LMFDB - Embedded newform 650.2.e.j.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(451,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.451"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,0,-3,0,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.155554 + 0.269427i$ of defining polynomial
Character	$\chi$	$=$	650.451
Dual form			650.2.e.j.601.1

$q$-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} +(-1.10716 + 1.91766i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.10716 - 1.91766i) q^{6} +(1.95161 + 3.38028i) q^{7} +1.00000 q^{8} +(-0.951606 - 1.64823i) q^{9} +(-0.533338 + 0.923769i) q^{11} +2.21432 q^{12} +(2.82148 + 2.24483i) q^{13} -3.90321 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.655554 - 1.13545i) q^{17} +1.90321 q^{18} +(3.29605 + 5.70893i) q^{19} -8.64296 q^{21} +(-0.533338 - 0.923769i) q^{22} +(-1.07382 + 1.85991i) q^{23} +(-1.10716 + 1.91766i) q^{24} +(-3.35482 + 1.32106i) q^{26} -2.42864 q^{27} +(1.95161 - 3.38028i) q^{28} +(4.52543 - 7.83827i) q^{29} -6.92396 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.18098 - 2.04552i) q^{33} +1.31111 q^{34} +(-0.951606 + 1.64823i) q^{36} +(-2.51037 + 4.34809i) q^{37} -6.59210 q^{38} +(-7.42864 + 2.92525i) q^{39} +(2.97703 - 5.15637i) q^{41} +(4.32148 - 7.48502i) q^{42} +(-1.00000 - 1.73205i) q^{43} +1.06668 q^{44} +(-1.07382 - 1.85991i) q^{46} -0.0967881 q^{47} +(-1.10716 - 1.91766i) q^{48} +(-4.11753 + 7.13177i) q^{49} +2.90321 q^{51} +(0.533338 - 3.56589i) q^{52} -1.49532 q^{53} +(1.21432 - 2.10326i) q^{54} +(1.95161 + 3.38028i) q^{56} -14.5970 q^{57} +(4.52543 + 7.83827i) q^{58} +(-3.59210 - 6.22171i) q^{59} +(-3.94370 - 6.83068i) q^{61} +(3.46198 - 5.99632i) q^{62} +(3.71432 - 6.43339i) q^{63} +1.00000 q^{64} +2.36196 q^{66} +(4.21432 - 7.29942i) q^{67} +(-0.655554 + 1.13545i) q^{68} +(-2.37778 - 4.11844i) q^{69} +(7.73975 + 13.4056i) q^{71} +(-0.951606 - 1.64823i) q^{72} -15.3526 q^{73} +(-2.51037 - 4.34809i) q^{74} +(3.29605 - 5.70893i) q^{76} -4.16346 q^{77} +(1.18098 - 7.89601i) q^{78} +4.30174 q^{79} +(5.54371 - 9.60199i) q^{81} +(2.97703 + 5.15637i) q^{82} +9.69381 q^{83} +(4.32148 + 7.48502i) q^{84} +2.00000 q^{86} +(10.0207 + 17.3564i) q^{87} +(-0.533338 + 0.923769i) q^{88} +(-2.26271 + 3.91914i) q^{89} +(-2.08173 + 13.9184i) q^{91} +2.14764 q^{92} +(7.66593 - 13.2778i) q^{93} +(0.0483940 - 0.0838209i) q^{94} +2.21432 q^{96} +(2.13013 + 3.68949i) q^{97} +(-4.11753 - 7.13177i) q^{98} +2.03011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 5 q^{7} + 6 q^{8} + q^{9} - 3 q^{11} - 3 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{18} + 13 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{27} + 5 q^{28} + 14 q^{29} + 12 q^{31}+ \cdots + 26 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 5 * q^7 + 6 * q^8 + q^9 - 3 * q^11 - 3 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 2 * q^18 + 13 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^27 + 5 * q^28 + 14 * q^29 + 12 * q^31 - 3 * q^32 + 6 * q^33 + 8 * q^34 + q^36 + 5 * q^37 - 26 * q^38 - 18 * q^39 - 2 * q^41 + 6 * q^42 - 6 * q^43 + 6 * q^44 - 14 * q^47 + 2 * q^49 + 4 * q^51 + 3 * q^52 + 18 * q^53 - 6 * q^54 + 5 * q^56 - 8 * q^57 + 14 * q^58 - 8 * q^59 - 4 * q^61 - 6 * q^62 + 9 * q^63 + 6 * q^64 - 12 * q^66 + 12 * q^67 - 4 * q^68 - 14 * q^69 + 20 * q^71 + q^72 - 12 * q^73 + 5 * q^74 + 13 * q^76 - 38 * q^77 - 6 * q^78 - 28 * q^79 + 13 * q^81 - 2 * q^82 - 8 * q^83 + 6 * q^84 + 12 * q^86 + 20 * q^87 - 3 * q^88 - 7 * q^89 - 19 * q^91 + 26 * q^93 + 7 * q^94 + 26 * q^97 + 2 * q^98 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.10716	+	1.91766i	−0.639219	+	1.10716i	0.346385	+	0.938092i	$0.387409\pi$
$3$	−1.10716	+	1.91766i	−0.639219	+	1.10716i	−0.985604	+	0.169068i	$0.945924\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.10716	−	1.91766i	−0.451996	−	0.782880i
$7$	1.95161	+	3.38028i	0.737638	+	1.27763i	0.953556	+	0.301215i	$0.0973921\pi$
$7$	1.95161	+	3.38028i	0.737638	+	1.27763i	−0.215919	+	0.976411i	$0.569275\pi$
$8$	1.00000			0.353553
$9$	−0.951606	−	1.64823i	−0.317202	−	0.549410i
$10$		0			0
$11$	−0.533338	+	0.923769i	−0.160808	+	0.278527i	−0.935159	−	0.354229i	$-0.884743\pi$
$11$	−0.533338	+	0.923769i	−0.160808	+	0.278527i	0.774351	+	0.632756i	$0.218077\pi$
$12$	2.21432			0.639219
$13$	2.82148	+	2.24483i	0.782538	+	0.622603i
$13$	2.82148	+	2.24483i	0.782538	+	0.622603i
$14$	−3.90321			−1.04318
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.655554	−	1.13545i	−0.158995	−	0.275388i	0.775511	−	0.631334i	$-0.217492\pi$
$17$	−0.655554	−	1.13545i	−0.158995	−	0.275388i	−0.934507	+	0.355946i	$0.884159\pi$
$18$	1.90321			0.448591
$19$	3.29605	+	5.70893i	0.756166	+	1.30972i	0.944792	+	0.327669i	$0.106263\pi$
$19$	3.29605	+	5.70893i	0.756166	+	1.30972i	−0.188626	+	0.982049i	$0.560403\pi$
$20$		0			0
$21$	−8.64296			−1.88605
$22$	−0.533338	−	0.923769i	−0.113708	−	0.196948i
$23$	−1.07382	+	1.85991i	−0.223907	+	0.387819i	−0.955991	−	0.293396i	$-0.905215\pi$
$23$	−1.07382	+	1.85991i	−0.223907	+	0.387819i	0.732084	+	0.681215i	$0.238548\pi$
$24$	−1.10716	+	1.91766i	−0.225998	+	0.391440i
$25$		0			0
$26$	−3.35482	+	1.32106i	−0.657934	+	0.259081i
$27$	−2.42864			−0.467392
$28$	1.95161	−	3.38028i	0.368819	−	0.638813i
$29$	4.52543	−	7.83827i	0.840351	−	1.45553i	−0.0492475	−	0.998787i	$-0.515682\pi$
$29$	4.52543	−	7.83827i	0.840351	−	1.45553i	0.889598	−	0.456744i	$-0.150984\pi$
$30$		0			0
$31$	−6.92396			−1.24358			−0.621790	−	0.783184i	$-0.713594\pi$
$31$	−6.92396			−1.24358			−0.621790	+	0.783184i	$0.713594\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.18098	−	2.04552i	−0.205582	−	0.356079i
$34$	1.31111			0.224853
$35$		0			0
$36$	−0.951606	+	1.64823i	−0.158601	+	0.274705i
$37$	−2.51037	+	4.34809i	−0.412703	+	0.714822i	−0.995184	−	0.0980220i	$-0.968748\pi$
$37$	−2.51037	+	4.34809i	−0.412703	+	0.714822i	0.582482	+	0.812844i	$0.302082\pi$
$38$	−6.59210			−1.06938
$39$	−7.42864	+	2.92525i	−1.18953	+	0.468414i
$40$		0			0
$41$	2.97703	−	5.15637i	0.464935	−	0.805290i	−0.534264	−	0.845318i	$-0.679411\pi$
$41$	2.97703	−	5.15637i	0.464935	−	0.805290i	0.999199	+	0.0400274i	$0.0127445\pi$
$42$	4.32148	−	7.48502i	0.666819	−	1.15496i
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	1.06668			0.160808
$45$		0			0
$46$	−1.07382	−	1.85991i	−0.158326	−	0.274229i
$47$	−0.0967881			−0.0141180			−0.00705900	−	0.999975i	$-0.502247\pi$
$47$	−0.0967881			−0.0141180			−0.00705900	+	0.999975i	$0.502247\pi$
$48$	−1.10716	−	1.91766i	−0.159805	−	0.276790i
$49$	−4.11753	+	7.13177i	−0.588219	+	1.01882i
$50$		0			0
$51$	2.90321			0.406531
$52$	0.533338	−	3.56589i	0.0739607	−	0.494500i
$53$	−1.49532			−0.205397			−0.102699	−	0.994713i	$-0.532748\pi$
$53$	−1.49532			−0.205397			−0.102699	+	0.994713i	$0.532748\pi$
$54$	1.21432	−	2.10326i	0.165248	−	0.286218i
$55$		0			0
$56$	1.95161	+	3.38028i	0.260794	+	0.451709i
$57$	−14.5970			−1.93342
$58$	4.52543	+	7.83827i	0.594218	+	1.02922i
$59$	−3.59210	−	6.22171i	−0.467652	−	0.809997i	0.531665	−	0.846955i	$-0.321567\pi$
$59$	−3.59210	−	6.22171i	−0.467652	−	0.809997i	−0.999317	+	0.0369577i	$0.988233\pi$
$60$		0			0
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	−0.999984	−	0.00571183i	$-0.998182\pi$
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	0.495045	−	0.868867i	$-0.335151\pi$
$62$	3.46198	−	5.99632i	0.439672	−	0.761534i
$63$	3.71432	−	6.43339i	0.467960	−	0.810531i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.36196			0.290738
$67$	4.21432	−	7.29942i	0.514861	−	0.891766i	−0.484990	−	0.874520i	$-0.661177\pi$
$67$	4.21432	−	7.29942i	0.514861	−	0.891766i	0.999851	−	0.0172460i	$-0.00548984\pi$
$68$	−0.655554	+	1.13545i	−0.0794976	+	0.137694i
$69$	−2.37778	−	4.11844i	−0.286252	−	0.495802i
$70$		0			0
$71$	7.73975	+	13.4056i	0.918539	+	1.59096i	0.801636	+	0.597813i	$0.203963\pi$
