LMFDB - Embedded newform 169.2.h.a.12.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

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

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, degree $12$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.11
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05649 - 0.729245i) q^{2} +(-0.277577 - 0.145684i) q^{3} +(-0.124830 + 0.329149i) q^{4} +(2.67487 + 3.01931i) q^{5} +(-0.399497 + 0.0485078i) q^{6} +(0.147281 + 0.597543i) q^{7} +(0.722584 + 2.93164i) q^{8} +(-1.64837 - 2.38807i) q^{9} +O(q^{10})$	\(q+(1.05649 - 0.729245i) q^{2} +(-0.277577 - 0.145684i) q^{3} +(-0.124830 + 0.329149i) q^{4} +(2.67487 + 3.01931i) q^{5} +(-0.399497 + 0.0485078i) q^{6} +(0.147281 + 0.597543i) q^{7} +(0.722584 + 2.93164i) q^{8} +(-1.64837 - 2.38807i) q^{9} +(5.02780 + 1.23924i) q^{10} +(-4.66304 - 3.21866i) q^{11} +(0.0826014 - 0.0731785i) q^{12} +(1.36417 - 3.33752i) q^{13} +(0.591356 + 0.523896i) q^{14} +(-0.302619 - 1.22778i) q^{15} +(2.37430 + 2.10344i) q^{16} +(3.65404 - 0.900639i) q^{17} +(-3.48298 - 1.32092i) q^{18} -4.14676i q^{19} +(-1.32770 + 0.503531i) q^{20} +(0.0461704 - 0.187321i) q^{21} -7.27366 q^{22} -0.237017 q^{23} +(0.226519 - 0.919024i) q^{24} +(-1.35859 + 11.1890i) q^{25} +(-0.992633 - 4.52088i) q^{26} +(0.223005 + 1.83661i) q^{27} +(-0.215065 - 0.0261137i) q^{28} +(-1.37916 - 1.99806i) q^{29} +(-1.21506 - 1.07645i) q^{30} +(-3.53027 + 0.428653i) q^{31} +(-1.95237 - 0.237060i) q^{32} +(0.825446 + 1.57276i) q^{33} +(3.20368 - 3.61621i) q^{34} +(-1.41021 + 2.04304i) q^{35} +(0.991797 - 0.244456i) q^{36} +(1.18387 - 0.143748i) q^{37} +(-3.02400 - 4.38103i) q^{38} +(-0.864884 + 0.727682i) q^{39} +(-6.91869 + 10.0235i) q^{40} +(-2.81798 + 5.36921i) q^{41} +(-0.0878239 - 0.231572i) q^{42} +(-0.697683 + 5.74593i) q^{43} +(1.64150 - 1.13305i) q^{44} +(2.80115 - 11.3647i) q^{45} +(-0.250406 + 0.172843i) q^{46} +(3.58791 - 1.36071i) q^{47} +(-0.352613 - 0.929765i) q^{48} +(5.86283 - 3.07705i) q^{49} +(6.72416 + 12.8118i) q^{50} +(-1.14549 - 0.282337i) q^{51} +(0.928251 + 0.865636i) q^{52} +(4.32424 - 1.06583i) q^{53} +(1.57494 + 1.77774i) q^{54} +(-2.75490 - 22.6886i) q^{55} +(-1.64536 + 0.863550i) q^{56} +(-0.604116 + 1.15105i) q^{57} +(-2.91415 - 1.10519i) q^{58} +(5.19283 + 5.86150i) q^{59} +(0.441896 + 0.0536559i) q^{60} +(-2.34193 - 0.577233i) q^{61} +(-3.41712 + 3.02730i) q^{62} +(1.18420 - 1.33669i) q^{63} +(-7.85292 + 4.12153i) q^{64} +(13.7260 - 4.80859i) q^{65} +(2.01900 + 1.05965i) q^{66} +(-8.97327 + 3.40311i) q^{67} +(-0.159688 + 1.31515i) q^{68} +(0.0657904 + 0.0345295i) q^{69} +3.18684i q^{70} +(-4.12424 + 7.85809i) q^{71} +(5.80989 - 6.55801i) q^{72} +(-11.9374 - 8.23982i) q^{73} +(1.14593 - 1.01520i) q^{74} +(2.00716 - 2.90788i) q^{75} +(1.36490 + 0.517639i) q^{76} +(1.23651 - 3.26041i) q^{77} +(-0.383086 + 1.39950i) q^{78} +(-6.09571 - 16.0731i) q^{79} +12.7952i q^{80} +(-2.88124 + 7.59720i) q^{81} +(0.938292 + 7.72753i) q^{82} +(1.29186 + 2.46144i) q^{83} +(0.0558929 + 0.0385801i) q^{84} +(12.4934 + 8.62356i) q^{85} +(3.45309 + 6.57932i) q^{86} +(0.0917389 + 0.755538i) q^{87} +(6.06652 - 15.9961i) q^{88} +2.78330i q^{89} +(-5.32826 - 14.0495i) q^{90} +(2.19523 + 0.323596i) q^{91} +(0.0295867 - 0.0780137i) q^{92} +(1.04237 + 0.395319i) q^{93} +(2.79831 - 4.05405i) q^{94} +(12.5203 - 11.0921i) q^{95} +(0.507396 + 0.350230i) q^{96} +(-5.77891 + 6.52304i) q^{97} +(3.95012 - 7.52632i) q^{98} +16.4412i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

Coefficient data

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

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

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

$2$	1.05649	−	0.729245i	0.747054	−	0.515654i	−0.132658	−	0.991162i	$-0.542351\pi$
$2$	1.05649	−	0.729245i	0.747054	−	0.515654i	0.879711	+	0.475508i	$0.157736\pi$
$3$	−0.277577	−	0.145684i	−0.160259	−	0.0841105i	0.382687	−	0.923878i	$-0.374999\pi$
$3$	−0.277577	−	0.145684i	−0.160259	−	0.0841105i	−0.542946	+	0.839768i	$0.682691\pi$
$4$	−0.124830	+	0.329149i	−0.0624148	+	0.164574i
$5$	2.67487	+	3.01931i	1.19624	+	1.35027i	0.921319	+	0.388807i	$0.127113\pi$
$5$	2.67487	+	3.01931i	1.19624	+	1.35027i	0.274920	+	0.961467i	$0.411349\pi$
$6$	−0.399497	+	0.0485078i	−0.163094	+	0.0198032i
$7$	0.147281	+	0.597543i	0.0556670	+	0.225850i	0.992186	−	0.124767i	$-0.0398182\pi$
$7$	0.147281	+	0.597543i	0.0556670	+	0.225850i	−0.936519	+	0.350617i	$0.885972\pi$
$8$	0.722584	+	2.93164i	0.255472	+	1.03649i
$9$	−1.64837	−	2.38807i	−0.549456	−	0.796025i
$10$	5.02780	+	1.23924i	1.58993	+	0.391882i
$11$	−4.66304	−	3.21866i	−1.40596	−	0.970463i	−0.998357	−	0.0573033i	$-0.981750\pi$
$11$	−4.66304	−	3.21866i	−1.40596	−	0.970463i	−0.407602	−	0.913160i	$-0.633635\pi$
$12$	0.0826014	−	0.0731785i	0.0238450	−	0.0211248i
$13$	1.36417	−	3.33752i	0.378352	−	0.925662i
$13$	1.36417	−	3.33752i	0.378352	−	0.925662i
$14$	0.591356	+	0.523896i	0.158047	+	0.140017i
$15$	−0.302619	−	1.22778i	−0.0781360	−	0.317010i
$16$	2.37430	+	2.10344i	0.593575	+	0.525861i
$17$	3.65404	−	0.900639i	0.886234	−	0.218437i	0.230177	−	0.973149i	$-0.426069\pi$
$17$	3.65404	−	0.900639i	0.886234	−	0.218437i	0.656057	+	0.754712i	$0.272223\pi$
$18$	−3.48298	−	1.32092i	−0.820947	−	0.311344i
$19$		−	4.14676i		−	0.951332i	−0.879626	−	0.475666i	$-0.842207\pi$
$19$		−	4.14676i		−	0.951332i	0.879626	−	0.475666i	$-0.157793\pi$
$20$	−1.32770	+	0.503531i	−0.296883	+	0.112593i
$21$	0.0461704	−	0.187321i	0.0100752	−	0.0408767i
$22$	−7.27366			−1.55075
$23$	−0.237017			−0.0494214			−0.0247107	−	0.999695i	$-0.507866\pi$
$23$	−0.237017			−0.0494214			−0.0247107	+	0.999695i	$0.507866\pi$
$24$	0.226519	−	0.919024i	0.0462380	−	0.187595i
$25$	−1.35859	+	11.1890i	−0.271717	+	2.23779i
$26$	−0.992633	−	4.52088i	−0.194671	−	0.886618i
$27$	0.223005	+	1.83661i	0.0429174	+	0.353456i
$28$	−0.215065	−	0.0261137i	−0.0406435	−	0.00493502i
$29$	−1.37916	−	1.99806i	−0.256104	−	0.371031i	0.673750	−	0.738959i	$-0.264683\pi$
$29$	−1.37916	−	1.99806i	−0.256104	−	0.371031i	−0.929854	+	0.367928i	$0.880067\pi$
$30$	−1.21506	−	1.07645i	−0.221839	−	0.196532i
$31$	−3.53027	+	0.428653i	−0.634056	+	0.0769883i	−0.431253	−	0.902231i	$-0.641928\pi$
$31$	−3.53027	+	0.428653i	−0.634056	+	0.0769883i	−0.202803	+	0.979220i	$0.565005\pi$
$32$	−1.95237	−	0.237060i	−0.345133	−	0.0419067i
$33$	0.825446	+	1.57276i	0.143692	+	0.273782i
$34$	3.20368	−	3.61621i	0.549426	−	0.620174i
$35$	−1.41021	+	2.04304i	−0.238368	+	0.345336i
$36$	0.991797	−	0.244456i	0.165299	−	0.0407427i
$37$	1.18387	−	0.143748i	0.194628	−	0.0236321i	−0.0226423	−	0.999744i	$-0.507208\pi$
$37$	1.18387	−	0.143748i	0.194628	−	0.0236321i	0.217270	+	0.976112i	$0.430285\pi$
$38$	−3.02400	−	4.38103i	−0.490558	−	0.710696i
$39$	−0.864884	+	0.727682i	−0.138492	+	0.116522i
$40$	−6.91869	+	10.0235i	−1.09394	+	1.58485i
$41$	−2.81798	+	5.36921i	−0.440094	+	0.838530i	0.559856	+	0.828590i	$0.310856\pi$
$41$	−2.81798	+	5.36921i	−0.440094	+	0.838530i	−0.999951	+	0.00993983i	$0.996836\pi$
$42$	−0.0878239	−	0.231572i	−0.0135515	−	0.0357324i
$43$	−0.697683	+	5.74593i	−0.106396	+	0.876247i	0.837599	+	0.546286i	$0.183959\pi$
$43$	−0.697683	+	5.74593i	−0.106396	+	0.876247i	−0.943995	+	0.329961i	$0.892964\pi$
$44$	1.64150	−	1.13305i	0.247466	−	0.170813i
$45$	2.80115	−	11.3647i	0.417571	−	1.69415i
$46$	−0.250406	+	0.172843i	−0.0369204	+	0.0254843i
