LMFDB - Embedded newform 546.2.g.a.209.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(209,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("546.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.g (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.1
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.a.209.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +1.23607i q^{10} +(1.61803 - 0.618034i) q^{12} +1.00000i q^{13} +(-2.61803 - 0.381966i) q^{14} +(2.00000 - 0.763932i) q^{15} +1.00000 q^{16} -6.47214 q^{17} +(-2.00000 - 2.23607i) q^{18} +6.00000i q^{19} +1.23607 q^{20} +(1.00000 + 4.47214i) q^{21} +1.23607i q^{23} +(-0.618034 - 1.61803i) q^{24} -3.47214 q^{25} +1.00000 q^{26} +(-2.38197 + 4.61803i) q^{27} +(-0.381966 + 2.61803i) q^{28} +7.70820i q^{29} +(-0.763932 - 2.00000i) q^{30} +2.76393i q^{31} -1.00000i q^{32} +6.47214i q^{34} +(-0.472136 + 3.23607i) q^{35} +(-2.23607 + 2.00000i) q^{36} -4.76393 q^{37} +6.00000 q^{38} +(-0.618034 - 1.61803i) q^{39} -1.23607i q^{40} -0.763932 q^{41} +(4.47214 - 1.00000i) q^{42} -1.52786 q^{43} +(-2.76393 + 2.47214i) q^{45} +1.23607 q^{46} +2.47214 q^{47} +(-1.61803 + 0.618034i) q^{48} +(-6.70820 - 2.00000i) q^{49} +3.47214i q^{50} +(10.4721 - 4.00000i) q^{51} -1.00000i q^{52} +1.23607i q^{53} +(4.61803 + 2.38197i) q^{54} +(2.61803 + 0.381966i) q^{56} +(-3.70820 - 9.70820i) q^{57} +7.70820 q^{58} +4.47214 q^{59} +(-2.00000 + 0.763932i) q^{60} -4.47214i q^{61} +2.76393 q^{62} +(-4.38197 - 6.61803i) q^{63} -1.00000 q^{64} -1.23607i q^{65} -10.9443 q^{67} +6.47214 q^{68} +(-0.763932 - 2.00000i) q^{69} +(3.23607 + 0.472136i) q^{70} +5.52786i q^{71} +(2.00000 + 2.23607i) q^{72} +1.23607i q^{73} +4.76393i q^{74} +(5.61803 - 2.14590i) q^{75} -6.00000i q^{76} +(-1.61803 + 0.618034i) q^{78} +8.94427 q^{79} -1.23607 q^{80} +(1.00000 - 8.94427i) q^{81} +0.763932i q^{82} +14.0000 q^{83} +(-1.00000 - 4.47214i) q^{84} +8.00000 q^{85} +1.52786i q^{86} +(-4.76393 - 12.4721i) q^{87} -16.1803 q^{89} +(2.47214 + 2.76393i) q^{90} +(2.61803 + 0.381966i) q^{91} -1.23607i q^{92} +(-1.70820 - 4.47214i) q^{93} -2.47214i q^{94} -7.41641i q^{95} +(0.618034 + 1.61803i) q^{96} -5.23607i q^{97} +(-2.00000 + 6.70820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 6 * q^7	$ 4 q - 2 q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{12} - 6 q^{14} + 8 q^{15} + 4 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{24} + 4 q^{25} + 4 q^{26} - 14 q^{27} - 6 q^{28} - 12 q^{30} + 16 q^{35} - 28 q^{37} + 24 q^{38} + 2 q^{39} - 12 q^{41} - 24 q^{43} - 20 q^{45} - 4 q^{46} - 8 q^{47} - 2 q^{48} + 24 q^{51} + 14 q^{54} + 6 q^{56} + 12 q^{57} + 4 q^{58} - 8 q^{60} + 20 q^{62} - 22 q^{63} - 4 q^{64} - 8 q^{67} + 8 q^{68} - 12 q^{69} + 4 q^{70} + 8 q^{72} + 18 q^{75} - 2 q^{78} + 4 q^{80} + 4 q^{81} + 56 q^{83} - 4 q^{84} + 32 q^{85} - 28 q^{87} - 20 q^{89} - 8 q^{90} + 6 q^{91} + 20 q^{93} - 2 q^{96} - 8 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^12 - 6 * q^14 + 8 * q^15 + 4 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^21 + 2 * q^24 + 4 * q^25 + 4 * q^26 - 14 * q^27 - 6 * q^28 - 12 * q^30 + 16 * q^35 - 28 * q^37 + 24 * q^38 + 2 * q^39 - 12 * q^41 - 24 * q^43 - 20 * q^45 - 4 * q^46 - 8 * q^47 - 2 * q^48 + 24 * q^51 + 14 * q^54 + 6 * q^56 + 12 * q^57 + 4 * q^58 - 8 * q^60 + 20 * q^62 - 22 * q^63 - 4 * q^64 - 8 * q^67 + 8 * q^68 - 12 * q^69 + 4 * q^70 + 8 * q^72 + 18 * q^75 - 2 * q^78 + 4 * q^80 + 4 * q^81 + 56 * q^83 - 4 * q^84 + 32 * q^85 - 28 * q^87 - 20 * q^89 - 8 * q^90 + 6 * q^91 + 20 * q^93 - 2 * q^96 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.61803	+	0.618034i	−0.934172	+	0.356822i
$3$	−1.61803	+	0.618034i	−0.934172	+	0.356822i
$4$	−1.00000			−0.500000
$5$	−1.23607			−0.552786			−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607			−0.552786			−0.276393	+	0.961045i	$0.589139\pi$
$6$	0.618034	+	1.61803i	0.252311	+	0.660560i
$7$	0.381966	−	2.61803i	0.144370	−	0.989524i
$7$	0.381966	−	2.61803i	0.144370	−	0.989524i
$8$			1.00000i			0.353553i
$9$	2.23607	−	2.00000i	0.745356	−	0.666667i
$10$			1.23607i			0.390879i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	1.61803	−	0.618034i	0.467086	−	0.178411i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−2.61803	−	0.381966i	−0.699699	−	0.102085i
$15$	2.00000	−	0.763932i	0.516398	−	0.197246i
$16$	1.00000			0.250000
$17$	−6.47214			−1.56972			−0.784862	−	0.619671i	$-0.787266\pi$
$17$	−6.47214			−1.56972			−0.784862	+	0.619671i	$0.787266\pi$
$18$	−2.00000	−	2.23607i	−0.471405	−	0.527046i
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$	1.23607			0.276393
$21$	1.00000	+	4.47214i	0.218218	+	0.975900i
$22$		0			0
$23$			1.23607i			0.257738i	0.991662	+	0.128869i	$0.0411347\pi$
$23$			1.23607i			0.257738i	−0.991662	+	0.128869i	$0.958865\pi$
$24$	−0.618034	−	1.61803i	−0.126156	−	0.330280i
$25$	−3.47214			−0.694427
$26$	1.00000			0.196116
$27$	−2.38197	+	4.61803i	−0.458410	+	0.888741i
$28$	−0.381966	+	2.61803i	−0.0721848	+	0.494762i
$29$			7.70820i			1.43138i	0.698419	+	0.715689i	$0.253887\pi$
$29$			7.70820i			1.43138i	−0.698419	+	0.715689i	$0.746113\pi$
$30$	−0.763932	−	2.00000i	−0.139474	−	0.365148i
$31$			2.76393i			0.496417i	0.968707	+	0.248208i	$0.0798418\pi$
$31$			2.76393i			0.496417i	−0.968707	+	0.248208i	$0.920158\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$			6.47214i			1.10996i
$35$	−0.472136	+	3.23607i	−0.0798055	+	0.546995i
$36$	−2.23607	+	2.00000i	−0.372678	+	0.333333i
$37$	−4.76393			−0.783186			−0.391593	−	0.920139i	$-0.628076\pi$
$37$	−4.76393			−0.783186			−0.391593	+	0.920139i	$0.628076\pi$
$38$	6.00000			0.973329
$39$	−0.618034	−	1.61803i	−0.0989646	−	0.259093i
$40$		−	1.23607i		−	0.195440i
$41$	−0.763932			−0.119306			−0.0596531	−	0.998219i	$-0.518999\pi$
$41$	−0.763932			−0.119306			−0.0596531	+	0.998219i	$0.518999\pi$
$42$	4.47214	−	1.00000i	0.690066	−	0.154303i
$43$	−1.52786			−0.232997			−0.116499	−	0.993191i	$-0.537167\pi$
$43$	−1.52786			−0.232997			−0.116499	+	0.993191i	$0.537167\pi$
$44$		0			0
$45$	−2.76393	+	2.47214i	−0.412023	+	0.368524i
$46$	1.23607			0.182248
$47$	2.47214			0.360598			0.180299	−	0.983612i	$-0.442293\pi$
$47$	2.47214			0.360598			0.180299	+	0.983612i	$0.442293\pi$
$48$	−1.61803	+	0.618034i	−0.233543	+	0.0892055i
$49$	−6.70820	−	2.00000i	−0.958315	−	0.285714i
$50$			3.47214i			0.491034i
$51$	10.4721	−	4.00000i	1.46639	−	0.560112i
$52$		−	1.00000i		−	0.138675i
$53$			1.23607i			0.169787i	0.996390	+	0.0848935i	$0.0270550\pi$
$53$			1.23607i			0.169787i	−0.996390	+	0.0848935i	$0.972945\pi$
$54$	4.61803	+	2.38197i	0.628435	+	0.324145i
$55$		0			0
$56$	2.61803	+	0.381966i	0.349850	+	0.0510424i
$57$	−3.70820	−	9.70820i	−0.491164	−	1.28588i
$58$	7.70820			1.01214
$59$	4.47214			0.582223			0.291111	−	0.956689i	$-0.405975\pi$
$59$	4.47214			0.582223			0.291111	+	0.956689i	$0.405975\pi$
$60$	−2.00000	+	0.763932i	−0.258199	+	0.0986232i
$61$		−	4.47214i		−	0.572598i	−0.958140	−	0.286299i	$-0.907575\pi$
$61$		−	4.47214i		−	0.572598i	0.958140	−	0.286299i	$-0.0924251\pi$
$62$	2.76393			0.351020
$63$	−4.38197	−	6.61803i	−0.552076	−	0.833794i
$64$	−1.00000			−0.125000
$65$		−	1.23607i		−	0.153315i
$66$		0			0
$67$	−10.9443			−1.33706			−0.668528	−	0.743687i	$-0.733075\pi$
$67$	−10.9443			−1.33706			−0.668528	+	0.743687i	$0.733075\pi$
