LMFDB - Embedded newform 512.2.o.a.157.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			157.50
Character	$\chi$	$=$	512.157
Dual form			512.2.o.a.437.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07983 + 0.913223i) q^{2} +(2.64744 - 1.02123i) q^{3} +(0.332047 + 1.97224i) q^{4} +(1.55916 - 1.99788i) q^{5} +(3.79139 + 1.31495i) q^{6} +(-1.13754 + 3.17922i) q^{7} +(-1.44255 + 2.43291i) q^{8} +(3.74319 - 3.39263i) q^{9} +O(q^{10})$	\(q+(1.07983 + 0.913223i) q^{2} +(2.64744 - 1.02123i) q^{3} +(0.332047 + 1.97224i) q^{4} +(1.55916 - 1.99788i) q^{5} +(3.79139 + 1.31495i) q^{6} +(-1.13754 + 3.17922i) q^{7} +(-1.44255 + 2.43291i) q^{8} +(3.74319 - 3.39263i) q^{9} +(3.50813 - 0.733500i) q^{10} +(-0.780850 - 3.47728i) q^{11} +(2.89319 + 4.88231i) q^{12} +(-1.23502 + 0.341775i) q^{13} +(-4.13169 + 2.39417i) q^{14} +(2.08749 - 6.88153i) q^{15} +(-3.77949 + 1.30976i) q^{16} +(-4.92788 + 1.49486i) q^{17} +(7.14022 - 0.245081i) q^{18} +(-1.81402 - 3.60383i) q^{19} +(4.45802 + 2.41165i) q^{20} +(0.235139 + 9.57851i) q^{21} +(2.33235 - 4.46795i) q^{22} +(-4.93694 + 0.732326i) q^{23} +(-1.33449 + 7.91417i) q^{24} +(-0.345639 - 1.37987i) q^{25} +(-1.64572 - 0.758788i) q^{26} +(2.61780 - 5.20067i) q^{27} +(-6.64792 - 1.18786i) q^{28} +(1.64013 + 9.45233i) q^{29} +(8.53850 - 5.52451i) q^{30} +(3.11475 - 4.66155i) q^{31} +(-5.27729 - 2.03721i) q^{32} +(-5.61837 - 8.40848i) q^{33} +(-6.68639 - 2.88607i) q^{34} +(4.57809 + 7.22959i) q^{35} +(7.93401 + 6.25597i) q^{36} +(7.25401 - 6.25736i) q^{37} +(1.33228 - 5.54811i) q^{38} +(-2.92061 + 2.16607i) q^{39} +(2.61151 + 6.67533i) q^{40} +(1.23985 - 4.94977i) q^{41} +(-8.49340 + 10.5579i) q^{42} +(-1.05869 - 2.38837i) q^{43} +(6.59877 - 2.69465i) q^{44} +(-0.941831 - 12.7681i) q^{45} +(-5.99981 - 3.71774i) q^{46} +(5.56539 + 6.78145i) q^{47} +(-8.66842 + 7.32724i) q^{48} +(-3.40237 - 2.79226i) q^{49} +(0.886897 - 1.80566i) q^{50} +(-11.5197 + 8.99006i) q^{51} +(-1.08415 - 2.32227i) q^{52} +(-0.471829 + 2.71922i) q^{53} +(7.57613 - 3.22518i) q^{54} +(-8.16466 - 3.86159i) q^{55} +(-6.09381 - 7.35372i) q^{56} +(-8.48285 - 7.68840i) q^{57} +(-6.86103 + 11.7047i) q^{58} +(-1.37423 + 4.96583i) q^{59} +(14.2652 + 1.83205i) q^{60} +(10.0710 + 0.247228i) q^{61} +(7.62042 - 2.18920i) q^{62} +(6.52788 + 15.7597i) q^{63} +(-3.83813 - 7.01917i) q^{64} +(-1.24276 + 3.00030i) q^{65} +(1.61196 - 14.2105i) q^{66} +(9.21282 - 8.77134i) q^{67} +(-4.58451 - 9.22262i) q^{68} +(-12.3224 + 6.98055i) q^{69} +(-1.65869 + 11.9875i) q^{70} +(-10.4011 + 0.510975i) q^{71} +(2.85425 + 14.0009i) q^{72} +(0.933193 + 2.60810i) q^{73} +(13.5474 - 0.132321i) q^{74} +(-2.32422 - 3.30014i) q^{75} +(6.50529 - 4.77432i) q^{76} +(11.9433 + 1.47307i) q^{77} +(-5.13185 - 0.328188i) q^{78} +(-13.7660 + 1.35583i) q^{79} +(-3.27609 + 9.59308i) q^{80} +(0.133871 - 1.35921i) q^{81} +(5.85907 - 4.21263i) q^{82} +(3.43404 + 2.96223i) q^{83} +(-18.8131 + 3.64427i) q^{84} +(-4.69681 + 12.1760i) q^{85} +(1.03791 - 3.54584i) q^{86} +(13.9952 + 23.3496i) q^{87} +(9.58633 + 3.11640i) q^{88} +(-12.2004 - 1.80975i) q^{89} +(10.6431 - 14.6474i) q^{90} +(0.318307 - 4.31518i) q^{91} +(-3.08362 - 9.49368i) q^{92} +(3.48560 - 15.5221i) q^{93} +(-0.183323 + 12.4052i) q^{94} +(-10.0284 - 1.99476i) q^{95} +(-16.0518 - 0.00405885i) q^{96} +(2.96716 - 0.590205i) q^{97} +(-1.12402 - 6.12228i) q^{98} +(-14.7200 - 10.3670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{91}{128}\right)$	$1$

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 $

$2$	1.07983	+	0.913223i	0.763552	+	0.645746i
$2$	1.07983	+	0.913223i	0.763552	+	0.645746i
$3$	2.64744	−	1.02123i	1.52850	−	0.589608i	0.557817	−	0.829964i	$-0.311639\pi$
$3$	2.64744	−	1.02123i	1.52850	−	0.589608i	0.970685	+	0.240355i	$0.0772640\pi$
$4$	0.332047	+	1.97224i	0.166024	+	0.986122i
$5$	1.55916	−	1.99788i	0.697277	−	0.893478i	−0.300910	−	0.953652i	$-0.597291\pi$
$5$	1.55916	−	1.99788i	0.697277	−	0.893478i	0.998188	+	0.0601740i	$0.0191655\pi$
$6$	3.79139	+	1.31495i	1.54783	+	0.536828i
$7$	−1.13754	+	3.17922i	−0.429951	+	1.20163i	0.509955	+	0.860201i	$0.329662\pi$
$7$	−1.13754	+	3.17922i	−0.429951	+	1.20163i	−0.939906	+	0.341432i	$0.889088\pi$
$8$	−1.44255	+	2.43291i	−0.510017	+	0.860164i
$9$	3.74319	−	3.39263i	1.24773	−	1.13088i
$10$	3.50813	−	0.733500i	1.10937	−	0.231953i
$11$	−0.780850	−	3.47728i	−0.235435	−	1.04844i	−0.940632	−	0.339428i	$-0.889766\pi$
$11$	−0.780850	−	3.47728i	−0.235435	−	1.04844i	0.705197	−	0.709012i	$-0.250859\pi$
$12$	2.89319	+	4.88231i	0.835193	+	1.40940i
$13$	−1.23502	+	0.341775i	−0.342532	+	0.0947914i	−0.433734	−	0.901041i	$-0.642804\pi$
$13$	−1.23502	+	0.341775i	−0.342532	+	0.0947914i	0.0912017	+	0.995832i	$0.470929\pi$
$14$	−4.13169	+	2.39417i	−1.10424	+	0.639870i
$15$	2.08749	−	6.88153i	0.538988	−	1.77680i
$16$	−3.77949	+	1.30976i	−0.944872	+	0.327439i
$17$	−4.92788	+	1.49486i	−1.19519	+	0.362556i	−0.824317	−	0.566129i	$-0.808440\pi$
$17$	−4.92788	+	1.49486i	−1.19519	+	0.362556i	−0.370870	+	0.928685i	$0.620940\pi$
$18$	7.14022	−	0.245081i	1.68297	−	0.0577662i
$19$	−1.81402	−	3.60383i	−0.416164	−	0.826775i	−0.999890	−	0.0148247i	$-0.995281\pi$
$19$	−1.81402	−	3.60383i	−0.416164	−	0.826775i	0.583727	−	0.811950i	$-0.301594\pi$
$20$	4.45802	+	2.41165i	0.996843	+	0.539262i
$21$	0.235139	+	9.57851i	0.0513116	+	2.09020i
$22$	2.33235	−	4.46795i	0.497259	−	0.952570i
$23$	−4.93694	+	0.732326i	−1.02942	+	0.152700i	−0.640013	−	0.768364i	$-0.721071\pi$
$23$	−4.93694	+	0.732326i	−1.02942	+	0.152700i	−0.389410	+	0.921065i	$0.627321\pi$
$24$	−1.33449	+	7.91417i	−0.272401	+	1.61547i
$25$	−0.345639	−	1.37987i	−0.0691277	−	0.275973i
$26$	−1.64572	−	0.758788i	−0.322752	−	0.148811i
$27$	2.61780	−	5.20067i	0.503795	−	1.00087i
$28$	−6.64792	−	1.18786i	−1.25634	−	0.224485i
$29$	1.64013	+	9.45233i	0.304565	+	1.75525i	0.600103	+	0.799923i	$0.295126\pi$
$29$	1.64013	+	9.45233i	0.304565	+	1.75525i	−0.295538	+	0.955331i	$0.595499\pi$
$30$	8.53850	−	5.52451i	1.55891	−	1.00863i
$31$	3.11475	−	4.66155i	0.559425	−	0.837239i	−0.438688	−	0.898639i	$-0.644557\pi$
$31$	3.11475	−	4.66155i	0.559425	−	0.837239i	0.998113	+	0.0614005i	$0.0195567\pi$
$32$	−5.27729	−	2.03721i	−0.932902	−	0.360131i
$33$	−5.61837	−	8.40848i	−0.978032	−	1.46373i
$34$	−6.68639	−	2.88607i	−1.14671	−	0.494957i
$35$	4.57809	+	7.22959i	0.773838	+	1.22202i
$36$	7.93401	+	6.25597i	1.32233	+	1.04266i
$37$	7.25401	−	6.25736i	1.19255	−	1.02870i	0.193688	−	0.981063i	$-0.437955\pi$
$37$	7.25401	−	6.25736i	1.19255	−	1.02870i	0.998865	−	0.0476397i	$-0.0151699\pi$
$38$	1.33228	−	5.54811i	0.216124	−	0.900022i
$39$	−2.92061	+	2.16607i	−0.467671	+	0.346849i
$40$	2.61151	+	6.67533i	0.412915	+	1.05546i
$41$	1.23985	−	4.94977i	0.193632	−	0.773024i	−0.792885	−	0.609371i	$-0.791422\pi$
$41$	1.23985	−	4.94977i	0.193632	−	0.773024i	0.986518	−	0.163653i	$-0.0523279\pi$
$42$	−8.49340	+	10.5579i	−1.31056	+	1.62911i
$43$	−1.05869	−	2.38837i	−0.161449	−	0.364223i	0.815163	−	0.579231i	$-0.196647\pi$
$43$	−1.05869	−	2.38837i	−0.161449	−	0.364223i	−0.976612	+	0.215008i	$0.931022\pi$
$44$	6.59877	−	2.69465i	0.994802	−	0.406233i
$45$	−0.941831	−	12.7681i	−0.140400	−	1.90335i
$46$	−5.99981	−	3.71774i	−0.884624	−	0.548151i
$47$	5.56539	+	6.78145i	0.811796	+	0.989176i	0.999975	+	0.00704122i	$0.00224131\pi$
$47$	5.56539	+	6.78145i	0.811796	+	0.989176i	−0.188180	+	0.982135i	$0.560259\pi$
$48$	−8.66842	+	7.32724i	−1.25118	+	1.05760i
$49$	−3.40237	−	2.79226i	−0.486053	−	0.398894i
$50$	0.886897	−	1.80566i	0.125426	−	0.255359i
$51$	−11.5197	+	8.99006i	−1.61308	+	1.25886i
$52$	−1.08415	−	2.32227i	−0.150344	−	0.322041i
$53$	−0.471829	+	2.71922i	−0.0648107	+	0.373514i	0.935011	+	0.354619i	$0.115390\pi$
$53$	−0.471829	+	2.71922i	−0.0648107	+	0.373514i	−0.999821	+	0.0188942i	$0.993985\pi$
$54$	7.57613	−	3.22518i	1.03098	−	0.438892i
$55$	−8.16466	−	3.86159i	−1.10092	−	0.520697i
$56$	−6.09381	−	7.35372i	−0.814320	−	0.982682i
$57$	−8.48285	−	7.68840i	−1.12358	−	1.01835i
$58$	−6.86103	+	11.7047i	−0.900897	+	1.53690i
$59$	−1.37423	+	4.96583i	−0.178910	+	0.646496i	0.818496	+	0.574512i	$0.194808\pi$
$59$	−1.37423	+	4.96583i	−0.178910	+	0.646496i	−0.997406	+	0.0719841i	$0.977067\pi$
$60$	14.2652	+	1.83205i	1.84163	+	0.236516i
$61$	10.0710	+	0.247228i	1.28945	+	0.0316543i	0.663483	−	0.748192i	$-0.269078\pi$
$61$	10.0710	+	0.247228i	1.28945	+	0.0316543i	0.625972	+	0.779846i	$0.284703\pi$
$62$	7.62042	−	2.18920i	0.967794	−	0.278029i
$63$	6.52788	+	15.7597i	0.822436	+	1.98554i
$64$	−3.83813	−	7.01917i	−0.479766	−	0.877397i
$65$	−1.24276	+	3.00030i	−0.154146	+	0.372141i
$66$	1.61196	−	14.2105i	0.198419	−	1.74919i
$67$	9.21282	−	8.77134i	1.12553	−	1.07159i	0.128723	−	0.991681i	$-0.458912\pi$
$67$	9.21282	−	8.77134i	1.12553	−	1.07159i	0.996802	−	0.0799086i	$-0.0254628\pi$
$68$	−4.58451	−	9.22262i	−0.555954	−	1.11841i
$69$	−12.3224	+	6.98055i	−1.48344	+	0.840359i
$70$	−1.65869	+	11.9875i	−0.198252	+	1.43278i
$71$	−10.4011	+	0.510975i	−1.23439	+	0.0606415i	−0.655772	−	0.754959i	$-0.727657\pi$
$71$	−10.4011	+	0.510975i	−1.23439	+	0.0606415i	−0.578615	+	0.815601i	$0.696407\pi$
$72$	2.85425	+	14.0009i	0.336377	+	1.65002i
$73$	0.933193	+	2.60810i	0.109222	+	0.305255i	0.983702	−	0.179807i	$-0.0575472\pi$
$73$	0.933193	+	2.60810i	0.109222	+	0.305255i	−0.874480	+	0.485062i	$0.838797\pi$
