LMFDB - Embedded newform 175.2.x.a.103.8

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			103.8
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.802384 - 0.0420512i) q^{2} +(-1.97492 - 2.43882i) q^{3} +(-1.34699 - 0.141575i) q^{4} +(-1.30893 - 1.81293i) q^{5} +(1.48209 + 2.03992i) q^{6} +(2.52724 + 0.782993i) q^{7} +(2.66204 + 0.421625i) q^{8} +(-1.42381 + 6.69848i) q^{9} +(0.974030 + 1.50970i) q^{10} +(-4.90608 + 1.04282i) q^{11} +(2.31492 + 3.56467i) q^{12} +(-0.816789 - 0.416175i) q^{13} +(-1.99489 - 0.734535i) q^{14} +(-1.83636 + 6.77262i) q^{15} +(0.531383 + 0.112949i) q^{16} +(0.185757 + 0.483913i) q^{17} +(1.42412 - 5.31488i) q^{18} +(-0.116377 - 1.10725i) q^{19} +(1.50646 + 2.62731i) q^{20} +(-3.08150 - 7.70982i) q^{21} +(3.98041 - 0.630435i) q^{22} +(0.270445 - 5.16039i) q^{23} +(-4.22903 - 7.32490i) q^{24} +(-1.57340 + 4.74599i) q^{25} +(0.637878 + 0.368279i) q^{26} +(10.7599 - 5.48243i) q^{27} +(-3.29331 - 1.41248i) q^{28} +(-3.39698 + 4.67555i) q^{29} +(1.75827 - 5.35702i) q^{30} +(-0.139259 + 0.312781i) q^{31} +(-5.62839 - 1.50812i) q^{32} +(12.2323 + 9.90555i) q^{33} +(-0.128699 - 0.396095i) q^{34} +(-1.88847 - 5.60657i) q^{35} +(2.86619 - 8.82122i) q^{36} +(-5.35336 + 3.47651i) q^{37} +(0.0468178 + 0.893337i) q^{38} +(0.598115 + 2.81391i) q^{39} +(-2.72005 - 5.37795i) q^{40} +(-6.75808 + 2.19583i) q^{41} +(2.14834 + 6.31581i) q^{42} +(-3.02167 - 3.02167i) q^{43} +(6.75609 - 0.710093i) q^{44} +(14.0075 - 6.18660i) q^{45} +(-0.434001 + 4.12924i) q^{46} +(-11.9164 - 4.57426i) q^{47} +(-0.773974 - 1.51901i) q^{48} +(5.77384 + 3.95762i) q^{49} +(1.46204 - 3.74194i) q^{50} +(0.813322 - 1.40871i) q^{51} +(1.04129 + 0.676221i) q^{52} +(4.55606 - 3.68942i) q^{53} +(-8.86410 + 3.94655i) q^{54} +(8.31228 + 7.52937i) q^{55} +(6.39747 + 3.14990i) q^{56} +(-2.47056 + 2.47056i) q^{57} +(2.92230 - 3.60874i) q^{58} +(5.88478 - 6.53571i) q^{59} +(3.43240 - 8.86268i) q^{60} +(-1.07623 + 0.969040i) q^{61} +(0.124892 - 0.245114i) q^{62} +(-8.84316 + 15.8138i) q^{63} +(3.41938 + 1.11102i) q^{64} +(0.314627 + 2.02552i) q^{65} +(-9.39849 - 8.46244i) q^{66} +(1.31334 - 0.504146i) q^{67} +(-0.181703 - 0.678125i) q^{68} +(-13.1194 + 9.53177i) q^{69} +(1.27952 + 4.57804i) q^{70} +(-6.16371 - 4.47820i) q^{71} +(-6.61447 + 17.2313i) q^{72} +(-0.656834 + 1.01144i) q^{73} +(4.44164 - 2.56438i) q^{74} +(14.6819 - 5.53571i) q^{75} +1.50794i q^{76} +(-13.2153 - 1.20598i) q^{77} +(-0.361590 - 2.28299i) q^{78} +(1.97771 + 4.44201i) q^{79} +(-0.490776 - 1.11120i) q^{80} +(-15.8523 - 7.05789i) q^{81} +(5.51491 - 1.47772i) q^{82} +(0.543025 - 3.42852i) q^{83} +(3.05924 + 10.8213i) q^{84} +(0.634155 - 0.970172i) q^{85} +(2.29747 + 2.55160i) q^{86} +(18.1116 - 0.949187i) q^{87} +(-13.4998 + 0.707497i) q^{88} +(-2.10268 - 2.33526i) q^{89} +(-11.4996 + 4.37500i) q^{90} +(-1.73836 - 1.69131i) q^{91} +(-1.09487 + 6.91272i) q^{92} +(1.03784 - 0.278088i) q^{93} +(9.36915 + 4.17141i) q^{94} +(-1.85504 + 1.66030i) q^{95} +(7.43756 + 16.7050i) q^{96} +(0.557021 + 3.51689i) q^{97} +(-4.46642 - 3.41833i) q^{98} -34.3480i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.802384	−	0.0420512i	−0.567371	−	0.0297347i	−0.233506	−	0.972355i	$-0.575020\pi$
$2$	−0.802384	−	0.0420512i	−0.567371	−	0.0297347i	−0.333865	+	0.942621i	$0.608353\pi$
$3$	−1.97492	−	2.43882i	−1.14022	−	1.40805i	−0.899203	−	0.437531i	$-0.855853\pi$
$3$	−1.97492	−	2.43882i	−1.14022	−	1.40805i	−0.241015	−	0.970521i	$-0.577480\pi$
$4$	−1.34699	−	0.141575i	−0.673496	−	0.0707873i
$5$	−1.30893	−	1.81293i	−0.585372	−	0.810765i
$5$	−1.30893	−	1.81293i	−0.585372	−	0.810765i
$6$	1.48209	+	2.03992i	0.605059	+	0.832792i
$7$	2.52724	+	0.782993i	0.955205	+	0.295944i
$7$	2.52724	+	0.782993i	0.955205	+	0.295944i
$8$	2.66204	+	0.421625i	0.941172	+	0.149067i
$9$	−1.42381	+	6.69848i	−0.474602	+	2.23283i
$10$	0.974030	+	1.50970i	0.308015	+	0.477410i
$11$	−4.90608	+	1.04282i	−1.47924	+	0.314422i	−0.875678	−	0.482895i	$-0.839585\pi$
$11$	−4.90608	+	1.04282i	−1.47924	+	0.314422i	−0.603560	+	0.797317i	$0.706252\pi$
$12$	2.31492	+	3.56467i	0.668260	+	1.02903i
$13$	−0.816789	−	0.416175i	−0.226536	−	0.115426i	0.337039	−	0.941491i	$-0.390575\pi$
$13$	−0.816789	−	0.416175i	−0.226536	−	0.115426i	−0.563575	+	0.826065i	$0.690575\pi$
$14$	−1.99489	−	0.734535i	−0.533156	−	0.196313i
$15$	−1.83636	+	6.77262i	−0.474147	+	1.74868i
$16$	0.531383	+	0.112949i	0.132846	+	0.0282372i
$17$	0.185757	+	0.483913i	0.0450526	+	0.117366i	0.954261	−	0.298976i	$-0.0966451\pi$
$17$	0.185757	+	0.483913i	0.0450526	+	0.117366i	−0.909208	+	0.416342i	$0.863312\pi$
$18$	1.42412	−	5.31488i	0.335668	−	1.25273i
$19$	−0.116377	−	1.10725i	−0.0266987	−	0.254022i	−0.999728	−	0.0233383i	$-0.992571\pi$
$19$	−0.116377	−	1.10725i	−0.0266987	−	0.254022i	0.973029	−	0.230683i	$-0.0740961\pi$
$20$	1.50646	+	2.62731i	0.336854	+	0.587484i
$21$	−3.08150	−	7.70982i	−0.672439	−	1.68242i
$22$	3.98041	−	0.630435i	0.848626	−	0.134409i
$23$	0.270445	−	5.16039i	0.0563916	−	1.07602i	−0.813118	−	0.582099i	$-0.802232\pi$
$23$	0.270445	−	5.16039i	0.0563916	−	1.07602i	0.869509	−	0.493916i	$-0.164435\pi$
$24$	−4.22903	−	7.32490i	−0.863248	−	1.49519i
$25$	−1.57340	+	4.74599i	−0.314679	+	0.949198i
$26$	0.637878	+	0.368279i	0.125098	+	0.0722254i
$27$	10.7599	−	5.48243i	2.07074	−	1.05509i
$28$	−3.29331	−	1.41248i	−0.622378	−	0.266933i
$29$	−3.39698	+	4.67555i	−0.630804	+	0.868227i	−0.998083	−	0.0618834i	$-0.980289\pi$
$29$	−3.39698	+	4.67555i	−0.630804	+	0.868227i	0.367279	+	0.930111i	$0.380289\pi$
$30$	1.75827	−	5.35702i	0.321014	−	0.978054i
$31$	−0.139259	+	0.312781i	−0.0250116	+	0.0561771i	−0.925619	−	0.378456i	$-0.876455\pi$
$31$	−0.139259	+	0.312781i	−0.0250116	+	0.0561771i	0.900608	+	0.434633i	$0.143122\pi$
$32$	−5.62839	−	1.50812i	−0.994968	−	0.266601i
$33$	12.2323	+	9.90555i	2.12938	+	1.72434i
$34$	−0.128699	−	0.396095i	−0.0220717	−	0.0679298i
$35$	−1.88847	−	5.60657i	−0.319210	−	0.947684i
$36$	2.86619	−	8.82122i	0.477698	−	1.47020i
$37$	−5.35336	+	3.47651i	−0.880086	+	0.571535i	−0.903690	−	0.428187i	$-0.859153\pi$
$37$	−5.35336	+	3.47651i	−0.880086	+	0.571535i	0.0236039	+	0.999721i	$0.492486\pi$
$38$	0.0468178	+	0.893337i	0.00759485	+	0.144918i
$39$	0.598115	+	2.81391i	0.0957751	+	0.450586i
$40$	−2.72005	−	5.37795i	−0.430078	−	0.850329i
$41$	−6.75808	+	2.19583i	−1.05543	+	0.342931i	−0.784799	−	0.619750i	$-0.787234\pi$
$41$	−6.75808	+	2.19583i	−1.05543	+	0.342931i	−0.270635	+	0.962682i	$0.587234\pi$
$42$	2.14834	+	6.31581i	0.331496	+	0.974551i
$43$	−3.02167	−	3.02167i	−0.460800	−	0.460800i	0.438118	−	0.898918i	$-0.355645\pi$
$43$	−3.02167	−	3.02167i	−0.460800	−	0.460800i	−0.898918	+	0.438118i	$0.855645\pi$
$44$	6.75609	−	0.710093i	1.01852	−	0.107051i
$45$	14.0075	−	6.18660i	2.08812	−	0.922244i
$46$	−0.434001	+	4.12924i	−0.0639899	+	0.608824i
$47$	−11.9164	−	4.57426i	−1.73818	−	0.667225i	−0.738207	−	0.674574i	$-0.764327\pi$
$47$	−11.9164	−	4.57426i	−1.73818	−	0.667225i	−0.999973	+	0.00734880i	$0.997661\pi$
$48$	−0.773974	−	1.51901i	−0.111714	−	0.219250i
$49$	5.77384	+	3.95762i	0.824835	+	0.565374i
$50$	1.46204	−	3.74194i	0.206764	−	0.529191i
$51$	0.813322	−	1.40871i	0.113888	−	0.197260i
$52$	1.04129	+	0.676221i	0.144401	+	0.0937749i
$53$	4.55606	−	3.68942i	0.625822	−	0.506781i	−0.263142	−	0.964757i	$-0.584759\pi$
$53$	4.55606	−	3.68942i	0.625822	−	0.506781i	0.888965	+	0.457976i	$0.151425\pi$
$54$	−8.86410	+	3.94655i	−1.20625	+	0.537057i
$55$	8.31228	+	7.52937i	1.12083	+	1.01526i
$56$	6.39747	+	3.14990i	0.854897	+	0.420924i
$57$	−2.47056	+	2.47056i	−0.327233	+	0.327233i
$58$	2.92230	−	3.60874i	0.383717	−	0.473850i
$59$	5.88478	−	6.53571i	0.766133	−	0.850876i	−0.226250	−	0.974069i	$-0.572647\pi$
$59$	5.88478	−	6.53571i	0.766133	−	0.850876i	0.992383	+	0.123193i	$0.0393134\pi$
$60$	3.43240	−	8.86268i	0.443121	−	1.14417i
$61$	−1.07623	+	0.969040i	−0.137797	+	0.124073i	−0.735147	−	0.677908i	$-0.762887\pi$
$61$	−1.07623	+	0.969040i	−0.137797	+	0.124073i	0.597350	+	0.801981i	$0.296220\pi$
$62$	0.124892	−	0.245114i	0.0158613	−	0.0311295i
$63$	−8.84316	+	15.8138i	−1.11413	+	1.99235i
$64$	3.41938	+	1.11102i	0.427422	+	0.138878i
$65$	0.314627	+	2.02552i	0.0390247	+	0.251235i
$66$	−9.39849	−	8.46244i	−1.15687	−	1.04165i
$67$	1.31334	−	0.504146i	0.160451	−	0.0615912i	−0.276817	−	0.960923i	$-0.589280\pi$
$67$	1.31334	−	0.504146i	0.160451	−	0.0615912i	0.437268	+	0.899331i	$0.355946\pi$
$68$	−0.181703	−	0.678125i	−0.0220347	−	0.0822348i
$69$	−13.1194	+	9.53177i	−1.57939	+	1.14749i
$70$	1.27952	+	4.57804i	0.152931	+	0.547180i
$71$	−6.16371	−	4.47820i	−0.731498	−	0.531465i	0.158539	−	0.987353i	$-0.449322\pi$
$71$	−6.16371	−	4.47820i	−0.731498	−	0.531465i	−0.890037	+	0.455888i	$0.849322\pi$
$72$	−6.61447	+	17.2313i	−0.779523	+	2.03073i
$73$	−0.656834	+	1.01144i	−0.0768766	+	0.118380i	−0.875018	−	0.484091i	$-0.839150\pi$
$73$	−0.656834	+	1.01144i	−0.0768766	+	0.118380i	0.798141	+	0.602471i	$0.205817\pi$
$74$	4.44164	−	2.56438i	0.516330	−	0.298103i
$75$	14.6819	−	5.53571i	1.69532	−	0.639209i
$76$			1.50794i			0.172972i
$77$	−13.2153	−	1.20598i	−1.50603	−	0.137434i
$78$	−0.361590	−	2.28299i	−0.0409420	−	0.258497i
$79$	1.97771	+	4.44201i	0.222510	+	0.499765i	0.989961	−	0.141343i	$-0.0451420\pi$
$79$	1.97771	+	4.44201i	0.222510	+	0.499765i	−0.767451	+	0.641107i	$0.778475\pi$
$80$	−0.490776	−	1.11120i	−0.0548704	−	0.124236i
$81$	−15.8523	−	7.05789i	−1.76136	−	0.784210i
