LMFDB - Embedded newform 175.2.x.a.103.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			103.15
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.01652 + 0.105681i) q^{2} +(-0.0343174 - 0.0423785i) q^{3} +(2.06612 + 0.217158i) q^{4} +(1.94852 + 1.09694i) q^{5} +(-0.0647231 - 0.0890837i) q^{6} +(-2.64536 + 0.0453616i) q^{7} +(0.154579 + 0.0244829i) q^{8} +(0.623117 - 2.93153i) q^{9} +(3.81329 + 2.41792i) q^{10} +(-3.71299 + 0.789220i) q^{11} +(-0.0617013 - 0.0950116i) q^{12} +(2.72389 + 1.38789i) q^{13} +(-5.33921 - 0.188092i) q^{14} +(-0.0203814 - 0.120220i) q^{15} +(-3.75509 - 0.798169i) q^{16} +(1.21589 + 3.16750i) q^{17} +(1.56633 - 5.84563i) q^{18} +(-0.387098 - 3.68300i) q^{19} +(3.78767 + 2.68956i) q^{20} +(0.0927044 + 0.110550i) q^{21} +(-7.57071 + 1.19908i) q^{22} +(0.300717 - 5.73802i) q^{23} +(-0.00426721 - 0.00739102i) q^{24} +(2.59344 + 4.27482i) q^{25} +(5.34609 + 3.08657i) q^{26} +(-0.291380 + 0.148466i) q^{27} +(-5.47550 - 0.480740i) q^{28} +(1.14694 - 1.57863i) q^{29} +(-0.0283944 - 0.244579i) q^{30} +(-1.84036 + 4.13351i) q^{31} +(-7.79020 - 2.08738i) q^{32} +(0.160866 + 0.130267i) q^{33} +(2.11711 + 6.51580i) q^{34} +(-5.20429 - 2.81342i) q^{35} +(1.92404 - 5.92160i) q^{36} +(-6.86909 + 4.46084i) q^{37} +(-0.391367 - 7.46773i) q^{38} +(-0.0346602 - 0.163063i) q^{39} +(0.274343 + 0.217269i) q^{40} +(-7.75457 + 2.51961i) q^{41} +(0.175257 + 0.232723i) q^{42} +(5.09273 + 5.09273i) q^{43} +(-7.84288 + 0.824320i) q^{44} +(4.42988 - 5.02862i) q^{45} +(1.21280 - 11.5390i) q^{46} +(8.71792 + 3.34650i) q^{47} +(0.0950399 + 0.186526i) q^{48} +(6.99588 - 0.239996i) q^{49} +(4.77794 + 8.89432i) q^{50} +(0.0925076 - 0.160228i) q^{51} +(5.32650 + 3.45907i) q^{52} +(5.17366 - 4.18955i) q^{53} +(-0.603263 + 0.268590i) q^{54} +(-8.10055 - 2.53512i) q^{55} +(-0.410028 - 0.0577542i) q^{56} +(-0.142796 + 0.142796i) q^{57} +(2.47966 - 3.06212i) q^{58} +(-2.16617 + 2.40578i) q^{59} +(-0.0160038 - 0.252815i) q^{60} +(10.5258 - 9.47749i) q^{61} +(-4.14794 + 8.14080i) q^{62} +(-1.51539 + 7.78324i) q^{63} +(-8.18628 - 2.65988i) q^{64} +(3.78511 + 5.69228i) q^{65} +(0.310623 + 0.279686i) q^{66} +(13.1621 - 5.05246i) q^{67} +(1.82433 + 6.80848i) q^{68} +(-0.253489 + 0.184170i) q^{69} +(-10.1972 - 6.22330i) q^{70} +(1.76180 + 1.28002i) q^{71} +(0.168093 - 0.437898i) q^{72} +(1.19576 - 1.84131i) q^{73} +(-14.3231 + 8.26943i) q^{74} +(0.0921603 - 0.256607i) q^{75} -7.69359i q^{76} +(9.78640 - 2.25620i) q^{77} +(-0.0526601 - 0.332483i) q^{78} +(-2.66490 - 5.98546i) q^{79} +(-6.44131 - 5.67436i) q^{80} +(-8.19747 - 3.64975i) q^{81} +(-15.9035 + 4.26133i) q^{82} +(-1.08205 + 6.83177i) q^{83} +(0.167532 + 0.248541i) q^{84} +(-1.10538 + 7.50568i) q^{85} +(9.73137 + 10.8078i) q^{86} +(-0.106260 + 0.00556886i) q^{87} +(-0.593272 + 0.0310921i) q^{88} +(-2.55687 - 2.83969i) q^{89} +(9.46435 - 9.67214i) q^{90} +(-7.26863 - 3.54791i) q^{91} +(1.86738 - 11.7902i) q^{92} +(0.238328 - 0.0638599i) q^{93} +(17.2262 + 7.66959i) q^{94} +(3.28576 - 7.60101i) q^{95} +(0.178880 + 0.401770i) q^{96} +(0.674820 + 4.26064i) q^{97} +(14.1327 + 0.255378i) q^{98} +11.3765i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	2.01652	+	0.105681i	1.42589	+	0.0747278i	0.749593	−	0.661899i	$-0.230249\pi$
$2$	2.01652	+	0.105681i	1.42589	+	0.0747278i	0.676299	+	0.736627i	$0.263583\pi$
$3$	−0.0343174	−	0.0423785i	−0.0198132	−	0.0244673i	0.767143	−	0.641476i	$-0.221678\pi$
$3$	−0.0343174	−	0.0423785i	−0.0198132	−	0.0244673i	−0.786956	+	0.617009i	$0.788344\pi$
$4$	2.06612	+	0.217158i	1.03306	+	0.108579i
$5$	1.94852	+	1.09694i	0.871403	+	0.490567i
$5$	1.94852	+	1.09694i	0.871403	+	0.490567i
$6$	−0.0647231	−	0.0890837i	−0.0264231	−	0.0363683i
$7$	−2.64536	+	0.0453616i	−0.999853	+	0.0171451i
$7$	−2.64536	+	0.0453616i	−0.999853	+	0.0171451i
$8$	0.154579	+	0.0244829i	0.0546519	+	0.00865601i
$9$	0.623117	−	2.93153i	0.207706	−	0.977178i
$10$	3.81329	+	2.41792i	1.20587	+	0.764614i
$11$	−3.71299	+	0.789220i	−1.11951	+	0.237959i	−0.730257	−	0.683173i	$-0.760600\pi$
$11$	−3.71299	+	0.789220i	−1.11951	+	0.237959i	−0.389251	+	0.921132i	$0.627266\pi$
$12$	−0.0617013	−	0.0950116i	−0.0178116	−	0.0274275i
$13$	2.72389	+	1.38789i	0.755471	+	0.384932i	0.788910	−	0.614509i	$-0.210646\pi$
$13$	2.72389	+	1.38789i	0.755471	+	0.384932i	−0.0334387	+	0.999441i	$0.510646\pi$
$14$	−5.33921	−	0.188092i	−1.42696	−	0.0502698i
$15$	−0.0203814	−	0.120220i	−0.00526245	−	0.0310405i
$16$	−3.75509	−	0.798169i	−0.938773	−	0.199542i
$17$	1.21589	+	3.16750i	0.294896	+	0.768230i	0.998346	+	0.0574860i	$0.0183084\pi$
$17$	1.21589	+	3.16750i	0.294896	+	0.768230i	−0.703450	+	0.710744i	$0.748358\pi$
$18$	1.56633	−	5.84563i	0.369188	−	1.37783i
$19$	−0.387098	−	3.68300i	−0.0888065	−	0.844937i	−0.944733	−	0.327840i	$-0.893679\pi$
$19$	−0.387098	−	3.68300i	−0.0888065	−	0.844937i	0.855927	−	0.517097i	$-0.172987\pi$
$20$	3.78767	+	2.68956i	0.846949	+	0.601403i
$21$	0.0927044	+	0.110550i	0.0202298	+	0.0241240i
$22$	−7.57071	+	1.19908i	−1.61408	+	0.255645i
$23$	0.300717	−	5.73802i	0.0627038	−	1.19646i	−0.768262	−	0.640136i	$-0.778878\pi$
$23$	0.300717	−	5.73802i	0.0627038	−	1.19646i	0.830966	−	0.556324i	$-0.187789\pi$
$24$	−0.00426721	−	0.00739102i	−0.000871040	−	0.00150869i
$25$	2.59344	+	4.27482i	0.518688	+	0.854964i
$26$	5.34609	+	3.08657i	1.04846	+	0.605326i
$27$	−0.291380	+	0.148466i	−0.0560761	+	0.0285722i
$28$	−5.47550	−	0.480740i	−1.03477	−	0.0908513i
$29$	1.14694	−	1.57863i	0.212982	−	0.293144i	−0.689138	−	0.724630i	$-0.742011\pi$
$29$	1.14694	−	1.57863i	0.212982	−	0.293144i	0.902120	+	0.431486i	$0.142011\pi$
$30$	−0.0283944	−	0.244579i	−0.00518409	−	0.0446537i
$31$	−1.84036	+	4.13351i	−0.330538	+	0.742400i	−1.00000		0.000446135i	$-0.999858\pi$
$31$	−1.84036	+	4.13351i	−0.330538	+	0.742400i	0.669462	+	0.742846i	$0.266525\pi$
$32$	−7.79020	−	2.08738i	−1.37712	−	0.369000i
$33$	0.160866	+	0.130267i	0.0280032	+	0.0226766i
$34$	2.11711	+	6.51580i	0.363082	+	1.11745i
$35$	−5.20429	−	2.81342i	−0.879686	−	0.475555i
$36$	1.92404	−	5.92160i	0.320674	−	0.986933i
$37$	−6.86909	+	4.46084i	−1.12927	+	0.733358i	−0.967350	−	0.253446i	$-0.918436\pi$
$37$	−6.86909	+	4.46084i	−1.12927	+	0.733358i	−0.161922	+	0.986803i	$0.551769\pi$
$38$	−0.391367	−	7.46773i	−0.0634881	−	1.21143i
$39$	−0.0346602	−	0.163063i	−0.00555007	−	0.0261110i
$40$	0.274343	+	0.217269i	0.0433775	+	0.0343533i
$41$	−7.75457	+	2.51961i	−1.21106	+	0.393497i	−0.843819	−	0.536628i	$-0.819698\pi$
$41$	−7.75457	+	2.51961i	−1.21106	+	0.393497i	−0.367242	+	0.930126i	$0.619698\pi$
$42$	0.175257	+	0.232723i	0.0270427	+	0.0359099i
$43$	5.09273	+	5.09273i	0.776634	+	0.776634i	0.979257	−	0.202623i	$-0.0649464\pi$
$43$	5.09273	+	5.09273i	0.776634	+	0.776634i	−0.202623	+	0.979257i	$0.564946\pi$
$44$	−7.84288	+	0.824320i	−1.18236	+	0.124271i
$45$	4.42988	−	5.02862i	0.660367	−	0.749623i
$46$	1.21280	−	11.5390i	0.178818	−	1.70134i
$47$	8.71792	+	3.34650i	1.27164	+	0.488137i	0.898228	−	0.439529i	$-0.144855\pi$
$47$	8.71792	+	3.34650i	1.27164	+	0.488137i	0.373411	+	0.927666i	$0.378188\pi$
$48$	0.0950399	+	0.186526i	0.0137178	+	0.0269228i
$49$	6.99588	−	0.239996i	0.999412	−	0.0342851i
$50$	4.77794	+	8.89432i	0.675703	+	1.25785i
$51$	0.0925076	−	0.160228i	0.0129537	−	0.0224364i
$52$	5.32650	+	3.45907i	0.738653	+	0.479687i
$53$	5.17366	−	4.18955i	0.710657	−	0.575479i	−0.204359	−	0.978896i	$-0.565511\pi$
$53$	5.17366	−	4.18955i	0.710657	−	0.575479i	0.915016	+	0.403417i	$0.132178\pi$
$54$	−0.603263	+	0.268590i	−0.0820937	+	0.0365505i
$55$	−8.10055	−	2.53512i	−1.09228	−	0.341836i
$56$	−0.410028	−	0.0577542i	−0.0547923	−	0.00771773i
$57$	−0.142796	+	0.142796i	−0.0189138	+	0.0189138i
$58$	2.47966	−	3.06212i	0.325595	−	0.402077i
$59$	−2.16617	+	2.40578i	−0.282011	+	0.313205i	−0.867463	−	0.497502i	$-0.834251\pi$
$59$	−2.16617	+	2.40578i	−0.282011	+	0.313205i	0.585451	+	0.810707i	$0.300917\pi$
$60$	−0.0160038	−	0.252815i	−0.00206608	−	0.0326382i
$61$	10.5258	−	9.47749i	1.34769	−	1.21347i	0.391694	−	0.920095i	$-0.371889\pi$
$61$	10.5258	−	9.47749i	1.34769	−	1.21347i	0.955998	−	0.293372i	$-0.0947775\pi$
$62$	−4.14794	+	8.14080i	−0.526789	+	1.03388i
$63$	−1.51539	+	7.78324i	−0.190921	+	0.980596i
$64$	−8.18628	−	2.65988i	−1.02329	−	0.332485i
$65$	3.78511	+	5.69228i	0.469485	+	0.706040i
$66$	0.310623	+	0.279686i	0.0382350	+	0.0344270i
$67$	13.1621	−	5.05246i	1.60801	−	0.617257i	0.621861	−	0.783127i	$-0.286377\pi$
$67$	13.1621	−	5.05246i	1.60801	−	0.617257i	0.986148	+	0.165871i	$0.0530434\pi$
$68$	1.82433	+	6.80848i	0.221232	+	0.825650i
$69$	−0.253489	+	0.184170i	−0.0305164	+	0.0221715i
$70$	−10.1972	−	6.22330i	−1.21880	−	0.743827i
$71$	1.76180	+	1.28002i	0.209087	+	0.151910i	0.687400	−	0.726279i	$-0.258752\pi$
$71$	1.76180	+	1.28002i	0.209087	+	0.151910i	−0.478314	+	0.878189i	$0.658752\pi$
$72$	0.168093	−	0.437898i	0.0198100	−	0.0516068i
$73$	1.19576	−	1.84131i	0.139953	−	0.215509i	−0.761743	−	0.647879i	$-0.775656\pi$
$73$	1.19576	−	1.84131i	0.139953	−	0.215509i	0.901696	+	0.432370i	$0.142323\pi$
$74$	−14.3231	+	8.26943i	−1.66502	+	0.961301i
$75$	0.0921603	−	0.256607i	0.0106418	−	0.0296304i
$76$		−	7.69359i		−	0.882515i
$77$	9.78640	−	2.25620i	1.11526	−	0.257118i
$78$	−0.0526601	−	0.332483i	−0.00596258	−	0.0376463i
$79$	−2.66490	−	5.98546i	−0.299825	−	0.673417i	0.699318	−	0.714810i	$-0.253487\pi$
$79$	−2.66490	−	5.98546i	−0.299825	−	0.673417i	−0.999143	+	0.0413931i	$0.986820\pi$
$80$	−6.44131	−	5.67436i	−0.720161	−	0.634413i
$81$	−8.19747	−	3.64975i	−0.910830	−	0.405528i