$74$	13.5474	−	0.132321i	1.57486	−	0.0153820i
$75$	−2.32422	−	3.30014i	−0.268378	−	0.381068i
$76$	6.50529	−	4.77432i	0.746208	−	0.547652i
$77$	11.9433	+	1.47307i	1.36107	+	0.167871i
$78$	−5.13185	−	0.328188i	−0.581068	−	0.0371599i
$79$	−13.7660	+	1.35583i	−1.54879	+	0.152543i	−0.835960	−	0.548790i	$-0.815089\pi$
$79$	−13.7660	+	1.35583i	−1.54879	+	0.152543i	−0.712834	+	0.701333i	$0.752589\pi$
$80$	−3.27609	+	9.59308i	−0.366278	+	1.07254i
$81$	0.133871	−	1.35921i	0.0148745	−	0.151024i
$82$	5.85907	−	4.21263i	0.647026	−	0.465207i
$83$	3.43404	+	2.96223i	0.376935	+	0.325147i	0.821085	−	0.570806i	$-0.193369\pi$
$83$	3.43404	+	2.96223i	0.376935	+	0.325147i	−0.444150	+	0.895953i	$0.646494\pi$
$84$	−18.8131	+	3.64427i	−2.05267	+	0.397622i
$85$	−4.69681	+	12.1760i	−0.509441	+	1.32068i
$86$	1.03791	−	3.54584i	0.111921	−	0.382358i
$87$	13.9952	+	23.3496i	1.50044	+	2.50333i
$88$	9.58633	+	3.11640i	1.02191	+	0.332209i
$89$	−12.2004	−	1.80975i	−1.29324	−	0.191833i	−0.535578	−	0.844485i	$-0.679906\pi$
$89$	−12.2004	−	1.80975i	−1.29324	−	0.191833i	−0.757658	+	0.652652i	$0.773656\pi$
$90$	10.6431	−	14.6474i	1.12188	−	1.54397i
$91$	0.318307	−	4.31518i	0.0333676	−	0.452354i
$92$	−3.08362	−	9.49368i	−0.321490	−	0.989784i
$93$	3.48560	−	15.5221i	0.361440	−	1.60956i
$94$	−0.183323	+	12.4052i	−0.0189083	+	1.27950i
$95$	−10.0284	−	1.99476i	−1.02889	−	0.204658i
$96$	−16.0518	−	0.00405885i	−1.63828	−	0.000414255i
$97$	2.96716	−	0.590205i	0.301270	−	0.0599263i	−0.0421408	−	0.999112i	$-0.513418\pi$
$97$	2.96716	−	0.590205i	0.301270	−	0.0599263i	0.343410	+	0.939185i	$0.388418\pi$
$98$	−1.12402	−	6.12228i	−0.113543	−	0.618443i
$99$	−14.7200	−	10.3670i	−1.47942	−	1.04192i
$100$	2.60667	−	1.13986i	0.260667	−	0.113986i
$101$	3.65024	−	1.20588i	0.363213	−	0.119989i	−0.126285	−	0.991994i	$-0.540305\pi$
$101$	3.65024	−	1.20588i	0.363213	−	0.119989i	0.489497	+	0.872005i	$0.337180\pi$
$102$	−20.6492	−	0.812355i	−2.04457	−	0.0804351i
$103$	−1.36931	−	0.820732i	−0.134922	−	0.0808692i	0.445049	−	0.895506i	$-0.353186\pi$
$103$	−1.36931	−	0.820732i	−0.134922	−	0.0808692i	−0.579971	+	0.814637i	$0.696936\pi$
$104$	0.950059	−	3.49772i	0.0931609	−	0.342979i
$105$	19.5033	+	14.4646i	1.90333	+	1.41160i
$106$	−2.99275	+	2.50540i	−0.290681	+	0.243346i
$107$	−7.86518	−	7.48827i	−0.760356	−	0.723919i	0.206722	−	0.978400i	$-0.433720\pi$
$107$	−7.86518	−	7.48827i	−0.760356	−	0.723919i	−0.967078	+	0.254481i	$0.918095\pi$
$108$	11.1262	+	3.43606i	1.07062	+	0.330635i
$109$	0.386037	−	1.16855i	0.0369756	−	0.111927i	−0.929390	−	0.369100i	$-0.879666\pi$
$109$	0.386037	−	1.16855i	0.0369756	−	0.111927i	0.966365	+	0.257173i	$0.0827910\pi$
$110$	−5.28991	−	11.6260i	−0.504373	−	1.10850i
$111$	12.8144	−	23.9740i	1.21629	−	2.27551i
$112$	0.135329	−	13.5057i	0.0127874	−	1.27617i
$113$	10.8333	−	5.79052i	1.01911	−	0.544726i	0.124805	−	0.992181i	$-0.460170\pi$
$113$	10.8333	−	5.79052i	1.01911	−	0.544726i	0.894306	+	0.447455i	$0.147670\pi$
$114$	−2.13877	−	16.0489i	−0.200314	−	1.50311i
$115$	−6.23438	+	11.0052i	−0.581359	+	1.02624i
$116$	−18.0977	+	6.37337i	−1.68033	+	0.591752i
$117$	−3.46339	+	5.46929i	−0.320190	+	0.505636i
$118$	−6.01884	+	4.10725i	−0.554079	+	0.378103i
$119$	0.853201	−	17.3673i	0.0782128	−	1.59206i
$120$	13.7309	+	15.0056i	1.25345	+	1.36982i
$121$	−1.53788	+	0.727363i	−0.139807	+	0.0661239i
$122$	10.6491	+	9.46400i	0.964125	+	0.856830i
$123$	−1.77242	−	14.3704i	−0.159814	−	1.29574i
$124$	10.2280	+	4.59519i	0.918497	+	0.412660i
$125$	8.28853	+	3.67405i	0.741349	+	0.328617i
$126$	−7.34315	+	22.9791i	−0.654179	+	2.04714i
$127$	−0.00974942	+	0.00974942i	−0.000865121	+	0.000865121i	−0.707539	−	0.706674i	$-0.750195\pi$
$127$	−0.00974942	+	0.00974942i	−0.000865121	+	0.000865121i	0.706674	+	0.707539i	$0.250195\pi$
$128$	2.26556	−	11.0845i	0.200249	−	0.979745i
$129$	−5.24190	−	5.24190i	−0.461524	−	0.461524i
$130$	−4.08191	+	2.10488i	−0.358007	+	0.184610i
$131$	−8.80326	+	19.8598i	−0.769144	+	1.73516i	−0.0963299	+	0.995349i	$0.530710\pi$
$131$	−8.80326	+	19.8598i	−0.769144	+	1.73516i	−0.672814	+	0.739812i	$0.734915\pi$
$132$	14.7180	−	13.8728i	1.28104	−	1.20747i
$133$	13.5209	−	1.66764i	1.17241	−	0.144603i
$134$	17.9584	−	1.05815i	1.55137	−	0.0914105i
$135$	−6.30874	−	13.3387i	−0.542970	−	1.14801i
$136$	3.47184	−	14.1455i	0.297708	−	1.21297i
$137$	12.5109	+	0.614622i	1.06888	+	0.0525107i	0.575892	−	0.817526i	$-0.304655\pi$
$137$	12.5109	+	0.614622i	1.06888	+	0.0525107i	0.492987	+	0.870036i	$0.335905\pi$
$138$	−19.6808	−	3.71532i	−1.67534	−	0.316269i
$139$	−5.86796	−	3.71584i	−0.497714	−	0.315174i	0.262405	−	0.964958i	$-0.415484\pi$
$139$	−5.86796	−	3.71584i	−0.497714	−	0.315174i	−0.760119	+	0.649784i	$0.774859\pi$
$140$	−12.7384	+	11.4297i	−1.07659	+	0.965983i
$141$	21.6595	+	12.2699i	1.82406	+	1.03332i
$142$	−11.6980	−	8.94678i	−0.981678	−	0.750798i
$143$	2.15281	+	4.02763i	0.180027	+	0.336807i
$144$	−9.70383	+	17.7251i	−0.808652	+	1.47709i
$145$	21.4418	+	11.4609i	1.78065	+	0.951776i
$146$	−1.37409	+	3.66851i	−0.113721	+	0.303608i
$147$	−11.8591	−	3.91773i	−0.978125	−	0.323129i
$148$	14.7497	+	12.2289i	1.21242	+	1.00521i
$149$	−13.6705	+	14.3585i	−1.11993	+	1.17630i	−0.137334	+	0.990525i	$0.543853\pi$
$149$	−13.6705	+	14.3585i	−1.11993	+	1.17630i	−0.982593	+	0.185772i	$0.940522\pi$
$150$	0.504011	−	5.68611i	0.0411523	−	0.464269i
$151$	1.37554	−	1.85470i	0.111940	−	0.150933i	−0.743684	−	0.668531i	$-0.766923\pi$
$151$	1.37554	−	1.85470i	0.111940	−	0.150933i	0.855624	+	0.517597i	$0.173173\pi$
$152$	11.3846	+	0.785346i	0.923413	+	0.0636999i
$153$	−13.3745	+	22.3140i	−1.08126	+	1.80398i
$154$	11.5514	+	12.4976i	0.930842	+	1.00708i
$155$	−4.45682	−	13.4910i	−0.357980	−	1.08362i
$156$	−5.24180	−	5.04091i	−0.419680	−	0.403596i
$157$	5.65071	−	8.02340i	0.450976	−	0.640337i	−0.526800	−	0.849989i	$-0.676608\pi$
$157$	5.65071	−	8.02340i	0.450976	−	0.640337i	0.977776	+	0.209653i	$0.0672333\pi$
$158$	−16.1030	−	11.1074i	−1.28109	−	0.883653i
$159$	1.52781	+	7.68083i	0.121163	+	0.609129i
$160$	−12.2982	+	7.36705i	−0.972261	+	0.582416i
$161$	3.28776	−	16.5287i	0.259112	−	1.30264i
$162$	1.38582	−	1.34546i	0.108880	−	0.105709i
$163$	−2.23606	−	0.502124i	−0.175142	−	0.0393294i	0.130646	−	0.991429i	$-0.458295\pi$
$163$	−2.23606	−	0.502124i	−0.175142	−	0.0393294i	−0.305788	+	0.952100i	$0.598920\pi$
$164$	10.1738	+	0.801734i	0.794443	+	0.0626049i
$165$	−25.5590	−	1.88535i	−1.98977	−	0.146774i
$166$	1.00300	+	6.33474i	0.0778475	+	0.491671i
$167$	2.02960	−	13.6824i	0.157055	−	1.05878i	−0.757066	−	0.653338i	$-0.773368\pi$
$167$	2.02960	−	13.6824i	0.157055	−	1.05878i	0.914121	−	0.405441i	$-0.132882\pi$
$168$	−23.6429	−	13.2454i	−1.82409	−	1.02190i
$169$	−9.74201	+	5.83914i	−0.749386	+	0.449165i
$170$	−16.1912	+	8.85875i	−1.24181	+	0.679435i
$171$	−19.0167	−	7.33553i	−1.45424	−	0.560962i
$172$	4.35891	−	2.88105i	0.332364	−	0.219678i
$173$	−4.57643	+	5.30536i	−0.347940	+	0.403359i	−0.903826	−	0.427899i	$-0.859254\pi$
$173$	−4.57643	+	5.30536i	−0.347940	+	0.403359i	0.555887	+	0.831258i	$0.312379\pi$
$174$	−6.21099	+	37.9942i	−0.470854	+	2.88033i
$175$	4.78008	+	0.470797i	0.361340	+	0.0355889i
$176$	7.50560	+	12.1196i	0.565756	+	0.913551i
$177$	1.43307	+	14.5502i	0.107716	+	1.09366i
$178$	−11.5216	−	13.0959i	−0.863578	−	0.981577i
$179$	3.22794	−	26.1714i	0.241268	−	1.95615i	−0.0478575	−	0.998854i	$-0.515239\pi$
$179$	3.22794	−	26.1714i	0.241268	−	1.95615i	0.289125	−	0.957291i	$-0.406636\pi$
$180$	24.8690	−	6.09713i	1.85363	−	0.454453i
$181$	3.71513	−	2.61649i	0.276143	−	0.194482i	−0.429466	−	0.903083i	$-0.641298\pi$
$181$	3.71513	−	2.61649i	0.276143	−	0.194482i	0.705609	+	0.708601i	$0.250673\pi$
$182$	4.28444	−	4.36896i	0.317584	−	0.323849i
$183$	26.9148	−	9.63026i	1.98960	−	0.711889i
$184$	5.34007	−	13.0676i	0.393675	−	0.963353i
$185$	−1.19127	−	24.2489i	−0.0875839	−	1.78281i
$186$	17.9389	−	13.5780i	1.31535	−	0.995587i
$187$	9.04597	+	15.9684i	0.661507	+	1.16772i
$188$	−11.5267	+	13.2281i	−0.840671	+	0.964756i
$189$	13.5562	+	14.2385i	0.986070	+	1.03570i
$190$	−9.00721	−	11.3121i	−0.653452	−	0.820667i
$191$	14.6967	+	6.08755i	1.06341	+	0.440480i	0.844661	−	0.535301i	$-0.179802\pi$
$191$	14.6967	+	6.08755i	1.06341	+	0.440480i	0.218751	+	0.975781i	$0.429802\pi$
$192$	−17.3294	−	14.6632i	−1.25064	−	1.05823i
$193$	19.7093	−	8.16387i	1.41871	−	0.587648i	0.464172	−	0.885745i	$-0.346352\pi$
$193$	19.7093	−	8.16387i	1.41871	−	0.587648i	0.954536	+	0.298097i	$0.0963519\pi$
$194$	3.74301	+	2.07236i	0.268732	+	0.148787i
$195$	−0.226148	+	9.21226i	−0.0161948	+	0.659704i
$196$	4.37726	−	7.63747i	0.312661	−	0.545534i
$197$	−12.6015	−	3.48732i	−0.897823	−	0.248461i	−0.212898	−	0.977074i	$-0.568290\pi$
$197$	−12.6015	−	3.48732i	−0.897823	−	0.248461i	−0.684925	+	0.728613i	$0.740165\pi$
$198$	−6.42766	−	24.6372i	−0.456794	−	1.75089i
$199$	−5.94531	+	6.55964i	−0.421452	+	0.465001i	−0.914254	−	0.405141i	$-0.867223\pi$
$199$	−5.94531	+	6.55964i	−0.421452	+	0.465001i	0.492802	+	0.870141i	$0.335973\pi$
$200$	3.85570	+	1.14961i	0.272639	+	0.0812898i
$201$	15.4329	−	32.6300i	1.08855	−	2.30155i
$202$	5.04286	+	2.03135i	0.354814	+	0.142925i
$203$	−31.9168	−	5.53809i	−2.24012	−	0.388698i
$204$	−21.5557	−	19.7345i	−1.50920	−	1.38169i
$205$	−7.95591	−	10.1946i	−0.555665	−	0.712019i
$206$	−0.729104	−	2.13673i	−0.0507991	−	0.148873i