$82$	5.51491	−	1.47772i	0.609020	−	0.163186i
$83$	0.543025	−	3.42852i	0.0596047	−	0.376329i	−0.939797	−	0.341734i	$-0.888986\pi$
$83$	0.543025	−	3.42852i	0.0596047	−	0.376329i	0.999401	−	0.0345952i	$-0.0110142\pi$
$84$	3.05924	+	10.8213i	0.333791	+	1.18070i
$85$	0.634155	−	0.970172i	0.0687838	−	0.105230i
$86$	2.29747	+	2.55160i	0.247743	+	0.275146i
$87$	18.1116	−	0.949187i	1.94176	−	0.101764i
$88$	−13.4998	+	0.707497i	−1.43909	+	0.0754194i
$89$	−2.10268	−	2.33526i	−0.222884	−	0.247537i	0.621324	−	0.783554i	$-0.286595\pi$
$89$	−2.10268	−	2.33526i	−0.222884	−	0.247537i	−0.844208	+	0.536016i	$0.819929\pi$
$90$	−11.4996	+	4.37500i	−1.21216	+	0.461165i
$91$	−1.73836	−	1.69131i	−0.182229	−	0.177298i
$92$	−1.09487	+	6.91272i	−0.114148	+	0.720700i
$93$	1.03784	−	0.278088i	0.107619	−	0.0288364i
$94$	9.36915	+	4.17141i	0.966354	+	0.430248i
$95$	−1.85504	+	1.66030i	−0.190323	+	0.170344i
$96$	7.43756	+	16.7050i	0.759093	+	1.70495i
$97$	0.557021	+	3.51689i	0.0565569	+	0.357086i	0.999695	+	0.0246858i	$0.00785852\pi$
$97$	0.557021	+	3.51689i	0.0565569	+	0.357086i	−0.943138	+	0.332400i	$0.892141\pi$
$98$	−4.46642	−	3.41833i	−0.451176	−	0.345303i
$99$		−	34.3480i		−	3.45211i
$100$	2.79126	−	6.17006i	0.279126	−	0.617006i
$101$	−8.57568	+	4.95117i	−0.853312	+	0.492660i	−0.861767	−	0.507304i	$-0.830642\pi$
$101$	−8.57568	+	4.95117i	−0.853312	+	0.492660i	0.00845468	+	0.999964i	$0.497309\pi$
$102$	−0.711834	+	1.09613i	−0.0704821	+	0.108533i
$103$	2.66143	−	6.93326i	0.262238	−	0.683154i	−0.737729	−	0.675097i	$-0.764102\pi$
$103$	2.66143	−	6.93326i	0.262238	−	0.683154i	0.999968	−	0.00805736i	$-0.00256477\pi$
$104$	−1.99885	−	1.45225i	−0.196004	−	0.142405i
$105$	−9.94384	+	15.6782i	−0.970420	+	1.53003i
$106$	−3.81085	+	2.76875i	−0.370143	+	0.268924i
$107$	0.403711	+	1.50667i	0.0390282	+	0.145655i	0.982691	−	0.185255i	$-0.0593110\pi$
$107$	0.403711	+	1.50667i	0.0390282	+	0.145655i	−0.943662	+	0.330910i	$0.892644\pi$
$108$	−15.2696	+	5.86147i	−1.46932	+	0.564020i
$109$	−4.44021	−	3.99798i	−0.425295	−	0.382937i	0.428504	−	0.903540i	$-0.359041\pi$
$109$	−4.44021	−	3.99798i	−0.425295	−	0.382937i	−0.853799	+	0.520603i	$0.825707\pi$
$110$	−6.35302	−	6.39099i	−0.605736	−	0.609357i
$111$	19.0510	+	6.19005i	1.80824	+	0.587533i
$112$	1.25449	+	0.701517i	0.118538	+	0.0662872i
$113$	1.14628	−	2.24970i	0.107833	−	0.211634i	−0.830784	−	0.556595i	$-0.812108\pi$
$113$	1.14628	−	2.24970i	0.107833	−	0.211634i	0.938617	+	0.344960i	$0.112108\pi$
$114$	2.08623	−	1.87845i	0.195393	−	0.175933i
$115$	−9.70939	+	6.26430i	−0.905406	+	0.584149i
$116$	5.23765	−	5.81700i	0.486303	−	0.540095i
$117$	3.95069	−	4.87869i	0.365241	−	0.451035i
$118$	−4.99668	+	4.99668i	−0.459982	+	0.459982i
$119$	0.0905506	+	1.36841i	0.00830076	+	0.125442i
$120$	−7.74398	+	17.2547i	−0.706925	+	1.57513i
$121$	12.9331	−	5.75820i	1.17574	−	0.523473i
$122$	0.904298	−	0.732286i	0.0818713	−	0.0662981i
$123$	18.7019	+	12.1451i	1.68629	+	1.09509i
$124$	0.231863	−	0.401598i	0.0208219	−	0.0360645i
$125$	10.6636	−	3.35973i	0.953781	−	0.300503i
$126$	7.76060	−	12.3169i	0.691369	−	1.09728i
$127$	−4.18519	−	8.21389i	−0.371375	−	0.728865i	0.627381	−	0.778712i	$-0.284127\pi$
$127$	−4.18519	−	8.21389i	−0.371375	−	0.728865i	−0.998757	+	0.0498468i	$0.984127\pi$
$128$	8.18289	+	3.14112i	0.723272	+	0.277638i
$129$	−1.40176	+	13.3368i	−0.123418	+	1.17424i
$130$	−0.167276	−	1.63848i	−0.0146711	−	0.143704i
$131$	5.58590	−	0.587102i	0.488043	−	0.0512953i	0.142688	−	0.989768i	$-0.454425\pi$
$131$	5.58590	−	0.587102i	0.488043	−	0.0512953i	0.345354	+	0.938472i	$0.387759\pi$
$132$	−15.0745	−	15.0745i	−1.31207	−	1.31207i
$133$	0.572860	−	2.88942i	0.0496733	−	0.250544i
$134$	−1.07501	+	0.349291i	−0.0928664	+	0.0301741i
$135$	−24.0232	−	12.3307i	−2.06759	−	1.06126i
$136$	0.290462	+	1.36651i	0.0249069	+	0.117178i
$137$	0.226254	+	4.31718i	0.0193302	+	0.368841i	0.991118	+	0.132985i	$0.0424562\pi$
$137$	0.226254	+	4.31718i	0.0193302	+	0.368841i	−0.971788	+	0.235857i	$0.924210\pi$
$138$	10.9276	−	7.09646i	0.930218	−	0.604091i
$139$	1.99140	−	6.12890i	0.168908	−	0.519847i	−0.830395	−	0.557176i	$-0.811885\pi$
$139$	1.99140	−	6.12890i	0.168908	−	0.519847i	0.999303	+	0.0373290i	$0.0118849\pi$
$140$	1.75001	+	7.81937i	0.147903	+	0.660857i
$141$	12.3780	+	38.0956i	1.04242	+	3.20823i
$142$	4.75735	+	3.85243i	0.399228	+	0.323289i
$143$	4.44123	+	1.19002i	0.371394	+	0.0995147i
$144$	−1.51317	+	3.39864i	−0.126098	+	0.283220i
$145$	12.9228	+	0.0385051i	1.07318	+	0.00319767i
$146$	0.569565	−	0.783939i	0.0471376	−	0.0648793i
$147$	−1.75094	−	21.8973i	−0.144415	−	1.80606i
$148$	7.70311	−	3.92493i	0.633192	−	0.322627i
$149$	1.92554	+	1.11171i	0.157746	+	0.0910749i	0.576795	−	0.816889i	$-0.304303\pi$
$149$	1.92554	+	1.11171i	0.157746	+	0.0910749i	−0.419049	+	0.907964i	$0.637636\pi$
$150$	−12.0133	+	3.82437i	−0.980884	+	0.312259i
$151$	6.19286	+	10.7263i	0.503968	+	0.872897i	0.999989	+	0.00458736i	$0.00146021\pi$
$151$	6.19286	+	10.7263i	0.503968	+	0.872897i	−0.496022	+	0.868310i	$0.665206\pi$
$152$	0.157046	−	2.99662i	0.0127381	−	0.243058i
$153$	−3.50596	+	0.555290i	−0.283440	+	0.0448925i
$154$	10.5531	+	1.52338i	0.850390	+	0.122757i
$155$	0.749329	−	0.156943i	0.0601875	−	0.0126059i
$156$	−0.407278	−	3.87499i	−0.0326083	−	0.310248i
$157$	4.35511	−	16.2535i	0.347576	−	1.29717i	−0.541998	−	0.840380i	$-0.682332\pi$
$157$	4.35511	−	16.2535i	0.347576	−	1.29717i	0.889574	−	0.456791i	$-0.151001\pi$
$158$	−1.40009	−	3.64736i	−0.111385	−	0.290168i
$159$	−17.9957	−	3.82509i	−1.42715	−	0.303350i
$160$	4.63306	+	12.1779i	0.366276	+	0.962746i
$161$	4.72403	−	12.8298i	0.372306	−	1.01113i
$162$	12.4228	+	6.32974i	0.976029	+	0.497312i
$163$	−9.91155	−	15.2625i	−0.776333	−	1.19545i	−0.976464	−	0.215679i	$-0.930804\pi$
$163$	−9.91155	−	15.2625i	−0.776333	−	1.19545i	0.200132	−	0.979769i	$-0.435863\pi$
$164$	9.41395	−	2.00100i	0.735106	−	0.156252i
$165$	1.94673	−	35.1420i	0.151553	−	2.73580i
$166$	−0.579888	+	2.72816i	−0.0450080	+	0.211746i
$167$	0.334099	+	0.0529161i	0.0258534	+	0.00409477i	0.169348	−	0.985556i	$-0.445834\pi$
$167$	0.334099	+	0.0529161i	0.0258534	+	0.00409477i	−0.143494	+	0.989651i	$0.545834\pi$
$168$	−4.95242	−	21.8231i	−0.382087	−	1.68369i
$169$	−7.14727	−	9.83737i	−0.549790	−	0.756721i
$170$	−0.549633	+	0.751784i	−0.0421549	+	0.0576592i
$171$	7.58262	+	0.796965i	0.579857	+	0.0609455i
$172$	3.64237	+	4.49795i	0.277728	+	0.342966i
$173$	−17.7761	−	0.931608i	−1.35149	−	0.0708288i	−0.637213	−	0.770687i	$-0.719913\pi$
$173$	−17.7761	−	0.931608i	−1.35149	−	0.0708288i	−0.714281	+	0.699859i	$0.753246\pi$
$174$	−14.5723			−1.10473
$175$	−7.69242	+	10.7623i	−0.581492	+	0.813552i
$176$	−2.72479			−0.205389
$177$	−27.5613	−	1.44443i	−2.07164	−	0.108570i
$178$	1.58896	+	1.96220i	0.119097	+	0.147073i
$179$	−9.80573	−	1.03062i	−0.732915	−	0.0770324i	−0.269284	−	0.963061i	$-0.586787\pi$
$179$	−9.80573	−	1.03062i	−0.732915	−	0.0770324i	−0.463631	+	0.886028i	$0.653454\pi$
$180$	−19.7439	+	6.35019i	−1.47162	+	0.473316i
$181$	−12.6158	−	17.3642i	−0.937727	−	1.29067i	−0.956768	−	0.290852i	$-0.906061\pi$
$181$	−12.6158	−	17.3642i	−0.937727	−	1.29067i	0.0190405	−	0.999819i	$-0.493939\pi$
$182$	1.32371	+	1.43018i	0.0981197	+	0.106012i
$183$	4.48877	+	0.710952i	0.331820	+	0.0525551i
$184$	2.89568	−	13.6231i	0.213473	−	1.00431i
$185$	13.3098	+	5.15472i	0.978558	+	0.378983i
$186$	−0.844440	+	0.179491i	−0.0619174	+	0.0131609i
$187$	−1.41597	−	2.18040i	−0.103546	−	0.159447i
$188$	15.4036	+	7.84855i	1.12343	+	0.572414i
$189$	31.4855	−	5.43048i	2.29023	−	0.395010i
$190$	1.55827	−	1.25419i	0.113049	−	0.0909888i
$191$	−0.709623	−	0.150835i	−0.0513465	−	0.0109140i	0.182167	−	0.983268i	$-0.441689\pi$
$191$	−0.709623	−	0.150835i	−0.0513465	−	0.0109140i	−0.233513	+	0.972354i	$0.575022\pi$
$192$	−4.04340	−	10.5334i	−0.291807	−	0.760185i
$193$	−3.80877	+	14.2145i	−0.274161	+	1.02318i	0.682240	+	0.731128i	$0.261006\pi$
$193$	−3.80877	+	14.2145i	−0.274161	+	1.02318i	−0.956401	+	0.292055i	$0.905661\pi$
$194$	−0.299055	−	2.84532i	−0.0214709	−	0.204282i
$195$	4.31852	−	4.76755i	0.309255	−	0.341412i
$196$	−7.21702	−	6.14831i	−0.515502	−	0.439165i
$197$	24.1329	−	3.82227i	1.71940	−	0.272326i	0.782683	−	0.622420i	$-0.213851\pi$
$197$	24.1329	−	3.82227i	1.71940	−	0.272326i	0.936714	+	0.350095i	$0.113851\pi$
$198$	−1.44438	+	27.5603i	−0.102647	+	1.95863i
$199$	0.487743	+	0.844796i	0.0345752	+	0.0598860i	0.882795	−	0.469758i	$-0.155659\pi$
$199$	0.487743	+	0.844796i	0.0345752	+	0.0598860i	−0.848220	+	0.529644i	$0.822326\pi$
$200$	−6.18947	+	11.9706i	−0.437661	+	0.846451i
$201$	−3.82326	−	2.20736i	−0.269672	−	0.155695i
$202$	7.08919	−	3.61212i	0.498794	−	0.254148i
$203$	−12.2459	+	9.15640i	−0.859494	+	0.642653i
$204$	−1.29498	+	1.78238i	−0.0906665	+	0.124792i
$205$	12.8267	+	9.37769i	0.895859	+	0.654967i
$206$	−2.42704	+	5.45122i	−0.169100	+	0.379804i
$207$	34.1817	+	9.15896i	2.37579	+	0.636592i
$208$	−0.387021	−	0.313403i	−0.0268351	−	0.0217306i
$209$	1.72562	+	5.31092i	0.119364	+	0.367364i
$210$	8.63807	−	12.1617i	0.596083	−	0.839240i
$211$	−8.83060	+	27.1778i	−0.607923	+	1.87100i	−0.132636	+	0.991165i	$0.542344\pi$
$211$	−8.83060	+	27.1778i	−0.607923	+	1.87100i	−0.475287	+	0.879831i	$0.657656\pi$
$212$	−6.65930	+	4.32460i	−0.457363	+	0.297015i
$213$	1.25130	+	23.8762i	0.0857377	+	1.63597i
$214$	−0.260574	−	1.22591i	−0.0178125	−	0.0838012i
