LMFDB - Embedded newform 196.2.p.a.103.26

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			103.26
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41415 - 0.0137562i) q^{2} +(-1.25831 - 0.857901i) q^{3} +(1.99962 - 0.0389066i) q^{4} +(-0.263482 - 0.0197452i) q^{5} +(-1.79123 - 1.19589i) q^{6} +(2.03749 - 1.68779i) q^{7} +(2.82722 - 0.0825269i) q^{8} +(-0.248675 - 0.633613i) q^{9} +O(q^{10})$	\(q+(1.41415 - 0.0137562i) q^{2} +(-1.25831 - 0.857901i) q^{3} +(1.99962 - 0.0389066i) q^{4} +(-0.263482 - 0.0197452i) q^{5} +(-1.79123 - 1.19589i) q^{6} +(2.03749 - 1.68779i) q^{7} +(2.82722 - 0.0825269i) q^{8} +(-0.248675 - 0.633613i) q^{9} +(-0.372873 - 0.0242981i) q^{10} +(1.57812 + 0.619368i) q^{11} +(-2.54952 - 1.66652i) q^{12} +(-2.83949 + 2.26441i) q^{13} +(2.85809 - 2.41481i) q^{14} +(0.314602 + 0.250887i) q^{15} +(3.99697 - 0.155597i) q^{16} +(0.766969 + 0.826596i) q^{17} +(-0.360379 - 0.892601i) q^{18} +(-0.734495 + 1.27218i) q^{19} +(-0.527632 - 0.0292318i) q^{20} +(-4.01175 + 0.375802i) q^{21} +(2.24022 + 0.854168i) q^{22} +(-2.17000 + 2.33870i) q^{23} +(-3.62832 - 2.32163i) q^{24} +(-4.87512 - 0.734806i) q^{25} +(-3.98430 + 3.24127i) q^{26} +(-1.24732 + 5.46488i) q^{27} +(4.00854 - 3.45422i) q^{28} +(1.25645 + 5.50485i) q^{29} +(0.448345 + 0.350463i) q^{30} +(-2.89828 - 5.01997i) q^{31} +(5.65016 - 0.275020i) q^{32} +(-1.45441 - 2.13323i) q^{33} +(1.09598 + 1.15838i) q^{34} +(-0.570167 + 0.404472i) q^{35} +(-0.521908 - 1.25731i) q^{36} +(-2.55647 - 0.788567i) q^{37} +(-1.02118 + 1.80916i) q^{38} +(5.51559 - 0.413337i) q^{39} +(-0.746551 - 0.0340798i) q^{40} +(2.59789 + 5.39457i) q^{41} +(-5.66803 + 0.586626i) q^{42} +(-4.36671 + 9.06756i) q^{43} +(3.17975 + 1.17710i) q^{44} +(0.0530105 + 0.171856i) q^{45} +(-3.03652 + 3.33711i) q^{46} +(5.64667 - 0.851098i) q^{47} +(-5.16291 - 3.23322i) q^{48} +(1.30271 - 6.87771i) q^{49} +(-6.90424 - 0.972061i) q^{50} +(-0.255947 - 1.69810i) q^{51} +(-5.58980 + 4.63845i) q^{52} +(-0.0663065 + 0.0204529i) q^{53} +(-1.68872 + 7.74530i) q^{54} +(-0.403577 - 0.194353i) q^{55} +(5.62114 - 4.93991i) q^{56} +(2.01563 - 0.970675i) q^{57} +(1.85253 + 7.76738i) q^{58} +(-0.838464 - 11.1885i) q^{59} +(0.638846 + 0.489438i) q^{60} +(0.0587480 - 0.190456i) q^{61} +(-4.16765 - 7.05911i) q^{62} +(-1.57608 - 0.871268i) q^{63} +(7.98638 - 0.466644i) q^{64} +(0.792864 - 0.540566i) q^{65} +(-2.08610 - 2.99669i) q^{66} +(12.8699 - 7.43043i) q^{67} +(1.56581 + 1.62304i) q^{68} +(4.73690 - 1.08117i) q^{69} +(-0.800735 + 0.579826i) q^{70} +(-3.45509 - 0.788602i) q^{71} +(-0.755350 - 1.77084i) q^{72} +(0.419429 - 2.78273i) q^{73} +(-3.62608 - 1.07998i) q^{74} +(5.50402 + 5.10698i) q^{75} +(-1.41922 + 2.57246i) q^{76} +(4.26077 - 1.40159i) q^{77} +(7.79417 - 0.660392i) q^{78} +(-13.0282 - 7.52182i) q^{79} +(-1.05620 - 0.0379242i) q^{80} +(4.76095 - 4.41752i) q^{81} +(3.74800 + 7.59297i) q^{82} +(-3.20201 + 4.01519i) q^{83} +(-8.00735 + 0.907546i) q^{84} +(-0.185761 - 0.232937i) q^{85} +(-6.05043 + 12.8829i) q^{86} +(3.14162 - 8.00471i) q^{87} +(4.51282 + 1.62085i) q^{88} +(16.7269 - 6.56481i) q^{89} +(0.0773287 + 0.242300i) q^{90} +(-1.96356 + 9.40618i) q^{91} +(-4.24818 + 4.76094i) q^{92} +(-0.659702 + 8.80311i) q^{93} +(7.97351 - 1.28125i) q^{94} +(0.218646 - 0.320694i) q^{95} +(-7.34559 - 4.50122i) q^{96} -7.85046i q^{97} +(1.74762 - 9.74402i) q^{98} -1.15394i 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 $

$2$	1.41415	−	0.0137562i	0.999953	−	0.00972712i
$2$	1.41415	−	0.0137562i	0.999953	−	0.00972712i
$3$	−1.25831	−	0.857901i	−0.726485	−	0.495309i	0.142719	−	0.989763i	$-0.454416\pi$
$3$	−1.25831	−	0.857901i	−0.726485	−	0.495309i	−0.869204	+	0.494454i	$0.835368\pi$
$4$	1.99962	−	0.0389066i	0.999811	−	0.0194533i
$5$	−0.263482	−	0.0197452i	−0.117833	−	0.00883034i	0.0156832	−	0.999877i	$-0.495008\pi$
$5$	−0.263482	−	0.0197452i	−0.117833	−	0.00883034i	−0.133516	+	0.991047i	$0.542627\pi$
$6$	−1.79123	−	1.19589i	−0.731269	−	0.488219i
$7$	2.03749	−	1.68779i	0.770098	−	0.637926i
$7$	2.03749	−	1.68779i	0.770098	−	0.637926i
$8$	2.82722	−	0.0825269i	0.999574	−	0.0291777i
$9$	−0.248675	−	0.633613i	−0.0828916	−	0.211204i
$10$	−0.372873	−	0.0242981i	−0.117913	−	0.00768375i
$11$	1.57812	+	0.619368i	0.475822	+	0.186747i	0.591119	−	0.806585i	$-0.298686\pi$
$11$	1.57812	+	0.619368i	0.475822	+	0.186747i	−0.115296	+	0.993331i	$0.536782\pi$
$12$	−2.54952	−	1.66652i	−0.735983	−	0.481083i
$13$	−2.83949	+	2.26441i	−0.787532	+	0.628036i	−0.932405	−	0.361415i	$-0.882294\pi$
$13$	−2.83949	+	2.26441i	−0.787532	+	0.628036i	0.144874	+	0.989450i	$0.453722\pi$
$14$	2.85809	−	2.41481i	0.763856	−	0.645386i
$15$	0.314602	+	0.250887i	0.0812299	+	0.0647787i
$16$	3.99697	−	0.155597i	0.999243	−	0.0388993i
$17$	0.766969	+	0.826596i	0.186017	+	0.200479i	0.819175	−	0.573544i	$-0.194432\pi$
$17$	0.766969	+	0.826596i	0.186017	+	0.200479i	−0.633157	+	0.774023i	$0.718241\pi$
$18$	−0.360379	−	0.892601i	−0.0849421	−	0.210388i
$19$	−0.734495	+	1.27218i	−0.168505	+	0.291859i	−0.937894	−	0.346921i	$-0.887227\pi$
$19$	−0.734495	+	1.27218i	−0.168505	+	0.291859i	0.769390	+	0.638780i	$0.220561\pi$
$20$	−0.527632	−	0.0292318i	−0.117982	−	0.00653643i
$21$	−4.01175	+	0.375802i	−0.875435	+	0.0820068i
$22$	2.24022	+	0.854168i	0.477616	+	0.182109i
$23$	−2.17000	+	2.33870i	−0.452475	+	0.487652i	−0.917551	−	0.397619i	$-0.869837\pi$
$23$	−2.17000	+	2.33870i	−0.452475	+	0.487652i	0.465075	+	0.885271i	$0.346027\pi$
$24$	−3.62832	−	2.32163i	−0.740628	−	0.473901i
$25$	−4.87512	−	0.734806i	−0.975024	−	0.146961i
$26$	−3.98430	+	3.24127i	−0.781385	+	0.635666i
$27$	−1.24732	+	5.46488i	−0.240047	+	1.05172i
$28$	4.00854	−	3.45422i	0.757543	−	0.652786i
$29$	1.25645	+	5.50485i	0.233316	+	1.02223i	0.946868	+	0.321623i	$0.104228\pi$
$29$	1.25645	+	5.50485i	0.233316	+	1.02223i	−0.713552	+	0.700603i	$0.752915\pi$
$30$	0.448345	+	0.350463i	0.0818562	+	0.0639855i
$31$	−2.89828	−	5.01997i	−0.520547	−	0.901614i	−0.999715	−	0.0238903i	$-0.992395\pi$
$31$	−2.89828	−	5.01997i	−0.520547	−	0.901614i	0.479168	−	0.877723i	$-0.340939\pi$
$32$	5.65016	−	0.275020i	0.998817	−	0.0486172i
$33$	−1.45441	−	2.13323i	−0.253181	−	0.371348i
$34$	1.09598	+	1.15838i	0.187959	+	0.198660i
$35$	−0.570167	+	0.404472i	−0.0963758	+	0.0683682i
$36$	−0.521908	−	1.25731i	−0.0869846	−	0.209552i
$37$	−2.55647	−	0.788567i	−0.420282	−	0.129640i	0.0773988	−	0.997000i	$-0.475339\pi$
$37$	−2.55647	−	0.788567i	−0.420282	−	0.129640i	−0.497680	+	0.867361i	$0.665815\pi$
$38$	−1.02118	+	1.80916i	−0.165658	+	0.293484i
$39$	5.51559	−	0.413337i	0.883202	−	0.0661868i
$40$	−0.746551	−	0.0340798i	−0.118040	−	0.00538849i
$41$	2.59789	+	5.39457i	0.405722	+	0.842490i	0.999289	+	0.0377054i	$0.0120049\pi$
$41$	2.59789	+	5.39457i	0.405722	+	0.842490i	−0.593567	+	0.804784i	$0.702281\pi$
$42$	−5.66803	+	0.586626i	−0.874596	+	0.0905183i
$43$	−4.36671	+	9.06756i	−0.665917	+	1.38279i	0.244724	+	0.969593i	$0.421302\pi$
$43$	−4.36671	+	9.06756i	−0.665917	+	1.38279i	−0.910641	+	0.413198i	$0.864412\pi$
$44$	3.17975	+	1.17710i	0.479365	+	0.177455i
$45$	0.0530105	+	0.171856i	0.00790233	+	0.0256187i
$46$	−3.03652	+	3.33711i	−0.447710	+	0.492031i
$47$	5.64667	−	0.851098i	0.823651	−	0.124145i	0.276324	−	0.961064i	$-0.410884\pi$
$47$	5.64667	−	0.851098i	0.823651	−	0.124145i	0.547327	+	0.836919i	$0.315646\pi$
$48$	−5.16291	−	3.23322i	−0.745202	−	0.466674i
$49$	1.30271	−	6.87771i	0.186102	−	0.982530i
$50$	−6.90424	−	0.972061i	−0.976408	−	0.137470i
