LMFDB - Embedded newform 546.2.bq.a.503.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.503
Dual form			546.2.bq.a.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.46410 q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.46410 q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +1.73205 q^{12} +(-3.50000 - 0.866025i) q^{13} +(-1.73205 + 2.00000i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +3.00000i q^{18} +(1.73205 + 3.00000i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(2.59808 + 1.50000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +7.00000 q^{25} +(2.59808 + 2.50000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(5.19615 + 3.00000i) q^{29} +(-5.19615 + 3.00000i) q^{30} -1.73205i q^{31} +(0.866025 - 0.500000i) q^{32} -1.73205i q^{34} +(1.73205 - 9.00000i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(-4.33013 + 4.50000i) q^{39} -3.46410i q^{40} +(-3.46410 + 6.00000i) q^{41} +(1.50000 + 4.33013i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(-5.19615 - 9.00000i) q^{45} +(-1.50000 - 2.59808i) q^{46} +3.46410 q^{47} +(0.866025 + 1.50000i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-6.06218 - 3.50000i) q^{50} +3.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} -9.00000i q^{53} +(4.50000 + 2.59808i) q^{54} +(-2.59808 - 0.500000i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-0.866025 - 1.50000i) q^{59} +6.00000 q^{60} +(-10.5000 + 6.06218i) q^{61} +(-0.866025 + 1.50000i) q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-12.1244 - 3.00000i) q^{65} +(3.50000 - 6.06218i) q^{67} +(-0.866025 + 1.50000i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-6.00000 + 6.92820i) q^{70} +(12.9904 - 7.50000i) q^{71} +(-2.59808 + 1.50000i) q^{72} +13.8564i q^{73} +(3.46410 - 2.00000i) q^{74} +(6.06218 - 10.5000i) q^{75} +(6.00000 - 1.73205i) q^{78} -10.0000 q^{79} +(-1.73205 + 3.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} +12.1244 q^{83} +(0.866025 - 4.50000i) q^{84} +(3.00000 + 5.19615i) q^{85} +1.00000i q^{86} +(9.00000 - 5.19615i) q^{87} +(-7.79423 + 13.5000i) q^{89} +10.3923i q^{90} +(-4.00000 + 8.66025i) q^{91} +3.00000i q^{92} +(-2.59808 - 1.50000i) q^{93} +(-3.00000 - 1.73205i) q^{94} -1.73205i q^{96} +(15.0000 - 8.66025i) q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9} - 12 q^{10} - 14 q^{13} + 12 q^{15} - 2 q^{16} - 6 q^{24} + 28 q^{25} + 10 q^{28} + 6 q^{36} - 8 q^{37} + 6 q^{42} - 2 q^{43} - 6 q^{46} - 26 q^{49} + 12 q^{51} - 4 q^{52} + 18 q^{54} - 12 q^{58} + 24 q^{60} - 42 q^{61} - 30 q^{63} - 4 q^{64} + 14 q^{67} + 18 q^{69} - 24 q^{70} + 24 q^{78} - 40 q^{79} - 18 q^{81} + 24 q^{82} + 12 q^{85} + 36 q^{87} - 16 q^{91} - 12 q^{94} + 60 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9 - 12 * q^10 - 14 * q^13 + 12 * q^15 - 2 * q^16 - 6 * q^24 + 28 * q^25 + 10 * q^28 + 6 * q^36 - 8 * q^37 + 6 * q^42 - 2 * q^43 - 6 * q^46 - 26 * q^49 + 12 * q^51 - 4 * q^52 + 18 * q^54 - 12 * q^58 + 24 * q^60 - 42 * q^61 - 30 * q^63 - 4 * q^64 + 14 * q^67 + 18 * q^69 - 24 * q^70 + 24 * q^78 - 40 * q^79 - 18 * q^81 + 24 * q^82 + 12 * q^85 + 36 * q^87 - 16 * q^91 - 12 * q^94 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.46410			1.54919			0.774597	−	0.632456i	$-0.217953\pi$
$5$	3.46410			1.54919			0.774597	+	0.632456i	$0.217953\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−3.00000	−	1.73205i	−0.948683	−	0.547723i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	1.73205			0.500000
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	−1.73205	+	2.00000i	−0.462910	+	0.534522i
$15$	3.00000	−	5.19615i	0.774597	−	1.34164i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.866025	+	1.50000i	0.210042	+	0.363803i	0.951727	−	0.306944i	$-0.0993066\pi$
$17$	0.866025	+	1.50000i	0.210042	+	0.363803i	−0.741685	+	0.670748i	$0.765973\pi$
$18$			3.00000i			0.707107i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	1.73205	+	3.00000i	0.387298	+	0.670820i
$21$	−3.46410	−	3.00000i	−0.755929	−	0.654654i
$22$		0			0
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	7.00000			1.40000
$26$	2.59808	+	2.50000i	0.509525	+	0.490290i
$27$	−5.19615			−1.00000
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.897678	−	0.440652i	$-0.145253\pi$
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.0672232	+	0.997738i	$0.478586\pi$
$30$	−5.19615	+	3.00000i	−0.948683	+	0.547723i
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	1.73205i		−	0.297044i
$35$	1.73205	−	9.00000i	0.292770	−	1.52128i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	−4.33013	+	4.50000i	−0.693375	+	0.720577i
$40$		−	3.46410i		−	0.547723i
$41$	−3.46410	+	6.00000i	−0.541002	+	0.937043i	0.457845	+	0.889032i	$0.348621\pi$
$41$	−3.46410	+	6.00000i	−0.541002	+	0.937043i	−0.998847	+	0.0480106i	$0.984712\pi$
$42$	1.50000	+	4.33013i	0.231455	+	0.668153i
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$	−5.19615	−	9.00000i	−0.774597	−	1.34164i
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$	0.866025	+	1.50000i	0.125000	+	0.216506i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−6.06218	−	3.50000i	−0.857321	−	0.494975i
$51$	3.00000			0.420084
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$		−	9.00000i		−	1.23625i	−0.786082	−	0.618123i	$-0.787894\pi$
$53$		−	9.00000i		−	1.23625i	0.786082	−	0.618123i	$-0.212106\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		0			0
$56$	−2.59808	−	0.500000i	−0.347183	−	0.0668153i
$57$		0			0
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	0.804130	−	0.594454i	$-0.202632\pi$
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	−0.916877	+	0.399170i	$0.869298\pi$
$60$	6.00000			0.774597
$61$	−10.5000	+	6.06218i	−1.34439	+	0.776182i	−0.987448	−	0.157945i	$-0.949513\pi$
$61$	−10.5000	+	6.06218i	−1.34439	+	0.776182i	−0.356939	+	0.934128i	$0.616180\pi$
$62$	−0.866025	+	1.50000i	−0.109985	+	0.190500i
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	−1.00000			−0.125000
$65$	−12.1244	−	3.00000i	−1.50384	−	0.372104i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−0.866025	+	1.50000i	−0.105021	+	0.181902i
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$	−6.00000	+	6.92820i	−0.717137	+	0.828079i
$71$	12.9904	−	7.50000i	1.54167	−	0.890086i	0.542941	−	0.839771i	$-0.317311\pi$
$71$	12.9904	−	7.50000i	1.54167	−	0.890086i	0.998733	−	0.0503155i	$-0.0160227\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$			13.8564i			1.62177i	0.585206	+	0.810885i	$0.301014\pi$
$73$			13.8564i			1.62177i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	3.46410	−	2.00000i	0.402694	−	0.232495i
$75$	6.06218	−	10.5000i	0.700000	−	1.21244i
$76$		0			0
$77$		0			0
$78$	6.00000	−	1.73205i	0.679366	−	0.196116i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.73205	+	3.00000i	−0.193649	+	0.335410i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	6.00000	−	3.46410i	0.662589	−	0.382546i
$83$	12.1244			1.33082			0.665410	−	0.746478i	$-0.268257\pi$
$83$	12.1244			1.33082			0.665410	+	0.746478i	$0.268257\pi$
$84$	0.866025	−	4.50000i	0.0944911	−	0.490990i
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$			1.00000i			0.107833i
$87$	9.00000	−	5.19615i	0.964901	−	0.557086i
$88$		0			0
$89$	−7.79423	+	13.5000i	−0.826187	+	1.43100i	0.0748225	+	0.997197i	$0.476161\pi$