$82$	−15.9035	+	4.26133i	−1.75625	+	0.470585i
$83$	−1.08205	+	6.83177i	−0.118770	+	0.749884i	0.854369	+	0.519667i	$0.173944\pi$
$83$	−1.08205	+	6.83177i	−0.118770	+	0.749884i	−0.973139	+	0.230218i	$0.926056\pi$
$84$	0.167532	+	0.248541i	0.0182793	+	0.0271181i
$85$	−1.10538	+	7.50568i	−0.119895	+	0.814105i
$86$	9.73137	+	10.8078i	1.04936	+	1.16543i
$87$	−0.106260	+	0.00556886i	−0.0113923	+	0.000597045i
$88$	−0.593272	+	0.0310921i	−0.0632430	+	0.00331443i
$89$	−2.55687	−	2.83969i	−0.271027	−	0.301006i	0.592232	−	0.805768i	$-0.298247\pi$
$89$	−2.55687	−	2.83969i	−0.271027	−	0.301006i	−0.863259	+	0.504762i	$0.831580\pi$
$90$	9.46435	−	9.67214i	0.997630	−	1.01953i
$91$	−7.26863	−	3.54791i	−0.761960	−	0.371923i
$92$	1.86738	−	11.7902i	0.194688	−	1.22921i
$93$	0.238328	−	0.0638599i	0.0247135	−	0.00662196i
$94$	17.2262	+	7.66959i	1.77674	+	0.791057i
$95$	3.28576	−	7.60101i	0.337112	−	0.779847i
$96$	0.178880	+	0.401770i	0.0182568	+	0.0410055i
$97$	0.674820	+	4.26064i	0.0685176	+	0.432603i	0.997971	+	0.0636644i	$0.0202787\pi$
$97$	0.674820	+	4.26064i	0.0685176	+	0.432603i	−0.929454	+	0.368939i	$0.879721\pi$
$98$	14.1327	+	0.255378i	1.42762	+	0.0257970i
$99$			11.3765i			1.14338i
$100$	4.43005	+	9.39550i	0.443005	+	0.939550i
$101$	−6.04964	+	3.49276i	−0.601962	+	0.347543i	−0.769813	−	0.638270i	$-0.779651\pi$
$101$	−6.04964	+	3.49276i	−0.601962	+	0.347543i	0.167851	+	0.985812i	$0.446317\pi$
$102$	0.203476	−	0.313326i	0.0201471	−	0.0310239i
$103$	−3.45648	+	9.00444i	−0.340577	+	0.887234i	0.651159	+	0.758941i	$0.274283\pi$
$103$	−3.45648	+	9.00444i	−0.340577	+	0.887234i	−0.991736	+	0.128293i	$0.959050\pi$
$104$	0.387076	+	0.281228i	0.0379560	+	0.0275766i
$105$	0.0593695	+	0.317100i	0.00579387	+	0.0309458i
$106$	10.8755	−	7.90153i	1.05632	−	0.767465i
$107$	0.858034	+	3.20223i	0.0829493	+	0.309571i	0.994918	−	0.100689i	$-0.0321047\pi$
$107$	0.858034	+	3.20223i	0.0829493	+	0.309571i	−0.911969	+	0.410260i	$0.865438\pi$
$108$	−0.634268	+	0.243473i	−0.0610325	+	0.0234282i
$109$	−7.25346	−	6.53104i	−0.694755	−	0.625560i	0.244150	−	0.969738i	$-0.421491\pi$
$109$	−7.25346	−	6.53104i	−0.694755	−	0.625560i	−0.938905	+	0.344177i	$0.888158\pi$
$110$	−16.0670	−	5.96819i	−1.53193	−	0.569045i
$111$	0.424774	+	0.138017i	0.0403177	+	0.0131000i
$112$	9.96978	+	1.94111i	0.942056	+	0.183418i
$113$	−2.12247	+	4.16559i	−0.199666	+	0.391866i	−0.969030	−	0.246945i	$-0.920573\pi$
$113$	−2.12247	+	4.16559i	−0.199666	+	0.391866i	0.769364	+	0.638811i	$0.220573\pi$
$114$	−0.303041	+	0.272859i	−0.0283824	+	0.0255556i
$115$	6.88022	−	10.8508i	0.641584	−	1.01184i
$116$	2.71254	−	3.01258i	0.251853	−	0.279711i
$117$	5.76595	−	7.12036i	0.533062	−	0.658277i
$118$	−4.62236	+	4.62236i	−0.425523	+	0.425523i
$119$	−3.36015	−	8.32402i	−0.308024	−	0.763061i
$120$	−0.000207210	−	0.0190824i	−1.89156e−5	−	0.00174198i
$121$	3.11442	−	1.38663i	0.283129	−	0.126057i
$122$	22.2271	−	17.9991i	2.01234	−	1.62956i
$123$	0.372895	+	0.242161i	0.0336228	+	0.0218349i
$124$	−4.70003	+	8.14070i	−0.422075	+	0.731056i
$125$	0.364133	+	11.1744i	0.0325690	+	0.999469i
$126$	−3.87835	+	15.5349i	−0.345511	+	1.38396i
$127$	−5.56395	−	10.9199i	−0.493721	−	0.968982i	−0.994631	−	0.103483i	$-0.967001\pi$
$127$	−5.56395	−	10.9199i	−0.493721	−	0.968982i	0.500910	−	0.865499i	$-0.332999\pi$
$128$	−1.16801	−	0.448356i	−0.103238	−	0.0396295i
$129$	0.0410529	−	0.390592i	0.00361450	−	0.0343897i
$130$	7.03117	+	11.8786i	0.616674	+	1.04182i
$131$	−10.2399	+	1.07626i	−0.894665	+	0.0940331i	−0.540690	−	0.841222i	$-0.681837\pi$
$131$	−10.2399	+	1.07626i	−0.894665	+	0.0940331i	−0.353975	+	0.935255i	$0.615170\pi$
$132$	0.304081	+	0.304081i	0.0264669	+	0.0264669i
$133$	1.19108	+	9.72530i	0.103280	+	0.843290i
$134$	27.0756	−	8.79739i	2.33897	−	0.759979i
$135$	−0.730617	−	0.0303392i	−0.0628815	−	0.00261119i
$136$	0.110401	+	0.519397i	0.00946682	+	0.0445379i
$137$	0.974016	+	18.5853i	0.0832158	+	1.58785i	0.647366	+	0.762179i	$0.275871\pi$
$137$	0.974016	+	18.5853i	0.0832158	+	1.58785i	−0.564150	+	0.825672i	$0.690796\pi$
$138$	−0.530627	+	0.344593i	−0.0451700	+	0.0293337i
$139$	4.94661	−	15.2241i	0.419566	−	1.29129i	−0.488537	−	0.872543i	$-0.662469\pi$
$139$	4.94661	−	15.2241i	0.419566	−	1.29129i	0.908103	−	0.418747i	$-0.137531\pi$
$140$	−10.1418	−	6.94303i	−0.857135	−	0.586793i
$141$	−0.157357	−	0.484296i	−0.0132519	−	0.0407851i
$142$	3.41741	+	2.76737i	0.286783	+	0.232232i
$143$	−11.2091	−	3.00348i	−0.937354	−	0.251163i
$144$	−4.67972	+	10.5108i	−0.389977	+	0.875902i
$145$	3.96650	−	1.81786i	0.329400	−	0.150965i
$146$	2.60586	−	3.58666i	0.215663	−	0.296834i
$147$	−0.250252	−	0.288239i	−0.0206404	−	0.0237736i
$148$	−15.1611	+	7.72497i	−1.24624	+	0.634989i
$149$	−1.52167	−	0.878534i	−0.124660	−	0.0719723i	0.436373	−	0.899766i	$-0.356263\pi$
$149$	−1.52167	−	0.878534i	−0.124660	−	0.0719723i	−0.561033	+	0.827793i	$0.689596\pi$
$150$	0.212961	−	0.507712i	0.0173882	−	0.0414545i
$151$	0.749583	+	1.29832i	0.0610002	+	0.105655i	0.894913	−	0.446241i	$-0.147238\pi$
$151$	0.749583	+	1.29832i	0.0610002	+	0.105655i	−0.833913	+	0.551897i	$0.813904\pi$
$152$	0.0303332	−	0.578791i	0.00246034	−	0.0469462i
$153$	10.0433	−	1.59070i	0.811949	−	0.128600i
$154$	19.9729	−	3.51543i	1.60946	−	0.283281i
$155$	−8.12018	+	6.03545i	−0.652229	+	0.484779i
$156$	−0.0362017	−	0.344436i	−0.00289845	−	0.0275769i
$157$	1.02623	−	3.82995i	0.0819023	−	0.305664i	−0.912807	−	0.408391i	$-0.866090\pi$
$157$	1.02623	−	3.82995i	0.0819023	−	0.305664i	0.994710	+	0.102727i	$0.0327568\pi$
$158$	−4.74126	−	12.3514i	−0.377195	−	0.982626i
$159$	−0.355094	−	0.0754775i	−0.0281608	−	0.00598576i
$160$	−12.8896	−	12.6127i	−1.01901	−	0.997120i
$161$	−0.535219	+	15.1928i	−0.0421812	+	1.19736i
$162$	−16.1446	−	8.22609i	−1.26844	−	0.646303i
$163$	−5.90369	−	9.09088i	−0.462412	−	0.712053i	0.528144	−	0.849155i	$-0.322888\pi$
$163$	−5.90369	−	9.09088i	−0.462412	−	0.712053i	−0.990557	+	0.137102i	$0.956221\pi$
$164$	−16.5691	+	3.52186i	−1.29383	+	0.275011i
$165$	0.170555	+	0.430288i	0.0132777	+	0.0334979i
$166$	−2.90395	+	13.6620i	−0.225390	+	1.06038i
$167$	−12.4850	−	1.97743i	−0.966117	−	0.153018i	−0.346610	−	0.938009i	$-0.612667\pi$
$167$	−12.4850	−	1.97743i	−0.966117	−	0.153018i	−0.619507	+	0.784991i	$0.712667\pi$
$168$	0.0116236	+	0.0193584i	0.000896778	+	0.00149353i
$169$	−2.14788	−	2.95630i	−0.165221	−	0.227407i
$170$	−3.02222	+	15.0185i	−0.231794	+	1.15187i
$171$	−11.0380	−	1.16014i	−0.844100	−	0.0887185i
$172$	9.41629	+	11.6282i	0.717985	+	0.886638i
$173$	−13.3952	−	0.702015i	−1.01842	−	0.0533732i	−0.464190	−	0.885736i	$-0.653654\pi$
$173$	−13.3952	−	0.702015i	−1.01842	−	0.0533732i	−0.554231	+	0.832363i	$0.686988\pi$
$174$	−0.214864			−0.0162888
$175$	−7.05450	−	11.1908i	−0.533270	−	0.845945i
$176$	14.5725			1.09845
$177$	0.176291	+	0.00923900i	0.0132508	+	0.000694446i
$178$	−4.85586	−	5.99649i	−0.363962	−	0.449456i
$179$	−5.36488	−	0.563872i	−0.400990	−	0.0421457i	−0.0981127	−	0.995175i	$-0.531281\pi$
$179$	−5.36488	−	0.563872i	−0.400990	−	0.0421457i	−0.302877	+	0.953030i	$0.597947\pi$
$180$	10.2447	−	9.42778i	0.763594	−	0.702705i
$181$	−12.4457	−	17.1301i	−0.925085	−	1.27327i	−0.961746	−	0.273942i	$-0.911672\pi$
$181$	−12.4457	−	17.1301i	−0.925085	−	1.27327i	0.0366616	−	0.999328i	$-0.488328\pi$
$182$	−14.2824	−	7.92258i	−1.05868	−	0.587261i
$183$	−0.762861	−	0.120825i	−0.0563923	−	0.00893166i
$184$	0.186968	−	0.879615i	0.0137835	−	0.0648460i
$185$	−18.2778	+	1.15703i	−1.34381	+	0.0850667i
$186$	0.487342	−	0.103588i	0.0357336	−	0.00759542i
$187$	−7.01443	−	10.8013i	−0.512946	−	0.789867i
$188$	17.2856	+	8.80745i	1.26068	+	0.642349i
$189$	0.764072	−	0.405963i	0.0555780	−	0.0295295i
$190$	7.42908	−	14.9803i	0.538962	−	1.08679i
$191$	14.7908	+	3.14389i	1.07023	+	0.227484i	0.709154	−	0.705053i	$-0.249077\pi$
$191$	14.7908	+	3.14389i	1.07023	+	0.227484i	0.361074	+	0.932537i	$0.382410\pi$
$192$	0.168210	+	0.438203i	0.0121395	+	0.0316246i
$193$	3.46038	−	12.9143i	0.249084	−	0.929593i	−0.722203	−	0.691681i	$-0.756870\pi$
$193$	3.46038	−	12.9143i	0.249084	−	0.929593i	0.971287	−	0.237912i	$-0.0764629\pi$
$194$	0.910515	+	8.66297i	0.0653712	+	0.621965i
$195$	0.111335	−	0.355752i	0.00797286	−	0.0254759i
$196$	14.5065	+	1.02335i	1.03618	+	0.0730967i
$197$	−9.33538	+	1.47858i	−0.665118	+	0.105344i	−0.479859	−	0.877345i	$-0.659312\pi$
$197$	−9.33538	+	1.47858i	−0.665118	+	0.105344i	−0.185259	+	0.982690i	$0.559312\pi$
$198$	−1.20228	+	22.9410i	−0.0854426	+	1.63034i
$199$	6.97072	+	12.0736i	0.494141	+	0.855878i	0.999977	−	0.00675174i	$-0.00214916\pi$
$199$	6.97072	+	12.0736i	0.494141	+	0.855878i	−0.505836	+	0.862630i	$0.668816\pi$
$200$	0.296231	+	0.724292i	0.0209467	+	0.0512152i
$201$	−0.665806	−	0.384403i	−0.0469624	−	0.0271137i
$202$	−12.5683	+	6.40388i	−0.884304	+	0.450575i
$203$	−2.96247	+	4.22808i	−0.207925	+	0.296753i
$204$	0.225927	−	0.310962i	0.0158181	−	0.0217717i
$205$	−17.8738	−	3.59680i	−1.24836	−	0.251212i
$206$	−7.92165	+	17.7923i	−0.551928	+	1.23965i
$207$	−16.6338	−	4.45702i	−1.15613	−	0.309784i
$208$	−9.12068	−	7.38578i	−0.632405	−	0.512112i
$209$	4.34399	+	13.3694i	0.300480	+	0.924782i
$210$	0.0862081	+	0.645711i	0.00594892	+	0.0445583i
$211$	−1.35065	+	4.15686i	−0.0929824	+	0.286170i	−0.986723	−	0.162415i	$-0.948072\pi$
$211$	−1.35065	+	4.15686i	−0.0929824	+	0.286170i	0.893740	+	0.448585i	$0.148072\pi$
$212$	11.5992	−	7.53263i	0.796638	−	0.517343i
$213$	−0.00621500	−	0.118589i	−0.000425845	−	0.00812560i
$214$	1.39182	+	6.54802i	0.0951432	+	0.447613i
$215$	4.33685	+	15.5097i	0.295770	+	1.05775i
