LMFDB - Embedded newform 546.2.g.a.209.4

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			209.4
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.a.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +3.23607 q^{5} +(-1.61803 + 0.618034i) q^{6} +(2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +3.23607 q^{5} +(-1.61803 + 0.618034i) q^{6} +(2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(-2.23607 + 2.00000i) q^{9} +3.23607i q^{10} +(-0.618034 - 1.61803i) q^{12} -1.00000i q^{13} +(-0.381966 + 2.61803i) q^{14} +(2.00000 + 5.23607i) q^{15} +1.00000 q^{16} +2.47214 q^{17} +(-2.00000 - 2.23607i) q^{18} -6.00000i q^{19} -3.23607 q^{20} +(1.00000 + 4.47214i) q^{21} +3.23607i q^{23} +(1.61803 - 0.618034i) q^{24} +5.47214 q^{25} +1.00000 q^{26} +(-4.61803 - 2.38197i) q^{27} +(-2.61803 - 0.381966i) q^{28} +5.70820i q^{29} +(-5.23607 + 2.00000i) q^{30} -7.23607i q^{31} +1.00000i q^{32} +2.47214i q^{34} +(8.47214 + 1.23607i) q^{35} +(2.23607 - 2.00000i) q^{36} -9.23607 q^{37} +6.00000 q^{38} +(1.61803 - 0.618034i) q^{39} -3.23607i q^{40} -5.23607 q^{41} +(-4.47214 + 1.00000i) q^{42} -10.4721 q^{43} +(-7.23607 + 6.47214i) q^{45} -3.23607 q^{46} -6.47214 q^{47} +(0.618034 + 1.61803i) q^{48} +(6.70820 + 2.00000i) q^{49} +5.47214i q^{50} +(1.52786 + 4.00000i) q^{51} +1.00000i q^{52} +3.23607i q^{53} +(2.38197 - 4.61803i) q^{54} +(0.381966 - 2.61803i) q^{56} +(9.70820 - 3.70820i) q^{57} -5.70820 q^{58} -4.47214 q^{59} +(-2.00000 - 5.23607i) q^{60} -4.47214i q^{61} +7.23607 q^{62} +(-6.61803 + 4.38197i) q^{63} -1.00000 q^{64} -3.23607i q^{65} +6.94427 q^{67} -2.47214 q^{68} +(-5.23607 + 2.00000i) q^{69} +(-1.23607 + 8.47214i) q^{70} -14.4721i q^{71} +(2.00000 + 2.23607i) q^{72} +3.23607i q^{73} -9.23607i q^{74} +(3.38197 + 8.85410i) q^{75} +6.00000i q^{76} +(0.618034 + 1.61803i) q^{78} -8.94427 q^{79} +3.23607 q^{80} +(1.00000 - 8.94427i) q^{81} -5.23607i q^{82} +14.0000 q^{83} +(-1.00000 - 4.47214i) q^{84} +8.00000 q^{85} -10.4721i q^{86} +(-9.23607 + 3.52786i) q^{87} +6.18034 q^{89} +(-6.47214 - 7.23607i) q^{90} +(0.381966 - 2.61803i) q^{91} -3.23607i q^{92} +(11.7082 - 4.47214i) q^{93} -6.47214i q^{94} -19.4164i q^{95} +(-1.61803 + 0.618034i) q^{96} +0.763932i q^{97} +(-2.00000 + 6.70820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.618034	+	1.61803i	0.356822	+	0.934172i
$3$	0.618034	+	1.61803i	0.356822	+	0.934172i
$4$	−1.00000			−0.500000
$5$	3.23607			1.44721			0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607			1.44721			0.723607	+	0.690212i	$0.242483\pi$
$6$	−1.61803	+	0.618034i	−0.660560	+	0.252311i
$7$	2.61803	+	0.381966i	0.989524	+	0.144370i
$7$	2.61803	+	0.381966i	0.989524	+	0.144370i
$8$		−	1.00000i		−	0.353553i
$9$	−2.23607	+	2.00000i	−0.745356	+	0.666667i
$10$			3.23607i			1.02333i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	−0.618034	−	1.61803i	−0.178411	−	0.467086i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.381966	+	2.61803i	−0.102085	+	0.699699i
$15$	2.00000	+	5.23607i	0.516398	+	1.35195i
$16$	1.00000			0.250000
$17$	2.47214			0.599581			0.299791	−	0.954005i	$-0.403083\pi$
$17$	2.47214			0.599581			0.299791	+	0.954005i	$0.403083\pi$
$18$	−2.00000	−	2.23607i	−0.471405	−	0.527046i
$19$		−	6.00000i		−	1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$		−	6.00000i		−	1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$	−3.23607			−0.723607
$21$	1.00000	+	4.47214i	0.218218	+	0.975900i
$22$		0			0
$23$			3.23607i			0.674767i	0.941367	+	0.337383i	$0.109542\pi$
$23$			3.23607i			0.674767i	−0.941367	+	0.337383i	$0.890458\pi$
$24$	1.61803	−	0.618034i	0.330280	−	0.126156i
$25$	5.47214			1.09443
$26$	1.00000			0.196116
$27$	−4.61803	−	2.38197i	−0.888741	−	0.458410i
$28$	−2.61803	−	0.381966i	−0.494762	−	0.0721848i
$29$			5.70820i			1.05999i	0.848002	+	0.529993i	$0.177806\pi$
$29$			5.70820i			1.05999i	−0.848002	+	0.529993i	$0.822194\pi$
$30$	−5.23607	+	2.00000i	−0.955971	+	0.365148i
$31$		−	7.23607i		−	1.29964i	−0.760090	−	0.649818i	$-0.774845\pi$
$31$		−	7.23607i		−	1.29964i	0.760090	−	0.649818i	$-0.225155\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			2.47214i			0.423968i
$35$	8.47214	+	1.23607i	1.43205	+	0.208934i
$36$	2.23607	−	2.00000i	0.372678	−	0.333333i
$37$	−9.23607			−1.51840			−0.759200	−	0.650857i	$-0.774410\pi$
$37$	−9.23607			−1.51840			−0.759200	+	0.650857i	$0.774410\pi$
$38$	6.00000			0.973329
$39$	1.61803	−	0.618034i	0.259093	−	0.0989646i
$40$		−	3.23607i		−	0.511667i
$41$	−5.23607			−0.817736			−0.408868	−	0.912593i	$-0.634076\pi$
$41$	−5.23607			−0.817736			−0.408868	+	0.912593i	$0.634076\pi$
$42$	−4.47214	+	1.00000i	−0.690066	+	0.154303i
$43$	−10.4721			−1.59699			−0.798493	−	0.602004i	$-0.794369\pi$
$43$	−10.4721			−1.59699			−0.798493	+	0.602004i	$0.794369\pi$
$44$		0			0
$45$	−7.23607	+	6.47214i	−1.07869	+	0.964809i
$46$	−3.23607			−0.477132
$47$	−6.47214			−0.944058			−0.472029	−	0.881583i	$-0.656478\pi$
$47$	−6.47214			−0.944058			−0.472029	+	0.881583i	$0.656478\pi$
$48$	0.618034	+	1.61803i	0.0892055	+	0.233543i
$49$	6.70820	+	2.00000i	0.958315	+	0.285714i
$50$			5.47214i			0.773877i
$51$	1.52786	+	4.00000i	0.213944	+	0.560112i
$52$			1.00000i			0.138675i
$53$			3.23607i			0.444508i	0.974989	+	0.222254i	$0.0713414\pi$
$53$			3.23607i			0.444508i	−0.974989	+	0.222254i	$0.928659\pi$
$54$	2.38197	−	4.61803i	0.324145	−	0.628435i
$55$		0			0
$56$	0.381966	−	2.61803i	0.0510424	−	0.349850i
$57$	9.70820	−	3.70820i	1.28588	−	0.491164i
$58$	−5.70820			−0.749524
$59$	−4.47214			−0.582223			−0.291111	−	0.956689i	$-0.594025\pi$
$59$	−4.47214			−0.582223			−0.291111	+	0.956689i	$0.594025\pi$
$60$	−2.00000	−	5.23607i	−0.258199	−	0.675973i
$61$		−	4.47214i		−	0.572598i	−0.958140	−	0.286299i	$-0.907575\pi$
$61$		−	4.47214i		−	0.572598i	0.958140	−	0.286299i	$-0.0924251\pi$
$62$	7.23607			0.918982
$63$	−6.61803	+	4.38197i	−0.833794	+	0.552076i
$64$	−1.00000			−0.125000
$65$		−	3.23607i		−	0.401385i
$66$		0			0
$67$	6.94427			0.848378			0.424189	−	0.905574i	$-0.360559\pi$
$67$	6.94427			0.848378			0.424189	+	0.905574i	$0.360559\pi$
$68$	−2.47214			−0.299791
$69$	−5.23607	+	2.00000i	−0.630349	+	0.240772i
$70$	−1.23607	+	8.47214i	−0.147738	+	1.01261i
$71$		−	14.4721i		−	1.71753i	−0.512373	−	0.858763i	$-0.671233\pi$
$71$		−	14.4721i		−	1.71753i	0.512373	−	0.858763i	$-0.328767\pi$
$72$	2.00000	+	2.23607i	0.235702	+	0.263523i
$73$			3.23607i			0.378753i	0.981905	+	0.189377i	$0.0606467\pi$
$73$			3.23607i			0.378753i	−0.981905	+	0.189377i	$0.939353\pi$
$74$		−	9.23607i		−	1.07367i
$75$	3.38197	+	8.85410i	0.390516	+	1.02238i
$76$			6.00000i			0.688247i
$77$		0			0
$78$	0.618034	+	1.61803i	0.0699786	+	0.183206i
$79$	−8.94427			−1.00631			−0.503155	−	0.864196i	$-0.667827\pi$
$79$	−8.94427			−1.00631			−0.503155	+	0.864196i	$0.667827\pi$
$80$	3.23607			0.361803
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$		−	5.23607i		−	0.578227i
