LMFDB - Embedded newform 175.2.x.a.47.3

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			47.3
Character	$\chi$	$=$	175.47
Dual form			175.2.x.a.108.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.128358 + 2.44921i) q^{2} +(-2.33133 + 1.88788i) q^{3} +(-3.99310 - 0.419692i) q^{4} +(0.975297 + 2.01216i) q^{5} +(-4.32456 - 5.95224i) q^{6} +(1.49568 + 2.18242i) q^{7} +(0.773125 - 4.88132i) q^{8} +(1.24730 - 5.86809i) q^{9} +(-5.05339 + 2.13043i) q^{10} +(3.31278 - 0.704153i) q^{11} +(10.1016 - 6.56004i) q^{12} +(0.306584 - 0.601706i) q^{13} +(-5.53718 + 3.38310i) q^{14} +(-6.07245 - 2.84978i) q^{15} +(4.00142 + 0.850527i) q^{16} +(2.65746 - 1.02010i) q^{17} +(14.2121 + 3.80811i) q^{18} +(0.332985 + 3.16814i) q^{19} +(-3.04997 - 8.44409i) q^{20} +(-7.60706 - 2.26428i) q^{21} +(1.29940 + 8.20407i) q^{22} +(-5.31061 - 0.278317i) q^{23} +(7.41291 + 12.8395i) q^{24} +(-3.09759 + 3.92491i) q^{25} +(1.43435 + 0.828123i) q^{26} +(4.08462 + 8.01652i) q^{27} +(-5.05646 - 9.34234i) q^{28} +(5.40952 - 7.44556i) q^{29} +(7.75915 - 14.5069i) q^{30} +(-2.24826 + 5.04968i) q^{31} +(-0.0384776 + 0.143600i) q^{32} +(-6.39384 + 7.89573i) q^{33} +(2.15734 + 6.63961i) q^{34} +(-2.93265 + 5.13805i) q^{35} +(-7.44339 + 22.9084i) q^{36} +(-0.910134 - 1.40148i) q^{37} +(-7.80217 + 0.408894i) q^{38} +(0.421196 + 1.98157i) q^{39} +(10.5760 - 3.20508i) q^{40} +(-0.985611 + 0.320244i) q^{41} +(6.52212 - 18.3406i) q^{42} +(3.97930 - 3.97930i) q^{43} +(-13.5238 + 1.42141i) q^{44} +(13.0240 - 3.21336i) q^{45} +(1.36331 - 12.9711i) q^{46} +(-0.987046 + 2.57134i) q^{47} +(-10.9343 + 5.57132i) q^{48} +(-2.52589 + 6.52839i) q^{49} +(-9.21532 - 8.09044i) q^{50} +(-4.26959 + 7.39515i) q^{51} +(-1.47675 + 2.27400i) q^{52} +(-2.51939 - 3.11118i) q^{53} +(-20.1584 + 8.97511i) q^{54} +(4.64781 + 5.97909i) q^{55} +(11.8094 - 5.61361i) q^{56} +(-6.75735 - 6.75735i) q^{57} +(17.5414 + 14.2047i) q^{58} +(0.797763 - 0.886005i) q^{59} +(23.0519 + 13.9280i) q^{60} +(4.35276 - 3.91924i) q^{61} +(-12.0791 - 6.15462i) q^{62} +(14.6722 - 6.05465i) q^{63} +(7.43442 + 2.41559i) q^{64} +(1.50974 + 0.0300560i) q^{65} +(-18.5176 - 16.6733i) q^{66} +(2.67924 + 6.97967i) q^{67} +(-11.0396 + 2.95806i) q^{68} +(12.9062 - 9.37692i) q^{69} +(-12.2077 - 7.84217i) q^{70} +(7.96131 + 5.78423i) q^{71} +(-27.6797 - 10.6252i) q^{72} +(4.33497 + 2.81516i) q^{73} +(3.54935 - 2.04922i) q^{74} +(-0.188223 - 14.9981i) q^{75} -12.7904i q^{76} +(6.49161 + 6.17668i) q^{77} +(-4.90734 + 0.777246i) q^{78} +(-1.61674 - 3.63126i) q^{79} +(2.19117 + 8.88102i) q^{80} +(-8.21521 - 3.65765i) q^{81} +(-0.657835 - 2.45507i) q^{82} +(7.87661 + 1.24753i) q^{83} +(29.4255 + 12.2341i) q^{84} +(4.64442 + 4.35233i) q^{85} +(9.23537 + 10.2569i) q^{86} +(1.44491 + 27.5706i) q^{87} +(-0.876003 - 16.7151i) q^{88} +(-8.29060 - 9.20765i) q^{89} +(6.19844 + 32.3110i) q^{90} +(1.77172 - 0.230864i) q^{91} +(21.0890 + 3.34017i) q^{92} +(-4.29172 - 16.0169i) q^{93} +(-6.17106 - 2.74753i) q^{94} +(-6.05005 + 3.75989i) q^{95} +(-0.181395 - 0.407421i) q^{96} +(-16.7616 + 2.65478i) q^{97} +(-15.6652 - 7.02439i) q^{98} -20.3180i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.128358	+	2.44921i	−0.0907625	+	1.73185i	0.452045	+	0.891995i	$0.350695\pi$
$2$	−0.128358	+	2.44921i	−0.0907625	+	1.73185i	−0.542808	+	0.839857i	$0.682639\pi$
$3$	−2.33133	+	1.88788i	−1.34600	+	1.08997i	−0.358295	+	0.933609i	$0.616642\pi$
$3$	−2.33133	+	1.88788i	−1.34600	+	1.08997i	−0.987701	+	0.156357i	$0.950025\pi$
$4$	−3.99310	−	0.419692i	−1.99655	−	0.209846i
$5$	0.975297	+	2.01216i	0.436166	+	0.899866i
$5$	0.975297	+	2.01216i	0.436166	+	0.899866i
$6$	−4.32456	−	5.95224i	−1.76549	−	2.42999i
$7$	1.49568	+	2.18242i	0.565314	+	0.824876i
$7$	1.49568	+	2.18242i	0.565314	+	0.824876i
$8$	0.773125	−	4.88132i	0.273341	−	1.72581i
$9$	1.24730	−	5.86809i	0.415767	−	1.95603i
$10$	−5.05339	+	2.13043i	−1.59802	+	0.673701i
$11$	3.31278	−	0.704153i	0.998840	−	0.212310i	0.320651	−	0.947197i	$-0.396098\pi$
$11$	3.31278	−	0.704153i	0.998840	−	0.212310i	0.678189	+	0.734887i	$0.262765\pi$
$12$	10.1016	−	6.56004i	2.91607	−	1.89372i
$13$	0.306584	−	0.601706i	0.0850312	−	0.166883i	−0.844575	−	0.535437i	$-0.820147\pi$
$13$	0.306584	−	0.601706i	0.0850312	−	0.166883i	0.929606	+	0.368554i	$0.120147\pi$
$14$	−5.53718	+	3.38310i	−1.47987	+	0.904172i
$15$	−6.07245	−	2.84978i	−1.56790	−	0.735810i
$16$	4.00142	+	0.850527i	1.00035	+	0.212632i
$17$	2.65746	−	1.02010i	0.644528	−	0.247411i	−0.0140758	−	0.999901i	$-0.504481\pi$
$17$	2.65746	−	1.02010i	0.644528	−	0.247411i	0.658604	+	0.752490i	$0.271147\pi$
$18$	14.2121	+	3.80811i	3.34982	+	0.897581i
$19$	0.332985	+	3.16814i	0.0763919	+	0.726821i	0.963943	+	0.266110i	$0.0857386\pi$
$19$	0.332985	+	3.16814i	0.0763919	+	0.726821i	−0.887551	+	0.460710i	$0.847595\pi$
$20$	−3.04997	−	8.44409i	−0.681994	−	1.88816i
$21$	−7.60706	−	2.26428i	−1.66000	−	0.494107i
$22$	1.29940	+	8.20407i	0.277032	+	1.74911i
$23$	−5.31061	−	0.278317i	−1.10734	−	0.0580332i	−0.510114	−	0.860107i	$-0.670397\pi$
$23$	−5.31061	−	0.278317i	−1.10734	−	0.0580332i	−0.597225	+	0.802074i	$0.703730\pi$
$24$	7.41291	+	12.8395i	1.51315	+	2.62086i
$25$	−3.09759	+	3.92491i	−0.619519	+	0.784982i
$26$	1.43435	+	0.828123i	0.281299	+	0.162408i
$27$	4.08462	+	8.01652i	0.786086	+	1.54278i
$28$	−5.05646	−	9.34234i	−0.955580	−	1.76554i
$29$	5.40952	−	7.44556i	1.00452	−	1.38261i	0.0820132	−	0.996631i	$-0.473865\pi$
$29$	5.40952	−	7.44556i	1.00452	−	1.38261i	0.922509	−	0.385975i	$-0.126135\pi$
$30$	7.75915	−	14.5069i	1.41662	−	2.64859i
$31$	−2.24826	+	5.04968i	−0.403800	+	0.906949i	0.591149	+	0.806562i	$0.298674\pi$
$31$	−2.24826	+	5.04968i	−0.403800	+	0.906949i	−0.994949	+	0.100386i	$0.967992\pi$
$32$	−0.0384776	+	0.143600i	−0.00680194	+	0.0253852i
$33$	−6.39384	+	7.89573i	−1.11302	+	1.37447i
$34$	2.15734	+	6.63961i	0.369981	+	1.13868i
$35$	−2.93265	+	5.13805i	−0.495708	+	0.868489i
$36$	−7.44339	+	22.9084i	−1.24056	+	3.81807i
$37$	−0.910134	−	1.40148i	−0.149625	−	0.230402i	0.755908	−	0.654678i	$-0.227196\pi$
$37$	−0.910134	−	1.40148i	−0.149625	−	0.230402i	−0.905533	+	0.424275i	$0.860529\pi$
$38$	−7.80217	+	0.408894i	−1.26568	+	0.0663314i
$39$	0.421196	+	1.98157i	0.0674453	+	0.317305i
$40$	10.5760	−	3.20508i	1.67222	−	0.506768i
$41$	−0.985611	+	0.320244i	−0.153927	+	0.0500138i	−0.384967	−	0.922930i	$-0.625787\pi$
$41$	−0.985611	+	0.320244i	−0.153927	+	0.0500138i	0.231040	+	0.972944i	$0.425787\pi$
$42$	6.52212	−	18.3406i	1.00639	−	2.83002i
$43$	3.97930	−	3.97930i	0.606838	−	0.606838i	−0.335280	−	0.942118i	$-0.608831\pi$
$43$	3.97930	−	3.97930i	0.606838	−	0.606838i	0.942118	+	0.335280i	$0.108831\pi$
$44$	−13.5238	+	1.42141i	−2.03879	+	0.214285i
$45$	13.0240	−	3.21336i	1.94151	−	0.479019i
$46$	1.36331	−	12.9711i	0.201010	−	1.91248i
$47$	−0.987046	+	2.57134i	−0.143976	+	0.375069i	−0.986539	−	0.163529i	$-0.947712\pi$
$47$	−0.987046	+	2.57134i	−0.143976	+	0.375069i	0.842563	+	0.538598i	$0.181046\pi$
$48$	−10.9343	+	5.57132i	−1.57823	+	0.804150i
$49$	−2.52589	+	6.52839i	−0.360841	+	0.932627i
$50$	−9.21532	−	8.09044i	−1.30324	−	1.14416i
$51$	−4.26959	+	7.39515i	−0.597862	+	1.03553i
$52$	−1.47675	+	2.27400i	−0.204789	+	0.315347i
$53$	−2.51939	−	3.11118i	−0.346064	−	0.427354i	0.574161	−	0.818742i	$-0.305328\pi$
$53$	−2.51939	−	3.11118i	−0.346064	−	0.427354i	−0.920226	+	0.391388i	$0.871995\pi$
$54$	−20.1584	+	8.97511i	−2.74321	+	1.22136i
$55$	4.64781	+	5.97909i	0.626711	+	0.806220i
$56$	11.8094	−	5.61361i	1.57810	−	0.750150i
$57$	−6.75735	−	6.75735i	−0.895033	−	0.895033i
$58$	17.5414	+	14.2047i	2.30330	+	1.86517i
$59$	0.797763	−	0.886005i	0.103860	−	0.115348i	−0.688974	−	0.724787i	$-0.741938\pi$
$59$	0.797763	−	0.886005i	0.103860	−	0.115348i	0.792833	+	0.609438i	$0.208605\pi$
$60$	23.0519	+	13.9280i	2.97599	+	1.79810i
$61$	4.35276	−	3.91924i	0.557313	−	0.501807i	−0.341652	−	0.939826i	$-0.610987\pi$
$61$	4.35276	−	3.91924i	0.557313	−	0.501807i	0.898966	+	0.438019i	$0.144320\pi$
$62$	−12.0791	−	6.15462i	−1.53405	−	0.781638i
$63$	14.6722	−	6.05465i	1.84852	−	0.762814i
$64$	7.43442	+	2.41559i	0.929302	+	0.301949i
$65$	1.50974	+	0.0300560i	0.187260	+	0.00372798i
$66$	−18.5176	−	16.6733i	−2.27936	−	2.05234i
$67$	2.67924	+	6.97967i	0.327322	+	0.852702i	0.994201	+	0.107536i	$0.0342962\pi$
$67$	2.67924	+	6.97967i	0.327322	+	0.852702i	−0.666880	+	0.745166i	$0.732370\pi$
$68$	−11.0396	+	2.95806i	−1.33875	+	0.358717i
$69$	12.9062	−	9.37692i	1.55373	−	1.12885i
$70$	−12.2077	−	7.84217i	−1.45910	−	0.937319i
$71$	7.96131	+	5.78423i	0.944833	+	0.686462i	0.949579	−	0.313527i	$-0.101511\pi$
$71$	7.96131	+	5.78423i	0.944833	+	0.686462i	−0.00474583	+	0.999989i	$0.501511\pi$
$72$	−27.6797	−	10.6252i	−3.26208	−	1.25220i
$73$	4.33497	+	2.81516i	0.507370	+	0.329490i	0.772810	−	0.634638i	$-0.218851\pi$
$73$	4.33497	+	2.81516i	0.507370	+	0.329490i	−0.265440	+	0.964127i	$0.585517\pi$
$74$	3.54935	−	2.04922i	0.412603	−	0.238217i
$75$	−0.188223	−	14.9981i	−0.0217341	−	1.73184i
$76$		−	12.7904i		−	1.46716i
$77$	6.49161	+	6.17668i	0.739788	+	0.703898i
$78$	−4.90734	+	0.777246i	−0.555647	+	0.0880058i
$79$	−1.61674	−	3.63126i	−0.181897	−	0.408548i	0.799465	−	0.600712i	$-0.205116\pi$
$79$	−1.61674	−	3.63126i	−0.181897	−	0.408548i	−0.981363	+	0.192164i	$0.938450\pi$
$80$	2.19117	+	8.88102i	0.244980	+	0.992928i
