LMFDB - Embedded newform 169.2.h.a.12.7

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			12.7
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156578 - 0.108078i) q^{2} +(2.47375 + 1.29833i) q^{3} +(-0.696374 + 1.83619i) q^{4} +(0.268145 + 0.302673i) q^{5} +(0.527655 - 0.0640690i) q^{6} +(-0.983215 - 3.98906i) q^{7} +(0.180477 + 0.732225i) q^{8} +(2.72961 + 3.95452i) q^{9} +O(q^{10})$	\(q+(0.156578 - 0.108078i) q^{2} +(2.47375 + 1.29833i) q^{3} +(-0.696374 + 1.83619i) q^{4} +(0.268145 + 0.302673i) q^{5} +(0.527655 - 0.0640690i) q^{6} +(-0.983215 - 3.98906i) q^{7} +(0.180477 + 0.732225i) q^{8} +(2.72961 + 3.95452i) q^{9} +(0.0746977 + 0.0184113i) q^{10} +(-3.14047 - 2.16771i) q^{11} +(-4.10663 + 3.63815i) q^{12} +(-0.132396 + 3.60312i) q^{13} +(-0.585079 - 0.518335i) q^{14} +(0.270356 + 1.09688i) q^{15} +(-2.83246 - 2.50934i) q^{16} +(5.36554 - 1.32249i) q^{17} +(0.854793 + 0.324180i) q^{18} -2.02432i q^{19} +(-0.742492 + 0.281590i) q^{20} +(2.74687 - 11.1445i) q^{21} -0.726011 q^{22} -4.36801 q^{23} +(-0.504210 + 2.04566i) q^{24} +(0.582974 - 4.80122i) q^{25} +(0.368687 + 0.578478i) q^{26} +(0.607870 + 5.00626i) q^{27} +(8.00935 + 0.972511i) q^{28} +(4.82210 + 6.98602i) q^{29} +(0.160880 + 0.142527i) q^{30} +(4.58503 - 0.556723i) q^{31} +(-2.21198 - 0.268584i) q^{32} +(-4.95436 - 9.43975i) q^{33} +(0.697193 - 0.786968i) q^{34} +(0.943736 - 1.36724i) q^{35} +(-9.16207 + 2.25825i) q^{36} +(-9.27923 + 1.12670i) q^{37} +(-0.218784 - 0.316963i) q^{38} +(-5.00554 + 8.74134i) q^{39} +(-0.173230 + 0.250968i) q^{40} +(-0.934182 + 1.77994i) q^{41} +(-0.774374 - 2.04186i) q^{42} +(0.751651 - 6.19040i) q^{43} +(6.16727 - 4.25696i) q^{44} +(-0.464996 + 1.88656i) q^{45} +(-0.683934 + 0.472085i) q^{46} +(-3.09675 + 1.17444i) q^{47} +(-3.74886 - 9.88494i) q^{48} +(-8.74771 + 4.59115i) q^{49} +(-0.427625 - 0.814772i) q^{50} +(14.9900 + 3.69471i) q^{51} +(-6.52381 - 2.75222i) q^{52} +(-6.07185 + 1.49658i) q^{53} +(0.636245 + 0.718172i) q^{54} +(-0.185994 - 1.53180i) q^{55} +(2.74344 - 1.43987i) q^{56} +(2.62822 - 5.00766i) q^{57} +(1.51007 + 0.572693i) q^{58} +(6.58214 + 7.42969i) q^{59} +(-2.20234 - 0.267412i) q^{60} +(-4.30087 - 1.06007i) q^{61} +(0.657745 - 0.582711i) q^{62} +(13.0910 - 14.7767i) q^{63} +(6.32598 - 3.32013i) q^{64} +(-1.12607 + 0.926084i) q^{65} +(-1.79597 - 0.942599i) q^{66} +(-4.35852 + 1.65297i) q^{67} +(-1.30809 + 10.7731i) q^{68} +(-10.8054 - 5.67110i) q^{69} -0.316076i q^{70} +(-4.93011 + 9.39353i) q^{71} +(-2.40297 + 2.71239i) q^{72} +(6.97287 + 4.81303i) q^{73} +(-1.33115 + 1.17930i) q^{74} +(7.67569 - 11.1202i) q^{75} +(3.71702 + 1.40968i) q^{76} +(-5.55938 + 14.6589i) q^{77} +(0.160989 + 1.90969i) q^{78} +(-2.88713 - 7.61275i) q^{79} -1.53017i q^{80} +(0.115704 - 0.305087i) q^{81} +(0.0460994 + 0.379663i) q^{82} +(1.74252 + 3.32009i) q^{83} +(18.5505 + 12.8045i) q^{84} +(1.83902 + 1.26938i) q^{85} +(-0.551354 - 1.05052i) q^{86} +(2.85856 + 23.5423i) q^{87} +(1.02047 - 2.69076i) q^{88} +3.64179i q^{89} +(0.131088 + 0.345650i) q^{90} +(14.5032 - 3.01451i) q^{91} +(3.04177 - 8.02048i) q^{92} +(12.0650 + 4.57567i) q^{93} +(-0.357951 + 0.518582i) q^{94} +(0.612705 - 0.542809i) q^{95} +(-5.12319 - 3.53629i) q^{96} +(7.28820 - 8.22667i) q^{97} +(-0.873495 + 1.66431i) q^{98} -18.3361i 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 $

$2$	0.156578	−	0.108078i	0.110717	−	0.0764226i	−0.511419	−	0.859331i	$-0.670880\pi$
$2$	0.156578	−	0.108078i	0.110717	−	0.0764226i	0.622137	+	0.782909i	$0.286265\pi$
$3$	2.47375	+	1.29833i	1.42822	+	0.749589i	0.988878	−	0.148730i	$-0.0475186\pi$
$3$	2.47375	+	1.29833i	1.42822	+	0.749589i	0.439344	+	0.898319i	$0.355211\pi$
$4$	−0.696374	+	1.83619i	−0.348187	+	0.918094i
$5$	0.268145	+	0.302673i	0.119918	+	0.135359i	0.805404	−	0.592727i	$-0.201949\pi$
$5$	0.268145	+	0.302673i	0.119918	+	0.135359i	−0.685486	+	0.728086i	$0.740410\pi$
$6$	0.527655	−	0.0640690i	0.215414	−	0.0261560i
$7$	−0.983215	−	3.98906i	−0.371620	−	1.50772i	−0.797709	−	0.603042i	$-0.793955\pi$
$7$	−0.983215	−	3.98906i	−0.371620	−	1.50772i	0.426089	−	0.904681i	$-0.359891\pi$
$8$	0.180477	+	0.732225i	0.0638083	+	0.258881i
$9$	2.72961	+	3.95452i	0.909870	+	1.31817i
$10$	0.0746977	+	0.0184113i	0.0236215	+	0.00582218i
$11$	−3.14047	−	2.16771i	−0.946889	−	0.653590i	−0.00879126	−	0.999961i	$-0.502798\pi$
$11$	−3.14047	−	2.16771i	−0.946889	−	0.653590i	−0.938098	+	0.346371i	$0.887414\pi$
$12$	−4.10663	+	3.63815i	−1.18548	+	1.05024i
$13$	−0.132396	+	3.60312i	−0.0367199	+	0.999326i
$13$	−0.132396	+	3.60312i	−0.0367199	+	0.999326i
$14$	−0.585079	−	0.518335i	−0.156369	−	0.138531i
$15$	0.270356	+	1.09688i	0.0698055	+	0.283212i
$16$	−2.83246	−	2.50934i	−0.708115	−	0.627335i
$17$	5.36554	−	1.32249i	1.30133	−	0.320750i	0.473039	−	0.881042i	$-0.343157\pi$
$17$	5.36554	−	1.32249i	1.30133	−	0.320750i	0.828295	+	0.560292i	$0.189311\pi$
$18$	0.854793	+	0.324180i	0.201477	+	0.0764100i
$19$		−	2.02432i		−	0.464410i	−0.972667	−	0.232205i	$-0.925406\pi$
$19$		−	2.02432i		−	0.464410i	0.972667	−	0.232205i	$-0.0745940\pi$
$20$	−0.742492	+	0.281590i	−0.166026	+	0.0629655i
$21$	2.74687	−	11.1445i	0.599416	−	2.43193i
$22$	−0.726011			−0.154786
$23$	−4.36801			−0.910793			−0.455396	−	0.890289i	$-0.650502\pi$
$23$	−4.36801			−0.910793			−0.455396	+	0.890289i	$0.650502\pi$
$24$	−0.504210	+	2.04566i	−0.102921	+	0.417569i
$25$	0.582974	−	4.80122i	0.116595	−	0.960245i
$26$	0.368687	+	0.578478i	0.0723056	+	0.113449i
$27$	0.607870	+	5.00626i	0.116985	+	0.963455i
$28$	8.00935	+	0.972511i	1.51362	+	0.183787i
$29$	4.82210	+	6.98602i	0.895441	+	1.29727i	0.954253	+	0.299002i	$0.0966537\pi$
$29$	4.82210	+	6.98602i	0.895441	+	1.29727i	−0.0588110	+	0.998269i	$0.518731\pi$
$30$	0.160880	+	0.142527i	0.0293725	+	0.0260218i
$31$	4.58503	−	0.556723i	0.823496	−	0.0999905i	0.302068	−	0.953286i	$-0.402323\pi$
$31$	4.58503	−	0.556723i	0.823496	−	0.0999905i	0.521427	+	0.853296i	$0.325400\pi$
$32$	−2.21198	−	0.268584i	−0.391027	−	0.0474793i
$33$	−4.95436	−	9.43975i	−0.862444	−	1.64325i
$34$	0.697193	−	0.786968i	0.119568	−	0.134964i
$35$	0.943736	−	1.36724i	0.159520	−	0.231105i
$36$	−9.16207	+	2.25825i	−1.52701	+	0.376375i
$37$	−9.27923	+	1.12670i	−1.52550	+	0.185229i	−0.839895	−	0.542749i	$-0.817384\pi$
$37$	−9.27923	+	1.12670i	−1.52550	+	0.185229i	−0.685601	+	0.727978i	$0.740460\pi$
$38$	−0.218784	−	0.316963i	−0.0354914	−	0.0514182i
$39$	−5.00554	+	8.74134i	−0.801527	+	1.39973i
$40$	−0.173230	+	0.250968i	−0.0273901	+	0.0396815i
$41$	−0.934182	+	1.77994i	−0.145895	+	0.277979i	−0.947427	−	0.319973i	$-0.896326\pi$
$41$	−0.934182	+	1.77994i	−0.145895	+	0.277979i	0.801532	+	0.597952i	$0.204019\pi$
$42$	−0.774374	−	2.04186i	−0.119488	−	0.315065i
$43$	0.751651	−	6.19040i	0.114626	−	0.944028i	−0.815999	−	0.578053i	$-0.803813\pi$
$43$	0.751651	−	6.19040i	0.114626	−	0.944028i	0.930625	−	0.365975i	$-0.119264\pi$
$44$	6.16727	−	4.25696i	0.929751	−	0.641761i
$45$	−0.464996	+	1.88656i	−0.0693175	+	0.281232i
$46$	−0.683934	+	0.472085i	−0.100841	+	0.0696052i
$47$	−3.09675	+	1.17444i	−0.451708	+	0.171310i	−0.569958	−	0.821674i	$-0.693041\pi$
$47$	−3.09675	+	1.17444i	−0.451708	+	0.171310i	0.118251	+	0.992984i	$0.462271\pi$
$48$	−3.74886	−	9.88494i	−0.541102	−	1.42677i
$49$	−8.74771	+	4.59115i	−1.24967	+	0.655879i
$50$	−0.427625	−	0.814772i	−0.0604754	−	0.115226i