$68$	6.47214			0.784862
$69$	−0.763932	−	2.00000i	−0.0919666	−	0.240772i
$70$	3.23607	+	0.472136i	0.386784	+	0.0564310i
$71$			5.52786i			0.656037i	0.944671	+	0.328018i	$0.106381\pi$
$71$			5.52786i			0.656037i	−0.944671	+	0.328018i	$0.893619\pi$
$72$	2.00000	+	2.23607i	0.235702	+	0.263523i
$73$			1.23607i			0.144671i	0.997380	+	0.0723354i	$0.0230452\pi$
$73$			1.23607i			0.144671i	−0.997380	+	0.0723354i	$0.976955\pi$
$74$			4.76393i			0.553796i
$75$	5.61803	−	2.14590i	0.648715	−	0.247787i
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$	−1.61803	+	0.618034i	−0.183206	+	0.0699786i
$79$	8.94427			1.00631			0.503155	−	0.864196i	$-0.332173\pi$
$79$	8.94427			1.00631			0.503155	+	0.864196i	$0.332173\pi$
$80$	−1.23607			−0.138197
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$			0.763932i			0.0843622i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$	−1.00000	−	4.47214i	−0.109109	−	0.487950i
$85$	8.00000			0.867722
$86$			1.52786i			0.164754i
$87$	−4.76393	−	12.4721i	−0.510747	−	1.33715i
$88$		0			0
$89$	−16.1803			−1.71511			−0.857556	−	0.514390i	$-0.828018\pi$
$89$	−16.1803			−1.71511			−0.857556	+	0.514390i	$0.828018\pi$
$90$	2.47214	+	2.76393i	0.260586	+	0.291344i
$91$	2.61803	+	0.381966i	0.274445	+	0.0400409i
$92$		−	1.23607i		−	0.128869i
$93$	−1.70820	−	4.47214i	−0.177132	−	0.463739i
$94$		−	2.47214i		−	0.254981i
$95$		−	7.41641i		−	0.760907i
$96$	0.618034	+	1.61803i	0.0630778	+	0.165140i
$97$		−	5.23607i		−	0.531642i	−0.964022	−	0.265821i	$-0.914357\pi$
$97$		−	5.23607i		−	0.531642i	0.964022	−	0.265821i	$-0.0856430\pi$
$98$	−2.00000	+	6.70820i	−0.202031	+	0.677631i
$99$		0			0
$100$	3.47214			0.347214
$101$	−4.18034			−0.415959			−0.207980	−	0.978133i	$-0.566689\pi$
$101$	−4.18034			−0.415959			−0.207980	+	0.978133i	$0.566689\pi$
$102$	−4.00000	−	10.4721i	−0.396059	−	1.03690i
$103$			5.70820i			0.562446i	0.959642	+	0.281223i	$0.0907401\pi$
$103$			5.70820i			0.562446i	−0.959642	+	0.281223i	$0.909260\pi$
$104$	−1.00000			−0.0980581
$105$	−1.23607	−	5.52786i	−0.120628	−	0.539464i
$106$	1.23607			0.120058
$107$			6.47214i			0.625685i	0.949805	+	0.312842i	$0.101281\pi$
$107$			6.47214i			0.625685i	−0.949805	+	0.312842i	$0.898719\pi$
$108$	2.38197	−	4.61803i	0.229205	−	0.444371i
$109$	−16.1803			−1.54980			−0.774898	−	0.632087i	$-0.782199\pi$
$109$	−16.1803			−1.54980			−0.774898	+	0.632087i	$0.782199\pi$
$110$		0			0
$111$	7.70820	−	2.94427i	0.731630	−	0.279458i
$112$	0.381966	−	2.61803i	0.0360924	−	0.247381i
$113$		−	16.0000i		−	1.50515i	−0.658505	−	0.752577i	$-0.728811\pi$
$113$		−	16.0000i		−	1.50515i	0.658505	−	0.752577i	$-0.271189\pi$
$114$	−9.70820	+	3.70820i	−0.909257	+	0.347305i
$115$		−	1.52786i		−	0.142474i
$116$		−	7.70820i		−	0.715689i
$117$	2.00000	+	2.23607i	0.184900	+	0.206725i
$118$		−	4.47214i		−	0.411693i
$119$	−2.47214	+	16.9443i	−0.226620	+	1.55328i
$120$	0.763932	+	2.00000i	0.0697371	+	0.182574i
$121$	11.0000			1.00000
$122$	−4.47214			−0.404888
$123$	1.23607	−	0.472136i	0.111452	−	0.0425711i
$124$		−	2.76393i		−	0.248208i
$125$	10.4721			0.936656
$126$	−6.61803	+	4.38197i	−0.589581	+	0.390377i
$127$	−20.9443			−1.85850			−0.929252	−	0.369447i	$-0.879547\pi$
$127$	−20.9443			−1.85850			−0.929252	+	0.369447i	$0.879547\pi$
$128$			1.00000i			0.0883883i
$129$	2.47214	−	0.944272i	0.217659	−	0.0831385i
$130$	−1.23607			−0.108410
$131$	−0.763932			−0.0667451			−0.0333725	−	0.999443i	$-0.510625\pi$
$131$	−0.763932			−0.0667451			−0.0333725	+	0.999443i	$0.510625\pi$
$132$		0			0
$133$	15.7082	+	2.29180i	1.36207	+	0.198724i
$134$			10.9443i			0.945441i
$135$	2.94427	−	5.70820i	0.253403	−	0.491284i
$136$		−	6.47214i		−	0.554981i
$137$			16.4721i			1.40731i	0.710542	+	0.703655i	$0.248450\pi$
$137$			16.4721i			1.40731i	−0.710542	+	0.703655i	$0.751550\pi$
$138$	−2.00000	+	0.763932i	−0.170251	+	0.0650302i
$139$		−	10.1803i		−	0.863485i	−0.901997	−	0.431743i	$-0.857899\pi$
$139$		−	10.1803i		−	0.863485i	0.901997	−	0.431743i	$-0.142101\pi$
$140$	0.472136	−	3.23607i	0.0399028	−	0.273498i
$141$	−4.00000	+	1.52786i	−0.336861	+	0.128669i
$142$	5.52786			0.463888
$143$		0			0
$144$	2.23607	−	2.00000i	0.186339	−	0.166667i
$145$		−	9.52786i		−	0.791246i
$146$	1.23607			0.102298
$147$	12.0902	−	0.909830i	0.997180	−	0.0750415i
$148$	4.76393			0.391593
$149$			9.41641i			0.771422i	0.922620	+	0.385711i	$0.126044\pi$
$149$			9.41641i			0.771422i	−0.922620	+	0.385711i	$0.873956\pi$
$150$	−2.14590	−	5.61803i	−0.175212	−	0.458711i
$151$	−9.70820			−0.790042			−0.395021	−	0.918672i	$-0.629263\pi$
$151$	−9.70820			−0.790042			−0.395021	+	0.918672i	$0.629263\pi$
$152$	−6.00000			−0.486664
$153$	−14.4721	+	12.9443i	−1.17000	+	1.04648i
$154$		0			0
$155$		−	3.41641i		−	0.274412i
$156$	0.618034	+	1.61803i	0.0494823	+	0.129546i
$157$		−	21.4164i		−	1.70922i	−0.519274	−	0.854608i	$-0.673798\pi$
$157$		−	21.4164i		−	1.70922i	0.519274	−	0.854608i	$-0.326202\pi$
$158$		−	8.94427i		−	0.711568i
$159$	−0.763932	−	2.00000i	−0.0605838	−	0.158610i
$160$			1.23607i			0.0977198i
$161$	3.23607	+	0.472136i	0.255038	+	0.0372095i
$162$	−8.94427	−	1.00000i	−0.702728	−	0.0785674i
$163$	17.4164			1.36416			0.682079	−	0.731278i	$-0.261076\pi$
$163$	17.4164			1.36416			0.682079	+	0.731278i	$0.261076\pi$
$164$	0.763932			0.0596531
$165$		0			0
$166$		−	14.0000i		−	1.08661i
$167$	−0.944272			−0.0730700			−0.0365350	−	0.999332i	$-0.511632\pi$
$167$	−0.944272			−0.0730700			−0.0365350	+	0.999332i	$0.511632\pi$
$168$	−4.47214	+	1.00000i	−0.345033	+	0.0771517i
$169$	−1.00000			−0.0769231
$170$		−	8.00000i		−	0.613572i
$171$	12.0000	+	13.4164i	0.917663	+	1.02598i
$172$	1.52786			0.116499
$173$	−23.2361			−1.76661			−0.883303	−	0.468803i	$-0.844685\pi$
$173$	−23.2361			−1.76661			−0.883303	+	0.468803i	$0.844685\pi$
$174$	−12.4721	+	4.76393i	−0.945510	+	0.361153i
$175$	−1.32624	+	9.09017i	−0.100254	+	0.687152i
$176$		0			0
$177$	−7.23607	+	2.76393i	−0.543896	+	0.207750i
$178$			16.1803i			1.21277i
$179$			1.52786i			0.114198i	0.998369	+	0.0570990i	$0.0181851\pi$
$179$			1.52786i			0.114198i	−0.998369	+	0.0570990i	$0.981815\pi$
$180$	2.76393	−	2.47214i	0.206011	−	0.184262i
$181$		−	4.47214i		−	0.332411i	−0.986091	−	0.166206i	$-0.946848\pi$
$181$		−	4.47214i		−	0.332411i	0.986091	−	0.166206i	$-0.0531515\pi$
$182$	0.381966	−	2.61803i	0.0283132	−	0.194062i
$183$	2.76393	+	7.23607i	0.204316	+	0.534906i
$184$	−1.23607			−0.0911241
$185$	5.88854			0.432934
$186$	−4.47214	+	1.70820i	−0.327913	+	0.125252i
$187$		0			0
$188$	−2.47214			−0.180299
$189$	11.1803	+	8.00000i	0.813250	+	0.581914i
$190$	−7.41641			−0.538043
$191$		−	8.29180i		−	0.599973i	−0.953943	−	0.299987i	$-0.903018\pi$
$191$		−	8.29180i		−	0.599973i	0.953943	−	0.299987i	$-0.0969822\pi$
$192$	1.61803	−	0.618034i	0.116772	−	0.0446028i
$193$	−23.8885			−1.71954			−0.859768	−	0.510686i	$-0.829392\pi$
$193$	−23.8885			−1.71954			−0.859768	+	0.510686i	$0.829392\pi$
$194$	−5.23607			−0.375928
$195$	0.763932	+	2.00000i	0.0547063	+	0.143223i
$196$	6.70820	+	2.00000i	0.479157	+	0.142857i
$197$		−	1.41641i		−	0.100915i	−0.998726	−	0.0504574i	$-0.983932\pi$
$197$		−	1.41641i		−	0.100915i	0.998726	−	0.0504574i	$-0.0160679\pi$
$198$		0			0
$199$			14.2918i			1.01312i	0.862205	+	0.506559i	$0.169083\pi$
$199$			14.2918i			1.01312i	−0.862205	+	0.506559i	$0.830917\pi$
$200$		−	3.47214i		−	0.245517i