$216$	−0.0486761	+	0.0158158i	−0.00331199	+	0.00107613i
$217$	4.68091	−	11.0181i	0.317761	−	0.747958i
$218$	−13.9365	−	13.9365i	−0.943899	−	0.943899i
$219$	−0.119067	+	0.0125145i	−0.00804583	+	0.000845651i
$220$	−16.1862	−	6.99698i	−1.09128	−	0.471737i
$221$	−1.08420	+	10.3154i	−0.0729309	+	0.693891i
$222$	0.841977	+	0.323205i	0.0565098	+	0.0216921i
$223$	−2.56478	−	5.03366i	−0.171750	−	0.337079i	0.789046	−	0.614334i	$-0.210575\pi$
$223$	−2.56478	−	5.03366i	−0.171750	−	0.337079i	−0.960796	+	0.277255i	$0.910575\pi$
$224$	20.7026	+	5.16849i	1.38325	+	0.345334i
$225$	14.1478	−	4.93904i	0.943186	−	0.329269i
$226$	−4.72023	+	8.17568i	−0.313985	+	0.543838i
$227$	13.8633	+	9.00292i	0.920139	+	0.597545i	0.915445	−	0.402444i	$-0.131839\pi$
$227$	13.8633	+	9.00292i	0.920139	+	0.597545i	0.00469399	+	0.999989i	$0.498506\pi$
$228$	−0.326043	+	0.264024i	−0.0215927	+	0.0174854i
$229$	25.5136	−	11.3594i	1.68599	−	0.750650i	0.686259	−	0.727357i	$-0.259252\pi$
$229$	25.5136	−	11.3594i	1.68599	−	0.750650i	0.999729	−	0.0232932i	$-0.00741512\pi$
$230$	15.0208	−	21.1536i	0.990442	−	1.39483i
$231$	−0.431459	−	0.337306i	−0.0283879	−	0.0221931i
$232$	0.215943	−	0.215943i	0.0141773	−	0.0141773i
$233$	10.1385	−	12.5200i	0.664194	−	0.820211i	−0.328031	−	0.944667i	$-0.606385\pi$
$233$	10.1385	−	12.5200i	0.664194	−	0.820211i	0.992225	+	0.124456i	$0.0397185\pi$
$234$	12.3796	−	13.7490i	0.809281	−	0.898798i
$235$	13.3161	+	16.0838i	0.868647	+	1.04919i
$236$	−4.99801	+	4.50023i	−0.325343	+	0.292940i
$237$	−0.162203	+	0.318340i	−0.0105362	+	0.0206784i
$238$	−5.89610	−	17.1406i	−0.382187	−	1.11106i
$239$	−14.3559	−	4.66452i	−0.928606	−	0.301722i	−0.194614	−	0.980880i	$-0.562345\pi$
$239$	−14.3559	−	4.66452i	−0.928606	−	0.301722i	−0.733993	+	0.679157i	$0.762345\pi$
$240$	−0.0194216	+	0.467703i	−0.00125366	+	0.0301901i
$241$	18.5815	+	16.7308i	1.19694	+	1.07773i	0.995157	+	0.0982968i	$0.0313394\pi$
$241$	18.5815	+	16.7308i	1.19694	+	1.07773i	0.201781	+	0.979431i	$0.435327\pi$
$242$	6.42681	−	2.46702i	0.413131	−	0.158586i
$243$	0.380565	+	1.42029i	0.0244133	+	0.0911115i
$244$	23.8058	−	17.2959i	1.52401	−	1.10726i
$245$	13.8949	+	7.20644i	0.887710	+	0.460403i
$246$	0.726356	+	0.527729i	0.0463108	+	0.0336467i
$247$	4.05718	−	10.5693i	0.258152	−	0.672510i
$248$	−0.385681	+	0.593896i	−0.0244908	+	0.0377125i
$249$	0.326653	−	0.188593i	0.0207008	−	0.0119516i
$250$	−0.446645	+	22.5719i	−0.0282483	+	1.42757i
$251$			12.4908i			0.788410i	0.919023	+	0.394205i	$0.128980\pi$
$251$			12.4908i			0.788410i	−0.919023	+	0.394205i	$0.871020\pi$
$252$	−4.82118	+	15.7521i	−0.303706	+	0.992286i
$253$	3.41200	+	21.5425i	0.214511	+	1.35437i
$254$	−10.0658	−	22.6081i	−0.631583	−	1.41856i
$255$	0.356013	−	0.210731i	0.0222944	−	0.0131965i
$256$	13.4189	+	5.97447i	0.838680	+	0.373404i
$257$	5.56457	−	1.49102i	0.347109	−	0.0930075i	−0.0810527	−	0.996710i	$-0.525828\pi$
$257$	5.56457	−	1.49102i	0.347109	−	0.0930075i	0.428161	+	0.903702i	$0.359162\pi$
$258$	0.124062	−	0.783297i	0.00772376	−	0.0487659i
$259$	17.9689	−	12.1121i	1.11653	−	0.752612i
$260$	6.58438	+	12.5829i	0.408346	+	0.780360i
$261$	−3.91313	−	4.34597i	−0.242217	−	0.269009i
$262$	−20.7627	+	1.08813i	−1.28272	+	0.0672247i
$263$	−6.45881	+	0.338492i	−0.398267	+	0.0208723i	−0.250418	−	0.968138i	$-0.580568\pi$
$263$	−6.45881	+	0.338492i	−0.398267	+	0.0208723i	−0.147849	+	0.989010i	$0.547235\pi$
$264$	0.0216772	+	0.0240750i	0.00133414	+	0.00148171i
$265$	14.6767	−	2.48820i	0.901580	−	0.152849i
$266$	1.37406	+	19.7371i	0.0842488	+	1.21016i
$267$	−0.0325966	+	0.205807i	−0.00199488	+	0.0125952i
$268$	28.2918	−	7.58076i	1.72819	−	0.463068i
$269$	−13.9620	−	6.21630i	−0.851281	−	0.379015i	−0.0657492	−	0.997836i	$-0.520944\pi$
$269$	−13.9620	−	6.21630i	−0.851281	−	0.379015i	−0.785532	+	0.618822i	$0.787610\pi$
$270$	−1.47010	−	0.138392i	−0.0894672	−	0.00842227i
$271$	−1.83475	−	4.12091i	−0.111453	−	0.250327i	0.849204	−	0.528065i	$-0.177082\pi$
$271$	−1.83475	−	4.12091i	−0.111453	−	0.250327i	−0.960657	+	0.277737i	$0.910415\pi$
$272$	−2.03757	−	12.8647i	−0.123546	−	0.780038i
$273$	0.0990855	+	0.429789i	0.00599693	+	0.0260120i
$274$			37.5806i			2.27032i
$275$	−13.0032	−	13.8256i	−0.784121	−	0.833713i
$276$	−0.563733	+	0.325471i	−0.0339327	+	0.0195911i
$277$	−3.08529	+	4.75093i	−0.185377	+	0.285456i	−0.919125	−	0.393966i	$-0.871103\pi$
$277$	−3.08529	+	4.75093i	−0.185377	+	0.285456i	0.733748	+	0.679422i	$0.237769\pi$
$278$	11.5838	−	30.1769i	0.694751	−	1.80989i
$279$	10.9708	+	7.97073i	0.656803	+	0.477195i
$280$	−0.735594	−	0.562312i	−0.0439601	−	0.0336046i
$281$	8.30707	−	6.03544i	0.495558	−	0.360044i	−0.311760	−	0.950161i	$-0.600918\pi$
$281$	8.30707	−	6.03544i	0.495558	−	0.360044i	0.807318	+	0.590117i	$0.200918\pi$
$282$	−0.266133	−	0.993220i	−0.0158480	−	0.0591454i
$283$	−26.4125	+	10.1388i	−1.57006	+	0.602689i	−0.978986	−	0.203929i	$-0.934629\pi$
$283$	−26.4125	+	10.1388i	−1.57006	+	0.602689i	−0.591073	+	0.806618i	$0.701296\pi$
$284$	3.36212	+	3.02727i	0.199505	+	0.179635i
$285$	−0.434878	+	0.121601i	−0.0257600	+	0.00720304i
$286$	−22.2860	−	7.24115i	−1.31780	−	0.428178i
$287$	20.3994	−	7.01705i	1.20414	−	0.414203i
$288$	−10.9734	+	21.5365i	−0.646615	+	1.26905i
$289$	4.07882	−	3.67258i	0.239931	−	0.216034i
$290$	8.19063	−	3.24656i	0.480970	−	0.190645i
$291$	0.157402	−	0.174812i	0.00922705	−	0.0102477i
$292$	2.87045	−	3.54470i	0.167980	−	0.207438i
$293$	−13.4826	+	13.4826i	−0.787661	+	0.787661i	−0.981110	−	0.193449i	$-0.938032\pi$
$293$	−13.4826	+	13.4826i	−0.787661	+	0.787661i	0.193449	+	0.981110i	$0.438032\pi$
$294$	−0.474175	−	0.607686i	−0.0276544	−	0.0354410i
$295$	−6.85981	+	2.31153i	−0.399394	+	0.134583i
$296$	−1.17103	+	0.521377i	−0.0680648	+	0.0303044i
$297$	0.964719	−	0.781214i	0.0559787	−	0.0453307i
$298$	−2.97562	−	1.93239i	−0.172373	−	0.111940i
$299$	8.78286	−	15.2124i	0.507926	−	0.879754i
$300$	0.246139	−	0.510169i	0.0142108	−	0.0294546i
$301$	−13.7031	−	13.2411i	−0.789836	−	0.763205i
$302$	1.37434	+	2.69729i	0.0790843	+	0.155212i
$303$	0.355626	+	0.136512i	0.0204302	+	0.00784242i
$304$	−1.48606	+	14.1390i	−0.0852316	+	0.810925i
$305$	30.9060	−	6.92084i	1.76967	−	0.396286i
$306$	20.4205	−	2.14628i	1.16736	−	0.122695i
$307$	13.9902	+	13.9902i	0.798461	+	0.798461i	0.982853	−	0.184392i	$-0.0590316\pi$
$307$	13.9902	+	13.9902i	0.798461	+	0.798461i	−0.184392	+	0.982853i	$0.559032\pi$
$308$	20.7099	−	2.53639i	1.18005	−	0.144524i
$309$	0.500213	−	0.162529i	0.0284561	−	0.00924595i
$310$	−17.0123	+	11.3124i	−0.966235	+	0.642503i
$311$	0.0370841	+	0.174467i	0.00210285	+	0.00989311i	0.979187	−	0.202962i	$-0.0650569\pi$
$311$	0.0370841	+	0.174467i	0.00210285	+	0.00989311i	−0.977084	+	0.212856i	$0.931724\pi$
$312$	−0.00136547	−	0.0260547i	−7.73046e−5	−	0.00147506i
$313$	11.5257	−	7.48485i	0.651469	−	0.423069i	−0.176147	−	0.984364i	$-0.556363\pi$
$313$	11.5257	−	7.48485i	0.651469	−	0.423069i	0.827616	+	0.561295i	$0.189697\pi$
$314$	2.47417	−	7.61471i	0.139625	−	0.429723i
$315$	−11.4905	+	13.5035i	−0.647417	+	0.760835i
$316$	−4.20622	−	12.9454i	−0.236619	−	0.728237i
$317$	−9.48600	−	7.68161i	−0.532787	−	0.431442i	0.324799	−	0.945783i	$-0.394703\pi$
$317$	−9.48600	−	7.68161i	−0.532787	−	0.431442i	−0.857586	+	0.514341i	$0.828037\pi$
$318$	−0.708076	−	0.189728i	−0.0397069	−	0.0106394i
$319$	−3.01270	+	6.76663i	−0.168679	+	0.378859i
$320$	−13.0334	−	14.1627i	−0.728588	−	0.791719i
$321$	0.106260	−	0.146254i	0.00593086	−	0.00816313i
$322$	−2.68487	+	30.5799i	−0.149622	+	1.70415i
$323$	11.1952	−	5.70424i	0.622918	−	0.317392i
$324$	−16.1444	−	9.32098i	−0.896912	−	0.517832i
$325$	1.13126	+	15.2435i	0.0627508	+	0.845560i
$326$	−10.9441	−	18.9558i	−0.606140	−	1.04987i
$327$	−0.0278557	+	0.531519i	−0.00154043	+	0.0293931i
$328$	−1.26038	+	0.199625i	−0.0695929	+	0.0110224i
$329$	−23.2139	−	8.45724i	−1.27982	−	0.466263i
$330$	0.298455	+	0.885708i	0.0164294	+	0.0487566i
$331$	−0.898409	−	8.54779i	−0.0493810	−	0.469829i	−0.991070	−	0.133344i	$-0.957429\pi$
$331$	−0.898409	−	8.54779i	−0.0493810	−	0.469829i	0.941689	−	0.336485i	$-0.109238\pi$
$332$	−3.71922	+	13.8803i	−0.204119	+	0.761781i
$333$	8.79686	+	22.9166i	0.482065	+	1.25582i
$334$	−24.9672	−	5.30694i	−1.36614	−	0.290383i
$335$	31.1889	+	4.59326i	1.70403	+	0.250957i
$336$	−0.259876	−	0.489119i	−0.0141774	−	0.0266836i
$337$	−6.18213	−	3.14995i	−0.336762	−	0.171589i	0.277429	−	0.960746i	$-0.410518\pi$
$337$	−6.18213	−	3.14995i	−0.336762	−	0.171589i	−0.614191	+	0.789157i	$0.710518\pi$
$338$	−4.01880	−	6.18841i	−0.218594	−	0.336605i
$339$	0.249370	−	0.0530051i	0.0135439	−	0.00287884i
$340$	−3.91377	+	15.2676i	−0.212254	+	0.828003i
$341$	3.57098	−	16.8001i	0.193379	−	0.909777i
$342$	−22.1358	−	3.50596i	−1.19697	−	0.189581i
$343$	−18.4958	+	0.952220i	−0.998677	+	0.0514151i
$344$	0.662544	+	0.911914i	0.0357220	+	0.0491671i
$345$	−0.695951	+	0.0807967i	−0.0374687	+	0.00434995i
$346$	−26.9375	−	2.83125i	−1.44817	−	0.152209i
$347$	−9.61213	−	11.8700i	−0.516006	−	0.637214i	0.450831	−	0.892609i	$-0.351128\pi$
$347$	−9.61213	−	11.8700i	−0.516006	−	0.637214i	−0.966837	+	0.255395i	$0.917794\pi$
$348$	−0.220756	−	0.0115693i	−0.0118338	−	0.000620182i
$349$	−27.7967			−1.48792			−0.743961	−	0.668224i	$-0.767055\pi$
$349$	−27.7967			−1.48792			−0.743961	+	0.668224i	$0.767055\pi$
$350$	−13.0429	−	23.3120i	−0.697170	−	1.24608i
$351$	−0.999742			−0.0533623
$352$	30.5723	+	1.60223i	1.62951	+	0.0853990i
$353$	7.82342	+	9.66111i	0.416398	+	0.514209i	0.941584	−	0.336779i	$-0.109337\pi$
