LMFDB - Embedded newform 490.2.i.b.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(79,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("490.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.i (of order $6$, degree $2$, not 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:	$3.91266969904$
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:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	490.79
Dual form			490.2.i.b.459.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +3.00000 q^{6} +1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +3.00000 q^{6} +1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(-0.133975 - 2.23205i) q^{10} +(2.59808 + 1.50000i) q^{12} +2.00000i q^{13} +(-6.00000 - 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(5.19615 - 3.00000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(0.866025 + 0.500000i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(-1.00000 + 1.73205i) q^{26} -9.00000i q^{27} +1.00000 q^{29} +(-3.69615 - 5.59808i) q^{30} +(5.00000 + 8.66025i) q^{31} +(-0.866025 + 0.500000i) q^{32} -2.00000 q^{34} +6.00000 q^{36} +(-6.92820 - 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(1.86603 - 1.23205i) q^{40} +3.00000 q^{41} +5.00000i q^{43} +(-13.3923 + 0.803848i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-6.92820 - 4.00000i) q^{47} +3.00000i q^{48} +(-4.00000 + 3.00000i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(4.50000 - 7.79423i) q^{54} -6.00000i q^{57} +(0.866025 + 0.500000i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(-0.401924 - 6.69615i) q^{60} +(-4.50000 + 7.79423i) q^{61} +10.0000i q^{62} -1.00000 q^{64} +(3.73205 - 2.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +3.00000 q^{69} +6.00000 q^{71} +(5.19615 + 3.00000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(1.79423 + 14.8923i) q^{75} +2.00000 q^{76} +6.00000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(2.23205 - 0.133975i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 1.50000i) q^{82} +9.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(2.59808 - 1.50000i) q^{87} +(3.50000 - 6.06218i) q^{89} +(-12.0000 - 6.00000i) q^{90} +1.00000i q^{92} +(25.9808 + 15.0000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(-4.46410 + 0.267949i) q^{95} +(-1.50000 + 2.59808i) q^{96} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{5} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^5 + 12 * q^6 + 12 * q^9	$ 4 q + 2 q^{4} + 2 q^{5} + 12 q^{6} + 12 q^{9} - 4 q^{10} - 24 q^{15} - 2 q^{16} + 4 q^{19} + 4 q^{20} + 6 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{29} + 6 q^{30} + 20 q^{31} - 8 q^{34} + 24 q^{36} + 12 q^{39} + 4 q^{40} + 12 q^{41} - 12 q^{45} + 2 q^{46} - 16 q^{50} - 12 q^{51} + 18 q^{54} - 4 q^{59} - 12 q^{60} - 18 q^{61} - 4 q^{64} + 8 q^{65} + 12 q^{69} + 24 q^{71} - 16 q^{74} - 24 q^{75} + 8 q^{76} - 20 q^{79} + 2 q^{80} - 18 q^{81} + 16 q^{85} - 10 q^{86} + 14 q^{89} - 48 q^{90} - 16 q^{94} - 4 q^{95} - 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^5 + 12 * q^6 + 12 * q^9 - 4 * q^10 - 24 * q^15 - 2 * q^16 + 4 * q^19 + 4 * q^20 + 6 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^29 + 6 * q^30 + 20 * q^31 - 8 * q^34 + 24 * q^36 + 12 * q^39 + 4 * q^40 + 12 * q^41 - 12 * q^45 + 2 * q^46 - 16 * q^50 - 12 * q^51 + 18 * q^54 - 4 * q^59 - 12 * q^60 - 18 * q^61 - 4 * q^64 + 8 * q^65 + 12 * q^69 + 24 * q^71 - 16 * q^74 - 24 * q^75 + 8 * q^76 - 20 * q^79 + 2 * q^80 - 18 * q^81 + 16 * q^85 - 10 * q^86 + 14 * q^89 - 48 * q^90 - 16 * q^94 - 4 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	1.00000			$0$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$	3.00000			1.22474
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$	−0.133975	−	2.23205i	−0.0423665	−	0.705836i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	2.59808	+	1.50000i	0.750000	+	0.433013i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$	−6.00000	−	3.00000i	−1.54919	−	0.774597i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$	5.19615	−	3.00000i	1.22474	−	0.707107i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$		0			0
$22$		0			0
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	0.587565	−	0.809177i	$-0.300087\pi$
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	−0.406986	+	0.913434i	$0.633420\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		−	9.00000i		−	1.73205i
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	−3.69615	−	5.59808i	−0.674822	−	1.02206i
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.830014	+	0.557743i	$0.188333\pi$
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	6.00000			1.00000
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.192809	−	0.981236i	$-0.561760\pi$
$37$	−6.92820	−	4.00000i	−1.13899	−	0.657596i	−0.946180	+	0.323640i	$0.895093\pi$
$38$	1.73205	−	1.00000i	0.280976	−	0.162221i
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$	1.86603	−	1.23205i	0.295045	−	0.194804i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$			5.00000i			0.762493i	0.924473	+	0.381246i	$0.124505\pi$
$43$			5.00000i			0.762493i	−0.924473	+	0.381246i	$0.875495\pi$
$44$		0			0
$45$	−13.3923	+	0.803848i	−1.99641	+	0.119831i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.0992202	−	0.995066i	$-0.531635\pi$
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.911362	+	0.411606i	$0.864968\pi$
$48$			3.00000i			0.433013i
$49$		0			0
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	4.50000	−	7.79423i	0.612372	−	1.06066i
$55$		0			0
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	0.866025	+	0.500000i	0.113715	+	0.0656532i
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$	−0.401924	−	6.69615i	−0.0518881	−	0.864470i
$61$	−4.50000	+	7.79423i	−0.576166	+	0.997949i	0.419748	+	0.907641i	$0.362118\pi$
$61$	−4.50000	+	7.79423i	−0.576166	+	0.997949i	−0.995914	+	0.0903080i	$0.971215\pi$
$62$			10.0000i			1.27000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.73205	−	2.46410i	0.462904	−	0.305634i
$66$		0			0
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$	−1.73205	−	1.00000i	−0.210042	−	0.121268i
$69$	3.00000			0.361158
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	5.19615	+	3.00000i	0.612372	+	0.353553i
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.101361	−	0.994850i	$-0.467680\pi$
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.912245	+	0.409644i	$0.134347\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	1.79423	+	14.8923i	0.207180	+	1.71962i
$76$	2.00000			0.229416
$77$		0			0
$78$			6.00000i			0.679366i
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	2.23205	−	0.133975i	0.249551	−	0.0149788i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.59808	+	1.50000i	0.286910	+	0.165647i
