LMFDB - Embedded newform 175.2.x.a.117.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			117.16
Character	$\chi$	$=$	175.117
Dual form			175.2.x.a.3.16

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$

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	0.967418	+	0.253185i	$0.0814780\pi$
$2$	1.13877	+	1.75355i	0.805229	+	1.23994i	−0.162189	+	0.986760i	$0.551855\pi$
$3$	0.297680	+	0.775483i	0.171866	+	0.447725i	0.992276	−	0.124050i	$-0.0395883\pi$
$3$	0.297680	+	0.775483i	0.171866	+	0.447725i	−0.820410	+	0.571775i	$0.806255\pi$
$4$	−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	−0.839718	−	0.543023i	$-0.817280\pi$
$11$	−0.702779	+	0.780515i	−0.211896	+	0.235334i	0.627822	+	0.778357i	$0.283946\pi$
$12$	−1.96737	−	0.103106i	−0.567932	−	0.0297640i
$13$	4.08239	−	2.08008i	1.13225	−	0.576911i	0.215554	−	0.976492i	$-0.430844\pi$
$13$	4.08239	−	2.08008i	1.13225	−	0.576911i	0.916698	+	0.399580i	$0.130844\pi$
$14$	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	0.919641	−	0.392761i	$-0.128480\pi$
$17$	1.41941	+	1.75283i	0.344259	+	0.425124i	−0.575382	+	0.817885i	$0.695147\pi$
$18$	4.66535	+	1.25008i	1.09963	+	0.294646i
$19$	−4.55223	+	2.02678i	−1.04435	+	0.464976i	−0.855919	−	0.517110i	$-0.827008\pi$
$19$	−4.55223	+	2.02678i	−1.04435	+	0.464976i	−0.188434	+	0.982086i	$0.560341\pi$
$20$	−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	0.129793	−	0.991541i	$-0.458569\pi$
$23$	5.21979	−	3.38977i	1.08840	−	0.706816i	0.958609	+	0.284725i	$0.0919022\pi$
$24$	−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	0.734402	−	0.678714i	$-0.237463\pi$
$29$	−0.743348	−	1.02313i	−0.138036	−	0.189991i	−0.872439	+	0.488724i	$0.837463\pi$
$30$	−1.63959	−	3.52049i	−0.299347	−	0.642751i
$31$	−10.1310	−	1.06481i	−1.81959	−	0.191246i	−0.867574	−	0.497308i	$-0.834322\pi$
$31$	−10.1310	−	1.06481i	−1.81959	−	0.191246i	−0.952012	+	0.306062i	$0.900989\pi$
$32$	−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	−0.827940	−	0.560817i	$-0.810487\pi$
$37$	0.328991	−	6.27752i	0.0540858	−	1.03202i	0.882026	−	0.471202i	$-0.156180\pi$
$38$	−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	−0.137697	−	0.990474i	$-0.543970\pi$
$41$	−5.32280	−	1.72948i	−0.831282	−	0.270100i	−0.693585	+	0.720374i	$0.743970\pi$
$42$	4.35431	−	1.46797i	0.671885	−	0.226513i
$43$	4.80861	−	4.80861i	0.733306	−	0.733306i	−0.237968	−	0.971273i	$-0.576481\pi$
$43$	4.80861	−	4.80861i	0.733306	−	0.733306i	0.971273	+	0.237968i	$0.0764812\pi$
$44$	−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	0.646897	−	0.762577i	$-0.276066\pi$
$47$	0.243253	+	0.196982i	0.0354821	+	0.0287328i	−0.611415	+	0.791310i	$0.709400\pi$
$48$	−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	−0.340341	−	0.940302i	$-0.610543\pi$
$53$	0.261509	−	0.100384i	0.0359210	−	0.0137888i	0.376262	+	0.926513i	$0.377209\pi$
$54$	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	0.251875	−	0.967760i	$-0.418953\pi$
$59$	6.72559	−	1.42957i	0.875597	−	0.186114i	0.623722	+	0.781646i	$0.285620\pi$
$60$	2.33619	−	3.73473i	0.301600	−	0.482151i
$61$	1.10261	−	5.18739i	0.141175	−	0.664178i	−0.849461	−	0.527651i	$-0.823073\pi$
$61$	1.10261	−	5.18739i	0.141175	−	0.664178i	0.990636	−	0.136527i	$-0.0435939\pi$
$62$	−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	−0.999135	−	0.0415894i	$-0.986758\pi$
$67$	−9.54564	+	7.72991i	−1.16619	+	0.944359i	−0.167051	+	0.985948i	$0.553425\pi$
$68$	−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	−0.682228	−	0.731140i	$-0.738989\pi$
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	0.484535	+	0.874772i	$0.338989\pi$
$72$	−1.12985	+	1.39524i	−0.133154	+	0.164431i
$73$	−1.29435	+	0.0678338i	−0.151492	+	0.00793934i	−0.127931	−	0.991783i	$-0.540834\pi$
$73$	−1.29435	+	0.0678338i	−0.151492	+	0.00793934i	−0.0235607	+	0.999722i	$0.507500\pi$
$74$	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	−0.689090	−	0.724676i	$-0.741989\pi$
$79$	−10.7765	+	1.13266i	−1.21245	+	0.127434i	−0.523363	+	0.852110i	$0.675323\pi$
$80$	−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	−0.998860	−	0.0477399i	$-0.984798\pi$
$83$	−0.579789	−	3.66064i	−0.0636401	−	0.401808i	0.935220	−	0.354068i	$-0.115202\pi$
$84$	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	−0.377811	−	0.925883i	$-0.623323\pi$
$89$	−10.3731	−	2.20488i	−1.09955	−	0.233716i	−0.721738	+	0.692166i	$0.756656\pi$
$90$	−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	0.916533	+	0.399958i	$0.130975\pi$
$97$	−0.775456	+	4.89604i	−0.0787356	+	0.497117i	−0.995269	+	0.0971587i	$0.969025\pi$
$98$	−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	0.327767	−	0.944758i	$-0.393704\pi$
$101$	13.1637	−	7.60006i	1.30984	−	0.756234i	0.982069	+	0.188524i	$0.0603704\pi$
$102$	−3.91190	+	0.205014i	−0.387336	+	0.0202994i
$103$	−4.27261	+	5.27623i	−0.420993	+	0.519883i	−0.942880	−	0.333132i	$-0.891895\pi$
$103$	−4.27261	+	5.27623i	−0.420993	+	0.519883i	0.521888	+	0.853014i	$0.325228\pi$
$104$	−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	−0.998572	−	0.0534166i	$-0.982989\pi$
$107$	−18.9985	+	5.09063i	−1.83665	+	0.492130i	−0.838081	+	0.545546i	$0.816322\pi$
$108$	−8.12981	+	6.58339i	−0.782292	+	0.633487i
