LMFDB - Embedded newform 175.2.x.a.3.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.16
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13877 - 1.75355i) q^{2} +(0.297680 - 0.775483i) q^{3} +(-0.964662 - 2.16667i) q^{4} +(-1.08500 - 1.95519i) q^{5} +(-1.02086 - 1.40509i) q^{6} +(-2.15744 + 1.53148i) q^{7} +(-0.767632 - 0.121581i) q^{8} +(1.71667 + 1.54570i) q^{9} +O(q^{10})$	\(q+(1.13877 - 1.75355i) q^{2} +(0.297680 - 0.775483i) q^{3} +(-0.964662 - 2.16667i) q^{4} +(-1.08500 - 1.95519i) q^{5} +(-1.02086 - 1.40509i) q^{6} +(-2.15744 + 1.53148i) q^{7} +(-0.767632 - 0.121581i) q^{8} +(1.71667 + 1.54570i) q^{9} +(-4.66408 - 0.323915i) q^{10} +(-0.702779 - 0.780515i) q^{11} +(-1.96737 + 0.103106i) q^{12} +(4.08239 + 2.08008i) q^{13} +(0.228707 + 5.52718i) q^{14} +(-1.83920 + 0.259375i) q^{15} +(2.08662 - 2.31743i) q^{16} +(1.41941 - 1.75283i) q^{17} +(4.66535 - 1.25008i) q^{18} +(-4.55223 - 2.02678i) q^{19} +(-3.18960 + 4.23693i) q^{20} +(0.545413 + 2.12895i) q^{21} +(-2.16897 + 0.343531i) q^{22} +(5.21979 + 3.38977i) q^{23} +(-0.322792 + 0.559093i) q^{24} +(-2.64556 + 4.24276i) q^{25} +(8.29642 - 4.78994i) q^{26} +(3.93004 - 2.00245i) q^{27} +(5.39942 + 3.19709i) q^{28} +(-0.743348 + 1.02313i) q^{29} +(-1.63959 + 3.52049i) q^{30} +(-10.1310 + 1.06481i) q^{31} +(-2.08985 - 7.79943i) q^{32} +(-0.814479 + 0.312649i) q^{33} +(-1.45729 - 4.48507i) q^{34} +(5.33517 + 2.55656i) q^{35} +(1.69301 - 5.21054i) q^{36} +(0.328991 + 6.27752i) q^{37} +(-8.73799 + 5.67452i) q^{38} +(2.82832 - 2.54663i) q^{39} +(0.595164 + 1.63278i) q^{40} +(-5.32280 + 1.72948i) q^{41} +(4.35431 + 1.46797i) q^{42} +(4.80861 + 4.80861i) q^{43} +(-1.01317 + 2.27562i) q^{44} +(1.15956 - 5.03351i) q^{45} +(11.8882 - 5.29299i) q^{46} +(0.243253 - 0.196982i) q^{47} +(-1.17598 - 2.30799i) q^{48} +(2.30911 - 6.60818i) q^{49} +(4.42720 + 9.47062i) q^{50} +(-0.936759 - 1.62251i) q^{51} +(0.568717 - 10.8518i) q^{52} +(0.261509 + 0.100384i) q^{53} +(0.963998 - 9.17183i) q^{54} +(-0.763545 + 2.22093i) q^{55} +(1.84232 - 0.913312i) q^{56} +(-2.92684 + 2.92684i) q^{57} +(0.947608 + 2.46860i) q^{58} +(6.72559 + 1.42957i) q^{59} +(2.33619 + 3.73473i) q^{60} +(1.10261 + 5.18739i) q^{61} +(-9.66967 + 18.9778i) q^{62} +(-6.07084 - 0.705699i) q^{63} +(-10.1249 - 3.28979i) q^{64} +(-0.362422 - 10.2388i) q^{65} +(-0.379257 + 1.78426i) q^{66} +(-9.54564 - 7.72991i) q^{67} +(-5.16706 - 1.38451i) q^{68} +(4.18254 - 3.03879i) q^{69} +(10.5586 - 6.44414i) q^{70} +(-1.66579 - 1.21027i) q^{71} +(-1.12985 - 1.39524i) q^{72} +(-1.29435 - 0.0678338i) q^{73} +(11.3826 + 6.57173i) q^{74} +(2.50266 + 3.31457i) q^{75} +11.8183i q^{76} +(2.71155 + 0.607621i) q^{77} +(-1.24484 - 7.85959i) q^{78} +(-10.7765 - 1.13266i) q^{79} +(-6.79499 - 1.56534i) q^{80} +(0.341411 + 3.24831i) q^{81} +(-3.02870 + 11.3033i) q^{82} +(-0.579789 + 3.66064i) q^{83} +(4.08659 - 3.23545i) q^{84} +(-4.96718 - 0.873412i) q^{85} +(13.9080 - 2.95623i) q^{86} +(0.572141 + 0.881019i) q^{87} +(0.444580 + 0.684593i) q^{88} +(-10.3731 + 2.20488i) q^{89} +(-7.50603 - 7.76533i) q^{90} +(-11.9931 + 1.76446i) q^{91} +(2.30917 - 14.5795i) q^{92} +(-2.19006 + 8.17341i) q^{93} +(-0.0684094 - 0.650872i) q^{94} +(0.976406 + 11.0995i) q^{95} +(-6.67043 - 0.701090i) q^{96} +(-0.775456 - 4.89604i) q^{97} +(-8.95821 - 11.5743i) q^{98} -2.42618i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	1.13877	−	1.75355i	0.805229	−	1.23994i	−0.162189	−	0.986760i	$-0.551855\pi$
$2$	1.13877	−	1.75355i	0.805229	−	1.23994i	0.967418	−	0.253185i	$-0.0814780\pi$
$3$	0.297680	−	0.775483i	0.171866	−	0.447725i	−0.820410	−	0.571775i	$-0.806255\pi$
$3$	0.297680	−	0.775483i	0.171866	−	0.447725i	0.992276	+	0.124050i	$0.0395883\pi$
$4$	−0.964662	−	2.16667i	−0.482331	−	1.08333i
$5$	−1.08500	−	1.95519i	−0.485226	−	0.874389i
$5$	−1.08500	−	1.95519i	−0.485226	−	0.874389i
$6$	−1.02086	−	1.40509i	−0.416763	−	0.573625i
$7$	−2.15744	+	1.53148i	−0.815436	+	0.578847i
$7$	−2.15744	+	1.53148i	−0.815436	+	0.578847i
$8$	−0.767632	−	0.121581i	−0.271399	−	0.0429853i
$9$	1.71667	+	1.54570i	0.572225	+	0.515234i
$10$	−4.66408	−	0.323915i	−1.47491	−	0.102431i
$11$	−0.702779	−	0.780515i	−0.211896	−	0.235334i	0.627822	−	0.778357i	$-0.283946\pi$
$11$	−0.702779	−	0.780515i	−0.211896	−	0.235334i	−0.839718	+	0.543023i	$0.817280\pi$
$12$	−1.96737	+	0.103106i	−0.567932	+	0.0297640i
$13$	4.08239	+	2.08008i	1.13225	+	0.576911i	0.916698	−	0.399580i	$-0.130844\pi$
$13$	4.08239	+	2.08008i	1.13225	+	0.576911i	0.215554	+	0.976492i	$0.430844\pi$
$14$	0.228707	+	5.52718i	0.0611245	+	1.47720i
$15$	−1.83920	+	0.259375i	−0.474879	+	0.0669703i
$16$	2.08662	−	2.31743i	0.521655	−	0.579357i
$17$	1.41941	−	1.75283i	0.344259	−	0.425124i	−0.575382	−	0.817885i	$-0.695147\pi$
$17$	1.41941	−	1.75283i	0.344259	−	0.425124i	0.919641	+	0.392761i	$0.128480\pi$
$18$	4.66535	−	1.25008i	1.09963	−	0.294646i
$19$	−4.55223	−	2.02678i	−1.04435	−	0.464976i	−0.188434	−	0.982086i	$-0.560341\pi$
$19$	−4.55223	−	2.02678i	−1.04435	−	0.464976i	−0.855919	+	0.517110i	$0.827008\pi$
$20$	−3.18960	+	4.23693i	−0.713215	+	0.947406i
$21$	0.545413	+	2.12895i	0.119019	+	0.464575i
$22$	−2.16897	+	0.343531i	−0.462426	+	0.0732411i
$23$	5.21979	+	3.38977i	1.08840	+	0.706816i	0.958609	−	0.284725i	$-0.0919022\pi$
$23$	5.21979	+	3.38977i	1.08840	+	0.706816i	0.129793	+	0.991541i	$0.458569\pi$
$24$	−0.322792	+	0.559093i	−0.0658897	+	0.114124i
$25$	−2.64556	+	4.24276i	−0.529112	+	0.848552i
$26$	8.29642	−	4.78994i	1.62706	−	0.939384i
$27$	3.93004	−	2.00245i	0.756336	−	0.385373i
$28$	5.39942	+	3.19709i	1.02039	+	0.604194i
$29$	−0.743348	+	1.02313i	−0.138036	+	0.189991i	−0.872439	−	0.488724i	$-0.837463\pi$
$29$	−0.743348	+	1.02313i	−0.138036	+	0.189991i	0.734402	+	0.678714i	$0.237463\pi$
$30$	−1.63959	+	3.52049i	−0.299347	+	0.642751i
$31$	−10.1310	+	1.06481i	−1.81959	+	0.191246i	−0.952012	−	0.306062i	$-0.900989\pi$
$31$	−10.1310	+	1.06481i	−1.81959	+	0.191246i	−0.867574	+	0.497308i	$0.834322\pi$
$32$	−2.08985	−	7.79943i	−0.369437	−	1.37876i
$33$	−0.814479	+	0.312649i	−0.141783	+	0.0544253i
$34$	−1.45729	−	4.48507i	−0.249923	−	0.769184i
$35$	5.33517	+	2.55656i	0.901808	+	0.432137i
$36$	1.69301	−	5.21054i	0.282168	−	0.868424i
$37$	0.328991	+	6.27752i	0.0540858	+	1.03202i	0.882026	+	0.471202i	$0.156180\pi$
$37$	0.328991	+	6.27752i	0.0540858	+	1.03202i	−0.827940	+	0.560817i	$0.810487\pi$
$38$	−8.73799	+	5.67452i	−1.41749	+	0.920528i
$39$	2.82832	−	2.54663i	0.452893	−	0.407787i
$40$	0.595164	+	1.63278i	0.0941037	+	0.258166i
$41$	−5.32280	+	1.72948i	−0.831282	+	0.270100i	−0.693585	−	0.720374i	$-0.743970\pi$
$41$	−5.32280	+	1.72948i	−0.831282	+	0.270100i	−0.137697	+	0.990474i	$0.543970\pi$
$42$	4.35431	+	1.46797i	0.671885	+	0.226513i
$43$	4.80861	+	4.80861i	0.733306	+	0.733306i	0.971273	−	0.237968i	$-0.0764812\pi$
$43$	4.80861	+	4.80861i	0.733306	+	0.733306i	−0.237968	+	0.971273i	$0.576481\pi$
$44$	−1.01317	+	2.27562i	−0.152741	+	0.343063i
$45$	1.15956	−	5.03351i	0.172856	−	0.750352i
$46$	11.8882	−	5.29299i	1.75283	−	0.780408i
$47$	0.243253	−	0.196982i	0.0354821	−	0.0287328i	−0.611415	−	0.791310i	$-0.709400\pi$
$47$	0.243253	−	0.196982i	0.0354821	−	0.0287328i	0.646897	+	0.762577i	$0.276066\pi$
$48$	−1.17598	−	2.30799i	−0.169738	−	0.333130i
$49$	2.30911	−	6.60818i	0.329873	−	0.944025i
$50$	4.42720	+	9.47062i	0.626101	+	1.33935i
$51$	−0.936759	−	1.62251i	−0.131172	−	0.227197i
