LMFDB - Embedded newform 169.2.k.a.127.2

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			127.2
Character	$\chi$	$=$	169.127
Dual form			169.2.k.a.4.2

$q$-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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{77}{78}\right)$

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	−0.875791	−	0.482690i	$-0.839660\pi$
$2$	−2.41817	+	0.0974488i	−1.70990	+	0.0689067i	−0.834111	+	0.551597i	$0.814019\pi$
$3$	−0.437408	−	1.51011i	−0.252538	−	0.871861i	−0.982166	−	0.188017i	$-0.939794\pi$
$3$	−0.437408	−	1.51011i	−0.252538	−	0.871861i	0.729628	−	0.683844i	$-0.239693\pi$
$4$	3.84452	−	0.310362i	1.92226	−	0.155181i
$5$	−2.71784	+	1.03074i	−1.21545	+	0.460961i	−0.877214	−	0.480099i	$-0.840601\pi$
$5$	−2.71784	+	1.03074i	−1.21545	+	0.460961i	−0.338240	+	0.941060i	$0.609832\pi$
$6$	1.20488	+	3.60907i	0.491891	+	1.47339i
$7$	−0.958962	+	2.25077i	−0.362453	+	0.850709i	0.634516	+	0.772910i	$0.281200\pi$
$7$	−0.958962	+	2.25077i	−0.362453	+	0.850709i	−0.996969	+	0.0777993i	$0.975211\pi$
$8$	−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	−0.694005	−	0.719970i	$-0.744155\pi$
$11$	0.842314	−	1.33201i	0.253967	−	0.401617i	0.947972	+	0.318353i	$0.103130\pi$
$12$	−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	0.596589	−	0.802547i	$-0.296522\pi$
$17$	1.77732	+	0.757244i	0.431062	+	0.183659i	−0.165527	+	0.986205i	$0.552932\pi$
$18$	−1.05213	+	0.726235i	−0.247990	+	0.171175i
$19$	6.36630	+	3.67559i	1.46053	+	0.843237i	0.999036	−	0.0439059i	$-0.0139802\pi$
$19$	6.36630	+	3.67559i	1.46053	+	0.843237i	0.461494	+	0.887143i	$0.347314\pi$
$20$	−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	0.999997	−	0.00228656i	$-0.000727835\pi$
$23$	2.38841	+	4.13685i	0.498018	+	0.862593i	−0.501979	+	0.864880i	$0.667395\pi$
$24$	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	0.767039	+	0.641601i	$0.221729\pi$
$29$	0.291416	+	7.23142i	0.0541147	+	1.34284i	−0.712924	+	0.701241i	$0.752630\pi$
$30$	−6.99469	−	8.56693i	−1.27705	−	1.56410i
$31$	3.48709	−	3.93612i	0.626301	−	0.706947i	−0.346641	−	0.937998i	$-0.612678\pi$
$31$	3.48709	−	3.93612i	0.626301	−	0.706947i	0.972942	+	0.231051i	$0.0742163\pi$
$32$	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	−0.637694	−	0.770290i	$-0.720112\pi$
$37$	−9.28405	−	1.89535i	−1.52629	−	0.311594i	−0.888593	+	0.458696i	$0.848317\pi$
$38$	−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	−0.396722	−	0.917939i	$-0.629852\pi$
$41$	−1.54584	+	0.447759i	−0.241420	+	0.0699283i	0.155302	+	0.987867i	$0.450365\pi$
$42$	−9.27860	−	0.749046i	−1.43172	−	0.115580i
$43$	0.644074	+	3.15488i	0.0982204	+	0.481115i	0.998911	+	0.0466544i	$0.0148560\pi$
$43$	0.644074	+	3.15488i	0.0982204	+	0.481115i	−0.900691	+	0.434461i	$0.856939\pi$
$44$	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	0.520145	−	0.854078i	$-0.325878\pi$
$47$	−0.644340	−	0.444756i	−0.0939867	−	0.0648743i	−0.614131	+	0.789204i	$0.710493\pi$
$48$	−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	0.700643	+	0.713512i	$0.252897\pi$
$53$	1.39133	+	11.4586i	0.191114	+	1.57397i	−0.509529	+	0.860454i	$0.670180\pi$
