LMFDB - Embedded newform 475.2.n.a.39.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.4
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12280 - 1.54541i) q^{2} +(1.41655 + 0.460266i) q^{3} +(-0.509559 + 1.56826i) q^{4} +(-0.295058 - 2.21652i) q^{5} +(-0.879213 - 2.70594i) q^{6} -3.52405i q^{7} +(-0.637733 + 0.207212i) q^{8} +(-0.632270 - 0.459371i) q^{9} +O(q^{10})$	\(q+(-1.12280 - 1.54541i) q^{2} +(1.41655 + 0.460266i) q^{3} +(-0.509559 + 1.56826i) q^{4} +(-0.295058 - 2.21652i) q^{5} +(-0.879213 - 2.70594i) q^{6} -3.52405i q^{7} +(-0.637733 + 0.207212i) q^{8} +(-0.632270 - 0.459371i) q^{9} +(-3.09413 + 2.94469i) q^{10} +(-3.11114 + 2.26038i) q^{11} +(-1.44364 + 1.98699i) q^{12} +(0.105032 - 0.144564i) q^{13} +(-5.44608 + 3.95681i) q^{14} +(0.602223 - 3.27562i) q^{15} +(3.70436 + 2.69138i) q^{16} +(0.288458 - 0.0937256i) q^{17} +1.49290i q^{18} +(-0.309017 - 0.951057i) q^{19} +(3.62642 + 0.666718i) q^{20} +(1.62200 - 4.99200i) q^{21} +(6.98640 + 2.27002i) q^{22} +(3.17832 + 4.37458i) q^{23} -0.998756 q^{24} +(-4.82588 + 1.30800i) q^{25} -0.341340 q^{26} +(-3.31065 - 4.55672i) q^{27} +(5.52662 + 1.79571i) q^{28} +(-1.12605 + 3.46561i) q^{29} +(-5.73834 + 2.74720i) q^{30} +(-2.50252 - 7.70198i) q^{31} -7.40552i q^{32} +(-5.44748 + 1.76999i) q^{33} +(-0.468726 - 0.340549i) q^{34} +(-7.81110 + 1.03980i) q^{35} +(1.04259 - 0.757488i) q^{36} +(4.72635 - 6.50526i) q^{37} +(-1.12280 + 1.54541i) q^{38} +(0.215321 - 0.156440i) q^{39} +(0.647456 + 1.35241i) q^{40} +(-2.64966 - 1.92509i) q^{41} +(-9.53586 + 3.09839i) q^{42} -2.18931i q^{43} +(-1.95955 - 6.03088i) q^{44} +(-0.831647 + 1.53698i) q^{45} +(3.19188 - 9.82359i) q^{46} +(4.11350 + 1.33656i) q^{47} +(4.00868 + 5.51747i) q^{48} -5.41890 q^{49} +(7.43991 + 5.98932i) q^{50} +0.451755 q^{51} +(0.173194 + 0.238381i) q^{52} +(2.80505 + 0.911416i) q^{53} +(-3.32477 + 10.2326i) q^{54} +(5.92813 + 6.22895i) q^{55} +(0.730224 + 2.24740i) q^{56} -1.48945i q^{57} +(6.62011 - 2.15100i) q^{58} +(-3.36526 - 2.44500i) q^{59} +(4.83016 + 2.61356i) q^{60} +(2.11026 - 1.53319i) q^{61} +(-9.09284 + 12.5152i) q^{62} +(-1.61885 + 2.22815i) q^{63} +(-4.03582 + 2.93219i) q^{64} +(-0.351419 - 0.190150i) q^{65} +(8.85180 + 6.43121i) q^{66} +(-3.00075 + 0.975002i) q^{67} +0.500136i q^{68} +(2.48879 + 7.65971i) q^{69} +(10.3772 + 10.9038i) q^{70} +(1.24418 - 3.82920i) q^{71} +(0.498407 + 0.161942i) q^{72} +(-1.26967 - 1.74756i) q^{73} -15.3600 q^{74} +(-7.43815 - 0.368339i) q^{75} +1.64897 q^{76} +(7.96567 + 10.9638i) q^{77} +(-0.483527 - 0.157107i) q^{78} +(4.71585 - 14.5139i) q^{79} +(4.87248 - 9.00488i) q^{80} +(-1.86789 - 5.74878i) q^{81} +6.25631i q^{82} +(7.76428 - 2.52277i) q^{83} +(7.00226 + 5.08744i) q^{84} +(-0.292856 - 0.611717i) q^{85} +(-3.38338 + 2.45817i) q^{86} +(-3.19021 + 4.39095i) q^{87} +(1.51570 - 2.08618i) q^{88} +(-7.24308 + 5.26240i) q^{89} +(3.30903 - 0.440491i) q^{90} +(-0.509450 - 0.370137i) q^{91} +(-8.48003 + 2.75533i) q^{92} -12.0621i q^{93} +(-2.55313 - 7.85772i) q^{94} +(-2.01685 + 0.965557i) q^{95} +(3.40851 - 10.4903i) q^{96} +(16.2159 + 5.26888i) q^{97} +(6.08435 + 8.37439i) q^{98} +3.00543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−1.12280	−	1.54541i	−0.793942	−	1.09277i	−0.993606	−	0.112903i	$-0.963985\pi$
$2$	−1.12280	−	1.54541i	−0.793942	−	1.09277i	0.199664	−	0.979864i	$-0.436015\pi$
$3$	1.41655	+	0.460266i	0.817848	+	0.265735i	0.687918	−	0.725788i	$-0.258525\pi$
$3$	1.41655	+	0.460266i	0.817848	+	0.265735i	0.129930	+	0.991523i	$0.458525\pi$
$4$	−0.509559	+	1.56826i	−0.254779	+	0.784131i
$5$	−0.295058	−	2.21652i	−0.131954	−	0.991256i
$5$	−0.295058	−	2.21652i	−0.131954	−	0.991256i
$6$	−0.879213	−	2.70594i	−0.358937	−	1.10470i
$7$		−	3.52405i		−	1.33196i	−0.745968	−	0.665982i	$-0.768013\pi$
$7$		−	3.52405i		−	1.33196i	0.745968	−	0.665982i	$-0.231987\pi$
$8$	−0.637733	+	0.207212i	−0.225473	+	0.0732605i
$9$	−0.632270	−	0.459371i	−0.210757	−	0.153124i
$10$	−3.09413	+	2.94469i	−0.978448	+	0.931194i
$11$	−3.11114	+	2.26038i	−0.938044	+	0.681529i	−0.947949	−	0.318422i	$-0.896847\pi$
$11$	−3.11114	+	2.26038i	−0.938044	+	0.681529i	0.00990473	+	0.999951i	$0.496847\pi$
$12$	−1.44364	+	1.98699i	−0.416742	+	0.573596i
$13$	0.105032	−	0.144564i	0.0291306	−	0.0400948i	−0.794203	−	0.607652i	$-0.792111\pi$
$13$	0.105032	−	0.144564i	0.0291306	−	0.0400948i	0.823334	+	0.567557i	$0.192111\pi$
$14$	−5.44608	+	3.95681i	−1.45553	+	1.05750i
$15$	0.602223	−	3.27562i	0.155493	−	0.845761i
$16$	3.70436	+	2.69138i	0.926090	+	0.672844i
$17$	0.288458	−	0.0937256i	0.0699613	−	0.0227318i	−0.273827	−	0.961779i	$-0.588290\pi$
$17$	0.288458	−	0.0937256i	0.0699613	−	0.0227318i	0.343789	+	0.939047i	$0.388290\pi$
$18$			1.49290i			0.351879i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	3.62642	+	0.666718i	0.810893	+	0.149083i
$21$	1.62200	−	4.99200i	0.353949	−	1.08934i
$22$	6.98640	+	2.27002i	1.48951	+	0.483970i
$23$	3.17832	+	4.37458i	0.662726	+	0.912164i	0.999568	−	0.0293973i	$-0.00935881\pi$
$23$	3.17832	+	4.37458i	0.662726	+	0.912164i	−0.336842	+	0.941561i	$0.609359\pi$
$24$	−0.998756			−0.203870
$25$	−4.82588	+	1.30800i	−0.965176	+	0.261600i
$26$	−0.341340			−0.0669423
$27$	−3.31065	−	4.55672i	−0.637134	−	0.876940i
$28$	5.52662	+	1.79571i	1.04443	+	0.339357i
$29$	−1.12605	+	3.46561i	−0.209101	+	0.643548i	0.790418	+	0.612567i	$0.209863\pi$
$29$	−1.12605	+	3.46561i	−0.209101	+	0.643548i	−0.999520	+	0.0309810i	$0.990137\pi$
$30$	−5.73834	+	2.74720i	−1.04767	+	0.501567i
$31$	−2.50252	−	7.70198i	−0.449467	−	1.38332i	−0.877510	−	0.479558i	$-0.840797\pi$
$31$	−2.50252	−	7.70198i	−0.449467	−	1.38332i	0.428043	−	0.903758i	$-0.359203\pi$
$32$		−	7.40552i		−	1.30912i
$33$	−5.44748	+	1.76999i	−0.948284	+	0.308116i
$34$	−0.468726	−	0.340549i	−0.0803858	−	0.0584037i
$35$	−7.81110	+	1.03980i	−1.32032	+	0.175758i
$36$	1.04259	−	0.757488i	0.173766	−	0.126248i
$37$	4.72635	−	6.50526i	0.777007	−	1.06946i	−0.218599	−	0.975815i	$-0.570149\pi$
$37$	4.72635	−	6.50526i	0.777007	−	1.06946i	0.995606	−	0.0936435i	$-0.0298514\pi$
$38$	−1.12280	+	1.54541i	−0.182143	+	0.250698i
$39$	0.215321	−	0.156440i	0.0344790	−	0.0250504i
$40$	0.647456	+	1.35241i	0.102372	+	0.213834i
$41$	−2.64966	−	1.92509i	−0.413808	−	0.300649i	0.361334	−	0.932437i	$-0.382322\pi$
$41$	−2.64966	−	1.92509i	−0.413808	−	0.300649i	−0.775142	+	0.631787i	$0.782322\pi$
$42$	−9.53586	+	3.09839i	−1.47141	+	0.478092i
$43$		−	2.18931i		−	0.333867i	−0.985968	−	0.166934i	$-0.946613\pi$
$43$		−	2.18931i		−	0.333867i	0.985968	−	0.166934i	$-0.0533866\pi$
$44$	−1.95955	−	6.03088i	−0.295413	−	0.909189i
$45$	−0.831647	+	1.53698i	−0.123975	+	0.229119i
$46$	3.19188	−	9.82359i	0.470617	−	1.44841i
$47$	4.11350	+	1.33656i	0.600016	+	0.194957i	0.593247	−	0.805020i	$-0.297846\pi$
$47$	4.11350	+	1.33656i	0.600016	+	0.194957i	0.00676816	+	0.999977i	$0.497846\pi$
$48$	4.00868	+	5.51747i	0.578603	+	0.796378i
$49$	−5.41890			−0.774128
$50$	7.43991	+	5.98932i	1.05216	+	0.847018i
$51$	0.451755			0.0632583
$52$	0.173194	+	0.238381i	0.0240177	+	0.0330575i
$53$	2.80505	+	0.911416i	0.385303	+	0.125193i	0.495262	−	0.868744i	$-0.335072\pi$
$53$	2.80505	+	0.911416i	0.385303	+	0.125193i	−0.109959	+	0.993936i	$0.535072\pi$
$54$	−3.32477	+	10.2326i	−0.452444	+	1.39248i
$55$	5.92813	+	6.22895i	0.799348	+	0.839912i
$56$	0.730224	+	2.24740i	0.0975803	+	0.300321i
$57$		−	1.48945i		−	0.197283i
$58$	6.62011	−	2.15100i	0.869263	−	0.282441i
$59$	−3.36526	−	2.44500i	−0.438120	−	0.318312i	0.346768	−	0.937951i	$-0.387279\pi$
$59$	−3.36526	−	2.44500i	−0.438120	−	0.318312i	−0.784887	+	0.619639i	$0.787279\pi$
$60$	4.83016	+	2.61356i	0.623571	+	0.337410i
$61$	2.11026	−	1.53319i	0.270191	−	0.196305i	−0.444437	−	0.895810i	$-0.646596\pi$
$61$	2.11026	−	1.53319i	0.270191	−	0.196305i	0.714628	+	0.699505i	$0.246596\pi$
$62$	−9.09284	+	12.5152i	−1.15479	+	1.58944i
$63$	−1.61885	+	2.22815i	−0.203955	+	0.280720i
$64$	−4.03582	+	2.93219i	−0.504477	+	0.366524i
$65$	−0.351419	−	0.190150i	−0.0435881	−	0.0235852i
$66$	8.85180	+	6.43121i	1.08958	+	0.791627i
$67$	−3.00075	+	0.975002i	−0.366599	+	0.119115i	−0.486523	−	0.873668i	$-0.661735\pi$
$67$	−3.00075	+	0.975002i	−0.366599	+	0.119115i	0.119924	+	0.992783i	$0.461735\pi$
$68$			0.500136i			0.0606504i
$69$	2.48879	+	7.65971i	0.299615	+	0.922121i
$70$	10.3772	+	10.9038i	1.24032	+	1.30326i
$71$	1.24418	−	3.82920i	0.147657	−	0.454442i	−0.849686	−	0.527289i	$-0.823209\pi$
$71$	1.24418	−	3.82920i	0.147657	−	0.454442i	0.997343	+	0.0728471i	$0.0232085\pi$
$72$	0.498407	+	0.161942i	0.0587378	+	0.0190851i
$73$	−1.26967	−	1.74756i	−0.148604	−	0.204536i	0.728225	−	0.685338i	$-0.240346\pi$
$73$	−1.26967	−	1.74756i	−0.148604	−	0.204536i	−0.876829	+	0.480802i	$0.840346\pi$
$74$	−15.3600			−1.78557
$75$	−7.43815	−	0.368339i	−0.858884	−	0.0425322i
$76$	1.64897			0.189150
$77$	7.96567	+	10.9638i	0.907772	+	1.24944i