$353$	7.82342	+	9.66111i	0.416398	+	0.514209i	−0.525185	+	0.850988i	$0.676004\pi$
$354$	0.354516	+	0.0372612i	0.0188423	+	0.00198041i
$355$	2.02878	+	4.42673i	0.107677	+	0.234946i
$356$	−4.66614	−	6.42239i	−0.247305	−	0.340386i
$357$	−0.237448	+	0.428057i	−0.0125671	+	0.0226552i
$358$	−10.7588	−	1.70402i	−0.568619	−	0.0900604i
$359$	−7.67344	+	36.1007i	−0.404989	+	1.90532i	0.0193382	+	0.999813i	$0.493844\pi$
$359$	−7.67344	+	36.1007i	−0.404989	+	1.90532i	−0.424327	+	0.905509i	$0.639489\pi$
$360$	0.807881	−	0.668863i	0.0425791	−	0.0352522i
$361$	5.17019	−	1.09896i	0.272115	−	0.0578399i
$362$	−23.2867	−	35.8584i	−1.22392	−	1.88467i
$363$	−0.165642	−	0.0843988i	−0.00869395	−	0.00442979i
$364$	−14.2474	−	8.90888i	−0.746769	−	0.466952i
$365$	4.34977	−	2.27614i	0.227677	−	0.119139i
$366$	−1.52555	−	0.324266i	−0.0797419	−	0.0169497i
$367$	5.19257	+	13.5271i	0.271050	+	0.706109i	0.999773	+	0.0213007i	$0.00678074\pi$
$367$	5.19257	+	13.5271i	0.271050	+	0.706109i	−0.728723	+	0.684808i	$0.759886\pi$
$368$	−5.70913	+	21.3068i	−0.297609	+	1.11069i
$369$	2.55433	+	24.3028i	0.132973	+	1.26515i
$370$	−36.9798	+	0.401552i	−1.92249	+	0.0208757i
$371$	−13.4962	+	11.3176i	−0.700686	+	0.587578i
$372$	0.506284	−	0.0801875i	0.0262496	−	0.00415753i
$373$	1.38894	−	26.5025i	0.0719163	−	1.37225i	−0.689643	−	0.724150i	$-0.742232\pi$
$373$	1.38894	−	26.5025i	0.0719163	−	1.37225i	0.761559	−	0.648096i	$-0.224434\pi$
$374$	−13.0032	−	22.5222i	−0.672380	−	1.16460i
$375$	0.461059	−	0.398909i	0.0238090	−	0.0205996i
$376$	1.26568	+	0.730738i	0.0652722	+	0.0376849i
$377$	5.31511	−	2.70819i	0.273742	−	0.139479i
$378$	1.58367	−	0.737883i	0.0814550	−	0.0379526i
$379$	−0.369609	+	0.508723i	−0.0189855	+	0.0261314i	−0.818404	−	0.574643i	$-0.805141\pi$
$379$	−0.369609	+	0.508723i	−0.0189855	+	0.0261314i	0.799419	+	0.600774i	$0.205141\pi$
$380$	8.43942	−	14.9911i	0.432933	−	0.769027i
$381$	−0.271827	+	0.610534i	−0.0139261	+	0.0312786i
$382$	29.4937	+	7.90282i	1.50903	+	0.404344i
$383$	9.13082	+	7.39400i	0.466563	+	0.377816i	0.833580	−	0.552399i	$-0.186287\pi$
$383$	9.13082	+	7.39400i	0.466563	+	0.377816i	−0.367017	+	0.930214i	$0.619621\pi$
$384$	0.0210824	+	0.0648849i	0.00107586	+	0.00331114i
$385$	21.5439	+	6.33886i	1.09798	+	0.323058i
$386$	8.34271	−	25.6762i	0.424633	−	1.30689i
$387$	18.1029	−	11.7562i	0.920221	−	0.597599i
$388$	0.469027	+	8.94957i	0.0238112	+	0.454345i
$389$	−1.05506	−	4.96367i	−0.0534937	−	0.251668i	0.943273	−	0.332018i	$-0.107730\pi$
$389$	−1.05506	−	4.96367i	−0.0534937	−	0.251668i	−0.996767	+	0.0803501i	$0.974396\pi$
$390$	0.262105	−	0.705613i	0.0132722	−	0.0357301i
$391$	18.5408	−	6.02427i	0.937648	−	0.304660i
$392$	1.08729	+	0.134181i	0.0549166	+	0.00677718i
$393$	0.397018	+	0.397018i	0.0200269	+	0.0200269i
$394$	−18.9812	+	1.99500i	−0.956259	+	0.100507i
$395$	1.37310	−	14.5860i	0.0690882	−	0.733902i
$396$	−2.47051	+	23.5053i	−0.124148	+	1.18119i
$397$	27.8532	+	10.6918i	1.39791	+	0.536608i	0.936528	−	0.350593i	$-0.114020\pi$
$397$	27.8532	+	10.6918i	1.39791	+	0.536608i	0.461383	+	0.887201i	$0.347353\pi$
$398$	12.7806	+	25.0834i	0.640634	+	1.25732i
$399$	0.371269	−	0.384224i	0.0185867	−	0.0192352i
$400$	−6.32657	−	18.1223i	−0.316328	−	0.906117i
$401$	8.26123	−	14.3089i	0.412546	−	0.714551i	−0.582621	−	0.812744i	$-0.697973\pi$
$401$	8.26123	−	14.3089i	0.412546	−	0.714551i	0.995167	+	0.0981931i	$0.0313063\pi$
$402$	−1.30198	−	0.845519i	−0.0649371	−	0.0421707i
$403$	−10.7498	+	8.70501i	−0.535485	+	0.433627i
$404$	−13.2578	+	5.90275i	−0.659600	+	0.293673i
$405$	−11.9693	−	16.1037i	−0.594762	−	0.800201i
$406$	−6.42070	+	8.21291i	−0.318654	+	0.407600i
$407$	21.9843	−	21.9843i	1.08972	−	1.08972i
$408$	0.0182226	−	0.0225030i	0.000902152	−	0.00111406i
$409$	−12.9141	+	14.3426i	−0.638562	+	0.709195i	−0.972370	−	0.233447i	$-0.925000\pi$
$409$	−12.9141	+	14.3426i	−0.638562	+	0.709195i	0.333808	+	0.942641i	$0.391666\pi$
$410$	−35.6627	−	9.14193i	−1.76125	−	0.451488i
$411$	0.754193	−	0.679078i	0.0372016	−	0.0334965i
$412$	−9.09692	+	17.8537i	−0.448173	+	0.879589i
$413$	5.62117	−	6.46241i	0.276600	−	0.317994i
$414$	−33.0713	−	10.7455i	−1.62537	−	0.528114i
$415$	−9.60244	+	12.1249i	−0.471365	+	0.595187i
$416$	−18.3226	−	16.4977i	−0.898338	−	0.808868i
$417$	−0.814929	+	0.312822i	−0.0399073	+	0.0153190i
$418$	7.34682	+	27.4187i	0.359345	+	1.34109i
$419$	19.1402	−	13.9062i	0.935062	−	0.679362i	−0.0121653	−	0.999926i	$-0.503872\pi$
$419$	19.1402	−	13.9062i	0.935062	−	0.679362i	0.947227	+	0.320564i	$0.103872\pi$
$420$	0.0538039	+	0.668060i	0.00262536	+	0.0325980i
$421$	−0.268667	−	0.195198i	−0.0130940	−	0.00951338i	0.581219	−	0.813747i	$-0.302576\pi$
$421$	−0.268667	−	0.195198i	−0.0130940	−	0.00951338i	−0.594313	+	0.804234i	$0.702576\pi$
$422$	−3.16290	+	8.23965i	−0.153968	+	0.401100i
$423$	15.2427	−	23.4716i	0.741123	−	1.14123i
$424$	0.902312	−	0.520950i	0.0438201	−	0.0252996i
$425$	−10.3871	+	13.4124i	−0.503850	+	0.650597i
$426$		−	0.239794i		−	0.0116181i
$427$	−27.4147	+	25.5489i	−1.32669	+	1.23640i
$428$	1.07742	+	6.80253i	0.0520788	+	0.328813i
$429$	0.257386	+	0.578098i	0.0124267	+	0.0279108i
$430$	7.10624	+	31.7339i	0.342693	+	1.53034i
$431$	31.2347	+	13.9066i	1.50452	+	0.669856i	0.983038	−	0.183405i	$-0.0587118\pi$
$431$	31.2347	+	13.9066i	1.50452	+	0.669856i	0.521484	+	0.853261i	$0.325378\pi$
$432$	1.21266	−	0.324931i	0.0583441	−	0.0156333i
$433$	0.570691	−	3.60320i	0.0274256	−	0.173159i	−0.970173	−	0.242412i	$-0.922062\pi$
$433$	0.570691	−	3.60320i	0.0274256	−	0.173159i	0.997599	+	0.0692529i	$0.0220616\pi$
$434$	10.6035	−	21.7235i	0.508986	−	1.04276i
$435$	−0.213159	−	0.105710i	−0.0102202	−	0.00506842i
$436$	−13.5683	−	15.0691i	−0.649802	−	0.721679i
$437$	−21.2495	+	1.11364i	−1.01650	+	0.0532726i
$438$	−0.241424	+	0.0126525i	−0.0115357	+	0.000604559i
$439$	20.5471	+	22.8199i	0.980659	+	1.08913i	0.996009	+	0.0892501i	$0.0284470\pi$
$439$	20.5471	+	22.8199i	0.980659	+	1.08913i	−0.0153501	+	0.999882i	$0.504886\pi$
$440$	−1.19011	−	0.590202i	−0.0567362	−	0.0281368i
$441$	3.65570	−	20.6582i	0.174081	−	0.983725i
$442$	−3.27644	+	20.6866i	−0.155844	+	0.983963i
$443$	6.25039	−	1.67479i	0.296965	−	0.0795715i	−0.107260	−	0.994231i	$-0.534208\pi$
$443$	6.25039	−	1.67479i	0.296965	−	0.0795715i	0.404225	+	0.914659i	$0.367541\pi$
$444$	0.847664	+	0.377404i	0.0402283	+	0.0179108i
$445$	−1.86713	−	8.33791i	−0.0885102	−	0.395255i
$446$	−4.63996	−	10.4215i	−0.219708	−	0.493473i
$447$	0.0149887	+	0.0946350i	0.000708941	+	0.00447608i
$448$	21.7763	+	6.66501i	1.02884	+	0.314892i
$449$			33.2556i			1.56943i	0.619856	+	0.784715i	$0.287191\pi$
$449$			33.2556i			1.56943i	−0.619856	+	0.784715i	$0.712809\pi$
$450$	29.0512	−	8.46450i	1.36949	−	0.399020i
$451$	26.8041	−	15.4754i	1.26216	−	0.728706i
$452$	−5.28989	+	8.14572i	−0.248816	+	0.383142i
$453$	0.0292969	−	0.0763211i	0.00137649	−	0.00358588i
$454$	27.0041	+	19.6196i	1.26737	+	0.920795i
$455$	−10.2712	−	14.8864i	−0.481521	−	0.697887i
$456$	−0.0255693	+	0.0185772i	−0.00119739	+	0.000869955i
$457$	7.18403	+	26.8112i	0.336055	+	1.25417i	0.902721	+	0.430226i	$0.141566\pi$
$457$	7.18403	+	26.8112i	0.336055	+	1.25417i	−0.566666	+	0.823947i	$0.691767\pi$
$458$	52.6491	−	20.2101i	2.46013	−	0.944356i
$459$	−0.824550	−	0.742428i	−0.0384867	−	0.0346536i
$460$	16.5717	−	20.9249i	0.772661	−	0.975630i
$461$	5.61141	+	1.82326i	0.261350	+	0.0849176i	0.436761	−	0.899578i	$-0.356126\pi$
$461$	5.61141	+	1.82326i	0.261350	+	0.0849176i	−0.175411	+	0.984495i	$0.556126\pi$
$462$	−0.834397	−	0.725780i	−0.0388196	−	0.0337664i
$463$	10.0954	−	19.8133i	0.469173	−	0.920804i	−0.528252	−	0.849088i	$-0.677152\pi$
$463$	10.0954	−	19.8133i	0.469173	−	0.920804i	0.997425	−	0.0717166i	$-0.0228477\pi$
$464$	−5.56689	+	5.01245i	−0.258436	+	0.232697i
$465$	0.534437	+	0.137000i	0.0247839	+	0.00635323i
$466$	21.7675	−	24.1753i	1.00836	−	1.11990i
$467$	−8.27546	+	10.2193i	−0.382943	+	0.472895i	−0.931774	−	0.363038i	$-0.881739\pi$
$467$	−8.27546	+	10.2193i	−0.382943	+	0.472895i	0.548832	+	0.835933i	$0.315073\pi$
$468$	13.4594	−	13.4594i	0.622162	−	0.622162i
$469$	−34.5894	+	13.9627i	−1.59719	+	0.644735i
$470$	25.1524	+	33.8404i	1.16019	+	1.56094i
$471$	−0.197526	+	0.0879440i	−0.00910150	+	0.00405225i
$472$	−0.393745	+	0.318848i	−0.0181236	+	0.0146762i
$473$	−22.9285	−	14.8900i	−1.05426	−	0.684642i
$474$	−0.360727	+	0.624797i	−0.0165687	+	0.0286979i
$475$	14.7402	−	11.2064i	0.676328	−	0.514185i
$476$	−5.13485	−	17.9281i	−0.235355	−	0.821735i
$477$	−9.05801	−	17.7773i	−0.414738	−	0.813969i
$478$	−28.4560	−	10.9232i	−1.30155	−	0.499616i
$479$	1.10249	−	10.4895i	0.0503742	−	0.479279i	−0.940031	−	0.341088i	$-0.889205\pi$
$479$	1.10249	−	10.4895i	0.0503742	−	0.479279i	0.990406	−	0.138191i	$-0.0441287\pi$
$480$	−0.0921685	+	0.979077i	−0.00420690	+	0.0446886i
$481$	−24.9018	+	2.61729i	−1.13543	+	0.119338i
$482$	35.7017	+	35.7017i	1.62617	+	1.62617i
$483$	0.662215	−	0.498696i	0.0301318	−	0.0226914i
$484$	6.73589	−	2.18862i	0.306177	−	0.0994829i
$485$	−3.35878	+	9.04218i	−0.152514	+	0.410584i
$486$	0.617318	+	2.90425i	0.0280021	+	0.131740i
$487$	−1.93592	−	36.9395i	−0.0877247	−	1.67389i	−0.588643	−	0.808393i	$-0.700338\pi$
$487$	−1.93592	−	36.9395i	−0.0877247	−	1.67389i	0.500918	−	0.865495i	$-0.332996\pi$
$488$	1.85911	−	1.20732i	0.0841578	−	0.0546527i
$489$	−0.182659	+	0.562165i	−0.00826011	+	0.0254220i
$490$	27.2576	+	16.0003i	1.23137	+	0.722821i
$491$	−8.54554	−	26.3005i	−0.385655	−	1.18692i	−0.936004	−	0.351989i	$-0.885506\pi$