$207$	−15.9954	+	19.4904i	−1.11176	+	1.35468i
$208$	4.22009	−	2.90931i	0.292611	−	0.201724i
$209$	−11.1151	+	9.12189i	−0.768844	+	0.630974i
$210$	7.85073	+	33.4302i	0.541752	+	2.30690i
$211$	10.5917	−	0.781293i	0.729164	−	0.0537864i	0.296110	−	0.955154i	$-0.404311\pi$
$211$	10.5917	−	0.781293i	0.729164	−	0.0537864i	0.433055	+	0.901368i	$0.357436\pi$
$212$	−5.51963	−	0.0276529i	−0.379090	−	0.00189921i
$213$	−27.0146	+	11.9747i	−1.85101	+	0.820495i
$214$	−1.65456	−	15.2687i	−0.113103	−	1.04375i
$215$	−6.42234	−	1.60871i	−0.438000	−	0.109713i
$216$	8.87648	+	13.8711i	0.603968	+	0.943806i
$217$	11.2769	+	15.2052i	0.765528	+	1.03220i
$218$	1.48400	−	0.909292i	0.100509	−	0.0615851i
$219$	5.13405	+	5.95179i	0.346927	+	0.402185i
$220$	4.90495	−	17.3849i	0.330692	−	1.17209i
$221$	5.57511	−	3.53040i	0.375023	−	0.237481i
$222$	35.7309	−	14.1854i	2.39810	−	0.952060i
$223$	−10.6629	+	7.12472i	−0.714040	+	0.477107i	−0.858768	−	0.512365i	$-0.828770\pi$
$223$	−10.6629	+	7.12472i	−0.714040	+	0.477107i	0.144727	+	0.989472i	$0.453770\pi$
$224$	12.4799	−	14.4603i	0.833847	−	0.966167i
$225$	−5.97517	−	3.99248i	−0.398345	−	0.266165i
$226$	16.9861	+	3.64047i	1.12990	+	0.242160i
$227$	0.491407	−	0.0852672i	0.0326158	−	0.00565938i	−0.154631	−	0.987972i	$-0.549419\pi$
$227$	0.491407	−	0.0852672i	0.0326158	−	0.00565938i	0.187246	+	0.982313i	$0.440044\pi$
$228$	12.3467	−	19.2832i	0.817680	−	1.27706i
$229$	−6.38274	−	3.21280i	−0.421783	−	0.212308i	0.226008	−	0.974125i	$-0.427432\pi$
$229$	−6.38274	−	3.21280i	−0.421783	−	0.212308i	−0.647792	+	0.761817i	$0.724307\pi$
$230$	−16.7823	+	6.19034i	−1.10659	+	0.408179i
$231$	33.1236	−	8.29702i	2.17937	−	0.545904i
$232$	−25.3627	−	9.64511i	−1.66514	−	0.633232i
$233$	−1.73624	−	11.7048i	−0.113745	−	0.766807i	−0.968723	−	0.248143i	$-0.920180\pi$
$233$	−1.73624	−	11.7048i	−0.113745	−	0.766807i	0.854978	−	0.518664i	$-0.173570\pi$
$234$	−8.73453	+	2.74303i	−0.570994	+	0.179318i
$235$	22.2258	−	0.545614i	1.44985	−	0.0355919i
$236$	−10.2501	−	1.06143i	−0.667227	−	0.0690930i
$237$	−35.0600	+	17.6477i	−2.27739	+	1.14634i
$238$	16.7815	−	17.9745i	1.08778	−	1.16511i
$239$	6.51192	+	21.4669i	0.421221	+	1.38858i	0.869167	+	0.494520i	$0.164656\pi$
$239$	6.51192	+	21.4669i	0.421221	+	1.38858i	−0.447945	+	0.894061i	$0.647844\pi$
$240$	1.12348	+	28.7428i	0.0725206	+	1.85534i
$241$	22.4903	+	6.82237i	1.44873	+	0.439467i	0.914055	−	0.405590i	$-0.132934\pi$
$241$	22.4903	+	6.82237i	1.44873	+	0.439467i	0.534675	+	0.845058i	$0.320434\pi$
$242$	−2.32489	−	0.619002i	−0.149449	−	0.0397909i
$243$	3.62503	+	13.0992i	0.232546	+	0.840313i
$244$	2.85644	+	19.9445i	0.182865	+	1.27681i
$245$	−10.8834	+	2.44396i	−0.695317	+	0.156139i
$246$	11.2095	−	17.1362i	0.714691	−	1.09256i
$247$	3.47204	+	3.83081i	0.220921	+	0.243748i
$248$	6.84798	+	14.3024i	0.434847	+	0.908203i
$249$	12.1166	+	4.33537i	0.767856	+	0.274743i
$250$	5.59494	+	11.5366i	0.353855	+	0.729640i
$251$	−11.6003	−	9.05300i	−0.732207	−	0.571420i	0.178763	−	0.983892i	$-0.442791\pi$
$251$	−11.6003	−	9.05300i	−0.732207	−	0.571420i	−0.910970	+	0.412472i	$0.864666\pi$
$252$	−28.9144	+	18.1075i	−1.82144	+	1.14067i
$253$	6.40151	+	16.5953i	0.402459	+	1.04334i
$254$	−0.0194311	+	0.00162428i	−0.00121921	+	0.000101916i
$255$			37.0319i			2.31903i
$256$	12.5691	−	9.90042i	0.785567	−	0.618776i
$257$		−	0.661570i		−	0.0412676i	−0.999787	−	0.0206338i	$-0.993432\pi$
$257$		−	0.661570i		−	0.0412676i	0.999787	−	0.0206338i	$-0.00656841\pi$
$258$	−0.873315	−	10.4474i	−0.0543702	−	0.650425i
$259$	11.6418	+	30.1801i	0.723384	+	1.87530i
$260$	−6.32997	−	1.45479i	−0.392568	−	0.0902224i
$261$	38.2076	+	29.8175i	2.36499	+	1.84566i
$262$	−27.6424	+	13.4058i	−1.70776	+	0.828214i
$263$	8.47826	+	3.03357i	0.522792	+	0.187058i	0.585043	−	0.811003i	$-0.301078\pi$
$263$	8.47826	+	3.03357i	0.522792	+	0.187058i	−0.0622506	+	0.998061i	$0.519828\pi$
$264$	28.5618	−	1.53938i	1.75786	−	0.0947425i
$265$	4.69701	+	5.18236i	0.288535	+	0.318350i
$266$	16.1231	+	10.5468i	0.988573	+	0.646668i
$267$	−34.1480	+	7.66818i	−2.08982	+	0.469285i
$268$	20.3583	+	15.2574i	1.24358	+	0.931996i
$269$	8.20805	+	29.6601i	0.500453	+	1.80841i	0.583815	+	0.811887i	$0.301559\pi$
$269$	8.20805	+	29.6601i	0.500453	+	1.80841i	−0.0833615	+	0.996519i	$0.526566\pi$
$270$	5.36888	−	20.1648i	0.326739	−	1.22719i
$271$	−16.1207	−	4.89016i	−0.979263	−	0.297056i	−0.240223	−	0.970718i	$-0.577221\pi$
$271$	−16.1207	−	4.89016i	−0.979263	−	0.297056i	−0.739040	+	0.673662i	$0.764721\pi$
$272$	16.6670	−	12.1041i	1.01058	−	0.733920i
$273$	−3.56410	−	11.7493i	−0.215709	−	0.711097i
$274$	12.9483	+	12.0889i	0.782236	+	0.730319i
$275$	−4.52829	+	2.27935i	−0.273066	+	0.137450i
$276$	−17.8590	−	21.9849i	−1.07498	−	1.32333i
$277$	5.86501	−	0.143978i	0.352394	−	0.00865079i	0.152040	−	0.988374i	$-0.451416\pi$
$277$	5.86501	−	0.143978i	0.352394	−	0.00865079i	0.200354	+	0.979724i	$0.435791\pi$
$278$	−2.94298	−	9.37122i	−0.176508	−	0.562048i
$279$	−4.15582	−	28.0162i	−0.248802	−	1.67729i
$280$	−24.1931	+	0.709077i	−1.44581	+	0.0423754i
$281$	14.7470	−	3.69394i	0.879735	−	0.220362i	0.223305	−	0.974749i	$-0.428316\pi$
$281$	14.7470	−	3.69394i	0.879735	−	0.220362i	0.656431	+	0.754386i	$0.272066\pi$
$282$	12.1833	+	33.0293i	0.725503	+	1.96687i
$283$	8.03464	+	4.04430i	0.477609	+	0.240408i	0.672050	−	0.740506i	$-0.265414\pi$
$283$	8.03464	+	4.04430i	0.477609	+	0.240408i	−0.194440	+	0.980914i	$0.562289\pi$
$284$	−4.46143	−	20.3439i	−0.264737	−	1.20719i
$285$	−28.5866	+	4.96025i	−1.69332	+	0.293820i
$286$	−1.35346	+	6.31513i	−0.0800318	+	0.373422i
$287$	14.3260	+	9.57235i	0.845639	+	0.565038i
$288$	−26.6654	+	10.2782i	−1.57127	+	0.605651i
$289$	7.91444	−	5.28826i	0.465555	−	0.311074i
$290$	12.6871	+	31.9570i	0.745012	+	1.87658i
$291$	7.25266	−	4.59269i	0.425158	−	0.269229i
$292$	−4.83394	+	2.70650i	−0.282885	+	0.158386i
$293$	7.97501	+	9.24526i	0.465905	+	0.540114i	0.940367	−	0.340163i	$-0.110482\pi$
$293$	7.97501	+	9.24526i	0.465905	+	0.540114i	−0.474461	+	0.880276i	$0.657357\pi$
$294$	−9.22804	−	15.0605i	−0.538190	−	0.878346i
$295$	7.77848	+	10.4881i	0.452881	+	0.610639i
$296$	4.75936	+	26.6749i	0.276632	+	1.55045i
$297$	−20.1283	−	5.04187i	−1.16796	−	0.292559i
$298$	−27.8742	+	3.02053i	−1.61471	+	0.174975i
$299$	5.84691	−	2.59176i	0.338136	−	0.149885i
$300$	5.73693	−	5.67974i	0.331222	−	0.327920i
$301$	8.79746	−	0.648940i	0.507077	−	0.0374043i
$302$	3.17910	−	0.746579i	0.182937	−	0.0429608i
$303$	8.43233	−	6.92023i	0.484425	−	0.397557i
$304$	11.5762	+	11.2447i	0.663940	+	0.644929i
$305$	16.1962	−	19.7351i	0.927390	−	1.13003i
$306$	−34.8198	+	11.8813i	−1.99052	+	0.679211i
$307$	12.8477	+	16.4628i	0.733257	+	0.939582i	0.999706	−	0.0242672i	$-0.00772524\pi$
$307$	12.8477	+	16.4628i	0.733257	+	0.939582i	−0.266449	+	0.963849i	$0.585850\pi$
$308$	1.06050	+	24.0442i	0.0604274	+	1.37005i
$309$	−4.46333	−	0.774461i	−0.253910	−	0.0440575i
$310$	7.50769	−	18.6380i	0.426408	−	1.05857i
$311$	−5.89614	+	12.4663i	−0.334339	+	0.706901i	−0.999197	−	0.0400688i	$-0.987242\pi$
$311$	−5.89614	+	12.4663i	−0.334339	+	0.706901i	0.664857	+	0.746970i	$0.268492\pi$
$312$	−1.05675	−	10.2302i	−0.0598267	−	0.579173i
$313$	5.97813	−	6.59585i	0.337904	−	0.372820i	−0.548167	−	0.836369i	$-0.684674\pi$
$313$	5.97813	−	6.59585i	0.337904	−	0.372820i	0.886071	+	0.463549i	$0.153424\pi$
$314$	13.4289	−	3.50351i	0.757839	−	0.197714i
$315$	41.6640	+	11.5300i	2.34750	+	0.649640i
$316$	−7.24499	−	26.6997i	−0.407562	−	1.50197i
$317$	0.735650	−	29.9670i	0.0413182	−	1.68312i	−0.518949	−	0.854805i	$-0.673677\pi$
$317$	0.735650	−	29.9670i	0.0413182	−	1.68312i	0.560267	−	0.828312i	$-0.310698\pi$
$318$	−5.36454	+	9.68919i	−0.300828	+	0.543343i
$319$	31.5877	−	13.0841i	1.76857	−	0.732567i
$320$	−20.0077	−	3.27590i	−1.11846	−	0.183128i
$321$	−28.4699	−	11.7926i	−1.58903	−	0.658199i
$322$	18.6446	−	14.8456i	1.03902	−	0.827315i
$323$	14.3265	+	15.0476i	0.797146	+	0.837268i
$324$	2.72515	−	0.187297i	0.151397	−	0.0104054i
$325$	0.898474	+	1.58603i	0.0498384	+	0.0879770i
$326$	−1.95600	−	2.58423i	−0.108333	−	0.143127i
$327$	−0.171350	−	3.48790i	−0.00947566	−	0.192881i
$328$	10.2538	+	10.1567i	0.566172	+	0.560811i
$329$	−27.8906	+	9.97942i	−1.53766	+	0.550183i
$330$	−25.8776	−	25.3770i	−1.42451	−	1.39696i
$331$	−3.38470	+	2.38377i	−0.186040	+	0.131024i	−0.665089	−	0.746764i	$-0.731606\pi$
$331$	−3.38470	+	2.38377i	−0.186040	+	0.131024i	0.479049	+	0.877788i	$0.340981\pi$
$332$	−4.70197	+	7.75637i	−0.258054	+	0.425686i
$333$	5.92426	−	48.0326i	0.324648	−	2.63217i
$334$	14.6867	−	12.9212i	0.803623	−	0.707015i
$335$	−3.15980	−	32.0820i	−0.172638	−	1.75283i
$336$	−13.4342	−	35.8939i	−0.732896	−	1.95817i
$337$	−3.21936	−	0.317079i	−0.175370	−	0.0172724i	0.00995116	−	0.999950i	$-0.496832\pi$
$337$	−3.21936	−	0.317079i	−0.175370	−	0.0172724i	−0.185321	+	0.982678i	$0.559332\pi$
$338$	−15.8521	−	2.59138i	−0.862241	−	0.140952i
$339$	22.7671	−	26.3934i	1.23654	−	1.43349i
$340$	−25.5737	−	5.22024i	−1.38693	−	0.283107i
$341$	−18.6417	−	7.19088i	−1.00950	−	0.389408i
$342$	−13.8357	−	25.2876i	−0.748149	−	1.36739i
$343$	−7.52592	+	4.51086i	−0.406362	+	0.243564i
$344$	7.33790	+	0.869627i	0.395633	+	0.0468872i
$345$	−5.26629	+	35.5024i	−0.283527	+	1.91139i
$346$	−9.78673	+	1.54956i	−0.526138	+	0.0833047i
$347$	−6.34439	−	0.467990i	−0.340585	−	0.0251230i	−0.0978081	−	0.995205i	$-0.531183\pi$