$201$	17.7082	−	6.76393i	1.24904	−	0.477091i
$202$			4.18034i			0.294128i
$203$	20.1803	+	2.94427i	1.41638	+	0.206647i
$204$	−10.4721	+	4.00000i	−0.733196	+	0.280056i
$205$	0.944272			0.0659508
$206$	5.70820			0.397709
$207$	2.47214	+	2.76393i	0.171825	+	0.192107i
$208$			1.00000i			0.0693375i
$209$		0			0
$210$	−5.52786	+	1.23607i	−0.381459	+	0.0852968i
$211$	9.88854			0.680755			0.340378	−	0.940289i	$-0.389445\pi$
$211$	9.88854			0.680755			0.340378	+	0.940289i	$0.389445\pi$
$212$		−	1.23607i		−	0.0848935i
$213$	−3.41641	−	8.94427i	−0.234088	−	0.612851i
$214$	6.47214			0.442426
$215$	1.88854			0.128798
$216$	−4.61803	−	2.38197i	−0.314217	−	0.162072i
$217$	7.23607	+	1.05573i	0.491216	+	0.0716675i
$218$			16.1803i			1.09587i
$219$	−0.763932	−	2.00000i	−0.0516217	−	0.135147i
$220$		0			0
$221$		−	6.47214i		−	0.435363i
$222$	−2.94427	−	7.70820i	−0.197607	−	0.517341i
$223$		−	13.2361i		−	0.886353i	−0.896434	−	0.443176i	$-0.853852\pi$
$223$		−	13.2361i		−	0.886353i	0.896434	−	0.443176i	$-0.146148\pi$
$224$	−2.61803	−	0.381966i	−0.174925	−	0.0255212i
$225$	−7.76393	+	6.94427i	−0.517595	+	0.462951i
$226$	−16.0000			−1.06430
$227$	12.4721			0.827805			0.413902	−	0.910321i	$-0.364165\pi$
$227$	12.4721			0.827805			0.413902	+	0.910321i	$0.364165\pi$
$228$	3.70820	+	9.70820i	0.245582	+	0.642942i
$229$			14.9443i			0.987545i	0.869591	+	0.493773i	$0.164382\pi$
$229$			14.9443i			0.987545i	−0.869591	+	0.493773i	$0.835618\pi$
$230$	−1.52786			−0.100744
$231$		0			0
$232$	−7.70820			−0.506068
$233$		−	24.9443i		−	1.63415i	−0.576529	−	0.817077i	$-0.695593\pi$
$233$		−	24.9443i		−	1.63415i	0.576529	−	0.817077i	$-0.304407\pi$
$234$	2.23607	−	2.00000i	0.146176	−	0.130744i
$235$	−3.05573			−0.199334
$236$	−4.47214			−0.291111
$237$	−14.4721	+	5.52786i	−0.940066	+	0.359073i
$238$	16.9443	+	2.47214i	1.09833	+	0.160245i
$239$		−	27.4164i		−	1.77342i	−0.462326	−	0.886710i	$-0.652985\pi$
$239$		−	27.4164i		−	1.77342i	0.462326	−	0.886710i	$-0.347015\pi$
$240$	2.00000	−	0.763932i	0.129099	−	0.0493116i
$241$			20.6525i			1.33034i	0.746691	+	0.665171i	$0.231642\pi$
$241$			20.6525i			1.33034i	−0.746691	+	0.665171i	$0.768358\pi$
$242$		−	11.0000i		−	0.707107i
$243$	3.90983	+	15.0902i	0.250816	+	0.968035i
$244$			4.47214i			0.286299i
$245$	8.29180	+	2.47214i	0.529743	+	0.157939i
$246$	−0.472136	−	1.23607i	−0.0301023	−	0.0788088i
$247$	−6.00000			−0.381771
$248$	−2.76393			−0.175510
$249$	−22.6525	+	8.65248i	−1.43554	+	0.548328i
$250$		−	10.4721i		−	0.662316i
$251$	19.2361			1.21417			0.607085	−	0.794637i	$-0.292339\pi$
$251$	19.2361			1.21417			0.607085	+	0.794637i	$0.292339\pi$
$252$	4.38197	+	6.61803i	0.276038	+	0.416897i
$253$		0			0
$254$			20.9443i			1.31416i
$255$	−12.9443	+	4.94427i	−0.810602	+	0.309622i
$256$	1.00000			0.0625000
$257$	−6.47214			−0.403721			−0.201860	−	0.979414i	$-0.564699\pi$
$257$	−6.47214			−0.403721			−0.201860	+	0.979414i	$0.564699\pi$
$258$	−0.944272	−	2.47214i	−0.0587878	−	0.153908i
$259$	−1.81966	+	12.4721i	−0.113068	+	0.774981i
$260$			1.23607i			0.0766577i
$261$	15.4164	+	17.2361i	0.954252	+	1.06689i
$262$			0.763932i			0.0471959i
$263$		−	4.29180i		−	0.264643i	−0.991207	−	0.132322i	$-0.957757\pi$
$263$		−	4.29180i		−	0.264643i	0.991207	−	0.132322i	$-0.0422432\pi$
$264$		0			0
$265$		−	1.52786i		−	0.0938559i
$266$	2.29180	−	15.7082i	0.140519	−	0.963132i
$267$	26.1803	−	10.0000i	1.60221	−	0.611990i
$268$	10.9443			0.668528
$269$	21.7082			1.32357			0.661786	−	0.749693i	$-0.269799\pi$
$269$	21.7082			1.32357			0.661786	+	0.749693i	$0.269799\pi$
$270$	−5.70820	−	2.94427i	−0.347390	−	0.179183i
$271$			26.1803i			1.59034i	0.606385	+	0.795171i	$0.292619\pi$
$271$			26.1803i			1.59034i	−0.606385	+	0.795171i	$0.707381\pi$
$272$	−6.47214			−0.392431
$273$	−4.47214	+	1.00000i	−0.270666	+	0.0605228i
$274$	16.4721			0.995118
$275$		0			0
$276$	0.763932	+	2.00000i	0.0459833	+	0.120386i
$277$	23.5279			1.41365			0.706826	−	0.707387i	$-0.250126\pi$
$277$	23.5279			1.41365			0.706826	+	0.707387i	$0.250126\pi$
$278$	−10.1803			−0.610576
$279$	5.52786	+	6.18034i	0.330945	+	0.370007i
$280$	−3.23607	−	0.472136i	−0.193392	−	0.0282155i
$281$			4.47214i			0.266785i	0.991063	+	0.133393i	$0.0425871\pi$
$281$			4.47214i			0.266785i	−0.991063	+	0.133393i	$0.957413\pi$
$282$	1.52786	+	4.00000i	0.0909830	+	0.238197i
$283$			19.1246i			1.13684i	0.822738	+	0.568420i	$0.192445\pi$
$283$			19.1246i			1.13684i	−0.822738	+	0.568420i	$0.807555\pi$
$284$		−	5.52786i		−	0.328018i
$285$	4.58359	+	12.0000i	0.271509	+	0.710819i
$286$		0			0
$287$	−0.291796	+	2.00000i	−0.0172242	+	0.118056i
$288$	−2.00000	−	2.23607i	−0.117851	−	0.131762i
$289$	24.8885			1.46403
$290$	−9.52786			−0.559495
$291$	3.23607	+	8.47214i	0.189702	+	0.496645i
$292$		−	1.23607i		−	0.0723354i
$293$	−27.7082			−1.61873			−0.809365	−	0.587306i	$-0.800189\pi$
$293$	−27.7082			−1.61873			−0.809365	+	0.587306i	$0.800189\pi$
$294$	−0.909830	−	12.0902i	−0.0530624	−	0.705113i
$295$	−5.52786			−0.321845
$296$		−	4.76393i		−	0.276898i
$297$		0			0
$298$	9.41641			0.545478
$299$	−1.23607			−0.0714837
$300$	−5.61803	+	2.14590i	−0.324357	+	0.123893i
$301$	−0.583592	+	4.00000i	−0.0336377	+	0.230556i
$302$			9.70820i			0.558644i
$303$	6.76393	−	2.58359i	0.388578	−	0.148423i
$304$			6.00000i			0.344124i
$305$			5.52786i			0.316525i
$306$	12.9443	+	14.4721i	0.739975	+	0.827317i
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$		0			0
$309$	−3.52786	−	9.23607i	−0.200693	−	0.525422i
$310$	−3.41641			−0.194039
$311$	−13.5279			−0.767095			−0.383547	−	0.923521i	$-0.625298\pi$
$311$	−13.5279			−0.767095			−0.383547	+	0.923521i	$0.625298\pi$
$312$	1.61803	−	0.618034i	0.0916031	−	0.0349893i
$313$		−	1.52786i		−	0.0863600i	−0.999067	−	0.0431800i	$-0.986251\pi$
$313$		−	1.52786i		−	0.0863600i	0.999067	−	0.0431800i	$-0.0137489\pi$
$314$	−21.4164			−1.20860
$315$	5.41641	+	8.18034i	0.305180	+	0.460910i
$316$	−8.94427			−0.503155
$317$			10.9443i			0.614692i	0.951598	+	0.307346i	$0.0994408\pi$
$317$			10.9443i			0.614692i	−0.951598	+	0.307346i	$0.900559\pi$
$318$	−2.00000	+	0.763932i	−0.112154	+	0.0428392i
$319$		0			0
$320$	1.23607			0.0690983
$321$	−4.00000	−	10.4721i	−0.223258	−	0.584498i
$322$	0.472136	−	3.23607i	0.0263111	−	0.180339i
$323$		−	38.8328i		−	2.16072i
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$		−	3.47214i		−	0.192599i
$326$		−	17.4164i		−	0.964606i
$327$	26.1803	−	10.0000i	1.44778	−	0.553001i
$328$		−	0.763932i		−	0.0421811i
$329$	0.944272	−	6.47214i	0.0520594	−	0.356820i
$330$		0			0
$331$	−30.3607			−1.66877			−0.834387	−	0.551179i	$-0.814178\pi$
$331$	−30.3607			−1.66877			−0.834387	+	0.551179i	$0.814178\pi$
$332$	−14.0000			−0.768350
$333$	−10.6525	+	9.52786i	−0.583752	+	0.522124i
$334$			0.944272i			0.0516683i
$335$	13.5279			0.739106
$336$	1.00000	+	4.47214i	0.0545545	+	0.243975i
$337$	15.8885			0.865504			0.432752	−	0.901513i	$-0.357543\pi$
$337$	15.8885			0.865504			0.432752	+	0.901513i	$0.357543\pi$
$338$			1.00000i			0.0543928i
$339$	9.88854	+	25.8885i	0.537072	+	1.40607i
$340$	−8.00000			−0.433861
$341$		0			0
$342$	13.4164	−	12.0000i	0.725476	−	0.648886i
$343$	−7.79837	+	16.7984i	−0.421073	+	0.907027i
$344$		−	1.52786i		−	0.0823769i
$345$	0.944272	+	2.47214i	0.0508379	+	0.133095i
$346$			23.2361i			1.24918i
$347$		−	20.3607i		−	1.09302i	−0.837453	−	0.546509i	$-0.815956\pi$