$81$	−8.21521	−	3.65765i	−0.912802	−	0.406405i
$82$	−0.657835	−	2.45507i	−0.0726457	−	0.271117i
$83$	7.87661	+	1.24753i	0.864570	+	0.136934i	0.572941	−	0.819597i	$-0.305803\pi$
$83$	7.87661	+	1.24753i	0.864570	+	0.136934i	0.291629	+	0.956531i	$0.405803\pi$
$84$	29.4255	+	12.2341i	3.21058	+	1.33485i
$85$	4.64442	+	4.35233i	0.503758	+	0.472077i
$86$	9.23537	+	10.2569i	0.995875	+	1.10603i
$87$	1.44491	+	27.5706i	0.154911	+	2.95588i
$88$	−0.876003	−	16.7151i	−0.0933822	−	1.78184i
$89$	−8.29060	−	9.20765i	−0.878802	−	0.976009i	0.121060	−	0.992645i	$-0.461371\pi$
$89$	−8.29060	−	9.20765i	−0.878802	−	0.976009i	−0.999862	+	0.0166367i	$0.994704\pi$
$90$	6.19844	+	32.3110i	0.653373	+	3.40588i
$91$	1.77172	−	0.230864i	0.185727	−	0.0242011i
$92$	21.0890	+	3.34017i	2.19868	+	0.348237i
$93$	−4.29172	−	16.0169i	−0.445030	−	1.66088i
$94$	−6.17106	−	2.74753i	−0.636496	−	0.283386i
$95$	−6.05005	+	3.75989i	−0.620722	+	0.385757i
$96$	−0.181395	−	0.407421i	−0.0185136	−	0.0415822i
$97$	−16.7616	+	2.65478i	−1.70189	+	0.269552i	−0.930361	−	0.366646i	$-0.880506\pi$
$97$	−16.7616	+	2.65478i	−1.70189	+	0.269552i	−0.771526	+	0.636198i	$0.780506\pi$
$98$	−15.6652	−	7.02439i	−1.58242	−	0.709571i
$99$		−	20.3180i		−	2.04203i
$100$	14.0163	−	14.3725i	1.40163	−	1.43725i
$101$	1.88364	−	1.08752i	0.187429	−	0.108212i	−0.403349	−	0.915046i	$-0.632154\pi$
$101$	1.88364	−	1.08752i	0.187429	−	0.108212i	0.590778	+	0.806834i	$0.298821\pi$
$102$	−17.5642	−	11.4063i	−1.73912	−	1.12940i
$103$	−2.30638	−	0.885336i	−0.227254	−	0.0872347i	0.242077	−	0.970257i	$-0.422171\pi$
$103$	−2.30638	−	0.885336i	−0.227254	−	0.0872347i	−0.469331	+	0.883022i	$0.655505\pi$
$104$	−2.70009	−	1.96173i	−0.264766	−	0.192363i
$105$	−2.86303	−	17.5150i	−0.279403	−	1.70929i
$106$	7.94332	−	5.77116i	0.771523	−	0.560544i
$107$	−1.72859	+	0.463175i	−0.167109	+	0.0447768i	−0.341404	−	0.939917i	$-0.610902\pi$
$107$	−1.72859	+	0.463175i	−0.167109	+	0.0447768i	0.174294	+	0.984694i	$0.444236\pi$
$108$	−12.9458	−	33.7251i	−1.24571	−	3.24520i
$109$	−1.82675	−	1.64482i	−0.174971	−	0.157545i	0.576992	−	0.816750i	$-0.304226\pi$
$109$	−1.82675	−	1.64482i	−0.174971	−	0.157545i	−0.751963	+	0.659205i	$0.770893\pi$
$110$	−15.2406	+	10.6160i	−1.45314	+	1.01220i
$111$	4.76765	+	1.54910i	0.452525	+	0.147034i
$112$	4.12863	+	10.0049i	0.390119	+	0.945372i
$113$	−1.65922	−	0.845414i	−0.156086	−	0.0795298i	0.374203	−	0.927347i	$-0.377916\pi$
$113$	−1.65922	−	0.845414i	−0.156086	−	0.0795298i	−0.530289	+	0.847817i	$0.677916\pi$
$114$	17.4175	−	15.6828i	1.63130	−	1.46883i
$115$	−4.61940	−	10.9573i	−0.430761	−	1.02177i
$116$	−24.7256	+	27.4606i	−2.29571	+	2.54965i
$117$	−3.14846	−	2.54957i	−0.291075	−	0.235708i
$118$	2.06761	+	2.06761i	0.190339	+	0.190339i
$119$	6.20099	+	4.27394i	0.568444	+	0.391791i
$120$	−18.6055	+	27.4383i	−1.69844	+	2.50477i
$121$	0.429674	−	0.191303i	0.0390612	−	0.0173912i
$122$	9.04032	+	11.1639i	0.818472	+	1.01073i
$123$	1.69321	−	2.60731i	0.152671	−	0.235093i
$124$	11.0968	−	19.2203i	0.996526	−	1.72603i
$125$	−10.9186	−	2.40491i	−0.976592	−	0.215102i
$126$	12.9458	+	36.7124i	1.15330	+	3.27060i
$127$	−10.4896	+	5.34472i	−0.930802	+	0.474268i	−0.852538	−	0.522665i	$-0.824938\pi$
$127$	−10.4896	+	5.34472i	−0.930802	+	0.474268i	−0.0782643	+	0.996933i	$0.524938\pi$
$128$	−6.97710	+	18.1760i	−0.616694	+	1.60654i
$129$	−1.76465	+	16.7895i	−0.155369	+	1.47823i
$130$	−0.267400	+	3.69381i	−0.0234525	+	0.323969i
$131$	−13.6348	+	1.43308i	−1.19128	+	0.125208i	−0.679347	−	0.733817i	$-0.737737\pi$
$131$	−13.6348	+	1.43308i	−1.19128	+	0.125208i	−0.511932	+	0.859026i	$0.671070\pi$
$132$	28.8450	−	28.8450i	2.51064	−	2.51064i
$133$	−6.41616	+	5.46523i	−0.556352	+	0.473895i
$134$	−17.4386	+	5.66613i	−1.50646	+	0.489479i
$135$	−12.1468	+	16.0374i	−1.04543	+	1.38028i
$136$	−2.92490	−	13.7606i	−0.250808	−	1.17996i
$137$	13.3958	−	0.702045i	1.14448	−	0.0599797i	0.529350	−	0.848404i	$-0.322436\pi$
$137$	13.3958	−	0.702045i	1.14448	−	0.0599797i	0.615132	+	0.788424i	$0.289103\pi$
$138$	21.3094	+	32.8136i	1.81398	+	2.79328i
$139$	3.08285	−	9.48803i	0.261484	−	0.804764i	−0.730999	−	0.682379i	$-0.760946\pi$
$139$	3.08285	−	9.48803i	0.261484	−	0.804764i	0.992483	−	0.122385i	$-0.0390544\pi$
$140$	13.8668	−	19.2860i	1.17195	−	1.62996i
$141$	−2.55324	−	7.85808i	−0.215022	−	0.661770i
$142$	−15.1887	+	18.7565i	−1.27461	+	1.57401i
$143$	0.591954	−	2.20920i	0.0495016	−	0.184743i
$144$	9.98194	−	22.4198i	0.831828	−	1.86832i
$145$	20.2576	+	3.62320i	1.68230	+	0.300890i
$146$	−7.45134	+	10.2559i	−0.616678	+	0.848784i
$147$	−6.43611	−	19.9884i	−0.530841	−	1.64862i
$148$	3.04607	+	5.97824i	0.250385	+	0.491408i
$149$	20.0681	+	11.5863i	1.64404	+	0.949187i	0.979376	+	0.202044i	$0.0647584\pi$
$149$	20.0681	+	11.5863i	1.64404	+	0.949187i	0.664663	+	0.747143i	$0.268575\pi$
$150$	36.7577	+	1.46413i	3.00126	+	0.119546i
$151$	−4.39641	−	7.61480i	−0.357775	−	0.619684i	0.629814	−	0.776746i	$-0.283131\pi$
$151$	−4.39641	−	7.61480i	−0.357775	−	0.619684i	−0.987589	+	0.157062i	$0.949798\pi$
$152$	15.7221	+	0.823962i	1.27523	+	0.0668321i
$153$	−2.67140	−	16.8666i	−0.215970	−	1.36358i
$154$	−15.9612	+	15.1065i	−1.28619	+	1.21731i
$155$	−12.3535	+	0.401067i	−0.992256	+	0.0322145i
$156$	−0.850228	−	8.08938i	−0.0680727	−	0.647669i
$157$	12.7655	+	3.42049i	1.01879	+	0.272985i	0.729299	−	0.684195i	$-0.239846\pi$
$157$	12.7655	+	3.42049i	1.01879	+	0.272985i	0.289495	+	0.957180i	$0.406513\pi$
$158$	9.10123	−	3.49363i	0.724055	−	0.277939i
$159$	11.7471	+	2.49691i	0.931602	+	0.198018i
$160$	−0.326474	+	0.0626297i	−0.0258100	+	0.00495131i
$161$	−7.33557	−	12.0062i	−0.578124	−	0.946225i
$162$	10.0128	−	19.6513i	0.786682	−	1.54395i
$163$	−10.0495	+	6.52620i	−0.787135	+	0.511171i	−0.874512	−	0.485004i	$-0.838818\pi$
$163$	−10.0495	+	6.52620i	−0.787135	+	0.511171i	0.0873771	+	0.996175i	$0.472151\pi$
$164$	4.07005	−	0.865116i	0.317817	−	0.0675542i
$165$	−22.1234	−	5.16476i	−1.72230	−	0.402076i
$166$	−4.06649	+	19.1313i	−0.315621	+	1.48488i
$167$	3.54656	−	22.3921i	0.274441	−	1.73275i	−0.337039	−	0.941491i	$-0.609425\pi$
$167$	3.54656	−	22.3921i	0.274441	−	1.73275i	0.611480	−	0.791260i	$-0.290575\pi$
$168$	−16.9339	+	35.3819i	−1.30648	+	2.72977i
$169$	7.37315	+	10.1483i	0.567166	+	0.780636i
$170$	−11.2559	+	10.8165i	−0.863289	+	0.829588i
$171$	19.0062	+	1.99764i	1.45344	+	0.152763i
$172$	−17.5598	+	14.2197i	−1.33893	+	1.08424i
$173$	0.220591	−	4.20912i	0.0167712	−	0.320013i	−0.977342	−	0.211666i	$-0.932111\pi$
$173$	0.220591	−	4.20912i	0.0167712	−	0.320013i	0.994113	−	0.108347i	$-0.0345557\pi$
$174$	−67.7116			−5.13320
$175$	−13.1988	−	0.889835i	−0.997735	−	0.0672652i
$176$	13.8547			1.04434
$177$	−0.187182	+	3.57165i	−0.0140695	+	0.268462i
$178$	23.6156	−	19.1235i	1.77006	−	1.43337i
$179$	−4.34914	−	0.457113i	−0.325070	−	0.0341662i	−0.0594118	−	0.998234i	$-0.518923\pi$
$179$	−4.34914	−	0.457113i	−0.325070	−	0.0341662i	−0.265658	+	0.964067i	$0.585589\pi$
$180$	−53.3549	+	7.36517i	−3.97684	+	0.548968i
$181$	14.5835	+	20.0725i	1.08399	+	1.49198i	0.855056	+	0.518536i	$0.173523\pi$
$181$	14.5835	+	20.0725i	1.08399	+	1.49198i	0.228931	+	0.973443i	$0.426477\pi$
$182$	0.338019	+	4.36896i	0.0250556	+	0.323849i
$183$	−2.74868	+	17.3545i	−0.203189	+	1.28288i
$184$	−5.46432	+	25.7076i	−0.402835	+	1.89519i
$185$	1.93236	−	3.19820i	0.142070	−	0.235136i
$186$	39.7796	−	8.45542i	2.91678	−	0.619981i
$187$	8.08526	−	5.25063i	0.591253	−	0.383964i
$188$	5.02055	−	9.85338i	0.366161	−	0.718632i
$189$	−11.3861	+	20.9045i	−0.828217	+	1.52058i
$190$	−8.43219	−	15.3004i	−0.611735	−	1.11001i
$191$	15.2799	+	3.24784i	1.10561	+	0.235005i	0.724330	−	0.689453i	$-0.242149\pi$
$191$	15.2799	+	3.24784i	1.10561	+	0.235005i	0.381283	+	0.924459i	$0.375483\pi$
$192$	−21.8924	+	8.40371i	−1.57995	+	0.606486i
$193$	19.7554	+	5.29344i	1.42202	+	0.381030i	0.886201	−	0.463301i	$-0.153335\pi$
$193$	19.7554	+	5.29344i	1.42202	+	0.381030i	0.535822	+	0.844331i	$0.320002\pi$
$194$	−4.35063	−	41.3935i	−0.312357	−	2.97188i
$195$	−3.57645	+	2.78013i	−0.256115	+	0.199089i
$196$	12.8260	−	25.0084i	0.916146	−	1.78632i
$197$	−2.13257	−	13.4645i	−0.151939	−	0.959306i	−0.939371	−	0.342904i	$-0.888590\pi$
$197$	−2.13257	−	13.4645i	−0.151939	−	0.959306i	0.787431	−	0.616402i	$-0.211410\pi$
$198$	49.7629	+	2.60797i	3.53650	+	0.185340i
$199$	−10.9166	−	18.9082i	−0.773859	−	1.34036i	−0.935434	−	0.353503i	$-0.884991\pi$
$199$	−10.9166	−	18.9082i	−0.773859	−	1.34036i	0.161574	−	0.986861i	$-0.448343\pi$
$200$	16.7639	+	18.1548i	1.18539	+	1.28374i
$201$	−19.4229	−	11.2138i	−1.36999	−	0.790964i
$202$	2.42178	+	4.75301i	0.170396	+	0.334421i
$203$	24.3402	+	0.669652i	1.70835	+	0.0470003i
$204$	20.1526	−	27.7377i	1.41096	−	1.94203i
$205$	−1.60565	−	1.67088i	−0.112143	−	0.116699i
$206$	2.46441	−	5.53516i	0.171704	−	0.385653i
$207$	−8.25712	+	30.8160i	−0.573910	+	2.14186i
$208$	1.73854	−	2.14692i	0.120546	−	0.148862i
$209$	3.33396	+	10.2609i	0.230615	+	0.709759i
$210$	43.2653	−	4.76398i	2.98559	−	0.328746i
$211$	2.71073	−	8.34277i	0.186614	−	0.574340i	−0.813358	−	0.581763i	$-0.802363\pi$
$211$	2.71073	−	8.34277i	0.186614	−	0.574340i	0.999972	+	0.00742360i	$0.00236303\pi$
$212$	8.75443	+	13.4806i	0.601256	+	0.925854i
$213$	−29.4804	+	1.54500i	−2.01996	+	0.105862i
$214$	−0.912534	−	4.29314i	−0.0623795	−	0.293473i
$215$	11.8880	+	4.12600i	0.810755	+	0.281391i
