	1.35234i	−0.0252257	−	0.0436923i
$959$	7.40388	−	12.8239i	0.239084	−	0.414105i
$960$	−0.280776	+	0.486319i	−0.00906202	+	0.0156959i
$961$	−21.2462			−0.685362
$962$	36.1231	−	14.6158i	1.16466	−	0.471233i
$963$	−13.5616			−0.437015
$964$	−11.8423	+	20.5115i	−0.381416	+	0.660631i
$965$	−1.22680	+	2.12488i	−0.0394921	+	0.0684024i
$966$	−0.438447	−	0.759413i	−0.0141068	−	0.0244337i
$967$	28.4924			0.916255			0.458127	−	0.888887i	$-0.348520\pi$
$967$	28.4924			0.916255			0.458127	+	0.888887i	$0.348520\pi$
$968$	4.28078	+	7.41452i	0.137589	+	0.238312i
$969$	−11.7116	−	20.2852i	−0.376232	−	0.651653i
$970$	−2.38447			−0.0765608
$971$	9.56155	+	16.5611i	0.306845	+	0.531471i	0.977670	−	0.210144i	$-0.0673934\pi$
$971$	9.56155	+	16.5611i	0.306845	+	0.531471i	−0.670826	+	0.741615i	$0.734060\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	2.34233	−	4.05703i	0.0750916	−	0.130063i
$974$	11.3153			0.362567
$975$	13.3153	+	10.3923i	0.426432	+	0.332820i
$976$	−1.00000			−0.0320092
$977$	17.5270	−	30.3576i	0.560738	−	0.971227i	−0.436694	−	0.899610i	$-0.643851\pi$
$977$	17.5270	−	30.3576i	0.560738	−	0.971227i	0.997432	−	0.0716167i	$-0.0228158\pi$
$978$	−3.56155	+	6.16879i	−0.113886	+	0.197256i
$979$	2.09612	+	3.63058i	0.0669922	+	0.116034i
$980$	0.561553			0.0179381
$981$	−4.56155	−	7.90084i	−0.145639	−	0.252254i
$982$	9.12311	+	15.8017i	0.291130	+	0.504252i
$983$	−27.2311			−0.868536			−0.434268	−	0.900784i	$-0.642993\pi$
$983$	−27.2311			−0.868536			−0.434268	+	0.900784i	$0.642993\pi$
$984$	2.06155	+	3.57071i	0.0657199	+	0.113830i
$985$	−1.00000	+	1.73205i	−0.0318626	+	0.0551877i
$986$	−2.50000	+	4.33013i	−0.0796162	+	0.137899i
$987$	−4.68466			−0.149114
$988$	13.3153	+	10.3923i	0.423617	+	0.330623i
$989$	9.75379			0.310152
$990$	0.438447	−	0.759413i	0.0139348	−	0.0241357i
$991$	2.78078	−	4.81645i	0.0883343	−	0.152999i	−0.818473	−	0.574545i	$-0.805179\pi$
$991$	2.78078	−	4.81645i	0.0883343	−	0.152999i	0.906807	+	0.421546i	$0.138512\pi$
$992$	1.56155	+	2.70469i	0.0495794	+	0.0858740i
$993$	−10.6307			−0.337355
$994$	−2.00000	−	3.46410i	−0.0634361	−	0.109875i
$995$	−6.63068	−	11.4847i	−0.210207	−	0.364089i
$996$	6.24621			0.197919
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$	1.31534	−	2.27824i	0.0416364	−	0.0721164i
$999$	−5.40388	+	9.35980i	−0.170971	+	0.296131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.i.295.2	yes	4
3.2	odd	2		1638.2.r.z.1387.1		4
13.3	even	3	inner	546.2.l.i.211.2	✓	4
13.4	even	6		7098.2.a.bq.1.1		2
13.9	even	3		7098.2.a.bw.1.2		2
39.29	odd	6		1638.2.r.z.757.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.i.211.2	✓	4	13.3	even	3	inner
546.2.l.i.295.2	yes	4	1.1	even	1	trivial
1638.2.r.z.757.1		4	39.29	odd	6
1638.2.r.z.1387.1		4	3.2	odd	2
7098.2.a.bq.1.1		2	13.4	even	6
7098.2.a.bw.1.2		2	13.9	even	3

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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.280776 + 0.486319i) q^{10} +(0.780776 - 1.35234i) q^{11} +1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.280776 + 0.486319i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(2.34233 + 4.05703i) q^{19} +(-0.280776 - 0.486319i) q^{20} -1.00000 q^{21} +(0.780776 + 1.35234i) q^{22} +(0.438447 - 0.759413i) q^{23} +(-0.500000 + 0.866025i) q^{24} -4.68466 q^{25} +(-2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.280776 - 0.486319i) q^{30} -3.12311 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.780776 + 1.35234i) q^{33} -5.00000 q^{34} +(0.280776 + 0.486319i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.40388 + 9.35980i) q^{37} -4.68466 q^{38} +(-2.84233 - 2.21837i) q^{39} +0.561553 q^{40} +(2.06155 - 3.57071i) q^{41} +(0.500000 - 0.866025i) q^{42} +(5.56155 + 9.63289i) q^{43} -1.56155 q^{44} +(-0.280776 - 0.486319i) q^{45} +(0.438447 + 0.759413i) q^{46} +4.68466 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.34233 - 4.05703i) q^{50} -5.00000 q^{51} +(3.34233 - 1.35234i) q^{52} -12.1231 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.438447 - 0.759413i) q^{55} +(0.500000 + 0.866025i) q^{56} -4.68466 q^{57} +(0.500000 + 0.866025i) q^{58} +(-2.43845 - 4.22351i) q^{59} +0.561553 q^{60} +(0.500000 + 0.866025i) q^{61} +(1.56155 - 2.70469i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-0.280776 + 2.00514i) q^{65} -1.56155 q^{66} +(3.56155 - 6.16879i) q^{67} +(2.50000 - 4.33013i) q^{68} +(0.438447 + 0.759413i) q^{69} -0.561553 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.56155 q^{73} +(-5.40388 - 9.35980i) q^{74} +(2.34233 - 4.05703i) q^{75} +(2.34233 - 4.05703i) q^{76} +1.56155 q^{77} +(3.34233 - 1.35234i) q^{78} +5.56155 q^{79} +(-0.280776 + 0.486319i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.06155 + 3.57071i) q^{82} +6.24621 q^{83} +(0.500000 + 0.866025i) q^{84} +(1.40388 + 2.43160i) q^{85} -11.1231 q^{86} +(0.500000 + 0.866025i) q^{87} +(0.780776 - 1.35234i) q^{88} +(-1.34233 + 2.32498i) q^{89} +0.561553 q^{90} +(-3.34233 + 1.35234i) q^{91} -0.876894 q^{92} +(1.56155 - 2.70469i) q^{93} +(-2.34233 + 4.05703i) q^{94} +(1.31534 + 2.27824i) q^{95} +1.00000 q^{96} +(2.12311 + 3.67733i) q^{97} +(-0.500000 - 0.866025i) q^{98} -1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 3 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 4 q^{14} + 3 q^{15} - 2 q^{16} + 10 q^{17} + 4 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} - q^{22} + 10 q^{23} - 2 q^{24} + 6 q^{25} + q^{26} + 4 q^{27} + 2 q^{28} + 2 q^{29} + 3 q^{30} + 4 q^{31} - 2 q^{32} - q^{33} - 20 q^{34} - 3 q^{35} - 2 q^{36} - q^{37} + 6 q^{38} + q^{39} - 6 q^{40} + 2 q^{42} + 14 q^{43} + 2 q^{44} + 3 q^{45} + 10 q^{46} - 6 q^{47} - 2 q^{48} - 2 q^{49} - 3 q^{50} - 20 q^{51} + q^{52} - 32 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 6 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 2 q^{61} - 2 q^{62} + 2 q^{63} + 4 q^{64} + 3 q^{65} + 2 q^{66} + 6 q^{67} + 10 q^{68} + 10 q^{69} + 6 q^{70} + 8 q^{71} - 2 q^{72} - 18 q^{73} - q^{74} - 3 q^{75} - 3 q^{76} - 2 q^{77} + q^{78} + 14 q^{79} + 3 q^{80} - 2 q^{81} - 8 q^{83} + 2 q^{84} - 15 q^{85} - 28 q^{86} + 2 q^{87} - q^{88} + 7 q^{89} - 6 q^{90} - q^{91} - 20 q^{92} - 2 q^{93} + 3 q^{94} + 30 q^{95} + 4 q^{96} - 8 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 3 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 3 * q^15 - 2 * q^16 + 10 * q^17 + 4 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 - q^22 + 10 * q^23 - 2 * q^24 + 6 * q^25 + q^26 + 4 * q^27 + 2 * q^28 + 2 * q^29 + 3 * q^30 + 4 * q^31 - 2 * q^32 - q^33 - 20 * q^34 - 3 * q^35 - 2 * q^36 - q^37 + 6 * q^38 + q^39 - 6 * q^40 + 2 * q^42 + 14 * q^43 + 2 * q^44 + 3 * q^45 + 10 * q^46 - 6 * q^47 - 2 * q^48 - 2 * q^49 - 3 * q^50 - 20 * q^51 + q^52 - 32 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 6 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 2 * q^61 - 2 * q^62 + 2 * q^63 + 4 * q^64 + 3 * q^65 + 2 * q^66 + 6 * q^67 + 10 * q^68 + 10 * q^69 + 6 * q^70 + 8 * q^71 - 2 * q^72 - 18 * q^73 - q^74 - 3 * q^75 - 3 * q^76 - 2 * q^77 + q^78 + 14 * q^79 + 3 * q^80 - 2 * q^81 - 8 * q^83 + 2 * q^84 - 15 * q^85 - 28 * q^86 + 2 * q^87 - q^88 + 7 * q^89 - 6 * q^90 - q^91 - 20 * q^92 - 2 * q^93 + 3 * q^94 + 30 * q^95 + 4 * q^96 - 8 * q^97 - 2 * q^98 + 2 * q^99

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