$71$	7.73975	+	13.4056i	0.918539	+	1.59096i	0.116903	+	0.993143i	$0.462703\pi$
$72$	−0.951606	−	1.64823i	−0.112148	−	0.194246i
$73$	−15.3526			−1.79689			−0.898443	−	0.439091i	$-0.855301\pi$
$73$	−15.3526			−1.79689			−0.898443	+	0.439091i	$0.855301\pi$
$74$	−2.51037	−	4.34809i	−0.291825	−	0.505455i
$75$		0			0
$76$	3.29605	−	5.70893i	0.378083	−	0.654859i
$77$	−4.16346			−0.474471
$78$	1.18098	−	7.89601i	0.133720	−	0.894048i
$79$	4.30174			0.483984			0.241992	−	0.970278i	$-0.422199\pi$
$79$	4.30174			0.483984			0.241992	+	0.970278i	$0.422199\pi$
$80$		0			0
$81$	5.54371	−	9.60199i	0.615968	−	1.06689i
$82$	2.97703	+	5.15637i	0.328758	+	0.569426i
$83$	9.69381			1.06403			0.532017	−	0.846734i	$-0.321434\pi$
$83$	9.69381			1.06403			0.532017	+	0.846734i	$0.321434\pi$
$84$	4.32148	+	7.48502i	0.471512	+	0.816683i
$85$		0			0
$86$	2.00000			0.215666
$87$	10.0207	+	17.3564i	1.07434	+	1.86081i
$88$	−0.533338	+	0.923769i	−0.0568541	+	0.0984741i
$89$	−2.26271	+	3.91914i	−0.239847	+	0.415428i	−0.960670	−	0.277692i	$-0.910431\pi$
$89$	−2.26271	+	3.91914i	−0.239847	+	0.415428i	0.720823	+	0.693119i	$0.243764\pi$
$90$		0			0
$91$	−2.08173	+	13.9184i	−0.218225	+	1.45905i
$92$	2.14764			0.223907
$93$	7.66593	−	13.2778i	0.794919	−	1.37684i
$94$	0.0483940	−	0.0838209i	0.00499146	−	0.00864547i
$95$		0			0
$96$	2.21432			0.225998
$97$	2.13013	+	3.68949i	0.216282	+	0.374611i	0.953668	−	0.300860i	$-0.0972738\pi$
$97$	2.13013	+	3.68949i	0.216282	+	0.374611i	−0.737387	+	0.675471i	$0.763940\pi$
$98$	−4.11753	−	7.13177i	−0.415934	−	0.720418i
$99$	2.03011			0.204034
$100$		0			0
$101$	−0.729376	+	1.26332i	−0.0725756	+	0.125705i	−0.900029	−	0.435829i	$-0.856455\pi$
$101$	−0.729376	+	1.26332i	−0.0725756	+	0.125705i	0.827454	+	0.561534i	$0.189789\pi$
$102$	−1.45161	+	2.51426i	−0.143730	+	0.248948i
$103$	−10.2444			−1.00941			−0.504707	−	0.863291i	$-0.668399\pi$
$103$	−10.2444			−1.00941			−0.504707	+	0.863291i	$0.668399\pi$
$104$	2.82148	+	2.24483i	0.276669	+	0.220123i
$105$		0			0
$106$	0.747658	−	1.29498i	0.0726190	−	0.125780i
$107$	1.10716	−	1.91766i	0.107033	−	0.185387i	−0.807534	−	0.589821i	$-0.799198\pi$
$107$	1.10716	−	1.91766i	0.107033	−	0.185387i	0.914567	+	0.404434i	$0.132532\pi$
$108$	1.21432	+	2.10326i	0.116848	+	0.202387i
$109$	0.133353			0.0127729			0.00638645	−	0.999980i	$-0.497967\pi$
$109$	0.133353			0.0127729			0.00638645	+	0.999980i	$0.497967\pi$
$110$		0			0
$111$	−5.55877	−	9.62806i	−0.527615	−	0.913855i
$112$	−3.90321			−0.368819
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$	7.29851	−	12.6414i	0.683568	−	1.18398i
$115$		0			0
$116$	−9.05086			−0.840351
$117$	1.01506	−	6.78664i	0.0938419	−	0.627425i
$118$	7.18421			0.661360
$119$	2.55877	−	4.43191i	0.234562	−	0.406273i
$120$		0			0
$121$	4.93110	+	8.54092i	0.448282	+	0.776447i
$122$	7.88739			0.714091
$123$	6.59210	+	11.4179i	0.594390	+	1.02951i
$124$	3.46198	+	5.99632i	0.310895	+	0.538486i
$125$		0			0
$126$	3.71432	+	6.43339i	0.330898	+	0.573132i
$127$	−4.99532	+	8.65214i	−0.443263	+	0.767753i	−0.997929	−	0.0643192i	$-0.979512\pi$
$127$	−4.99532	+	8.65214i	−0.443263	+	0.767753i	0.554667	+	0.832073i	$0.312846\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.42864			0.389920
$130$		0			0
$131$	9.25581			0.808684			0.404342	−	0.914608i	$-0.367501\pi$
$131$	9.25581			0.808684			0.404342	+	0.914608i	$0.367501\pi$
$132$	−1.18098	+	2.04552i	−0.102791	+	0.178040i
$133$	−12.8652	+	22.2832i	−1.11555	+	1.93220i
$134$	4.21432	+	7.29942i	0.364062	+	0.630573i
$135$		0			0
$136$	−0.655554	−	1.13545i	−0.0562133	−	0.0973643i
$137$	7.39530	+	12.8090i	0.631823	+	1.09435i	0.987179	+	0.159619i	$0.0510265\pi$
$137$	7.39530	+	12.8090i	0.631823	+	1.09435i	−0.355356	+	0.934731i	$0.615640\pi$
$138$	4.75557			0.404821
$139$	6.34691	+	10.9932i	0.538338	+	0.932428i	0.998994	+	0.0448494i	$0.0142808\pi$
$139$	6.34691	+	10.9932i	0.538338	+	0.932428i	−0.460656	+	0.887579i	$0.652386\pi$
$140$		0			0
$141$	0.107160	−	0.185606i	0.00902449	−	0.0156309i
$142$	−15.4795			−1.29901
$143$	−3.57851	+	1.40914i	−0.299250	+	0.117838i
$144$	1.90321			0.158601
$145$		0			0
$146$	7.67630	−	13.2957i	0.635295	−	1.10036i
$147$	−9.11753	−	15.7920i	−0.752001	−	1.30250i
$148$	5.02074			0.412703
$149$	−3.64296	−	6.30979i	−0.298443	−	0.516918i	0.677337	−	0.735673i	$-0.263134\pi$
$149$	−3.64296	−	6.30979i	−0.298443	−	0.516918i	−0.975780	+	0.218755i	$0.929801\pi$
$150$		0			0
$151$	20.1082			1.63638			0.818190	−	0.574949i	$-0.194978\pi$
$151$	20.1082			1.63638			0.818190	+	0.574949i	$0.194978\pi$
$152$	3.29605	+	5.70893i	0.267345	+	0.463055i
$153$	−1.24766	+	2.16101i	−0.100867	+	0.174707i
$154$	2.08173	−	3.60567i	0.167751	−	0.290553i
$155$		0			0
$156$	6.24766	+	4.97077i	0.500213	+	0.397980i
$157$	−1.98418			−0.158355			−0.0791773	−	0.996861i	$-0.525229\pi$
$157$	−1.98418			−0.158355			−0.0791773	+	0.996861i	$0.525229\pi$
$158$	−2.15087	+	3.72542i	−0.171114	+	0.296378i
$159$	1.65555	−	2.86750i	0.131294	−	0.227408i
$160$		0			0
$161$	−8.38271			−0.660650
$162$	5.54371	+	9.60199i	0.435555	+	0.754403i
$163$	2.35159	+	4.07308i	0.184191	+	0.319028i	0.943304	−	0.331931i	$-0.107700\pi$
$163$	2.35159	+	4.07308i	0.184191	+	0.319028i	−0.759113	+	0.650959i	$0.774367\pi$
$164$	−5.95407			−0.464935
$165$		0			0
$166$	−4.84691	+	8.39509i	−0.376193	+	0.651585i
$167$	4.84767	−	8.39642i	0.375124	−	0.649734i	−0.615221	−	0.788354i	$-0.710933\pi$
$167$	4.84767	−	8.39642i	0.375124	−	0.649734i	0.990346	+	0.138620i	$0.0442667\pi$
$168$	−8.64296			−0.666819
$169$	2.92149	+	12.6675i	0.224730	+	0.974421i
$170$		0			0
$171$	6.27309	−	10.8653i	0.479715	−	0.830890i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−12.0358	−	20.8466i	−0.915065	−	1.58494i	−0.806806	−	0.590816i	$-0.798806\pi$
$173$	−12.0358	−	20.8466i	−0.915065	−	1.58494i	−0.108259	−	0.994123i	$-0.534527\pi$
$174$	−20.0415			−1.51934
$175$		0			0
$176$	−0.533338	−	0.923769i	−0.0402019	−	0.0696317i
$177$	15.9081			1.19573
$178$	−2.26271	−	3.91914i	−0.169598	−	0.293752i
$179$	−1.52543	+	2.64212i	−0.114016	+	0.197481i	−0.917386	−	0.397999i	$-0.869705\pi$
$179$	−1.52543	+	2.64212i	−0.114016	+	0.197481i	0.803370	+	0.595480i	$0.203038\pi$
$180$		0			0
$181$	10.6430			0.791085			0.395542	−	0.918448i	$-0.370557\pi$
$181$	10.6430			0.791085			0.395542	+	0.918448i	$0.370557\pi$
$182$	−11.0128	−	8.76204i	−0.816325	−	0.649486i
$183$	17.4652			1.29107
$184$	−1.07382	+	1.85991i	−0.0791632	+	0.137115i
$185$		0			0
$186$	7.66593	+	13.2778i	0.562093	+	0.973574i
$187$	1.39853			0.102270
$188$	0.0483940	+	0.0838209i	0.00352950	+	0.00611327i
$189$	−4.73975	−	8.20948i	−0.344766	−	0.597152i
$190$		0			0
$191$	−7.36519	−	12.7569i	−0.532926	−	0.923056i	−0.999261	−	0.0384470i	$-0.987759\pi$
$191$	−7.36519	−	12.7569i	−0.532926	−	0.923056i	0.466334	−	0.884609i	$-0.345574\pi$
$192$	−1.10716	+	1.91766i	−0.0799024	+	0.138395i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−4.26025			−0.305868
$195$		0			0
$196$	8.23506			0.588219
$197$	5.20641	−	9.01776i	0.370941	−	0.642489i	−0.618769	−	0.785573i	$-0.712368\pi$
$197$	5.20641	−	9.01776i	0.370941	−	0.642489i	0.989711	+	0.143084i	$0.0457018\pi$
$198$	−1.01506	+	1.75813i	−0.0721369	+	0.124945i
$199$	2.18421	+	3.78316i	0.154834	+	0.268181i	0.932999	−	0.359880i	$-0.117182\pi$
$199$	2.18421	+	3.78316i	0.154834	+	0.268181i	−0.778164	+	0.628061i	$0.783849\pi$
$200$		0			0
$201$	9.33185	+	16.1632i	0.658218	+	1.14007i
$202$	−0.729376	−	1.26332i	−0.0513187	−	0.0888866i
$203$	35.3274			2.47950
$204$	−1.45161	−	2.51426i	−0.101633	−	0.176033i
$205$		0			0
$206$	5.12222	−	8.87194i	0.356882	−	0.618137i
$207$	4.08742			0.284095
$208$	−3.35482	+	1.32106i	−0.232615	+	0.0915990i
$209$	−7.03164			−0.486389
$210$		0			0
$211$	−2.74766	+	4.75908i	−0.189157	+	0.327629i	−0.944969	−	0.327159i	$-0.893909\pi$
$211$	−2.74766	+	4.75908i	−0.189157	+	0.327629i	0.755813	+	0.654788i	$0.227242\pi$
$212$	0.747658	+	1.29498i	0.0513494	+	0.0889397i