$51$	14.9900	+	3.69471i	2.09902	+	0.517363i
$52$	−6.52381	−	2.75222i	−0.904689	−	0.381665i
$53$	−6.07185	+	1.49658i	−0.834032	+	0.205570i	−0.633135	−	0.774042i	$-0.718232\pi$
$53$	−6.07185	+	1.49658i	−0.834032	+	0.205570i	−0.200898	+	0.979612i	$0.564386\pi$
$54$	0.636245	+	0.718172i	0.0865820	+	0.0977309i
$55$	−0.185994	−	1.53180i	−0.0250794	−	0.206547i
$56$	2.74344	−	1.43987i	0.366608	−	0.192411i
$57$	2.62822	−	5.00766i	0.348116	−	0.663280i
$58$	1.51007	+	0.572693i	0.198282	+	0.0751983i
$59$	6.58214	+	7.42969i	0.856921	+	0.967264i	0.999747	−	0.0224839i	$-0.00715746\pi$
$59$	6.58214	+	7.42969i	0.856921	+	0.967264i	−0.142826	+	0.989748i	$0.545619\pi$
$60$	−2.20234	−	0.267412i	−0.284321	−	0.0345228i
$61$	−4.30087	−	1.06007i	−0.550670	−	0.135728i	−0.0458432	−	0.998949i	$-0.514597\pi$
$61$	−4.30087	−	1.06007i	−0.550670	−	0.135728i	−0.504827	+	0.863221i	$0.668444\pi$
$62$	0.657745	−	0.582711i	0.0835337	−	0.0740044i
$63$	13.0910	−	14.7767i	1.64932	−	1.86169i
$64$	6.32598	−	3.32013i	0.790747	−	0.415016i
$65$	−1.12607	+	0.926084i	−0.139671	+	0.114867i
$66$	−1.79597	−	0.942599i	−0.221069	−	0.116026i
$67$	−4.35852	+	1.65297i	−0.532478	+	0.201942i	−0.606165	−	0.795339i	$-0.707293\pi$
$67$	−4.35852	+	1.65297i	−0.532478	+	0.201942i	0.0736864	+	0.997281i	$0.476524\pi$
$68$	−1.30809	+	10.7731i	−0.158629	+	1.30643i
$69$	−10.8054	−	5.67110i	−1.30081	−	0.682720i
$70$		−	0.316076i		−	0.0377783i
$71$	−4.93011	+	9.39353i	−0.585096	+	1.11481i	0.395445	+	0.918490i	$0.370591\pi$
$71$	−4.93011	+	9.39353i	−0.585096	+	1.11481i	−0.980540	+	0.196317i	$0.937102\pi$
$72$	−2.40297	+	2.71239i	−0.283192	+	0.319658i
$73$	6.97287	+	4.81303i	0.816113	+	0.563322i	0.901376	−	0.433036i	$-0.142558\pi$
$73$	6.97287	+	4.81303i	0.816113	+	0.563322i	−0.0852635	+	0.996358i	$0.527173\pi$
$74$	−1.33115	+	1.17930i	−0.154743	+	0.137090i
$75$	7.67569	−	11.1202i	0.886312	−	1.28404i
$76$	3.71702	+	1.40968i	0.426372	+	0.161701i
$77$	−5.55938	+	14.6589i	−0.633550	+	1.67053i
$78$	0.160989	+	1.90969i	0.0182284	+	0.216230i
$79$	−2.88713	−	7.61275i	−0.324828	−	0.856501i	−0.993592	−	0.113026i	$-0.963946\pi$
$79$	−2.88713	−	7.61275i	−0.324828	−	0.856501i	0.668764	−	0.743475i	$-0.266824\pi$
$80$		−	1.53017i		−	0.171079i
$81$	0.115704	−	0.305087i	0.0128560	−	0.0338986i
$82$	0.0460994	+	0.379663i	0.00509083	+	0.0419268i
$83$	1.74252	+	3.32009i	0.191266	+	0.364427i	0.962138	−	0.272563i	$-0.0878713\pi$
$83$	1.74252	+	3.32009i	0.191266	+	0.364427i	−0.770872	+	0.636991i	$0.780179\pi$
$84$	18.5505	+	12.8045i	2.02403	+	1.39709i
$85$	1.83902	+	1.26938i	0.199470	+	0.137684i
$86$	−0.551354	−	1.05052i	−0.0594540	−	0.113280i
$87$	2.85856	+	23.5423i	0.306470	+	2.52400i
$88$	1.02047	−	2.69076i	0.108782	−	0.286836i
$89$			3.64179i			0.386029i	0.981196	+	0.193014i	$0.0618264\pi$
$89$			3.64179i			0.386029i	−0.981196	+	0.193014i	$0.938174\pi$
$90$	0.131088	+	0.345650i	0.0138178	+	0.0364347i
$91$	14.5032	−	3.01451i	1.52035	−	0.316006i
$92$	3.04177	−	8.02048i	0.317126	−	0.836193i
$93$	12.0650	+	4.57567i	1.25109	+	0.474474i
$94$	−0.357951	+	0.518582i	−0.0369199	+	0.0534877i
$95$	0.612705	−	0.542809i	0.0628622	−	0.0556910i
$96$	−5.12319	−	3.53629i	−0.522884	−	0.360921i
$97$	7.28820	−	8.22667i	0.740004	−	0.835292i	−0.251158	−	0.967946i	$-0.580811\pi$
$97$	7.28820	−	8.22667i	0.740004	−	0.835292i	0.991162	+	0.132654i	$0.0423499\pi$
$98$	−0.873495	+	1.66431i	−0.0882364	+	0.168120i
$99$		−	18.3361i		−	1.84285i
$100$	8.40998	+	4.41390i	0.840998	+	0.441390i
$101$	−0.957265	+	7.88378i	−0.0952514	+	0.784466i	0.864309	+	0.502962i	$0.167756\pi$
$101$	−0.957265	+	7.88378i	−0.0952514	+	0.784466i	−0.959560	+	0.281504i	$0.909167\pi$
$102$	2.74642	−	1.04158i	0.271937	−	0.103132i
$103$	5.19618	+	2.72717i	0.511995	+	0.268716i	0.700875	−	0.713285i	$-0.252793\pi$
$103$	5.19618	+	2.72717i	0.511995	+	0.268716i	−0.188880	+	0.982000i	$0.560486\pi$
$104$	−2.66219	+	0.553337i	−0.261049	+	0.0542592i
$105$	4.10969	−	2.15693i	0.401065	−	0.210495i
$106$	−0.788970	+	0.890563i	−0.0766316	+	0.0864991i
$107$	−7.93123	+	7.02646i	−0.766741	+	0.679273i	−0.952913	−	0.303244i	$-0.901930\pi$
$107$	−7.93123	+	7.02646i	−0.766741	+	0.679273i	0.186172	+	0.982517i	$0.440392\pi$
$108$	−9.61573	−	2.37007i	−0.925274	−	0.228060i
$109$	0.805196	+	0.0977685i	0.0771238	+	0.00936453i	0.159008	−	0.987277i	$-0.449171\pi$
$109$	0.805196	+	0.0977685i	0.0771238	+	0.00936453i	−0.0818838	+	0.996642i	$0.526094\pi$
$110$	−0.194676	−	0.219744i	−0.0185616	−	0.0209517i
$111$	−24.4173	−	9.26028i	−2.31759	−	0.878947i
$112$	−7.22499	+	13.7661i	−0.682698	+	1.30077i
$113$	5.61914	−	2.94915i	0.528604	−	0.277433i	−0.179235	−	0.983806i	$-0.557362\pi$
$113$	5.61914	−	2.94915i	0.528604	−	0.277433i	0.707840	+	0.706373i	$0.249670\pi$
$114$	−0.129696	−	1.06814i	−0.0121471	−	0.100041i
$115$	−1.17126	−	1.32208i	−0.109220	−	0.123284i
$116$	−16.1856	+	3.98940i	−1.50280	+	0.370406i
$117$	−14.6100	+	9.31155i	−1.35070	+	0.860853i
$118$	1.83360	+	0.451943i	0.168797	+	0.0416047i
$119$	−10.5510	−	20.1032i	−0.967205	−	1.84285i
$120$	−0.754367	+	0.395922i	−0.0688640	+	0.0361426i
$121$	1.26295	+	3.33012i	0.114813	+	0.302738i
$122$	−0.787991	+	0.298846i	−0.0713414	+	0.0270562i
$123$	−4.62187	+	3.19025i	−0.416740	+	0.287655i
$124$	−2.17065	+	8.80666i	−0.194930	+	0.790861i
$125$	3.27346	−	2.25950i	0.292787	−	0.202096i
$126$	0.452729	−	3.72856i	0.0403323	−	0.332167i
$127$	−2.86624	−	7.55766i	−0.254338	−	0.670634i	−0.999991	−	0.00429931i	$-0.998631\pi$
$127$	−2.86624	−	7.55766i	−0.254338	−	0.670634i	0.745653	−	0.666335i	$-0.232138\pi$
$128$	2.70270	−	5.14956i	0.238887	−	0.455161i
$129$	9.89656	−	14.3376i	0.871343	−	1.26236i
$130$	−0.0762279	+	0.266707i	−0.00668563	+	0.0233918i
$131$	−1.39014	−	2.01397i	−0.121457	−	0.175961i	0.757539	−	0.652790i	$-0.226402\pi$
$131$	−1.39014	−	2.01397i	−0.121457	−	0.175961i	−0.878996	+	0.476829i	$0.841786\pi$
$132$	20.7832	−	2.52354i	1.80895	−	0.219646i
$133$	−8.07512	+	1.99034i	−0.700201	+	0.172584i
$134$	−0.503799	+	0.729879i	−0.0435216	+	0.0630519i
$135$	−1.35226	+	1.52639i	−0.116384	+	0.131370i
$136$	1.93671	+	3.69010i	0.166072	+	0.316424i
$137$	9.48606	+	1.15182i	0.810449	+	0.0984063i	0.515262	−	0.857033i	$-0.327695\pi$
$137$	9.48606	+	1.15182i	0.810449	+	0.0984063i	0.295188	+	0.955439i	$0.404618\pi$
$138$	−2.30480	+	0.279854i	−0.196198	+	0.0238227i
$139$	6.29596	+	5.57774i	0.534017	+	0.473098i	0.886505	−	0.462719i	$-0.153126\pi$
$139$	6.29596	+	5.57774i	0.534017	+	0.473098i	−0.352488	+	0.935816i	$0.614664\pi$
$140$	1.85331	+	2.68498i	0.156633	+	0.226923i
$141$	−9.18541	−	1.11531i	−0.773551	−	0.0939261i
$142$	0.243288	+	2.00365i	0.0204163	+	0.168143i
$143$	8.22632	−	11.0285i	0.687919	−	0.922250i
$144$	2.19173	−	18.0505i	0.182644	−	1.50421i
$145$	−0.821457	+	3.33278i	−0.0682183	+	0.276772i
$146$	1.61198			0.133408
$147$	−27.6005			−2.27645
$148$	4.39298	−	17.8230i	0.361100	−	1.46504i
$149$	−10.7339	+	4.07084i	−0.879357	+	0.333496i	−0.752632	−	0.658442i	$-0.771216\pi$
$149$	−10.7339	+	4.07084i	−0.879357	+	0.333496i	−0.126725	+	0.991938i	$0.540447\pi$
$150$		−	2.57074i		−	0.209900i
$151$	12.1024	+	4.58985i	0.984883	+	0.373517i	0.793881	−	0.608073i	$-0.208057\pi$
$151$	12.1024	+	4.58985i	0.984883	+	0.373517i	0.191002	+	0.981590i	$0.438826\pi$
$152$	1.48225	−	0.365343i	0.120227	−	0.0296332i
$153$	19.8756	+	17.6083i	1.60685	+	1.42354i