$89$	−7.79423	+	13.5000i	−0.826187	+	1.43100i	−0.901009	+	0.433800i	$0.857172\pi$
$90$			10.3923i			1.09545i
$91$	−4.00000	+	8.66025i	−0.419314	+	0.907841i
$92$			3.00000i			0.312772i
$93$	−2.59808	−	1.50000i	−0.269408	−	0.155543i
$94$	−3.00000	−	1.73205i	−0.309426	−	0.178647i
$95$		0			0
$96$		−	1.73205i		−	0.176777i
$97$	15.0000	−	8.66025i	1.52302	−	0.879316i	0.523390	−	0.852093i	$-0.324667\pi$
$97$	15.0000	−	8.66025i	1.52302	−	0.879316i	0.999629	−	0.0272222i	$-0.00866617\pi$
$98$	4.33013	+	5.50000i	0.437409	+	0.555584i
$99$		0			0
$100$	3.50000	+	6.06218i	0.350000	+	0.606218i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−2.59808	−	1.50000i	−0.257248	−	0.148522i
$103$		−	8.66025i		−	0.853320i	−0.904412	−	0.426660i	$-0.859690\pi$
$103$		−	8.66025i		−	0.853320i	0.904412	−	0.426660i	$-0.140310\pi$
$104$	−0.866025	+	3.50000i	−0.0849208	+	0.343203i
$105$	−12.0000	−	10.3923i	−1.17108	−	1.01419i
$106$	−4.50000	+	7.79423i	−0.437079	+	0.757042i
$107$	15.5885	+	9.00000i	1.50699	+	0.870063i	0.999967	+	0.00813215i	$0.00258857\pi$
$107$	15.5885	+	9.00000i	1.50699	+	0.870063i	0.507026	+	0.861931i	$0.330745\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$		0			0
$111$	3.46410	+	6.00000i	0.328798	+	0.569495i
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	−0.235269	−	0.971930i	$-0.575597\pi$
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	0.724082	+	0.689714i	$0.242264\pi$
$114$		0			0
$115$	9.00000	+	5.19615i	0.839254	+	0.484544i
$116$			6.00000i			0.557086i
$117$	3.00000	+	10.3923i	0.277350	+	0.960769i
$118$			1.73205i			0.159448i
$119$	4.33013	−	1.50000i	0.396942	−	0.137505i
$120$	−5.19615	−	3.00000i	−0.474342	−	0.273861i
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	12.1244			1.09769
$123$	6.00000	+	10.3923i	0.541002	+	0.937043i
$124$	1.50000	−	0.866025i	0.134704	−	0.0777714i
$125$	6.92820			0.619677
$126$	7.79423	+	1.50000i	0.694365	+	0.133631i
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.0443678	+	0.999015i	$0.514127\pi$
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.73205			−0.152499
$130$	9.00000	+	8.66025i	0.789352	+	0.759555i
$131$	−15.5885			−1.36197			−0.680985	−	0.732297i	$-0.738448\pi$
$131$	−15.5885			−1.36197			−0.680985	+	0.732297i	$0.738448\pi$
$132$		0			0
$133$		0			0
$134$	−6.06218	+	3.50000i	−0.523692	+	0.302354i
$135$	−18.0000			−1.54919
$136$	1.50000	−	0.866025i	0.128624	−	0.0742611i
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$	−5.19615			−0.442326
$139$	−6.00000	+	3.46410i	−0.508913	+	0.293821i	−0.732387	−	0.680889i	$-0.761594\pi$
$139$	−6.00000	+	3.46410i	−0.508913	+	0.293821i	0.223474	+	0.974710i	$0.428260\pi$
$140$	8.66025	−	3.00000i	0.731925	−	0.253546i
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	−15.0000			−1.25877
$143$		0			0
$144$	3.00000			0.250000
$145$	18.0000	+	10.3923i	1.49482	+	0.863034i
$146$	6.92820	−	12.0000i	0.573382	−	0.993127i
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	−4.00000			−0.328798
$149$	−18.1865	+	10.5000i	−1.48990	+	0.860194i	−0.999933	−	0.0115483i	$-0.996324\pi$
$149$	−18.1865	+	10.5000i	−1.48990	+	0.860194i	−0.489966	+	0.871742i	$0.662991\pi$
$150$	−10.5000	+	6.06218i	−0.857321	+	0.494975i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	2.59808	−	4.50000i	0.210042	−	0.363803i
$154$		0			0
$155$		−	6.00000i		−	0.481932i
$156$	−6.06218	−	1.50000i	−0.485363	−	0.120096i
$157$			13.8564i			1.10586i	0.833227	+	0.552931i	$0.186491\pi$
$157$			13.8564i			1.10586i	−0.833227	+	0.552931i	$0.813509\pi$
$158$	8.66025	+	5.00000i	0.688973	+	0.397779i
$159$	−13.5000	−	7.79423i	−1.07062	−	0.618123i
$160$	3.00000	−	1.73205i	0.237171	−	0.136931i
$161$	5.19615	−	6.00000i	0.409514	−	0.472866i
$162$	7.79423	−	4.50000i	0.612372	−	0.353553i
$163$	3.50000	+	6.06218i	0.274141	+	0.474826i	0.969918	−	0.243432i	$-0.0782731\pi$
$163$	3.50000	+	6.06218i	0.274141	+	0.474826i	−0.695777	+	0.718258i	$0.744940\pi$
$164$	−6.92820			−0.541002
$165$		0			0
$166$	−10.5000	−	6.06218i	−0.814958	−	0.470516i
$167$	3.46410	−	6.00000i	0.268060	−	0.464294i	−0.700301	−	0.713848i	$-0.746951\pi$
$167$	3.46410	−	6.00000i	0.268060	−	0.464294i	0.968361	+	0.249554i	$0.0802840\pi$
$168$	−3.00000	+	3.46410i	−0.231455	+	0.267261i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		−	6.00000i		−	0.460179i
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−10.3923			−0.787839
$175$	3.50000	−	18.1865i	0.264575	−	1.37477i
$176$		0			0
$177$	−3.00000			−0.225494
$178$	13.5000	−	7.79423i	1.01187	−	0.584202i
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	5.19615	−	9.00000i	0.387298	−	0.670820i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	7.79423	−	5.50000i	0.577747	−	0.407687i
$183$			21.0000i			1.55236i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−6.92820	+	12.0000i	−0.509372	+	0.882258i
$186$	1.50000	+	2.59808i	0.109985	+	0.190500i
$187$		0			0
$188$	1.73205	+	3.00000i	0.126323	+	0.218797i
$189$	−2.59808	+	13.5000i	−0.188982	+	0.981981i
$190$		0			0
$191$	−12.9904	+	7.50000i	−0.939951	+	0.542681i	−0.889945	−	0.456068i	$-0.849257\pi$
$191$	−12.9904	+	7.50000i	−0.939951	+	0.542681i	−0.0500060	+	0.998749i	$0.515924\pi$
$192$	−0.866025	+	1.50000i	−0.0625000	+	0.108253i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−17.3205			−1.24354
$195$	−15.0000	+	15.5885i	−1.07417	+	1.11631i
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	12.9904	+	7.50000i	0.925526	+	0.534353i	0.885394	−	0.464841i	$-0.153889\pi$
$197$	12.9904	+	7.50000i	0.925526	+	0.534353i	0.0401324	+	0.999194i	$0.487222\pi$
$198$		0			0
$199$	1.50000	−	0.866025i	0.106332	−	0.0613909i	−0.445891	−	0.895087i	$-0.647113\pi$
$199$	1.50000	−	0.866025i	0.106332	−	0.0613909i	0.552223	+	0.833696i	$0.313780\pi$
$200$		−	7.00000i		−	0.494975i
$201$	−6.06218	−	10.5000i	−0.427593	−	0.740613i
$202$		0			0
$203$	10.3923	−	12.0000i	0.729397	−	0.842235i
$204$	1.50000	+	2.59808i	0.105021	+	0.181902i
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	−4.33013	+	7.50000i	−0.301694	+	0.522550i
$207$		−	9.00000i		−	0.625543i
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$		0			0
$210$	5.19615	+	15.0000i	0.358569	+	1.03510i
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$	7.79423	−	4.50000i	0.535310	−	0.309061i
$213$		−	25.9808i		−	1.78017i
$214$	−9.00000	−	15.5885i	−0.615227	−	1.06561i
$215$	−1.73205	−	3.00000i	−0.118125	−	0.204598i
$216$			5.19615i			0.353553i
$217$	−4.50000	−	0.866025i	−0.305480	−	0.0587896i
$218$	−13.8564	−	8.00000i	−0.938474	−	0.541828i
$219$	20.7846	+	12.0000i	1.40449	+	0.810885i
$220$		0			0
$221$	−1.73205	−	6.00000i	−0.116510	−	0.403604i
$222$		−	6.92820i		−	0.464991i
$223$	−4.50000	−	2.59808i	−0.301342	−	0.173980i	0.341703	−	0.939808i	$-0.388996\pi$
$223$	−4.50000	−	2.59808i	−0.301342	−	0.173980i	−0.643046	+	0.765828i	$0.722329\pi$
$224$	−0.866025	−	2.50000i	−0.0578638	−	0.167038i
$225$	−10.5000	−	18.1865i	−0.700000	−	1.21244i
$226$	−6.00000			−0.399114
$227$	5.19615	+	9.00000i	0.344881	+	0.597351i	0.985332	−	0.170648i	$-0.0545860\pi$
$227$	5.19615	+	9.00000i	0.344881	+	0.597351i	−0.640451	+	0.767999i	$0.721253\pi$
$228$		0			0
$229$			15.5885i			1.03011i	0.857156	+	0.515057i	$0.172229\pi$
$229$			15.5885i			1.03011i	−0.857156	+	0.515057i	$0.827771\pi$