$109$	3.97502	+	18.7010i	0.380738	+	1.79123i	0.583618	+	0.812029i	$0.301637\pi$
$109$	3.97502	+	18.7010i	0.380738	+	1.79123i	−0.202880	+	0.979204i	$0.565030\pi$
$110$	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	0.998838	−	0.0481952i	$-0.0153470\pi$
$113$	3.96233	+	7.77652i	0.372745	+	0.731553i	−0.626093	+	0.779748i	$0.715347\pi$
$114$	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	−0.466390	−	0.884579i	$-0.654446\pi$
$127$	5.89827	−	11.5760i	0.523386	−	1.02720i	0.989777	−	0.142625i	$-0.0455542\pi$
$128$	−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	0.965487	−	0.260452i	$-0.0838716\pi$
$131$	1.44095	+	3.23643i	0.125896	+	0.282768i	−0.839590	+	0.543220i	$0.817205\pi$
$132$	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	0.786710	−	0.617323i	$-0.211783\pi$
$137$	6.35261	+	4.12544i	0.542740	+	0.352460i	−0.243969	+	0.969783i	$0.578450\pi$
$138$	−0.565729	+	10.7947i	−0.0481580	+	0.918910i
$139$	2.73221	+	8.40888i	0.231743	+	0.713232i	0.997537	+	0.0701455i	$0.0223463\pi$
$139$	2.73221	+	8.40888i	0.231743	+	0.713232i	−0.765794	+	0.643086i	$0.777654\pi$
$140$	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	0.561154	−	0.827711i	$-0.310357\pi$
$149$	1.52475	+	0.880317i	0.124913	+	0.0721183i	−0.436242	+	0.899830i	$0.643691\pi$
$150$	8.66219	+	0.614002i	0.707265	+	0.0501330i
$151$	−3.13479	−	5.42962i	−0.255106	−	0.441856i	0.709819	−	0.704385i	$-0.248777\pi$
$151$	−3.13479	−	5.42962i	−0.255106	−	0.441856i	−0.964924	+	0.262529i	$0.915444\pi$
$152$	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	0.650072	−	0.759872i	$-0.274739\pi$
$157$	10.4389	+	2.79709i	0.833115	+	0.223232i	0.183043	+	0.983105i	$0.441405\pi$
$158$	−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	0.269265	−	0.963066i	$-0.413219\pi$
$163$	5.57143	+	0.291986i	0.436388	+	0.0228701i	0.167122	+	0.985936i	$0.446552\pi$
$164$	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	0.257706	−	0.966223i	$-0.417033\pi$
$167$	10.3561	−	1.64024i	0.801379	−	0.126926i	0.543673	+	0.839297i	$0.317033\pi$
$168$	−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	0.431191	−	0.902260i	$-0.358093\pi$
$173$	−7.47674	−	11.5132i	−0.568446	−	0.875330i	−0.999637	+	0.0269305i	$0.991427\pi$
$174$	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	−0.936358	−	0.351047i	$-0.885826\pi$
$179$	−0.654680	+	1.47044i	−0.0489331	+	0.109906i	0.887425	+	0.460953i	$0.152492\pi$
$180$	−12.0245	−	2.34327i	−0.896255	−	0.174657i
$181$	2.04450	−	2.81402i	0.151967	−	0.209164i	−0.726245	−	0.687436i	$-0.758736\pi$
$181$	2.04450	−	2.81402i	0.151967	−	0.209164i	0.878212	+	0.478271i	$0.158736\pi$
$182$	−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	0.667089	−	0.744978i	$-0.267540\pi$
$191$	−1.98374	−	2.20317i	−0.143538	−	0.159415i	−0.810627	+	0.585563i	$0.800874\pi$
$192$	−5.56517	−	6.87242i	−0.401632	−	0.495974i
$193$	−16.4661	−	4.41207i	−1.18525	−	0.317588i	−0.388246	−	0.921556i	$-0.626919\pi$
$193$	−16.4661	−	4.41207i	−1.18525	−	0.317588i	−0.797009	+	0.603968i	$0.793586\pi$
$194$	−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	0.794320	−	0.607499i	$-0.207827\pi$
$197$	19.1171	+	3.02785i	1.36204	+	0.215725i	0.567716	+	0.823225i	$0.307827\pi$
$198$	−4.25441	+	2.76285i	−0.302348	+	0.196347i
$199$	0.0959424	+	0.166177i	0.00680118	+	0.0117800i	0.869406	−	0.494098i	$-0.164502\pi$
$199$	0.0959424	+	0.166177i	0.00680118	+	0.0117800i	−0.862605	+	0.505878i	$0.831168\pi$
$200$	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	0.995650	−	0.0931759i	$-0.0297019\pi$
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	−0.860265	+	0.509847i	$0.829702\pi$
$212$	−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	−0.594592	−	0.804027i	$-0.702687\pi$
$223$	6.05349	−	11.8807i	0.405372	−	0.795587i	0.999964	+	0.00843996i	$0.00268655\pi$
$224$	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	0.994025	+	0.109155i	$0.0348145\pi$
$227$	0.253949	+	4.84563i	0.0168552	+	0.321616i	−0.977170	+	0.212461i	$0.931852\pi$
$228$	9.16491	−	3.51808i	0.606961	−	0.232991i
$229$	−0.698945	−	6.65002i	−0.0461876	−	0.439446i	−0.993040	−	0.117777i	$-0.962423\pi$
$229$	−0.698945	−	6.65002i	−0.0461876	−	0.439446i	0.946852	−	0.321668i	$-0.104244\pi$
$230$	−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	−0.996819	−	0.0796953i	$-0.974605\pi$
$233$	−3.09426	+	8.06082i	−0.202712	+	0.528082i	0.794108	+	0.607777i	$0.207939\pi$
$234$	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	−0.832457	−	0.554090i	$-0.813066\pi$
$239$	−18.2461	+	5.92852i	−1.18024	+	0.383484i	−0.347785	+	0.937574i	$0.613066\pi$
$240$	−3.23663	−	4.80343i	−0.208924	−	0.310060i
$241$	−5.39578	−	25.3851i	−0.347572	−	1.63520i	−0.710725	−	0.703470i	$-0.751633\pi$
$241$	−5.39578	−	25.3851i	−0.347572	−	1.63520i	0.363152	−	0.931730i	$-0.381700\pi$
$242$	−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	$0.161705\pi$
$251$			15.4133i			0.972880i	−0.873714	+	0.486440i	$0.838295\pi$
$252$	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	0.538115	+	0.842871i	$0.319137\pi$
$257$	7.91188	+	29.5275i	0.493529	+	1.84188i	−0.0445856	+	0.999006i	$0.514197\pi$