$154$	0.713825	+	2.89610i	0.0575217	+	0.233375i
$155$	1.39796	+	1.23848i	0.112286	+	0.0994771i
$156$	−12.5650	−	15.2783i	−1.00601	−	1.22325i
$157$	3.92764	−	3.47958i	0.313460	−	0.277701i	−0.491693	−	0.870769i	$-0.663622\pi$
$157$	3.92764	−	3.47958i	0.313460	−	0.277701i	0.805153	+	0.593068i	$0.202083\pi$
$158$	−1.27483	−	0.879952i	−0.101420	−	0.0700052i
$159$	−16.9633	−	4.18108i	−1.34528	−	0.331581i
$160$	−0.511839	−	0.741526i	−0.0404644	−	0.0586228i
$161$	4.29469	+	17.4243i	0.338469	+	1.37322i
$162$	−0.0148565	−	0.0602750i	−0.00116723	−	0.00473565i
$163$	−19.9021	+	2.41655i	−1.55885	+	0.189279i	−0.854075	−	0.520150i	$-0.825876\pi$
$163$	−19.9021	+	2.41655i	−1.55885	+	0.189279i	−0.704777	+	0.709429i	$0.748953\pi$
$164$	−2.61775	−	2.95483i	−0.204412	−	0.230734i
$165$	1.52867	−	4.03077i	0.119007	−	0.313795i
$166$	0.631669	+	0.331525i	0.0490270	+	0.0257313i
$167$	20.1078	−	13.8794i	1.55599	−	1.07402i	0.592741	−	0.805393i	$-0.298046\pi$
$167$	20.1078	−	13.8794i	1.55599	−	1.07402i	0.963245	−	0.268626i	$-0.0865695\pi$
$168$	8.65601			0.667826
$169$	−12.9649	−	0.954075i	−0.997303	−	0.0733904i
$170$	0.425142			0.0326069
$171$	8.00520	−	5.52559i	0.612173	−	0.422552i
$172$	10.8433	+	5.69101i	0.826795	+	0.433935i
$173$	−8.04730	+	21.2190i	−0.611825	+	1.61325i	0.166965	+	0.985963i	$0.446603\pi$
$173$	−8.04730	+	21.2190i	−0.611825	+	1.61325i	−0.778789	+	0.627286i	$0.784166\pi$
$174$	2.99199	+	3.37726i	0.226822	+	0.256030i
$175$	−19.7256	+	2.39512i	−1.49111	+	0.181054i
$176$	3.45574	+	14.0205i	0.260486	+	1.05683i
$177$	6.63641	+	26.9250i	0.498823	+	2.02381i
$178$	0.393597	+	0.570224i	0.0295013	+	0.0427401i
$179$	−15.7741	−	3.88797i	−1.17901	−	0.290601i	−0.399349	−	0.916799i	$-0.630764\pi$
$179$	−15.7741	−	3.88797i	−1.17901	−	0.290601i	−0.779664	+	0.626198i	$0.784610\pi$
$180$	−3.14027	−	2.16757i	−0.234062	−	0.161561i
$181$	4.42668	−	3.92169i	0.329032	−	0.291497i	−0.482391	−	0.875956i	$-0.660232\pi$
$181$	4.42668	−	3.92169i	0.329032	−	0.291497i	0.811423	+	0.584459i	$0.198693\pi$
$182$	1.94508	−	2.03949i	0.144179	−	0.151177i
$183$	−9.26297	−	8.20628i	−0.684739	−	0.606626i
$184$	−0.788326	−	3.19836i	−0.0581162	−	0.235787i
$185$	−2.82920	−	2.50645i	−0.208007	−	0.184278i
$186$	2.38365	−	0.587516i	0.174777	−	0.0430788i
$187$	−19.7171	−	7.47771i	−1.44186	−	0.546825i
$188$		−	6.50407i		−	0.474358i
$189$	19.3726	−	7.34706i	1.40915	−	0.534420i
$190$	0.0372703	−	0.151212i	0.00270388	−	0.0109701i
$191$	21.9323			1.58697			0.793484	−	0.608591i	$-0.208265\pi$
$191$	21.9323			1.58697			0.793484	+	0.608591i	$0.208265\pi$
$192$	19.9595			1.44045
$193$	−0.638737	+	2.59146i	−0.0459773	+	0.186537i	−0.989440	−	0.144940i	$-0.953701\pi$
$193$	−0.638737	+	2.59146i	−0.0459773	+	0.186537i	0.943463	+	0.331478i	$0.107547\pi$
$194$	0.252049	−	2.07581i	0.0180960	−	0.149034i
$195$	−3.98797	+	0.828902i	−0.285584	+	0.0593589i
$196$	−2.33854	−	19.2596i	−0.167038	−	1.37568i
$197$	0.749130	+	0.0909608i	0.0533733	+	0.00648069i	0.147180	−	0.989110i	$-0.452980\pi$
$197$	0.749130	+	0.0909608i	0.0533733	+	0.00648069i	−0.0938065	+	0.995590i	$0.529903\pi$
$198$	−1.98173	−	2.87103i	−0.140835	−	0.204035i
$199$	−3.61022	−	3.19838i	−0.255922	−	0.226727i	0.525400	−	0.850855i	$-0.323916\pi$
$199$	−3.61022	−	3.19838i	−0.255922	−	0.226727i	−0.781322	+	0.624128i	$0.785454\pi$
$200$	3.62079	−	0.439643i	0.256028	−	0.0310875i
$201$	−12.9280	−	1.56974i	−0.911871	−	0.110721i
$202$	0.702176	+	1.33789i	0.0494050	+	0.0941333i
$203$	23.1265	−	26.1044i	1.62316	−	1.83217i
$204$	−17.2229	+	24.9516i	−1.20584	+	1.74696i
$205$	−0.789233	+	0.194529i	−0.0551225	+	0.0135865i
$206$	1.10835	−	0.134578i	0.0772227	−	0.00937653i
$207$	−11.9230	−	17.2734i	−0.828703	−	1.20058i
$208$	9.41645	−	9.87346i	0.652914	−	0.684601i
$209$	−4.38813	+	6.35731i	−0.303534	+	0.439744i
$210$	0.410370	−	0.781894i	0.0283182	−	0.0539558i
$211$	2.48767	+	6.55945i	0.171258	+	0.451571i	0.992975	−	0.118325i	$-0.0377525\pi$
$211$	2.48767	+	6.55945i	0.171258	+	0.451571i	−0.821717	+	0.569896i	$0.806983\pi$
$212$	1.48028	−	12.1912i	0.101666	−	0.837297i
$213$	−24.3917	+	16.8364i	−1.67129	+	1.15361i
$214$	−0.482451	+	1.95738i	−0.0329796	+	0.133804i
$215$	2.07522	−	1.43242i	0.141529	−	0.0976901i
$216$	−3.55600	+	1.34861i	−0.241955	+	0.0917615i
$217$	−6.72887	−	17.7426i	−0.456786	−	1.20445i
$218$	0.136643	−	0.0717156i	0.00925460	−	0.00485719i
$219$	11.0003	+	20.9593i	0.743331	+	1.41630i
$220$	2.94219	+	0.725184i	0.198362	+	0.0488919i
$221$	4.05470	+	19.5078i	0.272749	+	1.31223i
$222$	−4.82405	+	1.18902i	−0.323769	+	0.0798019i
$223$	3.09724	+	3.49606i	0.207407	+	0.234114i	0.843004	−	0.537907i	$-0.180785\pi$
$223$	3.09724	+	3.49606i	0.207407	+	0.234114i	−0.635598	+	0.772020i	$0.719246\pi$
$224$	1.10346	+	9.08782i	0.0737281	+	0.607205i
$225$	20.5778	−	10.8001i	1.37186	−	0.720006i
$226$	0.561095	−	1.06908i	0.0373235	−	0.0711140i
$227$	7.68708	+	2.91533i	0.510209	+	0.193497i	0.596256	−	0.802794i	$-0.296654\pi$
$227$	7.68708	+	2.91533i	0.510209	+	0.193497i	−0.0860468	+	0.996291i	$0.527423\pi$
$228$	7.36477	+	8.31311i	0.487744	+	0.550549i
$229$	−13.3643	−	1.62272i	−0.883140	−	0.107233i	−0.333615	−	0.942710i	$-0.608268\pi$
$229$	−13.3643	−	1.62272i	−0.883140	−	0.107233i	−0.549526	+	0.835477i	$0.685192\pi$
$230$	−0.326280	−	0.0804209i	−0.0215143	−	0.00530280i
$231$	−32.7845	+	29.0446i	−2.15706	+	1.91099i
$232$	−4.24506	+	4.79168i	−0.278702	+	0.314589i
$233$	17.9068	−	9.39820i	1.17311	−	0.615696i	0.238422	−	0.971162i	$-0.423370\pi$
$233$	17.9068	−	9.39820i	1.17311	−	0.615696i	0.934689	+	0.355465i	$0.115678\pi$
$234$	−1.28123	+	3.03700i	−0.0837567	+	0.198535i
$235$	−1.18585	−	0.622381i	−0.0773562	−	0.0405997i
$236$	−18.2259	+	6.91219i	−1.18641	+	0.449945i
$237$	2.74177	−	22.5805i	0.178097	−	1.46676i
$238$	−3.82476	−	2.00739i	−0.247922	−	0.130120i
$239$		−	22.5348i		−	1.45766i	−0.684697	−	0.728828i	$-0.740065\pi$
$239$		−	22.5348i		−	1.45766i	0.684697	−	0.728828i	$-0.259935\pi$
$240$	1.98666	−	3.78527i	0.128239	−	0.244338i
$241$	−6.73550	+	7.60281i	−0.433872	+	0.489740i	−0.924260	−	0.381764i	$-0.875317\pi$
$241$	−6.73550	+	7.60281i	−0.433872	+	0.489740i	0.490388	+	0.871504i	$0.336855\pi$
$242$	0.557662	+	0.384926i	0.0358479	+	0.0247440i
$243$	12.0066	−	10.6369i	0.770224	−	0.682359i
$244$	4.94150	−	7.15900i	0.316347	−	0.458308i
$245$	−3.73527	−	1.41660i	−0.238637	−	0.0905032i
$246$	−0.378888	+	0.999044i	−0.0241570	+	0.0636967i
$247$	7.29385	+	0.268010i	0.464097	+	0.0170531i
$248$	1.23514	+	3.25680i	0.0784314	+	0.206807i
$249$			10.4754i			0.663854i
$250$	0.268348	−	0.707577i	0.0169718	−	0.0447511i
$251$	−1.21635	−	10.0176i	−0.0767756	−	0.632304i	−0.979408	−	0.201892i	$-0.935291\pi$
$251$	−1.21635	−	10.0176i	−0.0767756	−	0.632304i	0.902632	−	0.430413i	$-0.141632\pi$
$252$	18.0166	+	34.3277i	1.13494	+	2.16244i
$253$	13.7176	+	9.46859i	0.862420	+	0.595285i
$254$	−1.26561	−	0.873585i	−0.0794112	−	0.0548136i
$255$	2.90121	+	5.52779i	0.181681	+	0.346164i
$256$	1.58893	+	13.0860i	0.0993083	+	0.817878i
$257$	8.82349	−	23.2656i	0.550394	−	1.45127i	−0.314472	−	0.949267i	$-0.601827\pi$
$257$	8.82349	−	23.2656i	0.550394	−	1.45127i	0.864866	−	0.502003i	$-0.167403\pi$
$258$		−	3.31456i		−	0.206355i
$259$	13.6180	+	35.9076i	0.846179	+	2.23119i
$260$	−0.916301	−	2.71257i	−0.0568266	−	0.168226i
$261$	−14.4639	+	38.1382i	−0.895294	+	2.36070i
