LMFDB - Embedded newform 169.2.k.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(4,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.k (of order $78$, degree $24$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	169.17
Dual form			169.2.k.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99584 + 0.407454i) q^{2} +(1.34046 + 0.217845i) q^{3} +(1.97740 - 0.842491i) q^{4} +(-0.647035 - 2.62512i) q^{5} +(-2.76410 + 0.111389i) q^{6} +(-3.12689 - 1.48373i) q^{7} +(-0.250449 + 0.172873i) q^{8} +(-1.09624 - 0.365979i) q^{9} +O(q^{10})$	\(q+(-1.99584 + 0.407454i) q^{2} +(1.34046 + 0.217845i) q^{3} +(1.97740 - 0.842491i) q^{4} +(-0.647035 - 2.62512i) q^{5} +(-2.76410 + 0.111389i) q^{6} +(-3.12689 - 1.48373i) q^{7} +(-0.250449 + 0.172873i) q^{8} +(-1.09624 - 0.365979i) q^{9} +(2.36099 + 4.97569i) q^{10} +(-0.457073 - 1.36910i) q^{11} +(2.83415 - 0.698555i) q^{12} +(-2.59114 + 2.50718i) q^{13} +(6.84532 + 1.68722i) q^{14} +(-0.295451 - 3.65982i) q^{15} +(-2.54846 + 2.65323i) q^{16} +(3.18715 - 6.71677i) q^{17} +(2.33704 + 0.283768i) q^{18} +(1.35625 - 0.783031i) q^{19} +(-3.49109 - 4.64579i) q^{20} +(-3.86824 - 2.67005i) q^{21} +(1.47009 + 2.54627i) q^{22} +(2.33811 - 4.04973i) q^{23} +(-0.373376 + 0.177169i) q^{24} +(-2.04534 + 1.07347i) q^{25} +(4.14995 - 6.05971i) q^{26} +(-4.99720 - 2.62273i) q^{27} +(-7.43313 - 0.299545i) q^{28} +(1.83251 + 8.97622i) q^{29} +(2.08088 + 7.18403i) q^{30} +(2.10123 - 4.00356i) q^{31} +(4.33054 - 6.84820i) q^{32} +(-0.314435 - 1.93479i) q^{33} +(-3.62426 + 14.7042i) q^{34} +(-1.87176 + 9.16849i) q^{35} +(-2.47604 + 0.199887i) q^{36} +(2.23182 + 3.52934i) q^{37} +(-2.38781 + 2.11541i) q^{38} +(-4.01949 + 2.79630i) q^{39} +(0.615861 + 0.545605i) q^{40} +(-0.705434 + 4.34071i) q^{41} +(8.80830 + 3.75287i) q^{42} +(6.97646 + 4.41165i) q^{43} +(-2.05727 - 2.32218i) q^{44} +(-0.251434 + 3.11457i) q^{45} +(-3.01642 + 9.03528i) q^{46} +(-4.62870 + 0.562026i) q^{47} +(-3.99409 + 3.00136i) q^{48} +(3.14887 + 3.85667i) q^{49} +(3.64477 - 2.97586i) q^{50} +(5.73545 - 8.30923i) q^{51} +(-3.01144 + 7.14072i) q^{52} +(-6.04755 - 8.76139i) q^{53} +(11.0423 + 3.19843i) q^{54} +(-3.29832 + 2.08573i) q^{55} +(1.03962 - 0.168955i) q^{56} +(1.98857 - 0.754166i) q^{57} +(-7.31479 - 17.1684i) q^{58} +(2.94149 - 2.82534i) q^{59} +(-3.66759 - 6.98800i) q^{60} +(-1.14441 - 0.0923863i) q^{61} +(-2.56246 + 8.84663i) q^{62} +(2.88481 + 2.77090i) q^{63} +(-3.24364 + 8.55277i) q^{64} +(8.25823 + 5.17984i) q^{65} +(1.41590 + 3.73342i) q^{66} +(2.26143 - 5.30777i) q^{67} +(0.643443 - 15.9669i) q^{68} +(4.01635 - 4.91914i) q^{69} -19.0615i q^{70} +(-5.41606 - 4.42208i) q^{71} +(0.337820 - 0.0978509i) q^{72} +(0.379675 - 0.428564i) q^{73} +(-5.89239 - 6.13463i) q^{74} +(-2.97554 + 0.993380i) q^{75} +(2.02215 - 2.69099i) q^{76} +(-0.602156 + 4.95920i) q^{77} +(6.88290 - 7.21873i) q^{78} +(0.816417 + 6.72380i) q^{79} +(8.61398 + 4.97329i) q^{80} +(-3.35539 - 2.52141i) q^{81} +(-0.360705 - 8.95080i) q^{82} +(-1.28793 - 0.488449i) q^{83} +(-9.89854 - 2.02080i) q^{84} +(-19.6945 - 4.02067i) q^{85} +(-15.7214 - 5.96236i) q^{86} +(0.500970 + 12.4314i) q^{87} +(0.351154 + 0.263875i) q^{88} +(13.8701 + 8.00792i) q^{89} +(-0.767221 - 6.31863i) q^{90} +(11.8222 - 3.99514i) q^{91} +(1.21152 - 9.97777i) q^{92} +(3.68877 - 4.90886i) q^{93} +(9.00915 - 3.00770i) q^{94} +(-2.93309 - 3.05367i) q^{95} +(7.29676 - 8.23633i) q^{96} +(-1.48629 + 0.430509i) q^{97} +(-7.85605 - 6.41427i) q^{98} +1.66815i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{73}{78}\right)$

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 $

$2$	−1.99584	+	0.407454i	−1.41127	+	0.288113i	−0.844409	−	0.535699i	$-0.820048\pi$
$2$	−1.99584	+	0.407454i	−1.41127	+	0.288113i	−0.566863	+	0.823812i	$0.691843\pi$
$3$	1.34046	+	0.217845i	0.773913	+	0.125773i	0.534527	−	0.845151i	$-0.320490\pi$
$3$	1.34046	+	0.217845i	0.773913	+	0.125773i	0.239386	+	0.970924i	$0.423054\pi$
$4$	1.97740	−	0.842491i	0.988700	−	0.421246i
$5$	−0.647035	−	2.62512i	−0.289363	−	1.17399i	−0.918092	−	0.396367i	$-0.870271\pi$
$5$	−0.647035	−	2.62512i	−0.289363	−	1.17399i	0.628730	−	0.777624i	$-0.283575\pi$
$6$	−2.76410	+	0.111389i	−1.12844	+	0.0454745i
$7$	−3.12689	−	1.48373i	−1.18185	−	0.560796i	−0.266652	−	0.963793i	$-0.585917\pi$
$7$	−3.12689	−	1.48373i	−1.18185	−	0.560796i	−0.915201	+	0.402997i	$0.867969\pi$
$8$	−0.250449	+	0.172873i	−0.0885471	+	0.0611197i
$9$	−1.09624	−	0.365979i	−0.365414	−	0.121993i
$10$	2.36099	+	4.97569i	0.746612	+	1.57345i
$11$	−0.457073	−	1.36910i	−0.137813	−	0.412800i	0.856902	−	0.515480i	$-0.172386\pi$
$11$	−0.457073	−	1.36910i	−0.137813	−	0.412800i	−0.994714	+	0.102680i	$0.967258\pi$
$12$	2.83415	−	0.698555i	0.818149	−	0.201656i
$13$	−2.59114	+	2.50718i	−0.718654	+	0.695368i
$13$	−2.59114	+	2.50718i	−0.718654	+	0.695368i
$14$	6.84532	+	1.68722i	1.82949	+	0.450928i
$15$	−0.295451	−	3.65982i	−0.0762851	−	0.944961i
$16$	−2.54846	+	2.65323i	−0.637114	+	0.663306i
$17$	3.18715	−	6.71677i	0.772997	−	1.62906i	−0.00435589	−	0.999991i	$-0.501387\pi$
$17$	3.18715	−	6.71677i	0.772997	−	1.62906i	0.777352	−	0.629065i	$-0.216562\pi$
$18$	2.33704	+	0.283768i	0.550846	+	0.0668848i
$19$	1.35625	−	0.783031i	0.311145	−	0.179640i	−0.336294	−	0.941757i	$-0.609174\pi$
$19$	1.35625	−	0.783031i	0.311145	−	0.179640i	0.647439	+	0.762118i	$0.275840\pi$
$20$	−3.49109	−	4.64579i	−0.780631	−	1.03883i
$21$	−3.86824	−	2.67005i	−0.844118	−	0.582653i
$22$	1.47009	+	2.54627i	0.313424	+	0.542867i
$23$	2.33811	−	4.04973i	0.487530	−	0.844427i	−0.512367	−	0.858767i	$-0.671231\pi$
$23$	2.33811	−	4.04973i	0.487530	−	0.844427i	0.999897	+	0.0143395i	$0.00456458\pi$
$24$	−0.373376	+	0.177169i	−0.0762150	+	0.0361645i
$25$	−2.04534	+	1.07347i	−0.409067	+	0.214695i
$26$	4.14995	−	6.05971i	0.813871	−	1.18841i
$27$	−4.99720	−	2.62273i	−0.961712	−	0.504745i
$28$	−7.43313	−	0.299545i	−1.40473	−	0.0566087i
$29$	1.83251	+	8.97622i	0.340288	+	1.66684i	0.685313	+	0.728249i	$0.259666\pi$
$29$	1.83251	+	8.97622i	0.340288	+	1.66684i	−0.345024	+	0.938594i	$0.612129\pi$
$30$	2.08088	+	7.18403i	0.379915	+	1.31162i
$31$	2.10123	−	4.00356i	0.377393	−	0.719061i	−0.620482	−	0.784220i	$-0.713063\pi$
$31$	2.10123	−	4.00356i	0.377393	−	0.719061i	0.997875	+	0.0651589i	$0.0207554\pi$
$32$	4.33054	−	6.84820i	0.765539	−	1.21060i
$33$	−0.314435	−	1.93479i	−0.0547360	−	0.336804i
$34$	−3.62426	+	14.7042i	−0.621556	+	2.52175i
$35$	−1.87176	+	9.16849i	−0.316385	+	1.54976i
$36$	−2.47604	+	0.199887i	−0.412674	+	0.0333145i
$37$	2.23182	+	3.52934i	0.366909	+	0.580220i	0.977295	−	0.211884i	$-0.0679601\pi$
$37$	2.23182	+	3.52934i	0.366909	+	0.580220i	−0.610386	+	0.792104i	$0.708986\pi$
$38$	−2.38781	+	2.11541i	−0.387353	+	0.343165i
$39$	−4.01949	+	2.79630i	−0.643634	+	0.447767i
$40$	0.615861	+	0.545605i	0.0973762	+	0.0862677i
$41$	−0.705434	+	4.34071i	−0.110170	+	0.677905i	0.871942	+	0.489609i	$0.162861\pi$
$41$	−0.705434	+	4.34071i	−0.110170	+	0.677905i	−0.982112	+	0.188296i	$0.939704\pi$
$42$	8.80830	+	3.75287i	1.35915	+	0.579080i
$43$	6.97646	+	4.41165i	1.06390	+	0.672770i	0.947280	−	0.320407i	$-0.103820\pi$
$43$	6.97646	+	4.41165i	1.06390	+	0.672770i	0.116620	+	0.993177i	$0.462794\pi$
$44$	−2.05727	−	2.32218i	−0.310146	−	0.350082i
$45$	−0.251434	+	3.11457i	−0.0374816	+	0.464293i
$46$	−3.01642	+	9.03528i	−0.444747	+	1.33218i
$47$	−4.62870	+	0.562026i	−0.675166	+	0.0819799i	−0.450936	−	0.892556i	$-0.648910\pi$