$213$	−34.2766			−2.34859
$214$	1.10716	+	1.91766i	0.0756839	+	0.131088i
$215$		0			0
$216$	−2.42864			−0.165248
$217$	−13.5128	−	23.4049i	−0.917311	−	1.58883i
$218$	−0.0666765	+	0.115487i	−0.00451591	+	0.00782178i
$219$	16.9978	−	29.4410i	1.14860	−	1.98944i
$220$		0			0
$221$	0.699264	−	4.67526i	0.0470376	−	0.314492i
$222$	11.1175			0.746160
$223$	10.0484	−	17.4043i	0.672890	−	1.16548i	−0.304191	−	0.952611i	$-0.598386\pi$
$223$	10.0484	−	17.4043i	0.672890	−	1.16548i	0.977081	−	0.212869i	$-0.0682807\pi$
$224$	1.95161	−	3.38028i	0.130397	−	0.225855i
$225$		0			0
$226$	−14.0000			−0.931266
$227$	−9.67952	−	16.7654i	−0.642453	−	1.11276i	−0.984884	−	0.173218i	$-0.944584\pi$
$227$	−9.67952	−	16.7654i	−0.642453	−	1.11276i	0.342431	−	0.939543i	$-0.388750\pi$
$228$	7.29851	+	12.6414i	0.483356	+	0.837197i
$229$	15.7255			1.03917			0.519584	−	0.854420i	$-0.326087\pi$
$229$	15.7255			1.03917			0.519584	+	0.854420i	$0.326087\pi$
$230$		0			0
$231$	4.60962	−	7.98410i	0.303291	−	0.525315i
$232$	4.52543	−	7.83827i	0.297109	−	0.514608i
$233$	−14.8825			−0.974983			−0.487491	−	0.873128i	$-0.662088\pi$
$233$	−14.8825			−0.974983			−0.487491	+	0.873128i	$0.662088\pi$
$234$	5.36987	+	4.27238i	0.351040	+	0.279294i
$235$		0			0
$236$	−3.59210	+	6.22171i	−0.233826	+	0.404999i
$237$	−4.76271	+	8.24926i	−0.309372	+	0.535847i
$238$	2.55877	+	4.43191i	0.165860	+	0.287278i
$239$	4.42219			0.286047			0.143024	−	0.989719i	$-0.454317\pi$
$239$	4.42219			0.286047			0.143024	+	0.989719i	$0.454317\pi$
$240$		0			0
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	0.988508	−	0.151170i	$-0.0483042\pi$
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	−0.625171	+	0.780488i	$0.714971\pi$
$242$	−9.86220			−0.633966
$243$	8.63259	+	14.9521i	0.553781	+	0.959176i
$244$	−3.94370	+	6.83068i	−0.252469	+	0.437290i
$245$		0			0
$246$	−13.1842			−0.840594
$247$	−3.51582	+	23.5067i	−0.223706	+	1.49570i
$248$	−6.92396			−0.439672
$249$	−10.7326	+	18.5894i	−0.680151	+	1.17806i
$250$		0			0
$251$	−1.32616	−	2.29698i	−0.0837067	−	0.144984i	0.821133	−	0.570737i	$-0.193343\pi$
$251$	−1.32616	−	2.29698i	−0.0837067	−	0.144984i	−0.904839	+	0.425753i	$0.860009\pi$
$252$	−7.42864			−0.467960
$253$	−1.14542	−	1.98393i	−0.0720120	−	0.124728i
$254$	−4.99532	−	8.65214i	−0.313434	−	0.542884i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.05086	+	3.55219i	−0.127929	+	0.221579i	−0.922874	−	0.385102i	$-0.874166\pi$
$257$	−2.05086	+	3.55219i	−0.127929	+	0.221579i	0.794945	+	0.606681i	$0.207500\pi$
$258$	−2.21432	+	3.83531i	−0.137858	+	0.238776i
$259$	−19.5970			−1.21770
$260$		0			0
$261$	−17.2257			−1.06624
$262$	−4.62790	+	8.01576i	−0.285913	+	0.495216i
$263$	5.40099	−	9.35479i	0.333039	−	0.576841i	−0.650067	−	0.759877i	$-0.725259\pi$
$263$	5.40099	−	9.35479i	0.333039	−	0.576841i	0.983106	+	0.183036i	$0.0585925\pi$
$264$	−1.18098	−	2.04552i	−0.0726844	−	0.125893i
$265$		0			0
$266$	−12.8652	−	22.2832i	−0.788815	−	1.36627i
$267$	−5.01037	−	8.67822i	−0.306630	−	0.531098i
$268$	−8.42864			−0.514861
$269$	9.29137	+	16.0931i	0.566505	+	0.981215i	0.996908	+	0.0785782i	$0.0250380\pi$
$269$	9.29137	+	16.0931i	0.566505	+	0.981215i	−0.430403	+	0.902637i	$0.641629\pi$
$270$		0			0
$271$	−9.88739	+	17.1255i	−0.600616	+	1.04030i	0.392112	+	0.919918i	$0.371745\pi$
$271$	−9.88739	+	17.1255i	−0.600616	+	1.04030i	−0.992728	+	0.120380i	$0.961589\pi$
$272$	1.31111			0.0794976
$273$	−24.3859	−	19.4020i	−1.47590	−	1.17426i
$274$	−14.7906			−0.893533
$275$		0			0
$276$	−2.37778	+	4.11844i	−0.143126	+	0.247901i
$277$	−0.102476	−	0.177493i	−0.00615718	−	0.0106645i	0.862930	−	0.505323i	$-0.168627\pi$
$277$	−0.102476	−	0.177493i	−0.00615718	−	0.0106645i	−0.869088	+	0.494658i	$0.835293\pi$
$278$	−12.6938			−0.761324
$279$	6.58888	+	11.4123i	0.394466	+	0.683235i
$280$		0			0
$281$	−20.4558			−1.22029			−0.610146	−	0.792289i	$-0.708889\pi$
$281$	−20.4558			−1.22029			−0.610146	+	0.792289i	$0.708889\pi$
$282$	0.107160	+	0.185606i	0.00638128	+	0.0110527i
$283$	−0.719004	+	1.24535i	−0.0427403	+	0.0740284i	−0.886604	−	0.462529i	$-0.846942\pi$
$283$	−0.719004	+	1.24535i	−0.0427403	+	0.0740284i	0.843864	+	0.536557i	$0.180275\pi$
$284$	7.73975	−	13.4056i	0.459270	−	0.795478i
$285$		0			0
$286$	0.568899	−	3.80365i	0.0336397	−	0.224914i
$287$	23.2400			1.37181
$288$	−0.951606	+	1.64823i	−0.0560739	+	0.0971229i
$289$	7.64050	−	13.2337i	0.449441	−	0.778455i
$290$		0			0
$291$	−9.43356			−0.553005
$292$	7.67630	+	13.2957i	0.449221	+	0.778074i
$293$	10.4573	+	18.1126i	0.610922	+	1.05815i	0.991085	+	0.133228i	$0.0425343\pi$
$293$	10.4573	+	18.1126i	0.610922	+	1.05815i	−0.380164	+	0.924919i	$0.624132\pi$
$294$	18.2351			1.06349
$295$		0			0
$296$	−2.51037	+	4.34809i	−0.145912	+	0.252728i
$297$	1.29529	−	2.24350i	0.0751601	−	0.130181i
$298$	7.28592			0.422062
$299$	−7.20495	+	2.83716i	−0.416673	+	0.164077i
$300$		0			0
$301$	3.90321	−	6.76056i	0.224977	−	0.389672i
$302$	−10.0541	+	17.4142i	−0.578547	+	1.00207i
$303$	−1.61507	−	2.79738i	−0.0927834	−	0.160706i
$304$	−6.59210			−0.378083
$305$		0			0
$306$	−1.24766	−	2.16101i	−0.0713239	−	0.123537i
$307$	12.5303			0.715145			0.357572	−	0.933885i	$-0.383605\pi$
$307$	12.5303			0.715145			0.357572	+	0.933885i	$0.383605\pi$
$308$	2.08173	+	3.60567i	0.118618	+	0.205452i
$309$	11.3422	−	19.6453i	0.645237	−	1.11758i
$310$		0			0
$311$	−9.78123			−0.554643			−0.277321	−	0.960777i	$-0.589447\pi$
$311$	−9.78123			−0.554643			−0.277321	+	0.960777i	$0.589447\pi$
$312$	−7.42864	+	2.92525i	−0.420564	+	0.165610i
$313$	17.2128			0.972924			0.486462	−	0.873702i	$-0.338287\pi$
$313$	17.2128			0.972924			0.486462	+	0.873702i	$0.338287\pi$
$314$	0.992089	−	1.71835i	0.0559868	−	0.0969720i
$315$		0			0
$316$	−2.15087	−	3.72542i	−0.120996	−	0.209571i
$317$	13.7447			0.771978			0.385989	−	0.922503i	$-0.373860\pi$
$317$	13.7447			0.771978			0.385989	+	0.922503i	$0.373860\pi$
$318$	1.65555	+	2.86750i	0.0928389	+	0.160802i
$319$	4.82717	+	8.36090i	0.270269	+	0.468120i
$320$		0			0
$321$	2.45161	+	4.24631i	0.136835	+	0.237006i
$322$	4.19135	−	7.25964i	0.233575	−	0.404564i
$323$	4.32148	−	7.48502i	0.240454	−	0.416478i
$324$	−11.0874			−0.615968
$325$		0			0
$326$	−4.70318			−0.260485
$327$	−0.147643	+	0.255726i	−0.00816469	+	0.0141417i
$328$	2.97703	−	5.15637i	0.164379	−	0.284713i
$329$	−0.188892	−	0.327171i	−0.0104140	−	0.0180375i
$330$		0			0
$331$	−9.69381	−	16.7902i	−0.532820	−	0.922872i	−0.999265	−	0.0383216i	$-0.987799\pi$
$331$	−9.69381	−	16.7902i	−0.532820	−	0.922872i	0.466445	−	0.884550i	$-0.345534\pi$
$332$	−4.84691	−	8.39509i	−0.266009	−	0.460740i
$333$	9.55554			0.523640
$334$	4.84767	+	8.39642i	0.265253	+	0.459431i
$335$		0			0
$336$	4.32148	−	7.48502i	0.235756	−	0.408341i
$337$	0.555539			0.0302621			0.0151311	−	0.999886i	$-0.495183\pi$
$337$	0.555539			0.0302621			0.0151311	+	0.999886i	$0.495183\pi$
$338$	−12.4311	−	3.80365i	−0.676163	−	0.206891i
$339$	−31.0005			−1.68371
$340$		0			0
$341$	3.69281	−	6.39614i	0.199977	−	0.346370i
$342$	6.27309	+	10.8653i	0.339210	+	0.587528i
$343$	−4.82071			−0.260294
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	24.0716			1.29410
$347$	−3.34222	−	5.78890i	−0.179420	−	0.310764i	0.762262	−	0.647269i	$-0.224089\pi$
$347$	−3.34222	−	5.78890i	−0.179420	−	0.310764i	−0.941682	+	0.336504i	$0.890755\pi$
$348$	10.0207	−	17.3564i	0.537168	−	0.930403i
$349$	−5.29137	+	9.16492i	−0.283240	+	0.490587i	−0.972181	−	0.234231i	$-0.924743\pi$
$349$	−5.29137	+	9.16492i	−0.283240	+	0.490587i	0.688941	+	0.724818i	$0.258076\pi$
$350$		0			0
$351$	−6.85236	−	5.45188i	−0.365752	−	0.291000i
$352$	1.06668			0.0568541
$353$	4.60470	−	7.97557i	0.245083	−	0.424497i	−0.717072	−	0.696999i	$-0.754518\pi$
$353$	4.60470	−	7.97557i	0.245083	−	0.424497i	0.962155	+	0.272503i	$0.0878513\pi$
$354$	−7.95407	+	13.7768i	−0.422754	+	0.732231i
$355$		0			0
$356$	4.52543			0.239847