$262$	−0.435331	−	0.165099i	−0.0268949	−	0.0101999i
$263$	−2.10878	+	3.05510i	−0.130033	+	0.188385i	−0.882592	−	0.470139i	$-0.844204\pi$
$263$	−2.10878	+	3.05510i	−0.130033	+	0.188385i	0.752559	+	0.658525i	$0.228819\pi$
$264$	6.01787	−	5.33136i	0.370374	−	0.328123i
$265$	−2.08110	−	1.43648i	−0.127841	−	0.0882425i
$266$	−1.04927	+	1.18438i	−0.0643351	+	0.0726193i
$267$	−4.72823	+	9.00889i	−0.289363	+	0.551335i
$268$		−	9.15415i		−	0.559179i
$269$	−2.37392	−	1.24593i	−0.144741	−	0.0759658i	0.390798	−	0.920476i	$-0.372199\pi$
$269$	−2.37392	−	1.24593i	−0.144741	−	0.0759658i	−0.535539	+	0.844511i	$0.679891\pi$
$270$	−0.0467654	+	0.385148i	−0.00284605	+	0.0234394i
$271$	−4.59141	+	1.74129i	−0.278909	+	0.105776i	−0.490093	−	0.871670i	$-0.663037\pi$
$271$	−4.59141	+	1.74129i	−0.278909	+	0.105776i	0.211184	+	0.977446i	$0.432268\pi$
$272$	−18.5162	−	9.71807i	−1.12271	−	0.589244i
$273$	39.7912	+	11.3728i	2.40828	+	0.688312i
$274$	1.60979	−	0.844885i	0.0972512	−	0.0510414i
$275$	−12.2385	+	13.8144i	−0.738009	+	0.833040i
$276$	17.9378	−	15.8915i	1.07973	−	0.956555i
$277$	21.9985	+	5.42215i	1.32176	+	0.325786i	0.836204	−	0.548418i	$-0.184770\pi$
$277$	21.9985	+	5.42215i	1.32176	+	0.325786i	0.485560	+	0.874204i	$0.338616\pi$
$278$	1.58864	+	0.192896i	0.0952803	+	0.0115691i
$279$	14.7169	+	16.6120i	0.881079	+	0.994532i
$280$	1.17145	+	0.444272i	0.0700074	+	0.0265503i
$281$	−5.33866	+	10.1720i	−0.318478	+	0.606809i	−0.991091	−	0.133185i	$-0.957480\pi$
$281$	−5.33866	+	10.1720i	−0.318478	+	0.606809i	0.672613	+	0.739994i	$0.265172\pi$
$282$	−1.55877	+	0.818107i	−0.0928235	+	0.0487175i
$283$	−0.801014	−	6.59694i	−0.0476153	−	0.392147i	−0.996960	−	0.0779116i	$-0.975175\pi$
$283$	−0.801014	−	6.59694i	−0.0476153	−	0.392147i	0.949345	−	0.314236i	$-0.101748\pi$
$284$	−13.8151	−	15.5940i	−0.819774	−	0.925334i
$285$	2.22042	−	0.547285i	0.131527	−	0.0324184i
$286$	0.0961207	−	2.61590i	0.00568373	−	0.154682i
$287$	8.01877	+	1.97645i	0.473333	+	0.116666i
$288$	−4.97574	−	9.48047i	−0.293198	−	0.558642i
$289$	11.9873	−	6.29141i	0.705134	−	0.370083i
$290$	0.231578	+	0.610621i	0.0135987	+	0.0358569i
$291$	28.7101	−	10.8883i	1.68302	−	0.638284i
$292$	−13.6933	+	9.45183i	−0.801342	+	0.553127i
$293$	6.87252	−	27.8829i	0.401497	−	1.62894i	−0.327806	−	0.944745i	$-0.606309\pi$
$293$	6.87252	−	27.8829i	0.401497	−	1.62894i	0.729302	−	0.684191i	$-0.239845\pi$
$294$	−4.32162	+	2.98300i	−0.252042	+	0.173972i
$295$	−0.483802	+	3.98446i	−0.0281680	+	0.231984i
$296$	−2.49969	−	6.59114i	−0.145291	−	0.383102i
$297$	8.94313	−	17.0397i	0.518933	−	0.988745i
$298$	−1.24073	+	1.79750i	−0.0718734	+	0.104127i
$299$	0.578305	−	15.7385i	0.0334443	−	0.910179i
$300$	15.0735	+	21.8378i	0.870271	+	1.26081i
$301$	−25.4329	+	3.08812i	−1.46593	+	0.177996i
$302$	2.39104	−	0.589338i	0.137589	−	0.0339126i
$303$	−12.6038	+	18.2597i	−0.724067	+	1.04899i
$304$	−5.07969	+	5.73379i	−0.291340	+	0.328855i
$305$	−0.832401	−	1.58601i	−0.0476631	−	0.0908145i
$306$	5.01515	+	0.608949i	0.286697	+	0.0348113i
$307$	4.04997	−	0.491756i	0.231144	−	0.0280660i	−0.00414489	−	0.999991i	$-0.501319\pi$
$307$	4.04997	−	0.491756i	0.231144	−	0.0280660i	0.235289	+	0.971925i	$0.424396\pi$
$308$	−23.0450	−	20.4161i	−1.31311	−	1.16332i
$309$	9.31332	+	13.4927i	0.529816	+	0.767571i
$310$	0.352741	+	0.0428306i	0.0200344	+	0.00243261i
$311$	−0.255721	−	2.10605i	−0.0145006	−	0.119423i	0.983661	−	0.180030i	$-0.0576195\pi$
$311$	−0.255721	−	2.10605i	−0.0145006	−	0.119423i	−0.998162	+	0.0606069i	$0.980696\pi$
$312$	−7.30401	−	2.08757i	−0.413508	−	0.118185i
$313$	−1.48117	+	12.1985i	−0.0837207	+	0.689502i	0.889063	+	0.457785i	$0.151357\pi$
$313$	−1.48117	+	12.1985i	−0.0837207	+	0.689502i	−0.972783	+	0.231716i	$0.925566\pi$
$314$	0.238915	−	0.969316i	0.0134828	−	0.0547017i
$315$	7.98280			0.449780
$316$	15.9890			0.899449
$317$	5.06422	−	20.5463i	0.284435	−	1.15400i	−0.638680	−	0.769473i	$-0.720519\pi$
$317$	5.06422	−	20.5463i	0.284435	−	1.15400i	0.923115	−	0.384525i	$-0.125635\pi$
$318$	−3.10796	+	1.17869i	−0.174286	+	0.0660978i
$319$		−	32.3923i		−	1.81362i
$320$	2.70119	+	1.02443i	0.151001	+	0.0572671i
$321$	−28.7425	+	7.08440i	−1.60425	+	0.395413i
$322$	2.55563	+	2.26409i	0.142420	+	0.126173i
$323$	−2.67713	−	10.8615i	−0.148959	−	0.604352i
$324$	0.479624	+	0.424910i	0.0266458	+	0.0236061i
$325$	17.2222	+	2.73619i	0.955316	+	0.151776i
$326$	−2.85505	+	2.52936i	−0.158127	+	0.140088i
$327$	1.86492	+	1.28726i	0.103130	+	0.0711858i
$328$	−1.47191	−	0.362793i	−0.0812727	−	0.0200319i
$329$	7.72970	+	11.1984i	0.426152	+	0.617388i
$330$	−0.196281	−	0.796344i	−0.0108049	−	0.0438373i
$331$	−5.04064	−	20.4507i	−0.277059	−	1.12407i	−0.930264	−	0.366891i	$-0.880422\pi$
$331$	−5.04064	−	20.4507i	−0.277059	−	1.12407i	0.653205	−	0.757181i	$-0.273424\pi$
$332$	−7.30975	+	0.887565i	−0.401175	+	0.0487115i
$333$	−29.7842	−	33.6195i	−1.63217	−	1.84234i
$334$	1.64838	−	4.34641i	0.0901951	−	0.237825i
$335$	−1.66902	−	0.875971i	−0.0911885	−	0.0478594i
$336$	−35.7457	+	24.6735i	−1.95009	+	1.34605i
$337$	−30.9964			−1.68848			−0.844242	−	0.535963i	$-0.819949\pi$
$337$	−30.9964			−1.68848			−0.844242	+	0.535963i	$0.819949\pi$
$338$	−2.13314	+	1.25184i	−0.116027	+	0.0680910i
$339$	17.7293			0.962925
$340$	−3.61147	+	2.49282i	−0.195860	+	0.135192i
$341$	−15.6060	−	8.19065i	−0.845112	−	0.443549i
$342$	0.656243	−	1.73037i	0.0354856	−	0.0935677i
$343$	7.84444	+	8.85454i	0.423560	+	0.478100i
$344$	4.66842	−	0.566849i	0.251704	−	0.0305625i
$345$	−1.18092	−	4.79117i	−0.0635784	−	0.257948i
$346$	1.03327	+	4.19216i	0.0555492	+	0.225372i
$347$	5.47397	+	7.93042i	0.293858	+	0.425727i	0.941908	−	0.335871i	$-0.109031\pi$
$347$	5.47397	+	7.93042i	0.293858	+	0.425727i	−0.648050	+	0.761598i	$0.724415\pi$
$348$	−45.2188	−	11.1454i	−2.42398	−	0.597458i
$349$	−1.46580	−	1.01177i	−0.0784626	−	0.0541588i	0.528188	−	0.849128i	$-0.322872\pi$
$349$	−1.46580	−	1.01177i	−0.0784626	−	0.0541588i	−0.606650	+	0.794969i	$0.707487\pi$
$350$	−2.82973	+	2.50692i	−0.151255	+	0.134001i
$351$	−18.1186	+	1.52742i	−0.967101	+	0.0815277i
$352$	6.36447	+	5.63843i	0.339227	+	0.300529i
$353$	1.60842	+	6.52562i	0.0856076	+	0.347324i	0.998089	−	0.0617948i	$-0.0196824\pi$
$353$	1.60842	+	6.52562i	0.0856076	+	0.347324i	−0.912481	+	0.409118i	$0.865836\pi$
$354$	3.94911	+	3.49861i	0.209893	+	0.185949i
$355$	−4.16515	+	1.02662i	−0.221063	+	0.0544871i
$356$	−6.68701	−	2.53605i	−0.354411	−	0.134410i
$357$		−	63.4289i		−	3.35701i
$358$	−2.89008	+	1.09606i	−0.152746	+	0.0579287i
$359$	0.540398	−	2.19248i	0.0285211	−	0.115715i	−0.954956	−	0.296748i	$-0.904098\pi$
$359$	0.540398	−	2.19248i	0.0285211	−	0.115715i	0.983477	+	0.181033i	$0.0579441\pi$
$360$	−1.46531			−0.0772285
$361$	14.9021			0.784324
$362$	0.269271	−	1.09248i	0.0141526	−	0.0574193i
$363$	−1.19936	+	9.87761i	−0.0629500	+	0.518440i
$364$	−4.56448	+	28.7299i	−0.239244	+	1.50586i
$365$	0.412966	+	3.40108i	0.0216156	+	0.178021i
$366$	−2.33729	−	0.283799i	−0.122172	−	0.0148344i
$367$	−5.70483	−	8.26487i	−0.297789	−	0.431423i	0.645316	−	0.763916i	$-0.276726\pi$
$367$	−5.70483	−	8.26487i	−0.297789	−	0.431423i	−0.943106	+	0.332493i	$0.892110\pi$
$368$	12.3722	+	10.9608i	0.644946	+	0.571372i
$369$	−9.58875	+	1.16428i	−0.499170	+	0.0606102i
$370$	−0.713881	−	0.0866809i	−0.0371129	−	0.00450633i
$371$	11.9399	+	22.7495i	0.619887	+	1.18110i
