LMFDB - Embedded newform 196.2.p.a.103.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(3,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("196.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.p (of order $42$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$26$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.16
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.301195 - 1.38177i) q^{2} +(2.71624 + 1.85190i) q^{3} +(-1.81856 - 0.832362i) q^{4} +(1.96396 + 0.147178i) q^{5} +(3.37701 - 3.19543i) q^{6} +(-2.22818 - 1.42661i) q^{7} +(-1.69787 + 2.26213i) q^{8} +(2.85240 + 7.26780i) q^{9} +O(q^{10})$	\(q+(0.301195 - 1.38177i) q^{2} +(2.71624 + 1.85190i) q^{3} +(-1.81856 - 0.832362i) q^{4} +(1.96396 + 0.147178i) q^{5} +(3.37701 - 3.19543i) q^{6} +(-2.22818 - 1.42661i) q^{7} +(-1.69787 + 2.26213i) q^{8} +(2.85240 + 7.26780i) q^{9} +(0.794901 - 2.66941i) q^{10} +(-4.60391 - 1.80690i) q^{11} +(-3.39820 - 5.62870i) q^{12} +(0.963118 - 0.768061i) q^{13} +(-2.64236 + 2.64913i) q^{14} +(5.06202 + 4.03683i) q^{15} +(2.61435 + 3.02741i) q^{16} +(-0.724645 - 0.780981i) q^{17} +(10.9015 - 1.75233i) q^{18} +(0.263430 - 0.456275i) q^{19} +(-3.44908 - 1.90238i) q^{20} +(-3.41032 - 8.00139i) q^{21} +(-3.88339 + 5.81730i) q^{22} +(1.53746 - 1.65699i) q^{23} +(-8.80107 + 3.00019i) q^{24} +(-1.10868 - 0.167107i) q^{25} +(-0.771196 - 1.56214i) q^{26} +(-3.51684 + 15.4083i) q^{27} +(2.86462 + 4.44904i) q^{28} +(-0.514512 - 2.25422i) q^{29} +(7.10262 - 5.77867i) q^{30} +(-2.23709 - 3.87476i) q^{31} +(4.97060 - 2.70058i) q^{32} +(-9.15911 - 13.4340i) q^{33} +(-1.29739 + 0.766063i) q^{34} +(-4.16608 - 3.12975i) q^{35} +(0.862170 - 15.5912i) q^{36} +(0.148440 + 0.0457878i) q^{37} +(-0.551122 - 0.501427i) q^{38} +(4.03843 - 0.302639i) q^{39} +(-3.66749 + 4.19284i) q^{40} +(1.00896 + 2.09513i) q^{41} +(-12.0832 + 2.30229i) q^{42} +(-4.03392 + 8.37653i) q^{43} +(6.86850 + 7.11808i) q^{44} +(4.53233 + 14.6935i) q^{45} +(-1.82650 - 2.62350i) q^{46} +(9.44316 - 1.42333i) q^{47} +(1.49473 + 13.0647i) q^{48} +(2.92955 + 6.35750i) q^{49} +(-0.564831 + 1.48161i) q^{50} +(-0.522009 - 3.46330i) q^{51} +(-2.39080 + 0.595104i) q^{52} +(-2.10418 + 0.649054i) q^{53} +(20.2314 + 9.50035i) q^{54} +(-8.77595 - 4.22627i) q^{55} +(7.01035 - 2.61821i) q^{56} +(1.56052 - 0.751505i) q^{57} +(-3.26978 + 0.0319754i) q^{58} +(0.949824 + 12.6745i) q^{59} +(-5.84551 - 11.5547i) q^{60} +(-0.310936 + 1.00803i) q^{61} +(-6.02781 + 1.92408i) q^{62} +(4.01269 - 20.2632i) q^{63} +(-2.23445 - 7.68162i) q^{64} +(2.00457 - 1.36669i) q^{65} +(-21.3213 + 8.60953i) q^{66} +(-0.898095 + 0.518515i) q^{67} +(0.667753 + 2.02343i) q^{68} +(7.24471 - 1.65356i) q^{69} +(-5.57939 + 4.81389i) q^{70} +(11.2417 + 2.56583i) q^{71} +(-21.2837 - 5.88730i) q^{72} +(0.954106 - 6.33008i) q^{73} +(0.107978 - 0.191319i) q^{74} +(-2.70198 - 2.50707i) q^{75} +(-0.858851 + 0.610495i) q^{76} +(7.68057 + 10.5941i) q^{77} +(0.798179 - 5.67133i) q^{78} +(-7.88112 - 4.55017i) q^{79} +(4.68890 + 6.33048i) q^{80} +(-20.9173 + 19.4084i) q^{81} +(3.19887 - 0.763107i) q^{82} +(5.49592 - 6.89167i) q^{83} +(-0.458178 + 17.3897i) q^{84} +(-1.30823 - 1.64047i) q^{85} +(10.3594 + 8.09691i) q^{86} +(2.77706 - 7.07583i) q^{87} +(11.9043 - 7.34674i) q^{88} +(-8.70248 + 3.41547i) q^{89} +(21.6681 - 1.83704i) q^{90} +(-3.24172 + 0.337379i) q^{91} +(-4.17519 + 1.73362i) q^{92} +(1.09919 - 14.6676i) q^{93} +(0.877523 - 13.4769i) q^{94} +(0.584520 - 0.857334i) q^{95} +(18.5026 + 1.86964i) q^{96} -7.11086i q^{97} +(9.66695 - 2.13311i) q^{98} -38.6142i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	0.301195	−	1.38177i	0.212977	−	0.977057i
$2$	0.301195	−	1.38177i	0.212977	−	0.977057i
$3$	2.71624	+	1.85190i	1.56822	+	1.06920i	0.961691	+	0.274136i	$0.0883918\pi$
$3$	2.71624	+	1.85190i	1.56822	+	1.06920i	0.606531	+	0.795060i	$0.292561\pi$
$4$	−1.81856	−	0.832362i	−0.909282	−	0.416181i
$5$	1.96396	+	0.147178i	0.878309	+	0.0658202i	0.506248	−	0.862388i	$-0.331032\pi$
$5$	1.96396	+	0.147178i	0.878309	+	0.0658202i	0.372061	+	0.928208i	$0.378651\pi$
$6$	3.37701	−	3.19543i	1.37866	−	1.30453i
$7$	−2.22818	−	1.42661i	−0.842172	−	0.539209i
$7$	−2.22818	−	1.42661i	−0.842172	−	0.539209i
$8$	−1.69787	+	2.26213i	−0.600289	+	0.799783i
$9$	2.85240	+	7.26780i	0.950800	+	2.42260i
$10$	0.794901	−	2.66941i	0.251370	−	0.844140i
$11$	−4.60391	−	1.80690i	−1.38813	−	0.544801i	−0.450606	−	0.892723i	$-0.648792\pi$
$11$	−4.60391	−	1.80690i	−1.38813	−	0.544801i	−0.937523	+	0.347922i	$0.886887\pi$
$12$	−3.39820	−	5.62870i	−0.980976	−	1.62486i
$13$	0.963118	−	0.768061i	0.267121	−	0.213022i	−0.480764	−	0.876850i	$-0.659641\pi$
$13$	0.963118	−	0.768061i	0.267121	−	0.213022i	0.747885	+	0.663828i	$0.231069\pi$
$14$	−2.64236	+	2.64913i	−0.706201	+	0.708011i
$15$	5.06202	+	4.03683i	1.30701	+	1.04231i
$16$	2.61435	+	3.02741i	0.653586	+	0.756852i
$17$	−0.724645	−	0.780981i	−0.175752	−	0.189416i	0.639032	−	0.769180i	$-0.279335\pi$
$17$	−0.724645	−	0.780981i	−0.175752	−	0.189416i	−0.814784	+	0.579764i	$0.803145\pi$
$18$	10.9015	−	1.75233i	2.56952	−	0.413028i
$19$	0.263430	−	0.456275i	0.0604351	−	0.104677i	−0.834225	−	0.551424i	$-0.814085\pi$
$19$	0.263430	−	0.456275i	0.0604351	−	0.104677i	0.894660	+	0.446748i	$0.147418\pi$
$20$	−3.44908	−	1.90238i	−0.771237	−	0.425385i
$21$	−3.41032	−	8.00139i	−0.744192	−	1.74605i
$22$	−3.88339	+	5.81730i	−0.827941	+	1.24025i
$23$	1.53746	−	1.65699i	0.320583	−	0.345507i	−0.552114	−	0.833769i	$-0.686179\pi$
$23$	1.53746	−	1.65699i	0.320583	−	0.345507i	0.872697	+	0.488262i	$0.162369\pi$
$24$	−8.80107	+	3.00019i	−1.79651	+	0.612412i
$25$	−1.10868	−	0.167107i	−0.221736	−	0.0334213i
$26$	−0.771196	−	1.56214i	−0.151244	−	0.306361i
$27$	−3.51684	+	15.4083i	−0.676816	+	2.96533i
$28$	2.86462	+	4.44904i	0.541363	+	0.840789i
$29$	−0.514512	−	2.25422i	−0.0955424	−	0.418599i	0.904425	−	0.426632i	$-0.140300\pi$
$29$	−0.514512	−	2.25422i	−0.0955424	−	0.418599i	−0.999968	+	0.00803334i	$0.997443\pi$
$30$	7.10262	−	5.77867i	1.29675	−	1.05504i
$31$	−2.23709	−	3.87476i	−0.401794	−	0.695927i	0.592149	−	0.805829i	$-0.298280\pi$
$31$	−2.23709	−	3.87476i	−0.401794	−	0.695927i	−0.993942	+	0.109902i	$0.964946\pi$
$32$	4.97060	−	2.70058i	0.878686	−	0.477399i
$33$	−9.15911	−	13.4340i	−1.59440	−	2.33855i
$34$	−1.29739	+	0.766063i	−0.222501	+	0.131379i
$35$	−4.16608	−	3.12975i	−0.704196	−	0.529024i
$36$	0.862170	−	15.5912i	0.143695	−	2.59853i
$37$	0.148440	+	0.0457878i	0.0244035	+	0.00752747i	0.306933	−	0.951731i	$-0.400697\pi$
$37$	0.148440	+	0.0457878i	0.0244035	+	0.00752747i	−0.282529	+	0.959259i	$0.591173\pi$
$38$	−0.551122	−	0.501427i	−0.0894038	−	0.0813422i
$39$	4.03843	−	0.302639i	0.646667	−	0.0484610i
$40$	−3.66749	+	4.19284i	−0.579881	+	0.662946i
$41$	1.00896	+	2.09513i	0.157573	+	0.327204i	0.964777	−	0.263069i	$-0.0847346\pi$
$41$	1.00896	+	2.09513i	0.157573	+	0.327204i	−0.807204	+	0.590272i	$0.799020\pi$
$42$	−12.0832	+	2.30229i	−1.86448	+	0.355251i
$43$	−4.03392	+	8.37653i	−0.615168	+	1.27741i	0.327870	+	0.944723i	$0.393669\pi$
$43$	−4.03392	+	8.37653i	−0.615168	+	1.27741i	−0.943038	+	0.332686i	$0.892045\pi$
$44$	6.86850	+	7.11808i	1.03547	+	1.07309i
$45$	4.53233	+	14.6935i	0.675640	+	2.19037i
$46$	−1.82650	−	2.62350i	−0.269303	−	0.386813i
$47$	9.44316	−	1.42333i	1.37743	−	0.207614i	0.581766	−	0.813356i	$-0.302362\pi$
$47$	9.44316	−	1.42333i	1.37743	−	0.207614i	0.795660	+	0.605743i	$0.207124\pi$
