LMFDB - Embedded newform 650.2.l.c.391.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (of order $5$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			391.2
Character	$\chi$	$=$	650.391
Dual form			650.2.l.c.261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.217795 - 0.670303i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.980398 + 2.00968i) q^{5} +(-0.217795 + 0.670303i) q^{6} -4.30334 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.02518 - 1.47138i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.217795 - 0.670303i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.980398 + 2.00968i) q^{5} +(-0.217795 + 0.670303i) q^{6} -4.30334 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.02518 - 1.47138i) q^{9} +(0.388103 - 2.20213i) q^{10} +(-1.42387 - 1.03450i) q^{11} +(0.570194 - 0.414270i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(3.48147 + 2.52944i) q^{14} +(1.13357 - 1.09486i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.12449 + 3.46084i) q^{17} -2.50326 q^{18} +(-0.417410 + 1.28466i) q^{19} +(-1.60836 + 1.55344i) q^{20} +(0.937244 + 2.88454i) q^{21} +(0.543870 + 1.67386i) q^{22} +(-4.83507 - 3.51288i) q^{23} -0.704799 q^{24} +(-3.07764 + 3.94057i) q^{25} +1.00000 q^{26} +(-3.13793 - 2.27984i) q^{27} +(-1.32980 - 4.09272i) q^{28} +(-3.16989 - 9.75592i) q^{29} +(-1.56062 + 0.219466i) q^{30} +(0.436598 - 1.34371i) q^{31} +1.00000 q^{32} +(-0.383319 + 1.17974i) q^{33} +(2.94396 - 2.13891i) q^{34} +(-4.21898 - 8.64834i) q^{35} +(2.02518 + 1.47138i) q^{36} +(-7.27136 + 5.28295i) q^{37} +(1.09279 - 0.793961i) q^{38} +(0.570194 + 0.414270i) q^{39} +(2.21428 - 0.311388i) q^{40} +(-8.06650 + 5.86066i) q^{41} +(0.937244 - 2.88454i) q^{42} -3.13015 q^{43} +(0.543870 - 1.67386i) q^{44} +(4.94248 + 2.62743i) q^{45} +(1.84683 + 5.68396i) q^{46} +(-0.687702 - 2.11653i) q^{47} +(0.570194 + 0.414270i) q^{48} +11.5187 q^{49} +(4.80608 - 1.37900i) q^{50} +2.56472 q^{51} +(-0.809017 - 0.587785i) q^{52} +(3.30815 + 10.1814i) q^{53} +(1.19858 + 3.68885i) q^{54} +(0.683062 - 3.87575i) q^{55} +(-1.32980 + 4.09272i) q^{56} +0.952018 q^{57} +(-3.16989 + 9.75592i) q^{58} +(-4.95163 + 3.59757i) q^{59} +(1.39157 + 0.739759i) q^{60} +(-2.86572 - 2.08207i) q^{61} +(-1.14303 + 0.830459i) q^{62} +(-8.71503 + 6.33184i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.97442 - 1.04960i) q^{65} +(1.00354 - 0.729116i) q^{66} +(2.94459 - 9.06251i) q^{67} -3.63894 q^{68} +(-1.30164 + 4.00605i) q^{69} +(-1.67014 + 9.47651i) q^{70} +(3.15082 + 9.69723i) q^{71} +(-0.773550 - 2.38074i) q^{72} +(-3.34187 - 2.42801i) q^{73} +8.98790 q^{74} +(3.31167 + 1.20472i) q^{75} -1.35077 q^{76} +(6.12740 + 4.45182i) q^{77} +(-0.217795 - 0.670303i) q^{78} +(-3.29896 - 10.1531i) q^{79} +(-1.97442 - 1.04960i) q^{80} +(1.47589 - 4.54232i) q^{81} +9.97074 q^{82} +(-4.06112 + 12.4989i) q^{83} +(-2.45374 + 1.78274i) q^{84} +(-8.05763 + 1.13312i) q^{85} +(2.53235 + 1.83986i) q^{86} +(-5.84904 + 4.24958i) q^{87} +(-1.42387 + 1.03450i) q^{88} +(10.7649 + 7.82117i) q^{89} +(-2.45419 - 5.03075i) q^{90} +(3.48147 - 2.52944i) q^{91} +(1.84683 - 5.68396i) q^{92} -0.995783 q^{93} +(-0.687702 + 2.11653i) q^{94} +(-2.99098 + 0.420612i) q^{95} +(-0.217795 - 0.670303i) q^{96} +(-1.46701 - 4.51499i) q^{97} +(-9.31884 - 6.77053i) q^{98} -4.40574 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.217795	−	0.670303i	−0.125744	−	0.387000i	0.868292	−	0.496053i	$-0.165218\pi$
$3$	−0.217795	−	0.670303i	−0.125744	−	0.387000i	−0.994036	+	0.109054i	$0.965218\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.980398	+	2.00968i	0.438447	+	0.898757i
$5$	0.980398	+	2.00968i	0.438447	+	0.898757i
$6$	−0.217795	+	0.670303i	−0.0889143	+	0.273650i
$7$	−4.30334			−1.62651			−0.813254	−	0.581908i	$-0.802306\pi$
$7$	−4.30334			−1.62651			−0.813254	+	0.581908i	$0.802306\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.02518	−	1.47138i	0.675060	−	0.490460i
$10$	0.388103	−	2.20213i	0.122729	−	0.696375i
$11$	−1.42387	−	1.03450i	−0.429313	−	0.311914i	0.352061	−	0.935977i	$-0.385481\pi$
$11$	−1.42387	−	1.03450i	−0.429313	−	0.311914i	−0.781374	+	0.624063i	$0.785481\pi$
$12$	0.570194	−	0.414270i	0.164601	−	0.119590i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	3.48147	+	2.52944i	0.930463	+	0.676021i
$15$	1.13357	−	1.09486i	0.292687	−	0.282692i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.12449	+	3.46084i	−0.272730	+	0.839376i	0.717081	+	0.696990i	$0.245478\pi$
$17$	−1.12449	+	3.46084i	−0.272730	+	0.839376i	−0.989811	+	0.142387i	$0.954522\pi$
$18$	−2.50326			−0.590024
$19$	−0.417410	+	1.28466i	−0.0957604	+	0.294720i	−0.987451	−	0.157925i	$-0.949520\pi$
$19$	−0.417410	+	1.28466i	−0.0957604	+	0.294720i	0.891691	+	0.452645i	$0.149520\pi$
$20$	−1.60836	+	1.55344i	−0.359641	+	0.347360i
$21$	0.937244	+	2.88454i	0.204523	+	0.629459i
$22$	0.543870	+	1.67386i	0.115954	+	0.356868i
$23$	−4.83507	−	3.51288i	−1.00818	−	0.732486i	−0.0443542	−	0.999016i	$-0.514123\pi$
$23$	−4.83507	−	3.51288i	−1.00818	−	0.732486i	−0.963827	+	0.266529i	$0.914123\pi$
$24$	−0.704799			−0.143866
$25$	−3.07764	+	3.94057i	−0.615528	+	0.788115i
$26$	1.00000			0.196116
$27$	−3.13793	−	2.27984i	−0.603894	−	0.438755i
$28$	−1.32980	−	4.09272i	−0.251309	−	0.773451i
$29$	−3.16989	−	9.75592i	−0.588634	−	1.81163i	−0.584160	−	0.811639i	$-0.698576\pi$
$29$	−3.16989	−	9.75592i	−0.588634	−	1.81163i	−0.00447429	−	0.999990i	$-0.501424\pi$
$30$	−1.56062	+	0.219466i	−0.284929	+	0.0400688i
$31$	0.436598	−	1.34371i	0.0784153	−	0.241338i	−0.904163	−	0.427188i	$-0.859504\pi$
$31$	0.436598	−	1.34371i	0.0784153	−	0.241338i	0.982578	+	0.185851i	$0.0595041\pi$
$32$	1.00000			0.176777
$33$	−0.383319	+	1.17974i	−0.0667273	+	0.205366i
$34$	2.94396	−	2.13891i	0.504886	−	0.366821i
$35$	−4.21898	−	8.64834i	−0.713138	−	1.46184i
$36$	2.02518	+	1.47138i	0.337530	+	0.245230i
$37$	−7.27136	+	5.28295i	−1.19540	+	0.868512i	−0.993825	−	0.110960i	$-0.964607\pi$
$37$	−7.27136	+	5.28295i	−1.19540	+	0.868512i	−0.201579	+	0.979472i	$0.564607\pi$
$38$	1.09279	−	0.793961i	0.177274	−	0.128797i
$39$	0.570194	+	0.414270i	0.0913041	+	0.0663363i
$40$	2.21428	−	0.311388i	0.350108	−	0.0492348i
$41$	−8.06650	+	5.86066i	−1.25978	+	0.915281i	−0.998747	−	0.0500504i	$-0.984062\pi$
$41$	−8.06650	+	5.86066i	−1.25978	+	0.915281i	−0.261029	+	0.965331i	$0.584062\pi$
$42$	0.937244	−	2.88454i	0.144620	−	0.445094i
$43$	−3.13015			−0.477344			−0.238672	−	0.971100i	$-0.576712\pi$
$43$	−3.13015			−0.477344			−0.238672	+	0.971100i	$0.576712\pi$
$44$	0.543870	−	1.67386i	0.0819916	−	0.252344i
$45$	4.94248	+	2.62743i	0.736782	+	0.391674i
$46$	1.84683	+	5.68396i	0.272300	+	0.838054i
$47$	−0.687702	−	2.11653i	−0.100312	−	0.308727i	0.888290	−	0.459283i	$-0.151894\pi$
$47$	−0.687702	−	2.11653i	−0.100312	−	0.308727i	−0.988602	+	0.150556i	$0.951894\pi$
$48$	0.570194	+	0.414270i	0.0823004	+	0.0597948i
$49$	11.5187			1.64553
$50$	4.80608	−	1.37900i	0.679682	−	0.195020i
$51$	2.56472			0.359133
$52$	−0.809017	−	0.587785i	−0.112190	−	0.0815111i
$53$	3.30815	+	10.1814i	0.454410	+	1.39853i	0.871827	+	0.489814i	$0.162935\pi$
$53$	3.30815	+	10.1814i	0.454410	+	1.39853i	−0.417417	+	0.908715i	$0.637065\pi$
$54$	1.19858	+	3.68885i	0.163106	+	0.501989i
$55$	0.683062	−	3.87575i	0.0921040	−	0.522606i
$56$	−1.32980	+	4.09272i	−0.177703	+	0.546912i
$57$	0.952018			0.126098
$58$	−3.16989	+	9.75592i	−0.416227	+	1.28102i
$59$	−4.95163	+	3.59757i	−0.644648	+	0.468364i	−0.861444	−	0.507853i	$-0.830439\pi$
$59$	−4.95163	+	3.59757i	−0.644648	+	0.468364i	0.216796	+	0.976217i	$0.430439\pi$
$60$	1.39157	+	0.739759i	0.179651	+	0.0955025i
$61$	−2.86572	−	2.08207i	−0.366918	−	0.266581i	0.389014	−	0.921232i	$-0.372816\pi$
$61$	−2.86572	−	2.08207i	−0.366918	−	0.266581i	−0.755932	+	0.654650i	$0.772816\pi$
$62$	−1.14303	+	0.830459i	−0.145165	+	0.105468i
$63$	−8.71503	+	6.33184i	−1.09799	+	0.797737i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.97442	−	1.04960i	−0.244897	−	0.130187i
$66$	1.00354	−	0.729116i	0.123528	−	0.0897480i
$67$	2.94459	−	9.06251i	0.359739	−	1.10716i	−0.593472	−	0.804855i	$-0.702243\pi$
$67$	2.94459	−	9.06251i	0.359739	−	1.10716i	0.953211	−	0.302307i	$-0.0977568\pi$
$68$	−3.63894			−0.441286
$69$	−1.30164	+	4.00605i	−0.156700	+	0.482272i
$70$	−1.67014	+	9.47651i	−0.199620	+	1.13266i
$71$	3.15082	+	9.69723i	0.373934	+	1.15085i	0.944195	+	0.329386i	$0.106842\pi$
$71$	3.15082	+	9.69723i	0.373934	+	1.15085i	−0.570262	+	0.821463i	$0.693158\pi$
$72$	−0.773550	−	2.38074i	−0.0911637	−	0.280573i
$73$	−3.34187	−	2.42801i	−0.391136	−	0.284177i	0.374785	−	0.927112i	$-0.377717\pi$
$73$	−3.34187	−	2.42801i	−0.391136	−	0.284177i	−0.765921	+	0.642935i	$0.777717\pi$
$74$	8.98790			1.04482
$75$	3.31167	+	1.20472i	0.382399	+	0.139109i
$76$	−1.35077			−0.154944
$77$	6.12740	+	4.45182i	0.698282	+	0.507332i