$47$	−4.62870	+	0.562026i	−0.675166	+	0.0819799i	−0.224230	+	0.974536i	$0.571987\pi$
$48$	−3.99409	+	3.00136i	−0.576497	+	0.433210i
$49$	3.14887	+	3.85667i	0.449839	+	0.550952i
$50$	3.64477	−	2.97586i	0.515448	−	0.420851i
$51$	5.73545	−	8.30923i	0.803124	−	1.16353i
$52$	−3.01144	+	7.14072i	−0.417612	+	0.990240i
$53$	−6.04755	−	8.76139i	−0.830695	−	1.20347i	−0.976790	−	0.214199i	$-0.931286\pi$
$53$	−6.04755	−	8.76139i	−0.830695	−	1.20347i	0.146095	−	0.989271i	$-0.453330\pi$
$54$	11.0423	+	3.19843i	1.50266	+	0.435251i
$55$	−3.29832	+	2.08573i	−0.444745	+	0.281240i
$56$	1.03962	−	0.168955i	0.138925	−	0.0225776i
$57$	1.98857	−	0.754166i	0.263393	−	0.0998917i
$58$	−7.31479	−	17.1684i	−0.960479	−	2.25433i
$59$	2.94149	−	2.82534i	0.382949	−	0.367827i	−0.476390	−	0.879234i	$-0.658055\pi$
$59$	2.94149	−	2.82534i	0.382949	−	0.367827i	0.859339	+	0.511407i	$0.170875\pi$
$60$	−3.66759	−	6.98800i	−0.473484	−	0.902147i
$61$	−1.14441	−	0.0923863i	−0.146527	−	0.0118289i	0.00698561	−	0.999976i	$-0.497776\pi$
$61$	−1.14441	−	0.0923863i	−0.146527	−	0.0118289i	−0.153512	+	0.988147i	$0.549058\pi$
$62$	−2.56246	+	8.84663i	−0.325432	+	1.12352i
$63$	2.88481	+	2.77090i	0.363452	+	0.349101i
$64$	−3.24364	+	8.55277i	−0.405455	+	1.06910i
$65$	8.25823	+	5.17984i	1.02431	+	0.642479i
$66$	1.41590	+	3.73342i	0.174285	+	0.459552i
$67$	2.26143	−	5.30777i	0.276277	−	0.648447i	−0.722815	−	0.691042i	$-0.757152\pi$
$67$	2.26143	−	5.30777i	0.276277	−	0.648447i	0.999092	+	0.0425946i	$0.0135624\pi$
$68$	0.643443	−	15.9669i	0.0780289	−	1.93627i
$69$	4.01635	−	4.91914i	0.483512	−	0.592195i
$70$		−	19.0615i		−	2.27828i
$71$	−5.41606	−	4.42208i	−0.642768	−	0.524804i	0.254057	−	0.967189i	$-0.418235\pi$
$71$	−5.41606	−	4.42208i	−0.642768	−	0.524804i	−0.896825	+	0.442385i	$0.854132\pi$
$72$	0.337820	−	0.0978509i	0.0398125	−	0.0115318i
$73$	0.379675	−	0.428564i	0.0444375	−	0.0501596i	−0.725872	−	0.687830i	$-0.758563\pi$
$73$	0.379675	−	0.428564i	0.0444375	−	0.0501596i	0.770309	+	0.637671i	$0.220102\pi$
$74$	−5.89239	−	6.13463i	−0.684977	−	0.713136i
$75$	−2.97554	+	0.993380i	−0.343585	+	0.114706i
$76$	2.02215	−	2.69099i	0.231956	−	0.308678i
$77$	−0.602156	+	4.95920i	−0.0686221	+	0.565154i
$78$	6.88290	−	7.21873i	0.779335	−	0.817360i
$79$	0.816417	+	6.72380i	0.0918541	+	0.756486i	0.963752	+	0.266799i	$0.0859660\pi$
$79$	0.816417	+	6.72380i	0.0918541	+	0.756486i	−0.871898	+	0.489687i	$0.837111\pi$
$80$	8.61398	+	4.97329i	0.963073	+	0.556030i
$81$	−3.35539	−	2.52141i	−0.372821	−	0.280157i
$82$	−0.360705	−	8.95080i	−0.0398332	−	0.988450i
$83$	−1.28793	−	0.488449i	−0.141369	−	0.0536143i	0.282906	−	0.959148i	$-0.408702\pi$
$83$	−1.28793	−	0.488449i	−0.141369	−	0.0536143i	−0.424275	+	0.905533i	$0.639471\pi$
$84$	−9.89854	−	2.02080i	−1.08002	−	0.220488i
$85$	−19.6945	−	4.02067i	−2.13617	−	0.436103i
$86$	−15.7214	−	5.96236i	−1.69529	−	0.642937i
$87$	0.500970	+	12.4314i	0.0537096	+	1.33279i
$88$	0.351154	+	0.263875i	0.0374331	+	0.0281292i
$89$	13.8701	+	8.00792i	1.47023	+	0.848837i	0.999442	−	0.0334089i	$-0.0106364\pi$
$89$	13.8701	+	8.00792i	1.47023	+	0.848837i	0.470788	+	0.882246i	$0.343970\pi$
$90$	−0.767221	−	6.31863i	−0.0808722	−	0.666042i
$91$	11.8222	−	3.99514i	1.23930	−	0.418804i
$92$	1.21152	−	9.97777i	0.126310	−	1.04025i
$93$	3.68877	−	4.90886i	0.382508	−	0.509025i
$94$	9.00915	−	3.00770i	0.929223	−	0.310220i
$95$	−2.93309	−	3.05367i	−0.300929	−	0.313300i
$96$	7.29676	−	8.23633i	0.744722	−	0.840617i
$97$	−1.48629	+	0.430509i	−0.150910	+	0.0437116i	−0.352813	−	0.935694i	$-0.614775\pi$
$97$	−1.48629	+	0.430509i	−0.150910	+	0.0437116i	0.201903	+	0.979406i	$0.435288\pi$
$98$	−7.85605	−	6.41427i	−0.793581	−	0.647939i
$99$			1.66815i			0.167655i
$100$	−3.14005	+	3.84586i	−0.314005	+	0.384586i
$101$	0.245955	−	6.10331i	0.0244734	−	0.607302i	−0.939695	−	0.342012i	$-0.888891\pi$
$101$	0.245955	−	6.10331i	0.0244734	−	0.607302i	0.964169	−	0.265289i	$-0.0854675\pi$
$102$	−8.06141	+	18.9208i	−0.798199	+	1.87344i
$103$	−4.19702	−	11.0666i	−0.413545	−	1.09043i	−0.966376	−	0.257134i	$-0.917222\pi$
$103$	−4.19702	−	11.0666i	−0.413545	−	1.09043i	0.552831	−	0.833293i	$-0.313547\pi$
$104$	0.215526	−	1.07586i	0.0211341	−	0.105497i
$105$	−4.50633	+	11.8822i	−0.439773	+	1.15958i
$106$	15.6398	+	15.0222i	1.51907	+	1.45909i
$107$	4.36722	−	15.0774i	0.422195	−	1.45759i	−0.414566	−	0.910019i	$-0.636067\pi$
$107$	4.36722	−	15.0774i	0.422195	−	1.45759i	0.836761	−	0.547568i	$-0.184446\pi$
$108$	−12.0911	−	0.976093i	−1.16347	−	0.0939246i
$109$	8.34150	+	15.8934i	0.798971	+	1.52231i	0.851894	+	0.523714i	$0.175454\pi$
$109$	8.34150	+	15.8934i	0.798971	+	1.52231i	−0.0529231	+	0.998599i	$0.516854\pi$
$110$	5.73308	−	5.50670i	0.546627	−	0.525043i
$111$	2.22281	+	5.21712i	0.210979	+	0.495187i
$112$	11.9054	−	4.51513i	1.12496	−	0.426639i
$113$	16.6925	−	2.71280i	1.57030	−	0.255199i	0.687939	−	0.725768i	$-0.258516\pi$
$113$	16.6925	−	2.71280i	1.57030	−	0.255199i	0.882363	+	0.470569i	$0.155951\pi$
$114$	−3.66158	+	2.31545i	−0.342939	+	0.216861i
$115$	−12.1439	−	3.51752i	−1.13242	−	0.328010i
$116$	11.1860	+	16.2057i	1.03859	+	1.50466i
$117$	3.75810	−	1.80018i	0.347436	−	0.166426i
$118$	−4.71954	+	6.83744i	−0.434469	+	0.629437i
$119$	−19.9317	+	16.2737i	−1.82714	+	1.49181i
$120$	0.706677	+	0.865523i	0.0645105	+	0.0790110i
$121$	7.12835	−	5.35660i	0.648031	−	0.486964i
$122$	2.32170	−	0.281906i	0.210197	−	0.0255225i
$123$	−1.89121	+	5.66486i	−0.170525	+	0.510783i
$124$	0.782009	−	9.68692i	0.0702265	−	0.869911i
$125$	−4.82297	−	5.44401i	−0.431380	−	0.486927i
$126$	−6.88664	−	4.35485i	−0.613510	−	0.387960i
$127$	−5.02428	−	2.14065i	−0.445833	−	0.189952i	0.157369	−	0.987540i	$-0.449699\pi$
$127$	−5.02428	−	2.14065i	−0.445833	−	0.189952i	−0.603203	+	0.797588i	$0.706109\pi$
$128$	0.389439	−	2.39632i	0.0344219	−	0.211806i
$129$	8.39059	+	7.43341i	0.738750	+	0.654475i
$130$	−18.5926	−	6.97328i	−1.63068	−	0.611597i
$131$	−8.32220	+	7.37283i	−0.727114	+	0.644167i	−0.943207	−	0.332206i	$-0.892207\pi$
$131$	−8.32220	+	7.37283i	−0.727114	+	0.644167i	0.216093	+	0.976373i	$0.430669\pi$
$132$	−2.25181	−	3.56095i	−0.195995	−	0.309941i
$133$	−5.40264	+	0.436146i	−0.468469	+	0.0378187i
$134$	−2.35078	+	11.5149i	−0.203076	+	0.994734i
$135$	−3.65163	+	14.8153i	−0.314283	+	1.27509i
$136$	0.362927	+	2.23318i	0.0311207	+	0.191494i
$137$	−0.432359	+	0.683721i	−0.0369389	+	0.0584142i	−0.863155	−	0.504940i	$-0.831515\pi$
$137$	−0.432359	+	0.683721i	−0.0369389	+	0.0584142i	0.826216	+	0.563354i	$0.190489\pi$
$138$	−6.01168	+	11.4543i	−0.511748	+	0.975054i
$139$	−1.53574	−	5.30200i	−0.130260	−	0.449710i	0.868698	−	0.495342i	$-0.164957\pi$
$139$	−1.53574	−	5.30200i	−0.130260	−	0.449710i	−0.998958	+	0.0456318i	$0.985470\pi$
$140$	4.02315	+	19.7067i	0.340018	+	1.66552i
$141$	−6.32701	−	0.254970i	−0.532830	−	0.0214723i
$142$	12.6114	+	6.61897i	1.05832	+	0.555451i
$143$	4.61693	+	2.40157i	0.386087	+	0.200830i
$144$	3.76475	−	1.97589i	0.313729	−	0.164658i
$145$	22.3780	−	10.6185i	1.85839	−	0.881817i
$146$	−0.583150	+	1.01004i	−0.0482618	+	0.0835919i
$147$	3.38077	+	5.85566i	0.278841	+	0.482967i
$148$	7.38663	+	5.09862i	0.607177	+	0.419104i
$149$	6.01119	+	7.99944i	0.492456	+	0.655340i	0.975434	−	0.220293i	$-0.0707012\pi$
$149$	6.01119	+	7.99944i	0.492456	+	0.655340i	−0.482978	+	0.875633i	$0.660445\pi$
$150$	5.53394	−	3.19502i	0.451844	−	0.260872i
$151$	7.83377	+	0.951191i	0.637503	+	0.0774068i	0.432905	−	0.901439i	$-0.357488\pi$