$215$	−1.52290	+	9.43321i	−0.103861	+	0.643340i
$216$	30.9547	−	10.0578i	2.10620	−	0.684347i
$217$	−0.596846	+	0.681432i	−0.0405165	+	0.0462586i
$218$	3.39463	+	3.39463i	0.229913	+	0.229913i
$219$	3.76390	−	0.395602i	0.254341	−	0.0267323i
$220$	−10.1306	−	11.3188i	−0.683005	−	0.763114i
$221$	0.0496683	−	0.472562i	0.00334105	−	0.0317880i
$222$	−15.0259	−	5.76791i	−1.00847	−	0.387117i
$223$	−10.1540	−	19.9284i	−0.679963	−	1.33450i	−0.930463	−	0.366385i	$-0.880595\pi$
$223$	−10.1540	−	19.9284i	−0.679963	−	1.33450i	0.250501	−	0.968116i	$-0.419405\pi$
$224$	−13.0434	−	8.21837i	−0.871500	−	0.549113i
$225$	−29.5507	−	17.2967i	−1.97005	−	1.15312i
$226$	−1.01436	+	1.75692i	−0.0674742	+	0.116869i
$227$	−4.67929	−	3.03877i	−0.310575	−	0.201690i	0.379934	−	0.925014i	$-0.375947\pi$
$227$	−4.67929	−	3.03877i	−0.310575	−	0.201690i	−0.690509	+	0.723324i	$0.742613\pi$
$228$	3.67759	−	2.97805i	0.243554	−	0.197226i
$229$	14.5622	−	6.48351i	0.962298	−	0.428443i	0.135398	−	0.990791i	$-0.456769\pi$
$229$	14.5622	−	6.48351i	0.962298	−	0.428443i	0.826900	+	0.562349i	$0.190102\pi$
$230$	8.05408	−	4.61809i	0.531071	−	0.304508i
$231$	23.1580	+	34.6115i	1.52369	+	2.27727i
$232$	−11.0142	+	11.0142i	−0.723119	+	0.723119i
$233$	−7.72921	+	9.54478i	−0.506357	+	0.625299i	−0.964660	−	0.263497i	$-0.915124\pi$
$233$	−7.72921	+	9.54478i	−0.506357	+	0.625299i	0.458303	+	0.888796i	$0.348458\pi$
$234$	−3.37512	+	3.74845i	−0.220639	+	0.245044i
$235$	7.30491	+	27.5909i	0.476520	+	1.79983i
$236$	−8.85204	+	7.97041i	−0.576218	+	0.518829i
$237$	6.92744	−	13.5959i	0.449985	−	0.883146i
$238$	−0.0151132	−	1.10180i	−0.000979641	−	0.0714189i
$239$	14.3549	+	4.66418i	0.928540	+	0.301701i	0.733965	−	0.679187i	$-0.237667\pi$
$239$	14.3549	+	4.66418i	0.928540	+	0.301701i	0.194574	+	0.980888i	$0.437667\pi$
$240$	−1.74077	+	3.39144i	−0.112366	+	0.218916i
$241$	−17.2487	−	15.5308i	−1.11108	−	1.00042i	−0.999978	−	0.00661623i	$-0.997894\pi$
$241$	−17.2487	−	15.5308i	−1.11108	−	1.00042i	−0.111106	−	0.993809i	$-0.535439\pi$
$242$	−10.6195	+	4.07644i	−0.682646	+	0.262043i
$243$	4.71744	+	17.6057i	0.302624	+	1.12941i
$244$	1.58686	−	1.15292i	0.101588	−	0.0738083i
$245$	−0.382702	−	15.6478i	−0.0244499	−	0.999701i
$246$	−14.4954	−	10.5315i	−0.924191	−	0.671464i
$247$	−0.365756	+	0.952826i	−0.0232725	+	0.0606269i
$248$	−0.502589	+	0.773919i	−0.0319144	+	0.0491439i
$249$	−9.43397	+	5.44671i	−0.597854	+	0.345171i
$250$	−8.69758	+	2.24738i	−0.550083	+	0.142137i
$251$			22.1623i			1.39887i	0.714697	+	0.699434i	$0.246565\pi$
$251$			22.1623i			1.39887i	−0.714697	+	0.699434i	$0.753435\pi$
$252$	14.1505	−	20.0491i	0.891398	−	1.26298i
$253$	4.05453	+	25.5993i	0.254906	+	1.60941i
$254$	3.01272	+	6.76669i	0.189035	+	0.424580i
$255$	−3.61848	+	0.369420i	−0.226598	+	0.0231340i
$256$	−13.0028	−	5.78920i	−0.812673	−	0.361825i
$257$	0.227789	−	0.0610358i	0.0142091	−	0.00380731i	−0.251708	−	0.967803i	$-0.580992\pi$
$257$	0.227789	−	0.0610358i	0.0142091	−	0.00380731i	0.265917	+	0.963996i	$0.414325\pi$
$258$	1.68558	−	10.6423i	0.104939	−	0.662562i
$259$	−16.2513	+	4.59432i	−1.00981	+	0.285477i
$260$	−0.137038	−	2.77290i	−0.00849875	−	0.171968i
$261$	−26.4824	−	29.4117i	−1.63922	−	1.82054i
$262$	−4.50673	+	0.236188i	−0.278427	+	0.0145917i
$263$	22.8710	−	1.19862i	1.41029	−	0.0739099i	0.668083	−	0.744086i	$-0.267115\pi$
$263$	22.8710	−	1.19862i	1.41029	−	0.0739099i	0.742202	+	0.670176i	$0.233782\pi$
$264$	28.3865	+	31.5264i	1.74707	+	1.94032i
$265$	−12.6522	−	3.43059i	−0.777219	−	0.210739i
$266$	−0.581157	+	2.29433i	−0.0356330	+	0.140674i
$267$	−1.54267	+	9.74001i	−0.0944096	+	0.596079i
$268$	−1.84044	+	0.493144i	−0.112423	+	0.0301236i
$269$	9.75209	+	4.34191i	0.594596	+	0.264731i	0.681894	−	0.731451i	$-0.261157\pi$
$269$	9.75209	+	4.34191i	0.594596	+	0.264731i	−0.0872981	+	0.996182i	$0.527823\pi$
$270$	18.7573	+	10.9042i	1.14153	+	0.663607i
$271$	−7.51186	−	16.8719i	−0.456313	−	1.02490i	−0.984438	−	0.175730i	$-0.943772\pi$
$271$	−7.51186	−	16.8719i	−0.456313	−	1.02490i	0.528125	−	0.849166i	$-0.322895\pi$
$272$	0.0440505	+	0.278124i	0.00267095	+	0.0168637i
$273$	−0.691695	+	7.57973i	−0.0418633	+	0.458746i
$274$		−	3.47355i		−	0.209845i
$275$	2.76999	−	24.9250i	0.167037	−	1.50303i
$276$	19.0211	−	10.9819i	1.14494	−	0.661030i
$277$	−5.68523	+	8.75448i	−0.341592	+	0.526006i	−0.967161	−	0.254163i	$-0.918200\pi$
$277$	−5.68523	+	8.75448i	−0.341592	+	0.526006i	0.625569	+	0.780169i	$0.284867\pi$
$278$	−1.85560	+	4.83399i	−0.111291	+	0.289924i
$279$	−1.89688	−	1.37816i	−0.113563	−	0.0825084i
$280$	−2.66331	−	15.7211i	−0.159163	−	0.939518i
$281$	23.9465	−	17.3981i	1.42853	−	1.03789i	0.438239	−	0.898858i	$-0.355602\pi$
$281$	23.9465	−	17.3981i	1.42853	−	1.03789i	0.990288	−	0.139028i	$-0.0443978\pi$
$282$	−8.32996	−	31.0878i	−0.496042	−	1.85125i
$283$	−26.0162	+	9.98669i	−1.54650	+	0.593647i	−0.974059	−	0.226296i	$-0.927338\pi$
$283$	−26.0162	+	9.98669i	−1.54650	+	0.593647i	−0.572445	+	0.819943i	$0.694005\pi$
$284$	7.66847	+	6.90472i	0.455040	+	0.409720i
$285$	7.71273	+	1.24514i	0.456862	+	0.0737560i
$286$	−3.51353	−	1.14161i	−0.207759	−	0.0675051i
$287$	−18.7986	+	0.257857i	−1.10965	+	0.0152208i
$288$	18.1159	−	35.5544i	1.06749	−	2.09506i
$289$	12.4338	−	11.1954i	0.731400	−	0.658555i
$290$	−10.3675	−	0.574316i	−0.608798	−	0.0337250i
$291$	7.47699	−	8.30404i	0.438309	−	0.486791i
$292$	1.02794	−	1.26940i	0.0601559	−	0.0742863i
$293$	−4.85076	+	4.85076i	−0.283385	+	0.283385i	−0.834457	−	0.551073i	$-0.814219\pi$
$293$	−4.85076	+	4.85076i	−0.283385	+	0.283385i	0.551073	+	0.834457i	$0.314219\pi$
$294$	0.484122	+	17.6437i	0.0282346	+	1.02900i
$295$	−19.5515	−	2.11387i	−1.13833	−	0.123074i
$296$	−15.7166	+	6.99749i	−0.913510	+	0.406721i
$297$	−47.0716	+	38.1178i	−2.73137	+	2.21182i
$298$	−1.49827	−	0.972990i	−0.0867926	−	0.0563638i
$299$	−2.36852	+	4.10240i	−0.136975	+	0.237248i
$300$	−20.5602	+	5.37797i	−1.18704	+	0.310497i
$301$	−5.27052	−	10.0024i	−0.303788	−	0.576529i
$302$	−4.51799	−	8.86706i	−0.259981	−	0.510242i
$303$	29.0113	+	11.1364i	1.66665	+	0.639768i
$304$	0.0632223	−	0.601520i	0.00362605	−	0.0344996i
$305$	3.16551	+	0.682714i	0.181256	+	0.0390921i
$306$	2.83648	−	0.298126i	0.162151	−	0.0170427i
$307$	−4.10345	−	4.10345i	−0.234196	−	0.234196i	0.580245	−	0.814442i	$-0.302957\pi$
$307$	−4.10345	−	4.10345i	−0.234196	−	0.234196i	−0.814442	+	0.580245i	$0.802957\pi$
$308$	17.6302	+	3.49540i	1.00457	+	0.199169i
$309$	−22.1650	+	7.20186i	−1.26093	+	0.409700i
$310$	−0.607849	+	0.0944181i	−0.0345235	+	0.00536259i
$311$	5.14856	+	24.2220i	0.291948	+	1.37351i	0.842496	+	0.538703i	$0.181085\pi$
$311$	5.14856	+	24.2220i	0.291948	+	1.37351i	−0.550548	+	0.834804i	$0.685581\pi$
$312$	0.405789	+	7.74291i	0.0229733	+	0.438356i
$313$	5.99503	−	3.89322i	0.338859	−	0.220058i	−0.363980	−	0.931407i	$-0.618582\pi$
$313$	5.99503	−	3.89322i	0.338859	−	0.220058i	0.702839	+	0.711349i	$0.251916\pi$
$314$	−4.17795	+	12.8584i	−0.235776	+	0.725642i
$315$	40.2443	−	4.66721i	2.26751	−	0.262968i
$316$	−2.03508	−	6.26334i	−0.114482	−	0.352340i
$317$	5.34470	+	4.32805i	0.300188	+	0.243088i	0.767566	−	0.640970i	$-0.221468\pi$
$317$	5.34470	+	4.32805i	0.300188	+	0.243088i	−0.467378	+	0.884058i	$0.654801\pi$
$318$	14.2786	+	3.82593i	0.800703	+	0.214548i
$319$	11.7901	−	26.4810i	0.660120	−	1.48265i
$320$	−2.46153	−	7.65333i	−0.137604	−	0.427834i
$321$	2.87720	−	3.96013i	0.160590	−	0.221033i
$322$	−4.32999	+	10.0957i	−0.241301	+	0.562614i
$323$	0.514197	−	0.261996i	0.0286107	−	0.0145779i
$324$	20.3537	+	11.7512i	1.13076	+	0.652844i
$325$	3.26029	−	3.22167i	0.180849	−	0.178706i
$326$	7.31107	+	12.6631i	0.404923	+	0.701347i
$327$	−0.981311	+	18.7245i	−0.0542666	+	1.03547i
$328$	−18.9161	+	2.99601i	−1.04447	+	0.165427i
$329$	−26.5338	−	20.8907i	−1.46286	−	1.15174i
$330$	−3.03979	+	28.1155i	−0.167335	+	1.54771i
$331$	−1.92457	−	18.3111i	−0.105784	−	1.00647i	−0.910697	−	0.413074i	$-0.864455\pi$
$331$	−1.92457	−	18.3111i	−0.105784	−	1.00647i	0.804913	−	0.593392i	$-0.202212\pi$
$332$	−1.21684	+	4.54131i	−0.0667828	+	0.249237i
$333$	−15.6652	−	40.8092i	−0.858447	−	2.23633i
$334$	−0.265851	−	0.0565083i	−0.0145467	−	0.00309200i
$335$	−2.63306	−	1.72110i	−0.143859	−	0.0940339i
$336$	−0.766641	−	4.44491i	−0.0418237	−	0.242490i
$337$	11.2377	+	5.72591i	0.612158	+	0.311910i	0.732442	−	0.680829i	$-0.238380\pi$
$337$	11.2377	+	5.72591i	0.612158	+	0.311910i	−0.120284	+	0.992740i	$0.538380\pi$
$338$	5.32118	+	8.19390i	0.289434	+	0.445689i
$339$	−7.75043	+	1.64740i	−0.420945	+	0.0894747i
$340$	−0.991554	+	1.21703i	−0.0537745	+	0.0660029i
$341$	0.357042	−	1.67975i	0.0193349	−	0.0909635i
$342$	−6.05066	−	0.958330i	−0.327182	−	0.0518206i
$343$	11.4931	+	14.5227i	0.620568	+	0.784153i
$344$	−6.76978	−	9.31780i	−0.365002	−	0.502382i
$345$	34.4527	+	11.3080i	1.85487	+	0.608801i
$346$	14.2241	+	1.49501i	0.764693	+	0.0803725i
$347$	−6.47761	−	7.99918i	−0.347736	−	0.429418i	0.573029	−	0.819535i	$-0.305768\pi$
$347$	−6.47761	−	7.99918i	−0.347736	−	0.429418i	−0.920766	+	0.390117i	$0.872435\pi$
$348$	−24.5305	−	1.28559i	−1.31497	−	0.0689149i
$349$	11.2771			0.603650			0.301825	−	0.953363i	$-0.402404\pi$
$349$	11.2771			0.603650			0.301825	+	0.953363i	$0.402404\pi$
$350$	6.62484	−	8.31201i	0.354113	−	0.444295i
$351$	−11.0702			−0.590883
$352$	29.1860	+	1.52957i	1.55562	+	0.0815266i
$353$	−10.4707	−	12.9303i	−0.557300	−	0.688208i	0.418163	−	0.908372i	$-0.362674\pi$
