LMFDB - Embedded newform 675.2.y.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.363246 + 1.70894i) q^{2} +(-0.961428 - 0.428055i) q^{4} +(-2.04050 + 0.914526i) q^{5} +(-3.25090 - 1.87691i) q^{7} +(-0.973104 + 1.33936i) q^{8} +O(q^{10})$	\(q+(-0.363246 + 1.70894i) q^{2} +(-0.961428 - 0.428055i) q^{4} +(-2.04050 + 0.914526i) q^{5} +(-3.25090 - 1.87691i) q^{7} +(-0.973104 + 1.33936i) q^{8} +(-0.821664 - 3.81928i) q^{10} +(0.651825 + 0.138550i) q^{11} +(-0.301380 - 1.41788i) q^{13} +(4.38839 - 4.87380i) q^{14} +(-3.34381 - 3.71368i) q^{16} +(2.20337 - 3.03268i) q^{17} +(4.05607 + 2.94691i) q^{19} +(2.35326 - 0.00580396i) q^{20} +(-0.473546 + 1.06360i) q^{22} +(-1.80341 - 1.62379i) q^{23} +(3.32728 - 3.73218i) q^{25} +2.53254 q^{26} +(2.32208 + 3.19608i) q^{28} +(-0.247116 - 2.35115i) q^{29} +(0.977492 - 9.30021i) q^{31} +(4.69359 - 2.70985i) q^{32} +(4.38229 + 4.86703i) q^{34} +(8.34994 + 0.856798i) q^{35} +(5.48696 + 1.78282i) q^{37} +(-6.50943 + 5.86112i) q^{38} +(0.760737 - 3.62290i) q^{40} +(-7.24962 + 1.54095i) q^{41} +(-8.90096 - 5.13897i) q^{43} +(-0.567376 - 0.412223i) q^{44} +(3.43004 - 2.49207i) q^{46} +(-10.9793 + 1.15397i) q^{47} +(3.54556 + 6.14109i) q^{49} +(5.16944 + 7.04182i) q^{50} +(-0.317176 + 1.49220i) q^{52} +(-6.87949 - 9.46881i) q^{53} +(-1.45676 + 0.313400i) q^{55} +(5.67732 - 2.52771i) q^{56} +(4.10773 + 0.431740i) q^{58} +(5.00582 - 1.06402i) q^{59} +(-1.86098 - 0.395563i) q^{61} +(15.5384 + 5.04873i) q^{62} +(-0.162441 - 0.499943i) q^{64} +(1.91165 + 2.61756i) q^{65} +(0.133224 + 0.0140024i) q^{67} +(-3.41653 + 1.97254i) q^{68} +(-4.49730 + 13.9583i) q^{70} +(-1.26087 + 0.916078i) q^{71} +(0.752348 - 0.244453i) q^{73} +(-5.03985 + 8.72927i) q^{74} +(-2.63818 - 4.56946i) q^{76} +(-1.85897 - 1.67383i) q^{77} +(1.78031 + 16.9385i) q^{79} +(10.2193 + 4.51976i) q^{80} -12.9489i q^{82} +(-1.34263 - 3.01560i) q^{83} +(-1.72251 + 8.20322i) q^{85} +(12.0154 - 13.3445i) q^{86} +(-0.819862 + 0.738207i) q^{88} +(1.31095 + 4.03469i) q^{89} +(-1.68147 + 5.17504i) q^{91} +(1.03877 + 2.33312i) q^{92} +(2.01612 - 19.1821i) q^{94} +(-10.9714 - 2.30378i) q^{95} +(-1.31796 + 0.138523i) q^{97} +(-11.7827 + 3.82842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.363246	+	1.70894i	−0.256854	+	1.20840i	0.640803	+	0.767705i	$0.278602\pi$
$2$	−0.363246	+	1.70894i	−0.256854	+	1.20840i	−0.897657	+	0.440696i	$0.854732\pi$
$3$		0			0
$3$		0			0
$4$	−0.961428	−	0.428055i	−0.480714	−	0.214028i
$5$	−2.04050	+	0.914526i	−0.912540	+	0.408989i
$5$	−2.04050	+	0.914526i	−0.912540	+	0.408989i
$6$		0			0
$7$	−3.25090	−	1.87691i	−1.22872	−	0.709404i	−0.261961	−	0.965078i	$-0.584369\pi$
$7$	−3.25090	−	1.87691i	−1.22872	−	0.709404i	−0.966763	+	0.255674i	$0.917703\pi$
$8$	−0.973104	+	1.33936i	−0.344044	+	0.473536i
$9$		0			0
$10$	−0.821664	−	3.81928i	−0.259833	−	1.20776i
$11$	0.651825	+	0.138550i	0.196533	+	0.0417743i	0.305126	−	0.952312i	$-0.401301\pi$
$11$	0.651825	+	0.138550i	0.196533	+	0.0417743i	−0.108593	+	0.994086i	$0.534635\pi$
$12$		0			0
$13$	−0.301380	−	1.41788i	−0.0835877	−	0.393249i	0.916388	−	0.400292i	$-0.131091\pi$
$13$	−0.301380	−	1.41788i	−0.0835877	−	0.393249i	−0.999975	+	0.00704319i	$0.997758\pi$
$14$	4.38839	−	4.87380i	1.17285	−	1.30258i
$15$		0			0
$16$	−3.34381	−	3.71368i	−0.835954	−	0.928421i
$17$	2.20337	−	3.03268i	0.534396	−	0.735532i	−0.453397	−	0.891309i	$-0.649788\pi$
$17$	2.20337	−	3.03268i	0.534396	−	0.735532i	0.987792	+	0.155776i	$0.0497879\pi$
$18$		0			0
$19$	4.05607	+	2.94691i	0.930526	+	0.676067i	0.946122	−	0.323811i	$-0.104964\pi$
$19$	4.05607	+	2.94691i	0.930526	+	0.676067i	−0.0155953	+	0.999878i	$0.504964\pi$
$20$	2.35326	−	0.00580396i	0.526205	−	0.00129780i
$21$		0			0
$22$	−0.473546	+	1.06360i	−0.100960	+	0.226761i
$23$	−1.80341	−	1.62379i	−0.376036	−	0.338585i	0.459343	−	0.888259i	$-0.348085\pi$
$23$	−1.80341	−	1.62379i	−0.376036	−	0.338585i	−0.835379	+	0.549675i	$0.814752\pi$
$24$		0			0
$25$	3.32728	−	3.73218i	0.665457	−	0.746436i
$26$	2.53254			0.496672
$27$		0			0
$28$	2.32208	+	3.19608i	0.438833	+	0.604001i
$29$	−0.247116	−	2.35115i	−0.0458883	−	0.436598i	−0.993212	−	0.116320i	$-0.962890\pi$
$29$	−0.247116	−	2.35115i	−0.0458883	−	0.436598i	0.947324	−	0.320278i	$-0.103776\pi$
$30$		0			0
$31$	0.977492	−	9.30021i	0.175563	−	1.67037i	−0.452165	−	0.891934i	$-0.649348\pi$
$31$	0.977492	−	9.30021i	0.175563	−	1.67037i	0.627728	−	0.778433i	$-0.283985\pi$
$32$	4.69359	−	2.70985i	0.829718	−	0.479038i
$33$		0			0
$34$	4.38229	+	4.86703i	0.751557	+	0.834688i
$35$	8.34994	+	0.856798i	1.41140	+	0.144825i
$36$		0			0
$37$	5.48696	+	1.78282i	0.902051	+	0.293094i	0.723083	−	0.690761i	$-0.242724\pi$
$37$	5.48696	+	1.78282i	0.902051	+	0.293094i	0.178968	+	0.983855i	$0.442724\pi$
$38$	−6.50943	+	5.86112i	−1.05597	+	0.950799i
$39$		0			0
$40$	0.760737	−	3.62290i	0.120283	−	0.572830i
$41$	−7.24962	+	1.54095i	−1.13220	+	0.240656i	−0.735653	−	0.677358i	$-0.763125\pi$
$41$	−7.24962	+	1.54095i	−1.13220	+	0.240656i	−0.396546	+	0.918015i	$0.629791\pi$
$42$		0			0
$43$	−8.90096	−	5.13897i	−1.35738	−	0.783686i	−0.368113	−	0.929781i	$-0.619996\pi$
$43$	−8.90096	−	5.13897i	−1.35738	−	0.783686i	−0.989271	+	0.146095i	$0.953329\pi$
$44$	−0.567376	−	0.412223i	−0.0855352	−	0.0621449i
$45$		0			0
$46$	3.43004	−	2.49207i	0.505732	−	0.367436i
$47$	−10.9793	+	1.15397i	−1.60149	+	0.168324i	−0.862738	−	0.505651i	$-0.831252\pi$
$47$	−10.9793	+	1.15397i	−1.60149	+	0.168324i	−0.738754	+	0.673975i	$0.764586\pi$
$48$		0			0
$49$	3.54556	+	6.14109i	0.506509	+	0.877299i
$50$	5.16944	+	7.04182i	0.731070	+	0.995864i
$51$		0			0
$52$	−0.317176	+	1.49220i	−0.0439844	+	0.206930i
$53$	−6.87949	−	9.46881i	−0.944971	−	1.30064i	−0.953725	−	0.300680i	$-0.902786\pi$
$53$	−6.87949	−	9.46881i	−0.944971	−	1.30064i	0.00875390	−	0.999962i	$-0.497214\pi$
$54$		0			0
$55$	−1.45676	+	0.313400i	−0.196429	+	0.0422589i
$56$	5.67732	−	2.52771i	0.758664	−	0.337779i
$57$		0			0
$58$	4.10773	+	0.431740i	0.539372	+	0.0566902i
$59$	5.00582	−	1.06402i	0.651703	−	0.138524i	0.129815	−	0.991538i	$-0.458562\pi$
$59$	5.00582	−	1.06402i	0.651703	−	0.138524i	0.521887	+	0.853015i	$0.325228\pi$
$60$		0			0
$61$	−1.86098	−	0.395563i	−0.238274	−	0.0506466i	0.0872269	−	0.996188i	$-0.472199\pi$
$61$	−1.86098	−	0.395563i	−0.238274	−	0.0506466i	−0.325501	+	0.945542i	$0.605533\pi$
$62$	15.5384	+	5.04873i	1.97338	+	0.641190i
$63$		0			0
$64$	−0.162441	−	0.499943i	−0.0203052	−	0.0624929i
$65$	1.91165	+	2.61756i	0.237111	+	0.324669i
$66$		0			0
$67$	0.133224	+	0.0140024i	0.0162759	+	0.00171066i	0.112663	−	0.993633i	$-0.464062\pi$
$67$	0.133224	+	0.0140024i	0.0162759	+	0.00171066i	−0.0963870	+	0.995344i	$0.530729\pi$
$68$	−3.41653	+	1.97254i	−0.414316	+	0.239205i
$69$		0			0
$70$	−4.49730	+	13.9583i	−0.537530	+	1.66834i
$71$	−1.26087	+	0.916078i	−0.149638	+	0.108718i	−0.660085	−	0.751191i	$-0.729480\pi$
$71$	−1.26087	+	0.916078i	−0.149638	+	0.108718i	0.510447	+	0.859909i	$0.329480\pi$
$72$		0			0
$73$	0.752348	−	0.244453i	0.0880557	−	0.0286110i	−0.264658	−	0.964342i	$-0.585259\pi$
$73$	0.752348	−	0.244453i	0.0880557	−	0.0286110i	0.352714	+	0.935731i	$0.385259\pi$
$74$	−5.03985	+	8.72927i	−0.585871	+	1.01476i
$75$		0			0
$76$	−2.63818	−	4.56946i	−0.302620	−	0.524153i
$77$	−1.85897	−	1.67383i	−0.211850	−	0.190750i
$78$		0			0
$79$	1.78031	+	16.9385i	0.200301	+	1.90573i	0.384966	+	0.922931i	$0.374213\pi$
$79$	1.78031	+	16.9385i	0.200301	+	1.90573i	−0.184666	+	0.982801i	$0.559120\pi$
$80$	10.2193	+	4.51976i	1.14255	+	0.505325i
$81$		0			0
$82$		−	12.9489i		−	1.42996i
$83$	−1.34263	−	3.01560i	−0.147373	−	0.331005i	0.824742	−	0.565509i	$-0.191320\pi$