$230$	−5.19615	−	9.00000i	−0.342624	−	0.593442i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	2.59808	−	10.5000i	0.169842	−	0.686406i
$235$	12.0000			0.782794
$236$	0.866025	−	1.50000i	0.0563735	−	0.0976417i
$237$	−8.66025	+	15.0000i	−0.562544	+	0.974355i
$238$	−4.50000	−	0.866025i	−0.291692	−	0.0561361i
$239$			21.0000i			1.35838i	0.733964	+	0.679189i	$0.237668\pi$
$239$			21.0000i			1.35838i	−0.733964	+	0.679189i	$0.762332\pi$
$240$	3.00000	+	5.19615i	0.193649	+	0.335410i
$241$	−9.00000	+	5.19615i	−0.579741	+	0.334714i	−0.761030	−	0.648716i	$-0.775306\pi$
$241$	−9.00000	+	5.19615i	−0.579741	+	0.334714i	0.181289	+	0.983430i	$0.441973\pi$
$242$			11.0000i			0.707107i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$	−10.5000	−	6.06218i	−0.672194	−	0.388091i
$245$	−22.5167	−	9.00000i	−1.43854	−	0.574989i
$246$		−	12.0000i		−	0.765092i
$247$		0			0
$248$	−1.73205			−0.109985
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	−9.52628	−	16.5000i	−0.601293	−	1.04147i	−0.992626	−	0.121221i	$-0.961319\pi$
$251$	−9.52628	−	16.5000i	−0.601293	−	1.04147i	0.391332	−	0.920250i	$-0.372014\pi$
$252$	−6.00000	−	5.19615i	−0.377964	−	0.327327i
$253$		0			0
$254$	17.3205	−	10.0000i	1.08679	−	0.627456i
$255$	10.3923			0.650791
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.79423	+	13.5000i	−0.486191	+	0.842107i	−0.999874	−	0.0158730i	$-0.994947\pi$
$257$	−7.79423	+	13.5000i	−0.486191	+	0.842107i	0.513683	+	0.857980i	$0.328281\pi$
$258$	1.50000	+	0.866025i	0.0933859	+	0.0539164i
$259$	8.00000	+	6.92820i	0.497096	+	0.430498i
$260$	−3.46410	−	12.0000i	−0.214834	−	0.744208i
$261$		−	18.0000i		−	1.11417i
$262$	13.5000	+	7.79423i	0.834033	+	0.481529i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		−	31.1769i		−	1.91518i
$266$		0			0
$267$	13.5000	+	23.3827i	0.826187	+	1.43100i
$268$	7.00000			0.427593
$269$	6.92820	+	12.0000i	0.422420	+	0.731653i	0.996176	−	0.0873736i	$-0.0278474\pi$
$269$	6.92820	+	12.0000i	0.422420	+	0.731653i	−0.573756	+	0.819027i	$0.694514\pi$
$270$	15.5885	+	9.00000i	0.948683	+	0.547723i
$271$	−7.50000	−	4.33013i	−0.455593	−	0.263036i	0.254597	−	0.967047i	$-0.418057\pi$
$271$	−7.50000	−	4.33013i	−0.455593	−	0.263036i	−0.710189	+	0.704011i	$0.751391\pi$
$272$	−1.73205			−0.105021
$273$	9.52628	+	13.5000i	0.576557	+	0.817057i
$274$	12.0000			0.724947
$275$		0			0
$276$	4.50000	+	2.59808i	0.270868	+	0.156386i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	6.92820			0.415526
$279$	−4.50000	+	2.59808i	−0.269408	+	0.155543i
$280$	−9.00000	−	1.73205i	−0.537853	−	0.103510i
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$	−5.19615	+	3.00000i	−0.309426	+	0.178647i
$283$	−21.0000	−	12.1244i	−1.24832	−	0.720718i	−0.277546	−	0.960712i	$-0.589521\pi$
$283$	−21.0000	−	12.1244i	−1.24832	−	0.720718i	−0.970774	+	0.239994i	$0.922854\pi$
$284$	12.9904	+	7.50000i	0.770837	+	0.445043i
$285$		0			0
$286$		0			0
$287$	13.8564	+	12.0000i	0.817918	+	0.708338i
$288$	−2.59808	−	1.50000i	−0.153093	−	0.0883883i
$289$	7.00000	−	12.1244i	0.411765	−	0.713197i
$290$	−10.3923	−	18.0000i	−0.610257	−	1.05700i
$291$		−	30.0000i		−	1.75863i
$292$	−12.0000	+	6.92820i	−0.702247	+	0.405442i
$293$	−8.66025	−	15.0000i	−0.505937	−	0.876309i	−0.999976	−	0.00686959i	$-0.997813\pi$
$293$	−8.66025	−	15.0000i	−0.505937	−	0.876309i	0.494039	−	0.869440i	$-0.335520\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$	−3.00000	−	5.19615i	−0.174667	−	0.302532i
$296$	3.46410	+	2.00000i	0.201347	+	0.116248i
$297$		0			0
$298$	21.0000			1.21650
$299$	−7.79423	−	7.50000i	−0.450752	−	0.433736i
$300$	12.1244			0.700000
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$	−13.8564	−	8.00000i	−0.797347	−	0.460348i
$303$		0			0
$304$		0			0
$305$	−36.3731	+	21.0000i	−2.08272	+	1.20246i
$306$	−4.50000	+	2.59808i	−0.257248	+	0.148522i
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$	−12.9904	−	7.50000i	−0.738997	−	0.426660i
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	13.8564			0.785725			0.392862	−	0.919597i	$-0.371485\pi$
$311$	13.8564			0.785725			0.392862	+	0.919597i	$0.371485\pi$
$312$	4.50000	+	4.33013i	0.254762	+	0.245145i
$313$		−	3.46410i		−	0.195803i	−0.995196	−	0.0979013i	$-0.968787\pi$
$313$		−	3.46410i		−	0.195803i	0.995196	−	0.0979013i	$-0.0312129\pi$
$314$	6.92820	−	12.0000i	0.390981	−	0.677199i
$315$	−25.9808	+	9.00000i	−1.46385	+	0.507093i
$316$	−5.00000	−	8.66025i	−0.281272	−	0.487177i
$317$		−	3.00000i		−	0.168497i	−0.996445	−	0.0842484i	$-0.973151\pi$
$317$		−	3.00000i		−	0.168497i	0.996445	−	0.0842484i	$-0.0268489\pi$
$318$	7.79423	+	13.5000i	0.437079	+	0.757042i
$319$		0			0
$320$	−3.46410			−0.193649
$321$	27.0000	−	15.5885i	1.50699	−	0.870063i
$322$	−7.50000	+	2.59808i	−0.417959	+	0.144785i
$323$		0			0
$324$	−9.00000			−0.500000
$325$	−24.5000	−	6.06218i	−1.35902	−	0.336269i
$326$		−	7.00000i		−	0.387694i
$327$	13.8564	−	24.0000i	0.766261	−	1.32720i
$328$	6.00000	+	3.46410i	0.331295	+	0.191273i
$329$	1.73205	−	9.00000i	0.0954911	−	0.496186i
$330$		0			0
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$	6.06218	+	10.5000i	0.332705	+	0.576262i
$333$	12.0000			0.657596
$334$	−6.00000	+	3.46410i	−0.328305	+	0.189547i
$335$	12.1244	−	21.0000i	0.662424	−	1.14735i
$336$	4.33013	−	1.50000i	0.236228	−	0.0818317i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−6.92820	−	11.0000i	−0.376845	−	0.598321i
$339$		−	10.3923i		−	0.564433i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$		0			0
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−0.866025	+	0.500000i	−0.0466930	+	0.0269582i
$345$	15.5885	−	9.00000i	0.839254	−	0.484544i
$346$		0			0
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$	9.00000	+	5.19615i	0.482451	+	0.278543i
$349$	−25.5000	−	14.7224i	−1.36498	−	0.788074i	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−25.5000	−	14.7224i	−1.36498	−	0.788074i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	−12.1244	+	14.0000i	−0.648074	+	0.748331i
$351$	18.1865	+	4.50000i	0.970725	+	0.240192i
$352$		0			0
$353$	6.06218	−	10.5000i	0.322657	−	0.558859i	−0.658378	−	0.752687i	$-0.728757\pi$
$353$	6.06218	−	10.5000i	0.322657	−	0.558859i	0.981035	+	0.193829i	$0.0620906\pi$
$354$	2.59808	+	1.50000i	0.138086	+	0.0797241i
$355$	45.0000	−	25.9808i	2.38835	−	1.37892i
$356$	−15.5885			−0.826187
$357$	1.50000	−	7.79423i	0.0793884	−	0.412514i
$358$		0			0
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$	−9.00000	+	5.19615i	−0.474342	+	0.273861i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$		0			0
$363$	−19.0526			−1.00000
$364$	−9.50000	+	0.866025i	−0.497935	+	0.0453921i
$365$			48.0000i			2.51243i
$366$	10.5000	−	18.1865i	0.548844	−	0.950625i
$367$	−10.5000	−	6.06218i	−0.548096	−	0.316443i	0.200258	−	0.979743i	$-0.435822\pi$
$367$	−10.5000	−	6.06218i	−0.548096	−	0.316443i	−0.748354	+	0.663300i	$0.769155\pi$
$368$	−2.59808	+	1.50000i	−0.135434	+	0.0781929i
$369$	20.7846			1.08200
$370$	12.0000	−	6.92820i	0.623850	−	0.360180i
$371$	−23.3827	−	4.50000i	−1.21397	−	0.233628i
$372$		−	3.00000i		−	0.155543i
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$		−	3.46410i		−	0.178647i
$377$	−15.5885	−	15.0000i	−0.802846	−	0.772539i
$378$	9.00000	−	10.3923i	0.462910	−	0.534522i
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$		0			0