$83$	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
$86$		−	10.4721i		−	1.12924i
$87$	−9.23607	+	3.52786i	−0.990210	+	0.378227i
$88$		0			0
$89$	6.18034			0.655115			0.327557	−	0.944831i	$-0.393775\pi$
$89$	6.18034			0.655115			0.327557	+	0.944831i	$0.393775\pi$
$90$	−6.47214	−	7.23607i	−0.682223	−	0.762749i
$91$	0.381966	−	2.61803i	0.0400409	−	0.274445i
$92$		−	3.23607i		−	0.337383i
$93$	11.7082	−	4.47214i	1.21408	−	0.463739i
$94$		−	6.47214i		−	0.667550i
$95$		−	19.4164i		−	1.99208i
$96$	−1.61803	+	0.618034i	−0.165140	+	0.0630778i
$97$			0.763932i			0.0775655i	0.999248	+	0.0387828i	$0.0123480\pi$
$97$			0.763932i			0.0775655i	−0.999248	+	0.0387828i	$0.987652\pi$
$98$	−2.00000	+	6.70820i	−0.202031	+	0.677631i
$99$		0			0
$100$	−5.47214			−0.547214
$101$	18.1803			1.80901			0.904506	−	0.426461i	$-0.140240\pi$
$101$	18.1803			1.80901			0.904506	+	0.426461i	$0.140240\pi$
$102$	−4.00000	+	1.52786i	−0.396059	+	0.151281i
$103$			7.70820i			0.759512i	0.925087	+	0.379756i	$0.123992\pi$
$103$			7.70820i			0.759512i	−0.925087	+	0.379756i	$0.876008\pi$
$104$	−1.00000			−0.0980581
$105$	3.23607	+	14.4721i	0.315808	+	1.41234i
$106$	−3.23607			−0.314315
$107$			2.47214i			0.238990i	0.992835	+	0.119495i	$0.0381276\pi$
$107$			2.47214i			0.238990i	−0.992835	+	0.119495i	$0.961872\pi$
$108$	4.61803	+	2.38197i	0.444371	+	0.229205i
$109$	6.18034			0.591969			0.295985	−	0.955193i	$-0.404352\pi$
$109$	6.18034			0.591969			0.295985	+	0.955193i	$0.404352\pi$
$110$		0			0
$111$	−5.70820	−	14.9443i	−0.541799	−	1.41845i
$112$	2.61803	+	0.381966i	0.247381	+	0.0360924i
$113$			16.0000i			1.50515i	0.658505	+	0.752577i	$0.271189\pi$
$113$			16.0000i			1.50515i	−0.658505	+	0.752577i	$0.728811\pi$
$114$	3.70820	+	9.70820i	0.347305	+	0.909257i
$115$			10.4721i			0.976532i
$116$		−	5.70820i		−	0.529993i
$117$	2.00000	+	2.23607i	0.184900	+	0.206725i
$118$		−	4.47214i		−	0.411693i
$119$	6.47214	+	0.944272i	0.593300	+	0.0865613i
$120$	5.23607	−	2.00000i	0.477985	−	0.182574i
$121$	11.0000			1.00000
$122$	4.47214			0.404888
$123$	−3.23607	−	8.47214i	−0.291786	−	0.763907i
$124$			7.23607i			0.649818i
$125$	1.52786			0.136656
$126$	−4.38197	−	6.61803i	−0.390377	−	0.589581i
$127$	−3.05573			−0.271152			−0.135576	−	0.990767i	$-0.543288\pi$
$127$	−3.05573			−0.271152			−0.135576	+	0.990767i	$0.543288\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.47214	−	16.9443i	−0.569840	−	1.49186i
$130$	3.23607			0.283822
$131$	−5.23607			−0.457477			−0.228739	−	0.973488i	$-0.573460\pi$
$131$	−5.23607			−0.457477			−0.228739	+	0.973488i	$0.573460\pi$
$132$		0			0
$133$	2.29180	−	15.7082i	0.198724	−	1.36207i
$134$			6.94427i			0.599894i
$135$	−14.9443	−	7.70820i	−1.28620	−	0.663417i
$136$		−	2.47214i		−	0.211984i
$137$		−	7.52786i		−	0.643149i	−0.946884	−	0.321574i	$-0.895788\pi$
$137$		−	7.52786i		−	0.643149i	0.946884	−	0.321574i	$-0.104212\pi$
$138$	−2.00000	−	5.23607i	−0.170251	−	0.445724i
$139$		−	12.1803i		−	1.03312i	−0.856250	−	0.516561i	$-0.827212\pi$
$139$		−	12.1803i		−	1.03312i	0.856250	−	0.516561i	$-0.172788\pi$
$140$	−8.47214	−	1.23607i	−0.716026	−	0.104467i
$141$	−4.00000	−	10.4721i	−0.336861	−	0.881913i
$142$	14.4721			1.21447
$143$		0			0
$144$	−2.23607	+	2.00000i	−0.186339	+	0.166667i
$145$			18.4721i			1.53403i
$146$	−3.23607			−0.267819
$147$	0.909830	+	12.0902i	0.0750415	+	0.997180i
$148$	9.23607			0.759200
$149$			17.4164i			1.42681i	0.700753	+	0.713404i	$0.252847\pi$
$149$			17.4164i			1.42681i	−0.700753	+	0.713404i	$0.747153\pi$
$150$	−8.85410	+	3.38197i	−0.722934	+	0.276136i
$151$	3.70820			0.301769			0.150885	−	0.988551i	$-0.451788\pi$
$151$	3.70820			0.301769			0.150885	+	0.988551i	$0.451788\pi$
$152$	−6.00000			−0.486664
$153$	−5.52786	+	4.94427i	−0.446901	+	0.399721i
$154$		0			0
$155$		−	23.4164i		−	1.88085i
$156$	−1.61803	+	0.618034i	−0.129546	+	0.0494823i
$157$		−	5.41641i		−	0.432276i	−0.976363	−	0.216138i	$-0.930654\pi$
$157$		−	5.41641i		−	0.432276i	0.976363	−	0.216138i	$-0.0693462\pi$
$158$		−	8.94427i		−	0.711568i
$159$	−5.23607	+	2.00000i	−0.415247	+	0.158610i
$160$			3.23607i			0.255834i
$161$	−1.23607	+	8.47214i	−0.0974158	+	0.667698i
$162$	8.94427	+	1.00000i	0.702728	+	0.0785674i
$163$	−9.41641			−0.737550			−0.368775	−	0.929519i	$-0.620223\pi$
$163$	−9.41641			−0.737550			−0.368775	+	0.929519i	$0.620223\pi$
$164$	5.23607			0.408868
$165$		0			0
$166$			14.0000i			1.08661i
$167$	16.9443			1.31119			0.655594	−	0.755114i	$-0.272418\pi$
$167$	16.9443			1.31119			0.655594	+	0.755114i	$0.272418\pi$
$168$	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
$172$	10.4721			0.798493
$173$	−18.7639			−1.42660			−0.713298	−	0.700861i	$-0.752799\pi$
$173$	−18.7639			−1.42660			−0.713298	+	0.700861i	$0.752799\pi$
$174$	−3.52786	−	9.23607i	−0.267447	−	0.700185i
$175$	14.3262	+	2.09017i	1.08296	+	0.158002i
$176$		0			0
$177$	−2.76393	−	7.23607i	−0.207750	−	0.543896i
$178$			6.18034i			0.463236i
$179$		−	10.4721i		−	0.782724i	−0.920237	−	0.391362i	$-0.872004\pi$
$179$		−	10.4721i		−	0.782724i	0.920237	−	0.391362i	$-0.127996\pi$
$180$	7.23607	−	6.47214i	0.539345	−	0.482405i
$181$		−	4.47214i		−	0.332411i	−0.986091	−	0.166206i	$-0.946848\pi$
$181$		−	4.47214i		−	0.332411i	0.986091	−	0.166206i	$-0.0531515\pi$
$182$	2.61803	+	0.381966i	0.194062	+	0.0283132i
$183$	7.23607	−	2.76393i	0.534906	−	0.204316i
$184$	3.23607			0.238566
$185$	−29.8885			−2.19745
$186$	4.47214	+	11.7082i	0.327913	+	0.858487i
$187$		0			0
$188$	6.47214			0.472029
$189$	−11.1803	−	8.00000i	−0.813250	−	0.581914i
$190$	19.4164			1.40861
$191$			21.7082i			1.57075i	0.619020	+	0.785375i	$0.287530\pi$
$191$			21.7082i			1.57075i	−0.619020	+	0.785375i	$0.712470\pi$
$192$	−0.618034	−	1.61803i	−0.0446028	−	0.116772i
$193$	11.8885			0.855756			0.427878	−	0.903836i	$-0.359261\pi$
$193$	11.8885			0.855756			0.427878	+	0.903836i	$0.359261\pi$
$194$	−0.763932			−0.0548471
$195$	5.23607	−	2.00000i	0.374963	−	0.143223i
$196$	−6.70820	−	2.00000i	−0.479157	−	0.142857i
$197$		−	25.4164i		−	1.81084i	−0.424513	−	0.905422i	$-0.639555\pi$
$197$		−	25.4164i		−	1.81084i	0.424513	−	0.905422i	$-0.360445\pi$
$198$		0			0
$199$		−	27.7082i		−	1.96418i	−0.188406	−	0.982091i	$-0.560332\pi$
$199$		−	27.7082i		−	1.96418i	0.188406	−	0.982091i	$-0.439668\pi$
$200$		−	5.47214i		−	0.386938i
$201$	4.29180	+	11.2361i	0.302720	+	0.792531i
$202$			18.1803i			1.27916i
$203$	−2.18034	+	14.9443i	−0.153030	+	1.04888i
$204$	−1.52786	−	4.00000i	−0.106972	−	0.280056i
$205$	−16.9443			−1.18344
$206$	−7.70820			−0.537056
$207$	−6.47214	−	7.23607i	−0.449845	−	0.502941i
$208$		−	1.00000i		−	0.0693375i
$209$		0			0
$210$	−14.4721	+	3.23607i	−0.998672	+	0.223310i
$211$	−25.8885			−1.78224			−0.891120	−	0.453767i	$-0.850080\pi$
$211$	−25.8885			−1.78224			−0.891120	+	0.453767i	$0.850080\pi$
$212$		−	3.23607i		−	0.222254i
$213$	23.4164	−	8.94427i	1.60447	−	0.612851i
$214$	−2.47214			−0.168992
$215$	−33.8885			−2.31118
$216$	−2.38197	+	4.61803i	−0.162072	+	0.314217i
