LMFDB - Embedded newform 504.2.br.a.155.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(155,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("504.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.br (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.1
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41306 + 0.0570983i) q^{2} +(0.376059 + 1.69073i) q^{3} +(1.99348 - 0.161367i) q^{4} +(1.12986 + 1.95698i) q^{5} +(-0.627932 - 2.36764i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.80769 + 0.341845i) q^{8} +(-2.71716 + 1.27163i) q^{9} +O(q^{10})$	\(q+(-1.41306 + 0.0570983i) q^{2} +(0.376059 + 1.69073i) q^{3} +(1.99348 - 0.161367i) q^{4} +(1.12986 + 1.95698i) q^{5} +(-0.627932 - 2.36764i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.80769 + 0.341845i) q^{8} +(-2.71716 + 1.27163i) q^{9} +(-1.70831 - 2.70082i) q^{10} +(3.30783 + 1.90978i) q^{11} +(1.02249 + 3.30976i) q^{12} +(3.49994 - 2.02069i) q^{13} +(-1.25230 - 0.657082i) q^{14} +(-2.88384 + 2.64624i) q^{15} +(3.94792 - 0.643363i) q^{16} +5.16096i q^{17} +(3.76690 - 1.95204i) q^{18} -4.38745 q^{19} +(2.56815 + 3.71888i) q^{20} +(-0.519690 + 1.65225i) q^{21} +(-4.78321 - 2.50976i) q^{22} +(-0.400728 - 0.694081i) q^{23} +(-1.63383 - 4.61851i) q^{24} +(-0.0531827 + 0.0921152i) q^{25} +(-4.83025 + 3.05520i) q^{26} +(-3.17180 - 4.11579i) q^{27} +(1.80709 + 0.856992i) q^{28} +(3.57701 - 6.19557i) q^{29} +(3.92394 - 3.90396i) q^{30} +(3.01785 - 1.74236i) q^{31} +(-5.54192 + 1.13453i) q^{32} +(-1.98499 + 6.31085i) q^{33} +(-0.294682 - 7.29275i) q^{34} +2.25973i q^{35} +(-5.21140 + 2.97343i) q^{36} -6.92403i q^{37} +(6.19974 - 0.250516i) q^{38} +(4.73263 + 5.15757i) q^{39} +(-3.84129 - 5.10836i) q^{40} +(-4.34488 + 2.50852i) q^{41} +(0.640013 - 2.36440i) q^{42} +(-6.13225 + 10.6214i) q^{43} +(6.90227 + 3.27333i) q^{44} +(-5.55857 - 3.88066i) q^{45} +(0.605884 + 0.957898i) q^{46} +(-4.90983 + 8.50407i) q^{47} +(2.57241 + 6.43294i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.0698908 - 0.133201i) q^{50} +(-8.72581 + 1.94082i) q^{51} +(6.65099 - 4.59298i) q^{52} -5.35295 q^{53} +(4.71695 + 5.63475i) q^{54} +8.63115i q^{55} +(-2.60246 - 1.10780i) q^{56} +(-1.64994 - 7.41801i) q^{57} +(-4.70078 + 8.95895i) q^{58} +(-0.549805 + 0.317430i) q^{59} +(-5.32186 + 5.74058i) q^{60} +(5.14843 + 2.97245i) q^{61} +(-4.16492 + 2.63437i) q^{62} +(-2.98894 - 0.257316i) q^{63} +(7.76628 - 1.91959i) q^{64} +(7.90891 + 4.56621i) q^{65} +(2.44457 - 9.03095i) q^{66} +(-4.63125 - 8.02155i) q^{67} +(0.832807 + 10.2883i) q^{68} +(1.02281 - 0.938539i) q^{69} +(-0.129027 - 3.19313i) q^{70} -4.14333 q^{71} +(7.19425 - 4.49920i) q^{72} +10.5544 q^{73} +(0.395351 + 9.78408i) q^{74} +(-0.175742 - 0.0552771i) q^{75} +(-8.74630 + 0.707989i) q^{76} +(1.90978 + 3.30783i) q^{77} +(-6.98198 - 7.01773i) q^{78} +(-3.13471 - 1.80983i) q^{79} +(5.71966 + 6.99909i) q^{80} +(5.76592 - 6.91044i) q^{81} +(5.99634 - 3.79277i) q^{82} +(8.83359 + 5.10008i) q^{83} +(-0.769374 + 3.37758i) q^{84} +(-10.0999 + 5.83118i) q^{85} +(8.05877 - 15.3588i) q^{86} +(11.8202 + 3.71788i) q^{87} +(-9.94023 - 4.23130i) q^{88} -15.9455i q^{89} +(8.07618 + 5.16622i) q^{90} +4.04138 q^{91} +(-0.910844 - 1.31897i) q^{92} +(4.08075 + 4.44715i) q^{93} +(6.45232 - 12.2971i) q^{94} +(-4.95722 - 8.58616i) q^{95} +(-4.00227 - 8.94325i) q^{96} +(-1.03421 + 1.79131i) q^{97} +(-0.755979 - 1.19520i) q^{98} +(-11.4164 - 0.982834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{6}+O(q^{10}) $ 144 * q + 6 * q^6	$ 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.41306	+	0.0570983i	−0.999185	+	0.0403746i
$2$	−1.41306	+	0.0570983i	−0.999185	+	0.0403746i
$3$	0.376059	+	1.69073i	0.217118	+	0.976145i
$3$	0.376059	+	1.69073i	0.217118	+	0.976145i
$4$	1.99348	−	0.161367i	0.996740	−	0.0806834i
$5$	1.12986	+	1.95698i	0.505290	+	0.875188i	0.999981	+	0.00611951i	$0.00194791\pi$
$5$	1.12986	+	1.95698i	0.505290	+	0.875188i	−0.494691	+	0.869069i	$0.664719\pi$
$6$	−0.627932	−	2.36764i	−0.256352	−	0.966583i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	−2.80769	+	0.341845i	−0.992669	+	0.120861i
$9$	−2.71716	+	1.27163i	−0.905720	+	0.423877i
$10$	−1.70831	−	2.70082i	−0.540214	−	0.854074i
$11$	3.30783	+	1.90978i	0.997349	+	0.575820i	0.907463	−	0.420132i	$-0.138016\pi$
$11$	3.30783	+	1.90978i	0.997349	+	0.575820i	0.0898862	+	0.995952i	$0.471350\pi$
$12$	1.02249	+	3.30976i	0.295168	+	0.955445i
$13$	3.49994	−	2.02069i	0.970709	−	0.560439i	0.0712564	−	0.997458i	$-0.477299\pi$
$13$	3.49994	−	2.02069i	0.970709	−	0.560439i	0.899452	+	0.437019i	$0.143966\pi$
$14$	−1.25230	−	0.657082i	−0.334690	−	0.175612i
$15$	−2.88384	+	2.64624i	−0.744604	+	0.683256i
$16$	3.94792	−	0.643363i	0.986980	−	0.160841i
$17$			5.16096i			1.25172i	0.779937	+	0.625858i	$0.215251\pi$
$17$			5.16096i			1.25172i	−0.779937	+	0.625858i	$0.784749\pi$
$18$	3.76690	−	1.95204i	0.887868	−	0.460099i
$19$	−4.38745			−1.00655			−0.503275	−	0.864126i	$-0.667872\pi$
$19$	−4.38745			−1.00655			−0.503275	+	0.864126i	$0.667872\pi$
$20$	2.56815	+	3.71888i	0.574256	+	0.831567i
$21$	−0.519690	+	1.65225i	−0.113406	+	0.360550i
$22$	−4.78321	−	2.50976i	−1.01978	−	0.535083i
$23$	−0.400728	−	0.694081i	−0.0835575	−	0.144726i	0.821218	−	0.570614i	$-0.193295\pi$
$23$	−0.400728	−	0.694081i	−0.0835575	−	0.144726i	−0.904776	+	0.425889i	$0.859962\pi$
$24$	−1.63383	−	4.61851i	−0.333503	−	0.942749i
$25$	−0.0531827	+	0.0921152i	−0.0106365	+	0.0184230i
$26$	−4.83025	+	3.05520i	−0.947290	+	0.599174i
$27$	−3.17180	−	4.11579i	−0.610413	−	0.792083i
$28$	1.80709	+	0.856992i	0.341507	+	0.161956i
$29$	3.57701	−	6.19557i	0.664234	−	1.15049i	−0.315258	−	0.949006i	$-0.602091\pi$
$29$	3.57701	−	6.19557i	0.664234	−	1.15049i	0.979492	−	0.201482i	$-0.0645756\pi$
$30$	3.92394	−	3.90396i	0.716411	−	0.712762i
$31$	3.01785	−	1.74236i	0.542022	−	0.312936i	−0.203876	−	0.978997i	$-0.565354\pi$
$31$	3.01785	−	1.74236i	0.542022	−	0.312936i	0.745898	+	0.666060i	$0.232021\pi$
$32$	−5.54192	+	1.13453i	−0.979682	+	0.200559i
$33$	−1.98499	+	6.31085i	−0.345542	+	1.09858i
$34$	−0.294682	−	7.29275i	−0.0505376	−	1.25070i
$35$			2.25973i			0.381964i
$36$	−5.21140	+	2.97343i	−0.868567	+	0.495571i
$37$		−	6.92403i		−	1.13830i	−0.822232	−	0.569152i	$-0.807272\pi$
$37$		−	6.92403i		−	1.13830i	0.822232	−	0.569152i	$-0.192728\pi$
$38$	6.19974	−	0.250516i	1.00573	−	0.0406391i
$39$	4.73263	+	5.15757i	0.757828	+	0.825872i
$40$	−3.84129	−	5.10836i	−0.607362	−	0.807703i
$41$	−4.34488	+	2.50852i	−0.678556	+	0.391765i	−0.799311	−	0.600918i	$-0.794802\pi$
$41$	−4.34488	+	2.50852i	−0.678556	+	0.391765i	0.120755	+	0.992682i	$0.461469\pi$
$42$	0.640013	−	2.36440i	0.0987562	−	0.364835i
$43$	−6.13225	+	10.6214i	−0.935159	+	1.61974i	−0.160808	+	0.986986i	$0.551410\pi$
$43$	−6.13225	+	10.6214i	−0.935159	+	1.61974i	−0.774350	+	0.632757i	$0.781923\pi$
$44$	6.90227	+	3.27333i	1.04056	+	0.493473i
$45$	−5.55857	−	3.88066i	−0.828623	−	0.578495i
$46$	0.605884	+	0.957898i	0.0893327	+	0.141234i
$47$	−4.90983	+	8.50407i	−0.716172	+	1.24045i	0.246334	+	0.969185i	$0.420774\pi$
$47$	−4.90983	+	8.50407i	−0.716172	+	1.24045i	−0.962506	+	0.271261i	$0.912559\pi$
$48$	2.57241	+	6.43294i	0.371295	+	0.928515i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.0698908	−	0.133201i	0.00988405	−	0.0188375i
$51$	−8.72581	+	1.94082i	−1.22186	+	0.271770i
$52$	6.65099	−	4.59298i	0.922326	−	0.636932i
$53$	−5.35295			−0.735284			−0.367642	−	0.929967i	$-0.619835\pi$
$53$	−5.35295			−0.735284			−0.367642	+	0.929967i	$0.619835\pi$
$54$	4.71695	+	5.63475i	0.641895	+	0.766792i
$55$			8.63115i			1.16382i
$56$	−2.60246	−	1.10780i	−0.347768	−	0.148036i
$57$	−1.64994	−	7.41801i	−0.218540	−	0.982540i
$58$	−4.70078	+	8.95895i	−0.617242	+	1.17637i
$59$	−0.549805	+	0.317430i	−0.0715785	+	0.0413259i	−0.535362	−	0.844623i	$-0.679825\pi$
$59$	−0.549805	+	0.317430i	−0.0715785	+	0.0413259i	0.463784	+	0.885949i	$0.346492\pi$
$60$	−5.32186	+	5.74058i	−0.687049	+	0.741105i
$61$	5.14843	+	2.97245i	0.659188	+	0.380583i	0.791968	−	0.610563i	$-0.209057\pi$
$61$	5.14843	+	2.97245i	0.659188	+	0.380583i	−0.132779	+	0.991146i	$0.542390\pi$
$62$	−4.16492	+	2.63437i	−0.528945	+	0.334565i
$63$	−2.98894	−	0.257316i	−0.376572	−	0.0324188i
$64$	7.76628	−	1.91959i	0.970785	−	0.239949i
$65$	7.90891	+	4.56621i	0.980979	+	0.566369i
$66$	2.44457	−	9.03095i	0.300905	−	1.11163i
$67$	−4.63125	−	8.02155i	−0.565797	−	0.979989i	−0.996975	−	0.0777219i	$-0.975235\pi$
$67$	−4.63125	−	8.02155i	−0.565797	−	0.979989i	0.431178	−	0.902267i	$-0.358098\pi$
$68$	0.832807	+	10.2883i	0.100993	+	1.24764i
$69$	1.02281	−	0.938539i	0.123132	−	0.112987i
$70$	−0.129027	−	3.19313i	−0.0154216	−	0.381652i
$71$	−4.14333			−0.491723			−0.245862	−	0.969305i	$-0.579071\pi$
$71$	−4.14333			−0.491723			−0.245862	+	0.969305i	$0.579071\pi$
$72$	7.19425	−	4.49920i	0.847851	−	0.530235i
$73$	10.5544			1.23530			0.617651	−	0.786452i	$-0.288084\pi$
$73$	10.5544			1.23530			0.617651	+	0.786452i	$0.288084\pi$
$74$	0.395351	+	9.78408i	0.0459586	+	1.13738i