$78$	−0.217795	−	0.670303i	−0.0246604	−	0.0758969i
$79$	−3.29896	−	10.1531i	−0.371161	−	1.14232i	−0.946032	−	0.324073i	$-0.894948\pi$
$79$	−3.29896	−	10.1531i	−0.371161	−	1.14232i	0.574871	−	0.818244i	$-0.305052\pi$
$80$	−1.97442	−	1.04960i	−0.220747	−	0.117349i
$81$	1.47589	−	4.54232i	0.163988	−	0.504703i
$82$	9.97074			1.10108
$83$	−4.06112	+	12.4989i	−0.445766	+	1.37193i	0.435875	+	0.900007i	$0.356439\pi$
$83$	−4.06112	+	12.4989i	−0.445766	+	1.37193i	−0.881641	+	0.471920i	$0.843561\pi$
$84$	−2.45374	+	1.78274i	−0.267725	+	0.194513i
$85$	−8.05763	+	1.13312i	−0.873973	+	0.122904i
$86$	2.53235	+	1.83986i	0.273070	+	0.198397i
$87$	−5.84904	+	4.24958i	−0.627083	+	0.455602i
$88$	−1.42387	+	1.03450i	−0.151785	+	0.110278i
$89$	10.7649	+	7.82117i	1.14108	+	0.829043i	0.987269	−	0.159058i	$-0.0508456\pi$
$89$	10.7649	+	7.82117i	1.14108	+	0.829043i	0.153810	+	0.988100i	$0.450846\pi$
$90$	−2.45419	−	5.03075i	−0.258694	−	0.530288i
$91$	3.48147	−	2.52944i	0.364958	−	0.265157i
$92$	1.84683	−	5.68396i	0.192545	−	0.592594i
$93$	−0.995783			−0.103258
$94$	−0.687702	+	2.11653i	−0.0709310	+	0.218303i
$95$	−2.99098	+	0.420612i	−0.306868	+	0.0431539i
$96$	−0.217795	−	0.670303i	−0.0222286	−	0.0684125i
$97$	−1.46701	−	4.51499i	−0.148952	−	0.458428i	0.848546	−	0.529122i	$-0.177479\pi$
$97$	−1.46701	−	4.51499i	−0.148952	−	0.458428i	−0.997498	+	0.0706942i	$0.977479\pi$
$98$	−9.31884	−	6.77053i	−0.941345	−	0.683927i
$99$	−4.40574			−0.442794
$100$	−4.69875	−	1.70931i	−0.469875	−	0.170931i
$101$	−2.96069			−0.294600			−0.147300	−	0.989092i	$-0.547058\pi$
$101$	−2.96069			−0.294600			−0.147300	+	0.989092i	$0.547058\pi$
$102$	−2.07490	−	1.50750i	−0.205446	−	0.149265i
$103$	−2.59634	−	7.99073i	−0.255825	−	0.787350i	−0.993666	−	0.112375i	$-0.964154\pi$
$103$	−2.59634	−	7.99073i	−0.255825	−	0.787350i	0.737841	−	0.674975i	$-0.235846\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$	−4.87814	+	4.71156i	−0.476057	+	0.459801i
$106$	3.30815	−	10.1814i	0.321316	−	0.988910i
$107$	10.5290			1.01788			0.508939	−	0.860803i	$-0.330038\pi$
$107$	10.5290			1.01788			0.508939	+	0.860803i	$0.330038\pi$
$108$	1.19858	−	3.68885i	0.115334	−	0.354960i
$109$	6.28295	−	4.56483i	0.601797	−	0.437231i	−0.244719	−	0.969594i	$-0.578696\pi$
$109$	6.28295	−	4.56483i	0.601797	−	0.437231i	0.846516	+	0.532363i	$0.178696\pi$
$110$	−2.83072	+	2.73406i	−0.269898	+	0.260682i
$111$	5.12484	+	3.72342i	0.486429	+	0.353411i
$112$	3.48147	−	2.52944i	0.328968	−	0.239009i
$113$	5.42710	−	3.94302i	0.510539	−	0.370928i	−0.302489	−	0.953153i	$-0.597818\pi$
$113$	5.42710	−	3.94302i	0.510539	−	0.370928i	0.813028	+	0.582225i	$0.197818\pi$
$114$	−0.770199	−	0.559582i	−0.0721358	−	0.0524097i
$115$	2.31948	−	13.1610i	0.216293	−	1.22727i
$116$	8.29888	−	6.02949i	0.770532	−	0.559824i
$117$	−0.773550	+	2.38074i	−0.0715147	+	0.220100i
$118$	6.12055			0.563443
$119$	4.83908	−	14.8931i	0.443598	−	1.36525i
$120$	−0.690983	−	1.41642i	−0.0630778	−	0.129301i
$121$	−2.44197	−	7.51562i	−0.221998	−	0.683238i
$122$	1.09461	+	3.36886i	0.0991011	+	0.305002i
$123$	5.68526	+	4.13058i	0.512622	+	0.372442i
$124$	1.41286			0.126879
$125$	−10.9366	−	2.32175i	−0.978200	−	0.207663i
$126$	10.7724			0.959679
$127$	−4.58538	−	3.33147i	−0.406887	−	0.295621i	0.365453	−	0.930830i	$-0.380914\pi$
$127$	−4.58538	−	3.33147i	−0.406887	−	0.295621i	−0.772340	+	0.635209i	$0.780914\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.681731	+	2.09815i	0.0600230	+	0.184732i
$130$	0.980398	+	2.00968i	0.0859866	+	0.176261i
$131$	−5.49051	+	16.8981i	−0.479708	+	1.47639i	0.359792	+	0.933032i	$0.382848\pi$
$131$	−5.49051	+	16.8981i	−0.479708	+	1.47639i	−0.839501	+	0.543358i	$0.817152\pi$
$132$	−1.24045			−0.107967
$133$	1.79626	−	5.52831i	0.155755	−	0.479365i
$134$	−7.70903	+	5.60094i	−0.665959	+	0.483847i
$135$	1.50533	−	8.54138i	0.129558	−	0.735125i
$136$	2.94396	+	2.13891i	0.252443	+	0.183410i
$137$	9.77934	−	7.10510i	0.835505	−	0.607030i	−0.0856064	−	0.996329i	$-0.527283\pi$
$137$	9.77934	−	7.10510i	0.835505	−	0.607030i	0.921111	+	0.389299i	$0.127283\pi$
$138$	3.40775	−	2.47587i	0.290087	−	0.210760i
$139$	13.9332	+	10.1230i	1.18180	+	0.858625i	0.992373	−	0.123271i	$-0.0393385\pi$
$139$	13.9332	+	10.1230i	1.18180	+	0.858625i	0.189422	+	0.981896i	$0.439338\pi$
$140$	6.92132	−	6.68497i	0.584958	−	0.564983i
$141$	−1.26894	+	0.921937i	−0.106864	+	0.0776411i
$142$	3.15082	−	9.69723i	0.264411	−	0.813774i
$143$	1.76000			0.147179
$144$	−0.773550	+	2.38074i	−0.0644625	+	0.198395i
$145$	16.4985	−	15.9352i	1.37013	−	1.32334i
$146$	1.27648	+	3.92860i	0.105642	+	0.325134i
$147$	−2.50872	−	7.72103i	−0.206915	−	0.636820i
$148$	−7.27136	−	5.28295i	−0.597702	−	0.434256i
$149$	−1.30772			−0.107133			−0.0535665	−	0.998564i	$-0.517059\pi$
$149$	−1.30772			−0.107133			−0.0535665	+	0.998564i	$0.517059\pi$
$150$	−1.97109	−	2.92119i	−0.160939	−	0.238514i
$151$	−20.1906			−1.64309			−0.821546	−	0.570142i	$-0.806888\pi$
$151$	−20.1906			−1.64309			−0.821546	+	0.570142i	$0.806888\pi$
$152$	1.09279	+	0.793961i	0.0886372	+	0.0643987i
$153$	2.81490	+	8.66337i	0.227571	+	0.700392i
$154$	−2.34046	−	7.20319i	−0.188600	−	0.580450i
$155$	3.12847	−	0.439948i	0.251285	−	0.0353375i
$156$	−0.217795	+	0.670303i	−0.0174375	+	0.0536672i
$157$	21.8082			1.74048			0.870242	−	0.492625i	$-0.163962\pi$
$157$	21.8082			1.74048			0.870242	+	0.492625i	$0.163962\pi$
$158$	−3.29896	+	10.1531i	−0.262451	+	0.807740i
$159$	6.10416	−	4.43493i	0.484091	−	0.351713i
$160$	0.980398	+	2.00968i	0.0775073	+	0.158879i
$161$	20.8069	+	15.1171i	1.63982	+	1.19140i
$162$	−3.86393	+	2.80731i	−0.303579	+	0.220563i
$163$	9.21900	−	6.69800i	0.722088	−	0.524628i	−0.164963	−	0.986300i	$-0.552750\pi$
$163$	9.21900	−	6.69800i	0.722088	−	0.524628i	0.887051	+	0.461672i	$0.152750\pi$
$164$	−8.06650	−	5.86066i	−0.629888	−	0.457640i
$165$	−2.74670	+	0.386260i	−0.213830	+	0.0300703i
$166$	10.6322	−	7.72472i	0.825216	−	0.599554i
$167$	−1.21063	+	3.72594i	−0.0936814	+	0.288322i	−0.986908	−	0.161286i	$-0.948436\pi$
$167$	−1.21063	+	3.72594i	−0.0936814	+	0.288322i	0.893226	+	0.449607i	$0.148436\pi$
$168$	3.03299			0.234000
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	7.18479	+	3.81944i	0.551048	+	0.292938i
$171$	1.04488	+	3.21583i	0.0799043	+	0.245920i
$172$	−0.967270	−	2.97695i	−0.0737536	−	0.226990i
$173$	−10.6822	−	7.76104i	−0.812149	−	0.590061i	0.102304	−	0.994753i	$-0.467379\pi$
$173$	−10.6822	−	7.76104i	−0.812149	−	0.590061i	−0.914453	+	0.404692i	$0.867379\pi$
$174$	7.22981			0.548091
$175$	13.2441	−	16.9576i	1.00116	−	1.28188i
$176$	1.76000			0.132665
$177$	3.48990	+	2.53556i	0.262317	+	0.190585i
$178$	−4.11183	−	12.6549i	−0.308195	−	0.948527i
$179$	−2.91525	−	8.97222i	−0.217896	−	0.670615i	−0.998935	−	0.0461330i	$-0.985310\pi$
$179$	−2.91525	−	8.97222i	−0.217896	−	0.670615i	0.781039	−	0.624482i	$-0.214690\pi$
$180$	−0.971522	+	5.51250i	−0.0724129	+	0.410878i
$181$	−3.83735	+	11.8101i	−0.285228	+	0.877841i	0.701103	+	0.713060i	$0.252691\pi$
$181$	−3.83735	+	11.8101i	−0.285228	+	0.877841i	−0.986330	+	0.164780i	$0.947309\pi$
$182$	−4.30334			−0.318985
$183$	−0.771478	+	2.37436i	−0.0570293	+	0.175518i
$184$	−4.83507	+	3.51288i	−0.356446	+	0.258973i
$185$	−17.7459	−	9.43372i	−1.30470	−	0.693581i
$186$	0.805605	+	0.585306i	0.0590698	+	0.0429167i
$187$	5.18138	−	3.76449i	0.378900	−	0.275287i
$188$	1.80043	−	1.30809i	0.131310	−	0.0954020i
$189$	13.5036	+	9.81091i	0.982239	+	0.713638i
$190$	2.66698	+	1.41777i	0.193483	+	0.102856i
$191$	−10.3141	+	7.49360i	−0.746299	+	0.542218i	−0.894678	−	0.446713i	$-0.852595\pi$
$191$	−10.3141	+	7.49360i	−0.746299	+	0.542218i	0.148378	+	0.988931i	$0.452595\pi$
$192$	−0.217795	+	0.670303i	−0.0157180	+	0.0483750i
$193$	−4.05694			−0.292025			−0.146013	−	0.989283i	$-0.546644\pi$
$193$	−4.05694			−0.292025			−0.146013	+	0.989283i	$0.546644\pi$
$194$	−1.46701	+	4.51499i	−0.105325	+	0.324157i
$195$	−0.273534	+	1.55206i	−0.0195882	+	0.111145i
$196$	3.55948	+	10.9549i	0.254248	+	0.782496i
$197$	−8.42954	−	25.9434i	−0.600580	−	1.84839i	−0.524719	−	0.851276i	$-0.675830\pi$
$197$	−8.42954	−	25.9434i	−0.600580	−	1.84839i	−0.0758609	−	0.997118i	$-0.524170\pi$
$198$	3.56432	+	2.58963i	0.253305	+	0.184037i
$199$	2.65754			0.188388			0.0941939	−	0.995554i	$-0.469973\pi$
$199$	2.65754			0.188388			0.0941939	+	0.995554i	$0.469973\pi$
$200$	2.79667	+	4.14471i	0.197754	+	0.293076i
$201$	−6.71595			−0.473706
$202$	2.39525	+	1.74025i	0.168529	+	0.122444i
$203$	13.6411	+	41.9830i	0.957418	+	2.94663i
$204$	0.792542	+	2.43919i	0.0554890	+	0.170778i
$205$	−19.6864	−	10.4653i	−1.37496	−	0.730930i
$206$	−2.59634	+	7.99073i	−0.180896	+	0.556740i
$207$	−14.9607			−1.03984
$208$	0.309017	−	0.951057i	0.0214265	−	0.0659439i
$209$	1.92332	−	1.39737i	0.133039	−	0.0966583i
$210$	6.71588	−	0.944435i	0.463440	−	0.0651722i
$211$	9.59132	+	6.96850i	0.660294	+	0.479732i	0.866762	−	0.498722i	$-0.166197\pi$
