LMFDB - Embedded newform 560.2.cz.c.213.79

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(157,560)] 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("560.157"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cz (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [360,2,-24,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$90$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			213.79
Character	$\chi$	$=$	560.213
Dual form			560.2.cz.c.397.79

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32364 - 0.497965i) q^{2} +(-0.623698 - 0.360092i) q^{3} +(1.50406 - 1.31826i) q^{4} +(0.842714 - 2.07119i) q^{5} +(-1.00487 - 0.166053i) q^{6} +(-2.59227 + 0.529295i) q^{7} +(1.33439 - 2.49387i) q^{8} +(-1.24067 - 2.14890i) q^{9} +(0.0840704 - 3.16116i) q^{10} +(-3.86774 + 1.03636i) q^{11} +(-1.41277 + 0.280593i) q^{12} -1.30220i q^{13} +(-3.16767 + 1.99146i) q^{14} +(-1.27142 + 0.988343i) q^{15} +(0.524399 - 3.96548i) q^{16} +(2.97541 - 0.797258i) q^{17} +(-2.71228 - 2.22657i) q^{18} +(3.10711 + 0.832549i) q^{19} +(-1.46287 - 4.22611i) q^{20} +(1.80739 + 0.603335i) q^{21} +(-4.60343 + 3.29776i) q^{22} +(1.57212 + 0.421249i) q^{23} +(-1.73028 + 1.07492i) q^{24} +(-3.57967 - 3.49084i) q^{25} +(-0.648449 - 1.72364i) q^{26} +3.94757i q^{27} +(-3.20118 + 4.21336i) q^{28} +(1.22355 + 1.22355i) q^{29} +(-1.19074 + 1.94134i) q^{30} +(4.67056 + 2.69655i) q^{31} +(-1.28055 - 5.51001i) q^{32} +(2.78548 + 0.746367i) q^{33} +(3.54137 - 2.53693i) q^{34} +(-1.08827 + 5.81512i) q^{35} +(-4.69884 - 1.59656i) q^{36} +(0.612879 + 1.06154i) q^{37} +(4.52729 - 0.445238i) q^{38} +(-0.468911 + 0.812178i) q^{39} +(-4.04077 - 4.86540i) q^{40} +5.53618 q^{41} +(2.69277 - 0.101416i) q^{42} -6.24099i q^{43} +(-4.45113 + 6.65741i) q^{44} +(-5.49631 + 0.758753i) q^{45} +(2.29070 - 0.225279i) q^{46} +(2.48511 - 9.27457i) q^{47} +(-1.75500 + 2.28443i) q^{48} +(6.43969 - 2.74415i) q^{49} +(-6.47652 - 2.83808i) q^{50} +(-2.14284 - 0.574172i) q^{51} +(-1.71663 - 1.95859i) q^{52} +(-4.64563 - 2.68216i) q^{53} +(1.96575 + 5.22517i) q^{54} +(-1.11290 + 8.88417i) q^{55} +(-2.13911 + 7.17107i) q^{56} +(-1.63811 - 1.63811i) q^{57} +(2.22883 + 1.01026i) q^{58} +(8.86473 - 2.37530i) q^{59} +(-0.609401 + 3.16258i) q^{60} +(-1.26482 + 4.72039i) q^{61} +(7.52494 + 1.24349i) q^{62} +(4.35354 + 4.91384i) q^{63} +(-4.43879 - 6.65561i) q^{64} +(-2.69710 - 1.09738i) q^{65} +(4.05865 - 0.399149i) q^{66} +(-7.00704 - 4.04552i) q^{67} +(3.42420 - 5.12147i) q^{68} +(-0.828841 - 0.828841i) q^{69} +(1.45525 + 8.23907i) q^{70} +14.6273i q^{71} +(-7.01462 + 0.226587i) q^{72} +(-6.30257 + 1.68877i) q^{73} +(1.33984 + 1.09990i) q^{74} +(0.975606 + 3.46624i) q^{75} +(5.77080 - 2.84377i) q^{76} +(9.47766 - 4.73368i) q^{77} +(-0.216234 + 1.30853i) q^{78} +(10.0365 - 5.79459i) q^{79} +(-7.77134 - 4.42789i) q^{80} +(-2.30051 + 3.98461i) q^{81} +(7.32792 - 2.75682i) q^{82} +9.57150i q^{83} +(3.51377 - 1.47515i) q^{84} +(0.856142 - 6.83450i) q^{85} +(-3.10779 - 8.26084i) q^{86} +(-0.322536 - 1.20372i) q^{87} +(-2.57654 + 11.0285i) q^{88} +(14.0247 - 8.09717i) q^{89} +(-6.89732 + 3.74129i) q^{90} +(0.689246 + 3.37564i) q^{91} +(2.91988 - 1.43888i) q^{92} +(-1.94201 - 3.36366i) q^{93} +(-1.32901 - 13.5137i) q^{94} +(4.34278 - 5.73383i) q^{95} +(-1.18543 + 3.89770i) q^{96} +(-0.176114 - 0.176114i) q^{97} +(7.15737 - 6.83901i) q^{98} +(7.02560 + 7.02560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.32364	−	0.497965i	0.935957	−	0.352115i
$2$	1.32364	−	0.497965i	0.935957	−	0.352115i
$3$	−0.623698	−	0.360092i	−0.360092	−	0.207899i	0.309029	−	0.951053i	$-0.399996\pi$
$3$	−0.623698	−	0.360092i	−0.360092	−	0.207899i	−0.669121	+	0.743153i	$0.733329\pi$
$4$	1.50406	−	1.31826i	0.752031	−	0.659128i
$5$	0.842714	−	2.07119i	0.376873	−	0.926265i
$5$	0.842714	−	2.07119i	0.376873	−	0.926265i
$6$	−1.00487	−	0.166053i	−0.410235	−	0.0677910i
$7$	−2.59227	+	0.529295i	−0.979785	+	0.200055i
$7$	−2.59227	+	0.529295i	−0.979785	+	0.200055i
$8$	1.33439	−	2.49387i	0.471779	−	0.881717i
$9$	−1.24067	−	2.14890i	−0.413556	−	0.716300i
$10$	0.0840704	−	3.16116i	0.0265854	−	0.999647i
$11$	−3.86774	+	1.03636i	−1.16617	+	0.312473i	−0.789426	−	0.613846i	$-0.789622\pi$
$11$	−3.86774	+	1.03636i	−1.16617	+	0.312473i	−0.376740	+	0.926319i	$0.622955\pi$
$12$	−1.41277	+	0.280593i	−0.407832	+	0.0810003i
$13$		−	1.30220i		−	0.361165i	−0.983560	−	0.180582i	$-0.942202\pi$
$13$		−	1.30220i		−	0.361165i	0.983560	−	0.180582i	$-0.0577982\pi$
$14$	−3.16767	+	1.99146i	−0.846594	+	0.532239i
$15$	−1.27142	+	0.988343i	−0.328279	+	0.255189i
$16$	0.524399	−	3.96548i	0.131100	−	0.991369i
$17$	2.97541	−	0.797258i	0.721642	−	0.193363i	0.120738	−	0.992684i	$-0.461474\pi$
$17$	2.97541	−	0.797258i	0.721642	−	0.193363i	0.600904	+	0.799321i	$0.294807\pi$
$18$	−2.71228	−	2.22657i	−0.639290	−	0.524807i
$19$	3.10711	+	0.832549i	0.712821	+	0.191000i	0.596966	−	0.802266i	$-0.296373\pi$
$19$	3.10711	+	0.832549i	0.712821	+	0.191000i	0.115855	+	0.993266i	$0.463039\pi$
$20$	−1.46287	−	4.22611i	−0.327107	−	0.944987i
$21$	1.80739	+	0.603335i	0.394404	+	0.131658i
$22$	−4.60343	+	3.29776i	−0.981455	+	0.703086i
$23$	1.57212	+	0.421249i	0.327810	+	0.0878365i	0.418971	−	0.908000i	$-0.362391\pi$
$23$	1.57212	+	0.421249i	0.327810	+	0.0878365i	−0.0911604	+	0.995836i	$0.529058\pi$
$24$	−1.73028	+	1.07492i	−0.353192	+	0.219417i
$25$	−3.57967	−	3.49084i	−0.715934	−	0.698168i
$26$	−0.648449	−	1.72364i	−0.127171	−	0.338035i
$27$			3.94757i			0.759710i
$28$	−3.20118	+	4.21336i	−0.604966	+	0.796251i
$29$	1.22355	+	1.22355i	0.227208	+	0.227208i	0.811525	−	0.584317i	$-0.198638\pi$
$29$	1.22355	+	1.22355i	0.227208	+	0.227208i	−0.584317	+	0.811525i	$0.698638\pi$
$30$	−1.19074	+	1.94134i	−0.217399	+	0.354438i
$31$	4.67056	+	2.69655i	0.838857	+	0.484314i	0.856876	−	0.515523i	$-0.172402\pi$
$31$	4.67056	+	2.69655i	0.838857	+	0.484314i	−0.0180184	+	0.999838i	$0.505736\pi$
$32$	−1.28055	−	5.51001i	−0.226372	−	0.974041i
$33$	2.78548	+	0.746367i	0.484890	+	0.129926i
$34$	3.54137	−	2.53693i	0.607340	−	0.435081i
$35$	−1.08827	+	5.81512i	−0.183951	+	0.982935i
$36$	−4.69884	−	1.59656i	−0.783140	−	0.266093i
$37$	0.612879	+	1.06154i	0.100757	+	0.174516i	0.911997	−	0.410198i	$-0.134540\pi$
$37$	0.612879	+	1.06154i	0.100757	+	0.174516i	−0.811240	+	0.584713i	$0.801207\pi$
$38$	4.52729	−	0.445238i	0.734424	−	0.0722271i
$39$	−0.468911	+	0.812178i	−0.0750859	+	0.130053i
$40$	−4.04077	−	4.86540i	−0.638902	−	0.769288i
$41$	5.53618			0.864606			0.432303	−	0.901728i	$-0.357701\pi$
$41$	5.53618			0.864606			0.432303	+	0.901728i	$0.357701\pi$
$42$	2.69277	−	0.101416i	0.415504	−	0.0156488i
$43$		−	6.24099i		−	0.951741i	−0.879515	−	0.475871i	$-0.842133\pi$
$43$		−	6.24099i		−	0.951741i	0.879515	−	0.475871i	$-0.157867\pi$
$44$	−4.45113	+	6.65741i	−0.671033	+	1.00364i
$45$	−5.49631	+	0.758753i	−0.819341	+	0.113108i
$46$	2.29070	−	0.225279i	0.337745	−	0.0332156i
$47$	2.48511	−	9.27457i	0.362491	−	1.35284i	−0.508299	−	0.861181i	$-0.669726\pi$
$47$	2.48511	−	9.27457i	0.362491	−	1.35284i	0.870790	−	0.491655i	$-0.163608\pi$
$48$	−1.75500	+	2.28443i	−0.253313	+	0.329729i
$49$	6.43969	−	2.74415i	0.919956	−	0.392021i
$50$	−6.47652	−	2.83808i	−0.915918	−	0.401365i
$51$	−2.14284	−	0.574172i	−0.300058	−	0.0804002i
$52$	−1.71663	−	1.95859i	−0.238054	−	0.271607i
$53$	−4.64563	−	2.68216i	−0.638127	−	0.368423i	0.145766	−	0.989319i	$-0.453435\pi$
$53$	−4.64563	−	2.68216i	−0.638127	−	0.368423i	−0.783893	+	0.620896i	$0.786769\pi$
$54$	1.96575	+	5.22517i	0.267505	+	0.711056i
$55$	−1.11290	+	8.88417i	−0.150063	+	1.19794i
$56$	−2.13911	+	7.17107i	−0.285851	+	0.958274i
$57$	−1.63811	−	1.63811i	−0.216972	−	0.216972i
$58$	2.22883	+	1.01026i	0.292660	+	0.132654i
$59$	8.86473	−	2.37530i	1.15409	−	0.309237i	0.369487	−	0.929236i	$-0.379534\pi$
$59$	8.86473	−	2.37530i	1.15409	−	0.309237i	0.784603	+	0.619999i	$0.212867\pi$
$60$	−0.609401	+	3.16258i	−0.0786733	+	0.408288i
$61$	−1.26482	+	4.72039i	−0.161944	+	0.604384i	0.836466	+	0.548019i	$0.184618\pi$
$61$	−1.26482	+	4.72039i	−0.161944	+	0.604384i	−0.998410	+	0.0563651i	$0.982049\pi$
$62$	7.52494	+	1.24349i	0.955668	+	0.157923i
$63$	4.35354	+	4.91384i	0.548495	+	0.619086i
$64$	−4.43879	−	6.65561i	−0.554848	−	0.831951i
$65$	−2.69710	−	1.09738i	−0.334534	−	0.136113i
$66$	4.05865	−	0.399149i	0.499585	−	0.0491319i
$67$	−7.00704	−	4.04552i	−0.856046	−	0.494239i	0.00664007	−	0.999978i	$-0.497886\pi$
$67$	−7.00704	−	4.04552i	−0.856046	−	0.494239i	−0.862686	+	0.505739i	$0.831220\pi$
$68$	3.42420	−	5.12147i	0.415246	−	0.621070i
$69$	−0.828841	−	0.828841i	−0.0997808	−	0.0997808i
$70$	1.45525	+	8.23907i	0.173936	+	0.984757i