$47$	3.58791	−	1.36071i	0.523350	−	0.198481i	−0.0787600	−	0.996894i	$-0.525096\pi$
$47$	3.58791	−	1.36071i	0.523350	−	0.198481i	0.602110	+	0.798413i	$0.294327\pi$
$48$	−0.352613	−	0.929765i	−0.0508953	−	0.134200i
$49$	5.86283	−	3.07705i	0.837547	−	0.439578i
$50$	6.72416	+	12.8118i	0.950939	+	1.81186i
$51$	−1.14549	−	0.282337i	−0.160400	−	0.0395351i
$52$	0.928251	+	0.865636i	0.128725	+	0.120042i
$53$	4.32424	−	1.06583i	0.593980	−	0.146403i	0.0691445	−	0.997607i	$-0.477973\pi$
$53$	4.32424	−	1.06583i	0.593980	−	0.146403i	0.524835	+	0.851204i	$0.324127\pi$
$54$	1.57494	+	1.77774i	0.214323	+	0.241920i
$55$	−2.75490	−	22.6886i	−0.371471	−	3.05934i
$56$	−1.64536	+	0.863550i	−0.219870	+	0.115397i
$57$	−0.604116	+	1.15105i	−0.0800171	+	0.152460i
$58$	−2.91415	−	1.10519i	−0.382647	−	0.145119i
$59$	5.19283	+	5.86150i	0.676049	+	0.763102i	0.981987	−	0.188950i	$-0.0605084\pi$
$59$	5.19283	+	5.86150i	0.676049	+	0.763102i	−0.305938	+	0.952052i	$0.598970\pi$
$60$	0.441896	+	0.0536559i	0.0570486	+	0.00692695i
$61$	−2.34193	−	0.577233i	−0.299853	−	0.0739072i	0.0865188	−	0.996250i	$-0.472426\pi$
$61$	−2.34193	−	0.577233i	−0.299853	−	0.0739072i	−0.386372	+	0.922343i	$0.626272\pi$
$62$	−3.41712	+	3.02730i	−0.433974	+	0.384468i
$63$	1.18420	−	1.33669i	0.149196	−	0.168407i
$64$	−7.85292	+	4.12153i	−0.981615	+	0.515192i
$65$	13.7260	−	4.80859i	1.70250	−	0.596433i
$66$	2.01900	+	1.05965i	0.248522	+	0.130434i
$67$	−8.97327	+	3.40311i	−1.09626	+	0.415756i	−0.835412	−	0.549624i	$-0.814771\pi$
$67$	−8.97327	+	3.40311i	−1.09626	+	0.415756i	−0.260847	+	0.965380i	$0.584002\pi$
$68$	−0.159688	+	1.31515i	−0.0193650	+	0.159485i
$69$	0.0657904	+	0.0345295i	0.00792023	+	0.00415686i
$70$			3.18684i			0.380900i
$71$	−4.12424	+	7.85809i	−0.489458	+	0.932584i	0.508002	+	0.861356i	$0.330384\pi$
$71$	−4.12424	+	7.85809i	−0.489458	+	0.932584i	−0.997460	+	0.0712281i	$0.977308\pi$
$72$	5.80989	−	6.55801i	0.684702	−	0.772868i
$73$	−11.9374	−	8.23982i	−1.39717	−	0.964398i	−0.998888	−	0.0471360i	$-0.984991\pi$
$73$	−11.9374	−	8.23982i	−1.39717	−	0.964398i	−0.398284	−	0.917262i	$-0.630394\pi$
$74$	1.14593	−	1.01520i	0.133211	−	0.118015i
$75$	2.00716	−	2.90788i	0.231767	−	0.335773i
$76$	1.36490	+	0.517639i	0.156565	+	0.0593772i
$77$	1.23651	−	3.26041i	0.140914	−	0.371558i
$78$	−0.383086	+	1.39950i	−0.0433760	+	0.158463i
$79$	−6.09571	−	16.0731i	−0.685821	−	1.80836i	−0.581055	−	0.813864i	$-0.697360\pi$
$79$	−6.09571	−	16.0731i	−0.685821	−	1.80836i	−0.104765	−	0.994497i	$-0.533409\pi$
$80$			12.7952i			1.43054i
$81$	−2.88124	+	7.59720i	−0.320137	+	0.844133i
$82$	0.938292	+	7.72753i	0.103617	+	0.853363i
$83$	1.29186	+	2.46144i	0.141801	+	0.270178i	0.945991	−	0.324194i	$-0.105093\pi$
$83$	1.29186	+	2.46144i	0.141801	+	0.270178i	−0.804190	+	0.594372i	$0.797401\pi$
$84$	0.0558929	+	0.0385801i	0.00609841	+	0.00420943i
$85$	12.4934	+	8.62356i	1.35510	+	0.935357i
$86$	3.45309	+	6.57932i	0.372357	+	0.709466i
$87$	0.0917389	+	0.755538i	0.00983545	+	0.0810022i
$88$	6.06652	−	15.9961i	0.646693	−	1.70519i
$89$			2.78330i			0.295030i	0.989060	+	0.147515i	$0.0471274\pi$
$89$			2.78330i			0.295030i	−0.989060	+	0.147515i	$0.952873\pi$
$90$	−5.32826	−	14.0495i	−0.561648	−	1.48094i
$91$	2.19523	+	0.323596i	0.230122	+	0.0339221i
$92$	0.0295867	−	0.0780137i	0.00308463	−	0.00813349i
$93$	1.04237	+	0.395319i	0.108089	+	0.0409927i
$94$	2.79831	−	4.05405i	0.288623	−	0.418143i
$95$	12.5203	−	11.0921i	1.28456	−	1.13802i
$96$	0.507396	+	0.350230i	0.0517859	+	0.0357452i
$97$	−5.77891	+	6.52304i	−0.586759	+	0.662314i	−0.964650	−	0.263536i	$-0.915111\pi$
$97$	−5.77891	+	6.52304i	−0.586759	+	0.662314i	0.377890	+	0.925850i	$0.376650\pi$
$98$	3.95012	−	7.52632i	0.399022	−	0.760273i
$99$			16.4412i			1.65241i
$100$	−3.51324	−	1.84389i	−0.351324	−	0.184389i
$101$	−1.54440	+	12.7193i	−0.153674	+	1.26562i	0.688031	+	0.725681i	$0.258475\pi$
$101$	−1.54440	+	12.7193i	−0.153674	+	1.26562i	−0.841705	+	0.539938i	$0.818448\pi$
$102$	−1.41609	+	0.537052i	−0.140214	+	0.0531761i
$103$	−3.19950	−	1.67922i	−0.315256	−	0.165459i	0.299672	−	0.954042i	$-0.403123\pi$
$103$	−3.19950	−	1.67922i	−0.315256	−	0.165459i	−0.614928	+	0.788583i	$0.710815\pi$
$104$	10.7701	+	1.58761i	1.05610	+	0.155678i
$105$	0.689078	−	0.361656i	0.0672471	−	0.0352940i
$106$	3.79128	−	4.27947i	0.368242	−	0.415659i
$107$	11.0152	−	9.75862i	1.06488	−	0.943401i	0.0663601	−	0.997796i	$-0.478861\pi$
$107$	11.0152	−	9.75862i	1.06488	−	0.943401i	0.998520	+	0.0543947i	$0.0173229\pi$
$108$	−0.632356	−	0.155862i	−0.0608485	−	0.0149978i
$109$	15.1624	+	1.84105i	1.45230	+	0.176341i	0.808338	−	0.588719i	$-0.200367\pi$
$109$	15.1624	+	1.84105i	1.45230	+	0.176341i	0.643960	+	0.765059i	$0.277290\pi$
$110$	−19.4561	−	21.9614i	−1.85507	−	2.09394i
$111$	−0.349558	−	0.132570i	−0.0331786	−	0.0125830i
$112$	−0.907209	+	1.72854i	−0.0857232	+	0.163332i
$113$	0.207083	−	0.108686i	0.0194808	−	0.0102243i	−0.454955	−	0.890515i	$-0.650345\pi$
$113$	0.207083	−	0.108686i	0.0194808	−	0.0102243i	0.474435	+	0.880290i	$0.342652\pi$
$114$	0.201150	+	1.65662i	0.0188394	+	0.155157i
$115$	−0.633989	−	0.715626i	−0.0591198	−	0.0667324i
$116$	0.829820	−	0.204532i	0.0770469	−	0.0189903i
$117$	−10.2189	+	2.24373i	−0.944738	+	0.207433i
$118$	9.76066	+	2.40579i	0.898541	+	0.221471i
$119$	1.07634	+	2.05080i	0.0986680	+	0.187996i
$120$	3.38072	−	1.77434i	0.308617	−	0.161974i
$121$	7.48347	+	19.7323i	0.680316	+	1.79385i
$122$	−2.89517	+	1.09799i	−0.262117	+	0.0994078i
$123$	1.56441	−	1.07984i	0.141058	−	0.0973655i
$124$	0.299592	−	1.21549i	0.0269042	−	0.109154i
$125$	−20.8184	+	14.3699i	−1.86205	+	1.28528i
$126$	0.276329	−	2.27578i	0.0246174	−	0.202742i
$127$	−2.16202	−	5.70078i	−0.191848	−	0.505863i	0.804232	−	0.594316i	$-0.202577\pi$
$127$	−2.16202	−	5.70078i	−0.191848	−	0.505863i	−0.996080	+	0.0884529i	$0.971808\pi$
$128$	−3.46301	+	6.59821i	−0.306089	+	0.583205i
$129$	1.03075	−	1.49330i	0.0907524	−	0.131478i
$130$	10.9948	−	15.0898i	0.964304	−	1.32347i
$131$	8.90953	+	12.9077i	0.778429	+	1.12775i	0.988671	+	0.150100i	$0.0479596\pi$
$131$	8.90953	+	12.9077i	0.778429	+	1.12775i	−0.210241	+	0.977649i	$0.567425\pi$
$132$	−0.620710	+	0.0753679i	−0.0540259	+	0.00655993i
$133$	2.47787	−	0.610740i	0.214858	−	0.0529578i
$134$	−6.99849	+	10.1391i	−0.604578	+	0.875882i
$135$	−4.94879	+	5.58602i	−0.425924	+	0.480768i
$136$	5.28070	+	10.0615i	0.452816	+	0.862769i
$137$	−5.04786	−	0.612921i	−0.431268	−	0.0523654i	−0.0979753	−	0.995189i	$-0.531237\pi$
$137$	−5.04786	−	0.612921i	−0.431268	−	0.0523654i	−0.333293	+	0.942823i	$0.608160\pi$
$138$	0.0946875	−	0.0114971i	0.00806034	−	0.000978702i
$139$	−9.32241	−	8.25894i	−0.790717	−	0.700514i	0.167715	−	0.985836i	$-0.446361\pi$
$139$	−9.32241	−	8.25894i	−0.790717	−	0.700514i	−0.958432	+	0.285322i	$0.907900\pi$
$140$	−0.496427	−	0.719199i	−0.0419558	−	0.0607834i
$141$	−1.19415	−	0.144997i	−0.100566	−	0.0122109i
$142$	1.37323	+	11.3096i	0.115239	+	0.949081i
$143$	−17.1035	+	11.1722i	−1.43027	+	0.934265i
$144$	1.10946	−	9.13726i	0.0924553	−	0.761438i
$145$	2.34368	−	9.50868i	0.194632	−	0.789653i
$146$	−18.6207			−1.54106
$147$	−2.07566			−0.171198
$148$	−0.100468	+	0.407614i	−0.00825841	+	0.0335057i
$149$	9.31900	−	3.53423i	0.763442	−	0.289535i	0.0580129	−	0.998316i	$-0.481524\pi$
$149$	9.31900	−	3.53423i	0.763442	−	0.289535i	0.705429	+	0.708780i	$0.250754\pi$
$150$		−	4.53586i		−	0.370352i
