LMFDB - Embedded newform 175.2.x.a.3.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.668598 - 1.02955i) q^{2} +(-0.0902073 + 0.234998i) q^{3} +(0.200523 + 0.450382i) q^{4} +(-0.532453 + 2.17175i) q^{5} +(0.181630 + 0.249992i) q^{6} +(1.56284 - 2.13484i) q^{7} +(3.02273 + 0.478753i) q^{8} +(2.18235 + 1.96499i) q^{9} +O(q^{10})$	\(q+(0.668598 - 1.02955i) q^{2} +(-0.0902073 + 0.234998i) q^{3} +(0.200523 + 0.450382i) q^{4} +(-0.532453 + 2.17175i) q^{5} +(0.181630 + 0.249992i) q^{6} +(1.56284 - 2.13484i) q^{7} +(3.02273 + 0.478753i) q^{8} +(2.18235 + 1.96499i) q^{9} +(1.87993 + 2.00021i) q^{10} +(-4.25460 - 4.72522i) q^{11} +(-0.123927 + 0.00649476i) q^{12} +(3.08865 + 1.57374i) q^{13} +(-1.15301 - 3.03637i) q^{14} +(-0.462326 - 0.321033i) q^{15} +(1.85412 - 2.05921i) q^{16} +(-2.43401 + 3.00575i) q^{17} +(3.48217 - 0.933045i) q^{18} +(-5.51153 - 2.45389i) q^{19} +(-1.08488 + 0.195678i) q^{20} +(0.360703 + 0.559843i) q^{21} +(-7.70946 + 1.22106i) q^{22} +(-1.49342 - 0.969836i) q^{23} +(-0.385178 + 0.667148i) q^{24} +(-4.43299 - 2.31271i) q^{25} +(3.68531 - 2.12772i) q^{26} +(-1.33148 + 0.678422i) q^{27} +(1.27488 + 0.275791i) q^{28} +(1.19010 - 1.63804i) q^{29} +(-0.639630 + 0.261346i) q^{30} +(1.49964 - 0.157619i) q^{31} +(0.703784 + 2.62656i) q^{32} +(1.49421 - 0.573575i) q^{33} +(1.46720 + 4.51558i) q^{34} +(3.80419 + 4.53080i) q^{35} +(-0.447387 + 1.37692i) q^{36} +(-0.403486 - 7.69898i) q^{37} +(-6.21140 + 4.03373i) q^{38} +(-0.648446 + 0.583863i) q^{39} +(-2.64919 + 6.30969i) q^{40} +(-2.44960 + 0.795924i) q^{41} +(0.817551 + 0.00294727i) q^{42} +(4.23024 + 4.23024i) q^{43} +(1.27501 - 2.86371i) q^{44} +(-5.42947 + 3.69324i) q^{45} +(-1.99699 + 0.889117i) q^{46} +(-2.04151 + 1.65318i) q^{47} +(0.316655 + 0.621471i) q^{48} +(-2.11506 - 6.67282i) q^{49} +(-5.34493 + 3.01771i) q^{50} +(-0.486781 - 0.843129i) q^{51} +(-0.0894413 + 1.70664i) q^{52} +(-2.84820 - 1.09332i) q^{53} +(-0.191754 + 1.82442i) q^{54} +(12.5274 - 6.72397i) q^{55} +(5.74610 - 5.70482i) q^{56} +(1.07384 - 1.07384i) q^{57} +(-0.890740 - 2.32046i) q^{58} +(-12.6346 - 2.68556i) q^{59} +(0.0518806 - 0.272598i) q^{60} +(0.0178842 + 0.0841387i) q^{61} +(0.840380 - 1.64934i) q^{62} +(7.60560 - 1.58799i) q^{63} +(8.44536 + 2.74406i) q^{64} +(-5.06234 + 5.86982i) q^{65} +(0.408504 - 1.92186i) q^{66} +(1.03031 + 0.834329i) q^{67} +(-1.84181 - 0.493512i) q^{68} +(0.362627 - 0.263464i) q^{69} +(7.20816 - 0.887327i) q^{70} +(1.14755 + 0.833741i) q^{71} +(5.65589 + 6.98445i) q^{72} +(13.2720 + 0.695556i) q^{73} +(-8.19625 - 4.73211i) q^{74} +(0.943370 - 0.833121i) q^{75} -2.97435i q^{76} +(-16.7368 + 1.69813i) q^{77} +(0.167567 + 1.05798i) q^{78} +(-4.39299 - 0.461722i) q^{79} +(3.48485 + 5.12312i) q^{80} +(0.881568 + 8.38756i) q^{81} +(-0.818354 + 3.05414i) q^{82} +(-0.0358492 + 0.226343i) q^{83} +(-0.179814 + 0.274715i) q^{84} +(-5.23175 - 6.88648i) q^{85} +(7.18357 - 1.52692i) q^{86} +(0.277580 + 0.427435i) q^{87} +(-10.5983 - 16.3199i) q^{88} +(12.6254 - 2.68362i) q^{89} +(0.172246 + 8.05921i) q^{90} +(8.18675 - 4.13425i) q^{91} +(0.137332 - 0.867081i) q^{92} +(-0.0982386 + 0.366631i) q^{93} +(0.337085 + 3.20715i) q^{94} +(8.26386 - 10.6631i) q^{95} +(-0.680723 - 0.0715469i) q^{96} +(-0.0559772 - 0.353426i) q^{97} +(-8.28413 - 2.28387i) q^{98} -18.6723i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.668598	−	1.02955i	0.472770	−	0.728002i	−0.519176	−	0.854668i	$-0.673761\pi$
$2$	0.668598	−	1.02955i	0.472770	−	0.728002i	0.991945	+	0.126666i	$0.0404276\pi$
$3$	−0.0902073	+	0.234998i	−0.0520812	+	0.135676i	−0.957153	−	0.289582i	$-0.906484\pi$
$3$	−0.0902073	+	0.234998i	−0.0520812	+	0.135676i	0.905072	+	0.425259i	$0.139817\pi$
$4$	0.200523	+	0.450382i	0.100261	+	0.225191i
$5$	−0.532453	+	2.17175i	−0.238120	+	0.971236i
$5$	−0.532453	+	2.17175i	−0.238120	+	0.971236i
$6$	0.181630	+	0.249992i	0.0741501	+	0.102059i
$7$	1.56284	−	2.13484i	0.590698	−	0.806893i
$7$	1.56284	−	2.13484i	0.590698	−	0.806893i
$8$	3.02273	+	0.478753i	1.06870	+	0.169265i
$9$	2.18235	+	1.96499i	0.727449	+	0.654998i
$10$	1.87993	+	2.00021i	0.594485	+	0.632523i
$11$	−4.25460	−	4.72522i	−1.28281	−	1.42471i	−0.853107	−	0.521736i	$-0.825284\pi$
$11$	−4.25460	−	4.72522i	−1.28281	−	1.42471i	−0.429704	−	0.902970i	$-0.641382\pi$
$12$	−0.123927	+	0.00649476i	−0.0357748	+	0.00187488i
$13$	3.08865	+	1.57374i	0.856637	+	0.436478i	0.826413	−	0.563065i	$-0.190378\pi$
$13$	3.08865	+	1.57374i	0.856637	+	0.436478i	0.0302242	+	0.999543i	$0.490378\pi$
$14$	−1.15301	−	3.03637i	−0.308155	−	0.811504i
$15$	−0.462326	−	0.321033i	−0.119372	−	0.0828904i
$16$	1.85412	−	2.05921i	0.463530	−	0.514802i
$17$	−2.43401	+	3.00575i	−0.590334	+	0.729002i	−0.981531	−	0.191305i	$-0.938728\pi$
$17$	−2.43401	+	3.00575i	−0.590334	+	0.729002i	0.391196	+	0.920307i	$0.372061\pi$
$18$	3.48217	−	0.933045i	0.820756	−	0.219921i
$19$	−5.51153	−	2.45389i	−1.26443	−	0.562961i	−0.338611	−	0.940926i	$-0.609957\pi$
$19$	−5.51153	−	2.45389i	−1.26443	−	0.562961i	−0.925820	+	0.377965i	$0.876624\pi$
$20$	−1.08488	+	0.195678i	−0.242588	+	0.0437550i
$21$	0.360703	+	0.559843i	0.0787119	+	0.122168i
$22$	−7.70946	+	1.22106i	−1.64366	+	0.260331i
$23$	−1.49342	−	0.969836i	−0.311399	−	0.202225i	0.379472	−	0.925203i	$-0.376106\pi$
$23$	−1.49342	−	0.969836i	−0.311399	−	0.202225i	−0.690870	+	0.722979i	$0.742772\pi$
$24$	−0.385178	+	0.667148i	−0.0786242	+	0.136181i
$25$	−4.43299	−	2.31271i	−0.886597	−	0.462542i
$26$	3.68531	−	2.12772i	0.722749	−	0.417279i
$27$	−1.33148	+	0.678422i	−0.256243	+	0.130562i
$28$	1.27488	+	0.275791i	0.240929	+	0.0521195i
$29$	1.19010	−	1.63804i	0.220997	−	0.304176i	−0.684095	−	0.729393i	$-0.739802\pi$
$29$	1.19010	−	1.63804i	0.220997	−	0.304176i	0.905091	+	0.425218i	$0.139802\pi$
$30$	−0.639630	+	0.261346i	−0.116780	+	0.0477149i
$31$	1.49964	−	0.157619i	0.269344	−	0.0283091i	0.0311061	−	0.999516i	$-0.490097\pi$
$31$	1.49964	−	0.157619i	0.269344	−	0.0283091i	0.238237	+	0.971207i	$0.423430\pi$
$32$	0.703784	+	2.62656i	0.124413	+	0.464314i
$33$	1.49421	−	0.573575i	0.260109	−	0.0998466i
$34$	1.46720	+	4.51558i	0.251623	+	0.774415i
$35$	3.80419	+	4.53080i	0.643026	+	0.765844i
$36$	−0.447387	+	1.37692i	−0.0745645	+	0.229486i
$37$	−0.403486	−	7.69898i	−0.0663327	−	1.26570i	−0.805668	−	0.592367i	$-0.798194\pi$
$37$	−0.403486	−	7.69898i	−0.0663327	−	1.26570i	0.739336	−	0.673337i	$-0.235140\pi$
$38$	−6.21140	+	4.03373i	−1.00762	+	0.654357i
$39$	−0.648446	+	0.583863i	−0.103834	+	0.0934930i
$40$	−2.64919	+	6.30969i	−0.418874	+	0.997650i
$41$	−2.44960	+	0.795924i	−0.382563	+	0.124302i	−0.493984	−	0.869471i	$-0.664460\pi$
$41$	−2.44960	+	0.795924i	−0.382563	+	0.124302i	0.111421	+	0.993773i	$0.464460\pi$
$42$	0.817551	+	0.00294727i	0.126151	+	0.000454774i
$43$	4.23024	+	4.23024i	0.645106	+	0.645106i	0.951806	−	0.306701i	$-0.0992250\pi$
$43$	4.23024	+	4.23024i	0.645106	+	0.645106i	−0.306701	+	0.951806i	$0.599225\pi$
$44$	1.27501	−	2.86371i	0.192214	−	0.431720i
$45$	−5.42947	+	3.69324i	−0.809378	+	0.550556i
$46$	−1.99699	+	0.889117i	−0.294440	+	0.131093i
$47$	−2.04151	+	1.65318i	−0.297785	+	0.241142i	−0.766555	−	0.642179i	$-0.778031\pi$
$47$	−2.04151	+	1.65318i	−0.297785	+	0.241142i	0.468770	+	0.883320i	$0.344697\pi$
$48$	0.316655	+	0.621471i	0.0457052	+	0.0897016i
$49$	−2.11506	−	6.67282i	−0.302152	−	0.953260i
$50$	−5.34493	+	3.01771i	−0.755888	+	0.426769i
$51$	−0.486781	−	0.843129i	−0.0681630	−	0.118062i
$52$	−0.0894413	+	1.70664i	−0.0124033	+	0.236669i