$71$			14.6273i			1.73594i	0.496619	+	0.867969i	$0.334575\pi$
$71$			14.6273i			1.73594i	−0.496619	+	0.867969i	$0.665425\pi$
$72$	−7.01462	+	0.226587i	−0.826680	+	0.0267036i
$73$	−6.30257	+	1.68877i	−0.737660	+	0.197655i	−0.608038	−	0.793908i	$-0.708043\pi$
$73$	−6.30257	+	1.68877i	−0.737660	+	0.197655i	−0.129622	+	0.991563i	$0.541376\pi$
$74$	1.33984	+	1.09990i	0.155753	+	0.127861i
$75$	0.975606	+	3.46624i	0.112653	+	0.400247i
$76$	5.77080	−	2.84377i	0.661957	−	0.326203i
$77$	9.47766	−	4.73368i	1.08008	−	0.539453i
$78$	−0.216234	+	1.30853i	−0.0244837	+	0.148162i
$79$	10.0365	−	5.79459i	1.12920	−	0.651942i	0.185464	−	0.982651i	$-0.440621\pi$
$79$	10.0365	−	5.79459i	1.12920	−	0.651942i	0.943733	+	0.330709i	$0.107288\pi$
$80$	−7.77134	−	4.42789i	−0.868863	−	0.495053i
$81$	−2.30051	+	3.98461i	−0.255613	+	0.442734i
$82$	7.32792	−	2.75682i	0.809234	−	0.304440i
$83$			9.57150i			1.05061i	0.850914	+	0.525305i	$0.176049\pi$
$83$			9.57150i			1.05061i	−0.850914	+	0.525305i	$0.823951\pi$
$84$	3.51377	−	1.47515i	0.383384	−	0.160952i
$85$	0.856142	−	6.83450i	0.0928617	−	0.741305i
$86$	−3.10779	−	8.26084i	−0.335122	−	0.890789i
$87$	−0.322536	−	1.20372i	−0.0345794	−	0.129052i
$88$	−2.57654	+	11.0285i	−0.274660	+	1.17565i
$89$	14.0247	−	8.09717i	1.48662	−	0.858298i	0.486732	−	0.873551i	$-0.338189\pi$
$89$	14.0247	−	8.09717i	1.48662	−	0.858298i	0.999884	+	0.0152534i	$0.00485550\pi$
$90$	−6.89732	+	3.74129i	−0.727041	+	0.394367i
$91$	0.689246	+	3.37564i	0.0722526	+	0.353864i
$92$	2.91988	−	1.43888i	0.304419	−	0.150013i
$93$	−1.94201	−	3.36366i	−0.201377	−	0.348796i
$94$	−1.32901	−	13.5137i	−0.137077	−	1.39383i
$95$	4.34278	−	5.73383i	0.445559	−	0.588278i
$96$	−1.18543	+	3.89770i	−0.120988	+	0.397807i
$97$	−0.176114	−	0.176114i	−0.0178817	−	0.0178817i	0.698109	−	0.715991i	$-0.254025\pi$
$97$	−0.176114	−	0.176114i	−0.0178817	−	0.0178817i	−0.715991	+	0.698109i	$0.754025\pi$
$98$	7.15737	−	6.83901i	0.723003	−	0.690845i
$99$	7.02560	+	7.02560i	0.706099	+	0.706099i
$100$	−9.98586	−	0.531520i	−0.998586	−	0.0531520i
$101$	3.17949	+	11.8660i	0.316371	+	1.18071i	0.922706	+	0.385503i	$0.125972\pi$
$101$	3.17949	+	11.8660i	0.316371	+	1.18071i	−0.606335	+	0.795209i	$0.707361\pi$
$102$	−3.12227	+	0.307061i	−0.309151	+	0.0304036i
$103$	−3.18347	+	11.8809i	−0.313676	+	1.17066i	0.611540	+	0.791214i	$0.290550\pi$
$103$	−3.18347	+	11.8809i	−0.313676	+	1.17066i	−0.925216	+	0.379441i	$0.876116\pi$
$104$	−3.24751	−	1.73764i	−0.318445	−	0.170390i
$105$	2.77273	−	3.23500i	0.270591	−	0.315704i
$106$	−7.48478	−	1.23685i	−0.726986	−	0.120134i
$107$	−2.02564	−	3.50852i	−0.195826	−	0.339181i	0.751345	−	0.659910i	$-0.229406\pi$
$107$	−2.02564	−	3.50852i	−0.195826	−	0.339181i	−0.947171	+	0.320729i	$0.896072\pi$
$108$	5.20391	+	5.93739i	0.500746	+	0.571325i
$109$	−1.17022	+	0.313558i	−0.112086	+	0.0300334i	−0.314426	−	0.949282i	$-0.601812\pi$
$109$	−1.17022	+	0.313558i	−0.112086	+	0.0300334i	0.202340	+	0.979315i	$0.435145\pi$
$110$	2.95093	+	12.3137i	0.281360	+	1.17406i
$111$		−	0.882771i		−	0.0837889i
$112$	0.739523	+	10.5571i	0.0698783	+	0.997556i
$113$	12.8737	+	12.8737i	1.21106	+	1.21106i	0.970679	+	0.240378i	$0.0772714\pi$
$113$	12.8737	+	12.8737i	1.21106	+	1.21106i	0.240378	+	0.970679i	$0.422729\pi$
$114$	−2.98399	−	1.35255i	−0.279476	−	0.126678i
$115$	2.19734	−	2.90118i	0.204903	−	0.270536i
$116$	3.45326	+	0.227342i	0.320627	+	0.0211081i
$117$	−2.79829	+	1.61559i	−0.258702	+	0.149362i
$118$	10.5509	−	7.55837i	0.971291	−	0.695805i
$119$	−7.29106	+	3.64157i	−0.668371	+	0.333822i
$120$	0.768227	+	4.48959i	0.0701293	+	0.409842i
$121$	4.35906	−	2.51671i	0.396278	−	0.228791i
$122$	0.676414	+	6.87795i	0.0612397	+	0.622700i
$123$	−3.45290	−	1.99353i	−0.311338	−	0.179751i
$124$	10.5795	−	2.10122i	0.950072	−	0.188695i
$125$	−10.2468	+	4.47240i	−0.916505	+	0.400023i
$126$	8.20946	+	4.33626i	0.731357	+	0.386305i
$127$	−13.9513	+	13.9513i	−1.23798	+	1.23798i	−0.277154	+	0.960825i	$0.589391\pi$
$127$	−13.9513	+	13.9513i	−1.23798	+	1.23798i	−0.960825	+	0.277154i	$0.910609\pi$
$128$	−9.18963	−	6.59929i	−0.812256	−	0.583300i
$129$	−2.24733	+	3.89249i	−0.197866	+	0.342715i
$130$	−4.11646	−	0.109476i	−0.361037	−	0.00960171i
$131$	0.366673	−	1.36844i	0.0320364	−	0.119561i	−0.948056	−	0.318104i	$-0.896954\pi$
$131$	0.366673	−	1.36844i	0.0320364	−	0.119561i	0.980092	+	0.198542i	$0.0636207\pi$
$132$	5.17344	−	2.54940i	0.450290	−	0.221897i
$133$	−8.49513	−	0.513610i	−0.736622	−	0.0445356i
$134$	−11.2893	−	1.86556i	−0.975251	−	0.161160i
$135$	8.17617	+	3.32667i	0.703693	+	0.286314i
$136$	1.98211	−	8.48414i	0.169964	−	0.727509i
$137$	6.46769	−	1.73301i	0.552572	−	0.148061i	0.0282805	−	0.999600i	$-0.490997\pi$
$137$	6.46769	−	1.73301i	0.552572	−	0.148061i	0.524292	+	0.851539i	$0.324330\pi$
$138$	−1.50982	−	0.684356i	−0.128525	−	0.0582562i
$139$	−4.62212	−	4.62212i	−0.392043	−	0.392043i	0.483372	−	0.875415i	$-0.339412\pi$
$139$	−4.62212	−	4.62212i	−0.392043	−	0.392043i	−0.875415	+	0.483372i	$0.839412\pi$
$140$	6.02900	+	10.1809i	0.509544	+	0.860445i
$141$	−4.88966	+	4.88966i	−0.411784	+	0.411784i
$142$	7.28387	+	19.3613i	0.611249	+	1.62476i
$143$	1.34954	+	5.03656i	0.112854	+	0.421178i
$144$	−9.17201	+	3.79296i	−0.764335	+	0.316080i
$145$	3.56532	−	1.50311i	0.296083	−	0.124826i
$146$	−7.50141	+	5.37379i	−0.620821	+	0.444738i
$147$	−5.00457	−	0.607365i	−0.412770	−	0.0500946i
$148$	2.32119	+	0.788685i	0.190800	+	0.0648295i
$149$	−6.33152	−	1.69653i	−0.518699	−	0.138985i	−0.0100340	−	0.999950i	$-0.503194\pi$
$149$	−6.33152	−	1.69653i	−0.518699	−	0.138985i	−0.508665	+	0.860965i	$0.669861\pi$
$150$	3.01742	+	4.10225i	0.246371	+	0.334947i
$151$	7.43917	+	4.29501i	0.605391	+	0.349523i	0.771159	−	0.636642i	$-0.219677\pi$
$151$	7.43917	+	4.29501i	0.605391	+	0.349523i	−0.165768	+	0.986165i	$0.553010\pi$
$152$	6.22238	−	6.63780i	0.504702	−	0.538396i
$153$	−5.40472	−	5.40472i	−0.436946	−	0.436946i
$154$	10.1878	−	10.9853i	0.820959	−	0.885217i
$155$	9.52101	−	7.40120i	0.764746	−	0.594479i
$156$	0.365388	+	1.83971i	0.0292544	+	0.147295i
$157$	11.3243	−	19.6143i	0.903780	−	1.56539i	0.0812343	−	0.996695i	$-0.474114\pi$
$157$	11.3243	−	19.6143i	0.903780	−	1.56539i	0.822546	−	0.568698i	$-0.192553\pi$
$158$	10.3993	−	12.6678i	0.827321	−	1.00780i
$159$	1.93165	+	3.34571i	0.153190	+	0.265332i
$160$	−12.4914	−	1.99109i	−0.987533	−	0.157409i
$161$	−4.29833	−	0.259874i	−0.338756	−	0.0204809i
$162$	−1.06086	+	6.41977i	−0.0833492	+	0.504385i
$163$	−10.6154	−	18.3864i	−0.831463	−	1.44014i	−0.896878	−	0.442278i	$-0.854170\pi$
$163$	−10.6154	−	18.3864i	−0.831463	−	1.44014i	0.0654148	−	0.997858i	$-0.479163\pi$
$164$	8.32675	−	7.29810i	0.650210	−	0.569886i
$165$	3.89323	−	5.14029i	0.303088	−	0.400171i
$166$	4.76628	+	12.6693i	0.369935	+	0.983325i
$167$	−5.40470	+	5.40470i	−0.418228	+	0.418228i	−0.884593	−	0.466365i	$-0.845563\pi$
$167$	−5.40470	+	5.40470i	−0.418228	+	0.418228i	0.466365	+	0.884593i	$0.345563\pi$
$168$	3.91640	−	3.70230i	0.302157	−	0.285639i
$169$	11.3043			0.869560
$170$	−2.27012	−	9.47276i	−0.174110	−	0.726528i
$171$	−2.06583	−	7.70979i	−0.157978	−	0.589583i
$172$	−8.22722	−	9.38682i	−0.627320	−	0.715739i
$173$	−22.3986	+	12.9318i	−1.70293	+	0.983187i	−0.760165	+	0.649730i	$0.774882\pi$
$173$	−22.3986	+	12.9318i	−1.70293	+	0.983187i	−0.942765	+	0.333457i	$0.891785\pi$
$174$	−1.02633	−	1.43268i	−0.0778060	−	0.108611i
$175$	11.1271	+	7.15450i	0.841133	+	0.540829i
$176$	2.08141	+	15.8809i	0.156892	+	1.19707i
$177$	−6.38424	−	1.71065i	−0.479869	−	0.128580i
$178$	14.5316	−	17.7016i	1.08919	−	1.32679i
$179$	−3.94762	+	1.05776i	−0.295059	+	0.0790608i	−0.403312	−	0.915063i	$-0.632141\pi$
$179$	−3.94762	+	1.05776i	−0.295059	+	0.0790608i	0.108253	+	0.994123i	$0.465474\pi$
$180$	−7.26655	+	8.38676i	−0.541617	+	0.625112i
$181$	9.97127	−	9.97127i	0.741159	−	0.741159i	−0.231642	−	0.972801i	$-0.574410\pi$
$181$	9.97127	−	9.97127i	0.741159	−	0.741159i	0.972801	+	0.231642i	$0.0744099\pi$
$182$	2.59327	+	4.12493i	0.192226	+	0.305760i
$183$	2.48864	−	2.48864i	0.183966	−	0.183966i
$184$	3.14837	−	3.35856i	0.232101	−	0.247596i
$185$	2.71513	−	0.374817i	0.199620	−	0.0275571i
$186$	−4.24552	−	3.48523i	−0.311296	−	0.255550i
$187$	−10.6818	+	6.16717i	−0.781134	+	0.450988i
$188$	−8.48850	−	17.2255i	−0.619088	−	1.25630i
$189$	−2.08943	−	10.2332i	−0.151984	−	0.744352i
$190$	2.89304	−	9.75209i	0.209883	−	0.707491i
$191$	−8.80890	−	15.2575i	−0.637390	−	1.10399i	−0.986003	−	0.166725i	$-0.946681\pi$
$191$	−8.80890	−	15.2575i	−0.637390	−	1.10399i	0.348614	−	0.937266i	$-0.386653\pi$
$192$	0.371828	+	5.74946i	0.0268344	+	0.414932i
$193$	24.7159	−	6.62260i	1.77909	−	0.476705i	0.788672	−	0.614815i	$-0.210769\pi$
