LMFDB - Embedded newform 175.2.x.a.108.18

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			108.18
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.127170 + 2.42654i) q^{2} +(-1.78675 - 1.44688i) q^{3} +(-3.88289 + 0.408108i) q^{4} +(-2.07076 - 0.843763i) q^{5} +(3.28370 - 4.51962i) q^{6} +(1.54352 - 2.14884i) q^{7} +(-0.723845 - 4.57018i) q^{8} +(0.475273 + 2.23598i) q^{9} +(1.78409 - 5.13210i) q^{10} +(-0.0163732 - 0.00348022i) q^{11} +(7.52823 + 4.88889i) q^{12} +(-1.39124 - 2.73047i) q^{13} +(5.41055 + 3.47216i) q^{14} +(2.47911 + 4.50374i) q^{15} +(3.35976 - 0.714139i) q^{16} +(-6.59423 - 2.53129i) q^{17} +(-5.36527 + 1.43762i) q^{18} +(0.331948 - 3.15828i) q^{19} +(8.38489 + 2.43114i) q^{20} +(-5.86701 + 1.60615i) q^{21} +(0.00636273 - 0.0401727i) q^{22} +(-5.46923 + 0.286630i) q^{23} +(-5.31918 + 9.21308i) q^{24} +(3.57613 + 3.49447i) q^{25} +(6.44868 - 3.72315i) q^{26} +(-0.745322 + 1.46278i) q^{27} +(-5.11637 + 8.97365i) q^{28} +(-0.0353871 - 0.0487062i) q^{29} +(-10.6132 + 6.58841i) q^{30} +(3.66733 + 8.23697i) q^{31} +(-0.235039 - 0.877177i) q^{32} +(0.0242193 + 0.0299083i) q^{33} +(5.30369 - 16.3231i) q^{34} +(-5.00939 + 3.14738i) q^{35} +(-2.75796 - 8.48811i) q^{36} +(4.57608 - 7.04654i) q^{37} +(7.70591 + 0.403850i) q^{38} +(-1.46486 + 6.89163i) q^{39} +(-2.35724 + 10.0745i) q^{40} +(5.83738 + 1.89668i) q^{41} +(-4.64350 - 14.0323i) q^{42} +(-3.18681 - 3.18681i) q^{43} +(0.0649954 + 0.00683130i) q^{44} +(0.902462 - 5.03121i) q^{45} +(-1.39104 - 13.2349i) q^{46} +(1.64959 + 4.29732i) q^{47} +(-7.03633 - 3.58519i) q^{48} +(-2.23507 - 6.63359i) q^{49} +(-8.02470 + 9.12201i) q^{50} +(8.11977 + 14.0639i) q^{51} +(6.51638 + 10.0343i) q^{52} +(2.73861 - 3.38191i) q^{53} +(-3.64427 - 1.62253i) q^{54} +(0.0309685 + 0.0210218i) q^{55} +(-10.9379 - 5.49875i) q^{56} +(-5.16276 + 5.16276i) q^{57} +(0.113687 - 0.0920622i) q^{58} +(1.67651 + 1.86195i) q^{59} +(-11.4641 - 16.4758i) q^{60} +(-9.91649 - 8.92884i) q^{61} +(-19.5210 + 9.94643i) q^{62} +(5.53838 + 2.43001i) q^{63} +(8.63203 - 2.80472i) q^{64} +(0.577069 + 6.82804i) q^{65} +(-0.0694938 + 0.0625725i) q^{66} +(0.113980 - 0.296929i) q^{67} +(26.6377 + 7.13755i) q^{68} +(10.1869 + 7.40119i) q^{69} +(-8.27429 - 11.7552i) q^{70} +(-6.35569 + 4.61768i) q^{71} +(9.87482 - 3.79059i) q^{72} +(-2.80391 + 1.82088i) q^{73} +(17.6807 + 10.2079i) q^{74} +(-1.33356 - 11.4180i) q^{75} +12.3987i q^{76} +(-0.0327508 + 0.0298116i) q^{77} +(-16.9091 - 2.67814i) q^{78} +(2.17913 - 4.89441i) q^{79} +(-7.55984 - 1.35603i) q^{80} +(9.71309 - 4.32455i) q^{81} +(-3.86003 + 14.4058i) q^{82} +(8.63403 - 1.36750i) q^{83} +(22.1255 - 8.63088i) q^{84} +(11.5193 + 10.8057i) q^{85} +(7.32766 - 8.13819i) q^{86} +(-0.00724415 + 0.138227i) q^{87} +(-0.00405361 + 0.0773474i) q^{88} +(5.60082 - 6.22034i) q^{89} +(12.3232 + 1.55004i) q^{90} +(-8.01478 - 1.22498i) q^{91} +(21.1194 - 3.34499i) q^{92} +(5.36531 - 20.0236i) q^{93} +(-10.2178 + 4.54928i) q^{94} +(-3.35223 + 6.25996i) q^{95} +(-0.849216 + 1.90737i) q^{96} +(6.79613 + 1.07640i) q^{97} +(15.8124 - 6.26707i) q^{98} -0.0382642i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.127170	+	2.42654i	0.0899225	+	1.71582i	0.556085	+	0.831125i	$0.312303\pi$
$2$	0.127170	+	2.42654i	0.0899225	+	1.71582i	−0.466163	+	0.884699i	$0.654364\pi$
$3$	−1.78675	−	1.44688i	−1.03158	−	0.835357i	−0.0450579	−	0.998984i	$-0.514347\pi$
$3$	−1.78675	−	1.44688i	−1.03158	−	0.835357i	−0.986522	+	0.163627i	$0.947681\pi$
$4$	−3.88289	+	0.408108i	−1.94144	+	0.204054i
$5$	−2.07076	−	0.843763i	−0.926074	−	0.377342i
$5$	−2.07076	−	0.843763i	−0.926074	−	0.377342i
$6$	3.28370	−	4.51962i	1.34056	−	1.84513i
$7$	1.54352	−	2.14884i	0.583397	−	0.812187i
$7$	1.54352	−	2.14884i	0.583397	−	0.812187i
$8$	−0.723845	−	4.57018i	−0.255918	−	1.61580i
$9$	0.475273	+	2.23598i	0.158424	+	0.745328i
$10$	1.78409	−	5.13210i	0.564178	−	1.62291i
$11$	−0.0163732	−	0.00348022i	−0.00493669	−	0.00104933i	0.205443	−	0.978669i	$-0.434137\pi$
$11$	−0.0163732	−	0.00348022i	−0.00493669	−	0.00104933i	−0.210379	+	0.977620i	$0.567470\pi$
$12$	7.52823	+	4.88889i	2.17321	+	1.41130i
$13$	−1.39124	−	2.73047i	−0.385862	−	0.757297i	0.613616	−	0.789605i	$-0.289714\pi$
$13$	−1.39124	−	2.73047i	−0.385862	−	0.757297i	−0.999478	+	0.0323079i	$0.989714\pi$
$14$	5.41055	+	3.47216i	1.44603	+	0.927973i
$15$	2.47911	+	4.50374i	0.640104	+	1.16286i
$16$	3.35976	−	0.714139i	0.839940	−	0.178535i
$17$	−6.59423	−	2.53129i	−1.59934	−	0.613928i	−0.614734	−	0.788735i	$-0.710737\pi$
$17$	−6.59423	−	2.53129i	−1.59934	−	0.613928i	−0.984603	+	0.174807i	$0.944070\pi$
$18$	−5.36527	+	1.43762i	−1.26461	+	0.338850i
$19$	0.331948	−	3.15828i	0.0761542	−	0.724559i	−0.888113	−	0.459626i	$-0.847984\pi$
$19$	0.331948	−	3.15828i	0.0761542	−	0.724559i	0.964267	−	0.264933i	$-0.0853498\pi$
$20$	8.38489	+	2.43114i	1.87492	+	0.543620i
$21$	−5.86701	+	1.60615i	−1.28029	+	0.350491i
$22$	0.00636273	−	0.0401727i	0.00135654	−	0.00856485i
$23$	−5.46923	+	0.286630i	−1.14041	+	0.0597665i	−0.613172	−	0.789949i	$-0.710107\pi$
$23$	−5.46923	+	0.286630i	−1.14041	+	0.0597665i	−0.527241	+	0.849716i	$0.676774\pi$
$24$	−5.31918	+	9.21308i	−1.08577	+	1.88061i
$25$	3.57613	+	3.49447i	0.715226	+	0.698894i
$26$	6.44868	−	3.72315i	1.26469	−	0.730169i
$27$	−0.745322	+	1.46278i	−0.143437	+	0.281512i
$28$	−5.11637	+	8.97365i	−0.966903	+	1.69586i
$29$	−0.0353871	−	0.0487062i	−0.00657122	−	0.00904451i	0.805719	−	0.592298i	$-0.201779\pi$
$29$	−0.0353871	−	0.0487062i	−0.00657122	−	0.00904451i	−0.812290	+	0.583254i	$0.801779\pi$
$30$	−10.6132	+	6.58841i	−1.93771	+	1.20287i
$31$	3.66733	+	8.23697i	0.658673	+	1.47940i	0.865440	+	0.501013i	$0.167039\pi$
$31$	3.66733	+	8.23697i	0.658673	+	1.47940i	−0.206767	+	0.978390i	$0.566294\pi$
$32$	−0.235039	−	0.877177i	−0.0415494	−	0.155065i
$33$	0.0242193	+	0.0299083i	0.00421603	+	0.00520637i
$34$	5.30369	−	16.3231i	0.909576	−	2.79939i
$35$	−5.00939	+	3.14738i	−0.846741	+	0.532005i
$36$	−2.75796	−	8.48811i	−0.459659	−	1.41469i
$37$	4.57608	−	7.04654i	0.752302	−	1.15844i	−0.230372	−	0.973103i	$-0.573994\pi$
$37$	4.57608	−	7.04654i	0.752302	−	1.15844i	0.982674	−	0.185341i	$-0.0593390\pi$
$38$	7.70591	+	0.403850i	1.25006	+	0.0655130i
$39$	−1.46486	+	6.89163i	−0.234566	+	1.10354i
$40$	−2.35724	+	10.0745i	−0.372712	+	1.59292i
$41$	5.83738	+	1.89668i	0.911646	+	0.296212i	0.727035	−	0.686600i	$-0.240898\pi$
$41$	5.83738	+	1.89668i	0.911646	+	0.296212i	0.184610	+	0.982812i	$0.440898\pi$
$42$	−4.64350	−	14.0323i	−0.716507	−	2.16523i
$43$	−3.18681	−	3.18681i	−0.485984	−	0.485984i	0.421052	−	0.907036i	$-0.361661\pi$
$43$	−3.18681	−	3.18681i	−0.485984	−	0.485984i	−0.907036	+	0.421052i	$0.861661\pi$
$44$	0.0649954	+	0.00683130i	0.00979843	+	0.00102986i
$45$	0.902462	−	5.03121i	0.134531	−	0.750009i
$46$	−1.39104	−	13.2349i	−0.205098	−	1.95137i
$47$	1.64959	+	4.29732i	0.240617	+	0.626828i	0.999708	−	0.0241558i	$-0.00768978\pi$
$47$	1.64959	+	4.29732i	0.240617	+	0.626828i	−0.759091	+	0.650984i	$0.774356\pi$
$48$	−7.03633	−	3.58519i	−1.01561	−	0.517477i
$49$	−2.23507	−	6.63359i	−0.319295	−	0.947655i
$50$	−8.02470	+	9.12201i	−1.13486	+	1.29005i
$51$	8.11977	+	14.0639i	1.13700	+	1.96933i
$52$	6.51638	+	10.0343i	0.903659	+	1.39151i
$53$	2.73861	−	3.38191i	0.376178	−	0.464541i	−0.553535	−	0.832826i	$-0.686722\pi$
$53$	2.73861	−	3.38191i	0.376178	−	0.464541i	0.929713	+	0.368285i	$0.120055\pi$
$54$	−3.64427	−	1.62253i	−0.495923	−	0.220799i
$55$	0.0309685	+	0.0210218i	0.00417579	+	0.00283458i
$56$	−10.9379	−	5.49875i	−1.46164	−	0.734802i
$57$	−5.16276	+	5.16276i	−0.683825	+	0.683825i
$58$	0.113687	−	0.0920622i	0.0149279	−	0.0120884i
$59$	1.67651	+	1.86195i	0.218263	+	0.242406i	0.842326	−	0.538968i	$-0.181186\pi$
$59$	1.67651	+	1.86195i	0.218263	+	0.242406i	−0.624063	+	0.781374i	$0.714519\pi$
$60$	−11.4641	−	16.4758i	−1.48001	−	2.12701i
$61$	−9.91649	−	8.92884i	−1.26968	−	1.14322i	−0.982684	−	0.185288i	$-0.940678\pi$
$61$	−9.91649	−	8.92884i	−1.26968	−	1.14322i	−0.286992	−	0.957933i	$-0.592655\pi$
$62$	−19.5210	+	9.94643i	−2.47917	+	1.26320i
$63$	5.53838	+	2.43001i	0.697770	+	0.306152i
$64$	8.63203	−	2.80472i	1.07900	−	0.350590i
$65$	0.577069	+	6.82804i	0.0715766	+	0.846915i
$66$	−0.0694938	+	0.0625725i	−0.00855409	+	0.00770214i
$67$	0.113980	−	0.296929i	0.0139249	−	0.0362757i	−0.926442	−	0.376438i	$-0.877149\pi$
$67$	0.113980	−	0.296929i	0.0139249	−	0.0362757i	0.940367	+	0.340162i	$0.110482\pi$
$68$	26.6377	+	7.13755i	3.23030	+	0.865556i
$69$	10.1869	+	7.40119i	1.22635	+	0.890999i
$70$	−8.27429	−	11.7552i	−0.988967	−	1.40502i
$71$	−6.35569	+	4.61768i	−0.754282	+	0.548018i	−0.897151	−	0.441724i	$-0.854367\pi$
$71$	−6.35569	+	4.61768i	−0.754282	+	0.548018i	0.142869	+	0.989742i	$0.454367\pi$
$72$	9.87482	−	3.79059i	1.16376	−	0.446725i
$73$	−2.80391	+	1.82088i	−0.328173	+	0.213118i	−0.698200	−	0.715903i	$-0.746015\pi$
$73$	−2.80391	+	1.82088i	−0.328173	+	0.213118i	0.370027	+	0.929021i	$0.379349\pi$
$74$	17.6807	+	10.2079i	2.05533	+	1.18665i
$75$	−1.33356	−	11.4180i	−0.153987	−	1.31843i
$76$			12.3987i			1.42223i
$77$	−0.0327508	+	0.0298116i	−0.00373230	+	0.00339734i
$78$	−16.9091	−	2.67814i	−1.91458	−	0.303240i
$79$	2.17913	−	4.89441i	0.245171	−	0.550664i	−0.748481	−	0.663156i	$-0.769217\pi$
$79$	2.17913	−	4.89441i	0.245171	−	0.550664i	0.993653	+	0.112492i	$0.0358833\pi$
$80$	−7.55984	−	1.35603i	−0.845216	−	0.151609i
$81$	9.71309	−	4.32455i	1.07923	−	0.480505i