$83$	−1.34263	−	3.01560i	−0.147373	−	0.331005i	−0.972115	+	0.234504i	$0.924653\pi$
$84$		0			0
$85$	−1.72251	+	8.20322i	−0.186833	+	0.889764i
$86$	12.0154	−	13.3445i	1.29566	−	1.43897i
$87$		0			0
$88$	−0.819862	+	0.738207i	−0.0873976	+	0.0786931i
$89$	1.31095	+	4.03469i	0.138960	+	0.427676i	0.996185	−	0.0872668i	$-0.0278133\pi$
$89$	1.31095	+	4.03469i	0.138960	+	0.427676i	−0.857225	+	0.514943i	$0.827813\pi$
$90$		0			0
$91$	−1.68147	+	5.17504i	−0.176266	+	0.542492i
$92$	1.03877	+	2.33312i	0.108299	+	0.243245i
$93$		0			0
$94$	2.01612	−	19.1821i	0.207947	−	1.97848i
$95$	−10.9714	−	2.30378i	−1.12565	−	0.236363i
$96$		0			0
$97$	−1.31796	+	0.138523i	−0.133819	+	0.0140649i	−0.171201	−	0.985236i	$-0.554765\pi$
$97$	−1.31796	+	0.138523i	−0.133819	+	0.0140649i	0.0373823	+	0.999301i	$0.488098\pi$
$98$	−11.7827	+	3.82842i	−1.19023	+	0.386728i
$99$		0			0
$100$	−4.79652	+	2.16396i	−0.479652	+	0.216396i
$101$	2.46584	−	4.27097i	0.245361	−	0.424977i	−0.716872	−	0.697204i	$-0.754427\pi$
$101$	2.46584	−	4.27097i	0.245361	−	0.424977i	0.962233	+	0.272227i	$0.0877603\pi$
$102$		0			0
$103$	−6.78415	+	15.2374i	−0.668462	+	1.50139i	0.186367	+	0.982480i	$0.440329\pi$
$103$	−6.78415	+	15.2374i	−0.668462	+	1.50139i	−0.854829	+	0.518910i	$0.826338\pi$
$104$	2.19233	+	0.976087i	0.214975	+	0.0957132i
$105$		0			0
$106$	18.6806	−	8.31712i	1.81442	−	0.807830i
$107$		−	11.4837i		−	1.11018i	−0.831792	−	0.555088i	$-0.812685\pi$
$107$		−	11.4837i		−	1.11018i	0.831792	−	0.555088i	$-0.187315\pi$
$108$		0			0
$109$	1.11921	−	3.44458i	0.107201	−	0.329931i	−0.883040	−	0.469298i	$-0.844507\pi$
$109$	1.11921	−	3.44458i	0.107201	−	0.329931i	0.990241	+	0.139367i	$0.0445069\pi$
$110$	−0.00642076	−	2.60335i	−0.000612195	−	0.248220i
$111$		0			0
$112$	3.90017	+	18.3488i	0.368531	+	1.73380i
$113$	0.342157	+	1.60972i	0.0321874	+	0.151430i	0.991306	−	0.131573i	$-0.0420028\pi$
$113$	0.342157	+	1.60972i	0.0321874	+	0.151430i	−0.959119	+	0.283003i	$0.908669\pi$
$114$		0			0
$115$	5.16486	+	1.66409i	0.481625	+	0.155177i
$116$	−0.768838	+	2.36624i	−0.0713848	+	0.219700i
$117$		0			0
$118$			8.94114i			0.823098i
$119$	−12.8550	+	5.72341i	−1.17841	+	0.524664i
$120$		0			0
$121$	−9.64332	−	4.29348i	−0.876665	−	0.390317i
$122$	1.35198	−	3.03661i	0.122403	−	0.274921i
$123$		0			0
$124$	−4.92079	+	8.52306i	−0.441900	+	0.765394i
$125$	−3.37615	+	10.6584i	−0.301972	+	0.953317i
$126$		0			0
$127$	−17.5734	+	5.70994i	−1.55939	+	0.506676i	−0.956644	−	0.291260i	$-0.905926\pi$
$127$	−17.5734	+	5.70994i	−1.55939	+	0.506676i	−0.602743	+	0.797935i	$0.705926\pi$
$128$	11.6934	−	1.22902i	1.03356	−	0.108631i
$129$		0			0
$130$	−5.16765	+	2.31608i	−0.453233	+	0.203133i
$131$	−0.417988	+	3.97689i	−0.0365198	+	0.347463i	0.960970	+	0.276653i	$0.0892251\pi$
$131$	−0.417988	+	3.97689i	−0.0365198	+	0.347463i	−0.997490	+	0.0708102i	$0.977442\pi$
$132$		0			0
$133$	−7.65480	−	17.1930i	−0.663755	−	1.49082i
$134$	−0.0723222	+	0.222585i	−0.00624769	+	0.0192284i
$135$		0			0
$136$	1.91775	+	5.90222i	0.164445	+	0.506111i
$137$	7.05143	−	6.34913i	0.602444	−	0.542443i	−0.310476	−	0.950581i	$-0.600488\pi$
$137$	7.05143	−	6.34913i	0.602444	−	0.542443i	0.912920	+	0.408138i	$0.133822\pi$
$138$		0			0
$139$	2.67464	−	2.97049i	0.226860	−	0.251954i	−0.618959	−	0.785423i	$-0.712445\pi$
$139$	2.67464	−	2.97049i	0.226860	−	0.251954i	0.845819	+	0.533469i	$0.179112\pi$
$140$	−7.66111	−	4.39799i	−0.647482	−	0.371698i
$141$		0			0
$142$	−1.10751	−	2.48752i	−0.0929404	−	0.208748i
$143$		−	0.965966i		−	0.0807781i
$144$		0			0
$145$	2.65443	+	4.57153i	0.220438	+	0.379645i
$146$	0.144467	+	1.37451i	0.0119562	+	0.113755i
$147$		0			0
$148$	−4.51217	−	4.06278i	−0.370898	−	0.333958i
$149$	−6.62708	−	11.4784i	−0.542912	−	0.940351i	−0.998735	−	0.0502807i	$-0.983988\pi$
$149$	−6.62708	−	11.4784i	−0.542912	−	0.940351i	0.455823	−	0.890070i	$-0.349345\pi$
$150$		0			0
$151$	5.09586	−	8.82629i	0.414695	−	0.718273i	−0.580701	−	0.814117i	$-0.697222\pi$
$151$	5.09586	−	8.82629i	0.414695	−	0.718273i	0.995396	+	0.0958437i	$0.0305549\pi$
$152$	−7.89395	+	2.56490i	−0.640284	+	0.208041i
$153$		0			0
$154$	3.53573	−	2.56886i	0.284917	−	0.207004i
$155$	6.51071	+	19.8710i	0.522953	+	1.59608i
$156$		0			0
$157$	11.9131	−	6.87804i	0.950770	−	0.548927i	0.0574498	−	0.998348i	$-0.481703\pi$
$157$	11.9131	−	6.87804i	0.950770	−	0.548927i	0.893320	+	0.449421i	$0.148370\pi$
$158$	−29.5936	−	3.11041i	−2.35434	−	0.247451i
$159$		0			0
$160$	−7.09905	+	9.82186i	−0.561229	+	0.776486i
$161$	2.81498	+	8.66362i	0.221852	+	0.682789i
$162$		0			0
$163$	−11.6985	−	3.80106i	−0.916295	−	0.297722i	−0.187349	−	0.982293i	$-0.559989\pi$
$163$	−11.6985	−	3.80106i	−0.916295	−	0.297722i	−0.728946	+	0.684571i	$0.759989\pi$
$164$	7.62960	+	1.62172i	0.595771	+	0.126635i
$165$		0			0
$166$	5.64117	−	1.19907i	0.437840	−	0.0930658i
$167$	−9.00288	−	0.946240i	−0.696663	−	0.0732223i	−0.250425	−	0.968136i	$-0.580570\pi$
$167$	−9.00288	−	0.946240i	−0.696663	−	0.0732223i	−0.446239	+	0.894914i	$0.647237\pi$
$168$		0			0
$169$	9.95654	−	4.43294i	0.765888	−	0.340995i
$170$	−13.3931	−	5.92345i	−1.02720	−	0.454308i
$171$		0			0
$172$	6.35787	+	8.75085i	0.484783	+	0.667246i
$173$	−0.0806049	+	0.379216i	−0.00612828	+	0.0288313i	−0.981106	−	0.193473i	$-0.938025\pi$
$173$	−0.0806049	+	0.379216i	−0.00612828	+	0.0288313i	0.974977	+	0.222305i	$0.0713580\pi$
$174$		0			0
$175$	−17.8216	+	5.88794i	−1.34719	+	0.445087i
$176$	−1.66505	−	2.88396i	−0.125508	−	0.217386i
$177$		0			0
$178$	−7.37122	+	0.774746i	−0.552496	+	0.0580697i
$179$	7.67121	−	5.57346i	0.573373	−	0.416580i	−0.262956	−	0.964808i	$-0.584697\pi$
$179$	7.67121	−	5.57346i	0.573373	−	0.416580i	0.836329	+	0.548228i	$0.184697\pi$
$180$		0			0
$181$	−17.3526	−	12.6074i	−1.28981	−	0.937103i	−0.290010	−	0.957024i	$-0.593659\pi$
$181$	−17.3526	−	12.6074i	−1.28981	−	0.937103i	−0.999802	+	0.0199210i	$0.993659\pi$
$182$	−8.23304	−	4.75335i	−0.610273	−	0.352342i
$183$		0			0
$184$	3.92975	−	0.835294i	0.289705	−	0.0615787i
$185$	−12.8266	+	1.38012i	−0.943030	+	0.101469i
$186$		0			0
$187$	1.85639	−	1.67150i	0.135753	−	0.122232i
$188$	11.0497	+	3.59028i	0.805886	+	0.261848i
$189$		0			0
$190$	7.92235	−	17.9127i	0.574748	−	1.29952i
$191$	−17.5024	−	19.4384i	−1.26643	−	1.40652i	−0.873409	−	0.486988i	$-0.838096\pi$
$191$	−17.5024	−	19.4384i	−1.26643	−	1.40652i	−0.393024	−	0.919528i	$-0.628571\pi$
$192$		0			0
$193$	3.23510	−	1.86779i	0.232868	−	0.134446i	−0.379027	−	0.925386i	$-0.623741\pi$
$193$	3.23510	−	1.86779i	0.232868	−	0.134446i	0.611894	+	0.790940i	$0.290408\pi$
$194$	0.242016	−	2.30263i	0.0173758	−	0.165319i
$195$		0			0
$196$	−0.780075	−	7.42191i	−0.0557196	−	0.530137i
$197$	7.70799	+	10.6091i	0.549171	+	0.755869i	0.989899	−	0.141771i	$-0.0452797\pi$
$197$	7.70799	+	10.6091i	0.549171	+	0.755869i	−0.440728	+	0.897641i	$0.645280\pi$
$198$		0			0
$199$	−2.91453			−0.206605			−0.103303	−	0.994650i	$-0.532941\pi$
$199$	−2.91453			−0.206605			−0.103303	+	0.994650i	$0.532941\pi$
$200$	1.76095	+	8.08824i	0.124518	+	0.571925i
$201$		0			0
$202$	6.40311	+	5.76538i	0.450521	+	0.405651i
$203$	−3.60954	+	8.10716i	−0.253340	+	0.569011i
$204$		0			0
$205$	13.3836	−	9.77428i	0.934751	−	0.682665i
$206$	−23.5755	−	17.1286i	−1.64258	−	1.19341i
$207$		0			0
$208$	−4.25780	+	5.86036i	−0.295225	+	0.406343i
$209$	2.23556	+	2.48284i	0.154637	+	0.171741i
$210$		0			0
$211$	−3.67623	+	4.08286i	−0.253082	+	0.281076i	−0.856276	−	0.516518i	$-0.827228\pi$
$211$	−3.67623	+	4.08286i	−0.253082	+	0.281076i	0.603194	+	0.797594i	$0.293894\pi$
$212$	2.56096	+	12.0484i	0.175888	+	0.827486i