$347$	−6.34439	−	0.467990i	−0.340585	−	0.0251230i	−0.242776	+	0.970082i	$0.578058\pi$
$348$	−41.4039	+	35.3551i	−2.21948	+	1.89523i
$349$	−11.2662	−	2.52991i	−0.603065	−	0.135423i	−0.0931565	−	0.995651i	$-0.529696\pi$
$349$	−11.2662	−	2.52991i	−0.603065	−	0.135423i	−0.509908	+	0.860229i	$0.670321\pi$
$350$	4.73171	+	4.87366i	0.252921	+	0.260508i
$351$	−1.45556	+	7.31761i	−0.0776922	+	0.390585i
$352$	−2.96318	+	19.9414i	−0.157938	+	1.06288i
$353$	6.83365	+	34.3551i	0.363719	+	1.82854i	0.536898	+	0.843647i	$0.319596\pi$
$353$	6.83365	+	34.3551i	0.363719	+	1.82854i	−0.173179	+	0.984890i	$0.555404\pi$
$354$	−11.7401	+	17.0203i	−0.623978	+	0.904621i
$355$	−15.1962	+	21.5769i	−0.806528	+	1.14518i
$356$	−0.481824	−	24.6630i	−0.0255366	−	1.30714i
$357$	−15.4772	−	46.8502i	−0.819142	−	2.47958i
$358$	27.3860	−	25.3128i	1.44739	−	1.33782i
$359$	−9.14998	+	15.2658i	−0.482918	+	0.805699i	−0.998698	−	0.0510219i	$-0.983752\pi$
$359$	−9.14998	+	15.2658i	−0.482918	+	0.805699i	0.515780	+	0.856721i	$0.327502\pi$
$360$	32.4223	+	16.1272i	1.70880	+	0.849976i
$361$	1.62135	−	2.18614i	0.0853344	−	0.115060i
$362$	6.40113	+	0.567389i	0.336436	+	0.0298213i
$363$	−3.32864	+	3.49618i	−0.174708	+	0.183502i
$364$	8.61628	−	0.805065i	0.451616	−	0.0421969i
$365$	6.66566	+	2.20204i	0.348897	+	0.115260i
$366$	37.8578	+	14.1802i	1.97886	+	0.741210i
$367$	−16.9618	−	9.06625i	−0.885397	−	0.473255i	−0.0349947	−	0.999387i	$-0.511141\pi$
$367$	−16.9618	−	9.06625i	−0.885397	−	0.473255i	−0.850402	+	0.526133i	$0.823641\pi$
$368$	17.6999	−	9.23400i	0.922673	−	0.481356i
$369$	−12.1517	−	22.7343i	−0.632594	−	1.18350i
$370$	20.8582	−	27.2724i	1.08437	−	1.41783i
$371$	−8.10828	−	4.59328i	−0.420961	−	0.238471i
$372$	31.7707	+	1.72039i	1.64723	+	0.0891978i
$373$	−16.8345	−	10.6603i	−0.871655	−	0.551970i	0.0224897	−	0.999747i	$-0.492841\pi$
$373$	−16.8345	−	10.6603i	−0.871655	−	0.551970i	−0.894145	+	0.447777i	$0.852216\pi$
$374$	−4.81461	+	25.5041i	−0.248958	+	1.31878i
$375$	25.6955	+	1.26234i	1.32691	+	0.0651869i
$376$	−24.5270	+	3.75756i	−1.26488	+	0.193782i
$377$	−5.25617	−	11.1132i	−0.270706	−	0.572361i
$378$	1.63539	+	27.7550i	0.0841153	+	1.42756i
$379$	−15.4186	+	1.90170i	−0.791999	+	0.0976838i	−0.508244	−	0.861213i	$-0.669705\pi$
$379$	−15.4186	+	1.90170i	−0.791999	+	0.0976838i	−0.283755	+	0.958897i	$0.591580\pi$
$380$	0.604272	−	20.4407i	0.0309985	−	1.04859i
$381$	−0.0158546	+	0.0357675i	−0.000812257	+	0.00183242i
$382$	10.3105	+	19.9948i	0.527533	+	1.02302i
$383$	−0.510896	−	0.510896i	−0.0261056	−	0.0261056i	0.693934	−	0.720039i	$-0.255876\pi$
$383$	−0.510896	−	0.510896i	−0.0261056	−	0.0261056i	−0.720039	+	0.693934i	$0.755876\pi$
$384$	−5.32195	−	31.6594i	−0.271584	−	1.61561i
$385$	21.5645	−	21.5645i	1.09903	−	1.09903i
$386$	28.7381	+	9.18345i	1.46273	+	0.467425i
$387$	−12.0657	−	5.34837i	−0.613336	−	0.271873i
$388$	2.14927	+	5.65599i	0.109112	+	0.287139i
$389$	−2.89804	−	23.4967i	−0.146936	−	1.19133i	−0.867319	−	0.497752i	$-0.834159\pi$
$389$	−2.89804	−	23.4967i	−0.146936	−	1.19133i	0.720383	−	0.693577i	$-0.243966\pi$
$390$	−8.65705	+	9.74112i	−0.438367	+	0.493261i
$391$	23.2339	−	10.9888i	1.17499	−	0.555729i
$392$	11.7014	−	4.24972i	0.591010	−	0.214643i
$393$	−3.02464	+	61.5679i	−0.152573	+	3.10569i
$394$	−10.4228	−	15.2737i	−0.525092	−	0.769479i
$395$	−18.7546	+	29.6167i	−0.943645	+	1.49018i
$396$	15.5585	−	32.4737i	0.781844	−	1.63187i
$397$	12.7335	−	22.4777i	0.639074	−	1.12812i	−0.342947	−	0.939355i	$-0.611425\pi$
$397$	12.7335	−	22.4777i	0.639074	−	1.12812i	0.982021	−	0.188769i	$-0.0604499\pi$
$398$	−12.4103	+	1.65387i	−0.622073	+	0.0829012i
$399$	34.0928	−	18.2230i	1.70677	−	0.912289i
$400$	3.11363	+	4.76249i	0.155681	+	0.238125i
$401$	−12.8794	+	24.0957i	−0.643168	+	1.20328i	0.323251	+	0.946313i	$0.395224\pi$
$401$	−12.8794	+	24.0957i	−0.643168	+	1.20328i	−0.966419	+	0.256970i	$0.917276\pi$
$402$	46.4633	−	21.1411i	2.31738	−	1.05442i
$403$	−2.25356	+	6.82164i	−0.112258	+	0.339810i
$404$	3.59034	+	6.79876i	0.178626	+	0.338251i
$405$	−2.50682	−	2.38669i	−0.124565	−	0.118595i
$406$	−29.4071	−	35.1273i	−1.45945	−	1.74334i
$407$	−27.4229	−	20.3382i	−1.35930	−	1.00813i
$408$	−5.25435	−	40.9950i	−0.260129	−	2.02955i
$409$	−18.6896	−	11.2021i	−0.924141	−	0.553909i	−0.0289449	−	0.999581i	$-0.509215\pi$
$409$	−18.6896	−	11.2021i	−0.924141	−	0.553909i	−0.895196	+	0.445672i	$0.852965\pi$
$410$	0.718908	−	18.2739i	0.0355043	−	0.902482i
$411$	33.7496	−	11.1494i	1.66475	−	0.549957i
$412$	1.16401	−	2.97313i	0.0573466	−	0.146476i
$413$	−14.2242	−	10.0178i	−0.699929	−	0.492945i
$414$	−35.0713	+	6.43892i	−1.72366	+	0.316456i
$415$	11.2724	−	2.24222i	0.553340	−	0.110066i
$416$	7.21381	+	0.712340i	0.353686	+	0.0349253i
$417$	−19.3298	−	3.84494i	−0.946586	−	0.188288i
$418$	−20.3326	−	0.300473i	−0.994502	−	0.0146966i
$419$	4.80150	−	21.3820i	0.234568	−	1.04458i	−0.706856	−	0.707357i	$-0.749887\pi$
$419$	4.80150	−	21.3820i	0.234568	−	1.04458i	0.941425	−	0.337224i	$-0.109488\pi$
$420$	−22.0518	+	43.2682i	−1.07602	+	2.11127i
$421$	−1.04585	+	14.1782i	−0.0509716	+	0.691005i	0.910044	+	0.414511i	$0.136047\pi$
$421$	−1.04585	+	14.1782i	−0.0509716	+	0.691005i	−0.961016	+	0.276494i	$0.910828\pi$
$422$	12.1507	+	8.82895i	0.591487	+	0.429786i
$423$	43.8393	+	6.50294i	2.13154	+	0.316184i
$424$	−5.93499	−	5.07052i	−0.288229	−	0.246246i
$425$	3.76597	+	6.28314i	0.182676	+	0.304777i
$426$	−40.1066	−	11.7397i	−1.94317	−	0.568790i
$427$	−12.2422	+	31.7366i	−0.592439	+	1.53584i
$428$	12.1571	−	17.9985i	0.587635	−	0.869991i
$429$	9.81259	+	8.46440i	0.473756	+	0.408665i
$430$	−5.46590	−	7.60216i	−0.263589	−	0.366609i
$431$	3.16898	−	32.1752i	0.152644	−	1.54983i	−0.548100	−	0.836413i	$-0.684649\pi$
$431$	3.16898	−	32.1752i	0.152644	−	1.54983i	0.700744	−	0.713413i	$-0.252851\pi$
$432$	−3.08233	+	23.0845i	−0.148298	+	1.11066i
$433$	−25.4020	+	2.50188i	−1.22074	+	0.120233i	−0.687789	−	0.725910i	$-0.741419\pi$
$433$	−25.4020	+	2.50188i	−1.22074	+	0.120233i	−0.532955	+	0.846143i	$0.678919\pi$
$434$	−1.70860	+	26.7173i	−0.0820156	+	1.28247i
$435$	68.4703	+	8.44501i	3.28290	+	0.404907i
$436$	2.43285	+	0.373345i	0.116512	+	0.0178800i
$437$	11.5949	+	16.4634i	0.554657	+	0.787553i
$438$	0.108567	+	11.1154i	0.00518752	+	0.531116i
$439$	−4.33509	−	12.1158i	−0.206903	−	0.578254i	0.792601	−	0.609740i	$-0.208726\pi$
$439$	−4.33509	−	12.1158i	−0.206903	−	0.578254i	−0.999504	+	0.0314856i	$0.989976\pi$
$440$	21.1728	−	14.2934i	1.00937	−	0.681410i
$441$	−22.2088	+	1.09105i	−1.05756	+	0.0519547i
$442$	9.24420	+	1.27910i	0.439702	+	0.0608408i
$443$	−9.95922	+	5.64183i	−0.473177	+	0.268051i	−0.710915	−	0.703278i	$-0.751719\pi$
$443$	−9.95922	+	5.64183i	−0.473177	+	0.268051i	0.237738	+	0.971329i	$0.423594\pi$
$444$	51.5376	+	17.3126i	2.44587	+	0.821618i
$445$	−22.6380	+	21.5532i	−1.07314	+	1.02172i
$446$	−18.0205	−	2.04415i	−0.853297	−	0.0967932i
$447$	−21.5284	+	51.9741i	−1.01826	+	2.45829i
$448$	26.6815	−	4.21764i	1.26058	−	0.199265i
$449$	−10.6298	−	25.6626i	−0.501651	−	1.21109i	−0.948584	−	0.316525i	$-0.897484\pi$
$449$	−10.6298	−	25.6626i	−0.501651	−	1.21109i	0.446933	−	0.894567i	$-0.352516\pi$
$450$	−2.80612	−	9.76784i	−0.132282	−	0.460461i
$451$	−18.1799	−	0.446291i	−0.856057	−	0.0210150i
$452$	15.0175	+	19.4432i	0.706363	+	0.914530i
$453$	1.74759	−	6.31496i	0.0821087	−	0.296703i
$454$	0.608502	+	0.356690i	0.0285584	+	0.0167403i
$455$	−8.12491	−	7.36399i	−0.380902	−	0.345229i
$456$	30.9421	−	9.54715i	1.44900	−	0.447086i
$457$	31.9906	+	15.1304i	1.49646	+	0.707771i	0.988162	−	0.153412i	$-0.0490262\pi$
$457$	31.9906	+	15.1304i	1.49646	+	0.707771i	0.508294	+	0.861183i	$0.330276\pi$
$458$	−3.95824	−	9.29813i	−0.184957	−	0.434473i
$459$	−5.12594	+	29.5415i	−0.239258	+	1.37888i
$460$	−23.7751	−	8.64146i	−1.10852	−	0.402910i
$461$	−10.6664	+	8.32418i	−0.496786	+	0.387696i	−0.832288	−	0.554344i	$-0.812969\pi$
$461$	−10.6664	+	8.32418i	−0.496786	+	0.387696i	0.335502	+	0.942040i	$0.391094\pi$
$462$	43.3447	+	21.2899i	2.01658	+	0.990494i
$463$	−20.8362	−	17.0998i	−0.968341	−	0.794697i	0.0103691	−	0.999946i	$-0.496699\pi$
$463$	−20.8362	−	17.0998i	−0.968341	−	0.794697i	−0.978710	+	0.205250i	$0.934199\pi$
$464$	−18.5791	−	33.5768i	−0.862514	−	1.55876i
$465$	−25.5766	−	31.1652i	−1.18609	−	1.44525i
$466$	8.81425	−	14.2247i	0.408312	−	0.658947i
$467$	1.06441	+	14.4299i	0.0492552	+	0.667737i	0.964372	+	0.264549i	$0.0852230\pi$
$467$	1.06441	+	14.4299i	0.0492552	+	0.667737i	−0.915117	+	0.403188i	$0.867902\pi$
$468$	−11.9368	−	5.01458i	−0.551777	−	0.231799i
$469$	17.4060	+	39.2674i	0.803736	+	1.81320i
$470$	24.4983	+	19.7080i	1.13002	+	0.909061i
$471$	6.76620	−	27.0122i	0.311770	−	1.24466i
$472$	−10.0990	−	10.5068i	−0.464846	−	0.483615i
$473$	−7.47835	+	5.54633i	−0.343855	+	0.255020i
$474$	−53.9751	−	12.9612i	−2.47916	−	0.595326i
$475$	−4.34581	+	3.74872i	−0.199399	+	0.172003i
$476$	34.5358	−	4.08404i	1.58295	−	0.187192i
$477$	7.45916	+	11.7793i	0.341531	+	0.539337i
$478$	−12.5724	+	29.1274i	−0.575046	+	1.33226i
$479$	0.824679	+	1.23422i	0.0376805	+	0.0563929i	0.849832	−	0.527054i	$-0.176704\pi$
$479$	0.824679	+	1.23422i	0.0376805	+	0.0563929i	−0.812151	+	0.583447i	$0.801704\pi$
$480$	−25.0354	+	32.0632i	−1.14270	+	1.46348i
$481$	−6.82022	+	10.2072i	−0.310975	+	0.465408i
$482$	18.0553	+	27.9057i	0.822396	+	1.27107i