$82$	−3.86003	+	14.4058i	−0.426270	+	1.59086i
$83$	8.63403	−	1.36750i	0.947708	−	0.150102i	0.336599	−	0.941648i	$-0.390723\pi$
$83$	8.63403	−	1.36750i	0.947708	−	0.150102i	0.611110	+	0.791546i	$0.290723\pi$
$84$	22.1255	−	8.63088i	2.41409	−	0.941706i
$85$	11.5193	+	10.8057i	1.24944	+	1.17204i
$86$	7.32766	−	8.13819i	0.790162	−	0.877564i
$87$	−0.00724415	+	0.138227i	−0.000776654	+	0.0148194i
$88$	−0.00405361	+	0.0773474i	−0.000432116	+	0.00824526i
$89$	5.60082	−	6.22034i	0.593686	−	0.659355i	−0.369173	−	0.929361i	$-0.620359\pi$
$89$	5.60082	−	6.22034i	0.593686	−	0.659355i	0.962859	+	0.270006i	$0.0870257\pi$
$90$	12.3232	+	1.55004i	1.29898	+	0.163389i
$91$	−8.01478	−	1.22498i	−0.840177	−	0.128413i
$92$	21.1194	−	3.34499i	2.20185	−	0.348739i
$93$	5.36531	−	20.0236i	0.556356	−	2.07635i
$94$	−10.2178	+	4.54928i	−1.05389	+	0.469222i
$95$	−3.35223	+	6.25996i	−0.343931	+	0.642259i
$96$	−0.849216	+	1.90737i	−0.0866727	+	0.194670i
$97$	6.79613	+	1.07640i	0.690043	+	0.109292i	0.491601	−	0.870821i	$-0.336412\pi$
$97$	6.79613	+	1.07640i	0.690043	+	0.109292i	0.198442	+	0.980113i	$0.436412\pi$
$98$	15.8124	−	6.26707i	1.59730	−	0.633070i
$99$		−	0.0382642i		−	0.00384569i
$100$	−15.3118	−	12.1092i	−1.53118	−	1.21092i
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.0321267	−	0.999484i	$-0.510228\pi$
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.881642	+	0.471919i	$0.843561\pi$
$102$	−33.0939	+	21.4915i	−3.27679	+	2.12797i
$103$	0.204272	−	0.0784125i	0.0201275	−	0.00772622i	−0.348283	−	0.937389i	$-0.613235\pi$
$103$	0.204272	−	0.0784125i	0.0201275	−	0.00772622i	0.368411	+	0.929663i	$0.379902\pi$
$104$	−11.4717	+	8.33468i	−1.12489	+	0.817282i
$105$	13.5044	+	1.62441i	1.31790	+	0.158526i
$106$	8.55461	+	6.21528i	0.830897	+	0.603682i
$107$	4.72847	+	1.26699i	0.457119	+	0.122485i	0.480028	−	0.877253i	$-0.340626\pi$
$107$	4.72847	+	1.26699i	0.457119	+	0.122485i	−0.0229097	+	0.999738i	$0.507293\pi$
$108$	2.29703	−	5.98397i	0.221032	−	0.575808i
$109$	−5.73459	+	5.16345i	−0.549274	+	0.494569i	−0.896398	−	0.443251i	$-0.853825\pi$
$109$	−5.73459	+	5.16345i	−0.549274	+	0.494569i	0.347123	+	0.937819i	$0.387158\pi$
$110$	−0.0470720	+	0.0778196i	−0.00448814	+	0.00741981i
$111$	−18.3718	+	5.96936i	−1.74377	+	0.566587i
$112$	3.65130	−	8.32190i	0.345015	−	0.786345i
$113$	−3.56746	+	1.81771i	−0.335599	+	0.170996i	−0.613666	−	0.789565i	$-0.710306\pi$
$113$	−3.56746	+	1.81771i	−0.335599	+	0.170996i	0.278068	+	0.960561i	$0.410306\pi$
$114$	−13.1842	−	11.8711i	−1.23481	−	1.11183i
$115$	11.5673	+	4.02119i	1.07866	+	0.374978i
$116$	0.157282	+	0.174679i	0.0146032	+	0.0162185i
$117$	5.44407	−	4.40852i	0.503304	−	0.407568i
$118$	−4.30491	+	4.30491i	−0.396299	+	0.396299i
$119$	−15.6177	+	10.2629i	−1.43167	+	0.940796i
$120$	18.7884	−	14.5900i	1.71514	−	1.33188i
$121$	−10.0487	−	4.47399i	−0.913522	−	0.406726i
$122$	20.4051	−	25.1982i	1.84739	−	2.28134i
$123$	−7.68566	−	11.8349i	−0.692993	−	1.06712i
$124$	−17.6014	−	30.4866i	−1.58065	−	2.73777i
$125$	−4.45681	−	10.2536i	−0.398630	−	0.917112i
$126$	−5.19220	+	13.7481i	−0.462558	+	1.22478i
$127$	6.49211	+	3.30790i	0.576082	+	0.293528i	0.717654	−	0.696399i	$-0.245216\pi$
$127$	6.49211	+	3.30790i	0.576082	+	0.293528i	−0.141572	+	0.989928i	$0.545216\pi$
$128$	7.25261	+	18.8937i	0.641047	+	1.66998i
$129$	1.08310	+	10.3050i	0.0953612	+	0.907301i
$130$	−16.4951	+	2.26860i	−1.44672	+	0.198970i
$131$	−11.7655	−	1.23661i	−1.02796	−	0.108043i	−0.424493	−	0.905431i	$-0.639548\pi$
$131$	−11.7655	−	1.23661i	−1.02796	−	0.108043i	−0.603466	+	0.797389i	$0.706214\pi$
$132$	−0.106246	−	0.106246i	−0.00924757	−	0.00924757i
$133$	−6.27428	−	5.58819i	−0.544049	−	0.484557i
$134$	0.735006	+	0.238818i	0.0634949	+	0.0206307i
$135$	2.77762	−	2.40019i	0.239060	−	0.206576i
$136$	−6.79524	+	31.9691i	−0.582687	+	2.74133i
$137$	3.28970	+	0.172406i	0.281058	+	0.0147296i	0.192344	−	0.981327i	$-0.438391\pi$
$137$	3.28970	+	0.172406i	0.281058	+	0.0147296i	0.0887140	+	0.996057i	$0.471724\pi$
$138$	−16.6638	+	25.6601i	−1.41852	+	2.18433i
$139$	−1.40509	−	4.32443i	−0.119179	−	0.366794i	0.873617	−	0.486614i	$-0.161768\pi$
$139$	−1.40509	−	4.32443i	−0.119179	−	0.366794i	−0.992796	+	0.119820i	$0.961768\pi$
$140$	18.1664	−	14.2653i	1.53534	−	1.20564i
$141$	3.27031	−	10.0650i	0.275410	−	0.847625i
$142$	−12.0133	−	14.8351i	−1.00813	−	1.24494i
$143$	0.0132764	+	0.0495483i	0.00111023	+	0.00414344i
$144$	3.19361	+	7.17296i	0.266134	+	0.597747i
$145$	0.0321819	+	0.130717i	0.00267256	+	0.0108555i
$146$	−4.77502	−	6.57225i	−0.395183	−	0.543923i
$147$	−5.60451	+	15.0864i	−0.462252	+	1.24431i
$148$	−14.8926	+	29.2285i	−1.22417	+	2.40256i
$149$	15.7486	−	9.09246i	1.29018	−	0.744884i	0.311491	−	0.950249i	$-0.399172\pi$
$149$	15.7486	−	9.09246i	1.29018	−	0.744884i	0.978685	+	0.205366i	$0.0658384\pi$
$150$	27.5366	−	4.68797i	2.24835	−	0.382771i
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	−0.169072	−	0.985604i	$-0.554077\pi$
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	0.938094	−	0.346381i	$-0.112590\pi$
$152$	−14.6742	+	0.769041i	−1.19023	+	0.0623775i
$153$	2.52586	−	15.9477i	0.204204	−	1.28929i
$154$	−0.0765039	−	0.0756801i	−0.00616486	−	0.00609848i
$155$	−0.644136	−	20.1512i	−0.0517382	−	1.61858i
$156$	2.87536	−	27.3573i	0.230213	−	2.19033i
$157$	−15.7038	+	4.20781i	−1.25330	+	0.335820i	−0.823609	−	0.567158i	$-0.808043\pi$
$157$	−15.7038	+	4.20781i	−1.25330	+	0.335820i	−0.429688	+	0.902978i	$0.641376\pi$
$158$	12.1536	+	4.66533i	0.966889	+	0.371154i
$159$	−9.78643	+	2.08017i	−0.776115	+	0.164968i
$160$	−0.253420	+	2.01474i	−0.0200346	+	0.159280i
$161$	−7.82597	+	12.1950i	−0.616773	+	0.961097i
$162$	11.7289	+	23.0193i	0.921510	+	1.80856i
$163$	7.85580	+	5.10162i	0.615314	+	0.399590i	0.814326	−	0.580407i	$-0.197107\pi$
$163$	7.85580	+	5.10162i	0.615314	+	0.399590i	−0.199012	+	0.979997i	$0.563773\pi$
$164$	−23.4399	−	4.98231i	−1.83035	−	0.389053i
$165$	−0.0249169	−	0.0823683i	−0.00193978	−	0.00641237i
$166$	4.41627	+	20.7769i	0.342769	+	1.61260i
$167$	1.18224	+	7.46435i	0.0914842	+	0.577608i	0.990263	+	0.139207i	$0.0444553\pi$
$167$	1.18224	+	7.46435i	0.0914842	+	0.577608i	−0.898779	+	0.438402i	$0.855545\pi$
$168$	11.5872	+	25.6507i	0.893972	+	1.97899i
$169$	2.12129	−	2.91971i	0.163177	−	0.224593i
$170$	−24.7555	+	29.3262i	−1.89866	+	2.24922i
$171$	7.21963	−	0.758813i	0.552099	−	0.0580279i
$172$	13.6746	+	11.0735i	1.04268	+	0.844343i
$173$	−1.22482	−	23.3710i	−0.0931217	−	1.77687i	−0.502572	−	0.864535i	$-0.667613\pi$
$173$	−1.22482	−	23.3710i	−0.0931217	−	1.77687i	0.409451	−	0.912332i	$-0.365720\pi$
$174$	−0.336334			−0.0254974
$175$	13.0289	−	2.29075i	0.984893	−	0.173164i
$176$	−0.0574953			−0.00433387
$177$	−0.301479	−	5.75255i	−0.0226605	−	0.432388i
$178$	15.8062	+	12.7996i	1.18472	+	0.959369i
$179$	−13.5506	+	1.42423i	−1.01282	+	0.106452i	−0.596373	−	0.802707i	$-0.703392\pi$
$179$	−13.5506	+	1.42423i	−1.01282	+	0.106452i	−0.416449	+	0.909159i	$0.636726\pi$
$180$	−1.45088	+	19.9039i	−0.108142	+	1.48355i
$181$	3.38018	−	4.65241i	0.251247	−	0.345811i	−0.664701	−	0.747110i	$-0.731441\pi$
$181$	3.38018	−	4.65241i	0.251247	−	0.345811i	0.915947	+	0.401298i	$0.131441\pi$
$182$	1.95323	−	19.6040i	0.144783	−	1.45314i
$183$	4.79930	+	30.3016i	0.354774	+	2.23996i
$184$	5.26883	+	24.7879i	0.388423	+	1.82739i
$185$	−15.4216	+	10.7306i	−1.13382	+	0.788929i
$186$	49.2704	+	10.4727i	3.61268	+	0.767899i
$187$	0.0991590	+	0.0643946i	0.00725122	+	0.00470900i
$188$	−8.15893	−	16.0128i	−0.595051	−	1.16785i
$189$	1.99286	+	3.85941i	0.144959	+	0.280731i
$190$	−15.6164	−	7.33824i	−1.13293	−	0.532372i
$191$	14.4947	−	3.08094i	1.04880	−	0.222929i	0.348892	−	0.937163i	$-0.386558\pi$
$191$	14.4947	−	3.08094i	1.04880	−	0.222929i	0.699907	+	0.714234i	$0.253225\pi$
$192$	−19.4814	−	7.47820i	−1.40595	−	0.539693i
$193$	−16.0726	+	4.30663i	−1.15693	+	0.309998i	−0.785739	−	0.618558i	$-0.787717\pi$
$193$	−16.0726	+	4.30663i	−1.15693	+	0.309998i	−0.371191	+	0.928557i	$0.621050\pi$
$194$	−1.74767	+	16.6280i	−0.125475	+	1.19382i
$195$	8.84829	−	13.0350i	0.633639	−	0.933452i
$196$	11.3857	+	24.8453i	0.813266	+	1.77467i
$197$	2.43376	−	15.3662i	0.173398	−	1.09479i	−0.735423	−	0.677608i	$-0.763017\pi$
$197$	2.43376	−	15.3662i	0.173398	−	1.09479i	0.908821	−	0.417185i	$-0.136983\pi$
$198$	0.0928496	−	0.00486604i	0.00659854	−	0.000345815i
$199$	0.988951	−	1.71291i	0.0701049	−	0.121425i	−0.828842	−	0.559482i	$-0.811000\pi$
$199$	0.988951	−	1.71291i	0.0701049	−	0.121425i	0.898947	+	0.438057i	$0.144333\pi$
$200$	13.3818	−	18.8730i	0.946235	−	1.33452i
$201$	−0.633276	+	0.365622i	−0.0446678	+	0.0257890i
$202$	11.6976	−	22.9578i	0.823039	−	1.61531i
$203$	−0.159283		0.000862231i	−0.0111795		6.05168e-5i
$204$	−37.2677	−	51.2946i	−2.60926	−	3.59134i
$205$	−10.4875	−	8.85294i	−0.732478	−	0.618316i
$206$	0.216248	+	0.485702i	0.0150667	+	0.0338405i
$207$	−3.24028	−	12.0929i	−0.225215	−	0.840514i
$208$	−6.62419	−	8.18019i	−0.459305	−	0.567194i
$209$	−0.0164266	+	0.0505557i	−0.00113625	+	0.00349701i
$210$	−2.22435	+	32.9756i	−0.153494	+	2.27553i
$211$	2.82445	+	8.69276i	0.194443	+	0.598434i	0.999983	+	0.00589215i	$0.00187554\pi$
$211$	2.82445	+	8.69276i	0.194443	+	0.598434i	−0.805540	+	0.592542i	$0.798124\pi$
$212$	−9.25355	+	14.2492i	−0.635536	+	0.978640i
$213$	18.0373	+	0.945293i	1.23589	+	0.0647704i
$214$	−2.47309	+	11.6350i	−0.169057	+	0.795349i
$215$	3.91022	+	9.28804i	0.266675	+	0.633439i
