LMFDB - Embedded newform 175.2.x.a.117.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			117.6
Character	$\chi$	$=$	175.117
Dual form			175.2.x.a.3.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.467632 - 0.720090i) q^{2} +(1.11331 + 2.90028i) q^{3} +(0.513623 - 1.15362i) q^{4} +(1.62243 - 1.53874i) q^{5} +(1.56784 - 2.15795i) q^{6} +(1.61121 - 2.09857i) q^{7} +(-2.76697 + 0.438245i) q^{8} +(-4.94272 + 4.45045i) q^{9} +(-1.86673 - 0.448731i) q^{10} +(-1.65194 + 1.83466i) q^{11} +(3.91763 + 0.205314i) q^{12} +(3.07959 - 1.56913i) q^{13} +(-2.26461 - 0.178856i) q^{14} +(6.26905 + 2.99240i) q^{15} +(-0.0804422 - 0.0893401i) q^{16} +(2.29486 + 2.83391i) q^{17} +(5.51610 + 1.47803i) q^{18} +(-6.48601 + 2.88776i) q^{19} +(-0.941799 - 2.66199i) q^{20} +(7.88023 + 2.33659i) q^{21} +(2.09362 + 0.331597i) q^{22} +(-1.71981 + 1.11686i) q^{23} +(-4.35154 - 7.53709i) q^{24} +(0.264555 - 4.99300i) q^{25} +(-2.57003 - 1.48381i) q^{26} +(-10.1063 - 5.14941i) q^{27} +(-1.59339 - 2.93659i) q^{28} +(0.594101 + 0.817710i) q^{29} +(-0.776811 - 5.91363i) q^{30} +(-3.62503 - 0.381006i) q^{31} +(-1.47686 + 5.51171i) q^{32} +(-7.16015 - 2.74852i) q^{33} +(0.967525 - 2.97773i) q^{34} +(-0.615085 - 5.88402i) q^{35} +(2.59541 + 7.98786i) q^{36} +(0.0472897 - 0.902341i) q^{37} +(5.11251 + 3.32010i) q^{38} +(7.97945 + 7.18473i) q^{39} +(-3.81487 + 4.96867i) q^{40} +(-2.23957 - 0.727680i) q^{41} +(-2.00249 - 6.76714i) q^{42} +(1.54846 - 1.54846i) q^{43} +(1.26802 + 2.84802i) q^{44} +(-1.17114 + 14.8261i) q^{45} +(1.60848 + 0.716140i) q^{46} +(-2.09481 - 1.69634i) q^{47} +(0.169554 - 0.332768i) q^{48} +(-1.80801 - 6.76248i) q^{49} +(-3.71912 + 2.14438i) q^{50} +(-5.66425 + 9.81076i) q^{51} +(-0.228425 - 4.35860i) q^{52} +(0.821669 - 0.315409i) q^{53} +(1.01798 + 9.68547i) q^{54} +(0.142917 + 5.51851i) q^{55} +(-3.53848 + 6.51279i) q^{56} +(-15.5963 - 15.5963i) q^{57} +(0.311004 - 0.810194i) q^{58} +(-1.20728 + 0.256616i) q^{59} +(6.67201 - 5.69511i) q^{60} +(2.25815 - 10.6238i) q^{61} +(1.42082 + 2.78852i) q^{62} +(1.37583 + 17.5433i) q^{63} +(4.43089 - 1.43968i) q^{64} +(2.58193 - 7.28448i) q^{65} +(1.36913 + 6.44125i) q^{66} +(-3.93146 + 3.18363i) q^{67} +(4.44794 - 1.19182i) q^{68} +(-5.15389 - 3.74452i) q^{69} +(-3.94939 + 3.19447i) q^{70} +(-11.9130 + 8.65529i) q^{71} +(11.7260 - 14.4804i) q^{72} +(8.24140 - 0.431913i) q^{73} +(-0.671881 + 0.387911i) q^{74} +(14.7756 - 4.79148i) q^{75} +8.96558i q^{76} +(1.18855 + 6.42273i) q^{77} +(1.44221 - 9.10574i) q^{78} +(15.0941 - 1.58645i) q^{79} +(-0.267983 - 0.0211684i) q^{80} +(1.59758 - 15.2000i) q^{81} +(0.523299 + 1.95298i) q^{82} +(-0.481396 - 3.03941i) q^{83} +(6.74299 - 7.89063i) q^{84} +(8.08390 + 1.06663i) q^{85} +(-1.83914 - 0.390922i) q^{86} +(-1.71017 + 2.63343i) q^{87} +(3.76683 - 5.80041i) q^{88} +(-9.19731 - 1.95495i) q^{89} +(11.2238 - 6.08984i) q^{90} +(1.66893 - 8.99093i) q^{91} +(0.405091 + 2.55764i) q^{92} +(-2.93077 - 10.9378i) q^{93} +(-0.241920 + 2.30172i) q^{94} +(-6.07958 + 14.6655i) q^{95} +(-17.6297 + 1.85296i) q^{96} +(-2.78673 + 17.5947i) q^{97} +(-4.02411 + 4.46428i) q^{98} -16.4201i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.467632	−	0.720090i	−0.330666	−	0.509181i	0.633762	−	0.773528i	$-0.281510\pi$
$2$	−0.467632	−	0.720090i	−0.330666	−	0.509181i	−0.964427	+	0.264348i	$0.914843\pi$
$3$	1.11331	+	2.90028i	0.642772	+	1.67448i	0.734428	+	0.678687i	$0.237451\pi$
$3$	1.11331	+	2.90028i	0.642772	+	1.67448i	−0.0916562	+	0.995791i	$0.529216\pi$
$4$	0.513623	−	1.15362i	0.256812	−	0.576808i
$5$	1.62243	−	1.53874i	0.725573	−	0.688146i
$5$	1.62243	−	1.53874i	0.725573	−	0.688146i
$6$	1.56784	−	2.15795i	0.640069	−	0.880979i
$7$	1.61121	−	2.09857i	0.608980	−	0.793186i
$7$	1.61121	−	2.09857i	0.608980	−	0.793186i
$8$	−2.76697	+	0.438245i	−0.978272	+	0.154943i
$9$	−4.94272	+	4.45045i	−1.64757	+	1.48348i
$10$	−1.86673	−	0.448731i	−0.590313	−	0.141901i
$11$	−1.65194	+	1.83466i	−0.498077	+	0.553171i	−0.938796	−	0.344474i	$-0.888057\pi$
$11$	−1.65194	+	1.83466i	−0.498077	+	0.553171i	0.440718	+	0.897645i	$0.354724\pi$
$12$	3.91763	+	0.205314i	1.13092	+	0.0592692i
$13$	3.07959	−	1.56913i	0.854124	−	0.435198i	0.0286171	−	0.999590i	$-0.490890\pi$
$13$	3.07959	−	1.56913i	0.854124	−	0.435198i	0.825506	+	0.564393i	$0.190890\pi$
$14$	−2.26461	−	0.178856i	−0.605244	−	0.0478014i
$15$	6.26905	+	2.99240i	1.61866	+	0.772634i
$16$	−0.0804422	−	0.0893401i	−0.0201105	−	0.0223350i
$17$	2.29486	+	2.83391i	0.556585	+	0.687325i	0.975323	−	0.220782i	$-0.0708609\pi$
$17$	2.29486	+	2.83391i	0.556585	+	0.687325i	−0.418738	+	0.908107i	$0.637528\pi$
$18$	5.51610	+	1.47803i	1.30016	+	0.348376i
$19$	−6.48601	+	2.88776i	−1.48799	+	0.662497i	−0.980024	−	0.198879i	$-0.936270\pi$
$19$	−6.48601	+	2.88776i	−1.48799	+	0.662497i	−0.507968	+	0.861376i	$0.669603\pi$
$20$	−0.941799	−	2.66199i	−0.210593	−	0.595240i
$21$	7.88023	+	2.33659i	1.71961	+	0.509886i
$22$	2.09362	+	0.331597i	0.446361	+	0.0706967i
$23$	−1.71981	+	1.11686i	−0.358605	+	0.232881i	−0.711349	−	0.702839i	$-0.751915\pi$
$23$	−1.71981	+	1.11686i	−0.358605	+	0.232881i	0.352744	+	0.935720i	$0.385249\pi$
$24$	−4.35154	−	7.53709i	−0.888254	−	1.53850i
$25$	0.264555	−	4.99300i	0.0529111	−	0.998599i
$26$	−2.57003	−	1.48381i	−0.504024	−	0.290998i
$27$	−10.1063	−	5.14941i	−1.94496	−	0.991005i
$28$	−1.59339	−	2.93659i	−0.301123	−	0.554964i
$29$	0.594101	+	0.817710i	0.110322	+	0.151845i	0.860608	−	0.509269i	$-0.170084\pi$
$29$	0.594101	+	0.817710i	0.110322	+	0.151845i	−0.750286	+	0.661114i	$0.770084\pi$
$30$	−0.776811	−	5.91363i	−0.141826	−	1.07968i
$31$	−3.62503	−	0.381006i	−0.651075	−	0.0684308i	−0.226768	−	0.973949i	$-0.572816\pi$
$31$	−3.62503	−	0.381006i	−0.651075	−	0.0684308i	−0.424308	+	0.905518i	$0.639482\pi$
$32$	−1.47686	+	5.51171i	−0.261074	+	0.974342i
$33$	−7.16015	−	2.74852i	−1.24642	−	0.478457i
$34$	0.967525	−	2.97773i	0.165929	−	0.510677i
$35$	−0.615085	−	5.88402i	−0.103968	−	0.994581i
$36$	2.59541	+	7.98786i	0.432569	+	1.33131i
$37$	0.0472897	−	0.902341i	0.00777438	−	0.148344i	−0.991984	−	0.126363i	$-0.959669\pi$
$37$	0.0472897	−	0.902341i	0.00777438	−	0.148344i	0.999758	−	0.0219806i	$-0.00699720\pi$
$38$	5.11251	+	3.32010i	0.829359	+	0.538592i
$39$	7.97945	+	7.18473i	1.27774	+	1.15048i
$40$	−3.81487	+	4.96867i	−0.603184	+	0.785616i
$41$	−2.23957	−	0.727680i	−0.349762	−	0.113644i	0.128867	−	0.991662i	$-0.458866\pi$
$41$	−2.23957	−	0.727680i	−0.349762	−	0.113644i	−0.478629	+	0.878017i	$0.658866\pi$
$42$	−2.00249	−	6.76714i	−0.308991	−	1.04419i
$43$	1.54846	−	1.54846i	0.236138	−	0.236138i	−0.579111	−	0.815249i	$-0.696600\pi$
$43$	1.54846	−	1.54846i	0.236138	−	0.236138i	0.815249	+	0.579111i	$0.196600\pi$
$44$	1.26802	+	2.84802i	0.191161	+	0.429356i
$45$	−1.17114	+	14.8261i	−0.174583	+	2.21015i
$46$	1.60848	+	0.716140i	0.237157	+	0.105589i
$47$	−2.09481	−	1.69634i	−0.305559	−	0.247437i	0.464260	−	0.885699i	$-0.346320\pi$
$47$	−2.09481	−	1.69634i	−0.305559	−	0.247437i	−0.769819	+	0.638262i	$0.779654\pi$
$48$	0.169554	−	0.332768i	0.0244730	−	0.0480310i
$49$	−1.80801	−	6.76248i	−0.258287	−	0.966068i
$50$	−3.71912	+	2.14438i	−0.525963	+	0.303261i
$51$	−5.66425	+	9.81076i	−0.793153	+	1.37378i
$52$	−0.228425	−	4.35860i	−0.0316768	−	0.604429i
$53$	0.821669	−	0.315409i	0.112865	−	0.0433248i	−0.301280	−	0.953536i	$-0.597414\pi$
$53$	0.821669	−	0.315409i	0.112865	−	0.0433248i	0.414145	+	0.910211i	$0.364081\pi$
$54$	1.01798	+	9.68547i	0.138530	+	1.31803i
$55$	0.142917	+	5.51851i	0.0192709	+	0.744115i
$56$	−3.53848	+	6.51279i	−0.472849	+	0.870309i
$57$	−15.5963	−	15.5963i	−2.06578	−	2.06578i
$58$	0.311004	−	0.810194i	0.0408369	−	0.106384i
$59$	−1.20728	+	0.256616i	−0.157175	+	0.0334085i	−0.285827	−	0.958281i	$-0.592268\pi$
$59$	−1.20728	+	0.256616i	−0.157175	+	0.0334085i	0.128652	+	0.991690i	$0.458935\pi$
$60$	6.67201	−	5.69511i	0.861353	−	0.735236i
$61$	2.25815	−	10.6238i	0.289127	−	1.36023i	−0.558440	−	0.829545i	$-0.688600\pi$
$61$	2.25815	−	10.6238i	0.289127	−	1.36023i	0.847566	−	0.530689i	$-0.178067\pi$
$62$	1.42082	+	2.78852i	0.180445	+	0.354143i
$63$	1.37583	+	17.5433i	0.173338	+	2.21024i
$64$	4.43089	−	1.43968i	0.553861	−	0.179960i
$65$	2.58193	−	7.28448i	0.320249	−	0.903529i
$66$	1.36913	+	6.44125i	0.168528	+	0.792864i
$67$	−3.93146	+	3.18363i	−0.480304	+	0.388942i	−0.838671	−	0.544638i	$-0.816667\pi$
$67$	−3.93146	+	3.18363i	−0.480304	+	0.388942i	0.358367	+	0.933581i	$0.383334\pi$
$68$	4.44794	−	1.19182i	0.539392	−	0.144530i
$69$	−5.15389	−	3.74452i	−0.620455	−	0.450787i
$70$	−3.94939	+	3.19447i	−0.472043	+	0.381812i
$71$	−11.9130	+	8.65529i	−1.41381	+	1.02719i	−0.421057	+	0.907034i	$0.638341\pi$
$71$	−11.9130	+	8.65529i	−1.41381	+	1.02719i	−0.992754	+	0.120161i	$0.961659\pi$
$72$	11.7260	−	14.4804i	1.38192	−	1.70653i
$73$	8.24140	−	0.431913i	0.964583	−	0.0505516i	0.436464	−	0.899722i	$-0.356231\pi$
$73$	8.24140	−	0.431913i	0.964583	−	0.0505516i	0.528119	+	0.849170i	$0.322897\pi$
$74$	−0.671881	+	0.387911i	−0.0781046	+	0.0450937i
$75$	14.7756	−	4.79148i	1.70614	−	0.553273i
$76$			8.96558i			1.02842i
$77$	1.18855	+	6.42273i	0.135448	+	0.731938i
$78$	1.44221	−	9.10574i	0.163298	−	1.03102i
$79$	15.0941	−	1.58645i	1.69822	−	0.178490i	0.794688	−	0.607019i	$-0.207635\pi$
$79$	15.0941	−	1.58645i	1.69822	−	0.178490i	0.903528	+	0.428529i	$0.140968\pi$
$80$	−0.267983	−	0.0211684i	−0.0299614	−	0.00236670i