$483$	−8.17545	−	47.1163i	−0.371996	−	2.14387i
$484$	−1.94518	−	2.79155i	−0.0884175	−	0.126889i
$485$	3.44712	−	6.84825i	0.156526	−	0.310963i
$486$	−8.04807	+	17.4553i	−0.365068	+	0.791788i
$487$	0.459457	+	1.83425i	0.0208200	+	0.0831180i	0.979551	−	0.201198i	$-0.0644835\pi$
$487$	0.459457	+	1.83425i	0.0208200	+	0.0831180i	−0.958731	+	0.284316i	$0.908233\pi$
$488$	−15.1293	+	24.1451i	−0.684871	+	1.09300i
$489$	−6.43263	+	0.954190i	−0.290893	+	0.0431500i
$490$	−13.9841	−	7.29995i	−0.631737	−	0.329778i
$491$	−0.207682	−	8.46001i	−0.00937254	−	0.381795i	−0.985989	−	0.166808i	$-0.946654\pi$
$491$	−0.207682	−	8.46001i	−0.00937254	−	0.381795i	0.976617	−	0.214987i	$-0.0689710\pi$
$492$	27.7534	−	8.26730i	1.25122	−	0.372719i
$493$	−22.2123	−	44.1282i	−1.00039	−	1.98743i
$494$	0.250818	+	7.30735i	0.0112848	+	0.328773i
$495$	−43.6628	+	13.2450i	−1.96250	+	0.595317i
$496$	−5.66666	+	21.6978i	−0.254441	+	0.974261i
$497$	10.2072	−	33.6487i	0.457857	−	1.50935i
$498$	9.12461	+	15.7466i	0.408883	+	0.705621i
$499$	26.3311	−	7.28679i	1.17874	−	0.326201i	0.378340	−	0.925667i	$-0.376495\pi$
$499$	26.3311	−	7.28679i	1.17874	−	0.326201i	0.800401	+	0.599465i	$0.204620\pi$
$500$	−4.49395	+	17.5670i	−0.200975	+	0.785619i
$501$	−8.59970	−	38.2962i	−0.384206	−	1.71095i
$502$	−4.25895	−	20.3694i	−0.190086	−	0.909129i
$503$	7.18715	−	6.51405i	0.320459	−	0.290447i	−0.495439	−	0.868643i	$-0.664993\pi$
$503$	7.18715	−	6.51405i	0.320459	−	0.290447i	0.815898	+	0.578195i	$0.196243\pi$
$504$	−47.7587	−	6.85231i	−2.12734	−	0.305226i
$505$	3.28211	−	9.17289i	0.146052	−	0.408188i
$506$	−8.24269	+	23.7660i	−0.366432	+	1.05653i
$507$	−19.8283	+	25.4076i	−0.880607	+	1.12839i
$508$	−0.0224655	−	0.0159910i	−0.000996746	−	0.000709485i
$509$	−26.9327	+	10.3891i	−1.19377	+	0.460488i	−0.873493	−	0.486836i	$-0.838151\pi$
$509$	−26.9327	+	10.3891i	−1.19377	+	0.460488i	−0.320276	+	0.947324i	$0.603776\pi$
$510$	−33.8184	+	39.9880i	−1.49750	+	1.77070i
$511$	−9.35328			−0.413765
$512$	22.6137	+	0.787644i	0.999394	+	0.0348093i
$513$	−23.4910			−1.03715
$514$	0.604161	−	0.714381i	0.0266484	−	0.0315100i
$515$	−3.77470	+	1.45606i	−0.166333	+	0.0641617i
$516$	8.59775	−	12.0789i	0.378495	−	0.531743i
$517$	19.2353	−	24.6477i	0.845966	−	1.08401i
$518$	−14.9901	+	43.2208i	−0.658628	+	1.89901i
$519$	−6.69785	+	18.7192i	−0.294003	+	0.821683i
$520$	−5.50672	−	7.35160i	−0.241486	−	0.322389i
$521$	−26.7687	+	24.2617i	−1.17276	+	1.06293i	−0.175845	+	0.984418i	$0.556266\pi$
$521$	−26.7687	+	24.2617i	−1.17276	+	1.06293i	−0.996913	+	0.0785080i	$0.974984\pi$
$522$	14.0275	+	67.0898i	0.613968	+	2.93644i
$523$	−6.63257	−	29.5362i	−0.290022	−	1.29153i	−0.876437	−	0.481517i	$-0.840086\pi$
$523$	−6.63257	−	29.5362i	−0.290022	−	1.29153i	0.586415	−	0.810011i	$-0.300539\pi$
$524$	−42.0915	−	10.7678i	−1.83878	−	0.470392i
$525$	13.1358	−	3.63516i	0.573293	−	0.158652i
$526$	6.38472	+	11.0183i	0.278387	+	0.480419i
$527$	−8.38076	+	27.6277i	−0.365072	+	1.20348i
$528$	32.2476	+	24.4211i	1.40340	+	1.06279i
$529$	1.82744	−	0.554346i	0.0794537	−	0.0241020i
$530$	0.339309	+	9.88546i	0.0147387	+	0.429397i
$531$	11.7032	+	23.2503i	0.507876	+	1.00898i
$532$	7.77857	+	26.1128i	0.337244	+	1.13213i
$533$	0.160469	+	6.53680i	0.00695070	+	0.283140i
$534$	−43.8766	−	22.9044i	−1.89873	−	0.991171i
$535$	−27.2237	+	4.03826i	−1.17698	+	0.174589i
$536$	8.04998	+	35.0670i	0.347706	+	1.51467i
$537$	−18.1813	−	72.5839i	−0.784582	−	3.13223i
$538$	−18.2230	+	39.5235i	−0.785649	+	1.70398i
$539$	−7.05272	+	14.0113i	−0.303782	+	0.603511i
$540$	24.2124	−	16.8715i	1.04194	−	0.726032i
$541$	−3.33439	−	19.2165i	−0.143356	−	0.826184i	−0.966177	−	0.257882i	$-0.916976\pi$
$541$	−3.33439	−	19.2165i	−0.143356	−	0.826184i	0.822820	−	0.568302i	$-0.192399\pi$
$542$	−12.9417	−	20.0023i	−0.555895	−	0.859173i
$543$	7.16355	−	10.7210i	0.307417	−	0.460082i
$544$	29.0512	+	2.15033i	1.24556	+	0.0921947i
$545$	−1.73273	−	2.59321i	−0.0742219	−	0.111081i
$546$	6.88109	−	15.9420i	0.294483	−	0.682253i
$547$	−14.4210	−	22.7732i	−0.616597	−	0.973713i	−0.998768	−	0.0496214i	$-0.984199\pi$
$547$	−14.4210	−	22.7732i	−0.616597	−	0.973713i	0.382171	−	0.924092i	$-0.375176\pi$
$548$	2.94203	+	24.8786i	0.125677	+	1.06276i
$549$	38.5363	−	33.2416i	1.64469	−	1.41872i
$550$	−6.97133	−	1.67404i	−0.297258	−	0.0713813i
$551$	31.0894	−	23.0574i	1.32445	−	0.982280i
$552$	0.792541	−	40.0491i	0.0337328	−	1.70460i
$553$	11.3489	−	45.3074i	0.482605	−	1.92667i
$554$	6.46467	+	5.20059i	0.274658	+	0.220952i
$555$	−27.9175	−	62.9809i	−1.18503	−	2.67339i
$556$	5.38011	−	12.8069i	0.228167	−	0.543133i
$557$	1.83222	+	24.8389i	0.0776339	+	1.05246i	0.885972	+	0.463738i	$0.153492\pi$
$557$	1.83222	+	24.8389i	0.0776339	+	1.05246i	−0.808338	+	0.588718i	$0.799633\pi$
$558$	21.0975	−	34.0479i	0.893129	−	1.44136i
$559$	2.12379	+	2.58784i	0.0898266	+	0.109454i
$560$	−26.7718	−	21.3280i	−1.13132	−	0.901272i
$561$	40.2561	+	33.0373i	1.69961	+	1.39484i
$562$	19.2976	+	9.47853i	0.814022	+	0.399828i
$563$	26.0768	−	20.3505i	1.09900	−	0.857672i	0.108357	−	0.994112i	$-0.465441\pi$
$563$	26.0768	−	20.3505i	1.09900	−	0.857672i	0.990648	+	0.136440i	$0.0435662\pi$
$564$	−17.0074	+	46.7920i	−0.716139	+	1.97030i
$565$	5.32209	−	30.6720i	0.223902	−	1.29038i
$566$	4.98266	+	11.7045i	0.209437	+	0.491979i
$567$	4.16896	+	1.97177i	0.175080	+	0.0828065i
$568$	13.7609	−	26.0421i	0.577396	−	1.09270i
$569$	30.0561	+	27.2413i	1.26002	+	1.14201i	0.983481	+	0.181011i	$0.0579370\pi$
$569$	30.0561	+	27.2413i	1.26002	+	1.14201i	0.276537	+	0.961003i	$0.410813\pi$
$570$	−35.3984	−	20.7497i	−1.48267	−	0.869111i
$571$	−0.277405	+	1.00241i	−0.0116090	+	0.0419496i	−0.969352	−	0.245675i	$-0.920990\pi$
$571$	−0.277405	+	1.00241i	−0.0116090	+	0.0419496i	0.957743	+	0.287624i	$0.0928655\pi$
$572$	−7.22863	+	5.58323i	−0.302244	+	0.233447i
$573$	45.1254	+	1.10777i	1.88514	+	0.0462776i
$574$	6.72793	+	23.4193i	0.280818	+	0.977504i
$575$	2.71691	+	6.55920i	0.113303	+	0.273538i
$576$	−38.1803	−	13.2527i	−1.59085	−	0.552198i
$577$	−6.01988	+	14.5333i	−0.250611	+	0.605028i	−0.998254	−	0.0590729i	$-0.981186\pi$
$577$	−6.01988	+	14.5333i	−0.250611	+	0.605028i	0.747643	+	0.664101i	$0.231186\pi$
$578$	13.3756	+	1.51725i	0.556351	+	0.0631093i
$579$	43.8421	−	41.7412i	1.82202	−	1.73470i
$580$	−15.4840	+	46.0941i	−0.642938	+	1.91395i
$581$	−13.3240	+	7.54793i	−0.552771	+	0.313141i
$582$	12.0258	+	1.66398i	0.498484	+	0.0689744i
$583$	9.82392	−	0.482618i	0.406865	−	0.0199880i
$584$	−7.69145	−	1.49192i	−0.318275	−	0.0617363i
$585$	5.52699	+	15.4469i	0.228513	+	0.638651i
$586$	0.168643	+	17.2662i	0.00696658	+	0.713261i
$587$	16.0498	+	22.7889i	0.662444	+	0.940599i	1.00000		0.000706996i	$-0.000225044\pi$
$587$	16.0498	+	22.7889i	0.662444	+	0.940599i	−0.337555	+	0.941306i	$0.609600\pi$
$588$	3.78892	−	24.6900i	0.156252	−	1.01820i
$589$	−22.4496	−	2.76890i	−0.925021	−	0.114090i
$590$	−1.17854	+	18.4288i	−0.0485198	+	0.758701i
$591$	−36.9232	+	3.63662i	−1.51882	+	0.149591i
$592$	−19.2209	+	33.1506i	−0.789972	+	1.36248i
$593$	−1.86440	+	18.9296i	−0.0765618	+	0.777345i	0.877867	+	0.478905i	$0.158966\pi$
$593$	−1.86440	+	18.9296i	−0.0765618	+	0.777345i	−0.954428	+	0.298440i	$0.903534\pi$
$594$	−17.1307	−	23.8260i	−0.702881	−	0.977591i
$595$	−33.3675	−	28.7830i	−1.36793	−	1.17999i
$596$	−32.8578	−	22.1938i	−1.34591	−	0.909092i
$597$	−9.04096	+	23.4378i	−0.370022	+	0.959246i
$598$	8.68050	+	2.54089i	0.354972	+	0.103905i
$599$	−9.33529	−	15.5750i	−0.381430	−	0.636377i	0.605812	−	0.795608i	$-0.292849\pi$
$599$	−9.33529	−	15.5750i	−0.381430	−	0.636377i	−0.987241	+	0.159231i	$0.949099\pi$
$600$	11.3818	−	0.894026i	0.464658	−	0.0364985i
$601$	22.8687	+	3.39225i	0.932833	+	0.138373i	0.595812	−	0.803124i	$-0.296831\pi$
$601$	22.8687	+	3.39225i	0.932833	+	0.138373i	0.337021	+	0.941497i	$0.390581\pi$
$602$	10.0924	+	7.33331i	0.411334	+	0.298883i
$603$	4.72745	−	64.0885i	0.192517	−	2.60988i
$604$	4.11467	+	2.09705i	0.167423	+	0.0853278i
$605$	−0.944617	+	4.20657i	−0.0384041	+	0.171021i
$606$	15.4252	+	0.227951i	0.626604	+	0.00925987i
$607$	4.20416	+	0.836259i	0.170641	+	0.0339427i	0.279671	−	0.960096i	$-0.409774\pi$
$607$	4.20416	+	0.836259i	0.170641	+	0.0339427i	−0.109030	+	0.994038i	$0.534774\pi$
$608$	2.23133	+	22.7140i	0.0904925	+	0.921173i
$609$	−90.1535	+	17.9327i	−3.65321	+	0.726668i
$610$	35.5116	−	6.51974i	1.43782	−	0.263977i
$611$	−9.19108	−	6.47309i	−0.371831	−	0.261873i
$612$	−48.4496	−	18.9685i	−1.95846	−	0.766755i
$613$	−2.22460	+	0.734910i	−0.0898509	+	0.0296827i	−0.358256	−	0.933623i	$-0.616628\pi$
$613$	−2.22460	+	0.734910i	−0.0898509	+	0.0296827i	0.268405	+	0.963306i	$0.413503\pi$
$614$	−1.16094	+	29.5098i	−0.0468516	+	1.19092i
$615$	−31.4738	−	18.8647i	−1.26915	−	0.760697i
$616$	−20.8126	+	26.9320i	−0.838563	+	1.08512i
$617$	2.02152	+	1.49926i	0.0813835	+	0.0603581i	0.635626	−	0.771997i	$-0.280742\pi$
$617$	2.02152	+	1.49926i	0.0813835	+	0.0603581i	−0.554243	+	0.832355i	$0.686992\pi$
$618$	−4.11236	−	4.91230i	−0.165423	−	0.197602i
$619$	27.8281	+	26.4946i	1.11851	+	1.06491i	0.997385	+	0.0722700i	$0.0230243\pi$
$619$	27.8281	+	26.4946i	1.11851	+	1.06491i	0.121122	+	0.992638i	$0.461351\pi$
$620$	25.1276	−	13.2696i	1.00915	−	0.532919i
$621$	−9.11532	+	27.5925i	−0.365785	+	1.10725i
$622$	−17.7514	+	8.07699i	−0.711765	+	0.323858i