$491$	−8.54554	−	26.3005i	−0.385655	−	1.18692i	0.550350	−	0.834934i	$-0.314494\pi$
$492$	0.717859	+	0.581311i	0.0323636	+	0.0262075i
$493$	6.39486	+	1.71350i	0.288010	+	0.0771720i
$494$	9.29835	−	20.8844i	0.418353	−	0.939636i
$495$	−12.4794	+	22.1674i	−0.560907	+	0.996349i
$496$	10.2099	−	14.0528i	0.458440	−	0.630989i
$497$	−4.71865	−	3.30620i	−0.211660	−	0.148303i
$498$	0.678633	−	0.345781i	0.0304103	−	0.0154948i
$499$	29.8613	+	17.2404i	1.33678	+	0.771788i	0.986328	−	0.164794i	$-0.0526959\pi$
$499$	29.8613	+	17.2404i	1.33678	+	0.771788i	0.350448	+	0.936582i	$0.386029\pi$
$500$	−1.67427	+	23.1668i	−0.0748758	+	1.03605i
$501$	0.344652	+	0.596956i	0.0153979	+	0.0266700i
$502$	−1.32004	+	25.1878i	−0.0589162	+	1.12419i
$503$	−4.83025	+	0.765036i	−0.215370	+	0.0341113i	−0.263187	−	0.964745i	$-0.584774\pi$
$503$	−4.83025	+	0.765036i	−0.215370	+	0.0341113i	0.0478169	+	0.998856i	$0.484774\pi$
$504$	−0.424804	+	1.16602i	−0.0189223	+	0.0519388i
$505$	−15.6192	+	0.169604i	−0.695045	+	0.00754727i
$506$	4.60372	+	43.8014i	0.204660	+	1.94721i
$507$	−0.0515739	+	0.192476i	−0.00229048	+	0.00854817i
$508$	−9.12448	−	23.7701i	−0.404833	−	1.05463i
$509$	−28.7283	−	6.10639i	−1.27336	−	0.270661i	−0.478841	−	0.877902i	$-0.658943\pi$
$509$	−28.7283	−	6.10639i	−1.27336	−	0.270661i	−0.794518	+	0.607241i	$0.792276\pi$
$510$	0.740177	−	0.387319i	0.0327756	−	0.0171508i
$511$	−3.07969	+	4.92517i	−0.136238	+	0.217877i
$512$	28.6575	+	14.6017i	1.26649	+	0.645311i
$513$	0.659591	+	1.01568i	0.0291217	+	0.0448434i
$514$	11.3786	−	2.41860i	0.501890	−	0.106680i
$515$	−16.6124	+	13.7538i	−0.732028	+	0.606063i
$516$	0.169641	−	0.798097i	0.00746802	−	0.0351343i
$517$	−35.0107	−	5.54515i	−1.53977	−	0.243875i
$518$	37.5146	−	22.5253i	1.64830	−	0.989707i
$519$	0.429940	+	0.591762i	0.0188723	+	0.0259755i
$520$	0.445735	+	0.972577i	0.0195468	+	0.0426503i
$521$	40.8957	+	4.29831i	1.79167	+	0.188312i	0.941232	−	0.337759i	$-0.109669\pi$
$521$	40.8957	+	4.29831i	1.79167	+	0.188312i	0.850440	+	0.526072i	$0.176336\pi$
$522$	−7.43161	−	9.17727i	−0.325273	−	0.401678i
$523$	−16.5929	−	0.869599i	−0.725558	−	0.0380249i	−0.314019	−	0.949417i	$-0.601675\pi$
$523$	−16.5929	−	0.869599i	−0.725558	−	0.0380249i	−0.411539	+	0.911392i	$0.635009\pi$
$524$	−21.3907			−0.934455
$525$	−0.232157	+	0.682999i	−0.0101322	+	0.0298085i
$526$	−13.0601			−0.569446
$527$	−15.3305	−	0.803439i	−0.667809	−	0.0349984i
$528$	−0.500092	−	0.617563i	−0.0217637	−	0.0268760i
$529$	−9.96042	−	1.04688i	−0.433062	−	0.0455166i
$530$	29.8587	−	3.46646i	1.29698	−	0.150573i
$531$	5.70284	+	7.84928i	0.247482	+	0.340630i
$532$	0.348994	+	20.3523i	0.0151308	+	0.882386i
$533$	−24.6195	−	3.89935i	−1.06639	−	0.168900i
$534$	−0.0874815	+	0.411568i	−0.00378570	+	0.0178103i
$535$	−1.84076	+	7.18081i	−0.0795831	+	0.310453i
$536$	2.15829	−	0.458758i	0.0932238	−	0.0198153i
$537$	0.160213	+	0.246706i	0.00691370	+	0.0106462i
$538$	−27.4977	−	14.0108i	−1.18551	−	0.604048i
$539$	−25.7862	+	6.41239i	−1.11069	+	0.276201i
$540$	−1.50296	−	0.221344i	−0.0646770	−	0.00952515i
$541$	−6.53994	−	1.39011i	−0.281174	−	0.0597654i	0.0651659	−	0.997874i	$-0.479242\pi$
$541$	−6.53994	−	1.39011i	−0.281174	−	0.0597654i	−0.346340	+	0.938109i	$0.612576\pi$
$542$	−3.26429	−	8.50377i	−0.140213	−	0.365268i
$543$	−0.298842	+	1.11529i	−0.0128245	+	0.0478618i
$544$	−2.86025	−	27.2134i	−0.122632	−	1.16677i
$545$	−6.96931	−	20.6825i	−0.298533	−	0.885939i
$546$	0.154387	+	0.877148i	0.00660715	+	0.0375385i
$547$	−9.20536	+	1.45799i	−0.393593	+	0.0623389i	−0.350094	−	0.936715i	$-0.613850\pi$
$547$	−9.20536	+	1.45799i	−0.393593	+	0.0623389i	−0.0434985	+	0.999053i	$0.513850\pi$
$548$	−2.02352	+	38.6111i	−0.0864406	+	1.64939i
$549$	−21.2248	−	36.7624i	−0.905851	−	1.56898i
$550$	−24.7600	−	29.2537i	−1.05577	−	1.24738i
$551$	−6.25807	−	3.61310i	−0.266603	−	0.153923i
$552$	−0.0436930	+	0.0222627i	−0.00185970	+	0.000947564i
$553$	7.32114	+	15.7128i	0.311326	+	0.668178i
$554$	−6.72363	+	9.25428i	−0.285660	+	0.393177i
$555$	0.676282	+	0.734881i	0.0287066	+	0.0311940i
$556$	13.5263	−	30.3807i	0.573645	−	1.28843i
$557$	−26.5262	−	7.10767i	−1.12395	−	0.301162i	−0.351469	−	0.936199i	$-0.614318\pi$
$557$	−26.5262	−	7.10767i	−1.12395	−	0.301162i	−0.772481	+	0.635038i	$0.780985\pi$
$558$	21.2804	+	17.2325i	0.900870	+	0.729510i
$559$	6.80388	+	20.9402i	0.287774	+	0.885676i
$560$	17.2970	+	14.7186i	0.730932	+	0.621972i
$561$	−0.217025	+	0.667933i	−0.00916279	+	0.0282002i
$562$	17.3892	−	11.2927i	0.733518	−	0.476352i
$563$	1.59530	+	30.4401i	0.0672339	+	1.28290i	0.798995	+	0.601338i	$0.205365\pi$
$563$	1.59530	+	30.4401i	0.0672339	+	1.28290i	−0.731761	+	0.681561i	$0.761301\pi$
$564$	−0.219951	−	1.03479i	−0.00926160	−	0.0435724i
$565$	−8.70509	+	5.78850i	−0.366226	+	0.243524i
$566$	−54.3327	+	17.6538i	−2.28377	+	0.742043i
$567$	21.8508	+	9.28306i	0.917649	+	0.389852i
$568$	0.240998	+	0.240998i	0.0101120	+	0.0101120i
$569$	8.85302	−	0.930489i	0.371138	−	0.0390081i	0.0828762	−	0.996560i	$-0.473589\pi$
$569$	8.85302	−	0.930489i	0.371138	−	0.0390081i	0.288262	+	0.957552i	$0.406923\pi$
$570$	−0.889790	+	0.199253i	−0.0372692	+	0.00834577i
$571$	−4.51357	+	42.9437i	−0.188887	+	1.79714i	0.331756	+	0.943365i	$0.392359\pi$
$571$	−4.51357	+	42.9437i	−0.188887	+	1.79714i	−0.520643	+	0.853774i	$0.674308\pi$
$572$	−22.5072	−	8.63971i	−0.941074	−	0.361244i
$573$	−0.374351	−	0.734705i	−0.0156387	−	0.0306927i
$574$	41.8772	−	11.9942i	1.74792	−	0.500627i
$575$	25.3089	−	13.5957i	1.05545	−	0.566979i
$576$	−12.8985	+	22.3409i	−0.537440	+	0.930873i
$577$	−2.33765	−	1.51809i	−0.0973175	−	0.0631987i	0.495063	−	0.868857i	$-0.335145\pi$
$577$	−2.33765	−	1.51809i	−0.0973175	−	0.0631987i	−0.592380	+	0.805658i	$0.701812\pi$
$578$	8.61313	−	6.97477i	0.358259	−	0.290112i
$579$	−0.666041	+	0.296541i	−0.0276797	+	0.0123238i
$580$	8.59006	−	2.89457i	0.356683	−	0.120190i
$581$	2.55250	−	18.1216i	0.105896	−	0.751810i
$582$	0.335877	−	0.335877i	0.0139226	−	0.0139226i
$583$	−15.9033	+	19.6389i	−0.658646	+	0.813360i
$584$	0.229920	−	0.255352i	0.00951415	−	0.0105665i
$585$	19.0457	−	7.54923i	0.787442	−	0.312122i
$586$	−28.6127	+	25.7630i	−1.18198	+	1.06426i
$587$	14.5534	−	28.5627i	0.600684	−	1.17891i	−0.367817	−	0.929898i	$-0.619895\pi$
$587$	14.5534	−	28.5627i	0.600684	−	1.17891i	0.968501	−	0.249011i	$-0.0801054\pi$
$588$	−0.454457	−	0.649882i	−0.0187415	−	0.0268007i
$589$	15.9361	+	5.17795i	0.656635	+	0.213354i
$590$	−14.0772	+	3.93629i	−0.579550	+	0.162054i
$591$	0.383026	+	0.344879i	0.0157556	+	0.0141864i
$592$	29.3546	−	11.2682i	1.20647	−	0.463119i
$593$	−3.56036	−	13.2874i	−0.146206	−	0.545650i	−0.999699	−	0.0245444i	$-0.992186\pi$
$593$	−3.56036	−	13.2874i	−0.146206	−	0.545650i	0.853492	−	0.521105i	$-0.174480\pi$
$594$	2.02793	−	1.47338i	0.0832070	−	0.0604535i
$595$	2.58366	−	19.9054i	0.105920	−	0.816041i
$596$	−2.95317	−	2.14560i	−0.120967	−	0.0878873i
$597$	0.272446	−	0.709746i	0.0111505	−	0.0290480i
$598$	19.3184	−	29.7478i	0.789990	−	1.21648i
$599$	27.9160	−	16.1173i	1.14062	−	0.658535i	0.194033	−	0.980995i	$-0.437843\pi$
$599$	27.9160	−	16.1173i	1.14062	−	0.658535i	0.946583	+	0.322460i	$0.104510\pi$
$600$	0.0205285	−	0.0374097i	0.000838074	−	0.00152724i
$601$		−	12.7293i		−	0.519238i	−0.965711	−	0.259619i	$-0.916403\pi$
$601$		−	12.7293i		−	0.519238i	0.965711	−	0.259619i	$-0.0835970\pi$
$602$	−26.2333	−	28.1491i	−1.06919	−	1.14727i
$603$	−6.60993	−	41.7335i	−0.269177	−	1.69952i
$604$	1.26679	+	2.84526i	0.0515450	+	0.115772i
$605$	7.58954	+	0.714465i	0.308559	+	0.0290471i
$606$	0.702699	+	0.312862i	0.0285452	+	0.0127091i
$607$	−11.2348	+	3.01036i	−0.456007	+	0.122187i	−0.479509	−	0.877537i	$-0.659185\pi$
$607$	−11.2348	+	3.01036i	−0.456007	+	0.122187i	0.0235020	+	0.999724i	$0.492518\pi$
$608$	−4.67223	+	29.4993i	−0.189484	+	1.19635i
$609$	0.280844	−	0.0195518i	0.0113804	−	0.000792278i
$610$	63.0538	−	10.6898i	2.55297	−	0.432818i
$611$	19.1021	+	21.2150i	0.772788	+	0.858268i
$612$	21.0961	−	1.10560i	0.852758	−	0.0446911i
$613$	23.9409	−	1.25469i	0.966964	−	0.0506764i	0.437689	−	0.899127i	$-0.355797\pi$
$613$	23.9409	−	1.25469i	0.966964	−	0.0506764i	0.529275	+	0.848450i	$0.322464\pi$
$614$	26.7329	+	29.6899i	1.07885	+	1.19819i
$615$	0.460955	+	0.880897i	0.0185875	+	0.0355212i
$616$	1.56801	−	0.109162i	0.0631769	−	0.00439825i
$617$	−7.33373	+	46.3033i	−0.295245	+	1.86410i	0.179194	+	0.983814i	$0.442651\pi$
$617$	−7.33373	+	46.3033i	−0.295245	+	1.86410i	−0.474439	+	0.880288i	$0.657349\pi$
$618$	1.02586	−	0.274879i	0.0412663	−	0.0110573i
$619$	−3.46545	−	1.54292i	−0.139288	−	0.0620152i	0.335909	−	0.941895i	$-0.390957\pi$
$619$	−3.46545	−	1.54292i	−0.139288	−	0.0620152i	−0.475197	+	0.879879i	$0.657623\pi$
$620$	−18.0880	+	10.7066i	−0.726430	+	0.429988i
$621$	0.764276	+	1.71659i	0.0306693	+	0.0688844i
$622$	0.0563428	+	0.355734i	0.00225914	+	0.0142637i
$623$	6.89265	+	7.39602i	0.276148	+	0.296315i
$624$			0.639982i			0.0256198i
$625$	−11.5482	+	22.1730i	−0.461926	+	0.886918i
$626$	24.0327	−	13.8753i	0.960539	−	0.554568i
$627$	0.417502	−	0.642896i	0.0166734	−	0.0256748i
$628$	2.95203	−	7.69031i	0.117799	−	0.306877i
$629$	−22.4817	−	16.3339i	−0.896406	−	0.651277i
$630$	−24.5979	+	26.0156i	−0.980003	+	1.03649i
$631$	−16.4374	+	11.9425i	−0.654362	+	0.475422i	−0.864754	−	0.502195i	$-0.832526\pi$
$631$	−16.4374	+	11.9425i	−0.654362	+	0.475422i	0.210392	+	0.977617i	$0.432526\pi$
$632$	−0.265396	−	0.990471i	−0.0105569	−	0.0393988i
$633$	0.222513	−	0.0854146i	0.00884408	−	0.00339492i
$634$	−18.3169	−	16.4926i	−0.727456	−	0.655004i