$216$	42.2891	−	13.7406i	2.87741	−	0.934927i
$217$	−14.3832	+	2.64605i	−0.976393	+	0.179626i
$218$	4.26298	−	4.26298i	0.288725	−	0.288725i
$219$	−15.4209	+	1.62080i	−1.04205	+	0.109524i
$220$	−16.0498	−	25.8258i	−1.08208	−	1.74117i
$221$	0.200934	−	1.91176i	0.0135163	−	0.128599i
$222$	−4.40604	+	11.4781i	−0.295714	+	0.770362i
$223$	−7.97499	+	4.06346i	−0.534045	+	0.272109i	−0.700146	−	0.713999i	$-0.746882\pi$
$223$	−7.97499	+	4.06346i	−0.534045	+	0.272109i	0.166102	+	0.986109i	$0.446882\pi$
$224$	−0.370946	+	0.130806i	−0.0247849	+	0.00873983i
$225$	19.1681	+	23.0725i	1.27787	+	1.53817i
$226$	2.28357	−	3.95525i	0.151901	−	0.263100i
$227$	9.17280	−	14.1249i	0.608820	−	0.937500i	−0.391033	−	0.920376i	$-0.627882\pi$
$227$	9.17280	−	14.1249i	0.608820	−	0.937500i	0.999853	−	0.0171240i	$-0.00545100\pi$
$228$	24.1468	+	29.8188i	1.59916	+	1.97480i
$229$	−0.0584255	+	0.0260127i	−0.00386087	+	0.00171897i	−0.408666	−	0.912684i	$-0.634006\pi$
$229$	−0.0584255	+	0.0260127i	−0.00386087	+	0.00171897i	0.404805	+	0.914403i	$0.367339\pi$
$230$	27.4295	−	9.90743i	1.80865	−	0.653277i
$231$	−26.7949	−	2.14454i	−1.76298	−	0.141100i
$232$	−32.1619	−	32.1619i	−2.11153	−	2.11153i
$233$	14.4276	+	11.6832i	0.945183	+	0.765394i	0.972178	−	0.234242i	$-0.0752607\pi$
$233$	14.4276	+	11.6832i	0.945183	+	0.765394i	−0.0269957	+	0.999636i	$0.508594\pi$
$234$	6.64856	−	7.38398i	0.434630	−	0.482706i
$235$	−6.13662	+	0.521725i	−0.400309	+	0.0340336i
$236$	−3.55740	+	3.20310i	−0.231567	+	0.208504i
$237$	10.6245	+	5.41346i	0.690137	+	0.351642i
$238$	−11.2637	+	14.6389i	−0.730117	+	0.948901i
$239$	−6.24077	−	2.02775i	−0.403682	−	0.131164i	0.100137	−	0.994974i	$-0.468072\pi$
$239$	−6.24077	−	2.02775i	−0.403682	−	0.131164i	−0.503819	+	0.863810i	$0.668072\pi$
$240$	−21.8746	−	16.5679i	−1.41200	−	1.06946i
$241$	3.27870	+	2.95215i	0.211199	+	0.190165i	0.767940	−	0.640521i	$-0.221282\pi$
$241$	3.27870	+	2.95215i	0.211199	+	0.190165i	−0.556741	+	0.830686i	$0.687948\pi$
$242$	0.413389	+	1.07692i	0.0265737	+	0.0692267i
$243$	−0.0141564	+	0.00379321i	−0.000908136	+	0.000243334i
$244$	−19.0259	+	13.8231i	−1.21801	+	0.884933i
$245$	−15.5997	+	1.28462i	−0.996626	+	0.0820714i
$246$	6.16850	+	4.48168i	0.393289	+	0.285741i
$247$	2.00837	+	0.770943i	0.127790	+	0.0490539i
$248$	22.9109	+	14.8785i	1.45484	+	0.944786i
$249$	−20.7182	+	11.9616i	−1.31296	+	0.758038i
$250$	7.29161	−	26.4333i	0.461162	−	1.67179i
$251$			4.66639i			0.294540i	0.989096	+	0.147270i	$0.0470486\pi$
$251$			4.66639i			0.294540i	−0.989096	+	0.147270i	$0.952951\pi$
$252$	−61.1286	+	18.0190i	−3.85074	+	1.13509i
$253$	−17.7889	+	2.81748i	−1.11838	+	0.177133i
$254$	−11.7439	−	26.3773i	−0.736879	−	1.65506i
$255$	−19.0444	−	1.37865i	−1.19260	−	0.0863342i
$256$	−29.3388	−	13.0625i	−1.83367	−	0.816404i
$257$	−1.87632	−	7.00253i	−0.117042	−	0.436806i	0.882390	−	0.470519i	$-0.155933\pi$
$257$	−1.87632	−	7.00253i	−0.117042	−	0.436806i	−0.999432	+	0.0337134i	$0.989267\pi$
$258$	−40.8945	−	6.47705i	−2.54598	−	0.403244i
$259$	1.69735	−	4.08246i	0.105468	−	0.253672i
$260$	−6.01593	−	0.753642i	−0.373092	−	0.0467389i
$261$	−36.9439	−	41.0304i	−2.28677	−	2.53972i
$262$	−1.75977	−	33.5784i	−0.108719	−	2.07448i
$263$	−0.586193	−	11.1852i	−0.0361462	−	0.689711i	−0.955269	−	0.295739i	$-0.904434\pi$
$263$	−0.586193	−	11.1852i	−0.0361462	−	0.689711i	0.919123	−	0.393972i	$-0.128899\pi$
$264$	33.5983	+	37.3147i	2.06784	+	2.29656i
$265$	3.80306	−	8.10374i	0.233620	−	0.497809i
$266$	−12.5619	−	16.4160i	−0.770221	−	1.00653i
$267$	36.7110	+	5.81446i	2.24668	+	0.355839i
$268$	−7.76918	−	28.9950i	−0.474578	−	1.77115i
$269$	−6.52032	−	2.90303i	−0.397551	−	0.177001i	0.198216	−	0.980158i	$-0.436485\pi$
$269$	−6.52032	−	2.90303i	−0.397551	−	0.177001i	−0.595767	+	0.803157i	$0.703152\pi$
$270$	−37.7198	−	31.8086i	−2.29555	−	1.93581i
$271$	7.04083	+	15.8140i	0.427700	+	0.960630i	0.990936	+	0.134334i	$0.0428894\pi$
$271$	7.04083	+	15.8140i	0.427700	+	0.960630i	−0.563236	+	0.826296i	$0.690444\pi$
$272$	11.5012	−	1.82161i	0.697364	−	0.110452i
$273$	−3.69464	+	3.88302i	−0.223610	+	0.235011i
$274$			32.8993i			1.98752i
$275$	−7.49791	+	15.1835i	−0.452141	+	0.915602i
$276$	−55.4713	+	32.0264i	−3.33898	+	1.92776i
$277$	−11.8624	−	7.70351i	−0.712741	−	0.462859i	0.136653	−	0.990619i	$-0.456365\pi$
$277$	−11.8624	−	7.70351i	−0.712741	−	0.462859i	−0.849394	+	0.527760i	$0.823032\pi$
$278$	22.8425	+	8.76840i	1.37000	+	0.525893i
$279$	26.8277	+	19.4915i	1.60613	+	1.16692i
$280$	22.8132	+	18.2875i	1.36335	+	1.09289i
$281$	8.33513	−	6.05583i	0.497232	−	0.361260i	−0.310727	−	0.950499i	$-0.600572\pi$
$281$	8.33513	−	6.05583i	0.497232	−	0.361260i	0.807959	+	0.589239i	$0.200572\pi$
$282$	19.5738	−	5.24478i	1.16560	−	0.312322i
$283$	1.05621	+	2.75152i	0.0627851	+	0.163561i	0.961384	−	0.275210i	$-0.0887473\pi$
$283$	1.05621	+	2.75152i	0.0627851	+	0.163561i	−0.898599	+	0.438771i	$0.855414\pi$
$284$	−29.3627	−	26.4383i	−1.74236	−	1.56883i
$285$	7.00646	−	20.1873i	0.415027	−	1.19579i
$286$	5.33481	+	1.73339i	0.315454	+	0.102497i
$287$	−2.17306	−	1.67203i	−0.128272	−	0.0986969i
$288$	0.794666	+	0.404903i	0.0468261	+	0.0238591i
$289$	−6.61199	+	5.95346i	−0.388941	+	0.350204i
$290$	−11.4742	+	49.1499i	−0.673787	+	2.88618i
$291$	34.0650	−	37.8331i	1.99693	−	2.21781i
$292$	−16.1285	−	13.0606i	−0.943847	−	0.764313i
$293$	−7.38784	−	7.38784i	−0.431602	−	0.431602i	0.457571	−	0.889173i	$-0.348720\pi$
$293$	−7.38784	−	7.38784i	−0.431602	−	0.431602i	−0.889173	+	0.457571i	$0.848720\pi$
$294$	49.7819	−	13.1977i	2.90334	−	0.769706i
$295$	2.56084	+	0.741110i	0.149098	+	0.0431491i
$296$	−7.54473	+	3.35913i	−0.438529	+	0.195246i
$297$	19.1763	+	23.6808i	1.11272	+	1.37410i
$298$	−30.9532	+	47.6637i	−1.79307	+	2.76108i
$299$	−1.79562	+	3.11010i	−0.103843	+	0.179862i
$300$	−5.54301	+	59.9681i	−0.320026	+	3.46226i
$301$	14.6363	+	2.73274i	0.843620	+	0.157512i
$302$	19.2145	−	9.79030i	1.10567	−	0.563368i
$303$	−2.33829	+	6.09144i	−0.134331	+	0.349944i
$304$	−1.36218	+	12.9603i	−0.0781262	+	0.743321i
$305$	12.1314	+	4.93603i	0.694640	+	0.282636i
$306$	41.6526	−	4.37787i	2.38112	−	0.250266i
$307$	19.3045	−	19.3045i	1.10176	−	1.10176i	0.107567	−	0.994198i	$-0.465694\pi$
$307$	19.3045	−	19.3045i	1.10176	−	1.10176i	0.994198	−	0.107567i	$-0.0343059\pi$
$308$	−23.3294	−	27.3886i	−1.32931	−	1.56061i
$309$	7.04834	−	2.29014i	0.400966	−	0.130282i
$310$	0.603368	−	30.3077i	0.0342690	−	1.72136i
$311$	−0.271828	−	1.27885i	−0.0154139	−	0.0725169i	0.969768	−	0.244027i	$-0.0784686\pi$
$311$	−0.271828	−	1.27885i	−0.0154139	−	0.0725169i	−0.985182	+	0.171510i	$0.945135\pi$
$312$	9.99831	−	0.523989i	0.566043	−	0.0296651i
$313$	−7.64733	−	11.7759i	−0.432252	−	0.665610i	0.553685	−	0.832726i	$-0.313221\pi$
$313$	−7.64733	−	11.7759i	−0.432252	−	0.665610i	−0.985937	+	0.167116i	$0.946555\pi$
$314$	−10.0160	+	30.8262i	−0.565238	+	1.73962i
$315$	26.4927	+	23.6177i	1.49269	+	1.33071i
$316$	4.93180	+	15.1785i	0.277435	+	0.853858i
$317$	18.3433	−	22.6520i	1.03026	−	1.27227i	0.0687096	−	0.997637i	$-0.478112\pi$
$317$	18.3433	−	22.6520i	1.03026	−	1.27227i	0.961550	−	0.274628i	$-0.0885549\pi$
$318$	−7.62328	+	28.4505i	−0.427492	+	1.59542i
$319$	12.6777	−	28.4746i	0.709816	−	1.59427i
$320$	2.39021	+	17.3152i	0.133617	+	0.967947i
$321$	3.15551	−	4.34318i	0.176123	−	0.242413i
$322$	30.3474	−	16.4252i	1.69119	−	0.915343i
$323$	4.11672	+	8.07951i	0.229060	+	0.449556i
$324$	31.2691	+	18.0532i	1.73717	+	1.00296i
$325$	1.41197	+	3.06716i	0.0783218	+	0.170135i
$326$	−14.6941	−	25.4509i	−0.813831	−	1.40960i
$327$	7.36398	+	0.385930i	0.407229	+	0.0213420i
$328$	0.801215	+	5.05867i	0.0442397	+	0.279318i
$329$	−7.08805	+	1.69176i	−0.390777	+	0.0932697i
$330$	15.4893	−	53.5218i	0.852656	−	2.94628i
$331$	0.881971	+	8.39139i	0.0484775	+	0.461233i	0.991653	+	0.128937i	$0.0411565\pi$
$331$	0.881971	+	8.39139i	0.0484775	+	0.461233i	−0.943175	+	0.332296i	$0.892177\pi$
$332$	−30.9285	−	8.28727i	−1.69742	−	0.454823i
$333$	−9.35924	+	3.59268i	−0.512883	+	0.196877i
$334$	54.3876	+	11.5604i	2.97596	+	0.632560i
$335$	−11.4312	+	12.1983i	−0.624551	+	0.666465i
$336$	−28.5132	−	15.5304i	−1.55552	−	0.847250i
$337$	−10.0363	+	19.6973i	−0.546710	+	1.07298i	0.438032	+	0.898959i	$0.355676\pi$
$337$	−10.0363	+	19.6973i	−0.546710	+	1.07298i	−0.984742	+	0.174019i	$0.944324\pi$
$338$	−25.8016	+	16.7558i	−1.40342	+	0.911394i
$339$	5.46422	−	1.16146i	0.296776	−	0.0630817i
$340$	−16.7190	−	19.3285i	−0.906715	−	1.04824i
$341$	−3.89225	+	18.3116i	−0.210777	+	0.991628i
$342$	−7.33222	+	46.2938i	−0.396481	+	2.50328i
$343$	−18.0256	+	4.25184i	−0.973290	+	0.229578i
$344$	−16.3478	−	22.5008i	−0.881412	−	1.21316i
$345$	31.4553	+	16.8241i	1.69350	+	0.905782i
$346$	10.2807	+	1.08054i	0.552694	+	0.0580904i
$347$	14.3215	−	11.5973i	0.768817	−	0.622576i	−0.162532	−	0.986703i	$-0.551966\pi$
$347$	14.3215	−	11.5973i	0.768817	−	0.622576i	0.931349	+	0.364128i	$0.118633\pi$
$348$	5.80147	−	110.699i	0.310991	−	5.93407i
$349$	30.5633			1.63602			0.818008	−	0.575207i	$-0.195078\pi$
$349$	30.5633			1.63602			0.818008	+	0.575207i	$0.195078\pi$
$350$	3.87356	−	32.2124i	0.207050	−	1.72182i
$351$	6.07587			0.324306
$352$	−0.0263512	+	0.502810i	−0.00140452	+	0.0267999i
$353$	−19.6438	+	15.9073i	−1.04554	+	0.846658i	−0.988425	−	0.151710i	$-0.951522\pi$