$81$	1.59758	−	15.2000i	0.177509	−	1.68889i
$82$	0.523299	+	1.95298i	0.0577887	+	0.215670i
$83$	−0.481396	−	3.03941i	−0.0528401	−	0.333619i	−0.999920	−	0.0126222i	$-0.995982\pi$
$83$	−0.481396	−	3.03941i	−0.0528401	−	0.333619i	0.947080	−	0.320997i	$-0.104018\pi$
$84$	6.74299	−	7.89063i	0.735721	−	0.860938i
$85$	8.08390	+	1.06663i	0.876822	+	0.115693i
$86$	−1.83914	−	0.390922i	−0.198320	−	0.0421542i
$87$	−1.71017	+	2.63343i	−0.183349	+	0.282333i
$88$	3.76683	−	5.80041i	0.401545	−	0.618325i
$89$	−9.19731	−	1.95495i	−0.974913	−	0.207224i	−0.307202	−	0.951644i	$-0.599393\pi$
$89$	−9.19731	−	1.95495i	−0.974913	−	0.207224i	−0.667711	+	0.744420i	$0.732726\pi$
$90$	11.2238	−	6.08984i	1.18309	−	0.641926i
$91$	1.66893	−	8.99093i	0.174951	−	0.942505i
$92$	0.405091	+	2.55764i	0.0422336	+	0.266653i
$93$	−2.93077	−	10.9378i	−0.303907	−	1.13420i
$94$	−0.241920	+	2.30172i	−0.0249521	+	0.237404i
$95$	−6.07958	+	14.6655i	−0.623752	+	1.50464i
$96$	−17.6297	+	1.85296i	−1.79933	+	0.189117i
$97$	−2.78673	+	17.5947i	−0.282949	+	1.78647i	0.280021	+	0.959994i	$0.409659\pi$
$97$	−2.78673	+	17.5947i	−0.282949	+	1.78647i	−0.562970	+	0.826477i	$0.690341\pi$
$98$	−4.02411	+	4.46428i	−0.406497	+	0.450961i
$99$		−	16.4201i		−	1.65028i
$100$	−5.62412	−	2.86971i	−0.562412	−	0.286971i
$101$	12.4991	−	7.21639i	1.24371	−	0.718057i	0.273864	−	0.961769i	$-0.411698\pi$
$101$	12.4991	−	7.21639i	1.24371	−	0.718057i	0.969848	+	0.243711i	$0.0783649\pi$
$102$	9.71342	−	0.509059i	0.961772	−	0.0504043i
$103$	9.43733	−	11.6541i	0.929888	−	1.14832i	−0.0587916	−	0.998270i	$-0.518725\pi$
$103$	9.43733	−	11.6541i	0.929888	−	1.14832i	0.988679	−	0.150045i	$-0.0479419\pi$
$104$	−7.83346	+	5.69134i	−0.768134	+	0.558082i
$105$	16.3805	−	8.33467i	1.59857	−	0.813381i
$106$	−0.611362	−	0.444181i	−0.0593807	−	0.0431426i
$107$	11.6252	−	3.11495i	1.12385	−	0.301134i	0.351408	−	0.936223i	$-0.385703\pi$
$107$	11.6252	−	3.11495i	1.12385	−	0.301134i	0.772439	+	0.635089i	$0.219037\pi$
$108$	−11.1313	+	9.01392i	−1.07111	+	0.867365i
$109$	−0.154346	−	0.726142i	−0.0147837	−	0.0695518i	0.970137	−	0.242556i	$-0.0779859\pi$
$109$	−0.154346	−	0.726142i	−0.0147837	−	0.0695518i	−0.984921	+	0.173004i	$0.944653\pi$
$110$	3.90699	−	2.68354i	0.372517	−	0.255866i
$111$	2.66969	−	0.867435i	0.253396	−	0.0823333i
$112$	−0.317096	+	0.0248682i	−0.0299627	+	0.00234982i
$113$	4.37867	+	8.59362i	0.411911	+	0.808420i	1.00000		0.000375885i	$-0.000119648\pi$
$113$	4.37867	+	8.59362i	0.411911	+	0.808420i	−0.588089	+	0.808796i	$0.700120\pi$
$114$	−3.93740	+	18.5240i	−0.368772	+	1.73493i
$115$	−1.07172	+	4.45836i	−0.0999380	+	0.415744i
$116$	1.24847	−	0.265370i	0.115917	−	0.0246390i
$117$	−8.23822	+	21.4613i	−0.761624	+	1.98410i
$118$	0.749350	+	0.749350i	0.0689833	+	0.0689833i
$119$	9.64467	−	0.249898i	0.884125	−	0.0229081i
$120$	−18.6577	−	5.53250i	−1.70321	−	0.505046i
$121$	0.512726	+	4.87826i	0.0466114	+	0.443478i
$122$	−8.70606	+	3.34194i	−0.788210	+	0.302565i
$123$	−0.382865	−	7.30551i	−0.0345218	−	0.658716i
$124$	−2.30144	+	3.98620i	−0.206675	+	0.357972i
$125$	−7.25370	−	8.50787i	−0.648791	−	0.760967i
$126$	11.9894	−	9.19451i	1.06810	−	0.819112i
$127$	−5.04425	+	9.89989i	−0.447605	+	0.878473i	0.551416	+	0.834230i	$0.314088\pi$
$127$	−5.04425	+	9.89989i	−0.447605	+	0.878473i	−0.999021	+	0.0442431i	$0.985912\pi$
$128$	5.76029	+	4.66459i	0.509142	+	0.412295i
$129$	6.21490	+	2.76705i	0.547191	+	0.243625i
$130$	−6.45288	+	1.54723i	−0.565955	+	0.135701i
$131$	5.81154	+	13.0529i	0.507756	+	1.14044i	0.967611	+	0.252445i	$0.0812348\pi$
$131$	5.81154	+	13.0529i	0.507756	+	1.14044i	−0.459855	+	0.887994i	$0.652099\pi$
$132$	−6.84836	+	6.84836i	−0.596073	+	0.596073i
$133$	−4.39015	+	18.2641i	−0.380674	+	1.58370i
$134$	4.13098	+	1.34224i	0.356862	+	0.115952i
$135$	−24.3203	+	7.19640i	−2.09316	+	0.619367i
$136$	−7.59176	−	6.83565i	−0.650988	−	0.586152i
$137$	1.46210	+	0.949498i	0.124916	+	0.0811211i	0.605584	−	0.795781i	$-0.292939\pi$
$137$	1.46210	+	0.949498i	0.124916	+	0.0811211i	−0.480669	+	0.876902i	$0.659606\pi$
$138$	−0.286268	+	5.46232i	−0.0243688	+	0.464983i
$139$	−3.24021	−	9.97233i	−0.274831	−	0.845842i	−0.989264	−	0.146138i	$-0.953315\pi$
$139$	−3.24021	−	9.97233i	−0.274831	−	0.845842i	0.714433	−	0.699703i	$-0.246685\pi$
$140$	−7.10382	−	2.31260i	−0.600382	−	0.195450i
$141$	2.58769	−	7.96409i	0.217923	−	0.670697i
$142$	11.8035	+	4.53094i	0.990527	+	0.380228i
$143$	−2.20846	+	8.24209i	−0.184681	+	0.689238i
$144$	0.795207	+	0.0835796i	0.0662673	+	0.00696497i
$145$	2.22213	+	0.412510i	0.184538	+	0.0342571i
$146$	−4.16496	−	5.73258i	−0.344695	−	0.474431i
$147$	17.6002	−	12.7725i	1.45164	−	1.05346i
$148$	−1.01667	−	0.518017i	−0.0835694	−	0.0425808i
$149$	−10.5057	−	6.06545i	−0.860658	−	0.496901i	0.00357448	−	0.999994i	$-0.498862\pi$
$149$	−10.5057	−	6.06545i	−0.860658	−	0.496901i	−0.864233	+	0.503092i	$0.832196\pi$
$150$	−10.3599	−	8.39913i	−0.845879	−	0.685786i
$151$	2.51055	+	4.34839i	0.204305	+	0.353867i	0.949911	−	0.312520i	$-0.101173\pi$
$151$	2.51055	+	4.34839i	0.204305	+	0.353867i	−0.745606	+	0.666387i	$0.767840\pi$
$152$	16.6811	−	10.8328i	1.35301	−	0.878656i
$153$	−23.9550	−	3.79410i	−1.93665	−	0.306735i
$154$	4.06914	−	3.85934i	0.327901	−	0.310994i
$155$	−6.46763	+	4.95983i	−0.519493	+	0.398383i
$156$	12.3869	−	5.51498i	0.991742	−	0.441552i
$157$	−4.61392	−	1.23630i	−0.368231	−	0.0986672i	0.0699583	−	0.997550i	$-0.477713\pi$
$157$	−4.61392	−	1.23630i	−0.368231	−	0.0986672i	−0.438189	+	0.898883i	$0.644380\pi$
$158$	−8.20086	−	10.1272i	−0.652425	−	0.805678i
$159$	1.82955	+	2.03192i	0.145093	+	0.161142i
$160$	6.08500	+	11.2149i	0.481061	+	0.886613i
$161$	−0.427167	+	5.40863i	−0.0336655	+	0.426260i
$162$	−11.6925	+	5.95761i	−0.918646	+	0.468074i
$163$	−1.11655	−	0.0585162i	−0.0874553	−	0.00458334i	0.00855810	−	0.999963i	$-0.497276\pi$
$163$	−1.11655	−	0.0585162i	−0.0874553	−	0.00458334i	−0.0960134	+	0.995380i	$0.530609\pi$
$164$	−1.98976	+	2.20985i	−0.155374	+	0.172560i
$165$	−15.8461	+	6.55833i	−1.23362	+	0.510565i
$166$	−1.96354	+	1.76798i	−0.152400	+	0.137222i
$167$	20.0374	−	3.17362i	1.55054	−	0.245582i	0.678349	−	0.734740i	$-0.262696\pi$
$167$	20.0374	−	3.17362i	1.55054	−	0.245582i	0.872195	+	0.489158i	$0.162696\pi$
$168$	−22.8284	−	3.01180i	−1.76125	−	0.232366i
$169$	−0.619519	+	0.852694i	−0.0476553	+	0.0655919i
$170$	−3.01222	−	6.31993i	−0.231027	−	0.484717i
$171$	19.2067	−	43.1390i	1.46878	−	3.29892i
$172$	−0.991005	−	2.58166i	−0.0755634	−	0.196849i
$173$	−4.85273	−	7.47255i	−0.368946	−	0.568128i	0.604625	−	0.796510i	$-0.293323\pi$
$173$	−4.85273	−	7.47255i	−0.368946	−	0.568128i	−0.973571	+	0.228383i	$0.926656\pi$
$174$	2.69604			0.204386
$175$	−10.0519	−	8.59995i	−0.759853	−	0.650095i
$176$	0.296794			0.0223717
$177$	−2.08834	−	3.21576i	−0.156969	−	0.241711i
$178$	2.89322	+	7.53709i	0.216856	+	0.564929i
$179$	−2.34621	+	5.26968i	−0.175364	+	0.393874i	−0.979748	−	0.200236i	$-0.935829\pi$
$179$	−2.34621	+	5.26968i	−0.175364	+	0.393874i	0.804383	+	0.594110i	$0.202496\pi$
$180$	16.5021	+	8.96607i	1.22999	+	0.668291i
$181$	3.29233	−	4.53150i	0.244717	−	0.336824i	−0.668935	−	0.743321i	$-0.733250\pi$
$181$	3.29233	−	4.53150i	0.244717	−	0.336824i	0.913652	+	0.406497i	$0.133250\pi$
$182$	−7.25472	+	3.00267i	−0.537756	+	0.222572i
$183$	33.3259	−	5.27831i	2.46352	−	0.390184i
$184$	4.26921	−	3.84401i	0.314730	−	0.283384i
$185$	−1.31174	−	1.53675i	−0.0964414	−	0.112984i
$186$	−6.50568	+	7.22529i	−0.477019	+	0.529784i
$187$	−8.99023	−	0.471158i	−0.657431	−	0.0344545i
$188$	−3.03287	+	1.54532i	−0.221195	+	0.112704i
$189$	−27.0898	+	12.9120i	−1.97049	+	0.939210i
$190$	13.4035	−	2.48019i	0.972390	−	0.179932i
$191$	−11.6643	−	12.9545i	−0.843997	−	0.937354i	0.154722	−	0.987958i	$-0.450552\pi$
$191$	−11.6643	−	12.9545i	−0.843997	−	0.937354i	−0.998719	+	0.0506044i	$0.983885\pi$
$192$	9.10845	+	11.2480i	0.657346	+	0.811754i
$193$	13.8891	+	3.72157i	0.999759	+	0.267885i	0.721345	−	0.692576i	$-0.243524\pi$
$193$	13.8891	+	3.72157i	0.999759	+	0.267885i	0.278415	+	0.960461i	$0.410191\pi$
$194$	13.9729	−	6.22115i	1.00320	−	0.446653i
$195$	24.0015	−	0.621586i	1.71879	−	0.0445127i
$196$	−8.72994	−	1.38761i	−0.623567	−	0.0991153i
$197$	7.84565	+	1.24263i	0.558979	+	0.0885336i	0.429530	−	0.903052i	$-0.358679\pi$
$197$	7.84565	+	1.24263i	0.558979	+	0.0885336i	0.129449	+	0.991586i	$0.458679\pi$
$198$	−11.8239	+	7.67855i	−0.840291	+	0.545691i
$199$	−3.08282	−	5.33960i	−0.218535	−	0.378514i	0.735825	−	0.677172i	$-0.236795\pi$
$199$	−3.08282	−	5.33960i	−0.218535	−	0.378514i	−0.954360	+	0.298657i	$0.903461\pi$
$200$	1.45614	+	13.9314i	0.102965	+	0.985100i
$201$	−13.6104	−	7.85795i	−0.960001	−	0.554257i
$202$	−11.0415	−	5.62590i	−0.776874	−	0.395837i
$203$	2.67325	+	0.0707378i	0.187625	+	0.00496482i
$204$	8.40857	+	11.5734i	0.588718	+	0.810300i
$205$	−4.75325	+	2.26550i	−0.331981	+	0.158230i
$206$	−12.8052	−	1.34588i	−0.892182	−	0.0937721i
$207$	3.53003	−	13.1742i	0.245354	−	0.915673i
$208$	−0.387915	−	0.148907i	−0.0268970	−	0.0103248i
$209$	5.41641	−	16.6700i	0.374661	−	1.15309i
$210$	−13.6618	−	7.89789i	−0.942752	−	0.545006i
$211$	5.44934	+	16.7713i	0.375148	+	1.15459i	0.943379	+	0.331717i	$0.107628\pi$
$211$	5.44934	+	16.7713i	0.375148	+	1.15459i	−0.568231	+	0.822869i	$0.692372\pi$
$212$	0.0581670	−	1.10989i	0.00399493	−	0.0762277i
$213$	−38.3657	−	24.9150i	−2.62877	−	1.70714i
$214$	−7.67935	−	6.91451i	−0.524949	−	0.472666i
