LMFDB - Embedded newform 169.2.k.a.4.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	169.4
Dual form			169.2.k.a.127.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99581 + 0.0804286i) q^{2} +(-0.751408 + 2.59416i) q^{3} +(1.98329 + 0.160108i) q^{4} +(1.41011 + 0.534785i) q^{5} +(-1.70832 + 5.11703i) q^{6} +(-1.63799 - 3.84451i) q^{7} +(-0.0203394 - 0.00246965i) q^{8} +(-3.62949 - 2.29515i) q^{9} +O(q^{10})$	\(q+(1.99581 + 0.0804286i) q^{2} +(-0.751408 + 2.59416i) q^{3} +(1.98329 + 0.160108i) q^{4} +(1.41011 + 0.534785i) q^{5} +(-1.70832 + 5.11703i) q^{6} +(-1.63799 - 3.84451i) q^{7} +(-0.0203394 - 0.00246965i) q^{8} +(-3.62949 - 2.29515i) q^{9} +(2.77131 + 1.18074i) q^{10} +(3.00913 + 4.75856i) q^{11} +(-1.90561 + 5.02467i) q^{12} +(-0.967139 - 3.47342i) q^{13} +(-2.95992 - 7.80467i) q^{14} +(-2.44689 + 3.25621i) q^{15} +(-3.96835 - 0.644919i) q^{16} +(6.45100 - 2.74851i) q^{17} +(-7.05919 - 4.87261i) q^{18} +(-1.84691 + 1.06631i) q^{19} +(2.71104 + 1.28640i) q^{20} +(11.2041 - 1.36042i) q^{21} +(5.62295 + 9.73923i) q^{22} +(0.789020 - 1.36662i) q^{23} +(0.0216898 - 0.0509079i) q^{24} +(-2.04014 - 1.80740i) q^{25} +(-1.65087 - 7.01008i) q^{26} +(2.61650 - 2.31802i) q^{27} +(-2.63308 - 7.88704i) q^{28} +(-0.179760 + 4.46070i) q^{29} +(-5.14542 + 6.30200i) q^{30} +(-2.69431 - 3.04125i) q^{31} +(-7.82806 - 1.59811i) q^{32} +(-14.6056 + 4.23056i) q^{33} +(13.0961 - 4.96668i) q^{34} +(-0.253767 - 6.29716i) q^{35} +(-6.83086 - 5.13306i) q^{36} +(3.77702 - 0.771085i) q^{37} +(-3.77184 + 1.97962i) q^{38} +(9.73733 + 0.101040i) q^{39} +(-0.0273601 - 0.0143597i) q^{40} +(-4.49274 - 1.30134i) q^{41} +(22.4707 - 1.81402i) q^{42} +(-0.625951 + 3.06611i) q^{43} +(5.20610 + 9.91940i) q^{44} +(-3.89057 - 5.17741i) q^{45} +(1.68465 - 2.66406i) q^{46} +(-6.46667 + 4.46362i) q^{47} +(4.65487 - 9.80994i) q^{48} +(-7.24819 + 7.54616i) q^{49} +(-3.92636 - 3.77132i) q^{50} +(2.28276 + 18.8002i) q^{51} +(-1.36200 - 7.04365i) q^{52} +(-0.932805 + 7.68234i) q^{53} +(5.40848 - 4.41589i) q^{54} +(1.69841 + 8.31934i) q^{55} +(0.0238212 + 0.0822403i) q^{56} +(-1.37840 - 5.59241i) q^{57} +(-0.717536 + 8.88828i) q^{58} +(-0.475472 - 2.92570i) q^{59} +(-5.37423 + 6.06625i) q^{60} +(2.12835 - 1.59935i) q^{61} +(-5.13275 - 6.28647i) q^{62} +(-2.87865 + 17.7131i) q^{63} +(-7.68766 - 1.89484i) q^{64} +(0.493758 - 5.41512i) q^{65} +(-29.4903 + 7.26870i) q^{66} +(0.307874 + 3.81370i) q^{67} +(13.2343 - 4.41825i) q^{68} +(2.95236 + 3.07374i) q^{69} -12.5884i q^{70} +(-0.130995 + 0.125823i) q^{71} +(0.0681534 + 0.0556455i) q^{72} +(3.18128 - 6.06142i) q^{73} +(7.60025 - 1.23516i) q^{74} +(6.22167 - 3.93434i) q^{75} +(-3.83367 + 1.81910i) q^{76} +(13.3654 - 19.3631i) q^{77} +(19.4258 + 0.984817i) q^{78} +(5.93723 + 8.60156i) q^{79} +(-5.25092 - 3.03162i) q^{80} +(-1.47554 - 3.10963i) q^{81} +(-8.86200 - 2.95857i) q^{82} +(-1.37302 + 5.57058i) q^{83} +(22.4388 - 0.904252i) q^{84} +(10.5665 - 0.425815i) q^{85} +(-1.49588 + 6.06904i) q^{86} +(-11.4367 - 3.81814i) q^{87} +(-0.0494519 - 0.104218i) q^{88} +(-6.07451 - 3.50712i) q^{89} +(-7.34845 - 10.6461i) q^{90} +(-11.7694 + 9.40762i) q^{91} +(1.78366 - 2.58408i) q^{92} +(9.91403 - 4.70427i) q^{93} +(-13.2653 + 8.38844i) q^{94} +(-3.17459 + 0.515921i) q^{95} +(10.0278 - 19.1064i) q^{96} +(-7.22423 - 5.89840i) q^{97} +(-15.0730 + 14.4778i) q^{98} -24.1776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.99581	+	0.0804286i	1.41125	+	0.0568716i	0.734136	−	0.679003i	$-0.237588\pi$
$2$	1.99581	+	0.0804286i	1.41125	+	0.0568716i	0.677118	+	0.735874i	$0.263229\pi$
$3$	−0.751408	+	2.59416i	−0.433826	+	1.49774i	0.384576	+	0.923093i	$0.374348\pi$
$3$	−0.751408	+	2.59416i	−0.433826	+	1.49774i	−0.818402	+	0.574647i	$0.805139\pi$
$4$	1.98329	+	0.160108i	0.991645	+	0.0800539i
$5$	1.41011	+	0.534785i	0.630621	+	0.239163i	0.649144	−	0.760666i	$-0.275127\pi$
$5$	1.41011	+	0.534785i	0.630621	+	0.239163i	−0.0185232	+	0.999828i	$0.505896\pi$
$6$	−1.70832	+	5.11703i	−0.697417	+	2.08902i
$7$	−1.63799	−	3.84451i	−0.619103	−	1.45309i	−0.873905	−	0.486096i	$-0.838421\pi$
$7$	−1.63799	−	3.84451i	−0.619103	−	1.45309i	0.254802	−	0.966993i	$-0.417990\pi$
$8$	−0.0203394	−	0.00246965i	−0.00719106	−	0.000873153i
$9$	−3.62949	−	2.29515i	−1.20983	−	0.765050i
$10$	2.77131	+	1.18074i	0.876364	+	0.373384i
$11$	3.00913	+	4.75856i	0.907288	+	1.43476i	0.900535	+	0.434784i	$0.143175\pi$
$11$	3.00913	+	4.75856i	0.907288	+	1.43476i	0.00675289	+	0.999977i	$0.497850\pi$
$12$	−1.90561	+	5.02467i	−0.550101	+	1.45050i
$13$	−0.967139	−	3.47342i	−0.268236	−	0.963353i
$13$	−0.967139	−	3.47342i	−0.268236	−	0.963353i
$14$	−2.95992	−	7.80467i	−0.791073	−	2.08589i
$15$	−2.44689	+	3.25621i	−0.631783	+	0.840751i
$16$	−3.96835	−	0.644919i	−0.992087	−	0.161230i
$17$	6.45100	−	2.74851i	1.56460	−	0.666613i	0.576035	−	0.817425i	$-0.304599\pi$
$17$	6.45100	−	2.74851i	1.56460	−	0.666613i	0.988562	+	0.150812i	$0.0481889\pi$
$18$	−7.05919	−	4.87261i	−1.66387	−	1.14849i
$19$	−1.84691	+	1.06631i	−0.423709	+	0.244629i	−0.696663	−	0.717399i	$-0.745333\pi$
$19$	−1.84691	+	1.06631i	−0.423709	+	0.244629i	0.272954	+	0.962027i	$0.411999\pi$
$20$	2.71104	+	1.28640i	0.606206	+	0.287648i
$21$	11.2041	−	1.36042i	2.44493	−	0.296869i
$22$	5.62295	+	9.73923i	1.19882	+	2.07641i
$23$	0.789020	−	1.36662i	0.164522	−	0.284960i	−0.771963	−	0.635667i	$-0.780725\pi$
$23$	0.789020	−	1.36662i	0.164522	−	0.284960i	0.936485	+	0.350707i	$0.114059\pi$
$24$	0.0216898	−	0.0509079i	0.00442742	−	0.0103915i
$25$	−2.04014	−	1.80740i	−0.408027	−	0.361480i
$26$	−1.65087	−	7.01008i	−0.323762	−	1.37479i
$27$	2.61650	−	2.31802i	0.503546	−	0.446103i
$28$	−2.63308	−	7.88704i	−0.497606	−	1.49051i
$29$	−0.179760	+	4.46070i	−0.0333806	+	0.828332i	0.892620	+	0.450810i	$0.148865\pi$
$29$	−0.179760	+	4.46070i	−0.0333806	+	0.828332i	−0.926001	+	0.377522i	$0.876776\pi$
$30$	−5.14542	+	6.30200i	−0.939421	+	1.15058i
$31$	−2.69431	−	3.04125i	−0.483913	−	0.546225i	0.454949	−	0.890517i	$-0.349657\pi$
$31$	−2.69431	−	3.04125i	−0.483913	−	0.546225i	−0.938863	+	0.344292i	$0.888119\pi$
$32$	−7.82806	−	1.59811i	−1.38382	−	0.282509i
$33$	−14.6056	+	4.23056i	−2.54250	+	0.736445i
$34$	13.0961	−	4.96668i	2.24596	−	0.851778i
$35$	−0.253767	−	6.29716i	−0.0428945	−	1.06441i
$36$	−6.83086	−	5.13306i	−1.13848	−	0.855510i
$37$	3.77702	−	0.771085i	0.620939	−	0.126766i	0.120751	−	0.992683i	$-0.461470\pi$
$37$	3.77702	−	0.771085i	0.620939	−	0.126766i	0.500187	+	0.865917i	$0.333265\pi$
$38$	−3.77184	+	1.97962i	−0.611873	+	0.321136i
$39$	9.73733	+	0.101040i	1.55922	+	0.0161794i
$40$	−0.0273601	−	0.0143597i	−0.00432601	−	0.00227046i
$41$	−4.49274	−	1.30134i	−0.701648	−	0.203235i	−0.0918280	−	0.995775i	$-0.529271\pi$
$41$	−4.49274	−	1.30134i	−0.701648	−	0.203235i	−0.609820	+	0.792540i	$0.708758\pi$
$42$	22.4707	−	1.81402i	3.46730	−	0.279910i
$43$	−0.625951	+	3.06611i	−0.0954566	+	0.467577i	0.903761	+	0.428037i	$0.140795\pi$
$43$	−0.625951	+	3.06611i	−0.0954566	+	0.467577i	−0.999218	+	0.0395406i	$0.987411\pi$
$44$	5.20610	+	9.91940i	0.784849	+	1.49541i
$45$	−3.89057	−	5.17741i	−0.579972	−	0.771803i
$46$	1.68465	−	2.66406i	0.248388	−	0.392795i
$47$	−6.46667	+	4.46362i	−0.943260	+	0.651085i	−0.937161	−	0.348896i	$-0.886557\pi$
$47$	−6.46667	+	4.46362i	−0.943260	+	0.651085i	−0.00609861	+	0.999981i	$0.501941\pi$
$48$	4.65487	−	9.80994i	0.671873	−	1.41594i
$49$	−7.24819	+	7.54616i	−1.03546	+	1.07802i