$151$	7.83377	+	0.951191i	0.637503	+	0.0774068i	0.204597	+	0.978846i	$0.434411\pi$
$152$	−0.204307	+	0.430567i	−0.0165715	+	0.0349236i
$153$	−5.95208	+	6.19677i	−0.481197	+	0.500979i
$154$	−0.818838	−	10.1431i	−0.0659838	−	0.817356i
$155$	−11.8694	−	2.92555i	−0.953375	−	0.234986i
$156$	−5.59228	+	8.91580i	−0.447741	+	0.713835i
$157$	6.30630	−	1.55436i	0.503298	−	0.124052i	0.0205108	−	0.999790i	$-0.493471\pi$
$157$	6.30630	−	1.55436i	0.503298	−	0.124052i	0.482787	+	0.875738i	$0.339625\pi$
$158$	−4.36907	−	13.0870i	−0.347585	−	1.04114i
$159$	−6.19785	−	13.0617i	−0.491522	−	1.03586i
$160$	−20.7794	−	6.93718i	−1.64275	−	0.548432i
$161$	−13.3197	+	9.19393i	−1.04974	+	0.724584i
$162$	7.72417	+	3.66516i	0.606868	+	0.287963i
$163$	3.43491	−	0.138422i	0.269043	−	0.0108421i	0.0946223	−	0.995513i	$-0.469836\pi$
$163$	3.43491	−	0.138422i	0.269043	−	0.0108421i	0.174421	+	0.984671i	$0.444195\pi$
$164$	2.26209	+	9.17764i	0.176639	+	0.716653i
$165$	−4.87562	+	2.07731i	−0.379567	+	0.161718i
$166$	2.76953	+	0.450093i	0.214957	+	0.0349340i
$167$	−10.0033	+	2.04219i	−0.774079	+	0.158029i	−0.570797	−	0.821091i	$-0.693366\pi$
$167$	−10.0033	+	2.04219i	−0.774079	+	0.158029i	−0.203282	+	0.979120i	$0.565161\pi$
$168$	1.43037			0.110356
$169$	0.428052	−	12.9930i	0.0329271	−	0.999458i
$170$	40.9454			3.14037
$171$	−1.77335	+	0.362032i	−0.135611	+	0.0276853i
$172$	17.5120	+	2.84598i	1.33528	+	0.217004i
$173$	7.96615	−	3.39406i	0.605655	−	0.258046i	−0.0672953	−	0.997733i	$-0.521437\pi$
$173$	7.96615	−	3.39406i	0.605655	−	0.258046i	0.672950	+	0.739688i	$0.265027\pi$
$174$	−6.06509	−	24.6070i	−0.459793	−	1.86546i
$175$	7.98828	−	0.321917i	0.603857	−	0.0243346i
$176$	4.79737	+	2.27638i	0.361615	+	0.171589i
$177$	4.55842	−	3.14645i	0.342632	−	0.236502i
$178$	−30.9454	−	10.3311i	−2.31946	−	0.774348i
$179$	−6.42291	−	13.5360i	−0.480071	−	1.01173i	−0.988584	−	0.150673i	$-0.951856\pi$
$179$	−6.42291	−	13.5360i	−0.480071	−	1.01173i	0.508513	−	0.861054i	$-0.330195\pi$
$180$	2.12681	+	6.37058i	0.158523	+	0.474835i
$181$	6.10303	−	1.50426i	0.453634	−	0.111811i	−0.00587692	−	0.999983i	$-0.501871\pi$
$181$	6.10303	−	1.50426i	0.453634	−	0.111811i	0.459511	+	0.888172i	$0.348025\pi$
$182$	−21.9674	+	12.7906i	−1.62833	+	0.948106i
$183$	−1.51391	−	0.373144i	−0.111911	−	0.0275836i
$184$	0.114509	+	1.41845i	0.00844170	+	0.104569i
$185$	7.82088	−	8.14240i	0.575003	−	0.598641i
$186$	−5.36206	+	11.3003i	−0.393165	+	0.828579i
$187$	−10.6527	−	1.29347i	−0.779003	−	0.0945881i
$188$	−8.67929	+	5.01099i	−0.633002	+	0.365464i
$189$	11.7343	+	15.6155i	0.853542	+	1.13586i
$190$	7.09821	+	4.89954i	0.514958	+	0.355450i
$191$	−2.27209	−	3.93538i	−0.164403	−	0.284754i	0.772040	−	0.635574i	$-0.219236\pi$
$191$	−2.27209	−	3.93538i	−0.164403	−	0.284754i	−0.936443	+	0.350820i	$0.885903\pi$
$192$	−6.21114	+	10.7580i	−0.448250	+	0.776392i
$193$	−3.69510	+	1.75335i	−0.265979	+	0.126209i	−0.557012	−	0.830504i	$-0.688052\pi$
$193$	−3.69510	+	1.75335i	−0.265979	+	0.126209i	0.291033	+	0.956713i	$0.406001\pi$
$194$	2.79099	−	1.46482i	0.200381	−	0.105168i
$195$	9.94139	+	8.74236i	0.711918	+	0.626054i
$196$	9.47578	+	4.97327i	0.676841	+	0.355234i
$197$	−8.32247	−	0.335384i	−0.592951	−	0.0238951i	−0.258023	−	0.966139i	$-0.583071\pi$
$197$	−8.32247	−	0.335384i	−0.592951	−	0.0238951i	−0.334928	+	0.942244i	$0.608712\pi$
$198$	−0.679692	−	3.32935i	−0.0483036	−	0.236607i
$199$	−6.04448	−	20.8680i	−0.428482	−	1.47929i	−0.827038	−	0.562146i	$-0.809976\pi$
$199$	−6.04448	−	20.8680i	−0.428482	−	1.47929i	0.398556	−	0.917144i	$-0.369511\pi$
$200$	0.326678	−	0.622433i	0.0230996	−	0.0440127i
$201$	4.18762	−	6.62219i	0.295372	−	0.467093i
$202$	1.99593	+	12.2814i	0.140433	+	0.864119i
$203$	7.58821	−	30.7866i	0.532588	−	2.16080i
$204$	4.34082	−	21.2627i	0.303918	−	1.48869i
$205$	11.8513	−	0.956739i	0.827734	−	0.0668216i
$206$	12.8857	+	20.3771i	0.897790	+	1.41974i
$207$	−4.04525	+	3.58378i	−0.281165	+	0.249090i
$208$	−0.0487057	−	13.2643i	−0.00337713	−	0.919717i
$209$	−1.69195	−	1.49894i	−0.117035	−	0.103684i
$210$	4.15246	−	25.5511i	0.286547	−	1.76319i
$211$	22.1462	+	9.43563i	1.52461	+	0.649576i	0.981738	−	0.190240i	$-0.0609265\pi$
$211$	22.1462	+	9.43563i	1.52461	+	0.649576i	0.542872	+	0.839815i	$0.317337\pi$
$212$	−19.3398	−	12.2298i	−1.32826	−	0.839944i
$213$	−6.29667	−	7.10747i	−0.431441	−	0.486996i
$214$	−2.57293	+	31.8715i	−0.175882	+	2.17869i
$215$	7.06710	−	21.1686i	0.481972	−	1.44368i
$216$	1.70494	−	0.207018i	0.116007	−	0.0140858i
$217$	−12.5105	+	9.40105i	−0.849269	+	0.638185i
$218$	−23.1241	−	28.3219i	−1.56616	−	1.91820i
$219$	0.602298	−	0.491761i	0.0406995	−	0.0332301i
$220$	−4.76488	+	6.90312i	−0.321248	+	0.465409i
$221$	8.58182	+	25.3949i	0.577276	+	1.70824i
$222$	−6.56210	−	9.50684i	−0.440419	−	0.638057i
$223$	9.11836	+	2.64117i	0.610611	+	0.176865i	0.569094	−	0.822272i	$-0.307294\pi$
$223$	9.11836	+	2.64117i	0.610611	+	0.176865i	0.0415163	+	0.999138i	$0.486781\pi$
$224$	−23.7020	+	14.9882i	−1.58366	+	1.00144i
$225$	2.63505	−	0.428237i	0.175670	−	0.0285492i
$226$	−32.2103	+	12.2158i	−2.14260	+	0.812580i
$227$	−8.61999	−	20.2319i	−0.572129	−	1.34284i	−0.915000	−	0.403453i	$-0.867810\pi$
$227$	−8.61999	−	20.2319i	−0.572129	−	1.34284i	0.342871	−	0.939382i	$-0.388600\pi$
$228$	3.29682	−	3.16664i	0.218337	−	0.209716i
$229$	9.84511	+	18.7583i	0.650583	+	1.23958i	0.957661	+	0.287898i	$0.0929566\pi$
$229$	9.84511	+	18.7583i	0.650583	+	1.23958i	−0.307078	+	0.951684i	$0.599351\pi$
$230$	25.6705	+	2.07233i	1.69266	+	0.136646i
$231$	−1.88750	+	6.51642i	−0.124189	+	0.428749i
$232$	−2.01069	−	1.93130i	−0.132008	−	0.126796i
$233$	−7.20397	+	18.9953i	−0.471948	+	1.24442i	0.461957	+	0.886902i	$0.347147\pi$
$233$	−7.20397	+	18.9953i	−0.471948	+	1.24442i	−0.933905	+	0.357522i	$0.883622\pi$
$234$	−6.76707	+	5.12411i	−0.442377	+	0.334974i
$235$	4.47032	+	11.7873i	0.291611	+	0.768916i
$236$	3.43617	−	8.06499i	0.223676	−	0.524986i
$237$	−0.370377	+	9.19081i	−0.0240586	+	0.597007i
$238$	33.1497	−	40.6010i	2.14878	−	2.63177i
$239$		−	11.8144i		−	0.764210i	−0.924119	−	0.382105i	$-0.875199\pi$
$239$		−	11.8144i		−	0.764210i	0.924119	−	0.382105i	$-0.124801\pi$
$240$	10.4633	+	8.54299i	0.675401	+	0.551448i
$241$	−21.9046	+	6.34476i	−1.41100	+	0.408702i	−0.894302	−	0.447465i	$-0.852327\pi$
$241$	−21.9046	+	6.34476i	−1.41100	+	0.408702i	−0.516700	+	0.856166i	$0.672840\pi$
$242$	−12.0445	+	13.5954i	−0.774248	+	0.873945i
$243$	7.78000	+	8.09984i	0.499087	+	0.519605i
$244$	−2.34079	+	0.781470i	−0.149854	+	0.0500285i
$245$	8.08679	−	10.7616i	0.516646	−	0.687531i
$246$	1.46638	−	12.0767i	0.0934930	−	0.769984i
$247$	−1.55103	+	5.42931i	−0.0986899	+	0.345459i
$248$	0.165855	+	1.36593i	0.0105318	+	0.0867369i
$249$	−1.62001	−	0.935316i	−0.102664	−	0.0592732i
$250$	11.8441	+	8.90024i	0.749085	+	0.562901i
$251$	0.811317	+	20.1326i	0.0512099	+	1.27076i	0.796754	+	0.604304i	$0.206549\pi$
$251$	0.811317	+	20.1326i	0.0512099	+	1.27076i	−0.745544	+	0.666457i	$0.767810\pi$
$252$	8.03888	+	3.04875i	0.506402	+	0.192053i
$253$	−6.61318	−	1.35009i	−0.415767	−	0.0848795i
$254$	10.8999	+	2.22523i	0.683919	+	0.139623i
$255$	−25.5238	−	9.67990i	−1.59836	−	0.606179i
$256$	−0.537511	−	13.3382i	−0.0335944	−	0.833637i
$257$	15.9028	+	11.9502i	0.991991	+	0.745433i	0.967136	−	0.254258i	$-0.0818312\pi$
$257$	15.9028	+	11.9502i	0.991991	+	0.745433i	0.0248549	+	0.999691i	$0.492088\pi$
$258$	−19.7750	−	11.4171i	−1.23114	−	0.710799i
