LMFDB - Embedded newform 250.2.g.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([38]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.g (of order $25$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	250.11
Dual form			250.2.g.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.728969 + 0.684547i) q^{2} +(0.930915 + 1.46689i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.692574 + 2.12611i) q^{5} +(-1.68276 - 0.432060i) q^{6} +(-0.369827 + 1.13821i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.00781785 + 0.0166138i) q^{9} +O(q^{10})$	\(q+(-0.728969 + 0.684547i) q^{2} +(0.930915 + 1.46689i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.692574 + 2.12611i) q^{5} +(-1.68276 - 0.432060i) q^{6} +(-0.369827 + 1.13821i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.00781785 + 0.0166138i) q^{9} +(-1.96029 - 1.07577i) q^{10} +(1.12049 - 1.05221i) q^{11} +(1.52245 - 0.836971i) q^{12} +(-2.33636 + 4.96502i) q^{13} +(-0.509567 - 1.08288i) q^{14} +(-2.47404 + 2.99516i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.259976 - 4.13220i) q^{17} +(-0.00567395 - 0.0174626i) q^{18} +(1.13746 - 1.79236i) q^{19} +(2.16540 - 0.557708i) q^{20} +(-2.01391 + 0.517083i) q^{21} +(-0.0965150 + 1.53406i) q^{22} +(-0.391837 + 2.05408i) q^{23} +(-0.536869 + 1.65231i) q^{24} +(-4.04068 + 2.94498i) q^{25} +(-1.69566 - 5.21869i) q^{26} +(5.13928 - 0.649242i) q^{27} +(1.11274 + 0.440567i) q^{28} +(-1.21184 - 0.479801i) q^{29} +(-0.246830 - 3.87697i) q^{30} +(0.207270 + 3.29447i) q^{31} +(0.809017 - 0.587785i) q^{32} +(2.58656 + 0.664117i) q^{33} +(3.01820 + 2.83428i) q^{34} +(-2.67610 + 0.00200210i) q^{35} +(0.0160901 + 0.00884561i) q^{36} +(-4.62657 - 0.584472i) q^{37} +(0.397777 + 2.08522i) q^{38} +(-9.45807 + 1.19483i) q^{39} +(-1.19673 + 1.88887i) q^{40} +(-1.42621 - 7.47648i) q^{41} +(1.11411 - 1.75555i) q^{42} +(6.13285 + 4.45577i) q^{43} +(-0.979781 - 1.18435i) q^{44} +(-0.0407372 - 0.00511534i) q^{45} +(-1.12048 - 1.76559i) q^{46} +(6.01160 - 7.26677i) q^{47} +(-0.739725 - 1.57200i) q^{48} +(4.50437 + 3.27261i) q^{49} +(0.929557 - 4.91283i) q^{50} +(5.81945 - 4.22808i) q^{51} +(4.80852 + 2.64351i) q^{52} +(10.0000 - 2.56757i) q^{53} +(-3.30194 + 3.99136i) q^{54} +(3.01315 + 1.65356i) q^{55} +(-1.11274 + 0.440567i) q^{56} +3.68806 q^{57} +(1.21184 - 0.479801i) q^{58} +(0.299588 - 0.164700i) q^{59} +(2.83390 + 2.65722i) q^{60} +(1.74933 - 9.17029i) q^{61} +(-2.40631 - 2.25968i) q^{62} +(-0.0160187 - 0.0150426i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(-12.1743 - 1.52872i) q^{65} +(-2.34014 + 1.28650i) q^{66} +(12.5324 - 4.96193i) q^{67} -4.14037 q^{68} +(-3.37788 + 1.33740i) q^{69} +(1.94942 - 1.83337i) q^{70} +(4.07883 - 4.93046i) q^{71} +(-0.0177844 + 0.00456626i) q^{72} +(-9.73478 - 5.35174i) q^{73} +(3.77272 - 2.74104i) q^{74} +(-8.08148 - 3.18570i) q^{75} +(-1.71740 - 1.24776i) q^{76} +(0.783253 + 1.66450i) q^{77} +(6.07672 - 7.34549i) q^{78} +(3.27431 + 5.15948i) q^{79} +(-0.420641 - 2.19615i) q^{80} +(5.77171 + 6.97680i) q^{81} +(6.15767 + 4.47381i) q^{82} +(-2.61606 + 4.12225i) q^{83} +(0.389609 + 2.04240i) q^{84} +(8.60545 - 3.41459i) q^{85} +(-7.52084 + 0.950103i) q^{86} +(-0.424305 - 2.22429i) q^{87} +(1.52497 + 0.192649i) q^{88} +(-8.29671 - 4.56116i) q^{89} +(0.0331978 - 0.0241576i) q^{90} +(-4.78719 - 4.49547i) q^{91} +(2.02543 + 0.520041i) q^{92} +(-4.63966 + 3.37091i) q^{93} +(0.592183 + 9.41247i) q^{94} +(4.59852 + 1.17703i) q^{95} +(1.61534 + 0.639559i) q^{96} +(-8.17237 - 3.23567i) q^{97} +(-5.52380 + 0.697818i) q^{98} +(0.00872139 + 0.0268417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9}+O(q^{10}) $ 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9	$ 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9} - 20 q^{10} + 20 q^{12} - 20 q^{14} - 10 q^{15} - 5 q^{17} + 25 q^{18} - 60 q^{19} + 5 q^{20} + 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} + 55 q^{25} + 5 q^{26} - 90 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} - 45 q^{31} + 30 q^{32} - 15 q^{33} - 10 q^{34} + 15 q^{35} + 10 q^{36} + 10 q^{37} + 10 q^{39} - 55 q^{41} - 5 q^{42} + 5 q^{43} - 40 q^{44} + 85 q^{45} - 20 q^{46} + 90 q^{47} - 5 q^{48} - 20 q^{49} - 30 q^{50} + 60 q^{51} + 5 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} - 120 q^{57} + 10 q^{58} - 75 q^{59} + 15 q^{60} - 85 q^{61} - 15 q^{62} - 45 q^{63} + 5 q^{65} - 15 q^{66} - 25 q^{67} - 70 q^{68} + 5 q^{69} - 65 q^{70} + 55 q^{71} + 5 q^{72} - 30 q^{73} - 70 q^{74} - 20 q^{75} - 5 q^{76} - 130 q^{77} + 60 q^{78} + 10 q^{79} + 5 q^{80} - 65 q^{81} + 80 q^{82} - 135 q^{83} + 20 q^{84} - 30 q^{85} + 10 q^{86} - 200 q^{87} - 80 q^{90} + 175 q^{91} - 5 q^{92} + 50 q^{93} + 35 q^{94} - 20 q^{95} - 15 q^{98} - 120 q^{99}+O(q^{100}) $ 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9 - 20 * q^10 + 20 * q^12 - 20 * q^14 - 10 * q^15 - 5 * q^17 + 25 * q^18 - 60 * q^19 + 5 * q^20 + 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 + 55 * q^25 + 5 * q^26 - 90 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 - 45 * q^31 + 30 * q^32 - 15 * q^33 - 10 * q^34 + 15 * q^35 + 10 * q^36 + 10 * q^37 + 10 * q^39 - 55 * q^41 - 5 * q^42 + 5 * q^43 - 40 * q^44 + 85 * q^45 - 20 * q^46 + 90 * q^47 - 5 * q^48 - 20 * q^49 - 30 * q^50 + 60 * q^51 + 5 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 - 120 * q^57 + 10 * q^58 - 75 * q^59 + 15 * q^60 - 85 * q^61 - 15 * q^62 - 45 * q^63 + 5 * q^65 - 15 * q^66 - 25 * q^67 - 70 * q^68 + 5 * q^69 - 65 * q^70 + 55 * q^71 + 5 * q^72 - 30 * q^73 - 70 * q^74 - 20 * q^75 - 5 * q^76 - 130 * q^77 + 60 * q^78 + 10 * q^79 + 5 * q^80 - 65 * q^81 + 80 * q^82 - 135 * q^83 + 20 * q^84 - 30 * q^85 + 10 * q^86 - 200 * q^87 - 80 * q^90 + 175 * q^91 - 5 * q^92 + 50 * q^93 + 35 * q^94 - 20 * q^95 - 15 * q^98 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	−0.728969	+	0.684547i	−0.515459	+	0.484048i
$2$	−0.728969	+	0.684547i	−0.515459	+	0.484048i
$3$	0.930915	+	1.46689i	0.537464	+	0.846908i	0.999195	−	0.0401121i	$-0.0127715\pi$
$3$	0.930915	+	1.46689i	0.537464	+	0.846908i	−0.461731	+	0.887020i	$0.652772\pi$
$4$	0.0627905	−	0.998027i	0.0313953	−	0.499013i
$5$	0.692574	+	2.12611i	0.309728	+	0.950825i
$5$	0.692574	+	2.12611i	0.309728	+	0.950825i
$6$	−1.68276	−	0.432060i	−0.686984	−	0.176388i
$7$	−0.369827	+	1.13821i	−0.139782	+	0.430204i	−0.996303	−	0.0859078i	$-0.972621\pi$
$7$	−0.369827	+	1.13821i	−0.139782	+	0.430204i	0.856521	+	0.516111i	$0.172621\pi$
$8$	0.637424	+	0.770513i	0.225363	+	0.272418i
$9$	−0.00781785	+	0.0166138i	−0.00260595	+	0.00553793i
$10$	−1.96029	−	1.07577i	−0.619897	−	0.340188i
$11$	1.12049	−	1.05221i	0.337842	−	0.317254i	−0.496994	−	0.867754i	$-0.665563\pi$
$11$	1.12049	−	1.05221i	0.337842	−	0.317254i	0.834835	+	0.550500i	$0.185563\pi$
$12$	1.52245	−	0.836971i	0.439492	−	0.241613i
$13$	−2.33636	+	4.96502i	−0.647990	+	1.37705i	0.263071	+	0.964776i	$0.415264\pi$
$13$	−2.33636	+	4.96502i	−0.647990	+	1.37705i	−0.911061	+	0.412272i	$0.864736\pi$
$14$	−0.509567	−	1.08288i	−0.136188	−	0.289413i
$15$	−2.47404	+	2.99516i	−0.638793	+	0.773346i
$16$	−0.992115	−	0.125333i	−0.248029	−	0.0313333i
$17$	−0.259976	−	4.13220i	−0.0630534	−	1.00220i	−0.894634	−	0.446800i	$-0.852563\pi$
$17$	−0.259976	−	4.13220i	−0.0630534	−	1.00220i	0.831580	−	0.555405i	$-0.187437\pi$
$18$	−0.00567395	−	0.0174626i	−0.00133736	−	0.00411598i
$19$	1.13746	−	1.79236i	0.260952	−	0.411194i	−0.688438	−	0.725296i	$-0.741703\pi$
$19$	1.13746	−	1.79236i	0.260952	−	0.411194i	0.949390	+	0.314101i	$0.101703\pi$
$20$	2.16540	−	0.557708i	0.484198	−	0.124707i
$21$	−2.01391	+	0.517083i	−0.439470	+	0.112837i
$22$	−0.0965150	+	1.53406i	−0.0205771	+	0.327063i
$23$	−0.391837	+	2.05408i	−0.0817037	+	0.428306i	0.917807	+	0.397027i	$0.129958\pi$
$23$	−0.391837	+	2.05408i	−0.0817037	+	0.428306i	−0.999511	+	0.0312790i	$0.990042\pi$
$24$	−0.536869	+	1.65231i	−0.109588	+	0.337277i
$25$	−4.04068	+	2.94498i	−0.808137	+	0.588995i
$26$	−1.69566	−	5.21869i	−0.332545	−	1.02347i
$27$	5.13928	−	0.649242i	0.989055	−	0.124947i
$28$	1.11274	+	0.440567i	0.210289	+	0.0832593i
$29$	−1.21184	−	0.479801i	−0.225033	−	0.0890969i	0.252903	−	0.967492i	$-0.418615\pi$
$29$	−1.21184	−	0.479801i	−0.225033	−	0.0890969i	−0.477936	+	0.878395i	$0.658615\pi$
$30$	−0.246830	−	3.87697i	−0.0450648	−	0.707834i
$31$	0.207270	+	3.29447i	0.0372268	+	0.591704i	0.971781	+	0.235884i	$0.0757984\pi$
$31$	0.207270	+	3.29447i	0.0372268	+	0.591704i	−0.934554	+	0.355820i	$0.884202\pi$
$32$	0.809017	−	0.587785i	0.143015	−	0.103907i
$33$	2.58656	+	0.664117i	0.450263	+	0.115608i
$34$	3.01820	+	2.83428i	0.517617	+	0.486074i
$35$	−2.67610	+	0.00200210i	−0.452343	+	0.000338417i
$36$	0.0160901	+	0.00884561i	0.00268169	+	0.00147427i
$37$	−4.62657	−	0.584472i	−0.760604	−	0.0960866i	−0.264542	−	0.964374i	$-0.585221\pi$
$37$	−4.62657	−	0.584472i	−0.760604	−	0.0960866i	−0.496061	+	0.868287i	$0.665221\pi$
$38$	0.397777	+	2.08522i	0.0645279	+	0.338267i
$39$	−9.45807	+	1.19483i	−1.51450	+	0.191326i
$40$	−1.19673	+	1.88887i	−0.189220	+	0.298657i
$41$	−1.42621	−	7.47648i	−0.222737	−	1.16763i	−0.901336	−	0.433120i	$-0.857412\pi$
$41$	−1.42621	−	7.47648i	−0.222737	−	1.16763i	0.678599	−	0.734509i	$-0.262588\pi$
$42$	1.11411	−	1.75555i	0.171910	−	0.270887i
$43$	6.13285	+	4.45577i	0.935250	+	0.679499i	0.947273	−	0.320429i	$-0.103827\pi$
$43$	6.13285	+	4.45577i	0.935250	+	0.679499i	−0.0120223	+	0.999928i	$0.503827\pi$
$44$	−0.979781	−	1.18435i	−0.147708	−	0.178548i
$45$	−0.0407372	−	0.00511534i	−0.00607274	−	0.000762550i
$46$	−1.12048	−	1.76559i	−0.165206	−	0.260322i
$47$	6.01160	−	7.26677i	0.876882	−	1.05997i	−0.120851	−	0.992671i	$-0.538562\pi$
$47$	6.01160	−	7.26677i	0.876882	−	1.05997i	0.997733	−	0.0672974i	$-0.0214376\pi$
$48$	−0.739725	−	1.57200i	−0.106770	−	0.226898i
$49$	4.50437	+	3.27261i	0.643481	+	0.467516i
$50$	0.929557	−	4.91283i	0.131459	−	0.694779i
$51$	5.81945	−	4.22808i	0.814886	−	0.592050i
$52$	4.80852	+	2.64351i	0.666821	+	0.366588i