$50$	−3.92636	−	3.77132i	−0.555272	−	0.533346i
$51$	2.28276	+	18.8002i	0.319650	+	2.63255i
$52$	−1.36200	−	7.04365i	−0.188875	−	0.976778i
$53$	−0.932805	+	7.68234i	−0.128131	+	1.05525i	0.776817	+	0.629727i	$0.216833\pi$
$53$	−0.932805	+	7.68234i	−0.128131	+	1.05525i	−0.904947	+	0.425524i	$0.860090\pi$
$54$	5.40848	−	4.41589i	0.736002	−	0.600927i
$55$	1.69841	+	8.31934i	0.229013	+	1.12178i
$56$	0.0238212	+	0.0822403i	0.00318324	+	0.0109898i
$57$	−1.37840	−	5.59241i	−0.182574	−	0.740732i
$58$	−0.717536	+	8.88828i	−0.0942171	+	1.16709i
$59$	−0.475472	−	2.92570i	−0.0619012	−	0.380893i	−0.999454	−	0.0330497i	$-0.989478\pi$
$59$	−0.475472	−	2.92570i	−0.0619012	−	0.380893i	0.937552	−	0.347844i	$-0.113086\pi$
$60$	−5.37423	+	6.06625i	−0.693810	+	0.783150i
$61$	2.12835	−	1.59935i	0.272507	−	0.204776i	−0.455699	−	0.890134i	$-0.650611\pi$
$61$	2.12835	−	1.59935i	0.272507	−	0.204776i	0.728206	+	0.685358i	$0.240354\pi$
$62$	−5.13275	−	6.28647i	−0.651860	−	0.798383i
$63$	−2.87865	+	17.7131i	−0.362676	+	2.23164i
$64$	−7.68766	−	1.89484i	−0.960957	−	0.236855i
$65$	0.493758	−	5.41512i	0.0612431	−	0.671663i
$66$	−29.4903	+	7.26870i	−3.63000	+	0.894715i
$67$	0.307874	+	3.81370i	0.0376128	+	0.465918i	0.987958	+	0.154721i	$0.0494478\pi$
$67$	0.307874	+	3.81370i	0.0376128	+	0.465918i	−0.950345	+	0.311197i	$0.899270\pi$
$68$	13.2343	−	4.41825i	1.60489	−	0.535791i
$69$	2.95236	+	3.07374i	0.355423	+	0.370034i
$70$		−	12.5884i		−	1.50460i
$71$	−0.130995	+	0.125823i	−0.0155463	+	0.0149324i	−0.700457	−	0.713694i	$-0.747021\pi$
$71$	−0.130995	+	0.125823i	−0.0155463	+	0.0149324i	0.684911	+	0.728627i	$0.259841\pi$
$72$	0.0681534	+	0.0556455i	0.00803196	+	0.00655789i
$73$	3.18128	−	6.06142i	0.372340	−	0.709435i	−0.625130	−	0.780521i	$-0.714954\pi$
$73$	3.18128	−	6.06142i	0.372340	−	0.709435i	0.997470	+	0.0710856i	$0.0226463\pi$
$74$	7.60025	−	1.23516i	0.883511	−	0.143585i
$75$	6.22167	−	3.93434i	0.718416	−	0.454299i
$76$	−3.83367	+	1.81910i	−0.439753	+	0.208665i
$77$	13.3654	−	19.3631i	1.52313	−	2.20664i
$78$	19.4258	+	0.984817i	2.19954	+	0.111509i
$79$	5.93723	+	8.60156i	0.667990	+	0.967751i	0.999703	+	0.0243703i	$0.00775807\pi$
$79$	5.93723	+	8.60156i	0.667990	+	0.967751i	−0.331713	+	0.943380i	$0.607627\pi$
$80$	−5.25092	−	3.03162i	−0.587070	−	0.338945i
$81$	−1.47554	−	3.10963i	−0.163949	−	0.345514i
$82$	−8.86200	−	2.95857i	−0.978645	−	0.326720i
$83$	−1.37302	+	5.57058i	−0.150709	+	0.611451i	0.846199	+	0.532868i	$0.178886\pi$
$83$	−1.37302	+	5.57058i	−0.150709	+	0.611451i	−0.996908	+	0.0785829i	$0.974960\pi$
$84$	22.4388	−	0.904252i	2.44827	−	0.0986620i
$85$	10.5665	−	0.425815i	1.14610	−	0.0461861i
$86$	−1.49588	+	6.06904i	−0.161305	+	0.654441i
$87$	−11.4367	−	3.81814i	−1.22614	−	0.409347i
$88$	−0.0494519	−	0.104218i	−0.00527160	−	0.0111097i
$89$	−6.07451	−	3.50712i	−0.643897	−	0.371754i	0.142217	−	0.989835i	$-0.454577\pi$
$89$	−6.07451	−	3.50712i	−0.643897	−	0.371754i	−0.786114	+	0.618081i	$0.787910\pi$
$90$	−7.34845	−	10.6461i	−0.774595	−	1.12219i
$91$	−11.7694	+	9.40762i	−1.23377	+	0.986186i
$92$	1.78366	−	2.58408i	0.185960	−	0.269409i
$93$	9.91403	−	4.70427i	1.02804	−	0.487810i
$94$	−13.2653	+	8.38844i	−1.36821	+	0.865202i
$95$	−3.17459	+	0.515921i	−0.325706	+	0.0529324i
$96$	10.0278	−	19.1064i	1.02346	−	1.95004i
$97$	−7.22423	−	5.89840i	−0.733510	−	0.598892i	0.190308	−	0.981724i	$-0.439051\pi$
$97$	−7.22423	−	5.89840i	−0.733510	−	0.598892i	−0.923818	+	0.382832i	$0.874949\pi$
$98$	−15.0730	+	14.4778i	−1.52260	+	1.46248i
$99$		−	24.1776i		−	2.42994i
$100$	−3.75680	−	3.91124i	−0.375680	−	0.391124i
$101$	7.16845	−	2.39318i	0.713287	−	0.238130i	0.0632120	−	0.998000i	$-0.479866\pi$
$101$	7.16845	−	2.39318i	0.713287	−	0.238130i	0.650075	+	0.759870i	$0.274737\pi$
$102$	3.04389	+	37.7053i	0.301390	+	3.73338i
$103$	9.68310	−	2.38667i	0.954105	−	0.235166i	0.268615	−	0.963248i	$-0.413434\pi$
$103$	9.68310	−	2.38667i	0.954105	−	0.235166i	0.685490	+	0.728082i	$0.259588\pi$
$104$	0.0110929	+	0.0730357i	0.00108775	+	0.00716174i
$105$	16.5265	+	4.07343i	1.61283	+	0.397526i
$106$	−2.47958	+	15.2575i	−0.240838	+	1.48194i
$107$	3.24006	+	3.96836i	0.313229	+	0.383635i	0.907093	−	0.420930i	$-0.138296\pi$
$107$	3.24006	+	3.96836i	0.313229	+	0.383635i	−0.593865	+	0.804565i	$0.702399\pi$
$108$	5.56041	−	4.17838i	0.535051	−	0.402065i
$109$	1.10737	−	1.24996i	0.106067	−	0.119725i	−0.693080	−	0.720861i	$-0.743747\pi$
$109$	1.10737	−	1.24996i	0.106067	−	0.119725i	0.799147	+	0.601136i	$0.205285\pi$
$110$	2.72059	+	16.7405i	0.259398	+	1.59614i
$111$	−0.837767	+	10.3776i	−0.0795173	+	0.984999i
$112$	4.02073	+	16.3127i	0.379923	+	1.54141i
$113$	2.35579	+	8.13314i	0.221614	+	0.765101i	0.991858	+	0.127351i	$0.0406475\pi$
$113$	2.35579	+	8.13314i	0.221614	+	0.765101i	−0.770243	+	0.637750i	$0.779865\pi$
$114$	−2.30125	−	11.2723i	−0.215532	−	1.05574i
$115$	1.84345	−	1.50513i	0.171903	−	0.140354i
$116$	−1.07071	+	8.81809i	−0.0994129	+	0.818739i
$117$	−4.46180	+	14.8265i	−0.412493	+	1.37071i
$118$	−0.713644	−	5.87739i	−0.0656963	−	0.541058i
$119$	−21.1334	−	20.2989i	−1.93730	−	1.86080i
$120$	0.0578099	−	0.0601865i	0.00527730	−	0.00549425i
$121$	−8.87343	+	18.7003i	−0.806675	+	1.70003i
$122$	4.37642	−	3.02083i	0.396223	−	0.273493i
$123$	6.75176	−	10.6771i	0.608786	−	0.962718i
$124$	−4.85668	−	6.46307i	−0.436143	−	0.580401i
$125$	−5.41452	−	10.3165i	−0.484290	−	0.922737i
$126$	−7.16989	+	35.1205i	−0.638745	+	3.12878i
$127$	12.6305	−	1.01964i	1.12078	−	0.0904786i	0.493844	−	0.869550i	$-0.335591\pi$
$127$	12.6305	−	1.01964i	1.12078	−	0.0904786i	0.626935	+	0.779072i	$0.284309\pi$
$128$	0.157437	+	0.0456021i	0.0139156	+	0.00403069i
$129$	−7.48364	−	3.92772i	−0.658898	−	0.345816i
$130$	1.42098	−	10.7679i	0.124628	−	0.944403i
$131$	−2.41869	+	1.26943i	−0.211322	+	0.110911i	−0.567064	−	0.823674i	$-0.691921\pi$
$131$	−2.41869	+	1.26943i	−0.211322	+	0.110911i	0.355741	+	0.934584i	$0.384228\pi$
$132$	−29.6444	+	6.05195i	−2.58022	+	0.526755i
$133$	7.12467	+	5.35384i	0.617787	+	0.464237i
$134$	0.307728	+	7.63620i	0.0265837	+	0.659667i
$135$	4.92920	−	1.86940i	0.424238	−	0.160892i
$136$	−0.137997	+	0.0399714i	−0.0118332	+	0.00342752i
$137$	8.80398	+	1.79735i	0.752175	+	0.153558i	0.560791	−	0.827958i	$-0.310497\pi$
$137$	8.80398	+	1.79735i	0.752175	+	0.153558i	0.191384	+	0.981515i	$0.438702\pi$
$138$	5.64515	+	6.37206i	0.480547	+	0.542426i
$139$	−5.46241	+	6.69024i	−0.463316	+	0.567459i	−0.952429	−	0.304762i	$-0.901423\pi$
$139$	−5.46241	+	6.69024i	−0.463316	+	0.567459i	0.489113	+	0.872220i	$0.337321\pi$
$140$	0.504931	−	12.5297i	0.0426745	−	1.05896i
$141$	−6.72024	−	20.1296i	−0.565946	−	1.69522i
$142$	−0.271562	+	0.240583i	−0.0227890	+	0.0201893i
$143$	13.6182	−	15.0542i	1.13881	−	1.25889i
$144$	12.9229	+	11.4487i	1.07691	+	0.954057i
$145$	−2.63900	+	6.19395i	−0.219157	+	0.514380i
$146$	6.83675	−	11.8416i	0.565813	−	0.980017i
$147$	−14.1296	−	24.4732i	−1.16539	−	2.01852i
$148$	7.61439	−	0.924554i	0.625899	−	0.0759979i
$149$	16.1993	+	7.68667i	1.32710	+	0.629717i	0.954482	−	0.298268i	$-0.0964089\pi$
$149$	16.1993	+	7.68667i	1.32710	+	0.629717i	0.372618	+	0.927985i	$0.378460\pi$
$150$	12.7337	−	7.35182i	1.03970	−	0.600274i
$151$	1.80201	+	1.24384i	0.146645	+	0.101222i	0.639128	−	0.769100i	$-0.279295\pi$
$151$	1.80201	+	1.24384i	0.146645	+	0.101222i	−0.492483	+	0.870322i	$0.663911\pi$
$152$	0.0401983	−	0.0171269i	0.00326052	−	0.00138918i