$78$	−0.483527	−	0.157107i	−0.0547486	−	0.0177889i
$79$	4.71585	−	14.5139i	0.530574	−	1.63294i	−0.222448	−	0.974945i	$-0.571405\pi$
$79$	4.71585	−	14.5139i	0.530574	−	1.63294i	0.753022	−	0.657995i	$-0.228595\pi$
$80$	4.87248	−	9.00488i	0.544759	−	1.00678i
$81$	−1.86789	−	5.74878i	−0.207544	−	0.638753i
$82$			6.25631i			0.690894i
$83$	7.76428	−	2.52277i	0.852240	−	0.276910i	0.149856	−	0.988708i	$-0.452119\pi$
$83$	7.76428	−	2.52277i	0.852240	−	0.276910i	0.702384	+	0.711798i	$0.252119\pi$
$84$	7.00226	+	5.08744i	0.764009	+	0.555085i
$85$	−0.292856	−	0.611717i	−0.0317647	−	0.0663500i
$86$	−3.38338	+	2.45817i	−0.364839	+	0.265071i
$87$	−3.19021	+	4.39095i	−0.342026	+	0.470759i
$88$	1.51570	−	2.08618i	0.161574	−	0.222388i
$89$	−7.24308	+	5.26240i	−0.767765	+	0.557814i	−0.901282	−	0.433233i	$-0.857373\pi$
$89$	−7.24308	+	5.26240i	−0.767765	+	0.557814i	0.133517	+	0.991046i	$0.457373\pi$
$90$	3.30903	−	0.440491i	0.348803	−	0.0464318i
$91$	−0.509450	−	0.370137i	−0.0534049	−	0.0388009i
$92$	−8.48003	+	2.75533i	−0.884105	+	0.287263i
$93$		−	12.0621i		−	1.25078i
$94$	−2.55313	−	7.85772i	−0.263335	−	0.810462i
$95$	−2.01685	+	0.965557i	−0.206925	+	0.0990641i
$96$	3.40851	−	10.4903i	0.347880	−	1.07066i
$97$	16.2159	+	5.26888i	1.64648	+	0.534974i	0.977973	−	0.208732i	$-0.0669337\pi$
$97$	16.2159	+	5.26888i	1.64648	+	0.534974i	0.668507	+	0.743706i	$0.266934\pi$
$98$	6.08435	+	8.37439i	0.614613	+	0.845942i
$99$	3.00543			0.302058
$100$	0.407787	−	8.23475i	0.0407787	−	0.823475i
$101$	−12.4597			−1.23979			−0.619895	−	0.784685i	$-0.712825\pi$
$101$	−12.4597			−1.23979			−0.619895	+	0.784685i	$0.712825\pi$
$102$	−0.507232	−	0.698145i	−0.0502234	−	0.0691266i
$103$	−1.21182	−	0.393744i	−0.119404	−	0.0387968i	0.248705	−	0.968579i	$-0.419995\pi$
$103$	−1.21182	−	0.393744i	−0.119404	−	0.0387968i	−0.368110	+	0.929782i	$0.619995\pi$
$104$	−0.0370269	+	0.113957i	−0.00363078	+	0.0111744i
$105$	−11.5434	−	2.12226i	−1.12652	−	0.207111i
$106$	−1.74101	−	5.35828i	−0.169102	−	0.520442i
$107$		−	0.206171i		−	0.0199313i	−0.999950	−	0.00996565i	$-0.996828\pi$
$107$		−	0.206171i		−	0.0199313i	0.999950	−	0.00996565i	$-0.00317222\pi$
$108$	8.83309	−	2.87005i	0.849965	−	0.276170i
$109$	−10.1092	−	7.34479i	−0.968289	−	0.703503i	−0.0132282	−	0.999913i	$-0.504211\pi$
$109$	−10.1092	−	7.34479i	−0.968289	−	0.703503i	−0.955061	+	0.296409i	$0.904211\pi$
$110$	2.97014	−	16.1552i	0.283192	−	1.54034i
$111$	9.68928	−	7.03968i	0.919666	−	0.668176i
$112$	9.48453	−	13.0543i	0.896204	−	1.23352i
$113$	9.00933	−	12.4003i	0.847527	−	1.16652i	−0.136876	−	0.990588i	$-0.543706\pi$
$113$	9.00933	−	12.4003i	0.847527	−	1.16652i	0.984402	−	0.175932i	$-0.0562940\pi$
$114$	−2.30181	+	1.67236i	−0.215584	+	0.156631i
$115$	8.75855	−	8.33555i	0.816739	−	0.777294i
$116$	−4.86120	−	3.53187i	−0.451351	−	0.327926i
$117$	−0.132817	+	0.0431549i	−0.0122789	+	0.00398967i
$118$			7.94595i			0.731484i
$119$	−0.330293	−	1.01654i	−0.0302779	−	0.0931859i
$120$	0.294690	+	2.21376i	0.0269014	+	0.202087i
$121$	1.17071	−	3.60308i	0.106428	−	0.327553i
$122$	−4.73881	−	1.53973i	−0.429032	−	0.139401i
$123$	−2.86734	−	3.94655i	−0.258539	−	0.355848i
$124$	13.3539			1.19922
$125$	4.32311	+	10.3107i	0.386671	+	0.922218i
$126$	5.26104			0.468691
$127$	11.4924	+	15.8179i	1.01978	+	1.40361i	0.912357	+	0.409396i	$0.134260\pi$
$127$	11.4924	+	15.8179i	1.01978	+	1.40361i	0.107424	+	0.994213i	$0.465740\pi$
$128$	−5.02328	−	1.63216i	−0.443999	−	0.144264i
$129$	1.00767	−	3.10128i	0.0887202	−	0.273053i
$130$	0.100715	+	0.756586i	0.00883329	+	0.0663569i
$131$	−2.30859	−	7.10509i	−0.201702	−	0.620775i	−0.999833	−	0.0182906i	$-0.994178\pi$
$131$	−2.30859	−	7.10509i	−0.201702	−	0.620775i	0.798131	−	0.602484i	$-0.205822\pi$
$132$		−	9.44498i		−	0.822080i
$133$	−3.35157	+	1.08899i	−0.290618	+	0.0944274i
$134$	4.87602	+	3.54264i	0.421224	+	0.306037i
$135$	−9.12320	+	8.68260i	−0.785200	+	0.747279i
$136$	−0.164538	+	0.119544i	−0.0141090	+	0.0102508i
$137$	10.9292	−	15.0427i	0.933741	−	1.28518i	−0.0246410	−	0.999696i	$-0.507844\pi$
$137$	10.9292	−	15.0427i	0.933741	−	1.28518i	0.958382	−	0.285488i	$-0.0921557\pi$
$138$	9.04294	−	12.4465i	0.769786	−	1.05952i
$139$	2.18843	−	1.58998i	0.185620	−	0.134861i	−0.491095	−	0.871106i	$-0.663403\pi$
$139$	2.18843	−	1.58998i	0.185620	−	0.134861i	0.676715	+	0.736245i	$0.263403\pi$
$140$	2.34954	−	12.7797i	0.198573	−	1.08008i
$141$	5.21182	+	3.78661i	0.438915	+	0.318890i
$142$	−7.31463	+	2.37667i	−0.613830	+	0.199446i
$143$			0.687170i			0.0574641i
$144$	−1.10582	−	3.40335i	−0.0921514	−	0.283613i
$145$	8.01383	+	1.47334i	0.665513	+	0.122354i
$146$	−1.27509	+	3.92433i	−0.105527	+	0.324780i
$147$	−7.67616	−	2.49414i	−0.633119	−	0.205713i
$148$	7.79360	+	10.7270i	0.640630	+	0.881751i
$149$	15.4329			1.26431			0.632155	−	0.774842i	$-0.282171\pi$
$149$	15.4329			1.26431			0.632155	+	0.774842i	$0.282171\pi$
$150$	7.78235	+	11.9085i	0.635426	+	0.972328i
$151$	9.90035			0.805679			0.402840	−	0.915271i	$-0.368023\pi$
$151$	9.90035			0.805679			0.402840	+	0.915271i	$0.368023\pi$
$152$	0.394141	+	0.542488i	0.0319690	+	0.0440016i
$153$	−0.225438	−	0.0732493i	−0.0182256	−	0.00592186i
$154$	7.99965	−	24.6204i	0.644630	−	1.98397i
$155$	−16.3332	+	7.81941i	−1.31191	+	0.628070i
$156$	0.135620	+	0.417395i	0.0108583	+	0.0334184i
$157$			15.9637i			1.27404i	0.770847	+	0.637021i	$0.219833\pi$
$157$			15.9637i			1.27404i	−0.770847	+	0.637021i	$0.780167\pi$
$158$	−27.7248	+	9.00834i	−2.20567	+	0.716665i
$159$	3.55401	+	2.58214i	0.281851	+	0.204777i
$160$	−16.4145	+	2.18506i	−1.29768	+	0.172744i
$161$	15.4162	−	11.2005i	1.21497	−	0.882727i
$162$	−6.78692	+	9.34140i	−0.533231	+	0.733930i
$163$	14.0665	−	19.3609i	1.10177	−	1.51646i	0.268761	−	0.963207i	$-0.413386\pi$
$163$	14.0665	−	19.3609i	1.10177	−	1.51646i	0.833012	−	0.553254i	$-0.186614\pi$
$164$	4.36921	−	3.17442i	0.341178	−	0.247880i
$165$	5.53053	+	11.5522i	0.430551	+	0.899335i
$166$	−12.6165	−	9.16639i	−0.979227	−	0.711450i
$167$	−20.2543	+	6.58103i	−1.56733	+	0.509255i	−0.958753	−	0.284241i	$-0.908258\pi$
$167$	−20.2543	+	6.58103i	−1.56733	+	0.509255i	−0.608574	+	0.793497i	$0.708258\pi$
$168$			3.51966i			0.271548i
$169$	4.00735	+	12.3334i	0.308258	+	0.948721i
$170$	−0.616531	+	1.13942i	−0.0472858	+	0.0873895i
$171$	−0.241506	+	0.743278i	−0.0184684	+	0.0568399i
$172$	3.43342	+	1.11558i	0.261796	+	0.0850625i
$173$	−0.547688	−	0.753827i	−0.0416399	−	0.0573124i	0.787689	−	0.616073i	$-0.211277\pi$
$173$	−0.547688	−	0.753827i	−0.0416399	−	0.0573124i	−0.829329	+	0.558760i	$0.811277\pi$
$174$	10.3678			0.785979
$175$	4.60945	+	17.0066i	0.348442	+	1.28558i
$176$	−17.6083			−1.32728
$177$	−3.64172	−	5.01240i	−0.273728	−	0.376755i
$178$	16.2651	+	5.28485i	1.21912	+	0.396116i
$179$	3.27897	−	10.0916i	0.245081	−	0.754283i	−0.750542	−	0.660823i	$-0.770207\pi$
$179$	3.27897	−	10.0916i	0.245081	−	0.754283i	0.995623	−	0.0934599i	$-0.0297927\pi$
$180$	−1.98661	−	2.08742i	−0.148073	−	0.155587i
$181$	−0.0327195	−	0.100700i	−0.00243202	−	0.00748499i	0.949833	−	0.312757i	$-0.101253\pi$
$181$	−0.0327195	−	0.100700i	−0.00243202	−	0.00748499i	−0.952265	+	0.305272i	$0.901253\pi$
$182$			1.20290i			0.0891647i
$183$	3.69497	−	1.20057i	0.273140	−	0.0887486i
$184$	−2.93339	−	2.13123i	−0.216252	−	0.157116i
$185$	−15.8136	−	8.55660i	−1.16264	−	0.629094i
$186$	−18.6408	+	13.5434i	−1.36681	+	0.993048i
$187$	−0.685578	+	0.943617i	−0.0501344	+	0.0690041i
$188$	−4.19214	+	5.76999i	−0.305743	+	0.420820i
$189$	−16.0581	+	11.6669i	−1.16805	+	0.848640i
$190$	3.75671	+	2.03273i	0.272540	+	0.147470i
$191$	14.9837	+	10.8863i	1.08418	+	0.787706i	0.978408	−	0.206684i	$-0.0662673\pi$
$191$	14.9837	+	10.8863i	1.08418	+	0.787706i	0.105776	+	0.994390i	$0.466267\pi$
$192$	−7.06655	+	2.29606i	−0.509984	+	0.165704i
$193$			17.5834i			1.26568i	0.774283	+	0.632839i	$0.218111\pi$
$193$			17.5834i			1.26568i	−0.774283	+	0.632839i	$0.781889\pi$
$194$	−10.0648	−	30.9761i	−0.722607	−	2.22396i
$195$	−0.410284	−	0.431104i	−0.0293810	−	0.0308720i
$196$	2.76125	−	8.49824i	0.197232	−	0.607017i
$197$	−2.08109	−	0.676188i	−0.148272	−	0.0481764i	0.233941	−	0.972251i	$-0.424838\pi$
$197$	−2.08109	−	0.676188i	−0.148272	−	0.0481764i	−0.382213	+	0.924074i	$0.624838\pi$
$198$	−3.37451	−	4.64462i	−0.239816	−	0.330079i
$199$	21.8332			1.54772			0.773858	−	0.633359i	$-0.218324\pi$
$199$	21.8332			1.54772			0.773858	+	0.633359i	$0.218324\pi$
$200$	2.80659	−	1.83413i	0.198456	−	0.129693i
$201$	−4.69948			−0.331476
$202$	13.9898	+	19.2554i	0.984321	+	1.35480i
$203$	12.2130	+	3.96824i	0.857183	+	0.278516i
$204$	−0.230196	+	0.708470i	−0.0161169	+	0.0496028i
$205$	−3.48520	+	6.44103i	−0.243417	+	0.449861i
$206$	0.752141	+	2.31485i	0.0524041	+	0.161283i
$207$		−	4.22595i		−	0.293724i
$208$	0.778152	−	0.252837i	0.0539551	−	0.0175311i
$209$	3.11114	+	2.26038i	0.215202	+	0.156354i
$210$	9.68125	+	20.2222i	0.668070	+	1.39546i