$83$			9.00000i			0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$			9.00000i			0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$		0			0
$85$	4.00000	+	2.00000i	0.433861	+	0.216930i
$86$	−2.50000	+	4.33013i	−0.269582	+	0.466930i
$87$	2.59808	−	1.50000i	0.278543	−	0.160817i
$88$		0			0
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$	−12.0000	−	6.00000i	−1.26491	−	0.632456i
$91$		0			0
$92$			1.00000i			0.104257i
$93$	25.9808	+	15.0000i	2.69408	+	1.55543i
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	−4.46410	+	0.267949i	−0.458007	+	0.0274910i
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		0			0
$99$		0			0
$100$	−4.96410	+	0.598076i	−0.496410	+	0.0598076i
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$	−5.19615	+	3.00000i	−0.514496	+	0.297044i
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.0491146	−	0.998793i	$-0.515640\pi$
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.889538	+	0.456862i	$0.848973\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−6.06218	−	3.50000i	−0.586053	−	0.338358i	0.177482	−	0.984124i	$-0.443205\pi$
$107$	−6.06218	−	3.50000i	−0.586053	−	0.338358i	−0.763535	+	0.645766i	$0.776538\pi$
$108$	7.79423	−	4.50000i	0.750000	−	0.433013i
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$		0			0
$111$	−24.0000			−2.27798
$112$		0			0
$113$		−	10.0000i		−	0.940721i	−0.882474	−	0.470360i	$-0.844124\pi$
$113$		−	10.0000i		−	0.940721i	0.882474	−	0.470360i	$-0.155876\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$	−0.133975	−	2.23205i	−0.0124932	−	0.208140i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	10.3923	+	6.00000i	0.960769	+	0.554700i
$118$		−	2.00000i		−	0.184115i
$119$		0			0
$120$	3.00000	−	6.00000i	0.273861	−	0.547723i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−7.79423	+	4.50000i	−0.705656	+	0.407411i
$123$	7.79423	−	4.50000i	0.702782	−	0.405751i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	7.50000	+	12.9904i	0.660338	+	1.14374i
$130$	4.46410	−	0.267949i	0.391528	−	0.0235007i
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.0155672	−	0.999879i	$-0.495045\pi$
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$132$		0			0
$133$		0			0
$134$	7.00000			0.604708
$135$	−16.7942	+	11.0885i	−1.44542	+	0.954342i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−13.8564	+	8.00000i	−1.18383	+	0.683486i	−0.956898	−	0.290424i	$-0.906204\pi$
$137$	−13.8564	+	8.00000i	−1.18383	+	0.683486i	−0.226935	+	0.973910i	$0.572870\pi$
$138$	2.59808	+	1.50000i	0.221163	+	0.127688i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$		0			0
$144$	3.00000	+	5.19615i	0.250000	+	0.433013i
$145$	−1.23205	−	1.86603i	−0.102316	−	0.154965i
$146$	10.0000			0.827606
$147$		0			0
$148$		−	8.00000i		−	0.657596i
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$	−5.89230	+	13.7942i	−0.481105	+	1.12629i
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	0.717752	−	0.696299i	$-0.245171\pi$
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	−0.961888	+	0.273442i	$0.911838\pi$
$152$	1.73205	+	1.00000i	0.140488	+	0.0811107i
$153$			12.0000i			0.970143i
$154$		0			0
$155$	10.0000	−	20.0000i	0.803219	−	1.60644i
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	−8.66025	+	5.00000i	−0.688973	+	0.397779i
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$	2.00000	+	1.00000i	0.158114	+	0.0790569i
$161$		0			0
$162$		−	9.00000i		−	0.707107i
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	0.0343508	−	0.999410i	$-0.489064\pi$
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	−0.848339	+	0.529454i	$0.822397\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$		−	9.00000i		−	0.696441i	−0.937413	−	0.348220i	$-0.886786\pi$
$167$		−	9.00000i		−	0.696441i	0.937413	−	0.348220i	$-0.113214\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	2.46410	+	3.73205i	0.188988	+	0.286235i
$171$	−6.00000	−	10.3923i	−0.458831	−	0.794719i
$172$	−4.33013	+	2.50000i	−0.330169	+	0.190623i
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	0.840002	−	0.542583i	$-0.182554\pi$
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	−0.0498898	+	0.998755i	$0.515887\pi$
$174$	3.00000			0.227429
$175$		0			0
$176$		0			0
$177$	−5.19615	−	3.00000i	−0.390567	−	0.225494i
$178$	6.06218	−	3.50000i	0.454379	−	0.262336i
$179$	−13.0000	−	22.5167i	−0.971666	−	1.68297i	−0.690526	−	0.723307i	$-0.742621\pi$
$179$	−13.0000	−	22.5167i	−0.971666	−	1.68297i	−0.281139	−	0.959667i	$-0.590712\pi$
$180$	−7.39230	−	11.1962i	−0.550990	−	0.834512i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$			27.0000i			1.99590i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	1.07180	+	17.8564i	0.0788001	+	1.31283i
$186$	15.0000	+	25.9808i	1.09985	+	1.90500i
$187$		0			0
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$	−4.00000	−	2.00000i	−0.290191	−	0.145095i
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$	−2.59808	+	1.50000i	−0.187500	+	0.108253i
$193$	17.3205	−	10.0000i	1.24676	−	0.719816i	0.276296	−	0.961073i	$-0.410893\pi$
$193$	17.3205	−	10.0000i	1.24676	−	0.719816i	0.970461	+	0.241257i	$0.0775596\pi$
$194$		0			0
$195$	6.00000	−	12.0000i	0.429669	−	0.859338i
$196$		0			0
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$		0			0
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	0.571122	−	0.820865i	$-0.306508\pi$
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	−0.996451	+	0.0841740i	$0.973175\pi$
$200$	−4.59808	−	1.96410i	−0.325133	−	0.138883i
$201$	10.5000	−	18.1865i	0.740613	−	1.28278i
$202$		−	15.0000i		−	1.05540i
$203$		0			0
$204$	−6.00000			−0.420084
$205$	−3.69615	−	5.59808i	−0.258150	−	0.390987i
$206$	−5.50000	−	9.52628i	−0.383203	−	0.663727i
$207$	5.19615	−	3.00000i	0.361158	−	0.208514i
$208$	−1.73205	−	1.00000i	−0.120096	−	0.0693375i
$209$		0			0
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$	15.5885	−	9.00000i	1.06810	−	0.616670i
$214$	−3.50000	−	6.06218i	−0.239255	−	0.414402i
$215$	9.33013	−	6.16025i	0.636309	−	0.420126i
$216$	9.00000			0.612372
$217$		0			0
$218$			5.00000i			0.338643i
$219$	15.0000	−	25.9808i	1.01361	−	1.75562i
$220$		0			0
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$	−20.7846	−	12.0000i	−1.39497	−	0.805387i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	18.0000	+	24.0000i	1.20000	+	1.60000i
$226$	5.00000	−	8.66025i	0.332595	−	0.576072i
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$	5.19615	−	3.00000i	0.344124	−	0.198680i
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	1.00000	−	2.00000i	0.0659380	−	0.131876i
$231$		0			0
$232$			1.00000i			0.0656532i
$233$	12.1244	+	7.00000i	0.794293	+	0.458585i	0.841472	−	0.540301i	$-0.181690\pi$
