LMFDB - Embedded newform 490.2.e.b.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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([0, 4]))

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.2.e.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 + 3.46410i) q^{11} +(-1.00000 + 1.73205i) q^{12} +2.00000 q^{13} +2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.00000 - 5.19615i) q^{19} +1.00000 q^{20} -4.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.00000 - 6.92820i) q^{33} +8.00000 q^{34} +1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(3.00000 + 5.19615i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-0.500000 + 0.866025i) q^{40} +4.00000 q^{41} +4.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-2.00000 + 3.46410i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(-8.00000 + 13.8564i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(2.00000 - 3.46410i) q^{54} -4.00000 q^{55} -12.0000 q^{57} +(3.00000 - 5.19615i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(5.00000 - 8.66025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(4.00000 + 6.92820i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-4.00000 + 6.92820i) q^{68} -8.00000 q^{69} +12.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-1.00000 + 1.73205i) q^{75} -6.00000 q^{76} +4.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-2.00000 + 3.46410i) q^{82} -2.00000 q^{83} +8.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(6.00000 + 10.3923i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-4.00000 + 6.92820i) q^{89} +1.00000 q^{90} -4.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(3.00000 + 5.19615i) q^{95} +(-1.00000 + 1.73205i) q^{96} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{13} + 4 q^{15} - q^{16} - 8 q^{17} - q^{18} + 6 q^{19} + 2 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{24} - q^{25} - 2 q^{26} - 8 q^{27} - 12 q^{29} - 2 q^{30} - 4 q^{31} - q^{32} + 8 q^{33} + 16 q^{34} + 2 q^{36} + 10 q^{37} + 6 q^{38} - 4 q^{39} - q^{40} + 8 q^{41} + 8 q^{43} + 4 q^{44} - q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 2 q^{50} - 16 q^{51} - 2 q^{52} - 10 q^{53} + 4 q^{54} - 8 q^{55} - 24 q^{57} + 6 q^{58} + 14 q^{59} - 2 q^{60} + 10 q^{61} + 8 q^{62} + 2 q^{64} - 2 q^{65} + 8 q^{66} + 4 q^{67} - 8 q^{68} - 16 q^{69} + 24 q^{71} - q^{72} - 4 q^{73} + 10 q^{74} - 2 q^{75} - 12 q^{76} + 8 q^{78} - 4 q^{79} - q^{80} + 11 q^{81} - 4 q^{82} - 4 q^{83} + 16 q^{85} - 4 q^{86} + 12 q^{87} + 4 q^{88} - 8 q^{89} + 2 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9 - q^10 + 4 * q^11 - 2 * q^12 + 4 * q^13 + 4 * q^15 - q^16 - 8 * q^17 - q^18 + 6 * q^19 + 2 * q^20 - 8 * q^22 + 4 * q^23 - 2 * q^24 - q^25 - 2 * q^26 - 8 * q^27 - 12 * q^29 - 2 * q^30 - 4 * q^31 - q^32 + 8 * q^33 + 16 * q^34 + 2 * q^36 + 10 * q^37 + 6 * q^38 - 4 * q^39 - q^40 + 8 * q^41 + 8 * q^43 + 4 * q^44 - q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 2 * q^50 - 16 * q^51 - 2 * q^52 - 10 * q^53 + 4 * q^54 - 8 * q^55 - 24 * q^57 + 6 * q^58 + 14 * q^59 - 2 * q^60 + 10 * q^61 + 8 * q^62 + 2 * q^64 - 2 * q^65 + 8 * q^66 + 4 * q^67 - 8 * q^68 - 16 * q^69 + 24 * q^71 - q^72 - 4 * q^73 + 10 * q^74 - 2 * q^75 - 12 * q^76 + 8 * q^78 - 4 * q^79 - q^80 + 11 * q^81 - 4 * q^82 - 4 * q^83 + 16 * q^85 - 4 * q^86 + 12 * q^87 + 4 * q^88 - 8 * q^89 + 2 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^99

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	2.00000			0.816497
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.275029	−	0.961436i	$-0.588688\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−4.00000			−0.852803
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	4.00000	−	6.92820i	0.696311	−	1.20605i
$34$	8.00000			1.37199
$35$		0			0
$36$	1.00000			0.166667
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	−0.974219	−	0.225605i	$-0.927564\pi$
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	0.682489	+	0.730896i	$0.260898\pi$
$48$	2.00000			0.288675
$49$		0			0
$50$	1.00000			0.141421
$51$	−8.00000	+	13.8564i	−1.12022	+	1.94029i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	−0.972867	−	0.231367i	$-0.925680\pi$
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	0.286064	−	0.958211i	$-0.407653\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	−4.00000			−0.539360
$56$		0			0
$57$	−12.0000			−1.58944
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.812198	+	0.583382i	$0.198271\pi$
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.0991242	+	0.995075i	$0.468396\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$	4.00000	+	6.92820i	0.492366	+	0.852803i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−4.00000	+	6.92820i	−0.485071	+	0.840168i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$	−6.00000			−0.688247
$77$		0			0
$78$	4.00000			0.452911
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	8.00000			0.867722
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	−0.996326	−	0.0856373i	$-0.972707\pi$
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	0.572327	+	0.820025i	$0.306041\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	−4.00000			−0.417029
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	−1.00000	+	1.73205i	−0.102062	+	0.176777i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	−8.00000	−	13.8564i	−0.792118	−	1.37199i