$216$	7.22465	+	2.34743i	0.491575	+	0.159722i
$217$	23.3606	+	4.83343i	1.58582	+	0.328115i
$218$	−13.2586	−	13.2586i	−0.897985	−	0.897985i
$219$	7.64448	+	0.803468i	0.516566	+	0.0542933i
$220$	−0.128826	−	0.0689868i	−0.00868546	−	0.00465109i
$221$	2.26258	+	21.5270i	0.152198	+	1.44806i
$222$	−16.8212	−	43.8208i	−1.12897	−	2.94106i
$223$	6.62726	+	3.37676i	0.443794	+	0.226124i	0.661584	−	0.749871i	$-0.269885\pi$
$223$	6.62726	+	3.37676i	0.443794	+	0.226124i	−0.217789	+	0.975996i	$0.569885\pi$
$224$	−2.24771	−	0.848882i	−0.150181	−	0.0567183i
$225$	−6.11394	+	9.65699i	−0.407596	+	0.643800i
$226$	−4.86443	−	8.42544i	−0.323577	−	0.560452i
$227$	−6.38180	−	9.82711i	−0.423575	−	0.652249i	0.560877	−	0.827899i	$-0.310464\pi$
$227$	−6.38180	−	9.82711i	−0.423575	−	0.652249i	−0.984453	+	0.175650i	$0.943797\pi$
$228$	17.9395	−	22.1534i	1.18807	−	1.46714i
$229$	24.6116	+	10.9578i	1.62638	+	0.724110i	0.998529	−	0.0542256i	$-0.0172690\pi$
$229$	24.6116	+	10.9578i	1.62638	+	0.724110i	0.627849	+	0.778335i	$0.283936\pi$
$230$	−8.28657	+	28.5800i	−0.546401	+	1.88451i
$231$	0.101651	−	0.00587925i	0.00668816	−	0.000386826i
$232$	−0.196981	+	0.196981i	−0.0129324	+	0.0129324i
$233$	−16.9779	+	13.7484i	−1.11226	+	0.900689i	−0.995713	−	0.0924959i	$-0.970515\pi$
$233$	−16.9779	+	13.7484i	−1.11226	+	0.900689i	−0.116546	+	0.993185i	$0.537182\pi$
$234$	11.3898	+	12.6496i	0.744573	+	0.826932i
$235$	0.210015	−	10.2906i	0.0136998	−	0.671284i
$236$	−7.26958	−	6.54556i	−0.473209	−	0.426080i
$237$	−10.9752	+	5.59214i	−0.712915	+	0.363248i
$238$	−26.8894	−	36.5919i	−1.74298	−	2.37190i
$239$	−4.05851	+	1.31869i	−0.262523	+	0.0852989i	−0.437321	−	0.899305i	$-0.644073\pi$
$239$	−4.05851	+	1.31869i	−0.262523	+	0.0852989i	0.174798	+	0.984604i	$0.444073\pi$
$240$	11.5455	+	13.3611i	0.745260	+	0.862453i
$241$	−0.122038	+	0.109884i	−0.00786117	+	0.00707823i	−0.673052	−	0.739595i	$-0.735017\pi$
$241$	−0.122038	+	0.109884i	−0.00786117	+	0.00707823i	0.665191	+	0.746674i	$0.268350\pi$
$242$	9.57843	−	24.9527i	0.615725	−	1.60402i
$243$	−18.8546	−	5.05209i	−1.20953	−	0.324092i
$244$	42.1485	+	30.6227i	2.69828	+	1.96042i
$245$	−0.968881	+	15.6225i	−0.0618996	+	0.998082i
$246$	27.7405	−	20.1546i	1.76867	−	1.28501i
$247$	−9.08541	+	3.48756i	−0.578091	+	0.221908i
$248$	34.9898	−	22.7227i	2.22186	−	1.44289i
$249$	−17.4055	−	10.0490i	−1.10303	−	0.636832i
$250$	24.3141	−	12.1186i	1.53776	−	0.766447i
$251$		−	0.132304i		−	0.00835098i	−0.999991	−	0.00417549i	$-0.998671\pi$
$251$		−	0.132304i		−	0.00835098i	0.999991	−	0.00417549i	$-0.00132910\pi$
$252$	−22.4966	−	7.17519i	−1.41715	−	0.451995i
$253$	0.0905461	+	0.0143411i	0.00569259	+	0.000901617i
$254$	−7.20115	+	16.1741i	−0.451840	+	1.01485i
$255$	−4.94757	−	35.9741i	−0.309829	−	2.25278i
$256$	−28.3409	+	12.6182i	−1.77131	+	0.788637i
$257$	−2.37849	+	8.87663i	−0.148366	+	0.553709i	0.851217	+	0.524815i	$0.175865\pi$
$257$	−2.37849	+	8.87663i	−0.148366	+	0.553709i	−0.999582	+	0.0288944i	$0.990801\pi$
$258$	−24.8677	+	3.93865i	−1.54819	+	0.245210i
$259$	−8.07863	−	20.7098i	−0.501982	−	1.28684i
$260$	−5.02727	−	26.2770i	−0.311778	−	1.62963i
$261$	0.0920877	−	0.102274i	0.00570008	−	0.00633058i
$262$	1.50446	−	28.7068i	0.0929458	−	1.77351i
$263$	1.09475	−	20.8891i	0.0675052	−	1.28808i	−0.729449	−	0.684036i	$-0.760223\pi$
$263$	1.09475	−	20.8891i	0.0675052	−	1.28808i	0.796954	−	0.604040i	$-0.206443\pi$
$264$	0.119155	−	0.132335i	0.00733350	−	0.00814468i
$265$	−8.52455	+	4.69239i	−0.523659	+	0.288251i
$266$	12.7621	−	15.9354i	0.782492	−	0.977065i
$267$	−19.0074	+	3.01047i	−1.16323	+	0.184238i
$268$	−0.321394	+	1.19946i	−0.0196323	+	0.0732687i
$269$	1.38180	−	0.615216i	0.0842497	−	0.0375104i	−0.364179	−	0.931329i	$-0.618650\pi$
$269$	1.38180	−	0.615216i	0.0842497	−	0.0375104i	0.448429	+	0.893819i	$0.351984\pi$
$270$	6.17739	+	6.43479i	0.375944	+	0.391609i
$271$	3.69590	−	8.30112i	0.224510	−	0.504257i	−0.765809	−	0.643068i	$-0.777661\pi$
$271$	3.69590	−	8.30112i	0.224510	−	0.504257i	0.990319	+	0.138811i	$0.0443279\pi$
$272$	−23.9627	−	3.79533i	−1.45295	−	0.230125i
$273$	12.5480	+	13.7852i	0.759439	+	0.834316i
$274$			8.00453i			0.483571i
$275$	−0.0463910	−	0.0696612i	−0.00279748	−	0.00420073i
$276$	−42.5749	−	24.5807i	−2.56271	−	1.47958i
$277$	−11.4597	+	7.44201i	−0.688546	+	0.447147i	−0.840908	−	0.541177i	$-0.817979\pi$
$277$	−11.4597	+	7.44201i	−0.688546	+	0.447147i	0.152362	+	0.988325i	$0.451312\pi$
$278$	10.3147	−	3.95946i	0.618637	−	0.237472i
$279$	−16.6747	+	12.1149i	−0.998291	+	0.725301i
$280$	18.0101	+	20.6156i	1.07631	+	1.23202i
$281$	−3.22462	−	2.34282i	−0.192365	−	0.139761i	0.487434	−	0.873160i	$-0.337933\pi$
$281$	−3.22462	−	2.34282i	−0.192365	−	0.139761i	−0.679799	+	0.733399i	$0.737933\pi$
$282$	24.8390	+	6.65559i	1.47914	+	0.396334i
$283$	−6.77206	+	17.6418i	−0.402557	+	1.04870i	0.571140	+	0.820853i	$0.306501\pi$
$283$	−6.77206	+	17.6418i	−0.402557	+	1.04870i	−0.973697	+	0.227845i	$0.926832\pi$
$284$	22.7939	−	20.5238i	1.35257	−	1.21786i
$285$	15.0470	−	6.33471i	0.891308	−	0.375236i
$286$	−0.118543	+	0.0385168i	−0.00700957	+	0.00227755i
$287$	13.0858	−	9.61605i	0.772431	−	0.567618i
$288$	1.84965	−	0.942442i	0.108991	−	0.0555339i
$289$	24.4430	+	22.0086i	1.43783	+	1.29462i
$290$	−0.313098	+	0.0947139i	−0.0183858	+	0.00556179i
$291$	−10.5856	−	11.7565i	−0.620536	−	0.689176i
$292$	10.1442	−	8.21458i	0.593642	−	0.480722i
$293$	4.94524	−	4.94524i	0.288904	−	0.288904i	−0.547743	−	0.836647i	$-0.684513\pi$
$293$	4.94524	−	4.94524i	0.288904	−	0.288904i	0.836647	+	0.547743i	$0.184513\pi$
$294$	−37.3206	−	11.6810i	−2.17658	−	0.681252i
$295$	−1.90061	−	5.27024i	−0.110658	−	0.306845i
$296$	−35.5163	−	15.8129i	−2.06434	−	0.919105i
$297$	0.0172941	−	0.0213564i	0.00100350	−	0.00123922i
$298$	24.0660	+	37.0584i	1.39410	+	2.14673i
$299$	8.39168	+	14.5348i	0.485303	+	0.840570i
$300$	9.83785	+	43.7905i	0.567988	+	2.52824i
$301$	−11.7669	+	1.92904i	−0.678231	+	0.111188i
$302$	40.9187	+	20.8491i	2.35460	+	1.19973i
$303$	8.73688	+	22.7604i	0.501921	+	1.30755i
$304$	−1.14018	−	10.8481i	−0.0653940	−	0.622182i
$305$	13.0009	+	26.8567i	0.744428	+	1.53781i
$306$	39.0189	+	4.10105i	2.23056	+	0.234441i
$307$	4.76473	+	4.76473i	0.271938	+	0.271938i	0.829880	−	0.557942i	$-0.188409\pi$
$307$	4.76473	+	4.76473i	0.271938	+	0.271938i	−0.557942	+	0.829880i	$0.688409\pi$
$308$	0.115001	−	0.129121i	0.00655282	−	0.00735734i
$309$	−0.478436	−	0.155453i	−0.0272173	−	0.00884342i
$310$	48.8158	−	4.12564i	2.77255	−	0.234321i
$311$	−0.546587	+	2.57149i	−0.0309941	+	0.145816i	−0.990924	−	0.134425i	$-0.957081\pi$
$311$	−0.546587	+	2.57149i	−0.0309941	+	0.145816i	0.959930	+	0.280241i	$0.0904145\pi$
$312$	32.5563	+	1.70621i	1.84314	+	0.0965948i
$313$	−2.36870	+	3.64748i	−0.133887	+	0.206168i	−0.899255	−	0.437425i	$-0.855890\pi$
$313$	−2.36870	+	3.64748i	−0.133887	+	0.206168i	0.765368	+	0.643593i	$0.222557\pi$
$314$	−12.2075	−	37.5707i	−0.688908	−	2.12024i
$315$	−9.41832	−	9.70505i	−0.530662	−	0.546818i
$316$	−6.46387	+	19.8938i	−0.363621	+	1.11911i
$317$	13.0585	+	16.1259i	0.733440	+	0.905723i	0.998283	−	0.0585688i	$-0.0186537\pi$
$317$	13.0585	+	16.1259i	0.733440	+	0.905723i	−0.264844	+	0.964291i	$0.585320\pi$
$318$	−6.29216	−	23.4827i	−0.352847	−	1.31684i
$319$	0.000409890	0	0.000920629i	2.29494e−5	0	5.15453e-5i
$320$	−20.2414	−	1.47548i	−1.13153	−	0.0824819i
$321$	−6.61541	−	9.10533i	−0.369236	−	0.508210i
$322$	−30.5868	−	17.4392i	−1.70453	−	0.971849i
$323$	−10.1835	+	19.9862i	−0.566623	+	1.11206i
$324$	−35.9500	+	20.7557i	−1.99722	+	1.15310i
$325$	4.56628	−	14.6262i	0.253291	−	0.811314i
$326$	−11.3803	+	19.7112i	−0.630295	+	1.09170i
$327$	17.7172	−	0.928518i	0.979762	−	0.0513471i
$328$	4.44281	−	28.0508i	0.245313	−	1.54884i
$329$	11.7804	+	3.08831i	0.649477	+	0.170264i
$330$	0.196702	−	0.0709366i	0.0108281	−	0.00390493i
$331$	−1.66114	+	15.8047i	−0.0913045	+	0.868705i	0.849005	+	0.528385i	$0.177202\pi$
$331$	−1.66114	+	15.8047i	−0.0913045	+	0.868705i	−0.940310	+	0.340320i	$0.889465\pi$
$332$	−32.9669	+	8.83346i	−1.80929	+	0.484799i
$333$	17.9308	+	6.88300i	0.982604	+	0.377186i
$334$	−17.9622	+	3.81798i	−0.982848	+	0.208911i
$335$	−0.486565	+	0.518698i	−0.0265839	+	0.0283395i
$336$	−18.5647	+	9.58615i	−1.01279	+	0.522967i
$337$	−11.6113	−	22.7884i	−0.632508	−	1.24137i	−0.955507	−	0.294967i	$-0.904691\pi$
$337$	−11.6113	−	22.7884i	−0.632508	−	1.24137i	0.323000	−	0.946399i	$-0.395309\pi$
$338$	7.35457	+	4.77611i	0.400036	+	0.259786i
$339$	9.00418	+	1.91390i	0.489040	+	0.103949i
$340$	−49.1380	−	37.2561i	−2.66488	−	2.02050i
$341$	−0.0313794	−	0.147628i	−0.00169929	−	0.00799452i
$342$	2.75941	+	17.4222i	0.149212	+	0.942086i
$343$	−17.7044	−	5.43629i	−0.955949	−	0.293532i
$344$	−12.2575	+	16.8710i	−0.660882	+	0.909626i
$345$	−14.8497	−	23.9214i	−0.799483	−	1.28789i
$346$	56.5550	−	5.94418i	3.04042	−	0.319561i
$347$	11.7761	+	9.53608i	0.632173	+	0.511923i	0.891002	−	0.454000i	$-0.150003\pi$
$347$	11.7761	+	9.53608i	0.632173	+	0.511923i	−0.258829	+	0.965923i	$0.583337\pi$
$348$	−0.0282832	−	0.539675i	−0.00151614	−	0.0289296i
$349$	1.48928			0.0797192			0.0398596	−	0.999205i	$-0.487309\pi$
$349$	1.48928			0.0797192			0.0398596	+	0.999205i	$0.487309\pi$
$350$	7.21547	+	31.3239i	0.385683	+	1.67433i
$351$	5.03100			0.268535
$352$	0.000795558		0.0151802i	4.24034e−5		0.000809105i
$353$	−7.30497	−	5.91545i	−0.388804	−	0.314847i	0.414911	−	0.909862i	$-0.363813\pi$