$381$	17.3205	+	30.0000i	0.887357	+	1.53695i
$382$	15.0000			0.767467
$383$	12.1244	+	21.0000i	0.619526	+	1.07305i	0.989572	+	0.144037i	$0.0460083\pi$
$383$	12.1244	+	21.0000i	0.619526	+	1.07305i	−0.370047	+	0.929013i	$0.620658\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$	−12.1244	+	7.00000i	−0.617113	+	0.356291i
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	15.0000	+	8.66025i	0.761510	+	0.439658i
$389$			9.00000i			0.456318i	0.973624	+	0.228159i	$0.0732706\pi$
$389$			9.00000i			0.456318i	−0.973624	+	0.228159i	$0.926729\pi$
$390$	20.7846	−	6.00000i	1.05247	−	0.303822i
$391$			5.19615i			0.262781i
$392$	−2.59808	+	6.50000i	−0.131223	+	0.328300i
$393$	−13.5000	+	23.3827i	−0.680985	+	1.17950i
$394$	−7.50000	−	12.9904i	−0.377845	−	0.654446i
$395$	−34.6410			−1.74298
$396$		0			0
$397$	−10.5000	+	6.06218i	−0.526980	+	0.304252i	−0.739786	−	0.672843i	$-0.765073\pi$
$397$	−10.5000	+	6.06218i	−0.526980	+	0.304252i	0.212806	+	0.977095i	$0.431740\pi$
$398$	−1.73205			−0.0868199
$399$		0			0
$400$	−3.50000	+	6.06218i	−0.175000	+	0.303109i
$401$	15.5885	+	9.00000i	0.778450	+	0.449439i	0.835881	−	0.548911i	$-0.184957\pi$
$401$	15.5885	+	9.00000i	0.778450	+	0.449439i	−0.0574304	+	0.998350i	$0.518291\pi$
$402$			12.1244i			0.604708i
$403$	−1.50000	+	6.06218i	−0.0747203	+	0.301979i
$404$		0			0
$405$	−15.5885	+	27.0000i	−0.774597	+	1.34164i
$406$	−15.0000	+	5.19615i	−0.744438	+	0.257881i
$407$		0			0
$408$		−	3.00000i		−	0.148522i
$409$	−12.0000	+	6.92820i	−0.593362	+	0.342578i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	−12.0000	+	6.92820i	−0.593362	+	0.342578i	0.173064	+	0.984911i	$0.444633\pi$
$410$	20.7846	−	12.0000i	1.02648	−	0.592638i
$411$			20.7846i			1.02523i
$412$	7.50000	−	4.33013i	0.369498	−	0.213330i
$413$	−4.33013	+	1.50000i	−0.213072	+	0.0738102i
$414$	−4.50000	+	7.79423i	−0.221163	+	0.383065i
$415$	42.0000			2.06170
$416$	−3.46410	+	1.00000i	−0.169842	+	0.0490290i
$417$			12.0000i			0.587643i
$418$		0			0
$419$	−9.52628	+	16.5000i	−0.465389	+	0.806078i	−0.999219	−	0.0395142i	$-0.987419\pi$
$419$	−9.52628	+	16.5000i	−0.465389	+	0.806078i	0.533830	+	0.845592i	$0.320752\pi$
$420$	3.00000	−	15.5885i	0.146385	−	0.760639i
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	−17.3205	+	10.0000i	−0.843149	+	0.486792i
$423$	−5.19615	−	9.00000i	−0.252646	−	0.437595i
$424$	−9.00000			−0.437079
$425$	6.06218	+	10.5000i	0.294059	+	0.509325i
$426$	−12.9904	+	22.5000i	−0.629386	+	1.09013i
$427$	10.5000	+	30.3109i	0.508131	+	1.46685i
$428$			18.0000i			0.870063i
$429$		0			0
$430$			3.46410i			0.167054i
$431$	−2.59808	−	1.50000i	−0.125145	−	0.0722525i	0.436121	−	0.899888i	$-0.356352\pi$
$431$	−2.59808	−	1.50000i	−0.125145	−	0.0722525i	−0.561266	+	0.827636i	$0.689685\pi$
$432$	2.59808	−	4.50000i	0.125000	−	0.216506i
$433$	6.00000	−	3.46410i	0.288342	−	0.166474i	−0.348852	−	0.937178i	$-0.613428\pi$
$433$	6.00000	−	3.46410i	0.288342	−	0.166474i	0.637194	+	0.770704i	$0.280095\pi$
$434$	3.46410	+	3.00000i	0.166282	+	0.144005i
$435$	31.1769	−	18.0000i	1.49482	−	0.863034i
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$		0			0
$438$	−12.0000	−	20.7846i	−0.573382	−	0.993127i
$439$	−3.00000	−	1.73205i	−0.143182	−	0.0826663i	0.426698	−	0.904394i	$-0.359677\pi$
$439$	−3.00000	−	1.73205i	−0.143182	−	0.0826663i	−0.569880	+	0.821728i	$0.693010\pi$
$440$		0			0
$441$	3.00000	+	20.7846i	0.142857	+	0.989743i
$442$	−1.50000	+	6.06218i	−0.0713477	+	0.288348i
$443$		−	18.0000i		−	0.855206i	−0.903967	−	0.427603i	$-0.859358\pi$
$443$		−	18.0000i		−	0.855206i	0.903967	−	0.427603i	$-0.140642\pi$
$444$	−3.46410	+	6.00000i	−0.164399	+	0.284747i
$445$	−27.0000	+	46.7654i	−1.27992	+	2.21689i
$446$	2.59808	+	4.50000i	0.123022	+	0.213081i
$447$			36.3731i			1.72039i
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−5.19615	+	3.00000i	−0.245222	+	0.141579i	−0.617574	−	0.786513i	$-0.711885\pi$
$449$	−5.19615	+	3.00000i	−0.245222	+	0.141579i	0.372353	+	0.928091i	$0.378551\pi$
$450$			21.0000i			0.989949i
$451$		0			0
$452$	5.19615	+	3.00000i	0.244406	+	0.141108i
$453$	13.8564	−	24.0000i	0.651031	−	1.12762i
$454$		−	10.3923i		−	0.487735i
$455$	−13.8564	+	30.0000i	−0.649598	+	1.40642i
$456$		0			0
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	7.79423	−	13.5000i	0.364200	−	0.630814i
$459$	−4.50000	−	7.79423i	−0.210042	−	0.363803i
$460$			10.3923i			0.484544i
$461$	−3.46410	−	6.00000i	−0.161339	−	0.279448i	0.774010	−	0.633173i	$-0.218248\pi$
$461$	−3.46410	−	6.00000i	−0.161339	−	0.279448i	−0.935349	+	0.353726i	$0.884915\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	−5.19615	+	3.00000i	−0.241225	+	0.139272i
$465$	−9.00000	−	5.19615i	−0.417365	−	0.240966i
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	15.5885			0.721348			0.360674	−	0.932692i	$-0.382547\pi$
$467$	15.5885			0.721348			0.360674	+	0.932692i	$0.382547\pi$
$468$	−7.50000	+	7.79423i	−0.346688	+	0.360288i
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$	−10.3923	−	6.00000i	−0.479361	−	0.276759i
$471$	20.7846	+	12.0000i	0.957704	+	0.552931i
$472$	−1.50000	+	0.866025i	−0.0690431	+	0.0398621i
$473$		0			0
$474$	15.0000	−	8.66025i	0.688973	−	0.397779i
$475$		0			0
$476$	3.46410	+	3.00000i	0.158777	+	0.137505i
$477$	−23.3827	+	13.5000i	−1.07062	+	0.618123i
$478$	10.5000	−	18.1865i	0.480259	−	0.831833i
$479$	12.1244	−	21.0000i	0.553976	−	0.959514i	−0.444006	−	0.896024i	$-0.646443\pi$
$479$	12.1244	−	21.0000i	0.553976	−	0.959514i	0.997982	−	0.0634909i	$-0.0202234\pi$
$480$		−	6.00000i		−	0.273861i
$481$	10.0000	−	10.3923i	0.455961	−	0.473848i
$482$	10.3923			0.473357
$483$	−4.50000	−	12.9904i	−0.204757	−	0.591083i
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	51.9615	−	30.0000i	2.35945	−	1.36223i
$486$		−	15.5885i		−	0.707107i
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$	6.06218	+	10.5000i	0.274422	+	0.475313i
$489$	12.1244			0.548282
$490$	15.0000	+	19.0526i	0.677631	+	0.860707i
$491$	−31.1769	−	18.0000i	−1.40699	−	0.812329i	−0.411897	−	0.911230i	$-0.635134\pi$
$491$	−31.1769	−	18.0000i	−1.40699	−	0.812329i	−0.995097	+	0.0989017i	$0.968467\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$			10.3923i			0.468046i
$494$		0			0
$495$		0			0
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	−12.9904	−	37.5000i	−0.582698	−	1.68210i
$498$	−18.1865	+	10.5000i	−0.814958	+	0.470516i
$499$	−17.0000			−0.761025			−0.380512	−	0.924776i	$-0.624252\pi$
$499$	−17.0000			−0.761025			−0.380512	+	0.924776i	$0.624252\pi$
$500$	3.46410	+	6.00000i	0.154919	+	0.268328i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$			19.0526i			0.850357i
$503$	−3.46410	−	6.00000i	−0.154457	−	0.267527i	0.778404	−	0.627763i	$-0.216029\pi$
$503$	−3.46410	−	6.00000i	−0.154457	−	0.267527i	−0.932861	+	0.360236i	$0.882696\pi$
$504$	2.59808	+	7.50000i	0.115728	+	0.334077i
$505$		0			0
$506$		0			0
$507$	19.0526	−	12.0000i	0.846154	−	0.532939i
$508$	−20.0000			−0.887357
$509$	1.73205	−	3.00000i	0.0767718	−	0.132973i	−0.825084	−	0.565011i	$-0.808872\pi$
$509$	1.73205	−	3.00000i	0.0767718	−	0.132973i	0.901855	+	0.432038i	$0.142205\pi$
$510$	−9.00000	−	5.19615i	−0.398527	−	0.230089i
$511$	36.0000	+	6.92820i	1.59255	+	0.306486i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	13.5000	−	7.79423i	0.595459	−	0.343789i