$51$	−0.255947	−	1.69810i	−0.0358397	−	0.237781i
$52$	−5.58980	+	4.63845i	−0.775165	+	0.643237i
$53$	−0.0663065	+	0.0204529i	−0.00910790	+	0.00280942i	−0.299306	−	0.954157i	$-0.596755\pi$
$53$	−0.0663065	+	0.0204529i	−0.00910790	+	0.00280942i	0.290198	+	0.956967i	$0.406279\pi$
$54$	−1.68872	+	7.74530i	−0.229806	+	1.05400i
$55$	−0.403577	−	0.194353i	−0.0544184	−	0.0262065i
$56$	5.62114	−	4.93991i	0.751157	−	0.660124i
$57$	2.01563	−	0.970675i	0.266976	−	0.128569i
$58$	1.85253	+	7.76738i	0.243249	+	1.01991i
$59$	−0.838464	−	11.1885i	−0.109159	−	1.45662i	−0.735739	−	0.677265i	$-0.763165\pi$
$59$	−0.838464	−	11.1885i	−0.109159	−	1.45662i	0.626580	−	0.779357i	$-0.284454\pi$
$60$	0.638846	+	0.489438i	0.0824747	+	0.0631862i
$61$	0.0587480	−	0.190456i	0.00752192	−	0.0243855i	−0.951734	−	0.306924i	$-0.900700\pi$
$61$	0.0587480	−	0.190456i	0.00752192	−	0.0243855i	0.959256	+	0.282538i	$0.0911765\pi$
$62$	−4.16765	−	7.05911i	−0.529292	−	0.896508i
$63$	−1.57608	−	0.871268i	−0.198567	−	0.109769i
$64$	7.98638	−	0.466644i	0.998297	−	0.0583305i
$65$	0.792864	−	0.540566i	0.0983427	−	0.0670489i
$66$	−2.08610	−	2.99669i	−0.256781	−	0.368867i
$67$	12.8699	−	7.43043i	1.57231	−	0.907772i	0.576421	−	0.817153i	$-0.304449\pi$
$67$	12.8699	−	7.43043i	1.57231	−	0.907772i	0.995886	−	0.0906187i	$-0.0288844\pi$
$68$	1.56581	+	1.62304i	0.189882	+	0.196822i
$69$	4.73690	−	1.08117i	0.570255	−	0.130157i
$70$	−0.800735	+	0.579826i	−0.0957062	+	0.0693024i
$71$	−3.45509	−	0.788602i	−0.410044	−	0.0935898i	0.0125231	−	0.999922i	$-0.496014\pi$
$71$	−3.45509	−	0.788602i	−0.410044	−	0.0935898i	−0.422567	+	0.906332i	$0.638871\pi$
$72$	−0.755350	−	1.77084i	−0.0890188	−	0.208696i
$73$	0.419429	−	2.78273i	0.0490904	−	0.325694i	−0.950784	−	0.309854i	$-0.899720\pi$
$73$	0.419429	−	2.78273i	0.0490904	−	0.325694i	0.999875	−	0.0158397i	$-0.00504213\pi$
$74$	−3.62608	−	1.07998i	−0.421523	−	0.125545i
$75$	5.50402	+	5.10698i	0.635549	+	0.589704i
$76$	−1.41922	+	2.57246i	−0.162795	+	0.295082i
$77$	4.26077	−	1.40159i	0.485560	−	0.159726i
$78$	7.79417	−	0.660392i	0.882516	−	0.0747747i
$79$	−13.0282	−	7.52182i	−1.46578	−	0.846271i	−0.466516	−	0.884513i	$-0.654491\pi$
$79$	−13.0282	−	7.52182i	−1.46578	−	0.846271i	−0.999269	+	0.0382418i	$0.987824\pi$
$80$	−1.05620	−	0.0379242i	−0.118087	−	0.00424005i
$81$	4.76095	−	4.41752i	0.528995	−	0.490835i
$82$	3.74800	+	7.59297i	0.413898	+	0.838504i
$83$	−3.20201	+	4.01519i	−0.351466	+	0.440725i	−0.925867	−	0.377850i	$-0.876664\pi$
$83$	−3.20201	+	4.01519i	−0.351466	+	0.440725i	0.574401	+	0.818574i	$0.305235\pi$
$84$	−8.00735	+	0.907546i	−0.873674	+	0.0990213i
$85$	−0.185761	−	0.232937i	−0.0201486	−	0.0252656i
$86$	−6.05043	+	12.8829i	−0.652435	+	1.38920i
$87$	3.14162	−	8.00471i	0.336817	−	0.858195i
$88$	4.51282	+	1.62085i	0.481069	+	0.172784i
$89$	16.7269	−	6.56481i	1.77304	−	0.695868i	0.775094	−	0.631846i	$-0.217702\pi$
$89$	16.7269	−	6.56481i	1.77304	−	0.695868i	0.997948	−	0.0640224i	$-0.0203929\pi$
$90$	0.0773287	+	0.242300i	0.00815116	+	0.0255407i
$91$	−1.96356	+	9.40618i	−0.205837	+	0.986036i
$92$	−4.24818	+	4.76094i	−0.442903	+	0.496362i
$93$	−0.659702	+	8.80311i	−0.0684079	+	0.912840i
$94$	7.97351	−	1.28125i	0.822404	−	0.132151i
$95$	0.218646	−	0.320694i	0.0224326	−	0.0329025i
$96$	−7.34559	−	4.50122i	−0.749706	−	0.459404i
$97$		−	7.85046i		−	0.797093i	−0.917148	−	0.398547i	$-0.869515\pi$
$97$		−	7.85046i		−	0.797093i	0.917148	−	0.398547i	$-0.130485\pi$
$98$	1.74762	−	9.74402i	0.176536	−	0.984294i
$99$		−	1.15394i		−	0.115976i
$100$	−9.77699	−	1.27966i	−0.977699	−	0.127966i
$101$	−5.91976	+	8.68269i	−0.589038	+	0.863960i	−0.998837	−	0.0482161i	$-0.984646\pi$
$101$	−5.91976	+	8.68269i	−0.589038	+	0.863960i	0.409799	+	0.912176i	$0.365599\pi$
$102$	−0.385306	−	2.39784i	−0.0381510	−	0.237421i
$103$	−1.09066	+	14.5538i	−0.107465	+	1.43403i	0.639309	+	0.768950i	$0.279221\pi$
$103$	−1.09066	+	14.5538i	−0.107465	+	1.43403i	−0.746774	+	0.665077i	$0.768399\pi$
$104$	−7.84098	+	6.63634i	−0.768872	+	0.650747i
$105$	1.06444	−	0.0198041i	0.103879	−	0.00193269i
$106$	−0.0934858	+	0.0298355i	−0.00908014	+	0.00289788i
$107$	−12.6495	+	4.96456i	−1.22287	+	0.479942i	−0.886914	−	0.461934i	$-0.847156\pi$
$107$	−12.6495	+	4.96456i	−1.22287	+	0.479942i	−0.335959	+	0.941877i	$0.609060\pi$
$108$	−2.28155	+	10.9762i	−0.219543	+	1.05619i
$109$	0.785682	−	2.00188i	0.0752547	−	0.191746i	−0.888296	−	0.459271i	$-0.848111\pi$
$109$	0.785682	−	2.00188i	0.0752547	−	0.191746i	0.963551	+	0.267525i	$0.0862059\pi$
$110$	−0.573391	−	0.269291i	−0.0546707	−	0.0256759i
$111$	2.54032	+	3.18546i	0.241117	+	0.302351i
$112$	7.88117	−	7.06309i	0.744700	−	0.667399i
$113$	5.55898	−	6.97074i	0.522945	−	0.655752i	−0.448287	−	0.893890i	$-0.647966\pi$
$113$	5.55898	−	6.97074i	0.522945	−	0.655752i	0.971231	+	0.238138i	$0.0765370\pi$
$114$	2.83704	−	1.40040i	0.265713	−	0.131160i
$115$	0.617932	−	0.573357i	0.0576225	−	0.0534659i
$116$	2.72659	+	10.9587i	0.253158	+	1.01749i
$117$	2.14087	+	1.23603i	0.197924	+	0.114271i
$118$	−1.33962	−	15.8107i	−0.123322	−	1.45549i
$119$	2.95781	+	0.389695i	0.271142	+	0.0357233i
$120$	0.910155	+	0.683350i	0.0830854	+	0.0623810i
$121$	−5.95671	−	5.52702i	−0.541519	−	0.502456i
$122$	0.0804584	−	0.270142i	0.00728436	−	0.0244575i
$123$	1.35906	−	9.01676i	0.122542	−	0.813014i
$124$	−5.99078	−	9.92528i	−0.537988	−	0.891317i
$125$	2.55798	+	0.583842i	0.228792	+	0.0522204i
$126$	−2.24079	−	1.21042i	−0.199626	−	0.107833i
$127$	−2.54858	+	0.581696i	−0.226150	+	0.0516172i	−0.334094	−	0.942540i	$-0.608430\pi$
$127$	−2.54858	+	0.581696i	−0.226150	+	0.0516172i	0.107944	+	0.994157i	$0.465573\pi$
$128$	11.2875	−	0.769765i	0.997683	−	0.0680383i
$129$	13.2737	−	7.66360i	1.16869	−	0.674742i
$130$	1.11379	−	0.775346i	0.0976859	−	0.0680023i
$131$	13.9469	−	9.50885i	1.21855	−	0.830792i	0.228780	−	0.973478i	$-0.426526\pi$
$131$	13.9469	−	9.50885i	1.21855	−	0.830792i	0.989768	+	0.142686i	$0.0455741\pi$
$132$	−2.99127	−	4.20907i	−0.260357	−	0.366352i
$133$	0.650655	+	3.83173i	0.0564190	+	0.332253i
$134$	18.0977	−	10.6848i	1.56340	−	0.923023i
$135$	0.436552	−	1.41527i	0.0375724	−	0.121807i
$136$	2.23661	+	2.27368i	0.191788	+	0.194966i
$137$	0.792228	+	10.5716i	0.0676846	+	0.903189i	0.922931	+	0.384966i	$0.125787\pi$
$137$	0.792228	+	10.5716i	0.0676846	+	0.903189i	−0.855246	+	0.518222i	$0.826594\pi$
$138$	6.68379	−	1.59409i	0.568962	−	0.135698i
$139$	8.84674	−	4.26036i	0.750370	−	0.361359i	−0.0192890	−	0.999814i	$-0.506140\pi$
$139$	8.84674	−	4.26036i	0.750370	−	0.361359i	0.769660	+	0.638455i	$0.220426\pi$
$140$	−1.12438	+	0.830974i	−0.0950276	+	0.0702301i
$141$	−7.83541	−	3.77333i	−0.659860	−	0.317772i
$142$	−4.89685	−	1.06767i	−0.410935	−	0.0895968i
$143$	−5.88357	+	1.81484i	−0.492009	+	0.151765i
$144$	−1.09254	−	2.49384i	−0.0910446	−	0.207820i
$145$	−0.222356	−	1.47524i	−0.0184657	−	0.122512i
$146$	0.554854	−	3.94096i	0.0459201	−	0.326156i
$147$	−7.53961	+	7.53669i	−0.621857	+	0.621616i
$148$	−5.14266	−	1.47737i	−0.422724	−	0.121439i
$149$	14.8661	−	2.24071i	1.21788	−	0.183566i	0.491511	−	0.870871i	$-0.336445\pi$
$149$	14.8661	−	2.24071i	1.21788	−	0.183566i	0.726368	+	0.687306i	$0.241207\pi$
$150$	7.85374	+	7.14631i	0.641255	+	0.583494i
$151$	0.285261	+	0.924792i	0.0232142	+	0.0752585i	0.966439	−	0.256897i	$-0.0827002\pi$
$151$	0.285261	+	0.924792i	0.0232142	+	0.0752585i	−0.943225	+	0.332156i	$0.892224\pi$
$152$	−1.97159	+	3.65736i	−0.159917	+	0.296651i
$153$	0.333016	−	0.691516i	0.0269228	−	0.0559057i