$353$	−19.6438	+	15.9073i	−1.04554	+	0.846658i	−0.0571106	+	0.998368i	$0.518189\pi$
$354$	−8.72369	−	0.916897i	−0.463659	−	0.0487325i
$355$	−3.87417	+	21.6608i	−0.205620	+	1.14963i
$356$	29.2408	+	40.2466i	1.54976	+	2.13306i
$357$	−22.5252	+	1.74274i	−1.19216	+	0.0922356i
$358$	1.67781	−	10.5933i	0.0886749	−	0.559872i
$359$	7.31316	−	34.4057i	0.385974	−	1.81586i	−0.170925	−	0.985284i	$-0.554676\pi$
$359$	7.31316	−	34.4057i	0.385974	−	1.81586i	0.556899	−	0.830580i	$-0.311991\pi$
$360$	−5.61621	−	66.0588i	−0.296000	−	3.48160i
$361$	8.65859	−	1.84044i	0.455715	−	0.0968653i
$362$	−51.0337	+	33.1417i	−2.68227	+	1.74189i
$363$	−0.640556	+	1.25716i	−0.0336205	+	0.0659839i
$364$	−7.17157	+	0.178284i	−0.375892	+	0.00934461i
$365$	−1.43668	+	11.4683i	−0.0751994	+	0.600277i
$366$	−42.1520	−	8.95968i	−2.20332	−	0.468330i
$367$	−2.14770	+	0.824426i	−0.112109	+	0.0430347i	−0.413776	−	0.910379i	$-0.635790\pi$
$367$	−2.14770	+	0.824426i	−0.112109	+	0.0430347i	0.301667	+	0.953413i	$0.402457\pi$
$368$	−21.0133	−	5.63048i	−1.09539	−	0.293509i
$369$	0.649869	+	6.18309i	0.0338308	+	0.321879i
$370$	7.58502	+	5.14327i	0.394327	+	0.267386i
$371$	3.02170	−	10.1517i	0.156879	−	0.527049i
$372$	10.4151	+	65.7584i	0.539998	+	3.40941i
$373$	−13.0628	−	0.684593i	−0.676367	−	0.0354469i	−0.288940	−	0.957347i	$-0.593303\pi$
$373$	−13.0628	−	0.684593i	−0.676367	−	0.0354469i	−0.387427	+	0.921900i	$0.626636\pi$
$374$	11.8221	+	20.4764i	0.611305	+	1.05881i
$375$	29.9951	−	15.0064i	1.54894	−	0.774926i
$376$	11.7884	+	6.80606i	0.607942	+	0.350996i
$377$	−2.82156	−	5.53763i	−0.145318	−	0.285203i
$378$	−49.7379	−	30.5702i	−2.55824	−	1.57236i
$379$	−11.2000	+	15.4155i	−0.575307	+	0.791842i	−0.993171	−	0.116667i	$-0.962779\pi$
$379$	−11.2000	+	15.4155i	−0.575307	+	0.791842i	0.417864	+	0.908510i	$0.362779\pi$
$380$	25.7365	−	12.4745i	1.32025	−	0.639927i
$381$	14.3646	−	32.2634i	0.735920	−	1.65290i
$382$	−9.91592	+	37.0067i	−0.507342	+	1.89343i
$383$	12.9263	−	15.9626i	0.660501	−	0.815650i	−0.331289	−	0.943529i	$-0.607484\pi$
$383$	12.9263	−	15.9626i	0.660501	−	0.815650i	0.991790	+	0.127879i	$0.0408169\pi$
$384$	−18.0480	−	55.5461i	−0.921009	−	2.83457i
$385$	−6.09723	+	19.0863i	−0.310744	+	0.972726i
$386$	−15.5005	+	47.7056i	−0.788954	+	2.42815i
$387$	−18.3875	−	28.3143i	−0.934690	−	1.43930i
$388$	68.0451	−	3.56609i	3.45447	−	0.181041i
$389$	8.14472	+	38.3179i	0.412954	+	1.94279i	0.321193	+	0.947014i	$0.395916\pi$
$389$	8.14472	+	38.3179i	0.412954	+	1.94279i	0.0917605	+	0.995781i	$0.470751\pi$
$390$	−6.35006	−	9.11632i	−0.321548	−	0.461623i
$391$	−14.3966	+	4.67775i	−0.728069	+	0.236564i
$392$	29.9143	+	17.3769i	1.51090	+	0.877667i
$393$	29.0818	−	29.0818i	1.46698	−	1.46698i
$394$	33.2511	−	3.49483i	1.67517	−	0.176067i
$395$	5.72988	−	6.79469i	0.288301	−	0.341878i
$396$	−8.52729	+	81.1317i	−0.428512	+	4.07702i
$397$	5.42600	−	14.1352i	0.272323	−	0.709426i	−0.727407	−	0.686206i	$-0.759275\pi$
$397$	5.42600	−	14.1352i	0.272323	−	0.709426i	0.999730	−	0.0232199i	$-0.00739178\pi$
$398$	47.7112	−	24.3101i	2.39155	−	1.21855i
$399$	4.64053	−	24.8542i	0.232317	−	1.24427i
$400$	−15.7330	+	13.0706i	−0.786650	+	0.653531i
$401$	11.4812	−	19.8860i	0.573343	−	0.993059i	−0.422877	−	0.906187i	$-0.638980\pi$
$401$	11.4812	−	19.8860i	0.573343	−	0.993059i	0.996220	−	0.0868716i	$-0.0276870\pi$
$402$	29.9581	−	46.1315i	1.49418	−	2.30083i
$403$	2.34914	+	2.90094i	0.117019	+	0.144506i
$404$	−7.97798	+	3.55203i	−0.396920	+	0.176720i
$405$	−0.652487	−	20.0976i	−0.0324224	−	0.998660i
$406$	−4.76437	+	59.5283i	−0.236452	+	2.95434i
$407$	−4.00193	−	4.00193i	−0.198368	−	0.198368i
$408$	32.7972	+	26.5586i	1.62370	+	1.31485i
$409$	−15.3308	+	17.0266i	−0.758059	+	0.841910i	−0.991452	−	0.130473i	$-0.958350\pi$
$409$	−15.3308	+	17.0266i	−0.758059	+	0.841910i	0.233393	+	0.972383i	$0.425017\pi$
$410$	4.29842	−	3.71809i	0.212284	−	0.183624i
$411$	−29.9047	+	26.9263i	−1.47509	+	1.32818i
$412$	8.83804	+	4.50320i	0.435419	+	0.221857i
$413$	3.12683	+	0.415871i	0.153861	+	0.0204637i
$414$	−74.4149	−	24.1789i	−3.65729	−	1.18833i
$415$	5.17179	+	17.0657i	0.253873	+	0.837724i
$416$	0.0746085	+	0.0671778i	0.00365798	+	0.00329366i
$417$	10.7251	+	27.9398i	0.525209	+	1.36822i
$418$	−25.5589	+	6.84850i	−1.25013	+	0.334971i
$419$	−25.0790	+	18.2210i	−1.22519	+	0.890153i	−0.996520	−	0.0833506i	$-0.973438\pi$
$419$	−25.0790	+	18.2210i	−1.22519	+	0.890153i	−0.228671	+	0.973504i	$0.573438\pi$
$420$	4.08148	+	71.1407i	0.199156	+	3.47131i
$421$	−18.7028	−	13.5884i	−0.911518	−	0.662257i	0.0298801	−	0.999553i	$-0.490487\pi$
$421$	−18.7028	−	13.5884i	−0.911518	−	0.662257i	−0.941398	+	0.337297i	$0.890487\pi$
$422$	20.0852	+	7.71000i	0.977734	+	0.375317i
$423$	13.8577	+	8.99932i	0.673786	+	0.437562i
$424$	−17.1345	+	9.89259i	−0.832124	+	0.480427i
$425$	−4.22791	+	13.5901i	−0.205084	+	0.659219i
$426$		−	72.4019i		−	3.50788i
$427$	15.0637	+	3.63760i	0.728985	+	0.176036i
$428$	7.09684	−	1.12403i	0.343039	−	0.0543320i
$429$	2.79066	+	6.26792i	0.134734	+	0.302618i
$430$	−11.6314	+	28.5866i	−0.560914	+	1.37857i
$431$	−4.05026	−	1.80329i	−0.195094	−	0.0868615i	0.306864	−	0.951753i	$-0.400720\pi$
$431$	−4.05026	−	1.80329i	−0.195094	−	0.0868615i	−0.501958	+	0.864892i	$0.667387\pi$
$432$	9.52600	+	35.5515i	0.458320	+	1.71047i
$433$	−23.2113	−	3.67631i	−1.11546	−	0.176672i	−0.428626	−	0.903482i	$-0.641002\pi$
$433$	−23.2113	−	3.67631i	−1.11546	−	0.176672i	−0.686839	+	0.726810i	$0.741002\pi$
$434$	−4.63454	−	35.5670i	−0.222465	−	1.70727i
$435$	−54.0673	+	29.7969i	−2.59233	+	1.42865i
$436$	6.60410	+	7.33460i	0.316279	+	0.351264i
$437$	−0.886605	−	16.9174i	−0.0424120	−	0.809270i
$438$	−1.99030	−	37.9771i	−0.0951000	−	1.81462i
$439$	−21.8140	−	24.2270i	−1.04113	−	1.15629i	−0.987482	−	0.157729i	$-0.949583\pi$
$439$	−21.8140	−	24.2270i	−1.04113	−	1.15629i	−0.0536454	−	0.998560i	$-0.517084\pi$
$440$	32.7792	−	18.0649i	1.56269	−	0.861209i
$441$	35.1586	+	22.9650i	1.67422	+	1.09357i
$442$	4.65650	+	0.737516i	0.221487	+	0.0350801i
$443$	−1.59298	−	5.94509i	−0.0756849	−	0.282460i	0.917703	−	0.397267i	$-0.130041\pi$
$443$	−1.59298	−	5.94509i	−0.0756849	−	0.282460i	−0.993388	+	0.114808i	$0.963375\pi$
$444$	−18.3876	−	8.18667i	−0.872635	−	0.388522i
$445$	10.4415	−	25.6622i	0.494974	−	1.21651i
$446$	−8.92861	−	20.0540i	−0.422782	−	0.949583i
$447$	−68.6588	+	10.8745i	−3.24745	+	0.514346i
$448$	5.84768	+	19.8379i	0.276277	+	0.937255i
$449$			11.7708i			0.555497i	0.960654	+	0.277748i	$0.0895882\pi$
$449$			11.7708i			0.555497i	−0.960654	+	0.277748i	$0.910412\pi$
$450$	−58.9697	+	43.9851i	−2.77986	+	2.07348i
$451$	−3.03961	+	1.75492i	−0.143130	+	0.0826359i
$452$	6.27061	+	4.07218i	0.294945	+	0.191539i
$453$	24.6253	+	9.45276i	1.15700	+	0.444129i
$454$	33.4173	+	24.2791i	1.56835	+	1.13948i
$455$	2.19249	+	3.33984i	0.102786	+	0.156574i
$456$	−38.2090	+	27.7605i	−1.78930	+	1.30000i
$457$	−7.83968	+	2.10064i	−0.366725	+	0.0982637i	−0.437475	−	0.899230i	$-0.644127\pi$
$457$	−7.83968	+	2.10064i	−0.366725	+	0.0982637i	0.0707504	+	0.997494i	$0.477461\pi$
$458$	−0.0562112	−	0.146435i	−0.00262658	−	0.00684247i
$459$	19.0324	+	17.1368i	0.888355	+	0.799879i
$460$	13.8471	+	45.6922i	0.645623	+	2.13041i
$461$	10.6651	+	3.46531i	0.496724	+	0.161395i	0.546656	−	0.837357i	$-0.315900\pi$
$461$	10.6651	+	3.46531i	0.496724	+	0.161395i	−0.0499320	+	0.998753i	$0.515900\pi$
$462$	8.69175	−	65.3510i	0.404377	−	3.04041i
$463$	4.85570	+	2.47410i	0.225664	+	0.114981i	0.563167	−	0.826343i	$-0.309583\pi$
$463$	4.85570	+	2.47410i	0.225664	+	0.114981i	−0.337504	+	0.941324i	$0.609583\pi$
$464$	27.9784	−	25.1919i	1.29886	−	1.16950i
$465$	28.0429	−	24.2569i	1.30046	−	1.12489i
$466$	−30.4666	+	33.8365i	−1.41134	+	1.56745i
$467$	−5.72965	−	4.63978i	−0.265136	−	0.214703i	0.487528	−	0.873107i	$-0.337899\pi$
$467$	−5.72965	−	4.63978i	−0.265136	−	0.214703i	−0.752665	+	0.658404i	$0.771232\pi$
$468$	11.5021	+	11.5021i	0.531684	+	0.531684i
$469$	−11.2253	+	16.2866i	−0.518334	+	0.752044i
$470$	−0.490132	−	15.0968i	−0.0226081	−	0.696365i
$471$	−36.2180	+	16.1253i	−1.66884	+	0.743014i
$472$	−3.70811	−	4.57913i	−0.170679	−	0.210771i
$473$	10.3805	−	15.9846i	0.477297	−	0.734972i
$474$	−14.6224	+	25.3268i	−0.671631	+	1.16330i
$475$	−13.4661	−	8.50667i	−0.617867	−	0.390313i
$476$	−22.9675	−	19.6688i	−1.05271	−	0.901516i
$477$	−21.3991	+	10.9034i	−0.979799	+	0.499232i
$478$	5.76743	−	15.0247i	0.263796	−	0.687212i
$479$	−1.04715	+	9.96298i	−0.0478456	+	0.455220i	0.944203	+	0.329364i	$0.106834\pi$
$479$	−1.04715	+	9.96298i	−0.0478456	+	0.455220i	−0.992049	+	0.125856i	$0.959832\pi$
$480$	0.642882	−	0.762353i	0.0293434	−	0.0347965i
$481$	−1.12231	+	0.117960i	−0.0511731	+	0.00537851i
$482$	−7.65128	+	7.65128i	−0.348506	+	0.348506i
$483$	39.7679	+	14.1419i	1.80950	+	0.643479i
$484$	−1.79602	+	0.583562i	−0.0816372	+	0.0265255i
$485$	−21.6894	−	31.1379i	−0.984866	−	1.41390i
$486$	−0.00747327	−	0.0351590i	−0.000338994	−	0.00159484i
$487$	−18.5946	+	0.974503i	−0.842603	+	0.0441589i	−0.468752	−	0.883330i	$-0.655296\pi$
$487$	−18.5946	+	0.974503i	−0.842603	+	0.0441589i	−0.373851	+	0.927489i	$0.621963\pi$
$488$	−15.7658	−	24.2773i	−0.713686	−	1.09898i
$489$	11.1080	−	34.1869i	0.502321	−	1.54598i
$490$	−1.14397	−	38.3717i	−0.0516792	−	1.73346i
$491$	3.16161	+	9.73045i	0.142682	+	0.439129i	0.996706	−	0.0811048i	$-0.0258448\pi$
