LMFDB - Embedded newform 544.2.bd.b.69.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(69,544)] 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("544.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			69.11
Character	$\chi$	$=$	544.69
Dual form			544.2.bd.b.205.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.780220 - 1.17952i) q^{2} +(0.998357 + 2.41025i) q^{3} +(-0.782513 + 1.84056i) q^{4} +(1.73773 + 0.719793i) q^{5} +(2.06399 - 3.05810i) q^{6} +(1.04993 + 1.04993i) q^{7} +(2.78151 - 0.513058i) q^{8} +(-2.69125 + 2.69125i) q^{9} +(-0.506808 - 2.61128i) q^{10} +(0.811901 - 1.96010i) q^{11} +(-5.21744 - 0.0485113i) q^{12} +(6.13950 - 2.54307i) q^{13} +(0.419231 - 2.05758i) q^{14} +4.90698i q^{15} +(-2.77535 - 2.88053i) q^{16} +1.00000i q^{17} +(5.27414 + 1.07460i) q^{18} +(1.33228 - 0.551850i) q^{19} +(-2.68463 + 2.63516i) q^{20} +(-1.48238 + 3.57878i) q^{21} +(-2.94543 + 0.571661i) q^{22} +(-3.13956 + 3.13956i) q^{23} +(4.01353 + 6.19190i) q^{24} +(-1.03391 - 1.03391i) q^{25} +(-7.78975 - 5.25749i) q^{26} +(-1.94267 - 0.804680i) q^{27} +(-2.75404 + 1.11088i) q^{28} +(1.68013 + 4.05620i) q^{29} +(5.78786 - 3.82852i) q^{30} -9.53824 q^{31} +(-1.23225 + 5.52101i) q^{32} +5.53490 q^{33} +(1.17952 - 0.780220i) q^{34} +(1.06876 + 2.58022i) q^{35} +(-2.84748 - 7.05936i) q^{36} +(-3.42874 - 1.42023i) q^{37} +(-1.69039 - 1.14089i) q^{38} +(12.2588 + 12.2588i) q^{39} +(5.20281 + 1.11055i) q^{40} +(1.23599 - 1.23599i) q^{41} +(5.37782 - 1.04375i) q^{42} +(-2.48552 + 6.00058i) q^{43} +(2.97237 + 3.02816i) q^{44} +(-6.61383 + 2.73954i) q^{45} +(6.15270 + 1.25361i) q^{46} +1.60091i q^{47} +(4.17200 - 9.56506i) q^{48} -4.79531i q^{49} +(-0.412837 + 2.02620i) q^{50} +(-2.41025 + 0.998357i) q^{51} +(-0.123571 + 13.2901i) q^{52} +(-1.26060 + 3.04336i) q^{53} +(0.566577 + 2.91924i) q^{54} +(2.82174 - 2.82174i) q^{55} +(3.45905 + 2.38170i) q^{56} +(2.66019 + 2.66019i) q^{57} +(3.47347 - 5.14647i) q^{58} +(-4.37346 - 1.81155i) q^{59} +(-9.03161 - 3.83978i) q^{60} +(-5.32147 - 12.8472i) q^{61} +(7.44192 + 11.2505i) q^{62} -5.65124 q^{63} +(7.47354 - 2.85415i) q^{64} +12.4993 q^{65} +(-4.31844 - 6.52850i) q^{66} +(0.0148947 + 0.0359589i) q^{67} +(-1.84056 - 0.782513i) q^{68} +(-10.7015 - 4.43271i) q^{69} +(2.20954 - 3.27377i) q^{70} +(0.520151 + 0.520151i) q^{71} +(-6.10496 + 8.86650i) q^{72} +(10.2953 - 10.2953i) q^{73} +(0.999989 + 5.15235i) q^{74} +(1.45977 - 3.52420i) q^{75} +(-0.0268151 + 2.88398i) q^{76} +(2.91040 - 1.20553i) q^{77} +(4.89490 - 24.0241i) q^{78} -12.6309i q^{79} +(-2.74943 - 7.00327i) q^{80} +5.93234i q^{81} +(-2.42222 - 0.493527i) q^{82} +(-2.38751 + 0.988939i) q^{83} +(-5.42700 - 5.52886i) q^{84} +(-0.719793 + 1.73773i) q^{85} +(9.01703 - 1.75006i) q^{86} +(-8.09906 + 8.09906i) q^{87} +(1.25266 - 5.86859i) q^{88} +(1.06110 + 1.06110i) q^{89} +(8.39157 + 5.66367i) q^{90} +(9.11606 + 3.77600i) q^{91} +(-3.32181 - 8.23529i) q^{92} +(-9.52256 - 22.9895i) q^{93} +(1.88830 - 1.24906i) q^{94} +2.71238 q^{95} +(-14.5372 + 2.54191i) q^{96} +9.46176 q^{97} +(-5.65614 + 3.74139i) q^{98} +(3.09010 + 7.46016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) $ 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.780220	−	1.17952i	−0.551699	−	0.834043i
$2$	−0.780220	−	1.17952i	−0.551699	−	0.834043i
$3$	0.998357	+	2.41025i	0.576402	+	1.39156i	0.896022	+	0.444011i	$0.146445\pi$
$3$	0.998357	+	2.41025i	0.576402	+	1.39156i	−0.319620	+	0.947546i	$0.603555\pi$
$4$	−0.782513	+	1.84056i	−0.391257	+	0.920282i
$5$	1.73773	+	0.719793i	0.777139	+	0.321901i	0.735760	−	0.677242i	$-0.236825\pi$
$5$	1.73773	+	0.719793i	0.777139	+	0.321901i	0.0413784	+	0.999144i	$0.486825\pi$
$6$	2.06399	−	3.05810i	0.842618	−	1.24846i
$7$	1.04993	+	1.04993i	0.396835	+	0.396835i	0.877115	−	0.480280i	$-0.159465\pi$
$7$	1.04993	+	1.04993i	0.396835	+	0.396835i	−0.480280	+	0.877115i	$0.659465\pi$
$8$	2.78151	−	0.513058i	0.983411	−	0.181393i
$9$	−2.69125	+	2.69125i	−0.897084	+	0.897084i
$10$	−0.506808	−	2.61128i	−0.160267	−	0.825760i
$11$	0.811901	−	1.96010i	0.244797	−	0.590993i	−0.752950	−	0.658078i	$-0.771370\pi$
$11$	0.811901	−	1.96010i	0.244797	−	0.590993i	0.997747	+	0.0670847i	$0.0213698\pi$
$12$	−5.21744	−	0.0485113i	−1.50614	−	0.0140040i
$13$	6.13950	−	2.54307i	1.70279	−	0.705320i	0.702810	−	0.711377i	$-0.251928\pi$
$13$	6.13950	−	2.54307i	1.70279	−	0.705320i	0.999982	+	0.00605760i	$0.00192821\pi$
$14$	0.419231	−	2.05758i	0.112044	−	0.549911i
$15$			4.90698i			1.26698i
$16$	−2.77535	−	2.88053i	−0.693836	−	0.720133i
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$	5.27414	+	1.07460i	1.24313	+	0.253287i
$19$	1.33228	−	0.551850i	0.305647	−	0.126603i	−0.224588	−	0.974454i	$-0.572104\pi$
$19$	1.33228	−	0.551850i	0.305647	−	0.126603i	0.530235	+	0.847851i	$0.322104\pi$
$20$	−2.68463	+	2.63516i	−0.600301	+	0.589240i
$21$	−1.48238	+	3.57878i	−0.323482	+	0.780955i
$22$	−2.94543	+	0.571661i	−0.627968	+	0.121879i
$23$	−3.13956	+	3.13956i	−0.654643	+	0.654643i	−0.954107	−	0.299465i	$-0.903192\pi$
$23$	−3.13956	+	3.13956i	−0.654643	+	0.654643i	0.299465	+	0.954107i	$0.403192\pi$
$24$	4.01353	+	6.19190i	0.819258	+	1.26392i
$25$	−1.03391	−	1.03391i	−0.206783	−	0.206783i
$26$	−7.78975	−	5.25749i	−1.52770	−	1.03108i
$27$	−1.94267	−	0.804680i	−0.373867	−	0.154861i
$28$	−2.75404	+	1.11088i	−0.520464	+	0.209936i
$29$	1.68013	+	4.05620i	0.311993	+	0.753217i	0.999631	+	0.0271635i	$0.00864748\pi$
$29$	1.68013	+	4.05620i	0.311993	+	0.753217i	−0.687638	+	0.726053i	$0.741353\pi$
$30$	5.78786	−	3.82852i	1.05671	−	0.698990i
$31$	−9.53824			−1.71312			−0.856559	−	0.516049i	$-0.827402\pi$
$31$	−9.53824			−1.71312			−0.856559	+	0.516049i	$0.827402\pi$
$32$	−1.23225	+	5.52101i	−0.217833	+	0.975986i
$33$	5.53490			0.963502
$34$	1.17952	−	0.780220i	0.202285	−	0.133807i
$35$	1.06876	+	2.58022i	0.180654	+	0.436138i
$36$	−2.84748	−	7.05936i	−0.474580	−	1.17656i
$37$	−3.42874	−	1.42023i	−0.563682	−	0.233485i	0.0826008	−	0.996583i	$-0.473677\pi$
$37$	−3.42874	−	1.42023i	−0.563682	−	0.233485i	−0.646283	+	0.763098i	$0.723677\pi$
$38$	−1.69039	−	1.14089i	−0.274218	−	0.185076i
$39$	12.2588	+	12.2588i	1.96298	+	1.96298i
$40$	5.20281	+	1.11055i	0.822637	+	0.175593i
$41$	1.23599	−	1.23599i	0.193030	−	0.193030i	−0.603974	−	0.797004i	$-0.706417\pi$
$41$	1.23599	−	1.23599i	0.193030	−	0.193030i	0.797004	+	0.603974i	$0.206417\pi$
$42$	5.37782	−	1.04375i	0.829815	−	0.161054i
$43$	−2.48552	+	6.00058i	−0.379039	+	0.915080i	0.613108	+	0.789999i	$0.289919\pi$
$43$	−2.48552	+	6.00058i	−0.379039	+	0.915080i	−0.992147	+	0.125081i	$0.960081\pi$
$44$	2.97237	+	3.02816i	0.448101	+	0.456513i
$45$	−6.61383	+	2.73954i	−0.985931	+	0.408386i
$46$	6.15270	+	1.25361i	0.907166	+	0.184835i
$47$			1.60091i			0.233517i	0.993160	+	0.116758i	$0.0372503\pi$
$47$			1.60091i			0.233517i	−0.993160	+	0.116758i	$0.962750\pi$
$48$	4.17200	−	9.56506i	0.602177	−	1.38060i
$49$		−	4.79531i		−	0.685044i
$50$	−0.412837	+	2.02620i	−0.0583840	+	0.286548i
$51$	−2.41025	+	0.998357i	−0.337502	+	0.139798i
$52$	−0.123571	+	13.2901i	−0.0171362	+	1.84301i
$53$	−1.26060	+	3.04336i	−0.173157	+	0.418038i	−0.986503	−	0.163742i	$-0.947643\pi$
$53$	−1.26060	+	3.04336i	−0.173157	+	0.418038i	0.813346	+	0.581780i	$0.197643\pi$
$54$	0.566577	+	2.91924i	0.0771014	+	0.397258i
$55$	2.82174	−	2.82174i	0.380483	−	0.380483i
$56$	3.45905	+	2.38170i	0.462235	+	0.318269i
$57$	2.66019	+	2.66019i	0.352351	+	0.352351i
$58$	3.47347	−	5.14647i	0.456090	−	0.675764i
$59$	−4.37346	−	1.81155i	−0.569376	−	0.235843i	0.0793740	−	0.996845i	$-0.474708\pi$
$59$	−4.37346	−	1.81155i	−0.569376	−	0.235843i	−0.648750	+	0.761002i	$0.724708\pi$
$60$	−9.03161	−	3.83978i	−1.16598	−	0.495713i
$61$	−5.32147	−	12.8472i	−0.681344	−	1.64491i	−0.761529	−	0.648131i	$-0.775551\pi$
$61$	−5.32147	−	12.8472i	−0.681344	−	1.64491i	0.0801847	−	0.996780i	$-0.474449\pi$
$62$	7.44192	+	11.2505i	0.945125	+	1.42881i
$63$	−5.65124			−0.711989
$64$	7.47354	−	2.85415i	0.934193	−	0.356768i
$65$	12.4993			1.55035
$66$	−4.31844	−	6.52850i	−0.531563	−	0.803602i
$67$	0.0148947	+	0.0359589i	0.00181967	+	0.00439308i	0.924787	−	0.380486i	$-0.124243\pi$
$67$	0.0148947	+	0.0359589i	0.00181967	+	0.00439308i	−0.922967	+	0.384879i	$0.874243\pi$
$68$	−1.84056	−	0.782513i	−0.223201	−	0.0948937i
$69$	−10.7015	−	4.43271i	−1.28831	−	0.533635i
$70$	2.20954	−	3.27377i	0.264091	−	0.391290i
$71$	0.520151	+	0.520151i	0.0617306	+	0.0617306i	0.737298	−	0.675568i	$-0.236101\pi$
$71$	0.520151	+	0.520151i	0.0617306	+	0.0617306i	−0.675568	+	0.737298i	$0.736101\pi$
$72$	−6.10496	+	8.86650i	−0.719477	+	1.04493i
$73$	10.2953	−	10.2953i	1.20497	−	1.20497i	0.232334	−	0.972636i	$-0.425364\pi$
$73$	10.2953	−	10.2953i	1.20497	−	1.20497i	0.972636	−	0.232334i	$-0.0746362\pi$
$74$	0.999989	+	5.15235i	0.116246	+	0.598949i
$75$	1.45977	−	3.52420i	0.168560	−	0.406940i
$76$	−0.0268151	+	2.88398i	−0.00307590	+	0.330816i