$217$	2.76393	−	18.9443i	0.187628	−	1.28602i
$218$			6.18034i			0.418585i
$219$	−5.23607	+	2.00000i	−0.353821	+	0.135147i
$220$		0			0
$221$		−	2.47214i		−	0.166294i
$222$	14.9443	−	5.70820i	1.00299	−	0.383110i
$223$			8.76393i			0.586876i	0.955978	+	0.293438i	$0.0947995\pi$
$223$			8.76393i			0.586876i	−0.955978	+	0.293438i	$0.905201\pi$
$224$	−0.381966	+	2.61803i	−0.0255212	+	0.174925i
$225$	−12.2361	+	10.9443i	−0.815738	+	0.729618i
$226$	−16.0000			−1.06430
$227$	3.52786			0.234153			0.117076	−	0.993123i	$-0.462648\pi$
$227$	3.52786			0.234153			0.117076	+	0.993123i	$0.462648\pi$
$228$	−9.70820	+	3.70820i	−0.642942	+	0.245582i
$229$			2.94427i			0.194563i	0.995257	+	0.0972815i	$0.0310147\pi$
$229$			2.94427i			0.194563i	−0.995257	+	0.0972815i	$0.968985\pi$
$230$	−10.4721			−0.690512
$231$		0			0
$232$	5.70820			0.374762
$233$			7.05573i			0.462236i	0.972926	+	0.231118i	$0.0742384\pi$
$233$			7.05573i			0.462236i	−0.972926	+	0.231118i	$0.925762\pi$
$234$	−2.23607	+	2.00000i	−0.146176	+	0.130744i
$235$	−20.9443			−1.36625
$236$	4.47214			0.291111
$237$	−5.52786	−	14.4721i	−0.359073	−	0.940066i
$238$	−0.944272	+	6.47214i	−0.0612081	+	0.419526i
$239$			0.583592i			0.0377494i	0.999822	+	0.0188747i	$0.00600837\pi$
$239$			0.583592i			0.0377494i	−0.999822	+	0.0188747i	$0.993992\pi$
$240$	2.00000	+	5.23607i	0.129099	+	0.337987i
$241$			10.6525i			0.686186i	0.939301	+	0.343093i	$0.111475\pi$
$241$			10.6525i			0.686186i	−0.939301	+	0.343093i	$0.888525\pi$
$242$			11.0000i			0.707107i
$243$	15.0902	−	3.90983i	0.968035	−	0.250816i
$244$			4.47214i			0.286299i
$245$	21.7082	+	6.47214i	1.38689	+	0.413490i
$246$	8.47214	−	3.23607i	0.540164	−	0.206324i
$247$	−6.00000			−0.381771
$248$	−7.23607			−0.459491
$249$	8.65248	+	22.6525i	0.548328	+	1.43554i
$250$			1.52786i			0.0966306i
$251$	14.7639			0.931891			0.465946	−	0.884813i	$-0.345714\pi$
$251$	14.7639			0.931891			0.465946	+	0.884813i	$0.345714\pi$
$252$	6.61803	−	4.38197i	0.416897	−	0.276038i
$253$		0			0
$254$		−	3.05573i		−	0.191733i
$255$	4.94427	+	12.9443i	0.309622	+	0.810602i
$256$	1.00000			0.0625000
$257$	2.47214			0.154208			0.0771038	−	0.997023i	$-0.475433\pi$
$257$	2.47214			0.154208			0.0771038	+	0.997023i	$0.475433\pi$
$258$	16.9443	−	6.47214i	1.05490	−	0.402938i
$259$	−24.1803	−	3.52786i	−1.50249	−	0.219211i
$260$			3.23607i			0.200692i
$261$	−11.4164	−	12.7639i	−0.706658	−	0.790068i
$262$		−	5.23607i		−	0.323485i
$263$			17.7082i			1.09193i	0.837806	+	0.545967i	$0.183838\pi$
$263$			17.7082i			1.09193i	−0.837806	+	0.545967i	$0.816162\pi$
$264$		0			0
$265$			10.4721i			0.643298i
$266$	15.7082	+	2.29180i	0.963132	+	0.140519i
$267$	3.81966	+	10.0000i	0.233759	+	0.611990i
$268$	−6.94427			−0.424189
$269$	8.29180			0.505560			0.252780	−	0.967524i	$-0.418655\pi$
$269$	8.29180			0.505560			0.252780	+	0.967524i	$0.418655\pi$
$270$	7.70820	−	14.9443i	0.469106	−	0.909479i
$271$		−	3.81966i		−	0.232028i	−0.993248	−	0.116014i	$-0.962988\pi$
$271$		−	3.81966i		−	0.232028i	0.993248	−	0.116014i	$-0.0370117\pi$
$272$	2.47214			0.149895
$273$	4.47214	−	1.00000i	0.270666	−	0.0605228i
$274$	7.52786			0.454775
$275$		0			0
$276$	5.23607	−	2.00000i	0.315174	−	0.120386i
$277$	32.4721			1.95106			0.975531	−	0.219863i	$-0.0705610\pi$
$277$	32.4721			1.95106			0.975531	+	0.219863i	$0.0705610\pi$
$278$	12.1803			0.730528
$279$	14.4721	+	16.1803i	0.866424	+	0.968692i
$280$	1.23607	−	8.47214i	0.0738692	−	0.506307i
$281$			4.47214i			0.266785i	0.991063	+	0.133393i	$0.0425871\pi$
$281$			4.47214i			0.266785i	−0.991063	+	0.133393i	$0.957413\pi$
$282$	10.4721	−	4.00000i	0.623607	−	0.238197i
$283$			21.1246i			1.25573i	0.778323	+	0.627864i	$0.216071\pi$
$283$			21.1246i			1.25573i	−0.778323	+	0.627864i	$0.783929\pi$
$284$			14.4721i			0.858763i
$285$	31.4164	−	12.0000i	1.86095	−	0.710819i
$286$		0			0
$287$	−13.7082	−	2.00000i	−0.809170	−	0.118056i
$288$	−2.00000	−	2.23607i	−0.117851	−	0.131762i
$289$	−10.8885			−0.640503
$290$	−18.4721			−1.08472
$291$	−1.23607	+	0.472136i	−0.0724596	+	0.0276771i
$292$		−	3.23607i		−	0.189377i
$293$	−14.2918			−0.834936			−0.417468	−	0.908692i	$-0.637082\pi$
$293$	−14.2918			−0.834936			−0.417468	+	0.908692i	$0.637082\pi$
$294$	−12.0902	+	0.909830i	−0.705113	+	0.0530624i
$295$	−14.4721			−0.842600
$296$			9.23607i			0.536836i
$297$		0			0
$298$	−17.4164			−1.00891
$299$	3.23607			0.187147
$300$	−3.38197	−	8.85410i	−0.195258	−	0.511192i
$301$	−27.4164	−	4.00000i	−1.58026	−	0.230556i
$302$			3.70820i			0.213383i
$303$	11.2361	+	29.4164i	0.645495	+	1.68993i
$304$		−	6.00000i		−	0.344124i
$305$		−	14.4721i		−	0.828672i
$306$	−4.94427	−	5.52786i	−0.282645	−	0.316007i
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$		0			0
$309$	−12.4721	+	4.76393i	−0.709515	+	0.271011i
$310$	23.4164			1.32996
$311$	−22.4721			−1.27428			−0.637139	−	0.770749i	$-0.719882\pi$
$311$	−22.4721			−1.27428			−0.637139	+	0.770749i	$0.719882\pi$
$312$	−0.618034	−	1.61803i	−0.0349893	−	0.0916031i
$313$			10.4721i			0.591920i	0.955200	+	0.295960i	$0.0956395\pi$
$313$			10.4721i			0.591920i	−0.955200	+	0.295960i	$0.904360\pi$
$314$	5.41641			0.305666
$315$	−21.4164	+	14.1803i	−1.20668	+	0.798972i
$316$	8.94427			0.503155
$317$			6.94427i			0.390029i	0.980800	+	0.195015i	$0.0624754\pi$
$317$			6.94427i			0.390029i	−0.980800	+	0.195015i	$0.937525\pi$
$318$	−2.00000	−	5.23607i	−0.112154	−	0.293624i
$319$		0			0
$320$	−3.23607			−0.180902
$321$	−4.00000	+	1.52786i	−0.223258	+	0.0852771i
$322$	−8.47214	−	1.23607i	−0.472134	−	0.0688834i
$323$		−	14.8328i		−	0.825320i
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$		−	5.47214i		−	0.303539i
$326$		−	9.41641i		−	0.521527i
$327$	3.81966	+	10.0000i	0.211228	+	0.553001i
$328$			5.23607i			0.289113i
$329$	−16.9443	−	2.47214i	−0.934168	−	0.136293i
$330$		0			0
$331$	14.3607			0.789334			0.394667	−	0.918824i	$-0.370860\pi$
$331$	14.3607			0.789334			0.394667	+	0.918824i	$0.370860\pi$
$332$	−14.0000			−0.768350
$333$	20.6525	−	18.4721i	1.13175	−	1.01227i
$334$			16.9443i			0.927149i
$335$	22.4721			1.22778
$336$	1.00000	+	4.47214i	0.0545545	+	0.243975i
$337$	−19.8885			−1.08340			−0.541699	−	0.840573i	$-0.682219\pi$
$337$	−19.8885			−1.08340			−0.541699	+	0.840573i	$0.682219\pi$
$338$		−	1.00000i		−	0.0543928i
$339$	−25.8885	+	9.88854i	−1.40607	+	0.537072i
$340$	−8.00000			−0.433861
$341$		0			0
$342$	−13.4164	+	12.0000i	−0.725476	+	0.648886i
$343$	16.7984	+	7.79837i	0.907027	+	0.421073i
$344$			10.4721i			0.564620i
$345$	−16.9443	+	6.47214i	−0.912249	+	0.348448i
$346$		−	18.7639i		−	1.00876i
$347$		−	24.3607i		−	1.30775i	−0.756603	−	0.653875i	$-0.773142\pi$
$347$		−	24.3607i		−	1.30775i	0.756603	−	0.653875i	$-0.226858\pi$
$348$	9.23607	−	3.52786i	0.495105	−	0.189113i
$349$			35.3050i			1.88983i	0.327315	+	0.944915i	$0.393856\pi$
$349$			35.3050i			1.88983i	−0.327315	+	0.944915i	$0.606144\pi$
$350$	−2.09017	+	14.3262i	−0.111724	+	0.765770i
