LMFDB - Embedded newform 507.2.m.b.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(40,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [204] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			79.1
Character	$\chi$	$=$	507.79
Dual form			507.2.m.b.430.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.42650 - 1.27353i) q^{2} +(-0.970942 - 0.239316i) q^{3} +(3.12991 + 4.53445i) q^{4} +(-0.0390694 - 0.103018i) q^{5} +(2.05122 + 1.81722i) q^{6} +(-0.184062 - 1.51589i) q^{7} +(-1.15934 - 9.54803i) q^{8} +(0.885456 + 0.464723i) q^{9} +(-0.0363936 + 0.299728i) q^{10} +(-4.15382 + 2.18010i) q^{11} +(-1.95379 - 5.15172i) q^{12} +(2.77782 + 2.29863i) q^{13} +(-1.48389 + 3.91271i) q^{14} +(0.0132804 + 0.109374i) q^{15} +(-5.43893 + 14.3413i) q^{16} +(-0.263861 - 2.17309i) q^{17} +(-1.55672 - 2.25530i) q^{18} +0.661441 q^{19} +(0.344845 - 0.499594i) q^{20} +(-0.184062 + 1.51589i) q^{21} +12.8557 q^{22} +5.40640 q^{23} +(-1.15934 + 9.54803i) q^{24} +(3.73347 - 3.30756i) q^{25} +(-3.81301 - 9.11526i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(6.29762 - 5.57920i) q^{28} +(5.46494 + 2.86822i) q^{29} +(0.107066 - 0.282309i) q^{30} +(-3.97739 - 3.52366i) q^{31} +(17.0630 - 15.1165i) q^{32} +(4.55485 - 1.12267i) q^{33} +(-2.12723 + 5.60905i) q^{34} +(-0.148972 + 0.0781865i) q^{35} +(0.664129 + 5.46960i) q^{36} +(-1.15032 - 1.01910i) q^{37} +(-1.60499 - 0.842362i) q^{38} +(-2.14700 - 2.89662i) q^{39} +(-0.938320 + 0.492468i) q^{40} +(-0.726940 - 0.179175i) q^{41} +(2.37715 - 3.44389i) q^{42} +(-6.59539 + 5.84301i) q^{43} +(-22.8866 - 12.0118i) q^{44} +(0.0132804 - 0.109374i) q^{45} +(-13.1186 - 6.88519i) q^{46} +(5.87910 - 8.51734i) q^{47} +(8.71298 - 12.6229i) q^{48} +(4.53256 - 1.11718i) q^{49} +(-13.2715 + 3.27114i) q^{50} +(-0.263861 + 2.17309i) q^{51} +(-1.72874 + 19.7904i) q^{52} +(-0.977751 - 8.05251i) q^{53} +(0.971758 + 2.56231i) q^{54} +(0.386876 + 0.342742i) q^{55} +(-14.2603 + 3.51486i) q^{56} +(-0.642221 - 0.158293i) q^{57} +(-9.60791 - 13.9195i) q^{58} +(0.0224213 + 0.0591201i) q^{59} +(-0.454385 + 0.402550i) q^{60} +(1.47461 - 12.1445i) q^{61} +(5.16366 + 13.6155i) q^{62} +(0.541489 - 1.42779i) q^{63} +(-30.8699 + 7.60875i) q^{64} +(0.128272 - 0.375971i) q^{65} +(-12.4821 - 3.07656i) q^{66} +(3.85753 - 5.58860i) q^{67} +(9.02793 - 7.99804i) q^{68} +(-5.24930 - 1.29384i) q^{69} +0.461053 q^{70} +(-6.34492 - 1.56388i) q^{71} +(3.41064 - 8.99313i) q^{72} +(1.75867 - 0.923022i) q^{73} +(1.49341 + 3.93781i) q^{74} +(-4.41653 + 2.31797i) q^{75} +(2.07025 + 2.99927i) q^{76} +(4.06934 + 5.89546i) q^{77} +(1.52078 + 9.76290i) q^{78} +(7.20919 - 10.4443i) q^{79} +1.68990 q^{80} +(0.568065 + 0.822984i) q^{81} +(1.53574 + 1.36054i) q^{82} +(8.54375 - 2.10584i) q^{83} +(-7.44981 + 3.90996i) q^{84} +(-0.213558 + 0.112084i) q^{85} +(23.4449 - 5.77866i) q^{86} +(-4.61972 - 4.09272i) q^{87} +(25.6313 + 37.1334i) q^{88} +7.62832 q^{89} +(-0.171516 + 0.248483i) q^{90} +(2.97318 - 4.63395i) q^{91} +(16.9215 + 24.5151i) q^{92} +(3.01855 + 4.37312i) q^{93} +(-25.1127 + 13.1801i) q^{94} +(-0.0258421 - 0.0681401i) q^{95} +(-20.1848 + 10.5938i) q^{96} +(1.64391 - 4.33464i) q^{97} +(-12.4210 - 3.06150i) q^{98} -4.69117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{13}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.42650	−	1.27353i	−1.71579	−	0.900518i	−0.972938	−	0.231068i	$-0.925778\pi$
$2$	−2.42650	−	1.27353i	−1.71579	−	0.900518i	−0.742857	−	0.669450i	$-0.766530\pi$
$3$	−0.970942	−	0.239316i	−0.560574	−	0.138169i
$3$	−0.970942	−	0.239316i	−0.560574	−	0.138169i
$4$	3.12991	+	4.53445i	1.56495	+	2.26723i
$5$	−0.0390694	−	0.103018i	−0.0174724	−	0.0460709i	0.925996	−	0.377533i	$-0.123227\pi$
$5$	−0.0390694	−	0.103018i	−0.0174724	−	0.0460709i	−0.943469	+	0.331462i	$0.892458\pi$
$6$	2.05122	+	1.81722i	0.837405	+	0.741876i
$7$	−0.184062	−	1.51589i	−0.0695689	−	0.572951i	−0.985259	−	0.171067i	$-0.945278\pi$
$7$	−0.184062	−	1.51589i	−0.0695689	−	0.572951i	0.915690	−	0.401884i	$-0.131645\pi$
$8$	−1.15934	−	9.54803i	−0.409889	−	3.37574i
$9$	0.885456	+	0.464723i	0.295152	+	0.154908i
$10$	−0.0363936	+	0.299728i	−0.0115087	+	0.0947824i
$11$	−4.15382	+	2.18010i	−1.25243	+	0.657324i	−0.954769	−	0.297349i	$-0.903897\pi$
$11$	−4.15382	+	2.18010i	−1.25243	+	0.657324i	−0.297657	+	0.954673i	$0.596205\pi$
$12$	−1.95379	−	5.15172i	−0.564011	−	1.48717i
$13$	2.77782	+	2.29863i	0.770428	+	0.637527i
$13$	2.77782	+	2.29863i	0.770428	+	0.637527i
$14$	−1.48389	+	3.91271i	−0.396587	+	1.04572i
$15$	0.0132804	+	0.109374i	0.00342899	+	0.0282403i
$16$	−5.43893	+	14.3413i	−1.35973	+	3.58532i
$17$	−0.263861	−	2.17309i	−0.0639958	−	0.527053i	−0.989090	−	0.147314i	$-0.952937\pi$
$17$	−0.263861	−	2.17309i	−0.0639958	−	0.527053i	0.925094	−	0.379738i	$-0.123986\pi$
$18$	−1.55672	−	2.25530i	−0.366923	−	0.531580i
$19$	0.661441			0.151745			0.0758725	−	0.997118i	$-0.475826\pi$
$19$	0.661441			0.151745			0.0758725	+	0.997118i	$0.475826\pi$
$20$	0.344845	−	0.499594i	0.0771096	−	0.111713i
$21$	−0.184062	+	1.51589i	−0.0401656	+	0.330794i
$22$	12.8557			2.74084
$23$	5.40640			1.12731			0.563657	−	0.826009i	$-0.309394\pi$
$23$	5.40640			1.12731			0.563657	+	0.826009i	$0.309394\pi$
$24$	−1.15934	+	9.54803i	−0.236649	+	1.94898i
$25$	3.73347	−	3.30756i	0.746694	−	0.661513i
$26$	−3.81301	−	9.11526i	−0.747792	−	1.78765i
$27$	−0.748511	−	0.663123i	−0.144051	−	0.127618i
$28$	6.29762	−	5.57920i	1.19014	−	1.05437i
$29$	5.46494	+	2.86822i	1.01481	+	0.532615i	0.888258	−	0.459345i	$-0.151916\pi$
$29$	5.46494	+	2.86822i	1.01481	+	0.532615i	0.126555	+	0.991960i	$0.459608\pi$
$30$	0.107066	−	0.282309i	0.0195474	−	0.0515423i
$31$	−3.97739	−	3.52366i	−0.714360	−	0.632868i	0.225573	−	0.974226i	$-0.427575\pi$
$31$	−3.97739	−	3.52366i	−0.714360	−	0.632868i	−0.939933	+	0.341358i	$0.889113\pi$
$32$	17.0630	−	15.1165i	3.01634	−	2.67224i
$33$	4.55485	−	1.12267i	0.792898	−	0.195432i
$34$	−2.12723	+	5.60905i	−0.364817	+	0.961944i
$35$	−0.148972	+	0.0781865i	−0.0251808	+	0.0132159i
$36$	0.664129	+	5.46960i	0.110688	+	0.911599i
$37$	−1.15032	−	1.01910i	−0.189112	−	0.167539i	0.563254	−	0.826284i	$-0.309549\pi$
$37$	−1.15032	−	1.01910i	−0.189112	−	0.167539i	−0.752366	+	0.658745i	$0.771088\pi$
$38$	−1.60499	−	0.842362i	−0.260363	−	0.136649i
$39$	−2.14700	−	2.89662i	−0.343795	−	0.463830i
$40$	−0.938320	+	0.492468i	−0.148361	+	0.0778661i
$41$	−0.726940	−	0.179175i	−0.113529	−	0.0279824i	0.182142	−	0.983272i	$-0.441697\pi$
$41$	−0.726940	−	0.179175i	−0.113529	−	0.0279824i	−0.295671	+	0.955290i	$0.595543\pi$
$42$	2.37715	−	3.44389i	0.366802	−	0.531404i
$43$	−6.59539	+	5.84301i	−1.00579	+	0.891050i	−0.994055	−	0.108881i	$-0.965273\pi$
$43$	−6.59539	+	5.84301i	−1.00579	+	0.891050i	−0.0117332	+	0.999931i	$0.503735\pi$
$44$	−22.8866	−	12.0118i	−3.45029	−	1.81085i
$45$	0.0132804	−	0.109374i	0.00197973	−	0.0163045i
$46$	−13.1186	−	6.88519i	−1.93424	−	1.01517i
$47$	5.87910	−	8.51734i	0.857554	−	1.24238i	−0.111060	−	0.993814i	$-0.535425\pi$
$47$	5.87910	−	8.51734i	0.857554	−	1.24238i	0.968614	−	0.248568i	$-0.0799600\pi$
$48$	8.71298	−	12.6229i	1.25761	−	1.82196i
$49$	4.53256	−	1.11718i	0.647508	−	0.159596i
$50$	−13.2715	+	3.27114i	−1.87688	+	0.462609i
$51$	−0.263861	+	2.17309i	−0.0369480	+	0.304294i
$52$	−1.72874	+	19.7904i	−0.239733	+	2.74443i
$53$	−0.977751	−	8.05251i	−0.134304	−	1.10610i	−0.891536	−	0.452950i	$-0.850372\pi$
$53$	−0.977751	−	8.05251i	−0.134304	−	1.10610i	0.757231	−	0.653147i	$-0.226552\pi$
$54$	0.971758	+	2.56231i	0.132239	+	0.348687i
$55$	0.386876	+	0.342742i	0.0521663	+	0.0462153i
$56$	−14.2603	+	3.51486i	−1.90562	+	0.469693i
$57$	−0.642221	−	0.158293i	−0.0850643	−	0.0209665i
$58$	−9.60791	−	13.9195i	−1.26158	−	1.82772i
$59$	0.0224213	+	0.0591201i	0.00291900	+	0.00769678i	0.936468	−	0.350753i	$-0.114074\pi$
$59$	0.0224213	+	0.0591201i	0.00291900	+	0.00769678i	−0.933549	+	0.358450i	$0.883305\pi$
$60$	−0.454385	+	0.402550i	−0.0586608	+	0.0519690i
$61$	1.47461	−	12.1445i	0.188804	−	1.55494i	−0.522856	−	0.852421i	$-0.675133\pi$
$61$	1.47461	−	12.1445i	0.188804	−	1.55494i	0.711660	−	0.702524i	$-0.247943\pi$
$62$	5.16366	+	13.6155i	0.655786	+	1.72917i
$63$	0.541489	−	1.42779i	0.0682212	−	0.179885i
$64$	−30.8699	+	7.60875i	−3.85874	+	0.951094i
$65$	0.128272	−	0.375971i	0.0159102	−	0.0466334i
$66$	−12.4821	−	3.07656i	−1.53644	−	0.378699i
$67$	3.85753	−	5.58860i	0.471273	−	0.682756i	−0.513205	−	0.858266i	$-0.671542\pi$
$67$	3.85753	−	5.58860i	0.471273	−	0.682756i	0.984478	+	0.175510i	$0.0561574\pi$
$68$	9.02793	−	7.99804i	1.09480	−	0.969905i
$69$	−5.24930	−	1.29384i	−0.631942	−	0.155760i
$70$	0.461053			0.0551063
$71$	−6.34492	−	1.56388i	−0.753004	−	0.185599i	−0.155911	−	0.987771i	$-0.549831\pi$
$71$	−6.34492	−	1.56388i	−0.753004	−	0.185599i	−0.597093	+	0.802172i	$0.703678\pi$
$72$	3.41064	−	8.99313i	0.401948	−	1.05985i
$73$	1.75867	−	0.923022i	0.205837	−	0.108032i	−0.358655	−	0.933470i	$-0.616764\pi$
$73$	1.75867	−	0.923022i	0.205837	−	0.108032i	0.564492	+	0.825439i	$0.309072\pi$
$74$	1.49341	+	3.93781i	0.173606	+	0.457761i
$75$	−4.41653	+	2.31797i	−0.509977	+	0.267657i
$76$	2.07025	+	2.99927i	0.237474	+	0.344040i