$211$	−15.4115	+	11.1971i	−1.06097	+	0.770840i	−0.974268	−	0.225395i	$-0.927633\pi$
$211$	−15.4115	+	11.1971i	−1.06097	+	0.770840i	−0.0867021	+	0.996234i	$0.527633\pi$
$212$	−2.85868	+	3.93463i	−0.196335	+	0.270231i
$213$	3.52490	−	4.85161i	0.241522	−	0.332427i
$214$	−0.318618	+	0.231489i	−0.0217803	+	0.0158243i
$215$	−4.85265	+	0.645974i	−0.330948	+	0.0440550i
$216$	3.05551	+	2.21996i	0.207901	+	0.151049i
$217$	−27.1421	+	8.81901i	−1.84253	+	0.598673i
$218$			23.8696i			1.61666i
$219$	−0.994221	−	3.05990i	−0.0671832	−	0.206769i
$220$	−12.7894	+	6.12283i	−0.862258	+	0.412801i
$221$	0.0167479	−	0.0515448i	0.00112659	−	0.00346728i
$222$	−21.7583	−	7.06971i	−1.46032	−	0.474488i
$223$	−14.2312	−	19.5875i	−0.952990	−	1.31168i	−0.950186	−	0.311682i	$-0.899108\pi$
$223$	−14.2312	−	19.5875i	−0.952990	−	1.31168i	−0.00280365	−	0.999996i	$-0.500892\pi$
$224$	−26.0974			−1.74371
$225$	3.65212	+	1.38986i	0.243475	+	0.0926575i
$226$	−29.2792			−1.94762
$227$	−11.3649	−	15.6424i	−0.754312	−	1.03822i	−0.997666	−	0.0682837i	$-0.978248\pi$
$227$	−11.3649	−	15.6424i	−0.754312	−	1.03822i	0.243354	−	0.969938i	$-0.421752\pi$
$228$	2.33585	+	0.758964i	0.154696	+	0.0502636i
$229$	−8.75891	+	26.9572i	−0.578805	+	1.78138i	0.0440353	+	0.999030i	$0.485979\pi$
$229$	−8.75891	+	26.9572i	−0.578805	+	1.78138i	−0.622840	+	0.782349i	$0.714021\pi$
$230$	−22.7159	−	4.17632i	−1.49784	−	0.275379i
$231$	6.23753	+	19.1972i	0.410400	+	1.26308i
$232$		−	2.44347i		−	0.160421i
$233$	12.6967	−	4.12539i	0.831786	−	0.270264i	0.137988	−	0.990434i	$-0.455936\pi$
$233$	12.6967	−	4.12539i	0.831786	−	0.270264i	0.693797	+	0.720170i	$0.255936\pi$
$234$	0.215819	+	0.156802i	0.0141085	+	0.0102505i
$235$	1.74878	−	9.51200i	0.114078	−	0.620494i
$236$	5.54920	−	4.03173i	0.361222	−	0.262443i
$237$	13.3605	−	18.3892i	0.867858	−	1.19450i
$238$	−1.20011	+	1.65181i	−0.0777916	+	0.107071i
$239$	−10.8760	+	7.90191i	−0.703513	+	0.511132i	−0.881074	−	0.472978i	$-0.843179\pi$
$239$	−10.8760	+	7.90191i	−0.703513	+	0.511132i	0.177561	+	0.984110i	$0.443179\pi$
$240$	11.0468	−	10.5133i	0.713066	−	0.678629i
$241$	11.2591	+	8.18018i	0.725259	+	0.526932i	0.888060	−	0.459727i	$-0.152053\pi$
$241$	11.2591	+	8.18018i	0.725259	+	0.526932i	−0.162801	+	0.986659i	$0.552053\pi$
$242$	−6.88270	+	2.23632i	−0.442437	+	0.143756i
$243$			7.89405i			0.506403i
$244$	1.32915	+	4.09069i	0.0850898	+	0.261879i
$245$	1.59889	+	12.0111i	0.102149	+	0.767359i
$246$	−2.87957	+	8.86240i	−0.183595	+	0.565046i
$247$	−0.169945	−	0.0552185i	−0.0108133	−	0.00351347i
$248$	3.19188	+	4.39325i	0.202685	+	0.278972i
$249$	12.1597			0.770587
$250$	11.0802	−	18.2579i	0.700775	−	1.15473i
$251$	5.16015			0.325706			0.162853	−	0.986650i	$-0.447930\pi$
$251$	5.16015			0.325706			0.162853	+	0.986650i	$0.447930\pi$
$252$	−2.66942	−	3.67415i	−0.168158	−	0.231449i
$253$	−19.7764	−	6.42575i	−1.24333	−	0.403983i
$254$	11.5414	−	35.5207i	0.724170	−	2.22877i
$255$	−0.133294	−	1.00132i	−0.00834718	−	0.0627052i
$256$	6.20089	+	19.0844i	0.387556	+	1.19277i
$257$			9.08335i			0.566604i	0.959031	+	0.283302i	$0.0914298\pi$
$257$			9.08335i			0.566604i	−0.959031	+	0.283302i	$0.908570\pi$
$258$	−5.92415	+	1.92487i	−0.368822	+	0.119837i
$259$	−22.9248	−	16.6559i	−1.42448	−	1.03495i
$260$	0.477273	−	0.454224i	0.0295992	−	0.0281697i
$261$	2.30397	−	1.67393i	0.142612	−	0.103614i
$262$	−8.38817	+	11.5453i	−0.518223	+	0.713273i
$263$	0.372798	−	0.513113i	0.0229877	−	0.0316399i	−0.797368	−	0.603493i	$-0.793775\pi$
$263$	0.372798	−	0.513113i	0.0229877	−	0.0316399i	0.820356	+	0.571853i	$0.193775\pi$
$264$	3.10727	−	2.25756i	0.191239	−	0.138943i
$265$	1.19252	−	6.48635i	0.0732557	−	0.398454i
$266$	5.44608	+	3.95681i	0.333921	+	0.242608i
$267$	−12.6823	+	4.12073i	−0.776145	+	0.252185i
$268$		−	5.20277i		−	0.317810i
$269$	−0.444619	−	1.36840i	−0.0271089	−	0.0834326i	0.936587	−	0.350436i	$-0.113967\pi$
$269$	−0.444619	−	1.36840i	−0.0271089	−	0.0834326i	−0.963696	+	0.267003i	$0.913967\pi$
$270$	23.6617	+	4.35020i	1.44000	+	0.264745i
$271$	2.45809	−	7.56522i	0.149318	−	0.459554i	−0.848223	−	0.529640i	$-0.822327\pi$
$271$	2.45809	−	7.56522i	0.149318	−	0.459554i	0.997541	+	0.0700853i	$0.0223271\pi$
$272$	1.32080	+	0.429155i	0.0800854	+	0.0260213i
$273$	−0.551302	−	0.758802i	−0.0333663	−	0.0459248i
$274$	−35.5184			−2.14574
$275$	12.0574	−	14.9777i	0.727090	−	0.903188i
$276$	−13.2806			−0.799399
$277$	7.71020	+	10.6122i	0.463261	+	0.637624i	0.975181	−	0.221409i	$-0.0710656\pi$
$277$	7.71020	+	10.6122i	0.463261	+	0.637624i	−0.511920	+	0.859033i	$0.671066\pi$
$278$	−4.91434	−	1.59677i	−0.294743	−	0.0957677i
$279$	−1.95580	+	6.01932i	−0.117090	+	0.360367i
$280$	4.76594	−	2.28167i	0.284819	−	0.136356i
$281$	5.86696	+	18.0566i	0.349993	+	1.07717i	0.958856	+	0.283893i	$0.0916261\pi$
$281$	5.86696	+	18.0566i	0.349993	+	1.07717i	−0.608863	+	0.793276i	$0.708374\pi$
$282$		−	12.3060i		−	0.732812i
$283$	−28.7470	+	9.34045i	−1.70883	+	0.555232i	−0.990138	−	0.140097i	$-0.955259\pi$
$283$	−28.7470	+	9.34045i	−1.70883	+	0.555232i	−0.718692	+	0.695329i	$0.755259\pi$
$284$	5.37120	+	3.90240i	0.318722	+	0.231565i
$285$	−3.30140	+	0.439474i	−0.195558	+	0.0260322i
$286$	1.06196	−	0.771557i	0.0627948	−	0.0456231i
$287$	−6.78412	+	9.33754i	−0.400454	+	0.551177i
$288$	−3.40188	+	4.68229i	−0.200458	+	0.275907i
$289$	−13.6789	+	9.93828i	−0.804639	+	0.584605i
$290$	−6.72105	−	14.0389i	−0.394673	−	0.824393i
$291$	20.5457	+	14.9273i	1.20441	+	0.875054i
$292$	3.38760	−	1.10070i	0.198244	−	0.0644135i
$293$		−	14.1357i		−	0.825817i	−0.910773	−	0.412908i	$-0.864513\pi$
$293$		−	14.1357i		−	0.825817i	0.910773	−	0.412908i	$-0.135487\pi$
$294$	4.76437	+	14.6632i	0.277863	+	0.855176i
$295$	−4.42644	+	8.18057i	−0.257718	+	0.476291i
$296$	−1.66618	+	5.12797i	−0.0968447	+	0.298057i
$297$	20.5998	+	6.69328i	1.19532	+	0.388383i
$298$	−17.3281	−	23.8500i	−1.00379	−	1.38160i
$299$	0.966232			0.0558786
$300$	4.36783	−	11.4773i	0.252177	−	0.662641i
$301$	−7.71524			−0.444699
$302$	−11.1161	−	15.3001i	−0.639662	−	0.880420i
$303$	−17.6499	−	5.73480i	−1.01396	−	0.329455i
$304$	1.41494	−	4.35474i	0.0811524	−	0.249761i
$305$	−4.02099	−	4.22504i	−0.230241	−	0.241925i
$306$	0.139923	+	0.430638i	0.00799885	+	0.0246179i
$307$			3.61939i			0.206569i	0.994652	+	0.103285i	$0.0329353\pi$
$307$			3.61939i			0.206569i	−0.994652	+	0.103285i	$0.967065\pi$
$308$	−21.2531	+	6.90555i	−1.21101	+	0.393480i
$309$	−1.53538	−	1.11552i	−0.0873448	−	0.0634597i
$310$	30.4231	+	16.4617i	1.72792	+	0.934963i
$311$	−22.7401	+	16.5217i	−1.28947	+	0.936857i	−0.999795	−	0.0202671i	$-0.993548\pi$
$311$	−22.7401	+	16.5217i	−1.28947	+	0.936857i	−0.289678	+	0.957124i	$0.593548\pi$
$312$	−0.104901	+	0.144384i	−0.00593886	+	0.00817414i
$313$	11.4997	−	15.8279i	0.649999	−	0.894647i	−0.349100	−	0.937086i	$-0.613513\pi$
$313$	11.4997	−	15.8279i	0.649999	−	0.894647i	0.999099	+	0.0424383i	$0.0135126\pi$
$314$	24.6704	−	17.9241i	1.39223	−	1.01151i
$315$	5.41638	+	2.93076i	0.305178	+	0.165130i
$316$	20.3586	+	14.7914i	1.14526	+	0.832079i
$317$	25.3832	−	8.24749i	1.42566	−	0.463225i	0.508264	−	0.861201i	$-0.330287\pi$
$317$	25.3832	−	8.24749i	1.42566	−	0.463225i	0.917396	+	0.397976i	$0.130287\pi$
$318$		−	8.39162i		−	0.470579i
$319$	−4.33030	−	13.3273i	−0.242450	−	0.746186i
$320$	7.69005	+	8.08029i	0.429887	+	0.451702i
$321$	0.0948935	−	0.292052i	0.00529644	−	0.0163008i
$322$	−34.6188	−	11.2483i	−1.92923	−	0.626845i
$323$	−0.178277	−	0.245377i	−0.00991958	−	0.0136531i
$324$	9.96739			0.553744
$325$	−0.317782	+	0.835030i	−0.0176274	+	0.0463191i
$326$	−45.7143			−2.53188
$327$	−10.9397	−	15.0572i	−0.604968	−	0.832667i
$328$	2.08868	+	0.678653i	0.115328	+	0.0374724i
$329$	4.71009	−	14.4962i	0.259676	−	0.799199i
$330$	11.6431	−	21.5177i	0.640931	−	1.18451i
$331$	0.261947	+	0.806190i	0.0143979	+	0.0443122i	0.957997	−	0.286777i	$-0.0925839\pi$
$331$	0.261947	+	0.806190i	0.0143979	+	0.0443122i	−0.943599	+	0.331089i	$0.892584\pi$
$332$			13.4619i			0.738818i
$333$	−5.97666	+	1.94193i	−0.327519	+	0.106417i
$334$	32.9120	+	23.9120i	1.80086	+	1.30840i
$335$	3.04650	+	6.36352i	0.166448	+	0.347676i
$336$	19.4438	−	14.1268i	1.06075	−	0.770678i
$337$	9.82706	−	13.5258i	0.535314	−	0.736797i	−0.452615	−	0.891706i	$-0.649509\pi$
$337$	9.82706	−	13.5258i	0.535314	−	0.736797i	0.987929	+	0.154910i	$0.0495086\pi$
$338$	14.5606	−	20.0409i	0.791992	−	1.09008i
$339$	18.4696	−	13.4190i	1.00313	−	0.728819i
$340$	1.10856	−	0.147569i	0.0601201	−	0.00800305i
$341$	25.1951	+	18.3053i	1.36439	+	0.991287i
$342$	1.41983	−	0.461331i	0.0767756	−	0.0249459i
$343$		−	5.57188i		−	0.300853i
$344$	0.453652	+	1.39620i	0.0244593	+	0.0752779i
$345$	16.2435	−	7.77650i	0.874522	−	0.418673i
$346$	−0.550024	+	1.69280i	−0.0295695	+	0.0910055i
$347$	−16.8959	−	5.48980i	−0.907017	−	0.294708i	−0.181887	−	0.983319i	$-0.558220\pi$
$347$	−16.8959	−	5.48980i	−0.907017	−	0.294708i	−0.725130	+	0.688612i	$0.758220\pi$