$353$	−10.4707	−	12.9303i	−0.557300	−	0.688208i	−0.975463	+	0.220164i	$0.929341\pi$
$354$	22.0540	+	2.31797i	1.17216	+	0.123199i
$355$	−0.0507607	+	17.0360i	−0.00269410	+	0.904177i
$356$	2.50168	+	3.44327i	0.132589	+	0.182493i
$357$	3.15847	−	2.92333i	0.167164	−	0.154719i
$358$	7.82462	+	1.23930i	0.413544	+	0.0654990i
$359$	−3.60963	+	16.9820i	−0.190509	+	0.896275i	0.774197	+	0.632945i	$0.218154\pi$
$359$	−3.60963	+	16.9820i	−0.190509	+	0.896275i	−0.964706	+	0.263330i	$0.915179\pi$
$360$	39.8969	−	10.5630i	2.10275	−	0.556721i
$361$	17.3723	−	3.69260i	0.914333	−	0.194348i
$362$	9.39256	+	14.4633i	0.493662	+	0.760173i
$363$	−39.5851	−	20.1696i	−2.07768	−	1.05863i
$364$	2.10211	+	2.52429i	0.110180	+	0.132309i
$365$	2.69341	−	0.133109i	0.140979	−	0.00696727i
$366$	−3.57182	−	0.759215i	−0.186702	−	0.0396848i
$367$	2.67456	+	6.96747i	0.139611	+	0.363699i	0.985504	−	0.169654i	$-0.0542651\pi$
$367$	2.67456	+	6.96747i	0.139611	+	0.363699i	−0.845893	+	0.533353i	$0.820932\pi$
$368$	0.726570	−	2.71160i	0.0378751	−	0.141352i
$369$	−5.08655	−	48.3953i	−0.264795	−	2.51936i
$370$	−10.4628	−	4.69576i	−0.543937	−	0.244121i
$371$	14.4030	−	5.75668i	0.747768	−	0.298872i
$372$	−1.43733	+	0.227651i	−0.0745222	+	0.0118032i
$373$	−1.54467	+	29.4741i	−0.0799802	+	1.52611i	0.604219	+	0.796818i	$0.293485\pi$
$373$	−1.54467	+	29.4741i	−0.0799802	+	1.52611i	−0.684199	+	0.729295i	$0.739848\pi$
$374$	1.04446	+	1.80906i	0.0540080	+	0.0935445i
$375$	−29.2535	−	19.3714i	−1.51064	−	1.00033i
$376$	−29.7932	−	17.2011i	−1.53647	−	0.887079i
$377$	4.72046	−	2.40520i	0.243116	−	0.123874i
$378$	−25.4918	+	3.03333i	−1.31116	+	0.156018i
$379$	−0.558890	+	0.769246i	−0.0287082	+	0.0395135i	−0.823130	−	0.567853i	$-0.807774\pi$
$379$	−0.558890	+	0.769246i	−0.0287082	+	0.0395135i	0.794422	+	0.607367i	$0.207774\pi$
$380$	2.73378	−	1.97379i	0.140240	−	0.101253i
$381$	−11.7668	+	26.4287i	−0.602831	+	1.35398i
$382$	0.563048	+	0.150868i	0.0288080	+	0.00771909i
$383$	−7.87866	−	6.38001i	−0.402581	−	0.326003i	0.406554	−	0.913627i	$-0.366730\pi$
$383$	−7.87866	−	6.38001i	−0.402581	−	0.326003i	−0.809135	+	0.587623i	$0.800064\pi$
$384$	−8.49991	−	26.1600i	−0.433759	−	1.33497i
$385$	15.1116	+	25.5370i	0.770160	+	1.30148i
$386$	3.65383	−	11.2453i	0.185975	−	0.572373i
$387$	24.5428	−	15.9383i	1.24758	−	0.810190i
$388$	−0.252400	−	4.81608i	−0.0128137	−	0.244500i
$389$	2.79772	+	13.1622i	0.141850	+	0.667352i	0.990399	+	0.138235i	$0.0441431\pi$
$389$	2.79772	+	13.1622i	0.141850	+	0.667352i	−0.848549	+	0.529116i	$0.822524\pi$
$390$	−3.66559	+	3.64381i	−0.185614	+	0.184512i
$391$	2.54742	−	0.827706i	0.128828	−	0.0418589i
$392$	13.7016	+	12.9697i	0.692033	+	0.655070i
$393$	−12.4635	−	12.4635i	−0.628702	−	0.628702i
$394$	−19.5246	+	2.05212i	−0.983634	+	0.103384i
$395$	5.46434	−	9.39972i	0.274941	−	0.472951i
$396$	−4.86281	+	46.2665i	−0.244365	+	2.32498i
$397$	25.1838	+	9.66717i	1.26394	+	0.485181i	0.895745	−	0.444567i	$-0.146643\pi$
$397$	25.1838	+	9.66717i	1.26394	+	0.485181i	0.368195	+	0.929749i	$0.379976\pi$
$398$	−0.355833	−	0.698361i	−0.0178363	−	0.0350057i
$399$	−8.17811	+	4.30925i	−0.409418	+	0.215732i
$400$	−1.37213	+	2.34422i	−0.0686065	+	0.117211i
$401$	−7.65133	+	13.2525i	−0.382089	+	0.661798i	−0.991361	−	0.131164i	$-0.958129\pi$
$401$	−7.65133	+	13.2525i	−0.382089	+	0.661798i	0.609271	+	0.792962i	$0.291462\pi$
$402$	2.97490	+	1.93193i	0.148375	+	0.0963557i
$403$	0.243917	−	0.197520i	0.0121504	−	0.00983916i
$404$	12.2523	−	5.45509i	0.609577	−	0.271401i
$405$	7.95413	+	37.9773i	0.395244	+	1.88711i
$406$	10.2110	−	6.83199i	0.506761	−	0.339066i
$407$	22.6386	−	22.6386i	1.12215	−	1.12215i
$408$	2.75904	−	3.40713i	0.136593	−	0.168678i
$409$	−8.68351	+	9.64401i	−0.429372	+	0.476866i	−0.918542	−	0.395322i	$-0.870633\pi$
$409$	−8.68351	+	9.64401i	−0.429372	+	0.476866i	0.489171	+	0.872188i	$0.337300\pi$
$410$	−9.89763	−	8.06389i	−0.488809	−	0.398247i
$411$	10.0820	−	9.07786i	0.497308	−	0.447778i
$412$	−4.56649	+	8.96225i	−0.224975	+	0.441538i
$413$	19.9896	−	11.9095i	0.983625	−	0.586030i
$414$	−27.0417	−	8.78639i	−1.32903	−	0.431827i
$415$	−6.92644	+	3.50324i	−0.340005	+	0.171967i
$416$	3.96956	+	3.57421i	0.194624	+	0.175240i
$417$	−18.8801	+	7.24740i	−0.924564	+	0.354907i
$418$	−1.16128	−	4.33396i	−0.0568001	−	0.211981i
$419$	−14.8800	+	10.8109i	−0.726935	+	0.528149i	−0.888592	−	0.458698i	$-0.848316\pi$
$419$	−14.8800	+	10.8109i	−0.726935	+	0.528149i	0.161658	+	0.986847i	$0.448316\pi$
$420$	15.6139	−	19.7106i	0.761881	−	0.961776i
$421$	19.9632	+	14.5041i	0.972947	+	0.706887i	0.956121	−	0.292971i	$-0.0946441\pi$
$421$	19.9632	+	14.5041i	0.972947	+	0.706887i	0.0168253	+	0.999858i	$0.494644\pi$
$422$	8.22839	−	21.4357i	0.400552	−	1.04347i
$423$	47.6072	−	73.3087i	2.31474	−	3.56439i
$424$	13.6839	−	7.90043i	0.664551	−	0.383679i
$425$	−2.58892	+	0.120214i	−0.125581	+	0.00583122i
$426$		−	19.2105i		−	0.930754i
$427$	−3.47864	+	1.60631i	−0.168343	+	0.0777350i
$428$	−0.330490	−	2.08663i	−0.0159748	−	0.100861i
$429$	−5.86880	−	13.1815i	−0.283348	−	0.636411i
$430$	1.61863	−	7.50502i	0.0780572	−	0.361924i
$431$	−27.9846	−	12.4596i	−1.34797	−	0.600156i	−0.399417	−	0.916769i	$-0.630787\pi$
$431$	−27.9846	−	12.4596i	−1.34797	−	0.600156i	−0.948555	+	0.316614i	$0.897454\pi$
$432$	6.33685	−	1.69795i	0.304882	−	0.0816928i
$433$	4.05772	−	25.6195i	0.195002	−	1.23119i	−0.674878	−	0.737929i	$-0.735804\pi$
$433$	4.05772	−	25.6195i	0.195002	−	1.23119i	0.869880	−	0.493263i	$-0.164196\pi$
$434$	0.507554	−	0.521672i	0.0243634	−	0.0250411i
$435$	−25.4276	−	31.5925i	−1.21916	−	1.51474i
$436$	5.41491	+	6.01387i	0.259327	+	0.288012i
$437$	−5.74534	+	0.301100i	−0.274837	+	0.0144036i
$438$	−3.03673	+	0.159148i	−0.145101	+	0.00760440i
$439$	−8.91058	−	9.89620i	−0.425279	−	0.472320i	0.491983	−	0.870605i	$-0.336272\pi$
$439$	−8.91058	−	9.89620i	−0.425279	−	0.472320i	−0.917262	+	0.398285i	$0.869606\pi$
$440$	18.9530	+	23.5481i	0.903549	+	1.12261i
$441$	−34.7309	+	33.0411i	−1.65385	+	1.57339i
$442$	−0.0597248	+	0.377088i	−0.00284082	+	0.0179362i
$443$	14.5088	−	3.88763i	0.689335	−	0.184707i	0.102886	−	0.994693i	$-0.467192\pi$
$443$	14.5088	−	3.88763i	0.689335	−	0.184707i	0.586449	+	0.809986i	$0.300526\pi$
$444$	−24.7852	−	11.0351i	−1.17625	−	0.523702i
$445$	−1.48139	+	6.86871i	−0.0702247	+	0.325608i
$446$	7.30940	+	16.4172i	0.346110	+	0.777376i
$447$	−1.09152	−	6.89157i	−0.0516270	−	0.325960i
$448$	7.77166	+	5.48517i	0.367176	+	0.259150i
$449$		−	3.87012i		−	0.182642i	−0.995822	−	0.0913211i	$-0.970891\pi$
$449$		−	3.87012i		−	0.182642i	0.995822	−	0.0913211i	$-0.0291090\pi$
$450$	22.9837	+	15.1213i	1.08346	+	0.712823i
$451$	30.8658	−	17.8204i	1.45341	−	0.839129i
$452$	−1.86253	+	2.86805i	−0.0876062	+	0.134902i
$453$	13.9292	−	36.2869i	0.654452	−	1.70491i
$454$	3.62680	+	2.63503i	0.170214	+	0.123668i
$455$	−0.790832	+	5.36532i	−0.0370748	+	0.251530i
$456$	−7.61836	+	5.53507i	−0.356763	+	0.259203i
$457$	10.9654	+	40.9235i	0.512941	+	1.91432i	0.386304	+	0.922371i	$0.373751\pi$
$457$	10.9654	+	40.9235i	0.512941	+	1.91432i	0.126636	+	0.991949i	$0.459582\pi$
$458$	−11.9571	+	4.58991i	−0.558720	+	0.214472i
$459$	4.65174	+	4.18845i	0.217125	+	0.195500i
$460$	13.9653	−	7.06336i	0.651137	−	0.329331i
$461$	−21.8890	−	7.11217i	−1.01947	−	0.331247i	−0.248852	−	0.968541i	$-0.580053\pi$
$461$	−21.8890	−	7.11217i	−1.01947	−	0.331247i	−0.770620	+	0.637295i	$0.780053\pi$
$462$	−17.1262	−	28.7455i	−0.796782	−	1.33736i
$463$	8.19728	−	16.0881i	0.380960	−	0.747676i	−0.618308	−	0.785936i	$-0.712182\pi$
$463$	8.19728	−	16.0881i	0.380960	−	0.747676i	0.999268	+	0.0382600i	$0.0121815\pi$
$464$	−2.33320	+	2.10082i	−0.108316	+	0.0975281i
$465$	−1.86262	−	1.51753i	−0.0863767	−	0.0703737i
$466$	6.60317	−	7.33356i	0.305886	−	0.339721i
$467$	−17.2567	+	21.3103i	−0.798545	+	0.986121i	0.201433	+	0.979502i	$0.435440\pi$
$467$	−17.2567	+	21.3103i	−0.798545	+	0.986121i	−0.999978	+	0.00661861i	$0.997893\pi$
$468$	−6.01224	+	6.01224i	−0.277916	+	0.277916i
$469$	3.71387	−	0.245755i	0.171491	−	0.0113479i
$470$	−4.70112	−	22.4457i	−0.216846	−	1.03534i
$471$	−48.2403	+	21.4780i	−2.22280	+	0.989653i
$472$	18.4211	−	14.9171i	0.847900	−	0.686616i
$473$	17.9756	+	11.6735i	0.826518	+	0.536747i
$474$	−6.13019	+	10.6178i	−0.281569	+	0.487691i
$475$	5.43813	+	1.18982i	0.249518	+	0.0545929i
$476$	0.0717609	−	1.85606i	0.00328916	−	0.0850721i
$477$	18.2266	+	35.7717i	0.834538	+	1.63787i
$478$	−11.3220	−	4.34610i	−0.517856	−	0.198786i
$479$	−3.81683	+	36.3147i	−0.174396	+	1.65926i	0.461242	+	0.887275i	$0.347404\pi$
$479$	−3.81683	+	36.3147i	−0.174396	+	1.65926i	−0.635637	+	0.771988i	$0.719263\pi$
$480$	20.5497	−	35.3495i	0.937962	−	1.61348i
$481$	5.81940	−	0.611643i	0.265342	−	0.0278885i
$482$	13.1870	+	13.1870i	0.600650	+	0.600650i
$483$	−40.6190	+	13.8167i	−1.84823	+	0.628680i
$484$	−18.2360	+	5.92525i	−0.828911	+	0.269330i
$485$	5.64676	−	5.61321i	0.256406	−	0.254883i
$486$	−3.04486	−	14.3249i	−0.138118	−	0.649792i
$487$	−1.88760	−	36.0175i	−0.0855352	−	1.63211i	−0.618368	−	0.785888i	$-0.712206\pi$
$487$	−1.88760	−	36.0175i	−0.0855352	−	1.63211i	0.532833	−	0.846220i	$-0.321127\pi$
$488$	−3.27353	+	2.12586i	−0.148186	+	0.0962330i
$489$	−17.6479	+	54.3145i	−0.798064	+	2.45619i
$490$	−0.350934	+	12.5716i	−0.0158536	+	0.567929i
$491$	2.89375	+	8.90606i	0.130593	+	0.401925i	0.994879	−	0.101077i	$-0.0322289\pi$
$491$	2.89375	+	8.90606i	0.130593	+	0.401925i	−0.864285	+	0.503002i	$0.832229\pi$