$347$		−	20.3607i		−	1.09302i	0.837453	−	0.546509i	$-0.184044\pi$
$348$	4.76393	+	12.4721i	0.255374	+	0.668577i
$349$			27.3050i			1.46160i	0.682591	+	0.730800i	$0.260853\pi$
$349$			27.3050i			1.46160i	−0.682591	+	0.730800i	$0.739147\pi$
$350$	9.09017	+	1.32624i	0.485890	+	0.0708904i
$351$	−4.61803	−	2.38197i	−0.246492	−	0.127140i
$352$		0			0
$353$	−21.1246			−1.12435			−0.562175	−	0.827018i	$-0.690035\pi$
$353$	−21.1246			−1.12435			−0.562175	+	0.827018i	$0.690035\pi$
$354$	2.76393	+	7.23607i	0.146901	+	0.384593i
$355$		−	6.83282i		−	0.362648i
$356$	16.1803			0.857556
$357$	−6.47214	−	28.9443i	−0.342542	−	1.53189i
$358$	1.52786			0.0807501
$359$			13.8885i			0.733009i	0.930416	+	0.366505i	$0.119446\pi$
$359$			13.8885i			0.733009i	−0.930416	+	0.366505i	$0.880554\pi$
$360$	−2.47214	−	2.76393i	−0.130293	−	0.145672i
$361$	−17.0000			−0.894737
$362$	−4.47214			−0.235050
$363$	−17.7984	+	6.79837i	−0.934172	+	0.356822i
$364$	−2.61803	−	0.381966i	−0.137222	−	0.0200205i
$365$		−	1.52786i		−	0.0799721i
$366$	7.23607	−	2.76393i	0.378235	−	0.144473i
$367$		−	18.6525i		−	0.973651i	−0.873499	−	0.486826i	$-0.838155\pi$
$367$		−	18.6525i		−	0.973651i	0.873499	−	0.486826i	$-0.161845\pi$
$368$			1.23607i			0.0644345i
$369$	−1.70820	+	1.52786i	−0.0889255	+	0.0795374i
$370$		−	5.88854i		−	0.306131i
$371$	3.23607	+	0.472136i	0.168008	+	0.0245121i
$372$	1.70820	+	4.47214i	0.0885662	+	0.231869i
$373$	−9.41641			−0.487563			−0.243782	−	0.969830i	$-0.578388\pi$
$373$	−9.41641			−0.487563			−0.243782	+	0.969830i	$0.578388\pi$
$374$		0			0
$375$	−16.9443	+	6.47214i	−0.874998	+	0.334220i
$376$			2.47214i			0.127491i
$377$	−7.70820			−0.396993
$378$	8.00000	−	11.1803i	0.411476	−	0.575055i
$379$	−30.0000			−1.54100			−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000			−1.54100			−0.770498	+	0.637442i	$0.779993\pi$
$380$			7.41641i			0.380454i
$381$	33.8885	−	12.9443i	1.73616	−	0.663155i
$382$	−8.29180			−0.424245
$383$	−21.5279			−1.10002			−0.550011	−	0.835157i	$-0.685377\pi$
$383$	−21.5279			−1.10002			−0.550011	+	0.835157i	$0.685377\pi$
$384$	−0.618034	−	1.61803i	−0.0315389	−	0.0825700i
$385$		0			0
$386$			23.8885i			1.21589i
$387$	−3.41641	+	3.05573i	−0.173666	+	0.155331i
$388$			5.23607i			0.265821i
$389$			34.5410i			1.75130i	0.482947	+	0.875650i	$0.339566\pi$
$389$			34.5410i			1.75130i	−0.482947	+	0.875650i	$0.660434\pi$
$390$	2.00000	−	0.763932i	0.101274	−	0.0386832i
$391$		−	8.00000i		−	0.404577i
$392$	2.00000	−	6.70820i	0.101015	−	0.338815i
$393$	1.23607	−	0.472136i	0.0623514	−	0.0238161i
$394$	−1.41641			−0.0713576
$395$	−11.0557			−0.556274
$396$		0			0
$397$		−	24.8328i		−	1.24632i	−0.782093	−	0.623162i	$-0.785848\pi$
$397$		−	24.8328i		−	1.24632i	0.782093	−	0.623162i	$-0.214152\pi$
$398$	14.2918			0.716383
$399$	−26.8328	+	6.00000i	−1.34332	+	0.300376i
$400$	−3.47214			−0.173607
$401$			1.05573i			0.0527205i	0.999653	+	0.0263603i	$0.00839171\pi$
$401$			1.05573i			0.0527205i	−0.999653	+	0.0263603i	$0.991608\pi$
$402$	−6.76393	−	17.7082i	−0.337354	−	0.883205i
$403$	−2.76393			−0.137681
$404$	4.18034			0.207980
$405$	−1.23607	+	11.0557i	−0.0614207	+	0.549364i
$406$	2.94427	−	20.1803i	0.146122	−	1.00153i
$407$		0			0
$408$	4.00000	+	10.4721i	0.198030	+	0.518448i
$409$			7.70820i			0.381146i	0.981673	+	0.190573i	$0.0610346\pi$
$409$			7.70820i			0.381146i	−0.981673	+	0.190573i	$0.938965\pi$
$410$		−	0.944272i		−	0.0466343i
$411$	−10.1803	−	26.6525i	−0.502159	−	1.31467i
$412$		−	5.70820i		−	0.281223i
$413$	1.70820	−	11.7082i	0.0840552	−	0.576123i
$414$	2.76393	−	2.47214i	0.135840	−	0.121499i
$415$	−17.3050			−0.849467
$416$	1.00000			0.0490290
$417$	6.29180	+	16.4721i	0.308111	+	0.806644i
$418$		0			0
$419$	1.70820			0.0834512			0.0417256	−	0.999129i	$-0.486714\pi$
$419$	1.70820			0.0834512			0.0417256	+	0.999129i	$0.486714\pi$
$420$	1.23607	+	5.52786i	0.0603139	+	0.269732i
$421$	19.2361			0.937509			0.468754	−	0.883329i	$-0.344703\pi$
$421$	19.2361			0.937509			0.468754	+	0.883329i	$0.344703\pi$
$422$		−	9.88854i		−	0.481367i
$423$	5.52786	−	4.94427i	0.268774	−	0.240399i
$424$	−1.23607			−0.0600288
$425$	22.4721			1.09006
$426$	−8.94427	+	3.41641i	−0.433351	+	0.165526i
$427$	−11.7082	−	1.70820i	−0.566600	−	0.0826658i
$428$		−	6.47214i		−	0.312842i
$429$		0			0
$430$		−	1.88854i		−	0.0910737i
$431$		−	20.0000i		−	0.963366i	−0.876346	−	0.481683i	$-0.840026\pi$
$431$		−	20.0000i		−	0.963366i	0.876346	−	0.481683i	$-0.159974\pi$
$432$	−2.38197	+	4.61803i	−0.114602	+	0.222185i
$433$			7.41641i			0.356410i	0.983993	+	0.178205i	$0.0570290\pi$
$433$			7.41641i			0.356410i	−0.983993	+	0.178205i	$0.942971\pi$
$434$	1.05573	−	7.23607i	0.0506766	−	0.347342i
$435$	5.88854	+	15.4164i	0.282334	+	0.739160i
$436$	16.1803			0.774898
$437$	−7.41641			−0.354775
$438$	−2.00000	+	0.763932i	−0.0955637	+	0.0365021i
$439$		−	32.5410i		−	1.55310i	−0.630057	−	0.776549i	$-0.716968\pi$
$439$		−	32.5410i		−	1.55310i	0.630057	−	0.776549i	$-0.283032\pi$
$440$		0			0
$441$	−19.0000	+	8.94427i	−0.904762	+	0.425918i
$442$	−6.47214			−0.307848
$443$			38.4721i			1.82787i	0.405865	+	0.913933i	$0.366970\pi$
$443$			38.4721i			1.82787i	−0.405865	+	0.913933i	$0.633030\pi$
$444$	−7.70820	+	2.94427i	−0.365815	+	0.139729i
$445$	20.0000			0.948091
$446$	−13.2361			−0.626746
$447$	−5.81966	−	15.2361i	−0.275260	−	0.720641i
$448$	−0.381966	+	2.61803i	−0.0180462	+	0.123690i
$449$		−	26.3607i		−	1.24404i	−0.783002	−	0.622019i	$-0.786313\pi$
$449$		−	26.3607i		−	1.24404i	0.783002	−	0.622019i	$-0.213687\pi$
$450$	6.94427	+	7.76393i	0.327356	+	0.365995i
$451$		0			0
$452$			16.0000i			0.752577i
$453$	15.7082	−	6.00000i	0.738036	−	0.281905i
$454$		−	12.4721i		−	0.585346i
$455$	−3.23607	−	0.472136i	−0.151709	−	0.0221341i
$456$	9.70820	−	3.70820i	0.454628	−	0.173653i
$457$	9.05573			0.423609			0.211805	−	0.977312i	$-0.432066\pi$
$457$	9.05573			0.423609			0.211805	+	0.977312i	$0.432066\pi$
$458$	14.9443			0.698300
$459$	15.4164	−	29.8885i	0.719576	−	1.39508i
$460$			1.52786i			0.0712370i
$461$	−25.2361			−1.17536			−0.587680	−	0.809093i	$-0.699959\pi$
$461$	−25.2361			−1.17536			−0.587680	+	0.809093i	$0.699959\pi$
$462$		0			0
$463$	2.29180			0.106509			0.0532544	−	0.998581i	$-0.483041\pi$
$463$	2.29180			0.106509			0.0532544	+	0.998581i	$0.483041\pi$
$464$			7.70820i			0.357844i
$465$	2.11146	+	5.52786i	0.0979164	+	0.256349i
$466$	−24.9443			−1.15552
$467$	4.18034			0.193443			0.0967215	−	0.995311i	$-0.469164\pi$
$467$	4.18034			0.193443			0.0967215	+	0.995311i	$0.469164\pi$
$468$	−2.00000	−	2.23607i	−0.0924500	−	0.103362i
$469$	−4.18034	+	28.6525i	−0.193030	+	1.32305i
$470$			3.05573i			0.140950i
$471$	13.2361	+	34.6525i	0.609886	+	1.59670i
$472$			4.47214i			0.205847i
$473$		0			0
$474$	5.52786	+	14.4721i	0.253903	+	0.664727i
$475$		−	20.8328i		−	0.955875i
$476$	2.47214	−	16.9443i	0.113310	−	0.776639i
$477$	2.47214	+	2.76393i	0.113191	+	0.126552i
$478$	−27.4164			−1.25400
$479$	5.52786			0.252575			0.126287	−	0.991994i	$-0.459694\pi$
$479$	5.52786			0.252575			0.126287	+	0.991994i	$0.459694\pi$
$480$	−0.763932	−	2.00000i	−0.0348686	−	0.0912871i
$481$		−	4.76393i		−	0.217217i
$482$	20.6525			0.940694
$483$	−5.52786	+	1.23607i	−0.251527	+	0.0562430i
$484$	−11.0000			−0.500000
$485$			6.47214i			0.293885i
$486$	15.0902	−	3.90983i	0.684504	−	0.177353i