$52$	0.568717	−	10.8518i	0.0788669	−	1.50487i
$53$	0.261509	+	0.100384i	0.0359210	+	0.0137888i	0.376262	−	0.926513i	$-0.377209\pi$
$53$	0.261509	+	0.100384i	0.0359210	+	0.0137888i	−0.340341	+	0.940302i	$0.610543\pi$
$54$	0.963998	−	9.17183i	0.131184	−	1.24813i
$55$	−0.763545	+	2.22093i	−0.102956	+	0.299470i
$56$	1.84232	−	0.913312i	0.246190	−	0.122046i
$57$	−2.92684	+	2.92684i	−0.387670	+	0.387670i
$58$	0.947608	+	2.46860i	0.124427	+	0.324143i
$59$	6.72559	+	1.42957i	0.875597	+	0.186114i	0.623722	−	0.781646i	$-0.285620\pi$
$59$	6.72559	+	1.42957i	0.875597	+	0.186114i	0.251875	+	0.967760i	$0.418953\pi$
$60$	2.33619	+	3.73473i	0.301600	+	0.482151i
$61$	1.10261	+	5.18739i	0.141175	+	0.664178i	0.990636	+	0.136527i	$0.0435939\pi$
$61$	1.10261	+	5.18739i	0.141175	+	0.664178i	−0.849461	+	0.527651i	$0.823073\pi$
$62$	−9.66967	+	18.9778i	−1.22805	+	2.41018i
$63$	−6.07084	−	0.705699i	−0.764854	−	0.0889097i
$64$	−10.1249	−	3.28979i	−1.26562	−	0.411224i
$65$	−0.362422	−	10.2388i	−0.0449529	−	1.26996i
$66$	−0.379257	+	1.78426i	−0.0466833	+	0.219627i
$67$	−9.54564	−	7.72991i	−1.16619	−	0.944359i	−0.167051	−	0.985948i	$-0.553425\pi$
$67$	−9.54564	−	7.72991i	−1.16619	−	0.944359i	−0.999135	+	0.0415894i	$0.986758\pi$
$68$	−5.16706	−	1.38451i	−0.626598	−	0.167896i
$69$	4.18254	−	3.03879i	0.503518	−	0.365827i
$70$	10.5586	−	6.44414i	1.26199	−	0.770222i
$71$	−1.66579	−	1.21027i	−0.197693	−	0.143632i	0.484535	−	0.874772i	$-0.338989\pi$
$71$	−1.66579	−	1.21027i	−0.197693	−	0.143632i	−0.682228	+	0.731140i	$0.738989\pi$
$72$	−1.12985	−	1.39524i	−0.133154	−	0.164431i
$73$	−1.29435	−	0.0678338i	−0.151492	−	0.00793934i	−0.0235607	−	0.999722i	$-0.507500\pi$
$73$	−1.29435	−	0.0678338i	−0.151492	−	0.00793934i	−0.127931	+	0.991783i	$0.540834\pi$
$74$	11.3826	+	6.57173i	1.32320	+	0.763948i
$75$	2.50266	+	3.31457i	0.288982	+	0.382734i
$76$			11.8183i			1.35566i
$77$	2.71155	+	0.607621i	0.309010	+	0.0692448i
$78$	−1.24484	−	7.85959i	−0.140950	−	0.889924i
$79$	−10.7765	−	1.13266i	−1.21245	−	0.127434i	−0.523363	−	0.852110i	$-0.675323\pi$
$79$	−10.7765	−	1.13266i	−1.21245	−	0.127434i	−0.689090	+	0.724676i	$0.741989\pi$
$80$	−6.79499	−	1.56534i	−0.759703	−	0.175011i
$81$	0.341411	+	3.24831i	0.0379346	+	0.360923i
$82$	−3.02870	+	11.3033i	−0.334464	+	1.24824i
$83$	−0.579789	+	3.66064i	−0.0636401	+	0.401808i	0.935220	+	0.354068i	$0.115202\pi$
$83$	−0.579789	+	3.66064i	−0.0636401	+	0.401808i	−0.998860	+	0.0477399i	$0.984798\pi$
$84$	4.08659	−	3.23545i	0.445883	−	0.353016i
$85$	−4.96718	−	0.873412i	−0.538767	−	0.0947349i
$86$	13.9080	−	2.95623i	1.49974	−	0.318779i
$87$	0.572141	+	0.881019i	0.0613399	+	0.0944552i
$88$	0.444580	+	0.684593i	0.0473924	+	0.0729778i
$89$	−10.3731	+	2.20488i	−1.09955	+	0.233716i	−0.721738	−	0.692166i	$-0.756656\pi$
$89$	−10.3731	+	2.20488i	−1.09955	+	0.233716i	−0.377811	+	0.925883i	$0.623323\pi$
$90$	−7.50603	−	7.76533i	−0.791205	−	0.818537i
$91$	−11.9931	+	1.76446i	−1.25722	+	0.184966i
$92$	2.30917	−	14.5795i	0.240748	−	1.52002i
$93$	−2.19006	+	8.17341i	−0.227098	+	0.847543i
$94$	−0.0684094	−	0.650872i	−0.00705589	−	0.0671323i
$95$	0.976406	+	11.0995i	0.100177	+	1.13879i
$96$	−6.67043	−	0.701090i	−0.680798	−	0.0715547i
$97$	−0.775456	−	4.89604i	−0.0787356	−	0.497117i	−0.995269	−	0.0971587i	$-0.969025\pi$
$97$	−0.775456	−	4.89604i	−0.0787356	−	0.497117i	0.916533	−	0.399958i	$-0.130975\pi$
$98$	−8.95821	−	11.5743i	−0.904916	−	1.16918i
$99$		−	2.42618i		−	0.243840i
$100$	11.7447	+	1.63922i	1.17447	+	0.163922i
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.982069	−	0.188524i	$-0.0603704\pi$
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.327767	+	0.944758i	$0.393704\pi$
$102$	−3.91190	−	0.205014i	−0.387336	−	0.0202994i
$103$	−4.27261	−	5.27623i	−0.420993	−	0.519883i	0.521888	−	0.853014i	$-0.325228\pi$
$103$	−4.27261	−	5.27623i	−0.420993	−	0.519883i	−0.942880	+	0.333132i	$0.891895\pi$
$104$	−2.88088	−	2.09308i	−0.282493	−	0.205243i
$105$	3.57074	−	3.37629i	0.348468	−	0.329492i
$106$	0.473825	−	0.344254i	0.0460220	−	0.0334369i
$107$	−18.9985	−	5.09063i	−1.83665	−	0.492130i	−0.838081	−	0.545546i	$-0.816322\pi$
$107$	−18.9985	−	5.09063i	−1.83665	−	0.492130i	−0.998572	+	0.0534166i	$0.982989\pi$
$108$	−8.12981	−	6.58339i	−0.782292	−	0.633487i
$109$	3.97502	−	18.7010i	0.380738	−	1.79123i	−0.202880	−	0.979204i	$-0.565030\pi$
$109$	3.97502	−	18.7010i	0.380738	−	1.79123i	0.583618	−	0.812029i	$-0.301637\pi$
$110$	3.02500	+	3.86803i	0.288422	+	0.368802i
$111$	4.96605	+	1.61357i	0.471356	+	0.153153i
$112$	−0.952659	+	8.19534i	−0.0900178	+	0.774387i
$113$	3.96233	−	7.77652i	0.372745	−	0.731553i	−0.626093	−	0.779748i	$-0.715347\pi$
$113$	3.96233	−	7.77652i	0.372745	−	0.731553i	0.998838	+	0.0481952i	$0.0153470\pi$
$114$	1.79937	+	8.46535i	0.168526	+	0.792852i
$115$	0.964199	−	13.8836i	0.0899120	−	1.29465i
$116$	2.93386	+	0.623612i	0.272402	+	0.0579009i
$117$	3.79296	+	9.88099i	0.350659	+	0.913498i
$118$	10.1657	−	10.1657i	0.935827	−	0.935827i
$119$	−0.377871	+	5.95544i	−0.0346393	+	0.545934i
$120$	1.44336	+	0.0245072i	0.131760	+	0.00223719i
$121$	1.03451	−	9.84268i	0.0940461	−	0.894789i
$122$	10.3520	+	3.97374i	0.937222	+	0.359766i
$123$	−0.243307	+	4.64257i	−0.0219383	+	0.418607i
$124$	12.0801	+	20.9234i	1.08483	+	1.87897i
$125$	11.1658	+	0.569199i	0.998703	+	0.0509107i
$126$	−8.15074	+	9.84188i	−0.726126	+	0.876784i
$127$	5.89827	+	11.5760i	0.523386	+	1.02720i	0.989777	+	0.142625i	$0.0455542\pi$
$127$	5.89827	+	11.5760i	0.523386	+	1.02720i	−0.466390	+	0.884579i	$0.654446\pi$
$128$	−4.74853	+	3.84528i	−0.419715	+	0.339878i
$129$	5.16042	−	2.29757i	0.454349	−	0.202289i
$130$	−18.3668	−	11.0240i	−1.61088	−	0.966871i
$131$	1.44095	−	3.23643i	0.125896	−	0.282768i	−0.839590	−	0.543220i	$-0.817205\pi$
$131$	1.44095	−	3.23643i	0.125896	−	0.282768i	0.965487	+	0.260452i	$0.0838716\pi$
$132$	1.46310	+	1.46310i	0.127347	+	0.127347i
$133$	12.9252	−	2.59900i	1.12075	−	0.225362i
$134$	−24.4250	+	7.93617i	−2.11000	+	0.685580i
$135$	−8.17927	−	5.51133i	−0.703959	−	0.474339i
$136$	−1.30270	+	1.17295i	−0.111705	+	0.100580i
$137$	6.35261	−	4.12544i	0.542740	−	0.352460i	−0.243969	−	0.969783i	$-0.578450\pi$
$137$	6.35261	−	4.12544i	0.542740	−	0.352460i	0.786710	+	0.617323i	$0.211783\pi$
$138$	−0.565729	−	10.7947i	−0.0481580	−	0.918910i
$139$	2.73221	−	8.40888i	0.231743	−	0.713232i	−0.765794	−	0.643086i	$-0.777654\pi$
$139$	2.73221	−	8.40888i	0.231743	−	0.713232i	0.997537	−	0.0701455i	$-0.0223463\pi$
$140$	0.392577	−	14.0257i	0.0331788	−	1.18539i
$141$	−0.0803449	−	0.247276i	−0.00676626	−	0.0208244i
$142$	−4.01920	+	1.54283i	−0.337284	+	0.129471i
$143$	−1.24548	−	4.64821i	−0.104153	−	0.388703i
$144$	7.16410	−	0.752977i	0.597008	−	0.0627481i
$145$	2.80695	+	0.343295i	0.233104	+	0.0285091i
$146$	−1.59291	+	2.19245i	−0.131830	+	0.181448i
$147$	−4.43715	−	3.75780i	−0.365970	−	0.309938i
$148$	13.2839	−	6.76851i	1.09193	−	0.556368i
$149$	1.52475	−	0.880317i	0.124913	−	0.0721183i	−0.436242	−	0.899830i	$-0.643691\pi$
$149$	1.52475	−	0.880317i	0.124913	−	0.0721183i	0.561154	+	0.827711i	$0.310357\pi$
$150$	8.66219	−	0.614002i	0.707265	−	0.0501330i
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	−0.964924	−	0.262529i	$-0.915444\pi$
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	0.709819	+	0.704385i	$0.248777\pi$
$152$	3.24802	+	2.10929i	0.263449	+	0.171086i
$153$	5.14602	−	0.815050i	0.416031	−	0.0658929i
$154$	4.15332	−	4.06289i	0.334684	−	0.327397i