$153$	−29.7221	−	4.83031i	−2.40289	−	0.390508i
$154$	28.2322	−	37.5703i	2.27502	−	3.02750i
$155$	−2.17287	−	5.72938i	−0.174529	−	0.460195i
$156$	19.2958	+	1.75941i	1.54490	+	0.140866i
$157$	4.27634	−	11.2758i	0.341289	−	0.899906i	−0.648988	−	0.760799i	$-0.724807\pi$
$157$	4.27634	−	11.2758i	0.341289	−	0.899906i	0.990277	−	0.139107i	$-0.0444234\pi$
$158$	11.1578	+	17.6446i	0.887666	+	1.40373i
$159$	−19.2283	−	8.19242i	−1.52490	−	0.649701i
$160$	−10.1838	−	6.43984i	−0.805099	−	0.509114i
$161$	−6.54641	−	0.794878i	−0.515929	−	0.0626451i
$162$	−2.69479	−	6.32491i	−0.211723	−	0.496932i
$163$	−2.19300	+	6.56885i	−0.171769	+	0.514512i	−0.998869	−	0.0475431i	$-0.984861\pi$
$163$	−2.19300	+	6.56885i	−0.171769	+	0.514512i	0.827100	+	0.562055i	$0.189989\pi$
$164$	−8.70205	−	3.30025i	−0.679516	−	0.257706i
$165$	−22.8579	−	1.84528i	−1.77949	−	0.143655i
$166$	−3.18834	+	11.0074i	−0.247463	+	0.854341i
$167$	9.37859	+	0.377944i	0.725737	+	0.0292462i	0.400385	−	0.916347i	$-0.368876\pi$
$167$	9.37859	+	0.377944i	0.725737	+	0.0292462i	0.325352	+	0.945593i	$0.394517\pi$
$168$	−0.231244			−0.0178409
$169$	−11.1293	+	6.71856i	−0.856099	+	0.516812i
$170$	21.1230			1.62006
$171$	9.15067	+	0.368759i	0.699769	+	0.0281997i
$172$	−1.73235	+	5.98076i	−0.132090	+	0.456029i
$173$	−0.252651	−	0.0203961i	−0.0192087	−	0.00155069i	0.0708585	−	0.997486i	$-0.477426\pi$
$173$	−0.252651	−	0.0203961i	−0.0192087	−	0.00155069i	−0.0900672	+	0.995936i	$0.528708\pi$
$174$	−22.5185	−	8.54013i	−1.70712	−	0.647425i
$175$	−3.60685	+	10.8038i	−0.272652	+	0.816694i
$176$	−8.87240	−	20.8243i	−0.668782	−	1.56969i
$177$	7.94701	+	0.964941i	0.597334	+	0.0725294i
$178$	−11.8415	−	7.48813i	−0.887560	−	0.561259i
$179$	−11.8180	−	5.03517i	−0.883317	−	0.376346i	−0.0978144	−	0.995205i	$-0.531185\pi$
$179$	−11.8180	−	5.03517i	−0.883317	−	0.376346i	−0.785502	+	0.618859i	$0.787595\pi$
$180$	−6.88719	−	10.8912i	−0.513341	−	0.811784i
$181$	−6.15382	+	16.2263i	−0.457410	+	1.20609i	0.485852	+	0.874041i	$0.338509\pi$
$181$	−6.15382	+	16.2263i	−0.457410	+	1.20609i	−0.943262	+	0.332050i	$0.892260\pi$
$182$	−24.2463	+	17.8293i	−1.79725	+	1.32159i
$183$	2.54972	+	6.72305i	0.188480	+	0.496982i
$184$	−0.0194233	+	0.0258477i	−0.00143190	+	0.00190551i
$185$	5.73838	+	0.932578i	0.421894	+	0.0685645i
$186$	20.1649	−	8.59147i	1.47856	−	0.629957i
$187$	32.4909	+	22.4269i	2.37597	+	1.64001i
$188$	−13.5399	+	7.81728i	−0.987501	+	0.570134i
$189$	−13.1975	−	6.26227i	−0.959974	−	0.455513i
$190$	−6.37738	+	0.774354i	−0.462664	+	0.0561776i
$191$	−8.94862	−	15.4995i	−0.647500	−	1.12150i	−0.983718	−	0.179718i	$-0.942481\pi$
$191$	−8.94862	−	15.4995i	−0.647500	−	1.12150i	0.336219	−	0.941784i	$-0.390852\pi$
$192$	10.6921	−	18.5192i	0.771634	−	1.33651i
$193$	7.49253	−	17.5856i	0.539324	−	1.26584i	−0.398001	−	0.917385i	$-0.630296\pi$
$193$	7.49253	−	17.5856i	0.539324	−	1.26584i	0.937325	−	0.348455i	$-0.113294\pi$
$194$	−13.9438	−	12.3532i	−1.00111	−	0.886905i
$195$	13.6767	+	5.34985i	0.979407	+	0.383111i
$196$	−15.5835	+	13.8057i	−1.11310	+	0.986124i
$197$	−7.59567	−	22.7518i	−0.541169	−	1.62100i	−0.763344	−	0.645992i	$-0.776444\pi$
$197$	−7.59567	−	22.7518i	−0.541169	−	1.62100i	0.222176	−	0.975007i	$-0.428684\pi$
$198$	1.94457	−	48.2539i	0.138194	−	3.42926i
$199$	8.96125	−	10.9755i	0.635246	−	0.778035i	−0.352211	−	0.935920i	$-0.614570\pi$
$199$	8.96125	−	10.9755i	0.635246	−	0.778035i	0.987457	+	0.157885i	$0.0504676\pi$
$200$	0.0370315	+	0.0417999i	0.00261852	+	0.00295570i
$201$	−10.1247	−	2.06697i	−0.714141	−	0.145793i
$202$	14.4994	−	4.19979i	1.02017	−	0.295496i
$203$	17.4437	−	6.61552i	1.22431	−	0.464318i
$204$	1.51731	+	37.6517i	0.106233	+	2.63615i
$205$	−5.63932	−	4.23768i	−0.393867	−	0.295972i
$206$	19.5176	−	3.98455i	1.35986	−	0.277617i
$207$	−6.00034	+	3.14922i	−0.417053	+	0.218886i
$208$	1.59787	+	14.4075i	0.110792	+	0.998978i
$209$	−10.6317	−	5.57994i	−0.735410	−	0.385973i
$210$	32.6563	+	9.45901i	2.25350	+	0.652734i
$211$	−25.5484	+	2.06248i	−1.75882	+	0.141987i	−0.917290	−	0.398220i	$-0.869628\pi$
$211$	−25.5484	+	2.06248i	−1.75882	+	0.141987i	−0.841532	+	0.540207i	$0.818346\pi$
$212$	−3.08002	+	15.0870i	−0.211537	+	1.03618i
$213$	−0.227973	−	0.434367i	−0.0156205	−	0.0297623i
$214$	6.14739	+	8.18069i	0.420227	+	0.559221i
$215$	−2.52237	+	3.98880i	−0.172024	+	0.272034i
$216$	−0.0589427	+	0.0406852i	−0.00401054	+	0.00276828i
$217$	−7.27886	+	15.3399i	−0.494121	+	1.04134i
$218$	2.31064	−	2.40563i	0.156496	−	0.162930i
$219$	13.3339	+	12.8073i	0.901019	+	0.865440i
$220$	2.03644	+	16.7716i	0.137297	+	1.13074i
$221$	−15.7858	−	19.7488i	−1.06187	−	1.32845i
$222$	−2.50668	+	20.6444i	−0.168238	+	1.38556i
$223$	13.0486	−	10.6539i	0.873800	−	0.713435i	−0.0853450	−	0.996351i	$-0.527199\pi$
$223$	13.0486	−	10.6539i	0.873800	−	0.713435i	0.959145	+	0.282916i	$0.0913018\pi$
$224$	6.67836	+	32.7128i	0.446217	+	2.18571i
$225$	3.25639	+	11.2424i	0.217093	+	0.749491i
$226$	4.04759	+	16.4217i	0.269241	+	1.09236i
$227$	0.337296	−	4.17817i	0.0223871	−	0.277315i	−0.975872	−	0.218342i	$-0.929935\pi$
$227$	0.337296	−	4.17817i	0.0223871	−	0.277315i	0.998260	−	0.0589731i	$-0.0187826\pi$
$228$	−1.83839	−	11.3121i	−0.121750	−	0.749159i
$229$	2.42838	−	2.74108i	0.160472	−	0.181135i	−0.662775	−	0.748818i	$-0.730622\pi$
$229$	2.42838	−	2.74108i	0.160472	−	0.181135i	0.823247	+	0.567683i	$0.192160\pi$
$230$	3.80025	−	2.85570i	0.250581	−	0.188299i
$231$	40.1883	+	49.2217i	2.64419	+	3.23855i
$232$	0.0146726	−	0.0902840i	0.000963302	−	0.00592744i
$233$	11.5935	+	2.85754i	0.759515	+	0.187204i	0.600009	−	0.799993i	$-0.295164\pi$
$233$	11.5935	+	2.85754i	0.759515	+	0.187204i	0.159506	+	0.987197i	$0.449010\pi$
$234$	−10.0974	+	29.2320i	−0.660087	+	1.91096i
$235$	−11.5058	+	2.83592i	−0.750555	+	0.184995i
$236$	−0.474573	−	5.87864i	−0.0308920	−	0.382667i
$237$	−26.7751	+	8.93884i	−1.73923	+	0.580640i
$238$	−40.5457	−	42.2126i	−2.62819	−	2.73623i
$239$		−	15.5704i		−	1.00717i	−0.863946	−	0.503584i	$-0.832015\pi$
$239$		−	15.5704i		−	1.00717i	0.863946	−	0.503584i	$-0.167985\pi$
$240$	11.8101	−	11.3437i	0.762338	−	0.732236i
$241$	5.78675	+	4.72473i	0.372757	+	0.304347i	0.800244	−	0.599675i	$-0.204703\pi$
$241$	5.78675	+	4.72473i	0.372757	+	0.304347i	−0.427487	+	0.904022i	$0.640601\pi$
$242$	−19.2137	+	36.6087i	−1.23511	+	2.35330i
$243$	19.5266	−	3.17339i	1.25263	−	0.203573i
$244$	4.47720	−	2.83121i	0.286624	−	0.181250i
$245$	−14.2563	+	6.76471i	−0.910803	+	0.432181i
$246$	14.3340	−	20.7664i	0.913902	−	1.32402i
$247$	5.48996	+	5.38381i	0.349318	+	0.342563i
$248$	0.0472899	+	0.0685112i	0.00300291	+	0.00435047i
$249$	−13.4193	−	7.74763i	−0.850413	−	0.490986i
$250$	−9.97664	−	21.0253i	−0.630978	−	1.32976i
$251$	0.653774	+	0.218262i	0.0412658	+	0.0137766i	0.337226	−	0.941424i	$-0.390511\pi$
$251$	0.653774	+	0.218262i	0.0412658	+	0.0137766i	−0.295960	+	0.955200i	$0.595640\pi$
$252$	−8.54521	+	34.6693i	−0.538297	+	2.18396i
$253$	8.87742	−	0.357748i	0.558119	−	0.0224914i
$254$	25.2902	−	1.01916i	1.58685	−	0.0639478i
$255$	−6.83511	+	27.7311i	−0.428031	+	1.73659i
$256$	15.3311	+	5.11826i	0.958191	+	0.319891i
$257$	5.15529	+	10.8645i	0.321578	+	0.677712i	0.998285	−	0.0585410i	$-0.0186448\pi$
$257$	5.15529	+	10.8645i	0.321578	+	0.677712i	−0.676707	+	0.736253i	$0.736594\pi$
$258$	−14.6200	−	8.44089i	−0.910204	−	0.525507i
$259$	−9.15118	−	13.2578i	−0.568627	−	0.823798i
$260$	1.84627	−	10.6607i	0.114501	−	0.661148i