$151$	10.4903	+	3.97845i	0.853689	+	0.323762i	0.742343	−	0.670020i	$-0.233715\pi$
$151$	10.4903	+	3.97845i	0.853689	+	0.323762i	0.111346	+	0.993782i	$0.464484\pi$
$152$	12.1568	−	2.99638i	0.986047	−	0.243039i
$153$	−8.17400	−	7.24153i	−0.660828	−	0.585443i
$154$	−1.07127	−	4.34632i	−0.0863256	−	0.350237i
$155$	−10.7373	−	9.51238i	−0.862438	−	0.764053i
$156$	−0.131552	−	0.375512i	−0.0105326	−	0.0300650i
$157$	−8.77032	+	7.76982i	−0.699947	+	0.620099i	−0.936148	−	0.351605i	$-0.885636\pi$
$157$	−8.77032	+	7.76982i	−0.699947	+	0.620099i	0.236201	+	0.971704i	$0.424098\pi$
$158$	−18.1613	−	12.5358i	−1.44483	−	0.997296i
$159$	−1.35558	−	0.334121i	−0.107505	−	0.0264975i
$160$	−4.50657	−	6.52890i	−0.356276	−	0.516155i
$161$	−0.0349081	−	0.141628i	−0.00275114	−	0.0111618i
$162$	2.49621	+	10.1275i	0.196121	+	0.795693i
$163$	2.79411	−	0.339267i	0.218852	−	0.0265734i	−0.0103762	−	0.999946i	$-0.503303\pi$
$163$	2.79411	−	0.339267i	0.218852	−	0.0265734i	0.229228	+	0.973373i	$0.426380\pi$
$164$	−1.41550	−	1.59777i	−0.110532	−	0.124765i
$165$	−2.54067	+	6.69919i	−0.197791	+	0.521531i
$166$	3.15984	+	1.65841i	0.245251	+	0.128718i
$167$	6.44840	−	4.45101i	0.498992	−	0.344429i	−0.291835	−	0.956469i	$-0.594266\pi$
$167$	6.44840	−	4.45101i	0.498992	−	0.344429i	0.790827	+	0.612039i	$0.209651\pi$
$168$	0.582518			0.0449423
$169$	−9.27808	−	9.10589i	−0.713699	−	0.700453i
$170$	19.4879			1.49465
$171$	−9.90278	+	6.83539i	−0.757284	+	0.522716i
$172$	−1.80417	−	0.946904i	−0.137567	−	0.0722007i
$173$	5.26767	−	13.8897i	0.400493	−	1.05601i	−0.571416	−	0.820660i	$-0.693606\pi$
$173$	5.26767	−	13.8897i	0.400493	−	1.05601i	0.971910	−	0.235354i	$-0.0756249\pi$
$174$	0.647894	+	0.731321i	0.0491167	+	0.0554413i
$175$	−6.88598	+	0.836109i	−0.520531	+	0.0632039i
$176$	−4.30116	−	17.4505i	−0.324212	−	1.31538i
$177$	−0.587487	−	2.38353i	−0.0441582	−	0.179157i
$178$	2.02971	+	2.94054i	0.152133	+	0.220403i
$179$	17.9096	+	4.41433i	1.33863	+	0.329942i	0.842682	−	0.538411i	$-0.180975\pi$
$179$	17.9096	+	4.41433i	1.33863	+	0.329942i	0.495946	+	0.868353i	$0.334821\pi$
$180$	3.39102	+	2.34065i	0.252751	+	0.174462i
$181$	−4.76371	+	4.22028i	−0.354084	+	0.313691i	−0.821349	−	0.570426i	$-0.806778\pi$
$181$	−4.76371	+	4.22028i	−0.354084	+	0.313691i	0.467265	+	0.884118i	$0.345240\pi$
$182$	2.55522	−	1.25898i	0.189406	−	0.0933219i
$183$	0.565972	+	0.501407i	0.0418378	+	0.0370651i
$184$	−0.171264	−	0.694847i	−0.0126258	−	0.0512248i
$185$	3.60073	+	3.18997i	0.264731	+	0.234531i
$186$	1.38954	−	0.342491i	0.101886	−	0.0251127i
$187$	−19.9378	−	7.56140i	−1.45799	−	0.552944i
$188$			1.35081i			0.0985181i
$189$	−1.06461	+	0.403753i	−0.0774390	+	0.0293687i
$190$	5.13883	−	20.8491i	0.372810	−	1.51255i
$191$	6.96811			0.504195			0.252097	−	0.967702i	$-0.418880\pi$
$191$	6.96811			0.504195			0.252097	+	0.967702i	$0.418880\pi$
$192$	2.78023			0.200646
$193$	−3.42240	+	13.8852i	−0.246349	+	0.999479i	0.709285	+	0.704922i	$0.249018\pi$
$193$	−3.42240	+	13.8852i	−0.246349	+	0.999479i	−0.955634	+	0.294557i	$0.904828\pi$
$194$	−1.34849	+	11.1058i	−0.0968157	+	0.797349i
$195$	−4.51055	−	0.664895i	−0.323007	−	0.0476141i
$196$	0.280952	+	2.31385i	0.0200680	+	0.165275i
$197$	−17.7596	−	2.15640i	−1.26532	−	0.153637i	−0.539772	−	0.841811i	$-0.681490\pi$
$197$	−17.7596	−	2.15640i	−1.26532	−	0.153637i	−0.725546	+	0.688174i	$0.758413\pi$
$198$	11.9897	+	17.3700i	0.852069	+	1.23444i
$199$	−8.12589	−	7.19891i	−0.576029	−	0.510317i	0.324052	−	0.946039i	$-0.394955\pi$
$199$	−8.12589	−	7.19891i	−0.576029	−	0.510317i	−0.900081	+	0.435722i	$0.856493\pi$
$200$	−33.7837	+	4.10208i	−2.38887	+	0.290061i
$201$	2.98655	+	0.362633i	0.210655	+	0.0255782i
$202$	7.64384	+	14.5641i	0.537819	+	1.02473i
$203$	0.990804	−	1.11839i	0.0695408	−	0.0784953i
$204$	0.235921	−	0.341791i	0.0165178	−	0.0239301i
$205$	−23.7490	+	5.85361i	−1.65870	+	0.408834i
$206$	−4.60481	+	0.559125i	−0.320832	+	0.0389561i
$207$	0.390691	+	0.566013i	0.0271549	+	0.0393407i
$208$	10.2592	−	5.05481i	0.711350	−	0.350488i
$209$	−13.3470	+	19.3365i	−0.923233	+	1.33753i
$210$	0.464271	−	0.884594i	0.0320377	−	0.0610428i
$211$	−5.23303	−	13.7984i	−0.360256	−	0.949918i	−0.985528	−	0.169511i	$-0.945781\pi$
$211$	−5.23303	−	13.7984i	−0.360256	−	0.949918i	0.625272	−	0.780407i	$-0.284988\pi$
$212$	−0.188977	+	1.55636i	−0.0129790	+	0.106892i
$213$	2.28959	−	1.58039i	0.156880	−	0.108287i
$214$	4.52107	−	18.3427i	0.309054	−	1.25388i
$215$	−19.2149	+	13.2631i	−1.31045	+	0.904537i
$216$	−5.22314	+	1.98088i	−0.355390	+	0.134782i
$217$	−0.776081	−	2.04636i	−0.0526838	−	0.138916i
$218$	17.3616	−	9.11206i	1.17587	−	0.617147i
$219$	2.11315	+	4.02628i	0.142794	+	0.272071i
$220$	7.81183	+	1.92544i	0.526673	+	0.129813i
$221$	1.97882	−	13.4240i	0.133110	−	0.902999i
$222$	−0.465981	+	0.114854i	−0.0312746	+	0.00770850i
$223$	3.02855	+	3.41853i	0.202807	+	0.228921i	0.841111	−	0.540863i	$-0.181902\pi$
$223$	3.02855	+	3.41853i	0.202807	+	0.228921i	−0.638304	+	0.769784i	$0.720364\pi$
$224$	−0.145893	−	1.20154i	−0.00974789	−	0.0802811i
$225$	28.9595	−	15.1991i	1.93064	−	1.01328i
$226$	0.139524	−	0.265840i	0.00928098	−	0.0176834i
$227$	26.0286	+	9.87135i	1.72758	+	0.655184i	0.999539	−	0.0303511i	$-0.00966252\pi$
$227$	26.0286	+	9.87135i	1.72758	+	0.655184i	0.728039	+	0.685535i	$0.240432\pi$
$228$	−0.303454	−	0.342528i	−0.0200967	−	0.0226845i
$229$	25.5964	+	3.10797i	1.69146	+	0.205381i	0.908848	−	0.417128i	$-0.136963\pi$
$229$	25.5964	+	3.10797i	1.69146	+	0.205381i	0.782613	+	0.622508i	$0.213886\pi$
$230$	−1.19167	−	0.293721i	−0.0785765	−	0.0193674i
$231$	−0.818216	+	0.724876i	−0.0538347	+	0.0476933i
$232$	4.86104	−	5.48698i	0.319143	−	0.360238i
$233$	25.3547	−	13.3072i	1.66104	−	0.871781i	0.669377	−	0.742923i	$-0.266561\pi$
$233$	25.3547	−	13.3072i	1.66104	−	0.871781i	0.991663	−	0.128858i	$-0.0411311\pi$
$234$	−9.15997	+	9.82256i	−0.598806	+	0.642121i
$235$	13.7056	+	7.19325i	0.894055	+	0.469236i
$236$	−2.57752	+	0.977525i	−0.167782	+	0.0636315i
$237$	−0.649554	+	5.34956i	−0.0421931	+	0.347491i
$238$	2.63268	+	1.38174i	0.170651	+	0.0895647i
$239$			3.89120i			0.251701i	0.992049	+	0.125850i	$0.0401660\pi$
$239$			3.89120i			0.251701i	−0.992049	+	0.125850i	$0.959834\pi$
$240$	1.86405	−	3.55165i	0.120324	−	0.229258i
$241$	9.60583	−	10.8427i	0.618766	−	0.698442i	−0.352669	−	0.935748i	$-0.614726\pi$
$241$	9.60583	−	10.8427i	0.618766	−	0.698442i	0.971435	+	0.237306i	$0.0762644\pi$
$242$	22.2959	+	15.3898i	1.43324	+	0.989291i
$243$	6.06102	−	5.36959i	0.388814	−	0.344459i
$244$	0.482337	−	0.698786i	0.0308785	−	0.0447352i
$245$	24.9729	+	9.47096i	1.59546	+	0.605077i
$246$	0.865326	−	2.28168i	0.0551712	−	0.145474i
$247$	−13.8399	−	5.65688i	−0.880612	−	0.359939i
$248$	−3.80757	−	10.0397i	−0.241781	−	0.637525i
$249$		−	0.871443i		−	0.0552255i
$250$	−11.5153	+	30.3634i	−0.728293	+	1.92035i
$251$	−1.88166	−	15.4969i	−0.118769	−	0.978153i	−0.923257	−	0.384183i	$-0.874483\pi$
$251$	−1.88166	−	15.4969i	−0.118769	−	0.978153i	0.804488	−	0.593970i	$-0.202440\pi$
$252$	0.292146	+	0.556637i	0.0184035	+	0.0350648i
$253$	1.10522	+	0.762876i	0.0694844	+	0.0479616i
$254$	−6.44143	−	4.44619i	−0.404171	−	0.278979i
$255$	−2.21157	−	4.21379i	−0.138494	−	0.263877i
$256$	−0.984964	−	8.11191i	−0.0615603	−	0.506994i
$257$	−0.901021	+	2.37580i	−0.0562042	+	0.148198i	−0.960178	−	0.279390i	$-0.909868\pi$
$257$	−0.901021	+	2.37580i	−0.0562042	+	0.148198i	0.903973	+	0.427589i	$0.140637\pi$