$213$		0			0
$214$	19.6250	+	4.17142i	1.34154	+	0.285153i
$215$	22.8621	+	2.34591i	1.55918	+	0.159990i
$216$		0			0
$217$	−20.6334	+	28.3994i	−1.40068	+	1.92788i
$218$	5.48002	+	3.16389i	0.371154	+	0.214286i
$219$		0			0
$220$	1.53472	+	0.322261i	0.103471	+	0.0217268i
$221$	−4.96402	−	2.21013i	−0.333916	−	0.148669i
$222$		0			0
$223$	−1.39865	+	6.58011i	−0.0936602	+	0.440637i	0.906182	+	0.422887i	$0.138983\pi$
$223$	−1.39865	+	6.58011i	−0.0936602	+	0.440637i	−0.999842	+	0.0177493i	$0.994350\pi$
$224$	−20.3445			−1.35933
$225$		0			0
$226$	−2.87520			−0.191255
$227$	−5.14623	+	24.2111i	−0.341568	+	1.60695i	0.387070	+	0.922050i	$0.373487\pi$
$227$	−5.14623	+	24.2111i	−0.341568	+	1.60695i	−0.728638	+	0.684899i	$0.759846\pi$
$228$		0			0
$229$	−9.38718	−	4.17944i	−0.620323	−	0.276185i	0.0724156	−	0.997375i	$-0.476929\pi$
$229$	−9.38718	−	4.17944i	−0.620323	−	0.276185i	−0.692738	+	0.721189i	$0.743596\pi$
$230$	−4.71994	+	8.22194i	−0.311224	+	0.542139i
$231$		0			0
$232$	3.38951	+	1.95693i	0.222532	+	0.128479i
$233$	−6.13944	+	8.45022i	−0.402208	+	0.553592i	−0.961296	−	0.275516i	$-0.911151\pi$
$233$	−6.13944	+	8.45022i	−0.402208	+	0.553592i	0.559088	+	0.829108i	$0.311151\pi$
$234$		0			0
$235$	21.3479	−	12.3955i	1.39258	−	0.808594i
$236$	−5.26820	−	1.11979i	−0.342930	−	0.0728921i
$237$		0			0
$238$	−5.11143	−	24.0474i	−0.331324	−	1.55876i
$239$	15.1896	−	16.8697i	0.982531	−	1.09121i	−0.0132930	−	0.999912i	$-0.504231\pi$
$239$	15.1896	−	16.8697i	0.982531	−	1.09121i	0.995824	−	0.0912990i	$-0.0291019\pi$
$240$		0			0
$241$	17.2240	+	19.1292i	1.10950	+	1.23222i	0.970287	+	0.241958i	$0.0777895\pi$
$241$	17.2240	+	19.1292i	1.10950	+	1.23222i	0.139210	+	0.990263i	$0.455544\pi$
$242$	10.8402	−	14.9202i	0.696834	−	0.959109i
$243$		0			0
$244$	1.61987	+	1.17691i	0.103702	+	0.0753437i
$245$	−12.8509	−	9.28839i	−0.821014	−	0.593414i
$246$		0			0
$247$	2.95594	−	6.63916i	0.188082	−	0.422439i
$248$	11.5052	+	10.3593i	0.730578	+	0.657815i
$249$		0			0
$250$	−16.9882	−	9.64124i	−1.07443	−	0.609766i
$251$	−25.3114			−1.59764			−0.798819	−	0.601571i	$-0.794542\pi$
$251$	−25.3114			−1.59764			−0.798819	+	0.601571i	$0.794542\pi$
$252$		0			0
$253$	−0.950530	−	1.30829i	−0.0597593	−	0.0822516i
$254$	−3.37447	−	32.1059i	−0.211733	−	2.01451i
$255$		0			0
$256$	−2.03735	+	19.3841i	−0.127335	+	1.21151i
$257$	16.8281	−	9.71573i	1.04971	−	0.606051i	0.127143	−	0.991884i	$-0.459419\pi$
$257$	16.8281	−	9.71573i	1.04971	−	0.606051i	0.922568	+	0.385834i	$0.126086\pi$
$258$		0			0
$259$	−14.4914	−	16.0943i	−0.900450	−	1.00005i
$260$	−0.717455	−	3.33489i	−0.0444946	−	0.206821i
$261$		0			0
$262$	−6.64443	−	2.15891i	−0.410494	−	0.133378i
$263$	16.3100	−	14.6856i	1.00572	−	0.905551i	0.0101813	−	0.999948i	$-0.496759\pi$
$263$	16.3100	−	14.6856i	1.00572	−	0.905551i	0.995535	+	0.0943975i	$0.0300925\pi$
$264$		0			0
$265$	22.6971	+	13.0296i	1.39427	+	0.800404i
$266$	32.1623	−	6.83630i	1.97200	−	0.419161i
$267$		0			0
$268$	−0.122091	−	0.0704895i	−0.00745792	−	0.00430583i
$269$	5.24433	+	3.81023i	0.319752	+	0.232314i	0.736070	−	0.676906i	$-0.236679\pi$
$269$	5.24433	+	3.81023i	0.319752	+	0.232314i	−0.416317	+	0.909219i	$0.636679\pi$
$270$		0			0
$271$	3.01248	−	2.18869i	0.182995	−	0.132954i	−0.492516	−	0.870303i	$-0.663923\pi$
$271$	3.01248	−	2.18869i	0.182995	−	0.132954i	0.675512	+	0.737349i	$0.263923\pi$
$272$	−18.6301	+	1.95810i	−1.12961	+	0.118727i
$273$		0			0
$274$	8.28887	+	14.3567i	0.500749	+	0.867322i
$275$	2.68590	−	1.97174i	0.161966	−	0.118900i
$276$		0			0
$277$	−3.37893	+	15.8966i	−0.203020	+	0.955134i	0.752131	+	0.659014i	$0.229026\pi$
$277$	−3.37893	+	15.8966i	−0.203020	+	0.955134i	−0.955151	+	0.296120i	$0.904307\pi$
$278$	4.10483	+	5.64981i	0.246191	+	0.338853i
$279$		0			0
$280$	−9.27292	+	10.3498i	−0.554163	+	0.618521i
$281$	0.979194	−	0.435965i	0.0584138	−	0.0260075i	−0.377322	−	0.926082i	$-0.623155\pi$
$281$	0.979194	−	0.435965i	0.0584138	−	0.0260075i	0.435736	+	0.900075i	$0.356488\pi$
$282$		0			0
$283$	13.0563	+	1.37228i	0.776119	+	0.0815734i	0.484302	−	0.874901i	$-0.339074\pi$
$283$	13.0563	+	1.37228i	0.776119	+	0.0815734i	0.291817	+	0.956474i	$0.405740\pi$
$284$	1.60437	−	0.341020i	0.0952019	−	0.0202358i
$285$		0			0
$286$	1.65078	+	0.350883i	0.0976124	+	0.0207482i
$287$	26.4600	+	8.59737i	1.56188	+	0.507487i
$288$		0			0
$289$	0.910992	+	2.80374i	0.0535877	+	0.164926i
$290$	−8.77667	+	2.87566i	−0.515384	+	0.168865i
$291$		0			0
$292$	−0.827968	−	0.0870229i	−0.0484532	−	0.00509263i
$293$	11.4180	−	6.59221i	0.667049	−	0.385121i	−0.127909	−	0.991786i	$-0.540826\pi$
$293$	11.4180	−	6.59221i	0.667049	−	0.385121i	0.794958	+	0.606665i	$0.207493\pi$
$294$		0			0
$295$	−9.24131	+	6.74909i	−0.538050	+	0.392947i
$296$	−7.72723	+	5.61416i	−0.449136	+	0.326316i
$297$		0			0
$298$	22.0232	−	7.15577i	1.27577	−	0.414523i
$299$	−1.75884	+	3.04639i	−0.101716	+	0.176177i
$300$		0			0
$301$	19.2907	+	33.4126i	1.11190	+	1.92587i
$302$	13.2325	+	11.9146i	0.761446	+	0.685609i
$303$		0			0
$304$	−2.61887	−	24.9169i	−0.150202	−	1.42908i
$305$	4.15908	−	0.894766i	0.238148	−	0.0512341i
$306$		0			0
$307$			0.396378i			0.0226225i	0.999936	+	0.0113113i	$0.00360056\pi$
$307$			0.396378i			0.0226225i	−0.999936	+	0.0113113i	$0.996399\pi$
$308$	1.07078	+	2.40501i	0.0610133	+	0.137038i
$309$		0			0
$310$	−36.3233	+	3.90833i	−2.06303	+	0.221978i
$311$	−17.5452	+	19.4859i	−0.994895	+	1.10494i	−0.000416817		1.00000i	$0.500133\pi$
$311$	−17.5452	+	19.4859i	−0.994895	+	1.10494i	−0.994478	+	0.104943i	$0.966534\pi$
$312$		0			0
$313$	15.7460	−	14.1778i	0.890018	−	0.801376i	−0.0908873	−	0.995861i	$-0.528970\pi$
$313$	15.7460	−	14.1778i	0.890018	−	0.801376i	0.980905	+	0.194485i	$0.0623036\pi$
$314$	7.42675	+	22.8572i	0.419116	+	1.28991i
$315$		0			0
$316$	5.53898	−	17.0472i	0.311592	−	0.958982i
$317$	10.3298	+	23.2010i	0.580177	+	1.30310i	0.930439	+	0.366447i	$0.119426\pi$
$317$	10.3298	+	23.2010i	0.580177	+	1.30310i	−0.350262	+	0.936652i	$0.613908\pi$
$318$		0			0
$319$	0.164675	−	1.56678i	0.00922002	−	0.0877227i
$320$	0.788673	+	0.871578i	0.0440882	+	0.0487227i
$321$		0			0
$322$	−15.8281	+	1.66360i	−0.882066	+	0.0927089i
$323$	17.8740	−	5.80763i	0.994538	−	0.323145i
$324$		0			0
$325$	−6.29456	−	3.59288i	−0.349159	−	0.199297i
$326$	10.7452	−	18.6112i	0.595121	−	1.03078i
$327$		0			0
$328$	4.99073	−	11.2094i	0.275567	−	0.618934i
$329$	37.8584	+	16.8556i	2.08720	+	0.929282i
$330$		0			0
$331$	0.400161	−	0.178163i	0.0219948	−	0.00979273i	−0.395710	−	0.918376i	$-0.629501\pi$
$331$	0.400161	−	0.178163i	0.0219948	−	0.00979273i	0.417705	+	0.908583i	$0.362835\pi$
$332$			3.47400i			0.190661i
$333$		0			0
$334$	4.88732	−	15.0416i	0.267422	−	0.823041i
$335$	−0.284649	+	0.0932648i	−0.0155520	+	0.00509560i
$336$		0			0
$337$	1.96564	+	9.24763i	0.107075	+	0.503750i	0.998700	+	0.0509748i	$0.0162328\pi$
$337$	1.96564	+	9.24763i	0.107075	+	0.503750i	−0.891624	+	0.452776i	$0.850434\pi$
$338$	3.95894	+	18.6253i	0.215338	+	1.01309i
$339$		0			0
$340$	5.16750	−	7.14947i	0.280247	−	0.387735i
$341$	1.92570	−	5.92668i	0.104282	−	0.320948i
$342$		0			0
$343$		−	0.342055i		−	0.0184693i
$344$	15.5445	−	6.92086i	0.838103	−	0.373148i
$345$		0			0
$346$	−0.618777	−	0.275497i	−0.0332657	−	0.0148108i
$347$	7.06225	−	15.8621i	0.379121	−	0.851520i	−0.618705	−	0.785623i	$-0.712342\pi$
$347$	7.06225	−	15.8621i	0.379121	−	0.851520i	0.997826	−	0.0658971i	$-0.0209909\pi$
$348$		0			0
$349$	−3.51770	+	6.09284i	−0.188298	+	0.326142i	−0.944683	−	0.327985i	$-0.893630\pi$
$349$	−3.51770	+	6.09284i	−0.188298	+	0.326142i	0.756385	+	0.654127i	$0.226964\pi$