$635$	1.13700	−	27.3809i	0.0451206	−	1.08658i
$636$	−0.717277	−	0.233058i	−0.0284419	−	0.00924133i
$637$	19.3891	+	9.05580i	0.768224	+	0.358804i
$638$	−6.79026	+	13.3266i	−0.268829	+	0.527606i
$639$	4.85022	−	4.36716i	0.191872	−	0.172762i
$640$	−1.78406	−	2.15487i	−0.0705213	−	0.0851786i
$641$	−7.34951	+	8.16245i	−0.290288	+	0.322398i	−0.870595	−	0.492000i	$-0.836266\pi$
$641$	−7.34951	+	8.16245i	−0.290288	+	0.322398i	0.580307	+	0.814398i	$0.302933\pi$
$642$	0.229732	−	0.283695i	0.00906678	−	0.0111965i
$643$	1.99706	−	1.99706i	0.0787564	−	0.0787564i	−0.666631	−	0.745388i	$-0.732264\pi$
$643$	1.99706	−	1.99706i	0.0787564	−	0.0787564i	0.745388	+	0.666631i	$0.232264\pi$
$644$	−4.40507	+	31.2740i	−0.173584	+	1.23237i
$645$	0.508449	−	0.716043i	0.0200202	−	0.0281942i
$646$	23.1781	−	10.3196i	0.911932	−	0.406018i
$647$	−17.4663	+	14.1439i	−0.686671	+	0.556055i	−0.907910	−	0.419164i	$-0.862323\pi$
$647$	−17.4663	+	14.1439i	−0.686671	+	0.556055i	0.221239	+	0.975220i	$0.428990\pi$
$648$	−1.17780	−	0.764872i	−0.0462683	−	0.0300470i
$649$	6.14428	−	10.6422i	0.241184	−	0.417743i
$650$	0.670242	+	30.8584i	0.0262891	+	1.21037i
$651$	−0.627568	+	0.179743i	−0.0245963	+	0.00704470i
$652$	−10.2236	−	20.0649i	−0.400387	−	0.785803i
$653$	−7.09333	−	2.72287i	−0.277583	−	0.106554i	0.215594	−	0.976483i	$-0.430831\pi$
$653$	−7.09333	−	2.72287i	−0.277583	−	0.106554i	−0.493177	+	0.869929i	$0.664165\pi$
$654$	−0.112343	+	1.06887i	−0.00439296	+	0.0417963i
$655$	−21.1332	−	9.13548i	−0.825744	−	0.356953i
$656$	31.1302	−	3.27191i	1.21543	−	0.127747i
$657$	−4.65276	−	4.65276i	−0.181522	−	0.181522i
$658$	−45.9174	−	19.5074i	−1.79005	−	0.760479i
$659$	39.6715	−	12.8900i	1.54538	−	0.502125i	0.592526	−	0.805551i	$-0.298131\pi$
$659$	39.6715	−	12.8900i	1.54538	−	0.502125i	0.952855	+	0.303426i	$0.0981306\pi$
$660$	0.258948	+	0.926067i	0.0100795	+	0.0360471i
$661$	−9.10948	−	42.8567i	−0.354318	−	1.66693i	−0.689122	−	0.724646i	$-0.742003\pi$
$661$	−9.10948	−	42.8567i	−0.354318	−	1.66693i	0.334804	−	0.942288i	$-0.391330\pi$
$662$	−0.908316	−	17.3317i	−0.0353027	−	0.673616i
$663$	0.474359	−	0.308053i	0.0184226	−	0.0119638i
$664$	−0.334523	+	1.02956i	−0.0129820	+	0.0399545i
$665$	−8.34724	+	20.2565i	−0.323692	+	0.785512i
$666$	15.3172	+	47.1414i	0.593528	+	1.82669i
$667$	−8.71331	−	7.05590i	−0.337381	−	0.273206i
$668$	−25.3661	−	6.79683i	−0.981445	−	0.262977i
$669$	−0.125302	+	0.281434i	−0.00484447	+	0.0108809i
$670$	62.4074	+	12.5585i	2.41101	+	0.485176i
$671$	−31.6024	+	43.4970i	−1.22000	+	1.67918i
$672$	−0.491427	−	1.05471i	−0.0189572	−	0.0406865i
$673$	25.6305	−	13.0594i	0.987982	−	0.503402i	0.116163	−	0.993230i	$-0.462940\pi$
$673$	25.6305	−	13.0594i	0.987982	−	0.503402i	0.871819	+	0.489828i	$0.162940\pi$
$674$	−12.1335	−	7.00526i	−0.467364	−	0.269833i
$675$	−1.39034	−	0.860561i	−0.0535142	−	0.0331230i
$676$	−3.79579	−	6.57451i	−0.145992	−	0.252866i
$677$	−2.17334	+	41.4698i	−0.0835283	+	1.59382i	0.560066	+	0.828448i	$0.310776\pi$
$677$	−2.17334	+	41.4698i	−0.0835283	+	1.59382i	−0.643594	+	0.765367i	$0.722557\pi$
$678$	0.508459	−	0.0805320i	0.0195273	−	0.00309281i
$679$	−1.97841	−	11.2403i	−0.0759245	−	0.431365i
$680$	−0.354629	+	1.13316i	−0.0135994	+	0.0434546i
$681$	−0.0942220	−	0.896463i	−0.00361060	−	0.0343525i
$682$	8.97638	−	33.5003i	0.343724	−	1.28279i
$683$	1.65579	+	4.31348i	0.0633570	+	0.165051i	0.961604	−	0.274440i	$-0.0884924\pi$
$683$	1.65579	+	4.31348i	0.0633570	+	0.165051i	−0.898247	+	0.439490i	$0.855159\pi$
$684$	−22.5540	−	4.79401i	−0.862375	−	0.183303i
$685$	−18.4891	+	37.2823i	−0.706433	+	1.42448i
$686$	−37.3976	−	0.0344856i	−1.42785	−	0.00131667i
$687$	−1.35696	−	0.691404i	−0.0517711	−	0.0263787i
$688$	−15.0588	−	23.1885i	−0.574112	−	0.884055i
$689$	19.9071	−	4.23139i	0.758401	−	0.161203i
$690$	−1.41193	+	0.0893790i	−0.0537514	+	0.00340260i
$691$	0.0490610	−	0.230814i	0.00186637	−	0.00878057i	−0.977205	−	0.212300i	$-0.931905\pi$
$691$	0.0490610	−	0.230814i	0.00186637	−	0.00878057i	0.979071	+	0.203519i	$0.0652380\pi$
$692$	−27.5238	−	4.35934i	−1.04630	−	0.165717i
$693$	−0.516058	−	30.0950i	−0.0196034	−	1.14322i
$694$	−18.1286	−	24.9518i	−0.688151	−	0.947159i
$695$	26.3385	−	24.2383i	0.999075	−	0.919409i
$696$	−0.0165619	−	0.00174073i	−0.000627779	−	6.59822e-5i
$697$	−17.4095	−	21.4990i	−0.659434	−	0.814333i
$698$	−56.0524	−	2.93758i	−2.12162	−	0.111189i
$699$	−0.878505			−0.0332281
$700$	−12.1453	−	24.6535i	−0.459049	−	0.931816i
$701$	−8.97311			−0.338910			−0.169455	−	0.985538i	$-0.554201\pi$
$701$	−8.97311			−0.338910			−0.169455	+	0.985538i	$0.554201\pi$
$702$	−2.01600	−	0.105654i	−0.0760888	−	0.00398765i
$703$	19.0883	+	23.5721i	0.719928	+	0.889037i
$704$	32.4948	+	3.41534i	1.22469	+	0.128721i
$705$	0.224631	−	1.11627i	0.00846009	−	0.0420412i
$706$	14.7550	+	20.3086i	0.555313	+	0.764323i
$707$	15.8451	−	9.51404i	0.595915	−	0.357812i
$708$	0.362232	+	0.0573719i	0.0136135	+	0.00215617i
$709$	3.68095	−	17.3175i	0.138241	−	0.650372i	−0.853391	−	0.521272i	$-0.825458\pi$
$709$	3.68095	−	17.3175i	0.138241	−	0.650372i	0.991632	−	0.129100i	$-0.0412090\pi$
$710$	3.62325	+	9.14097i	0.135978	+	0.343054i
$711$	−19.2071	+	4.08260i	−0.720324	+	0.153110i
$712$	−0.325714	−	0.501555i	−0.0122066	−	0.0187966i
$713$	23.1647	+	11.8030i	0.867526	+	0.442026i
$714$	−0.524055	+	0.838090i	−0.0196123	+	0.0313647i
$715$	−18.5465	−	18.1481i	−0.693601	−	0.678700i
$716$	−10.9621	−	2.33006i	−0.409671	−	0.0870784i
$717$	0.294983	+	0.768456i	0.0110163	+	0.0286985i
$718$	−19.2888	+	71.9867i	−0.719851	+	2.68652i
$719$	−0.0402153	−	0.382623i	−0.00149978	−	0.0142694i	0.993746	−	0.111660i	$-0.0356169\pi$
$719$	−0.0402153	−	0.382623i	−0.00149978	−	0.0142694i	−0.995246	+	0.0973911i	$0.968950\pi$
$720$	−20.6483	+	15.3471i	−0.769516	+	0.571954i
$721$	8.73519	−	23.9768i	0.325316	−	0.892943i
$722$	10.5419	−	1.66967i	0.392329	−	0.0621388i
$723$	0.0713592	−	1.36161i	0.00265388	−	0.0506390i
$724$	−21.9945	−	38.0956i	−0.817419	−	1.41581i
$725$	9.72289	+	0.808890i	0.361099	+	0.0300414i
$726$	−0.325100	−	0.187697i	−0.0120656	−	0.00696608i
$727$	29.7326	−	15.1495i	1.10272	−	0.561864i	0.194731	−	0.980857i	$-0.437617\pi$
$727$	29.7326	−	15.1495i	1.10272	−	0.561864i	0.907990	+	0.418992i	$0.137617\pi$
$728$	−1.03671	−	0.726390i	−0.0384232	−	0.0269218i
$729$	−15.7759	+	21.7137i	−0.584292	+	0.804210i
$730$	9.01192	−	4.13019i	0.333546	−	0.152865i
$731$	−9.93902	+	22.3234i	−0.367608	+	0.825661i
$732$	−1.54993	−	0.415302i	−0.0572870	−	0.0153500i
$733$	−38.1040	−	30.8560i	−1.40740	−	1.13969i	−0.970758	−	0.240059i	$-0.922833\pi$
$733$	−38.1040	−	30.8560i	−1.40740	−	1.13969i	−0.436645	−	0.899634i	$-0.643833\pi$
$734$	9.04134	+	27.8264i	0.333722	+	1.02709i
$735$	−0.171438	−	0.836150i	−0.00632358	−	0.0308419i
$736$	−14.3200	+	44.0726i	−0.527844	+	1.62454i
$737$	−44.8833	+	29.1476i	−1.65330	+	1.07366i
$738$	2.58249	+	49.2769i	0.0950629	+	1.81391i
$739$	0.295688	+	1.39110i	0.0108771	+	0.0511726i	0.983251	−	0.182254i	$-0.0583394\pi$
$739$	0.295688	+	1.39110i	0.0108771	+	0.0511726i	−0.972374	+	0.233427i	$0.925006\pi$
$740$	−38.0155	−	1.57861i	−1.39748	−	0.0580310i
$741$	−0.587145	+	0.190775i	−0.0215693	+	0.00700829i
$742$	−28.4113	+	21.3958i	−1.04301	+	0.785463i
$743$	−28.2843	−	28.2843i	−1.03765	−	1.03765i	−0.999263	−	0.0383888i	$-0.987777\pi$
$743$	−28.2843	−	28.2843i	−1.03765	−	1.03765i	−0.0383888	−	0.999263i	$-0.512223\pi$
$744$	0.0384040	−	0.00403643i	0.00140796	−	0.000147983i
$745$	−2.00129	−	3.38102i	−0.0733216	−	0.123871i
$746$	5.60162	−	53.2959i	0.205090	−	1.95130i
$747$	19.3533	+	7.42905i	0.708101	+	0.271815i
$748$	−12.1471	−	23.8400i	−0.444142	−	0.871677i
$749$	−2.41507	−	8.43213i	−0.0882447	−	0.308103i
$750$	0.971890	−	0.755680i	0.0354884	−	0.0275935i
$751$	−14.2895	+	24.7501i	−0.521430	+	0.903143i	0.478260	+	0.878218i	$0.341268\pi$
$751$	−14.2895	+	24.7501i	−0.521430	+	0.903143i	−0.999689	+	0.0249242i	$0.992066\pi$
$752$	−30.0655	−	19.5248i	−1.09638	−	0.711995i
$753$	0.529340	−	0.428651i	0.0192902	−	0.0156209i
$754$	11.0042	−	4.89939i	0.400750	−	0.178425i
$755$	0.0363987	+	3.35204i	0.00132469	+	0.121993i
$756$	1.66683	−	0.672845i	0.0606219	−	0.0244711i
$757$	9.94771	−	9.94771i	0.361556	−	0.361556i	−0.502830	−	0.864385i	$-0.667708\pi$
$757$	9.94771	−	9.94771i	0.361556	−	0.361556i	0.864385	+	0.502830i	$0.167708\pi$
$758$	−0.799085	+	0.986788i	−0.0290241	+	0.0358417i
$759$	0.795849	−	0.883880i	0.0288875	−	0.0320828i
$760$	0.694005	−	1.09451i	0.0251742	−	0.0397021i
$761$	17.7877	−	16.0161i	0.644803	−	0.580583i	−0.280480	−	0.959860i	$-0.590494\pi$
$761$	17.7877	−	16.0161i	0.644803	−	0.580583i	0.925283	+	0.379276i	$0.123827\pi$
$762$	−0.612666	+	1.20243i	−0.0221946	+	0.0435593i
$763$	19.4843	+	16.9479i	0.705378	+	0.613557i
$764$	29.8770	+	9.70763i	1.08091	+	0.351210i
$765$	21.3144	+	7.91737i	0.770623	+	0.286253i
$766$	17.6310	+	15.8751i	0.637036	+	0.573589i
$767$	−9.23936	+	3.54666i	−0.333614	+	0.128062i
$768$	−0.207313	−	0.773701i	−0.00748075	−	0.0279185i
$769$	18.1484	−	13.1856i	0.654450	−	0.475486i	−0.210334	−	0.977630i	$-0.567455\pi$
$769$	18.1484	−	13.1856i	0.654450	−	0.475486i	0.864784	+	0.502144i	$0.167455\pi$
$770$	42.7737	+	15.0592i	1.54146	+	0.542696i
$771$	−0.254149	−	0.184650i	−0.00915296	−	0.00665002i
$772$	9.95403	−	25.9311i	0.358253	−	0.933282i
$773$	0.484394	−	0.745901i	0.0174224	−	0.0268282i	−0.829852	−	0.557983i	$-0.811575\pi$
$773$	0.484394	−	0.745901i	0.0174224	−	0.0268282i	0.847274	+	0.531155i	$0.178242\pi$
$774$	37.7472	−	21.7933i	1.35679	−	0.783345i
$775$	−22.4429	+	2.85281i	−0.806171	+	0.102476i