$77$	2.91040	−	1.20553i	0.331671	−	0.137383i
$78$	4.89490	−	24.0241i	0.554238	−	2.72019i
$79$		−	12.6309i		−	1.42109i	−0.703654	−	0.710543i	$-0.748450\pi$
$79$		−	12.6309i		−	1.42109i	0.703654	−	0.710543i	$-0.251550\pi$
$80$	−2.74943	−	7.00327i	−0.307395	−	0.782990i
$81$			5.93234i			0.659149i
$82$	−2.42222	−	0.493527i	−0.267490	−	0.0545009i
$83$	−2.38751	+	0.988939i	−0.262063	+	0.108550i	−0.509847	−	0.860265i	$-0.670298\pi$
$83$	−2.38751	+	0.988939i	−0.262063	+	0.108550i	0.247783	+	0.968815i	$0.420298\pi$
$84$	−5.42700	−	5.52886i	−0.592134	−	0.603248i
$85$	−0.719793	+	1.73773i	−0.0780725	+	0.188484i
$86$	9.01703	−	1.75006i	0.972332	−	0.188714i
$87$	−8.09906	+	8.09906i	−0.868311	+	0.868311i
$88$	1.25266	−	5.86859i	0.133534	−	0.625594i
$89$	1.06110	+	1.06110i	0.112477	+	0.112477i	0.761105	−	0.648628i	$-0.224657\pi$
$89$	1.06110	+	1.06110i	0.112477	+	0.112477i	−0.648628	+	0.761105i	$0.724657\pi$
$90$	8.39157	+	5.66367i	0.884549	+	0.597003i
$91$	9.11606	+	3.77600i	0.955623	+	0.395832i
$92$	−3.32181	−	8.23529i	−0.346322	−	0.858589i
$93$	−9.52256	−	22.9895i	−0.987444	−	2.38390i
$94$	1.88830	−	1.24906i	0.194763	−	0.128831i
$95$	2.71238			0.278284
$96$	−14.5372	+	2.54191i	−1.48370	+	0.259433i
$97$	9.46176			0.960696			0.480348	−	0.877078i	$-0.340510\pi$
$97$	9.46176			0.960696			0.480348	+	0.877078i	$0.340510\pi$
$98$	−5.65614	+	3.74139i	−0.571356	+	0.377938i
$99$	3.09010	+	7.46016i	0.310567	+	0.749774i
$100$	2.71204	−	1.09393i	0.271204	−	0.109393i
$101$	−10.3678	−	4.29447i	−1.03163	−	0.427316i	−0.198331	−	0.980135i	$-0.563552\pi$
$101$	−10.3678	−	4.29447i	−1.03163	−	0.427316i	−0.833301	+	0.552819i	$0.813552\pi$
$102$	3.05810	+	2.06399i	0.302797	+	0.204365i
$103$	7.20019	+	7.20019i	0.709456	+	0.709456i	0.966421	−	0.256965i	$-0.0827226\pi$
$103$	7.20019	+	7.20019i	0.709456	+	0.709456i	−0.256965	+	0.966421i	$0.582723\pi$
$104$	15.7723	−	10.2235i	1.54660	−	1.00249i
$105$	−5.15197	+	5.15197i	−0.502781	+	0.502781i
$106$	4.57324	−	0.887592i	0.444192	−	0.0862106i
$107$	0.818630	−	1.97635i	0.0791399	−	0.191061i	−0.879357	−	0.476162i	$-0.842027\pi$
$107$	0.818630	−	1.97635i	0.0791399	−	0.191061i	0.958497	+	0.285102i	$0.0920274\pi$
$108$	3.00123	−	2.94593i	0.288794	−	0.283473i
$109$	−13.4659	+	5.57777i	−1.28980	+	0.534254i	−0.918927	−	0.394428i	$-0.870943\pi$
$109$	−13.4659	+	5.57777i	−1.28980	+	0.534254i	−0.370876	+	0.928682i	$0.620943\pi$
$110$	−5.52986	−	1.12671i	−0.527251	−	0.107427i
$111$		−	9.68202i		−	0.918976i
$112$	0.110436	−	5.93826i	0.0104353	−	0.561113i
$113$		−	11.9134i		−	1.12072i	−0.828248	−	0.560361i	$-0.810662\pi$
$113$		−	11.9134i		−	1.12072i	0.828248	−	0.560361i	$-0.189338\pi$
$114$	1.06220	−	5.21327i	0.0994843	−	0.488267i
$115$	−7.71554	+	3.19588i	−0.719478	+	0.298018i
$116$	−8.78041	−	0.0816396i	−0.815241	−	0.00758005i
$117$	−9.67892	+	23.3670i	−0.894817	+	2.16028i
$118$	1.27551	+	6.57197i	0.117421	+	0.604999i
$119$	−1.04993	+	1.04993i	−0.0962467	+	0.0962467i
$120$	2.51756	+	13.6488i	0.229821	+	1.24596i
$121$	4.59536	+	4.59536i	0.417760	+	0.417760i
$122$	−11.0015	+	16.3004i	−0.996030	+	1.47577i
$123$	4.21301	+	1.74509i	0.379875	+	0.157349i
$124$	7.46380	−	17.5557i	0.670269	−	1.57655i
$125$	−4.65143	−	11.2295i	−0.416037	−	1.00440i
$126$	4.40921	+	6.66572i	0.392803	+	0.593830i
$127$	9.02208			0.800580			0.400290	−	0.916389i	$-0.368909\pi$
$127$	9.02208			0.800580			0.400290	+	0.916389i	$0.368909\pi$
$128$	−9.19752	−	6.58830i	−0.812953	−	0.582329i
$129$	−16.9443			−1.49186
$130$	−9.75221	−	14.7431i	−0.855326	−	1.29306i
$131$	6.12073	+	14.7768i	0.534771	+	1.29105i	0.928332	+	0.371753i	$0.121243\pi$
$131$	6.12073	+	14.7768i	0.534771	+	1.29105i	−0.393561	+	0.919299i	$0.628757\pi$
$132$	−4.33113	+	10.1873i	−0.376977	+	0.886693i
$133$	1.97820	+	0.819399i	0.171532	+	0.0710509i
$134$	0.0307930	−	0.0456243i	0.00266011	−	0.00394134i
$135$	−2.79664	−	2.79664i	−0.240697	−	0.240697i
$136$	0.513058	+	2.78151i	0.0439943	+	0.238512i
$137$	−9.76805	+	9.76805i	−0.834541	+	0.834541i	−0.988134	−	0.153593i	$-0.950915\pi$
$137$	−9.76805	+	9.76805i	−0.834541	+	0.834541i	0.153593	+	0.988134i	$0.450915\pi$
$138$	3.12108	+	16.0811i	0.265684	+	1.36891i
$139$	0.0457461	−	0.110441i	0.00388014	−	0.00936748i	−0.921928	−	0.387362i	$-0.873386\pi$
$139$	0.0457461	−	0.110441i	0.00388014	−	0.00936748i	0.925808	+	0.377995i	$0.123386\pi$
$140$	−5.58539	−	0.0519325i	−0.472052	−	0.00438910i
$141$	−3.85859	+	1.59828i	−0.324952	+	0.134599i
$142$	0.207694	−	1.01936i	0.0174293	−	0.0855427i
$143$		−	14.0988i		−	1.17900i
$144$	15.2214	+	0.283079i	1.26845	+	0.0235899i
$145$			8.25794i			0.685785i
$146$	−20.1760	−	4.11085i	−1.66978	−	0.340217i
$147$	11.5579	−	4.78743i	0.953277	−	0.394860i
$148$	5.29707	−	5.19947i	0.435416	−	0.427394i
$149$	−9.27185	+	22.3842i	−0.759579	+	1.83379i	−0.266388	+	0.963866i	$0.585830\pi$
$149$	−9.27185	+	22.3842i	−0.759579	+	1.83379i	−0.493192	+	0.869921i	$0.664170\pi$
$150$	−5.29580	+	1.02783i	−0.432400	+	0.0839220i
$151$	−7.22570	+	7.22570i	−0.588019	+	0.588019i	−0.937095	−	0.349075i	$-0.886496\pi$
$151$	−7.22570	+	7.22570i	−0.588019	+	0.588019i	0.349075	+	0.937095i	$0.386496\pi$
$152$	3.42263	−	2.21851i	0.277612	−	0.179945i
$153$	−2.69125	−	2.69125i	−0.217575	−	0.217575i
$154$	−3.69269	−	2.49229i	−0.297566	−	0.200834i
$155$	−16.5749	−	6.86556i	−1.33133	−	0.551455i
$156$	−32.1559	+	12.9705i	−2.57453	+	1.03847i
$157$	−1.29107	−	3.11692i	−0.103039	−	0.248757i	0.863950	−	0.503578i	$-0.167983\pi$
$157$	−1.29107	−	3.11692i	−0.103039	−	0.248757i	−0.966988	+	0.254821i	$0.917983\pi$
$158$	−14.8983	+	9.85487i	−1.18525	+	0.784011i
$159$	−8.59378			−0.681531
$160$	−6.11531	+	8.70709i	−0.483458	+	0.688356i
$161$	−6.59261			−0.519570
$162$	6.99729	−	4.62853i	0.549759	−	0.363652i
$163$	−2.63563	−	6.36298i	−0.206439	−	0.498387i	0.786419	−	0.617694i	$-0.211933\pi$
$163$	−2.63563	−	6.36298i	−0.206439	−	0.498387i	−0.992857	+	0.119307i	$0.961933\pi$
$164$	1.30774	+	3.24211i	0.102118	+	0.253166i
$165$	9.61818	+	3.98398i	0.748774	+	0.310153i
$166$	3.02925	+	2.04451i	0.235116	+	0.158685i
$167$	−10.9280	−	10.9280i	−0.845635	−	0.845635i	0.143950	−	0.989585i	$-0.454020\pi$
$167$	−10.9280	−	10.9280i	−0.845635	−	0.845635i	−0.989585	+	0.143950i	$0.954020\pi$
$168$	−2.28713	+	10.7150i	−0.176456	+	0.826677i
$169$	22.0339	−	22.0339i	1.69492	−	1.69492i
$170$	2.61128	−	0.506808i	0.200276	−	0.0388704i
$171$	−2.10034	+	5.07068i	−0.160617	+	0.387765i
$172$	−9.09949	−	9.27030i	−0.693830	−	0.706853i
$173$	7.59855	−	3.14742i	0.577707	−	0.239294i	−0.0746452	−	0.997210i	$-0.523782\pi$
$173$	7.59855	−	3.14742i	0.577707	−	0.239294i	0.652352	+	0.757916i	$0.273782\pi$
$174$	15.8720	+	3.23392i	1.20325	+	0.245163i
$175$		−	2.17107i		−	0.164117i
$176$	−7.89944	+	3.10126i	−0.595443	+	0.233766i
$177$		−	12.3497i		−	0.928259i
$178$	0.423694	−	2.07948i	0.0317572	−	0.155864i
$179$	18.1483	−	7.51726i	1.35647	−	0.561867i	0.418381	−	0.908272i	$-0.362598\pi$
$179$	18.1483	−	7.51726i	1.35647	−	0.561867i	0.938085	+	0.346405i	$0.112598\pi$
$180$	0.133117	−	14.3169i	0.00992198	−	1.06712i
$181$	6.78605	−	16.3830i	0.504403	−	1.21774i	−0.442660	−	0.896690i	$-0.645965\pi$
$181$	6.78605	−	16.3830i	0.504403	−	1.21774i	0.947063	−	0.321047i	$-0.104035\pi$
$182$	−2.65869	−	13.6986i	−0.197075	−	1.01541i
$183$	25.6521	−	25.6521i	1.89626	−	1.89626i
$184$	−7.12192	+	10.3435i	−0.525035	+	0.762530i
$185$	−4.93597	−	4.93597i	−0.362900	−	0.362900i
$186$	−19.6868	+	29.1689i	−1.44350	+	2.13877i
$187$	1.96010	+	0.811901i	0.143337	+	0.0593721i
$188$	−2.94658	−	1.25273i	−0.214901	−	0.0913650i
$189$	−1.19481	−	2.88452i	−0.0869094	−	0.209818i
$190$	−2.11625	−	3.19929i	−0.153529	−	0.232101i
$191$	0.380739			0.0275493			0.0137746	−	0.999905i	$-0.495615\pi$
$191$	0.380739			0.0275493			0.0137746	+	0.999905i	$0.495615\pi$
$192$	14.3405	+	15.1636i	1.03493	+	1.09434i
$193$	2.76728			0.199193			0.0995966	−	0.995028i	$-0.468245\pi$
$193$	2.76728			0.199193			0.0995966	+	0.995028i	$0.468245\pi$
$194$	−7.38226	−	11.1603i	−0.530015	−	0.801262i
$195$	12.4788	+	30.1264i	0.893623	+	2.15740i
$196$	8.82606	+	3.75239i	0.630433	+	0.268028i
$197$	−13.7475	−	5.69442i	−0.979472	−	0.405711i	−0.165242	−	0.986253i	$-0.552841\pi$
$197$	−13.7475	−	5.69442i	−0.979472	−	0.405711i	−0.814230	+	0.580542i	$0.802841\pi$
$198$	6.38842	−	9.46539i	0.454005	−	0.672676i
$199$	14.7524	+	14.7524i	1.04577	+	1.04577i	0.998901	+	0.0468725i	$0.0149255\pi$
$199$	14.7524	+	14.7524i	1.04577	+	1.04577i	0.0468725	+	0.998901i	$0.485075\pi$
$200$	−3.40630	−	2.34538i	−0.240862	−	0.165843i
$201$	−0.0717996	+	0.0717996i	−0.00506435	+	0.00506435i
$202$	3.02375	+	15.5796i	0.212750	+	1.09618i
$203$	−2.49470	+	6.02273i	−0.175093	+	0.422713i
$204$	0.0485113	−	5.21744i	0.00339647	−	0.365294i
$205$	3.03749	−	1.25817i	0.212147	−	0.0878744i
$206$	2.87500	−	14.1105i	0.200311	−	0.983122i
$207$		−	16.8987i		−	1.17454i
$208$	−24.3646	−	10.6271i	−1.68938	−	0.736860i
$209$		−	3.05946i		−	0.211627i