$258$	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	−0.831758	−	0.555138i	$-0.812665\pi$
$263$	0.222055	−	0.341935i	0.0136925	−	0.0210846i	0.845451	+	0.534054i	$0.179332\pi$
$264$	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	−0.746335	−	0.665570i	$-0.768188\pi$
$269$	2.00211	−	19.0488i	0.122071	−	1.16142i	0.868406	−	0.495854i	$-0.165145\pi$
$270$	−18.9786	−	8.06661i	−1.15500	−	0.490918i
$271$	−19.2007	+	2.01808i	−1.16636	+	0.122589i	−0.667851	−	0.744295i	$-0.732786\pi$
$271$	−19.2007	+	2.01808i	−1.16636	+	0.122589i	−0.498509	+	0.866884i	$0.666119\pi$
$272$	−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	0.178497	−	0.983940i	$-0.442876\pi$
$277$	7.63707	−	0.400242i	0.458867	−	0.0240482i	0.280369	+	0.959892i	$0.409543\pi$
$278$	−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	0.939329	−	0.343019i	$-0.111449\pi$
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	−0.0359618	+	0.999353i	$0.511449\pi$
$282$	−0.525104	+	0.140701i	−0.0312695	+	0.00837864i
$283$	2.21463	−	1.79337i	0.131646	−	0.106605i	−0.561236	−	0.827656i	$-0.689674\pi$
$283$	2.21463	−	1.79337i	0.131646	−	0.106605i	0.692882	+	0.721051i	$0.256341\pi$
$284$	−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	0.689814	−	0.723987i	$-0.257692\pi$
$293$	−0.584948	−	0.584948i	−0.0341730	−	0.0341730i	−0.723987	+	0.689814i	$0.757692\pi$
$294$	−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	−0.345007	−	0.938600i	$-0.612123\pi$
$307$	10.4006	−	10.4006i	0.593593	−	0.593593i	0.938600	+	0.345007i	$0.112123\pi$
$308$	−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	0.880377	−	0.474275i	$-0.157290\pi$
$311$	8.83036	+	7.95089i	0.500724	+	0.450854i	−0.379653	+	0.925129i	$0.623957\pi$
$312$	−2.48073	−	1.61100i	−0.140443	−	0.0912050i
$313$	0.527196	−	10.0595i	0.0297989	−	0.568597i	−0.942407	−	0.334469i	$-0.891443\pi$
$313$	0.527196	−	10.0595i	0.0297989	−	0.568597i	0.972206	−	0.234128i	$-0.0752235\pi$
$314$	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	−0.191981	−	0.981399i	$-0.561491\pi$
$317$	−17.6502	−	6.77528i	−0.991335	−	0.380538i	−0.799354	+	0.600861i	$0.794825\pi$
$318$	−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	0.570302	−	0.821435i	$-0.306826\pi$
$331$	28.4245	−	12.6554i	1.56235	−	0.695605i	0.992052	+	0.125830i	$0.0401594\pi$
$332$	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	−0.700696	+	0.713460i	$0.747127\pi$
$337$	−31.0198	+	15.8054i	−1.68976	+	0.860974i	−0.989060	+	0.147514i	$0.952873\pi$
$338$	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	−0.904008	−	0.427515i	$-0.859389\pi$
$347$	−9.65416	−	25.1500i	−0.518263	−	1.35012i	0.385746	−	0.922605i	$-0.373944\pi$
$348$	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	0.998710	−	0.0507745i	$-0.0161690\pi$
$353$	4.18132	+	10.8927i	0.222549	+	0.579760i	−0.776161	+	0.630535i	$0.782836\pi$
$354$	−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	−0.577192	−	0.816608i	$-0.695852\pi$
$359$	3.30837	−	2.97887i	0.174609	−	0.157219i	0.751802	+	0.659389i	$0.229185\pi$
$360$	−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	−0.998545	−	0.0539306i	$-0.982825\pi$
$367$	−16.1627	−	19.9593i	−0.843688	−	1.04187i	0.154857	−	0.987937i	$-0.450508\pi$
$368$	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	−0.573544	+	0.819175i	$0.694432\pi$
$373$	−30.0355	+	19.5053i	−1.55518	+	1.00994i	−0.981635	+	0.190770i	$0.938902\pi$
$374$	−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	0.314567	−	0.949235i	$-0.398141\pi$
$379$	−13.3436	−	18.3659i	−0.685416	−	0.943394i	−0.999983	+	0.00584095i	$0.998141\pi$
$380$	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	0.816770	−	0.576964i	$-0.195763\pi$
$383$	20.3079	+	7.79546i	1.03768	+	0.398330i	0.220914	+	0.975293i	$0.429096\pi$
$384$	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	0.876641	−	0.481145i	$-0.159779\pi$
$389$	9.65968	+	8.69762i	0.489765	+	0.440987i	−0.386876	+	0.922132i	$0.626446\pi$
$390$	−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	0.531592	−	0.847001i	$-0.321594\pi$
$397$	−3.71351	−	3.00714i	−0.186376	−	0.150924i	−0.717968	+	0.696077i	$0.754927\pi$
$398$	−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	−0.612171	−	0.790725i	$-0.709704\pi$
$401$	7.58351	−	13.1350i	0.378702	−	0.655932i	0.990874	+	0.134793i	$0.0430370\pi$
$402$	−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	0.0474592	−	0.998873i	$-0.484888\pi$
$409$	10.0531	−	2.13685i	0.497094	−	0.105661i	0.449634	+	0.893213i	$0.351554\pi$
$410$	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	0.882414	−	0.470473i	$-0.155917\pi$
$419$	14.4852	+	10.5241i	0.707648	+	0.514137i	−0.174766	+	0.984610i	$0.555917\pi$
$420$	−10.7599	+	4.47962i	−0.525027	+	0.218583i
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	−0.205227	−	0.978714i	$-0.565793\pi$
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	0.867394	+	0.497621i	$0.165793\pi$
$422$	−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	−0.948650	−	0.316326i	$-0.897551\pi$
$431$	0.935006	−	8.89599i	0.0450377	−	0.428505i	0.993688	−	0.112178i	$-0.0357828\pi$
$432$	3.55996	+	13.2859i	0.171278	+	0.639220i
$433$	2.75652	+	17.4040i	0.132470	+	0.836382i	0.961022	+	0.276471i	$0.0891649\pi$