$77$	4.06934	+	5.89546i	0.463744	+	0.671850i
$78$	1.52078	+	9.76290i	0.172195	+	1.10543i
$79$	7.20919	−	10.4443i	0.811098	−	1.17508i	−0.170733	−	0.985317i	$-0.554614\pi$
$79$	7.20919	−	10.4443i	0.811098	−	1.17508i	0.981830	−	0.189760i	$-0.0607711\pi$
$80$	1.68990			0.188937
$81$	0.568065	+	0.822984i	0.0631183	+	0.0914427i
$82$	1.53574	+	1.36054i	0.169594	+	0.150247i
$83$	8.54375	−	2.10584i	0.937798	−	0.231146i	0.259340	−	0.965786i	$-0.416495\pi$
$83$	8.54375	−	2.10584i	0.937798	−	0.231146i	0.678458	+	0.734640i	$0.262649\pi$
$84$	−7.44981	+	3.90996i	−0.812841	+	0.426612i
$85$	−0.213558	+	0.112084i	−0.0231636	+	0.0121572i
$86$	23.4449	−	5.77866i	2.52813	−	0.623129i
$87$	−4.61972	−	4.09272i	−0.495286	−	0.438785i
$88$	25.6313	+	37.1334i	2.73231	+	3.95843i
$89$	7.62832			0.808601			0.404300	−	0.914626i	$-0.367515\pi$
$89$	7.62832			0.808601			0.404300	+	0.914626i	$0.367515\pi$
$90$	−0.171516	+	0.248483i	−0.0180793	+	0.0261924i
$91$	2.97318	−	4.63395i	0.311674	−	0.485770i
$92$	16.9215	+	24.5151i	1.76419	+	2.55587i
$93$	3.01855	+	4.37312i	0.313009	+	0.453471i
$94$	−25.1127	+	13.1801i	−2.59017	+	1.35943i
$95$	−0.0258421	−	0.0681401i	−0.00265135	−	0.00699103i
$96$	−20.1848	+	10.5938i	−2.06010	+	1.08122i
$97$	1.64391	−	4.33464i	0.166914	−	0.440116i	−0.825295	−	0.564702i	$-0.808991\pi$
$97$	1.64391	−	4.33464i	0.166914	−	0.440116i	0.992209	+	0.124586i	$0.0397604\pi$
$98$	−12.4210	−	3.06150i	−1.25471	−	0.309258i
$99$	−4.69117			−0.471480
$100$	26.6834	+	6.57686i	2.66834	+	0.657686i
$101$	−10.2373	+	9.06945i	−1.01865	+	0.902444i	−0.995257	−	0.0972826i	$-0.968985\pi$
$101$	−10.2373	+	9.06945i	−1.01865	+	0.902444i	−0.0233917	+	0.999726i	$0.507446\pi$
$102$	3.40775	−	4.93698i	0.337418	−	0.488834i
$103$	−13.5367	−	3.33650i	−1.33381	−	0.328755i	−0.492976	−	0.870043i	$-0.664091\pi$
$103$	−13.5367	−	3.33650i	−1.33381	−	0.328755i	−0.840838	+	0.541288i	$0.817937\pi$
$104$	18.7270	−	29.1876i	1.83633	−	2.86208i
$105$	0.163354	−	0.0402632i	0.0159417	−	0.00392929i
$106$	−7.88256	+	20.7846i	−0.765622	+	2.01878i
$107$	2.80991	+	7.40913i	0.271644	+	0.716267i	0.999533	+	0.0305716i	$0.00973276\pi$
$107$	2.80991	+	7.40913i	0.271644	+	0.716267i	−0.727888	+	0.685696i	$0.759498\pi$
$108$	0.664129	−	5.46960i	0.0639059	−	0.526312i
$109$	15.4511	−	13.6885i	1.47995	−	1.31112i	0.640113	−	0.768281i	$-0.278888\pi$
$109$	15.4511	−	13.6885i	1.47995	−	1.31112i	0.839836	−	0.542840i	$-0.182651\pi$
$110$	−0.502263	−	1.32436i	−0.0478889	−	0.126273i
$111$	0.873011	+	1.26477i	0.0828625	+	0.120047i
$112$	22.7409	+	5.60512i	2.14881	+	0.529634i
$113$	12.3977	−	3.05576i	1.16628	−	0.287462i	0.391794	−	0.920053i	$-0.371855\pi$
$113$	12.3977	−	3.05576i	1.16628	−	0.287462i	0.774486	+	0.632591i	$0.218009\pi$
$114$	1.35676	+	1.20198i	0.127072	+	0.112576i
$115$	−0.211225	−	0.556955i	−0.0196968	−	0.0519363i
$116$	4.09893	+	33.7577i	0.380576	+	3.13433i
$117$	1.39141	+	3.32626i	0.128636	+	0.307513i
$118$	0.0208857	−	0.172009i	0.00192268	−	0.0158347i
$119$	−3.24560	+	0.799968i	−0.297524	+	0.0733330i
$120$	1.02891	−	0.253604i	0.0939262	−	0.0231507i
$121$	6.25273	−	9.05865i	0.568430	−	0.823513i
$122$	−19.0445	+	27.5907i	−1.72421	+	2.49794i
$123$	0.662938	+	0.347936i	0.0597751	+	0.0313724i
$124$	3.52901	−	29.0640i	0.316914	−	2.61002i
$125$	−0.974388	−	0.511398i	−0.0871519	−	0.0457408i
$126$	−3.13225	+	2.77493i	−0.279043	+	0.247210i
$127$	5.10096	−	7.39002i	0.452637	−	0.655758i	−0.528531	−	0.848914i	$-0.677257\pi$
$127$	5.10096	−	7.39002i	0.452637	−	0.655758i	0.981168	+	0.193156i	$0.0618724\pi$
$128$	40.3288	+	9.94016i	3.56460	+	0.878594i
$129$	7.80207	−	4.09484i	0.686934	−	0.360531i
$130$	−0.790060	+	0.748935i	−0.0692929	+	0.0656859i
$131$	−3.18853	−	1.67347i	−0.278583	−	0.146212i	0.319646	−	0.947537i	$-0.396436\pi$
$131$	−3.18853	−	1.67347i	−0.278583	−	0.146212i	−0.598228	+	0.801326i	$0.704128\pi$
$132$	19.3470	+	17.1399i	1.68394	+	1.49184i
$133$	−0.121746	−	1.00267i	−0.0105567	−	0.0869426i
$134$	−16.4775	+	8.64807i	−1.42344	+	0.747080i
$135$	−0.0390694	+	0.103018i	−0.00336256	+	0.00886635i
$136$	−20.4429	+	5.03871i	−1.75296	+	0.432066i
$137$	−4.42106	+	3.91672i	−0.377716	+	0.334628i	−0.830526	−	0.556980i	$-0.811960\pi$
$137$	−4.42106	+	3.91672i	−0.377716	+	0.334628i	0.452810	+	0.891607i	$0.350422\pi$
$138$	11.0897	+	9.82462i	0.944018	+	0.836327i
$139$	−6.49480	+	17.1254i	−0.550881	+	1.45256i	0.313436	+	0.949609i	$0.398520\pi$
$139$	−6.49480	+	17.1254i	−0.550881	+	1.45256i	−0.864318	+	0.502946i	$0.832249\pi$
$140$	−0.820801	−	0.430789i	−0.0693703	−	0.0364084i
$141$	−7.74659	+	6.86288i	−0.652381	+	0.577959i
$142$	13.4043	+	11.8752i	1.12486	+	0.996543i
$143$	−16.5498	−	3.49222i	−1.38397	−	0.292034i
$144$	−11.4807	+	10.1710i	−0.956722	+	0.847582i
$145$	0.0819652	−	0.675044i	0.00680684	−	0.0560594i
$146$	−5.44291			−0.450458
$147$	−4.66821			−0.385027
$148$	1.02064	−	8.40576i	0.0838964	−	0.690949i
$149$	−10.6518	+	15.4318i	−0.872630	+	1.26422i	0.0906934	+	0.995879i	$0.471092\pi$
$149$	−10.6518	+	15.4318i	−0.872630	+	1.26422i	−0.963323	+	0.268344i	$0.913524\pi$
$150$	13.6687			1.11605
$151$	10.6965	+	15.4965i	0.870466	+	1.26109i	0.964116	+	0.265483i	$0.0855314\pi$
$151$	10.6965	+	15.4965i	0.870466	+	1.26109i	−0.0936491	+	0.995605i	$0.529853\pi$
$152$	−0.766836	−	6.31546i	−0.0621986	−	0.512251i
$153$	0.776249	−	2.04680i	0.0627560	−	0.165474i
$154$	−2.36624	−	19.4877i	−0.190677	−	1.57037i
$155$	−0.207605	+	0.547409i	−0.0166752	+	0.0439689i
$156$	6.41465	−	18.8016i	0.513583	−	1.50533i
$157$	−6.11782	−	16.1314i	−0.488256	−	1.28742i	−0.922280	−	0.386523i	$-0.873676\pi$
$157$	−6.11782	−	16.1314i	−0.488256	−	1.28742i	0.434024	−	0.900901i	$-0.357093\pi$
$158$	−30.7942	+	16.1620i	−2.44986	+	1.28578i
$159$	−0.977751	+	8.05251i	−0.0775407	+	0.638605i
$160$	−2.22391	−	1.16720i	−0.175815	−	0.0922749i
$161$	−0.995114	−	8.19550i	−0.0784259	−	0.645896i
$162$	−0.330318	−	2.72042i	−0.0259522	−	0.213736i
$163$	4.23350	+	3.75056i	0.331593	+	0.293766i	0.812447	−	0.583035i	$-0.198135\pi$
$163$	4.23350	+	3.75056i	0.331593	+	0.293766i	−0.480854	+	0.876801i	$0.659673\pi$
$164$	−1.46280	−	3.85708i	−0.114225	−	0.301187i
$165$	−0.293610	−	0.425368i	−0.0228575	−	0.0331149i
$166$	−23.4132	−	5.77085i	−1.81722	−	0.447905i
$167$	16.4803	+	8.64953i	1.27528	+	0.669321i	0.960086	−	0.279705i	$-0.0902366\pi$
$167$	16.4803	+	8.64953i	1.27528	+	0.669321i	0.315198	+	0.949026i	$0.397929\pi$
$168$	14.6871			1.13314
$169$	2.43256	+	12.7704i	0.187120	+	0.982337i
$170$	0.660940			0.0506918
$171$	0.585677	+	0.307387i	0.0447879	+	0.0235065i
$172$	−47.1378	−	11.6184i	−3.59422	−	0.885896i
$173$	9.42892	+	13.6601i	0.716867	+	1.03856i	0.996908	+	0.0785736i	$0.0250366\pi$
$173$	9.42892	+	13.6601i	0.716867	+	1.03856i	−0.280041	+	0.959988i	$0.590348\pi$
$174$	5.99758	+	15.8143i	0.454675	+	1.19888i
$175$	−5.70108	−	5.05072i	−0.430961	−	0.381798i
$176$	−8.67300	−	71.4286i	−0.653752	−	5.38413i
$177$	−0.00762141	−	0.0627679i	−0.000572860	−	0.00471793i
$178$	−18.5101	−	9.71486i	−1.38739	−	0.728160i
$179$	2.67612	−	22.0398i	0.200023	−	1.64733i	−0.454104	−	0.890949i	$-0.650041\pi$
$179$	2.67612	−	22.0398i	0.200023	−	1.64733i	0.654127	−	0.756385i	$-0.273036\pi$
$180$	0.537518	−	0.282111i	0.0400642	−	0.0210273i
$181$	4.98928	+	13.1557i	0.370851	+	0.977853i	0.982424	+	0.186665i	$0.0597678\pi$
$181$	4.98928	+	13.1557i	0.370851	+	0.977853i	−0.611573	+	0.791188i	$0.709463\pi$
$182$	−13.1159	+	7.45786i	−0.972213	+	0.552814i
$183$	−4.33813	+	11.4387i	−0.320684	+	0.845574i
$184$	−6.26786	−	51.6205i	−0.462073	−	3.80551i
$185$	−0.0600425	+	0.158319i	−0.00441441	+	0.0116399i
$186$	−1.75522	−	14.4556i	−0.128699	−	1.05993i
$187$	5.83359	+	8.45141i	0.426594	+	0.618028i
$188$	57.0225			4.15879
$189$	−0.867447	+	1.25671i	−0.0630975	+	0.0914125i
$190$	−0.0240722	+	0.198253i	−0.00174638	+	0.0143828i
$191$	1.95922			0.141764			0.0708819	−	0.997485i	$-0.477419\pi$
$191$	1.95922			0.141764			0.0708819	+	0.997485i	$0.477419\pi$
$192$	31.7938			2.29452
$193$	−1.28305	+	10.5669i	−0.0923561	+	0.760621i	0.870793	+	0.491651i	$0.163606\pi$
$193$	−1.28305	+	10.5669i	−0.0923561	+	0.760621i	−0.963149	+	0.268970i	$0.913317\pi$
$194$	−9.50922	+	8.42443i	−0.682722	+	0.604839i
$195$	−0.214520	+	0.334348i	−0.0153621	+	0.0239432i
$196$	19.2523	+	17.0560i	1.37516	+	1.21829i
$197$	10.5203	−	9.32014i	0.749538	−	0.664033i	−0.199249	−	0.979949i	$-0.563850\pi$
$197$	10.5203	−	9.32014i	0.749538	−	0.664033i	0.948787	+	0.315916i	$0.102312\pi$
$198$	11.3831	+	5.97432i	0.808963	+	0.424577i
$199$	5.36494	−	14.1462i	0.380311	−	1.00280i	−0.599056	−	0.800707i	$-0.704457\pi$
$199$	5.36494	−	14.1462i	0.380311	−	1.00280i	0.979367	−	0.202090i	$-0.0647734\pi$
$200$	−35.9091	−	31.8127i	−2.53915	−	2.24949i
$201$	−5.08288	+	4.50304i	−0.358519	+	0.317620i
$202$	36.3910	−	8.96957i	2.56046	−	0.631096i
$203$	3.34201	−	8.81216i	0.234563	−	0.618492i
$204$	−10.6796	+	5.60511i	−0.747725	+	0.392436i
$205$	0.00994299	+	0.0818879i	0.000694449	+	0.00571930i
$206$	28.5977	+	25.3354i	1.99250	+	1.76520i
$207$	4.78713	+	2.51248i	0.332729	+	0.174629i
$208$	−48.0738	+	27.3354i	−3.33332	+	1.89537i
$209$	−2.74751	+	1.44201i	−0.190049	+	0.0997456i