$53$	10.0000	−	2.56757i	1.37361	−	0.352683i	0.511447	−	0.859315i	$-0.329110\pi$
$53$	10.0000	−	2.56757i	1.37361	−	0.352683i	0.862162	+	0.506632i	$0.169110\pi$
$54$	−3.30194	+	3.99136i	−0.449337	+	0.543155i
$55$	3.01315	+	1.65356i	0.406292	+	0.222966i
$56$	−1.11274	+	0.440567i	−0.148697	+	0.0588732i
$57$	3.68806			0.488496
$58$	1.21184	−	0.479801i	0.159122	−	0.0630010i
$59$	0.299588	−	0.164700i	0.0390031	−	0.0214421i	−0.462133	−	0.886811i	$-0.652916\pi$
$59$	0.299588	−	0.164700i	0.0390031	−	0.0214421i	0.501136	+	0.865369i	$0.332916\pi$
$60$	2.83390	+	2.65722i	0.365855	+	0.343046i
$61$	1.74933	−	9.17029i	0.223978	−	1.17414i	−0.675564	−	0.737301i	$-0.736100\pi$
$61$	1.74933	−	9.17029i	0.223978	−	1.17414i	0.899542	−	0.436834i	$-0.143900\pi$
$62$	−2.40631	−	2.25968i	−0.305602	−	0.286979i
$63$	−0.0160187	−	0.0150426i	−0.00201817	−	0.00189519i
$64$	−0.187381	+	0.982287i	−0.0234227	+	0.122786i
$65$	−12.1743	−	1.52872i	−1.51003	−	0.189614i
$66$	−2.34014	+	1.28650i	−0.288052	+	0.158358i
$67$	12.5324	−	4.96193i	1.53108	−	0.606196i	0.556618	−	0.830768i	$-0.312099\pi$
$67$	12.5324	−	4.96193i	1.53108	−	0.606196i	0.974457	+	0.224573i	$0.0720987\pi$
$68$	−4.14037			−0.502093
$69$	−3.37788	+	1.33740i	−0.406648	+	0.161003i
$70$	1.94942	−	1.83337i	0.233000	−	0.219130i
$71$	4.07883	−	4.93046i	0.484068	−	0.585138i	−0.470773	−	0.882254i	$-0.656025\pi$
$71$	4.07883	−	4.93046i	0.484068	−	0.585138i	0.954841	+	0.297116i	$0.0960250\pi$
$72$	−0.0177844	+	0.00456626i	−0.00209591	+	0.000538139i
$73$	−9.73478	−	5.35174i	−1.13937	−	0.626374i	−0.203624	−	0.979049i	$-0.565272\pi$
$73$	−9.73478	−	5.35174i	−1.13937	−	0.626374i	−0.935746	+	0.352675i	$0.885272\pi$
$74$	3.77272	−	2.74104i	0.438570	−	0.318640i
$75$	−8.08148	−	3.18570i	−0.933169	−	0.367853i
$76$	−1.71740	−	1.24776i	−0.196999	−	0.143128i
$77$	0.783253	+	1.66450i	0.0892599	+	0.189687i
$78$	6.07672	−	7.34549i	0.688053	−	0.831713i
$79$	3.27431	+	5.15948i	0.368388	+	0.580487i	0.977068	−	0.212929i	$-0.0683004\pi$
$79$	3.27431	+	5.15948i	0.368388	+	0.580487i	−0.608679	+	0.793416i	$0.708300\pi$
$80$	−0.420641	−	2.19615i	−0.0470290	−	0.245537i
$81$	5.77171	+	6.97680i	0.641301	+	0.775200i
$82$	6.15767	+	4.47381i	0.680001	+	0.494049i
$83$	−2.61606	+	4.12225i	−0.287150	+	0.452476i	−0.957028	−	0.289995i	$-0.906346\pi$
$83$	−2.61606	+	4.12225i	−0.287150	+	0.452476i	0.669878	+	0.742471i	$0.266346\pi$
$84$	0.389609	+	2.04240i	0.0425098	+	0.222844i
$85$	8.60545	−	3.41459i	0.933392	−	0.370364i
$86$	−7.52084	+	0.950103i	−0.810993	+	0.102452i
$87$	−0.424305	−	2.22429i	−0.0454903	−	0.238469i
$88$	1.52497	+	0.192649i	0.162563	+	0.0205365i
$89$	−8.29671	−	4.56116i	−0.879450	−	0.483482i	−0.0230140	−	0.999735i	$-0.507326\pi$
$89$	−8.29671	−	4.56116i	−0.879450	−	0.483482i	−0.856436	+	0.516253i	$0.827326\pi$
$90$	0.0331978	−	0.0241576i	0.00349936	−	0.00254643i
$91$	−4.78719	−	4.49547i	−0.501834	−	0.471253i
$92$	2.02543	+	0.520041i	0.211165	+	0.0542180i
$93$	−4.63966	+	3.37091i	−0.481110	+	0.349547i
$94$	0.592183	+	9.41247i	0.0610790	+	0.970823i
$95$	4.59852	+	1.17703i	0.471798	+	0.120761i
$96$	1.61534	+	0.639559i	0.164865	+	0.0652747i
$97$	−8.17237	−	3.23567i	−0.829778	−	0.328533i	−0.0854468	−	0.996343i	$-0.527232\pi$
$97$	−8.17237	−	3.23567i	−0.829778	−	0.328533i	−0.744332	+	0.667810i	$0.767232\pi$
$98$	−5.52380	+	0.697818i	−0.557988	+	0.0704903i
$99$	0.00872139	+	0.0268417i	0.000876533	+	0.00269769i
$100$	2.68545	+	4.21763i	0.268545	+	0.421763i
$101$	−4.49255	+	13.8266i	−0.447025	+	1.37580i	0.433223	+	0.901287i	$0.357376\pi$
$101$	−4.49255	+	13.8266i	−0.447025	+	1.37580i	−0.880248	+	0.474515i	$0.842624\pi$
$102$	−1.34788	+	7.06583i	−0.133460	+	0.699621i
$103$	−0.149787	+	2.38080i	−0.0147590	+	0.234587i	0.983731	+	0.179649i	$0.0574962\pi$
$103$	−0.149787	+	2.38080i	−0.0147590	+	0.234587i	−0.998490	+	0.0549382i	$0.982504\pi$
$104$	−5.31486	+	1.36462i	−0.521165	+	0.133812i
$105$	−2.49415	−	3.92367i	−0.243405	−	0.382911i
$106$	−5.53208	+	8.71717i	−0.537323	+	0.846686i
$107$	−2.07509	−	6.38646i	−0.200606	−	0.617402i	−0.999865	−	0.0164158i	$-0.994774\pi$
$107$	−2.07509	−	6.38646i	−0.200606	−	0.617402i	0.799259	−	0.600987i	$-0.205226\pi$
$108$	−0.325263	−	5.16991i	−0.0312984	−	0.497475i
$109$	6.53503	+	0.825566i	0.625942	+	0.0790749i	0.431905	−	0.901919i	$-0.357842\pi$
$109$	6.53503	+	0.825566i	0.625942	+	0.0790749i	0.194037	+	0.980994i	$0.437842\pi$
$110$	−3.32843	+	0.857249i	−0.317353	+	0.0817355i
$111$	−3.44959	−	7.33075i	−0.327421	−	0.695804i
$112$	0.509567	−	1.08288i	0.0481496	−	0.102323i
$113$	−1.38466	+	0.761221i	−0.130258	+	0.0716097i	−0.545550	−	0.838078i	$-0.683679\pi$
$113$	−1.38466	+	0.761221i	−0.130258	+	0.0716097i	0.415293	+	0.909688i	$0.363679\pi$
$114$	−2.68848	+	2.52465i	−0.251800	+	0.236456i
$115$	−4.63858	+	0.589515i	−0.432550	+	0.0549726i
$116$	−0.554947	+	1.17932i	−0.0515255	+	0.109497i
$117$	−0.0642224	−	0.0776315i	−0.00593736	−	0.00717704i
$118$	−0.105646	+	0.325144i	−0.00972547	+	0.0299319i
$119$	4.79946	+	1.23229i	0.439966	+	0.112964i
$120$	−3.88482	+	0.00290640i	−0.354634	+	0.000265317i
$121$	−0.542343	+	8.62030i	−0.0493039	+	0.783663i
$122$	5.00229	+	7.88235i	0.452886	+	0.713635i
$123$	9.63947	−	9.05206i	0.869161	−	0.816197i
$124$	3.30098			0.296437
$125$	−9.05981	−	6.55132i	−0.810334	−	0.585968i
$126$	0.0219745			0.00195765
$127$	−11.3203	+	10.6304i	−1.00451	+	0.943299i	−0.998392	−	0.0566825i	$-0.981948\pi$
$127$	−11.3203	+	10.6304i	−1.00451	+	0.943299i	−0.00611897	+	0.999981i	$0.501948\pi$
$128$	−0.535827	−	0.844328i	−0.0473608	−	0.0746288i
$129$	−0.826959	+	13.1441i	−0.0728097	+	1.15728i
$130$	9.92114	−	7.21948i	0.870141	−	0.633190i
$131$	1.07872	+	0.276969i	0.0942485	+	0.0241989i	0.295520	−	0.955337i	$-0.404507\pi$
$131$	1.07872	+	0.276969i	0.0942485	+	0.0241989i	−0.201271	+	0.979536i	$0.564507\pi$
$132$	0.825218	−	2.53976i	0.0718260	−	0.221058i
$133$	1.61941	+	1.95754i	0.140421	+	0.169740i
$134$	−5.73905	+	12.1961i	−0.495778	+	1.05358i
$135$	4.93969	+	10.4770i	0.425141	+	0.901719i
$136$	3.01820	−	2.83428i	0.258808	−	0.243037i
$137$	−15.9394	+	8.76274i	−1.36179	+	0.748651i	−0.984156	−	0.177303i	$-0.943263\pi$
$137$	−15.9394	+	8.76274i	−1.36179	+	0.748651i	−0.377635	+	0.925955i	$0.623263\pi$
$138$	1.54685	−	3.28723i	0.131677	−	0.279828i
$139$	−4.42618	−	9.40612i	−0.375424	−	0.797817i	−0.999860	−	0.0167406i	$-0.994671\pi$
$139$	−4.42618	−	9.40612i	−0.375424	−	0.797817i	0.624436	−	0.781076i	$-0.285329\pi$
$140$	−0.166035	+	2.67094i	−0.0140325	+	0.225736i
$141$	16.2558	+	2.05359i	1.36899	+	0.172943i
$142$	0.401792	+	6.38630i	0.0337176	+	0.535927i
$143$	2.60638	+	8.02162i	0.217957	+	0.670801i
$144$	0.00983847	−	0.0155029i	0.000819872	−	0.00129191i
$145$	0.180822	−	2.90880i	0.0150164	−	0.241563i
$146$	10.7599	−	2.76267i	0.890493	−	0.228640i
$147$	−0.607373	+	9.65392i	−0.0500953	+	0.796242i
$148$	−0.873824	+	4.58074i	−0.0718279	+	0.376535i
$149$	2.02755	−	6.24017i	0.166104	−	0.511215i	−0.833012	−	0.553255i	$-0.813386\pi$
$149$	2.02755	−	6.24017i	0.166104	−	0.511215i	0.999116	+	0.0420398i	$0.0133856\pi$
$150$	8.07191	−	3.20987i	0.659069	−	0.262085i
$151$	−3.14103	−	9.66708i	−0.255613	−	0.786696i	−0.993708	−	0.112000i	$-0.964274\pi$
$151$	−3.14103	−	9.66708i	−0.255613	−	0.786696i	0.738095	−	0.674697i	$-0.235726\pi$
$152$	2.10608	−	0.266060i	0.170826	−	0.0215803i
$153$	0.0706839	+	0.0279857i	0.00571445	+	0.00226251i
$154$	−1.71039	−	0.677192i	−0.137827	−	0.0545697i
$155$	−6.86085	+	2.72234i	−0.551076	+	0.218664i
$156$	0.598597	+	9.51443i	0.0479261	+	0.761764i
$157$	−15.0186	+	10.9117i	−1.19862	+	0.870846i	−0.994148	−	0.108027i	$-0.965547\pi$
$157$	−15.0186	+	10.9117i	−1.19862	+	0.870846i	−0.204469	+	0.978873i	$0.565547\pi$
$158$	−5.91877	−	1.51968i	−0.470872	−	0.120899i
$159$	13.0755	+	12.2787i	1.03696	+	0.973766i
$160$	1.81000	+	1.31297i	0.143093	+	0.103800i
$161$	−2.19307	−	1.20565i	−0.172838	−	0.0950185i
$162$	−8.98335	−	1.13486i	−0.705798	−	0.0891631i
$163$	3.57340	+	18.7324i	0.279891	+	1.46724i	0.793162	+	0.609011i	$0.208434\pi$
$163$	3.57340	+	18.7324i	0.279891	+	1.46724i	−0.513271	+	0.858227i	$0.671566\pi$
$164$	−7.55128	+	0.953948i	−0.589656	+	0.0744908i
$165$	0.379401	+	5.95927i	0.0295364	+	0.463928i
$166$	−0.914849	−	4.79581i	−0.0710060	−	0.372227i
$167$	13.0105	−	20.5013i	1.00678	−	1.58644i	0.214095	−	0.976813i	$-0.431320\pi$
$167$	13.0105	−	20.5013i	1.00678	−	1.58644i	0.792689	−	0.609626i	$-0.208680\pi$
$168$	−1.68213	−	1.22214i	−0.129779	−	0.0942902i
$169$	−10.9063	−	13.1835i	−0.838946	−	1.01411i
$170$	−3.93566	+	8.37996i	−0.301851	+	0.642714i
$171$	0.0208853	+	0.0329099i	0.00159714	+	0.00251669i
$172$	4.83207	−	5.84096i	0.368442	−	0.445369i
$173$	−8.39521	−	17.8407i	−0.638276	−	1.35641i	−0.918098	−	0.396354i	$-0.870275\pi$
$173$	−8.39521	−	17.8407i	−0.638276	−	1.35641i	0.279822	−	0.960052i	$-0.409725\pi$
$174$	1.83193	+	1.33098i	0.138879	+	0.100901i
$175$	−1.85765	−	5.68829i	−0.140425	−	0.429994i
$176$	−1.24354	+	0.903481i	−0.0937350	+	0.0681025i
$177$	0.520488	+	0.286141i	0.0391223	+	0.0215077i
$178$	9.17037	−	2.35455i	0.687348	−	0.176481i
$179$	14.4527	−	17.4703i	1.08025	−	1.30579i	0.130958	−	0.991388i	$-0.458195\pi$
$179$	14.4527	−	17.4703i	1.08025	−	1.30579i	0.949289	−	0.314406i	$-0.101805\pi$
$180$	−0.00766315	+	0.0403356i	−0.000571178	+	0.00300644i
$181$	−11.7840	+	4.66560i	−0.875894	+	0.346791i	−0.762677	−	0.646779i	$-0.776116\pi$
$181$	−11.7840	+	4.66560i	−0.875894	+	0.346791i	−0.113217	+	0.993570i	$0.536116\pi$
$182$	6.56707			0.486784
$183$	15.0803	−	5.97070i	1.11476	−	0.441367i
$184$	−1.83246	+	1.00741i	−0.135091	+	0.0742669i
$185$	−1.96159	−	10.2414i	−0.144219	−	0.752962i
$186$	1.07462	−	5.63335i	0.0787949	−	0.413058i
$187$	−4.63925	−	4.35655i	−0.339256	−	0.318582i
$188$	−6.87496	−	6.45602i	−0.501408	−	0.470854i
$189$	−1.16167	+	6.08970i	−0.0844992	+	0.442960i
$190$	−4.15791	+	2.28988i	−0.301647	+	0.166126i
$191$	2.50187	−	1.37541i	0.181029	−	0.0995213i	−0.388663	−	0.921380i	$-0.627063\pi$