$357$	5.66593	+	9.81367i	0.299873	+	0.519395i
$358$	−1.52543	−	2.64212i	−0.0806214	−	0.139640i
$359$	−4.19358			−0.221328			−0.110664	−	0.993858i	$-0.535298\pi$
$359$	−4.19358			−0.221328			−0.110664	+	0.993858i	$0.535298\pi$
$360$		0			0
$361$	−12.2279	+	21.1794i	−0.643575	+	1.11470i
$362$	−5.32148	+	9.21707i	−0.279691	+	0.484439i
$363$	−21.8381			−1.14620
$364$	13.0946	−	5.15637i	0.686342	−	0.270267i
$365$		0			0
$366$	−8.73260	+	15.1253i	−0.456460	+	0.790613i
$367$	−6.98418	+	12.0970i	−0.364571	+	0.631456i	−0.988707	−	0.149860i	$-0.952118\pi$
$367$	−6.98418	+	12.0970i	−0.364571	+	0.631456i	0.624136	+	0.781316i	$0.285451\pi$
$368$	−1.07382	−	1.85991i	−0.0559768	−	0.0969547i
$369$	−11.3319			−0.589913
$370$		0			0
$371$	−2.91827	−	5.05459i	−0.151509	−	0.262421i
$372$	−15.3319			−0.794919
$373$	−5.92396	−	10.2606i	−0.306731	−	0.531273i	0.670914	−	0.741535i	$-0.265902\pi$
$373$	−5.92396	−	10.2606i	−0.306731	−	0.531273i	−0.977645	+	0.210262i	$0.932568\pi$
$374$	−0.699264	+	1.21116i	−0.0361581	+	0.0626276i
$375$		0			0
$376$	−0.0967881			−0.00499146
$377$	30.3640	−	11.9567i	1.56382	−	0.615802i
$378$	9.47949			0.487573
$379$	−0.303197	+	0.525153i	−0.0155742	+	0.0269753i	−0.873707	−	0.486452i	$-0.838291\pi$
$379$	−0.303197	+	0.525153i	−0.0155742	+	0.0269753i	0.858133	+	0.513427i	$0.171624\pi$
$380$		0			0
$381$	−11.0612	−	19.1586i	−0.566684	−	0.981525i
$382$	14.7304			0.753672
$383$	17.3899	+	30.1201i	0.888580	+	1.53907i	0.841555	+	0.540172i	$0.181641\pi$
$383$	17.3899	+	30.1201i	0.888580	+	1.53907i	0.0470252	+	0.998894i	$0.485026\pi$
$384$	−1.10716	−	1.91766i	−0.0564995	−	0.0978600i
$385$		0			0
$386$	7.00000	+	12.1244i	0.356291	+	0.617113i
$387$	−1.90321	+	3.29646i	−0.0967457	+	0.167568i
$388$	2.13013	−	3.68949i	0.108141	−	0.187305i
$389$	−18.6844			−0.947339			−0.473670	−	0.880703i	$-0.657071\pi$
$389$	−18.6844			−0.947339			−0.473670	+	0.880703i	$0.657071\pi$
$390$		0			0
$391$	2.81579			0.142401
$392$	−4.11753	+	7.13177i	−0.207967	+	0.360209i
$393$	−10.2477	+	17.7495i	−0.516926	+	0.895342i
$394$	5.20641	+	9.01776i	0.262295	+	0.454308i
$395$		0			0
$396$	−1.01506	−	1.75813i	−0.0510085	−	0.0883493i
$397$	−11.4874	−	19.8968i	−0.576536	−	0.998590i	−0.995873	−	0.0907594i	$-0.971071\pi$
$397$	−11.4874	−	19.8968i	−0.576536	−	0.998590i	0.419337	−	0.907831i	$-0.362263\pi$
$398$	−4.36842			−0.218969
$399$	−28.4876	−	49.3420i	−1.42617	−	2.47019i
$400$		0			0
$401$	2.18667	−	3.78742i	0.109197	−	0.189135i	−0.806248	−	0.591577i	$-0.798505\pi$
$401$	2.18667	−	3.78742i	0.109197	−	0.189135i	0.915445	+	0.402443i	$0.131839\pi$
$402$	−18.6637			−0.930861
$403$	−19.5358	−	15.5431i	−0.973147	−	0.774256i
$404$	1.45875			0.0725756
$405$		0			0
$406$	−17.6637	+	30.5944i	−0.876635	+	1.51838i
$407$	−2.67775	−	4.63801i	−0.132731	−	0.229897i
$408$	2.90321			0.143730
$409$	1.88493	+	3.26479i	0.0932038	+	0.161434i	0.908858	−	0.417107i	$-0.136956\pi$
$409$	1.88493	+	3.26479i	0.0932038	+	0.161434i	−0.815654	+	0.578540i	$0.803623\pi$
$410$		0			0
$411$	−32.7511			−1.61549
$412$	5.12222	+	8.87194i	0.252353	+	0.437089i
$413$	14.0207	−	24.2846i	0.689916	−	1.19497i
$414$	−2.04371	+	3.53981i	−0.100443	+	0.173972i
$415$		0			0
$416$	0.533338	−	3.56589i	0.0261491	−	0.174832i
$417$	−28.1082			−1.37646
$418$	3.51582	−	6.08958i	0.171964	−	0.297851i
$419$	−3.72615	+	6.45388i	−0.182034	+	0.315293i	−0.942573	−	0.334000i	$-0.891602\pi$
$419$	−3.72615	+	6.45388i	−0.182034	+	0.315293i	0.760539	+	0.649292i	$0.224935\pi$
$420$		0			0
$421$	27.6751			1.34880			0.674400	−	0.738366i	$-0.264402\pi$
$421$	27.6751			1.34880			0.674400	+	0.738366i	$0.264402\pi$
$422$	−2.74766	−	4.75908i	−0.133754	−	0.231669i
$423$	0.0921041	+	0.159529i	0.00447825	+	0.00775657i
$424$	−1.49532			−0.0726190
$425$		0			0
$426$	17.1383	−	29.6844i	0.830352	−	1.43821i
$427$	15.3931	−	26.6616i	0.744923	−	1.29024i
$428$	−2.21432			−0.107033
$429$	1.25973	−	8.42249i	0.0608201	−	0.406642i
$430$		0			0
$431$	−9.84468	+	17.0515i	−0.474202	+	0.821342i	−0.999564	−	0.0295373i	$-0.990597\pi$
$431$	−9.84468	+	17.0515i	−0.474202	+	0.821342i	0.525362	+	0.850879i	$0.323930\pi$
$432$	1.21432	−	2.10326i	0.0584240	−	0.101193i
$433$	6.87310	+	11.9046i	0.330300	+	0.572097i	0.982571	−	0.185890i	$-0.0595167\pi$
$433$	6.87310	+	11.9046i	0.330300	+	0.572097i	−0.652270	+	0.757986i	$0.726183\pi$
$434$	27.0257			1.29727
$435$		0			0
$436$	−0.0666765	−	0.115487i	−0.00319323	−	0.00553083i
$437$	−14.1575			−0.677244
$438$	16.9978	+	29.4410i	0.812185	+	1.40675i
$439$	−20.9114	+	36.2195i	−0.998045	+	1.72866i	−0.444894	+	0.895583i	$0.646758\pi$
$439$	−20.9114	+	36.2195i	−0.998045	+	1.72866i	−0.553151	+	0.833081i	$0.686575\pi$
$440$		0			0
$441$	15.6731			0.746337
$442$	3.69926	+	2.94321i	0.175956	+	0.139994i
$443$	−23.6829			−1.12521			−0.562605	−	0.826726i	$-0.690201\pi$
$443$	−23.6829			−1.12521			−0.562605	+	0.826726i	$0.690201\pi$
$444$	−5.55877	+	9.62806i	−0.263807	+	0.456928i
$445$		0			0
$446$	10.0484	+	17.4043i	0.475805	+	0.824119i
$447$	16.1334			0.763081
$448$	1.95161	+	3.38028i	0.0922047	+	0.159703i
$449$	−3.52789	−	6.11048i	−0.166491	−	0.288371i	0.770693	−	0.637207i	$-0.219910\pi$
$449$	−3.52789	−	6.11048i	−0.166491	−	0.288371i	−0.937184	+	0.348836i	$0.886577\pi$
$450$		0			0
$451$	3.17553	+	5.50018i	0.149530	+	0.258993i
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$	−22.2630	+	38.5606i	−1.04600	+	1.81173i
$454$	19.3590			0.908565
$455$		0			0
$456$	−14.5970			−0.683568
$457$	17.8398	−	30.8994i	0.834509	−	1.44541i	−0.0599208	−	0.998203i	$-0.519085\pi$
$457$	17.8398	−	30.8994i	0.834509	−	1.44541i	0.894430	−	0.447209i	$-0.147582\pi$
$458$	−7.86273	+	13.6186i	−0.367401	+	0.636358i
$459$	1.59210	+	2.75761i	0.0743131	+	0.128714i
$460$		0			0
$461$	7.30074	+	12.6452i	0.340029	+	0.588948i	0.984438	−	0.175734i	$-0.0562297\pi$
$461$	7.30074	+	12.6452i	0.340029	+	0.588948i	−0.644409	+	0.764681i	$0.722896\pi$
$462$	4.60962	+	7.98410i	0.214459	+	0.371454i
$463$	30.7511			1.42913			0.714563	−	0.699571i	$-0.246626\pi$
$463$	30.7511			1.42913			0.714563	+	0.699571i	$0.246626\pi$
$464$	4.52543	+	7.83827i	0.210088	+	0.363883i
$465$		0			0
$466$	7.44123	−	12.8886i	0.344709	−	0.597053i
$467$	−20.5620			−0.951496			−0.475748	−	0.879582i	$-0.657822\pi$
$467$	−20.5620			−0.951496			−0.475748	+	0.879582i	$0.657822\pi$
$468$	−6.38493	+	2.51426i	−0.295143	+	0.116221i
$469$	32.8988			1.51912
$470$		0			0
$471$	2.19680	−	3.80497i	0.101223	−	0.175324i
$472$	−3.59210	−	6.22171i	−0.165340	−	0.286377i
$473$	2.13335			0.0980917
$474$	−4.76271	−	8.24926i	−0.218759	−	0.378901i
$475$		0			0
$476$	−5.11753			−0.234562
$477$	1.42295	+	2.46462i	0.0651525	+	0.112847i
$478$	−2.21109	+	3.82973i	−0.101133	+	0.175168i
$479$	−5.96666	+	10.3346i	−0.272624	+	0.472198i	−0.969533	−	0.244961i	$-0.921225\pi$
$479$	−5.96666	+	10.3346i	−0.272624	+	0.472198i	0.696909	+	0.717159i	$0.254558\pi$
$480$		0			0
$481$	−16.8437	+	6.63270i	−0.768006	+	0.302425i
$482$	−11.2810			−0.513835
$483$	9.28100	−	16.0752i	0.422300	−	0.731445i
$484$	4.93110	−	8.54092i	0.224141	−	0.388223i
$485$		0			0
$486$	−17.2652			−0.783164
$487$	13.9859	+	24.2244i	0.633764	+	1.09771i	0.986776	+	0.162092i	$0.0518242\pi$
$487$	13.9859	+	24.2244i	0.633764	+	1.09771i	−0.353012	+	0.935619i	$0.614842\pi$
$488$	−3.94370	−	6.83068i	−0.178523	−	0.309210i
$489$	−10.4143			−0.470953
$490$		0			0
$491$	10.3906	−	17.9971i	0.468922	−	0.812197i	−0.530447	−	0.847718i	$-0.677976\pi$
$491$	10.3906	−	17.9971i	0.468922	−	0.812197i	0.999369	+	0.0355214i	$0.0113092\pi$
$492$	6.59210	−	11.4179i	0.297195	−	0.514757i
$493$	−11.8666			−0.534447
$494$	−18.5995	−	14.7981i	−0.836830	−	0.665800i
$495$		0			0
$496$	3.46198	−	5.99632i	0.155447	−	0.269243i
$497$	−30.2099	+	52.3250i	−1.35510	+	2.34710i
$498$	−10.7326	−	18.5894i	−0.480939	−	0.833011i
$499$	34.2908			1.53507			0.767534	−	0.641008i	$-0.221483\pi$
$499$	34.2908			1.53507			0.767534	+	0.641008i	$0.221483\pi$