$154$	6.00608	−	2.04067i	0.483984	−	0.164442i
$155$	0.664524	+	1.37990i	0.0533759	+	0.110836i
$156$	11.0130	−	1.04111i	0.881747	−	0.0833555i
$157$	−21.4307	+	1.60601i	−1.71036	+	0.128173i	−0.893616	−	0.448833i	$-0.851840\pi$
$157$	−21.4307	+	1.60601i	−1.71036	+	0.128173i	−0.816740	+	0.577006i	$0.804221\pi$
$158$	−18.5272	−	10.4577i	−1.47395	−	0.831973i
$159$	0.100981	+	0.0311484i	0.00800828	+	0.00247023i
$160$	−1.49415	−	0.0391010i	−0.118123	−	0.00309120i
$161$	−0.474102	+	8.42757i	−0.0373644	+	0.664186i
$162$	6.67192	−	6.31251i	0.524195	−	0.495958i
$163$	−5.94541	−	8.72031i	−0.465680	−	0.683028i	0.519515	−	0.854461i	$-0.326113\pi$
$163$	−5.94541	−	8.72031i	−0.465680	−	0.683028i	−0.985196	+	0.171433i	$0.945160\pi$
$164$	5.40467	+	10.6860i	0.422034	+	0.834438i
$165$	0.341090	+	0.590785i	0.0265538	+	0.0459926i
$166$	−4.47288	+	5.72212i	−0.347163	+	0.444123i
$167$	1.02069	+	4.47192i	0.0789830	+	0.346047i	0.998943	−	0.0459649i	$-0.0146362\pi$
$167$	1.02069	+	4.47192i	0.0789830	+	0.346047i	−0.919960	+	0.392012i	$0.871779\pi$
$168$	−11.3111	+	1.39355i	−0.872670	+	0.107515i
$169$	0.0423353	−	0.185483i	0.00325656	−	0.0142679i
$170$	−0.265898	−	0.326852i	−0.0203934	−	0.0250684i
$171$	0.988723	+	0.149026i	0.0756095	+	0.0113963i
$172$	−8.37898	+	18.3016i	−0.638891	+	1.39548i
$173$	−17.0843	+	18.4125i	−1.29890	+	1.39988i	−0.431620	+	0.902056i	$0.642058\pi$
$173$	−17.0843	+	18.4125i	−1.29890	+	1.39988i	−0.867278	+	0.497824i	$0.834133\pi$
$174$	4.33259	−	11.3631i	0.328453	−	0.861431i
$175$	−11.1732	+	6.73103i	−0.844615	+	0.508818i
$176$	6.40409	+	2.23005i	0.482727	+	0.168096i
$177$	−8.54359	+	14.7979i	−0.642176	+	1.11228i
$178$	23.5639	−	9.51370i	1.76619	−	0.713082i
$179$	−10.0609	−	10.8431i	−0.751987	−	0.810450i	0.234873	−	0.972026i	$-0.424533\pi$
$179$	−10.0609	−	10.8431i	−0.751987	−	0.810450i	−0.986860	+	0.161577i	$0.948342\pi$
$180$	0.112687	+	0.341584i	0.00839921	+	0.0254602i
$181$	−17.7841	−	14.1823i	−1.32188	−	1.05416i	−0.993993	−	0.109446i	$-0.965092\pi$
$181$	−17.7841	−	14.1823i	−1.32188	−	1.05416i	−0.327886	−	0.944717i	$-0.606336\pi$
$182$	−2.64736	+	13.3287i	−0.196236	+	0.987991i
$183$	−0.237316	+	0.189253i	−0.0175429	+	0.0139900i
$184$	−5.94205	+	6.79111i	−0.438054	+	0.500647i
$185$	0.658014	+	0.258251i	0.0483781	+	0.0189870i
$186$	−0.811818	+	12.4580i	−0.0595254	+	0.913463i
$187$	0.698405	+	1.77951i	0.0510724	+	0.130130i
$188$	11.2581	−	1.92157i	0.821080	−	0.140145i
$189$	6.68217	+	13.2398i	0.486057	+	0.963057i
$190$	0.304785	−	0.456516i	0.0221115	−	0.0331192i
$191$	16.7906	+	1.25828i	1.21492	+	0.0910458i	0.666725	−	0.745304i	$-0.267696\pi$
$191$	16.7906	+	1.25828i	1.21492	+	0.0910458i	0.548197	+	0.836350i	$0.315315\pi$
$192$	−10.4497	−	6.26434i	−0.754140	−	0.452090i
$193$	−8.47699	−	5.77951i	−0.610187	−	0.416019i	0.218415	−	0.975856i	$-0.429911\pi$
$193$	−8.47699	−	5.77951i	−0.610187	−	0.416019i	−0.828603	+	0.559837i	$0.810864\pi$
$194$	−0.107993	−	11.1017i	−0.00775342	−	0.797056i
$195$	−1.46142			−0.104654
$196$	2.33735	−	13.8035i	0.166953	−	0.985965i
$197$	−17.3198			−1.23398			−0.616992	−	0.786969i	$-0.711649\pi$
$197$	−17.3198			−1.23398			−0.616992	+	0.786969i	$0.711649\pi$
$198$	−0.0158739	−	1.63184i	−0.00112811	−	0.115970i
$199$	18.5474	+	12.6454i	1.31479	+	0.896411i	0.998632	−	0.0522945i	$-0.0166534\pi$
$199$	18.5474	+	12.6454i	1.31479	+	0.896411i	0.316162	+	0.948705i	$0.397606\pi$
$200$	−13.8437	−	1.67513i	−0.978897	−	0.118450i
$201$	−22.5689	−	1.69130i	−1.59188	−	0.119295i
$202$	−8.25196	+	12.3600i	−0.580606	+	0.869648i
$203$	11.8510	+	9.09545i	0.831780	+	0.638375i
$204$	−0.577864	−	3.38559i	−0.0404586	−	0.237039i
$205$	−0.577979	−	1.47267i	−0.0403678	−	0.102855i
$206$	−1.34214	+	20.5962i	−0.0935115	+	1.43500i
$207$	2.02145	+	0.793362i	0.140501	+	0.0551425i
$208$	−10.9970	+	9.49262i	−0.762506	+	0.658195i
$209$	−1.94707	+	1.55274i	−0.134682	+	0.107405i
$210$	1.50501	−	0.0426487i	0.103855	−	0.00294304i
$211$	−2.24783	−	1.79259i	−0.154747	−	0.123407i	0.543055	−	0.839697i	$-0.317267\pi$
$211$	−2.24783	−	1.79259i	−0.154747	−	0.123407i	−0.697803	+	0.716290i	$0.745839\pi$
$212$	−0.131792	+	0.0434777i	−0.00905153	+	0.00298606i
$213$	3.67103	+	3.95643i	0.251535	+	0.271090i
$214$	−17.8200	+	7.19463i	−1.21815	+	0.491815i
$215$	1.32959	−	2.30292i	0.0906772	−	0.157058i
$216$	−3.07546	+	15.5534i	−0.209259	+	1.05827i
$217$	−14.3779	−	5.33643i	−0.976034	−	0.362261i
$218$	1.08353	−	2.84177i	0.0733860	−	0.192469i
$219$	−2.91508	+	3.14170i	−0.196983	+	0.212297i
$220$	−0.814564	−	0.372930i	−0.0549179	−	0.0251429i
$221$	−4.04955	−	0.610372i	−0.272402	−	0.0410581i
$222$	3.63621	+	4.46976i	0.244046	+	0.299991i
$223$	1.04391	−	4.57365i	0.0699051	−	0.306274i	−0.927873	−	0.372896i	$-0.878365\pi$
$223$	1.04391	−	4.57365i	0.0699051	−	0.306274i	0.997778	+	0.0666216i	$0.0212220\pi$
$224$	11.0480	−	10.0967i	0.738173	−	0.674611i
$225$	0.746737	+	3.27167i	0.0497825	+	0.218111i
$226$	7.76532	−	9.93412i	0.516541	−	0.660808i
$227$	−5.34275	−	9.25391i	−0.354611	−	0.614204i	0.632441	−	0.774609i	$-0.282053\pi$
$227$	−5.34275	−	9.25391i	−0.354611	−	0.614204i	−0.987051	+	0.160405i	$0.948720\pi$
$228$	3.99273	−	2.01940i	0.264425	−	0.133738i
$229$	4.02135	+	5.89824i	0.265739	+	0.389767i	0.935796	−	0.352543i	$-0.114683\pi$
$229$	4.02135	+	5.89824i	0.265739	+	0.389767i	−0.670057	+	0.742309i	$0.733730\pi$
$230$	0.865960	−	0.819312i	0.0570997	−	0.0540238i
$231$	−6.56380	−	1.89169i	−0.431866	−	0.124464i
$232$	4.00655	+	15.4598i	0.263043	+	1.01498i
$233$	13.5728	+	4.18664i	0.889181	+	0.274276i	0.705500	−	0.708710i	$-0.250722\pi$
$233$	13.5728	+	4.18664i	0.889181	+	0.274276i	0.183681	+	0.982986i	$0.441199\pi$
$234$	3.04451	+	1.71848i	0.199026	+	0.112341i
$235$	−1.50460	+	0.112754i	−0.0981492	+	0.00735527i
$236$	−2.11192	−	22.3402i	−0.137474	−	1.45422i
$237$	9.94050	+	20.6417i	0.645705	+	1.34082i
$238$	4.18814	+	0.510398i	0.271477	+	0.0330842i
$239$	0.477666	−	0.991884i	0.0308977	−	0.0641597i	−0.884949	−	0.465688i	$-0.845807\pi$
$239$	0.477666	−	0.991884i	0.0308977	−	0.0641597i	0.915846	+	0.401529i	$0.131521\pi$
$240$	1.29649	+	0.953836i	0.0836883	+	0.0615699i
$241$	−4.68170	−	15.1777i	−0.301575	−	0.977683i	−0.971856	−	0.235575i	$-0.924303\pi$
$241$	−4.68170	−	15.1777i	−0.301575	−	0.977683i	0.670281	−	0.742107i	$-0.266174\pi$
$242$	−8.49969	−	7.73407i	−0.546381	−	0.497165i
$243$	6.84789	−	1.03215i	0.439293	−	0.0662127i
$244$	0.110064	−	0.383127i	0.00704612	−	0.0245272i
$245$	−0.479044	+	1.78643i	−0.0306050	+	0.114131i
$246$	1.79787	−	12.7697i	0.114628	−	0.814167i
$247$	−0.795161	−	5.27555i	−0.0505949	−	0.335675i
$248$	−8.60837	−	13.9534i	−0.546632	−	0.886041i
$249$	7.47375	−	2.30535i	0.473630	−	0.146095i
$250$	3.62539	+	0.790449i	0.229290	+	0.0499924i
$251$	17.3367	+	8.34890i	1.09428	+	0.526978i	0.891856	−	0.452320i	$-0.149403\pi$
$251$	17.3367	+	8.34890i	1.09428	+	0.526978i	0.202425	+	0.979298i	$0.435118\pi$
$252$	−3.18546	−	1.68089i	−0.200665	−	0.105886i
$253$	−4.87304	+	2.34673i	−0.306365	+	0.147538i
$254$	−3.59606	+	0.857662i	−0.225637	+	0.0538145i
$255$	0.0339080	+	0.452471i	0.00212340	+	0.0283348i
$256$	15.9516	−	1.24383i	0.996974	−	0.0777396i
$257$	3.75030	−	12.1582i	0.233937	−	0.758406i	−0.760143	−	0.649756i	$-0.774871\pi$
$257$	3.75030	−	12.1582i	0.233937	−	0.758406i	0.994080	−	0.108650i	$-0.0346528\pi$
$258$	18.6656	−	11.0200i	1.16207	−	0.686078i
$259$	−6.53972	+	2.70810i	−0.406358	+	0.168273i
$260$	1.56440	−	1.11177i	0.0970198	−	0.0689493i
$261$	3.17550	−	2.16502i	0.196559	−	0.134011i