$211$	9.59132	+	6.96850i	0.660294	+	0.479732i	−0.206468	+	0.978453i	$0.566197\pi$
$212$	−8.66086	+	6.29248i	−0.594830	+	0.432169i
$213$	5.81385	−	4.22401i	0.398359	−	0.289425i
$214$	−8.51814	−	6.18879i	−0.582288	−	0.423057i
$215$	−3.06879	−	6.29061i	−0.209290	−	0.429016i
$216$	−3.13793	+	2.27984i	−0.213509	+	0.155123i
$217$	−1.87883	+	5.78244i	−0.127543	+	0.392538i
$218$	−7.76615			−0.525990
$219$	−0.899662	+	2.76887i	−0.0607935	+	0.187103i
$220$	3.89714	−	0.548043i	0.262745	−	0.0369491i
$221$	−1.12449	−	3.46084i	−0.0756417	−	0.232801i
$222$	−1.95752	−	6.02462i	−0.131380	−	0.404346i
$223$	−5.29388	−	3.84623i	−0.354504	−	0.257562i	0.396252	−	0.918142i	$-0.370311\pi$
$223$	−5.29388	−	3.84623i	−0.354504	−	0.257562i	−0.750756	+	0.660579i	$0.770311\pi$
$224$	−4.30334			−0.287529
$225$	−0.434695	+	12.5087i	−0.0289797	+	0.833916i
$226$	−6.70827			−0.446227
$227$	−1.31157	−	0.952911i	−0.0870520	−	0.0632469i	0.543408	−	0.839469i	$-0.317134\pi$
$227$	−1.31157	−	0.952911i	−0.0870520	−	0.0632469i	−0.630460	+	0.776222i	$0.717134\pi$
$228$	0.294190	+	0.905423i	0.0194832	+	0.0599631i
$229$	0.100965	+	0.310739i	0.00667197	+	0.0205342i	0.954337	−	0.298732i	$-0.0965636\pi$
$229$	0.100965	+	0.310739i	0.00667197	+	0.0205342i	−0.947665	+	0.319266i	$0.896564\pi$
$230$	−9.61232	+	9.28409i	−0.633818	+	0.612174i
$231$	1.64955	−	5.07680i	0.108533	−	0.334029i
$232$	−10.2580			−0.673469
$233$	0.507209	−	1.56103i	0.0332284	−	0.102266i	−0.933067	−	0.359703i	$-0.882878\pi$
$233$	0.507209	−	1.56103i	0.0332284	−	0.102266i	0.966295	+	0.257437i	$0.0828779\pi$
$234$	2.02518	−	1.47138i	0.132390	−	0.0961870i
$235$	3.57933	−	3.45710i	0.233489	−	0.225516i
$236$	−4.95163	−	3.59757i	−0.322324	−	0.234182i
$237$	−6.08719	+	4.42260i	−0.395405	+	0.287279i
$238$	−12.6689	+	9.20447i	−0.821201	+	0.596637i
$239$	3.92795	+	2.85382i	0.254078	+	0.184598i	0.707532	−	0.706681i	$-0.249808\pi$
$239$	3.92795	+	2.85382i	0.254078	+	0.184598i	−0.453454	+	0.891280i	$0.649808\pi$
$240$	−0.273534	+	1.55206i	−0.0176566	+	0.100185i
$241$	8.40132	−	6.10391i	0.541176	−	0.393188i	−0.283345	−	0.959018i	$-0.591444\pi$
$241$	8.40132	−	6.10391i	0.541176	−	0.393188i	0.824522	+	0.565830i	$0.191444\pi$
$242$	−2.44197	+	7.51562i	−0.156976	+	0.483123i
$243$	−15.0022			−0.962394
$244$	1.09461	−	3.36886i	0.0700751	−	0.215669i
$245$	11.2929	+	23.1489i	0.721478	+	1.47893i
$246$	−2.17158	−	6.68342i	−0.138455	−	0.426119i
$247$	−0.417410	−	1.28466i	−0.0265592	−	0.0817407i
$248$	−1.14303	−	0.830459i	−0.0725824	−	0.0527342i
$249$	9.26252			0.586988
$250$	7.48322	+	8.30671i	0.473280	+	0.525363i
$251$	11.6701			0.736609			0.368305	−	0.929705i	$-0.379938\pi$
$251$	11.6701			0.736609			0.368305	+	0.929705i	$0.379938\pi$
$252$	−8.71503	−	6.33184i	−0.548995	−	0.398868i
$253$	3.25043	+	10.0038i	0.204353	+	0.628932i
$254$	1.75146	+	5.39044i	0.109896	+	0.338226i
$255$	2.51445	+	5.15427i	0.157461	+	0.322773i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.77596			0.360294			0.180147	−	0.983640i	$-0.442343\pi$
$257$	5.77596			0.360294			0.180147	+	0.983640i	$0.442343\pi$
$258$	0.681731	−	2.09815i	0.0424427	−	0.130625i
$259$	31.2911	−	22.7343i	1.94434	−	1.41264i
$260$	0.388103	−	2.20213i	0.0240691	−	0.136570i
$261$	−20.7742	−	15.0934i	−1.28589	−	0.934256i
$262$	14.3744	−	10.4436i	0.888051	−	0.645206i
$263$	9.08007	−	6.59705i	0.559901	−	0.406792i	−0.271522	−	0.962432i	$-0.587527\pi$
$263$	9.08007	−	6.59705i	0.559901	−	0.406792i	0.831423	+	0.555640i	$0.187527\pi$
$264$	1.00354	+	0.729116i	0.0617638	+	0.0448740i
$265$	−17.2182	+	16.6302i	−1.05770	+	1.02159i
$266$	−4.70266	+	3.41668i	−0.288338	+	0.209490i
$267$	2.89802	−	8.91917i	0.177356	−	0.545845i
$268$	9.52889			0.582069
$269$	−0.492308	+	1.51517i	−0.0300165	+	0.0923814i	−0.964942	−	0.262462i	$-0.915466\pi$
$269$	−0.492308	+	1.51517i	−0.0300165	+	0.0923814i	0.934926	+	0.354843i	$0.115466\pi$
$270$	−6.23833	+	6.02531i	−0.379653	+	0.366689i
$271$	8.45487	+	26.0214i	0.513597	+	1.58069i	0.785821	+	0.618454i	$0.212241\pi$
$271$	8.45487	+	26.0214i	0.513597	+	1.58069i	−0.272224	+	0.962234i	$0.587759\pi$
$272$	−1.12449	−	3.46084i	−0.0681825	−	0.209844i
$273$	−2.45374	−	1.78274i	−0.148507	−	0.107897i
$274$	−12.0879			−0.730258
$275$	8.45870	−	2.42704i	0.510079	−	0.146356i
$276$	−4.21221			−0.253545
$277$	1.91803	+	1.39353i	0.115244	+	0.0837293i	0.643914	−	0.765098i	$-0.277309\pi$
$277$	1.91803	+	1.39353i	0.115244	+	0.0837293i	−0.528671	+	0.848827i	$0.677309\pi$
$278$	−5.32199	−	16.3794i	−0.319192	−	0.982372i
$279$	−1.09292	−	3.36366i	−0.0654313	−	0.201377i
$280$	−9.52880	+	1.34001i	−0.569454	+	0.0800808i
$281$	−8.61824	+	26.5242i	−0.514121	+	1.58230i	0.270754	+	0.962649i	$0.412727\pi$
$281$	−8.61824	+	26.5242i	−0.514121	+	1.58230i	−0.784875	+	0.619654i	$0.787273\pi$
$282$	1.56849			0.0934024
$283$	9.88435	−	30.4209i	0.587564	−	1.80833i	−0.00115839	−	0.999999i	$-0.500369\pi$
$283$	9.88435	−	30.4209i	0.587564	−	1.80833i	0.588722	−	0.808336i	$-0.299631\pi$
$284$	−8.24896	+	5.99322i	−0.489486	+	0.355632i
$285$	0.933357	+	1.91325i	0.0552873	+	0.113331i
$286$	−1.42387	−	1.03450i	−0.0841953	−	0.0611715i
$287$	34.7129	−	25.2204i	2.04904	−	1.48871i
$288$	2.02518	−	1.47138i	0.119335	−	0.0867018i
$289$	3.04038	+	2.20897i	0.178846	+	0.129939i
$290$	−22.7140	+	3.19421i	−1.33381	+	0.187571i
$291$	−2.70690	+	1.96668i	−0.158682	+	0.115289i
$292$	1.27648	−	3.92860i	0.0747004	−	0.229904i
$293$	19.4002			1.13337			0.566687	−	0.823933i	$-0.308225\pi$
$293$	19.4002			1.13337			0.566687	+	0.823933i	$0.308225\pi$
$294$	−2.50872	+	7.72103i	−0.146311	+	0.450300i
$295$	−12.0845	−	6.42415i	−0.703589	−	0.374029i
$296$	2.77741	+	8.54800i	0.161434	+	0.496842i
$297$	2.10950	+	6.49239i	0.122406	+	0.376727i
$298$	1.05797	+	0.768661i	0.0612866	+	0.0445273i
$299$	5.97647			0.345628
$300$	−0.122389	+	3.52187i	−0.00706616	+	0.203335i
$301$	13.4701			0.776404
$302$	16.3346	+	11.8678i	0.939949	+	0.682913i
$303$	0.644823	+	1.98456i	0.0370441	+	0.114010i
$304$	−0.417410	−	1.28466i	−0.0239401	−	0.0736800i
$305$	1.37475	−	7.80044i	0.0787178	−	0.446652i
$306$	2.81490	−	8.66337i	0.160917	−	0.495252i
$307$	−19.6871			−1.12360			−0.561801	−	0.827273i	$-0.689891\pi$
$307$	−19.6871			−1.12360			−0.561801	+	0.827273i	$0.689891\pi$
$308$	−2.34046	+	7.20319i	−0.133360	+	0.410440i
$309$	−4.79074	+	3.48068i	−0.272536	+	0.198009i
$310$	−2.78958	−	1.48294i	−0.158438	−	0.0842255i
$311$	−24.1170	−	17.5220i	−1.36755	−	0.993581i	−0.997924	−	0.0643992i	$-0.979487\pi$
$311$	−24.1170	−	17.5220i	−1.36755	−	0.993581i	−0.369623	−	0.929182i	$-0.620513\pi$
$312$	0.570194	−	0.414270i	0.0322809	−	0.0234534i
$313$	−8.16842	+	5.93470i	−0.461706	+	0.335449i	−0.794200	−	0.607656i	$-0.792110\pi$
$313$	−8.16842	+	5.93470i	−0.461706	+	0.335449i	0.332494	+	0.943105i	$0.392110\pi$
$314$	−17.6432	−	12.8185i	−0.995664	−	0.723392i
$315$	−21.2692	−	11.3067i	−1.19838	−	0.637061i
$316$	8.63678	−	6.27499i	0.485857	−	0.352996i
$317$	−10.4045	+	32.0219i	−0.584377	+	1.79853i	0.0173804	+	0.999849i	$0.494467\pi$
$317$	−10.4045	+	32.0219i	−0.584377	+	1.79853i	−0.601757	+	0.798679i	$0.705533\pi$
$318$	−7.54516			−0.423111
$319$	−5.57901	+	17.1704i	−0.312365	+	0.961360i
$320$	0.388103	−	2.20213i	0.0216956	−	0.123103i
$321$	−2.29316	−	7.05763i	−0.127992	−	0.393918i
$322$	−7.94754	−	24.4600i	−0.442899	−	1.36310i
$323$	−3.97661	−	2.88917i	−0.221264	−	0.160758i
$324$	4.77608			0.265338
$325$	0.173652	−	4.99698i	0.00963246	−	0.277183i
$326$	−11.3953			−0.631128
$327$	−4.42821	−	3.21729i	−0.244881	−	0.177916i
$328$	3.08113	+	9.48274i	0.170127	+	0.523597i
$329$	2.95941	+	9.10813i	0.163158	+	0.502148i
$330$	2.44916	+	1.30198i	0.134822	+	0.0716715i
$331$	2.84383	−	8.75240i	0.156311	−	0.481076i	−0.841980	−	0.539508i	$-0.818610\pi$
$331$	2.84383	−	8.75240i	0.156311	−	0.481076i	0.998291	+	0.0584325i	$0.0186102\pi$
$332$	−13.1421			−0.721265
$333$	−6.95258	+	21.3978i	−0.380999	+	1.17259i
$334$	3.16947	−	2.30276i	0.173426	−	0.126001i
$335$	21.0996	−	2.96718i	1.15280	−	0.162114i
$336$	−2.45374	−	1.78274i	−0.133862	−	0.0972567i
$337$	−11.2333	+	8.16149i	−0.611918	+	0.444584i	−0.850089	−	0.526639i	$-0.823452\pi$
$337$	−11.2333	+	8.16149i	−0.611918	+	0.444584i	0.238171	+	0.971223i	$0.423452\pi$
$338$	−0.809017	+	0.587785i	−0.0440047	+	0.0319713i
$339$	−3.82502	−	2.77904i	−0.207746	−	0.150937i
$340$	−3.56761	−	7.31311i	−0.193481	−	0.396609i
$341$	−2.01173	+	1.46161i	−0.108941	+	0.0791506i
$342$	1.04488	−	3.21583i	0.0565009	−	0.173892i
$343$	−19.4456			−1.04996
$344$	−0.967270	+	2.97695i	−0.0521517	+	0.160506i
$345$	−9.32701	+	1.31163i	−0.502149	+	0.0706158i
$346$	4.08022	+	12.5576i	0.219354	+	0.675102i
$347$	10.9646	+	33.7455i	0.588609	+	1.81155i	0.584267	+	0.811562i	$0.301382\pi$
$347$	10.9646	+	33.7455i	0.588609	+	1.81155i	0.00434253	+	0.999991i	$0.498618\pi$
$348$	−5.84904	−	4.24958i	−0.313541	−	0.227801i