$191$	2.50187	−	1.37541i	0.181029	−	0.0995213i	0.569691	+	0.821859i	$0.307063\pi$
$192$	−1.61534	+	0.639559i	−0.116577	+	0.0461562i
$193$	4.82380			0.347225			0.173612	−	0.984814i	$-0.444456\pi$
$193$	4.82380			0.347225			0.173612	+	0.984814i	$0.444456\pi$
$194$	8.17237	−	3.23567i	0.586742	−	0.232308i
$195$	−9.09076	−	19.2814i	−0.651003	−	1.38077i
$196$	3.54899	−	4.28999i	0.253499	−	0.306428i
$197$	−16.0641	+	4.12455i	−1.14452	+	0.293862i	−0.772903	−	0.634524i	$-0.781196\pi$
$197$	−16.0641	+	4.12455i	−1.14452	+	0.293862i	−0.371615	+	0.928387i	$0.621196\pi$
$198$	−0.0247320	−	0.0135965i	−0.00175763	−	0.000966264i
$199$	7.36550	−	5.35135i	0.522127	−	0.379347i	−0.295278	−	0.955411i	$-0.595412\pi$
$199$	7.36550	−	5.35135i	0.522127	−	0.379347i	0.817404	+	0.576064i	$0.195412\pi$
$200$	−4.84477	−	1.23620i	−0.342577	−	0.0874127i
$201$	18.9452	+	13.7645i	1.33629	+	0.970871i
$202$	−6.19006	−	13.1545i	−0.435531	−	0.925550i
$203$	0.994287	−	1.20189i	0.0697853	−	0.0843559i
$204$	−3.85433	−	6.07345i	−0.269857	−	0.425227i
$205$	14.9081	−	8.21030i	1.04122	−	0.573432i
$206$	−1.52058	−	1.83806i	−0.105944	−	0.128064i
$207$	−0.0310628	−	0.0225684i	−0.00215901	−	0.00156861i
$208$	2.94022	−	4.63304i	0.203867	−	0.321244i
$209$	−0.611420	−	3.20518i	−0.0422928	−	0.221707i
$210$	4.50410	+	1.15286i	0.310812	+	0.0795552i
$211$	−20.6007	+	2.60248i	−1.41821	+	0.179162i	−0.796763	−	0.604292i	$-0.793456\pi$
$211$	−20.6007	+	2.60248i	−1.41821	+	0.179162i	−0.621450	+	0.783454i	$0.713456\pi$
$212$	−1.93460	−	10.1415i	−0.132869	−	0.696522i
$213$	11.0295	+	1.39335i	0.755727	+	0.0954705i
$214$	5.88451	+	3.23503i	0.402257	+	0.221142i
$215$	−5.22601	+	16.1251i	−0.356411	+	1.09972i
$216$	3.77615	+	3.54604i	0.256935	+	0.241278i
$217$	−3.82645	−	0.982467i	−0.259757	−	0.0666942i
$218$	−5.32897	+	3.87172i	−0.360923	+	0.262226i
$219$	−1.21185	−	19.2619i	−0.0818894	−	1.30160i
$220$	1.83949	−	2.90337i	0.124018	−	0.195745i
$221$	21.1238	+	8.36351i	1.42094	+	0.562591i
$222$	7.53289	+	2.98248i	0.505574	+	0.200171i
$223$	−24.8534	+	3.13972i	−1.66431	+	0.210251i	−0.900397	−	0.435070i	$-0.856724\pi$
$223$	−24.8534	+	3.13972i	−1.66431	+	0.210251i	−0.763911	+	0.645321i	$0.776724\pi$
$224$	0.369827	+	1.13821i	0.0247101	+	0.0760500i
$225$	−0.0173377	−	0.0901544i	−0.00115585	−	0.00601029i
$226$	0.488279	−	1.50277i	0.0324799	−	0.0999627i
$227$	0.0913422	−	0.478832i	0.00606259	−	0.0317812i	−0.979127	−	0.203247i	$-0.934850\pi$
$227$	0.0913422	−	0.478832i	0.00606259	−	0.0317812i	0.985190	+	0.171466i	$0.0548504\pi$
$228$	0.231575	−	3.68079i	0.0153365	−	0.243766i
$229$	23.1242	−	5.93729i	1.52809	−	0.392347i	0.611198	−	0.791478i	$-0.290688\pi$
$229$	23.1242	−	5.93729i	1.52809	−	0.392347i	0.916894	+	0.399130i	$0.130688\pi$
$230$	2.97783	−	3.60507i	0.196352	−	0.237711i
$231$	−1.71249	+	2.69845i	−0.112673	+	0.177545i
$232$	−0.402762	−	1.23958i	−0.0264427	−	0.0813821i
$233$	1.11344	+	17.6977i	0.0729442	+	1.15941i	0.848874	+	0.528595i	$0.177281\pi$
$233$	1.11344	+	17.6977i	0.0729442	+	1.15941i	−0.775930	+	0.630819i	$0.782719\pi$
$234$	0.0999586	+	0.0126277i	0.00653450	+	0.000825499i
$235$	19.6134	+	7.74854i	1.27944	+	0.505459i
$236$	−0.145564	−	0.309339i	−0.00947540	−	0.0201362i
$237$	−4.52028	+	9.60608i	−0.293623	+	0.623982i
$238$	−4.34222	+	2.38715i	−0.281464	+	0.154736i
$239$	−6.78297	+	6.36964i	−0.438754	+	0.412018i	−0.872190	−	0.489167i	$-0.837301\pi$
$239$	−6.78297	+	6.36964i	−0.438754	+	0.412018i	0.433436	+	0.901184i	$0.357301\pi$
$240$	2.82992	−	2.66146i	0.182671	−	0.171796i
$241$	5.97924	−	12.7065i	0.385157	−	0.818499i	−0.614408	−	0.788989i	$-0.710605\pi$
$241$	5.97924	−	12.7065i	0.385157	−	0.818499i	0.999564	−	0.0295109i	$-0.00939496\pi$
$242$	−5.50565	−	6.65519i	−0.353916	−	0.427812i
$243$	−0.0589646	+	0.181474i	−0.00378258	+	0.0116416i
$244$	−9.04235	−	2.32168i	−0.578877	−	0.148630i
$245$	−3.83833	+	11.8433i	−0.245222	+	0.756641i
$246$	−0.830306	+	13.1973i	−0.0529384	+	0.841431i
$247$	6.24155	+	9.83511i	0.397140	+	0.625793i
$248$	−2.40631	+	2.25968i	−0.152801	+	0.143490i
$249$	−8.48220			−0.537538
$250$	11.0890	−	1.42616i	0.701330	−	0.0901983i
$251$	22.2602			1.40505			0.702527	−	0.711657i	$-0.252055\pi$
$251$	22.2602			1.40505			0.702527	+	0.711657i	$0.252055\pi$
$252$	−0.0160187	+	0.0150426i	−0.00100909	+	0.000947595i
$253$	1.72228	+	2.71388i	0.108279	+	0.170620i
$254$	0.975084	−	15.4985i	0.0611822	−	0.972463i
$255$	13.0198	+	9.44453i	0.815329	+	0.591440i
$256$	0.968583	+	0.248690i	0.0605364	+	0.0155431i
$257$	−1.63535	+	5.03308i	−0.102010	+	0.313955i	−0.989017	−	0.147801i	$-0.952780\pi$
$257$	−1.63535	+	5.03308i	−0.102010	+	0.313955i	0.887007	+	0.461756i	$0.152780\pi$
$258$	−8.39496	−	10.1478i	−0.522647	−	0.631772i
$259$	2.37629	−	5.04986i	0.147655	−	0.313783i
$260$	−2.29013	+	12.0543i	−0.142028	+	0.747573i
$261$	0.0174453	−	0.0163822i	0.00107984	−	0.00101403i
$262$	−0.975954	+	0.536535i	−0.0602946	+	0.0331473i
$263$	1.26678	−	2.69205i	0.0781130	−	0.165999i	−0.861956	−	0.506984i	$-0.830760\pi$
$263$	1.26678	−	2.69205i	0.0781130	−	0.165999i	0.940069	+	0.340985i	$0.110760\pi$
$264$	1.13703	+	2.41630i	0.0699792	+	0.148713i
$265$	12.3847	+	19.4829i	0.760786	+	1.19683i
$266$	−2.52053	−	0.318417i	−0.154543	−	0.0195234i
$267$	−1.03283	−	16.4164i	−0.0632083	−	1.00467i
$268$	−4.16522	−	12.8192i	−0.254431	−	0.783059i
$269$	10.7702	−	16.9711i	0.656669	−	1.03474i	−0.338911	−	0.940819i	$-0.610058\pi$
$269$	10.7702	−	16.9711i	0.656669	−	1.03474i	0.995579	−	0.0939255i	$-0.0299415\pi$
$270$	−10.7729	−	4.25597i	−0.655618	−	0.259010i
$271$	−21.2740	+	5.46225i	−1.29231	+	0.331808i	−0.831417	−	0.555650i	$-0.812470\pi$
$271$	−21.2740	+	5.46225i	−1.29231	+	0.331808i	−0.460890	+	0.887457i	$0.652470\pi$
$272$	−0.259976	+	4.13220i	−0.0157633	+	0.250551i
$273$	2.13788	−	11.2072i	0.129391	−	0.678289i
$274$	5.62079	−	17.2990i	0.339564	−	1.04507i
$275$	−1.42882	+	7.55149i	−0.0861609	+	0.455372i
$276$	1.12266	+	3.45519i	0.0675761	+	0.207978i
$277$	4.08017	−	0.515446i	0.245154	−	0.0309701i	−0.00179605	−	0.999998i	$-0.500572\pi$
$277$	4.08017	−	0.515446i	0.245154	−	0.0309701i	0.246950	+	0.969028i	$0.420572\pi$
$278$	9.66548	+	3.82684i	0.579697	+	0.229518i
$279$	−0.0563540	−	0.0223121i	−0.00337382	−	0.00133579i
$280$	−1.70735	−	2.06069i	−0.102034	−	0.123150i
$281$	0.697892	+	11.0927i	0.0416327	+	0.661733i	0.962403	+	0.271627i	$0.0875617\pi$
$281$	0.697892	+	11.0927i	0.0416327	+	0.661733i	−0.920770	+	0.390106i	$0.872438\pi$
$282$	−13.2558	+	9.63088i	−0.789369	+	0.573510i
$283$	−1.88149	−	0.483084i	−0.111843	−	0.0287164i	0.192354	−	0.981326i	$-0.438388\pi$
$283$	−1.88149	−	0.483084i	−0.111843	−	0.0287164i	−0.304196	+	0.952609i	$0.598388\pi$
$284$	−4.66462	−	4.38037i	−0.276794	−	0.259927i
$285$	2.55426	+	7.84123i	0.151301	+	0.464474i
$286$	−7.39115	−	4.06332i	−0.437048	−	0.240269i
$287$	9.03727	+	1.14167i	0.533453	+	0.0673908i
$288$	0.00344056	+	0.0180361i	0.000202737	+	0.00106278i
$289$	−0.141513	+	0.0178773i	−0.00832432	+	0.00105161i
$290$	1.85940	+	2.24421i	0.109188	+	0.131784i
$291$	−2.86142	−	15.0001i	−0.167739	−	0.879320i
$292$	−5.95243	+	9.37954i	−0.348340	+	0.548896i
$293$	−3.38096	−	2.45641i	−0.197518	−	0.143505i	0.484630	−	0.874719i	$-0.338954\pi$
$293$	−3.38096	−	2.45641i	−0.197518	−	0.143505i	−0.682148	+	0.731214i	$0.738954\pi$
$294$	−6.16581	−	7.45318i	−0.359597	−	0.434678i
$295$	0.557658	+	0.522891i	0.0324681	+	0.0304439i
$296$	−2.49874	−	3.93739i	−0.145237	−	0.228856i
$297$	5.07539	−	6.13509i	0.294504	−	0.355994i
$298$	2.79367	+	5.93685i	0.161833	+	0.343912i
$299$	−9.28308	−	6.74455i	−0.536855	−	0.390048i
$300$	−3.68686	+	7.86550i	−0.212861	+	0.454115i
$301$	−7.33971	+	5.33261i	−0.423054	+	0.307367i
$302$	8.90728	+	4.89682i	0.512557	+	0.281780i
$303$	−24.4643	+	6.28136i	−1.40544	+	0.360855i
$304$	−1.35314	+	1.63566i	−0.0776076	+	0.0938115i
$305$	20.7086	−	2.63184i	1.18577	−	0.150699i
$306$	−0.0706839	+	0.0279857i	−0.00404073	+	0.00159984i
$307$	−32.6709			−1.86462			−0.932312	−	0.361654i	$-0.882212\pi$
$307$	−32.6709			−1.86462			−0.932312	+	0.361654i	$0.882212\pi$
$308$	1.71039	−	0.677192i	0.0974587	−	0.0385866i
$309$	−3.63180	+	1.99660i	−0.206606	+	0.113583i
$310$	3.13777	−	6.68107i	0.178213	−	0.379459i
$311$	−4.55066	+	23.8554i	−0.258044	+	1.35271i	0.583318	+	0.812244i	$0.301754\pi$
$311$	−4.55066	+	23.8554i	−0.258044	+	1.35271i	−0.841363	+	0.540471i	$0.818246\pi$
$312$	−6.94944	−	6.52596i	−0.393434	−	0.369459i
$313$	−22.1628	−	20.8123i	−1.25272	−	1.17638i	−0.976555	−	0.215267i	$-0.930938\pi$
$313$	−22.1628	−	20.8123i	−1.25272	−	1.17638i	−0.276160	−	0.961112i	$-0.589062\pi$
$314$	3.47855	−	18.2352i	0.196306	−	1.02907i
$315$	0.0208881	−	0.0444757i	0.00117691	−	0.00250592i
$316$	5.35489	−	2.94388i	0.301236	−	0.165606i
$317$	−3.54813	+	1.40480i	−0.199283	+	0.0789017i	−0.465646	−	0.884971i	$-0.654178\pi$
$317$	−3.54813	+	1.40480i	−0.199283	+	0.0789017i	0.266363	+	0.963873i	$0.414178\pi$
$318$	−17.9370			−1.00586
$319$	−1.86271	+	0.737500i	−0.104292	+	0.0412921i
$320$	−2.21823	+	0.281913i	−0.124003	+	0.0157594i
$321$	7.43649	−	8.98917i	0.415064	−	0.501727i
$322$	2.42400	−	0.622378i	0.135084	−	0.0346838i
$323$	−7.70208	−	4.23425i	−0.428555	−	0.235600i
$324$	7.32544	−	5.32225i	0.406969	−	0.295680i
$325$	−5.18136	−	26.9426i	−0.287410	−	1.49451i
$326$	−15.4281	−	11.2092i	−0.854486	−	0.620820i
$327$	4.87254	+	10.3547i	0.269452	+	0.572615i
$328$	4.85162	−	5.86460i	0.267886	−	0.323819i
$329$	6.04787	+	9.52993i	0.333430	+	0.525402i
$330$	−4.35597	−	4.08440i	−0.239788	−	0.224839i
$331$	−8.06935	−	9.75417i	−0.443532	−	0.536138i	0.500612	−	0.865672i	$-0.333108\pi$
$331$	−8.06935	−	9.75417i	−0.443532	−	0.536138i	−0.944144	+	0.329534i	$0.893108\pi$
$332$	3.94985	+	2.86973i	0.216776	+	0.157497i
$333$	0.0458802	−	0.0722956i	0.00251422	−	0.00396177i
$334$	4.54984	+	23.8511i	0.248956	+	1.30508i
$335$	19.2292	+	23.2087i	1.05060	+	1.26803i
$336$	2.06283	−	0.260597i	0.112537	−	0.0142167i
$337$	−2.81046	−	14.7329i	−0.153095	−	0.802554i	−0.973133	−	0.230244i	$-0.926047\pi$