$53$	−2.84820	−	1.09332i	−0.391230	−	0.150179i	0.154798	−	0.987946i	$-0.450527\pi$
$53$	−2.84820	−	1.09332i	−0.391230	−	0.150179i	−0.546028	+	0.837767i	$0.683861\pi$
$54$	−0.191754	+	1.82442i	−0.0260944	+	0.248271i
$55$	12.5274	−	6.72397i	1.68919	−	0.906660i
$56$	5.74610	−	5.70482i	0.767855	−	0.762338i
$57$	1.07384	−	1.07384i	0.142234	−	0.142234i
$58$	−0.890740	−	2.32046i	−0.116960	−	0.304691i
$59$	−12.6346	−	2.68556i	−1.64488	−	0.349630i	−0.709893	−	0.704310i	$-0.751257\pi$
$59$	−12.6346	−	2.68556i	−1.64488	−	0.349630i	−0.934988	+	0.354680i	$0.884590\pi$
$60$	0.0518806	−	0.272598i	0.00669776	−	0.0351922i
$61$	0.0178842	+	0.0841387i	0.00228984	+	0.0107729i	0.979278	−	0.202522i	$-0.0649138\pi$
$61$	0.0178842	+	0.0841387i	0.00228984	+	0.0107729i	−0.976988	+	0.213295i	$0.931580\pi$
$62$	0.840380	−	1.64934i	0.106728	−	0.209466i
$63$	7.60560	−	1.58799i	0.958216	−	0.200067i
$64$	8.44536	+	2.74406i	1.05567	+	0.343008i
$65$	−5.06234	+	5.86982i	−0.627906	+	0.728062i
$66$	0.408504	−	1.92186i	0.0502833	−	0.236564i
$67$	1.03031	+	0.834329i	0.125872	+	0.101930i	0.690190	−	0.723629i	$-0.257527\pi$
$67$	1.03031	+	0.834329i	0.125872	+	0.101930i	−0.564317	+	0.825558i	$0.690860\pi$
$68$	−1.84181	−	0.493512i	−0.223352	−	0.0598471i
$69$	0.362627	−	0.263464i	0.0436551	−	0.0317173i
$70$	7.20816	−	0.887327i	0.861539	−	0.106056i
$71$	1.14755	+	0.833741i	0.136189	+	0.0989469i	0.653794	−	0.756673i	$-0.273176\pi$
$71$	1.14755	+	0.833741i	0.136189	+	0.0989469i	−0.517605	+	0.855620i	$0.673176\pi$
$72$	5.65589	+	6.98445i	0.666554	+	0.823125i
$73$	13.2720	+	0.695556i	1.55337	+	0.0814087i	0.809582	−	0.587007i	$-0.199694\pi$
$73$	13.2720	+	0.695556i	1.55337	+	0.0814087i	0.743788	+	0.668416i	$0.233027\pi$
$74$	−8.19625	−	4.73211i	−0.952795	−	0.550096i
$75$	0.943370	−	0.833121i	0.108931	−	0.0962005i
$76$		−	2.97435i		−	0.341182i
$77$	−16.7368	+	1.69813i	−1.90734	+	0.193520i
$78$	0.167567	+	1.05798i	0.0189732	+	0.119792i
$79$	−4.39299	−	0.461722i	−0.494250	−	0.0519478i	−0.145875	−	0.989303i	$-0.546600\pi$
$79$	−4.39299	−	0.461722i	−0.494250	−	0.0519478i	−0.348375	+	0.937355i	$0.613266\pi$
$80$	3.48485	+	5.12312i	0.389618	+	0.572782i
$81$	0.881568	+	8.38756i	0.0979520	+	0.931951i
$82$	−0.818354	+	3.05414i	−0.0903721	+	0.337273i
$83$	−0.0358492	+	0.226343i	−0.00393496	+	0.0248444i	−0.989578	−	0.144000i	$-0.954004\pi$
$83$	−0.0358492	+	0.226343i	−0.00393496	+	0.0248444i	0.985643	+	0.168844i	$0.0540035\pi$
$84$	−0.179814	+	0.274715i	−0.0196193	+	0.0299739i
$85$	−5.23175	−	6.88648i	−0.567462	−	0.746944i
$86$	7.18357	−	1.52692i	0.774624	−	0.164652i
$87$	0.277580	+	0.427435i	0.0297597	+	0.0458258i
$88$	−10.5983	−	16.3199i	−1.12978	−	1.73971i
$89$	12.6254	−	2.68362i	1.33829	−	0.284463i	0.517498	−	0.855684i	$-0.326863\pi$
$89$	12.6254	−	2.68362i	1.33829	−	0.284463i	0.820796	+	0.571221i	$0.193530\pi$
$90$	0.172246	+	8.05921i	0.0181564	+	0.849515i
$91$	8.18675	−	4.13425i	0.858205	−	0.433387i
$92$	0.137332	−	0.867081i	0.0143179	−	0.0903995i
$93$	−0.0982386	+	0.366631i	−0.0101869	+	0.0380179i
$94$	0.337085	+	3.20715i	0.0347677	+	0.330793i
$95$	8.26386	−	10.6631i	0.847854	−	1.09401i
$96$	−0.680723	−	0.0715469i	−0.0694760	−	0.00730222i
$97$	−0.0559772	−	0.353426i	−0.00568363	−	0.0358850i	0.984684	−	0.174351i	$-0.0557828\pi$
$97$	−0.0559772	−	0.353426i	−0.00568363	−	0.0358850i	−0.990367	+	0.138466i	$0.955783\pi$
$98$	−8.28413	−	2.28387i	−0.836823	−	0.230705i
$99$		−	18.6723i		−	1.87664i
$100$	0.152687	−	2.46029i	0.0152687	−	0.246029i
$101$	−3.72935	−	2.15314i	−0.371084	−	0.214246i	0.302848	−	0.953039i	$-0.402063\pi$
$101$	−3.72935	−	2.15314i	−0.371084	−	0.214246i	−0.673932	+	0.738793i	$0.735396\pi$
$102$	−1.19350	−	0.0625489i	−0.118175	−	0.00619327i
$103$	6.82272	+	8.42536i	0.672263	+	0.830175i	0.993138	−	0.116946i	$-0.0373105\pi$
$103$	6.82272	+	8.42536i	0.672263	+	0.830175i	−0.320876	+	0.947121i	$0.603977\pi$
$104$	8.58271	+	6.23570i	0.841604	+	0.611461i
$105$	−1.40790	+	0.485267i	−0.137396	+	0.0473572i
$106$	−3.02993	+	2.20137i	−0.294293	+	0.213816i
$107$	9.62039	+	2.57778i	0.930038	+	0.249203i	0.691871	−	0.722021i	$-0.256787\pi$
$107$	9.62039	+	2.57778i	0.930038	+	0.249203i	0.238167	+	0.971224i	$0.423453\pi$
$108$	−0.572541	−	0.463634i	−0.0550928	−	0.0446132i
$109$	−0.595124	+	2.79984i	−0.0570026	+	0.268176i	−0.997415	−	0.0718609i	$-0.977106\pi$
$109$	−0.595124	+	2.79984i	−0.0570026	+	0.268176i	0.940412	+	0.340037i	$0.110440\pi$
$110$	1.45309	−	17.3932i	0.138547	−	1.65837i
$111$	1.84564	+	0.599686i	0.175181	+	0.0569197i
$112$	−1.49838	−	7.17646i	−0.141584	−	0.678112i
$113$	−4.40329	+	8.64195i	−0.414227	+	0.812966i	0.585770	+	0.810477i	$0.300792\pi$
$113$	−4.40329	+	8.64195i	−0.414227	+	0.812966i	−0.999997	+	0.00248866i	$0.999208\pi$
$114$	−0.387605	−	1.82354i	−0.0363025	−	0.170790i
$115$	2.90141	−	2.72693i	0.270558	−	0.254288i
$116$	0.976384	+	0.207537i	0.0906550	+	0.0192693i
$117$	3.64810	+	9.50364i	0.337267	+	0.878611i
$118$	−11.2124	+	11.2124i	−1.03218	+	1.03218i
$119$	2.61283	+	9.89373i	0.239517	+	0.906957i
$120$	−1.24379	−	1.19174i	−0.113542	−	0.108790i
$121$	−3.07620	+	29.2681i	−0.279655	+	2.66074i
$122$	0.0985823	+	0.0378422i	0.00892523	+	0.00342607i
$123$	0.0339314	−	0.647450i	0.00305949	−	0.0583786i
$124$	0.371701	+	0.643805i	0.0333797	+	0.0578154i
$125$	7.38298	−	8.39593i	0.660354	−	0.750954i
$126$	3.45018	−	8.89207i	0.307366	−	0.792169i
$127$	3.47660	+	6.82321i	0.308498	+	0.605462i	0.992251	−	0.124252i	$-0.0396532\pi$
$127$	3.47660	+	6.82321i	0.308498	+	0.605462i	−0.683753	+	0.729714i	$0.739653\pi$
$128$	4.24525	−	3.43773i	0.375230	−	0.303856i
$129$	−1.37570	+	0.612500i	−0.121123	+	0.0539276i
$130$	2.65861	+	9.13648i	0.233175	+	0.801322i
$131$	−3.45729	+	7.76520i	−0.302065	+	0.678448i	−0.999261	−	0.0384316i	$-0.987764\pi$
$131$	−3.45729	+	7.76520i	−0.302065	+	0.678448i	0.697197	+	0.716880i	$0.254430\pi$
$132$	0.557951	+	0.557951i	0.0485634	+	0.0485634i
$133$	−13.8523	+	7.93118i	−1.20115	+	0.687720i
$134$	1.54785	−	0.502926i	0.133714	−	0.0434462i
$135$	−0.764413	−	3.25287i	−0.0657902	−	0.279962i
$136$	−8.79637	+	7.92028i	−0.754282	+	0.679159i
$137$	14.3330	−	9.30796i	1.22455	−	0.795233i	0.240076	−	0.970754i	$-0.422828\pi$
$137$	14.3330	−	9.30796i	1.22455	−	0.795233i	0.984476	+	0.175521i	$0.0561611\pi$
$138$	−0.0287977	−	0.549494i	−0.00245143	−	0.0467760i
$139$	4.98856	−	15.3532i	0.423124	−	1.30224i	−0.481656	−	0.876361i	$-0.659964\pi$
$139$	4.98856	−	15.3532i	0.423124	−	1.30224i	0.904779	−	0.425880i	$-0.140036\pi$
$140$	−1.27776	+	2.62187i	−0.107990	+	0.221588i
$141$	−0.204336	−	0.628881i	−0.0172082	−	0.0529613i
$142$	1.62563	−	0.624019i	0.136419	−	0.0523665i
$143$	−5.70469	−	21.2902i	−0.477050	−	1.78038i
$144$	8.09267	−	0.850574i	0.674389	−	0.0708811i
$145$	2.92373	+	3.45678i	0.242803	+	0.287070i
$146$	9.58974	−	13.1991i	0.793652	−	1.09237i
$147$	1.75889	+	0.104901i	0.145071	+	0.00865210i
$148$	3.38657	−	1.72554i	0.278374	−	0.141839i
$149$	−13.1522	+	7.59345i	−1.07747	+	0.622080i	−0.930214	−	0.367018i	$-0.880379\pi$
$149$	−13.1522	+	7.59345i	−1.07747	+	0.622080i	−0.147260	+	0.989098i	$0.547045\pi$
$150$	−0.227004	−	1.52827i	−0.0185348	−	0.124783i
$151$	−7.07212	+	12.2493i	−0.575521	+	0.996832i	0.420464	+	0.907309i	$0.361867\pi$
$151$	−7.07212	+	12.2493i	−0.575521	+	0.996832i	−0.995985	+	0.0895225i	$0.971466\pi$
$152$	−15.4850	−	10.0561i	−1.25600	−	0.815657i
$153$	−11.2181	+	1.77678i	−0.906934	+	0.143644i
$154$	−9.44189	+	18.3668i	−0.760849	+	1.48004i
$155$	−0.456181	+	3.34077i	−0.0366413	+	0.268337i