$210$	−0.447655	−	0.110337i	−0.0308912	−	0.00761399i
$211$	−9.27713	+	13.4402i	−0.638664	+	0.925264i	−0.999974	−	0.00718145i	$-0.997714\pi$
$211$	−9.27713	+	13.4402i	−0.638664	+	0.925264i	0.361311	+	0.932446i	$0.382329\pi$
$212$	33.4534	−	29.6372i	2.29759	−	2.03549i
$213$	5.78629	+	3.03688i	0.396470	+	0.208084i
$214$	2.61746	−	21.5567i	0.178926	−	1.47359i
$215$	0.859611	+	0.451159i	0.0586250	+	0.0307688i
$216$	−5.46373	+	7.91559i	−0.371760	+	0.538587i
$217$	−4.60938	+	6.67784i	−0.312905	+	0.453322i
$218$	−54.9248	+	13.5377i	−3.71998	+	0.916892i
$219$	−1.92846	+	0.475323i	−0.130313	+	0.0321194i
$220$	−0.343262	+	2.82702i	−0.0231427	+	0.190598i
$221$	4.26219	−	6.64298i	0.286706	−	0.446855i
$222$	−0.507638	−	4.18078i	−0.0340704	−	0.280595i
$223$	−5.83164	−	15.3768i	−0.390515	−	1.02970i	−0.975759	−	0.218847i	$-0.929770\pi$
$223$	−5.83164	−	15.3768i	−0.390515	−	1.02970i	0.585244	−	0.810857i	$-0.300999\pi$
$224$	−26.0555	−	23.0832i	−1.74091	−	1.54231i
$225$	4.84292	−	1.19367i	0.322862	−	0.0795782i
$226$	−33.9747	−	8.37400i	−2.25996	−	0.557030i
$227$	−1.83475	−	2.65809i	−0.121777	−	0.176424i	0.757354	−	0.653004i	$-0.226492\pi$
$227$	−1.83475	−	2.65809i	−0.121777	−	0.176424i	−0.879131	+	0.476580i	$0.841876\pi$
$228$	−1.29232	−	3.40756i	−0.0855859	−	0.225671i
$229$	7.16232	−	6.34526i	0.473300	−	0.419307i	−0.392458	−	0.919770i	$-0.628375\pi$
$229$	7.16232	−	6.34526i	0.473300	−	0.419307i	0.865758	+	0.500463i	$0.166837\pi$
$230$	−0.196758	+	1.62045i	−0.0129739	+	0.106849i
$231$	−2.54022	−	6.69800i	−0.167134	−	0.440696i
$232$	21.0501	−	55.5046i	1.38201	−	3.64405i
$233$	−17.4950	+	4.31214i	−1.14614	+	0.282498i	−0.766255	−	0.642537i	$-0.777882\pi$
$233$	−17.4950	+	4.31214i	−1.14614	+	0.282498i	−0.379883	+	0.925035i	$0.624036\pi$
$234$	0.859822	−	9.84315i	0.0562083	−	0.643467i
$235$	−1.10713	−	0.272883i	−0.0722211	−	0.0178009i
$236$	−0.197901	+	0.286708i	−0.0128822	+	0.0186631i
$237$	−9.49920	+	8.41555i	−0.617039	+	0.546649i
$238$	8.89422	+	2.19223i	0.576527	+	0.142101i
$239$	−11.9852			−0.775261			−0.387630	−	0.921815i	$-0.626706\pi$
$239$	−11.9852			−0.775261			−0.387630	+	0.921815i	$0.626706\pi$
$240$	−1.64080	−	0.404420i	−0.105913	−	0.0261052i
$241$	−7.64297	+	20.1528i	−0.492327	+	1.29816i	0.426853	+	0.904321i	$0.359622\pi$
$241$	−7.64297	+	20.1528i	−0.492327	+	1.29816i	−0.919180	+	0.393838i	$0.871147\pi$
$242$	−26.7087	+	14.0178i	−1.71690	+	0.901098i
$243$	−0.354605	−	0.935016i	−0.0227479	−	0.0599813i
$244$	59.6841	−	31.3246i	3.82088	−	2.00535i
$245$	−0.292173	−	0.423286i	−0.0186663	−	0.0270427i
$246$	−1.16551	−	1.68854i	−0.0743103	−	0.107657i
$247$	1.83736	+	1.52041i	0.116909	+	0.0967415i
$248$	−29.0328	+	42.0613i	−1.84359	+	2.67090i
$249$	−8.79944			−0.557642
$250$	1.71307	+	2.48182i	0.108344	+	0.156964i
$251$	4.84773	+	4.29471i	0.305986	+	0.271080i	0.802116	−	0.597168i	$-0.203708\pi$
$251$	4.84773	+	4.29471i	0.305986	+	0.271080i	−0.496130	+	0.868248i	$0.665246\pi$
$252$	8.16905	−	2.01349i	0.514602	−	0.126838i
$253$	−22.4573	+	11.7865i	−1.41188	+	0.741009i
$254$	−21.7889	+	11.4357i	−1.36715	+	0.717538i
$255$	0.234176	−	0.0577192i	0.0146647	−	0.00361451i
$256$	−37.6028	−	33.3132i	−2.35017	−	2.08207i
$257$	−9.59657	−	13.9030i	−0.598618	−	0.867248i	0.400171	−	0.916440i	$-0.368951\pi$
$257$	−9.59657	−	13.9030i	−0.598618	−	0.867248i	−0.998789	+	0.0491926i	$0.984335\pi$
$258$	−24.1466			−1.50330
$259$	−1.33311	+	1.93134i	−0.0828352	+	0.120007i
$260$	2.10630	−	0.595109i	0.130627	−	0.0369071i
$261$	3.50603	+	5.07936i	0.217018	+	0.314405i
$262$	5.60575	+	8.12134i	0.346325	+	0.501738i
$263$	−4.00426	+	2.10160i	−0.246913	+	0.129590i	−0.583640	−	0.812012i	$-0.698372\pi$
$263$	−4.00426	+	2.10160i	−0.246913	+	0.129590i	0.336727	+	0.941602i	$0.390680\pi$
$264$	−15.9999	−	42.1883i	−0.984727	−	2.59651i
$265$	−0.791350	+	0.415333i	−0.0486122	+	0.0255137i
$266$	−0.981509	+	2.58803i	−0.0601802	+	0.158682i
$267$	−7.40666	−	1.82558i	−0.453280	−	0.111724i
$268$	37.4149			2.28548
$269$	26.4134	+	6.51032i	1.61045	+	0.396941i	0.938948	−	0.344059i	$-0.111802\pi$
$269$	26.4134	+	6.51032i	1.61045	+	0.396941i	0.671505	+	0.741000i	$0.265648\pi$
$270$	0.225998	−	0.200216i	0.0137538	−	0.0121848i
$271$	−11.6127	+	16.8238i	−0.705419	+	1.02198i	0.292422	+	0.956289i	$0.405539\pi$
$271$	−11.6127	+	16.8238i	−0.705419	+	1.02198i	−0.997840	+	0.0656858i	$0.979077\pi$
$272$	32.6001	+	8.03520i	1.97667	+	0.487206i
$273$	−3.99576	+	3.78777i	−0.241835	+	0.229246i
$274$	15.7157	−	3.87358i	0.949422	−	0.234012i
$275$	−8.29737	+	21.8784i	−0.500350	+	1.31931i
$276$	−10.5630	−	27.8523i	−0.635817	−	1.67651i
$277$	0.778188	−	6.40895i	0.0467568	−	0.385077i	−0.950480	−	0.310786i	$-0.899408\pi$
$277$	0.778188	−	6.40895i	0.0467568	−	0.385077i	0.997237	−	0.0742905i	$-0.0236692\pi$
$278$	37.5692	−	33.2834i	2.25325	−	1.99621i
$279$	−1.88428	−	4.96843i	−0.112809	−	0.297452i
$280$	0.919236	+	1.33174i	0.0549348	+	0.0795869i
$281$	5.85174	+	1.44232i	0.349086	+	0.0860419i	0.409960	−	0.912104i	$-0.365543\pi$
$281$	5.85174	+	1.44232i	0.349086	+	0.0860419i	−0.0608742	+	0.998145i	$0.519389\pi$
$282$	27.5372	−	6.78730i	1.63981	−	0.404178i
$283$	−5.04498	−	4.46946i	−0.299893	−	0.265682i	0.499734	−	0.866179i	$-0.333431\pi$
$283$	−5.04498	−	4.46946i	−0.299893	−	0.265682i	−0.799627	+	0.600497i	$0.794970\pi$
$284$	−12.7677	−	33.6656i	−0.757621	−	1.99768i
$285$	0.00878422	+	0.0723445i	0.000520332	+	0.00428532i
$286$	35.7107	+	29.5505i	2.11162	+	1.74736i
$287$	−0.137807	+	1.13494i	−0.00813446	+	0.0669933i
$288$	22.1335	−	5.45542i	1.30423	−	0.321464i
$289$	11.8533	−	2.92158i	0.697253	−	0.171857i
$290$	−1.05857	+	1.53361i	−0.0621616	+	0.0900567i
$291$	−2.63349	+	3.81527i	−0.154378	+	0.223655i
$292$	9.68988	+	5.08564i	0.567057	+	0.297615i
$293$	1.58373	−	13.0432i	0.0925223	−	0.761990i	−0.870425	−	0.492301i	$-0.836156\pi$
$293$	1.58373	−	13.0432i	0.0925223	−	0.761990i	0.962947	−	0.269689i	$-0.0869209\pi$
$294$	11.3274	+	5.94508i	0.660628	+	0.346724i
$295$	0.00521442	−	0.00461958i	0.000303595	−	0.000268962i
$296$	−8.39675	+	12.1648i	−0.488051	+	0.707064i
$297$	4.55485	+	1.12267i	0.264299	+	0.0651440i
$298$	45.4994	−	23.8799i	2.63571	−	1.38333i
$299$	15.0180	+	12.4273i	0.868514	+	0.718692i
$300$	−24.3341	−	12.7715i	−1.40493	−	0.737363i
$301$	10.0713	+	8.92240i	0.580500	+	0.514278i
$302$	−6.21978	−	51.2245i	−0.357908	−	2.94764i
$303$	12.1103	−	6.35596i	0.695717	−	0.365140i
$304$	−3.59754	+	9.48592i	−0.206333	+	0.544055i
$305$	−1.30871	+	0.322568i	−0.0749365	+	0.0184702i
$306$	−4.49022	+	3.97799i	−0.256689	+	0.227407i
$307$	−14.5653	−	12.9037i	−0.831283	−	0.736452i	0.135849	−	0.990730i	$-0.456624\pi$
$307$	−14.5653	−	12.9037i	−0.831283	−	0.736452i	−0.967131	+	0.254277i	$0.918162\pi$
$308$	−13.9960	+	36.9044i	−0.797497	+	2.10283i
$309$	12.3449	+	6.47910i	0.702277	+	0.368583i
$310$	1.20089	−	1.06390i	0.0682060	−	0.0604253i
$311$	3.66838	+	3.24990i	0.208015	+	0.184285i	0.760697	−	0.649107i	$-0.224857\pi$
$311$	3.66838	+	3.24990i	0.208015	+	0.184285i	−0.552682	+	0.833392i	$0.686396\pi$
$312$	−25.1679	+	23.8578i	−1.42485	+	1.35068i
$313$	−15.8843	+	14.0722i	−0.897832	+	0.795410i	−0.979541	−	0.201247i	$-0.935501\pi$
$313$	−15.8843	+	14.0722i	−0.897832	+	0.795410i	0.0817086	+	0.996656i	$0.473962\pi$
$314$	−5.69882	+	46.9340i	−0.321603	+	2.64864i
$315$	−0.168243			−0.00947943
$316$	69.9233			3.93350
$317$	−1.38685	+	11.4217i	−0.0778932	+	0.641508i	0.900515	+	0.434825i	$0.143190\pi$
$317$	−1.38685	+	11.4217i	−0.0778932	+	0.641508i	−0.978408	+	0.206683i	$0.933733\pi$
$318$	12.6276	−	18.2942i	0.708120	−	1.02589i
$319$	−28.9534			−1.62108
$320$	1.98991	+	2.88288i	0.111239	+	0.161158i
$321$	−0.955140	−	7.86629i	−0.0533107	−	0.439053i
$322$	−8.02253	+	21.1537i	−0.447078	+	1.17885i
$323$	−0.174529	−	1.43737i	−0.00971104	−	0.0799776i
$324$	−1.95379	+	5.15172i	−0.108544	+	0.286207i
$325$	17.9738	−	0.605934i	0.997006	−	0.0336112i
$326$	−5.49616	−	14.4922i	−0.304404	−	0.802648i
$327$	−18.2780	+	9.59304i	−1.01078	+	0.530496i
$328$	−0.867994	+	7.14857i	−0.0479269	+	0.394714i
$329$	−13.9934	−	7.34433i	−0.771484	−	0.404906i
$330$	0.170729	+	1.40608i	0.00939830	+	0.0774019i
$331$	0.463772	+	3.81951i	0.0254912	+	0.209939i	0.999889	−	0.0148914i	$-0.00474025\pi$
$331$	0.463772	+	3.81951i	0.0254912	+	0.209939i	−0.974398	+	0.224830i	$0.927817\pi$
$332$	36.2900	+	32.1501i	1.99167	+	1.76447i
$333$	−0.544962	−	1.43695i	−0.0298638	−	0.0787443i
$334$	−28.9741	−	41.9762i	−1.58539	−	2.29683i
$335$	−0.726436	−	0.179050i	−0.0396894	−	0.00978257i
$336$	−20.7387	−	10.8845i	−1.13139	−	0.593798i
$337$	24.5055			1.33490			0.667449	−	0.744656i	$-0.267386\pi$
$337$	24.5055			1.33490			0.667449	+	0.744656i	$0.267386\pi$
$338$	10.3608	−	34.0853i	0.563554	−	1.85399i
$339$	−12.7688			−0.693504
$340$	−1.17666	−	0.617556i	−0.0638131	−	0.0334917i
$341$	24.2033	+	5.96558i	1.31068	+	0.323054i
$342$	−1.02968	−	1.49175i	−0.0556787	−	0.0806646i
$343$	−6.31821	−	16.6597i	−0.341151	−	0.899541i
$344$	63.4355	+	56.1990i	3.42021	+	3.03004i
$345$	0.0717993	+	0.591320i	0.00386554	+	0.0318356i
$346$	−5.48273	−	45.1543i	−0.294753	−	2.42751i
$347$	−2.10564	−	1.10512i	−0.113037	−	0.0593262i	0.407257	−	0.913314i	$-0.366485\pi$