$48$	1.49473	+	13.0647i	0.215746	+	1.88572i
$49$	2.92955	+	6.35750i	0.418507	+	0.908214i
$50$	−0.564831	+	1.48161i	−0.0798792	+	0.209531i
$51$	−0.522009	−	3.46330i	−0.0730959	−	0.484959i
$52$	−2.39080	+	0.595104i	−0.331544	+	0.0825261i
$53$	−2.10418	+	0.649054i	−0.289031	+	0.0891544i	−0.435881	−	0.900005i	$-0.643563\pi$
$53$	−2.10418	+	0.649054i	−0.289031	+	0.0891544i	0.146849	+	0.989159i	$0.453087\pi$
$54$	20.2314	+	9.50035i	2.75315	+	1.29283i
$55$	−8.77595	−	4.22627i	−1.18335	−	0.569870i
$56$	7.01035	−	2.61821i	0.936797	−	0.349874i
$57$	1.56052	−	0.751505i	0.206695	−	0.0995393i
$58$	−3.26978	+	0.0319754i	−0.429343	+	0.00419857i
$59$	0.949824	+	12.6745i	0.123657	+	1.65008i	0.621938	+	0.783067i	$0.286346\pi$
$59$	0.949824	+	12.6745i	0.123657	+	1.65008i	−0.498281	+	0.867016i	$0.666035\pi$
$60$	−5.84551	−	11.5547i	−0.754652	−	1.49170i
$61$	−0.310936	+	1.00803i	−0.0398113	+	0.129065i	−0.973297	−	0.229550i	$-0.926275\pi$
$61$	−0.310936	+	1.00803i	−0.0398113	+	0.129065i	0.933486	+	0.358615i	$0.116751\pi$
$62$	−6.02781	+	1.92408i	−0.765533	+	0.244359i
$63$	4.01269	−	20.2632i	0.505551	−	2.55292i
$64$	−2.23445	−	7.68162i	−0.279307	−	0.960202i
$65$	2.00457	−	1.36669i	0.248636	−	0.169517i
$66$	−21.3213	+	8.60953i	−2.62447	+	1.05976i
$67$	−0.898095	+	0.518515i	−0.109720	+	0.0633467i	−0.553856	−	0.832613i	$-0.686844\pi$
$67$	−0.898095	+	0.518515i	−0.109720	+	0.0633467i	0.444136	+	0.895959i	$0.353511\pi$
$68$	0.667753	+	2.02343i	0.0809769	+	0.245377i
$69$	7.24471	−	1.65356i	0.872160	−	0.199065i
$70$	−5.57939	+	4.81389i	−0.666865	+	0.575370i
$71$	11.2417	+	2.56583i	1.33414	+	0.304508i	0.829347	−	0.558733i	$-0.188712\pi$
$71$	11.2417	+	2.56583i	1.33414	+	0.304508i	0.504791	+	0.863242i	$0.331570\pi$
$72$	−21.2837	−	5.88730i	−2.50831	−	0.693825i
$73$	0.954106	−	6.33008i	0.111670	−	0.740880i	−0.860986	−	0.508628i	$-0.830153\pi$
$73$	0.954106	−	6.33008i	0.111670	−	0.740880i	0.972656	−	0.232251i	$-0.0746092\pi$
$74$	0.107978	−	0.191319i	0.0125521	−	0.0222404i
$75$	−2.70198	−	2.50707i	−0.311997	−	0.289491i
$76$	−0.858851	+	0.610495i	−0.0985170	+	0.0700286i
$77$	7.68057	+	10.5941i	0.875282	+	1.20731i
$78$	0.798179	−	5.67133i	0.0903759	−	0.642152i
$79$	−7.88112	−	4.55017i	−0.886696	−	0.511934i	−0.0138353	−	0.999904i	$-0.504404\pi$
$79$	−7.88112	−	4.55017i	−0.886696	−	0.511934i	−0.872860	+	0.487970i	$0.837737\pi$
$80$	4.68890	+	6.33048i	0.524235	+	0.707769i
$81$	−20.9173	+	19.4084i	−2.32414	+	2.15649i
$82$	3.19887	−	0.763107i	0.353256	−	0.0842710i
$83$	5.49592	−	6.89167i	0.603256	−	0.756459i	−0.382626	−	0.923903i	$-0.624980\pi$
$83$	5.49592	−	6.89167i	0.603256	−	0.756459i	0.985881	+	0.167445i	$0.0535516\pi$
$84$	−0.458178	+	17.3897i	−0.0499913	+	1.89737i
$85$	−1.30823	−	1.64047i	−0.141897	−	0.177934i
$86$	10.3594	+	8.09691i	1.11709	+	0.873113i
$87$	2.77706	−	7.07583i	0.297732	−	0.758609i
$88$	11.9043	−	7.34674i	1.26900	−	0.783165i
$89$	−8.70248	+	3.41547i	−0.922461	+	0.362039i	−0.778573	−	0.627554i	$-0.784056\pi$
$89$	−8.70248	+	3.41547i	−0.922461	+	0.362039i	−0.143889	+	0.989594i	$0.545961\pi$
$90$	21.6681	−	1.83704i	2.28401	−	0.193641i
$91$	−3.24172	+	0.337379i	−0.339825	+	0.0353669i
$92$	−4.17519	+	1.73362i	−0.435294	+	0.180742i
$93$	1.09919	−	14.6676i	0.113980	−	1.52096i
$94$	0.877523	−	13.4769i	0.0905095	−	1.39004i
$95$	0.584520	−	0.857334i	0.0599705	−	0.0879606i
$96$	18.5026	+	1.86964i	1.88841	+	0.190819i
$97$		−	7.11086i		−	0.721999i	−0.932566	−	0.360999i	$-0.882436\pi$
$97$		−	7.11086i		−	0.721999i	0.932566	−	0.360999i	$-0.117564\pi$
$98$	9.66695	−	2.13311i	0.976509	−	0.215476i
$99$		−	38.6142i		−	3.88088i
$100$	1.87711	+	1.22672i	0.187711	+	0.122672i
$101$	1.88397	−	2.76327i	0.187462	−	0.274956i	−0.720990	−	0.692945i	$-0.756313\pi$
$101$	1.88397	−	2.76327i	0.187462	−	0.274956i	0.908452	+	0.417990i	$0.137265\pi$
$102$	−4.94271	−	0.321834i	−0.489401	−	0.0318663i
$103$	−1.32714	+	17.7094i	−0.130767	+	1.74496i	0.417515	+	0.908670i	$0.362901\pi$
$103$	−1.32714	+	17.7094i	−0.130767	+	1.74496i	−0.548282	+	0.836293i	$0.684718\pi$
$104$	0.102201	+	3.48277i	0.0100216	+	0.341513i
$105$	−5.52009	−	16.2163i	−0.538706	−	1.58255i
$106$	0.263073	+	3.10298i	0.0255519	+	0.301388i
$107$	10.0086	−	3.92809i	0.967570	−	0.379743i	0.171659	−	0.985156i	$-0.445087\pi$
$107$	10.0086	−	3.92809i	0.967570	−	0.379743i	0.795911	+	0.605413i	$0.206992\pi$
$108$	19.2209	−	25.0937i	1.84953	−	2.41464i
$109$	2.35069	−	5.98947i	0.225156	−	0.573687i	−0.772999	−	0.634407i	$-0.781244\pi$
$109$	2.35069	−	5.98947i	0.225156	−	0.573687i	0.998155	+	0.0607199i	$0.0193396\pi$
$110$	−8.48300	+	10.8534i	−0.808822	+	1.03483i
$111$	0.318405	+	0.399268i	0.0302217	+	0.0378968i
$112$	−1.50628	−	10.4753i	−0.142331	−	0.989819i
$113$	11.5011	−	14.4220i	1.08194	−	1.35670i	0.152254	−	0.988341i	$-0.451347\pi$
$113$	11.5011	−	14.4220i	1.08194	−	1.35670i	0.929682	−	0.368363i	$-0.120082\pi$
$114$	−0.568386	−	2.38262i	−0.0532342	−	0.223153i
$115$	3.26339	−	3.02798i	0.304313	−	0.282361i
$116$	−0.940658	+	4.52771i	−0.0873379	+	0.420387i
$117$	8.32931	+	4.80893i	0.770045	+	0.444586i
$118$	17.7993	+	2.50506i	1.63856	+	0.230610i
$119$	0.500478	+	2.77395i	0.0458788	+	0.254288i
$120$	−17.7265	+	4.59693i	−1.61820	+	0.419640i
$121$	9.86749	+	9.15569i	0.897044	+	0.832335i
$122$	1.29921	+	0.733256i	0.117625	+	0.0663859i
$123$	−1.13939	+	7.55936i	−0.102735	+	0.681605i
$124$	0.843092	+	8.90856i	0.0757119	+	0.800012i
$125$	−11.7532	−	2.68260i	−1.05124	−	0.239939i
$126$	−26.7904	−	11.6478i	−2.38668	−	1.03767i
$127$	−11.8888	+	2.71355i	−1.05496	+	0.240789i	−0.714621	−	0.699512i	$-0.753401\pi$
$127$	−11.8888	+	2.71355i	−1.05496	+	0.240789i	−0.340344	+	0.940301i	$0.610544\pi$
$128$	−11.2872	+	0.773833i	−0.997658	+	0.0683978i
$129$	−26.4696	+	15.2822i	−2.33052	+	1.34553i
$130$	−1.28468	−	3.18148i	−0.112674	−	0.279035i
$131$	10.5985	−	7.22593i	0.925995	−	0.631332i	−0.00356925	−	0.999994i	$-0.501136\pi$
$131$	10.5985	−	7.22593i	0.925995	−	0.631332i	0.929564	+	0.368661i	$0.120184\pi$
$132$	5.47451	+	32.0542i	0.476495	+	2.78996i
$133$	−1.23790	+	0.640848i	−0.107339	+	0.0555686i
$134$	0.445966	+	1.39713i	0.0385256	+	0.120694i
$135$	−9.17470	+	29.7436i	−0.789632	+	2.55992i
$136$	2.99703	−	0.313233i	0.256994	−	0.0268595i
$137$	0.212903	+	2.84099i	0.0181895	+	0.242722i	0.998886	+	0.0471864i	$0.0150255\pi$
$137$	0.212903	+	2.84099i	0.0181895	+	0.242722i	−0.980697	+	0.195536i	$0.937355\pi$
$138$	−0.102764	−	10.5085i	−0.00874783	−	0.894547i
$139$	−4.87181	+	2.34614i	−0.413222	+	0.198997i	−0.628932	−	0.777460i	$-0.716508\pi$
$139$	−4.87181	+	2.34614i	−0.413222	+	0.198997i	0.215710	+	0.976457i	$0.430793\pi$
$140$	4.97120	+	9.15934i	0.420143	+	0.774106i
$141$	28.2857	+	13.6217i	2.38209	+	1.14715i
$142$	6.93131	−	14.7605i	0.581663	−	1.23868i
$143$	−5.82191	+	1.79582i	−0.486853	+	0.150174i
$144$	−14.5454	+	27.6359i	−1.21212	+	2.30299i
$145$	−0.678707	−	4.50293i	−0.0563635	−	0.373948i
$146$	−8.45933	−	3.22494i	−0.700099	−	0.266898i
$147$	−3.81610	+	22.6937i	−0.314747	+	1.87175i
$148$	−0.231836	−	0.206824i	−0.0190568	−	0.0170009i
$149$	19.5642	−	2.94882i	1.60276	−	0.241577i	0.714065	−	0.700079i	$-0.246852\pi$
$149$	19.5642	−	2.94882i	1.60276	−	0.241577i	0.888693	+	0.458502i	$0.151614\pi$
$150$	−4.27801	+	2.97839i	−0.349298	+	0.243184i
$151$	−1.19308	−	3.86787i	−0.0970915	−	0.314763i	0.893978	−	0.448111i	$-0.147903\pi$
$151$	−1.19308	−	3.86787i	−0.0970915	−	0.314763i	−0.991069	+	0.133349i	$0.957427\pi$