$351$	−2.38197	+	4.61803i	−0.127140	+	0.246492i
$352$		0			0
$353$	19.1246			1.01790			0.508950	−	0.860796i	$-0.330034\pi$
$353$	19.1246			1.01790			0.508950	+	0.860796i	$0.330034\pi$
$354$	7.23607	−	2.76393i	0.384593	−	0.146901i
$355$		−	46.8328i		−	2.48563i
$356$	−6.18034			−0.327557
$357$	2.47214	+	11.0557i	0.130839	+	0.585131i
$358$	10.4721			0.553470
$359$			21.8885i			1.15523i	0.816308	+	0.577617i	$0.196017\pi$
$359$			21.8885i			1.15523i	−0.816308	+	0.577617i	$0.803983\pi$
$360$	6.47214	+	7.23607i	0.341112	+	0.381374i
$361$	−17.0000			−0.894737
$362$	4.47214			0.235050
$363$	6.79837	+	17.7984i	0.356822	+	0.934172i
$364$	−0.381966	+	2.61803i	−0.0200205	+	0.137222i
$365$			10.4721i			0.548137i
$366$	2.76393	+	7.23607i	0.144473	+	0.378235i
$367$		−	12.6525i		−	0.660454i	−0.943902	−	0.330227i	$-0.892875\pi$
$367$		−	12.6525i		−	0.660454i	0.943902	−	0.330227i	$-0.107125\pi$
$368$			3.23607i			0.168692i
$369$	11.7082	−	10.4721i	0.609505	−	0.545158i
$370$		−	29.8885i		−	1.55383i
$371$	−1.23607	+	8.47214i	−0.0641735	+	0.439851i
$372$	−11.7082	+	4.47214i	−0.607042	+	0.231869i
$373$	17.4164			0.901787			0.450894	−	0.892578i	$-0.351105\pi$
$373$	17.4164			0.901787			0.450894	+	0.892578i	$0.351105\pi$
$374$		0			0
$375$	0.944272	+	2.47214i	0.0487620	+	0.127661i
$376$			6.47214i			0.333775i
$377$	5.70820			0.293987
$378$	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	$0.779993\pi$
$380$			19.4164i			0.996041i
$381$	−1.88854	−	4.94427i	−0.0967530	−	0.253303i
$382$	−21.7082			−1.11069
$383$	−30.4721			−1.55705			−0.778527	−	0.627611i	$-0.784033\pi$
$383$	−30.4721			−1.55705			−0.778527	+	0.627611i	$0.784033\pi$
$384$	1.61803	−	0.618034i	0.0825700	−	0.0315389i
$385$		0			0
$386$			11.8885i			0.605111i
$387$	23.4164	−	20.9443i	1.19032	−	1.06466i
$388$		−	0.763932i		−	0.0387828i
$389$			32.5410i			1.64990i	0.565209	+	0.824948i	$0.308795\pi$
$389$			32.5410i			1.64990i	−0.565209	+	0.824948i	$0.691205\pi$
$390$	2.00000	+	5.23607i	0.101274	+	0.265139i
$391$			8.00000i			0.404577i
$392$	2.00000	−	6.70820i	0.101015	−	0.338815i
$393$	−3.23607	−	8.47214i	−0.163238	−	0.427363i
$394$	25.4164			1.28046
$395$	−28.9443			−1.45634
$396$		0			0
$397$		−	28.8328i		−	1.44708i	−0.690284	−	0.723539i	$-0.742514\pi$
$397$		−	28.8328i		−	1.44708i	0.690284	−	0.723539i	$-0.257486\pi$
$398$	27.7082			1.38889
$399$	26.8328	−	6.00000i	1.34332	−	0.300376i
$400$	5.47214			0.273607
$401$		−	18.9443i		−	0.946032i	−0.881054	−	0.473016i	$-0.843165\pi$
$401$		−	18.9443i		−	0.946032i	0.881054	−	0.473016i	$-0.156835\pi$
$402$	−11.2361	+	4.29180i	−0.560404	+	0.214055i
$403$	−7.23607			−0.360454
$404$	−18.1803			−0.904506
$405$	3.23607	−	28.9443i	0.160802	−	1.43825i
$406$	−14.9443	−	2.18034i	−0.741672	−	0.108208i
$407$		0			0
$408$	4.00000	−	1.52786i	0.198030	−	0.0756405i
$409$			5.70820i			0.282253i	0.989992	+	0.141126i	$0.0450724\pi$
$409$			5.70820i			0.282253i	−0.989992	+	0.141126i	$0.954928\pi$
$410$		−	16.9443i		−	0.836818i
$411$	12.1803	−	4.65248i	0.600812	−	0.229490i
$412$		−	7.70820i		−	0.379756i
$413$	−11.7082	−	1.70820i	−0.576123	−	0.0840552i
$414$	7.23607	−	6.47214i	0.355633	−	0.318088i
$415$	45.3050			2.22393
$416$	1.00000			0.0490290
$417$	19.7082	−	7.52786i	0.965115	−	0.368641i
$418$		0			0
$419$	−11.7082			−0.571983			−0.285992	−	0.958232i	$-0.592323\pi$
$419$	−11.7082			−0.571983			−0.285992	+	0.958232i	$0.592323\pi$
$420$	−3.23607	−	14.4721i	−0.157904	−	0.706168i
$421$	14.7639			0.719550			0.359775	−	0.933039i	$-0.382853\pi$
$421$	14.7639			0.719550			0.359775	+	0.933039i	$0.382853\pi$
$422$		−	25.8885i		−	1.26023i
$423$	14.4721	−	12.9443i	0.703659	−	0.629372i
$424$	3.23607			0.157157
$425$	13.5279			0.656198
$426$	8.94427	+	23.4164i	0.433351	+	1.13453i
$427$	1.70820	−	11.7082i	0.0826658	−	0.566600i
$428$		−	2.47214i		−	0.119495i
$429$		0			0
$430$		−	33.8885i		−	1.63425i
$431$			20.0000i			0.963366i	0.876346	+	0.481683i	$0.159974\pi$
$431$			20.0000i			0.963366i	−0.876346	+	0.481683i	$0.840026\pi$
$432$	−4.61803	−	2.38197i	−0.222185	−	0.114602i
$433$			19.4164i			0.933093i	0.884497	+	0.466547i	$0.154502\pi$
$433$			19.4164i			0.933093i	−0.884497	+	0.466547i	$0.845498\pi$
$434$	18.9443	+	2.76393i	0.909354	+	0.132673i
$435$	−29.8885	+	11.4164i	−1.43305	+	0.547375i
$436$	−6.18034			−0.295985
$437$	19.4164			0.928813
$438$	−2.00000	−	5.23607i	−0.0955637	−	0.250189i
$439$		−	34.5410i		−	1.64855i	−0.566188	−	0.824276i	$-0.691582\pi$
$439$		−	34.5410i		−	1.64855i	0.566188	−	0.824276i	$-0.308418\pi$
$440$		0			0
$441$	−19.0000	+	8.94427i	−0.904762	+	0.425918i
$442$	2.47214			0.117588
$443$		−	29.5279i		−	1.40291i	−0.712713	−	0.701456i	$-0.752534\pi$
$443$		−	29.5279i		−	1.40291i	0.712713	−	0.701456i	$-0.247466\pi$
$444$	5.70820	+	14.9443i	0.270899	+	0.709224i
$445$	20.0000			0.948091
$446$	−8.76393			−0.414984
$447$	−28.1803	+	10.7639i	−1.33288	+	0.509117i
$448$	−2.61803	−	0.381966i	−0.123690	−	0.0180462i
$449$		−	18.3607i		−	0.866494i	−0.901275	−	0.433247i	$-0.857368\pi$
$449$		−	18.3607i		−	0.866494i	0.901275	−	0.433247i	$-0.142632\pi$
$450$	−10.9443	−	12.2361i	−0.515918	−	0.576814i
$451$		0			0
$452$		−	16.0000i		−	0.752577i
$453$	2.29180	+	6.00000i	0.107678	+	0.281905i
$454$			3.52786i			0.165571i
$455$	1.23607	−	8.47214i	0.0579478	−	0.397180i
$456$	−3.70820	−	9.70820i	−0.173653	−	0.454628i
$457$	26.9443			1.26040			0.630200	−	0.776433i	$-0.282973\pi$
$457$	26.9443			1.26040			0.630200	+	0.776433i	$0.282973\pi$
$458$	−2.94427			−0.137577
$459$	−11.4164	−	5.88854i	−0.532872	−	0.274854i
$460$		−	10.4721i		−	0.488266i
$461$	−20.7639			−0.967073			−0.483536	−	0.875324i	$-0.660648\pi$
$461$	−20.7639			−0.967073			−0.483536	+	0.875324i	$0.660648\pi$
$462$		0			0
$463$	15.7082			0.730022			0.365011	−	0.931003i	$-0.381065\pi$
$463$	15.7082			0.730022			0.365011	+	0.931003i	$0.381065\pi$
$464$			5.70820i			0.264997i
$465$	37.8885	−	14.4721i	1.75704	−	0.671129i
$466$	−7.05573			−0.326850
$467$	−18.1803			−0.841286			−0.420643	−	0.907226i	$-0.638195\pi$
$467$	−18.1803			−0.841286			−0.420643	+	0.907226i	$0.638195\pi$
$468$	−2.00000	−	2.23607i	−0.0924500	−	0.103362i
$469$	18.1803	+	2.65248i	0.839490	+	0.122480i
$470$		−	20.9443i		−	0.966087i
$471$	8.76393	−	3.34752i	0.403821	−	0.154246i
$472$			4.47214i			0.205847i
$473$		0			0
$474$	14.4721	−	5.52786i	0.664727	−	0.253903i
$475$		−	32.8328i		−	1.50647i
$476$	−6.47214	−	0.944272i	−0.296650	−	0.0432806i
$477$	−6.47214	−	7.23607i	−0.296339	−	0.331317i
$478$	−0.583592			−0.0266929
$479$	14.4721			0.661249			0.330624	−	0.943762i	$-0.392741\pi$
$479$	14.4721			0.661249			0.330624	+	0.943762i	$0.392741\pi$
$480$	−5.23607	+	2.00000i	−0.238993	+	0.0912871i
$481$			9.23607i			0.421128i
$482$	−10.6525			−0.485207
$483$	−14.4721	+	3.23607i	−0.658505	+	0.147246i
$484$	−11.0000			−0.500000
$485$			2.47214i			0.112254i
$486$	3.90983	+	15.0902i	0.177353	+	0.684504i
$487$	10.7639			0.487760			0.243880	−	0.969805i	$-0.421580\pi$