$233$	12.1244	+	7.00000i	0.794293	+	0.458585i	−0.0471787	+	0.998886i	$0.515023\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$	1.07180	+	17.8564i	0.0699163	+	1.16482i
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$			30.0000i			1.94871i
$238$		0			0
$239$	10.0000			0.646846			0.323423	−	0.946254i	$-0.395166\pi$
$239$	10.0000			0.646846			0.323423	+	0.946254i	$0.395166\pi$
$240$	5.59808	−	3.69615i	0.361354	−	0.238586i
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	0.995509	+	0.0946700i	$0.0301796\pi$
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	9.52628	−	5.50000i	0.612372	−	0.353553i
$243$		0			0
$244$	−9.00000			−0.576166
$245$		0			0
$246$	9.00000			0.573819
$247$	3.46410	+	2.00000i	0.220416	+	0.127257i
$248$	−8.66025	+	5.00000i	−0.549927	+	0.317500i
$249$	13.5000	+	23.3827i	0.855528	+	1.48182i
$250$	10.5263	+	3.76795i	0.665740	+	0.238306i
$251$	10.0000			0.631194			0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000			0.631194			0.315597	+	0.948893i	$0.397795\pi$
$252$		0			0
$253$		0			0
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	13.3923	−	0.803848i	0.838659	−	0.0503389i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$			15.0000i			0.933859i
$259$		0			0
$260$	4.00000	+	2.00000i	0.248069	+	0.124035i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	17.3205	−	10.0000i	1.07006	−	0.617802i
$263$	18.1865	−	10.5000i	1.12143	−	0.647458i	0.179664	−	0.983728i	$-0.442499\pi$
$263$	18.1865	−	10.5000i	1.12143	−	0.647458i	0.941766	+	0.336270i	$0.109166\pi$
$264$		0			0
$265$	12.0000	+	6.00000i	0.737154	+	0.368577i
$266$		0			0
$267$		−	21.0000i		−	1.28518i
$268$	6.06218	+	3.50000i	0.370306	+	0.213797i
$269$	−2.50000	−	4.33013i	−0.152428	−	0.264013i	0.779692	−	0.626164i	$-0.215376\pi$
$269$	−2.50000	−	4.33013i	−0.152428	−	0.264013i	−0.932119	+	0.362151i	$0.882042\pi$
$270$	−20.0885	+	1.20577i	−1.22254	+	0.0733809i
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	−0.760405	−	0.649449i	$-0.775000\pi$
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	0.942642	+	0.333805i	$0.108333\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	−16.0000			−0.966595
$275$		0			0
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	22.5167	−	13.0000i	1.35290	−	0.781094i	0.364241	−	0.931305i	$-0.381328\pi$
$277$	22.5167	−	13.0000i	1.35290	−	0.781094i	0.988654	+	0.150210i	$0.0479951\pi$
$278$	−6.92820	−	4.00000i	−0.415526	−	0.239904i
$279$	60.0000			3.59211
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−20.7846	−	12.0000i	−1.23771	−	0.714590i
$283$	−6.92820	+	4.00000i	−0.411839	+	0.237775i	−0.691580	−	0.722300i	$-0.743085\pi$
$283$	−6.92820	+	4.00000i	−0.411839	+	0.237775i	0.279741	+	0.960076i	$0.409752\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	−11.1962	+	7.39230i	−0.663203	+	0.437882i
$286$		0			0
$287$		0			0
$288$			6.00000i			0.353553i
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$	−0.133975	−	2.23205i	−0.00786726	−	0.131071i
$291$		0			0
$292$	8.66025	+	5.00000i	0.506803	+	0.292603i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	−2.00000	+	4.00000i	−0.116445	+	0.232889i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$	−12.9904	+	7.50000i	−0.752513	+	0.434463i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$	−12.0000	+	9.00000i	−0.692820	+	0.519615i
$301$		0			0
$302$		−	6.00000i		−	0.345261i
$303$	−38.9711	−	22.5000i	−2.23883	−	1.29259i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	20.0885	−	1.20577i	1.15026	−	0.0690423i
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$		−	19.0000i		−	1.08439i	−0.840254	−	0.542194i	$-0.817594\pi$
$307$		−	19.0000i		−	1.08439i	0.840254	−	0.542194i	$-0.182406\pi$
$308$		0			0
$309$	−33.0000			−1.87730
$310$	18.6603	−	12.3205i	1.05983	−	0.699758i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$	−5.19615	+	3.00000i	−0.294174	+	0.169842i
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	0.682855	−	0.730554i	$-0.260738\pi$
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	−0.291250	+	0.956647i	$0.594071\pi$
$314$	−12.0000			−0.677199
$315$		0			0
$316$	−10.0000			−0.562544
$317$	19.0526	+	11.0000i	1.07010	+	0.617822i	0.928208	−	0.372061i	$-0.121349\pi$
$317$	19.0526	+	11.0000i	1.07010	+	0.617822i	0.141890	+	0.989882i	$0.454682\pi$
$318$	−15.5885	+	9.00000i	−0.874157	+	0.504695i
$319$		0			0
$320$	1.23205	+	1.86603i	0.0688737	+	0.104314i
$321$	−21.0000			−1.17211
$322$		0			0
$323$			4.00000i			0.222566i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−9.19615	−	3.92820i	−0.510111	−	0.217898i
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$	12.9904	+	7.50000i	0.718370	+	0.414751i
$328$			3.00000i			0.165647i
$329$		0			0
$330$		0			0
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$332$	−7.79423	+	4.50000i	−0.427764	+	0.246970i
$333$	−41.5692	+	24.0000i	−2.27798	+	1.31519i
$334$	4.50000	−	7.79423i	0.246229	−	0.426481i
$335$	−14.0000	−	7.00000i	−0.764902	−	0.382451i
$336$		0			0
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$	−15.0000	−	25.9808i	−0.814688	−	1.41108i
$340$	0.267949	+	4.46410i	0.0145316	+	0.242100i
$341$		0			0
$342$		−	12.0000i		−	0.648886i
$343$		0			0
$344$	−5.00000			−0.269582
$345$	−3.69615	−	5.59808i	−0.198994	−	0.301390i
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.901152	−	0.433503i	$-0.857278\pi$
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.0751519	+	0.997172i	$0.523944\pi$
$348$	2.59808	+	1.50000i	0.139272	+	0.0804084i
$349$	−9.00000			−0.481759			−0.240879	−	0.970555i	$-0.577436\pi$
$349$	−9.00000			−0.481759			−0.240879	+	0.970555i	$0.577436\pi$
$350$		0			0
$351$	18.0000			0.960769
$352$		0			0
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	−0.355303	−	0.934751i	$-0.615622\pi$
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	0.631867	+	0.775077i	$0.282289\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	−7.39230	−	11.1962i	−0.392343	−	0.594230i
$356$	7.00000			0.370999
$357$		0			0
$358$		−	26.0000i		−	1.37414i
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	−0.989479	−	0.144677i	$-0.953786\pi$
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	0.620033	+	0.784576i	$0.287119\pi$
$360$	−0.803848	−	13.3923i	−0.0423665	−	0.705836i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−4.33013	−	2.50000i	−0.227586	−	0.131397i
$363$		−	33.0000i		−	1.73205i
$364$		0			0
$365$	−20.0000	−	10.0000i	−1.04685	−	0.523424i
$366$	−13.5000	+	23.3827i	−0.705656	+	1.22223i
$367$	−19.9186	+	11.5000i	−1.03974	+	0.600295i	−0.919760	−	0.392481i	$-0.871617\pi$
$367$	−19.9186	+	11.5000i	−1.03974	+	0.600295i	−0.119982	+	0.992776i	$0.538284\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	9.00000	−	15.5885i	0.468521	−	0.811503i
$370$	−8.00000	+	16.0000i	−0.415900	+	0.831800i