$155$	13.0741	+	18.6528i	1.05013	+	1.49823i
$156$	−8.24606	−	3.67138i	−0.660213	−	0.293946i
$157$	10.4389	−	2.79709i	0.833115	−	0.223232i	0.183043	−	0.983105i	$-0.441405\pi$
$157$	10.4389	−	2.79709i	0.833115	−	0.223232i	0.650072	+	0.759872i	$0.274739\pi$
$158$	−14.2581	+	17.6073i	−1.13431	+	1.40076i
$159$	0.155692	−	0.172913i	0.0123472	−	0.0137129i
$160$	−12.9819	+	12.5484i	−1.02631	+	0.992040i
$161$	−16.4528	+	0.680794i	−1.29666	+	0.0536541i
$162$	6.08485	+	3.10038i	0.478071	+	0.243589i
$163$	5.57143	−	0.291986i	0.436388	−	0.0228701i	0.167122	−	0.985936i	$-0.446552\pi$
$163$	5.57143	−	0.291986i	0.436388	−	0.0228701i	0.269265	+	0.963066i	$0.413219\pi$
$164$	8.88192	+	9.86438i	0.693562	+	0.770278i
$165$	1.49500	+	1.25324i	0.116385	+	0.0975647i
$166$	5.75886	+	5.18530i	0.446975	+	0.402458i
$167$	10.3561	+	1.64024i	0.801379	+	0.126926i	0.543673	−	0.839297i	$-0.317033\pi$
$167$	10.3561	+	1.64024i	0.801379	+	0.126926i	0.257706	+	0.966223i	$0.417033\pi$
$168$	−0.159836	−	1.70056i	−0.0123316	−	0.131201i
$169$	4.69799	+	6.46623i	0.361384	+	0.497402i
$170$	−7.18803	+	7.71557i	−0.551297	+	0.591757i
$171$	−4.68190	−	10.5157i	−0.358034	−	0.804157i
$172$	5.77997	−	15.0573i	0.440718	−	1.14811i
$173$	−7.47674	+	11.5132i	−0.568446	+	0.875330i	−0.999637	−	0.0269305i	$-0.991427\pi$
$173$	−7.47674	+	11.5132i	−0.568446	+	0.875330i	0.431191	+	0.902260i	$0.358093\pi$
$174$	2.19644			0.166512
$175$	−0.790077	−	13.2051i	−0.0597242	−	0.998215i
$176$	−3.27522			−0.246879
$177$	3.11068	−	4.79002i	0.233813	−	0.360040i
$178$	−7.94621	+	20.7006i	−0.595594	+	1.55158i
$179$	−0.654680	−	1.47044i	−0.0489331	−	0.109906i	0.887425	−	0.460953i	$-0.152492\pi$
$179$	−0.654680	−	1.47044i	−0.0489331	−	0.109906i	−0.936358	+	0.351047i	$0.885826\pi$
$180$	−12.0245	+	2.34327i	−0.896255	+	0.174657i
$181$	2.04450	+	2.81402i	0.151967	+	0.209164i	0.878212	−	0.478271i	$-0.158736\pi$
$181$	2.04450	+	2.81402i	0.151967	+	0.209164i	−0.726245	+	0.687436i	$0.758736\pi$
$182$	−10.5633	+	23.0398i	−0.783005	+	1.70783i
$183$	4.35096	+	0.689125i	0.321632	+	0.0509416i
$184$	−3.59475	−	3.23672i	−0.265008	−	0.238614i
$185$	11.9168	−	7.45434i	0.876142	−	0.548054i
$186$	11.8385	+	13.1480i	0.868040	+	0.964056i
$187$	−2.36565	+	0.123978i	−0.172993	+	0.00906619i
$188$	−0.661452	−	0.337027i	−0.0482414	−	0.0245802i
$189$	−5.41210	+	10.3390i	−0.393672	+	0.752050i
$190$	20.5755	+	10.9276i	1.49270	+	0.792773i
$191$	−1.98374	+	2.20317i	−0.143538	+	0.159415i	−0.810627	−	0.585563i	$-0.800874\pi$
$191$	−1.98374	+	2.20317i	−0.143538	+	0.159415i	0.667089	+	0.744978i	$0.267540\pi$
$192$	−5.56517	+	6.87242i	−0.401632	+	0.495974i
$193$	−16.4661	+	4.41207i	−1.18525	+	0.317588i	−0.797009	−	0.603968i	$-0.793586\pi$
$193$	−16.4661	+	4.41207i	−1.18525	+	0.317588i	−0.388246	+	0.921556i	$0.626919\pi$
$194$	−9.46849	−	4.21564i	−0.679798	−	0.302665i
$195$	−8.04786	−	2.76682i	−0.576319	−	0.198136i
$196$	−16.5452	+	1.37159i	−1.18180	+	0.0979705i
$197$	19.1171	−	3.02785i	1.36204	−	0.215725i	0.567716	−	0.823225i	$-0.307827\pi$
$197$	19.1171	−	3.02785i	1.36204	−	0.215725i	0.794320	+	0.607499i	$0.207827\pi$
$198$	−4.25441	−	2.76285i	−0.302348	−	0.196347i
$199$	0.0959424	−	0.166177i	0.00680118	−	0.0117800i	−0.862605	−	0.505878i	$-0.831168\pi$
$199$	0.0959424	−	0.166177i	0.00680118	−	0.0117800i	0.869406	+	0.494098i	$0.164502\pi$
$200$	2.54665	−	2.93523i	0.180076	−	0.207552i
$201$	−8.83596	+	5.10144i	−0.623240	+	0.359828i
$202$	28.3174	−	14.4284i	1.99241	−	1.01518i
$203$	0.0368211	−	3.34577i	0.00258434	−	0.234827i
$204$	−2.61179	+	3.59482i	−0.182862	+	0.251688i
$205$	9.15670	+	8.53062i	0.639532	+	0.595805i
$206$	−14.1176	+	1.48382i	−0.983621	+	0.103383i
$207$	3.72111	+	13.8874i	0.258635	+	0.965239i
$208$	13.3388	−	5.12030i	0.924883	−	0.355029i
$209$	1.61728	+	4.97747i	0.111869	+	0.344299i
$210$	−1.85425	−	10.1063i	−0.127955	−	0.697398i
$211$	1.96658	−	6.05250i	0.135385	−	0.416671i	−0.860265	−	0.509847i	$-0.829702\pi$
$211$	1.96658	−	6.05250i	0.135385	−	0.416671i	0.995650	+	0.0931759i	$0.0297019\pi$
$212$	−0.0347694	−	0.663440i	−0.00238797	−	0.0455652i
$213$	−1.43441	+	0.931518i	−0.0982843	+	0.0638266i
$214$	−30.5615	+	27.5177i	−2.08914	+	1.88107i
$215$	4.18443	−	14.6191i	0.285376	−	0.997013i
$216$	−3.26028	+	1.05933i	−0.221834	+	0.0720783i
$217$	20.2263	−	17.8128i	1.37305	−	1.20921i
$218$	−28.2665	−	28.2665i	−1.91445	−	1.91445i
$219$	−0.437905	+	0.983550i	−0.0295908	+	0.0664621i
$220$	5.54857	−	0.488097i	0.374085	−	0.0329075i
$221$	9.44064	−	4.20325i	0.635046	−	0.282741i
$222$	8.48463	−	6.87072i	0.569451	−	0.461132i
$223$	6.05349	+	11.8807i	0.405372	+	0.795587i	0.999964	−	0.00843996i	$-0.00268655\pi$
$223$	6.05349	+	11.8807i	0.405372	+	0.795587i	−0.594592	+	0.804027i	$0.702687\pi$
$224$	16.4534	+	13.6262i	1.09934	+	0.910441i
$225$	−11.0996	+	3.19419i	−0.739974	+	0.212946i
$226$	−9.12431	−	15.8038i	−0.606940	−	1.05125i
$227$	0.253949	−	4.84563i	0.0168552	−	0.321616i	−0.977170	−	0.212461i	$-0.931852\pi$
$227$	0.253949	−	4.84563i	0.0168552	−	0.321616i	0.994025	−	0.109155i	$-0.0348145\pi$
$228$	9.16491	+	3.51808i	0.606961	+	0.232991i
$229$	−0.698945	+	6.65002i	−0.0461876	+	0.439446i	0.946852	+	0.321668i	$0.104244\pi$
$229$	−0.698945	+	6.65002i	−0.0461876	+	0.439446i	−0.993040	+	0.117777i	$0.962423\pi$
$230$	−23.2475	−	17.5009i	−1.53290	−	1.15398i
$231$	1.27837	−	1.92189i	0.0841108	−	0.126451i
$232$	0.695011	−	0.695011i	0.0456297	−	0.0456297i
$233$	−3.09426	−	8.06082i	−0.202712	−	0.528082i	0.794108	−	0.607777i	$-0.207939\pi$
$233$	−3.09426	−	8.06082i	−0.202712	−	0.528082i	−0.996819	+	0.0796953i	$0.974605\pi$
$234$	21.6461	+	4.60101i	1.41505	+	0.300778i
$235$	−0.649068	−	0.261881i	−0.0423405	−	0.0170832i
$236$	−3.39053	−	15.9512i	−0.220704	−	1.03833i
$237$	−4.08631	+	8.01983i	−0.265434	+	0.520944i
$238$	10.0128	+	7.44447i	0.649036	+	0.482553i
$239$	−18.2461	−	5.92852i	−1.18024	−	0.383484i	−0.347785	−	0.937574i	$-0.613066\pi$
$239$	−18.2461	−	5.92852i	−1.18024	−	0.383484i	−0.832457	+	0.554090i	$0.813066\pi$
$240$	−3.23663	+	4.80343i	−0.208924	+	0.310060i
$241$	−5.39578	+	25.3851i	−0.347572	+	1.63520i	0.363152	+	0.931730i	$0.381700\pi$
$241$	−5.39578	+	25.3851i	−0.347572	+	1.63520i	−0.710725	+	0.703470i	$0.751633\pi$
$242$	−16.0815	−	13.0226i	−1.03376	−	0.837122i
$243$	15.4021	+	4.12698i	0.988046	+	0.264746i
$244$	10.1757	−	7.39308i	0.651433	−	0.473294i
$245$	−15.4256	+	2.65510i	−0.985508	+	0.169628i
$246$	7.86390	+	5.71346i	0.501384	+	0.364277i
$247$	−14.3681	−	17.7432i	−0.914222	−	1.12897i
$248$	7.90636	+	0.414355i	0.502054	+	0.0263115i
$249$	2.66617	+	1.53932i	0.168962	+	0.0975502i
$250$	13.7134	−	18.9316i	0.867312	−	1.19734i
$251$		−	15.4133i		−	0.972880i	−0.873714	−	0.486440i	$-0.838295\pi$
$251$		−	15.4133i		−	0.972880i	0.873714	−	0.486440i	$-0.161705\pi$
$252$	4.32730	+	13.8343i	0.272594	+	0.871476i
$253$	−1.02259	−	6.45639i	−0.0642898	−	0.405910i
$254$	27.0158	+	2.83947i	1.69512	+	0.178164i
$255$	−2.15595	+	3.59197i	−0.135011	+	0.224938i
$256$	−0.890203	−	8.46971i	−0.0556377	−	0.529357i
$257$	7.91188	−	29.5275i	0.493529	−	1.84188i	−0.0445856	−	0.999006i	$-0.514197\pi$
$257$	7.91188	−	29.5275i	0.493529	−	1.84188i	0.538115	−	0.842871i	$-0.319137\pi$
$258$	1.84762	−	11.6654i	0.115028	−	0.726257i
$259$	−10.3237	−	13.0395i	−0.641484	−	0.810238i
$260$	−21.8344	+	10.6622i	−1.35411	+	0.661241i
$261$	−2.85754	+	0.607389i	−0.176877	+	0.0375964i