$353$	−7.30497	−	5.91545i	−0.388804	−	0.314847i	−0.803715	+	0.595015i	$0.797146\pi$
$354$	13.9205	−	1.46310i	0.739865	−	0.0777629i
$355$	17.0574	−	4.19943i	0.905311	−	0.222883i
$356$	−19.2088	+	26.4386i	−1.01806	+	1.40124i
$357$	42.7541	+	4.25978i	2.26279	+	0.225451i
$358$	−5.17918	−	32.7001i	−0.273728	−	1.72825i
$359$	−1.27728	−	6.00914i	−0.0674124	−	0.317150i	0.931502	−	0.363736i	$-0.118499\pi$
$359$	−1.27728	−	6.00914i	−0.0674124	−	0.317150i	−0.998914	+	0.0465862i	$0.985166\pi$
$360$	−23.6468	−	0.482594i	−1.24630	−	0.0254349i
$361$	8.72027	+	1.85355i	0.458962	+	0.0975553i
$362$	11.7191	+	7.61049i	0.615944	+	0.399999i
$363$	11.4813	+	22.5332i	0.602610	+	1.18269i
$364$	31.6204	+	1.48557i	1.65736	+	0.0778648i
$365$	7.34263	−	1.40478i	0.384331	−	0.0735295i
$366$	−72.9177	+	15.4991i	−3.81147	+	0.810153i
$367$	33.6866	+	12.9311i	1.75843	+	0.674997i	0.999722	+	0.0235632i	$0.00750108\pi$
$367$	33.6866	+	12.9311i	1.75843	+	0.674997i	0.758705	+	0.651434i	$0.225832\pi$
$368$	−18.1706	+	4.86880i	−0.947209	+	0.253804i
$369$	−1.46660	+	13.9537i	−0.0763479	+	0.726402i
$370$	−27.9994	−	36.0565i	−1.45562	−	1.87449i
$371$	−3.04007	−	11.1049i	−0.157833	−	0.576538i
$372$	−12.6611	+	79.9390i	−0.656447	+	4.14464i
$373$	−18.5645	+	0.972924i	−0.961233	+	0.0503761i	−0.526493	−	0.850180i	$-0.676493\pi$
$373$	−18.5645	+	0.972924i	−0.961233	+	0.0503761i	−0.434741	+	0.900556i	$0.643160\pi$
$374$	−0.143646	+	0.248802i	−0.00742777	+	0.0128653i
$375$	−6.87256	+	24.7691i	−0.354898	+	1.27907i
$376$	18.4455	−	10.6495i	0.951252	−	0.549206i
$377$	−0.0837587	+	0.164386i	−0.00431379	+	0.00846629i
$378$	−9.11160	+	5.32655i	−0.468650	+	0.273968i
$379$	−13.0838	−	18.0083i	−0.672068	−	0.925022i	0.327737	−	0.944769i	$-0.393714\pi$
$379$	−13.0838	−	18.0083i	−0.672068	−	0.925022i	−0.999805	+	0.0197466i	$0.993714\pi$
$380$	10.4616	−	25.6748i	0.536667	−	1.31709i
$381$	−6.81365	−	15.3037i	−0.349074	−	0.784032i
$382$	9.31932	+	34.7802i	0.476818	+	1.77951i
$383$	−9.68844	−	11.9642i	−0.495056	−	0.611344i	0.466979	−	0.884268i	$-0.345342\pi$
$383$	−9.68844	−	11.9642i	−0.495056	−	0.611344i	−0.962035	+	0.272925i	$0.912009\pi$
$384$	14.3783	−	44.2520i	0.733742	−	2.25822i
$385$	0.0929731	−	0.0340988i	0.00473835	−	0.00173783i
$386$	−12.4942	−	38.4531i	−0.635937	−	1.95721i
$387$	5.61105	−	8.64026i	0.285226	−	0.439209i
$388$	−26.8279	−	1.40599i	−1.36198	−	0.0713784i
$389$	2.47851	−	11.6605i	0.125666	−	0.591211i	−0.869578	−	0.493795i	$-0.835609\pi$
$389$	2.47851	−	11.6605i	0.125666	−	0.591211i	0.995244	−	0.0974152i	$-0.0310575\pi$
$390$	32.7551	+	19.8131i	1.65862	+	1.00327i
$391$	36.7909	+	11.9541i	1.86060	+	0.604545i
$392$	−28.6988	+	15.0163i	−1.44951	+	0.758440i
$393$	19.2328	+	19.2328i	0.970168	+	0.970168i
$394$	37.5961	+	3.95151i	1.89407	+	0.199074i
$395$	−8.64219	+	8.29649i	−0.434836	+	0.417442i
$396$	0.0156159	+	0.148576i	0.000784729	+	0.00746620i
$397$	−2.42929	−	6.32850i	−0.121922	−	0.317619i	0.859013	−	0.511954i	$-0.171078\pi$
$397$	−2.42929	−	6.32850i	−0.121922	−	0.317619i	−0.980935	+	0.194336i	$0.937745\pi$
$398$	4.28222	+	2.18190i	0.214648	+	0.109369i
$399$	3.12512	+	19.0628i	0.156452	+	0.954335i
$400$	14.5105	+	9.18673i	0.725524	+	0.459336i
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	0.542220	−	0.840237i	$-0.317584\pi$
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	−0.998776	+	0.0494575i	$0.984251\pi$
$402$	−0.967730	−	1.49017i	−0.0482660	−	0.0743231i
$403$	17.3887	−	21.4732i	0.866190	−	1.06966i
$404$	37.8213	+	16.8391i	1.88168	+	0.837779i
$405$	−23.7624	+	0.759570i	−1.18076	+	0.0377433i
$406$	−0.0223482	−	0.386397i	−0.00110912	−	0.0191765i
$407$	−0.0994483	+	0.0994483i	−0.00492947	+	0.00492947i
$408$	58.3969	−	47.2888i	2.89108	−	2.34115i
$409$	−10.6452	−	11.8226i	−0.526369	−	0.584592i	0.420063	−	0.907495i	$-0.362008\pi$
$409$	−10.6452	−	11.8226i	−0.526369	−	0.584592i	−0.946432	+	0.322903i	$0.895341\pi$
$410$	20.1483	−	26.5742i	0.995056	−	1.31240i
$411$	−5.62843	−	5.06786i	−0.277630	−	0.249979i
$412$	−0.761163	+	0.387832i	−0.0374998	+	0.0191071i
$413$	6.58878	−	0.728590i	0.324213	−	0.0358516i
$414$	28.9318	−	9.40052i	1.42192	−	0.462010i
$415$	−19.0329	−	4.45332i	−0.934288	−	0.218605i
$416$	−2.06811	+	1.86214i	−0.101397	+	0.0912987i
$417$	−3.74639	+	9.75968i	−0.183462	+	0.477934i
$418$	−0.124765	−	0.0334306i	−0.00610243	−	0.00163514i
$419$	−28.7560	−	20.8925i	−1.40482	−	1.02066i	−0.994050	−	0.108926i	$-0.965259\pi$
$419$	−28.7560	−	20.8925i	−1.40482	−	1.02066i	−0.410773	−	0.911738i	$-0.634741\pi$
$420$	−53.0991	−	0.796143i	−2.59097	−	0.0388478i
$421$	−11.3679	+	8.25925i	−0.554037	+	0.402531i	−0.829272	−	0.558846i	$-0.811244\pi$
$421$	−11.3679	+	8.25925i	−0.554037	+	0.402531i	0.275235	+	0.961377i	$0.411244\pi$
$422$	−20.7342	+	7.95910i	−1.00932	+	0.387443i
$423$	−8.82473	+	5.73085i	−0.429073	+	0.278643i
$424$	−17.4383	−	10.0680i	−0.846876	−	0.488944i
$425$	−14.7363	−	32.0956i	−0.714816	−	1.55686i
$426$			43.8884i			2.12640i
$427$	−34.4930	+	7.52710i	−1.66923	+	0.364262i
$428$	−18.8772	−	2.98985i	−0.912464	−	0.144520i
$429$	0.0479688	−	0.107740i	0.00231596	−	0.00520172i
$430$	−22.0406	+	10.6695i	−1.06289	+	0.514527i
$431$	3.47670	−	1.54793i	0.167467	−	0.0745610i	−0.321291	−	0.946980i	$-0.604117\pi$
$431$	3.47670	−	1.54793i	0.167467	−	0.0745610i	0.488758	+	0.872419i	$0.337450\pi$
$432$	−1.45948	+	5.44685i	−0.0702192	+	0.262061i
$433$	−1.22529	+	0.194066i	−0.0588836	+	0.00932624i	−0.185807	−	0.982586i	$-0.559490\pi$
$433$	−1.22529	+	0.194066i	−0.0588836	+	0.00932624i	0.126923	+	0.991913i	$0.459490\pi$
$434$	−8.75776	+	57.3001i	−0.420386	+	2.75049i
$435$	0.131631	−	0.280122i	0.00631124	−	0.0134308i
$436$	20.1595	−	22.3894i	0.965467	−	1.07226i
$437$	−0.910245	+	17.3685i	−0.0435429	+	0.830848i
$438$	−0.977501	+	18.6518i	−0.0467068	+	0.891219i
$439$	−3.64427	+	4.04738i	−0.173932	+	0.193171i	−0.823807	−	0.566870i	$-0.808154\pi$
$439$	−3.64427	+	4.04738i	−0.173932	+	0.193171i	0.649876	+	0.760041i	$0.274821\pi$
$440$	0.0736569	−	0.156748i	0.00351146	−	0.00747266i
$441$	13.7703	−	8.15034i	0.655730	−	0.388111i
$442$	−51.9485	+	8.22783i	−2.47094	+	0.391358i
$443$	−4.73507	+	17.6715i	−0.224970	+	0.839599i	0.757447	+	0.652897i	$0.226447\pi$
$443$	−4.73507	+	17.6715i	−0.224970	+	0.839599i	−0.982417	+	0.186702i	$0.940220\pi$
$444$	68.8995	−	30.6760i	3.26983	−	1.45582i
$445$	−16.8465	+	8.15509i	−0.798599	+	0.386589i
$446$	−7.35106	+	16.5107i	−0.348083	+	0.781807i
$447$	−41.2945	−	6.54041i	−1.95316	−	0.309351i
$448$	7.29685	−	22.8780i	0.344744	−	1.08089i
$449$		−	7.28927i		−	0.344002i	−0.985097	−	0.172001i	$-0.944977\pi$
$449$		−	7.28927i		−	0.344002i	0.985097	−	0.172001i	$-0.0550232\pi$
$450$	−24.2106	−	13.6076i	−1.14130	−	0.641471i
$451$	−0.0889755	−	0.0513700i	−0.00418969	−	0.00241892i
$452$	13.1102	−	8.51389i	0.616654	−	0.400460i
$453$	−40.5667	+	15.5721i	−1.90599	+	0.731641i
$454$	23.0343	−	16.7354i	1.08105	−	0.785432i
$455$	15.5631	+	9.29922i	0.729611	+	0.435954i
$456$	27.3318	+	19.8577i	1.27993	+	0.929922i
$457$	−11.4145	−	3.05849i	−0.533946	−	0.143070i	−0.0182361	−	0.999834i	$-0.505805\pi$
$457$	−11.4145	−	3.05849i	−0.533946	−	0.143070i	−0.515710	+	0.856763i	$0.672472\pi$
$458$	−23.4596	+	61.1145i	−1.09620	+	2.85569i
$459$	8.61754	−	7.75927i	0.402232	−	0.362172i
$460$	−46.5558	−	10.8931i	−2.17067	−	0.507894i
$461$	0.809532	−	0.263033i	0.0377037	−	0.0122507i	−0.290104	−	0.956995i	$-0.593690\pi$
$461$	0.809532	−	0.263033i	0.0377037	−	0.0122507i	0.327808	+	0.944744i	$0.393690\pi$
$462$	0.0271932	+	0.245913i	0.00126514	+	0.0114409i
$463$	34.4372	−	17.5466i	1.60043	−	0.815460i	0.600557	−	0.799582i	$-0.294945\pi$
$463$	34.4372	−	17.5466i	1.60043	−	0.815460i	0.999874	−	0.0158788i	$-0.00505458\pi$
$464$	−0.153675	−	0.138370i	−0.00713419	−	0.00642365i
$465$	−28.0055	+	36.9371i	−1.29872	+	1.71292i
$466$	−35.5202	−	39.4492i	−1.64544	−	1.82745i
$467$	−6.95024	+	5.62819i	−0.321619	+	0.260442i	−0.776509	−	0.630106i	$-0.783012\pi$
$467$	−6.95024	+	5.62819i	−0.321619	+	0.260442i	0.454891	+	0.890547i	$0.349678\pi$
$468$	−19.3396	+	19.3396i	−0.893972	+	0.893972i
$469$	−0.462123	−	0.703244i	−0.0213389	−	0.0324728i
$470$	24.9973	−	0.799042i	1.15304	−	0.0368570i
$471$	34.1469	+	15.2032i	1.57341	+	0.700525i
$472$	7.29593	−	9.00972i	0.335822	−	0.414706i
$473$	0.0410873	+	0.0632689i	0.00188920	+	0.00290911i
$474$	−14.9653	−	25.9206i	−0.687377	−	1.19057i
$475$	12.2236	−	10.1344i	0.560857	−	0.464999i
$476$	56.4535	−	46.2233i	2.58754	−	2.11864i
$477$	8.86348	+	4.51617i	0.405831	+	0.206781i
$478$	−3.71597	−	9.68044i	−0.169965	−	0.442773i
$479$	0.101310	+	0.963902i	0.00462898	+	0.0440418i	0.996593	−	0.0824819i	$-0.0262847\pi$
$479$	0.101310	+	0.963902i	0.00462898	+	0.0440418i	−0.991964	+	0.126524i	$0.959618\pi$
$480$	3.36789	−	3.23318i	0.153723	−	0.147574i
$481$	−25.6068	−	2.69138i	−1.16757	−	0.122717i
$482$	−0.282157	−	0.282157i	−0.0128519	−	0.0128519i
$483$	31.6277	−	10.4661i	1.43911	−	0.476223i
$484$	40.8440	+	13.2710i	1.85655	+	0.603228i
$485$	−13.1650	−	7.96330i	−0.597790	−	0.361595i
$486$	9.86136	−	46.3941i	0.447320	−	2.10448i
$487$	34.6240	+	1.81457i	1.56896	+	0.0822258i	0.816866	−	0.576827i	$-0.195709\pi$
$487$	34.6240	+	1.81457i	1.56896	+	0.0822258i	0.752096	+	0.659053i	$0.229043\pi$
$488$	−33.6284	+	51.7832i	−1.52229	+	2.34412i
$489$	−6.65491	−	20.4817i	−0.300946	−	0.926215i
$490$	−38.0318	−	0.364328i	−1.71810	−	0.0164587i
$491$	1.58176	−	4.86817i	0.0713840	−	0.219697i	−0.908999	−	0.416798i	$-0.863152\pi$