$500$		0			0
$501$	10.7343	+	18.5923i	0.479573	+	0.830645i
$502$	2.65233			0.118379
$503$	10.1128	+	17.5160i	0.450910	+	0.780998i	0.998443	−	0.0557857i	$-0.0177663\pi$
$503$	10.1128	+	17.5160i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$504$	3.71432	−	6.43339i	0.165449	−	0.286566i
$505$		0			0
$506$	2.29084			0.101840
$507$	−27.5264	−	8.42249i	−1.22249	−	0.374056i
$508$	9.99063			0.443263
$509$	13.6889	−	23.7099i	0.606749	−	1.05092i	−0.385023	−	0.922907i	$-0.625806\pi$
$509$	13.6889	−	23.7099i	0.606749	−	1.05092i	0.991772	−	0.128014i	$-0.0408602\pi$
$510$		0			0
$511$	−29.9622	−	51.8961i	−1.32545	−	2.29575i
$512$	1.00000			0.0441942
$513$	−8.00492	−	13.8649i	−0.353426	−	0.612152i
$514$	−2.05086	−	3.55219i	−0.0904593	−	0.156680i
$515$		0			0
$516$	−2.21432	−	3.83531i	−0.0974800	−	0.168840i
$517$	0.0516208	−	0.0894098i	0.00227028	−	0.00393224i
$518$	9.79851	−	16.9715i	0.430522	−	0.745686i
$519$	53.3022			2.33971
$520$		0			0
$521$	−31.2034			−1.36705			−0.683523	−	0.729929i	$-0.739553\pi$
$521$	−31.2034			−1.36705			−0.683523	+	0.729929i	$0.739553\pi$
$522$	8.61285	−	14.9179i	0.376974	−	0.652938i
$523$	4.92396	−	8.52854i	0.215310	−	0.372927i	−0.738059	−	0.674736i	$-0.764257\pi$
$523$	4.92396	−	8.52854i	0.215310	−	0.372927i	0.953368	+	0.301809i	$0.0975906\pi$
$524$	−4.62790	−	8.01576i	−0.202171	−	0.350170i
$525$		0			0
$526$	5.40099	+	9.35479i	0.235494	+	0.407888i
$527$	4.53903	+	7.86182i	0.197723	+	0.342466i
$528$	2.36196			0.102791
$529$	9.19381	+	15.9242i	0.399731	+	0.692355i
$530$		0			0
$531$	−6.83654	+	11.8412i	−0.296680	+	0.513865i
$532$	25.7304			1.11555
$533$	19.9748	−	7.86567i	0.865205	−	0.340700i
$534$	10.0207			0.433640
$535$		0			0
$536$	4.21432	−	7.29942i	0.182031	−	0.315287i
$537$	−3.37778	−	5.85049i	−0.145762	−	0.252467i
$538$	−18.5827			−0.801159
$539$	−4.39207	−	7.60730i	−0.189180	−	0.327669i
$540$		0			0
$541$	41.6149			1.78916			0.894581	−	0.446905i	$-0.147474\pi$
$541$	41.6149			1.78916			0.894581	+	0.446905i	$0.147474\pi$
$542$	−9.88739	−	17.1255i	−0.424700	−	0.735602i
$543$	−11.7835	+	20.4095i	−0.505677	+	0.875857i
$544$	−0.655554	+	1.13545i	−0.0281066	+	0.0486821i
$545$		0			0
$546$	28.9956	−	11.4179i	1.24090	−	0.488639i
$547$	6.77430			0.289648			0.144824	−	0.989457i	$-0.453738\pi$
$547$	6.77430			0.289648			0.144824	+	0.989457i	$0.453738\pi$
$548$	7.39530	−	12.8090i	0.315912	−	0.547175i
$549$	−7.50569	+	13.0002i	−0.320335	+	0.554836i
$550$		0			0
$551$	59.6642			2.54178
$552$	−2.37778	−	4.11844i	−0.101205	−	0.175293i
$553$	8.39530	+	14.5411i	0.357005	+	0.618350i
$554$	0.204952			0.00870757
$555$		0			0
$556$	6.34691	−	10.9932i	0.269169	−	0.466214i
$557$	−12.7225	+	22.0360i	−0.539068	+	0.933694i	0.459886	+	0.887978i	$0.347890\pi$
$557$	−12.7225	+	22.0360i	−0.539068	+	0.933694i	−0.998954	+	0.0457158i	$0.985443\pi$
$558$	−13.1778			−0.557859
$559$	1.06668	−	7.13177i	0.0451156	−	0.301642i
$560$		0			0
$561$	−1.54839	+	2.68190i	−0.0653732	+	0.113230i
$562$	10.2279	−	17.7153i	0.431439	−	0.747274i
$563$	−6.59210	−	11.4179i	−0.277824	−	0.481205i	0.693020	−	0.720919i	$-0.256280\pi$
$563$	−6.59210	−	11.4179i	−0.277824	−	0.481205i	−0.970844	+	0.239713i	$0.922947\pi$
$564$	−0.214320			−0.00902449
$565$		0			0
$566$	−0.719004	−	1.24535i	−0.0302220	−	0.0523460i
$567$	43.2766			1.81744
$568$	7.73975	+	13.4056i	0.324753	+	0.562488i
$569$	12.2304	−	21.1836i	0.512724	−	0.888064i	−0.487167	−	0.873309i	$-0.661970\pi$
$569$	12.2304	−	21.1836i	0.512724	−	0.888064i	0.999891	−	0.0147555i	$-0.00469698\pi$
$570$		0			0
$571$	24.3526			1.01912			0.509562	−	0.860434i	$-0.329807\pi$
$571$	24.3526			1.01912			0.509562	+	0.860434i	$0.329807\pi$
$572$	3.00961	+	2.39451i	0.125838	+	0.100119i
$573$	32.6178			1.36263
$574$	−11.6200	+	20.1264i	−0.485009	+	0.840060i
$575$		0			0
$576$	−0.951606	−	1.64823i	−0.0396502	−	0.0686762i
$577$	−42.0479			−1.75048			−0.875239	−	0.483690i	$-0.839296\pi$
$577$	−42.0479			−1.75048			−0.875239	+	0.483690i	$0.839296\pi$
$578$	7.64050	+	13.2337i	0.317803	+	0.550451i
$579$	15.5002	+	26.8472i	0.644168	+	1.11573i
$580$		0			0
$581$	18.9185	+	32.7678i	0.784872	+	1.35944i
$582$	4.71678	−	8.16970i	0.195517	−	0.338645i
$583$	0.797509	−	1.38133i	0.0330295	−	0.0572087i
$584$	−15.3526			−0.635295
$585$		0			0
$586$	−20.9146			−0.863974
$587$	3.67307	−	6.36195i	0.151604	−	0.262586i	−0.780213	−	0.625513i	$-0.784890\pi$
$587$	3.67307	−	6.36195i	0.151604	−	0.262586i	0.931817	+	0.362928i	$0.118223\pi$
$588$	−9.11753	+	15.7920i	−0.376001	+	0.651252i
$589$	−22.8217	−	39.5284i	−0.940353	−	1.62874i
$590$		0			0
$591$	11.5287	+	19.9682i	0.474225	+	0.821383i
$592$	−2.51037	−	4.34809i	−0.103176	−	0.178705i
$593$	4.19358			0.172210			0.0861048	−	0.996286i	$-0.472558\pi$
$593$	4.19358			0.172210			0.0861048	+	0.996286i	$0.472558\pi$
$594$	1.29529	+	2.24350i	0.0531462	+	0.0920520i
$595$		0			0
$596$	−3.64296	+	6.30979i	−0.149221	+	0.258459i
$597$	−9.67307			−0.395892
$598$	1.14542	−	7.65825i	0.0468397	−	0.313169i
$599$	9.33630			0.381471			0.190735	−	0.981641i	$-0.438913\pi$
$599$	9.33630			0.381471			0.190735	+	0.981641i	$0.438913\pi$
$600$		0			0
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	−0.834132	−	0.551565i	$-0.814031\pi$
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	0.894735	+	0.446597i	$0.147364\pi$
$602$	3.90321	+	6.76056i	0.159083	+	0.275540i
$603$	−16.0415			−0.653260
$604$	−10.0541	−	17.4142i	−0.409095	−	0.708573i
$605$		0			0
$606$	3.23014			0.131216
$607$	8.57160	+	14.8464i	0.347910	+	0.602599i	0.985878	−	0.167465i	$-0.0535580\pi$
$607$	8.57160	+	14.8464i	0.347910	+	0.602599i	−0.637968	+	0.770063i	$0.720225\pi$
$608$	3.29605	−	5.70893i	0.133673	−	0.231528i
$609$	−39.1131	+	67.7459i	−1.58494	+	2.74520i
$610$		0			0
$611$	−0.273086	−	0.217273i	−0.0110479	−	0.00878991i
$612$	2.49532			0.100867
$613$	14.6422	−	25.3610i	0.591393	−	1.02432i	−0.402653	−	0.915353i	$-0.631912\pi$
$613$	14.6422	−	25.3610i	0.591393	−	1.02432i	0.994045	−	0.108969i	$-0.0347550\pi$
$614$	−6.26517	+	10.8516i	−0.252842	+	0.437935i
$615$		0			0
$616$	−4.16346			−0.167751
$617$	6.60793	+	11.4453i	0.266025	+	0.460769i	0.967832	−	0.251599i	$-0.0809563\pi$
$617$	6.60793	+	11.4453i	0.266025	+	0.460769i	−0.701807	+	0.712368i	$0.747623\pi$
$618$	11.3422	+	19.6453i	0.456251	+	0.790250i
$619$	−18.9333			−0.760995			−0.380497	−	0.924782i	$-0.624247\pi$
$619$	−18.9333			−0.760995			−0.380497	+	0.924782i	$0.624247\pi$
$620$		0			0
$621$	2.60793	−	4.51706i	0.104652	−	0.181263i
$622$	4.89062	−	8.47080i	0.196096	−	0.339648i
$623$	−17.6637			−0.707681
$624$	1.18098	−	7.89601i	0.0472771	−	0.316094i
$625$		0			0
$626$	−8.60639	+	14.9067i	−0.343981	+	0.595792i
$627$	7.78515	−	13.4843i	0.310909	−	0.538510i
$628$	0.992089	+	1.71835i	0.0395887	+	0.0685696i
$629$	6.58274			0.262471
$630$		0			0
$631$	−1.21432	−	2.10326i	−0.0483413	−	0.0837296i	0.840842	−	0.541280i	$-0.182060\pi$
$631$	−1.21432	−	2.10326i	−0.0483413	−	0.0837296i	−0.889184	+	0.457551i	$0.848727\pi$
$632$	4.30174			0.171114
$633$	−6.08419	−	10.5381i	−0.241825	−	0.418853i
$634$	−6.87233	+	11.9032i	−0.272935	+	0.472738i
$635$		0			0
$636$	−3.31111			−0.131294
$637$	−27.6271	+	10.8790i	−1.09463	+	0.431042i
$638$	−9.65433			−0.382219
$639$	14.7304	−	25.5138i	0.582725	−	1.00931i
$640$		0			0
$641$	−7.54371	−	13.0661i	−0.297959	−	0.516079i	0.677710	−	0.735329i	$-0.262972\pi$
$641$	−7.54371	−	13.0661i	−0.297959	−	0.516079i	−0.975669	+	0.219250i	$0.929639\pi$
$642$	−4.90321			−0.193514
$643$	3.35159	+	5.80513i	0.132174	+	0.228932i	0.924514	−	0.381147i	$-0.124471\pi$
$643$	3.35159	+	5.80513i	0.132174	+	0.228932i	−0.792340	+	0.610079i	$0.791138\pi$
$644$	4.19135	+	7.25964i	0.165162	+	0.286070i
$645$		0			0
$646$	4.32148	+	7.48502i	0.170026	+	0.294494i
$647$	−11.1867	+	19.3759i	−0.439793	+	0.761744i	−0.997673	−	0.0681773i	$-0.978282\pi$
$647$	−11.1867	+	19.3759i	−0.439793	+	0.761744i	0.557880	+	0.829922i	$0.311615\pi$
