LMFDB - Embedded newform 169.2.k.a.4.2

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			4.2
Character	$\chi$	$=$	169.4
Dual form			169.2.k.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41817 - 0.0974488i) q^{2} +(-0.437408 + 1.51011i) q^{3} +(3.84452 + 0.310362i) q^{4} +(-2.71784 - 1.03074i) q^{5} +(1.20488 - 3.60907i) q^{6} +(-0.958962 - 2.25077i) q^{7} +(-4.46148 - 0.541722i) q^{8} +(0.446473 + 0.282332i) q^{9} +O(q^{10})$	\(q+(-2.41817 - 0.0974488i) q^{2} +(-0.437408 + 1.51011i) q^{3} +(3.84452 + 0.310362i) q^{4} +(-2.71784 - 1.03074i) q^{5} +(1.20488 - 3.60907i) q^{6} +(-0.958962 - 2.25077i) q^{7} +(-4.46148 - 0.541722i) q^{8} +(0.446473 + 0.282332i) q^{9} +(6.47174 + 2.75735i) q^{10} +(0.842314 + 1.33201i) q^{11} +(-2.15030 + 5.66988i) q^{12} +(2.05596 - 2.96193i) q^{13} +(2.09959 + 5.53618i) q^{14} +(2.74533 - 3.65337i) q^{15} +(3.12165 + 0.507318i) q^{16} +(1.77732 - 0.757244i) q^{17} +(-1.05213 - 0.726235i) q^{18} +(6.36630 - 3.67559i) q^{19} +(-10.1289 - 4.80621i) q^{20} +(3.81835 - 0.463632i) q^{21} +(-1.90705 - 3.30311i) q^{22} +(2.38841 - 4.13685i) q^{23} +(2.76954 - 6.50036i) q^{24} +(2.58167 + 2.28716i) q^{25} +(-5.26030 + 6.96208i) q^{26} +(-4.15202 + 3.67837i) q^{27} +(-2.98820 - 8.95074i) q^{28} +(0.291416 - 7.23142i) q^{29} +(-6.99469 + 8.56693i) q^{30} +(3.48709 + 3.93612i) q^{31} +(1.30761 + 0.266950i) q^{32} +(-2.37992 + 0.689352i) q^{33} +(-4.37164 + 1.65794i) q^{34} +(0.286348 + 7.10566i) q^{35} +(1.62885 + 1.22400i) q^{36} +(-9.28405 + 1.89535i) q^{37} +(-15.7530 + 8.26779i) q^{38} +(3.57353 + 4.40029i) q^{39} +(11.5672 + 6.07094i) q^{40} +(-1.54584 - 0.447759i) q^{41} +(-9.27860 + 0.749046i) q^{42} +(0.644074 - 3.15488i) q^{43} +(2.82489 + 5.38238i) q^{44} +(-0.922430 - 1.22753i) q^{45} +(-6.17871 + 9.77085i) q^{46} +(-0.644340 + 0.444756i) q^{47} +(-2.13154 + 4.49212i) q^{48} +(0.702733 - 0.731622i) q^{49} +(-6.02002 - 5.78230i) q^{50} +(0.366107 + 3.01516i) q^{51} +(8.82346 - 10.7491i) q^{52} +(1.39133 - 11.4586i) q^{53} +(10.3987 - 8.49031i) q^{54} +(-0.916314 - 4.48840i) q^{55} +(3.05910 + 10.5612i) q^{56} +(2.76586 + 11.2215i) q^{57} +(-1.40939 + 17.4584i) q^{58} +(-0.344613 - 2.12049i) q^{59} +(11.6883 - 13.1934i) q^{60} +(-7.39192 + 5.55467i) q^{61} +(-8.04881 - 9.85800i) q^{62} +(0.207314 - 1.27565i) q^{63} +(-9.27741 - 2.28668i) q^{64} +(-8.64075 + 5.93088i) q^{65} +(5.82221 - 1.43505i) q^{66} +(-0.146501 - 1.81474i) q^{67} +(7.06795 - 2.35963i) q^{68} +(5.20238 + 5.41625i) q^{69} -17.2106i q^{70} +(8.24282 - 7.91734i) q^{71} +(-1.83898 - 1.50148i) q^{72} +(-3.61262 + 6.88327i) q^{73} +(22.6351 - 3.67856i) q^{74} +(-4.58309 + 2.89817i) q^{75} +(25.6161 - 12.1550i) q^{76} +(2.19030 - 3.17320i) q^{77} +(-8.21259 - 10.9889i) q^{78} +(3.01380 + 4.36625i) q^{79} +(-7.96123 - 4.59642i) q^{80} +(-3.05923 - 6.44720i) q^{81} +(3.69448 + 1.23340i) q^{82} +(0.682568 - 2.76929i) q^{83} +(14.8236 - 0.597372i) q^{84} +(-5.61098 + 0.226115i) q^{85} +(-1.86492 + 7.56627i) q^{86} +(10.7928 + 3.60315i) q^{87} +(-3.03639 - 6.39905i) q^{88} +(10.7109 + 6.18392i) q^{89} +(2.11097 + 3.05827i) q^{90} +(-8.63819 - 1.78712i) q^{91} +(10.4662 - 15.1629i) q^{92} +(-7.46924 + 3.54420i) q^{93} +(1.60146 - 1.01270i) q^{94} +(-21.0912 + 3.42765i) q^{95} +(-0.975080 + 1.85786i) q^{96} +(-10.8183 - 8.83290i) q^{97} +(-1.77062 + 1.70070i) q^{98} +0.832521i 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{78}\right)$

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 $

$2$	−2.41817	−	0.0974488i	−1.70990	−	0.0689067i	−0.834111	−	0.551597i	$-0.814019\pi$
$2$	−2.41817	−	0.0974488i	−1.70990	−	0.0689067i	−0.875791	+	0.482690i	$0.839660\pi$
$3$	−0.437408	+	1.51011i	−0.252538	+	0.871861i	0.729628	+	0.683844i	$0.239693\pi$
$3$	−0.437408	+	1.51011i	−0.252538	+	0.871861i	−0.982166	+	0.188017i	$0.939794\pi$
$4$	3.84452	+	0.310362i	1.92226	+	0.155181i
$5$	−2.71784	−	1.03074i	−1.21545	−	0.460961i	−0.338240	−	0.941060i	$-0.609832\pi$
$5$	−2.71784	−	1.03074i	−1.21545	−	0.460961i	−0.877214	+	0.480099i	$0.840601\pi$
$6$	1.20488	−	3.60907i	0.491891	−	1.47339i
$7$	−0.958962	−	2.25077i	−0.362453	−	0.850709i	−0.996969	−	0.0777993i	$-0.975211\pi$
$7$	−0.958962	−	2.25077i	−0.362453	−	0.850709i	0.634516	−	0.772910i	$-0.281200\pi$
$8$	−4.46148	−	0.541722i	−1.57737	−	0.191528i
$9$	0.446473	+	0.282332i	0.148824	+	0.0941108i
$10$	6.47174	+	2.75735i	2.04654	+	0.871951i
$11$	0.842314	+	1.33201i	0.253967	+	0.401617i	0.947972	−	0.318353i	$-0.103130\pi$
$11$	0.842314	+	1.33201i	0.253967	+	0.401617i	−0.694005	+	0.719970i	$0.744155\pi$
$12$	−2.15030	+	5.66988i	−0.620739	+	1.63675i
$13$	2.05596	−	2.96193i	0.570222	−	0.821491i
$13$	2.05596	−	2.96193i	0.570222	−	0.821491i
$14$	2.09959	+	5.53618i	0.561140	+	1.47961i
$15$	2.74533	−	3.65337i	0.708841	−	0.943297i
$16$	3.12165	+	0.507318i	0.780413	+	0.126829i
$17$	1.77732	−	0.757244i	0.431062	−	0.183659i	−0.165527	−	0.986205i	$-0.552932\pi$
$17$	1.77732	−	0.757244i	0.431062	−	0.183659i	0.596589	+	0.802547i	$0.296522\pi$
$18$	−1.05213	−	0.726235i	−0.247990	−	0.171175i
$19$	6.36630	−	3.67559i	1.46053	−	0.843237i	0.461494	−	0.887143i	$-0.347314\pi$
$19$	6.36630	−	3.67559i	1.46053	−	0.843237i	0.999036	+	0.0439059i	$0.0139802\pi$
$20$	−10.1289	−	4.80621i	−2.26489	−	1.07470i
$21$	3.81835	−	0.463632i	0.833233	−	0.101173i
$22$	−1.90705	−	3.30311i	−0.406585	−	0.704226i
$23$	2.38841	−	4.13685i	0.498018	−	0.862593i	−0.501979	−	0.864880i	$-0.667395\pi$
$23$	2.38841	−	4.13685i	0.498018	−	0.862593i	0.999997	+	0.00228656i	$0.000727835\pi$
$24$	2.76954	−	6.50036i	0.565331	−	1.32688i
$25$	2.58167	+	2.28716i	0.516333	+	0.457431i
$26$	−5.26030	+	6.96208i	−1.03163	+	1.36538i
$27$	−4.15202	+	3.67837i	−0.799057	+	0.707903i
$28$	−2.98820	−	8.95074i	−0.564716	−	1.69153i
$29$	0.291416	−	7.23142i	0.0541147	−	1.34284i	−0.712924	−	0.701241i	$-0.752630\pi$
$29$	0.291416	−	7.23142i	0.0541147	−	1.34284i	0.767039	−	0.641601i	$-0.221729\pi$
$30$	−6.99469	+	8.56693i	−1.27705	+	1.56410i
$31$	3.48709	+	3.93612i	0.626301	+	0.706947i	0.972942	−	0.231051i	$-0.0742163\pi$
$31$	3.48709	+	3.93612i	0.626301	+	0.706947i	−0.346641	+	0.937998i	$0.612678\pi$
$32$	1.30761	+	0.266950i	0.231154	+	0.0471905i
$33$	−2.37992	+	0.689352i	−0.414290	+	0.120001i
$34$	−4.37164	+	1.65794i	−0.749730	+	0.284335i
$35$	0.286348	+	7.10566i	0.0484017	+	1.20108i
$36$	1.62885	+	1.22400i	0.271475	+	0.204000i
$37$	−9.28405	+	1.89535i	−1.52629	+	0.311594i	−0.888593	−	0.458696i	$-0.848317\pi$
$37$	−9.28405	+	1.89535i	−1.52629	+	0.311594i	−0.637694	+	0.770290i	$0.720112\pi$
$38$	−15.7530	+	8.26779i	−2.55547	+	1.34121i
$39$	3.57353	+	4.40029i	0.572223	+	0.704611i
$40$	11.5672	+	6.07094i	1.82894	+	0.959899i
$41$	−1.54584	−	0.447759i	−0.241420	−	0.0699283i	0.155302	−	0.987867i	$-0.450365\pi$
$41$	−1.54584	−	0.447759i	−0.241420	−	0.0699283i	−0.396722	+	0.917939i	$0.629852\pi$
$42$	−9.27860	+	0.749046i	−1.43172	+	0.115580i
$43$	0.644074	−	3.15488i	0.0982204	−	0.481115i	−0.900691	−	0.434461i	$-0.856939\pi$
$43$	0.644074	−	3.15488i	0.0982204	−	0.481115i	0.998911	−	0.0466544i	$-0.0148560\pi$
$44$	2.82489	+	5.38238i	0.425868	+	0.811424i
$45$	−0.922430	−	1.22753i	−0.137508	−	0.182990i
$46$	−6.17871	+	9.77085i	−0.911001	+	1.44063i
$47$	−0.644340	+	0.444756i	−0.0939867	+	0.0648743i	−0.614131	−	0.789204i	$-0.710493\pi$
$47$	−0.644340	+	0.444756i	−0.0939867	+	0.0648743i	0.520145	+	0.854078i	$0.325878\pi$