$193$	24.7159	−	6.62260i	1.77909	−	0.476705i	0.990417	+	0.138109i	$0.0441025\pi$
$194$	−0.320811	−	0.145413i	−0.0230329	−	0.0104401i
$195$	1.28702	+	1.65564i	0.0921653	+	0.118563i
$196$	6.06821	−	12.6165i	0.433443	−	0.901181i
$197$	−18.7829			−1.33822			−0.669112	−	0.743161i	$-0.733326\pi$
$197$	−18.7829			−1.33822			−0.669112	+	0.743161i	$0.733326\pi$
$198$	12.7979	+	5.80088i	0.909506	+	0.412251i
$199$	−7.71789	−	4.45592i	−0.547106	−	0.315872i	0.200848	−	0.979622i	$-0.435630\pi$
$199$	−7.71789	−	4.45592i	−0.547106	−	0.315872i	−0.747954	+	0.663750i	$0.768964\pi$
$200$	−13.4824	+	4.26907i	−0.953349	+	0.301869i
$201$	2.91352	+	5.04636i	0.205504	+	0.355943i
$202$	10.1174	+	14.1231i	0.711856	+	0.993697i
$203$	−3.81940	−	2.52416i	−0.268069	−	0.177161i
$204$	−3.97987	+	1.96122i	−0.278647	+	0.137313i
$205$	4.66541	−	11.4665i	0.325847	−	0.800854i
$206$	1.70248	+	17.3113i	0.118618	+	1.20613i
$207$	−1.04526	−	3.90097i	−0.0726506	−	0.271136i
$208$	−5.16384	−	0.682872i	−0.358048	−	0.0473486i
$209$	−12.8803			−0.890950
$210$	2.05919	−	5.66271i	0.142097	−	0.390764i
$211$	−6.90757	+	6.90757i	−0.475537	+	0.475537i	−0.903701	−	0.428164i	$-0.859161\pi$
$211$	−6.90757	+	6.90757i	−0.475537	+	0.475537i	0.428164	+	0.903701i	$0.359161\pi$
$212$	−10.5231	+	2.09001i	−0.722729	+	0.143542i
$213$	5.26716	−	9.12299i	0.360900	−	0.625097i
$214$	−4.42835	−	3.63532i	−0.302716	−	0.248505i
$215$	−12.9263	−	5.25936i	−0.881565	−	0.358686i
$216$	9.84473	+	5.26761i	0.669849	+	0.358416i
$217$	−13.5346	−	4.51807i	−0.918789	−	0.306707i
$218$	−1.39281	+	0.997766i	−0.0943327	+	0.0675772i
$219$	4.53901	+	1.21622i	0.306718	+	0.0821848i
$220$	10.0377	+	14.8294i	0.676745	+	0.999800i
$221$	−1.03819	−	3.87457i	−0.0698361	−	0.260632i
$222$	−0.439589	−	1.16847i	−0.0295033	−	0.0784228i
$223$	−4.16871	+	4.16871i	−0.279157	+	0.279157i	−0.832773	−	0.553615i	$-0.813248\pi$
$223$	−4.16871	+	4.16871i	−0.279157	+	0.279157i	0.553615	+	0.832773i	$0.313248\pi$
$224$	6.23595	+	13.6056i	0.416657	+	0.909064i
$225$	−3.06029	+	12.0233i	−0.204019	+	0.801555i
$226$	23.4509	+	10.6295i	1.55993	+	0.707066i
$227$	7.18744	−	12.4490i	0.477047	−	0.826270i	−0.522607	−	0.852574i	$-0.675040\pi$
$227$	7.18744	−	12.4490i	0.477047	−	0.826270i	0.999654	+	0.0263039i	$0.00837376\pi$
$228$	−4.62326	−	0.304367i	−0.306183	−	0.0201572i
$229$	−1.03029	+	3.84511i	−0.0680838	+	0.254092i	−0.991576	−	0.129524i	$-0.958655\pi$
$229$	−1.03029	+	3.84511i	−0.0680838	+	0.254092i	0.923492	+	0.383617i	$0.125322\pi$
$230$	1.46381	−	4.93432i	0.0965205	−	0.325359i
$231$	−7.61576	−	0.460443i	−0.501080	−	0.0302949i
$232$	4.68408	−	1.41868i	0.307525	−	0.0931410i
$233$	0.543375	+	0.145597i	0.0355977	+	0.00953837i	0.276574	−	0.960993i	$-0.410801\pi$
$233$	0.543375	+	0.145597i	0.0355977	+	0.00953837i	−0.240976	+	0.970531i	$0.577468\pi$
$234$	−2.89943	+	3.53192i	−0.189542	+	0.230889i
$235$	−17.1152	−	12.9630i	−1.11647	−	0.845610i
$236$	10.2018	−	15.2586i	0.664083	−	0.993249i
$237$	−8.34634			−0.542153
$238$	−7.83739	+	8.45084i	−0.508022	+	0.547787i
$239$			16.8638i			1.09083i	0.838167	+	0.545414i	$0.183628\pi$
$239$			16.8638i			1.09083i	−0.838167	+	0.545414i	$0.816372\pi$
$240$	3.25252	+	5.56007i	0.209949	+	0.358901i
$241$	5.17220	+	2.98617i	0.333170	+	0.192356i	0.657248	−	0.753675i	$-0.271720\pi$
$241$	5.17220	+	2.98617i	0.333170	+	0.192356i	−0.324077	+	0.946031i	$0.605054\pi$
$242$	4.51661	−	5.50188i	0.290339	−	0.353674i
$243$	13.1257	−	7.57815i	0.842017	−	0.486138i
$244$	4.32031	+	8.76712i	0.276580	+	0.561257i
$245$	−0.256833	−	15.6504i	−0.0164085	−	0.999865i
$246$	−5.56312	−	0.919301i	−0.354692	−	0.0586125i
$247$	1.08414	−	4.04608i	0.0689824	−	0.257446i
$248$	12.9572	−	8.04952i	0.822784	−	0.511145i
$249$	3.44662	−	5.96973i	0.218421	−	0.378316i
$250$	−11.3361	+	11.0224i	−0.716955	+	0.697119i
$251$	0.424636	−	0.424636i	0.0268028	−	0.0268028i	−0.693578	−	0.720381i	$-0.743967\pi$
$251$	0.424636	−	0.424636i	0.0268028	−	0.0268028i	0.720381	+	0.693578i	$0.243967\pi$
$252$	13.0257	+	1.65163i	0.820542	+	0.104043i
$253$	−6.51712			−0.409728
$254$	−11.5193	+	25.4138i	−0.722785	+	1.59461i
$255$	−2.99502	+	3.95437i	−0.187556	+	0.247632i
$256$	−15.4500	−	4.15899i	−0.965626	−	0.259937i
$257$	−2.68019	+	10.0026i	−0.167185	+	0.623945i	0.830566	+	0.556920i	$0.188017\pi$
$257$	−2.68019	+	10.0026i	−0.167185	+	0.623945i	−0.997751	+	0.0670243i	$0.978650\pi$
$258$	−1.03634	+	6.27136i	−0.0645195	+	0.390438i
$259$	−2.15061	−	2.42739i	−0.133632	−	0.150831i
$260$	−5.50323	+	1.90494i	−0.341296	+	0.118140i
$261$	1.11127	−	4.14731i	0.0687859	−	0.256712i
$262$	−0.196093	−	1.99392i	−0.0121146	−	0.123185i
$263$	5.39358	+	20.1291i	0.332582	+	1.24121i	0.906466	+	0.422278i	$0.138769\pi$
$263$	5.39358	+	20.1291i	0.332582	+	1.24121i	−0.573884	+	0.818937i	$0.694564\pi$
$264$	5.57827	−	5.95068i	0.343319	−	0.366239i
$265$	−9.47020	+	7.36170i	−0.581750	+	0.452226i
$266$	−11.5003	+	3.55045i	−0.705128	+	0.217692i
$267$	−11.6629			−0.713758
$268$	−15.8720	+	3.15237i	−0.969539	+	0.192562i
$269$	7.70811	+	28.7671i	0.469972	+	1.75396i	0.639856	+	0.768495i	$0.278994\pi$
$269$	7.70811	+	28.7671i	0.469972	+	1.75396i	−0.169884	+	0.985464i	$0.554339\pi$
$270$	12.4789	+	0.331874i	0.759442	+	0.0201972i
$271$	−3.82804	+	2.21012i	−0.232537	+	0.134255i	−0.611742	−	0.791058i	$-0.709531\pi$
$271$	−3.82804	+	2.21012i	−0.232537	+	0.134255i	0.379205	+	0.925313i	$0.376197\pi$
$272$	−1.60121	−	12.2170i	−0.0970874	−	0.740764i
$273$	0.785661	−	2.35357i	0.0475504	−	0.142445i
$274$	7.69793	−	5.51457i	0.465049	−	0.333148i
$275$	17.4630	+	9.79184i	1.05306	+	0.590470i
$276$	−2.33925	−	0.154002i	−0.140807	−	0.00926986i
$277$	4.24736	−	7.35664i	0.255199	−	0.442018i	−0.709751	−	0.704453i	$-0.751192\pi$
$277$	4.24736	−	7.35664i	0.255199	−	0.442018i	0.964950	+	0.262435i	$0.0845257\pi$
$278$	−8.41969	−	3.81638i	−0.504979	−	0.228891i
$279$		−	13.3821i		−	0.801164i
$280$	13.0500	+	10.4737i	0.779886	+	0.625921i
$281$		−	1.51577i		−	0.0904234i	−0.998977	−	0.0452117i	$-0.985604\pi$
$281$		−	1.51577i		−	0.0904234i	0.998977	−	0.0452117i	$-0.0143962\pi$
$282$	−4.03728	+	8.90704i	−0.240417	+	0.530407i
$283$	6.13216	−	10.6212i	0.364519	−	0.631365i	−0.624180	−	0.781281i	$-0.714567\pi$
$283$	6.13216	−	10.6212i	0.364519	−	0.631365i	0.988699	+	0.149915i	$0.0479001\pi$
$284$	19.2825	+	22.0003i	1.14421	+	1.30548i
$285$	−4.77329	+	2.01238i	−0.282745	+	0.119203i
$286$	4.29434	+	5.99458i	0.253930	+	0.354467i
$287$	−14.3512	+	2.93027i	−0.847128	+	0.172968i
$288$	−10.2517	+	9.58787i	−0.604088	+	0.564970i
$289$	−6.50500	+	3.75567i	−0.382647	+	0.220922i
$290$	3.97071	−	3.76498i	0.233168	−	0.221087i
$291$	0.0464247	+	0.173259i	0.00272146	+	0.0101566i
$292$	−7.25322	+	10.8484i	−0.424463	+	0.634856i
$293$	−0.845374			−0.0493873			−0.0246936	−	0.999695i	$-0.507861\pi$
$293$	−0.845374			−0.0493873			−0.0246936	+	0.999695i	$0.507861\pi$
$294$	−6.92671	+	1.68817i	−0.403974	+	0.0984559i
$295$	2.55073	−	20.3622i	0.148509	−	1.18554i
$296$	3.46516	−	0.111932i	0.201408	−	0.00650593i
$297$	−4.09109	−	15.2682i	−0.237389	−	0.885948i
$298$	−9.22549	+	0.907284i	−0.534418	+	0.0525575i
$299$	0.548550	−	2.04722i	0.0317235	−	0.118394i
$300$	6.03676	+	3.92734i	0.348533	+	0.226745i
$301$	3.30332	+	16.1783i	0.190400	+	0.932502i
$302$	11.9856	+	1.98061i	0.689692	+	0.113971i
$303$	2.28982	−	8.54571i	0.131547	−	0.490938i
$304$	4.93082	−	11.8846i	0.282802	−	0.681629i
$305$	8.71094	+	6.59763i	0.498787	+	0.377779i
$306$	−9.84528	−	4.46255i	−0.562817	−	0.255107i
$307$	−16.2854			−0.929459			−0.464730	−	0.885453i	$-0.653848\pi$
$307$	−16.2854			−0.929459			−0.464730	+	0.885453i	$0.653848\pi$
$308$	8.01477	−	19.6137i	0.456684	−	1.11760i
$309$	6.26372	−	6.26372i	0.356331	−	0.356331i
$310$	8.91688	−	14.5377i	0.506445	−	0.825685i
$311$	−1.90495	+	3.29948i	−0.108020	+	0.187096i	−0.914968	−	0.403526i	$-0.867784\pi$
$311$	−1.90495	+	3.29948i	−0.108020	+	0.187096i	0.806948	+	0.590622i	$0.201118\pi$
$312$	1.39975	+	2.25317i	0.0792455	+	0.127561i
$313$	6.08353	−	22.7040i	0.343861	−	1.28331i	−0.550075	−	0.835115i	$-0.685401\pi$
$313$	6.08353	−	22.7040i	0.343861	−	1.28331i	0.893937	−	0.448193i	$-0.147932\pi$
$314$	5.22212	−	31.6015i	0.294701	−	1.78338i
$315$	13.8463	−	4.87606i	0.780150	−	0.274735i
$316$	7.45678	−	21.9461i	0.419477	−	1.23457i
$317$	0.0246702	−	0.0142434i	0.00138562	−	0.000799987i	−0.499307	−	0.866425i	$-0.666412\pi$
$317$	0.0246702	−	0.0142434i	0.00138562	−	0.000799987i	0.500693	+	0.865625i	$0.333079\pi$
$318$	4.22286	+	3.46663i	0.236806	+	0.194399i
$319$	−6.00042	−	3.46434i	−0.335959	−	0.193966i
$320$	−17.5257	+	3.58480i	−0.979715	+	0.200397i
$321$			2.91767i			0.162849i
$322$	−5.81886	+	1.79644i	−0.324272	+	0.100112i