$433$	2.75652	+	17.4040i	0.132470	+	0.836382i	−0.828552	+	0.559912i	$0.810835\pi$
$434$	−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	−0.482363	−	0.875972i	$-0.660221\pi$
$439$	−26.8046	−	5.69749i	−1.27931	−	0.271926i	−0.796950	+	0.604045i	$0.793555\pi$
$440$	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	0.999989	+	0.00464732i	$0.00147929\pi$
$443$	2.86872	+	10.7062i	0.136297	+	0.508667i	−0.863692	+	0.504019i	$0.831854\pi$
$444$	−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	$0.395489\pi$
$449$			40.1154i			1.89316i	−0.322465	+	0.946581i	$0.604511\pi$
$450$	−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	0.610620	−	0.791924i	$-0.290920\pi$
$457$	32.8230	−	8.79489i	1.53539	−	0.411408i	0.924774	+	0.380516i	$0.124254\pi$
$458$	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	−0.909060	−	0.416666i	$-0.863198\pi$
$461$	−30.0506	+	9.76402i	−1.39959	+	0.454756i	−0.490535	+	0.871422i	$0.663198\pi$
$462$	−1.91435	+	4.43027i	−0.0890634	+	0.206115i
$463$	−8.64582	−	16.9684i	−0.401805	−	0.788587i	0.598113	−	0.801412i	$-0.295918\pi$
$463$	−8.64582	−	16.9684i	−0.401805	−	0.788587i	−0.999918	+	0.0128250i	$0.995918\pi$
$464$	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	−0.974072	−	0.226236i	$-0.927358\pi$
$467$	−2.13538	+	5.56287i	−0.0988138	+	0.257419i	0.875259	+	0.483655i	$0.160691\pi$
$468$	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	0.792794	−	0.609490i	$-0.208626\pi$
$479$	19.0483	+	8.48083i	0.870338	+	0.387499i	0.0775436	+	0.996989i	$0.475292\pi$
$480$	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	0.964474	−	0.264176i	$-0.0851001\pi$
$487$	24.6153	+	15.9853i	1.11542	+	0.724365i	0.150950	+	0.988541i	$0.451767\pi$
$488$	−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	0.743476	+	0.668762i	$0.233176\pi$
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	−0.994574	+	0.104036i	$0.966824\pi$
$492$	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	0.393339	−	0.919394i	$-0.371320\pi$
$499$	−4.60639	−	2.65950i	−0.206210	−	0.119056i	−0.599549	+	0.800338i	$0.704653\pi$
$500$	−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	0.707801	−	0.706412i	$-0.249687\pi$
$503$	26.0759	+	4.13001i	1.16267	+	0.184148i	0.454865	+	0.890560i	$0.349687\pi$
$504$	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	0.805855	−	0.592113i	$-0.201706\pi$
$509$	2.99499	+	3.32627i	0.132750	+	0.147434i	−0.673104	+	0.739548i	$0.735040\pi$
$510$	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	0.525987	+	0.850492i	$0.323696\pi$
$521$	−10.4542	+	23.4805i	−0.458006	+	1.02870i	−0.983993	+	0.178206i	$0.942971\pi$
$522$	−2.18899	−	5.70250i	−0.0958093	−	0.249592i
$523$	−11.9816	−	18.4501i	−0.523920	−	0.806766i	0.473330	−	0.880885i	$-0.343052\pi$
$523$	−11.9816	−	18.4501i	−0.523920	−	0.806766i	−0.997249	+	0.0741198i	$0.976385\pi$
$524$	−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	0.848343	−	0.529447i	$-0.177601\pi$
$541$	5.42224	+	6.02201i	0.233120	+	0.258906i	−0.615223	+	0.788353i	$0.710934\pi$
$542$	−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	0.550444	−	0.834872i	$-0.314458\pi$
$547$	19.0836	+	3.02255i	0.815958	+	0.129235i	0.265514	+	0.964107i	$0.414458\pi$
$548$	−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	−0.785336	−	0.619069i	$-0.787510\pi$
$557$	4.82211	−	17.9964i	0.204320	−	0.762531i	0.989656	−	0.143462i	$-0.0458234\pi$
$558$	−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	0.866926	−	0.498436i	$-0.166092\pi$
$563$	18.1325	+	11.7754i	0.764193	+	0.496273i	−0.102734	+	0.994709i	$0.532759\pi$
$564$	−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	−0.835898	−	0.548885i	$-0.815053\pi$
$569$	−16.3273	−	36.6716i	−0.684474	−	1.53735i	0.151424	−	0.988469i	$-0.451614\pi$
$570$	14.5991	+	12.7030i	0.611488	+	0.532070i
$571$	30.4188	+	13.5433i	1.27299	+	0.566770i	0.928260	−	0.371932i	$-0.121305\pi$
$571$	30.4188	+	13.5433i	1.27299	+	0.566770i	0.344727	+	0.938703i	$0.387971\pi$
$572$	−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	−0.997739	−	0.0672061i	$-0.978592\pi$
$577$	−0.300036	−	5.72503i	−0.0124907	−	0.238336i	0.985248	−	0.171130i	$-0.0547418\pi$
$578$	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	0.749785	−	0.661682i	$-0.230157\pi$
$587$	−5.48135	−	10.7577i	−0.226239	−	0.444020i	−0.976024	+	0.217662i	$0.930157\pi$
$588$	−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	0.743802	−	0.668401i	$-0.233021\pi$
$593$	41.9372	−	11.2370i	1.72215	−	0.461449i	0.978351	+	0.206951i	$0.0663541\pi$
$594$	−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	−0.486092	−	0.873908i	$-0.661578\pi$
$599$	0.677665	−	0.391250i	0.0276887	−	0.0159860i	0.513780	+	0.857922i	$0.328245\pi$
$600$	−1.51813	+	2.84864i	−0.0619774	+	0.116295i
$601$			7.23002i			0.294919i	0.989068	+	0.147459i	$0.0471095\pi$
$601$			7.23002i			0.294919i	−0.989068	+	0.147459i	$0.952890\pi$
$602$	−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	0.955970	−	0.293464i	$-0.0948080\pi$
$607$	−0.459640	−	1.71540i	−0.0186562	−	0.0696260i	−0.974626	+	0.223838i	$0.928141\pi$
$608$	−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	−0.826414	−	0.563063i	$-0.809623\pi$