$215$	0.129589	−	4.89495i	0.00883792	−	0.333833i
$216$	30.2205	+	9.81924i	2.05625	+	0.668115i
$217$	−6.64026	+	6.99352i	−0.450770	+	0.474751i
$218$	−0.450710	+	0.450710i	−0.0305260	+	0.0305260i
$219$	10.4279	+	23.4215i	0.704654	+	1.58268i
$220$	6.43965	+	2.66956i	0.434161	+	0.179982i
$221$	11.5140	+	5.12636i	0.774514	+	0.344836i
$222$	−1.87306	−	1.51678i	−0.125712	−	0.101799i
$223$	−3.91951	+	7.69248i	−0.262470	+	0.515126i	−0.984203	−	0.177046i	$-0.943346\pi$
$223$	−3.91951	+	7.69248i	−0.262470	+	0.515126i	0.721733	+	0.692172i	$0.243346\pi$
$224$	9.18720	+	11.9798i	0.613846	+	0.800435i
$225$	20.9134	+	25.8564i	1.39423	+	1.72376i
$226$	4.14058	−	7.17169i	0.275427	−	0.477054i
$227$	−0.571138	−	10.8980i	−0.0379078	−	0.723324i	−0.949793	−	0.312879i	$-0.898707\pi$
$227$	−0.571138	−	10.8980i	−0.0379078	−	0.723324i	0.911885	−	0.410445i	$-0.134627\pi$
$228$	−26.0027	+	9.98150i	−1.72207	+	0.661041i
$229$	−1.02433	−	9.74582i	−0.0676894	−	0.644022i	−0.974793	−	0.223113i	$-0.928378\pi$
$229$	−1.02433	−	9.74582i	−0.0676894	−	0.644022i	0.907103	−	0.420909i	$-0.138289\pi$
$230$	3.71159	−	1.31314i	0.244735	−	0.0865860i
$231$	−17.3045	+	10.5976i	−1.13855	+	0.697274i
$232$	−2.00222	−	2.00222i	−0.131452	−	0.131452i
$233$	1.20987	−	3.15183i	0.0792614	−	0.206483i	−0.888224	−	0.459411i	$-0.848060\pi$
$233$	1.20987	−	3.15183i	0.0792614	−	0.206483i	0.967485	+	0.252928i	$0.0813937\pi$
$234$	19.3065	−	4.10373i	1.26211	−	0.268269i
$235$	−6.00891	+	0.471170i	−0.391978	+	0.0307358i
$236$	−0.324052	+	1.52454i	−0.0210940	+	0.0992393i
$237$	21.4056	+	42.0108i	1.39044	+	2.72890i
$238$	−4.69011	−	6.82817i	−0.304014	−	0.442605i
$239$	−14.2076	+	4.61631i	−0.919010	+	0.298604i	−0.730061	−	0.683382i	$-0.760508\pi$
$239$	−14.2076	+	4.61631i	−0.919010	+	0.298604i	−0.188949	+	0.981987i	$0.560508\pi$
$240$	−0.236955	−	0.800793i	−0.0152954	−	0.0516910i
$241$	5.52248	+	25.9812i	0.355734	+	1.67360i	0.684365	+	0.729140i	$0.260080\pi$
$241$	5.52248	+	25.9812i	0.355734	+	1.67360i	−0.328631	+	0.944459i	$0.606587\pi$
$242$	3.27302	−	2.65044i	0.210398	−	0.170377i
$243$	12.9947	−	3.48192i	0.833610	−	0.223365i
$244$	−11.0959	−	8.06166i	−0.710343	−	0.516095i
$245$	−13.3391	−	8.18958i	−0.852202	−	0.523213i
$246$	−5.08159	+	3.69199i	−0.323990	+	0.235393i
$247$	−15.4430	+	19.0705i	−0.982612	+	1.21342i
$248$	10.1973	−	0.534420i	0.647532	−	0.0339357i
$249$	8.27921	−	4.78000i	0.524673	−	0.302920i
$250$	−2.73437	+	9.20187i	−0.172937	+	0.581978i
$251$		−	6.13565i		−	0.387279i	−0.981073	−	0.193639i	$-0.937971\pi$
$251$		−	6.13565i		−	0.387279i	0.981073	−	0.193639i	$-0.0620292\pi$
$252$	20.9448	+	7.42345i	1.31940	+	0.467633i
$253$	0.791961	−	5.00024i	0.0497901	−	0.314363i
$254$	9.48767	−	0.997194i	0.595309	−	0.0625695i
$255$	5.90638	+	24.6331i	0.369872	+	1.54258i
$256$	1.63921	−	15.5960i	0.102450	−	0.974751i
$257$	−4.17077	−	15.5655i	−0.260166	−	0.970951i	−0.965143	−	0.261722i	$-0.915710\pi$
$257$	−4.17077	−	15.5655i	−0.260166	−	0.970951i	0.704978	−	0.709230i	$-0.250957\pi$
$258$	−0.913759	−	5.76925i	−0.0568882	−	0.359178i
$259$	−1.81743	−	1.55310i	−0.112930	−	0.0965050i
$260$	−7.07736	−	6.72004i	−0.438919	−	0.416759i
$261$	−6.57566	−	1.39770i	−0.407023	−	0.0865154i
$262$	6.68162	−	10.2888i	0.412792	−	0.635644i
$263$	11.3920	−	17.5421i	0.702458	−	1.08169i	−0.289751	−	0.957102i	$-0.593572\pi$
$263$	11.3920	−	17.5421i	0.702458	−	1.08169i	0.992209	−	0.124588i	$-0.0397609\pi$
$264$	21.0165	+	4.46719i	1.29347	+	0.274936i
$265$	0.847767	−	1.77607i	0.0520779	−	0.109103i
$266$	15.2048	−	5.37959i	0.932266	−	0.329844i
$267$	−4.56959	−	28.8512i	−0.279654	−	1.76567i
$268$	1.65340	+	6.17058i	0.100998	+	0.376928i
$269$	2.36733	−	22.5237i	0.144339	−	1.37329i	−0.647268	−	0.762262i	$-0.724089\pi$
$269$	2.36733	−	22.5237i	0.144339	−	1.37329i	0.791607	−	0.611030i	$-0.209245\pi$
$270$	16.5550	+	14.1476i	1.00751	+	0.860994i
$271$	11.4809	−	1.20670i	0.697417	−	0.0733015i	0.250816	−	0.968035i	$-0.419301\pi$
$271$	11.4809	−	1.20670i	0.697417	−	0.0733015i	0.446601	+	0.894733i	$0.352634\pi$
$272$	0.0685787	−	0.432989i	0.00415820	−	0.0262538i
$273$	27.9342	−	5.16935i	1.69066	−	0.312863i
$274$		−	1.49686i		−	0.0904286i
$275$	8.72342	+	8.73348i	0.526042	+	0.526649i
$276$	−6.96689	+	4.02234i	−0.419357	+	0.242116i
$277$	−25.3650	+	1.32933i	−1.52404	+	0.0798714i	−0.795845	−	0.605501i	$-0.792973\pi$
$277$	−25.3650	+	1.32933i	−1.52404	+	0.0798714i	−0.728193	+	0.685372i	$0.759640\pi$
$278$	−5.66575	+	6.99662i	−0.339809	+	0.419630i
$279$	19.6132	−	14.2498i	1.17421	−	0.853114i
$280$	4.28056	+	16.0114i	0.255813	+	0.956861i
$281$	1.65462	+	1.20215i	0.0987061	+	0.0717142i	0.636044	−	0.771653i	$-0.280570\pi$
$281$	1.65462	+	1.20215i	0.0987061	+	0.0717142i	−0.537337	+	0.843367i	$0.680570\pi$
$282$	−6.94495	+	1.86089i	−0.413566	+	0.110815i
$283$	16.1101	−	13.0457i	0.957646	−	0.775486i	−0.0168580	−	0.999858i	$-0.505366\pi$
$283$	16.1101	−	13.0457i	0.957646	−	0.775486i	0.974504	+	0.224372i	$0.0720330\pi$
$284$	3.86610	+	18.1886i	0.229411	+	1.07929i
$285$	−49.3024	−	1.30524i	−2.92042	−	0.0773156i
$286$	6.96780	−	2.26398i	0.412015	−	0.133872i
$287$	−5.13550	+	3.52745i	−0.303139	+	0.208219i
$288$	−17.2299	−	33.8156i	−1.01528	−	1.99260i
$289$	0.769805	−	3.62165i	0.0452827	−	0.213038i
$290$	−0.742096	−	1.79304i	−0.0435774	−	0.105291i
$291$	−54.1321	+	11.5061i	−3.17328	+	0.674501i
$292$	3.73471	−	9.72925i	0.218557	−	0.569361i
$293$	−12.1262	−	12.1262i	−0.708422	−	0.708422i	0.257781	−	0.966203i	$-0.417009\pi$
$293$	−12.1262	−	12.1262i	−0.708422	−	0.708422i	−0.966203	+	0.257781i	$0.917009\pi$
$294$	−17.4278	−	6.70090i	−1.01641	−	0.390805i
$295$	−1.56386	+	2.27403i	−0.0910517	+	0.132399i
$296$	0.264597	+	2.51748i	0.0153794	+	0.146325i
$297$	26.1424	−	10.0351i	1.51693	−	0.582296i
$298$	0.545116	+	10.4014i	0.0315777	+	0.602539i
$299$	−3.54381	+	6.13806i	−0.204944	+	0.354973i
$300$	2.06157	−	19.5064i	0.119025	−	1.12620i
$301$	−0.754663	−	5.74445i	−0.0434981	−	0.331105i
$302$	1.95722	−	3.84127i	0.112626	−	0.221040i
$303$	34.8450	+	28.2169i	2.00179	+	1.62102i
$304$	0.779741	+	0.347163i	0.0447212	+	0.0199112i
$305$	−12.6835	−	20.7110i	−0.726257	−	1.18591i
$306$	8.47005	+	19.0240i	0.484200	+	1.08753i
$307$	−3.57700	+	3.57700i	−0.204150	+	0.204150i	−0.801775	−	0.597625i	$-0.796111\pi$
$307$	−3.57700	+	3.57700i	−0.204150	+	0.204150i	0.597625	+	0.801775i	$0.296111\pi$
$308$	8.01983	+	1.92773i	0.456972	+	0.109842i
$309$	44.3069	+	14.3962i	2.52053	+	0.818971i
$310$	6.59600	+	2.33790i	0.374628	+	0.132784i
$311$	2.30262	+	2.07329i	0.130569	+	0.117565i	0.731828	−	0.681489i	$-0.238667\pi$
$311$	2.30262	+	2.07329i	0.130569	+	0.117565i	−0.601259	+	0.799054i	$0.705334\pi$
$312$	−25.2276	−	16.3830i	−1.42823	−	0.927504i
$313$	0.0182272	−	0.347795i	0.00103026	−	0.0196585i	−0.998066	−	0.0621627i	$-0.980200\pi$
$313$	0.0182272	−	0.347795i	0.00103026	−	0.0196585i	0.999096	+	0.0425042i	$0.0135336\pi$
$314$	1.26737	+	3.90057i	0.0715220	+	0.220122i
$315$	29.2267	+	26.3457i	1.64674	+	1.48441i
$316$	5.92251	−	18.2276i	0.333167	−	1.02538i
$317$	−1.29367	−	0.496593i	−0.0726597	−	0.0278914i	0.321767	−	0.946819i	$-0.395723\pi$
$317$	−1.29367	−	0.496593i	−0.0726597	−	0.0278914i	−0.394426	+	0.918928i	$0.629057\pi$
$318$	0.607611	−	2.26763i	0.0340731	−	0.127163i
$319$	−2.48164	−	0.260831i	−0.138945	−	0.0146037i
$320$	4.97351	−	9.15377i	0.278027	−	0.511711i
$321$	21.9767	+	30.2483i	1.22662	+	1.68830i
$322$	4.09446	−	2.22165i	0.228175	−	0.123808i
$323$	−23.0681	−	11.7538i	−1.28354	−	0.653999i
$324$	−16.7144	−	9.65007i	−0.928579	−	0.536115i
$325$	−7.01993	−	15.7915i	−0.389395	−	0.875954i
$326$	0.480000	+	0.831384i	0.0265847	+	0.0460461i
$327$	1.93418	−	1.25607i	0.106960	−	0.0694608i
$328$	6.51572	+	1.03199i	0.359771	+	0.0569821i
$329$	−6.93507	+	1.66294i	−0.382343	+	0.0916811i
$330$	12.1327	+	8.34374i	0.667885	+	0.459308i
$331$	11.6622	−	5.19234i	0.641012	−	0.285397i	−0.0603768	−	0.998176i	$-0.519230\pi$
$331$	11.6622	−	5.19234i	0.641012	−	0.285397i	0.701389	+	0.712779i	$0.252564\pi$
$332$	−3.75357	−	1.00577i	−0.206004	−	0.0551986i
$333$	3.78208	+	4.67048i	0.207257	+	0.255941i
$334$	−11.6554	−	12.9447i	−0.637757	−	0.708301i
$335$	−1.47973	+	11.2147i	−0.0808463	+	0.612725i
$336$	−0.425152	−	0.891981i	−0.0231939	−	0.0486615i
$337$	2.29665	−	1.17020i	0.125106	−	0.0637448i	−0.390317	−	0.920680i	$-0.627635\pi$
$337$	2.29665	−	1.17020i	0.125106	−	0.0637448i	0.515423	+	0.856936i	$0.327635\pi$
$338$	0.903724	+	0.0473622i	0.0491561	+	0.00257616i
$339$	−20.0491	+	22.2668i	−1.08892	+	1.20936i
$340$	5.38257	−	8.77787i	0.291911	−	0.476047i
$341$	6.68734	−	6.02131i	0.362140	−	0.326072i
$342$	−40.0457	+	6.34261i	−2.16542	+	0.342969i
$343$	−17.1046	−	7.10152i	−0.923563	−	0.383446i
$344$	−3.60594	+	4.96315i	−0.194419	+	0.267595i
$345$	−14.1237	+	1.85528i	−0.760392	+	0.0998848i
$346$	−3.11162	+	6.98881i	−0.167282	+	0.375721i
$347$	2.23182	+	5.81410i	0.119811	+	0.312117i	0.980350	−	0.197267i	$-0.0632066\pi$
$347$	2.23182	+	5.81410i	0.119811	+	0.312117i	−0.860539	+	0.509384i	$0.829873\pi$
$348$	2.15958	+	3.32547i	0.115766	+	0.178264i
$349$	6.37223			0.341098			0.170549	−	0.985349i	$-0.445446\pi$
$349$	6.37223			0.341098			0.170549	+	0.985349i	$0.445446\pi$
$350$	−1.49215	+	11.2599i	−0.0797585	+	0.601867i
$351$	−39.2033			−2.09252
$352$	−7.67245	−	11.8145i	−0.408943	−	0.629717i
$353$	−0.236809	−	0.616908i	−0.0126041	−	0.0328347i	0.927134	−	0.374730i	$-0.122265\pi$