$54$	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	−0.999784	−	0.0208031i	$-0.993378\pi$
$59$	−0.344613	+	2.12049i	−0.0448647	+	0.276064i	0.954919	+	0.296867i	$0.0959418\pi$
$60$	11.6883	+	13.1934i	1.50896	+	1.70326i
$61$	−7.39192	−	5.55467i	−0.946439	−	0.711202i	0.0109697	−	0.999940i	$-0.496508\pi$
$61$	−7.39192	−	5.55467i	−0.946439	−	0.711202i	−0.957408	+	0.288737i	$0.906765\pi$
$62$	−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	0.981625	+	0.190821i	$0.0611149\pi$
$67$	−0.146501	+	1.81474i	−0.0178980	+	0.221706i	−0.999523	+	0.0308858i	$0.990167\pi$
$68$	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	0.998187	−	0.0601862i	$-0.0191695\pi$
$71$	8.24282	+	7.91734i	0.978243	+	0.939615i	−0.0199445	+	0.999801i	$0.506349\pi$
$72$	−1.83898	+	1.50148i	−0.216726	+	0.176952i
$73$	−3.61262	−	6.88327i	−0.422825	−	0.805626i	0.577114	−	0.816663i	$-0.304179\pi$
$73$	−3.61262	−	6.88327i	−0.422825	−	0.805626i	−0.999939	+	0.0110379i	$0.996486\pi$
$74$	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	−0.615936	−	0.787796i	$-0.711222\pi$
$79$	3.01380	−	4.36625i	0.339080	−	0.491242i	0.955016	+	0.296554i	$0.0958376\pi$
$80$	−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	0.996434	−	0.0843812i	$-0.0268914\pi$
$83$	0.682568	+	2.76929i	0.0749215	+	0.303969i	−0.921512	+	0.388350i	$0.873045\pi$
$84$	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	0.190075	−	0.981770i	$-0.439127\pi$
$89$	10.7109	−	6.18392i	1.13535	−	0.655494i	0.945275	+	0.326275i	$0.105794\pi$
$90$	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	−0.995205	−	0.0978123i	$-0.968816\pi$
$97$	−10.8183	+	8.83290i	−1.09844	+	0.896845i	−0.103231	+	0.994657i	$0.532918\pi$
$98$	−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	−0.277999	−	0.960581i	$-0.589671\pi$
$101$	−10.8268	−	3.61451i	−1.07731	−	0.359658i	−0.799306	+	0.600924i	$0.794800\pi$
$102$	−0.591484	+	7.32684i	−0.0585656	+	0.725465i
$103$	13.2430	+	3.26412i	1.30488	+	0.321623i	0.829671	−	0.558252i	$-0.188528\pi$
$103$	13.2430	+	3.26412i	1.30488	+	0.321623i	0.475205	+	0.879875i	$0.342374\pi$
$104$	−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	−0.0594690	−	0.998230i	$-0.518941\pi$
$107$	9.62499	−	11.7885i	0.930483	−	1.13963i	0.989952	−	0.141404i	$-0.0451618\pi$
$108$	−17.1042	−	12.8529i	−1.64585	−	1.23678i
$109$	5.56485	+	6.28142i	0.533016	+	0.601651i	0.951907	−	0.306386i	$-0.0991197\pi$
$109$	5.56485	+	6.28142i	0.533016	+	0.601651i	−0.418891	+	0.908036i	$0.637581\pi$
$110$	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	−0.362307	−	0.932059i	$-0.618011\pi$
$113$	4.69921	−	16.2236i	0.442065	−	1.52619i	0.804372	−	0.594126i	$-0.202502\pi$
$114$	−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	0.726161	−	0.687524i	$-0.241302\pi$
$127$	15.0180	+	1.21238i	1.33263	+	0.107581i	0.606471	+	0.795105i	$0.292585\pi$
$128$	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	−0.0353286	−	0.999376i	$-0.511248\pi$
$131$	−10.0477	−	5.27342i	−0.877868	−	0.460740i	−0.842539	+	0.538635i	$0.818940\pi$
$132$	−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	−0.214515	−	0.976721i	$-0.568817\pi$
$137$	−0.339690	+	0.0693483i	−0.0290217	+	0.00592482i	0.185493	+	0.982646i	$0.440612\pi$