$372$	−16.8036	+	18.9673i	−0.871224	+	0.983408i
$373$	16.3372	−	23.6685i	0.845908	−	1.22551i	−0.126440	−	0.991974i	$-0.540355\pi$
$373$	16.3372	−	23.6685i	0.845908	−	1.22551i	0.972348	−	0.233536i	$-0.0750296\pi$
$374$	−3.89544	+	0.960140i	−0.201428	+	0.0496476i
$375$	11.0313	−	1.33944i	0.569653	−	0.0691685i
$376$	−1.41885	−	2.05556i	−0.0731715	−	0.106007i
$377$	−25.8099	+	16.4497i	−1.32928	+	0.847202i
$378$	2.23927	−	3.24414i	0.115175	−	0.166860i
$379$	10.8967	−	20.7618i	0.559723	−	1.06646i	−0.427030	−	0.904237i	$-0.640440\pi$
$379$	10.8967	−	20.7618i	0.559723	−	1.06646i	0.986754	−	0.162227i	$-0.0518675\pi$
$380$	0.570027	+	1.50304i	0.0292418	+	0.0771043i
$381$	2.72193	−	22.4171i	0.139449	−	1.14846i
$382$	3.43412	−	2.37040i	0.175705	−	0.121280i
$383$	7.52907	−	30.5466i	0.384718	−	1.56086i	−0.385271	−	0.922803i	$-0.625892\pi$
$383$	7.52907	−	30.5466i	0.384718	−	1.56086i	0.769989	−	0.638057i	$-0.220262\pi$
$384$	13.3716	−	9.22975i	0.682367	−	0.471004i
$385$	−5.92756	+	2.24803i	−0.302096	+	0.114570i
$386$	0.180067	+	0.474798i	0.00916518	+	0.0241666i
$387$	26.5318	−	13.9250i	1.34869	−	0.707846i
$388$	10.0304	+	19.1113i	0.509217	+	0.970231i
$389$	−11.1195	−	2.74072i	−0.563783	−	0.138960i	−0.0528841	−	0.998601i	$-0.516841\pi$
$389$	−11.1195	−	2.74072i	−0.563783	−	0.138960i	−0.510899	+	0.859641i	$0.670688\pi$
$390$	−0.534842	+	0.560799i	−0.0270828	+	0.0283972i
$391$	−23.4367	+	5.77663i	−1.18525	+	0.292137i
$392$	−4.94051	−	5.57669i	−0.249534	−	0.281665i
$393$	−0.824081	−	6.78692i	−0.0415694	−	0.342355i
$394$	0.127128	−	0.0667219i	0.00640462	−	0.00336140i
$395$	1.53000	−	2.91517i	0.0769827	−	0.146678i
$396$	33.6685	+	12.7688i	1.69191	+	0.641655i
$397$	−1.78641	−	2.01644i	−0.0896571	−	0.101202i	0.701970	−	0.712207i	$-0.252304\pi$
$397$	−1.78641	−	2.01644i	−0.0896571	−	0.101202i	−0.791627	+	0.611005i	$0.790766\pi$
$398$	−0.910955	−	0.110610i	−0.0456621	−	0.00554438i
$399$	−22.5600	−	5.56053i	−1.12941	−	0.278375i
$400$	−13.6992	+	12.1364i	−0.684958	+	0.606819i
$401$	−17.0452	+	19.2401i	−0.851197	+	0.960803i	−0.999604	−	0.0281237i	$-0.991047\pi$
$401$	−17.0452	+	19.2401i	−0.851197	+	0.960803i	0.148408	+	0.988926i	$0.452585\pi$
$402$	−2.19389	+	1.15144i	−0.109422	+	0.0574288i
$403$	1.39890	+	16.5941i	0.0696843	+	0.826612i
$404$	−13.8095	−	7.24778i	−0.687048	−	0.360590i
$405$	0.123367	−	0.0467869i	0.00613016	−	0.00232486i
$406$	0.799787	−	6.58684i	0.0396928	−	0.326899i
$407$	31.5836	+	16.5763i	1.56554	+	0.821658i
$408$			11.6429i			0.576409i
$409$	12.7706	−	24.3323i	0.631465	−	1.20316i	−0.333988	−	0.942577i	$-0.608395\pi$
$409$	12.7706	−	24.3323i	0.631465	−	1.20316i	0.965453	−	0.260578i	$-0.0839131\pi$
$410$	−0.102552	+	0.115758i	−0.00506470	+	0.00571686i
$411$	21.9707	+	15.1653i	1.08374	+	0.748050i
$412$	−8.62607	+	7.64203i	−0.424976	+	0.376496i
$413$	23.1659	−	33.5615i	1.13992	−	1.65145i
$414$	−3.73374	−	1.41602i	−0.183504	−	0.0695937i
$415$	−0.537654	+	1.41768i	−0.0263924	+	0.0695910i
$416$	1.26060	−	7.93449i	0.0618058	−	0.389020i
$417$	8.33294	+	21.9722i	0.408066	+	1.07598i
$418$			1.46967i			0.0718841i
$419$	−13.9902	+	36.8893i	−0.683468	+	1.80216i	−0.0921103	+	0.995749i	$0.529361\pi$
$419$	−13.9902	+	36.8893i	−0.683468	+	1.80216i	−0.591358	+	0.806409i	$0.701408\pi$
$420$	1.09865	+	9.04819i	0.0536086	+	0.441506i
$421$	7.88093	+	15.0159i	0.384093	+	0.731828i	0.998359	−	0.0572713i	$-0.0182400\pi$
$421$	7.88093	+	15.0159i	0.384093	+	0.731828i	−0.614266	+	0.789099i	$0.710548\pi$
$422$	1.09845	+	0.758203i	0.0534715	+	0.0369087i
$423$	−13.0973	−	9.04040i	−0.636812	−	0.439559i
$424$	−2.19166	−	4.17586i	−0.106436	−	0.202798i
$425$	−3.22158	−	26.5321i	−0.156270	−	1.28700i
$426$	−1.99956	+	5.27241i	−0.0968791	+	0.255449i
$427$			18.1987i			0.880697i
$428$	−7.37879	−	19.4563i	−0.356667	−	0.940454i
$429$	34.6685	−	16.6014i	1.67381	−	0.801522i
$430$	0.170120	−	0.448570i	0.00820393	−	0.0216320i
$431$	22.7213	+	8.61706i	1.09445	+	0.415069i	0.834755	−	0.550622i	$-0.185609\pi$
$431$	22.7213	+	8.61706i	1.09445	+	0.415069i	0.259693	+	0.965691i	$0.416379\pi$
$432$	10.8406	−	15.7054i	0.521570	−	0.755625i
$433$	−12.5934	+	11.1568i	−0.605202	+	0.536162i	−0.909119	−	0.416537i	$-0.863244\pi$
$433$	−12.5934	+	11.1568i	−0.605202	+	0.536162i	0.303917	+	0.952698i	$0.401705\pi$
$434$	−2.97117	−	2.05085i	−0.142621	−	0.0984441i
$435$	−6.35911	+	7.17796i	−0.304896	+	0.344157i
$436$	−0.740239	+	1.41041i	−0.0354510	+	0.0675463i
$437$			8.84223i			0.422981i
$438$	3.98764	+	2.09287i	0.190537	+	0.100001i
$439$	−1.23762	+	10.1927i	−0.0590682	+	0.486470i	0.932915	+	0.360098i	$0.117257\pi$
$439$	−1.23762	+	10.1927i	−0.0590682	+	0.486470i	−0.991983	+	0.126373i	$0.959666\pi$
$440$	1.08805	−	0.412643i	0.0518708	−	0.0196720i
$441$	−42.0336	−	22.0610i	−2.00160	−	1.05052i
$442$	2.74324	+	2.61626i	0.130482	+	0.124443i
$443$	23.6811	−	12.4288i	1.12512	−	0.590509i	0.203684	−	0.979037i	$-0.434708\pi$
$443$	23.6811	−	12.4288i	1.12512	−	0.590509i	0.921437	+	0.388527i	$0.127016\pi$
$444$	34.0072	−	38.3862i	1.61391	−	1.82173i
$445$	−1.10227	+	0.976526i	−0.0522526	+	0.0462918i
$446$	0.862807	+	0.212663i	0.0408551	+	0.0100699i
$447$	−31.8384	−	3.86588i	−1.50590	−	0.182850i
$448$	−19.4640	−	21.9703i	−0.919587	−	1.03800i
$449$	19.3469	+	7.33731i	0.913037	+	0.346269i	0.765984	−	0.642859i	$-0.222252\pi$
$449$	19.3469	+	7.33731i	0.913037	+	0.346269i	0.147053	+	0.989129i	$0.453021\pi$
$450$	2.05478	−	3.91506i	0.0968635	−	0.184558i
$451$	6.79216	−	3.56480i	0.319831	−	0.167860i
$452$	1.50217	+	12.3715i	0.0706563	+	0.581907i
$453$	23.9793	+	27.0671i	1.12665	+	1.27172i
$454$	1.51871	−	0.374328i	0.0712766	−	0.0175681i
$455$	4.80137	+	3.58141i	0.225092	+	0.167899i
$456$	4.14106	+	1.02068i	0.193923	+	0.0477977i
$457$	16.0836	+	30.6447i	0.752359	+	1.43350i	0.896085	+	0.443882i	$0.146399\pi$
$457$	16.0836	+	30.6447i	0.752359	+	1.43350i	−0.143726	+	0.989617i	$0.545908\pi$
$458$	−2.26794	+	1.19031i	−0.105974	+	0.0556194i
$459$	9.88226	+	26.0574i	0.461264	+	1.21625i
$460$	3.24321	−	1.22999i	0.151216	−	0.0573485i
$461$	−27.1787	+	18.7601i	−1.26584	+	0.873745i	−0.996017	−	0.0891651i	$-0.971580\pi$
$461$	−27.1787	+	18.7601i	−1.26584	+	0.873745i	−0.269822	+	0.962910i	$0.586965\pi$
$462$	−1.99426	+	8.09102i	−0.0927812	+	0.376428i
$463$	−5.08591	+	3.51055i	−0.236362	+	0.163149i	−0.680358	−	0.732880i	$-0.738176\pi$
$463$	−5.08591	+	3.51055i	−0.236362	+	0.163149i	0.443996	+	0.896029i	$0.353560\pi$
$464$	3.87189	−	31.8879i	0.179748	−	1.48036i
$465$	1.85025	+	4.87870i	0.0858031	+	0.226244i
$466$	1.78807	−	3.40688i	0.0828306	−	0.157820i
$467$	1.10026	−	1.59400i	0.0509141	−	0.0737617i	−0.796700	−	0.604375i	$-0.793423\pi$
$467$	1.10026	−	1.59400i	0.0509141	−	0.0737617i	0.847614	+	0.530613i	$0.178038\pi$
$468$	−6.92372	−	33.3110i	−0.320049	−	1.53980i
$469$	10.8792	+	15.7612i	0.502353	+	0.727784i
$470$	−0.252943	+	0.0307129i	−0.0116674	+	0.00141668i
$471$	14.2336	−	3.50828i	0.655851	−	0.161653i
$472$	−4.25228	+	6.16049i	−0.195727	+	0.283560i
$473$	−15.7796	+	17.8114i	−0.725545	+	0.818971i
$474$	−2.01115	−	3.83193i	−0.0923753	−	0.176006i
$475$	−9.71919	−	1.18012i	−0.445947	−	0.0541478i
$476$	44.2606	−	5.37421i	2.02868	−	0.246327i
$477$	−22.4920	−	19.9262i	−1.02984	−	0.912357i
$478$	−2.43552	−	3.52845i	−0.111398	−	0.161388i
$479$	−40.4461	−	4.91104i	−1.84803	−	0.224391i	−0.879954	−	0.475059i	$-0.842427\pi$