$323$	9.90869			0.551334
$324$	1.79262	+	9.02576i	0.0995900	+	0.501431i
$325$	−4.54577	+	4.66144i	−0.252154	+	0.258570i
$326$	−23.2068	−	19.0510i	−1.28531	−	1.05514i
$327$	0.842770	+	0.225820i	0.0466053	+	0.0124879i
$328$	7.38744	−	13.8065i	0.407903	−	0.762337i
$329$	−1.53310	+	25.3575i	−0.0845224	+	1.39801i
$330$	2.59356	−	8.74260i	0.142771	−	0.481265i
$331$	0.342677	−	1.27889i	0.0188352	−	0.0702941i	−0.955869	−	0.293795i	$-0.905082\pi$
$331$	0.342677	−	1.27889i	0.0188352	−	0.0702941i	0.974704	+	0.223501i	$0.0717485\pi$
$332$	12.6177	+	14.3961i	0.692486	+	0.790090i
$333$	1.52076	−	2.63403i	0.0833370	−	0.144344i
$334$	−4.46254	+	9.84524i	−0.244179	+	0.538708i
$335$	−14.2840	+	11.1037i	−0.780416	+	0.606660i
$336$	3.34030	−	6.85076i	0.182228	−	0.373739i
$337$	9.95073	−	9.95073i	0.542051	−	0.542051i	−0.382079	−	0.924130i	$-0.624792\pi$
$337$	9.95073	−	9.95073i	0.542051	−	0.542051i	0.924130	+	0.382079i	$0.124792\pi$
$338$	14.9628	−	5.62914i	0.813871	−	0.306185i
$339$	−3.39358	−	12.6650i	−0.184314	−	0.687870i
$340$	−7.72193	−	11.4081i	−0.418781	−	0.618692i
$341$	−20.8591	−	5.58917i	−1.12958	−	0.302671i
$342$	−6.57363	−	9.17630i	−0.355461	−	0.496197i
$343$	−15.2409	+	10.5221i	−0.822934	+	0.568138i
$344$	−15.5642	−	8.32793i	−0.839166	−	0.449012i
$345$	−2.41516	+	1.01821i	−0.130028	+	0.0548188i
$346$	−23.2081	+	28.2708i	−1.24767	+	1.51985i
$347$	4.25411	−	7.36834i	0.228373	−	0.395553i	−0.728953	−	0.684563i	$-0.759993\pi$
$347$	4.25411	−	7.36834i	0.228373	−	0.395553i	0.957326	+	0.289010i	$0.0933262\pi$
$348$	−2.07192	−	1.38528i	−0.111067	−	0.0742589i
$349$	−21.0228	+	21.0228i	−1.12532	+	1.12532i	−0.134397	+	0.990928i	$0.542910\pi$
$349$	−21.0228	+	21.0228i	−1.12532	+	1.12532i	−0.990928	+	0.134397i	$0.957090\pi$
$350$	18.2910	+	3.92907i	0.977698	+	0.210018i
$351$	5.14052			0.274381
$352$	10.6632	+	19.9841i	0.568349	+	1.06516i
$353$	−3.61815	−	13.5031i	−0.192574	−	0.718698i	−0.992881	−	0.119107i	$-0.961997\pi$
$353$	−3.61815	−	13.5031i	−0.192574	−	0.718698i	0.800307	−	0.599591i	$-0.204670\pi$
$354$	−9.30230	+	0.914837i	−0.494411	+	0.0486231i
$355$	30.2959	+	12.3266i	1.60794	+	0.654228i
$356$	10.4199	−	30.6668i	0.552252	−	1.62534i
$357$	5.85872	+	0.354214i	0.310076	+	0.0187470i
$358$	−4.69851	+	3.36588i	−0.248324	+	0.177892i
$359$	−11.6770	−	20.2251i	−0.616287	−	1.06744i	−0.990157	−	0.139959i	$-0.955303\pi$
$359$	−11.6770	−	20.2251i	−0.616287	−	1.06744i	0.373870	−	0.927481i	$-0.378030\pi$
$360$	−5.44201	+	14.7196i	−0.286819	+	0.775789i
$361$	−7.49346	−	4.32635i	−0.394393	−	0.227703i
$362$	8.23305	−	18.1637i	0.432720	−	0.954665i
$363$	−3.62498			−0.190262
$364$	5.48663	+	4.16857i	0.287578	+	0.218493i
$365$	−1.81350	+	14.4770i	−0.0949229	+	0.757760i
$366$	2.05482	−	4.53333i	0.107407	−	0.236961i
$367$	6.79376	−	1.82038i	0.354631	−	0.0950232i	−0.0771051	−	0.997023i	$-0.524568\pi$
$367$	6.79376	−	1.82038i	0.354631	−	0.0950232i	0.431736	+	0.902000i	$0.357901\pi$
$368$	2.49487	−	6.01332i	0.130054	−	0.313466i
$369$	−6.86856	−	11.8967i	−0.357563	−	0.619317i
$370$	3.40721	−	1.84816i	0.177133	−	0.0960815i
$371$	13.4624	+	4.49396i	0.698932	+	0.233315i
$372$	−7.35507	−	2.49908i	−0.381343	−	0.129571i
$373$	−24.8817	+	14.3654i	−1.28832	+	0.743814i	−0.978355	−	0.206932i	$-0.933652\pi$
$373$	−24.8817	+	14.3654i	−1.28832	+	0.743814i	−0.309969	+	0.950747i	$0.600319\pi$
$374$	−11.0679	+	13.4823i	−0.572308	+	0.697154i
$375$	8.00140	+	0.900381i	0.413191	+	0.0464955i
$376$	−19.8135	−	18.5735i	−1.02180	−	0.957854i
$377$	1.59331	−	1.59331i	0.0820595	−	0.0820595i
$378$	−7.86141	−	12.5046i	−0.404347	−	0.643166i
$379$	12.2721	−	12.2721i	0.630375	−	0.630375i	−0.317787	−	0.948162i	$-0.602940\pi$
$379$	12.2721	−	12.2721i	0.630375	−	0.630375i	0.948162	+	0.317787i	$0.102940\pi$
$380$	−1.02686	−	14.3489i	−0.0526767	−	0.736084i
$381$	13.7252	−	3.67765i	0.703162	−	0.188412i
$382$	−19.2575	−	15.8089i	−0.985301	−	0.808854i
$383$	14.5025	+	3.88593i	0.741042	+	0.198562i	0.609541	−	0.792754i	$-0.291354\pi$
$383$	14.5025	+	3.88593i	0.741042	+	0.198562i	0.131501	+	0.991316i	$0.458020\pi$
$384$	3.35520	+	7.42508i	0.171219	+	0.378909i
$385$	−1.81741	−	23.6192i	−0.0926238	−	1.20375i
$386$	29.4172	−	21.0736i	1.49730	−	1.07262i
$387$	−13.4112	+	7.74299i	−0.681732	+	0.393598i
$388$	−0.497050	−	0.0327228i	−0.0252339	−	0.00166125i
$389$	6.53876	+	24.4030i	0.331528	+	1.23728i	0.907584	+	0.419870i	$0.137924\pi$
$389$	6.53876	+	24.4030i	0.331528	+	1.23728i	−0.576056	+	0.817410i	$0.695409\pi$
$390$	2.52800	+	1.55058i	0.128010	+	0.0785168i
$391$	5.01355			0.253546
$392$	1.74954	−	19.7215i	0.0883652	−	0.996088i
$393$	−0.721458	+	0.721458i	−0.0363928	+	0.0363928i
$394$	−24.8618	+	9.35322i	−1.25252	+	0.471209i
$395$	−3.54379	−	25.6707i	−0.178307	−	1.29163i
$396$	19.8285	+	1.30539i	0.996418	+	0.0655982i
$397$	6.09474	+	10.5564i	0.305886	+	0.529811i	0.977458	−	0.211129i	$-0.0677139\pi$
$397$	6.09474	+	10.5564i	0.305886	+	0.529811i	−0.671572	+	0.740939i	$0.734381\pi$
$398$	−12.4346	−	2.05481i	−0.623291	−	0.102998i
$399$	5.11345	+	3.37937i	0.255993	+	0.169180i
$400$	−15.7200	+	12.3645i	−0.786001	+	0.618225i
$401$	17.8560	+	30.9276i	0.891688	+	1.54445i	0.837851	+	0.545899i	$0.183812\pi$
$401$	17.8560	+	30.9276i	0.891688	+	1.54445i	0.0538373	+	0.998550i	$0.482855\pi$
$402$	6.36937	+	5.22875i	0.317675	+	0.260786i
$403$	3.51144	−	6.08199i	0.174917	−	0.302966i
$404$	20.4246	+	13.6558i	1.01616	+	0.679403i
$405$	6.31421	+	8.12269i	0.313756	+	0.403620i
$406$	−6.31246	−	1.43915i	−0.313282	−	0.0714240i
$407$	−3.47058	−	3.47058i	−0.172030	−	0.172030i
$408$	−4.29131	+	4.57780i	−0.212451	+	0.226635i
$409$	−13.5323	−	7.81290i	−0.669131	−	0.386323i	0.126616	−	0.991952i	$-0.459588\pi$
$409$	−13.5323	−	7.81290i	−0.669131	−	0.386323i	−0.795747	+	0.605629i	$0.792922\pi$
$410$	0.465429	−	17.5007i	0.0229859	−	0.864300i
$411$	−4.65793	−	1.24809i	−0.229759	−	0.0615636i
$412$	10.8739	+	22.0662i	0.535718	+	1.08712i
$413$	−21.7225	+	10.8495i	−1.06889	+	0.533867i
$414$	−3.32610	−	4.64298i	−0.163469	−	0.228190i
$415$	19.8244	+	8.06604i	0.973142	+	0.395946i
$416$	−7.17512	+	1.66753i	−0.351789	+	0.0817575i
$417$	1.21842	+	4.54719i	0.0596661	+	0.222677i
$418$	−17.0489	+	6.41395i	−0.833891	+	0.313717i
$419$	−3.05027	+	3.05027i	−0.149016	+	0.149016i	−0.777678	−	0.628663i	$-0.783603\pi$
$419$	−3.05027	+	3.05027i	−0.149016	+	0.149016i	0.628663	+	0.777678i	$0.283603\pi$
$420$	−0.0942085	−	8.52081i	−0.00459690	−	0.415773i
$421$	21.6422	+	21.6422i	1.05478	+	1.05478i	0.998410	+	0.0563674i	$0.0179518\pi$
$421$	21.6422	+	21.6422i	1.05478	+	1.05478i	0.0563674	+	0.998410i	$0.482048\pi$
$422$	−5.70343	+	12.5829i	−0.277638	+	0.612525i
$423$	−23.0133	+	6.16640i	−1.11895	+	0.299821i
$424$	−12.8881	+	8.00656i	−0.625899	+	0.388833i
$425$	−13.4341	−	7.53276i	−0.651648	−	0.365392i
$426$	2.42891	−	14.6984i	0.117681	−	0.712142i
$427$	0.780286	−	12.9060i	0.0377607	−	0.624564i
$428$	−7.67181	−	2.60671i	−0.370831	−	0.126000i
$429$	0.971918	−	3.62725i	0.0469246	−	0.175125i
$430$	−19.7288	−	0.524682i	−0.951405	−	0.0253024i
$431$	2.56467	−	4.44214i	0.123536	−	0.213970i	−0.797624	−	0.603155i	$-0.793910\pi$
$431$	2.56467	−	4.44214i	0.123536	−	0.213970i	0.921160	+	0.389185i	$0.127243\pi$
$432$	15.6540	+	2.07010i	0.753153	+	0.0995979i
$433$	29.1874	−	29.1874i	1.40266	−	1.40266i	0.611117	−	0.791540i	$-0.290720\pi$
$433$	29.1874	−	29.1874i	1.40266	−	1.40266i	0.791540	−	0.611117i	$-0.209280\pi$
$434$	−20.1648	+	0.759451i	−0.967943	+	0.0364548i
$435$	−2.76494	−	0.346358i	−0.132569	−	0.0166066i
$436$	−1.34672	+	2.01425i	−0.0644964	+	0.0964653i
$437$	4.53406	+	2.61774i	0.216893	+	0.125223i
$438$	6.61367	−	0.650423i	0.316013	−	0.0310784i
$439$	27.2269	−	15.7195i	1.29947	−	0.750250i	0.319158	−	0.947701i	$-0.396600\pi$
$439$	27.2269	−	15.7195i	1.29947	−	0.750250i	0.980313	+	0.197452i	$0.0632666\pi$
$440$	20.6709	+	14.6304i	0.985448	+	0.697478i
$441$	−13.8864	−	10.4337i	−0.661258	−	0.496842i
$442$	−3.30359	−	4.61156i	−0.157136	−	0.219350i
$443$	−12.4689	+	7.19894i	−0.592417	+	0.342032i	−0.766053	−	0.642778i	$-0.777782\pi$
$443$	−12.4689	+	7.19894i	−0.592417	+	0.342032i	0.173636	+	0.984810i	$0.444448\pi$
$444$	−1.16372	−	1.32774i	−0.0552276	−	0.0630118i
$445$	−4.95197	−	35.8714i	−0.234746	−	1.70047i
$446$	−3.44201	+	7.59375i	−0.162984	+	0.359575i
$447$	3.33805	+	3.33805i	0.157884	+	0.157884i
$448$	15.0293	+	14.9037i	0.710068	+	0.704133i
$449$			24.3063i			1.14709i	0.819175	+	0.573544i	$0.194432\pi$
$449$			24.3063i			1.14709i	−0.819175	+	0.573544i	$0.805568\pi$
$450$	1.93646	+	17.4385i	0.0912858	+	0.822059i
$451$	−21.4125	+	5.73745i	−1.00827	+	0.270166i
$452$	36.3337	+	2.39199i	1.70899	+	0.112510i