$337$	−2.81046	−	14.7329i	−0.153095	−	0.802554i	0.820037	−	0.572310i	$-0.193953\pi$
$338$	16.9750	+	2.14445i	0.923321	+	0.116643i
$339$	−2.40562	−	1.32250i	−0.130656	−	0.0718285i
$340$	−2.86751	−	8.80287i	−0.155513	−	0.477403i
$341$	3.69873	+	3.47334i	0.200297	+	0.188092i
$342$	−0.0377531	−	0.00969335i	−0.00204145	−	0.000524156i
$343$	−12.1683	+	8.84079i	−0.657027	+	0.477358i
$344$	0.475991	+	7.56566i	0.0256637	+	0.407913i
$345$	−5.18288	−	6.25549i	−0.279037	−	0.336784i
$346$	18.3327	+	7.25842i	0.985570	+	0.390215i
$347$	24.7215	+	9.78792i	1.32712	+	0.525443i	0.921421	−	0.388565i	$-0.127029\pi$
$347$	24.7215	+	9.78792i	1.32712	+	0.525443i	0.405696	+	0.914008i	$0.367029\pi$
$348$	−2.24654	+	0.283804i	−0.120427	+	0.0152135i
$349$	1.24629	+	3.83569i	0.0667125	+	0.205320i	0.978856	−	0.204551i	$-0.0655736\pi$
$349$	1.24629	+	3.83569i	0.0667125	+	0.205320i	−0.912143	+	0.409871i	$0.865574\pi$
$350$	5.24807	+	2.87493i	0.280521	+	0.153672i
$351$	−8.78371	+	27.0335i	−0.468840	+	1.44294i
$352$	0.288023	−	1.50987i	0.0153517	−	0.0804762i
$353$	1.62575	−	25.8405i	0.0865297	−	1.37535i	−0.680033	−	0.733181i	$-0.738035\pi$
$353$	1.62575	−	25.8405i	0.0865297	−	1.37535i	0.766563	−	0.642169i	$-0.221965\pi$
$354$	−0.575296	+	0.147711i	−0.0305767	+	0.00785075i
$355$	13.3076	+	5.25733i	0.706293	+	0.279030i
$356$	−5.07311	+	7.99394i	−0.268874	+	0.423678i
$357$	2.66026	+	8.18743i	0.140796	+	0.433325i
$358$	1.42369	+	22.6289i	0.0752443	+	1.19597i
$359$	−27.9185	−	3.52693i	−1.47348	−	0.186144i	−0.652801	−	0.757530i	$-0.726406\pi$
$359$	−27.9185	−	3.52693i	−1.47348	−	0.186144i	−0.820682	+	0.571386i	$0.806406\pi$
$360$	−0.0220254	−	0.0346492i	−0.00116084	−	0.00182617i
$361$	6.17109	+	13.1142i	0.324794	+	0.690223i
$362$	5.39631	−	11.4677i	0.283624	−	0.602731i
$363$	−13.1499	+	7.22921i	−0.690190	+	0.379435i
$364$	−4.78719	+	4.49547i	−0.250917	+	0.235627i
$365$	4.63633	−	24.4037i	0.242677	−	1.27735i
$366$	−6.90581	+	14.6756i	−0.360973	+	0.767106i
$367$	23.2865	+	28.1486i	1.21555	+	1.46934i	0.840041	+	0.542523i	$0.182531\pi$
$367$	23.2865	+	28.1486i	1.21555	+	1.46934i	0.375506	+	0.926820i	$0.377469\pi$
$368$	0.646192	−	1.98878i	0.0336851	−	0.103672i
$369$	0.135363	+	0.0347552i	0.00704669	+	0.00180928i
$370$	8.44065	+	6.12285i	0.438809	+	0.318312i
$371$	−0.775845	+	12.3317i	−0.0402799	+	0.640230i
$372$	3.07293	+	4.84217i	0.159324	+	0.251055i
$373$	15.2889	−	14.3572i	0.791628	−	0.743388i	−0.179033	−	0.983843i	$-0.557297\pi$
$373$	15.2889	−	14.3572i	0.791628	−	0.743388i	0.970660	+	0.240455i	$0.0772968\pi$
$374$	6.36413			0.329082
$375$	1.17614	−	19.3884i	0.0607354	−	1.00122i
$376$	9.43108			0.486371
$377$	5.21352	−	4.89582i	0.268510	−	0.252147i
$378$	−3.32186	−	5.23442i	−0.170858	−	0.269229i
$379$	−0.981182	+	15.5954i	−0.0503999	+	0.801084i	0.888924	+	0.458054i	$0.151453\pi$
$379$	−0.981182	+	15.5954i	−0.0503999	+	0.801084i	−0.939324	+	0.343030i	$0.888547\pi$
$380$	1.46345	−	4.51554i	0.0750736	−	0.231642i
$381$	−26.1319	−	6.70952i	−1.33878	−	0.343739i
$382$	−0.882247	+	2.71528i	−0.0451397	+	0.138926i
$383$	7.97031	+	9.63445i	0.407264	+	0.492297i	0.933770	−	0.357874i	$-0.116498\pi$
$383$	7.97031	+	9.63445i	0.407264	+	0.492297i	−0.526506	+	0.850171i	$0.676498\pi$
$384$	0.739725	−	1.57200i	0.0377489	−	0.0802205i
$385$	−2.99644	+	2.81807i	−0.152713	+	0.143622i
$386$	−3.51640	+	3.30212i	−0.178980	+	0.168073i
$387$	−0.121973	+	0.0670552i	−0.00620023	+	0.00340861i
$388$	−3.74243	+	7.95307i	−0.189993	+	0.403756i
$389$	9.62791	+	20.4604i	0.488155	+	1.03738i	0.985476	+	0.169815i	$0.0543170\pi$
$389$	9.62791	+	20.4604i	0.488155	+	1.03738i	−0.497321	+	0.867566i	$0.665683\pi$
$390$	19.8259	+	7.83247i	1.00392	+	0.396613i
$391$	8.58974	+	1.08514i	0.434402	+	0.0548777i
$392$	0.349599	+	5.55672i	0.0176574	+	0.280656i
$393$	0.597917	+	1.84020i	0.0301609	+	0.0928258i
$394$	8.88676	−	14.0033i	0.447708	−	0.705476i
$395$	−8.70192	+	10.5349i	−0.437841	+	0.530066i
$396$	0.0273363	−	0.00701878i	0.00137370	−	0.000352707i
$397$	0.757440	−	12.0392i	0.0380148	−	0.604228i	−0.932194	−	0.361959i	$-0.882108\pi$
$397$	0.757440	−	12.0392i	0.0380148	−	0.604228i	0.970209	−	0.242270i	$-0.0778918\pi$
$398$	−1.70597	+	8.94300i	−0.0855125	+	0.448272i
$399$	−1.36395	+	4.19780i	−0.0682828	+	0.210153i
$400$	4.37792	−	2.41532i	0.218896	−	0.120766i
$401$	6.52715	+	20.0885i	0.325951	+	1.00317i	0.971010	+	0.239040i	$0.0768327\pi$
$401$	6.52715	+	20.0885i	0.325951	+	1.00317i	−0.645059	+	0.764133i	$0.723167\pi$
$402$	−23.2329	+	2.93499i	−1.15875	+	0.146384i
$403$	−16.8413	−	6.66796i	−0.838927	−	0.332155i
$404$	13.5173	+	5.35186i	0.672509	+	0.266265i
$405$	−10.8361	+	17.1032i	−0.538451	+	0.849867i
$406$	0.0979439	+	1.55677i	0.00486087	+	0.0772614i
$407$	−5.79903	+	4.21324i	−0.287447	+	0.208843i
$408$	6.96725	+	1.78889i	0.344930	+	0.0885630i
$409$	2.66414	+	2.50179i	0.131733	+	0.123706i	0.747614	−	0.664134i	$-0.231200\pi$
$409$	2.66414	+	2.50179i	0.131733	+	0.123706i	−0.615880	+	0.787840i	$0.711200\pi$
$410$	−5.24716	+	16.1903i	−0.259139	+	0.799583i
$411$	−27.6921	−	15.2239i	−1.36595	−	0.750939i
$412$	2.36670	+	0.298983i	0.116599	+	0.0147299i
$413$	0.0766676	+	0.401906i	0.00377257	+	0.0197765i
$414$	0.0380929	−	0.00481226i	0.00187217	−	0.000236509i
$415$	−10.5762	−	2.70707i	−0.519164	−	0.132885i
$416$	1.02821	+	5.39006i	0.0504121	+	0.264269i
$417$	9.67732	−	15.2490i	0.473900	−	0.746747i
$418$	2.63980	+	1.91793i	0.129117	+	0.0938089i
$419$	−2.06289	−	2.49360i	−0.100779	−	0.121821i	0.717713	−	0.696339i	$-0.245189\pi$
$419$	−2.06289	−	2.49360i	−0.100779	−	0.121821i	−0.818491	+	0.574519i	$0.805189\pi$
$420$	−4.07253	+	2.24286i	−0.198719	+	0.109441i
$421$	−16.5490	−	26.0771i	−0.806549	−	1.27092i	−0.959225	−	0.282642i	$-0.908789\pi$
$421$	−16.5490	−	26.0771i	−0.806549	−	1.27092i	0.152676	−	0.988276i	$-0.451211\pi$
$422$	13.2358	−	15.9993i	0.644307	−	0.778833i
$423$	0.0737308	+	0.156686i	0.00358492	+	0.00761833i
$424$	8.35260	+	6.06852i	0.405638	+	0.294713i
$425$	13.2197	+	15.9313i	0.641250	+	0.772780i
$426$	−8.99395	+	6.53449i	−0.435758	+	0.316597i
$427$	9.79078	+	5.38253i	0.473809	+	0.260479i
$428$	−6.50415	+	1.66998i	−0.314390	+	0.0807217i
$429$	−9.34049	+	11.2907i	−0.450963	+	0.545121i
$430$	−7.22876	−	15.3321i	−0.348602	−	0.739380i
$431$	20.7423	−	8.21247i	0.999123	−	0.395581i	0.189086	−	0.981960i	$-0.439447\pi$
$431$	20.7423	−	8.21247i	0.999123	−	0.395581i	0.810036	+	0.586380i	$0.199447\pi$
$432$	−5.18013			−0.249229
$433$	17.1304	−	6.78241i	0.823235	−	0.325942i	0.0815322	−	0.996671i	$-0.474019\pi$
$433$	17.1304	−	6.78241i	0.823235	−	0.325942i	0.741702	+	0.670729i	$0.234019\pi$
$434$	3.46191	−	1.90320i	0.166177	−	0.0913566i
$435$	4.43521	−	2.44260i	0.212652	−	0.117114i
$436$	1.23427	−	6.47030i	0.0591110	−	0.309871i
$437$	3.23595	+	3.03875i	0.154796	+	0.145363i
$438$	14.0690	+	13.2117i	0.672245	+	0.631280i
$439$	0.483345	−	2.53379i	0.0230688	−	0.120931i	−0.968890	−	0.247491i	$-0.920394\pi$
$439$	0.483345	−	2.53379i	0.0230688	−	0.120931i	0.991959	+	0.126560i	$0.0403938\pi$
$440$	0.646564	+	3.37569i	0.0308237	+	0.160929i
$441$	−0.0895850	+	0.0492497i	−0.00426595	+	0.00234523i
$442$	−21.1238	+	8.36351i	−1.00476	+	0.397812i
$443$	−33.4086			−1.58729			−0.793645	−	0.608381i	$-0.791819\pi$
$443$	−33.4086			−1.58729			−0.793645	+	0.608381i	$0.791819\pi$
$444$	−7.53289	+	2.98248i	−0.357495	+	0.141542i
$445$	3.95143	−	20.7987i	0.187316	−	0.985951i
$446$	15.9681	−	19.3021i	0.756110	−	0.913980i
$447$	11.0411	−	2.83488i	0.522227	−	0.134085i
$448$	−1.04875	−	0.576556i	−0.0495489	−	0.0272397i
$449$	1.25678	−	0.913101i	0.0593109	−	0.0430919i	−0.557735	−	0.830019i	$-0.688329\pi$
$449$	1.25678	−	0.913101i	0.0593109	−	0.0430919i	0.617046	+	0.786927i	$0.288329\pi$
$450$	0.0743536	+	0.0538513i	0.00350506	+	0.00253857i
$451$	−9.46491	−	6.87666i	−0.445685	−	0.323809i
$452$	0.672776	+	1.42972i	0.0316447	+	0.0672484i
$453$	11.2565	−	13.6068i	0.528876	−	0.639302i
$454$	0.261198	+	0.411582i	0.0122586	+	0.0193165i
$455$	6.24238	−	13.2915i	0.292647	−	0.623117i
$456$	2.35086	+	2.84170i	0.110089	+	0.133075i
$457$	10.8145	+	7.85719i	0.505881	+	0.367544i	0.811259	−	0.584687i	$-0.198783\pi$
$457$	10.8145	+	7.85719i	0.505881	+	0.367544i	−0.305378	+	0.952231i	$0.598783\pi$
$458$	−12.7925	+	20.1577i	−0.597754	+	0.941909i
$459$	−4.01889	−	21.0677i	−0.187586	−	0.983358i
$460$	0.297093	+	4.66644i	0.0138520	+	0.217574i
$461$	−23.9964	+	3.03145i	−1.11762	+	0.141189i	−0.662373	−	0.749174i	$-0.730450\pi$
$461$	−23.9964	+	3.03145i	−1.11762	+	0.141189i	−0.455251	+	0.890363i	$0.650450\pi$
$462$	−0.598865	−	3.13936i	−0.0278617	−	0.146056i
$463$	29.1260	+	3.67947i	1.35360	+	0.171000i	0.768442	−	0.639919i	$-0.221032\pi$
$463$	29.1260	+	3.67947i	1.35360	+	0.171000i	0.585159	+	0.810919i	$0.301032\pi$
$464$	1.14215	+	0.627902i	0.0530229	+	0.0291496i
$465$	−10.3802	−	7.52982i	−0.481372	−	0.349187i
$466$	−12.9266	−	12.1389i	−0.598812	−	0.562322i
$467$	−31.8689	−	8.18255i	−1.47472	−	0.378643i	−0.576102	−	0.817378i	$-0.695427\pi$
$467$	−31.8689	−	8.18255i	−1.47472	−	0.378643i	−0.898617	+	0.438735i	$0.855427\pi$
$468$	−0.0815109	+	0.0592211i	−0.00376784	+	0.00273750i
$469$	1.01290	+	16.0996i	0.0467713	+	0.743409i
$470$	−19.6018	+	7.77788i	−0.904165	+	0.358767i
$471$	−29.9873	−	11.8728i	−1.38174	−	0.547070i
$472$	0.317869	+	0.125853i	0.0146311	+	0.00579286i
$473$	11.5602	−	1.46040i	0.531540	−	0.0671492i
$474$	−3.28067	−	10.0969i	−0.150686	−	0.463765i
$475$	0.682314	+	10.5921i	0.0313067	+	0.486001i
$476$	1.53122	−	4.71261i	0.0701834	−	0.216002i
$477$	−0.0355217	+	0.186211i	−0.00162643	+	0.00852602i
$478$	0.584259	−	9.28653i	0.0267234	−	0.424756i
$479$	2.54413	−	0.653220i	0.116244	−	0.0298464i	−0.190120	−	0.981761i	$-0.560888\pi$
$479$	2.54413	−	0.653220i	0.116244	−	0.0298464i	0.306364	+	0.951915i	$0.400888\pi$
$480$	−0.241029	+	3.87733i	−0.0110014	+	0.176975i
$481$	13.7112	−	21.6055i	0.625179	−	0.985125i
$482$	4.33954	+	13.3557i	0.197661	+	0.608337i