$156$	−0.392990	−	0.174970i	−0.0314643	−	0.0140088i
$157$	4.44121	−	1.19002i	0.354447	−	0.0949739i	−0.0772018	−	0.997015i	$-0.524599\pi$
$157$	4.44121	−	1.19002i	0.354447	−	0.0949739i	0.431649	+	0.902042i	$0.357932\pi$
$158$	−3.41251	+	4.21410i	−0.271485	+	0.335256i
$159$	0.513857	−	0.570696i	0.0407515	−	0.0452591i
$160$	−6.07896	+	0.129923i	−0.480584	+	0.0102713i
$161$	−4.40441	+	1.67250i	−0.347116	+	0.131812i
$162$	9.22483	+	4.70028i	0.724771	+	0.369289i
$163$	9.72937	−	0.509895i	0.762063	−	0.0399381i	0.332655	−	0.943049i	$-0.392055\pi$
$163$	9.72937	−	0.509895i	0.762063	−	0.0399381i	0.429408	+	0.903110i	$0.358722\pi$
$164$	−0.849670	−	0.943654i	−0.0663481	−	0.0736870i
$165$	0.450062	+	3.55046i	0.0350373	+	0.276403i
$166$	0.209063	+	0.188241i	0.0162264	+	0.0146103i
$167$	−17.9190	−	2.83810i	−1.38662	−	0.219618i	−0.581892	−	0.813266i	$-0.697687\pi$
$167$	−17.9190	−	2.83810i	−1.38662	−	0.219618i	−0.804725	+	0.593648i	$0.797687\pi$
$168$	0.822281	+	1.86494i	0.0634404	+	0.143883i
$169$	−0.578133	−	0.795732i	−0.0444718	−	0.0612101i
$170$	−10.5879	+	0.782056i	−0.812056	+	0.0599810i
$171$	−7.20619	−	16.1854i	−0.551071	−	1.23773i
$172$	−1.05696	+	2.75348i	−0.0805927	+	0.209951i
$173$	−6.81817	+	10.4991i	−0.518376	+	0.798228i	−0.996803	−	0.0798987i	$-0.974540\pi$
$173$	−6.81817	+	10.4991i	−0.518376	+	0.798228i	0.478427	+	0.878127i	$0.341207\pi$
$174$	0.625655			0.0474308
$175$	−11.8653	+	5.84931i	−0.896933	+	0.442167i
$176$	−17.6187			−1.32806
$177$	1.77083	−	2.72684i	0.133104	−	0.204962i
$178$	5.67842	−	14.7928i	0.425615	−	1.10877i
$179$	6.52722	+	14.6604i	0.487868	+	1.09577i	0.974952	+	0.222414i	$0.0713936\pi$
$179$	6.52722	+	14.6604i	0.487868	+	1.09577i	−0.487085	+	0.873355i	$0.661940\pi$
$180$	−2.75210	−	1.70476i	−0.205130	−	0.127065i
$181$	−8.02423	−	11.0444i	−0.596436	−	0.820924i	0.398940	−	0.916977i	$-0.369378\pi$
$181$	−8.02423	−	11.0444i	−0.596436	−	0.820924i	−0.995376	+	0.0960528i	$0.969378\pi$
$182$	1.21722	−	11.1928i	0.0902267	−	0.829667i
$183$	−0.0213857	−	0.00338717i	−0.00158088	−	0.000250387i
$184$	−4.04988	−	3.64653i	−0.298561	−	0.268826i
$185$	16.9351	+	3.22307i	1.24509	+	0.236965i
$186$	0.311783	+	0.346270i	0.0228611	+	0.0253898i
$187$	24.5586	−	1.28706i	1.79590	−	0.0941192i
$188$	−1.15393	−	0.587958i	−0.0841592	−	0.0428813i
$189$	−0.632566	+	3.90276i	−0.0460124	+	0.283884i
$190$	−5.45297	−	15.6374i	−0.395600	−	1.13445i
$191$	0.744251	−	0.826574i	0.0538521	−	0.0598088i	−0.715617	−	0.698493i	$-0.753854\pi$
$191$	0.744251	−	0.826574i	0.0538521	−	0.0598088i	0.769469	+	0.638684i	$0.220521\pi$
$192$	−1.40668	+	1.73711i	−0.101519	+	0.125365i
$193$	10.1893	−	2.73020i	0.733438	−	0.196524i	0.127278	−	0.991867i	$-0.459376\pi$
$193$	10.1893	−	2.73020i	0.733438	−	0.196524i	0.606160	+	0.795343i	$0.292709\pi$
$194$	−0.401296	−	0.178669i	−0.0288114	−	0.0128277i
$195$	−0.922738	−	1.71914i	−0.0660786	−	0.123110i
$196$	2.58120	−	2.29064i	0.184371	−	0.163617i
$197$	0.109704	−	0.0173753i	0.00781605	−	0.00123794i	−0.152525	−	0.988300i	$-0.548741\pi$
$197$	0.109704	−	0.0173753i	0.00781605	−	0.00123794i	0.160341	+	0.987062i	$0.448741\pi$
$198$	−19.2241	−	12.4843i	−1.36620	−	0.887219i
$199$	−9.56773	+	16.5718i	−0.678239	+	1.17474i	0.297272	+	0.954793i	$0.403923\pi$
$199$	−9.56773	+	16.5718i	−0.678239	+	1.17474i	−0.975511	+	0.219951i	$0.929410\pi$
$200$	−12.2925	−	9.11300i	−0.869211	−	0.644386i
$201$	−0.289007	+	0.166858i	−0.0203850	+	0.0117693i
$202$	−4.71020	+	2.39997i	−0.331409	+	0.168861i
$203$	−1.63700	−	5.10067i	−0.114895	−	0.357997i
$204$	0.282119	−	0.388304i	0.0197523	−	0.0271867i
$205$	−0.424248	−	5.74371i	−0.0296308	−	0.401158i
$206$	13.2360	−	1.39116i	0.922195	−	0.0969266i
$207$	−1.35343	−	5.05107i	−0.0940700	−	0.351074i
$208$	8.96739	−	3.44226i	0.621777	−	0.238678i
$209$	11.8542	+	36.4835i	0.819972	+	2.52362i
$210$	−0.441708	+	1.77395i	−0.0304808	+	0.122414i
$211$	−5.50057	+	16.9290i	−0.378675	+	1.16544i	0.562290	+	0.826940i	$0.309920\pi$
$211$	−5.50057	+	16.9290i	−0.378675	+	1.16544i	−0.940966	+	0.338502i	$0.890080\pi$
$212$	−0.0787171	−	1.50201i	−0.00540632	−	0.103159i
$213$	−0.299445	+	0.194462i	−0.0205176	+	0.0133243i
$214$	9.08612	−	8.18118i	0.621114	−	0.559254i
$215$	−11.4394	+	6.93461i	−0.780162	+	0.472937i
$216$	−4.34949	+	1.41324i	−0.295946	+	0.0961585i
$217$	2.00721	−	3.44782i	0.136258	−	0.234053i
$218$	2.48468	+	2.48468i	0.168283	+	0.168283i
$219$	−1.36069	+	3.05615i	−0.0919466	+	0.206516i
$220$	5.54038	+	4.29378i	0.373532	+	0.289487i
$221$	−12.2481	+	5.45320i	−0.823896	+	0.366822i
$222$	1.85140	−	1.49923i	0.124258	−	0.100622i
$223$	3.11940	+	6.12217i	0.208891	+	0.409971i	0.971552	−	0.236827i	$-0.0761075\pi$
$223$	3.11940	+	6.12217i	0.208891	+	0.409971i	−0.762661	+	0.646798i	$0.776108\pi$
$224$	6.70718	+	2.60243i	0.448142	+	0.173882i
$225$	−5.12986	−	13.7579i	−0.341991	−	0.917195i
$226$	5.95329	+	10.3114i	0.396007	+	0.685904i
$227$	0.447330	−	8.53557i	0.0296903	−	0.566525i	−0.942768	−	0.333449i	$-0.891787\pi$
$227$	0.447330	−	8.53557i	0.0296903	−	0.566525i	0.972458	−	0.233076i	$-0.0748792\pi$
$228$	0.698967	+	0.268308i	0.0462902	+	0.0177692i
$229$	0.934425	−	8.89046i	0.0617485	−	0.587498i	−0.919276	−	0.393614i	$-0.871225\pi$
$229$	0.934425	−	8.89046i	0.0617485	−	0.587498i	0.981024	−	0.193884i	$-0.0621086\pi$
$230$	−0.867635	−	4.81037i	−0.0572102	−	0.317187i
$231$	1.11073	−	4.08631i	0.0730805	−	0.268859i
$232$	4.38157	−	4.38157i	0.287664	−	0.287664i
$233$	−2.24413	−	5.84615i	−0.147018	−	0.382994i	0.840221	−	0.542245i	$-0.182425\pi$
$233$	−2.24413	−	5.84615i	−0.147018	−	0.382994i	−0.987238	+	0.159251i	$0.949092\pi$
$234$	12.2236	+	2.59820i	0.799081	+	0.169850i
$235$	−2.50329	−	5.31389i	−0.163297	−	0.346640i
$236$	−1.32399	−	6.22889i	−0.0861845	−	0.405466i
$237$	0.504784	−	0.990694i	0.0327892	−	0.0643525i
$238$	11.9330	+	3.92489i	0.773503	+	0.254413i
$239$	22.1170	+	7.18624i	1.43063	+	0.464839i	0.918963	−	0.394345i	$-0.129028\pi$
$239$	22.1170	+	7.18624i	1.43063	+	0.464839i	0.511666	+	0.859184i	$0.329028\pi$
$240$	−1.51828	+	0.356791i	−0.0980047	+	0.0230308i
$241$	−0.777157	+	3.65624i	−0.0500611	+	0.235519i	−0.996064	−	0.0886400i	$-0.971748\pi$
$241$	−0.777157	+	3.65624i	−0.0500611	+	0.235519i	0.946003	+	0.324159i	$0.105081\pi$
$242$	28.0762	+	22.7357i	1.80481	+	1.46150i
$243$	−6.38089	−	1.70975i	−0.409334	−	0.109681i
$244$	−0.0343083	+	0.0249265i	−0.00219637	+	0.00159575i
$245$	15.6179	−	1.04042i	0.997788	−	0.0664702i
$246$	−0.643896	−	0.467817i	−0.0410533	−	0.0298270i
$247$	−13.1614	−	16.2529i	−0.837438	−	1.03415i
$248$	4.60847	+	0.241520i	0.292638	+	0.0153365i
$249$	−0.0499564	−	0.0288423i	−0.00316586	−	0.00182781i
$250$	−3.70778	−	13.2146i	−0.234501	−	0.835768i
$251$		−	7.23085i		−	0.456407i	−0.973613	−	0.228204i	$-0.926715\pi$
$251$		−	7.23085i		−	0.456407i	0.973613	−	0.228204i	$-0.0732852\pi$
$252$	2.24030	+	3.10700i	0.141125	+	0.195722i
$253$	1.77121	+	11.1830i	0.111355	+	0.703068i
$254$	9.34928	+	0.982649i	0.586626	+	0.0616569i
$255$	2.09025	−	0.608239i	0.130897	−	0.0380894i
$256$	1.15546	+	10.9935i	0.0722165	+	0.687094i
$257$	5.53721	−	20.6651i	0.345401	−	1.28906i	−0.546741	−	0.837302i	$-0.684132\pi$
$257$	5.53721	−	20.6651i	0.345401	−	1.28906i	0.892143	−	0.451754i	$-0.149202\pi$
$258$	−0.289189	+	1.82587i	−0.0180041	+	0.113673i
$259$	−17.0667	−	11.1709i	−1.06047	−	0.694125i
$260$	−3.65878	−	1.10295i	−0.226908	−	0.0684021i
$261$	5.81595	−	1.23622i	0.359998	−	0.0765200i
$262$	5.68312	+	8.75124i	0.351105	+	0.540654i