$262$	19.5922	−	13.6388i	1.21041	−	0.842605i
$263$	−5.30249	+	3.06139i	−0.326965	+	0.188774i	−0.654493	−	0.756068i	$-0.727118\pi$
$263$	−5.30249	+	3.06139i	−0.326965	+	0.188774i	0.327528	+	0.944842i	$0.393785\pi$
$264$	−4.28800	−	5.91109i	−0.263908	−	0.363802i
$265$	0.0178744	−	0.00407972i	0.00109802	−	0.000250615i
$266$	0.972832	+	5.40968i	0.0596482	+	0.331689i
$267$	−26.6795	−	6.08942i	−1.63276	−	0.372667i
$268$	25.4458	−	15.3588i	1.55435	−	0.938186i
$269$	−0.267378	+	1.77394i	−0.0163023	+	0.108159i	−0.995502	−	0.0947398i	$-0.969798\pi$
$269$	−0.267378	+	1.77394i	−0.0163023	+	0.108159i	0.979200	+	0.202899i	$0.0650362\pi$
$270$	0.597880	−	2.00740i	0.0363858	−	0.122167i
$271$	−8.08714	−	7.50377i	−0.491259	−	0.455821i	0.395223	−	0.918585i	$-0.370667\pi$
$271$	−8.08714	−	7.50377i	−0.491259	−	0.455821i	−0.886482	+	0.462764i	$0.846858\pi$
$272$	3.19417	+	3.18454i	0.193675	+	0.193091i
$273$	10.5403	−	10.1513i	0.637930	−	0.614387i
$274$	1.26575	+	14.9388i	0.0764669	+	0.902488i
$275$	−7.23843	−	4.17911i	−0.436494	−	0.252010i
$276$	9.42993	−	2.34622i	0.567615	−	0.141226i
$277$	10.4875	−	9.73095i	0.630131	−	0.584676i	−0.299079	−	0.954228i	$-0.596679\pi$
$277$	10.4875	−	9.73095i	0.630131	−	0.584676i	0.929210	+	0.369552i	$0.120489\pi$
$278$	12.4520	−	6.14648i	0.746820	−	0.368641i
$279$	−2.45999	+	3.08473i	−0.147276	+	0.184678i
$280$	−1.57861	+	1.19059i	−0.0943399	+	0.0711511i
$281$	14.6964	+	18.4288i	0.876716	+	1.09937i	0.994333	+	0.106309i	$0.0339031\pi$
$281$	14.6964	+	18.4288i	0.876716	+	1.09937i	−0.117617	+	0.993059i	$0.537525\pi$
$282$	−11.1323	−	5.22826i	−0.662920	−	0.311338i
$283$	1.17291	−	2.98854i	0.0697226	−	0.177650i	−0.891765	−	0.452499i	$-0.850533\pi$
$283$	1.17291	−	2.98854i	0.0697226	−	0.177650i	0.961487	+	0.274849i	$0.0886278\pi$
$284$	−6.93955	−	1.44248i	−0.411787	−	0.0855954i
$285$	−0.550248	+	0.215956i	−0.0325939	+	0.0127921i
$286$	−8.29526	+	2.64739i	−0.490509	+	0.156543i
$287$	14.3981	+	6.60667i	0.849891	+	0.389980i
$288$	−1.57931	−	3.51163i	−0.0930618	−	0.206925i
$289$	1.17539	−	15.6845i	0.0691407	−	0.922619i
$290$	−0.334738	−	2.08314i	−0.0196565	−	0.122326i
$291$	−6.73491	+	9.87830i	−0.394808	+	0.579076i
$292$	0.730433	−	5.58072i	0.0427453	−	0.326587i
$293$		−	19.4225i		−	1.13467i	−0.823486	−	0.567336i	$-0.807974\pi$
$293$		−	19.4225i		−	1.13467i	0.823486	−	0.567336i	$-0.192026\pi$
$294$	−10.5584	+	10.7617i	−0.615781	+	0.627635i
$295$			2.96453i			0.172602i
$296$	−7.29280	−	2.01848i	−0.423885	−	0.117322i
$297$	−5.35320	+	7.85171i	−0.310624	+	0.455602i
$298$	20.9920	−	3.37319i	1.21604	−	0.195403i
$299$	0.865888	−	11.5545i	0.0500756	−	0.668212i
$300$	11.2046	+	9.99789i	0.646901	+	0.577228i
$301$	6.40705	+	25.8451i	0.369296	+	1.48969i
$302$	0.416122	+	1.30387i	0.0239451	+	0.0750291i
$303$	14.8978	−	5.84694i	0.855854	−	0.335898i
$304$	−2.73781	+	5.19917i	−0.157024	+	0.298193i
$305$	−0.0192396	+	0.0490218i	−0.00110166	+	0.00280698i
$306$	0.461421	−	0.982485i	0.0263777	−	0.0561650i
$307$	9.70679	+	12.1719i	0.553996	+	0.694689i	0.977435	−	0.211235i	$-0.0677487\pi$
$307$	9.70679	+	12.1719i	0.553996	+	0.694689i	−0.423439	+	0.905925i	$0.639177\pi$
$308$	8.46541	−	2.96842i	0.482361	−	0.169142i
$309$	13.8581	−	17.3775i	0.788359	−	0.988571i
$310$	0.958717	+	1.94224i	0.0544514	+	0.110312i
$311$	−15.6099	+	14.4838i	−0.885154	+	0.821303i	−0.984795	−	0.173720i	$-0.944421\pi$
$311$	−15.6099	+	14.4838i	−0.885154	+	0.821303i	0.0996406	+	0.995023i	$0.468231\pi$
$312$	15.5597	−	1.62378i	0.880895	−	0.0919284i
$313$	8.32645	+	4.80728i	0.470639	+	0.271723i	0.716507	−	0.697580i	$-0.245740\pi$
$313$	8.32645	+	4.80728i	0.470639	+	0.271723i	−0.245868	+	0.969303i	$0.579073\pi$
$314$	−30.2841	+	2.56594i	−1.70903	+	0.144804i
$315$	0.398065	+	0.260683i	0.0224284	+	0.0146878i
$316$	−26.3441	−	14.5339i	−1.48197	−	0.817597i
$317$	−6.32362	−	5.86746i	−0.355170	−	0.329550i	0.482327	−	0.875991i	$-0.339792\pi$
$317$	−6.32362	−	5.86746i	−0.355170	−	0.329550i	−0.837497	+	0.546441i	$0.815982\pi$
$318$	0.143230	+	0.0426593i	0.00803193	+	0.00239221i
$319$	−1.42670	+	9.46555i	−0.0798799	+	0.529969i
$320$	−2.11348	−	0.0347407i	−0.118147	−	0.00194206i
$321$	20.1761	+	4.60506i	1.12612	+	0.257029i
$322$	−0.554518	+	11.9243i	−0.0309021	+	0.664518i
$323$	−1.61492	+	0.368594i	−0.0898563	+	0.0205091i
$324$	9.34823	−	9.01860i	0.519346	−	0.501033i
$325$	15.5067	−	8.95282i	0.860159	−	0.496613i
$326$	−8.52764	−	12.2500i	−0.472302	−	0.678466i
$327$	−2.70605	+	1.84495i	−0.149645	+	0.102026i
$328$	7.79000	+	15.0372i	0.430131	+	0.830293i
$329$	10.0685	−	11.2645i	0.555096	−	0.621032i
$330$	0.490478	+	0.830765i	0.0269999	+	0.0457321i
$331$	9.35325	−	30.3225i	0.514101	−	1.66667i	−0.210569	−	0.977579i	$-0.567532\pi$
$331$	9.35325	−	30.3225i	0.514101	−	1.66667i	0.724670	−	0.689096i	$-0.241992\pi$
$332$	−6.24659	+	8.15344i	−0.342826	+	0.447478i
$333$	0.136084	+	1.81591i	0.00745735	+	0.0995114i
$334$	1.50492	+	6.30990i	0.0823453	+	0.345263i
$335$	−3.53770	+	1.70366i	−0.193285	+	0.0930811i
$336$	−15.9764	+	2.12629i	−0.871582	+	0.115998i
$337$	3.27627	+	1.57777i	0.178470	+	0.0859465i	0.520985	−	0.853566i	$-0.325565\pi$
$337$	3.27627	+	1.57777i	0.178470	+	0.0859465i	−0.342516	+	0.939512i	$0.611279\pi$
$338$	0.0573168	−	0.262883i	0.00311762	−	0.0142989i
$339$	−12.9751	+	4.00229i	−0.704711	+	0.217375i
$340$	−0.380515	−	0.458558i	−0.0206363	−	0.0248688i
$341$	−1.46464	−	9.71724i	−0.0793146	−	0.526218i
$342$	1.40025	+	0.197143i	0.0757168	+	0.0106603i
$343$	−8.95389	−	16.2120i	−0.483464	−	0.875364i
$344$	−11.5973	+	25.9964i	−0.625287	+	1.40163i
$345$	−1.26943	+	0.191336i	−0.0683440	+	0.0103012i
$346$	−23.9065	+	26.2730i	−1.28522	+	1.41245i
$347$	0.409643	+	1.32803i	0.0219908	+	0.0712924i	0.965903	−	0.258904i	$-0.0833613\pi$
$347$	0.409643	+	1.32803i	0.0219908	+	0.0712924i	−0.943912	+	0.330196i	$0.892885\pi$
$348$	5.97061	−	16.1286i	0.320058	−	0.864585i
$349$	5.31392	−	11.0345i	0.284448	−	0.590662i	−0.708966	−	0.705242i	$-0.750838\pi$
$349$	5.31392	−	11.0345i	0.284448	−	0.590662i	0.993414	+	0.114581i	$0.0365525\pi$
$350$	−15.7080	+	9.67237i	−0.839625	+	0.517010i
$351$	−8.83299	−	18.3419i	−0.471470	−	0.979018i
$352$	9.08700	+	3.06552i	0.484339	+	0.163393i
$353$	−3.11273	+	0.233267i	−0.165674	+	0.0124155i	−0.157309	−	0.987549i	$-0.550282\pi$
$353$	−3.11273	+	0.233267i	−0.165674	+	0.0124155i	−0.00836506	+	0.999965i	$0.502663\pi$
$354$	−11.8783	+	21.0440i	−0.631326	+	1.11848i
$355$	0.894782	+	0.276004i	0.0474901	+	0.0146488i
$356$	33.1920	−	13.7779i	1.75917	−	0.730228i
$357$	−3.38752	−	3.02787i	−0.179287	−	0.160252i
$358$	−14.3768	−	15.1953i	−0.759835	−	0.803097i
$359$	16.6231	+	24.3816i	0.877334	+	1.28681i	0.957029	+	0.289993i	$0.0936531\pi$
$359$	16.6231	+	24.3816i	0.877334	+	1.28681i	−0.0796946	+	0.996819i	$0.525395\pi$
$360$	0.164055	+	0.481500i	0.00864647	+	0.0253773i
$361$	8.42103	+	14.5857i	0.443212	+	0.767666i
$362$	−25.3444	−	19.8112i	−1.33207	−	1.04126i
$363$	2.75375	+	12.0650i	0.144534	+	0.633246i
$364$	−3.56041	+	18.8852i	−0.186616	+	0.989853i
$365$	−0.165458	+	0.724917i	−0.00866044	+	0.0379439i
$366$	−0.332996	+	0.270896i	−0.0174060	+	0.0141600i
$367$	25.5823	+	3.85591i	1.33539	+	0.201277i	0.777627	−	0.628726i	$-0.216423\pi$
$367$	25.5823	+	3.85591i	1.33539	+	0.201277i	0.557759	+	0.830003i	$0.311661\pi$
$368$	−8.30952	+	9.68536i	−0.433164	+	0.504884i
$369$	2.77204	−	2.98755i	0.144307	−	0.155526i
$370$	0.934080	+	0.356153i	0.0485605	+	0.0185155i
$371$	−0.100579	+	0.153584i	−0.00522178	+	0.00797369i