$48$	−2.13154	+	4.49212i	−0.307661	+	0.648382i
$49$	0.702733	−	0.731622i	0.100390	−	0.104517i
$50$	−6.02002	−	5.78230i	−0.851359	−	0.817741i
$51$	0.366107	+	3.01516i	0.0512652	+	0.422207i
$52$	8.82346	−	10.7491i	1.22359	−	1.49063i
$53$	1.39133	−	11.4586i	0.191114	−	1.57397i	−0.509529	−	0.860454i	$-0.670180\pi$
$53$	1.39133	−	11.4586i	0.191114	−	1.57397i	0.700643	−	0.713512i	$-0.252897\pi$
$54$	10.3987	−	8.49031i	1.41509	−	1.15538i
$55$	−0.916314	−	4.48840i	−0.123556	−	0.605216i
$56$	3.05910	+	10.5612i	0.408789	+	1.41130i
$57$	2.76586	+	11.2215i	0.366347	+	1.48633i
$58$	−1.40939	+	17.4584i	−0.185062	+	2.29240i
$59$	−0.344613	−	2.12049i	−0.0448647	−	0.276064i	0.954919	−	0.296867i	$-0.0959418\pi$
$59$	−0.344613	−	2.12049i	−0.0448647	−	0.276064i	−0.999784	+	0.0208031i	$0.993378\pi$
$60$	11.6883	−	13.1934i	1.50896	−	1.70326i
$61$	−7.39192	+	5.55467i	−0.946439	+	0.711202i	−0.957408	−	0.288737i	$-0.906765\pi$
$61$	−7.39192	+	5.55467i	−0.946439	+	0.711202i	0.0109697	+	0.999940i	$0.496508\pi$
$62$	−8.04881	−	9.85800i	−1.02220	−	1.25197i
$63$	0.207314	−	1.27565i	0.0261191	−	0.160717i
$64$	−9.27741	−	2.28668i	−1.15968	−	0.285835i
$65$	−8.64075	+	5.93088i	−1.07175	+	0.735635i
$66$	5.82221	−	1.43505i	0.716665	−	0.176642i
$67$	−0.146501	−	1.81474i	−0.0178980	−	0.221706i	−0.999523	−	0.0308858i	$-0.990167\pi$
$67$	−0.146501	−	1.81474i	−0.0178980	−	0.221706i	0.981625	−	0.190821i	$-0.0611149\pi$
$68$	7.06795	−	2.35963i	0.857115	−	0.286147i
$69$	5.20238	+	5.41625i	0.626293	+	0.652040i
$70$		−	17.2106i		−	2.05706i
$71$	8.24282	−	7.91734i	0.978243	−	0.939615i	−0.0199445	−	0.999801i	$-0.506349\pi$
$71$	8.24282	−	7.91734i	0.978243	−	0.939615i	0.998187	+	0.0601862i	$0.0191695\pi$
$72$	−1.83898	−	1.50148i	−0.216726	−	0.176952i
$73$	−3.61262	+	6.88327i	−0.422825	+	0.805626i	−0.999939	−	0.0110379i	$-0.996486\pi$
$73$	−3.61262	+	6.88327i	−0.422825	+	0.805626i	0.577114	+	0.816663i	$0.304179\pi$
$74$	22.6351	−	3.67856i	2.63127	−	0.427624i
$75$	−4.58309	+	2.89817i	−0.529210	+	0.334652i
$76$	25.6161	−	12.1550i	2.93837	−	1.39428i
$77$	2.19030	−	3.17320i	0.249608	−	0.361620i
$78$	−8.21259	−	10.9889i	−0.929893	−	1.24425i
$79$	3.01380	+	4.36625i	0.339080	+	0.491242i	0.955016	−	0.296554i	$-0.0958376\pi$
$79$	3.01380	+	4.36625i	0.339080	+	0.491242i	−0.615936	+	0.787796i	$0.711222\pi$
$80$	−7.96123	−	4.59642i	−0.890093	−	0.513895i
$81$	−3.05923	−	6.44720i	−0.339915	−	0.716355i
$82$	3.69448	+	1.23340i	0.407987	+	0.136206i
$83$	0.682568	−	2.76929i	0.0749215	−	0.303969i	−0.921512	−	0.388350i	$-0.873045\pi$
$83$	0.682568	−	2.76929i	0.0749215	−	0.303969i	0.996434	+	0.0843812i	$0.0268914\pi$
$84$	14.8236	−	0.597372i	1.61739	−	0.0651786i
$85$	−5.61098	+	0.226115i	−0.608596	+	0.0245256i
$86$	−1.86492	+	7.56627i	−0.201099	+	0.815892i
$87$	10.7928	+	3.60315i	1.15710	+	0.386298i
$88$	−3.03639	−	6.39905i	−0.323680	−	0.682141i
$89$	10.7109	+	6.18392i	1.13535	+	0.655494i	0.945275	−	0.326275i	$-0.105794\pi$
$89$	10.7109	+	6.18392i	1.13535	+	0.655494i	0.190075	+	0.981770i	$0.439127\pi$
$90$	2.11097	+	3.05827i	0.222516	+	0.322370i
$91$	−8.63819	−	1.78712i	−0.905529	−	0.187341i
$92$	10.4662	−	15.1629i	1.09118	−	1.58085i
$93$	−7.46924	+	3.54420i	−0.774524	+	0.367516i
$94$	1.60146	−	1.01270i	0.165178	−	0.104452i
$95$	−21.0912	+	3.42765i	−2.16391	+	0.351669i
$96$	−0.975080	+	1.85786i	−0.0995187	+	0.189617i
$97$	−10.8183	−	8.83290i	−1.09844	−	0.896845i	−0.103231	−	0.994657i	$-0.532918\pi$
$97$	−10.8183	−	8.83290i	−1.09844	−	0.896845i	−0.995205	+	0.0978123i	$0.968816\pi$
$98$	−1.77062	+	1.70070i	−0.178860	+	0.171797i
$99$			0.832521i			0.0836715i
$100$	9.21542	+	9.59427i	0.921542	+	0.959427i
$101$	−10.8268	+	3.61451i	−1.07731	+	0.359658i	−0.799306	−	0.600924i	$-0.794800\pi$
$101$	−10.8268	+	3.61451i	−1.07731	+	0.359658i	−0.277999	+	0.960581i	$0.589671\pi$
$102$	−0.591484	−	7.32684i	−0.0585656	−	0.725465i
$103$	13.2430	−	3.26412i	1.30488	−	0.321623i	0.475205	−	0.879875i	$-0.342374\pi$
$103$	13.2430	−	3.26412i	1.30488	−	0.321623i	0.829671	+	0.558252i	$0.188528\pi$
$104$	−10.7772	+	12.1008i	−1.05679	+	1.18658i
$105$	−10.8556	−	2.67565i	−1.05939	−	0.261117i
$106$	−4.48110	+	27.5733i	−0.435243	+	2.67816i
$107$	9.62499	+	11.7885i	0.930483	+	1.13963i	0.989952	+	0.141404i	$0.0451618\pi$
$107$	9.62499	+	11.7885i	0.930483	+	1.13963i	−0.0594690	+	0.998230i	$0.518941\pi$
$108$	−17.1042	+	12.8529i	−1.64585	+	1.23678i
$109$	5.56485	−	6.28142i	0.533016	−	0.601651i	−0.418891	−	0.908036i	$-0.637581\pi$
$109$	5.56485	−	6.28142i	0.533016	−	0.601651i	0.951907	+	0.306386i	$0.0991197\pi$
$110$	1.77841	+	10.9430i	0.169565	+	1.04337i
$111$	1.19873	−	14.8489i	0.113778	−	1.40940i
$112$	−1.85169	−	7.51260i	−0.174968	−	0.709874i
$113$	4.69921	+	16.2236i	0.442065	+	1.52619i	0.804372	+	0.594126i	$0.202502\pi$
$113$	4.69921	+	16.2236i	0.442065	+	1.52619i	−0.362307	+	0.932059i	$0.618011\pi$
$114$	−5.59478	−	27.4051i	−0.523999	−	2.56672i
$115$	−10.7553	+	8.78146i	−1.00294	+	0.818876i
$116$	3.36471	−	27.7109i	0.312406	−	2.57289i
$117$	1.75418	−	0.741956i	0.162174	−	0.0685938i
$118$	0.626692	+	5.16127i	0.0576917	+	0.475134i
$119$	−3.40876	−	3.27415i	−0.312480	−	0.300141i
$120$	−14.2273	+	14.8122i	−1.29877	+	1.35217i
$121$	3.65085	−	7.69401i	0.331896	−	0.699455i
$122$	18.4162	−	12.7118i	1.66732	−	1.15087i
$123$	1.35233	−	2.13854i	0.121935	−	0.192825i
$124$	12.1846	+	16.2147i	1.09421	+	1.45613i
$125$	2.09503	+	3.99175i	0.187386	+	0.357033i
$126$	−0.625630	+	3.06454i	−0.0557355	+	0.273011i
$127$	15.0180	−	1.21238i	1.33263	−	0.107581i	0.606471	−	0.795105i	$-0.292585\pi$
$127$	15.0180	−	1.21238i	1.33263	−	0.107581i	0.726161	+	0.687524i	$0.241302\pi$
$128$	19.6477	+	5.69103i	1.73663	+	0.503021i
$129$	4.48249	+	2.35259i	0.394661	+	0.207134i
$130$	21.4727	−	13.4998i	1.88328	−	1.18401i
$131$	−10.0477	+	5.27342i	−0.877868	+	0.460740i	−0.842539	−	0.538635i	$-0.818940\pi$
$131$	−10.0477	+	5.27342i	−0.877868	+	0.460740i	−0.0353286	+	0.999376i	$0.511248\pi$
$132$	−9.36359	+	1.91159i	−0.814996	+	0.166383i
$133$	−14.3779	−	10.8043i	−1.24672	−	0.936852i
$134$	0.177420	+	4.40263i	0.0153268	+	0.380329i
$135$	15.0760	−	5.71756i	1.29753	−	0.492089i
$136$	−8.33967	+	2.41562i	−0.715121	+	0.207137i
$137$	−0.339690	−	0.0693483i	−0.0290217	−	0.00592482i	0.185493	−	0.982646i	$-0.440612\pi$
$137$	−0.339690	−	0.0693483i	−0.0290217	−	0.00592482i	−0.214515	+	0.976721i	$0.568817\pi$
$138$	−12.0524	−	13.6044i	−1.02597	−	1.15808i
$139$	6.27836	−	7.68959i	0.532524	−	0.652223i	−0.436351	−	0.899777i	$-0.643729\pi$
$139$	6.27836	−	7.68959i	0.532524	−	0.652223i	0.968874	+	0.247554i	$0.0796267\pi$
$140$	−1.10445	+	27.4067i	−0.0933433	+	2.31629i
$141$	−0.389790	−	1.16756i	−0.0328262	−	0.0983265i
$142$	−20.7040	+	18.3422i	−1.73745	+	1.53924i
$143$	5.67709	+	0.243697i	0.474743	+	0.0203790i
$144$	1.25050	+	1.10785i	0.104208	+	0.0923206i
$145$	−8.24574	+	19.3535i	−0.684772	+	1.60722i
$146$	9.40668	−	16.2928i	0.778502	−	1.34841i
$147$	0.797447	+	1.38122i	0.0657723	+	0.113921i
$148$	−36.2809	+	4.40530i	−2.98228	+	0.362114i
$149$	−7.46452	−	3.54196i	−0.611518	−	0.290169i	0.0976366	−	0.995222i	$-0.468872\pi$
$149$	−7.46452	−	3.54196i	−0.611518	−	0.290169i	−0.709154	+	0.705053i	$0.750923\pi$
$150$	11.3651	−	6.56164i	0.927957	−	0.535756i
$151$	−7.03976	−	4.85919i	−0.572887	−	0.395436i	0.246102	−	0.969244i	$-0.420850\pi$
$151$	−7.03976	−	4.85919i	−0.572887	−	0.395436i	−0.818990	+	0.573808i	$0.805465\pi$