$259$	−1.74207	−	14.3473i	−0.108247	−	0.891495i
$260$	20.6938	+	3.28512i	1.28337	+	0.203734i
$261$	1.27624	−	10.5108i	0.0789972	−	0.650600i
$262$	13.6057	−	18.1059i	0.840563	−	1.11859i
$263$	−26.1751	+	8.73854i	−1.61403	+	0.538842i	−0.973420	−	0.229027i	$-0.926446\pi$
$263$	−26.1751	+	8.73854i	−1.61403	+	0.538842i	−0.640608	+	0.767868i	$0.721317\pi$
$264$	0.413222	+	0.430210i	0.0254321	+	0.0264776i
$265$	−19.0868	+	21.5445i	−1.17249	+	1.32347i
$266$	10.6051	−	3.07180i	0.650240	−	0.188344i
$267$	16.8478	+	13.7558i	1.03107	+	0.841842i
$268$		−	12.4008i		−	0.757500i
$269$	−4.38696	+	5.37305i	−0.267478	+	0.327601i	−0.890827	−	0.454343i	$-0.849874\pi$
$269$	−4.38696	+	5.37305i	−0.267478	+	0.327601i	0.623349	+	0.781944i	$0.285772\pi$
$270$	1.25154	−	31.0568i	0.0761666	−	1.89005i
$271$	−5.84265	+	13.7132i	−0.354916	+	0.833018i	0.642836	+	0.766004i	$0.277758\pi$
$271$	−5.84265	+	13.7132i	−0.354916	+	0.833018i	−0.997752	+	0.0670145i	$0.978653\pi$
$272$	9.69879	+	25.5736i	0.588076	+	1.55063i
$273$	16.7175	−	2.77990i	1.01179	−	0.168247i
$274$	0.584334	−	1.54076i	0.0353009	−	0.0930809i
$275$	2.40456	+	2.30962i	0.145001	+	0.139275i
$276$	3.79760	−	13.1108i	0.228589	−	0.789180i
$277$	8.19712	+	0.661740i	0.492517	+	0.0397601i	0.324231	−	0.945978i	$-0.394895\pi$
$277$	8.19712	+	0.661740i	0.492517	+	0.0397601i	0.168286	+	0.985738i	$0.446177\pi$
$278$	5.22542	+	9.95620i	0.313400	+	0.597133i
$279$	−3.76868	+	3.61987i	−0.225625	+	0.216716i
$280$	−1.11620	−	2.61982i	−0.0667057	−	0.156564i
$281$	23.1226	−	8.76924i	1.37938	−	0.523129i	0.450255	−	0.892900i	$-0.351333\pi$
$281$	23.1226	−	8.76924i	1.37938	−	0.523129i	0.929123	+	0.369771i	$0.120564\pi$
$282$	12.7316	−	2.06908i	0.758155	−	0.123212i
$283$	−14.0566	+	8.88886i	−0.835578	+	0.528388i	−0.882392	−	0.470516i	$-0.844068\pi$
$283$	−14.0566	+	8.88886i	−0.835578	+	0.528388i	0.0468131	+	0.998904i	$0.485093\pi$
$284$	−14.4353	−	4.18123i	−0.856576	−	0.248110i
$285$	−3.26645	−	4.73227i	−0.193488	−	0.280316i
$286$	−10.1932	−	2.91197i	−0.602736	−	0.172188i
$287$	8.64625	−	12.5263i	0.510372	−	0.739401i
$288$	−7.25362	+	5.92240i	−0.427424	+	0.348981i
$289$	−24.2055	−	29.6464i	−1.42385	−	1.74390i
$290$	−40.3363	+	30.3108i	−2.36863	+	1.77991i
$291$	−2.08609	+	0.253298i	−0.122289	+	0.0148486i
$292$	0.389707	−	1.16731i	0.0228059	−	0.0683119i
$293$	0.140226	−	1.73702i	0.00819212	−	0.101478i	−0.991369	−	0.131101i	$-0.958149\pi$
$293$	0.140226	−	1.73702i	0.00819212	−	0.101478i	0.999561	+	0.0296235i	$0.00943082\pi$
$294$	−9.13338	−	10.3095i	−0.532670	−	0.601260i
$295$	−9.32010	−	5.89367i	−0.542637	−	0.343143i
$296$	−1.16908	−	0.498099i	−0.0679515	−	0.0289514i
$297$	−1.30670	+	8.04046i	−0.0758225	+	0.466555i
$298$	−15.2568	−	13.5163i	−0.883801	−	0.782980i
$299$	4.09503	+	16.3555i	0.236822	+	0.945864i
$300$	−5.04691	+	4.47117i	−0.291383	+	0.258143i
$301$	−15.2689	−	24.1459i	−0.880087	−	1.39175i
$302$	−16.0225	+	1.29347i	−0.921992	+	0.0744309i
$303$	1.65927	−	8.12764i	0.0953225	−	0.466921i
$304$	−1.37879	+	5.59395i	−0.0790788	+	0.320835i
$305$	0.497947	+	3.06399i	0.0285124	+	0.175444i
$306$	9.35450	−	14.7930i	0.534761	−	0.845657i
$307$	9.06808	−	17.2778i	0.517543	−	0.986095i	−0.476712	−	0.879059i	$-0.658172\pi$
$307$	9.06808	−	17.2778i	0.517543	−	0.986095i	0.994255	−	0.107036i	$-0.0341360\pi$
$308$	2.98738	+	10.3136i	0.170222	+	0.587674i
$309$	−3.21511	−	15.7486i	−0.182901	−	0.895909i
$310$	24.8815	+	1.00269i	1.41317	+	0.0569489i
$311$	−17.5336	−	9.20232i	−0.994237	−	0.521816i	−0.112548	−	0.993646i	$-0.535901\pi$
$311$	−17.5336	−	9.20232i	−0.994237	−	0.521816i	−0.881689	+	0.471831i	$0.843593\pi$
$312$	0.523275	−	1.39519i	0.0296246	−	0.0789872i
$313$	1.14134	−	0.599021i	0.0645123	−	0.0338586i	−0.432159	−	0.901798i	$-0.642248\pi$
$313$	1.14134	−	0.599021i	0.0645123	−	0.0338586i	0.496671	+	0.867939i	$0.334556\pi$
$314$	−11.9530	+	5.67178i	−0.674549	+	0.320077i
$315$	5.40738	−	9.36585i	0.304671	−	0.527706i
$316$	7.27912	+	12.6078i	0.409483	+	0.709245i
$317$	4.60209	+	3.17659i	0.258479	+	0.178415i	0.690256	−	0.723565i	$-0.257498\pi$
$317$	4.60209	+	3.17659i	0.258479	+	0.178415i	−0.431777	+	0.901980i	$0.642113\pi$
$318$	17.6920	+	23.5437i	0.992116	+	1.32027i
$319$	11.4518	−	6.61168i	0.641176	−	0.370183i
$320$	24.5508	+	2.98101i	1.37243	+	0.166643i
$321$	9.13862	−	19.2592i	0.510068	−	1.07495i
$322$	22.8379	−	23.7768i	1.27271	−	1.32503i
$323$	−0.936872	−	11.6052i	−0.0521290	−	0.645733i
$324$	−8.75920	−	2.15895i	−0.486622	−	0.119942i
$325$	2.60836	−	7.90956i	0.144686	−	0.438743i
$326$	−6.79914	+	1.67584i	−0.376569	+	0.0928160i
$327$	7.71912	+	23.1216i	0.426868	+	1.27863i
$328$	−0.573714	−	1.20908i	−0.0316781	−	0.0667601i
$329$	15.3073	+	5.11034i	0.843920	+	0.281742i
$330$	8.88455	−	6.13256i	0.489078	−	0.337586i
$331$	8.12738	+	3.85649i	0.446721	+	0.211972i	0.638745	−	0.769418i	$-0.279454\pi$
$331$	8.12738	+	3.85649i	0.446721	+	0.211972i	−0.192024	+	0.981390i	$0.561505\pi$
$332$	−2.95828	+	0.119214i	−0.162356	+	0.00654274i
$333$	−1.15495	−	4.68581i	−0.0632907	−	0.256781i
$334$	19.1329	−	8.15177i	1.04691	−	0.446045i
$335$	−15.3968	−	2.50222i	−0.841215	−	0.136711i
$336$	16.9423	−	3.45879i	0.924277	−	0.188693i
$337$	−13.4769			−0.734135			−0.367067	−	0.930194i	$-0.619638\pi$
$337$	−13.4769			−0.734135			−0.367067	+	0.930194i	$0.619638\pi$
$338$	4.43970	+	26.1063i	0.241488	+	1.41999i
$339$	22.9666			1.24737
$340$	−42.3313	+	8.64200i	−2.29574	+	0.468679i
$341$	−6.44171	−	1.04688i	−0.348838	−	0.0566917i
$342$	3.39181	−	1.44511i	0.183408	−	0.0781429i
$343$	1.67406	+	6.79193i	0.0903908	+	0.366730i
$344$	−2.50990	+	0.101146i	−0.135325	+	0.00545340i
$345$	−15.5121	−	7.36057i	−0.835142	−	0.396280i
$346$	−14.5162	+	10.0198i	−0.780398	+	0.538670i
$347$	29.6704	+	9.90544i	1.59279	+	0.531752i	0.968409	−	0.249367i	$-0.0802226\pi$
$347$	29.6704	+	9.90544i	1.59279	+	0.531752i	0.624382	+	0.781119i	$0.285351\pi$
$348$	11.4640	+	24.1599i	0.614535	+	1.29510i
$349$	−8.30961	−	24.8903i	−0.444803	−	1.33235i	−0.897630	−	0.440750i	$-0.854713\pi$
$349$	−8.30961	−	24.8903i	−0.444803	−	1.33235i	0.452827	−	0.891599i	$-0.350416\pi$
$350$	−15.8122	+	3.89735i	−0.845196	+	0.208322i
$351$	19.5241	−	5.73302i	1.04212	−	0.306006i
$352$	−11.3553	−	2.79882i	−0.605238	−	0.149178i
$353$	0.745481	+	9.23443i	0.0396779	+	0.491499i	0.985827	+	0.167767i	$0.0536557\pi$
$353$	0.745481	+	9.23443i	0.0396779	+	0.491499i	−0.946149	+	0.323732i	$0.895062\pi$
$354$	−7.81585	+	8.13716i	−0.415408	+	0.432485i
$355$	−8.10412	+	17.0791i	−0.430122	+	0.906463i
$356$	34.1734	+	4.14940i	1.81118	+	0.219918i
$357$	−30.2628	+	17.4722i	−1.60167	+	0.924727i
$358$	18.3344	+	24.3986i	0.969002	+	1.28951i
$359$	1.96186	+	1.35418i	0.103543	+	0.0714706i	0.618711	−	0.785619i	$-0.287655\pi$
$359$	1.96186	+	1.35418i	0.103543	+	0.0714706i	−0.515168	+	0.857089i	$0.672271\pi$
$360$	−0.475452	−	0.823507i	−0.0250585	−	0.0434026i
$361$	−8.27373	+	14.3305i	−0.435459	+	0.754238i
$362$	−11.5677	+	5.48897i	−0.607987	+	0.288494i
$363$	10.7222	−	5.62742i	0.562767	−	0.295363i
$364$	20.0113	−	17.8601i	1.04888	−	0.936122i
$365$	−1.37070	−	0.719397i	−0.0717455	−	0.0376549i
$366$	3.17355	+	0.127890i	0.165884	+	0.00668491i
$367$	2.87149	+	14.0655i	0.149891	+	0.734214i	0.983363	+	0.181652i	$0.0581444\pi$
$367$	2.87149	+	14.0655i	0.149891	+	0.734214i	−0.833472	+	0.552562i	$0.813650\pi$
$368$	4.78627	+	16.5241i	0.249501	+	0.861379i
$369$	2.36194	−	4.50029i	0.122958	−	0.234276i