$648$	5.54371	−	9.60199i	0.217777	−	0.377202i
$649$	7.66323			0.300808
$650$		0			0
$651$	59.8435			2.34545
$652$	2.35159	−	4.07308i	0.0920954	−	0.159514i
$653$	−8.20641	+	14.2139i	−0.321142	+	0.556234i	−0.980724	−	0.195399i	$-0.937400\pi$
$653$	−8.20641	+	14.2139i	−0.321142	+	0.556234i	0.659582	+	0.751632i	$0.270733\pi$
$654$	−0.147643	−	0.255726i	−0.00577331	−	0.00999966i
$655$		0			0
$656$	2.97703	+	5.15637i	0.116234	+	0.201323i
$657$	14.6096	+	25.3046i	0.569976	+	0.987227i
$658$	0.377784			0.0147276
$659$	−4.33407	−	7.50684i	−0.168832	−	0.292425i	0.769178	−	0.639035i	$-0.220666\pi$
$659$	−4.33407	−	7.50684i	−0.168832	−	0.292425i	−0.938009	+	0.346610i	$0.887333\pi$
$660$		0			0
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	−0.984241	−	0.176834i	$-0.943414\pi$
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	0.645263	+	0.763960i	$0.276748\pi$
$662$	19.3876			0.753522
$663$	8.19135	+	6.51721i	0.318126	+	0.253108i
$664$	9.69381			0.376193
$665$		0			0
$666$	−4.77777	+	8.27534i	−0.185135	+	0.320663i
$667$	9.71900	+	16.8338i	0.376321	+	0.651808i
$668$	−9.69535			−0.375124
$669$	22.2504	+	38.5387i	0.860249	+	1.48999i
$670$		0			0
$671$	8.41329			0.324792
$672$	4.32148	+	7.48502i	0.166705	+	0.288741i
$673$	−20.2415	+	35.0593i	−0.780253	+	1.35144i	0.151541	+	0.988451i	$0.451576\pi$
$673$	−20.2415	+	35.0593i	−0.780253	+	1.35144i	−0.931794	+	0.362987i	$0.881757\pi$
$674$	−0.277770	+	0.481111i	−0.0106993	+	0.0185317i
$675$		0			0
$676$	9.50961	−	8.86382i	0.365754	−	0.340916i
$677$	40.0228			1.53820			0.769100	−	0.639129i	$-0.220705\pi$
$677$	40.0228			1.53820			0.769100	+	0.639129i	$0.220705\pi$
$678$	15.5002	−	26.8472i	0.595283	−	1.03106i
$679$	−8.31433	+	14.4008i	−0.319075	+	0.552654i
$680$		0			0
$681$	42.8671			1.64267
$682$	3.69281	+	6.39614i	0.141405	+	0.244921i
$683$	−21.6543	−	37.5064i	−0.828580	−	1.43514i	−0.899152	−	0.437636i	$-0.855816\pi$
$683$	−21.6543	−	37.5064i	−0.828580	−	1.43514i	0.0705721	−	0.997507i	$-0.477518\pi$
$684$	−12.5462			−0.479715
$685$		0			0
$686$	2.41036	−	4.17486i	0.0920279	−	0.159397i
$687$	−17.4106	+	30.1560i	−0.664256	+	1.15052i
$688$	2.00000			0.0762493
$689$	−4.21900	−	3.35673i	−0.160731	−	0.127881i
$690$		0			0
$691$	−14.1741	+	24.5502i	−0.539207	+	0.933934i	0.459740	+	0.888054i	$0.347943\pi$
$691$	−14.1741	+	24.5502i	−0.539207	+	0.933934i	−0.998947	+	0.0458806i	$0.985391\pi$
$692$	−12.0358	+	20.8466i	−0.457532	+	0.792469i
$693$	3.96198	+	6.86235i	0.150503	+	0.260679i
$694$	6.68445			0.253738
$695$		0			0
$696$	10.0207	+	17.3564i	0.379835	+	0.657894i
$697$	−7.80642			−0.295689
$698$	−5.29137	−	9.16492i	−0.200281	−	0.346897i
$699$	16.4773	−	28.5395i	0.623228	−	1.07946i
$700$		0			0
$701$	12.8080			0.483750			0.241875	−	0.970307i	$-0.422238\pi$
$701$	12.8080			0.483750			0.241875	+	0.970307i	$0.422238\pi$
$702$	8.14764	−	3.20838i	0.307513	−	0.121092i
$703$	−33.0973			−1.24829
$704$	−0.533338	+	0.923769i	−0.0201009	+	0.0348159i
$705$		0			0
$706$	4.60470	+	7.97557i	0.173300	+	0.300165i
$707$	−5.69381			−0.214138
$708$	−7.95407	−	13.7768i	−0.298932	−	0.517766i
$709$	−1.26126	−	2.18456i	−0.0473675	−	0.0820429i	0.841370	−	0.540460i	$-0.181750\pi$
$709$	−1.26126	−	2.18456i	−0.0473675	−	0.0820429i	−0.888737	+	0.458417i	$0.848417\pi$
$710$		0			0
$711$	−4.09356	−	7.09026i	−0.153521	−	0.265905i
$712$	−2.26271	+	3.91914i	−0.0847988	+	0.146876i
$713$	7.43509	−	12.8780i	0.278446	−	0.482283i
$714$	−11.3319			−0.424084
$715$		0			0
$716$	3.05086			0.114016
$717$	−4.89607	+	8.48024i	−0.182847	+	0.316700i
$718$	2.09679	−	3.63174i	0.0782514	−	0.135535i
$719$	−8.51114	−	14.7417i	−0.317412	−	0.549773i	0.662535	−	0.749031i	$-0.269480\pi$
$719$	−8.51114	−	14.7417i	−0.317412	−	0.549773i	−0.979947	+	0.199257i	$0.936147\pi$
$720$		0			0
$721$	−19.9931	−	34.6291i	−0.744582	−	1.28965i
$722$	−12.2279	−	21.1794i	−0.455076	−	0.788215i
$723$	−24.9797			−0.929006
$724$	−5.32148	−	9.21707i	−0.197771	−	0.342550i
$725$		0			0
$726$	10.9190	−	18.9123i	0.405243	−	0.701902i
$727$	−30.5353			−1.13249			−0.566245	−	0.824237i	$-0.691605\pi$
$727$	−30.5353			−1.13249			−0.566245	+	0.824237i	$0.691605\pi$
$728$	−2.08173	+	13.9184i	−0.0771541	+	0.515851i
$729$	−4.96836			−0.184013
$730$		0			0
$731$	−1.31111	+	2.27091i	−0.0484931	+	0.0839925i
$732$	−8.73260	−	15.1253i	−0.322766	−	0.559048i
$733$	24.4499			0.903076			0.451538	−	0.892252i	$-0.350876\pi$
$733$	24.4499			0.903076			0.451538	+	0.892252i	$0.350876\pi$
$734$	−6.98418	−	12.0970i	−0.257791	−	0.446507i
$735$		0			0
$736$	2.14764			0.0791632
$737$	4.49532	+	7.78612i	0.165587	+	0.286805i
$738$	5.66593	−	9.81367i	0.208566	−	0.361246i
$739$	5.39776	−	9.34920i	0.198560	−	0.343916i	−0.749502	−	0.662002i	$-0.769707\pi$
$739$	5.39776	−	9.34920i	0.198560	−	0.343916i	0.948062	+	0.318086i	$0.103040\pi$
$740$		0			0
$741$	−41.1852	−	32.7678i	−1.51298	−	1.20376i
$742$	5.83654			0.214266
$743$	−14.9677	+	25.9248i	−0.549110	+	0.951087i	0.449225	+	0.893418i	$0.351700\pi$
$743$	−14.9677	+	25.9248i	−0.549110	+	0.951087i	−0.998336	+	0.0576686i	$0.981633\pi$
$744$	7.66593	−	13.2778i	0.281046	−	0.486787i
$745$		0			0
$746$	11.8479			0.433783
$747$	−9.22469	−	15.9776i	−0.337514	−	0.584591i
$748$	−0.699264	−	1.21116i	−0.0255676	−	0.0442844i
$749$	8.64296			0.315807
$750$		0			0
$751$	−13.4588	+	23.3112i	−0.491117	+	0.850639i	−0.999948	−	0.0102272i	$-0.996745\pi$
$751$	−13.4588	+	23.3112i	−0.491117	+	0.850639i	0.508831	+	0.860866i	$0.330078\pi$
$752$	0.0483940	−	0.0838209i	0.00176475	−	0.00305663i
$753$	5.87310			0.214028
$754$	−4.82717	+	32.2743i	−0.175795	+	1.17536i
$755$		0			0
$756$	−4.73975	+	8.20948i	−0.172383	+	0.298576i
$757$	17.9533	−	31.0960i	0.652524	−	1.13020i	−0.329985	−	0.943986i	$-0.607044\pi$
$757$	17.9533	−	31.0960i	0.652524	−	1.13020i	0.982508	−	0.186218i	$-0.0596231\pi$
$758$	−0.303197	−	0.525153i	−0.0110126	−	0.0190744i
$759$	5.07265			0.184126
$760$		0			0
$761$	−11.2699	−	19.5200i	−0.408532	−	0.707598i	0.586193	−	0.810171i	$-0.300626\pi$
$761$	−11.2699	−	19.5200i	−0.408532	−	0.707598i	−0.994725	+	0.102573i	$0.967293\pi$
$762$	22.1225			0.801412
$763$	0.260253	+	0.450771i	0.00942178	+	0.0163190i
$764$	−7.36519	+	12.7569i	−0.266463	+	0.461528i
$765$		0			0
$766$	−34.7797			−1.25664
$767$	3.83161	−	25.6181i	0.138352	−	0.925015i
$768$	2.21432			0.0799024
$769$	−1.23729	+	2.14304i	−0.0446177	+	0.0772801i	−0.887472	−	0.460862i	$-0.847540\pi$
$769$	−1.23729	+	2.14304i	−0.0446177	+	0.0772801i	0.842854	+	0.538142i	$0.180874\pi$
$770$		0			0
$771$	−4.54125	−	7.86567i	−0.163549	−	0.283275i
$772$	−14.0000			−0.503871
$773$	22.1003	+	38.2788i	0.794891	+	1.37679i	0.922908	+	0.385019i	$0.125805\pi$
$773$	22.1003	+	38.2788i	0.794891	+	1.37679i	−0.128018	+	0.991772i	$0.540861\pi$
$774$	−1.90321	−	3.29646i	−0.0684095	−	0.118489i
$775$		0			0
$776$	2.13013	+	3.68949i	0.0764671	+	0.132445i
$777$	21.6970	−	37.5804i	0.778377	−	1.34819i
$778$	9.34222	−	16.1812i	0.334935	−	0.580124i
$779$	39.2498			1.40627
$780$		0			0
$781$	−16.5116			−0.590832
$782$	−1.40790	+	2.43855i	−0.0503463	+	0.0872023i
$783$	−10.9906	+	19.0363i	−0.392773	+	0.680303i
$784$	−4.11753	−	7.13177i	−0.147055	−	0.254706i
$785$		0			0
$786$	−10.2477	−	17.7495i	−0.365522	−	0.633102i
$787$	−17.0153	−	29.4714i	−0.606530	−	1.05054i	−0.991808	−	0.127740i	$-0.959228\pi$
$787$	−17.0153	−	29.4714i	−0.606530	−	1.05054i	0.385278	−	0.922801i	$-0.374106\pi$
$788$	−10.4128			−0.370941
$789$	11.9595	+	20.7145i	0.425770	+	0.737455i
$790$		0			0
$791$	−27.3225	+	47.3239i	−0.971476	+	1.68265i
$792$	2.03011			0.0721369
$793$	4.20665	−	28.1255i	0.149382	−	0.998767i
$794$	22.9748			0.815346
$795$		0			0
$796$	2.18421	−	3.78316i	0.0774172	−	0.134091i
$797$	−4.06890	−	7.04754i	−0.144128	−	0.249637i	0.784919	−	0.619598i	$-0.212704\pi$
$797$	−4.06890	−	7.04754i	−0.144128	−	0.249637i	−0.929047	+	0.369961i	$0.879371\pi$