$613$	0.596749	−	0.918913i	0.0241025	−	0.0371145i	0.850516	+	0.525948i	$0.176290\pi$
$614$	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	0.853494	+	0.521103i	$0.174479\pi$
$617$	5.03752	+	31.8056i	0.202803	+	1.28045i	−0.650691	+	0.759343i	$0.725521\pi$
$618$	−3.05185	−	11.3897i	−0.122764	−	0.458160i
$619$	−1.93430	+	18.4036i	−0.0777461	+	0.739705i	0.884319	+	0.466884i	$0.154623\pi$
$619$	−1.93430	+	18.4036i	−0.0777461	+	0.739705i	−0.962065	+	0.272821i	$0.912043\pi$
$620$	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	0.916425	−	0.400206i	$-0.131061\pi$
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	−0.0974273	+	0.995243i	$0.531061\pi$
$632$	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	−0.862840	−	0.505478i	$-0.831316\pi$
$641$	−36.5968	+	7.77889i	−1.44549	+	0.307248i	−0.582647	+	0.812725i	$0.697983\pi$
$642$	12.2419	−	31.8914i	0.483151	−	1.25865i
$643$	−14.7951	−	14.7951i	−0.583460	−	0.583460i	0.352392	−	0.935852i	$-0.385368\pi$
$643$	−14.7951	−	14.7951i	−0.583460	−	0.583460i	−0.935852	+	0.352392i	$0.885368\pi$
$644$	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	−0.783006	−	0.622014i	$-0.786315\pi$
$647$	−24.1309	+	9.26299i	−0.948684	+	0.364166i	−0.165678	+	0.986180i	$0.552981\pi$
$648$	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	0.939503	−	0.342542i	$-0.111288\pi$
$653$	20.4375	+	16.5499i	0.799780	+	0.647649i	−0.139723	+	0.990191i	$0.544621\pi$
$654$	−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	0.195906	−	0.980623i	$-0.437235\pi$
$659$	−5.69893	−	1.85169i	−0.221999	−	0.0721317i	−0.417904	+	0.908491i	$0.637235\pi$
$660$	1.27319	+	4.44812i	0.0495588	+	0.173143i
$661$	−34.1915	−	30.7862i	−1.32990	−	1.19744i	−0.963725	−	0.266897i	$-0.914002\pi$
$661$	−34.1915	−	30.7862i	−1.32990	−	1.19744i	−0.366171	−	0.930547i	$-0.619332\pi$
$662$	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	0.127030	−	0.991899i	$-0.459456\pi$
$673$	−15.5853	−	7.94108i	−0.600767	−	0.306106i	−0.727797	+	0.685793i	$0.759456\pi$
$674$	−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	0.159008	−	0.987277i	$-0.449170\pi$
$677$	29.2874	−	19.0194i	1.12560	−	0.730976i	0.966597	+	0.256301i	$0.0825038\pi$
$678$	−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	0.977709	+	0.209965i	$0.0673349\pi$
$683$	25.6066	+	31.6215i	0.979808	+	1.20996i	0.00209925	+	0.999998i	$0.499332\pi$
$684$	−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	−0.378106	−	0.925762i	$-0.623425\pi$
$691$	13.2239	−	11.9069i	0.503062	−	0.452959i	0.881168	+	0.472803i	$0.156758\pi$
$692$	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	−0.658233	−	0.752814i	$-0.728696\pi$
$709$	0.576558	−	0.519135i	0.0216531	−	0.0194965i	0.679886	+	0.733318i	$0.262029\pi$
$710$	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	−0.923506	−	0.383583i	$-0.874690\pi$
$719$	−33.6892	+	14.9994i	−1.25639	+	0.559383i	−0.332888	+	0.942966i	$0.608023\pi$
$720$	−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	0.0928967	−	0.995676i	$-0.470387\pi$
$727$	−17.7421	−	9.04006i	−0.658019	−	0.335277i	−0.750915	+	0.660398i	$0.770387\pi$
$728$	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	0.357677	−	0.933845i	$-0.383569\pi$
$733$	−0.0374092	−	0.0143601i	−0.00138174	−	0.000530401i	−0.359059	+	0.933315i	$0.616902\pi$
$734$	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	0.361384	−	0.932417i	$-0.382304\pi$
$739$	−14.3575	−	12.9276i	−0.528151	−	0.475549i	−0.889534	+	0.456868i	$0.848971\pi$
$740$	−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	−0.328831	−	0.944389i	$-0.606655\pi$
$743$	16.7789	−	16.7789i	0.615557	−	0.615557i	0.944389	+	0.328831i	$0.106655\pi$
$744$	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	−0.961306	−	0.275482i	$-0.911163\pi$
$751$	−6.63402	+	11.4905i	−0.242079	+	0.419293i	0.719227	+	0.694775i	$0.244496\pi$
$752$	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	0.727448	−	0.686163i	$-0.240706\pi$
$757$	1.13591	+	1.13591i	0.0412853	+	0.0412853i	−0.686163	+	0.727448i	$0.740706\pi$
$758$	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	−0.680020	−	0.733194i	$-0.738029\pi$
$761$	6.60486	−	31.0734i	0.239426	−	1.12641i	0.919446	−	0.393217i	$-0.128638\pi$
$762$	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
$767$	24.4829	−	19.8259i	0.884026	−	0.715870i
$768$	−6.83311	+	1.83093i	−0.246569	+	0.0660679i
$769$	11.1412	+	8.09458i	0.401763	+	0.291898i	0.770259	−	0.637731i	$-0.220127\pi$
$769$	11.1412	+	8.09458i	0.401763	+	0.291898i	−0.368495	+	0.929630i	$0.620127\pi$
$770$	−12.4501	+	3.71230i	−0.448670	+	0.133782i
$771$	−20.5429	+	14.9253i	−0.739834	+	0.537521i
$772$	25.4437	−	31.4204i	0.915739	−	1.13084i
$773$	10.0294	−	0.525618i	0.360732	−	0.0189052i	0.128891	−	0.991659i	$-0.458858\pi$
$773$	10.0294	−	0.525618i	0.360732	−	0.0189052i	0.231841	+	0.972754i	$0.425525\pi$
$774$	28.4449	−	16.4227i	1.02243	−	0.590302i
$775$	22.2845	+	45.8005i	0.800483	+	1.64520i
$776$		−	3.85263i		−	0.138301i
$777$	−13.1851	−	4.12425i	−0.473013	−	0.147957i
$778$	−4.25155	+	26.8433i	−0.152426	+	0.962377i
$779$	27.7359	−	2.91516i	0.993743	−	0.104447i
$780$	1.76869	−	20.1061i	0.0633294	−	0.719913i
$781$	0.226050	−	2.15072i	0.00808871	−	0.0769590i