$350$	−3.58849	−	32.5948i	−0.191813	−	1.74227i
$351$		0			0
$352$	3.43485	−	1.11605i	0.183078	−	0.0594857i
$353$	12.6331	−	1.32779i	0.672392	−	0.0706712i	0.237821	−	0.971309i	$-0.423567\pi$
$353$	12.6331	−	1.32779i	0.672392	−	0.0706712i	0.434571	+	0.900638i	$0.356900\pi$
$354$		0			0
$355$	1.73504	−	3.02236i	0.0920861	−	0.160410i
$356$	0.466686	−	4.44022i	0.0247343	−	0.235331i
$357$		0			0
$358$	6.73816	+	15.1342i	0.356123	+	0.799865i
$359$	8.11078	−	24.9624i	0.428071	−	1.31747i	−0.471952	−	0.881624i	$-0.656451\pi$
$359$	8.11078	−	24.9624i	0.428071	−	1.31747i	0.900023	−	0.435842i	$-0.143549\pi$
$360$		0			0
$361$	1.89612	+	5.83565i	0.0997957	+	0.307140i
$362$	27.8486	−	25.0750i	1.46369	−	1.31791i
$363$		0			0
$364$	3.83182	−	4.25567i	0.200842	−	0.223058i
$365$	−1.31161	+	1.18685i	−0.0686527	+	0.0621225i
$366$		0			0
$367$	−7.74844	−	17.4033i	−0.404465	−	0.908444i	−0.994853	−	0.101324i	$-0.967692\pi$
$367$	−7.74844	−	17.4033i	−0.404465	−	0.908444i	0.590388	−	0.807119i	$-0.298975\pi$
$368$			12.1270i			0.632161i
$369$		0			0
$370$	2.30066	−	22.4212i	0.119606	−	1.16562i
$371$	4.59246	+	43.6943i	0.238429	+	2.26850i
$372$		0			0
$373$	−16.5294	−	14.8831i	−0.855860	−	0.770619i	0.119128	−	0.992879i	$-0.461990\pi$
$373$	−16.5294	−	14.8831i	−0.855860	−	0.770619i	−0.974988	+	0.222260i	$0.928657\pi$
$374$	2.18216	+	3.77962i	0.112837	+	0.195439i
$375$		0			0
$376$	9.13839	−	15.8282i	0.471277	−	0.816275i
$377$	−3.25917	+	1.05897i	−0.167856	+	0.0545397i
$378$		0			0
$379$	6.01160	−	4.36768i	0.308795	−	0.224353i	−0.422584	−	0.906324i	$-0.638877\pi$
$379$	6.01160	−	4.36768i	0.308795	−	0.224353i	0.731379	+	0.681971i	$0.238877\pi$
$380$	9.56210	+	6.91130i	0.490525	+	0.354542i
$381$		0			0
$382$	39.5768	−	22.8497i	2.02492	−	1.16909i
$383$	−9.45757	−	0.994031i	−0.483259	−	0.0507926i	−0.140233	−	0.990118i	$-0.544785\pi$
$383$	−9.45757	−	0.994031i	−0.483259	−	0.0507926i	−0.343026	+	0.939326i	$0.611452\pi$
$384$		0			0
$385$	5.32399	+	1.71537i	0.271336	+	0.0874231i
$386$	2.01679	+	6.20705i	0.102652	+	0.315931i
$387$		0			0
$388$	1.32642	+	0.430980i	0.0673388	+	0.0218797i
$389$	5.61954	+	1.19447i	0.284922	+	0.0605620i	0.348156	−	0.937437i	$-0.386808\pi$
$389$	5.61954	+	1.19447i	0.284922	+	0.0605620i	−0.0632338	+	0.997999i	$0.520141\pi$
$390$		0			0
$391$	−8.89802	+	1.89133i	−0.449992	+	0.0956488i
$392$	−11.6753	−	1.22713i	−0.589694	−	0.0619793i
$393$		0			0
$394$	−20.9302	+	9.31874i	−1.05445	+	0.469471i
$395$	−19.1234	−	32.9349i	−0.962205	−	1.65714i
$396$		0			0
$397$	−5.75674	−	7.92348i	−0.288923	−	0.397668i	0.639741	−	0.768590i	$-0.279042\pi$
$397$	−5.75674	−	7.92348i	−0.288923	−	0.397668i	−0.928664	+	0.370922i	$0.879042\pi$
$398$	1.05869	−	4.98074i	0.0530673	−	0.249662i
$399$		0			0
$400$	−24.9860	+	0.123249i	−1.24930	+	0.00616244i
$401$	10.4437	+	18.0890i	0.521532	+	0.903320i	0.999686	+	0.0250444i	$0.00797272\pi$
$401$	10.4437	+	18.0890i	0.521532	+	0.903320i	−0.478154	+	0.878276i	$0.658694\pi$
$402$		0			0
$403$	−13.4812	+	1.41693i	−0.671545	+	0.0705822i
$404$	−4.19894	+	3.05071i	−0.208905	+	0.151778i
$405$		0			0
$406$	−12.5435	−	9.11337i	−0.622523	−	0.452289i
$407$	3.32953	+	1.92231i	0.165039	+	0.0952852i
$408$		0			0
$409$	−15.6930	+	3.33565i	−0.775969	+	0.164937i	−0.578841	−	0.815440i	$-0.696495\pi$
$409$	−15.6930	+	3.33565i	−0.775969	+	0.164937i	−0.197128	+	0.980378i	$0.563162\pi$
$410$	11.8421	+	26.4222i	0.584839	+	1.30490i
$411$		0			0
$412$	13.0449	−	11.7457i	0.642678	−	0.578670i
$413$	−18.2705	−	5.93644i	−0.899032	−	0.292113i
$414$		0			0
$415$	5.49748	+	4.92546i	0.269861	+	0.241781i
$416$	−5.25679	−	5.83826i	−0.257735	−	0.286244i
$417$		0			0
$418$	−5.05507	+	2.91854i	−0.247251	+	0.142751i
$419$	−1.86837	+	17.7763i	−0.0912756	+	0.868429i	0.849086	+	0.528254i	$0.177153\pi$
$419$	−1.86837	+	17.7763i	−0.0912756	+	0.868429i	−0.940362	+	0.340175i	$0.889514\pi$
$420$		0			0
$421$	1.83004	+	17.4117i	0.0891908	+	0.848594i	0.944065	+	0.329759i	$0.106967\pi$
$421$	1.83004	+	17.4117i	0.0891908	+	0.848594i	−0.854874	+	0.518835i	$0.826366\pi$
$422$	−5.64198	−	7.76553i	−0.274648	−	0.378020i
$423$		0			0
$424$	19.3766			0.941012
$425$	−3.98727	−	18.3140i	−0.193411	−	0.888357i
$426$		0			0
$427$	5.30741	+	4.77882i	0.256844	+	0.231263i
$428$	−4.91568	+	11.0408i	−0.237608	+	0.533677i
$429$		0			0
$430$	−12.3136	+	38.2178i	−0.593814	+	1.84303i
$431$	−14.7408	−	10.7098i	−0.710038	−	0.515873i	0.173148	−	0.984896i	$-0.444606\pi$
$431$	−14.7408	−	10.7098i	−0.710038	−	0.515873i	−0.883186	+	0.469023i	$0.844606\pi$
$432$		0			0
$433$	9.61568	−	13.2348i	0.462100	−	0.636026i	−0.512843	−	0.858483i	$-0.671408\pi$
$433$	9.61568	−	13.2348i	0.462100	−	0.636026i	0.974943	+	0.222456i	$0.0714075\pi$
$434$	−41.0378	−	45.5771i	−1.96988	−	2.18777i
$435$		0			0
$436$	−2.55051	+	2.83263i	−0.122147	+	0.135658i
$437$	−2.52957	−	11.9007i	−0.121006	−	0.569288i
$438$		0			0
$439$	−8.17881	−	1.73846i	−0.390353	−	0.0829722i	0.00855392	−	0.999963i	$-0.497277\pi$
$439$	−8.17881	−	1.73846i	−0.390353	−	0.0829722i	−0.398907	+	0.916991i	$0.630611\pi$
$440$	0.997819	−	2.25610i	0.0475692	−	0.107555i
$441$		0			0
$442$	5.58013	−	7.68038i	0.265420	−	0.365319i
$443$	−13.9314	−	8.04332i	−0.661903	−	0.382150i	0.131099	−	0.991369i	$-0.458150\pi$
$443$	−13.9314	−	8.04332i	−0.661903	−	0.382150i	−0.793002	+	0.609219i	$0.791483\pi$
$444$		0			0
$445$	−6.36482	−	7.03388i	−0.301721	−	0.333438i
$446$	−10.7369	−	4.78039i	−0.508409	−	0.226358i
$447$		0			0
$448$	−0.410267	+	1.93015i	−0.0193833	+	0.0911911i
$449$	−9.82336			−0.463593			−0.231797	−	0.972764i	$-0.574460\pi$
$449$	−9.82336			−0.463593			−0.231797	+	0.972764i	$0.574460\pi$
$450$		0			0
$451$	−4.93898			−0.232568
$452$	0.360091	−	1.69409i	0.0169372	−	0.0796835i
$453$		0			0
$454$	−39.5060	−	17.5892i	−1.85411	−	0.825501i
$455$	−1.30167	−	12.0974i	−0.0610230	−	0.567136i
$456$		0			0
$457$	30.7197	+	17.7360i	1.43701	+	0.829657i	0.997641	−	0.0686509i	$-0.0218695\pi$
$457$	30.7197	+	17.7360i	1.43701	+	0.829657i	0.439367	+	0.898308i	$0.355203\pi$
$458$	10.5523	−	14.5239i	0.493075	−	0.678659i
$459$		0			0
$460$	−4.25331	−	3.81075i	−0.198312	−	0.177677i
$461$	19.4142	+	4.12661i	0.904207	+	0.192195i	0.636474	−	0.771298i	$-0.280392\pi$
$461$	19.4142	+	4.12661i	0.904207	+	0.192195i	0.267733	+	0.963493i	$0.413725\pi$
$462$		0			0
$463$	0.343862	+	1.61774i	0.0159806	+	0.0751830i	0.985415	−	0.170167i	$-0.0544306\pi$
$463$	0.343862	+	1.61774i	0.0159806	+	0.0751830i	−0.969435	+	0.245350i	$0.921097\pi$
$464$	−7.90512	+	8.77952i	−0.366986	+	0.407579i
$465$		0			0
$466$	−12.2108	−	13.5614i	−0.565653	−	0.628221i
$467$	−13.9659	+	19.2225i	−0.646267	+	0.889510i	−0.998930	−	0.0462404i	$-0.985276\pi$
$467$	−13.9659	+	19.2225i	−0.646267	+	0.889510i	0.352664	+	0.935750i	$0.385276\pi$
$468$		0			0
$469$	−0.406816	−	0.295569i	−0.0187850	−	0.0136481i
$470$	13.4286	+	40.9848i	0.619416	+	1.89049i
$471$		0			0
$472$	−3.44607	+	7.74001i	−0.158618	+	0.356263i
$473$	−5.08987	−	4.58294i	−0.234032	−	0.210724i
$474$		0			0
$475$	24.4941	−	5.33279i	1.12387	−	0.244685i
$476$	14.8091			0.678773
$477$		0			0
$478$	23.3117	+	32.0858i	1.06625	+	1.46757i
$479$	3.30027	+	31.4000i	0.150793	+	1.43470i	0.764223	+	0.644952i	$0.223123\pi$
$479$	3.30027	+	31.4000i	0.150793	+	1.43470i	−0.613430	+	0.789749i	$0.710211\pi$
$480$		0			0
$481$	0.874169	−	8.31716i	0.0398587	−	0.379230i
$482$	−38.9472	+	22.4862i	−1.77399	+	1.02422i
$483$		0			0
$484$	7.43351	+	8.25575i	0.337887	+	0.375261i
$485$	2.56262	−	1.48797i	0.116362	−	0.0675651i
$486$		0			0
$487$	31.6451	+	10.2821i	1.43398	+	0.465928i	0.920015	−	0.391884i	$-0.128177\pi$