$371$		0			0
$372$			30.0000i			1.55543i
$373$	−6.92820	−	4.00000i	−0.358729	−	0.207112i	0.309794	−	0.950804i	$-0.399740\pi$
$373$	−6.92820	−	4.00000i	−0.358729	−	0.207112i	−0.668523	+	0.743691i	$0.733073\pi$
$374$		0			0
$375$	25.5788	−	21.6962i	1.32089	−	1.12038i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$			2.00000i			0.103005i
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	−2.46410	−	3.73205i	−0.126406	−	0.191450i
$381$	12.0000	+	20.7846i	0.614779	+	1.06483i
$382$	17.3205	−	10.0000i	0.886194	−	0.511645i
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	0.287469	−	0.957790i	$-0.407186\pi$
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	−0.685736	+	0.727851i	$0.740519\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	20.0000			1.01797
$387$	25.9808	+	15.0000i	1.32068	+	0.762493i
$388$		0			0
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$	11.1962	−	7.39230i	0.566939	−	0.374324i
$391$	−2.00000			−0.101144
$392$		0			0
$393$		−	60.0000i		−	3.02660i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	22.3205	−	1.33975i	1.12307	−	0.0674099i
$396$		0			0
$397$	27.7128	+	16.0000i	1.39087	+	0.803017i	0.993411	−	0.114605i	$-0.0365601\pi$
$397$	27.7128	+	16.0000i	1.39087	+	0.803017i	0.397455	+	0.917622i	$0.369893\pi$
$398$		−	12.0000i		−	0.601506i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	18.1865	−	10.5000i	0.907062	−	0.523692i
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$	7.50000	−	12.9904i	0.373139	−	0.646296i
$405$	−9.00000	+	18.0000i	−0.447214	+	0.894427i
$406$		0			0
$407$		0			0
$408$	−5.19615	−	3.00000i	−0.257248	−	0.148522i
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	0.995968	−	0.0897044i	$-0.0285922\pi$
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	−0.575670	+	0.817682i	$0.695259\pi$
$410$	−0.401924	−	6.69615i	−0.0198496	−	0.330699i
$411$	−24.0000	+	41.5692i	−1.18383	+	2.05046i
$412$		−	11.0000i		−	0.541931i
$413$		0			0
$414$	6.00000			0.294884
$415$	16.7942	−	11.0885i	0.824396	−	0.544311i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−20.7846	+	12.0000i	−1.01783	+	0.587643i
$418$		0			0
$419$	−40.0000			−1.95413			−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000			−1.95413			−0.977064	+	0.212946i	$0.931694\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$	−15.5885	−	9.00000i	−0.758834	−	0.438113i
$423$	−41.5692	+	24.0000i	−2.02116	+	1.16692i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−1.19615	−	9.92820i	−0.0580219	−	0.481589i
$426$	18.0000			0.872103
$427$		0			0
$428$		−	7.00000i		−	0.338358i
$429$		0			0
$430$	11.1603	−	0.669873i	0.538195	−	0.0323041i
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	−0.937184	−	0.348836i	$-0.886577\pi$
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	0.166491	−	0.986043i	$-0.446756\pi$
$432$	7.79423	+	4.50000i	0.375000	+	0.216506i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$		0			0
$435$	−6.00000	−	3.00000i	−0.287678	−	0.143839i
$436$	−2.50000	+	4.33013i	−0.119728	+	0.207375i
$437$	1.73205	−	1.00000i	0.0828552	−	0.0478365i
$438$	25.9808	−	15.0000i	1.24141	−	0.716728i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$		0			0
$442$		−	4.00000i		−	0.190261i
$443$	2.59808	+	1.50000i	0.123438	+	0.0712672i	0.560448	−	0.828190i	$-0.310629\pi$
$443$	2.59808	+	1.50000i	0.123438	+	0.0712672i	−0.437009	+	0.899457i	$0.643962\pi$
$444$	−12.0000	−	20.7846i	−0.569495	−	0.986394i
$445$	−15.6244	+	0.937822i	−0.740665	+	0.0444570i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$			45.0000i			2.12843i
$448$		0			0
$449$	−23.0000			−1.08544			−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000			−1.08544			−0.542719	+	0.839915i	$0.682605\pi$
$450$	3.58846	+	29.7846i	0.169161	+	1.40406i
$451$		0			0
$452$	8.66025	−	5.00000i	0.407344	−	0.235180i
$453$	−15.5885	−	9.00000i	−0.732410	−	0.422857i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.979772	−	0.200118i	$-0.0641325\pi$
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.316579	+	0.948566i	$0.397466\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$	9.00000	+	15.5885i	0.420084	+	0.727607i
$460$	1.86603	−	1.23205i	0.0870039	−	0.0574447i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$			25.0000i			1.16185i	0.813958	+	0.580924i	$0.197309\pi$
$463$			25.0000i			1.16185i	−0.813958	+	0.580924i	$0.802691\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	−4.01924	−	66.9615i	−0.186388	−	3.10527i
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−0.866025	−	0.500000i	−0.0400749	−	0.0231372i	0.479829	−	0.877362i	$-0.340699\pi$
$467$	−0.866025	−	0.500000i	−0.0400749	−	0.0231372i	−0.519904	+	0.854225i	$0.674032\pi$
$468$			12.0000i			0.554700i
$469$		0			0
$470$	−8.00000	+	16.0000i	−0.369012	+	0.738025i
$471$	−18.0000	+	31.1769i	−0.829396	+	1.43656i
$472$	1.73205	−	1.00000i	0.0797241	−	0.0460287i
$473$		0			0
$474$	−15.0000	+	25.9808i	−0.688973	+	1.19334i
$475$	6.00000	+	8.00000i	0.275299	+	0.367065i
$476$		0			0
$477$			36.0000i			1.64833i
$478$	8.66025	+	5.00000i	0.396111	+	0.228695i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$	6.69615	−	0.401924i	0.305636	−	0.0183452i
$481$	8.00000	−	13.8564i	0.364769	−	0.631798i
$482$			18.0000i			0.819878i
$483$		0			0
$484$	11.0000			0.500000
$485$		0			0
$486$		0			0
$487$	−3.46410	+	2.00000i	−0.156973	+	0.0906287i	−0.576429	−	0.817147i	$-0.695554\pi$
$487$	−3.46410	+	2.00000i	−0.156973	+	0.0906287i	0.419456	+	0.907776i	$0.362221\pi$
$488$	−7.79423	−	4.50000i	−0.352828	−	0.203705i
$489$	−36.0000			−1.62798
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	7.79423	+	4.50000i	0.351391	+	0.202876i
$493$	−1.73205	+	1.00000i	−0.0780076	+	0.0450377i
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$		0			0
$496$	−10.0000			−0.449013
$497$		0			0
$498$			27.0000i			1.20990i
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	7.23205	+	8.52628i	0.323427	+	0.381307i
$501$	−13.5000	−	23.3827i	−0.603136	−	1.04466i
$502$	8.66025	+	5.00000i	0.386526	+	0.223161i
$503$			5.00000i			0.222939i	0.993768	+	0.111469i	$0.0355557\pi$
$503$			5.00000i			0.222939i	−0.993768	+	0.111469i	$0.964444\pi$
$504$		0			0
$505$	−15.0000	+	30.0000i	−0.667491	+	1.33498i
$506$		0			0
$507$	23.3827	−	13.5000i	1.03846	−	0.599556i
$508$	−6.92820	+	4.00000i	−0.307389	+	0.177471i
$509$	−17.5000	+	30.3109i	−0.775674	+	1.34351i	0.158741	+	0.987320i	$0.449256\pi$
$509$	−17.5000	+	30.3109i	−0.775674	+	1.34351i	−0.934415	+	0.356186i	$0.884077\pi$
$510$	12.0000	+	6.00000i	0.531369	+	0.265684i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−15.5885	−	9.00000i	−0.688247	−	0.397360i
$514$	−6.00000	−	10.3923i	−0.264649	−	0.458385i
$515$	1.47372	+	24.5526i	0.0649399	+	1.08192i
$516$	−7.50000	+	12.9904i	−0.330169	+	0.571870i