$138$	−12.0524	+	13.6044i	−1.02597	+	1.15808i
$139$	6.27836	+	7.68959i	0.532524	+	0.652223i	0.968874	−	0.247554i	$-0.0796267\pi$
$139$	6.27836	+	7.68959i	0.532524	+	0.652223i	−0.436351	+	0.899777i	$0.643729\pi$
$140$	−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	−0.709154	−	0.705053i	$-0.750923\pi$
$149$	−7.46452	+	3.54196i	−0.611518	+	0.290169i	0.0976366	+	0.995222i	$0.468872\pi$
$150$	11.3651	+	6.56164i	0.927957	+	0.535756i
$151$	−7.03976	+	4.85919i	−0.572887	+	0.395436i	−0.818990	−	0.573808i	$-0.805465\pi$
$151$	−7.03976	+	4.85919i	−0.572887	+	0.395436i	0.246102	+	0.969244i	$0.420850\pi$
$152$	−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	−0.764525	−	0.644594i	$-0.777026\pi$
$157$	−7.76500	−	20.4746i	−0.619715	−	1.63405i	0.144810	−	0.989459i	$-0.453743\pi$
$158$	−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	0.944173	−	0.329449i	$-0.106863\pi$
$163$	−0.109202	−	0.327101i	−0.00855338	−	0.0256205i	−0.952727	+	0.303829i	$0.901735\pi$
$164$	−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	0.589428	−	0.807821i	$-0.299353\pi$
$167$	16.0495	−	0.646773i	1.24195	−	0.0500488i	0.652520	+	0.757772i	$0.273712\pi$
$168$	−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	−0.332137	−	0.943231i	$-0.607770\pi$
$173$	−6.69049	+	0.540112i	−0.508668	+	0.0410640i	−0.176531	+	0.984295i	$0.556488\pi$
$174$	−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	−0.951383	−	0.308011i	$-0.900337\pi$
$179$	−18.5741	+	7.91367i	−1.38829	+	0.591495i	−0.436907	+	0.899506i	$0.643926\pi$
$180$	−3.16532	+	5.00556i	−0.235929	+	0.373092i
$181$	−2.55442	−	6.73546i	−0.189869	−	0.500643i	0.805951	−	0.591982i	$-0.201654\pi$
$181$	−2.55442	−	6.73546i	−0.189869	−	0.500643i	−0.995820	+	0.0913394i	$0.970885\pi$
$182$	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	0.193373	+	0.981125i	$0.438057\pi$
$191$	−10.4066	+	18.0247i	−0.752993	+	1.30422i	−0.946366	+	0.323096i	$0.895276\pi$
$192$	7.51114	+	13.0097i	0.542070	+	0.938892i
$193$	−3.24871	−	7.62501i	−0.233847	−	0.548860i	0.761171	−	0.648551i	$-0.224625\pi$
$193$	−3.24871	−	7.62501i	−0.233847	−	0.548860i	−0.995018	+	0.0996912i	$0.968215\pi$
$194$	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	−0.961630	−	0.274351i	$-0.911537\pi$
$197$	−0.393664	+	1.17917i	−0.0280474	+	0.0840122i	0.933582	+	0.358363i	$0.116665\pi$
$198$	0.0811282	+	2.01317i	0.00576553	+	0.143070i
$199$	−9.72543	−	11.9115i	−0.689418	−	0.844383i	0.304727	−	0.952440i	$-0.401435\pi$
$199$	−9.72543	−	11.9115i	−0.689418	−	0.844383i	−0.994145	+	0.108056i	$0.965537\pi$
$200$	−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	0.482522	−	0.875884i	$-0.339721\pi$
$211$	11.8864	+	0.959571i	0.818295	+	0.0660596i	0.335772	+	0.941943i	$0.391003\pi$
$212$	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	0.711258	−	0.702931i	$-0.248126\pi$
$223$	2.46102	+	2.00936i	0.164802	+	0.134557i	−0.546456	+	0.837488i	$0.684023\pi$
$224$	−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	−0.837868	−	0.545873i	$-0.816198\pi$
$227$	−1.48276	−	18.3673i	−0.0984143	−	1.21908i	0.739454	−	0.673207i	$-0.235084\pi$
$228$	7.15066	−	43.9998i	0.473564	−	2.91396i