$487$	10.7639			0.487760			0.243880	+	0.969805i	$0.421580\pi$
$488$	−4.47214			−0.202444
$489$	−5.81966	−	15.2361i	−0.263174	−	0.688999i
$490$	−6.47214	+	21.7082i	−0.292381	+	0.980677i
$491$		−	3.41641i		−	0.154180i	−0.997024	−	0.0770902i	$-0.975437\pi$
$491$		−	3.41641i		−	0.154180i	0.997024	−	0.0770902i	$-0.0245629\pi$
$492$	3.23607	+	8.47214i	0.145893	+	0.381953i
$493$			14.1115i			0.635548i
$494$		−	6.00000i		−	0.269953i
$495$		0			0
$496$		−	7.23607i		−	0.324909i
$497$	5.52786	−	37.8885i	0.247959	−	1.69953i
$498$	−22.6525	+	8.65248i	−1.01508	+	0.387727i
$499$	−10.0000			−0.447661			−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000			−0.447661			−0.223831	+	0.974628i	$0.571856\pi$
$500$	−1.52786			−0.0683282
$501$	10.4721	+	27.4164i	0.467861	+	1.22487i
$502$			14.7639i			0.658947i
$503$	−4.94427			−0.220454			−0.110227	−	0.993906i	$-0.535158\pi$
$503$	−4.94427			−0.220454			−0.110227	+	0.993906i	$0.535158\pi$
$504$	4.38197	+	6.61803i	0.195188	+	0.294791i
$505$	58.8328			2.61803
$506$		0			0
$507$	−0.618034	−	1.61803i	−0.0274479	−	0.0718594i
$508$	3.05573			0.135576
$509$	−7.23607			−0.320733			−0.160367	−	0.987058i	$-0.551268\pi$
$509$	−7.23607			−0.320733			−0.160367	+	0.987058i	$0.551268\pi$
$510$	−12.9443	+	4.94427i	−0.573182	+	0.218936i
$511$	−1.23607	+	8.47214i	−0.0546804	+	0.374785i
$512$			1.00000i			0.0441942i
$513$	−14.2918	+	27.7082i	−0.630998	+	1.22335i
$514$			2.47214i			0.109041i
$515$			24.9443i			1.09918i
$516$	6.47214	+	16.9443i	0.284920	+	0.745930i
$517$		0			0
$518$	3.52786	−	24.1803i	0.155005	−	1.06242i
$519$	−11.5967	−	30.3607i	−0.509041	−	1.33269i
$520$	−3.23607			−0.141911
$521$	−34.8328			−1.52605			−0.763027	−	0.646367i	$-0.776288\pi$
$521$	−34.8328			−1.52605			−0.763027	+	0.646367i	$0.776288\pi$
$522$	12.7639	−	11.4164i	0.558662	−	0.499683i
$523$		−	2.29180i		−	0.100213i	−0.998744	−	0.0501066i	$-0.984044\pi$
$523$		−	2.29180i		−	0.100213i	0.998744	−	0.0501066i	$-0.0159561\pi$
$524$	5.23607			0.228739
$525$	5.47214	+	24.4721i	0.238824	+	1.06805i
$526$	−17.7082			−0.772114
$527$		−	17.8885i		−	0.779237i
$528$		0			0
$529$	12.5279			0.544690
$530$	−10.4721			−0.454881
$531$	10.0000	−	8.94427i	0.433963	−	0.388148i
$532$	−2.29180	+	15.7082i	−0.0993620	+	0.681037i
$533$			5.23607i			0.226799i
$534$	−10.0000	+	3.81966i	−0.432742	+	0.165293i
$535$			8.00000i			0.345870i
$536$		−	6.94427i		−	0.299947i
$537$	16.9443	−	6.47214i	0.731199	−	0.279293i
$538$			8.29180i			0.357485i
$539$		0			0
$540$	14.9443	+	7.70820i	0.643099	+	0.331708i
$541$	−28.6525			−1.23187			−0.615933	−	0.787798i	$-0.711221\pi$
$541$	−28.6525			−1.23187			−0.615933	+	0.787798i	$0.711221\pi$
$542$	3.81966			0.164068
$543$	7.23607	−	2.76393i	0.310529	−	0.118612i
$544$			2.47214i			0.105992i
$545$	20.0000			0.856706
$546$	1.00000	+	4.47214i	0.0427960	+	0.191390i
$547$	22.4721			0.960839			0.480420	−	0.877039i	$-0.340484\pi$
$547$	22.4721			0.960839			0.480420	+	0.877039i	$0.340484\pi$
$548$			7.52786i			0.321574i
$549$	8.94427	+	10.0000i	0.381732	+	0.426790i
$550$		0			0
$551$	34.2492			1.45907
$552$	2.00000	+	5.23607i	0.0851257	+	0.222862i
$553$	−23.4164	−	3.41641i	−0.995767	−	0.145280i
$554$			32.4721i			1.37961i
$555$	−18.4721	−	48.3607i	−0.784099	−	2.05280i
$556$			12.1803i			0.516561i
$557$		−	22.0000i		−	0.932170i	−0.884740	−	0.466085i	$-0.845664\pi$
$557$		−	22.0000i		−	0.932170i	0.884740	−	0.466085i	$-0.154336\pi$
$558$	−16.1803	+	14.4721i	−0.684968	+	0.612654i
$559$			10.4721i			0.442924i
$560$	8.47214	+	1.23607i	0.358013	+	0.0522334i
$561$		0			0
$562$	−4.47214			−0.188646
$563$	−9.81966			−0.413849			−0.206925	−	0.978357i	$-0.566346\pi$
$563$	−9.81966			−0.413849			−0.206925	+	0.978357i	$0.566346\pi$
$564$	4.00000	+	10.4721i	0.168430	+	0.440956i
$565$			51.7771i			2.17828i
$566$	−21.1246			−0.887934
$567$	6.03444	−	23.0344i	0.253423	−	0.967356i
$568$	−14.4721			−0.607237
$569$		−	8.36068i		−	0.350498i	−0.984524	−	0.175249i	$-0.943927\pi$
$569$		−	8.36068i		−	0.350498i	0.984524	−	0.175249i	$-0.0560730\pi$
$570$	12.0000	+	31.4164i	0.502625	+	1.31589i
$571$	−22.4721			−0.940430			−0.470215	−	0.882552i	$-0.655824\pi$
$571$	−22.4721			−0.940430			−0.470215	+	0.882552i	$0.655824\pi$
$572$		0			0
$573$	−35.1246	+	13.4164i	−1.46735	+	0.560478i
$574$	2.00000	−	13.7082i	0.0834784	−	0.572169i
$575$			17.7082i			0.738483i
$576$	2.23607	−	2.00000i	0.0931695	−	0.0833333i
$577$			2.87539i			0.119704i	0.998207	+	0.0598520i	$0.0190629\pi$
$577$			2.87539i			0.119704i	−0.998207	+	0.0598520i	$0.980937\pi$
$578$		−	10.8885i		−	0.452904i
$579$	7.34752	+	19.2361i	0.305353	+	0.799424i
$580$		−	18.4721i		−	0.767014i
$581$	36.6525	+	5.34752i	1.52060	+	0.221853i
$582$	−0.472136	−	1.23607i	−0.0195707	−	0.0512367i
$583$		0			0
$584$	3.23607			0.133909
$585$	6.47214	+	7.23607i	0.267590	+	0.299175i
$586$		−	14.2918i		−	0.590389i
$587$	−5.41641			−0.223559			−0.111780	−	0.993733i	$-0.535655\pi$
$587$	−5.41641			−0.223559			−0.111780	+	0.993733i	$0.535655\pi$
$588$	−0.909830	−	12.0902i	−0.0375208	−	0.498590i
$589$	−43.4164			−1.78894
$590$		−	14.4721i		−	0.595808i
$591$	41.1246	−	15.7082i	1.69164	−	0.646149i
$592$	−9.23607			−0.379600
$593$	−40.0689			−1.64543			−0.822716	−	0.568453i	$-0.807542\pi$
$593$	−40.0689			−1.64543			−0.822716	+	0.568453i	$0.807542\pi$
$594$		0			0
$595$	20.9443	+	3.05573i	0.858631	+	0.125273i
$596$		−	17.4164i		−	0.713404i
$597$	44.8328	−	17.1246i	1.83488	−	0.700864i
$598$			3.23607i			0.132333i
$599$			32.5410i			1.32959i	0.747026	+	0.664795i	$0.231481\pi$
$599$			32.5410i			1.32959i	−0.747026	+	0.664795i	$0.768519\pi$
$600$	8.85410	−	3.38197i	0.361467	−	0.138068i
$601$			3.41641i			0.139358i	0.997569	+	0.0696791i	$0.0221975\pi$
$601$			3.41641i			0.139358i	−0.997569	+	0.0696791i	$0.977802\pi$
$602$	4.00000	−	27.4164i	0.163028	−	1.11741i
$603$	−15.5279	+	13.8885i	−0.632344	+	0.565585i
$604$	−3.70820			−0.150885
$605$	35.5967			1.44721
$606$	−29.4164	+	11.2361i	−1.19496	+	0.456434i
$607$			23.1246i			0.938599i	0.883039	+	0.469300i	$0.155494\pi$
$607$			23.1246i			0.938599i	−0.883039	+	0.469300i	$0.844506\pi$
$608$	6.00000			0.243332
$609$	−25.5279	+	5.70820i	−1.03444	+	0.231308i
$610$	14.4721			0.585960
$611$			6.47214i			0.261835i
$612$	5.52786	−	4.94427i	0.223451	−	0.199860i
$613$	15.7082			0.634448			0.317224	−	0.948351i	$-0.397249\pi$
$613$	15.7082			0.634448			0.317224	+	0.948351i	$0.397249\pi$
$614$	−18.0000			−0.726421
$615$	−10.4721	−	27.4164i	−0.422277	−	1.10554i
$616$		0			0
$617$			33.7771i			1.35981i	0.733298	+	0.679907i	$0.237980\pi$
$617$			33.7771i			1.35981i	−0.733298	+	0.679907i	$0.762020\pi$
$618$	−4.76393	−	12.4721i	−0.191633	−	0.501703i
$619$			8.47214i			0.340524i	0.985399	+	0.170262i	$0.0544614\pi$
$619$			8.47214i			0.340524i	−0.985399	+	0.170262i	$0.945539\pi$
$620$			23.4164i			0.940426i
$621$	7.70820	−	14.9443i	0.309320	−	0.599693i
$622$		−	22.4721i		−	0.901051i
$623$	16.1803	+	2.36068i	0.648252	+	0.0945786i