$347$	−2.10564	−	1.10512i	−0.113037	−	0.0593262i	−0.520294	+	0.853987i	$0.674178\pi$
$348$	4.09893	−	33.7577i	0.219726	−	1.80960i
$349$	5.73074	−	3.00772i	0.306759	−	0.161000i	−0.304318	−	0.952570i	$-0.598429\pi$
$349$	5.73074	−	3.00772i	0.306759	−	0.161000i	0.611078	+	0.791571i	$0.290736\pi$
$350$	7.40146	+	19.5160i	0.395625	+	1.04318i
$351$	−0.554950	−	3.56259i	−0.0296211	−	0.190157i
$352$	−37.9213	+	99.9902i	−2.02121	+	5.32949i
$353$	−3.08928	−	25.4425i	−0.164426	−	1.35417i	−0.808180	−	0.588936i	$-0.799547\pi$
$353$	−3.08928	−	25.4425i	−0.164426	−	1.35417i	0.643754	−	0.765233i	$-0.277376\pi$
$354$	−0.0614432	+	0.162012i	−0.00326567	+	0.00861086i
$355$	0.0867850	+	0.714739i	0.00460607	+	0.0379344i
$356$	23.8759	+	34.5903i	1.26542	+	1.83328i
$357$	3.34273			0.176916
$358$	−34.5619	+	50.0715i	−1.82665	+	2.64636i
$359$	0.445744	−	3.67103i	0.0235254	−	0.193749i	−0.976208	−	0.216836i	$-0.930426\pi$
$359$	0.445744	−	3.67103i	0.0235254	−	0.193749i	0.999733	+	0.0230866i	$0.00734935\pi$
$360$	−1.05970			−0.0558512
$361$	−18.5625			−0.976973
$362$	4.64757	−	38.2762i	0.244271	−	2.01175i
$363$	−8.23892	+	7.29904i	−0.432431	+	0.383100i
$364$	30.3182	−	1.02209i	1.58911	−	0.0535721i
$365$	−0.163798	−	0.145112i	−0.00857357	−	0.00759552i
$366$	25.0940	−	22.2313i	1.31168	−	1.16205i
$367$	−5.83693	−	3.06346i	−0.304685	−	0.159911i	0.305451	−	0.952208i	$-0.401193\pi$
$367$	−5.83693	−	3.06346i	−0.304685	−	0.159911i	−0.610136	+	0.792297i	$0.708885\pi$
$368$	−29.4051	+	77.5348i	−1.53285	+	4.04178i
$369$	−0.560407	−	0.496477i	−0.0291736	−	0.0258456i
$370$	0.347317	−	0.307696i	0.0180561	−	0.0159963i
$371$	−12.0267	+	2.96432i	−0.624397	+	0.153900i
$372$	−10.3819	+	27.3749i	−0.538278	+	1.41932i
$373$	−3.50923	+	1.84179i	−0.181701	+	0.0953642i	−0.553121	−	0.833101i	$-0.686563\pi$
$373$	−3.50923	+	1.84179i	−0.181701	+	0.0953642i	0.371420	+	0.928465i	$0.378871\pi$
$374$	−3.39211	−	27.9366i	−0.175402	−	1.44457i
$375$	0.823688	+	0.729724i	0.0425351	+	0.0376828i
$376$	−88.1397	−	46.2593i	−4.54546	−	2.38564i
$377$	8.58761	+	20.5293i	0.442284	+	1.05731i
$378$	3.70532	−	1.94470i	0.190581	−	0.100025i
$379$	−18.6118	−	4.58739i	−0.956023	−	0.235638i	−0.269707	−	0.962942i	$-0.586927\pi$
$379$	−18.6118	−	4.58739i	−0.956023	−	0.235638i	−0.686316	+	0.727304i	$0.740773\pi$
$380$	0.228095	−	0.330452i	0.0117010	−	0.0169518i
$381$	−6.72128	+	5.95454i	−0.344342	+	0.305060i
$382$	−4.75404	−	2.49511i	−0.243238	−	0.127661i
$383$	3.33193	−	27.4409i	0.170253	−	1.40216i	−0.617693	−	0.786419i	$-0.711933\pi$
$383$	3.33193	−	27.4409i	0.170253	−	1.40216i	0.787946	−	0.615744i	$-0.211144\pi$
$384$	−36.7781	−	19.3026i	−1.87682	−	0.985033i
$385$	0.448349	−	0.649546i	0.0228500	−	0.0331039i
$386$	16.5705	−	24.0065i	0.843417	−	1.22190i
$387$	−8.55531	+	2.10870i	−0.434891	+	0.107191i
$388$	24.8005	−	6.11277i	1.25905	−	0.310329i
$389$	−1.76171	+	14.5090i	−0.0893221	+	0.735634i	0.877392	+	0.479774i	$0.159282\pi$
$389$	−1.76171	+	14.5090i	−0.0893221	+	0.735634i	−0.966714	+	0.255859i	$0.917642\pi$
$390$	0.946335	−	0.538098i	0.0479195	−	0.0272477i
$391$	−1.42654	−	11.7486i	−0.0721433	−	0.594153i
$392$	−15.9216	−	41.9818i	−0.804162	−	2.12040i
$393$	2.69539	+	2.38790i	0.135964	+	0.120454i
$394$	−37.3969	+	9.21750i	−1.88403	+	0.464371i
$395$	−1.35761	−	0.334620i	−0.0683087	−	0.0168366i
$396$	−14.6829	−	21.2719i	−0.737844	−	1.06895i
$397$	10.6873	+	28.1800i	0.536378	+	1.41431i	0.879896	+	0.475166i	$0.157612\pi$
$397$	10.6873	+	28.1800i	0.536378	+	1.41431i	−0.343518	+	0.939146i	$0.611619\pi$
$398$	−31.0336	+	27.4933i	−1.55557	+	1.37812i
$399$	−0.121746	+	1.00267i	−0.00609494	+	0.0501963i
$400$	27.1286	+	71.5324i	1.35643	+	3.57662i
$401$	3.33306	−	8.78855i	0.166445	−	0.438879i	−0.825679	−	0.564140i	$-0.809208\pi$
$401$	3.33306	−	8.78855i	0.166445	−	0.438879i	0.992124	+	0.125261i	$0.0399769\pi$
$402$	18.0683	−	4.45345i	0.901167	−	0.222118i
$403$	−2.94886	−	18.9307i	−0.146893	−	0.943003i
$404$	−73.1667	−	18.0340i	−3.64018	−	0.897224i
$405$	0.0625879	−	0.0906742i	0.00311002	−	0.00450564i
$406$	−19.3319	+	17.1266i	−0.959426	+	0.849977i
$407$	6.99997	+	1.72534i	0.346976	+	0.0855218i
$408$	21.0547			1.04236
$409$	12.6129	+	3.10880i	0.623668	+	0.153720i	0.538472	−	0.842644i	$-0.319002\pi$
$409$	12.6129	+	3.10880i	0.623668	+	0.153720i	0.0851968	+	0.996364i	$0.472848\pi$
$410$	0.0801597	−	0.211364i	0.00395880	−	0.0104385i
$411$	5.22992	−	2.74487i	0.257973	−	0.135395i
$412$	−27.2395	−	71.8246i	−1.34199	−	3.53854i
$413$	0.0854925	−	0.0448699i	0.00420681	−	0.00220790i
$414$	−8.41627	−	12.1931i	−0.413637	−	0.599257i
$415$	−0.550738	−	0.797882i	−0.0270347	−	0.0391665i
$416$	82.1452	−	2.76929i	4.02750	−	0.135775i
$417$	10.4044	−	15.0734i	0.509508	−	0.738149i
$418$	8.50327			0.415908
$419$	13.4784	+	19.5268i	0.658461	+	0.953946i	0.999901	+	0.0140421i	$0.00446990\pi$
$419$	13.4784	+	19.5268i	0.658461	+	0.953946i	−0.341440	+	0.939903i	$0.610915\pi$
$420$	0.693855	+	0.614702i	0.0338567	+	0.0299944i
$421$	20.1096	−	4.95657i	0.980081	−	0.241568i	0.283441	−	0.958990i	$-0.408524\pi$
$421$	20.1096	−	4.95657i	0.980081	−	0.241568i	0.696639	+	0.717421i	$0.254678\pi$
$422$	39.6274	−	20.7981i	1.92903	−	1.01243i
$423$	9.16389	−	4.80958i	0.445563	−	0.233850i
$424$	−75.7520	+	18.6712i	−3.67884	+	0.906753i
$425$	−8.17276	−	7.24044i	−0.396437	−	0.351213i
$426$	−10.1729	−	14.7380i	−0.492878	−	0.714057i
$427$	−18.6811			−0.904043
$428$	−24.8016	+	35.9313i	−1.19883	+	1.73680i
$429$	15.2332	+	7.35137i	0.735464	+	0.354927i
$430$	−1.51128	−	2.18947i	−0.0728806	−	0.105586i
$431$	3.42904	+	4.96782i	0.165171	+	0.239292i	0.896826	−	0.442384i	$-0.145867\pi$
$431$	3.42904	+	4.96782i	0.165171	+	0.239292i	−0.731655	+	0.681675i	$0.761252\pi$
$432$	13.5811	−	7.12793i	0.653423	−	0.342943i
$433$	0.972586	+	2.56450i	0.0467395	+	0.123242i	0.956353	−	0.292213i	$-0.0943916\pi$
$433$	0.972586	+	2.56450i	0.0467395	+	0.123242i	−0.909614	+	0.415455i	$0.863622\pi$
$434$	19.6891	−	10.3336i	0.945106	−	0.496030i
$435$	−0.241132	+	0.635813i	−0.0115614	+	0.0304849i
$436$	110.430	+	27.2186i	5.28866	+	1.30354i
$437$	3.57602			0.171064
$438$	5.28475	+	1.30257i	0.252515	+	0.0622394i
$439$	−7.42631	+	6.57914i	−0.354439	+	0.314005i	−0.821488	−	0.570226i	$-0.806856\pi$
$439$	−7.42631	+	6.57914i	−0.354439	+	0.314005i	0.467049	+	0.884231i	$0.345317\pi$
$440$	2.82399	−	4.09126i	0.134628	−	0.195043i
$441$	4.53256	+	1.11718i	0.215836	+	0.0531988i
$442$	−18.8022	+	10.6912i	−0.894330	+	0.508528i
$443$	−29.3311	+	7.22947i	−1.39356	+	0.343483i	−0.863446	−	0.504441i	$-0.831699\pi$
$443$	−29.3311	+	7.22947i	−1.39356	+	0.343483i	−0.530118	+	0.847924i	$0.677852\pi$
$444$	−3.00262	+	7.91725i	−0.142498	+	0.375736i
$445$	−0.298034	−	0.785852i	−0.0141282	−	0.0372529i
$446$	−5.43223	+	44.7385i	−0.257224	+	2.11843i
$447$	14.0354	−	12.4342i	0.663849	−	0.588119i
$448$	17.2160	+	45.3948i	0.813379	+	2.14470i
$449$	9.27106	+	13.4314i	0.437528	+	0.633869i	0.978274	−	0.207317i	$-0.0664732\pi$
$449$	9.27106	+	13.4314i	0.437528	+	0.633869i	−0.540745	+	0.841186i	$0.681858\pi$
$450$	−13.2715	−	3.27114i	−0.625626	−	0.154203i
$451$	3.41020	−	0.840539i	0.160580	−	0.0395794i
$452$	52.6599	+	46.6526i	2.47691	+	2.19435i
$453$	−6.67709	−	17.6060i	−0.313717	−	0.827204i
$454$	1.06687	+	8.78646i	0.0500707	+	0.412369i
$455$	−0.593539	−	0.125244i	−0.0278255	−	0.00587153i
$456$	−0.766836	+	6.31546i	−0.0359104	+	0.295749i
$457$	−26.9821	+	6.65048i	−1.26217	+	0.311096i	−0.812954	−	0.582328i	$-0.802142\pi$
$457$	−26.9821	+	6.65048i	−1.26217	+	0.311096i	−0.449213	+	0.893424i	$0.648296\pi$
$458$	−25.4602	+	6.27538i	−1.18968	+	0.293229i
$459$	−1.24352	+	1.80156i	−0.0580428	+	0.0840895i
$460$	1.86437	−	2.70101i	0.0869267	−	0.125935i
$461$	15.0618	+	7.90503i	0.701497	+	0.368174i	0.777456	−	0.628937i	$-0.216510\pi$
$461$	15.0618	+	7.90503i	0.701497	+	0.368174i	−0.0759594	+	0.997111i	$0.524202\pi$
$462$	−2.36624	+	19.4877i	−0.110087	+	0.906651i
$463$	33.9524	+	17.8196i	1.57790	+	0.828146i	0.999927	+	0.0120897i	$0.00384838\pi$
$463$	33.9524	+	17.8196i	1.57790	+	0.828146i	0.577973	+	0.816056i	$0.303844\pi$
$464$	−70.8574	+	62.7742i	−3.28947	+	2.91422i
$465$	0.332576	−	0.481819i	0.0154228	−	0.0223438i
$466$	47.9433	+	11.8170i	2.22093	+	0.547410i
$467$	8.85822	−	4.64915i	0.409910	−	0.215137i	−0.247148	−	0.968978i	$-0.579493\pi$
$467$	8.85822	−	4.64915i	0.409910	−	0.215137i	0.657057	+	0.753841i	$0.271801\pi$
$468$	−10.7278	+	16.7201i	−0.495891	+	0.772889i
$469$	−9.18171	−	4.81893i	−0.423972	−	0.222518i
$470$	2.33893	+	2.07211i	0.107887	+	0.0955792i
$471$	2.07956	+	17.1267i	0.0958211	+	0.789158i
$472$	0.538486	−	0.282619i	0.0247858	−	0.0130086i
$473$	14.6578	−	38.6494i	0.673966	−	1.77710i
$474$	33.7672	−	8.32287i	1.55098	−	0.382282i
$475$	2.46947	−	2.18776i	0.113307	−	0.100381i
$476$	−13.7858	−	12.2132i	−0.631873	−	0.559790i
$477$	2.87643	−	7.58453i	0.131703	−	0.347272i
$478$	29.0822	+	15.2635i	1.33019	+	0.698137i
$479$	−17.9912	+	15.9388i	−0.822040	+	0.728264i	−0.965222	−	0.261433i	$-0.915805\pi$
$479$	−17.9912	+	15.9388i	−0.822040	+	0.728264i	0.143182	+	0.989696i	$0.454267\pi$
$480$	1.87995	+	1.66549i	0.0858078	+	0.0760191i
$481$	−0.852857	−	5.47504i	−0.0388869	−	0.249640i