$229$	−6.06220	−	6.84281i	−0.400602	−	0.452186i	0.513247	−	0.858241i	$-0.328442\pi$
$229$	−6.06220	−	6.84281i	−0.400602	−	0.452186i	−0.913848	+	0.406055i	$0.866904\pi$
$230$	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	0.833546	−	0.552449i	$-0.186307\pi$
$233$	27.9086	−	6.87884i	1.82835	−	0.450648i	0.994805	+	0.101801i	$0.0324606\pi$
$234$	−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	$-0.807466\pi$
$239$		−	17.5823i		−	1.13730i	0.822579	−	0.568651i	$-0.192534\pi$
$240$	10.4234	+	10.0118i	0.672827	+	0.646259i
$241$	−7.47584	+	6.10384i	−0.481561	+	0.393183i	−0.841896	−	0.539641i	$-0.818560\pi$
$241$	−7.47584	+	6.10384i	−0.481561	+	0.393183i	0.360334	+	0.932823i	$0.382663\pi$
$242$	−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	0.0100743	−	0.999949i	$-0.496793\pi$
$251$	9.80427	−	3.27315i	0.618840	−	0.206599i	0.608766	+	0.793350i	$0.291665\pi$
$252$	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	0.367116	+	0.930175i	$0.380345\pi$
$257$	−9.38761	+	19.7840i	−0.585583	+	1.23409i	−0.952699	+	0.303915i	$0.901706\pi$
$258$	−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	0.146099	−	0.989270i	$-0.453328\pi$
$263$	−11.1092	−	7.02506i	−0.685026	−	0.433184i	−0.831125	+	0.556086i	$0.812303\pi$
$264$	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	−0.946540	−	0.322586i	$-0.895448\pi$
$269$	−9.61280	+	10.0080i	−0.586103	+	0.610198i	0.360437	+	0.932783i	$0.382627\pi$
$270$	−37.0134	−	12.3569i	−2.25256	−	0.752016i
$271$	0.759241	−	9.40489i	0.0461206	−	0.571306i	−0.931889	−	0.362745i	$-0.881840\pi$
$271$	0.759241	−	9.40489i	0.0461206	−	0.571306i	0.978009	−	0.208562i	$-0.0668782\pi$
$272$	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	0.938059	−	0.346475i	$-0.112622\pi$
$277$	14.4172	+	10.8338i	0.866247	+	0.650943i	−0.0718116	+	0.997418i	$0.522878\pi$
$278$	−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	−0.932161	−	0.362043i	$-0.882079\pi$
$281$	1.03053	−	4.18104i	0.0614764	−	0.249420i	0.993638	+	0.112624i	$0.0359254\pi$
$282$	0.828799	−	2.86134i	0.0493542	−	0.170391i
$283$	1.11476	−	5.46047i	0.0662658	−	0.324591i	−0.933123	−	0.359558i	$-0.882927\pi$
$283$	1.11476	−	5.46047i	0.0662658	−	0.324591i	0.999388	+	0.0349668i	$0.0111325\pi$
$284$	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	−0.958555	−	0.284909i	$-0.908037\pi$
$293$	−7.15857	+	9.52632i	−0.418208	+	0.556534i	0.540347	+	0.841442i	$0.318293\pi$
$294$	−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	−0.899901	−	0.436094i	$-0.856362\pi$
$307$	−6.28170	+	7.09058i	−0.358516	+	0.404681i	0.541385	+	0.840775i	$0.317900\pi$
$308$	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	0.683104	−	0.730321i	$-0.260629\pi$
$311$	0.713301	+	0.631929i	0.0404476	+	0.0358334i	−0.642657	+	0.766154i	$0.722168\pi$
$312$	−13.5595	+	21.5677i	−0.767656	+	1.22103i
$313$	−12.8396	+	11.3749i	−0.725740	+	0.642949i	−0.942858	−	0.333196i	$-0.891873\pi$
$313$	−12.8396	+	11.3749i	−0.725740	+	0.642949i	0.217118	+	0.976145i	$0.430334\pi$
$314$	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	0.487945	−	0.872874i	$-0.337747\pi$
$317$	13.4036	+	1.62749i	0.752819	+	0.0914088i	0.264874	+	0.964283i	$0.414670\pi$