$453$	−3.09319	−	5.35757i	−0.145331	−	0.251721i
$454$	3.31443	−	20.0571i	0.155554	−	0.941328i
$455$	7.57244	+	1.41714i	0.355002	+	0.0664366i
$456$	−6.27110	+	1.89935i	−0.293671	+	0.0889451i
$457$	2.79803	−	10.4424i	0.130886	−	0.488474i	−0.869095	−	0.494646i	$-0.835298\pi$
$457$	2.79803	−	10.4424i	0.130886	−	0.488474i	0.999981	+	0.00617169i	$0.00196452\pi$
$458$	0.550990	+	5.60261i	0.0257461	+	0.261793i
$459$	3.14723	+	11.7456i	0.146900	+	0.548239i
$460$	−0.519565	−	7.26020i	−0.0242248	−	0.338509i
$461$	−9.72905	−	9.72905i	−0.453127	−	0.453127i	0.443264	−	0.896391i	$-0.353820\pi$
$461$	−9.72905	−	9.72905i	−0.453127	−	0.453127i	−0.896391	+	0.443264i	$0.853820\pi$
$462$	−10.3098	+	3.18292i	−0.479657	+	0.148083i
$463$	−17.8524	−	17.8524i	−0.829671	−	0.829671i	0.157800	−	0.987471i	$-0.449560\pi$
$463$	−17.8524	−	17.8524i	−0.829671	−	0.829671i	−0.987471	+	0.157800i	$0.949560\pi$
$464$	5.49360	−	4.21034i	0.255034	−	0.195460i
$465$	−8.60335	+	1.18767i	−0.398971	+	0.0550770i
$466$	0.791736	−	0.0778636i	0.0366765	−	0.00360696i
$467$	0.164592	+	0.285082i	0.00761641	+	0.0131920i	0.869808	−	0.493389i	$-0.164242\pi$
$467$	0.164592	+	0.285082i	0.00761641	+	0.0131920i	−0.862192	+	0.506582i	$0.830909\pi$
$468$	−2.07903	+	6.11882i	−0.0961034	+	0.282843i
$469$	20.3054	+	6.77827i	0.937616	+	0.312991i
$470$	−29.1095	−	8.63556i	−1.34272	−	0.398329i
$471$	−14.1259	+	8.15561i	−0.650888	+	0.375790i
$472$	5.90535	−	25.2771i	0.271816	−	1.16347i
$473$	6.46789	+	24.1385i	0.297394	+	1.10989i
$474$	−11.0476	+	4.15619i	−0.507432	+	0.190900i
$475$	−8.21614	−	13.8267i	−0.376982	−	0.634412i
$476$	−6.16568	+	15.0886i	−0.282603	+	0.691587i
$477$			13.3107i			0.609453i
$478$	8.39759	+	22.3216i	0.384097	+	1.02097i
$479$	8.80324	−	15.2477i	0.402230	−	0.696683i	−0.591764	−	0.806111i	$-0.701568\pi$
$479$	8.80324	−	15.2477i	0.402230	−	0.696683i	0.993995	+	0.109428i	$0.0349018\pi$
$480$	7.07389	+	5.73990i	0.322878	+	0.261989i
$481$	1.38233	−	0.798089i	0.0630289	−	0.0363897i
$482$	8.33315	+	1.37705i	0.379565	+	0.0627228i
$483$	2.58728	+	1.70988i	0.117725	+	0.0778021i
$484$	3.23863	−	9.53164i	0.147211	−	0.433256i
$485$	−0.513180	+	0.216352i	−0.0233023	+	0.00982405i
$486$	13.6001	−	16.5669i	0.616915	−	0.751491i
$487$	15.7620	−	4.22342i	0.714245	−	0.191381i	0.116643	−	0.993174i	$-0.462787\pi$
$487$	15.7620	−	4.22342i	0.714245	−	0.191381i	0.597603	+	0.801793i	$0.296120\pi$
$488$	10.0843	+	9.45317i	0.456493	+	0.427925i
$489$			15.2901i			0.691442i
$490$	−8.13330	−	20.5876i	−0.367425	−	0.930053i
$491$	26.7226	+	26.7226i	1.20597	+	1.20597i	0.972320	+	0.233652i	$0.0750676\pi$
$491$	26.7226	+	26.7226i	1.20597	+	1.20597i	0.233652	+	0.972320i	$0.424932\pi$
$492$	−7.82136	+	1.55341i	−0.352614	+	0.0700333i
$493$	4.61606	+	2.66508i	0.207897	+	0.120029i
$494$	−0.579788	−	5.89543i	−0.0260859	−	0.265248i
$495$	20.4719	−	8.63079i	0.920145	−	0.387925i
$496$	13.1423	−	17.1069i	0.590108	−	0.768124i
$497$	−7.74213	−	37.9178i	−0.347282	−	1.70084i
$498$	1.58938	−	9.61808i	0.0712219	−	0.430997i
$499$	10.3634	−	38.6769i	0.463931	−	1.73142i	−0.196476	−	0.980509i	$-0.562950\pi$
$499$	10.3634	−	38.6769i	0.463931	−	1.73142i	0.660408	−	0.750907i	$-0.270383\pi$
$500$	−9.51610	+	20.2347i	−0.425573	+	0.904924i
$501$	5.31709	−	1.42471i	0.237550	−	0.0636513i
$502$	0.350613	−	0.773521i	0.0156486	−	0.0345239i
$503$	16.4835	+	16.4835i	0.734965	+	0.734965i	0.971599	−	0.236634i	$-0.0760443\pi$
$503$	16.4835	+	16.4835i	0.734965	+	0.734965i	−0.236634	+	0.971599i	$0.576044\pi$
$504$	18.0638	−	4.30017i	0.804627	−	0.191545i
$505$	27.2562	+	3.41432i	1.21288	+	0.151935i
$506$	−8.62634	+	3.24530i	−0.383488	+	0.144271i
$507$	−7.05045	−	4.07058i	−0.313122	−	0.180781i
$508$	−2.59222	+	39.3751i	−0.115011	+	1.74699i
$509$	−28.8827	−	7.73911i	−1.28020	−	0.343030i	−0.446273	−	0.894897i	$-0.647249\pi$
$509$	−28.8827	−	7.73911i	−1.28020	−	0.343030i	−0.833932	+	0.551867i	$0.813916\pi$
$510$	−1.99520	+	6.72559i	−0.0883490	+	0.297814i
$511$	15.4441	−	7.71366i	0.683206	−	0.341232i
$512$	−22.5213	+	2.18856i	−0.995311	+	0.0967215i
$513$	−3.28654	+	12.2656i	−0.145105	+	0.541537i
$514$	1.43333	+	14.5745i	0.0632217	+	0.642854i
$515$	21.9248	+	16.6057i	0.966121	+	0.731736i
$516$	1.75118	+	8.81710i	0.0770913	+	0.388151i
$517$			38.4471i			1.69090i
$518$	−4.05540	−	2.14207i	−0.178184	−	0.0941173i
$519$	18.6266			0.817616
$520$	−6.33572	+	5.26189i	−0.277840	+	0.230749i
$521$	−15.0914	+	26.1390i	−0.661165	+	1.14517i	0.319145	+	0.947706i	$0.396604\pi$
$521$	−15.0914	+	26.1390i	−0.661165	+	1.14517i	−0.980310	+	0.197465i	$0.936729\pi$
$522$	−0.594295	−	6.04294i	−0.0260116	−	0.264492i
$523$	4.48449	+	7.76736i	0.196093	+	0.339643i	0.947258	−	0.320471i	$-0.103841\pi$
$523$	4.48449	+	7.76736i	0.196093	+	0.339643i	−0.751165	+	0.660114i	$0.770508\pi$
$524$	−1.25246	−	2.54159i	−0.0547139	−	0.111030i
$525$	−4.36369	−	8.46904i	−0.190447	−	0.369619i
$526$	17.1628	+	23.9580i	0.748333	+	1.04462i
$527$	16.0467	+	4.29969i	0.699003	+	0.187297i
$528$	4.42041	−	10.6544i	0.192374	−	0.463672i
$529$	−17.6245	−	10.1755i	−0.766281	−	0.442413i
$530$	−8.86929	+	14.4601i	−0.385257	+	0.628107i
$531$	−16.1025	−	16.1025i	−0.698787	−	0.698787i
$532$	−13.4543	+	10.4263i	−0.583317	+	0.452036i
$533$		−	7.20920i		−	0.312265i
$534$	−15.4375	+	5.80772i	−0.668047	+	0.251325i
$535$	−8.97384	+	1.23882i	−0.387973	+	0.0535588i
$536$	−19.4391	+	12.0763i	−0.839643	+	0.521619i
$537$	2.84301	+	0.761783i	0.122685	+	0.0328734i
$538$	24.5278	+	34.2389i	1.05747	+	1.47615i
$539$	−22.0631	+	17.2874i	−0.950326	+	0.744623i
$540$	16.6829	−	5.77478i	0.717916	−	0.248507i
$541$	2.57671	+	0.690427i	0.110781	+	0.0296838i	0.313784	−	0.949494i	$-0.398403\pi$
$541$	2.57671	+	0.690427i	0.110781	+	0.0296838i	−0.203003	+	0.979178i	$0.565070\pi$
$542$	−3.96639	+	4.83164i	−0.170371	+	0.207537i
$543$	−9.80963	+	2.62848i	−0.420972	+	0.112799i
$544$	−8.20306	−	15.3736i	−0.351703	−	0.659137i
$545$	−0.336717	+	2.68798i	−0.0144234	+	0.115140i
$546$	−0.132063	−	3.50652i	−0.00565178	−	0.150065i
$547$			9.41386i			0.402508i	0.979539	+	0.201254i	$0.0645016\pi$
$547$			9.41386i			0.402508i	−0.979539	+	0.201254i	$0.935498\pi$
$548$	7.44325	−	11.1326i	0.317960	−	0.475562i
$549$	11.7129	−	3.13845i	0.499893	−	0.133946i
$550$	27.9907	+	4.26495i	1.19353	+	0.181858i
$551$	2.78305	+	4.82039i	0.118562	+	0.205355i
$552$	−3.17302	+	0.961023i	−0.135053	+	0.0409039i
$553$	−22.9503	+	20.3334i	−0.975945	+	0.864664i
$554$	1.95863	−	11.8526i	0.0832144	−	0.503569i
$555$	−1.82839	−	0.743923i	−0.0776107	−	0.0315778i
$556$	−13.0451	−	0.858810i	−0.553235	−	0.0364217i
$557$	20.6283	+	11.9097i	0.874048	+	0.504632i	0.868691	−	0.495354i	$-0.164962\pi$
$557$	20.6283	+	11.9097i	0.874048	+	0.504632i	0.00535649	+	0.999986i	$0.498295\pi$
$558$	−6.66381	−	17.7131i	−0.282102	−	0.749855i
$559$	−8.12700			−0.343735
$560$	22.4891	+	7.36495i	0.950336	+	0.311226i
$561$	8.88299			0.375040
$562$	−0.754802	−	2.00634i	−0.0318394	−	0.0846324i
$563$	23.6088	+	13.6305i	0.994992	+	0.574459i	0.906763	−	0.421641i	$-0.138546\pi$
$563$	23.6088	+	13.6305i	0.994992	+	0.574459i	0.0882292	+	0.996100i	$0.471879\pi$
$564$	−0.908521	+	13.8002i	−0.0382556	+	0.581092i
$565$	37.5128	−	15.8151i	1.57817	−	0.665345i
$566$	2.82779	−	17.1123i	0.118861	−	0.719283i
$567$	3.85451	−	11.5468i	0.161874	−	0.484921i
$568$	36.4785	+	19.5185i	1.53060	+	0.818979i
$569$	18.6660	+	32.3304i	0.782519	+	1.35536i	0.930470	+	0.366368i	$0.119399\pi$
$569$	18.6660	+	32.3304i	0.782519	+	1.35536i	−0.147951	+	0.988995i	$0.547268\pi$
$570$	−5.31603	+	5.04060i	−0.222664	+	0.211127i
$571$	−21.9928	+	5.89295i	−0.920369	+	0.246612i	−0.687743	−	0.725954i	$-0.741398\pi$
$571$	−21.9928	+	5.89295i	−0.920369	+	0.246612i	−0.232626	+	0.972566i	$0.574732\pi$
$572$	8.66927	+	5.79625i	0.362480	+	0.242353i
$573$			12.6881i			0.530051i
$574$	−17.5368	+	11.0251i	−0.731970	+	0.460177i
$575$	−4.15716	−	6.99597i	−0.173366	−	0.291752i
$576$	−8.79518	+	17.7959i	−0.366466	+	0.741496i
$577$	2.95800	−	0.792593i	0.123143	−	0.0329961i	−0.196721	−	0.980459i	$-0.563029\pi$
$577$	2.95800	−	0.792593i	0.123143	−	0.0329961i	0.319864	+	0.947463i	$0.396363\pi$
$578$	−6.74011	+	8.21043i	−0.280352	+	0.341509i
$579$	−17.8000	−	4.76949i	−0.739742	−	0.198213i
$580$	3.38097	−	6.96077i	0.140387	−	0.289030i
$581$	−5.06615	−	24.8119i	−0.210179	−	1.02937i
$582$	0.147727	+	0.206215i	0.00612347	+	0.00854791i
$583$	20.7478	+	5.55934i	0.859284	+	0.230244i
$584$	−4.19854	+	17.9713i	−0.173737	+	0.743657i
$585$	0.988047	+	7.15728i	0.0408507	+	0.295917i
$586$	−1.11897	+	0.420967i	−0.0462243	+	0.0173900i
$587$			16.5240i			0.682019i	0.940060	+	0.341010i	$0.110769\pi$
$587$			16.5240i			0.682019i	−0.940060	+	0.341010i	$0.889231\pi$