$491$	1.58176	−	4.86817i	0.0713840	−	0.219697i	0.980383	+	0.197100i	$0.0631524\pi$
$492$	34.6725	+	42.8170i	1.56316	+	1.93034i
$493$	0.110061	+	0.410755i	0.00495692	+	0.0184995i
$494$	−9.61810	−	21.6026i	−0.432739	−	0.971948i
$495$	−0.0322859	+	0.0792361i	−0.00145114	+	0.00356140i
$496$	18.2037	+	25.0553i	0.817371	+	1.12501i
$497$	0.112513	+	20.7849i	0.00504690	+	0.932330i
$498$	22.1710	−	43.5130i	0.993506	−	1.94986i
$499$	−31.5502	+	18.2155i	−1.41238	+	0.815438i	−0.995612	−	0.0935745i	$-0.970171\pi$
$499$	−31.5502	+	18.2155i	−1.41238	+	0.815438i	−0.416768	+	0.909013i	$0.636837\pi$
$500$	21.4899	+	37.9948i	0.961058	+	1.69918i
$501$	8.68766	−	15.0475i	0.388136	−	0.672271i
$502$	0.321042	−	0.0168251i	0.0143288	−	0.000750941i
$503$	−0.209162	+	1.32059i	−0.00932605	+	0.0588824i	−0.991912	−	0.126924i	$-0.959490\pi$
$503$	−0.209162	+	1.32059i	−0.00932605	+	0.0588824i	0.982586	+	0.185806i	$0.0594896\pi$
$504$	7.09664	−	27.0703i	0.316110	−	1.20581i
$505$	14.5428	+	18.7276i	0.647145	+	0.833367i
$506$	−0.0232846	+	0.221538i	−0.00103512	+	0.00984855i
$507$	−8.01470	+	2.14753i	−0.355945	+	0.0953752i
$508$	−26.5581	−	10.1947i	−1.17833	−	0.452317i
$509$	−18.7407	+	3.98347i	−0.830669	+	0.176564i	−0.603573	−	0.797308i	$-0.706257\pi$
$509$	−18.7407	+	3.98347i	−0.830669	+	0.176564i	−0.227097	+	0.973872i	$0.572923\pi$
$510$	86.6634	−	16.5803i	3.83752	−	0.734188i
$511$	−0.415114	+	8.83574i	−0.0183636	+	0.390870i
$512$	−15.8470	−	31.1015i	−0.700346	−	1.37451i
$513$	4.37245	+	2.83950i	0.193048	+	0.125367i
$514$	−21.8420	−	4.64266i	−0.963409	−	0.204779i
$515$	−0.489160	−	0.00998298i	−0.0215550	−	0.000439903i
$516$	−8.41107	−	39.5710i	−0.370277	−	1.74202i
$517$	−0.0120533	−	0.0761016i	−0.000530104	−	0.00334694i
$518$	49.2258	−	22.2368i	2.16286	−	0.977028i
$519$	−31.6267	+	43.5304i	−1.38826	+	1.91077i
$520$	30.7877	−	7.57976i	1.35013	−	0.332394i
$521$	14.5325	−	1.52742i	0.636678	−	0.0669176i	0.219310	−	0.975655i	$-0.429619\pi$
$521$	14.5325	−	1.52742i	0.636678	−	0.0669176i	0.417368	+	0.908738i	$0.362953\pi$
$522$	0.259882	+	0.210448i	0.0113747	+	0.00921108i
$523$	1.82151	+	34.7566i	0.0796493	+	1.51980i	0.687755	+	0.725943i	$0.258596\pi$
$523$	1.82151	+	34.7566i	0.0796493	+	1.51980i	−0.608106	+	0.793856i	$0.708070\pi$
$524$	46.1889			2.01777
$525$	−26.5938	−	14.7583i	−1.16065	−	0.644105i
$526$	50.8274			2.21618
$527$	−3.33311	−	63.5996i	−0.145193	−	2.77044i
$528$	0.102730	+	0.0831888i	0.00447073	+	0.00362033i
$529$	6.95634	−	0.731141i	0.302449	−	0.0317887i
$530$	−12.4703	−	20.0884i	−0.541677	−	0.872586i
$531$	−3.36650	+	4.63359i	−0.146094	+	0.201081i
$532$	26.6429	+	19.1377i	1.15512	+	0.829725i
$533$	−2.94239	−	18.5775i	−0.127449	−	0.804683i
$534$	−9.72219	−	45.7393i	−0.420720	−	1.97933i
$535$	−8.72251	−	6.61335i	−0.377107	−	0.285920i
$536$	−1.43952	−	0.305980i	−0.0621780	−	0.0132163i
$537$	26.2723	+	17.0614i	1.13373	+	0.736255i
$538$	1.66857	+	3.27475i	0.0719372	+	0.141185i
$539$	0.0135087	+	0.116391i	0.000581862	+	0.00501333i
$540$	−9.80566	+	10.4532i	−0.421969	+	0.449836i
$541$	16.9335	−	3.59933i	0.728028	−	0.154747i	0.171036	−	0.985265i	$-0.445289\pi$
$541$	16.9335	−	3.59933i	0.728028	−	0.154747i	0.556992	+	0.830518i	$0.311955\pi$
$542$	20.6130	+	7.91260i	0.885405	+	0.339875i
$543$	−12.7710	+	3.42198i	−0.548057	+	0.146851i
$544$	−0.670488	+	6.37926i	−0.0287469	+	0.273509i
$545$	16.2317	−	5.85365i	0.695290	−	0.250743i
$546$	−31.8546	+	32.2013i	−1.36325	+	1.37809i
$547$	1.54775	−	9.77211i	0.0661770	−	0.417825i	−0.932253	−	0.361808i	$-0.882160\pi$
$547$	1.54775	−	9.77211i	0.0661770	−	0.417825i	0.998430	−	0.0560177i	$-0.0178403\pi$
$548$	−12.8439	+	0.673121i	−0.548665	+	0.0287543i
$549$	15.2517	−	26.4167i	0.650927	−	1.12744i
$550$	0.163136	−	0.121428i	0.00695615	−	0.00517773i
$551$	−0.165574	+	0.0955944i	−0.00705370	+	0.00407246i
$552$	26.4511	−	51.9131i	1.12583	−	2.20957i
$553$	−7.15378	−	12.2373i	−0.304210	−	0.520381i
$554$	−19.5157	−	26.8610i	−0.829142	−	1.14122i
$555$	43.0804	+	3.14031i	1.82866	+	0.133299i
$556$	7.22066	+	16.2179i	0.306224	+	0.687791i
$557$	−4.19928	−	15.6719i	−0.177929	−	0.664041i	−0.996034	−	0.0889717i	$-0.971642\pi$
$557$	−4.19928	−	15.6719i	−0.177929	−	0.664041i	0.818105	−	0.575069i	$-0.195025\pi$
$558$	−31.5179	−	38.9213i	−1.33426	−	1.64767i
$559$	−4.26786	+	13.1351i	−0.180511	+	0.555557i
$560$	−14.5827	+	14.1519i	−0.616231	+	0.598025i
$561$	−0.0840009	−	0.258528i	−0.00354652	−	0.0109151i
$562$	5.27488	−	8.12260i	0.222507	−	0.342631i
$563$	30.9666	+	1.62289i	1.30509	+	0.0683966i	0.692160	−	0.721744i	$-0.256659\pi$
$563$	30.9666	+	1.62289i	1.30509	+	0.0683966i	0.612925	+	0.790141i	$0.289993\pi$
$564$	−8.59065	+	40.4158i	−0.361732	+	1.70181i
$565$	8.92109	−	0.753962i	0.375313	−	0.0317194i
$566$	−43.6698	−	14.1892i	−1.83558	−	0.596416i
$567$	5.69961	−	27.5470i	0.239361	−	1.15686i
$568$	25.7042	+	25.7042i	1.07852	+	1.07852i
$569$	−13.2566	−	1.39333i	−0.555746	−	0.0584112i	−0.177507	−	0.984119i	$-0.556803\pi$
$569$	−13.2566	−	1.39333i	−0.555746	−	0.0584112i	−0.378238	+	0.925708i	$0.623470\pi$
$570$	17.2850	+	35.7066i	0.723988	+	1.49559i
$571$	−0.872701	−	8.30320i	−0.0365214	−	0.347478i	−0.997489	−	0.0708179i	$-0.977439\pi$
$571$	−0.872701	−	8.30320i	−0.0365214	−	0.347478i	0.960968	−	0.276660i	$-0.0892276\pi$
$572$	−0.0717719	−	0.186972i	−0.00300093	−	0.00781770i
$573$	−30.3562	−	15.4672i	−1.26815	−	0.646153i
$574$	24.9979	+	30.5304i	1.04339	+	1.27431i
$575$	−20.5603	−	18.0870i	−0.857424	−	0.754281i
$576$	10.3739	+	17.9681i	0.432245	+	0.748670i
$577$	18.8463	+	29.0208i	0.784582	+	1.20815i	0.974065	+	0.226267i	$0.0726522\pi$
$577$	18.8463	+	29.0208i	0.784582	+	1.20815i	−0.189483	+	0.981884i	$0.560681\pi$
$578$	−50.2964	+	62.1109i	−2.09205	+	2.58347i
$579$	34.9489	+	15.5602i	1.45242	+	0.646661i
$580$	−0.178305	−	0.494427i	−0.00740373	−	0.0205300i
$581$	10.3883	−	20.6640i	0.430979	−	0.857286i
$582$	27.1814	−	27.1814i	1.12670	−	1.12670i
$583$	−0.0566095	+	0.0458415i	−0.00234453	+	0.00189856i
$584$	10.3514	+	11.4963i	0.428342	+	0.475722i
$585$	−14.9931	+	4.53550i	−0.619890	+	0.187520i
$586$	12.6287	+	11.3709i	0.521687	+	0.469729i
$587$	−17.8813	+	9.11097i	−0.738039	+	0.376050i	−0.782244	−	0.622973i	$-0.785925\pi$
$587$	−17.8813	+	9.11097i	−0.738039	+	0.376050i	0.0442042	+	0.999023i	$0.485925\pi$
$588$	15.6048	−	60.8662i	0.643531	−	2.51008i
$589$	27.2320	−	8.84822i	1.12208	−	0.364584i
$590$	12.5468	−	5.28212i	0.516542	−	0.217462i
$591$	−26.5815	+	23.9341i	−1.09342	+	0.984518i
$592$	10.3423	−	26.9426i	0.425066	−	1.10734i
$593$	17.9557	+	4.81121i	0.737352	+	0.197573i	0.607901	−	0.794013i	$-0.292012\pi$
$593$	17.9557	+	4.81121i	0.737352	+	0.197573i	0.129451	+	0.991586i	$0.458678\pi$
$594$	0.0540215	+	0.0392489i	0.00221653	+	0.00161040i
$595$	41.0000	−	8.07436i	1.68084	−	0.331016i
$596$	−57.4394	+	41.7321i	−2.35281	+	1.70942i
$597$	−4.24539	+	1.62965i	−0.173752	+	0.0666972i
$598$	−34.2022	+	22.2111i	−1.39863	+	0.908281i
$599$	−30.6038	−	17.6691i	−1.25044	−	0.721941i	−0.279241	−	0.960221i	$-0.590083\pi$
$599$	−30.6038	−	17.6691i	−1.25044	−	0.721941i	−0.971196	+	0.238280i	$0.923416\pi$
$600$	−51.2169	+	14.3595i	−2.09092	+	0.586223i
$601$		−	0.819532i		−	0.0334294i	−0.999860	−	0.0167147i	$-0.994679\pi$
$601$		−	0.819532i		−	0.0334294i	0.999860	−	0.0167147i	$-0.00532070\pi$
$602$	−6.17729	−	28.3075i	−0.251767	−	1.15373i
$603$	0.718101	+	0.113736i	0.0292433	+	0.00463169i
$604$	−30.0131	+	67.4105i	−1.22122	+	2.74290i
$605$	17.0336	+	17.7433i	0.692514	+	0.721369i
$606$	−54.1179	+	24.0948i	−2.19839	+	0.978786i
$607$	3.58282	−	13.3713i	0.145422	−	0.542724i	−0.854314	−	0.519757i	$-0.826022\pi$
$607$	3.58282	−	13.3713i	0.145422	−	0.542724i	0.999736	−	0.0229662i	$-0.00731101\pi$
$608$	−2.84839	+	0.451141i	−0.115518	+	0.0182962i
$609$	0.285846	+	0.228923i	0.0115831	+	0.00927642i
$610$	−63.5156	+	34.9625i	−2.57167	+	1.41559i
$611$	9.43873	−	10.4828i	0.381850	−	0.424087i
$612$	−3.29927	+	62.9538i	−0.133365	+	2.54476i
$613$	−2.00609	+	38.2785i	−0.0810253	+	1.54605i	0.591697	+	0.806160i	$0.298458\pi$
$613$	−2.00609	+	38.2785i	−0.0810253	+	1.54605i	−0.672723	+	0.739895i	$0.734875\pi$
$614$	−10.9559	+	12.1678i	−0.442144	+	0.491051i
$615$	5.92936	+	30.9921i	0.239095	+	1.24972i
$616$	0.159951	+	0.128098i	0.00644460	+	0.00516122i
$617$	−16.5933	+	2.62812i	−0.668022	+	0.105804i	−0.481229	−	0.876595i	$-0.659809\pi$
$617$	−16.5933	+	2.62812i	−0.668022	+	0.105804i	−0.186793	+	0.982399i	$0.559809\pi$
$618$	0.316371	−	1.18071i	0.0127263	−	0.0474952i
$619$	−5.67928	+	2.52858i	−0.228269	+	0.101632i	−0.517685	−	0.855572i	$-0.673206\pi$
$619$	−5.67928	+	2.52858i	−0.228269	+	0.101632i	0.289415	+	0.957204i	$0.406539\pi$
$620$	10.7250	+	77.9819i	0.430725	+	3.13183i
$621$	3.65706	−	8.21390i	0.146753	−	0.329612i
$622$	−6.30933	−	0.999300i	−0.252981	−	0.0400683i
$623$	−4.72154	−	21.6365i	−0.189165	−	0.866850i
$624$			24.2004i			0.968790i
$625$	0.577384	+	24.9933i	0.0230954	+	0.999733i
$626$	−9.15199	−	5.28391i	−0.365787	−	0.211187i
$627$	0.102498	−	0.0665632i	0.00409339	−	0.00265828i
$628$	59.2587	−	22.7473i	2.36468	−	0.907716i
$629$	−48.0125	+	34.8832i	−1.91439	+	1.39088i
$630$	22.3520	−	24.0881i	0.890524	−	0.959695i
$631$	−16.6120	−	12.0693i	−0.661312	−	0.480471i	0.205794	−	0.978595i	$-0.434022\pi$
$631$	−16.6120	−	12.0693i	−0.661312	−	0.480471i	−0.867106	+	0.498124i	$0.834022\pi$
$632$	−23.9457	−	6.41622i	−0.952508	−	0.255224i
$633$	7.53080	−	19.6184i	0.299323	−	0.779762i