$487$	31.6451	+	10.2821i	1.43398	+	0.465928i	0.513964	+	0.857812i	$0.328177\pi$
$488$	2.34073	−	2.10760i	0.105960	−	0.0954065i
$489$		0			0
$490$	20.5413	−	18.5874i	0.927962	−	0.839694i
$491$	1.63163	−	0.346814i	0.0736345	−	0.0156515i	−0.170947	−	0.985280i	$-0.554683\pi$
$491$	1.63163	−	0.346814i	0.0736345	−	0.0156515i	0.244582	+	0.969629i	$0.421349\pi$
$492$		0			0
$493$	−7.67477	−	4.43103i	−0.345654	−	0.199564i
$494$	10.2722	+	7.46317i	0.462167	+	0.335784i
$495$		0			0
$496$	−37.8066	+	27.4681i	−1.69757	+	1.23335i
$497$	5.81837	−	0.611535i	0.260989	−	0.0274311i
$498$		0			0
$499$	−4.43912	−	7.68878i	−0.198722	−	0.344197i	0.749392	−	0.662126i	$-0.230346\pi$
$499$	−4.43912	−	7.68878i	−0.198722	−	0.344197i	−0.948114	+	0.317929i	$0.897013\pi$
$500$	7.80831	−	8.80211i	0.349198	−	0.393642i
$501$		0			0
$502$	9.19425	−	43.2555i	0.410359	−	1.93059i
$503$	−19.2085	−	26.4383i	−0.856467	−	1.17883i	−0.982401	−	0.186786i	$-0.940193\pi$
$503$	−19.2085	−	26.4383i	−0.856467	−	1.17883i	0.125934	−	0.992039i	$-0.459807\pi$
$504$		0			0
$505$	−1.12564	+	10.9700i	−0.0500905	+	0.488158i
$506$	2.58107	−	1.14916i	0.114742	−	0.0510866i
$507$		0			0
$508$	19.3397	+	2.03269i	0.858062	+	0.0901859i
$509$	−32.5108	+	6.91039i	−1.44102	+	0.306298i	−0.861124	−	0.508395i	$-0.830239\pi$
$509$	−32.5108	+	6.91039i	−1.44102	+	0.306298i	−0.579893	+	0.814692i	$0.696906\pi$
$510$		0			0
$511$	−2.90462	−	0.617397i	−0.128493	−	0.0273120i
$512$	−10.0215	−	3.25619i	−0.442893	−	0.143905i
$513$		0			0
$514$	10.4908	+	32.2874i	0.462731	+	1.42414i
$515$	−0.0919856	−	37.2963i	−0.00405337	−	1.64347i
$516$		0			0
$517$	−7.31645	−	0.768990i	−0.321777	−	0.0338202i
$518$	32.7681	−	18.9187i	1.43975	−	0.831238i
$519$		0			0
$520$	−5.36610	+	0.0132347i	−0.235319	+	0.000580379i
$521$	−1.75489	+	1.27500i	−0.0768832	+	0.0558589i	−0.625563	−	0.780174i	$-0.715131\pi$
$521$	−1.75489	+	1.27500i	−0.0768832	+	0.0558589i	0.548680	+	0.836033i	$0.315131\pi$
$522$		0			0
$523$	−6.96385	+	2.26269i	−0.304508	+	0.0989406i	−0.457285	−	0.889320i	$-0.651178\pi$
$523$	−6.96385	+	2.26269i	−0.304508	+	0.0989406i	0.152778	+	0.988261i	$0.451178\pi$
$524$	2.10420	−	3.64457i	0.0919222	−	0.159214i
$525$		0			0
$526$	19.1722	+	33.2072i	0.835947	+	1.44790i
$527$	−26.0508	−	23.4562i	−1.13479	−	1.02177i
$528$		0			0
$529$	−1.78859	−	17.0173i	−0.0777647	−	0.739882i
$530$	−30.5115	+	34.0549i	−1.32533	+	1.47925i
$531$		0			0
$532$			19.8065i			0.858720i
$533$	4.36977	+	9.81467i	0.189276	+	0.425121i
$534$		0			0
$535$	10.5022	+	23.4326i	0.454049	+	1.01308i
$536$	−0.148395	+	0.164809i	−0.00640968	+	0.00711867i
$537$		0			0
$538$	−8.41642	+	7.57818i	−0.362858	+	0.326719i
$539$	1.46024	+	4.49416i	0.0628970	+	0.193577i
$540$		0			0
$541$	8.25025	−	25.3916i	0.354706	−	1.09167i	−0.601474	−	0.798892i	$-0.705420\pi$
$541$	8.25025	−	25.3916i	0.354706	−	1.09167i	0.956180	−	0.292780i	$-0.0945803\pi$
$542$	2.64607	+	5.94317i	0.113658	+	0.255281i
$543$		0			0
$544$	2.12363	−	20.2049i	0.0910497	−	0.866280i
$545$	0.866406	+	8.05221i	0.0371128	+	0.344919i
$546$		0			0
$547$	−13.3649	+	1.40471i	−0.571442	+	0.0600609i	−0.385843	−	0.922565i	$-0.626089\pi$
$547$	−13.3649	+	1.40471i	−0.571442	+	0.0600609i	−0.185599	+	0.982626i	$0.559423\pi$
$548$	−9.49722	+	3.08583i	−0.405701	+	0.131820i
$549$		0			0
$550$	2.39393	+	5.30626i	0.102078	+	0.226260i
$551$	5.92630	−	10.2647i	0.252469	−	0.437289i
$552$		0			0
$553$	26.0044	−	58.4069i	1.10582	−	2.48371i
$554$	−25.9389	−	11.5488i	−1.10204	−	0.490659i
$555$		0			0
$556$	−3.84301	+	1.71102i	−0.162980	+	0.0725633i
$557$			28.5556i			1.20994i	0.796248	+	0.604970i	$0.206815\pi$
$557$			28.5556i			1.20994i	−0.796248	+	0.604970i	$0.793185\pi$
$558$		0			0
$559$	−4.60388	+	14.1693i	−0.194723	+	0.599296i
$560$	−24.7388	−	33.8740i	−1.04540	−	1.43144i
$561$		0			0
$562$	0.389349	+	1.83174i	0.0164237	+	0.0772674i
$563$	1.46405	+	6.88783i	0.0617025	+	0.290287i	0.998170	−	0.0604664i	$-0.0192588\pi$
$563$	1.46405	+	6.88783i	0.0617025	+	0.290287i	−0.936468	+	0.350754i	$0.885925\pi$
$564$		0			0
$565$	−2.17030	−	2.97173i	−0.0913054	−	0.125021i
$566$	−7.08779	+	21.8140i	−0.297922	+	0.916910i
$567$		0			0
$568$		−	2.58021i		−	0.108263i
$569$	8.31748	−	3.70318i	0.348687	−	0.155245i	−0.224918	−	0.974378i	$-0.572211\pi$
$569$	8.31748	−	3.70318i	0.348687	−	0.155245i	0.573605	+	0.819132i	$0.305545\pi$
$570$		0			0
$571$	−29.2397	−	13.0184i	−1.22364	−	0.544802i	−0.309775	−	0.950810i	$-0.600254\pi$
$571$	−29.2397	−	13.0184i	−1.22364	−	0.544802i	−0.913869	+	0.406008i	$0.866920\pi$
$572$	−0.413487	+	0.928707i	−0.0172888	+	0.0388312i
$573$		0			0
$574$	−24.3039	+	42.0955i	−1.01442	+	1.75703i
$575$	−12.0607	+	1.32782i	−0.502968	+	0.0553738i
$576$		0			0
$577$	1.49607	−	0.486103i	0.0622822	−	0.0202367i	−0.277710	−	0.960665i	$-0.589575\pi$
$577$	1.49607	−	0.486103i	0.0622822	−	0.0202367i	0.339992	+	0.940428i	$0.389575\pi$
$578$	−5.12234	+	0.538379i	−0.213061	+	0.0223936i
$579$		0			0
$580$	−0.595174	−	5.53144i	−0.0247133	−	0.229680i
$581$	−1.29524	+	12.3234i	−0.0537357	+	0.511261i
$582$		0			0
$583$	−3.17233	−	7.12516i	−0.131384	−	0.295094i
$584$	−0.404702	+	1.24554i	−0.0167467	+	0.0515410i
$585$		0			0
$586$	7.11811	+	21.9073i	0.294047	+	0.904982i
$587$	−0.231583	+	0.208519i	−0.00955847	+	0.00860648i	−0.673896	−	0.738826i	$-0.735380\pi$
$587$	−0.231583	+	0.208519i	−0.00955847	+	0.00860648i	0.664338	+	0.747433i	$0.268714\pi$
$588$		0			0
$589$	31.3716	−	34.8417i	1.29265	−	1.43563i
$590$	−8.17690	−	18.2444i	−0.336638	−	0.751110i
$591$		0			0
$592$	−11.7266	−	26.3383i	−0.481958	−	1.08250i
$593$			8.60462i			0.353350i	0.984269	+	0.176675i	$0.0565341\pi$
$593$			8.60462i			0.353350i	−0.984269	+	0.176675i	$0.943466\pi$
$594$		0			0
$595$	20.9964	−	23.4348i	0.860768	−	0.960735i
$596$	1.45805	+	13.8725i	0.0597242	+	0.568238i
$597$		0			0
$598$	−4.56720	−	4.11233i	−0.186767	−	0.168166i
$599$	2.26387	+	3.92114i	0.0924993	+	0.160213i	0.908562	−	0.417750i	$-0.137181\pi$
$599$	2.26387	+	3.92114i	0.0924993	+	0.160213i	−0.816063	+	0.577963i	$0.803848\pi$
$600$		0			0
$601$	−8.48989	+	14.7049i	−0.346310	+	0.599826i	−0.985591	−	0.169147i	$-0.945899\pi$
$601$	−8.48989	+	14.7049i	−0.346310	+	0.599826i	0.639281	+	0.768973i	$0.279232\pi$
$602$	−64.1072	+	20.8297i	−2.61282	+	0.848955i
$603$		0			0
$604$	−8.67744	+	6.30453i	−0.353080	+	0.256528i
$605$	23.6037	−	0.0582149i	0.959627	−	0.00236677i
$606$		0			0
$607$	4.98025	−	2.87535i	0.202142	−	0.116707i	−0.395512	−	0.918461i	$-0.629433\pi$
$607$	4.98025	−	2.87535i	0.202142	−	0.116707i	0.597654	+	0.801754i	$0.296100\pi$
$608$	27.0232	+	2.84025i	1.09594	+	0.115188i
$609$		0			0
$610$	0.0183314	+	7.43262i	0.000742217	+	0.300938i
$611$	4.94512	+	15.2195i	0.200058	+	0.615716i
$612$		0			0
$613$	18.5982	+	6.04292i	0.751174	+	0.244071i	0.659486	−	0.751716i	$-0.270774\pi$
$613$	18.5982	+	6.04292i	0.751174	+	0.244071i	0.0916880	+	0.995788i	$0.470774\pi$
$614$	−0.677386	−	0.143983i	−0.0273371	−	0.00581067i
$615$		0			0
$616$	4.05083	−	0.861031i	0.163213	−	0.0346919i
$617$	18.9641	+	1.99321i	0.763467	+	0.0802436i	0.478255	−	0.878221i	$-0.341269\pi$
$617$	18.9641	+	1.99321i	0.763467	+	0.0802436i	0.285212	+	0.958465i	$0.407936\pi$
$618$		0			0
$619$	−24.2178	+	10.7825i	−0.973395	+	0.433383i	−0.830906	−	0.556413i	$-0.812177\pi$
$619$	−24.2178	+	10.7825i	−0.973395	+	0.433383i	−0.142489	+	0.989796i	$0.545511\pi$
$620$	2.24632	−	21.8915i	0.0902142	−	0.879184i
$621$		0			0
$622$	−26.9269	−	37.0618i	−1.07967	−	1.48604i
$623$	3.31097	−	15.5769i	0.132651	−	0.624075i
$624$		0			0
$625$	−2.85836	−	24.8361i	−0.114335	−	0.993442i