$262$	−4.03432	−	6.21231i	−0.249241	−	0.383798i
$263$	0.222055	+	0.341935i	0.0136925	+	0.0210846i	0.845451	−	0.534054i	$-0.179332\pi$
$263$	0.222055	+	0.341935i	0.0136925	+	0.0210846i	−0.831758	+	0.555138i	$0.812665\pi$
$264$	0.663232	−	0.140974i	0.0408191	−	0.00867637i
$265$	−0.0874667	−	0.620217i	−0.00537304	−	0.0380996i
$266$	10.1613	−	25.6245i	0.623027	−	1.57114i
$267$	−1.37803	+	8.70053i	−0.0843340	+	0.532464i
$268$	−7.53982	+	28.1390i	−0.460568	+	1.71886i
$269$	2.00211	+	19.0488i	0.122071	+	1.16142i	0.868406	+	0.495854i	$0.165145\pi$
$269$	2.00211	+	19.0488i	0.122071	+	1.16142i	−0.746335	+	0.665570i	$0.768188\pi$
$270$	−18.9786	+	8.06661i	−1.15500	+	0.490918i
$271$	−19.2007	−	2.01808i	−1.16636	−	0.122589i	−0.498509	−	0.866884i	$-0.666119\pi$
$271$	−19.2007	−	2.01808i	−1.16636	−	0.122589i	−0.667851	+	0.744295i	$0.732786\pi$
$272$	−1.10028	−	6.94688i	−0.0667141	−	0.421216i
$273$	−2.20181	+	9.82572i	−0.133259	+	0.594680i
$274$		−	15.8375i		−	0.956779i
$275$	5.17078	−	0.916822i	0.311810	−	0.0552865i
$276$	−10.6188	−	6.13076i	−0.639176	−	0.369028i
$277$	7.63707	+	0.400242i	0.458867	+	0.0240482i	0.280369	−	0.959892i	$-0.409543\pi$
$277$	7.63707	+	0.400242i	0.458867	+	0.0240482i	0.178497	+	0.983940i	$0.442876\pi$
$278$	−11.6340	−	14.3668i	−0.697761	−	0.861664i
$279$	−19.0376	−	13.8316i	−1.13975	−	0.828076i
$280$	−3.78461	−	2.61115i	−0.226174	−	0.156046i
$281$	15.1432	−	11.0022i	0.903367	−	0.656334i	−0.0359618	−	0.999353i	$-0.511449\pi$
$281$	15.1432	−	11.0022i	0.903367	−	0.656334i	0.939329	+	0.343019i	$0.111449\pi$
$282$	−0.525104	−	0.140701i	−0.0312695	−	0.00837864i
$283$	2.21463	+	1.79337i	0.131646	+	0.106605i	0.692882	−	0.721051i	$-0.256341\pi$
$283$	2.21463	+	1.79337i	0.131646	+	0.106605i	−0.561236	+	0.827656i	$0.689674\pi$
$284$	−1.01532	+	4.77671i	−0.0602482	+	0.283446i
$285$	8.89816	+	2.54693i	0.527082	+	0.150867i
$286$	−9.56917	−	3.10921i	−0.565837	−	0.183852i
$287$	8.83496	−	11.8831i	0.521511	−	0.701434i
$288$	8.46799	−	16.6194i	0.498981	−	0.979305i
$289$	2.47682	+	11.6525i	0.145695	+	0.685443i
$290$	3.79844	−	4.53118i	0.223052	−	0.266080i
$291$	−4.02763	−	0.856099i	−0.236104	−	0.0501854i
$292$	1.10163	+	2.86985i	0.0644682	+	0.167945i
$293$	−0.584948	+	0.584948i	−0.0341730	+	0.0341730i	−0.723987	−	0.689814i	$-0.757692\pi$
$293$	−0.584948	+	0.584948i	−0.0341730	+	0.0341730i	0.689814	+	0.723987i	$0.257692\pi$
$294$	−11.6423	+	3.50150i	−0.678995	+	0.204212i
$295$	−4.50217	−	14.7009i	−0.262126	−	0.855920i
$296$	0.510683	−	4.85883i	0.0296829	−	0.282414i
$297$	−4.32490	−	1.66017i	−0.250956	−	0.0963330i
$298$	0.192661	−	3.67620i	0.0111606	−	0.212957i
$299$	14.2582	+	24.6960i	0.824575	+	1.42821i
$300$	4.76735	−	8.61986i	0.275243	−	0.497668i
$301$	−17.7386	−	3.00998i	−1.02244	−	0.173492i
$302$	5.95129	+	11.6801i	0.342458	+	0.672112i
$303$	9.81228	−	7.94583i	0.563701	−	0.456476i
$304$	−14.1957	+	6.32033i	−0.814179	+	0.362496i
$305$	8.94602	−	7.78414i	0.512248	−	0.445718i
$306$	4.43089	−	9.95194i	0.253297	−	0.568915i
$307$	10.4006	+	10.4006i	0.593593	+	0.593593i	0.938600	−	0.345007i	$-0.112123\pi$
$307$	10.4006	+	10.4006i	0.593593	+	0.593593i	−0.345007	+	0.938600i	$0.612123\pi$
$308$	−1.29922	−	6.46118i	−0.0740299	−	0.368160i
$309$	−5.36350	+	1.74271i	−0.305119	+	0.0991391i
$310$	47.5968	−	1.68479i	2.70332	−	0.0956895i
$311$	8.83036	−	7.95089i	0.500724	−	0.450854i	−0.379653	−	0.925129i	$-0.623957\pi$
$311$	8.83036	−	7.95089i	0.500724	−	0.450854i	0.880377	+	0.474275i	$0.157290\pi$
$312$	−2.48073	+	1.61100i	−0.140443	+	0.0912050i
$313$	0.527196	+	10.0595i	0.0297989	+	0.568597i	0.972206	+	0.234128i	$0.0752235\pi$
$313$	0.527196	+	10.0595i	0.0297989	+	0.568597i	−0.942407	+	0.334469i	$0.891443\pi$
$314$	6.98263	−	21.4903i	0.394053	−	1.21277i
$315$	5.20707	+	12.6354i	0.293385	+	0.711921i
$316$	7.94161	+	24.4418i	0.446750	+	1.37496i
$317$	−17.6502	+	6.77528i	−0.991335	+	0.380538i	−0.799354	−	0.600861i	$-0.794825\pi$
$317$	−17.6502	+	6.77528i	−0.991335	+	0.380538i	−0.191981	+	0.981399i	$0.561491\pi$
$318$	−0.125915	−	0.469921i	−0.00706096	−	0.0263519i
$319$	1.32098	−	0.138841i	0.0739606	−	0.00777358i
$320$	4.55336	+	23.3656i	0.254540	+	1.30618i
$321$	−9.60316	+	13.2176i	−0.535996	+	0.737736i
$322$	−17.5421	+	29.6260i	−0.977581	+	1.65099i
$323$	−10.0141	+	5.10245i	−0.557200	+	0.283908i
$324$	6.70866	−	3.87325i	0.372703	−	0.215180i
$325$	−19.6255	+	11.8176i	−1.08863	+	0.655524i
$326$	5.83254	−	10.1023i	0.323035	−	0.559512i
$327$	−13.3190	−	8.64948i	−0.736544	−	0.478317i
$328$	4.29622	−	0.680455i	0.237219	−	0.0375719i
$329$	−0.223129	+	0.797516i	−0.0123015	+	0.0439685i
$330$	3.90007	−	1.19440i	0.214692	−	0.0657495i
$331$	28.4245	+	12.6554i	1.56235	+	0.695605i	0.992052	−	0.125830i	$-0.0401594\pi$
$331$	28.4245	+	12.6554i	1.56235	+	0.695605i	0.570302	+	0.821435i	$0.306826\pi$
$332$	8.49070	−	2.27508i	0.465988	−	0.124861i
$333$	−9.13840	+	11.2850i	−0.500781	+	0.618414i
$334$	14.6694	−	16.2920i	0.802675	−	0.891461i
$335$	−4.75647	+	27.0505i	−0.259874	+	1.47793i
$336$	6.07176	+	3.17836i	0.331241	+	0.173394i
$337$	−31.0198	−	15.8054i	−1.68976	−	0.860974i	−0.989060	−	0.147514i	$-0.952873\pi$
$337$	−31.0198	−	15.8054i	−1.68976	−	0.860974i	−0.700696	−	0.713460i	$-0.747127\pi$
$338$	16.6887	−	0.874620i	0.907748	−	0.0475730i
$339$	−4.85105	−	5.38763i	−0.263473	−	0.292616i
$340$	2.89926	+	11.6048i	0.157235	+	0.629358i
$341$	7.95098	+	7.15909i	0.430570	+	0.387687i
$342$	−23.7714	−	3.76502i	−1.28541	−	0.203589i
$343$	5.13855	+	17.7931i	0.277456	+	0.960738i
$344$	−3.10660	−	4.27587i	−0.167497	−	0.230540i
$345$	−10.4795	−	4.88059i	−0.564195	−	0.262762i
$346$	11.6746	+	26.2216i	0.627631	+	1.40968i
$347$	−9.65416	+	25.1500i	−0.518263	+	1.35012i	0.385746	+	0.922605i	$0.373944\pi$
$347$	−9.65416	+	25.1500i	−0.518263	+	1.35012i	−0.904008	+	0.427515i	$0.859389\pi$
$348$	1.35695	−	2.08952i	0.0727403	−	0.112010i
$349$	−28.9278			−1.54847			−0.774236	−	0.632897i	$-0.781866\pi$
$349$	−28.9278			−1.54847			−0.774236	+	0.632897i	$0.781866\pi$
$350$	−24.0555	−	13.6521i	−1.28582	−	0.729737i
$351$	20.2092			1.07869
$352$	−4.61887	+	7.11244i	−0.246187	+	0.379094i
$353$	4.18132	−	10.8927i	0.222549	−	0.579760i	−0.776161	−	0.630535i	$-0.782836\pi$
$353$	4.18132	−	10.8927i	0.222549	−	0.579760i	0.998710	+	0.0507745i	$0.0161690\pi$
$354$	−4.85719	−	10.9094i	−0.258157	−	0.579830i
$355$	−0.558928	+	4.57008i	−0.0296648	+	0.242554i
$356$	14.7838	+	20.3482i	0.783540	+	1.07845i
$357$	4.50586	+	2.06585i	0.238475	+	0.109336i
$358$	−3.32401	−	0.526471i	−0.175679	−	0.0278248i
$359$	3.30837	+	2.97887i	0.174609	+	0.157219i	0.751802	−	0.659389i	$-0.229185\pi$
$359$	3.30837	+	2.97887i	0.174609	+	0.157219i	−0.577192	+	0.816608i	$0.695852\pi$
$360$	−1.50209	+	3.72290i	−0.0791671	+	0.196214i
$361$	3.90148	+	4.33303i	0.205341	+	0.228054i
$362$	7.26272	−	0.380623i	0.381720	−	0.0200051i
$363$	−7.32488	−	3.73221i	−0.384456	−	0.195890i
$364$	15.3923	+	24.2830i	0.806778	+	1.27278i
$365$	1.27173	+	2.60430i	0.0665656	+	0.136315i
$366$	6.16314	−	6.84486i	0.322152	−	0.357787i
$367$	−16.1627	+	19.9593i	−0.843688	+	1.04187i	0.154857	+	0.987937i	$0.450508\pi$
$367$	−16.1627	+	19.9593i	−0.843688	+	1.04187i	−0.998545	+	0.0539306i	$0.982825\pi$
$368$	18.7473	−	5.02332i	0.977269	−	0.261858i
$369$	−11.8108	−	5.25850i	−0.614845	−	0.273747i
$370$	0.498942	−	29.3854i	0.0259387	−	1.52768i
$371$	−0.717927	+	0.183925i	−0.0372729	+	0.00954889i
$372$	19.8217	−	3.13945i	1.02771	−	0.162773i