$258$		−	2.32933i		−	0.145018i
$259$	0.260258	+	0.686244i	0.0161716	+	0.0426411i
$260$	−0.130666	+	5.11814i	−0.00810353	+	0.317414i
$261$	−2.49815	+	6.58709i	−0.154632	+	0.407731i
$262$	18.8257	+	7.13965i	1.16306	+	0.441089i
$263$	−9.64281	+	13.9700i	−0.594601	+	0.861429i	−0.998576	−	0.0533413i	$-0.983013\pi$
$263$	−9.64281	+	13.9700i	−0.594601	+	0.861429i	0.403975	+	0.914770i	$0.367628\pi$
$264$	−4.01430	+	3.55636i	−0.247063	+	0.218879i
$265$	14.7848	+	10.2052i	0.908226	+	0.626903i
$266$	2.17247	−	2.45221i	0.133203	−	0.150355i
$267$	0.405482	−	0.772581i	0.0248151	−	0.0472812i
$268$		−	3.37835i		−	0.206365i
$269$	−13.2606	−	6.95971i	−0.808514	−	0.424341i	0.00920541	−	0.999958i	$-0.497070\pi$
$269$	−13.2606	−	6.95971i	−0.808514	−	0.424341i	−0.817720	+	0.575617i	$0.804762\pi$
$270$	−1.15478	+	9.51047i	−0.0702777	+	0.578789i
$271$	−19.7700	+	7.49777i	−1.20094	+	0.455457i	−0.872288	−	0.488993i	$-0.837364\pi$
$271$	−19.7700	+	7.49777i	−1.20094	+	0.455457i	−0.328655	+	0.944450i	$0.606595\pi$
$272$	10.5702	+	5.54768i	0.640914	+	0.336377i
$273$	−0.562202	−	0.409632i	−0.0340260	−	0.0247920i
$274$	−5.78000	+	3.03358i	−0.349183	+	0.183265i
$275$	42.3486	−	47.8017i	2.55372	−	2.88255i
$276$	−0.0195779	+	0.0173445i	−0.00117845	+	0.00104402i
$277$	12.8600	+	3.16971i	0.772683	+	0.190449i	0.605896	−	0.795544i	$-0.292815\pi$
$277$	12.8600	+	3.16971i	0.772683	+	0.190449i	0.166787	+	0.985993i	$0.446661\pi$
$278$	−15.8719	−	1.92719i	−0.951930	−	0.115585i
$279$	6.84285	+	7.72398i	0.409671	+	0.462422i
$280$	−7.00844	−	2.65795i	−0.418834	−	0.158843i
$281$	−9.96651	+	18.9896i	−0.594552	+	1.13282i	0.383319	+	0.923616i	$0.374781\pi$
$281$	−9.96651	+	18.9896i	−0.594552	+	1.13282i	−0.977871	+	0.209209i	$0.932911\pi$
$282$	−1.36735	+	0.717643i	−0.0814248	+	0.0427350i
$283$	−0.939128	−	7.73442i	−0.0558254	−	0.459763i	−0.993638	−	0.112621i	$-0.964075\pi$
$283$	−0.939128	−	7.73442i	−0.0558254	−	0.459763i	0.937813	−	0.347142i	$-0.112848\pi$
$284$	−2.07165	−	2.33841i	−0.122930	−	0.138759i
$285$	−5.09129	+	1.25489i	−0.301582	+	0.0743333i
$286$	−9.92250	+	24.2760i	−0.586730	+	1.43547i
$287$	−3.62337	−	0.893080i	−0.213881	−	0.0527168i
$288$	2.65210	+	5.05316i	0.156277	+	0.297760i
$289$	−2.51191	+	1.31835i	−0.147760	+	0.0775503i
$290$	−4.45807	−	11.7550i	−0.261787	−	0.690276i
$291$	2.55439	−	0.968753i	0.149741	−	0.0567893i
$292$	4.20227	−	2.90062i	0.245919	−	0.169746i
$293$	1.60772	−	6.52277i	0.0939240	−	0.381065i	−0.905102	−	0.425195i	$-0.860206\pi$
$293$	1.60772	−	6.52277i	0.0939240	−	0.381065i	0.999026	+	0.0441304i	$0.0140517\pi$
$294$	−2.19292	+	1.51367i	−0.127894	+	0.0882787i
$295$	−3.80749	+	31.3575i	−0.221681	+	1.82570i
$296$	1.27687	+	3.36682i	0.0742163	+	0.195692i
$297$	4.87155	−	9.28197i	0.282676	−	0.538595i
$298$	7.26814	−	10.5297i	0.421032	−	0.609970i
$299$	−0.323331	+	0.791048i	−0.0186987	+	0.0457475i
$300$	0.706570	+	1.02364i	0.0407938	+	0.0591001i
$301$	−3.53620	+	0.429372i	−0.203823	+	0.0247486i
$302$	13.9842	−	3.44680i	0.804700	−	0.198341i
$303$	2.28169	−	3.30560i	0.131080	−	0.189901i
$304$	8.72249	−	9.84565i	0.500269	−	0.564687i
$305$	−4.52151	−	8.61502i	−0.258901	−	0.493295i
$306$	−13.9166	−	1.68978i	−0.795560	−	0.0965985i
$307$	−15.9474	+	1.93636i	−0.910164	+	0.110514i	−0.562207	−	0.826996i	$-0.690048\pi$
$307$	−15.9474	+	1.93636i	−0.910164	+	0.110514i	−0.347957	+	0.937510i	$0.613125\pi$
$308$	0.918807	+	0.813992i	0.0523539	+	0.0463815i
$309$	0.643471	+	0.932229i	0.0366058	+	0.0530326i
$310$	−18.2807	−	2.21968i	−1.03827	−	0.126069i
$311$	−2.10029	−	17.2974i	−0.119096	−	0.980847i	−0.922656	−	0.385623i	$-0.873986\pi$
$311$	−2.10029	−	17.2974i	−0.119096	−	0.980847i	0.803560	−	0.595224i	$-0.202937\pi$
$312$	−2.75825	−	2.00972i	−0.156155	−	0.113778i
$313$	3.08829	−	25.4344i	0.174561	−	1.43764i	−0.597388	−	0.801952i	$-0.703795\pi$
$313$	3.08829	−	25.4344i	0.174561	−	1.43764i	0.771949	−	0.635685i	$-0.219282\pi$
$314$	−3.59968	+	14.6045i	−0.203142	+	0.824178i
$315$	7.20347			0.405869
$316$	6.05135			0.340415
$317$	−0.417869	+	1.69536i	−0.0234698	+	0.0952209i	−0.981509	−	0.191417i	$-0.938692\pi$
$317$	−0.417869	+	1.69536i	−0.0234698	+	0.0952209i	0.958039	+	0.286638i	$0.0925378\pi$
$318$	−1.67582	+	0.635555i	−0.0939754	+	0.0356402i
$319$			13.7561i			0.770194i
$320$	−33.4497	−	12.6858i	−1.86990	−	0.709158i
$321$	−4.47924	+	1.10403i	−0.250007	+	0.0616211i
$322$	−0.140161	−	0.124172i	−0.00781088	−	0.00691984i
$323$	−3.73474	−	15.1524i	−0.207806	−	0.843103i
$324$	−2.14094	−	1.89671i	−0.118941	−	0.105373i
$325$	35.4901	+	19.7980i	1.96863	+	1.09819i
$326$	2.70455	−	2.39603i	0.149791	−	0.132704i
$327$	−3.94053	−	2.71995i	−0.217912	−	0.150414i
$328$	−17.7768	−	4.38159i	−0.981560	−	0.241933i
$329$	1.34152	+	1.94352i	0.0739601	+	0.107150i
$330$	2.20115	+	8.93042i	0.121169	+	0.491603i
$331$	6.80569	+	27.6118i	0.374075	+	1.51768i	0.792751	+	0.609545i	$0.208648\pi$
$331$	6.80569	+	27.6118i	0.374075	+	1.51768i	−0.418676	+	0.908136i	$0.637506\pi$
$332$	−0.971443	+	0.117955i	−0.0533149	+	0.00647360i
$333$	−2.29474	−	2.59023i	−0.125751	−	0.141944i
$334$	3.56682	−	9.40492i	0.195168	−	0.514614i
$335$	−34.2774	−	17.9901i	−1.87277	−	0.982907i
$336$	0.503641	−	0.347638i	0.0274759	−	0.0189652i
$337$	−13.6513			−0.743636			−0.371818	−	0.928306i	$-0.621265\pi$
$337$	−13.6513			−0.743636			−0.371818	+	0.928306i	$0.621265\pi$
$338$	−16.4427	−	2.85431i	−0.894362	−	0.155254i
$339$	−0.0733153			−0.00398194
$340$	−4.39798	+	3.03570i	−0.238514	+	0.164634i
$341$	17.8415	+	9.36393i	0.966170	+	0.507085i
$342$	−5.47754	+	14.4431i	−0.296192	+	0.780993i
$343$	5.55887	+	6.27467i	0.300151	+	0.338800i
$344$	−17.3491	+	2.10657i	−0.935403	+	0.113578i
$345$	0.0717258	+	0.291003i	0.00386159	+	0.0156671i
$346$	−4.56373	−	18.5158i	−0.245348	−	0.995415i
$347$	−4.73333	−	6.85741i	−0.254098	−	0.368125i	0.675088	−	0.737738i	$-0.264106\pi$
$347$	−4.73333	−	6.85741i	−0.254098	−	0.368125i	−0.929186	+	0.369613i	$0.879490\pi$
$348$	−0.260136	−	0.0641178i	−0.0139448	−	0.00343707i
$349$	−12.1092	−	8.35835i	−0.648188	−	0.447412i	0.198068	−	0.980188i	$-0.436533\pi$
$349$	−12.1092	−	8.35835i	−0.648188	−	0.447412i	−0.846256	+	0.532776i	$0.821149\pi$
$350$	−6.66526	+	5.90491i	−0.356273	+	0.315631i
$351$	6.43395	+	1.76117i	0.343419	+	0.0940041i
$352$	8.34094	+	7.38943i	0.444574	+	0.393858i
$353$	−5.31201	−	21.5517i	−0.282730	−	1.14708i	−0.924806	−	0.380439i	$-0.875773\pi$
$353$	−5.31201	−	21.5517i	−0.282730	−	1.14708i	0.642076	−	0.766641i	$-0.278073\pi$
$354$	−2.35885	−	2.08976i	−0.125371	−	0.111069i
$355$	−34.7578	+	8.56703i	−1.84475	+	0.454691i
$356$	−0.916121	−	0.347439i	−0.0485543	−	0.0184142i
$357$		−	0.726059i		−	0.0384271i
$358$	22.1405	−	8.39679i	1.17016	−	0.443784i
$359$	−1.36833	+	5.55153i	−0.0722177	+	0.292999i	−0.995935	−	0.0900765i	$-0.971289\pi$
$359$	−1.36833	+	5.55153i	−0.0722177	+	0.292999i	0.923717	+	0.383075i	$0.125135\pi$
$360$	35.3413			1.86265
$361$	1.80437			0.0949666
$362$	−1.95521	+	7.93261i	−0.102764	+	0.416929i
$363$	0.797433	−	6.56745i	0.0418544	−	0.344702i
$364$	−0.380541	+	0.682162i	−0.0199457	+	0.0357550i
$365$	−7.05258	−	58.0833i	−0.369149	−	3.04022i
$366$	0.963594	+	0.117001i	0.0503679	+	0.00611577i
$367$	0.666386	+	0.965426i	0.0347851	+	0.0503949i	0.839991	−	0.542601i	$-0.182560\pi$
$367$	0.666386	+	0.965426i	0.0347851	+	0.0503949i	−0.805206	+	0.592996i	$0.797945\pi$
$368$	−0.562748	−	0.498551i	−0.0293353	−	0.0259888i