$588$	−8.32784	+	5.68379i	−0.343434	+	0.234396i
$589$	12.2670	+	12.2670i	0.505451	+	0.505451i
$590$	−6.76343	−	28.2225i	−0.278446	−	1.16190i
$591$	11.7148	+	6.76357i	0.481884	+	0.278216i
$592$	4.53089	−	1.87369i	0.186219	−	0.0770081i
$593$	−34.5811	−	9.26597i	−1.42007	−	0.380508i	−0.534564	−	0.845128i	$-0.679524\pi$
$593$	−34.5811	−	9.26597i	−1.42007	−	0.380508i	−0.885510	+	0.464620i	$0.846191\pi$
$594$	−13.0182	−	18.1724i	−0.534141	−	0.745621i
$595$	1.39811	+	18.1700i	0.0573171	+	0.744897i
$596$	−11.7595	+	5.79489i	−0.481686	+	0.237368i
$597$	3.20909	+	5.55830i	0.131339	+	0.227486i
$598$	−0.293358	−	2.98294i	−0.0119963	−	0.121982i
$599$	15.7308	−	27.2465i	0.642742	−	1.11326i	−0.342077	−	0.939672i	$-0.611130\pi$
$599$	15.7308	−	27.2465i	0.642742	−	1.11326i	0.984818	−	0.173589i	$-0.0555364\pi$
$600$	9.94620	+	2.19229i	0.406052	+	0.0895000i
$601$	42.9833			1.75333			0.876663	−	0.481104i	$-0.159764\pi$
$601$	42.9833			1.75333			0.876663	+	0.481104i	$0.159764\pi$
$602$	12.4287	+	19.7694i	0.506554	+	0.805739i
$603$			20.0766i			0.817581i
$604$	16.8509	−	3.34678i	0.685653	−	0.136179i
$605$	−1.53914	−	11.1493i	−0.0625749	−	0.453284i
$606$	−1.22457	−	12.4517i	−0.0497447	−	0.505817i
$607$	−3.38204	+	12.6219i	−0.137273	+	0.512308i	0.862706	+	0.505706i	$0.168768\pi$
$607$	−3.38204	+	12.6219i	−0.137273	+	0.512308i	−0.999978	+	0.00660186i	$0.997899\pi$
$608$	0.608527	−	18.1863i	0.0246790	−	0.737554i
$609$	1.47322	+	2.94964i	0.0596979	+	0.119526i
$610$	14.8156	+	4.39516i	0.599865	+	0.177955i
$611$	−12.0773	−	3.23611i	−0.488596	−	0.130919i
$612$	−15.2538	−	1.00422i	−0.616600	−	0.0405932i
$613$	32.2284	+	18.6071i	1.30169	+	0.751534i	0.980695	−	0.195546i	$-0.0626478\pi$
$613$	32.2284	+	18.6071i	1.30169	+	0.751534i	0.321000	+	0.947079i	$0.395981\pi$
$614$	−21.5561	+	8.10958i	−0.869934	+	0.327276i
$615$	−7.03880	+	5.47164i	−0.283832	+	0.220638i
$616$	0.841736	−	29.9527i	0.0339145	−	1.20683i
$617$	0.636726	+	0.636726i	0.0256336	+	0.0256336i	0.719807	−	0.694174i	$-0.244230\pi$
$617$	0.636726	+	0.636726i	0.0256336	+	0.0256336i	−0.694174	+	0.719807i	$0.744230\pi$
$618$	5.17181	−	11.4100i	0.208041	−	0.458979i
$619$	5.48706	−	1.47025i	0.220544	−	0.0590945i	−0.146855	−	0.989158i	$-0.546915\pi$
$619$	5.48706	−	1.47025i	0.220544	−	0.0590945i	0.367399	+	0.930064i	$0.380248\pi$
$620$	4.56350	−	23.6830i	0.183275	−	0.951132i
$621$	−1.66291	+	6.20607i	−0.0667303	+	0.249041i
$622$	−0.878454	+	5.31593i	−0.0352228	+	0.213149i
$623$	−32.0700	+	28.4132i	−1.28486	+	1.13835i
$624$	2.97478	+	2.28536i	0.119086	+	0.0914877i
$625$	0.628039	+	24.9921i	0.0251216	+	0.999684i
$626$	−3.25340	−	33.0814i	−0.130032	−	1.32220i
$627$	8.03342	+	4.63810i	0.320824	+	0.185228i
$628$	−8.82422	−	44.4295i	−0.352125	−	1.77293i
$629$	2.66988	+	2.66988i	0.106455	+	0.106455i
$630$	15.8994	−	13.3491i	0.633449	−	0.531842i
$631$		−	32.0044i		−	1.27408i	−0.770832	−	0.637038i	$-0.780159\pi$
$631$		−	32.0044i		−	1.27408i	0.770832	−	0.637038i	$-0.219841\pi$
$632$	−1.05829	−	32.7620i	−0.0420963	−	1.30320i
$633$	6.79560	−	1.82087i	0.270101	−	0.0723733i
$634$	0.0255619	−	0.0311380i	0.00101519	−	0.00123665i
$635$	17.1389	+	40.6528i	0.680136	+	1.61326i
$636$	7.31582	+	2.48575i	0.290091	+	0.0985663i
$637$	−3.57342	−	8.38576i	−0.141584	−	0.332256i
$638$	−9.66753	−	1.59755i	−0.382741	−	0.0632477i
$639$	31.4325	−	18.1476i	1.24345	−	0.717907i
$640$	−21.4126	+	13.4722i	−0.846408	+	0.532535i
$641$	−16.6572	+	28.8512i	−0.657921	+	1.13955i	0.323231	+	0.946320i	$0.395231\pi$
$641$	−16.6572	+	28.8512i	−0.657921	+	1.13955i	−0.981153	+	0.193233i	$0.938103\pi$
$642$	1.45290	+	3.86195i	0.0573413	+	0.152419i
$643$			5.26026i			0.207444i	0.994606	+	0.103722i	$0.0330753\pi$
$643$			5.26026i			0.207444i	−0.994606	+	0.103722i	$0.966925\pi$
$644$	−6.80753	+	5.27543i	−0.268254	+	0.207881i
$645$	6.16823	+	7.93490i	0.242874	+	0.312436i
$646$	13.1156	−	4.93418i	0.516025	−	0.194133i
$647$	11.1178	+	41.4921i	0.437085	+	1.63122i	0.736027	+	0.676952i	$0.236699\pi$
$647$	11.1178	+	41.4921i	0.437085	+	1.63122i	−0.298942	+	0.954271i	$0.596634\pi$
$648$	6.86731	+	11.0542i	0.269773	+	0.434251i
$649$	−31.8248	+	18.3740i	−1.24923	+	0.721244i
$650$	−3.69574	+	8.43371i	−0.144959	+	0.330797i
$651$	6.81458	+	7.69161i	0.267084	+	0.301458i
$652$	−40.2043	−	13.6605i	−1.57452	−	0.534986i
$653$	9.98010	+	17.2860i	0.390552	+	0.676455i	0.992522	−	0.122063i	$-0.0389510\pi$
$653$	9.98010	+	17.2860i	0.390552	+	0.676455i	−0.601971	+	0.798518i	$0.705618\pi$
$654$	1.22798	−	0.120766i	0.0480177	−	0.00472232i
$655$	−2.52531	−	1.91266i	−0.0986719	−	0.0747336i
$656$	2.90317	−	21.9536i	0.113350	−	0.857143i
$657$	11.4484	+	11.4484i	0.446644	+	0.446644i
$658$	10.5979	+	34.3277i	0.413149	+	1.33823i
$659$	−29.6719	−	29.6719i	−1.15585	−	1.15585i	−0.985359	−	0.170494i	$-0.945464\pi$
$659$	−29.6719	−	29.6719i	−1.15585	−	1.15585i	−0.170494	−	0.985359i	$-0.554536\pi$
$660$	−0.920562	−	12.8636i	−0.0358328	−	0.500715i
$661$	3.17323	+	11.8427i	0.123424	+	0.460626i	0.999779	−	0.0210412i	$-0.00669813\pi$
$661$	3.17323	+	11.8427i	0.123424	+	0.460626i	−0.876354	+	0.481667i	$0.840031\pi$
$662$	−0.183260	−	1.86343i	−0.00712260	−	0.0724244i
$663$	−0.747686	+	2.79040i	−0.0290377	+	0.108370i
$664$	23.8701	+	12.7722i	0.926339	+	0.495656i
$665$	−8.22275	+	17.1622i	−0.318865	+	0.665522i
$666$	0.701285	−	4.24380i	0.0271742	−	0.164444i
$667$	1.40816	+	2.43900i	0.0545240	+	0.0944384i
$668$	−1.00422	+	15.2538i	−0.0388543	+	0.590186i
$669$	4.10113	−	1.09889i	0.158559	−	0.0424857i
$670$	−13.3776	+	21.8103i	−0.516822	+	0.842604i
$671$		−	19.5680i		−	0.755415i
$672$	1.00993	−	10.7313i	0.0389588	−	0.413969i
$673$	20.2676	+	20.2676i	0.781258	+	0.781258i	0.980043	−	0.198785i	$-0.0636996\pi$
$673$	20.2676	+	20.2676i	0.781258	+	0.781258i	−0.198785	+	0.980043i	$0.563700\pi$
$674$	8.21609	−	18.1263i	0.316472	−	0.698200i
$675$	13.7803	−	14.1310i	0.530406	−	0.543902i
$676$	17.0023	−	14.9019i	0.653936	−	0.573152i
$677$	−6.08766	+	3.51471i	−0.233968	+	0.135081i	−0.612401	−	0.790547i	$-0.709796\pi$
$677$	−6.08766	+	3.51471i	−0.233968	+	0.135081i	0.378433	+	0.925629i	$0.376463\pi$
$678$	−10.7986	−	15.0741i	−0.414719	−	0.578917i
$679$	0.549751	+	0.363318i	0.0210975	+	0.0139429i
$680$	−15.9019	−	11.2550i	−0.609811	−	0.431610i
$681$	−8.96558	+	5.17628i	−0.343562	+	0.198355i
$682$	−30.3932	+	2.98903i	−1.16381	+	0.114456i
$683$	−41.2356	−	23.8074i	−1.57784	−	0.910965i	−0.995161	−	0.0982608i	$-0.968672\pi$
$683$	−41.2356	−	23.8074i	−1.57784	−	0.910965i	−0.582677	−	0.812704i	$-0.697995\pi$
$684$	−13.2706	−	8.87270i	−0.507415	−	0.339256i
$685$	1.86101	−	14.8563i	0.0711055	−	0.567628i
$686$	−14.9339	+	21.5169i	−0.570181	+	0.821519i
$687$	2.02719	−	2.02719i	0.0773420	−	0.0773420i
$688$	−24.7485	−	3.27277i	−0.943527	−	0.124773i
$689$	−3.49270	+	6.04953i	−0.133061	+	0.230469i
$690$	−2.68978	+	2.55042i	−0.102398	+	0.0970928i
$691$	−5.92635	+	22.1174i	−0.225449	+	0.841387i	0.756775	+	0.653675i	$0.226774\pi$
$691$	−5.92635	+	22.1174i	−0.225449	+	0.841387i	−0.982224	+	0.187712i	$0.939893\pi$
$692$	−16.6413	+	48.9773i	−0.632609	+	1.86184i
$693$	−21.9308	−	14.4936i	−0.833084	−	0.550567i
$694$	1.96175	−	11.8715i	0.0744670	−	0.450634i
$695$	−13.4684	+	5.67817i	−0.510886	+	0.215385i
$696$	−3.43231	−	0.801873i	−0.130101	−	0.0303949i
$697$	16.4724	−	4.41376i	0.623936	−	0.167183i
$698$	−17.3581	+	38.2953i	−0.657012	+	1.44950i
$699$	−0.286473	−	0.286473i	−0.0108354	−	0.0108354i
$700$	26.1674	−	3.90762i	0.989033	−	0.147694i
$701$	18.7237	−	18.7237i	0.707185	−	0.707185i	−0.258757	−	0.965942i	$-0.583313\pi$
$701$	18.7237	−	18.7237i	0.707185	−	0.707185i	0.965942	+	0.258757i	$0.0833130\pi$
$702$	6.80421	−	2.55980i	0.256808	−	0.0966134i
$703$	1.02050	+	3.80857i	0.0384890	+	0.143643i
$704$	24.0656	+	21.1420i	0.907008	+	0.796818i
$705$	6.00684	+	14.2480i	0.226231	+	0.536611i
$706$	−11.5132	−	16.0716i	−0.433305	−	0.604862i
$707$	−14.5227	−	29.0770i	−0.546182	−	1.09355i
$708$	−11.8574	+	5.84314i	−0.445627	+	0.219599i
$709$	−18.4310	−	4.93857i	−0.692190	−	0.185472i	−0.104460	−	0.994529i	$-0.533312\pi$
$709$	−18.4310	−	4.93857i	−0.692190	−	0.185472i	−0.587730	+	0.809057i	$0.699978\pi$
$710$	46.2391	+	1.22972i	1.73532	+	0.0461506i
$711$	−24.9040	−	14.3783i	−0.933971	−	0.539229i
$712$	−1.47881	−	45.7806i	−0.0554209	−	1.71570i
$713$	6.20678	+	6.20678i	0.232446	+	0.232446i
$714$	7.93124	−	2.44859i	0.296819	−	0.0916361i
$715$	11.5689	+	1.44922i	0.432654	+	0.0541976i
$716$	−4.54306	+	6.79492i	−0.169782	+	0.253938i
$717$	6.07252	−	10.5179i	0.226782	−	0.392799i
$718$	−25.5275	−	20.9561i	−0.952679	−	0.782074i
$719$	7.09781	+	12.2938i	0.264704	+	0.458480i	0.967486	−	0.252925i	$-0.0813925\pi$