$348$	−5.26055	−	7.24053i	−0.281995	−	0.388133i
$349$	28.0529			1.50164			0.750819	−	0.660509i	$-0.229659\pi$
$349$	28.0529			1.50164			0.750819	+	0.660509i	$0.229659\pi$
$350$	21.1066	−	26.2186i	1.12820	−	1.40144i
$351$	−1.00646			−0.0537209
$352$	16.7393	+	23.0396i	0.892206	+	1.22802i
$353$	23.0904	+	7.50254i	1.22898	+	0.399320i	0.850345	−	0.526226i	$-0.176393\pi$
$353$	23.0904	+	7.50254i	1.22898	+	0.399320i	0.378635	+	0.925546i	$0.376393\pi$
$354$	−3.65725	+	11.2559i	−0.194381	+	0.598243i
$355$	−8.85458	−	1.62791i	−0.469952	−	0.0864007i
$356$	−4.56205	−	14.0405i	−0.241788	−	0.744147i
$357$		−	1.59200i		−	0.0842578i
$358$	−19.2773	+	6.26357i	−1.01884	+	0.331040i
$359$	−16.1347	−	11.7226i	−0.851557	−	0.618693i	0.0740177	−	0.997257i	$-0.476418\pi$
$359$	−16.1347	−	11.7226i	−0.851557	−	0.618693i	−0.925575	+	0.378564i	$0.876418\pi$
$360$	0.211889	−	1.15251i	0.0111675	−	0.0607425i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−0.118885	+	0.163631i	−0.00624847	+	0.00860028i
$363$	3.31675	−	4.56512i	0.174084	−	0.239607i
$364$	0.840066	−	0.610344i	0.0440314	−	0.0319907i
$365$	−3.49886	+	3.32988i	−0.183139	+	0.174294i
$366$	−6.00409	−	4.36223i	−0.313839	−	0.228017i
$367$	29.0552	−	9.44062i	1.51667	−	0.492796i	0.571843	−	0.820363i	$-0.306228\pi$
$367$	29.0552	−	9.44062i	1.51667	−	0.492796i	0.944828	+	0.327566i	$0.106228\pi$
$368$			24.7591i			1.29066i
$369$	0.790971	+	2.43436i	0.0411763	+	0.126728i
$370$	4.53209	+	34.0457i	0.235612	+	1.76995i
$371$	3.21187	−	9.88512i	0.166752	−	0.513210i
$372$	18.9165	+	6.14635i	0.980776	+	0.318673i
$373$	−14.7488	−	20.2999i	−0.763663	−	1.05109i	−0.996901	−	0.0786718i	$-0.974932\pi$
$373$	−14.7488	−	20.2999i	−0.763663	−	1.05109i	0.233238	−	0.972420i	$-0.425068\pi$
$374$	2.22804			0.115209
$375$	1.37825	+	16.5955i	0.0711727	+	0.856986i
$376$	−2.90026			−0.149570
$377$	0.382732	+	0.526785i	0.0197117	+	0.0271308i
$378$	36.0601	+	11.7166i	1.85473	+	0.602639i
$379$	−9.49641	+	29.2269i	−0.487798	+	1.50129i	0.340090	+	0.940393i	$0.389543\pi$
$379$	−9.49641	+	29.2269i	−0.487798	+	1.50129i	−0.827888	+	0.560894i	$0.810457\pi$
$380$	−0.486540	−	3.65496i	−0.0249590	−	0.187496i
$381$	8.99911	+	27.6964i	0.461038	+	1.41893i
$382$		−	35.3791i		−	1.81015i
$383$	−9.81225	+	3.18819i	−0.501382	+	0.162909i	−0.548780	−	0.835967i	$-0.684907\pi$
$383$	−9.81225	+	3.18819i	−0.501382	+	0.162909i	0.0473972	+	0.998876i	$0.484907\pi$
$384$	−6.36452	−	4.62409i	−0.324788	−	0.235972i
$385$	21.9511	−	20.8910i	1.11873	−	1.06470i
$386$	27.1734	−	19.7427i	1.38309	−	1.00487i
$387$	−1.00571	+	1.38424i	−0.0511230	+	0.0703648i
$388$	−16.5260	+	22.7460i	−0.838978	+	1.15475i
$389$	3.70753	−	2.69368i	0.187979	−	0.136575i	−0.489815	−	0.871826i	$-0.662936\pi$
$389$	3.70753	−	2.69368i	0.187979	−	0.136575i	0.677795	+	0.735251i	$0.262936\pi$
$390$	−0.205563	+	1.11810i	−0.0104091	+	0.0566172i
$391$	1.32682	+	0.963993i	0.0671003	+	0.0487512i
$392$	3.45581	−	1.12286i	0.174545	−	0.0567130i
$393$		−	11.1273i		−	0.561299i
$394$	1.29167	+	3.97536i	0.0650735	+	0.200276i
$395$	−33.5617	−	6.17032i	−1.68867	−	0.310462i
$396$	−1.53145	+	4.71331i	−0.0769581	+	0.236853i
$397$	−3.56569	−	1.15856i	−0.178957	−	0.0581466i	0.218168	−	0.975911i	$-0.429992\pi$
$397$	−3.56569	−	1.15856i	−0.178957	−	0.0581466i	−0.397125	+	0.917765i	$0.629992\pi$
$398$	−24.5144	−	33.7412i	−1.22880	−	1.69129i
$399$	−5.24890			−0.262774
$400$	−21.3971	−	8.14296i	−1.06986	−	0.407148i
$401$	−10.6326			−0.530968			−0.265484	−	0.964115i	$-0.585532\pi$
$401$	−10.6326			−0.530968			−0.265484	+	0.964115i	$0.585532\pi$
$402$	5.27659	+	7.26261i	0.263172	+	0.362226i
$403$	−1.37627	−	0.447178i	−0.0685570	−	0.0222755i
$404$	6.34897	−	19.5401i	0.315873	−	0.972157i
$405$	−12.1911	+	5.83643i	−0.605782	+	0.290015i
$406$	−7.58023	−	23.3296i	−0.376201	−	1.15783i
$407$			30.9221i			1.53275i
$408$	−0.288099	+	0.0936090i	−0.0142630	+	0.00463434i
$409$	−12.2313	−	8.88657i	−0.604799	−	0.439413i	0.242780	−	0.970081i	$-0.421941\pi$
$409$	−12.2313	−	8.88657i	−0.604799	−	0.439413i	−0.847579	+	0.530669i	$0.821941\pi$
$410$	13.8672	−	1.84597i	0.684852	−	0.0911660i
$411$	22.4054	−	16.2785i	1.10518	−	0.802958i
$412$	1.23499	−	1.69981i	0.0608434	−	0.0837438i
$413$	−8.61631	+	11.8593i	−0.423981	+	0.583559i
$414$	−6.53081	+	4.74491i	−0.320972	+	0.233200i
$415$	−7.88266	−	16.4653i	−0.386944	−	0.808249i
$416$	−1.07057	−	0.777816i	−0.0524891	−	0.0381355i
$417$	3.83184	−	1.24504i	0.187646	−	0.0609699i
$418$		−	7.34594i		−	0.359301i
$419$	1.60700	+	4.94584i	0.0785072	+	0.241620i	0.982606	−	0.185704i	$-0.0594564\pi$
$419$	1.60700	+	4.94584i	0.0785072	+	0.241620i	−0.904099	+	0.427324i	$0.859456\pi$
$420$	9.21032	−	17.0217i	0.449417	−	0.830574i
$421$	−0.244737	+	0.753224i	−0.0119278	+	0.0367099i	−0.956843	−	0.290605i	$-0.906144\pi$
$421$	−0.244737	+	0.753224i	−0.0119278	+	0.0367099i	0.944915	+	0.327314i	$0.106144\pi$
$422$	34.6081	+	11.2449i	1.68470	+	0.547391i
$423$	−1.98687	−	2.73469i	−0.0966048	−	0.132965i
$424$	−1.97773			−0.0960470
$425$	−1.26947	+	0.829611i	−0.0615784	+	0.0402421i
$426$	−11.4555			−0.555020
$427$	−5.40304	−	7.43665i	−0.261471	−	0.359884i
$428$	0.323330	+	0.105056i	0.0156287	+	0.00507809i
$429$	−0.316281	+	0.973414i	−0.0152702	+	0.0469969i
$430$	6.44686	+	6.77401i	0.310895	+	0.326672i
$431$	−10.6950	−	32.9159i	−0.515161	−	1.58550i	−0.782989	−	0.622036i	$-0.786306\pi$
$431$	−10.6950	−	32.9159i	−0.515161	−	1.58550i	0.267827	−	0.963467i	$-0.413694\pi$
$432$		−	25.7899i		−	1.24082i
$433$	−13.4885	+	4.38269i	−0.648218	+	0.210619i	−0.614628	−	0.788817i	$-0.710694\pi$
$433$	−13.4885	+	4.38269i	−0.648218	+	0.210619i	−0.0335898	+	0.999436i	$0.510694\pi$
$434$	44.1042	+	32.0436i	2.11707	+	1.53814i
$435$	10.6739	+	5.77557i	0.511774	+	0.276917i
$436$	16.6698	−	12.1113i	0.798339	−	0.580027i
$437$	3.17832	−	4.37458i	0.152040	−	0.209265i
$438$	−3.61247	+	4.97214i	−0.172611	+	0.237578i
$439$	−13.7675	+	10.0027i	−0.657088	+	0.477403i	−0.865678	−	0.500600i	$-0.833113\pi$
$439$	−13.7675	+	10.0027i	−0.657088	+	0.477403i	0.208590	+	0.978003i	$0.433113\pi$
$440$	−5.07127	−	2.74403i	−0.241763	−	0.130816i
$441$	3.42621	+	2.48929i	0.163153	+	0.118537i
$442$	−0.0984622	+	0.0319923i	−0.00468337	+	0.00152172i
$443$		−	22.9664i		−	1.09116i	−0.838057	−	0.545582i	$-0.816308\pi$
$443$		−	22.9664i		−	1.09116i	0.838057	−	0.545582i	$-0.183692\pi$
$444$	6.10279	+	18.7825i	0.289626	+	0.891376i
$445$	13.8013	+	14.5017i	0.654245	+	0.687445i
$446$	−14.2919	+	43.9859i	−0.676740	+	2.08279i
$447$	21.8615	+	7.10323i	1.03401	+	0.335971i
$448$	10.3332	+	14.2224i	0.488197	+	0.671946i
$449$	−21.9462			−1.03571			−0.517853	−	0.855469i	$-0.673269\pi$
$449$	−21.9462			−1.03571			−0.517853	+	0.855469i	$0.673269\pi$
$450$	−1.95271	−	7.20455i	−0.0920516	−	0.339626i
$451$	12.5949			0.593071
$452$	14.8561	+	20.4477i	0.698772	+	0.961777i
$453$	14.0244	+	4.55680i	0.658923	+	0.214097i
$454$	−11.4133	+	35.1266i	−0.535654	+	1.64857i
$455$	−0.670097	+	1.23842i	−0.0314146	+	0.0580578i
$456$	0.308633	+	0.949873i	0.0144530	+	0.0444819i
$457$		−	33.9191i		−	1.58667i	−0.608786	−	0.793334i	$-0.708343\pi$
$457$		−	33.9191i		−	1.58667i	0.608786	−	0.793334i	$-0.291657\pi$
$458$	51.4943	−	16.7315i	2.40617	−	0.781812i
$459$	−1.38206	−	1.00413i	−0.0645092	−	0.0468687i
$460$	8.60933	+	17.9831i	0.401412	+	0.838468i
$461$	−1.56610	+	1.13783i	−0.0729403	+	0.0529943i	−0.623658	−	0.781697i	$-0.714354\pi$
$461$	−1.56610	+	1.13783i	−0.0729403	+	0.0529943i	0.550718	+	0.834692i	$0.314354\pi$
$462$	22.6639	−	31.1941i	1.05442	−	1.45128i
$463$	−15.3997	+	21.1958i	−0.715682	+	0.985052i	0.283974	+	0.958832i	$0.408347\pi$
$463$	−15.3997	+	21.1958i	−0.715682	+	0.985052i	−0.999656	+	0.0262203i	$0.991653\pi$
$464$	−13.4985	+	9.80727i	−0.626654	+	0.455291i
$465$	−26.7358	+	3.55901i	−1.23984	+	0.165045i
$466$	−20.6313	−	14.9895i	−0.955725	−	0.694375i
$467$	−28.4948	+	9.25852i	−1.31858	+	0.428433i	−0.882008	−	0.471235i	$-0.843808\pi$
$467$	−28.4948	+	9.25852i	−1.31858	+	0.428433i	−0.436574	+	0.899668i	$0.643808\pi$
$468$		−	0.230282i		−	0.0106448i
$469$	3.43595	+	10.5748i	0.158657	+	0.488297i
$470$	−16.6634	+	7.97752i	−0.768627	+	0.367976i
$471$	−7.34755	+	22.6134i	−0.338557	+	1.04197i
$472$	2.65277	+	0.861937i	0.122104	+	0.0396739i
$473$	4.94867	+	6.81126i	0.227540	+	0.313182i
$474$	−43.4199			−1.99434
$475$	2.73526	+	4.18549i	0.125502	+	0.192044i
$476$	1.76250			0.0807841
$477$	−1.35487	−	1.86482i	−0.0620353	−	0.0853842i
$478$	24.4233	+	7.93562i	1.11710	+	0.362967i
$479$	−9.29832	+	28.6173i	−0.424851	+	1.30756i	0.478285	+	0.878204i	$0.341258\pi$
$479$	−9.29832	+	28.6173i	−0.424851	+	1.30756i	−0.903137	+	0.429353i	$0.858742\pi$
$480$	−24.2577	−	4.45977i	−1.10721	−	0.203560i
$481$	−0.444009	−	1.36652i	−0.0202451	−	0.0623079i
$482$		−	26.5845i		−	1.21089i
$483$	26.9932	−	8.77061i	1.22823	−	0.399077i
$484$	5.05402	+	3.67196i	0.229728	+	0.166907i