$318$	−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	−0.927142	−	0.374711i	$-0.877742\pi$
$331$	−0.266451	+	0.625385i	−0.0146455	+	0.0343742i	0.912496	+	0.409085i	$0.134152\pi$
$332$	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	−0.505722	−	0.862696i	$-0.668774\pi$
$347$	1.05958	−	0.670041i	0.0568815	−	0.0359697i	0.562604	+	0.826727i	$0.309800\pi$
$348$	40.3747	−	17.2020i	2.16431	−	0.922126i
$349$	0.566237	−	0.895433i	0.0303100	−	0.0479314i	−0.829695	−	0.558217i	$-0.811486\pi$
$349$	0.566237	−	0.895433i	0.0303100	−	0.0479314i	0.860005	+	0.510285i	$0.170460\pi$
$350$	−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	0.774699	−	0.632331i	$-0.217902\pi$
$353$	−0.905614	−	1.20515i	−0.0482010	−	0.0641438i	−0.822900	+	0.568187i	$0.807645\pi$
$354$	−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	0.503671	−	0.863896i	$-0.331982\pi$
$359$	14.8919	+	1.80820i	0.785962	+	0.0954331i	0.282291	+	0.959329i	$0.408906\pi$
$360$	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	−0.759348	−	0.650684i	$-0.774482\pi$
$367$	−1.05021	−	26.0608i	−0.0548207	−	1.36036i	0.704528	−	0.709676i	$-0.251159\pi$
$368$	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	−0.981521	−	0.191353i	$-0.938712\pi$
$373$	0.235906	−	5.85396i	0.0122148	−	0.303106i	0.993736	−	0.111753i	$-0.0356466\pi$
$374$	−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	0.0944934	−	0.995525i	$-0.469877\pi$
$379$	13.7528	−	3.98354i	0.706433	−	0.204621i	0.611939	+	0.790905i	$0.290390\pi$
$380$	−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	−0.272268	−	0.962221i	$-0.587774\pi$
$383$	14.2416	−	18.9521i	0.727712	−	0.968409i	0.999981	−	0.00618801i	$-0.00196972\pi$
$384$	−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	−0.971078	−	0.238762i	$-0.923258\pi$
$389$	0.570424	−	4.69787i	0.0289217	−	0.238191i	1.00000		0.000570414i	$0.000181568\pi$
$390$	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	0.913021	+	0.407912i	$0.133743\pi$
$397$	−1.63753	+	10.0761i	−0.0821852	+	0.505706i	−0.995207	+	0.0977943i	$0.968821\pi$
$398$	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	−0.992407	−	0.122999i	$-0.960749\pi$
$401$	−1.80270	−	11.0925i	−0.0900228	−	0.553932i	0.902384	−	0.430933i	$-0.141815\pi$
$402$	−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	0.999791	−	0.0204511i	$-0.00651023\pi$
$409$	20.6204	+	19.8062i	1.01961	+	0.979352i	0.0198231	+	0.999804i	$0.493690\pi$
$410$	−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	−0.532194	−	0.846622i	$-0.678632\pi$
$419$	9.41980	−	19.8518i	0.460187	−	0.969824i	0.992382	−	0.123202i	$-0.0393163\pi$
$420$	−40.9040	+	13.6558i	−1.99591	+	0.666332i
$421$	−0.0574544	−	0.233101i	−0.00280015	−	0.0113607i	0.969525	−	0.244992i	$-0.0787853\pi$
$421$	−0.0574544	−	0.233101i	−0.00280015	−	0.0113607i	−0.972325	+	0.233631i	$0.924939\pi$
$422$	−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	−0.0419424	−	0.999120i	$-0.513355\pi$
$431$	−17.4885	−	8.29840i	−0.842392	−	0.399720i	−0.800450	+	0.599400i	$0.795406\pi$
$432$	−14.8273	−	9.37620i	−0.713377	−	0.451113i
$433$	12.6799	+	2.06069i	0.609359	+	0.0990305i	0.457258	−	0.889334i	$-0.348832\pi$