$349$	−6.88122			−0.368343			−0.184172	−	0.982894i	$-0.558960\pi$
$349$	−6.88122			−0.368343			−0.184172	+	0.982894i	$0.558960\pi$
$350$	−20.6822	+	5.93430i	−1.10551	+	0.317202i
$351$	3.87869			0.207029
$352$	−1.42387	−	1.03450i	−0.0758926	−	0.0551392i
$353$	4.93566	+	15.1904i	0.262699	+	0.808503i	0.992215	+	0.124539i	$0.0397453\pi$
$353$	4.93566	+	15.1904i	0.262699	+	0.808503i	−0.729516	+	0.683964i	$0.760255\pi$
$354$	−1.33302	−	4.10263i	−0.0708494	−	0.218052i
$355$	−16.3993	+	15.8393i	−0.870384	+	0.840662i
$356$	−4.11183	+	12.6549i	−0.217927	+	0.670710i
$357$	−11.0369			−0.584132
$358$	−2.91525	+	8.97222i	−0.154076	+	0.474196i
$359$	−12.8137	+	9.30972i	−0.676283	+	0.491348i	−0.872122	−	0.489288i	$-0.837257\pi$
$359$	−12.8137	+	9.30972i	−0.676283	+	0.491348i	0.195840	+	0.980636i	$0.437257\pi$
$360$	4.02614	−	3.88866i	0.212196	−	0.204950i
$361$	13.8952	+	10.0955i	0.731327	+	0.531340i
$362$	10.0463	−	7.29907i	0.528022	−	0.383630i
$363$	−4.50590	+	3.27373i	−0.236498	+	0.171826i
$364$	3.48147	+	2.52944i	0.182479	+	0.132579i
$365$	1.60317	−	9.09651i	0.0839136	−	0.476133i
$366$	2.01976	−	1.46744i	0.105574	−	0.0767042i
$367$	−4.37342	+	13.4600i	−0.228291	+	0.702607i	0.769650	+	0.638466i	$0.220431\pi$
$367$	−4.37342	+	13.4600i	−0.228291	+	0.702607i	−0.997941	+	0.0641409i	$0.979569\pi$
$368$	5.97647			0.311545
$369$	−7.71286	+	23.7378i	−0.401516	+	1.23574i
$370$	8.81171	+	18.0628i	0.458099	+	0.939041i
$371$	−14.2361	−	43.8142i	−0.739101	−	2.27472i
$372$	−0.307714	−	0.947046i	−0.0159542	−	0.0491020i
$373$	−11.8060	−	8.57757i	−0.611292	−	0.444130i	0.238577	−	0.971124i	$-0.423319\pi$
$373$	−11.8060	−	8.57757i	−0.611292	−	0.444130i	−0.849869	+	0.526994i	$0.823319\pi$
$374$	−6.40454			−0.331171
$375$	0.825662	+	7.83651i	0.0426370	+	0.404676i
$376$	−2.22545			−0.114769
$377$	8.29888	+	6.02949i	0.427414	+	0.310535i
$378$	−5.15790	−	15.8744i	−0.265294	−	0.816490i
$379$	−7.16376	−	22.0478i	−0.367978	−	1.13252i	−0.948095	−	0.317986i	$-0.896994\pi$
$379$	−7.16376	−	22.0478i	−0.367978	−	1.13252i	0.580118	−	0.814533i	$-0.303006\pi$
$380$	−1.32429	−	2.71461i	−0.0679346	−	0.139257i
$381$	−1.23443	+	3.79917i	−0.0632416	+	0.194638i
$382$	12.7489			0.652289
$383$	−9.44212	+	29.0599i	−0.482470	+	1.48489i	0.353143	+	0.935570i	$0.385113\pi$
$383$	−9.44212	+	29.0599i	−0.482470	+	1.48489i	−0.835612	+	0.549320i	$0.814887\pi$
$384$	0.570194	−	0.414270i	0.0290976	−	0.0211406i
$385$	−2.93944	+	16.6787i	−0.149808	+	0.850024i
$386$	3.28214	+	2.38461i	0.167056	+	0.121373i
$387$	−6.33912	+	4.60564i	−0.322235	+	0.234118i
$388$	3.84068	−	2.79042i	0.194981	−	0.141662i
$389$	−14.6953	−	10.6768i	−0.745084	−	0.541335i	0.149215	−	0.988805i	$-0.452325\pi$
$389$	−14.6953	−	10.6768i	−0.745084	−	0.541335i	−0.894299	+	0.447470i	$0.852325\pi$
$390$	1.13357	−	1.09486i	0.0574006	−	0.0554405i
$391$	17.5945	−	12.7832i	0.889793	−	0.646472i
$392$	3.55948	−	10.9549i	0.179781	−	0.553308i
$393$	12.5226			0.631683
$394$	−8.42954	+	25.9434i	−0.424674	+	1.30701i
$395$	17.1703	−	16.5840i	0.863931	−	0.834430i
$396$	−1.36145	−	4.19011i	−0.0684154	−	0.210561i
$397$	6.73882	+	20.7400i	0.338212	+	1.04091i	0.965118	+	0.261814i	$0.0843207\pi$
$397$	6.73882	+	20.7400i	0.338212	+	1.04091i	−0.626907	+	0.779094i	$0.715679\pi$
$398$	−2.14999	−	1.56206i	−0.107769	−	0.0782991i
$399$	−4.09686			−0.205099
$400$	0.173652	−	4.99698i	0.00868258	−	0.249849i
$401$	−25.3192			−1.26438			−0.632189	−	0.774814i	$-0.717844\pi$
$401$	−25.3192			−1.26438			−0.632189	+	0.774814i	$0.717844\pi$
$402$	5.43331	+	3.94753i	0.270989	+	0.196885i
$403$	0.436598	+	1.34371i	0.0217485	+	0.0669350i
$404$	−0.914904	−	2.81579i	−0.0455182	−	0.140091i
$405$	10.5756	−	1.48721i	0.525505	−	0.0739003i
$406$	13.6411	−	41.9830i	0.676997	−	2.08358i
$407$	15.8187			0.784104
$408$	0.792542	−	2.43919i	0.0392367	−	0.120758i
$409$	−0.296478	+	0.215404i	−0.0146599	+	0.0106510i	−0.595091	−	0.803658i	$-0.702884\pi$
$409$	−0.296478	+	0.215404i	−0.0146599	+	0.0106510i	0.580431	+	0.814309i	$0.302884\pi$
$410$	9.77529	+	20.0380i	0.482767	+	0.989607i
$411$	−6.89246	−	5.00767i	−0.339980	−	0.247010i
$412$	6.79732	−	4.93854i	0.334880	−	0.243304i
$413$	21.3085	−	15.4816i	1.04852	−	0.761798i
$414$	12.1034	+	8.79365i	0.594851	+	0.432184i
$415$	−29.1002	+	4.09228i	−1.42847	+	0.200882i
$416$	−0.809017	+	0.587785i	−0.0396653	+	0.0288185i
$417$	3.75093	−	11.5442i	0.183684	−	0.565321i
$418$	−2.37735			−0.116280
$419$	−5.45078	+	16.7758i	−0.266288	+	0.819551i	0.725106	+	0.688638i	$0.241791\pi$
$419$	−5.45078	+	16.7758i	−0.266288	+	0.819551i	−0.991394	+	0.130913i	$0.958209\pi$
$420$	−5.98839	−	3.18343i	−0.292203	−	0.155336i
$421$	−9.11501	−	28.0531i	−0.444238	−	1.36722i	−0.883317	−	0.468776i	$-0.844695\pi$
$421$	−9.11501	−	28.0531i	−0.444238	−	1.36722i	0.439079	−	0.898449i	$-0.355305\pi$
$422$	−3.66356	−	11.2753i	−0.178339	−	0.548872i
$423$	−4.50693	−	3.27448i	−0.219135	−	0.159211i
$424$	10.7054			0.519901
$425$	−10.1769	−	15.0824i	−0.493652	−	0.731602i
$426$	−7.18632			−0.348178
$427$	12.3322	+	8.95984i	0.596795	+	0.433597i
$428$	3.25364	+	10.0137i	0.157271	+	0.484029i
$429$	−0.383319	−	1.17974i	−0.0185068	−	0.0569581i
$430$	−1.21482	+	6.89300i	−0.0585838	+	0.332410i
$431$	−6.29548	+	19.3755i	−0.303243	+	0.933285i	0.677085	+	0.735905i	$0.263243\pi$
$431$	−6.29548	+	19.3755i	−0.303243	+	0.933285i	−0.980327	+	0.197379i	$0.936757\pi$
$432$	3.87869			0.186614
$433$	−2.98064	+	9.17348i	−0.143241	+	0.440849i	−0.996781	−	0.0801782i	$-0.974451\pi$
$433$	−2.98064	+	9.17348i	−0.143241	+	0.440849i	0.853540	+	0.521027i	$0.174451\pi$
$434$	4.91884	−	3.57375i	0.236112	−	0.171545i
$435$	−14.2747	−	7.58843i	−0.684419	−	0.363838i
$436$	6.28295	+	4.56483i	0.300899	+	0.218616i
$437$	6.53105	−	4.74508i	0.312422	−	0.226988i
$438$	2.35535	−	1.71126i	0.112543	−	0.0817671i
$439$	−24.1445	−	17.5420i	−1.15235	−	0.837234i	−0.163561	−	0.986533i	$-0.552298\pi$
$439$	−24.1445	−	17.5420i	−1.15235	−	0.837234i	−0.988792	+	0.149300i	$0.952298\pi$
$440$	−3.47498	−	1.84730i	−0.165663	−	0.0880667i
$441$	23.3275	−	16.9484i	1.11083	−	0.807066i
$442$	−1.12449	+	3.46084i	−0.0534867	+	0.164615i
$443$	9.11437			0.433037			0.216518	−	0.976279i	$-0.430530\pi$
$443$	9.11437			0.433037			0.216518	+	0.976279i	$0.430530\pi$
$444$	−1.95752	+	6.02462i	−0.0928996	+	0.285916i
$445$	−5.16416	+	29.3019i	−0.244805	+	1.38904i
$446$	2.02208	+	6.22333i	0.0957483	+	0.294683i
$447$	0.284815	+	0.876572i	0.0134713	+	0.0414604i
$448$	3.48147	+	2.52944i	0.164484	+	0.119505i
$449$	11.8592			0.559669			0.279834	−	0.960048i	$-0.409720\pi$
$449$	11.8592			0.559669			0.279834	+	0.960048i	$0.409720\pi$
$450$	7.70413	−	9.86428i	0.363176	−	0.465007i
$451$	17.5485			0.826328
$452$	5.42710	+	3.94302i	0.255269	+	0.185464i
$453$	4.39742	+	13.5339i	0.206609	+	0.635876i
$454$	0.500975	+	1.54184i	0.0235119	+	0.0723623i
$455$	8.49659	+	4.51680i	0.398326	+	0.211751i
$456$	0.294190	−	0.905423i	0.0137767	−	0.0424003i
$457$	−0.464889			−0.0217466			−0.0108733	−	0.999941i	$-0.503461\pi$
$457$	−0.464889			−0.0217466			−0.0108733	+	0.999941i	$0.503461\pi$
$458$	0.100965	−	0.310739i	0.00471780	−	0.0145199i
$459$	11.4187	−	8.29619i	0.532980	−	0.387233i
$460$	13.2336	−	1.86100i	0.617019	−	0.0867696i
$461$	−23.3521	−	16.9663i	−1.08761	−	0.790198i	−0.108619	−	0.994083i	$-0.534643\pi$
$461$	−23.3521	−	16.9663i	−1.08761	−	0.790198i	−0.978995	+	0.203885i	$0.934643\pi$
$462$	−4.31858	+	3.13763i	−0.200919	+	0.145976i
$463$	16.8288	−	12.2269i	0.782102	−	0.568231i	−0.123507	−	0.992344i	$-0.539414\pi$
$463$	16.8288	−	12.2269i	0.782102	−	0.568231i	0.905609	+	0.424113i	$0.139414\pi$
$464$	8.29888	+	6.02949i	0.385266	+	0.279912i
$465$	−0.976263	−	2.00121i	−0.0452731	−	0.0928037i
$466$	−1.32789	+	0.964768i	−0.0615133	+	0.0446920i
$467$	−2.55424	+	7.86113i	−0.118196	+	0.363770i	−0.992600	−	0.121428i	$-0.961253\pi$
$467$	−2.55424	+	7.86113i	−0.118196	+	0.363770i	0.874404	+	0.485198i	$0.161253\pi$
$468$	−2.50326			−0.115713
$469$	−12.6716	+	38.9990i	−0.585118	+	1.80081i
$470$	−4.92777	+	0.692978i	−0.227301	+	0.0319647i
$471$	−4.74971	−	14.6181i	−0.218855	−	0.673567i
$472$	1.89135	+	5.82099i	0.0870567	+	0.267933i
$473$	4.45693	+	3.23815i	0.204930	+	0.148890i
$474$	7.52418			0.345597
$475$	−3.77764	−	5.59854i	−0.173330	−	0.256879i
$476$	15.6596			0.717756
$477$	21.6804	+	15.7517i	0.992676	+	0.721221i
$478$	−1.50034	−	4.61758i	−0.0686241	−	0.211203i
$479$	−0.888668	−	2.73504i	−0.0406043	−	0.124967i	0.928700	−	0.370833i	$-0.120928\pi$
$479$	−0.888668	−	2.73504i	−0.0406043	−	0.124967i	−0.969304	+	0.245866i	$0.920928\pi$
$480$	1.13357	−	1.09486i	0.0517402	−	0.0499734i
$481$	2.77741	−	8.54800i	0.126639	−	0.389755i
$482$	−10.3846			−0.473006
$483$	5.60141	−	17.2394i	0.254873	−	0.784419i
$484$	6.39317	−	4.64491i	0.290599	−	0.211132i
$485$	7.63544	−	7.37470i	0.346707	−	0.334868i