$624$	1.61803	−	0.618034i	0.0647732	−	0.0247412i
$625$	−22.4164			−0.896656
$626$	−10.4721			−0.418551
$627$		0			0
$628$			5.41641i			0.216138i
$629$	−22.8328			−0.910404
$630$	−14.1803	−	21.4164i	−0.564958	−	0.853250i
$631$	25.8197			1.02786			0.513932	−	0.857831i	$-0.328188\pi$
$631$	25.8197			1.02786			0.513932	+	0.857831i	$0.328188\pi$
$632$			8.94427i			0.355784i
$633$	−16.0000	−	41.8885i	−0.635943	−	1.66492i
$634$	−6.94427			−0.275792
$635$	−9.88854			−0.392415
$636$	5.23607	−	2.00000i	0.207624	−	0.0793052i
$637$	2.00000	−	6.70820i	0.0792429	−	0.265789i
$638$		0			0
$639$	28.9443	+	32.3607i	1.14502	+	1.28017i
$640$		−	3.23607i		−	0.127917i
$641$		−	34.4721i		−	1.36157i	−0.732484	−	0.680784i	$-0.761639\pi$
$641$		−	34.4721i		−	1.36157i	0.732484	−	0.680784i	$-0.238361\pi$
$642$	−1.52786	−	4.00000i	−0.0603000	−	0.157867i
$643$		−	31.8885i		−	1.25756i	−0.777583	−	0.628781i	$-0.783554\pi$
$643$		−	31.8885i		−	1.25756i	0.777583	−	0.628781i	$-0.216446\pi$
$644$	1.23607	−	8.47214i	0.0487079	−	0.333849i
$645$	−20.9443	−	54.8328i	−0.824680	−	2.15904i
$646$	14.8328			0.583589
$647$	20.3607			0.800461			0.400230	−	0.916415i	$-0.368930\pi$
$647$	20.3607			0.800461			0.400230	+	0.916415i	$0.368930\pi$
$648$	−8.94427	−	1.00000i	−0.351364	−	0.0392837i
$649$		0			0
$650$	5.47214			0.214635
$651$	32.3607	−	7.23607i	1.26832	−	0.283604i
$652$	9.41641			0.368775
$653$			5.34752i			0.209265i	0.994511	+	0.104632i	$0.0333666\pi$
$653$			5.34752i			0.209265i	−0.994511	+	0.104632i	$0.966633\pi$
$654$	−10.0000	+	3.81966i	−0.391031	+	0.149361i
$655$	−16.9443			−0.662067
$656$	−5.23607			−0.204434
$657$	−6.47214	−	7.23607i	−0.252502	−	0.282306i
$658$	2.47214	−	16.9443i	0.0963739	−	0.660556i
$659$			1.88854i			0.0735672i	0.999323	+	0.0367836i	$0.0117112\pi$
$659$			1.88854i			0.0735672i	−0.999323	+	0.0367836i	$0.988289\pi$
$660$		0			0
$661$		−	33.4164i		−	1.29975i	−0.760042	−	0.649874i	$-0.774822\pi$
$661$		−	33.4164i		−	1.29975i	0.760042	−	0.649874i	$-0.225178\pi$
$662$			14.3607i			0.558144i
$663$	4.00000	−	1.52786i	0.155347	−	0.0593373i
$664$		−	14.0000i		−	0.543305i
$665$	7.41641	−	50.8328i	0.287596	−	1.97121i
$666$	18.4721	+	20.6525i	0.715781	+	0.800267i
$667$	−18.4721			−0.715244
$668$	−16.9443			−0.655594
$669$	−14.1803	+	5.41641i	−0.548244	+	0.209410i
$670$			22.4721i			0.868174i
$671$		0			0
$672$	−4.47214	+	1.00000i	−0.172516	+	0.0385758i
$673$	−12.8328			−0.494669			−0.247334	−	0.968930i	$-0.579555\pi$
$673$	−12.8328			−0.494669			−0.247334	+	0.968930i	$0.579555\pi$
$674$		−	19.8885i		−	0.766078i
$675$	−25.2705	−	13.0344i	−0.972662	−	0.501696i
$676$	1.00000			0.0384615
$677$	8.65248			0.332542			0.166271	−	0.986080i	$-0.446827\pi$
$677$	8.65248			0.332542			0.166271	+	0.986080i	$0.446827\pi$
$678$	−9.88854	−	25.8885i	−0.379767	−	0.994244i
$679$	−0.291796	+	2.00000i	−0.0111981	+	0.0767530i
$680$		−	8.00000i		−	0.306786i
$681$	2.18034	+	5.70820i	0.0835508	+	0.218739i
$682$		0			0
$683$			42.8328i			1.63895i	0.573113	+	0.819476i	$0.305735\pi$
$683$			42.8328i			1.63895i	−0.573113	+	0.819476i	$0.694265\pi$
$684$	−12.0000	−	13.4164i	−0.458831	−	0.512989i
$685$		−	24.3607i		−	0.930774i
$686$	−7.79837	+	16.7984i	−0.297743	+	0.641365i
$687$	−4.76393	+	1.81966i	−0.181755	+	0.0694244i
$688$	−10.4721			−0.399246
$689$	3.23607			0.123284
$690$	−6.47214	−	16.9443i	−0.246390	−	0.645057i
$691$		−	10.0000i		−	0.380418i	−0.981744	−	0.190209i	$-0.939083\pi$
$691$		−	10.0000i		−	0.380418i	0.981744	−	0.190209i	$-0.0609166\pi$
$692$	18.7639			0.713298
$693$		0			0
$694$	24.3607			0.924719
$695$		−	39.4164i		−	1.49515i
$696$	3.52786	+	9.23607i	0.133723	+	0.350092i
$697$	−12.9443			−0.490299
$698$	−35.3050			−1.33631
$699$	−11.4164	+	4.36068i	−0.431808	+	0.164936i
$700$	−14.3262	−	2.09017i	−0.541481	−	0.0790010i
$701$			12.7639i			0.482087i	0.970514	+	0.241044i	$0.0774897\pi$
$701$			12.7639i			0.482087i	−0.970514	+	0.241044i	$0.922510\pi$
$702$	−4.61803	−	2.38197i	−0.174296	−	0.0899015i
$703$			55.4164i			2.09007i
$704$		0			0
$705$	−12.9443	−	33.8885i	−0.487509	−	1.27632i
$706$			19.1246i			0.719764i
$707$	47.5967	+	6.94427i	1.79006	+	0.261166i
$708$	2.76393	+	7.23607i	0.103875	+	0.271948i
$709$	2.76393			0.103802			0.0519008	−	0.998652i	$-0.483472\pi$
$709$	2.76393			0.103802			0.0519008	+	0.998652i	$0.483472\pi$
$710$	46.8328			1.75760
$711$	20.0000	−	17.8885i	0.750059	−	0.670873i
$712$		−	6.18034i		−	0.231618i
$713$	23.4164			0.876951
$714$	−11.0557	+	2.47214i	−0.413750	+	0.0925174i
$715$		0			0
$716$			10.4721i			0.391362i
$717$	−0.944272	+	0.360680i	−0.0352645	+	0.0134698i
$718$	−21.8885			−0.816873
$719$	44.7214			1.66783			0.833913	−	0.551896i	$-0.186096\pi$
$719$	44.7214			1.66783			0.833913	+	0.551896i	$0.186096\pi$
$720$	−7.23607	+	6.47214i	−0.269672	+	0.241202i
$721$	−2.94427	+	20.1803i	−0.109650	+	0.751555i
$722$		−	17.0000i		−	0.632674i
$723$	−17.2361	+	6.58359i	−0.641016	+	0.244846i
$724$			4.47214i			0.166206i
$725$			31.2361i			1.16008i
$726$	−17.7984	+	6.79837i	−0.660560	+	0.252311i
$727$		−	38.1803i		−	1.41603i	−0.706197	−	0.708015i	$-0.749591\pi$
$727$		−	38.1803i		−	1.41603i	0.706197	−	0.708015i	$-0.250409\pi$
$728$	−2.61803	−	0.381966i	−0.0970308	−	0.0141566i
$729$	15.6525	+	22.0000i	0.579721	+	0.814815i
$730$	−10.4721			−0.387591
$731$	−25.8885			−0.957522
$732$	−7.23607	+	2.76393i	−0.267453	+	0.102158i
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$	12.6525			0.467011
$735$	2.94427	+	39.1246i	0.108601	+	1.44313i
$736$	−3.23607			−0.119283
$737$		0			0
$738$	10.4721	+	11.7082i	0.385485	+	0.430985i
$739$	−16.8328			−0.619205			−0.309603	−	0.950866i	$-0.600196\pi$
$739$	−16.8328			−0.619205			−0.309603	+	0.950866i	$0.600196\pi$
$740$	29.8885			1.09872
$741$	−3.70820	−	9.70820i	−0.136224	−	0.356640i
$742$	−8.47214	−	1.23607i	−0.311022	−	0.0453775i
$743$			17.3050i			0.634857i	0.948282	+	0.317429i	$0.102819\pi$
$743$			17.3050i			0.634857i	−0.948282	+	0.317429i	$0.897181\pi$
$744$	−4.47214	−	11.7082i	−0.163956	−	0.429244i
$745$			56.3607i			2.06490i
$746$			17.4164i			0.637660i
$747$	−31.3050	+	28.0000i	−1.14539	+	1.02447i
$748$		0			0
$749$	−0.944272	+	6.47214i	−0.0345029	+	0.236487i
$750$	−2.47214	+	0.944272i	−0.0902696	+	0.0344799i
$751$	33.3050			1.21531			0.607657	−	0.794199i	$-0.292109\pi$
$751$	33.3050			1.21531			0.607657	+	0.794199i	$0.292109\pi$
$752$	−6.47214			−0.236015
$753$	9.12461	+	23.8885i	0.332519	+	0.870547i
$754$			5.70820i			0.207881i
$755$	12.0000			0.436725
$756$	11.1803	+	8.00000i	0.406625	+	0.290957i
$757$	10.3607			0.376565			0.188283	−	0.982115i	$-0.439708\pi$
$757$	10.3607			0.376565			0.188283	+	0.982115i	$0.439708\pi$
$758$		−	30.0000i		−	1.08965i
$759$		0			0
$760$	−19.4164			−0.704307
$761$	−39.7082			−1.43942			−0.719711	−	0.694274i	$-0.755726\pi$
$761$	−39.7082			−1.43942			−0.719711	+	0.694274i	$0.755726\pi$
$762$	4.94427	−	1.88854i	0.179112	−	0.0684147i
$763$	16.1803	+	2.36068i	0.585768	+	0.0854623i