$369$	17.4671	−	2.12089i	0.909303	−	0.110409i
$370$	6.13041	+	0.744367i	0.318705	+	0.0386978i
$371$	1.27376	+	2.42694i	0.0661302	+	0.126001i
$372$	−0.260237	+	0.293747i	−0.0134927	+	0.0152301i
$373$	7.28414	−	10.5529i	0.377159	−	0.546408i	−0.587734	−	0.809054i	$-0.699980\pi$
$373$	7.28414	−	10.5529i	0.377159	−	0.546408i	0.964892	+	0.262646i	$0.0845951\pi$
$374$	−26.5782	+	6.55094i	−1.37433	+	0.338741i
$375$	7.87217	−	0.955854i	0.406517	−	0.0493601i
$376$	6.58169	+	9.53522i	0.339425	+	0.491741i
$377$	−8.54999	+	1.87729i	−0.440347	+	0.0966853i
$378$	−0.830319	+	1.20292i	−0.0427070	+	0.0618717i
$379$	0.340934	−	0.649595i	0.0175126	−	0.0333674i	−0.876543	−	0.481324i	$-0.840156\pi$
$379$	0.340934	−	0.649595i	0.0175126	−	0.0333674i	0.894055	+	0.447957i	$0.147848\pi$
$380$	2.08803	+	5.50567i	0.107113	+	0.282435i
$381$	−0.230383	+	1.89738i	−0.0118029	+	0.0972056i
$382$	7.36176	−	5.08145i	0.376660	−	0.259990i
$383$	−8.38380	+	34.0144i	−0.428392	+	1.73806i	0.218837	+	0.975761i	$0.429774\pi$
$383$	−8.38380	+	34.0144i	−0.428392	+	1.73806i	−0.647230	+	0.762295i	$0.724073\pi$
$384$	1.92250	−	1.32701i	0.0981073	−	0.0677186i
$385$	13.1517	−	4.98778i	0.670272	−	0.254201i
$386$	6.50997	+	17.1654i	0.331349	+	0.873695i
$387$	14.8718	−	7.80530i	0.755974	−	0.396766i
$388$	−1.42567	−	2.71639i	−0.0723774	−	0.137904i
$389$	14.3326	+	3.53266i	0.726690	+	0.179113i	0.585272	−	0.810837i	$-0.300988\pi$
$389$	14.3326	+	3.53266i	0.726690	+	0.179113i	0.141418	+	0.989950i	$0.454834\pi$
$390$	−5.25023	+	2.58684i	−0.265856	+	0.130990i
$391$	−0.866068	+	0.213466i	−0.0437989	+	0.0107955i
$392$	13.2572	+	14.9643i	0.669589	+	0.755809i
$393$	−0.592643	−	4.88085i	−0.0298949	−	0.246206i
$394$	−20.3354	+	10.6729i	−1.02448	+	0.537691i
$395$	32.2243	−	61.3982i	1.62138	−	3.08928i
$396$	−5.41161	−	2.05235i	−0.271943	−	0.103135i
$397$	−14.8552	−	16.7680i	−0.745559	−	0.841562i	0.246261	−	0.969203i	$-0.420798\pi$
$397$	−14.8552	−	16.7680i	−0.745559	−	0.841562i	−0.991820	+	0.127641i	$0.959259\pi$
$398$	−13.8347	−	1.67984i	−0.693471	−	0.0842027i
$399$	−0.776774	−	0.191458i	−0.0388873	−	0.00958487i
$400$	−26.7611	+	23.7082i	−1.33805	+	1.18541i
$401$	−12.0831	+	13.6390i	−0.603403	+	0.681101i	−0.968255	−	0.249964i	$-0.919581\pi$
$401$	−12.0831	+	13.6390i	−0.603403	+	0.681101i	0.364852	+	0.931065i	$0.381120\pi$
$402$	3.41972	−	1.79481i	0.170560	−	0.0895168i
$403$	−3.38525	+	12.3671i	−0.168631	+	0.616050i
$404$	−3.99376	−	2.09609i	−0.198697	−	0.104284i
$405$	−30.6452	+	11.6222i	−1.52277	+	0.577511i
$406$	0.231200	−	1.90411i	0.0114743	−	0.0944992i
$407$	−5.98312	−	3.14019i	−0.296572	−	0.155653i
$408$		−	3.56216i		−	0.176353i
$409$	−4.34647	+	8.28150i	−0.214919	+	0.409494i	−0.968918	−	0.247381i	$-0.920430\pi$
$409$	−4.34647	+	8.28150i	−0.214919	+	0.409494i	0.753999	+	0.656875i	$0.228122\pi$
$410$	−20.8220	+	23.5031i	−1.02832	+	1.16074i
$411$	1.31188	+	0.905524i	0.0647101	+	0.0446662i
$412$	0.952106	−	0.843493i	0.0469069	−	0.0415559i
$413$	−2.73769	+	3.96623i	−0.134713	+	0.195165i
$414$	0.825524	+	0.313080i	0.0405723	+	0.0153870i
$415$	−3.97627	+	10.4846i	−0.195188	+	0.514668i
$416$	−3.45455	+	6.19267i	−0.169373	+	0.303621i
$417$	1.38450	+	3.65061i	0.0677990	+	0.178771i
$418$			30.1621i			1.47528i
$419$	7.07596	−	18.6578i	0.345683	−	0.911492i	−0.643584	−	0.765375i	$-0.722553\pi$
$419$	7.07596	−	18.6578i	0.345683	−	0.911492i	0.989267	−	0.146116i	$-0.0466774\pi$
$420$	0.0330212	+	0.271954i	0.00161127	+	0.0132700i
$421$	1.58500	+	3.01997i	0.0772482	+	0.147184i	0.921017	−	0.389523i	$-0.127360\pi$
$421$	1.58500	+	3.01997i	0.0772482	+	0.147184i	−0.843768	+	0.536707i	$0.819668\pi$
$422$	−15.5910	−	10.7617i	−0.758960	−	0.523872i
$423$	−9.16368	−	6.32523i	−0.445553	−	0.307543i
$424$	6.24925	+	11.9070i	0.303490	+	0.578253i
$425$	5.11290	+	42.1085i	0.248012	+	2.04256i
$426$	1.26645	−	3.33934i	0.0613595	−	0.161792i
$427$		−	1.48442i		−	0.0718360i
$428$	1.83701	+	4.84380i	0.0887953	+	0.234134i
$429$	6.37515	−	0.609437i	0.307795	−	0.0294239i
$430$	−10.6284	+	28.0248i	−0.512547	+	1.35148i
$431$	16.3677	+	6.20744i	0.788403	+	0.299002i	0.715751	−	0.698356i	$-0.246085\pi$
$431$	16.3677	+	6.20744i	0.788403	+	0.299002i	0.0726519	+	0.997357i	$0.476854\pi$
$432$	−3.33373	+	4.82975i	−0.160394	+	0.232371i
$433$	−10.7005	+	9.47984i	−0.514235	+	0.455572i	−0.879889	−	0.475178i	$-0.842384\pi$
$433$	−10.7005	+	9.47984i	−0.514235	+	0.455572i	0.365655	+	0.930751i	$0.380845\pi$
$434$	−2.31222	−	1.59601i	−0.110990	−	0.0766109i
$435$	−2.03581	+	2.29796i	−0.0976096	+	0.110179i
$436$	−2.49870	+	4.76088i	−0.119666	+	0.228005i
$437$			0.982851i			0.0470162i
$438$	5.16867	+	2.71273i	0.246969	+	0.129619i
$439$	−0.899113	+	7.40486i	−0.0429123	+	0.353415i	0.955399	+	0.295319i	$0.0954259\pi$
$439$	−0.899113	+	7.40486i	−0.0429123	+	0.353415i	−0.998311	+	0.0580957i	$0.981497\pi$
$440$	64.5242	−	24.4708i	3.07607	−	1.16660i
$441$	−17.0123	−	8.92876i	−0.810111	−	0.425179i
$442$	−7.69880	−	15.6255i	−0.366195	−	0.743227i
$443$	12.6032	−	6.61465i	0.598794	−	0.314271i	−0.137954	−	0.990439i	$-0.544053\pi$
$443$	12.6032	−	6.61465i	0.598794	−	0.314271i	0.736748	+	0.676167i	$0.236360\pi$
$444$	0.0872704	−	0.0985079i	0.00414167	−	0.00467498i
$445$	−8.40365	+	7.44498i	−0.398371	+	0.352926i
$446$	5.69258	+	1.40310i	0.269552	+	0.0664385i
$447$	−3.10162	−	0.376605i	−0.146702	−	0.0178128i
$448$	−3.61938	−	4.08543i	−0.171000	−	0.193019i
$449$	−15.2324	−	5.77687i	−0.718859	−	0.272627i	−0.0320716	−	0.999486i	$-0.510210\pi$
$449$	−15.2324	−	5.77687i	−0.718859	−	0.272627i	−0.686787	+	0.726858i	$0.740980\pi$
$450$	19.5117	−	37.1764i	0.919789	−	1.75251i
$451$	30.4220	−	15.9667i	1.43252	−	0.751842i
$452$	0.00992362	+	0.0817284i	0.000466768	+	0.00384418i
$453$	−2.33227	−	2.63259i	−0.109580	−	0.123690i
$454$	34.6977	−	8.55221i	1.62844	−	0.401375i
$455$	4.89492	+	7.49364i	0.229477	+	0.351307i
$456$	−3.81097	−	0.939321i	−0.178465	−	0.0439877i
$457$	−7.65811	−	14.5913i	−0.358231	−	0.682553i	0.637929	−	0.770095i	$-0.279791\pi$
$457$	−7.65811	−	14.5913i	−0.358231	−	0.682553i	−0.996161	+	0.0875418i	$0.972099\pi$
$458$	29.3089	−	15.3825i	1.36952	−	0.718778i
$459$	2.46899	+	6.51020i	0.115243	+	0.303870i
$460$	0.314688	−	0.119345i	0.0146724	−	0.00556450i
$461$	17.8162	−	12.2976i	0.829783	−	0.572758i	−0.0757047	−	0.997130i	$-0.524121\pi$
$461$	17.8162	−	12.2976i	0.829783	−	0.572758i	0.905488	+	0.424372i	$0.139505\pi$
$462$	−0.335828	+	1.36251i	−0.0156241	+	0.0633895i
$463$	22.0050	−	15.1889i	1.02266	−	0.705889i	0.0662131	−	0.997806i	$-0.478908\pi$
$463$	22.0050	−	15.1889i	1.02266	−	0.705889i	0.956444	+	0.291916i	$0.0942929\pi$
$464$	0.928270	−	7.64499i	0.0430939	−	0.354910i
$465$	1.59462	+	4.20466i	0.0739487	+	0.194987i
$466$	17.0829	−	32.5487i	0.791348	−	1.50779i
$467$	−16.0731	+	23.2859i	−0.743773	+	1.07754i	0.250230	+	0.968186i	$0.419494\pi$
$467$	−16.0731	+	23.2859i	−0.743773	+	1.07754i	−0.994003	+	0.109354i	$0.965122\pi$
$468$	0.537102	−	3.64362i	0.0248275	−	0.168426i
$469$	−3.35510	−	4.86070i	−0.154924	−	0.224446i
$470$	19.7255	−	2.39511i	0.909870	−	0.110478i
$471$	3.56637	−	0.879032i	0.164330	−	0.0405037i
$472$	−13.4315	+	19.4589i	−0.618236	+	0.895670i
$473$	21.7475	−	24.5479i	0.999953	−	1.12871i
$474$	3.21489	+	6.12546i	0.147665	+	0.281352i
$475$	46.3980	+	5.63373i	2.12889	+	0.258493i
$476$	−0.809376	+	0.0982760i	−0.0370977	+	0.00450448i
$477$	−9.67322	−	8.56973i	−0.442906	−	0.392381i
$478$	2.83764	+	4.11103i	0.129791	+	0.188034i