$483$	−0.273008	−	4.33934i	−0.0124223	−	0.197447i
$484$	8.56923	+	1.08255i	0.389511	+	0.0492066i
$485$	1.21942	−	19.6163i	0.0553710	−	0.890730i
$486$	−0.0812444	−	0.172653i	−0.00368532	−	0.00783170i
$487$	−9.67414	+	20.5586i	−0.438377	+	0.931598i	0.556533	+	0.830826i	$0.312131\pi$
$487$	−9.67414	+	20.5586i	−0.438377	+	0.931598i	−0.994909	+	0.100773i	$0.967869\pi$
$488$	8.18089	−	4.49748i	0.370332	−	0.203592i
$489$	−24.1518	+	22.6801i	−1.09218	+	1.02563i
$490$	−5.30928	−	11.2609i	−0.239849	−	0.508716i
$491$	−7.15141	+	15.1975i	−0.322739	+	0.685854i	−0.998694	−	0.0510880i	$-0.983731\pi$
$491$	−7.15141	+	15.1975i	−0.322739	+	0.685854i	0.675956	+	0.736942i	$0.263731\pi$
$492$	−8.42893	−	10.1888i	−0.380006	−	0.459348i
$493$	−1.66758	+	5.13230i	−0.0751042	+	0.231147i
$494$	−11.2825	−	2.89685i	−0.507623	−	0.130335i
$495$	−0.0510282	+	0.0371325i	−0.00229355	+	0.00166898i
$496$	0.207270	−	3.29447i	0.00930671	−	0.147926i
$497$	4.10344	+	6.46599i	0.184065	+	0.290039i
$498$	6.18326	−	5.80647i	0.277078	−	0.260194i
$499$	−4.65347			−0.208318			−0.104159	−	0.994561i	$-0.533215\pi$
$499$	−4.65347			−0.208318			−0.104159	+	0.994561i	$0.533215\pi$
$500$	−7.10726	+	8.63057i	−0.317847	+	0.385971i
$501$	42.1848			1.88468
$502$	−16.2270	+	15.2382i	−0.724247	+	0.680113i
$503$	−2.53061	−	3.98761i	−0.112834	−	0.177799i	0.783218	−	0.621748i	$-0.213577\pi$
$503$	−2.53061	−	3.98761i	−0.112834	−	0.177799i	−0.896052	+	0.443949i	$0.853577\pi$
$504$	0.00137979	−	0.0219312i	6.14608e−5	−	0.000976892i
$505$	−32.5084	+	0.0243209i	−1.44660	+	0.00108227i
$506$	−3.11327	−	0.799352i	−0.138402	−	0.0355355i
$507$	9.18580	−	28.2710i	0.407956	−	1.25556i
$508$	9.89866	+	11.9654i	0.439182	+	0.530880i
$509$	−6.24749	+	13.2766i	−0.276915	+	0.588474i	−0.994107	−	0.108401i	$-0.965427\pi$
$509$	−6.24749	+	13.2766i	−0.276915	+	0.588474i	0.717192	+	0.696875i	$0.245427\pi$
$510$	−15.9562	+	2.02787i	−0.706554	+	0.0897956i
$511$	9.69161	−	9.10102i	0.428731	−	0.402606i
$512$	−0.876307	+	0.481754i	−0.0387276	+	0.0212907i
$513$	4.68207	−	9.94991i	0.206719	−	0.439299i
$514$	−2.25326	−	4.78843i	−0.0993871	−	0.211208i
$515$	−5.16558	+	1.33042i	−0.227623	+	0.0586251i
$516$	13.0663	+	1.65066i	0.575211	+	0.0726660i
$517$	−0.910241	−	14.4679i	−0.0400323	−	0.636296i
$518$	1.72463	+	5.30787i	0.0757760	+	0.233215i
$519$	18.3551	−	28.9230i	0.805700	−	1.26958i
$520$	−6.58228	−	10.3549i	−0.288652	−	0.454091i
$521$	18.5217	−	4.75558i	0.811452	−	0.208346i	0.179906	−	0.983684i	$-0.442421\pi$
$521$	18.5217	−	4.75558i	0.811452	−	0.208346i	0.631546	+	0.775338i	$0.282421\pi$
$522$	−0.00150267	+	0.0238843i	−6.57701e−5	+	0.00104539i
$523$	0.676849	−	3.54817i	0.0295965	−	0.155151i	−0.964421	−	0.264371i	$-0.914836\pi$
$523$	0.676849	−	3.54817i	0.0295965	−	0.155151i	0.994018	+	0.109221i	$0.0348356\pi$
$524$	0.344156	−	1.05920i	0.0150345	−	0.0462715i
$525$	6.61476	−	8.02027i	0.288692	−	0.350033i
$526$	0.919389	+	2.82959i	0.0400873	+	0.123376i
$527$	13.5595	−	1.71296i	0.590661	−	0.0746178i
$528$	−2.48293	−	0.983062i	−0.108056	−	0.0427823i
$529$	17.3191	+	6.85713i	0.753006	+	0.298136i
$530$	−22.3650	−	5.72453i	−0.971475	−	0.248658i
$531$	0.000394154		0.00626490i	1.71048e−5		0.000271874i
$532$	2.05536	−	1.49330i	0.0891110	−	0.0647430i
$533$	40.4530	+	10.3866i	1.75221	+	0.449892i
$534$	11.9907	+	11.2600i	0.518888	+	0.487268i
$535$	12.1412	−	8.83496i	0.524908	−	0.381969i
$536$	11.8117	+	6.49352i	0.510187	+	0.280478i
$537$	39.0813	+	4.93711i	1.68648	+	0.213052i
$538$	3.76638	+	19.7441i	0.162380	+	0.851227i
$539$	8.49060	−	1.07261i	0.365716	−	0.0462007i
$540$	10.7665	−	4.27209i	0.463317	−	0.183841i
$541$	−4.05403	−	21.2520i	−0.174297	−	0.913695i	−0.956734	−	0.290965i	$-0.906024\pi$
$541$	−4.05403	−	21.2520i	−0.174297	−	0.913695i	0.782437	−	0.622730i	$-0.213976\pi$
$542$	11.7689	−	18.5449i	0.505520	−	0.796571i
$543$	−17.8138	−	12.9425i	−0.764462	−	0.555414i
$544$	−2.63917	−	3.19021i	−0.113153	−	0.136779i
$545$	2.77075	+	14.4660i	0.118686	+	0.619653i
$546$	6.11339	+	9.63316i	0.261629	+	0.412261i
$547$	8.38610	−	10.1371i	0.358564	−	0.433429i	−0.560127	−	0.828407i	$-0.689248\pi$
$547$	8.38610	−	10.1371i	0.358564	−	0.433429i	0.918691	+	0.394978i	$0.129248\pi$
$548$	7.74460	+	16.4581i	0.330833	+	0.703056i
$549$	0.138677	+	0.100755i	0.00591860	+	0.00430012i
$550$	−4.12779	−	6.48289i	−0.176009	−	0.276431i
$551$	−2.23840	+	1.62629i	−0.0953589	+	0.0692823i
$552$	−3.18362	−	1.75021i	−0.135504	−	0.0744939i
$553$	−7.08351	+	1.81874i	−0.301221	+	0.0773405i
$554$	−2.62147	+	3.16881i	−0.111376	+	0.134630i
$555$	13.1969	−	12.4113i	0.560177	−	0.526830i
$556$	−9.66548	+	3.82684i	−0.409908	+	0.162294i
$557$	−31.5720			−1.33775			−0.668875	−	0.743375i	$-0.733224\pi$
$557$	−31.5720			−1.33775			−0.668875	+	0.743375i	$0.733224\pi$
$558$	0.0563540	−	0.0223121i	0.00238565	−	0.000944547i
$559$	−36.4515	+	20.0394i	−1.54174	+	0.847576i
$560$	2.65524	+	0.333417i	0.112205	+	0.0140895i
$561$	2.07182	−	10.8608i	0.0874722	−	0.458545i
$562$	−8.10220	−	7.60847i	−0.341771	−	0.320944i
$563$	−16.3550	−	15.3584i	−0.689281	−	0.647278i	0.258569	−	0.965993i	$-0.416749\pi$
$563$	−16.3550	−	15.3584i	−0.689281	−	0.647278i	−0.947851	+	0.318714i	$0.896749\pi$
$564$	3.07025	−	16.0948i	0.129281	−	0.677714i
$565$	−2.57742	−	2.41673i	−0.108433	−	0.101673i
$566$	1.70224	−	0.935814i	0.0715505	−	0.0393352i
$567$	−10.0756	+	3.98922i	−0.423136	+	0.167531i
$568$	6.39893			0.268493
$569$	−19.3390	+	7.65687i	−0.810735	+	0.320993i	−0.736663	−	0.676260i	$-0.763599\pi$
$569$	−19.3390	+	7.65687i	−0.810735	+	0.320993i	−0.0740719	+	0.997253i	$0.523599\pi$
$570$	−7.22966	−	3.96750i	−0.302817	−	0.166180i
$571$	21.0251	−	25.4150i	0.879872	−	1.06358i	−0.117638	−	0.993057i	$-0.537532\pi$
$571$	21.0251	−	25.4150i	0.879872	−	1.06358i	0.997510	−	0.0705264i	$-0.0224679\pi$
$572$	8.16945	−	2.09756i	0.341582	−	0.0877033i
$573$	4.34660	+	2.38956i	0.181582	+	0.0998254i
$574$	−7.36941	+	5.35419i	−0.307593	+	0.223480i
$575$	−4.46593	−	9.45385i	−0.186242	−	0.394253i
$576$	−0.0148546	−	0.0107925i	−0.000618941	−	0.000449687i
$577$	−0.498346	−	1.05904i	−0.0207464	−	0.0440884i	0.894185	−	0.447697i	$-0.147756\pi$
$577$	−0.498346	−	1.05904i	−0.0207464	−	0.0440884i	−0.914932	+	0.403609i	$0.867756\pi$
$578$	0.0909210	−	0.109905i	0.00378181	−	0.00457143i
$579$	4.49055	+	7.07598i	0.186621	+	0.294067i
$580$	−2.89171	−	0.363110i	−0.120072	−	0.0150773i
$581$	−3.72450	−	4.50215i	−0.154518	−	0.186781i
$582$	12.3541	+	8.97581i	0.512096	+	0.372059i
$583$	8.50333	−	13.3991i	0.352172	−	0.554934i
$584$	−2.08160	−	10.9121i	−0.0861371	−	0.451546i
$585$	0.120574	−	0.190309i	0.00498514	−	0.00786833i
$586$	4.14614	−	0.523780i	0.171276	−	0.0216371i
$587$	−7.86288	−	41.2186i	−0.324536	−	1.70128i	−0.653495	−	0.756931i	$-0.726698\pi$
$587$	−7.86288	−	41.2186i	−0.324536	−	1.70128i	0.328959	−	0.944344i	$-0.393302\pi$
$588$	9.59673	+	1.21235i	0.395763	+	0.0499964i
$589$	6.14062	+	3.37583i	0.253020	+	0.139099i
$590$	−0.764458		0.000571925i	−0.0314723		2.35458e-5i
$591$	−21.0045	−	19.7246i	−0.864012	−	0.811361i
$592$	4.51684	+	1.15973i	0.185641	+	0.0476645i
$593$	10.0702	−	7.31640i	0.413532	−	0.300449i	−0.361498	−	0.932373i	$-0.617735\pi$
$593$	10.0702	−	7.31640i	0.413532	−	0.300449i	0.775030	+	0.631924i	$0.217735\pi$
$594$	0.499960	+	7.94664i	0.0205136	+	0.326054i
$595$	0.703993	+	11.0576i	0.0288609	+	0.453319i
$596$	−6.10055	−	2.41538i	−0.249888	−	0.0989377i
$597$	14.7065	+	5.82271i	0.601896	+	0.238308i
$598$	11.3840	−	1.43814i	0.465528	−	0.0588099i
$599$	4.81368	+	14.8150i	0.196682	+	0.605324i	0.999953	+	0.00971030i	$0.00309093\pi$
$599$	4.81368	+	14.8150i	0.196682	+	0.605324i	−0.803271	+	0.595613i	$0.796909\pi$
$600$	−2.69670	−	8.25753i	−0.110092	−	0.337112i
$601$	−5.30102	+	16.3149i	−0.216233	+	0.665497i	0.782831	+	0.622235i	$0.213775\pi$
$601$	−5.30102	+	16.3149i	−0.216233	+	0.665497i	−0.999064	+	0.0432622i	$0.986225\pi$
$602$	1.69999	−	8.91168i	0.0692866	−	0.363213i
$603$	−0.0155401	+	0.247002i	−0.000632840	+	0.0100587i
$604$	−9.84523	+	2.52783i	−0.400597	+	0.102856i
$605$	−18.7033	+	4.81711i	−0.760398	+	0.195843i
$606$	13.5338	−	21.3259i	0.549774	−	0.866305i
$607$	0.0730491	+	0.224822i	0.00296497	+	0.00912524i	0.952528	−	0.304451i	$-0.0984729\pi$
$607$	0.0730491	+	0.224822i	0.00296497	+	0.00912524i	−0.949563	+	0.313576i	$0.898473\pi$
$608$	−0.133293	−	2.11863i	−0.00540574	−	0.0859218i
$609$	2.68863	+	0.339653i	0.108949	+	0.0137634i
$610$	−13.2943	+	16.0945i	−0.538270	+	0.651648i
$611$	22.0344	+	46.8255i	0.891417	+	1.89436i
$612$	0.0323688	−	0.0687872i	0.00130843	−	0.00278056i
$613$	−24.4575	+	13.4456i	−0.987830	+	0.543064i	−0.891856	−	0.452320i	$-0.850597\pi$
$613$	−24.4575	+	13.4456i	−0.987830	+	0.543064i	−0.0959743	+	0.995384i	$0.530597\pi$
$614$	23.8160	−	22.3647i	0.961137	−	0.902568i
$615$	25.9217	+	14.2253i	1.04526	+	0.573621i
$616$	−0.783253	+	1.66450i	−0.0315581	+	0.0670645i
$617$	8.83465	+	10.6793i	0.355670	+	0.429931i	0.917754	−	0.397149i	$-0.130000\pi$
$617$	8.83465	+	10.6793i	0.355670	+	0.429931i	−0.562084	+	0.827080i	$0.690000\pi$
$618$	1.28070	−	3.94160i	0.0515175	−	0.158554i
$619$	40.0322	+	10.2785i	1.60903	+	0.413128i	0.942999	−	0.332797i	$-0.107992\pi$
$619$	40.0322	+	10.2785i	1.60903	+	0.413128i	0.666030	+	0.745925i	$0.267992\pi$
$620$	2.28617	+	7.01824i	0.0918149	+	0.281860i
$621$	−0.680165	+	10.8109i	−0.0272941	+	0.433827i
$622$	−13.0128	−	20.5050i	−0.521768	−	0.822174i
$623$	8.25991	−	7.75658i	0.330926	−	0.310761i
$624$	9.53324			0.381635
$625$	7.65424	−	23.7994i	0.306170	−	0.951977i
$626$	30.4030			1.21515
$627$	4.13245	−	3.88063i	0.165034	−	0.154977i
$628$	9.94711	+	15.6741i	0.396933	+	0.625466i
$629$	−1.21236	+	19.2699i	−0.0483398	+	0.768339i
$630$	0.0152190	+	0.0467203i	0.000606339	+	0.00186138i
$631$	−24.1135	−	6.19129i	−0.959942	−	0.246471i	−0.263963	−	0.964533i	$-0.585030\pi$
$631$	−24.1135	−	6.19129i	−0.959942	−	0.246471i	−0.695980	+	0.718062i	$0.745030\pi$
$632$	−1.88833	+	5.81167i	−0.0751136	+	0.231176i