$517$		0			0
$518$		0			0
$519$	36.0000			1.58022
$520$	2.46410	+	3.73205i	0.108058	+	0.163661i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	5.19615	−	3.00000i	0.227429	−	0.131306i
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	0.573822	−	0.818980i	$-0.305460\pi$
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	−0.422347	+	0.906434i	$0.638794\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	21.0000			0.915644
$527$	−17.3205	−	10.0000i	−0.754493	−	0.435607i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$	7.39230	+	11.1962i	0.321101	+	0.486330i
$531$	−12.0000			−0.520756
$532$		0			0
$533$			6.00000i			0.259889i
$534$	10.5000	−	18.1865i	0.454379	−	0.787008i
$535$	0.937822	+	15.6244i	0.0405456	+	0.675500i
$536$	3.50000	+	6.06218i	0.151177	+	0.261846i
$537$	−67.5500	−	39.0000i	−2.91500	−	1.68297i
$538$		−	5.00000i		−	0.215565i
$539$		0			0
$540$	−18.0000	−	9.00000i	−0.774597	−	0.387298i
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	5.19615	−	3.00000i	0.223194	−	0.128861i
$543$	−12.9904	+	7.50000i	−0.557471	+	0.321856i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	5.00000	−	10.0000i	0.214176	−	0.428353i
$546$		0			0
$547$		−	37.0000i		−	1.58201i	−0.611812	−	0.791003i	$-0.709559\pi$
$547$		−	37.0000i		−	1.58201i	0.611812	−	0.791003i	$-0.290441\pi$
$548$	−13.8564	−	8.00000i	−0.591916	−	0.341743i
$549$	27.0000	+	46.7654i	1.15233	+	1.99590i
$550$		0			0
$551$	1.00000	−	1.73205i	0.0426014	−	0.0737878i
$552$			3.00000i			0.127688i
$553$		0			0
$554$	26.0000			1.10463
$555$	29.5692	+	44.7846i	1.25514	+	1.90100i
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	3.46410	−	2.00000i	0.146779	−	0.0847427i	−0.424812	−	0.905282i	$-0.639660\pi$
$557$	3.46410	−	2.00000i	0.146779	−	0.0847427i	0.571591	+	0.820539i	$0.306326\pi$
$558$	51.9615	+	30.0000i	2.19971	+	1.27000i
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$	15.5885	+	9.00000i	0.657559	+	0.379642i
$563$	−9.52628	+	5.50000i	−0.401485	+	0.231797i	−0.687124	−	0.726540i	$-0.741127\pi$
$563$	−9.52628	+	5.50000i	−0.401485	+	0.231797i	0.285640	+	0.958337i	$0.407794\pi$
$564$	−12.0000	−	20.7846i	−0.505291	−	0.875190i
$565$	−18.6603	+	12.3205i	−0.785043	+	0.518328i
$566$	−8.00000			−0.336265
$567$		0			0
$568$			6.00000i			0.251754i
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$	−13.3923	+	0.803848i	−0.560942	+	0.0336695i
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	0.951476	−	0.307722i	$-0.0995665\pi$
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	−0.742233	+	0.670142i	$0.766233\pi$
$572$		0			0
$573$		−	60.0000i		−	2.50654i
$574$		0			0
$575$	−4.00000	+	3.00000i	−0.166812	+	0.125109i
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	−13.8564	+	8.00000i	−0.576850	+	0.333044i	−0.759880	−	0.650063i	$-0.774743\pi$
$577$	−13.8564	+	8.00000i	−0.576850	+	0.333044i	0.183031	+	0.983107i	$0.441409\pi$
$578$	−11.2583	+	6.50000i	−0.468285	+	0.270364i
$579$	30.0000	−	51.9615i	1.24676	−	2.15945i
$580$	1.00000	−	2.00000i	0.0415227	−	0.0830455i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$	−1.60770	−	26.7846i	−0.0664700	−	1.10741i
$586$	12.0000	−	20.7846i	0.495715	−	0.858604i
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$	−3.73205	+	2.46410i	−0.153646	+	0.101445i
$591$	12.0000	+	20.7846i	0.493614	+	0.854965i
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.999974	−	0.00727173i	$-0.00231468\pi$
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.493689	+	0.869638i	$0.335648\pi$
$594$		0			0
$595$		0			0
$596$	−15.0000			−0.614424
$597$	−31.1769	−	18.0000i	−1.27599	−	0.736691i
$598$	−1.73205	+	1.00000i	−0.0708288	+	0.0408930i
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$	−14.8923	+	1.79423i	−0.607976	+	0.0732491i
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$		−	42.0000i		−	1.71037i
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	−24.5526	+	1.47372i	−0.998203	+	0.0599153i
$606$	−22.5000	−	38.9711i	−0.914000	−	1.58309i
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	0.409542	−	0.912291i	$-0.365689\pi$
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	−0.585296	+	0.810819i	$0.699022\pi$
$608$			2.00000i			0.0811107i
$609$		0			0
$610$	18.0000	+	9.00000i	0.728799	+	0.364399i
$611$	8.00000	−	13.8564i	0.323645	−	0.560570i
$612$	−10.3923	+	6.00000i	−0.420084	+	0.242536i
$613$	15.5885	−	9.00000i	0.629612	−	0.363507i	−0.150990	−	0.988535i	$-0.548246\pi$
$613$	15.5885	−	9.00000i	0.629612	−	0.363507i	0.780602	+	0.625029i	$0.214913\pi$
$614$	9.50000	−	16.4545i	0.383389	−	0.664049i
$615$	−18.0000	−	9.00000i	−0.725830	−	0.362915i
$616$		0			0
$617$		−	20.0000i		−	0.805170i	−0.915383	−	0.402585i	$-0.868112\pi$
$617$		−	20.0000i		−	0.805170i	0.915383	−	0.402585i	$-0.131888\pi$
$618$	−28.5788	−	16.5000i	−1.14961	−	0.663727i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$	22.3205	−	1.33975i	0.896413	−	0.0538055i
$621$	4.50000	−	7.79423i	0.180579	−	0.312772i
$622$			6.00000i			0.240578i
$623$		0			0
$624$	−6.00000			−0.240192
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	4.00000	+	6.92820i	0.159872	+	0.276907i
$627$		0			0
$628$	−10.3923	−	6.00000i	−0.414698	−	0.239426i
$629$	16.0000			0.637962
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$	−8.66025	−	5.00000i	−0.344486	−	0.198889i
$633$	−46.7654	+	27.0000i	−1.85876	+	1.07315i
$634$	11.0000	+	19.0526i	0.436866	+	0.756674i
$635$	14.9282	−	9.85641i	0.592408	−	0.391140i
$636$	−18.0000			−0.713746
$637$		0			0
$638$		0			0
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$	0.133975	+	2.23205i	0.00529581	+	0.0882296i
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	0.971442	+	0.237276i	$0.0762547\pi$
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	−0.280234	+	0.959932i	$0.590412\pi$
$642$	−18.1865	−	10.5000i	−0.717765	−	0.414402i
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$		0			0
$645$	15.0000	−	30.0000i	0.590624	−	1.18125i
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	−0.0979182	−	0.995194i	$-0.531218\pi$
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	0.812905	+	0.582397i	$0.197885\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$		0			0
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$	−36.3731	−	21.0000i	−1.42339	−	0.821794i	−0.426801	−	0.904345i	$-0.640360\pi$
$653$	−36.3731	−	21.0000i	−1.42339	−	0.821794i	−0.996587	+	0.0825519i	$0.973693\pi$
$654$	7.50000	+	12.9904i	0.293273	+	0.507964i
$655$	−44.6410	+	2.67949i	−1.74427	+	0.104696i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		−	60.0000i		−	2.34082i
$658$		0			0
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	−20.5000	−	35.5070i	−0.797358	−	1.38106i	−0.921331	−	0.388778i	$-0.872897\pi$