$479$	−5.74639	−	0.697738i	−0.262559	−	0.0318805i	−0.0118016	−	0.999930i	$-0.503757\pi$
$479$	−5.74639	−	0.697738i	−0.262559	−	0.0318805i	−0.250758	+	0.968050i	$0.580680\pi$
$480$	0.299767	+	2.46881i	0.0136824	+	0.112685i
$481$	1.13524	−	4.14730i	0.0517625	−	0.189101i
$482$	2.24148	−	18.4603i	0.102097	−	0.840843i
$483$	−0.0109431	+	0.0443981i	−0.000497931	+	0.00202018i
$484$	−7.42902			−0.337683
$485$	−35.1529			−1.59621
$486$	2.48768	−	10.0929i	0.112843	−	0.457823i
$487$	19.5789	−	7.42531i	0.887207	−	0.336473i	0.131448	−	0.991323i	$-0.458037\pi$
$487$	19.5789	−	7.42531i	0.887207	−	0.336473i	0.755759	+	0.654850i	$0.227268\pi$
$488$		−	7.28278i		−	0.329676i
$489$	−0.825007	−	0.312884i	−0.0373081	−	0.0141491i
$490$	33.2903	−	8.20532i	1.50390	−	0.370679i
$491$	19.7827	+	17.5260i	0.892782	+	0.790936i	0.978685	−	0.205368i	$-0.0658391\pi$
$491$	19.7827	+	17.5260i	0.892782	+	0.790936i	−0.0859032	+	0.996303i	$0.527378\pi$
$492$	0.160141	+	0.649719i	0.00721973	+	0.0292916i
$493$	−6.83905	−	6.05887i	−0.308015	−	0.272878i
$494$	−18.7470	+	4.11621i	−0.843468	+	0.185197i
$495$	−49.6411	+	43.9782i	−2.23120	+	1.97667i
$496$	−9.28357	−	6.40799i	−0.416845	−	0.287727i
$497$	−5.30297	−	1.30706i	−0.237871	−	0.0586298i
$498$	−0.635495	−	0.920674i	−0.0284772	−	0.0412564i
$499$	10.0347	+	40.7125i	0.449216	+	1.82254i	0.559741	+	0.828668i	$0.310901\pi$
$499$	10.0347	+	40.7125i	0.449216	+	1.82254i	−0.110525	+	0.993873i	$0.535253\pi$
$500$	−2.13108	−	8.64613i	−0.0953048	−	0.386667i
$501$	−2.43837	+	0.296071i	−0.108938	+	0.0132275i
$502$	−13.2890	−	15.0001i	−0.593115	−	0.669489i
$503$	−11.1500	+	29.4002i	−0.497155	+	1.31089i	0.418241	+	0.908336i	$0.362647\pi$
$503$	−11.1500	+	29.4002i	−0.497155	+	1.31089i	−0.915396	+	0.402555i	$0.868122\pi$
$504$	4.77438	+	2.50579i	0.212668	+	0.111617i
$505$	−42.5346	+	29.3595i	−1.89276	+	1.30648i
$506$	1.72398			0.0766402
$507$	1.24880	+	3.87925i	0.0554614	+	0.172284i
$508$	2.14629			0.0952262
$509$	6.11533	−	4.22111i	0.271057	−	0.187097i	−0.424780	−	0.905296i	$-0.639649\pi$
$509$	6.11533	−	4.22111i	0.271057	−	0.187097i	0.695838	+	0.718199i	$0.255033\pi$
$510$	−5.40938	−	2.83906i	−0.239532	−	0.125716i
$511$	3.16549	−	8.34670i	0.140033	−	0.369236i
$512$	−16.8390	−	19.0073i	−0.744188	−	0.840014i
$513$	7.61600	−	0.924749i	0.336254	−	0.0408287i
$514$	0.780615	+	3.16708i	0.0344314	+	0.139694i
$515$	−3.48815	−	14.1520i	−0.153706	−	0.623610i
$516$	0.362849	+	0.525677i	0.0159735	+	0.0231417i
$517$	−21.1102	−	5.20320i	−0.928427	−	0.228837i
$518$	0.775400	+	0.535220i	0.0340691	+	0.0235162i
$519$	−3.48569	+	3.08805i	−0.153005	+	0.135550i
$520$	24.0152	+	36.7650i	1.05314	+	1.61225i
$521$	−28.3216	−	25.0908i	−1.24079	−	1.09925i	−0.991403	−	0.130845i	$-0.958231\pi$
$521$	−28.3216	−	25.0908i	−1.24079	−	1.09925i	−0.249391	−	0.968403i	$-0.580230\pi$
$522$	2.16432	+	8.78098i	0.0947296	+	0.384333i
$523$	21.9771	+	19.4700i	0.960992	+	0.851364i	0.988951	−	0.148245i	$-0.0473623\pi$
$523$	21.9771	+	19.4700i	0.960992	+	0.851364i	−0.0279590	+	0.999609i	$0.508901\pi$
$524$	−5.36072	+	1.32130i	−0.234184	+	0.0577212i
$525$	2.03320	+	0.771090i	0.0887360	+	0.0336531i
$526$			21.7912i			0.950142i
$527$	−12.5137	+	4.74582i	−0.545105	+	0.206731i
$528$	−1.34835	+	5.47047i	−0.0586794	+	0.238072i
$529$	−22.9438			−0.997558
$530$	23.0622			1.00176
$531$	5.43799	−	22.0628i	0.235989	−	0.957443i
$532$	−0.108287	+	0.891825i	−0.00469484	+	0.0386655i
$533$	14.0756	+	16.7296i	0.609684	+	0.724638i
$534$	−0.135012	−	1.11192i	−0.00584253	−	0.0481176i
$535$	58.9285	+	7.15521i	2.54770	+	0.309347i
$536$	−16.4606	−	23.8473i	−0.710991	−	1.03005i
$537$	−4.32821	−	3.83446i	−0.186776	−	0.165469i
$538$	−19.0851	+	2.31735i	−0.822817	+	0.0999080i
$539$	−37.2426	−	4.52207i	−1.60415	−	0.194779i
$540$	−1.22088	−	2.32619i	−0.0525382	−	0.100103i
$541$	17.5030	−	19.7568i	0.752513	−	0.849412i	−0.240098	−	0.970749i	$-0.577180\pi$
$541$	17.5030	−	19.7568i	0.752513	−	0.849412i	0.992611	+	0.121337i	$0.0387181\pi$
$542$	−15.4192	+	22.3385i	−0.662310	+	0.959522i
$543$	1.93712	−	0.477458i	0.0831300	−	0.0204897i
$544$	−7.34753	+	0.892151i	−0.315023	+	0.0382507i
$545$	34.9989	+	50.7046i	1.49919	+	2.17195i
$546$	−0.892684	−	0.0227901i	−0.0382034	−	0.000975328i
$547$	25.4024	−	36.8018i	1.08613	−	1.57353i	0.301607	−	0.953432i	$-0.402477\pi$
$547$	25.4024	−	36.8018i	1.08613	−	1.57353i	0.784524	−	0.620099i	$-0.212908\pi$
$548$	0.831865	−	1.58499i	0.0355355	−	0.0677072i
$549$	2.48188	+	6.54419i	0.105924	+	0.279299i
$550$	9.88189	−	81.3847i	0.421365	−	3.47026i
$551$	−8.28549	+	5.71906i	−0.352974	+	0.243640i
$552$	−0.0536888	+	0.217824i	−0.00228515	+	0.00927121i
$553$	8.70656	−	6.00971i	0.370241	−	0.255559i
$554$	15.8980	−	6.02932i	0.675441	−	0.256161i
$555$	−0.534754	−	1.41003i	−0.0226990	−	0.0598524i
$556$	3.88213	−	2.03750i	0.164639	−	0.0864092i
$557$	−3.35111	−	6.38501i	−0.141991	−	0.270542i	0.804067	−	0.594539i	$-0.202665\pi$
$557$	−3.35111	−	6.38501i	−0.141991	−	0.270542i	−0.946058	+	0.323997i	$0.894973\pi$
$558$	12.8621	+	3.17022i	0.544496	+	0.134206i
$559$	18.2254	+	10.1670i	0.770853	+	0.430016i
$560$	−7.64567	+	1.88449i	−0.323088	+	0.0796341i
$561$	4.43269	+	5.00348i	0.187148	+	0.211247i
$562$	3.31851	+	27.3304i	0.139983	+	1.15286i
$563$	2.37398	−	1.24596i	0.100051	−	0.0525110i	−0.413955	−	0.910297i	$-0.635853\pi$
$563$	2.37398	−	1.24596i	0.100051	−	0.0525110i	0.514007	+	0.857786i	$0.328161\pi$
$564$	0.196791	−	0.374954i	0.00828641	−	0.0157884i
$565$	0.882077	+	0.334528i	0.0371092	+	0.0140737i
$566$	−6.63246	−	7.48650i	−0.278783	−	0.314681i
$567$	−4.96400	−	0.602739i	−0.208468	−	0.0253127i
$568$	−26.0172	−	6.41266i	−1.09166	−	0.269069i
$569$	−8.32818	+	7.37813i	−0.349136	+	0.309307i	−0.819404	−	0.573216i	$-0.805696\pi$
$569$	−8.32818	+	7.37813i	−0.349136	+	0.309307i	0.470269	+	0.882523i	$0.344157\pi$
$570$	−4.46379	+	5.03858i	−0.186968	+	0.211043i
$571$	0.669203	−	0.351225i	0.0280053	−	0.0146983i	−0.450662	−	0.892694i	$-0.648812\pi$
$571$	0.669203	−	0.351225i	0.0280053	−	0.0146983i	0.478668	+	0.877996i	$0.341120\pi$
$572$	−1.54228	−	7.02422i	−0.0644860	−	0.293697i
$573$	−1.93419	−	1.01514i	−0.0808018	−	0.0424081i
$574$	−4.47934	+	1.69879i	−0.186964	+	0.0709060i
$575$	0.322008	−	2.65197i	0.0134286	−	0.110595i
$576$	22.7870	+	11.9596i	0.949460	+	0.498315i
$577$		−	44.9989i		−	1.87333i	−0.350229	−	0.936664i	$-0.613896\pi$
$577$		−	44.9989i		−	1.87333i	0.350229	−	0.936664i	$-0.386104\pi$
$578$	−1.69242	+	3.22463i	−0.0703953	+	0.134127i
$579$	2.97283	−	3.35563i	0.123546	−	0.139455i
$580$	2.83721	+	1.95838i	0.117809	+	0.0813174i
$581$	−1.28055	+	1.13447i	−0.0531262	+	0.0470657i
$582$	1.99224	−	2.88626i	0.0825810	−	0.119639i
$583$	−23.5946	−	8.94826i	−0.977190	−	0.370599i
$584$	15.5304	−	40.9502i	0.642652	−	1.69453i
$585$	−34.1087	−	24.8523i	−1.41022	−	1.02752i
$586$	−3.05815	−	8.06369i	−0.126331	−	0.333108i
$587$			4.44919i			0.183638i	0.995776	+	0.0918189i	$0.0292681\pi$
$587$			4.44919i			0.183638i	−0.995776	+	0.0918189i	$0.970732\pi$
$588$	0.259104	−	0.683201i	0.0106853	−	0.0281747i
$589$	1.77752	+	14.6392i	0.0732415	+	0.603198i
$590$	18.8447	+	35.9056i	0.775824	+	1.47821i
$591$	4.61550	+	3.18585i	0.189856	+	0.131048i
$592$	3.11324	+	2.14891i	0.127953	+	0.0883197i
$593$	−3.18730	−	6.07289i	−0.130887	−	0.249384i	0.811189	−	0.584784i	$-0.198821\pi$
$593$	−3.18730	−	6.07289i	−0.130887	−	0.249384i	−0.942076	+	0.335400i	$0.891128\pi$