$263$	8.88784	+	13.6861i	0.548048	+	0.843920i	0.998812	−	0.0487233i	$-0.0155153\pi$
$263$	8.88784	+	13.6861i	0.548048	+	0.843920i	−0.450765	+	0.892643i	$0.648849\pi$
$264$	4.79120	−	1.01840i	0.294878	−	0.0626783i
$265$	3.89095	−	5.60343i	0.239019	−	0.344216i
$266$	−1.09606	+	19.5644i	−0.0672039	+	1.19957i
$267$	−0.508262	+	3.20904i	−0.0311051	+	0.196390i
$268$	−0.169166	+	0.631335i	−0.0103334	+	0.0385649i
$269$	−1.57606	−	14.9952i	−0.0960942	−	0.914275i	−0.931279	−	0.364306i	$-0.881306\pi$
$269$	−1.57606	−	14.9952i	−0.0960942	−	0.914275i	0.835185	−	0.549969i	$-0.185361\pi$
$270$	−3.86007	−	1.38786i	−0.234917	−	0.0844623i
$271$	5.10011	+	0.536043i	0.309809	+	0.0325623i	0.258157	−	0.966103i	$-0.416885\pi$
$271$	5.10011	+	0.536043i	0.309809	+	0.0325623i	0.0516520	+	0.998665i	$0.483551\pi$
$272$	1.67653	+	10.5852i	0.101654	+	0.641820i
$273$	0.233036	+	2.29681i	0.0141040	+	0.139009i
$274$		−	20.9798i		−	1.26744i
$275$	7.93255	+	30.7865i	0.478351	+	1.85649i
$276$	0.191374	+	0.110490i	0.0115194	+	0.00665071i
$277$	0.285419	+	0.0149582i	0.0171492	+	0.000898750i	0.0609086	−	0.998143i	$-0.480600\pi$
$277$	0.285419	+	0.0149582i	0.0171492	+	0.000898750i	−0.0437594	+	0.999042i	$0.513934\pi$
$278$	−12.4715	−	15.4011i	−0.747994	−	0.923695i
$279$	3.58246	+	2.60281i	0.214476	+	0.155826i
$280$	9.32990	+	15.5166i	0.557568	+	0.927296i
$281$	−0.915304	+	0.665008i	−0.0546025	+	0.0396710i	−0.614752	−	0.788721i	$-0.710744\pi$
$281$	−0.915304	+	0.665008i	−0.0546025	+	0.0396710i	0.560149	+	0.828392i	$0.310744\pi$
$282$	−0.784083	−	0.210094i	−0.0466915	−	0.0125109i
$283$	2.43928	+	1.97529i	0.145000	+	0.117419i	0.699076	−	0.715047i	$-0.253595\pi$
$283$	2.43928	+	1.97529i	0.145000	+	0.117419i	−0.554076	+	0.832466i	$0.686928\pi$
$284$	−0.145393	+	0.684018i	−0.00862746	+	0.0405890i
$285$	1.76034	+	2.90388i	0.104274	+	0.172011i
$286$	−25.7335	−	8.36131i	−1.52165	−	0.494414i
$287$	−2.12917	+	6.47340i	−0.125681	+	0.382113i
$288$	−3.62527	+	7.11500i	−0.213621	+	0.419255i
$289$	0.424355	+	1.99643i	0.0249620	+	0.117437i
$290$	5.51373	−	0.698929i	0.323777	−	0.0410425i
$291$	0.0881041	+	0.0187271i	0.00516476	+	0.00109780i
$292$	2.34807	+	6.11694i	0.137411	+	0.357967i
$293$	1.98002	−	1.98002i	0.115674	−	0.115674i	−0.646900	−	0.762575i	$-0.723935\pi$
$293$	1.98002	−	1.98002i	0.115674	−	0.115674i	0.762575	+	0.646900i	$0.223935\pi$
$294$	1.28399	−	1.74073i	0.0748840	−	0.101522i
$295$	12.5597	−	26.0092i	0.731253	−	1.51431i
$296$	2.46628	−	23.4651i	0.143350	−	1.36388i
$297$	8.87061	+	3.40511i	0.514725	+	0.197584i
$298$	−0.975720	+	18.6178i	−0.0565219	+	1.07850i
$299$	−3.08636	−	5.34574i	−0.178489	−	0.309152i
$300$	0.564390	+	0.257817i	0.0325850	+	0.0148851i
$301$	15.6421	−	2.41969i	0.901594	−	0.139469i
$302$	7.88284	+	15.4709i	0.453606	+	0.890253i
$303$	0.842399	−	0.682161i	0.0483946	−	0.0391891i
$304$	−15.2721	+	6.79958i	−0.875915	+	0.389983i
$305$	−0.192251	−	0.00595985i	−0.0110082	−	0.000341260i
$306$	−5.67114	+	12.7376i	−0.324198	+	0.728160i
$307$	−18.7431	−	18.7431i	−1.06973	−	1.06973i	−0.997379	−	0.0723483i	$-0.976951\pi$
$307$	−18.7431	−	18.7431i	−1.06973	−	1.06973i	−0.0723483	−	0.997379i	$-0.523049\pi$
$308$	−4.12092	−	7.19745i	−0.234811	−	0.410113i
$309$	−2.59540	+	0.843298i	−0.147647	+	0.0479735i
$310$	3.13449	+	2.70329i	0.178027	+	0.153537i
$311$	22.4840	−	20.2447i	1.27495	−	1.14797i	0.293562	−	0.955940i	$-0.405159\pi$
$311$	22.4840	−	20.2447i	1.27495	−	1.14797i	0.981389	−	0.192031i	$-0.0615075\pi$
$312$	−2.23960	+	1.45441i	−0.126792	+	0.0823400i
$313$	−1.04388	−	19.9185i	−0.0590038	−	1.12586i	−0.854348	−	0.519701i	$-0.826043\pi$
$313$	−1.04388	−	19.9185i	−0.0590038	−	1.12586i	0.795344	−	0.606158i	$-0.207290\pi$
$314$	1.74420	−	5.36809i	0.0984308	−	0.302939i
$315$	−0.600921	+	17.3630i	−0.0338581	+	0.978294i
$316$	−0.672944	−	2.07111i	−0.0378561	−	0.116509i
$317$	16.1871	−	6.21364i	0.909157	−	0.348993i	0.141563	−	0.989929i	$-0.454787\pi$
$317$	16.1871	−	6.21364i	0.909157	−	0.348993i	0.767594	+	0.640937i	$0.221454\pi$
$318$	−0.243997	−	0.910607i	−0.0136826	−	0.0510643i
$319$	−12.8035	+	1.34570i	−0.716858	+	0.0753448i
$320$	−10.4562	+	16.8801i	−0.584518	+	0.943627i
$321$	−1.47360	+	2.02824i	−0.0822485	+	0.113205i
$322$	−1.22285	+	5.65279i	−0.0681470	+	0.315018i
$323$	20.7909	−	10.5935i	1.15684	−	0.589438i
$324$	−3.60083	+	2.07894i	−0.200046	+	0.115497i
$325$	−10.0523	−	14.1195i	−0.557603	−	0.783211i
$326$	5.98007	−	10.3578i	0.331206	−	0.573665i
$327$	−0.604272	−	0.392419i	−0.0334163	−	0.0217008i
$328$	−7.78553	+	1.23311i	−0.429884	+	0.0680869i
$329$	0.338723	+	6.94196i	0.0186744	+	0.382723i
$330$	3.95628	+	1.91047i	0.217786	+	0.105168i
$331$	−5.73969	−	2.55547i	−0.315482	−	0.140462i	0.242887	−	0.970055i	$-0.421906\pi$
$331$	−5.73969	−	2.55547i	−0.315482	−	0.140462i	−0.558368	+	0.829593i	$0.688572\pi$
$332$	−0.109129	+	0.0292411i	−0.00598925	+	0.00160482i
$333$	14.2479	−	17.5947i	0.780780	−	0.964183i
$334$	−14.9026	+	16.5510i	−0.815433	+	0.905630i
$335$	−2.36055	+	1.79333i	−0.128970	+	0.0979803i
$336$	1.82162	+	0.295252i	0.0993775	+	0.0161073i
$337$	−28.1439	−	14.3400i	−1.53310	−	0.781152i	−0.535123	−	0.844774i	$-0.679735\pi$
$337$	−28.1439	−	14.3400i	−1.53310	−	0.781152i	−0.997974	+	0.0636218i	$0.979735\pi$
$338$	−1.20578	+	0.0631925i	−0.0655860	+	0.00343722i
$339$	−1.63363	−	1.81433i	−0.0887267	−	0.0985410i
$340$	2.05246	−	3.73718i	0.111310	−	0.202677i
$341$	−7.12516	−	6.41552i	−0.385849	−	0.347420i
$342$	−21.4817	−	3.40236i	−1.16160	−	0.183979i
$343$	−17.5509	−	5.91323i	−0.947659	−	0.319284i
$344$	10.7616	+	14.8121i	0.580228	+	0.798615i
$345$	0.379095	+	0.927816i	0.0204098	+	0.0499520i
$346$	6.25069	+	14.0393i	0.336039	+	0.754757i
$347$	−4.55257	+	11.8599i	−0.244395	+	0.636670i	−0.999828	−	0.0185555i	$-0.994093\pi$
$347$	−4.55257	+	11.8599i	−0.244395	+	0.636670i	0.755433	+	0.655226i	$0.227427\pi$
$348$	−0.136848	+	0.210727i	−0.00733581	+	0.0112962i
$349$	−18.9164			−1.01257			−0.506287	−	0.862365i	$-0.668982\pi$
$349$	−18.9164			−1.01257			−0.506287	+	0.862365i	$0.668982\pi$
$350$	−1.91095	+	16.1268i	−0.102145	+	0.862012i
$351$	−5.18013			−0.276495
$352$	9.41673	−	14.5005i	0.501914	−	0.772879i
$353$	−10.2699	+	26.7541i	−0.546613	+	1.42398i	0.330552	+	0.943788i	$0.392765\pi$
$353$	−10.2699	+	26.7541i	−0.546613	+	1.42398i	−0.877165	+	0.480189i	$0.840568\pi$
$354$	−1.62345	−	3.64632i	−0.0862852	−	0.193800i
$355$	−2.42169	+	2.04825i	−0.128530	+	0.108710i
$356$	3.74034	+	5.14814i	0.198238	+	0.272851i
$357$	−2.56070	−	0.278478i	−0.135527	−	0.0147386i
$358$	19.4577	+	3.08179i	1.02837	+	0.162878i
$359$	−23.5570	−	21.2109i	−1.24329	−	1.11947i	−0.988300	−	0.152523i	$-0.951260\pi$
$359$	−23.5570	−	21.2109i	−1.24329	−	1.11947i	−0.254993	−	0.966943i	$-0.582073\pi$
$360$	−18.1800	+	8.56429i	−0.958168	+	0.451378i
$361$	11.6419	+	12.9296i	0.612730	+	0.680506i
$362$	−16.7358	+	0.877084i	−0.879612	+	0.0460985i
$363$	−6.60045	−	3.36310i	−0.346434	−	0.176517i
$364$	3.50362	+	2.85815i	0.183640	+	0.149808i
$365$	−8.57729	+	28.4531i	−0.448956	+	1.48930i
$366$	−0.0177857	+	0.0197530i	−0.000929674	+	0.00103251i
$367$	8.36452	−	10.3293i	0.436624	−	0.539186i	−0.510574	−	0.859834i	$-0.670567\pi$
$367$	8.36452	−	10.3293i	0.436624	−	0.539186i	0.947199	+	0.320647i	$0.103900\pi$
$368$	−4.76607	+	1.27706i	−0.248448	+	0.0665716i
$369$	−6.90987	−	3.07647i	−0.359713	−	0.160155i
$370$	14.6411	−	15.2806i	0.761153	−	0.794399i
$371$	−6.78534	+	4.37176i	−0.352277	+	0.226970i