$487$	15.2361			0.690412			0.345206	−	0.938527i	$-0.387809\pi$
$487$	15.2361			0.690412			0.345206	+	0.938527i	$0.387809\pi$
$488$	4.47214			0.202444
$489$	−28.1803	+	10.7639i	−1.27436	+	0.486762i
$490$	2.47214	−	8.29180i	0.111680	−	0.374585i
$491$		−	23.4164i		−	1.05677i	−0.849006	−	0.528384i	$-0.822798\pi$
$491$		−	23.4164i		−	1.05677i	0.849006	−	0.528384i	$-0.177202\pi$
$492$	−1.23607	+	0.472136i	−0.0557262	+	0.0212855i
$493$		−	49.8885i		−	2.24687i
$494$			6.00000i			0.269953i
$495$		0			0
$496$			2.76393i			0.124104i
$497$	14.4721	+	2.11146i	0.649164	+	0.0947118i
$498$	8.65248	+	22.6525i	0.387727	+	1.01508i
$499$	−10.0000			−0.447661			−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000			−0.447661			−0.223831	+	0.974628i	$0.571856\pi$
$500$	−10.4721			−0.468328
$501$	1.52786	−	0.583592i	0.0682599	−	0.0260730i
$502$		−	19.2361i		−	0.858548i
$503$	12.9443			0.577157			0.288578	−	0.957456i	$-0.406817\pi$
$503$	12.9443			0.577157			0.288578	+	0.957456i	$0.406817\pi$
$504$	6.61803	−	4.38197i	0.294791	−	0.195188i
$505$	5.16718			0.229937
$506$		0			0
$507$	1.61803	−	0.618034i	0.0718594	−	0.0274479i
$508$	20.9443			0.929252
$509$	−2.76393			−0.122509			−0.0612546	−	0.998122i	$-0.519510\pi$
$509$	−2.76393			−0.122509			−0.0612546	+	0.998122i	$0.519510\pi$
$510$	4.94427	+	12.9443i	0.218936	+	0.573182i
$511$	3.23607	+	0.472136i	0.143155	+	0.0208861i
$512$		−	1.00000i		−	0.0441942i
$513$	−27.7082	−	14.2918i	−1.22335	−	0.630998i
$514$			6.47214i			0.285474i
$515$		−	7.05573i		−	0.310913i
$516$	−2.47214	+	0.944272i	−0.108830	+	0.0415693i
$517$		0			0
$518$	12.4721	+	1.81966i	0.547994	+	0.0799513i
$519$	37.5967	−	14.3607i	1.65031	−	0.630364i
$520$	1.23607			0.0542052
$521$	18.8328			0.825081			0.412540	−	0.910939i	$-0.364642\pi$
$521$	18.8328			0.825081			0.412540	+	0.910939i	$0.364642\pi$
$522$	17.2361	−	15.4164i	0.754402	−	0.674758i
$523$			15.7082i			0.686872i	0.939176	+	0.343436i	$0.111591\pi$
$523$			15.7082i			0.686872i	−0.939176	+	0.343436i	$0.888409\pi$
$524$	0.763932			0.0333725
$525$	−3.47214	−	15.5279i	−0.151536	−	0.677692i
$526$	−4.29180			−0.187131
$527$		−	17.8885i		−	0.779237i
$528$		0			0
$529$	21.4721			0.933571
$530$	−1.52786			−0.0663662
$531$	10.0000	−	8.94427i	0.433963	−	0.388148i
$532$	−15.7082	−	2.29180i	−0.681037	−	0.0993620i
$533$		−	0.763932i		−	0.0330896i
$534$	−10.0000	−	26.1803i	−0.432742	−	1.13293i
$535$		−	8.00000i		−	0.345870i
$536$		−	10.9443i		−	0.472721i
$537$	−0.944272	−	2.47214i	−0.0407483	−	0.106681i
$538$		−	21.7082i		−	0.935907i
$539$		0			0
$540$	−2.94427	+	5.70820i	−0.126701	+	0.245642i
$541$	2.65248			0.114039			0.0570194	−	0.998373i	$-0.481840\pi$
$541$	2.65248			0.114039			0.0570194	+	0.998373i	$0.481840\pi$
$542$	26.1803			1.12454
$543$	2.76393	+	7.23607i	0.118612	+	0.310529i
$544$			6.47214i			0.277491i
$545$	20.0000			0.856706
$546$	1.00000	+	4.47214i	0.0427960	+	0.191390i
$547$	13.5279			0.578410			0.289205	−	0.957267i	$-0.406609\pi$
$547$	13.5279			0.578410			0.289205	+	0.957267i	$0.406609\pi$
$548$		−	16.4721i		−	0.703655i
$549$	−8.94427	−	10.0000i	−0.381732	−	0.426790i
$550$		0			0
$551$	−46.2492			−1.97028
$552$	2.00000	−	0.763932i	0.0851257	−	0.0325151i
$553$	3.41641	−	23.4164i	0.145280	−	0.995767i
$554$		−	23.5279i		−	0.999603i
$555$	−9.52786	+	3.63932i	−0.404435	+	0.154481i
$556$			10.1803i			0.431743i
$557$			22.0000i			0.932170i	0.884740	+	0.466085i	$0.154336\pi$
$557$			22.0000i			0.932170i	−0.884740	+	0.466085i	$0.845664\pi$
$558$	6.18034	−	5.52786i	0.261635	−	0.234013i
$559$		−	1.52786i		−	0.0646218i
$560$	−0.472136	+	3.23607i	−0.0199514	+	0.136749i
$561$		0			0
$562$	4.47214			0.188646
$563$	−32.1803			−1.35624			−0.678120	−	0.734951i	$-0.737205\pi$
$563$	−32.1803			−1.35624			−0.678120	+	0.734951i	$0.737205\pi$
$564$	4.00000	−	1.52786i	0.168430	−	0.0643347i
$565$			19.7771i			0.832028i
$566$	19.1246			0.803867
$567$	−23.0344	−	6.03444i	−0.967356	−	0.253423i
$568$	−5.52786			−0.231944
$569$		−	36.3607i		−	1.52432i	−0.647389	−	0.762159i	$-0.724139\pi$
$569$		−	36.3607i		−	1.52432i	0.647389	−	0.762159i	$-0.275861\pi$
$570$	12.0000	−	4.58359i	0.502625	−	0.191986i
$571$	−13.5279			−0.566123			−0.283062	−	0.959102i	$-0.591350\pi$
$571$	−13.5279			−0.566123			−0.283062	+	0.959102i	$0.591350\pi$
$572$		0			0
$573$	5.12461	+	13.4164i	0.214084	+	0.560478i
$574$	2.00000	+	0.291796i	0.0834784	+	0.0121793i
$575$		−	4.29180i		−	0.178980i
$576$	−2.23607	+	2.00000i	−0.0931695	+	0.0833333i
$577$		−	43.1246i		−	1.79530i	−0.440708	−	0.897651i	$-0.645273\pi$
$577$		−	43.1246i		−	1.79530i	0.440708	−	0.897651i	$-0.354727\pi$
$578$		−	24.8885i		−	1.03523i
$579$	38.6525	−	14.7639i	1.60634	−	0.613568i
$580$			9.52786i			0.395623i
$581$	5.34752	−	36.6525i	0.221853	−	1.52060i
$582$	8.47214	−	3.23607i	0.351181	−	0.134139i
$583$		0			0
$584$	−1.23607			−0.0511489
$585$	−2.47214	−	2.76393i	−0.102210	−	0.114275i
$586$			27.7082i			1.14462i
$587$	21.4164			0.883950			0.441975	−	0.897027i	$-0.354278\pi$
$587$	21.4164			0.883950			0.441975	+	0.897027i	$0.354278\pi$
$588$	−12.0902	+	0.909830i	−0.498590	+	0.0375208i
$589$	−16.5836			−0.683315
$590$			5.52786i			0.227579i
$591$	0.875388	+	2.29180i	0.0360087	+	0.0942719i
$592$	−4.76393			−0.195796
$593$	18.0689			0.742000			0.371000	−	0.928633i	$-0.379015\pi$
$593$	18.0689			0.742000			0.371000	+	0.928633i	$0.379015\pi$
$594$		0			0
$595$	3.05573	−	20.9443i	0.125273	−	0.858631i
$596$		−	9.41641i		−	0.385711i
$597$	−8.83282	−	23.1246i	−0.361503	−	0.946427i
$598$			1.23607i			0.0505466i
$599$			34.5410i			1.41131i	0.708557	+	0.705654i	$0.249347\pi$
$599$			34.5410i			1.41131i	−0.708557	+	0.705654i	$0.750653\pi$
$600$	2.14590	+	5.61803i	0.0876059	+	0.229355i
$601$			23.4164i			0.955175i	0.878584	+	0.477588i	$0.158489\pi$
$601$			23.4164i			0.955175i	−0.878584	+	0.477588i	$0.841511\pi$
$602$	4.00000	+	0.583592i	0.163028	+	0.0237854i
$603$	−24.4721	+	21.8885i	−0.996582	+	0.891370i
$604$	9.70820			0.395021
$605$	−13.5967			−0.552786
$606$	−2.58359	−	6.76393i	−0.104951	−	0.274766i
$607$			17.1246i			0.695067i	0.937668	+	0.347533i	$0.112981\pi$
$607$			17.1246i			0.695067i	−0.937668	+	0.347533i	$0.887019\pi$
$608$	6.00000			0.243332
$609$	−34.4721	+	7.70820i	−1.39688	+	0.312352i
$610$	5.52786			0.223817
$611$			2.47214i			0.100012i
$612$	14.4721	−	12.9443i	0.585001	−	0.523241i
$613$	2.29180			0.0925648			0.0462824	−	0.998928i	$-0.485263\pi$
$613$	2.29180			0.0925648			0.0462824	+	0.998928i	$0.485263\pi$
$614$	−18.0000			−0.726421
$615$	−1.52786	+	0.583592i	−0.0616094	+	0.0235327i
$616$		0			0
$617$			37.7771i			1.52085i	0.649427	+	0.760424i	$0.275009\pi$
$617$			37.7771i			1.52085i	−0.649427	+	0.760424i	$0.724991\pi$
$618$	−9.23607	+	3.52786i	−0.371529	+	0.141912i
$619$			0.472136i			0.0189767i	0.999955	+	0.00948837i	$0.00302029\pi$
$619$			0.472136i			0.0189767i	−0.999955	+	0.00948837i	$0.996980\pi$
$620$			3.41641i			0.137206i
$621$	−5.70820	−	2.94427i	−0.229062	−	0.118150i
$622$			13.5279i			0.542418i
$623$	−6.18034	+	42.3607i	−0.247610	+	1.69714i
$624$	−0.618034	−	1.61803i	−0.0247412	−	0.0647732i
$625$	4.41641			0.176656
$626$	−1.52786			−0.0610657
$627$		0			0
$628$			21.4164i			0.854608i
$629$	30.8328			1.22938
$630$	8.18034	−	5.41641i	0.325913	−	0.215795i
$631$	48.1803			1.91803			0.959015	−	0.283357i	$-0.0914481\pi$