$372$	−0.976655	+	17.6286i	−0.0506372	+	0.913998i
$373$	−8.63010	+	14.9478i	−0.446850	+	0.773967i	−0.998179	−	0.0603212i	$-0.980788\pi$
$373$	−8.63010	+	14.9478i	−0.446850	+	0.773967i	0.551329	+	0.834288i	$0.314121\pi$
$374$	1.01213	+	2.50688i	0.0523358	+	0.129628i
$375$	−2.71785	−	2.92914i	−0.140349	−	0.151260i
$376$	15.8941	−	2.87225i	0.819678	−	0.148125i
$377$	−16.0329	−	12.7858i	−0.825738	−	0.658504i
$378$	9.63171	+	18.6312i	0.495401	+	0.958284i
$379$	4.60730	−	3.67420i	0.236661	−	0.188731i	−0.497977	−	0.867190i	$-0.665924\pi$
$379$	4.60730	−	3.67420i	0.236661	−	0.188731i	0.734638	+	0.678460i	$0.237352\pi$
$380$	0.424731	−	0.649774i	0.0217883	−	0.0333327i
$381$	3.70593	+	1.45447i	0.189861	+	0.0745148i
$382$	23.7616	+	1.54841i	1.21575	+	0.0792238i
$383$	−9.56634	−	24.3746i	−0.488817	−	1.24549i	−0.936302	−	0.351195i	$-0.885776\pi$
$383$	−9.56634	−	24.3746i	−0.488817	−	1.24549i	0.447485	−	0.894291i	$-0.352320\pi$
$384$	−14.8635	−	8.71494i	−0.758502	−	0.444733i
$385$	−1.15031	+	0.285164i	−0.0586253	+	0.0145333i
$386$	−12.0672	−	8.05647i	−0.614205	−	0.410063i
$387$	6.83122	+	0.511929i	0.347250	+	0.0260228i
$388$	−0.305435	−	15.6979i	−0.0155061	−	0.796942i
$389$	5.33873	+	3.63988i	0.270684	+	0.184549i	0.691053	−	0.722804i	$-0.257147\pi$
$389$	5.33873	+	3.63988i	0.270684	+	0.184549i	−0.420369	+	0.907353i	$0.638099\pi$
$390$	−2.06666	+	0.0201036i	−0.104649	+	0.00101799i
$391$	−3.59748			−0.181932
$392$	3.11547	−	19.5523i	0.157355	−	0.987542i
$393$	−25.7072			−1.29676
$394$	−24.4927	+	0.238255i	−1.23393	+	0.0120031i
$395$	3.28417	+	2.23911i	0.165244	+	0.112662i
$396$	−0.0448960	−	2.30745i	−0.00225611	−	0.115954i
$397$	7.25469	+	0.543664i	0.364102	+	0.0272857i	0.255525	−	0.966802i	$-0.417752\pi$
$397$	7.25469	+	0.543664i	0.364102	+	0.0272857i	0.108577	+	0.994088i	$0.465371\pi$
$398$	26.4028	+	17.6274i	1.32345	+	0.883579i
$399$	2.46852	−	5.37970i	0.123581	−	0.269322i
$400$	−19.6001	−	2.17845i	−0.980003	−	0.108922i
$401$	−13.3656	−	34.0551i	−0.667449	−	1.70063i	−0.712524	−	0.701648i	$-0.752448\pi$
$401$	−13.3656	−	34.0551i	−0.667449	−	1.70063i	0.0450757	−	0.998984i	$-0.485647\pi$
$402$	−31.9389	−	2.08129i	−1.59297	−	0.103805i
$403$	19.5969	+	7.69123i	0.976193	+	0.383127i
$404$	−11.4995	+	17.5924i	−0.572119	+	0.875255i
$405$	−1.34165	+	1.06993i	−0.0666671	+	0.0531652i
$406$	16.8842	+	12.6993i	0.837950	+	0.630254i
$407$	−3.54602	−	2.82786i	−0.175770	−	0.140172i
$408$	−0.863757	−	4.77977i	−0.0427624	−	0.236634i
$409$	20.8393	+	22.4594i	1.03044	+	1.11055i	0.993796	+	0.111219i	$0.0354755\pi$
$409$	20.8393	+	22.4594i	1.03044	+	1.11055i	0.0366415	+	0.999328i	$0.488334\pi$
$410$	−0.837605	−	2.07462i	−0.0413664	−	0.102458i
$411$	8.07247	−	13.9819i	0.398186	−	0.689678i
$412$	−1.61466	+	29.1445i	−0.0795486	+	1.43585i
$413$	−20.5923	−	21.3813i	−1.01328	−	1.05211i
$414$	2.86955	+	1.09412i	0.141031	+	0.0537732i
$415$	0.922952	−	0.994706i	0.0453059	−	0.0488282i
$416$	−15.4208	+	13.5752i	−0.756067	+	0.665580i
$417$	−14.7869	−	2.22877i	−0.724118	−	0.109143i
$418$	−2.73209	+	2.22259i	−0.133631	+	0.108710i
$419$	4.50328	−	19.7301i	0.219999	−	0.963880i	−0.737478	−	0.675371i	$-0.763983\pi$
$419$	4.50328	−	19.7301i	0.219999	−	0.963880i	0.957477	−	0.288509i	$-0.0931595\pi$
$420$	2.12771	−	0.0810147i	0.103822	−	0.00395311i
$421$	3.98667	+	17.4667i	0.194298	+	0.851277i	0.974256	+	0.225444i	$0.0723834\pi$
$421$	3.98667	+	17.4667i	0.194298	+	0.851277i	−0.779958	+	0.625832i	$0.784759\pi$
$422$	−3.20343	−	2.50406i	−0.155940	−	0.121896i
$423$	−1.94345	−	3.36616i	−0.0944938	−	0.163668i
$424$	−0.185775	+	0.0632969i	−0.00902205	+	0.00307397i
$425$	−3.13168	−	4.59333i	−0.151909	−	0.222809i
$426$	5.24580	+	5.54447i	0.254160	+	0.268630i
$427$	−0.201753	−	0.487207i	−0.00976349	−	0.0235776i
$428$	−25.1011	+	10.4194i	−1.21331	+	0.503641i
$429$	8.96030	+	2.76389i	0.432607	+	0.133442i
$430$	1.84855	−	3.27495i	0.0891452	−	0.157932i
$431$	−30.6869	+	2.29967i	−1.47814	+	0.110771i	−0.789239	−	0.614086i	$-0.789525\pi$
$431$	−30.6869	+	2.29967i	−1.47814	+	0.110771i	−0.688899	+	0.724857i	$0.741906\pi$
$432$	−4.13520	+	22.0371i	−0.198955	+	1.06026i
$433$	14.5644	+	30.2432i	0.699918	+	1.45340i	0.882552	+	0.470214i	$0.155823\pi$
$433$	14.5644	+	30.2432i	0.699918	+	1.45340i	−0.182634	+	0.983181i	$0.558462\pi$
$434$	−20.4058	−	7.34872i	−0.979512	−	0.352750i
$435$	−0.985814	+	2.04706i	−0.0472662	+	0.0981492i
$436$	1.49318	−	4.03358i	0.0715103	−	0.193173i
$437$	−1.38140	−	4.47839i	−0.0660814	−	0.214231i
$438$	−4.07913	+	4.48293i	−0.194908	+	0.214203i
$439$	−30.6661	+	4.62217i	−1.46361	+	0.220604i	−0.832041	−	0.554714i	$-0.812828\pi$
$439$	−30.6661	+	4.62217i	−1.46361	+	0.220604i	−0.631571	+	0.775318i	$0.717590\pi$
$440$	−1.15704	−	0.516172i	−0.0551599	−	0.0246076i
$441$	−4.68176	+	0.884897i	−0.222941	+	0.0421380i
$442$	−5.73506	−	0.807449i	−0.272789	−	0.0384064i
$443$	4.34114	+	28.8016i	0.206254	+	1.36840i	0.817028	+	0.576599i	$0.195620\pi$
$443$	4.34114	+	28.8016i	0.206254	+	1.36840i	−0.610774	+	0.791805i	$0.709142\pi$
$444$	5.20361	+	6.27088i	0.246953	+	0.297603i
$445$	−4.53684	+	1.39943i	−0.215067	+	0.0663394i
$446$	1.41332	−	6.48217i	0.0669226	−	0.306940i
$447$	−20.6285	−	9.93414i	−0.975693	−	0.469869i
$448$	15.4846	−	14.4301i	0.731576	−	0.681760i
$449$	17.5297	−	8.44186i	0.827278	−	0.398396i	0.0281843	−	0.999603i	$-0.491027\pi$
$449$	17.5297	−	8.44186i	0.827278	−	0.398396i	0.799093	+	0.601207i	$0.205313\pi$
$450$	1.10100	+	4.61635i	0.0519017	+	0.217617i
$451$	0.758565	+	10.1223i	0.0357194	+	0.476643i
$452$	10.8446	−	14.1551i	0.510089	−	0.665801i
$453$	0.434434	−	1.40840i	0.0204115	−	0.0661724i
$454$	−7.68273	−	13.0129i	−0.360568	−	0.610725i
$455$	0.703089	−	2.43959i	0.0329613	−	0.114370i
$456$	5.61852	−	2.91066i	0.263111	−	0.136304i
$457$	−19.0440	+	12.9840i	−0.890840	+	0.607364i	−0.919874	−	0.392214i	$-0.871709\pi$
$457$	−19.0440	+	12.9840i	−0.890840	+	0.607364i	0.0290342	+	0.999578i	$0.490757\pi$
$458$	5.76792	+	8.28566i	0.269517	+	0.387164i
$459$	−5.47390	+	3.16036i	−0.255500	+	0.147513i
$460$	1.21332	−	1.17054i	0.0565715	−	0.0545767i
$461$	−12.3886	+	2.82762i	−0.576995	+	0.131695i	−0.501053	−	0.865417i	$-0.667054\pi$
$461$	−12.3886	+	2.82762i	−0.576995	+	0.131695i	−0.0759425	+	0.997112i	$0.524197\pi$
$462$	−9.30819	−	2.58483i	−0.433056	−	0.120257i
$463$	33.6271	+	7.67517i	1.56278	+	0.356695i	0.914462	−	0.404671i	$-0.132614\pi$
$463$	33.6271	+	7.67517i	1.56278	+	0.356695i	0.648322	+	0.761366i	$0.275471\pi$
$464$	5.87852	+	21.8072i	0.272904	+	1.01238i
$465$	0.347639	−	2.30643i	0.0161214	−	0.106958i
$466$	19.2515	+	5.73382i	0.891807	+	0.265614i
$467$	−0.247445	−	0.229595i	−0.0114504	−	0.0106244i	0.674427	−	0.738342i	$-0.264391\pi$
$467$	−0.247445	−	0.229595i	−0.0114504	−	0.0106244i	−0.685877	+	0.727717i	$0.740581\pi$
$468$	4.32902	+	2.38830i	0.200109	+	0.110399i
$469$	13.6812	−	36.8611i	0.631740	−	1.70209i
$470$	−2.12617	+	0.180148i	−0.0980730	+	0.00830963i
$471$	28.3442	+	16.3646i	1.30603	+	0.754039i
$472$	−3.29388	−	31.5633i	−0.151613	−	1.45282i
$473$	−12.5074	+	11.6051i	−0.575090	+	0.533605i
$474$	14.3413	+	29.0536i	0.658716	+	1.33448i
$475$	4.51556	−	5.66233i	0.207188	−	0.259806i
$476$	5.92967	+	0.664164i	0.271786	+	0.0304419i
$477$	0.0294480	+	0.0369266i	0.00134833	+	0.00169075i
$478$	0.661846	−	1.40924i	0.0302721	−	0.0644572i
$479$	−9.13747	+	23.2819i	−0.417501	+	1.06378i	0.555200	+	0.831717i	$0.312642\pi$
$479$	−9.13747	+	23.2819i	−0.417501	+	1.06378i	−0.972702	+	0.232060i	$0.925454\pi$