$479$	−40.4461	−	4.91104i	−1.84803	−	0.224391i	−0.968073	+	0.250668i	$0.919350\pi$
$480$	−0.303420	−	2.49889i	−0.0138492	−	0.114058i
$481$	−2.83111	−	33.5833i	−0.129088	−	1.53127i
$482$	−0.232935	+	1.91839i	−0.0106099	+	0.0873803i
$483$	−11.9984	+	48.6792i	−0.545944	+	2.21498i
$484$	−6.99421			−0.317918
$485$	4.44428			0.201804
$486$	0.730353	−	2.96316i	0.0331295	−	0.134412i
$487$	−27.4356	+	10.4049i	−1.24322	+	0.471493i	−0.886505	−	0.462718i	$-0.846874\pi$
$487$	−27.4356	+	10.4049i	−1.24322	+	0.471493i	−0.356720	+	0.934211i	$0.616105\pi$
$488$		−	3.34052i		−	0.151218i
$489$	−52.3703	−	19.8614i	−2.36827	−	0.898166i
$490$	−0.737963	+	0.181892i	−0.0333378	+	0.00821702i
$491$	12.7834	+	11.3251i	0.576909	+	0.511097i	0.900359	−	0.435149i	$-0.143304\pi$
$491$	12.7834	+	11.3251i	0.576909	+	0.511097i	−0.323450	+	0.946245i	$0.604843\pi$
$492$	−2.63934	−	10.7082i	−0.118991	−	0.482764i
$493$	35.1121	+	31.1066i	1.58137	+	1.40097i
$494$	1.17102	−	0.746340i	0.0526868	−	0.0335794i
$495$	5.54983	−	4.91672i	0.249446	−	0.220990i
$496$	−14.3839	−	9.92850i	−0.645857	−	0.445803i
$497$	42.3187	+	10.4306i	1.89825	+	0.467878i
$498$	1.13216	+	1.64022i	0.0507335	+	0.0735001i
$499$	0.877449	+	3.55995i	0.0392800	+	0.159365i	0.987307	−	0.158826i	$-0.0507708\pi$
$499$	0.877449	+	3.55995i	0.0392800	+	0.159365i	−0.948027	+	0.318191i	$0.896925\pi$
$500$	1.86932	+	7.58414i	0.0835986	+	0.339173i
$501$	67.7616	−	8.22775i	3.02737	−	0.367589i
$502$	−1.27313	−	1.43707i	−0.0568227	−	0.0641396i
$503$	−3.54081	+	9.33636i	−0.157877	+	0.416288i	−0.990493	−	0.137563i	$-0.956073\pi$
$503$	−3.54081	+	9.33636i	−0.157877	+	0.416288i	0.832616	+	0.553851i	$0.186842\pi$
$504$	13.1825	+	6.91872i	0.587196	+	0.308184i
$505$	−2.64289	+	1.82426i	−0.117607	+	0.0811783i
$506$	3.17122			0.140978
$507$	−30.8334	−	19.1929i	−1.36936	−	0.852385i
$508$	15.8733			0.704262
$509$	−25.3014	+	17.4643i	−1.12147	+	0.774092i	−0.976537	−	0.215351i	$-0.930911\pi$
$509$	−25.3014	+	17.4643i	−1.12147	+	0.774092i	−0.144928	+	0.989442i	$0.546295\pi$
$510$	1.05170	+	0.551973i	0.0465699	+	0.0244418i
$511$	12.3436	−	32.5475i	0.546050	−	1.43981i
$512$	9.37617	+	10.5835i	0.414372	+	0.467729i
$513$	10.1342	−	1.23052i	0.447438	−	0.0543288i
$514$	−1.13294	−	4.59651i	−0.0499717	−	0.202743i
$515$	0.567889	+	2.30402i	0.0250242	+	0.101527i
$516$	19.4349	+	28.1563i	0.855573	+	1.23951i
$517$	12.2711	+	3.02456i	0.539683	+	0.133020i
$518$	6.01309	+	4.15054i	0.264200	+	0.182364i
$519$	−47.4562	+	42.0425i	−2.08309	+	1.84546i
$520$	−0.881331	−	0.657397i	−0.0386489	−	0.0288288i
$521$	−29.1926	−	25.8624i	−1.27895	−	1.13305i	−0.984120	−	0.177505i	$-0.943198\pi$
$521$	−29.1926	−	25.8624i	−1.27895	−	1.13305i	−0.294833	−	0.955549i	$-0.595264\pi$
$522$	1.85717	+	7.53483i	0.0812861	+	0.329791i
$523$	27.8142	+	24.6412i	1.21623	+	1.07749i	0.994751	+	0.102320i	$0.0326267\pi$
$523$	27.8142	+	24.6412i	1.21623	+	1.07749i	0.221478	+	0.975165i	$0.428912\pi$
$524$	4.66608	−	1.15009i	0.203839	−	0.0502418i
$525$	−51.9058	−	19.6853i	−2.26536	−	0.859136i
$526$			0.706274i			0.0307950i
$527$	23.8649	−	9.05076i	1.03957	−	0.394257i
$528$	−9.65450	+	39.1699i	−0.420158	+	1.70465i
$529$	−3.92049			−0.170456
$530$	−0.481107			−0.0208980
$531$	−11.4142	+	46.3094i	−0.495336	+	2.00966i
$532$	1.96867	−	16.2134i	0.0853526	−	0.702942i
$533$	−6.28964	−	3.60163i	−0.272434	−	0.156004i
$534$	0.233326	+	1.92161i	0.0100970	+	0.0831562i
$535$	−4.25343	−	0.516460i	−0.183892	−	0.0223285i
$536$	−1.99696	−	2.89310i	−0.0862555	−	0.124963i
$537$	−33.9734	−	30.0978i	−1.46606	−	1.29882i
$538$	−0.506362	+	0.0614835i	−0.0218308	+	0.00265074i
$539$	37.4242	+	4.54413i	1.61198	+	0.195729i
$540$	−1.86105	−	3.54594i	−0.0800870	−	0.152593i
$541$	−2.37096	+	2.67626i	−0.101935	+	0.115061i	−0.797264	−	0.603630i	$-0.793720\pi$
$541$	−2.37096	+	2.67626i	−0.101935	+	0.115061i	0.695329	+	0.718692i	$0.255259\pi$
$542$	−0.530719	+	0.768878i	−0.0227963	+	0.0330262i
$543$	16.0421	−	3.95403i	0.688434	−	0.169684i
$544$	−12.2237	+	1.48422i	−0.524086	+	0.0636356i
$545$	0.186317	+	0.269927i	0.00798095	+	0.0115624i
$546$	7.45958	−	2.51983i	0.319240	−	0.107839i
$547$	5.21634	−	7.55718i	0.223035	−	0.323122i	−0.695453	−	0.718572i	$-0.744796\pi$
$547$	5.21634	−	7.55718i	0.223035	−	0.323122i	0.918487	+	0.395450i	$0.129411\pi$
$548$	−8.72080	+	16.6161i	−0.372534	+	0.709804i
$549$	−7.54763	−	19.9015i	−0.322125	−	0.849374i
$550$	−0.423246	+	3.48574i	−0.0180473	+	0.148633i
$551$	14.1419	−	9.76145i	0.602465	−	0.415852i
$552$	2.20239	−	8.93547i	0.0937401	−	0.380319i
$553$	−27.5290	+	19.0019i	−1.17065	+	0.808044i
$554$	4.03050	−	1.52857i	0.171240	−	0.0649426i
$555$	−3.74455	−	9.87356i	−0.158947	−	0.419109i
$556$	−14.6261	+	7.67638i	−0.620286	+	0.325551i
$557$	6.92080	+	13.1865i	0.293244	+	0.558729i	0.986853	−	0.161623i	$-0.0516727\pi$
$557$	6.92080	+	13.1865i	0.293244	+	0.558729i	−0.693609	+	0.720352i	$0.743980\pi$
$558$	4.09973	+	1.01049i	0.173555	+	0.0427776i
$559$	22.2052	+	3.52787i	0.939182	+	0.149213i
$560$	−6.10396	+	1.50449i	−0.257939	+	0.0635763i
$561$	−39.0668	−	44.0972i	−1.64940	−	1.86179i
$562$	0.263449	+	2.16970i	0.0111129	+	0.0915232i
$563$	−8.74816	+	4.59139i	−0.368691	+	0.193504i	−0.638886	−	0.769302i	$-0.720604\pi$
$563$	−8.74816	+	4.59139i	−0.368691	+	0.193504i	0.270195	+	0.962806i	$0.412912\pi$
$564$	8.44440	−	16.0895i	0.355573	−	0.677488i
$565$	2.39937	+	0.909961i	0.100942	+	0.0382823i
$566$	−0.838405	−	0.946363i	−0.0352408	−	0.0397786i
$567$	−1.33077	−	0.161585i	−0.0558873	−	0.00678594i
$568$	−7.76795	−	1.91463i	−0.325936	−	0.0803360i
$569$	18.2074	−	16.1304i	0.763295	−	0.676220i	−0.188803	−	0.982015i	$-0.560461\pi$
$569$	18.2074	−	16.1304i	0.763295	−	0.676220i	0.952097	+	0.305795i	$0.0989222\pi$
$570$	0.288520	−	0.325671i	0.0120848	−	0.0136409i
$571$	4.90851	−	2.57618i	0.205415	−	0.107810i	−0.358879	−	0.933384i	$-0.616841\pi$
$571$	4.90851	−	2.57618i	0.205415	−	0.107810i	0.564294	+	0.825574i	$0.309149\pi$
$572$	14.5218	+	22.7850i	0.607188	+	0.952690i
$573$	54.2552	+	28.4753i	2.26654	+	1.18957i
$574$	1.46917	−	0.557184i	0.0613221	−	0.0232564i
$575$	−2.54644	+	20.9718i	−0.106194	+	0.874584i
$576$	30.3970	+	15.9536i	1.26654	+	0.664732i
$577$		−	21.0609i		−	0.876777i	−0.898786	−	0.438389i	$-0.855549\pi$
$577$		−	21.0609i		−	0.876777i	0.898786	−	0.438389i	$-0.144451\pi$
$578$	1.19698	−	2.28066i	0.0497878	−	0.0948628i
$579$	−4.94463	+	5.58134i	−0.205492	+	0.231952i
$580$	−5.54757	−	3.82921i	−0.230350	−	0.158999i
$581$	11.5308	−	10.2154i	0.478377	−	0.423805i
$582$	3.31858	−	4.80780i	0.137560	−	0.199290i
$583$	22.3126	+	8.46206i	0.924095	+	0.350463i
$584$	−2.26577	+	5.97435i	−0.0937583	+	0.247220i
$585$	−6.73594	−	1.92521i	−0.278497	−	0.0795975i
$586$	−1.93744	−	5.10861i	−0.0800350	−	0.211035i
$587$			4.92853i			0.203422i	0.994814	+	0.101711i	$0.0324317\pi$
$587$			4.92853i			0.203422i	−0.994814	+	0.101711i	$0.967568\pi$
$588$	19.2203	−	50.6796i	0.792630	−	2.08999i
$589$	−1.12698	−	9.28154i	−0.0464365	−	0.382439i
$590$	0.354880	+	0.676167i	0.0146102	+	0.0278374i
$591$	1.73507	+	1.19763i	0.0713710	+	0.0492639i
$592$	29.1103	+	20.0934i	1.19643	+	0.825833i
$593$	−4.83227	−	9.20712i	−0.198437	−	0.378091i	0.765821	−	0.643053i	$-0.222333\pi$
$593$	−4.83227	−	9.20712i	−0.198437	−	0.378091i	−0.964259	+	0.264963i	$0.914640\pi$
$594$	−0.441320	−	3.63460i	−0.0181076	−	0.149129i