$261$	10.8904	−	15.7775i	0.674101	−	0.976603i
$262$	−4.92936	+	2.33901i	−0.304537	+	0.144505i
$263$	−4.78435	+	3.02544i	−0.295016	+	0.186557i	−0.673771	−	0.738940i	$-0.735327\pi$
$263$	−4.78435	+	3.02544i	−0.295016	+	0.186557i	0.378755	+	0.925497i	$0.376352\pi$
$264$	0.307516	−	0.0499763i	0.0189263	−	0.00307583i
$265$	−5.42375	+	10.3341i	−0.333179	+	0.634819i
$266$	13.7889	+	11.2583i	0.845452	+	0.690290i
$267$	13.6625	−	13.1230i	0.836130	−	0.803114i
$268$			7.61297i			0.465036i
$269$	21.9131	+	22.8139i	1.33606	+	1.39099i	0.858871	+	0.512191i	$0.171166\pi$
$269$	21.9131	+	22.8139i	1.33606	+	1.39099i	0.477193	+	0.878799i	$0.341654\pi$
$270$	9.98811	−	3.33452i	0.607857	−	0.202933i
$271$	0.959838	+	11.8897i	0.0583060	+	0.722249i	0.958192	+	0.286125i	$0.0923672\pi$
$271$	0.959838	+	11.8897i	0.0583060	+	0.722249i	−0.899886	+	0.436125i	$0.856351\pi$
$272$	−27.3724	+	6.74669i	−1.65969	+	0.409078i
$273$	−15.5612	−	37.6008i	−0.941809	−	2.27570i
$274$	17.4266	+	4.29526i	1.05278	+	0.259486i
$275$	2.46160	−	15.1468i	0.148440	−	0.913388i
$276$	5.36326	+	6.56881i	0.322831	+	0.395396i
$277$	−16.4414	+	12.3549i	−0.987870	+	0.742336i	−0.966297	−	0.257431i	$-0.917124\pi$
$277$	−16.4414	+	12.3549i	−0.987870	+	0.742336i	−0.0215736	+	0.999767i	$0.506868\pi$
$278$	−11.4400	+	12.9131i	−0.686128	+	0.774479i
$279$	2.79886	+	17.2221i	0.167563	+	1.03106i
$280$	−0.0103903	+	0.128707i	−0.000620940	+	0.00769172i
$281$	5.68800	+	23.0771i	0.339318	+	1.37667i	0.854440	+	0.519549i	$0.173900\pi$
$281$	5.68800	+	23.0771i	0.339318	+	1.37667i	−0.515123	+	0.857116i	$0.672254\pi$
$282$	−11.7934	−	40.7154i	−0.702284	−	2.42457i
$283$	−2.94812	−	14.4408i	−0.175248	−	0.858419i	−0.968401	−	0.249398i	$-0.919767\pi$
$283$	−2.94812	−	14.4408i	−0.175248	−	0.858419i	0.793154	−	0.609022i	$-0.208438\pi$
$284$	−0.279947	+	0.228569i	−0.0166118	+	0.0135631i
$285$	1.04703	−	8.62306i	0.0620207	−	0.510786i
$286$	28.3903	−	28.9500i	1.67875	−	1.71185i
$287$	2.35607	+	19.4040i	0.139074	+	1.14538i
$288$	24.7440	+	23.7669i	1.45805	+	1.40048i
$289$	22.2848	−	23.2009i	1.31087	−	1.36476i
$290$	−5.76512	+	12.1497i	−0.338539	+	0.713457i
$291$	20.7298	−	14.3087i	1.21520	−	0.838792i
$292$	7.27987	−	11.5122i	0.426022	−	0.673701i
$293$	7.46258	+	9.93089i	0.435969	+	0.580169i	0.962941	−	0.269714i	$-0.0869291\pi$
$293$	7.46258	+	9.93089i	0.435969	+	0.580169i	−0.526972	+	0.849883i	$0.676673\pi$
$294$	−26.2317	−	49.9804i	−1.52987	−	2.91492i
$295$	0.894150	−	4.37983i	0.0520594	−	0.255004i
$296$	−0.0787266	+	0.00635547i	−0.00457589	+	0.000369404i
$297$	18.9038	+	5.47556i	1.09691	+	0.317724i
$298$	31.7126	+	16.6441i	1.83706	+	0.964165i
$299$	−5.50994	−	1.41888i	−0.318648	−	0.0820561i
$300$	12.9693	−	6.80681i	0.748782	−	0.392991i
$301$	12.8130	−	2.61579i	0.738529	−	0.150772i
$302$	3.49643	+	2.62740i	0.201197	+	0.151190i
$303$	0.821865	+	20.3944i	0.0472149	+	1.17163i
$304$	8.01684	−	3.04039i	0.459798	−	0.174378i
$305$	3.85652	−	1.11705i	0.220824	−	0.0639623i
$306$	−58.9313	−	12.0309i	−3.36888	−	0.687761i
$307$	−19.7940	−	22.3428i	−1.12970	−	1.27517i	−0.956966	−	0.290201i	$-0.906278\pi$
$307$	−19.7940	−	22.3428i	−1.12970	−	1.27517i	−0.172736	−	0.984968i	$-0.555261\pi$
$308$	29.6077	−	36.2628i	1.68705	−	2.06627i
$309$	−1.08455	+	26.9129i	−0.0616981	+	1.53102i
$310$	−3.87583	−	11.6095i	−0.220133	−	0.659378i
$311$	11.7558	−	10.4147i	0.666609	−	0.590564i	−0.260446	−	0.965488i	$-0.583870\pi$
$311$	11.7558	−	10.4147i	0.666609	−	0.590564i	0.927056	+	0.374924i	$0.122331\pi$
$312$	−0.197802	−	0.0261029i	−0.0111983	−	0.00147778i
$313$	0.273059	+	0.241909i	0.0154342	+	0.0136735i	0.670805	−	0.741634i	$-0.265949\pi$
$313$	0.273059	+	0.241909i	0.0154342	+	0.0136735i	−0.655370	+	0.755308i	$0.727487\pi$
$314$	9.44168	−	22.1604i	0.532825	−	1.25059i
$315$	−13.5319	+	23.4379i	−0.762436	+	1.32058i
$316$	10.3981	+	18.0100i	0.584937	+	1.01314i
$317$	−14.6380	+	1.77738i	−0.822154	+	0.0998276i	−0.520794	−	0.853683i	$-0.674364\pi$
$317$	−14.6380	+	1.77738i	−0.822154	+	0.0998276i	−0.301361	+	0.953510i	$0.597441\pi$
$318$	−37.7172	−	17.8970i	−2.11508	−	1.00362i
$319$	−21.7675	+	12.5675i	−1.21874	+	0.703642i
$320$	−9.82712	−	6.78317i	−0.549353	−	0.379191i
$321$	−12.7292	+	5.42339i	−0.710473	+	0.302704i
$322$	−13.0015	−	2.11295i	−0.724544	−	0.117750i
$323$	−8.98362	+	11.9550i	−0.499862	+	0.665195i
$324$	−2.42854	−	6.40354i	−0.134919	−	0.355752i
$325$	−4.30477	+	8.83425i	−0.238786	+	0.490036i
$326$	−4.90515	+	12.9338i	−0.271671	+	0.716338i
$327$	2.41052	+	3.81193i	0.133302	+	0.210800i
$328$	0.0881657	+	0.0375639i	0.00486814	+	0.00207412i
$329$	27.7528	+	17.5498i	1.53006	+	0.967552i
$330$	−45.4717	−	5.52127i	−2.50314	−	0.303936i
$331$	−0.782037	−	1.83551i	−0.0429847	−	0.100889i	0.897103	−	0.441821i	$-0.145667\pi$
$331$	−0.782037	−	1.83551i	−0.0429847	−	0.100889i	−0.940088	+	0.340933i	$0.889257\pi$
$332$	−3.61500	+	10.8282i	−0.198399	+	0.594277i
$333$	−15.4784	−	5.87019i	−0.848212	−	0.321685i
$334$	18.6875	+	1.50861i	1.02254	+	0.0825476i
$335$	−1.60537	+	5.54239i	−0.0877108	+	0.302813i
$336$	−45.3391	−	1.82710i	−2.47345	−	0.0996766i
$337$	11.4442			0.623404			0.311702	−	0.950180i	$-0.399101\pi$
$337$	11.4442			0.623404			0.311702	+	0.950180i	$0.399101\pi$
$338$	−22.7523	+	12.5139i	−1.23756	+	0.680665i
$339$	−22.8688			−1.24206
$340$	21.0246	+	0.847262i	1.14022	+	0.0459492i
$341$	6.36444	−	21.9726i	0.344654	−	1.18988i
$342$	18.2334	+	1.47195i	0.985948	+	0.0795940i
$343$	13.5323	+	5.13214i	0.730678	+	0.277110i
$344$	0.0203037	−	0.0608169i	0.00109470	−	0.00327903i
$345$	2.51937	+	5.91319i	0.135638	+	0.318355i
$346$	−0.502604	−	0.0610272i	−0.0270202	−	0.00328084i
$347$	−20.7503	−	13.1217i	−1.11393	−	0.704410i	−0.154966	−	0.987920i	$-0.549527\pi$
$347$	−20.7503	−	13.1217i	−1.11393	−	0.704410i	−0.958969	+	0.283510i	$0.908501\pi$
$348$	−22.0710	−	9.40358i	−1.18313	−	0.504085i
$349$	−11.7946	−	18.6516i	−0.631348	−	0.998398i	−0.997691	−	0.0679177i	$-0.978364\pi$
$349$	−11.7946	−	18.6516i	−0.631348	−	0.998398i	0.366342	−	0.930480i	$-0.380610\pi$
$350$	−8.06754	+	21.2724i	−0.431228	+	1.13706i
$351$	−10.5820	−	6.84636i	−0.564824	−	0.365432i
$352$	−15.9510	−	42.0593i	−0.850190	−	2.24177i
$353$	−11.3408	+	15.0918i	−0.603608	+	0.803256i	−0.993037	−	0.117800i	$-0.962416\pi$
$353$	−11.3408	+	15.0918i	−0.603608	+	0.803256i	0.389430	+	0.921056i	$0.372672\pi$
$354$	15.7831	+	2.56501i	0.838865	+	0.136329i
$355$	−0.252006	+	0.107370i	−0.0133751	+	0.00569859i
$356$	−11.4860	−	7.92822i	−0.608757	−	0.420195i
$357$	68.5385	−	39.5707i	3.62744	−	2.09430i
$358$	−23.1815	−	10.9998i	−1.22518	−	0.581356i
$359$	−7.74831	+	0.940816i	−0.408940	+	0.0496543i	−0.322422	−	0.946596i	$-0.604497\pi$
$359$	−7.74831	+	0.940816i	−0.408940	+	0.0496543i	−0.0865180	+	0.996250i	$0.527574\pi$
$360$	0.0663455	+	0.114914i	0.00349671	+	0.00605649i
$361$	−7.22596	+	12.5157i	−0.380314	+	0.658723i
$362$	−13.5869	+	31.8897i	−0.714114	+	1.67609i
$363$	−41.8442	−	37.0707i	−2.19625	−	1.94571i
$364$	−24.8484	+	16.7737i	−1.30241	+	0.879179i
$365$	7.72750	−	6.84597i	0.404476	−	0.358335i
$366$	4.54803	+	13.6230i	0.237730	+	0.712087i
$367$	0.257734	−	6.39561i	0.0134536	−	0.333848i	−0.978420	−	0.206624i	$-0.933752\pi$
$367$	0.257734	−	6.39561i	0.0134536	−	0.333848i	0.991874	−	0.127224i	$-0.0406067\pi$
$368$	−4.01246	+	4.91438i	−0.209164	+	0.256180i
$369$	13.3196	+	15.0347i	0.693390	+	0.782675i
$370$	11.3777	+	2.32278i	0.591501	+	0.120756i
$371$	31.0628	−	8.99744i	1.61270	−	0.467124i