$152$	0.584881	+	1.37061i	0.0474401	+	0.111171i
$153$	3.60904	−	7.49424i	0.291773	−	0.605873i
$154$	16.9519	−	7.42188i	1.36602	−	0.598072i
$155$	−3.82328	−	7.93912i	−0.307093	−	0.637685i
$156$	−7.59605	−	2.81107i	−0.608171	−	0.225066i
$157$	−8.56317	+	0.641721i	−0.683415	+	0.0512149i	−0.411913	−	0.911223i	$-0.635139\pi$
$157$	−8.56317	+	0.641721i	−0.683415	+	0.0512149i	−0.271502	+	0.962438i	$0.587520\pi$
$158$	−8.66103	+	9.51939i	−0.689034	+	0.757322i
$159$	−6.91744	−	2.13375i	−0.548589	−	0.169217i
$160$	10.1595	−	4.57226i	0.803181	−	0.361469i
$161$	−5.78963	+	1.49871i	−0.456287	+	0.118115i
$162$	20.5177	+	34.7486i	1.61203	+	2.73010i
$163$	1.91619	+	2.81053i	0.150087	+	0.220138i	0.893918	−	0.448230i	$-0.147946\pi$
$163$	1.91619	+	2.81053i	0.150087	+	0.220138i	−0.743831	+	0.668368i	$0.766993\pi$
$164$	−0.0909528	−	4.64994i	−0.00710222	−	0.363099i
$165$	−16.0109	−	27.7318i	−1.24645	−	2.15891i
$166$	−7.86734	−	9.66982i	−0.610624	−	0.750524i
$167$	−2.23388	−	9.78726i	−0.172863	−	0.757361i	−0.984811	−	0.173631i	$-0.944450\pi$
$167$	−2.23388	−	9.78726i	−0.172863	−	0.757361i	0.811948	−	0.583730i	$-0.198407\pi$
$168$	23.8905	+	5.87077i	1.84319	+	0.452940i
$169$	−2.55509	+	11.1946i	−0.196546	+	0.861123i
$170$	−2.66078	+	1.31357i	−0.204072	+	0.100746i
$171$	4.06752	+	0.613080i	0.311051	+	0.0468834i
$172$	14.3083	−	11.8756i	1.09099	−	0.905503i
$173$	−2.25477	+	2.43007i	−0.171427	+	0.184754i	−0.812922	−	0.582373i	$-0.802124\pi$
$173$	−2.25477	+	2.43007i	−0.171427	+	0.184754i	0.641494	+	0.767128i	$0.278315\pi$
$174$	−8.94072	−	5.96846i	−0.677794	−	0.452467i
$175$	2.23194	+	1.95400i	0.168719	+	0.147709i
$176$	−6.56598	−	18.6618i	−0.494929	−	1.40668i
$177$	−20.8920	+	36.1860i	−1.57034	+	2.71991i
$178$	2.09825	+	13.0535i	0.157270	+	0.978404i
$179$	2.37065	+	2.55496i	0.177191	+	0.190967i	0.815402	−	0.578895i	$-0.196516\pi$
$179$	2.37065	+	2.55496i	0.177191	+	0.190967i	−0.638211	+	0.769861i	$0.720325\pi$
$180$	3.98795	−	30.4935i	0.297244	−	2.27285i
$181$	−9.55201	−	7.61747i	−0.709995	−	0.566202i	0.200514	−	0.979691i	$-0.435739\pi$
$181$	−9.55201	−	7.61747i	−0.709995	−	0.566202i	−0.910509	+	0.413488i	$0.864310\pi$
$182$	−0.510212	+	4.58093i	−0.0378194	+	0.339561i
$183$	−2.71135	+	2.16223i	−0.200429	+	0.159837i
$184$	1.13791	+	6.29131i	0.0838879	+	0.463801i
$185$	0.284792	+	0.111773i	0.0209383	+	0.00821769i
$186$	−19.9362	−	5.93664i	−1.46179	−	0.435296i
$187$	1.92504	+	4.90492i	0.140773	+	0.358684i
$188$	−18.3577	−	5.27172i	−1.33887	−	0.384480i
$189$	29.8178	−	29.3152i	2.16893	−	2.13237i
$190$	−1.00858	−	1.06590i	−0.0731702	−	0.0773282i
$191$	18.0766	+	1.35466i	1.30798	+	0.0980195i	0.710404	−	0.703794i	$-0.248512\pi$
$191$	18.0766	+	1.35466i	1.30798	+	0.0980195i	0.597575	+	0.801813i	$0.296131\pi$
$192$	8.15628	−	25.0031i	0.588629	−	1.80444i
$193$	14.4433	+	9.84726i	1.03965	+	0.708822i	0.957686	−	0.287814i	$-0.0929284\pi$
$193$	14.4433	+	9.84726i	1.03965	+	0.708822i	0.0819638	+	0.996635i	$0.473881\pi$
$194$	−9.82556	−	2.14175i	−0.705434	−	0.153769i
$195$	7.97586			0.571163
$196$	−0.0358260	−	14.0000i	−0.00255900	−	0.999997i
$197$	−5.26437			−0.375071			−0.187535	−	0.982258i	$-0.560050\pi$
$197$	−5.26437			−0.375071			−0.187535	+	0.982258i	$0.560050\pi$
$198$	−53.3559	−	11.6304i	−3.79184	−	0.826537i
$199$	−13.4449	−	9.16660i	−0.953086	−	0.649803i	−0.0163597	−	0.999866i	$-0.505208\pi$
$199$	−13.4449	−	9.16660i	−0.953086	−	0.649803i	−0.936726	+	0.350063i	$0.886160\pi$
$200$	2.26041	−	2.22425i	0.159835	−	0.157278i
$201$	−3.39968	−	0.254771i	−0.239795	−	0.0179701i
$202$	−3.25076	−	3.43549i	−0.228722	−	0.241720i
$203$	−2.06948	+	5.75682i	−0.145249	+	0.404049i
$204$	−1.93342	+	6.73274i	−0.135366	+	0.471386i
$205$	1.67320	+	4.26324i	0.116861	+	0.297758i
$206$	24.0706	+	7.16779i	1.67708	+	0.499404i
$207$	16.4281	+	6.44757i	1.14183	+	0.448137i
$208$	4.84316	+	0.907774i	0.335813	+	0.0629428i
$209$	−2.03725	+	1.62465i	−0.140920	+	0.112380i
$210$	−24.0698	+	2.74321i	−1.66098	+	0.189299i
$211$	11.0880	+	8.84237i	0.763328	+	0.608734i	0.925815	−	0.377977i	$-0.123380\pi$
$211$	11.0880	+	8.84237i	0.763328	+	0.608734i	−0.162487	+	0.986711i	$0.551952\pi$
$212$	4.36683	+	0.571095i	0.299915	+	0.0392230i
$213$	25.7834	+	27.7878i	1.76665	+	1.90399i
$214$	−2.41317	−	15.0127i	−0.164961	−	1.02625i
$215$	−9.15531	+	15.8575i	−0.624387	+	1.08147i
$216$	−28.8844	−	34.1169i	−1.96533	−	2.32136i
$217$	−0.543144	+	11.8251i	−0.0368710	+	0.802741i
$218$	−7.56804	−	5.05211i	−0.512572	−	0.342172i
$219$	14.3143	−	15.4271i	0.967268	−	1.04247i
$220$	12.4418	+	14.9905i	0.838828	+	1.01066i
$221$	−1.29776	−	0.195606i	−0.0872967	−	0.0131579i
$222$	0.647597	−	0.319705i	0.0434639	−	0.0214572i
$223$	−0.293880	+	1.28757i	−0.0196797	+	0.0862222i	−0.983814	−	0.179192i	$-0.942652\pi$
$223$	−0.293880	+	1.28757i	−0.0196797	+	0.0862222i	0.964134	+	0.265414i	$0.0855088\pi$
$224$	−14.9281	−	1.07376i	−0.997423	−	0.0717435i
$225$	−1.94790	−	8.53432i	−0.129860	−	0.568954i
$226$	−16.4637	−	20.2357i	−1.09515	−	1.34606i
$227$	1.81535	+	3.14428i	0.120489	+	0.208693i	0.919961	−	0.392011i	$-0.128220\pi$
$227$	1.81535	+	3.14428i	0.120489	+	0.208693i	−0.799472	+	0.600704i	$0.794887\pi$
$228$	−3.46342	+	0.0677446i	−0.229371	+	0.00448649i
$229$	−3.53991	−	5.19209i	−0.233924	−	0.343103i	0.691271	−	0.722595i	$-0.257051\pi$
$229$	−3.53991	−	5.19209i	−0.233924	−	0.343103i	−0.925195	+	0.379492i	$0.876099\pi$
$230$	−3.20105	−	5.42126i	−0.211071	−	0.357467i
$231$	1.24307	+	42.9997i	0.0817878	+	2.82918i
$232$	5.97292	+	2.66349i	0.392141	+	0.174867i
$233$	−18.3353	−	5.65570i	−1.20119	−	0.370517i	−0.371334	−	0.928499i	$-0.621099\pi$
$233$	−18.3353	−	5.65570i	−1.20119	−	0.370517i	−0.829853	+	0.557983i	$0.811576\pi$
$234$	9.15356	−	10.0607i	0.598387	−	0.657691i
$235$	18.7555	−	1.40553i	1.22347	−	0.0916865i
$236$	8.82248	−	23.8400i	0.574295	−	1.55185i
$237$	−12.9806	−	26.9544i	−0.843178	−	1.75088i
$238$	3.98370	+	0.143955i	0.258225	+	0.00933125i
$239$	2.16666	−	4.49912i	0.140150	−	0.291024i	−0.819066	−	0.573700i	$-0.805508\pi$
$239$	2.16666	−	4.49912i	0.140150	−	0.291024i	0.959216	+	0.282676i	$0.0912220\pi$
$240$	1.01275	+	25.8785i	0.0653730	+	1.67045i
$241$	3.17073	+	10.2793i	0.204245	+	0.662145i	0.998510	+	0.0545735i	$0.0173799\pi$
$241$	3.17073	+	10.2793i	0.204245	+	0.662145i	−0.794265	+	0.607571i	$0.792144\pi$
$242$	15.6231	−	10.8769i	1.00429	−	0.699195i
$243$	−45.8748	+	6.91452i	−2.94287	+	0.443566i
$244$	1.40451	−	1.57436i	0.0899142	−	0.100788i
$245$	4.81782	+	12.9170i	0.307799	+	0.825239i
$246$	10.1021	+	3.85121i	0.644086	+	0.245544i
$247$	−0.0967324	−	0.641777i	−0.00615493	−	0.0408353i
$248$	12.5635	+	1.51826i	0.797783	+	0.0964093i
$249$	27.6909	−	8.54152i	1.75484	−	0.541297i
$250$	−7.24675	+	15.4323i	−0.458325	+	0.976022i
$251$	−7.86305	−	3.78664i	−0.496311	−	0.239011i	0.168946	−	0.985625i	$-0.445964\pi$
$251$	−7.86305	−	3.78664i	−0.496311	−	0.239011i	−0.665257	+	0.746615i	$0.731678\pi$
$252$	−24.1637	+	33.5099i	−1.52217	+	2.11093i
$253$	−10.0724	+	4.85059i	−0.633244	+	0.304954i
$254$	0.168639	+	17.2449i	0.0105814	+	1.08204i
$255$	−0.515481	−	6.87861i	−0.0322807	−	0.430755i
$256$	−2.33039	+	15.8294i	−0.145650	+	0.989336i
$257$	−2.17267	+	7.04363i	−0.135528	+	0.439370i	−0.997741	−	0.0671752i	$-0.978601\pi$
$257$	−2.17267	+	7.04363i	−0.135528	+	0.439370i	0.862214	+	0.506545i	$0.169078\pi$
$258$	13.1440	+	41.1778i	0.818309	+	2.56362i
$259$	−0.265430	−	0.313791i	−0.0164930	−	0.0194980i