$482$	44.2108	−	39.1674i	2.01375	−	1.78402i
$483$	−0.995114	+	8.19550i	−0.0452792	+	0.372908i
$484$	60.6465			2.75666
$485$	−0.510771			−0.0231929
$486$	−0.330318	+	2.72042i	−0.0149835	+	0.123401i
$487$	−17.8859	+	25.9122i	−0.810486	+	1.17419i	0.171490	+	0.985186i	$0.445142\pi$
$487$	−17.8859	+	25.9122i	−0.810486	+	1.17419i	−0.981976	+	0.189006i	$0.939473\pi$
$488$	−117.666			−5.32647
$489$	−3.21292	−	4.65471i	−0.145293	−	0.210493i
$490$	0.169893	+	1.39919i	0.00767498	+	0.0632091i
$491$	10.5861	−	27.9134i	0.477746	−	1.25971i	−0.452167	−	0.891933i	$-0.649349\pi$
$491$	10.5861	−	27.9134i	0.477746	−	1.25971i	0.929913	−	0.367780i	$-0.119882\pi$
$492$	0.497231	+	4.09507i	0.0224169	+	0.184620i
$493$	4.79092	−	12.6326i	0.215772	−	0.568945i
$494$	−2.52208	−	6.02921i	−0.113474	−	0.271267i
$495$	0.183281	+	0.483273i	0.00823788	+	0.0217215i
$496$	72.1666	−	37.8759i	3.24037	−	1.70068i
$497$	−1.20281	+	9.90604i	−0.0539535	+	0.444347i
$498$	21.3518	+	11.2063i	0.956799	+	0.502167i
$499$	−0.634084	−	5.22215i	−0.0283855	−	0.233776i	0.971611	−	0.236586i	$-0.0760285\pi$
$499$	−0.634084	−	5.22215i	−0.0283855	−	0.233776i	−0.999996	+	0.00281034i	$0.999105\pi$
$500$	−0.730832	−	6.01894i	−0.0326838	−	0.269175i
$501$	−13.9315	−	12.3422i	−0.622411	−	0.551408i
$502$	−6.29358	−	16.5948i	−0.280896	−	0.740663i
$503$	−16.8305	−	24.3833i	−0.750437	−	1.08720i	−0.993121	−	0.117090i	$-0.962643\pi$
$503$	−16.8305	−	24.3833i	−0.750437	−	1.08720i	0.242684	−	0.970105i	$-0.421972\pi$
$504$	−14.2603	−	3.51486i	−0.635206	−	0.156564i
$505$	1.33428	+	0.700283i	0.0593746	+	0.0311622i
$506$	69.5029			3.08978
$507$	0.694283	−	12.9814i	0.0308342	−	0.576526i
$508$	49.4752			2.19511
$509$	−25.6596	−	13.4672i	−1.13734	−	0.596923i	−0.212457	−	0.977170i	$-0.568147\pi$
$509$	−25.6596	−	13.4672i	−1.13734	−	0.596923i	−0.924885	+	0.380247i	$0.875839\pi$
$510$	−0.641735	−	0.158173i	−0.0284165	−	0.00700403i
$511$	−1.72290	−	2.49606i	−0.0762167	−	0.110419i
$512$	19.3604	+	51.0493i	0.855619	+	2.25608i
$513$	−0.495096	−	0.438617i	−0.0218590	−	0.0193654i
$514$	5.58021	+	45.9572i	0.246133	+	2.02709i
$515$	0.185154	+	1.52488i	0.00815884	+	0.0671941i
$516$	42.9876	+	22.5616i	1.89242	+	0.993220i
$517$	−5.85212	+	48.1965i	−0.257376	+	2.11968i
$518$	5.69439	−	2.98865i	0.250197	−	0.131314i
$519$	−5.88584	−	15.5197i	−0.258360	−	0.681239i
$520$	−3.73849	−	0.788867i	−0.163944	−	0.0345941i
$521$	4.44719	−	11.7263i	0.194835	−	0.513737i	−0.801623	−	0.597830i	$-0.796030\pi$
$521$	4.44719	−	11.7263i	0.194835	−	0.513737i	0.996458	+	0.0840925i	$0.0267991\pi$
$522$	−2.03869	−	16.7901i	−0.0892309	−	0.734883i
$523$	5.03128	−	13.2664i	0.220003	−	0.580099i	−0.778889	−	0.627161i	$-0.784217\pi$
$523$	5.03128	−	13.2664i	0.220003	−	0.580099i	0.998892	+	0.0470621i	$0.0149859\pi$
$524$	−2.39153	−	19.6960i	−0.104474	−	0.860424i
$525$	4.32670	+	6.26831i	0.188833	+	0.273572i
$526$	12.3928			0.540350
$527$	−6.60776	+	9.57300i	−0.287839	+	0.417006i
$528$	−8.67300	+	71.4286i	−0.377444	+	3.10853i
$529$	6.22920			0.270835
$530$	2.44915			0.106384
$531$	−0.00762141	+	0.0627679i	−0.000330741	+	0.00272390i
$532$	4.16551	−	3.69032i	0.180598	−	0.159995i
$533$	−1.60745	−	2.16869i	−0.0696265	−	0.0939362i
$534$	15.6473	+	13.8623i	0.677126	+	0.599882i
$535$	0.653489	−	0.578941i	0.0282528	−	0.0250298i
$536$	−57.8323	−	30.3527i	−2.49798	−	1.31104i
$537$	−7.87283	+	20.7589i	−0.339738	+	0.895815i
$538$	−55.8010	−	49.4354i	−2.40575	−	2.13131i
$539$	−16.3919	+	14.5220i	−0.706049	+	0.625505i
$540$	−0.589412	+	0.145277i	−0.0253643	+	0.00625173i
$541$	−7.51596	+	19.8180i	−0.323136	+	0.852040i	0.670755	+	0.741679i	$0.265970\pi$
$541$	−7.51596	+	19.8180i	−0.323136	+	0.852040i	−0.993892	+	0.110362i	$0.964799\pi$
$542$	49.6037	−	26.0340i	2.13066	−	1.11826i
$543$	−1.69595	−	13.9674i	−0.0727801	−	0.599398i
$544$	−37.3518	−	33.0908i	−1.60145	−	1.41876i
$545$	−2.01382	−	1.05694i	−0.0862627	−	0.0452742i
$546$	14.5195	−	4.10232i	0.621379	−	0.175563i
$547$	15.7692	−	8.27631i	0.674242	−	0.353870i	−0.0926017	−	0.995703i	$-0.529518\pi$
$547$	15.7692	−	8.27631i	0.674242	−	0.353870i	0.766844	+	0.641834i	$0.221826\pi$
$548$	−31.5976	−	7.78812i	−1.34978	−	0.332692i
$549$	6.94954	−	10.0681i	0.296599	−	0.429698i
$550$	47.9962	−	42.5209i	2.04656	−	1.81310i
$551$	3.61473	+	1.89716i	0.153993	+	0.0808217i
$552$	−6.26786	+	51.6205i	−0.266778	+	2.19711i
$553$	−17.1593	−	9.00592i	−0.729690	−	0.382971i
$554$	−10.0502	+	14.5603i	−0.426993	+	0.618607i
$555$	0.0961860	−	0.139350i	0.00408287	−	0.00591506i
$556$	−97.9823	+	24.1505i	−4.15537	+	1.02421i
$557$	−19.9607	+	4.91987i	−0.845762	+	0.208462i	−0.638306	−	0.769783i	$-0.720365\pi$
$557$	−19.9607	+	4.91987i	−0.845762	+	0.208462i	−0.207456	+	0.978244i	$0.566518\pi$
$558$	−1.75522	+	14.4556i	−0.0743046	+	0.611953i
$559$	−31.7518	+	1.07042i	−1.34296	+	0.0452739i
$560$	−0.311047	−	2.56170i	−0.0131441	−	0.108252i
$561$	−3.64152	−	9.60189i	−0.153745	−	0.405392i
$562$	−12.3624	−	10.9521i	−0.521477	−	0.461988i
$563$	31.1054	−	7.66680i	1.31094	−	0.323117i	0.478917	−	0.877860i	$-0.341030\pi$
$563$	31.1054	−	7.66680i	1.31094	−	0.323117i	0.832022	+	0.554743i	$0.187183\pi$
$564$	−55.3655	−	13.6464i	−2.33131	−	0.574616i
$565$	−0.799169	−	1.15780i	−0.0336213	−	0.0487089i
$566$	6.54967	+	17.2701i	0.275303	+	0.725915i
$567$	1.14299	−	1.01260i	0.0480011	−	0.0425253i
$568$	−7.57607	+	62.3946i	−0.317885	+	2.61802i
$569$	−14.7628	−	38.9264i	−0.618890	−	1.63188i	−0.766062	−	0.642767i	$-0.777786\pi$
$569$	−14.7628	−	38.9264i	−0.618890	−	1.63188i	0.147173	−	0.989111i	$-0.452983\pi$
$570$	0.0708177	−	0.186731i	0.00296623	−	0.00782130i
$571$	2.55407	−	0.629521i	0.106884	−	0.0263447i	−0.185511	−	0.982642i	$-0.559394\pi$
$571$	2.55407	−	0.629521i	0.106884	−	0.0263447i	0.292395	+	0.956298i	$0.405548\pi$
$572$	−35.9641	−	85.9746i	−1.50373	−	3.59478i
$573$	−1.90228	−	0.468871i	−0.0794690	−	0.0195874i
$574$	1.77976	−	2.57843i	0.0742858	−	0.107622i
$575$	20.1846	−	17.8820i	0.841757	−	0.745732i
$576$	−30.8699	−	7.60875i	−1.28625	−	0.317031i
$577$	−6.95608			−0.289585			−0.144793	−	0.989462i	$-0.546252\pi$
$577$	−6.95608			−0.289585			−0.144793	+	0.989462i	$0.546252\pi$
$578$	−32.4827	−	8.00627i	−1.35110	−	0.333017i
$579$	3.77459	−	9.95277i	0.156867	−	0.413623i
$580$	3.31750	−	1.74116i	0.137752	−	0.0722976i
$581$	−4.76480	−	12.5637i	−0.197677	−	0.521232i
$582$	11.2490	−	5.90393i	0.466286	−	0.244726i
$583$	21.6166	+	31.3171i	0.895270	+	1.29702i
$584$	−10.8519	−	15.7218i	−0.449057	−	0.650571i
$585$	0.288302	−	0.273294i	0.0119198	−	0.0112993i
$586$	−20.4537	+	29.6323i	−0.844935	+	1.22410i
$587$	5.86347			0.242011			0.121006	−	0.992652i	$-0.461388\pi$
$587$	5.86347			0.242011			0.121006	+	0.992652i	$0.461388\pi$
$588$	−14.6110	−	21.1678i	−0.602549	−	0.872943i
$589$	−2.63081	−	2.33069i	−0.108401	−	0.0960346i
$590$	−0.0185359	+	0.00456870i	−0.000763113	+	0.000188090i
$591$	−12.4450	+	6.53165i	−0.511920	+	0.268676i
$592$	20.8717	−	10.9543i	0.857822	−	0.450220i
$593$	32.4569	−	7.99990i	1.33284	−	0.328517i	0.492378	−	0.870381i	$-0.336128\pi$
$593$	32.4569	−	7.99990i	1.33284	−	0.328517i	0.840466	+	0.541865i	$0.182281\pi$
$594$	−9.62260	−	8.52488i	−0.394820	−	0.349780i
$595$	0.209215	+	0.303100i	0.00857696	+	0.0124259i
$596$	−103.314			−4.23190
$597$	−8.59445	+	12.4512i	−0.351748	+	0.509594i
$598$	−20.6147	−	49.2808i	−0.842996	−	2.01524i
$599$	21.0140	+	30.4440i	0.858607	+	1.24391i	0.968262	+	0.249937i	$0.0804100\pi$
$599$	21.0140	+	30.4440i	0.858607	+	1.24391i	−0.109655	+	0.993970i	$0.534975\pi$
$600$	27.2523	+	39.4818i	1.11257	+	1.61184i
$601$	24.6788	−	12.9524i	1.00667	−	0.528340i	0.120997	−	0.992653i	$-0.461391\pi$
$601$	24.6788	−	12.9524i	1.00667	−	0.528340i	0.885671	+	0.464313i	$0.153699\pi$
$602$	−13.0751	−	34.4763i	−0.532902	−	1.40515i
$603$	6.01283	−	3.15578i	0.244861	−	0.128513i
$604$	−36.7892	+	97.0052i	−1.49693	+	3.94709i
$605$	−1.17749	−	0.290226i	−0.0478718	−	0.0117993i
$606$	−37.4801			−1.52252
$607$	−5.67937	−	1.39984i	−0.230519	−	0.0568177i	0.122364	−	0.992485i	$-0.460952\pi$
$607$	−5.67937	−	1.39984i	−0.230519	−	0.0568177i	−0.352883	+	0.935668i	$0.614799\pi$
$608$	11.2862	−	9.99867i	0.457714	−	0.405500i
$609$	−5.35378	+	7.75629i	−0.216946	+	0.314301i
$610$	3.58638	+	0.883964i	0.145208	+	0.0357907i
$611$	35.9093	−	10.1457i	1.45274	−	0.410453i
$612$	11.7107	−	2.88643i	0.473377	−	0.116677i
$613$	5.29855	−	13.9711i	0.214006	−	0.564289i	−0.784428	−	0.620220i	$-0.787043\pi$
$613$	5.29855	−	13.9711i	0.214006	−	0.564289i	0.998435	+	0.0559311i	$0.0178127\pi$
$614$	18.9094	+	49.8600i	0.763122	+	2.01219i
$615$	0.00994299	−	0.0818879i	0.000400940	−	0.00330204i
$616$	51.5722	−	45.6890i	2.07790	−	1.84086i
$617$	−10.1017	−	26.6360i	−0.406679	−	1.07232i	−0.969359	−	0.245649i	$-0.920999\pi$
$617$	−10.1017	−	26.6360i	−0.406679	−	1.07232i	0.562680	−	0.826675i	$-0.309770\pi$
$618$	−21.7036	−	31.4431i	−0.873046	−	1.26483i
$619$	−5.78022	−	1.42470i	−0.232327	−	0.0572634i	0.121433	−	0.992600i	$-0.461251\pi$
$619$	−5.78022	−	1.42470i	−0.232327	−	0.0572634i	−0.353760	+	0.935336i	$0.615097\pi$
$620$	−3.13198	+	0.771964i	−0.125783	+	0.0310028i
$621$	−4.04675	−	3.58511i	−0.162391	−	0.143865i