$372$	−0.184823	+	0.0292731i	−0.00958263	+	0.00151774i
$373$	−19.1176	−	12.4151i	−0.989871	−	0.642830i	−0.0552493	−	0.998473i	$-0.517595\pi$
$373$	−19.1176	−	12.4151i	−0.989871	−	0.642830i	−0.934622	+	0.355643i	$0.884262\pi$
$374$	15.0947	−	26.1448i	0.780529	−	1.35192i
$375$	1.30703	+	2.49236i	0.0674946	+	0.128705i
$376$	−6.96240	+	4.01974i	−0.359058	+	0.207302i
$377$	6.25366	−	3.18640i	0.322080	−	0.164108i
$378$	3.59515	+	3.26063i	0.184915	+	0.167709i
$379$	8.90518	−	12.2569i	0.457428	−	0.629596i	−0.516545	−	0.856260i	$-0.672782\pi$
$379$	8.90518	−	12.2569i	0.457428	−	0.629596i	0.973973	+	0.226664i	$0.0727820\pi$
$380$	6.45954	+	1.58370i	0.331368	+	0.0812422i
$381$	−1.91706	+	0.201491i	−0.0982137	+	0.0103227i
$382$	−0.353395	−	1.31889i	−0.0180813	−	0.0674802i
$383$	−3.27535	+	1.25729i	−0.167362	+	0.0642444i	−0.440607	−	0.897700i	$-0.645237\pi$
$383$	−3.27535	+	1.25729i	−0.167362	+	0.0642444i	0.273244	+	0.961945i	$0.411903\pi$
$384$	0.424909	+	1.30773i	0.0216835	+	0.0667350i
$385$	5.22366	−	37.2524i	0.266222	−	1.89856i
$386$	4.00163	−	12.3158i	0.203678	−	0.626855i
$387$	0.919455	+	17.5443i	0.0467385	+	0.891825i
$388$	0.147952	−	0.0960812i	0.00751113	−	0.00487778i
$389$	2.95236	−	2.65832i	0.149691	−	0.134782i	−0.590883	−	0.806757i	$-0.701221\pi$
$389$	2.95236	−	2.65832i	0.149691	−	0.134782i	0.740574	+	0.671975i	$0.234554\pi$
$390$	−2.38688	−	0.199410i	−0.120864	−	0.0100975i
$391$	6.55008	−	2.12825i	0.331252	−	0.107630i
$392$	−3.19863	−	21.1827i	−0.161555	−	1.06989i
$393$	−1.51293	−	1.51293i	−0.0763174	−	0.0763174i
$394$	0.0554587	−	0.124562i	0.00279397	−	0.00627536i
$395$	3.34181	−	9.29463i	0.168145	−	0.467664i
$396$	8.40968	−	3.74423i	0.422602	−	0.188155i
$397$	−25.0612	+	20.2941i	−1.25778	+	1.01853i	−0.259173	+	0.965831i	$0.583450\pi$
$397$	−25.0612	+	20.2941i	−1.25778	+	1.01853i	−0.998610	+	0.0527017i	$0.983217\pi$
$398$	10.6645	+	20.9303i	0.534565	+	1.04914i
$399$	−0.614234	−	3.97071i	−0.0307502	−	0.198784i
$400$	−12.9816	+	4.84041i	−0.649082	+	0.242020i
$401$	7.36782	+	12.7614i	0.367932	+	0.637276i	0.989242	−	0.146288i	$-0.0467327\pi$
$401$	7.36782	+	12.7614i	0.367932	+	0.637276i	−0.621310	+	0.783565i	$0.713399\pi$
$402$	−0.0214405	+	0.409109i	−0.00106935	+	0.0204045i
$403$	4.87992	+	1.87322i	0.243086	+	0.0933119i
$404$	0.221915	−	2.11138i	0.0110407	−	0.105045i
$405$	−18.6851	−	2.55144i	−0.928469	−	0.126782i
$406$	−6.34589	−	1.72492i	−0.314941	−	0.0856062i
$407$	−34.6627	+	34.6627i	−1.71816	+	1.71816i
$408$	−1.06776	−	2.78160i	−0.0528618	−	0.137710i
$409$	16.0700	+	3.41578i	0.794611	+	0.168900i	0.587293	−	0.809374i	$-0.300193\pi$
$409$	16.0700	+	3.41578i	0.794611	+	0.168900i	0.207317	+	0.978274i	$0.433527\pi$
$410$	−6.19709	−	3.40345i	−0.306052	−	0.168084i
$411$	0.894412	+	4.20788i	0.0441181	+	0.207559i
$412$	−2.42652	+	4.76230i	−0.119546	+	0.234622i
$413$	−25.4790	+	22.7756i	−1.25374	+	1.12072i
$414$	−6.10523	−	1.98371i	−0.300056	−	0.0974941i
$415$	−0.472472	−	0.198373i	−0.0231928	−	0.00973773i
$416$	−1.95979	+	9.22009i	−0.0960867	+	0.452052i
$417$	3.15797	+	2.55727i	0.154646	+	0.125230i
$418$	45.4873	+	12.1883i	2.22485	+	0.596148i
$419$	7.57258	−	5.50180i	0.369945	−	0.268781i	−0.387243	−	0.921978i	$-0.626573\pi$
$419$	7.57258	−	5.50180i	0.369945	−	0.268781i	0.757188	+	0.653197i	$0.226573\pi$
$420$	−0.500871	−	0.536783i	−0.0244400	−	0.0261923i
$421$	−9.78581	−	7.10980i	−0.476931	−	0.346511i	0.323205	−	0.946329i	$-0.395240\pi$
$421$	−9.78581	−	7.10980i	−0.476931	−	0.346511i	−0.800136	+	0.599818i	$0.795240\pi$
$422$	13.7516	+	16.9818i	0.669418	+	0.826662i
$423$	−7.70379	−	0.403738i	−0.374571	−	0.0196304i
$424$	−8.08590	−	4.66840i	−0.392686	−	0.226717i
$425$	17.7414	−	7.69531i	0.860583	−	0.373277i
$426$			0.438310i			0.0212362i
$427$	0.207573	+	0.0933154i	0.0100451	+	0.00451585i
$428$	0.768125	+	4.84975i	0.0371287	+	0.234422i
$429$	5.51776	+	0.579940i	0.266400	+	0.0279998i
$430$	−0.508839	+	16.4139i	−0.0245384	+	0.791550i
$431$	−2.84276	−	27.0471i	−0.136931	−	1.30281i	−0.819960	−	0.572421i	$-0.806004\pi$
$431$	−2.84276	−	27.0471i	−0.136931	−	1.30281i	0.683029	−	0.730391i	$-0.260662\pi$
$432$	−1.07171	+	3.99967i	−0.0515626	+	0.192434i
$433$	−4.60452	+	29.0718i	−0.221279	+	1.39710i	0.587612	+	0.809143i	$0.300068\pi$
$433$	−4.60452	+	29.0718i	−0.221279	+	1.39710i	−0.808891	+	0.587959i	$0.799932\pi$
$434$	−2.20769	−	4.37173i	−0.105973	−	0.209850i
$435$	−1.07608	+	0.375244i	−0.0515941	+	0.0179916i
$436$	−1.38033	+	0.293399i	−0.0661059	+	0.0140512i
$437$	5.85113	+	9.00996i	0.279898	+	0.431005i
$438$	2.23671	+	3.44423i	0.106874	+	0.164572i
$439$	2.21580	−	0.470982i	0.105754	−	0.0224788i	−0.154731	−	0.987957i	$-0.549451\pi$
$439$	2.21580	−	0.470982i	0.105754	−	0.0224788i	0.260485	+	0.965478i	$0.416118\pi$
$440$	41.0859	−	14.3272i	1.95869	−	0.683024i
$441$	8.49625	−	18.7185i	0.404583	−	0.891357i
$442$	−2.57470	+	16.2560i	−0.122466	+	0.773220i
$443$	−3.88631	+	14.5039i	−0.184644	+	0.689102i	0.810062	+	0.586344i	$0.199433\pi$
$443$	−3.88631	+	14.5039i	−0.184644	+	0.689102i	−0.994706	+	0.102758i	$0.967233\pi$
$444$	0.100006	+	0.951494i	0.00474608	+	0.0451559i
$445$	−0.894307	+	28.8482i	−0.0423942	+	1.36754i
$446$	8.38871	+	0.881689i	0.397217	+	0.0417492i
$447$	−0.598018	−	3.77574i	−0.0282853	−	0.178586i
$448$	19.0569	−	13.7409i	0.900353	−	0.649198i
$449$		−	16.3116i		−	0.769793i	−0.922960	−	0.384897i	$-0.874237\pi$
$449$		−	16.3116i		−	0.769793i	0.922960	−	0.384897i	$-0.125763\pi$
$450$	−17.5943	−	3.91708i	−0.829403	−	0.184653i
$451$	14.1830	+	8.18855i	0.667851	+	0.385584i
$452$	−4.77513	−	0.250254i	−0.224603	−	0.0117710i
$453$	−2.24060	−	2.76691i	−0.105273	−	0.130001i
$454$	−8.48871	−	6.16741i	−0.398395	−	0.289451i
$455$	4.61949	+	19.9809i	0.216565	+	0.936717i
$456$	3.76003	−	2.73182i	0.176079	−	0.127929i
$457$	1.28545	+	0.344436i	0.0601310	+	0.0161121i	0.288759	−	0.957402i	$-0.406757\pi$
$457$	1.28545	+	0.344436i	0.0601310	+	0.0161121i	−0.228628	+	0.973514i	$0.573424\pi$
$458$	−8.52842	−	6.90618i	−0.398507	−	0.322704i
$459$	1.20166	−	5.65338i	0.0560889	−	0.263877i
$460$	1.80996	+	0.759931i	0.0843898	+	0.0354320i
$461$	24.7473	+	8.04087i	1.15259	+	0.374501i	0.822120	−	0.569314i	$-0.192791\pi$
$461$	24.7473	+	8.04087i	1.15259	+	0.374501i	0.330474	+	0.943815i	$0.392791\pi$
$462$	−3.46443	−	3.87565i	−0.161180	−	0.180311i
$463$	14.0944	−	27.6618i	0.655023	−	1.28555i	−0.289522	−	0.957171i	$-0.593496\pi$
$463$	14.0944	−	27.6618i	0.655023	−	1.28555i	0.944545	−	0.328383i	$-0.106504\pi$
$464$	−1.16647	−	5.48779i	−0.0541518	−	0.254764i
$465$	−0.743924	−	0.408563i	−0.0344986	−	0.0189467i
$466$	−7.51932	−	1.59828i	−0.348326	−	0.0740389i
$467$	2.59522	+	6.76079i	0.120093	+	0.312852i	0.980428	−	0.196876i	$-0.0630795\pi$
$467$	2.59522	+	6.76079i	0.120093	+	0.312852i	−0.860336	+	0.509728i	$0.829746\pi$
$468$	−3.54874	+	3.54874i	−0.164040	+	0.164040i
$469$	3.39137	−	0.895623i	0.156599	−	0.0413560i
$470$	−7.14461	−	0.975594i	−0.329556	−	0.0450008i
$471$	−0.120978	+	1.15102i	−0.00557435	+	0.0530364i
$472$	−36.9051	−	14.1666i	−1.69870	−	0.652068i
$473$	1.99080	−	37.9868i	0.0915372	−	1.74663i
$474$	−0.682472	−	1.18208i	−0.0313470	−	0.0542946i
$475$	18.7574	+	23.6246i	0.860648	+	1.08397i
$476$	−3.93202	+	3.16069i	−0.180224	+	0.144870i
$477$	−4.06739	−	7.98270i	−0.186233	−	0.365503i
$478$	22.1860	−	17.9658i	1.01476	−	0.821738i
$479$	−16.5055	+	7.34871i	−0.754154	+	0.335771i	−0.747548	−	0.664207i	$-0.768769\pi$
$479$	−16.5055	+	7.34871i	−0.754154	+	0.335771i	−0.00660539	+	0.999978i	$0.502103\pi$