$260$	−4.78301	+	0.816887i	−0.296630	+	0.0506612i
$261$	14.9156	−	10.1693i	0.923255	−	0.629464i
$262$	−6.79235	−	16.8211i	−0.419632	−	1.03921i
$263$	−20.7820	+	11.9985i	−1.28148	+	0.739860i	−0.977118	−	0.212698i	$-0.931775\pi$
$263$	−20.7820	+	11.9985i	−1.28148	+	0.739860i	−0.304357	+	0.952558i	$0.598442\pi$
$264$	45.9403	+	2.09005i	2.82743	+	0.128634i
$265$	−4.22805	+	0.965025i	−0.259727	+	0.0592810i
$266$	0.512654	+	1.90351i	0.0314329	+	0.116712i
$267$	−29.9632	−	6.83889i	−1.83372	−	0.418534i
$268$	2.06483	−	0.195413i	0.126130	−	0.0119367i
$269$	−1.02434	+	6.79604i	−0.0624550	+	0.414362i	0.935655	+	0.352915i	$0.114810\pi$
$269$	−1.02434	+	6.79604i	−0.0624550	+	0.414362i	−0.998110	+	0.0614467i	$0.980429\pi$
$270$	38.3354	+	21.6359i	2.33302	+	1.31672i
$271$	−14.5506	−	13.5009i	−0.883883	−	0.820124i	0.100722	−	0.994915i	$-0.467885\pi$
$271$	−14.5506	−	13.5009i	−0.883883	−	0.820124i	−0.984606	+	0.174791i	$0.944075\pi$
$272$	0.469877	−	4.23555i	0.0284905	−	0.256818i
$273$	−9.43009	−	5.08695i	−0.570735	−	0.307876i
$274$	3.98971	+	0.561509i	0.241027	+	0.0339220i
$275$	4.80231	+	2.77262i	0.289590	+	0.167195i
$276$	−14.5513	−	3.02312i	−0.875887	−	0.181971i
$277$	−9.86248	+	9.15104i	−0.592579	+	0.549833i	−0.918428	−	0.395589i	$-0.870540\pi$
$277$	−9.86248	+	9.15104i	−0.592579	+	0.549833i	0.325849	+	0.945422i	$0.394350\pi$
$278$	1.77446	+	7.43836i	0.106425	+	0.446123i
$279$	21.7799	−	27.3111i	1.30393	−	1.63507i
$280$	14.1534	−	4.11030i	0.845826	−	0.245637i
$281$	−5.71210	−	7.16275i	−0.340755	−	0.427294i	0.581697	−	0.813406i	$-0.302389\pi$
$281$	−5.71210	−	7.16275i	−0.340755	−	0.427294i	−0.922452	+	0.386112i	$0.873818\pi$
$282$	27.3415	−	34.9815i	1.62816	−	2.08312i
$283$	−2.38440	+	6.07534i	−0.141738	+	0.361142i	−0.984061	−	0.177831i	$-0.943092\pi$
$283$	−2.38440	+	6.07534i	−0.141738	+	0.361142i	0.842323	+	0.538972i	$0.181187\pi$
$284$	−18.3080	−	14.0233i	−1.08638	−	0.832127i
$285$	3.17540	−	1.24625i	0.188094	−	0.0738215i
$286$	0.727879	+	8.58542i	0.0430404	+	0.507667i
$287$	0.740795	−	6.10771i	0.0437278	−	0.360527i
$288$	33.8054	+	28.4222i	1.99200	+	1.67479i
$289$	1.18559	−	15.8206i	0.0697406	−	0.930623i
$290$	−6.42642	−	0.418443i	−0.377372	−	0.0245718i
$291$	13.1686	−	19.3148i	0.771958	−	1.13225i
$292$	−7.00402	+	10.7175i	−0.409879	+	0.627194i
$293$			16.4670i			0.962010i	0.876718	+	0.481005i	$0.159728\pi$
$293$			16.4670i			0.962010i	−0.876718	+	0.481005i	$0.840272\pi$
$294$	30.2081	+	12.1082i	1.76177	+	0.706164i
$295$			25.0320i			1.45742i
$296$	−0.355611	+	0.258050i	−0.0206695	+	0.0149988i
$297$	44.0324	−	64.5837i	2.55502	−	3.74753i
$298$	1.81804	−	27.9213i	0.105316	−	1.61744i
$299$	0.208088	−	2.77675i	0.0120341	−	0.160583i
$300$	2.82693	+	6.80829i	0.163213	+	0.393077i
$301$	20.9384	−	12.9095i	1.20687	−	0.744094i
$302$	−5.70385	+	0.483577i	−0.328220	+	0.0278267i
$303$	10.2346	−	4.01679i	0.587963	−	0.230758i
$304$	2.07003	−	0.395349i	0.118724	−	0.0226748i
$305$	−0.759027	+	1.93397i	−0.0434618	+	0.110739i
$306$	−9.26827	−	7.24407i	−0.529832	−	0.414116i
$307$	−9.43588	−	11.8322i	−0.538534	−	0.675300i	0.435895	−	0.899998i	$-0.356432\pi$
$307$	−9.43588	−	11.8322i	−0.538534	−	0.675300i	−0.974429	+	0.224698i	$0.927861\pi$
$308$	−5.14948	−	25.6590i	−0.293419	−	1.46206i
$309$	−36.4010	+	45.6454i	−2.07078	+	2.59667i
$310$	−12.1216	+	2.89166i	−0.688459	+	0.164235i
$311$	−1.64734	+	1.52851i	−0.0934123	+	0.0866739i	−0.725497	−	0.688225i	$-0.758390\pi$
$311$	−1.64734	+	1.52851i	−0.0934123	+	0.0866739i	0.632085	+	0.774899i	$0.282200\pi$
$312$	−6.17214	+	9.64930i	−0.349429	+	0.546284i
$313$	−16.3112	−	9.41728i	−0.921964	−	0.532296i	−0.0377029	−	0.999289i	$-0.512004\pi$
$313$	−16.3112	−	9.41728i	−0.921964	−	0.532296i	−0.884261	+	0.466993i	$0.845337\pi$
$314$	−1.69247	+	12.0256i	−0.0955117	+	0.678643i
$315$	10.8631	−	39.2055i	0.612064	−	2.20898i
$316$	10.5449	+	14.8347i	0.593199	+	0.834518i
$317$	−7.72732	−	7.16991i	−0.434010	−	0.402702i	0.432682	−	0.901547i	$-0.357567\pi$
$317$	−7.72732	−	7.16991i	−0.434010	−	0.402702i	−0.866691	+	0.498845i	$0.833758\pi$
$318$	−5.03184	+	8.91563i	−0.282172	+	0.499963i
$319$	−1.70439	+	11.3079i	−0.0954276	+	0.633121i
$320$	−3.25781	−	15.4152i	−0.182117	−	0.861738i
$321$	34.4603	+	7.86533i	1.92338	+	0.439000i
$322$	0.327055	+	8.45133i	0.0182261	+	0.470974i
$323$	−0.547236	+	0.124903i	−0.0304490	+	0.00694979i
$324$	54.1943	−	17.8847i	3.01079	−	0.993592i
$325$	−1.19614	+	0.690591i	−0.0663498	+	0.0383071i
$326$	4.46065	−	1.80121i	0.247052	−	0.0997597i
$327$	17.4770	−	11.9156i	0.966478	−	0.658933i
$328$	−6.45253	−	1.27486i	−0.356281	−	0.0703925i
$329$	−23.0716	−	10.3003i	−1.27198	−	0.567875i
$330$	−43.1412	+	13.7707i	−2.37485	+	0.758054i
$331$	2.46170	−	7.98064i	0.135307	−	0.438655i	−0.862408	−	0.506214i	$-0.831045\pi$
$331$	2.46170	−	7.98064i	0.135307	−	0.438655i	0.997715	+	0.0675583i	$0.0215209\pi$
$332$	−15.7310	+	7.95834i	−0.863353	+	0.436770i
$333$	0.0906350	+	1.20944i	0.00496677	+	0.0662769i
$334$	−14.1965	+	0.138829i	−0.776801	+	0.00759638i
$335$	−1.84014	+	0.886162i	−0.100537	+	0.0484162i
$336$	15.3077	−	31.2428i	0.835105	−	1.70444i
$337$	−10.5799	−	5.09500i	−0.576323	−	0.277542i	0.122932	−	0.992415i	$-0.460770\pi$
$337$	−10.5799	−	5.09500i	−0.576323	−	0.277542i	−0.699255	+	0.714873i	$0.746485\pi$
$338$	14.6987	+	6.90230i	0.799507	+	0.375436i
$339$	57.9479	−	17.8746i	3.14730	−	0.970813i
$340$	1.01363	+	4.07221i	0.0549720	+	0.220847i
$341$	3.29806	+	21.8812i	0.178600	+	1.18493i
$342$	2.07225	−	5.43571i	0.112054	−	0.293930i
$343$	2.54214	−	18.3450i	0.137263	−	0.990535i
$344$	−12.0997	−	23.3475i	−0.652372	−	1.25882i
$345$	14.4717	−	2.18125i	0.779129	−	0.117435i
$346$	2.67866	+	3.84749i	0.144006	+	0.206842i
$347$	6.00148	+	19.4563i	0.322176	+	1.04447i	0.961332	+	0.275393i	$0.0888079\pi$
$347$	6.00148	+	19.4563i	0.322176	+	1.04447i	−0.639155	+	0.769078i	$0.720716\pi$
$348$	−10.9399	+	10.5563i	−0.586441	+	0.565879i
$349$	3.68089	−	7.64345i	0.197034	−	0.409145i	−0.778920	−	0.627124i	$-0.784232\pi$
$349$	3.68089	−	7.64345i	0.197034	−	0.409145i	0.975953	+	0.217979i	$0.0699464\pi$
$350$	3.37222	−	2.49549i	0.180253	−	0.133389i
$351$	8.44737	+	17.5411i	0.450887	+	0.936277i
$352$	−27.7639	+	3.45183i	−1.47982	+	0.183983i
$353$	−21.7781	+	1.63204i	−1.15913	+	0.0868648i	−0.640378	−	0.768060i	$-0.721222\pi$
$353$	−21.7781	+	1.63204i	−1.15913	+	0.0868648i	−0.518752	+	0.854925i	$0.673603\pi$
$354$	43.7081	+	39.7670i	2.32306	+	2.11359i
$355$	21.7005	+	6.69372i	1.15174	+	0.355266i
$356$	18.6689	+	1.03237i	0.989451	+	0.0547153i
$357$	−3.77767	+	8.46156i	−0.199935	+	0.447833i
$358$	4.24439	−	2.50615i	0.224323	−	0.132454i
$359$	−12.9862	−	19.0473i	−0.685386	−	1.00528i	−0.998456	−	0.0555464i	$-0.982310\pi$
$359$	−12.9862	−	19.0473i	−0.685386	−	1.00528i	0.313070	−	0.949730i	$-0.398642\pi$
$360$	−40.9338	−	14.6949i	−2.15740	−	0.774490i
$361$	9.36121	+	16.2141i	0.492695	+	0.853373i
$362$	−13.4026	+	10.9043i	−0.704425	+	0.573118i
$363$	9.84703	+	43.1427i	0.516835	+	2.26440i
$364$	6.17610	+	2.08474i	0.323716	+	0.109270i
$365$	2.80548	−	12.2916i	0.146845	−	0.643372i
$366$	2.17106	+	4.39771i	0.113483	+	0.229872i
$367$	−37.2856	−	5.61991i	−1.94629	−	0.293357i	−0.946708	−	0.322094i	$-0.895613\pi$
$367$	−37.2856	−	5.61991i	−1.94629	−	0.293357i	−0.999587	+	0.0287376i	$0.990851\pi$
$368$	9.03585	+	0.322580i	0.471026	+	0.0168156i
$369$	−12.3490	+	13.3091i	−0.642863	+	0.692842i