$622$	−4.76249	−	12.5576i	−0.190958	−	0.503516i
$623$	−1.40408	−	11.5637i	−0.0562535	−	0.463289i
$624$	53.2186	−	15.0363i	2.13045	−	0.601932i
$625$	2.99149	−	24.6371i	0.119659	−	0.985484i
$626$	56.4645	−	13.9173i	2.25678	−	0.556245i
$627$	3.01277	−	0.742581i	0.120318	−	0.0296558i
$628$	53.9987	−	78.2306i	2.15478	−	3.12174i
$629$	−1.91107	+	2.76866i	−0.0761993	+	0.110394i
$630$	0.408242	+	0.214262i	0.0162647	+	0.00853640i
$631$	3.31358	−	27.2898i	0.131912	−	1.08639i	−0.764953	−	0.644086i	$-0.777238\pi$
$631$	3.31358	−	27.2898i	0.131912	−	1.08639i	0.896865	−	0.442305i	$-0.145839\pi$
$632$	−108.081	−	56.7250i	−4.29921	−	2.25640i
$633$	12.2240	−	10.8295i	0.485861	−	0.430435i
$634$	17.9110	−	25.9486i	0.711339	−	1.03055i
$635$	−0.960594	−	0.236765i	−0.0381200	−	0.00939573i
$636$	−39.5740	+	20.7700i	−1.56921	+	0.823585i
$637$	15.1586	+	7.31538i	0.600606	+	0.289846i
$638$	70.2554	+	36.8729i	2.78144	+	1.45981i
$639$	−4.89138	−	4.33338i	−0.193500	−	0.171426i
$640$	−0.551612	−	4.54293i	−0.0218044	−	0.179575i
$641$	−38.9636	+	20.4497i	−1.53897	+	0.807713i	−0.999414	−	0.0342368i	$-0.989100\pi$
$641$	−38.9636	+	20.4497i	−1.53897	+	0.807713i	−0.539555	+	0.841950i	$0.681408\pi$
$642$	−7.70027	+	20.3039i	−0.303905	+	0.801333i
$643$	−31.8347	+	7.84656i	−1.25544	+	0.309438i	−0.810296	−	0.586021i	$-0.800693\pi$
$643$	−31.8347	+	7.84656i	−1.25544	+	0.309438i	−0.445143	+	0.895459i	$0.646847\pi$
$644$	34.0475	−	30.1634i	1.34166	−	1.18861i
$645$	−0.726663	−	0.643767i	−0.0286123	−	0.0253483i
$646$	−1.40704	+	3.71006i	−0.0553592	+	0.145970i
$647$	−22.2837	−	11.6954i	−0.876062	−	0.459793i	−0.0341554	−	0.999417i	$-0.510874\pi$
$647$	−22.2837	−	11.6954i	−0.876062	−	0.459793i	−0.841906	+	0.539624i	$0.818566\pi$
$648$	7.19929	−	6.37802i	0.282815	−	0.250552i
$649$	−0.222022	−	0.196694i	−0.00871511	−	0.00772091i
$650$	−44.3850	−	21.4198i	−1.74092	−	0.840152i
$651$	6.07356	−	5.38070i	0.238041	−	0.210886i
$652$	−3.75625	+	30.9355i	−0.147106	+	1.21153i
$653$	−32.3198			−1.26477			−0.632386	−	0.774653i	$-0.717925\pi$
$653$	−32.3198			−1.26477			−0.632386	+	0.774653i	$0.717925\pi$
$654$	56.5686			2.21201
$655$	−0.0478227	+	0.393856i	−0.00186859	+	0.0153892i
$656$	6.52338	−	9.45074i	0.254695	−	0.368990i
$657$	1.98618			0.0774881
$658$	24.6019	+	35.6420i	0.959082	+	1.38947i
$659$	−0.389197	−	3.20533i	−0.0151610	−	0.124862i	0.983163	−	0.182729i	$-0.0584931\pi$
$659$	−0.389197	−	3.20533i	−0.0151610	−	0.124862i	−0.998324	+	0.0578672i	$0.981570\pi$
$660$	1.00984	−	2.66272i	0.0393079	−	0.103646i
$661$	5.37722	+	44.2854i	0.209150	+	1.72250i	0.598251	+	0.801309i	$0.295862\pi$
$661$	5.37722	+	44.2854i	0.209150	+	1.72250i	−0.389102	+	0.921195i	$0.627214\pi$
$662$	3.73890	−	9.85866i	0.145316	−	0.383168i
$663$	−5.72811	+	5.42994i	−0.222461	+	0.210881i
$664$	−30.0118	−	79.1345i	−1.16468	−	3.07102i
$665$	−0.0985362	+	0.0517158i	−0.00382107	+	0.00200545i
$666$	−0.507638	+	4.18078i	−0.0196706	+	0.162002i
$667$	29.5456	+	15.5067i	1.14401	+	0.600424i
$668$	12.3609	+	101.801i	0.478258	+	3.93881i
$669$	1.98228	+	16.3255i	0.0766394	+	0.631182i
$670$	1.53467	+	1.35960i	0.0592895	+	0.0525259i
$671$	20.3509	+	53.6609i	0.785638	+	2.07156i
$672$	19.7742	+	28.6479i	0.762808	+	1.10512i
$673$	−0.491606	−	0.121170i	−0.0189500	−	0.00467076i	0.229829	−	0.973231i	$-0.426183\pi$
$673$	−0.491606	−	0.121170i	−0.0189500	−	0.00467076i	−0.248779	+	0.968560i	$0.580029\pi$
$674$	−59.4625	−	31.2083i	−2.29041	−	1.20210i
$675$	−4.98786			−0.191983
$676$	−50.2930	+	51.0004i	−1.93435	+	1.96155i
$677$	−8.94006			−0.343594			−0.171797	−	0.985132i	$-0.554957\pi$
$677$	−8.94006			−0.343594			−0.171797	+	0.985132i	$0.554957\pi$
$678$	30.9834	+	16.2613i	1.18991	+	0.624513i
$679$	−6.87340	−	1.69414i	−0.263777	−	0.0650152i
$680$	1.31777	+	1.90911i	0.0505340	+	0.0732112i
$681$	1.14531	+	3.01994i	0.0438884	+	0.115724i
$682$	−51.1320	−	45.2990i	−1.95794	−	1.73459i
$683$	−0.905937	−	7.46106i	−0.0346647	−	0.285490i	−0.999725	−	0.0234607i	$-0.992532\pi$
$683$	−0.905937	−	7.46106i	−0.0346647	−	0.285490i	0.965060	−	0.262029i	$-0.0843915\pi$
$684$	0.439283	+	3.61782i	0.0167964	+	0.138331i
$685$	0.576219	+	0.302423i	0.0220162	+	0.0115550i
$686$	−5.88548	+	48.4713i	−0.224709	+	1.85064i
$687$	−8.47272	+	4.44683i	−0.323254	+	0.169657i
$688$	−47.9244	−	126.366i	−1.82710	−	4.81767i
$689$	15.7938	−	24.6159i	0.601694	−	0.937791i
$690$	0.578840	−	1.52628i	0.0220361	−	0.0581044i
$691$	−2.14981	−	17.7053i	−0.0817826	−	0.673540i	−0.974731	−	0.223381i	$-0.928290\pi$
$691$	−2.14981	−	17.7053i	−0.0817826	−	0.673540i	0.892949	−	0.450159i	$-0.148633\pi$
$692$	−32.4296	+	85.5099i	−1.23279	+	3.25060i
$693$	0.863466	+	7.11128i	0.0328004	+	0.270135i
$694$	3.70193	+	5.36317i	0.140523	+	0.203583i
$695$	2.01796			0.0765457
$696$	−33.7216	+	48.8541i	−1.27821	+	1.85181i
$697$	−0.197552	+	1.62699i	−0.00748282	+	0.0616265i
$698$	−17.7360			−0.671319
$699$	18.0186			0.681527
$700$	5.05839	−	41.6595i	0.191189	−	1.57458i
$701$	15.0041	−	13.2925i	0.566698	−	0.502051i	−0.330424	−	0.943832i	$-0.607192\pi$
$701$	15.0041	−	13.2925i	0.566698	−	0.502051i	0.897123	+	0.441782i	$0.145653\pi$
$702$	−3.19046	+	9.35136i	−0.120416	+	0.352944i
$703$	−0.760871	−	0.674073i	−0.0286968	−	0.0254232i
$704$	111.640	−	98.9048i	4.20761	−	3.72762i
$705$	1.00965	+	0.529907i	0.0380257	+	0.0199574i
$706$	−24.9056	+	65.6705i	−0.937333	+	2.47154i
$707$	15.6326	+	13.8492i	0.587923	+	0.520854i
$708$	0.260764	−	0.231017i	0.00980010	−	0.00868213i
$709$	−5.82554	+	1.43587i	−0.218783	+	0.0539251i	−0.347183	−	0.937797i	$-0.612862\pi$
$709$	−5.82554	+	1.43587i	−0.218783	+	0.0539251i	0.128400	+	0.991722i	$0.459016\pi$
$710$	0.699654	−	1.84484i	0.0262576	−	0.0692355i
$711$	11.2371	−	5.89771i	0.421426	−	0.221181i
$712$	−8.84382	−	72.8354i	−0.331436	−	2.72962i
$713$	−21.5034	−	19.0503i	−0.805308	−	0.713440i
$714$	−8.11114	−	4.25705i	−0.303552	−	0.159316i
$715$	0.286832	+	1.84136i	0.0107269	+	0.0688630i
$716$	108.314	−	56.8478i	4.04790	−	2.12450i
$717$	11.6370	+	2.86826i	0.434591	+	0.107117i
$718$	−5.75675	+	8.34009i	−0.214840	+	0.311249i
$719$	37.1669	−	32.9270i	1.38609	−	1.22797i	0.442541	−	0.896749i	$-0.354077\pi$
$719$	37.1669	−	32.9270i	1.38609	−	1.22797i	0.943553	−	0.331223i	$-0.107461\pi$
$720$	1.49633	+	0.785336i	0.0557651	+	0.0292678i
$721$	−2.56617	+	21.1343i	−0.0955690	+	0.787082i
$722$	45.0419	+	23.6398i	1.67629	+	0.879783i
$723$	12.2438	−	17.7382i	0.455351	−	0.659689i
$724$	−44.0377	+	63.7996i	−1.63665	+	2.37109i
$725$	29.8900	−	7.36722i	1.11009	−	0.273612i
$726$	29.2872	−	7.21866i	1.08695	−	0.267910i
$727$	−1.33722	+	11.0130i	−0.0495947	+	0.408449i	0.946677	+	0.322183i	$0.104417\pi$
$727$	−1.33722	+	11.0130i	−0.0495947	+	0.408449i	−0.996272	+	0.0862662i	$0.972506\pi$
$728$	−47.6920	−	23.0157i	−1.76758	−	0.853018i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	0.212651	+	0.560716i	0.00787058	+	0.0207530i
$731$	14.4377	+	12.7907i	0.533997	+	0.473080i
$732$	−65.4462	+	16.1310i	−2.41896	+	0.596220i
$733$	−45.2288	−	11.1479i	−1.67056	−	0.411757i	−0.713273	−	0.700886i	$-0.752788\pi$
$733$	−45.2288	−	11.1479i	−1.67056	−	0.411757i	−0.957290	+	0.289130i	$0.906634\pi$
$734$	10.2619	+	14.8669i	0.378774	+	0.548749i
$735$	0.182384	+	0.480908i	0.00672734	+	0.0177385i
$736$	92.2494	−	81.7258i	3.40036	−	3.01245i
$737$	−3.83983	+	31.6239i	−0.141442	+	1.16488i
$738$	0.727551	+	1.91839i	0.0267815	+	0.0706171i
$739$	−2.56229	+	6.75620i	−0.0942553	+	0.248531i	−0.973850	−	0.227194i	$-0.927045\pi$
$739$	−2.56229	+	6.75620i	−0.0942553	+	0.248531i	0.879594	+	0.475725i	$0.157814\pi$
$740$	−0.905818	+	0.223264i	−0.0332985	+	0.00820735i
$741$	−1.42012	−	1.91594i	−0.0521692	−	0.0703839i
$742$	32.9580	+	8.12341i	1.20993	+	0.298220i
$743$	−23.6585	+	34.2752i	−0.867945	+	1.25743i	0.0970803	+	0.995277i	$0.469050\pi$
$743$	−23.6585	+	34.2752i	−0.867945	+	1.25743i	−0.965025	+	0.262158i	$0.915566\pi$
$744$	38.2551	−	33.8911i	1.40250	−	1.24251i
$745$	2.00591	+	0.494412i	0.0734908	+	0.0181138i
$746$	10.8607			0.397639
$747$	8.54375	+	2.10584i	0.312599	+	0.0770488i
$748$	−20.0639	+	52.9042i	−0.733610	+	1.93437i
$749$	10.7142	−	5.62325i	0.391489	−	0.205469i
$750$	−1.06936	−	2.81966i	−0.0390474	−	0.102960i
$751$	0.370955	−	0.194692i	0.0135363	−	0.00710442i	−0.457941	−	0.888982i	$-0.651413\pi$
$751$	0.370955	−	0.194692i	0.0135363	−	0.00710442i	0.471478	+	0.881878i	$0.343721\pi$
$752$	90.1736	+	130.639i	3.28829	+	4.76392i
$753$	−3.67907	−	5.33005i	−0.134073	−	0.194238i
$754$	5.30673	−	60.7508i	0.193260	−	2.21242i
$755$	1.17851	−	1.70736i	0.0428903	−	0.0621374i
$756$	−8.41353			−0.305997
$757$	16.5447	+	23.9691i	0.601328	+	0.871173i	0.998924	−	0.0463873i	$-0.0147708\pi$
$757$	16.5447	+	23.9691i	0.601328	+	0.871173i	−0.397596	+	0.917561i	$0.630155\pi$
$758$	39.3193	+	34.8339i	1.42814	+	1.26522i
$759$	24.6254	−	6.06961i	0.893844	−	0.220313i
$760$	−0.620644	+	0.325739i	−0.0225131	+	0.0118158i
$761$	−22.1152	+	11.6070i	−0.801676	+	0.420752i	−0.815216	−	0.579156i	$-0.803382\pi$
$761$	−22.1152	+	11.6070i	−0.801676	+	0.420752i	0.0135406	+	0.999908i	$0.495690\pi$
$762$	23.8924	−	5.88896i	0.865532	−	0.213334i
$763$	−23.5942	−	20.9026i	−0.854167	−	0.756726i