$486$	12.1371	+	8.81810i	0.550549	+	0.399997i
$487$	7.81792	−	5.68005i	0.354264	−	0.257388i	−0.396392	−	0.918081i	$-0.629738\pi$
$487$	7.81792	−	5.68005i	0.354264	−	0.257388i	0.750655	+	0.660694i	$0.229738\pi$
$488$	−2.86572	+	2.08207i	−0.129725	+	0.0942508i
$489$	−6.49754	−	4.72074i	−0.293829	−	0.213479i
$490$	4.47044	−	25.3657i	0.201954	−	1.14591i
$491$	−0.650801	+	0.472834i	−0.0293702	+	0.0213387i	−0.602374	−	0.798214i	$-0.705778\pi$
$491$	−0.650801	+	0.472834i	−0.0293702	+	0.0213387i	0.573003	+	0.819553i	$0.305778\pi$
$492$	−2.17158	+	6.68342i	−0.0979022	+	0.301312i
$493$	37.3282			1.68118
$494$	−0.417410	+	1.28466i	−0.0187802	+	0.0577994i
$495$	−4.31938	−	8.85414i	−0.194142	−	0.397964i
$496$	0.436598	+	1.34371i	0.0196038	+	0.0603344i
$497$	−13.5590	−	41.7305i	−0.608206	−	1.87187i
$498$	−7.49353	−	5.44437i	−0.335793	−	0.243968i
$499$	−20.0876			−0.899244			−0.449622	−	0.893219i	$-0.648441\pi$
$499$	−20.0876			−0.899244			−0.449622	+	0.893219i	$0.648441\pi$
$500$	−1.17149	−	11.1188i	−0.0523905	−	0.497248i
$501$	2.76118			0.123360
$502$	−9.44130	−	6.85950i	−0.421386	−	0.306155i
$503$	0.512352	+	1.57686i	0.0228446	+	0.0703086i	0.961829	−	0.273652i	$-0.0882315\pi$
$503$	0.512352	+	1.57686i	0.0228446	+	0.0703086i	−0.938984	+	0.343960i	$0.888231\pi$
$504$	3.32884	+	10.2451i	0.148279	+	0.456354i
$505$	−2.90266	−	5.95005i	−0.129167	−	0.264774i
$506$	3.25043	−	10.0038i	0.144499	−	0.444722i
$507$	−0.704799			−0.0313012
$508$	1.75146	−	5.39044i	0.0777084	−	0.239162i
$509$	31.2081	−	22.6740i	1.38327	−	1.00501i	0.386707	−	0.922203i	$-0.373612\pi$
$509$	31.2081	−	22.6740i	1.38327	−	1.00501i	0.996566	−	0.0828042i	$-0.0263876\pi$
$510$	0.995375	−	5.64785i	0.0440759	−	0.250091i
$511$	14.3812	+	10.4486i	0.636187	+	0.462217i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	4.23861	−	3.07953i	0.187139	−	0.135964i
$514$	−4.67285	−	3.39502i	−0.206110	−	0.149748i
$515$	13.5134	−	13.0519i	0.595470	−	0.575136i
$516$	−1.78479	+	1.29673i	−0.0785712	+	0.0570853i
$517$	−1.21036	+	3.72509i	−0.0532314	+	0.163829i
$518$	−38.6779			−1.69941
$519$	−2.87573	+	8.85060i	−0.126231	+	0.388498i
$520$	−1.60836	+	1.55344i	−0.0705313	+	0.0681228i
$521$	−11.1719	−	34.3837i	−0.489451	−	1.50638i	−0.825429	−	0.564506i	$-0.809067\pi$
$521$	−11.1719	−	34.3837i	−0.489451	−	1.50638i	0.335978	−	0.941870i	$-0.390933\pi$
$522$	7.93506	+	24.4216i	0.347308	+	1.06890i
$523$	8.80804	+	6.39942i	0.385149	+	0.279827i	0.763465	−	0.645850i	$-0.223497\pi$
$523$	8.80804	+	6.39942i	0.385149	+	0.279827i	−0.378316	+	0.925677i	$0.623497\pi$
$524$	−17.7677			−0.776185
$525$	−14.2513	−	5.18430i	−0.621976	−	0.226261i
$526$	−11.2236			−0.489371
$527$	4.15941	+	3.02199i	0.181187	+	0.131640i
$528$	−0.383319	−	1.17974i	−0.0166818	−	0.0513414i
$529$	3.93014	+	12.0957i	0.170876	+	0.525901i
$530$	23.7048	−	3.33353i	1.02967	−	0.144799i
$531$	−4.73455	+	14.5714i	−0.205462	+	0.632347i
$532$	5.81281			0.252017
$533$	3.08113	−	9.48274i	0.133458	−	0.410743i
$534$	−7.58710	+	5.51235i	−0.328326	+	0.238543i
$535$	10.3226	+	21.1599i	0.446286	+	0.914824i
$536$	−7.70903	−	5.60094i	−0.332979	−	0.241924i
$537$	−5.37918	+	3.90820i	−0.232129	+	0.168651i
$538$	1.28888	−	0.936426i	0.0555675	−	0.0403722i
$539$	−16.4012	−	11.9161i	−0.706448	−	0.513265i
$540$	8.58851	−	1.20778i	0.369590	−	0.0519744i
$541$	0.566400	−	0.411513i	0.0243514	−	0.0176923i	−0.575543	−	0.817772i	$-0.695209\pi$
$541$	0.566400	−	0.411513i	0.0243514	−	0.0176923i	0.599894	+	0.800079i	$0.295209\pi$
$542$	8.45487	−	26.0214i	0.363168	−	1.11772i
$543$	8.75213			0.375590
$544$	−1.12449	+	3.46084i	−0.0482123	+	0.148382i
$545$	15.3336	+	8.15138i	0.656821	+	0.349167i
$546$	0.937244	+	2.88454i	0.0401104	+	0.123447i
$547$	1.79931	+	5.53771i	0.0769330	+	0.236775i	0.982126	−	0.188226i	$-0.0602737\pi$
$547$	1.79931	+	5.53771i	0.0769330	+	0.236775i	−0.905193	+	0.425001i	$0.860274\pi$
$548$	9.77934	+	7.10510i	0.417753	+	0.303515i
$549$	−8.86711			−0.378439
$550$	−8.26981	−	3.00838i	−0.352626	−	0.128278i
$551$	13.8561			0.590291
$552$	3.40775	+	2.47587i	0.145043	+	0.105380i
$553$	14.1965	+	43.6924i	0.603697	+	1.85799i
$554$	−0.732624	−	2.25479i	−0.0311262	−	0.0957966i
$555$	−2.45850	+	13.9497i	−0.104357	+	0.592133i
$556$	−5.32199	+	16.3794i	−0.225703	+	0.694642i
$557$	−36.8259			−1.56036			−0.780181	−	0.625553i	$-0.784873\pi$
$557$	−36.8259			−1.56036			−0.780181	+	0.625553i	$0.784873\pi$
$558$	−1.09292	+	3.36366i	−0.0462669	+	0.142395i
$559$	2.53235	−	1.83986i	0.107107	−	0.0778177i
$560$	8.49659	+	4.51680i	0.359047	+	0.190870i
$561$	−3.65183	−	2.65321i	−0.154180	−	0.112019i
$562$	22.5629	−	16.3929i	0.951757	−	0.691492i
$563$	15.3922	−	11.1831i	0.648703	−	0.471311i	−0.214126	−	0.976806i	$-0.568690\pi$
$563$	15.3922	−	11.1831i	0.648703	−	0.471311i	0.862829	+	0.505495i	$0.168690\pi$
$564$	−1.26894	−	0.921937i	−0.0534319	−	0.0388206i
$565$	13.2449	+	7.04102i	0.557219	+	0.296218i
$566$	−25.8776	+	18.8012i	−1.08772	+	0.790271i
$567$	−6.35126	+	19.5472i	−0.266728	+	0.820903i
$568$	10.1963			0.427826
$569$	−3.32453	+	10.2319i	−0.139372	+	0.428942i	−0.996244	−	0.0865861i	$-0.972404\pi$
$569$	−3.32453	+	10.2319i	−0.139372	+	0.428942i	0.856873	+	0.515528i	$0.172404\pi$
$570$	0.369481	−	2.09647i	0.0154759	−	0.0878114i
$571$	0.732929	+	2.25572i	0.0306721	+	0.0943991i	0.965221	−	0.261437i	$-0.0841963\pi$
$571$	0.732929	+	2.25572i	0.0306721	+	0.0943991i	−0.934549	+	0.355836i	$0.884196\pi$
$572$	0.543870	+	1.67386i	0.0227404	+	0.0699877i
$573$	7.26934	+	5.28148i	0.303681	+	0.220637i
$574$	−42.9075			−1.79092
$575$	28.7234	−	8.24156i	1.19785	−	0.343697i
$576$	−2.50326			−0.104302
$577$	−3.20750	−	2.33038i	−0.133530	−	0.0970151i	0.519015	−	0.854765i	$-0.326299\pi$
$577$	−3.20750	−	2.33038i	−0.133530	−	0.0970151i	−0.652545	+	0.757750i	$0.726299\pi$
$578$	−1.16132	−	3.57419i	−0.0483047	−	0.148667i
$579$	0.883581	+	2.71938i	0.0367204	+	0.113014i
$580$	20.2536	+	10.7668i	0.840983	+	0.447067i
$581$	17.4764	−	53.7868i	0.725043	−	2.23145i
$582$	3.34592			0.138693
$583$	5.82235	−	17.9194i	0.241137	−	0.742144i
$584$	−3.34187	+	2.42801i	−0.138288	+	0.100472i
$585$	−5.54292	+	0.779485i	−0.229171	+	0.0322277i
$586$	−15.6951	−	11.4032i	−0.648360	−	0.471061i
$587$	−24.4323	+	17.7511i	−1.00843	+	0.732666i	−0.963879	−	0.266341i	$-0.914185\pi$
$587$	−24.4323	+	17.7511i	−1.00843	+	0.732666i	−0.0445493	+	0.999007i	$0.514185\pi$
$588$	6.56790	−	4.77186i	0.270856	−	0.196788i
$589$	1.54397	+	1.12176i	0.0636180	+	0.0462212i
$590$	6.00058	+	12.3004i	0.247040	+	0.506398i
$591$	−15.5541	+	11.3007i	−0.639809	+	0.464848i
$592$	2.77741	−	8.54800i	0.114151	−	0.351320i
$593$	−3.09691			−0.127175			−0.0635875	−	0.997976i	$-0.520254\pi$
$593$	−3.09691			−0.127175			−0.0635875	+	0.997976i	$0.520254\pi$
$594$	2.10950	−	6.49239i	0.0865540	−	0.266386i
$595$	34.6747	−	4.87621i	1.42152	−	0.199905i
$596$	−0.404109	−	1.24372i	−0.0165529	−	0.0509447i
$597$	−0.578798	−	1.78136i	−0.0236886	−	0.0729061i
$598$	−4.83507	−	3.51288i	−0.197721	−	0.143652i
$599$	13.9569			0.570263			0.285132	−	0.958488i	$-0.407963\pi$
$599$	13.9569			0.570263			0.285132	+	0.958488i	$0.407963\pi$
$600$	2.16912	−	2.77731i	0.0885538	−	0.113383i
$601$	−26.9507			−1.09934			−0.549672	−	0.835381i	$-0.685247\pi$
$601$	−26.9507			−1.09934			−0.549672	+	0.835381i	$0.685247\pi$
$602$	−10.8975	−	7.91753i	−0.444151	−	0.322694i
$603$	−7.37107	−	22.6858i	−0.300173	−	0.923838i
$604$	−6.23925	−	19.2024i	−0.253872	−	0.781337i
$605$	12.7099	−	12.2759i	0.516731	−	0.499086i
$606$	0.644823	−	1.98456i	0.0261942	−	0.0806173i
$607$	−47.8930			−1.94392			−0.971959	−	0.235148i	$-0.924442\pi$
$607$	−47.8930			−1.94392			−0.971959	+	0.235148i	$0.924442\pi$
$608$	−0.417410	+	1.28466i	−0.0169282	+	0.0520997i
$609$	25.1704	−	18.2874i	1.01996	−	0.741041i
$610$	−5.69718	+	5.50263i	−0.230672	+	0.222795i
$611$	1.80043	+	1.30809i	0.0728374	+	0.0529195i
$612$	−7.36950	+	5.35426i	−0.297895	+	0.216433i
$613$	34.1885	−	24.8394i	1.38086	−	1.00325i	0.384061	−	0.923308i	$-0.374525\pi$
$613$	34.1885	−	24.8394i	1.38086	−	1.00325i	0.996799	−	0.0799465i	$-0.0254749\pi$
$614$	15.9272	+	11.5718i	0.642769	+	0.466999i
$615$	−2.72734	+	15.4752i	−0.109977	+	0.624019i
$616$	6.12740	−	4.45182i	0.246880	−	0.179369i
$617$	4.20462	−	12.9405i	0.169271	−	0.520964i	−0.830054	−	0.557683i	$-0.811691\pi$
$617$	4.20462	−	12.9405i	0.169271	−	0.520964i	0.999326	+	0.0367188i	$0.0116906\pi$
$618$	5.92168			0.238205
$619$	7.62821	−	23.4772i	0.306604	−	0.943629i	−0.672470	−	0.740124i	$-0.734767\pi$
$619$	7.62821	−	23.4772i	0.306604	−	0.943629i	0.979074	−	0.203505i	$-0.0652333\pi$
$620$	1.38517	+	2.83940i	0.0556296	+	0.114033i
$621$	7.16328	+	22.0463i	0.287453	+	0.884688i
$622$	9.21186	+	28.3512i	0.369362	+	1.13678i
$623$	−46.3251	−	33.6572i	−1.85598	−	1.34845i
$624$	−0.704799			−0.0282145
$625$	−6.05626	−	24.2553i	−0.242250	−	0.970214i
$626$	10.0967			0.403546