$485$	6.89392	−	37.4975i	0.313037	−	1.70267i
$486$	12.1995	−	8.86346i	0.553381	−	0.402055i
$487$	−9.51570	+	13.0972i	−0.431197	+	0.593492i	−0.968228	−	0.250071i	$-0.919546\pi$
$487$	−9.51570	+	13.0972i	−0.431197	+	0.593492i	0.537030	+	0.843563i	$0.319546\pi$
$488$	−1.02809	+	1.41504i	−0.0465392	+	0.0640557i
$489$	28.8371	−	20.9514i	1.30406	−	0.947455i
$490$	16.7667	−	15.9570i	0.757444	−	0.720863i
$491$	−24.8959	−	18.0879i	−1.12353	−	0.816295i	−0.138793	−	0.990321i	$-0.544322\pi$
$491$	−24.8959	−	18.0879i	−1.12353	−	0.816295i	−0.984741	+	0.174026i	$0.944322\pi$
$492$	7.65030	−	2.48573i	0.344902	−	0.112065i
$493$			1.10522i			0.0497767i
$494$	0.105480	+	0.324634i	0.00474576	+	0.0146060i
$495$	−0.886776	−	6.66159i	−0.0398576	−	0.299416i
$496$	11.4587	−	35.2661i	0.514509	−	1.58350i
$497$	−13.4943	−	4.38455i	−0.605300	−	0.196674i
$498$	−13.6529	−	18.7916i	−0.611801	−	0.842072i
$499$	7.43734			0.332941			0.166471	−	0.986046i	$-0.446763\pi$
$499$	7.43734			0.332941			0.166471	+	0.986046i	$0.446763\pi$
$500$	−18.3728	+	1.52586i	−0.821655	+	0.0682385i
$501$	−31.7204			−1.41716
$502$	−5.79383	−	7.97453i	−0.258591	−	0.355921i
$503$	−3.87202	−	1.25810i	−0.172645	−	0.0560958i	0.221419	−	0.975179i	$-0.428931\pi$
$503$	−3.87202	−	1.25810i	−0.172645	−	0.0560958i	−0.394064	+	0.919083i	$0.628931\pi$
$504$	0.570692	−	1.75641i	0.0254206	−	0.0782366i
$505$	3.67634	+	27.6172i	0.163595	+	1.22895i
$506$	12.2746	+	37.7774i	0.545674	+	1.67941i
$507$			19.3153i			0.857824i
$508$	−30.6626	+	9.96288i	−1.36043	+	0.442031i
$509$	28.1595	+	20.4591i	1.24815	+	0.906833i	0.998113	−	0.0614032i	$-0.0195576\pi$
$509$	28.1595	+	20.4591i	1.24815	+	0.906833i	0.250036	+	0.968237i	$0.419558\pi$
$510$	−1.39779	+	1.33028i	−0.0618950	+	0.0589058i
$511$	−6.15847	+	4.47439i	−0.272435	+	0.197935i
$512$	16.3216	−	22.4648i	0.721321	−	0.992813i
$513$	−3.31065	+	4.55672i	−0.146169	+	0.201184i
$514$	14.0375	−	10.1988i	0.619166	−	0.449850i
$515$	−0.515183	+	2.80219i	−0.0227017	+	0.123479i
$516$	4.35015	+	3.16057i	0.191505	+	0.139136i
$517$	−15.8188	+	5.13984i	−0.695710	+	0.226050i
$518$			54.1294i			2.37831i
$519$	−0.428868	−	1.31992i	−0.0188252	−	0.0579380i
$520$	0.263513	+	0.0484468i	0.0115558	+	0.00212453i
$521$	4.12606	−	12.6987i	0.180766	−	0.556341i	−0.819084	−	0.573674i	$-0.805518\pi$
$521$	4.12606	−	12.6987i	0.180766	−	0.556341i	0.999850	+	0.0173332i	$0.00551759\pi$
$522$	−5.17381	−	1.68107i	−0.226451	−	0.0735785i
$523$	2.86690	+	3.94595i	0.125361	+	0.172544i	0.867084	−	0.498162i	$-0.165991\pi$
$523$	2.86690	+	3.94595i	0.125361	+	0.172544i	−0.741724	+	0.670706i	$0.765991\pi$
$524$	12.3190			0.538158
$525$	−1.29804	+	26.2124i	−0.0566513	+	1.14400i
$526$	−1.21155			−0.0528259
$527$	−1.44375	−	1.98715i	−0.0628905	−	0.0865614i
$528$	−24.9431	−	8.10451i	−1.08551	−	0.352704i
$529$	−1.92787	+	5.93337i	−0.0838204	+	0.257973i
$530$	−11.3630	+	5.43998i	−0.493578	+	0.236298i
$531$	1.00459	+	3.09181i	0.0435955	+	0.134173i
$532$		−	5.81104i		−	0.251940i
$533$	−0.556598	+	0.180850i	−0.0241089	+	0.00783347i
$534$	20.6080	+	14.9726i	0.891793	+	0.647926i
$535$	−0.456981	+	0.0608323i	−0.0197570	+	0.00263001i
$536$	1.71164	−	1.24358i	0.0739317	−	0.0537145i
$537$	9.28967	−	12.7861i	0.400879	−	0.551762i
$538$	−1.61551	+	2.22356i	−0.0696495	+	0.0958644i
$539$	16.8590	−	12.2487i	0.726166	−	0.527591i
$540$	−8.96777	−	18.7319i	−0.385911	−	0.806091i
$541$	25.3594	+	18.4247i	1.09029	+	0.792138i	0.979447	−	0.201700i	$-0.0646466\pi$
$541$	25.3594	+	18.4247i	1.09029	+	0.792138i	0.110838	+	0.993839i	$0.464647\pi$
$542$	−14.4513	+	4.69551i	−0.620736	+	0.201689i
$543$		−	0.157707i		−	0.00676786i
$544$	−0.694087	−	2.13618i	−0.0297587	−	0.0915880i
$545$	−13.2970	+	24.5744i	−0.569582	+	1.05265i
$546$	−0.553653	+	1.70397i	−0.0236942	+	0.0729232i
$547$	5.67292	+	1.84324i	0.242557	+	0.0788115i	0.427773	−	0.903886i	$-0.359298\pi$
$547$	5.67292	+	1.84324i	0.242557	+	0.0788115i	−0.185216	+	0.982698i	$0.559298\pi$
$548$	18.0218	+	24.8049i	0.769854	+	1.05961i
$549$	−2.03856			−0.0870035
$550$	−36.6847	−	1.81664i	−1.56424	−	0.0774617i
$551$	3.64396			0.155238
$552$	−3.17437	−	4.36914i	−0.135110	−	0.185963i
$553$	−51.1476	−	16.6189i	−2.17502	−	0.706706i
$554$	7.74309	−	23.8308i	0.328972	−	1.01247i
$555$	−18.4624	−	19.3993i	−0.783687	−	0.823456i
$556$	1.37838	+	4.24221i	0.0584563	+	0.179910i
$557$			27.8984i			1.18209i	0.806637	+	0.591047i	$0.201285\pi$
$557$			27.8984i			1.18209i	−0.806637	+	0.591047i	$0.798715\pi$
$558$	11.4983	−	3.73601i	0.486761	−	0.158158i
$559$	−0.316496	−	0.229948i	−0.0133863	−	0.00972575i
$560$	−31.7336	−	17.1708i	−1.34099	−	0.725600i
$561$	−1.40547	+	1.02114i	−0.0593391	+	0.0431124i
$562$	21.3174	−	29.3409i	0.899220	−	1.23767i
$563$	−10.4656	+	14.4047i	−0.441073	+	0.607084i	−0.970450	−	0.241302i	$-0.922426\pi$
$563$	−10.4656	+	14.4047i	−0.441073	+	0.607084i	0.529378	+	0.848386i	$0.322426\pi$
$564$	−8.59413	+	6.24400i	−0.361878	+	0.262920i
$565$	−30.1437	−	16.3105i	−1.26815	−	0.686189i
$566$	46.7120	+	33.9382i	1.96345	+	1.42653i
$567$	−20.2590	+	6.58254i	−0.850796	+	0.276441i
$568$			2.69981i			0.113282i
$569$	6.21995	+	19.1430i	0.260754	+	0.802518i	0.992641	+	0.121092i	$0.0386397\pi$
$569$	6.21995	+	19.1430i	0.260754	+	0.802518i	−0.731887	+	0.681426i	$0.761360\pi$
$570$	4.38599	+	4.60855i	0.183709	+	0.193031i
$571$	4.44494	−	13.6801i	0.186015	−	0.572495i	−0.813950	−	0.580935i	$-0.802687\pi$
$571$	4.44494	−	13.6801i	0.186015	−	0.572495i	0.999964	+	0.00844089i	$0.00268685\pi$
$572$	−1.07766	−	0.350154i	−0.0450593	−	0.0146407i
$573$	16.2146	+	22.3175i	0.677377	+	0.932329i
$574$	22.0475			0.920245
$575$	−21.0602	−	16.9540i	−0.878269	−	0.707030i
$576$	3.89869			0.162446
$577$	25.2681	+	34.7786i	1.05193	+	1.44785i	0.887127	+	0.461525i	$0.152698\pi$
$577$	25.2681	+	34.7786i	1.05193	+	1.44785i	0.164799	+	0.986327i	$0.447302\pi$
$578$	30.7174	+	9.98067i	1.27767	+	0.415141i
$579$	−8.09303	+	24.9078i	−0.336335	+	1.03513i
$580$	−6.39411	+	11.8170i	−0.265501	+	0.490675i
$581$	−8.89034	−	27.3617i	−0.368834	−	1.13515i
$582$		−	48.5118i		−	2.01088i
$583$	−10.7870	+	3.50492i	−0.446754	+	0.145159i
$584$	1.17183	+	0.851383i	0.0484906	+	0.0352305i
$585$	0.134842	+	0.281658i	0.00557503	+	0.0116451i
$586$	−21.8454	+	15.8716i	−0.902425	+	0.655650i
$587$	2.23519	−	3.07648i	0.0922562	−	0.126980i	−0.760394	−	0.649462i	$-0.774994\pi$
$587$	2.23519	−	3.07648i	0.0922562	−	0.126980i	0.852650	+	0.522483i	$0.174994\pi$
$588$	7.82291	−	10.7673i	0.322611	−	0.444037i
$589$	−6.55169	+	4.76008i	−0.269958	+	0.196136i
$590$	17.6123	−	2.34451i	0.725088	−	0.0965221i
$591$	−2.63675	−	1.91571i	−0.108461	−	0.0788019i
$592$	35.0162	−	11.3775i	1.43916	−	0.467610i
$593$		−	1.36970i		−	0.0562470i	−0.999604	−	0.0281235i	$-0.991047\pi$
$593$		−	1.36970i		−	0.0562470i	0.999604	−	0.0281235i	$-0.00895316\pi$
$594$	−12.7857	−	39.3503i	−0.524603	−	1.61456i
$595$	−2.15572	+	1.03204i	−0.0883758	+	0.0423094i
$596$	−7.86395	+	24.2028i	−0.322120	+	0.991384i
$597$	30.9279	+	10.0491i	1.26580	+	0.411282i
$598$	−1.08489	−	1.49322i	−0.0443644	−	0.0610623i
$599$	18.1072			0.739842			0.369921	−	0.929063i	$-0.379385\pi$
$599$	18.1072			0.739842			0.369921	+	0.929063i	$0.379385\pi$
$600$	4.81988	−	1.30637i	0.196771	−	0.0533324i
$601$	32.0520			1.30743			0.653714	−	0.756742i	$-0.273210\pi$
$601$	32.0520			1.30743			0.653714	+	0.756742i	$0.273210\pi$
$602$	8.66270	+	11.9232i	0.353065	+	0.485953i
$603$	2.34517	+	0.761992i	0.0955027	+	0.0310307i
$604$	−5.04481	+	15.5263i	−0.205271	+	0.631758i
$605$	−8.33171	−	1.53178i	−0.338732	−	0.0622759i
$606$	10.9548	+	33.7153i	0.445007	+	1.36959i
$607$		−	44.9625i		−	1.82497i	−0.409110	−	0.912485i	$-0.634161\pi$
$607$		−	44.9625i		−	1.82497i	0.409110	−	0.912485i	$-0.365839\pi$
$608$	−7.04307	+	2.28843i	−0.285634	+	0.0928082i
$609$	15.4739	+	11.2424i	0.627034	+	0.455567i
$610$	−2.01462	+	10.9580i	−0.0815696	+	0.443675i
$611$	0.625266	−	0.454283i	0.0252956	−	0.0183783i
$612$	0.229748	−	0.316221i	0.00928702	−	0.0127825i
$613$	−19.3693	+	26.6595i	−0.782317	+	1.07677i	0.212706	+	0.977116i	$0.431772\pi$
$613$	−19.3693	+	26.6595i	−0.782317	+	1.07677i	−0.995023	+	0.0996503i	$0.968228\pi$
$614$	5.59342	−	4.06386i	0.225732	−	0.164004i
$615$	−7.90156	+	7.51996i	−0.318622	+	0.303234i
$616$	−7.35180	−	5.34139i	−0.296212	−	0.215211i
$617$	39.3159	−	12.7745i	1.58280	−	0.514282i	0.620023	−	0.784584i	$-0.287123\pi$
$617$	39.3159	−	12.7745i	1.58280	−	0.514282i	0.962776	+	0.270301i	$0.0871234\pi$
$618$			3.62530i			0.145831i
$619$	3.19955	+	9.84719i	0.128601	+	0.395792i	0.994540	−	0.104357i	$-0.0332785\pi$
$619$	3.19955	+	9.84719i	0.128601	+	0.395792i	−0.865939	+	0.500149i	$0.833279\pi$
$620$	−3.94017	−	29.5991i	−0.158241	−	1.18873i
$621$	9.41143	−	28.9654i	0.377668	−	1.16234i
$622$	51.0653	+	16.5921i	2.04753	+	0.665284i
$623$	18.5449	+	25.5249i	0.742988	+	1.02263i
$624$	1.21867			0.0487857
$625$	21.5783	−	12.6245i	0.863131	−	0.504980i