$373$	−30.0355	−	19.5053i	−1.55518	−	1.00994i	−0.981635	−	0.190770i	$-0.938902\pi$
$373$	−30.0355	−	19.5053i	−1.55518	−	1.00994i	−0.573544	−	0.819175i	$-0.694432\pi$
$374$	−2.47652	+	4.28945i	−0.128058	+	0.221802i
$375$	3.76525	−	8.48948i	0.194437	−	0.438395i
$376$	−0.210678	+	0.121635i	−0.0108649	+	0.00627285i
$377$	−5.16284	+	2.63060i	−0.265900	+	0.135483i
$378$	11.9667	+	21.2640i	0.615503	+	1.09370i
$379$	−13.3436	+	18.3659i	−0.685416	+	0.943394i	−0.999983	−	0.00584095i	$-0.998141\pi$
$379$	−13.3436	+	18.3659i	−0.685416	+	0.943394i	0.314567	+	0.949235i	$0.398141\pi$
$380$	23.1071	−	12.8229i	1.18537	−	0.657799i
$381$	10.7328	−	1.12806i	0.549857	−	0.0577923i
$382$	1.60434	+	5.98747i	0.0820850	+	0.306346i
$383$	20.3079	−	7.79546i	1.03768	−	0.398330i	0.220914	−	0.975293i	$-0.429096\pi$
$383$	20.3079	−	7.79546i	1.03768	−	0.398330i	0.816770	+	0.576964i	$0.195763\pi$
$384$	1.56841	+	4.82707i	0.0800375	+	0.246330i
$385$	−1.75401	−	5.96088i	−0.0893927	−	0.303794i
$386$	−11.0142	+	33.8984i	−0.560610	+	1.72538i
$387$	0.822146	+	15.6875i	0.0417920	+	0.797439i
$388$	−9.86003	+	6.40318i	−0.500567	+	0.325072i
$389$	9.65968	−	8.69762i	0.489765	−	0.440987i	−0.386876	−	0.922132i	$-0.626446\pi$
$389$	9.65968	−	8.69762i	0.489765	−	0.440987i	0.876641	+	0.481145i	$0.159779\pi$
$390$	−14.0164	+	10.9615i	−0.709747	+	0.555059i
$391$	13.3507	−	4.33792i	0.675176	−	0.219378i
$392$	−2.57597	+	4.79190i	−0.130106	+	0.242028i
$393$	−2.08085	−	2.08085i	−0.104965	−	0.104965i
$394$	16.4604	−	36.9707i	0.829264	−	1.86256i
$395$	9.47793	+	22.2991i	0.476886	+	1.12199i
$396$	−5.25672	+	2.34044i	−0.264160	+	0.117612i
$397$	−3.71351	+	3.00714i	−0.186376	+	0.150924i	−0.717968	−	0.696077i	$-0.754927\pi$
$397$	−3.71351	+	3.00714i	−0.186376	+	0.150924i	0.531592	+	0.847001i	$0.321594\pi$
$398$	−0.182143	−	0.357476i	−0.00913002	−	0.0179187i
$399$	1.83208	−	10.7969i	0.0917187	−	0.540522i
$400$	4.31200	+	14.9839i	0.215600	+	0.749196i
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	0.990874	−	0.134793i	$-0.0430370\pi$
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	−0.612171	+	0.790725i	$0.709704\pi$
$402$	−1.11647	+	21.3036i	−0.0556847	+	1.06253i
$403$	−43.5737	−	16.7264i	−2.17056	−	0.833201i
$404$	3.76828	−	35.8528i	0.187479	−	1.78374i
$405$	5.98064	−	4.19193i	0.297180	−	0.208299i
$406$	−5.82504	−	3.87462i	−0.289092	−	0.192294i
$407$	4.66850	−	4.66850i	0.231409	−	0.231409i
$408$	0.521819	+	1.35938i	0.0258339	+	0.0672996i
$409$	10.0531	+	2.13685i	0.497094	+	0.105661i	0.449634	−	0.893213i	$-0.351554\pi$
$409$	10.0531	+	2.13685i	0.497094	+	0.105661i	0.0474592	+	0.998873i	$0.484888\pi$
$410$	25.3862	−	6.34232i	1.25373	−	0.313225i
$411$	−1.30816	−	6.15440i	−0.0645267	−	0.303574i
$412$	−7.31021	+	14.3471i	−0.360148	+	0.706831i
$413$	−16.6994	+	7.21593i	−0.821725	+	0.355073i
$414$	28.5896	+	9.28933i	1.40510	+	0.456546i
$415$	7.78634	−	2.83819i	0.382216	−	0.139321i
$416$	7.69187	−	36.1874i	0.377125	−	1.77423i
$417$	−5.70761	−	4.62194i	−0.279503	−	0.226337i
$418$	10.5699	+	2.83220i	0.516992	+	0.138528i
$419$	14.4852	−	10.5241i	0.707648	−	0.514137i	−0.174766	−	0.984610i	$-0.555917\pi$
$419$	14.4852	−	10.5241i	0.707648	−	0.514137i	0.882414	+	0.470473i	$0.155917\pi$
$420$	−10.7599	−	4.47962i	−0.525027	−	0.218583i
$421$	13.5865	+	9.87120i	0.662168	+	0.481093i	0.867394	−	0.497621i	$-0.165793\pi$
$421$	13.5865	+	9.87120i	0.662168	+	0.481093i	−0.205227	+	0.978714i	$0.565793\pi$
$422$	−8.37387	−	10.3409i	−0.407634	−	0.503386i
$423$	0.722062	+	0.0378417i	0.0351079	+	0.00183992i
$424$	−0.188538	−	0.108852i	−0.00915621	−	0.00528634i
$425$	3.68169	+	10.6595i	0.178588	+	0.517059i
$426$			3.57609i			0.173262i
$427$	−10.3232	−	9.50286i	−0.499577	−	0.459876i
$428$	7.29743	+	46.0741i	0.352734	+	2.22708i
$429$	−3.97536	−	0.417827i	−0.191932	−	0.0201729i
$430$	−20.8701	−	23.9853i	−1.00645	−	1.15667i
$431$	0.935006	+	8.89599i	0.0450377	+	0.428505i	0.993688	+	0.112178i	$0.0357828\pi$
$431$	0.935006	+	8.89599i	0.0450377	+	0.428505i	−0.948650	+	0.316326i	$0.897551\pi$
$432$	3.55996	−	13.2859i	0.171278	−	0.639220i
$433$	2.75652	−	17.4040i	0.132470	−	0.836382i	−0.828552	−	0.559912i	$-0.810835\pi$
$433$	2.75652	−	17.4040i	0.132470	−	0.836382i	0.961022	−	0.276471i	$-0.0891649\pi$
$434$	−8.20245	−	55.7524i	−0.393730	−	2.67620i
$435$	1.10179	−	2.07455i	0.0528269	−	0.0994670i
$436$	−44.3534	+	9.42761i	−2.12414	+	0.451501i
$437$	−16.8914	−	26.0104i	−0.808024	−	1.24425i
$438$	1.22603	+	1.88792i	0.0585819	+	0.0902083i
$439$	−26.8046	+	5.69749i	−1.27931	+	0.271926i	−0.796950	−	0.604045i	$-0.793555\pi$
$439$	−26.8046	+	5.69749i	−1.27931	+	0.271926i	−0.482363	+	0.875972i	$0.660221\pi$
$440$	0.856143	−	1.61202i	0.0408150	−	0.0768501i
$441$	14.1783	−	7.77490i	0.675155	−	0.370233i
$442$	3.38010	−	21.3411i	0.160775	−	1.01509i
$443$	2.86872	−	10.7062i	0.136297	−	0.508667i	−0.863692	−	0.504019i	$-0.831854\pi$
$443$	2.86872	−	10.7062i	0.136297	−	0.508667i	0.999989	−	0.00464732i	$-0.00147929\pi$
$444$	−1.29450	−	12.3163i	−0.0614341	−	0.584506i
$445$	15.5658	+	17.8892i	0.737889	+	0.848029i
$446$	27.7268	+	2.91420i	1.31290	+	0.137992i
$447$	−0.228782	−	1.44447i	−0.0108210	−	0.0683212i
$448$	26.8823	−	8.40866i	1.27007	−	0.397272i
$449$		−	40.1154i		−	1.89316i	−0.322465	−	0.946581i	$-0.604511\pi$
$449$		−	40.1154i		−	1.89316i	0.322465	−	0.946581i	$-0.395489\pi$
$450$	−7.03869	+	23.1011i	−0.331807	+	1.08900i
$451$	5.09064	+	2.93909i	0.239709	+	0.138396i
$452$	−20.6714	−	1.08334i	−0.972303	−	0.0509562i
$453$	3.27741	+	4.04726i	0.153986	+	0.190157i
$454$	−8.20786	−	5.96336i	−0.385214	−	0.279874i
$455$	16.4624	+	21.5345i	0.771769	+	1.00955i
$456$	2.60259	−	1.89089i	0.121877	−	0.0885490i
$457$	32.8230	+	8.79489i	1.53539	+	0.411408i	0.924774	−	0.380516i	$-0.124254\pi$
$457$	32.8230	+	8.79489i	1.53539	+	0.411408i	0.610620	+	0.791924i	$0.290920\pi$
$458$	10.8652	+	8.79845i	0.507697	+	0.411125i
$459$	2.06839	−	9.73101i	0.0965441	−	0.454204i
$460$	−31.0113	+	11.3039i	−1.44591	+	0.527046i
$461$	−30.0506	−	9.76402i	−1.39959	−	0.454756i	−0.490535	−	0.871422i	$-0.663198\pi$
$461$	−30.0506	−	9.76402i	−1.39959	−	0.454756i	−0.909060	+	0.416666i	$0.863198\pi$
$462$	−1.91435	−	4.43027i	−0.0890634	−	0.206115i
$463$	−8.64582	+	16.9684i	−0.401805	+	0.788587i	−0.999918	−	0.0128250i	$-0.995918\pi$
$463$	−8.64582	+	16.9684i	−0.401805	+	0.788587i	0.598113	+	0.801412i	$0.295918\pi$
$464$	0.819946	+	3.85754i	0.0380650	+	0.179082i
$465$	18.3568	−	4.58614i	0.851276	−	0.212677i
$466$	−17.6587	−	3.75346i	−0.818021	−	0.173876i
$467$	−2.13538	−	5.56287i	−0.0988138	−	0.257419i	0.875259	−	0.483655i	$-0.160691\pi$
$467$	−2.13538	−	5.56287i	−0.0988138	−	0.257419i	−0.974072	+	0.226236i	$0.927358\pi$
$468$	17.7499	−	17.7499i	0.820489	−	0.820489i
$469$	32.4324	+	2.05782i	1.49759	+	0.0950215i
$470$	−1.19836	+	0.839948i	−0.0552761	+	0.0387439i
$471$	0.938352	−	8.92782i	0.0432370	−	0.411372i
$472$	−4.98897	−	1.91509i	−0.229636	−	0.0881489i
$473$	0.373803	−	7.13258i	0.0171875	−	0.327956i
$474$	9.40980	+	16.2982i	0.432206	+	0.748603i
$475$	20.6424	−	13.9520i	0.947137	−	0.640164i
$476$	13.2680	−	4.92627i	0.608137	−	0.225795i
$477$	0.293762	+	0.576541i	0.0134505	+	0.0263980i
$478$	−31.1740	+	25.2442i	−1.42586	+	1.15464i
$479$	19.0483	−	8.48083i	0.870338	−	0.387499i	0.0775436	−	0.996989i	$-0.475292\pi$
$479$	19.0483	−	8.48083i	0.870338	−	0.387499i	0.792794	+	0.609490i	$0.208626\pi$