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	10.0000			0.971286
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	−20.0000			−1.89832
$112$		0			0
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$	6.00000	−	10.3923i	0.561951	−	0.973329i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−14.0000			−1.28880
$119$		0			0
$120$	2.00000			0.182574
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$	−8.00000			−0.696311
$133$		0			0
$134$	−4.00000			−0.345547
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$	−4.00000	−	6.92820i	−0.342997	−	0.594089i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	4.00000			0.331042
$147$		0			0
$148$	−10.0000			−0.821995
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	8.00000			0.646762
$154$		0			0
$155$	4.00000			0.321288
$156$	−2.00000	+	3.46410i	−0.160128	+	0.277350i
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	−10.0000	+	17.3205i	−0.793052	+	1.37361i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−11.0000			−0.864242
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$	4.00000	+	6.92820i	0.311400	+	0.539360i
$166$	1.00000	−	1.73205i	0.0776151	−	0.134433i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	−4.00000			−0.301511
$177$	14.0000	−	24.2487i	1.05230	−	1.82264i
$178$	−4.00000	−	6.92820i	−0.299813	−	0.519291i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$		0			0
$183$	−20.0000			−1.47844
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	16.0000	−	27.7128i	1.17004	−	2.02656i
$188$	4.00000			0.291730
$189$		0			0
$190$	−6.00000			−0.435286
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$	−2.00000			−0.140720
$203$		0			0
$204$	16.0000			1.12022
$205$	−2.00000	+	3.46410i	−0.139686	+	0.241943i
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	24.0000			1.66011
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$	−12.0000	−	20.7846i	−0.822226	−	1.42414i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−2.00000	+	3.46410i	−0.136399	+	0.236250i
$216$	−4.00000			−0.272166
$217$		0			0
$218$	10.0000			0.677285
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	−8.00000	−	13.8564i	−0.538138	−	0.932083i
$222$	10.0000	−	17.3205i	0.671156	−	1.16248i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$	−4.00000			−0.263752
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	0.240112	+	0.970745i	$0.422816\pi$
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	−0.960746	+	0.277429i	$0.910518\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	−2.00000	−	3.46410i	−0.130466	−	0.225973i
$236$	7.00000	−	12.1244i	0.455661	−	0.789228i
$237$	8.00000			0.519656
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$	−1.00000	+	1.73205i	−0.0645497	+	0.111803i
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	0.794393	−	0.607404i	$-0.207789\pi$
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	−0.923224	+	0.384262i	$0.874456\pi$
$242$	−2.50000	−	4.33013i	−0.160706	−	0.278351i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	8.00000			0.510061
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	2.00000	+	3.46410i	0.126745	+	0.219529i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	22.0000			1.38863			0.694314	−	0.719672i	$-0.255708\pi$
$251$	22.0000			1.38863			0.694314	+	0.719672i	$0.255708\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$	−8.00000	−	13.8564i	−0.500979	−	0.867722i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	8.00000			0.498058
$259$		0			0
$260$	2.00000			0.124035
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−9.00000	−	15.5885i	−0.556022	−	0.963058i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	4.00000	−	6.92820i	0.246183	−	0.426401i
$265$	10.0000			0.614295
$266$		0			0
$267$	16.0000			0.979184
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−13.0000	−	22.5167i	−0.792624	−	1.37287i	−0.924337	−	0.381577i	$-0.875381\pi$
$269$	−13.0000	−	22.5167i	−0.792624	−	1.37287i	0.131713	−	0.991288i	$-0.457952\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$	8.00000			0.485071
$273$		0			0
$274$	−2.00000			−0.120824
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	−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	$0.852470\pi$
$278$	5.00000	−	8.66025i	0.299880	−	0.519408i
$279$	4.00000			0.239474
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	−4.00000	+	6.92820i	−0.238197	+	0.412568i
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	0.936039	+	0.351895i	$0.114463\pi$
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	−0.163270	+	0.986581i	$0.552204\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	6.00000	−	10.3923i	0.355409	−	0.615587i
$286$	−8.00000			−0.473050
$287$		0			0
$288$	1.00000			0.0589256
$289$	−23.5000	+	40.7032i	−1.38235	+	2.39431i
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$		0			0
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	−14.0000			−0.815112
$296$	5.00000	−	8.66025i	0.290619	−	0.503367i
$297$	−8.00000	−	13.8564i	−0.464207	−	0.804030i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$	2.00000			0.115470
$301$		0			0
$302$		0			0
$303$	2.00000	−	3.46410i	0.114897	−	0.199007i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	−8.00000	−	13.8564i	−0.453638	−	0.785725i	0.544970	−	0.838455i	$-0.316541\pi$
$311$	−8.00000	−	13.8564i	−0.453638	−	0.785725i	−0.998609	+	0.0527306i	$0.983208\pi$