$764$		−	21.7082i		−	0.785375i
$765$	−17.8885	+	16.0000i	−0.646762	+	0.578481i
$766$		−	30.4721i		−	1.10100i
$767$			4.47214i			0.161479i
$768$	0.618034	+	1.61803i	0.0223014	+	0.0583858i
$769$			52.5410i			1.89468i	0.320233	+	0.947339i	$0.396239\pi$
$769$			52.5410i			1.89468i	−0.320233	+	0.947339i	$0.603761\pi$
$770$		0			0
$771$	1.52786	+	4.00000i	0.0550247	+	0.144056i
$772$	−11.8885			−0.427878
$773$	−14.2918			−0.514040			−0.257020	−	0.966406i	$-0.582741\pi$
$773$	−14.2918			−0.514040			−0.257020	+	0.966406i	$0.582741\pi$
$774$	20.9443	+	23.4164i	0.752826	+	0.841685i
$775$		−	39.5967i		−	1.42236i
$776$	0.763932			0.0274236
$777$	−9.23607	−	41.3050i	−0.331342	−	1.48181i
$778$	−32.5410			−1.16665
$779$			31.4164i			1.12561i
$780$	−5.23607	+	2.00000i	−0.187481	+	0.0716115i
$781$		0			0
$782$	−8.00000			−0.286079
$783$	13.5967	−	26.3607i	0.485908	−	0.942054i
$784$	6.70820	+	2.00000i	0.239579	+	0.0714286i
$785$		−	17.5279i		−	0.625596i
$786$	8.47214	−	3.23607i	0.302191	−	0.115427i
$787$		−	18.5836i		−	0.662434i	−0.943555	−	0.331217i	$-0.892541\pi$
$787$		−	18.5836i		−	0.662434i	0.943555	−	0.331217i	$-0.107459\pi$
$788$			25.4164i			0.905422i
$789$	−28.6525	+	10.9443i	−1.02006	+	0.389626i
$790$		−	28.9443i		−	1.02979i
$791$	−6.11146	+	41.8885i	−0.217298	+	1.48939i
$792$		0			0
$793$	−4.47214			−0.158810
$794$	28.8328			1.02324
$795$	−16.9443	+	6.47214i	−0.600951	+	0.229543i
$796$			27.7082i			0.982091i
$797$	−27.1246			−0.960803			−0.480402	−	0.877049i	$-0.659509\pi$
$797$	−27.1246			−0.960803			−0.480402	+	0.877049i	$0.659509\pi$
$798$	6.00000	+	26.8328i	0.212398	+	0.949871i
$799$	−16.0000			−0.566039
$800$			5.47214i			0.193469i
$801$	−13.8197	+	12.3607i	−0.488294	+	0.436743i
$802$	18.9443			0.668945
$803$		0			0
$804$	−4.29180	−	11.2361i	−0.151360	−	0.396266i
$805$	−4.00000	+	27.4164i	−0.140981	+	0.966301i
$806$		−	7.23607i		−	0.254880i
$807$	5.12461	+	13.4164i	0.180395	+	0.472280i
$808$		−	18.1803i		−	0.639582i
$809$			27.4164i			0.963910i	0.876196	+	0.481955i	$0.160073\pi$
$809$			27.4164i			0.963910i	−0.876196	+	0.481955i	$0.839927\pi$
$810$	28.9443	+	3.23607i	1.01700	+	0.113704i
$811$			31.3050i			1.09927i	0.835406	+	0.549633i	$0.185232\pi$
$811$			31.3050i			1.09927i	−0.835406	+	0.549633i	$0.814768\pi$
$812$	2.18034	−	14.9443i	0.0765149	−	0.524441i
$813$	6.18034	−	2.36068i	0.216754	−	0.0827927i
$814$		0			0
$815$	−30.4721			−1.06739
$816$	1.52786	+	4.00000i	0.0534859	+	0.140028i
$817$			62.8328i			2.19824i
$818$	−5.70820			−0.199583
$819$	4.38197	+	6.61803i	0.153118	+	0.231253i
$820$	16.9443			0.591720
$821$		−	18.9443i		−	0.661160i	−0.943778	−	0.330580i	$-0.892756\pi$
$821$		−	18.9443i		−	0.661160i	0.943778	−	0.330580i	$-0.107244\pi$
$822$	4.65248	+	12.1803i	0.162274	+	0.424838i
$823$	15.0557			0.524810			0.262405	−	0.964958i	$-0.415484\pi$
$823$	15.0557			0.524810			0.262405	+	0.964958i	$0.415484\pi$
$824$	7.70820			0.268528
$825$		0			0
$826$	1.70820	−	11.7082i	0.0594360	−	0.407381i
$827$			36.9443i			1.28468i	0.766421	+	0.642339i	$0.222036\pi$
$827$			36.9443i			1.28468i	−0.766421	+	0.642339i	$0.777964\pi$
$828$	6.47214	+	7.23607i	0.224922	+	0.251471i
$829$		−	2.58359i		−	0.0897319i	−0.998993	−	0.0448659i	$-0.985714\pi$
$829$		−	2.58359i		−	0.0897319i	0.998993	−	0.0448659i	$-0.0142861\pi$
$830$			45.3050i			1.57256i
$831$	20.0689	+	52.5410i	0.696182	+	1.82263i
$832$			1.00000i			0.0346688i
$833$	16.5836	+	4.94427i	0.574587	+	0.171309i
$834$	7.52786	+	19.7082i	0.260669	+	0.682439i
$835$	54.8328			1.89757
$836$		0			0
$837$	−17.2361	+	33.4164i	−0.595766	+	1.15504i
$838$		−	11.7082i		−	0.404453i
$839$	44.7214			1.54395			0.771976	−	0.635651i	$-0.219268\pi$
$839$	44.7214			1.54395			0.771976	+	0.635651i	$0.219268\pi$
$840$	14.4721	−	3.23607i	0.499336	−	0.111655i
$841$	−3.58359			−0.123572
$842$			14.7639i			0.508799i
$843$	−7.23607	+	2.76393i	−0.249223	+	0.0951949i
$844$	25.8885			0.891120
$845$	−3.23607			−0.111324
$846$	12.9443	+	14.4721i	0.445033	+	0.497562i
$847$	28.7984	+	4.20163i	0.989524	+	0.144370i
$848$			3.23607i			0.111127i
$849$	−34.1803	+	13.0557i	−1.17307	+	0.448071i
$850$			13.5279i			0.464002i
$851$		−	29.8885i		−	1.02457i
$852$	−23.4164	+	8.94427i	−0.802233	+	0.306426i
$853$			27.3050i			0.934904i	0.884019	+	0.467452i	$0.154828\pi$
$853$			27.3050i			0.934904i	−0.884019	+	0.467452i	$0.845172\pi$
$854$	11.7082	+	1.70820i	0.400646	+	0.0584535i
$855$	38.8328	+	43.4164i	1.32805	+	1.48481i
$856$	2.47214			0.0844959
$857$	−36.7214			−1.25438			−0.627189	−	0.778867i	$-0.715795\pi$
$857$	−36.7214			−1.25438			−0.627189	+	0.778867i	$0.715795\pi$
$858$		0			0
$859$			5.70820i			0.194761i	0.995247	+	0.0973807i	$0.0310464\pi$
$859$			5.70820i			0.194761i	−0.995247	+	0.0973807i	$0.968954\pi$
$860$	33.8885			1.15559
$861$	−5.23607	−	23.4164i	−0.178445	−	0.798029i
$862$	−20.0000			−0.681203
$863$		−	45.3050i		−	1.54220i	−0.636715	−	0.771099i	$-0.719707\pi$
$863$		−	45.3050i		−	1.54220i	0.636715	−	0.771099i	$-0.280293\pi$
$864$	2.38197	−	4.61803i	0.0810361	−	0.157109i
$865$	−60.7214			−2.06459
$866$	−19.4164			−0.659796
$867$	−6.72949	−	17.6180i	−0.228545	−	0.598340i
$868$	−2.76393	+	18.9443i	−0.0938140	+	0.643010i
$869$		0			0
$870$	−11.4164	−	29.8885i	−0.387052	−	1.01332i
$871$		−	6.94427i		−	0.235298i
$872$		−	6.18034i		−	0.209293i
$873$	−1.52786	−	1.70820i	−0.0517104	−	0.0578139i
$874$			19.4164i			0.656770i
$875$	4.00000	+	0.583592i	0.135225	+	0.0197290i
$876$	5.23607	−	2.00000i	0.176910	−	0.0675737i
$877$	−0.291796			−0.00985325			−0.00492663	−	0.999988i	$-0.501568\pi$
$877$	−0.291796			−0.00985325			−0.00492663	+	0.999988i	$0.501568\pi$
$878$	34.5410			1.16570
$879$	−8.83282	−	23.1246i	−0.297923	−	0.779974i
$880$		0			0
$881$	26.4721			0.891869			0.445934	−	0.895066i	$-0.352871\pi$
$881$	26.4721			0.891869			0.445934	+	0.895066i	$0.352871\pi$
$882$	−8.94427	−	19.0000i	−0.301169	−	0.639763i
$883$	9.52786			0.320638			0.160319	−	0.987065i	$-0.448748\pi$
$883$	9.52786			0.320638			0.160319	+	0.987065i	$0.448748\pi$
$884$			2.47214i			0.0831469i
$885$	−8.94427	−	23.4164i	−0.300658	−	0.787134i
$886$	29.5279			0.992008
$887$	45.8885			1.54079			0.770393	−	0.637569i	$-0.220060\pi$
$887$	45.8885			1.54079			0.770393	+	0.637569i	$0.220060\pi$
$888$	−14.9443	+	5.70820i	−0.501497	+	0.191555i
$889$	−8.00000	−	1.16718i	−0.268311	−	0.0391461i
$890$			20.0000i			0.670402i
$891$		0			0
$892$		−	8.76393i		−	0.293438i
$893$			38.8328i			1.29949i
$894$	−10.7639	−	28.1803i	−0.360000	−	0.942492i
$895$		−	33.8885i		−	1.13277i
$896$	0.381966	−	2.61803i	0.0127606	−	0.0874624i
$897$	2.00000	+	5.23607i	0.0667781	+	0.174827i
$898$	18.3607			0.612704
$899$	41.3050			1.37760
$900$	12.2361	−	10.9443i	0.407869	−	0.364809i
$901$			8.00000i			0.266519i
$902$		0			0
$903$	−10.4721	−	46.8328i	−0.348491	−	1.55850i
$904$	16.0000			0.532152
$905$		−	14.4721i		−	0.481070i
$906$	−6.00000	+	2.29180i	−0.199337	+	0.0761398i