$782$	7.59663	+	28.3510i	0.271655	+	1.01383i
$783$	−0.872614	−	5.50947i	−0.0311847	−	0.196892i
$784$	−10.4957	+	19.1399i	−0.374847	+	0.683570i
$785$	−16.7950	+	17.3752i	−0.599441	+	0.620148i
$786$	−6.01847	−	1.27927i	−0.214672	−	0.0456299i
$787$	11.7250	−	18.0549i	0.417950	−	0.643586i	−0.565504	−	0.824746i	$-0.691318\pi$
$787$	11.7250	−	18.0549i	0.417950	−	0.643586i	0.983454	+	0.181159i	$0.0579850\pi$
$788$	−25.0019	+	38.4995i	−0.890655	+	1.37149i
$789$	0.331266	+	0.0704127i	0.0117934	+	0.00250676i
$790$	49.8956	−	8.77348i	1.77521	−	0.312146i
$791$	3.36111	−	22.8456i	0.119507	−	0.812297i
$792$	−0.294977	−	1.86241i	−0.0104815	−	0.0661779i
$793$	−6.28891	−	23.4705i	−0.223326	−	0.833463i
$794$	1.04434	−	9.93624i	0.0370623	−	0.352624i
$795$	−0.507004	+	0.116797i	−0.0179816	+	0.00414237i
$796$	−0.452602	+	0.0475704i	−0.0160421	+	0.00168609i
$797$	0.825084	−	5.20937i	0.0292260	−	0.184526i	−0.968757	−	0.248013i	$-0.920222\pi$
$797$	0.825084	−	5.20937i	0.0292260	−	0.184526i	0.997983	+	0.0634877i	$0.0202224\pi$
$798$	−16.8466	+	15.5078i	−0.596362	+	0.548970i
$799$			0.705981i			0.0249758i
$800$	38.6199	−	11.7671i	1.36542	−	0.416031i
$801$	−21.2154	+	12.2487i	−0.749608	+	0.432786i
$802$	31.6687	−	1.65969i	1.11826	−	0.0586056i
$803$	0.856694	−	1.05793i	0.0302321	−	0.0373335i
$804$	19.5768	−	14.2234i	0.690422	−	0.501621i
$805$	19.1823	−	31.4297i	0.676088	−	1.10775i
$806$	−78.9508	−	57.3611i	−2.78092	−	2.02046i
$807$	15.3680	−	4.11784i	0.540979	−	0.144955i
$808$	−9.18084	+	7.43450i	−0.322981	+	0.261545i
$809$	−1.72341	−	8.10801i	−0.0605919	−	0.285063i	0.937411	−	0.348224i	$-0.113215\pi$
$809$	−1.72341	−	8.10801i	−0.0605919	−	0.285063i	−0.998003	+	0.0631613i	$0.979882\pi$
$810$	−0.540193	+	15.2610i	−0.0189805	+	0.536216i
$811$	22.9445	−	7.45511i	0.805689	−	0.261784i	0.122918	−	0.992417i	$-0.460775\pi$
$811$	22.9445	−	7.45511i	0.805689	−	0.261784i	0.682771	+	0.730632i	$0.260775\pi$
$812$	−7.28469	−	3.14776i	−0.255643	−	0.110465i
$813$	−7.28065	−	14.2891i	−0.255343	−	0.501140i
$814$	−2.87010	+	13.5028i	−0.100597	+	0.473271i
$815$	−6.61587	+	10.5764i	−0.231744	+	0.370475i
$816$	−5.71472	+	1.21470i	−0.200055	+	0.0425230i
$817$	−12.1439	+	31.6359i	−0.424861	+	1.10680i
$818$	15.1952	+	15.1952i	0.531288	+	0.531288i
$819$	−23.3157	+	15.5088i	−0.814715	+	0.541921i
$820$	9.64990	+	28.0687i	0.336989	+	0.980202i
$821$	−1.17488	−	11.1783i	−0.0410037	−	0.390124i	−0.995707	−	0.0925640i	$-0.970494\pi$
$821$	−1.17488	−	11.1783i	−0.0410037	−	0.390124i	0.954703	−	0.297560i	$-0.0961729\pi$
$822$	−12.2817	+	4.71451i	−0.428374	+	0.164437i
$823$	0.898326	+	17.1411i	0.0313137	+	0.597501i	0.968552	+	0.248811i	$0.0800399\pi$
$823$	0.898326	+	17.1411i	0.0313137	+	0.597501i	−0.937238	+	0.348689i	$0.886627\pi$
$824$	2.63830	−	4.56967i	0.0919096	−	0.159192i
$825$	0.828259	+	4.28277i	0.0288363	+	0.149107i
$826$	−6.36329	−	37.5005i	−0.221407	−	1.30481i
$827$	10.5674	−	20.7397i	0.367465	−	0.721190i	−0.631046	−	0.775745i	$-0.717374\pi$
$827$	10.5674	−	20.7397i	0.367465	−	0.721190i	0.998511	+	0.0545555i	$0.0173742\pi$
$828$	26.4997	+	21.4590i	0.920928	+	0.745753i
$829$	−23.1374	−	10.3014i	−0.803596	−	0.357784i	−0.0365142	−	0.999333i	$-0.511625\pi$
$829$	−23.1374	−	10.3014i	−0.803596	−	0.357784i	−0.767082	+	0.641549i	$0.778292\pi$
$830$	3.88992	+	16.8857i	0.135021	+	0.586112i
$831$	2.58378	+	5.80327i	0.0896304	+	0.201313i
$832$	−34.4910	+	34.4910i	−1.19576	+	1.19576i
$833$	−8.30543	+	13.4272i	−0.287766	+	0.465226i
$834$	−14.6044	−	4.74526i	−0.505710	−	0.164315i
$835$	−8.02934	+	22.0278i	−0.277867	+	0.762304i
$836$	9.22439	+	8.30568i	0.319032	+	0.287258i
$837$	−37.6831	−	24.4717i	−1.30252	−	0.845865i
$838$	−1.95926	+	37.3850i	−0.0676816	+	1.29144i
$839$	17.1783	+	52.8695i	0.593062	+	1.82526i	0.564144	+	0.825677i	$0.309206\pi$
$839$	17.1783	+	52.8695i	0.593062	+	1.82526i	0.0289189	+	0.999582i	$0.490794\pi$
$840$	−3.15150	−	2.15762i	−0.108737	−	0.0744448i
$841$	8.46726	−	26.0596i	0.291975	−	0.898605i
$842$	32.7815	+	12.5836i	1.12973	+	0.433661i
$843$	−4.02417	+	15.0184i	−0.138600	+	0.517261i
$844$	−15.0108	−	1.57770i	−0.516694	−	0.0543068i
$845$	7.54542	+	16.2013i	0.259570	+	0.557342i
$846$	0.888617	+	1.22308i	0.0305513	+	0.0420502i
$847$	12.8420	−	22.8193i	0.441257	−	0.784082i
$848$	0.778302	+	0.396565i	0.0267270	+	0.0136181i
$849$	2.04998	+	1.18355i	0.0703550	+	0.0406195i
$850$	22.8844	−	5.68261i	0.784930	−	0.194912i
$851$	−19.5621	−	33.8826i	−0.670581	−	1.16148i
$852$	3.40201	−	2.20929i	0.116551	−	0.0756892i
$853$	−41.8419	−	6.62710i	−1.43264	−	0.226908i	−0.608616	−	0.793465i	$-0.708275\pi$
$853$	−41.8419	−	6.62710i	−1.43264	−	0.226908i	−0.824023	+	0.566557i	$0.808275\pi$
$854$	−28.4195	−	7.28074i	−0.972494	−	0.249142i
$855$	−15.4804	−	20.5635i	−0.529419	−	0.703258i
$856$	13.9649	−	6.21758i	0.477311	−	0.212513i
$857$	−36.7601	−	9.84983i	−1.25570	−	0.336464i	−0.431164	−	0.902274i	$-0.641897\pi$
$857$	−36.7601	−	9.84983i	−1.25570	−	0.336464i	−0.824536	+	0.565810i	$0.808564\pi$
$858$	−5.25969	−	6.49517i	−0.179563	−	0.221742i
$859$	34.3314	+	38.1289i	1.17137	+	1.30094i	0.945064	+	0.326884i	$0.105999\pi$
$859$	34.3314	+	38.1289i	1.17137	+	1.30094i	0.226307	+	0.974056i	$0.427335\pi$