$372$	20.4156	−	7.74261i	1.05850	−	0.401436i
$373$	0.476693	+	11.8290i	0.0246822	+	0.612484i	0.963443	+	0.267914i	$0.0863342\pi$
$373$	0.476693	+	11.8290i	0.0246822	+	0.612484i	−0.938761	+	0.344570i	$0.888025\pi$
$374$	63.0420	+	47.3730i	3.25983	+	2.44960i
$375$	30.8312	−	6.29424i	1.59212	−	0.325033i
$376$	0.142552	−	0.0748168i	0.00735154	−	0.00385838i
$377$	15.6677	−	3.68974i	0.806930	−	0.190031i
$378$	−25.8360	−	13.5598i	−1.32886	−	0.697440i
$379$	−14.1547	−	4.09995i	−0.727077	−	0.210600i	−0.106018	−	0.994364i	$-0.533810\pi$
$379$	−14.1547	−	4.09995i	−0.727077	−	0.210600i	−0.621059	+	0.783764i	$0.713297\pi$
$380$	−6.37873	+	0.514945i	−0.327222	+	0.0264161i
$381$	−6.84557	+	33.5318i	−0.350709	+	1.71789i
$382$	−16.6132	−	31.6538i	−0.850005	−	1.61955i
$383$	−0.706777	−	0.940549i	−0.0361146	−	0.0480598i	0.781024	−	0.624501i	$-0.214698\pi$
$383$	−0.706777	−	0.940549i	−0.0361146	−	0.0480598i	−0.817139	+	0.576441i	$0.804441\pi$
$384$	−0.236598	+	0.374150i	−0.0120739	+	0.0190933i
$385$	29.2018	−	20.1566i	1.48826	−	1.02727i
$386$	16.3681	−	34.4950i	0.833113	−	1.75575i
$387$	9.30906	−	9.69176i	0.473206	−	0.492660i
$388$	−13.3834	−	12.8549i	−0.679438	−	0.652609i
$389$	4.58196	+	37.7358i	0.232315	+	1.91328i	0.381315	+	0.924445i	$0.375471\pi$
$389$	4.58196	+	37.7358i	0.232315	+	1.91328i	−0.149001	+	0.988837i	$0.547606\pi$
$390$	26.8658	+	11.7773i	1.36040	+	0.596367i
$391$	1.33379	−	10.9847i	0.0674524	−	0.555521i
$392$	0.166060	−	0.135584i	0.00838730	−	0.00684802i
$393$	−1.47568	−	7.22834i	−0.0744381	−	0.364622i
$394$	−13.3296	−	46.0193i	−0.671538	−	2.31842i
$395$	3.77217	+	15.3043i	0.189798	+	0.770042i
$396$	3.87102	−	47.9512i	0.194526	−	2.40964i
$397$	−4.13292	−	25.4309i	−0.207425	−	1.27634i	−0.856711	−	0.515796i	$-0.827496\pi$
$397$	−4.13292	−	25.4309i	−0.207425	−	1.27634i	0.649286	−	0.760544i	$-0.275068\pi$
$398$	18.7677	−	21.1844i	0.940741	−	1.06188i
$399$	−19.2423	+	14.4596i	−0.963318	+	0.723886i
$400$	6.93034	+	8.48812i	0.346517	+	0.424406i
$401$	−3.49577	+	21.5103i	−0.174570	+	1.07418i	0.740848	+	0.671672i	$0.234424\pi$
$401$	−3.49577	+	21.5103i	−0.174570	+	1.07418i	−0.915419	+	0.402503i	$0.868140\pi$
$402$	−20.0408	−	4.93961i	−0.999543	−	0.246365i
$403$	−7.95777	+	12.2998i	−0.396405	+	0.612697i
$404$	14.6003	−	3.59865i	0.726391	−	0.179039i
$405$	−0.417690	−	5.17402i	−0.0207552	−	0.257099i
$406$	35.3464	−	11.8004i	1.75421	−	0.585642i
$407$	15.0348	+	15.6529i	0.745248	+	0.775886i
$408$		−	0.388022i		−	0.0192100i
$409$	−16.7058	+	16.0462i	−0.826051	+	0.793433i	−0.980902	−	0.194505i	$-0.937690\pi$
$409$	−16.7058	+	16.0462i	−0.826051	+	0.793433i	0.154850	+	0.987938i	$0.450510\pi$
$410$	−10.9142	−	8.91118i	−0.539015	−	0.440092i
$411$	−11.2780	+	21.4884i	−0.556302	+	1.05995i
$412$	19.5865	−	3.18312i	0.964959	−	0.156821i
$413$	−10.4691	+	6.62024i	−0.515149	+	0.325760i
$414$	−12.2289	+	5.80266i	−0.601016	+	0.285185i
$415$	−4.91518	+	7.12086i	−0.241277	+	0.349550i
$416$	2.01992	+	28.7357i	0.0990346	+	1.40889i
$417$	−13.2511	−	19.1975i	−0.648907	−	0.940105i
$418$	−20.7701	−	11.9916i	−1.01590	−	0.586529i
$419$	2.05380	+	4.32829i	0.100335	+	0.211451i	0.947410	−	0.320022i	$-0.103690\pi$
$419$	2.05380	+	4.32829i	0.100335	+	0.211451i	−0.847076	+	0.531472i	$0.821639\pi$
$420$	32.1247	+	10.7248i	1.56753	+	0.523317i
$421$	3.40791	−	13.8264i	0.166091	−	0.673859i	−0.827562	−	0.561374i	$-0.810273\pi$
$421$	3.40791	−	13.8264i	0.166091	−	0.673859i	0.993653	−	0.112485i	$-0.0358810\pi$
$422$	−51.1557	+	2.06150i	−2.49022	+	0.100352i
$423$	33.7154	−	1.35868i	1.63930	−	0.0660614i
$424$	0.0379454	−	0.153950i	0.00184279	−	0.00747649i
$425$	−18.1286	−	6.05221i	−0.879366	−	0.293575i
$426$	−0.420057	−	0.885251i	−0.0203518	−	0.0428906i
$427$	−9.63495	−	5.56274i	−0.466268	−	0.269200i
$428$	5.79062	+	8.38916i	0.279900	+	0.405505i
$429$	28.8201	+	46.6397i	1.39145	+	2.25179i
$430$	−5.35499	+	7.75804i	−0.258241	+	0.374126i
$431$	19.6971	−	9.34639i	0.948776	−	0.450200i	0.109549	−	0.993981i	$-0.465059\pi$
$431$	19.6971	−	9.34639i	0.948776	−	0.450200i	0.839227	+	0.543782i	$0.183008\pi$
$432$	−11.8781	+	7.51127i	−0.571486	+	0.361386i
$433$	25.9555	−	4.21818i	1.24734	−	0.202713i	0.499338	−	0.866407i	$-0.333577\pi$
$433$	25.9555	−	4.21818i	1.24734	−	0.202713i	0.748004	+	0.663694i	$0.231012\pi$
$434$	−15.7610	+	30.0301i	−0.756553	+	1.44149i
$435$	−14.0852	−	11.5002i	−0.675332	−	0.551391i
$436$	2.39636	−	2.30174i	0.114765	−	0.110233i
$437$			3.36536i			0.160987i
$438$	25.5818	+	26.6335i	1.22235	+	1.27260i
$439$	−13.4758	+	4.49890i	−0.643167	+	0.214721i	−0.619497	−	0.784999i	$-0.712663\pi$
$439$	−13.4758	+	4.49890i	−0.643167	+	0.214721i	−0.0236700	+	0.999720i	$0.507535\pi$
$440$	−0.0139987	−	0.173405i	−0.000667361	−	0.00826675i
$441$	43.6268	−	10.7530i	2.07747	−	0.512050i
$442$	−29.9171	−	40.6846i	−1.42301	−	1.93517i
$443$	−18.8633	−	4.64938i	−0.896222	−	0.220899i	−0.235807	−	0.971800i	$-0.575773\pi$
$443$	−18.8633	−	4.64938i	−0.896222	−	0.220899i	−0.660415	+	0.750901i	$0.729619\pi$
$444$	−3.32307	+	20.4477i	−0.157706	+	0.970404i
$445$	−6.69018	−	8.19399i	−0.317145	−	0.388432i
$446$	26.8995	−	20.2136i	1.27373	−	0.957144i
$447$	−32.1128	+	36.2478i	−1.51888	+	1.71446i
$448$	5.30761	+	32.6590i	0.250761	+	1.54299i
$449$	2.30623	−	28.5678i	0.108838	−	1.34820i	−0.679827	−	0.733372i	$-0.737945\pi$
$449$	2.30623	−	28.5678i	0.108838	−	1.34820i	0.788665	−	0.614823i	$-0.210773\pi$
$450$	5.59494	+	22.6996i	0.263748	+	1.07007i
$451$	−7.32675	−	25.2949i	−0.345003	−	1.19109i
$452$	3.37004	+	16.5076i	0.158513	+	0.776450i
$453$	−4.58076	+	3.74007i	−0.215223	+	0.175724i
$454$	1.00922	−	8.31171i	0.0473653	−	0.390088i
$455$	−21.6273	+	6.97167i	−1.01390	+	0.326837i
$456$	0.0142246	+	0.117150i	0.000666129	+	0.00548606i
$457$	23.8794	+	22.9365i	1.11703	+	1.07292i	0.996780	+	0.0801796i	$0.0255494\pi$
$457$	23.8794	+	22.9365i	1.11703	+	1.07292i	0.120251	+	0.992744i	$0.461630\pi$
$458$	5.06706	−	5.27537i	0.236768	−	0.246502i
$459$	10.5079	−	22.1450i	0.490469	−	1.03364i
$460$	3.89709	−	2.68997i	0.181703	−	0.125420i
$461$	−18.1033	+	28.6280i	−0.843153	+	1.33334i	0.0979394	+	0.995192i	$0.468775\pi$
$461$	−18.1033	+	28.6280i	−0.843153	+	1.33334i	−0.941093	+	0.338148i	$0.890199\pi$
$462$	76.2495	+	101.470i	3.54745	+	4.72079i
$463$	12.5829	+	23.9748i	0.584779	+	1.11420i	0.980627	+	0.195887i	$0.0627585\pi$
$463$	12.5829	+	23.9748i	0.584779	+	1.11420i	−0.395848	+	0.918316i	$0.629549\pi$
$464$	3.59014	−	17.5857i	0.166668	−	0.816395i
$465$	16.4957	−	1.33167i	0.764968	−	0.0617546i
$466$	22.9086	+	6.63557i	1.06122	+	0.307387i
$467$	−19.4378	−	10.2018i	−0.899476	−	0.472082i	−0.0494229	−	0.998778i	$-0.515738\pi$
$467$	−19.4378	−	10.2018i	−0.899476	−	0.472082i	−0.850054	+	0.526696i	$0.823431\pi$
$468$	−11.2229	+	28.6908i	−0.518778	+	1.32623i
$469$	14.1575	−	7.43044i	0.653734	−	0.343106i
$470$	−23.1915	+	4.73458i	−1.06974	+	0.218390i
$471$	26.0380	+	19.5663i	1.19977	+	0.901565i
$472$	0.00244537	+	0.0606812i	0.000112557	+	0.00279308i
$473$	−16.4738	+	6.24770i	−0.757468	+	0.287270i
$474$	−54.1571	+	15.6868i	−2.48752	+	0.720518i
$475$	5.69519	+	1.16268i	0.261313	+	0.0533475i
$476$	−38.6637	−	43.6422i	−1.77215	−	2.00034i
$477$	21.0177	−	25.7420i	0.962336	−	1.17865i
$478$	1.25231	−	31.0757i	0.0572792	−	1.42137i
$479$	−3.45774	−	10.3572i	−0.157988	−	0.473232i	0.839556	−	0.543273i	$-0.182815\pi$
$479$	−3.45774	−	10.3572i	−0.157988	−	0.473232i	−0.997544	+	0.0700410i	$0.977687\pi$