$312$	−2.00000	−	3.46410i	−0.113228	−	0.196116i
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	4.00000			0.225018
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−10.0000	−	17.3205i	−0.560772	−	0.971286i
$319$	−12.0000	−	20.7846i	−0.671871	−	1.16371i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−24.0000			−1.33955
$322$		0			0
$323$	−48.0000			−2.67079
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	−10.0000	+	17.3205i	−0.553001	+	0.957826i
$328$	4.00000			0.220863
$329$		0			0
$330$	−8.00000			−0.440386
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	1.00000	+	1.73205i	0.0548821	+	0.0950586i
$333$	5.00000	+	8.66025i	0.273998	+	0.474579i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	2.00000	+	3.46410i	0.108625	+	0.188144i
$340$	−4.00000	−	6.92820i	−0.216930	−	0.375735i
$341$	8.00000	−	13.8564i	0.433224	−	0.750366i
$342$	−6.00000			−0.324443
$343$		0			0
$344$	4.00000			0.215666
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$	6.00000	−	10.3923i	0.321634	−	0.557086i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−8.00000			−0.427008
$352$	2.00000	−	3.46410i	0.106600	−	0.184637i
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	0.980352	−	0.197256i	$-0.0632029\pi$
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	−0.661004	+	0.750382i	$0.729870\pi$
$354$	14.0000	+	24.2487i	0.744092	+	1.28880i
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$	8.00000			0.423999
$357$		0			0
$358$	4.00000			0.211407
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	−0.740951	−	0.671559i	$-0.765625\pi$
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	0.952063	+	0.305903i	$0.0989582\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−13.0000	+	22.5167i	−0.683265	+	1.18345i
$363$	10.0000			0.524864
$364$		0			0
$365$	4.00000			0.209370
$366$	10.0000	−	17.3205i	0.522708	−	0.905357i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	−2.00000	+	3.46410i	−0.104116	+	0.180334i
$370$	−10.0000			−0.519875
$371$		0			0
$372$	8.00000			0.414781
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$	16.0000	+	27.7128i	0.827340	+	1.43300i
$375$	−1.00000	−	1.73205i	−0.0516398	−	0.0894427i
$376$	−2.00000	+	3.46410i	−0.103142	+	0.178647i
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	12.0000	+	20.7846i	0.614779	+	1.06483i
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	−10.0000	+	17.3205i	−0.510976	+	0.885037i	0.488943	+	0.872316i	$0.337383\pi$
$383$	−10.0000	+	17.3205i	−0.510976	+	0.885037i	−0.999919	+	0.0127209i	$0.995951\pi$
$384$	2.00000			0.102062
$385$		0			0
$386$	−18.0000			−0.916176
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$		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	$0.984165\pi$
$390$	−2.00000	+	3.46410i	−0.101274	+	0.175412i
$391$	−32.0000			−1.61831
$392$		0			0
$393$	36.0000			1.81596
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−2.00000	−	3.46410i	−0.100631	−	0.174298i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	0.330075	+	0.943955i	$0.392926\pi$
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	−0.982526	+	0.186124i	$0.940407\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	−0.636609	−	0.771187i	$-0.719663\pi$
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	0.986172	+	0.165726i	$0.0529966\pi$
$402$	4.00000	+	6.92820i	0.199502	+	0.345547i
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$	1.00000	−	1.73205i	0.0497519	−	0.0861727i
$405$	−11.0000			−0.546594
$406$		0			0
$407$	40.0000			1.98273
$408$	−8.00000	+	13.8564i	−0.396059	+	0.685994i
$409$	10.0000	+	17.3205i	0.494468	+	0.856444i	0.999980	−	0.00637586i	$-0.00202951\pi$
$409$	10.0000	+	17.3205i	0.494468	+	0.856444i	−0.505511	+	0.862820i	$0.668696\pi$
$410$	−2.00000	−	3.46410i	−0.0987730	−	0.171080i
$411$	2.00000	−	3.46410i	0.0986527	−	0.170872i
$412$	4.00000			0.197066
$413$		0			0
$414$	−4.00000			−0.196589
$415$	1.00000	−	1.73205i	0.0490881	−	0.0850230i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	10.0000	+	17.3205i	0.489702	+	0.848189i
$418$	−12.0000	+	20.7846i	−0.586939	+	1.01661i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	−10.0000	+	17.3205i	−0.486792	+	0.843149i
$423$	−2.00000	−	3.46410i	−0.0972433	−	0.168430i
$424$	−5.00000	−	8.66025i	−0.242821	−	0.420579i
$425$	−4.00000	+	6.92820i	−0.194029	+	0.336067i
$426$	24.0000			1.16280
$427$		0			0
$428$	−12.0000			−0.580042
$429$	8.00000	−	13.8564i	0.386244	−	0.668994i
$430$	−2.00000	−	3.46410i	−0.0964486	−	0.167054i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−40.0000			−1.92228			−0.961139	−	0.276066i	$-0.910969\pi$
$433$	−40.0000			−1.92228			−0.961139	+	0.276066i	$0.910969\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$	−4.00000	−	6.92820i	−0.191127	−	0.331042i
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	16.0000			0.761042
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	−0.909618	−	0.415445i	$-0.863626\pi$
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	0.814595	+	0.580030i	$0.196959\pi$
$444$	10.0000	+	17.3205i	0.474579	+	0.821995i
$445$	−4.00000	−	6.92820i	−0.189618	−	0.328428i
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$	−20.0000			−0.945968
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	8.00000	+	13.8564i	0.376705	+	0.652473i
$452$	1.00000	+	1.73205i	0.0470360	+	0.0814688i
$453$		0			0
$454$	−18.0000			−0.844782
$455$		0			0