$631$	48.1803			1.91803			0.959015	+	0.283357i	$0.0914481\pi$
$632$			8.94427i			0.355784i
$633$	−16.0000	+	6.11146i	−0.635943	+	0.242909i
$634$	10.9443			0.434653
$635$	25.8885			1.02736
$636$	0.763932	+	2.00000i	0.0302919	+	0.0793052i
$637$	2.00000	−	6.70820i	0.0792429	−	0.265789i
$638$		0			0
$639$	11.0557	+	12.3607i	0.437358	+	0.488981i
$640$		−	1.23607i		−	0.0488599i
$641$			25.5279i			1.00829i	0.863619	+	0.504145i	$0.168192\pi$
$641$			25.5279i			1.00829i	−0.863619	+	0.504145i	$0.831808\pi$
$642$	−10.4721	+	4.00000i	−0.413302	+	0.157867i
$643$		−	3.88854i		−	0.153349i	−0.997056	−	0.0766746i	$-0.975570\pi$
$643$		−	3.88854i		−	0.153349i	0.997056	−	0.0766746i	$-0.0244303\pi$
$644$	−3.23607	−	0.472136i	−0.127519	−	0.0186048i
$645$	−3.05573	+	1.16718i	−0.120319	+	0.0459578i
$646$	−38.8328			−1.52786
$647$	−24.3607			−0.957717			−0.478859	−	0.877892i	$-0.658949\pi$
$647$	−24.3607			−0.957717			−0.478859	+	0.877892i	$0.658949\pi$
$648$	8.94427	+	1.00000i	0.351364	+	0.0392837i
$649$		0			0
$650$	−3.47214			−0.136188
$651$	−12.3607	+	2.76393i	−0.484453	+	0.108327i
$652$	−17.4164			−0.682079
$653$		−	36.6525i		−	1.43432i	−0.696907	−	0.717161i	$-0.745441\pi$
$653$		−	36.6525i		−	1.43432i	0.696907	−	0.717161i	$-0.254559\pi$
$654$	−10.0000	−	26.1803i	−0.391031	−	1.02373i
$655$	0.944272			0.0368958
$656$	−0.763932			−0.0298265
$657$	2.47214	+	2.76393i	0.0964472	+	0.107831i
$658$	−6.47214	−	0.944272i	−0.252310	−	0.0368116i
$659$			33.8885i			1.32011i	0.751217	+	0.660055i	$0.229467\pi$
$659$			33.8885i			1.32011i	−0.751217	+	0.660055i	$0.770533\pi$
$660$		0			0
$661$			6.58359i			0.256072i	0.991770	+	0.128036i	$0.0408673\pi$
$661$			6.58359i			0.256072i	−0.991770	+	0.128036i	$0.959133\pi$
$662$			30.3607i			1.18000i
$663$	4.00000	+	10.4721i	0.155347	+	0.406704i
$664$			14.0000i			0.543305i
$665$	−19.4164	−	2.83282i	−0.752936	−	0.109852i
$666$	9.52786	+	10.6525i	0.369197	+	0.412775i
$667$	−9.52786			−0.368920
$668$	0.944272			0.0365350
$669$	8.18034	+	21.4164i	0.316270	+	0.828006i
$670$		−	13.5279i		−	0.522627i
$671$		0			0
$672$	4.47214	−	1.00000i	0.172516	−	0.0385758i
$673$	40.8328			1.57399			0.786995	−	0.616960i	$-0.211636\pi$
$673$	40.8328			1.57399			0.786995	+	0.616960i	$0.211636\pi$
$674$		−	15.8885i		−	0.612004i
$675$	8.27051	−	16.0344i	0.318332	−	0.617166i
$676$	1.00000			0.0384615
$677$	−22.6525			−0.870605			−0.435303	−	0.900284i	$-0.643359\pi$
$677$	−22.6525			−0.870605			−0.435303	+	0.900284i	$0.643359\pi$
$678$	25.8885	−	9.88854i	0.994244	−	0.379767i
$679$	−13.7082	−	2.00000i	−0.526073	−	0.0767530i
$680$			8.00000i			0.306786i
$681$	−20.1803	+	7.70820i	−0.773312	+	0.295379i
$682$		0			0
$683$			10.8328i			0.414506i	0.978287	+	0.207253i	$0.0664524\pi$
$683$			10.8328i			0.414506i	−0.978287	+	0.207253i	$0.933548\pi$
$684$	−12.0000	−	13.4164i	−0.458831	−	0.512989i
$685$		−	20.3607i		−	0.777942i
$686$	16.7984	+	7.79837i	0.641365	+	0.297743i
$687$	−9.23607	−	24.1803i	−0.352378	−	0.922538i
$688$	−1.52786			−0.0582493
$689$	−1.23607			−0.0470904
$690$	2.47214	−	0.944272i	0.0941126	−	0.0359478i
$691$			10.0000i			0.380418i	0.981744	+	0.190209i	$0.0609166\pi$
$691$			10.0000i			0.380418i	−0.981744	+	0.190209i	$0.939083\pi$
$692$	23.2361			0.883303
$693$		0			0
$694$	−20.3607			−0.772881
$695$			12.5836i			0.477323i
$696$	12.4721	−	4.76393i	0.472755	−	0.180576i
$697$	4.94427			0.187278
$698$	27.3050			1.03351
$699$	15.4164	+	40.3607i	0.583102	+	1.52658i
$700$	1.32624	−	9.09017i	0.0501271	−	0.343576i
$701$		−	17.2361i		−	0.650997i	−0.945543	−	0.325499i	$-0.894468\pi$
$701$		−	17.2361i		−	0.650997i	0.945543	−	0.325499i	$-0.105532\pi$
$702$	−2.38197	+	4.61803i	−0.0899015	+	0.174296i
$703$		−	28.5836i		−	1.07805i
$704$		0			0
$705$	4.94427	−	1.88854i	0.186212	−	0.0711267i
$706$			21.1246i			0.795035i
$707$	−1.59675	+	10.9443i	−0.0600519	+	0.411602i
$708$	7.23607	−	2.76393i	0.271948	−	0.103875i
$709$	7.23607			0.271756			0.135878	−	0.990726i	$-0.456614\pi$
$709$	7.23607			0.271756			0.135878	+	0.990726i	$0.456614\pi$
$710$	−6.83282			−0.256431
$711$	20.0000	−	17.8885i	0.750059	−	0.670873i
$712$		−	16.1803i		−	0.606384i
$713$	−3.41641			−0.127945
$714$	−28.9443	+	6.47214i	−1.08321	+	0.242214i
$715$		0			0
$716$		−	1.52786i		−	0.0570990i
$717$	16.9443	+	44.3607i	0.632795	+	1.65668i
$718$	13.8885			0.518316
$719$	−44.7214			−1.66783			−0.833913	−	0.551896i	$-0.813904\pi$
$719$	−44.7214			−1.66783			−0.833913	+	0.551896i	$0.813904\pi$
$720$	−2.76393	+	2.47214i	−0.103006	+	0.0921311i
$721$	14.9443	+	2.18034i	0.556554	+	0.0812001i
$722$			17.0000i			0.632674i
$723$	−12.7639	−	33.4164i	−0.474696	−	1.24277i
$724$			4.47214i			0.166206i
$725$		−	26.7639i		−	0.993987i
$726$	6.79837	+	17.7984i	0.252311	+	0.660560i
$727$			15.8197i			0.586719i	0.956002	+	0.293359i	$0.0947732\pi$
$727$			15.8197i			0.586719i	−0.956002	+	0.293359i	$0.905227\pi$
$728$	−0.381966	+	2.61803i	−0.0141566	+	0.0970308i
$729$	−15.6525	−	22.0000i	−0.579721	−	0.814815i
$730$	−1.52786			−0.0565488
$731$	9.88854			0.365741
$732$	−2.76393	−	7.23607i	−0.102158	−	0.267453i
$733$			14.0000i			0.517102i	0.965998	+	0.258551i	$0.0832450\pi$
$733$			14.0000i			0.517102i	−0.965998	+	0.258551i	$0.916755\pi$
$734$	−18.6525			−0.688475
$735$	−14.9443	+	1.12461i	−0.551228	+	0.0414819i
$736$	1.23607			0.0455621
$737$		0			0
$738$	1.52786	+	1.70820i	0.0562415	+	0.0628799i
$739$	36.8328			1.35492			0.677459	−	0.735561i	$-0.263081\pi$
$739$	36.8328			1.35492			0.677459	+	0.735561i	$0.263081\pi$
$740$	−5.88854			−0.216467
$741$	9.70820	−	3.70820i	0.356640	−	0.136224i
$742$	0.472136	−	3.23607i	0.0173327	−	0.118800i
$743$			45.3050i			1.66208i	0.556215	+	0.831039i	$0.312253\pi$
$743$			45.3050i			1.66208i	−0.556215	+	0.831039i	$0.687747\pi$
$744$	4.47214	−	1.70820i	0.163956	−	0.0626258i
$745$		−	11.6393i		−	0.426432i
$746$			9.41641i			0.344759i
$747$	31.3050	−	28.0000i	1.14539	−	1.02447i
$748$		0			0
$749$	16.9443	+	2.47214i	0.619130	+	0.0903299i
$750$	6.47214	+	16.9443i	0.236329	+	0.618717i
$751$	−29.3050			−1.06935			−0.534676	−	0.845057i	$-0.679567\pi$
$751$	−29.3050			−1.06935			−0.534676	+	0.845057i	$0.679567\pi$
$752$	2.47214			0.0901495
$753$	−31.1246	+	11.8885i	−1.13424	+	0.433243i
$754$			7.70820i			0.280716i
$755$	12.0000			0.436725
$756$	−11.1803	−	8.00000i	−0.406625	−	0.290957i
$757$	−34.3607			−1.24886			−0.624430	−	0.781081i	$-0.714669\pi$
$757$	−34.3607			−1.24886			−0.624430	+	0.781081i	$0.714669\pi$
$758$			30.0000i			1.08965i
$759$		0			0
$760$	7.41641			0.269021
$761$	−26.2918			−0.953077			−0.476538	−	0.879154i	$-0.658109\pi$
$761$	−26.2918			−0.953077			−0.476538	+	0.879154i	$0.658109\pi$
$762$	−12.9443	−	33.8885i	−0.468921	−	1.22765i
$763$	−6.18034	+	42.3607i	−0.223743	+	1.53356i
$764$			8.29180i			0.299987i
$765$	17.8885	−	16.0000i	0.646762	−	0.578481i
$766$			21.5279i			0.777833i
$767$			4.47214i			0.161479i
$768$	−1.61803	+	0.618034i	−0.0583858	+	0.0223014i
$769$			14.5410i			0.524363i	0.965019	+	0.262181i	$0.0844418\pi$
$769$			14.5410i			0.524363i	−0.965019	+	0.262181i	$0.915558\pi$
$770$		0			0
$771$	10.4721	−	4.00000i	0.377145	−	0.144056i
$772$	23.8885			0.859768
$773$	−27.7082			−0.996595			−0.498297	−	0.867006i	$-0.666041\pi$
$773$	−27.7082			−0.996595			−0.498297	+	0.867006i	$0.666041\pi$
$774$	3.05573	+	3.41641i	0.109836	+	0.122800i
$775$		−	9.59675i		−	0.344725i