$491$	3.16161	+	9.73045i	0.142682	+	0.439129i	−0.854024	+	0.520234i	$0.825845\pi$
$492$	−7.85541	+	9.70062i	−0.354149	+	0.437338i
$493$	6.78033	−	25.3045i	0.305371	−	1.13966i
$494$	−2.14599	+	4.81997i	−0.0965526	+	0.216861i
$495$	40.8831	−	19.8160i	1.83756	−	0.890665i
$496$	−13.2911	+	18.2936i	−0.596789	+	0.821409i
$497$	−0.716037	+	26.0262i	−0.0321187	+	1.16744i
$498$	−26.6372	−	52.2785i	−1.19364	−	2.34266i
$499$	−8.93457	−	5.15838i	−0.399966	−	0.230921i	0.286503	−	0.958079i	$-0.407507\pi$
$499$	−8.93457	−	5.15838i	−0.399966	−	0.230921i	−0.686470	+	0.727159i	$0.740840\pi$
$500$	42.5899	+	14.1855i	1.90468	+	0.634395i
$501$	34.0053	+	58.8988i	1.51924	+	2.63141i
$502$	−11.4290	−	0.598967i	−0.510100	−	0.0267332i
$503$	4.07688	+	25.7404i	0.181779	+	1.14771i	0.894768	+	0.446532i	$0.147341\pi$
$503$	4.07688	+	25.7404i	0.181779	+	1.14771i	−0.712989	+	0.701176i	$0.752659\pi$
$504$	−18.2112	−	76.3006i	−0.811193	−	3.39870i
$505$	4.02537	+	2.72953i	0.179127	+	0.121463i
$506$	−4.61726	−	43.9303i	−0.205262	−	1.95294i
$507$	−36.3479	−	9.73940i	−1.61427	−	0.432542i
$508$	44.1292	−	16.9396i	1.95792	−	0.751574i
$509$	−10.6675	−	2.26746i	−0.472831	−	0.100503i	−0.0346678	−	0.999399i	$-0.511037\pi$
$509$	−10.6675	−	2.26746i	−0.472831	−	0.100503i	−0.438163	+	0.898896i	$0.644371\pi$
$510$	5.82108	−	46.4666i	0.257762	−	2.05758i
$511$	0.339866	+	13.6713i	0.0150348	+	0.604782i
$512$	18.0810	−	35.4859i	0.799074	−	1.56827i
$513$	−24.0373	+	15.6100i	−1.06127	+	0.689199i
$514$	17.3915	−	3.69667i	0.767106	−	0.163053i
$515$	−0.467964	−	5.50427i	−0.0206210	−	0.242547i
$516$	14.0928	−	66.3016i	0.620403	−	2.91877i
$517$	−1.45925	+	9.21333i	−0.0641776	+	0.405202i
$518$	9.78093	+	4.68119i	0.429749	+	0.205679i
$519$	7.43202	+	10.2293i	0.326230	+	0.449017i
$520$	1.31393	−	7.34629i	0.0576197	−	0.322156i
$521$	−20.6341	−	2.16873i	−0.903996	−	0.0950138i	−0.358889	−	0.933380i	$-0.616844\pi$
$521$	−20.6341	−	2.16873i	−0.903996	−	0.0950138i	−0.545107	+	0.838367i	$0.683511\pi$
$522$	105.234	−	85.2168i	4.60597	−	3.72984i
$523$	−0.218055	+	4.16073i	−0.00953487	+	0.181936i	0.989710	+	0.143086i	$0.0457027\pi$
$523$	−0.218055	+	4.16073i	−0.00953487	+	0.181936i	−0.999245	+	0.0388497i	$0.987631\pi$
$524$	55.0466			2.40472
$525$	32.4507	−	22.8432i	1.41626	−	0.996958i
$526$	27.4702			1.19776
$527$	−0.823471	+	15.7128i	−0.0358709	+	0.684458i
$528$	−32.2999	+	26.1560i	−1.40567	+	1.13829i
$529$	5.25113	+	0.551916i	0.228310	+	0.0239964i
$530$	19.3596	+	10.3547i	0.840927	+	0.449777i
$531$	−4.20411	−	5.78646i	−0.182443	−	0.251111i
$532$	27.9141	−	19.1304i	1.21023	−	0.829408i
$533$	−0.109480	+	0.691230i	−0.00474211	+	0.0299405i
$534$	−18.9530	+	89.1667i	−0.820175	+	3.85862i
$535$	−2.61787	−	3.02648i	−0.113181	−	0.130846i
$536$	36.1414	−	7.68209i	1.56107	−	0.331816i
$537$	11.0023	−	7.14495i	0.474782	−	0.308327i
$538$	7.94707	−	15.5970i	0.342622	−	0.672434i
$539$	−3.77072	+	23.4057i	−0.162417	+	1.00816i
$540$	55.2343	−	58.9411i	2.37690	−	2.53642i
$541$	1.83101	+	0.389192i	0.0787211	+	0.0167327i	0.247104	−	0.968989i	$-0.420521\pi$
$541$	1.83101	+	0.389192i	0.0787211	+	0.0167327i	−0.168383	+	0.985722i	$0.553854\pi$
$542$	−39.6354	+	15.2146i	−1.70249	+	0.653524i
$543$	−71.8935	−	19.2638i	−3.08525	−	0.826689i
$544$	0.0442345	+	0.420863i	0.00189654	+	0.0180443i
$545$	1.52801	−	5.27991i	0.0654528	−	0.226167i
$546$	−9.03608	−	9.54735i	−0.386709	−	0.408589i
$547$	−1.28862	−	8.13603i	−0.0550974	−	0.347871i	−0.999801	−	0.0199460i	$-0.993651\pi$
$547$	−1.28862	−	8.13603i	−0.0550974	−	0.347871i	0.944704	−	0.327925i	$-0.106349\pi$
$548$	−53.7855	−	2.81878i	−2.29760	−	0.120412i
$549$	−17.5692	−	30.4308i	−0.749837	−	1.29876i
$550$	−36.2252	−	20.3129i	−1.54465	−	0.866143i
$551$	25.3899	+	14.6588i	1.08164	+	0.624488i
$552$	−35.7936	−	70.2490i	−1.52348	−	2.98999i
$553$	5.50679	−	8.95960i	0.234173	−	0.381001i
$554$	20.3901	−	28.0646i	0.866294	−	1.19235i
$555$	1.53283	+	11.1041i	0.0650648	+	0.471344i
$556$	−16.2922	+	36.5928i	−0.690942	+	1.55188i
$557$	−0.506336	+	1.88967i	−0.0214541	+	0.0800679i	−0.975823	−	0.218563i	$-0.929863\pi$
$557$	−0.506336	+	1.88967i	−0.0214541	+	0.0800679i	0.954369	+	0.298631i	$0.0965298\pi$
$558$	−51.1822	+	63.2047i	−2.16671	+	2.67567i
$559$	−1.17438	−	3.61436i	−0.0496709	−	0.152871i
$560$	−16.1048	+	18.0652i	−0.680552	+	0.763394i
$561$	−8.93690	+	27.5049i	−0.377316	+	1.16126i
$562$	13.7621	+	21.1918i	0.580519	+	0.893921i
$563$	−33.0391	+	1.73151i	−1.39243	+	0.0729743i	−0.733736	−	0.679434i	$-0.762225\pi$
$563$	−33.0391	+	1.73151i	−1.39243	+	0.0729743i	−0.658697	+	0.752409i	$0.728892\pi$
$564$	6.89739	+	32.4497i	0.290433	+	1.36638i
$565$	0.0828800	−	4.16314i	0.00348679	−	0.175145i
$566$	−6.87462	+	2.23370i	−0.288962	+	0.0938894i
$567$	−4.30481	−	23.3997i	−0.180785	−	0.982695i
$568$	34.3898	−	34.3898i	1.44296	−	1.44296i
$569$	22.9184	−	2.40883i	0.960791	−	0.100983i	0.388871	−	0.921292i	$-0.372865\pi$
$569$	22.9184	−	2.40883i	0.960791	−	0.100983i	0.571920	+	0.820309i	$0.306199\pi$
$570$	48.5436	+	19.7515i	2.03327	+	0.827298i
$571$	1.93329	−	18.3940i	0.0809057	−	0.769766i	−0.876574	−	0.481267i	$-0.840177\pi$
$571$	1.93329	−	18.3940i	0.0809057	−	0.769766i	0.957480	−	0.288500i	$-0.0931565\pi$
$572$	−3.29091	+	8.57313i	−0.137600	+	0.358460i
$573$	−41.7540	+	21.2747i	−1.74430	+	0.888764i
$574$	4.37408	−	5.10767i	0.182571	−	0.213190i
$575$	17.5425	−	19.9816i	0.731572	−	0.833289i
$576$	23.4478	−	40.6129i	0.976993	−	1.69220i
$577$	14.6287	−	22.5262i	0.609000	−	0.937779i	−0.390849	−	0.920455i	$-0.627819\pi$
$577$	14.6287	−	22.5262i	0.609000	−	0.937779i	0.999850	−	0.0173239i	$-0.00551464\pi$
$578$	−13.7326	−	16.9583i	−0.571200	−	0.705373i
$579$	−56.0497	+	24.9549i	−2.32935	+	1.03709i
$580$	−79.3699	−	22.9697i	−3.29566	−	0.953766i
$581$	9.05824	+	19.0560i	0.375799	+	0.790574i
$582$	88.2886	+	88.2886i	3.65968	+	3.65968i
$583$	−10.5369	−	8.53263i	−0.436394	−	0.353385i
$584$	17.0932	−	18.9839i	0.707321	−	0.785559i
$585$	2.05947	−	8.82180i	0.0851487	−	0.364737i
$586$	19.0426	−	17.1461i	0.786644	−	0.708298i
$587$	0.477303	+	0.243198i	0.0197004	+	0.0100379i	0.463813	−	0.885933i	$-0.346481\pi$
$587$	0.477303	+	0.243198i	0.0197004	+	0.0100379i	−0.444113	+	0.895971i	$0.646481\pi$
$588$	17.3111	+	82.5170i	0.713896	+	3.40294i
$589$	−16.7467	−	5.44133i	−0.690036	−	0.224206i
$590$	−2.14384	+	6.17691i	−0.0882604	+	0.254299i
$591$	30.3910	+	27.3642i	1.25012	+	1.12561i
$592$	−2.44982	−	6.38201i	−0.100687	−	0.262299i
$593$	16.6711	−	4.46701i	0.684600	−	0.183438i	0.100277	−	0.994960i	$-0.468027\pi$
$593$	16.6711	−	4.46701i	0.684600	−	0.183438i	0.584323	+	0.811521i	$0.301360\pi$
$594$	−60.4605	+	43.9272i	−2.48073	+	1.80235i
$595$	−2.55204	+	16.6458i	−0.104624	+	0.682410i
$596$	−75.2712	−	54.6877i	−3.08323	−	2.24010i
$597$	61.1465	+	23.4720i	2.50256	+	0.960643i
$598$	−7.38680	−	4.79704i	−0.302069	−	0.196166i
$599$	8.98779	−	5.18910i	0.367231	−	0.212021i	−0.305017	−	0.952347i	$-0.598662\pi$
$599$	8.98779	−	5.18910i	0.367231	−	0.212021i	0.672248	+	0.740326i	$0.265329\pi$
$600$	−73.3562	−	10.6767i	−2.99476	−	0.435873i
$601$			15.2610i			0.622508i	0.950327	+	0.311254i	$0.100749\pi$
$601$			15.2610i			0.622508i	−0.950327	+	0.311254i	$0.899251\pi$
$602$	−8.57172	+	35.4965i	−0.349357	+	1.44673i
$603$	44.2991	−	7.01629i	1.80400	−	0.285726i
$604$	14.3594	+	32.2518i	0.584277	+	1.31231i
$605$	0.803992	+	0.677996i	0.0326869	+	0.0275644i
$606$	−14.6191	−	6.50883i	−0.593859	−	0.264403i
$607$	−2.31963	−	8.65699i	−0.0941510	−	0.351376i	0.902738	−	0.430190i	$-0.141553\pi$
$607$	−2.31963	−	8.65699i	−0.0941510	−	0.351376i	−0.996889	+	0.0788137i	$0.974887\pi$
$608$	−0.467758	−	0.0740856i	−0.0189701	−	0.00300457i
$609$	−58.0094	+	44.3901i	−2.35066	+	1.79878i
$610$	−13.6465	+	29.0787i	−0.552531	+	1.17736i
$611$	1.24458	+	1.38225i	0.0503503	+	0.0559197i
$612$	3.58842	+	68.4711i	0.145053	+	2.76778i
$613$	−0.865859	−	16.5216i	−0.0349717	−	0.667300i	−0.958729	−	0.284322i	$-0.908232\pi$
$613$	−0.865859	−	16.5216i	−0.0349717	−	0.667300i	0.923757	−	0.382979i	$-0.125102\pi$
$614$	44.8028	+	49.7586i	1.80809	+	2.00809i
$615$	6.89770	+	0.864105i	0.278142	+	0.0348441i
$616$	35.1692	−	26.9123i	1.41701	−	1.08433i
$617$	−20.5016	−	3.24713i	−0.825362	−	0.130725i	−0.270556	−	0.962704i	$-0.587208\pi$
$617$	−20.5016	−	3.24713i	−0.825362	−	0.130725i	−0.554806	+	0.831980i	$0.687208\pi$
$618$	4.70433	+	17.5568i	0.189236	+	0.706238i
$619$	40.5114	+	18.0368i	1.62829	+	0.724962i	0.998651	−	0.0519243i	$-0.0165354\pi$
$619$	40.5114	+	18.0368i	1.62829	+	0.724962i	0.629641	+	0.776886i	$0.283202\pi$
$620$	49.4971	+	3.58316i	1.98785	+	0.143903i
$621$	−19.4607	−	43.7094i	−0.780931	−	1.75400i
$622$	3.16706	−	0.501613i	0.126988	−	0.0201128i
$623$	7.69484	−	31.8652i	0.308287	−	1.27665i
$624$			8.28732i			0.331758i
$625$	−5.80983	−	24.3155i	−0.232393	−	0.972622i
$626$	29.8231	−	17.2184i	1.19197	−	0.688185i
$627$	−27.1438	−	17.6274i	−1.08402	−	0.703970i
$628$	−49.5382	−	19.0159i	−1.97679	−	0.758818i
$629$	−3.84830	−	2.79595i	−0.153442	−	0.111482i
$630$	−61.2453	+	61.8545i	−2.44007	+	2.46434i
$631$	39.2726	−	28.5332i	1.56342	−	1.13589i	0.630281	−	0.776367i	$-0.282940\pi$
$631$	39.2726	−	28.5332i	1.56342	−	1.13589i	0.933136	−	0.359523i	$-0.117060\pi$
$632$	−18.9753	+	5.08441i	−0.754796	+	0.202247i
$633$	9.43049	+	24.5673i	0.374828	+	0.976462i
$634$	53.1251	+	47.8340i	2.10987	+	1.89973i