$480$	24.3582	−	21.5795i	1.11179	−	0.984963i
$481$	−6.33121	−	12.3734i	−0.288678	−	0.564180i
$482$	11.1693	+	9.89511i	0.508746	+	0.450710i
$483$	6.98106	−	16.3852i	0.317649	−	0.745550i
$484$	−20.5927	+	35.6675i	−0.936030	+	1.62125i
$485$	−7.03260	−	12.1808i	−0.319334	−	0.553102i
$486$	39.2268	−	4.76299i	1.77936	−	0.216054i
$487$	−36.3107	−	17.2297i	−1.64540	−	0.780750i	−0.999855	−	0.0170241i	$-0.994581\pi$
$487$	−36.3107	−	17.2297i	−1.64540	−	0.780750i	−0.645541	−	0.763726i	$-0.723368\pi$
$488$	−0.0472392	+	0.0272735i	−0.00213842	+	0.00123462i
$489$	−15.3928	−	10.6249i	−0.696087	−	0.480474i
$490$	−28.9970	+	12.3545i	−1.30995	+	0.558119i
$491$	−7.26513	−	1.18070i	−0.327871	−	0.0532842i	−0.00575195	−	0.999983i	$-0.501831\pi$
$491$	−7.26513	−	1.18070i	−0.327871	−	0.0532842i	−0.322119	+	0.946699i	$0.604395\pi$
$492$	15.1002	−	20.0947i	0.680769	−	0.905939i
$493$	11.1007	+	29.2701i	0.499949	+	1.31826i
$494$	10.5239	+	11.1866i	0.473494	+	0.503310i
$495$	12.9298	−	34.0931i	0.581151	−	1.53237i
$496$	8.73061	+	13.8064i	0.392016	+	0.619924i
$497$	0.698296	+	0.297516i	0.0313229	+	0.0133454i
$498$	−26.1593	−	16.5421i	−1.17222	−	0.741270i
$499$	17.4844	+	2.12299i	0.782709	+	0.0950381i	0.502129	−	0.864793i	$-0.332550\pi$
$499$	17.4844	+	2.12299i	0.782709	+	0.0950381i	0.280580	+	0.959831i	$0.409473\pi$
$500$	−9.08682	−	21.3275i	−0.406375	−	0.953797i
$501$	−8.02760	+	24.0456i	−0.358647	+	1.07428i
$502$	1.28726	+	0.488192i	0.0574531	+	0.0217891i
$503$	12.1173	+	0.978209i	0.540284	+	0.0436162i	0.347597	−	0.937644i	$-0.386998\pi$
$503$	12.1173	+	0.978209i	0.540284	+	0.0436162i	0.192687	+	0.981260i	$0.438280\pi$
$504$	0.102295	−	0.353164i	0.00455659	−	0.0157312i
$505$	11.3881	+	0.458926i	0.506766	+	0.0204220i
$506$	17.7465			0.788926
$507$	−9.06640	−	33.9195i	−0.402653	−	1.50642i
$508$	25.2133			1.11866
$509$	−39.7729	−	1.60279i	−1.76290	−	0.0710426i	−0.862489	−	0.506076i	$-0.831096\pi$
$509$	−39.7729	−	1.60279i	−1.76290	−	0.0710426i	−0.900414	+	0.435033i	$0.856737\pi$
$510$	−15.8720	+	54.7965i	−0.702824	+	2.42643i
$511$	−28.5141	−	2.30190i	−1.26139	−	0.101830i
$512$	29.8798	+	11.3319i	1.32051	+	0.500804i
$513$	−2.36070	+	7.07116i	−0.104228	+	0.312200i
$514$	9.41518	+	22.0982i	0.415286	+	0.974712i
$515$	14.9306	+	1.81290i	0.657921	+	0.0798861i
$516$	−14.2134	−	8.98799i	−0.625709	−	0.395674i
$517$	−40.6995	−	17.3404i	−1.78996	−	0.762631i
$518$	−17.1978	−	27.1961i	−0.755626	−	1.19493i
$519$	0.242755	−	0.640092i	0.0106558	−	0.0280969i
$520$	−0.0234162	+	0.108921i	−0.00102687	+	0.00477649i
$521$	−8.99446	−	23.7164i	−0.394055	−	1.03904i	−0.974431	−	0.224688i	$-0.927864\pi$
$521$	−8.99446	−	23.7164i	−0.394055	−	1.03904i	0.580376	−	0.814348i	$-0.302905\pi$
$522$	23.0042	−	30.6131i	1.00687	−	1.33990i
$523$	−0.834172	−	0.135566i	−0.0364758	−	0.00592790i	0.142146	−	0.989846i	$-0.454600\pi$
$523$	−0.834172	−	0.135566i	−0.0364758	−	0.00592790i	−0.178622	+	0.983918i	$0.557164\pi$
$524$	−5.00022	+	2.13039i	−0.218436	+	0.0930667i
$525$	−25.3167	−	17.4749i	−1.10491	−	0.762665i
$526$	−9.79201	+	5.65342i	−0.426952	+	0.246501i
$527$	−25.7400	−	12.2138i	−1.12125	−	0.532040i
$528$	60.6883	−	7.36890i	2.64112	−	0.320690i
$529$	10.2549	+	17.7620i	0.445865	+	0.772261i
$530$	−11.6560	+	20.1887i	−0.506303	+	0.876942i
$531$	−4.98920	+	11.7101i	−0.216513	+	0.508174i
$532$	13.2731	+	11.7589i	0.575462	+	0.509814i
$533$	−0.174988	+	16.8637i	−0.00757958	+	0.730450i
$534$	28.3232	−	25.0922i	1.22567	−	1.08585i
$535$	2.44663	+	7.32856i	0.105777	+	0.316841i
$536$	0.00315654	−	0.0783287i	0.000136342	−	0.00338328i
$537$	21.9422	−	26.8743i	0.946874	−	1.15971i
$538$	41.8995	+	47.2948i	1.80642	+	2.03902i
$539$	−57.7196	−	11.7835i	−2.48616	−	0.507553i
$540$	10.0753	−	2.91836i	0.433573	−	0.125586i
$541$	−18.9242	+	7.17698i	−0.813613	+	0.308563i	−0.726090	−	0.687600i	$-0.758664\pi$
$541$	−18.9242	+	7.17698i	−0.813613	+	0.308563i	−0.0875230	+	0.996162i	$0.527895\pi$
$542$	0.959384	+	23.8069i	0.0412091	+	1.02259i
$543$	−37.4696	−	28.1566i	−1.60797	−	1.20831i
$544$	−54.8913	+	11.2061i	−2.35344	+	0.480459i
$545$	2.22997	−	1.17038i	0.0955216	−	0.0501336i
$546$	−28.0332	−	76.2957i	−1.19971	−	3.26516i
$547$	8.94300	+	4.69365i	0.382375	+	0.200686i	0.644948	−	0.764226i	$-0.276879\pi$
$547$	8.94300	+	4.69365i	0.382375	+	0.200686i	−0.262573	+	0.964912i	$0.584571\pi$
$548$	17.1731	+	4.97425i	0.733598	+	0.212489i
$549$	−11.3956	+	0.919946i	−0.486351	+	0.0392623i
$550$	6.13113	−	30.0323i	0.261432	−	1.28058i
$551$	−4.42450	−	8.43018i	−0.188490	−	0.359138i
$552$	−0.0524582	−	0.0698092i	−0.00223277	−	0.00297128i
$553$	23.3437	−	36.9150i	0.992673	−	1.56979i
$554$	−33.8077	+	23.3358i	−1.43635	+	0.991443i
$555$	−6.73113	+	14.1856i	−0.285720	+	0.602143i
$556$	−11.9047	+	12.3941i	−0.504872	+	0.525628i
$557$	10.5868	+	10.1687i	0.448576	+	0.430863i	0.882662	−	0.470009i	$-0.155749\pi$
$557$	10.5868	+	10.1687i	0.448576	+	0.430863i	−0.434086	+	0.900871i	$0.642929\pi$
$558$	4.20085	+	34.5971i	0.177836	+	1.46461i
$559$	11.2553	−	0.791165i	0.476047	−	0.0334627i
$560$	−3.05413	+	25.1530i	−0.129060	+	1.06291i
$561$	−82.5928	+	67.4349i	−3.48707	+	2.84711i
$562$	9.49613	+	46.5151i	0.400570	+	1.96212i
$563$	0.216310	+	0.746788i	0.00911637	+	0.0314734i	0.964947	−	0.262443i	$-0.0845283\pi$
$563$	0.216310	+	0.746788i	0.00911637	+	0.0314734i	−0.955831	+	0.293917i	$0.905041\pi$
$564$	−10.1053	−	40.9988i	−0.425509	−	1.72636i
$565$	−1.02755	+	12.7285i	−0.0432293	+	0.535491i
$566$	−4.72244	−	29.0584i	−0.198499	−	1.22141i
$567$	−9.53809	+	10.7663i	−0.400562	+	0.452141i
$568$	0.00297510	−	0.00223564i	0.000124832	−	9.38055e-5i
$569$	−0.582071	−	0.712908i	−0.0244017	−	0.0298866i	0.762260	−	0.647271i	$-0.224090\pi$
$569$	−0.582071	−	0.712908i	−0.0244017	−	0.0298866i	−0.786662	+	0.617384i	$0.788192\pi$
$570$	2.78322	−	17.1258i	0.116576	−	0.717322i
$571$	17.1250	+	4.22093i	0.716658	+	0.176640i	0.580751	−	0.814081i	$-0.302759\pi$
$571$	17.1250	+	4.22093i	0.716658	+	0.176640i	0.135907	+	0.990722i	$0.456605\pi$
$572$	29.4192	−	27.6764i	1.23008	−	1.15721i
$573$	46.9322	−	11.5677i	1.96062	−	0.483250i
$574$	3.14164	+	38.9162i	0.131130	+	1.62433i
$575$	−4.07974	+	1.36202i	−0.170137	+	0.0568001i
$576$	23.5533	+	24.5216i	0.981389	+	1.02173i
$577$		−	28.6096i		−	1.19103i	−0.803342	−	0.595517i	$-0.796947\pi$
$577$		−	28.6096i		−	1.19103i	0.803342	−	0.595517i	$-0.203053\pi$
$578$	46.3423	−	44.5123i	1.92758	−	1.85147i
$579$	39.9900	+	32.6508i	1.66193	+	1.35692i
$580$	−6.22560	+	11.8619i	−0.258504	+	0.492538i
$581$	23.6652	−	3.84597i	0.981797	−	0.159558i
$582$	42.5236	−	26.8903i	1.76266	−	1.11464i
$583$	−39.3638	+	18.6784i	−1.63028	+	0.773579i
$584$	−0.0796748	+	0.115429i	−0.00329697	+	0.00477648i
$585$	−14.2206	+	18.5209i	−0.587950	+	0.765744i
$586$	14.0952	+	20.4204i	0.582267	+	0.843560i
$587$	23.4935	+	13.5640i	0.969682	+	0.559846i	0.899139	−	0.437662i	$-0.144194\pi$
$587$	23.4935	+	13.5640i	0.969682	+	0.559846i	0.0705428	+	0.997509i	$0.477527\pi$
$588$	−24.1048	−	50.7997i	−0.994064	−	2.09495i
$589$	8.21907	+	2.74393i	0.338661	+	0.113062i
$590$	2.13682	−	8.66942i	0.0879715	−	0.356914i
$591$	64.7293	−	2.60850i	2.66261	−	0.107299i
$592$	−15.4858	+	0.624057i	−0.636463	+	0.0256486i
$593$	6.81419	−	27.6463i	0.279825	−	1.13530i	−0.647808	−	0.761804i	$-0.724314\pi$
$593$	6.81419	−	27.6463i	0.279825	−	1.13530i	0.927633	−	0.373492i	$-0.121840\pi$
$594$	37.2881	+	12.4486i	1.52995	+	0.510773i