$595$	3.25550	−	8.58404i	0.133462	−	0.351911i
$596$		−	22.5443i		−	0.923451i
$597$	−4.77826	−	12.5992i	−0.195561	−	0.515653i
$598$	−1.61043	−	2.52680i	−0.0658554	−	0.103328i
$599$	−3.92630	+	10.3528i	−0.160424	+	0.423004i	−0.990993	−	0.133912i	$-0.957246\pi$
$599$	−3.92630	+	10.3528i	−0.160424	+	0.423004i	0.830569	+	0.556916i	$0.188015\pi$
$600$	9.52774	+	3.61339i	0.388968	+	0.147516i
$601$	2.14006	−	3.10041i	0.0872948	−	0.126468i	−0.776904	−	0.629620i	$-0.783211\pi$
$601$	2.14006	−	3.10041i	0.0872948	−	0.126468i	0.864198	+	0.503151i	$0.167826\pi$
$602$	−3.64848	+	3.23227i	−0.148701	+	0.131737i
$603$	−18.4338	−	12.7239i	−0.750681	−	0.518158i
$604$	−16.8557	+	19.0261i	−0.685847	+	0.774161i
$605$	−0.669283	+	1.27521i	−0.0272102	+	0.0518448i
$606$			4.22125i			0.171477i
$607$	11.6463	+	6.11246i	0.472709	+	0.248097i	0.684216	−	0.729280i	$-0.260145\pi$
$607$	11.6463	+	6.11246i	0.472709	+	0.248097i	−0.211507	+	0.977377i	$0.567837\pi$
$608$	−0.543698	+	4.47775i	−0.0220499	+	0.181597i
$609$	91.1013	−	34.5502i	3.69161	−	1.40004i
$610$	−0.301748	−	0.158370i	−0.0122174	−	0.00641220i
$611$	−3.82166	−	11.3135i	−0.154608	−	0.457693i
$612$	−46.1730	+	24.2334i	−1.86643	+	0.979579i
$613$	20.8023	−	23.4810i	0.840198	−	0.948387i	−0.159046	−	0.987271i	$-0.550842\pi$
$613$	20.8023	−	23.4810i	0.840198	−	0.948387i	0.999244	+	0.0388841i	$0.0123803\pi$
$614$	0.580989	−	0.514711i	0.0234468	−	0.0207720i
$615$	−2.20493	−	0.543466i	−0.0889114	−	0.0219147i
$616$	−11.7369	−	1.42512i	−0.472894	−	0.0574198i
$617$	15.3100	+	17.2814i	0.616357	+	0.695723i	0.970946	−	0.239299i	$-0.0769176\pi$
$617$	15.3100	+	17.2814i	0.616357	+	0.695723i	−0.354589	+	0.935022i	$0.615379\pi$
$618$	2.91652	+	1.10609i	0.117320	+	0.0444935i
$619$	−20.1606	+	38.4128i	−0.810322	+	1.54394i	0.0285390	+	0.999593i	$0.490915\pi$
$619$	−20.1606	+	38.4128i	−0.810322	+	1.54394i	−0.838861	+	0.544346i	$0.816778\pi$
$620$	−3.24758	+	1.70446i	−0.130426	+	0.0684529i
$621$	−2.65518	−	21.8674i	−0.106549	−	0.877508i
$622$	−0.267658	−	0.302123i	−0.0107321	−	0.0121140i
$623$	14.5273	−	3.58066i	0.582025	−	0.143456i
$624$	36.1130	−	12.1989i	1.44568	−	0.488346i
$625$	−21.9181	−	5.40232i	−0.876724	−	0.216093i
$626$	1.08647	+	2.07010i	0.0434242	+	0.0827379i
$627$	−19.1090	+	10.0292i	−0.763141	+	0.400527i
$628$	3.65406	+	9.63497i	0.145813	+	0.384477i
$629$	−48.2980	+	18.3170i	−1.92577	+	0.730347i
$630$	1.24993	−	0.862765i	0.0497984	−	0.0343734i
$631$	−7.46121	+	30.2713i	−0.297026	+	1.20508i	0.612849	+	0.790200i	$0.290023\pi$
$631$	−7.46121	+	30.2713i	−0.297026	+	1.20508i	−0.909875	+	0.414882i	$0.863823\pi$
$632$	5.05318	−	3.48796i	0.201005	−	0.138743i
$633$	−2.36242	+	19.4563i	−0.0938977	+	0.773317i
$634$	−1.42766	−	3.76443i	−0.0566997	−	0.149505i
$635$	1.51893	−	2.89408i	0.0602769	−	0.114848i
$636$	19.4900	−	28.2362i	0.772830	−	1.11964i
$637$	−15.3843	−	32.1269i	−0.609548	−	1.27291i
$638$	−3.50090	−	5.07193i	−0.138602	−	0.200799i
$639$	−50.6042	+	6.14446i	−2.00187	+	0.243071i
$640$	2.28334	−	0.562794i	0.0902571	−	0.0222464i
$641$	−15.1569	+	21.9586i	−0.598664	+	0.867314i	−0.998792	−	0.0491454i	$-0.984350\pi$
$641$	−15.1569	+	21.9586i	−0.598664	+	0.867314i	0.400128	+	0.916459i	$0.368966\pi$
$642$	−3.73478	+	4.21569i	−0.147400	+	0.166380i
$643$	−8.41917	−	16.0414i	−0.332020	−	0.632610i	0.661023	−	0.750366i	$-0.270123\pi$
$643$	−8.41917	−	16.0414i	−0.332020	−	0.632610i	−0.993043	+	0.117755i	$0.962430\pi$
$644$	−34.9849	−	4.24794i	−1.37860	−	0.167392i
$645$	6.99332	−	0.849143i	0.275362	−	0.0334350i
$646$	−1.59307	−	1.41134i	−0.0626786	−	0.0555284i
$647$	−24.3719	−	35.3088i	−0.958159	−	1.38813i	−0.921317	−	0.388812i	$-0.872885\pi$
$647$	−24.3719	−	35.3088i	−0.958159	−	1.38813i	−0.0368424	−	0.999321i	$-0.511730\pi$
$648$	0.244274	+	0.0296603i	0.00959600	+	0.00116517i
$649$	−4.56558	−	37.6010i	−0.179215	−	1.47597i
$650$	2.99234	−	1.43291i	0.117369	−	0.0562035i
$651$	6.39008	−	52.6270i	0.250447	−	2.06262i
$652$	9.42206	−	38.2268i	0.368996	−	1.49708i
$653$	−45.8864			−1.79567			−0.897836	−	0.440329i	$-0.854862\pi$
$653$	−45.8864			−1.79567			−0.897836	+	0.440329i	$0.854862\pi$
$654$	0.431130			0.0168585
$655$	0.236814	−	0.960793i	0.00925310	−	0.0375413i
$656$	7.11249	−	2.69741i	0.277696	−	0.105316i
$657$			40.7121i			1.58833i
$658$	2.42060	+	0.918012i	0.0943648	+	0.0357878i
$659$	−9.26131	+	2.28271i	−0.360769	+	0.0889216i	−0.415534	−	0.909578i	$-0.636405\pi$
$659$	−9.26131	+	2.28271i	−0.360769	+	0.0889216i	0.0547647	+	0.998499i	$0.482559\pi$
$660$	6.33672	+	5.61384i	0.246656	+	0.218518i
$661$	9.69730	+	39.3435i	0.377181	+	1.53028i	0.786324	+	0.617814i	$0.211981\pi$
$661$	9.69730	+	39.3435i	0.377181	+	1.53028i	−0.409143	+	0.912470i	$0.634172\pi$
$662$	−2.99952	−	2.65734i	−0.116580	−	0.103281i
$663$	−15.2971	+	53.5217i	−0.594090	+	2.07861i
$664$	−2.11657	+	1.87512i	−0.0821388	+	0.0727686i
$665$	−2.76772	−	1.91042i	−0.107328	−	0.0740829i
$666$	−8.29708	−	2.04505i	−0.321505	−	0.0792439i
$667$	−21.0630	−	30.5150i	−0.815562	−	1.18155i
$668$	11.4826	+	46.5869i	0.444276	+	1.80250i
$669$	3.12278	+	12.6696i	0.120734	+	0.489836i
$670$	−0.356005	+	0.0432269i	−0.0137537	+	0.00167000i
$671$	11.2088	+	12.6522i	0.432713	+	0.488432i
$672$	−9.06926	+	23.9137i	−0.349854	+	0.922490i
$673$	−8.89790	−	4.66998i	−0.342989	−	0.180014i	0.284429	−	0.958697i	$-0.408196\pi$
$673$	−8.89790	−	4.66998i	−0.342989	−	0.180014i	−0.627418	+	0.778683i	$0.715888\pi$
$674$	−4.85336	+	3.35003i	−0.186944	+	0.129038i
$675$	24.3905			0.938793
$676$	10.7803	−	23.1417i	0.414627	−	0.890064i
$677$	−23.3435			−0.897162			−0.448581	−	0.893742i	$-0.648070\pi$
$677$	−23.3435			−0.897162			−0.448581	+	0.893742i	$0.648070\pi$
$678$	2.77602	−	1.91615i	0.106612	−	0.0735893i
$679$	−39.9826	−	20.9845i	−1.53439	−	0.805310i
$680$	−0.597573	+	1.57567i	−0.0229159	+	0.0604242i
$681$	15.2309	+	17.1921i	0.583649	+	0.658804i
$682$	−3.32878	+	0.404187i	−0.127466	+	0.0154771i
$683$	−0.308530	−	1.25176i	−0.0118056	−	0.0478971i	0.964744	−	0.263191i	$-0.0847751\pi$
$683$	−0.308530	−	1.25176i	−0.0118056	−	0.0478971i	−0.976549	+	0.215294i	$0.930929\pi$
$684$	4.57141	+	18.5469i	0.174792	+	0.709159i
$685$	2.19501	+	3.18003i	0.0838671	+	0.121503i
$686$	2.18525	+	0.538615i	0.0834331	+	0.0205644i
$687$	−30.9532	−	21.3655i	−1.18094	−	0.815144i
$688$	−17.6628	+	15.6479i	−0.673390	+	0.596571i
$689$	−4.58846	−	22.0757i	−0.174806	−	0.841018i
$690$	−0.702725	−	0.622560i	−0.0267523	−	0.0237004i
$691$	−2.53908	−	10.3015i	−0.0965912	−	0.391886i	0.902669	−	0.430335i	$-0.141604\pi$
$691$	−2.53908	−	10.3015i	−0.0965912	−	0.391886i	−0.999261	+	0.0384490i	$0.987758\pi$
$692$	−33.3581	−	29.5527i	−1.26808	−	1.12342i
$693$	−73.1438	+	18.0283i	−2.77850	+	0.684839i
$694$	1.71421	+	0.650113i	0.0650704	+	0.0246779i
$695$			3.40126i			0.129017i
$696$	−16.7224	+	6.34196i	−0.633860	+	0.240391i
$697$	−2.65845	+	10.7858i	−0.100696	+	0.408540i
$698$	−0.338862			−0.0128261
$699$	56.4988			2.13698
$700$	9.33849	−	37.8877i	0.352962	−	1.43202i
$701$	0.176313	−	1.45207i	0.00665926	−	0.0548439i	−0.989000	−	0.147913i	$-0.952745\pi$
$701$	0.176313	−	1.45207i	0.00665926	−	0.0548439i	0.995660	+	0.0930687i	$0.0296676\pi$
$702$	−2.67190	+	2.19738i	−0.100844	+	0.0829349i
$703$	2.28080	+	18.7841i	0.0860220	+	0.708455i
$704$	−27.0637	−	3.28612i	−1.02000	−	0.123850i
$705$	−2.12544	−	3.07924i	−0.0800488	−	0.115971i