$370$	0.240222	−	0.359851i	0.0124885	−	0.0187078i
$371$	5.61444	+	1.55565i	0.291487	+	0.0807651i
$372$	−14.2077	+	25.7591i	−0.736637	+	1.33555i
$373$	−14.0240	+	24.2903i	−0.726135	+	1.25770i	0.232370	+	0.972627i	$0.425352\pi$
$373$	−14.0240	+	24.2903i	−0.726135	+	1.25770i	−0.958505	+	0.285076i	$0.907981\pi$
$374$	7.35728	−	1.18262i	0.380436	−	0.0611519i
$375$	−26.9567	−	29.0524i	−1.39204	−	1.50026i
$376$	−12.8135	+	23.7783i	−0.660808	+	1.22627i
$377$	−2.22692	−	1.77591i	−0.114692	−	0.0914638i
$378$	−31.5258	−	50.0309i	−1.62151	−	2.57331i
$379$	5.15435	−	4.11046i	0.264761	−	0.211140i	−0.482107	−	0.876113i	$-0.660128\pi$
$379$	5.15435	−	4.11046i	0.264761	−	0.211140i	0.746868	+	0.664973i	$0.231557\pi$
$380$	−1.77660	+	1.07258i	−0.0911377	+	0.0550224i
$381$	−37.3182	−	14.6463i	−1.91187	−	0.750353i
$382$	7.31640	−	24.5697i	0.374340	−	1.25709i
$383$	−5.44098	−	13.8634i	−0.278021	−	0.708386i	−0.999867	−	0.0163317i	$-0.994801\pi$
$383$	−5.44098	−	13.8634i	−0.278021	−	0.708386i	0.721846	−	0.692054i	$-0.243294\pi$
$384$	−32.0918	−	18.8009i	−1.63768	−	0.959429i
$385$	13.5251	+	21.9368i	0.689303	+	1.11800i
$386$	17.9569	−	16.9913i	0.913981	−	0.864835i
$387$	−72.3853	−	5.42453i	−3.67955	−	0.275744i
$388$	−5.91881	+	12.9316i	−0.300482	+	0.656500i
$389$	11.8078	+	8.05043i	0.598680	+	0.408173i	0.824391	−	0.566021i	$-0.191518\pi$
$389$	11.8078	+	8.05043i	0.598680	+	0.408173i	−0.225711	+	0.974194i	$0.572470\pi$
$390$	2.40229	−	11.0208i	0.121645	−	0.558059i
$391$	−2.40820			−0.121788
$392$	−19.3555	−	4.16721i	−0.977599	−	0.210476i
$393$	42.1698			2.12718
$394$	−1.58560	+	7.27414i	−0.0798814	+	0.366466i
$395$	−14.8085	−	10.0963i	−0.745097	−	0.507999i
$396$	−32.1410	+	70.2224i	−1.61515	+	3.52881i
$397$	36.7676	+	2.75535i	1.84531	+	0.138287i	0.951008	−	0.309168i	$-0.100050\pi$
$397$	36.7676	+	2.75535i	1.84531	+	0.138287i	0.894307	+	0.447455i	$0.147669\pi$
$398$	−16.7156	+	15.8168i	−0.837880	+	0.792826i
$399$	−4.54921	−	0.551768i	−0.227746	−	0.0276229i
$400$	−2.39257	−	3.79330i	−0.119629	−	0.189665i
$401$	−2.48236	−	6.32496i	−0.123963	−	0.315853i	0.855398	−	0.517972i	$-0.173313\pi$
$401$	−2.48236	−	6.32496i	−0.123963	−	0.315853i	−0.979361	+	0.202118i	$0.935217\pi$
$402$	−1.37600	+	4.62083i	−0.0686286	+	0.230466i
$403$	−5.13063	−	2.01363i	−0.255575	−	0.100306i
$404$	−5.72615	+	3.45704i	−0.284887	+	0.171994i
$405$	−43.9372	+	35.0388i	−2.18326	+	1.74109i
$406$	7.33126	+	4.59347i	0.363845	+	0.227970i
$407$	−0.600672	−	0.479020i	−0.0297742	−	0.0237441i
$408$	8.72074	+	4.69940i	0.431741	+	0.232655i
$409$	−14.5767	−	15.7099i	−0.720769	−	0.776804i	0.261314	−	0.965254i	$-0.415844\pi$
$409$	−14.5767	−	15.7099i	−0.720769	−	0.776804i	−0.982083	+	0.188449i	$0.939654\pi$
$410$	6.39477	−	1.02791i	0.315815	−	0.0507646i
$411$	−4.68294	+	8.11108i	−0.230992	+	0.400090i
$412$	17.1542	−	31.1011i	0.845125	−	1.53224i
$413$	15.9653	−	29.5961i	0.785600	−	1.45633i
$414$	13.8571	−	20.7579i	0.681040	−	1.02020i
$415$	11.8081	−	12.7261i	0.579635	−	0.624698i
$416$	2.71307	−	6.41870i	0.133019	−	0.314703i
$417$	−17.5778	−	2.64943i	−0.860791	−	0.129743i
$418$	1.63128	+	3.30435i	0.0797888	+	0.161621i
$419$	5.91313	−	25.9071i	0.288875	−	1.26565i	−0.597195	−	0.802096i	$-0.703718\pi$
$419$	5.91313	−	25.9071i	0.288875	−	1.26565i	0.886071	−	0.463550i	$-0.153425\pi$
$420$	−3.45922	+	34.0851i	−0.168793	+	1.66318i
$421$	−4.40656	−	19.3064i	−0.214763	−	0.940937i	−0.961281	−	0.275571i	$-0.911133\pi$
$421$	−4.40656	−	19.3064i	−0.214763	−	0.940937i	0.746518	−	0.665365i	$-0.231724\pi$
$422$	15.5577	−	12.6577i	0.757339	−	0.616169i
$423$	37.2801	+	64.5710i	1.81262	+	3.13955i
$424$	2.10439	−	5.86194i	0.102198	−	0.284681i
$425$	0.672892	+	0.986951i	0.0326401	+	0.0478742i
$426$	46.1622	−	27.2570i	2.23656	−	1.32061i
$427$	2.13089	−	1.80249i	0.103121	−	0.0872284i
$428$	−21.4709	−	1.18731i	−1.03784	−	0.0573908i
$429$	−19.1394	−	5.90372i	−0.924059	−	0.285034i
$430$	19.1538	+	17.4267i	0.923678	+	0.840390i
$431$	−18.4564	+	1.38312i	−0.889013	+	0.0666223i	−0.511402	−	0.859342i	$-0.670874\pi$
$431$	−18.4564	+	1.38312i	−0.889013	+	0.0666223i	−0.377612	+	0.925964i	$0.623255\pi$
$432$	−55.8414	+	29.6357i	−2.68667	+	1.42585i
$433$	15.0973	+	31.3498i	0.725528	+	1.50657i	0.857034	+	0.515259i	$0.172304\pi$
$433$	15.0973	+	31.3498i	0.725528	+	1.50657i	−0.131506	+	0.991315i	$0.541981\pi$
$434$	16.1760	+	4.31216i	0.776471	+	0.206990i
$435$	6.49544	−	13.4879i	0.311433	−	0.646697i
$436$	−9.26029	+	8.93560i	−0.443488	+	0.427938i
$437$	−0.351029	−	1.13801i	−0.0167920	−	0.0544383i
$438$	−17.0053	−	24.4256i	−0.812544	−	1.16710i
$439$	34.6170	−	5.21767i	1.65218	−	0.249026i	0.744174	−	0.667986i	$-0.232844\pi$
$439$	34.6170	−	5.21767i	1.65218	−	0.249026i	0.908004	+	0.418961i	$0.137605\pi$
$440$	24.4608	−	12.6766i	1.16612	−	0.604335i
$441$	−37.8487	+	39.4255i	−1.80232	+	1.87740i
$442$	−0.661160	+	1.73429i	−0.0314482	+	0.0824916i
$443$	1.87199	+	12.4198i	0.0889410	+	0.590085i	0.988259	+	0.152789i	$0.0488256\pi$
$443$	1.87199	+	12.4198i	0.0889410	+	0.590085i	−0.899318	+	0.437296i	$0.855936\pi$
$444$	−0.246705	−	0.991123i	−0.0117081	−	0.0470366i
$445$	−17.5940	+	5.42703i	−0.834036	+	0.257266i
$446$	1.69061	+	0.793884i	0.0800527	+	0.0375915i
$447$	58.6019	+	28.2212i	2.77177	+	1.33482i
$448$	−5.97994	+	20.3037i	−0.282526	+	0.959260i
$449$	28.4836	−	13.7170i	1.34422	−	0.647344i	0.383164	−	0.923681i	$-0.374835\pi$
$449$	28.4836	−	13.7170i	1.34422	−	0.647344i	0.961061	+	0.276336i	$0.0891203\pi$
$450$	−12.3791	+	0.121056i	−0.583558	+	0.00570665i
$451$	−0.859472	−	11.4689i	−0.0404709	−	0.540047i
$452$	−32.9198	+	16.6542i	−1.54842	+	0.783345i
$453$	3.92222	−	12.7155i	0.184282	−	0.597428i
$454$	4.89144	−	1.56135i	0.229567	−	0.0732779i
$455$	−6.41627	+	0.185486i	−0.300799	+	0.00869572i
$456$	−0.949558	+	4.80605i	−0.0444671	+	0.225064i
$457$	−23.2631	+	15.8605i	−1.08820	+	0.741923i	−0.968031	−	0.250831i	$-0.919296\pi$
$457$	−23.2631	+	15.8605i	−1.08820	+	0.741923i	−0.120170	+	0.992753i	$0.538344\pi$
$458$	−8.24047	+	3.32750i	−0.385052	+	0.155484i
$459$	14.5820	−	8.41894i	0.680631	−	0.392963i
$460$	−8.45506	+	2.79026i	−0.394219	+	0.130096i
$461$	21.2703	−	4.85482i	0.990659	−	0.226111i	0.303668	−	0.952778i	$-0.401789\pi$
$461$	21.2703	−	4.85482i	0.990659	−	0.226111i	0.686991	+	0.726666i	$0.258931\pi$
$462$	59.7900	+	11.2337i	2.78168	+	0.522637i
$463$	2.42360	+	0.553172i	0.112634	+	0.0257081i	0.278467	−	0.960446i	$-0.410174\pi$
$463$	2.42360	+	0.553172i	0.112634	+	0.0257081i	−0.165832	+	0.986154i	$0.553031\pi$
$464$	5.47934	−	7.45095i	0.254372	−	0.345902i
$465$	4.31752	−	28.6449i	0.200220	−	1.32837i
$466$	−13.3374	+	23.6317i	−0.617841	+	1.09472i
$467$	11.7602	+	10.9118i	0.544196	+	0.504940i	0.903678	−	0.428212i	$-0.140856\pi$
$467$	11.7602	+	10.9118i	0.544196	+	0.504940i	−0.359482	+	0.933152i	$0.617047\pi$
$468$	−11.1446	−	15.6783i	−0.515159	−	0.724732i
$469$	2.74083	+	0.125890i	0.126560	+	0.00581308i
$470$	3.70693	−	26.3390i	0.170988	−	1.21493i
$471$	−24.4480	−	14.1151i	−1.12651	−	0.650388i
$472$	−30.2841	−	19.3711i	−1.39394	−	0.891628i
$473$	33.7074	−	31.2759i	1.54987	−	1.43807i
$474$	−41.1544	+	9.81759i	−1.89028	+	0.450937i
$475$	−0.368307	+	0.461842i	−0.0168991	+	0.0211908i
$476$	1.39878	−	5.46119i	0.0641131	−	0.250313i
$477$	−10.7192	−	13.4414i	−0.490796	−	0.615439i
$478$	−5.56415	−	4.34894i	−0.254498	−	0.198916i
$479$	−3.20767	+	8.17300i	−0.146562	+	0.373434i	−0.985236	−	0.171199i	$-0.945236\pi$