$623$	19.6321	−	36.7290i	0.786542	−	1.47152i
$624$	8.20138	−	12.0119i	0.328318	−	0.480862i
$625$	26.5361	−	14.1839i	1.06144	−	0.567354i
$626$	12.4788	−	1.66300i	0.498754	−	0.0664670i
$627$	−20.1109	+	35.5007i	−0.803153	+	1.41776i
$628$	17.7004	+	8.48043i	0.706323	+	0.338406i
$629$	−26.3931	+	41.6792i	−1.05236	+	1.66186i
$630$	34.4604	+	50.4989i	1.37293	+	2.01192i
$631$	0.276058	−	5.61929i	0.0109897	−	0.223700i	−0.987018	−	0.160609i	$-0.948654\pi$
$631$	0.276058	−	5.61929i	0.0109897	−	0.223700i	0.998008	−	0.0630912i	$-0.0200959\pi$
$632$	16.5594	−	35.4473i	0.658699	−	1.41002i
$633$	27.2431	−	12.8850i	1.08282	−	0.512134i
$634$	28.1610	−	31.6874i	1.11842	−	1.25847i
$635$	0.00427726	+	0.0346791i	0.000169738	+	0.00137620i
$636$	−14.6412	+	5.56361i	−0.580560	+	0.220612i
$637$	5.15631	+	2.28564i	0.204301	+	0.0905602i
$638$	46.0579	+	14.7181i	1.82345	+	0.582696i
$639$	−37.1998	+	37.1998i	−1.47160	+	1.47160i
$640$	−18.6132	−	21.8089i	−0.735752	−	0.862072i
$641$	−4.96862	−	4.96862i	−0.196249	−	0.196249i	0.602141	−	0.798390i	$-0.294315\pi$
$641$	−4.96862	−	4.96862i	−0.196249	−	0.196249i	−0.798390	+	0.602141i	$0.794315\pi$
$642$	−19.9732	−	38.7333i	−0.788280	−	1.52868i
$643$	7.83020	−	17.6647i	0.308793	−	0.696626i	−0.690859	−	0.722989i	$-0.742768\pi$
$643$	7.83020	−	17.6647i	0.308793	−	0.696626i	0.999652	+	0.0263631i	$0.00839261\pi$
$644$	33.6903	+	0.995958i	1.32758	+	0.0392462i
$645$	−18.6457	+	2.29972i	−0.734172	+	0.0905515i
$646$	1.72831	+	29.3320i	0.0679994	+	1.15405i
$647$	0.813408	+	1.71981i	0.0319784	+	0.0676126i	0.919346	−	0.393450i	$-0.128718\pi$
$647$	0.813408	+	1.71981i	0.0319784	+	0.0676126i	−0.887368	+	0.461062i	$0.847468\pi$
$648$	3.11373	+	2.28642i	0.122319	+	0.0898191i
$649$	18.3407	+	0.901019i	0.719934	+	0.0353681i
$650$	−0.478202	+	2.53314i	−0.0187566	+	0.0993580i
$651$	45.3831	+	28.7385i	1.77870	+	1.12635i
$652$	0.247833	−	4.57678i	0.00970590	−	0.179241i
$653$	−9.03459	−	5.11803i	−0.353551	−	0.200284i	0.305843	−	0.952082i	$-0.401062\pi$
$653$	−9.03459	−	5.11803i	−0.353551	−	0.200284i	−0.659394	+	0.751798i	$0.729187\pi$
$654$	3.00020	−	3.92281i	0.117317	−	0.153394i
$655$	25.9518	+	48.5525i	1.01402	+	1.89710i
$656$	1.79698	+	20.3315i	0.0701603	+	0.793812i
$657$	12.3414	+	6.59663i	0.481485	+	0.257359i
$658$	−39.2304	−	14.6943i	−1.52936	−	0.572844i
$659$	−15.6181	−	5.15952i	−0.608394	−	0.200986i	−0.00704847	−	0.999975i	$-0.502244\pi$
$659$	−15.6181	−	5.15952i	−0.608394	−	0.200986i	−0.601346	+	0.798989i	$0.705369\pi$
$660$	−4.76845	−	51.0347i	−0.185611	−	1.98652i
$661$	6.65593	−	6.99094i	0.258886	−	0.271916i	−0.581929	−	0.813240i	$-0.697702\pi$
$661$	6.65593	−	6.99094i	0.258886	−	0.271916i	0.840814	+	0.541324i	$0.182077\pi$
$662$	−5.83180	−	0.516925i	−0.226659	−	0.0200908i
$663$	11.1544	−	15.0400i	0.433203	−	0.584106i
$664$	−12.1606	+	4.08158i	−0.471923	+	0.158396i
$665$	17.7495	−	29.6132i	0.688296	−	1.14835i
$666$	50.2617	−	46.4567i	1.94760	−	1.80016i
$667$	−15.0194	−	45.4645i	−0.581555	−	1.76039i
$668$	27.6590	−	0.540355i	1.07016	−	0.0209070i
$669$	−20.9534	+	29.7516i	−0.810106	+	1.15026i
$670$	25.8860	−	37.5286i	1.00006	−	1.44986i
$671$	−7.00422	−	35.2126i	−0.270395	−	1.35937i
$672$	18.2725	−	51.0276i	0.704878	−	1.96843i
$673$	1.86172	−	9.35950i	0.0717641	−	0.360782i	−0.928171	−	0.372153i	$-0.878620\pi$
$673$	1.86172	−	9.35950i	0.0717641	−	0.360782i	0.999935	+	0.0113710i	$0.00361957\pi$
$674$	−3.18678	−	3.28238i	−0.122750	−	0.126433i
$675$	−8.08104	−	1.81466i	−0.311039	−	0.0698462i
$676$	−14.7510	−	17.2748i	−0.567347	−	0.664414i
$677$	−20.8882	−	1.54081i	−0.802800	−	0.0592181i	−0.334057	−	0.942553i	$-0.608418\pi$
$677$	−20.8882	−	1.54081i	−0.802800	−	0.0592181i	−0.468743	+	0.883335i	$0.655293\pi$
$678$	48.6875	−	7.70883i	1.86983	−	0.296056i
$679$	−1.49888	+	10.1046i	−0.0575219	+	0.387781i
$680$	−22.8479	−	28.9914i	−0.876175	−	1.11177i
$681$	1.21389	−	0.727580i	0.0465165	−	0.0278809i
$682$	−13.5629	−	24.7889i	−0.519349	−	0.949216i
$683$	−13.6692	−	5.27278i	−0.523036	−	0.201757i	0.0839499	−	0.996470i	$-0.473246\pi$
$683$	−13.6692	−	5.27278i	−0.523036	−	0.201757i	−0.606986	+	0.794713i	$0.707621\pi$
$684$	8.15303	−	39.9412i	0.311739	−	1.52719i
$685$	20.7344	−	24.0370i	0.792223	−	0.918406i
$686$	−12.2461	−	2.00190i	−0.467559	−	0.0764328i
$687$	−20.1790	−	1.98745i	−0.769875	−	0.0758261i
$688$	7.12949	+	7.64019i	0.271809	+	0.291279i
$689$	−0.346645	−	3.51954i	−0.0132061	−	0.134084i
$690$	−38.1083	+	33.5271i	−1.45076	+	1.27636i
$691$	−4.41015	+	35.7566i	−0.167770	+	1.36024i	0.638922	+	0.769272i	$0.279381\pi$
$691$	−4.41015	+	35.7566i	−0.167770	+	1.36024i	−0.806692	+	0.590972i	$0.798744\pi$
$692$	−11.9830	−	7.26421i	−0.455527	−	0.276144i
$693$	49.7036	−	35.0052i	1.88808	−	1.32974i
$694$	−6.42345	−	6.29919i	−0.243831	−	0.239114i
$695$	−16.5729	+	5.92987i	−0.628645	+	0.224933i
$696$	−76.9961	+	0.366275i	−2.91853	+	0.0138836i
$697$	1.28935	+	26.2453i	0.0488375	+	0.994111i
$698$	−9.85514	−	13.0204i	−0.373023	−	0.492829i
$699$	−16.5499	−	29.2147i	−0.625975	−	1.10500i
$700$	0.658687	+	9.58381i	0.0248960	+	0.362234i
$701$	−14.1006	−	14.8103i	−0.532572	−	0.559378i	0.401777	−	0.915738i	$-0.368393\pi$
$701$	−14.1006	−	14.8103i	−0.532572	−	0.559378i	−0.934349	+	0.356360i	$0.884018\pi$
$702$	−8.25437	+	6.57249i	−0.311541	+	0.248063i
$703$	−35.7093	−	14.7913i	−1.34680	−	0.557864i
$704$	−21.4106	+	18.8272i	−0.806944	+	0.709576i
$705$	58.2845	−	24.1422i	2.19512	−	0.909248i
$706$	−23.9947	+	43.3382i	−0.903053	+	1.63105i
$707$	−0.318559	+	12.9767i	−0.0119807	+	0.488038i
$708$	−28.2206	+	7.65770i	−1.06060	+	0.287794i
$709$	21.8452	+	6.04537i	0.820412	+	0.227039i	0.651554	−	0.758602i	$-0.274117\pi$
$709$	21.8452	+	6.04537i	0.820412	+	0.227039i	0.168858	+	0.985640i	$0.445992\pi$
$710$	−36.1137	+	9.42179i	−1.35532	+	0.353594i
$711$	−46.9289	+	51.7780i	−1.75997	+	1.94183i
$712$	22.0026	−	27.0718i	0.824580	−	1.01456i
$713$	−11.9635	+	25.2948i	−0.448038	+	0.947297i
$714$	26.0720	−	64.7243i	0.975721	−	2.42224i
$715$	11.4033	+	1.97866i	0.426459	+	0.0739976i
$716$	52.6883	−	2.32387i	1.96905	−	0.0868472i
$717$	39.1627	+	50.1823i	1.46256	+	1.87409i
$718$	−23.8215	+	8.12845i	−0.889010	+	0.303351i
$719$	14.7800	−	18.0095i	0.551201	−	0.671640i	−0.420654	−	0.907221i	$-0.638199\pi$
$719$	14.7800	−	18.0095i	0.551201	−	0.671640i	0.971855	+	0.235581i	$0.0756994\pi$
$720$	20.2827	+	47.0233i	0.755892	+	1.75245i
$721$	4.16694	−	3.41972i	0.155185	−	0.127357i
$722$	3.74722	−	0.879995i	0.139457	−	0.0327500i
$723$	66.5091	−	4.90601i	2.47350	−	0.182456i
$724$	6.39395	+	6.45834i	0.237629	+	0.240022i
$725$	12.4761	−	5.53026i	0.463349	−	0.205389i
$726$	−6.78715	+	0.735475i	−0.251895	+	0.0272960i
$727$	0.436118	+	0.109242i	0.0161747	+	0.00405156i	0.251059	−	0.967972i	$-0.419221\pi$
$727$	0.436118	+	0.109242i	0.0161747	+	0.00405156i	−0.234884	+	0.972023i	$0.575471\pi$
$728$	10.0393	+	6.99925i	0.372080	+	0.259410i
$729$	25.4152	+	34.2684i	0.941302	+	1.26920i
$730$	5.18680	+	8.46505i	0.191972	+	0.313306i
$731$	8.78738	+	10.1870i	0.325013	+	0.376780i
$732$	27.9302	+	49.8848i	1.03233	+	1.84379i
$733$	8.41555	−	5.32909i	0.310836	−	0.196834i	−0.370450	−	0.928853i	$-0.620796\pi$
$733$	8.41555	−	5.32909i	0.310836	−	0.196834i	0.681285	+	0.732018i	$0.261421\pi$
$734$	−10.0362	−	25.2799i	−0.370444	−	0.933096i
$735$	−26.3174	+	17.5847i	−0.970733	+	0.648623i
$736$	27.5456	+	6.19288i	1.01534	+	0.228273i
$737$	−37.6942	−	25.1865i	−1.38848	−	0.927756i
$738$	7.63972	−	35.6463i	0.281222	−	1.31216i
$739$	−32.6348	+	5.66268i	−1.20049	+	0.208305i	−0.735819	−	0.677178i	$-0.763203\pi$
$739$	−32.6348	+	5.66268i	−1.20049	+	0.208305i	−0.464672	+	0.885483i	$0.653828\pi$
$740$	47.4291	−	10.4012i	1.74353	−	0.382357i
$741$	13.1042	+	6.59608i	0.481394	+	0.242313i
$742$	−4.56083	−	12.3646i	−0.167434	−	0.453919i
$743$	−14.1439	+	3.54286i	−0.518890	+	0.129975i	−0.493573	−	0.869704i	$-0.664309\pi$
$743$	−14.1439	+	3.54286i	−0.518890	+	0.129975i	−0.0253167	+	0.999679i	$0.508059\pi$
$744$	32.7357	+	30.8714i	1.20015	+	1.13180i
$745$	7.37217	+	49.6991i	0.270095	+	1.82084i
$746$	−8.44305	−	26.8849i	−0.309122	−	0.984326i
$747$	22.9040	−	0.562262i	0.838014	−	0.0205721i
$748$	−28.4898	+	23.1431i	−1.04169	+	0.846196i
$749$	32.7539	−	16.4869i	1.19680	−	0.602419i
$750$	26.5939	+	24.8288i	0.971070	+	0.906620i
$751$	8.60134	+	28.3548i	0.313867	+	1.03468i	0.961976	+	0.273134i	$0.0880602\pi$
$751$	8.60134	+	28.3548i	0.313867	+	1.03468i	−0.648109	+	0.761548i	$0.724440\pi$
$752$	−29.9164	−	18.3411i	−1.09094	−	0.668831i
$753$	−39.9565	−	12.1207i	−1.45609	−	0.441702i
$754$	4.47312	−	16.8004i	0.162901	−	0.611835i
$755$	−1.56078	−	5.63994i	−0.0568026	−	0.205258i
$756$	−23.5806	+	31.4640i	−0.857617	+	1.14434i
$757$	−21.5164	+	4.83168i	−0.782029	+	0.175610i	−0.591752	−	0.806120i	$-0.701563\pi$
$757$	−21.5164	+	4.83168i	−0.782029	+	0.175610i	−0.190277	+	0.981731i	$0.560938\pi$
$758$	−18.3861	−	12.0271i	−0.667812	−	0.436844i
$759$	33.8953	+	37.3977i	1.23032	+	1.35745i
$760$	19.3194	−	21.5206i	0.700790	−	0.780633i
$761$	−23.2917	−	8.33391i	−0.844324	−	0.302104i	−0.121034	−	0.992648i	$-0.538621\pi$
$761$	−23.2917	−	8.33391i	−0.844324	−	0.302104i	−0.723290	+	0.690544i	$0.757371\pi$
$762$	−0.0497839	+	0.0241438i	−0.00180348	+	0.000874638i
$763$	3.27595	+	2.55657i	0.118597	+	0.0925541i
$764$	−7.12615	+	31.0067i	−0.257815	+	1.12178i