$594$	−1.62206	−	13.3589i	−0.0665541	−	0.548122i
$595$	−3.31291	+	8.73542i	−0.135816	+	0.358117i
$596$			3.50851i			0.143714i
$597$	1.20680	+	3.18206i	0.0493909	+	0.130233i
$598$	0.235271	+	1.07152i	0.00962093	+	0.0438179i
$599$	−8.08973	+	21.3309i	−0.330537	+	0.871556i	0.661988	+	0.749515i	$0.269713\pi$
$599$	−8.08973	+	21.3309i	−0.330537	+	0.871556i	−0.992525	+	0.122041i	$0.961056\pi$
$600$	9.97519	+	3.78309i	0.407235	+	0.154444i
$601$	−5.46268	+	7.91406i	−0.222828	+	0.322821i	−0.918414	−	0.395621i	$-0.870529\pi$
$601$	−5.46268	+	7.91406i	−0.222828	+	0.322821i	0.695586	+	0.718443i	$0.255145\pi$
$602$	−3.42285	+	3.03238i	−0.139505	+	0.123591i
$603$	22.9181	+	15.8192i	0.933299	+	0.644210i
$604$	−2.61900	+	2.95624i	−0.106566	+	0.120288i
$605$	−39.5605	+	75.3763i	−1.60836	+	3.06448i
$606$		−	5.15625i		−	0.209458i
$607$	4.54929	+	2.38765i	0.184650	+	0.0969118i	0.554515	−	0.832174i	$-0.312904\pi$
$607$	4.54929	+	2.38765i	0.184650	+	0.0969118i	−0.369865	+	0.929085i	$0.620596\pi$
$608$	−0.983032	+	8.09600i	−0.0398672	+	0.328336i
$609$	−0.437955	+	0.166094i	−0.0177468	+	0.00673048i
$610$	−11.0594	−	5.80442i	−0.447782	−	0.235014i
$611$	0.353103	−	13.8310i	0.0142850	−	0.559541i
$612$	3.40390	−	1.78650i	0.137594	−	0.0722151i
$613$	2.32850	−	2.62833i	0.0940473	−	0.106157i	−0.699603	−	0.714532i	$-0.746640\pi$
$613$	2.32850	−	2.62833i	0.0940473	−	0.106157i	0.793650	+	0.608375i	$0.208178\pi$
$614$	−15.4362	+	13.6753i	−0.622955	+	0.551890i
$615$	7.44496	+	1.83502i	0.300210	+	0.0739950i
$616$	10.4518	+	1.26908i	0.421116	+	0.0511328i
$617$	13.4484	+	15.1801i	0.541410	+	0.611126i	0.954006	−	0.299788i	$-0.0969161\pi$
$617$	13.4484	+	15.1801i	0.541410	+	0.611126i	−0.412595	+	0.910914i	$0.635378\pi$
$618$	1.35965	+	0.515645i	0.0546930	+	0.0207423i
$619$	−11.7821	+	22.4488i	−0.473561	+	0.902295i	0.525124	+	0.851026i	$0.324019\pi$
$619$	−11.7821	+	22.4488i	−0.473561	+	0.902295i	−0.998685	+	0.0512692i	$0.983673\pi$
$620$	4.47132	−	2.34673i	0.179572	−	0.0942468i
$621$	−0.0528559	−	0.435308i	−0.00212104	−	0.0174683i
$622$	−14.8330	−	16.7430i	−0.594749	−	0.671333i
$623$	−1.66314	+	0.409928i	−0.0666324	+	0.0164234i
$624$	−3.58413	−	0.0915025i	−0.143480	−	0.00366303i
$625$	−44.3555	−	10.9327i	−1.77422	−	0.437306i
$626$	−15.2851	−	29.1234i	−0.610917	−	1.16400i
$627$	6.52184	−	3.42293i	0.260457	−	0.136698i
$628$	−1.46263	−	3.85664i	−0.0583653	−	0.153897i
$629$	4.19645	−	1.59150i	0.167324	−	0.0634575i
$630$	7.61041	−	5.25309i	0.303206	−	0.209288i
$631$	0.842945	−	3.41996i	0.0335571	−	0.136147i	−0.951774	−	0.306800i	$-0.900742\pi$
$631$	0.842945	−	3.41996i	0.0335571	−	0.136147i	0.985331	+	0.170654i	$0.0545879\pi$
$632$	42.7158	−	29.4846i	1.69914	−	1.17283i
$633$	−0.557627	+	4.59247i	−0.0221637	+	0.182534i
$634$	0.794856	+	2.09586i	0.0315678	+	0.0832374i
$635$	11.4293	−	21.7767i	0.453557	−	0.864180i
$636$	0.279192	−	0.404480i	0.0110707	−	0.0160387i
$637$	−2.27183	−	23.7649i	−0.0900130	−	0.941600i
$638$	10.0316	+	14.5332i	0.397153	+	0.575376i
$639$	25.5640	−	3.10403i	1.01130	−	0.122794i
$640$	−29.1851	+	7.19348i	−1.15364	+	0.284347i
$641$	4.47209	−	6.47894i	0.176637	−	0.255903i	−0.724658	−	0.689109i	$-0.758002\pi$
$641$	4.47209	−	6.47894i	0.176637	−	0.255903i	0.901295	+	0.433206i	$0.142618\pi$
$642$	−3.92717	+	4.43286i	−0.154993	+	0.174951i
$643$	−0.967152	−	1.84275i	−0.0381408	−	0.0726711i	0.865640	−	0.500667i	$-0.166912\pi$
$643$	−0.967152	−	1.84275i	−0.0381408	−	0.0726711i	−0.903781	+	0.427996i	$0.859220\pi$
$644$	0.0509741	+	0.00618937i	0.00200866	+	0.000243895i
$645$	7.26585	−	0.882233i	0.286092	−	0.0347379i
$646$	−14.9955	−	13.2849i	−0.589992	−	0.522687i
$647$	−3.67601	−	5.32561i	−0.144519	−	0.209372i	0.744039	−	0.668136i	$-0.232908\pi$
$647$	−3.67601	−	5.32561i	−0.144519	−	0.209372i	−0.888558	+	0.458764i	$0.848292\pi$
$648$	−24.3542	−	2.95713i	−0.956722	−	0.116167i
$649$	−5.34819	−	44.0463i	−0.209935	−	1.72897i
$650$	51.9326	−	4.96453i	2.03696	−	0.194725i
$651$	−0.0826986	+	0.681084i	−0.00324121	+	0.0266938i
$652$	−0.237119	+	0.962029i	−0.00928629	+	0.0376760i
$653$	−4.93481			−0.193114			−0.0965570	−	0.995327i	$-0.530783\pi$
$653$	−4.93481			−0.193114			−0.0965570	+	0.995327i	$0.530783\pi$
$654$	−6.14666			−0.240353
$655$	−15.1404	+	61.4270i	−0.591584	+	2.40015i
$656$	−17.9846	+	6.82064i	−0.702179	+	0.266301i
$657$			42.0898i			1.64208i
$658$	2.83460	+	1.07502i	0.110504	+	0.0419088i
$659$	−3.25931	+	0.803349i	−0.126965	+	0.0312940i	−0.302286	−	0.953217i	$-0.597750\pi$
$659$	−3.25931	+	0.803349i	−0.126965	+	0.0312940i	0.175321	+	0.984511i	$0.443904\pi$
$660$	−1.88788	−	1.67251i	−0.0734856	−	0.0651025i
$661$	−2.01450	−	8.17313i	−0.0783548	−	0.317898i	0.918666	−	0.395036i	$-0.129268\pi$
$661$	−2.01450	−	8.17313i	−0.0783548	−	0.317898i	−0.997020	+	0.0771382i	$0.975422\pi$
$662$	27.3259	+	24.2086i	1.06205	+	0.940896i
$663$	−2.50494	+	3.43793i	−0.0972838	+	0.133518i
$664$	−6.28258	+	5.56588i	−0.243811	+	0.215998i
$665$	8.47199	+	5.84779i	0.328530	+	0.226768i
$666$	−4.31329	−	1.06313i	−0.167137	−	0.0411955i
$667$	0.326885	+	0.473574i	0.0126570	+	0.0183369i
$668$	0.660092	+	2.67810i	0.0255397	+	0.103619i
$669$	−0.342632	−	1.39011i	−0.0132469	−	0.0537449i
$670$	−49.3330	+	5.99011i	−1.90590	+	0.231418i
$671$	9.06258	+	10.2295i	0.349857	+	0.394907i
$672$	−0.134548	+	0.354773i	−0.00519029	+	0.0136857i
$673$	24.6133	+	12.9181i	0.948773	+	0.497954i	0.866787	−	0.498679i	$-0.166181\pi$
$673$	24.6133	+	12.9181i	0.948773	+	0.497954i	0.0819862	+	0.996633i	$0.473874\pi$
$674$	−14.4226	+	9.95517i	−0.555536	+	0.383459i
$675$	−20.8528			−0.802623
$676$	4.15537	−	1.91718i	0.159822	−	0.0737379i
$677$	11.6742			0.448676			0.224338	−	0.974511i	$-0.427978\pi$
$677$	11.6742			0.448676			0.224338	+	0.974511i	$0.427978\pi$
$678$	−0.0774571	+	0.0534648i	−0.00297472	+	0.00205330i
$679$	−4.74892	−	2.49242i	−0.182247	−	0.0956505i
$680$	−16.2536	+	42.8573i	−0.623299	+	1.64350i
$681$	−5.78685	−	6.53200i	−0.221752	−	0.250307i
$682$	25.6780	−	3.11787i	0.983261	−	0.119390i
$683$	1.85348	+	7.51985i	0.0709213	+	0.287739i	0.995684	−	0.0928045i	$-0.0295831\pi$
$683$	1.85348	+	7.51985i	0.0709213	+	0.287739i	−0.924763	+	0.380543i	$0.875737\pi$
$684$	−1.01370	−	4.11274i	−0.0387598	−	0.157255i
$685$	−11.6518	−	16.8805i	−0.445192	−	0.644972i
$686$	10.4487	+	2.57537i	0.398932	+	0.0983280i
$687$	−6.65221	−	4.59169i	−0.253798	−	0.175184i
$688$	−13.7428	+	12.1750i	−0.523938	+	0.464168i
$689$	2.34177	−	15.8862i	0.0892142	−	0.605216i
$690$	0.287990	+	0.255137i	0.0109636	+	0.00971290i
$691$	−4.68472	−	19.0066i	−0.178215	−	0.723047i	−0.990234	−	0.139416i	$-0.955478\pi$
$691$	−4.68472	−	19.0066i	−0.178215	−	0.723047i	0.812019	−	0.583631i	$-0.198369\pi$
$692$	3.91421	+	3.46769i	0.148796	+	0.131822i
$693$	−9.82433	+	2.42148i	−0.373196	+	0.0919845i
$694$	−10.0015	−	3.79305i	−0.379650	−	0.143982i
$695$		−	50.2388i		−	1.90567i
$696$	−2.14868	+	0.814885i	−0.0814453	+	0.0308881i
$697$	−5.46128	+	22.1573i	−0.206861	+	0.839266i
$698$	−18.8885			−0.714941
$699$	−8.97651			−0.339523
$700$	0.584370	−	2.37088i	0.0220871	−	0.0896109i
$701$	−0.800917	+	6.59615i	−0.0302502	+	0.249133i	0.969737	+	0.244150i	$0.0785091\pi$
$701$	−0.800917	+	6.59615i	−0.0302502	+	0.249133i	−0.999988	+	0.00498259i	$0.998414\pi$
$702$	8.08174	−	2.83126i	0.305026	−	0.106859i
$703$	−0.596090	−	4.90924i	−0.0224820	−	0.185156i
$704$	49.8843	+	6.05705i	1.88008	+	0.228284i