$456$	−12.0000			−0.561951
$457$	−3.00000	+	5.19615i	−0.140334	+	0.243066i	−0.927622	−	0.373519i	$-0.878151\pi$
$457$	−3.00000	+	5.19615i	−0.140334	+	0.243066i	0.787288	+	0.616585i	$0.211484\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$	16.0000	+	27.7128i	0.746816	+	1.29352i
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	−11.0000	−	19.0526i	−0.509565	−	0.882593i
$467$	5.00000	−	8.66025i	0.231372	−	0.400749i	−0.726840	−	0.686807i	$-0.759012\pi$
$467$	5.00000	−	8.66025i	0.231372	−	0.400749i	0.958212	+	0.286058i	$0.0923451\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$	4.00000			0.184506
$471$	−2.00000	+	3.46410i	−0.0921551	+	0.159617i
$472$	7.00000	+	12.1244i	0.322201	+	0.558069i
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$	−6.00000			−0.275299
$476$		0			0
$477$	10.0000			0.457869
$478$	4.00000	−	6.92820i	0.182956	−	0.316889i
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	0.816711	−	0.577047i	$-0.195795\pi$
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	−0.908093	+	0.418769i	$0.862462\pi$
$480$	−1.00000	−	1.73205i	−0.0456435	−	0.0790569i
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$	4.00000			0.182195
$483$		0			0
$484$	5.00000			0.227273
$485$		0			0
$486$	5.00000	+	8.66025i	0.226805	+	0.392837i
$487$	22.0000	+	38.1051i	0.996915	+	1.72671i	0.566429	+	0.824110i	$0.308325\pi$
$487$	22.0000	+	38.1051i	0.996915	+	1.72671i	0.430486	+	0.902597i	$0.358342\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−4.00000	+	6.92820i	−0.180334	+	0.312348i
$493$	24.0000	+	41.5692i	1.08091	+	1.87218i
$494$	6.00000	+	10.3923i	0.269953	+	0.467572i
$495$	2.00000	−	3.46410i	0.0898933	−	0.155700i
$496$	4.00000			0.179605
$497$		0			0
$498$	−4.00000			−0.179244
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−12.0000	−	20.7846i	−0.536120	−	0.928588i
$502$	−11.0000	+	19.0526i	−0.490954	+	0.850357i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	−2.00000			−0.0889988
$506$	−8.00000	+	13.8564i	−0.355643	+	0.615992i
$507$	9.00000	+	15.5885i	0.399704	+	0.692308i
$508$	6.00000	+	10.3923i	0.266207	+	0.461084i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$	16.0000			0.708492
$511$		0			0
$512$	1.00000			0.0441942
$513$	−12.0000	+	20.7846i	−0.529813	+	0.917663i
$514$	−6.00000	−	10.3923i	−0.264649	−	0.458385i
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	−16.0000			−0.703679
$518$		0			0
$519$	36.0000			1.58022
$520$	−1.00000	+	1.73205i	−0.0438529	+	0.0759555i
$521$	6.00000	+	10.3923i	0.262865	+	0.455295i	0.967002	−	0.254769i	$-0.0819994\pi$
$521$	6.00000	+	10.3923i	0.262865	+	0.455295i	−0.704137	+	0.710064i	$0.748666\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	17.0000	−	29.4449i	0.743358	−	1.28753i	−0.207600	−	0.978214i	$-0.566565\pi$
$523$	17.0000	−	29.4449i	0.743358	−	1.28753i	0.950958	−	0.309320i	$-0.100101\pi$
$524$	18.0000			0.786334
$525$		0			0
$526$		0			0
$527$	−16.0000	+	27.7128i	−0.696971	+	1.20719i
$528$	4.00000	+	6.92820i	0.174078	+	0.301511i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−5.00000	+	8.66025i	−0.217186	+	0.376177i
$531$	−14.0000			−0.607548
$532$		0			0
$533$	8.00000			0.346518
$534$	−8.00000	+	13.8564i	−0.346194	+	0.599625i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	−4.00000	+	6.92820i	−0.172613	+	0.298974i
$538$	26.0000			1.12094
$539$		0			0
$540$	−4.00000			−0.172133
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	−26.0000	−	45.0333i	−1.11577	−	1.93256i
$544$	−4.00000	+	6.92820i	−0.171499	+	0.297044i
$545$	10.0000			0.428353
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	−18.0000	+	31.1769i	−0.766826	+	1.32818i
$552$	−8.00000			−0.340503
$553$		0			0
$554$	2.00000			0.0849719
$555$	10.0000	−	17.3205i	0.424476	−	0.735215i
$556$	5.00000	+	8.66025i	0.212047	+	0.367277i
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	0.922557	−	0.385860i	$-0.126095\pi$
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	−0.795443	+	0.606028i	$0.792762\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	8.00000			0.338364
$560$		0			0
$561$	−64.0000			−2.70208
$562$	5.00000	−	8.66025i	0.210912	−	0.365311i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$	−4.00000	−	6.92820i	−0.168430	−	0.291730i
$565$	1.00000	−	1.73205i	0.0420703	−	0.0728679i
$566$	−26.0000			−1.09286
$567$		0			0
$568$	12.0000			0.503509
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	−0.125347	−	0.992113i	$-0.540004\pi$
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	0.921869	−	0.387503i	$-0.126662\pi$
$570$	6.00000	+	10.3923i	0.251312	+	0.435286i
$571$	18.0000	+	31.1769i	0.753277	+	1.30471i	0.946227	+	0.323505i	$0.104861\pi$
$571$	18.0000	+	31.1769i	0.753277	+	1.30471i	−0.192950	+	0.981209i	$0.561806\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$	24.0000			1.00261
$574$		0			0
$575$	−4.00000			−0.166812
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	10.0000	+	17.3205i	0.416305	+	0.721062i	0.995565	−	0.0940813i	$-0.0299914\pi$
$577$	10.0000	+	17.3205i	0.416305	+	0.721062i	−0.579259	+	0.815144i	$0.696658\pi$
$578$	−23.5000	−	40.7032i	−0.977471	−	1.69303i
$579$	18.0000	−	31.1769i	0.748054	−	1.29567i
$580$	−6.00000			−0.249136
$581$		0			0
$582$		0			0
$583$	20.0000	−	34.6410i	0.828315	−	1.43468i
$584$	−2.00000	−	3.46410i	−0.0827606	−	0.143346i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	−3.00000	+	5.19615i	−0.123929	+	0.214651i