$492$	−23.4718	−	19.0071i	−1.05819	−	0.856907i
$493$	−2.89357	−	0.775330i	−0.130320	−	0.0349191i
$494$	0.333544	−	0.749152i	0.0150069	−	0.0337060i
$495$	−62.2704	+	44.9592i	−2.79885	+	2.02077i
$496$	−0.109328	+	0.150477i	−0.00490897	+	0.00675662i
$497$	−12.0708	−	16.1436i	−0.541447	−	0.724140i
$498$	7.79871	−	3.97364i	0.349468	−	0.178063i
$499$	−27.8046	−	16.0530i	−1.24470	−	0.718630i	−0.274656	−	0.961543i	$-0.588564\pi$
$499$	−27.8046	−	16.0530i	−1.24470	−	0.718630i	−0.970048	+	0.242912i	$0.921897\pi$
$500$	−14.8394	+	3.01584i	−0.663639	+	0.134872i
$501$	−0.530765	−	0.919313i	−0.0237128	−	0.0410719i
$502$	0.931948	−	17.7826i	0.0415949	−	0.793678i
$503$	31.9663	−	5.06296i	1.42531	−	0.225746i	0.604342	−	0.796725i	$-0.293436\pi$
$503$	31.9663	−	5.06296i	1.42531	−	0.225746i	0.820965	+	0.570979i	$0.193436\pi$
$504$	−30.2083	+	38.3685i	−1.34559	+	1.70907i
$505$	20.2011	+	9.06632i	0.898937	+	0.403446i
$506$	−2.17681	−	20.7110i	−0.0967710	−	0.920715i
$507$	−9.87630	+	36.8589i	−0.438622	+	1.63696i
$508$	4.47454	+	11.6566i	0.198525	+	0.517177i
$509$	25.8085	+	5.48576i	1.14394	+	0.243152i	0.740631	−	0.671912i	$-0.234527\pi$
$509$	25.8085	+	5.48576i	1.14394	+	0.243152i	0.403309	+	0.915064i	$0.367860\pi$
$510$	2.91894	−	0.144255i	0.129253	−	0.00638774i
$511$	−2.45192	+	2.04184i	−0.108467	+	0.0903257i
$512$	−5.42969	−	2.76657i	−0.239961	−	0.122266i
$513$	−7.32265	−	11.2759i	−0.323303	−	0.497843i
$514$	−0.185341	+	0.0393954i	−0.00817502	+	0.00173765i
$515$	−16.0531	+	4.25019i	−0.707384	+	0.187286i
$516$	3.77631	−	17.7662i	0.166243	−	0.782111i
$517$	63.2328	+	10.0151i	2.78097	+	0.440463i
$518$	13.2330	−	3.00302i	0.581423	−	0.131945i
$519$	32.8344	+	45.1926i	1.44127	+	1.98374i
$520$	−0.0164614	+	5.52467i	−0.000721879	+	0.242273i
$521$	8.94847	+	0.940522i	0.392039	+	0.0412050i	0.298498	−	0.954410i	$-0.403514\pi$
$521$	8.94847	+	0.940522i	0.392039	+	0.0412050i	0.0935417	+	0.995615i	$0.470181\pi$
$522$	20.0123	+	24.7131i	0.875913	+	1.08166i
$523$	−6.80248	−	0.356503i	−0.297452	−	0.0155888i	−0.0969736	−	0.995287i	$-0.530916\pi$
$523$	−6.80248	−	0.356503i	−0.297452	−	0.0155888i	−0.200478	+	0.979698i	$0.564250\pi$
$524$	−7.60728			−0.332326
$525$	41.4391	−	2.49419i	1.80855	−	0.108855i
$526$	−18.4017			−0.802353
$527$	−0.177227	−	0.00928807i	−0.00772013	−	0.000404595i
$528$	5.38123	+	6.64527i	0.234188	+	0.289198i
$529$	−3.68248	−	0.387044i	−0.160108	−	0.0168280i
$530$	10.0077	+	3.28469i	0.434705	+	0.142678i
$531$	35.4005	+	48.7246i	1.53625	+	2.11447i
$532$	−1.18071	+	3.81092i	−0.0511901	+	0.165224i
$533$	6.43377	+	1.01901i	0.278678	+	0.0441382i
$534$	1.64739	−	7.75036i	0.0712895	−	0.335391i
$535$	2.20305	−	2.70403i	0.0952462	−	0.116905i
$536$	3.70873	−	0.788315i	0.160193	−	0.0340500i
$537$	16.8520	+	25.9498i	0.727217	+	1.11982i
$538$	−7.64234	−	3.89397i	−0.329485	−	0.167881i
$539$	−32.4540	−	13.3953i	−1.39789	−	0.576977i
$540$	30.6133	+	20.0105i	1.31739	+	0.861113i
$541$	−3.42812	−	0.728670i	−0.147387	−	0.0313280i	0.133628	−	0.991032i	$-0.457337\pi$
$541$	−3.42812	−	0.728670i	−0.147387	−	0.0313280i	−0.281014	+	0.959704i	$0.590671\pi$
$542$	5.31791	+	13.8536i	0.228424	+	0.595065i
$543$	−17.4329	+	65.0606i	−0.748118	+	2.79202i
$544$	−0.315711	−	3.00379i	−0.0135360	−	0.128787i
$545$	−1.43611	+	13.2828i	−0.0615162	+	0.568975i
$546$	0.873742	−	6.05277i	0.0373927	−	0.259035i
$547$	−29.8893	+	4.73400i	−1.27798	+	0.202411i	−0.758274	−	0.651936i	$-0.773957\pi$
$547$	−29.8893	+	4.73400i	−1.27798	+	0.202411i	−0.519702	+	0.854348i	$0.673957\pi$
$548$	0.306441	−	5.84724i	0.0130905	−	0.249782i
$549$	−4.95876	−	8.58882i	−0.211635	−	0.366562i
$550$	−3.27072	+	19.8829i	−0.139464	+	0.847810i
$551$	5.57235	+	3.21720i	0.237390	+	0.137057i
$552$	−38.9431	+	19.8425i	−1.65753	+	0.844552i
$553$	1.52007	+	12.7745i	0.0646402	+	0.543228i
$554$	4.92987	−	6.78539i	0.209450	−	0.288283i
$555$	−13.7144	−	42.6404i	−0.582143	−	1.80998i
$556$	−3.55010	+	7.97365i	−0.150558	+	0.338158i
$557$	−14.5926	−	3.91007i	−0.618307	−	0.165675i	−0.0639490	−	0.997953i	$-0.520370\pi$
$557$	−14.5926	−	3.91007i	−0.618307	−	0.165675i	−0.554358	+	0.832278i	$0.687036\pi$
$558$	1.46407	+	1.18558i	0.0619791	+	0.0501897i
$559$	1.21052	+	3.72561i	0.0511997	+	0.157576i
$560$	−0.370245	−	3.19254i	−0.0156457	−	0.134909i
$561$	−2.52119	+	7.75941i	−0.106445	+	0.327603i
$562$	−19.9459	+	12.9530i	−0.841367	+	0.546390i
$563$	1.83668	+	35.0459i	0.0774067	+	1.47701i	0.710918	+	0.703275i	$0.248280\pi$
$563$	1.83668	+	35.0459i	0.0774067	+	1.47701i	−0.633511	+	0.773734i	$0.718387\pi$
$564$	−11.2797	−	53.0669i	−0.474962	−	2.23452i
$565$	−5.57895	+	0.866587i	−0.234708	+	0.0364576i
$566$	21.2950	−	6.91915i	0.895094	−	0.290834i
$567$	−34.5362	−	30.2492i	−1.45038	−	1.27035i
$568$	−14.5199	−	14.5199i	−0.609242	−	0.609242i
$569$	−2.55943	+	0.269006i	−0.107297	+	0.0112773i	−0.158025	−	0.987435i	$-0.550513\pi$
$569$	−2.55943	+	0.269006i	−0.107297	+	0.0112773i	0.0507279	+	0.998713i	$0.483846\pi$
$570$	−6.13621	−	1.32341i	−0.257017	−	0.0554317i
$571$	2.11736	−	20.1454i	0.0886089	−	0.843058i	−0.856466	−	0.516204i	$-0.827345\pi$
$571$	2.11736	−	20.1454i	0.0886089	−	0.843058i	0.945075	−	0.326854i	$-0.105989\pi$
$572$	−5.81382	−	2.23172i	−0.243088	−	0.0933127i
$573$	1.03359	+	2.02853i	0.0431787	+	0.0847430i
$574$	15.0945	+	0.583602i	0.630033	+	0.0243591i
$575$	24.0656	+	9.40286i	1.00361	+	0.392126i
$576$	−12.3107	+	21.3228i	−0.512946	+	0.888449i
$577$	−33.6097	−	21.8264i	−1.39919	−	0.908645i	−0.399225	−	0.916853i	$-0.630721\pi$
$577$	−33.6097	−	21.8264i	−1.39919	−	0.908645i	−0.999966	+	0.00820794i	$0.997387\pi$
$578$	−10.4475	+	8.46019i	−0.434557	+	0.351897i
$579$	42.1886	−	18.7836i	1.75330	−	0.780619i
$580$	−17.4015	−	1.88141i	−0.722558	−	0.0781213i
$581$	4.05686	−	8.23950i	0.168307	−	0.341832i
$582$	−6.34861	+	6.34861i	−0.263158	+	0.263158i
$583$	−18.5050	+	22.8517i	−0.766397	+	0.946422i
$584$	−2.17496	+	2.41554i	−0.0900006	+	0.0999558i
$585$	−14.0159	−	0.776425i	−0.579486	−	0.0321012i
$586$	4.09615	−	3.68819i	0.169211	−	0.152358i
$587$	8.81418	−	17.2988i	0.363800	−	0.713998i	−0.634460	−	0.772955i	$-0.718778\pi$
$587$	8.81418	−	17.2988i	0.363800	−	0.713998i	0.998261	+	0.0589574i	$0.0187776\pi$
$588$	−0.741595	+	29.7434i	−0.0305829	+	1.22660i
$589$	0.362534	+	0.117795i	0.0149380	+	0.00485364i
$590$	15.5989	+	2.51830i	0.642198	+	0.103677i
$591$	−56.9823	−	51.3071i	−2.34394	−	2.11049i
$592$	−3.23735	+	1.24270i	−0.133054	+	0.0510747i
$593$	−4.61082	−	17.2078i	−0.189344	−	0.706640i	−0.993659	−	0.112437i	$-0.964134\pi$
$593$	−4.61082	−	17.2078i	−0.189344	−	0.706640i	0.804315	−	0.594203i	$-0.202532\pi$
$594$	39.3724	−	28.6057i	1.61547	−	1.17371i
$595$	2.36230	−	1.95532i	0.0968448	−	0.0801601i
$596$	−2.43630	−	1.77007i	−0.0997945	−	0.0725050i
$597$	1.09705	−	2.85792i	0.0448994	−	0.116967i
$598$	2.07297	−	3.19210i	0.0847702	−	0.130535i
$599$	12.9831	−	7.49578i	0.530474	−	0.306269i	−0.210735	−	0.977543i	$-0.567586\pi$
$599$	12.9831	−	7.49578i	0.530474	−	0.306269i	0.741209	+	0.671274i	$0.234253\pi$
$600$	41.4178	−	8.54599i	1.69088	−	0.348889i
$601$		−	20.7383i		−	0.845932i	−0.906145	−	0.422966i	$-0.860989\pi$
$601$		−	20.7383i		−	0.845932i	0.906145	−	0.422966i	$-0.139011\pi$
$602$	3.80837	+	8.24741i	0.155217	+	0.336139i
$603$	1.50706	+	9.51522i	0.0613723	+	0.387490i
$604$	−6.82315	−	15.3250i	−0.277630	−	0.623567i
$605$	−27.3678	−	15.9097i	−1.11266	−	0.646822i
$606$	−22.8099	−	10.1556i	−0.926588	−	0.412544i
$607$	20.9910	−	5.62452i	0.851999	−	0.228292i	0.193711	−	0.981059i	$-0.437948\pi$
$607$	20.9910	−	5.62452i	0.851999	−	0.228292i	0.658288	+	0.752766i	$0.271281\pi$
$608$	−1.01486	+	6.40757i	−0.0411580	+	0.259861i
$609$	46.5154	+	11.7824i	1.88490	+	0.477448i
$610$	−2.51124	−	0.680912i	−0.101677	−	0.0275693i
$611$	7.82946	+	8.69550i	0.316746	+	0.351782i
$612$	4.80112	−	0.251616i	0.194074	−	0.0101710i
$613$	−7.07221	+	0.370639i	−0.285644	+	0.0149700i	−0.194620	−	0.980879i	$-0.562347\pi$
$613$	−7.07221	+	0.370639i	−0.285644	+	0.0149700i	−0.0910239	+	0.995849i	$0.529014\pi$
$614$	3.11999	+	3.46510i	0.125913	+	0.139840i
$615$	−2.46125	−	49.8023i	−0.0992472	−	2.00822i
$616$	−34.6713	−	8.78228i	−1.39694	−	0.353848i
$617$	1.94396	−	12.2737i	0.0782608	−	0.494119i	−0.917159	−	0.398521i	$-0.869524\pi$
$617$	1.94396	−	12.2737i	0.0782608	−	0.494119i	0.995420	−	0.0955982i	$-0.0304764\pi$
$618$	18.0877	−	4.84659i	0.727595	−	0.194959i
$619$	25.0310	+	11.1445i	1.00608	+	0.447937i	0.842560	−	0.538603i	$-0.181048\pi$
$619$	25.0310	+	11.1445i	1.00608	+	0.447937i	0.163522	+	0.986540i	$0.447714\pi$
$620$	−1.03156	+	0.105315i	−0.0414284	+	0.00422953i
$621$	−25.3815	−	57.0079i	−1.01853	−	2.28765i
$622$	−3.11255	−	19.6519i	−0.124802	−	0.787969i
$623$	−3.48548	−	7.54815i	−0.139643	−	0.302410i
$624$			1.56282i			0.0625628i
$625$	−20.0489	−	14.9346i	−0.801954	−	0.597385i
$626$	−4.97403	+	2.87176i	−0.198802	+	0.114778i
$627$	9.54440	−	14.6971i	0.381167	−	0.586945i
$628$	−8.16739	+	21.2768i	−0.325914	+	0.849036i
$629$	−2.67675	−	1.94477i	−0.106729	−	0.0775432i
$630$	−32.4877	+	2.05258i	−1.29434	+	0.0817766i
$631$	29.5709	−	21.4845i	1.17720	−	0.855286i	0.185347	−	0.982673i	$-0.440659\pi$
$631$	29.5709	−	21.4845i	1.17720	−	0.855286i	0.991853	+	0.127387i	$0.0406590\pi$
$632$	3.39187	+	12.6586i	0.134921	+	0.503534i
$633$	83.7214	−	32.1376i	3.32762	−	1.27736i
$634$	−4.10650	−	3.69751i	−0.163090	−	0.146847i