$479$	−3.20767	+	8.17300i	−0.146562	+	0.373434i	0.838674	+	0.544633i	$0.183331\pi$
$480$	36.0631	+	6.39507i	1.64605	+	0.291894i
$481$	0.178134	−	0.0699123i	0.00812219	−	0.00318772i
$482$	15.1585	−	1.28515i	0.690453	−	0.0585372i
$483$	−18.5015	−	6.65098i	−0.841847	−	0.302630i
$484$	−10.3238	−	24.8635i	−0.469264	−	1.13016i
$485$	1.04657	−	13.9654i	0.0475221	−	0.634138i
$486$	−4.26300	+	65.4710i	−0.193374	+	2.96982i
$487$	−15.4038	+	22.5932i	−0.698012	+	1.02380i	0.299555	+	0.954079i	$0.403162\pi$
$487$	−15.4038	+	22.5932i	−0.698012	+	1.02380i	−0.997567	+	0.0697166i	$0.977790\pi$
$488$	−1.75237	−	2.41489i	−0.0793259	−	0.109317i
$489$			11.1827i			0.505698i
$490$	19.2994	−	2.76657i	0.871860	−	0.124981i
$491$			40.7964i			1.84111i	0.390607	+	0.920557i	$0.372265\pi$
$491$			40.7964i			1.84111i	−0.390607	+	0.920557i	$0.627735\pi$
$492$	8.36418	−	12.7988i	0.377086	−	0.577014i
$493$	−1.38767	+	2.03533i	−0.0624974	+	0.0916668i
$494$	−0.915922	−	0.0596383i	−0.0412093	−	0.00268325i
$495$	5.68318	−	75.8368i	0.255440	−	3.40861i
$496$	5.88194	−	16.9025i	0.264107	−	0.758947i
$497$	−21.3879	−	21.7546i	−0.959380	−	0.975828i
$498$	−3.46203	−	40.8351i	−0.155137	−	1.82986i
$499$	10.2577	−	4.02584i	0.459197	−	0.180222i	−0.124455	−	0.992225i	$-0.539718\pi$
$499$	10.2577	−	4.02584i	0.459197	−	0.180222i	0.583652	+	0.812004i	$0.301623\pi$
$500$	19.1411	+	14.6614i	0.856017	+	0.655680i
$501$	12.0573	−	30.7215i	0.538680	−	1.37253i
$502$	−7.60057	+	9.72438i	−0.339230	+	0.434021i
$503$	−10.7541	−	13.4852i	−0.479500	−	0.601274i	0.481969	−	0.876188i	$-0.339922\pi$
$503$	−10.7541	−	13.4852i	−0.479500	−	0.601274i	−0.961469	+	0.274915i	$0.911350\pi$
$504$	39.0250	+	43.4816i	1.73831	+	1.93682i
$505$	4.10673	−	5.14967i	0.182747	−	0.229157i
$506$	3.66865	+	15.3786i	0.163091	+	0.683664i
$507$	−27.6715	+	25.6754i	−1.22894	+	1.14029i
$508$	23.8793	+	4.96106i	1.05947	+	0.220112i
$509$	1.92974	+	1.11413i	0.0855341	+	0.0493832i	0.542157	−	0.840277i	$-0.317608\pi$
$509$	1.92974	+	1.11413i	0.0855341	+	0.0493832i	−0.456623	+	0.889660i	$0.650941\pi$
$510$	−9.65990	−	1.35953i	−0.427748	−	0.0602009i
$511$	−11.1565	+	12.7434i	−0.493534	+	0.563735i
$512$	21.1706	+	7.98779i	0.935618	+	0.353014i
$513$	6.10397	+	5.66366i	0.269497	+	0.250057i
$514$	9.07827	+	5.12363i	0.400425	+	0.225994i
$515$	−5.21289	+	34.5853i	−0.229708	+	1.52401i
$516$	60.8570	−	5.75941i	2.67908	−	0.253544i
$517$	−46.0472	−	10.5100i	−2.02515	−	0.462228i
$518$	−0.513532	+	0.272251i	−0.0225633	+	0.0119620i
$519$	−10.6247	+	2.42503i	−0.466374	+	0.106447i
$520$	−0.311870	+	6.85505i	−0.0136764	+	0.300614i
$521$	−0.728955	+	0.420862i	−0.0319361	+	0.0184383i	−0.515883	−	0.856659i	$-0.672536\pi$
$521$	−0.728955	+	0.420862i	−0.0319361	+	0.0184383i	0.483947	+	0.875097i	$0.339203\pi$
$522$	−9.55911	−	23.6729i	−0.418391	−	1.03613i
$523$	1.73171	−	1.18066i	0.0757222	−	0.0516265i	−0.524867	−	0.851184i	$-0.675885\pi$
$523$	1.73171	−	1.18066i	0.0757222	−	0.0516265i	0.600589	+	0.799558i	$0.294933\pi$
$524$	−25.2886	+	4.31903i	−1.10474	+	0.188677i
$525$	2.44386	+	9.44087i	0.106659	+	0.412033i
$526$	10.3197	+	32.3298i	0.449961	+	1.40965i
$527$	−1.40502	+	4.55495i	−0.0612034	+	0.198417i
$528$	16.7250	−	62.8494i	0.727860	−	2.73517i
$529$	1.33696	+	17.8406i	0.0581289	+	0.775676i
$530$	0.0599735	+	6.13285i	0.00260508	+	0.266394i
$531$	−89.4066	+	43.0559i	−3.87991	+	1.86847i
$532$	2.78461	−	0.135043i	0.120728	−	0.00585486i
$533$	2.58093	+	1.24291i	0.111793	+	0.0538365i
$534$	−18.4745	+	39.3423i	−0.799470	+	1.70251i
$535$	20.2347	−	6.24156i	0.874820	−	0.269846i
$536$	0.351903	−	2.91198i	0.0151999	−	0.125778i
$537$	1.70774	+	11.3301i	0.0736943	+	0.488930i
$538$	9.08202	+	3.46233i	0.391554	+	0.149272i
$539$	−2.00000	−	34.5627i	−0.0861460	−	1.48872i
$540$	41.4422	−	46.4540i	1.78339	−	1.99906i
$541$	6.91274	−	1.04193i	0.297202	−	0.0447960i	0.00125127	−	0.999999i	$-0.499602\pi$
$541$	6.91274	−	1.04193i	0.297202	−	0.0447960i	0.295951	+	0.955203i	$0.404364\pi$
$542$	−23.0377	+	16.0391i	−0.989554	+	0.688937i
$543$	−11.8387	−	38.3803i	−0.508049	−	1.64706i
$544$	−5.71102	−	1.92499i	−0.244858	−	0.0825331i
$545$	5.49819	−	11.4171i	0.235516	−	0.489055i
$546$	−9.86928	+	11.4980i	−0.422366	+	0.492070i
$547$	10.6051	+	22.0217i	0.453441	+	0.941580i	0.994901	+	0.100854i	$0.0321574\pi$
$547$	10.6051	+	22.0217i	0.453441	+	0.941580i	−0.541460	+	0.840726i	$0.682128\pi$
$548$	1.97756	−	5.34373i	0.0844770	−	0.228273i
$549$	−8.21308	+	0.615485i	−0.350526	+	0.0262683i
$550$	5.27754	−	5.80058i	0.225035	−	0.247338i
$551$	−1.16408	−	0.359072i	−0.0495916	−	0.0152970i
$552$	−8.56004	+	19.1960i	−0.364339	+	0.817036i
$553$	11.0692	+	21.3819i	0.470710	+	0.909251i
$554$	9.67409	+	16.3839i	0.411013	+	0.696085i
$555$	0.566572	+	0.831008i	0.0240496	+	0.0352743i
$556$	10.8125	−	0.211493i	0.458554	−	0.00896932i
$557$	7.53323	+	13.0479i	0.319193	+	0.552859i	0.980320	−	0.197415i	$-0.0632548\pi$
$557$	7.53323	+	13.0479i	0.319193	+	0.552859i	−0.661127	+	0.750274i	$0.729921\pi$
$558$	−31.1776	−	38.3207i	−1.31985	−	1.62224i
$559$	2.54854	+	11.1659i	0.107792	+	0.472267i
$560$	−1.41655	−	20.7947i	−0.0598601	−	0.878736i
$561$	−3.85456	+	16.8879i	−0.162740	+	0.713009i
$562$	−11.6177	+	5.73541i	−0.490063	+	0.241934i
$563$	12.1382	+	1.82954i	0.511564	+	0.0771059i	0.399752	−	0.916623i	$-0.369096\pi$
$563$	12.1382	+	1.82954i	0.511564	+	0.0771059i	0.111812	+	0.993729i	$0.464334\pi$
$564$	−40.1012	−	48.3159i	−1.68857	−	2.03447i
$565$	24.7104	−	26.6314i	1.03957	−	1.12039i
$566$	7.67654	+	5.12454i	0.322669	+	0.215401i
$567$	74.2957	−	13.4045i	3.12013	−	0.562935i
$568$	−24.8911	+	21.0736i	−1.04441	+	0.884229i
$569$	15.0982	−	26.1509i	0.632950	−	1.09630i	−0.353996	−	0.935247i	$-0.615177\pi$
$569$	15.0982	−	26.1509i	0.632950	−	1.09630i	0.986946	−	0.161054i	$-0.0514893\pi$
$570$	−0.765617	−	4.76302i	−0.0320682	−	0.199501i
$571$	18.4461	+	19.8801i	0.771944	+	0.831958i	0.989567	−	0.144075i	$-0.0460207\pi$
$571$	18.4461	+	19.8801i	0.771944	+	0.831958i	−0.217623	+	0.976033i	$0.569830\pi$
$572$	12.0823	+	1.58012i	0.505186	+	0.0660683i
$573$	46.5918	+	37.1557i	1.94640	+	1.55220i
$574$	−8.21631	−	2.86322i	−0.342942	−	0.119508i
$575$	−1.98145	+	1.58015i	−0.0826322	+	0.0658970i
$576$	49.4549	−	38.1506i	2.06062	−	1.58961i
$577$	25.1296	+	9.86263i	1.04616	+	0.410587i	0.825285	−	0.564716i	$-0.191014\pi$
$577$	25.1296	+	9.86263i	1.04616	+	0.410587i	0.220873	+	0.975303i	$0.429109\pi$
$578$	−21.5033	−	6.40329i	−0.894419	−	0.266342i
$579$	20.9953	+	53.4951i	0.872533	+	2.22318i
$580$	−2.51379	+	8.75379i	−0.104380	+	0.363481i
$581$	−22.0776	+	7.51530i	−0.915935	+	0.311787i
$582$	−22.7223	−	24.0135i	−0.941868	−	0.995391i
$583$	10.8602	+	0.813861i	0.449784	+	0.0337067i
$584$	12.6995	+	12.9060i	0.525509	+	0.534053i
$585$	15.6506	+	10.6704i	0.647075	+	0.441168i
$586$	22.7535	+	4.95976i	0.939939	+	0.204886i
$587$	4.51677			0.186427			0.0932136	−	0.995646i	$-0.470286\pi$
$587$	4.51677			0.186427			0.0932136	+	0.995646i	$0.470286\pi$
$588$	25.8292	−	38.0936i	1.06518	−	1.57095i
$589$	−2.35727			−0.0971297
$590$	34.5885	+	7.53952i	1.42398	+	0.310397i
$591$	−14.2993	−	9.74910i	−0.588195	−	0.401024i
$592$	0.249456	+	0.569095i	0.0102526	+	0.0233897i
$593$	−23.3135	−	1.74710i	−0.957369	−	0.0717449i	−0.413127	−	0.910673i	$-0.635564\pi$
$593$	−23.3135	−	1.74710i	−0.957369	−	0.0717449i	−0.544242	+	0.838928i	$0.683183\pi$
$594$	−75.9773	−	80.2948i	−3.11739	−	3.29454i
$595$	0.574653	+	5.52159i	0.0235585	+	0.226363i