$515$		−	30.0000i		−	1.32196i
$516$	−0.866025	−	1.50000i	−0.0381246	−	0.0660338i
$517$		0			0
$518$	−3.46410	−	10.0000i	−0.152204	−	0.439375i
$519$		0			0
$520$	−3.00000	+	12.1244i	−0.131559	+	0.531688i
$521$	−13.8564			−0.607060			−0.303530	−	0.952822i	$-0.598165\pi$
$521$	−13.8564			−0.607060			−0.303530	+	0.952822i	$0.598165\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	−18.0000	−	10.3923i	−0.787085	−	0.454424i	0.0518503	−	0.998655i	$-0.483488\pi$
$523$	−18.0000	−	10.3923i	−0.787085	−	0.454424i	−0.838935	+	0.544231i	$0.816821\pi$
$524$	−7.79423	−	13.5000i	−0.340492	−	0.589750i
$525$	−24.2487	−	21.0000i	−1.05830	−	0.916515i
$526$		0			0
$527$	2.59808	−	1.50000i	0.113174	−	0.0653410i
$528$		0			0
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$	−15.5885	+	27.0000i	−0.677119	+	1.17281i
$531$	−2.59808	+	4.50000i	−0.112747	+	0.195283i
$532$		0			0
$533$	17.3205	−	18.0000i	0.750234	−	0.779667i
$534$		−	27.0000i		−	1.16840i
$535$	54.0000	+	31.1769i	2.33462	+	1.34790i
$536$	−6.06218	−	3.50000i	−0.261846	−	0.151177i
$537$		0			0
$538$		−	13.8564i		−	0.597392i
$539$		0			0
$540$	−9.00000	−	15.5885i	−0.387298	−	0.670820i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	4.33013	+	7.50000i	0.185995	+	0.322153i
$543$		0			0
$544$	1.50000	+	0.866025i	0.0643120	+	0.0371305i
$545$	55.4256			2.37417
$546$	−1.50000	−	16.4545i	−0.0641941	−	0.704187i
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−10.3923	−	6.00000i	−0.443937	−	0.256307i
$549$	31.5000	+	18.1865i	1.34439	+	0.776182i
$550$		0			0
$551$		0			0
$552$	−2.59808	−	4.50000i	−0.110581	−	0.191533i
$553$	−5.00000	+	25.9808i	−0.212622	+	1.10481i
$554$			2.00000i			0.0849719i
$555$	12.0000	+	20.7846i	0.509372	+	0.882258i
$556$	−6.00000	−	3.46410i	−0.254457	−	0.146911i
$557$	−18.1865	−	10.5000i	−0.770588	−	0.444899i	0.0624962	−	0.998045i	$-0.480094\pi$
$557$	−18.1865	−	10.5000i	−0.770588	−	0.444899i	−0.833084	+	0.553146i	$0.813427\pi$
$558$	5.19615			0.219971
$559$	1.00000	+	3.46410i	0.0422955	+	0.146516i
$560$	6.92820	+	6.00000i	0.292770	+	0.253546i
$561$		0			0
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	−5.19615	−	9.00000i	−0.218992	−	0.379305i	0.735508	−	0.677516i	$-0.236943\pi$
$563$	−5.19615	−	9.00000i	−0.218992	−	0.379305i	−0.954500	+	0.298211i	$0.903610\pi$
$564$	6.00000			0.252646
$565$	18.0000	−	10.3923i	0.757266	−	0.437208i
$566$	12.1244	+	21.0000i	0.509625	+	0.882696i
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$	−7.50000	−	12.9904i	−0.314693	−	0.545064i
$569$	−15.5885	−	9.00000i	−0.653502	−	0.377300i	0.136295	−	0.990668i	$-0.456481\pi$
$569$	−15.5885	−	9.00000i	−0.653502	−	0.377300i	−0.789797	+	0.613369i	$0.789814\pi$
$570$		0			0
$571$	−37.0000			−1.54840			−0.774201	−	0.632940i	$-0.781848\pi$
$571$	−37.0000			−1.54840			−0.774201	+	0.632940i	$0.781848\pi$
$572$		0			0
$573$			25.9808i			1.08536i
$574$	−6.00000	−	17.3205i	−0.250435	−	0.722944i
$575$	18.1865	+	10.5000i	0.758431	+	0.437880i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$		−	10.3923i		−	0.432637i	−0.976323	−	0.216319i	$-0.930595\pi$
$577$		−	10.3923i		−	0.432637i	0.976323	−	0.216319i	$-0.0694050\pi$
$578$	−12.1244	+	7.00000i	−0.504307	+	0.291162i
$579$	−12.1244	−	21.0000i	−0.503871	−	0.872730i
$580$			20.7846i			0.863034i
$581$	6.06218	−	31.5000i	0.251502	−	1.30684i
$582$	−15.0000	+	25.9808i	−0.621770	+	1.07694i
$583$		0			0
$584$	13.8564			0.573382
$585$	10.3923	+	36.0000i	0.429669	+	1.48842i
$586$			17.3205i			0.715504i
$587$	−2.59808	+	4.50000i	−0.107234	+	0.185735i	−0.914649	−	0.404249i	$-0.867533\pi$
$587$	−2.59808	+	4.50000i	−0.107234	+	0.185735i	0.807415	+	0.589984i	$0.200866\pi$
$588$	−11.2583	−	4.50000i	−0.464286	−	0.185577i
$589$		0			0
$590$			6.00000i			0.247016i
$591$	22.5000	−	12.9904i	0.925526	−	0.534353i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	−39.8372			−1.63592			−0.817958	−	0.575278i	$-0.804894\pi$
$593$	−39.8372			−1.63592			−0.817958	+	0.575278i	$0.804894\pi$
$594$		0			0
$595$	15.0000	−	5.19615i	0.614940	−	0.213021i
$596$	−18.1865	−	10.5000i	−0.744949	−	0.430097i
$597$		−	3.00000i		−	0.122782i
$598$	3.00000	+	10.3923i	0.122679	+	0.424973i
$599$		−	33.0000i		−	1.34834i	−0.738575	−	0.674172i	$-0.764501\pi$
$599$		−	33.0000i		−	1.34834i	0.738575	−	0.674172i	$-0.235499\pi$
$600$	−10.5000	−	6.06218i	−0.428661	−	0.247487i
$601$	27.0000	+	15.5885i	1.10135	+	0.635866i	0.936576	−	0.350464i	$-0.113976\pi$
$601$	27.0000	+	15.5885i	1.10135	+	0.635866i	0.164777	+	0.986331i	$0.447310\pi$
$602$	2.59808	+	0.500000i	0.105890	+	0.0203785i
$603$	−21.0000			−0.855186
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	−19.0526	−	33.0000i	−0.774597	−	1.34164i
$606$		0			0
$607$	4.50000	−	2.59808i	0.182649	−	0.105453i	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	4.50000	−	2.59808i	0.182649	−	0.105453i	0.588537	+	0.808470i	$0.299704\pi$
$608$		0			0
$609$	−9.00000	−	25.9808i	−0.364698	−	1.05279i
$610$	42.0000			1.70053
$611$	−12.1244	−	3.00000i	−0.490499	−	0.121367i
$612$	5.19615			0.210042
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	12.1244	−	21.0000i	0.489299	−	0.847491i
$615$	20.7846	+	36.0000i	0.838116	+	1.45166i
$616$		0			0
$617$	41.5692	−	24.0000i	1.67351	−	0.966204i	0.707867	−	0.706346i	$-0.249658\pi$
$617$	41.5692	−	24.0000i	1.67351	−	0.966204i	0.965647	−	0.259858i	$-0.0836757\pi$
$618$	7.50000	+	12.9904i	0.301694	+	0.522550i
$619$		−	38.1051i		−	1.53157i	−0.643094	−	0.765787i	$-0.722350\pi$
$619$		−	38.1051i		−	1.53157i	0.643094	−	0.765787i	$-0.277650\pi$
$620$	5.19615	−	3.00000i	0.208683	−	0.120483i
$621$	−13.5000	−	7.79423i	−0.541736	−	0.312772i
$622$	−12.0000	−	6.92820i	−0.481156	−	0.277796i
$623$	31.1769	+	27.0000i	1.24908	+	1.08173i
$624$	−1.73205	−	6.00000i	−0.0693375	−	0.240192i
$625$	−11.0000			−0.440000
$626$	−1.73205	+	3.00000i	−0.0692267	+	0.119904i
$627$		0			0
$628$	−12.0000	+	6.92820i	−0.478852	+	0.276465i
$629$	−6.92820			−0.276246
$630$	27.0000	+	5.19615i	1.07571	+	0.207020i
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$			10.0000i			0.397779i
$633$	−17.3205	−	30.0000i	−0.688428	−	1.19239i
$634$	−1.50000	+	2.59808i	−0.0595726	+	0.103183i
$635$	−34.6410	+	60.0000i	−1.37469	+	2.38103i
$636$		−	15.5885i		−	0.618123i
$637$	20.5000	+	14.7224i	0.812240	+	0.583324i
$638$		0			0
$639$	−38.9711	−	22.5000i	−1.54167	−	0.890086i
$640$	3.00000	+	1.73205i	0.118585	+	0.0684653i
$641$	10.3923	−	6.00000i	0.410471	−	0.236986i	−0.280521	−	0.959848i	$-0.590507\pi$
$641$	10.3923	−	6.00000i	0.410471	−	0.236986i	0.690992	+	0.722862i	$0.257174\pi$
$642$	−31.1769			−1.23045
$643$	−6.00000	+	3.46410i	−0.236617	+	0.136611i	−0.613621	−	0.789601i	$-0.710288\pi$
$643$	−6.00000	+	3.46410i	−0.236617	+	0.136611i	0.377004	+	0.926212i	$0.376954\pi$
$644$	7.79423	+	1.50000i	0.307136	+	0.0591083i
$645$	−6.00000			−0.236250
$646$		0			0
$647$	−10.3923	+	18.0000i	−0.408564	+	0.707653i	−0.994729	−	0.102538i	$-0.967304\pi$
$647$	−10.3923	+	18.0000i	−0.408564	+	0.707653i	0.586165	+	0.810191i	$0.300637\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$		0			0
$650$	18.1865	+	17.5000i	0.713335	+	0.686406i
$651$	−5.19615	+	6.00000i	−0.203653	+	0.235159i
$652$	−3.50000	+	6.06218i	−0.137071	+	0.237413i
$653$	33.7750	+	19.5000i	1.32172	+	0.763094i	0.984003	−	0.178154i	$-0.0570127\pi$