$353$	−0.236809	−	0.616908i	−0.0126041	−	0.0328347i	−0.939738	+	0.341895i	$0.888931\pi$
$354$	−1.33906	+	3.00759i	−0.0711704	+	0.159851i
$355$	−6.00974	+	32.3736i	−0.318964	+	1.71821i
$356$	−6.97921	+	9.60606i	−0.369897	+	0.509120i
$357$	11.4623	+	27.6940i	0.606650	+	1.46572i
$358$	4.89181	−	0.774787i	0.258540	−	0.0409488i
$359$	−13.9304	+	12.5430i	−0.735221	+	0.661996i	−0.949139	−	0.314856i	$-0.898044\pi$
$359$	−13.9304	+	12.5430i	−0.735221	+	0.661996i	0.213919	+	0.976851i	$0.431377\pi$
$360$	−3.25697	−	41.5367i	−0.171657	−	2.18917i
$361$	21.0157	−	23.3403i	1.10609	−	1.22844i
$362$	−4.80269	−	0.251698i	−0.252424	−	0.0132290i
$363$	−13.5775	+	6.91808i	−0.712633	+	0.363105i
$364$	−9.51488	−	6.54325i	−0.498715	−	0.342960i
$365$	12.7065	−	13.3821i	0.665088	−	0.700452i
$366$	−19.3851	−	21.5294i	−1.01328	−	1.12536i
$367$	19.6025	+	24.2070i	1.02324	+	1.26360i	0.964154	+	0.265343i	$0.0854853\pi$
$367$	19.6025	+	24.2070i	1.02324	+	1.26360i	0.0590860	+	0.998253i	$0.481181\pi$
$368$	0.238125	+	0.0638055i	0.0124131	+	0.00332609i
$369$	14.3081	−	6.37036i	0.744848	−	0.331628i
$370$	−0.493186	+	1.66321i	−0.0256395	+	0.0864661i
$371$	0.661972	−	2.23252i	0.0343679	−	0.115907i
$372$	−14.1233	−	2.23692i	−0.732260	−	0.115979i
$373$	−6.76376	+	4.39244i	−0.350214	+	0.227432i	−0.707742	−	0.706471i	$-0.750286\pi$
$373$	−6.76376	+	4.39244i	−0.350214	+	0.227432i	0.357528	+	0.933902i	$0.383620\pi$
$374$	3.86484	+	6.69411i	0.199846	+	0.346144i
$375$	16.5996	−	30.5097i	0.857197	−	1.57551i
$376$	6.53969	+	3.77569i	0.337259	+	0.194716i
$377$	3.11268	+	1.58599i	0.160311	+	0.0816826i
$378$	21.9658	+	13.4690i	1.12980	+	0.692771i
$379$	−8.68157	−	11.9492i	−0.445942	−	0.613787i	0.525577	−	0.850746i	$-0.323849\pi$
$379$	−8.68157	−	11.9492i	−0.445942	−	0.613787i	−0.971520	+	0.236959i	$0.923849\pi$
$380$	13.7957	+	14.5460i	0.707705	+	0.746195i
$381$	−34.3283	−	3.60805i	−1.75869	−	0.184846i
$382$	−3.87381	+	14.4573i	−0.198201	+	0.739698i
$383$	23.2265	+	8.91581i	1.18682	+	0.455577i	0.870068	−	0.492932i	$-0.164075\pi$
$383$	23.2265	+	8.91581i	1.18682	+	0.455577i	0.316750	+	0.948509i	$0.397408\pi$
$384$	−7.11561	+	21.8996i	−0.363117	+	1.11756i
$385$	11.8113	+	8.59155i	0.601957	+	0.437866i
$386$	−3.81512	−	11.7417i	−0.194185	−	0.597639i
$387$	−0.762269	+	14.5450i	−0.0387483	+	0.739362i
$388$	18.8662	+	12.2519i	0.957786	+	0.621994i
$389$	21.2173	+	19.1041i	1.07576	+	0.968618i	0.999594	−	0.0284772i	$-0.00906580\pi$
$389$	21.2173	+	19.1041i	1.07576	+	0.968618i	0.0761649	+	0.997095i	$0.475732\pi$
$390$	−11.6715	−	16.9926i	−0.591009	−	0.860454i
$391$	−7.11180	−	2.31076i	−0.359659	−	0.116860i
$392$	7.96634	+	17.9192i	0.402361	+	0.905058i
$393$	−31.3871	+	31.3871i	−1.58327	+	1.58327i
$394$	−2.77407	−	6.23067i	−0.139756	−	0.313896i
$395$	22.0479	−	25.7998i	1.10935	−	1.29813i
$396$	−18.9425	−	8.43373i	−0.951895	−	0.423811i
$397$	−6.02439	−	4.87845i	−0.302355	−	0.244843i	0.466121	−	0.884721i	$-0.345651\pi$
$397$	−6.02439	−	4.87845i	−0.302355	−	0.244843i	−0.768476	+	0.639879i	$0.778985\pi$
$398$	−2.40337	+	4.71688i	−0.120470	+	0.236436i
$399$	−57.8587	+	7.60104i	−2.89656	+	0.380528i
$400$	−0.467356	+	0.378012i	−0.0233678	+	0.0189006i
$401$	18.2018	−	31.5265i	0.908956	−	1.57436i	0.0934398	−	0.995625i	$-0.470214\pi$
$401$	18.2018	−	31.5265i	0.908956	−	1.57436i	0.815517	−	0.578734i	$-0.196453\pi$
$402$	0.706211	+	13.4753i	0.0352226	+	0.672088i
$403$	−11.7615	+	4.51480i	−0.585880	+	0.224898i
$404$	−1.90509	−	18.1257i	−0.0947818	−	0.901788i
$405$	−20.7969	−	27.1192i	−1.03341	−	1.34756i
$406$	−1.19916	−	1.95806i	−0.0595132	−	0.0971768i
$407$	1.57737	+	1.57737i	0.0781873	+	0.0781873i
$408$	11.3733	−	29.6284i	0.563062	−	1.46683i
$409$	−11.5158	+	2.44775i	−0.569418	+	0.121034i	−0.483619	−	0.875279i	$-0.660678\pi$
$409$	−11.5158	+	2.44775i	−0.569418	+	0.121034i	−0.0857996	+	0.996312i	$0.527344\pi$
$410$	3.85414	+	2.36335i	0.190342	+	0.116717i
$411$	−1.12604	+	5.29759i	−0.0555433	+	0.261311i
$412$	−8.59716	−	16.8729i	−0.423552	−	0.831267i
$413$	−1.40666	+	2.94703i	−0.0692170	+	0.145014i
$414$	−11.1374	+	3.61876i	−0.547373	+	0.177852i
$415$	−5.45790	−	4.19049i	−0.267918	−	0.205703i
$416$	4.10047	+	19.2912i	0.201042	+	0.945828i
$417$	25.3152	−	20.4998i	1.23969	−	1.00388i
$418$	−14.5368	+	3.89512i	−0.711018	+	0.190517i
$419$	−4.95298	−	3.59855i	−0.241969	−	0.175801i	0.460191	−	0.887820i	$-0.347781\pi$
$419$	−4.95298	−	3.59855i	−0.241969	−	0.175801i	−0.702160	+	0.712019i	$0.747781\pi$
$420$	−1.20160	−	23.1777i	−0.0586322	−	1.13096i
$421$	−19.6842	+	14.3014i	−0.959351	+	0.697009i	−0.953000	−	0.302971i	$-0.902022\pi$
$421$	−19.6842	+	14.3014i	−0.959351	+	0.697009i	−0.00635102	+	0.999980i	$0.502022\pi$
$422$	9.52859	−	11.7668i	0.463844	−	0.572800i
$423$	17.9035	−	0.938285i	0.870500	−	0.0456210i
$424$	−2.13531	+	1.23282i	−0.103700	+	0.0598711i
$425$	14.7568	−	10.7085i	0.715812	−	0.519438i
$426$			39.2778i			1.90301i
$427$	−18.6564	−	21.8560i	−0.902846	−	1.05769i
$428$	2.37749	−	15.0109i	0.114920	−	0.725578i
$429$	−26.3631	+	2.77087i	−1.27282	+	0.133779i
$430$	−3.58541	+	2.19572i	−0.172904	+	0.105887i
$431$	−0.230809	+	2.19600i	−0.0111177	+	0.105777i	−0.998673	−	0.0514918i	$-0.983602\pi$
$431$	−0.230809	+	2.19600i	−0.0111177	+	0.105777i	0.987556	+	0.157269i	$0.0502691\pi$
$432$	0.352923	+	1.31713i	0.0169800	+	0.0633703i
$433$	4.68698	+	29.5924i	0.225242	+	1.42212i	0.798129	+	0.602487i	$0.205824\pi$
$433$	4.68698	+	29.5924i	0.225242	+	1.42212i	−0.572887	+	0.819635i	$0.694176\pi$
$434$	8.14116	+	1.51119i	0.390788	+	0.0725396i
$435$	1.27753	+	6.90406i	0.0612531	+	0.331024i
$436$	−0.916965	−	0.194907i	−0.0439146	−	0.00933434i
$437$	7.92948	−	12.2103i	0.379319	−	0.584100i
$438$	11.9892	−	18.4617i	0.572865	−	0.882134i
$439$	−5.09440	−	1.08285i	−0.243142	−	0.0516815i	0.0847284	−	0.996404i	$-0.472998\pi$
$439$	−5.09440	−	1.08285i	−0.243142	−	0.0516815i	−0.327871	+	0.944723i	$0.606331\pi$
$440$	−2.81391	−	15.2069i	−0.134148	−	0.724961i
$441$	39.0325	+	25.3786i	1.85869	+	1.20850i
$442$	−1.69287	−	10.6884i	−0.0805216	−	0.508393i
$443$	9.11243	+	34.0081i	0.432945	+	1.61577i	0.745937	+	0.666016i	$0.232002\pi$
$443$	9.11243	+	34.0081i	0.432945	+	1.61577i	−0.312992	+	0.949756i	$0.601331\pi$
$444$	0.370527	−	3.52533i	0.0175844	−	0.167305i
$445$	−17.9301	+	10.9805i	−0.849970	+	0.520526i
$446$	7.37217	−	0.774846i	0.349082	−	0.0366900i
$447$	5.89541	−	37.2221i	0.278843	−	1.76055i
$448$	4.11781	−	11.6182i	0.194548	−	0.548907i
$449$		−	11.0263i		−	0.520361i	−0.965560	−	0.260181i	$-0.916218\pi$
$449$		−	11.0263i		−	0.520361i	0.965560	−	0.260181i	$-0.0837821\pi$
$450$	8.83914	−	27.1508i	0.416681	−	1.27990i
$451$	5.03467	−	2.90677i	0.237073	−	0.136874i
$452$	12.1627	−	0.637422i	0.572087	−	0.0299818i
$453$	−9.81654	+	12.1224i	−0.461221	+	0.569561i
$454$	−7.58044	+	5.50751i	−0.355768	+	0.258480i
$455$	−11.1270	−	17.1552i	−0.521641	−	0.804248i
$456$	49.9894	+	36.3194i	2.34097	+	1.70081i
$457$	−4.78308	+	1.28162i	−0.223743	+	0.0599518i	−0.368949	−	0.929450i	$-0.620282\pi$
$457$	−4.78308	+	1.28162i	−0.223743	+	0.0599518i	0.145206	+	0.989401i	$0.453616\pi$
$458$	−6.53886	+	5.29507i	−0.305541	+	0.247422i
$459$	−8.59951	−	40.4575i	−0.401391	−	1.88840i
$460$	4.59278	+	3.52627i	0.214140	+	0.164413i
$461$	−9.15490	+	2.97461i	−0.426386	+	0.138541i	−0.514346	−	0.857583i	$-0.671965\pi$
$461$	−9.15490	+	2.97461i	−0.426386	+	0.138541i	0.0879597	+	0.996124i	$0.471965\pi$
$462$	15.7234	+	7.50499i	0.731518	+	0.349164i
$463$	9.49875	+	18.6423i	0.441444	+	0.866383i	0.999335	+	0.0364685i	$0.0116109\pi$
$463$	9.49875	+	18.6423i	0.441444	+	0.866383i	−0.557891	+	0.829914i	$0.688389\pi$
$464$	0.0252635	−	0.118855i	0.00117283	−	0.00551773i
$465$	−21.5854	−	13.2361i	−1.00100	−	0.613810i
$466$	−2.83538	+	0.602678i	−0.131346	+	0.0279185i
$467$	0.108162	−	0.281771i	0.00500512	−	0.0130388i	−0.931055	−	0.364879i	$-0.881110\pi$
$467$	0.108162	−	0.281771i	0.00500512	−	0.0130388i	0.936060	+	0.351840i	$0.114444\pi$
$468$	20.5268	+	20.5268i	0.948850	+	0.948850i
$469$	0.346680	+	13.3799i	0.0160082	+	0.617828i
$470$	3.14924	+	4.10662i	0.145264	+	0.189424i
$471$	−1.55113	−	14.7581i	−0.0714725	−	0.680015i
$472$	3.22805	−	1.23913i	0.148583	−	0.0570357i
$473$	0.282942	+	5.39886i	0.0130097	+	0.248240i
$474$	20.2416	−	35.0596i	0.929730	−	1.61034i
$475$	12.7026	+	33.1486i	0.582838	+	1.52096i
$476$	4.66544	−	11.2546i	0.213840	−	0.515854i
$477$	−2.65757	+	5.21578i	−0.121682	+	0.238814i
$478$	9.96807	+	8.07198i	0.455929	+	0.369204i
$479$	−14.4131	−	6.41713i	−0.658552	−	0.293206i	0.0501214	−	0.998743i	$-0.484039\pi$
$479$	−14.4131	−	6.41713i	−0.658552	−	0.293206i	−0.708673	+	0.705537i	$0.750706\pi$
$480$	−25.7518	+	30.1339i	−1.17540	+	1.37542i
$481$	−1.27026	−	2.85304i	−0.0579187	−	0.130087i
$482$	16.1263	−	16.1263i	0.734535	−	0.734535i
$483$	−16.1621	+	4.78260i	−0.735402	+	0.217616i
$484$	5.89098	+	1.91410i	0.267772	+	0.0870044i
$485$	22.5524	+	32.8342i	1.02405	+	1.49092i
$486$	−8.58403	−	7.72910i	−0.389380	−	0.350599i
$487$	−5.93909	−	3.85689i	−0.269126	−	0.174772i	0.403020	−	0.915191i	$-0.367961\pi$
$487$	−5.93909	−	3.85689i	−0.269126	−	0.174772i	−0.672146	+	0.740419i	$0.734627\pi$
$488$	−1.59243	+	30.3853i	−0.0720857	+	1.37548i
$489$	−1.07336	−	3.30347i	−0.0485391	−	0.149388i
$490$	0.340536	+	13.4350i	0.0153838	+	0.606934i
$491$	−6.72096	+	20.6850i	−0.303313	+	0.933500i	0.676989	+	0.735993i	$0.263285\pi$