$764$	6.13216	+	8.88396i	0.221854	+	0.321411i
$765$	−0.241184			−0.00872004
$766$	−43.0316	+	62.3420i	−1.55479	+	2.25251i
$767$	−0.0736132	+	0.215763i	−0.00265802	+	0.00779076i
$768$	28.5378	+	41.3441i	1.02977	+	1.49188i
$769$	2.22566	+	3.22443i	0.0802594	+	0.116276i	0.861057	−	0.508508i	$-0.169803\pi$
$769$	2.22566	+	3.22443i	0.0802594	+	0.116276i	−0.780798	+	0.624783i	$0.785187\pi$
$770$	−1.91513	+	1.00514i	−0.0690166	+	0.0362227i
$771$	5.99050	+	15.7957i	0.215743	+	0.568867i
$772$	−51.9308	+	27.2554i	−1.86903	+	0.980943i
$773$	1.25330	−	3.30469i	0.0450782	−	0.118861i	−0.910586	−	0.413319i	$-0.864370\pi$
$773$	1.25330	−	3.30469i	0.0450782	−	0.118861i	0.955665	+	0.294457i	$0.0951388\pi$
$774$	23.4449	+	5.77866i	0.842711	+	0.207710i
$775$	−26.5042			−0.952058
$776$	−43.2931	−	10.6708i	−1.55413	−	0.383059i
$777$	1.75657	−	1.55618i	0.0630165	−	0.0558278i
$778$	22.7523	−	32.9624i	0.815710	−	1.18176i
$779$	−0.480829	−	0.118514i	−0.0172275	−	0.00424619i
$780$	−2.18751	+	0.0737457i	−0.0783256	+	0.00264052i
$781$	29.7651	−	7.33644i	1.06508	−	0.262519i
$782$	−11.5007	+	30.3248i	−0.411263	+	1.08441i
$783$	−2.18858	−	5.77082i	−0.0782135	−	0.206232i
$784$	−8.63055	+	71.0790i	−0.308234	+	2.53853i
$785$	−1.42280	+	1.26049i	−0.0507818	+	0.0449887i
$786$	−3.49930	−	9.22689i	−0.124816	−	0.329112i
$787$	−8.28640	−	12.0049i	−0.295378	−	0.427929i	0.646994	−	0.762495i	$-0.276026\pi$
$787$	−8.28640	−	12.0049i	−0.295378	−	0.427929i	−0.942372	+	0.334566i	$0.891410\pi$
$788$	75.1892	+	18.5325i	2.67850	+	0.660192i
$789$	4.39085	−	1.08225i	0.156318	−	0.0385290i
$790$	2.86809	+	2.54090i	0.102042	+	0.0904013i
$791$	−6.91414	−	18.2311i	−0.245839	−	0.648223i
$792$	5.43866	+	44.7914i	0.193254	+	1.59159i
$793$	32.0120	−	30.3456i	1.13678	−	1.07761i
$794$	9.95529	−	81.9892i	0.353300	−	2.90969i
$795$	0.867750	−	0.213881i	0.0307759	−	0.00758559i
$796$	80.9370	−	19.9492i	2.86874	−	0.707080i
$797$	11.1437	−	16.1444i	0.394730	−	0.571865i	−0.574351	−	0.818609i	$-0.694745\pi$
$797$	11.1437	−	16.1444i	0.394730	−	0.571865i	0.969081	+	0.246744i	$0.0793607\pi$
$798$	1.57234	−	2.27793i	0.0556604	−	0.0806380i
$799$	−20.0602	−	10.5284i	−0.709681	−	0.372469i
$800$	13.7054	−	112.874i	0.484558	−	3.99069i
$801$	6.75454	+	3.54506i	0.238660	+	0.125258i
$802$	−19.2801	+	17.0807i	−0.680804	+	0.603140i
$803$	−5.29294	+	7.66815i	−0.186784	+	0.270603i
$804$	−36.3277	−	8.95398i	−1.28118	−	0.315783i
$805$	−0.805402	+	0.422708i	−0.0283867	+	0.0148985i
$806$	−16.9533	+	49.6907i	−0.597153	+	1.75028i
$807$	−24.0878	−	12.6423i	−0.847932	−	0.445029i
$808$	98.4638	+	87.2313i	3.46395	+	3.06879i
$809$	−1.40101	−	11.5383i	−0.0492568	−	0.405667i	−0.996395	−	0.0848395i	$-0.972962\pi$
$809$	−1.40101	−	11.5383i	−0.0492568	−	0.405667i	0.947138	−	0.320827i	$-0.103961\pi$
$810$	−0.267345	+	0.140314i	−0.00939356	+	0.00493012i
$811$	−5.29283	+	13.9560i	−0.185856	+	0.490063i	−0.995267	−	0.0971805i	$-0.969018\pi$
$811$	−5.29283	+	13.9560i	−0.185856	+	0.490063i	0.809410	+	0.587243i	$0.199787\pi$
$812$	50.4185	−	12.4270i	1.76934	−	0.436103i
$813$	15.3014	−	13.5559i	0.536644	−	0.475425i
$814$	−14.7882	−	13.1012i	−0.518325	−	0.459196i
$815$	0.220973	−	0.582657i	0.00774034	−	0.0204096i
$816$	−29.7298	−	15.6034i	−1.04075	−	0.546229i
$817$	−4.36247	+	3.86481i	−0.152623	+	0.135213i
$818$	−26.6461	−	23.6064i	−0.931659	−	0.825378i
$819$	4.78612	−	2.72145i	0.167241	−	0.0950953i
$820$	−0.340196	+	0.301387i	−0.0118802	+	0.0105249i
$821$	−1.28066	+	10.5472i	−0.0446953	+	0.368099i	0.953151	+	0.302496i	$0.0978200\pi$
$821$	−1.28066	+	10.5472i	−0.0446953	+	0.368099i	−0.997846	+	0.0656025i	$0.979103\pi$
$822$	−16.1861			−0.564554
$823$	−22.7370			−0.792561			−0.396281	−	0.918129i	$-0.629699\pi$
$823$	−22.7370			−0.792561			−0.396281	+	0.918129i	$0.629699\pi$
$824$	−16.1634	+	133.117i	−0.563077	+	4.63736i
$825$	13.2921	−	19.2569i	0.462771	−	0.670440i
$826$	−0.264590			−0.00920628
$827$	19.1264	+	27.7094i	0.665091	+	0.963551i	0.999775	+	0.0212202i	$0.00675511\pi$
$827$	19.1264	+	27.7094i	0.665091	+	0.963551i	−0.334684	+	0.942330i	$0.608630\pi$
$828$	3.59055	+	29.5708i	0.124780	+	1.02766i
$829$	18.8477	−	49.6972i	0.654607	−	1.72606i	−0.0324723	−	0.999473i	$-0.510338\pi$
$829$	18.8477	−	49.6972i	0.654607	−	1.72606i	0.687079	−	0.726583i	$-0.258893\pi$
$830$	0.320243	+	2.63744i	0.0111158	+	0.0915469i
$831$	−2.28934	+	6.03649i	−0.0794162	+	0.209403i
$832$	−103.241	−	49.8229i	−3.57923	−	1.72730i
$833$	−3.62369	−	9.55489i	−0.125554	−	0.331057i
$834$	−44.4428	+	23.3254i	−1.53893	+	0.807691i
$835$	0.247178	−	2.03569i	0.00855395	−	0.0704481i
$836$	−15.1382	−	7.94512i	−0.523564	−	0.274788i
$837$	0.640500	+	5.27499i	0.0221389	+	0.182330i
$838$	−7.83740	−	64.5468i	−0.270738	−	2.22973i
$839$	21.1517	+	18.7388i	0.730238	+	0.646934i	0.943998	−	0.329952i	$-0.107033\pi$
$839$	21.1517	+	18.7388i	0.730238	+	0.646934i	−0.213760	+	0.976886i	$0.568571\pi$
$840$	−0.573818	−	1.51303i	−0.0197986	−	0.0522046i
$841$	5.16496	+	7.48273i	0.178102	+	0.258025i
$842$	−55.1082	−	13.5829i	−1.89915	−	0.468099i
$843$	−5.33653	−	2.80083i	−0.183800	−	0.0964656i
$844$	−89.9806			−3.09726
$845$	1.22054	−	0.749528i	0.0419877	−	0.0257845i
$846$	−28.3613			−0.975081
$847$	−14.8828	−	7.81109i	−0.511378	−	0.268392i
$848$	120.801	+	29.7748i	4.14833	+	1.02247i
$849$	3.82877	+	5.54693i	0.131403	+	0.190370i
$850$	10.6103	+	27.9771i	0.363931	+	0.959608i
$851$	−6.21911	−	5.50965i	−0.213188	−	0.188868i
$852$	4.33996	+	35.7428i	0.148685	+	1.22453i
$853$	5.11122	+	42.0947i	0.175005	+	1.44129i	0.770246	+	0.637747i	$0.220133\pi$
$853$	5.11122	+	42.0947i	0.175005	+	1.44129i	−0.595241	+	0.803547i	$0.702944\pi$
$854$	45.3297	+	23.7909i	1.55115	+	0.814107i
$855$	0.00878422	−	0.0723445i	0.000300414	−	0.00247413i
$856$	67.4849	−	35.4188i	2.30659	−	1.21059i
$857$	0.342130	+	0.902123i	0.0116869	+	0.0308159i	0.940733	−	0.339149i	$-0.110139\pi$
$857$	0.342130	+	0.902123i	0.0116869	+	0.0308159i	−0.929046	+	0.369965i	$0.879370\pi$
$858$	−27.6011	−	37.2379i	−0.942287	−	1.27128i
$859$	1.11238	−	2.93311i	0.0379540	−	0.100077i	−0.914699	−	0.404135i	$-0.867573\pi$
$859$	1.11238	−	2.93311i	0.0379540	−	0.100077i	0.952653	+	0.304058i	$0.0983418\pi$
$860$	0.644744	+	5.30995i	0.0219856	+	0.181068i
$861$	0.405411	−	1.06898i	0.0138164	−	0.0364308i
$862$	−1.99392	−	16.4214i	−0.0679131	−	0.559315i
$863$	27.9300	+	40.4636i	0.950747	+	1.37740i	0.925927	+	0.377704i	$0.123286\pi$
$863$	27.9300	+	40.4636i	0.950747	+	1.37740i	0.0248210	+	0.999692i	$0.492098\pi$
$864$	−22.7959			−0.775533
$865$	1.03885	−	1.50504i	0.0353221	−	0.0511729i
$866$	0.905974	−	7.46137i	0.0307862	−	0.253548i
$867$	−12.2080			−0.414607
$868$	−44.7073			−1.51746
$869$	−7.17611	+	59.1006i	−0.243433	+	2.00485i
$870$	1.39483	−	1.23571i	0.0472892	−	0.0418946i
$871$	23.5617	−	6.65706i	0.798357	−	0.225566i
$872$	−148.611	−	131.658i	−5.03261	−	4.45851i
$873$	3.47002	−	3.07417i	0.117442	−	0.104045i
$874$	−8.67721	−	4.55415i	−0.293511	−	0.154046i
$875$	−0.595874	+	1.57119i	−0.0201442	+	0.0531160i
$876$	−8.19123	−	7.25680i	−0.276756	−	0.245185i
$877$	−28.3877	+	25.1493i	−0.958586	+	0.849233i	−0.988638	−	0.150316i	$-0.951971\pi$
$877$	−28.3877	+	25.1493i	−0.958586	+	0.849233i	0.0300525	+	0.999548i	$0.490433\pi$
$878$	26.3986	−	6.50668i	0.890911	−	0.219590i
$879$	−4.65914	+	12.2851i	−0.157149	+	0.414368i
$880$	−7.01956	+	3.68415i	−0.236629	+	0.124193i
$881$	1.50553	+	12.3992i	0.0507227	+	0.417739i	0.995848	+	0.0910310i	$0.0290162\pi$
$881$	1.50553	+	12.3992i	0.0507227	+	0.417739i	−0.945125	+	0.326708i	$0.894061\pi$
$882$	−9.57550	−	8.48315i	−0.322424	−	0.285643i
$883$	40.6208	+	21.3195i	1.36700	+	0.717457i	0.978934	−	0.204175i	$-0.0654511\pi$
$883$	40.6208	+	21.3195i	1.36700	+	0.717457i	0.388065	+	0.921632i	$0.373143\pi$
$884$	43.4625	−	1.46521i	1.46180	−	0.0492805i
$885$	−0.00616844	+	0.00323745i	−0.000207350	+	0.000108826i
$886$	80.3789	+	19.8116i	2.70038	+	0.665584i
$887$	−15.3283	+	22.2069i	−0.514675	+	0.745635i	−0.991033	−	0.133616i	$-0.957341\pi$
$887$	−15.3283	+	22.2069i	−0.514675	+	0.745635i	0.476359	+	0.879251i	$0.341956\pi$
$888$	11.0640	−	9.80184i	0.371283	−	0.328928i
$889$	−12.1413	−	6.37226i	−0.407207	−	0.213719i
$890$	−0.277622	+	2.28642i	−0.00930591	+	0.0766411i
$891$	−4.15382	−	2.18010i	−0.139158	−	0.0730359i
$892$	51.4727	−	74.5711i	1.72343	−	2.49683i
$893$	3.88868	−	5.63372i	0.130130	−	0.188525i
$894$	−49.8921	+	12.2973i	−1.66864	+	0.411283i
$895$	−2.37504	+	0.585396i	−0.0793890	+	0.0195676i
$896$	7.64515	−	62.9635i	0.255407	−	2.10346i
$897$	−11.6076	−	15.6603i	−0.387565	−	0.522881i
$898$	−5.39093	−	44.3983i	−0.179898	−	1.48159i
$899$	−11.6295	−	30.6646i	−0.387867	−	1.02272i
$900$	20.5705	+	18.2239i	0.685685	+	0.607464i
$901$	−17.2409	+	4.24949i	−0.574377	+	0.141571i
$902$	−9.34530	−	2.30341i	−0.311164	−	0.0766952i
$903$	−7.64338	−	11.0733i	−0.254356	−	0.368498i
$904$	−43.5497	−	114.831i	−1.44844	−	3.81923i
$905$	1.16034	−	1.02797i	0.0385709	−	0.0341708i
$906$	−6.21978	+	51.2245i	−0.206638	+	1.70182i
$907$	18.6439	+	49.1600i	0.619062	+	1.63233i	0.765742	+	0.643148i	$0.222372\pi$
$907$	18.6439	+	49.1600i	0.619062	+	1.63233i	−0.146680	+	0.989184i	$0.546859\pi$