$860$	−35.7112	−	5.03621i	−1.21774	−	0.171733i
$861$	−6.58511	+	10.3887i	−0.224420	+	0.354046i
$862$	16.6643	−	8.49088i	0.567588	−	0.289200i
$863$	21.8237	+	1.14373i	0.742887	+	0.0389331i	0.420025	−	0.907513i	$-0.362021\pi$
$863$	21.8237	+	1.14373i	0.742887	+	0.0389331i	0.322863	+	0.946446i	$0.395355\pi$
$864$	−23.8312	+	26.4672i	−0.810754	+	0.900433i
$865$	30.6227	−	2.12671i	1.04120	−	0.0723103i
$866$	−27.3797	+	24.6528i	−0.930399	+	0.837735i
$867$	9.77363	−	1.54799i	0.331930	−	0.0525725i
$868$	−58.1060	+	26.6404i	−1.97224	+	0.904236i
$869$	6.68946	−	9.20725i	0.226924	−	0.312334i
$870$	−2.38313	+	4.29447i	−0.0807958	+	0.145596i
$871$	−22.8902	+	51.4123i	−0.775606	+	1.74204i
$872$	−5.32504	−	13.8722i	−0.180329	−	0.469772i
$873$	6.23660	+	9.60352i	0.211077	+	0.325030i
$874$	−64.8458			−2.19344
$875$	−24.9614	−	15.8723i	−0.843848	−	0.536582i
$876$	2.55345			0.0862732
$877$	0.771263	+	1.18764i	0.0260437	+	0.0401038i	0.851453	−	0.524431i	$-0.175722\pi$
$877$	0.771263	+	1.18764i	0.0260437	+	0.0401038i	−0.825409	+	0.564535i	$0.809055\pi$
$878$	−20.5333	−	53.4912i	−0.692967	−	1.80524i
$879$	0.279490	−	0.627744i	0.00942695	−	0.0211733i
$880$	3.55361	−	6.40369i	0.119792	−	0.215868i
$881$	−5.05676	+	6.96003i	−0.170367	+	0.234489i	−0.885659	−	0.464335i	$-0.846293\pi$
$881$	−5.05676	+	6.96003i	−0.170367	+	0.234489i	0.715293	+	0.698825i	$0.246293\pi$
$882$	2.51208	+	33.7160i	0.0845860	+	1.13528i
$883$	40.2254	−	6.37108i	1.35369	−	0.214404i	0.562919	−	0.826512i	$-0.309678\pi$
$883$	40.2254	−	6.37108i	1.35369	−	0.214404i	0.790774	+	0.612108i	$0.209678\pi$
$884$	−18.2141	+	16.4000i	−0.612605	+	0.551592i
$885$	−12.7405	+	0.884812i	−0.428267	+	0.0297426i
$886$	−15.5070	+	17.2223i	−0.520968	+	0.578594i
$887$	24.7751	+	1.29841i	0.831866	+	0.0435963i	0.463514	−	0.886090i	$-0.346589\pi$
$887$	24.7751	+	1.29841i	0.831866	+	0.0435963i	0.368353	+	0.929686i	$0.379922\pi$
$888$	−3.61591	+	1.84240i	−0.121342	+	0.0618269i
$889$	−30.4536	+	15.9414i	−1.02138	+	0.534659i
$890$	49.0953	+	6.92371i	1.64568	+	0.232083i
$891$	2.29542	+	2.54932i	0.0768994	+	0.0854055i
$892$	19.9018	+	24.5767i	0.666363	+	0.822890i
$893$	−1.50658	−	0.403688i	−0.0504159	−	0.0135089i
$894$	−2.79348	+	1.24374i	−0.0934279	+	0.0415968i
$895$	−2.16466	−	2.87545i	−0.0723566	−	0.0961156i
$896$	4.35568	+	15.5683i	0.145513	+	0.520100i
$897$	23.3957	+	3.70552i	0.781160	+	0.123724i
$898$	−70.3442	+	45.6821i	−2.34742	+	1.52443i
$899$	6.44144	+	11.1569i	0.214834	+	0.372103i
$900$	17.6281	−	20.9678i	0.587604	−	0.698928i
$901$	0.547146	+	0.315895i	0.0182281	+	0.0105240i
$902$	10.9509	+	5.57975i	0.364624	+	0.185785i
$903$	−7.61461	−	12.8600i	−0.253398	−	0.427953i
$904$	−3.98709	−	5.48776i	−0.132609	−	0.182520i
$905$	3.28367	+	7.05060i	0.109153	+	0.234370i
$906$	10.8293	+	1.13820i	0.359778	+	0.0378142i
$907$	−8.07670	+	30.1426i	−0.268182	+	1.00087i	0.692091	+	0.721810i	$0.256690\pi$
$907$	−8.07670	+	30.1426i	−0.268182	+	1.00087i	−0.960274	+	0.279060i	$0.909977\pi$
$908$	−10.7439	−	4.12418i	−0.356547	−	0.136866i
$909$	10.8504	−	33.3940i	0.359883	−	1.10761i
$910$	56.5085	+	4.34485i	1.87324	+	0.144030i
$911$	−11.4702	−	35.3017i	−0.380025	−	1.16960i	−0.940025	−	0.341105i	$-0.889199\pi$
$911$	−11.4702	−	35.3017i	−0.380025	−	1.16960i	0.560000	−	0.828492i	$-0.310801\pi$
$912$	0.675534	−	12.8900i	0.0223692	−	0.426829i
$913$	3.26465	+	2.12009i	0.108044	+	0.0701647i
$914$	52.8000	+	47.5413i	1.74647	+	1.57253i
$915$	−3.37341	+	9.25467i	−0.111521	+	0.305950i
$916$	15.0826	+	4.90064i	0.498344	+	0.161922i
$917$	1.84777	−	9.18920i	0.0610188	−	0.303454i
$918$	−14.7084	+	14.7084i	−0.485448	+	0.485448i
$919$	17.2862	+	38.8255i	0.570220	+	1.28074i	0.936643	+	0.350287i	$0.113916\pi$
$919$	17.2862	+	38.8255i	0.570220	+	1.28074i	−0.366422	+	0.930449i	$0.619417\pi$
$920$	−2.42813	−	10.5403i	−0.0800531	−	0.347502i
$921$	11.1615	+	4.96943i	0.367785	+	0.163748i
$922$	−51.3422	−	41.5761i	−1.69087	−	1.36924i
$923$	−4.28295	+	8.40577i	−0.140975	+	0.276679i
$924$	−5.39729	+	0.915841i	−0.177558	+	0.0301290i
$925$	−27.5044	+	15.2117i	−0.904339	+	0.500159i
$926$	19.9093	−	34.4838i	0.654259	−	1.13321i
$927$	0.820797	+	15.6617i	0.0269585	+	0.514399i
$928$	9.53332	−	3.65950i	0.312947	−	0.120129i
$929$	1.58633	+	15.0929i	0.0520459	+	0.495183i	0.989232	+	0.146354i	$0.0467539\pi$
$929$	1.58633	+	15.0929i	0.0520459	+	0.495183i	−0.937186	+	0.348829i	$0.886579\pi$
$930$	12.8621	+	37.4120i	0.421765	+	1.22679i
$931$	−23.9050	−	25.4019i	−0.783453	−	0.832513i
$932$	−14.4802	−	14.4802i	−0.474315	−	0.474315i
$933$	−3.53716	+	9.21461i	−0.115801	+	0.301673i
$934$	−12.1864	+	2.59031i	−0.398753	+	0.0847575i
$935$	2.80912	−	4.49078i	0.0918681	−	0.146864i
$936$	−1.71025	+	8.04611i	−0.0559014	+	0.262995i
$937$	−11.3453	−	22.2665i	−0.370636	−	0.727415i	0.628076	−	0.778152i	$-0.283843\pi$
$937$	−11.3453	−	22.2665i	−0.370636	−	0.727415i	−0.998712	+	0.0507375i	$0.983843\pi$
$938$	40.5414	+	54.5283i	1.32372	+	1.78041i
$939$	7.95790	−	2.58568i	0.259696	−	0.0843805i
$940$	0.0587216	−	1.65894i	0.00191529	−	0.0541087i
$941$	−3.46764	−	16.3140i	−0.113042	−	0.531820i	−0.997831	−	0.0658284i	$-0.979031\pi$
$941$	−3.46764	−	16.3140i	−0.113042	−	0.531820i	0.884789	−	0.465992i	$-0.154302\pi$