$75$	−0.175742	−	0.0552771i	−0.0202930	−	0.00638285i
$76$	−8.74630	+	0.707989i	−1.00327	+	0.0812119i
$77$	1.90978	+	3.30783i	0.217639	+	0.376963i
$78$	−6.98198	−	7.01773i	−0.790554	−	0.794601i
$79$	−3.13471	−	1.80983i	−0.352683	−	0.203622i	0.313183	−	0.949693i	$-0.398605\pi$
$79$	−3.13471	−	1.80983i	−0.352683	−	0.203622i	−0.665866	+	0.746071i	$0.731938\pi$
$80$	5.71966	+	6.99909i	0.639478	+	0.782523i
$81$	5.76592	−	6.91044i	0.640657	−	0.767827i
$82$	5.99634	−	3.79277i	0.662185	−	0.418842i
$83$	8.83359	+	5.10008i	0.969613	+	0.559806i	0.899118	−	0.437706i	$-0.144209\pi$
$83$	8.83359	+	5.10008i	0.969613	+	0.559806i	0.0704944	+	0.997512i	$0.477542\pi$
$84$	−0.769374	+	3.37758i	−0.0839456	+	0.368524i
$85$	−10.0999	+	5.83118i	−1.09549	+	0.632480i
$86$	8.05877	−	15.3588i	0.869000	−	1.65618i
$87$	11.8202	+	3.71788i	1.26726	+	0.398598i
$88$	−9.94023	−	4.23130i	−1.05963	−	0.451058i
$89$		−	15.9455i		−	1.69022i	−0.534590	−	0.845112i	$-0.679534\pi$
$89$		−	15.9455i		−	1.69022i	0.534590	−	0.845112i	$-0.320466\pi$
$90$	8.07618	+	5.16622i	0.851304	+	0.544568i
$91$	4.04138			0.423652
$92$	−0.910844	−	1.31897i	−0.0949621	−	0.137512i
$93$	4.08075	+	4.44715i	0.423154	+	0.461148i
$94$	6.45232	−	12.2971i	0.665506	−	1.26835i
$95$	−4.95722	−	8.58616i	−0.508600	−	0.880922i
$96$	−4.00227	−	8.94325i	−0.408480	−	0.912767i
$97$	−1.03421	+	1.79131i	−0.105008	+	0.181880i	−0.913742	−	0.406296i	$-0.866820\pi$
$97$	−1.03421	+	1.79131i	−0.105008	+	0.181880i	0.808733	+	0.588175i	$0.200154\pi$
$98$	−0.755979	−	1.19520i	−0.0763654	−	0.120733i
$99$	−11.4164	−	0.982834i	−1.14740	−	0.0987785i
$100$	−0.0911544	+	0.192212i	−0.00911544	+	0.0192212i
$101$	4.00188	−	6.93147i	0.398202	−	0.689707i	−0.595302	−	0.803502i	$-0.702968\pi$
$101$	4.00188	−	6.93147i	0.398202	−	0.689707i	0.993504	+	0.113795i	$0.0363009\pi$
$102$	12.2193	−	3.24073i	1.20989	−	0.320880i
$103$	2.47708	−	1.43015i	0.244074	−	0.140916i	−0.372974	−	0.927842i	$-0.621662\pi$
$103$	2.47708	−	1.43015i	0.244074	−	0.140916i	0.617048	+	0.786926i	$0.288328\pi$
$104$	−9.13599	+	6.86992i	−0.895858	+	0.673651i
$105$	−3.82060	+	0.849790i	−0.372852	+	0.0829310i
$106$	7.56404	−	0.305645i	0.734685	−	0.0296868i
$107$		−	11.1353i		−	1.07649i	−0.842789	−	0.538245i	$-0.819088\pi$
$107$		−	11.1353i		−	1.07649i	0.842789	−	0.538245i	$-0.180912\pi$
$108$	−6.98707	−	7.69291i	−0.672331	−	0.740251i
$109$		−	5.59452i		−	0.535858i	−0.963439	−	0.267929i	$-0.913661\pi$
$109$		−	5.59452i		−	0.535858i	0.963439	−	0.267929i	$-0.0863392\pi$
$110$	−0.492825	−	12.1963i	−0.0469890	−	1.16288i
$111$	11.7067	−	2.60384i	1.11115	−	0.247146i
$112$	3.74068	+	1.41679i	0.353461	+	0.133874i
$113$	2.13565	−	1.23302i	0.200905	−	0.115993i	−0.396172	−	0.918176i	$-0.629662\pi$
$113$	2.13565	−	1.23302i	0.200905	−	0.115993i	0.597078	+	0.802183i	$0.296328\pi$
$114$	2.75502	+	10.3879i	0.258031	+	0.972915i
$115$	0.905536	−	1.56843i	0.0844416	−	0.146257i
$116$	6.13094	−	12.9279i	0.569244	−	1.20033i
$117$	−6.94032	+	9.94117i	−0.641633	+	0.919061i
$118$	0.758783	−	0.479941i	0.0698516	−	0.0441821i
$119$	−2.58048	+	4.46952i	−0.236552	+	0.409720i
$120$	7.19233	−	8.41565i	0.656567	−	0.768240i
$121$	1.79450	+	3.10817i	0.163137	+	0.282561i
$122$	−7.44476	−	3.90628i	−0.674017	−	0.353658i
$123$	−5.87516	−	6.40268i	−0.529746	−	0.577310i
$124$	5.73486	−	3.96033i	0.515006	−	0.355648i
$125$	11.0583			0.989082
$126$	4.23825	+	0.192940i	0.377573	+	0.0171884i
$127$			20.1325i			1.78647i	0.449592	+	0.893234i	$0.351569\pi$
$127$			20.1325i			1.78647i	−0.449592	+	0.893234i	$0.648431\pi$
$128$	−10.8646	+	3.15594i	−0.960306	+	0.278949i
$129$	−20.2640	−	6.37374i	−1.78414	−	0.561177i
$130$	−11.4365	−	6.00074i	−1.00305	−	0.526300i
$131$	−1.55482	+	0.897674i	−0.135845	+	0.0784301i	−0.566382	−	0.824143i	$-0.691657\pi$
$131$	−1.55482	+	0.897674i	−0.135845	+	0.0784301i	0.430537	+	0.902573i	$0.358324\pi$
$132$	−2.93867	+	12.9009i	−0.255778	+	1.12288i
$133$	−3.79965	−	2.19373i	−0.329471	−	0.190220i
$134$	7.00225	+	11.0705i	0.604902	+	0.956346i
$135$	4.47082	−	10.8574i	0.384786	−	0.934458i
$136$	−1.76425	−	14.4904i	−0.151283	−	1.24254i
$137$	13.8648	+	8.00482i	1.18455	+	0.683898i	0.957062	−	0.289884i	$-0.0936168\pi$
$137$	13.8648	+	8.00482i	1.18455	+	0.683898i	0.227484	+	0.973782i	$0.426950\pi$
$138$	−1.39170	+	1.38461i	−0.118470	+	0.117866i
$139$	−1.10069	−	1.90646i	−0.0933597	−	0.161704i	0.815563	−	0.578668i	$-0.196427\pi$
$139$	−1.10069	−	1.90646i	−0.0933597	−	0.161704i	−0.908923	+	0.416964i	$0.863094\pi$
$140$	0.364645	+	4.50472i	0.0308181	+	0.380718i
$141$	−16.2245	−	5.10318i	−1.36635	−	0.429766i
$142$	5.85478	−	0.236577i	0.491322	−	0.0198531i
$143$	15.4363			1.29085
$144$	−9.90901	+	6.76841i	−0.825751	+	0.564035i
$145$	16.1661			1.34252
$146$	−14.9140	+	0.602640i	−1.23429	+	0.0498749i
$147$	−1.27619	+	1.17104i	−0.105258	+	0.0965860i
$148$	−1.11731	−	13.8029i	−0.0918423	−	1.13459i
$149$	−10.3890	−	17.9942i	−0.851098	−	1.47415i	−0.880218	−	0.474570i	$-0.842604\pi$
$149$	−10.3890	−	17.9942i	−0.851098	−	1.47415i	0.0291196	−	0.999576i	$-0.490730\pi$
$150$	0.251490	+	0.0680753i	0.0205341	+	0.00555833i
$151$	13.9896	+	8.07690i	1.13846	+	0.657289i	0.946048	−	0.324026i	$-0.105037\pi$
$151$	13.9896	+	8.07690i	1.13846	+	0.657289i	0.192409	+	0.981315i	$0.438370\pi$
$152$	12.3186	−	1.49983i	0.999172	−	0.121652i
$153$	−6.56283	−	14.0232i	−0.530573	−	1.13370i
$154$	−2.88750	−	4.56512i	−0.232682	−	0.367868i
$155$	6.81952	+	3.93725i	0.547757	+	0.316247i
$156$	10.2667	+	9.51781i	0.821991	+	0.762035i
$157$	20.4542	−	11.8093i	1.63243	−	0.942482i	0.649085	−	0.760716i	$-0.275152\pi$
$157$	20.4542	−	11.8093i	1.63243	−	0.942482i	0.983342	−	0.181766i	$-0.0581814\pi$
$158$	4.53288	+	2.37841i	0.360617	+	0.189216i
$159$	−2.01302	−	9.05041i	−0.159643	−	0.717745i
$160$	−8.48186	−	9.56356i	−0.670550	−	0.756066i
$161$		−	0.801456i		−	0.0631636i
$162$	−7.75301	+	10.0941i	−0.609134	+	0.793067i
$163$	9.70763			0.760360			0.380180	−	0.924913i	$-0.375862\pi$
$163$	9.70763			0.760360			0.380180	+	0.924913i	$0.375862\pi$
$164$	−8.25664	+	5.70180i	−0.644735	+	0.445235i
$165$	−14.5930	+	3.24582i	−1.13606	+	0.252687i
$166$	−12.7736	−	6.70233i	−0.991424	−	0.520202i
$167$	−4.08809	−	7.08077i	−0.316346	−	0.547927i	0.663377	−	0.748285i	$-0.269123\pi$
$167$	−4.08809	−	7.08077i	−0.316346	−	0.547927i	−0.979723	+	0.200359i	$0.935789\pi$
$168$	0.894318	−	4.81666i	0.0689981	−	0.371613i
$169$	1.66638	−	2.88626i	0.128183	−	0.222020i
$170$	13.9388	−	8.81650i	1.06906	−	0.676194i
$171$	11.9214	−	5.57922i	0.911653	−	0.426653i
$172$	−10.5106	+	22.1630i	−0.801424	+	1.68991i
$173$	−5.25508	+	9.10207i	−0.399536	+	0.692017i	−0.993669	−	0.112350i	$-0.964162\pi$
$173$	−5.25508	+	9.10207i	−0.399536	+	0.692017i	0.594132	+	0.804367i	$0.297496\pi$
$174$	−16.9150	−	4.57867i	−1.28232	−	0.347108i
$175$	−0.0921152	+	0.0531827i	−0.00696326	+	0.00402024i
$176$	14.2877	+	5.41152i	1.07698	+	0.407908i
$177$	−0.743449	−	0.810201i	−0.0558810	−	0.0608985i
$178$	0.910464	+	22.5320i	0.0682421	+	1.68885i
$179$		−	16.8090i		−	1.25636i	−0.778067	−	0.628182i	$-0.783800\pi$
$179$		−	16.8090i		−	1.25636i	0.778067	−	0.628182i	$-0.216200\pi$
$180$	−11.7071	−	6.83905i	−0.872597	−	0.509753i
$181$		−	13.0346i		−	0.968855i	−0.874831	−	0.484428i	$-0.839028\pi$
$181$		−	13.0346i		−	0.968855i	0.874831	−	0.484428i	$-0.160972\pi$
$182$	−5.71072	+	0.230756i	−0.423307	+	0.0171048i
$183$	−3.08950	+	9.82243i	−0.228383	+	0.726095i
$184$	1.36239	+	1.81178i	0.100437	+	0.133566i
$185$	13.5502	−	7.82321i	0.996231	−	0.575174i
$186$	−6.02027	−	6.05109i	−0.441428	−	0.443687i
$187$	−9.85629	+	17.0716i	−0.720763	+	1.24840i
$188$	−8.41537	+	17.7450i	−0.613754	+	1.29419i
$189$	−0.688965	−	5.15027i	−0.0501148	−	0.374627i
$190$	7.49511	+	11.8497i	0.543752	+	0.859669i
$191$	8.30601	−	14.3864i	0.601002	−	1.04097i	−0.391668	−	0.920107i	$-0.628102\pi$
$191$	8.30601	−	14.3864i	0.601002	−	1.04097i	0.992670	−	0.120859i	$-0.0385648\pi$
$192$	6.16610	+	12.4088i	0.445000	+	0.895531i
$193$	4.09630	+	7.09500i	0.294858	+	0.510709i	0.974952	−	0.222416i	$-0.0713943\pi$
$193$	4.09630	+	7.09500i	0.294858	+	0.510709i	−0.680094	+	0.733125i	$0.738061\pi$
$194$	1.35912	−	2.59028i	0.0975793	−	0.185971i
$195$	−4.74603	+	15.0890i	−0.339870	+	1.08055i
$196$	1.13649	+	1.64572i	0.0811777	+	0.117551i
$197$	−8.71068			−0.620610			−0.310305	−	0.950637i	$-0.600431\pi$
$197$	−8.71068			−0.620610			−0.310305	+	0.950637i	$0.600431\pi$
$198$	16.1882	+	0.736943i	1.15045	+	0.0523723i
$199$			18.2167i			1.29135i	0.763614	+	0.645673i	$0.223423\pi$
$199$			18.2167i			1.29135i	−0.763614	+	0.645673i	$0.776577\pi$
$200$	0.117832	−	0.276812i	0.00833196	−	0.0195735i
$201$	11.8207	−	10.8468i	0.833767	−	0.765073i
$202$	−5.25913	+	10.0231i	−0.370031	+	0.705222i
$203$	6.19557	−	3.57701i	0.434843	−	0.251057i
$204$	−17.0815	+	5.27705i	−1.19595	+	0.369467i
$205$	−9.81824	−	5.66856i	−0.685736	−	0.395910i
$206$	−3.41861	+	2.16232i	−0.238186	+	0.150656i
$207$	1.97146	+	1.37635i	0.137026	+	0.0956630i
$208$	12.5174	−	10.2293i	0.867929	−	0.709272i