$595$	−18.9449	−	39.9255i	−0.776665	−	1.63679i
$596$	30.8973	+	17.8385i	1.26560	+	0.730695i
$597$	21.7388	+	31.4940i	0.889708	+	1.28897i
$598$	−10.8827	−	3.27498i	−0.445027	−	0.133924i
$599$	12.1147	−	17.5511i	0.494992	−	0.717120i	−0.493272	−	0.869875i	$-0.664199\pi$
$599$	12.1147	−	17.5511i	0.494992	−	0.717120i	0.988264	+	0.152755i	$0.0488147\pi$
$600$	−0.136261	+	0.0646568i	−0.00556285	+	0.00263960i
$601$	−34.7696	+	21.9870i	−1.41828	+	0.896868i	−0.999935	−	0.0114183i	$-0.996365\pi$
$601$	−34.7696	+	21.9870i	−1.41828	+	0.896868i	−0.418349	+	0.908286i	$0.637391\pi$
$602$	25.7827	−	4.19010i	1.05083	−	0.170776i
$603$	7.63559	−	14.5484i	0.310945	−	0.592457i
$604$	3.37476	+	2.75540i	0.137317	+	0.112116i
$605$	−22.5132	+	21.6242i	−0.915291	+	0.879149i
$606$			40.7695i			1.65615i
$607$	2.11058	+	2.19735i	0.0856659	+	0.0891876i	0.762655	−	0.646805i	$-0.223895\pi$
$607$	2.11058	+	2.19735i	0.0856659	+	0.0891876i	−0.676990	+	0.735993i	$0.736716\pi$
$608$	16.1618	−	5.39559i	0.655446	−	0.218820i
$609$	4.05439	+	50.2227i	0.164292	+	2.03513i
$610$	7.78673	−	1.91926i	0.315276	−	0.0777085i
$611$	21.7582	+	18.1445i	0.880242	+	0.734048i
$612$	−58.1742	−	14.3387i	−2.35155	−	0.579606i
$613$	2.22353	−	13.6819i	0.0898074	−	0.552607i	−0.902685	−	0.430302i	$-0.858407\pi$
$613$	2.22353	−	13.6819i	0.0898074	−	0.552607i	0.992493	−	0.122305i	$-0.0390288\pi$
$614$	−37.7081	−	46.1840i	−1.52177	−	1.86384i
$615$	15.2307	−	11.4451i	0.614159	−	0.461511i
$616$	−0.319665	+	0.360827i	−0.0128797	+	0.0145381i
$617$	−3.72393	−	22.9143i	−0.149920	−	0.922494i	−0.947611	−	0.319427i	$-0.896509\pi$
$617$	−3.72393	−	22.9143i	−0.149920	−	0.922494i	0.797691	−	0.603067i	$-0.206055\pi$
$618$	−4.32913	+	53.6259i	−0.174143	+	2.15715i
$619$	−5.41183	−	21.9566i	−0.217520	−	0.882512i	−0.973642	−	0.228082i	$-0.926755\pi$
$619$	−5.41183	−	21.9566i	−0.217520	−	0.882512i	0.756122	−	0.654430i	$-0.227091\pi$
$620$	−3.39211	−	11.7109i	−0.136230	−	0.470322i
$621$	−1.10338	−	5.40473i	−0.0442773	−	0.216884i
$622$	24.3000	−	19.8403i	0.974341	−	0.795525i
$623$	−3.53316	+	29.0982i	−0.141553	+	1.16579i
$624$	−38.5759	−	6.68075i	−1.54427	−	0.267444i
$625$	−0.475298	−	3.91443i	−0.0190119	−	0.156577i
$626$	0.525519	+	0.504768i	0.0210040	+	0.0201746i
$627$	22.4640	−	23.3875i	0.897126	−	0.934008i
$628$	10.2866	−	21.6785i	0.410479	−	0.865066i
$629$	22.2462	−	15.3555i	0.887016	−	0.612263i
$630$	−28.8922	+	45.6894i	−1.15109	+	1.82031i
$631$	−22.9172	−	30.4972i	−0.912318	−	1.21407i	−0.976365	−	0.216128i	$-0.930657\pi$
$631$	−22.9172	−	30.4972i	−0.912318	−	1.21407i	0.0640471	−	0.997947i	$-0.479599\pi$
$632$	−0.0995167	−	0.189613i	−0.00395856	−	0.00754241i
$633$	13.8469	−	67.8264i	0.550363	−	2.69586i
$634$	−29.3578	+	2.37000i	−1.16595	+	0.0941249i
$635$	18.3558	+	5.31681i	0.728426	+	0.210991i
$636$	−36.8236	−	19.3265i	−1.46015	−	0.766347i
$637$	33.2210	+	17.8778i	1.31626	+	0.708344i
$638$	−44.4546	+	23.3316i	−1.75997	+	0.923706i
$639$	0.764228	−	0.156018i	0.0302324	−	0.00617199i
$640$	0.197616	+	0.148499i	0.00781145	+	0.00586993i
$641$	−1.37995	−	34.2432i	−0.0545049	−	1.35253i	−0.762812	−	0.646621i	$-0.776182\pi$
$641$	−1.37995	−	34.2432i	−0.0545049	−	1.35253i	0.708307	−	0.705905i	$-0.249459\pi$
$642$	−25.8412	+	9.80029i	−1.01987	+	0.386787i
$643$	20.4143	−	5.91307i	0.805061	−	0.233189i	0.149922	−	0.988698i	$-0.452098\pi$
$643$	20.4143	−	5.91307i	0.805061	−	0.233189i	0.655138	+	0.755509i	$0.272610\pi$
$644$	−12.8562	−	2.62460i	−0.506604	−	0.103424i
$645$	−8.45228	−	9.54065i	−0.332808	−	0.375663i
$646$	−18.8912	+	23.1375i	−0.743262	+	0.910331i
$647$	0.147247	−	3.65391i	0.00578889	−	0.143650i	−0.993710	−	0.111987i	$-0.964279\pi$
$647$	0.147247	−	3.65391i	0.00578889	−	0.143650i	0.999499	−	0.0316632i	$-0.0100804\pi$
$648$	0.0223318	+	0.0668920i	0.000877277	+	0.00262777i
$649$	12.4914	−	11.0664i	0.490329	−	0.434393i
$650$	−9.30205	+	17.2853i	−0.364856	+	0.677985i
$651$	−34.3247	−	30.4091i	−1.34529	−	1.19183i
$652$	−5.40109	+	12.6768i	−0.211523	+	0.496462i
$653$	18.9152	−	32.7622i	0.740211	−	1.28208i	−0.212188	−	0.977229i	$-0.568059\pi$
$653$	18.9152	−	32.7622i	0.740211	−	1.28208i	0.952399	−	0.304854i	$-0.0986076\pi$
$654$	4.50435	+	7.80177i	0.176134	+	0.305073i
$655$	−4.08950	+	0.496555i	−0.159790	+	0.0194020i
$656$	16.9895	+	8.06161i	0.663328	+	0.314753i
$657$	−25.4583	+	14.6983i	−0.993222	+	0.573437i
$658$	53.9779	+	37.2583i	2.10428	+	1.45248i
$659$	14.3482	−	6.11321i	0.558928	−	0.238137i	−0.0939804	−	0.995574i	$-0.529959\pi$
$659$	14.3482	−	6.11321i	0.558928	−	0.238137i	0.652908	+	0.757437i	$0.273549\pi$
$660$	−45.0384	−	7.31946i	−1.75312	−	0.284909i
$661$	22.7924	−	30.3311i	0.886520	−	1.17974i	−0.0963319	−	0.995349i	$-0.530711\pi$
$661$	22.7924	−	30.3311i	0.886520	−	1.17974i	0.982852	−	0.184395i	$-0.0590326\pi$
$662$	−1.41317	−	3.72623i	−0.0549246	−	0.144824i
$663$	63.0932	−	26.1114i	2.45034	−	1.01408i
$664$	0.0416839	−	0.109911i	0.00161765	−	0.00426539i
$665$	7.18342	+	11.3597i	0.278561	+	0.440509i
$666$	−30.4199	−	12.9607i	−1.17875	−	0.502218i
$667$	5.95426	+	3.76525i	0.230550	+	0.145791i
$668$	18.5400	+	2.25116i	0.717333	+	0.0870999i
$669$	17.8330	+	41.8556i	0.689464	+	1.61823i
$670$	−3.64979	+	10.9325i	−0.141004	+	0.422358i
$671$	14.0151	+	5.31523i	0.541047	+	0.205192i
$672$	−89.8804	−	7.25590i	−3.46721	−	0.279902i
$673$	−12.0086	+	41.4586i	−0.462899	+	1.59811i	0.301565	+	0.953446i	$0.402491\pi$
$673$	−12.0086	+	41.4586i	−0.462899	+	1.59811i	−0.764464	+	0.644667i	$0.776996\pi$
$674$	22.8404	+	0.920438i	0.879781	+	0.0354540i
$675$	−9.52761			−0.366718
$676$	−23.1483	+	11.5430i	−0.890319	+	0.443960i
$677$	−18.7128			−0.719191			−0.359595	−	0.933108i	$-0.617085\pi$
$677$	−18.7128			−0.719191			−0.359595	+	0.933108i	$0.617085\pi$
$678$	−45.6419	−	1.83931i	−1.75287	−	0.0706382i
$679$	−10.8432	+	37.4352i	−0.416125	+	1.43663i
$680$	−0.215968	−	0.0174347i	−0.00828198	−	0.000668590i
$681$	10.5854	+	4.01451i	0.405633	+	0.153836i
$682$	14.4695	−	43.3413i	0.554064	−	1.65963i
$683$	11.1375	+	26.1407i	0.426166	+	1.00025i	0.985248	+	0.171135i	$0.0547434\pi$
$683$	11.1375	+	26.1407i	0.426166	+	1.00025i	−0.559082	+	0.829112i	$0.688846\pi$
$684$	18.0894	+	2.19645i	0.691665	+	0.0839834i
$685$	11.4534	+	7.24269i	0.437612	+	0.276729i
$686$	26.5953	+	11.3312i	1.01541	+	0.432627i
$687$	5.28609	+	8.35928i	0.201677	+	0.318926i
$688$	4.46138	−	11.7637i	0.170089	−	0.448487i
$689$	27.5861	−	4.18987i	1.05095	−	0.159621i
$690$	4.55261	+	12.0042i	0.173315	+	0.456994i
$691$	−27.1424	+	36.1200i	−1.03254	+	1.37407i	−0.107502	+	0.994205i	$0.534285\pi$
$691$	−27.1424	+	36.1200i	−1.03254	+	1.37407i	−0.925043	+	0.379863i	$0.875971\pi$
$692$	−0.497815	−	0.0809028i	−0.0189241	−	0.00307546i
$693$	−92.9510	+	39.6027i	−3.53092	+	1.50438i
$694$	−40.3584	−	27.8574i	−1.53198	−	1.05745i
$695$	−11.2804	+	6.51277i	−0.427892	+	0.247043i
$696$	0.223186	+	0.105903i	0.00845986	+	0.00401425i
$697$	−32.5594	+	3.95343i	−1.23328	+	0.149747i
$698$	−22.0396	−	38.1738i	−0.834212	−	1.44490i
$699$	−16.1244	+	27.9282i	−0.609880	+	1.05634i
$700$	−8.88321	+	20.8497i	−0.335754	+	0.788043i
$701$	−0.0187671	−	0.0166262i	−0.000708823	−	0.000627962i	0.662768	−	0.748825i	$-0.269381\pi$
$701$	−0.0187671	−	0.0166262i	−0.000708823	−	0.000627962i	−0.663477	+	0.748197i	$0.730920\pi$
$702$	−20.5690	−	14.5152i	−0.776327	−	0.547839i
$703$	−6.15359	+	5.45160i	−0.232087	+	0.205611i
$704$	−14.1165	−	42.2840i	−0.532035	−	1.59364i