$596$	−38.0332	−	10.9218i	−1.55790	−	0.447376i
$597$	−19.5440	−	49.7974i	−0.799884	−	2.03807i
$598$	−3.77414	−	1.12387i	−0.154336	−	0.0459585i
$599$	−37.6231	−	14.7660i	−1.53724	−	0.603322i	−0.562525	−	0.826780i	$-0.690170\pi$
$599$	−37.6231	−	14.7660i	−1.53724	−	0.603322i	−0.974713	+	0.223458i	$0.928265\pi$
$600$	10.2589	−	1.85554i	0.418819	−	0.0757519i
$601$	18.8492	−	15.0317i	0.768873	−	0.613156i	−0.158472	−	0.987363i	$-0.550657\pi$
$601$	18.8492	−	15.0317i	0.768873	−	0.613156i	0.927345	+	0.374208i	$0.122085\pi$
$602$	−11.5315	−	32.8203i	−0.469987	−	1.33765i
$603$	−6.33019	−	5.04816i	−0.257785	−	0.205577i
$604$	−1.04978	+	8.02705i	−0.0427149	+	0.326616i
$605$	18.0318	+	19.4337i	0.733098	+	0.790091i
$606$	−2.46766	−	15.3517i	−0.100242	−	0.623620i
$607$	8.04470	−	13.9338i	0.326524	−	0.565557i	−0.655295	−	0.755373i	$-0.727456\pi$
$607$	8.04470	−	13.9338i	0.326524	−	0.565557i	0.981820	+	0.189816i	$0.0607892\pi$
$608$	0.0772011	−	2.97938i	0.00313092	−	0.120830i
$609$	−16.2823	+	11.8044i	−0.659791	+	0.478339i
$610$	2.44368	+	1.63130i	0.0989418	+	0.0660494i
$611$	8.00167	−	8.62375i	0.323713	−	0.348880i
$612$	−12.8012	+	10.6247i	−0.517457	+	0.429479i
$613$	−1.26958	−	0.191359i	−0.0512779	−	0.00772891i	0.123353	−	0.992363i	$-0.460635\pi$
$613$	−1.26958	−	0.191359i	−0.0512779	−	0.00772891i	−0.174631	+	0.984634i	$0.555873\pi$
$614$	−19.1914	+	9.47439i	−0.774502	+	0.382355i
$615$	−3.35029	+	14.6786i	−0.135097	+	0.591898i
$616$	−37.0058	−	0.612980i	−1.49101	−	0.0246977i
$617$	6.30244	+	27.6128i	0.253727	+	1.11165i	0.927827	+	0.373010i	$0.121674\pi$
$617$	6.30244	+	27.6128i	0.253727	+	1.11165i	−0.674101	+	0.738639i	$0.735469\pi$
$618$	52.1075	+	64.0458i	2.09607	+	2.57630i
$619$	−20.3893	−	35.3152i	−0.819513	−	1.41944i	−0.906041	−	0.423189i	$-0.860911\pi$
$619$	−20.3893	−	35.3152i	−0.819513	−	1.41944i	0.0865280	−	0.996249i	$-0.472423\pi$
$620$	0.344650	+	17.6201i	0.0138415	+	0.707642i
$621$	20.1244	+	29.5171i	0.807564	+	1.18448i
$622$	1.61588	+	2.73662i	0.0647907	+	0.109729i
$623$	24.2632	+	4.80480i	0.972086	+	0.192500i
$624$	11.4741	+	11.4348i	0.459330	+	0.457758i
$625$	−17.3311	−	5.34594i	−0.693245	−	0.213838i
$626$	−17.9253	+	19.7019i	−0.716441	+	0.787445i
$627$	−8.54236	+	0.640162i	−0.341149	+	0.0255656i
$628$	16.1068	+	5.96065i	0.642731	+	0.237856i
$629$	−0.0718072	−	0.149109i	−0.00286314	−	0.00594537i
$630$	−50.9010	−	26.8187i	−2.02795	−	1.06848i
$631$	12.6347	−	26.2362i	0.502980	−	1.04445i	−0.482695	−	0.875789i	$-0.660342\pi$
$631$	12.6347	−	26.2362i	0.502980	−	1.04445i	0.985674	−	0.168660i	$-0.0539438\pi$
$632$	23.6742	−	10.1025i	0.941710	−	0.401856i
$633$	13.7424	+	44.5518i	0.546212	+	1.77078i
$634$	−12.2346	+	8.51783i	−0.485897	+	0.338286i
$635$	−23.7486	+	3.57952i	−0.942434	+	0.142049i
$636$	10.8038	+	9.63818i	0.428397	+	0.382179i
$637$	7.70444	+	3.87295i	0.305261	+	0.153452i
$638$	15.1115	+	5.76095i	0.598271	+	0.228078i
$639$	13.4177	+	89.0208i	0.530797	+	3.52161i
$640$	−22.2815	−	0.141457i	−0.880754	−	0.00559159i
$641$	−5.50743	+	1.69882i	−0.217530	+	0.0670993i	−0.401605	−	0.915813i	$-0.631547\pi$
$641$	−5.50743	+	1.69882i	−0.217530	+	0.0670993i	0.184074	+	0.982912i	$0.441071\pi$
$642$	21.2473	−	45.2471i	0.838564	−	1.78576i
$643$	6.88143	+	3.31392i	0.271377	+	0.130688i	0.564623	−	0.825349i	$-0.309021\pi$
$643$	6.88143	+	3.31392i	0.271377	+	0.130688i	−0.293247	+	0.956037i	$0.594736\pi$
$644$	11.7763	+	2.09358i	0.464050	+	0.0824986i
$645$	−54.2345	+	26.1179i	−2.13548	+	1.02839i
$646$	0.00776235	+	0.793773i	0.000305406	+	0.0312306i
$647$	−0.772862	−	10.3131i	−0.0303844	−	0.405451i	−0.991572	−	0.129556i	$-0.958645\pi$
$647$	−0.772862	−	10.3131i	−0.0303844	−	0.405451i	0.961188	−	0.275895i	$-0.0889742\pi$
$648$	−8.38942	−	80.2706i	−0.329567	−	3.15333i
$649$	18.5287	−	60.0685i	0.727315	−	2.35790i
$650$	0.593965	+	1.86079i	0.0232972	+	0.0729861i
$651$	−23.3742	+	31.1140i	−0.916109	+	1.21945i
$652$	−1.14533	−	6.70609i	−0.0448545	−	0.262631i
$653$	8.64278	−	5.89254i	0.338218	−	0.230593i	−0.382286	−	0.924044i	$-0.624863\pi$
$653$	8.64278	−	5.89254i	0.338218	−	0.230593i	0.720504	+	0.693451i	$0.243911\pi$
$654$	−11.2006	−	27.7380i	−0.437978	−	1.08464i
$655$	21.8785	−	12.6316i	0.854864	−	0.493556i
$656$	−3.70503	+	8.53192i	−0.144657	+	0.333115i
$657$	48.7272	−	11.1217i	1.90103	−	0.433898i
$658$	−21.1817	+	28.7771i	−0.825748	+	1.12185i
$659$	37.9549	+	8.66297i	1.47851	+	0.337461i	0.884328	−	0.466866i	$-0.154617\pi$
$659$	37.9549	+	8.66297i	1.47851	+	0.337461i	0.594186	+	0.804327i	$0.297474\pi$
$660$	6.03403	+	63.7589i	0.234874	+	2.48181i
$661$	6.95859	−	46.1672i	0.270658	−	1.79570i	−0.278982	−	0.960296i	$-0.589997\pi$
$661$	6.95859	−	46.1672i	0.270658	−	1.79570i	0.549640	−	0.835401i	$-0.314765\pi$
$662$	−10.2859	−	5.80522i	−0.399774	−	0.225626i
$663$	−3.16278	−	2.93463i	−0.122832	−	0.113972i
$664$	6.25846	+	24.1337i	0.242875	+	0.936568i
$665$	−2.52550	+	1.07641i	−0.0979347	+	0.0417413i
$666$	1.69846	+	0.239041i	0.0658141	+	0.00926263i
$667$	−4.52627	−	2.61324i	−0.175258	−	0.101185i
$668$	−4.08410	+	19.6581i	−0.158018	+	0.760596i
$669$	−3.18271	+	2.95312i	−0.123051	+	0.114174i
$670$	0.670231	+	2.80955i	0.0258933	+	0.108542i
$671$	3.25293	−	4.07905i	0.125578	−	0.157470i
$672$	−38.5597	−	30.5619i	−1.48747	−	1.17895i
$673$	−20.9509	−	26.2716i	−0.807598	−	1.01270i	−0.999511	−	0.0312837i	$-0.990040\pi$
$673$	−20.9509	−	26.2716i	−0.807598	−	1.01270i	0.191913	−	0.981412i	$-0.438531\pi$
$674$	−10.2267	+	13.0843i	−0.393918	+	0.503990i
$675$	6.47388	−	16.4952i	0.249180	−	0.634899i
$676$	13.9646	−	18.2313i	0.537098	−	0.701205i
$677$	0.162376	−	0.0637278i	0.00624061	−	0.00244926i	−0.362219	−	0.932093i	$-0.617981\pi$
$677$	0.162376	−	0.0637278i	0.00624061	−	0.00244926i	0.368459	+	0.929644i	$0.379885\pi$
$678$	−7.24488	−	85.4543i	−0.278238	−	3.28185i
$679$	−10.1445	+	15.8443i	−0.389308	+	0.608047i
$680$	5.93215	−	0.174077i	0.227488	−	0.00667555i
$681$	−0.891967	+	11.9025i	−0.0341802	+	0.456104i
$682$	31.2281	+	2.03335i	1.19579	+	0.0778611i
$683$	13.5029	−	19.8051i	0.516673	−	0.757820i	−0.475897	−	0.879501i	$-0.657876\pi$
$683$	13.5029	−	19.8051i	0.516673	−	0.757820i	0.992569	+	0.121682i	$0.0388287\pi$
$684$	−6.88674	−	4.50058i	−0.263321	−	0.172084i
$685$			5.61092i			0.214382i
$686$	−24.5828	−	9.03806i	−0.938575	−	0.345075i
$687$		−	20.6585i		−	0.788172i
$688$	−35.9052	+	9.68681i	−1.36887	+	0.369306i
$689$	−1.52806	+	2.24125i	−0.0582145	+	0.0853850i
$690$	1.34481	−	20.6535i	0.0511959	−	0.786265i
$691$	−0.135141	+	1.80334i	−0.00514102	+	0.0686021i	−0.999184	−	0.0403848i	$-0.987142\pi$
$691$	−0.135141	+	1.80334i	−0.00514102	+	0.0686021i	0.994043	+	0.108987i	$0.0347607\pi$
$692$	6.12314	−	2.54244i	0.232767	−	0.0966491i
$693$	−55.0876	+	86.0394i	−2.09261	+	3.26837i
$694$	28.6917	−	2.43251i	1.08912	−	0.0923368i
$695$	−9.91335	+	3.89070i	−0.376035	+	0.147583i
$696$	11.2914	+	18.2959i	0.427998	+	0.693506i
$697$	0.905117	−	2.30620i	0.0342838	−	0.0873536i
$698$	−9.45281	−	7.38831i	−0.357794	−	0.279652i
$699$	−39.3293	−	49.3174i	−1.48757	−	1.86536i
$700$	−2.43249	−	5.41126i	−0.0919393	−	0.204526i
$701$	−19.1596	+	24.0253i	−0.723647	+	0.907424i	−0.998538	−	0.0540510i	$-0.982787\pi$
$701$	−19.1596	+	24.0253i	−0.723647	+	0.907424i	0.274891	+	0.961475i	$0.411358\pi$
$702$	26.7821	−	6.38900i	1.01082	−	0.241137i
$703$	0.0599956	−	0.0556678i	0.00226278	−	0.00209955i
$704$	−3.59270	+	39.4029i	−0.135405	+	1.48505i