$719$	7.09781	+	12.2938i	0.264704	+	0.458480i	−0.702782	+	0.711405i	$0.748059\pi$
$720$	0.126558	+	22.1934i	0.00471653	+	0.827098i
$721$	1.96392	−	32.4833i	0.0731401	−	1.20974i
$722$	−12.0730	−	1.99506i	−0.449312	−	0.0742485i
$723$	−2.15059	−	3.72493i	−0.0799814	−	0.138532i
$724$	1.85271	−	28.1421i	0.0688553	−	1.04589i
$725$	−0.108682	−	8.65114i	−0.00403636	−	0.321295i
$726$	−4.79818	+	1.80512i	−0.178077	+	0.0669941i
$727$	5.68905	−	5.68905i	0.210995	−	0.210995i	−0.593695	−	0.804690i	$-0.702331\pi$
$727$	5.68905	−	5.68905i	0.210995	−	0.210995i	0.804690	+	0.593695i	$0.202331\pi$
$728$	9.33815	+	2.78555i	0.346095	+	0.103239i
$729$	2.88776			0.106954
$730$	4.80861	+	20.0654i	0.177975	+	0.742654i
$731$	−4.97568	−	18.5695i	−0.184032	−	0.686817i
$732$	0.462401	−	7.02374i	0.0170908	−	0.259605i
$733$	11.0423	−	6.37528i	0.407857	−	0.235476i	−0.282012	−	0.959411i	$-0.591002\pi$
$733$	11.0423	−	6.37528i	0.407857	−	0.235476i	0.689869	+	0.723935i	$0.257668\pi$
$734$	8.08602	−	5.79259i	0.298461	−	0.213808i
$735$	−5.47539	+	9.85358i	−0.201963	+	0.363455i
$736$	0.307900	−	9.20184i	0.0113493	−	0.339185i
$737$	31.2940	+	8.38520i	1.15273	+	0.308873i
$738$	−15.0157	−	12.3267i	−0.552734	−	0.453751i
$739$	10.4001	−	2.78670i	0.382574	−	0.102510i	−0.0624060	−	0.998051i	$-0.519877\pi$
$739$	10.4001	−	2.78670i	0.382574	−	0.102510i	0.444980	+	0.895540i	$0.353211\pi$
$740$	3.58961	−	4.14298i	0.131957	−	0.152299i
$741$	−2.13314	+	2.13314i	−0.0783628	+	0.0783628i
$742$	20.0572	−	0.755398i	0.736323	−	0.0277315i
$743$	12.8147	−	12.8147i	0.470126	−	0.470126i	−0.431829	−	0.901955i	$-0.642132\pi$
$743$	12.8147	−	12.8147i	0.470126	−	0.470126i	0.901955	+	0.431829i	$0.142132\pi$
$744$	−10.9799	+	0.354676i	−0.402544	+	0.0130031i
$745$	−8.84949	+	11.6841i	−0.324220	+	0.428073i
$746$	−25.7810	+	31.4049i	−0.943908	+	1.14982i
$747$	20.5682	−	11.8751i	0.752551	−	0.434485i
$748$	−7.93624	+	23.3572i	−0.290178	+	0.854024i
$749$	7.10804	+	8.02285i	0.259722	+	0.293148i
$750$	11.0394	−	2.79264i	0.403100	−	0.101973i
$751$	−25.4233	−	44.0345i	−0.927711	−	1.60684i	−0.787142	−	0.616772i	$-0.788440\pi$
$751$	−25.4233	−	44.0345i	−0.927711	−	1.60684i	−0.140569	−	0.990071i	$-0.544893\pi$
$752$	−35.4749	−	14.7182i	−1.29364	−	0.536719i
$753$	−0.417753	+	0.111937i	−0.0152238	+	0.00407919i
$754$	1.31556	−	2.90238i	0.0479098	−	0.105699i
$755$	15.1649	−	11.7885i	0.551906	−	0.429027i
$756$	−16.6326	−	12.6369i	−0.604920	−	0.459599i
$757$	−16.7501			−0.608791			−0.304396	−	0.952546i	$-0.598454\pi$
$757$	−16.7501			−0.608791			−0.304396	+	0.952546i	$0.598454\pi$
$758$	10.1328	−	22.3550i	0.368040	−	0.811968i
$759$	4.06471	+	2.34676i	0.147540	+	0.0851821i
$760$	−8.50446	−	18.4815i	−0.308489	−	0.670395i
$761$	−3.95436	−	6.84916i	−0.143346	−	0.248282i	0.785409	−	0.618977i	$-0.212453\pi$
$761$	−3.95436	−	6.84916i	−0.143346	−	0.248282i	−0.928754	+	0.370695i	$0.879119\pi$
$762$	16.3359	−	11.7025i	0.591786	−	0.423939i
$763$	2.86755	−	1.43222i	0.103812	−	0.0518497i
$764$	−33.3624	−	11.3358i	−1.20701	−	0.410114i
$765$	−15.7488	+	6.63958i	−0.569400	+	0.240054i
$766$	21.1312	−	2.07815i	0.763500	−	0.0750867i
$767$	−3.09311	−	11.5436i	−0.111686	−	0.416816i
$768$	8.13852	+	8.15738i	0.293673	+	0.294354i
$769$	−32.4594			−1.17052			−0.585258	−	0.810847i	$-0.699007\pi$
$769$	−32.4594			−1.17052			−0.585258	+	0.810847i	$0.699007\pi$
$770$	−14.1671	−	30.3584i	−0.510548	−	1.09404i
$771$	5.27348	−	5.27348i	0.189920	−	0.189920i
$772$	28.4439	−	42.5427i	1.02372	−	1.53114i
$773$	0.911466	−	1.57871i	0.0327832	−	0.0567821i	−0.849168	−	0.528122i	$-0.822896\pi$
$773$	0.911466	−	1.57871i	0.0327832	−	0.0567821i	0.881951	+	0.471340i	$0.156230\pi$
$774$	−13.8960	+	16.9273i	−0.499480	+	0.608439i
$775$	−7.30582	−	25.9569i	−0.262433	−	0.932401i
$776$	−0.674211	+	0.204200i	−0.0242028	+	0.00733037i
$777$	0.467246	+	2.28838i	0.0167624	+	0.0820951i
$778$	20.8068	+	29.0448i	0.745961	+	1.04131i
$779$	17.2015	+	4.60914i	0.616309	+	0.165140i
$780$	4.11831	+	0.793561i	0.147459	+	0.0284140i
$781$	−15.1591	−	56.5744i	−0.542434	−	2.02439i
$782$	6.63615	−	2.49658i	0.237308	−	0.0892773i
$783$	−4.83006	+	4.83006i	−0.172612	+	0.172612i
$784$	−7.50488	−	26.9755i	−0.268031	−	0.963410i
$785$	−31.0818	−	39.9841i	−1.10936	−	1.42709i
$786$	−0.595692	+	1.31421i	−0.0212476	+	0.0468765i
$787$	−16.5605	+	28.6835i	−0.590316	+	1.02246i	0.403873	+	0.914815i	$0.367664\pi$
$787$	−16.5605	+	28.6835i	−0.590316	+	1.02246i	−0.994190	+	0.107643i	$0.965670\pi$
$788$	−28.2506	+	24.7607i	−1.00639	+	0.882062i
$789$	3.88437	−	14.4967i	0.138287	−	0.516095i
$790$	−17.4738	−	32.2142i	−0.621691	−	1.14613i
$791$	−40.1861	−	26.5581i	−1.42885	−	0.944298i
$792$	26.8959	−	8.14602i	0.955703	−	0.289456i
$793$	6.14688	+	1.64705i	0.218282	+	0.0584885i
$794$	13.3240	+	10.9379i	0.472851	+	0.388173i
$795$	8.55743	−	1.18133i	0.303501	−	0.0418976i
$796$	−17.4822	+	3.47217i	−0.619641	+	0.123068i
$797$	37.6739			1.33448			0.667238	−	0.744844i	$-0.267476\pi$
$797$	37.6739			1.33448			0.667238	+	0.744844i	$0.267476\pi$
$798$	8.45119	+	1.92676i	0.299169	+	0.0682064i
$799$		−	29.5769i		−	1.04636i
$800$	−14.6506	+	24.1942i	−0.517978	+	0.855394i
$801$	−34.8000	−	20.0918i	−1.22960	−	0.709908i
$802$	39.0359	+	32.0454i	1.37840	+	1.13156i
$803$	22.6265	−	13.0634i	0.798472	−	0.460998i
$804$	11.0345	+	3.74927i	0.389157	+	0.132227i
$805$	−4.16051	+	8.68366i	−0.146639	+	0.306059i
$806$	1.61927	−	9.79896i	0.0570364	−	0.345154i
$807$	5.55126	−	20.7176i	0.195414	−	0.729293i
$808$	33.8350	+	7.90470i	1.19031	+	0.278086i
$809$	−0.337958	+	0.585360i	−0.0118820	+	0.0205802i	−0.871905	−	0.489675i	$-0.837116\pi$
$809$	−0.337958	+	0.585360i	−0.0118820	+	0.0205802i	0.860023	+	0.510255i	$0.170449\pi$
$810$	12.4026	+	7.60728i	0.435782	+	0.267293i
$811$	−8.03712	+	8.03712i	−0.282222	+	0.282222i	−0.833994	−	0.551773i	$-0.813952\pi$
$811$	−8.03712	+	8.03712i	−0.282222	+	0.282222i	0.551773	+	0.833994i	$0.313952\pi$
$812$	−9.07209	+	1.23846i	−0.318368	+	0.0434614i
$813$	3.18338			0.111646
$814$	−6.32204	−	2.86558i	−0.221588	−	0.100439i
$815$	−47.0276	+	6.49205i	−1.64730	+	0.227407i
$816$	−3.40057	+	8.19629i	−0.119044	+	0.286928i
$817$	5.19593	−	19.3915i	0.181782	−	0.678421i
$818$	−21.8025	−	3.60285i	−0.762308	−	0.125971i
$819$	6.39879	−	5.66917i	0.223592	−	0.198097i
$820$	−8.09870	−	23.3965i	−0.282819	−	0.817041i
$821$	6.62898	−	24.7397i	0.231353	−	0.863421i	−0.748406	−	0.663241i	$-0.769181\pi$
$821$	6.62898	−	24.7397i	0.231353	−	0.863421i	0.979759	−	0.200180i	$-0.0641528\pi$
$822$	−6.78694	+	0.667464i	−0.236722	+	0.0232805i
$823$	2.10830	+	7.86830i	0.0734909	+	0.274272i	0.992887	−	0.119062i	$-0.0379886\pi$
$823$	2.10830	+	7.86830i	0.0734909	+	0.274272i	−0.919396	+	0.393333i	$0.871322\pi$
$824$	25.3813	+	23.7929i	0.884200	+	0.828864i
$825$	−7.36565	−	12.3954i	−0.256439	−	0.431553i
$826$	−23.3502	+	25.1779i	−0.812457	+	0.876050i
$827$	24.7546			0.860801			0.430400	−	0.902638i	$-0.358372\pi$
$827$	24.7546			0.860801			0.430400	+	0.902638i	$0.358372\pi$
$828$	−6.71461	−	4.48937i	−0.233349	−	0.156016i
$829$	5.97792	+	22.3099i	0.207622	+	0.774854i	0.988634	+	0.150339i	$0.0480366\pi$
$829$	5.97792	+	22.3099i	0.207622	+	0.774854i	−0.781013	+	0.624515i	$0.785297\pi$
$830$	30.2571	+	0.804680i	1.05024	+	0.0279309i
$831$	−5.29813	+	3.05888i	−0.183790	+	0.106111i
$832$	−8.66692	+	5.78018i	−0.300472	+	0.200392i
$833$	16.9729	−	13.2990i	0.588077	−	0.460785i
$834$	3.87709	+	5.41213i	0.134253	+	0.187407i
$835$	6.63955	+	15.7488i	0.229771	+	0.545009i
$836$	−19.3728	+	16.9796i	−0.670022	+	0.587250i
$837$	−10.6448	+	18.4374i	−0.367939	+	0.637288i
$838$	−2.51854	+	5.55640i	−0.0870016	+	0.191943i
$839$		−	9.36329i		−	0.323257i	−0.986852	−	0.161628i	$-0.948325\pi$
$839$		−	9.36329i		−	0.323257i	0.986852	−	0.161628i	$-0.0516746\pi$
$840$	−4.36777	−	11.2316i	−0.150702	−	0.387527i
$841$		−	26.0058i		−	0.896753i
$842$	39.4237	+	17.8695i	1.35863	+	0.615824i
$843$	−0.545817	+	0.945384i	−0.0187990	+	0.0325607i
$844$	−1.28346	+	19.4954i	−0.0441784	+	0.671058i
$845$	9.52627	−	23.4133i	0.327714	−	0.805443i
$846$	−27.3908	+	19.6219i	−0.941714	+	0.674616i
$847$	−9.96777	+	8.83120i	−0.342497	+	0.303444i
$848$	−13.0722	+	17.0156i	−0.448901	+	0.584319i
$849$	−7.64923	+	4.41628i	−0.262521	+	0.151566i
$850$	−21.5330	−	3.28098i	−0.738575	−	0.112537i
$851$	0.516349	+	1.92704i	0.0177002	+	0.0660582i
$852$	−4.10431	−	20.6650i	−0.140611	−	0.707972i
$853$	−14.6246			−0.500735			−0.250368	−	0.968151i	$-0.580551\pi$
$853$	−14.6246			−0.500735			−0.250368	+	0.968151i	$0.580551\pi$
$854$	−5.39391	−	17.4715i	−0.184576	−	0.597861i
$855$	−17.7094	−	2.21841i	−0.605647	−	0.0758681i
$856$	−11.4528	+	0.369950i	−0.391448	+	0.0126446i