$634$	−37.4696	+	33.7378i	−1.48811	+	1.33990i
$635$	−10.6526	−	12.3277i	−0.422734	−	0.489209i
$636$	37.1507	−	12.0710i	1.47312	−	0.478646i
$637$	−15.0033	+	15.3317i	−0.594452	+	0.607465i
$638$	−0.00218182	+	0.00111169i	−8.63790e−5	+	4.40123e-5i
$639$	−13.3458	−	12.0166i	−0.527950	−	0.475368i
$640$	0.923356	−	45.2439i	0.0364989	−	1.78842i
$641$	6.22319	+	6.91155i	0.245801	+	0.272990i	0.853403	−	0.521252i	$-0.174535\pi$
$641$	6.22319	+	6.91155i	0.245801	+	0.272990i	−0.607602	+	0.794242i	$0.707868\pi$
$642$	21.2532	−	17.2105i	0.838796	−	0.679244i
$643$	10.6811	−	10.6811i	0.421223	−	0.421223i	−0.464402	−	0.885625i	$-0.653731\pi$
$643$	10.6811	−	10.6811i	0.421223	−	0.421223i	0.885625	+	0.464402i	$0.153731\pi$
$644$	25.4105	−	50.5455i	1.00131	−	1.99177i
$645$	6.45211	−	22.2530i	0.254052	−	0.876212i
$646$	−49.7923	−	22.1690i	−1.95905	−	0.872226i
$647$	9.53557	−	11.7754i	0.374882	−	0.462940i	−0.554433	−	0.832228i	$-0.687065\pi$
$647$	9.53557	−	11.7754i	0.374882	−	0.462940i	0.929315	+	0.369288i	$0.120398\pi$
$648$	−26.7947	−	41.2603i	−1.05260	−	1.62086i
$649$	−0.0209698	−	0.0363207i	−0.000823135	−	0.00142571i
$650$	36.0717	+	9.22025i	1.41485	+	0.361648i
$651$	−34.7461	−	42.4361i	−1.36181	−	1.66320i
$652$	−32.5852	−	16.6030i	−1.27614	−	0.650223i
$653$	−12.9236	−	33.6671i	−0.505740	−	1.31750i	−0.914401	−	0.404811i	$-0.867337\pi$
$653$	−12.9236	−	33.6671i	−0.505740	−	1.31750i	0.408661	−	0.912686i	$-0.365996\pi$
$654$	4.50617	+	42.8734i	0.176205	+	1.67648i
$655$	23.3202	+	12.4880i	0.911197	+	0.487948i
$656$	20.9667	+	2.20369i	0.818612	+	0.0860396i
$657$	−5.40409	−	5.40409i	−0.210833	−	0.210833i
$658$	−5.99580	+	28.9785i	−0.233741	+	1.12970i
$659$	30.6779	+	9.96786i	1.19504	+	0.388293i	0.837935	−	0.545771i	$-0.183763\pi$
$659$	30.6779	+	9.96786i	1.19504	+	0.388293i	0.357107	+	0.934063i	$0.383763\pi$
$660$	0.130365	+	0.309658i	0.00507443	+	0.0120534i
$661$	3.78793	−	17.8208i	0.147333	−	0.693149i	−0.841024	−	0.540998i	$-0.818047\pi$
$661$	3.78793	−	17.8208i	0.147333	−	0.693149i	0.988357	−	0.152151i	$-0.0486199\pi$
$662$	−38.5620	−	2.02095i	−1.49875	−	0.0785464i
$663$	27.1044	−	41.7371i	1.05265	−	1.62093i
$664$	−12.4994	−	38.4692i	−0.485071	−	1.49290i
$665$	8.27745	+	16.8658i	0.320986	+	0.654028i
$666$	−14.4216	+	44.3852i	−0.558827	+	1.71989i
$667$	0.207501	+	0.256242i	0.00803447	+	0.00992174i
$668$	−7.63675	−	28.5007i	−0.295475	−	1.10273i
$669$	−6.95549	−	15.6223i	−0.268915	−	0.603992i
$670$	−1.32052	−	1.11471i	−0.0510161	−	0.0430649i
$671$	0.131290	+	0.180705i	0.00506839	+	0.00697604i
$672$	2.78786	+	4.76890i	0.107544	+	0.183964i
$673$	−8.71675	+	17.1076i	−0.336006	+	0.659449i	−0.995756	−	0.0920367i	$-0.970662\pi$
$673$	−8.71675	+	17.1076i	−0.336006	+	0.659449i	0.659750	+	0.751485i	$0.270662\pi$
$674$	53.8205	−	31.0733i	2.07309	−	1.19690i
$675$	−7.77700	+	2.62657i	−0.299337	+	0.101097i
$676$	−7.04519	+	12.2026i	−0.270969	+	0.469332i
$677$	35.4419	−	1.85743i	1.36214	−	0.0713870i	0.642797	−	0.766037i	$-0.277774\pi$
$677$	35.4419	−	1.85743i	1.36214	−	0.0713870i	0.719348	+	0.694650i	$0.244441\pi$
$678$	−3.49909	+	22.0924i	−0.134382	+	0.848453i
$679$	12.8030	−	12.9424i	0.491335	−	0.496683i
$680$	41.0457	−	60.4669i	1.57403	−	2.31880i
$681$	−2.81598	+	26.7923i	−0.107909	+	1.02668i
$682$	0.354236	−	0.0949172i	0.0135644	−	0.00363457i
$683$	8.91129	+	3.42072i	0.340981	+	0.130890i	0.522832	−	0.852436i	$-0.324876\pi$
$683$	8.91129	+	3.42072i	0.340981	+	0.130890i	−0.181851	+	0.983326i	$0.558209\pi$
$684$	−27.7233	+	5.89278i	−1.06003	+	0.225316i
$685$	−6.66673	−	3.13274i	−0.254723	−	0.119696i
$686$	10.9399	−	43.6519i	0.417688	−	1.66664i
$687$	−28.1201	−	55.1888i	−1.07285	−	2.10558i
$688$	−12.9827	−	8.43109i	−0.494962	−	0.321432i
$689$	−13.0443	−	2.77265i	−0.496948	−	0.105629i
$690$	56.1579	−	39.0756i	2.13789	−	1.48758i
$691$	10.4781	+	49.2956i	0.398606	+	1.87529i	0.477855	+	0.878439i	$0.341415\pi$
$691$	10.4781	+	49.2956i	0.398606	+	1.87529i	−0.0792486	+	0.996855i	$0.525252\pi$
$692$	14.2938	+	90.2473i	0.543367	+	3.43069i
$693$	−0.0822238	−	0.0590617i	−0.00312342	−	0.00224357i
$694$	−21.6421	+	29.7878i	−0.821524	+	1.13073i
$695$	−0.739180	+	10.1405i	−0.0280387	+	0.384649i
$696$	0.636964	−	0.0669476i	0.0241441	−	0.00253764i
$697$	−33.6920	−	27.2832i	−1.27618	−	1.03343i
$698$	0.189391	+	3.61379i	0.00716855	+	0.136784i
$699$	50.2276			1.89978
$700$	−49.6549	+	14.2119i	−1.87678	+	0.537160i
$701$	41.2864			1.55936			0.779682	−	0.626176i	$-0.215381\pi$
$701$	41.2864			1.55936			0.779682	+	0.626176i	$0.215381\pi$
$702$	0.639790	+	12.2079i	0.0241473	+	0.460758i
$703$	−20.7359	−	16.7916i	−0.782070	−	0.633307i
$704$	−0.151095	+	0.0158807i	−0.00569460	+	0.000598526i
$705$	−15.2645	+	18.0828i	−0.574895	+	0.681039i
$706$	13.4251	−	18.4781i	0.505261	−	0.695431i
$707$	−25.5677	+	11.5497i	−0.961571	+	0.434371i
$708$	3.51827	+	22.2135i	0.132225	+	0.834834i
$709$	0.400572	+	1.88454i	0.0150438	+	0.0707755i	0.985029	−	0.172388i	$-0.0551482\pi$
$709$	0.400572	+	1.88454i	0.0150438	+	0.0707755i	−0.969985	+	0.243163i	$0.921815\pi$
$710$	12.3593	+	40.8564i	0.463835	+	1.53331i
$711$	11.9795	+	2.54632i	0.449266	+	0.0954945i
$712$	−32.4822	−	21.0942i	−1.21732	−	0.790538i
$713$	−22.4185	−	43.9987i	−0.839578	−	1.64777i
$714$	−4.89950	+	104.286i	−0.183359	+	3.90282i
$715$	0.0143147	−	0.113805i	0.000535338	−	0.00425606i
$716$	52.0344	−	11.0603i	1.94462	−	0.413341i
$717$	9.15952	+	3.51601i	0.342069	+	0.131308i
$718$	14.4190	−	3.86356i	0.538112	−	0.144187i
$719$	5.06873	−	48.2257i	0.189032	−	1.79852i	−0.330230	−	0.943900i	$-0.607126\pi$
$719$	5.06873	−	48.2257i	0.189032	−	1.79852i	0.519262	−	0.854615i	$-0.326207\pi$
$720$	−0.560930	−	17.5482i	−0.0209046	−	0.653981i
$721$	0.146802	−	0.559980i	0.00546719	−	0.0208547i
$722$	−3.38876	+	21.3958i	−0.126117	+	0.796270i
$723$	0.377040	−	0.0197598i	0.0140223	−	0.000734876i
$724$	−11.2262	+	19.4443i	−0.417217	+	0.722641i
$725$	0.0436533	−	0.297839i	0.00162124	−	0.0110614i
$726$	−53.2178	+	30.7253i	−1.97510	+	1.14032i
$727$	3.31875	−	6.51342i	0.123086	−	0.241569i	−0.821239	−	0.570584i	$-0.806717\pi$
$727$	3.31875	−	6.51342i	0.123086	−	0.241569i	0.944325	+	0.329015i	$0.106717\pi$
$728$	0.203080	+	37.5157i	0.00752665	+	1.39042i
$729$	7.63022	+	10.5021i	0.282601	+	0.388967i
$730$	4.34251	+	17.6386i	0.160724	+	0.652832i
$731$	12.9478	+	29.0813i	0.478893	+	1.07561i
$732$	−31.0015	−	115.699i	−1.14585	−	4.27636i
$733$	−6.48565	−	8.00911i	−0.239553	−	0.295823i	0.643164	−	0.765729i	$-0.277621\pi$
$733$	−6.48565	−	8.00911i	−0.239553	−	0.295823i	−0.882717	+	0.469905i	$0.844288\pi$
$734$	−27.0939	+	83.3864i	−1.00005	+	3.07785i
$735$	24.3350	−	26.5116i	0.897610	−	0.977894i
$736$	1.53691	+	4.73012i	0.0566512	+	0.174354i
$737$	−0.00289960	+	0.00446499i	−0.000106808	+	0.000164470i
$738$	−34.0458	−	1.78427i	−1.25324	−	0.0656797i
$739$	4.57499	−	21.5236i	0.168294	−	0.791759i	−0.810309	−	0.586002i	$-0.800701\pi$
$739$	4.57499	−	21.5236i	0.168294	−	0.791759i	0.978603	−	0.205757i	$-0.0659657\pi$
$740$	55.5010	−	47.9594i	2.04026	−	1.76302i
$741$	21.2794	+	6.91411i	0.781720	+	0.253996i
$742$	26.5599	−	8.78907i	0.975045	−	0.322657i
$743$	−32.3075	−	32.3075i	−1.18525	−	1.18525i	−0.978366	−	0.206883i	$-0.933668\pi$
$743$	−32.3075	−	32.3075i	−1.18525	−	1.18525i	−0.206883	−	0.978366i	$-0.566332\pi$
$744$	−95.3951	−	10.0264i	−3.49735	−	0.367587i
$745$	−40.2835	+	5.54025i	−1.47587	+	0.202979i
$746$	−4.72168	−	44.9238i	−0.172873	−	1.64478i
$747$	7.16123	+	18.6556i	0.262016	+	0.682574i
$748$	−0.411303	−	0.209569i	−0.0150387	−	0.00766262i
$749$	10.0211	−	8.20512i	0.366162	−	0.299809i
$750$	−60.9773	−	13.5267i	−2.22658	−	0.493924i
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	0.591254	−	0.806485i	$-0.298633\pi$
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	−0.994064	+	0.108798i	$0.965300\pi$
$752$	8.61110	+	13.2599i	0.314014	+	0.483540i
$753$	−0.191429	+	0.236395i	−0.00697605	+	0.00861471i
$754$	−0.409540	−	0.182339i	−0.0149146	−	0.00664040i
$755$	−33.3790	+	25.9202i	−1.21479	+	0.943332i
$756$	−9.31310	−	14.1724i	−0.338714	−	0.515444i
$757$	2.36580	−	2.36580i	0.0859865	−	0.0859865i	−0.662805	−	0.748792i	$-0.730634\pi$
$757$	2.36580	−	2.36580i	0.0859865	−	0.0859865i	0.748792	+	0.662805i	$0.230634\pi$
$758$	42.0339	−	34.0384i	1.52674	−	1.23633i
$759$	−0.141033	−	0.156633i	−0.00511919	−	0.00568543i
$760$	31.0356	+	10.7890i	1.12578	+	0.391359i
$761$	27.8157	+	25.0454i	1.00832	+	0.907895i	0.995757	−	0.0920256i	$-0.0293342\pi$
$761$	27.8157	+	25.0454i	1.00832	+	0.907895i	0.0125634	+	0.999921i	$0.496001\pi$
$762$	36.2686	−	18.4798i	1.31387	−	0.669451i
$763$	2.24397	+	20.2927i	0.0812371	+	0.734643i
$764$	−55.0239	+	17.8784i	−1.99070	+	0.646816i
$765$	−18.6865	+	30.8926i	−0.675612	+	1.11692i
$766$	27.7996	−	25.0309i	1.00444	−	0.904403i
$767$	2.75157	−	7.16810i	0.0993536	−	0.258825i
$768$	68.8951	+	18.4604i	2.48604	+	0.666132i
$769$	31.5396	+	22.9148i	1.13735	+	0.826330i	0.986747	−	0.162264i	$-0.0518798\pi$
$769$	31.5396	+	22.9148i	1.13735	+	0.826330i	0.150599	+	0.988595i	$0.451880\pi$
$770$	0.0945655	+	0.221267i	0.00340790	+	0.00797390i
$771$	17.0932	−	12.4189i	0.615596	−	0.447257i
$772$	60.6505	−	23.2815i	2.18286	−	0.837920i
$773$	19.4971	−	12.6616i	0.701263	−	0.455405i	−0.144124	−	0.989560i	$-0.546037\pi$
$773$	19.4971	−	12.6616i	0.701263	−	0.455405i	0.845387	+	0.534154i	$0.179370\pi$
$774$	21.6795	+	12.5167i	0.779254	+	0.449902i
$775$	−15.6690	+	42.2718i	−0.562846	+	1.51845i