$210$	10.0965	+	2.05716i	0.696725	+	0.141957i
$211$	21.8571	−	9.05350i	1.50470	−	0.623268i	0.530246	−	0.847844i	$-0.322099\pi$
$211$	21.8571	−	9.05350i	1.50470	−	0.623268i	0.974457	+	0.224575i	$0.0720995\pi$
$212$	−4.61506	−	4.70169i	−0.316964	−	0.322913i
$213$	−0.734396	+	1.77299i	−0.0503200	+	0.121483i
$214$	−2.96984	+	0.576399i	−0.203014	+	0.0394018i
$215$	−8.63836	+	8.63836i	−0.589131	+	0.589131i
$216$	−5.81639	−	1.24152i	−0.395756	−	0.0844748i
$217$	−10.0145	−	10.0145i	−0.679825	−	0.679825i
$218$	17.0855	+	11.5314i	1.15717	+	0.781004i
$219$	35.0925	+	14.5358i	2.37133	+	0.982237i
$220$	2.98554	+	7.40163i	0.201285	+	0.499018i
$221$	2.54307	+	6.13950i	0.171065	+	0.412988i
$222$	−11.4201	+	7.55410i	−0.766466	+	0.506998i
$223$	−22.0446			−1.47622			−0.738109	−	0.674682i	$-0.764281\pi$
$223$	−22.0446			−1.47622			−0.738109	+	0.674682i	$0.764281\pi$
$224$	−7.09043	+	4.50289i	−0.473749	+	0.300862i
$225$	5.56505			0.371003
$226$	−14.0521	+	9.29511i	−0.934731	+	0.618301i
$227$	−0.882729	−	2.13110i	−0.0585888	−	0.141446i	0.891874	−	0.452283i	$-0.149390\pi$
$227$	−0.882729	−	2.13110i	−0.0585888	−	0.141446i	−0.950463	+	0.310838i	$0.899390\pi$
$228$	−6.97788	+	2.81461i	−0.462122	+	0.186402i
$229$	2.58627	+	1.07127i	0.170906	+	0.0707915i	0.466496	−	0.884523i	$-0.345516\pi$
$229$	2.58627	+	1.07127i	0.170906	+	0.0707915i	−0.295590	+	0.955315i	$0.595516\pi$
$230$	9.78942	+	6.60711i	0.645495	+	0.435660i
$231$	5.81124	+	5.81124i	0.382351	+	0.382351i
$232$	6.75436	+	10.4203i	0.443445	+	0.684128i
$233$	20.5341	−	20.5341i	1.34523	−	1.34523i	0.454470	−	0.890762i	$-0.349829\pi$
$233$	20.5341	−	20.5341i	1.34523	−	1.34523i	0.890762	−	0.454470i	$-0.150171\pi$
$234$	35.1134	−	6.81495i	2.29544	−	0.445507i
$235$	−1.15232	+	2.78196i	−0.0751693	+	0.181475i
$236$	6.75656	−	6.63207i	0.439814	−	0.431711i
$237$	30.4435	−	12.6101i	1.97752	−	0.819116i
$238$	2.05758	+	0.419231i	0.133373	+	0.0271747i
$239$			25.1591i			1.62741i	0.581278	+	0.813705i	$0.302553\pi$
$239$			25.1591i			1.62741i	−0.581278	+	0.813705i	$0.697447\pi$
$240$	14.1347	−	13.6186i	0.912391	−	0.879075i
$241$		−	3.89585i		−	0.250954i	−0.992097	−	0.125477i	$-0.959954\pi$
$241$		−	3.89585i		−	0.250954i	0.992097	−	0.125477i	$-0.0400461\pi$
$242$	1.83490	−	9.00568i	0.117952	−	0.578907i
$243$	−20.1264	+	8.33664i	−1.29111	+	0.534795i
$244$	27.8101	+	0.258576i	1.78036	+	0.0165537i
$245$	3.45163	−	8.33297i	0.220517	−	0.532374i
$246$	−1.22872	−	6.33087i	−0.0783403	−	0.403641i
$247$	6.77617	−	6.77617i	0.431158	−	0.431158i
$248$	−26.5307	+	4.89367i	−1.68470	+	0.310748i
$249$	−4.76717	−	4.76717i	−0.302107	−	0.302107i
$250$	−9.61628	+	14.2480i	−0.608187	+	0.901120i
$251$	−12.0508	−	4.99160i	−0.760639	−	0.315067i	−0.0315647	−	0.999502i	$-0.510049\pi$
$251$	−12.0508	−	4.99160i	−0.760639	−	0.315067i	−0.729074	+	0.684435i	$0.760049\pi$
$252$	4.42217	−	10.4015i	0.278570	−	0.655230i
$253$	3.60484	+	8.70286i	0.226634	+	0.547144i
$254$	−7.03920	−	10.6417i	−0.441679	−	0.667718i
$255$	−4.90698			−0.307287
$256$	−0.594913	+	15.9889i	−0.0371820	+	0.999309i
$257$	−9.40432			−0.586625			−0.293313	−	0.956017i	$-0.594758\pi$
$257$	−9.40432			−0.586625			−0.293313	+	0.956017i	$0.594758\pi$
$258$	13.2203	+	19.9861i	0.823060	+	1.24428i
$259$	−2.10879	−	5.09107i	−0.131034	−	0.316344i
$260$	−9.78088	+	23.0058i	−0.606584	+	1.42676i
$261$	−15.4379	−	6.39459i	−0.955582	−	0.395815i
$262$	12.6539	−	18.7486i	0.781760	−	1.15829i
$263$	3.47874	+	3.47874i	0.214508	+	0.214508i	0.806180	−	0.591671i	$-0.201532\pi$
$263$	3.47874	+	3.47874i	0.214508	+	0.214508i	−0.591671	+	0.806180i	$0.701532\pi$
$264$	15.3953	−	2.83972i	0.947518	−	0.174773i
$265$	−4.38118	+	4.38118i	−0.269134	+	0.269134i
$266$	−0.576941	−	2.97263i	−0.0353745	−	0.182264i
$267$	−1.49816	+	3.61688i	−0.0916861	+	0.221350i
$268$	−0.0778399		0.000723749i	−0.00475483		4.42100e-5i
$269$	−9.42178	+	3.90263i	−0.574456	+	0.237948i	−0.650948	−	0.759123i	$-0.725628\pi$
$269$	−9.42178	+	3.90263i	−0.574456	+	0.237948i	0.0764913	+	0.997070i	$0.475628\pi$
$270$	−1.11669	+	5.48068i	−0.0679594	+	0.333543i
$271$		−	4.93771i		−	0.299944i	−0.988690	−	0.149972i	$-0.952082\pi$
$271$		−	4.93771i		−	0.299944i	0.988690	−	0.149972i	$-0.0479184\pi$
$272$	2.88053	−	2.77535i	0.174658	−	0.168280i
$273$			25.7418i			1.55796i
$274$	19.1428	+	3.90034i	1.15646	+	0.235628i
$275$	−2.86601	+	1.18714i	−0.172827	+	0.0715874i
$276$	16.5327	−	16.2281i	0.995154	−	0.976819i
$277$	6.11627	−	14.7660i	0.367491	−	0.887202i	−0.626669	−	0.779286i	$-0.715582\pi$
$277$	6.11627	−	14.7660i	0.367491	−	0.887202i	0.994160	−	0.107916i	$-0.0344178\pi$
$278$	−0.165959	+	0.0322100i	−0.00995355	+	0.00193182i
$279$	25.6698	−	25.6698i	1.53681	−	1.53681i
$280$	4.29658	+	6.62857i	0.256770	+	0.396133i
$281$	17.6210	+	17.6210i	1.05118	+	1.05118i	0.998618	+	0.0525613i	$0.0167385\pi$
$281$	17.6210	+	17.6210i	1.05118	+	1.05118i	0.0525613	+	0.998618i	$0.483261\pi$
$282$	4.89574	+	3.30425i	0.291537	+	0.196765i
$283$	−15.8643	−	6.57120i	−0.943034	−	0.390617i	−0.142425	−	0.989806i	$-0.545490\pi$
$283$	−15.8643	−	6.57120i	−0.943034	−	0.390617i	−0.800608	+	0.599188i	$0.795490\pi$
$284$	−1.36440	+	0.550346i	−0.0809620	+	0.0326570i
$285$	2.70792	+	6.53749i	0.160403	+	0.387248i
$286$	−16.6297	+	11.0001i	−0.983336	+	0.650452i
$287$	2.59541			0.153202
$288$	−11.5421	−	18.1747i	−0.680127	−	1.07096i
$289$	−1.00000			−0.0588235
$290$	9.74037	−	6.44301i	0.571974	−	0.378347i
$291$	9.44621	+	22.8052i	0.553747	+	1.33686i
$292$	10.8929	+	27.0053i	0.637459	+	1.58036i
$293$	16.4141	+	6.79893i	0.958919	+	0.397197i	0.806576	−	0.591130i	$-0.201318\pi$
$293$	16.4141	+	6.79893i	0.958919	+	0.397197i	0.152343	+	0.988328i	$0.451318\pi$
$294$	−14.6645	−	9.89744i	−0.855253	−	0.577230i
$295$	−6.29597	−	6.29597i	−0.366566	−	0.366566i
$296$	−10.2657	−	2.19124i	−0.596683	−	0.127363i
$297$	−3.15451	+	3.15451i	−0.183043	+	0.183043i
$298$	33.6366	−	6.52833i	1.94852	−	0.378176i
$299$	−11.2912	+	27.2594i	−0.652988	+	1.57645i
$300$	5.34423	+	5.44454i	0.308549	+	0.314341i
$301$	−8.90979	+	3.69056i	−0.513552	+	0.212720i
$302$	14.1605	+	2.88519i	0.814843	+	0.166024i
$303$		−	29.2763i		−	1.68188i
$304$	−5.28717	−	2.30611i	−0.303240	−	0.132265i
$305$		−	26.1553i		−	1.49765i
$306$	−1.07460	+	5.27414i	−0.0614310	+	0.301503i
$307$	−13.6374	+	5.64879i	−0.778326	+	0.322393i	−0.736240	−	0.676721i	$-0.763401\pi$
$307$	−13.6374	+	5.64879i	−0.778326	+	0.322393i	−0.0420865	+	0.999114i	$0.513401\pi$
$308$	−0.0585780	+	6.30012i	−0.00333779	+	0.358983i
$309$	−10.1659	+	24.5426i	−0.578316	+	1.39618i
$310$	4.83406	+	24.9070i	0.274556	+	1.41462i
$311$	11.3131	−	11.3131i	0.641507	−	0.641507i	−0.309419	−	0.950926i	$-0.600134\pi$
$311$	11.3131	−	11.3131i	0.641507	−	0.641507i	0.950926	+	0.309419i	$0.100134\pi$
$312$	40.3875	+	27.8085i	2.28649	+	1.57435i
$313$	9.51015	+	9.51015i	0.537545	+	0.537545i	0.922807	−	0.385262i	$-0.125889\pi$
$313$	9.51015	+	9.51015i	0.537545	+	0.537545i	−0.385262	+	0.922807i	$0.625889\pi$
$314$	−2.66914	+	3.95472i	−0.150628	+	0.223178i
$315$	−9.82035	−	4.06772i	−0.553314	−	0.229190i
$316$	23.2479	+	9.88383i	1.30780	+	0.556009i
$317$	8.59025	+	20.7387i	0.482476	+	1.16480i	0.958429	+	0.285330i	$0.0921033\pi$
$317$	8.59025	+	20.7387i	0.482476	+	1.16480i	−0.475953	+	0.879471i	$0.657897\pi$
$318$	6.70504	+	10.1365i	0.376000	+	0.568426i
$319$	9.31466			0.521521
$320$	15.0414	+	0.419659i	0.840842	+	0.0234596i
$321$	5.58077			0.311488
$322$	5.14368	+	7.77608i	0.286646	+	0.433344i
$323$	0.551850	+	1.33228i	0.0307058	+	0.0741303i
$324$	−10.9189	−	4.64214i	−0.606603	−	0.257897i
$325$	−8.97704	−	3.71841i	−0.497956	−	0.206260i
$326$	−5.44886	+	8.07329i	−0.301784	+	0.447138i
$327$	−26.8876	−	26.8876i	−1.48689	−	1.48689i
$328$	2.80379	−	4.07206i	0.154813	−	0.224842i
$329$	−1.68084	+	1.68084i	−0.0926676	+	0.0926676i
$330$	−2.80513	−	14.4532i	−0.154417	−	0.795621i
$331$	9.71570	−	23.4558i	0.534023	−	1.28925i	−0.394815	−	0.918761i	$-0.629191\pi$
$331$	9.71570	−	23.4558i	0.534023	−	1.28925i	0.928838	−	0.370485i	$-0.120809\pi$
$332$	0.0480537	−	5.16822i	0.00263729	−	0.283643i
$333$	13.0498	−	5.40541i	0.715125	−	0.296215i
$334$	−4.36351	+	21.4160i	−0.238761	+	1.17183i
$335$			0.0732081i			0.00399979i
$336$	14.4229	−	5.66232i	0.786835	−	0.308905i
$337$		−	22.3097i		−	1.21529i	−0.794209	−	0.607644i	$-0.792115\pi$
$337$		−	22.3097i		−	1.21529i	0.794209	−	0.607644i	$-0.207885\pi$
$338$	−43.1807	−	8.79805i	−2.34872	−	0.478551i
$339$	28.7143	−	11.8939i	1.55955	−	0.645986i
$340$	−2.63516	−	2.68463i	−0.142912	−	0.145594i
$341$	−7.74410	+	18.6959i	−0.419367	+	1.01244i
$342$	7.61968	−	1.47886i	0.412025	−	0.0799675i
$343$	12.3842	−	12.3842i	0.668685	−	0.668685i
$344$	−3.83485	+	17.9659i	−0.206761	+	0.968654i
$345$	−15.4057	−	15.4057i	−0.829417	−	0.829417i
$346$	−9.64097	−	6.50692i	−0.518302	−	0.349814i
$347$	11.8752	+	4.91885i	0.637491	+	0.264058i	0.677932	−	0.735124i	$-0.262876\pi$