$480$	5.86663	+	13.8027i	0.267774	+	0.630002i
$481$	−11.7147	+	26.3117i	−0.534145	+	1.19971i
$482$	38.3695	+	38.3695i	1.74768	+	1.74768i
$483$	−4.36972	+	12.9615i	−0.198829	+	0.589769i
$484$	−22.3238	+	7.25343i	−1.01472	+	0.329701i
$485$	−8.73133	+	6.82835i	−0.396469	+	0.310060i
$486$	24.7763	−	22.3086i	1.12387	−	1.01194i
$487$	24.6153	−	15.9853i	1.11542	−	0.724365i	0.150950	−	0.988541i	$-0.451767\pi$
$487$	24.6153	−	15.9853i	1.11542	−	0.724365i	0.964474	+	0.264176i	$0.0851001\pi$
$488$	−0.215714	−	4.11607i	−0.00976491	−	0.186326i
$489$	1.43207	−	4.40746i	0.0647605	−	0.199312i
$490$	−12.9104	+	30.0731i	−0.583231	+	1.35856i
$491$	−5.56395	−	17.1241i	−0.251097	−	0.772798i	−0.994574	−	0.104036i	$-0.966824\pi$
$491$	−5.56395	−	17.1241i	−0.251097	−	0.772798i	0.743476	−	0.668762i	$-0.233176\pi$
$492$	10.2936	−	3.95135i	0.464072	−	0.178141i
$493$	0.738256	+	2.75521i	0.0332494	+	0.124088i
$494$	−47.4754	+	4.98986i	−2.13602	+	0.224505i
$495$	−4.74364	+	2.63240i	−0.213211	+	0.118317i
$496$	−18.6720	+	25.6998i	−0.838396	+	1.15395i
$497$	5.44735	+	0.0599495i	0.244347	+	0.00268910i
$498$	5.73541	−	2.92234i	0.257010	−	0.130953i
$499$	−4.60639	+	2.65950i	−0.206210	+	0.119056i	−0.599549	−	0.800338i	$-0.704653\pi$
$499$	−4.60639	+	2.65950i	−0.206210	+	0.119056i	0.393339	+	0.919394i	$0.371320\pi$
$500$	−9.53800	−	24.7417i	−0.426552	−	1.10648i
$501$	4.35478	−	7.54270i	0.194557	−	0.336983i
$502$	−27.0280	−	17.5522i	−1.20632	−	0.783391i
$503$	26.0759	−	4.13001i	1.16267	−	0.184148i	0.454865	−	0.890560i	$-0.349687\pi$
$503$	26.0759	−	4.13001i	1.16267	−	0.184148i	0.707801	+	0.706412i	$0.249687\pi$
$504$	4.57437	+	1.27982i	0.203759	+	0.0570075i
$505$	0.577015	−	33.9836i	0.0256768	−	1.51225i
$506$	−12.4861	−	5.55916i	−0.555073	−	0.247135i
$507$	6.41294	−	1.71834i	0.284809	−	0.0763143i
$508$	19.3915	−	23.9465i	0.860359	−	1.06245i
$509$	2.99499	−	3.32627i	0.132750	−	0.147434i	−0.673104	−	0.739548i	$-0.735040\pi$
$509$	2.99499	−	3.32627i	0.132750	−	0.147434i	0.805855	+	0.592113i	$0.201706\pi$
$510$	3.84356	+	7.87096i	0.170196	+	0.348532i
$511$	2.89636	−	1.83592i	0.128127	−	0.0812164i
$512$	−26.7543	−	13.6320i	−1.18238	−	0.602454i
$513$	−21.9490	+	1.15030i	−0.969072	+	0.0507869i
$514$	−42.7681	−	47.4988i	−1.88642	−	2.09508i
$515$	−5.68028	+	14.0785i	−0.250303	+	0.620372i
$516$	−9.95612	−	8.96453i	−0.438294	−	0.394641i
$517$	−0.324701	−	0.0514276i	−0.0142803	−	0.00226178i
$518$	−34.6217	+	3.25411i	−1.52119	+	0.142977i
$519$	6.70259	+	9.22532i	0.294211	+	0.404947i
$520$	−0.966631	+	7.90366i	−0.0423896	+	0.346598i
$521$	−10.4542	−	23.4805i	−0.458006	−	1.02870i	−0.983993	−	0.178206i	$-0.942971\pi$
$521$	−10.4542	−	23.4805i	−0.458006	−	1.02870i	0.525987	−	0.850492i	$-0.323696\pi$
$522$	−2.18899	+	5.70250i	−0.0958093	+	0.249592i
$523$	−11.9816	+	18.4501i	−0.523920	+	0.806766i	−0.997249	−	0.0741198i	$-0.976385\pi$
$523$	−11.9816	+	18.4501i	−0.523920	+	0.806766i	0.473330	+	0.880885i	$0.343052\pi$
$524$	−8.40229			−0.367056
$525$	−10.4755	−	3.31821i	−0.457190	−	0.144819i
$526$	0.852467			0.0371693
$527$	−12.5137	+	19.2694i	−0.545105	+	0.839388i
$528$	−0.974967	+	2.53988i	−0.0424300	+	0.110534i
$529$	6.40073	+	14.3763i	0.278292	+	0.625055i
$530$	−1.18718	−	0.552905i	−0.0515679	−	0.0240167i
$531$	9.33596	+	12.8499i	0.405146	+	0.557636i
$532$	−18.0996	−	25.4974i	−0.784717	−	1.10545i
$533$	−25.3273	−	4.01144i	−1.09705	−	0.173755i
$534$	13.6875	+	12.3243i	0.592317	+	0.533325i
$535$	10.6601	+	42.6690i	0.460878	+	1.84474i
$536$	6.38773	+	7.09429i	0.275908	+	0.306427i
$537$	−1.33518	+	0.0699740i	−0.0576174	+	0.00301960i
$538$	35.6828	+	18.1813i	1.53840	+	0.783852i
$539$	−6.78058	+	2.84179i	−0.292060	+	0.122405i
$540$	−4.05098	+	23.0383i	−0.174326	+	0.991412i
$541$	5.42224	−	6.02201i	0.233120	−	0.258906i	−0.615223	−	0.788353i	$-0.710934\pi$
$541$	5.42224	−	6.02201i	0.233120	−	0.258906i	0.848343	+	0.529447i	$0.177601\pi$
$542$	−25.4039	+	31.3712i	−1.09119	+	1.34751i
$543$	2.79083	−	0.747801i	0.119766	−	0.0320912i
$544$	−16.6374	−	7.40747i	−0.713324	−	0.317592i
$545$	−40.8770	+	12.5186i	−1.75098	+	0.536239i
$546$	14.7225	+	15.0502i	0.630065	+	0.644088i
$547$	19.0836	−	3.02255i	0.815958	−	0.129235i	0.265514	−	0.964107i	$-0.414458\pi$
$547$	19.0836	−	3.02255i	0.815958	−	0.129235i	0.550444	+	0.834872i	$0.314458\pi$
$548$	−15.0666	−	9.78435i	−0.643612	−	0.417967i
$549$	−6.12533	+	10.6094i	−0.261423	+	0.452797i
$550$	4.28062	−	10.1113i	0.182526	−	0.431145i
$551$	5.45756	−	3.15092i	0.232500	−	0.134234i
$552$	−3.58011	+	1.82416i	−0.152379	+	0.0776412i
$553$	24.9844	−	14.0604i	1.06244	−	0.597910i
$554$	9.39867	−	12.9362i	0.399311	−	0.549605i
$555$	−2.23331	−	11.4603i	−0.0947989	−	0.486462i
$556$	−20.8549	+	2.19194i	−0.884445	+	0.0929589i
$557$	4.82211	+	17.9964i	0.204320	+	0.762531i	0.989656	+	0.143462i	$0.0458234\pi$
$557$	4.82211	+	17.9964i	0.204320	+	0.762531i	−0.785336	+	0.619069i	$0.787510\pi$
$558$	−45.9337	+	17.6323i	−1.94453	+	0.746434i
$559$	9.62832	+	29.6329i	0.407235	+	1.25334i
$560$	17.0571	−	7.02929i	0.720794	−	0.297042i
$561$	−0.608062	+	1.87142i	−0.0256724	+	0.0790116i
$562$	−2.04826	−	39.0832i	−0.0864007	−	1.64862i
$563$	18.1325	−	11.7754i	0.764193	−	0.496273i	−0.102734	−	0.994709i	$-0.532759\pi$
$563$	18.1325	−	11.7754i	0.764193	−	0.496273i	0.866926	+	0.498436i	$0.166092\pi$
$564$	−0.458259	+	0.412619i	−0.0192962	+	0.0173744i
$565$	−19.5037	+	0.690374i	−0.820527	+	0.0290443i
$566$	5.66670	−	1.84122i	0.238189	−	0.0773923i
$567$	−5.71131	−	6.48517i	−0.239852	−	0.272352i
$568$	1.13157	+	1.13157i	0.0474795	+	0.0474795i
$569$	−16.3273	+	36.6716i	−0.684474	+	1.53735i	0.151424	+	0.988469i	$0.451614\pi$
$569$	−16.3273	+	36.6716i	−0.684474	+	1.53735i	−0.835898	+	0.548885i	$0.815053\pi$
$570$	14.5991	−	12.7030i	0.611488	−	0.532070i
$571$	30.4188	−	13.5433i	1.27299	−	0.566770i	0.344727	−	0.938703i	$-0.387971\pi$
$571$	30.4188	−	13.5433i	1.27299	−	0.566770i	0.928260	+	0.371932i	$0.121305\pi$
$572$	−8.86966	+	7.18251i	−0.370859	+	0.300316i
$573$	1.11800	+	2.19419i	0.0467050	+	0.0916638i
$574$	−10.7765	−	29.0245i	−0.449803	−	1.21146i
$575$	−28.1913	+	13.1785i	−1.17566	+	0.549580i
$576$	−12.2962	−	21.2976i	−0.512342	−	0.887402i
$577$	−0.300036	+	5.72503i	−0.0124907	+	0.238336i	0.985248	+	0.171130i	$0.0547418\pi$
$577$	−0.300036	+	5.72503i	−0.0124907	+	0.238336i	−0.997739	+	0.0672061i	$0.978592\pi$
$578$	23.2538	+	8.92628i	0.967229	+	0.371284i
$579$	−1.48014	+	14.0825i	−0.0615123	+	0.585251i
$580$	−1.96395	−	6.41289i	−0.0815487	−	0.266281i
$581$	−4.35536	−	8.78556i	−0.180691	−	0.364487i
$582$	−6.08774	+	6.08774i	−0.252345	+	0.252345i
$583$	−0.105432	−	0.274660i	−0.00436654	−	0.0113752i
$584$	0.985333	+	0.209439i	0.0407734	+	0.00866665i
$585$	15.2039	−	18.1368i	0.628604	−	0.749865i
$586$	0.359614	+	1.69185i	0.0148555	+	0.0698898i
$587$	−5.48135	+	10.7577i	−0.226239	+	0.444020i	−0.976024	−	0.217662i	$-0.930157\pi$
$587$	−5.48135	+	10.7577i	−0.226239	+	0.444020i	0.749785	+	0.661682i	$0.230157\pi$
$588$	−3.86154	+	13.2388i	−0.159247	+	0.545960i
$589$	48.2769	+	15.6861i	1.98922	+	0.646335i
$590$	−30.9056	−	8.84614i	−1.27236	−	0.364190i
$591$	3.34273	−	15.7263i	0.137501	−	0.646893i
$592$	15.2342	+	12.3364i	0.626121	+	0.507023i
$593$	41.9372	+	11.2370i	1.72215	+	0.461449i	0.978351	−	0.206951i	$-0.0663541\pi$
$593$	41.9372	+	11.2370i	1.72215	+	0.461449i	0.743802	+	0.668401i	$0.233021\pi$
$594$	−7.83623	+	5.69336i	−0.321525	+	0.233601i