$209$	−14.5130	−	8.37906i	−1.00388	−	0.579592i
$210$	5.35021	−	1.41895i	0.369200	−	0.0979171i
$211$	11.3159	+	19.5998i	0.779022	+	1.34931i	0.932506	+	0.361154i	$0.117617\pi$
$211$	11.3159	+	19.5998i	0.779022	+	1.34931i	−0.153484	+	0.988151i	$0.549049\pi$
$212$	−10.6710	+	0.863789i	−0.732887	+	0.0593253i
$213$	−1.55814	−	7.00527i	−0.106762	−	0.479993i
$214$	0.635807	+	15.7348i	0.0434628	+	1.07561i
$215$	−27.7144			−1.89011
$216$	10.3124	+	10.4716i	0.701670	+	0.712502i
$217$	3.48471			0.236558
$218$	0.319438	+	7.90539i	0.0216351	+	0.535421i
$219$	3.96908	+	17.8447i	0.268206	+	1.20583i
$220$	1.39278	+	17.2060i	0.0939013	+	1.16003i
$221$	10.4287	+	18.0630i	0.701511	+	1.21505i
$222$	−16.3936	+	4.34782i	−1.10027	+	0.291807i
$223$	−5.59246	−	3.22881i	−0.374499	−	0.216217i	0.300923	−	0.953648i	$-0.402705\pi$
$223$	−5.59246	−	3.22881i	−0.374499	−	0.216217i	−0.675422	+	0.737431i	$0.736039\pi$
$224$	−5.36671	−	1.78843i	−0.358578	−	0.119494i
$225$	0.0273696	−	0.317921i	0.00182464	−	0.0211947i
$226$	−2.94740	+	1.86427i	−0.196058	+	0.124010i
$227$	2.99379	+	1.72846i	0.198705	+	0.114722i	0.596051	−	0.802947i	$-0.296736\pi$
$227$	2.99379	+	1.72846i	0.198705	+	0.114722i	−0.397347	+	0.917669i	$0.630069\pi$
$228$	−4.48614	−	14.5214i	−0.297102	−	0.961704i
$229$	8.46450	−	4.88698i	0.559350	−	0.322941i	−0.193535	−	0.981093i	$-0.561995\pi$
$229$	8.46450	−	4.88698i	0.559350	−	0.322941i	0.752885	+	0.658153i	$0.228662\pi$
$230$	−1.19002	+	2.26800i	−0.0784677	+	0.149547i
$231$	−4.87447	+	4.47286i	−0.320717	+	0.294293i
$232$	−7.92522	+	18.6180i	−0.520317	+	1.22233i
$233$			14.5341i			0.952159i	0.879402	+	0.476080i	$0.157943\pi$
$233$			14.5341i			0.952159i	−0.879402	+	0.476080i	$0.842057\pi$
$234$	9.23947	−	14.4438i	0.604003	−	0.944218i
$235$	−22.1897			−1.44750
$236$	−1.04480	+	0.721511i	−0.0680108	+	0.0469663i
$237$	1.88110	−	5.98057i	0.122191	−	0.388480i
$238$	3.39117	−	6.46305i	0.219817	−	0.418937i
$239$	−4.79900	−	8.31212i	−0.310422	−	0.537666i	0.668032	−	0.744133i	$-0.267137\pi$
$239$	−4.79900	−	8.31212i	−0.310422	−	0.537666i	−0.978454	+	0.206466i	$0.933804\pi$
$240$	−9.68268	+	12.3025i	−0.625014	+	0.794122i
$241$	−8.26406	+	14.3138i	−0.532335	+	0.922031i	0.466953	+	0.884282i	$0.345352\pi$
$241$	−8.26406	+	14.3138i	−0.532335	+	0.922031i	−0.999287	+	0.0377484i	$0.987981\pi$
$242$	−2.71321	−	4.28957i	−0.174412	−	0.275744i
$243$	13.8520	+	7.14989i	0.888609	+	0.458666i
$244$	10.7429	+	5.09472i	0.687746	+	0.326156i
$245$	−1.12986	+	1.95698i	−0.0721843	+	0.125027i
$246$	8.66754	+	8.71192i	0.552622	+	0.555451i
$247$	−15.3558	+	8.86569i	−0.977067	+	0.564110i
$248$	−7.87758	+	5.92364i	−0.500227	+	0.376151i
$249$	−5.30092	+	16.8532i	−0.335932	+	1.06803i
$250$	−15.6260	+	0.631409i	−0.988276	+	0.0399338i
$251$		−	28.0214i		−	1.76869i	−0.466832	−	0.884346i	$-0.654605\pi$
$251$		−	28.0214i		−	1.76869i	0.466832	−	0.884346i	$-0.345395\pi$
$252$	−5.99992	−	0.0306381i	−0.377960	−	0.00193002i
$253$		−	3.06121i		−	0.192456i
$254$	−1.14953	−	28.4484i	−0.0721280	−	1.78501i
$255$	−13.6571	−	14.8834i	−0.855242	−	0.932033i
$256$	15.1722	−	5.07989i	0.948261	−	0.317493i
$257$	−2.01486	+	1.16328i	−0.125684	+	0.0725635i	−0.561524	−	0.827461i	$-0.689785\pi$
$257$	−2.01486	+	1.16328i	−0.125684	+	0.0725635i	0.435840	+	0.900024i	$0.356451\pi$
$258$	28.9982	+	7.84944i	1.80535	+	0.488685i
$259$	3.46202	−	5.99639i	0.215119	−	0.372598i
$260$	16.5031	+	7.82641i	1.02348	+	0.485373i
$261$	−1.84085	+	21.3830i	−0.113945	+	1.32357i
$262$	2.14579	−	1.35724i	0.132568	−	0.0838508i
$263$	1.56134	−	2.70432i	0.0962762	−	0.166755i	−0.813864	−	0.581055i	$-0.802640\pi$
$263$	1.56134	−	2.70432i	0.0962762	−	0.166755i	0.910141	+	0.414300i	$0.135973\pi$
$264$	3.41590	−	18.3975i	0.210234	−	1.13229i
$265$	−6.04810	−	10.4756i	−0.371532	−	0.643512i
$266$	5.49439	+	2.88291i	0.336882	+	0.176763i
$267$	26.9597	−	5.99646i	1.64990	−	0.366977i
$268$	−10.5267	−	15.2435i	−0.643021	−	0.931143i
$269$	13.7534			0.838561			0.419281	−	0.907857i	$-0.362282\pi$
$269$	13.7534			0.838561			0.419281	+	0.907857i	$0.362282\pi$
$270$	−5.69759	+	15.5975i	−0.346744	+	0.949232i
$271$		−	15.2903i		−	0.928818i	−0.885621	−	0.464409i	$-0.846267\pi$
$271$		−	15.2903i		−	0.928818i	0.885621	−	0.464409i	$-0.153733\pi$
$272$	3.32037	+	20.3751i	0.201327	+	1.23542i
$273$	1.51980	+	6.83290i	0.0919823	+	0.413546i
$274$	−20.0488	−	10.5196i	−1.21119	−	0.635514i
$275$	−0.351839	+	0.203134i	−0.0212167	+	0.0122495i
$276$	1.88750	−	2.03601i	0.113614	−	0.122553i
$277$	−7.56397	−	4.36706i	−0.454475	−	0.262391i	0.255243	−	0.966877i	$-0.417844\pi$
$277$	−7.56397	−	4.36706i	−0.454475	−	0.262391i	−0.709718	+	0.704486i	$0.751178\pi$
$278$	1.66420	+	2.63109i	0.0998123	+	0.157803i
$279$	−5.98435	+	8.57185i	−0.358273	+	0.513183i
$280$	−0.772477	−	6.34462i	−0.0461643	−	0.379164i
$281$	5.98458	+	3.45520i	0.357010	+	0.206120i	0.667768	−	0.744369i	$-0.267250\pi$
$281$	5.98458	+	3.45520i	0.357010	+	0.206120i	−0.310758	+	0.950489i	$0.600583\pi$
$282$	23.2176	+	6.28471i	1.38259	+	0.374249i
$283$	−0.138945	−	0.240660i	−0.00825944	−	0.0143058i	0.861866	−	0.507136i	$-0.169296\pi$
$283$	−0.138945	−	0.240660i	−0.00825944	−	0.0143058i	−0.870126	+	0.492830i	$0.835962\pi$
$284$	−8.25965	+	0.668597i	−0.490120	+	0.0396739i
$285$	12.6527	−	11.6102i	0.749481	−	0.687731i
$286$	−21.8124	+	0.881386i	−1.28979	+	0.0521175i
$287$	−5.01703			−0.296146
$288$	13.6156	−	10.1300i	0.802305	−	0.596914i
$289$	−9.63550			−0.566794
$290$	−22.8437	+	0.923060i	−1.34143	+	0.0542039i
$291$	−3.41755	−	1.07494i	−0.200340	−	0.0630141i
$292$	21.0400	−	1.70313i	1.23127	−	0.0996684i
$293$	13.1703	+	22.8116i	0.769415	+	1.33267i	0.937881	+	0.346958i	$0.112785\pi$
$293$	13.1703	+	22.8116i	0.769415	+	1.33267i	−0.168466	+	0.985708i	$0.553881\pi$
$294$	1.73647	−	1.72762i	0.101273	−	0.100757i
$295$	−1.24241	−	0.717305i	−0.0723359	−	0.0417631i
$296$	2.36695	+	19.4406i	0.137576	+	1.12996i
$297$	−2.63154	−	19.6718i	−0.152698	−	1.14147i
$298$	15.7077	+	24.8338i	0.909922	+	1.43858i
$299$	−2.80505	−	1.61949i	−0.162220	−	0.0936578i
$300$	−0.359258	−	0.0818349i	−0.0207418	−	0.00472474i
$301$	−10.6214	+	6.13225i	−0.612205	+	0.353457i
$302$	−20.2293	−	10.6144i	−1.16407	−	0.610788i
$303$	13.2242	+	4.15948i	0.759711	+	0.238956i
$304$	−17.3213	+	2.82272i	−0.993446	+	0.161894i
$305$			13.4338i			0.769219i
$306$	10.0744	+	19.4408i	0.575914	+	1.11136i
$307$	14.6693			0.837223			0.418612	−	0.908165i	$-0.362517\pi$
$307$	14.6693			0.837223			0.418612	+	0.908165i	$0.362517\pi$
$308$	4.34088	+	6.28592i	0.247344	+	0.358174i
$309$	3.34952	+	3.65027i	0.190548	+	0.207657i
$310$	−9.86120	−	5.17419i	−0.560078	−	0.293874i
$311$	5.55222	+	9.61673i	0.314838	+	0.545315i	0.979403	−	0.201915i	$-0.0647166\pi$
$311$	5.55222	+	9.61673i	0.314838	+	0.545315i	−0.664565	+	0.747230i	$0.731383\pi$
$312$	−15.0509	−	12.8630i	−0.852088	−	0.728226i
$313$	−12.6698	+	21.9448i	−0.716140	+	1.24039i	0.246378	+	0.969174i	$0.420760\pi$
$313$	−12.6698	+	21.9448i	−0.716140	+	1.24039i	−0.962518	+	0.271218i	$0.912574\pi$
$314$	−28.2288	+	17.8551i	−1.59304	+	1.00762i
$315$	−2.87354	−	6.14004i	−0.161905	−	0.345952i
$316$	−6.54104	−	3.10202i	−0.367962	−	0.174502i
$317$	0.808447	−	1.40027i	0.0454069	−	0.0786470i	−0.842429	−	0.538808i	$-0.818875\pi$
$317$	0.808447	−	1.40027i	0.0454069	−	0.0786470i	0.887836	+	0.460161i	$0.152208\pi$
$318$	3.36129	+	12.6738i	0.188492	+	0.710714i
$319$	23.6643	−	13.6626i	1.32495	−	0.764958i
$320$	12.5314	+	13.0296i	0.700529	+	0.728376i
$321$	18.8268	−	4.18752i	1.05081	−	0.233725i
$322$	0.0457618	+	1.13251i	0.00255021	+	0.0631121i
$323$		−	22.6435i		−	1.25992i
$324$	10.3791	−	14.7063i	0.576618	−	0.817014i
$325$			0.429864i			0.0238445i
$326$	−13.7175	+	0.554289i	−0.759740	+	0.0306993i
$327$	9.45884	−	2.10387i	0.523075	−	0.116344i
$328$	11.3416	−	8.52842i	0.626233	−	0.470903i
$329$	−8.50407	+	4.90983i	−0.468845	+	0.270688i
$330$	20.4354	−	5.41977i	1.12493	−	0.298349i
$331$	4.08150	−	7.06936i	0.224339	−	0.388567i	−0.731782	−	0.681539i	$-0.761311\pi$
$331$	4.08150	−	7.06936i	0.224339	−	0.388567i	0.956121	+	0.292972i	$0.0946443\pi$
$332$	18.4326	+	8.74145i	1.01162	+	0.479749i
$333$	8.80481	+	18.8137i	0.482501	+	1.03098i
$334$	6.18101	+	9.77214i	0.338210	+	0.534707i
$335$	10.4653	−	18.1265i	0.571783	−	0.990357i
$336$	−0.988702	+	6.85729i	−0.0539381	+	0.374096i
$337$	−7.51325	−	13.0133i	−0.409273	−	0.708881i	0.585536	−	0.810647i	$-0.300884\pi$
$337$	−7.51325	−	13.0133i	−0.409273	−	0.708881i	−0.994808	+	0.101765i	$0.967551\pi$
$338$	−2.18990	+	4.17361i	−0.119115	+	0.227015i
$339$	2.88784	+	3.14713i	0.156846	+	0.170929i
$340$	−19.1930	+	13.2541i	−1.04089	+	0.718806i
$341$	13.3101			0.720780
$342$	−16.5271	+	8.56446i	−0.893684	+	0.463113i
$343$			1.00000i			0.0539949i
$344$	13.5866	−	31.9178i	0.732541	−	1.72089i
$345$	2.99234	+	0.941196i	0.161102	+	0.0506723i
$346$	6.90603	−	13.1618i	0.371271	−	0.707584i
$347$	−5.52936	+	3.19238i	−0.296832	+	0.171376i	−0.641019	−	0.767525i	$-0.721488\pi$