$347$	11.8752	+	4.91885i	0.637491	+	0.264058i	−0.0404408	+	0.999182i	$0.512876\pi$
$348$	−8.56921	−	21.2445i	−0.459358	−	1.13882i
$349$	−3.41436	−	8.24300i	−0.182767	−	0.441238i	0.805768	−	0.592231i	$-0.201753\pi$
$349$	−3.41436	−	8.24300i	−0.182767	−	0.441238i	−0.988535	+	0.150993i	$0.951753\pi$
$350$	−2.56081	+	1.69391i	−0.136881	+	0.0905434i
$351$	−13.9734			−0.745844
$352$	9.82128	+	6.89785i	0.523476	+	0.367657i
$353$	5.77631			0.307442			0.153721	−	0.988114i	$-0.450874\pi$
$353$	5.77631			0.307442			0.153721	+	0.988114i	$0.450874\pi$
$354$	−14.5666	+	9.63547i	−0.774208	+	0.512119i
$355$	0.529483	+	1.27829i	0.0281021	+	0.0678444i
$356$	−2.78336	+	1.12270i	−0.147518	+	0.0595031i
$357$	−3.57878	−	1.48238i	−0.189409	−	0.0784559i
$358$	−23.0264	−	15.5411i	−1.21698	−	0.821370i
$359$	−24.8622	−	24.8622i	−1.31218	−	1.31218i	−0.919809	−	0.392366i	$-0.871657\pi$
$359$	−24.8622	−	24.8622i	−1.31218	−	1.31218i	−0.392366	−	0.919809i	$-0.628343\pi$
$360$	−16.9909	+	11.0133i	−0.895497	+	0.580452i
$361$	−11.9646	+	11.9646i	−0.629715	+	0.629715i
$362$	−24.6186	+	4.77807i	−1.29392	+	0.251130i
$363$	−6.48814	+	15.6637i	−0.340539	+	0.822133i
$364$	−14.0834	+	13.8239i	−0.738171	+	0.724571i
$365$	25.3009	−	10.4800i	1.32431	−	0.548547i
$366$	−50.2713	−	10.2428i	−2.62773	−	0.535398i
$367$			8.57061i			0.447382i	0.974660	+	0.223691i	$0.0718107\pi$
$367$			8.57061i			0.447382i	−0.974660	+	0.223691i	$0.928189\pi$
$368$	17.7569	+	0.330234i	0.925644	+	0.0172146i
$369$			6.65274i			0.346328i
$370$	−1.97091	+	9.67320i	−0.102463	+	0.502886i
$371$	−4.51884	+	1.87177i	−0.234607	+	0.0971773i
$372$	49.7652	+	0.462713i	2.58020	+	0.0239905i
$373$	−4.48842	+	10.8360i	−0.232402	+	0.561068i	−0.996459	−	0.0840811i	$-0.973205\pi$
$373$	−4.48842	+	10.8360i	−0.232402	+	0.561068i	0.764057	+	0.645149i	$0.223205\pi$
$374$	−0.571661	−	2.94543i	−0.0295599	−	0.152305i
$375$	22.4222	−	22.4222i	1.15788	−	1.15788i
$376$	0.821359	+	4.45294i	0.0423584	+	0.229643i
$377$	20.6304	+	20.6304i	1.06252	+	1.06252i
$378$	−2.47012	+	3.65985i	−0.127049	+	0.188242i
$379$	−20.1508	−	8.34674i	−1.03508	−	0.428743i	−0.200535	−	0.979687i	$-0.564268\pi$
$379$	−20.1508	−	8.34674i	−1.03508	−	0.428743i	−0.834543	+	0.550943i	$0.814268\pi$
$380$	−2.12247	+	4.99230i	−0.108880	+	0.256099i
$381$	9.00725	+	21.7454i	0.461455	+	1.11405i
$382$	−0.297060	−	0.449087i	−0.0151989	−	0.0229773i
$383$	−20.4826			−1.04661			−0.523305	−	0.852146i	$-0.675301\pi$
$383$	−20.4826			−1.04661			−0.523305	+	0.852146i	$0.675301\pi$
$384$	6.69702	−	28.7458i	0.341756	−	1.46693i
$385$	5.92524			0.301978
$386$	−2.15909	−	3.26405i	−0.109895	−	0.166136i
$387$	−9.45991	−	22.8382i	−0.480874	−	1.16093i
$388$	−7.40395	+	17.4150i	−0.375879	+	0.884111i
$389$	−1.01696	−	0.421238i	−0.0515619	−	0.0213576i	0.356753	−	0.934199i	$-0.383884\pi$
$389$	−1.01696	−	0.421238i	−0.0515619	−	0.0213576i	−0.408315	+	0.912841i	$0.633884\pi$
$390$	25.7984	−	38.2241i	1.30635	−	1.93555i
$391$	−3.13956	−	3.13956i	−0.158774	−	0.158774i
$392$	−2.46027	−	13.3382i	−0.124262	−	0.673679i
$393$	−29.5050	+	29.5050i	−1.48833	+	1.48833i
$394$	4.00946	+	20.6583i	0.201993	+	1.04075i
$395$	9.09162	−	21.9491i	0.457449	−	1.10438i
$396$	−16.1489	−	0.150152i	−0.811515	−	0.00754540i
$397$	6.27895	−	2.60083i	0.315132	−	0.130532i	−0.219511	−	0.975610i	$-0.570446\pi$
$397$	6.27895	−	2.60083i	0.315132	−	0.130532i	0.534643	+	0.845078i	$0.320446\pi$
$398$	5.89059	−	28.9109i	0.295268	−	1.44917i
$399$			5.58601i			0.279650i
$400$	−0.108752	+	5.84769i	−0.00543761	+	0.292385i
$401$		−	16.6913i		−	0.833524i	−0.909016	−	0.416762i	$-0.863165\pi$
$401$		−	16.6913i		−	0.833524i	0.909016	−	0.416762i	$-0.136835\pi$
$402$	0.140708	+	0.0286693i	0.00701789	+	0.00142989i
$403$	−58.5600	+	24.2564i	−2.91708	+	1.20830i
$404$	16.0172	−	15.7221i	0.796884	−	0.782202i
$405$	−4.27006	+	10.3088i	−0.212181	+	0.512250i
$406$	9.05031	−	1.75652i	0.449159	−	0.0871747i
$407$	−5.56760	+	5.56760i	−0.275976	+	0.275976i
$408$	−6.19190	+	4.01353i	−0.306545	+	0.198699i
$409$	22.2782	+	22.2782i	1.10159	+	1.10159i	0.994219	+	0.107369i	$0.0342427\pi$
$409$	22.2782	+	22.2782i	1.10159	+	1.10159i	0.107369	+	0.994219i	$0.465757\pi$
$410$	−3.85394	−	2.60112i	−0.190333	−	0.128460i
$411$	−33.2954	−	13.7914i	−1.64234	−	0.680280i
$412$	−18.8866	+	7.61816i	−0.930478	+	0.375320i
$413$	−2.68982	−	6.49380i	−0.132357	−	0.319539i
$414$	−19.9322	+	13.1847i	−0.979616	+	0.647992i
$415$	−4.86069			−0.238602
$416$	6.47489	+	37.0300i	0.317458	+	1.81554i
$417$	0.311861			0.0152719
$418$	−3.60868	+	2.38705i	−0.176506	+	0.116755i
$419$	9.48648	+	22.9024i	0.463445	+	1.11886i	0.966974	+	0.254877i	$0.0820349\pi$
$419$	9.48648	+	22.9024i	0.463445	+	1.11886i	−0.503529	+	0.863979i	$0.667965\pi$
$420$	−5.45104	−	13.5140i	−0.265984	−	0.659416i
$421$	6.23372	+	2.58209i	0.303813	+	0.125843i	0.529382	−	0.848384i	$-0.322424\pi$
$421$	6.23372	+	2.58209i	0.303813	+	0.125843i	−0.225569	+	0.974227i	$0.572424\pi$
$422$	−27.7321	−	18.7170i	−1.34998	−	0.911131i
$423$	−4.30845	−	4.30845i	−0.209484	−	0.209484i
$424$	−1.94495	+	9.11188i	−0.0944551	+	0.442512i
$425$	1.03391	−	1.03391i	0.0501522	−	0.0501522i
$426$	2.66426	−	0.517090i	0.129084	−	0.0250531i
$427$	7.90143	−	19.0757i	0.382377	−	0.923140i
$428$	2.99700	+	3.05326i	0.144866	+	0.147585i
$429$	33.9815	−	14.0756i	1.64064	−	0.679577i
$430$	16.9289	+	3.44926i	0.816384	+	0.166338i
$431$			10.9887i			0.529307i	0.964344	+	0.264653i	$0.0852576\pi$
$431$			10.9887i			0.529307i	−0.964344	+	0.264653i	$0.914742\pi$
$432$	3.07367	+	7.82919i	0.147882	+	0.376682i
$433$			31.8392i			1.53009i	0.643975	+	0.765047i	$0.277284\pi$
$433$			31.8392i			1.53009i	−0.643975	+	0.765047i	$0.722716\pi$
$434$	−3.99872	+	19.6257i	−0.191945	+	0.942063i
$435$	−19.9037	+	8.24437i	−0.954308	+	0.395287i
$436$	0.271031	−	29.1496i	0.0129800	−	1.39601i
$437$	−2.45022	+	5.91535i	−0.117210	+	0.282969i
$438$	−10.2347	−	52.7332i	−0.489032	−	2.51969i
$439$	−19.3399	+	19.3399i	−0.923043	+	0.923043i	−0.997243	−	0.0742006i	$-0.976359\pi$
$439$	−19.3399	+	19.3399i	−0.923043	+	0.923043i	0.0742006	+	0.997243i	$0.476359\pi$
$440$	6.40096	−	9.29639i	0.305154	−	0.443188i
$441$	12.9054	+	12.9054i	0.614542	+	0.614542i
$442$	5.25749	−	7.78975i	0.250073	−	0.370521i
$443$	−27.8468	−	11.5345i	−1.32304	−	0.548021i	−0.394377	−	0.918949i	$-0.629040\pi$
$443$	−27.8468	−	11.5345i	−1.32304	−	0.548021i	−0.928662	+	0.370928i	$0.879040\pi$
$444$	17.8204	+	7.57631i	0.845717	+	0.359556i
$445$	1.08014	+	2.60769i	0.0512037	+	0.123617i
$446$	17.1997	+	26.0020i	0.814428	+	1.23123i
$447$	−63.2081			−2.98964
$448$	10.8433	+	4.85003i	0.512299	+	0.229142i
$449$	−5.68405			−0.268247			−0.134124	−	0.990965i	$-0.542822\pi$
$449$	−5.68405			−0.268247			−0.134124	+	0.990965i	$0.542822\pi$
$450$	−4.34196	−	6.56406i	−0.204682	−	0.309433i
$451$	−1.41917	−	3.42618i	−0.0668261	−	0.161333i
$452$	21.9274	+	9.32243i	1.03138	+	0.438490i
$453$	−24.6296	−	10.2019i	−1.15720	−	0.479327i
$454$	−1.82494	+	2.70392i	−0.0856486	+	0.126901i
$455$	13.1234	+	13.1234i	0.615233	+	0.615233i
$456$	8.76417	+	6.03450i	0.410420	+	0.282591i
$457$	−17.3734	+	17.3734i	−0.812695	+	0.812695i	−0.985037	−	0.172342i	$-0.944867\pi$
$457$	−17.3734	+	17.3734i	−0.812695	+	0.812695i	0.172342	+	0.985037i	$0.444867\pi$
$458$	−0.754283	−	3.88637i	−0.0352453	−	0.181598i
$459$	0.804680	−	1.94267i	0.0375593	−	0.0906761i
$460$	0.155292	−	16.7018i	0.00724051	−	0.778724i
$461$	10.5670	−	4.37701i	0.492156	−	0.203858i	−0.122781	−	0.992434i	$-0.539181\pi$
$461$	10.5670	−	4.37701i	0.492156	−	0.203858i	0.614937	+	0.788576i	$0.289181\pi$
$462$	2.32040	−	11.3885i	0.107955	−	0.529840i
$463$		−	14.2699i		−	0.663177i	−0.943424	−	0.331588i	$-0.892415\pi$
$463$		−	14.2699i		−	0.663177i	0.943424	−	0.331588i	$-0.107585\pi$
$464$	7.02105	−	16.0970i	0.325944	−	0.747285i
$465$		−	46.8039i		−	2.17048i
$466$	−40.2414	−	8.19916i	−1.86414	−	0.379819i
$467$	−4.88302	+	2.02261i	−0.225959	+	0.0935953i	−0.492791	−	0.870148i	$-0.664023\pi$
$467$	−4.88302	+	2.02261i	−0.225959	+	0.0935953i	0.266832	+	0.963743i	$0.414023\pi$
$468$	−35.4345	−	36.0996i	−1.63796	−	1.66871i
$469$	−0.0221159	+	0.0533925i	−0.00102122	+	0.00246544i
$470$	4.18043	−	0.811354i	0.192829	−	0.0374250i
$471$	6.22360	−	6.22360i	0.286768	−	0.286768i
$472$	−13.0942	−	2.79499i	−0.602711	−	0.128650i
$473$	9.74376	+	9.74376i	0.448018	+	0.448018i
$474$	−38.6265	−	26.0700i	−1.77417	−	1.19743i
$475$	−1.94803	−	0.806902i	−0.0893819	−	0.0370232i
$476$	−1.11088	−	2.75404i	−0.0509169	−	0.126231i
$477$	−4.79785	−	11.5830i	−0.219679	−	0.530351i
$478$	29.6756	−	19.6297i	1.35733	−	0.897840i
$479$	−2.32994			−0.106457			−0.0532287	−	0.998582i	$-0.516951\pi$
$479$	−2.32994			−0.106457			−0.0532287	+	0.998582i	$0.516951\pi$
$480$	−27.0915	−	6.04663i	−1.23655	−	0.275989i
$481$	−24.6625			−1.12451
$482$	−4.59521	+	3.03962i	−0.209306	+	0.138451i
$483$	−6.58177	−	15.8898i	−0.299481	−	0.723011i