$635$	−20.9849	−	15.8941i	−0.832762	−	0.630738i
$636$	−45.8592	−	14.9006i	−1.81844	−	0.590846i
$637$	3.15377	+	3.52134i	0.124957	+	0.139521i
$638$	68.1130	+	34.7053i	2.69662	+	1.37400i
$639$	43.8725	−	39.5030i	1.73557	−	1.56271i
$640$	−43.3777	+	3.68790i	−1.71465	+	0.145777i
$641$	−17.0972	+	18.9883i	−0.675297	+	0.749994i	−0.979242	−	0.202696i	$-0.935030\pi$
$641$	−17.0972	+	18.9883i	−0.675297	+	0.749994i	0.303944	+	0.952690i	$0.401696\pi$
$642$	10.2323	+	8.28597i	0.403838	+	0.327021i
$643$	8.37217	+	8.37217i	0.330166	+	0.330166i	0.852650	−	0.522483i	$-0.174994\pi$
$643$	8.37217	+	8.37217i	0.330166	+	0.330166i	−0.522483	+	0.852650i	$0.674994\pi$
$644$	24.2527	+	51.0208i	0.955692	+	2.01050i
$645$	−35.5043	+	12.8240i	−1.39798	+	0.504944i
$646$	−20.3168	+	9.04563i	−0.799355	+	0.355896i
$647$	−14.7539	−	18.2196i	−0.580038	−	0.716287i	0.399683	−	0.916653i	$-0.369120\pi$
$647$	−14.7539	−	18.2196i	−0.580038	−	0.716287i	−0.979721	+	0.200366i	$0.935787\pi$
$648$	−24.2055	+	37.2733i	−0.950883	+	1.46423i
$649$	2.01893	−	3.49689i	0.0792499	−	0.137265i
$650$	−7.69334	+	3.06451i	−0.301758	+	0.120200i
$651$	28.5365	−	33.3225i	1.11844	−	1.30601i
$652$	42.8675	−	21.8421i	1.67882	−	0.855403i
$653$	−6.61869	+	17.2423i	−0.259009	+	0.674743i	0.740985	+	0.671521i	$0.234359\pi$
$653$	−6.61869	+	17.2423i	−0.259009	+	0.674743i	−0.999995	+	0.00322157i	$0.998975\pi$
$654$	−1.89045	+	17.9864i	−0.0739223	+	0.703324i
$655$	−16.1816	−	26.0378i	−0.632266	−	1.01738i
$656$	−4.21622	+	0.443142i	−0.164616	+	0.0173018i
$657$	21.9266	−	21.9266i	0.855439	−	0.855439i
$658$	−3.23366	−	17.5773i	−0.126061	−	0.685233i
$659$	41.0738	−	13.3457i	1.60001	−	0.519875i	0.632899	−	0.774234i	$-0.281865\pi$
$659$	41.0738	−	13.3457i	1.60001	−	0.519875i	0.967110	+	0.254359i	$0.0818646\pi$
$660$	86.1733	+	29.9084i	3.35429	+	1.16418i
$661$	−0.780289	−	3.67097i	−0.0303497	−	0.142784i	0.960364	−	0.278749i	$-0.0899198\pi$
$661$	−0.780289	−	3.67097i	−0.0303497	−	0.142784i	−0.990714	+	0.135965i	$0.956587\pi$
$662$	−20.6655	+	1.08303i	−0.803187	+	0.0420932i
$663$	3.14071	+	4.83627i	0.121975	+	0.187825i
$664$	12.1792	−	37.4837i	0.472645	−	1.45465i
$665$	−17.2546	−	7.58013i	−0.669104	−	0.293945i
$666$	−7.59788	−	23.3839i	−0.294412	−	0.906107i
$667$	−30.8001	+	38.0349i	−1.19258	+	1.47272i
$668$	−23.5595	+	87.9254i	−0.911546	+	3.40194i
$669$	10.9210	−	24.5291i	0.422232	−	0.948348i
$670$	−28.4089	−	29.5630i	−1.09753	−	1.14212i
$671$	11.6600	−	16.0486i	0.450128	−	0.619548i
$672$	0.617853	−	1.00525i	0.0238342	−	0.0387784i
$673$	13.3247	+	26.1511i	0.513628	+	1.00805i	0.991559	+	0.129654i	$0.0413868\pi$
$673$	13.3247	+	26.1511i	0.513628	+	1.00805i	−0.477931	+	0.878397i	$0.658613\pi$
$674$	−46.9545	−	27.1092i	−1.80862	−	1.04421i
$675$	−44.1166	−	8.80015i	−1.69805	−	0.338718i
$676$	−25.1826	−	43.6175i	−0.968562	−	1.67760i
$677$	9.67944	+	0.507278i	0.372011	+	0.0194963i	0.237426	−	0.971406i	$-0.423696\pi$
$677$	9.67944	+	0.507278i	0.372011	+	0.0194963i	0.134585	+	0.990902i	$0.457030\pi$
$678$	2.14327	+	13.5321i	0.0823120	+	0.519697i
$679$	−30.8639	−	32.6102i	−1.18445	−	1.25146i
$680$	24.8358	−	19.3060i	0.952411	−	0.740351i
$681$	5.28116	+	50.2469i	0.202374	+	1.92546i
$682$	−44.3493	−	11.8834i	−1.69822	−	0.455037i
$683$	−21.9187	+	8.41379i	−0.838694	+	0.321945i	−0.739528	−	0.673126i	$-0.764951\pi$
$683$	−21.9187	+	8.41379i	−0.838694	+	0.321945i	−0.0991667	+	0.995071i	$0.531618\pi$
$684$	−75.0555	−	15.9535i	−2.86982	−	0.609999i
$685$	14.4775	+	26.2698i	0.553158	+	1.00372i
$686$	−8.09991	−	44.6942i	−0.309256	−	1.70643i
$687$	0.0871006	−	0.170944i	0.00332309	−	0.00652194i
$688$	19.3074	−	12.5383i	0.736086	−	0.478020i
$689$	−2.64442	+	0.562089i	−0.100744	+	0.0214139i
$690$	−45.2434	+	74.8811i	−1.72239	+	2.85067i
$691$	6.20027	−	29.1700i	0.235869	−	1.10968i	−0.687625	−	0.726066i	$-0.741347\pi$
$691$	6.20027	−	29.1700i	0.235869	−	1.10968i	0.923494	−	0.383612i	$-0.125320\pi$
$692$	−2.64737	+	16.7149i	−0.100638	+	0.635404i
$693$	44.3423	−	30.3892i	1.68442	−	1.15439i
$694$	26.5659	+	36.5649i	1.00843	+	1.38798i
$695$	22.0981	−	3.05045i	0.838230	−	0.115710i
$696$	135.698	+	14.2624i	5.14362	+	0.540616i
$697$	−2.29254	+	1.85646i	−0.0868360	+	0.0703184i
$698$	−3.92303	+	74.8559i	−0.148489	+	2.83334i
$699$	−55.6920			−2.10646
$700$	52.3307	+	9.09263i	1.97791	+	0.343669i
$701$	−51.6850			−1.95212			−0.976058	−	0.217508i	$-0.930207\pi$
$701$	−51.6850			−1.95212			−0.976058	+	0.217508i	$0.930207\pi$
$702$	−0.779884	+	14.8811i	−0.0294348	+	0.561650i
$703$	4.13703	−	3.35010i	0.156031	−	0.126351i
$704$	26.3295	+	2.76734i	0.992331	+	0.104298i
$705$	13.3216	−	12.8015i	0.501719	−	0.482132i
$706$	−36.4388	−	50.1537i	−1.37139	−	1.88756i
$707$	5.19074	+	2.48430i	0.195218	+	0.0934319i
$708$	2.24643	−	14.1834i	0.0844260	−	0.533045i
$709$	1.56789	−	7.37635i	0.0588834	−	0.277025i	−0.938849	−	0.344329i	$-0.888106\pi$
$709$	1.56789	−	7.37635i	0.0588834	−	0.277025i	0.997732	+	0.0673043i	$0.0214398\pi$
$710$	−52.5545	−	12.2690i	−1.97233	−	0.460446i
$711$	−23.3251	+	4.95790i	−0.874760	+	0.185936i
$712$	−51.3551	+	33.3504i	−1.92462	+	1.24986i
$713$	13.3451	−	26.1911i	0.499776	−	0.980866i
$714$	−1.37705	−	55.3927i	−0.0515349	−	2.07302i
$715$	5.02260	−	0.963519i	0.187835	−	0.0360336i
$716$	17.1747	+	3.65059i	0.641849	+	0.136429i
$717$	18.3774	−	7.05444i	0.686318	−	0.263453i
$718$	83.3281	+	22.3277i	3.10978	+	0.833262i
$719$	1.32961	+	12.6504i	0.0495861	+	0.471780i	0.990935	+	0.134345i	$0.0428929\pi$
$719$	1.32961	+	12.6504i	0.0495861	+	0.471780i	−0.941349	+	0.337436i	$0.890440\pi$
$720$	54.8476	−	1.78068i	2.04405	−	0.0663619i
$721$	−1.51743	−	6.35766i	−0.0565121	−	0.236772i
$722$	3.39623	+	21.4429i	0.126394	+	0.798023i
$723$	−13.2170	−	0.692675i	−0.491547	−	0.0257609i
$724$	−49.8093	−	86.2722i	−1.85115	−	3.20628i
$725$	12.4667	+	44.2952i	0.463001	+	1.64508i
$726$	−2.99683	−	1.73022i	−0.111223	−	0.0642145i
$727$	−2.99184	−	5.87181i	−0.110961	−	0.217774i	0.828848	−	0.559474i	$-0.188997\pi$
$727$	−2.99184	−	5.87181i	−0.110961	−	0.217774i	−0.939809	+	0.341701i	$0.888997\pi$
$728$	0.242845	−	8.82684i	0.00900044	−	0.327145i
$729$	15.8831	−	21.8612i	0.588264	−	0.809676i
$730$	−27.9038	−	4.99077i	−1.03277	−	0.184717i
$731$	6.51553	−	14.6341i	0.240986	−	0.541263i
$732$	18.2593	−	68.1447i	0.674884	−	2.51870i
$733$	25.1012	−	30.9974i	0.927135	−	1.14492i	−0.0620254	−	0.998075i	$-0.519756\pi$
$733$	25.1012	−	30.9974i	0.927135	−	1.14492i	0.989160	−	0.146841i	$-0.0469107\pi$
$734$	−1.74352	−	5.36599i	−0.0643544	−	0.198062i
$735$	33.9428	−	32.4451i	1.25200	−	1.19676i
$736$	0.244306	−	0.751896i	0.00900524	−	0.0277153i
$737$	13.7905	+	21.2355i	0.507979	+	0.782220i
$738$	−15.2271	+	0.798019i	−0.560517	+	0.0293755i
$739$	−6.76642	−	31.8335i	−0.248907	−	1.17101i	−0.908005	−	0.418958i	$-0.862395\pi$
$739$	−6.76642	−	31.8335i	−0.248907	−	1.17101i	0.659099	−	0.752057i	$-0.270938\pi$
$740$	−9.05837	+	11.9597i	−0.332992	+	0.439649i
$741$	−6.13763	+	1.99424i	−0.225472	+	0.0732602i
$742$	24.4757	+	8.70383i	0.898532	+	0.319528i
$743$	−30.1810	+	30.1810i	−1.10723	+	1.10723i	−0.113722	+	0.993513i	$0.536277\pi$
$743$	−30.1810	+	30.1810i	−1.10723	+	1.10723i	−0.993513	+	0.113722i	$0.963723\pi$
$744$	−81.5017	+	8.56617i	−2.98800	+	0.314051i
$745$	−3.74120	+	51.6803i	−0.137067	+	1.89342i
$746$	3.35342	−	31.9057i	0.122778	−	1.16815i
$747$	17.1451	−	44.6646i	0.627308	−	1.63419i
$748$	−34.4889	+	17.5730i	−1.26104	+	0.642532i
$749$	−3.59626	−	3.07975i	−0.131405	−	0.112532i
$750$	32.9036	+	75.3905i	1.20147	+	2.75287i
$751$	−3.97735	+	6.88897i	−0.145136	+	0.251382i	−0.929424	−	0.369015i	$-0.879695\pi$
$751$	−3.97735	+	6.88897i	−0.145136	+	0.251382i	0.784288	+	0.620397i	$0.213028\pi$
$752$	−6.13658	+	9.44951i	−0.223778	+	0.344588i
$753$	−8.80957	−	10.8789i	−0.321038	−	0.396449i
$754$	13.9250	−	6.19980i	0.507118	−	0.225783i
$755$	11.0344	−	16.2730i	0.401583	−	0.592234i
$756$	54.2393	−	78.6951i	1.97267	−	2.86211i
$757$	−13.7537	−	13.7537i	−0.499888	−	0.499888i	0.411515	−	0.911403i	$-0.365000\pi$
$757$	−13.7537	−	13.7537i	−0.499888	−	0.499888i	−0.911403	+	0.411515i	$0.865000\pi$
$758$	−36.3182	−	29.4099i	−1.31914	−	1.06822i
$759$	36.1527	−	40.1516i	1.31226	−	1.45741i
$760$	13.6758	+	32.4391i	0.496073	+	1.17669i
$761$	−27.0346	+	24.3421i	−0.980005	+	0.882400i	−0.993071	−	0.117514i	$-0.962507\pi$
$761$	−27.0346	+	24.3421i	−0.980005	+	0.882400i	0.0130662	+	0.999915i	$0.495841\pi$
$762$	77.1760	+	39.3231i	2.79579	+	1.42453i
$763$	0.857439	−	6.44686i	0.0310414	−	0.233392i
$764$	−59.6510	−	19.3818i	−2.15810	−	0.701208i
$765$	31.3329	−	21.8252i	1.13284	−	0.789092i
$766$	37.4365	+	33.7080i	1.35264	+	1.21792i
$767$	−0.288533	−	0.751654i	−0.0104183	−	0.0271407i
$768$	93.0587	−	24.9350i	3.35797	−	0.899764i
$769$	−22.4668	+	16.3231i	−0.810173	+	0.588625i	−0.913881	−	0.405983i	$-0.866929\pi$
$769$	−22.4668	+	16.3231i	−0.810173	+	0.588625i	0.103708	+	0.994608i	$0.466929\pi$
$770$	−45.9636	−	17.3833i	−1.65641	−	0.626449i
$771$	17.5942	+	12.7830i	0.633641	+	0.460367i
$772$	−76.6637	−	29.4284i	−2.75919	−	1.05915i
$773$	27.2366	+	17.6877i	0.979633	+	0.636181i	0.931914	−	0.362680i	$-0.118138\pi$
$773$	27.2366	+	17.6877i	0.979633	+	0.636181i	0.0477191	+	0.998861i	$0.484805\pi$
$774$	71.7078	−	41.4005i	2.57748	−	1.48811i
$775$	−12.8553	−	24.4661i	−0.461777	−	0.878847i
$776$			83.8714i			3.01081i