$633$	−22.9951	−	27.7963i	−0.913972	−	1.10480i
$634$	1.62482	−	3.45292i	0.0645299	−	0.137133i
$635$	−30.4416	−	16.7058i	−1.20804	−	0.662948i
$636$	13.0755	−	12.2787i	0.518478	−	0.486883i
$637$	−26.7724	+	14.7182i	−1.06076	+	0.583158i
$638$	0.853005	−	1.81273i	0.0337708	−	0.0717666i
$639$	0.0500259	+	0.106310i	0.00197899	+	0.00420558i
$640$	1.42403	−	1.72399i	0.0562899	−	0.0681465i
$641$	25.4359	+	3.21330i	1.00466	+	0.126918i	0.610409	−	0.792086i	$-0.291005\pi$
$641$	25.4359	+	3.21330i	1.00466	+	0.126918i	0.394248	+	0.919004i	$0.371005\pi$
$642$	0.732544	+	11.6435i	0.0289112	+	0.459530i
$643$	12.8434	+	39.5279i	0.506494	+	1.55883i	0.798244	+	0.602334i	$0.205763\pi$
$643$	12.8434	+	39.5279i	0.506494	+	1.55883i	−0.291750	+	0.956495i	$0.594237\pi$
$644$	−1.34097	+	2.11304i	−0.0528418	+	0.0832654i
$645$	−28.5186	+	7.34508i	−1.12292	+	0.289212i
$646$	8.51312	−	2.18580i	0.334944	−	0.0859990i
$647$	−0.0641823	+	1.02015i	−0.00252327	+	0.0401062i	−0.999087	−	0.0427247i	$-0.986396\pi$
$647$	−0.0641823	+	1.02015i	−0.00252327	+	0.0401062i	0.996564	+	0.0828309i	$0.0263961\pi$
$648$	−1.69669	+	8.89436i	−0.0666523	+	0.349404i
$649$	0.162387	−	0.499777i	0.00637426	−	0.0196179i
$650$	22.2205	+	16.0934i	0.871560	+	0.631235i
$651$	−2.12094	−	6.52757i	−0.0831260	−	0.255836i
$652$	18.9199	−	2.39013i	0.740959	−	0.0936048i
$653$	20.7737	+	8.22489i	0.812938	+	0.321865i	0.737553	−	0.675290i	$-0.235981\pi$
$653$	20.7737	+	8.22489i	0.812938	+	0.321865i	0.0753853	+	0.997154i	$0.475981\pi$
$654$	−10.6402	−	4.21275i	−0.416065	−	0.164732i
$655$	0.158229	+	2.48531i	0.00618252	+	0.0971089i
$656$	0.477917	+	7.59628i	0.0186595	+	0.296585i
$657$	0.165018	−	0.119892i	0.00643796	−	0.00467745i
$658$	−10.9324	−	2.80696i	−0.426189	−	0.109427i
$659$	−26.7590	−	25.1283i	−1.04238	−	0.978861i	−0.0425860	−	0.999093i	$-0.513560\pi$
$659$	−26.7590	−	25.1283i	−1.04238	−	0.978861i	−0.999795	+	0.0202316i	$0.993560\pi$
$660$	5.97133	−	0.00446741i	0.232434	−	0.000173894i
$661$	0.555889	+	0.305603i	0.0216216	+	0.0118866i	0.492528	−	0.870297i	$-0.336073\pi$
$661$	0.555889	+	0.305603i	0.0216216	+	0.0118866i	−0.470906	+	0.882183i	$0.656073\pi$
$662$	12.5595	+	1.58663i	0.488138	+	0.0616662i
$663$	7.39615	+	38.7720i	0.287243	+	1.50578i
$664$	−4.84379	+	0.611912i	−0.187975	+	0.0237468i
$665$	−3.04037	+	4.79879i	−0.117901	+	0.186089i
$666$	0.0160445	+	0.0841083i	0.000621713	+	0.00325913i
$667$	1.46040	−	2.30122i	0.0565467	−	0.0891034i
$668$	−19.6439	−	14.2721i	−0.760046	−	0.552206i
$669$	−27.7420	−	33.5344i	−1.07257	−	1.29651i
$670$	−29.9050	−	3.75515i	−1.15533	−	0.145074i
$671$	−7.68900	−	12.1159i	−0.296830	−	0.467730i
$672$	−1.32535	+	1.60207i	−0.0511265	+	0.0618013i
$673$	7.67105	+	16.3018i	0.295697	+	0.628389i	0.996373	−	0.0850911i	$-0.0271181\pi$
$673$	7.67105	+	16.3018i	0.295697	+	0.628389i	−0.700676	+	0.713480i	$0.747118\pi$
$674$	12.1341	+	8.81596i	0.467389	+	0.339578i
$675$	−18.8542	+	17.7584i	−0.725699	+	0.683523i
$676$	−13.8423	+	10.0570i	−0.532394	+	0.386807i
$677$	26.4627	+	14.5480i	1.01705	+	0.559126i	0.900864	−	0.434102i	$-0.142934\pi$
$677$	26.4627	+	14.5480i	1.01705	+	0.559126i	0.116182	+	0.993228i	$0.462934\pi$
$678$	2.65894	−	0.682700i	0.102116	−	0.0262189i
$679$	6.70524	−	8.10525i	0.257324	−	0.311051i
$680$	8.11631	+	4.45407i	0.311246	+	0.170806i
$681$	0.787425	−	0.311764i	0.0301742	−	0.0119468i
$682$	−5.07392			−0.194290
$683$	32.0221	−	12.6784i	1.22529	−	0.485127i	0.335736	−	0.941956i	$-0.391015\pi$
$683$	32.0221	−	12.6784i	1.22529	−	0.485127i	0.889555	+	0.456829i	$0.151015\pi$
$684$	0.0341564	−	0.0187776i	0.00130600	−	0.000717981i
$685$	−29.6697	−	27.8200i	−1.13362	−	1.06295i
$686$	2.81838	−	14.7744i	0.107606	−	0.564091i
$687$	30.2360	+	28.3935i	1.15358	+	1.08328i
$688$	−5.52603	−	5.18929i	−0.210678	−	0.197840i
$689$	−10.6156	+	55.6491i	−0.404423	+	2.12006i
$690$	8.06033	+	1.01213i	0.306852	+	0.0385312i
$691$	16.1719	−	8.89060i	0.615210	−	0.338214i	−0.143493	−	0.989651i	$-0.545834\pi$
$691$	16.1719	−	8.89060i	0.615210	−	0.338214i	0.758703	+	0.651437i	$0.225834\pi$
$692$	−18.3327	+	7.25842i	−0.696904	+	0.275924i
$693$	−0.0337769			−0.00128308
$694$	−24.7215	+	9.78792i	−0.938414	+	0.371544i
$695$	16.9330	−	15.9250i	0.642305	−	0.604069i
$696$	1.44338	−	1.74475i	0.0547112	−	0.0661345i
$697$	−30.5235	+	7.83710i	−1.15616	+	0.296851i
$698$	−3.53422	−	1.94295i	−0.133772	−	0.0735419i
$699$	−24.9240	+	18.1083i	−0.942712	+	0.684920i
$700$	−5.79370	+	1.49681i	−0.218981	+	0.0565743i
$701$	−5.93950	−	4.31530i	−0.224332	−	0.162987i	0.469943	−	0.882697i	$-0.344275\pi$
$701$	−5.93950	−	4.31530i	−0.224332	−	0.162987i	−0.694274	+	0.719710i	$0.744275\pi$
$702$	−12.1026	−	25.7194i	−0.456785	−	0.970717i
$703$	−6.31014	+	7.62764i	−0.237991	+	0.287682i
$704$	0.823616	+	1.29781i	0.0310412	+	0.0489131i
$705$	6.89221	+	35.9839i	0.259576	+	1.35523i
$706$	16.5039	+	19.9498i	0.621133	+	0.750821i
$707$	−14.0762	−	10.2269i	−0.529389	−	0.384624i
$708$	0.318258	−	0.501494i	0.0119609	−	0.0188473i
$709$	0.687175	+	3.60230i	0.0258074	+	0.135287i	0.992859	−	0.119293i	$-0.0380628\pi$
$709$	0.687175	+	3.60230i	0.0258074	+	0.135287i	−0.967052	+	0.254580i	$0.918063\pi$
$710$	−13.2997	+	5.27724i	−0.499129	+	0.198051i
$711$	−0.111317	+	0.0140625i	−0.00417470	+	0.000527387i
$712$	−1.77409	−	9.30012i	−0.0664869	−	0.348537i
$713$	−6.84832	−	0.865144i	−0.256472	−	0.0323999i
$714$	−7.54392	−	4.14731i	−0.282324	−	0.155209i
$715$	−15.2497	+	11.0970i	−0.570307	+	0.415005i
$716$	−16.5284	−	15.5212i	−0.617694	−	0.580053i
$717$	−15.6579	−	4.02027i	−0.584755	−	0.150140i
$718$	22.7661	−	16.5405i	0.849622	−	0.617286i
$719$	1.85334	+	29.4580i	0.0691179	+	1.09860i	0.867823	+	0.496874i	$0.165519\pi$
$719$	1.85334	+	29.4580i	0.0691179	+	1.09860i	−0.798705	+	0.601723i	$0.794481\pi$
$720$	0.0397748	+	0.0101807i	0.00148232	+	0.000379413i
$721$	−2.65446	−	1.05097i	−0.0988572	−	0.0391403i
$722$	−13.4758	−	5.33547i	−0.501519	−	0.198565i
$723$	24.2052	−	3.05783i	0.900201	−	0.113722i
$724$	3.91647	+	12.0537i	0.145554	+	0.447971i
$725$	6.30966	−	1.63011i	0.234335	−	0.0605409i
$726$	4.63712	−	14.2716i	0.172100	−	0.529668i
$727$	−3.71850	+	19.4930i	−0.137911	+	0.722957i	0.844402	+	0.535711i	$0.179956\pi$
$727$	−3.71850	+	19.4930i	−0.137911	+	0.722957i	−0.982313	+	0.187246i	$0.940044\pi$
$728$	0.412350	−	6.55411i	0.0152827	−	0.242912i
$729$	25.9897	−	6.67303i	0.962583	−	0.247149i
$730$	13.3257	+	20.9633i	0.493208	+	0.775887i
$731$	16.8177	−	26.5005i	0.622027	−	0.980157i
$732$	−5.01202	−	15.4254i	−0.185249	−	0.570139i
$733$	1.92372	+	30.5767i	0.0710544	+	1.12938i	0.858439	+	0.512915i	$0.171434\pi$
$733$	1.92372	+	30.5767i	0.0710544	+	1.12938i	−0.787385	+	0.616462i	$0.788566\pi$
$734$	−36.2442	−	4.57870i	−1.33780	−	0.169003i
$735$	−20.9459	+	5.39471i	−0.772603	+	0.198987i
$736$	0.890357	+	1.89210i	0.0328190	+	0.0697439i
$737$	8.82146	−	18.7466i	0.324943	−	0.690538i
$738$	−0.122467	+	0.0673266i	−0.00450806	+	0.00247833i
$739$	18.9669	−	17.8111i	0.697710	−	0.655193i	−0.252215	−	0.967671i	$-0.581159\pi$
$739$	18.9669	−	17.8111i	0.697710	−	0.655193i	0.949925	+	0.312478i	$0.101159\pi$
$740$	−10.3443	+	1.31466i	−0.380266	+	0.0483278i
$741$	−8.61664	+	18.3113i	−0.316540	+	0.672682i
$742$	−7.87607	−	9.52053i	−0.289139	−	0.349510i
$743$	9.85657	−	30.3354i	0.361603	−	1.11290i	−0.590479	−	0.807053i	$-0.701061\pi$
$743$	9.85657	−	30.3354i	0.361603	−	1.11290i	0.952081	−	0.305845i	$-0.0989390\pi$
$744$	−5.55476	−	1.42622i	−0.203647	−	0.0522878i
$745$	14.6715	−	0.0109764i	0.537523	−	0.000402144i
$746$	−1.31692	+	20.9319i	−0.0482160	+	0.766371i
$747$	−0.0480342	−	0.0756898i	−0.00175748	−	0.00276934i
$748$	−4.63925	+	4.35655i	−0.169628	+	0.159291i
$749$	8.03657			0.293650
$750$	12.4149	+	14.9387i	0.453329	+	0.545484i
$751$	−46.6150			−1.70101			−0.850503	−	0.525970i	$-0.823703\pi$
$751$	−46.6150			−1.70101			−0.850503	+	0.525970i	$0.823703\pi$
$752$	−6.87496	+	6.45602i	−0.250704	+	0.235427i
$753$	20.7224	+	32.6533i	0.755166	+	1.18995i
$754$	−0.449072	+	7.13779i	−0.0163542	+	0.259943i
$755$	18.3779	−	13.3733i	0.668840	−	0.486705i
$756$	6.00474	+	1.54176i	0.218390	+	0.0560731i
$757$	4.14281	−	12.7502i	0.150573	−	0.463415i	−0.847113	−	0.531413i	$-0.821661\pi$
$757$	4.14281	−	12.7502i	0.150573	−	0.463415i	0.997685	+	0.0679979i	$0.0216611\pi$
$758$	−9.96056	−	12.0403i	−0.361784	−	0.437322i
$759$	−2.37766	+	5.05279i	−0.0863037	+	0.183405i
$760$	2.02429	+	4.29349i	0.0734286	+	0.155741i
$761$	3.75704	−	3.52809i	0.136192	−	0.127893i	−0.613458	−	0.789728i	$-0.710222\pi$
$761$	3.75704	−	3.52809i	0.136192	−	0.127893i	0.749650	+	0.661834i	$0.230222\pi$
$762$	23.6423	−	12.9975i	0.856470	−	0.470848i
$763$	−3.35650	+	7.13293i	−0.121514	+	0.258229i
$764$	−1.21560	−	2.58329i	−0.0439790	−	0.0934602i
$765$	−0.0105469	+	0.169664i	−0.000381325	+	0.00613421i
$766$	−12.4053	−	1.56716i	−0.448223	−	0.0566237i
$767$	0.117793	+	1.87226i	0.00425325	+	0.0676034i
$768$	0.536869	+	1.65231i	0.0193726	+	0.0596227i
$769$	−24.9197	+	39.2672i	−0.898628	+	1.41601i	0.0107061	+	0.999943i	$0.496592\pi$
$769$	−24.9197	+	39.2672i	−0.898628	+	1.41601i	−0.909334	+	0.416068i	$0.863408\pi$
$770$	0.255212	−	4.10549i	0.00919720	−	0.147952i
$771$	−8.90532	+	2.28650i	−0.320717	+	0.0823462i
$772$	0.302889	−	4.81428i	0.0109012	−	0.173270i
$773$	−2.59841	+	13.6214i	−0.0934584	+	0.489926i	0.904523	+	0.426424i	$0.140227\pi$
$773$	−2.59841	+	13.6214i	−0.0934584	+	0.489926i	−0.997982	+	0.0635018i	$0.979773\pi$
$774$	0.0430120	−	0.132377i	0.00154604	−	0.00475821i
$775$	−10.5396	−	12.7015i	−0.378595	−	0.456251i
$776$	−2.71614	−	8.35941i	−0.0975037	−	0.300085i
$777$	9.61970	−	1.21525i	0.345105	−	0.0435969i
$778$	−21.0245	−	8.32420i	−0.753766	−	0.298437i
$779$	−15.0228	−	5.94793i	−0.538247	−	0.213107i
$780$	−19.8142	+	7.86213i	−0.709461	+	0.281509i
$781$	−0.617592	−	9.81635i	−0.0220992	−	0.351257i
$782$	−7.00448	+	5.08905i	−0.250480	+	0.181984i
$783$	−6.53949	−	1.67906i	−0.233702	−	0.0600046i
$784$	−4.05868	−	3.81135i	−0.144953	−	0.136120i