$626$	−37.3724			−1.49370
$627$	3.36673	+	4.63390i	0.134454	+	0.185060i
$628$	−25.0352	−	8.13444i	−0.999015	−	0.324600i
$629$	0.753643	−	2.31947i	0.0300497	−	0.0924835i
$630$	−1.55231	−	11.6612i	−0.0618455	−	0.464592i
$631$	−13.8244	−	42.5471i	−0.550340	−	1.69377i	−0.707943	−	0.706269i	$-0.750377\pi$
$631$	−13.8244	−	42.5471i	−0.550340	−	1.69377i	0.157603	−	0.987502i	$-0.449623\pi$
$632$			10.2332i			0.407053i
$633$	−26.9848	+	8.76790i	−1.07255	+	0.348493i
$634$	−41.2460	−	29.9670i	−1.63809	−	1.19014i
$635$	31.6696	−	30.1402i	1.25677	−	1.19608i
$636$	−5.86045	+	4.25786i	−0.232382	+	0.168835i
$637$	−0.569157	+	0.783377i	−0.0225508	+	0.0310385i
$638$	−15.7340	+	21.6560i	−0.622916	+	0.857370i
$639$	−2.54568	+	1.84955i	−0.100706	+	0.0731669i
$640$	−2.13556	+	11.6158i	−0.0844153	+	0.459153i
$641$	20.0948	+	14.5997i	0.793695	+	0.576653i	0.909058	−	0.416670i	$-0.136803\pi$
$641$	20.0948	+	14.5997i	0.793695	+	0.576653i	−0.115363	+	0.993323i	$0.536803\pi$
$642$	−0.557886	+	0.181268i	−0.0220180	+	0.00715409i
$643$		−	3.38289i		−	0.133408i	−0.997773	−	0.0667041i	$-0.978752\pi$
$643$		−	3.38289i		−	0.133408i	0.997773	−	0.0667041i	$-0.0212483\pi$
$644$	9.70991	+	29.8840i	0.382624	+	1.17760i
$645$	−7.17136	−	1.31845i	−0.282372	−	0.0519141i
$646$	−0.179037	+	0.551020i	−0.00704413	+	0.0216796i
$647$	11.5811	+	3.76294i	0.455302	+	0.147937i	0.527685	−	0.849440i	$-0.323060\pi$
$647$	11.5811	+	3.76294i	0.455302	+	0.147937i	−0.0723827	+	0.997377i	$0.523060\pi$
$648$	2.38243	+	3.27914i	0.0935908	+	0.128817i
$649$	15.9964			0.627915
$650$	1.64727	−	0.446473i	0.0646111	−	0.0175121i
$651$	−42.5074			−1.66600
$652$	23.1952	+	31.9255i	0.908394	+	1.25030i
$653$	17.4181	+	5.65949i	0.681624	+	0.221473i	0.629306	−	0.777158i	$-0.283339\pi$
$653$	17.4181	+	5.65949i	0.681624	+	0.221473i	0.0523176	+	0.998630i	$0.483339\pi$
$654$	−10.9864	+	33.8126i	−0.429602	+	1.32218i
$655$	−15.0674	+	7.21343i	−0.588732	+	0.281852i
$656$	−4.63416	−	14.2625i	−0.180934	−	0.556856i
$657$			1.68818i			0.0658622i
$658$	−27.6910	+	8.99734i	−1.07951	+	0.350753i
$659$	22.8671	+	16.6139i	0.890777	+	0.647187i	0.936080	−	0.351786i	$-0.114426\pi$
$659$	22.8671	+	16.6139i	0.890777	+	0.647187i	−0.0453038	+	0.998973i	$0.514426\pi$
$660$	−20.9349	+	2.78681i	−0.814892	+	0.108477i
$661$	19.8893	−	14.4504i	0.773604	−	0.562056i	−0.129449	−	0.991586i	$-0.541321\pi$
$661$	19.8893	−	14.4504i	0.773604	−	0.562056i	0.903053	+	0.429530i	$0.141321\pi$
$662$	0.951776	−	1.31001i	0.0369918	−	0.0509149i
$663$	0.0474486	−	0.0653075i	0.00184275	−	0.00253633i
$664$	−4.42879	+	3.21770i	−0.171870	+	0.124871i
$665$	3.40267	+	7.10748i	0.131950	+	0.275616i
$666$	9.71169	+	7.05596i	0.376320	+	0.273413i
$667$	−18.7396	+	6.08885i	−0.725598	+	0.235761i
$668$		−	35.1175i		−	1.35874i
$669$	−11.1437	−	34.2969i	−0.430842	−	1.32600i
$670$	6.41360	−	11.8531i	0.247779	−	0.457924i
$671$	−3.09972	+	9.53996i	−0.119663	+	0.368286i
$672$	−36.9684	−	12.0118i	−1.42609	−	0.463363i
$673$	−11.2529	−	15.4883i	−0.433767	−	0.597028i	0.535046	−	0.844823i	$-0.320294\pi$
$673$	−11.2529	−	15.4883i	−0.433767	−	0.597028i	−0.968813	+	0.247794i	$0.920294\pi$
$674$	−31.9367			−1.23016
$675$	21.9370	+	17.6598i	0.844355	+	0.679728i
$676$	−21.3839			−0.822459
$677$	6.09121	+	8.38383i	0.234104	+	0.322217i	0.909865	−	0.414904i	$-0.136185\pi$
$677$	6.09121	+	8.38383i	0.234104	+	0.322217i	−0.675761	+	0.737121i	$0.736185\pi$
$678$	−41.4755	−	13.4762i	−1.59286	−	0.517551i
$679$	18.5678	−	57.1457i	0.712566	−	2.19305i
$680$	0.313519	+	0.329429i	0.0120229	+	0.0126330i
$681$	−8.89927	−	27.3891i	−0.341021	−	1.04955i
$682$		−	59.4899i		−	2.27799i
$683$	43.1132	−	14.0083i	1.64968	−	0.536014i	0.671010	−	0.741449i	$-0.265861\pi$
$683$	43.1132	−	14.0083i	1.64968	−	0.536014i	0.978671	+	0.205435i	$0.0658609\pi$
$684$	−1.04259	−	0.757488i	−0.0398645	−	0.0289633i
$685$	−36.5671	−	19.7862i	−1.39716	−	0.755992i
$686$	−8.61082	+	6.25613i	−0.328763	+	0.238860i
$687$	−24.8149	+	34.1548i	−0.946749	+	1.30309i
$688$	5.89227	−	8.11001i	0.224641	−	0.309191i
$689$	0.426377	−	0.309781i	0.0162437	−	0.0118017i
$690$	−30.2561	−	16.3714i	−1.15183	−	0.623248i
$691$	−32.1042	−	23.3251i	−1.22130	−	0.887328i	−0.225095	−	0.974337i	$-0.572269\pi$
$691$	−32.1042	−	23.3251i	−1.22130	−	0.887328i	−0.996208	+	0.0870085i	$0.972269\pi$
$692$	1.46128	−	0.474798i	0.0555494	−	0.0180491i
$693$		−	10.5913i		−	0.402330i
$694$	10.4868	+	32.2749i	0.398072	+	1.22514i
$695$	−4.16994	−	4.38154i	−0.158175	−	0.166201i
$696$	1.12464	−	3.46130i	0.0426296	−	0.131200i
$697$	−0.944747	−	0.306967i	−0.0357848	−	0.0116272i
$698$	−31.4979	−	43.3531i	−1.19221	−	1.64094i
$699$	19.8843			0.752093
$700$	−29.0196	−	1.43706i	−1.09684	−	0.0543157i
$701$	28.9835			1.09469			0.547346	−	0.836906i	$-0.315638\pi$
$701$	28.9835			1.09469			0.547346	+	0.836906i	$0.315638\pi$
$702$	1.13006	+	1.55539i	0.0426512	+	0.0587044i
$703$	−7.64739	−	2.48479i	−0.288427	−	0.0937156i
$704$	5.92814	−	18.2449i	0.223425	−	0.687632i
$705$	6.85529	−	12.6694i	0.258185	−	0.477155i
$706$	−14.3315	−	44.1080i	−0.539375	−	1.66003i
$707$			43.9087i			1.65136i
$708$	9.71642	−	3.15706i	0.365165	−	0.118649i
$709$	1.18482	+	0.860819i	0.0444967	+	0.0323287i	0.609811	−	0.792547i	$-0.291245\pi$
$709$	1.18482	+	0.860819i	0.0444967	+	0.0323287i	−0.565315	+	0.824875i	$0.691245\pi$
$710$	7.42616	+	15.5117i	0.278699	+	0.582145i
$711$	−9.64895	+	7.01037i	−0.361864	+	0.262910i
$712$	3.52871	−	4.85686i	0.132244	−	0.182018i
$713$	25.7391	−	35.4269i	0.963938	−	1.32675i
$714$	−2.46029	+	1.78751i	−0.0920742	+	0.0668958i
$715$	1.52312	−	0.202755i	0.0569616	−	0.00758260i
$716$	14.1555	+	10.2845i	0.529015	+	0.384352i
$717$	−19.0435	+	6.18761i	−0.711192	+	0.231080i
$718$			38.0968i			1.42176i
$719$	−1.27879	−	3.93570i	−0.0476907	−	0.146777i	0.924375	−	0.381484i	$-0.124587\pi$
$719$	−1.27879	−	3.93570i	−0.0476907	−	0.146777i	−0.972066	+	0.234707i	$0.924587\pi$
$720$	−7.21731	+	3.45524i	−0.268973	+	0.128769i
$721$	−1.38757	+	4.27051i	−0.0516759	+	0.159042i
$722$	1.81673	+	0.590293i	0.0676118	+	0.0219684i
$723$	12.1840	+	16.7698i	0.453128	+	0.623677i
$724$	0.174597			0.00648884
$725$	0.901145	−	18.1975i	0.0334677	−	0.675838i
$726$	−10.7790			−0.400047
$727$	5.47855	+	7.54057i	0.203188	+	0.279664i	0.898435	−	0.439107i	$-0.144705\pi$
$727$	5.47855	+	7.54057i	0.203188	+	0.279664i	−0.695247	+	0.718771i	$0.744705\pi$
$728$	0.401590	+	0.130484i	0.0148839	+	0.00483607i
$729$	−9.23704	+	28.4287i	−0.342113	+	1.05291i
$730$	9.07455	+	1.66836i	0.335864	+	0.0617486i
$731$	−0.205195	−	0.631525i	−0.00758940	−	0.0233578i
$732$			6.40644i			0.236789i
$733$	−0.628430	+	0.204189i	−0.0232116	+	0.00754190i	−0.320600	−	0.947215i	$-0.603884\pi$
$733$	−0.628430	+	0.204189i	−0.0232116	+	0.00754190i	0.297388	+	0.954757i	$0.403884\pi$
$734$	−47.2129	−	34.3022i	−1.74266	−	1.26612i
$735$	−3.26338	+	17.7502i	−0.120372	+	0.654727i
$736$	32.3961	−	23.5371i	1.19414	−	0.867590i
$737$	7.13187	−	9.81618i	0.262706	−	0.361584i
$738$	2.87397	−	3.95568i	0.105792	−	0.145611i
$739$	25.2296	−	18.3304i	0.928086	−	0.674294i	−0.0174372	−	0.999848i	$-0.505551\pi$
$739$	25.2296	−	18.3304i	0.928086	−	0.674294i	0.945524	+	0.325554i	$0.105551\pi$
$740$	21.4769	−	20.4397i	0.789507	−	0.751378i
$741$	−0.215321	−	0.156440i	−0.00791002	−	0.00574697i
$742$	−18.8828	+	6.13540i	−0.693210	+	0.225238i
$743$			9.70425i			0.356014i	0.984029	+	0.178007i	$0.0569650\pi$
$743$			9.70425i			0.356014i	−0.984029	+	0.178007i	$0.943035\pi$
$744$	2.49941	+	7.69240i	0.0916328	+	0.282017i
$745$	−4.55358	−	34.2072i	−0.166830	−	1.25325i
$746$	−14.8117	+	45.5857i	−0.542295	+	1.66901i
$747$	−6.06801	−	1.97161i	−0.222017	−	0.0721376i
$748$	−1.13050	−	1.55599i	−0.0413350	−	0.0568928i
$749$	−0.726556			−0.0265478
$750$	24.0992	−	20.7634i	0.879979	−	0.758172i
$751$	−11.7290			−0.427997			−0.213998	−	0.976834i	$-0.568649\pi$
$751$	−11.7290			−0.427997			−0.213998	+	0.976834i	$0.568649\pi$
$752$	11.6407	+	16.0221i	0.424493	+	0.584264i
$753$	7.30963	+	2.37504i	0.266378	+	0.0865514i
$754$	0.384365	−	1.18295i	0.0139977	−	0.0430806i
$755$	−2.92117	−	21.9443i	−0.106312	−	0.798634i
$756$	−10.1142	−	31.1282i	−0.367849	−	1.13212i
$757$			15.3224i			0.556901i	0.960451	+	0.278451i	$0.0898208\pi$
$757$			15.3224i			0.556901i	−0.960451	+	0.278451i	$0.910179\pi$
$758$	55.8301	−	18.1403i	2.02784	−	0.658885i
$759$	−25.0568	−	18.2048i	−0.909504	−	0.660794i
$760$	1.08614	−	1.03368i	0.0393984	−	0.0374957i
$761$	−24.2407	+	17.6119i	−0.878725	+	0.638431i	−0.932914	−	0.360100i	$-0.882743\pi$
$761$	−24.2407	+	17.6119i	−0.878725	+	0.638431i	0.0541888	+	0.998531i	$0.482743\pi$
$762$	32.6980	−	45.0049i	1.18452	−	1.63036i
$763$	−25.8834	+	35.6254i	−0.937041	+	1.28973i
$764$	−24.7077	+	17.9512i	−0.893892	+	0.649450i
$765$	−0.0958410	+	0.521300i	−0.00346514	+	0.0188476i
$766$	15.9443	+	11.5842i	0.576090	+	0.418554i
$767$	−0.706919	+	0.229692i	−0.0255254	+	0.00829369i