$777$	3.75009	+	12.7220i	0.134534	+	0.456398i
$778$	−94.8940	+	15.0297i	−3.40211	+	0.538842i
$779$	−1.34277	−	3.01591i	−0.0481098	−	0.108056i
$780$	15.4479	−	9.60034i	0.553124	−	0.343747i
$781$	30.4470	+	13.5559i	1.08948	+	0.485068i
$782$	−9.60887	−	35.8608i	−0.343612	−	1.28238i
$783$	81.7833	+	12.9532i	2.92270	+	0.462910i
$784$	−15.6597	+	23.9745i	−0.559275	+	0.856231i
$785$	5.56752	+	29.0222i	0.198713	+	1.03585i
$786$	67.4945	+	74.9603i	2.40745	+	2.67374i
$787$	0.953698	+	18.1976i	0.0339957	+	0.648676i	0.961490	+	0.274839i	$0.0886246\pi$
$787$	0.953698	+	18.1976i	0.0339957	+	0.648676i	−0.927495	+	0.373837i	$0.878042\pi$
$788$	2.86462	+	54.6602i	0.102048	+	1.94719i
$789$	22.4829	+	24.9698i	0.800414	+	0.888950i
$790$	15.9062	+	14.9058i	0.565915	+	0.530325i
$791$	−0.636612	−	4.88557i	−0.0226353	−	0.173711i
$792$	−99.1785	−	15.7083i	−3.52416	−	0.558171i
$793$	−1.02374	−	3.82066i	−0.0363541	−	0.135675i
$794$	33.9236	+	15.1038i	1.20390	+	0.536012i
$795$	6.43267	+	26.0722i	0.228143	+	0.924686i
$796$	35.6556	+	80.0838i	1.26378	+	2.83849i
$797$	−14.1304	+	2.23804i	−0.500525	+	0.0792753i	−0.401592	−	0.915819i	$-0.631543\pi$
$797$	−14.1304	+	2.23804i	−0.500525	+	0.0792753i	−0.0989330	+	0.995094i	$0.531543\pi$
$798$	60.2774	+	14.5558i	2.13380	+	0.515271i
$799$			7.84013i			0.277364i
$800$	−0.444430	−	0.595836i	−0.0157130	−	0.0210660i
$801$	−64.3722	+	37.1653i	−2.27448	+	1.31317i
$802$	47.2312	+	30.6723i	1.66779	+	1.08308i
$803$	16.3431	+	6.27353i	0.576735	+	0.221388i
$804$	72.8515	+	52.9297i	2.56927	+	1.86669i
$805$	17.0042	−	26.4700i	0.599318	−	0.932945i
$806$	−7.40654	+	5.38117i	−0.260884	+	0.189544i
$807$	20.6816	−	5.54162i	0.728027	−	0.195074i
$808$	−3.85224	−	10.0354i	−0.135521	−	0.353045i
$809$	0.231313	+	0.208275i	0.00813253	+	0.00732256i	0.673187	−	0.739472i	$-0.264925\pi$
$809$	0.231313	+	0.208275i	0.00813253	+	0.00732256i	−0.665054	+	0.746795i	$0.731592\pi$
$810$	49.3070	+	0.981606i	1.73247	+	0.0344901i
$811$	−3.46924	−	1.12722i	−0.121822	−	0.0395822i	0.247472	−	0.968895i	$-0.420400\pi$
$811$	−3.46924	−	1.12722i	−0.121822	−	0.0395822i	−0.369293	+	0.929313i	$0.620400\pi$
$812$	−96.9120	−	12.8894i	−3.40094	−	0.452329i
$813$	−46.2693	−	23.5754i	−1.62274	−	0.826825i
$814$	10.3152	−	9.28788i	0.361549	−	0.325540i
$815$	−22.9330	−	13.8562i	−0.803307	−	0.485361i
$816$	−23.3742	+	25.9597i	−0.818260	+	0.908770i
$817$	13.9320	+	11.2819i	0.487420	+	0.394705i
$818$	−39.7338	−	39.7338i	−1.38926	−	1.38926i
$819$	0.855145	−	10.6846i	0.0298812	−	0.373350i
$820$	5.71026	+	7.34585i	0.199411	+	0.256528i
$821$	−26.2728	+	11.6974i	−0.916928	+	0.408243i	−0.810272	−	0.586054i	$-0.800681\pi$
$821$	−26.2728	+	11.6974i	−0.916928	+	0.408243i	−0.106655	+	0.994296i	$0.534014\pi$
$822$	−62.1097	−	76.6991i	−2.16632	−	2.67519i
$823$	13.9301	−	21.4505i	0.485574	−	0.747719i	−0.507944	−	0.861390i	$-0.669594\pi$
$823$	13.9301	−	21.4505i	0.485574	−	0.747719i	0.993518	+	0.113671i	$0.0362610\pi$
$824$	−6.10473	+	10.5737i	−0.212668	+	0.368352i
$825$	−11.1845	−	49.5530i	−0.389395	−	1.72521i
$826$	−1.41991	+	7.60488i	−0.0494049	+	0.264608i
$827$	−19.3175	+	9.84275i	−0.671735	+	0.342266i	−0.756368	−	0.654146i	$-0.773028\pi$
$827$	−19.3175	+	9.84275i	−0.671735	+	0.342266i	0.0846335	+	0.996412i	$0.473028\pi$
$828$	45.9048	−	119.586i	1.59530	−	4.15590i
$829$	2.15065	−	20.4621i	0.0746952	−	0.710678i	−0.891527	−	0.452967i	$-0.850365\pi$
$829$	2.15065	−	20.4621i	0.0746952	−	0.710678i	0.966222	−	0.257710i	$-0.0829680\pi$
$830$	−42.4614	+	10.4763i	−1.47386	+	0.363637i
$831$	42.1984	−	4.43523i	1.46385	−	0.153856i
$832$	3.73275	−	3.73275i	0.129410	−	0.129410i
$833$	−0.0528130	+	19.9256i	−0.00182986	+	0.690381i
$834$	−69.8070	+	22.6817i	−2.41722	+	0.785402i
$835$	48.5154	−	14.7027i	1.67895	−	0.508807i
$836$	−9.00643	−	42.3719i	−0.311494	−	1.46546i
$837$	−49.6641	+	2.60279i	−1.71664	+	0.0899654i
$838$	−41.4079	−	63.7626i	−1.43041	−	2.20264i
$839$	−10.5057	+	32.3333i	−0.362698	+	1.11627i	0.588713	+	0.808342i	$0.299635\pi$
$839$	−10.5057	+	32.3333i	−0.362698	+	1.11627i	−0.951410	+	0.307926i	$0.900365\pi$
$840$	−87.7097	+	0.434104i	−3.02627	+	0.0149780i
$841$	−17.2120	−	52.9732i	−0.593518	−	1.82666i
$842$	35.6814	−	44.0629i	1.22966	−	1.51851i
$843$	−7.99931	+	29.8538i	−0.275511	+	1.02822i
$844$	−14.3256	+	32.1758i	−0.493108	+	1.10754i
$845$	−13.2290	+	24.7336i	−0.455090	+	0.850860i
$846$	−23.8199	+	32.7853i	−0.818947	+	1.12718i
$847$	1.06016	+	0.651599i	0.0364274	+	0.0223892i
$848$	−7.43497	−	14.5919i	−0.255318	−	0.501089i
$849$	−7.65690	−	4.42072i	−0.262784	−	0.151719i
$850$	−32.7424	−	12.0994i	−1.12306	−	0.415007i
$851$	4.44331	+	7.69604i	0.152315	+	0.263817i
$852$	118.367	+	6.20333i	4.05517	+	0.212522i
$853$	−2.16517	−	13.6703i	−0.0741339	−	0.468063i	−0.996628	−	0.0820518i	$-0.973853\pi$
$853$	−2.16517	−	13.6703i	−0.0741339	−	0.468063i	0.922494	−	0.386011i	$-0.126147\pi$
$854$	−10.8428	+	36.4273i	−0.371033	+	1.24652i
$855$	14.5172	+	40.1919i	0.496476	+	1.37454i
$856$	0.924487	+	8.79591i	0.0315983	+	0.300638i
$857$	40.9109	+	10.9620i	1.39749	+	0.374456i	0.877443	−	0.479681i	$-0.159248\pi$
$857$	40.9109	+	10.9620i	1.39749	+	0.374456i	0.520047	+	0.854137i	$0.325914\pi$
$858$	−15.7096	+	6.03036i	−0.536318	+	0.205873i
$859$	−43.0244	−	9.14512i	−1.46797	−	0.312027i	−0.596557	−	0.802571i	$-0.703465\pi$
$859$	−43.0244	−	9.14512i	−1.46797	−	0.312027i	−0.871417	+	0.490543i	$0.836798\pi$
$860$	−45.7384	−	21.4648i	−1.55967	−	0.731945i
$861$	8.22272	−	0.204415i	0.280230	−	0.00696645i
$862$	4.93652	−	9.68847i	0.168139	−	0.329991i
$863$	24.2255	−	15.7322i	0.824646	−	0.535531i	−0.0619482	−	0.998079i	$-0.519731\pi$
$863$	24.2255	−	15.7322i	0.824646	−	0.535531i	0.886594	+	0.462548i	$0.153065\pi$
$864$	−1.30834	+	0.278096i	−0.0445107	+	0.00946103i
$865$	8.68457	−	3.66128i	0.295284	−	0.124487i
$866$	11.9834	−	56.3775i	0.407212	−	1.91578i
$867$	4.17535	−	26.3621i	0.141802	−	0.895304i
$868$	58.5440	−	4.52946i	1.98711	−	0.153740i
$869$	−7.91286	−	10.8911i	−0.268425	−	0.369456i
$870$	−66.0389	−	136.247i	−2.23893	−	4.61919i
$871$	5.02112	+	0.527741i	0.170134	+	0.0178818i
$872$	−9.44119	+	7.64532i	−0.319719	+	0.258903i
$873$	−5.32830	+	101.670i	−0.180336	+	3.44101i
$874$	41.5481			1.40539
$875$	−11.0822	−	27.4260i	−0.374648	−	0.927167i
$876$	62.2576			2.10349
$877$	1.44886	−	27.6459i	0.0489245	−	0.933536i	−0.858368	−	0.513035i	$-0.828521\pi$
$877$	1.44886	−	27.6459i	0.0489245	−	0.933536i	0.907292	−	0.420501i	$-0.138146\pi$
$878$	62.1369	−	50.3174i	2.09702	−	1.69813i
$879$	31.1708	+	3.27619i	1.05137	+	0.110503i
$880$	13.5125	+	27.8779i	0.455505	+	0.939765i
$881$	−21.9771	−	30.2489i	−0.740427	−	1.01911i	−0.998594	−	0.0530096i	$-0.983119\pi$
$881$	−21.9771	−	30.2489i	−0.740427	−	1.01911i	0.258167	−	0.966100i	$-0.416881\pi$
$882$	−60.7590	+	83.1631i	−2.04586	+	2.80025i
$883$	1.16366	−	7.34708i	0.0391604	−	0.247249i	−0.960341	−	0.278829i	$-0.910054\pi$
$883$	1.16366	−	7.34708i	0.0391604	−	0.247249i	0.999501	+	0.0315798i	$0.0100538\pi$
$884$	−1.60470	+	7.54950i	−0.0539718	+	0.253917i
$885$	−7.36930	+	3.10678i	−0.247716	+	0.104433i
$886$	14.7652	−	3.13845i	0.496048	−	0.105438i
$887$	−0.106040	+	0.0688632i	−0.00356047	+	0.00231220i	−0.546418	−	0.837513i	$-0.684009\pi$
$887$	−0.106040	+	0.0688632i	−0.00356047	+	0.00231220i	0.542858	+	0.839825i	$0.317342\pi$
$888$	11.2477	−	22.0748i	0.377447	−	0.740781i
$889$	−27.3535	−	14.8987i	−0.917407	−	0.499687i
$890$	61.5119	+	28.8673i	2.06188	+	0.967634i
$891$	−29.7907	−	6.33222i	−0.998027	−	0.212137i
$892$	33.5503	−	12.8788i	1.12335	−	0.431213i
$893$	−8.47504	−	2.27088i	−0.283606	−	0.0759921i
$894$	−17.8210	−	169.556i	−0.596024	−	5.67079i
$895$	−3.32191	−	9.19699i	−0.111039	−	0.307421i
$896$	−50.1030	+	11.9585i	−1.67382	+	0.399504i
$897$	−1.68530	−	10.6406i	−0.0562706	−	0.355278i
$898$	−28.8291	−	1.51087i	−0.962038	−	0.0504183i
$899$	25.4357	+	44.0559i	0.848327	+	1.46935i
$900$	−66.8568	−	100.176i	−2.22856	−	3.33918i
$901$	−9.86889	−	5.69780i	−0.328780	−	0.189821i
$902$	−3.90801	−	7.66990i	−0.130122	−	0.255380i
$903$	−39.2811	+	21.2605i	−1.30719	+	0.707506i
$904$	−5.40952	+	7.44556i	−0.179918	+	0.247636i
$905$	−26.1659	+	48.9211i	−0.869784	+	1.62619i
$906$	−26.3126	+	59.0991i	−0.874178	+	1.96344i
$907$	−10.7414	+	40.0873i	−0.356661	+	1.33108i	0.521720	+	0.853117i	$0.325290\pi$
$907$	−10.7414	+	40.0873i	−0.356661	+	1.33108i	−0.878381	+	0.477960i	$0.841376\pi$
$908$	−42.5560	+	52.5523i	−1.41227	+	1.74401i
$909$	−4.03220	−	12.4098i	−0.133739	−	0.411608i
$910$	−8.46138	+	4.94118i	−0.280492	+	0.163798i
$911$	10.0535	−	30.9415i	0.333087	−	1.02514i	−0.634569	−	0.772866i	$-0.718822\pi$
$911$	10.0535	−	30.9415i	0.333087	−	1.02514i	0.967656	−	0.252272i	$-0.0811776\pi$
$912$	−21.2917	−	32.7863i	−0.705037	−	1.08566i
$913$	26.9719	−	1.41354i	0.892640	−	0.0467813i
$914$	−4.13861	−	19.4707i	−0.136893	−	0.644032i
$915$	−37.6009	+	11.3950i	−1.24305	+	0.376707i
$916$	0.244216	−	0.0793507i	0.00806914	−	0.00262182i
$917$	−23.5209	−	27.6134i	−0.776728	−	0.911875i
$918$	−44.4146	+	44.4146i	−1.46590	+	1.46590i
$919$	−25.9627	+	2.72879i	−0.856432	+	0.0900146i	−0.522559	−	0.852603i	$-0.675022\pi$
$919$	−25.9627	+	2.72879i	−0.856432	+	0.0900146i	−0.333873	+	0.942618i	$0.608356\pi$
$920$	−57.0572	+	14.0774i	−1.88112	+	0.464120i
$921$	−8.56070	+	81.4496i	−0.282085	+	2.68386i