$706$	0.957118	+	0.847933i	0.0360216	+	0.0319124i
$707$	32.3901	−	3.93287i	1.21815	−	0.147911i
$708$	−54.0607	−	6.56416i	−2.03173	−	0.246696i
$709$	10.1337	+	19.3082i	0.380580	+	0.725135i	0.998113	−	0.0614105i	$-0.0195599\pi$
$709$	10.1337	+	19.3082i	0.380580	+	0.725135i	−0.617532	+	0.786545i	$0.711868\pi$
$710$	−0.541215	+	0.610906i	−0.0203114	+	0.0229269i
$711$	22.2240	−	32.1971i	0.833466	−	1.20748i
$712$	−2.66661	+	0.657260i	−0.0999354	+	0.0246319i
$713$	−20.0275	+	2.43177i	−0.750034	+	0.0910706i
$714$	−6.85526	−	9.93156i	−0.256552	−	0.371679i
$715$	5.54387	−	0.467355i	0.207329	−	0.0174781i
$716$	18.1237	−	26.2567i	0.677315	−	0.981261i
$717$	29.2575	−	55.7456i	1.09264	−	2.08186i
$718$	−0.152344	−	0.401699i	−0.00568544	−	0.0149913i
$719$	−4.31315	+	35.5220i	−0.160853	+	1.32475i	0.658987	+	0.752154i	$0.270985\pi$
$719$	−4.31315	+	35.5220i	−0.160853	+	1.32475i	−0.819841	+	0.572592i	$0.805938\pi$
$720$	6.05110	−	4.17678i	0.225511	−	0.155659i
$721$	5.76987	−	23.4093i	0.214881	−	0.871807i
$722$	2.33335	−	1.61059i	0.0868382	−	0.0599401i
$723$	−26.5329	+	10.0626i	−0.986768	+	0.374232i
$724$	4.11834	+	10.8592i	0.153057	+	0.403578i
$725$	36.3526	−	19.0793i	1.35010	−	0.708588i
$726$	0.879758	+	1.67624i	0.0326509	+	0.0622111i
$727$	24.6806	+	6.08323i	0.915354	+	0.225614i	0.668737	−	0.743499i	$-0.266835\pi$
$727$	24.6806	+	6.08323i	0.915354	+	0.225614i	0.246616	+	0.969113i	$0.420681\pi$
$728$	4.82480	+	10.0756i	0.178819	+	0.373426i
$729$	42.5612	−	10.4904i	1.57634	−	0.388533i
$730$	0.432243	+	0.487902i	0.0159980	+	0.0180581i
$731$	−4.15371	−	34.2089i	−0.153631	−	1.26526i
$732$	21.5188	−	11.2939i	0.795356	−	0.417435i
$733$	3.44446	−	6.56286i	0.127224	−	0.242405i	−0.813510	−	0.581551i	$-0.802446\pi$
$733$	3.44446	−	6.56286i	0.127224	−	0.242405i	0.940734	+	0.339146i	$0.110138\pi$
$734$	−1.78650	−	0.677530i	−0.0659409	−	0.0250081i
$735$	−7.40092	−	8.35391i	−0.272987	−	0.308139i
$736$	9.66197	+	1.17318i	0.356145	+	0.0432438i
$737$	17.2710	+	4.25692i	0.636185	+	0.156806i
$738$	−1.37555	+	1.21863i	−0.0506348	+	0.0448585i
$739$	24.8788	−	28.0823i	0.915180	−	1.03302i	−0.0841513	−	0.996453i	$-0.526818\pi$
$739$	24.8788	−	28.0823i	0.915180	−	1.03302i	0.999331	−	0.0365714i	$-0.0116436\pi$
$740$	6.57249	−	3.44951i	0.241610	−	0.126806i
$741$	17.6952	+	10.1328i	0.650050	+	0.372237i
$742$	4.32824	+	2.27164i	0.158895	+	0.0833943i
$743$	−25.9712	+	9.84956i	−0.952789	+	0.361345i	−0.781521	−	0.623879i	$-0.785556\pi$
$743$	−25.9712	+	9.84956i	−0.952789	+	0.361345i	−0.171268	+	0.985224i	$0.554787\pi$
$744$	−1.17295	+	9.66012i	−0.0430025	+	0.354157i
$745$	−4.11038	−	2.15729i	−0.150592	−	0.0790370i
$746$		−	5.47166i		−	0.200332i
$747$	−8.37298	+	15.9534i	−0.306351	+	0.583704i
$748$	27.4610	−	30.9970i	1.00407	−	1.13336i
$749$	35.8271	+	24.7297i	1.30909	+	0.903602i
$750$	1.58249	−	1.40197i	0.0577845	−	0.0511926i
$751$	−6.01103	+	8.70847i	−0.219345	+	0.317777i	−0.917173	−	0.398489i	$-0.869535\pi$
$751$	−6.01103	+	8.70847i	−0.219345	+	0.317777i	0.697828	+	0.716266i	$0.254150\pi$
$752$	11.7185	+	4.44424i	0.427330	+	0.162065i
$753$	9.99713	−	26.3603i	0.364315	−	0.960621i
$754$	−2.26341	+	5.36514i	−0.0824285	+	0.195387i
$755$	1.85598	+	4.89382i	0.0675461	+	0.178104i
$756$			40.6880i			1.47981i
$757$	3.52061	−	9.28307i	0.127959	−	0.337399i	−0.855692	−	0.517485i	$-0.826868\pi$
$757$	3.52061	−	9.28307i	0.127959	−	0.337399i	0.983651	+	0.180086i	$0.0576376\pi$
$758$	−0.537721	−	4.42853i	−0.0195309	−	0.160852i
$759$	21.6407	+	41.2329i	0.785508	+	1.49666i
$760$	0.508037	+	0.350673i	0.0184285	+	0.0127202i
$761$	0.350957	+	0.242248i	0.0127222	+	0.00878150i	0.574409	−	0.818569i	$-0.305232\pi$
$761$	0.350957	+	0.242248i	0.0127222	+	0.00878150i	−0.561687	+	0.827350i	$0.689847\pi$
$762$	−1.99660	−	3.80420i	−0.0723292	−	0.137812i
$763$	−0.401677	−	3.30811i	−0.0145417	−	0.119761i
$764$	−15.2731	+	40.2719i	−0.552562	+	1.45699i
$765$			10.7374i			0.388210i
$766$	−2.12253	−	5.59666i	−0.0766902	−	0.202215i
$767$	−27.6415

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)

\(f(q)\)	\(=\)	\(q+(0.156578 - 0.108078i) q^{2} +(2.47375 + 1.29833i) q^{3} +(-0.696374 + 1.83619i) q^{4} +(0.268145 + 0.302673i) q^{5} +(0.527655 - 0.0640690i) q^{6} +(-0.983215 - 3.98906i) q^{7} +(0.180477 + 0.732225i) q^{8} +(2.72961 + 3.95452i) q^{9} +O(q^{10})\)	\(q+(0.156578 - 0.108078i) q^{2} +(2.47375 + 1.29833i) q^{3} +(-0.696374 + 1.83619i) q^{4} +(0.268145 + 0.302673i) q^{5} +(0.527655 - 0.0640690i) q^{6} +(-0.983215 - 3.98906i) q^{7} +(0.180477 + 0.732225i) q^{8} +(2.72961 + 3.95452i) q^{9} +(0.0746977 + 0.0184113i) q^{10} +(-3.14047 - 2.16771i) q^{11} +(-4.10663 + 3.63815i) q^{12} +(-0.132396 + 3.60312i) q^{13} +(-0.585079 - 0.518335i) q^{14} +(0.270356 + 1.09688i) q^{15} +(-2.83246 - 2.50934i) q^{16} +(5.36554 - 1.32249i) q^{17} +(0.854793 + 0.324180i) q^{18} -2.02432i q^{19} +(-0.742492 + 0.281590i) q^{20} +(2.74687 - 11.1445i) q^{21} -0.726011 q^{22} -4.36801 q^{23} +(-0.504210 + 2.04566i) q^{24} +(0.582974 - 4.80122i) q^{25} +(0.368687 + 0.578478i) q^{26} +(0.607870 + 5.00626i) q^{27} +(8.00935 + 0.972511i) q^{28} +(4.82210 + 6.98602i) q^{29} +(0.160880 + 0.142527i) q^{30} +(4.58503 - 0.556723i) q^{31} +(-2.21198 - 0.268584i) q^{32} +(-4.95436 - 9.43975i) q^{33} +(0.697193 - 0.786968i) q^{34} +(0.943736 - 1.36724i) q^{35} +(-9.16207 + 2.25825i) q^{36} +(-9.27923 + 1.12670i) q^{37} +(-0.218784 - 0.316963i) q^{38} +(-5.00554 + 8.74134i) q^{39} +(-0.173230 + 0.250968i) q^{40} +(-0.934182 + 1.77994i) q^{41} +(-0.774374 - 2.04186i) q^{42} +(0.751651 - 6.19040i) q^{43} +(6.16727 - 4.25696i) q^{44} +(-0.464996 + 1.88656i) q^{45} +(-0.683934 + 0.472085i) q^{46} +(-3.09675 + 1.17444i) q^{47} +(-3.74886 - 9.88494i) q^{48} +(-8.74771 + 4.59115i) q^{49} +(-0.427625 - 0.814772i) q^{50} +(14.9900 + 3.69471i) q^{51} +(-6.52381 - 2.75222i) q^{52} +(-6.07185 + 1.49658i) q^{53} +(0.636245 + 0.718172i) q^{54} +(-0.185994 - 1.53180i) q^{55} +(2.74344 - 1.43987i) q^{56} +(2.62822 - 5.00766i) q^{57} +(1.51007 + 0.572693i) q^{58} +(6.58214 + 7.42969i) q^{59} +(-2.20234 - 0.267412i) q^{60} +(-4.30087 - 1.06007i) q^{61} +(0.657745 - 0.582711i) q^{62} +(13.0910 - 14.7767i) q^{63} +(6.32598 - 3.32013i) q^{64} +(-1.12607 + 0.926084i) q^{65} +(-1.79597 - 0.942599i) q^{66} +(-4.35852 + 1.65297i) q^{67} +(-1.30809 + 10.7731i) q^{68} +(-10.8054 - 5.67110i) q^{69} -0.316076i q^{70} +(-4.93011 + 9.39353i) q^{71} +(-2.40297 + 2.71239i) q^{72} +(6.97287 + 4.81303i) q^{73} +(-1.33115 + 1.17930i) q^{74} +(7.67569 - 11.1202i) q^{75} +(3.71702 + 1.40968i) q^{76} +(-5.55938 + 14.6589i) q^{77} +(0.160989 + 1.90969i) q^{78} +(-2.88713 - 7.61275i) q^{79} -1.53017i q^{80} +(0.115704 - 0.305087i) q^{81} +(0.0460994 + 0.379663i) q^{82} +(1.74252 + 3.32009i) q^{83} +(18.5505 + 12.8045i) q^{84} +(1.83902 + 1.26938i) q^{85} +(-0.551354 - 1.05052i) q^{86} +(2.85856 + 23.5423i) q^{87} +(1.02047 - 2.69076i) q^{88} +3.64179i q^{89} +(0.131088 + 0.345650i) q^{90} +(14.5032 - 3.01451i) q^{91} +(3.04177 - 8.02048i) q^{92} +(12.0650 + 4.57567i) q^{93} +(-0.357951 + 0.518582i) q^{94} +(0.612705 - 0.542809i) q^{95} +(-5.12319 - 3.53629i) q^{96} +(7.28820 - 8.22667i) q^{97} +(-0.873495 + 1.66431i) q^{98} -18.3361i 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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