$705$	−2.75642	−	3.99336i	−0.103813	−	0.150399i
$706$	−21.3285	−	18.8954i	−0.802710	−	0.711139i
$707$	−7.82780	+	0.950467i	−0.294395	+	0.0357460i
$708$	0.857870	+	0.104164i	0.0322407	+	0.00391474i
$709$	−19.3732	−	36.9126i	−0.727577	−	1.38628i	−0.914776	−	0.403961i	$-0.867633\pi$
$709$	−19.3732	−	36.9126i	−0.727577	−	1.38628i	0.187199	−	0.982322i	$-0.440059\pi$
$710$	−30.4739	+	34.3979i	−1.14367	+	1.29093i
$711$	−28.3357	+	41.0513i	−1.06267	+	1.53955i
$712$	−8.15964	+	2.01117i	−0.305795	+	0.0753718i
$713$	0.836733	−	0.101598i	0.0313359	−	0.00380487i
$714$	−0.529475	−	0.767077i	−0.0198151	−	0.0287071i
$715$	−79.4820	−	21.7566i	−2.97246	−	0.813651i
$716$	−3.68862	+	5.34389i	−0.137850	+	0.199711i
$717$	0.566885	−	1.08011i	0.0211707	−	0.0403374i
$718$	2.60279	+	6.86300i	0.0971354	+	0.256125i
$719$	3.39762	−	27.9819i	0.126710	−	1.04355i	−0.781170	−	0.624318i	$-0.785377\pi$
$719$	3.39762	−	27.9819i	0.126710	−	1.04355i	0.907880	−	0.419231i	$-0.137700\pi$
$720$	30.5558	−	21.0912i	1.13875	−	0.786022i
$721$	0.532184	−	2.15915i	0.0198196	−	0.0804111i
$722$	1.90630	−	1.31582i	0.0709452	−	0.0489699i
$723$	−4.24597	+	1.61028i	−0.157909	+	0.0598871i
$724$	−0.794448	−	2.09479i	−0.0295254	−	0.0778521i
$725$	24.2300	−	12.7169i	0.899879	−	0.472293i
$726$	−3.94680	−	7.51999i	−0.146479	−	0.279093i
$727$	−6.24507	−	1.53927i	−0.231617	−	0.0570885i	0.121799	−	0.992555i	$-0.461134\pi$
$727$	−6.24507	−	1.53927i	−0.231617	−	0.0570885i	−0.353416	+	0.935466i	$0.614980\pi$
$728$	0.637570	+	6.66944i	0.0236299	+	0.247186i
$729$	21.2026	−	5.22598i	0.785283	−	0.193555i
$730$	−49.8079	−	56.2215i	−1.84347	−	2.08085i
$731$	2.62566	+	21.6242i	0.0971134	+	0.799800i
$732$	−0.235688	+	0.123698i	−0.00871126	+	0.00457202i
$733$	−0.163936	+	0.312354i	−0.00605511	+	0.0115371i	−0.888465	−	0.458945i	$-0.848228\pi$
$733$	−0.163936	+	0.312354i	−0.00605511	+	0.0115371i	0.882410	+	0.470482i	$0.155920\pi$
$734$	1.40806	+	0.534008i	0.0519726	+	0.0197106i
$735$	−5.55213	−	6.26706i	−0.204793	−	0.231164i
$736$	0.462743	+	0.0561872i	0.0170569	+	0.00207109i
$737$	52.7961	+	13.0131i	1.94477	+	0.479343i
$738$	16.9073	−	14.9785i	0.622365	−	0.551367i
$739$	17.5218	−	19.7780i	0.644548	−	0.727545i	−0.331896	−	0.943316i	$-0.607688\pi$
$739$	17.5218	−	19.7780i	0.644548	−	0.727545i	0.976444	+	0.215771i	$0.0692266\pi$
$740$	−1.49945	+	0.786973i	−0.0551209	+	0.0289297i
$741$	3.01752	+	3.58647i	0.110851	+	0.131752i
$742$	3.11555	+	1.63517i	0.114375	+	0.0600289i
$743$	−46.0776	+	17.4749i	−1.69042	+	0.641093i	−0.996851	−	0.0792952i	$-0.974733\pi$
$743$	−46.0776	+	17.4749i	−1.69042	+	0.641093i	−0.693571	+	0.720388i	$0.743964\pi$
$744$	−0.405732	+	3.34150i	−0.0148749	+	0.122506i
$745$	35.5980	+	18.6833i	1.30421	+	0.684503i
$746$		−	16.4610i		−	0.602680i
$747$	3.74864	−	7.14243i	0.137156	−	0.261328i
$748$	4.97765	−	5.61860i	0.182001	−	0.205436i
$749$	7.45352	+	5.14479i	0.272346	+	0.187987i
$750$	7.61984	−	6.75059i	0.278237	−	0.246497i
$751$	−11.4866	+	16.6412i	−0.419152	+	0.607247i	−0.974504	−	0.224368i	$-0.927968\pi$
$751$	−11.4866	+	16.6412i	−0.419152	+	0.607247i	0.555352	+	0.831615i	$0.312583\pi$
$752$	11.3809	+	4.31622i	0.415021	+	0.157397i
$753$	−1.73533	+	4.57570i	−0.0632391	+	0.166748i
$754$	−7.66400	+	8.21838i	−0.279106	+	0.299296i
$755$	16.0481	+	42.3153i	0.584049	+	1.54001i
$756$		−	0.400815i		−	0.0145775i
$757$	9.91962	−	26.1559i	0.360535	−	0.950652i	−0.624916	−	0.780692i	$-0.714867\pi$
$757$	9.91962	−	26.1559i	0.360535	−	0.950652i	0.985451	−	0.169960i	$-0.0543640\pi$
$758$	−0.113519	−	0.934916i	−0.00412321	−	0.0339577i
$759$	−0.195644	−	0.372769i	−0.00710144	−	0.0135307i
$760$	41.5649	+	28.6902i	1.50772	+	1.04070i
$761$	12.8538	+	8.87231i	0.465949	+	0.321621i	0.777802	−	0.628509i	$-0.216334\pi$
$761$	12.8538	+	8.87231i	0.465949	+	0.321621i	−0.311854	+	0.950130i	$0.600950\pi$
$762$	1.14025	+	2.17257i	0.0413070	+	0.0787040i
$763$	1.13303	+	9.33136i	0.0410185	+	0.337818i
$764$	−0.869826	+	2.29354i	−0.0314692	+	0.0829775i
$765$		−	44.0499i		−	1.59263i
$766$	15.9474	+	42.0499i	0.576203	+	1.51932i

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.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05649 - 0.729245i) q^{2} +(-0.277577 - 0.145684i) q^{3} +(-0.124830 + 0.329149i) q^{4} +(2.67487 + 3.01931i) q^{5} +(-0.399497 + 0.0485078i) q^{6} +(0.147281 + 0.597543i) q^{7} +(0.722584 + 2.93164i) q^{8} +(-1.64837 - 2.38807i) q^{9} +O(q^{10})\)	\(q+(1.05649 - 0.729245i) q^{2} +(-0.277577 - 0.145684i) q^{3} +(-0.124830 + 0.329149i) q^{4} +(2.67487 + 3.01931i) q^{5} +(-0.399497 + 0.0485078i) q^{6} +(0.147281 + 0.597543i) q^{7} +(0.722584 + 2.93164i) q^{8} +(-1.64837 - 2.38807i) q^{9} +(5.02780 + 1.23924i) q^{10} +(-4.66304 - 3.21866i) q^{11} +(0.0826014 - 0.0731785i) q^{12} +(1.36417 - 3.33752i) q^{13} +(0.591356 + 0.523896i) q^{14} +(-0.302619 - 1.22778i) q^{15} +(2.37430 + 2.10344i) q^{16} +(3.65404 - 0.900639i) q^{17} +(-3.48298 - 1.32092i) q^{18} -4.14676i q^{19} +(-1.32770 + 0.503531i) q^{20} +(0.0461704 - 0.187321i) q^{21} -7.27366 q^{22} -0.237017 q^{23} +(0.226519 - 0.919024i) q^{24} +(-1.35859 + 11.1890i) q^{25} +(-0.992633 - 4.52088i) q^{26} +(0.223005 + 1.83661i) q^{27} +(-0.215065 - 0.0261137i) q^{28} +(-1.37916 - 1.99806i) q^{29} +(-1.21506 - 1.07645i) q^{30} +(-3.53027 + 0.428653i) q^{31} +(-1.95237 - 0.237060i) q^{32} +(0.825446 + 1.57276i) q^{33} +(3.20368 - 3.61621i) q^{34} +(-1.41021 + 2.04304i) q^{35} +(0.991797 - 0.244456i) q^{36} +(1.18387 - 0.143748i) q^{37} +(-3.02400 - 4.38103i) q^{38} +(-0.864884 + 0.727682i) q^{39} +(-6.91869 + 10.0235i) q^{40} +(-2.81798 + 5.36921i) q^{41} +(-0.0878239 - 0.231572i) q^{42} +(-0.697683 + 5.74593i) q^{43} +(1.64150 - 1.13305i) q^{44} +(2.80115 - 11.3647i) q^{45} +(-0.250406 + 0.172843i) q^{46} +(3.58791 - 1.36071i) q^{47} +(-0.352613 - 0.929765i) q^{48} +(5.86283 - 3.07705i) q^{49} +(6.72416 + 12.8118i) q^{50} +(-1.14549 - 0.282337i) q^{51} +(0.928251 + 0.865636i) q^{52} +(4.32424 - 1.06583i) q^{53} +(1.57494 + 1.77774i) q^{54} +(-2.75490 - 22.6886i) q^{55} +(-1.64536 + 0.863550i) q^{56} +(-0.604116 + 1.15105i) q^{57} +(-2.91415 - 1.10519i) q^{58} +(5.19283 + 5.86150i) q^{59} +(0.441896 + 0.0536559i) q^{60} +(-2.34193 - 0.577233i) q^{61} +(-3.41712 + 3.02730i) q^{62} +(1.18420 - 1.33669i) q^{63} +(-7.85292 + 4.12153i) q^{64} +(13.7260 - 4.80859i) q^{65} +(2.01900 + 1.05965i) q^{66} +(-8.97327 + 3.40311i) q^{67} +(-0.159688 + 1.31515i) q^{68} +(0.0657904 + 0.0345295i) q^{69} +3.18684i q^{70} +(-4.12424 + 7.85809i) q^{71} +(5.80989 - 6.55801i) q^{72} +(-11.9374 - 8.23982i) q^{73} +(1.14593 - 1.01520i) q^{74} +(2.00716 - 2.90788i) q^{75} +(1.36490 + 0.517639i) q^{76} +(1.23651 - 3.26041i) q^{77} +(-0.383086 + 1.39950i) q^{78} +(-6.09571 - 16.0731i) q^{79} +12.7952i q^{80} +(-2.88124 + 7.59720i) q^{81} +(0.938292 + 7.72753i) q^{82} +(1.29186 + 2.46144i) q^{83} +(0.0558929 + 0.0385801i) q^{84} +(12.4934 + 8.62356i) q^{85} +(3.45309 + 6.57932i) q^{86} +(0.0917389 + 0.755538i) q^{87} +(6.06652 - 15.9961i) q^{88} +2.78330i q^{89} +(-5.32826 - 14.0495i) q^{90} +(2.19523 + 0.323596i) q^{91} +(0.0295867 - 0.0780137i) q^{92} +(1.04237 + 0.395319i) q^{93} +(2.79831 - 4.05405i) q^{94} +(12.5203 - 11.0921i) q^{95} +(0.507396 + 0.350230i) q^{96} +(-5.77891 + 6.52304i) q^{97} +(3.95012 - 7.52632i) q^{98} +16.4412i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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