$480$	0.517835	−	1.44026i	0.0236358	−	0.0657388i
$481$	10.8700	−	24.4144i	0.495629	−	1.11320i
$482$	3.24467	+	3.24467i	0.147791	+	0.147791i
$483$	0.00427517	−	1.18590i	0.000194527	−	0.0539604i
$484$	−13.7987	+	4.48346i	−0.627212	+	0.203793i
$485$	0.797359	+	0.0666145i	0.0362062	+	0.00302481i
$486$	−6.02652	+	5.42631i	−0.273369	+	0.246142i
$487$	−18.4169	+	11.9600i	−0.834547	+	0.541961i	−0.889715	−	0.456516i	$-0.849097\pi$
$487$	−18.4169	+	11.9600i	−0.834547	+	0.541961i	0.0551681	+	0.998477i	$0.482431\pi$
$488$	0.0137775	+	0.262890i	0.000623678	+	0.0119005i
$489$	−0.757837	+	2.33238i	−0.0342706	+	0.105474i
$490$	9.37089	−	16.7750i	0.423334	−	0.757817i
$491$	0.143207	+	0.440744i	0.00646282	+	0.0198905i	0.954236	−	0.299055i	$-0.0966714\pi$
$491$	0.143207	+	0.440744i	0.00646282	+	0.0198905i	−0.947773	+	0.318945i	$0.896671\pi$
$492$	0.298404	−	0.114546i	0.0134531	−	0.00516415i
$493$	2.02681	+	7.56416i	0.0912829	+	0.340673i
$494$	−25.5329	+	2.68361i	−1.14878	+	0.120741i
$495$	40.5516	+	9.94214i	1.82266	+	0.446866i
$496$	2.45594	−	3.38032i	0.110275	−	0.151781i
$497$	3.57333	−	1.14682i	0.160286	−	0.0514420i
$498$	−0.0630953	+	0.0321487i	−0.00282737	+	0.00144062i
$499$	−7.05051	+	4.07061i	−0.315624	+	0.182226i	−0.649440	−	0.760412i	$-0.724997\pi$
$499$	−7.05051	+	4.07061i	−0.315624	+	0.182226i	0.333816	+	0.942638i	$0.391663\pi$
$500$	5.26183	+	1.64158i	0.235316	+	0.0734139i
$501$	2.28338	−	3.95492i	0.102014	−	0.176693i
$502$	−7.44452	−	4.83453i	−0.332265	−	0.215776i
$503$	20.1887	−	3.19758i	0.900171	−	0.142573i	0.310838	−	0.950463i	$-0.399390\pi$
$503$	20.1887	−	3.19758i	0.900171	−	0.142573i	0.589334	+	0.807890i	$0.299390\pi$
$504$	23.7499	−	1.15884i	1.05791	−	0.0516190i
$505$	6.66179	−	6.95277i	0.296446	−	0.309394i
$506$	12.6977	+	5.65336i	0.564480	+	0.251323i
$507$	0.239147	−	0.0640793i	0.0106209	−	0.00284586i
$508$	−2.37591	+	2.93400i	−0.105414	+	0.130175i
$509$	27.2532	−	30.2678i	1.20798	−	1.34160i	0.284155	−	0.958778i	$-0.408287\pi$
$509$	27.2532	−	30.2678i	1.20798	−	1.34160i	0.923824	−	0.382818i	$-0.125046\pi$
$510$	0.771326	−	2.55869i	0.0341549	−	0.113301i
$511$	22.2269	−	27.2465i	0.983260	−	1.20531i
$512$	21.8254	+	11.1206i	0.964554	+	0.491465i
$513$	9.00325	−	0.471841i	0.397503	−	0.0208323i
$514$	−17.5736	−	19.5175i	−0.775139	−	0.860880i
$515$	−21.9305	+	10.3311i	−0.966375	+	0.455244i
$516$	−0.551717	−	0.496769i	−0.0242880	−	0.0218690i
$517$	16.4975	+	2.61294i	0.725558	+	0.114917i
$518$	−22.9117	+	10.1021i	−1.00668	+	0.443863i
$519$	−1.85221	−	2.54935i	−0.0813030	−	0.111904i
$520$	−18.1123	+	15.3193i	−0.794275	+	0.671794i
$521$	5.76944	+	12.9584i	0.252764	+	0.567716i	0.994708	−	0.102745i	$-0.0327627\pi$
$521$	5.76944	+	12.9584i	0.252764	+	0.567716i	−0.741944	+	0.670462i	$0.766096\pi$
$522$	2.61578	−	6.81435i	0.114490	−	0.298256i
$523$	−11.2240	+	17.2834i	−0.490790	+	0.755751i	−0.994113	−	0.108348i	$-0.965444\pi$
$523$	−11.2240	+	17.2834i	−0.490790	+	0.755751i	0.503323	+	0.864098i	$0.332111\pi$
$524$	−4.19057			−0.183066
$525$	−0.304240	−	3.31598i	−0.0132781	−	0.144721i
$526$	20.0329			0.873475
$527$	−3.17638	+	4.89120i	−0.138365	+	0.213064i
$528$	1.58934	−	4.14037i	0.0691672	−	0.180187i
$529$	−8.06523	−	18.1148i	−0.350662	−	0.787600i
$530$	−3.16753	−	7.75237i	−0.137589	−	0.336741i
$531$	−22.2959	−	30.6877i	−0.967560	−	1.33173i
$532$	−6.34976	−	4.64843i	−0.275297	−	0.201535i
$533$	−8.81854	−	1.39672i	−0.381973	−	0.0604986i
$534$	2.96404	+	2.66884i	0.128267	+	0.115492i
$535$	−10.7207	+	19.5205i	−0.463496	+	0.843946i
$536$	2.71491	+	3.01521i	0.117266	+	0.130237i
$537$	−4.03397	+	0.211411i	−0.174079	+	0.00912307i
$538$	−16.4921	−	8.40314i	−0.711025	−	0.362285i
$539$	−22.5317	+	38.3843i	−0.970511	+	1.65333i
$540$	1.31175	−	0.996551i	0.0564487	−	0.0428847i
$541$	−12.2065	+	13.5567i	−0.524797	+	0.582846i	−0.946019	−	0.324111i	$-0.894935\pi$
$541$	−12.2065	+	13.5567i	−0.524797	+	0.582846i	0.421222	+	0.906958i	$0.361601\pi$
$542$	3.96180	−	4.89242i	0.170174	−	0.210147i
$543$	3.31926	−	0.889393i	0.142443	−	0.0381675i
$544$	−9.60781	−	4.27767i	−0.411931	−	0.183404i
$545$	−5.76367	−	2.78324i	−0.246889	−	0.119221i
$546$	2.52049	+	1.29572i	0.107867	+	0.0554517i
$547$	29.6025	−	4.68857i	1.26571	−	0.200469i	0.512752	−	0.858537i	$-0.328626\pi$
$547$	29.6025	−	4.68857i	1.26571	−	0.200469i	0.752959	+	0.658068i	$0.228626\pi$
$548$	7.06623	+	4.58886i	0.301854	+	0.196027i
$549$	−0.126302	+	0.218762i	−0.00539046	+	0.00933655i
$550$	36.9999	+	12.4168i	1.57768	+	0.529454i
$551$	−10.5788	+	6.10770i	−0.450674	+	0.260197i
$552$	1.22226	−	0.622770i	0.0520227	−	0.0265069i
$553$	−7.85124	+	8.65673i	−0.333869	+	0.368121i
$554$	0.206231	−	0.283852i	0.00876190	−	0.0120597i
$555$	−2.28509	+	3.68897i	−0.0969965	+	0.156588i
$556$	7.91512	−	0.831912i	0.335676	−	0.0352809i
$557$	−6.17658	−	23.0513i	−0.261710	−	0.976716i	−0.964233	−	0.265055i	$-0.914610\pi$
$557$	−6.17658	−	23.0513i	−0.261710	−	0.976716i	0.702523	−	0.711661i	$-0.252057\pi$
$558$	5.07494	−	1.94809i	0.214840	−	0.0824692i
$559$	6.40840	+	19.7230i	0.271047	+	0.834196i
$560$	16.3833	+	0.567014i	0.692320	+	0.0239607i
$561$	−1.91291	+	5.88733i	−0.0807630	+	0.248563i
$562$	0.0726882	+	1.38697i	0.00306617	+	0.0585060i
$563$	3.07725	−	1.99839i	0.129691	−	0.0842222i	−0.478163	−	0.878271i	$-0.658697\pi$
$563$	3.07725	−	1.99839i	0.129691	−	0.0842222i	0.607854	+	0.794049i	$0.292031\pi$
$564$	0.242262	−	0.218134i	0.0102011	−	0.00918510i
$565$	−16.4236	−	14.1643i	−0.690946	−	0.595896i
$566$	3.66456	−	1.19069i	0.154033	−	0.0500483i
$567$	19.2838	+	11.2264i	0.809845	+	0.471465i
$568$	3.06956	+	3.06956i	0.128796	+	0.128796i
$569$	16.5717	−	37.2207i	0.694723	−	1.56037i	−0.127900	−	0.991787i	$-0.540824\pi$
$569$	16.5717	−	37.2207i	0.694723	−	1.56037i	0.822623	−	0.568587i	$-0.192510\pi$
$570$	4.16665	+	0.129168i	0.174522	+	0.00541025i
$571$	9.71455	−	4.32520i	0.406541	−	0.181004i	−0.193269	−	0.981146i	$-0.561909\pi$
$571$	9.71455	−	4.32520i	0.406541	−	0.181004i	0.599811	+	0.800142i	$0.295242\pi$
$572$	8.44479	−	6.83846i	0.353094	−	0.285930i
$573$	0.127107	+	0.249461i	0.00530995	+	0.0104214i
$574$	5.24113	+	6.52018i	0.218761	+	0.272147i
$575$	4.37735	+	7.75311i	0.182548	+	0.323327i
$576$	13.0386	+	22.5836i	0.543277	+	0.940983i
$577$	1.71681	−	32.7588i	0.0714719	−	1.36377i	−0.693851	−	0.720119i	$-0.744087\pi$
$577$	1.71681	−	32.7588i	0.0714719	−	1.36377i	0.765323	−	0.643647i	$-0.222579\pi$
$578$	2.33915	+	0.897915i	0.0972957	+	0.0373483i
$579$	−0.277553	+	2.64074i	−0.0115347	+	0.109745i
$580$	−0.970597	+	2.00996i	−0.0403019	+	0.0834590i
$581$	0.427179	+	0.430270i	0.0177224	+	0.0178506i
$582$	0.0781867	−	0.0781867i	0.00324094	−	0.00324094i
$583$	6.95178	+	18.1100i	0.287913	+	0.750040i
$584$	39.7846	+	8.45648i	1.64630	+	0.349932i
$585$	−22.5820	+	2.86253i	−0.933649	+	0.118351i
$586$	−0.714694	−	3.36237i	−0.0295237	−	0.138898i
$587$	−14.7169	+	28.8836i	−0.607433	+	1.19215i	0.358541	+	0.933514i	$0.383274\pi$
$587$	−14.7169	+	28.8836i	−0.607433	+	1.19215i	−0.965974	+	0.258640i	$0.916726\pi$
$588$	0.305453	+	0.813209i	0.0125967	+	0.0335362i
$589$	−8.65209	−	2.81124i	−0.356503	−	0.115835i
$590$	−18.3804	−	30.3205i	−0.756708	−	1.24827i
$591$	−0.00581289	+	0.0273475i	−0.000239110	+	0.00112493i
$592$	−16.6019	−	13.4440i	−0.682335	−	0.552544i
$593$	37.8985	+	10.1549i	1.55631	+	0.417011i	0.931492	−	0.363762i	$-0.118508\pi$
$593$	37.8985	+	10.1549i	1.55631	+	0.417011i	0.624815	+	0.780773i	$0.285174\pi$
$594$	9.43659	−	6.85609i	0.387188	−	0.281309i