$626$	18.5093	+	32.0590i	0.739779	+	1.28134i
$627$		0			0
$628$	−14.3978	+	1.51327i	−0.574534	+	0.0603859i
$629$	17.4965	−	12.7120i	0.697633	−	0.506860i
$630$		0			0
$631$	−31.6402	−	22.9880i	−1.25958	−	0.915136i	−0.260840	−	0.965382i	$-0.584000\pi$
$631$	−31.6402	−	22.9880i	−1.25958	−	0.915136i	−0.998737	+	0.0502455i	$0.984000\pi$
$632$	−24.4192	−	14.0985i	−0.971345	−	0.560806i
$633$		0			0
$634$	−43.4013	+	9.22523i	−1.72369	+	0.366381i
$635$	30.6366	−	27.7225i	1.21578	−	1.10013i
$636$		0			0
$637$	7.63877	−	6.87798i	0.302659	−	0.272515i
$638$	2.61771	+	0.850544i	0.103636	+	0.0336734i
$639$		0			0
$640$	−22.7364	+	13.2017i	−0.898735	+	0.521844i
$641$	−12.5942	−	13.9873i	−0.497443	−	0.552466i	0.441177	−	0.897420i	$-0.354561\pi$
$641$	−12.5942	−	13.9873i	−0.497443	−	0.552466i	−0.938620	+	0.344954i	$0.887894\pi$
$642$		0			0
$643$	−18.4572	+	10.6563i	−0.727881	+	0.420242i	−0.817646	−	0.575721i	$-0.804722\pi$
$643$	−18.4572	+	10.6563i	−0.727881	+	0.420242i	0.0897654	+	0.995963i	$0.471388\pi$
$644$	1.00211	−	9.53441i	0.0394886	−	0.375709i
$645$		0			0
$646$	3.43220	+	32.6552i	0.135038	+	1.28480i
$647$	−21.2702	−	29.2760i	−0.836219	−	1.15096i	−0.986733	−	0.162349i	$-0.948093\pi$
$647$	−21.2702	−	29.2760i	−0.836219	−	1.15096i	0.150514	−	0.988608i	$-0.451907\pi$
$648$		0			0
$649$	3.41034			0.133868
$650$	8.42649	−	9.45191i	0.330514	−	0.370734i
$651$		0			0
$652$	9.62017	+	8.66204i	0.376755	+	0.339232i
$653$	1.87939	−	4.22118i	0.0735463	−	0.165188i	−0.873031	−	0.487665i	$-0.837849\pi$
$653$	1.87939	−	4.22118i	0.0735463	−	0.165188i	0.946577	+	0.322477i	$0.104516\pi$
$654$		0			0
$655$	−2.78407	−	8.49711i	−0.108783	−	0.332010i
$656$	29.9640	+	21.7701i	1.16990	+	0.849980i
$657$		0			0
$658$	−42.5572	+	58.5749i	−1.65905	+	2.28349i
$659$	14.5964	+	16.2110i	0.568597	+	0.631491i	0.957031	−	0.289986i	$-0.0936506\pi$
$659$	14.5964	+	16.2110i	0.568597	+	0.631491i	−0.388434	+	0.921476i	$0.626984\pi$
$660$		0			0
$661$	4.52703	−	5.02777i	0.176081	−	0.195558i	−0.648644	−	0.761092i	$-0.724663\pi$
$661$	4.52703	−	5.02777i	0.176081	−	0.195558i	0.824725	+	0.565535i	$0.191330\pi$
$662$	0.159113	+	0.748567i	0.00618409	+	0.0290939i
$663$		0			0
$664$	5.34550	+	1.13622i	0.207446	+	0.0440939i
$665$	31.3430	+	28.0817i	1.21543	+	1.08896i
$666$		0			0
$667$	−3.37214	+	4.64135i	−0.130570	+	0.179714i
$668$	8.25057	+	4.76347i	0.319224	+	0.184304i
$669$		0			0
$670$	−0.0559862	−	0.520325i	−0.00216294	−	0.0201019i
$671$	−1.15823	−	0.515676i	−0.0447129	−	0.0199074i
$672$		0			0
$673$	−3.37090	+	15.8588i	−0.129938	+	0.611313i	0.864195	+	0.503156i	$0.167828\pi$
$673$	−3.37090	+	15.8588i	−0.129938	+	0.611313i	−0.994134	+	0.108156i	$0.965505\pi$
$674$	−16.5176			−0.636235
$675$		0			0
$676$	−11.4700			−0.441155
$677$	3.63779	−	17.1145i	0.139812	−	0.657762i	−0.851294	−	0.524688i	$-0.824182\pi$
$677$	3.63779	−	17.1145i	0.139812	−	0.657762i	0.991106	−	0.133074i	$-0.0424848\pi$
$678$		0			0
$679$	4.54455	+	2.02337i	0.174404	+	0.0776497i
$680$	−9.31090	−	10.2896i	−0.357057	−	0.394590i
$681$		0			0
$682$	9.42883	+	5.44374i	0.361048	+	0.208451i
$683$	4.49194	−	6.18262i	0.171879	−	0.236571i	−0.714383	−	0.699754i	$-0.753293\pi$
$683$	4.49194	−	6.18262i	0.171879	−	0.236571i	0.886263	+	0.463183i	$0.153293\pi$
$684$		0			0
$685$	−8.58199	+	19.4041i	−0.327901	+	0.741393i
$686$	0.584551	+	0.124250i	0.0223183	+	0.00474390i
$687$		0			0
$688$	10.6787	+	50.2391i	0.407120	+	1.91535i
$689$	−11.3523	+	12.6080i	−0.432488	+	0.480327i
$690$		0			0
$691$	−5.95581	−	6.61459i	−0.226570	−	0.251631i	0.619132	−	0.785287i	$-0.287484\pi$
$691$	−5.95581	−	6.61459i	−0.226570	−	0.251631i	−0.845702	+	0.533656i	$0.820818\pi$
$692$	0.239821	−	0.330086i	0.00911664	−	0.0125480i
$693$		0			0
$694$	24.5419	+	17.8308i	0.931599	+	0.676847i
$695$	−2.74102	+	8.50731i	−0.103973	+	0.322701i
$696$		0			0
$697$	−11.3004	+	25.3810i	−0.428032	+	0.961375i
$698$	−9.13449	−	8.22473i	−0.345745	−	0.311311i
$699$		0			0
$700$	19.6546	+	1.96781i	0.742873	+	0.0743761i
$701$	41.8416			1.58034			0.790168	−	0.612891i	$-0.209993\pi$
$701$	41.8416			1.58034			0.790168	+	0.612891i	$0.209993\pi$
$702$		0			0
$703$	17.0017	+	23.4008i	0.641231	+	0.882579i
$704$	−0.0366164	−	0.348382i	−0.00138003	−	0.0131301i
$705$		0			0
$706$	−2.31981	+	22.0715i	−0.0873071	+	0.830671i
$707$	−16.0324	+	9.25632i	−0.602961	+	0.348120i
$708$		0			0
$709$	−3.75850	−	4.17424i	−0.141154	−	0.156767i	0.668423	−	0.743782i	$-0.266970\pi$
$709$	−3.75850	−	4.17424i	−0.141154	−	0.156767i	−0.809576	+	0.587015i	$0.800303\pi$
$710$	4.53478	+	4.06293i	0.170187	+	0.152479i
$711$		0			0
$712$	−6.67959	−	2.17033i	−0.250328	−	0.0813366i
$713$	−16.8645	+	15.1848i	−0.631579	+	0.568676i
$714$		0			0
$715$	0.883401	+	1.97105i	0.0330373	+	0.0737132i
$716$	−9.76107	+	2.07478i	−0.364788	+	0.0775381i
$717$		0			0
$718$	39.7130	+	22.9283i	1.48208	+	0.855677i
$719$	−3.88292	−	2.82111i	−0.144808	−	0.105210i	0.513022	−	0.858375i	$-0.328526\pi$
$719$	−3.88292	−	2.82111i	−0.144808	−	0.105210i	−0.657831	+	0.753166i	$0.728526\pi$
$720$		0			0
$721$	50.6539	−	36.8022i	1.88645	−	1.37058i
$722$	−10.6615	+	1.12057i	−0.396781	+	0.0417033i
$723$		0			0
$724$	11.2866	+	19.5490i	0.419464	+	0.726534i
$725$	−9.59714	−	6.90066i	−0.356429	−	0.256284i
$726$		0			0
$727$	−9.27710	+	43.6453i	−0.344068	+	1.61871i	0.377250	+	0.926111i	$0.376870\pi$
$727$	−9.27710	+	43.6453i	−0.344068	+	1.61871i	−0.721319	+	0.692603i	$0.756464\pi$
$728$	−5.29501	−	7.28796i	−0.196246	−	0.270110i
$729$		0			0
$730$	−1.55181	−	2.67257i	−0.0574352	−	0.0989164i
$731$	−35.1969	+	15.6707i	−1.30181	+	0.579601i
$732$		0			0
$733$	50.5491	+	5.31293i	1.86707	+	0.196237i	0.969578	−	0.244783i	$-0.0787168\pi$
$733$	50.5491	+	5.31293i	1.86707	+	0.196237i	0.897497	+	0.441021i	$0.145383\pi$
$734$	32.5557	−	6.91993i	1.20165	−	0.255419i
$735$		0			0
$736$	−12.8647	−	2.73448i	−0.474199	−	0.100794i
$737$	0.0848987	+	0.0275853i	0.00312728	+	0.00101612i
$738$		0			0
$739$	−2.35761	−	7.25597i	−0.0867260	−	0.266915i	0.898283	−	0.439417i	$-0.144815\pi$
$739$	−2.35761	−	7.25597i	−0.0867260	−	0.266915i	−0.985009	+	0.172502i	$0.944815\pi$
$740$	12.9226	+	4.16360i	0.475045	+	0.153057i
$741$		0			0
$742$	−76.3390	−	8.02356i	−2.80249	−	0.294554i
$743$	−22.0140	+	12.7098i	−0.807615	+	0.466277i	−0.846127	−	0.532981i	$-0.821072\pi$
$743$	−22.0140	+	12.7098i	−0.807615	+	0.466277i	0.0385118	+	0.999258i	$0.487738\pi$
$744$		0			0
$745$	24.0199	+	17.3611i	0.880021	+	0.636063i
$746$	31.4386	−	22.8415i	1.15105	−	0.836285i
$747$		0			0
$748$	−2.50028	+	0.812390i	−0.0914192	+	0.0297039i
$749$	−21.5539	+	37.3325i	−0.787564	+	1.36410i
$750$		0			0
$751$	4.27890	+	7.41128i	0.156139	+	0.270441i	0.933473	−	0.358647i	$-0.116762\pi$
$751$	4.27890	+	7.41128i	0.156139	+	0.270441i	−0.777334	+	0.629088i	$0.783428\pi$
$752$	40.9981	+	36.9149i	1.49505	+	1.34615i
$753$		0			0
$754$	−0.625831	−	5.95439i	−0.0227914	−	0.216846i
$755$	−2.32623	+	22.6703i	−0.0846603	+	0.825058i
$756$		0			0
$757$		−	23.1763i		−	0.842357i	−0.906978	−	0.421179i	$-0.861617\pi$
$757$		−	23.1763i		−	0.842357i	0.906978	−	0.421179i	$-0.138383\pi$
$758$	5.28041	+	11.8600i	0.191793	+	0.430774i
$759$		0			0
$760$	13.7619	−	12.4529i	0.499198	−	0.451714i
$761$	−16.1121	+	17.8943i	−0.584062	+	0.648667i	−0.960666	−	0.277708i	$-0.910425\pi$
$761$	−16.1121	+	17.8943i	−0.584062	+	0.648667i	0.376604	+	0.926375i	$0.377092\pi$
$762$		0			0
$763$	−10.1036	+	9.09732i	−0.365775	+	0.329345i
$764$	8.50662	+	26.1807i	0.307759	+	0.947184i
$765$		0			0
$766$	5.13416	−	15.8013i	0.185505	−	0.570925i
$767$	−3.01731	−	6.77698i	−0.108949	−	0.244703i