$595$	12.0540	−	5.72283i	0.494167	−	0.234613i
$596$	−3.37823	−	2.45442i	−0.138377	−	0.100537i
$597$	−0.100307	−	0.123869i	−0.00410531	−	0.00506963i
$598$	59.5424	+	3.12048i	2.43487	+	0.127606i
$599$	0.677665	+	0.391250i	0.0276887	+	0.0159860i	0.513780	−	0.857922i	$-0.328245\pi$
$599$	0.677665	+	0.391250i	0.0276887	+	0.0159860i	−0.486092	+	0.873908i	$0.661578\pi$
$600$	−1.51813	−	2.84864i	−0.0619774	−	0.116295i
$601$		−	7.23002i		−	0.294919i	−0.989068	−	0.147459i	$-0.952890\pi$
$601$		−	7.23002i		−	0.294919i	0.989068	−	0.147459i	$-0.0471095\pi$
$602$	−25.4783	+	27.6778i	−1.03842	+	1.12806i
$603$	−4.43864	−	28.0244i	−0.180755	−	1.14124i
$604$	14.7882	+	1.55430i	0.601723	+	0.0632436i
$605$	−20.3668	+	8.65662i	−0.828027	+	0.351942i
$606$	−2.75948	−	26.2547i	−0.112096	−	1.06653i
$607$	−0.459640	+	1.71540i	−0.0186562	+	0.0696260i	−0.974626	−	0.223838i	$-0.928141\pi$
$607$	−0.459640	+	1.71540i	−0.0186562	+	0.0696260i	0.955970	+	0.293464i	$0.0948080\pi$
$608$	−6.29427	+	39.7405i	−0.255267	+	1.61169i
$609$	−2.58363	−	1.02452i	−0.104694	−	0.0415158i
$610$	−3.46241	−	24.5516i	−0.140189	−	0.994064i
$611$	1.40279	−	0.298173i	0.0567510	−	0.0120628i
$612$	−6.73012	−	10.3635i	−0.272049	−	0.418919i
$613$	0.596749	+	0.918913i	0.0241025	+	0.0371145i	0.850516	−	0.525948i	$-0.176290\pi$
$613$	0.596749	+	0.918913i	0.0241025	+	0.0371145i	−0.826414	+	0.563063i	$0.809623\pi$
$614$	30.0818	−	6.39408i	1.21400	−	0.258044i
$615$	9.34112	−	4.56147i	0.376670	−	0.183936i
$616$	−2.00760	−	0.796102i	−0.0808884	−	0.0320759i
$617$	5.03752	−	31.8056i	0.202803	−	1.28045i	−0.650691	−	0.759343i	$-0.725521\pi$
$617$	5.03752	−	31.8056i	0.202803	−	1.28045i	0.853494	−	0.521103i	$-0.174479\pi$
$618$	−3.05185	+	11.3897i	−0.122764	+	0.458160i
$619$	−1.93430	−	18.4036i	−0.0777461	−	0.739705i	−0.962065	−	0.272821i	$-0.912043\pi$
$619$	−1.93430	−	18.4036i	−0.0777461	−	0.739705i	0.884319	−	0.466884i	$-0.154623\pi$
$620$	27.8023	−	46.3208i	1.11657	−	1.86029i
$621$	27.3018	+	2.86954i	1.09559	+	0.115151i
$622$	−3.88654	−	24.5386i	−0.155836	−	0.983910i
$623$	19.0027	−	20.6432i	0.761326	−	0.827051i
$624$		−	11.8683i		−	0.475111i
$625$	−11.0020	−	22.4490i	−0.440081	−	0.897958i
$626$	18.2402	+	10.5310i	0.729023	+	0.420902i
$627$	4.34137	+	0.227522i	0.173378	+	0.00908634i
$628$	−16.1304	−	19.9194i	−0.643673	−	0.794869i
$629$	11.4704	+	8.33374i	0.457355	+	0.332288i
$630$	28.0863	+	5.25787i	1.11899	+	0.209479i
$631$	20.5730	−	14.9472i	0.818998	−	0.595037i	−0.0974273	−	0.995243i	$-0.531061\pi$
$631$	20.5730	−	14.9472i	0.818998	−	0.595037i	0.916425	+	0.400206i	$0.131061\pi$
$632$	8.13469	+	2.17968i	0.323580	+	0.0867031i
$633$	−4.10820	−	3.32675i	−0.163286	−	0.132227i
$634$	−8.21870	+	38.6659i	−0.326406	+	1.53562i
$635$	16.2337	−	24.0922i	0.644215	−	0.956069i
$636$	−0.524836	−	0.170530i	−0.0208111	−	0.00676194i
$637$	23.1723	−	22.1740i	0.918118	−	0.878568i
$638$	1.26082	−	2.47450i	0.0499165	−	0.0979666i
$639$	−0.988908	−	4.65245i	−0.0391206	−	0.184048i
$640$	12.6704	+	5.11217i	0.500842	+	0.202076i
$641$	−36.5968	−	7.77889i	−1.44549	−	0.307248i	−0.582647	−	0.812725i	$-0.697983\pi$
$641$	−36.5968	−	7.77889i	−1.44549	−	0.307248i	−0.862840	+	0.505478i	$0.831316\pi$
$642$	12.2419	+	31.8914i	0.483151	+	1.25865i
$643$	−14.7951	+	14.7951i	−0.583460	+	0.583460i	−0.935852	−	0.352392i	$-0.885368\pi$
$643$	−14.7951	+	14.7951i	−0.583460	+	0.583460i	0.352392	+	0.935852i	$0.385368\pi$
$644$	17.3464	+	34.9910i	0.683545	+	1.37884i
$645$	−10.0912	−	7.59676i	−0.397341	−	0.299122i
$646$	−2.45636	+	23.3707i	−0.0966442	+	0.919508i
$647$	−24.1309	−	9.26299i	−0.948684	−	0.364166i	−0.165678	−	0.986180i	$-0.552981\pi$
$647$	−24.1309	−	9.26299i	−0.948684	−	0.364166i	−0.783006	+	0.622014i	$0.786315\pi$
$648$	0.132854	−	2.53501i	0.00521902	−	0.0995848i
$649$	−3.61080	−	6.25410i	−0.141736	−	0.245495i
$650$	−1.62612	+	47.8718i	−0.0637816	+	1.87769i
$651$	−7.79252	−	20.9877i	−0.305413	−	0.822572i
$652$	−6.00718	−	11.7898i	−0.235259	−	0.461723i
$653$	20.4375	−	16.5499i	0.799780	−	0.647649i	−0.139723	−	0.990191i	$-0.544621\pi$
$653$	20.4375	−	16.5499i	0.799780	−	0.647649i	0.939503	+	0.342542i	$0.111288\pi$
$654$	−30.3345	+	13.5058i	−1.18617	+	0.528118i
$655$	−7.89127	+	0.694179i	−0.308337	+	0.0271238i
$656$	−7.09872	+	15.9440i	−0.277158	+	0.622508i
$657$	−2.11712	−	2.11712i	−0.0825967	−	0.0825967i
$658$	1.14439	+	1.29945i	0.0446130	+	0.0506579i
$659$	−5.69893	+	1.85169i	−0.221999	+	0.0721317i	−0.417904	−	0.908491i	$-0.637235\pi$
$659$	−5.69893	+	1.85169i	−0.221999	+	0.0721317i	0.195906	+	0.980623i	$0.437235\pi$
$660$	1.27319	−	4.44812i	0.0495588	−	0.173143i
$661$	−34.1915	+	30.7862i	−1.32990	+	1.19744i	−0.366171	+	0.930547i	$0.619332\pi$
$661$	−34.1915	+	30.7862i	−1.32990	+	1.19744i	−0.963725	+	0.266897i	$0.914002\pi$
$662$	54.5608	−	35.4322i	2.12056	−	1.37711i
$663$	−0.449254	−	8.57228i	−0.0174476	−	0.332920i
$664$	0.890129	−	2.73954i	0.0345437	−	0.106315i
$665$	−19.1053	−	22.4513i	−0.740873	−	0.870623i
$666$	9.38224	+	28.8756i	0.363555	+	1.11891i
$667$	−7.34830	+	2.82075i	−0.284527	+	0.109220i
$668$	−6.43627	−	24.0205i	−0.249027	−	0.929381i
$669$	11.0152	−	1.15775i	0.425874	−	0.0447612i
$670$	42.0178	+	39.1449i	1.62329	+	1.51230i
$671$	3.27395	−	4.50620i	0.126389	−	0.173960i
$672$	15.4648	−	8.70309i	0.596566	−	0.335729i
$673$	−15.5853	+	7.94108i	−0.600767	+	0.306106i	−0.727797	−	0.685793i	$-0.759456\pi$
$673$	−15.5853	+	7.94108i	−0.600767	+	0.306106i	0.127030	+	0.991899i	$0.459456\pi$
$674$	−63.0398	+	36.3960i	−2.42820	+	1.40192i
$675$	−1.90122	+	21.9718i	−0.0731781	+	0.845696i
$676$	9.47819	−	16.4167i	0.364546	−	0.631412i
$677$	29.2874	+	19.0194i	1.12560	+	0.730976i	0.966597	−	0.256301i	$-0.0825038\pi$
$677$	29.2874	+	19.0194i	1.12560	+	0.730976i	0.159008	+	0.987277i	$0.449170\pi$
$678$	−14.9717	+	2.37128i	−0.574984	+	0.0910685i
$679$	9.17120	+	9.37531i	0.351959	+	0.359792i
$680$	3.70678	+	1.27437i	0.142148	+	0.0488700i
$681$	−3.68211	−	1.63938i	−0.141099	−	0.0628212i
$682$	21.6081	−	5.78987i	0.827417	−	0.221706i
$683$	25.6066	−	31.6215i	0.979808	−	1.20996i	0.00209925	−	0.999998i	$-0.499332\pi$
$683$	25.6066	−	31.6215i	0.979808	−	1.20996i	0.977709	−	0.209965i	$-0.0673349\pi$
$684$	−18.2676	+	20.2882i	−0.698479	+	0.775740i
$685$	−14.9586	−	7.94450i	−0.571538	−	0.303544i
$686$	37.0527	+	11.2515i	1.41468	+	0.429585i
$687$	4.94891	+	2.52160i	0.188813	+	0.0962049i
$688$	21.1773	−	1.10986i	0.807378	−	0.0423129i
$689$	0.858776	+	0.953767i	0.0327168	+	0.0363356i
$690$	−20.4920	+	12.8184i	−0.780117	+	0.487987i
$691$	13.2239	+	11.9069i	0.503062	+	0.452959i	0.881168	−	0.472803i	$-0.156758\pi$
$691$	13.2239	+	11.9069i	0.503062	+	0.452959i	−0.378106	+	0.925762i	$0.623425\pi$
$692$	32.1577	+	5.09328i	1.22245	+	0.193618i
$693$	3.71565	+	5.23434i	0.141146	+	0.198836i
$694$	33.1078	+	45.5689i	1.25675	+	1.72977i
$695$	−19.4054	+	3.78161i	−0.736090	+	0.143445i
$696$	−0.332078	−	0.745860i	−0.0125874	−	0.0282717i
$697$	−4.52377	+	11.7848i	−0.171350	+	0.446382i
$698$	−32.9421	+	50.7263i	−1.24688	+	1.92002i
$699$	−7.17212			−0.271275
$700$	−27.8490	+	14.4503i	−1.05259	+	0.546171i
$701$	−20.8675			−0.788156			−0.394078	−	0.919077i	$-0.628936\pi$
$701$	−20.8675			−0.788156			−0.394078	+	0.919077i	$0.628936\pi$
$702$	23.0136	−	35.4378i	0.868592	−	1.33752i
$703$	11.2255	−	29.2435i	0.423379	−	1.10294i
$704$	4.54787	+	10.2147i	0.171404	+	0.384980i
$705$	−0.396299	+	0.425384i	−0.0149255	+	0.0160209i