$595$	−22.8779	+	0.406455i	−0.937903	+	0.0166630i
$596$	−6.05727	−	4.40087i	−0.248116	−	0.180267i
$597$	−3.03126	−	3.74330i	−0.124061	−	0.153203i
$598$	−7.56724	−	0.396582i	−0.309447	−	0.0162175i
$599$	24.9966	+	14.4318i	1.02133	+	0.589668i	0.914490	−	0.404608i	$-0.132592\pi$
$599$	24.9966	+	14.4318i	1.02133	+	0.589668i	0.106845	+	0.994276i	$0.465925\pi$
$600$	3.25041	−	2.06665i	0.132697	−	0.0843708i
$601$		−	4.29834i		−	0.175333i	−0.996150	−	0.0876666i	$-0.972059\pi$
$601$		−	4.29834i		−	0.175333i	0.996150	−	0.0876666i	$-0.0279410\pi$
$602$	7.96706	−	17.7221i	0.324713	−	0.722298i
$603$	0.609044	+	3.84535i	0.0248022	+	0.156595i
$604$	−6.93497	−	0.728895i	−0.282180	−	0.0296583i
$605$	−61.9250	−	22.2646i	−2.51761	−	0.905186i
$606$	−0.139093	−	1.32338i	−0.00565027	−	0.0537588i
$607$	−1.79188	+	6.68738i	−0.0727301	+	0.271432i	−0.992709	−	0.120535i	$-0.961539\pi$
$607$	−1.79188	+	6.68738i	−0.0727301	+	0.271432i	0.919979	+	0.391968i	$0.128206\pi$
$608$	2.56636	−	16.2034i	0.104080	−	0.657133i
$609$	1.34632	+	0.0754252i	0.0545555	+	0.00305638i
$610$	−0.134674	+	0.193947i	−0.00545280	+	0.00785268i
$611$	−8.90720	+	1.89328i	−0.360347	+	0.0765941i
$612$	−3.04972	−	4.69616i	−0.123278	−	0.189831i
$613$	5.28880	+	8.14403i	0.213612	+	0.328934i	0.929192	−	0.369597i	$-0.120504\pi$
$613$	5.28880	+	8.14403i	0.213612	+	0.328934i	−0.715580	+	0.698531i	$0.753837\pi$
$614$	−31.8286	+	6.76538i	−1.28450	+	0.273029i
$615$	1.38803	+	0.418427i	0.0559708	+	0.0168726i
$616$	−51.4039	−	2.87982i	−2.07112	−	0.116031i
$617$	−0.775761	+	4.89796i	−0.0312310	+	0.197184i	−0.998371	−	0.0570609i	$-0.981827\pi$
$617$	−0.775761	+	4.89796i	−0.0312310	+	0.197184i	0.967140	+	0.254245i	$0.0818271\pi$
$618$	−0.867063	+	3.23592i	−0.0348784	+	0.130168i
$619$	3.61746	+	34.4178i	0.145398	+	1.38337i	0.787294	+	0.616578i	$0.211482\pi$
$619$	3.61746	+	34.4178i	0.145398	+	1.38337i	−0.641896	+	0.766792i	$0.721852\pi$
$620$	−1.59610	+	0.464445i	−0.0641007	+	0.0186526i
$621$	2.64641	+	0.278149i	0.106197	+	0.0111617i
$622$	−5.81017	−	36.6840i	−0.232967	−	1.47089i
$623$	14.0024	−	31.1473i	0.560996	−	1.24789i
$624$			2.41784i			0.0967910i
$625$	14.3028	+	20.5044i	0.572110	+	0.820177i
$626$	−21.2050	−	12.2427i	−0.847523	−	0.489318i
$627$	−9.64289	−	0.505362i	−0.385100	−	0.0201822i
$628$	1.42653	+	1.76161i	0.0569246	+	0.0702961i
$629$	24.1233	+	17.5266i	0.961860	+	0.698832i
$630$	17.4743	+	12.2275i	0.696193	+	0.487157i
$631$	−31.6801	+	23.0169i	−1.26116	+	0.916289i	−0.998814	−	0.0486840i	$-0.984497\pi$
$631$	−31.6801	+	23.0169i	−1.26116	+	0.916289i	−0.262349	+	0.964973i	$0.584497\pi$
$632$	−13.0578	−	3.49882i	−0.519410	−	0.139175i
$633$	−3.48210	−	2.81975i	−0.138401	−	0.112075i
$634$	4.42539	−	20.8198i	0.175755	−	0.826861i
$635$	−16.6694	+	3.91726i	−0.661506	+	0.155452i
$636$	0.360071	+	0.116994i	0.0142777	+	0.00463912i
$637$	3.96863	−	23.9386i	0.157243	−	0.948480i
$638$	−7.17492	+	14.0816i	−0.284058	+	0.557495i
$639$	0.866048	+	4.07444i	0.0342603	+	0.161182i
$640$	5.20550	+	11.0500i	0.205765	+	0.436791i
$641$	20.0822	+	4.26861i	0.793200	+	0.168600i	0.586655	−	0.809837i	$-0.300445\pi$
$641$	20.0822	+	4.26861i	0.793200	+	0.168600i	0.206545	+	0.978437i	$0.433778\pi$
$642$	1.10293	+	2.87322i	0.0435291	+	0.113397i
$643$	33.0301	−	33.0301i	1.30258	−	1.30258i	0.375934	−	0.926646i	$-0.377322\pi$
$643$	33.0301	−	33.0301i	1.30258	−	1.30258i	0.926646	−	0.375934i	$-0.122678\pi$
$644$	−1.63645	−	1.64829i	−0.0644852	−	0.0649518i
$645$	−0.597702	−	3.31380i	−0.0235345	−	0.130481i
$646$	2.99422	−	28.4881i	0.117806	−	1.12085i
$647$	4.43443	+	1.70222i	0.174335	+	0.0669211i	0.443970	−	0.896042i	$-0.353570\pi$
$647$	4.43443	+	1.70222i	0.174335	+	0.0669211i	−0.269635	+	0.962963i	$0.586903\pi$
$648$	−1.35083	+	25.7754i	−0.0530656	+	1.01255i
$649$	41.0652	+	71.1270i	1.61195	+	2.79198i
$650$	−21.2577	+	0.909082i	−0.833797	+	0.0356571i
$651$	0.629167	+	0.782709i	0.0246590	+	0.0306768i
$652$	2.18061	+	4.27969i	0.0853992	+	0.167605i
$653$	4.65894	−	3.77273i	0.182318	−	0.147638i	−0.533817	−	0.845600i	$-0.679243\pi$
$653$	4.65894	−	3.77273i	0.182318	−	0.147638i	0.716135	+	0.697962i	$0.245909\pi$
$654$	−0.808030	+	0.359758i	−0.0315965	+	0.0140677i
$655$	−15.0232	−	11.6430i	−0.587006	−	0.454928i
$656$	−2.90288	+	6.51998i	−0.113338	+	0.254562i
$657$	27.5973	+	27.5973i	1.07668	+	1.07668i
$658$	7.37356	+	4.29264i	0.287451	+	0.167345i
$659$	−27.7363	+	9.01207i	−1.08045	+	0.351060i	−0.794550	−	0.607198i	$-0.792293\pi$
$659$	−27.7363	+	9.01207i	−1.08045	+	0.351060i	−0.285903	+	0.958259i	$0.592293\pi$
$660$	−1.50881	+	0.914647i	−0.0587305	+	0.0356026i
$661$	−15.0457	+	13.5472i	−0.585211	+	0.526926i	−0.907685	−	0.419652i	$-0.862152\pi$
$661$	−15.0457	+	13.5472i	−0.585211	+	0.526926i	0.322474	+	0.946578i	$0.395485\pi$
$662$	−6.46853	+	4.20071i	−0.251407	+	0.163265i
$663$	−0.176625	−	3.37020i	−0.00685953	−	0.130888i
$664$	−0.216725	+	0.667011i	−0.00841056	+	0.0258850i
$665$	−9.84883	−	34.3067i	−0.381921	−	1.33036i
$666$	−8.58850	−	26.4327i	−0.332798	−	1.02425i
$667$	−3.36595	+	1.29207i	−0.130330	+	0.0500290i
$668$	−2.31495	−	8.63951i	−0.0895681	−	0.334273i
$669$	−1.72009	+	0.180789i	−0.0665026	+	0.00698971i
$670$	0.268073	+	3.62932i	0.0103566	+	0.140213i
$671$	0.321483	−	0.442484i	0.0124107	−	0.0170819i
$672$	−1.21660	+	1.34142i	−0.0469314	+	0.0517463i
$673$	−3.57412	+	1.82110i	−0.137772	+	0.0701984i	−0.521518	−	0.853240i	$-0.674634\pi$
$673$	−3.57412	+	1.82110i	−0.137772	+	0.0701984i	0.383746	+	0.923439i	$0.374634\pi$
$674$	−33.5808	+	19.3879i	−1.29348	+	0.746792i
$675$	7.47142	+	0.0718859i	0.287575	+	0.00276689i
$676$	0.242454	−	0.419943i	0.00932516	−	0.0161517i
$677$	41.5962	+	27.0129i	1.59867	+	1.03819i	0.964175	+	0.265265i	$0.0854596\pi$
$677$	41.5962	+	27.0129i	1.59867	+	1.03819i	0.634498	+	0.772925i	$0.281207\pi$
$678$	−2.96019	+	0.468848i	−0.113685	+	0.0180060i
$679$	−0.841992	−	0.432847i	−0.0323127	−	0.0166111i
$680$	−12.5172	−	23.3207i	−0.480013	−	0.894307i
$681$	1.96549	+	0.875093i	0.0753177	+	0.0335336i
$682$	−11.3690	+	3.04631i	−0.435340	+	0.116649i
$683$	9.13221	−	11.2773i	0.349434	−	0.431515i	−0.571878	−	0.820339i	$-0.693785\pi$
$683$	9.13221	−	11.2773i	0.349434	−	0.431515i	0.921312	+	0.388823i	$0.127118\pi$
$684$	5.84458	−	6.49107i	0.223473	−	0.248192i
$685$	12.5829	+	36.0837i	0.480768	+	1.37869i
$686$	−17.8224	+	14.1159i	−0.680464	+	0.538949i
$687$	2.00495	+	1.02157i	0.0764936	+	0.0389754i
$688$	16.5543	−	0.867575i	0.631128	−	0.0330760i
$689$	−7.07648	−	7.85922i	−0.269592	−	0.299413i
$690$	1.20870	+	0.230038i	0.0460143	+	0.00875740i
$691$	−2.25683	−	2.03206i	−0.0858540	−	0.0773033i	0.625086	−	0.780556i	$-0.285064\pi$
$691$	−2.25683	−	2.03206i	−0.0858540	−	0.0773033i	−0.710940	+	0.703252i	$0.751730\pi$
$692$	−6.09578	−	0.965477i	−0.231727	−	0.0367019i
$693$	−39.8624	−	29.1819i	−1.51425	−	1.10853i
$694$	9.16648	+	12.6166i	0.347955	+	0.478919i
$695$	30.6871	+	19.0087i	1.16403	+	0.721043i
$696$	0.634411	+	1.42491i	0.0240473	+	0.0540111i
$697$	3.57001	−	9.30018i	0.135224	−	0.352270i
$698$	−12.6475	+	19.4754i	−0.478715	+	0.737156i
$699$	1.57627			0.0596200
$700$	−5.01369	−	4.17100i	−0.189500	−	0.157649i
$701$	−14.2658			−0.538811			−0.269405	−	0.963027i	$-0.586827\pi$
$701$	−14.2658			−0.538811			−0.269405	+	0.963027i	$0.586827\pi$
$702$	−3.46342	+	5.33321i	−0.130719	+	0.201289i
$703$	−16.6686	+	43.4232i	−0.628669	+	1.63774i
$704$	−22.9654	−	51.5811i	−0.865540	−	1.94403i
$705$	1.47457	−	0.108916i	0.0555356	−	0.00410203i