$908$	6.31040	−	16.6392i	0.209418	−	0.552190i
$909$	−13.2795	+	3.27309i	−0.440452	+	0.108562i
$910$	1.28072	+	1.05979i	0.0424555	+	0.0351318i
$911$	−52.5059	−	12.9415i	−1.73960	−	0.428773i	−0.763449	−	0.645868i	$-0.776495\pi$
$911$	−52.5059	−	12.9415i	−1.73960	−	0.428773i	−0.976150	+	0.217096i	$0.930342\pi$
$912$	5.76313	−	8.34933i	0.190836	−	0.276474i
$913$	−30.8983	+	27.3735i	−1.02258	+	0.905930i
$914$	73.9415	+	18.2249i	2.44577	+	0.602828i
$915$	1.34788			0.0445594
$916$	51.1897	+	12.6171i	1.69135	+	0.416881i
$917$	−1.94990	+	5.14147i	−0.0643914	+	0.169786i
$918$	5.31174	−	2.78782i	0.175314	−	0.0920117i
$919$	10.8632	+	28.6439i	0.358344	+	0.944874i	0.986054	+	0.166427i	$0.0532231\pi$
$919$	10.8632	+	28.6439i	0.358344	+	0.944874i	−0.627710	+	0.778447i	$0.716008\pi$
$920$	−5.07294	+	2.66248i	−0.167250	+	0.0877795i
$921$	11.0540	+	16.0144i	0.364240	+	0.527693i
$922$	−26.4801	−	38.3631i	−0.872077	−	1.26342i
$923$	−14.0303	−	18.9288i	−0.461811	−	0.623051i
$924$	22.4211	−	32.4826i	0.737601	−	1.06860i
$925$	−7.66542			−0.252038
$926$	−59.6917	−	86.4784i	−1.96159	−	2.84186i
$927$	−10.4356	−	9.24516i	−0.342751	−	0.303651i
$928$	136.605	−	33.6702i	4.48430	−	1.10528i
$929$	−18.9466	+	9.94396i	−0.621619	+	0.326251i	−0.745962	−	0.665988i	$-0.768010\pi$
$929$	−18.9466	+	9.94396i	−0.621619	+	0.326251i	0.124343	+	0.992239i	$0.460318\pi$
$930$	−1.42060	+	0.745590i	−0.0465834	+	0.0244489i
$931$	2.99802	−	0.738946i	0.0982562	−	0.0242180i
$932$	−74.3110	−	65.8338i	−2.43414	−	2.15646i
$933$	−2.78403	−	4.03336i	−0.0911450	−	0.132046i
$934$	−27.4153			−0.897055
$935$	0.642729	−	0.931154i	0.0210195	−	0.0304520i
$936$	30.1461	−	17.1415i	0.985355	−	0.560286i
$937$	−12.6991	−	18.3978i	−0.414861	−	0.601030i	0.558724	−	0.829353i	$-0.311291\pi$
$937$	−12.6991	−	18.3978i	−0.414861	−	0.601030i	−0.973585	+	0.228324i	$0.926676\pi$
$938$	16.1424	+	23.3863i	0.527068	+	0.763589i
$939$	18.7904	−	9.86197i	0.613202	−	0.321833i
$940$	−2.22784	−	5.87432i	−0.0726640	−	0.191599i
$941$	4.71102	−	2.47253i	0.153575	−	0.0806022i	−0.386185	−	0.922421i	$-0.626207\pi$
$941$	4.71102	−	2.47253i	0.153575	−	0.0806022i	0.539760	+	0.841819i	$0.318515\pi$
$942$	16.7653	−	44.2064i	0.546242	−	1.44032i
$943$	−3.93013	−	0.968691i	−0.127983	−	0.0315449i
$944$	−0.969806			−0.0315645
$945$	0.163354	+	0.0402632i	0.00531392	+	0.00130976i
$946$	−84.7882	+	75.1157i	−2.75670	+	2.44222i
$947$	−8.23549	+	11.9312i	−0.267617	+	0.387711i	−0.933635	−	0.358225i	$-0.883382\pi$
$947$	−8.23549	+	11.9312i	−0.267617	+	0.387711i	0.666018	+	0.745936i	$0.267997\pi$
$948$	−67.8915	−	16.7338i	−2.20501	−	0.543487i
$949$	7.00696	+	1.47856i	0.227456	+	0.0479960i
$950$	−8.77834	+	2.16367i	−0.284807	+	0.0701986i
$951$	4.07995	−	10.7579i	0.132301	−	0.348850i
$952$	11.4009	+	30.0616i	0.369504	+	0.974303i
$953$	0.896673	−	7.38477i	0.0290461	−	0.239216i	−0.970954	−	0.239267i	$-0.923093\pi$
$953$	0.896673	−	7.38477i	0.0290461	−	0.239216i	1.00000		5.05180e-5i	$1.60804e-5\pi$
$954$	−16.6387	+	14.7406i	−0.538699	+	0.477246i
$955$	−0.0765454	−	0.201834i	−0.00247695	−	0.00653118i
$956$	−37.5127	−	54.3465i	−1.21325	−	1.75769i
$957$	28.1120	+	6.92900i	0.908733	+	0.223983i
$958$	63.9542	−	15.7633i	2.06627	−	0.509289i
$959$	6.75105	+	5.98091i	0.218003	+	0.193134i
$960$	−1.24217	−	3.27532i	−0.0400907	−	0.105711i
$961$	−0.333188	−	2.74405i	−0.0107480	−	0.0885177i
$962$	−4.90315	+	14.3713i	−0.158084	+	0.463350i
$963$	−0.955140	+	7.86629i	−0.0307790	+	0.253488i
$964$	−115.304	+	28.4198i	−3.71369	+	0.915342i
$965$	1.13870	−	0.280665i	0.0366561	−	0.00903493i
$966$	12.8518	−	18.6191i	0.413500	−	0.599059i
$967$	2.79699	−	4.05214i	0.0899451	−	0.130308i	−0.775428	−	0.631436i	$-0.782466\pi$
$967$	2.79699	−	4.05214i	0.0899451	−	0.130308i	0.865373	+	0.501128i	$0.167081\pi$
$968$	−93.7413	−	49.1992i	−3.01296	−	1.58132i
$969$	−0.174529	+	1.43737i	−0.00560667	+	0.0461751i
$970$	1.23938	+	0.650479i	0.0397942	+	0.0208856i
$971$	13.6285	−	12.0738i	0.437360	−	0.387467i	−0.415511	−	0.909588i	$-0.636397\pi$
$971$	13.6285	−	12.0738i	0.437360	−	0.387467i	0.852872	+	0.522121i	$0.174859\pi$
$972$	3.12991	−	4.53445i	0.100392	−	0.145443i
$973$	27.1556	+	6.69325i	0.870568	+	0.214576i
$974$	76.3999	−	40.0977i	2.44801	−	1.28481i
$975$	−17.5965	−	3.71308i	−0.563539	−	0.118914i
$976$	166.148	+	87.2010i	5.31825	+	2.79124i
$977$	34.7607	+	30.7953i	1.11209	+	0.985229i	0.999964	−	0.00846449i	$-0.00269436\pi$
$977$	34.7607	+	30.7953i	1.11209	+	0.985229i	0.112130	+	0.993694i	$0.464233\pi$
$978$	1.86825	+	15.3864i	0.0597399	+	0.492003i
$979$	−31.6867	+	16.6305i	−1.01271	+	0.531512i
$980$	1.00489	−	2.64969i	0.0321002	−	0.0846412i
$981$	20.0427	−	4.94007i	0.639913	−	0.157724i
$982$	−61.2357	+	54.2501i	−1.95411	+	1.73119i
$983$	−16.8381	−	14.9172i	−0.537051	−	0.475786i	0.350456	−	0.936579i	$-0.386027\pi$
$983$	−16.8381	−	14.9172i	−0.537051	−	0.475786i	−0.887508	+	0.460793i	$0.847565\pi$
$984$	2.55354	−	6.73312i	0.0814038	−	0.214644i
$985$	−1.37116	−	0.719640i	−0.0436888	−	0.0229296i
$986$	−27.7132	+	24.5517i	−0.882567	+	0.781886i
$987$	11.8292	+	10.4798i	0.376528	+	0.333575i
$988$	−1.14346	+	13.0902i	−0.0363782	+	0.416454i
$989$	−35.6574	+	31.5897i	−1.13384	+	1.00449i
$990$	0.170729	−	1.40608i	0.00542611	−	0.0446880i
$991$	3.49232			0.110937			0.0554686	−	0.998460i	$-0.482335\pi$
$991$	3.49232			0.110937			0.0554686	+	0.998460i	$0.482335\pi$
$992$	−121.131			−3.84593
$993$	0.463772	−	3.81951i	0.0147174	−	0.121208i
$994$	15.5342	−	22.5052i	0.492715	−	0.713821i
$995$	−1.66691			−0.0528447
$996$	−27.5414	−	39.9006i	−0.872683	−	1.26430i
$997$	−2.85489	−	23.5121i	−0.0904152	−	0.744636i	−0.965452	−	0.260580i	$-0.916086\pi$
$997$	−2.85489	−	23.5121i	−0.0904152	−	0.744636i	0.875037	−	0.484056i	$-0.160837\pi$
$998$	−5.11194	+	13.4791i	−0.161816	+	0.426673i
$999$	0.185243	+	1.52561i	0.00586082	+	0.0482682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.79.1	✓	204
169.92	even	13	inner	507.2.m.b.430.1	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.79.1	✓	204	1.1	even	1	trivial
507.2.m.b.430.1	yes	204	169.92	even	13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42650 - 1.27353i) q^{2} +(-0.970942 - 0.239316i) q^{3} +(3.12991 + 4.53445i) q^{4} +(-0.0390694 - 0.103018i) q^{5} +(2.05122 + 1.81722i) q^{6} +(-0.184062 - 1.51589i) q^{7} +(-1.15934 - 9.54803i) q^{8} +(0.885456 + 0.464723i) q^{9} +(-0.0363936 + 0.299728i) q^{10} +(-4.15382 + 2.18010i) q^{11} +(-1.95379 - 5.15172i) q^{12} +(2.77782 + 2.29863i) q^{13} +(-1.48389 + 3.91271i) q^{14} +(0.0132804 + 0.109374i) q^{15} +(-5.43893 + 14.3413i) q^{16} +(-0.263861 - 2.17309i) q^{17} +(-1.55672 - 2.25530i) q^{18} +0.661441 q^{19} +(0.344845 - 0.499594i) q^{20} +(-0.184062 + 1.51589i) q^{21} +12.8557 q^{22} +5.40640 q^{23} +(-1.15934 + 9.54803i) q^{24} +(3.73347 - 3.30756i) q^{25} +(-3.81301 - 9.11526i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(6.29762 - 5.57920i) q^{28} +(5.46494 + 2.86822i) q^{29} +(0.107066 - 0.282309i) q^{30} +(-3.97739 - 3.52366i) q^{31} +(17.0630 - 15.1165i) q^{32} +(4.55485 - 1.12267i) q^{33} +(-2.12723 + 5.60905i) q^{34} +(-0.148972 + 0.0781865i) q^{35} +(0.664129 + 5.46960i) q^{36} +(-1.15032 - 1.01910i) q^{37} +(-1.60499 - 0.842362i) q^{38} +(-2.14700 - 2.89662i) q^{39} +(-0.938320 + 0.492468i) q^{40} +(-0.726940 - 0.179175i) q^{41} +(2.37715 - 3.44389i) q^{42} +(-6.59539 + 5.84301i) q^{43} +(-22.8866 - 12.0118i) q^{44} +(0.0132804 - 0.109374i) q^{45} +(-13.1186 - 6.88519i) q^{46} +(5.87910 - 8.51734i) q^{47} +(8.71298 - 12.6229i) q^{48} +(4.53256 - 1.11718i) q^{49} +(-13.2715 + 3.27114i) q^{50} +(-0.263861 + 2.17309i) q^{51} +(-1.72874 + 19.7904i) q^{52} +(-0.977751 - 8.05251i) q^{53} +(0.971758 + 2.56231i) q^{54} +(0.386876 + 0.342742i) q^{55} +(-14.2603 + 3.51486i) q^{56} +(-0.642221 - 0.158293i) q^{57} +(-9.60791 - 13.9195i) q^{58} +(0.0224213 + 0.0591201i) q^{59} +(-0.454385 + 0.402550i) q^{60} +(1.47461 - 12.1445i) q^{61} +(5.16366 + 13.6155i) q^{62} +(0.541489 - 1.42779i) q^{63} +(-30.8699 + 7.60875i) q^{64} +(0.128272 - 0.375971i) q^{65} +(-12.4821 - 3.07656i) q^{66} +(3.85753 - 5.58860i) q^{67} +(9.02793 - 7.99804i) q^{68} +(-5.24930 - 1.29384i) q^{69} +0.461053 q^{70} +(-6.34492 - 1.56388i) q^{71} +(3.41064 - 8.99313i) q^{72} +(1.75867 - 0.923022i) q^{73} +(1.49341 + 3.93781i) q^{74} +(-4.41653 + 2.31797i) q^{75} +(2.07025 + 2.99927i) q^{76} +(4.06934 + 5.89546i) q^{77} +(1.52078 + 9.76290i) q^{78} +(7.20919 - 10.4443i) q^{79} +1.68990 q^{80} +(0.568065 + 0.822984i) q^{81} +(1.53574 + 1.36054i) q^{82} +(8.54375 - 2.10584i) q^{83} +(-7.44981 + 3.90996i) q^{84} +(-0.213558 + 0.112084i) q^{85} +(23.4449 - 5.77866i) q^{86} +(-4.61972 - 4.09272i) q^{87} +(25.6313 + 37.1334i) q^{88} +7.62832 q^{89} +(-0.171516 + 0.248483i) q^{90} +(2.97318 - 4.63395i) q^{91} +(16.9215 + 24.5151i) q^{92} +(3.01855 + 4.37312i) q^{93} +(-25.1127 + 13.1801i) q^{94} +(-0.0258421 - 0.0681401i) q^{95} +(-20.1848 + 10.5938i) q^{96} +(1.64391 - 4.33464i) q^{97} +(-12.4210 - 3.06150i) q^{98} -4.69117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

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