$768$			29.8881i			1.07849i
$769$	−2.30340	−	7.08914i	−0.0830627	−	0.255641i	0.900897	−	0.434034i	$-0.142910\pi$
$769$	−2.30340	−	7.08914i	−0.0830627	−	0.255641i	−0.983959	+	0.178393i	$0.942910\pi$
$770$	−56.9318	−	10.4669i	−2.05168	−	0.377201i
$771$	−4.18076	+	12.8671i	−0.150566	+	0.463396i
$772$	−27.5753	−	8.95976i	−0.992457	−	0.322469i
$773$	−24.3944	−	33.5760i	−0.877406	−	1.20765i	−0.977133	−	0.212631i	$-0.931797\pi$
$773$	−24.3944	−	33.5760i	−0.877406	−	1.20765i	0.0997269	−	0.995015i	$-0.468203\pi$
$774$	3.26842			0.117481
$775$	22.1511	+	33.8955i	0.795690	+	1.21756i
$776$	−11.4332			−0.410428
$777$	−24.8081	−	34.1455i	−0.889987	−	1.22496i
$778$	−8.32565	−	2.70517i	−0.298489	−	0.0969850i
$779$	−1.01208	+	3.11487i	−0.0362616	+	0.111602i
$780$	0.885147	−	0.423759i	0.0316934	−	0.0151730i
$781$	4.78460	+	14.7255i	0.171206	+	0.526919i
$782$		−	3.13285i		−	0.112031i
$783$	19.5198	−	6.34235i	0.697579	−	0.226657i
$784$	−20.0735	−	14.5843i	−0.716912	−	0.520867i
$785$	35.3838	−	4.71021i	1.26290	−	0.168115i
$786$	−17.1962	+	12.4938i	−0.613369	+	0.445639i
$787$	−25.9929	+	35.7762i	−0.926547	+	1.27528i	0.0346443	+	0.999400i	$0.488970\pi$
$787$	−25.9929	+	35.7762i	−0.926547	+	1.27528i	−0.961191	+	0.275883i	$0.911030\pi$
$788$	2.12088	−	2.91914i	0.0755531	−	0.103990i
$789$	0.764257	−	0.555265i	0.0272083	−	0.0197680i
$790$	28.1475	+	58.7945i	1.00144	+	2.09181i
$791$	−43.6992	−	31.7493i	−1.55376	−	1.12888i
$792$	−1.91666	+	0.622762i	−0.0681057	+	0.0221289i
$793$		−	0.466101i		−	0.0165517i
$794$	2.21312	+	6.81128i	0.0785406	+	0.241723i
$795$	4.67471	−	8.63940i	0.165795	−	0.306408i
$796$	−11.1253	+	34.2402i	−0.394326	+	1.21361i
$797$	6.72591	+	2.18538i	0.238244	+	0.0774102i	0.425705	−	0.904862i	$-0.360026\pi$
$797$	6.72591	+	2.18538i	0.238244	+	0.0774102i	−0.187461	+	0.982272i	$0.560026\pi$
$798$	5.89348	+	8.11168i	0.208627	+	0.287150i
$799$	1.31184			0.0464096
$800$	9.68642	+	35.7382i	0.342467	+	1.26354i
$801$	6.99698			0.247226
$802$	11.9383	+	16.4317i	0.421558	+	0.580224i
$803$	7.90027	+	2.56695i	0.278795	+	0.0905859i
$804$	2.39466	−	7.37001i	0.0844532	−	0.259920i
$805$	−29.3749	−	30.8655i	−1.03533	−	1.08787i
$806$	0.854212	+	2.62899i	0.0300883	+	0.0926024i
$807$		−	2.14305i		−	0.0754390i
$808$	7.94598	−	2.58181i	0.279539	−	0.0908276i
$809$	6.46648	+	4.69817i	0.227349	+	0.165179i	0.695629	−	0.718402i	$-0.255126\pi$
$809$	6.46648	+	4.69817i	0.227349	+	0.165179i	−0.468279	+	0.883580i	$0.655126\pi$
$810$	22.7079	+	12.2871i	0.797874	+	0.431724i
$811$	28.3587	−	20.6038i	0.995808	−	0.723497i	0.0346230	−	0.999400i	$-0.488977\pi$
$811$	28.3587	−	20.6038i	0.995808	−	0.723497i	0.961185	+	0.275903i	$0.0889770\pi$
$812$	−12.4465	+	17.1311i	−0.436785	+	0.601183i
$813$	6.96403	−	9.58517i	0.244239	−	0.336167i
$814$	47.7872	−	34.7195i	1.67494	−	1.21692i
$815$	−47.0641	−	25.4660i	−1.64858	−	0.892037i
$816$	1.67346	+	1.21584i	0.0585829	+	0.0425630i
$817$	−2.08216	+	0.676535i	−0.0728456	+	0.0236690i
$818$			28.8802i			1.00977i
$819$	0.152080	+	0.468053i	0.00531409	+	0.0163551i
$820$	−8.32531	−	8.74779i	−0.290733	−	0.305486i
$821$	−13.5247	+	41.6247i	−0.472015	+	1.45271i	0.377926	+	0.925836i	$0.376637\pi$
$821$	−13.5247	+	41.6247i	−0.472015	+	1.45271i	−0.849941	+	0.526878i	$0.823363\pi$
$822$	−50.3137	−	16.3479i	−1.75489	−	0.570199i
$823$	11.1880	+	15.3990i	0.389989	+	0.536774i	0.958196	−	0.286112i	$-0.0923628\pi$
$823$	11.1880	+	15.3990i	0.389989	+	0.536774i	−0.568207	+	0.822885i	$0.692363\pi$
$824$	0.854406			0.0297646
$825$	23.9737	−	15.6671i	0.834658	−	0.545457i
$826$	28.0019			0.974311
$827$	3.08342	+	4.24397i	0.107221	+	0.147577i	0.859256	−	0.511547i	$-0.170927\pi$
$827$	3.08342	+	4.24397i	0.107221	+	0.147577i	−0.752034	+	0.659124i	$0.770927\pi$
$828$	6.62739	+	2.15337i	0.230318	+	0.0748348i
$829$	−15.5870	+	47.9720i	−0.541360	+	1.66614i	0.188130	+	0.982144i	$0.439757\pi$
$829$	−15.5870	+	47.9720i	−0.541360	+	1.66614i	−0.729490	+	0.683991i	$0.760243\pi$
$830$	−16.5949	+	30.6692i	−0.576016	+	1.06454i
$831$	6.03749	+	18.5815i	0.209438	+	0.644584i
$832$			0.891408i			0.0309040i
$833$	−1.56312	+	0.507889i	−0.0541590	+	0.0175973i
$834$	−6.22650	−	4.52381i	−0.215606	−	0.156647i
$835$	20.5632	+	42.9523i	0.711617	+	1.48642i
$836$	−5.13017	+	3.72729i	−0.177431	+	0.128911i
$837$	−26.8108	+	36.9018i	−0.926715	+	1.27551i
$838$	5.83899	−	8.03668i	0.201705	−	0.277622i
$839$	−13.5670	+	9.85699i	−0.468384	+	0.340301i	−0.796811	−	0.604228i	$-0.793481\pi$
$839$	−13.5670	+	9.85699i	−0.468384	+	0.340301i	0.328427	+	0.944529i	$0.393481\pi$
$840$	7.80138	−	1.03850i	0.269173	−	0.0358317i
$841$	12.7190	+	9.24089i	0.438586	+	0.318651i
$842$	1.43883	−	0.467504i	0.0495853	−	0.0161112i
$843$			28.2786i			0.973966i
$844$	−9.70691	−	29.8748i	−0.334126	−	1.02833i
$845$	26.1547	−	12.5214i	0.899749	−	0.430750i
$846$	−1.99534	+	6.14103i	−0.0686013	+	0.211133i
$847$	−12.6974	−	4.12564i	−0.436288	−	0.141759i
$848$	7.93795	+	10.9257i	0.272590	+	0.375188i
$849$	−45.0207			−1.54511
$850$	2.70745	+	1.03036i	0.0928648	+	0.0353409i
$851$	43.4797			1.49046
$852$	5.81245	+	8.00014i	0.199131	+	0.274080i
$853$	14.6038	+	4.74506i	0.500024	+	0.162468i	0.548161	−	0.836373i	$-0.315328\pi$
$853$	14.6038	+	4.74506i	0.500024	+	0.162468i	−0.0481364	+	0.998841i	$0.515328\pi$
$854$	−5.42609	+	16.6998i	−0.185677	+	0.571455i
$855$	1.71875	+	0.315991i	0.0587799	+	0.0108067i
$856$	0.0427211	+	0.131482i	0.00146018	+	0.00449396i
$857$		−	30.1135i		−	1.02866i	−0.857593	−	0.514328i	$-0.828041\pi$
$857$		−	30.1135i		−	1.02866i	0.857593	−	0.514328i	$-0.171959\pi$
$858$	1.85944	−	0.604169i	0.0634803	−	0.0206260i
$859$	−23.2862	−	16.9184i	−0.794515	−	0.577249i	0.114785	−	0.993390i	$-0.463382\pi$
$859$	−23.2862	−	16.9184i	−0.794515	−	0.577249i	−0.909300	+	0.416141i	$0.863382\pi$
$860$	1.45965	−	7.93938i	0.0497738	−	0.270731i
$861$	−13.9078	+	10.1046i	−0.473977	+	0.344365i
$862$	−38.8600	+	53.4862i	−1.32358	+	1.82175i
$863$	24.9815	−	34.3841i	0.850379	−	1.17045i	−0.133400	−	0.991062i	$-0.542589\pi$
$863$	24.9815	−	34.3841i	0.850379	−	1.17045i	0.983779	−	0.179385i	$-0.0574106\pi$
$864$	−33.7449	+	24.5171i	−1.14802	+	0.834088i
$865$	−1.50927	+	1.43638i	−0.0513168	+	0.0488384i
$866$	21.9180	+	15.9244i	0.744805	+	0.541132i
$867$	−23.9511	+	7.78219i	−0.813422	+	0.264297i
$868$		−	47.0597i		−	1.59731i
$869$	18.1352	+	55.8143i	0.615194	+	1.89337i
$870$	−3.05909	−	22.9803i	−0.103713	−	0.779106i
$871$	−0.174224	+	0.536206i	−0.00590335	+	0.0181686i
$872$	7.96892	+	2.58926i	0.269862	+	0.0876834i
$873$	−7.83249	−	10.7805i	−0.265090	−	0.364864i
$874$	−10.3291			−0.349388
$875$	36.3354	−	15.2348i	1.22836	−	0.515032i
$876$	5.30533			0.179251
$877$	1.62908	+	2.24224i	0.0550103	+	0.0757152i	0.835636	−	0.549284i	$-0.185099\pi$
$877$	1.62908	+	2.24224i	0.0550103	+	0.0757152i	−0.780626	+	0.624999i	$0.785099\pi$
$878$	30.9165	+	10.0454i	1.04338	+	0.339015i
$879$	6.50619	−	20.0240i	0.219448	−	0.675393i
$880$	5.19547	+	39.0291i	0.175139	+	1.31567i
$881$	−7.18708	−	22.1196i	−0.242139	−	0.745227i	−0.996094	−	0.0883010i	$-0.971856\pi$
$881$	−7.18708	−	22.1196i	−0.242139	−	0.745227i	0.753955	−	0.656926i	$-0.228144\pi$
$882$		−	8.08986i		−	0.272400i
$883$	−7.72901	+	2.51131i	−0.260102	+	0.0845122i	−0.436165	−	0.899867i	$-0.643664\pi$
$883$	−7.72901	+	2.51131i	−0.260102	+	0.0845122i	0.176063	+	0.984379i	$0.443664\pi$
$884$	0.0723016	+	0.0525302i	0.00243177	+	0.00176678i
$885$	−10.0355	+	9.55087i	−0.337341	+	0.321049i
$886$	−35.4924	+	25.7867i	−1.19239	+	0.866322i
$887$	22.7430	−	31.3030i	0.763634	−	1.05105i	−0.233269	−	0.972412i	$-0.574942\pi$
$887$	22.7430	−	31.3030i	0.763634	−	1.05105i	0.996903	−	0.0786399i	$-0.0250577\pi$
$888$	−4.72047	+	6.49717i	−0.158409	+	0.218031i
$889$	55.7429	−	40.4996i	1.86956	−	1.35831i
$890$	6.91481	−	37.6112i	0.231785	−	1.26073i
$891$	18.8057	+	13.6631i	0.630014	+	0.457732i
$892$	37.9700	−	12.3372i	1.27133	−	0.413080i
$893$		−	4.32519i		−	0.144737i
$894$	−13.5688	−	41.7604i	−0.453808	−	1.39668i
$895$	−23.3357	−	4.29027i	−0.780027	−	0.143408i
$896$	−5.75181	+	17.7023i	−0.192155	+	0.591391i
$897$	1.36872	+	0.444724i	0.0457002	+	0.0148489i
$898$	24.6413	+	33.9158i	0.822291	+	1.13179i
$899$	29.5100			0.984215
$900$	−4.04064	+	5.01926i	−0.134688	+	0.167309i
$901$	0.894561			0.0298022
$902$	−14.1416	−	19.4643i	−0.470864	−	0.648089i
$903$	−10.9291	−	3.55107i	−0.363696	−	0.118172i
$904$	−3.17606	+	9.77491i	−0.105634	+	0.325109i
$905$	−0.213550	+	0.102236i	−0.00709863	+	0.00339843i
$906$	−8.70452	−	26.7898i	−0.289188	−	0.890030i
$907$		−	21.3277i		−	0.708174i	−0.935212	−	0.354087i	$-0.884792\pi$
$907$		−	21.3277i		−	0.708174i	0.935212	−	0.354087i	$-0.115208\pi$
$908$	30.3224	−	9.85234i	1.00628	−	0.326962i
$909$	7.87792	+	5.72364i	0.261294	+	0.189841i
$910$	2.66624	−	0.354924i	0.0883851	−	0.0117656i
$911$	1.93413	−	1.40523i	0.0640807	−	0.0465573i	−0.555284	−	0.831661i	$-0.687390\pi$