$433$	12.6799	+	2.06069i	0.609359	+	0.0990305i	0.152102	+	0.988365i	$0.451396\pi$
$434$	−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	0.337110	−	0.941465i	$-0.390551\pi$
$439$	0.859716	+	0.287015i	0.0410320	+	0.0136985i	−0.296078	+	0.955164i	$0.595679\pi$
$440$	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	−0.184585	−	0.982817i	$-0.559094\pi$
$443$	2.28809	−	0.563964i	0.108711	−	0.0267948i	0.293296	+	0.956022i	$0.405248\pi$
$444$	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	0.874849	+	0.484395i	$0.160960\pi$
$449$	1.88654	+	23.3690i	0.0890315	+	1.10285i	−0.785818	+	0.618458i	$0.787758\pi$
$450$	−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	0.152409	−	0.988317i	$-0.451297\pi$
$457$	24.5000	−	23.5326i	1.14606	−	1.10081i	0.993653	−	0.112490i	$-0.0358827\pi$
$458$	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	0.794605	−	0.607127i	$-0.207678\pi$
$461$	−2.02997	−	3.21013i	−0.0945450	−	0.149511i	−0.889150	+	0.457616i	$0.848704\pi$
$462$	−8.81323	+	11.7283i	−0.410029	+	0.545649i
$463$	9.33044	−	17.7777i	0.433622	−	0.826198i	−0.566376	−	0.824147i	$-0.691655\pi$
$463$	9.33044	−	17.7777i	0.433622	−	0.826198i	0.999998	−	0.00205110i	$-0.000652885\pi$
$464$	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	−0.974835	−	0.222926i	$-0.928439\pi$
$467$	−29.0687	+	15.2565i	−1.34514	+	0.705984i	−0.370305	+	0.928910i	$0.620747\pi$
$468$	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	−0.365224	−	0.930920i	$-0.619008\pi$
$479$	10.6365	−	31.8602i	0.485994	−	1.45573i	0.851219	−	0.524811i	$-0.175864\pi$
$480$	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	−0.494435	−	0.869215i	$-0.664625\pi$
$487$	−2.95358	+	1.40149i	−0.133839	+	0.0635075i	0.360595	+	0.932722i	$0.382574\pi$
$488$	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	0.0226868	−	0.999743i	$-0.492778\pi$
$491$	7.99463	−	1.29925i	0.360793	−	0.0586345i	0.338106	+	0.941108i	$0.390214\pi$
$492$	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	0.616928	−	0.787019i	$-0.288377\pi$
$499$	31.3692	−	3.80890i	1.40428	−	0.170510i	0.787348	+	0.616509i	$0.211454\pi$
$500$	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	0.0181848	−	0.999835i	$-0.494211\pi$
$503$	4.40746	−	0.355807i	0.196519	−	0.0158646i	0.178334	+	0.983970i	$0.442929\pi$
$504$	−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	0.0695458	−	0.997579i	$-0.477845\pi$
$509$	4.94398	−	0.199235i	0.219138	−	0.00883096i	0.149592	+	0.988748i	$0.452204\pi$
$510$	−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	0.539783	+	0.841804i	$0.318506\pi$
$521$	−9.64305	+	25.4266i	−0.422470	+	1.11396i	−0.962253	+	0.272157i	$0.912263\pi$
$522$	−5.55832	−	7.39679i	−0.243281	−	0.323749i
$523$	25.2140	−	4.09768i	1.10253	−	0.179179i	0.418205	−	0.908353i	$-0.362659\pi$
$523$	25.2140	−	4.09768i	1.10253	−	0.179179i	0.684329	+	0.729174i	$0.260095\pi$
$524$	−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	0.161143	−	0.986931i	$-0.448482\pi$
$541$	−8.66868	−	3.28759i	−0.372695	−	0.141345i	−0.533839	+	0.845586i	$0.679251\pi$
$542$	−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	−0.637380	−	0.770550i	$-0.719982\pi$
$547$	−8.54373	+	4.48410i	−0.365304	+	0.191726i	0.272077	+	0.962276i	$0.412290\pi$