$785$	−33.6009	−	24.3741i	−1.19927	−	0.869949i
$786$	−1.69557	−	0.932146i	−0.0604789	−	0.0332485i
$787$	20.0350	+	2.53101i	0.714172	+	0.0902209i	0.474019	−	0.880514i	$-0.342803\pi$
$787$	20.0350	+	2.53101i	0.714172	+	0.0902209i	0.240152	+	0.970735i	$0.422803\pi$
$788$	3.10774	+	16.2914i	0.110709	+	0.580356i
$789$	5.12819	−	0.647841i	0.182569	−	0.0230638i
$790$	−0.868176	−	13.6365i	−0.0308883	−	0.485163i
$791$	−0.354347	−	1.85755i	−0.0125991	−	0.0660470i
$792$	−0.0151227	+	0.0238295i	−0.000537360	+	0.000846744i
$793$	41.4436	+	30.1105i	1.47171	+	1.06926i
$794$	7.68922	+	9.29467i	0.272880	+	0.329856i
$795$	−17.0502	+	36.3039i	−0.604707	+	1.28757i
$796$	−4.87831	−	7.68698i	−0.172907	−	0.272458i
$797$	−17.9063	+	21.6450i	−0.634275	+	0.766706i	−0.985517	−	0.169578i	$-0.945759\pi$
$797$	−17.9063	+	21.6450i	−0.634275	+	0.766706i	0.351242	+	0.936285i	$0.385759\pi$
$798$	−1.87932	−	3.99375i	−0.0665271	−	0.141377i
$799$	−31.5906	−	22.9519i	−1.11760	−	0.811981i
$800$	−1.53797	+	4.75759i	−0.0543754	+	0.168206i
$801$	0.140641	−	0.102181i	0.00496929	−	0.00361040i
$802$	−18.5096	−	10.1758i	−0.653598	−	0.359318i
$803$	−16.5389	+	4.24648i	−0.583647	+	0.149855i
$804$	14.9269	−	18.0435i	0.526431	−	0.636346i
$805$	1.04448	−	5.49771i	0.0368131	−	0.193769i
$806$	16.8413	−	6.66796i	0.593211	−	0.234869i
$807$	34.9207			1.22927
$808$	−13.5173	+	5.35186i	−0.475536	+	0.188278i
$809$	−13.3013	+	7.31247i	−0.467650	+	0.257093i	−0.698112	−	0.715989i	$-0.745976\pi$
$809$	−13.3013	+	7.31247i	−0.467650	+	0.257093i	0.230462	+	0.973081i	$0.425976\pi$
$810$	−3.80879	−	19.8856i	−0.133827	−	0.698707i
$811$	−4.97767	+	26.0938i	−0.174789	+	0.916278i	0.781511	+	0.623892i	$0.214449\pi$
$811$	−4.97767	+	26.0938i	−0.174789	+	0.916278i	−0.956300	+	0.292387i	$0.905551\pi$
$812$	−1.13708	−	1.06779i	−0.0399038	−	0.0374722i
$813$	−27.8168	−	26.1217i	−0.975579	−	0.916129i
$814$	1.34315	−	7.04104i	0.0470774	−	0.246788i
$815$	−37.3524	+	20.5710i	−1.30840	+	0.720572i
$816$	−6.30348	+	3.46537i	−0.220666	+	0.121312i
$817$	14.9622	−	5.92396i	0.523462	−	0.207253i
$818$	−3.65467			−0.127783
$819$	0.112112	−	0.0443884i	0.00391752	−	0.00155106i
$820$	−7.25802	−	15.3942i	−0.253461	−	0.537587i
$821$	−1.00609	+	1.21616i	−0.0351129	+	0.0424442i	−0.787777	−	0.615960i	$-0.788768\pi$
$821$	−1.00609	+	1.21616i	−0.0351129	+	0.0424442i	0.752664	+	0.658404i	$0.228768\pi$
$822$	30.6082	−	7.85884i	1.06758	−	0.274109i
$823$	−25.7709	−	14.1677i	−0.898318	−	0.493855i	−0.0355004	−	0.999370i	$-0.511302\pi$
$823$	−25.7709	−	14.1677i	−0.898318	−	0.493855i	−0.862818	+	0.505515i	$0.831302\pi$
$824$	−1.92992	+	1.40217i	−0.0672318	+	0.0488468i
$825$	−12.4073	+	4.93388i	−0.431966	+	0.171776i
$826$	−0.331012	−	0.240494i	−0.0115174	−	0.00836786i
$827$	16.2881	+	34.6140i	0.566392	+	1.20365i	0.958860	+	0.283879i	$0.0916215\pi$
$827$	16.2881	+	34.6140i	0.566392	+	1.20365i	−0.392468	+	0.919766i	$0.628379\pi$
$828$	−0.0244743	+	0.0295844i	−0.000850542	+	0.00102813i
$829$	6.63758	+	10.4592i	0.230533	+	0.363261i	0.939827	−	0.341651i	$-0.110986\pi$
$829$	6.63758	+	10.4592i	0.230533	+	0.363261i	−0.709294	+	0.704913i	$0.750986\pi$
$830$	9.56281	−	5.26652i	0.331930	−	0.182803i
$831$	4.55439	+	5.50532i	0.157990	+	0.190977i
$832$	−4.43928	−	3.22533i	−0.153904	−	0.111818i
$833$	12.3521	−	19.4637i	0.427973	−	0.674378i
$834$	3.38421	+	17.7406i	0.117185	+	0.614308i
$835$	52.5988	+	13.4631i	1.82026	+	0.465911i
$836$	−3.23724	+	0.408959i	−0.111962	+	0.0141441i
$837$	3.20413	+	16.7966i	0.110751	+	0.580576i
$838$	3.21077	+	0.405615i	0.110914	+	0.0140117i
$839$	32.4567	+	17.8432i	1.12053	+	0.616016i	0.930694	−	0.365799i	$-0.119204\pi$
$839$	32.4567	+	17.8432i	1.12053	+	0.616016i	0.189836	+	0.981816i	$0.439204\pi$
$840$	1.43340	−	4.42282i	0.0494571	−	0.152602i
$841$	−19.9017	−	18.6890i	−0.686267	−	0.644448i
$842$	29.9147	+	7.68079i	1.03093	+	0.264697i
$843$	−15.6220	+	11.3501i	−0.538051	+	0.390917i
$844$	1.30381	+	20.7235i	0.0448790	+	0.713332i
$845$	20.4761	−	32.3185i	0.704398	−	1.11179i
$846$	−0.161006	−	0.0637469i	−0.00553551	−	0.00219167i
$847$	−9.61115	−	3.80532i	−0.330243	−	0.130752i
$848$	−10.2430	+	1.29399i	−0.351745	+	0.0444358i
$849$	−1.04288	−	3.20964i	−0.0357914	−	0.110155i
$850$	−20.5425	−	2.56389i	−0.704600	−	0.0879408i
$851$	3.01342	−	9.27434i	0.103299	−	0.317920i
$852$	2.08314	−	10.9202i	0.0713673	−	0.374121i
$853$	−2.31010	+	36.7179i	−0.0790962	+	1.25720i	0.735643	+	0.677370i	$0.236880\pi$
$853$	−2.31010	+	36.7179i	−0.0790962	+	1.25720i	−0.814739	+	0.579828i	$0.803120\pi$
$854$	−10.8218	+	2.77856i	−0.370313	+	0.0950803i
$855$	−0.0555055	+	0.0671970i	−0.00189825	+	0.00229809i
$856$	3.59814	−	5.66977i	0.122982	−	0.193789i
$857$	5.78869	+	17.8157i	0.197738	+	0.608574i	0.999934	+	0.0115134i	$0.00366490\pi$
$857$	5.78869	+	17.8157i	0.197738	+	0.608574i	−0.802196	+	0.597061i	$0.796335\pi$
$858$	−0.920101	−	14.6246i	−0.0314117	−	0.499275i
$859$	55.9767	+	7.07150i	1.90990	+	0.241276i	0.988933	−	0.148365i	$-0.0474011\pi$
$859$	55.9767	+	7.07150i	1.90990	+	0.241276i	0.920967	+	0.389642i	$0.127401\pi$
$860$	15.7651	+	6.22820i	0.537585	+	0.212380i
$861$	6.73822	+	14.3195i	0.229638	+	0.488006i
$862$	−9.49868	+	20.1857i	−0.323526	+	0.687529i
$863$	−3.50050	+	1.92442i	−0.119159	+	0.0655079i	−0.540218	−	0.841525i	$-0.681658\pi$
$863$	−3.50050	+	1.92442i	−0.119159	+	0.0655079i	0.421060	+	0.907033i	$0.361658\pi$
$864$	3.77615	−	3.54604i	0.128467	−	0.120639i
$865$	32.1171	−	30.2052i	1.09201	−	1.02701i
$866$	−7.84465	+	16.6707i	−0.266572	+	0.566494i
$867$	−0.157961	−	0.190942i	−0.00536463	−	0.00648473i
$868$	−1.22079	+	3.75721i	−0.0414364	+	0.127528i
$869$	9.09771	+	2.33590i	0.308619	+	0.0792398i
$870$	−1.56106	+	4.81669i	−0.0529247	+	0.163301i
$871$	−4.64413	+	73.8164i	−0.157360	+	2.50117i
$872$	3.52947	+	5.56156i	0.119523	+	0.188338i
$873$	0.117647	−	0.110478i	0.00398175	−	0.00373911i
$874$	−4.43907			−0.150154
$875$	10.8074	−	7.88913i	0.365355	−	0.266701i
$876$	−19.2999			−0.652084
$877$	11.6096	−	10.9021i	0.392027	−	0.368138i	−0.463322	−	0.886190i	$-0.653343\pi$
$877$	11.6096	−	10.9021i	0.392027	−	0.368138i	0.855349	+	0.518052i	$0.173343\pi$
$878$	1.38215	+	2.17792i	0.0466454	+	0.0735013i
$879$	0.455892	−	7.24620i	0.0153769	−	0.244408i
$880$	−2.78214	−	2.01817i	−0.0937859	−	0.0680323i
$881$	−50.9711	−	13.0871i	−1.71726	−	0.440917i	−0.743544	−	0.668687i	$-0.766857\pi$
$881$	−50.9711	−	13.0871i	−1.71726	−	0.440917i	−0.973715	+	0.227770i	$0.926857\pi$
$882$	0.0315908	−	0.0972266i	0.00106372	−	0.00327379i
$883$	−4.32353	−	5.22625i	−0.145498	−	0.175877i	0.692729	−	0.721198i	$-0.256408\pi$
$883$	−4.32353	−	5.22625i	−0.145498	−	0.175877i	−0.838228	+	0.545320i	$0.816408\pi$
$884$	9.67339	−	20.5570i	0.325351	−	0.691406i
$885$	−0.247890	+	1.30479i	−0.00833273	+	0.0438600i
$886$	24.3538	−	22.8698i	0.818183	−	0.768325i
$887$	23.9444	−	13.1635i	0.803973	−	0.441988i	−0.0260887	−	0.999660i	$-0.508305\pi$
$887$	23.9444	−	13.1635i	0.803973	−	0.441988i	0.830062	+	0.557672i	$0.188305\pi$
$888$	3.44959	−	7.33075i	0.115761	−	0.246004i
$889$	−7.91314	−	16.8163i	−0.265398	−	0.564000i
$890$	11.3572	+	17.8665i	0.380694	+	0.598887i
$891$	13.8083	+	1.74439i	0.462594	+	0.0584392i
$892$	1.57296	+	25.0015i	0.0526667	+	0.837113i
$893$	−6.18667	−	19.0406i	−0.207029	−	0.637170i
$894$	−6.10802	+	9.62470i	−0.204283	+	0.321898i
$895$	47.1534	+	18.6286i	1.57616	+	0.622684i
$896$	1.15919	−	0.297629i	0.0387257	−	0.00994308i
$897$	1.25174	−	19.8958i	0.0417944	−	0.664303i
$898$	−0.291090	+	1.52594i	−0.00971378	+	0.0509214i
$899$	1.32951	−	4.09181i	0.0443417	−	0.136470i
$900$	−0.0910652	+	0.0116427i	−0.00303551	+	0.000388089i
$901$	−13.2095	−	40.6546i	−0.440071	−	1.35440i
$902$	11.6070	−	1.46631i	0.386472	−	0.0488227i
$903$	−14.6550	−	5.80232i	−0.487687	−	0.193089i
$904$	−1.46914	−	0.581675i	−0.0488630	−	0.0193462i
$905$	−18.0808	−	21.8227i	−0.601027	−	0.725411i
$906$	1.10884	+	17.6245i	0.0368387	+	0.585535i
$907$	30.6908	−	22.2982i	1.01907	−	0.740398i	0.0529788	−	0.998596i	$-0.483128\pi$
$907$	30.6908	−	22.2982i	1.01907	−	0.740398i	0.966092	+	0.258197i	$0.0831284\pi$
$908$	−0.472152	−	0.121228i	−0.0156689	−	0.00402309i
$909$	−0.194591	−	0.182733i	−0.00645416	−	0.00606086i
$910$	4.54818	+	13.9623i	0.150771	+	0.462846i
$911$	−29.7579	−	16.3595i	−0.985923	−	0.542016i	−0.0946634	−	0.995509i	$-0.530177\pi$
$911$	−29.7579	−	16.3595i	−0.985923	−	0.542016i	−0.891260	+	0.453494i	$0.850177\pi$
$912$	−3.65898	−	0.462237i	−0.121161	−	0.0153062i
$913$	1.40621	+	7.37161i	0.0465387	+	0.243965i
$914$	−13.2620	+	1.67539i	−0.438669	+	0.0554168i
$915$	23.1385	+	27.9271i	0.764937	+	0.923242i
$916$	−4.47360	−	23.4514i	−0.147812	−	0.774856i
$917$	−0.714191	+	1.12538i	−0.0235847	+	0.0371635i
$918$	17.3515	+	12.6066i	0.572685	+	0.416080i
$919$	10.8548	+	13.1212i	0.358066	+	0.432827i	0.918530	−	0.395352i	$-0.129377\pi$
$919$	10.8548	+	13.1212i	0.358066	+	0.432827i	−0.560464	+	0.828179i	$0.689377\pi$
$920$	−3.41097	−	3.19832i	−0.112456	−	0.105445i
$921$	−30.4138	−	47.9245i	−1.00217	−	1.57917i
$922$	15.4175	−	18.6365i	0.507747	−	0.613760i
$923$	14.9502	+	31.7708i	0.492092	+	1.04575i
$924$	2.58560	+	1.87854i	0.0850598	+	0.0617996i
$925$	20.4158	−	11.2635i	0.671266	−	0.370341i
$926$	−23.7507	+	17.2559i	−0.780497	+	0.567064i
$927$	−0.0383831	−	0.0211013i	−0.00126067	−	0.000693057i
$928$	−1.26242	+	0.324134i	−0.0414409	+	0.0106402i
$929$	−14.0937	+	17.0363i	−0.462399	+	0.558944i	−0.949243	−	0.314545i	$-0.898148\pi$
$929$	−14.0937	+	17.0363i	−0.462399	+	0.558944i	0.486844	+	0.873489i	$0.338148\pi$
$930$	12.7214	−	1.61675i	0.417150	−	0.0530155i
$931$	10.9892	−	4.35095i	0.360158	−	0.142596i
$932$	17.7327			0.580853
$933$	−39.2294	+	15.5320i	−1.28431	+	0.508496i
$934$	28.8328	−	15.8510i	0.943438	−	0.518659i
$935$	6.04948	−	12.8808i	0.197839	−	0.421247i
$936$	0.0188792	−	0.0989684i	0.000617087	−	0.00323488i
$937$	−16.4899	−	15.4850i	−0.538700	−	0.505873i	0.366754	−	0.930318i	$-0.380469\pi$