$370$	−12.2916	+	19.4376i	−0.639009	+	1.01051i
$371$	5.91051	+	36.3688i	0.306858	+	1.88818i
$372$	3.15850	−	12.8145i	0.163761	−	0.664403i
$373$	−4.82209	+	23.6202i	−0.249678	+	1.22301i	0.640703	+	0.767789i	$0.278643\pi$
$373$	−4.82209	+	23.6202i	−0.249678	+	1.22301i	−0.890381	+	0.455216i	$0.849562\pi$
$374$	21.7881	−	1.75892i	1.12664	−	0.0909515i
$375$	−5.27904	−	8.34813i	−0.272608	−	0.431095i
$376$	1.06210	−	0.940934i	0.0547734	−	0.0485250i
$377$	−27.2533	−	18.6642i	−1.40362	−	0.961258i
$378$	−29.7823	−	26.3848i	−1.53184	−	1.35709i
$379$	−3.48094	+	21.4191i	−0.178804	+	1.10023i	0.730137	+	0.683301i	$0.239456\pi$
$379$	−3.48094	+	21.4191i	−0.178804	+	1.10023i	−0.908941	+	0.416925i	$0.863108\pi$
$380$	−8.37258	−	3.56722i	−0.429504	−	0.182995i
$381$	−6.26851	−	3.96396i	−0.321145	−	0.203080i
$382$	6.13822	+	6.92862i	0.314059	+	0.354499i
$383$	1.46898	−	18.1966i	0.0750614	−	0.929802i	−0.844168	−	0.536079i	$-0.819905\pi$
$383$	1.46898	−	18.1966i	0.0750614	−	0.929802i	0.919229	−	0.393723i	$-0.128813\pi$
$384$	1.04405	−	3.12732i	0.0532791	−	0.159590i
$385$	13.4081	−	1.62804i	0.683342	−	0.0829727i
$386$	6.66043	−	5.00499i	0.339007	−	0.254747i
$387$	−6.03332	−	7.38947i	−0.306691	−	0.375628i
$388$	−2.57629	+	2.10348i	−0.130791	+	0.106788i
$389$	2.54967	−	3.69384i	0.129274	−	0.187285i	−0.753002	−	0.658018i	$-0.771395\pi$
$389$	2.54967	−	3.69384i	0.129274	−	0.187285i	0.882276	+	0.470733i	$0.156010\pi$
$390$	−23.4035	−	13.3977i	−1.18508	−	0.678419i
$391$	−19.7492	−	28.6116i	−0.998760	−	1.44695i
$392$	−1.45534	−	0.421545i	−0.0735059	−	0.0212913i
$393$	−12.7617	+	8.07001i	−0.643742	+	0.407078i
$394$	16.7470	−	2.72165i	0.843700	−	0.137115i
$395$	17.1225	−	6.49372i	0.861529	−	0.326735i
$396$	1.40540	+	3.29859i	0.0706239	+	0.165760i
$397$	1.36751	−	1.31351i	0.0686335	−	0.0659234i	−0.657623	−	0.753347i	$-0.728438\pi$
$397$	1.36751	−	1.31351i	0.0686335	−	0.0659234i	0.726256	+	0.687424i	$0.241258\pi$
$398$	20.5665	+	39.1862i	1.03091	+	1.96423i
$399$	−7.33702	−	0.592306i	−0.367310	−	0.0296524i
$400$	2.36428	−	8.16244i	0.118214	−	0.408122i
$401$	−15.5436	−	14.9298i	−0.776211	−	0.745561i	0.195762	−	0.980651i	$-0.437282\pi$
$401$	−15.5436	−	14.9298i	−0.776211	−	0.745561i	−0.971974	+	0.235090i	$0.924461\pi$
$402$	−5.65958	+	14.9231i	−0.282274	+	0.744296i
$403$	4.59308	+	15.6420i	0.228798	+	0.779183i
$404$	−4.65563	−	12.2759i	−0.231626	−	0.610748i
$405$	−4.44796	+	10.4397i	−0.221021	+	0.518755i
$406$	−2.60075	+	64.5370i	−0.129073	+	3.20292i
$407$	3.81192	−	4.66875i	0.188950	−	0.231421i
$408$			3.07254i			0.152113i
$409$	10.0783	+	8.22867i	0.498340	+	0.406882i	0.848001	−	0.529994i	$-0.177806\pi$
$409$	10.0783	+	8.22867i	0.498340	+	0.406882i	−0.349662	+	0.936876i	$0.613703\pi$
$410$	−23.2636	+	6.73837i	−1.14890	+	0.332784i
$411$	−0.728504	+	0.822310i	−0.0359344	+	0.0405616i
$412$	−17.6227	−	18.3472i	−0.868209	−	0.903901i
$413$	−13.3897	+	4.47015i	−0.658865	+	0.219962i
$414$	6.61345	−	8.80091i	0.325033	−	0.432541i
$415$	−0.448901	+	3.69703i	−0.0220357	+	0.181480i
$416$	5.94866	+	28.6022i	0.291657	+	1.40234i
$417$	−0.903581	−	7.44166i	−0.0442485	−	0.364419i
$418$	3.98762	+	2.30225i	0.195041	+	0.112607i
$419$	4.65288	+	3.49641i	0.227308	+	0.170811i	0.708294	−	0.705917i	$-0.249465\pi$
$419$	4.65288	+	3.49641i	0.227308	+	0.170811i	−0.480986	+	0.876728i	$0.659721\pi$
$420$	1.09985	+	27.2924i	0.0536670	+	1.33173i
$421$	−2.10953	−	0.800040i	−0.102812	−	0.0389916i	0.302662	−	0.953098i	$-0.402125\pi$
$421$	−2.10953	−	0.800040i	−0.102812	−	0.0389916i	−0.405475	+	0.914106i	$0.632894\pi$
$422$	−48.0449	−	9.80844i	−2.33879	−	0.477467i
$423$	5.27987	+	1.07789i	0.256716	+	0.0524089i
$424$	3.02921	+	1.14883i	0.147111	+	0.0557920i
$425$	0.691499	+	17.1594i	0.0335426	+	0.832352i
$426$	15.4631	+	11.6198i	0.749190	+	0.562980i
$427$	3.44137	+	1.98687i	0.166539	+	0.0961515i
$428$	−4.06683	−	33.4934i	−0.196578	−	1.61896i
$429$	5.66563	+	4.22498i	0.273539	+	0.203984i
$430$	−5.47960	+	45.1286i	−0.264250	+	2.17629i
$431$	14.8592	−	19.7740i	0.715743	−	0.952480i	−0.284238	−	0.958754i	$-0.591740\pi$
$431$	14.8592	−	19.7740i	0.715743	−	0.952480i	0.999980	+	0.00627342i	$0.00199690\pi$
$432$	19.6939	−	6.57477i	0.947521	−	0.316329i
$433$	0.0650389	+	0.0677127i	0.00312557	+	0.00325406i	0.722763	−	0.691096i	$-0.242872\pi$
$433$	0.0650389	+	0.0677127i	0.00312557	+	0.00325406i	−0.719638	+	0.694350i	$0.755692\pi$
$434$	21.1385	−	23.8604i	1.01468	−	1.14534i
$435$	32.3099	−	9.35868i	1.54914	−	0.448714i
$436$	29.8845	+	24.4000i	1.43121	+	1.16855i
$437$		−	7.32325i		−	0.350319i
$438$	−1.00172	+	1.22688i	−0.0478641	+	0.0586228i
$439$	0.454911	−	11.2885i	0.0217117	−	0.538771i	−0.951334	−	0.308161i	$-0.900287\pi$
$439$	0.454911	−	11.2885i	0.0217117	−	0.538771i	0.973046	−	0.230611i	$-0.0740724\pi$
$440$	0.465495	−	1.09256i	0.0221916	−	0.0520857i
$441$	−2.04046	−	5.38026i	−0.0971649	−	0.256203i
$442$	−27.4752	−	47.1874i	−1.30686	−	2.24448i
$443$	−13.8305	+	36.4679i	−0.657105	+	1.73264i	0.0232177	+	0.999730i	$0.492609\pi$
$443$	−13.8305	+	36.4679i	−0.657105	+	1.73264i	−0.680323	+	0.732913i	$0.738160\pi$
$444$	8.79075	+	8.44363i	0.417190	+	0.400717i
$445$	12.0473	−	41.5922i	0.571098	−	1.97166i
$446$	−19.2749	−	1.55603i	−0.912695	−	0.0736803i
$447$	6.31510	+	12.0324i	0.298694	+	0.569114i
$448$	22.8325	−	21.9309i	1.07873	−	1.03614i
$449$	−9.96239	−	23.3826i	−0.470154	−	1.10349i	−0.971242	−	0.238096i	$-0.923477\pi$
$449$	−9.96239	−	23.3826i	−0.470154	−	1.10349i	0.501087	−	0.865397i	$-0.332934\pi$
$450$	−5.08465	+	1.92835i	−0.239693	+	0.0909035i
$451$	6.26531	−	1.01821i	0.295022	−	0.0479457i
$452$	30.7223	−	19.4276i	1.44506	−	0.913798i
$453$	10.2936	+	2.98158i	0.483636	+	0.140087i
$454$	25.4477	+	36.8673i	1.19432	+	1.73027i
$455$	−18.1371	−	28.4497i	−0.850280	−	1.33374i
$456$	−0.367662	+	0.532650i	−0.0172173	+	0.0249436i
$457$	17.2405	−	14.0764i	0.806475	−	0.658467i	−0.136755	−	0.990605i	$-0.543667\pi$
$457$	17.2405	−	14.0764i	0.806475	−	0.658467i	0.943231	+	0.332138i	$0.107770\pi$
$458$	−27.2924	−	33.4271i	−1.27529	−	1.56195i
$459$	−33.5431	+	25.2060i	−1.56566	+	1.17652i
$460$	−26.9768	+	3.27557i	−1.25780	+	0.152724i
$461$	2.94728	−	8.82819i	0.137269	−	0.411170i	−0.857355	−	0.514726i	$-0.827894\pi$
$461$	2.94728	−	8.82819i	0.137269	−	0.411170i	0.994624	+	0.103556i	$0.0330220\pi$
$462$	1.11202	−	13.7748i	0.0517357	−	0.640862i
$463$	21.8475	+	24.6607i	1.01534	+	1.14608i	0.989222	+	0.146420i	$0.0467752\pi$
$463$	21.8475	+	24.6607i	1.01534	+	1.14608i	0.0261151	+	0.999659i	$0.491686\pi$
$464$	−28.4860	−	18.0135i	−1.32243	−	0.836254i
$465$	−15.2731	−	6.50727i	−0.708274	−	0.301767i
$466$	6.63826	−	40.8469i	0.307512	−	1.89219i
$467$	−9.81858	−	8.69850i	−0.454350	−	0.402519i	0.404669	−	0.914463i	$-0.367387\pi$
$467$	−9.81858	−	8.69850i	−0.454350	−	0.402519i	−0.859018	+	0.511945i	$0.828925\pi$
$468$	5.91463	−	6.72583i	0.273404	−	0.310901i
$469$	−14.9465	+	13.2415i	−0.690166	+	0.611434i
$470$	−13.7248	−	21.7040i	−0.633078	−	1.00113i
$471$	8.79193	−	0.709758i	0.405111	−	0.0327039i
$472$	−0.248270	+	1.21610i	−0.0114275	+	0.0559758i
$473$	2.85124	−	11.5679i	0.131100	−	0.531894i
$474$	−3.00562	−	18.4943i	−0.138053	−	0.849471i
$475$	−1.93342	+	3.05746i	−0.0887114	+	0.140286i
$476$	−25.7025	+	48.9720i	−1.17807	+	2.24463i
$477$	3.42309	+	11.8179i	0.156733	+	0.541104i
$478$	4.81382	+	23.5796i	0.220179	+	1.07851i
$479$	17.7174	+	0.713987i	0.809529	+	0.0326229i	0.441579	−	0.897223i	$-0.354419\pi$