$776$			0.675128i			0.0242357i
$777$	−1.12994	−	0.345837i	−0.0405364	−	0.0124068i
$778$	−1.60298	−	10.1208i	−0.0574696	−	0.362849i
$779$	12.2815	+	27.5847i	0.440031	+	0.988325i
$780$	0.307286	−	0.710850i	0.0110026	−	0.0254525i
$781$	−7.55174	−	3.36225i	−0.270223	−	0.120311i
$782$	38.0244	−	10.1886i	1.35975	−	0.364344i
$783$	−0.0998239	+	0.630263i	−0.00356742	+	0.0225238i
$784$	−26.4617	−	4.68269i	−0.945062	−	0.167239i
$785$	6.20087	−	6.33701i	0.221319	−	0.226178i
$786$	0.758636	+	0.842550i	0.0270596	+	0.0300528i
$787$	−11.4467	+	0.599895i	−0.408030	+	0.0213839i	−0.255247	−	0.966876i	$-0.582157\pi$
$787$	−11.4467	+	0.599895i	−0.408030	+	0.0213839i	−0.152783	+	0.988260i	$0.548823\pi$
$788$	−19.6091	+	1.02767i	−0.698547	+	0.0366093i
$789$	0.235995	+	0.262098i	0.00840163	+	0.00933095i
$790$	4.31035	−	29.2678i	0.153355	−	1.04130i
$791$	5.42576	−	11.1158i	0.192918	−	0.395232i
$792$	−0.278530	+	1.75857i	−0.00989715	+	0.0624881i
$793$	41.8249	−	11.2069i	1.48524	−	0.397970i
$794$	55.0365	+	24.5038i	1.95317	+	0.869608i
$795$	−0.609112	−	0.536586i	−0.0216030	−	0.0190308i
$796$	11.7805	+	26.4594i	0.417548	+	0.937829i
$797$	1.06473	+	6.72244i	0.0377146	+	0.238121i	0.999343	−	0.0362333i	$-0.0115359\pi$
$797$	1.06473	+	6.72244i	0.0377146	+	0.238121i	−0.961629	+	0.274354i	$0.911536\pi$
$798$	0.789275	−	0.735557i	0.0279400	−	0.0260384i
$799$			31.6829i			1.12086i
$800$	−11.2802	−	38.7152i	−0.398817	−	1.36879i
$801$	−9.91786	+	5.72608i	−0.350430	+	0.202321i
$802$	18.1711	−	27.9810i	0.641643	−	0.988044i
$803$	−2.98665	+	7.78048i	−0.105396	+	0.274567i
$804$	−1.29216	−	0.938811i	−0.0455711	−	0.0331093i
$805$	−17.7085	+	29.0163i	−0.624142	+	1.02269i
$806$	−22.5971	+	16.4177i	−0.795948	+	0.578290i
$807$	0.215704	+	0.805018i	0.00759314	+	0.0283380i
$808$	−1.02066	+	0.391795i	−0.0359067	+	0.0137833i
$809$	15.0141	+	13.5188i	0.527868	+	0.475294i	0.889441	−	0.457049i	$-0.151094\pi$
$809$	15.0141	+	13.5188i	0.527868	+	0.475294i	−0.361573	+	0.932344i	$0.617760\pi$
$810$	−22.4345	−	33.7384i	−0.788269	−	1.18545i
$811$	44.8838	+	14.5836i	1.57608	+	0.512101i	0.961044	−	0.276394i	$-0.0891396\pi$
$811$	44.8838	+	14.5836i	1.57608	+	0.512101i	0.615041	+	0.788495i	$0.289140\pi$
$812$	−7.03900	+	8.09241i	−0.247020	+	0.283988i
$813$	−0.111674	+	0.219173i	−0.00391658	+	0.00768673i
$814$	46.6550	−	42.0083i	1.63526	−	1.47239i
$815$	−1.53127	−	24.1897i	−0.0536381	−	0.847330i
$816$	−0.475263	+	0.527833i	−0.0166375	+	0.0184779i
$817$	16.7851	−	20.7279i	0.587237	−	0.725178i
$818$	−27.5572	+	27.5572i	−0.963517	+	0.963517i
$819$	−14.9300	+	19.0975i	−0.521698	+	0.667320i
$820$	−36.1484	−	11.3129i	−1.26236	−	0.395063i
$821$	−38.8062	+	17.2776i	−1.35435	+	0.602994i	−0.950183	−	0.311693i	$-0.899104\pi$
$821$	−38.8062	+	17.2776i	−1.35435	+	0.602994i	−0.404163	+	0.914687i	$0.632437\pi$
$822$	1.59261	−	1.28967i	0.0555486	−	0.0449824i
$823$	−9.23367	−	5.99642i	−0.321866	−	0.209022i	0.373585	−	0.927596i	$-0.378128\pi$
$823$	−9.23367	−	5.99642i	−0.321866	−	0.209022i	−0.695450	+	0.718574i	$0.744795\pi$
$824$	−0.754754	+	1.30727i	−0.0262931	+	0.0455410i
$825$	−0.139671	+	1.02551i	−0.00486271	+	0.0357038i
$826$	12.0181	−	12.4375i	0.418165	−	0.432756i
$827$	−6.91433	−	13.5701i	−0.240435	−	0.471880i	0.738983	−	0.673724i	$-0.235307\pi$
$827$	−6.91433	−	13.5701i	−0.240435	−	0.471880i	−0.979418	+	0.201844i	$0.935307\pi$
$828$	−33.3997	−	12.8209i	−1.16072	−	0.445558i
$829$	2.62011	−	24.9287i	0.0910002	−	0.865809i	−0.849859	−	0.527010i	$-0.823313\pi$
$829$	2.62011	−	24.9287i	0.0910002	−	0.865809i	0.940859	−	0.338798i	$-0.110020\pi$
$830$	−20.6448	+	23.4352i	−0.716593	+	0.813449i
$831$	0.307217	−	0.0322898i	0.0106572	−	0.00112012i
$832$	−18.6069	−	18.6069i	−0.645078	−	0.645078i
$833$	9.26639	+	21.8676i	0.321062	+	0.757668i
$834$	−1.67638	+	0.544688i	−0.0580482	+	0.0188610i
$835$	−22.1581	−	17.5484i	−0.766812	−	0.607286i
$836$	6.07194	+	28.5662i	0.210002	+	0.987983i
$837$	−0.0774405	−	1.47765i	−0.00267673	−	0.0510751i
$838$	40.0662	−	26.0193i	1.38406	−	0.898822i
$839$	5.42302	−	16.6903i	0.187223	−	0.576214i	−0.812756	−	0.582604i	$-0.802034\pi$
$839$	5.42302	−	16.6903i	0.187223	−	0.576214i	0.999980	+	0.00638981i	$0.00203395\pi$
$840$	0.00141375	+	0.0504705i	4.87791e−5	+	0.00174140i
$841$	7.78489	+	23.9594i	0.268445	+	0.826188i
$842$	−0.521143	−	0.422013i	−0.0179598	−	0.0145435i
$843$	−0.540850	−	0.144920i	−0.0186279	−	0.00499132i
$844$	−3.69330	+	8.29530i	−0.127129	+	0.285536i
$845$	−0.942287	−	8.11649i	−0.0324157	−	0.279216i
$846$	33.2176	−	45.7201i	1.14204	−	1.57189i
$847$	−8.17586	+	3.80941i	−0.280926	+	0.130893i
$848$	−22.7715	+	11.6027i	−0.781978	+	0.398438i
$849$	1.33608	+	0.771384i	0.0458540	+	0.0264738i
$850$	−22.3633	+	25.9486i	−0.767054	+	0.890030i
$851$	23.5307	+	40.7564i	0.806623	+	1.39711i
$852$	0.0129117	−	0.246370i	0.000442347	−	0.00844049i
$853$	17.0873	−	2.70636i	0.585057	−	0.0926639i	0.143113	−	0.989706i	$-0.454289\pi$
$853$	17.0873	−	2.70636i	0.585057	−	0.0926639i	0.441944	+	0.897043i	$0.354289\pi$
$854$	−57.9822	+	48.6225i	−1.98411	+	1.66383i
$855$	−20.2352	−	14.3686i	−0.692029	−	0.491397i
$856$	0.0542342	+	0.516004i	0.00185369	+	0.0176367i
$857$	−7.83496	+	29.2405i	−0.267637	+	0.998836i	0.692979	+	0.720958i	$0.256298\pi$
$857$	−7.83496	+	29.2405i	−0.267637	+	0.998836i	−0.960616	+	0.277878i	$0.910369\pi$
$858$	0.457928	+	1.19294i	0.0156334	+	0.0407264i
$859$	−23.9309	−	5.08666i	−0.816511	−	0.173555i	−0.219319	−	0.975653i	$-0.570384\pi$
$859$	−23.9309	−	5.08666i	−0.816511	−	0.173555i	−0.597192	+	0.802098i	$0.703717\pi$
$860$	5.59240	+	32.9868i	0.190699	+	1.12484i
$861$	−0.997426	−	0.623687i	−0.0339922	−	0.0212552i
$862$	61.5156	+	31.3438i	2.09523	+	1.06757i
$863$	−17.8159	−	27.4340i	−0.606459	−	0.933864i	−0.999895	−	0.0145124i	$-0.995380\pi$
$863$	−17.8159	−	27.4340i	−0.606459	−	0.933864i	0.393436	−	0.919352i	$-0.371286\pi$
$864$	2.57981	−	0.548356i	0.0877670	−	0.0186555i
$865$	−25.3308	−	16.0617i	−0.861273	−	0.546114i
$866$	1.53160	−	7.20560i	0.0520458	−	0.244856i
$867$	−0.295613	−	0.0468206i	−0.0100396	−	0.00159011i
$868$	12.0640	−	21.7483i	0.409479	−	0.738185i
$869$	14.6186	+	20.1208i	0.495902	+	0.682550i
$870$	−0.418666	−	0.235693i	−0.0141941	−	0.00799075i
$871$	42.8644	+	4.50523i	1.45241	+	0.152654i
$872$	−0.961333	−	1.18715i	−0.0325548	−	0.0402019i
$873$	12.9107	+	0.676622i	0.436962	+	0.0229002i
$874$	−42.9677			−1.45340
$875$	−1.47015	−	29.5438i	−0.0497002	−	0.998764i
$876$	−0.248726			−0.00840366
$877$	−3.69340	−	0.193563i	−0.124717	−	0.00653615i	−0.0101248	−	0.999949i	$-0.503223\pi$
$877$	−3.69340	−	0.193563i	−0.124717	−	0.00653615i	−0.114592	+	0.993413i	$0.536556\pi$
$878$	39.0219	+	48.1880i	1.31693	+	1.62627i
$879$	1.03406	+	0.108684i	0.0348780	+	0.00366582i
$880$	28.3948	+	15.9852i	0.957190	+	0.538862i
$881$	−13.7300	−	18.8977i	−0.462575	−	0.636680i	0.512465	−	0.858708i	$-0.328732\pi$
$881$	−13.7300	−	18.8977i	−0.462575	−	0.636680i	−0.975040	+	0.222028i	$0.928732\pi$
$882$	9.55496	−	41.2713i	0.321732	−	1.38968i
$883$	44.4188	+	7.03524i	1.49481	+	0.236755i	0.849672	−	0.527311i	$-0.176800\pi$
$883$	44.4188	+	7.03524i	1.49481	+	0.236755i	0.645139	+	0.764066i	$0.276800\pi$
$884$	−4.48016	+	21.0775i	−0.150684	+	0.708914i
$885$	0.333371	+	0.211383i	0.0112061	+	0.00710556i
$886$	12.7810	−	2.71668i	0.429386	−	0.0912688i
$887$	28.1228	+	43.3053i	0.944270	+	1.45405i	0.890231	+	0.455509i	$0.150543\pi$
$887$	28.1228	+	43.3053i	0.944270	+	1.45405i	0.0540387	+	0.998539i	$0.482791\pi$
$888$	0.0622820	+	0.0317343i	0.00209005	+	0.00106493i
$889$	15.2140	+	28.6346i	0.510262	+	0.960375i
$890$	−2.88393	−	17.0108i	−0.0966695	−	0.570205i
$891$	33.3176	+	7.08187i	1.11618	+	0.237251i
$892$	−4.20605	−	10.9571i	−0.140829	−	0.366872i
$893$	8.95044	−	33.4035i	0.299515	−	1.11781i
$894$	0.0202238	+	0.192417i	0.000676386	+	0.00643538i
$895$	−9.83503	−	6.98367i	−0.328749	−	0.233438i
$896$	3.11014	+	1.13308i	0.103903	+	0.0378536i
$897$	−0.946083	+	0.149845i	−0.0315888	+	0.00500317i
$898$	−3.51449	+	67.0605i	−0.117280	+	2.23784i
$899$	4.41450	+	7.64614i	0.147232	+	0.255013i
$900$	30.3037	−	7.13236i	1.01012	−	0.237745i
$901$	19.5610	+	11.2935i	0.651670	+	0.376242i
$902$	55.6864	−	28.3736i	1.85415	−	0.944738i
$903$	−0.0908819	+	1.03512i	−0.00302436	+	0.0344466i
$904$	−0.430076	+	0.591949i	−0.0143041	+	0.0196879i
$905$	−5.46003	−	47.0305i	−0.181497	−	1.56335i
$906$	0.0671434	−	0.150807i	0.00223069	−	0.00501021i
$907$	1.89080	+	0.506638i	0.0627830	+	0.0168226i	0.290074	−	0.957004i	$-0.406320\pi$
$907$	1.89080	+	0.506638i	0.0627830	+	0.0168226i	−0.227291	+	0.973827i	$0.572987\pi$
$908$	26.6882	+	21.6117i	0.885680	+	0.717209i
$909$	6.46952	+	19.9111i	0.214580	+	0.660410i
$910$	−19.1388	−	31.1042i	−0.634446	−	1.03109i
$911$	12.2158	−	37.5963i	0.404726	−	1.24562i	−0.516397	−	0.856349i	$-0.672727\pi$
$911$	12.2158	−	37.5963i	0.404726	−	1.24562i	0.921124	−	0.389270i	$-0.127273\pi$
$912$	0.650186	−	0.422236i	0.0215298	−	0.0139816i
$913$	−1.37415	−	26.2203i	−0.0454776	−	0.867764i
$914$	11.6533	+	54.8244i	0.385456	+	1.81343i
$915$	−1.35391	−	1.07224i	−0.0447589	−	0.0354473i
$916$	55.1811	−	17.9294i	1.82324	−	0.592405i
$917$	27.0395	−	3.31159i	0.892922	−	0.109358i
$918$	−1.58426	−	1.58426i	−0.0522883	−	0.0522883i
$919$	−3.80368	+	0.399783i	−0.125472	+	0.0131876i	−0.167056	−	0.985947i	$-0.553426\pi$
$919$	−3.80368	+	0.399783i	−0.125472	+	0.0131876i	0.0415844	+	0.999135i	$0.486759\pi$
$920$	1.32920	−	1.50885i	0.0438223	−	0.0497454i
$921$	0.112776	−	1.07299i	0.00371609	−	0.0353562i