$705$	1.28870	−	31.9788i	0.0485353	−	1.20439i
$706$	−23.8479	+	29.2083i	−0.897526	+	1.09927i
$707$	−20.9425	−	23.6392i	−0.787623	−	0.889043i
$708$	15.6067	+	3.18614i	0.586537	+	0.119742i
$709$	7.34085	−	2.12630i	0.275691	−	0.0798550i	−0.137492	−	0.990503i	$-0.543904\pi$
$709$	7.34085	−	2.12630i	0.275691	−	0.0798550i	0.413183	+	0.910648i	$0.364417\pi$
$710$	−0.511592	+	0.194021i	−0.0191997	+	0.00728149i
$711$	−1.80724	−	44.8461i	−0.0677766	−	1.68186i
$712$	0.114891	+	0.0863346i	0.00430570	+	0.00323553i
$713$	−6.28211	+	1.28250i	−0.235267	+	0.0480301i
$714$	139.973	−	73.4633i	5.23834	−	2.74929i
$715$	27.2540	−	13.9452i	1.01924	−	0.521522i
$716$	−22.6323	−	11.8784i	−0.845809	−	0.443915i
$717$	40.3922	+	11.6997i	1.50847	+	0.436935i
$718$	−15.5399	+	1.25451i	−0.579942	+	0.0468178i
$719$	8.08174	−	39.5870i	0.301398	−	1.47635i	−0.493576	−	0.869703i	$-0.664310\pi$
$719$	8.08174	−	39.5870i	0.301398	−	1.47635i	0.794974	−	0.606643i	$-0.207484\pi$
$720$	12.1001	+	23.0549i	0.450945	+	0.859204i
$721$	−25.0365	−	33.3175i	−0.932406	−	1.24081i
$722$	−15.4283	+	24.3979i	−0.574182	+	0.907996i
$723$	−16.6049	+	11.4616i	−0.617544	+	0.426260i
$724$	−14.8028	+	31.1962i	−0.550141	+	1.15940i
$725$	8.42902	−	8.77554i	0.313046	−	0.325915i
$726$	−80.5316	−	77.3517i	−2.98881	−	2.87079i
$727$	−3.13307	−	25.8031i	−0.116199	−	0.956985i	−0.927879	−	0.372882i	$-0.878370\pi$
$727$	−3.13307	−	25.8031i	−0.116199	−	0.956985i	0.811680	−	0.584103i	$-0.198554\pi$
$728$	0.262617	−	0.162279i	0.00973322	−	0.00601445i
$729$	−5.19555	+	42.7892i	−0.192428	+	1.58479i
$730$	15.9733	−	13.0418i	0.591197	−	0.482698i
$731$	4.38924	+	21.4999i	0.162342	+	0.795203i
$732$	3.98041	+	13.7420i	0.147120	+	0.507918i
$733$	3.87323	+	15.7143i	0.143061	+	0.580422i	0.998086	+	0.0618355i	$0.0196954\pi$
$733$	3.87323	+	15.7143i	0.143061	+	0.580422i	−0.855025	+	0.518586i	$0.826458\pi$
$734$	1.02878	−	12.7437i	0.0379730	−	0.470380i
$735$	−6.83643	−	42.0662i	−0.252166	−	1.55164i
$736$	−8.36051	+	9.43706i	−0.308172	+	0.347855i
$737$	−17.2213	+	12.9410i	−0.634355	+	0.476687i
$738$	25.3742	+	31.0777i	0.934037	+	1.14399i
$739$	4.87315	−	29.9857i	0.179262	−	1.10304i	−0.728961	−	0.684555i	$-0.759996\pi$
$739$	4.87315	−	29.9857i	0.179262	−	1.10304i	0.908223	−	0.418487i	$-0.137440\pi$
$740$	11.2316	+	2.76833i	0.412881	+	0.101766i
$741$	−18.0917	+	10.1964i	−0.664614	+	0.374575i
$742$	62.7192	−	15.4589i	2.30249	−	0.567514i
$743$	0.174255	+	2.15853i	0.00639279	+	0.0791890i	0.999167	−	0.0408086i	$-0.0129934\pi$
$743$	0.174255	+	2.15853i	0.00639279	+	0.0791890i	−0.992774	+	0.119998i	$0.961711\pi$
$744$	−0.213263	+	0.0711977i	−0.00781861	+	0.00261023i
$745$	18.7321	+	19.5022i	0.686292	+	0.714506i
$746$			23.6469i			0.865774i
$747$	17.7687	−	17.0671i	0.650123	−	0.624452i
$748$	60.8482	+	49.6810i	2.22483	+	1.81652i
$749$	9.94919	−	18.9566i	0.363536	−	0.692659i
$750$	62.0396	−	10.0824i	2.26537	−	0.368158i
$751$	−20.1482	+	12.7409i	−0.735218	+	0.464924i	−0.848873	−	0.528597i	$-0.822718\pi$
$751$	−20.1482	+	12.7409i	−0.735218	+	0.464924i	0.113655	+	0.993520i	$0.463744\pi$
$752$	28.5406	−	13.5427i	1.04077	−	0.493852i
$753$	−1.05746	+	1.53199i	−0.0385359	+	0.0558289i
$754$	31.5667	−	6.10390i	1.14959	−	0.222291i
$755$	1.87585	+	2.71763i	0.0682691	+	0.0989048i
$756$	−25.1718	−	14.5329i	−0.915488	−	0.528557i
$757$	−0.938828	−	1.97854i	−0.0341223	−	0.0719112i	0.885674	−	0.464309i	$-0.153697\pi$
$757$	−0.938828	−	1.97854i	−0.0341223	−	0.0719112i	−0.919796	+	0.392397i	$0.871646\pi$
$758$	−27.9204	−	9.32118i	−1.01411	−	0.338561i
$759$	−5.74251	+	23.2983i	−0.208440	+	0.845674i
$760$	0.0658433	−	0.00265340i	0.00238839	−	9.62488e-5i
$761$	−17.7931	+	0.717037i	−0.644999	+	0.0259926i	−0.360610	−	0.932717i	$-0.617432\pi$
$761$	−17.7931	+	0.717037i	−0.644999	+	0.0259926i	−0.284388	+	0.958709i	$0.591791\pi$
$762$	−16.3594	+	66.3727i	−0.592639	+	2.40443i
$763$	−6.61936	−	2.20987i	−0.239637	−	0.0800025i
$764$	−15.2661	−	32.1727i	−0.552309	−	1.16397i
$765$	−39.3283	−	22.7062i	−1.42192	−	0.820944i
$766$	−1.33495	−	1.93401i	−0.0482336	−	0.0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.99581 + 0.0804286i) q^{2} +(-0.751408 + 2.59416i) q^{3} +(1.98329 + 0.160108i) q^{4} +(1.41011 + 0.534785i) q^{5} +(-1.70832 + 5.11703i) q^{6} +(-1.63799 - 3.84451i) q^{7} +(-0.0203394 - 0.00246965i) q^{8} +(-3.62949 - 2.29515i) q^{9} +O(q^{10})\)	\(q+(1.99581 + 0.0804286i) q^{2} +(-0.751408 + 2.59416i) q^{3} +(1.98329 + 0.160108i) q^{4} +(1.41011 + 0.534785i) q^{5} +(-1.70832 + 5.11703i) q^{6} +(-1.63799 - 3.84451i) q^{7} +(-0.0203394 - 0.00246965i) q^{8} +(-3.62949 - 2.29515i) q^{9} +(2.77131 + 1.18074i) q^{10} +(3.00913 + 4.75856i) q^{11} +(-1.90561 + 5.02467i) q^{12} +(-0.967139 - 3.47342i) q^{13} +(-2.95992 - 7.80467i) q^{14} +(-2.44689 + 3.25621i) q^{15} +(-3.96835 - 0.644919i) q^{16} +(6.45100 - 2.74851i) q^{17} +(-7.05919 - 4.87261i) q^{18} +(-1.84691 + 1.06631i) q^{19} +(2.71104 + 1.28640i) q^{20} +(11.2041 - 1.36042i) q^{21} +(5.62295 + 9.73923i) q^{22} +(0.789020 - 1.36662i) q^{23} +(0.0216898 - 0.0509079i) q^{24} +(-2.04014 - 1.80740i) q^{25} +(-1.65087 - 7.01008i) q^{26} +(2.61650 - 2.31802i) q^{27} +(-2.63308 - 7.88704i) q^{28} +(-0.179760 + 4.46070i) q^{29} +(-5.14542 + 6.30200i) q^{30} +(-2.69431 - 3.04125i) q^{31} +(-7.82806 - 1.59811i) q^{32} +(-14.6056 + 4.23056i) q^{33} +(13.0961 - 4.96668i) q^{34} +(-0.253767 - 6.29716i) q^{35} +(-6.83086 - 5.13306i) q^{36} +(3.77702 - 0.771085i) q^{37} +(-3.77184 + 1.97962i) q^{38} +(9.73733 + 0.101040i) q^{39} +(-0.0273601 - 0.0143597i) q^{40} +(-4.49274 - 1.30134i) q^{41} +(22.4707 - 1.81402i) q^{42} +(-0.625951 + 3.06611i) q^{43} +(5.20610 + 9.91940i) q^{44} +(-3.89057 - 5.17741i) q^{45} +(1.68465 - 2.66406i) q^{46} +(-6.46667 + 4.46362i) q^{47} +(4.65487 - 9.80994i) q^{48} +(-7.24819 + 7.54616i) q^{49} +(-3.92636 - 3.77132i) q^{50} +(2.28276 + 18.8002i) q^{51} +(-1.36200 - 7.04365i) q^{52} +(-0.932805 + 7.68234i) q^{53} +(5.40848 - 4.41589i) q^{54} +(1.69841 + 8.31934i) q^{55} +(0.0238212 + 0.0822403i) q^{56} +(-1.37840 - 5.59241i) q^{57} +(-0.717536 + 8.88828i) q^{58} +(-0.475472 - 2.92570i) q^{59} +(-5.37423 + 6.06625i) q^{60} +(2.12835 - 1.59935i) q^{61} +(-5.13275 - 6.28647i) q^{62} +(-2.87865 + 17.7131i) q^{63} +(-7.68766 - 1.89484i) q^{64} +(0.493758 - 5.41512i) q^{65} +(-29.4903 + 7.26870i) q^{66} +(0.307874 + 3.81370i) q^{67} +(13.2343 - 4.41825i) q^{68} +(2.95236 + 3.07374i) q^{69} -12.5884i q^{70} +(-0.130995 + 0.125823i) q^{71} +(0.0681534 + 0.0556455i) q^{72} +(3.18128 - 6.06142i) q^{73} +(7.60025 - 1.23516i) q^{74} +(6.22167 - 3.93434i) q^{75} +(-3.83367 + 1.81910i) q^{76} +(13.3654 - 19.3631i) q^{77} +(19.4258 + 0.984817i) q^{78} +(5.93723 + 8.60156i) q^{79} +(-5.25092 - 3.03162i) q^{80} +(-1.47554 - 3.10963i) q^{81} +(-8.86200 - 2.95857i) q^{82} +(-1.37302 + 5.57058i) q^{83} +(22.4388 - 0.904252i) q^{84} +(10.5665 - 0.425815i) q^{85} +(-1.49588 + 6.06904i) q^{86} +(-11.4367 - 3.81814i) q^{87} +(-0.0494519 - 0.104218i) q^{88} +(-6.07451 - 3.50712i) q^{89} +(-7.34845 - 10.6461i) q^{90} +(-11.7694 + 9.40762i) q^{91} +(1.78366 - 2.58408i) q^{92} +(9.91403 - 4.70427i) q^{93} +(-13.2653 + 8.38844i) q^{94} +(-3.17459 + 0.515921i) q^{95} +(10.0278 - 19.1064i) q^{96} +(-7.22423 - 5.89840i) q^{97} +(-15.0730 + 14.4778i) q^{98} -24.1776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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