$484$	−12.0540	+	4.86212i	−0.547908	+	0.221005i
$485$	16.4420	+	6.81051i	0.746594	+	0.309249i
$486$	25.5362	+	17.2350i	1.15835	+	0.781796i
$487$	14.5798	+	14.5798i	0.660673	+	0.660673i	0.955539	−	0.294865i	$-0.0952748\pi$
$487$	14.5798	+	14.5798i	0.660673	+	0.660673i	−0.294865	+	0.955539i	$0.595275\pi$
$488$	−21.3930	−	33.0042i	−0.968417	−	1.49403i
$489$	12.7050	−	12.7050i	0.574542	−	0.574542i
$490$	−12.5219	+	2.43030i	−0.565682	+	0.109790i
$491$	−5.86943	+	14.1701i	−0.264884	+	0.639486i	−0.999228	−	0.0392917i	$-0.987490\pi$
$491$	−5.86943	+	14.1701i	−0.264884	+	0.639486i	0.734344	+	0.678777i	$0.237490\pi$
$492$	−6.50868	+	6.38876i	−0.293434	+	0.288028i
$493$	−4.05620	+	1.68013i	−0.182682	+	0.0756693i
$494$	−13.2795	−	2.70570i	−0.597473	−	0.121735i
$495$			15.1880i			0.682650i
$496$	26.4719	+	27.4752i	1.18862	+	1.23367i
$497$			1.09224i			0.0489937i
$498$	−1.90351	+	9.34240i	−0.0852983	+	0.418643i
$499$	−14.8192	+	6.13832i	−0.663399	+	0.274789i	−0.688868	−	0.724887i	$-0.741892\pi$
$499$	−14.8192	+	6.13832i	−0.663399	+	0.274789i	0.0254693	+	0.999676i	$0.491892\pi$
$500$	24.3085	+	0.226019i	1.08711	+	0.0101079i
$501$	15.4292	−	37.2493i	0.689324	−	1.66418i
$502$	3.51460	+	18.1086i	0.156864	+	0.808228i
$503$	−0.0609239	+	0.0609239i	−0.00271646	+	0.00271646i	−0.708464	−	0.705747i	$-0.750611\pi$
$503$	−0.0609239	+	0.0609239i	−0.00271646	+	0.00271646i	0.705747	+	0.708464i	$0.250611\pi$
$504$	−15.7189	+	2.89941i	−0.700177	+	0.129150i
$505$	−14.9253	−	14.9253i	−0.664168	−	0.664168i
$506$	7.45259	−	11.0421i	0.331308	−	0.490882i
$507$	75.1050	+	31.1095i	3.33553	+	1.38162i
$508$	−7.05989	+	16.6057i	−0.313232	+	0.736759i
$509$	16.4962	+	39.8253i	0.731181	+	1.76523i	0.638624	+	0.769519i	$0.279504\pi$
$509$	16.4962	+	39.8253i	0.731181	+	1.76523i	0.0925566	+	0.995707i	$0.470496\pi$
$510$	3.82852	+	5.78786i	0.169530	+	0.256291i
$511$	21.6186			0.956349
$512$	19.3234	−	11.7732i	0.853980	−	0.520306i
$513$	−3.03225			−0.133877
$514$	7.33744	+	11.0925i	0.323641	+	0.489271i
$515$	7.32937	+	17.6947i	0.322971	+	0.779720i
$516$	13.2592	−	31.1871i	0.583702	−	1.37293i
$517$	3.13795	+	1.29978i	0.138007	+	0.0571643i
$518$	−4.35968	+	6.45951i	−0.191553	+	0.283814i
$519$	15.1721	+	15.1721i	0.665982	+	0.665982i
$520$	34.7669	−	6.41287i	1.52463	−	0.281223i
$521$	4.41693	−	4.41693i	0.193509	−	0.193509i	−0.603701	−	0.797211i	$-0.706308\pi$
$521$	4.41693	−	4.41693i	0.193509	−	0.193509i	0.797211	+	0.603701i	$0.206308\pi$
$522$	4.50245	+	23.1984i	0.197067	+	1.01537i
$523$	7.31304	−	17.6552i	0.319777	−	0.772010i	−0.679488	−	0.733686i	$-0.737798\pi$
$523$	7.31304	−	17.6552i	0.319777	−	0.772010i	0.999265	−	0.0383238i	$-0.0122018\pi$
$524$	−31.9871	−	0.297414i	−1.39736	−	0.0129926i
$525$	5.23281	−	2.16750i	0.228379	−	0.0945976i
$526$	1.38905	−	6.81742i	0.0605653	−	0.297253i
$527$		−	9.53824i		−	0.415492i
$528$	−15.3613	−	15.9434i	−0.668513	−	0.693849i
$529$			3.28639i			0.142886i
$530$	8.58595	+	1.74938i	0.372950	+	0.0759884i
$531$	16.6454	−	6.89475i	0.722349	−	0.299207i
$532$	−3.05613	+	2.99982i	−0.132500	+	0.130059i
$533$	4.44518	−	10.7316i	0.192542	−	0.464837i
$534$	5.43507	−	1.05486i	0.235198	−	0.0456482i
$535$	2.84512	−	2.84512i	0.123005	−	0.123005i
$536$	0.0598786	+	0.0923780i	0.00258636	+	0.00399012i
$537$	36.2369	+	36.2369i	1.56374	+	1.56374i
$538$	11.9543	+	8.06823i	0.515385	+	0.347846i
$539$	−9.39929	−	3.89331i	−0.404856	−	0.167697i
$540$	7.33581	−	2.95899i	0.315683	−	0.127334i
$541$	2.06339	+	4.98146i	0.0887120	+	0.214170i	0.962009	−	0.273019i	$-0.0880223\pi$
$541$	2.06339	+	4.98146i	0.0887120	+	0.214170i	−0.873297	+	0.487189i	$0.838022\pi$
$542$	−5.82410	+	3.85250i	−0.250167	+	0.165479i
$543$	46.2619			1.98529
$544$	−5.52101	−	1.23225i	−0.236711	−	0.0528323i
$545$	−27.4151			−1.17433
$546$	30.3628	−	20.0842i	1.29941	−	0.859526i
$547$	−9.04145	−	21.8280i	−0.386585	−	0.933298i	−0.990658	−	0.136369i	$-0.956457\pi$
$547$	−9.04145	−	21.8280i	−0.386585	−	0.933298i	0.604073	−	0.796929i	$-0.293543\pi$
$548$	−10.3351	−	25.6223i	−0.441493	−	1.09453i
$549$	48.8964	+	20.2535i	2.08685	+	0.864400i
$550$	3.63637	+	2.45428i	0.155056	+	0.104651i
$551$	4.47683	+	4.47683i	0.190719	+	0.190719i
$552$	−32.0405	−	6.83911i	−1.36373	−	0.291092i
$553$	13.2615	−	13.2615i	0.563937	−	0.563937i
$554$	−22.1887	+	4.30648i	−0.942709	+	0.182965i
$555$	6.96905	−	16.8248i	0.295820	−	0.714172i
$556$	0.167477	+	0.170620i	0.00710259	+	0.00723591i
$557$	−37.9425	+	15.7163i	−1.60767	+	0.665921i	−0.992475	−	0.122451i	$-0.960925\pi$
$557$	−37.9425	+	15.7163i	−1.60767	+	0.665921i	−0.615200	+	0.788371i	$0.710925\pi$
$558$	−50.3060	−	10.2498i	−2.12962	−	0.433910i
$559$			43.1614i			1.82553i
$560$	4.46623	−	10.2396i	0.188733	−	0.432703i
$561$			5.53490i			0.233684i
$562$	7.03597	−	34.5324i	0.296795	−	1.45666i
$563$	13.6260	−	5.64408i	0.574268	−	0.237869i	−0.0765984	−	0.997062i	$-0.524406\pi$
$563$	13.6260	−	5.64408i	0.574268	−	0.237869i	0.650866	+	0.759193i	$0.274406\pi$
$564$	0.0776623	−	8.35265i	0.00327017	−	0.351710i
$565$	8.57521	−	20.7024i	0.360762	−	0.870956i
$566$	4.62680	+	23.8391i	0.194479	+	1.00203i
$567$	−6.22853	+	6.22853i	−0.261574	+	0.261574i
$568$	1.71367	+	1.17994i	0.0719040	+	0.0495090i
$569$	22.4328	+	22.4328i	0.940432	+	0.940432i	0.998323	−	0.0578912i	$-0.0184377\pi$
$569$	22.4328	+	22.4328i	0.940432	+	0.940432i	−0.0578912	+	0.998323i	$0.518438\pi$
$570$	5.59830	−	8.29471i	0.234487	−	0.347427i
$571$	−18.9110	−	7.83320i	−0.791402	−	0.327809i	−0.0498948	−	0.998754i	$-0.515889\pi$
$571$	−18.9110	−	7.83320i	−0.791402	−	0.327809i	−0.741507	+	0.670945i	$0.765889\pi$
$572$	25.9497	+	11.0325i	1.08501	+	0.461291i
$573$	0.380113	+	0.917674i	0.0158794	+	0.0383364i
$574$	−2.02499	−	3.06132i	−0.0845214	−	0.127777i
$575$	6.49206			0.270738
$576$	−12.4320	+	27.7944i	−0.517998	+	1.15810i
$577$	−39.0569			−1.62596			−0.812981	−	0.582291i	$-0.802157\pi$
$577$	−39.0569			−1.62596			−0.812981	+	0.582291i	$0.802157\pi$
$578$	0.780220	+	1.17952i	0.0324529	+	0.0490614i
$579$	2.76273	+	6.66983i	0.114815	+	0.277189i
$580$	−15.1993	−	6.46195i	−0.631115	−	0.268318i
$581$	−3.54502	−	1.46840i	−0.147072	−	0.0609194i
$582$	19.5289	−	28.9350i	0.809500	−	1.19939i
$583$	4.94181	+	4.94181i	0.204669	+	0.204669i
$584$	23.3543	−	33.9184i	0.966407	−	1.40355i
$585$	−33.6388	+	33.6388i	−1.39079	+	1.39079i
$586$	−4.78714	−	24.6653i	−0.197755	−	1.01891i
$587$	15.9565	−	38.5224i	0.658595	−	1.58999i	−0.141379	−	0.989956i	$-0.545154\pi$
$587$	15.9565	−	38.5224i	0.658595	−	1.58999i	0.799974	−	0.600034i	$-0.204846\pi$
$588$	−0.232627	+	25.0192i	−0.00959336	+	1.03178i
$589$	−12.7076	+	5.26368i	−0.523609	+	0.216886i
$590$	−2.51395	+	12.3384i	−0.103498	+	0.507966i
$591$		−	38.8200i		−	1.59684i
$592$	5.42493	+	13.8182i	0.222963	+	0.567926i
$593$		−	28.1275i		−	1.15506i	−0.816370	−	0.577530i	$-0.804017\pi$
$593$		−	28.1275i		−	1.15506i	0.816370	−	0.577530i	$-0.195983\pi$
$594$	6.18201	+	1.25958i	0.253651	+	0.0516813i
$595$	−2.58022	+	1.06876i	−0.105779	+	0.0438151i
$596$	−33.9442	−	34.5814i	−1.39041	−	1.41651i
$597$	−20.8288	+	50.2852i	−0.852467	+	2.05804i
$598$	40.9625	−	7.95017i	1.67508	−	0.325107i
$599$	−26.7753	+	26.7753i	−1.09401	+	1.09401i	−0.0989141	+	0.995096i	$0.531537\pi$
$599$	−26.7753	+	26.7753i	−1.09401	+	1.09401i	−0.995096	+	0.0989141i	$0.968463\pi$
$600$	2.25225	−	10.5515i	0.0919476	−	0.430765i
$601$	−4.23005	−	4.23005i	−0.172547	−	0.172547i	0.615550	−	0.788098i	$-0.288934\pi$
$601$	−4.23005	−	4.23005i	−0.172547	−	0.172547i	−0.788098	+	0.615550i	$0.788934\pi$
$602$	11.3047	+	7.62979i	0.460744	+	0.310967i
$603$	−0.136860	−	0.0566892i	−0.00557336	−	0.00230856i
$604$	−7.64515	−	18.9536i	−0.311077	−	0.771210i
$605$	4.67780	+	11.2932i	0.190180	+	0.459135i
$606$	−34.5319	+	22.8420i	−1.40276	+	0.927891i
$607$	28.6818			1.16416			0.582079	−	0.813132i	$-0.302239\pi$
$607$	28.6818			1.16416			0.582079	+	0.813132i	$0.302239\pi$
$608$	1.40506	+	8.03557i	0.0569829	+	0.325886i
$609$	−17.0069			−0.689152
$610$	−30.8506	+	20.4069i	−1.24910	+	0.826251i
$611$	4.07122	+	9.82879i	0.164704	+	0.397630i
$612$	7.05936	−	2.84748i	0.285358	−	0.115102i
$613$	−15.6380	−	6.47749i	−0.631615	−	0.261623i	0.0438242	−	0.999039i	$-0.486046\pi$
$613$	−15.6380	−	6.47749i	−0.631615	−	0.261623i	−0.675439	+	0.737416i	$0.736046\pi$
$614$	17.3030	+	11.6782i	0.698292	+	0.471294i
$615$	6.06500	+	6.06500i	0.244564	+	0.244564i
$616$	7.47679	−	4.84639i	0.301249	−	0.195266i
$617$	16.2575	−	16.2575i	0.654504	−	0.654504i	−0.299570	−	0.954074i	$-0.596843\pi$
$617$	16.2575	−	16.2575i	0.654504	−	0.654504i	0.954074	+	0.299570i	$0.0968433\pi$
$618$	36.8800	−	7.15781i	1.48353	−	0.287929i
$619$	12.6336	−	30.5001i	0.507786	−	1.22590i	−0.437369	−	0.899282i	$-0.644090\pi$
$619$	12.6336	−	30.5001i	0.507786	−	1.22590i	0.945155	−	0.326622i	$-0.105910\pi$
$620$	25.6066	−	25.1348i	1.02839	−	1.00944i
$621$	8.62546	−	3.57278i	0.346128	−	0.143371i
$622$	−22.1707	−	4.51727i	−0.888964	−	0.181126i