$347$	−5.52936	+	3.19238i	−0.296832	+	0.171376i	0.344187	+	0.938901i	$0.388155\pi$
$348$	24.1633	+	5.50412i	1.29529	+	0.295052i
$349$	3.96982	+	2.29198i	0.212500	+	0.122687i	0.602473	−	0.798140i	$-0.294182\pi$
$349$	3.96982	+	2.29198i	0.212500	+	0.122687i	−0.389973	+	0.920826i	$0.627516\pi$
$350$	0.127128	−	0.0804101i	0.00679526	−	0.00429810i
$351$	−19.4178	−	7.99578i	−1.03645	−	0.426783i
$352$	−20.4984	−	6.83099i	−1.09257	−	0.364093i
$353$	−8.31089	−	4.79830i	−0.442344	−	0.255388i	0.262247	−	0.965001i	$-0.415536\pi$
$353$	−8.31089	−	4.79830i	−0.442344	−	0.255388i	−0.704591	+	0.709613i	$0.748870\pi$
$354$	1.09680	+	1.10241i	0.0582942	+	0.0585926i
$355$	−4.68140	−	8.10843i	−0.248463	−	0.430351i
$356$	−2.57308	−	31.7871i	−0.136373	−	1.68471i
$357$	−8.52718	−	2.68210i	−0.451306	−	0.141952i
$358$	0.959766	+	23.7521i	0.0507252	+	1.25534i
$359$	−31.6107			−1.66835			−0.834176	−	0.551499i	$-0.814056\pi$
$359$	−31.6107			−1.66835			−0.834176	+	0.551499i	$0.814056\pi$
$360$	16.9334	+	8.99553i	0.892466	+	0.474106i
$361$	0.249740			0.0131442
$362$	0.744255	+	18.4187i	0.0391172	+	0.968065i
$363$	−4.58025	+	4.20288i	−0.240401	+	0.220594i
$364$	8.05641	−	0.652145i	0.422271	−	0.0341817i
$365$	11.9251	+	20.6548i	0.624186	+	1.08112i
$366$	3.80481	−	14.0561i	0.198881	−	0.734724i
$367$	−20.2718	−	11.7039i	−1.05818	−	0.610941i	−0.133252	−	0.991082i	$-0.542542\pi$
$367$	−20.2718	−	11.7039i	−1.05818	−	0.610941i	−0.924928	+	0.380141i	$0.875875\pi$
$368$	−2.02859	−	2.48236i	−0.105747	−	0.129402i
$369$	8.61582	−	12.3411i	0.448522	−	0.642453i
$370$	−18.7006	+	11.8284i	−0.972196	+	0.614927i
$371$	−4.63579	−	2.67648i	−0.240678	−	0.138956i
$372$	8.85251	+	8.20681i	0.458981	+	0.425503i
$373$	−28.2693	+	16.3213i	−1.46373	+	0.845084i	−0.999181	−	0.0404635i	$-0.987117\pi$
$373$	−28.2693	+	16.3213i	−1.46373	+	0.845084i	−0.464548	+	0.885548i	$0.653783\pi$
$374$	12.9528	−	24.6860i	0.669772	−	1.27648i
$375$	4.15856	+	18.6966i	0.214747	+	0.965488i
$376$	10.8782	−	25.5552i	0.561001	−	1.31791i
$377$		−	28.9121i		−	1.48905i
$378$	1.26762	+	7.23831i	0.0651994	+	0.372299i
$379$	−36.1439			−1.85659			−0.928293	−	0.371849i	$-0.878724\pi$
$379$	−36.1439			−1.85659			−0.928293	+	0.371849i	$0.878724\pi$
$380$	−11.2676	−	16.3164i	−0.578018	−	0.837014i
$381$	−34.0386	+	7.57099i	−1.74385	+	0.387874i
$382$	−10.9155	+	20.8032i	−0.558483	+	1.06438i
$383$	−9.62916	−	16.6782i	−0.492027	−	0.852216i	0.507931	−	0.861398i	$-0.330411\pi$
$383$	−9.62916	−	16.6782i	−0.492027	−	0.852216i	−0.999958	+	0.00918191i	$0.997077\pi$
$384$	−9.42160	−	17.1824i	−0.480794	−	0.876834i
$385$	−4.31558	+	7.47480i	−0.219942	+	0.380951i
$386$	−6.19343	−	9.79177i	−0.315237	−	0.498388i
$387$	3.15585	−	36.6579i	0.160421	−	1.86343i
$388$	−1.77262	+	3.73782i	−0.0899912	+	0.189759i
$389$	−4.50524	+	7.80331i	−0.228425	+	0.395643i	−0.957341	−	0.288959i	$-0.906691\pi$
$389$	−4.50524	+	7.80331i	−0.228425	+	0.395643i	0.728917	+	0.684602i	$0.240024\pi$
$390$	5.84487	−	21.5927i	0.295967	−	1.09339i
$391$	3.58212	−	2.06814i	0.181156	−	0.104590i
$392$	−1.69989	−	2.26061i	−0.0858576	−	0.114178i
$393$	−2.10243	−	2.29120i	−0.106054	−	0.115576i
$394$	12.3087	−	0.497365i	0.620104	−	0.0250569i
$395$		−	8.17944i		−	0.411552i
$396$	−22.9170	−	0.117024i	−1.15162	−	0.00588067i
$397$		−	31.6444i		−	1.58818i	−0.607797	−	0.794092i	$-0.707947\pi$
$397$		−	31.6444i		−	1.58818i	0.607797	−	0.794092i	$-0.292053\pi$
$398$	−1.04014	−	25.7413i	−0.0521376	−	1.29029i
$399$	2.28012	−	7.24916i	0.114149	−	0.362912i
$400$	−0.150698	+	0.397879i	−0.00753489	+	0.0198940i
$401$	−18.4050	+	10.6261i	−0.919101	+	0.530643i	−0.883348	−	0.468718i	$-0.844716\pi$
$401$	−18.4050	+	10.6261i	−0.919101	+	0.530643i	−0.0357527	+	0.999361i	$0.511383\pi$
$402$	−16.0840	+	16.0021i	−0.802198	+	0.798112i
$403$	7.04153	−	12.1963i	0.350763	−	0.607540i
$404$	6.85916	−	14.4635i	0.341256	−	0.719586i
$405$	20.0383	+	3.47593i	0.995711	+	0.172720i
$406$	−8.55047	+	5.40829i	−0.424353	+	0.268409i
$407$	13.2234	−	22.9035i	0.655458	−	1.13529i
$408$	23.8359	−	8.43211i	1.18005	−	0.417452i
$409$	4.86952	+	8.43425i	0.240782	+	0.417047i	0.960937	−	0.276766i	$-0.0892627\pi$
$409$	4.86952	+	8.43425i	0.240782	+	0.417047i	−0.720155	+	0.693813i	$0.755929\pi$
$410$	14.1974	+	7.44942i	0.701161	+	0.367900i
$411$	−8.32005	+	26.4519i	−0.410398	+	1.30477i
$412$	4.70724	−	3.25068i	0.231909	−	0.160150i
$413$	−0.634860			−0.0312394
$414$	−2.86437	−	1.83230i	−0.140776	−	0.0900527i
$415$			23.0496i			1.13146i
$416$	−17.1038	+	15.1693i	−0.838585	+	0.743736i
$417$	2.80939	−	2.57792i	0.137576	−	0.126241i
$418$	20.9861	+	11.0115i	1.02646	+	0.538588i
$419$	−5.47817	+	3.16283i	−0.267626	+	0.154514i	−0.627808	−	0.778368i	$-0.716048\pi$
$419$	−5.47817	+	3.16283i	−0.267626	+	0.154514i	0.360182	+	0.932882i	$0.382715\pi$
$420$	−7.47915	+	2.31056i	−0.364945	+	0.112744i
$421$	22.4959	+	12.9880i	1.09638	+	0.632998i	0.935269	−	0.353938i	$-0.115158\pi$
$421$	22.4959	+	12.9880i	1.09638	+	0.632998i	0.161115	+	0.986936i	$0.448491\pi$
$422$	−17.1092	−	27.0496i	−0.832864	−	1.31675i
$423$	2.52676	−	29.3504i	0.122855	−	1.42707i
$424$	15.0294	−	1.82988i	0.729894	−	0.0888669i
$425$	−0.475403	−	0.274474i	−0.0230604	−	0.0133139i
$426$	2.60173	+	9.80991i	0.126054	+	0.475292i
$427$	2.97245	+	5.14843i	0.143847	+	0.249150i
$428$	−1.79687	−	22.1980i	−0.0868548	−	1.07298i
$429$	5.80495	+	26.0986i	0.280266	+	1.26005i
$430$	39.1621	−	1.58245i	1.88857	−	0.0763123i
$431$	−13.1059			−0.631290			−0.315645	−	0.948877i	$-0.602221\pi$
$431$	−13.1059			−0.631290			−0.315645	+	0.948877i	$0.602221\pi$
$432$	−15.1700	−	14.2082i	−0.729865	−	0.683591i
$433$	21.8854			1.05174			0.525872	−	0.850564i	$-0.323739\pi$
$433$	21.8854			1.05174			0.525872	+	0.850564i	$0.323739\pi$
$434$	−4.92411	+	0.198971i	−0.236365	+	0.00955093i
$435$	6.07942	+	27.3326i	0.291486	+	1.31050i
$436$	−0.902770	−	11.1526i	−0.0432348	−	0.534111i
$437$	1.75817	+	3.04525i	0.0841049	+	0.145674i
$438$	−6.62746	−	24.9890i	−0.316672	−	1.19402i
$439$	3.73057	+	2.15384i	0.178050	+	0.102797i	0.586376	−	0.810039i	$-0.300554\pi$
$439$	3.73057	+	2.15384i	0.178050	+	0.102797i	−0.408326	+	0.912836i	$0.633887\pi$
$440$	−2.95052	−	24.2336i	−0.140661	−	1.15529i
$441$	−2.45984	−	1.71731i	−0.117135	−	0.0817769i
$442$	−15.7678	−	24.9287i	−0.749996	−	1.18574i
$443$	9.82529	+	5.67264i	0.466814	+	0.269515i	0.714905	−	0.699222i	$-0.246470\pi$
$443$	9.82529	+	5.67264i	0.466814	+	0.269515i	−0.248091	+	0.968737i	$0.579803\pi$
$444$	22.9169	−	7.07978i	1.08759	−	0.335991i
$445$	31.2051	−	18.0163i	1.47926	−	0.854054i
$446$	8.08685	+	4.24318i	0.382923	+	0.200920i
$447$	26.5166	−	24.3319i	1.25419	−	1.15086i
$448$	7.68560	+	2.22072i	0.363110	+	0.104919i
$449$			19.8155i			0.935149i	0.883954	+	0.467575i	$0.154872\pi$
$449$			19.8155i			0.935149i	−0.883954	+	0.467575i	$0.845128\pi$
$450$	−0.0205221	+	0.450804i	−0.000967421	+	0.0212511i
$451$	−19.1628			−0.902343
$452$	4.05841	−	2.80262i	0.190892	−	0.131824i
$453$	−8.39498	+	26.6901i	−0.394430	+	1.25401i
$454$	−4.32909	−	2.27148i	−0.203174	−	0.106606i
$455$	4.56621	+	7.90891i	0.214067	+	0.370775i
$456$	7.16834	+	20.2635i	0.335688	+	0.948924i
$457$	−7.59514	+	13.1552i	−0.355286	+	0.615373i	−0.987167	−	0.159692i	$-0.948950\pi$
$457$	−7.59514	+	13.1552i	−0.355286	+	0.615373i	0.631881	+	0.775065i	$0.282283\pi$
$458$	−11.6818	+	7.38891i	−0.545855	+	0.345261i
$459$	21.2414	−	16.3695i	0.991464	−	0.764064i
$460$	1.55207	−	3.27276i	0.0723658	−	0.152593i
$461$	21.1956	−	36.7119i	0.987178	−	1.70984i	0.355351	−	0.934733i	$-0.384361\pi$
$461$	21.1956	−	36.7119i	0.987178	−	1.70984i	0.631827	−	0.775109i	$-0.282305\pi$
$462$	6.63253	−	6.59875i	0.308573	−	0.307002i
$463$	−26.0480	+	15.0388i	−1.21055	+	0.698914i	−0.962880	−	0.269929i	$-0.913000\pi$
$463$	−26.0480	+	15.0388i	−1.21055	+	0.698914i	−0.247674	+	0.968843i	$0.579666\pi$
$464$	10.1358	−	26.7609i	0.470541	−	1.24234i
$465$	−4.09230	+	13.0106i	−0.189776	+	0.603353i
$466$	−0.829872	−	20.5375i	−0.0384431	−	0.951383i
$467$			37.3626i			1.72893i	0.502690	+	0.864467i	$0.332344\pi$
$467$			37.3626i			1.72893i	−0.502690	+	0.864467i	$0.667656\pi$
$468$	−12.2312	+	20.9375i	−0.565388	+	0.967834i
$469$		−	9.26249i		−	0.427702i
$470$	31.3555	−	1.26700i	1.44632	−	0.0584422i
$471$	27.6583	+	30.1417i	1.27443	+	1.38886i
$472$	1.43517	−	1.07919i	0.0660591	−	0.0496740i
$473$	−40.5689	+	23.4225i	−1.86536	+	1.07697i
$474$	−2.31663	+	8.55831i	−0.106406	+	0.393096i
$475$	0.233337	−	0.404151i	0.0107062	−	0.0185437i
$476$	−4.42290	+	9.32630i	−0.202723	+	0.427470i
$477$	14.5448	−	6.80697i	0.665962	−	0.311670i
$478$	7.25589	+	11.4715i	0.331877	+	0.524695i
$479$	−8.90532	+	15.4245i	−0.406895	+	0.704762i	−0.994540	−	0.104357i	$-0.966722\pi$
$479$	−8.90532	+	15.4245i	−0.406895	+	0.704762i	0.587645	+	0.809119i	$0.300055\pi$
$480$	12.9798	−	17.9370i	0.592442	−	0.818710i
$481$	−13.9913	−	24.2337i	−0.637950	−	1.10496i
$482$	10.8603	−	20.6981i	0.494674	−	0.942772i
$483$	1.35505	−	0.301394i	0.0616568	−	0.0137139i
$484$	4.07886	+	5.90650i	0.185403	+	0.268477i
$485$	−4.67407			−0.212239