$776$	5.23607			0.187964
$777$	−4.76393	−	21.3050i	−0.170905	−	0.764311i
$778$	34.5410			1.23836
$779$		−	4.58359i		−	0.164224i
$780$	−0.763932	−	2.00000i	−0.0273532	−	0.0716115i
$781$		0			0
$782$	−8.00000			−0.286079
$783$	−35.5967	−	18.3607i	−1.27212	−	0.656157i
$784$	−6.70820	−	2.00000i	−0.239579	−	0.0714286i
$785$			26.4721i			0.944831i
$786$	−0.472136	−	1.23607i	−0.0168405	−	0.0440891i
$787$			45.4164i			1.61892i	0.587175	+	0.809460i	$0.300240\pi$
$787$			45.4164i			1.61892i	−0.587175	+	0.809460i	$0.699760\pi$
$788$			1.41641i			0.0504574i
$789$	2.65248	+	6.94427i	0.0944306	+	0.247223i
$790$			11.0557i			0.393345i
$791$	−41.8885	−	6.11146i	−1.48939	−	0.217298i
$792$		0			0
$793$	4.47214			0.158810
$794$	−24.8328			−0.881284
$795$	0.944272	+	2.47214i	0.0334899	+	0.0876776i
$796$		−	14.2918i		−	0.506559i
$797$	13.1246			0.464898			0.232449	−	0.972609i	$-0.425326\pi$
$797$	13.1246			0.464898			0.232449	+	0.972609i	$0.425326\pi$
$798$	6.00000	+	26.8328i	0.212398	+	0.949871i
$799$	−16.0000			−0.566039
$800$			3.47214i			0.122759i
$801$	−36.1803	+	32.3607i	−1.27837	+	1.14341i
$802$	1.05573			0.0372791
$803$		0			0
$804$	−17.7082	+	6.76393i	−0.624520	+	0.238545i
$805$	−4.00000	−	0.583592i	−0.140981	−	0.0205689i
$806$			2.76393i			0.0973554i
$807$	−35.1246	+	13.4164i	−1.23644	+	0.472280i
$808$		−	4.18034i		−	0.147064i
$809$		−	0.583592i		−	0.0205180i	−0.999947	−	0.0102590i	$-0.996734\pi$
$809$		−	0.583592i		−	0.0205180i	0.999947	−	0.0102590i	$-0.00326560\pi$
$810$	11.0557	+	1.23607i	0.388459	+	0.0434310i
$811$			31.3050i			1.09927i	0.835406	+	0.549633i	$0.185232\pi$
$811$			31.3050i			1.09927i	−0.835406	+	0.549633i	$0.814768\pi$
$812$	−20.1803	−	2.94427i	−0.708191	−	0.103324i
$813$	−16.1803	−	42.3607i	−0.567469	−	1.48565i
$814$		0			0
$815$	−21.5279			−0.754088
$816$	10.4721	−	4.00000i	0.366598	−	0.140028i
$817$		−	9.16718i		−	0.320719i
$818$	7.70820			0.269511
$819$	6.61803	−	4.38197i	0.231253	−	0.153118i
$820$	−0.944272			−0.0329754
$821$			1.05573i			0.0368452i	0.999830	+	0.0184226i	$0.00586442\pi$
$821$			1.05573i			0.0368452i	−0.999830	+	0.0184226i	$0.994136\pi$
$822$	−26.6525	+	10.1803i	−0.929612	+	0.355080i
$823$	32.9443			1.14837			0.574183	−	0.818727i	$-0.305320\pi$
$823$	32.9443			1.14837			0.574183	+	0.818727i	$0.305320\pi$
$824$	−5.70820			−0.198855
$825$		0			0
$826$	−11.7082	−	1.70820i	−0.407381	−	0.0594360i
$827$		−	19.0557i		−	0.662633i	−0.943520	−	0.331316i	$-0.892507\pi$
$827$		−	19.0557i		−	0.662633i	0.943520	−	0.331316i	$-0.107493\pi$
$828$	−2.47214	−	2.76393i	−0.0859127	−	0.0960533i
$829$			29.4164i			1.02167i	0.859678	+	0.510837i	$0.170664\pi$
$829$			29.4164i			1.02167i	−0.859678	+	0.510837i	$0.829336\pi$
$830$			17.3050i			0.600664i
$831$	−38.0689	+	14.5410i	−1.32059	+	0.504422i
$832$		−	1.00000i		−	0.0346688i
$833$	43.4164	+	12.9443i	1.50429	+	0.448492i
$834$	16.4721	−	6.29180i	0.570383	−	0.217867i
$835$	1.16718			0.0403921
$836$		0			0
$837$	−12.7639	−	6.58359i	−0.441186	−	0.227562i
$838$		−	1.70820i		−	0.0590089i
$839$	−44.7214			−1.54395			−0.771976	−	0.635651i	$-0.780732\pi$
$839$	−44.7214			−1.54395			−0.771976	+	0.635651i	$0.780732\pi$
$840$	5.52786	−	1.23607i	0.190729	−	0.0426484i
$841$	−30.4164			−1.04884
$842$		−	19.2361i		−	0.662919i
$843$	−2.76393	−	7.23607i	−0.0951949	−	0.249223i
$844$	−9.88854			−0.340378
$845$	1.23607			0.0425220
$846$	−4.94427	−	5.52786i	−0.169988	−	0.190052i
$847$	4.20163	−	28.7984i	0.144370	−	0.989524i
$848$			1.23607i			0.0424467i
$849$	−11.8197	−	30.9443i	−0.405650	−	1.06200i
$850$		−	22.4721i		−	0.770788i
$851$		−	5.88854i		−	0.201857i
$852$	3.41641	+	8.94427i	0.117044	+	0.306426i
$853$			35.3050i			1.20882i	0.796674	+	0.604409i	$0.206591\pi$
$853$			35.3050i			1.20882i	−0.796674	+	0.604409i	$0.793409\pi$
$854$	−1.70820	+	11.7082i	−0.0584535	+	0.400646i
$855$	−14.8328	−	16.5836i	−0.507272	−	0.567147i
$856$	−6.47214			−0.221213
$857$	52.7214			1.80093			0.900464	−	0.434931i	$-0.143227\pi$
$857$	52.7214			1.80093			0.900464	+	0.434931i	$0.143227\pi$
$858$		0			0
$859$			7.70820i			0.263001i	0.991316	+	0.131500i	$0.0419794\pi$
$859$			7.70820i			0.263001i	−0.991316	+	0.131500i	$0.958021\pi$
$860$	−1.88854			−0.0643988
$861$	−0.763932	−	3.41641i	−0.0260347	−	0.116431i
$862$	−20.0000			−0.681203
$863$		−	17.3050i		−	0.589067i	−0.955641	−	0.294534i	$-0.904836\pi$
$863$		−	17.3050i		−	0.589067i	0.955641	−	0.294534i	$-0.0951643\pi$
$864$	4.61803	+	2.38197i	0.157109	+	0.0810361i
$865$	28.7214			0.976556
$866$	7.41641			0.252020
$867$	−40.2705	+	15.3820i	−1.36766	+	0.522399i
$868$	−7.23607	−	1.05573i	−0.245608	−	0.0358337i
$869$		0			0
$870$	15.4164	−	5.88854i	0.522665	−	0.199640i
$871$		−	10.9443i		−	0.370833i
$872$		−	16.1803i		−	0.547935i
$873$	−10.4721	−	11.7082i	−0.354428	−	0.396263i
$874$			7.41641i			0.250864i
$875$	4.00000	−	27.4164i	0.135225	−	0.926844i
$876$	0.763932	+	2.00000i	0.0258109	+	0.0675737i
$877$	−13.7082			−0.462893			−0.231447	−	0.972848i	$-0.574346\pi$
$877$	−13.7082			−0.462893			−0.231447	+	0.972848i	$0.574346\pi$
$878$	−32.5410			−1.09821
$879$	44.8328	−	17.1246i	1.51217	−	0.577599i
$880$		0			0
$881$	17.5279			0.590529			0.295264	−	0.955416i	$-0.404592\pi$
$881$	17.5279			0.590529			0.295264	+	0.955416i	$0.404592\pi$
$882$	8.94427	+	19.0000i	0.301169	+	0.639763i
$883$	18.4721			0.621637			0.310818	−	0.950469i	$-0.399397\pi$
$883$	18.4721			0.621637			0.310818	+	0.950469i	$0.399397\pi$
$884$			6.47214i			0.217681i
$885$	8.94427	−	3.41641i	0.300658	−	0.114841i
$886$	38.4721			1.29250
$887$	10.1115			0.339509			0.169755	−	0.985486i	$-0.445702\pi$
$887$	10.1115			0.339509			0.169755	+	0.985486i	$0.445702\pi$
$888$	2.94427	+	7.70820i	0.0988033	+	0.258670i
$889$	−8.00000	+	54.8328i	−0.268311	+	1.83903i
$890$		−	20.0000i		−	0.670402i
$891$		0			0
$892$			13.2361i			0.443176i
$893$			14.8328i			0.496361i
$894$	−15.2361	+	5.81966i	−0.509570	+	0.194639i
$895$		−	1.88854i		−	0.0631271i
$896$	2.61803	+	0.381966i	0.0874624	+	0.0127606i
$897$	2.00000	−	0.763932i	0.0667781	−	0.0255069i
$898$	−26.3607			−0.879667
$899$	−21.3050			−0.710560
$900$	7.76393	−	6.94427i	0.258798	−	0.231476i
$901$		−	8.00000i		−	0.266519i
$902$		0			0
$903$	−1.52786	−	6.83282i	−0.0508441	−	0.227382i
$904$	16.0000			0.532152
$905$			5.52786i			0.183752i
$906$	−6.00000	−	15.7082i	−0.199337	−	0.521870i
$907$	34.8328			1.15660			0.578302	−	0.815823i	$-0.303715\pi$
$907$	34.8328			1.15660			0.578302	+	0.815823i	$0.303715\pi$
$908$	−12.4721			−0.413902
$909$	−9.34752	+	8.36068i	−0.310038	+	0.277306i
$910$	−0.472136	+	3.23607i	−0.0156512	+	0.107275i
$911$			11.7082i			0.387910i	0.981010	+	0.193955i	$0.0621316\pi$
$911$			11.7082i			0.387910i	−0.981010	+	0.193955i	$0.937868\pi$
$912$	−3.70820	−	9.70820i	−0.122791	−	0.321471i
$913$		0			0
$914$		−	9.05573i		−	0.299537i
$915$	−3.41641	−	8.94427i	−0.112943	−	0.295689i
$916$		−	14.9443i		−	0.493773i
$917$	−0.291796	+	2.00000i	−0.00963596	+	0.0660458i
$918$	−29.8885	−	15.4164i	−0.986469	−	0.508817i
$919$	44.7214			1.47522			0.737611	−	0.675226i	$-0.235954\pi$
$919$	44.7214			1.47522			0.737611	+	0.675226i	$0.235954\pi$
$920$	1.52786			0.0503722
$921$	11.1246	+	29.1246i	0.366568	+	0.959689i
$922$			25.2361i			0.831106i
$923$	−5.52786			−0.181952
$924$		0			0
$925$	16.5410			0.543865
$926$		−	2.29180i		−	0.0753131i