$152$	−30.3943	+	12.9498i	−2.46530	+	1.05037i
$153$	1.00732	+	0.163705i	0.0814369	+	0.0132348i
$154$	−5.60574	+	7.45989i	−0.451724	+	0.601135i
$155$	−5.42025	−	14.2920i	−0.435365	−	1.14796i
$156$	12.3728	+	18.0261i	0.990620	+	1.44324i
$157$	−7.76500	+	20.4746i	−0.619715	+	1.63405i	0.144810	+	0.989459i	$0.453743\pi$
$157$	−7.76500	+	20.4746i	−0.619715	+	1.63405i	−0.764525	+	0.644594i	$0.777026\pi$
$158$	−6.86240	−	10.8520i	−0.545943	−	0.863340i
$159$	16.6952	+	7.11316i	1.32402	+	0.564110i
$160$	−3.27871	−	2.07333i	−0.259205	−	0.163911i
$161$	−11.6015	−	1.40867i	−0.914325	−	0.111019i
$162$	6.76947	+	15.8885i	0.531860	+	1.24832i
$163$	−0.109202	+	0.327101i	−0.00855338	+	0.0256205i	−0.952727	−	0.303829i	$-0.901735\pi$
$163$	−0.109202	+	0.327101i	−0.00855338	+	0.0256205i	0.944173	+	0.329449i	$0.106863\pi$
$164$	−5.80406	−	2.20119i	−0.453221	−	0.171884i
$165$	7.17877	+	0.579530i	0.558867	+	0.0451164i
$166$	−1.92043	+	6.63008i	−0.149054	+	0.514594i
$167$	16.0495	+	0.646773i	1.24195	+	0.0500488i	0.652520	−	0.757772i	$-0.273712\pi$
$167$	16.0495	+	0.646773i	1.24195	+	0.0500488i	0.589428	+	0.807821i	$0.299353\pi$
$168$	−17.2867			−1.33370
$169$	−4.54603	−	12.1792i	−0.349694	−	0.936864i
$170$	13.5903			1.04233
$171$	3.88012	+	0.156363i	0.296720	+	0.0119574i
$172$	3.45531	−	11.9291i	0.263465	−	0.909587i
$173$	−6.69049	−	0.540112i	−0.508668	−	0.0410640i	−0.176531	−	0.984295i	$-0.556488\pi$
$173$	−6.69049	−	0.540112i	−0.508668	−	0.0410640i	−0.332137	+	0.943231i	$0.607770\pi$
$174$	−25.7476	−	9.76476i	−1.95192	−	0.740265i
$175$	2.67213	−	8.00402i	0.201994	−	0.605047i
$176$	1.95366	+	4.58540i	0.147262	+	0.345638i
$177$	3.35290	+	0.407116i	0.252019	+	0.0306007i
$178$	−25.2980	−	15.9975i	−1.89617	−	1.19906i
$179$	−18.5741	−	7.91367i	−1.38829	−	0.591495i	−0.436907	−	0.899506i	$-0.643926\pi$
$179$	−18.5741	−	7.91367i	−1.38829	−	0.591495i	−0.951383	+	0.308011i	$0.900337\pi$
$180$	−3.16532	−	5.00556i	−0.235929	−	0.373092i
$181$	−2.55442	+	6.73546i	−0.189869	+	0.500643i	−0.995820	−	0.0913394i	$-0.970885\pi$
$181$	−2.55442	+	6.73546i	−0.189869	+	0.500643i	0.805951	+	0.591982i	$0.201654\pi$
$182$	20.7144	+	5.16333i	1.53546	+	0.382731i
$183$	−5.15486	−	13.5922i	−0.381058	−	1.00477i
$184$	−12.8969	+	17.1626i	−0.950770	+	1.26525i
$185$	27.1861	+	4.41818i	1.99877	+	0.324831i
$186$	18.4072	−	7.84259i	1.34968	−	0.575047i
$187$	2.50572	+	1.72957i	0.183236	+	0.126479i
$188$	−2.61521	+	1.50989i	−0.190734	+	0.110120i
$189$	12.2608	+	5.81781i	0.891841	+	0.423184i
$190$	51.3359	−	6.23331i	3.72430	−	0.452212i
$191$	−10.4066	−	18.0247i	−0.752993	−	1.30422i	−0.946366	−	0.323096i	$-0.895276\pi$
$191$	−10.4066	−	18.0247i	−0.752993	−	1.30422i	0.193373	−	0.981125i	$-0.438057\pi$
$192$	7.51114	−	13.0097i	0.542070	−	0.938892i
$193$	−3.24871	+	7.62501i	−0.233847	+	0.548860i	−0.995018	−	0.0996912i	$-0.968215\pi$
$193$	−3.24871	+	7.62501i	−0.233847	+	0.548860i	0.761171	+	0.648551i	$0.224625\pi$
$194$	25.2998	+	22.4137i	1.81642	+	1.60921i
$195$	−5.17672	−	15.6427i	−0.370713	−	1.12020i
$196$	2.92874	−	2.59464i	0.209196	−	0.185331i
$197$	−0.393664	−	1.17917i	−0.0280474	−	0.0840122i	0.933582	−	0.358363i	$-0.116665\pi$
$197$	−0.393664	−	1.17917i	−0.0280474	−	0.0840122i	−0.961630	+	0.274351i	$0.911537\pi$
$198$	0.0811282	−	2.01317i	0.00576553	−	0.143070i
$199$	−9.72543	+	11.9115i	−0.689418	+	0.844383i	−0.994145	−	0.108056i	$-0.965537\pi$
$199$	−9.72543	+	11.9115i	−0.689418	+	0.844383i	0.304727	+	0.952440i	$0.401435\pi$
$200$	−10.2790	−	11.6026i	−0.726838	−	0.820431i
$201$	2.80454	+	0.572551i	0.197817	+	0.0403846i
$202$	26.5332	−	7.68544i	1.86687	−	0.540746i
$203$	−16.5557	+	6.27875i	−1.16198	+	0.440682i
$204$	0.471715	+	11.7055i	0.0330266	+	0.819547i
$205$	3.73983	+	2.81030i	0.261201	+	0.196280i
$206$	−32.3420	+	6.60266i	−2.25337	+	0.460029i
$207$	2.23433	−	1.17267i	0.155297	−	0.0815060i
$208$	7.92064	−	8.20308i	0.549198	−	0.568781i
$209$	10.2584	+	5.38400i	0.709585	+	0.372419i
$210$	25.9898	+	7.52804i	1.79347	+	0.519484i
$211$	11.8864	−	0.959571i	0.818295	−	0.0660596i	0.335772	−	0.941943i	$-0.391003\pi$
$211$	11.8864	−	0.959571i	0.818295	−	0.0660596i	0.482522	+	0.875884i	$0.339721\pi$
$212$	8.90533	−	43.6212i	0.611620	−	2.99591i
$213$	8.35055	+	15.9106i	0.572170	+	1.09018i
$214$	−22.1261	−	29.4444i	−1.51251	−	2.01278i
$215$	−5.00236	+	7.91059i	−0.341158	+	0.539498i
$216$	20.5168	−	14.1617i	1.39599	−	0.963584i
$217$	5.51528	−	11.6232i	0.374402	−	0.789035i
$218$	−14.0689	+	14.6472i	−0.952863	+	0.992035i
$219$	−8.81428	−	8.46623i	−0.595614	−	0.572095i
$220$	−2.12976	−	17.5402i	−0.143588	−	1.18256i
$221$	1.41120	−	6.82115i	0.0949273	−	0.458840i
$222$	−4.34574	+	35.7904i	−0.291667	+	2.40209i
$223$	2.46102	−	2.00936i	0.164802	−	0.134557i	−0.546456	−	0.837488i	$-0.684023\pi$
$223$	2.46102	−	2.00936i	0.164802	−	0.134557i	0.711258	+	0.702931i	$0.248126\pi$
$224$	−0.653103	−	3.19911i	−0.0436373	−	0.213750i
$225$	0.506906	+	1.75004i	0.0337937	+	0.116669i
$226$	−9.78252	−	39.6892i	−0.650723	−	2.64009i
$227$	−1.48276	+	18.3673i	−0.0984143	+	1.21908i	0.739454	+	0.673207i	$0.235084\pi$
$227$	−1.48276	+	18.3673i	−0.0984143	+	1.21908i	−0.837868	+	0.545873i	$0.816198\pi$
$228$	7.15066	+	43.9998i	0.473564	+	2.91396i
$229$	−6.06220	+	6.84281i	−0.400602	+	0.452186i	−0.913848	−	0.406055i	$-0.866904\pi$
$229$	−6.06220	+	6.84281i	−0.400602	+	0.452186i	0.513247	+	0.858241i	$0.328442\pi$
$230$	26.8639	−	20.1869i	1.77136	−	1.33109i
$231$	3.83382	+	4.69557i	0.252247	+	0.308946i
$232$	−5.21757	+	32.1050i	−0.342550	+	2.10780i
$233$	27.9086	+	6.87884i	1.82835	+	0.450648i	0.994805	−	0.101801i	$-0.0324606\pi$
$233$	27.9086	+	6.87884i	1.82835	+	0.450648i	0.833546	+	0.552449i	$0.186307\pi$
$234$	−4.31420	+	1.62323i	−0.282028	+	0.106114i
$235$	2.20964	−	0.544627i	0.144141	−	0.0355276i
$236$	−0.666752	−	8.25921i	−0.0434019	−	0.537629i
$237$	−7.91177	+	2.64134i	−0.513924	+	0.171573i
$238$	7.92388	+	8.24963i	0.513629	+	0.534744i
$239$			17.5823i			1.13730i	0.822579	+	0.568651i	$0.192534\pi$
$239$			17.5823i			1.13730i	−0.822579	+	0.568651i	$0.807466\pi$
$240$	10.4234	−	10.0118i	0.672827	−	0.646259i
$241$	−7.47584	−	6.10384i	−0.481561	−	0.393183i	0.360334	−	0.932823i	$-0.382663\pi$
$241$	−7.47584	−	6.10384i	−0.481561	−	0.393183i	−0.841896	+	0.539641i	$0.818560\pi$
$242$	−9.57814	+	18.2496i	−0.615706	+	1.17313i
$243$	−5.35154	+	0.869711i	−0.343302	+	0.0557920i
$244$	−30.1424	+	19.0609i	−1.92967	+	1.22025i
$245$	−2.66403	+	1.26410i	−0.170198	+	0.0807602i
$246$	−3.47855	+	5.03956i	−0.221785	+	0.321310i
$247$	2.20206	−	26.4134i	0.140114	−	1.68064i
$248$	−13.4253	−	19.4499i	−0.852509	−	1.23507i
$249$	3.88336	+	2.24206i	0.246098	+	0.142085i
$250$	−4.67715	−	9.85689i	−0.295809	−	0.623404i
$251$	9.80427	+	3.27315i	0.618840	+	0.206599i	0.608766	−	0.793350i	$-0.291665\pi$
$251$	9.80427	+	3.27315i	0.618840	+	0.206599i	0.0100743	+	0.999949i	$0.496793\pi$
$252$	1.19294	−	4.83993i	0.0751478	−	0.304887i
$253$	7.52214	−	0.303132i	0.472913	−	0.0190577i
$254$	−36.4342	+	1.46825i	−2.28608	+	0.0921261i
$255$	2.11283	−	8.57208i	0.132310	−	0.536805i
$256$	−28.8302	−	9.62495i	−1.80189	−	0.601559i
$257$	−9.38761	−	19.7840i	−0.585583	−	1.23409i	−0.952699	−	0.303915i	$-0.901706\pi$
$257$	−9.38761	−	19.7840i	−0.585583	−	1.23409i	0.367116	−	0.930175i	$-0.380345\pi$
$258$	−10.6102	−	6.12577i	−0.660559	−	0.381374i
$259$	13.1690	+	19.0786i	0.818284	+	1.18549i
$260$	−35.0603	+	20.1196i	−2.17435	+	1.24777i