$486$	−19.9820	−	9.31230i	−0.906403	−	0.422415i
$487$		−	37.5010i		−	1.69933i	−0.527322	−	0.849666i	$-0.676804\pi$
$487$		−	37.5010i		−	1.69933i	0.527322	−	0.849666i	$-0.323196\pi$
$488$	−15.4713	−	6.58575i	−0.700354	−	0.298123i
$489$	3.65064	+	16.4130i	0.165088	+	0.742222i
$490$	1.48482	−	2.82985i	0.0670776	−	0.127839i
$491$	−0.201710	+	0.116458i	−0.00910306	+	0.00525566i	−0.504545	−	0.863386i	$-0.668340\pi$
$491$	−0.201710	+	0.116458i	−0.00910306	+	0.00525566i	0.495442	+	0.868641i	$0.335006\pi$
$492$	−12.7452	−	11.8156i	−0.574598	−	0.532687i
$493$	31.9751	+	18.4608i	1.44008	+	0.831433i
$494$	21.1925	−	13.4045i	0.953495	−	0.603099i
$495$	−10.9756	−	23.4522i	−0.493318	−	1.05410i
$496$	10.7933	−	8.82026i	0.484632	−	0.396041i
$497$	−3.58823	−	2.07167i	−0.160954	−	0.0929270i
$498$	6.52823	−	24.1172i	0.292537	−	1.08072i
$499$	−20.1583	−	34.9152i	−0.902408	−	1.56302i	−0.824359	−	0.566068i	$-0.808464\pi$
$499$	−20.1583	−	34.9152i	−0.902408	−	1.56302i	−0.0780497	−	0.996949i	$-0.524869\pi$
$500$	22.0444	−	1.78444i	0.985858	−	0.0798025i
$501$	10.4343	−	9.57465i	0.466172	−	0.427764i
$502$	1.59997	+	39.5959i	0.0714103	+	1.76725i
$503$	1.78194			0.0794526			0.0397263	−	0.999211i	$-0.487351\pi$
$503$	1.78194			0.0794526			0.0397263	+	0.999211i	$0.487351\pi$
$504$	8.48000	−	0.299292i	0.377729	−	0.0133315i
$505$	18.0863			0.804831
$506$	0.174790	+	4.32567i	0.00777035	+	0.192299i
$507$	5.50656	+	1.73201i	0.244555	+	0.0769212i
$508$	3.24871	+	40.1337i	0.144138	+	1.78064i
$509$	2.18758	+	3.78900i	0.0969629	+	0.167945i	0.910426	−	0.413672i	$-0.135754\pi$
$509$	2.18758	+	3.78900i	0.0969629	+	0.167945i	−0.813463	+	0.581616i	$0.802421\pi$
$510$	20.1482	+	20.2513i	0.892175	+	0.896743i
$511$	9.14040	+	5.27721i	0.404348	+	0.233450i
$512$	−21.1491	+	8.04450i	−0.934669	+	0.355520i
$513$	13.9161	+	18.0578i	0.614412	+	0.797272i
$514$	2.78070	−	1.75883i	0.122651	−	0.0775787i
$515$	5.59753	+	3.23174i	0.246657	+	0.142407i
$516$	−41.4243	−	9.43599i	−1.82360	−	0.415396i
$517$	−32.4818	+	18.7534i	−1.42855	+	0.824772i
$518$	−4.54966	+	8.67094i	−0.199900	+	0.380979i
$519$	−17.3654	−	5.46203i	−0.762256	−	0.239757i
$520$	−23.7667	−	10.1169i	−1.04224	−	0.443655i
$521$			12.6198i			0.552884i	0.961031	+	0.276442i	$0.0891553\pi$
$521$			12.6198i			0.552884i	−0.961031	+	0.276442i	$0.910845\pi$
$522$	1.38029	−	30.3205i	0.0604138	−	1.32709i
$523$	29.6471			1.29638			0.648189	−	0.761480i	$-0.275527\pi$
$523$	29.6471			1.29638			0.648189	+	0.761480i	$0.275527\pi$
$524$	−2.95464	+	2.04039i	−0.129074	+	0.0891348i
$525$	−0.124559	−	0.135742i	−0.00543618	−	0.00592429i
$526$	−2.05185	+	3.91051i	−0.0894650	+	0.170506i
$527$	8.99223	+	15.5750i	0.391708	+	0.678458i
$528$	−3.77640	+	26.1918i	−0.164347	+	1.13985i
$529$	11.1788	−	19.3623i	0.486036	−	0.841840i
$530$	9.14448	+	14.4574i	0.397211	+	0.627987i
$531$	1.09025	−	1.56166i	0.0473130	−	0.0677701i
$532$	−7.92851	−	3.76001i	−0.343745	−	0.163017i
$533$	−10.1379	+	17.5593i	−0.439120	+	0.760578i
$534$	−37.7532	+	10.0127i	−1.63374	+	0.433292i
$535$	21.7916	−	12.5814i	0.942131	−	0.543940i
$536$	15.7452	+	20.9389i	0.680091	+	0.904422i
$537$	28.4195	−	6.32117i	1.22639	−	0.272778i
$538$	−19.4344	+	0.785298i	−0.837877	+	0.0338566i
$539$			3.81956i			0.164520i
$540$	7.16045	−	22.3655i	0.308137	−	0.962458i
$541$		−	5.41227i		−	0.232692i	−0.993209	−	0.116346i	$-0.962882\pi$
$541$		−	5.41227i		−	0.232692i	0.993209	−	0.116346i	$-0.0371181\pi$
$542$	0.873049	+	21.6061i	0.0375007	+	0.928060i
$543$	22.0381	−	4.90178i	0.945743	−	0.210355i
$544$	−5.85526	−	28.6016i	−0.251042	−	1.22628i
$545$	10.9484	−	6.32104i	0.468977	−	0.270764i
$546$	−2.53771	−	9.56852i	−0.108604	−	0.409495i
$547$	−1.38415	+	2.39741i	−0.0591819	+	0.102506i	−0.894098	−	0.447871i	$-0.852183\pi$
$547$	−1.38415	+	2.39741i	−0.0591819	+	0.102506i	0.834917	+	0.550377i	$0.185516\pi$
$548$	28.9308	+	13.7201i	1.23586	+	0.586095i
$549$	−17.7689	−	1.52972i	−0.758360	−	0.0652867i
$550$	0.485571	−	0.307131i	0.0207048	−	0.0130961i
$551$	−15.6940	+	27.1827i	−0.668585	+	1.15802i
$552$	−2.55090	+	2.98477i	−0.108573	+	0.127040i
$553$	−1.80983	−	3.13471i	−0.0769617	−	0.133302i
$554$	10.9377	+	5.73903i	0.464698	+	0.243828i
$555$	18.3226	+	19.9678i	0.777753	+	0.847586i
$556$	−2.50185	−	3.62287i	−0.106102	−	0.153644i
$557$	−46.6890			−1.97828			−0.989139	−	0.146983i	$-0.953044\pi$
$557$	−46.6890			−1.97828			−0.989139	+	0.146983i	$0.953044\pi$
$558$	7.96681	−	12.4542i	0.337262	−	0.527230i
$559$			49.5655i			2.09640i
$560$	1.45382	+	8.92122i	0.0614353	+	0.376991i
$561$	−32.5700	−	10.2444i	−1.37511	−	0.432520i
$562$	−8.65386	−	4.54069i	−0.365041	−	0.191538i
$563$	16.7870	−	9.69199i	0.707489	−	0.408469i	−0.102642	−	0.994718i	$-0.532730\pi$
$563$	16.7870	−	9.69199i	0.707489	−	0.408469i	0.810130	+	0.586250i	$0.199396\pi$
$564$	−33.1667	−	7.55499i	−1.39657	−	0.318123i
$565$	4.82599	+	2.78629i	0.203031	+	0.117220i
$566$	0.210079	+	0.332134i	0.00883029	+	0.0139606i
$567$	8.44865	−	3.10166i	0.354810	−	0.130258i
$568$	11.6332	−	1.41638i	0.488119	−	0.0594300i
$569$	−3.37682	−	1.94961i	−0.141564	−	0.0817318i	0.427545	−	0.903994i	$-0.359378\pi$
$569$	−3.37682	−	1.94961i	−0.141564	−	0.0817318i	−0.569109	+	0.822262i	$0.692712\pi$
$570$	−17.2161	+	17.1284i	−0.721103	+	0.717431i
$571$	8.50678	+	14.7342i	0.355998	+	0.616606i	0.987288	−	0.158940i	$-0.0508078\pi$
$571$	8.50678	+	14.7342i	0.355998	+	0.616606i	−0.631291	+	0.775546i	$0.717474\pi$
$572$	30.7719	−	2.49090i	1.28664	−	0.104150i
$573$	27.4472	+	8.63311i	1.14662	+	0.360653i
$574$	7.08937	−	0.286464i	0.295905	−	0.0119568i
$575$	0.0852472			0.00355506
$576$	−18.6612	+	15.0917i	−0.777551	+	0.628820i
$577$	−21.9438			−0.913532			−0.456766	−	0.889587i	$-0.650992\pi$
$577$	−21.9438			−0.913532			−0.456766	+	0.889587i	$0.650992\pi$
$578$	13.6155	−	0.550171i	0.566332	−	0.0228841i
$579$	−10.4553	+	9.59388i	−0.434507	+	0.398708i
$580$	32.2269	−	2.60868i	1.33815	−	0.108319i
$581$	5.10008	+	8.83359i	0.211587	+	0.366479i
$582$	4.89058	+	1.32382i	0.202721	+	0.0548740i
$583$	−17.7067	−	10.2229i	−0.733335	−	0.423391i
$584$	−29.6336	+	3.60798i	−1.22625	+	0.149299i
$585$	−27.2963	−	2.34992i	−1.12856	−	0.0971572i
$586$	−19.9129	−	31.4821i	−0.822593	−	1.30051i
$587$	3.73905	+	2.15874i	0.154327	+	0.0891007i	0.575175	−	0.818031i	$-0.304934\pi$
$587$	3.73905	+	2.15874i	0.154327	+	0.0891007i	−0.420848	+	0.907131i	$0.638267\pi$
$588$	−2.35509	+	2.54038i	−0.0971222	+	0.104764i
$589$	−13.2407	+	7.64450i	−0.545572	+	0.314986i
$590$	1.79656	+	0.942656i	0.0739630	+	0.0388085i
$591$	−3.27573	−	14.7274i	−0.134745	−	0.605806i
$592$	−4.45467	−	27.3355i	−0.183086	−	1.12348i
$593$		−	24.0556i		−	0.987846i	−0.869506	−	0.493923i	$-0.835562\pi$
$593$		−	24.0556i		−	0.987846i	0.869506	−	0.493923i	$-0.164438\pi$
$594$	4.84175	+	27.6471i	0.198659	+	1.13438i
$595$	−11.6624			−0.478110
$596$	−23.6139	−	34.1947i	−0.967263	−	1.40067i
$597$	−30.7995	+	6.85053i	−1.26054	+	0.280374i
$598$	4.05617	+	2.12828i	0.165869	+	0.0870318i
$599$	1.73639	+	3.00752i	0.0709470	+	0.122884i	0.899317	−	0.437298i	$-0.144065\pi$
$599$	1.73639	+	3.00752i	0.0709470	+	0.122884i	−0.828370	+	0.560182i	$0.810731\pi$
$600$	0.512326	+	0.0951246i	0.0209156	+	0.00388345i
$601$	−3.47104	+	6.01202i	−0.141587	+	0.245235i	−0.928094	−	0.372345i	$-0.878554\pi$
$601$	−3.47104	+	6.01202i	−0.141587	+	0.245235i	0.786508	+	0.617581i	$0.211887\pi$
$602$	14.6585	−	9.27170i	0.597435	−	0.377886i
$603$	22.7843	+	15.9066i	0.927848	+	0.647767i
$604$	29.1913	+	13.8437i	1.18778	+	0.563291i
$605$	−4.05509	+	7.02362i	−0.164863	+	0.285551i
$606$	−18.9241	−	5.12252i	−0.768739	−	0.208088i
$607$	−11.8273	+	6.82851i	−0.480057	+	0.277161i	−0.720440	−	0.693517i	$-0.756060\pi$
$607$	−11.8273	+	6.82851i	−0.480057	+	0.277161i	0.240383	+	0.970678i	$0.422727\pi$
$608$	24.3149	−	4.97770i	0.986099	−	0.201872i
$609$	8.37767	+	9.12988i	0.339480	+	0.369962i
$610$	−0.767049	−	18.9828i	−0.0310569	−	0.768592i
$611$			39.6850i			1.60548i
$612$	−15.3457	−	26.8958i	−0.620315	−	1.08720i
$613$		−	9.27795i		−	0.374733i	−0.982290	−	0.187366i	$-0.940005\pi$
$613$		−	9.27795i		−	0.374733i	0.982290	−	0.187366i	$-0.0599952\pi$
$614$	−20.7287	+	0.837595i	−0.836541	+	0.0338026i
$615$	5.89180	−	18.7317i	0.237580	−	0.755337i
$616$	−6.49284	−	8.63453i	−0.261604	−	0.347895i
$617$	−20.4524	+	11.8082i	−0.823384	+	0.475381i	−0.851582	−	0.524221i	$-0.824356\pi$
$617$	−20.4524	+	11.8082i	−0.823384	+	0.475381i	0.0281981	+	0.999602i	$0.491023\pi$
$618$	−4.94150	−	4.96680i	−0.198776	−	0.199794i
$619$	13.7092	−	23.7451i	0.551020	−	0.954394i	−0.447181	−	0.894443i	$-0.647572\pi$
$619$	13.7092	−	23.7451i	0.551020	−	0.954394i	0.998201	−	0.0599512i	$-0.0190945\pi$
$620$	14.2299	+	6.74838i	0.571487	+	0.271022i
$621$	−1.58566	+	3.85080i	−0.0636304	+	0.154527i
$622$	−8.39472	−	13.2720i	−0.336598	−	0.532159i
$623$	7.97277	−	13.8092i	0.319422	−	0.553256i
$624$	22.0022	+	17.3169i	0.880795	+	0.693230i
$625$	12.7603	+	22.1014i	0.510410	+	0.884057i
$626$	16.6502	−	31.7327i	0.665476	−	1.26829i