$765$	23.7277	+	61.5117i	0.857877	+	2.22396i
$766$	−0.0851166	−	1.01824i	−0.00307539	−	0.0367905i
$767$		−	6.60256i		−	0.238405i
$768$	23.1653	−	39.0467i	0.835906	−	1.40898i
$769$			14.0839i			0.507878i	0.967220	+	0.253939i	$0.0817263\pi$
$769$			14.0839i			0.507878i	−0.967220	+	0.253939i	$0.918274\pi$
$770$	42.9791	−	3.59271i	1.54886	−	0.129472i
$771$	−0.675616	−	1.75147i	−0.0243317	−	0.0630776i
$772$	22.6456	+	36.1608i	0.815032	+	1.30146i
$773$	14.6386	+	11.4240i	0.526512	+	0.410894i	0.843171	−	0.537645i	$-0.180686\pi$
$773$	14.6386	+	11.4240i	0.526512	+	0.410894i	−0.316659	+	0.948539i	$0.602561\pi$
$774$	−8.14463	−	16.7940i	−0.292753	−	0.603649i
$775$	−7.50890	−	2.68673i	−0.269727	−	0.0965100i
$776$	−2.84435	+	8.07024i	−0.102106	+	0.289705i
$777$	61.6418	+	68.0113i	2.21139	+	2.43989i
$778$	18.3283	−	28.0189i	0.657103	−	1.00453i
$779$	−20.0872	+	4.51074i	−0.719700	+	0.161614i
$780$	−18.2439	+	2.61289i	−0.653237	+	0.0935564i
$781$	9.89852	+	35.7687i	0.354197	+	1.27990i
$782$	35.1238	+	9.35174i	1.25603	+	0.334417i
$783$	53.4520	+	16.2145i	1.91022	+	0.579458i
$784$	16.5164	+	6.09702i	0.589872	+	0.217751i
$785$	−7.21941	−	23.7992i	−0.257672	−	0.849430i
$786$	−59.4913	+	63.7205i	−2.12199	+	2.27283i
$787$	−39.4685	+	19.8668i	−1.40690	+	0.708175i	−0.980529	−	0.196373i	$-0.937084\pi$
$787$	−39.4685	+	19.8668i	−1.40690	+	0.708175i	−0.426372	+	0.904548i	$0.640209\pi$
$788$	2.69353	−	26.0113i	0.0959531	−	0.926613i
$789$	25.5437	−	0.627062i	0.909380	−	0.0223240i
$790$	−47.2984	+	14.8538i	−1.68280	+	0.528474i
$791$	6.08599	+	41.0284i	0.216393	+	1.45880i
$792$	46.4562	−	20.8576i	1.65075	−	0.741143i
$793$	−12.5223	+	3.13667i	−0.444680	+	0.111387i
$794$	34.2771	−	12.6435i	1.21645	−	0.448702i
$795$	17.7275	+	8.92326i	0.628728	+	0.316475i
$796$	−14.9113	−	9.54749i	−0.528518	−	0.338402i
$797$	21.6105	−	3.74979i	0.765485	−	0.132824i	0.225207	−	0.974311i	$-0.427694\pi$
$797$	21.6105	−	3.74979i	0.765485	−	0.132824i	0.540278	+	0.841487i	$0.318319\pi$
$798$	53.4559	+	11.4567i	1.89232	+	0.405562i
$799$	−37.5629	−	25.0987i	−1.32888	−	0.887929i
$800$	−0.987041	+	7.98610i	−0.0348972	+	0.282351i
$801$	−51.8081	+	34.6171i	−1.83055	+	1.22313i
$802$	−35.9123	+	14.2574i	−1.26811	+	0.503446i
$803$	8.34041	−	5.28151i	0.294327	−	0.186380i
$804$	69.4788	+	19.6026i	2.45033	+	0.691332i
$805$	−27.8961	−	32.3394i	−0.983210	−	1.13981i
$806$	−8.66313	+	5.30817i	−0.305146	+	0.186972i
$807$	52.0201	+	70.1410i	1.83120	+	2.46908i
$808$	−2.33184	+	10.6202i	−0.0820340	+	0.373619i
$809$	−6.56489	−	1.64442i	−0.230809	−	0.0578147i	0.125850	−	0.992049i	$-0.459834\pi$
$809$	−6.56489	−	1.64442i	−0.230809	−	0.0578147i	−0.356659	+	0.934235i	$0.616084\pi$
$810$	−0.527347	−	4.86649i	−0.0185291	−	0.170991i
$811$	19.8363	−	8.79283i	0.696547	−	0.308758i	−0.0264101	−	0.999651i	$-0.508408\pi$
$811$	19.8363	−	8.79283i	0.696547	−	0.308758i	0.722957	+	0.690893i	$0.242783\pi$
$812$	0.324576	−	64.7866i	0.0113904	−	2.27356i
$813$	−47.6726	+	3.51654i	−1.67195	+	0.123331i
$814$	−11.0386	−	47.0049i	−0.386904	−	1.64752i
$815$	−4.48956	+	3.68448i	−0.157262	+	0.129062i
$816$	31.7638	−	49.0658i	1.11195	−	1.71765i
$817$	−6.68679	+	8.14788i	−0.233941	+	0.285058i
$818$	−9.95148	−	29.1641i	−0.347945	−	1.01970i
$819$	−13.4483	−	17.2324i	−0.469922	−	0.602150i
$820$	17.4644	−	19.0761i	0.609884	−	0.666165i
$821$	−23.4845	−	4.07495i	−0.819615	−	0.142217i	−0.254336	−	0.967116i	$-0.581857\pi$
$821$	−23.4845	−	4.07495i	−0.819615	−	0.142217i	−0.565280	+	0.824899i	$0.691232\pi$
$822$	46.6255	+	18.7815i	1.62625	+	0.655082i
$823$	8.21268	−	17.3643i	0.286276	−	0.605280i	−0.708687	−	0.705523i	$-0.750712\pi$
$823$	8.21268	−	17.3643i	0.286276	−	0.605280i	0.994963	+	0.100243i	$0.0319621\pi$
$824$	3.97206	−	2.14747i	0.138373	−	0.0748105i
$825$	−9.66066	+	10.6589i	−0.336341	+	0.371095i
$826$	−6.21117	−	23.8074i	−0.216114	−	0.828366i
$827$	35.2065	+	9.74294i	1.22425	+	0.338795i	0.818135	−	0.575027i	$-0.195008\pi$
$827$	35.2065	+	9.74294i	1.22425	+	0.338795i	0.406114	+	0.913822i	$0.366883\pi$
$828$	−43.7511	−	25.0751i	−1.52046	−	0.871418i
$829$	0.803111	−	32.7151i	0.0278932	−	1.13624i	−0.808632	−	0.588315i	$-0.799792\pi$
$829$	0.803111	−	32.7151i	0.0278932	−	1.13624i	0.836525	−	0.547928i	$-0.184583\pi$
$830$	14.2199	+	7.87300i	0.493579	+	0.273276i
$831$	15.3802	−	6.37071i	0.533535	−	0.220997i
$832$	7.13913	+	7.35702i	0.247505	+	0.255059i
$833$	20.9405	+	8.67385i	0.725546	+	0.300531i
$834$	−17.3616	−	21.8043i	−0.601181	−	0.755021i
$835$	−24.1714	−	25.3880i	−0.836486	−	0.878588i
$836$	−21.6813	−	18.8927i	−0.749864	−	0.653418i
$837$	−16.0894	−	28.4017i	−0.556131	−	0.981708i
$838$	24.7114	−	18.7040i	0.853639	−	0.646120i
$839$	−0.794248	−	16.1673i	−0.0274205	−	0.558157i	−0.972724	−	0.231965i	$-0.925484\pi$
$839$	−0.794248	−	16.1673i	−0.0274205	−	0.558157i	0.945304	−	0.326192i	$-0.105766\pi$
$840$	−63.3256	+	26.5840i	−2.18494	+	0.917234i
$841$	−59.3517	+	21.2364i	−2.04661	+	0.732289i
$842$	−14.0772	+	14.3549i	−0.485133	+	0.494704i
$843$	35.2696	−	24.8397i	1.21475	−	0.855523i
$844$	5.05785	+	20.6300i	0.174098	+	0.710115i
$845$	−3.52347	+	28.5675i	−0.121211	+	0.982752i
$846$	41.4001	+	47.0571i	1.42337	+	1.61785i
$847$	−0.563042	−	5.71667i	−0.0193464	−	0.196427i
$848$	−1.77824	−	10.8952i	−0.0610650	−	0.374144i
$849$	25.4014	+	2.50182i	0.871774	+	0.0858622i
$850$	−1.67132	+	10.2239i	−0.0573257	+	0.350676i
$851$	−31.2302	+	36.2045i	−1.07056	+	1.24107i
$852$	−32.5872	−	49.3031i	−1.11642	−	1.68910i
$853$	25.7073	+	9.91639i	0.880200	+	0.339531i	0.757439	−	0.652906i	$-0.226450\pi$
$853$	25.7073	+	9.91639i	0.880200	+	0.339531i	0.122761	+	0.992436i	$0.460825\pi$
$854$	−42.2020	+	23.0902i	−1.44412	+	0.790129i
$855$	−44.3055	+	26.5557i	−1.51522	+	0.908186i
$856$	29.5642	−	8.33312i	1.01048	−	0.284820i
$857$	1.57296	−	10.6041i	0.0537314	−	0.362228i	−0.945589	−	0.325364i	$-0.894513\pi$
$857$	1.57296	−	10.6041i	0.0537314	−	0.362228i	0.999320	−	0.0368639i	$-0.0117368\pi$
$858$	2.86600	+	18.1012i	0.0978437	+	0.617963i
$859$	5.04438	+	0.372096i	0.172112	+	0.0126958i	0.159346	−	0.987223i	$-0.449061\pi$
$859$	5.04438	+	0.372096i	0.172112	+	0.0126958i	0.0127659	+	0.999919i	$0.495936\pi$
$860$	1.04025	−	13.2006i	0.0354723	−	0.450136i
$861$	47.7029	+	10.7121i	1.62571	+	0.365066i
$862$	32.8051	−	31.8496i	1.11735	−	1.08480i
$863$	5.41345	−	27.2153i	0.184276	−	0.926418i	−0.772372	−	0.635171i	$-0.780930\pi$
$863$	5.41345	−	27.2153i	0.184276	−	0.926418i	0.956648	−	0.291247i	$-0.0940703\pi$
$864$	−24.4097	+	22.1124i	−0.830435	+	0.752280i
$865$	3.46407	+	17.4151i	0.117782	+	0.592130i
$866$	−29.7146	−	20.4961i	−1.00974	−	0.696487i
$867$	15.5525	−	22.0828i	0.528190	−	0.749973i
$868$	−26.2439	+	27.2897i	−0.890775	+	0.926273i
$869$	15.4638	+	46.8095i	0.524572	+	1.58790i
$870$	66.2238	+	71.6478i	2.24520	+	2.42909i
$871$	−8.38017	+	13.9815i	−0.283951	+	0.473744i
$872$	2.28610	+	2.62488i	0.0774172	+	0.0888896i
$873$	9.10430	−	12.2757i	0.308134	−	0.415471i
$874$	−2.51436	+	28.3663i	−0.0850495	+	0.959505i
$875$	−21.1092	+	22.1717i	−0.713621	+	0.749540i
$876$	−10.0336	+	12.1019i	−0.339005	+	0.408884i
$877$	−11.4025	−	3.76687i	−0.385035	−	0.127198i	0.114649	−	0.993406i	$-0.463426\pi$
$877$	−11.4025	−	3.76687i	−0.385035	−	0.127198i	−0.499684	+	0.866208i	$0.666551\pi$
$878$	6.38326	−	17.0418i	0.215425	−	0.575134i
$879$	30.5549	+	16.3320i	1.03059	+	0.550863i
$880$	35.9160	+	3.90115i	1.21073	+	0.131508i
$881$	−16.6424	−	31.1357i	−0.560696	−	1.04899i	−0.989355	−	0.145522i	$-0.953514\pi$
$881$	−16.6424	−	31.1357i	−0.560696	−	1.04899i	0.428659	−	0.903466i	$-0.358986\pi$
$882$	−24.9780	−	19.1035i	−0.841054	−	0.643247i
$883$	44.3802	+	25.1411i	1.49351	+	0.846065i	0.999723	−	0.0235158i	$-0.00748600\pi$
$883$	44.3802	+	25.1411i	1.49351	+	0.846065i	0.493790	+	0.869581i	$0.335611\pi$
$884$	8.81401	+	9.82322i	0.296447	+	0.330391i
$885$	31.3038	+	19.8229i	1.05227	+	0.666341i
$886$	−15.9065	−	3.00280i	−0.534388	−	0.100881i
$887$	28.5424	+	1.40220i	0.958360	+	0.0470812i	0.522232	−	0.852803i	$-0.325099\pi$
$887$	28.5424	+	1.40220i	0.958360	+	0.0470812i	0.436128	+	0.899885i	$0.356349\pi$
$888$	39.8414	+	65.7599i	1.33699	+	2.20676i
$889$	−0.0199052	−	0.0420860i	−0.000667599	−	0.00141152i
$890$	−44.1279	+	2.60012i	−1.47917	+	0.0871562i
$891$	−4.83090	+	0.595834i	−0.161841	+	0.0199612i
$892$	−17.5923	−	18.6641i	−0.589033	−	0.624920i
$893$	14.3435	−	32.3584i	0.479986	−	1.08283i
$894$	−70.7108	+	36.4628i	−2.36492	+	1.21950i
$895$	−47.2545	−	47.2545i	−1.57954	−	1.57954i
$896$	32.6631	+	19.8119i	1.09120	+	0.661869i
$897$	12.8326	−	12.8326i	0.428468	−	0.428468i
$898$	11.9573	−	37.4185i	0.399022	−	1.24867i
$899$	49.1711	+	21.7961i	1.63995	+	0.726939i
$900$	5.89010	−	13.1102i	0.196337	−	0.437006i
$901$	−1.73972	−	14.1053i	−0.0579586	−	0.469916i
$902$	−19.2235	−	17.0842i	−0.640074	−	0.568842i
$903$	22.6281	−	10.7023i	0.753015	−	0.356150i
$904$	−1.53970	+	34.7096i	−0.0512095	+	1.15442i
$905$	0.565052	−	11.5019i	0.0187830	−	0.382336i
$906$	7.65406	−	5.22312i	0.254289	−	0.173527i
$907$	−22.4559	+	35.4617i	−0.745636	+	1.17749i	0.233118	+	0.972448i	$0.425107\pi$
$907$	−22.4559	+	35.4617i	−0.745636	+	1.17749i	−0.978754	+	0.205039i	$0.934268\pi$
$908$	0.331338	+	0.940861i	0.0109958	+	0.0312236i
$909$	9.57245	−	16.8977i	0.317498	−	0.560463i
$910$	−2.04852	−	15.3717i	−0.0679079	−	0.509566i