$491$	−6.72096	+	20.6850i	−0.303313	+	0.933500i	−0.980301	+	0.197507i	$0.936715\pi$
$492$	−8.62440	−	3.31060i	−0.388818	−	0.149253i
$493$	−0.953942	+	3.56016i	−0.0429634	+	0.160342i
$494$	20.9541	+	2.20236i	0.942769	+	0.0990890i
$495$	−25.2662	−	26.6404i	−1.13563	−	1.19740i
$496$	0.257567	+	0.354510i	0.0115651	+	0.0159180i
$497$	−1.03056	+	38.9458i	−0.0462269	+	1.74696i
$498$	−7.31366	−	3.72649i	−0.327733	−	0.166988i
$499$	−3.54008	−	2.04386i	−0.158476	−	0.0914959i	0.418665	−	0.908141i	$-0.362498\pi$
$499$	−3.54008	−	2.04386i	−0.158476	−	0.0914959i	−0.577141	+	0.816645i	$0.695832\pi$
$500$	−13.5405	+	3.99815i	−0.605549	+	0.178803i
$501$	31.5123	+	54.5810i	1.40787	+	2.43850i
$502$	−4.41822	+	2.86923i	−0.197195	+	0.128060i
$503$	−37.4748	−	5.93543i	−1.67092	−	0.264648i	−0.752020	−	0.659140i	$-0.770921\pi$
$503$	−37.4748	−	5.93543i	−1.67092	−	0.264648i	−0.918899	+	0.394492i	$0.870921\pi$
$504$	−11.4951	−	47.9388i	−0.512033	−	2.13536i
$505$	9.17484	−	30.9410i	0.408275	−	1.37686i
$506$	−3.97097	+	1.76799i	−0.176531	+	0.0785968i
$507$	−3.16277	−	0.847462i	−0.140464	−	0.0376371i
$508$	8.82983	+	10.9039i	0.391761	+	0.483784i
$509$	19.4921	+	21.6481i	0.863971	+	0.959537i	0.999512	−	0.0312348i	$-0.00994395\pi$
$509$	19.4921	+	21.6481i	0.863971	+	0.959537i	−0.135541	+	0.990772i	$0.543277\pi$
$510$	14.9760	−	15.7723i	0.663150	−	0.698411i
$511$	12.3722	−	17.9911i	0.547315	−	0.795878i
$512$	1.21138	−	0.617229i	0.0535360	−	0.0272779i
$513$	80.4197	+	4.21462i	3.55062	+	0.186080i
$514$	−9.25821	+	10.2823i	−0.408362	+	0.453532i
$515$	−2.62128	−	33.4296i	−0.115507	−	1.47308i
$516$	6.38423	−	5.74838i	0.281050	−	0.253058i
$517$	6.57270	−	1.04101i	0.289067	−	0.0457837i
$518$	−0.268482	+	2.03500i	−0.0117964	+	0.0894126i
$519$	16.2699	−	22.3936i	0.714169	−	0.982969i
$520$	−3.95174	+	21.2875i	−0.173295	+	0.933517i
$521$	−4.23899	+	9.52093i	−0.185714	+	0.417120i	−0.982277	−	0.187436i	$-0.939982\pi$
$521$	−4.23899	+	9.52093i	−0.185714	+	0.417120i	0.796563	+	0.604555i	$0.206649\pi$
$522$	2.06852	+	5.38868i	0.0905366	+	0.235856i
$523$	−7.35048	−	11.3187i	−0.321414	−	0.494934i	0.640622	−	0.767856i	$-0.278677\pi$
$523$	−7.35048	−	11.3187i	−0.321414	−	0.494934i	−0.962036	+	0.272922i	$0.912010\pi$
$524$	18.0430			0.788212
$525$	13.7513	−	38.7278i	0.600158	−	1.69022i
$526$	−17.9591			−0.783055
$527$	−7.23920	−	11.1474i	−0.315345	−	0.485588i
$528$	0.330425	+	0.860786i	0.0143799	+	0.0374609i
$529$	−7.64457	+	17.1700i	−0.332373	+	0.746521i
$530$	−1.67537	+	0.220076i	−0.0727734	+	0.00955949i
$531$	4.82520	−	6.64132i	0.209396	−	0.288209i
$532$	18.8149	+	14.4454i	0.815730	+	0.626289i
$533$	−8.03876	+	1.27322i	−0.348198	+	0.0551491i
$534$	−18.6386	+	16.7823i	−0.806572	+	0.726240i
$535$	14.0679	−	22.9419i	0.608208	−	0.991865i
$536$	9.48302	−	10.5320i	0.409604	−	0.454911i
$537$	−17.8956	−	0.937870i	−0.772253	−	0.0404721i
$538$	−17.3261	+	8.82810i	−0.746982	+	0.380606i
$539$	15.3936	+	7.85409i	0.663048	+	0.338300i
$540$	−4.18961	+	31.7526i	−0.180292	+	1.36641i
$541$	−7.56010	−	8.39634i	−0.325034	−	0.360987i	0.558376	−	0.829588i	$-0.311425\pi$
$541$	−7.56010	−	8.39634i	−0.325034	−	0.360987i	−0.883410	+	0.468601i	$0.844758\pi$
$542$	−6.23778	−	7.70302i	−0.267936	−	0.330873i
$543$	16.8080	+	4.50370i	0.721301	+	0.193272i
$544$	−19.0089	+	8.46331i	−0.815000	+	0.362861i
$545$	−1.36776	−	0.940615i	−0.0585884	−	0.0402915i
$546$	−16.7854	−	17.6978i	−0.718347	−	0.757397i
$547$	−30.3524	−	4.80735i	−1.29778	−	0.205547i	−0.530950	−	0.847403i	$-0.678165\pi$
$547$	−30.3524	−	4.80735i	−1.29778	−	0.205547i	−0.766826	+	0.641856i	$0.778165\pi$
$548$	1.84632	−	1.19902i	0.0788711	−	0.0512195i
$549$	36.1191	+	62.5602i	1.54153	+	2.67000i
$550$	2.20954	−	10.3657i	0.0942151	−	0.441995i
$551$	−6.21469	−	3.58806i	−0.264755	−	0.152856i
$552$	15.9017	+	8.10230i	0.676820	+	0.344857i
$553$	20.9904	−	34.2321i	0.892604	−	1.45570i
$554$	12.8187	+	17.6435i	0.544616	+	0.749600i
$555$	2.99663	−	5.51531i	0.127200	−	0.234112i
$556$	−13.1685	−	1.38406i	−0.558468	−	0.0586974i
$557$	−0.808291	+	3.01658i	−0.0342484	+	0.127817i	−0.980934	−	0.194344i	$-0.937742\pi$
$557$	−0.808291	+	3.01658i	−0.0342484	+	0.127817i	0.946685	+	0.322160i	$0.104409\pi$
$558$	−19.4329	−	7.45960i	−0.822661	−	0.315790i
$559$	2.33889	−	7.19835i	0.0989244	−	0.304458i
$560$	−0.476200	+	0.528275i	−0.0201231	+	0.0223237i
$561$	−8.64245	−	26.5987i	−0.364885	−	1.12300i
$562$	0.0919042	−	1.75364i	0.00387675	−	0.0739727i
$563$	−24.7112	−	16.0476i	−1.04145	−	0.676327i	−0.0937868	−	0.995592i	$-0.529897\pi$
$563$	−24.7112	−	16.0476i	−1.04145	−	0.676327i	−0.947665	+	0.319265i	$0.896564\pi$
$564$	−7.85841	−	7.07574i	−0.330899	−	0.297942i
$565$	20.3274	+	7.20491i	0.855182	+	0.303113i
$566$	−16.9277	−	5.50014i	−0.711523	−	0.231188i
$567$	−29.3243	−	27.8430i	−1.23150	−	1.16930i
$568$	29.1698	−	29.1698i	1.22394	−	1.22394i
$569$	−3.24840	−	7.29602i	−0.136180	−	0.305865i	0.832564	−	0.553929i	$-0.186872\pi$
$569$	−3.24840	−	7.29602i	−0.136180	−	0.305865i	−0.968744	+	0.248064i	$0.920206\pi$
$570$	22.1155	+	36.1126i	0.926317	+	1.51259i
$571$	28.3513	+	12.6228i	1.18646	+	0.528248i	0.902543	−	0.430600i	$-0.141698\pi$
$571$	28.3513	+	12.6228i	1.18646	+	0.528248i	0.283921	+	0.958848i	$0.408365\pi$
$572$	8.37389	+	6.78105i	0.350130	+	0.283530i
$573$	24.5856	−	48.2521i	1.02708	−	2.01576i
$574$	4.94161	+	2.04847i	0.206259	+	0.0855017i
$575$	5.12148	+	8.88247i	0.213580	+	0.370425i
$576$	−15.4934	+	26.8354i	−0.645559	+	1.11814i
$577$	−1.71926	−	32.8055i	−0.0715739	−	1.36571i	−0.764463	−	0.644667i	$-0.776996\pi$
$577$	−1.71926	−	32.8055i	−0.0715739	−	1.36571i	0.692889	−	0.721044i	$-0.256337\pi$
$578$	−2.96790	+	1.13927i	−0.123448	+	0.0473874i
$579$	4.66931	+	44.4256i	0.194050	+	1.84626i
$580$	1.61722	−	2.35161i	0.0671512	−	0.0976454i
$581$	−7.15406	−	3.88689i	−0.296800	−	0.161255i
$582$	33.5993	+	33.5993i	1.39274	+	1.39274i
$583$	−0.778676	+	2.02852i	−0.0322495	+	0.0840127i
$584$	−22.6144	+	4.80685i	−0.935792	+	0.198909i
$585$	19.6574	+	47.4959i	0.812735	+	1.96372i
$586$	−3.06137	+	14.4026i	−0.126464	+	0.594966i
$587$	−17.4894	−	34.3249i	−0.721865	−	1.41674i	−0.901399	−	0.432989i	$-0.857459\pi$
$587$	−17.4894	−	34.3249i	−0.721865	−	1.41674i	0.179534	−	0.983752i	$-0.442541\pi$
$588$	−5.69469	−	26.8641i	−0.234845	−	1.10786i
$589$	24.6123	−	7.99701i	1.01413	−	0.329511i
$590$	2.36882	+	0.0627124i	0.0975229	+	0.00258183i
$591$	5.13069	+	24.1380i	0.211048	+	0.992905i
$592$	−0.0844193	+	0.0683614i	−0.00346961	+	0.00280964i
$593$	22.2798	−	5.96985i	0.914922	−	0.245153i	0.229508	−	0.973307i	$-0.426288\pi$
$593$	22.2798	−	5.96985i	0.914922	−	0.245153i	0.685413	+	0.728154i	$0.259622\pi$
$594$	−19.4512	−	14.1321i	−0.798092	−	0.579848i
$595$	15.2633	−	15.2461i	0.625733	−	0.625029i
$596$	−12.3932	+	9.00416i	−0.507644	+	0.368825i
$597$	12.0542	−	14.8857i	0.493345	−	0.609231i
$598$	6.07716	−	0.318490i	0.248513	−	0.0130240i
$599$	−15.2982	+	8.83240i	−0.625066	+	0.360882i	−0.778839	−	0.627224i	$-0.784191\pi$
$599$	−15.2982	+	8.83240i	−0.625066	+	0.360882i	0.153773	+	0.988106i	$0.450858\pi$
$600$	−38.7839	+	19.7332i	−1.58334	+	0.805606i
$601$		−	22.6811i		−	0.925181i	−0.886572	−	0.462591i	$-0.846920\pi$
$601$		−	22.6811i		−	0.925181i	0.886572	−	0.462591i	$-0.153080\pi$
$602$	−3.78362	+	3.22972i	−0.154209	+	0.131633i
$603$	5.26352	−	33.2325i	0.214347	−	1.35333i
$604$	6.30585	−	0.662772i	0.256581	−	0.0269678i
$605$	8.33823	+	7.12568i	0.338997	+	0.289700i
$606$	4.02409	−	38.2867i	0.163468	−	1.55529i
$607$	−3.64430	−	13.6007i	−0.147917	−	0.552036i	−0.999608	−	0.0279907i	$-0.991089\pi$
$607$	−3.64430	−	13.6007i	−0.147917	−	0.552036i	0.851691	−	0.524045i	$-0.175578\pi$
$608$	−6.33757	−	40.0138i	−0.257022	−	1.62277i
$609$	2.77100	+	7.83191i	0.112287	+	0.317365i
$610$	−8.98259	+	18.8184i	−0.363694	+	0.761936i
$611$	−9.11292	−	1.93701i	−0.368669	−	0.0783631i
$612$	−16.6808	+	25.6862i	−0.674281	+	1.03830i
$613$	−6.73359	+	10.3688i	−0.271967	+	0.418792i	−0.948093	−	0.317994i	$-0.896991\pi$
$613$	−6.73359	+	10.3688i	−0.271967	+	0.418792i	0.676126	+	0.736786i	$0.263658\pi$
$614$	4.24848	+	0.903043i	0.171455	+	0.0364438i
$615$	−11.8625	−	11.2635i	−0.478340	−	0.454190i
$616$	−6.10342	−	17.2506i	−0.245914	−	0.695048i
$617$	4.15259	+	26.2184i	0.167177	+	1.05551i	0.918454	+	0.395527i	$0.129438\pi$
$617$	4.15259	+	26.2184i	0.167177	+	1.05551i	−0.751277	+	0.659987i	$0.770562\pi$
$618$	−10.3528	−	38.6371i	−0.416450	−	1.55421i
$619$	−4.12571	+	39.2535i	−0.165826	+	1.57773i	0.522699	+	0.852517i	$0.324925\pi$
$619$	−4.12571	+	39.2535i	−0.165826	+	1.57773i	−0.688525	+	0.725213i	$0.741741\pi$
$620$	2.39982	+	10.0086i	0.0963789	+	0.401957i
$621$	23.1320	−	2.43128i	0.928257	−	0.0975637i
$622$	0.416175	−	2.62763i	0.0166871	−	0.105358i
$623$	−18.9214	+	16.1514i	−0.758069	+	0.647092i
$624$		−	1.29084i		−	0.0516750i
$625$	−24.8600	−	2.64185i	−0.994401	−	0.105674i
$626$	−0.258967	+	0.149515i	−0.0103504	+	0.00597581i
$627$	54.3779	−	2.84982i	2.17164	−	0.113811i
$628$	−3.79603	+	4.68770i	−0.151478	+	0.187060i
$629$	2.66568	−	1.93673i	0.106288	−	0.0772225i
$630$	5.30391	−	33.3660i	0.211313	−	1.32933i
$631$	−2.56712	−	1.86512i	−0.102195	−	0.0742493i	0.535514	−	0.844526i	$-0.320118\pi$
$631$	−2.56712	−	1.86512i	−0.102195	−	0.0742493i	−0.637709	+	0.770277i	$0.720118\pi$
$632$	−41.0696	+	11.0046i	−1.63366	+	0.437738i
$633$	−42.5747	+	34.4763i	−1.69219	+	1.37031i