$627$	8.70904	−	27.6886i	0.347805	−	1.10577i
$628$	38.8695	−	26.8422i	1.55106	−	1.07112i
$629$	35.7347			1.42483
$630$	4.41107	+	8.51217i	0.175741	+	0.339133i
$631$		−	32.6178i		−	1.29849i	−0.760577	−	0.649247i	$-0.775084\pi$
$631$		−	32.6178i		−	1.29849i	0.760577	−	0.649247i	$-0.224916\pi$
$632$	9.42000	+	4.00986i	0.374707	+	0.159503i
$633$	−28.8826	+	26.5029i	−1.14798	+	1.05340i
$634$	−1.06243	+	2.02483i	−0.0421945	+	0.0804162i
$635$	−39.3989	+	22.7469i	−1.56350	+	0.902685i
$636$	−5.47336	−	17.7170i	−0.217033	−	0.702524i
$637$	3.49994	+	2.02069i	0.138673	+	0.0800627i
$638$	−32.6590	+	20.6573i	−1.29298	+	0.817829i
$639$	11.2581	−	5.26879i	0.445364	−	0.208430i
$640$	−18.4517	−	17.6961i	−0.729366	−	0.699499i
$641$	−12.1518	−	7.01586i	−0.479968	−	0.277110i	0.240435	−	0.970665i	$-0.422710\pi$
$641$	−12.1518	−	7.01586i	−0.479968	−	0.277110i	−0.720403	+	0.693555i	$0.756043\pi$
$642$	−26.3643	+	6.99220i	−1.04052	+	0.275960i
$643$	9.96898	+	17.2668i	0.393138	+	0.680936i	0.992862	−	0.119272i	$-0.0380560\pi$
$643$	9.96898	+	17.2668i	0.393138	+	0.680936i	−0.599723	+	0.800207i	$0.704723\pi$
$644$	−0.129328	−	1.59769i	−0.00509625	−	0.0629576i
$645$	−10.4222	−	46.8577i	−0.410375	−	1.84502i
$646$	1.29290	+	31.9966i	0.0508686	+	1.25889i
$647$	25.9899			1.02177			0.510883	−	0.859650i	$-0.329318\pi$
$647$	25.9899			1.02177			0.510883	+	0.859650i	$0.329318\pi$
$648$	−13.8266	+	21.3735i	−0.543161	+	0.839629i
$649$	−2.42488			−0.0951850
$650$	−0.0245445	−	0.607423i	−0.000962714	−	0.0238251i
$651$	1.31046	+	5.89172i	0.0513608	+	0.230915i
$652$	19.3520	−	1.56649i	0.757881	−	0.0613484i
$653$	−3.48413	−	6.03470i	−0.136345	−	0.236156i	0.789766	−	0.613409i	$-0.210202\pi$
$653$	−3.48413	−	6.03470i	−0.136345	−	0.236156i	−0.926110	+	0.377253i	$0.876869\pi$
$654$	−13.2458	+	3.51298i	−0.517951	+	0.137368i
$655$	−3.51346	−	2.02850i	−0.137282	−	0.0792599i
$656$	−15.5394	+	12.6988i	−0.606710	+	0.495803i
$657$	−28.6781	+	13.4213i	−1.11884	+	0.523616i
$658$	11.7364	−	7.42345i	0.457534	−	0.289396i
$659$	−2.93482	−	1.69442i	−0.114324	−	0.0660051i	0.441748	−	0.897139i	$-0.354359\pi$
$659$	−2.93482	−	1.69442i	−0.114324	−	0.0660051i	−0.556072	+	0.831134i	$0.687692\pi$
$660$	−28.5670	+	8.82530i	−1.11197	+	0.343524i
$661$	−37.6384	+	21.7305i	−1.46396	+	0.845220i	−0.999191	−	0.0402104i	$-0.987197\pi$
$661$	−37.6384	+	21.7305i	−1.46396	+	0.845220i	−0.464772	+	0.885430i	$0.653864\pi$
$662$	−5.36375	+	10.2225i	−0.208468	+	0.397308i
$663$	−26.6180	+	24.4249i	−1.03376	+	0.948585i
$664$	−26.5454	−	11.2997i	−1.03016	−	0.438514i
$665$		−	9.91444i		−	0.384466i
$666$	−13.5160	−	26.0822i	−0.523733	−	1.01066i
$667$	−5.73363			−0.222007
$668$	−9.29212	−	13.4557i	−0.359523	−	0.520616i
$669$	3.35596	−	10.6696i	0.129749	−	0.412510i
$670$	−13.7532	+	26.2114i	−0.531332	+	1.01264i
$671$	11.3534	+	19.6647i	0.438294	+	0.759147i
$672$	1.00556	−	9.74622i	0.0387902	−	0.375969i
$673$	21.3052	−	36.9017i	0.821255	−	1.42246i	−0.0834933	−	0.996508i	$-0.526608\pi$
$673$	21.3052	−	36.9017i	0.821255	−	1.42246i	0.904748	−	0.425947i	$-0.140059\pi$
$674$	11.3597	+	17.9596i	0.437560	+	0.691779i
$675$	0.547812	−	0.0732821i	0.0210853	−	0.00282063i
$676$	2.85616	−	6.02261i	0.109852	−	0.231639i
$677$	−12.4102	+	21.4950i	−0.476962	+	0.826122i	−0.999651	−	0.0264012i	$-0.991595\pi$
$677$	−12.4102	+	21.4950i	−0.476962	+	0.826122i	0.522690	+	0.852523i	$0.324929\pi$
$678$	−4.26039	−	4.28220i	−0.163619	−	0.164457i
$679$	−1.79131	+	1.03421i	−0.0687440	+	0.0396894i
$680$	26.3641	−	19.8248i	1.01102	−	0.760245i
$681$	−1.79653	+	5.71170i	−0.0688432	+	0.218873i
$682$	−18.8079	+	0.759982i	−0.720192	+	0.0291012i
$683$		−	8.52318i		−	0.326130i	−0.986615	−	0.163065i	$-0.947862\pi$
$683$		−	8.52318i		−	0.326130i	0.986615	−	0.163065i	$-0.0521381\pi$
$684$	22.8648	−	13.0458i	0.874257	−	0.498818i
$685$			36.1774i			1.38227i
$686$	−0.0570983	−	1.41306i	−0.00218002	−	0.0539509i
$687$	11.4457	+	12.4734i	0.436682	+	0.475891i
$688$	−17.3762	+	45.8776i	−0.662463	+	1.74907i
$689$	−18.7350	+	10.8167i	−0.713747	+	0.412082i
$690$	−4.28209	−	1.15911i	−0.163017	−	0.0441266i
$691$	6.24960	−	10.8246i	0.237746	−	0.411788i	−0.722321	−	0.691558i	$-0.756925\pi$
$691$	6.24960	−	10.8246i	0.237746	−	0.411788i	0.960067	+	0.279770i	$0.0902581\pi$
$692$	−9.00712	+	18.9928i	−0.342399	+	0.721997i
$693$	−9.39551	−	6.55938i	−0.356906	−	0.249170i
$694$	7.63104	−	4.82674i	0.289670	−	0.183220i
$695$	2.48727	−	4.30808i	0.0943475	−	0.163415i
$696$	−34.4585	−	6.39797i	−1.30615	−	0.242515i
$697$	−12.9464	−	22.4237i	−0.490378	−	0.849360i
$698$	−5.74047	−	3.01203i	−0.217280	−	0.114007i
$699$	−24.5733	+	5.46567i	−0.929446	+	0.206731i
$700$	−0.175048	+	0.120883i	−0.00661619	+	0.00456895i
$701$	47.4340			1.79156			0.895778	−	0.444502i	$-0.146619\pi$
$701$	47.4340			1.79156			0.895778	+	0.444502i	$0.146619\pi$
$702$	27.8951	+	10.1898i	1.05283	+	0.384589i
$703$			30.3789i			1.14576i
$704$	29.3556	+	8.48218i	1.10638	+	0.319684i
$705$	−8.34465	−	37.5169i	−0.314278	−	1.41297i
$706$	12.0178	+	6.30574i	0.452295	+	0.237320i
$707$	6.93147	−	4.00188i	0.260685	−	0.150506i
$708$	−1.61279	−	1.49515i	−0.0606123	−	0.0561913i
$709$	10.0930	+	5.82717i	0.379049	+	0.218844i	0.677404	−	0.735611i	$-0.263105\pi$
$709$	10.0930	+	5.82717i	0.379049	+	0.218844i	−0.298356	+	0.954455i	$0.596438\pi$
$710$	7.07808	+	11.1904i	0.265636	+	0.419968i
$711$	10.8190	+	0.931396i	0.405742	+	0.0349301i
$712$	5.45091	+	44.7702i	0.204281	+	1.67783i
$713$	−2.41867	−	1.39642i	−0.0905800	−	0.0522964i
$714$	12.2026	+	3.30308i	0.456670	+	0.123615i
$715$	17.4409	+	30.2085i	0.652252	+	1.12973i
$716$	−2.71241	−	33.5084i	−0.101368	−	1.25227i
$717$	12.2489	−	11.2397i	0.457442	−	0.419754i
$718$	44.6679	−	1.80492i	1.66699	−	0.0673590i
$719$	26.4879			0.987831			0.493915	−	0.869510i	$-0.335565\pi$
$719$	26.4879			0.987831			0.493915	+	0.869510i	$0.335565\pi$
$720$	−24.4415	−	11.7444i	−0.910881	−	0.437687i
$721$	2.86029			0.106523
$722$	−0.352898	+	0.0142597i	−0.0131335	+	0.000530692i
$723$	−27.3085	−	8.58950i	−1.01562	−	0.319447i
$724$	−2.10335	−	25.9842i	−0.0781705	−	0.965696i
$725$	0.380471	+	0.658994i	0.0141303	+	0.0244744i
$726$	6.23220	−	6.20045i	0.231298	−	0.230120i
$727$	2.88678	+	1.66668i	0.107065	+	0.0618139i	0.552576	−	0.833462i	$-0.313645\pi$
$727$	2.88678	+	1.66668i	0.107065	+	0.0618139i	−0.445511	+	0.895276i	$0.646978\pi$
$728$	−11.3470	+	1.38153i	−0.420546	+	0.0512028i
$729$	−6.87939	+	26.1089i	−0.254792	+	0.966996i
$730$	−18.0302	−	28.5056i	−0.667327	−	1.05504i
$731$	−54.8164	−	31.6483i	−2.02746	−	1.17055i
$732$	−4.57385	+	20.0794i	−0.169054	+	0.742154i
$733$	8.25486	−	4.76594i	0.304900	−	0.176034i	−0.339742	−	0.940519i	$-0.610340\pi$
$733$	8.25486	−	4.76594i	0.304900	−	0.176034i	0.644642	+	0.764485i	$0.277006\pi$
$734$	29.3136	+	15.3809i	1.08198	+	0.567719i
$735$	−3.73363	−	1.17436i	−0.137717	−	0.0433169i
$736$	3.00826	+	3.39190i	0.110886	+	0.125027i
$737$		−	35.3786i		−	1.30319i
$738$	−11.4700	+	17.9307i	−0.422217	+	0.660038i
$739$	−4.44786			−0.163617			−0.0818087	−	0.996648i	$-0.526070\pi$
$739$	−4.44786			−0.163617			−0.0818087	+	0.996648i	$0.526070\pi$
$740$	25.7496	−	17.7820i	0.946576	−	0.653678i
$741$	−20.7642	−	22.6286i	−0.762792	−	0.831282i
$742$	6.70348	+	3.51733i	0.246092	+	0.129125i
$743$	−10.5142	−	18.2112i	−0.385730	−	0.668103i	0.606140	−	0.795358i	$-0.292717\pi$
$743$	−10.5142	−	18.2112i	−0.385730	−	0.668103i	−0.991870	+	0.127254i	$0.959384\pi$
$744$	−12.9777	−	11.0913i	−0.475787	−	0.406625i
$745$	23.4763	−	40.6621i	0.860103	−	1.48974i
$746$	39.0143	−	24.6771i	1.42842	−	0.903493i
$747$	−30.4877	−	2.62466i	−1.11549	−	0.0960314i
$748$	−16.8935	+	35.6223i	−0.617688	+	1.30248i
$749$	5.56765	−	9.64344i	0.203437	−	0.352364i
$750$	−6.94384	−	26.1820i	−0.253553	−	0.956031i
$751$	−1.90216	+	1.09821i	−0.0694107	+	0.0400743i	−0.534304	−	0.845293i	$-0.679426\pi$
$751$	−1.90216	+	1.09821i	−0.0694107	+	0.0400743i	0.464893	+	0.885367i	$0.346093\pi$
$752$	−13.9124	+	36.7322i	−0.507334	+	1.33949i
$753$	47.3766	−	10.5377i	1.72650	−	0.384014i
$754$	1.65084	+	40.8546i	0.0601199	+	1.48784i
$755$			36.5032i			1.32849i
$756$	−2.20452	−	10.1558i	−0.0801777	−	0.369363i
$757$			23.9222i			0.869469i	0.900559	+	0.434734i	$0.143158\pi$
$757$			23.9222i			0.869469i	−0.900559	+	0.434734i	$0.856842\pi$
$758$	51.0735	−	2.06376i	1.85507	−	0.0749590i
$759$	5.17568	−	1.15119i	0.187865	−	0.0417856i
$760$	16.8535	+	22.4127i	0.611341	+	0.812994i
$761$	−19.2494	+	11.1136i	−0.697789	+	0.402868i	−0.806523	−	0.591202i	$-0.798653\pi$
$761$	−19.2494	+	11.1136i	−0.697789	+	0.402868i	0.108735	+	0.994071i	$0.465320\pi$
$762$	47.6664	−	12.6418i	1.72677	−	0.457965i
$763$	2.79726	−	4.84500i	0.101268	−	0.175401i
$764$	14.2364	−	30.0194i	0.515054	−	1.08606i
$765$	20.0279	−	28.6876i	0.724112	−	1.03720i
$766$	14.5589	+	23.0175i	0.526034	+	0.831656i
$767$	−1.28286	+	2.22197i	−0.0463213	+	0.0802308i
$768$	14.2944	+	23.7418i	0.515804	+	0.856707i
$769$	−6.50215	−	11.2620i	−0.234473	−	0.406120i	0.724646	−	0.689121i	$-0.242003\pi$