$480$	1.84655	+	1.33103i	0.0842832	+	0.0607529i
$481$	9.04471	−	3.54979i	0.412403	−	0.161856i
$482$	−6.82941	−	21.3991i	−0.311071	−	0.974703i
$483$	7.82658	−	10.1978i	0.356122	−	0.464014i
$484$	−12.1262	−	10.8202i	−0.551191	−	0.491827i
$485$	−0.155009	+	2.06845i	−0.00703860	+	0.0939236i
$486$	9.66973	−	1.55382i	0.438628	−	0.0704826i
$487$	−3.89188	+	5.70833i	−0.176358	+	0.258669i	−0.904232	−	0.427041i	$-0.859556\pi$
$487$	−3.89188	+	5.70833i	−0.176358	+	0.258669i	0.727875	+	0.685710i	$0.240508\pi$
$488$	0.150376	−	0.543311i	0.00680720	−	0.0245945i
$489$			16.0734i			0.726865i
$490$	−0.652863	+	2.53286i	−0.0294934	+	0.114423i
$491$			16.2303i			0.732462i	0.930524	+	0.366231i	$0.119352\pi$
$491$			16.2303i			0.732462i	−0.930524	+	0.366231i	$0.880648\pi$
$492$	2.36679	−	18.0830i	0.106703	−	0.815244i
$493$	−3.58663	+	5.26062i	−0.161534	+	0.236927i
$494$	−1.19705	−	7.44946i	−0.0538576	−	0.335167i
$495$	−0.0227849	+	0.304043i	−0.00102410	+	0.0136657i
$496$	−12.3654	−	19.6137i	−0.555225	−	0.880682i
$497$	−8.37070	+	4.22471i	−0.375477	+	0.189504i
$498$	10.5373	−	3.36291i	0.472186	−	0.150696i
$499$	−16.6354	+	6.52892i	−0.744703	+	0.292274i	−0.707192	−	0.707022i	$-0.750038\pi$
$499$	−16.6354	+	6.52892i	−0.744703	+	0.292274i	−0.0375113	+	0.999296i	$0.511943\pi$
$500$	5.13770	+	1.06794i	0.229765	+	0.0477597i
$501$	2.55212	−	6.50270i	0.114020	−	0.290519i
$502$	24.6314	+	11.5681i	1.09935	+	0.516309i
$503$	−20.3569	−	25.5267i	−0.907667	−	1.13818i	−0.989929	−	0.141568i	$-0.954786\pi$
$503$	−20.3569	−	25.5267i	−0.907667	−	1.13818i	0.0822611	−	0.996611i	$-0.473786\pi$
$504$	−4.52783	−	2.33320i	−0.201686	−	0.103929i
$505$	1.73119	−	2.17084i	0.0770369	−	0.0966012i
$506$	−6.85891	+	3.38566i	−0.304916	+	0.150511i
$507$	−0.212397	+	0.197076i	−0.00943288	+	0.00875244i
$508$	−5.07356	+	1.26233i	−0.225103	+	0.0560068i
$509$	9.51075	+	5.49103i	0.421557	+	0.243386i	0.695743	−	0.718291i	$-0.255075\pi$
$509$	9.51075	+	5.49103i	0.421557	+	0.243386i	−0.274186	+	0.961677i	$0.588409\pi$
$510$	0.0541752	+	0.639394i	0.00239892	+	0.0283128i
$511$	−3.84209	−	6.37769i	−0.169964	−	0.282132i
$512$	22.5408	−	1.97840i	0.996170	−	0.0874336i
$513$	−6.03617	−	5.60075i	−0.266504	−	0.247279i
$514$	5.13623	−	17.2450i	0.226549	−	0.760646i
$515$	0.574736	−	3.81312i	0.0253259	−	0.168026i
$516$	26.2443	−	15.8407i	1.15534	−	0.697349i
$517$	9.43828	+	2.15423i	0.415095	+	0.0947428i
$518$	−9.21087	+	3.91961i	−0.404702	+	0.172218i
$519$	37.2935	−	8.51200i	1.63700	−	0.373635i
$520$	2.19699	−	1.59373i	0.0963445	−	0.0698898i
$521$	13.9034	−	8.02712i	0.609118	−	0.351675i	−0.163502	−	0.986543i	$-0.552279\pi$
$521$	13.9034	−	8.02712i	0.609118	−	0.351675i	0.772620	+	0.634868i	$0.218946\pi$
$522$	4.46084	−	3.10534i	0.195246	−	0.135917i
$523$	−20.9806	+	14.3043i	−0.917416	+	0.625484i	−0.927240	−	0.374468i	$-0.877825\pi$
$523$	−20.9806	+	14.3043i	−0.917416	+	0.625484i	0.00982360	+	0.999952i	$0.496873\pi$
$524$	27.5186	−	19.5567i	1.20216	−	0.854339i
$525$	19.8339	+	1.11578i	0.865622	+	0.0486965i
$526$	−7.45638	+	4.40220i	−0.325114	+	0.191945i
$527$	1.92660	−	6.24587i	0.0839238	−	0.272074i
$528$	−6.14517	−	8.30016i	−0.267434	−	0.361218i
$529$	0.958160	+	12.7858i	0.0416591	+	0.555902i
$530$	0.0252209	−	0.00601520i	0.00109553	−	0.000261284i
$531$	−6.88069	+	3.31357i	−0.298597	+	0.143797i
$532$	1.45014	+	7.63670i	0.0628717	+	0.331093i
$533$	−19.5922	−	9.43511i	−0.848632	−	0.408680i
$534$	−37.8125	−	8.24433i	−1.63631	−	0.356767i
$535$	3.43094	−	1.05830i	0.148332	−	0.0457545i
$536$	35.7728	−	22.0696i	1.54515	−	0.953261i
$537$	3.35745	+	22.2752i	0.144884	+	0.961246i
$538$	−0.353709	+	2.51228i	−0.0152495	+	0.108312i
$539$	6.31568	−	10.0470i	0.272036	−	0.432756i
$540$	0.817876	−	2.84698i	0.0351958	−	0.122515i
$541$	36.7348	−	5.53688i	1.57935	−	0.238049i	0.699972	−	0.714170i	$-0.253196\pi$
$541$	36.7348	−	5.53688i	1.57935	−	0.238049i	0.879379	+	0.476122i	$0.157958\pi$
$542$	−11.5396	−	10.5002i	−0.495669	−	0.451021i
$543$	10.2108	+	33.1027i	0.438189	+	1.42057i
$544$	4.56083	+	4.45947i	0.195544	+	0.191198i
$545$	−0.246541	+	0.511947i	−0.0105606	+	0.0219294i
$546$	14.7659	−	14.5005i	0.631923	−	0.620563i
$547$	8.17165	+	16.9686i	0.349394	+	0.725525i	0.999408	−	0.0343973i	$-0.0109512\pi$
$547$	8.17165	+	16.9686i	0.349394	+	0.725525i	−0.650014	+	0.759922i	$0.725237\pi$
$548$	1.99546	+	21.1083i	0.0852418	+	0.901701i
$549$	−0.135285	+	0.0101382i	−0.00577382	+	0.000432688i
$550$	−10.2937	−	5.81030i	−0.438925	−	0.247752i
$551$	−7.92603	−	2.44486i	−0.337660	−	0.104154i
$552$	13.3030	−	3.44762i	0.566215	−	0.146740i
$553$	−39.2400	+	6.66324i	−1.66866	+	0.283350i
$554$	14.6970	−	13.9053i	0.624414	−	0.590778i
$555$	−0.606430	−	0.889470i	−0.0257415	−	0.0377559i
$556$	17.5244	−	8.86331i	0.743199	−	0.375888i
$557$	−3.41050	−	5.90716i	−0.144508	−	0.250295i	0.784682	−	0.619899i	$-0.212826\pi$
$557$	−3.41050	−	5.90716i	−0.144508	−	0.250295i	−0.929189	+	0.369605i	$0.879493\pi$
$558$	−3.43635	+	4.39610i	−0.145472	+	0.186102i
$559$	−8.13352	−	35.6353i	−0.344011	−	1.50721i
$560$	−2.21601	+	1.70538i	−0.0936434	+	0.0720654i
$561$	0.647831	−	2.83833i	0.0273514	−	0.119834i
$562$	21.0364	+	25.8588i	0.887369	+	1.09079i
$563$	−25.5068	−	3.84453i	−1.07498	−	0.162028i	−0.412390	−	0.911007i	$-0.635306\pi$
$563$	−25.5068	−	3.84453i	−1.07498	−	0.162028i	−0.662593	+	0.748979i	$0.730544\pi$
$564$	−15.8147	−	7.24039i	−0.665917	−	0.304875i
$565$	−1.60233	+	1.72690i	−0.0674105	+	0.0726512i
$566$	1.61756	−	4.24237i	0.0679912	−	0.178320i
$567$	2.24453	−	17.0361i	0.0942614	−	0.715450i
$568$	−9.83339	−	1.94441i	−0.412600	−	0.0815858i
$569$	−18.2427	+	31.5972i	−0.764773	+	1.32462i	0.175594	+	0.984463i	$0.443815\pi$
$569$	−18.2427	+	31.5972i	−0.764773	+	1.32462i	−0.940367	+	0.340162i	$0.889518\pi$
$570$	−0.775160	+	0.312963i	−0.0324679	+	0.0131086i
$571$	−6.06637	−	6.53799i	−0.253870	−	0.273606i	0.593239	−	0.805027i	$-0.297849\pi$
$571$	−6.06637	−	6.53799i	−0.253870	−	0.273606i	−0.847108	+	0.531420i	$0.821659\pi$
$572$	−11.6943	+	3.85790i	−0.488963	+	0.161307i
$573$	−20.0482	−	15.9879i	−0.837527	−	0.667905i
$574$	20.4519	+	9.14474i	0.853644	+	0.381694i
$575$	12.2975	−	9.80691i	0.512840	−	0.408977i
$576$	−2.28168	−	4.94423i	−0.0950702	−	0.206010i
$577$	−12.3632	−	4.85218i	−0.514685	−	0.201999i	0.0937602	−	0.995595i	$-0.470111\pi$
$577$	−12.3632	−	4.85218i	−0.514685	−	0.201999i	−0.608445	+	0.793596i	$0.708207\pi$
$578$	1.44642	−	22.1964i	0.0601630	−	0.923248i
$579$	5.70842	+	14.5448i	0.237234	+	0.604462i
$580$	−0.502025	−	2.94126i	−0.0208454	−	0.122129i
$581$	0.252756	+	13.5852i	0.0104861	+	0.563610i
$582$	−9.38827	+	14.0620i	−0.389156	+	0.582889i
$583$	−0.117308	−	0.00879100i	−0.00485839	−	0.000364086i
$584$	0.956169	−	7.90201i	0.0395666	−	0.326987i
$585$	−0.539675	−	0.367944i	−0.0223128	−	0.0152126i
$586$	−0.267180	−	27.4662i	−0.0110371	−	1.13462i
$587$	5.02774			0.207517			0.103759	−	0.994603i	$-0.466913\pi$
$587$	5.02774			0.207517			0.103759	+	0.994603i	$0.466913\pi$
$588$	−14.7831	+	15.3639i	−0.609646	+	0.633595i
$589$	8.51510			0.350858
$590$	0.0407807	+	4.19228i	0.00167892	+	0.172593i
$591$	21.7936	+	14.8587i	0.896471	+	0.611203i
$592$	−10.3409	−	2.75410i	−0.425006	−	0.113193i
$593$	−23.6004	−	1.76860i	−0.969150	−	0.0726278i	−0.419261	−	0.907866i	$-0.637711\pi$
$593$	−23.6004	−	1.76860i	−0.969150	−	0.0726278i	−0.549889	+	0.835238i	$0.685330\pi$
$594$	−7.46220	+	11.1771i	−0.306178	+	0.458602i
$595$	−0.771635	−	0.161080i	−0.0316340	−	0.00660365i