$634$	0.247369	+	1.16378i	0.00982429	+	0.0462197i
$635$	7.04943	+	23.8237i	0.279748	+	0.945413i
$636$	3.28376	−	1.06696i	0.130209	−	0.0423076i
$637$	−16.1791	−	17.9886i	−0.641040	−	0.712736i
$638$	0.972672	+	1.90898i	0.0385085	+	0.0755771i
$639$	20.3627	−	95.7989i	0.805535	−	3.78974i
$640$	16.5233	−	1.29562i	0.653139	−	0.0512139i
$641$	4.77373	−	1.01469i	0.188551	−	0.0400778i	−0.112668	−	0.993633i	$-0.535940\pi$
$641$	4.77373	−	1.01469i	0.188551	−	0.0400778i	0.301219	+	0.953555i	$0.402606\pi$
$642$	11.5045	−	29.9703i	0.454047	−	1.18283i
$643$	0.430113	+	0.430113i	0.0169620	+	0.0169620i	0.715537	−	0.698575i	$-0.246182\pi$
$643$	0.430113	+	0.430113i	0.0169620	+	0.0169620i	−0.698575	+	0.715537i	$0.746182\pi$
$644$	6.02009	+	3.27079i	0.237225	+	0.128887i
$645$	14.3410	−	5.07377i	0.564676	−	0.199779i
$646$	2.32360	+	22.1076i	0.0914208	+	0.869811i
$647$	−15.2032	+	5.83596i	−0.597700	+	0.229435i	−0.638360	−	0.769738i	$-0.720387\pi$
$647$	−15.2032	+	5.83596i	−0.597700	+	0.229435i	0.0406607	+	0.999173i	$0.487054\pi$
$648$	2.24086	+	42.7581i	0.0880292	+	1.67970i
$649$	1.52355	−	2.63886i	0.0598045	−	0.103584i
$650$	−8.08855	+	12.4396i	−0.317259	+	0.487921i
$651$	−27.6758	−	11.4726i	−1.08470	−	0.449648i
$652$	−0.640993	+	1.25802i	−0.0251032	+	0.0492679i
$653$	−36.7888	−	29.7910i	−1.43966	−	1.16581i	−0.957032	−	0.289983i	$-0.906350\pi$
$653$	−36.7888	−	29.7910i	−1.43966	−	1.16581i	−0.482624	−	0.875828i	$-0.660316\pi$
$654$	−1.80897	−	0.805404i	−0.0707363	−	0.0314938i
$655$	29.5139	+	12.2350i	1.15320	+	0.478061i
$656$	0.115145	+	0.258619i	0.00449565	+	0.0100974i
$657$	−38.8127	+	38.8127i	−1.51423	+	1.51423i
$658$	4.44053	+	4.21623i	0.173110	+	0.164366i
$659$	−12.4558	−	4.04712i	−0.485208	−	0.157654i	0.0561901	−	0.998420i	$-0.482105\pi$
$659$	−12.4558	−	4.04712i	−0.485208	−	0.157654i	−0.541398	+	0.840767i	$0.682105\pi$
$660$	−0.573133	+	21.6488i	−0.0223092	+	0.842680i
$661$	22.5948	+	20.3444i	0.878836	+	0.791307i	0.979042	−	0.203659i	$-0.0652835\pi$
$661$	22.5948	+	20.3444i	0.878836	+	0.791307i	−0.100206	+	0.994967i	$0.531950\pi$
$662$	−9.19258	−	5.96973i	−0.357280	−	0.232020i
$663$	−2.04920	+	39.1010i	−0.0795842	+	1.51856i
$664$	2.66402	+	8.19900i	0.103384	+	0.318183i
$665$	20.9811	+	36.3876i	0.813610	+	1.41105i
$666$	1.59455	−	4.90751i	0.0617874	−	0.190162i
$667$	−1.93501	−	0.742780i	−0.0749238	−	0.0287605i
$668$	6.63055	−	24.7456i	0.256544	−	0.957434i
$669$	−26.6740	−	2.80355i	−1.03128	−	0.108391i
$670$	8.76757	−	4.17882i	0.338721	−	0.161442i
$671$	15.7607	+	21.6927i	0.608435	+	0.837439i
$672$	−24.5166	+	39.9827i	−0.945748	+	1.54237i
$673$	12.8773	+	6.56131i	0.496383	+	0.252920i	0.684214	−	0.729282i	$-0.260146\pi$
$673$	12.8773	+	6.56131i	0.496383	+	0.252920i	−0.187830	+	0.982201i	$0.560146\pi$
$674$	−1.91663	−	1.10657i	−0.0738260	−	0.0426235i
$675$	−28.3847	+	49.0983i	−1.09253	+	1.88980i
$676$	0.665483	+	1.15265i	0.0255955	+	0.0443327i
$677$	−16.2360	+	10.5438i	−0.623999	+	0.405230i	−0.817548	−	0.575861i	$-0.804667\pi$
$677$	−16.2360	+	10.5438i	−0.623999	+	0.405230i	0.193549	+	0.981091i	$0.438000\pi$
$678$	25.4097	+	4.02450i	0.975853	+	0.154560i
$679$	32.4337	+	34.1969i	1.24469	+	1.31236i
$680$	−22.8354	+	0.591385i	−0.875697	+	0.0226786i
$681$	30.9713	−	13.7893i	1.18682	−	0.528408i
$682$	−7.46310	−	1.99973i	−0.285777	−	0.0765737i
$683$	−28.0404	−	34.6270i	−1.07294	−	1.32497i	−0.942759	−	0.333476i	$-0.891778\pi$
$683$	−28.0404	−	34.6270i	−1.07294	−	1.32497i	−0.130178	−	0.991491i	$-0.541555\pi$
$684$	−39.9009	−	44.3144i	−1.52565	−	1.69440i
$685$	3.83318	−	0.709297i	0.146458	−	0.0271008i
$686$	2.88494	+	15.6378i	0.110147	+	0.597053i
$687$	27.1252	−	13.8210i	1.03489	−	0.527303i
$688$	−0.262901	−	0.0137781i	−0.0100230	−	0.000525284i
$689$	2.03548	−	2.26063i	0.0775458	−	0.0861233i
$690$	7.94064	+	9.30272i	0.302295	+	0.354149i
$691$	2.22126	−	2.00003i	0.0845008	−	0.0760849i	−0.625798	−	0.779985i	$-0.715227\pi$
$691$	2.22126	−	2.00003i	0.0845008	−	0.0760849i	0.710299	+	0.703900i	$0.248560\pi$
$692$	−11.1129	+	1.76012i	−0.422450	+	0.0669096i
$693$	−34.4587	−	26.4562i	−1.30898	−	1.00499i
$694$	3.14300	−	4.32597i	0.119307	−	0.164212i
$695$	−20.6018	−	11.1936i	−0.781472	−	0.424596i
$696$	3.57790	−	8.03609i	0.135620	−	0.304607i
$697$	−3.07731	−	8.01666i	−0.116561	−	0.303653i
$698$	−2.97986	−	4.58858i	−0.112789	−	0.173680i
$699$	10.4882			0.396698
$700$	−15.0839	+	7.17891i	−0.570119	+	0.271337i
$701$	−27.5603			−1.04094			−0.520469	−	0.853880i	$-0.674243\pi$
$701$	−27.5603			−1.04094			−0.520469	+	0.853880i	$0.674243\pi$
$702$	18.3327	+	28.2299i	0.691923	+	1.06547i
$703$	2.29902	+	5.98915i	0.0867092	+	0.225885i
$704$	−4.67821	+	10.5074i	−0.176317	+	0.396014i
$705$	−8.05632	−	16.9030i	−0.303419	−	0.636602i
$706$	−0.333490	+	0.459010i	−0.0125511	+	0.0172751i
$707$	4.99463	−	37.8575i	0.187842	−	1.42378i
$708$	−4.78237	+	0.757453i	−0.179733	+	0.0284668i
$709$	−20.4491	+	18.4125i	−0.767982	+	0.691495i	−0.956874	−	0.290503i	$-0.906177\pi$
$709$	−20.4491	+	18.4125i	−0.767982	+	0.691495i	0.188891	+	0.981998i	$0.439511\pi$
$710$	26.1223	−	10.8114i	0.980351	−	0.405744i
$711$	−67.5454	+	75.0168i	−2.53315	+	2.81335i
$712$	26.3054	+	1.37861i	0.985838	+	0.0516656i
$713$	6.65990	−	3.39339i	0.249415	−	0.127083i
$714$	14.5821	−	21.2045i	0.545720	−	0.793559i
$715$	9.09937	+	16.7705i	0.340297	+	0.627180i
$716$	4.87412	+	5.41326i	0.182154	+	0.202303i
$717$	−29.2061	−	36.0665i	−1.09072	−	1.34693i
$718$	15.5464	+	4.16565i	0.580188	+	0.155461i
$719$	2.18213	−	0.971547i	0.0813797	−	0.0362326i	−0.365643	−	0.930755i	$-0.619151\pi$
$719$	2.18213	−	0.971547i	0.0813797	−	0.0362326i	0.447023	+	0.894523i	$0.352484\pi$
$720$	1.41877	−	1.08802i	0.0528746	−	0.0405479i
$721$	−9.25152	−	38.5822i	−0.344545	−	1.43687i
$722$	−26.6347	−	4.21852i	−0.991241	−	0.156997i
$723$	−69.2046	+	44.9420i	−2.57375	+	1.67141i
$724$	−3.53660	−	6.12557i	−0.131437	−	0.227655i
$725$	4.24000	−	2.75002i	0.157470	−	0.102133i
$726$	11.3309	+	6.54190i	0.420530	+	0.242793i
$727$	42.2271	+	21.5158i	1.56612	+	0.797976i	0.999659	−	0.0261149i	$-0.00831358\pi$
$727$	42.2271	+	21.5158i	1.56612	+	0.797976i	0.566457	+	0.824091i	$0.308314\pi$
$728$	−0.677651	+	25.6090i	−0.0251154	+	0.949134i
$729$	−2.38496	−	3.28261i	−0.0883317	−	0.121578i
$730$	−15.5783	−	2.89191i	−0.576579	−	0.107034i
$731$	7.94171	+	0.834707i	0.293735	+	0.0308728i
$732$	11.0278	−	41.1564i	0.407600	−	1.52118i
$733$	−11.5764	−	4.44376i	−0.427584	−	0.164134i	0.135053	−	0.990838i	$-0.456880\pi$
$733$	−11.5764	−	4.44376i	−0.427584	−	0.164134i	−0.562637	+	0.826704i	$0.690213\pi$
$734$	8.26450	−	25.4355i	0.305048	−	0.938842i
$735$	8.90153	−	47.8046i	0.328338	−	1.76330i
$736$	−3.61588	−	11.1285i	−0.133283	−	0.410203i
$737$	0.653632	−	12.4720i	0.0240768	−	0.459414i
$738$	−11.2781	−	7.32411i	−0.415154	−	0.269604i
$739$	−2.37066	−	2.13455i	−0.0872060	−	0.0785207i	0.624375	−	0.781125i	$-0.285354\pi$
$739$	−2.37066	−	2.13455i	−0.0872060	−	0.0785207i	−0.711581	+	0.702604i	$0.752020\pi$
$740$	−2.44656	+	0.723939i	−0.0899375	+	0.0266125i
$741$	−72.5025	−	23.5575i	−2.66345	−	0.865407i
$742$	−1.91718	+	0.567320i	−0.0703818	+	0.0208270i
$743$	−14.5667	+	14.5667i	−0.534401	+	0.534401i	−0.921879	−	0.387478i	$-0.873346\pi$
$743$	−14.5667	+	14.5667i	−0.534401	+	0.534401i	0.387478	+	0.921879i	$0.373346\pi$
$744$	12.9028	+	28.9802i	0.473040	+	1.06246i
$745$	−26.3779	+	6.32473i	−0.966410	+	0.231720i
$746$	6.32591	+	2.81647i	0.231608	+	0.103118i
$747$	15.9062	+	12.8806i	0.581976	+	0.471275i
$748$	−5.16112	+	10.1293i	−0.188709	+	0.370363i
$749$	12.1936	−	29.4151i	0.445545	−	1.07480i
$750$	−29.7322	+	2.31413i	−1.08567	+	0.0845002i
$751$	−5.27493	+	9.13644i	−0.192485	+	0.333394i	−0.946073	−	0.323953i	$-0.894988\pi$
$751$	−5.27493	+	9.13644i	−0.192485	+	0.333394i	0.753588	+	0.657347i	$0.228321\pi$
$752$	0.0169596	+	0.323608i	0.000618452	+	0.0118008i
$753$	17.7951	−	6.83090i	0.648490	−	0.248932i
$754$	−0.313533	−	2.98307i	−0.0114182	−	0.108637i
$755$	10.7642	+	3.19188i	0.391751	+	0.116165i
$756$	0.981568	+	37.8831i	0.0356993	+	1.37779i
$757$	18.5968	+	18.5968i	0.675912	+	0.675912i	0.959072	−	0.283161i	$-0.0913830\pi$
$757$	18.5968	+	18.5968i	0.675912	+	0.675912i	−0.283161	+	0.959072i	$0.591383\pi$
$758$	−4.54469	+	11.8393i	−0.165071	+	0.430024i
$759$	15.3838	−	3.26993i	0.558397	−	0.118691i
$760$	10.3950	−	43.2433i	0.377065	−	1.56860i
$761$	−7.55377	+	35.5377i	−0.273824	+	1.28824i	0.599214	+	0.800589i	$0.295480\pi$
$761$	−7.55377	+	35.5377i	−0.273824	+	1.28824i	−0.873038	+	0.487652i	$0.837854\pi$
$762$	13.4549	+	26.4067i	0.487419	+	0.956614i
$763$	−1.77254	−	0.846059i	−0.0641704	−	0.0306294i
$764$	−20.9355	+	6.80237i	−0.757421	+	0.246101i
$765$	−44.7035	+	30.7049i	−1.61626	+	1.11014i
$766$	−4.44126	−	20.8945i	−0.160469	−	0.754949i
$767$	−3.31526	+	2.68465i	−0.119707	+	0.0969370i
$768$	47.0578	−	12.6091i	1.69805	−	0.454991i
$769$	12.1604	+	8.83501i	0.438514	+	0.318599i	0.785044	−	0.619440i	$-0.212640\pi$
$769$	12.1604	+	8.83501i	0.438514	+	0.318599i	−0.346530	+	0.938039i	$0.612640\pi$
$770$	0.663368	−	12.5229i	0.0239061	−	0.451292i
$771$	40.5010	−	29.4257i	1.45861	−	1.05974i
$772$	11.4270	−	14.1112i	0.411268	−	0.507873i
$773$	44.1321	−	2.31286i	1.58732	−	0.0831879i	0.761895	−	0.647700i	$-0.224269\pi$
$773$	44.1321	−	2.31286i	1.58732	−	0.0831879i	0.825425	+	0.564512i	$0.190936\pi$
$774$	10.8302	−	6.25279i	0.389282	−	0.224752i
$775$	−2.86139	+	17.9990i	−0.102784	+	0.646543i