$942$	−14.5868	+	11.8121i	−0.475263	+	0.384861i
$943$	−33.6465	+	9.01555i	−1.09568	+	0.293587i
$944$	17.3467	+	12.6031i	0.564586	+	0.410196i
$945$	26.0868	+	0.636056i	0.848604	+	0.0206909i
$946$	−12.0816	+	8.77782i	−0.392808	+	0.285392i
$947$	15.0527	−	18.5885i	0.489147	−	0.604047i	−0.471483	−	0.881875i	$-0.656281\pi$
$947$	15.0527	−	18.5885i	0.489147	−	0.604047i	0.960631	+	0.277828i	$0.0896146\pi$
$948$	21.3182	−	1.11724i	0.692383	−	0.0362863i
$949$	−5.14293	+	2.96927i	−0.166947	+	0.0963866i
$950$	−0.958726	+	52.0855i	−0.0311052	+	1.68988i
$951$		−	15.7043i		−	0.509247i
$952$	1.01413	+	4.52564i	0.0328683	+	0.146677i
$953$	8.33470	−	52.6232i	0.269987	−	1.70463i	−0.364090	−	0.931364i	$-0.618620\pi$
$953$	8.33470	−	52.6232i	0.269987	−	1.70463i	0.634077	−	0.773270i	$-0.281380\pi$
$954$	1.34552	−	0.141420i	0.0435628	−	0.00457863i
$955$	6.45997	−	1.48816i	0.209040	−	0.0481559i
$956$	4.75620	−	45.2522i	0.153827	−	1.46356i
$957$	0.285561	+	1.06573i	0.00923086	+	0.0344500i
$958$	6.81999	+	43.0597i	0.220344	+	1.39120i
$959$	−7.38735	−	18.6293i	−0.238550	−	0.601572i
$960$	19.4751	−	3.42443i	0.628556	−	0.110523i
$961$	71.1813	+	15.1300i	2.29617	+	0.488066i
$962$	32.7984	−	50.5051i	1.05746	−	1.62835i
$963$	−24.7456	+	38.1049i	−0.797417	+	1.22791i
$964$	60.2062	+	12.7972i	1.93911	+	0.412171i
$965$	26.4921	−	27.4073i	0.852811	−	0.882272i
$966$	17.7525	−	22.4226i	0.571178	−	0.721436i
$967$	−4.98535	−	31.4763i	−0.160318	−	1.01221i	−0.928326	−	0.371768i	$-0.878752\pi$
$967$	−4.98535	−	31.4763i	−0.160318	−	1.01221i	0.768008	−	0.640441i	$-0.221248\pi$
$968$	−1.99080	−	7.42978i	−0.0639868	−	0.238802i
$969$	0.975858	−	9.28467i	0.0313491	−	0.298266i
$970$	2.03089	−	23.0867i	0.0652080	−	0.741269i
$971$	−38.5053	+	4.04707i	−1.23569	+	0.129877i	−0.699757	−	0.714381i	$-0.746708\pi$
$971$	−38.5053	+	4.04707i	−1.23569	+	0.129877i	−0.535937	+	0.844258i	$0.680042\pi$
$972$	−5.91604	+	37.3524i	−0.189757	+	1.19808i
$973$	6.98348	−	22.3260i	0.223880	−	0.715739i
$974$			61.3676i			1.96634i
$975$	3.32224	−	18.7371i	0.106397	−	0.600068i
$976$	14.3221	−	8.26889i	0.458441	−	0.264681i
$977$	−28.8691	+	1.51297i	−0.923604	+	0.0484040i	−0.508206	−	0.861236i	$-0.669691\pi$
$977$	−28.8691	+	1.51297i	−0.923604	+	0.0484040i	−0.415398	+	0.909640i	$0.636358\pi$
$978$	−6.09789	+	7.53027i	−0.194989	+	0.240792i
$979$	9.01096	−	6.54684i	0.287991	−	0.209238i
$980$	20.6333	−	30.8610i	0.659105	−	0.985817i
$981$	35.7300	+	25.9594i	1.14077	+	0.828818i
$982$	−36.3639	+	9.74367i	−1.16042	+	0.310933i
$983$	7.60355	−	6.15724i	0.242516	−	0.196385i	−0.500355	−	0.865820i	$-0.666797\pi$
$983$	7.60355	−	6.15724i	0.242516	−	0.196385i	0.742871	+	0.669435i	$0.233464\pi$
$984$	0.751219	+	3.53421i	0.0239480	+	0.112666i
$985$	−26.6620	+	34.0924i	−0.849523	+	1.08627i
$986$	5.67209	−	1.84297i	0.180636	−	0.0586922i
$987$	0.552039	−	0.410437i	0.0175716	−	0.0130644i
$988$	−24.5831	−	48.2471i	−0.782093	−	1.53494i
$989$	8.79984	−	41.4000i	0.279819	−	1.31644i
$990$	−0.785875	−	11.3159i	−0.0249767	−	0.359642i
$991$	23.8969	−	5.07944i	0.759110	−	0.161354i	0.187934	−	0.982182i	$-0.439821\pi$
$991$	23.8969	−	5.07944i	0.759110	−	0.161354i	0.571176	+	0.820828i	$0.306487\pi$
$992$	29.4773	−	76.7909i	0.935904	−	2.43811i
$993$	18.2755	+	18.2755i	0.579955	+	0.579955i
$994$	6.30838	+	9.48391i	0.200090	+	0.300811i
$995$	−0.429006	+	0.00728418i	−0.0136004	+	0.000230924i
$996$	0.763228	+	7.26163i	0.0241838	+	0.230094i
$997$	20.3902	−	7.82705i	0.645763	−	0.247885i	−0.0133710	−	0.999911i	$-0.504256\pi$
$997$	20.3902	−	7.82705i	0.645763	−	0.247885i	0.659134	+	0.752025i	$0.270923\pi$
$998$	−0.582044	−	11.1061i	−0.0184243	−	0.351556i
$999$	13.8634	−	24.0121i	0.438619	−	0.759710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.117.16	yes	288
5.2	odd	4		875.2.bb.a.768.3		288
5.3	odd	4		875.2.bb.b.768.16		288
5.4	even	2		875.2.bb.c.607.3		288
7.3	odd	6	inner	175.2.x.a.17.3	yes	288
25.3	odd	20	inner	175.2.x.a.103.3	yes	288
25.4	even	10		875.2.bb.a.257.3		288
25.21	even	5		875.2.bb.b.257.16		288
25.22	odd	20		875.2.bb.c.243.16		288
35.3	even	12		875.2.bb.b.143.16		288
35.17	even	12		875.2.bb.a.143.3		288
35.24	odd	6		875.2.bb.c.857.16		288
175.3	even	60	inner	175.2.x.a.3.16	✓	288
175.122	even	60		875.2.bb.c.493.3		288
175.129	odd	30		875.2.bb.a.507.3		288
175.171	odd	30		875.2.bb.b.507.16		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.16	✓	288	175.3	even	60	inner
175.2.x.a.17.3	yes	288	7.3	odd	6	inner
175.2.x.a.103.3	yes	288	25.3	odd	20	inner
175.2.x.a.117.16	yes	288	1.1	even	1	trivial
875.2.bb.a.143.3		288	35.17	even	12
875.2.bb.a.257.3		288	25.4	even	10
875.2.bb.a.507.3		288	175.129	odd	30
875.2.bb.a.768.3		288	5.2	odd	4
875.2.bb.b.143.16		288	35.3	even	12
875.2.bb.b.257.16		288	25.21	even	5
875.2.bb.b.507.16		288	175.171	odd	30
875.2.bb.b.768.16		288	5.3	odd	4
875.2.bb.c.243.16		288	25.22	odd	20
875.2.bb.c.493.3		288	175.122	even	60
875.2.bb.c.607.3		288	5.4	even	2
875.2.bb.c.857.16		288	35.24	odd	6

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 $\F_{q}$
Belyi maps

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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