$635$	−9.41305	+	18.3389i	−0.373545	+	0.727756i
$636$	23.6985	+	7.70010i	0.939705	+	0.305329i
$637$	−3.06895	−	5.63547i	−0.121596	−	0.223285i
$638$	−10.5738	+	20.7522i	−0.418619	+	0.821587i
$639$	38.7731	−	34.9114i	1.53384	−	1.38107i
$640$	−5.01624	−	18.9465i	−0.198284	−	0.748925i
$641$	29.7244	−	33.0123i	1.17404	−	1.30391i	0.230339	−	0.973110i	$-0.426016\pi$
$641$	29.7244	−	33.0123i	1.17404	−	1.30391i	0.943703	−	0.330795i	$-0.107317\pi$
$642$	−2.47515	+	3.05655i	−0.0976863	+	0.120633i
$643$	9.86123	−	9.86123i	0.388889	−	0.388889i	−0.485402	−	0.874291i	$-0.661327\pi$
$643$	9.86123	−	9.86123i	0.388889	−	0.388889i	0.874291	+	0.485402i	$0.161327\pi$
$644$	−8.17960	+	16.6128i	−0.322321	+	0.654636i
$645$	26.0135	−	14.9157i	1.02428	−	0.587306i
$646$	−0.423601	+	0.188599i	−0.0166663	+	0.00742033i
$647$	37.7000	−	30.5289i	1.48214	−	1.20021i	0.551554	−	0.834139i	$-0.314035\pi$
$647$	37.7000	−	30.5289i	1.48214	−	1.20021i	0.930586	−	0.366074i	$-0.119298\pi$
$648$	−39.2236	−	25.4721i	−1.54085	−	1.00064i
$649$	−22.0556	+	38.2014i	−0.865759	+	1.49954i
$650$	−2.75148	+	2.44791i	−0.107922	+	0.0960151i
$651$	2.84061	+	0.109827i	0.111332	+	0.00430445i
$652$	11.1900	+	21.9616i	0.438235	+	0.860084i
$653$	−42.3671	−	16.2632i	−1.65795	−	0.636428i	−0.664151	−	0.747599i	$-0.731207\pi$
$653$	−42.3671	−	16.2632i	−1.65795	−	0.636428i	−0.993801	+	0.111171i	$0.964540\pi$
$654$	1.57478	−	14.9830i	0.0615786	−	0.585882i
$655$	−8.37594	−	9.35835i	−0.327275	−	0.365661i
$656$	−3.83914	+	0.403510i	−0.149893	+	0.0157544i
$657$	−5.83988	−	5.83988i	−0.227835	−	0.227835i
$658$	20.4119	+	17.8781i	0.795737	+	0.696962i
$659$	22.0985	−	7.18025i	0.860837	−	0.279703i	0.154859	−	0.987937i	$-0.450508\pi$
$659$	22.0985	−	7.18025i	0.860837	−	0.279703i	0.705978	+	0.708234i	$0.250508\pi$
$660$	−7.59744	+	47.0604i	−0.295730	+	1.83182i
$661$	−2.48937	−	11.7116i	−0.0968254	−	0.455528i	−0.999673	−	0.0255671i	$-0.991861\pi$
$661$	−2.48937	−	11.7116i	−0.0968254	−	0.455528i	0.902848	−	0.429960i	$-0.141472\pi$
$662$	0.774242	+	14.7734i	0.0300918	+	0.574186i
$663$	−1.25058	+	0.812139i	−0.0485686	+	0.0315408i
$664$	2.89110	−	8.89790i	0.112197	−	0.345306i
$665$	−5.98813	+	2.74349i	−0.232210	+	0.106388i
$666$	10.8534	+	33.4034i	0.420562	+	1.29436i
$667$	23.2090	+	18.7942i	0.898654	+	0.727716i
$668$	−0.442538	−	0.118578i	−0.0171223	−	0.00458790i
$669$	−28.5483	+	64.1206i	−1.10374	+	2.47905i
$670$	2.04035	+	1.49171i	0.0788255	+	0.0576297i
$671$	4.26953	−	5.87650i	0.164823	−	0.226860i
$672$	5.71654	+	48.0411i	0.220520	+	1.85323i
$673$	−20.5664	+	10.4791i	−0.792775	+	0.403939i	−0.802978	−	0.596009i	$-0.796752\pi$
$673$	−20.5664	+	10.4791i	−0.792775	+	0.403939i	0.0102030	+	0.999948i	$0.496752\pi$
$674$	−8.77620	−	5.06694i	−0.338046	−	0.195171i
$675$	9.09003	+	59.6923i	0.349875	+	2.29756i
$676$	8.23459	+	14.2627i	0.316715	+	0.548566i
$677$	0.604301	−	11.5308i	0.0232252	−	0.443163i	−0.962124	−	0.272613i	$-0.912112\pi$
$677$	0.604301	−	11.5308i	0.0232252	−	0.443163i	0.985349	−	0.170550i	$-0.0545545\pi$
$678$	6.28809	−	0.995936i	0.241493	−	0.0382487i
$679$	−1.34598	+	9.32416i	−0.0516539	+	0.357828i
$680$	2.09719	−	2.31526i	0.0804237	−	0.0887861i
$681$	1.83021	+	17.4132i	0.0701336	+	0.667277i
$682$	−0.357120	+	1.33279i	−0.0136748	+	0.0510352i
$683$	5.18841	+	13.5163i	0.198529	+	0.517186i	0.996316	−	0.0857529i	$-0.0273296\pi$
$683$	5.18841	+	13.5163i	0.198529	+	0.517186i	−0.797787	+	0.602939i	$0.793996\pi$
$684$	−10.1009	−	2.14701i	−0.386217	−	0.0820931i
$685$	7.53057	−	6.06107i	0.287728	−	0.231582i
$686$	−8.61116	−	12.1361i	−0.328776	−	0.463358i
$687$	−44.5713	−	22.7102i	−1.70050	−	0.866448i
$688$	−1.26437	−	1.94695i	−0.0482036	−	0.0742270i
$689$	−5.25678	+	1.11736i	−0.200267	+	0.0425681i
$690$	−27.1688	−	10.5221i	−1.03430	−	0.400570i
$691$	−9.11485	+	42.8820i	−0.346745	+	1.63131i	0.366518	+	0.930411i	$0.380550\pi$
$691$	−9.11485	+	42.8820i	−0.346745	+	1.63131i	−0.713263	+	0.700896i	$0.752784\pi$
$692$	23.8124	+	3.77152i	0.905213	+	0.143372i
$693$	26.8943	−	86.8056i	1.02163	−	3.29747i
$694$	4.86115	+	6.69080i	0.184527	+	0.253979i
$695$	−13.7179	+	4.41206i	−0.520348	+	0.167359i
$696$	48.6139	+	5.10952i	1.84270	+	0.193676i
$697$	−2.31795	−	2.86243i	−0.0877986	−	0.108422i
$698$	−9.04857	−	0.474216i	−0.342494	−	0.0179493i
$699$	38.5425			1.45781
$700$	11.8853	−	13.4077i	0.449222	−	0.506762i
$701$	−30.4358			−1.14955			−0.574773	−	0.818313i	$-0.694910\pi$
$701$	−30.4358			−1.14955			−0.574773	+	0.818313i	$0.694910\pi$
$702$	8.88255	+	0.465515i	0.335250	+	0.0175697i
$703$	4.47239	+	5.52294i	0.168679	+	0.208302i
$704$	−17.9343	−	1.88498i	−0.675926	−	0.0710427i
$705$	52.8625	−	72.3050i	1.99092	−	2.72316i
$706$	7.85780	+	10.8153i	0.295732	+	0.407041i
$707$	−25.5495	+	5.79808i	−0.960888	+	0.218059i
$708$	36.9204	+	5.84762i	1.38755	+	0.219767i
$709$	−0.889983	+	4.18704i	−0.0334240	+	0.157248i	−0.991695	−	0.128615i	$-0.958947\pi$
$709$	−0.889983	+	4.18704i	−0.0334240	+	0.157248i	0.958271	+	0.285863i	$0.0922801\pi$
$710$	0.757114	−	13.6673i	0.0284140	−	0.512924i
$711$	−32.5706	+	6.92309i	−1.22149	+	0.259636i
$712$	−4.61281	−	7.10310i	−0.172872	−	0.266200i
$713$	1.57641	+	0.803220i	0.0590370	+	0.0300808i
$714$	−2.65724	+	2.21281i	−0.0994445	+	0.0828125i
$715$	−3.65584	−	9.60927i	−0.136721	−	0.359366i
$716$	13.0623	+	2.77648i	0.488162	+	0.103762i
$717$	−16.9746	−	44.2203i	−0.633927	−	1.65144i
$718$	3.61042	−	13.4743i	0.134740	−	0.502856i
$719$	1.92780	+	18.3418i	0.0718947	+	0.684033i	0.969810	+	0.243864i	$0.0784149\pi$
$719$	1.92780	+	18.3418i	0.0718947	+	0.684033i	−0.897915	+	0.440169i	$0.854918\pi$
$720$	8.14212	−	1.70532i	0.303439	−	0.0635535i
$721$	12.1547	−	15.4381i	0.452667	−	0.574945i
$722$	−14.0946	+	2.23236i	−0.524545	+	0.0830798i
$723$	−3.81205	+	72.7383i	−0.141772	+	2.70517i
$724$	14.5351	+	25.1755i	0.540193	+	0.935641i
$725$	−16.8453	−	23.4785i	−0.625619	−	0.871971i
$726$	30.9143	+	17.8484i	1.14734	+	0.662415i
$727$	−30.7663	+	15.6762i	−1.14106	+	0.581398i	−0.919243	−	0.393690i	$-0.871198\pi$
$727$	−30.7663	+	15.6762i	−1.14106	+	0.581398i	−0.221816	+	0.975089i	$0.571198\pi$
$728$	−3.91447	−	5.23527i	−0.145080	−	0.194032i
$729$	3.02204	−	4.15948i	0.111927	−	0.154055i
$730$	−2.16675	−	0.00645606i	−0.0801948	−	0.000238950i
$731$	0.900929	−	2.02352i	0.0333221	−	0.0748426i
$732$	−5.94569	−	1.59314i	−0.219759	−	0.0588843i
$733$	21.7471	+	17.6104i	0.803247	+	0.650456i	0.940391	−	0.340095i	$-0.110459\pi$
$733$	21.7471	+	17.6104i	0.803247	+	0.650456i	−0.137144	+	0.990551i	$0.543792\pi$
$734$	−1.85303	−	5.70305i	−0.0683967	−	0.210504i
$735$	−37.4063	+	31.8364i	−1.37975	+	1.17430i
$736$	−9.30467	+	28.6368i	−0.342975	+	1.05557i
$737$	−5.91764	+	3.84296i	−0.217979	+	0.141557i
$738$	2.04629	+	39.0455i	0.0753249	+	1.43728i
$739$	1.73453	+	8.16031i	0.0638056	+	0.300182i	0.998467	−	0.0553586i	$-0.0176302\pi$
$739$	1.73453	+	8.16031i	0.0638056	+	0.300182i	−0.934661	+	0.355540i	$0.884297\pi$
$740$	−17.1985	−	8.82770i	−0.632228	−	0.324513i
$741$	3.04611	−	0.989740i	0.111902	−	0.0363590i
$742$	−11.7988	+	4.01340i	−0.433149	+	0.147337i
$743$	−31.5650	−	31.5650i	−1.15801	−	1.15801i	−0.984903	−	0.173106i	$-0.944620\pi$
$743$	−31.5650	−	31.5650i	−1.15801	−	1.15801i	−0.173106	−	0.984903i	$-0.555380\pi$
$744$	2.88002	−	0.302702i	0.105587	−	0.0110976i
$745$	−0.504951	−	4.94601i	−0.0185000	−	0.181208i
$746$	2.47884	−	23.5846i	0.0907569	−	0.863495i
$747$	22.1927	+	8.51899i	0.811989	+	0.311694i
$748$	1.59861	+	3.13745i	0.0584510	+	0.114717i
$749$	−0.159440	+	4.12382i	−0.00582580	+	0.150681i
$750$	22.6579	+	16.7734i	0.827351	+	0.612479i
$751$	22.8072	−	39.5032i	0.832247	−	1.44149i	−0.0640055	−	0.997950i	$-0.520388\pi$
$751$	22.8072	−	39.5032i	0.832247	−	1.44149i	0.896252	−	0.443544i	$-0.146279\pi$
$752$	−5.81549	−	3.77662i	−0.212069	−	0.137719i
$753$	54.0497	−	43.7686i	1.96968	−	1.59502i
$754$	−3.88877	+	1.73139i	−0.141621	+	0.0630535i
$755$	11.3400	−	25.2672i	0.412706	−	0.919569i
$756$	−43.1795	+	2.85728i	−1.57042	+	0.103918i
$757$	11.9819	−	11.9819i	0.435488	−	0.435488i	−0.455002	−	0.890490i	$-0.650362\pi$
$757$	11.9819	−	11.9819i	0.435488	−	0.435488i	0.890490	+	0.455002i	$0.150362\pi$
$758$	0.480792	−	0.593728i	0.0174631	−	0.0215652i
$759$	54.4247	−	60.4447i	1.97549	−	2.19401i
$760$	−5.63821	+	3.63766i	−0.204519	+	0.131952i
$761$	−17.1557	+	15.4470i	−0.621892	+	0.559954i	−0.918687	−	0.394987i	$-0.870749\pi$
$761$	−17.1557	+	15.4470i	−0.621892	+	0.559954i	0.296794	+	0.954941i	$0.404082\pi$
$762$	10.5528	−	20.7111i	0.382289	−	0.750285i
$763$	−8.09106	−	13.5805i	−0.292916	−	0.491647i
$764$	0.934503	+	0.303638i	0.0338091	+	0.0109852i
$765$	5.59577	+	5.62921i	0.202315	+	0.203525i
$766$	6.05342	+	5.45053i	0.218719	+	0.196936i
$767$	−7.52662	+	2.88920i	−0.271770	+	0.104323i
$768$	11.5606	+	43.1446i	0.417155	+	1.55685i
$769$	−33.2899	+	24.1865i	−1.20046	+	0.872188i	−0.994330	−	0.106336i	$-0.966088\pi$
$769$	−33.2899	+	24.1865i	−1.20046	+	0.872188i	−0.206133	+	0.978524i	$0.566088\pi$
$770$	−11.0515	−	21.1259i	−0.398267	−	0.761325i
$771$	−0.598719	−	0.434994i	−0.0215623	−	0.0156659i
$772$	7.14280	−	18.6076i	0.257075	−	0.669703i
$773$	9.85916	−	15.1818i	0.354609	−	0.546050i	−0.615681	−	0.787996i	$-0.711119\pi$
$773$	9.85916	−	15.1818i	0.354609	−	0.546050i	0.970290	+	0.241945i	$0.0777855\pi$
$774$	−20.3630	+	11.7566i	−0.731933	+	0.422582i
$775$	−1.26535	−	1.15305i	−0.0454525	−	0.0414188i
$776$			9.59695i			0.344510i