$261$	2.17178	−	3.14636i	0.134430	−	0.194755i
$262$	24.8108	−	11.7729i	1.53282	−	0.727330i
$263$	−11.1092	+	7.02506i	−0.685026	+	0.433184i	−0.831125	−	0.556086i	$-0.812303\pi$
$263$	−11.1092	+	7.02506i	−0.685026	+	0.433184i	0.146099	+	0.989270i	$0.453328\pi$
$264$	10.9914	−	1.78627i	0.676473	−	0.109938i
$265$	−15.5923	+	29.7086i	−0.957827	+	1.82499i
$266$	33.7153	+	27.5277i	2.06722	+	1.68783i
$267$	−14.0234	+	13.4697i	−0.858218	+	0.824329i
$268$		−	7.02229i		−	0.428955i
$269$	−9.61280	−	10.0080i	−0.586103	−	0.610198i	0.360437	−	0.932783i	$-0.382627\pi$
$269$	−9.61280	−	10.0080i	−0.586103	−	0.610198i	−0.946540	+	0.322586i	$0.895448\pi$
$270$	−37.0134	+	12.3569i	−2.25256	+	0.752016i
$271$	0.759241	+	9.40489i	0.0461206	+	0.571306i	0.978009	+	0.208562i	$0.0668782\pi$
$271$	0.759241	+	9.40489i	0.0461206	+	0.571306i	−0.931889	+	0.362745i	$0.881840\pi$
$272$	5.93232	−	1.46219i	0.359700	−	0.0886581i
$273$	6.47715	−	12.2629i	0.392015	−	0.742184i
$274$	0.814670	+	0.200798i	0.0492160	+	0.0121307i
$275$	−0.871949	+	5.36532i	−0.0525805	+	0.323541i
$276$	18.3197	+	22.4375i	1.10271	+	1.35058i
$277$	14.4172	−	10.8338i	0.866247	−	0.650943i	−0.0718116	−	0.997418i	$-0.522878\pi$
$277$	14.4172	−	10.8338i	0.866247	−	0.650943i	0.938059	+	0.346475i	$0.112622\pi$
$278$	−15.9315	+	17.9829i	−0.955506	+	1.07854i
$279$	0.445600	+	2.74189i	0.0266774	+	0.164153i
$280$	2.57175	−	31.8569i	0.153692	−	1.90381i
$281$	1.03053	+	4.18104i	0.0614764	+	0.249420i	0.993638	−	0.112624i	$-0.0359254\pi$
$281$	1.03053	+	4.18104i	0.0614764	+	0.249420i	−0.932161	+	0.362043i	$0.882079\pi$
$282$	0.828799	+	2.86134i	0.0493542	+	0.170391i
$283$	1.11476	+	5.46047i	0.0662658	+	0.324591i	0.999388	−	0.0349668i	$-0.0111325\pi$
$283$	1.11476	+	5.46047i	0.0662658	+	0.324591i	−0.933123	+	0.359558i	$0.882927\pi$
$284$	34.1469	−	27.8801i	2.02625	−	1.65438i
$285$	4.04932	−	33.3492i	0.239861	−	1.97543i
$286$	−13.7044	−	1.14253i	−0.810359	−	0.0675590i
$287$	0.474604	+	3.90872i	0.0280150	+	0.230724i
$288$	0.508443	+	0.488366i	0.0299603	+	0.0287772i
$289$	−9.19088	+	9.56872i	−0.540640	+	0.562866i
$290$	21.8255	−	45.9964i	1.28164	−	2.70100i
$291$	18.0706	−	12.4733i	1.05932	−	0.731196i
$292$	−16.0251	+	25.3416i	−0.937797	+	1.48301i
$293$	−7.15857	−	9.52632i	−0.418208	−	0.556534i	0.540347	−	0.841442i	$-0.318293\pi$
$293$	−7.15857	−	9.52632i	−0.418208	−	0.556534i	−0.958555	+	0.284909i	$0.908037\pi$
$294$	−1.79376	−	3.41773i	−0.104614	−	0.199326i
$295$	−1.24907	+	6.11835i	−0.0727236	+	0.356224i
$296$	42.4473	−	3.42670i	2.46720	−	0.199173i
$297$	−8.39695	−	2.43221i	−0.487240	−	0.141131i
$298$	17.7053	+	9.29246i	1.02564	+	0.538298i
$299$	−7.34257	−	15.5795i	−0.424632	−	0.900987i
$300$	−18.5193	+	9.71966i	−1.06921	+	0.561165i
$301$	−7.71855	+	1.57575i	−0.444890	+	0.0908249i
$302$	16.5498	+	12.4364i	0.952333	+	0.715632i
$303$	−0.722579	−	17.9306i	−0.0415111	−	1.03009i
$304$	21.7381	−	8.24416i	1.24676	−	0.472835i
$305$	25.8155	−	7.47754i	1.47819	−	0.428163i
$306$	−2.41991	−	0.494028i	−0.138337	−	0.0282417i
$307$	−6.28170	−	7.09058i	−0.358516	−	0.404681i	0.541385	−	0.840775i	$-0.317900\pi$
$307$	−6.28170	−	7.09058i	−0.358516	−	0.404681i	−0.899901	+	0.436094i	$0.856362\pi$
$308$	9.40550	−	11.5197i	0.535928	−	0.656393i
$309$	−0.863445	+	21.4262i	−0.0491197	+	1.21889i
$310$	11.7143	+	35.0887i	0.665329	+	1.99290i
$311$	0.713301	−	0.631929i	0.0404476	−	0.0358334i	−0.642657	−	0.766154i	$-0.722168\pi$
$311$	0.713301	−	0.631929i	0.0404476	−	0.0358334i	0.683104	+	0.730321i	$0.260629\pi$
$312$	−13.5595	−	21.5677i	−0.767656	−	1.22103i
$313$	−12.8396	−	11.3749i	−0.725740	−	0.642949i	0.217118	−	0.976145i	$-0.430334\pi$
$313$	−12.8396	−	11.3749i	−0.725740	−	0.642949i	−0.942858	+	0.333196i	$0.891873\pi$
$314$	20.7723	−	48.7544i	1.17225	−	2.75137i
$315$	−1.87831	+	3.25333i	−0.105831	+	0.183304i
$316$	10.2315	+	17.7215i	0.575568	+	0.996913i
$317$	13.4036	−	1.62749i	0.752819	−	0.0914088i	0.264874	−	0.964283i	$-0.414670\pi$
$317$	13.4036	−	1.62749i	0.752819	−	0.0914088i	0.487945	+	0.872874i	$0.337747\pi$
$318$	−39.6786	−	18.8277i	−2.22507	−	1.05581i
$319$	9.87782	−	5.70296i	0.553052	−	0.319305i
$320$	22.8575	+	15.7774i	1.27777	+	0.881984i
$321$	−22.0119	+	9.37839i	−1.22858	+	0.523451i
$322$	27.9170	+	4.53696i	1.55576	+	0.252835i
$323$	8.53162	−	11.3535i	0.474712	−	0.631727i
$324$	−9.76032	−	25.7359i	−0.542240	−	1.42977i
$325$	12.0822	−	2.94440i	0.670200	−	0.163326i
$326$	0.295945	−	0.780342i	0.0163909	−	0.0432192i
$327$	7.05150	+	11.1511i	0.389949	+	0.616655i
$328$	6.65419	+	2.83509i	0.367416	+	0.156541i
$329$	1.61894	+	1.02375i	0.0892550	+	0.0564414i
$330$	−17.3030	−	2.10096i	−0.952499	−	0.115654i
$331$	−0.266451	−	0.625385i	−0.0146455	−	0.0343742i	0.912496	−	0.409085i	$-0.134152\pi$
$331$	−0.266451	−	0.625385i	−0.0146455	−	0.0343742i	−0.927142	+	0.374711i	$0.877742\pi$
$332$	3.48363	−	10.4347i	0.191189	−	0.572680i
$333$	−4.68020	−	1.77496i	−0.256473	−	0.0972674i
$334$	−38.7474	−	3.12801i	−2.12016	−	0.171157i
$335$	−1.47236	+	5.08319i	−0.0804438	+	0.277724i
$336$	12.1548	+	0.489821i	0.663097	+	0.0267219i
$337$	−3.40754			−0.185620			−0.0928102	−	0.995684i	$-0.529585\pi$
$337$	−3.40754			−0.185620			−0.0928102	+	0.995684i	$0.529585\pi$
$338$	9.80620	+	29.8944i	0.533387	+	1.62604i
$339$	−26.5548			−1.44226
$340$	−21.6417	−	0.872131i	−1.17369	−	0.0472979i
$341$	−2.30573	+	7.96030i	−0.124862	+	0.431075i
$342$	−9.36754	−	0.756226i	−0.506539	−	0.0408920i
$343$	−18.3335	−	6.95297i	−0.989915	−	0.375425i
$344$	−4.58259	+	13.7265i	−0.247077	+	0.740086i
$345$	−8.55648	−	20.0828i	−0.460665	−	1.08122i
$346$	16.1261	+	1.95806i	0.866944	+	0.105266i
$347$	1.05958	+	0.670041i	0.0568815	+	0.0359697i	0.562604	−	0.826727i	$-0.309800\pi$
$347$	1.05958	+	0.670041i	0.0568815	+	0.0359697i	−0.505722	+	0.862696i	$0.668774\pi$
$348$	40.3747	+	17.2020i	2.16431	+	0.922126i
$349$	0.566237	+	0.895433i	0.0303100	+	0.0479314i	0.860005	−	0.510285i	$-0.170460\pi$
$349$	0.566237	+	0.895433i	0.0303100	+	0.0479314i	−0.829695	+	0.558217i	$0.811486\pi$
$350$	−7.24165	+	19.0947i	−0.387082	+	1.02065i
$351$	2.35866	+	19.8606i	0.125896	+	1.06008i
$352$	0.745835	+	1.96661i	0.0397531	+	0.104820i
$353$	−0.905614	+	1.20515i	−0.0482010	+	0.0641438i	−0.822900	−	0.568187i	$-0.807645\pi$
$353$	−0.905614	+	1.20515i	−0.0482010	+	0.0641438i	0.774699	+	0.632331i	$0.217902\pi$
$354$	−8.06819	−	1.31121i	−0.428820	−	0.0696900i
$355$	−30.5634	+	13.0218i	−1.62213	+	0.691127i
$356$	39.2589	+	27.0984i	2.08072	+	1.43621i
$357$	6.43534	−	3.71544i	0.340594	−	0.196642i
$358$	44.1440	+	20.9466i	2.33308	+	1.10706i
$359$	14.8919	−	1.80820i	0.785962	−	0.0954331i	0.282291	−	0.959329i	$-0.408906\pi$
$359$	14.8919	−	1.80820i	0.785962	−	0.0954331i	0.503671	+	0.863896i	$0.331982\pi$
$360$	3.45042	+	5.97631i	0.181853	+	0.314979i
$361$	17.5199	−	30.3453i	0.922098	−	1.59712i
$362$	6.83338	−	16.0385i	0.359155	−	0.842967i
$363$	10.0219	+	8.87859i	0.526011	+	0.466005i
$364$	−32.6551	−	9.55157i	−1.71159	−	0.500638i
$365$	16.9134	−	14.9839i	0.885286	−	0.784295i
$366$	11.1408	+	33.3707i	0.582337	+	1.74431i
$367$	−1.05021	+	26.0608i	−0.0548207	+	1.36036i	0.704528	+	0.709676i	$0.251159\pi$
$367$	−1.05021	+	26.0608i	−0.0548207	+	1.36036i	−0.759348	+	0.650684i	$0.774482\pi$
$368$	9.55449	−	11.7021i	0.498062	−	0.610015i
$369$	−0.563761	−	0.636354i	−0.0293482	−	0.0331273i
$370$	−65.3101	−	13.3332i	−3.39531	−	0.693158i