$907$	−18.8328			−0.625333			−0.312667	−	0.949863i	$-0.601222\pi$
$907$	−18.8328			−0.625333			−0.312667	+	0.949863i	$0.601222\pi$
$908$	−3.52786			−0.117076
$909$	−40.6525	+	36.3607i	−1.34836	+	1.20601i
$910$	8.47214	+	1.23607i	0.280849	+	0.0409753i
$911$			1.70820i			0.0565953i	0.999600	+	0.0282977i	$0.00900863\pi$
$911$			1.70820i			0.0565953i	−0.999600	+	0.0282977i	$0.990991\pi$
$912$	9.70820	−	3.70820i	0.321471	−	0.122791i
$913$		0			0
$914$			26.9443i			0.891237i
$915$	23.4164	−	8.94427i	0.774123	−	0.295689i
$916$		−	2.94427i		−	0.0972815i
$917$	−13.7082	−	2.00000i	−0.452685	−	0.0660458i
$918$	5.88854	−	11.4164i	0.194351	−	0.376798i
$919$	−44.7214			−1.47522			−0.737611	−	0.675226i	$-0.764046\pi$
$919$	−44.7214			−1.47522			−0.737611	+	0.675226i	$0.764046\pi$
$920$	10.4721			0.345256
$921$	−29.1246	+	11.1246i	−0.959689	+	0.366568i
$922$		−	20.7639i		−	0.683824i
$923$	−14.4721			−0.476356
$924$		0			0
$925$	−50.5410			−1.66178
$926$			15.7082i			0.516204i
$927$	−15.4164	−	17.2361i	−0.506341	−	0.566107i
$928$	−5.70820			−0.187381
$929$	42.7639			1.40304			0.701520	−	0.712650i	$-0.252505\pi$
$929$	42.7639			1.40304			0.701520	+	0.712650i	$0.252505\pi$
$930$	14.4721	+	37.8885i	0.474560	+	1.24241i
$931$	12.0000	−	40.2492i	0.393284	−	1.31912i
$932$		−	7.05573i		−	0.231118i
$933$	−13.8885	−	36.3607i	−0.454691	−	1.19040i
$934$		−	18.1803i		−	0.594879i
$935$		0			0
$936$	2.23607	−	2.00000i	0.0730882	−	0.0653720i
$937$			10.1115i			0.330327i	0.986266	+	0.165163i	$0.0528152\pi$
$937$			10.1115i			0.330327i	−0.986266	+	0.165163i	$0.947185\pi$
$938$	−2.65248	+	18.1803i	−0.0866064	+	0.593609i
$939$	−16.9443	+	6.47214i	−0.552955	+	0.211210i
$940$	20.9443			0.683127
$941$	−51.0132			−1.66298			−0.831491	−	0.555539i	$-0.812512\pi$
$941$	−51.0132			−1.66298			−0.831491	+	0.555539i	$0.812512\pi$
$942$	3.34752	+	8.76393i	0.109068	+	0.285544i
$943$		−	16.9443i		−	0.551781i
$944$	−4.47214			−0.145556
$945$	−36.1803	−	25.8885i	−1.17695	−	0.842154i
$946$		0			0
$947$		−	23.0557i		−	0.749210i	−0.927184	−	0.374605i	$-0.877778\pi$
$947$		−	23.0557i		−	0.749210i	0.927184	−	0.374605i	$-0.122222\pi$
$948$	5.52786	+	14.4721i	0.179537	+	0.470033i
$949$	3.23607			0.105047
$950$	32.8328			1.06524
$951$	−11.2361	+	4.29180i	−0.364354	+	0.139171i
$952$	0.944272	−	6.47214i	0.0306040	−	0.209763i
$953$			17.3050i			0.560562i	0.959918	+	0.280281i	$0.0904277\pi$
$953$			17.3050i			0.560562i	−0.959918	+	0.280281i	$0.909572\pi$
$954$	7.23607	−	6.47214i	0.234276	−	0.209543i
$955$			70.2492i			2.27321i
$956$		−	0.583592i		−	0.0188747i
$957$		0			0
$958$			14.4721i			0.467573i
$959$	2.87539	−	19.7082i	0.0928511	−	0.636411i
$960$	−2.00000	−	5.23607i	−0.0645497	−	0.168993i
$961$	−21.3607			−0.689054
$962$	−9.23607			−0.297783
$963$	−4.94427	−	5.52786i	−0.159327	−	0.178133i
$964$		−	10.6525i		−	0.343093i
$965$	38.4721			1.23846
$966$	−3.23607	−	14.4721i	−0.104119	−	0.465633i
$967$	34.1803			1.09917			0.549583	−	0.835439i	$-0.314787\pi$
$967$	34.1803			1.09917			0.549583	+	0.835439i	$0.314787\pi$
$968$		−	11.0000i		−	0.353553i
$969$	24.0000	−	9.16718i	0.770991	−	0.294492i
$970$	−2.47214			−0.0793755
$971$	0.291796			0.00936418			0.00468209	−	0.999989i	$-0.498510\pi$
$971$	0.291796			0.00936418			0.00468209	+	0.999989i	$0.498510\pi$
$972$	−15.0902	+	3.90983i	−0.484017	+	0.125408i
$973$	4.65248	−	31.8885i	0.149152	−	1.02230i
$974$			10.7639i			0.344899i
$975$	8.85410	−	3.38197i	0.283558	−	0.108310i
$976$		−	4.47214i		−	0.143150i
$977$			21.4164i			0.685172i	0.939487	+	0.342586i	$0.111303\pi$
$977$			21.4164i			0.685172i	−0.939487	+	0.342586i	$0.888697\pi$
$978$	15.2361	−	5.81966i	0.487196	−	0.186092i
$979$		0			0
$980$	−21.7082	−	6.47214i	−0.693443	−	0.206745i
$981$	−13.8197	+	12.3607i	−0.441228	+	0.394646i
$982$	3.41641			0.109022
$983$	61.8885			1.97394			0.986969	−	0.160911i	$-0.0514431\pi$
$983$	61.8885			1.97394			0.986969	+	0.160911i	$0.0514431\pi$
$984$	−8.47214	+	3.23607i	−0.270082	+	0.103162i
$985$		−	82.2492i		−	2.62068i
$986$	−14.1115			−0.449400
$987$	−6.47214	−	28.9443i	−0.206010	−	0.921306i
$988$	6.00000			0.190885
$989$		−	33.8885i		−	1.07759i
$990$		0			0
$991$	24.3607			0.773842			0.386921	−	0.922113i	$-0.373539\pi$
$991$	24.3607			0.773842			0.386921	+	0.922113i	$0.373539\pi$
$992$	7.23607			0.229745
$993$	8.87539	+	23.2361i	0.281652	+	0.737374i
$994$	37.8885	+	5.52786i	1.20175	+	0.175333i
$995$		−	89.6656i		−	2.84259i
$996$	−8.65248	−	22.6525i	−0.274164	−	0.717771i
$997$			46.9443i			1.48674i	0.668880	+	0.743370i	$0.266774\pi$
$997$			46.9443i			1.48674i	−0.668880	+	0.743370i	$0.733226\pi$
$998$		−	10.0000i		−	0.316544i
$999$	42.6525	+	22.0000i	1.34946	+	0.696049i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +3.23607 q^{5} +(-1.61803 + 0.618034i) q^{6} +(2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +3.23607 q^{5} +(-1.61803 + 0.618034i) q^{6} +(2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(-2.23607 + 2.00000i) q^{9} +3.23607i q^{10} +(-0.618034 - 1.61803i) q^{12} -1.00000i q^{13} +(-0.381966 + 2.61803i) q^{14} +(2.00000 + 5.23607i) q^{15} +1.00000 q^{16} +2.47214 q^{17} +(-2.00000 - 2.23607i) q^{18} -6.00000i q^{19} -3.23607 q^{20} +(1.00000 + 4.47214i) q^{21} +3.23607i q^{23} +(1.61803 - 0.618034i) q^{24} +5.47214 q^{25} +1.00000 q^{26} +(-4.61803 - 2.38197i) q^{27} +(-2.61803 - 0.381966i) q^{28} +5.70820i q^{29} +(-5.23607 + 2.00000i) q^{30} -7.23607i q^{31} +1.00000i q^{32} +2.47214i q^{34} +(8.47214 + 1.23607i) q^{35} +(2.23607 - 2.00000i) q^{36} -9.23607 q^{37} +6.00000 q^{38} +(1.61803 - 0.618034i) q^{39} -3.23607i q^{40} -5.23607 q^{41} +(-4.47214 + 1.00000i) q^{42} -10.4721 q^{43} +(-7.23607 + 6.47214i) q^{45} -3.23607 q^{46} -6.47214 q^{47} +(0.618034 + 1.61803i) q^{48} +(6.70820 + 2.00000i) q^{49} +5.47214i q^{50} +(1.52786 + 4.00000i) q^{51} +1.00000i q^{52} +3.23607i q^{53} +(2.38197 - 4.61803i) q^{54} +(0.381966 - 2.61803i) q^{56} +(9.70820 - 3.70820i) q^{57} -5.70820 q^{58} -4.47214 q^{59} +(-2.00000 - 5.23607i) q^{60} -4.47214i q^{61} +7.23607 q^{62} +(-6.61803 + 4.38197i) q^{63} -1.00000 q^{64} -3.23607i q^{65} +6.94427 q^{67} -2.47214 q^{68} +(-5.23607 + 2.00000i) q^{69} +(-1.23607 + 8.47214i) q^{70} -14.4721i q^{71} +(2.00000 + 2.23607i) q^{72} +3.23607i q^{73} -9.23607i q^{74} +(3.38197 + 8.85410i) q^{75} +6.00000i q^{76} +(0.618034 + 1.61803i) q^{78} -8.94427 q^{79} +3.23607 q^{80} +(1.00000 - 8.94427i) q^{81} -5.23607i q^{82} +14.0000 q^{83} +(-1.00000 - 4.47214i) q^{84} +8.00000 q^{85} -10.4721i q^{86} +(-9.23607 + 3.52786i) q^{87} +6.18034 q^{89} +(-6.47214 - 7.23607i) q^{90} +(0.381966 - 2.61803i) q^{91} -3.23607i q^{92} +(11.7082 - 4.47214i) q^{93} -6.47214i q^{94} -19.4164i q^{95} +(-1.61803 + 0.618034i) q^{96} +0.763932i q^{97} +(-2.00000 + 6.70820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 6 q^{7}+O(q^{10}) \) 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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