$769$	−6.50215	−	11.2620i	−0.234473	−	0.406120i	−0.959120	+	0.283001i	$0.908670\pi$
$770$	5.67137	−	10.8088i	0.204382	−	0.389520i
$771$	−2.72450	−	2.96913i	−0.0981206	−	0.106931i
$772$	9.31078	+	13.4827i	0.335102	+	0.485254i
$773$	−44.5857			−1.60364			−0.801819	−	0.597568i	$-0.796134\pi$
$773$	−44.5857			−1.60364			−0.801819	+	0.597568i	$0.796134\pi$
$774$	−2.36631	+	51.9800i	−0.0850551	+	1.86838i
$775$			0.370653i			0.0133143i
$776$	2.29140	−	5.38298i	0.0822564	−	0.193238i
$777$	11.4402	+	3.59835i	0.410416	+	0.129090i
$778$	5.92062	−	11.2838i	0.212265	−	0.404543i
$779$	19.0629	−	11.0060i	0.683001	−	0.394331i
$780$	−7.02625	+	30.8455i	−0.251580	+	1.10445i
$781$	−13.7055	−	7.91285i	−0.490420	−	0.283144i
$782$	−4.94367	+	3.12694i	−0.176785	+	0.111819i
$783$	−36.8452	+	4.92887i	−1.31674	+	0.176144i
$784$	2.53113	+	3.09732i	0.0903975	+	0.110619i
$785$	46.2210	+	26.6857i	1.64970	+	0.952454i
$786$	3.10168	+	3.11756i	0.110633	+	0.111200i
$787$	2.19802	+	3.80709i	0.0783511	+	0.135708i	0.902539	−	0.430609i	$-0.141701\pi$
$787$	2.19802	+	3.80709i	0.0783511	+	0.135708i	−0.824188	+	0.566317i	$0.808368\pi$
$788$	−17.3646	+	1.40561i	−0.618587	+	0.0500729i
$789$	5.15943	+	1.62282i	0.183681	+	0.0577741i
$790$	0.467032	+	11.5580i	0.0166163	+	0.411216i
$791$	2.46604			0.0876823
$792$	32.3898	−	1.14316i	1.15092	−	0.0406205i
$793$	24.0256			0.853173
$794$	1.80684	+	44.7154i	0.0641224	+	1.58689i
$795$	15.4370	−	14.1652i	0.547496	−	0.502387i
$796$	2.93957	+	36.3146i	0.104190	+	1.28714i
$797$	−16.7293	−	28.9760i	−0.592583	−	1.02638i	−0.993883	−	0.110437i	$-0.964775\pi$
$797$	−16.7293	−	28.9760i	−0.592583	−	1.02638i	0.401300	−	0.915947i	$-0.368558\pi$
$798$	−2.80803	+	10.3737i	−0.0994031	+	0.367225i
$799$	−43.8892	−	25.3394i	−1.55269	−	0.896444i
$800$	0.190227	−	0.570832i	0.00672553	−	0.0201820i
$801$	20.2768	+	43.3266i	0.716446	+	1.53087i
$802$	25.4006	−	16.0662i	0.896927	−	0.567319i
$803$	34.9123	+	20.1566i	1.23203	+	0.711311i
$804$	21.8140	−	23.5303i	0.769320	−	0.829849i
$805$	1.56843	−	0.905536i	0.0552800	−	0.0319159i
$806$	−9.25372	+	17.6361i	−0.325948	+	0.621207i
$807$	5.17209	+	23.2534i	0.182066	+	0.818558i
$808$	−8.86657	+	20.8295i	−0.311925	+	0.732778i
$809$			47.7828i			1.67995i	0.542622	+	0.839977i	$0.317432\pi$
$809$			47.7828i			1.67995i	−0.542622	+	0.839977i	$0.682568\pi$
$810$	−28.5138	−	3.76754i	−1.00187	−	0.132378i
$811$	−31.5182			−1.10675			−0.553377	−	0.832931i	$-0.686661\pi$
$811$	−31.5182			−1.10675			−0.553377	+	0.832931i	$0.686661\pi$
$812$	11.7735	−	8.13046i	0.413170	−	0.285323i
$813$	25.8518	−	5.75004i	0.906661	−	0.201663i
$814$	−17.3777	+	33.1191i	−0.609087	+	1.16082i
$815$	10.9683	+	18.9976i	0.384203	+	0.665458i
$816$	−33.2001	+	13.2761i	−1.16224	+	0.464756i
$817$	26.9049	−	46.6007i	0.941285	−	1.63035i
$818$	−7.36250	−	11.6401i	−0.257424	−	0.406985i
$819$	−10.9811	+	5.13914i	−0.383710	+	0.179576i
$820$	−20.4872	−	9.71583i	−0.715443	−	0.339291i
$821$	−0.875428	+	1.51629i	−0.0305526	+	0.0529187i	−0.880897	−	0.473307i	$-0.843060\pi$
$821$	−0.875428	+	1.51629i	−0.0305526	+	0.0529187i	0.850345	+	0.526226i	$0.176393\pi$
$822$	10.2464	−	37.8532i	0.357384	−	1.32028i
$823$	46.4707	−	26.8299i	1.61987	−	0.935230i	0.632913	−	0.774223i	$-0.281859\pi$
$823$	46.4707	−	26.8299i	1.61987	−	0.935230i	0.986953	−	0.161008i	$-0.0514744\pi$
$824$	−6.46600	+	4.86219i	−0.225254	+	0.169382i
$825$	−0.475758	−	0.518476i	−0.0165638	−	0.0180510i
$826$	0.897096	−	0.0362495i	0.0312140	−	0.00126128i
$827$		−	18.1913i		−	0.632573i	−0.948664	−	0.316287i	$-0.897564\pi$
$827$		−	18.1913i		−	0.632573i	0.948664	−	0.316287i	$-0.102436\pi$
$828$	4.15215	+	2.42560i	0.144297	+	0.0842955i
$829$		−	14.0203i		−	0.486945i	−0.969908	−	0.243472i	$-0.921713\pi$
$829$		−	14.0203i		−	0.486945i	0.969908	−	0.243472i	$-0.0782866\pi$
$830$	−1.31609	−	32.5704i	−0.0456822	−	1.13054i
$831$	4.53904	−	14.4309i	0.157458	−	0.500604i
$832$	23.3026	−	22.4117i	0.807873	−	0.776987i
$833$	−4.46952	+	2.58048i	−0.154860	+	0.0894083i
$834$	−3.82264	+	3.80317i	−0.132367	+	0.131693i
$835$	9.23796	−	16.0006i	0.319693	−	0.553724i
$836$	−30.2834	−	14.3616i	−1.04737	−	0.496705i
$837$	−16.7432	−	6.89442i	−0.578729	−	0.238306i
$838$	7.56040	−	4.78206i	0.261170	−	0.165193i
$839$	−5.61935	+	9.73301i	−0.194002	+	0.336021i	−0.946573	−	0.322490i	$-0.895480\pi$
$839$	−5.61935	+	9.73301i	−0.194002	+	0.336021i	0.752571	+	0.658511i	$0.228813\pi$
$840$	10.4366	−	3.69200i	0.360096	−	0.127386i
$841$	−11.0900	−	19.2085i	−0.382414	−	0.662361i
$842$	−32.5297	−	17.0684i	−1.12105	−	0.588215i
$843$	−3.59127	+	11.4177i	−0.123690	+	0.393246i
$844$	25.7209	+	37.2458i	0.885349	+	1.28205i
$845$	7.53115			0.259079
$846$	−1.89460	+	41.6182i	−0.0651377	+	1.43086i
$847$			3.58901i			0.123320i
$848$	−21.1330	+	3.44389i	−0.725711	+	0.118264i
$849$	0.354641	−	0.325422i	0.0121712	−	0.0111684i
$850$	0.687445	+	0.360704i	0.0235792	+	0.0123720i
$851$	−4.80584	+	2.77465i	−0.164742	+	0.0951139i
$852$	−4.23653	−	13.7134i	−0.145141	−	0.469815i
$853$	−42.1625	−	24.3425i	−1.44362	−	0.833472i	−0.445528	−	0.895268i	$-0.646984\pi$
$853$	−42.1625	−	24.3425i	−1.44362	−	0.833472i	−0.998089	+	0.0617956i	$0.980317\pi$
$854$	−4.49421	−	7.10532i	−0.153789	−	0.243139i
$855$	24.3880	+	17.0262i	0.834051	+	0.582284i
$856$	3.80655	+	31.2645i	0.130105	+	1.06860i
$857$	19.3571	+	11.1758i	0.661227	+	0.381759i	0.792744	−	0.609554i	$-0.208652\pi$
$857$	19.3571	+	11.1758i	0.661227	+	0.381759i	−0.131518	+	0.991314i	$0.541985\pi$
$858$	−9.69293	−	36.5475i	−0.330911	−	1.24771i
$859$	−8.62068	−	14.9314i	−0.294134	−	0.509454i	0.680649	−	0.732609i	$-0.261698\pi$
$859$	−8.62068	−	14.9314i	−0.294134	−	0.509454i	−0.974783	+	0.223155i	$0.928364\pi$
$860$	−55.2481	+	4.47219i	−1.88394	+	0.152500i
$861$	−1.88670	−	8.48247i	−0.0642985	−	0.289082i
$862$	18.5194	−	0.748326i	0.630775	−	0.0254881i
$863$	−8.85631			−0.301472			−0.150736	−	0.988574i	$-0.548164\pi$
$863$	−8.85631			−0.301472			−0.150736	+	0.988574i	$0.548164\pi$
$864$	22.2473	+	19.2108i	0.756869	+	0.653566i
$865$	−23.7501			−0.807527
$866$	−30.9253	+	1.24962i	−1.05089	+	0.0424637i
$867$	−3.62351	−	16.2911i	−0.123061	−	0.553273i
$868$	6.94670	−	0.562317i	0.235786	−	0.0190863i
$869$	−6.91274	−	11.9732i	−0.234499	−	0.406164i
$870$	−10.1512	−	38.2755i	−0.344159	−	1.29766i
$871$	−32.4182	−	18.7166i	−1.09845	−	0.634189i
$872$	1.91246	+	15.7077i	0.0647641	+	0.531930i
$873$	0.532239	−	6.18240i	0.0180135	−	0.209243i
$874$	−2.65829	−	4.20273i	−0.0899178	−	0.142159i
$875$	9.57675	+	5.52914i	0.323753	+	0.186919i
$876$	10.7918	+	34.9326i	0.364622	+	1.18026i
$877$	−23.6408	+	13.6490i	−0.798294	+	0.460895i	−0.842874	−	0.538111i	$-0.819138\pi$
$877$	−23.6408	+	13.6490i	−0.798294	+	0.460895i	0.0445805	+	0.999006i	$0.485805\pi$
$878$	−5.39450	−	2.83050i	−0.182055	−	0.0955248i
$879$	−33.6155	+	30.8459i	−1.13382	+	1.04041i
$880$	5.55296	+	34.0751i	0.187190	+	1.14867i
$881$			15.0327i			0.506464i	0.967406	+	0.253232i	$0.0814936\pi$
$881$			15.0327i			0.506464i	−0.967406	+	0.253232i	$0.918506\pi$
$882$	3.57396	+	2.28622i	0.120342	+	0.0769809i
$883$	2.68685			0.0904196			0.0452098	−	0.998978i	$-0.485604\pi$
$883$	2.68685			0.0904196			0.0452098	+	0.998978i	$0.485604\pi$
$884$	23.7042	+	34.3255i	0.797258	+	1.15449i
$885$	0.745553	−	2.37033i	0.0250615	−	0.0796778i
$886$	−14.2076	−	7.45477i	−0.477315	−	0.250448i
$887$	−3.38051	−	5.85522i	−0.113507	−	0.196599i	0.803675	−	0.595068i	$-0.202875\pi$
$887$	−3.38051	−	5.85522i	−0.113507	−	0.196599i	−0.917182	+	0.398469i	$0.869542\pi$
$888$	−31.9787	+	11.3127i	−1.07313	+	0.379628i
$889$	−10.0662	+	17.4352i	−0.337611	+	0.584759i
$890$	−43.0660	+	27.2399i	−1.44358	+	0.913082i
$891$	32.2701	−	11.8470i	1.08109	−	0.396888i
$892$	−11.6695	−	5.53413i	−0.390723	−	0.185296i
$893$	21.5416	−	37.3112i	0.720864	−	1.24857i
$894$	−36.0802	+	35.8965i	−1.20670	+	1.20056i
$895$	32.8949	−	18.9919i	1.09955	−	0.634828i
$896$	−10.9870	−	2.69918i	−0.367050	−	0.0901734i
$897$	1.68327	−	5.35161i	0.0562028	−	0.178685i
$898$	−1.13143	−	28.0004i	−0.0377563	−	0.934387i
$899$		−	24.9297i		−	0.831452i
$900$	0.00325884	−	0.638185i	0.000108628	−	0.0212728i
$901$		−	27.6264i		−	0.920368i
$902$	27.0783	−	1.09417i	0.901607	−	0.0364318i
$903$	−14.3623	−	15.6518i	−0.477946	−	0.520860i
$904$	−5.57476	+	4.19201i	−0.185414	+	0.139424i
$905$	25.5085	−	14.7273i	0.847931	−	0.489553i
$906$	10.3386	−	38.1940i	0.343479	−	1.26891i
$907$	13.0591	−	22.6190i	0.433620	−	0.751051i	−0.563562	−	0.826074i	$-0.690570\pi$
$907$	13.0591	−	22.6190i	0.433620	−	0.751051i	0.997182	+	0.0750225i	$0.0239028\pi$
$908$	6.24697	+	2.96256i	0.207313	+	0.0983159i
$909$	−2.05950	+	23.9228i	−0.0683093	+	0.793470i
$910$	−6.90392	−	10.9150i	−0.228863	−	0.361830i
$911$	13.0546	−	22.6112i	0.432517	−	0.749142i	−0.564572	−	0.825384i	$-0.690959\pi$
$911$	13.0546	−	22.6112i	0.432517	−	0.749142i	0.997089	+	0.0762421i	$0.0242922\pi$
$912$	−11.2863	−	28.2242i	−0.373727	−	0.934597i
$913$	19.4800	+	33.7404i	0.644695	+	1.11664i
$914$	9.98125	−	19.0227i	0.330151	−	0.629216i