$371$	−27.1249	+	7.85684i	−1.40826	+	0.407907i
$372$	−29.8156	+	11.3076i	−1.54587	+	0.586270i
$373$	0.235906	+	5.85396i	0.0122148	+	0.303106i	0.993736	+	0.111753i	$0.0356466\pi$
$373$	0.235906	+	5.85396i	0.0122148	+	0.303106i	−0.981521	+	0.191353i	$0.938712\pi$
$374$	−5.89070	−	4.42657i	−0.304601	−	0.228893i
$375$	−6.94436	+	1.41770i	−0.358605	+	0.0732098i
$376$	3.11564	−	1.63522i	0.160677	−	0.0843298i
$377$	−20.8198	−	15.7307i	−1.07227	−	0.810172i
$378$	−29.0817	−	15.2632i	−1.49580	−	0.785056i
$379$	13.7528	+	3.98354i	0.706433	+	0.204621i	0.611939	−	0.790905i	$-0.290390\pi$
$379$	13.7528	+	3.98354i	0.706433	+	0.204621i	0.0944934	+	0.995525i	$0.469877\pi$
$380$	−82.1492	+	6.63177i	−4.21416	+	0.340202i
$381$	−4.73817	+	23.2091i	−0.242744	+	1.18904i
$382$	23.4083	+	44.6008i	1.19767	+	2.28198i
$383$	14.2416	+	18.9521i	0.727712	+	0.968409i	0.999981	+	0.00618801i	$0.00196972\pi$
$383$	14.2416	+	18.9521i	0.727712	+	0.968409i	−0.272268	+	0.962221i	$0.587774\pi$
$384$	−17.1881	+	27.1809i	−0.877128	+	1.38707i
$385$	−9.22363	+	6.36662i	−0.470080	+	0.324473i
$386$	8.59898	−	18.1220i	0.437676	−	0.922383i
$387$	1.17829	−	1.22673i	0.0598957	−	0.0623581i
$388$	−38.8499	−	37.3159i	−1.97231	−	1.89443i
$389$	0.570424	+	4.69787i	0.0289217	+	0.238191i	1.00000		0.000570414i	$-0.000181568\pi$
$389$	0.570424	+	4.69787i	0.0289217	+	0.238191i	−0.971078	+	0.238762i	$0.923258\pi$
$390$	10.9938	+	38.3311i	0.556694	+	1.94097i
$391$	1.11236	−	9.16110i	0.0562544	−	0.463297i
$392$	−3.53156	+	2.88343i	−0.178371	+	0.145635i
$393$	−3.56850	−	17.4797i	−0.180007	−	0.881732i
$394$	0.837037	+	2.88979i	0.0421693	+	0.145585i
$395$	−3.69056	−	14.9732i	−0.185692	−	0.753384i
$396$	−0.258383	+	3.20064i	−0.0129842	+	0.160838i
$397$	−1.63753	−	10.0761i	−0.0821852	−	0.505706i	−0.995207	−	0.0977943i	$-0.968821\pi$
$397$	−1.63753	−	10.0761i	−0.0821852	−	0.505706i	0.913021	−	0.407912i	$-0.133743\pi$
$398$	24.6785	−	27.8562i	1.23702	−	1.39631i
$399$	22.6047	−	16.9863i	1.13165	−	0.850379i
$400$	6.89874	+	8.44943i	0.344937	+	0.422471i
$401$	−1.80270	+	11.0925i	−0.0900228	+	0.553932i	0.902384	+	0.430933i	$0.141815\pi$
$401$	−1.80270	+	11.0925i	−0.0900228	+	0.553932i	−0.992407	+	0.122999i	$0.960749\pi$
$402$	−6.72605	−	1.65782i	−0.335465	−	0.0826846i
$403$	18.8278	−	2.23601i	0.937881	−	0.111384i
$404$	−42.7456	+	10.5358i	−2.12667	+	0.524178i
$405$	1.66912	+	20.6757i	0.0829391	+	1.02738i
$406$	40.6463	−	13.5697i	2.01724	−	0.673454i
$407$	−10.3447	−	10.7700i	−0.512769	−	0.533849i
$408$		−	13.6504i		−	0.675796i
$409$	20.6204	−	19.8062i	1.01961	−	0.979352i	0.0198231	−	0.999804i	$-0.493690\pi$
$409$	20.6204	−	19.8062i	1.01961	−	0.979352i	0.999791	+	0.0204511i	$0.00651023\pi$
$410$	−8.76968	−	7.16022i	−0.433103	−	0.353618i
$411$	0.253307	−	0.482635i	0.0124947	−	0.0238066i
$412$	51.9262	−	8.43883i	2.55822	−	0.415752i
$413$	−4.44225	+	2.80911i	−0.218589	+	0.138227i
$414$	−5.51726	+	2.61797i	−0.271158	+	0.128666i
$415$	−4.70952	+	6.82292i	−0.231181	+	0.334924i
$416$	3.47908	−	3.32420i	0.170576	−	0.162982i
$417$	8.86591	+	12.8445i	0.434165	+	0.628997i
$418$	−24.2818	−	14.0191i	−1.18766	−	0.685696i
$419$	9.41980	+	19.8518i	0.460187	+	0.969824i	0.992382	+	0.123202i	$0.0393163\pi$
$419$	9.41980	+	19.8518i	0.460187	+	0.969824i	−0.532194	+	0.846622i	$0.678632\pi$
$420$	−40.9040	−	13.6558i	−1.99591	−	0.666332i
$421$	−0.0574544	+	0.233101i	−0.00280015	+	0.0113607i	−0.972325	−	0.233631i	$-0.924939\pi$
$421$	−0.0574544	+	0.233101i	−0.00280015	+	0.0113607i	0.969525	+	0.244992i	$0.0787853\pi$
$422$	−28.8368	+	1.16209i	−1.40376	+	0.0565694i
$423$	−0.413250	+	0.0166534i	−0.0200929	+	0.000809715i
$424$	−12.4148	+	50.3688i	−0.602915	+	2.44612i
$425$	6.32037	+	2.11005i	0.306583	+	0.102352i
$426$	−18.6425	−	39.2883i	−0.903234	−	1.90353i
$427$	19.5908	+	11.3108i	0.948066	+	0.547366i
$428$	33.3448	+	48.3083i	1.61178	+	2.33507i
$429$	−2.85121	+	8.46643i	−0.137658	+	0.408763i
$430$	12.8674	−	18.6417i	0.620522	−	0.898981i
$431$	−17.4885	+	8.29840i	−0.842392	+	0.399720i	−0.800450	−	0.599400i	$-0.795406\pi$
$431$	−17.4885	+	8.29840i	−0.842392	+	0.399720i	−0.0419424	+	0.999120i	$0.513355\pi$
$432$	−14.8273	+	9.37620i	−0.713377	+	0.451113i
$433$	12.6799	−	2.06069i	0.609359	−	0.0990305i	0.152102	−	0.988365i	$-0.451396\pi$
$433$	12.6799	−	2.06069i	0.609359	−	0.0990305i	0.457258	+	0.889334i	$0.348832\pi$
$434$	−14.4695	+	27.5694i	−0.694560	+	1.32337i
$435$	−25.6190	−	20.9173i	−1.22834	−	1.00291i
$436$	23.3437	−	22.4219i	1.11796	−	1.07382i
$437$		−	35.1153i		−	1.67979i
$438$	20.4894	+	21.3317i	0.979021	+	1.01927i
$439$	0.859716	−	0.287015i	0.0410320	−	0.0136985i	−0.296078	−	0.955164i	$-0.595679\pi$
$439$	0.859716	−	0.287015i	0.0410320	−	0.0136985i	0.337110	+	0.941465i	$0.390551\pi$
$440$	1.65665	+	20.5213i	0.0789778	+	0.978315i
$441$	0.520312	−	0.128245i	0.0247768	−	0.00610692i
$442$	−4.07722	+	16.3572i	−0.193934	+	0.778030i
$443$	2.28809	+	0.563964i	0.108711	+	0.0267948i	0.293296	−	0.956022i	$-0.405248\pi$
$443$	2.28809	+	0.563964i	0.108711	+	0.0267948i	−0.184585	+	0.982817i	$0.559094\pi$
$444$	9.21709	−	56.7150i	0.437424	−	2.69158i
$445$	−22.7364	−	27.8470i	−1.07781	−	1.32007i
$446$	−6.14696	+	4.61914i	−0.291067	+	0.218723i
$447$	8.61378	−	9.72295i	0.407418	−	0.459880i
$448$	3.74991	+	23.0741i	0.177166	+	1.09015i
$449$	1.88654	−	23.3690i	0.0890315	−	1.10285i	−0.785818	−	0.618458i	$-0.787758\pi$
$449$	1.88654	−	23.3690i	0.0890315	−	1.10285i	0.874849	−	0.484395i	$-0.160960\pi$
$450$	−1.05524	−	4.28129i	−0.0497446	−	0.201822i
$451$	−0.705665	−	2.43624i	−0.0332285	−	0.114718i
$452$	13.0310	+	63.8303i	0.612929	+	3.00232i
$453$	10.4171	−	8.50534i	0.489440	−	0.399616i
$454$	5.37543	−	44.2707i	0.252282	−	2.07773i
$455$	21.6352	+	13.7608i	1.01427	+	0.645118i
$456$	−6.26087	−	51.5629i	−0.293192	−	2.41466i
$457$	24.5000	+	23.5326i	1.14606	+	1.10081i	0.993653	+	0.112490i	$0.0358827\pi$
$457$	24.5000	+	23.5326i	1.14606	+	1.10081i	0.152409	+	0.988317i	$0.451297\pi$
$458$	15.3262	−	15.9563i	0.716148	−	0.745589i
$459$	−4.59403	+	9.68172i	−0.214431	+	0.451904i
$460$	−44.0745	+	30.4225i	−2.05499	+	1.41845i
$461$	−2.02997	+	3.21013i	−0.0945450	+	0.149511i	−0.889150	−	0.457616i	$-0.848704\pi$
$461$	−2.02997	+	3.21013i	−0.0945450	+	0.149511i	0.794605	+	0.607127i	$0.207678\pi$
$462$	−8.81323	−	11.7283i	−0.410029	−	0.545649i
$463$	9.33044	+	17.7777i	0.433622	+	0.826198i	0.999998	+	0.00205110i	$0.000652885\pi$
$463$	9.33044	+	17.7777i	0.433622	+	0.826198i	−0.566376	+	0.824147i	$0.691655\pi$
$464$	4.57833	−	22.4261i	0.212544	−	1.04111i
$465$	23.9533	−	1.93371i	1.11081	−	0.0896738i
$466$	−66.8172	−	19.3539i	−3.09525	−	0.896550i
$467$	−29.0687	−	15.2565i	−1.34514	−	0.705984i	−0.370305	−	0.928910i	$-0.620747\pi$
$467$	−29.0687	−	15.2565i	−1.34514	−	0.705984i	−0.974835	+	0.222926i	$0.928439\pi$
$468$	6.97426	−	2.30803i	0.322385	−	0.106689i
$469$	−3.94407	+	2.07001i	−0.182120	+	0.0955842i
$470$	−5.39635	+	1.10167i	−0.248915	+	0.0508164i
$471$	−27.5224	−	20.6817i	−1.26817	−	0.952965i
$472$	0.388769	+	9.64719i	0.0178945	+	0.444048i
$473$	4.74486	−	1.79949i	0.218169	−	0.0827406i
$474$	19.3894	−	5.61620i	0.890583	−	0.257961i
$475$	24.8423	+	5.07159i	1.13984	+	0.232701i
$476$	−12.0889	−	13.6455i	−0.554092	−	0.625440i
$477$	3.85634	−	4.72316i	0.176570	−	0.216259i
$478$	1.71337	−	42.5168i	0.0783677	−	1.94467i
$479$	10.6365	+	31.8602i	0.485994	+	1.45573i	0.851219	+	0.524811i	$0.175864\pi$