$479$	17.7174	+	0.713987i	0.809529	+	0.0326229i	0.367950	+	0.929846i	$0.380060\pi$
$480$	−26.3426	−	13.8257i	−1.20237	−	0.631053i
$481$	−14.6317	−	3.54944i	−0.667146	−	0.161841i
$482$	41.1330	−	21.5882i	1.87355	−	0.983317i
$483$	−19.8574	+	9.42243i	−0.903541	+	0.428736i
$484$	9.58269	−	16.5977i	0.435577	−	0.754442i
$485$	2.09182	+	3.62314i	0.0949847	+	0.164518i
$486$	−18.8279	−	12.9960i	−0.854053	−	0.589510i
$487$	0.220056	+	0.292841i	0.00997169	+	0.0132699i	0.804401	−	0.594087i	$-0.202486\pi$
$487$	0.220056	+	0.292841i	0.00997169	+	0.0132699i	−0.794429	+	0.607357i	$0.792230\pi$
$488$	0.302587	−	0.174699i	0.0136975	−	0.00790825i
$489$	4.63451	+	0.562731i	0.209580	+	0.0254476i
$490$	−11.7551	+	24.7734i	−0.531041	+	1.11915i
$491$	12.8909	−	13.4209i	0.581759	−	0.605675i	−0.363660	−	0.931532i	$-0.618473\pi$
$491$	12.8909	−	13.4209i	0.581759	−	0.605675i	0.945419	+	0.325856i	$0.105653\pi$
$492$	1.03292	+	12.7950i	0.0465677	+	0.576844i
$493$	66.1317	+	16.3000i	2.97842	+	0.734115i
$494$	0.883422	−	11.4680i	0.0397470	−	0.515970i
$495$	4.37909	−	1.07935i	0.196825	−	0.0485131i
$496$	5.26746	+	15.7780i	0.236516	+	0.708451i
$497$	10.3743	+	21.8633i	0.465350	+	0.980703i
$498$	3.61439	+	1.20666i	0.161965	+	0.0540717i
$499$	3.01408	−	2.08047i	0.134929	−	0.0931344i	−0.498689	−	0.866781i	$-0.666185\pi$
$499$	3.01408	−	2.08047i	0.134929	−	0.0931344i	0.633617	+	0.773647i	$0.281569\pi$
$500$	−14.1235	−	6.70167i	−0.631621	−	0.299708i
$501$	−13.8539	+	0.558292i	−0.618946	+	0.0249427i
$502$	−9.82237	−	39.8509i	−0.438394	−	1.77863i
$503$	28.0334	−	11.9439i	1.24995	−	0.532552i	0.337336	−	0.941384i	$-0.390474\pi$
$503$	28.0334	−	11.9439i	1.24995	−	0.532552i	0.912610	+	0.408832i	$0.134064\pi$
$504$	−1.20151	−	0.195265i	−0.0535196	−	0.00869778i
$505$	−16.1811	+	3.30339i	−0.720048	+	0.146999i
$506$	13.7490			0.611215
$507$	3.40424	−	17.3232i	0.151188	−	0.769352i
$508$	−11.7385			−0.520811
$509$	−0.0254264	+	0.00519084i	−0.00112701	+	0.000230080i	−0.200589	−	0.979675i	$-0.564286\pi$
$509$	−0.0254264	+	0.00519084i	−0.00112701	+	0.000230080i	0.199462	+	0.979906i	$0.436081\pi$
$510$	54.8855	+	8.91976i	2.43037	+	0.394974i
$511$	−1.82307	+	0.776738i	−0.0806480	+	0.0343609i
$512$	7.66948	+	31.1163i	0.338946	+	1.37516i
$513$	−8.83113	+	0.355882i	−0.389904	+	0.0157126i
$514$	−36.6087	−	17.3710i	−1.61474	−	0.766203i
$515$	−26.3356	+	18.1782i	−1.16049	+	0.801027i
$516$	22.8541	+	7.62983i	1.00610	+	0.335884i
$517$	2.88513	+	6.08028i	0.126888	+	0.267410i
$518$	9.32274	+	27.9250i	0.409618	+	1.22695i
$519$	11.4177	−	2.81420i	0.501180	−	0.123530i
$520$	−2.96372	+	0.130336i	−0.129968	+	0.00571559i
$521$	−24.1345	−	5.94861i	−1.05735	−	0.260613i	−0.327946	−	0.944697i	$-0.606356\pi$
$521$	−24.1345	−	5.94861i	−1.05735	−	0.260613i	−0.729404	+	0.684083i	$0.760203\pi$
$522$	1.73548	+	21.4978i	0.0759600	+	0.940934i
$523$	−19.6729	+	20.4816i	−0.860235	+	0.895599i	−0.995457	−	0.0952159i	$-0.969646\pi$
$523$	−19.6729	+	20.4816i	−0.860235	+	0.895599i	0.135222	+	0.990815i	$0.456825\pi$
$524$	−10.2448	+	21.5904i	−0.447545	+	0.943181i
$525$	10.7781	+	1.30869i	0.470394	+	0.0571161i
$526$	48.6808	−	28.1059i	2.12258	−	1.22547i
$527$	−20.1941	−	26.8734i	−0.879668	−	1.17063i
$528$	5.93477	+	4.09647i	0.258278	+	0.178276i
$529$	0.566459	+	0.981136i	0.0246286	+	0.0426581i
$530$	29.3157	−	50.7763i	1.27339	−	2.20558i
$531$	−4.25859	+	2.02073i	−0.184807	+	0.0876921i
$532$	−10.3157	+	5.41411i	−0.447244	+	0.234732i
$533$	−9.05508	−	13.0161i	−0.392219	−	0.563788i
$534$	−39.2304	−	20.5897i	−1.69766	−	0.891003i
$535$	−42.4058	−	1.70889i	−1.83336	−	0.0738819i
$536$	0.351195	+	1.72026i	0.0151693	+	0.0743041i
$537$	−5.66087	−	19.5436i	−0.244285	−	0.843369i
$538$	6.56640	−	12.5112i	0.283098	−	0.539398i
$539$	3.84090	−	6.07390i	0.165439	−	0.261622i
$540$	5.26099	+	32.3722i	0.226397	+	1.39308i
$541$	−0.594343	+	2.41134i	−0.0255528	+	0.103672i	−0.982334	−	0.187138i	$-0.940079\pi$
$541$	−0.594343	+	2.41134i	−0.0255528	+	0.103672i	0.956781	+	0.290810i	$0.0939248\pi$
$542$	6.07350	−	29.7500i	0.260879	−	1.27787i
$543$	8.50854	−	0.686880i	0.365136	−	0.0294769i
$544$	−32.1957	−	50.9135i	−1.38038	−	2.18290i
$545$	36.3249	−	32.1811i	1.55599	−	1.37848i
$546$	−32.2327	+	12.3598i	−1.37943	+	0.528951i
$547$	10.2667	+	9.09547i	0.438971	+	0.388894i	0.853459	−	0.521161i	$-0.174501\pi$
$547$	10.2667	+	9.09547i	0.438971	+	0.388894i	−0.414488	+	0.910055i	$0.636039\pi$
$548$	−0.278917	+	1.71625i	−0.0119148	+	0.0733144i
$549$	1.22074	+	0.520108i	0.0520998	+	0.0221977i
$550$	−5.74019	−	3.62987i	−0.244762	−	0.154778i
$551$	9.51399	+	10.7391i	0.405310	+	0.457500i
$552$	−0.155508	+	1.92631i	−0.00661886	+	0.0819893i
$553$	7.42344	−	22.2359i	0.315677	−	0.945567i
$554$	−16.6298	+	2.01922i	−0.706531	+	0.0857884i
$555$	12.2573	−	9.21079i	0.520295	−	0.390976i
$556$	−7.50366	−	9.19032i	−0.318226	−	0.389756i
$557$	11.9942	−	9.79294i	0.508209	−	0.414940i	−0.343343	−	0.939210i	$-0.611559\pi$
$557$	11.9942	−	9.79294i	0.508209	−	0.414940i	0.851552	+	0.524270i	$0.175662\pi$
$558$	6.04675	−	8.76024i	0.255980	−	0.370850i
$559$	−29.1378	+	6.06006i	−1.23240	+	0.256313i
$560$	−19.5560	−	28.3317i	−0.826391	−	1.19723i
$561$	−13.9977	−	4.05449i	−0.590984	−	0.171181i
$562$	−42.5759	+	26.9234i	−1.79596	+	1.13569i
$563$	12.0409	−	1.95684i	0.507464	−	0.0824709i	0.0987111	−	0.995116i	$-0.468528\pi$
$563$	12.0409	−	1.95684i	0.507464	−	0.0824709i	0.408753	+	0.912645i	$0.365964\pi$
$564$	−12.7258	+	4.82627i	−0.535854	+	0.203223i
$565$	−17.9221	−	42.0647i	−0.753988	−	1.76967i
$566$	24.4329	−	23.4681i	1.02699	−	0.986440i
$567$	6.75084	+	12.8626i	0.283509	+	0.540180i
$568$	2.12090	+	0.171217i	0.0889912	+	0.00718411i
$569$	−10.7535	+	37.1254i	−0.450810	+	1.55638i	0.337638	+	0.941276i	$0.390372\pi$
$569$	−10.7535	+	37.1254i	−0.450810	+	1.55638i	−0.788448	+	0.615101i	$0.789115\pi$
$570$	8.44750	+	8.11393i	0.353827	+	0.339855i
$571$	6.05784	−	15.9732i	0.253513	−	0.668458i	−0.746483	−	0.665405i	$-0.768259\pi$
$571$	6.05784	−	15.9732i	0.253513	−	0.668458i	0.999995	−	0.00305317i	$-0.000971854\pi$
$572$	11.1528	+	0.859142i	0.466323	+	0.0359225i
$573$	−2.18834	−	5.77017i	−0.0914191	−	0.241052i
$574$	−12.1527	+	28.5233i	−0.507242	+	1.19054i
$575$	−0.434941	+	10.7930i	−0.0181383	+	0.450098i
$576$	6.68595	−	8.18880i	0.278581	−	0.341200i
$577$			13.4756i			0.560998i	0.959854	+	0.280499i	$0.0904999\pi$
$577$			13.4756i			0.560998i	−0.959854	+	0.280499i	$0.909500\pi$
$578$	60.3898	+	49.3068i	2.51189	+	2.05089i
$579$	−5.33509	+	1.54533i	−0.221719	+	0.0642216i
$580$	35.3042	−	39.8502i	1.46593	−	1.65469i
$581$	3.30250	+	3.43827i	0.137011	+	0.142644i
$582$	4.06030	−	1.35553i	0.168305	−	0.0561884i
$583$	−9.23107	+	12.2843i	−0.382312	+	0.508764i
$584$	−0.0210022	+	0.172969i	−0.000869078	+	0.00715750i
$585$	−7.15730	−	8.70069i	−0.295918	−	0.359729i
$586$	0.427884	+	3.52394i	0.0176757	+	0.145573i
$587$	−21.5551	−	12.4449i	−0.889675	−	0.513654i	−0.0158390	−	0.999875i	$-0.505042\pi$
$587$	−21.5551	−	12.4449i	−0.889675	−	0.513654i	−0.873836	+	0.486220i	$0.838375\pi$
$588$	11.6185	+	8.73071i	0.479138	+	0.360049i
$589$	−0.285119	−	7.07516i	−0.0117481	−	0.291527i
$590$	21.0028	+	7.96532i	0.864672	+	0.327927i
$591$	−11.0828	−	2.26258i	−0.455887	−	0.0930701i
$592$	−15.0518	−	3.07285i	−0.618626	−	0.126293i
$593$	4.21478	+	1.59846i	0.173080	+	0.0656407i	0.439623	−	0.898182i	$-0.355112\pi$
$593$	4.21478	+	1.59846i	0.173080	+	0.0656407i	−0.266543	+	0.963823i	$0.585881\pi$