$653$	33.7750	+	19.5000i	1.32172	+	0.763094i	0.337715	+	0.941248i	$0.390346\pi$
$654$	−24.0000	+	13.8564i	−0.938474	+	0.541828i
$655$	−54.0000			−2.10995
$656$	−3.46410	−	6.00000i	−0.135250	−	0.234261i
$657$	36.0000	−	20.7846i	1.40449	−	0.810885i
$658$	−6.00000	+	6.92820i	−0.233904	+	0.270089i
$659$	−5.19615	+	3.00000i	−0.202413	+	0.116863i	−0.597781	−	0.801660i	$-0.703951\pi$
$659$	−5.19615	+	3.00000i	−0.202413	+	0.116863i	0.395367	+	0.918523i	$0.370617\pi$
$660$		0			0
$661$	10.5000	+	6.06218i	0.408403	+	0.235791i	0.690103	−	0.723711i	$-0.257565\pi$
$661$	10.5000	+	6.06218i	0.408403	+	0.235791i	−0.281701	+	0.959502i	$0.590898\pi$
$662$			28.0000i			1.08825i
$663$	−10.5000	−	2.59808i	−0.407786	−	0.100901i
$664$		−	12.1244i		−	0.470516i
$665$		0			0
$666$	−10.3923	−	6.00000i	−0.402694	−	0.232495i
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	6.92820			0.268060
$669$	−7.79423	+	4.50000i	−0.301342	+	0.173980i
$670$	−21.0000	+	12.1244i	−0.811301	+	0.468405i
$671$		0			0
$672$	−4.50000	−	0.866025i	−0.173591	−	0.0334077i
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	−0.135615	−	0.990762i	$-0.543301\pi$
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	0.925832	−	0.377934i	$-0.123365\pi$
$674$	12.1244	+	7.00000i	0.467013	+	0.269630i
$675$	−36.3731			−1.40000
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−20.7846			−0.798817			−0.399409	−	0.916773i	$-0.630785\pi$
$677$	−20.7846			−0.798817			−0.399409	+	0.916773i	$0.630785\pi$
$678$	−5.19615	+	9.00000i	−0.199557	+	0.345643i
$679$	−15.0000	−	43.3013i	−0.575647	−	1.66175i
$680$	5.19615	−	3.00000i	0.199263	−	0.115045i
$681$	18.0000			0.689761
$682$		0			0
$683$	10.3923	−	6.00000i	0.397650	−	0.229584i	−0.287819	−	0.957685i	$-0.592930\pi$
$683$	10.3923	−	6.00000i	0.397650	−	0.229584i	0.685470	+	0.728101i	$0.259597\pi$
$684$		0			0
$685$	−36.0000	+	20.7846i	−1.37549	+	0.794139i
$686$	16.4545	−	8.50000i	0.628235	−	0.324532i
$687$	23.3827	+	13.5000i	0.892105	+	0.515057i
$688$	1.00000			0.0381246
$689$	−7.79423	+	31.5000i	−0.296936	+	1.20005i
$690$	−18.0000			−0.685248
$691$	−39.0000	−	22.5167i	−1.48363	−	0.856574i	−0.483803	−	0.875177i	$-0.660745\pi$
$691$	−39.0000	−	22.5167i	−1.48363	−	0.856574i	−0.999827	+	0.0186028i	$0.994078\pi$
$692$		0			0
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−20.7846	+	12.0000i	−0.788405	+	0.455186i
$696$	−5.19615	−	9.00000i	−0.196960	−	0.341144i
$697$	−12.0000			−0.454532
$698$	14.7224	+	25.5000i	0.557252	+	0.965189i
$699$	−27.0000	−	15.5885i	−1.02123	−	0.589610i
$700$	17.5000	−	6.06218i	0.661438	−	0.229129i
$701$			33.0000i			1.24639i	0.782065	+	0.623196i	$0.214166\pi$
$701$			33.0000i			1.24639i	−0.782065	+	0.623196i	$0.785834\pi$
$702$	−13.5000	−	12.9904i	−0.509525	−	0.490290i
$703$		0			0
$704$		0			0
$705$	10.3923	−	18.0000i	0.391397	−	0.677919i
$706$	−10.5000	+	6.06218i	−0.395173	+	0.228153i
$707$		0			0
$708$	−1.50000	−	2.59808i	−0.0563735	−	0.0976417i
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	−0.999549	−	0.0300298i	$-0.990440\pi$
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	0.473768	−	0.880650i	$-0.342894\pi$
$710$	−51.9615			−1.95008
$711$	15.0000	+	25.9808i	0.562544	+	0.974355i
$712$	13.5000	+	7.79423i	0.505934	+	0.292101i
$713$	2.59808	−	4.50000i	0.0972987	−	0.168526i
$714$	−5.19615	+	6.00000i	−0.194461	+	0.224544i
$715$		0			0
$716$		0			0
$717$	31.5000	+	18.1865i	1.17639	+	0.679189i
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$	12.1244	+	21.0000i	0.452162	+	0.783168i	0.998520	−	0.0543839i	$-0.0173195\pi$
$719$	12.1244	+	21.0000i	0.452162	+	0.783168i	−0.546358	+	0.837552i	$0.683986\pi$
$720$	10.3923			0.387298
$721$	−22.5000	−	4.33013i	−0.837944	−	0.161262i
$722$	16.4545	−	9.50000i	0.612372	−	0.353553i
$723$			18.0000i			0.669427i
$724$		0			0
$725$	36.3731	+	21.0000i	1.35086	+	0.779920i
$726$	16.5000	+	9.52628i	0.612372	+	0.353553i
$727$			12.1244i			0.449667i	0.974397	+	0.224834i	$0.0721839\pi$
$727$			12.1244i			0.449667i	−0.974397	+	0.224834i	$0.927816\pi$
$728$	8.66025	+	4.00000i	0.320970	+	0.148250i
$729$	27.0000			1.00000
$730$	24.0000	−	41.5692i	0.888280	−	1.53855i
$731$	0.866025	−	1.50000i	0.0320311	−	0.0554795i
$732$	−18.1865	+	10.5000i	−0.672194	+	0.388091i
$733$		−	8.66025i		−	0.319874i	−0.987127	−	0.159937i	$-0.948871\pi$
$733$		−	8.66025i		−	0.319874i	0.987127	−	0.159937i	$-0.0511291\pi$
$734$	6.06218	+	10.5000i	0.223759	+	0.387562i
$735$	−33.0000	+	25.9808i	−1.21722	+	0.958315i
$736$	3.00000			0.110581
$737$		0			0
$738$	−18.0000	−	10.3923i	−0.662589	−	0.382546i
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	−0.794443	−	0.607339i	$-0.792237\pi$
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$740$	−13.8564			−0.509372
$741$		0			0
$742$	18.0000	+	15.5885i	0.660801	+	0.572270i
$743$	−23.3827	−	13.5000i	−0.857828	−	0.495267i	0.00545664	−	0.999985i	$-0.498263\pi$
$743$	−23.3827	−	13.5000i	−0.857828	−	0.495267i	−0.863284	+	0.504718i	$0.831596\pi$
$744$	−1.50000	+	2.59808i	−0.0549927	+	0.0952501i
$745$	−63.0000	+	36.3731i	−2.30814	+	1.33261i
$746$			14.0000i			0.512576i
$747$	−18.1865	−	31.5000i	−0.665410	−	1.15252i
$748$		0			0
$749$	31.1769	−	36.0000i	1.13918	−	1.31541i
$750$	−10.3923	+	6.00000i	−0.379473	+	0.219089i
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	−1.73205	+	3.00000i	−0.0631614	+	0.109399i
$753$	−33.0000			−1.20259
$754$	6.00000	+	20.7846i	0.218507	+	0.756931i
$755$	55.4256			2.01715
$756$	−12.9904	+	4.50000i	−0.472456	+	0.163663i
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	−0.993701	−	0.112062i	$-0.964254\pi$
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	0.593899	+	0.804539i	$0.297588\pi$
$758$	−17.3205	+	10.0000i	−0.629109	+	0.363216i
$759$		0			0
$760$		0			0
$761$	−24.2487	−	42.0000i	−0.879015	−	1.52250i	−0.852423	−	0.522852i	$-0.824868\pi$
$761$	−24.2487	−	42.0000i	−0.879015	−	1.52250i	−0.0265919	−	0.999646i	$-0.508465\pi$
$762$		−	34.6410i		−	1.25491i
$763$	8.00000	−	41.5692i	0.289619	−	1.50491i
$764$	−12.9904	−	7.50000i	−0.469975	−	0.271340i
$765$	9.00000	−	15.5885i	0.325396	−	0.563602i
$766$		−	24.2487i		−	0.876142i
$767$	1.73205	+	6.00000i	0.0625407	+	0.216647i
$768$	−1.73205			−0.0625000
$769$	36.0000	+	20.7846i	1.29819	+	0.749512i	0.980092	−	0.198545i	$-0.0636214\pi$
$769$	36.0000	+	20.7846i	1.29819	+	0.749512i	0.318101	+	0.948057i	$0.396955\pi$
$770$		0			0
$771$	13.5000	+	23.3827i	0.486191	+	0.842107i
$772$	14.0000			0.503871
$773$	−17.3205	−	30.0000i	−0.622975	−	1.07903i	−0.988929	−	0.148392i	$-0.952590\pi$
$773$	−17.3205	−	30.0000i	−0.622975	−	1.07903i	0.365953	−	0.930633i	$-0.380743\pi$
$774$	2.59808	−	1.50000i	0.0933859	−	0.0539164i
$775$		−	12.1244i		−	0.435520i
$776$	−8.66025	−	15.0000i	−0.310885	−	0.538469i
$777$	17.3205	−	6.00000i	0.621370	−	0.215249i
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$		0			0
$780$	−21.0000	−	5.19615i	−0.751921	−	0.186052i
$781$		0			0
$782$	2.59808	−	4.50000i	0.0929070	−	0.160920i
$783$	−27.0000	−	15.5885i	−0.964901	−	0.557086i
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$			48.0000i			1.71319i
$786$	23.3827	−	13.5000i	0.834033	−	0.481529i
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.221162	−	0.975237i	$-0.429015\pi$
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.955161	+	0.296087i	$0.0956817\pi$