$587$	2.00000			0.0825488			0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000			0.0825488			0.0412744	+	0.999148i	$0.486858\pi$
$588$		0			0
$589$	−24.0000			−0.988903
$590$	7.00000	−	12.1244i	0.288185	−	0.499152i
$591$	−18.0000	−	31.1769i	−0.740421	−	1.28245i
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	10.0000	−	17.3205i	0.410651	−	0.711268i	−0.584310	−	0.811530i	$-0.698635\pi$
$593$	10.0000	−	17.3205i	0.410651	−	0.711268i	0.994961	+	0.100262i	$0.0319682\pi$
$594$	16.0000			0.656488
$595$		0			0
$596$	−10.0000			−0.409616
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$	4.00000	+	6.92820i	0.163572	+	0.283315i
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	0.996358	+	0.0852695i	$0.0271751\pi$
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	−0.424333	+	0.905506i	$0.639492\pi$
$600$	−1.00000	+	1.73205i	−0.0408248	+	0.0707107i
$601$	40.0000			1.63163			0.815817	−	0.578310i	$-0.196288\pi$
$601$	40.0000			1.63163			0.815817	+	0.578310i	$0.196288\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$	2.00000	+	3.46410i	0.0812444	+	0.140720i
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	−6.00000			−0.243332
$609$		0			0
$610$	−10.0000			−0.404888
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$	−4.00000	−	6.92820i	−0.161690	−	0.280056i
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$	8.00000			0.322591
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	3.00000	+	5.19615i	0.120580	+	0.208851i	0.919997	−	0.391926i	$-0.128191\pi$
$619$	3.00000	+	5.19615i	0.120580	+	0.208851i	−0.799416	+	0.600777i	$0.794858\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$	−8.00000	+	13.8564i	−0.321029	+	0.556038i
$622$	16.0000			0.641542
$623$		0			0
$624$	4.00000			0.160128
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	4.00000	+	6.92820i	0.159872	+	0.276907i
$627$	−24.0000	−	41.5692i	−0.958468	−	1.66011i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−80.0000			−3.18981
$630$		0			0
$631$	4.00000			0.159237			0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000			0.159237			0.0796187	+	0.996825i	$0.474630\pi$
$632$	−2.00000	+	3.46410i	−0.0795557	+	0.137795i
$633$	−20.0000	−	34.6410i	−0.794929	−	1.37686i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$	20.0000			0.793052
$637$		0			0
$638$	24.0000			0.950169
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	12.0000	−	20.7846i	0.473602	−	0.820303i
$643$	18.0000			0.709851			0.354925	−	0.934895i	$-0.384506\pi$
$643$	18.0000			0.709851			0.354925	+	0.934895i	$0.384506\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$	24.0000	−	41.5692i	0.944267	−	1.63552i
$647$	−14.0000	−	24.2487i	−0.550397	−	0.953315i	−0.998246	−	0.0592060i	$-0.981143\pi$
$647$	−14.0000	−	24.2487i	−0.550397	−	0.953315i	0.447849	−	0.894109i	$-0.352190\pi$
$648$	5.50000	+	9.52628i	0.216060	+	0.374228i
$649$	−28.0000	+	48.4974i	−1.09910	+	1.90369i
$650$	2.00000			0.0784465
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	−10.0000	−	17.3205i	−0.391031	−	0.677285i
$655$	−9.00000	−	15.5885i	−0.351659	−	0.609091i
$656$	−2.00000	+	3.46410i	−0.0780869	+	0.135250i
$657$	4.00000			0.156055
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$	4.00000	−	6.92820i	0.155700	−	0.269680i
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	0.884818	−	0.465937i	$-0.154283\pi$
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	−0.845922	+	0.533306i	$0.820949\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$	−16.0000	+	27.7128i	−0.621389	+	1.07628i
$664$	−2.00000			−0.0776151
$665$		0			0
$666$	−10.0000			−0.387492
$667$	−12.0000	+	20.7846i	−0.464642	+	0.804783i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	40.0000			1.54418
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	23.0000	−	39.8372i	0.883962	−	1.53107i	0.0370628	−	0.999313i	$-0.488200\pi$
$677$	23.0000	−	39.8372i	0.883962	−	1.53107i	0.846899	−	0.531754i	$-0.178467\pi$
$678$	−4.00000			−0.153619
$679$		0			0
$680$	8.00000			0.306786
$681$	18.0000	−	31.1769i	0.689761	−	1.19470i
$682$	8.00000	+	13.8564i	0.306336	+	0.530589i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	3.00000	−	5.19615i	0.114708	−	0.198680i
$685$	−2.00000			−0.0764161
$686$		0			0
$687$	−28.0000			−1.06827
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−10.0000	−	17.3205i	−0.380970	−	0.659859i
$690$	4.00000	+	6.92820i	0.152277	+	0.263752i
$691$	23.0000	−	39.8372i	0.874961	−	1.51548i	0.0181572	−	0.999835i	$-0.494220\pi$
$691$	23.0000	−	39.8372i	0.874961	−	1.51548i	0.856804	−	0.515642i	$-0.172447\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−4.00000			−0.151838
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$	6.00000	+	10.3923i	0.227429	+	0.393919i
$697$	−16.0000	−	27.7128i	−0.606043	−	1.04970i
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	44.0000			1.66423
$700$		0			0
$701$	−38.0000			−1.43524			−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000			−1.43524			−0.717620	+	0.696435i	$0.754769\pi$
$702$	4.00000	−	6.92820i	0.150970	−	0.261488i
$703$	−30.0000	−	51.9615i	−1.13147	−	1.95977i
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$	−12.0000			−0.451626
$707$		0			0
$708$	−28.0000			−1.05230
$709$	−21.0000	+	36.3731i	−0.788672	+	1.36602i	0.138109	+	0.990417i	$0.455897\pi$