$776$		−	31.8387i		−	1.14294i
$777$	−15.5301	+	48.6920i	−0.557139	+	1.74682i
$778$	28.6099	+	4.53136i	1.02571	+	0.162457i
$779$	7.92795	−	17.8065i	0.284048	−	0.637983i
$780$	−29.0372	+	54.2243i	−1.03970	+	1.94154i
$781$	0.120133	−	0.0534868i	0.00429871	−	0.00191391i
$782$	−24.3284	+	90.7949i	−0.869983	+	3.24682i
$783$	0.0976210	−	0.0154617i	0.00348869	−	0.000552554i
$784$	−12.2466	−	20.6911i	−0.437378	−	0.738969i
$785$	36.0692	+	4.53687i	1.28736	+	0.161928i
$786$	−44.2234	+	49.1151i	−1.57740	+	1.75188i
$787$	0.863994	−	16.4860i	0.0307981	−	0.587662i	−0.939024	−	0.343850i	$-0.888269\pi$
$787$	0.863994	−	16.4860i	0.0307981	−	0.587662i	0.969823	−	0.243812i	$-0.0783979\pi$
$788$	−3.17897	+	60.6583i	−0.113246	+	2.16086i
$789$	−32.1801	+	35.7396i	−1.14564	+	1.27236i
$790$	−21.2308	−	19.9156i	−0.755358	−	0.708564i
$791$	−1.60048	+	10.4716i	−0.0569066	+	0.372327i
$792$	−0.174874	+	0.0276973i	−0.00621388	+	0.000984182i
$793$	−10.5837	+	39.4989i	−0.375838	+	1.40265i
$794$	15.0474	−	6.69956i	0.534014	−	0.237758i
$795$	22.0206	+	3.94989i	0.780989	+	0.140088i
$796$	−3.14093	+	7.05465i	−0.111327	+	0.250045i
$797$	43.0687	+	6.82142i	1.52557	+	0.241627i	0.862164	−	0.506630i	$-0.169109\pi$
$797$	43.0687	+	6.82142i	1.52557	+	0.241627i	0.663409	+	0.748257i	$0.269109\pi$
$798$	−45.8593	+	10.0075i	−1.62340	+	0.354260i
$799$		−	32.5131i		−	1.15023i
$800$	2.22474	−	3.95823i	0.0786564	−	0.139945i
$801$	16.5705	+	9.56698i	0.585490	+	0.338033i
$802$	37.2625	−	24.1985i	1.31578	−	0.854480i
$803$	0.0522459	−	0.0200553i	0.00184372	−	0.000707738i
$804$	2.30973	−	1.67811i	0.0814578	−	0.0591825i
$805$	26.4954	−	18.6496i	0.933839	−	0.657312i
$806$	54.3169	+	39.4635i	1.91323	+	1.39004i
$807$	−3.35907	−	0.900061i	−0.118245	−	0.0316836i
$808$	−17.5836	+	45.8069i	−0.618590	+	1.61148i
$809$	10.9422	−	9.85244i	0.384709	−	0.346393i	−0.453973	−	0.891016i	$-0.649994\pi$
$809$	10.9422	−	9.85244i	0.384709	−	0.346393i	0.838681	+	0.544622i	$0.183327\pi$
$810$	−4.86499	−	57.5639i	−0.170938	−	2.02259i
$811$	−24.6251	+	8.00118i	−0.864704	+	0.280959i	−0.707592	−	0.706621i	$-0.750218\pi$
$811$	−24.6251	+	8.00118i	−0.864704	+	0.280959i	−0.157112	+	0.987581i	$0.550218\pi$
$812$	0.618125	−	0.0683525i	0.0216920	−	0.00239870i
$813$	−18.6144	+	9.48450i	−0.652835	+	0.332636i
$814$	−0.253962	−	0.228669i	−0.00890137	−	0.00801483i
$815$	−11.9630	−	17.1927i	−0.419044	−	0.602233i
$816$	37.3240	+	41.4525i	1.30660	+	1.45113i
$817$	−11.1227	+	9.00697i	−0.389134	+	0.315114i
$818$	27.3344	−	27.3344i	0.955725	−	0.955725i
$819$	−1.07017	−	18.5031i	−0.0373948	−	0.646551i
$820$	44.3347	+	30.0950i	1.54823	+	1.05096i
$821$	44.7779	+	19.9364i	1.56276	+	0.695785i	0.992106	−	0.125406i	$-0.0400233\pi$
$821$	44.7779	+	19.9364i	1.56276	+	0.695785i	0.570653	+	0.821191i	$0.306690\pi$
$822$	11.5816	−	14.3021i	0.403955	−	0.498843i
$823$	28.8436	+	44.4153i	1.00543	+	1.54822i	0.825393	+	0.564558i	$0.190953\pi$
$823$	28.8436	+	44.4153i	1.00543	+	1.54822i	0.180032	+	0.983661i	$0.442380\pi$
$824$	−0.506220	−	0.876799i	−0.0176350	−	0.0305447i
$825$	−0.0179024	+	0.191589i	−0.000623282	+	0.00667028i
$826$	2.60585	+	15.8953i	0.0906690	+	0.553068i
$827$	4.78458	+	2.43786i	0.166376	+	0.0847728i	0.535196	−	0.844728i	$-0.320238\pi$
$827$	4.78458	+	2.43786i	0.166376	+	0.0847728i	−0.368819	+	0.929501i	$0.620238\pi$
$828$	17.5168	+	45.6330i	0.608753	+	1.58585i
$829$	−3.66391	−	34.8598i	−0.127253	−	1.21073i	−0.852681	−	0.522432i	$-0.825025\pi$
$829$	−3.66391	−	34.8598i	−0.127253	−	1.21073i	0.725428	−	0.688298i	$-0.241642\pi$
$830$	8.38575	−	46.7504i	0.291074	−	1.62273i
$831$	31.2433	+	3.28380i	1.08382	+	0.113914i
$832$	−19.6675	−	19.6675i	−0.681847	−	0.681847i
$833$	−2.05298	+	49.4010i	−0.0711316	+	1.71164i
$834$	−24.1587	−	7.84964i	−0.836548	−	0.271811i
$835$	3.85001	−	16.4544i	0.133235	−	0.569429i
$836$	0.0431503	−	0.203006i	0.00149238	−	0.00702111i
$837$	−14.7822	−	0.774702i	−0.510947	−	0.0267776i
$838$	47.0395	−	72.4345i	1.62495	−	2.50221i
$839$	4.17081	+	12.8364i	0.143992	+	0.443163i	0.996880	−	0.0789314i	$-0.0251508\pi$
$839$	4.17081	+	12.8364i	0.143992	+	0.443163i	−0.852888	+	0.522095i	$0.825151\pi$
$840$	−2.35126	−	62.8934i	−0.0811262	−	2.17003i
$841$	8.96037	−	27.5772i	0.308978	−	0.950938i
$842$	−21.4871	−	26.5343i	−0.740493	−	0.914433i
$843$	2.37180	+	8.85167i	0.0816891	+	0.304868i
$844$	−14.5146	−	32.6003i	−0.499613	−	1.12215i
$845$	−6.85625	+	4.25616i	−0.235862	+	0.146417i
$846$	−15.0284	−	20.6848i	−0.516686	−	0.711158i
$847$	−25.1244	+	14.6875i	−0.863284	+	0.504668i
$848$	6.78594	−	13.3182i	0.233030	−	0.457347i
$849$	37.6256	−	21.7232i	1.29131	−	0.745537i
$850$	76.0072	−	39.8399i	2.60703	−	1.36650i
$851$	−23.0079	+	39.8508i	−0.788699	+	1.36607i
$852$	−70.4225	+	3.69069i	−2.41263	+	0.126441i
$853$	−5.33840	+	33.7053i	−0.182783	+	1.15405i	0.710214	+	0.703986i	$0.248598\pi$
$853$	−5.33840	+	33.7053i	−0.182783	+	1.15405i	−0.892997	+	0.450063i	$0.851402\pi$
$854$	−22.6513	−	82.7416i	−0.775111	−	2.83136i
$855$	−15.5904	−	4.52033i	−0.533181	−	0.154592i
$856$	2.36769	−	22.5271i	0.0809260	−	0.769960i
$857$	6.63141	−	1.77688i	0.226525	−	0.0606971i	−0.143771	−	0.989611i	$-0.545923\pi$
$857$	6.63141	−	1.77688i	0.226525	−	0.0606971i	0.370296	+	0.928914i	$0.379256\pi$
$858$	0.267535	+	0.102697i	0.00913350	+	0.00350602i
$859$	43.3468	−	9.21364i	1.47897	−	0.314365i	0.603395	−	0.797442i	$-0.293814\pi$
$859$	43.3468	−	9.21364i	1.47897	−	0.314365i	0.875578	+	0.483077i	$0.160481\pi$
$860$	−18.9735	−	34.4686i	−0.646990	−	1.17537i
$861$	−37.2943	−	1.75213i	−1.27099	−	0.0597126i
$862$	4.19824	+	8.23950i	0.142993	+	0.280639i
$863$	1.69343	+	1.09973i	0.0576452	+	0.0374352i	0.573140	−	0.819458i	$-0.305725\pi$
$863$	1.69343	+	1.09973i	0.0576452	+	0.0374352i	−0.515495	+	0.856893i	$0.672392\pi$
$864$	1.45829	+	0.309970i	0.0496122	+	0.0105454i
$865$	−17.1833	+	49.4294i	−0.584250	+	1.68065i
$866$	−0.626730	−	2.94853i	−0.0212971	−	0.100195i
$867$	−11.8297	−	74.6900i	−0.401759	−	2.53661i
$868$	−92.6791	−	9.23402i	−3.14573	−	0.313423i
$869$	−0.0527129	+	0.0725531i	−0.00178816	+	0.00246119i
$870$	0.696468	+	0.283786i	0.0236125	+	0.00962125i
$871$	−0.969332	+	0.101881i	−0.0328446	+	0.00345210i
$872$	27.7488	+	22.4706i	0.939694	+	0.760950i
$873$	0.823202	+	15.7076i	0.0278612	+	0.531623i
$874$	−42.2612			−1.42950
$875$	−28.9126	−	6.24971i	−0.977426	−	0.211279i
$876$	−30.0106			−1.01396
$877$	−2.45627	−	46.8683i	−0.0829422	−	1.58263i	−0.650635	−	0.759391i	$-0.725497\pi$
$877$	−2.45627	−	46.8683i	−0.0829422	−	1.58263i	0.567693	−	0.823240i	$-0.307836\pi$
$878$	−10.2846	−	8.32828i	−0.347087	−	0.281066i
$879$	−15.9911	+	1.68073i	−0.539365	+	0.0566896i
$880$	0.119059	+	0.0485124i	0.00401348	+	0.00163535i
$881$	12.9945	−	17.8855i	0.437797	−	0.602576i	−0.531924	−	0.846792i	$-0.678531\pi$
$881$	12.9945	−	17.8855i	0.437797	−	0.602576i	0.969721	+	0.244216i	$0.0785306\pi$
$882$	21.5283	+	32.3778i	0.724896	+	1.09022i
$883$	2.48456	+	15.6869i	0.0836122	+	0.527906i	0.993571	+	0.113208i	$0.0361128\pi$
$883$	2.48456	+	15.6869i	0.0836122	+	0.527906i	−0.909959	+	0.414698i	$0.863887\pi$
$884$	−17.5707	−	82.6636i	−0.590966	−	2.78028i
$885$	−4.22950	+	12.1666i	−0.142173	+	0.408974i
$886$	−43.4828	−	9.24256i	−1.46083	−	0.310510i
$887$	−14.7196	−	9.55901i	−0.494236	−	0.320960i	0.273341	−	0.961917i	$-0.411871\pi$
$887$	−14.7196	−	9.55901i	−0.494236	−	0.320960i	−0.767577	+	0.640957i	$0.778538\pi$
$888$	40.5794	+	79.6415i	1.36175	+	2.67259i
$889$	17.1289	−	8.84473i	0.574485	−	0.296643i
$890$	−21.9310	−	39.8416i	−0.735130	−	1.33549i
$891$	−0.174084	+	0.0370028i	−0.00583205	+	0.00123964i
$892$	−27.1110	−	10.4069i	−0.907743	−	0.348450i
$893$	14.1197	−	3.78336i	0.472498	−	0.126605i
$894$	10.6192	−	101.035i	0.355158	−	3.37910i
$895$	29.2619	+	8.48429i	0.978117	+	0.283598i
$896$	51.7942	+	13.5782i	1.73032	+	0.453614i
$897$	6.03632	−	38.1118i	0.201547	−	1.27252i
$898$	17.6877	−	0.926974i	0.590246	−	0.0309335i
$899$	0.271415	−	0.470104i	0.00905219	−	0.0156789i
$900$	19.7986	−	39.9922i	0.659955	−	1.33307i
$901$	−26.6196	+	15.3689i	−0.886829	+	0.512011i
$902$	0.113336	−	0.222435i	0.00377369	−	0.00740629i
$903$	23.8155	+	13.5786i	0.792532	+	0.451866i
$904$	10.8896	+	14.9882i	0.362182	+	0.498500i
$905$	−10.9251	+	6.78198i	−0.363162	+	0.225441i
$906$	−42.9452	−	96.4565i	−1.42676	−	3.20455i
$907$	7.69450	+	28.7163i	0.255492	+	0.953508i	0.967816	+	0.251658i	$0.0809757\pi$
$907$	7.69450	+	28.7163i	0.255492	+	0.953508i	−0.712325	+	0.701850i	$0.752358\pi$
$908$	28.7904	+	35.5531i	0.955441	+	1.17987i
$909$	7.49054	−	23.0535i	0.248445	−	0.764636i
$910$	−20.5858	+	38.9471i	−0.682412	+	1.29109i
$911$	12.1969	+	37.5382i	0.404101	+	1.24370i	0.921643	+	0.388038i	$0.126847\pi$
$911$	12.1969	+	37.5382i	0.404101	+	1.24370i	−0.517542	+	0.855658i	$0.673153\pi$
$912$	−13.6587	+	21.0326i	−0.452285	+	0.696458i
$913$	−0.146126	−	0.00765812i	−0.00483605	−	0.000253447i
$914$	5.96999	−	28.0866i	0.197470	−	0.929022i
$915$	15.6291	−	66.7969i	0.516683	−	2.20824i
$916$	−100.036	−	32.5036i	−3.30528	−	1.07395i
$917$	−20.8177	+	23.3736i	−0.687459	+	0.771863i
$918$	19.9241	+	19.9241i	0.657593	+	0.657593i
$919$	−14.7138	−	1.54648i	−0.485363	−	0.0510137i	−0.141313	−	0.989965i	$-0.545132\pi$
$919$	−14.7138	−	1.54648i	−0.485363	−	0.0510137i	−0.344050	+	0.938951i	$0.611799\pi$
$920$	10.0046	−	55.7755i	0.329842	−	1.83886i
$921$	−1.61938	−	15.4074i	−0.0533605	−	0.507691i
$922$	0.741208	+	1.93091i	0.0244104	+	0.0635912i