$623$			2.22816i			0.0892695i
$624$	1.28944	−	69.3344i	0.0516191	−	2.77560i
$625$		−	15.5512i		−	0.622046i
$626$	3.79736	−	18.6374i	0.151773	−	0.744899i
$627$	7.37406	−	3.05443i	0.294491	−	0.121982i
$628$	6.74717	+	0.0627347i	0.269241	+	0.00250339i
$629$	1.42023	−	3.42874i	0.0566284	−	0.136713i
$630$	2.86409	+	14.7570i	0.114108	+	0.587932i
$631$	9.20252	−	9.20252i	0.366347	−	0.366347i	−0.499796	−	0.866143i	$-0.666592\pi$
$631$	9.20252	−	9.20252i	0.366347	−	0.366347i	0.866143	+	0.499796i	$0.166592\pi$
$632$	−6.48037	−	35.1329i	−0.257775	−	1.39751i
$633$	43.6423	+	43.6423i	1.73463	+	1.73463i
$634$	17.7593	−	26.3131i	0.705313	−	1.04503i
$635$	15.6780	+	6.49403i	0.622161	+	0.257708i
$636$	6.72475	−	15.8174i	0.266654	−	0.627200i
$637$	−12.1948	−	29.4408i	−0.483175	−	1.16649i
$638$	−7.26749	−	10.9868i	−0.287723	−	0.434971i
$639$	−2.79972			−0.110755
$640$	−11.2406	−	18.0690i	−0.444325	−	0.714241i
$641$	44.4863			1.75710			0.878552	−	0.477646i	$-0.158510\pi$
$641$	44.4863			1.75710			0.878552	+	0.477646i	$0.158510\pi$
$642$	−4.35423	−	6.58260i	−0.171848	−	0.259795i
$643$	8.31005	+	20.0622i	0.327716	+	0.791177i	0.998761	+	0.0497603i	$0.0158457\pi$
$643$	8.31005	+	20.0622i	0.327716	+	0.791177i	−0.671045	+	0.741417i	$0.734154\pi$
$644$	5.15880	−	12.1341i	0.203285	−	0.478151i
$645$	−29.4447	−	12.1964i	−1.15939	−	0.480233i
$646$	1.14089	−	1.69039i	0.0448875	−	0.0665075i
$647$	−28.4035	−	28.4035i	−1.11666	−	1.11666i	−0.992229	−	0.124429i	$-0.960290\pi$
$647$	−28.4035	−	28.4035i	−1.11666	−	1.11666i	−0.124429	−	0.992229i	$-0.539710\pi$
$648$	3.04363	+	16.5008i	0.119565	+	0.648214i
$649$	−7.10163	+	7.10163i	−0.278763	+	0.278763i
$650$	2.61814	+	13.4897i	0.102692	+	0.529111i
$651$	14.1393	−	34.1353i	0.554163	−	1.33787i
$652$	13.7739	+	0.128068i	0.539427	+	0.00501555i
$653$	−22.7727	+	9.43274i	−0.891163	+	0.369132i	−0.780816	−	0.624761i	$-0.785196\pi$
$653$	−22.7727	+	9.43274i	−0.891163	+	0.369132i	−0.110347	+	0.993893i	$0.535196\pi$
$654$	−10.7361	+	52.6926i	−0.419815	+	2.06044i
$655$			30.0837i			1.17547i
$656$	−6.99063	−	0.130008i	−0.272938	−	0.00507596i
$657$			55.4143i			2.16192i
$658$	3.29400	+	0.671151i	0.128413	+	0.0261642i
$659$	−7.96230	+	3.29809i	−0.310167	+	0.128476i	−0.532337	−	0.846532i	$-0.678686\pi$
$659$	−7.96230	+	3.29809i	−0.310167	+	0.128476i	0.222170	+	0.975008i	$0.428686\pi$
$660$	−14.8591	+	14.5854i	−0.578391	+	0.567734i
$661$	0.939899	−	2.26912i	0.0365578	−	0.0882584i	−0.904546	−	0.426376i	$-0.859790\pi$
$661$	0.939899	−	2.26912i	0.0365578	−	0.0882584i	0.941104	+	0.338117i	$0.109790\pi$
$662$	−35.2468	+	6.84085i	−1.36991	+	0.265877i
$663$	−12.2588	+	12.2588i	−0.476094	+	0.476094i
$664$	−6.13349	+	3.97567i	−0.238025	+	0.154286i
$665$	2.84780	+	2.84780i	0.110433	+	0.110433i
$666$	−16.5575	−	11.1750i	−0.641590	−	0.433024i
$667$	−18.0095	−	7.45979i	−0.697331	−	0.288844i
$668$	28.6650	−	11.5624i	1.10908	−	0.447362i
$669$	−22.0084	−	53.1330i	−0.850894	−	2.05424i
$670$	0.0863501	−	0.0571184i	0.00333599	−	0.00220668i
$671$	−29.5023			−1.13892
$672$	−17.9318	−	12.5942i	−0.691736	−	0.485832i
$673$	−40.9167			−1.57722			−0.788612	−	0.614892i	$-0.789200\pi$
$673$	−40.9167			−1.57722			−0.788612	+	0.614892i	$0.789200\pi$
$674$	−26.3147	+	17.4065i	−1.01360	+	0.670473i
$675$	1.17658	+	2.84053i	0.0452867	+	0.109332i
$676$	23.3130	+	57.7967i	0.896654	+	2.22295i
$677$	−9.91951	−	4.10880i	−0.381238	−	0.157914i	0.183831	−	0.982958i	$-0.441150\pi$
$677$	−9.91951	−	4.10880i	−0.381238	−	0.157914i	−0.565068	+	0.825044i	$0.691150\pi$
$678$	−36.4325	−	24.5892i	−1.39918	−	0.944341i
$679$	9.93416	+	9.93416i	0.381238	+	0.381238i
$680$	−1.11055	+	5.20281i	−0.0425877	+	0.199519i
$681$	4.25519	−	4.25519i	0.163059	−	0.163059i
$682$	28.0942	−	5.45264i	1.07578	−	0.208792i
$683$	6.32576	−	15.2717i	0.242048	−	0.584356i	−0.755438	−	0.655221i	$-0.772576\pi$
$683$	6.32576	−	15.2717i	0.242048	−	0.584356i	0.997486	+	0.0708642i	$0.0225757\pi$
$684$	−7.68936	−	7.83369i	−0.294010	−	0.299529i
$685$	−24.0053	+	9.94330i	−0.917194	+	0.379914i
$686$	−24.2698	−	4.94496i	−0.926624	−	0.188799i
$687$			7.30306i			0.278629i
$688$	24.1830	−	9.49406i	0.921970	−	0.361958i
$689$			21.8905i			0.833962i
$690$	−6.15144	+	30.1912i	−0.234181	+	1.14936i
$691$	−30.4462	+	12.6112i	−1.15823	+	0.479753i	−0.877284	−	0.479971i	$-0.840647\pi$
$691$	−30.4462	+	12.6112i	−1.15823	+	0.479753i	−0.280943	+	0.959725i	$0.590647\pi$
$692$	−0.152937	+	16.4485i	−0.00581379	+	0.625278i
$693$	−4.58824	+	11.0770i	−0.174293	+	0.420780i
$694$	−3.46337	−	17.8447i	−0.131468	−	0.677376i
$695$	0.158989	−	0.158989i	0.00603081	−	0.00603081i
$696$	−18.3723	+	26.6829i	−0.696400	+	1.01141i
$697$	1.23599	+	1.23599i	0.0468166	+	0.0468166i
$698$	−7.05879	+	10.4586i	−0.267179	+	0.395866i
$699$	69.9925	+	28.9918i	2.64736	+	1.09657i
$700$	3.99599	+	1.69889i	0.151034	+	0.0642120i
$701$	6.85850	+	16.5579i	0.259042	+	0.625383i	0.998876	−	0.0474070i	$-0.0150958\pi$
$701$	6.85850	+	16.5579i	0.259042	+	0.625383i	−0.739834	+	0.672790i	$0.765096\pi$
$702$	10.9023	+	16.4818i	0.411481	+	0.622066i
$703$	−5.35182			−0.201848
$704$	0.473360	−	16.9662i	0.0178404	−	0.639438i
$705$	−7.85563			−0.295860
$706$	−4.50679	−	6.81325i	−0.169615	−	0.256420i
$707$	−6.37652	−	15.3943i	−0.239814	−	0.578962i
$708$	22.7304	+	9.66379i	0.854260	+	0.363188i
$709$	−16.1578	−	6.69279i	−0.606820	−	0.251353i	0.0580483	−	0.998314i	$-0.481512\pi$
$709$	−16.1578	−	6.69279i	−0.606820	−	0.251353i	−0.664868	+	0.746961i	$0.731512\pi$
$710$	1.09464	−	1.62188i	0.0410813	−	0.0608680i
$711$	33.9929	+	33.9929i	1.27483	+	1.27483i
$712$	3.49588	+	2.40706i	0.131013	+	0.0902084i
$713$	29.9458	−	29.9458i	1.12148	−	1.12148i
$714$	1.04375	+	5.37782i	0.0390613	+	0.201260i
$715$	10.1482	−	24.4999i	0.379521	−	0.916245i
$716$	−0.365273	+	39.2854i	−0.0136509	+	1.46816i
$717$	−60.6397	+	25.1178i	−2.26463	+	0.938041i
$718$	−9.92735	+	48.7233i	−0.370485	+	1.81834i
$719$			46.2184i			1.72366i	0.507200	+	0.861828i	$0.330680\pi$
$719$			46.2184i			1.72366i	−0.507200	+	0.861828i	$0.669320\pi$
$720$	26.2470	+	11.4482i	0.978167	+	0.426648i
$721$			15.1193i			0.563074i
$722$	23.4474	+	4.77740i	0.872623	+	0.177797i
$723$	9.38996	−	3.88945i	0.349216	−	0.144650i
$724$	24.8437	+	25.3100i	0.923310	+	0.940641i
$725$	2.45665	−	5.93087i	0.0912376	−	0.220267i
$726$	23.5378	−	4.56831i	0.873570	−	0.169546i
$727$	−12.5873	+	12.5873i	−0.466836	+	0.466836i	−0.900888	−	0.434052i	$-0.857083\pi$
$727$	−12.5873	+	12.5873i	−0.466836	+	0.466836i	0.434052	+	0.900888i	$0.357083\pi$
$728$	27.2937	+	5.82589i	1.01157	+	0.215922i
$729$	−27.6023	−	27.6023i	−1.02231	−	1.02231i
$730$	−32.1016	−	21.6661i	−1.18813	−	0.801899i
$731$	−6.00058	−	2.48552i	−0.221940	−	0.0919304i
$732$	27.1412	+	67.2874i	1.00317	+	2.48702i
$733$	10.0169	+	24.1830i	0.369984	+	0.893220i	0.993752	+	0.111610i	$0.0356009\pi$
$733$	10.0169	+	24.1830i	0.369984	+	0.893220i	−0.623768	+	0.781609i	$0.714399\pi$
$734$	10.1092	−	6.68697i	0.373136	−	0.246820i
$735$	23.5305			0.867934
$736$	−13.4648	−	21.2022i	−0.496319	−	0.781525i
$737$	0.0825761			0.00304173
$738$	7.84701	−	5.19060i	0.288853	−	0.191069i
$739$	13.3870	+	32.3190i	0.492448	+	1.18887i	0.953470	+	0.301486i	$0.0974828\pi$
$739$	13.3870	+	32.3190i	0.492448	+	1.18887i	−0.461022	+	0.887389i	$0.652517\pi$
$740$	12.9474	−	5.22251i	0.475957	−	0.191983i
$741$	23.0973	+	9.56721i	0.848500	+	0.351460i
$742$	5.73347	+	3.86966i	0.210482	+	0.142060i
$743$	−10.5401	−	10.5401i	−0.386680	−	0.386680i	0.486821	−	0.873502i	$-0.338156\pi$
$743$	−10.5401	−	10.5401i	−0.386680	−	0.386680i	−0.873502	+	0.486821i	$0.838156\pi$
$744$	−38.2820	−	59.0598i	−1.40349	−	2.16524i
$745$	−32.2240	+	32.2240i	−1.18060	+	1.18060i
$746$	16.2832	−	3.16031i	0.596170	−	0.115707i
$747$	3.76391	−	9.08687i	0.137714	−	0.332471i
$748$	−3.02816	+	2.97237i	−0.110721	+	0.108681i
$749$	2.93452	−	1.21552i	0.107225	−	0.0444141i
$750$	−43.9416	−	8.95308i	−1.60452	−	0.326920i
$751$			34.2205i			1.24872i	0.781136	+	0.624361i	$0.214641\pi$
$751$			34.2205i			1.24872i	−0.781136	+	0.624361i	$0.785359\pi$
$752$	4.61147	−	4.44308i	0.168163	−	0.162022i
$753$		−	34.0288i		−	1.24008i
$754$	8.23760	−	40.4300i	0.299996	−	1.47238i
$755$	−17.7574	+	7.35534i	−0.646257	+	0.267688i
$756$	6.24409	+	0.0580570i	0.227095	+	0.00211151i
$757$	7.07598	−	17.0829i	0.257181	−	0.620889i	−0.741569	−	0.670877i	$-0.765918\pi$
$757$	7.07598	−	17.0829i	0.257181	−	0.620889i	0.998750	+	0.0499872i	$0.0159180\pi$
$758$	5.87696	+	30.2805i	0.213461	+	1.09984i
$759$	−17.3771	+	17.3771i	−0.630749	+	0.630749i
$760$	7.54449	−	1.39160i	0.273667	−	0.0504788i
$761$	17.0045	+	17.0045i	0.616414	+	0.616414i	0.944610	−	0.328196i	$-0.106441\pi$
$761$	17.0045	+	17.0045i	0.616414	+	0.616414i	−0.328196	+	0.944610i	$0.606441\pi$
$762$	18.6214	−	27.5904i	0.674583	−	0.999495i
$763$	−19.9945	−	8.28200i	−0.723850	−	0.299828i
$764$	−0.297933	+	0.700773i	−0.0107788	+	0.0253531i