$596$	29.6394	−	5.05895i	1.21408	−	0.207223i
$597$	−12.4899	−	31.8237i	−0.511177	−	1.30246i
$598$	1.06555	−	16.3516i	0.0435734	−	0.668668i
$599$	−22.0537	−	8.65543i	−0.901088	−	0.353651i	−0.130846	−	0.991403i	$-0.541769\pi$
$599$	−22.0537	−	8.65543i	−0.901088	−	0.353651i	−0.770242	+	0.637752i	$0.779865\pi$
$600$	15.9825	+	13.9843i	0.652485	+	0.570909i
$601$	−29.3205	+	23.3824i	−1.19601	+	0.953786i	−0.999642	−	0.0267443i	$-0.991486\pi$
$601$	−29.3205	+	23.3824i	−1.19601	+	0.953786i	−0.196368	+	0.980530i	$0.562915\pi$
$602$	9.41604	+	36.4607i	0.383769	+	1.48603i
$603$	−7.90844	−	6.30677i	−0.322057	−	0.256831i
$604$	0.606394	+	1.83814i	0.0246738	+	0.0747927i
$605$	1.46035	+	1.57389i	0.0593718	+	0.0639876i
$606$	20.9872	−	8.47337i	0.852546	−	0.344207i
$607$	−16.7349	+	28.9857i	−0.679249	+	1.17649i	0.295958	+	0.955201i	$0.404361\pi$
$607$	−16.7349	+	28.9857i	−0.679249	+	1.17649i	−0.975207	+	0.221293i	$0.928972\pi$
$608$	−3.80014	+	7.39004i	−0.154116	+	0.299706i
$609$	−7.10928	−	21.6119i	−0.288083	−	0.875758i
$610$	−0.0265333	+	0.0695887i	−0.00107430	+	0.00281756i
$611$	−14.1064	+	15.2031i	−0.570683	+	0.615050i
$612$	0.639002	−	1.39573i	0.0258301	−	0.0564189i
$613$	12.0968	+	1.82330i	0.488585	+	0.0736424i	0.388715	−	0.921358i	$-0.372919\pi$
$613$	12.0968	+	1.82330i	0.488585	+	0.0736424i	0.0998703	+	0.995000i	$0.468157\pi$
$614$	13.8943	+	17.0794i	0.560727	+	0.689267i
$615$	−0.536125	+	2.34892i	−0.0216186	+	0.0947175i
$616$	11.9305	−	4.31424i	0.480693	−	0.173826i
$617$	4.56028	+	19.9799i	0.183590	+	0.804360i	0.979903	+	0.199475i	$0.0639237\pi$
$617$	4.56028	+	19.9799i	0.183590	+	0.804360i	−0.796313	+	0.604885i	$0.793219\pi$
$618$	19.3583	−	24.7650i	0.778706	−	0.996192i
$619$	10.0376	+	17.3856i	0.403444	+	0.698786i	0.994139	−	0.108109i	$-0.0344795\pi$
$619$	10.0376	+	17.3856i	0.403444	+	0.698786i	−0.590695	+	0.806895i	$0.701146\pi$
$620$	1.38248	+	2.73342i	0.0555219	+	0.109777i
$621$	−10.0740	−	14.7759i	−0.404257	−	0.592935i
$622$	−21.8754	+	20.6970i	−0.877124	+	0.829874i
$623$	23.0007	−	41.6072i	0.921505	−	1.66696i
$624$	21.9814	−	2.51030i	0.879959	−	0.100493i
$625$	22.8933	+	7.06165i	0.915733	+	0.282466i
$626$	11.8409	+	6.68365i	0.473259	+	0.267133i
$627$	3.78212	−	0.283431i	0.151043	−	0.0113191i
$628$	−42.7908	+	4.04521i	−1.70754	+	0.161421i
$629$	−1.30891	−	2.71798i	−0.0521896	−	0.108373i
$630$	0.566508	+	0.363169i	0.0225702	+	0.0144690i
$631$	16.0221	−	33.2703i	0.637830	−	1.32447i	−0.291978	−	0.956425i	$-0.594313\pi$
$631$	16.0221	−	33.2703i	0.637830	−	1.32447i	0.929809	−	0.368044i	$-0.119972\pi$
$632$	−37.4543	−	20.1907i	−1.48985	−	0.803143i
$633$	1.29061	+	4.18405i	0.0512971	+	0.166301i
$634$	−9.02324	−	8.21047i	−0.358359	−	0.326079i
$635$	0.682989	−	0.102944i	0.0271036	−	0.00408521i
$636$	0.203135	+	0.0583562i	0.00805482	+	0.00231397i
$637$	11.8750	+	22.4791i	0.470503	+	0.890653i
$638$	−1.88736	+	13.4053i	−0.0747211	+	0.530721i
$639$	0.359526	+	2.38530i	0.0142226	+	0.0943609i
$640$	−2.98925	−	0.0200550i	−0.118160	−	0.000792742i
$641$	−15.0682	+	4.64792i	−0.595158	+	0.183582i	−0.577677	−	0.816265i	$-0.696041\pi$
$641$	−15.0682	+	4.64792i	−0.595158	+	0.183582i	−0.0174806	+	0.999847i	$0.505565\pi$
$642$	28.5953	+	6.23468i	1.12857	+	0.246063i
$643$	−7.44922	−	3.58735i	−0.293768	−	0.141471i	0.281195	−	0.959651i	$-0.409269\pi$
$643$	−7.44922	−	3.58735i	−0.293768	−	0.141471i	−0.574963	+	0.818179i	$0.694984\pi$
$644$	−0.620136	+	16.8704i	−0.0244368	+	0.664787i
$645$	−3.64871	+	1.75712i	−0.143668	+	0.0691867i
$646$	−2.27866	+	0.543461i	−0.0896526	+	0.0213822i
$647$	0.442714	+	5.90761i	0.0174049	+	0.232252i	0.999122	+	0.0419043i	$0.0133425\pi$
$647$	0.442714	+	5.90761i	0.0174049	+	0.232252i	−0.981717	+	0.190348i	$0.939038\pi$
$648$	13.0957	−	12.8822i	0.514448	−	0.506061i
$649$	5.60662	−	18.1762i	0.220079	−	0.713478i
$650$	21.8057	−	12.8739i	0.855288	−	0.504957i
$651$	13.5137	+	19.0497i	0.529643	+	0.746616i
$652$	−12.2278	−	17.2060i	−0.478879	−	0.673839i
$653$	−7.87320	+	5.36785i	−0.308102	+	0.210060i	−0.707493	−	0.706720i	$-0.750174\pi$
$653$	−7.87320	+	5.36785i	−0.308102	+	0.210060i	0.399391	+	0.916781i	$0.369222\pi$
$654$	−3.80137	+	2.64626i	−0.148645	+	0.103477i
$655$	−3.86251	+	2.23002i	−0.150921	+	0.0871342i
$656$	11.2231	+	21.1577i	0.438187	+	0.826070i
$657$	−1.86748	+	0.426239i	−0.0728572	+	0.0166292i
$658$	14.0834	−	16.0682i	0.549029	−	0.626402i
$659$	41.0401	+	9.36715i	1.59870	+	0.364892i	0.926742	−	0.375699i	$-0.122597\pi$
$659$	41.0401	+	9.36715i	1.59870	+	0.364892i	0.671956	+	0.740591i	$0.265455\pi$
$660$	0.705036	+	1.16808i	0.0274435	+	0.0454673i
$661$	1.64378	−	10.9058i	0.0639358	−	0.424186i	−0.933849	−	0.357667i	$-0.883572\pi$
$661$	1.64378	−	10.9058i	0.0639358	−	0.424186i	0.997785	−	0.0665196i	$-0.0211895\pi$
$662$	12.8097	−	43.0091i	0.497865	−	1.67160i
$663$	4.57195	+	4.24215i	0.177560	+	0.164751i
$664$	−8.72143	+	11.6161i	−0.338457	+	0.450792i
$665$	−0.0957774	−	1.02244i	−0.00371409	−	0.0396485i
$666$	0.217423	+	2.56609i	0.00842495	+	0.0994341i
$667$	−15.6007	−	9.00705i	−0.604061	−	0.348755i
$668$	2.21497	+	8.90243i	0.0856998	+	0.344445i
$669$	−5.23729	+	4.85950i	−0.202485	+	0.187879i
$670$	−4.97938	+	2.45790i	−0.192370	+	0.0949568i
$671$	0.210674	−	0.264177i	0.00813300	−	0.0101985i
$672$	−22.5637	+	3.22666i	−0.870413	+	0.124471i
$673$	8.21635	+	10.3030i	0.316717	+	0.397151i	0.914552	−	0.404469i	$-0.132544\pi$
$673$	8.21635	+	10.3030i	0.316717	+	0.397151i	−0.597835	+	0.801619i	$0.703972\pi$
$674$	4.65483	+	2.18613i	0.179297	+	0.0842064i
$675$	10.0965	−	25.7254i	0.388614	−	0.990171i
$676$	0.0774381	−	0.372543i	0.00297839	−	0.0143286i
$677$	16.9005	−	6.63295i	0.649539	−	0.254925i	−0.0176155	−	0.999845i	$-0.505607\pi$
$677$	16.9005	−	6.63295i	0.649539	−	0.254925i	0.667154	+	0.744920i	$0.267512\pi$
$678$	−18.2937	+	5.83832i	−0.702564	+	0.224219i
$679$	−13.2499	−	15.9952i	−0.508486	−	0.613840i
$680$	−0.544411	−	0.643234i	−0.0208772	−	0.0246669i
$681$	−1.21611	+	16.2278i	−0.0466013	+	0.621852i
$682$	−2.20489	−	13.7215i	−0.0844295	−	0.525422i
$683$	2.20788	−	3.23836i	0.0844820	−	0.123912i	−0.781672	−	0.623690i	$-0.785633\pi$
$683$	2.20788	−	3.23836i	0.0844820	−	0.123912i	0.866154	+	0.499778i	$0.166585\pi$
$684$	1.98287	+	0.259528i	0.0758169	+	0.00992329i
$685$		−	2.80105i		−	0.107023i
$686$	−12.8851	−	22.8029i	−0.491956	−	0.870620i
$687$		−	10.8717i		−	0.414783i
$688$	−16.0427	+	36.9223i	−0.611623	+	1.40765i
$689$	0.141963	−	0.208221i	0.00540835	−	0.00793259i
$690$	−1.79253	+	0.288040i	−0.0682406	+	0.0109655i
$691$	0.0990365	−	1.32155i	0.00376752	−	0.0502741i	−0.995003	−	0.0998434i	$-0.968166\pi$
$691$	0.0990365	−	1.32155i	0.00376752	−	0.0502741i	0.998771	+	0.0495693i	$0.0157849\pi$
$692$	−33.4458	+	37.4828i	−1.27142	+	1.42488i
$693$	−1.94761	−	2.35114i	−0.0739838	−	0.0893126i
$694$	0.597564	+	1.87240i	0.0226832	+	0.0710752i
$695$	−2.41508	+	0.947848i	−0.0916091	+	0.0359539i
$696$	8.22145	−	22.8904i	0.311633	−	0.867657i
$697$	−2.46663	+	6.28487i	−0.0934302	+	0.238056i
$698$	7.36287	−	15.6775i	0.278689	−	0.593401i
$699$	−13.4870	−	16.9122i	−0.510125	−	0.639677i
$700$	−22.0803	+	13.8942i	−0.834557	+	0.525153i
$701$	16.8610	−	21.1430i	0.636832	−	0.798562i	−0.353771	−	0.935332i	$-0.615101\pi$
$701$	16.8610	−	21.1430i	0.636832	−	0.798562i	0.990603	+	0.136770i	$0.0436722\pi$
$702$	−12.7435	−	25.8166i	−0.480971	−	0.974386i
$703$	2.88092	−	2.67310i	0.108656	−	0.100818i
$704$	12.8925	+	4.21009i	0.485905	+	0.158674i
$705$	1.98998	+	1.14892i	0.0749471	+	0.0432707i