$627$	−1.35555	−	0.984866i	−0.0541355	−	0.0393318i
$628$	6.73910	+	20.7408i	0.268920	+	0.827649i
$629$	−10.1068	−	31.1056i	−0.402986	−	1.24026i
$630$	10.5612	+	21.6490i	0.420769	+	0.862518i
$631$	1.70575	−	5.24976i	0.0679049	−	0.208990i	−0.911346	−	0.411641i	$-0.864956\pi$
$631$	1.70575	−	5.24976i	0.0679049	−	0.208990i	0.979251	+	0.202651i	$0.0649558\pi$
$632$	−10.6756			−0.424654
$633$	2.58207	−	7.94680i	0.102628	−	0.315857i
$634$	27.2394	−	19.7906i	1.08182	−	0.785985i
$635$	2.19970	−	12.4813i	0.0872926	−	0.495306i
$636$	6.10416	+	4.43493i	0.242046	+	0.175856i
$637$	−9.31884	+	6.77053i	−0.369226	+	0.268258i
$638$	14.6060	−	10.6119i	0.578259	−	0.420130i
$639$	20.6493	+	15.0026i	0.816873	+	0.593493i
$640$	−1.60836	+	1.55344i	−0.0635761	+	0.0614051i
$641$	−3.60285	+	2.61762i	−0.142304	+	0.103390i	−0.656660	−	0.754187i	$-0.728031\pi$
$641$	−3.60285	+	2.61762i	−0.142304	+	0.103390i	0.514356	+	0.857577i	$0.328031\pi$
$642$	−2.29316	+	7.05763i	−0.0905039	+	0.278542i
$643$	2.71186			0.106946			0.0534728	−	0.998569i	$-0.482971\pi$
$643$	2.71186			0.106946			0.0534728	+	0.998569i	$0.482971\pi$
$644$	−7.94754	+	24.4600i	−0.313177	+	0.963859i
$645$	−3.54825	+	3.42708i	−0.139712	+	0.134941i
$646$	1.51893	+	4.67478i	0.0597615	+	0.183927i
$647$	1.29752	+	3.99337i	0.0510109	+	0.156996i	0.973317	−	0.229465i	$-0.0736976\pi$
$647$	1.29752	+	3.99337i	0.0510109	+	0.156996i	−0.922306	+	0.386460i	$0.873698\pi$
$648$	−3.86393	−	2.80731i	−0.151790	−	0.110282i
$649$	10.7722			0.422845
$650$	−3.07764	+	3.94057i	−0.120715	+	0.154562i
$651$	4.28519			0.167950
$652$	9.21900	+	6.69800i	0.361044	+	0.262314i
$653$	−0.163576	−	0.503435i	−0.00640122	−	0.0197009i	0.947805	−	0.318851i	$-0.103297\pi$
$653$	−0.163576	−	0.503435i	−0.00640122	−	0.0197009i	−0.954206	+	0.299150i	$0.903297\pi$
$654$	1.69143	+	5.20568i	0.0661400	+	0.203558i
$655$	−39.3426	+	5.53264i	−1.53724	+	0.216178i
$656$	3.08113	−	9.48274i	0.120298	−	0.370239i
$657$	−10.3404			−0.403418
$658$	2.95941	−	9.10813i	0.115370	−	0.355072i
$659$	27.0745	−	19.6707i	1.05467	−	0.766263i	0.0815758	−	0.996667i	$-0.474005\pi$
$659$	27.0745	−	19.6707i	1.05467	−	0.766263i	0.973095	+	0.230404i	$0.0740047\pi$
$660$	−1.21613	−	2.49290i	−0.0473378	−	0.0970361i
$661$	10.1922	+	7.40506i	0.396430	+	0.288023i	0.768085	−	0.640347i	$-0.221210\pi$
$661$	10.1922	+	7.40506i	0.396430	+	0.288023i	−0.371655	+	0.928371i	$0.621210\pi$
$662$	−7.44524	+	5.40928i	−0.289367	+	0.210238i
$663$	−2.07490	+	1.50750i	−0.0805825	+	0.0585466i
$664$	10.6322	+	7.72472i	0.412608	+	0.299777i
$665$	12.8712	−	1.81004i	0.499123	−	0.0701902i
$666$	18.2021	−	13.2246i	0.705317	−	0.512443i
$667$	−18.9448	+	58.3060i	−0.733544	+	2.25762i
$668$	−3.91768			−0.151580
$669$	−1.42516	+	4.38619i	−0.0550999	+	0.169580i
$670$	−18.8140	−	10.0016i	−0.726849	−	0.386394i
$671$	1.92651	+	5.92919i	0.0743721	+	0.228894i
$672$	0.937244	+	2.88454i	0.0361550	+	0.111274i
$673$	−23.6104	−	17.1540i	−0.910114	−	0.661237i	0.0309294	−	0.999522i	$-0.490153\pi$
$673$	−23.6104	−	17.1540i	−0.910114	−	0.661237i	−0.941044	+	0.338285i	$0.890153\pi$
$674$	13.8851			0.534836
$675$	18.6413	−	5.34871i	0.717503	−	0.205872i
$676$	1.00000			0.0384615
$677$	5.69726	+	4.13930i	0.218963	+	0.159086i	0.691860	−	0.722032i	$-0.256792\pi$
$677$	5.69726	+	4.13930i	0.218963	+	0.159086i	−0.472897	+	0.881118i	$0.656792\pi$
$678$	1.46103	+	4.49657i	0.0561104	+	0.172690i
$679$	6.31303	+	19.4295i	0.242272	+	0.745637i
$680$	−1.41228	+	8.01342i	−0.0541586	+	0.307301i
$681$	−0.353087	+	1.08669i	−0.0135303	+	0.0416420i
$682$	2.48664			0.0952183
$683$	−1.59253	+	4.90130i	−0.0609364	+	0.187543i	−0.976891	−	0.213740i	$-0.931436\pi$
$683$	−1.59253	+	4.90130i	−0.0609364	+	0.187543i	0.915954	+	0.401283i	$0.131436\pi$
$684$	−2.73554	+	1.98749i	−0.104596	+	0.0759936i
$685$	23.8666	+	12.6875i	0.911897	+	0.484765i
$686$	15.7318	+	11.4298i	0.600642	+	0.436392i
$687$	0.186300	−	0.135355i	0.00710778	−	0.00516410i
$688$	2.53235	−	1.83986i	0.0965448	−	0.0701439i
$689$	−8.66086	−	6.29248i	−0.329952	−	0.239724i
$690$	8.31667	+	4.42115i	0.316610	+	0.168310i
$691$	−11.2357	+	8.16318i	−0.427424	+	0.310542i	−0.780618	−	0.625008i	$-0.785096\pi$
$691$	−11.2357	+	8.16318i	−0.427424	+	0.310542i	0.353194	+	0.935550i	$0.385096\pi$
$692$	4.08022	−	12.5576i	0.155107	−	0.477369i
$693$	18.9594			0.720208
$694$	10.9646	−	33.7455i	0.416209	−	1.28096i
$695$	−6.68404	+	37.9258i	−0.253540	+	1.43861i
$696$	2.23413	+	6.87596i	0.0846846	+	0.260633i
$697$	−11.2120	−	34.5071i	−0.424686	−	1.30705i
$698$	5.56702	+	4.04468i	0.210715	+	0.153093i
$699$	−1.15683			−0.0437553
$700$	20.2203	+	7.35572i	0.764256	+	0.278020i
$701$	−9.24325			−0.349113			−0.174556	−	0.984647i	$-0.555849\pi$
$701$	−9.24325			−0.349113			−0.174556	+	0.984647i	$0.555849\pi$
$702$	−3.13793	−	2.27984i	−0.118433	−	0.0860469i
$703$	−3.75164	−	11.5463i	−0.141496	−	0.435479i
$704$	0.543870	+	1.67386i	0.0204979	+	0.0630860i
$705$	−3.09686	−	1.64630i	−0.116635	−	0.0620031i
$706$	4.93566	−	15.1904i	0.185756	−	0.571698i
$707$	12.7409			0.479169
$708$	−1.33302	+	4.10263i	−0.0500981	+	0.154186i
$709$	−19.3937	+	14.0903i	−0.728345	+	0.529173i	−0.889039	−	0.457831i	$-0.848627\pi$
$709$	−19.3937	+	14.0903i	−0.728345	+	0.529173i	0.160695	+	0.987004i	$0.448627\pi$
$710$	22.5774	−	3.17500i	0.847315	−	0.119155i
$711$	−21.6201	−	15.7079i	−0.810817	−	0.589093i
$712$	10.7649	−	7.82117i	0.403433	−	0.293111i
$713$	−6.83128	+	4.96321i	−0.255833	+	0.185874i
$714$	8.92900	+	6.48730i	0.334160	+	0.242781i
$715$	1.72550	+	3.53704i	0.0645301	+	0.132278i
$716$	7.63222	−	5.54513i	0.285230	−	0.207231i
$717$	1.05744	−	3.25446i	0.0394908	−	0.121540i
$718$	15.8386			0.591093
$719$	−10.7917	+	33.2133i	−0.402461	+	1.23865i	0.520535	+	0.853840i	$0.325732\pi$
$719$	−10.7917	+	33.2133i	−0.402461	+	1.23865i	−0.922997	+	0.384808i	$0.874268\pi$
$720$	−5.54292	+	0.779485i	−0.206572	+	0.0290497i
$721$	11.1729	+	34.3868i	0.416102	+	1.28063i
$722$	−5.30750	−	16.3348i	−0.197525	−	0.607918i
$723$	−5.92124	−	4.30203i	−0.220213	−	0.159994i
$724$	−12.4179			−0.461508
$725$	48.1997	+	17.5340i	1.79009	+	0.651197i
$726$	5.56960			0.206707
$727$	−4.54812	−	3.30440i	−0.168680	−	0.122553i	0.500242	−	0.865885i	$-0.333244\pi$
$727$	−4.54812	−	3.30440i	−0.168680	−	0.122553i	−0.668923	+	0.743332i	$0.733244\pi$
$728$	−1.32980	−	4.09272i	−0.0492858	−	0.151686i
$729$	−1.16026	−	3.57092i	−0.0429726	−	0.132256i
$730$	−6.64378	+	6.41692i	−0.245898	+	0.237501i
$731$	3.51984	−	10.8329i	0.130186	−	0.400671i
$732$	−2.49655			−0.0922753
$733$	15.9708	−	49.1532i	0.589897	−	1.81551i	0.0112494	−	0.999937i	$-0.496419\pi$
$733$	15.9708	−	49.1532i	0.589897	−	1.81551i	0.578647	−	0.815578i	$-0.303581\pi$
$734$	11.4498	−	8.31875i	0.422619	−	0.307051i
$735$	13.0573	−	12.6114i	0.481625	−	0.465179i
$736$	−4.83507	−	3.51288i	−0.178223	−	0.129487i
$737$	−13.5679	+	9.85766i	−0.499780	+	0.363112i
$738$	20.1925	−	14.6707i	0.743298	−	0.540037i
$739$	−29.2853	−	21.2770i	−1.07728	−	0.782687i	−0.100070	−	0.994980i	$-0.531907\pi$
$739$	−29.2853	−	21.2770i	−1.07728	−	0.782687i	−0.977206	+	0.212293i	$0.931907\pi$
$740$	3.48823	−	19.7925i	0.128230	−	0.727587i
$741$	−0.770199	+	0.559582i	−0.0282940	+	0.0205568i
$742$	−14.2361	+	43.8142i	−0.522624	+	1.60847i
$743$	−51.4177			−1.88633			−0.943165	−	0.332324i	$-0.892167\pi$
$743$	−51.4177			−1.88633			−0.943165	+	0.332324i	$0.892167\pi$
$744$	−0.307714	+	0.947046i	−0.0112813	+	0.0347204i
$745$	−1.28209	−	2.62811i	−0.0469721	−	0.0962865i
$746$	4.50950	+	13.8788i	0.165104	+	0.508139i
$747$	10.1660	+	31.2879i	0.371956	+	1.14476i
$748$	5.18138	+	3.76449i	0.189450	+	0.137644i
$749$	−45.3099			−1.65559
$750$	3.93821	−	6.82518i	0.143803	−	0.249220i
$751$	−0.596811			−0.0217779			−0.0108890	−	0.999941i	$-0.503466\pi$
$751$	−0.596811			−0.0217779			−0.0108890	+	0.999941i	$0.503466\pi$
$752$	1.80043	+	1.30809i	0.0656548	+	0.0477010i
$753$	−2.54168	−	7.82250i	−0.0926241	−	0.285068i
$754$	−3.16989	−	9.75592i	−0.115441	−	0.355290i
$755$	−19.7949	−	40.5768i	−0.720409	−	1.47674i
$756$	−5.15790	+	15.8744i	−0.187591	+	0.577346i
$757$	5.35477			0.194622			0.0973112	−	0.995254i	$-0.468976\pi$
$757$	5.35477			0.194622			0.0973112	+	0.995254i	$0.468976\pi$
$758$	−7.16376	+	22.0478i	−0.260199	+	0.800811i
$759$	5.99764	−	4.35754i	0.217701	−	0.158169i
$760$	−0.524236	+	2.97456i	−0.0190160	+	0.107899i
$761$	−33.9226	−	24.6462i	−1.22969	−	0.893423i	−0.232825	−	0.972519i	$-0.574797\pi$
$761$	−33.9226	−	24.6462i	−1.22969	−	0.893423i	−0.996867	+	0.0790952i	$0.974797\pi$
$762$	3.23177	−	2.34802i	0.117075	−	0.0850597i
$763$	−27.0377	+	19.6440i	−0.978829	+	0.711161i
$764$	−10.3141	−	7.49360i	−0.373150	−	0.271109i
$765$	−14.6509	+	14.1506i	−0.529704	+	0.511616i
$766$	24.7198	−	17.9600i	0.893162	−	0.648920i
$767$	1.89135	−	5.82099i	0.0682929	−	0.210184i
$768$	−0.704799			−0.0254322