$765$	−2.73954	−	6.61383i	−0.0990482	−	0.239123i
$766$	15.9809	+	24.1595i	0.577413	+	0.872918i
$767$	−31.4578			−1.13587
$768$	−39.1312	+	14.5288i	−1.41203	+	0.524262i
$769$	−8.03831			−0.289869			−0.144935	−	0.989441i	$-0.546297\pi$
$769$	−8.03831			−0.289869			−0.144935	+	0.989441i	$0.546297\pi$
$770$	−4.62299	−	6.98891i	−0.166601	−	0.251863i
$771$	−9.38887	−	22.6667i	−0.338132	−	0.816322i
$772$	−2.16543	+	5.09335i	−0.0779357	+	0.183314i
$773$	12.4643	+	5.16289i	0.448311	+	0.185696i	0.595404	−	0.803426i	$-0.296992\pi$
$773$	12.4643	+	5.16289i	0.448311	+	0.185696i	−0.147094	+	0.989123i	$0.546992\pi$
$774$	−19.5572	+	28.9770i	−0.702971	+	1.04156i
$775$	9.86172	+	9.86172i	0.354243	+	0.354243i
$776$	26.3179	−	4.85443i	0.944759	−	0.174264i
$777$	10.1654	−	10.1654i	0.364682	−	0.364682i
$778$	0.296595	+	1.52818i	0.0106334	+	0.0547878i
$779$	0.964612	−	2.32878i	0.0345608	−	0.0834372i
$780$	−65.2144	−	0.606358i	−2.33505	−	0.0217111i
$781$	1.44186	−	0.597238i	0.0515938	−	0.0213709i
$782$	−1.25361	+	6.15270i	−0.0448290	+	0.220020i
$783$		−	9.23182i		−	0.329918i
$784$	−13.8130	+	13.3086i	−0.493322	+	0.475308i
$785$		−	6.34569i		−	0.226487i
$786$	57.8219	+	11.7812i	2.06244	+	0.420221i
$787$	14.8100	−	6.13451i	0.527920	−	0.218672i	−0.102772	−	0.994705i	$-0.532771\pi$
$787$	14.8100	−	6.13451i	0.527920	−	0.218672i	0.630692	+	0.776033i	$0.282771\pi$
$788$	21.2386	−	20.8473i	0.756593	−	0.742653i
$789$	−4.91160	+	11.8577i	−0.174858	+	0.422144i
$790$	−32.9828	+	6.40143i	−1.17348	+	0.227753i
$791$	12.5082	−	12.5082i	0.444742	−	0.444742i
$792$	12.4226	+	19.1651i	0.441419	+	0.681001i
$793$	−65.3424	−	65.3424i	−2.32038	−	2.32038i
$794$	−7.96668	−	5.37690i	−0.282727	−	0.190819i
$795$	−14.9337	−	6.18574i	−0.529644	−	0.219386i
$796$	−38.6968	+	15.6088i	−1.37157	+	0.553240i
$797$	6.04234	+	14.5875i	0.214031	+	0.516716i	0.994035	−	0.109058i	$-0.0347834\pi$
$797$	6.04234	+	14.5875i	0.214031	+	0.516716i	−0.780005	+	0.625774i	$0.784783\pi$
$798$	6.58879	−	4.35832i	0.233241	−	0.154283i
$799$	−1.60091			−0.0566361
$800$	6.98229	−	4.43421i	0.246861	−	0.156773i
$801$	−5.71140			−0.201802
$802$	−19.6877	+	13.0229i	−0.695195	+	0.459854i
$803$	−11.8210	−	28.5385i	−0.417155	−	1.00710i
$804$	−0.0759676	−	0.188336i	−0.00267917	−	0.00664210i
$805$	−11.4562	−	4.74531i	−0.403778	−	0.167250i
$806$	74.3005	+	50.1472i	2.61712	+	1.76636i
$807$	−18.8126	−	18.8126i	−0.662235	−	0.662235i
$808$	−31.0413	−	6.62583i	−1.09203	−	0.233096i
$809$	29.7903	−	29.7903i	1.04737	−	1.04737i	0.0485504	−	0.998821i	$-0.484540\pi$
$809$	29.7903	−	29.7903i	1.04737	−	1.04737i	0.998821	−	0.0485504i	$-0.0154601\pi$
$810$	15.4910	−	3.00656i	0.544299	−	0.105640i
$811$	10.3850	−	25.0715i	0.364665	−	0.880380i	−0.629940	−	0.776644i	$-0.716920\pi$
$811$	10.3850	−	25.0715i	0.364665	−	0.880380i	0.994605	−	0.103736i	$-0.0330796\pi$
$812$	−9.13308	−	9.30451i	−0.320508	−	0.326524i
$813$	11.9011	−	4.92959i	0.417390	−	0.172888i
$814$	10.9110	+	2.22312i	0.382431	+	0.0779202i
$815$		−	12.9543i		−	0.453768i
$816$	9.56506	+	4.17200i	0.334844	+	0.146049i
$817$			9.36612i			0.327679i
$818$	8.89560	−	43.6595i	0.311027	−	1.52652i
$819$	−34.6958	+	14.3715i	−1.21237	+	0.502180i
$820$	−0.0611359	+	6.57523i	−0.00213496	+	0.229617i
$821$	−2.02373	+	4.88572i	−0.0706288	+	0.170513i	−0.955252	−	0.295794i	$-0.904416\pi$
$821$	−2.02373	+	4.88572i	−0.0706288	+	0.170513i	0.884623	+	0.466307i	$0.154416\pi$
$822$	9.71057	+	50.0328i	0.338695	+	1.74509i
$823$	34.1819	−	34.1819i	1.19150	−	1.19150i	0.214860	−	0.976645i	$-0.431071\pi$
$823$	34.1819	−	34.1819i	1.19150	−	1.19150i	0.976645	−	0.214860i	$-0.0689294\pi$
$824$	23.7215	+	16.3332i	0.826377	+	0.568996i
$825$	−5.72261	−	5.72261i	−0.199236	−	0.199236i
$826$	−5.56089	+	8.23928i	−0.193488	+	0.286681i
$827$	9.59895	+	3.97602i	0.333788	+	0.138260i	0.543282	−	0.839550i	$-0.317182\pi$
$827$	9.59895	+	3.97602i	0.333788	+	0.138260i	−0.209494	+	0.977810i	$0.567182\pi$
$828$	31.1031	+	13.2234i	1.08091	+	0.459546i
$829$	−11.4250	−	27.5824i	−0.396807	−	0.957976i	−0.988418	−	0.151753i	$-0.951508\pi$
$829$	−11.4250	−	27.5824i	−0.396807	−	0.957976i	0.591612	−	0.806223i	$-0.298492\pi$
$830$	3.79241	+	5.73326i	0.131636	+	0.199004i
$831$	41.6959			1.44641
$832$	38.6256	−	36.5288i	1.33910	−	1.26641i
$833$	4.79531			0.166148
$834$	−0.243320	−	0.367845i	−0.00842548	−	0.0127374i
$835$	−11.1241	−	26.8559i	−0.384965	−	0.929387i
$836$	5.63113	+	2.39407i	0.194757	+	0.0828006i
$837$	18.5296	+	7.67523i	0.640478	+	0.265295i
$838$	19.6122	−	29.0584i	0.677492	−	1.00380i
$839$	−13.0580	−	13.0580i	−0.450812	−	0.450812i	0.444812	−	0.895624i	$-0.353270\pi$
$839$	−13.0580	−	13.0580i	−0.450812	−	0.450812i	−0.895624	+	0.444812i	$0.853270\pi$
$840$	−11.6870	+	16.9735i	−0.403239	+	0.585641i
$841$	6.87621	−	6.87621i	0.237111	−	0.237111i
$842$	−1.81806	−	9.36737i	−0.0626544	−	0.322821i
$843$	−24.8789	+	60.0629i	−0.856874	+	2.06868i
$844$	−0.439920	+	47.3138i	−0.0151427	+	1.62861i
$845$	54.1490	−	22.4293i	1.86278	−	0.771590i
$846$	−1.72034	+	8.44342i	−0.0591467	+	0.290291i
$847$			9.64958i			0.331563i
$848$	12.2651	−	4.81518i	0.421185	−	0.165354i
$849$		−	44.7972i		−	1.53744i
$850$	−2.02620	−	0.412837i	−0.0694981	−	0.0141602i
$851$	15.2236	−	6.30583i	0.521859	−	0.216161i
$852$	−2.68862	−	2.73909i	−0.0921107	−	0.0938397i
$853$	−10.7093	+	25.8544i	−0.366678	+	0.885238i	0.627612	+	0.778526i	$0.284032\pi$
$853$	−10.7093	+	25.8544i	−0.366678	+	0.885238i	−0.994290	+	0.106712i	$0.965968\pi$
$854$	−28.6650	+	5.56342i	−0.980896	+	0.190376i
$855$	−7.29968	+	7.29968i	−0.249644	+	0.249644i
$856$	1.26304	−	5.91722i	0.0431699	−	0.202247i
$857$	16.2324	+	16.2324i	0.554489	+	0.554489i	0.927733	−	0.373244i	$-0.121755\pi$
$857$	16.2324	+	16.2324i	0.554489	+	0.554489i	−0.373244	+	0.927733i	$0.621755\pi$
$858$	−43.1155	−	29.0997i	−1.47194	−	0.993446i
$859$	23.7858	+	9.85239i	0.811560	+	0.336159i	0.749576	−	0.661918i	$-0.230257\pi$
$859$	23.7858	+	9.85239i	0.811560	+	0.336159i	0.0619839	+	0.998077i	$0.480257\pi$
$860$	−9.13981	−	22.6591i	−0.311665	−	0.772668i
$861$	2.59114	+	6.25557i	0.0883059	+	0.213189i
$862$	12.9613	−	8.57360i	0.441465	−	0.292018i
$863$	6.03655			0.205487			0.102743	−	0.994708i	$-0.467238\pi$
$863$	6.03655			0.205487			0.102743	+	0.994708i	$0.467238\pi$
$864$	6.83650	−	9.73394i	0.232583	−	0.331155i
$865$	15.4697			0.525987
$866$	37.5548	−	24.8416i	1.27616	−	0.844151i
$867$	−0.998357	−	2.41025i	−0.0339060	−	0.0818563i
$868$	26.2687	−	10.5958i	0.891617	−	0.359645i
$869$	−24.7578	−	10.2550i	−0.839852	−	0.347878i
$870$	25.2536	+	17.0443i	0.856178	+	0.577855i
$871$	0.182892	+	0.182892i	0.00619705	+	0.00619705i
$872$	−34.5939	+	22.4234i	−1.17150	+	0.759353i
$873$	−25.4640	+	25.4640i	−0.861825	+	0.861825i
$874$	8.88895	−	1.72520i	0.300673	−	0.0583559i
$875$	6.90654	−	16.6739i	0.233484	−	0.563680i
$876$	−54.2144	+	53.2155i	−1.83173	+	1.79798i
$877$	1.06893	−	0.442765i	0.0360951	−	0.0149511i	−0.364563	−	0.931179i	$-0.618782\pi$
$877$	1.06893	−	0.442765i	0.0360951	−	0.0149511i	0.400658	+	0.916228i	$0.368782\pi$
$878$	37.9011	+	7.72233i	1.27910	+	0.260616i
$879$			46.3497i			1.56334i
$880$	−15.9594	−	0.296804i	−0.537991	−	0.0100053i
$881$			44.1045i			1.48592i	0.669336	+	0.742960i	$0.266579\pi$
$881$			44.1045i			1.48592i	−0.669336	+	0.742960i	$0.733421\pi$
$882$	5.15306	−	25.2911i	0.173512	−	0.851596i
$883$	−12.0673	+	4.99843i	−0.406096	+	0.168211i	−0.576375	−	0.817185i	$-0.695533\pi$
$883$	−12.0673	+	4.99843i	−0.406096	+	0.168211i	0.170279	+	0.985396i	$0.445533\pi$
$884$	−13.2901	−	0.123571i	−0.446995	−	0.00415613i
$885$	8.88922	−	21.4605i	0.298808	−	0.721386i
$886$	8.12147	+	41.8451i	0.272846	+	1.40581i
$887$	0.445012	−	0.445012i	0.0149421	−	0.0149421i	−0.699596	−	0.714538i	$-0.746637\pi$
$887$	0.445012	−	0.445012i	0.0149421	−	0.0149421i	0.714538	+	0.699596i	$0.246637\pi$
$888$	−4.96743	−	26.9306i	−0.166696	−	0.903731i
$889$	9.47252	+	9.47252i	0.317698	+	0.317698i
$890$	2.23307	−	3.30862i	0.0748526	−	0.110905i
$891$	11.6280	+	4.81647i	0.389553	+	0.161358i
$892$	17.2502	−	40.5745i	0.577580	−	1.35854i
$893$	0.883463	+	2.13287i	0.0295639	+	0.0713737i
$894$	49.3162	+	74.5549i	1.64938	+	2.49349i
$895$	36.9478			1.23503
$896$	−2.73949	−	16.5740i	−0.0915199	−	0.553697i
$897$	−76.9746			−2.57011
$898$	4.43481	+	6.70443i	0.147992	+	0.223730i
$899$	−16.0255	−	38.6890i	−0.534480	−	1.29035i
$900$	−4.35473	+	10.2428i	−0.145158	+	0.341427i
$901$	−3.04336	−	1.26060i	−0.101389	−	0.0419967i
$902$	−2.93397	+	4.34711i	−0.0976904	+	0.144743i
$903$	−17.7903	−	17.7903i	−0.592024	−	0.592024i
$904$	−6.11228	−	33.1373i	−0.203291	−	1.10213i
$905$	23.5847	−	23.5847i	0.783982	−	0.783982i
$906$	7.18318	+	37.0107i	0.238645	+	1.22960i
$907$	−10.9826	+	26.5142i	−0.364670	+	0.880391i	0.629934	+	0.776648i	$0.283082\pi$
$907$	−10.9826	+	26.5142i	−0.364670	+	0.880391i	−0.994604	+	0.103742i	$0.966918\pi$
$908$	4.61317	+	0.0428929i	0.153093	+	0.00142345i