$479$	10.6365	+	31.8602i	0.485994	+	1.45573i	−0.365224	+	0.930920i	$0.619008\pi$
$480$	4.56508	−	4.04431i	0.208366	−	0.184597i
$481$	−13.4738	+	31.3954i	−0.614351	+	1.43151i
$482$	17.4830	+	15.4886i	0.796330	+	0.705487i
$483$	7.20183	−	16.9033i	0.327694	−	0.769127i
$484$	16.4237	−	28.4467i	0.746532	−	1.29303i
$485$	20.2981	+	35.1573i	0.921688	+	1.59641i
$486$	13.0257	−	1.58160i	0.590857	−	0.0717430i
$487$	−2.95358	−	1.40149i	−0.133839	−	0.0635075i	0.360595	−	0.932722i	$-0.382574\pi$
$487$	−2.95358	−	1.40149i	−0.133839	−	0.0635075i	−0.494435	+	0.869215i	$0.664625\pi$
$488$	35.9880	−	20.7777i	1.62910	−	0.940561i
$489$	−0.446191	−	0.307983i	−0.0201775	−	0.0139275i
$490$	6.56525	−	2.79719i	0.296588	−	0.126364i
$491$	7.99463	+	1.29925i	0.360793	+	0.0586345i	0.338106	−	0.941108i	$-0.390214\pi$
$491$	7.99463	+	1.29925i	0.360793	+	0.0586345i	0.0226868	+	0.999743i	$0.492778\pi$
$492$	5.86278	−	7.80194i	0.264314	−	0.351738i
$493$	−4.95801	−	13.0732i	−0.223298	−	0.588787i
$494$	−7.89891	+	63.6574i	−0.355389	+	2.86408i
$495$	0.858113	−	2.26266i	0.0385693	−	0.101699i
$496$	8.88863	+	14.0562i	0.399111	+	0.631144i
$497$	−25.7246	−	10.9602i	−1.15391	−	0.491634i
$498$	−9.17212	−	5.80010i	−0.411013	−	0.259909i
$499$	31.3692	+	3.80890i	1.40428	+	0.170510i	0.787348	−	0.616509i	$-0.211454\pi$
$499$	31.3692	+	3.80890i	1.40428	+	0.170510i	0.616928	+	0.787019i	$0.288377\pi$
$500$	6.81551	+	15.9966i	0.304799	+	0.715390i
$501$	−7.99688	+	23.9536i	−0.357274	+	1.07017i
$502$	−23.3894	−	8.87043i	−1.04392	−	0.395907i
$503$	4.40746	+	0.355807i	0.196519	+	0.0158646i	0.178334	−	0.983970i	$-0.442929\pi$
$503$	4.40746	+	0.355807i	0.196519	+	0.0158646i	0.0181848	+	0.999835i	$0.494211\pi$
$504$	−1.61597	+	5.57899i	−0.0719812	+	0.248508i
$505$	33.1511	+	1.33594i	1.47520	+	0.0594487i
$506$	−18.2193			−0.809948
$507$	20.3804	−	1.53770i	0.905126	−	0.0682916i
$508$	58.1133			2.57836
$509$	4.94398	+	0.199235i	0.219138	+	0.00883096i	0.149592	−	0.988748i	$-0.452204\pi$
$509$	4.94398	+	0.199235i	0.219138	+	0.00883096i	0.0695458	+	0.997579i	$0.477845\pi$
$510$	−5.94451	+	20.5228i	−0.263227	+	0.908766i
$511$	18.9570	+	1.53037i	0.838607	+	0.0676994i
$512$	30.5262	+	11.5771i	1.34908	+	0.511639i
$513$	−12.9129	+	38.6787i	−0.570117	+	1.70771i
$514$	20.7729	+	48.7558i	0.916253	+	2.15052i
$515$	−39.3569	−	4.77880i	−1.73427	−	0.210579i
$516$	16.5029	+	10.4358i	0.726498	+	0.459410i
$517$	−1.13516	−	0.483646i	−0.0499242	−	0.0212707i
$518$	−29.9857	−	47.4186i	−1.31750	−	2.08346i
$519$	3.74210	−	9.86710i	0.164260	−	0.433118i
$520$	41.7634	−	21.7796i	1.83145	−	0.955098i
$521$	−9.64305	−	25.4266i	−0.422470	−	1.11396i	−0.962253	−	0.272157i	$-0.912263\pi$
$521$	−9.64305	−	25.4266i	−0.422470	−	1.11396i	0.539783	−	0.841804i	$-0.318506\pi$
$522$	−5.55832	+	7.39679i	−0.243281	+	0.323749i
$523$	25.2140	+	4.09768i	1.10253	+	0.179179i	0.684329	−	0.729174i	$-0.260095\pi$
$523$	25.2140	+	4.09768i	1.10253	+	0.179179i	0.418205	+	0.908353i	$0.362659\pi$
$524$	−40.2651	+	17.1553i	−1.75899	+	0.749435i
$525$	10.9181	+	7.53623i	0.476505	+	0.328908i
$526$	27.5486	−	15.9052i	1.20118	−	0.693499i
$527$	9.17827	+	4.35514i	0.399812	+	0.189713i
$528$	−7.77899	+	0.944541i	−0.338537	+	0.0411059i
$529$	0.0909695	+	0.157564i	0.00395520	+	0.00685060i
$530$	40.5998	−	70.3210i	1.76354	−	3.05455i
$531$	0.444822	−	1.04404i	0.0193036	−	0.0453073i
$532$	−51.9230	−	45.9997i	−2.25115	−	1.99434i
$533$	−4.50443	+	3.65810i	−0.195109	+	0.158450i
$534$	35.2235	−	31.2053i	1.52427	−	1.35039i
$535$	−14.0083	−	41.9600i	−0.605632	−	1.81409i
$536$	−0.329474	+	8.17581i	−0.0142311	+	0.353141i
$537$	20.0749	−	24.5873i	0.866297	−	1.06102i
$538$	22.2701	+	25.1377i	0.960132	+	1.08376i
$539$	1.56645	+	0.319794i	0.0674719	+	0.0137745i
$540$	59.7344	−	17.3023i	2.57056	−	0.744571i
$541$	−8.66868	+	3.28759i	−0.372695	+	0.141345i	−0.533839	−	0.845586i	$-0.679251\pi$
$541$	−8.66868	+	3.28759i	−0.372695	+	0.141345i	0.161143	+	0.986931i	$0.448482\pi$
$542$	−0.919477	−	22.8166i	−0.0394949	−	0.980056i
$543$	−9.05394	−	6.80359i	−0.388542	−	0.291970i
$544$	2.52618	−	0.515723i	0.108309	−	0.0221114i
$545$	−21.5989	+	11.3360i	−0.925194	+	0.485579i
$546$	−16.8578	+	29.0225i	−0.721449	+	1.24205i
$547$	−8.54373	−	4.48410i	−0.365304	−	0.191726i	0.272077	−	0.962276i	$-0.412290\pi$
$547$	−8.54373	−	4.48410i	−0.365304	−	0.191726i	−0.637380	+	0.770550i	$0.719982\pi$
$548$	−1.28442	−	0.372038i	−0.0548678	−	0.0158927i
$549$	−4.86856	+	0.393031i	−0.207785	+	0.0167741i
$550$	2.63136	−	12.8893i	0.112202	−	0.549600i
$551$	−24.7245	−	47.1086i	−1.05330	−	2.00689i
$552$	−20.2762	−	26.9827i	−0.863013	−	1.14846i
$553$	6.93728	−	10.9704i	0.295003	−	0.466510i
$554$	−35.9190	+	24.7931i	−1.52605	+	1.05336i
$555$	−18.5634	+	39.1214i	−0.787971	+	1.66061i
$556$	26.5238	−	27.6142i	1.12486	−	1.17110i
$557$	−1.78315	−	1.71274i	−0.0755546	−	0.0725712i	0.653996	−	0.756498i	$-0.273091\pi$
$557$	−1.78315	−	1.71274i	−0.0755546	−	0.0725712i	−0.729551	+	0.683927i	$0.760271\pi$
$558$	−0.810342	−	6.67377i	−0.0343045	−	0.282523i
$559$	−8.02035	−	8.39403i	−0.339224	−	0.355030i
$560$	−2.71095	+	22.3267i	−0.114558	+	0.943473i
$561$	−3.70786	+	3.02737i	−0.156546	+	0.127816i
$562$	−2.08456	−	10.2109i	−0.0879320	−	0.430719i
$563$	−2.11109	−	7.28833i	−0.0889718	−	0.307166i	0.903674	−	0.428221i	$-0.140860\pi$
$563$	−2.11109	−	7.28833i	−0.0889718	−	0.307166i	−0.992646	+	0.121055i	$0.961372\pi$
$564$	−1.13619	−	4.60969i	−0.0478421	−	0.194103i
$565$	3.95058	−	48.9367i	0.166202	−	2.05878i
$566$	−2.16357	−	13.3130i	−0.0909415	−	0.559586i
$567$	−11.5774	+	13.0682i	−0.486207	+	0.548814i
$568$	−41.0642	+	30.8577i	−1.72301	+	1.29476i
$569$	−4.12408	−	5.05108i	−0.172890	−	0.211752i	0.680890	−	0.732386i	$-0.261593\pi$
$569$	−4.12408	−	5.05108i	−0.172890	−	0.211752i	−0.853780	+	0.520633i	$0.825696\pi$
$570$	−13.0418	+	80.2493i	−0.546260	+	3.36127i
$571$	0.636898	+	0.156981i	0.0266533	+	0.00656946i	0.252620	−	0.967566i	$-0.418708\pi$
$571$	0.636898	+	0.156981i	0.0266533	+	0.00656946i	−0.225966	+	0.974135i	$0.572554\pi$
$572$	21.7501	+	2.69885i	0.909416	+	0.112845i
$573$	31.7711	−	7.83088i	1.32726	−	0.327140i
$574$	−0.766772	−	9.49818i	−0.0320045	−	0.396446i
$575$	15.6277	−	5.21730i	0.651720	−	0.217576i
$576$	−3.49651	−	3.64025i	−0.145688	−	0.151677i
$577$			12.4648i			0.518916i	0.965754	+	0.259458i	$0.0835440\pi$
$577$			12.4648i			0.518916i	−0.965754	+	0.259458i	$0.916456\pi$
$578$	23.1575	−	22.2431i	0.963227	−	0.925192i
$579$	−10.0936	−	8.24114i	−0.419474	−	0.342490i
$580$	−37.7075	+	71.8456i	−1.56572	+	2.98323i
$581$	−6.88757	+	1.11934i	−0.285745	+	0.0464380i
$582$	−44.9133	+	28.4015i	−1.86172	+	1.17728i
$583$	16.4350	−	7.79851i	0.680668	−	0.322981i
$584$	19.8464	−	28.7525i	0.821251	−	1.18979i
$585$	−5.53234	+	0.208411i	−0.228734	+	0.00861674i
$586$	16.3823	+	23.7338i	0.676746	+	0.980436i
$587$	−27.3535	−	15.7925i	−1.12900	−	0.651828i	−0.185316	−	0.982679i	$-0.559331\pi$
$587$	−27.3535	−	15.7925i	−1.12900	−	0.651828i	−0.943683	+	0.330851i	$0.892664\pi$
$588$	2.63712	+	5.55762i	0.108753	+	0.229192i
$589$	36.6674	+	12.2414i	1.51086	+	0.504398i
$590$	3.61668	−	14.6735i	0.148897	−	0.604097i
$591$	1.95286	−	0.0786976i	0.0803299	−	0.00323719i
$592$	−29.9431	+	1.20667i	−1.23065	+	0.0495937i
$593$	−4.47834	+	18.1694i	−0.183904	+	0.746126i	0.804459	+	0.594008i	$0.202455\pi$
$593$	−4.47834	+	18.1694i	−0.183904	+	0.746126i	−0.988362	+	0.152118i	$0.951391\pi$