$915$	−22.7130	+	5.05191i	−0.750870	+	0.167011i
$916$	16.0852	−	11.1080i	0.531471	−	0.367018i
$917$	−1.79535			−0.0592876
$918$	−29.0807	+	24.3440i	−0.959807	+	0.803471i
$919$		−	3.60841i		−	0.119031i	−0.998227	−	0.0595153i	$-0.981044\pi$
$919$		−	3.60841i		−	0.119031i	0.998227	−	0.0595153i	$-0.0189555\pi$
$920$	−2.00630	+	4.71323i	−0.0661459	+	0.155391i
$921$	5.51653	+	24.8019i	0.181776	+	0.817252i
$922$	−27.8545	+	53.0863i	−0.917339	+	1.74831i
$923$	−14.5014	+	8.37240i	−0.477320	+	0.275581i
$924$	−8.99539	+	9.70314i	−0.295927	+	0.319210i
$925$	0.637809	+	0.368239i	0.0209710	+	0.0121076i
$926$	35.9487	−	22.7381i	1.18135	−	0.747220i
$927$	−4.91202	+	7.03587i	−0.161332	+	0.231088i
$928$	−12.7944	+	38.3935i	−0.419998	+	1.26033i
$929$	24.6429	+	14.2276i	0.808506	+	0.466791i	0.846437	−	0.532489i	$-0.178743\pi$
$929$	24.6429	+	14.2276i	0.808506	+	0.466791i	−0.0379309	+	0.999280i	$0.512077\pi$
$930$	5.03978	−	18.6185i	0.165261	−	0.610523i
$931$	−2.19373	−	3.79965i	−0.0718965	−	0.124528i
$932$	2.34532	+	28.9734i	0.0768235	+	0.949055i
$933$	−14.1714	+	13.0038i	−0.463950	+	0.425725i
$934$	−2.13334	−	52.7956i	−0.0698050	−	1.72752i
$935$	−44.5450			−1.45678
$936$	16.0880	−	30.2843i	0.525851	−	0.989872i
$937$	−3.05642			−0.0998489			−0.0499244	−	0.998753i	$-0.515898\pi$
$937$	−3.05642			−0.0998489			−0.0499244	+	0.998753i	$0.515898\pi$
$938$	0.528873	+	13.0885i	0.0172683	+	0.427353i
$939$	−41.8673	−	13.1688i	−1.36629	−	0.429746i
$940$	−44.2348	+	3.58069i	−1.44278	+	0.116789i
$941$	17.9485	+	31.0876i	0.585103	+	1.01343i	0.994863	+	0.101235i	$0.0322793\pi$
$941$	17.9485	+	31.0876i	0.585103	+	1.01343i	−0.409760	+	0.912194i	$0.634387\pi$
$942$	−40.8039	−	41.0128i	−1.32946	−	1.33627i
$943$	3.48223	+	2.01047i	0.113397	+	0.0654698i
$944$	−1.96636	+	1.60691i	−0.0639997	+	0.0523006i
$945$	9.30055	−	7.16740i	0.302547	−	0.233155i
$946$	55.9889	−	35.4138i	1.82036	−	1.15140i
$947$	−9.20400	−	5.31393i	−0.299090	−	0.172680i	0.342944	−	0.939356i	$-0.388576\pi$
$947$	−9.20400	−	5.31393i	−0.299090	−	0.172680i	−0.642034	+	0.766676i	$0.721909\pi$
$948$	2.78487	−	12.2257i	0.0904484	−	0.397072i
$949$	36.9399	−	21.3272i	1.19912	−	0.692311i
$950$	−0.306643	+	0.584413i	−0.00994880	+	0.0189609i
$951$	2.67151	+	0.840284i	0.0866296	+	0.0272481i
$952$	5.71731	−	13.4312i	0.185299	−	0.435307i
$953$		−	44.2132i		−	1.43221i	−0.697994	−	0.716104i	$-0.745924\pi$
$953$		−	44.2132i		−	1.43221i	0.697994	−	0.716104i	$-0.254076\pi$
$954$	−20.1640	+	10.4491i	−0.652835	+	0.338304i
$955$	37.5386			1.21472
$956$	−10.9080	−	15.7956i	−0.352790	−	0.510867i
$957$	31.9990	+	34.8721i	1.03438	+	1.12726i
$958$	11.7030	−	22.3042i	0.378108	−	0.720616i
$959$	8.00482	+	13.8648i	0.258489	+	0.447716i
$960$	−17.3170	+	26.0872i	−0.558904	+	0.841962i
$961$	−9.42839	+	16.3305i	−0.304142	+	0.526789i
$962$	21.1543	+	33.4448i	0.682042	+	1.07830i
$963$	14.1600	+	30.2564i	0.456299	+	0.974998i
$964$	−14.1645	+	29.8677i	−0.456207	+	0.961975i
$965$	−9.25651	+	16.0328i	−0.297978	+	0.516113i
$966$	−1.89756	+	0.503259i	−0.0610529	+	0.0161921i
$967$	2.52416	−	1.45733i	0.0811716	−	0.0468644i	−0.458865	−	0.888506i	$-0.651744\pi$
$967$	2.52416	−	1.45733i	0.0811716	−	0.0468644i	0.540036	+	0.841642i	$0.318410\pi$
$968$	−6.10093	−	8.11335i	−0.196091	−	0.260773i
$969$	38.2841	−	8.51527i	1.22986	−	0.273550i
$970$	6.60474	−	0.266882i	0.212066	−	0.00856905i
$971$			48.3893i			1.55289i	0.630188	+	0.776443i	$0.282978\pi$
$971$			48.3893i			1.55289i	−0.630188	+	0.776443i	$0.717022\pi$
$972$	28.7675	+	12.0179i	0.922718	+	0.385475i
$973$		−	2.20139i		−	0.0705733i
$974$	2.14124	+	52.9911i	0.0686099	+	1.69795i
$975$	−0.726785	+	0.161654i	−0.0232757	+	0.00517707i
$976$	22.2379	+	8.42267i	0.711819	+	0.269603i
$977$	30.0139	−	17.3285i	0.960230	−	0.554389i	0.0639860	−	0.997951i	$-0.479619\pi$
$977$	30.0139	−	17.3285i	0.960230	−	0.554389i	0.896244	+	0.443562i	$0.146285\pi$
$978$	−6.09573	−	22.9841i	−0.194920	−	0.734951i
$979$	30.4524	−	52.7452i	0.973264	−	1.68574i
$980$	−1.93657	+	4.08352i	−0.0618614	+	0.130443i
$981$	7.11416	+	15.2012i	0.227138	+	0.485337i
$982$	0.278380	−	0.176079i	0.00888345	−	0.00561890i
$983$	−9.56861	+	16.5733i	−0.305191	+	0.528607i	−0.977304	−	0.211842i	$-0.932054\pi$
$983$	−9.56861	+	16.5733i	−0.305191	+	0.528607i	0.672113	+	0.740449i	$0.265387\pi$
$984$	18.6844	+	15.9684i	0.595636	+	0.509053i
$985$	−9.84188	−	17.0466i	−0.313588	−	0.543151i
$986$	−46.2368	−	24.2605i	−1.47248	−	0.772612i
$987$	−11.4992	−	12.5317i	−0.366025	−	0.398890i
$988$	−29.1809	+	20.1515i	−0.928368	+	0.641104i
$989$	9.82945			0.312558
$990$	16.8483	+	32.5127i	0.535475	+	1.03332i
$991$			34.3176i			1.09013i	0.838392	+	0.545067i	$0.183496\pi$
$991$			34.3176i			1.09013i	−0.838392	+	0.545067i	$0.816504\pi$
$992$	−14.7479	+	13.0798i	−0.468247	+	0.415285i
$993$	13.4873	+	4.24223i	0.428006	+	0.134623i
$994$	5.18868	+	2.72251i	0.164575	+	0.0863527i
$995$	−35.6497	+	20.5823i	−1.13017	+	0.652504i
$996$	−7.84774	+	34.4519i	−0.248665	+	1.09165i
$997$	0.473822	+	0.273562i	0.0150061	+	0.00866378i	0.507484	−	0.861661i	$-0.330576\pi$
$997$	0.473822	+	0.273562i	0.0150061	+	0.00866378i	−0.492478	+	0.870325i	$0.663909\pi$
$998$	30.4785	+	48.1862i	0.964779	+	1.52531i
$999$	−28.4978	+	21.9616i	−0.901632	+	0.694836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.1	✓	144
8.3	odd	2	inner	504.2.br.a.155.24	yes	144
9.5	odd	6	inner	504.2.br.a.491.24	yes	144
72.59	even	6	inner	504.2.br.a.491.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.1	✓	144	1.1	even	1	trivial
504.2.br.a.155.24	yes	144	8.3	odd	2	inner
504.2.br.a.491.1	yes	144	72.59	even	6	inner
504.2.br.a.491.24	yes	144	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41306 + 0.0570983i) q^{2} +(0.376059 + 1.69073i) q^{3} +(1.99348 - 0.161367i) q^{4} +(1.12986 + 1.95698i) q^{5} +(-0.627932 - 2.36764i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.80769 + 0.341845i) q^{8} +(-2.71716 + 1.27163i) q^{9} +O(q^{10})\)	\(q+(-1.41306 + 0.0570983i) q^{2} +(0.376059 + 1.69073i) q^{3} +(1.99348 - 0.161367i) q^{4} +(1.12986 + 1.95698i) q^{5} +(-0.627932 - 2.36764i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.80769 + 0.341845i) q^{8} +(-2.71716 + 1.27163i) q^{9} +(-1.70831 - 2.70082i) q^{10} +(3.30783 + 1.90978i) q^{11} +(1.02249 + 3.30976i) q^{12} +(3.49994 - 2.02069i) q^{13} +(-1.25230 - 0.657082i) q^{14} +(-2.88384 + 2.64624i) q^{15} +(3.94792 - 0.643363i) q^{16} +5.16096i q^{17} +(3.76690 - 1.95204i) q^{18} -4.38745 q^{19} +(2.56815 + 3.71888i) q^{20} +(-0.519690 + 1.65225i) q^{21} +(-4.78321 - 2.50976i) q^{22} +(-0.400728 - 0.694081i) q^{23} +(-1.63383 - 4.61851i) q^{24} +(-0.0531827 + 0.0921152i) q^{25} +(-4.83025 + 3.05520i) q^{26} +(-3.17180 - 4.11579i) q^{27} +(1.80709 + 0.856992i) q^{28} +(3.57701 - 6.19557i) q^{29} +(3.92394 - 3.90396i) q^{30} +(3.01785 - 1.74236i) q^{31} +(-5.54192 + 1.13453i) q^{32} +(-1.98499 + 6.31085i) q^{33} +(-0.294682 - 7.29275i) q^{34} +2.25973i q^{35} +(-5.21140 + 2.97343i) q^{36} -6.92403i q^{37} +(6.19974 - 0.250516i) q^{38} +(4.73263 + 5.15757i) q^{39} +(-3.84129 - 5.10836i) q^{40} +(-4.34488 + 2.50852i) q^{41} +(0.640013 - 2.36440i) q^{42} +(-6.13225 + 10.6214i) q^{43} +(6.90227 + 3.27333i) q^{44} +(-5.55857 - 3.88066i) q^{45} +(0.605884 + 0.957898i) q^{46} +(-4.90983 + 8.50407i) q^{47} +(2.57241 + 6.43294i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.0698908 - 0.133201i) q^{50} +(-8.72581 + 1.94082i) q^{51} +(6.65099 - 4.59298i) q^{52} -5.35295 q^{53} +(4.71695 + 5.63475i) q^{54} +8.63115i q^{55} +(-2.60246 - 1.10780i) q^{56} +(-1.64994 - 7.41801i) q^{57} +(-4.70078 + 8.95895i) q^{58} +(-0.549805 + 0.317430i) q^{59} +(-5.32186 + 5.74058i) q^{60} +(5.14843 + 2.97245i) q^{61} +(-4.16492 + 2.63437i) q^{62} +(-2.98894 - 0.257316i) q^{63} +(7.76628 - 1.91959i) q^{64} +(7.90891 + 4.56621i) q^{65} +(2.44457 - 9.03095i) q^{66} +(-4.63125 - 8.02155i) q^{67} +(0.832807 + 10.2883i) q^{68} +(1.02281 - 0.938539i) q^{69} +(-0.129027 - 3.19313i) q^{70} -4.14333 q^{71} +(7.19425 - 4.49920i) q^{72} +10.5544 q^{73} +(0.395351 + 9.78408i) q^{74} +(-0.175742 - 0.0552771i) q^{75} +(-8.74630 + 0.707989i) q^{76} +(1.90978 + 3.30783i) q^{77} +(-6.98198 - 7.01773i) q^{78} +(-3.13471 - 1.80983i) q^{79} +(5.71966 + 6.99909i) q^{80} +(5.76592 - 6.91044i) q^{81} +(5.99634 - 3.79277i) q^{82} +(8.83359 + 5.10008i) q^{83} +(-0.769374 + 3.37758i) q^{84} +(-10.0999 + 5.83118i) q^{85} +(8.05877 - 15.3588i) q^{86} +(11.8202 + 3.71788i) q^{87} +(-9.94023 - 4.23130i) q^{88} -15.9455i q^{89} +(8.07618 + 5.16622i) q^{90} +4.04138 q^{91} +(-0.910844 - 1.31897i) q^{92} +(4.08075 + 4.44715i) q^{93} +(6.45232 - 12.2971i) q^{94} +(-4.95722 - 8.58616i) q^{95} +(-4.00227 - 8.94325i) q^{96} +(-1.03421 + 1.79131i) q^{97} +(-0.755979 - 1.19520i) q^{98} +(-11.4164 - 0.982834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{6}+O(q^{10}) \) 144 * q + 6 * q^6	\( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

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