$788$			15.0000i			0.534353i
$789$		0			0
$790$	30.0000	+	17.3205i	1.06735	+	0.616236i
$791$	−5.19615	−	15.0000i	−0.184754	−	0.533339i
$792$		0			0
$793$	42.0000	−	12.1244i	1.49146	−	0.430548i
$794$	12.1244			0.430277
$795$	−46.7654	−	27.0000i	−1.65860	−	0.957591i
$796$	1.50000	+	0.866025i	0.0531661	+	0.0306955i
$797$	15.5885	+	27.0000i	0.552171	+	0.956389i	0.998118	+	0.0613293i	$0.0195340\pi$
$797$	15.5885	+	27.0000i	0.552171	+	0.956389i	−0.445946	+	0.895060i	$0.647133\pi$
$798$		0			0
$799$	3.00000	+	5.19615i	0.106132	+	0.183827i
$800$	6.06218	−	3.50000i	0.214330	−	0.123744i
$801$	46.7654			1.65237
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$		0			0
$804$	6.06218	−	10.5000i	0.213797	−	0.370306i
$805$	18.0000	−	20.7846i	0.634417	−	0.732561i
$806$	4.33013	−	4.50000i	0.152522	−	0.158506i
$807$	24.0000			0.844840
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$	27.0000	−	15.5885i	0.948683	−	0.547723i
$811$		−	48.4974i		−	1.70297i	−0.524375	−	0.851487i	$-0.675701\pi$
$811$		−	48.4974i		−	1.70297i	0.524375	−	0.851487i	$-0.324299\pi$
$812$	15.5885	+	3.00000i	0.547048	+	0.105279i
$813$	−12.9904	+	7.50000i	−0.455593	+	0.263036i
$814$		0			0
$815$	12.1244	+	21.0000i	0.424698	+	0.735598i
$816$	−1.50000	+	2.59808i	−0.0525105	+	0.0909509i
$817$		0			0
$818$	13.8564			0.484478
$819$	28.5000	−	2.59808i	0.995871	−	0.0907841i
$820$	−24.0000			−0.838116
$821$	−2.59808	−	1.50000i	−0.0906735	−	0.0523504i	0.453978	−	0.891013i	$-0.350005\pi$
$821$	−2.59808	−	1.50000i	−0.0906735	−	0.0523504i	−0.544651	+	0.838663i	$0.683338\pi$
$822$	10.3923	−	18.0000i	0.362473	−	0.627822i
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$	−8.66025			−0.301694
$825$		0			0
$826$	4.50000	+	0.866025i	0.156575	+	0.0301329i
$827$		−	42.0000i		−	1.46048i	−0.683189	−	0.730242i	$-0.739408\pi$
$827$		−	42.0000i		−	1.46048i	0.683189	−	0.730242i	$-0.260592\pi$
$828$	7.79423	−	4.50000i	0.270868	−	0.156386i
$829$	−24.0000	−	13.8564i	−0.833554	−	0.481253i	0.0215137	−	0.999769i	$-0.493151\pi$
$829$	−24.0000	−	13.8564i	−0.833554	−	0.481253i	−0.855068	+	0.518516i	$0.826485\pi$
$830$	−36.3731	−	21.0000i	−1.26253	−	0.728921i
$831$	−3.46410			−0.120168
$832$	3.50000	+	0.866025i	0.121341	+	0.0300240i
$833$	−1.73205	−	12.0000i	−0.0600120	−	0.415775i
$834$	6.00000	−	10.3923i	0.207763	−	0.359856i
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$		0			0
$837$			9.00000i			0.311086i
$838$	16.5000	−	9.52628i	0.569983	−	0.329080i
$839$	8.66025	+	15.0000i	0.298985	+	0.517858i	0.975904	−	0.218200i	$-0.0700186\pi$
$839$	8.66025	+	15.0000i	0.298985	+	0.517858i	−0.676919	+	0.736058i	$0.736685\pi$
$840$	−10.3923	+	12.0000i	−0.358569	+	0.414039i
$841$	3.50000	+	6.06218i	0.120690	+	0.209041i
$842$	−12.1244	−	7.00000i	−0.417833	−	0.241236i
$843$	−18.0000	−	10.3923i	−0.619953	−	0.357930i
$844$	20.0000			0.688428
$845$	39.8372	+	21.0000i	1.37044	+	0.722422i
$846$			10.3923i			0.357295i
$847$	−27.5000	+	9.52628i	−0.944911	+	0.327327i
$848$	7.79423	+	4.50000i	0.267655	+	0.154531i
$849$	−36.3731	+	21.0000i	−1.24832	+	0.720718i
$850$		−	12.1244i		−	0.415862i
$851$	−10.3923	+	6.00000i	−0.356244	+	0.205677i
$852$	22.5000	−	12.9904i	0.770837	−	0.445043i
$853$		−	12.1244i		−	0.415130i	−0.978221	−	0.207565i	$-0.933446\pi$
$853$		−	12.1244i		−	0.415130i	0.978221	−	0.207565i	$-0.0665539\pi$
$854$	6.06218	−	31.5000i	0.207443	−	1.07791i
$855$		0			0
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	34.6410			1.18331			0.591657	−	0.806190i	$-0.298474\pi$
$857$	34.6410			1.18331			0.591657	+	0.806190i	$0.298474\pi$
$858$		0			0
$859$		−	27.7128i		−	0.945549i	−0.881183	−	0.472774i	$-0.843253\pi$
$859$		−	27.7128i		−	0.945549i	0.881183	−	0.472774i	$-0.156747\pi$
$860$	1.73205	−	3.00000i	0.0590624	−	0.102299i
$861$	30.0000	−	10.3923i	1.02240	−	0.354169i
$862$	1.50000	+	2.59808i	0.0510902	+	0.0884908i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		0			0
$866$	−6.92820			−0.235430
$867$	−12.1244	−	21.0000i	−0.411765	−	0.713197i
$868$	−1.50000	−	4.33013i	−0.0509133	−	0.146974i
$869$		0			0
$870$	−36.0000			−1.22051
$871$	−17.5000	+	18.1865i	−0.592965	+	0.616227i
$872$		−	16.0000i		−	0.541828i
$873$	−45.0000	−	25.9808i	−1.52302	−	0.879316i
$874$		0			0
$875$	3.46410	−	18.0000i	0.117108	−	0.608511i
$876$			24.0000i			0.810885i
$877$	14.0000	+	24.2487i	0.472746	+	0.818821i	0.999514	−	0.0311889i	$-0.00992933\pi$
$877$	14.0000	+	24.2487i	0.472746	+	0.818821i	−0.526767	+	0.850010i	$0.676596\pi$
$878$	1.73205	+	3.00000i	0.0584539	+	0.101245i
$879$	−30.0000			−1.01187
$880$		0			0
$881$	−2.59808	+	4.50000i	−0.0875314	+	0.151609i	−0.906467	−	0.422276i	$-0.861231\pi$
$881$	−2.59808	+	4.50000i	−0.0875314	+	0.151609i	0.818936	+	0.573885i	$0.194564\pi$
$882$	7.79423	−	19.5000i	0.262445	−	0.656599i
$883$	−47.0000			−1.58168			−0.790838	−	0.612026i	$-0.790355\pi$
$883$	−47.0000			−1.58168			−0.790838	+	0.612026i	$0.790355\pi$
$884$	4.33013	−	4.50000i	0.145638	−	0.151351i
$885$	−10.3923			−0.349334
$886$	−9.00000	+	15.5885i	−0.302361	+	0.523704i
$887$	−22.5167	+	39.0000i	−0.756035	+	1.30949i	0.188822	+	0.982011i	$0.439533\pi$
$887$	−22.5167	+	39.0000i	−0.756035	+	1.30949i	−0.944858	+	0.327481i	$0.893800\pi$
$888$	6.00000	−	3.46410i	0.201347	−	0.116248i
$889$	40.0000	+	34.6410i	1.34156	+	1.16182i
$890$	46.7654	−	27.0000i	1.56758	−	0.905042i
$891$		0			0
$892$		−	5.19615i		−	0.173980i
$893$		0			0
$894$	18.1865	−	31.5000i	0.608249	−	1.05352i
$895$		0			0
$896$	1.73205	−	2.00000i	0.0578638	−	0.0668153i
$897$	−18.0000	+	5.19615i	−0.601003	+	0.173494i
$898$	6.00000			0.200223
$899$	5.19615	−	9.00000i	0.173301	−	0.300167i
$900$	10.5000	−	18.1865i	0.350000	−	0.606218i
$901$	13.5000	−	7.79423i	0.449750	−	0.259663i
$902$		0			0
$903$	−0.866025	+	4.50000i	−0.0288195	+	0.149751i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$		0			0
$906$	−24.0000	+	13.8564i	−0.797347	+	0.460348i
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$	−5.19615	+	9.00000i	−0.172440	+	0.298675i
$909$		0			0
$910$	27.0000	−	19.0526i	0.895041	−	0.631586i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	26.8468	−	15.5000i	0.888013	−	0.512694i
$915$			72.7461i			2.40491i
$916$	−13.5000	+	7.79423i	−0.446053	+	0.257529i
$917$	−7.79423	+	40.5000i	−0.257388	+	1.33743i
$918$			9.00000i			0.297044i
$919$	7.00000	+	12.1244i	0.230909	+	0.399946i	0.958076	−	0.286515i	$-0.0924968\pi$
$919$	7.00000	+	12.1244i	0.230909	+	0.399946i	−0.727167	+	0.686461i	$0.759163\pi$
$920$	5.19615	−	9.00000i	0.171312	−	0.296721i
$921$	36.3731	+	21.0000i	1.19853	+	0.691974i
$922$			6.92820i			0.228168i
$923$	−51.9615	+	15.0000i	−1.71033	+	0.493731i
$924$		0			0
$925$	−14.0000	+	24.2487i	−0.460317	+	0.797293i
$926$	−12.1244	−	7.00000i	−0.398431	−	0.230034i
$927$	−22.5000	+	12.9904i	−0.738997	+	0.426660i
$928$	6.00000			0.196960
$929$	26.8468	+	46.5000i	0.880815	+	1.52562i	0.850437	+	0.526077i	$0.176338\pi$
$929$	26.8468	+	46.5000i	0.880815	+	1.52562i	0.0303776	+	0.999538i	$0.490329\pi$
$930$	5.19615	+	9.00000i	0.170389	+	0.295122i
$931$		0			0
$932$	15.5885	−	9.00000i	0.510617	−	0.294805i
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$	−13.5000	−	7.79423i	−0.441733	−	0.255035i
$935$		0			0
$936$	10.3923	−	3.00000i	0.339683	−	0.0980581i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	6.06218	+	17.5000i	0.197937	+	0.571395i