$911$	1.93413	−	1.40523i	0.0640807	−	0.0465573i	0.619364	+	0.785104i	$0.287390\pi$
$912$	4.00868	−	5.51747i	0.132741	−	0.182702i
$913$	−18.4534	+	25.3989i	−0.610717	+	0.840580i
$914$	−52.4188	+	38.0845i	−1.73386	+	1.25972i
$915$	−3.75131	−	7.83573i	−0.124014	−	0.259041i
$916$	−37.8127	−	27.4725i	−1.24937	−	0.907718i
$917$	−25.0387	+	8.13556i	−0.826850	+	0.268660i
$918$			3.26329i			0.107705i
$919$	14.8591	+	45.7315i	0.490156	+	1.50854i	0.824372	+	0.566048i	$0.191528\pi$
$919$	14.8591	+	45.7315i	0.490156	+	1.50854i	−0.334217	+	0.942496i	$0.608472\pi$
$920$	−3.85839	+	7.13073i	−0.127207	+	0.235093i
$921$	−1.66588	+	5.12706i	−0.0548927	+	0.168942i
$922$	3.51683	+	1.14269i	0.115821	+	0.0376324i
$923$	−0.422885	−	0.582051i	−0.0139194	−	0.0191584i
$924$	−33.2845			−1.09498
$925$	−14.2999	+	37.5757i	−0.470179	+	1.23548i
$926$	50.0469			1.64464
$927$	0.585323	+	0.805628i	0.0192245	+	0.0264603i
$928$	25.6647	+	8.33896i	0.842484	+	0.273740i
$929$	5.07790	−	15.6282i	0.166600	−	0.512743i	−0.832550	−	0.553950i	$-0.813120\pi$
$929$	5.07790	−	15.6282i	0.166600	−	0.512743i	0.999151	+	0.0412062i	$0.0131201\pi$
$930$	35.5192	+	37.3216i	1.16472	+	1.22382i
$931$	1.67453	+	5.15368i	0.0548805	+	0.168905i
$932$			22.0138i			0.721086i
$933$	−39.8169	+	12.9373i	−1.30355	+	0.423549i
$934$	46.3022	+	33.6405i	1.51506	+	1.10075i
$935$	2.29383	+	1.24117i	0.0750161	+	0.0405907i
$936$	0.0757596	−	0.0550425i	0.00247628	−	0.00179912i
$937$	−16.5333	+	22.7561i	−0.540118	+	0.743409i	−0.988630	−	0.150368i	$-0.951954\pi$
$937$	−16.5333	+	22.7561i	−0.540118	+	0.743409i	0.448512	+	0.893777i	$0.351954\pi$
$938$	12.4844	−	17.1833i	0.407631	−	0.561055i
$939$	23.5750	−	17.1282i	0.769340	−	0.558958i
$940$	14.0262	+	7.58947i	0.457484	+	0.247541i
$941$	−20.9857	−	15.2470i	−0.684113	−	0.497037i	0.190607	−	0.981666i	$-0.438954\pi$
$941$	−20.9857	−	15.2470i	−0.684113	−	0.497037i	−0.874720	+	0.484629i	$0.838954\pi$
$942$	43.1968	−	14.0355i	1.40743	−	0.457301i
$943$		−	17.7097i		−	0.576709i
$944$	−5.88571	−	18.1144i	−0.191564	−	0.589572i
$945$	30.5979	+	32.1506i	0.995349	+	1.04586i
$946$	4.96978	−	15.2954i	0.161582	−	0.497297i
$947$	29.8291	+	9.69207i	0.969317	+	0.314950i	0.750540	−	0.660825i	$-0.229793\pi$
$947$	29.8291	+	9.69207i	0.969317	+	0.314950i	0.218777	+	0.975775i	$0.429793\pi$
$948$	22.0310	+	30.3231i	0.715535	+	0.984849i
$949$	−0.385990			−0.0125298
$950$	3.39713	−	8.92657i	0.110217	−	0.289616i
$951$	39.7527			1.28907
$952$	0.421278	+	0.579839i	0.0136537	+	0.0187927i
$953$	−5.66786	−	1.84160i	−0.183600	−	0.0596552i	0.215774	−	0.976443i	$-0.430773\pi$
$953$	−5.66786	−	1.84160i	−0.183600	−	0.0596552i	−0.399374	+	0.916788i	$0.630773\pi$
$954$	−1.36065	+	4.18765i	−0.0440527	+	0.135580i
$955$	19.7086	−	36.4237i	0.637756	−	1.17864i
$956$	−6.85027	−	21.0830i	−0.221554	−	0.681872i
$957$		−	20.8719i		−	0.674694i
$958$	54.6655	−	17.7619i	1.76616	−	0.573861i
$959$	−53.0112	−	38.5149i	−1.71182	−	1.24371i
$960$	7.17429	+	14.9856i	0.231549	+	0.483660i
$961$	−27.9783	+	20.3274i	−0.902526	+	0.655724i
$962$	−1.61329	+	2.22051i	−0.0520146	+	0.0715920i
$963$	−0.0947090	+	0.130356i	−0.00305196	+	0.00420066i
$964$	−18.5658	+	13.4889i	−0.597964	+	0.434447i
$965$	38.9738	−	5.18810i	1.25461	−	0.167011i
$966$	−43.8622	−	31.8677i	−1.41124	−	1.02533i
$967$	21.1989	−	6.88792i	0.681709	−	0.221501i	0.0523656	−	0.998628i	$-0.483324\pi$
$967$	21.1989	−	6.88792i	0.681709	−	0.221501i	0.629343	+	0.777127i	$0.283324\pi$
$968$			2.54039i			0.0816511i
$969$	−0.139600	−	0.429644i	−0.00448460	−	0.0138022i
$970$	−65.6894	+	31.4484i	−2.10916	+	1.00975i
$971$	1.01222	−	3.11529i	0.0324837	−	0.0999745i	−0.933500	−	0.358577i	$-0.883262\pi$
$971$	1.01222	−	3.11529i	0.0324837	−	0.0999745i	0.965984	+	0.258603i	$0.0832620\pi$
$972$	−12.3799	−	4.02248i	−0.397086	−	0.129021i
$973$	−5.60318	−	7.71211i	−0.179630	−	0.247239i
$974$	30.9248			0.990895
$975$	−0.834491	+	1.03660i	−0.0267251	+	0.0331978i
$976$	11.9436			0.382304
$977$	22.8022	+	31.3845i	0.729507	+	1.00408i	0.999154	+	0.0411206i	$0.0130928\pi$
$977$	22.8022	+	31.3845i	0.729507	+	1.00408i	−0.269648	+	0.962959i	$0.586907\pi$
$978$	−64.7568	−	21.0408i	−2.07070	−	0.672810i
$979$	10.6392	−	32.7442i	0.340031	−	1.04651i
$980$	−19.6512	−	3.61288i	−0.627735	−	0.115409i
$981$	3.01778	+	9.28779i	0.0963504	+	0.296536i
$982$			58.7834i			1.87585i
$983$	16.2319	−	5.27405i	0.517716	−	0.168216i	−0.0384927	−	0.999259i	$-0.512256\pi$
$983$	16.2319	−	5.27405i	0.517716	−	0.168216i	0.556208	+	0.831043i	$0.312256\pi$
$984$	2.64637	+	1.92270i	0.0843631	+	0.0612934i
$985$	−0.884738	+	4.81229i	−0.0281901	+	0.153332i
$986$	1.70802	−	1.24095i	0.0543944	−	0.0395198i
$987$	13.3442	−	18.3667i	0.424750	−	0.584618i
$988$	0.173194	−	0.238381i	0.00551004	−	0.00758392i
$989$	9.57734	−	6.95834i	0.304542	−	0.221262i
$990$	−9.29919	+	8.85009i	−0.295548	+	0.281274i
$991$	8.61911	+	6.26215i	0.273795	+	0.198924i	0.716206	−	0.697889i	$-0.245877\pi$
$991$	8.61911	+	6.26215i	0.273795	+	0.198924i	−0.442411	+	0.896812i	$0.645877\pi$
$992$	−57.0372	+	18.5325i	−1.81093	+	0.588408i
$993$			1.26258i			0.0400667i
$994$	8.37549	+	25.7771i	0.265654	+	0.817600i
$995$	−6.44206	−	48.3937i	−0.204227	−	1.53418i
$996$	−6.19606	+	19.0695i	−0.196330	+	0.604241i
$997$	−15.0777	−	4.89904i	−0.477515	−	0.155154i	0.0603634	−	0.998176i	$-0.480774\pi$
$997$	−15.0777	−	4.89904i	−0.477515	−	0.155154i	−0.537878	+	0.843022i	$0.680774\pi$
$998$	−8.35067	−	11.4937i	−0.264336	−	0.363827i
$999$	−45.2899			−1.43291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.4	✓	80
25.9	even	10	inner	475.2.n.a.134.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.4	✓	80	1.1	even	1	trivial
475.2.n.a.134.4	yes	80	25.9	even	10	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12280 - 1.54541i) q^{2} +(1.41655 + 0.460266i) q^{3} +(-0.509559 + 1.56826i) q^{4} +(-0.295058 - 2.21652i) q^{5} +(-0.879213 - 2.70594i) q^{6} -3.52405i q^{7} +(-0.637733 + 0.207212i) q^{8} +(-0.632270 - 0.459371i) q^{9} +O(q^{10})\)	\(q+(-1.12280 - 1.54541i) q^{2} +(1.41655 + 0.460266i) q^{3} +(-0.509559 + 1.56826i) q^{4} +(-0.295058 - 2.21652i) q^{5} +(-0.879213 - 2.70594i) q^{6} -3.52405i q^{7} +(-0.637733 + 0.207212i) q^{8} +(-0.632270 - 0.459371i) q^{9} +(-3.09413 + 2.94469i) q^{10} +(-3.11114 + 2.26038i) q^{11} +(-1.44364 + 1.98699i) q^{12} +(0.105032 - 0.144564i) q^{13} +(-5.44608 + 3.95681i) q^{14} +(0.602223 - 3.27562i) q^{15} +(3.70436 + 2.69138i) q^{16} +(0.288458 - 0.0937256i) q^{17} +1.49290i q^{18} +(-0.309017 - 0.951057i) q^{19} +(3.62642 + 0.666718i) q^{20} +(1.62200 - 4.99200i) q^{21} +(6.98640 + 2.27002i) q^{22} +(3.17832 + 4.37458i) q^{23} -0.998756 q^{24} +(-4.82588 + 1.30800i) q^{25} -0.341340 q^{26} +(-3.31065 - 4.55672i) q^{27} +(5.52662 + 1.79571i) q^{28} +(-1.12605 + 3.46561i) q^{29} +(-5.73834 + 2.74720i) q^{30} +(-2.50252 - 7.70198i) q^{31} -7.40552i q^{32} +(-5.44748 + 1.76999i) q^{33} +(-0.468726 - 0.340549i) q^{34} +(-7.81110 + 1.03980i) q^{35} +(1.04259 - 0.757488i) q^{36} +(4.72635 - 6.50526i) q^{37} +(-1.12280 + 1.54541i) q^{38} +(0.215321 - 0.156440i) q^{39} +(0.647456 + 1.35241i) q^{40} +(-2.64966 - 1.92509i) q^{41} +(-9.53586 + 3.09839i) q^{42} -2.18931i q^{43} +(-1.95955 - 6.03088i) q^{44} +(-0.831647 + 1.53698i) q^{45} +(3.19188 - 9.82359i) q^{46} +(4.11350 + 1.33656i) q^{47} +(4.00868 + 5.51747i) q^{48} -5.41890 q^{49} +(7.43991 + 5.98932i) q^{50} +0.451755 q^{51} +(0.173194 + 0.238381i) q^{52} +(2.80505 + 0.911416i) q^{53} +(-3.32477 + 10.2326i) q^{54} +(5.92813 + 6.22895i) q^{55} +(0.730224 + 2.24740i) q^{56} -1.48945i q^{57} +(6.62011 - 2.15100i) q^{58} +(-3.36526 - 2.44500i) q^{59} +(4.83016 + 2.61356i) q^{60} +(2.11026 - 1.53319i) q^{61} +(-9.09284 + 12.5152i) q^{62} +(-1.61885 + 2.22815i) q^{63} +(-4.03582 + 2.93219i) q^{64} +(-0.351419 - 0.190150i) q^{65} +(8.85180 + 6.43121i) q^{66} +(-3.00075 + 0.975002i) q^{67} +0.500136i q^{68} +(2.48879 + 7.65971i) q^{69} +(10.3772 + 10.9038i) q^{70} +(1.24418 - 3.82920i) q^{71} +(0.498407 + 0.161942i) q^{72} +(-1.26967 - 1.74756i) q^{73} -15.3600 q^{74} +(-7.43815 - 0.368339i) q^{75} +1.64897 q^{76} +(7.96567 + 10.9638i) q^{77} +(-0.483527 - 0.157107i) q^{78} +(4.71585 - 14.5139i) q^{79} +(4.87248 - 9.00488i) q^{80} +(-1.86789 - 5.74878i) q^{81} +6.25631i q^{82} +(7.76428 - 2.52277i) q^{83} +(7.00226 + 5.08744i) q^{84} +(-0.292856 - 0.611717i) q^{85} +(-3.38338 + 2.45817i) q^{86} +(-3.19021 + 4.39095i) q^{87} +(1.51570 - 2.08618i) q^{88} +(-7.24308 + 5.26240i) q^{89} +(3.30903 - 0.440491i) q^{90} +(-0.509450 - 0.370137i) q^{91} +(-8.48003 + 2.75533i) q^{92} -12.0621i q^{93} +(-2.55313 - 7.85772i) q^{94} +(-2.01685 + 0.965557i) q^{95} +(3.40851 - 10.4903i) q^{96} +(16.2159 + 5.26888i) q^{97} +(6.08435 + 8.37439i) q^{98} +3.00543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

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