$709$	−21.0000	+	36.3731i	−0.788672	+	1.36602i	−0.926781	+	0.375602i	$0.877436\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	−4.00000	+	6.92820i	−0.149906	+	0.259645i
$713$	−16.0000			−0.599205
$714$		0			0
$715$	−8.00000			−0.299183
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$	8.00000	+	13.8564i	0.298765	+	0.517477i
$718$	4.00000	+	6.92820i	0.149279	+	0.258558i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	17.0000			0.632674
$723$	−4.00000	+	6.92820i	−0.148762	+	0.257663i
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	20.0000			0.741759			0.370879	−	0.928681i	$-0.379056\pi$
$727$	20.0000			0.741759			0.370879	+	0.928681i	$0.379056\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−2.00000	+	3.46410i	−0.0740233	+	0.128212i
$731$	−16.0000	−	27.7128i	−0.591781	−	1.02500i
$732$	10.0000	+	17.3205i	0.369611	+	0.640184i
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−8.00000	+	13.8564i	−0.294684	+	0.510407i
$738$	−2.00000	−	3.46410i	−0.0736210	−	0.127515i
$739$	−6.00000	−	10.3923i	−0.220714	−	0.382287i	0.734311	−	0.678813i	$-0.237505\pi$
$739$	−6.00000	−	10.3923i	−0.220714	−	0.382287i	−0.955025	+	0.296526i	$0.904172\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$	−24.0000			−0.881662
$742$		0			0
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$	5.00000	+	8.66025i	0.183186	+	0.317287i
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	1.00000	−	1.73205i	0.0365881	−	0.0633724i
$748$	−32.0000			−1.17004
$749$		0			0
$750$	2.00000			0.0730297
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	0.227153	+	0.973859i	$0.427058\pi$
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	−0.956963	+	0.290209i	$0.906275\pi$
$752$	−2.00000	−	3.46410i	−0.0729325	−	0.126323i
$753$	−22.0000	−	38.1051i	−0.801725	−	1.38863i
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$		0			0
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	2.00000	−	3.46410i	0.0726433	−	0.125822i
$759$	−16.0000	−	27.7128i	−0.580763	−	1.00591i
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	−24.0000			−0.869428
$763$		0			0
$764$	12.0000			0.434145
$765$	−4.00000	+	6.92820i	−0.144620	+	0.250490i
$766$	−10.0000	−	17.3205i	−0.361315	−	0.625815i
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$	−1.00000	+	1.73205i	−0.0360844	+	0.0625000i
$769$	28.0000			1.00971			0.504853	−	0.863205i	$-0.331547\pi$
$769$	28.0000			1.00971			0.504853	+	0.863205i	$0.331547\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	9.00000	−	15.5885i	0.323917	−	0.561041i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$		0			0
$777$		0			0
$778$	18.0000			0.645331
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$	−2.00000	−	3.46410i	−0.0716115	−	0.124035i
$781$	24.0000	+	41.5692i	0.858788	+	1.48746i
$782$	16.0000	−	27.7128i	0.572159	−	0.991008i
$783$	24.0000			0.857690
$784$		0			0
$785$	2.00000			0.0713831
$786$	−18.0000	+	31.1769i	−0.642039	+	1.11204i
$787$	−3.00000	−	5.19615i	−0.106938	−	0.185223i	0.807590	−	0.589744i	$-0.200771\pi$
$787$	−3.00000	−	5.19615i	−0.106938	−	0.185223i	−0.914529	+	0.404521i	$0.867438\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$		0			0
$790$	4.00000			0.142314
$791$		0			0
$792$	−4.00000			−0.142134
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	−13.0000	−	22.5167i	−0.461353	−	0.799086i
$795$	−10.0000	−	17.3205i	−0.354663	−	0.614295i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$		0			0
$799$	32.0000			1.13208
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−4.00000	−	6.92820i	−0.141333	−	0.244796i
$802$	7.00000	+	12.1244i	0.247179	+	0.428126i
$803$	8.00000	−	13.8564i	0.282314	−	0.488982i
$804$	−8.00000			−0.282138
$805$		0			0
$806$	8.00000			0.281788
$807$	−26.0000	+	45.0333i	−0.915243	+	1.58525i
$808$	1.00000	+	1.73205i	0.0351799	+	0.0609333i
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	0.940435	−	0.339975i	$-0.110418\pi$
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	−0.764644	+	0.644453i	$0.777085\pi$
$810$	5.50000	−	9.52628i	0.193250	−	0.334719i
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$	−20.0000	+	34.6410i	−0.701000	+	1.21417i
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$	−8.00000	−	13.8564i	−0.280056	−	0.485071i
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$	−20.0000			−0.699284
$819$		0			0
$820$	4.00000			0.139686
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	2.00000	+	3.46410i	0.0697580	+	0.120824i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$	−8.00000			−0.278524
$826$		0			0
$827$	44.0000			1.53003			0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000			1.53003			0.765015	+	0.644013i	$0.222732\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$	1.00000	+	1.73205i	0.0347105	+	0.0601204i
$831$	−2.00000	+	3.46410i	−0.0693792	+	0.120168i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−20.0000			−0.692543
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$	−12.0000	−	20.7846i	−0.415029	−	0.718851i
$837$	8.00000	+	13.8564i	0.276520	+	0.478947i
$838$	−3.00000	+	5.19615i	−0.103633	+	0.179498i
$839$	−36.0000			−1.24286			−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000			−1.24286			−0.621429	+	0.783470i	$0.713448\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	17.0000	−	29.4449i	0.585859	−	1.01474i
$843$	10.0000	+	17.3205i	0.344418	+	0.596550i
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	4.00000			0.137523
$847$		0			0