$594$	−0.668147	−	16.5799i	−0.0274144	−	0.680281i
$595$	55.6171	+	41.7935i	2.28008	+	1.71337i
$596$	18.6260	+	10.7537i	0.762950	+	0.440489i
$597$	−3.55637	−	29.2894i	−0.145553	−	1.19873i
$598$	−14.8371	−	30.9744i	−0.606736	−	1.26664i
$599$	−4.66539	+	38.4229i	−0.190623	+	1.56992i	0.512397	+	0.858748i	$0.328757\pi$
$599$	−4.66539	+	38.4229i	−0.190623	+	1.56992i	−0.703020	+	0.711170i	$0.748166\pi$
$600$	0.573492	−	0.763179i	0.0234127	−	0.0311567i
$601$	−30.0712	+	10.0392i	−1.22663	+	0.409509i	−0.854881	−	0.518824i	$-0.826370\pi$
$601$	−30.0712	+	10.0392i	−1.22663	+	0.409509i	−0.371749	+	0.928333i	$0.621242\pi$
$602$	40.3127	+	41.9700i	1.64302	+	1.71057i
$603$	−4.42160	+	4.99096i	−0.180062	+	0.203248i
$604$	16.2919	−	4.71899i	0.662906	−	0.192013i
$605$	−18.6740	−	15.2469i	−0.759207	−	0.619874i
$606$			16.8975i			0.686416i
$607$	2.21518	−	2.71310i	0.0899113	−	0.110121i	−0.727690	−	0.685906i	$-0.759406\pi$
$607$	2.21518	−	2.71310i	0.0899113	−	0.110121i	0.817601	+	0.575785i	$0.195303\pi$
$608$	0.510939	−	12.6788i	0.0207213	−	0.514194i
$609$	16.8784	−	39.6150i	0.683947	−	1.60528i
$610$	−2.24226	−	5.91235i	−0.0907864	−	0.239384i
$611$	10.5845	−	13.0613i	0.428204	−	0.528404i
$612$	−6.54891	+	17.2681i	−0.264724	+	0.698020i
$613$	25.6194	+	24.6078i	1.03476	+	0.993900i	0.999985	−	0.00549524i	$-0.00174920\pi$
$613$	25.6194	+	24.6078i	1.03476	+	0.993900i	0.0347745	+	0.999395i	$0.488929\pi$
$614$	−11.0585	+	38.1785i	−0.446286	+	1.54076i
$615$	16.0946	+	1.29929i	0.648998	+	0.0523925i
$616$	−0.706500	−	1.34612i	−0.0284657	−	0.0542369i
$617$	−32.6896	+	31.3988i	−1.31603	+	1.26407i	−0.374468	+	0.927240i	$0.622175\pi$
$617$	−32.6896	+	31.3988i	−1.31603	+	1.26407i	−0.941566	+	0.336828i	$0.890646\pi$
$618$	12.8337	+	30.1218i	0.516246	+	1.21167i
$619$	11.1348	−	4.22288i	0.447546	−	0.169732i	−0.120527	−	0.992710i	$-0.538458\pi$
$619$	11.1348	−	4.22288i	0.447546	−	0.169732i	0.568073	+	0.822978i	$0.307689\pi$
$620$	−25.9353	+	4.21490i	−1.04159	+	0.169275i
$621$	−22.3054	+	14.1051i	−0.895084	+	0.566017i
$622$	38.7437	+	11.2222i	1.55348	+	0.449971i
$623$	−31.4888	−	45.6193i	−1.26157	−	1.82770i
$624$	2.82429	−	17.7909i	0.113062	−	0.712205i
$625$	−17.7315	+	25.6885i	−0.709260	+	1.02754i
$626$	−2.03386	+	1.66059i	−0.0812892	+	0.0663706i
$627$	−1.94145	−	2.37785i	−0.0775342	−	0.0949621i
$628$	11.1605	−	8.38660i	0.445354	−	0.334662i
$629$	30.8189	−	3.74209i	1.22883	−	0.149207i
$630$	−6.97611	+	20.8960i	−0.277935	+	0.832517i
$631$	−2.35467	+	29.1678i	−0.0937377	+	1.16115i	0.763352	+	0.645983i	$0.223552\pi$
$631$	−2.35467	+	29.1678i	−0.0937377	+	1.16115i	−0.857090	+	0.515167i	$0.827730\pi$
$632$	−1.36683	−	1.54283i	−0.0543696	−	0.0613706i
$633$	27.6306	+	17.4725i	1.09822	+	0.694470i
$634$	−10.4793	−	4.46483i	−0.416188	−	0.177321i
$635$	−2.36858	+	14.5744i	−0.0939941	+	0.578369i
$636$	−23.2600	−	20.6066i	−0.922319	−	0.817103i
$637$	−17.8285	−	2.09838i	−0.706393	−	0.0831407i
$638$	−20.1620	+	17.8619i	−0.798219	+	0.707161i
$639$	4.31892	+	6.82983i	0.170854	+	0.270184i
$640$	−6.54260	+	0.528174i	−0.258619	+	0.0208779i
$641$	0.990553	−	4.85205i	0.0391245	−	0.191644i	−0.955532	−	0.294889i	$-0.904717\pi$
$641$	0.990553	−	4.85205i	0.0391245	−	0.191644i	0.994656	+	0.103245i	$0.0329225\pi$
$642$	−10.3920	+	42.1619i	−0.410138	+	1.66400i
$643$	3.72884	+	22.9445i	0.147051	+	0.904841i	0.950785	+	0.309852i	$0.100280\pi$
$643$	3.72884	+	22.9445i	0.147051	+	0.904841i	−0.803734	+	0.594989i	$0.797156\pi$
$644$	−18.5926	+	29.4018i	−0.732650	+	1.15859i
$645$	14.0846	−	26.8360i	0.554581	−	1.05667i
$646$	6.59844	+	22.7805i	0.259612	+	0.896286i
$647$	0.265425	+	1.30014i	0.0104349	+	0.0511136i	0.984675	−	0.174401i	$-0.0557988\pi$
$647$	0.265425	+	1.30014i	0.0104349	+	0.0511136i	−0.974240	+	0.225514i	$0.927594\pi$
$648$	1.27624	+	0.0514306i	0.0501353	+	0.00202038i
$649$	−5.21265	−	2.73581i	−0.204614	−	0.107390i
$650$	−1.98309	+	16.8490i	−0.0777831	+	0.660872i
$651$	−18.8178	+	9.87634i	−0.737527	+	0.387084i
$652$	6.67558	−	3.16760i	0.261436	−	0.124053i
$653$	−1.69876	+	2.94233i	−0.0664774	+	0.115142i	−0.897348	−	0.441323i	$-0.854509\pi$
$653$	−1.69876	+	2.94233i	−0.0664774	+	0.115142i	0.830871	+	0.556465i	$0.187843\pi$
$654$	−24.8271	−	43.0018i	−0.970816	−	1.68150i
$655$	24.7393	+	17.0763i	0.966646	+	0.667227i
$656$	−9.71912	−	12.9338i	−0.379468	−	0.504980i
$657$	−0.573061	+	0.330857i	−0.0223572	+	0.0129079i
$658$	−32.6332	−	3.96239i	−1.27217	−	0.154470i
$659$	−7.24058	+	15.2592i	−0.282053	+	0.594414i	−0.994192	−	0.107625i	$-0.965675\pi$
$659$	−7.24058	+	15.2592i	−0.282053	+	0.594414i	0.712139	+	0.702039i	$0.247727\pi$
$660$	−7.89093	+	8.21533i	−0.307154	+	0.319781i
$661$	3.50810	+	43.4557i	0.136449	+	1.69023i	0.596719	+	0.802451i	$0.296471\pi$
$661$	3.50810	+	43.4557i	0.136449	+	1.69023i	−0.460269	+	0.887779i	$0.652247\pi$
$662$	−17.7923	−	4.38541i	−0.691517	−	0.170444i
$663$	5.97141	+	35.9102i	0.231910	+	1.39464i
$664$	0.407002	−	0.100317i	0.0157947	−	0.00389305i
$665$	4.64063	+	13.9004i	0.179956	+	0.539034i
$666$	4.21434	+	8.88153i	0.163302	+	0.344152i
$667$	40.6359	+	13.5663i	1.57343	+	0.525287i
$668$	−18.0600	+	12.4659i	−0.698762	+	0.482321i
$669$	11.6474	+	5.52676i	0.450315	+	0.213677i
$670$	31.7490	−	1.27944i	1.22657	−	0.0494291i
$671$	0.396593	+	1.60904i	0.0153103	+	0.0621163i
$672$	−35.0366	+	14.9277i	−1.35157	+	0.575849i
$673$	−17.8765	−	2.90521i	−0.689087	−	0.111988i	−0.194222	−	0.980958i	$-0.562218\pi$
$673$	−17.8765	−	2.90521i	−0.689087	−	0.111988i	−0.494865	+	0.868970i	$0.664782\pi$
$674$	26.8978	−	5.49122i	1.03606	−	0.211514i
$675$	13.0364			0.501771
$676$	−10.1000	−	26.0529i	−0.388462	−	1.00203i
$677$	39.7823			1.52896			0.764478	−	0.644650i	$-0.222997\pi$
$677$	39.7823			1.52896			0.764478	+	0.644650i	$0.222997\pi$
$678$	−45.8377	+	9.35782i	−1.76038	+	0.359385i
$679$	5.28622	+	0.859095i	0.202867	+	0.0329690i
$680$	5.62754	−	2.39767i	0.215806	−	0.0919465i
$681$	−7.14731	−	28.9978i	−0.273885	−	1.11120i
$682$	13.2832	−	0.535293i	0.508639	−	0.0204974i
$683$	17.5182	+	8.31251i	0.670317	+	0.318069i	0.733261	−	0.679948i	$-0.237998\pi$
$683$	17.5182	+	8.31251i	0.670317	+	0.318069i	−0.0629437	+	0.998017i	$0.520049\pi$
$684$	−3.20161	+	2.20991i	−0.122417	+	0.0844981i
$685$	2.07460	+	0.692604i	0.0792664	+	0.0264630i
$686$	−6.10855	−	12.8735i	−0.233226	−	0.491513i
$687$	9.11054	+	27.2894i	0.347589	+	1.04116i
$688$	−29.4843	+	7.26723i	−1.12408	+	0.277061i
$689$	37.6365	+	7.53970i	1.43384	+	0.287240i
$690$	33.9587	+	8.37007i	1.29279	+	0.318643i
$691$	−3.87669	−	48.0214i	−0.147476	−	1.82682i	−0.472746	−	0.881199i	$-0.656737\pi$
$691$	−3.87669	−	48.0214i	−0.147476	−	1.82682i	0.325270	−	0.945621i	$-0.394545\pi$
$692$	12.8928	−	13.4228i	0.490110	−	0.510259i
$693$	2.47507	−	5.21611i	0.0940203	−	0.198144i
$694$	−63.2534	−	7.68035i	−2.40107	−	0.291542i
$695$	−12.9247	+	7.46209i	−0.490263	+	0.283053i
$696$	−2.27452	−	3.02684i	−0.0862156	−	0.114732i
$697$	26.9072	+	18.5727i	1.01918	+	0.703492i
$698$	26.7263	+	46.2913i	1.01161	+	1.75215i
$699$	−13.7946	+	23.8930i	−0.521762	+	0.903717i
$700$	15.5248	−	7.36661i	0.586783	−	0.278432i
$701$	−39.9471	+	20.9659i	−1.50878	+	0.791869i	−0.997708	−	0.0676680i	$-0.978444\pi$
$701$	−39.9471	+	20.9659i	−1.50878	+	0.791869i	−0.511073	+	0.859537i	$0.670752\pi$
$702$	−36.6311	+	19.3974i	−1.38255	+	0.732107i
$703$	5.79048	+	3.03908i	0.218392	+	0.114621i
$704$	13.1922	+	0.531627i	0.497199	+	0.0200365i