$777$	43.2996	+	30.5605i	1.55337	+	1.09635i
$778$	−1.69136	−	10.6788i	−0.0606381	−	0.382854i
$779$	3.21783	+	7.22737i	0.115291	+	0.258947i
$780$	−6.49197	+	5.81047i	−0.232450	+	0.208048i
$781$	34.9096	+	15.5428i	1.24916	+	0.556164i
$782$	−2.07881	+	0.557016i	−0.0743382	+	0.0199189i
$783$	−10.9178	+	68.9320i	−0.390169	+	2.46343i
$784$	2.62111	+	2.75516i	0.0936111	+	0.0983985i
$785$	−35.1669	+	13.3792i	−1.25516	+	0.477525i
$786$	9.47643	+	10.5246i	0.338013	+	0.375401i
$787$	−15.3321	+	0.803521i	−0.546530	+	0.0286424i	−0.323603	−	0.946193i	$-0.604894\pi$
$787$	−15.3321	+	0.803521i	−0.546530	+	0.0286424i	−0.222927	+	0.974835i	$0.571561\pi$
$788$	−33.0480	+	1.73197i	−1.17728	+	0.0616989i
$789$	−48.0915	−	53.4110i	−1.71210	−	1.90148i
$790$	−4.77977	+	7.31240i	−0.170056	+	0.260164i
$791$	4.65843	−	4.78800i	0.165635	−	0.170242i
$792$	14.4820	−	91.4358i	0.514596	−	3.24903i
$793$	1.28234	−	0.343602i	0.0455373	−	0.0122017i
$794$	−19.8006	−	8.81579i	−0.702697	−	0.312861i
$795$	16.6205	+	37.6316i	0.589468	+	1.33465i
$796$	−0.537385	−	1.20699i	−0.0190471	−	0.0427805i
$797$	2.39964	+	15.1507i	0.0849997	+	0.536667i	0.993039	+	0.117783i	$0.0375787\pi$
$797$	2.39964	+	15.1507i	0.0849997	+	0.536667i	−0.908040	+	0.418884i	$0.862421\pi$
$798$	6.74319	−	3.11377i	0.238706	−	0.110226i
$799$		−	6.61618i		−	0.234064i
$800$	16.0132	−	24.3394i	0.566153	−	0.860528i
$801$	18.6365	−	10.7598i	0.658489	−	0.380179i
$802$	6.69659	−	10.3118i	0.236465	−	0.364124i
$803$	2.16773	−	5.64714i	0.0764977	−	0.199283i
$804$	4.83740	+	3.51458i	0.170602	+	0.123950i
$805$	−29.4428	+	8.22898i	−1.03772	+	0.290033i
$806$	−0.204021	+	0.148230i	−0.00718632	+	0.00522117i
$807$	−8.67043	−	32.3585i	−0.305214	−	1.13907i
$808$	−24.9163	+	9.56448i	−0.876553	+	0.336477i
$809$	−15.3954	−	13.8621i	−0.541275	−	0.487366i	0.352544	−	0.935795i	$-0.385317\pi$
$809$	−15.3954	−	13.8621i	−0.541275	−	0.487366i	−0.893818	+	0.448430i	$0.851984\pi$
$810$	−4.78527	−	30.8068i	−0.168137	−	1.08244i
$811$	−27.8184	−	9.03875i	−0.976837	−	0.317394i	−0.223264	−	0.974758i	$-0.571671\pi$
$811$	−27.8184	−	9.03875i	−0.976837	−	0.317394i	−0.753573	+	0.657364i	$0.771671\pi$
$812$	17.7914	−	10.5999i	0.624357	−	0.371983i
$813$	−26.3122	+	51.6407i	−0.922811	+	1.81112i
$814$	−19.1168	+	17.2129i	−0.670045	+	0.603311i
$815$	−14.6961	+	37.9464i	−0.514783	+	1.32920i
$816$	0.591298	−	0.656703i	0.0206996	−	0.0229892i
$817$	−2.99410	+	3.69741i	−0.104750	+	0.129356i
$818$	7.37305	−	7.37305i	0.257793	−	0.257793i
$819$	13.8043	−	9.23625i	0.482361	−	0.322741i
$820$	−15.9499	−	14.4476i	−0.556994	−	0.504533i
$821$	27.1109	−	12.0706i	0.946179	−	0.421266i	0.125140	−	0.992139i	$-0.460062\pi$
$821$	27.1109	−	12.0706i	0.946179	−	0.421266i	0.821038	+	0.570873i	$0.193395\pi$
$822$	−8.47136	+	6.85997i	−0.295472	+	0.239269i
$823$	12.4789	+	8.10388i	0.434986	+	0.282484i	0.743499	−	0.668737i	$-0.233165\pi$
$823$	12.4789	+	8.10388i	0.434986	+	0.282484i	−0.308513	+	0.951220i	$0.599831\pi$
$824$	10.0081	−	17.3345i	0.348647	−	0.603875i
$825$	−66.2580	+	42.4692i	−2.30681	+	1.47859i
$826$	−16.5402	+	8.71543i	−0.575506	+	0.303249i
$827$	16.7900	+	32.9522i	0.583844	+	1.14586i	0.974304	+	0.225239i	$0.0723162\pi$
$827$	16.7900	+	32.9522i	0.583844	+	1.14586i	−0.390459	+	0.920620i	$0.627684\pi$
$828$	−44.7458	−	17.1763i	−1.55502	−	0.596918i
$829$	4.28022	−	40.7236i	0.148658	−	1.41439i	−0.624920	−	0.780689i	$-0.714869\pi$
$829$	4.28022	−	40.7236i	0.148658	−	1.41439i	0.773579	−	0.633700i	$-0.218465\pi$
$830$	5.70498	−	2.51968i	0.198023	−	0.0874593i
$831$	32.5784	−	3.42413i	1.13013	−	0.118782i
$832$	−2.33053	−	2.33053i	−0.0807967	−	0.0807967i
$833$	−0.842612	+	3.52919i	−0.0291948	+	0.122279i
$834$	15.4539	−	5.02127i	0.535124	−	0.173872i
$835$	−0.341380	−	0.674961i	−0.0118140	−	0.0233580i
$836$	−1.57251	−	7.39807i	−0.0543863	−	0.255867i
$837$	0.216390	+	4.12896i	0.00747952	+	0.142718i
$838$	12.3941	−	8.04880i	0.428146	−	0.278041i
$839$	−6.83090	+	21.0234i	−0.235829	+	0.725807i	0.761181	+	0.648539i	$0.224620\pi$
$839$	−6.83090	+	21.0234i	−0.235829	+	0.725807i	−0.997010	+	0.0772679i	$0.975380\pi$
$840$	−33.0812	+	37.5432i	−1.14141	+	1.29537i
$841$	−1.35975	−	4.18488i	−0.0468879	−	0.144306i
$842$	−15.4082	−	12.4773i	−0.531003	−	0.429998i
$843$	−89.7232	−	24.0413i	−3.09023	−	0.828025i
$844$	15.7424	−	35.3581i	0.541877	−	1.21707i
$845$	−8.47913	+	25.8339i	−0.291691	+	0.888713i
$846$	−41.2820	+	56.8198i	−1.41930	+	1.95350i
$847$	37.1937	−	4.42578i	1.27799	−	0.152072i
$848$	2.83772	−	1.44589i	0.0974479	−	0.0496522i
$849$	75.7356	+	43.7260i	2.59924	+	1.50067i
$850$	2.08236	+	0.0124094i	0.0714243	+	0.000425638i
$851$	16.4924	+	28.5656i	0.565351	+	0.979217i
$852$	1.69478	−	32.3383i	0.0580621	−	1.10789i
$853$	14.5805	−	2.30932i	0.499226	−	0.0790697i	0.0982567	−	0.995161i	$-0.468673\pi$
$853$	14.5805	−	2.30932i	0.499226	−	0.0790697i	0.400969	+	0.916091i	$0.368673\pi$
$854$	2.85875	−	1.14260i	0.0978244	−	0.0390990i
$855$	−8.48029	−	14.7899i	−0.290020	−	0.505804i
$856$	0.439444	+	4.18103i	0.0150199	+	0.142905i
$857$	4.99249	−	18.6322i	0.170540	−	0.636465i	−0.826728	−	0.562602i	$-0.809800\pi$
$857$	4.99249	−	18.6322i	0.170540	−	0.636465i	0.997268	−	0.0738633i	$-0.0235328\pi$
$858$	4.15473	+	10.8234i	0.141840	+	0.369506i
$859$	29.3200	+	6.23216i	1.00039	+	0.212639i	0.678864	−	0.734264i	$-0.262472\pi$
$859$	29.3200	+	6.23216i	1.00039	+	0.212639i	0.321522	+	0.946902i	$0.395806\pi$
$860$	3.38684	−	12.4909i	0.115490	−	0.425935i
$861$	37.7545	+	45.3371i	1.28667	+	1.54508i
$862$	21.9305	+	11.1741i	0.746955	+	0.380592i
$863$	−14.0374	−	21.6157i	−0.477839	−	0.735807i	0.514749	−	0.857341i	$-0.327885\pi$
$863$	−14.0374	−	21.6157i	−0.477839	−	0.735807i	−0.992587	+	0.121534i	$0.961219\pi$
$864$	−68.8289	+	14.6300i	−2.34161	+	0.497724i
$865$	21.5788	+	33.4462i	0.733702	+	1.13721i
$866$	−4.33318	+	20.3860i	−0.147247	+	0.692745i
$867$	−51.8593	−	8.21371i	−1.76124	−	0.278952i
$868$	0.900420	−	0.833385i	0.0305622	−	0.0282869i
$869$	−14.3350	−	19.7304i	−0.486282	−	0.669309i
$870$	19.0742	+	26.4186i	0.646676	+	0.895674i
$871$	−1.28254	−	0.134800i	−0.0434571	−	0.00456753i
$872$	−10.1343	−	12.5149i	−0.343192	−	0.423807i
$873$	−24.3509	−	1.27618i	−0.824154	−	0.0431921i
$874$	4.62263			0.156363
$875$	29.5801	−	0.141310i	0.999989	−	0.00477715i
$876$	−5.12595			−0.173190
$877$	−21.5554	−	1.12967i	−0.727876	−	0.0381463i	−0.315201	−	0.949025i	$-0.602072\pi$
$877$	−21.5554	−	1.12967i	−0.727876	−	0.0381463i	−0.412674	+	0.910879i	$0.635405\pi$
$878$	6.73356	+	8.31526i	0.227247	+	0.280626i
$879$	21.4100	+	2.25028i	0.722141	+	0.0759000i
$880$	3.56656	+	4.93984i	0.120229	+	0.166522i
$881$	−18.9856	−	26.1314i	−0.639640	−	0.880388i	0.358957	−	0.933354i	$-0.383133\pi$
$881$	−18.9856	−	26.1314i	−0.639640	−	0.880388i	−0.998596	+	0.0529657i	$0.983133\pi$
$882$	29.2569	−	25.0512i	0.985131	−	0.843517i
$883$	−17.4297	−	2.76060i	−0.586557	−	0.0929015i	−0.143899	−	0.989592i	$-0.545964\pi$
$883$	−17.4297	−	2.76060i	−0.586557	−	0.0929015i	−0.442657	+	0.896691i	$0.645964\pi$
$884$	−0.133806	+	0.629506i	−0.00450037	+	0.0211726i
$885$	33.4573	+	51.8573i	1.12465	+	1.74316i
$886$	−11.8051	+	2.50926i	−0.396601	+	0.0843001i
$887$	−12.5598	−	19.3404i	−0.421717	−	0.649387i	0.562409	−	0.826859i	$-0.309875\pi$
$887$	−12.5598	−	19.3404i	−0.421717	−	0.649387i	−0.984126	+	0.177472i	$0.943208\pi$
$888$	48.1046	+	24.5105i	1.61429	+	0.822519i
$889$	−4.14553	−	24.0354i	−0.139037	−	0.806122i
$890$	1.47748	−	5.44904i	0.0495253	−	0.182652i
$891$	85.1326	+	18.0955i	2.85205	+	0.606222i
$892$	10.8560	+	28.2809i	0.363486	+	0.946914i
$893$	−3.67808	+	13.7268i	−0.123082	+	0.459349i
$894$	0.586018	+	5.57559i	0.0195994	+	0.186476i
$895$	10.9666	+	19.1261i	0.366573	+	0.639314i
$896$	18.2206	+	14.3455i	0.608708	+	0.479249i
$897$	14.6826	−	2.32550i	0.490239	−	0.0776462i
$898$	−0.162743	+	3.10532i	−0.00543080	+	0.103626i
$899$	−0.989361	−	1.71362i	−0.0329970	−	0.0571525i
$900$	37.3558	+	27.4822i	1.24519	+	0.916073i
$901$	2.63168	+	1.51940i	0.0876739	+	0.0506185i
$902$	−25.5156	+	13.0008i	−0.849576	+	0.432881i
$903$	−13.9852	+	32.6078i	−0.465399	+	1.08512i
$904$	3.99998	−	5.50549i	0.133037	−	0.183110i
$905$	−14.9667	+	45.6001i	−0.497511	+	1.51580i
$906$	−12.7025	+	28.5303i	−0.422012	+	0.947855i
$907$	−39.8182	−	10.6692i	−1.32214	−	0.354266i	−0.472361	−	0.881405i	$-0.656598\pi$
$907$	−39.8182	−	10.6692i	−1.32214	−	0.354266i	−0.849779	+	0.527139i	$0.823265\pi$
$908$	5.87275	+	4.75566i	0.194894	+	0.157822i
$909$	−20.9552	−	64.4936i	−0.695041	−	2.13912i
$910$	0.860169	−	4.27179i	0.0285143	−	0.141609i
$911$	0.709840	−	2.18466i	0.0235181	−	0.0723812i	−0.938609	−	0.344984i	$-0.887884\pi$
$911$	0.709840	−	2.18466i	0.0235181	−	0.0723812i	0.962127	+	0.272603i	$0.0878844\pi$
$912$	−1.59186	+	1.03376i	−0.0527117	+	0.0342314i
$913$	0.911208	+	17.3869i	0.0301566	+	0.575422i
$914$	−7.07760	−	33.2975i	−0.234106	−	1.10138i
$915$	−4.58660	−	9.06840i	−0.151628	−	0.299792i
$916$	−20.5331	+	6.67160i	−0.678432	+	0.220436i
$917$	14.5766	+	2.88998i	0.481361	+	0.0954355i
$918$	−3.55635	−	3.55635i	−0.117377	−	0.117377i
$919$	−25.3891	+	2.66851i	−0.837511	+	0.0880259i	−0.513566	−	0.858050i	$-0.671676\pi$
$919$	−25.3891	+	2.66851i	−0.837511	+	0.0880259i	−0.323945	+	0.946076i	$0.605009\pi$
$920$	−28.4880	+	12.5821i	−0.939220	+	0.414819i
$921$	−1.90360	+	18.1116i	−0.0627258	+	0.596796i
$922$	17.2643	+	6.62715i	0.568570	+	0.218254i
$923$	3.17074	+	6.22293i	0.104366	+	0.204830i