$798$	56.9753			2.01690
$799$	0.0634498	+	0.109898i	0.00224469	+	0.00388792i
$800$		0			0
$801$	8.61285			0.304320
$802$	2.18667	+	3.78742i	0.0772140	+	0.133739i
$803$	8.18813	−	14.1823i	0.288953	−	0.500481i
$804$	9.33185	−	16.1632i	0.329109	−	0.570034i
$805$		0			0
$806$	23.2286	−	9.14695i	0.818193	−	0.322188i
$807$	−41.1481			−1.44848
$808$	−0.729376	+	1.26332i	−0.0256593	+	0.0444433i
$809$	3.92618	−	6.80034i	0.138037	−	0.239087i	−0.788716	−	0.614757i	$-0.789254\pi$
$809$	3.92618	−	6.80034i	0.138037	−	0.239087i	0.926754	+	0.375670i	$0.122587\pi$
$810$		0			0
$811$	9.33477			0.327788			0.163894	−	0.986478i	$-0.447595\pi$
$811$	9.33477			0.327788			0.163894	+	0.986478i	$0.447595\pi$
$812$	−17.6637	−	30.5944i	−0.619874	−	1.07365i
$813$	−21.8938	−	37.9213i	−0.767851	−	1.32996i
$814$	5.35551			0.187711
$815$		0			0
$816$	−1.45161	+	2.51426i	−0.0508164	+	0.0880165i
$817$	6.59210	−	11.4179i	0.230629	−	0.399460i
$818$	−3.76986			−0.131810
$819$	24.9217	−	9.81367i	0.870836	−	0.342917i
$820$		0			0
$821$	23.7659	−	41.1638i	0.829437	−	1.43663i	−0.0690434	−	0.997614i	$-0.521995\pi$
$821$	23.7659	−	41.1638i	0.829437	−	1.43663i	0.898480	−	0.439013i	$-0.144672\pi$
$822$	16.3756	−	28.3633i	0.571163	−	0.989284i
$823$	0.693576	+	1.20131i	0.0241765	+	0.0418750i	0.877861	−	0.478916i	$-0.158970\pi$
$823$	0.693576	+	1.20131i	0.0241765	+	0.0418750i	−0.853684	+	0.520791i	$0.825637\pi$
$824$	−10.2444			−0.356882
$825$		0			0
$826$	14.0207	+	24.2846i	0.487844	+	0.844971i
$827$	−31.5131			−1.09582			−0.547910	−	0.836537i	$-0.684576\pi$
$827$	−31.5131			−1.09582			−0.547910	+	0.836537i	$0.684576\pi$
$828$	−2.04371	−	3.53981i	−0.0710238	−	0.123017i
$829$	14.4128	−	24.9637i	0.500578	−	0.867026i	−0.499422	−	0.866359i	$-0.666454\pi$
$829$	14.4128	−	24.9637i	0.500578	−	0.867026i	1.00000		0.000667386i	$-0.000212436\pi$
$830$		0			0
$831$	0.453829			0.0157431
$832$	2.82148	+	2.24483i	0.0978172	+	0.0778254i
$833$	10.7971			0.374096
$834$	14.0541	−	24.3424i	0.486653	−	0.842908i
$835$		0			0
$836$	3.51582	+	6.08958i	0.121597	+	0.210613i
$837$	16.8158			0.581239
$838$	−3.72615	−	6.45388i	−0.128718	−	0.222946i
$839$	−4.21755	−	7.30500i	−0.145606	−	0.252197i	0.783993	−	0.620770i	$-0.213180\pi$
$839$	−4.21755	−	7.30500i	−0.145606	−	0.252197i	−0.929599	+	0.368573i	$0.879846\pi$
$840$		0			0
$841$	−26.4590	−	45.8283i	−0.912379	−	1.58029i
$842$	−13.8375	+	23.9673i	−0.476873	+	0.825968i
$843$	22.6479	−	39.2273i	0.780034	−	1.35106i
$844$	5.49532			0.189157
$845$		0			0
$846$	−0.184208			−0.00633321
$847$	−19.2471	+	33.3370i	−0.661339	+	1.14547i
$848$	0.747658	−	1.29498i	0.0256747	−	0.0444699i
$849$	−1.59210	−	2.75761i	−0.0546409	−	0.0946408i
$850$		0			0
$851$	−5.39138	−	9.33815i	−0.184814	−	0.320108i
$852$	17.1383	+	29.6844i	0.587148	+	1.01697i
$853$	−40.0656			−1.37182			−0.685910	−	0.727686i	$-0.740596\pi$
$853$	−40.0656			−1.37182			−0.685910	+	0.727686i	$0.740596\pi$
$854$	15.3931	+	26.6616i	0.526740	+	0.912341i
$855$		0			0
$856$	1.10716	−	1.91766i	0.0378419	−	0.0655442i
$857$	32.0479			1.09474			0.547368	−	0.836892i	$-0.315630\pi$
$857$	32.0479			1.09474			0.547368	+	0.836892i	$0.315630\pi$
$858$	6.66423	+	5.30220i	0.227513	+	0.181014i
$859$	−26.6894			−0.910630			−0.455315	−	0.890331i	$-0.650473\pi$
$859$	−26.6894			−0.910630			−0.455315	+	0.890331i	$0.650473\pi$
$860$		0			0
$861$	−25.7304	+	44.5663i	−0.876889	+	1.51882i
$862$	−9.84468	−	17.0515i	−0.335311	−	0.580776i
$863$	30.6593			1.04365			0.521827	−	0.853052i	$-0.325251\pi$
$863$	30.6593			1.04365			0.521827	+	0.853052i	$0.325251\pi$
$864$	1.21432	+	2.10326i	0.0413120	+	0.0715545i
$865$		0			0
$866$	−13.7462			−0.467115
$867$	16.9185	+	29.3037i	0.574583	+	0.995206i
$868$	−13.5128	+	23.4049i	−0.458655	+	0.794415i
$869$	−2.29428	+	3.97381i	−0.0778282	+	0.134802i
$870$		0			0
$871$	28.2766	−	11.1347i	0.958114	−	0.377286i
$872$	0.133353			0.00451591
$873$	4.05408	−	7.02188i	0.137210	−	0.237654i
$874$	7.07874	−	12.2607i	0.239442	−	0.414726i
$875$		0			0
$876$	−33.9956			−1.14860
$877$	−10.4652	−	18.1263i	−0.353385	−	0.612081i	0.633455	−	0.773779i	$-0.281636\pi$
$877$	−10.4652	−	18.1263i	−0.353385	−	0.612081i	−0.986840	+	0.161699i	$0.948303\pi$
$878$	−20.9114	−	36.2195i	−0.705724	−	1.22235i
$879$	−46.3116			−1.56205
$880$		0			0
$881$	−10.7351	+	18.5937i	−0.361673	+	0.626437i	−0.988236	−	0.152934i	$-0.951128\pi$
$881$	−10.7351	+	18.5937i	−0.361673	+	0.626437i	0.626563	+	0.779371i	$0.284461\pi$
$882$	−7.83654	+	13.5733i	−0.263870	+	0.457036i
$883$	−7.73530			−0.260314			−0.130157	−	0.991493i	$-0.541548\pi$
$883$	−7.73530			−0.260314			−0.130157	+	0.991493i	$0.541548\pi$
$884$	−4.39853	+	1.73205i	−0.147939	+	0.0582552i
$885$		0			0
$886$	11.8415	−	20.5100i	0.397822	−	0.689047i
$887$	24.2232	−	41.9559i	0.813337	−	1.40874i	−0.0971796	−	0.995267i	$-0.530982\pi$
$887$	24.2232	−	41.9559i	0.813337	−	1.40874i	0.910516	−	0.413473i	$-0.135685\pi$
$888$	−5.55877	−	9.62806i	−0.186540	−	0.323097i
$889$	−38.9956			−1.30787
$890$		0			0
$891$	5.91335	+	10.2422i	0.198105	+	0.343127i
$892$	−20.0968			−0.672890
$893$	−0.319019	−	0.552556i	−0.0106755	−	0.0184906i
$894$	−8.06668	+	13.9719i	−0.269790	+	0.467290i
$895$		0			0
$896$	−3.90321			−0.130397
$897$	2.53633	−	16.9578i	0.0846855	−	0.566205i
$898$	7.05578			0.235454
$899$	−31.3339	+	54.2718i	−1.04504	+	1.81007i
$900$		0			0
$901$	0.980260	+	1.69786i	0.0326572	+	0.0565639i
$902$	−6.35106			−0.211467
$903$	8.64296	+	14.9700i	0.287620	+	0.498172i
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$		0			0
$906$	−22.2630	−	38.5606i	−0.739637	−	1.28109i
$907$	−6.00545	+	10.4017i	−0.199408	+	0.345384i	−0.948337	−	0.317266i	$-0.897235\pi$
$907$	−6.00545	+	10.4017i	−0.199408	+	0.345384i	0.748929	+	0.662650i	$0.230568\pi$
$908$	−9.67952	+	16.7654i	−0.321226	+	0.556380i
$909$	2.77631			0.0920845
$910$		0			0
$911$	−8.10171			−0.268422			−0.134211	−	0.990953i	$-0.542850\pi$
$911$	−8.10171			−0.268422			−0.134211	+	0.990953i	$0.542850\pi$
$912$	7.29851	−	12.6414i	0.241678	−	0.418598i
$913$	−5.17008	+	8.95485i	−0.171105	+	0.296362i
$914$	17.8398	+	30.8994i	0.590087	+	1.02206i
$915$		0			0
$916$	−7.86273	−	13.6186i	−0.259792	−	0.449973i
$917$	18.0637	+	31.2872i	0.596516	+	1.03320i
$918$	−3.18421			−0.105095
$919$	−8.29682	−	14.3705i	−0.273687	−	0.474039i	0.696116	−	0.717929i	$-0.254910\pi$
$919$	−8.29682	−	14.3705i	−0.273687	−	0.474039i	−0.969803	+	0.243890i	$0.921576\pi$
$920$		0			0
$921$	−13.8731	+	24.0289i	−0.457134	+	0.791780i
$922$	−14.6015			−0.480874
$923$	−8.25581	+	55.1981i	−0.271743	+	1.81687i
$924$	−9.21924			−0.303291
$925$		0			0
$926$	−15.3756	+	26.6313i	−0.505272	+	0.875157i
$927$	9.74866	+	16.8852i	0.320188	+	0.554582i
$928$	−9.05086			−0.297109
$929$	−28.5605	−	49.4682i	−0.937038	−	1.62300i	−0.770958	−	0.636886i	$-0.780222\pi$
$929$	−28.5605	−	49.4682i	−0.937038	−	1.62300i	−0.166080	−	0.986112i	$-0.553111\pi$
$930$		0			0
$931$	−54.2864			−1.77916
$932$	7.44123	+	12.8886i	0.243746	+	0.422180i
$933$	10.8294	−	18.7571i	0.354538	−	0.614078i
$934$	10.2810	−	17.8072i	0.336404	−	0.582670i
$935$		0			0
$936$	1.01506	−	6.78664i	0.0331781	−	0.221828i
$937$	−11.1842			−0.365372			−0.182686	−	0.983171i	$-0.558479\pi$
$937$	−11.1842			−0.365372			−0.182686	+	0.983171i	$0.558479\pi$
$938$	−16.4494	+	28.4912i	−0.537091	+	0.930270i
$939$	−19.0573	+	33.0082i	−0.621912	+	1.07718i
$940$		0			0
$941$	−7.68598			−0.250556			−0.125278	−	0.992122i	$-0.539982\pi$
$941$	−7.68598			−0.250556			−0.125278	+	0.992122i	$0.539982\pi$
$942$	2.19680	+	3.80497i	0.0715757	+	0.123973i
$943$	6.39361	+	11.0741i	0.208204	+	0.360621i
$944$	7.18421			0.233826
$945$		0			0
$946$	−1.06668	+	1.84754i	−0.0346806	+	0.0600686i
$947$	−10.3373	+	17.9047i	−0.335917	+	0.581826i	−0.983661	−	0.180033i	$-0.942380\pi$
$947$	−10.3373	+	17.9047i	−0.335917	+	0.581826i	0.647743	+	0.761859i	$0.275713\pi$
$948$	9.52543			0.309372