$661$	−20.5000	−	35.5070i	−0.797358	−	1.38106i	0.123974	−	0.992286i	$-0.460436\pi$
$662$	−12.1244	+	7.00000i	−0.471226	+	0.272063i
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$	−9.00000			−0.349268
$665$		0			0
$666$	−48.0000			−1.85996
$667$	0.866025	+	0.500000i	0.0335326	+	0.0193601i
$668$	7.79423	−	4.50000i	0.301568	−	0.174110i
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$	−8.62436	−	13.0622i	−0.333188	−	0.504636i
$671$		0			0
$672$		0			0
$673$			20.0000i			0.770943i	0.922720	+	0.385472i	$0.125961\pi$
$673$			20.0000i			0.770943i	−0.922720	+	0.385472i	$0.874039\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	41.3827	+	17.6769i	1.59282	+	0.680385i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	0.532915	−	0.846169i	$-0.321097\pi$
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	−0.466347	+	0.884602i	$0.654430\pi$
$678$		−	30.0000i		−	1.15214i
$679$		0			0
$680$	−2.00000	+	4.00000i	−0.0766965	+	0.153393i
$681$	18.0000	−	31.1769i	0.689761	−	1.19470i
$682$		0			0
$683$	21.6506	−	12.5000i	0.828439	−	0.478299i	−0.0248792	−	0.999690i	$-0.507920\pi$
$683$	21.6506	−	12.5000i	0.828439	−	0.478299i	0.853318	+	0.521391i	$0.174587\pi$
$684$	6.00000	−	10.3923i	0.229416	−	0.397360i
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$		0			0
$687$			30.0000i			1.14457i
$688$	−4.33013	−	2.50000i	−0.165085	−	0.0953116i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$	−0.401924	−	6.69615i	−0.0153010	−	0.254918i
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	−21.0000			−0.797149
$695$	9.85641	+	14.9282i	0.373875	+	0.566259i
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$	−5.19615	+	3.00000i	−0.196818	+	0.113633i
$698$	−7.79423	−	4.50000i	−0.295016	−	0.170328i
$699$	42.0000			1.58859
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$	15.5885	+	9.00000i	0.588348	+	0.339683i
$703$	−13.8564	+	8.00000i	−0.522604	+	0.301726i
$704$		0			0
$705$	29.5692	+	44.7846i	1.11364	+	1.68669i
$706$	6.00000			0.225813
$707$		0			0
$708$		−	6.00000i		−	0.225494i
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	−0.938069	−	0.346449i	$-0.887387\pi$
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	0.769068	+	0.639167i	$0.220721\pi$
$710$	−0.803848	−	13.3923i	−0.0301679	−	0.502604i
$711$	30.0000	+	51.9615i	1.12509	+	1.94871i
$712$	6.06218	+	3.50000i	0.227190	+	0.131168i
$713$			10.0000i			0.374503i
$714$		0			0
$715$		0			0
$716$	13.0000	−	22.5167i	0.485833	−	0.841487i
$717$	25.9808	−	15.0000i	0.970269	−	0.560185i
$718$	−12.1244	+	7.00000i	−0.452477	+	0.261238i
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	−0.990016	−	0.140955i	$-0.954983\pi$
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	0.617079	+	0.786901i	$0.288316\pi$
$720$	6.00000	−	12.0000i	0.223607	−	0.447214i
$721$		0			0
$722$			15.0000i			0.558242i
$723$	46.7654	+	27.0000i	1.73922	+	1.00414i
$724$	−2.50000	−	4.33013i	−0.0929118	−	0.160928i
$725$	−1.96410	+	4.59808i	−0.0729449	+	0.170768i
$726$	16.5000	−	28.5788i	0.612372	−	1.06066i
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−12.3205	−	18.6603i	−0.456002	−	0.690647i
$731$	−5.00000	−	8.66025i	−0.184932	−	0.320311i
$732$	−23.3827	+	13.5000i	−0.864249	+	0.498974i
$733$	−13.8564	−	8.00000i	−0.511798	−	0.295487i	0.221774	−	0.975098i	$-0.428815\pi$
$733$	−13.8564	−	8.00000i	−0.511798	−	0.295487i	−0.733572	+	0.679611i	$0.762148\pi$
$734$	−23.0000			−0.848945
$735$		0			0
$736$	−1.00000			−0.0368605
$737$		0			0
$738$	15.5885	−	9.00000i	0.573819	−	0.331295i
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	−14.9282	+	9.85641i	−0.548772	+	0.362329i
$741$	12.0000			0.440831
$742$		0			0
$743$		−	3.00000i		−	0.110059i	−0.998485	−	0.0550297i	$-0.982475\pi$
$743$		−	3.00000i		−	0.110059i	0.998485	−	0.0550297i	$-0.0175253\pi$
$744$	−15.0000	+	25.9808i	−0.549927	+	0.952501i
$745$	33.4808	−	2.00962i	1.22664	−	0.0736267i
$746$	−4.00000	−	6.92820i	−0.146450	−	0.253660i
$747$	46.7654	+	27.0000i	1.71106	+	0.987878i
$748$		0			0
$749$		0			0
$750$	33.0000	−	6.00000i	1.20499	−	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	$0.189918\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$	25.9808	−	15.0000i	0.946792	−	0.546630i
$754$	−1.00000	+	1.73205i	−0.0364179	+	0.0630776i
$755$	−6.00000	+	12.0000i	−0.218362	+	0.436725i
$756$		0			0
$757$			6.00000i			0.218074i	0.994038	+	0.109037i	$0.0347767\pi$
$757$			6.00000i			0.218074i	−0.994038	+	0.109037i	$0.965223\pi$
$758$	1.73205	+	1.00000i	0.0629109	+	0.0363216i
$759$		0			0
$760$	−0.267949	−	4.46410i	−0.00971954	−	0.161930i
$761$	−25.0000	+	43.3013i	−0.906249	+	1.56967i	−0.0870179	+	0.996207i	$0.527734\pi$
$761$	−25.0000	+	43.3013i	−0.906249	+	1.56967i	−0.819231	+	0.573463i	$0.805600\pi$
$762$			24.0000i			0.869428i
$763$		0			0
$764$	20.0000			0.723575
$765$	22.3923	−	14.7846i	0.809595	−	0.534539i
$766$	−4.50000	−	7.79423i	−0.162592	−	0.281617i
$767$	3.46410	−	2.00000i	0.125081	−	0.0722158i
$768$	−2.59808	−	1.50000i	−0.0937500	−	0.0541266i
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$	17.3205	+	10.0000i	0.623379	+	0.359908i
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$	15.0000	+	25.9808i	0.539164	+	0.933859i
$775$	−49.6410	+	5.98076i	−1.78316	+	0.214835i
$776$		0			0
$777$		0			0
$778$		−	18.0000i		−	0.645331i
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	13.3923	−	0.803848i	0.479521	−	0.0287824i
$781$		0			0
$782$	−1.73205	−	1.00000i	−0.0619380	−	0.0357599i
$783$		−	9.00000i		−	0.321634i
$784$		0			0
$785$	24.0000	+	12.0000i	0.856597	+	0.428298i
$786$	30.0000	−	51.9615i	1.07006	−	1.85341i
$787$	18.1865	−	10.5000i	0.648280	−	0.374285i	−0.139517	−	0.990220i	$-0.544555\pi$
$787$	18.1865	−	10.5000i	0.648280	−	0.374285i	0.787797	+	0.615935i	$0.211222\pi$
$788$	−6.92820	+	4.00000i	−0.246807	+	0.142494i
$789$	31.5000	−	54.5596i	1.12143	−	1.94237i
$790$	20.0000	+	10.0000i	0.711568	+	0.355784i
$791$		0			0
$792$		0			0
$793$	−15.5885	−	9.00000i	−0.553562	−	0.319599i
$794$	16.0000	+	27.7128i	0.567819	+	0.983491i
$795$	40.1769	−	2.41154i	1.42493	−	0.0855286i
$796$	6.00000	−	10.3923i	0.212664	−	0.368345i
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	−0.598076	−	4.96410i	−0.0211452	−	0.175507i
$801$	−21.0000	−	36.3731i	−0.741999	−	1.28518i
$802$	−2.59808	+	1.50000i	−0.0917413	+	0.0529668i
$803$		0			0
$804$	21.0000			0.740613
$805$		0			0
$806$	−20.0000			−0.704470
$807$	−12.9904	−	7.50000i	−0.457283	−	0.264013i
$808$	12.9904	−	7.50000i	0.457000	−	0.263849i
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	0.997649	−	0.0685291i	$-0.0218306\pi$
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	−0.558173	+	0.829725i	$0.688497\pi$
$810$	−16.7942	+	11.0885i	−0.590089	+	0.389609i
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$		0			0