$911$	−20.7797	+	11.1070i	−0.688462	+	0.367991i	−0.778236	−	0.627972i	$-0.783885\pi$
$911$	−20.7797	+	11.1070i	−0.688462	+	0.367991i	0.0897743	+	0.995962i	$0.471385\pi$
$912$	42.1308	+	17.9478i	1.39509	+	0.594310i
$913$	7.61902	−	14.2542i	0.252153	−	0.471745i
$914$	20.7268	+	45.5528i	0.685582	+	1.50675i
$915$	22.7243	−	68.7876i	0.751244	−	2.27405i
$916$	4.21706	−	13.6551i	0.139335	−	0.451178i
$917$	−53.1247	−	50.5789i	−1.75433	−	1.67026i
$918$	−32.5131	+	27.2186i	−1.07309	+	0.898346i
$919$	−18.4351	−	13.6724i	−0.608117	−	0.451011i	0.247308	−	0.968937i	$-0.420454\pi$
$919$	−18.4351	−	13.6724i	−0.608117	−	0.451011i	−0.855425	+	0.517926i	$0.826704\pi$
$920$	−17.7814	−	31.0432i	−0.586234	−	1.02346i
$921$	50.8259	+	30.4639i	1.67477	+	1.00382i
$922$	−19.1197	−	0.752185i	−0.629675	−	0.0247719i
$923$	12.6709	−	4.18591i	0.417069	−	0.137781i
$924$	27.3623	+	62.5727i	0.900155	+	2.05849i
$925$	−11.1416	−	7.84679i	−0.366333	−	0.258001i
$926$	−6.88351	−	37.4929i	−0.226206	−	1.23209i
$927$	−7.91003	+	1.57340i	−0.259799	+	0.0516773i
$928$	10.6009	−	53.2240i	0.347992	−	1.74716i
$929$	−9.37967	−	1.86573i	−0.307737	−	0.0612127i	0.0388060	−	0.999247i	$-0.487645\pi$
$929$	−9.37967	−	1.86573i	−0.307737	−	0.0612127i	−0.346543	+	0.938034i	$0.612645\pi$
$930$	0.842488	−	57.0101i	0.0276263	−	1.86943i
$931$	−3.89086	+	17.3268i	−0.127518	+	0.567862i
$932$	22.5082	−	7.31084i	0.737280	−	0.239474i
$933$	−2.87868	+	39.0253i	−0.0942436	+	1.27763i
$934$	−12.0283	+	16.5538i	−0.393580	+	0.541658i
$935$	46.0070	+	6.82449i	1.50459	+	0.223185i
$936$	−8.31020	−	16.3158i	−0.271627	−	0.533299i
$937$	−25.0210	−	41.7450i	−0.817399	−	1.36375i	−0.929032	−	0.369999i	$-0.879358\pi$
$937$	−25.0210	−	41.7450i	−0.817399	−	1.36375i	0.111633	−	0.993750i	$-0.464392\pi$
$938$	−17.0644	+	58.2975i	−0.557172	+	1.90348i
$939$	9.09087	−	23.5672i	0.296669	−	0.769086i
$940$	8.45611	+	43.6536i	0.275808	+	1.42382i
$941$	−22.5542	−	19.4554i	−0.735246	−	0.634227i	0.203406	−	0.979095i	$-0.434799\pi$
$941$	−22.5542	−	19.4554i	−0.735246	−	0.634227i	−0.938652	+	0.344867i	$0.887924\pi$
$942$	31.9745	−	22.9894i	1.04178	−	0.749035i
$943$	−2.49623	+	25.3447i	−0.0812885	+	0.825336i
$944$	−1.31014	−	20.5682i	−0.0426414	−	0.669438i
$945$	49.5832	−	4.88352i	1.61294	−	0.158861i
$946$	−13.1404	−	0.840341i	−0.427230	−	0.0273218i
$947$	60.1578	+	7.41975i	1.95486	+	0.241110i	0.998667	−	0.0516127i	$-0.0164361\pi$
$947$	60.1578	+	7.41975i	1.95486	+	0.241110i	0.956198	+	0.292722i	$0.0945611\pi$
$948$	−46.4472	−	63.2871i	−1.50854	−	2.05547i
$949$	−2.04389	−	2.90211i	−0.0663476	−	0.0942063i
$950$	−8.11614	+	0.0792721i	−0.263322	+	0.00257193i
$951$	−28.6557	−	80.0873i	−0.929225	−	2.59701i
$952$	41.0223	+	27.1289i	1.32954	+	0.879252i
$953$	−23.5689	+	1.15786i	−0.763470	+	0.0375069i	−0.427078	−	0.904215i	$-0.640457\pi$
$953$	−23.5689	+	1.15786i	−0.763470	+	0.0375069i	−0.336392	+	0.941722i	$0.609207\pi$
$954$	−2.70254	+	19.5315i	−0.0874978	+	0.632354i
$955$	35.0766	−	19.8707i	1.13505	−	0.642999i
$956$	−40.1758	+	19.9711i	−1.29938	+	0.645913i
$957$	70.2648	−	66.8977i	2.27134	−	2.16250i
$958$	−0.236608	+	2.08586i	−0.00764445	+	0.0673910i
$959$	−16.1857	+	39.0758i	−0.522664	+	1.26182i
$960$	−56.3147	+	11.7597i	−1.81755	+	0.379544i
$961$	−0.165200	−	0.398829i	−0.00532904	−	0.0128654i
$962$	−16.6861	+	4.79360i	−0.537981	+	0.154552i
$963$	−54.8458	−	1.34639i	−1.76738	−	0.0433868i
$964$	−5.98752	+	46.6218i	−0.192845	+	1.50159i
$965$	14.4196	−	52.1056i	0.464182	−	1.67734i
$966$	34.1996	−	58.3434i	1.10035	−	1.87717i
$967$	0.229868	+	0.208340i	0.00739204	+	0.00669976i	0.675247	−	0.737592i	$-0.264037\pi$
$967$	0.229868	+	0.208340i	0.00739204	+	0.00669976i	−0.667855	+	0.744292i	$0.732787\pi$
$968$	0.448850	−	4.79078i	0.0144266	−	0.153981i
$969$	53.2955	+	25.2069i	1.71210	+	0.809763i
$970$	9.97627	−	4.24693i	0.320319	−	0.136361i
$971$	6.67972	−	38.4961i	0.214362	−	1.23540i	−0.660425	−	0.750892i	$-0.729624\pi$
$971$	6.67972	−	38.4961i	0.214362	−	1.23540i	0.874787	−	0.484508i	$-0.161001\pi$
$972$	−24.6311	+	11.4990i	−0.790043	+	0.368830i
$973$	18.4886	−	14.4286i	0.592716	−	0.462560i
$974$	−1.17895	+	2.40026i	−0.0377760	+	0.0769093i
$975$	3.99836	+	3.28137i	0.128050	+	0.105088i
$976$	−38.3869	+	12.2561i	−1.22873	+	0.392308i
$977$	−26.1656	−	31.8829i	−0.837112	−	1.02002i	−0.999446	−	0.0332878i	$-0.989402\pi$
$977$	−26.1656	−	31.8829i	−0.837112	−	1.02002i	0.162334	−	0.986736i	$-0.448098\pi$
$978$	−7.81751	−	4.84406i	−0.249976	−	0.154896i
$979$	3.23363	+	43.8373i	0.103347	+	1.40104i
$980$	−8.43389	−	20.6533i	−0.269411	−	0.659744i
$981$	−2.51945	−	5.68378i	−0.0804398	−	0.181469i
$982$	7.50162	−	9.32500i	0.239386	−	0.297573i
$983$	−12.4592	+	49.7400i	−0.397388	+	1.58646i	0.359648	+	0.933088i	$0.382897\pi$
$983$	−12.4592	+	49.7400i	−0.397388	+	1.58646i	−0.757036	+	0.653373i	$0.773353\pi$
$984$	37.5188	+	16.4178i	1.19605	+	0.523381i
$985$	−26.6151	+	19.7391i	−0.848026	+	0.628939i
$986$	16.3135	−	67.9355i	0.519528	−	2.16351i
$987$	−63.6475	+	54.9027i	−2.02592	+	1.74757i
$988$	−6.40240	+	8.11972i	−0.203687	+	0.258323i
$989$	6.97576	+	11.0159i	0.221816	+	0.350286i
$990$	−59.2438	−	25.5716i	−1.88289	−	0.812720i
$991$	26.8770	+	40.2243i	0.853776	+	1.27777i	0.959025	+	0.283320i	$0.0914360\pi$
$991$	26.8770	+	40.2243i	0.853776	+	1.27777i	−0.105249	+	0.994446i	$0.533564\pi$
$992$	−25.9340	+	18.2550i	−0.823404	+	0.579595i
$993$	−6.52641	+	9.76747i	−0.207109	+	0.309961i
$994$	41.7508	−	27.0133i	1.32426	−	0.856810i
$995$	3.83567	+	22.1055i	0.121599	+	0.700793i
$996$	−4.52714	+	25.3364i	−0.143448	+	0.802813i
$997$	−19.7450	+	39.2265i	−0.625330	+	1.24232i	0.329216	+	0.944255i	$0.393215\pi$
$997$	−19.7450	+	39.2265i	−0.625330	+	1.24232i	−0.954546	+	0.298063i	$0.903660\pi$
$998$	35.0874	+	16.1777i	1.11067	+	0.512095i
$999$	−13.5529	−	54.1062i	−0.428795	−	1.71184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.157.50	✓	4032
512.437	even	128	inner	512.2.o.a.437.50	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.157.50	✓	4032	1.1	even	1	trivial
512.2.o.a.437.50	yes	4032	512.437	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07983 + 0.913223i) q^{2} +(2.64744 - 1.02123i) q^{3} +(0.332047 + 1.97224i) q^{4} +(1.55916 - 1.99788i) q^{5} +(3.79139 + 1.31495i) q^{6} +(-1.13754 + 3.17922i) q^{7} +(-1.44255 + 2.43291i) q^{8} +(3.74319 - 3.39263i) q^{9} +O(q^{10})\)	\(q+(1.07983 + 0.913223i) q^{2} +(2.64744 - 1.02123i) q^{3} +(0.332047 + 1.97224i) q^{4} +(1.55916 - 1.99788i) q^{5} +(3.79139 + 1.31495i) q^{6} +(-1.13754 + 3.17922i) q^{7} +(-1.44255 + 2.43291i) q^{8} +(3.74319 - 3.39263i) q^{9} +(3.50813 - 0.733500i) q^{10} +(-0.780850 - 3.47728i) q^{11} +(2.89319 + 4.88231i) q^{12} +(-1.23502 + 0.341775i) q^{13} +(-4.13169 + 2.39417i) q^{14} +(2.08749 - 6.88153i) q^{15} +(-3.77949 + 1.30976i) q^{16} +(-4.92788 + 1.49486i) q^{17} +(7.14022 - 0.245081i) q^{18} +(-1.81402 - 3.60383i) q^{19} +(4.45802 + 2.41165i) q^{20} +(0.235139 + 9.57851i) q^{21} +(2.33235 - 4.46795i) q^{22} +(-4.93694 + 0.732326i) q^{23} +(-1.33449 + 7.91417i) q^{24} +(-0.345639 - 1.37987i) q^{25} +(-1.64572 - 0.758788i) q^{26} +(2.61780 - 5.20067i) q^{27} +(-6.64792 - 1.18786i) q^{28} +(1.64013 + 9.45233i) q^{29} +(8.53850 - 5.52451i) q^{30} +(3.11475 - 4.66155i) q^{31} +(-5.27729 - 2.03721i) q^{32} +(-5.61837 - 8.40848i) q^{33} +(-6.68639 - 2.88607i) q^{34} +(4.57809 + 7.22959i) q^{35} +(7.93401 + 6.25597i) q^{36} +(7.25401 - 6.25736i) q^{37} +(1.33228 - 5.54811i) q^{38} +(-2.92061 + 2.16607i) q^{39} +(2.61151 + 6.67533i) q^{40} +(1.23985 - 4.94977i) q^{41} +(-8.49340 + 10.5579i) q^{42} +(-1.05869 - 2.38837i) q^{43} +(6.59877 - 2.69465i) q^{44} +(-0.941831 - 12.7681i) q^{45} +(-5.99981 - 3.71774i) q^{46} +(5.56539 + 6.78145i) q^{47} +(-8.66842 + 7.32724i) q^{48} +(-3.40237 - 2.79226i) q^{49} +(0.886897 - 1.80566i) q^{50} +(-11.5197 + 8.99006i) q^{51} +(-1.08415 - 2.32227i) q^{52} +(-0.471829 + 2.71922i) q^{53} +(7.57613 - 3.22518i) q^{54} +(-8.16466 - 3.86159i) q^{55} +(-6.09381 - 7.35372i) q^{56} +(-8.48285 - 7.68840i) q^{57} +(-6.86103 + 11.7047i) q^{58} +(-1.37423 + 4.96583i) q^{59} +(14.2652 + 1.83205i) q^{60} +(10.0710 + 0.247228i) q^{61} +(7.62042 - 2.18920i) q^{62} +(6.52788 + 15.7597i) q^{63} +(-3.83813 - 7.01917i) q^{64} +(-1.24276 + 3.00030i) q^{65} +(1.61196 - 14.2105i) q^{66} +(9.21282 - 8.77134i) q^{67} +(-4.58451 - 9.22262i) q^{68} +(-12.3224 + 6.98055i) q^{69} +(-1.65869 + 11.9875i) q^{70} +(-10.4011 + 0.510975i) q^{71} +(2.85425 + 14.0009i) q^{72} +(0.933193 + 2.60810i) q^{73} +(13.5474 - 0.132321i) q^{74} +(-2.32422 - 3.30014i) q^{75} +(6.50529 - 4.77432i) q^{76} +(11.9433 + 1.47307i) q^{77} +(-5.13185 - 0.328188i) q^{78} +(-13.7660 + 1.35583i) q^{79} +(-3.27609 + 9.59308i) q^{80} +(0.133871 - 1.35921i) q^{81} +(5.85907 - 4.21263i) q^{82} +(3.43404 + 2.96223i) q^{83} +(-18.8131 + 3.64427i) q^{84} +(-4.69681 + 12.1760i) q^{85} +(1.03791 - 3.54584i) q^{86} +(13.9952 + 23.3496i) q^{87} +(9.58633 + 3.11640i) q^{88} +(-12.2004 - 1.80975i) q^{89} +(10.6431 - 14.6474i) q^{90} +(0.318307 - 4.31518i) q^{91} +(-3.08362 - 9.49368i) q^{92} +(3.48560 - 15.5221i) q^{93} +(-0.183323 + 12.4052i) q^{94} +(-10.0284 - 1.99476i) q^{95} +(-16.0518 - 0.00405885i) q^{96} +(2.96716 - 0.590205i) q^{97} +(-1.12402 - 6.12228i) q^{98} +(-14.7200 - 10.3670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more