$548$	−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	−0.729551	−	0.683927i	$-0.760271\pi$
$557$	−1.78315	+	1.71274i	−0.0755546	+	0.0725712i	0.653996	+	0.756498i	$0.273091\pi$
$558$	−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	−0.992646	−	0.121055i	$-0.961372\pi$
$563$	−2.11109	+	7.28833i	−0.0889718	+	0.307166i	0.903674	+	0.428221i	$0.140860\pi$
$564$	−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	−0.853780	−	0.520633i	$-0.825696\pi$
$569$	−4.12408	+	5.05108i	−0.172890	+	0.211752i	0.680890	+	0.732386i	$0.261593\pi$
$570$	−13.0418	−	80.2493i	−0.546260	−	3.36127i
$571$	0.636898	−	0.156981i	0.0266533	−	0.00656946i	−0.225966	−	0.974135i	$-0.572554\pi$
$571$	0.636898	−	0.156981i	0.0266533	−	0.00656946i	0.252620	+	0.967566i	$0.418708\pi$
$572$	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	$-0.916456\pi$
$577$		−	12.4648i		−	0.518916i	0.965754	−	0.259458i	$-0.0835440\pi$
$578$	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	−0.943683	−	0.330851i	$-0.892664\pi$
$587$	−27.3535	+	15.7925i	−1.12900	+	0.651828i	−0.185316	+	0.982679i	$0.559331\pi$
$588$	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	−0.988362	−	0.152118i	$-0.951391\pi$
$593$	−4.47834	−	18.1694i	−0.183904	−	0.746126i	0.804459	−	0.594008i	$-0.202455\pi$
$594$	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	0.471564	−	0.881832i	$-0.343690\pi$
$599$	−12.7312	−	18.4443i	−0.520182	−	0.753614i	−0.991746	+	0.128218i	$0.959074\pi$
$600$	22.0174	+	10.4474i	0.898855	+	0.426512i
$601$	11.1889	+	7.07545i	0.456406	+	0.288614i	0.742819	−	0.669493i	$-0.233488\pi$
$601$	11.1889	+	7.07545i	0.456406	+	0.288614i	−0.286413	+	0.958106i	$0.592463\pi$
$602$	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	−0.499384	−	0.866381i	$-0.666440\pi$
$607$	9.51994	−	9.91131i	0.386402	−	0.402288i	0.885786	+	0.464093i	$0.153620\pi$
$608$	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	0.999955	−	0.00945109i	$-0.00300842\pi$
$613$	1.20002	+	7.38403i	0.0484684	+	0.298238i	−0.951487	+	0.307689i	$0.900444\pi$
$614$	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	−0.992792	−	0.119849i	$-0.961759\pi$
$617$	−0.326394	+	2.00839i	−0.0131401	+	0.0808546i	0.979652	+	0.200704i	$0.0643229\pi$
$618$	4.17591	+	51.7279i	0.167980	+	2.08080i
$619$	8.56309	−	34.7418i	0.344179	−	1.39639i	−0.502633	−	0.864500i	$-0.667635\pi$
$619$	8.56309	−	34.7418i	0.344179	−	1.39639i	0.846813	−	0.531891i	$-0.178518\pi$
$620$	−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	0.200947	+	0.979602i	$0.435598\pi$
$631$	−19.9924	+	26.6051i	−0.795885	+	1.05913i	−0.996833	+	0.0795290i	$0.974658\pi$
$632$	−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	−0.955321	−	0.295569i	$-0.904491\pi$
$641$	0.523719	−	12.9959i	0.0206856	−	0.513309i	0.976007	−	0.217740i	$-0.0698684\pi$
$642$	54.1424	+	20.5335i	2.13683	+	0.810392i
$643$	−1.19493	−	0.346117i	−0.0471236	−	0.0136495i	0.254572	−	0.967054i	$-0.418065\pi$
$643$	−1.19493	−	0.346117i	−0.0471236	−	0.0136495i	−0.301696	+	0.953404i	$0.597553\pi$
$644$	−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	−0.664153	−	0.747596i	$-0.731208\pi$