$949$	−43.3170	−	34.4639i	−1.40613	−	1.11875i
$950$		0			0
$951$	−15.2175	+	26.3576i	−0.493463	+	0.854703i
$952$	2.55877	−	4.43191i	0.0829301	−	0.143639i
$953$	15.4876	+	26.8254i	0.501694	+	0.868959i	0.999998	+	0.00195715i	$0.000622981\pi$
$953$	15.4876	+	26.8254i	0.501694	+	0.868959i	−0.498304	+	0.867002i	$0.666044\pi$
$954$	−2.84590			−0.0921395
$955$		0			0
$956$	−2.21109	−	3.82973i	−0.0715119	−	0.123862i
$957$	−21.3778			−0.691046
$958$	−5.96666	−	10.3346i	−0.192774	−	0.333895i
$959$	−28.8654	+	49.9964i	−0.932113	+	1.61447i
$960$		0			0
$961$	16.9412			0.546489
$962$	2.67775	−	17.9034i	0.0863343	−	0.577229i
$963$	−4.21432			−0.135805
$964$	5.64050	−	9.76963i	0.181668	−	0.314659i
$965$		0			0
$966$	9.28100	+	16.0752i	0.298611	+	0.517210i
$967$	−0.529873			−0.0170396			−0.00851979	−	0.999964i	$-0.502712\pi$
$967$	−0.529873			−0.0170396			−0.00851979	+	0.999964i	$0.502712\pi$
$968$	4.93110	+	8.54092i	0.158492	+	0.274515i
$969$	9.56914	+	16.5742i	0.307405	+	0.532441i
$970$		0			0
$971$	17.1620	+	29.7255i	0.550755	+	0.953936i	0.998220	+	0.0596344i	$0.0189935\pi$
$971$	17.1620	+	29.7255i	0.550755	+	0.953936i	−0.447465	+	0.894301i	$0.647673\pi$
$972$	8.63259	−	14.9521i	0.276890	−	0.479588i
$973$	−24.7733	+	42.9087i	−0.794196	+	1.37559i
$974$	−27.9719			−0.896277
$975$		0			0
$976$	7.88739			0.252469
$977$	−9.98418	+	17.2931i	−0.319422	+	0.553255i	−0.980368	−	0.197179i	$-0.936822\pi$
$977$	−9.98418	+	17.2931i	−0.319422	+	0.553255i	0.660945	+	0.750434i	$0.270155\pi$
$978$	5.20717	−	9.01909i	0.166507	−	0.288399i
$979$	−2.41358	−	4.18045i	−0.0771385	−	0.133608i
$980$		0			0
$981$	−0.126900	−	0.219797i	−0.00405159	−	0.00701756i
$982$	10.3906	+	17.9971i	0.331578	+	0.574310i
$983$	−20.8524			−0.665087			−0.332543	−	0.943088i	$-0.607907\pi$
$983$	−20.8524			−0.665087			−0.332543	+	0.943088i	$0.607907\pi$
$984$	6.59210	+	11.4179i	0.210149	+	0.363988i
$985$		0			0
$986$	5.93332	−	10.2768i	0.188956	−	0.327281i
$987$	0.836535			0.0266272
$988$	22.1153	−	8.70856i	0.703582	−	0.277056i
$989$	4.29529			0.136582
$990$		0			0
$991$	1.47949	−	2.56256i	0.0469977	−	0.0814024i	−0.841570	−	0.540149i	$-0.818368\pi$
$991$	1.47949	−	2.56256i	0.0469977	−	0.0814024i	0.888567	+	0.458746i	$0.151701\pi$
$992$	3.46198	+	5.99632i	0.109918	+	0.190383i
$993$	42.9304			1.36236
$994$	−30.2099	−	52.3250i	−0.958199	−	1.65965i
$995$		0			0
$996$	21.4652			0.680151
$997$	10.5240	+	18.2281i	0.333297	+	0.577288i	0.983156	−	0.182767i	$-0.0585053\pi$
$997$	10.5240	+	18.2281i	0.333297	+	0.577288i	−0.649859	+	0.760055i	$0.725172\pi$
$998$	−17.1454	+	29.6967i	−0.542729	+	0.940034i
$999$	6.09679	−	10.5599i	0.192894	−	0.334102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.j.451.1		6
5.2	odd	4		130.2.n.a.9.3	✓	12
5.3	odd	4		130.2.n.a.9.4	yes	12
5.4	even	2		650.2.e.k.451.3		6
13.3	even	3	inner	650.2.e.j.601.1		6
13.4	even	6		8450.2.a.bt.1.3		3
13.9	even	3		8450.2.a.cb.1.3		3
15.2	even	4		1170.2.bp.h.919.4		12
15.8	even	4		1170.2.bp.h.919.1		12
20.3	even	4		1040.2.dh.b.529.6		12
20.7	even	4		1040.2.dh.b.529.1		12
65.3	odd	12		130.2.n.a.29.3	yes	12
65.4	even	6		8450.2.a.ca.1.1		3
65.7	even	12		1690.2.c.b.1689.1		6
65.9	even	6		8450.2.a.bu.1.1		3
65.17	odd	12		1690.2.b.b.339.1		6
65.22	odd	12		1690.2.b.c.339.4		6
65.29	even	6		650.2.e.k.601.3		6
65.32	even	12		1690.2.c.c.1689.1		6
65.33	even	12		1690.2.c.c.1689.6		6
65.42	odd	12		130.2.n.a.29.4	yes	12
65.43	odd	12		1690.2.b.b.339.6		6
65.48	odd	12		1690.2.b.c.339.3		6
65.58	even	12		1690.2.c.b.1689.6		6
195.68	even	12		1170.2.bp.h.289.4		12
195.107	even	12		1170.2.bp.h.289.1		12
260.3	even	12		1040.2.dh.b.289.1		12
260.107	even	12		1040.2.dh.b.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.3	✓	12	5.2	odd	4
130.2.n.a.9.4	yes	12	5.3	odd	4
130.2.n.a.29.3	yes	12	65.3	odd	12
130.2.n.a.29.4	yes	12	65.42	odd	12
650.2.e.j.451.1		6	1.1	even	1	trivial
650.2.e.j.601.1		6	13.3	even	3	inner
650.2.e.k.451.3		6	5.4	even	2
650.2.e.k.601.3		6	65.29	even	6
1040.2.dh.b.289.1		12	260.3	even	12
1040.2.dh.b.289.6		12	260.107	even	12
1040.2.dh.b.529.1		12	20.7	even	4
1040.2.dh.b.529.6		12	20.3	even	4
1170.2.bp.h.289.1		12	195.107	even	12
1170.2.bp.h.289.4		12	195.68	even	12
1170.2.bp.h.919.1		12	15.8	even	4
1170.2.bp.h.919.4		12	15.2	even	4
1690.2.b.b.339.1		6	65.17	odd	12
1690.2.b.b.339.6		6	65.43	odd	12
1690.2.b.c.339.3		6	65.48	odd	12
1690.2.b.c.339.4		6	65.22	odd	12
1690.2.c.b.1689.1		6	65.7	even	12
1690.2.c.b.1689.6		6	65.58	even	12
1690.2.c.c.1689.1		6	65.32	even	12
1690.2.c.c.1689.6		6	65.33	even	12
8450.2.a.bt.1.3		3	13.4	even	6
8450.2.a.bu.1.1		3	65.9	even	6
8450.2.a.ca.1.1		3	65.4	even	6
8450.2.a.cb.1.3		3	13.9	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.10716 + 1.91766i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.10716 - 1.91766i) q^{6} +(1.95161 + 3.38028i) q^{7} +1.00000 q^{8} +(-0.951606 - 1.64823i) q^{9} +(-0.533338 + 0.923769i) q^{11} +2.21432 q^{12} +(2.82148 + 2.24483i) q^{13} -3.90321 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.655554 - 1.13545i) q^{17} +1.90321 q^{18} +(3.29605 + 5.70893i) q^{19} -8.64296 q^{21} +(-0.533338 - 0.923769i) q^{22} +(-1.07382 + 1.85991i) q^{23} +(-1.10716 + 1.91766i) q^{24} +(-3.35482 + 1.32106i) q^{26} -2.42864 q^{27} +(1.95161 - 3.38028i) q^{28} +(4.52543 - 7.83827i) q^{29} -6.92396 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.18098 - 2.04552i) q^{33} +1.31111 q^{34} +(-0.951606 + 1.64823i) q^{36} +(-2.51037 + 4.34809i) q^{37} -6.59210 q^{38} +(-7.42864 + 2.92525i) q^{39} +(2.97703 - 5.15637i) q^{41} +(4.32148 - 7.48502i) q^{42} +(-1.00000 - 1.73205i) q^{43} +1.06668 q^{44} +(-1.07382 - 1.85991i) q^{46} -0.0967881 q^{47} +(-1.10716 - 1.91766i) q^{48} +(-4.11753 + 7.13177i) q^{49} +2.90321 q^{51} +(0.533338 - 3.56589i) q^{52} -1.49532 q^{53} +(1.21432 - 2.10326i) q^{54} +(1.95161 + 3.38028i) q^{56} -14.5970 q^{57} +(4.52543 + 7.83827i) q^{58} +(-3.59210 - 6.22171i) q^{59} +(-3.94370 - 6.83068i) q^{61} +(3.46198 - 5.99632i) q^{62} +(3.71432 - 6.43339i) q^{63} +1.00000 q^{64} +2.36196 q^{66} +(4.21432 - 7.29942i) q^{67} +(-0.655554 + 1.13545i) q^{68} +(-2.37778 - 4.11844i) q^{69} +(7.73975 + 13.4056i) q^{71} +(-0.951606 - 1.64823i) q^{72} -15.3526 q^{73} +(-2.51037 - 4.34809i) q^{74} +(3.29605 - 5.70893i) q^{76} -4.16346 q^{77} +(1.18098 - 7.89601i) q^{78} +4.30174 q^{79} +(5.54371 - 9.60199i) q^{81} +(2.97703 + 5.15637i) q^{82} +9.69381 q^{83} +(4.32148 + 7.48502i) q^{84} +2.00000 q^{86} +(10.0207 + 17.3564i) q^{87} +(-0.533338 + 0.923769i) q^{88} +(-2.26271 + 3.91914i) q^{89} +(-2.08173 + 13.9184i) q^{91} +2.14764 q^{92} +(7.66593 - 13.2778i) q^{93} +(0.0483940 - 0.0838209i) q^{94} +2.21432 q^{96} +(2.13013 + 3.68949i) q^{97} +(-4.11753 - 7.13177i) q^{98} +2.03011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 5 q^{7} + 6 q^{8} + q^{9} - 3 q^{11} - 3 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{18} + 13 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{27} + 5 q^{28} + 14 q^{29} + 12 q^{31}+ \cdots + 26 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 5 * q^7 + 6 * q^8 + q^9 - 3 * q^11 - 3 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 2 * q^18 + 13 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^27 + 5 * q^28 + 14 * q^29 + 12 * q^31 - 3 * q^32 + 6 * q^33 + 8 * q^34 + q^36 + 5 * q^37 - 26 * q^38 - 18 * q^39 - 2 * q^41 + 6 * q^42 - 6 * q^43 + 6 * q^44 - 14 * q^47 + 2 * q^49 + 4 * q^51 + 3 * q^52 + 18 * q^53 - 6 * q^54 + 5 * q^56 - 8 * q^57 + 14 * q^58 - 8 * q^59 - 4 * q^61 - 6 * q^62 + 9 * q^63 + 6 * q^64 - 12 * q^66 + 12 * q^67 - 4 * q^68 - 14 * q^69 + 20 * q^71 + q^72 - 12 * q^73 + 5 * q^74 + 13 * q^76 - 38 * q^77 - 6 * q^78 - 28 * q^79 + 13 * q^81 - 2 * q^82 - 8 * q^83 + 6 * q^84 + 12 * q^86 + 20 * q^87 - 3 * q^88 - 7 * q^89 - 19 * q^91 + 26 * q^93 + 7 * q^94 + 26 * q^97 + 2 * q^98 + 26 * q^99

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