$924$	−26.2936	−	49.9000i	−0.864995	−	1.64159i
$925$	−8.07654	−	30.8769i	−0.265555	−	1.01523i
$926$	−7.25389	+	12.5641i	−0.238378	+	0.412882i
$927$	42.6529	+	27.6991i	1.40091	+	0.909759i
$928$	26.1708	−	21.1927i	0.859100	−	0.695685i
$929$	−41.0517	+	18.2774i	−1.34686	+	0.599662i	−0.948270	−	0.317466i	$-0.897168\pi$
$929$	−41.0517	+	18.2774i	−1.34686	+	0.599662i	−0.398593	+	0.917128i	$0.630501\pi$
$930$	1.43072	+	1.29597i	0.0469151	+	0.0424964i
$931$	3.71015	−	6.85369i	0.121595	−	0.224621i
$932$	11.7625	−	11.7625i	0.385293	−	0.385293i
$933$	48.9052	−	60.3929i	1.60108	−	1.97718i
$934$	14.7426	−	16.3733i	0.482393	−	0.535752i
$935$	−2.09950	+	5.42105i	−0.0686610	+	0.177287i
$936$	12.5739	−	11.3216i	0.410989	−	0.370057i
$937$	−25.9319	+	50.8942i	−0.847158	+	1.66264i	−0.102956	+	0.994686i	$0.532830\pi$
$937$	−25.9319	+	50.8942i	−0.847158	+	1.66264i	−0.744202	+	0.667955i	$0.767170\pi$
$938$	−2.99029	+	0.0410173i	−0.0976363	+	0.00133926i
$939$	−21.3345	−	6.93200i	−0.696226	−	0.226217i
$940$	−5.93349	−	38.1989i	−0.193529	−	1.24591i
$941$	24.2474	+	21.8325i	0.790444	+	0.711719i	0.961879	−	0.273477i	$-0.0881736\pi$
$941$	24.2474	+	21.8325i	0.790444	+	0.711719i	−0.171435	+	0.985195i	$0.554840\pi$
$942$	39.6104	−	15.2050i	1.29058	−	0.495407i
$943$	9.50367	+	35.4682i	0.309482	+	1.15500i
$944$	3.86527	−	2.80828i	0.125804	−	0.0914018i
$945$	−51.0574	−	49.9726i	−1.66090	−	1.62561i
$946$	−13.9324	−	10.1225i	−0.452983	−	0.329111i
$947$	−13.1382	+	34.2262i	−0.426934	+	1.11220i	0.536415	+	0.843954i	$0.319778\pi$
$947$	−13.1382	+	34.2262i	−0.426934	+	1.11220i	−0.963350	+	0.268248i	$0.913555\pi$
$948$	−11.2560	+	17.3328i	−0.365579	+	0.562942i
$949$	0.957429	−	0.552772i	0.0310795	−	0.0179437i
$950$	−4.31343	−	1.18338i	−0.139946	−	0.0383938i
$951$		−	21.5823i		−	0.699854i
$952$	−0.335907	+	3.68093i	−0.0108868	+	0.119300i
$953$	−7.31025	−	46.1551i	−0.236802	−	1.49511i	−0.763916	−	0.645316i	$-0.776726\pi$
$953$	−7.31025	−	46.1551i	−0.236802	−	1.49511i	0.527113	−	0.849795i	$-0.323274\pi$
$954$	−13.1205	−	29.4691i	−0.424791	−	0.954096i
$955$	0.655396	+	1.48393i	0.0212081	+	0.0480188i
$956$	−18.6756	−	8.31490i	−0.604011	−	0.268923i
$957$	−87.8669	+	23.5439i	−2.84034	+	0.761065i
$958$	4.58964	−	28.9779i	0.148285	−	0.936232i
$959$	−2.80853	+	11.0877i	−0.0906920	+	0.358040i
$960$	−13.8038	+	21.1179i	−0.445515	+	0.681578i
$961$	20.6646	+	22.9504i	0.666600	+	0.740335i
$962$	−4.69511	+	0.246060i	−0.151377	+	0.00793331i
$963$	−10.6672	+	0.559045i	−0.343746	+	0.0180150i
$964$	21.0351	+	23.3618i	0.677493	+	0.752433i
$965$	30.7553	−	11.7008i	0.990047	−	0.376663i
$966$	33.1731	−	9.37819i	1.06733	−	0.301738i
$967$	−1.12542	+	7.10565i	−0.0361912	+	0.228502i	−0.999154	−	0.0411332i	$-0.986903\pi$
$967$	−1.12542	+	7.10565i	−0.0361912	+	0.228502i	0.962962	+	0.269635i	$0.0869032\pi$
$968$	36.8563	−	9.87561i	1.18461	−	0.317414i
$969$	−1.65446	−	0.736612i	−0.0531488	−	0.0236634i
$970$	−4.76691	+	4.26649i	−0.153056	+	0.136989i
$971$	9.07173	+	20.3754i	0.291126	+	0.653879i	0.998602	−	0.0528579i	$-0.0168330\pi$
$971$	9.07173	+	20.3754i	0.291126	+	0.653879i	−0.707476	+	0.706737i	$0.750166\pi$
$972$	−3.86183	−	24.3826i	−0.123868	−	0.782074i
$973$	9.83163	−	13.9299i	0.315188	−	0.446573i
$974$			28.9792i			0.928555i
$975$	−14.2959	−	1.58874i	−0.457834	−	0.0508805i
$976$	−0.681341	+	0.393372i	−0.0218092	+	0.0125915i
$977$	31.2438	−	48.1113i	0.999579	−	1.53922i	0.166516	−	0.986039i	$-0.446748\pi$
$977$	31.2438	−	48.1113i	0.999579	−	1.53922i	0.833063	−	0.553178i	$-0.186585\pi$
$978$	16.4444	−	42.8390i	0.525832	−	1.36984i
$979$	12.7512	+	9.26427i	0.407529	+	0.296087i
$980$	−1.69983	+	21.1316i	−0.0542992	+	0.675025i
$981$	33.1024	−	24.0503i	1.05688	−	0.767867i
$982$	−1.94739	−	7.26776i	−0.0621438	−	0.231924i
$983$	−17.3870	+	6.67425i	−0.554560	+	0.212875i	−0.619477	−	0.785015i	$-0.712655\pi$
$983$	−17.3870	+	6.67425i	−0.554560	+	0.212875i	0.0649169	+	0.997891i	$0.479322\pi$
$984$	44.6644	+	40.2160i	1.42385	+	1.28204i
$985$	−38.5178	−	38.7480i	−1.22728	−	1.23461i
$986$	2.28915	+	0.743790i	0.0729014	+	0.0236871i
$987$	1.45355	+	105.969i	0.0462671	+	3.37302i
$988$	0.627566	−	1.23167i	0.0199655	−	0.0391846i
$989$	−16.4102	+	14.7758i	−0.521813	+	0.469843i
$990$	51.8554	−	33.4560i	1.64807	−	1.06330i
$991$	−28.2917	+	31.4211i	−0.898714	+	0.998123i	0.101280	+	0.994858i	$0.467706\pi$
$991$	−28.2917	+	31.4211i	−0.898714	+	0.998123i	−0.999995	+	0.00326534i	$0.998961\pi$
$992$	1.25552	−	1.55043i	0.0398626	−	0.0492263i
$993$	−40.8565	+	40.8565i	−1.29654	+	1.29654i
$994$	9.00652	+	13.4610i	0.285670	+	0.426956i
$995$	0.893130	−	1.99002i	0.0283141	−	0.0630880i
$996$	13.4786	−	6.00106i	0.427086	−	0.190151i
$997$	13.2661	−	10.7426i	0.420140	−	0.340223i	−0.395823	−	0.918327i	$-0.629541\pi$
$997$	13.2661	−	10.7426i	0.420140	−	0.340223i	0.815963	+	0.578104i	$0.196207\pi$
$998$	21.6349	+	14.0499i	0.684841	+	0.444741i
$999$	−38.5417	+	66.7562i	−1.21941	+	2.11207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.8	yes	288
5.2	odd	4		875.2.bb.b.257.11		288
5.3	odd	4		875.2.bb.a.257.8		288
5.4	even	2		875.2.bb.c.243.11		288
7.3	odd	6	inner	175.2.x.a.3.11	✓	288
25.6	even	5		875.2.bb.b.768.11		288
25.8	odd	20		875.2.bb.c.607.8		288
25.17	odd	20	inner	175.2.x.a.117.11	yes	288
25.19	even	10		875.2.bb.a.768.8		288
35.3	even	12		875.2.bb.a.507.8		288
35.17	even	12		875.2.bb.b.507.11		288
35.24	odd	6		875.2.bb.c.493.8		288
175.17	even	60	inner	175.2.x.a.17.8	yes	288
175.31	odd	30		875.2.bb.b.143.11		288
175.94	odd	30		875.2.bb.a.143.8		288
175.108	even	60		875.2.bb.c.857.11		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.11	✓	288	7.3	odd	6	inner
175.2.x.a.17.8	yes	288	175.17	even	60	inner
175.2.x.a.103.8	yes	288	1.1	even	1	trivial
175.2.x.a.117.11	yes	288	25.17	odd	20	inner
875.2.bb.a.143.8		288	175.94	odd	30
875.2.bb.a.257.8		288	5.3	odd	4
875.2.bb.a.507.8		288	35.3	even	12
875.2.bb.a.768.8		288	25.19	even	10
875.2.bb.b.143.11		288	175.31	odd	30
875.2.bb.b.257.11		288	5.2	odd	4
875.2.bb.b.507.11		288	35.17	even	12
875.2.bb.b.768.11		288	25.6	even	5
875.2.bb.c.243.11		288	5.4	even	2
875.2.bb.c.493.8		288	35.24	odd	6
875.2.bb.c.607.8		288	25.8	odd	20
875.2.bb.c.857.11		288	175.108	even	60

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+(-0.802384 - 0.0420512i) q^{2} +(-1.97492 - 2.43882i) q^{3} +(-1.34699 - 0.141575i) q^{4} +(-1.30893 - 1.81293i) q^{5} +(1.48209 + 2.03992i) q^{6} +(2.52724 + 0.782993i) q^{7} +(2.66204 + 0.421625i) q^{8} +(-1.42381 + 6.69848i) q^{9} +(0.974030 + 1.50970i) q^{10} +(-4.90608 + 1.04282i) q^{11} +(2.31492 + 3.56467i) q^{12} +(-0.816789 - 0.416175i) q^{13} +(-1.99489 - 0.734535i) q^{14} +(-1.83636 + 6.77262i) q^{15} +(0.531383 + 0.112949i) q^{16} +(0.185757 + 0.483913i) q^{17} +(1.42412 - 5.31488i) q^{18} +(-0.116377 - 1.10725i) q^{19} +(1.50646 + 2.62731i) q^{20} +(-3.08150 - 7.70982i) q^{21} +(3.98041 - 0.630435i) q^{22} +(0.270445 - 5.16039i) q^{23} +(-4.22903 - 7.32490i) q^{24} +(-1.57340 + 4.74599i) q^{25} +(0.637878 + 0.368279i) q^{26} +(10.7599 - 5.48243i) q^{27} +(-3.29331 - 1.41248i) q^{28} +(-3.39698 + 4.67555i) q^{29} +(1.75827 - 5.35702i) q^{30} +(-0.139259 + 0.312781i) q^{31} +(-5.62839 - 1.50812i) q^{32} +(12.2323 + 9.90555i) q^{33} +(-0.128699 - 0.396095i) q^{34} +(-1.88847 - 5.60657i) q^{35} +(2.86619 - 8.82122i) q^{36} +(-5.35336 + 3.47651i) q^{37} +(0.0468178 + 0.893337i) q^{38} +(0.598115 + 2.81391i) q^{39} +(-2.72005 - 5.37795i) q^{40} +(-6.75808 + 2.19583i) q^{41} +(2.14834 + 6.31581i) q^{42} +(-3.02167 - 3.02167i) q^{43} +(6.75609 - 0.710093i) q^{44} +(14.0075 - 6.18660i) q^{45} +(-0.434001 + 4.12924i) q^{46} +(-11.9164 - 4.57426i) q^{47} +(-0.773974 - 1.51901i) q^{48} +(5.77384 + 3.95762i) q^{49} +(1.46204 - 3.74194i) q^{50} +(0.813322 - 1.40871i) q^{51} +(1.04129 + 0.676221i) q^{52} +(4.55606 - 3.68942i) q^{53} +(-8.86410 + 3.94655i) q^{54} +(8.31228 + 7.52937i) q^{55} +(6.39747 + 3.14990i) q^{56} +(-2.47056 + 2.47056i) q^{57} +(2.92230 - 3.60874i) q^{58} +(5.88478 - 6.53571i) q^{59} +(3.43240 - 8.86268i) q^{60} +(-1.07623 + 0.969040i) q^{61} +(0.124892 - 0.245114i) q^{62} +(-8.84316 + 15.8138i) q^{63} +(3.41938 + 1.11102i) q^{64} +(0.314627 + 2.02552i) q^{65} +(-9.39849 - 8.46244i) q^{66} +(1.31334 - 0.504146i) q^{67} +(-0.181703 - 0.678125i) q^{68} +(-13.1194 + 9.53177i) q^{69} +(1.27952 + 4.57804i) q^{70} +(-6.16371 - 4.47820i) q^{71} +(-6.61447 + 17.2313i) q^{72} +(-0.656834 + 1.01144i) q^{73} +(4.44164 - 2.56438i) q^{74} +(14.6819 - 5.53571i) q^{75} +1.50794i q^{76} +(-13.2153 - 1.20598i) q^{77} +(-0.361590 - 2.28299i) q^{78} +(1.97771 + 4.44201i) q^{79} +(-0.490776 - 1.11120i) q^{80} +(-15.8523 - 7.05789i) q^{81} +(5.51491 - 1.47772i) q^{82} +(0.543025 - 3.42852i) q^{83} +(3.05924 + 10.8213i) q^{84} +(0.634155 - 0.970172i) q^{85} +(2.29747 + 2.55160i) q^{86} +(18.1116 - 0.949187i) q^{87} +(-13.4998 + 0.707497i) q^{88} +(-2.10268 - 2.33526i) q^{89} +(-11.4996 + 4.37500i) q^{90} +(-1.73836 - 1.69131i) q^{91} +(-1.09487 + 6.91272i) q^{92} +(1.03784 - 0.278088i) q^{93} +(9.36915 + 4.17141i) q^{94} +(-1.85504 + 1.66030i) q^{95} +(7.43756 + 16.7050i) q^{96} +(0.557021 + 3.51689i) q^{97} +(-4.46642 - 3.41833i) q^{98} -34.3480i 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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Groups

Database

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