$768$		0			0
$769$	−3.65020	+	34.7293i	−0.131630	+	1.25237i	0.706820	+	0.707393i	$0.250129\pi$
$769$	−3.65020	+	34.7293i	−0.131630	+	1.25237i	−0.838450	+	0.544979i	$0.816538\pi$
$770$	−4.86537	+	8.47527i	−0.175336	+	0.305428i
$771$		0			0
$772$	−3.90983	+	0.410940i	−0.140718	+	0.0147901i
$773$	13.1421	−	4.27014i	0.472689	−	0.153586i	−0.0629784	−	0.998015i	$-0.520060\pi$
$773$	13.1421	−	4.27014i	0.472689	−	0.153586i	0.535668	+	0.844429i	$0.320060\pi$
$774$		0			0
$775$	−31.4577	−	34.5926i	−1.12999	−	1.24260i
$776$	1.09698	−	1.90003i	0.0393793	−	0.0682069i
$777$		0			0
$778$	−4.08255	+	9.16955i	−0.146366	+	0.328744i
$779$	−33.9460	−	15.1137i	−1.21624	−	0.541506i
$780$		0			0
$781$	−0.948792	+	0.422429i	−0.0339504	+	0.0151157i
$782$		−	15.8932i		−	0.568339i
$783$		0			0
$784$	10.9504	−	33.7018i	0.391085	−	1.20363i
$785$	−18.0186	+	24.9295i	−0.643110	+	0.889772i
$786$		0			0
$787$	−10.1538	−	47.7699i	−0.361944	−	1.70281i	−0.662510	−	0.749053i	$-0.730509\pi$
$787$	−10.1538	−	47.7699i	−0.361944	−	1.70281i	0.300566	−	0.953761i	$-0.402824\pi$
$788$	−2.86938	−	13.4994i	−0.102217	−	0.480895i
$789$		0			0
$790$	63.2302	−	20.7173i	2.24963	−	0.737088i
$791$	1.90898	−	5.87524i	0.0678755	−	0.208899i
$792$		0			0
$793$			2.75786i			0.0979343i
$794$	15.6318	−	6.95974i	0.554753	−	0.246992i
$795$		0			0
$796$	2.80211	+	1.24758i	0.0993180	+	0.0442192i
$797$	16.1888	−	36.3605i	0.573435	−	1.28796i	−0.361246	−	0.932470i	$-0.617649\pi$
$797$	16.1888	−	36.3605i	0.573435	−	1.28796i	0.934682	−	0.355486i	$-0.115685\pi$
$798$		0			0
$799$	−20.6918	+	35.8392i	−0.732023	+	1.26790i
$800$	5.50327	−	26.5338i	0.194570	−	0.938111i
$801$		0			0
$802$	−34.7065	+	11.2768i	−1.22553	+	0.398199i
$803$	0.524269	−	0.0551028i	0.0185010	−	0.00194454i
$804$		0			0
$805$	−13.6671	−	15.1037i	−0.481701	−	0.532337i
$806$	2.47554	−	23.5532i	0.0871971	−	0.829625i
$807$		0			0
$808$	3.32085	+	7.45875i	0.116827	+	0.262398i
$809$	−1.36669	+	4.20622i	−0.0480501	+	0.147883i	−0.972203	−	0.234140i	$-0.924773\pi$
$809$	−1.36669	+	4.20622i	−0.0480501	+	0.147883i	0.924153	+	0.382023i	$0.124773\pi$
$810$		0			0
$811$	4.98095	+	15.3298i	0.174905	+	0.538301i	0.999629	−	0.0272334i	$-0.00866975\pi$
$811$	4.98095	+	15.3298i	0.174905	+	0.538301i	−0.824724	+	0.565535i	$0.808670\pi$
$812$	6.94063	−	6.24937i	0.243568	−	0.219310i
$813$		0			0
$814$	−4.49454	+	4.99169i	−0.157534	+	0.174959i
$815$	27.3469	−	2.94248i	0.957920	−	0.103071i
$816$		0			0
$817$	−20.9588	−	47.0743i	−0.733257	−	1.64692i
$818$		−	28.0300i		−	0.980047i
$819$		0			0
$820$	−17.0513	+	3.66834i	−0.595457	+	0.128104i
$821$	−4.35674	−	41.4516i	−0.152051	−	1.44667i	−0.758565	−	0.651598i	$-0.774099\pi$
$821$	−4.35674	−	41.4516i	−0.152051	−	1.44667i	0.606514	−	0.795073i	$-0.292568\pi$
$822$		0			0
$823$	41.6242	+	37.4786i	1.45093	+	1.30642i	0.870553	+	0.492075i	$0.163761\pi$
$823$	41.6242	+	37.4786i	1.45093	+	1.30642i	0.580377	+	0.814348i	$0.302905\pi$
$824$	−13.8068	−	23.9140i	−0.480982	−	0.833085i
$825$		0			0
$826$	16.7817	−	29.0667i	0.583909	−	1.01136i
$827$	19.1562	−	6.22424i	0.666128	−	0.216438i	0.0436158	−	0.999048i	$-0.486112\pi$
$827$	19.1562	−	6.22424i	0.666128	−	0.216438i	0.622512	+	0.782610i	$0.286112\pi$
$828$		0			0
$829$	1.14834	−	0.834320i	0.0398836	−	0.0289771i	−0.567665	−	0.823260i	$-0.692153\pi$
$829$	1.14834	−	0.834320i	0.0398836	−	0.0289771i	0.607548	+	0.794283i	$0.292153\pi$
$830$	−10.4142	+	7.60570i	−0.361483	+	0.263998i
$831$		0			0
$832$	−0.659903	+	0.380995i	−0.0228780	+	0.0132086i
$833$	26.4361	+	2.77855i	0.915958	+	0.0962710i
$834$		0			0
$835$	19.2357	−	6.30256i	0.665680	−	0.218109i
$836$	−1.08653	−	3.34401i	−0.0375786	−	0.115655i
$837$		0			0
$838$	−29.6999	−	9.65009i	−1.02597	−	0.333357i
$839$	26.5147	+	5.63588i	0.915390	+	0.194572i	0.641441	−	0.767172i	$-0.278337\pi$
$839$	26.5147	+	5.63588i	0.915390	+	0.194572i	0.273949	+	0.961744i	$0.411670\pi$
$840$		0			0
$841$	22.8994	−	4.86743i	0.789636	−	0.167842i
$842$	−30.4202	−	3.19730i	−1.04835	−	0.110186i
$843$		0			0
$844$	5.28212	−	2.35175i	0.181818	−	0.0809506i
$845$	−16.2623	+	18.1509i	−0.559440	+	0.624411i
$846$		0			0
$847$	23.2910	+	32.0573i	0.800288	+	1.10150i
$848$	−12.1604	+	57.2102i	−0.417590	+	1.96461i
$849$		0			0
$850$	32.7458	−	0.161526i	1.12317	−	0.00554029i
$851$	−7.00029	−	12.1249i	−0.239967	−	0.415635i
$852$		0			0
$853$	−46.4395	+	4.88098i	−1.59006	+	0.167122i	−0.857828	−	0.513937i	$-0.828186\pi$
$853$	−46.4395	+	4.88098i	−1.59006	+	0.167122i	−0.732229	+	0.681059i	$0.761520\pi$
$854$	−10.0946	+	7.33415i	−0.345430	+	0.250969i
$855$		0			0
$856$	15.3809	+	11.1749i	0.525708	+	0.381949i
$857$	37.4303	+	21.6104i	1.27860	+	0.738198i	0.976590	−	0.215108i	$-0.0690105\pi$
$857$	37.4303	+	21.6104i	1.27860	+	0.738198i	0.302006	+	0.953306i	$0.402344\pi$
$858$		0			0
$859$	−8.36680	+	1.77842i	−0.285472	+	0.0606789i	−0.348422	−	0.937338i	$-0.613282\pi$
$859$	−8.36680	+	1.77842i	−0.285472	+	0.0606789i	0.0629504	+	0.998017i	$0.479949\pi$
$860$	−20.9761	−	12.0417i	−0.715280	−	0.410618i
$861$		0			0
$862$	23.6569	−	21.3008i	0.805758	−	0.725507i
$863$	9.08388	+	2.95153i	0.309219	+	0.100471i	0.459516	−	0.888170i	$-0.348023\pi$
$863$	9.08388	+	2.95153i	0.309219	+	0.100471i	−0.150297	+	0.988641i	$0.548023\pi$
$864$		0			0
$865$	−0.182329	−	0.847506i	−0.00619936	−	0.0288161i
$866$	19.1247	+	21.2401i	0.649883	+	0.721768i
$867$		0			0
$868$	31.9940	−	18.4717i	1.08595	−	0.626972i
$869$	−1.18638	+	11.2876i	−0.0402451	+	0.382906i
$870$		0			0
$871$	−0.0202973	−	0.193115i	−0.000687746	−	0.00654347i
$872$	3.52443	+	4.85096i	0.119352	+	0.164274i
$873$		0			0
$874$	21.2564			0.719009
$875$	30.9803	−	28.3127i	1.04733	−	0.957143i
$876$		0			0
$877$	−23.7355	−	21.3716i	−0.801492	−	0.721667i	0.162756	−	0.986666i	$-0.447962\pi$
$877$	−23.7355	−	21.3716i	−0.801492	−	0.721667i	−0.964249	+	0.264999i	$0.914628\pi$
$878$	5.94184	−	13.3456i	0.200527	−	0.450392i
$879$		0			0
$880$	6.03500	+	4.36198i	0.203440	+	0.147042i
$881$	0.509770	+	0.370370i	0.0171746	+	0.0124781i	0.596339	−	0.802732i	$-0.296621\pi$
$881$	0.509770	+	0.370370i	0.0171746	+	0.0124781i	−0.579165	+	0.815210i	$0.696621\pi$
$882$		0			0
$883$	25.3022	−	34.8256i	0.851488	−	1.17197i	−0.132045	−	0.991244i	$-0.542154\pi$
$883$	25.3022	−	34.8256i	0.851488	−	1.17197i	0.983533	−	0.180729i	$-0.0578458\pi$
$884$	3.82649	+	4.24975i	0.128699	+	0.142935i
$885$		0			0
$886$	18.8061	−	20.8863i	0.631803	−	0.701688i
$887$	−0.0237201	−	0.111594i	−0.000796442	−	0.00374696i	0.977748	−	0.209785i	$-0.0672763\pi$
$887$	−0.0237201	−	0.111594i	−0.000796442	−	0.00374696i	−0.978544	+	0.206038i	$0.933943\pi$
$888$		0			0
$889$	67.8464	+	14.4212i	2.27549	+	0.483671i
$890$	14.3325	−	8.32204i	0.480425	−	0.278956i
$891$		0			0
$892$	4.16135	−	5.72760i	0.139332	−	0.191774i
$893$	−47.9334	−	27.6743i	−1.60403	−	0.926086i
$894$		0			0
$895$	−10.5560	+	18.3882i	−0.352849	+	0.614649i
$896$	−40.3208	−	17.9520i	−1.34702	−	0.599733i
$897$		0			0
$898$	3.56830	−	16.7875i	0.119076	−	0.560206i
$899$	−22.1077			−0.737335
$900$		0			0
$901$	−43.8739			−1.46165
$902$	1.79406	−	8.44041i	0.0597358	−	0.281035i
$903$		0			0
$904$	−2.48895	−	1.10815i	−0.0827814	−	0.0368567i
$905$	46.9379	+	9.85602i	1.56027	+	0.327625i
$906$		0			0
$907$	−25.2748	−	14.5924i	−0.839236	−	0.484533i	0.0177683	−	0.999842i	$-0.494344\pi$
$907$	−25.2748	−	14.5924i	−0.839236	−	0.484533i	−0.857005	+	0.515309i	$0.827677\pi$
$908$	15.3114	−	21.0744i	0.508128	−	0.699378i
$909$		0			0
$910$	21.1466	+	2.16988i	0.701002	+	0.0719307i
$911$	25.2235	+	5.36141i	0.835691	+	0.177632i	0.605832	−	0.795593i	$-0.292840\pi$