$922$	−9.85621	+	25.6763i	−0.324597	+	0.845604i
$923$	5.92122	−	3.01701i	0.194899	−	0.0993061i
$924$	106.095	+	19.8090i	3.49026	+	0.651667i
$925$	8.31992	+	0.769032i	0.273557	+	0.0252856i
$926$	−6.68286	+	11.5751i	−0.219612	+	0.380380i
$927$	−8.07198	+	12.4298i	−0.265118	+	0.408247i
$928$	0.861040	+	1.06330i	0.0282650	+	0.0349044i
$929$	37.5816	−	16.7324i	1.23301	−	0.548972i	0.316353	−	0.948642i	$-0.397542\pi$
$929$	37.5816	−	16.7324i	1.23301	−	0.548972i	0.916659	+	0.399669i	$0.130875\pi$
$930$	55.8106	+	71.7965i	1.83010	+	2.35430i
$931$	−21.5239	−	5.82851i	−0.705418	−	0.191022i
$932$	−52.7075	−	52.7075i	−1.72649	−	1.72649i
$933$	3.04803	+	2.46825i	0.0997880	+	0.0808067i
$934$	12.0992	−	13.4375i	0.395899	−	0.439690i
$935$	18.4506	+	11.1479i	0.603401	+	0.364577i
$936$	−14.8794	+	13.3975i	−0.486349	+	0.437911i
$937$	27.5551	+	14.0400i	0.900186	+	0.458668i	0.841901	−	0.539632i	$-0.181437\pi$
$937$	27.5551	+	14.0400i	0.900186	+	0.458668i	0.0582855	+	0.998300i	$0.481437\pi$
$938$	−38.4483	−	29.5835i	−1.25538	−	0.965935i
$939$	40.0598	+	13.0162i	1.30730	+	0.424768i
$940$	24.7231	+	0.492189i	0.806380	+	0.0160534i
$941$	−13.9378	−	12.5497i	−0.454359	−	0.409107i	0.409918	−	0.912122i	$-0.365557\pi$
$941$	−13.9378	−	12.5497i	−0.454359	−	0.409107i	−0.864277	+	0.503015i	$0.832224\pi$
$942$	−34.8453	−	90.7752i	−1.13532	−	2.95762i
$943$	5.32333	−	1.42638i	0.173351	−	0.0464494i
$944$	3.94575	−	2.86676i	0.128423	−	0.0933050i
$945$	−53.1680	−	2.52262i	−1.72956	−	0.0820608i
$946$	37.8172	+	27.4758i	1.22954	+	0.893315i
$947$	52.9910	+	20.3413i	1.72198	+	0.661005i	0.999537	−	0.0304292i	$-0.00968741\pi$
$947$	52.9910	+	20.3413i	1.72198	+	0.661005i	0.722440	+	0.691434i	$0.243021\pi$
$948$	−40.1528	−	26.0755i	−1.30410	−	0.846894i
$949$	3.02293	−	1.74529i	0.0981286	−	0.0566545i
$950$	22.5631	−	31.8894i	0.732043	−	1.03463i
$951$			87.4392i			2.83541i
$952$	25.6566	−	26.9647i	0.831535	−	0.873932i
$953$	30.4878	−	4.82879i	0.987595	−	0.156420i	0.358317	−	0.933600i	$-0.383351\pi$
$953$	30.4878	−	4.82879i	0.987595	−	0.156420i	0.629278	+	0.777180i	$0.283351\pi$
$954$	−23.9580	−	53.8105i	−0.775668	−	1.74218i
$955$	8.36723	+	33.9132i	0.270757	+	1.09740i
$956$	24.0690	+	10.7162i	0.778447	+	0.346587i
$957$	24.2006	+	90.3178i	0.782294	+	2.91956i
$958$	−24.2670	−	3.84351i	−0.784031	−	0.124178i
$959$	21.5680	+	28.1852i	0.696467	+	0.910148i
$960$	−38.2612	−	35.8550i	−1.23488	−	1.15722i
$961$	0.298499	+	0.331517i	0.00962901	+	0.0106941i
$962$	−0.144851	−	2.76392i	−0.00467018	−	0.0891124i
$963$	0.561877	+	10.7213i	0.0181062	+	0.345488i
$964$	−11.8532	−	13.1643i	−0.381765	−	0.423993i
$965$	8.61610	+	44.9137i	0.277362	+	1.44582i
$966$	−39.7410	+	95.5847i	−1.27865	+	3.07539i
$967$	23.7132	+	3.75580i	0.762565	+	0.120778i	0.525591	−	0.850738i	$-0.323844\pi$
$967$	23.7132	+	3.75580i	0.762565	+	0.120778i	0.236974	+	0.971516i	$0.423844\pi$
$968$	−0.601620	−	2.24528i	−0.0193368	−	0.0721659i
$969$	−24.8506	−	11.0642i	−0.798315	−	0.355433i
$970$	79.0473	−	49.1251i	2.53806	−	1.57731i
$971$	6.33721	+	14.2336i	0.203371	+	0.456778i	0.986221	−	0.165432i	$-0.0529017\pi$
$971$	6.33721	+	14.2336i	0.203371	+	0.456778i	−0.782850	+	0.622210i	$0.786235\pi$
$972$	0.0581201	−	0.00920532i	0.00186420	−	0.000295261i
$973$	25.3178	−	7.46299i	0.811651	−	0.239252i
$974$		−	45.6672i		−	1.46327i
$975$	−9.08217	−	4.48494i	−0.290862	−	0.143633i
$976$	20.7506	−	11.9804i	0.664211	−	0.383482i
$977$	−32.6511	−	21.2039i	−1.04460	−	0.678372i	−0.0961736	−	0.995365i	$-0.530660\pi$
$977$	−32.6511	−	21.2039i	−1.04460	−	0.678372i	−0.948428	+	0.316992i	$0.897327\pi$
$978$	82.3050	+	31.5939i	2.63182	+	1.01026i
$979$	−33.9485	−	24.6650i	−1.08500	−	0.788298i
$980$	62.8302	+	1.41743i	2.00704	+	0.0452782i
$981$	−11.9304	+	8.66798i	−0.380910	+	0.276747i
$982$	−24.2377	+	6.49448i	−0.773456	+	0.207247i
$983$	−15.6652	−	40.8094i	−0.499644	−	1.30162i	−0.919166	−	0.393871i	$-0.871136\pi$
$983$	−15.6652	−	40.8094i	−0.499644	−	1.30162i	0.419522	−	0.907745i	$-0.362198\pi$
$984$	−11.4180	−	10.2808i	−0.363994	−	0.327742i
$985$	25.0129	−	17.4230i	0.796976	−	0.555141i
$986$	61.1058	+	19.8545i	1.94600	+	0.632295i
$987$	13.3308	−	17.3254i	0.424323	−	0.551474i
$988$	−7.69609	−	3.92135i	−0.244845	−	0.124755i
$989$	−22.2400	+	20.0250i	−0.707192	+	0.636759i
$990$	43.2860	+	102.675i	1.37572	+	3.26321i
$991$	−16.4088	+	18.2238i	−0.521242	+	0.578898i	−0.945080	−	0.326840i	$-0.894016\pi$
$991$	−16.4088	+	18.2238i	−0.521242	+	0.578898i	0.423837	+	0.905738i	$0.360683\pi$
$992$	−0.638627	−	0.517150i	−0.0202764	−	0.0164195i
$993$	−17.8981	−	17.8981i	−0.567978	−	0.567978i
$994$	−63.6518	−	5.09439i	−2.01891	−	0.161584i
$995$	27.3993	−	40.4071i	0.868617	−	1.28099i
$996$	87.7500	−	39.0688i	2.78047	−	1.23794i
$997$	35.8237	+	44.2386i	1.13455	+	1.40105i	0.903757	+	0.428046i	$0.140798\pi$
$997$	35.8237	+	44.2386i	1.13455	+	1.40105i	0.230790	+	0.973004i	$0.425869\pi$
$998$	13.7808	−	21.2205i	0.436222	−	0.671724i
$999$	7.51747	−	13.0206i	0.237842	−	0.411955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.47.3	yes	288
5.2	odd	4		875.2.bb.a.243.3		288
5.3	odd	4		875.2.bb.b.243.16		288
5.4	even	2		875.2.bb.c.257.16		288
7.3	odd	6	inner	175.2.x.a.122.3	yes	288
25.6	even	5		875.2.bb.b.607.3		288
25.8	odd	20	inner	175.2.x.a.33.3	✓	288
25.17	odd	20		875.2.bb.c.768.16		288
25.19	even	10		875.2.bb.a.607.16		288
35.3	even	12		875.2.bb.b.493.3		288
35.17	even	12		875.2.bb.a.493.16		288
35.24	odd	6		875.2.bb.c.507.16		288
175.17	even	60		875.2.bb.c.143.16		288
175.31	odd	30		875.2.bb.b.857.16		288
175.94	odd	30		875.2.bb.a.857.3		288
175.108	even	60	inner	175.2.x.a.108.3	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.3	✓	288	25.8	odd	20	inner
175.2.x.a.47.3	yes	288	1.1	even	1	trivial
175.2.x.a.108.3	yes	288	175.108	even	60	inner
175.2.x.a.122.3	yes	288	7.3	odd	6	inner
875.2.bb.a.243.3		288	5.2	odd	4
875.2.bb.a.493.16		288	35.17	even	12
875.2.bb.a.607.16		288	25.19	even	10
875.2.bb.a.857.3		288	175.94	odd	30
875.2.bb.b.243.16		288	5.3	odd	4
875.2.bb.b.493.3		288	35.3	even	12
875.2.bb.b.607.3		288	25.6	even	5
875.2.bb.b.857.16		288	175.31	odd	30
875.2.bb.c.143.16		288	175.17	even	60
875.2.bb.c.257.16		288	5.4	even	2
875.2.bb.c.507.16		288	35.24	odd	6
875.2.bb.c.768.16		288	25.17	odd	20

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+(-0.128358 + 2.44921i) q^{2} +(-2.33133 + 1.88788i) q^{3} +(-3.99310 - 0.419692i) q^{4} +(0.975297 + 2.01216i) q^{5} +(-4.32456 - 5.95224i) q^{6} +(1.49568 + 2.18242i) q^{7} +(0.773125 - 4.88132i) q^{8} +(1.24730 - 5.86809i) q^{9} +(-5.05339 + 2.13043i) q^{10} +(3.31278 - 0.704153i) q^{11} +(10.1016 - 6.56004i) q^{12} +(0.306584 - 0.601706i) q^{13} +(-5.53718 + 3.38310i) q^{14} +(-6.07245 - 2.84978i) q^{15} +(4.00142 + 0.850527i) q^{16} +(2.65746 - 1.02010i) q^{17} +(14.2121 + 3.80811i) q^{18} +(0.332985 + 3.16814i) q^{19} +(-3.04997 - 8.44409i) q^{20} +(-7.60706 - 2.26428i) q^{21} +(1.29940 + 8.20407i) q^{22} +(-5.31061 - 0.278317i) q^{23} +(7.41291 + 12.8395i) q^{24} +(-3.09759 + 3.92491i) q^{25} +(1.43435 + 0.828123i) q^{26} +(4.08462 + 8.01652i) q^{27} +(-5.05646 - 9.34234i) q^{28} +(5.40952 - 7.44556i) q^{29} +(7.75915 - 14.5069i) q^{30} +(-2.24826 + 5.04968i) q^{31} +(-0.0384776 + 0.143600i) q^{32} +(-6.39384 + 7.89573i) q^{33} +(2.15734 + 6.63961i) q^{34} +(-2.93265 + 5.13805i) q^{35} +(-7.44339 + 22.9084i) q^{36} +(-0.910134 - 1.40148i) q^{37} +(-7.80217 + 0.408894i) q^{38} +(0.421196 + 1.98157i) q^{39} +(10.5760 - 3.20508i) q^{40} +(-0.985611 + 0.320244i) q^{41} +(6.52212 - 18.3406i) q^{42} +(3.97930 - 3.97930i) q^{43} +(-13.5238 + 1.42141i) q^{44} +(13.0240 - 3.21336i) q^{45} +(1.36331 - 12.9711i) q^{46} +(-0.987046 + 2.57134i) q^{47} +(-10.9343 + 5.57132i) q^{48} +(-2.52589 + 6.52839i) q^{49} +(-9.21532 - 8.09044i) q^{50} +(-4.26959 + 7.39515i) q^{51} +(-1.47675 + 2.27400i) q^{52} +(-2.51939 - 3.11118i) q^{53} +(-20.1584 + 8.97511i) q^{54} +(4.64781 + 5.97909i) q^{55} +(11.8094 - 5.61361i) q^{56} +(-6.75735 - 6.75735i) q^{57} +(17.5414 + 14.2047i) q^{58} +(0.797763 - 0.886005i) q^{59} +(23.0519 + 13.9280i) q^{60} +(4.35276 - 3.91924i) q^{61} +(-12.0791 - 6.15462i) q^{62} +(14.6722 - 6.05465i) q^{63} +(7.43442 + 2.41559i) q^{64} +(1.50974 + 0.0300560i) q^{65} +(-18.5176 - 16.6733i) q^{66} +(2.67924 + 6.97967i) q^{67} +(-11.0396 + 2.95806i) q^{68} +(12.9062 - 9.37692i) q^{69} +(-12.2077 - 7.84217i) q^{70} +(7.96131 + 5.78423i) q^{71} +(-27.6797 - 10.6252i) q^{72} +(4.33497 + 2.81516i) q^{73} +(3.54935 - 2.04922i) q^{74} +(-0.188223 - 14.9981i) q^{75} -12.7904i q^{76} +(6.49161 + 6.17668i) q^{77} +(-4.90734 + 0.777246i) q^{78} +(-1.61674 - 3.63126i) q^{79} +(2.19117 + 8.88102i) q^{80} +(-8.21521 - 3.65765i) q^{81} +(-0.657835 - 2.45507i) q^{82} +(7.87661 + 1.24753i) q^{83} +(29.4255 + 12.2341i) q^{84} +(4.64442 + 4.35233i) q^{85} +(9.23537 + 10.2569i) q^{86} +(1.44491 + 27.5706i) q^{87} +(-0.876003 - 16.7151i) q^{88} +(-8.29060 - 9.20765i) q^{89} +(6.19844 + 32.3110i) q^{90} +(1.77172 - 0.230864i) q^{91} +(21.0890 + 3.34017i) q^{92} +(-4.29172 - 16.0169i) q^{93} +(-6.17106 - 2.74753i) q^{94} +(-6.05005 + 3.75989i) q^{95} +(-0.181395 - 0.407421i) q^{96} +(-16.7616 + 2.65478i) q^{97} +(-15.6652 - 7.02439i) q^{98} -20.3180i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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