$647$	−1.58493	−	39.3297i	−0.0623102	−	1.54621i	0.601843	−	0.798614i	$-0.294433\pi$
$648$	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	0.574330	−	0.818624i	$-0.305263\pi$
$653$	−10.7782	−	18.6684i	−0.421784	−	0.730552i	−0.996114	+	0.0880721i	$0.971929\pi$
$654$	−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	0.0336190	−	0.999435i	$-0.489297\pi$
$659$	−17.0426	−	7.26119i	−0.663887	−	0.282856i	−0.697506	+	0.716579i	$0.745707\pi$
$660$	27.4191	−	4.45603i	1.06729	−	0.173451i
$661$	−23.7847	−	31.6518i	−0.925119	−	1.23111i	−0.972658	−	0.232241i	$-0.925394\pi$
$661$	−23.7847	−	31.6518i	−0.925119	−	1.23111i	0.0475388	−	0.998869i	$-0.484862\pi$
$662$	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	−0.988803	−	0.149227i	$-0.952322\pi$
$673$	−6.04021	−	20.8532i	−0.232833	−	0.803833i	0.755970	−	0.654606i	$-0.227166\pi$
$674$	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	−0.464379	−	0.885637i	$-0.653722\pi$
$683$	12.9634	−	30.4262i	0.496031	−	1.16423i	0.960410	−	0.278591i	$-0.0898675\pi$
$684$	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	0.951918	−	0.306352i	$-0.0991086\pi$
$691$	10.3260	+	13.7415i	0.392821	+	0.522750i	−0.559097	+	0.829102i	$0.688852\pi$
$692$	−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	−0.125704	−	0.992068i	$-0.540119\pi$
$701$	22.3455	−	19.7964i	0.843979	−	0.747700i	0.969683	+	0.244368i	$0.0785805\pi$
$702$	−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	0.805821	−	0.592160i	$-0.201725\pi$
$709$	31.1644	+	9.02688i	1.17040	+	0.339011i	0.364583	+	0.931171i	$0.381212\pi$
$710$	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	−0.975080	−	0.221853i	$-0.928789\pi$
$719$	−4.42395	−	21.6699i	−0.164985	−	0.808152i	0.810095	−	0.586299i	$-0.199416\pi$
$720$	−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	−0.653985	−	0.756508i	$-0.726904\pi$
$727$	4.36909	−	35.9827i	0.162041	−	1.33452i	0.816025	−	0.578016i	$-0.196173\pi$
$728$	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	0.0713116	+	0.997454i	$0.477282\pi$
$733$	−12.3287	+	50.0196i	−0.455372	+	1.84752i	−0.526683	+	0.850062i	$0.676565\pi$
$734$	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	0.968288	+	0.249835i	$0.0803763\pi$
$739$	3.50535	+	21.5693i	0.128946	+	0.793438i	−0.839342	+	0.543603i	$0.817060\pi$
$740$	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	0.831908	+	0.554913i	$0.187249\pi$
$743$	−2.13270	+	26.4183i	−0.0782414	+	0.969193i	−0.910150	+	0.414280i	$0.864033\pi$
$744$	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	0.581632	−	0.813452i	$-0.302414\pi$
$751$	2.63246	+	1.66466i	0.0960597	+	0.0607445i	−0.485572	+	0.874197i	$0.661389\pi$
$752$	−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	−0.939792	−	0.341747i	$-0.888981\pi$
$757$	−2.22050	+	4.67961i	−0.0807056	+	0.170083i	0.859086	+	0.511831i	$0.171033\pi$
$758$	−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	0.0682607	−	0.997668i	$-0.478255\pi$
$761$	1.54541	+	0.0622780i	0.0560211	+	0.00225757i	−0.0122396	+	0.999925i	$0.503896\pi$
$762$	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

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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