$909$	39.4598	−	16.3448i	1.30880	−	0.542122i
$910$	5.24010	−	25.7183i	0.173708	−	0.852554i
$911$			29.3868i			0.973628i	0.873506	+	0.486814i	$0.161841\pi$
$911$			29.3868i			0.973628i	−0.873506	+	0.486814i	$0.838159\pi$
$912$	0.279812	−	15.0457i	0.00926550	−	0.498213i
$913$			5.48268i			0.181450i
$914$	34.0474	+	6.93714i	1.12619	+	0.229460i
$915$	63.0408	−	26.1123i	2.08406	−	0.863247i
$916$	−3.99553	+	3.92192i	−0.132016	+	0.129584i
$917$	−9.08819	+	21.9408i	−0.300119	+	0.724550i
$918$	−2.91924	+	0.566577i	−0.0963492	+	0.0186998i
$919$	9.53834	−	9.53834i	0.314641	−	0.314641i	−0.532064	−	0.846704i	$-0.678583\pi$
$919$	9.53834	−	9.53834i	0.314641	−	0.314641i	0.846704	+	0.532064i	$0.178583\pi$
$920$	−19.8212	+	12.8479i	−0.653484	+	0.423582i
$921$	−27.2299	−	27.2299i	−0.897257	−	0.897257i
$922$	−13.4074	−	9.04895i	−0.441548	−	0.298011i
$923$	4.51625	+	1.87069i	0.148654	+	0.0615746i
$924$	−15.2433	+	6.14858i	−0.501468	+	0.202273i
$925$	2.07663	+	5.01343i	0.0682792	+	0.164840i
$926$	−16.8315	+	11.1336i	−0.553118	+	0.365874i
$927$	−38.7550			−1.27288
$928$	−24.4647	+	4.27778i	−0.803091	+	0.140425i
$929$	−12.4566			−0.408689			−0.204344	−	0.978899i	$-0.565506\pi$
$929$	−12.4566			−0.408689			−0.204344	+	0.978899i	$0.565506\pi$
$930$	−55.2060	+	36.5174i	−1.81027	+	1.19745i
$931$	−2.64629	−	6.38871i	−0.0867287	−	0.209382i
$932$	21.7261	+	53.8625i	0.711661	+	1.76432i
$933$	38.5619	+	15.9729i	1.26246	+	0.522928i
$934$	6.19553	+	4.18151i	0.202724	+	0.136823i
$935$	2.82174	+	2.82174i	0.0922807	+	0.0922807i
$936$	−14.9334	+	69.9612i	−0.488112	+	2.28675i
$937$	41.9535	−	41.9535i	1.37056	−	1.37056i	0.510948	−	0.859611i	$-0.329294\pi$
$937$	41.9535	−	41.9535i	1.37056	−	1.37056i	0.859611	−	0.510948i	$-0.170706\pi$
$938$	0.0802326	−	0.0155719i	0.00261969	−	0.000508439i
$939$	−13.4273	+	32.4163i	−0.438183	+	1.05787i
$940$	−4.21866	−	4.29784i	−0.137597	−	0.140180i
$941$	−9.39211	+	3.89034i	−0.306174	+	0.126821i	−0.530480	−	0.847697i	$-0.677988\pi$
$941$	−9.39211	+	3.89034i	−0.306174	+	0.126821i	0.224306	+	0.974519i	$0.427988\pi$
$942$	−12.1966	−	2.48505i	−0.397387	−	0.0809674i
$943$			7.76094i			0.252731i
$944$	6.91965	+	17.6255i	0.225215	+	0.573663i
$945$		−	5.87254i		−	0.191034i
$946$	3.89064	−	19.0952i	0.126496	−	0.620838i
$947$	−36.2342	+	15.0087i	−1.17745	+	0.487718i	−0.883650	−	0.468148i	$-0.844921\pi$
$947$	−36.2342	+	15.0087i	−1.17745	+	0.487718i	−0.293805	+	0.955866i	$0.594921\pi$
$948$	−0.612741	+	65.9009i	−0.0199009	+	2.14036i
$949$	37.0263	−	89.3894i	1.20192	−	2.90170i
$950$	0.568142	+	2.92730i	0.0184330	+	0.0949741i
$951$	−41.4092	+	41.4092i	−1.34279	+	1.34279i
$952$	−2.38170	+	3.45905i	−0.0771915	+	0.112108i
$953$	−2.22029	−	2.22029i	−0.0719221	−	0.0719221i	0.670231	−	0.742153i	$-0.266195\pi$
$953$	−2.22029	−	2.22029i	−0.0719221	−	0.0719221i	−0.742153	+	0.670231i	$0.766195\pi$
$954$	−9.91900	+	14.6965i	−0.321139	+	0.475816i
$955$	0.661623	+	0.274053i	0.0214096	+	0.00886815i
$956$	−46.3070	−	19.6874i	−1.49767	−	0.636735i
$957$	9.29936	+	22.4506i	0.300606	+	0.725726i
$958$	1.81786	+	2.74820i	0.0587325	+	0.0887902i
$959$	−20.5115			−0.662350
$960$	14.0052	+	36.6725i	0.452017	+	1.18360i
$961$	59.9780			1.93477
$962$	19.2422	+	29.0898i	0.620393	+	0.937894i
$963$	3.11571	+	7.52199i	0.100402	+	0.242393i
$964$	7.17056	+	3.04855i	0.230948	+	0.0981873i
$965$	4.80880	+	1.99187i	0.154801	+	0.0641205i
$966$	−13.6070	+	20.1609i	−0.437799	+	0.648665i
$967$	29.6659	+	29.6659i	0.953990	+	0.953990i	0.998987	−	0.0449975i	$-0.0143280\pi$
$967$	29.6659	+	29.6659i	0.953990	+	0.953990i	−0.0449975	+	0.998987i	$0.514328\pi$
$968$	15.1397	+	10.4243i	0.486608	+	0.335050i
$969$	−2.66019	+	2.66019i	−0.0854576	+	0.0854576i
$970$	−4.79530	−	24.7073i	−0.153968	−	0.793304i
$971$	13.2755	−	32.0498i	0.426030	−	1.02853i	−0.554504	−	0.832181i	$-0.687092\pi$
$971$	13.2755	−	32.0498i	0.426030	−	1.02853i	0.980534	−	0.196347i	$-0.0629079\pi$
$972$	0.405087	−	43.5675i	0.0129932	−	1.39743i
$973$	0.163985	−	0.0679248i	0.00525712	−	0.00217757i
$974$	5.82164	−	28.5725i	0.186537	−	0.915523i
$975$		−	25.3492i		−	0.811823i
$976$	−22.2377	+	50.9840i	−0.711812	+	1.63196i
$977$			20.4525i			0.654332i	0.944967	+	0.327166i	$0.106094\pi$
$977$			20.4525i			0.654332i	−0.944967	+	0.327166i	$0.893906\pi$
$978$	−24.8985	−	5.07307i	−0.796167	−	0.162219i
$979$	2.94139	−	1.21836i	0.0940071	−	0.0389390i
$980$	12.6364	+	12.8736i	0.403655	+	0.411232i
$981$	21.2290	−	51.2514i	0.677791	−	1.63633i
$982$	21.2932	−	4.13268i	0.679495	−	0.131879i
$983$	32.0641	−	32.0641i	1.02269	−	1.02269i	0.0229508	−	0.999737i	$-0.492694\pi$
$983$	32.0641	−	32.0641i	1.02269	−	1.02269i	0.999737	−	0.0229508i	$-0.00730612\pi$
$984$	12.6139	+	2.69245i	0.402115	+	0.0858322i
$985$	−19.7908	−	19.7908i	−0.630587	−	0.630587i
$986$	5.14647	+	3.47347i	0.163897	+	0.110618i
$987$	−5.72931	−	2.37316i	−0.182366	−	0.0755385i
$988$	7.16953	+	17.7744i	0.228093	+	0.565480i
$989$	−11.0357	−	26.6426i	−0.350916	−	0.847185i
$990$	17.9145	−	11.8500i	0.569360	−	0.376617i
$991$	−13.1949			−0.419151			−0.209575	−	0.977793i	$-0.567208\pi$
$991$	−13.1949			−0.419151			−0.209575	+	0.977793i	$0.567208\pi$
$992$	11.7535	−	52.6607i	0.373174	−	1.67198i
$993$	66.2339			2.10187
$994$	1.28832	−	0.852189i	0.0408629	−	0.0270298i
$995$	15.0171	+	36.2546i	0.476075	+	1.14935i
$996$	12.5047	−	5.04391i	0.396225	−	0.159822i
$997$	−36.4315	−	15.0904i	−1.15380	−	0.477918i	−0.277992	−	0.960584i	$-0.589669\pi$
$997$	−36.4315	−	15.0904i	−1.15380	−	0.477918i	−0.875805	+	0.482665i	$0.839669\pi$
$998$	18.8025	+	12.6902i	0.595182	+	0.401703i
$999$	5.51809	+	5.51809i	0.174584	+	0.174584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bd.b.69.11	✓	128
32.13	even	8	inner	544.2.bd.b.205.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.11	✓	128	1.1	even	1	trivial
544.2.bd.b.205.11	yes	128	32.13	even	8	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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780220 - 1.17952i) q^{2} +(0.998357 + 2.41025i) q^{3} +(-0.782513 + 1.84056i) q^{4} +(1.73773 + 0.719793i) q^{5} +(2.06399 - 3.05810i) q^{6} +(1.04993 + 1.04993i) q^{7} +(2.78151 - 0.513058i) q^{8} +(-2.69125 + 2.69125i) q^{9} +(-0.506808 - 2.61128i) q^{10} +(0.811901 - 1.96010i) q^{11} +(-5.21744 - 0.0485113i) q^{12} +(6.13950 - 2.54307i) q^{13} +(0.419231 - 2.05758i) q^{14} +4.90698i q^{15} +(-2.77535 - 2.88053i) q^{16} +1.00000i q^{17} +(5.27414 + 1.07460i) q^{18} +(1.33228 - 0.551850i) q^{19} +(-2.68463 + 2.63516i) q^{20} +(-1.48238 + 3.57878i) q^{21} +(-2.94543 + 0.571661i) q^{22} +(-3.13956 + 3.13956i) q^{23} +(4.01353 + 6.19190i) q^{24} +(-1.03391 - 1.03391i) q^{25} +(-7.78975 - 5.25749i) q^{26} +(-1.94267 - 0.804680i) q^{27} +(-2.75404 + 1.11088i) q^{28} +(1.68013 + 4.05620i) q^{29} +(5.78786 - 3.82852i) q^{30} -9.53824 q^{31} +(-1.23225 + 5.52101i) q^{32} +5.53490 q^{33} +(1.17952 - 0.780220i) q^{34} +(1.06876 + 2.58022i) q^{35} +(-2.84748 - 7.05936i) q^{36} +(-3.42874 - 1.42023i) q^{37} +(-1.69039 - 1.14089i) q^{38} +(12.2588 + 12.2588i) q^{39} +(5.20281 + 1.11055i) q^{40} +(1.23599 - 1.23599i) q^{41} +(5.37782 - 1.04375i) q^{42} +(-2.48552 + 6.00058i) q^{43} +(2.97237 + 3.02816i) q^{44} +(-6.61383 + 2.73954i) q^{45} +(6.15270 + 1.25361i) q^{46} +1.60091i q^{47} +(4.17200 - 9.56506i) q^{48} -4.79531i q^{49} +(-0.412837 + 2.02620i) q^{50} +(-2.41025 + 0.998357i) q^{51} +(-0.123571 + 13.2901i) q^{52} +(-1.26060 + 3.04336i) q^{53} +(0.566577 + 2.91924i) q^{54} +(2.82174 - 2.82174i) q^{55} +(3.45905 + 2.38170i) q^{56} +(2.66019 + 2.66019i) q^{57} +(3.47347 - 5.14647i) q^{58} +(-4.37346 - 1.81155i) q^{59} +(-9.03161 - 3.83978i) q^{60} +(-5.32147 - 12.8472i) q^{61} +(7.44192 + 11.2505i) q^{62} -5.65124 q^{63} +(7.47354 - 2.85415i) q^{64} +12.4993 q^{65} +(-4.31844 - 6.52850i) q^{66} +(0.0148947 + 0.0359589i) q^{67} +(-1.84056 - 0.782513i) q^{68} +(-10.7015 - 4.43271i) q^{69} +(2.20954 - 3.27377i) q^{70} +(0.520151 + 0.520151i) q^{71} +(-6.10496 + 8.86650i) q^{72} +(10.2953 - 10.2953i) q^{73} +(0.999989 + 5.15235i) q^{74} +(1.45977 - 3.52420i) q^{75} +(-0.0268151 + 2.88398i) q^{76} +(2.91040 - 1.20553i) q^{77} +(4.89490 - 24.0241i) q^{78} -12.6309i q^{79} +(-2.74943 - 7.00327i) q^{80} +5.93234i q^{81} +(-2.42222 - 0.493527i) q^{82} +(-2.38751 + 0.988939i) q^{83} +(-5.42700 - 5.52886i) q^{84} +(-0.719793 + 1.73773i) q^{85} +(9.01703 - 1.75006i) q^{86} +(-8.09906 + 8.09906i) q^{87} +(1.25266 - 5.86859i) q^{88} +(1.06110 + 1.06110i) q^{89} +(8.39157 + 5.66367i) q^{90} +(9.11606 + 3.77600i) q^{91} +(-3.32181 - 8.23529i) q^{92} +(-9.52256 - 22.9895i) q^{93} +(1.88830 - 1.24906i) q^{94} +2.71238 q^{95} +(-14.5372 + 2.54191i) q^{96} +9.46176 q^{97} +(-5.65614 + 3.74139i) q^{98} +(3.09010 + 7.46016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) \) 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

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