$776$		−	49.9053i		−	1.79150i
$777$	2.48105	−	7.00016i	0.0890073	−	0.251129i
$778$	3.83482	−	24.2121i	0.137485	−	0.868045i
$779$	16.6272	−	1.74759i	0.595732	−	0.0626139i
$780$	11.6107	−	28.0078i	0.415729	−	1.00284i
$781$	3.79997	−	36.1543i	0.135974	−	1.29370i
$782$	1.66175	+	6.20172i	0.0594239	+	0.221773i
$783$	−1.79343	−	11.3233i	−0.0640921	−	0.404661i
$784$	−0.458720	+	0.705516i	−0.0163829	+	0.0251970i
$785$	−9.38810	+	5.09382i	−0.335076	+	0.181806i
$786$	37.2791	+	7.92393i	1.32970	+	0.282637i
$787$	−1.64203	+	2.52850i	−0.0585319	+	0.0901312i	−0.866725	−	0.498787i	$-0.833779\pi$
$787$	−1.64203	+	2.52850i	−0.0585319	+	0.0901312i	0.808193	+	0.588918i	$0.200446\pi$
$788$	5.46322	−	8.41262i	0.194619	−	0.299687i
$789$	63.5597	+	13.5100i	2.26279	+	0.480970i
$790$	−28.8885	−	3.81170i	−1.02781	−	0.135614i
$791$	25.0893	+	4.65717i	0.892073	+	0.165590i
$792$	7.19602	+	45.4339i	0.255699	+	1.61442i
$793$	−9.71588	−	36.2602i	−0.345021	−	1.28764i
$794$	−0.695730	+	6.61943i	−0.0246905	+	0.234915i
$795$	6.09492	+	0.481446i	0.216164	+	0.0170751i
$796$	−7.74326	+	0.813849i	−0.274452	+	0.0288461i
$797$	0.278785	−	1.76018i	0.00987509	−	0.0623488i	−0.982259	−	0.187531i	$-0.939952\pi$
$797$	0.278785	−	1.76018i	0.00987509	−	0.0623488i	0.992134	+	0.125182i	$0.0399515\pi$
$798$	32.5300	+	38.1090i	1.15155	+	1.34904i
$799$		−	9.82937i		−	0.347738i
$800$	27.1292	+	8.83210i	0.959164	+	0.312262i
$801$	54.1601	−	31.2694i	1.91365	−	1.10485i
$802$	−31.2137	+	1.63584i	−1.10219	+	0.0577635i
$803$	−12.8218	+	15.8337i	−0.452473	+	0.558758i
$804$	−16.0556	+	11.6651i	−0.566239	+	0.411397i
$805$	7.62944	+	9.43243i	0.268902	+	0.332449i
$806$	8.75110	+	6.35804i	0.308244	+	0.223953i
$807$	67.9605	−	18.2100i	2.39232	−	0.641021i
$808$	−31.4222	+	25.4452i	−1.10543	+	0.895160i
$809$	−7.19843	−	33.8660i	−0.253083	−	1.19066i	−0.902656	−	0.430364i	$-0.858385\pi$
$809$	−7.19843	−	33.8660i	−0.253083	−	1.19066i	0.649572	−	0.760300i	$-0.274948\pi$
$810$	−9.80298	+	27.6575i	−0.344442	+	0.971784i
$811$	47.4403	−	15.4143i	1.66585	−	0.541269i	0.683767	−	0.729700i	$-0.260340\pi$
$811$	47.4403	−	15.4143i	1.66585	−	0.541269i	0.982086	+	0.188432i	$0.0603404\pi$
$812$	1.45464	−	3.04757i	0.0510480	−	0.106949i
$813$	16.2816	+	31.9545i	0.571022	+	1.12069i
$814$	0.398220	−	1.87348i	0.0139576	−	0.0656654i
$815$	−1.90157	+	1.62315i	−0.0666092	+	0.0568565i
$816$	1.33214	−	0.283155i	0.0466342	−	0.00991241i
$817$	−5.57175	+	14.5149i	−0.194931	+	0.507813i
$818$	7.14775	+	7.14775i	0.249915	+	0.249915i
$819$	31.7646	+	51.8671i	1.10994	+	1.81238i
$820$	0.172144	+	6.64704i	0.00601151	+	0.232125i
$821$	−1.61272	−	15.3441i	−0.0562845	−	0.535511i	−0.985942	−	0.167087i	$-0.946564\pi$
$821$	−1.61272	−	15.3441i	−0.0562845	−	0.535511i	0.929658	−	0.368424i	$-0.120103\pi$
$822$	4.34131	−	1.66647i	0.151421	−	0.0581249i
$823$	−1.10792	−	21.1403i	−0.0386196	−	0.736906i	−0.947482	−	0.319809i	$-0.896381\pi$
$823$	−1.10792	−	21.1403i	−0.0386196	−	0.736906i	0.908862	−	0.417096i	$-0.136952\pi$
$824$	−21.0054	+	36.3825i	−0.731759	+	1.26744i
$825$	−15.6176	+	35.0235i	−0.543736	+	1.21936i
$826$	2.77992	−	0.365205i	0.0967259	−	0.0127071i
$827$	−0.614015	+	1.20507i	−0.0213514	+	0.0419045i	−0.901436	−	0.432913i	$-0.857486\pi$
$827$	−0.614015	+	1.20507i	−0.0213514	+	0.0419045i	0.880084	+	0.474817i	$0.157486\pi$
$828$	−13.3849	−	10.8389i	−0.465158	−	0.376677i
$829$	−29.9580	−	13.3382i	−1.04049	−	0.463254i	−0.185902	−	0.982568i	$-0.559521\pi$
$829$	−29.9580	−	13.3382i	−1.04049	−	0.463254i	−0.854583	+	0.519315i	$0.826187\pi$
$830$	−0.465243	+	5.88979i	−0.0161488	+	0.204438i
$831$	−32.0946	−	72.0858i	−1.11335	−	2.50063i
$832$	11.3863	−	11.3863i	0.394747	−	0.394747i
$833$	15.0152	−	20.6427i	0.520244	−	0.715226i
$834$	−26.5999	−	8.64284i	−0.921080	−	0.299277i
$835$	27.6260	−	35.9814i	0.956036	−	1.24519i
$836$	−16.4488	−	14.8106i	−0.568894	−	0.512234i
$837$	34.6737	+	22.5174i	1.19850	+	0.778314i
$838$	−0.275109	+	5.24940i	−0.00950349	+	0.181337i
$839$	−8.80454	−	27.0976i	−0.303966	−	0.935512i	−0.980061	−	0.198697i	$-0.936329\pi$
$839$	−8.80454	−	27.0976i	−0.303966	−	0.935512i	0.676094	−	0.736815i	$-0.263671\pi$
$840$	−41.6718	+	30.2405i	−1.43781	+	1.04340i
$841$	8.64580	−	26.6090i	0.298131	−	0.917553i
$842$	19.5033	+	7.48662i	0.672128	+	0.258006i
$843$	−1.64446	+	6.13722i	−0.0566383	+	0.211377i
$844$	22.1466	+	2.32770i	0.762317	+	0.0801227i
$845$	0.306950	+	2.33672i	0.0105594	+	0.0803854i
$846$	−9.04792	−	12.4534i	−0.311074	−	0.428157i
$847$	11.0635	+	6.78390i	0.380146	+	0.233098i
$848$	−0.0942756	−	0.0480358i	−0.00323744	−	0.00164956i
$849$	55.7717	+	32.1998i	1.91408	+	1.10510i
$850$	−14.6119	−	5.61862i	−0.501182	−	0.192717i
$851$	0.926457	+	1.60467i	0.0317585	+	0.0550074i
$852$	−48.4478	+	31.4624i	−1.65979	+	1.07788i
$853$	−9.12263	−	1.44488i	−0.312353	−	0.0494718i	−0.00170994	−	0.999999i	$-0.500544\pi$
$853$	−9.12263	−	1.44488i	−0.312353	−	0.0494718i	−0.310643	+	0.950527i	$0.600544\pi$
$854$	−7.01397	+	23.6549i	−0.240013	+	0.809453i
$855$	−35.2182	−	99.5442i	−1.20444	−	3.40434i
$856$	−30.8014	+	13.7137i	−1.05277	+	0.468723i
$857$	28.8945	+	7.74225i	0.987016	+	0.264470i	0.715997	−	0.698104i	$-0.245973\pi$
$857$	28.8945	+	7.74225i	0.987016	+	0.264470i	0.271019	+	0.962574i	$0.412639\pi$
$858$	14.3235	+	17.6881i	0.488996	+	0.603860i
$859$	−35.5236	−	39.4530i	−1.21205	−	1.34612i	−0.921073	−	0.389390i	$-0.872686\pi$
$859$	−35.5236	−	39.4530i	−1.21205	−	1.34612i	−0.290978	−	0.956730i	$-0.593981\pi$
$860$	−5.58033	−	2.66366i	−0.190288	−	0.0908299i
$861$	−15.9480	−	10.9672i	−0.543507	−	0.373762i
$862$	1.68925	−	0.860716i	0.0575361	−	0.0293161i
$863$	−7.64071	−	0.400432i	−0.260093	−	0.0136309i	−0.0781560	−	0.996941i	$-0.524903\pi$
$863$	−7.64071	−	0.400432i	−0.260093	−	0.0136309i	−0.181937	+	0.983310i	$0.558237\pi$
$864$	43.3076	−	48.0980i	1.47336	−	1.63633i
$865$	−19.3715	−	4.65660i	−0.658652	−	0.158329i
$866$	19.1174	−	17.2134i	0.649637	−	0.584936i
$867$	11.3608	−	1.79938i	0.385834	−	0.0611101i
$868$	4.65724	+	11.2523i	0.158077	+	0.381929i
$869$	−22.0238	+	30.3132i	−0.747108	+	1.02831i
$870$	4.37413	−	4.14850i	0.148297	−	0.140647i
$871$	−7.11174	+	15.9732i	−0.240972	+	0.541232i
$872$	0.745300	+	1.94157i	0.0252390	+	0.0657499i
$873$	−64.5303	−	99.3679i	−2.18402	−	3.36309i
$874$	−12.5006			−0.422840
$875$	−29.5416	+	1.51447i	−0.998689	+	0.0511983i
$876$	32.3755			1.09387
$877$	30.3097	+	46.6729i	1.02349	+	1.57603i	0.798796	+	0.601602i	$0.205471\pi$
$877$	30.3097	+	46.6729i	1.02349	+	1.57603i	0.224691	+	0.974430i	$0.427863\pi$
$878$	1.60256	+	4.17480i	0.0540837	+	0.140893i
$879$	21.6692	−	48.6698i	0.730883	−	1.64159i
$880$	0.481528	−	0.456689i	0.0162323	−	0.0153950i
$881$	−29.7627	+	40.9648i	−1.00273	+	1.38014i	−0.0790948	+	0.996867i	$0.525203\pi$
$881$	−29.7627	+	40.9648i	−1.00273	+	1.38014i	−0.923635	+	0.383273i	$0.874797\pi$
$882$	0.0220087	−	39.9748i	0.000741073	−	1.34602i
$883$	−29.5527	+	4.68068i	−0.994527	+	0.157518i	−0.632425	−	0.774621i	$-0.717941\pi$
$883$	−29.5527	+	4.68068i	−0.994527	+	0.157518i	−0.362101	+	0.932139i	$0.617941\pi$
$884$	11.8277	−	10.6497i	0.397808	−	0.358188i
$885$	−8.33640	−	2.00393i	−0.280225	−	0.0673615i
$886$	20.2276	−	22.4650i	0.679560	−	0.754728i
$887$	−1.14496	−	0.0600049i	−0.0384441	−	0.00201477i	0.0331042	−	0.999452i	$-0.489461\pi$
$887$	−1.14496	−	0.0600049i	−0.0384441	−	0.00201477i	−0.0715483	+	0.997437i	$0.522794\pi$
$888$	−7.00681	+	3.57015i	−0.235133	+	0.119806i
$889$	12.6483	+	26.5365i	0.424210	+	0.890006i
$890$	16.2917	+	7.77649i	0.546098	+	0.260668i
$891$	25.2477	+	28.0405i	0.845831	+	0.939391i
$892$	6.86101	+	8.47265i	0.229724	+	0.283685i
$893$	18.4856	+	4.95319i	0.618596	+	0.165752i
$894$	−29.5602	+	13.1610i	−0.988640	+	0.440171i
$895$	4.30211	+	12.1599i	0.143804	+	0.406461i
$896$	19.0700	−	4.57275i	0.637084	−	0.152765i
$897$	−21.7475	−	3.44446i	−0.726126	−	0.115007i
$898$	−7.93990	+	5.15623i	−0.264958	+	0.172066i
$899$	−1.84208	−	3.19058i	−0.0614370	−	0.106412i
$900$	40.5700	−	10.8457i	1.35233	−	0.361522i
$901$	2.77946	+	1.60472i	0.0925971	+	0.0534610i
$902$	−4.44751	−	2.26612i	−0.148086	−	0.0754535i
$903$	15.8203	−	8.58411i	0.526468	−	0.285661i
$904$	−15.8818	−	21.8594i	−0.528220	−	0.727032i
$905$	−1.63123	−	12.4181i	−0.0542241	−	0.412791i
$906$	13.3198	+	1.39996i	0.442519	+	0.0465107i
$907$	−9.17085	+	34.2261i	−0.304513	+	1.13646i	0.628851	+	0.777526i	$0.283526\pi$
$907$	−9.17085	+	34.2261i	−0.304513	+	1.13646i	−0.933364	+	0.358932i	$0.883141\pi$
$908$	−12.8654	−	4.93857i	−0.426954	−	0.163892i
$909$	−29.6637	+	91.2954i	−0.983882	+	3.02808i
$910$	−7.14996	+	16.0348i	−0.237019	+	0.531547i
$911$	−1.99352	−	6.13541i	−0.0660482	−	0.203275i	0.912586	−	0.408885i	$-0.134082\pi$
$911$	−1.99352	−	6.13541i	−0.0660482	−	0.203275i	−0.978634	+	0.205610i	$0.934082\pi$
$912$	−0.138774	+	2.64797i	−0.00459527	+	0.0876830i
$913$	6.37153	+	4.13772i	0.210867	+	0.136938i
$914$	3.15961	+	2.84492i	0.104511	+	0.0941017i
$915$	45.9470	−	59.8437i	1.51896	−	1.97837i
$916$	−11.7691	−	3.82400i	−0.388860	−	0.126348i
$917$	36.7561	+	8.83506i	1.21379	+	0.291759i
$918$	−25.1117	+	25.1117i	−0.828808	+	0.828808i
$919$	−10.5951	−	23.7969i	−0.349499	−	0.784987i	−0.999682	−	0.0252097i	$-0.991975\pi$
$919$	−10.5951	−	23.7969i	−0.349499	−	0.784987i	0.650183	−	0.759777i	$-0.274692\pi$
$920$	1.01155	−	12.8058i	0.0333499	−	0.422196i
$921$	−14.3566	−	6.39198i	−0.473067	−	0.210623i