$769$	3.93015	−	12.0958i	0.141725	−	0.436184i	−0.854851	−	0.518874i	$-0.826351\pi$
$769$	3.93015	−	12.0958i	0.141725	−	0.436184i	0.996575	+	0.0826904i	$0.0263512\pi$
$770$	12.1815	−	11.7656i	0.438992	−	0.424002i
$771$	−1.25797	−	3.87164i	−0.0453048	−	0.139434i
$772$	−1.25366	−	3.85838i	−0.0451204	−	0.138866i
$773$	14.3221	+	10.4056i	0.515131	+	0.374265i	0.814767	−	0.579789i	$-0.196865\pi$
$773$	14.3221	+	10.4056i	0.515131	+	0.374265i	−0.299636	+	0.954054i	$0.596865\pi$
$774$	7.83558			0.281644
$775$	3.95130	+	5.85591i	0.141935	+	0.210350i
$776$	−4.74734			−0.170420
$777$	−22.0539	−	16.0231i	−0.791181	−	0.574826i
$778$	5.61312	+	17.2754i	0.201240	+	0.619354i
$779$	−4.16189	−	12.8090i	−0.149115	−	0.458929i
$780$	−1.56062	+	0.219466i	−0.0558792	+	0.00785814i
$781$	5.54545	−	17.0671i	0.198432	−	0.610710i
$782$	−21.7480			−0.777707
$783$	−12.2950	+	37.8402i	−0.439388	+	1.35230i
$784$	−9.31884	+	6.77053i	−0.332816	+	0.241805i
$785$	21.3807	+	43.8275i	0.763110	+	1.56427i
$786$	−10.1310	−	7.36062i	−0.361362	−	0.262545i
$787$	11.8702	−	8.62422i	0.423128	−	0.307420i	−0.355767	−	0.934575i	$-0.615780\pi$
$787$	11.8702	−	8.62422i	0.423128	−	0.307420i	0.778895	+	0.627154i	$0.215780\pi$
$788$	22.0688	−	16.0339i	0.786169	−	0.571185i
$789$	−6.39962	−	4.64960i	−0.227832	−	0.165530i
$790$	−23.6389	+	3.32427i	−0.841033	+	0.118272i
$791$	−23.3547	+	16.9682i	−0.830396	+	0.603318i
$792$	−1.36145	+	4.19011i	−0.0483770	+	0.148889i
$793$	3.54222			0.125788
$794$	6.73882	−	20.7400i	0.239152	−	0.736033i
$795$	14.8973	+	7.91942i	0.528353	+	0.280873i
$796$	0.821224	+	2.52747i	0.0291075	+	0.0895837i
$797$	−3.23561	−	9.95818i	−0.114611	−	0.352737i	0.877255	−	0.480025i	$-0.159373\pi$
$797$	−3.23561	−	9.95818i	−0.114611	−	0.352737i	−0.991866	+	0.127289i	$0.959373\pi$
$798$	3.31443	+	2.40807i	0.117329	+	0.0852448i
$799$	8.09827			0.286496
$800$	−3.07764	+	3.94057i	−0.108811	+	0.139320i
$801$	33.3088			1.17691
$802$	20.4836	+	14.8822i	0.723302	+	0.525510i
$803$	2.24661	+	6.91435i	0.0792811	+	0.244002i
$804$	−2.07534	−	6.38724i	−0.0731917	−	0.225261i
$805$	−9.98153	+	56.6361i	−0.351803	+	1.99616i
$806$	0.436598	−	1.34371i	0.0153785	−	0.0473302i
$807$	1.12284			0.0395260
$808$	−0.914904	+	2.81579i	−0.0321862	+	0.0990590i
$809$	−39.4458	+	28.6590i	−1.38684	+	1.00760i	−0.390636	+	0.920545i	$0.627745\pi$
$809$	−39.4458	+	28.6590i	−1.38684	+	1.00760i	−0.996204	+	0.0870530i	$0.972255\pi$
$810$	−9.42999	−	5.01299i	−0.331336	−	0.176139i
$811$	20.2588	+	14.7189i	0.711384	+	0.516851i	0.883620	−	0.468205i	$-0.155099\pi$
$811$	20.2588	+	14.7189i	0.711384	+	0.516851i	−0.172236	+	0.985056i	$0.555099\pi$
$812$	−35.7129	+	25.9469i	−1.25328	+	0.910559i
$813$	15.6008	−	11.3347i	0.547144	−	0.397524i
$814$	−12.7976	−	9.29801i	−0.448556	−	0.325895i
$815$	22.4991	+	11.9606i	0.788110	+	0.418960i
$816$	−2.07490	+	1.50750i	−0.0726361	+	0.0527732i
$817$	1.30656	−	4.02117i	0.0457106	−	0.140683i
$818$	0.366467			0.0128132
$819$	3.32884	−	10.2451i	0.116319	−	0.357994i
$820$	3.86967	−	21.9569i	0.135135	−	0.766767i
$821$	−0.926452	−	2.85133i	−0.0323334	−	0.0995119i	0.933587	−	0.358350i	$-0.116660\pi$
$821$	−0.926452	−	2.85133i	−0.0323334	−	0.0995119i	−0.965921	+	0.258838i	$0.916660\pi$
$822$	2.63269	+	8.10258i	0.0918255	+	0.282610i
$823$	−12.5371	−	9.10874i	−0.437016	−	0.317511i	0.347432	−	0.937705i	$-0.387054\pi$
$823$	−12.5371	−	9.10874i	−0.437016	−	0.317511i	−0.784448	+	0.620194i	$0.787054\pi$
$824$	−8.40195			−0.292696
$825$	−3.46912	−	5.14130i	−0.120779	−	0.178997i
$826$	−26.3388			−0.916444
$827$	7.81363	+	5.67693i	0.271706	+	0.197406i	0.715292	−	0.698826i	$-0.246294\pi$
$827$	7.81363	+	5.67693i	0.271706	+	0.197406i	−0.443585	+	0.896232i	$0.646294\pi$
$828$	−4.62310	−	14.2284i	−0.160664	−	0.494472i
$829$	−12.1381	−	37.3572i	−0.421573	−	1.29747i	−0.906238	−	0.422769i	$-0.861058\pi$
$829$	−12.1381	−	37.3572i	−0.421573	−	1.29747i	0.484664	−	0.874700i	$-0.338942\pi$
$830$	25.9480	+	13.7940i	0.900667	+	0.478795i
$831$	0.516352	−	1.58917i	0.0179121	−	0.0551277i
$832$	1.00000			0.0346688
$833$	−12.9527	+	39.8644i	−0.448785	+	1.38122i
$834$	−9.82007	+	7.13470i	−0.340041	+	0.247054i
$835$	−8.67485	+	1.21992i	−0.300205	+	0.0422170i
$836$	1.92332	+	1.39737i	0.0665193	+	0.0483291i
$837$	−4.43345	+	3.22109i	−0.153243	+	0.111337i
$838$	14.2703	−	10.3680i	0.492961	−	0.358157i
$839$	−4.04468	−	2.93863i	−0.139638	−	0.101453i	0.515773	−	0.856725i	$-0.327505\pi$
$839$	−4.04468	−	2.93863i	−0.139638	−	0.101453i	−0.655411	+	0.755272i	$0.727505\pi$
$840$	2.97353	+	6.09534i	0.102597	+	0.210309i
$841$	−61.6683	+	44.8046i	−2.12649	+	1.54499i
$842$	−9.11501	+	28.0531i	−0.314124	+	0.966774i
$843$	19.6563			0.676998
$844$	−3.66356	+	11.2753i	−0.126105	+	0.388111i
$845$	2.21428	−	0.311388i	0.0761736	−	0.0107121i
$846$	1.72150	+	5.29822i	0.0591862	+	0.182156i
$847$	10.5086	+	32.3423i	0.361081	+	1.11129i
$848$	−8.66086	−	6.29248i	−0.297415	−	0.216085i
$849$	−22.5440			−0.773708
$850$	−0.631908	+	18.1837i	−0.0216743	+	0.623696i
$851$	53.7159			1.84136
$852$	5.81385	+	4.22401i	0.199179	+	0.144712i
$853$	−10.5657	−	32.5179i	−0.361763	−	1.11339i	−0.951983	−	0.306150i	$-0.900959\pi$
$853$	−10.5657	−	32.5179i	−0.361763	−	1.11339i	0.590220	−	0.807243i	$-0.299041\pi$
$854$	−4.71047	−	14.4973i	−0.161189	−	0.496088i
$855$	−5.43838	+	5.25267i	−0.185989	+	0.179638i
$856$	3.25364	−	10.0137i	0.111207	−	0.342261i
$857$	6.43509			0.219818			0.109909	−	0.993942i	$-0.464944\pi$
$857$	6.43509			0.219818			0.109909	+	0.993942i	$0.464944\pi$
$858$	−0.383319	+	1.17974i	−0.0130863	+	0.0402755i
$859$	8.25211	−	5.99551i	0.281558	−	0.204564i	−0.438038	−	0.898956i	$-0.644327\pi$
$859$	8.25211	−	5.99551i	0.281558	−	0.204564i	0.719597	+	0.694392i	$0.244327\pi$
$860$	5.03441	−	4.86250i	0.171672	−	0.165810i
$861$	−24.4656	−	17.7753i	−0.833785	−	0.605780i
$862$	16.4818	−	11.9747i	0.561372	−	0.407860i
$863$	−1.49337	+	1.08500i	−0.0508351	+	0.0369338i	−0.612913	−	0.790151i	$-0.710002\pi$
$863$	−1.49337	+	1.08500i	−0.0508351	+	0.0369338i	0.562078	+	0.827085i	$0.310002\pi$
$864$	−3.13793	−	2.27984i	−0.106754	−	0.0775616i
$865$	5.12446	−	29.0766i	0.174237	−	0.988636i
$866$	7.80343	−	5.66952i	0.265171	−	0.192658i
$867$	0.818499	−	2.51908i	0.0277977	−	0.0855525i
$868$	−6.08002			−0.206369
$869$	−5.80617	+	17.8695i	−0.196961	+	0.606183i
$870$	7.08809	+	14.5296i	0.240309	+	0.492600i
$871$	2.94459	+	9.06251i	0.0997736	+	0.307071i
$872$	−2.39987	−	7.38605i	−0.0812700	−	0.250123i
$873$	−9.61421	−	6.98513i	−0.325392	−	0.236411i
$874$	−8.07282			−0.273067
$875$	47.0639	+	9.99126i	1.59105	+	0.337766i
$876$	−2.91137			−0.0983660
$877$	6.96467	+	5.06013i	0.235180	+	0.170868i	0.699133	−	0.714991i	$-0.253569\pi$
$877$	6.96467	+	5.06013i	0.235180	+	0.170868i	−0.463953	+	0.885860i	$0.653569\pi$
$878$	9.22237	+	28.3835i	0.311240	+	0.957898i
$879$	−4.22527	−	13.0040i	−0.142515	−	0.438616i
$880$	1.72550	+	3.53704i	0.0581667	+	0.119234i
$881$	−15.0273	+	46.2494i	−0.506284	+	1.55818i	0.292316	+	0.956322i	$0.405574\pi$
$881$	−15.0273	+	46.2494i	−0.506284	+	1.55818i	−0.798601	+	0.601861i	$0.794426\pi$
$882$	−28.8343			−0.970902
$883$	−0.410179	+	1.26240i	−0.0138036	+	0.0424832i	−0.957721	−	0.287698i	$-0.907110\pi$
$883$	−0.410179	+	1.26240i	−0.0138036	+	0.0424832i	0.943917	+	0.330181i	$0.107110\pi$
$884$	2.94396	−	2.13891i	0.0990162	−	0.0719395i
$885$	−1.67418	+	9.49945i	−0.0562770	+	0.319321i
$886$	−7.37368	−	5.35729i	−0.247724	−	0.179982i
$887$	1.82344	−	1.32481i	0.0612252	−	0.0444827i	−0.556752	−	0.830679i	$-0.687953\pi$
$887$	1.82344	−	1.32481i	0.0612252	−	0.0444827i	0.617977	+	0.786196i	$0.287953\pi$
$888$	5.12484	−	3.72342i	0.171979	−	0.124950i
$889$	19.7324	+	14.3365i	0.661805	+	0.480829i
$890$	21.4011	−	20.6703i	0.717368	−	0.692871i
$891$	−6.80053	+	4.94087i	−0.227826	+	0.165525i
$892$	2.02208	−	6.22333i	0.0677043	−	0.208372i
$893$	3.00606			0.100594
$894$	0.284815	−	0.876572i	0.00952565	−	0.0293169i
$895$	15.1732	−	14.6551i	0.507184	−	0.489865i
$896$	−1.32980	−	4.09272i	−0.0444256	−	0.136728i
$897$	−1.30164	−	4.00605i	−0.0434606	−	0.133758i
$898$	−9.59427	−	6.97065i	−0.320165	−	0.232613i
$899$	−14.4931			−0.483372
$900$	−12.0309	+	3.45199i	−0.401028	+	0.115066i
$901$	−38.9563			−1.29782
$902$	−14.1971	−	10.3148i	−0.472710	−	0.343444i
$903$	−2.93372	−	9.02905i	−0.0976280	−	0.300468i
$904$	−2.07297	−	6.37994i	−0.0689459	−	0.212194i
$905$	−27.4967	+	3.86679i	−0.914023	+	0.128536i
$906$	4.39742	−	13.5339i	0.146094	−	0.449632i
$907$	13.4734			0.447376			0.223688	−	0.974661i	$-0.428190\pi$
$907$	13.4734			0.447376			0.223688	+	0.974661i	$0.428190\pi$
$908$	0.500975	−	1.54184i	0.0166254	−	0.0511679i
$909$	−5.99593	+	4.35630i	−0.198873	+	0.144489i
$910$	−4.21898	−	8.64834i	−0.139858	−	0.286690i
$911$	−8.11231	−	5.89394i	−0.268773	−	0.195275i	0.445233	−	0.895415i	$-0.353121\pi$
$911$	−8.11231	−	5.89394i	−0.268773	−	0.195275i	−0.714006	+	0.700140i	$0.753121\pi$