$705$	53.5472	+	30.9155i	2.01671	+	1.16435i
$706$	−4.30434	+	30.5838i	−0.161996	+	1.15104i
$707$	−8.13993	+	3.46936i	−0.306134	+	0.130479i
$708$	68.1133	−	48.4169i	2.55986	−	1.81962i
$709$	24.5814	+	22.8082i	0.923174	+	0.856581i	0.989983	−	0.141185i	$-0.0450913\pi$
$709$	24.5814	+	22.8082i	0.923174	+	0.856581i	−0.0668089	+	0.997766i	$0.521282\pi$
$710$	15.7852	−	27.9689i	0.592410	−	1.04966i
$711$	10.5896	−	70.2573i	0.397140	−	2.63485i
$712$	7.04947	−	25.4852i	0.264190	−	0.955098i
$713$	−9.85989	−	2.25046i	−0.369256	−	0.0842802i
$714$	10.5541	+	7.76843i	0.394977	+	0.290726i
$715$	−11.6983	+	2.67006i	−0.437492	+	0.0998547i
$716$	−2.18453	−	6.61960i	−0.0816399	−	0.247386i
$717$	14.2171	−	8.20825i	0.530948	−	0.306543i
$718$	−30.2303	+	12.2070i	−1.12818	+	0.455561i
$719$	−15.2549	+	10.4006i	−0.568911	+	0.387877i	−0.813339	−	0.581791i	$-0.802352\pi$
$719$	−15.2549	+	10.4006i	−0.568911	+	0.387877i	0.244428	+	0.969668i	$0.421400\pi$
$720$	−32.6340	+	52.1350i	−1.21620	+	1.94296i
$721$	28.2216	−	37.5665i	1.05103	−	1.39905i
$722$	25.2237	−	8.05142i	0.938727	−	0.299643i
$723$	−10.4237	+	33.7928i	−0.387661	+	1.25677i
$724$	11.0304	+	21.8036i	0.409943	+	0.810324i
$725$	0.193733	+	2.58519i	0.00719507	+	0.0960115i
$726$	62.5790	−	0.611964i	2.32252	−	0.0227121i
$727$	36.3515	−	17.5060i	1.34820	−	0.649260i	0.386229	−	0.922403i	$-0.373777\pi$
$727$	36.3515	−	17.5060i	1.34820	−	0.649260i	0.961974	+	0.273143i	$0.0880631\pi$
$728$	4.74084	−	7.90602i	0.175707	−	0.293017i
$729$	−60.2859	−	29.0321i	−2.23281	−	1.07526i
$730$	−16.1391	−	7.57868i	−0.597336	−	0.280500i
$731$	9.46507	−	2.91959i	0.350078	−	0.107985i
$732$	6.73053	−	1.67533i	0.248767	−	0.0619219i
$733$	3.19234	+	21.1798i	0.117912	+	0.782292i	0.967136	+	0.254260i	$0.0818319\pi$
$733$	3.19234	+	21.1798i	0.117912	+	0.782292i	−0.849224	+	0.528032i	$0.822930\pi$
$734$	−18.9956	+	49.8274i	−0.701142	+	1.83916i
$735$	−10.8347	+	44.0079i	−0.399644	+	1.62326i
$736$	3.16728	−	12.3883i	0.116748	−	0.456639i
$737$	5.07165	−	0.764428i	0.186817	−	0.0281581i
$738$	14.6706	+	21.0721i	0.540031	+	0.775673i
$739$	−0.228438	−	0.740579i	−0.00840325	−	0.0272427i	0.951274	−	0.308347i	$-0.0997756\pi$
$739$	−0.228438	−	0.740579i	−0.00840325	−	0.0272427i	−0.959677	+	0.281104i	$0.909299\pi$
$740$	−0.424877	−	0.440316i	−0.0156188	−	0.0161863i
$741$	0.925760	−	1.92236i	0.0340086	−	0.0706197i
$742$	3.84058	−	7.28929i	0.140992	−	0.267598i
$743$	1.75367	+	3.64153i	0.0643359	+	0.133595i	0.930657	−	0.365892i	$-0.119236\pi$
$743$	1.75367	+	3.64153i	0.0643359	+	0.133595i	−0.866321	+	0.499487i	$0.833522\pi$
$744$	31.3138	+	27.3903i	1.14802	+	1.00418i
$745$	38.8572	−	2.91195i	1.42362	−	0.106685i
$746$	29.3396	+	26.6940i	1.07420	+	0.977337i
$747$	65.7638	+	20.2854i	2.40617	+	0.742206i
$748$	0.581865	−	10.5222i	0.0212751	−	0.384731i
$749$	−27.9049	−	5.52595i	−1.01962	−	0.201914i
$750$	−48.2629	+	28.4975i	−1.76231	+	1.04058i
$751$	4.91873	+	7.21446i	0.179487	+	0.263259i	0.905430	−	0.424496i	$-0.139549\pi$
$751$	4.91873	+	7.21446i	0.179487	+	0.263259i	−0.725943	+	0.687755i	$0.758596\pi$
$752$	28.9967	+	24.8672i	1.05740	+	0.906814i
$753$	−14.3454	−	24.8470i	−0.522777	−	0.905476i
$754$	−3.12462	+	2.54219i	−0.113792	+	0.0925810i
$755$	−1.77389	−	7.77194i	−0.0645586	−	0.282850i
$756$	−78.6265	+	28.4923i	−2.85962	+	1.03626i
$757$	2.17827	−	9.54363i	0.0791706	−	0.346869i	−0.919792	−	0.392406i	$-0.871643\pi$
$757$	2.17827	−	9.54363i	0.0791706	−	0.346869i	0.998963	+	0.0455371i	$0.0144999\pi$
$758$	−4.12723	−	8.36016i	−0.149908	−	0.303655i
$759$	−36.3418	−	5.47764i	−1.31912	−	0.198826i
$760$	0.946958	+	2.77791i	0.0343498	+	0.100765i
$761$	8.32067	−	8.96754i	0.301624	−	0.325073i	−0.563994	−	0.825779i	$-0.690736\pi$
$761$	8.32067	−	8.96754i	0.301624	−	0.325073i	0.865617	+	0.500706i	$0.166926\pi$
$762$	−31.4778	+	47.1537i	−1.14032	+	1.70820i
$763$	−13.7824	+	9.99207i	−0.498957	+	0.361737i
$764$	−31.7459	−	17.5098i	−1.14853	−	0.633483i
$765$	8.19099	−	14.1872i	0.296146	−	0.512940i
$766$	−20.7948	+	3.34259i	−0.751345	+	0.120773i
$767$	10.6496	+	11.4775i	0.384535	+ <

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.301195 - 1.38177i) q^{2} +(2.71624 + 1.85190i) q^{3} +(-1.81856 - 0.832362i) q^{4} +(1.96396 + 0.147178i) q^{5} +(3.37701 - 3.19543i) q^{6} +(-2.22818 - 1.42661i) q^{7} +(-1.69787 + 2.26213i) q^{8} +(2.85240 + 7.26780i) q^{9} +O(q^{10})\)	\(q+(0.301195 - 1.38177i) q^{2} +(2.71624 + 1.85190i) q^{3} +(-1.81856 - 0.832362i) q^{4} +(1.96396 + 0.147178i) q^{5} +(3.37701 - 3.19543i) q^{6} +(-2.22818 - 1.42661i) q^{7} +(-1.69787 + 2.26213i) q^{8} +(2.85240 + 7.26780i) q^{9} +(0.794901 - 2.66941i) q^{10} +(-4.60391 - 1.80690i) q^{11} +(-3.39820 - 5.62870i) q^{12} +(0.963118 - 0.768061i) q^{13} +(-2.64236 + 2.64913i) q^{14} +(5.06202 + 4.03683i) q^{15} +(2.61435 + 3.02741i) q^{16} +(-0.724645 - 0.780981i) q^{17} +(10.9015 - 1.75233i) q^{18} +(0.263430 - 0.456275i) q^{19} +(-3.44908 - 1.90238i) q^{20} +(-3.41032 - 8.00139i) q^{21} +(-3.88339 + 5.81730i) q^{22} +(1.53746 - 1.65699i) q^{23} +(-8.80107 + 3.00019i) q^{24} +(-1.10868 - 0.167107i) q^{25} +(-0.771196 - 1.56214i) q^{26} +(-3.51684 + 15.4083i) q^{27} +(2.86462 + 4.44904i) q^{28} +(-0.514512 - 2.25422i) q^{29} +(7.10262 - 5.77867i) q^{30} +(-2.23709 - 3.87476i) q^{31} +(4.97060 - 2.70058i) q^{32} +(-9.15911 - 13.4340i) q^{33} +(-1.29739 + 0.766063i) q^{34} +(-4.16608 - 3.12975i) q^{35} +(0.862170 - 15.5912i) q^{36} +(0.148440 + 0.0457878i) q^{37} +(-0.551122 - 0.501427i) q^{38} +(4.03843 - 0.302639i) q^{39} +(-3.66749 + 4.19284i) q^{40} +(1.00896 + 2.09513i) q^{41} +(-12.0832 + 2.30229i) q^{42} +(-4.03392 + 8.37653i) q^{43} +(6.86850 + 7.11808i) q^{44} +(4.53233 + 14.6935i) q^{45} +(-1.82650 - 2.62350i) q^{46} +(9.44316 - 1.42333i) q^{47} +(1.49473 + 13.0647i) q^{48} +(2.92955 + 6.35750i) q^{49} +(-0.564831 + 1.48161i) q^{50} +(-0.522009 - 3.46330i) q^{51} +(-2.39080 + 0.595104i) q^{52} +(-2.10418 + 0.649054i) q^{53} +(20.2314 + 9.50035i) q^{54} +(-8.77595 - 4.22627i) q^{55} +(7.01035 - 2.61821i) q^{56} +(1.56052 - 0.751505i) q^{57} +(-3.26978 + 0.0319754i) q^{58} +(0.949824 + 12.6745i) q^{59} +(-5.84551 - 11.5547i) q^{60} +(-0.310936 + 1.00803i) q^{61} +(-6.02781 + 1.92408i) q^{62} +(4.01269 - 20.2632i) q^{63} +(-2.23445 - 7.68162i) q^{64} +(2.00457 - 1.36669i) q^{65} +(-21.3213 + 8.60953i) q^{66} +(-0.898095 + 0.518515i) q^{67} +(0.667753 + 2.02343i) q^{68} +(7.24471 - 1.65356i) q^{69} +(-5.57939 + 4.81389i) q^{70} +(11.2417 + 2.56583i) q^{71} +(-21.2837 - 5.88730i) q^{72} +(0.954106 - 6.33008i) q^{73} +(0.107978 - 0.191319i) q^{74} +(-2.70198 - 2.50707i) q^{75} +(-0.858851 + 0.610495i) q^{76} +(7.68057 + 10.5941i) q^{77} +(0.798179 - 5.67133i) q^{78} +(-7.88112 - 4.55017i) q^{79} +(4.68890 + 6.33048i) q^{80} +(-20.9173 + 19.4084i) q^{81} +(3.19887 - 0.763107i) q^{82} +(5.49592 - 6.89167i) q^{83} +(-0.458178 + 17.3897i) q^{84} +(-1.30823 - 1.64047i) q^{85} +(10.3594 + 8.09691i) q^{86} +(2.77706 - 7.07583i) q^{87} +(11.9043 - 7.34674i) q^{88} +(-8.70248 + 3.41547i) q^{89} +(21.6681 - 1.83704i) q^{90} +(-3.24172 + 0.337379i) q^{91} +(-4.17519 + 1.73362i) q^{92} +(1.09919 - 14.6676i) q^{93} +(0.877523 - 13.4769i) q^{94} +(0.584520 - 0.857334i) q^{95} +(18.5026 + 1.86964i) q^{96} -7.11086i q^{97} +(9.66695 - 2.13311i) q^{98} -38.6142i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

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