$706$	−4.39864	+	0.372693i	−0.165545	+	0.0140265i
$707$	2.59314	+	27.6822i	0.0975251	+	1.04110i
$708$	−16.5082	+	29.9227i	−0.620417	+	1.12456i
$709$	−7.92861	−	7.35667i	−0.297765	−	0.276286i	0.517114	−	0.855917i	$-0.327006\pi$
$709$	−7.92861	−	7.35667i	−0.297765	−	0.276286i	−0.814879	+	0.579631i	$0.803197\pi$
$710$	1.26915	+	0.378001i	0.0476303	+	0.0141861i
$711$	−1.52615	+	10.1253i	−0.0572349	+	0.379729i
$712$	46.7488	−	19.9406i	1.75198	−	0.747305i
$713$	18.0295	+	4.11511i	0.675209	+	0.154112i
$714$	−4.83211	−	4.23525i	−0.180837	−	0.158500i
$715$	1.58605	−	0.362005i	0.0593148	−	0.0135382i
$716$	−20.5399	−	21.2906i	−0.767611	−	0.795668i
$717$	−1.45199	+	0.838307i	−0.0542256	+	0.0313071i
$718$	23.8429	+	34.2505i	0.889810	+	1.27822i
$719$	−20.6067	+	14.0494i	−0.768501	+	0.523955i	−0.882946	−	0.469475i	$-0.844443\pi$
$719$	−20.6067	+	14.0494i	−0.768501	+	0.523955i	0.114445	+	0.993430i	$0.463491\pi$
$720$	0.238622	+	0.678654i	0.00889290	+	0.0252920i
$721$	22.3416	+	31.4940i	0.832044	+	1.17290i
$722$	12.1092	+	20.5104i	0.450659	+	0.763319i
$723$	−7.12994	+	23.1147i	−0.265165	+	0.859645i
$724$	−36.1132	−	27.6673i	−1.34214	−	1.02825i
$725$	−2.08033	−	27.7601i	−0.0772615	−	1.03098i
$726$	4.06017	+	17.0237i	0.150687	+	0.631811i
$727$	5.80239	−	2.79428i	0.215199	−	0.103634i	−0.323179	−	0.946338i	$-0.604752\pi$
$727$	5.80239	−	2.79428i	0.215199	−	0.103634i	0.538378	+	0.842704i	$0.319037\pi$
$728$	−4.77515	+	26.7554i	−0.176979	+	0.991622i
$729$	−27.0568	−	13.0299i	−1.00210	−	0.482588i
$730$	−0.224009	+	1.02741i	−0.00829095	+	0.0380263i
$731$	−10.8443	+	3.34504i	−0.401092	+	0.123721i
$732$	−0.467179	+	0.387668i	−0.0172674	+	0.0143286i
$733$	4.96258	+	32.9246i	0.183297	+	1.21610i	0.871433	+	0.490515i	$0.163191\pi$
$733$	4.96258	+	32.9246i	0.183297	+	1.21610i	−0.688135	+	0.725582i	$0.741571\pi$
$734$	36.2302	+	5.10091i	1.33728	+	0.188278i
$735$	2.13536	−	1.83691i	0.0787641	−	0.0677554i
$736$	−11.6176	+	13.8108i	−0.428232	+	0.509074i
$737$	24.9125	−	3.75495i	0.917662	−	0.138315i
$738$	3.87897	−	4.26297i	0.142787	−	0.156922i
$739$	−11.7170	−	37.9855i	−0.431016	−	1.39732i	−0.867423	−	0.497571i	$-0.834225\pi$
$739$	−11.7170	−	37.9855i	−0.431016	−	1.39732i	0.436407	−	0.899749i	$-0.356251\pi$
$740$	1.32583	+	0.490804i	0.0487383	+	0.0180423i
$741$	−3.52534	+	7.32044i	−0.129506	+	0.268923i
$742$	−0.140120	+	0.218574i	−0.00514397	+	0.00802410i
$743$	9.55016	+	19.8311i	0.350361	+	0.727533i	0.999449	−	0.0331805i	$-0.0105636\pi$
$743$	9.55016	+	19.8311i	0.350361	+	0.727533i	−0.649088	+	0.760713i	$0.724849\pi$
$744$	−1.13863	+	24.9428i	−0.0417442	+	0.914448i
$745$	−3.96119	+	0.296850i	−0.145127	+	0.0108758i
$746$	−11.9986	+	21.2571i	−0.439300	+	0.778277i
$747$	3.34034	+	1.03036i	0.122217	+	0.0376988i
$748$	1.46578	+	3.53117i	0.0535943	+	0.129112i
$749$	−17.3941	+	31.4650i	−0.635565	+	1.14970i
$750$	−3.88373	−	4.10485i	−0.141814	−	0.149888i
$751$	−0.747435	−	1.09629i	−0.0272743	−	0.0400040i	0.812359	−	0.583157i	$-0.198183\pi$
$751$	−0.747435	−	1.09629i	−0.0272743	−	0.0400040i	−0.839634	+	0.543153i	$0.817230\pi$
$752$	22.4371	−	4.28042i	0.818198	−	0.156091i
$753$	−14.6524	−	25.3786i	−0.533962	−	0.924849i
$754$	−22.8488	−	17.8605i	−0.832104	−	0.650441i
$755$	−0.0569007	−	0.249298i	−0.00207083	−	0.00907290i
$756$	13.8769	+	26.2147i	0.504699	+	0.953420i
$757$	7.47782	−	32.7625i	0.271786	−	1.19077i	−0.636118	−	0.771592i	$-0.719461\pi$
$757$	7.47782	−	32.7625i	0.271786	−	1.19077i	0.907903	−	0.419179i	$-0.137682\pi$
$758$	6.46485	−	5.25923i	0.234814	−	0.191024i
$759$	8.14505	+	1.22767i	0.295647	+	0.0445616i
$760$	0.591694	−	0.924718i	0.0214630	−	0.0335431i
$761$	−10.7488	+	11.5845i	−0.389644	+	0.419936i	−0.897160	−	0.441706i	$-0.854373\pi$
$761$	−10.7488	+	11.5845i	−0.389644	+	0.419936i	0.507516	+	0.861642i	$0.330564\pi$
$762$	5.26074	+	2.00586i	0.190577	+	0.0726645i
$763$	−1.77795	−	5.40488i	−0.0643661	−	0.195670i
$764$	33.6237	+	1.86282i	1.21646	+	0.0673943i
$765$	−0.101398	+	0.175626i	−0.00366605	+	0.00634978i
$766$	−13.8635	−	34.3377i	−0.500909	−	1.24067i

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)

\(f(q)\)	\(=\)	\(q+(1.41415 - 0.0137562i) q^{2} +(-1.25831 - 0.857901i) q^{3} +(1.99962 - 0.0389066i) q^{4} +(-0.263482 - 0.0197452i) q^{5} +(-1.79123 - 1.19589i) q^{6} +(2.03749 - 1.68779i) q^{7} +(2.82722 - 0.0825269i) q^{8} +(-0.248675 - 0.633613i) q^{9} +O(q^{10})\)	\(q+(1.41415 - 0.0137562i) q^{2} +(-1.25831 - 0.857901i) q^{3} +(1.99962 - 0.0389066i) q^{4} +(-0.263482 - 0.0197452i) q^{5} +(-1.79123 - 1.19589i) q^{6} +(2.03749 - 1.68779i) q^{7} +(2.82722 - 0.0825269i) q^{8} +(-0.248675 - 0.633613i) q^{9} +(-0.372873 - 0.0242981i) q^{10} +(1.57812 + 0.619368i) q^{11} +(-2.54952 - 1.66652i) q^{12} +(-2.83949 + 2.26441i) q^{13} +(2.85809 - 2.41481i) q^{14} +(0.314602 + 0.250887i) q^{15} +(3.99697 - 0.155597i) q^{16} +(0.766969 + 0.826596i) q^{17} +(-0.360379 - 0.892601i) q^{18} +(-0.734495 + 1.27218i) q^{19} +(-0.527632 - 0.0292318i) q^{20} +(-4.01175 + 0.375802i) q^{21} +(2.24022 + 0.854168i) q^{22} +(-2.17000 + 2.33870i) q^{23} +(-3.62832 - 2.32163i) q^{24} +(-4.87512 - 0.734806i) q^{25} +(-3.98430 + 3.24127i) q^{26} +(-1.24732 + 5.46488i) q^{27} +(4.00854 - 3.45422i) q^{28} +(1.25645 + 5.50485i) q^{29} +(0.448345 + 0.350463i) q^{30} +(-2.89828 - 5.01997i) q^{31} +(5.65016 - 0.275020i) q^{32} +(-1.45441 - 2.13323i) q^{33} +(1.09598 + 1.15838i) q^{34} +(-0.570167 + 0.404472i) q^{35} +(-0.521908 - 1.25731i) q^{36} +(-2.55647 - 0.788567i) q^{37} +(-1.02118 + 1.80916i) q^{38} +(5.51559 - 0.413337i) q^{39} +(-0.746551 - 0.0340798i) q^{40} +(2.59789 + 5.39457i) q^{41} +(-5.66803 + 0.586626i) q^{42} +(-4.36671 + 9.06756i) q^{43} +(3.17975 + 1.17710i) q^{44} +(0.0530105 + 0.171856i) q^{45} +(-3.03652 + 3.33711i) q^{46} +(5.64667 - 0.851098i) q^{47} +(-5.16291 - 3.23322i) q^{48} +(1.30271 - 6.87771i) q^{49} +(-6.90424 - 0.972061i) q^{50} +(-0.255947 - 1.69810i) q^{51} +(-5.58980 + 4.63845i) q^{52} +(-0.0663065 + 0.0204529i) q^{53} +(-1.68872 + 7.74530i) q^{54} +(-0.403577 - 0.194353i) q^{55} +(5.62114 - 4.93991i) q^{56} +(2.01563 - 0.970675i) q^{57} +(1.85253 + 7.76738i) q^{58} +(-0.838464 - 11.1885i) q^{59} +(0.638846 + 0.489438i) q^{60} +(0.0587480 - 0.190456i) q^{61} +(-4.16765 - 7.05911i) q^{62} +(-1.57608 - 0.871268i) q^{63} +(7.98638 - 0.466644i) q^{64} +(0.792864 - 0.540566i) q^{65} +(-2.08610 - 2.99669i) q^{66} +(12.8699 - 7.43043i) q^{67} +(1.56581 + 1.62304i) q^{68} +(4.73690 - 1.08117i) q^{69} +(-0.800735 + 0.579826i) q^{70} +(-3.45509 - 0.788602i) q^{71} +(-0.755350 - 1.77084i) q^{72} +(0.419429 - 2.78273i) q^{73} +(-3.62608 - 1.07998i) q^{74} +(5.50402 + 5.10698i) q^{75} +(-1.41922 + 2.57246i) q^{76} +(4.26077 - 1.40159i) q^{77} +(7.79417 - 0.660392i) q^{78} +(-13.0282 - 7.52182i) q^{79} +(-1.05620 - 0.0379242i) q^{80} +(4.76095 - 4.41752i) q^{81} +(3.74800 + 7.59297i) q^{82} +(-3.20201 + 4.01519i) q^{83} +(-8.00735 + 0.907546i) q^{84} +(-0.185761 - 0.232937i) q^{85} +(-6.05043 + 12.8829i) q^{86} +(3.14162 - 8.00471i) q^{87} +(4.51282 + 1.62085i) q^{88} +(16.7269 - 6.56481i) q^{89} +(0.0773287 + 0.242300i) q^{90} +(-1.96356 + 9.40618i) q^{91} +(-4.24818 + 4.76094i) q^{92} +(-0.659702 + 8.80311i) q^{93} +(7.97351 - 1.28125i) q^{94} +(0.218646 - 0.320694i) q^{95} +(-7.34559 - 4.50122i) q^{96} -7.85046i q^{97} +(1.74762 - 9.74402i) q^{98} -1.15394i 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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