$911$	25.2235	+	5.36141i	0.835691	+	0.177632i	0.229859	+	0.973224i	$0.426174\pi$
$912$		0			0
$913$	−0.457350	−	2.15166i	−0.0151361	−	0.0712097i
$914$	−41.4686	+	46.0555i	−1.37166	+	1.52338i
$915$		0			0
$916$	7.23607	+	8.03647i	0.239086	+	0.265532i
$917$	8.82310	−	12.1440i	0.291364	−	0.401029i
$918$		0			0
$919$	−36.6407	−	26.6210i	−1.20866	−	0.878146i	−0.213556	−	0.976931i	$-0.568504\pi$
$919$	−36.6407	−	26.6210i	−1.20866	−	0.878146i	−0.995109	+	0.0987849i	$0.968504\pi$
$920$	−7.25476	+	5.29828i	−0.239182	+	0.174679i
$921$		0			0
$922$	−14.1042	+	31.6786i	−0.464498	+	1.04328i
$923$	1.67889	+	1.51168i	0.0552613	+	0.0497575i
$924$		0			0
$925$	24.9105	−	14.5464i	0.819052	−	0.478282i
$926$	−2.88953			−0.0949559
$927$		0			0
$928$	−7.53112	−	10.3657i	−0.247221	−	0.340271i
$929$	−1.33486	−	12.7003i	−0.0437952	−	0.416684i	−0.994352	−	0.106133i	$-0.966153\pi$
$929$	−1.33486	−	12.7003i	−0.0437952	−	0.416684i	0.950557	−	0.310551i	$-0.100514\pi$
$930$		0			0
$931$	−3.71619	+	35.3571i	−0.121793	+	1.15878i
$932$	9.51979	−	5.49625i	0.311831	−	0.180036i
$933$		0			0
$934$	−27.7769	−	30.8494i	−0.908889	−	1.00942i
$935$	−2.25933	+	5.10841i	−0.0738880	+	0.167063i
$936$		0			0
$937$	−10.3930	−	3.37689i	−0.339525	−	0.110318i	0.134292	−	0.990942i	$-0.457124\pi$
$937$	−10.3930	−	3.37689i	−0.339525	−	0.110318i	−0.473817	+	0.880624i	$0.657124\pi$
$938$	0.652883	−	0.587859i	0.0213174	−	0.0191943i
$939$		0			0
$940$	−25.8304	+	2.77931i	−0.842495	+	0.0906512i
$941$	18.1546	−	3.85887i	0.591822	−	0.125796i	0.0977416	−	0.995212i	$-0.468838\pi$
$941$	18.1546	−	3.85887i	0.591822	−	0.125796i	0.494080	+	0.869416i	$0.335505\pi$
$942$		0			0
$943$	15.5762	+	8.99292i	0.507231	+	0.292850i
$944$	−20.6900	−	15.0321i	−0.673401	−	0.489255i
$945$		0			0
$946$	9.68083	−	7.03353i	0.314751	−	0.228680i
$947$	−46.1870	+	4.85445i	−1.50088	+	0.157748i	−0.819031	−	0.573749i	$-0.805489\pi$
$947$	−46.1870	+	4.85445i	−1.50088	+	0.157748i	−0.681845	+	0.731497i	$0.738822\pi$
$948$		0			0
$949$	−0.573347	−	0.993066i	−0.0186116	−	0.0322363i
$950$	0.216033	+	43.7960i	0.00700905	+	1.42093i
$951$		0			0
$952$	4.84352	−	22.7869i	0.156979	−	0.738529i
$953$	15.1247	+	20.8173i	0.489936	+	0.674339i	0.980376	−	0.197136i	$-0.0631640\pi$
$953$	15.1247	+	20.8173i	0.489936	+	0.674339i	−0.490440	+	0.871475i	$0.663164\pi$
$954$		0			0
$955$	53.4907	+	23.6577i	1.73092	+	0.765545i
$956$	−21.8248	+	9.71704i	−0.705865	+	0.314272i
$957$		0			0
$958$	−54.8594	−	5.76595i	−1.77243	−	0.186290i
$959$	−34.8402	+	7.40551i	−1.12505	+	0.239137i
$960$		0			0
$961$	−55.2159	−	11.7365i	−1.78116	−	0.378597i
$962$	13.8960	+	4.51507i	0.448024	+	0.145572i
$963$		0			0
$964$	−8.37129	−	25.7642i	−0.269621	−	0.829809i
$965$	−4.89309	+	6.76980i	−0.157514	+	0.217928i
$966$		0			0
$967$	33.2158	+	3.49112i	1.06815	+	0.112267i	0.622252	−	0.782817i	$-0.286218\pi$
$967$	33.2158	+	3.49112i	1.06815	+	0.112267i	0.445897	+	0.895084i	$0.352885\pi$
$968$	15.1345	−	8.73789i	0.486441	−	0.280847i
$969$		0			0
$970$	1.61198	+	4.91985i	0.0517576	+	0.157967i
$971$	27.7301	−	20.1471i	0.889903	−	0.646552i	−0.0459499	−	0.998944i	$-0.514631\pi$
$971$	27.7301	−	20.1471i	0.889903	−	0.646552i	0.935853	+	0.352392i	$0.114631\pi$
$972$		0			0
$973$	−14.2703	+	4.63671i	−0.457485	+	0.148646i
$974$	−29.0665	+	50.3446i	−0.931350	+	1.61315i
$975$		0			0
$976$	4.75377	+	8.23377i	0.152164	+	0.263556i
$977$	−13.9382	−	12.5500i	−0.445922	−	0.401510i	0.415344	−	0.909664i	$-0.363661\pi$
$977$	−13.9382	−	12.5500i	−0.445922	−	0.401510i	−0.861266	+	0.508155i	$0.830328\pi$
$978$		0			0
$979$	0.295505	+	2.81154i	0.00944438	+	0.0898573i
$980$	8.37928	+	14.4310i	0.267666	+	0.460982i
$981$		0			0
$982$			2.91433i			0.0930001i
$983$	−5.59499	−	12.5666i	−0.178453	−	0.400811i	0.802067	−	0.597235i	$-0.203734\pi$
$983$	−5.59499	−	12.5666i	−0.178453	−	0.400811i	−0.980519	+	0.196424i	$0.937067\pi$
$984$		0			0
$985$	−25.4305	−	14.5988i	−0.810282	−	0.465156i
$986$	10.3602	−	11.5061i	0.329935	−	0.366430i
$987$		0			0
$988$	−5.68385	+	5.11776i	−0.180827	+	0.162818i
$989$	7.70742	+	23.7210i	0.245082	+	0.754284i
$990$		0			0
$991$	−12.4935	+	38.4511i	−0.396870	+	1.22144i	0.530625	+	0.847607i	$0.321957\pi$
$991$	−12.4935	+	38.4511i	−0.396870	+	1.22144i	−0.927495	+	0.373834i	$0.878043\pi$
$992$	−20.6142	−	46.3003i	−0.654502	−	1.47003i
$993$		0			0
$994$	−1.06842	+	10.1654i	−0.0338883	+	0.322426i
$995$	5.94709	−	2.66541i	0.188535	−	0.0844992i
$996$		0			0
$997$	8.57791	−	0.901575i	0.271665	−	0.0285532i	0.0322837	−	0.999479i	$-0.489722\pi$
$997$	8.57791	−	0.901575i	0.271665	−	0.0285532i	0.239382	+	0.970926i	$0.423055\pi$
$998$	14.7521	−	4.79326i	0.466971	−	0.151728i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.7		224
3.2	odd	2		225.2.u.a.169.22	yes	224
9.4	even	3	inner	675.2.y.a.469.7		224
9.5	odd	6		225.2.u.a.94.22	yes	224
25.4	even	10	inner	675.2.y.a.154.7		224
75.29	odd	10		225.2.u.a.79.22	yes	224
225.4	even	30	inner	675.2.y.a.604.7		224
225.104	odd	30		225.2.u.a.4.22	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.22	✓	224	225.104	odd	30
225.2.u.a.79.22	yes	224	75.29	odd	10
225.2.u.a.94.22	yes	224	9.5	odd	6
225.2.u.a.169.22	yes	224	3.2	odd	2
675.2.y.a.19.7		224	1.1	even	1	trivial
675.2.y.a.154.7		224	25.4	even	10	inner
675.2.y.a.469.7		224	9.4	even	3	inner
675.2.y.a.604.7		224	225.4	even	30	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.363246 + 1.70894i) q^{2} +(-0.961428 - 0.428055i) q^{4} +(-2.04050 + 0.914526i) q^{5} +(-3.25090 - 1.87691i) q^{7} +(-0.973104 + 1.33936i) q^{8} +O(q^{10})\)	\(q+(-0.363246 + 1.70894i) q^{2} +(-0.961428 - 0.428055i) q^{4} +(-2.04050 + 0.914526i) q^{5} +(-3.25090 - 1.87691i) q^{7} +(-0.973104 + 1.33936i) q^{8} +(-0.821664 - 3.81928i) q^{10} +(0.651825 + 0.138550i) q^{11} +(-0.301380 - 1.41788i) q^{13} +(4.38839 - 4.87380i) q^{14} +(-3.34381 - 3.71368i) q^{16} +(2.20337 - 3.03268i) q^{17} +(4.05607 + 2.94691i) q^{19} +(2.35326 - 0.00580396i) q^{20} +(-0.473546 + 1.06360i) q^{22} +(-1.80341 - 1.62379i) q^{23} +(3.32728 - 3.73218i) q^{25} +2.53254 q^{26} +(2.32208 + 3.19608i) q^{28} +(-0.247116 - 2.35115i) q^{29} +(0.977492 - 9.30021i) q^{31} +(4.69359 - 2.70985i) q^{32} +(4.38229 + 4.86703i) q^{34} +(8.34994 + 0.856798i) q^{35} +(5.48696 + 1.78282i) q^{37} +(-6.50943 + 5.86112i) q^{38} +(0.760737 - 3.62290i) q^{40} +(-7.24962 + 1.54095i) q^{41} +(-8.90096 - 5.13897i) q^{43} +(-0.567376 - 0.412223i) q^{44} +(3.43004 - 2.49207i) q^{46} +(-10.9793 + 1.15397i) q^{47} +(3.54556 + 6.14109i) q^{49} +(5.16944 + 7.04182i) q^{50} +(-0.317176 + 1.49220i) q^{52} +(-6.87949 - 9.46881i) q^{53} +(-1.45676 + 0.313400i) q^{55} +(5.67732 - 2.52771i) q^{56} +(4.10773 + 0.431740i) q^{58} +(5.00582 - 1.06402i) q^{59} +(-1.86098 - 0.395563i) q^{61} +(15.5384 + 5.04873i) q^{62} +(-0.162441 - 0.499943i) q^{64} +(1.91165 + 2.61756i) q^{65} +(0.133224 + 0.0140024i) q^{67} +(-3.41653 + 1.97254i) q^{68} +(-4.49730 + 13.9583i) q^{70} +(-1.26087 + 0.916078i) q^{71} +(0.752348 - 0.244453i) q^{73} +(-5.03985 + 8.72927i) q^{74} +(-2.63818 - 4.56946i) q^{76} +(-1.85897 - 1.67383i) q^{77} +(1.78031 + 16.9385i) q^{79} +(10.2193 + 4.51976i) q^{80} -12.9489i q^{82} +(-1.34263 - 3.01560i) q^{83} +(-1.72251 + 8.20322i) q^{85} +(12.0154 - 13.3445i) q^{86} +(-0.819862 + 0.738207i) q^{88} +(1.31095 + 4.03469i) q^{89} +(-1.68147 + 5.17504i) q^{91} +(1.03877 + 2.33312i) q^{92} +(2.01612 - 19.1821i) q^{94} +(-10.9714 - 2.30378i) q^{95} +(-1.31796 + 0.138523i) q^{97} +(-11.7827 + 3.82842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Introduction

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