$922$	11.1228	+	4.26965i	0.366311	+	0.140613i
$923$	3.02241	+	5.93181i	0.0994838	+	0.195248i
$924$	−0.818199	−	0.790611i	−0.0269168	−	0.0260092i
$925$	−36.8839	−	17.7952i	−1.21273	−	0.585103i
$926$	22.4514	−	38.8870i	0.737800	−	1.27791i
$927$	24.2430	+	15.7436i	0.796246	+	0.517088i
$928$	−12.2301	+	9.90374i	−0.401473	+	0.325106i
$929$	−16.7546	+	7.45963i	−0.549701	+	0.244743i	−0.662742	−	0.748848i	$-0.730607\pi$
$929$	−16.7546	+	7.45963i	−0.549701	+	0.244743i	0.113041	+	0.993590i	$0.463941\pi$
$930$	1.06322	+	0.332743i	0.0348645	+	0.0109111i
$931$	−3.59200	−	25.6729i	−0.117723	−	0.841396i
$932$	23.6662	−	23.6662i	0.775212	−	0.775212i
$933$	0.00612102	−	0.00755883i	0.000200393	−	0.000247465i
$934$	−17.7676	+	19.7329i	−0.581373	+	0.645680i
$935$	−1.81937	−	28.7409i	−0.0594997	−	0.939927i
$936$	1.06562	−	0.959490i	0.0348309	−	0.0313619i
$937$	−16.8884	+	33.1453i	−0.551720	+	1.08281i	0.431793	+	0.901973i	$0.357881\pi$
$937$	−16.8884	+	33.1453i	−0.551720	+	1.08281i	−0.983513	+	0.180838i	$0.942119\pi$
$938$	−71.2256	+	24.5005i	−2.32560	+	0.799969i
$939$	−0.712728	−	0.231579i	−0.0232590	−	0.00755731i
$940$	24.0200	+	36.1228i	0.783447	+	1.17819i
$941$	−12.9524	−	11.6624i	−0.422236	−	0.380183i	0.430443	−	0.902618i	$-0.358357\pi$
$941$	−12.9524	−	11.6624i	−0.422236	−	0.380183i	−0.852679	+	0.522435i	$0.825024\pi$
$942$	−0.407607	+	0.156466i	−0.0132806	+	0.00509793i
$943$	12.1257	+	45.2536i	0.394866	+	1.47366i
$944$	10.0544	−	7.30493i	0.327242	−	0.237755i
$945$	1.93412	+	0.0471163i	0.0629171	+	0.00153269i
$946$	−44.6622	−	32.4490i	−1.45209	−	1.05501i
$947$	−8.51972	+	22.1946i	−0.276854	+	0.721229i	0.722694	+	0.691168i	$0.242903\pi$
$947$	−8.51972	+	22.1946i	−0.276854	+	0.721229i	−0.999548	+	0.0300608i	$0.990430\pi$
$948$	−0.404261	+	0.622507i	−0.0131298	+	0.0202181i
$949$	5.81265	−	3.35594i	0.188687	−	0.108938i
$950$	30.9082	−	21.0401i	1.00279	−	0.682632i
$951$			0.665616i			0.0215841i
$952$	−0.315612	−	1.36898i	−0.0102290	−	0.0443690i
$953$	4.35463	+	27.4941i	0.141060	+	0.890621i	0.952135	+	0.305678i	$0.0988830\pi$
$953$	4.35463	+	27.4941i	0.141060	+	0.890621i	−0.811075	+	0.584943i	$0.801117\pi$
$954$	−16.3869	−	36.8056i	−0.530545	−	1.19162i
$955$	25.3716	+	22.3506i	0.821004	+	0.723249i
$956$	−28.6482	−	12.7550i	−0.926548	−	0.412526i
$957$	0.390148	−	0.104540i	0.0126117	−	0.00337929i
$958$	3.33174	−	21.0358i	0.107644	−	0.679636i
$959$	−3.41969	−	49.1207i	−0.110427	−	1.58619i
$960$	−0.152922	+	1.03836i	−0.00493554	+	0.0335130i
$961$	7.04407	+	7.82323i	0.227228	+	0.252362i
$962$	−50.4915	+	2.64615i	−1.62791	+	0.0853152i
$963$	9.92209	−	0.519995i	0.319735	−	0.0167566i
$964$	34.7584	+	38.6031i	1.11949	+	1.24332i
$965$	20.9089	−	21.3679i	0.673080	−	0.687858i
$966$	1.38807	−	0.935644i	0.0446604	−	0.0301039i
$967$	2.80338	−	17.6999i	0.0901507	−	0.569189i	−0.900723	−	0.434394i	$-0.856962\pi$
$967$	2.80338	−	17.6999i	0.0901507	−	0.569189i	0.990874	−	0.134795i	$-0.0430376\pi$
$968$	0.515372	−	0.138094i	0.0165647	−	0.00443849i
$969$	−0.625928	−	0.278681i	−0.0201077	−	0.00895253i
$970$	−7.72862	+	17.8787i	−0.248151	+	0.574052i
$971$	−6.46406	−	14.5185i	−0.207442	−	0.465922i	0.779622	−	0.626250i	$-0.215411\pi$
$971$	−6.46406	−	14.5185i	−0.207442	−	0.465922i	−0.987064	+	0.160329i	$0.948745\pi$
$972$	0.477867	+	3.01714i	0.0153276	+	0.0967747i
$973$	−12.3950	+	40.4976i	−0.397365	+	1.29829i
$974$		−	74.6937i		−	2.39334i
$975$	0.607177	−	0.571061i	0.0194452	−	0.0182886i
$976$	−47.0900	+	27.1874i	−1.50731	+	0.870249i
$977$	2.97189	−	4.57631i	0.0950791	−	0.146409i	−0.787930	−	0.615765i	$-0.788847\pi$
$977$	2.97189	−	4.57631i	0.0950791	−	0.146409i	0.883009	+	0.469356i	$0.155514\pi$
$978$	−0.427744	+	1.11431i	−0.0136778	+	0.0356318i
$979$	11.7347	+	8.52579i	0.375044	+	0.272486i
$980$	27.1436	+	17.9068i	0.867070	+	0.572012i
$981$	−23.6657	+	17.1942i	−0.755588	+	0.548967i
$982$	−14.4527	−	53.9384i	−0.461206	−	1.72124i
$983$	−19.6948	+	7.56014i	−0.628168	+	0.241131i	−0.651562	−	0.758595i	$-0.725886\pi$
$983$	−19.6948	+	7.56014i	−0.628168	+	0.241131i	0.0233942	+	0.999726i	$0.492553\pi$
$984$	0.0517129	+	0.0465625i	0.00164855	+	0.00148436i
$985$	−19.8121	−	7.35933i	−0.631265	−	0.234488i
$986$	12.7143	+	4.13111i	0.404904	+	0.131561i
$987$	0.438235	+	1.27400i	0.0139492	+	0.0405519i
$988$	10.6779	−	20.9565i	0.339708	−	0.666715i
$989$	30.7537	−	27.6907i	0.977910	−	0.880514i
$990$	−27.5076	+	43.3820i	−0.874248	+	1.37877i
$991$	−2.67624	+	2.97226i	−0.0850134	+	0.0944170i	−0.784151	−	0.620571i	$-0.786901\pi$
$991$	−2.67624	+	2.97226i	−0.0850134	+	0.0944170i	0.699137	+	0.714988i	$0.253568\pi$
$992$	22.9649	−	28.3593i	0.729137	−	0.900409i
$993$	−0.331412	+	0.331412i	−0.0105170	+	0.0105170i
$994$	−9.16583	−	7.16567i	−0.290723	−	0.227281i
$995$	0.338489	+	31.1722i	0.0107308	+	0.988225i
$996$	0.715861	−	0.318722i	0.0226829	−	0.0100991i
$997$	2.20694	−	1.78714i	0.0698943	−	0.0565993i	−0.593737	−	0.804659i	$-0.702348\pi$
$997$	2.20694	−	1.78714i	0.0698943	−	0.0565993i	0.663631	+	0.748060i	$0.269015\pi$
$998$	58.3939	+	37.9214i	1.84843	+	1.20038i
$999$	1.33924	−	2.31963i	0.0423716	−	0.0733897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.15	yes	288
5.2	odd	4		875.2.bb.b.257.4		288
5.3	odd	4		875.2.bb.a.257.15		288
5.4	even	2		875.2.bb.c.243.4		288
7.3	odd	6	inner	175.2.x.a.3.4	✓	288
25.6	even	5		875.2.bb.b.768.4		288
25.8	odd	20		875.2.bb.c.607.15		288
25.17	odd	20	inner	175.2.x.a.117.4	yes	288
25.19	even	10		875.2.bb.a.768.15		288
35.3	even	12		875.2.bb.a.507.15		288
35.17	even	12		875.2.bb.b.507.4		288
35.24	odd	6		875.2.bb.c.493.15		288
175.17	even	60	inner	175.2.x.a.17.15	yes	288
175.31	odd	30		875.2.bb.b.143.4		288
175.94	odd	30		875.2.bb.a.143.15		288
175.108	even	60		875.2.bb.c.857.4		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.4	✓	288	7.3	odd	6	inner
175.2.x.a.17.15	yes	288	175.17	even	60	inner
175.2.x.a.103.15	yes	288	1.1	even	1	trivial
175.2.x.a.117.4	yes	288	25.17	odd	20	inner
875.2.bb.a.143.15		288	175.94	odd	30
875.2.bb.a.257.15		288	5.3	odd	4
875.2.bb.a.507.15		288	35.3	even	12
875.2.bb.a.768.15		288	25.19	even	10
875.2.bb.b.143.4		288	175.31	odd	30
875.2.bb.b.257.4		288	5.2	odd	4
875.2.bb.b.507.4		288	35.17	even	12
875.2.bb.b.768.4		288	25.6	even	5
875.2.bb.c.243.4		288	5.4	even	2
875.2.bb.c.493.15		288	35.24	odd	6
875.2.bb.c.607.15		288	25.8	odd	20
875.2.bb.c.857.4		288	175.108	even	60

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.01652 + 0.105681i) q^{2} +(-0.0343174 - 0.0423785i) q^{3} +(2.06612 + 0.217158i) q^{4} +(1.94852 + 1.09694i) q^{5} +(-0.0647231 - 0.0890837i) q^{6} +(-2.64536 + 0.0453616i) q^{7} +(0.154579 + 0.0244829i) q^{8} +(0.623117 - 2.93153i) q^{9} +(3.81329 + 2.41792i) q^{10} +(-3.71299 + 0.789220i) q^{11} +(-0.0617013 - 0.0950116i) q^{12} +(2.72389 + 1.38789i) q^{13} +(-5.33921 - 0.188092i) q^{14} +(-0.0203814 - 0.120220i) q^{15} +(-3.75509 - 0.798169i) q^{16} +(1.21589 + 3.16750i) q^{17} +(1.56633 - 5.84563i) q^{18} +(-0.387098 - 3.68300i) q^{19} +(3.78767 + 2.68956i) q^{20} +(0.0927044 + 0.110550i) q^{21} +(-7.57071 + 1.19908i) q^{22} +(0.300717 - 5.73802i) q^{23} +(-0.00426721 - 0.00739102i) q^{24} +(2.59344 + 4.27482i) q^{25} +(5.34609 + 3.08657i) q^{26} +(-0.291380 + 0.148466i) q^{27} +(-5.47550 - 0.480740i) q^{28} +(1.14694 - 1.57863i) q^{29} +(-0.0283944 - 0.244579i) q^{30} +(-1.84036 + 4.13351i) q^{31} +(-7.79020 - 2.08738i) q^{32} +(0.160866 + 0.130267i) q^{33} +(2.11711 + 6.51580i) q^{34} +(-5.20429 - 2.81342i) q^{35} +(1.92404 - 5.92160i) q^{36} +(-6.86909 + 4.46084i) q^{37} +(-0.391367 - 7.46773i) q^{38} +(-0.0346602 - 0.163063i) q^{39} +(0.274343 + 0.217269i) q^{40} +(-7.75457 + 2.51961i) q^{41} +(0.175257 + 0.232723i) q^{42} +(5.09273 + 5.09273i) q^{43} +(-7.84288 + 0.824320i) q^{44} +(4.42988 - 5.02862i) q^{45} +(1.21280 - 11.5390i) q^{46} +(8.71792 + 3.34650i) q^{47} +(0.0950399 + 0.186526i) q^{48} +(6.99588 - 0.239996i) q^{49} +(4.77794 + 8.89432i) q^{50} +(0.0925076 - 0.160228i) q^{51} +(5.32650 + 3.45907i) q^{52} +(5.17366 - 4.18955i) q^{53} +(-0.603263 + 0.268590i) q^{54} +(-8.10055 - 2.53512i) q^{55} +(-0.410028 - 0.0577542i) q^{56} +(-0.142796 + 0.142796i) q^{57} +(2.47966 - 3.06212i) q^{58} +(-2.16617 + 2.40578i) q^{59} +(-0.0160038 - 0.252815i) q^{60} +(10.5258 - 9.47749i) q^{61} +(-4.14794 + 8.14080i) q^{62} +(-1.51539 + 7.78324i) q^{63} +(-8.18628 - 2.65988i) q^{64} +(3.78511 + 5.69228i) q^{65} +(0.310623 + 0.279686i) q^{66} +(13.1621 - 5.05246i) q^{67} +(1.82433 + 6.80848i) q^{68} +(-0.253489 + 0.184170i) q^{69} +(-10.1972 - 6.22330i) q^{70} +(1.76180 + 1.28002i) q^{71} +(0.168093 - 0.437898i) q^{72} +(1.19576 - 1.84131i) q^{73} +(-14.3231 + 8.26943i) q^{74} +(0.0921603 - 0.256607i) q^{75} -7.69359i q^{76} +(9.78640 - 2.25620i) q^{77} +(-0.0526601 - 0.332483i) q^{78} +(-2.66490 - 5.98546i) q^{79} +(-6.44131 - 5.67436i) q^{80} +(-8.19747 - 3.64975i) q^{81} +(-15.9035 + 4.26133i) q^{82} +(-1.08205 + 6.83177i) q^{83} +(0.167532 + 0.248541i) q^{84} +(-1.10538 + 7.50568i) q^{85} +(9.73137 + 10.8078i) q^{86} +(-0.106260 + 0.00556886i) q^{87} +(-0.593272 + 0.0310921i) q^{88} +(-2.55687 - 2.83969i) q^{89} +(9.46435 - 9.67214i) q^{90} +(-7.26863 - 3.54791i) q^{91} +(1.86738 - 11.7902i) q^{92} +(0.238328 - 0.0638599i) q^{93} +(17.2262 + 7.66959i) q^{94} +(3.28576 - 7.60101i) q^{95} +(0.178880 + 0.401770i) q^{96} +(0.674820 + 4.26064i) q^{97} +(14.1327 + 0.255378i) q^{98} +11.3765i 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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