$912$	−0.770199	+	0.559582i	−0.0255038	+	0.0185296i
$913$	18.7126	−	13.5955i	0.619297	−	0.449946i
$914$	0.376103	+	0.273255i	0.0124404	+	0.00903846i
$915$	−5.52807	+	0.777397i	−0.182752	+	0.0257000i
$916$	−0.264330	+	0.192047i	−0.00873372	+	0.00634542i
$917$	23.6275	−	72.7181i	0.780250	−	2.40136i
$918$	−14.1143			−0.465842
$919$	−3.92632	+	12.0840i	−0.129517	+	0.398614i	−0.994697	−	0.102848i	$-0.967204\pi$
$919$	−3.92632	+	12.0840i	−0.129517	+	0.398614i	0.865180	+	0.501462i	$0.167204\pi$
$920$	−11.8001	−	6.27292i	−0.389036	−	0.206812i
$921$	4.28774	+	13.1963i	0.141286	+	0.434834i
$922$	8.91970	+	27.4520i	0.293755	+	0.904084i
$923$	−8.24896	−	5.99322i	−0.271518	−	0.197269i
$924$	5.33806			0.175609
$925$	1.56076	−	44.9124i	0.0513175	−	1.47671i
$926$	−20.8016			−0.683583
$927$	−17.0154	−	12.3624i	−0.558861	−	0.406036i
$928$	−3.16989	−	9.75592i	−0.104057	−	0.320254i
$929$	2.55612	+	7.86694i	0.0838637	+	0.258106i	0.984192	−	0.177106i	$-0.0566735\pi$
$929$	2.55612	+	7.86694i	0.0838637	+	0.258106i	−0.900328	+	0.435212i	$0.856674\pi$
$930$	−0.386466	+	2.19284i	−0.0126727	+	0.0719062i
$931$	−4.80803	+	14.7976i	−0.157577	+	0.484971i
$932$	1.64136			0.0537646
$933$	−6.49250	+	19.9819i	−0.212555	+	0.654177i
$934$	6.68708	−	4.85845i	0.218808	−	0.158973i
$935$	12.6452	+	6.72223i	0.413544	+	0.219840i
$936$	2.02518	+	1.47138i	0.0661950	+	0.0480935i
$937$	18.6898	−	13.5790i	0.610570	−	0.443605i	−0.239045	−	0.971009i	$-0.576834\pi$
$937$	18.6898	−	13.5790i	0.610570	−	0.443605i	0.849615	+	0.527403i	$0.176834\pi$
$938$	33.1746	−	24.1027i	1.08319	−	0.786982i
$939$	5.75709	+	4.18277i	0.187875	+	0.136500i
$940$	4.39397	+	2.33584i	0.143316	+	0.0761867i
$941$	38.5272	−	27.9916i	1.25595	−	0.912501i	0.257399	−	0.966305i	$-0.417135\pi$
$941$	38.5272	−	27.9916i	1.25595	−	0.912501i	0.998552	+	0.0538038i	$0.0171346\pi$
$942$	−4.74971	+	14.6181i	−0.154754	+	0.476284i
$943$	59.5898			1.94051
$944$	1.89135	−	5.82099i	0.0615584	−	0.189457i
$945$	−6.47794	+	36.7564i	−0.210728	+	1.19569i
$946$	−1.70240	−	5.23944i	−0.0553497	−	0.170349i
$947$	13.6886	+	42.1293i	0.444821	+	1.36902i	0.882680	+	0.469975i	$0.155737\pi$
$947$	13.6886	+	42.1293i	0.444821	+	1.36902i	−0.437858	+	0.899044i	$0.644263\pi$
$948$	−6.08719	−	4.42260i	−0.197703	−	0.143639i
$949$	4.13078			0.134091
$950$	−0.234563	+	6.74976i	−0.00761022	+	0.218991i
$951$	23.7304			0.769512
$952$	−12.6689	−	9.20447i	−0.410600	−	0.298319i
$953$	4.42327	+	13.6134i	0.143284	+	0.440982i	0.996786	−	0.0801067i	$-0.0255261\pi$
$953$	4.42327	+	13.6134i	0.143284	+	0.440982i	−0.853503	+	0.521089i	$0.825526\pi$
$954$	−8.28116	−	25.4868i	−0.268113	−	0.825166i
$955$	−25.1716	−	13.3813i	−0.814535	−	0.433008i
$956$	−1.50034	+	4.61758i	−0.0485245	+	0.149343i
$957$	12.7245			0.411324
$958$	−0.888668	+	2.73504i	−0.0287116	+	0.0883651i
$959$	−42.0838	+	30.5757i	−1.35896	+	0.987340i
$960$	−1.56062	+	0.219466i	−0.0503689	+	0.00708323i
$961$	23.4646	+	17.0480i	0.756922	+	0.549936i
$962$	−7.27136	+	5.28295i	−0.234438	+	0.170329i
$963$	21.3231	−	15.4922i	0.687128	−	0.499228i
$964$	8.40132	+	6.10391i	0.270588	+	0.196594i
$965$	−3.97742	−	8.15316i	−0.128038	−	0.262460i
$966$	−14.6647	+	10.6545i	−0.471829	+	0.342804i
$967$	−14.0280	+	43.1739i	−0.451111	+	1.38838i	0.424529	+	0.905414i	$0.360440\pi$
$967$	−14.0280	+	43.1739i	−0.451111	+	1.38838i	−0.875640	+	0.482964i	$0.839560\pi$
$968$	−7.90239			−0.253993
$969$	−1.07054	+	3.29478i	−0.0343907	+	0.105844i
$970$	−10.5119	+	1.47826i	−0.337518	+	0.0474642i
$971$	−9.71113	−	29.8878i	−0.311645	−	0.959145i	−0.977113	−	0.212719i	$-0.931768\pi$
$971$	−9.71113	−	29.8878i	−0.311645	−	0.959145i	0.665468	−	0.746426i	$-0.268232\pi$
$972$	−4.63595	−	14.2680i	−0.148698	−	0.457646i
$973$	−59.9591	−	43.5628i	−1.92220	−	1.39656i
$974$	−9.66348			−0.309638
$975$	−3.38732	+	0.971918i	−0.108481	+	0.0311263i
$976$	3.54222			0.113384
$977$	−30.2630	−	21.9874i	−0.968199	−	0.703438i	−0.0131587	−	0.999913i	$-0.504189\pi$
$977$	−30.2630	−	21.9874i	−0.968199	−	0.703438i	−0.955040	+	0.296476i	$0.904189\pi$
$978$	2.48184	+	7.63832i	0.0793605	+	0.244246i
$979$	−7.23684	−	22.2727i	−0.231290	−	0.711838i
$980$	−18.5263	+	17.8936i	−0.591799	+	0.571591i
$981$	6.00750	−	18.4892i	0.191805	−	0.590315i
$982$	0.804434			0.0256705
$983$	−14.5824	+	44.8801i	−0.465107	+	1.43145i	0.393741	+	0.919222i	$0.371181\pi$
$983$	−14.5824	+	44.8801i	−0.465107	+	1.43145i	−0.858848	+	0.512231i	$0.828819\pi$
$984$	5.68526	−	4.13058i	0.181239	−	0.131678i
$985$	43.8738	−	42.3756i	1.39793	−	1.35020i
$986$	−30.1991	−	21.9409i	−0.961736	−	0.698742i
$987$	5.46067	−	3.96741i	0.173815	−	0.126284i
$988$	1.09279	−	0.793961i	0.0347664	−	0.0252593i
$989$	15.1345	+	10.9959i	0.481249	+	0.349648i
$990$	−1.70988	+	9.70201i	−0.0543435	+	0.308350i
$991$	17.2868	−	12.5596i	0.549132	−	0.398968i	−0.278333	−	0.960485i	$-0.589782\pi$
$991$	17.2868	−	12.5596i	0.549132	−	0.398968i	0.827465	+	0.561517i	$0.189782\pi$
$992$	0.436598	−	1.34371i	0.0138620	−	0.0426629i
$993$	−6.48613			−0.205831
$994$	−13.5590	+	41.7305i	−0.430067	+	1.32361i
$995$	2.60544	+	5.34080i	0.0825981	+	0.169315i
$996$	2.86227	+	8.80918i	0.0906947	+	0.279129i
$997$	5.45649	+	16.7933i	0.172809	+	0.531850i	0.999527	−	0.0307663i	$-0.00979476\pi$
$997$	5.45649	+	16.7933i	0.172809	+	0.531850i	−0.826718	+	0.562617i	$0.809795\pi$
$998$	16.2512	+	11.8072i	0.514423	+	0.373750i
$999$	34.8613			1.10296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.391.2	yes	24
25.11	even	5	inner	650.2.l.c.261.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.261.2	✓	24	25.11	even	5	inner
650.2.l.c.391.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.217795 - 0.670303i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.980398 + 2.00968i) q^{5} +(-0.217795 + 0.670303i) q^{6} -4.30334 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.02518 - 1.47138i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.217795 - 0.670303i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.980398 + 2.00968i) q^{5} +(-0.217795 + 0.670303i) q^{6} -4.30334 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.02518 - 1.47138i) q^{9} +(0.388103 - 2.20213i) q^{10} +(-1.42387 - 1.03450i) q^{11} +(0.570194 - 0.414270i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(3.48147 + 2.52944i) q^{14} +(1.13357 - 1.09486i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.12449 + 3.46084i) q^{17} -2.50326 q^{18} +(-0.417410 + 1.28466i) q^{19} +(-1.60836 + 1.55344i) q^{20} +(0.937244 + 2.88454i) q^{21} +(0.543870 + 1.67386i) q^{22} +(-4.83507 - 3.51288i) q^{23} -0.704799 q^{24} +(-3.07764 + 3.94057i) q^{25} +1.00000 q^{26} +(-3.13793 - 2.27984i) q^{27} +(-1.32980 - 4.09272i) q^{28} +(-3.16989 - 9.75592i) q^{29} +(-1.56062 + 0.219466i) q^{30} +(0.436598 - 1.34371i) q^{31} +1.00000 q^{32} +(-0.383319 + 1.17974i) q^{33} +(2.94396 - 2.13891i) q^{34} +(-4.21898 - 8.64834i) q^{35} +(2.02518 + 1.47138i) q^{36} +(-7.27136 + 5.28295i) q^{37} +(1.09279 - 0.793961i) q^{38} +(0.570194 + 0.414270i) q^{39} +(2.21428 - 0.311388i) q^{40} +(-8.06650 + 5.86066i) q^{41} +(0.937244 - 2.88454i) q^{42} -3.13015 q^{43} +(0.543870 - 1.67386i) q^{44} +(4.94248 + 2.62743i) q^{45} +(1.84683 + 5.68396i) q^{46} +(-0.687702 - 2.11653i) q^{47} +(0.570194 + 0.414270i) q^{48} +11.5187 q^{49} +(4.80608 - 1.37900i) q^{50} +2.56472 q^{51} +(-0.809017 - 0.587785i) q^{52} +(3.30815 + 10.1814i) q^{53} +(1.19858 + 3.68885i) q^{54} +(0.683062 - 3.87575i) q^{55} +(-1.32980 + 4.09272i) q^{56} +0.952018 q^{57} +(-3.16989 + 9.75592i) q^{58} +(-4.95163 + 3.59757i) q^{59} +(1.39157 + 0.739759i) q^{60} +(-2.86572 - 2.08207i) q^{61} +(-1.14303 + 0.830459i) q^{62} +(-8.71503 + 6.33184i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.97442 - 1.04960i) q^{65} +(1.00354 - 0.729116i) q^{66} +(2.94459 - 9.06251i) q^{67} -3.63894 q^{68} +(-1.30164 + 4.00605i) q^{69} +(-1.67014 + 9.47651i) q^{70} +(3.15082 + 9.69723i) q^{71} +(-0.773550 - 2.38074i) q^{72} +(-3.34187 - 2.42801i) q^{73} +8.98790 q^{74} +(3.31167 + 1.20472i) q^{75} -1.35077 q^{76} +(6.12740 + 4.45182i) q^{77} +(-0.217795 - 0.670303i) q^{78} +(-3.29896 - 10.1531i) q^{79} +(-1.97442 - 1.04960i) q^{80} +(1.47589 - 4.54232i) q^{81} +9.97074 q^{82} +(-4.06112 + 12.4989i) q^{83} +(-2.45374 + 1.78274i) q^{84} +(-8.05763 + 1.13312i) q^{85} +(2.53235 + 1.83986i) q^{86} +(-5.84904 + 4.24958i) q^{87} +(-1.42387 + 1.03450i) q^{88} +(10.7649 + 7.82117i) q^{89} +(-2.45419 - 5.03075i) q^{90} +(3.48147 - 2.52944i) q^{91} +(1.84683 - 5.68396i) q^{92} -0.995783 q^{93} +(-0.687702 + 2.11653i) q^{94} +(-2.99098 + 0.420612i) q^{95} +(-0.217795 - 0.670303i) q^{96} +(-1.46701 - 4.51499i) q^{97} +(-9.31884 - 6.77053i) q^{98} -4.40574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Introduction

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