$813$		−	18.0000i		−	0.631288i
$814$		0			0
$815$	1.60770	+	26.7846i	0.0563151	+	0.938224i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	8.66025	+	5.00000i	0.302984	+	0.174928i
$818$			17.0000i			0.594391i
$819$		0			0
$820$	3.00000	−	6.00000i	0.104765	−	0.209529i
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$	−41.5692	+	24.0000i	−1.44989	+	0.837096i
$823$	−38.9711	+	22.5000i	−1.35845	+	0.784301i	−0.989415	−	0.145115i	$-0.953645\pi$
$823$	−38.9711	+	22.5000i	−1.35845	+	0.784301i	−0.369034	+	0.929416i	$0.620311\pi$
$824$	5.50000	−	9.52628i	0.191602	−	0.331864i
$825$		0			0
$826$		0			0
$827$			37.0000i			1.28662i	0.765607	+	0.643308i	$0.222439\pi$
$827$			37.0000i			1.28662i	−0.765607	+	0.643308i	$0.777561\pi$
$828$	5.19615	+	3.00000i	0.180579	+	0.104257i
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$	20.0885	−	1.20577i	0.697281	−	0.0418529i
$831$	39.0000	−	67.5500i	1.35290	−	2.34328i
$832$		−	2.00000i		−	0.0693375i
$833$		0			0
$834$	−24.0000			−0.831052
$835$	−16.7942	+	11.0885i	−0.581188	+	0.383732i
$836$		0			0
$837$	77.9423	−	45.0000i	2.69408	−	1.55543i
$838$	−34.6410	−	20.0000i	−1.19665	−	0.690889i
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	26.8468	+	15.5000i	0.925201	+	0.534165i
$843$	46.7654	−	27.0000i	1.61068	−	0.929929i
$844$	−9.00000	−	15.5885i	−0.309793	−	0.536577i
$845$	−11.0885	−	16.7942i	−0.381455	−	0.577739i
$846$	−48.0000			−1.65027
$847$		0			0
$848$		−	6.00000i		−	0.206041i
$849$	−12.0000	+	20.7846i	−0.411839	+	0.713326i
$850$	3.92820	−	9.19615i	0.134736	−	0.315425i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$	15.5885	+	9.00000i	0.534052	+	0.308335i
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$	−12.0000	+	24.0000i	−0.410391	+	0.820783i
$856$	3.50000	−	6.06218i	0.119628	−	0.207201i
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	−0.557998	−	0.829843i	$-0.688430\pi$
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	0.439666	+	0.898161i	$0.355097\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	10.0000	+	5.00000i	0.340997	+	0.170499i
$861$		0			0
$862$		−	32.0000i		−	1.08992i
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	0.653298	−	0.757101i	$-0.273385\pi$
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	−0.329020	+	0.944323i	$0.606718\pi$
$864$	4.50000	+	7.79423i	0.153093	+	0.265165i
$865$	−1.60770	−	26.7846i	−0.0546633	−	0.910704i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$			39.0000i			1.32451i
$868$		0			0
$869$		0			0
$870$	−3.69615	−	5.59808i	−0.125311	−	0.189793i
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$	−4.33013	+	2.50000i	−0.146637	+	0.0846607i
$873$		0			0
$874$	2.00000			0.0676510
$875$		0			0
$876$	30.0000			1.01361
$877$	−12.1244	−	7.00000i	−0.409410	−	0.236373i	0.281126	−	0.959671i	$-0.409292\pi$
$877$	−12.1244	−	7.00000i	−0.409410	−	0.236373i	−0.690536	+	0.723298i	$0.742625\pi$
$878$	−6.92820	+	4.00000i	−0.233816	+	0.134993i
$879$	−36.0000	−	62.3538i	−1.21425	−	2.10314i
$880$		0			0
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$		0			0
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$	0.803848	+	13.3923i	0.0270210	+	0.450177i
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	0.363407	−	0.931630i	$-0.381613\pi$
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	−0.625112	+	0.780535i	$0.714947\pi$
$888$		−	24.0000i		−	0.805387i
$889$		0			0
$890$	−14.0000	−	7.00000i	−0.469281	−	0.234641i
$891$		0			0
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$	−13.8564	+	8.00000i	−0.463687	+	0.267710i
$894$	−22.5000	+	38.9711i	−0.752513	+	1.30339i
$895$	−26.0000	+	52.0000i	−0.869084	+	1.73817i
$896$		0			0
$897$			6.00000i			0.200334i
$898$	−19.9186	−	11.5000i	−0.664692	−	0.383760i
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$	−11.7846	+	27.5885i	−0.392820	+	0.919615i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		0			0
$903$		0			0
$904$	10.0000			0.332595
$905$	6.16025	+	9.33013i	0.204774	+	0.310144i
$906$	−9.00000	−	15.5885i	−0.299005	−	0.517892i
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	−0.0954492	−	0.995434i	$-0.530429\pi$
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	0.814347	+	0.580379i	$0.197095\pi$
$908$	10.3923	+	6.00000i	0.344881	+	0.199117i
$909$	−90.0000			−2.98511
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$	5.19615	+	3.00000i	0.172062	+	0.0993399i
$913$		0			0
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$	50.3827	−	33.2654i	1.66560	−	1.09972i
$916$	−10.0000			−0.330409
$917$		0			0
$918$			18.0000i			0.594089i
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	0.996770	+	0.0803145i	$0.0255924\pi$
$920$	2.23205	−	0.133975i	0.0735885	−	0.00441701i
$921$	−28.5000	−	49.3634i	−0.939107	−	1.62658i
$922$	12.1244	+	7.00000i	0.399294	+	0.230533i
$923$			12.0000i			0.394985i
$924$		0			0
$925$	32.0000	−	24.0000i	1.05215	−	0.789115i
$926$	−12.5000	+	21.6506i	−0.410775	+	0.711484i
$927$	−57.1577	+	33.0000i	−1.87730	+	1.08386i
$928$	−0.866025	+	0.500000i	−0.0284287	+	0.0164133i
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$	30.0000	−	60.0000i	0.983739	−	1.96748i
$931$		0			0
$932$			14.0000i			0.458585i
$933$	15.5885	+	9.00000i	0.510343	+	0.294647i
$934$	−0.500000	−	0.866025i	−0.0163605	−	0.0283372i
$935$		0			0
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$		−	56.0000i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$937$		−	56.0000i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$938$		0			0
$939$	24.0000			0.783210
$940$	−14.9282	+	9.85641i	−0.486904	+	0.321481i
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	0.957273	−	0.289187i	$-0.0933848\pi$
$941$	7.00000	+	12.1244i	0.228193	+	0.395243i	−0.729079	+	0.684429i	$0.760051\pi$
$942$	−31.1769	+	18.0000i	−1.01580	+	0.586472i
$943$	2.59808	+	1.50000i	0.0846050	+	0.0488467i
$944$	2.00000			0.0650945
$945$		0			0
$946$		0			0
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	0.457193	−	0.889368i	$-0.348855\pi$
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	−0.541619	+	0.840624i	$0.682188\pi$
$948$	−25.9808	+	15.0000i	−0.843816	+	0.487177i
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$	1.19615	+	9.92820i	0.0388083	+	0.322113i
$951$	66.0000			2.14020
$952$		0			0
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$	−18.0000	+	31.1769i	−0.582772	+	1.00939i
$955$	−44.6410	+	2.67949i	−1.44455	+	0.0867063i
$956$	5.00000	+	8.66025i	0.161712	+	0.280093i
$957$		0			0
$958$		−	18.0000i		−	0.581554i
$959$		0			0
$960$	6.00000	+	3.00000i	0.193649	+	0.0968246i
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	13.8564	−	8.00000i	0.446748	−	0.257930i
$963$	−36.3731	+	21.0000i	−1.17211	+	0.676716i
$964$	−9.00000	+	15.5885i	−0.289870	+	0.502070i
$965$	−40.0000	−	20.0000i	−1.28765	−	0.643823i