$939$	−5.19615	−	3.00000i	−0.169570	−	0.0979013i
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$	38.1051			1.24219			0.621096	−	0.783735i	$-0.286688\pi$
$941$	38.1051			1.24219			0.621096	+	0.783735i	$0.286688\pi$
$942$	−12.0000	−	20.7846i	−0.390981	−	0.677199i
$943$	−18.0000	+	10.3923i	−0.586161	+	0.338420i
$944$	1.73205			0.0563735
$945$	−9.00000	+	46.7654i	−0.292770	+	1.52128i
$946$		0			0
$947$	−15.5885	−	9.00000i	−0.506557	−	0.292461i	0.224860	−	0.974391i	$-0.427807\pi$
$947$	−15.5885	−	9.00000i	−0.506557	−	0.292461i	−0.731417	+	0.681930i	$0.761141\pi$
$948$	−17.3205			−0.562544
$949$	12.0000	−	48.4974i	0.389536	−	1.57429i
$950$		0			0
$951$	−4.50000	−	2.59808i	−0.145922	−	0.0842484i
$952$	−1.50000	−	4.33013i	−0.0486153	−	0.140340i
$953$	31.1769	−	18.0000i	1.00992	−	0.583077i	0.0987513	−	0.995112i	$-0.468515\pi$
$953$	31.1769	−	18.0000i	1.00992	−	0.583077i	0.911168	+	0.412035i	$0.135182\pi$
$954$	27.0000			0.874157
$955$	−45.0000	+	25.9808i	−1.45617	+	0.840718i
$956$	−18.1865	+	10.5000i	−0.588195	+	0.339594i
$957$		0			0
$958$	−21.0000	+	12.1244i	−0.678479	+	0.391720i
$959$	10.3923	+	30.0000i	0.335585	+	0.968751i
$960$	−3.00000	+	5.19615i	−0.0968246	+	0.167705i
$961$	28.0000			0.903226
$962$	−13.8564	+	4.00000i	−0.446748	+	0.128965i
$963$		−	54.0000i		−	1.74013i
$964$	−9.00000	−	5.19615i	−0.289870	−	0.167357i
$965$	24.2487	−	42.0000i	0.780594	−	1.35203i
$966$	−2.59808	+	13.5000i	−0.0835917	+	0.434355i
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$	−9.52628	+	5.50000i	−0.306186	+	0.176777i
$969$		0			0
$970$	−60.0000			−1.92648
$971$	−6.06218	−	10.5000i	−0.194545	−	0.336961i	0.752207	−	0.658927i	$-0.228990\pi$
$971$	−6.06218	−	10.5000i	−0.194545	−	0.336961i	−0.946751	+	0.321966i	$0.895656\pi$
$972$	−7.79423	+	13.5000i	−0.250000	+	0.433013i
$973$	6.00000	+	17.3205i	0.192351	+	0.555270i
$974$		−	2.00000i		−	0.0640841i
$975$	−30.3109	+	31.5000i	−0.970725	+	1.00881i
$976$		−	12.1244i		−	0.388091i
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	0.794164	−	0.607704i	$-0.207909\pi$
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	−0.129205	+	0.991618i	$0.541243\pi$
$978$	−10.5000	−	6.06218i	−0.335753	−	0.193847i
$979$		0			0
$980$	−3.46410	−	24.0000i	−0.110657	−	0.766652i
$981$	−24.0000	−	41.5692i	−0.766261	−	1.32720i
$982$	18.0000	+	31.1769i	0.574403	+	0.994895i
$983$	−13.8564			−0.441951			−0.220975	−	0.975279i	$-0.570924\pi$
$983$	−13.8564			−0.441951			−0.220975	+	0.975279i	$0.570924\pi$
$984$	10.3923	−	6.00000i	0.331295	−	0.191273i
$985$	45.0000	+	25.9808i	1.43382	+	0.827816i
$986$	5.19615	−	9.00000i	0.165479	−	0.286618i
$987$	−12.0000	−	10.3923i	−0.381964	−	0.330791i
$988$		0			0
$989$		−	3.00000i		−	0.0953945i
$990$		0			0
$991$	7.00000	−	12.1244i	0.222362	−	0.385143i	−0.733163	−	0.680053i	$-0.761957\pi$
$991$	7.00000	−	12.1244i	0.222362	−	0.385143i	0.955525	+	0.294911i	$0.0952899\pi$
$992$	−0.866025	−	1.50000i	−0.0274963	−	0.0476250i
$993$	−48.4974			−1.53902
$994$	−7.50000	+	38.9711i	−0.237886	+	1.23609i
$995$	5.19615	−	3.00000i	0.164729	−	0.0951064i
$996$	21.0000			0.665410
$997$	43.5000	−	25.1147i	1.37766	−	0.795392i	0.385782	−	0.922590i	$-0.373932\pi$
$997$	43.5000	−	25.1147i	1.37766	−	0.795392i	0.991877	+	0.127198i	$0.0405985\pi$
$998$	14.7224	+	8.50000i	0.466030	+	0.269063i
$999$	10.3923	−	18.0000i	0.328798	−	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.a.503.1	yes	4
3.2	odd	2	inner	546.2.bq.a.503.2	yes	4
7.6	odd	2		546.2.bq.b.503.1	yes	4
13.3	even	3		546.2.bq.b.419.2	yes	4
21.20	even	2		546.2.bq.b.503.2	yes	4
39.29	odd	6		546.2.bq.b.419.1	yes	4
91.55	odd	6	inner	546.2.bq.a.419.2	yes	4
273.146	even	6	inner	546.2.bq.a.419.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.a.419.1	✓	4	273.146	even	6	inner
546.2.bq.a.419.2	yes	4	91.55	odd	6	inner
546.2.bq.a.503.1	yes	4	1.1	even	1	trivial
546.2.bq.a.503.2	yes	4	3.2	odd	2	inner
546.2.bq.b.419.1	yes	4	39.29	odd	6
546.2.bq.b.419.2	yes	4	13.3	even	3
546.2.bq.b.503.1	yes	4	7.6	odd	2
546.2.bq.b.503.2	yes	4	21.20	even	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.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.46410 q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.46410 q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +1.73205 q^{12} +(-3.50000 - 0.866025i) q^{13} +(-1.73205 + 2.00000i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +3.00000i q^{18} +(1.73205 + 3.00000i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(2.59808 + 1.50000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +7.00000 q^{25} +(2.59808 + 2.50000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(5.19615 + 3.00000i) q^{29} +(-5.19615 + 3.00000i) q^{30} -1.73205i q^{31} +(0.866025 - 0.500000i) q^{32} -1.73205i q^{34} +(1.73205 - 9.00000i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(-4.33013 + 4.50000i) q^{39} -3.46410i q^{40} +(-3.46410 + 6.00000i) q^{41} +(1.50000 + 4.33013i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(-5.19615 - 9.00000i) q^{45} +(-1.50000 - 2.59808i) q^{46} +3.46410 q^{47} +(0.866025 + 1.50000i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-6.06218 - 3.50000i) q^{50} +3.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} -9.00000i q^{53} +(4.50000 + 2.59808i) q^{54} +(-2.59808 - 0.500000i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(-0.866025 - 1.50000i) q^{59} +6.00000 q^{60} +(-10.5000 + 6.06218i) q^{61} +(-0.866025 + 1.50000i) q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-12.1244 - 3.00000i) q^{65} +(3.50000 - 6.06218i) q^{67} +(-0.866025 + 1.50000i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-6.00000 + 6.92820i) q^{70} +(12.9904 - 7.50000i) q^{71} +(-2.59808 + 1.50000i) q^{72} +13.8564i q^{73} +(3.46410 - 2.00000i) q^{74} +(6.06218 - 10.5000i) q^{75} +(6.00000 - 1.73205i) q^{78} -10.0000 q^{79} +(-1.73205 + 3.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} +12.1244 q^{83} +(0.866025 - 4.50000i) q^{84} +(3.00000 + 5.19615i) q^{85} +1.00000i q^{86} +(9.00000 - 5.19615i) q^{87} +(-7.79423 + 13.5000i) q^{89} +10.3923i q^{90} +(-4.00000 + 8.66025i) q^{91} +3.00000i q^{92} +(-2.59808 - 1.50000i) q^{93} +(-3.00000 - 1.73205i) q^{94} -1.73205i q^{96} +(15.0000 - 8.66025i) q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} - 6 q^{6} + 2 q^{7} - 6 q^{9} - 12 q^{10} - 14 q^{13} + 12 q^{15} - 2 q^{16} - 6 q^{24} + 28 q^{25} + 10 q^{28} + 6 q^{36} - 8 q^{37} + 6 q^{42} - 2 q^{43} - 6 q^{46} - 26 q^{49} + 12 q^{51} - 4 q^{52} + 18 q^{54} - 12 q^{58} + 24 q^{60} - 42 q^{61} - 30 q^{63} - 4 q^{64} + 14 q^{67} + 18 q^{69} - 24 q^{70} + 24 q^{78} - 40 q^{79} - 18 q^{81} + 24 q^{82} + 12 q^{85} + 36 q^{87} - 16 q^{91} - 12 q^{94} + 60 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^6 + 2 * q^7 - 6 * q^9 - 12 * q^10 - 14 * q^13 + 12 * q^15 - 2 * q^16 - 6 * q^24 + 28 * q^25 + 10 * q^28 + 6 * q^36 - 8 * q^37 + 6 * q^42 - 2 * q^43 - 6 * q^46 - 26 * q^49 + 12 * q^51 - 4 * q^52 + 18 * q^54 - 12 * q^58 + 24 * q^60 - 42 * q^61 - 30 * q^63 - 4 * q^64 + 14 * q^67 + 18 * q^69 - 24 * q^70 + 24 * q^78 - 40 * q^79 - 18 * q^81 + 24 * q^82 + 12 * q^85 + 36 * q^87 - 16 * q^91 - 12 * q^94 + 60 * q^97

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