$848$	10.0000			0.343401
$849$	26.0000	−	45.0333i	0.892318	−	1.54554i
$850$	−4.00000	−	6.92820i	−0.137199	−	0.237635i
$851$	−20.0000	−	34.6410i	−0.685591	−	1.18748i
$852$	−12.0000	+	20.7846i	−0.411113	+	0.712069i
$853$	50.0000			1.71197			0.855984	−	0.517003i	$-0.172952\pi$
$853$	50.0000			1.71197			0.855984	+	0.517003i	$0.172952\pi$
$854$		0			0
$855$	−6.00000			−0.205196
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	0.994880	−	0.101068i	$-0.0322260\pi$
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	−0.584967	+	0.811057i	$0.698893\pi$
$858$	8.00000	+	13.8564i	0.273115	+	0.473050i
$859$	−19.0000	+	32.9090i	−0.648272	+	1.12284i	0.335264	+	0.942124i	$0.391175\pi$
$859$	−19.0000	+	32.9090i	−0.648272	+	1.12284i	−0.983535	+	0.180715i	$0.942159\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$		0			0
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$	−9.00000	−	15.5885i	−0.306009	−	0.530023i
$866$	20.0000	−	34.6410i	0.679628	−	1.17715i
$867$	94.0000			3.19241
$868$		0			0
$869$	−16.0000			−0.542763
$870$	6.00000	−	10.3923i	0.203419	−	0.352332i
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$	8.00000			0.270295
$877$	21.0000	−	36.3731i	0.709120	−	1.22823i	−0.256064	−	0.966660i	$-0.582426\pi$
$877$	21.0000	−	36.3731i	0.709120	−	1.22823i	0.965184	−	0.261571i	$-0.0842407\pi$
$878$	16.0000	+	27.7128i	0.539974	+	0.935262i
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	−40.0000			−1.34763			−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000			−1.34763			−0.673817	+	0.738898i	$0.735346\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	−8.00000	+	13.8564i	−0.269069	+	0.466041i
$885$	14.0000	+	24.2487i	0.470605	+	0.815112i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$	−2.00000	+	3.46410i	−0.0671534	+	0.116313i	−0.897647	−	0.440715i	$-0.854725\pi$
$887$	−2.00000	+	3.46410i	−0.0671534	+	0.116313i	0.830494	+	0.557028i	$0.188058\pi$
$888$	−20.0000			−0.671156
$889$		0			0
$890$	8.00000			0.268161
$891$	−22.0000	+	38.1051i	−0.737028	+	1.27657i
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$	10.0000	−	17.3205i	0.334450	−	0.579284i
$895$	4.00000			0.133705
$896$		0			0
$897$	−16.0000			−0.534224
$898$	−9.00000	+	15.5885i	−0.300334	+	0.520194i
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−40.0000	+	69.2820i	−1.33259	+	2.30812i
$902$	−16.0000			−0.532742
$903$		0			0
$904$	−2.00000			−0.0665190
$905$	−13.0000	+	22.5167i	−0.432135	+	0.748479i
$906$		0			0
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$	6.00000	−	10.3923i	0.198680	−	0.344124i
$913$	−4.00000	−	6.92820i	−0.132381	−	0.229290i
$914$	−3.00000	−	5.19615i	−0.0992312	−	0.171873i
$915$	10.0000	−	17.3205i	0.330590	−	0.572598i
$916$	−14.0000			−0.462573
$917$		0			0
$918$	−32.0000			−1.05616
$919$	2.00000	−	3.46410i	0.0659739	−	0.114270i	−0.831152	−	0.556046i	$-0.812318\pi$
$919$	2.00000	−	3.46410i	0.0659739	−	0.114270i	0.897126	+	0.441776i	$0.145651\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	24.0000			0.789970
$924$		0			0
$925$	−10.0000			−0.328798
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	−2.00000	−	3.46410i	−0.0656886	−	0.113776i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	6.00000	−	10.3923i	0.196854	−	0.340960i	−0.750653	−	0.660697i	$-0.770261\pi$
$929$	6.00000	−	10.3923i	0.196854	−	0.340960i	0.947507	+	0.319736i	$0.103594\pi$
$930$	8.00000			0.262330
$931$		0			0
$932$	22.0000			0.720634
$933$	−16.0000	+	27.7128i	−0.523816	+	0.907277i
$934$	5.00000	+	8.66025i	0.163605	+	0.283372i
$935$	16.0000	+	27.7128i	0.523256	+	0.906306i
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	0.935942	−	0.352155i	$-0.114551\pi$
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	−0.772946	+	0.634472i	$0.781218\pi$
$942$	−2.00000	−	3.46410i	−0.0651635	−	0.112867i
$943$	8.00000	−	13.8564i	0.260516	−	0.451227i
$944$	−14.0000			−0.455661
$945$		0			0
$946$	−16.0000			−0.520205
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$	−4.00000	−	6.92820i	−0.129914	−	0.225018i
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$	3.00000	−	5.19615i	0.0973329	−	0.168585i
$951$	36.0000			1.16738
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$	−5.00000	+	8.66025i	−0.161881	+	0.280386i
$955$	−6.00000	−	10.3923i	−0.194155	−	0.336287i
$956$	4.00000	+	6.92820i	0.129369	+	0.224074i
$957$	−24.0000	+	41.5692i	−0.775810	+	1.34374i
$958$	4.00000			0.129234
$959$		0			0
$960$	2.00000			0.0645497
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	10.0000	+	17.3205i	0.322413	+	0.558436i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−2.00000	+	3.46410i	−0.0644157	+	0.111571i
$965$	−18.0000			−0.579441
$966$		0			0
$967$	−52.0000			−1.67221			−0.836104	−	0.548572i	$-0.815172\pi$
$967$	−52.0000			−1.67221			−0.836104	+	0.548572i	$0.815172\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	48.0000	+	83.1384i	1.54198	+	2.67079i
$970$		0			0
$971$	31.0000	−	53.6936i	0.994837	−	1.72311i	0.409532	−	0.912296i	$-0.365692\pi$
$971$	31.0000	−	53.6936i	0.994837	−	1.72311i	0.585305	−	0.810813i	$-0.300975\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	−44.0000			−1.40985
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	−32.0000			−1.02272
$980$		0			0
$981$	10.0000			0.319275
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	−10.0000	−	17.3205i	−0.318950	−	0.552438i	0.661319	−	0.750105i	$-0.269997\pi$