$706$	20.6782	+	28.4611i	0.778235	+	1.07115i
$707$	−10.4250	+	4.59654i	−0.392072	+	0.172871i
$708$	1.58321	+	0.250756i	0.0595008	+	0.00942399i
$709$	4.67089	+	4.20569i	0.175419	+	0.157948i	0.752163	−	0.658977i	$-0.229010\pi$
$709$	4.67089	+	4.20569i	0.175419	+	0.157948i	−0.576744	+	0.816925i	$0.695677\pi$
$710$	0.489643	+	3.86271i	0.0183760	+	0.144965i
$711$	−8.67975	−	9.63984i	−0.325516	−	0.361522i
$712$	39.4481	−	2.06739i	1.47838	−	0.0774785i
$713$	−2.39245	−	1.21902i	−0.0895981	−	0.0456525i
$714$	−1.99879	+	2.45018i	−0.0748028	+	0.0916958i
$715$	49.2744	−	1.05312i	1.84276	−	0.0393846i
$716$	−5.29391	+	5.87948i	−0.197843	+	0.219727i
$717$	−3.68387	+	4.54920i	−0.137577	+	0.169893i
$718$	−37.5878	+	10.0716i	−1.40276	+	0.375870i
$719$	−30.9003	−	13.7577i	−1.15239	−	0.513075i	−0.260562	−	0.965457i	$-0.583908\pi$
$719$	−30.9003	−	13.7577i	−1.15239	−	0.513075i	−0.891824	+	0.452382i	$0.850574\pi$
$720$	−2.46173	+	18.0281i	−0.0917434	+	0.671869i
$721$	28.6496	−	1.39792i	1.06697	−	0.0520611i
$722$	21.0954	−	3.34118i	0.785090	−	0.124346i
$723$	−0.789104	−	0.512450i	−0.0293471	−	0.0190582i
$724$	3.36516	−	5.82862i	0.125065	−	0.216619i
$725$	−9.06401	+	4.50903i	−0.336629	+	0.167461i
$726$	−7.87552	+	4.54694i	−0.292288	+	0.168753i
$727$	−0.691104	+	0.352135i	−0.0256316	+	0.0130600i	−0.466759	−	0.884384i	$-0.654579\pi$
$727$	−0.691104	+	0.352135i	−0.0256316	+	0.0130600i	0.441128	+	0.897444i	$0.354579\pi$
$728$	26.7256	−	8.57728i	0.990517	−	0.317895i
$729$	−13.8943	+	19.1239i	−0.514605	+	0.708293i
$730$	23.5591	+	27.8544i	0.871963	+	1.03094i
$731$	−23.0115	+	2.41861i	−0.851112	+	0.0894554i
$732$	−0.00276281	−	0.0103109i	−0.000102116	−	0.000381103i
$733$	−41.2853	+	15.8479i	−1.52491	+	0.585357i	−0.969255	−	0.246057i	$-0.920865\pi$
$733$	−41.2853	+	15.8479i	−1.52491	+	0.585357i	−0.555653	+	0.831415i	$0.687532\pi$
$734$	−5.04206	−	15.5179i	−0.186106	−	0.572774i
$735$	−1.16435	+	3.76402i	−0.0429476	+	0.138838i
$736$	1.49629	−	4.60510i	0.0551539	−	0.169746i
$737$	−0.441178	−	8.41818i	−0.0162510	−	0.310088i
$738$	−7.78730	+	5.05713i	−0.286654	+	0.186156i
$739$	3.53703	−	3.18475i	0.130112	−	0.117153i	−0.601506	−	0.798868i	$-0.705432\pi$
$739$	3.53703	−	3.18475i	0.130112	−	0.117153i	0.731618	+	0.681715i	$0.238766\pi$
$740$	1.94426	+	8.27355i	0.0714723	+	0.304142i
$741$	5.00666	−	1.62676i	0.183924	−	0.0597607i
$742$	−0.0357212	+	9.90880i	−0.00131137	+	0.363763i
$743$	−11.1811	−	11.1811i	−0.410196	−	0.410196i	0.471611	−	0.881807i	$-0.343673\pi$
$743$	−11.1811	−	11.1811i	−0.410196	−	0.410196i	−0.881807	+	0.471611i	$0.843673\pi$
$744$	−0.472474	+	1.06119i	−0.0173217	+	0.0389053i
$745$	−9.48811	−	32.6065i	−0.347618	−	1.19461i
$746$	−25.5639	+	11.3818i	−0.935963	+	0.416717i
$747$	−0.522998	+	0.423516i	−0.0191355	+	0.0154956i
$748$	5.50423	+	10.8027i	0.201254	+	0.394984i
$749$	20.5383	−	16.5093i	0.750452	−	0.603237i
$750$	3.43989	+	0.320736i	0.125607	+	0.0117116i
$751$	−25.2501	−	43.7345i	−0.921390	−	1.59589i	−0.797266	−	0.603628i	$-0.793721\pi$
$751$	−25.2501	−	43.7345i	−0.921390	−	1.59589i	−0.124124	−	0.992267i	$-0.539612\pi$
$752$	−0.380957	+	7.26910i	−0.0138921	+	0.265077i
$753$	1.69924	+	0.652276i	0.0619236	+	0.0237703i
$754$	0.900625	−	8.56888i	0.0327988	−	0.312060i
$755$	−22.8368	−	21.8810i	−0.831115	−	0.796333i
$756$	−1.88457	+	0.497695i	−0.0685413	+	0.0181010i
$757$	−6.78176	+	6.78176i	−0.246487	+	0.246487i	−0.819527	−	0.573040i	$-0.805764\pi$
$757$	−6.78176	+	6.78176i	−0.246487	+	0.246487i	0.573040	+	0.819527i	$0.305764\pi$
$758$	−6.66514	−	17.3633i	−0.242089	−	0.630663i
$759$	−2.78776	−	0.592556i	−0.101189	−	0.0215084i
$760$	30.0844	−	28.2752i	1.09128	−	1.02565i
$761$	0.693871	+	3.26440i	0.0251528	+	0.118335i	0.988933	−	0.148364i	$-0.0474006\pi$
$761$	0.693871	+	3.26440i	0.0251528	+	0.118335i	−0.963780	+	0.266698i	$0.914067\pi$
$762$	−1.07429	+	2.10842i	−0.0389176	+	0.0763800i
$763$	5.04712	+	5.64619i	0.182718	+	0.204406i
$764$	0.521513	+	0.169450i	0.0188677	+	0.00613048i
$765$	2.11442	−	25.3091i	0.0764470	−	0.915051i
$766$	−0.895448	+	4.21275i	−0.0323539

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.668598 - 1.02955i) q^{2} +(-0.0902073 + 0.234998i) q^{3} +(0.200523 + 0.450382i) q^{4} +(-0.532453 + 2.17175i) q^{5} +(0.181630 + 0.249992i) q^{6} +(1.56284 - 2.13484i) q^{7} +(3.02273 + 0.478753i) q^{8} +(2.18235 + 1.96499i) q^{9} +O(q^{10})\)	\(q+(0.668598 - 1.02955i) q^{2} +(-0.0902073 + 0.234998i) q^{3} +(0.200523 + 0.450382i) q^{4} +(-0.532453 + 2.17175i) q^{5} +(0.181630 + 0.249992i) q^{6} +(1.56284 - 2.13484i) q^{7} +(3.02273 + 0.478753i) q^{8} +(2.18235 + 1.96499i) q^{9} +(1.87993 + 2.00021i) q^{10} +(-4.25460 - 4.72522i) q^{11} +(-0.123927 + 0.00649476i) q^{12} +(3.08865 + 1.57374i) q^{13} +(-1.15301 - 3.03637i) q^{14} +(-0.462326 - 0.321033i) q^{15} +(1.85412 - 2.05921i) q^{16} +(-2.43401 + 3.00575i) q^{17} +(3.48217 - 0.933045i) q^{18} +(-5.51153 - 2.45389i) q^{19} +(-1.08488 + 0.195678i) q^{20} +(0.360703 + 0.559843i) q^{21} +(-7.70946 + 1.22106i) q^{22} +(-1.49342 - 0.969836i) q^{23} +(-0.385178 + 0.667148i) q^{24} +(-4.43299 - 2.31271i) q^{25} +(3.68531 - 2.12772i) q^{26} +(-1.33148 + 0.678422i) q^{27} +(1.27488 + 0.275791i) q^{28} +(1.19010 - 1.63804i) q^{29} +(-0.639630 + 0.261346i) q^{30} +(1.49964 - 0.157619i) q^{31} +(0.703784 + 2.62656i) q^{32} +(1.49421 - 0.573575i) q^{33} +(1.46720 + 4.51558i) q^{34} +(3.80419 + 4.53080i) q^{35} +(-0.447387 + 1.37692i) q^{36} +(-0.403486 - 7.69898i) q^{37} +(-6.21140 + 4.03373i) q^{38} +(-0.648446 + 0.583863i) q^{39} +(-2.64919 + 6.30969i) q^{40} +(-2.44960 + 0.795924i) q^{41} +(0.817551 + 0.00294727i) q^{42} +(4.23024 + 4.23024i) q^{43} +(1.27501 - 2.86371i) q^{44} +(-5.42947 + 3.69324i) q^{45} +(-1.99699 + 0.889117i) q^{46} +(-2.04151 + 1.65318i) q^{47} +(0.316655 + 0.621471i) q^{48} +(-2.11506 - 6.67282i) q^{49} +(-5.34493 + 3.01771i) q^{50} +(-0.486781 - 0.843129i) q^{51} +(-0.0894413 + 1.70664i) q^{52} +(-2.84820 - 1.09332i) q^{53} +(-0.191754 + 1.82442i) q^{54} +(12.5274 - 6.72397i) q^{55} +(5.74610 - 5.70482i) q^{56} +(1.07384 - 1.07384i) q^{57} +(-0.890740 - 2.32046i) q^{58} +(-12.6346 - 2.68556i) q^{59} +(0.0518806 - 0.272598i) q^{60} +(0.0178842 + 0.0841387i) q^{61} +(0.840380 - 1.64934i) q^{62} +(7.60560 - 1.58799i) q^{63} +(8.44536 + 2.74406i) q^{64} +(-5.06234 + 5.86982i) q^{65} +(0.408504 - 1.92186i) q^{66} +(1.03031 + 0.834329i) q^{67} +(-1.84181 - 0.493512i) q^{68} +(0.362627 - 0.263464i) q^{69} +(7.20816 - 0.887327i) q^{70} +(1.14755 + 0.833741i) q^{71} +(5.65589 + 6.98445i) q^{72} +(13.2720 + 0.695556i) q^{73} +(-8.19625 - 4.73211i) q^{74} +(0.943370 - 0.833121i) q^{75} -2.97435i q^{76} +(-16.7368 + 1.69813i) q^{77} +(0.167567 + 1.05798i) q^{78} +(-4.39299 - 0.461722i) q^{79} +(3.48485 + 5.12312i) q^{80} +(0.881568 + 8.38756i) q^{81} +(-0.818354 + 3.05414i) q^{82} +(-0.0358492 + 0.226343i) q^{83} +(-0.179814 + 0.274715i) q^{84} +(-5.23175 - 6.88648i) q^{85} +(7.18357 - 1.52692i) q^{86} +(0.277580 + 0.427435i) q^{87} +(-10.5983 - 16.3199i) q^{88} +(12.6254 - 2.68362i) q^{89} +(0.172246 + 8.05921i) q^{90} +(8.18675 - 4.13425i) q^{91} +(0.137332 - 0.867081i) q^{92} +(-0.0982386 + 0.366631i) q^{93} +(0.337085 + 3.20715i) q^{94} +(8.26386 - 10.6631i) q^{95} +(-0.680723 - 0.0715469i) q^{96} +(-0.0559772 - 0.353426i) q^{97} +(-8.28413 - 2.28387i) q^{98} -18.6723i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

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