$594$	20.0682	+	6.69975i	0.823409	+	0.274894i
$595$	5.88964	+	12.4122i	0.241452	+	0.508849i
$596$	−27.5982	−	15.9338i	−1.13047	−	0.652675i
$597$	−13.7336	−	19.8966i	−0.562081	−	0.814315i
$598$	16.2373	+	38.3894i	0.663994	+	1.56986i
$599$	−12.7312	+	18.4443i	−0.520182	+	0.753614i	−0.991746	−	0.128218i	$-0.959074\pi$
$599$	−12.7312	+	18.4443i	−0.520182	+	0.753614i	0.471564	+	0.881832i	$0.343690\pi$
$600$	22.0174	−	10.4474i	0.898855	−	0.426512i
$601$	11.1889	−	7.07545i	0.456406	−	0.288614i	−0.286413	−	0.958106i	$-0.592463\pi$
$601$	11.1889	−	7.07545i	0.456406	−	0.288614i	0.742819	+	0.669493i	$0.233488\pi$
$602$	18.8183	−	3.05827i	0.766976	−	0.124646i
$603$	0.446952	−	0.851596i	0.0182013	−	0.0346797i
$604$	−25.5564	−	20.8661i	−1.03987	−	0.849031i
$605$	−17.8529	+	17.1480i	−0.725825	+	0.697165i
$606$			43.4297i			1.76421i
$607$	9.51994	+	9.91131i	0.386402	+	0.402288i	0.885786	−	0.464093i	$-0.153620\pi$
$607$	9.51994	+	9.91131i	0.386402	+	0.402288i	−0.499384	+	0.866381i	$0.666440\pi$
$608$	9.30582	−	3.10674i	0.377401	−	0.125995i
$609$	−2.23999	−	27.7472i	−0.0907689	−	1.12438i
$610$	−63.1548	+	15.5663i	−2.55706	+	0.630259i
$611$	−0.00740514	+	2.82289i	−0.000299580	+	0.114202i
$612$	3.82185	+	0.942001i	0.154489	+	0.0380781i
$613$	1.20002	−	7.38403i	0.0484684	−	0.298238i	−0.951487	−	0.307689i	$-0.900444\pi$
$613$	1.20002	−	7.38403i	0.0484684	−	0.298238i	0.999955	+	0.00945109i	$0.00300842\pi$
$614$	14.4992	+	17.7583i	0.585142	+	0.716668i
$615$	−5.87969	+	4.41830i	−0.237092	+	0.178163i
$616$	−11.4910	+	12.9706i	−0.462985	+	0.522602i
$617$	−0.326394	−	2.00839i	−0.0131401	−	0.0808546i	0.979652	−	0.200704i	$-0.0643229\pi$
$617$	−0.326394	−	2.00839i	−0.0131401	−	0.0808546i	−0.992792	+	0.119849i	$0.961759\pi$
$618$	4.17591	−	51.7279i	0.167980	−	2.08080i
$619$	8.56309	+	34.7418i	0.344179	+	1.39639i	0.846813	+	0.531891i	$0.178518\pi$
$619$	8.56309	+	34.7418i	0.344179	+	1.39639i	−0.502633	+	0.864500i	$0.667635\pi$
$620$	−16.4026	−	56.6282i	−0.658742	−	2.27424i
$621$	5.30013	+	25.9618i	0.212687	+	1.04181i
$622$	−1.78646	+	1.45860i	−0.0716305	+	0.0584845i
$623$	3.64725	−	30.0378i	0.146124	−	1.20344i
$624$	8.92298	+	15.5491i	0.357205	+	0.622462i
$625$	−3.65820	−	30.1280i	−0.146328	−	1.20512i
$626$	29.9399	+	28.7577i	1.19664	+	1.14939i
$627$	−12.6175	+	13.1362i	−0.503895	+	0.524610i
$628$	−36.2073	+	76.3052i	−1.44483	+	3.04491i
$629$	−15.0654	+	10.3989i	−0.600698	+	0.414632i
$630$	4.85910	−	7.68405i	0.193591	−	0.306140i
$631$	−19.9924	−	26.6051i	−0.795885	−	1.05913i	−0.996833	−	0.0795290i	$-0.974658\pi$
$631$	−19.9924	−	26.6051i	−0.795885	−	1.05913i	0.200947	−	0.979602i	$-0.435598\pi$
$632$	−11.0807	−	21.1126i	−0.440768	−	0.839813i
$633$	−3.75016	+	18.3695i	−0.149055	+	0.730121i
$634$	−32.5706	+	2.62937i	−1.29355	+	0.104426i
$635$	−42.0662	−	12.1846i	−1.66934	−	0.483532i
$636$	61.9774	+	32.5282i	2.45756	+	1.28983i
$637$	−0.722219	−	3.58563i	−0.0286154	−	0.142068i
$638$	−24.4420	+	12.8281i	−0.967667	+	0.507871i
$639$	5.91552	−	1.20766i	0.234014	−	0.0477744i
$640$	−47.5334	−	35.7190i	−1.87892	−	1.41192i
$641$	0.523719	+	12.9959i	0.0206856	+	0.513309i	0.976007	+	0.217740i	$0.0698684\pi$
$641$	0.523719	+	12.9959i	0.0206856	+	0.513309i	−0.955321	+	0.295569i	$0.904491\pi$
$642$	54.1424	−	20.5335i	2.13683	−	0.810392i
$643$	−1.19493	+	0.346117i	−0.0471236	+	0.0136495i	−0.301696	−	0.953404i	$-0.597553\pi$
$643$	−1.19493	+	0.346117i	−0.0471236	+	0.0136495i	0.254572	+	0.967054i	$0.418065\pi$
$644$	−44.1649	−	9.01633i	−1.74034	−	0.355293i
$645$	−9.75777	−	11.0142i	−0.384212	−	0.433686i
$646$	−21.7373	+	26.6233i	−0.855241	+	1.04748i
$647$	−1.58493	+	39.3297i	−0.0623102	+	1.54621i	0.601843	+	0.798614i	$0.294433\pi$
$647$	−1.58493	+	39.3297i	−0.0623102	+	1.54621i	−0.664153	+	0.747596i	$0.731208\pi$
$648$	10.1561	+	30.4213i	0.398970	+	1.19506i
$649$	2.53425	−	2.24515i	0.0994778	−	0.0881297i
$650$	−29.5037	+	5.94265i	−1.15723	+	0.233090i
$651$	15.1399	+	13.4128i	0.593378	+	0.525687i
$652$	−0.521350	+	1.22365i	−0.0204176	+	0.0479219i
$653$	−10.7782	+	18.6684i	−0.421784	+	0.730552i	−0.996114	−	0.0880721i	$-0.971929\pi$
$653$	−10.7782	+	18.6684i	−0.421784	+	0.730552i	0.574330	+	0.818624i	$0.305263\pi$
$654$	−15.9651	−	27.6523i	−0.624283	−	1.08129i
$655$	32.7434	−	3.97577i	1.27939	−	0.155346i
$656$	−4.59843	−	2.18198i	−0.179539	−	0.0851921i
$657$	−3.55631	+	2.05323i	−0.138745	+	0.0801043i
$658$	−3.81510	−	2.63337i	−0.148728	−	0.102660i
$659$	−17.0426	+	7.26119i	−0.663887	+	0.282856i	−0.697506	−	0.716579i	$-0.745707\pi$
$659$	−17.0426	+	7.26119i	−0.663887	+	0.282856i	0.0336190	+	0.999435i	$0.489297\pi$
$660$	27.4191	+	4.45603i	1.06729	+	0.173451i
$661$	−23.7847	+	31.6518i	−0.925119	+	1.23111i	0.0475388	+	0.998869i	$0.484862\pi$
$661$	−23.7847	+	31.6518i	−0.925119	+	1.23111i	−0.972658	+	0.232241i	$0.925394\pi$
$662$	0.583381	+	1.53825i	0.0226738	+	0.0597858i
$663$	9.68339	+	5.11468i	0.376072	+	0.198638i
$664$	−4.54544	+	11.9854i	−0.176397	+	0.465122i
$665$	27.9404	+	44.1843i	1.08348	+	1.71339i
$666$	11.1445	+	4.74824i	0.431842	+	0.183991i
$667$	−29.2193	−	18.4772i	−1.13138	−	0.715439i
$668$	61.5019	+	7.46769i	2.37958	+	0.288933i
$669$	1.95788	+	4.59531i	0.0756959	+	0.177665i
$670$	4.05577	−	12.1485i	0.156688	−	0.469338i
$671$	−13.6252	−	5.16736i	−0.525996	−	0.199484i
$672$	5.11667	+	0.413060i	0.197380	+	0.0159341i
$673$	−6.04021	+	20.8532i	−0.232833	+	0.803833i	0.755970	+	0.654606i	$0.227166\pi$
$673$	−6.04021	+	20.8532i	−0.232833	+	0.803833i	−0.988803	+	0.149227i	$0.952322\pi$
$674$	8.24000	+	0.332061i	0.317393	+	0.0127905i
$675$	−19.1321			−0.736396
$676$	−13.6973	−	48.2342i	−0.526820	−	1.85516i
$677$	−5.76839			−0.221697			−0.110849	−	0.993837i	$-0.535357\pi$
$677$	−5.76839			−0.221697			−0.110849	+	0.993837i	$0.535357\pi$
$678$	64.2139	+	2.58773i	2.46612	+	0.0993813i
$679$	−9.50641	+	32.8200i	−0.364823	+	1.25951i
$680$	25.1558	+	2.03078i	0.964679	+	0.0778770i
$681$	−27.0880	−	10.2731i	−1.03801	−	0.393667i
$682$	6.35136	−	19.0247i	0.243206	−	0.728492i
$683$	12.9634	+	30.4262i	0.496031	+	1.16423i	0.960410	+	0.278591i	$0.0898675\pi$
$683$	12.9634	+	30.4262i	0.496031	+	1.16423i	−0.464379	+	0.885637i	$0.653722\pi$
$684$	14.8687	+	1.80538i	0.568518	+	0.0690306i
$685$	0.851743	+	0.538610i	0.0325434	+	0.0205792i
$686$	43.6559	+	18.6000i	1.66679	+	0.710152i
$687$	−7.68172	−	12.1477i	−0.293076	−	0.463463i
$688$	3.61110	−	9.52170i	0.137672	−	0.363011i
$689$	−31.0791	−	27.6796i	−1.18402	−	1.05451i
$690$	18.7339	+	49.3974i	0.713189	+	1.88053i
$691$	10.3260	−	13.7415i	0.392821	−	0.522750i	−0.559097	−	0.829102i	$-0.688852\pi$
$691$	10.3260	−	13.7415i	0.392821	−	0.522750i	0.951918	+	0.306352i	$0.0991086\pi$
$692$	−25.5541	−	4.15294i	−0.971421	−	0.157871i
$693$	1.87381	−	0.798355i	0.0711801	−	0.0303270i
$694$	−2.49696	−	1.72353i	−0.0947832	−	0.0654242i
$695$	−24.9895	+	14.4277i	−0.947907	+	0.547274i
$696$	−46.1997	−	21.9221i	−1.75120	−	0.830953i
$697$	−3.08652	+	0.374771i	−0.116910	+	0.0141955i
$698$	−1.28200	−	2.22049i	−0.0485243	−	0.0840466i
$699$	−22.5952	+	39.1361i	−0.854630	+	1.48026i
$700$	12.7572	−	29.9423i	0.482177	−	1.13171i
$701$	22.3455	+	19.7964i	0.843979	+	0.747700i	0.969683	−	0.244368i	$-0.0785805\pi$
$701$	22.3455	+	19.7964i	0.843979	+	0.747700i	−0.125704	+	0.992068i	$0.540119\pi$
$702$	−3.76825	−	48.2561i	−0.142223	−	1.82131i
$703$	−52.1385	+	46.1907i	−1.96644	+	1.74211i
$704$	−4.76861	−	14.2837i	−0.179724	−	0.538339i