$705$	3.42447	+	16.7741i	0.128973	+	0.631751i
$706$	−5.25046	−	18.1267i	−0.197604	−	0.682207i
$707$	−9.82472	+	18.7194i	−0.369497	+	0.704017i
$708$	6.36296	−	10.0622i	0.239135	−	0.378161i
$709$	−3.79625	−	23.3593i	−0.142571	−	0.877276i	−0.955517	−	0.294936i	$-0.904702\pi$
$709$	−3.79625	−	23.3593i	−0.142571	−	0.877276i	0.812946	−	0.582339i	$-0.197863\pi$
$710$	9.21559	−	37.3891i	0.345855	−	1.40319i
$711$	1.56578	−	7.66970i	0.0587213	−	0.287636i
$712$	−4.85811	+	0.392187i	−0.182065	+	0.0146978i
$713$	−11.3004	−	17.8702i	−0.423205	−	0.669245i
$714$	53.2805	−	47.2024i	1.99397	−	1.76651i
$715$	3.31711	−	13.6739i	0.124053	−	0.511376i
$716$	−24.1046	−	21.3548i	−0.900831	−	0.798067i
$717$	2.57371	−	15.8367i	0.0961171	−	0.591432i
$718$	−4.46733	−	1.90335i	−0.166719	−	0.0710324i
$719$	4.50633	+	2.84963i	0.168058	+	0.106273i	0.615847	−	0.787866i	$-0.288814\pi$
$719$	4.50633	+	2.84963i	0.168058	+	0.106273i	−0.447789	+	0.894139i	$0.647788\pi$
$720$	−7.62289	−	8.60446i	−0.284088	−	0.320669i
$721$	−3.29625	+	40.8314i	−0.122759	+	1.52064i
$722$	10.6740	−	31.9726i	0.397246	−	1.18990i
$723$	−30.7444	+	3.73305i	−1.14340	+	0.138833i
$724$	10.8008	−	8.11627i	0.401408	−	0.301639i
$725$	−13.3838	−	16.3922i	−0.497064	−	0.608792i
$726$	−19.1068	+	15.6002i	−0.709119	+	0.578978i
$727$	5.28256	−	7.65311i	0.195919	−	0.283838i	−0.712695	−	0.701474i	$-0.752526\pi$
$727$	5.28256	−	7.65311i	0.195919	−	0.283838i	0.908615	+	0.417636i	$0.137141\pi$
$728$	−2.27021	+	3.04431i	−0.0841395	+	0.112830i
$729$	15.8170	+	22.9149i	0.585815	+	0.848700i
$730$	3.02881	+	0.877305i	0.112101	+	0.0324705i
$731$	51.8670	−	32.7987i	1.91837	−	1.21310i
$732$	−3.30797	+	0.537597i	−0.122266	+	0.0198701i
$733$	11.3559	−	4.30672i	0.419439	−	0.159072i	−0.135850	−	0.990729i	$-0.543377\pi$
$733$	11.3559	−	4.30672i	0.419439	−	0.159072i	0.555290	+	0.831657i	$0.312607\pi$
$734$	−11.4621	−	26.9025i	−0.423073	−	0.992989i
$735$	13.1844	−	12.6637i	0.486312	−	0.467109i
$736$	−17.6081	−	33.5494i	−0.649043	−	1.23665i
$737$	−8.30051	−	0.670087i	−0.305753	−	0.0246830i
$738$	−2.88039	+	9.94425i	−0.106028	+	0.366053i
$739$	−5.82810	−	5.59797i	−0.214390	−	0.205925i	0.577835	−	0.816154i	$-0.303898\pi$
$739$	−5.82810	−	5.59797i	−0.214390	−	0.205925i	−0.792225	+	0.610229i	$0.791077\pi$
$740$	8.60510	−	22.6898i	0.316330	−	0.834093i
$741$	−3.26184	+	6.93987i	−0.119827	+	0.254942i
$742$	−26.6150	−	70.1781i	−0.977069	−	2.57632i
$743$	3.49446	−	8.20179i	0.128199	−	0.300895i	−0.843495	−	0.537137i	$-0.819506\pi$
$743$	3.49446	−	8.20179i	0.128199	−	0.300895i	0.971694	+	0.236243i	$0.0759160\pi$
$744$	−0.0752418	+	1.86711i	−0.00275850	+	0.0684515i
$745$	17.1101	−	20.9560i	0.626865	−	0.767770i
$746$		−	49.1068i		−	1.79793i
$747$	1.23313	+	1.00682i	0.0451177	+	0.0368375i
$748$	−22.1544	+	6.41710i	−0.810044	+	0.234632i
$749$	−36.0266	+	40.6656i	−1.31638	+	1.48589i
$750$	13.9376	+	14.5106i	0.508929	+	0.529851i
$751$	18.5847	−	6.20450i	0.678167	−	0.226405i	0.0433407	−	0.999060i	$-0.486200\pi$
$751$	18.5847	−	6.20450i	0.678167	−	0.226405i	0.634826	+	0.772655i	$0.281072\pi$
$752$	10.3049	−	13.7133i	0.375780	−	0.500072i
$753$	−3.29827	+	27.1637i	−0.120196	+	0.989899i
$754$	61.9981	+	26.1464i	2.25784	+	0.952195i
$755$	−2.57172	−	21.1800i	−0.0935946	−	0.770821i
$756$	36.3592	+	20.9920i	1.32237	+	0.763472i
$757$	4.88221	+	3.66875i	0.177447	+	0.133343i	0.685755	−	0.727833i	$-0.259472\pi$
$757$	4.88221	+	3.66875i	0.177447	+	0.133343i	−0.508308	+	0.861176i	$0.669729\pi$
$758$	−1.77989	−	44.1674i	−0.0646484	−	1.60423i
$759$	−8.57057	−	3.25039i	−0.311092	−	0.117982i
$760$	1.26249	+	0.257738i	0.0457952	+	0.00934915i
$761$	2.29304	+	0.468127i	0.0831226	+	0.0169696i	0.241407	−	0.970424i	$-0.422391\pi$
$761$	2.29304	+	0.468127i	0.0831226	+	0.0169696i	−0.158284	+	0.987394i	$0.550596\pi$
$762$	14.1261	+	5.35731i	0.511733	+	0.194075i
$763$	−2.50147	−	62.0734i	−0.0905594	−	2.24721i
$764$	−7.80836	−	5.86760i	−0.282496	−	0.212282i
$765$	20.1185	+	11.6154i	0.727386	+	0.419956i
$766$	4.48242	+	36.9160i	0.161956	+	1.33383i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.k (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99584 + 0.407454i) q^{2} +(1.34046 + 0.217845i) q^{3} +(1.97740 - 0.842491i) q^{4} +(-0.647035 - 2.62512i) q^{5} +(-2.76410 + 0.111389i) q^{6} +(-3.12689 - 1.48373i) q^{7} +(-0.250449 + 0.172873i) q^{8} +(-1.09624 - 0.365979i) q^{9} +O(q^{10})\)	\(q+(-1.99584 + 0.407454i) q^{2} +(1.34046 + 0.217845i) q^{3} +(1.97740 - 0.842491i) q^{4} +(-0.647035 - 2.62512i) q^{5} +(-2.76410 + 0.111389i) q^{6} +(-3.12689 - 1.48373i) q^{7} +(-0.250449 + 0.172873i) q^{8} +(-1.09624 - 0.365979i) q^{9} +(2.36099 + 4.97569i) q^{10} +(-0.457073 - 1.36910i) q^{11} +(2.83415 - 0.698555i) q^{12} +(-2.59114 + 2.50718i) q^{13} +(6.84532 + 1.68722i) q^{14} +(-0.295451 - 3.65982i) q^{15} +(-2.54846 + 2.65323i) q^{16} +(3.18715 - 6.71677i) q^{17} +(2.33704 + 0.283768i) q^{18} +(1.35625 - 0.783031i) q^{19} +(-3.49109 - 4.64579i) q^{20} +(-3.86824 - 2.67005i) q^{21} +(1.47009 + 2.54627i) q^{22} +(2.33811 - 4.04973i) q^{23} +(-0.373376 + 0.177169i) q^{24} +(-2.04534 + 1.07347i) q^{25} +(4.14995 - 6.05971i) q^{26} +(-4.99720 - 2.62273i) q^{27} +(-7.43313 - 0.299545i) q^{28} +(1.83251 + 8.97622i) q^{29} +(2.08088 + 7.18403i) q^{30} +(2.10123 - 4.00356i) q^{31} +(4.33054 - 6.84820i) q^{32} +(-0.314435 - 1.93479i) q^{33} +(-3.62426 + 14.7042i) q^{34} +(-1.87176 + 9.16849i) q^{35} +(-2.47604 + 0.199887i) q^{36} +(2.23182 + 3.52934i) q^{37} +(-2.38781 + 2.11541i) q^{38} +(-4.01949 + 2.79630i) q^{39} +(0.615861 + 0.545605i) q^{40} +(-0.705434 + 4.34071i) q^{41} +(8.80830 + 3.75287i) q^{42} +(6.97646 + 4.41165i) q^{43} +(-2.05727 - 2.32218i) q^{44} +(-0.251434 + 3.11457i) q^{45} +(-3.01642 + 9.03528i) q^{46} +(-4.62870 + 0.562026i) q^{47} +(-3.99409 + 3.00136i) q^{48} +(3.14887 + 3.85667i) q^{49} +(3.64477 - 2.97586i) q^{50} +(5.73545 - 8.30923i) q^{51} +(-3.01144 + 7.14072i) q^{52} +(-6.04755 - 8.76139i) q^{53} +(11.0423 + 3.19843i) q^{54} +(-3.29832 + 2.08573i) q^{55} +(1.03962 - 0.168955i) q^{56} +(1.98857 - 0.754166i) q^{57} +(-7.31479 - 17.1684i) q^{58} +(2.94149 - 2.82534i) q^{59} +(-3.66759 - 6.98800i) q^{60} +(-1.14441 - 0.0923863i) q^{61} +(-2.56246 + 8.84663i) q^{62} +(2.88481 + 2.77090i) q^{63} +(-3.24364 + 8.55277i) q^{64} +(8.25823 + 5.17984i) q^{65} +(1.41590 + 3.73342i) q^{66} +(2.26143 - 5.30777i) q^{67} +(0.643443 - 15.9669i) q^{68} +(4.01635 - 4.91914i) q^{69} -19.0615i q^{70} +(-5.41606 - 4.42208i) q^{71} +(0.337820 - 0.0978509i) q^{72} +(0.379675 - 0.428564i) q^{73} +(-5.89239 - 6.13463i) q^{74} +(-2.97554 + 0.993380i) q^{75} +(2.02215 - 2.69099i) q^{76} +(-0.602156 + 4.95920i) q^{77} +(6.88290 - 7.21873i) q^{78} +(0.816417 + 6.72380i) q^{79} +(8.61398 + 4.97329i) q^{80} +(-3.35539 - 2.52141i) q^{81} +(-0.360705 - 8.95080i) q^{82} +(-1.28793 - 0.488449i) q^{83} +(-9.89854 - 2.02080i) q^{84} +(-19.6945 - 4.02067i) q^{85} +(-15.7214 - 5.96236i) q^{86} +(0.500970 + 12.4314i) q^{87} +(0.351154 + 0.263875i) q^{88} +(13.8701 + 8.00792i) q^{89} +(-0.767221 - 6.31863i) q^{90} +(11.8222 - 3.99514i) q^{91} +(1.21152 - 9.97777i) q^{92} +(3.68877 - 4.90886i) q^{93} +(9.00915 - 3.00770i) q^{94} +(-2.93309 - 3.05367i) q^{95} +(7.29676 - 8.23633i) q^{96} +(-1.48629 + 0.430509i) q^{97} +(-7.85605 - 6.41427i) q^{98} +1.66815i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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