$923$	21.4508	+	10.9297i	0.706061	+	0.359756i
$924$	−0.392301	+	0.0643132i	−0.0129058	+	0.00211575i
$925$	40.9885	−	9.20837i	1.34769	−	0.302769i
$926$	46.9570	+	81.3318i	1.54310	+	2.67273i
$927$	0.272414	+	0.419481i	0.00894725	+	0.0137776i
$928$	−0.0344066	+	0.0424886i	−0.00112945	+	0.00139476i
$929$	15.8211	+	7.04399i	0.519072	+	0.231106i	0.649513	−	0.760350i	$-0.274973\pi$
$929$	15.8211	+	7.04399i	0.519072	+	0.231106i	−0.130441	+	0.991456i	$0.541639\pi$
$930$	−93.1908	−	63.2591i	−3.05585	−	2.07435i
$931$	−21.6926	+	4.85695i	−0.710948	+	0.159180i
$932$	60.3124	−	60.3124i	1.97560	−	1.97560i
$933$	4.69725	−	3.80376i	0.153781	−	0.124530i
$934$	−14.5409	−	16.1493i	−0.475793	−	0.528421i
$935$	−0.151001	−	0.217013i	−0.00493826	−	0.00709707i
$936$	−24.0884	−	21.6893i	−0.787354	−	0.708937i
$937$	−29.8820	+	15.2256i	−0.976202	+	0.497400i	−0.867911	−	0.496719i	$-0.834538\pi$
$937$	−29.8820	+	15.2256i	−0.976202	+	0.497400i	−0.108291	+	0.994119i	$0.534538\pi$
$938$	1.64768	−	1.21079i	0.0537987	−	0.0395338i
$939$	9.50975	−	3.08990i	0.310339	−	0.100835i
$940$	3.38421	+	40.0429i	0.110381	+	1.30606i
$941$	−32.3887	+	29.1630i	−1.05584	+	0.950685i	−0.998862	−	0.0476900i	$-0.984814\pi$
$941$	−32.3887	+	29.1630i	−1.05584	+	0.950685i	−0.0569808	+	0.998375i	$0.518147\pi$
$942$	−32.5487	+	84.7923i	−1.06049	+	2.76268i
$943$	−32.4696	−	8.70021i	−1.05736	−	0.283318i
$944$	6.96237	+	5.05846i	0.226606	+	0.164639i
$945$	−0.870308	−	9.67343i	−0.0283111	−	0.314677i
$946$	−0.148300	+	0.107746i	−0.00482164	+	0.00350312i
$947$	5.14526	−	1.97508i	0.167199	−	0.0641815i	−0.273329	−	0.961921i	$-0.588125\pi$
$947$	5.14526	−	1.97508i	0.167199	−	0.0641815i	0.440528	+	0.897739i	$0.354791\pi$
$948$	40.3332	−	26.1927i	1.30996	−	0.850699i
$949$	8.87279	+	5.12271i	0.288023	+	0.166290i
$950$	26.1461	+	28.3723i	0.848291	+	0.920518i
$951$		−	47.7071i		−	1.54701i
$952$	58.2080	+	63.9470i	1.88653	+	2.07253i
$953$	−6.68823	−	1.05931i	−0.216653	−	0.0343145i	0.0471642	−	0.998887i	$-0.484982\pi$
$953$	−6.68823	−	1.05931i	−0.216653	−	0.0343145i	−0.263817	+	0.964573i	$0.584982\pi$
$954$	−9.83150	+	22.0819i	−0.318307	+	0.714929i
$955$	−32.6147	−	5.85018i	−1.05539	−	0.189307i
$956$	15.2206	−	6.77663i	0.492268	−	0.219172i
$957$	0.000599669	−	0.00223799i	1.93845e−5	−	7.23441e-5i
$958$	−2.32607	+	0.368413i	−0.0751518	+	0.0119029i
$959$	5.44821	−	6.80295i	0.175932	−	0.219679i
$960$	34.0315	+	31.9232i	1.09836	+	1.03032i
$961$	−33.6553	+	37.3780i	−1.08565	+	1.20574i
$962$	3.27435	−	62.4783i	0.105569	−	2.01438i
$963$	−0.585655	+	11.1750i	−0.0188725	+	0.360108i
$964$	0.429016	−	0.476471i	0.0138177	−	0.0153461i
$965$	36.9163	+	4.64342i	1.18838	+	0.149477i
$966$	29.4184	+	75.4149i	0.946523	+	2.42644i
$967$	−57.0421	+	9.03458i	−1.83435	+	0.290533i	−0.975222	−	0.221228i	$-0.928994\pi$
$967$	−57.0421	+	9.03458i	−1.83435	+	0.290533i	−0.859128	+	0.511760i	$0.828994\pi$
$968$	−13.1732	+	49.1630i	−0.423403	+	1.58016i
$969$	47.1129	−	20.9760i	1.51348	−	0.673847i
$970$	17.6491	−	32.9580i	0.566678	−	1.05822i
$971$	−7.98460	+	17.9337i	−0.256238	+	0.575520i	−0.995160	−	0.0982714i	$-0.968669\pi$
$971$	−7.98460	+	17.9337i	−0.256238	+	0.575520i	0.738922	+	0.673791i	$0.235335\pi$
$972$	75.2723	+	11.9220i	2.41436	+	0.382397i
$973$	−11.4613	−	3.65554i	−0.367434	−	0.117191i
$974$			84.2473i			2.69946i
$975$	−29.3211	+	19.5265i	−0.939028	+	0.625347i
$976$	−39.6935	−	22.9170i	−1.27056	−	0.733556i
$977$	−20.6393	+	13.4033i	−0.660309	+	0.428810i	−0.830816	−	0.556547i	$-0.812126\pi$
$977$	−20.6393	+	13.4033i	−0.660309	+	0.428810i	0.170507	+	0.985356i	$0.445459\pi$
$978$	48.8534	−	18.7531i	1.56216	−	0.599657i
$979$	−0.113351	+	0.0823545i	−0.00362272	+	0.00263206i
$980$	−2.61359	−	61.0557i	−0.0834882	−	1.95035i
$981$	−14.2709	−	10.3684i	−0.455634	−	0.331038i
$982$	12.0140	+	3.21913i	0.383381	+	0.102727i
$983$	16.0960	−	41.9315i	0.513382	−	1.33741i	−0.394775	−	0.918778i	$-0.629177\pi$
$983$	16.0960	−	41.9315i	0.513382	−	1.33741i	0.908157	−	0.418629i	$-0.137489\pi$
$984$	−48.5243	+	43.6915i	−1.54690	+	1.39283i
$985$	−18.0051	+	29.7662i	−0.573691	+	0.948429i
$986$	−0.982717	+	0.319304i	−0.0312961	+	0.0101687i
$987$	−16.5803	−	22.5629i	−0.527756	−	0.718186i
$988$	33.8543	−	17.2496i	1.07705	−	0.548784i
$989$	18.3428	+	16.5160i	0.583268	+	0.525177i
$990$	−0.196375	−	0.0682666i	−0.00624122	−	0.00216966i
$991$	−31.0000	−	34.4290i	−0.984747	−	1.09367i	−0.995598	−	0.0937308i	$-0.970121\pi$
$991$	−31.0000	−	34.4290i	−0.984747	−	1.09367i	0.0108510	−	0.999941i	$-0.496546\pi$
$992$	6.36332	−	5.15291i	0.202035	−	0.163605i
$993$	25.8356	−	25.8356i	0.819867	−	0.819867i
$994$	−50.4211	+	2.91623i	−1.59926	+	0.0924971i
$995$	−3.49318	+	2.71260i	−0.110741	+	0.0859952i
$996$	71.6845	+	31.9160i	2.27141	+	1.01130i
$997$	−15.5757	+	19.2344i	−0.493286	+	0.609158i	−0.961617	−	0.274395i	$-0.911522\pi$
$997$	−15.5757	+	19.2344i	−0.493286	+	0.609158i	0.468331	+	0.883553i	$0.344856\pi$
$998$	−48.2129	−	74.2414i	−1.52615	−	2.35007i
$999$	6.89686	+	11.9457i	0.218207	+	0.377946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.18	yes	288
5.2	odd	4		875.2.bb.b.857.1		288
5.3	odd	4		875.2.bb.a.857.18		288
5.4	even	2		875.2.bb.c.143.1		288
7.5	odd	6	inner	175.2.x.a.33.18	✓	288
25.3	odd	20		875.2.bb.c.507.1		288
25.4	even	10		875.2.bb.a.493.1		288
25.21	even	5		875.2.bb.b.493.18		288
25.22	odd	20	inner	175.2.x.a.122.18	yes	288
35.12	even	12		875.2.bb.b.607.18		288
35.19	odd	6		875.2.bb.c.768.1		288
35.33	even	12		875.2.bb.a.607.1		288
175.47	even	60	inner	175.2.x.a.47.18	yes	288
175.54	odd	30		875.2.bb.a.243.18		288
175.96	odd	30		875.2.bb.b.243.1		288
175.103	even	60		875.2.bb.c.257.1		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.18	✓	288	7.5	odd	6	inner
175.2.x.a.47.18	yes	288	175.47	even	60	inner
175.2.x.a.108.18	yes	288	1.1	even	1	trivial
175.2.x.a.122.18	yes	288	25.22	odd	20	inner
875.2.bb.a.243.18		288	175.54	odd	30
875.2.bb.a.493.1		288	25.4	even	10
875.2.bb.a.607.1		288	35.33	even	12
875.2.bb.a.857.18		288	5.3	odd	4
875.2.bb.b.243.1		288	175.96	odd	30
875.2.bb.b.493.18		288	25.21	even	5
875.2.bb.b.607.18		288	35.12	even	12
875.2.bb.b.857.1		288	5.2	odd	4
875.2.bb.c.143.1		288	5.4	even	2
875.2.bb.c.257.1		288	175.103	even	60
875.2.bb.c.507.1		288	25.3	odd	20
875.2.bb.c.768.1		288	35.19	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+(0.127170 + 2.42654i) q^{2} +(-1.78675 - 1.44688i) q^{3} +(-3.88289 + 0.408108i) q^{4} +(-2.07076 - 0.843763i) q^{5} +(3.28370 - 4.51962i) q^{6} +(1.54352 - 2.14884i) q^{7} +(-0.723845 - 4.57018i) q^{8} +(0.475273 + 2.23598i) q^{9} +(1.78409 - 5.13210i) q^{10} +(-0.0163732 - 0.00348022i) q^{11} +(7.52823 + 4.88889i) q^{12} +(-1.39124 - 2.73047i) q^{13} +(5.41055 + 3.47216i) q^{14} +(2.47911 + 4.50374i) q^{15} +(3.35976 - 0.714139i) q^{16} +(-6.59423 - 2.53129i) q^{17} +(-5.36527 + 1.43762i) q^{18} +(0.331948 - 3.15828i) q^{19} +(8.38489 + 2.43114i) q^{20} +(-5.86701 + 1.60615i) q^{21} +(0.00636273 - 0.0401727i) q^{22} +(-5.46923 + 0.286630i) q^{23} +(-5.31918 + 9.21308i) q^{24} +(3.57613 + 3.49447i) q^{25} +(6.44868 - 3.72315i) q^{26} +(-0.745322 + 1.46278i) q^{27} +(-5.11637 + 8.97365i) q^{28} +(-0.0353871 - 0.0487062i) q^{29} +(-10.6132 + 6.58841i) q^{30} +(3.66733 + 8.23697i) q^{31} +(-0.235039 - 0.877177i) q^{32} +(0.0242193 + 0.0299083i) q^{33} +(5.30369 - 16.3231i) q^{34} +(-5.00939 + 3.14738i) q^{35} +(-2.75796 - 8.48811i) q^{36} +(4.57608 - 7.04654i) q^{37} +(7.70591 + 0.403850i) q^{38} +(-1.46486 + 6.89163i) q^{39} +(-2.35724 + 10.0745i) q^{40} +(5.83738 + 1.89668i) q^{41} +(-4.64350 - 14.0323i) q^{42} +(-3.18681 - 3.18681i) q^{43} +(0.0649954 + 0.00683130i) q^{44} +(0.902462 - 5.03121i) q^{45} +(-1.39104 - 13.2349i) q^{46} +(1.64959 + 4.29732i) q^{47} +(-7.03633 - 3.58519i) q^{48} +(-2.23507 - 6.63359i) q^{49} +(-8.02470 + 9.12201i) q^{50} +(8.11977 + 14.0639i) q^{51} +(6.51638 + 10.0343i) q^{52} +(2.73861 - 3.38191i) q^{53} +(-3.64427 - 1.62253i) q^{54} +(0.0309685 + 0.0210218i) q^{55} +(-10.9379 - 5.49875i) q^{56} +(-5.16276 + 5.16276i) q^{57} +(0.113687 - 0.0920622i) q^{58} +(1.67651 + 1.86195i) q^{59} +(-11.4641 - 16.4758i) q^{60} +(-9.91649 - 8.92884i) q^{61} +(-19.5210 + 9.94643i) q^{62} +(5.53838 + 2.43001i) q^{63} +(8.63203 - 2.80472i) q^{64} +(0.577069 + 6.82804i) q^{65} +(-0.0694938 + 0.0625725i) q^{66} +(0.113980 - 0.296929i) q^{67} +(26.6377 + 7.13755i) q^{68} +(10.1869 + 7.40119i) q^{69} +(-8.27429 - 11.7552i) q^{70} +(-6.35569 + 4.61768i) q^{71} +(9.87482 - 3.79059i) q^{72} +(-2.80391 + 1.82088i) q^{73} +(17.6807 + 10.2079i) q^{74} +(-1.33356 - 11.4180i) q^{75} +12.3987i q^{76} +(-0.0327508 + 0.0298116i) q^{77} +(-16.9091 - 2.67814i) q^{78} +(2.17913 - 4.89441i) q^{79} +(-7.55984 - 1.35603i) q^{80} +(9.71309 - 4.32455i) q^{81} +(-3.86003 + 14.4058i) q^{82} +(8.63403 - 1.36750i) q^{83} +(22.1255 - 8.63088i) q^{84} +(11.5193 + 10.8057i) q^{85} +(7.32766 - 8.13819i) q^{86} +(-0.00724415 + 0.138227i) q^{87} +(-0.00405361 + 0.0773474i) q^{88} +(5.60082 - 6.22034i) q^{89} +(12.3232 + 1.55004i) q^{90} +(-8.01478 - 1.22498i) q^{91} +(21.1194 - 3.34499i) q^{92} +(5.36531 - 20.0236i) q^{93} +(-10.2178 + 4.54928i) q^{94} +(-3.35223 + 6.25996i) q^{95} +(-0.849216 + 1.90737i) q^{96} +(6.79613 + 1.07640i) q^{97} +(15.8124 - 6.26707i) q^{98} -0.0382642i 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

Fields

Representations

Groups

Database

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