$937$	−16.4899	−	15.4850i	−0.538700	−	0.505873i	−0.905454	+	0.424445i	$0.860469\pi$
$938$	−11.7593	−	11.0427i	−0.383954	−	0.360557i
$939$	9.89755	−	51.8848i	0.322994	−	1.69320i
$940$	8.96479	−	19.0882i	0.292399	−	0.622588i
$941$	−1.42494	+	0.783366i	−0.0464516	+	0.0255370i	−0.504810	−	0.863230i	$-0.668438\pi$
$941$	−1.42494	+	0.783366i	−0.0464516	+	0.0255370i	0.458359	+	0.888767i	$0.348438\pi$
$942$	29.9873	−	11.8728i	0.977038	−	0.386837i
$943$	15.9161			0.518301
$944$	−0.317869	+	0.125853i	−0.0103457	+	0.00409617i
$945$	−13.7519	+	1.74772i	−0.447350	+	0.0568535i
$946$	−7.42734	+	8.97811i	−0.241484	+	0.291904i
$947$	−48.5236	+	12.4587i	−1.57681	+	0.404855i	−0.932866	−	0.360222i	$-0.882701\pi$
$947$	−48.5236	+	12.4587i	−1.57681	+	0.404855i	−0.643939	+	0.765077i	$0.722701\pi$
$948$	9.30329	+	5.11453i	0.302157	+	0.166112i
$949$	49.3154	−	35.8298i	1.60085	−	1.16308i
$950$	−7.74820	−	7.25426i	−0.251385	−	0.235359i
$951$	−5.36370	−	3.89695i	−0.173930	−	0.126367i
$952$	2.10979	+	4.48354i	0.0683788	+	0.145312i
$953$	9.81271	−	11.8615i	0.317865	−	0.384233i	−0.587246	−	0.809409i	$-0.699788\pi$
$953$	9.81271	−	11.8615i	0.317865	−	0.384233i	0.905111	+	0.425176i	$0.139788\pi$
$954$	−0.101576	−	0.160058i	−0.00328865	−	0.00518208i
$955$	4.65700	+	4.36666i	0.150697	+	0.141302i
$956$	5.93116	+	7.16954i	0.191827	+	0.231880i
$957$	−2.81586	−	2.04584i	−0.0910237	−	0.0661326i
$958$	−1.40743	+	2.21775i	−0.0454719	+	0.0716523i
$959$	−4.07904	−	21.3831i	−0.131719	−	0.690495i
$960$	−2.47851	−	2.99145i	−0.0799937	−	0.0965486i
$961$	19.9450	−	2.51964i	0.643387	−	0.0812787i
$962$	4.79489	+	25.1357i	0.154594	+	0.810408i
$963$	0.122326	+	0.0154534i	0.00394190	+	0.000497978i
$964$	−12.3060	−	6.76529i	−0.396350	−	0.217895i
$965$	3.34084	+	10.2559i	0.107545	+	0.330150i
$966$	3.16950	+	2.97636i	0.101977	+	0.0957627i
$967$	4.23654	+	1.08776i	0.136238	+	0.0349799i	0.316193	−	0.948695i	$-0.397595\pi$
$967$	4.23654	+	1.08776i	0.136238	+	0.0349799i	−0.179955	+	0.983675i	$0.557595\pi$
$968$	−6.98776	+	5.07690i	−0.224595	+	0.163178i
$969$	−0.958807	−	15.2398i	−0.0308013	−	0.489573i
$970$	12.5394	+	15.1344i	0.402615	+	0.485937i
$971$	−3.95362	−	1.56535i	−0.126878	−	0.0502344i	0.303828	−	0.952727i	$-0.401735\pi$
$971$	−3.95362	−	1.56535i	−0.126878	−	0.0502344i	−0.430706	+	0.902493i	$0.641735\pi$
$972$	0.177414	+	0.0702431i	0.00569055	+	0.00225305i
$973$	12.3431	−	1.55929i	0.395701	−	0.0499887i
$974$	−7.02118	−	21.6090i	−0.224973	−	0.692396i
$975$	34.6983	−	32.6817i	1.11124	−	1.04665i
$976$	−2.88487	+	8.87873i	−0.0923426	+	0.284201i
$977$	−0.0697486	+	0.365635i	−0.00223146	+	0.0116977i	−0.983386	−	0.181529i	$-0.941895\pi$
$977$	−0.0697486	+	0.365635i	−0.00223146	+	0.0116977i	0.981154	+	0.193227i	$0.0618953\pi$
$978$	2.08035	−	33.0662i	0.0665221	−	1.05734i
$979$	−14.0957	+	3.61917i	−0.450501	+	0.115669i
$980$	11.5789	+	4.57440i	0.369875	+	0.146124i
$981$	−0.0648057	+	0.102117i	−0.00206909	+	0.00326036i
$982$	−5.19026	−	15.9740i	−0.165628	−	0.509751i
$983$	−3.78648	−	60.1844i	−0.120770	−	1.91958i	−0.333983	−	0.942579i	$-0.608393\pi$
$983$	−3.78648	−	60.1844i	−0.120770	−	1.91958i	0.213213	−	0.977006i	$-0.431607\pi$
$984$	13.1192	+	1.65734i	0.418224	+	0.0528339i
$985$	−19.8948	−	31.2974i	−0.633901	−	0.997219i
$986$	−2.29768	−	4.88282i	−0.0731731	−	0.155501i
$987$	−8.34927	+	17.7431i	−0.265760	+	0.564769i
$988$	10.2076	−	5.61168i	0.324747	−	0.178531i
$989$	−11.5556	+	10.8514i	−0.367447	+	0.345056i
$990$	0.0117790	−	0.0619996i	0.000374361	−	0.00197048i
$991$	−8.08353	+	17.1784i	−0.256782	+	0.545689i	−0.991100	−	0.133116i	$-0.957502\pi$
$991$	−8.08353	+	17.1784i	−0.256782	+	0.545689i	0.734319	+	0.678805i	$0.237502\pi$
$992$	2.10412	+	2.54345i	0.0668060	+	0.0807546i
$993$	6.79639	−	20.9171i	0.215677	−	0.663785i
$994$	−7.41756	−	1.90451i	−0.235271	−	0.0604072i
$995$	16.4787	+	11.9537i	0.522410	+	0.378957i
$996$	−0.532602	+	8.46546i	−0.0168761	+	0.268239i
$997$	−4.09014	−	6.44503i	−0.129536	−	0.204116i	0.773369	−	0.633956i	$-0.218570\pi$
$997$	−4.09014	−	6.44503i	−0.129536	−	0.204116i	−0.902905	+	0.429840i	$0.858570\pi$
$998$	3.39224	−	3.18552i	0.107379	−	0.100836i
$999$	−24.1567			−0.764285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.a.11.5	✓	120
125.91	even	25	inner	250.2.g.a.91.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.a.11.5	✓	120	1.1	even	1	trivial
250.2.g.a.91.5	yes	120	125.91	even	25	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.728969 + 0.684547i) q^{2} +(0.930915 + 1.46689i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.692574 + 2.12611i) q^{5} +(-1.68276 - 0.432060i) q^{6} +(-0.369827 + 1.13821i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.00781785 + 0.0166138i) q^{9} +O(q^{10})\)	\(q+(-0.728969 + 0.684547i) q^{2} +(0.930915 + 1.46689i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.692574 + 2.12611i) q^{5} +(-1.68276 - 0.432060i) q^{6} +(-0.369827 + 1.13821i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.00781785 + 0.0166138i) q^{9} +(-1.96029 - 1.07577i) q^{10} +(1.12049 - 1.05221i) q^{11} +(1.52245 - 0.836971i) q^{12} +(-2.33636 + 4.96502i) q^{13} +(-0.509567 - 1.08288i) q^{14} +(-2.47404 + 2.99516i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.259976 - 4.13220i) q^{17} +(-0.00567395 - 0.0174626i) q^{18} +(1.13746 - 1.79236i) q^{19} +(2.16540 - 0.557708i) q^{20} +(-2.01391 + 0.517083i) q^{21} +(-0.0965150 + 1.53406i) q^{22} +(-0.391837 + 2.05408i) q^{23} +(-0.536869 + 1.65231i) q^{24} +(-4.04068 + 2.94498i) q^{25} +(-1.69566 - 5.21869i) q^{26} +(5.13928 - 0.649242i) q^{27} +(1.11274 + 0.440567i) q^{28} +(-1.21184 - 0.479801i) q^{29} +(-0.246830 - 3.87697i) q^{30} +(0.207270 + 3.29447i) q^{31} +(0.809017 - 0.587785i) q^{32} +(2.58656 + 0.664117i) q^{33} +(3.01820 + 2.83428i) q^{34} +(-2.67610 + 0.00200210i) q^{35} +(0.0160901 + 0.00884561i) q^{36} +(-4.62657 - 0.584472i) q^{37} +(0.397777 + 2.08522i) q^{38} +(-9.45807 + 1.19483i) q^{39} +(-1.19673 + 1.88887i) q^{40} +(-1.42621 - 7.47648i) q^{41} +(1.11411 - 1.75555i) q^{42} +(6.13285 + 4.45577i) q^{43} +(-0.979781 - 1.18435i) q^{44} +(-0.0407372 - 0.00511534i) q^{45} +(-1.12048 - 1.76559i) q^{46} +(6.01160 - 7.26677i) q^{47} +(-0.739725 - 1.57200i) q^{48} +(4.50437 + 3.27261i) q^{49} +(0.929557 - 4.91283i) q^{50} +(5.81945 - 4.22808i) q^{51} +(4.80852 + 2.64351i) q^{52} +(10.0000 - 2.56757i) q^{53} +(-3.30194 + 3.99136i) q^{54} +(3.01315 + 1.65356i) q^{55} +(-1.11274 + 0.440567i) q^{56} +3.68806 q^{57} +(1.21184 - 0.479801i) q^{58} +(0.299588 - 0.164700i) q^{59} +(2.83390 + 2.65722i) q^{60} +(1.74933 - 9.17029i) q^{61} +(-2.40631 - 2.25968i) q^{62} +(-0.0160187 - 0.0150426i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(-12.1743 - 1.52872i) q^{65} +(-2.34014 + 1.28650i) q^{66} +(12.5324 - 4.96193i) q^{67} -4.14037 q^{68} +(-3.37788 + 1.33740i) q^{69} +(1.94942 - 1.83337i) q^{70} +(4.07883 - 4.93046i) q^{71} +(-0.0177844 + 0.00456626i) q^{72} +(-9.73478 - 5.35174i) q^{73} +(3.77272 - 2.74104i) q^{74} +(-8.08148 - 3.18570i) q^{75} +(-1.71740 - 1.24776i) q^{76} +(0.783253 + 1.66450i) q^{77} +(6.07672 - 7.34549i) q^{78} +(3.27431 + 5.15948i) q^{79} +(-0.420641 - 2.19615i) q^{80} +(5.77171 + 6.97680i) q^{81} +(6.15767 + 4.47381i) q^{82} +(-2.61606 + 4.12225i) q^{83} +(0.389609 + 2.04240i) q^{84} +(8.60545 - 3.41459i) q^{85} +(-7.52084 + 0.950103i) q^{86} +(-0.424305 - 2.22429i) q^{87} +(1.52497 + 0.192649i) q^{88} +(-8.29671 - 4.56116i) q^{89} +(0.0331978 - 0.0241576i) q^{90} +(-4.78719 - 4.49547i) q^{91} +(2.02543 + 0.520041i) q^{92} +(-4.63966 + 3.37091i) q^{93} +(0.592183 + 9.41247i) q^{94} +(4.59852 + 1.17703i) q^{95} +(1.61534 + 0.639559i) q^{96} +(-8.17237 - 3.23567i) q^{97} +(-5.52380 + 0.697818i) q^{98} +(0.00872139 + 0.0268417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9	\( 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9} - 20 q^{10} + 20 q^{12} - 20 q^{14} - 10 q^{15} - 5 q^{17} + 25 q^{18} - 60 q^{19} + 5 q^{20} + 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} + 55 q^{25} + 5 q^{26} - 90 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} - 45 q^{31} + 30 q^{32} - 15 q^{33} - 10 q^{34} + 15 q^{35} + 10 q^{36} + 10 q^{37} + 10 q^{39} - 55 q^{41} - 5 q^{42} + 5 q^{43} - 40 q^{44} + 85 q^{45} - 20 q^{46} + 90 q^{47} - 5 q^{48} - 20 q^{49} - 30 q^{50} + 60 q^{51} + 5 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} - 120 q^{57} + 10 q^{58} - 75 q^{59} + 15 q^{60} - 85 q^{61} - 15 q^{62} - 45 q^{63} + 5 q^{65} - 15 q^{66} - 25 q^{67} - 70 q^{68} + 5 q^{69} - 65 q^{70} + 55 q^{71} + 5 q^{72} - 30 q^{73} - 70 q^{74} - 20 q^{75} - 5 q^{76} - 130 q^{77} + 60 q^{78} + 10 q^{79} + 5 q^{80} - 65 q^{81} + 80 q^{82} - 135 q^{83} + 20 q^{84} - 30 q^{85} + 10 q^{86} - 200 q^{87} - 80 q^{90} + 175 q^{91} - 5 q^{92} + 50 q^{93} + 35 q^{94} - 20 q^{95} - 15 q^{98} - 120 q^{99}+O(q^{100}) \) 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9 - 20 * q^10 + 20 * q^12 - 20 * q^14 - 10 * q^15 - 5 * q^17 + 25 * q^18 - 60 * q^19 + 5 * q^20 + 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 + 55 * q^25 + 5 * q^26 - 90 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 - 45 * q^31 + 30 * q^32 - 15 * q^33 - 10 * q^34 + 15 * q^35 + 10 * q^36 + 10 * q^37 + 10 * q^39 - 55 * q^41 - 5 * q^42 + 5 * q^43 - 40 * q^44 + 85 * q^45 - 20 * q^46 + 90 * q^47 - 5 * q^48 - 20 * q^49 - 30 * q^50 + 60 * q^51 + 5 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 - 120 * q^57 + 10 * q^58 - 75 * q^59 + 15 * q^60 - 85 * q^61 - 15 * q^62 - 45 * q^63 + 5 * q^65 - 15 * q^66 - 25 * q^67 - 70 * q^68 + 5 * q^69 - 65 * q^70 + 55 * q^71 + 5 * q^72 - 30 * q^73 - 70 * q^74 - 20 * q^75 - 5 * q^76 - 130 * q^77 + 60 * q^78 + 10 * q^79 + 5 * q^80 - 65 * q^81 + 80 * q^82 - 135 * q^83 + 20 * q^84 - 30 * q^85 + 10 * q^86 - 200 * q^87 - 80 * q^90 + 175 * q^91 - 5 * q^92 + 50 * q^93 + 35 * q^94 - 20 * q^95 - 15 * q^98 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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