$706$	−14.3393	−	19.7364i	−0.539667	−	0.742788i
$707$	−40.0393	+	3.76330i	−1.50583	+	0.141533i
$708$	−13.3791	−	2.11905i	−0.502819	−	0.0796387i
$709$	0.576558	+	0.519135i	0.0216531	+	0.0194965i	0.679886	−	0.733318i	$-0.262029\pi$
$709$	0.576558	+	0.519135i	0.0216531	+	0.0194965i	−0.658233	+	0.752814i	$0.728696\pi$
$710$	7.37735	+	6.18435i	0.276867	+	0.232095i
$711$	−16.7490	−	18.6017i	−0.628137	−	0.697617i
$712$	8.23081	−	0.431359i	0.308463	−	0.0161658i
$713$	−56.4913	−	28.7838i	−2.11562	−	1.07796i
$714$	8.75368	−	5.54871i	0.327598	−	0.207655i
$715$	−7.73680	+	7.47846i	−0.289340	+	0.279679i
$716$	−2.55440	+	2.83695i	−0.0954624	+	0.106022i
$717$	−10.0290	+	12.3847i	−0.374538	+	0.462516i
$718$	8.99106	−	2.40915i	0.335543	−	0.0899086i
$719$	−33.6892	−	14.9994i	−1.25639	−	0.559383i	−0.332888	−	0.942966i	$-0.608023\pi$
$719$	−33.6892	−	14.9994i	−1.25639	−	0.559383i	−0.923506	+	0.383583i	$0.874690\pi$
$720$	−9.24524	−	13.1902i	−0.344550	−	0.491570i
$721$	17.2984	+	4.83973i	0.644225	+	0.180241i
$722$	12.0411	−	1.90712i	0.448122	−	0.0709755i
$723$	18.0795	+	11.7410i	0.672384	+	0.436651i
$724$	4.12478	−	7.14434i	0.153296	−	0.265517i
$725$	−2.37433	−	5.86060i	−0.0881803	−	0.217657i
$726$	−14.8859	+	8.59439i	−0.552468	+	0.318968i
$727$	−17.7421	+	9.04006i	−0.658019	+	0.335277i	−0.750915	−	0.660398i	$-0.770387\pi$
$727$	−17.7421	+	9.04006i	−0.658019	+	0.335277i	0.0928967	+	0.995676i	$0.470387\pi$
$728$	9.42084	+	0.103679i	0.349160	+	0.00384259i
$729$	2.02583	−	2.78831i	0.0750307	−	0.103271i
$730$	6.01496	+	0.735640i	0.222624	+	0.0272272i
$731$	15.2541	−	1.60327i	0.564192	−	0.0592990i
$732$	−2.70410	−	10.0919i	−0.0999466	−	0.373006i
$733$	−0.0374092	+	0.0143601i	−0.00138174	+	0.000530401i	−0.359059	−	0.933315i	$-0.616902\pi$
$733$	−0.0374092	+	0.0143601i	−0.00138174	+	0.000530401i	0.357677	+	0.933845i	$0.383569\pi$
$734$	16.5940	+	51.0711i	0.612496	+	1.88507i
$735$	−2.53292	+	12.7527i	−0.0934282	+	0.470390i
$736$	15.5297	−	47.7955i	0.572432	−	1.76177i
$737$	0.675166	+	12.8829i	0.0248701	+	0.474549i
$738$	−22.6707	+	14.7226i	−0.834522	+	0.541945i
$739$	−14.3575	+	12.9276i	−0.528151	+	0.475549i	−0.889534	−	0.456868i	$-0.848971\pi$
$739$	−14.3575	+	12.9276i	−0.528151	+	0.475549i	0.361384	+	0.932417i	$0.382304\pi$
$740$	−27.6468	−	18.6289i	−1.01632	−	0.684811i
$741$	−18.0366	+	5.86045i	−0.662592	+	0.215289i
$742$	−0.495031	+	1.46836i	−0.0181731	+	0.0539054i
$743$	16.7789	+	16.7789i	0.615557	+	0.615557i	0.944389	−	0.328831i	$-0.106655\pi$
$743$	16.7789	+	16.7789i	0.615557	+	0.615557i	−0.328831	+	0.944389i	$0.606655\pi$
$744$	2.67489	−	6.00790i	0.0980661	−	0.220260i
$745$	−3.37554	−	2.02605i	−0.123670	−	0.0742286i
$746$	−68.4068	+	30.4567i	−2.50455	+	1.11510i
$747$	−6.65357	+	5.38795i	−0.243441	+	0.197135i
$748$	2.55067	+	5.00597i	0.0932617	+	0.183036i
$749$	48.7843	−	18.1132i	1.78254	−	0.661840i
$750$	−10.5989	−	16.2701i	−0.387019	−	0.594099i
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	0.719227	−	0.694775i	$-0.244496\pi$
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	−0.961306	+	0.275482i	$0.911163\pi$
$752$	0.0510844	−	0.974748i	0.00186286	−	0.0355454i
$753$	−11.9528	−	4.58823i	−0.435583	−	0.167205i
$754$	−1.26639	+	12.0489i	−0.0461193	+	0.438796i
$755$	14.0172	+	0.238001i	0.510138	+	0.00866174i
$756$	27.6220	+	1.75260i	1.00460	+	0.0637416i
$757$	1.13591	−	1.13591i	0.0412853	−	0.0412853i	−0.686163	−	0.727448i	$-0.740706\pi$
$757$	1.13591	−	1.13591i	0.0412853	−	0.0412853i	0.727448	+	0.686163i	$0.240706\pi$
$758$	17.0102	+	44.3132i	0.617839	+	1.60953i
$759$	−5.31122	−	1.12894i	−0.192785	−	0.0409778i
$760$	0.599974	−	8.63908i	0.0217633	−	0.313372i
$761$	6.60486	+	31.0734i	0.239426	+	1.12641i	0.919446	+	0.393217i	$0.128638\pi$
$761$	6.60486	+	31.0734i	0.239426	+	1.12641i	−0.680020	+	0.733194i	$0.738029\pi$
$762$	10.2440	−	20.1050i	0.371102	−	0.728328i
$763$	20.0644	+	46.4340i	0.726381	+	1.68102i
$764$	6.68717	+	2.17279i	0.241933	+	0.0786089i
$765$	−7.17700	−	9.17714i	−0.259485	−	0.331800i
$766$	9.45622	−	44.4880i	0.341667	−	1.60742i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13877 - 1.75355i) q^{2} +(0.297680 - 0.775483i) q^{3} +(-0.964662 - 2.16667i) q^{4} +(-1.08500 - 1.95519i) q^{5} +(-1.02086 - 1.40509i) q^{6} +(-2.15744 + 1.53148i) q^{7} +(-0.767632 - 0.121581i) q^{8} +(1.71667 + 1.54570i) q^{9} +O(q^{10})\)	\(q+(1.13877 - 1.75355i) q^{2} +(0.297680 - 0.775483i) q^{3} +(-0.964662 - 2.16667i) q^{4} +(-1.08500 - 1.95519i) q^{5} +(-1.02086 - 1.40509i) q^{6} +(-2.15744 + 1.53148i) q^{7} +(-0.767632 - 0.121581i) q^{8} +(1.71667 + 1.54570i) q^{9} +(-4.66408 - 0.323915i) q^{10} +(-0.702779 - 0.780515i) q^{11} +(-1.96737 + 0.103106i) q^{12} +(4.08239 + 2.08008i) q^{13} +(0.228707 + 5.52718i) q^{14} +(-1.83920 + 0.259375i) q^{15} +(2.08662 - 2.31743i) q^{16} +(1.41941 - 1.75283i) q^{17} +(4.66535 - 1.25008i) q^{18} +(-4.55223 - 2.02678i) q^{19} +(-3.18960 + 4.23693i) q^{20} +(0.545413 + 2.12895i) q^{21} +(-2.16897 + 0.343531i) q^{22} +(5.21979 + 3.38977i) q^{23} +(-0.322792 + 0.559093i) q^{24} +(-2.64556 + 4.24276i) q^{25} +(8.29642 - 4.78994i) q^{26} +(3.93004 - 2.00245i) q^{27} +(5.39942 + 3.19709i) q^{28} +(-0.743348 + 1.02313i) q^{29} +(-1.63959 + 3.52049i) q^{30} +(-10.1310 + 1.06481i) q^{31} +(-2.08985 - 7.79943i) q^{32} +(-0.814479 + 0.312649i) q^{33} +(-1.45729 - 4.48507i) q^{34} +(5.33517 + 2.55656i) q^{35} +(1.69301 - 5.21054i) q^{36} +(0.328991 + 6.27752i) q^{37} +(-8.73799 + 5.67452i) q^{38} +(2.82832 - 2.54663i) q^{39} +(0.595164 + 1.63278i) q^{40} +(-5.32280 + 1.72948i) q^{41} +(4.35431 + 1.46797i) q^{42} +(4.80861 + 4.80861i) q^{43} +(-1.01317 + 2.27562i) q^{44} +(1.15956 - 5.03351i) q^{45} +(11.8882 - 5.29299i) q^{46} +(0.243253 - 0.196982i) q^{47} +(-1.17598 - 2.30799i) q^{48} +(2.30911 - 6.60818i) q^{49} +(4.42720 + 9.47062i) q^{50} +(-0.936759 - 1.62251i) q^{51} +(0.568717 - 10.8518i) q^{52} +(0.261509 + 0.100384i) q^{53} +(0.963998 - 9.17183i) q^{54} +(-0.763545 + 2.22093i) q^{55} +(1.84232 - 0.913312i) q^{56} +(-2.92684 + 2.92684i) q^{57} +(0.947608 + 2.46860i) q^{58} +(6.72559 + 1.42957i) q^{59} +(2.33619 + 3.73473i) q^{60} +(1.10261 + 5.18739i) q^{61} +(-9.66967 + 18.9778i) q^{62} +(-6.07084 - 0.705699i) q^{63} +(-10.1249 - 3.28979i) q^{64} +(-0.362422 - 10.2388i) q^{65} +(-0.379257 + 1.78426i) q^{66} +(-9.54564 - 7.72991i) q^{67} +(-5.16706 - 1.38451i) q^{68} +(4.18254 - 3.03879i) q^{69} +(10.5586 - 6.44414i) q^{70} +(-1.66579 - 1.21027i) q^{71} +(-1.12985 - 1.39524i) q^{72} +(-1.29435 - 0.0678338i) q^{73} +(11.3826 + 6.57173i) q^{74} +(2.50266 + 3.31457i) q^{75} +11.8183i q^{76} +(2.71155 + 0.607621i) q^{77} +(-1.24484 - 7.85959i) q^{78} +(-10.7765 - 1.13266i) q^{79} +(-6.79499 - 1.56534i) q^{80} +(0.341411 + 3.24831i) q^{81} +(-3.02870 + 11.3033i) q^{82} +(-0.579789 + 3.66064i) q^{83} +(4.08659 - 3.23545i) q^{84} +(-4.96718 - 0.873412i) q^{85} +(13.9080 - 2.95623i) q^{86} +(0.572141 + 0.881019i) q^{87} +(0.444580 + 0.684593i) q^{88} +(-10.3731 + 2.20488i) q^{89} +(-7.50603 - 7.76533i) q^{90} +(-11.9931 + 1.76446i) q^{91} +(2.30917 - 14.5795i) q^{92} +(-2.19006 + 8.17341i) q^{93} +(-0.0684094 - 0.650872i) q^{94} +(0.976406 + 11.0995i) q^{95} +(-6.67043 - 0.701090i) q^{96} +(-0.775456 - 4.89604i) q^{97} +(-8.95821 - 11.5743i) q^{98} -2.42618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

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