$922$	6.42311	+	5.20134i	0.211534	+	0.171297i
$923$	−23.1058	+	45.3477i	−0.760537	+	1.49264i
$924$	3.33764	+	25.4059i	0.109800	+	0.835793i
$925$	−4.49288	−	0.474837i	−0.147725	−	0.0156125i
$926$	8.98225	−	15.5577i	0.295175	−	0.511258i
$927$	5.22000	+	99.6035i	0.171447	+	3.27141i
$928$	−5.38439	+	2.06687i	−0.176751	+	0.0678484i
$929$	4.70786	+	44.7923i	0.154460	+	1.46959i	0.747419	+	0.664353i	$0.231293\pi$
$929$	4.70786	+	44.7923i	0.154460	+	1.46959i	−0.592959	+	0.805233i	$0.702040\pi$
$930$	0.562838	+	21.7331i	0.0184562	+	0.712655i
$931$	31.2552	+	38.6404i	1.02435	+	1.26639i
$932$	−3.01458	−	3.01458i	−0.0987459	−	0.0987459i
$933$	−3.44957	+	8.98645i	−0.112934	+	0.294203i
$934$	−0.253480	+	0.0538789i	−0.00829413	+	0.00176297i
$935$	−15.3110	+	13.0692i	−0.500723	+	0.427409i
$936$	13.3896	−	62.9932i	0.437653	−	2.05900i
$937$	1.89104	+	3.71138i	0.0617776	+	0.121245i	0.919831	−	0.392316i	$-0.128326\pi$
$937$	1.89104	+	3.71138i	0.0617776	+	0.121245i	−0.858053	+	0.513561i	$0.828326\pi$
$938$	9.47265	−	6.50653i	0.309293	−	0.212446i
$939$	1.02899	−	0.334341i	0.0335800	−	0.0109108i
$940$	−2.54276	+	7.17398i	−0.0829358	+	0.233989i
$941$	9.49215	+	44.6571i	0.309435	+	1.45578i	0.808132	+	0.589002i	$0.200479\pi$
$941$	9.49215	+	44.6571i	0.309435	+	1.45578i	−0.498696	+	0.866777i	$0.666188\pi$
$942$	−9.90177	+	8.01830i	−0.322617	+	0.261250i
$943$	4.66434	−	1.24981i	0.151892	−	0.0406993i
$944$	0.120042	+	0.0872159i	0.00390705	+	0.00283864i
$945$	−24.0830	+	62.6329i	−0.783420	+	2.03745i
$946$	3.75535	−	2.72842i	0.122097	−	0.0887087i
$947$	−20.0118	+	24.7125i	−0.650297	+	0.803050i	−0.990531	−	0.137291i	$-0.956160\pi$
$947$	−20.0118	+	24.7125i	−0.650297	+	0.803050i	0.340234	+	0.940341i	$0.389494\pi$
$948$	59.4588	−	3.11610i	1.93113	−	0.101206i
$949$	24.7024	−	14.2619i	0.801873	−	0.462962i
$950$	17.9298	−	24.6484i	0.581720	−	0.799700i
$951$		−	4.30486i		−	0.139595i
$952$	−26.5770	+	4.91819i	−0.861366	+	0.159399i
$953$	−5.01517	+	31.6645i	−0.162457	+	1.02571i	0.762872	+	0.646549i	$0.223789\pi$
$953$	−5.01517	+	31.6645i	−0.162457	+	1.02571i	−0.925329	+	0.379165i	$0.876211\pi$
$954$	4.99860	−	0.525374i	0.161836	−	0.0170096i
$955$	−38.8581	−	3.06945i	−1.25742	−	0.0993252i
$956$	−1.97187	+	18.7611i	−0.0637749	+	0.606778i
$957$	−2.00636	−	7.48783i	−0.0648564	−	0.242047i
$958$	2.11912	+	13.3796i	0.0684657	+	0.432275i
$959$	4.34834	−	1.53848i	0.140415	−	0.0496801i
$960$	32.0856	+	4.23354i	1.03556	+	0.136637i
$961$	−17.3269	−	3.68294i	−0.558931	−	0.118804i
$962$	−1.46043	+	2.24887i	−0.0470863	+	0.0725066i
$963$	−43.5970	+	67.1335i	−1.40489	+	2.16335i
$964$	32.8088	+	6.97373i	1.05670	+	0.224609i
$965$	28.2606	−	15.3337i	0.909742	−	0.493610i
$966$	11.0018	+	9.40169i	0.353978	+	0.302494i
$967$	−2.94641	−	18.6029i	−0.0947502	−	0.598229i	−0.988682	−	0.150026i	$-0.952064\pi$
$967$	−2.94641	−	18.6029i	−0.0947502	−	0.598229i	0.893932	−	0.448203i	$-0.147936\pi$
$968$	−3.55657	−	13.2733i	−0.114312	−	0.426620i
$969$	8.40725	−	79.9897i	0.270080	−	2.56964i
$970$	13.0974	−	31.5941i	0.420531	−	1.01443i
$971$	−46.2521	+	4.86130i	−1.48430	+	0.156006i	−0.811733	−	0.584029i	$-0.801476\pi$
$971$	−46.2521	+	4.86130i	−1.48430	+	0.156006i	−0.672568	+	0.740035i	$0.734809\pi$
$972$	2.65758	−	16.7793i	0.0852418	−	0.538196i
$973$	−26.1483	−	9.26770i	−0.838276	−	0.297109i
$974$			6.08029i			0.194825i
$975$	37.9843	−	37.9406i	1.21647	−	1.21507i
$976$	−1.13078	+	0.652856i	−0.0361954	+	0.0208974i
$977$	−39.8515	+	2.08853i	−1.27496	+	0.0668180i	−0.677767	−	0.735277i	$-0.737052\pi$
$977$	−39.8515	+	2.08853i	−1.27496	+	0.0668180i	−0.597197	+	0.802095i	$0.703719\pi$
$978$	−1.87686	+	2.31773i	−0.0600153	+	0.0741127i
$979$	18.7800	−	13.6445i	0.600212	−	0.436080i
$980$	−16.2989	+	11.1818i	−0.520649	+	0.357190i
$981$	3.99455	+	2.90221i	0.127536	+	0.0926604i
$982$	18.0380	−	4.83327i	0.575616	−	0.154236i
$983$	34.0512	−	27.5741i	1.08606	−	0.879477i	0.0928385	−	0.995681i	$-0.470406\pi$
$983$	34.0512	−	27.5741i	1.08606	−	0.879477i	0.993225	+	0.116204i	$0.0370726\pi$
$984$	4.26098	+	20.0463i	0.135835	+	0.639054i
$985$	14.6411	−	10.0563i	0.466504	−	0.320422i
$986$	3.00973	−	0.977921i	0.0958494	−	0.0311434i
$987$	−12.5439	−	18.2623i	−0.399277	−	0.581294i
$988$	14.0681	+	27.6103i	0.447567	+	0.878400i
$989$	−0.933648	+	4.39247i	−0.0296883	+	0.139672i
$990$	−7.36820	+	30.6519i	−0.234177	+	0.974181i
$991$	−31.5828	+	6.71313i	−1.00326	+	0.213250i	−0.680119	−	0.733101i	$-0.738072\pi$
$991$	−31.5828	+	6.71313i	−1.00326	+	0.213250i	−0.323141	+	0.946351i	$0.604739\pi$
$992$	7.45366	−	19.4175i	0.236654	−	0.616505i
$993$	28.0429	+	28.0429i	0.889916	+	0.889916i
$994$	28.5264	−	17.4702i	0.904802	−	0.554121i
$995$	−13.2179	−	3.91947i	−0.419036	−	0.124255i
$996$	−1.26190	−	12.0061i	−0.0399847	−	0.380429i
$997$	−31.6171	+	12.1367i	−1.00132	+	0.384373i	−0.803139	−	0.595792i	$-0.796838\pi$
$997$	−31.6171	+	12.1367i	−1.00132	+	0.384373i	−0.198186	+	0.980164i	$0.563505\pi$
$998$	0.183687	+	3.50495i	0.00581450	+	0.110947i
$999$	−5.12445	+	8.87580i	−0.162130	+	0.280818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.117.6	yes	288
5.2	odd	4		875.2.bb.a.768.13		288
5.3	odd	4		875.2.bb.b.768.6		288
5.4	even	2		875.2.bb.c.607.13		288
7.3	odd	6	inner	175.2.x.a.17.13	yes	288
25.3	odd	20	inner	175.2.x.a.103.13	yes	288
25.4	even	10		875.2.bb.a.257.13		288
25.21	even	5		875.2.bb.b.257.6		288
25.22	odd	20		875.2.bb.c.243.6		288
35.3	even	12		875.2.bb.b.143.6		288
35.17	even	12		875.2.bb.a.143.13		288
35.24	odd	6		875.2.bb.c.857.6		288
175.3	even	60	inner	175.2.x.a.3.6	✓	288
175.122	even	60		875.2.bb.c.493.13		288
175.129	odd	30		875.2.bb.a.507.13		288
175.171	odd	30		875.2.bb.b.507.6		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.6	✓	288	175.3	even	60	inner
175.2.x.a.17.13	yes	288	7.3	odd	6	inner
175.2.x.a.103.13	yes	288	25.3	odd	20	inner
175.2.x.a.117.6	yes	288	1.1	even	1	trivial
875.2.bb.a.143.13		288	35.17	even	12
875.2.bb.a.257.13		288	25.4	even	10
875.2.bb.a.507.13		288	175.129	odd	30
875.2.bb.a.768.13		288	5.2	odd	4
875.2.bb.b.143.6		288	35.3	even	12
875.2.bb.b.257.6		288	25.21	even	5
875.2.bb.b.507.6		288	175.171	odd	30
875.2.bb.b.768.6		288	5.3	odd	4
875.2.bb.c.243.6		288	25.22	odd	20
875.2.bb.c.493.13		288	175.122	even	60
875.2.bb.c.607.13		288	5.4	even	2
875.2.bb.c.857.6		288	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.467632 - 0.720090i) q^{2} +(1.11331 + 2.90028i) q^{3} +(0.513623 - 1.15362i) q^{4} +(1.62243 - 1.53874i) q^{5} +(1.56784 - 2.15795i) q^{6} +(1.61121 - 2.09857i) q^{7} +(-2.76697 + 0.438245i) q^{8} +(-4.94272 + 4.45045i) q^{9} +(-1.86673 - 0.448731i) q^{10} +(-1.65194 + 1.83466i) q^{11} +(3.91763 + 0.205314i) q^{12} +(3.07959 - 1.56913i) q^{13} +(-2.26461 - 0.178856i) q^{14} +(6.26905 + 2.99240i) q^{15} +(-0.0804422 - 0.0893401i) q^{16} +(2.29486 + 2.83391i) q^{17} +(5.51610 + 1.47803i) q^{18} +(-6.48601 + 2.88776i) q^{19} +(-0.941799 - 2.66199i) q^{20} +(7.88023 + 2.33659i) q^{21} +(2.09362 + 0.331597i) q^{22} +(-1.71981 + 1.11686i) q^{23} +(-4.35154 - 7.53709i) q^{24} +(0.264555 - 4.99300i) q^{25} +(-2.57003 - 1.48381i) q^{26} +(-10.1063 - 5.14941i) q^{27} +(-1.59339 - 2.93659i) q^{28} +(0.594101 + 0.817710i) q^{29} +(-0.776811 - 5.91363i) q^{30} +(-3.62503 - 0.381006i) q^{31} +(-1.47686 + 5.51171i) q^{32} +(-7.16015 - 2.74852i) q^{33} +(0.967525 - 2.97773i) q^{34} +(-0.615085 - 5.88402i) q^{35} +(2.59541 + 7.98786i) q^{36} +(0.0472897 - 0.902341i) q^{37} +(5.11251 + 3.32010i) q^{38} +(7.97945 + 7.18473i) q^{39} +(-3.81487 + 4.96867i) q^{40} +(-2.23957 - 0.727680i) q^{41} +(-2.00249 - 6.76714i) q^{42} +(1.54846 - 1.54846i) q^{43} +(1.26802 + 2.84802i) q^{44} +(-1.17114 + 14.8261i) q^{45} +(1.60848 + 0.716140i) q^{46} +(-2.09481 - 1.69634i) q^{47} +(0.169554 - 0.332768i) q^{48} +(-1.80801 - 6.76248i) q^{49} +(-3.71912 + 2.14438i) q^{50} +(-5.66425 + 9.81076i) q^{51} +(-0.228425 - 4.35860i) q^{52} +(0.821669 - 0.315409i) q^{53} +(1.01798 + 9.68547i) q^{54} +(0.142917 + 5.51851i) q^{55} +(-3.53848 + 6.51279i) q^{56} +(-15.5963 - 15.5963i) q^{57} +(0.311004 - 0.810194i) q^{58} +(-1.20728 + 0.256616i) q^{59} +(6.67201 - 5.69511i) q^{60} +(2.25815 - 10.6238i) q^{61} +(1.42082 + 2.78852i) q^{62} +(1.37583 + 17.5433i) q^{63} +(4.43089 - 1.43968i) q^{64} +(2.58193 - 7.28448i) q^{65} +(1.36913 + 6.44125i) q^{66} +(-3.93146 + 3.18363i) q^{67} +(4.44794 - 1.19182i) q^{68} +(-5.15389 - 3.74452i) q^{69} +(-3.94939 + 3.19447i) q^{70} +(-11.9130 + 8.65529i) q^{71} +(11.7260 - 14.4804i) q^{72} +(8.24140 - 0.431913i) q^{73} +(-0.671881 + 0.387911i) q^{74} +(14.7756 - 4.79148i) q^{75} +8.96558i q^{76} +(1.18855 + 6.42273i) q^{77} +(1.44221 - 9.10574i) q^{78} +(15.0941 - 1.58645i) q^{79} +(-0.267983 - 0.0211684i) q^{80} +(1.59758 - 15.2000i) q^{81} +(0.523299 + 1.95298i) q^{82} +(-0.481396 - 3.03941i) q^{83} +(6.74299 - 7.89063i) q^{84} +(8.08390 + 1.06663i) q^{85} +(-1.83914 - 0.390922i) q^{86} +(-1.71017 + 2.63343i) q^{87} +(3.76683 - 5.80041i) q^{88} +(-9.19731 - 1.95495i) q^{89} +(11.2238 - 6.08984i) q^{90} +(1.66893 - 8.99093i) q^{91} +(0.405091 + 2.55764i) q^{92} +(-2.93077 - 10.9378i) q^{93} +(-0.241920 + 2.30172i) q^{94} +(-6.07958 + 14.6655i) q^{95} +(-17.6297 + 1.85296i) q^{96} +(-2.78673 + 17.5947i) q^{97} +(-4.02411 + 4.46428i) q^{98} -16.4201i 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

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