$705$	−0.144068	+	3.57502i	−0.00542592	+	0.134643i
$706$	2.30737	−	2.82601i	0.0868389	−	0.106358i
$707$	18.5179	+	20.9024i	0.696437	+	0.786115i
$708$	12.7639	+	2.60578i	0.479698	+	0.0979310i
$709$	31.1644	−	9.02688i	1.17040	−	0.339011i	0.364583	−	0.931171i	$-0.381212\pi$
$709$	31.1644	−	9.02688i	1.17040	−	0.339011i	0.805821	+	0.592160i	$0.201725\pi$
$710$	75.1763	−	28.5106i	2.82132	−	1.06998i
$711$	0.112849	+	2.80031i	0.00423215	+	0.105020i
$712$	−44.4363	−	33.3917i	−1.66532	−	1.25141i
$713$	24.6118	−	5.02453i	0.921717	−	0.188170i
$714$	−15.9238	+	8.35745i	−0.595933	+	0.312770i
$715$	−15.1782	−	6.51394i	−0.567634	−	0.243608i
$716$	−68.9522	−	36.1889i	−2.57687	−	1.35244i
$717$	−26.5511	−	7.69062i	−0.991568	−	0.287211i
$718$	−36.1872	+	2.92133i	−1.35049	+	0.109023i
$719$	−4.42395	+	21.6699i	−0.164985	+	0.808152i	0.810095	+	0.586299i	$0.199416\pi$
$719$	−4.42395	+	21.6699i	−0.164985	+	0.808152i	−0.975080	+	0.221853i	$0.928789\pi$
$720$	−2.25676	−	4.29989i	−0.0841044	−	0.160247i
$721$	−20.0463	−	26.6768i	−0.746565	−	0.993497i
$722$	−45.3231	+	71.6727i	−1.68675	+	2.66738i
$723$	12.4874	−	8.61946i	0.464413	−	0.320561i
$724$	−11.9110	+	25.1018i	−0.442667	+	0.932902i
$725$	17.2917	−	18.0026i	0.642199	−	0.668600i
$726$	−23.3693	−	22.4465i	−0.867317	−	0.833069i
$727$	4.36909	+	35.9827i	0.162041	+	1.33452i	0.816025	+	0.578016i	$0.196173\pi$
$727$	4.36909	+	35.9827i	0.162041	+	1.33452i	−0.653985	+	0.756508i	$0.726904\pi$
$728$	37.5710	+	12.6527i	1.39247	+	0.468940i
$729$	3.60797	−	29.7143i	0.133629	−	1.10053i
$730$	−42.3595	+	34.5855i	−1.56780	+	1.28007i
$731$	−1.24429	−	6.09495i	−0.0460218	−	0.225430i
$732$	−15.5994	−	53.8555i	−0.576572	−	1.99056i
$733$	−12.3287	−	50.0196i	−0.455372	−	1.84752i	−0.526683	−	0.850062i	$-0.676565\pi$
$733$	−12.3287	−	50.0196i	−0.455372	−	1.84752i	0.0713116	−	0.997454i	$-0.477282\pi$
$734$	5.07918	−	62.9169i	0.187476	−	2.32231i
$735$	−0.743655	−	4.57589i	−0.0274301	−	0.168784i
$736$	4.22744	−	4.77179i	0.155825	−	0.175890i
$737$	2.29386	−	1.72373i	0.0844956	−	0.0634943i
$738$	1.30126	+	1.59375i	0.0478999	+	0.0586667i
$739$	3.50535	−	21.5693i	0.128946	−	0.793438i	−0.839342	−	0.543603i	$-0.817060\pi$
$739$	3.50535	−	21.5693i	0.128946	−	0.793438i	0.968288	−	0.249835i	$-0.0803763\pi$
$740$	103.146	+	25.4233i	3.79174	+	0.934580i
$741$	38.9239	+	14.8788i	1.42990	+	0.546586i
$742$	66.3583	−	16.3559i	2.43609	−	0.600442i
$743$	−2.13270	−	26.4183i	−0.0782414	−	0.969193i	−0.910150	−	0.414280i	$-0.864033\pi$
$743$	−2.13270	−	26.4183i	−0.0782414	−	0.969193i	0.831908	−	0.554913i	$-0.187249\pi$
$744$	35.2438	−	11.7661i	1.29210	−	0.431367i
$745$	16.6365	+	17.3205i	0.609515	+	0.634572i
$746$		−	14.1788i		−	0.519124i
$747$	1.08661	−	1.04370i	0.0397569	−	0.0381870i
$748$	9.09649	+	7.42705i	0.332601	+	0.271560i
$749$	17.3031	−	32.9683i	0.632241	−	1.20463i
$750$	16.9308	−	2.75152i	0.618225	−	0.100471i
$751$	2.63246	−	1.66466i	0.0960597	−	0.0607445i	−0.485572	−	0.874197i	$-0.661389\pi$
$751$	2.63246	−	1.66466i	0.0960597	−	0.0607445i	0.581632	+	0.813452i	$0.302414\pi$
$752$	−2.23704	+	1.06149i	−0.0815764	+	0.0387085i
$753$	−9.23126	+	13.3738i	−0.336406	+	0.487368i
$754$	48.8128	+	40.0683i	1.77766	+	1.45920i
$755$	14.1244	+	20.4627i	0.514038	+	0.744713i
$756$	45.3312	+	26.1720i	1.64868	+	0.951866i
$757$	−2.22050	−	4.67961i	−0.0807056	−	0.170083i	0.859086	−	0.511831i	$-0.171033\pi$
$757$	−2.22050	−	4.67961i	−0.0807056	−	0.170083i	−0.939792	+	0.341747i	$0.888981\pi$
$758$	−32.8683	−	10.9731i	−1.19383	−	0.398559i
$759$	−2.83248	+	11.4918i	−0.102813	+	0.417127i
$760$	95.9546	−	3.86684i	3.48064	−	0.140265i
$761$	1.54541	−	0.0622780i	0.0560211	−	0.00225757i	−0.0122396	−	0.999925i	$-0.503896\pi$
$761$	1.54541	−	0.0622780i	0.0560211	−	0.00225757i	0.0682607	+	0.997668i	$0.478255\pi$
$762$	13.7194	−	55.6618i	0.497001	−	2.01641i
$763$	−19.4745	−	6.50153i	−0.705023	−	0.235371i
$764$	−34.4141	−	72.5261i	−1.24506	−	2.62390i
$765$	−2.56899	−	1.48321i	−0.0928820	−	0.0536255i
$766$	−32.5917	−	47.2173i	−1.17759	−	1.70603i
$767$

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)

\(f(q)\)	\(=\)	\(q+(-2.41817 - 0.0974488i) q^{2} +(-0.437408 + 1.51011i) q^{3} +(3.84452 + 0.310362i) q^{4} +(-2.71784 - 1.03074i) q^{5} +(1.20488 - 3.60907i) q^{6} +(-0.958962 - 2.25077i) q^{7} +(-4.46148 - 0.541722i) q^{8} +(0.446473 + 0.282332i) q^{9} +O(q^{10})\)	\(q+(-2.41817 - 0.0974488i) q^{2} +(-0.437408 + 1.51011i) q^{3} +(3.84452 + 0.310362i) q^{4} +(-2.71784 - 1.03074i) q^{5} +(1.20488 - 3.60907i) q^{6} +(-0.958962 - 2.25077i) q^{7} +(-4.46148 - 0.541722i) q^{8} +(0.446473 + 0.282332i) q^{9} +(6.47174 + 2.75735i) q^{10} +(0.842314 + 1.33201i) q^{11} +(-2.15030 + 5.66988i) q^{12} +(2.05596 - 2.96193i) q^{13} +(2.09959 + 5.53618i) q^{14} +(2.74533 - 3.65337i) q^{15} +(3.12165 + 0.507318i) q^{16} +(1.77732 - 0.757244i) q^{17} +(-1.05213 - 0.726235i) q^{18} +(6.36630 - 3.67559i) q^{19} +(-10.1289 - 4.80621i) q^{20} +(3.81835 - 0.463632i) q^{21} +(-1.90705 - 3.30311i) q^{22} +(2.38841 - 4.13685i) q^{23} +(2.76954 - 6.50036i) q^{24} +(2.58167 + 2.28716i) q^{25} +(-5.26030 + 6.96208i) q^{26} +(-4.15202 + 3.67837i) q^{27} +(-2.98820 - 8.95074i) q^{28} +(0.291416 - 7.23142i) q^{29} +(-6.99469 + 8.56693i) q^{30} +(3.48709 + 3.93612i) q^{31} +(1.30761 + 0.266950i) q^{32} +(-2.37992 + 0.689352i) q^{33} +(-4.37164 + 1.65794i) q^{34} +(0.286348 + 7.10566i) q^{35} +(1.62885 + 1.22400i) q^{36} +(-9.28405 + 1.89535i) q^{37} +(-15.7530 + 8.26779i) q^{38} +(3.57353 + 4.40029i) q^{39} +(11.5672 + 6.07094i) q^{40} +(-1.54584 - 0.447759i) q^{41} +(-9.27860 + 0.749046i) q^{42} +(0.644074 - 3.15488i) q^{43} +(2.82489 + 5.38238i) q^{44} +(-0.922430 - 1.22753i) q^{45} +(-6.17871 + 9.77085i) q^{46} +(-0.644340 + 0.444756i) q^{47} +(-2.13154 + 4.49212i) q^{48} +(0.702733 - 0.731622i) q^{49} +(-6.02002 - 5.78230i) q^{50} +(0.366107 + 3.01516i) q^{51} +(8.82346 - 10.7491i) q^{52} +(1.39133 - 11.4586i) q^{53} +(10.3987 - 8.49031i) q^{54} +(-0.916314 - 4.48840i) q^{55} +(3.05910 + 10.5612i) q^{56} +(2.76586 + 11.2215i) q^{57} +(-1.40939 + 17.4584i) q^{58} +(-0.344613 - 2.12049i) q^{59} +(11.6883 - 13.1934i) q^{60} +(-7.39192 + 5.55467i) q^{61} +(-8.04881 - 9.85800i) q^{62} +(0.207314 - 1.27565i) q^{63} +(-9.27741 - 2.28668i) q^{64} +(-8.64075 + 5.93088i) q^{65} +(5.82221 - 1.43505i) q^{66} +(-0.146501 - 1.81474i) q^{67} +(7.06795 - 2.35963i) q^{68} +(5.20238 + 5.41625i) q^{69} -17.2106i q^{70} +(8.24282 - 7.91734i) q^{71} +(-1.83898 - 1.50148i) q^{72} +(-3.61262 + 6.88327i) q^{73} +(22.6351 - 3.67856i) q^{74} +(-4.58309 + 2.89817i) q^{75} +(25.6161 - 12.1550i) q^{76} +(2.19030 - 3.17320i) q^{77} +(-8.21259 - 10.9889i) q^{78} +(3.01380 + 4.36625i) q^{79} +(-7.96123 - 4.59642i) q^{80} +(-3.05923 - 6.44720i) q^{81} +(3.69448 + 1.23340i) q^{82} +(0.682568 - 2.76929i) q^{83} +(14.8236 - 0.597372i) q^{84} +(-5.61098 + 0.226115i) q^{85} +(-1.86492 + 7.56627i) q^{86} +(10.7928 + 3.60315i) q^{87} +(-3.03639 - 6.39905i) q^{88} +(10.7109 + 6.18392i) q^{89} +(2.11097 + 3.05827i) q^{90} +(-8.63819 - 1.78712i) q^{91} +(10.4662 - 15.1629i) q^{92} +(-7.46924 + 3.54420i) q^{93} +(1.60146 - 1.01270i) q^{94} +(-21.0912 + 3.42765i) q^{95} +(-0.975080 + 1.85786i) q^{96} +(-10.8183 - 8.83290i) q^{97} +(-1.77062 + 1.70070i) q^{98} +0.832521i 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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