$983$	−10.0000	−	17.3205i	−0.318950	−	0.552438i	−0.980269	+	0.197666i	$0.936664\pi$
$984$	−4.00000	−	6.92820i	−0.127515	−	0.220863i
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−48.0000			−1.52863
$987$		0			0
$988$	−12.0000			−0.381771
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$	2.00000	+	3.46410i	0.0635642	+	0.110096i
$991$	18.0000	+	31.1769i	0.571789	+	0.990367i	0.996382	+	0.0849833i	$0.0270837\pi$
$991$	18.0000	+	31.1769i	0.571789	+	0.990367i	−0.424594	+	0.905384i	$0.639583\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−56.0000			−1.77711
$994$		0			0
$995$	4.00000			0.126809
$996$	2.00000	−	3.46410i	0.0633724	−	0.109764i
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	0.979265	+	0.202586i	$0.0649345\pi$
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	−0.314188	+	0.949361i	$0.601732\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$	−20.0000	+	34.6410i	−0.632772	+	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.b.471.1		2
7.2	even	3		490.2.a.i.1.1	yes	1
7.3	odd	6		490.2.e.e.361.1		2
7.4	even	3	inner	490.2.e.b.361.1		2
7.5	odd	6		490.2.a.f.1.1	✓	1
7.6	odd	2		490.2.e.e.471.1		2
21.2	odd	6		4410.2.a.i.1.1		1
21.5	even	6		4410.2.a.s.1.1		1
28.19	even	6		3920.2.a.bg.1.1		1
28.23	odd	6		3920.2.a.j.1.1		1
35.2	odd	12		2450.2.c.n.99.2		2
35.9	even	6		2450.2.a.d.1.1		1
35.12	even	12		2450.2.c.b.99.2		2
35.19	odd	6		2450.2.a.n.1.1		1
35.23	odd	12		2450.2.c.n.99.1		2
35.33	even	12		2450.2.c.b.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.a.f.1.1	✓	1	7.5	odd	6
490.2.a.i.1.1	yes	1	7.2	even	3
490.2.e.b.361.1		2	7.4	even	3	inner
490.2.e.b.471.1		2	1.1	even	1	trivial
490.2.e.e.361.1		2	7.3	odd	6
490.2.e.e.471.1		2	7.6	odd	2
2450.2.a.d.1.1		1	35.9	even	6
2450.2.a.n.1.1		1	35.19	odd	6
2450.2.c.b.99.1		2	35.33	even	12
2450.2.c.b.99.2		2	35.12	even	12
2450.2.c.n.99.1		2	35.23	odd	12
2450.2.c.n.99.2		2	35.2	odd	12
3920.2.a.j.1.1		1	28.23	odd	6
3920.2.a.bg.1.1		1	28.19	even	6
4410.2.a.i.1.1		1	21.2	odd	6
4410.2.a.s.1.1		1	21.5	even	6

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 + 3.46410i) q^{11} +(-1.00000 + 1.73205i) q^{12} +2.00000 q^{13} +2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.00000 - 5.19615i) q^{19} +1.00000 q^{20} -4.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -4.00000 q^{27} -6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.00000 - 6.92820i) q^{33} +8.00000 q^{34} +1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(3.00000 + 5.19615i) q^{38} +(-2.00000 - 3.46410i) q^{39} +(-0.500000 + 0.866025i) q^{40} +4.00000 q^{41} +4.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-2.00000 + 3.46410i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(-8.00000 + 13.8564i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(2.00000 - 3.46410i) q^{54} -4.00000 q^{55} -12.0000 q^{57} +(3.00000 - 5.19615i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(5.00000 - 8.66025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(4.00000 + 6.92820i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-4.00000 + 6.92820i) q^{68} -8.00000 q^{69} +12.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-1.00000 + 1.73205i) q^{75} -6.00000 q^{76} +4.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-2.00000 + 3.46410i) q^{82} -2.00000 q^{83} +8.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(6.00000 + 10.3923i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-4.00000 + 6.92820i) q^{89} +1.00000 q^{90} -4.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(3.00000 + 5.19615i) q^{95} +(-1.00000 + 1.73205i) q^{96} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{13} + 4 q^{15} - q^{16} - 8 q^{17} - q^{18} + 6 q^{19} + 2 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{24} - q^{25} - 2 q^{26} - 8 q^{27} - 12 q^{29} - 2 q^{30} - 4 q^{31} - q^{32} + 8 q^{33} + 16 q^{34} + 2 q^{36} + 10 q^{37} + 6 q^{38} - 4 q^{39} - q^{40} + 8 q^{41} + 8 q^{43} + 4 q^{44} - q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 2 q^{50} - 16 q^{51} - 2 q^{52} - 10 q^{53} + 4 q^{54} - 8 q^{55} - 24 q^{57} + 6 q^{58} + 14 q^{59} - 2 q^{60} + 10 q^{61} + 8 q^{62} + 2 q^{64} - 2 q^{65} + 8 q^{66} + 4 q^{67} - 8 q^{68} - 16 q^{69} + 24 q^{71} - q^{72} - 4 q^{73} + 10 q^{74} - 2 q^{75} - 12 q^{76} + 8 q^{78} - 4 q^{79} - q^{80} + 11 q^{81} - 4 q^{82} - 4 q^{83} + 16 q^{85} - 4 q^{86} + 12 q^{87} + 4 q^{88} - 8 q^{89} + 2 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - q^5 + 4 * q^6 + 2 * q^8 - q^9 - q^10 + 4 * q^11 - 2 * q^12 + 4 * q^13 + 4 * q^15 - q^16 - 8 * q^17 - q^18 + 6 * q^19 + 2 * q^20 - 8 * q^22 + 4 * q^23 - 2 * q^24 - q^25 - 2 * q^26 - 8 * q^27 - 12 * q^29 - 2 * q^30 - 4 * q^31 - q^32 + 8 * q^33 + 16 * q^34 + 2 * q^36 + 10 * q^37 + 6 * q^38 - 4 * q^39 - q^40 + 8 * q^41 + 8 * q^43 + 4 * q^44 - q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 2 * q^50 - 16 * q^51 - 2 * q^52 - 10 * q^53 + 4 * q^54 - 8 * q^55 - 24 * q^57 + 6 * q^58 + 14 * q^59 - 2 * q^60 + 10 * q^61 + 8 * q^62 + 2 * q^64 - 2 * q^65 + 8 * q^66 + 4 * q^67 - 8 * q^68 - 16 * q^69 + 24 * q^71 - q^72 - 4 * q^73 + 10 * q^74 - 2 * q^75 - 12 * q^76 + 8 * q^78 - 4 * q^79 - q^80 + 11 * q^81 - 4 * q^82 - 4 * q^83 + 16 * q^85 - 4 * q^86 + 12 * q^87 + 4 * q^88 - 8 * q^89 + 2 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^99

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