$966$		0			0
$967$		−	17.0000i		−	0.546683i	−0.961917	−	0.273342i	$-0.911871\pi$
$967$		−	17.0000i		−	0.546683i	0.961917	−	0.273342i	$-0.0881289\pi$
$968$	9.52628	+	5.50000i	0.306186	+	0.176777i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$		0			0
$974$	−4.00000			−0.128168
$975$	−29.7846	+	3.58846i	−0.953871	+	0.114923i
$976$	−4.50000	−	7.79423i	−0.144041	−	0.249487i
$977$	−31.1769	+	18.0000i	−0.997438	+	0.575871i	−0.907489	−	0.420075i	$-0.862004\pi$
$977$	−31.1769	+	18.0000i	−0.997438	+	0.575871i	−0.0899487	+	0.995946i	$0.528670\pi$
$978$	−31.1769	−	18.0000i	−0.996928	−	0.575577i
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$	−15.5885	−	9.00000i	−0.497448	−	0.287202i
$983$	−21.6506	+	12.5000i	−0.690548	+	0.398688i	−0.803817	−	0.594876i	$-0.797201\pi$
$983$	−21.6506	+	12.5000i	−0.690548	+	0.398688i	0.113269	+	0.993564i	$0.463868\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	14.9282	−	9.85641i	0.475652	−	0.314051i
$986$	−2.00000			−0.0636930
$987$		0			0
$988$			4.00000i			0.127257i
$989$	−2.50000	+	4.33013i	−0.0794954	+	0.137690i
$990$		0			0
$991$	13.0000	+	22.5167i	0.412959	+	0.715265i	0.995212	−	0.0977423i	$-0.0311621\pi$
$991$	13.0000	+	22.5167i	0.412959	+	0.715265i	−0.582253	+	0.813008i	$0.697829\pi$
$992$	−8.66025	−	5.00000i	−0.274963	−	0.158750i
$993$			42.0000i			1.33283i
$994$		0			0
$995$	−12.0000	+	24.0000i	−0.380426	+	0.760851i
$996$	−13.5000	+	23.3827i	−0.427764	+	0.740909i
$997$	29.4449	−	17.0000i	0.932528	−	0.538395i	0.0449179	−	0.998991i	$-0.485697\pi$
$997$	29.4449	−	17.0000i	0.932528	−	0.538395i	0.887610	+	0.460595i	$0.152364\pi$
$998$	13.8564	−	8.00000i	0.438617	−	0.253236i
$999$	−36.0000	+	62.3538i	−1.13899	+	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.i.b.79.2		4
5.4	even	2	inner	490.2.i.b.79.1		4
7.2	even	3		490.2.c.b.99.1		2
7.3	odd	6		70.2.i.a.39.1	yes	4
7.4	even	3	inner	490.2.i.b.459.1		4
7.5	odd	6		490.2.c.c.99.1		2
7.6	odd	2		70.2.i.a.9.2	yes	4
21.17	even	6		630.2.u.b.109.2		4
21.20	even	2		630.2.u.b.289.1		4
28.3	even	6		560.2.bw.c.529.1		4
28.27	even	2		560.2.bw.c.289.2		4
35.2	odd	12		2450.2.a.bh.1.1		1
35.3	even	12		350.2.e.g.151.1		2
35.4	even	6	inner	490.2.i.b.459.2		4
35.9	even	6		490.2.c.b.99.2		2
35.12	even	12		2450.2.a.s.1.1		1
35.13	even	4		350.2.e.g.51.1		2
35.17	even	12		350.2.e.f.151.1		2
35.19	odd	6		490.2.c.c.99.2		2
35.23	odd	12		2450.2.a.c.1.1		1
35.24	odd	6		70.2.i.a.39.2	yes	4
35.27	even	4		350.2.e.f.51.1		2
35.33	even	12		2450.2.a.r.1.1		1
35.34	odd	2		70.2.i.a.9.1	✓	4
105.59	even	6		630.2.u.b.109.1		4
105.104	even	2		630.2.u.b.289.2		4
140.59	even	6		560.2.bw.c.529.2		4
140.139	even	2		560.2.bw.c.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	35.34	odd	2
70.2.i.a.9.2	yes	4	7.6	odd	2
70.2.i.a.39.1	yes	4	7.3	odd	6
70.2.i.a.39.2	yes	4	35.24	odd	6
350.2.e.f.51.1		2	35.27	even	4
350.2.e.f.151.1		2	35.17	even	12
350.2.e.g.51.1		2	35.13	even	4
350.2.e.g.151.1		2	35.3	even	12
490.2.c.b.99.1		2	7.2	even	3
490.2.c.b.99.2		2	35.9	even	6
490.2.c.c.99.1		2	7.5	odd	6
490.2.c.c.99.2		2	35.19	odd	6
490.2.i.b.79.1		4	5.4	even	2	inner
490.2.i.b.79.2		4	1.1	even	1	trivial
490.2.i.b.459.1		4	7.4	even	3	inner
490.2.i.b.459.2		4	35.4	even	6	inner
560.2.bw.c.289.1		4	140.139	even	2
560.2.bw.c.289.2		4	28.27	even	2
560.2.bw.c.529.1		4	28.3	even	6
560.2.bw.c.529.2		4	140.59	even	6
630.2.u.b.109.1		4	105.59	even	6
630.2.u.b.109.2		4	21.17	even	6
630.2.u.b.289.1		4	21.20	even	2
630.2.u.b.289.2		4	105.104	even	2
2450.2.a.c.1.1		1	35.23	odd	12
2450.2.a.r.1.1		1	35.33	even	12
2450.2.a.s.1.1		1	35.12	even	12
2450.2.a.bh.1.1		1	35.2	odd	12

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +3.00000 q^{6} +1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +3.00000 q^{6} +1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(-0.133975 - 2.23205i) q^{10} +(2.59808 + 1.50000i) q^{12} +2.00000i q^{13} +(-6.00000 - 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(5.19615 - 3.00000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(1.00000 - 2.00000i) q^{20} +(0.866025 + 0.500000i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(-1.00000 + 1.73205i) q^{26} -9.00000i q^{27} +1.00000 q^{29} +(-3.69615 - 5.59808i) q^{30} +(5.00000 + 8.66025i) q^{31} +(-0.866025 + 0.500000i) q^{32} -2.00000 q^{34} +6.00000 q^{36} +(-6.92820 - 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(1.86603 - 1.23205i) q^{40} +3.00000 q^{41} +5.00000i q^{43} +(-13.3923 + 0.803848i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-6.92820 - 4.00000i) q^{47} +3.00000i q^{48} +(-4.00000 + 3.00000i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(4.50000 - 7.79423i) q^{54} -6.00000i q^{57} +(0.866025 + 0.500000i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(-0.401924 - 6.69615i) q^{60} +(-4.50000 + 7.79423i) q^{61} +10.0000i q^{62} -1.00000 q^{64} +(3.73205 - 2.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +3.00000 q^{69} +6.00000 q^{71} +(5.19615 + 3.00000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(1.79423 + 14.8923i) q^{75} +2.00000 q^{76} +6.00000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(2.23205 - 0.133975i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 1.50000i) q^{82} +9.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(2.59808 - 1.50000i) q^{87} +(3.50000 - 6.06218i) q^{89} +(-12.0000 - 6.00000i) q^{90} +1.00000i q^{92} +(25.9808 + 15.0000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(-4.46410 + 0.267949i) q^{95} +(-1.50000 + 2.59808i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^5 + 12 * q^6 + 12 * q^9	\( 4 q + 2 q^{4} + 2 q^{5} + 12 q^{6} + 12 q^{9} - 4 q^{10} - 24 q^{15} - 2 q^{16} + 4 q^{19} + 4 q^{20} + 6 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{29} + 6 q^{30} + 20 q^{31} - 8 q^{34} + 24 q^{36} + 12 q^{39} + 4 q^{40} + 12 q^{41} - 12 q^{45} + 2 q^{46} - 16 q^{50} - 12 q^{51} + 18 q^{54} - 4 q^{59} - 12 q^{60} - 18 q^{61} - 4 q^{64} + 8 q^{65} + 12 q^{69} + 24 q^{71} - 16 q^{74} - 24 q^{75} + 8 q^{76} - 20 q^{79} + 2 q^{80} - 18 q^{81} + 16 q^{85} - 10 q^{86} + 14 q^{89} - 48 q^{90} - 16 q^{94} - 4 q^{95} - 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^5 + 12 * q^6 + 12 * q^9 - 4 * q^10 - 24 * q^15 - 2 * q^16 + 4 * q^19 + 4 * q^20 + 6 * q^24 + 6 * q^25 - 4 * q^26 + 4 * q^29 + 6 * q^30 + 20 * q^31 - 8 * q^34 + 24 * q^36 + 12 * q^39 + 4 * q^40 + 12 * q^41 - 12 * q^45 + 2 * q^46 - 16 * q^50 - 12 * q^51 + 18 * q^54 - 4 * q^59 - 12 * q^60 - 18 * q^61 - 4 * q^64 + 8 * q^65 + 12 * q^69 + 24 * q^71 - 16 * q^74 - 24 * q^75 + 8 * q^76 - 20 * q^79 + 2 * q^80 - 18 * q^81 + 16 * q^85 - 10 * q^86 + 14 * q^89 - 48 * q^90 - 16 * q^94 - 4 * q^95 - 6 * q^96

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