$927$	11.4164	+	12.7639i	0.374964	+	0.419223i
$928$	7.70820			0.253034
$929$	47.2361			1.54977			0.774883	−	0.632105i	$-0.217809\pi$
$929$	47.2361			1.54977			0.774883	+	0.632105i	$0.217809\pi$
$930$	5.52786	−	2.11146i	0.181266	−	0.0692374i
$931$	12.0000	−	40.2492i	0.393284	−	1.31912i
$932$			24.9443i			0.817077i
$933$	21.8885	−	8.36068i	0.716599	−	0.273716i
$934$		−	4.18034i		−	0.136785i
$935$		0			0
$936$	−2.23607	+	2.00000i	−0.0730882	+	0.0653720i
$937$		−	45.8885i		−	1.49911i	−0.661940	−	0.749557i	$-0.730267\pi$
$937$		−	45.8885i		−	1.49911i	0.661940	−	0.749557i	$-0.269733\pi$
$938$	28.6525	+	4.18034i	0.935536	+	0.136493i
$939$	0.944272	+	2.47214i	0.0308151	+	0.0806751i
$940$	3.05573			0.0996669
$941$	25.0132			0.815406			0.407703	−	0.913115i	$-0.366330\pi$
$941$	25.0132			0.815406			0.407703	+	0.913115i	$0.366330\pi$
$942$	34.6525	−	13.2361i	1.12904	−	0.431254i
$943$		−	0.944272i		−	0.0307497i
$944$	4.47214			0.145556
$945$	−13.8197	−	9.88854i	−0.449554	−	0.321674i
$946$		0			0
$947$			40.9443i			1.33051i	0.746616	+	0.665255i	$0.231677\pi$
$947$			40.9443i			1.33051i	−0.746616	+	0.665255i	$0.768323\pi$
$948$	14.4721	−	5.52786i	0.470033	−	0.179537i
$949$	−1.23607			−0.0401245
$950$	−20.8328			−0.675906
$951$	−6.76393	−	17.7082i	−0.219336	−	0.574228i
$952$	−16.9443	−	2.47214i	−0.549167	−	0.0801224i
$953$			45.3050i			1.46757i	0.679381	+	0.733786i	$0.262248\pi$
$953$			45.3050i			1.46757i	−0.679381	+	0.733786i	$0.737752\pi$
$954$	2.76393	−	2.47214i	0.0894856	−	0.0800384i
$955$			10.2492i			0.331657i
$956$			27.4164i			0.886710i
$957$		0			0
$958$		−	5.52786i		−	0.178597i
$959$	43.1246	+	6.29180i	1.39257	+	0.203173i
$960$	−2.00000	+	0.763932i	−0.0645497	+	0.0246558i
$961$	23.3607			0.753570
$962$	−4.76393			−0.153595
$963$	12.9443	+	14.4721i	0.417123	+	0.466358i
$964$		−	20.6525i		−	0.665171i
$965$	29.5279			0.950536
$966$	1.23607	+	5.52786i	0.0397698	+	0.177856i
$967$	11.8197			0.380095			0.190047	−	0.981775i	$-0.439136\pi$
$967$	11.8197			0.380095			0.190047	+	0.981775i	$0.439136\pi$
$968$			11.0000i			0.353553i
$969$	24.0000	+	62.8328i	0.770991	+	2.01848i
$970$	6.47214			0.207808
$971$	13.7082			0.439917			0.219959	−	0.975509i	$-0.429408\pi$
$971$	13.7082			0.439917			0.219959	+	0.975509i	$0.429408\pi$
$972$	−3.90983	−	15.0902i	−0.125408	−	0.484017i
$973$	−26.6525	−	3.88854i	−0.854439	−	0.124661i
$974$		−	15.2361i		−	0.488195i
$975$	2.14590	+	5.61803i	0.0687237	+	0.179921i
$976$		−	4.47214i		−	0.143150i
$977$			5.41641i			0.173286i	0.996239	+	0.0866431i	$0.0276140\pi$
$977$			5.41641i			0.173286i	−0.996239	+	0.0866431i	$0.972386\pi$
$978$	10.7639	+	28.1803i	0.344193	+	0.901108i
$979$		0			0
$980$	−8.29180	−	2.47214i	−0.264872	−	0.0789695i
$981$	−36.1803	+	32.3607i	−1.15515	+	1.03320i
$982$	−23.4164			−0.747248
$983$	26.1115			0.832826			0.416413	−	0.909176i	$-0.363287\pi$
$983$	26.1115			0.832826			0.416413	+	0.909176i	$0.363287\pi$
$984$	0.472136	+	1.23607i	0.0150511	+	0.0394044i
$985$			1.75078i			0.0557844i
$986$	−49.8885			−1.58877
$987$	2.47214	+	11.0557i	0.0786890	+	0.351908i
$988$	6.00000			0.190885
$989$		−	1.88854i		−	0.0600522i
$990$		0			0
$991$	−20.3607			−0.646778			−0.323389	−	0.946266i	$-0.604822\pi$
$991$	−20.3607			−0.646778			−0.323389	+	0.946266i	$0.604822\pi$
$992$	2.76393			0.0877549
$993$	49.1246	−	18.7639i	1.55892	−	0.595455i
$994$	2.11146	−	14.4721i	0.0669713	−	0.459028i
$995$		−	17.6656i		−	0.560038i
$996$	22.6525	−	8.65248i	0.717771	−	0.274164i
$997$		−	29.0557i		−	0.920204i	−0.887866	−	0.460102i	$-0.847813\pi$
$997$		−	29.0557i		−	0.920204i	0.887866	−	0.460102i	$-0.152187\pi$
$998$			10.0000i			0.316544i
$999$	11.3475	−	22.0000i	0.359020	−	0.696049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.g.a.209.1	✓	4
3.2	odd	2		546.2.g.b.209.4	yes	4
7.6	odd	2		546.2.g.b.209.2	yes	4
21.20	even	2	inner	546.2.g.a.209.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.g.a.209.1	✓	4	1.1	even	1	trivial
546.2.g.a.209.3	yes	4	21.20	even	2	inner
546.2.g.b.209.2	yes	4	7.6	odd	2
546.2.g.b.209.4	yes	4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +1.23607i q^{10} +(1.61803 - 0.618034i) q^{12} +1.00000i q^{13} +(-2.61803 - 0.381966i) q^{14} +(2.00000 - 0.763932i) q^{15} +1.00000 q^{16} -6.47214 q^{17} +(-2.00000 - 2.23607i) q^{18} +6.00000i q^{19} +1.23607 q^{20} +(1.00000 + 4.47214i) q^{21} +1.23607i q^{23} +(-0.618034 - 1.61803i) q^{24} -3.47214 q^{25} +1.00000 q^{26} +(-2.38197 + 4.61803i) q^{27} +(-0.381966 + 2.61803i) q^{28} +7.70820i q^{29} +(-0.763932 - 2.00000i) q^{30} +2.76393i q^{31} -1.00000i q^{32} +6.47214i q^{34} +(-0.472136 + 3.23607i) q^{35} +(-2.23607 + 2.00000i) q^{36} -4.76393 q^{37} +6.00000 q^{38} +(-0.618034 - 1.61803i) q^{39} -1.23607i q^{40} -0.763932 q^{41} +(4.47214 - 1.00000i) q^{42} -1.52786 q^{43} +(-2.76393 + 2.47214i) q^{45} +1.23607 q^{46} +2.47214 q^{47} +(-1.61803 + 0.618034i) q^{48} +(-6.70820 - 2.00000i) q^{49} +3.47214i q^{50} +(10.4721 - 4.00000i) q^{51} -1.00000i q^{52} +1.23607i q^{53} +(4.61803 + 2.38197i) q^{54} +(2.61803 + 0.381966i) q^{56} +(-3.70820 - 9.70820i) q^{57} +7.70820 q^{58} +4.47214 q^{59} +(-2.00000 + 0.763932i) q^{60} -4.47214i q^{61} +2.76393 q^{62} +(-4.38197 - 6.61803i) q^{63} -1.00000 q^{64} -1.23607i q^{65} -10.9443 q^{67} +6.47214 q^{68} +(-0.763932 - 2.00000i) q^{69} +(3.23607 + 0.472136i) q^{70} +5.52786i q^{71} +(2.00000 + 2.23607i) q^{72} +1.23607i q^{73} +4.76393i q^{74} +(5.61803 - 2.14590i) q^{75} -6.00000i q^{76} +(-1.61803 + 0.618034i) q^{78} +8.94427 q^{79} -1.23607 q^{80} +(1.00000 - 8.94427i) q^{81} +0.763932i q^{82} +14.0000 q^{83} +(-1.00000 - 4.47214i) q^{84} +8.00000 q^{85} +1.52786i q^{86} +(-4.76393 - 12.4721i) q^{87} -16.1803 q^{89} +(2.47214 + 2.76393i) q^{90} +(2.61803 + 0.381966i) q^{91} -1.23607i q^{92} +(-1.70820 - 4.47214i) q^{93} -2.47214i q^{94} -7.41641i q^{95} +(0.618034 + 1.61803i) q^{96} -5.23607i q^{97} +(-2.00000 + 6.70820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 6 * q^7	\( 4 q - 2 q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{12} - 6 q^{14} + 8 q^{15} + 4 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{24} + 4 q^{25} + 4 q^{26} - 14 q^{27} - 6 q^{28} - 12 q^{30} + 16 q^{35} - 28 q^{37} + 24 q^{38} + 2 q^{39} - 12 q^{41} - 24 q^{43} - 20 q^{45} - 4 q^{46} - 8 q^{47} - 2 q^{48} + 24 q^{51} + 14 q^{54} + 6 q^{56} + 12 q^{57} + 4 q^{58} - 8 q^{60} + 20 q^{62} - 22 q^{63} - 4 q^{64} - 8 q^{67} + 8 q^{68} - 12 q^{69} + 4 q^{70} + 8 q^{72} + 18 q^{75} - 2 q^{78} + 4 q^{80} + 4 q^{81} + 56 q^{83} - 4 q^{84} + 32 q^{85} - 28 q^{87} - 20 q^{89} - 8 q^{90} + 6 q^{91} + 20 q^{93} - 2 q^{96} - 8 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^12 - 6 * q^14 + 8 * q^15 + 4 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^21 + 2 * q^24 + 4 * q^25 + 4 * q^26 - 14 * q^27 - 6 * q^28 - 12 * q^30 + 16 * q^35 - 28 * q^37 + 24 * q^38 + 2 * q^39 - 12 * q^41 - 24 * q^43 - 20 * q^45 - 4 * q^46 - 8 * q^47 - 2 * q^48 + 24 * q^51 + 14 * q^54 + 6 * q^56 + 12 * q^57 + 4 * q^58 - 8 * q^60 + 20 * q^62 - 22 * q^63 - 4 * q^64 - 8 * q^67 + 8 * q^68 - 12 * q^69 + 4 * q^70 + 8 * q^72 + 18 * q^75 - 2 * q^78 + 4 * q^80 + 4 * q^81 + 56 * q^83 - 4 * q^84 + 32 * q^85 - 28 * q^87 - 20 * q^89 - 8 * q^90 + 6 * q^91 + 20 * q^93 - 2 * q^96 - 8 * q^98

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