$857$	10.1631	+	37.9291i	0.347164	+	1.29563i	0.890064	+	0.455836i	$0.150660\pi$
$857$	10.1631	+	37.9291i	0.347164	+	1.29563i	−0.542900	+	0.839798i	$0.682674\pi$
$858$	−0.519771	−	5.28516i	−0.0177447	−	0.180432i
$859$	−7.70414	+	28.7522i	−0.262862	+	0.981013i	0.700684	+	0.713471i	$0.252878\pi$
$859$	−7.70414	+	28.7522i	−0.262862	+	0.981013i	−0.963546	+	0.267542i	$0.913789\pi$
$860$	−26.3751	+	9.12974i	−0.899383	+	0.311322i
$861$	10.0060	+	3.34017i	0.341004	+	0.113833i
$862$	1.18268	−	7.15692i	0.0402821	−	0.243766i
$863$	2.61211	−	9.74854i	0.0889174	−	0.331844i	−0.907110	−	0.420894i	$-0.861716\pi$
$863$	2.61211	−	9.74854i	0.0889174	−	0.331844i	0.996027	+	0.0890498i	$0.0283830\pi$
$864$	21.7511	−	5.05507i	0.739989	−	0.171977i
$865$	7.90869	+	57.2895i	0.268903	+	1.94790i
$866$	24.0994	−	53.1680i	0.818931	−	1.80672i
$867$	5.40954			0.183718
$868$	−26.3128	+	11.0466i	−0.893116	+	0.374947i
$869$	−32.8133	+	32.8133i	−1.11312	+	1.11312i
$870$	−3.83226	+	0.918389i	−0.129926	+	0.0311363i
$871$	−5.26806	+	9.12455i	−0.178501	+	0.309174i
$872$	−0.779554	+	3.33678i	−0.0263990	+	0.112997i
$873$	−0.159952	+	0.596950i	−0.00541357	+	0.0202037i
$874$	7.30502	+	1.20715i	0.247096	+	0.0408324i
$875$	24.1953	−	17.0172i	0.817951	−	0.575288i
$876$	8.43025	−	4.15431i	0.284832	−	0.140361i
$877$	−21.4403	+	12.3785i	−0.723986	+	0.417994i	−0.816218	−	0.577744i	$-0.803933\pi$
$877$	−21.4403	+	12.3785i	−0.723986	+	0.417994i	0.0922319	+	0.995738i	$0.470600\pi$
$878$	28.2110	−	34.3650i	0.952075	−	1.15976i
$879$	0.527258	+	0.304412i	0.0177840	+	0.0102676i
$880$	34.6464	+	9.07203i	1.16793	+	0.305818i
$881$			32.4793i			1.09426i	0.837049	+	0.547128i	$0.184279\pi$
$881$			32.4793i			1.09426i	−0.837049	+	0.547128i	$0.815721\pi$
$882$	−23.5763	−	6.89552i	−0.793854	−	0.232184i
$883$	−5.96843			−0.200854			−0.100427	−	0.994944i	$-0.532021\pi$
$883$	−5.96843			−0.200854			−0.100427	+	0.994944i	$0.532021\pi$
$884$	−6.66917	−	4.45899i	−0.224309	−	0.149972i
$885$	−8.92317	+	11.7814i	−0.299949	+	0.396027i
$886$	−12.9196	+	15.7379i	−0.434042	+	0.528726i
$887$	23.9104	+	6.40678i	0.802833	+	0.215118i	0.636827	−	0.771006i	$-0.280246\pi$
$887$	23.9104	+	6.40678i	0.802833	+	0.215118i	0.166006	+	0.986125i	$0.446913\pi$
$888$	−2.20152	−	1.17796i	−0.0738781	−	0.0395299i
$889$	28.7812	−	43.5499i	0.965290	−	1.46062i
$890$	−24.4174	−	45.0151i	−0.818472	−	1.50891i
$891$	4.76831	−	17.7956i	0.159744	−	0.596174i
$892$	−0.774565	+	11.7654i	−0.0259343	+	0.393935i
$893$	15.4431	−	26.7482i	0.516783	−	0.895094i
$894$	6.08062	+	2.75615i	0.203366	+	0.0921796i
$895$	−1.13589	+	9.06767i	−0.0379685	+	0.303099i
$896$	27.3150	+	12.2431i	0.912528	+	0.409013i
$897$	−1.07932	+	1.07932i	−0.0360373	+	0.0360373i
$898$	12.1037	+	32.1729i	0.403906	+	1.07362i
$899$	2.41531	+	9.01405i	0.0805550	+	0.300635i
$900$	11.2470	+	22.1181i	0.374898	+	0.737268i
$901$	−15.9610	−	4.27674i	−0.531739	−	0.142479i
$902$	−25.4854	+	18.2570i	−0.848571	+	0.607892i
$903$	3.76540	−	11.2799i	0.125305	−	0.375371i
$904$	49.2840	−	14.9268i	1.63916	−	0.496457i
$905$	−12.2495	−	29.0553i	−0.407187	−	0.965832i
$906$	−6.76217	−	5.55121i	−0.224658	−	0.184426i
$907$	−25.2867	+	43.7978i	−0.839630	+	1.45428i	0.0505746	+	0.998720i	$0.483895\pi$
$907$	−25.2867	+	43.7978i	−0.839630	+	1.45428i	−0.890204	+	0.455561i	$0.849439\pi$
$908$	−5.60064	−	28.1990i	−0.185864	−	0.935815i
$909$	21.5542	−	21.5542i	0.714907	−	0.714907i
$910$	10.7289	−	1.89503i	0.355659	−	0.0628195i
$911$	−29.4944			−0.977193			−0.488597	−	0.872510i	$-0.662491\pi$
$911$	−29.4944			−0.977193			−0.488597	+	0.872510i	$0.662491\pi$
$912$	−7.35489	+	5.63685i	−0.243545	+	0.186655i
$913$	−9.91949	−	37.0200i	−0.328287	−	1.22518i
$914$	−1.49635	−	15.2153i	−0.0494950	−	0.503277i
$915$	−3.05724	−	7.25167i	−0.101069	−	0.239733i
$916$	3.51922	+	7.14148i	0.116278	+	0.235961i
$917$	−0.226205	+	3.74145i	−0.00746995	+	0.123553i
$918$	10.0147	+	13.9798i	0.330535	+	0.461402i
$919$	−6.17836	−	10.7012i	−0.203805	−	0.353001i	0.745946	−	0.666006i	$-0.231998\pi$
$919$	−6.17836	−	10.7012i	−0.203805	−	0.353001i	−0.949751	+	0.313005i	$0.898664\pi$
$920$	−4.30305	−	9.35119i	−0.141867	−	0.308300i
$921$	10.1572	+	5.86426i	0.334691	+	0.193234i
$922$	−17.7225	−	8.03306i	−0.583660	−	0.264555i
$923$	19.0476			0.626959
$924$	−12.0615	+	9.34699i	−0.396796	+	0.307493i
$925$	1.51176	−	5.93941i	0.0497063	−	0.195287i
$926$	−32.5201	−	14.7403i	−1.06868	−	0.484397i
$927$	29.4804	−	7.89924i	0.968263	−	0.259445i
$928$	5.17496	−	8.30861i	0.169876	−	0.272743i
$929$	−29.2360	−	50.6382i	−0.959201	−	1.66138i	−0.724448	−	0.689330i	$-0.757905\pi$
$929$	−29.2360	−	50.6382i	−0.959201	−	1.66138i	−0.234753	−	0.972055i	$-0.575428\pi$
$930$	−10.7963	+	5.85622i	−0.354026	+	0.192033i
$931$	22.2935	−	3.16502i	0.730640	−	0.103729i
$932$	1.00920	−	0.497321i	0.0330575	−	0.0162903i
$933$	2.37623	−	1.37192i	0.0777943	−	0.0449146i
$934$	0.359822	+	0.295385i	0.0117737	+	0.00966531i
$935$	3.77164	+	27.3213i	0.123346	+	0.893502i
$936$	0.295062	+	9.13442i	0.00964439	+	0.298568i
$937$	−3.44627	+	3.44627i	−0.112585	+	0.112585i	−0.761155	−	0.648570i	$-0.775367\pi$
$937$	−3.44627	+	3.44627i	−0.112585	+	0.112585i	0.648570	+	0.761155i	$0.275367\pi$
$938$	30.2524	−	1.13937i	0.987777	−	0.0372018i
$939$	−11.9698	+	11.9698i	−0.390621	+	0.390621i
$940$	−42.8308	+	3.06511i	−1.39699	+	0.0999730i
$941$	37.3071	−	9.99642i	1.21618	−	0.325874i	0.406995	−	0.913430i	$-0.366577\pi$
$941$	37.3071	−	9.99642i	1.21618	−	0.325874i	0.809183	+	0.587557i	$0.199910\pi$
$942$	−14.6365	+	17.8293i	−0.476882	+	0.580911i
$943$	8.70356	+	2.33211i	0.283427	+	0.0759440i
$944$	−4.77053	−	36.3985i	−0.155267	−	1.18467i
$945$	−22.9556	−	4.29601i	−0.746746	−	0.139749i
$946$	20.5813	+	28.7299i	0.669156	+	0.934091i
$947$	−2.23642	+	1.29120i	−0.0726737	+	0.0419582i	−0.535897	−	0.844284i	$-0.680026\pi$
$947$	−2.23642	+	1.29120i	−0.0726737	+	0.0419582i	0.463223	+	0.886242i	$0.346693\pi$
$948$	−12.5534	+	11.0026i	−0.407715	+	0.357348i
$949$	2.19911	+	8.20719i	0.0713862	+	0.266417i
$950$	−17.7605	−	14.2103i	−0.576225	−	0.461042i
$951$	−0.0205157			−0.000665267
$952$	−0.647538	+	23.0423i	−0.0209868	+	0.746804i
$953$	−19.3433	+	19.3433i	−0.626592	+	0.626592i	−0.947209	−	0.320617i	$-0.896110\pi$
$953$	−19.3433	+	19.3433i	−0.626592	+	0.626592i	0.320617	+	0.947209i	$0.396110\pi$
$954$	6.62825	+	17.6186i	0.214597	+	0.570422i
$955$	−39.0245	+	5.38725i	−1.26280	+	0.174327i
$956$	22.2308	+	25.3642i	0.718996	+	0.820336i
$957$	2.49496	+	4.32140i	0.0806507	+	0.139691i
$958$	4.05954	−	24.5662i	0.131158	−	0.793697i
$959$	−15.8487	+	7.91574i	−0.511781	+	0.255613i
$960$	12.2216	+	4.07502i	0.394450	+	0.131521i
$961$	−0.957251	−	1.65801i	−0.0308791	−	0.0534841i
$962$	1.43229	−	1.74474i	0.0461790	−	0.0562526i
$963$	−5.02630	+	8.70580i	−0.161970	+	0.280541i
$964$	11.7158	−	2.32690i	0.377342	−	0.0749445i
$965$	7.11174	−	56.7723i	0.228935	−	1.82756i
$966$	4.27609	+	0.974891i	0.137581	+	0.0313666i
$967$	−17.8010	−	17.8010i	−0.572442	−	0.572442i	0.360368	−	0.932810i	$-0.382651\pi$
$967$	−17.8010	−	17.8010i	−0.572442	−	0.572442i	−0.932810	+	0.360368i	$0.882651\pi$
$968$	−0.459635	−	14.2292i	−0.0147732	−	0.457344i
$969$	−6.18003	−	3.56804i	−0.198531	−	0.114622i
$970$	−0.571531	+	0.541919i	−0.0183507	+	0.0174000i
$971$	44.9534	+	12.0452i	1.44262	+	0.386550i	0.893451	−	0.449160i	$-0.148277\pi$
$971$	44.9534	+	12.0452i	1.44262	+	0.386550i	0.549171	+	0.835710i	$0.314943\pi$
$972$	9.75197	−	28.7011i	0.312795	−	0.920588i
$973$	14.4282	+	9.53530i	0.462548	+	0.305688i
$974$	18.7602	−	13.4392i	0.601114	−	0.430621i
$975$	4.51373	−	1.27043i	0.144555	−	0.0406864i
$976$	18.0553	+	7.49100i	0.577937	+	0.239781i
$977$	−7.73241	−	28.8578i	−0.247382	−	0.923241i	−0.972171	−	0.234271i	$-0.924730\pi$
$977$	−7.73241	−	28.8578i	−0.247382	−	0.923241i	0.724790	−	0.688970i	$-0.241937\pi$
$978$	7.61394	+	20.2386i	0.243467	+	0.647160i
$979$	−45.8523	+	45.8523i	−1.46545	+	1.46545i
$980$	−21.0175	−	23.2005i	−0.671379	−	0.741114i
$981$	2.12565	+	2.12565i	0.0678669	+	0.0678669i
$982$	48.6780	+	22.0642i	1.55338	+	0.704097i
$983$	−6.59494	+	1.76711i	−0.210346	+	0.0563620i	−0.362453	−	0.932002i	$-0.618061\pi$
$983$	−6.59494	+	1.76711i	−0.210346	+	0.0563620i	0.152107	+	0.988364i	$0.451394\pi$
$984$	−9.57915	+	5.95093i	−0.305372	+	0.189709i
$985$	−15.8286	+	38.9029i	−0.504341	+	1.23955i
$986$	7.43713	+	1.22898i	0.236846	+	0.0391387i
$987$	10.0872	−	15.2634i	0.321080	−	0.485839i
$988$	−3.70315	−	7.51473i	−0.117813	−	0.239075i
$989$	2.62901	−	9.81160i	0.0835977	−	0.311991i
$990$	22.7997	−	21.6184i	0.724622	−	0.687078i
$991$	−22.3880	+	38.7772i	−0.711179	+	1.23180i	0.253236	+	0.967405i	$0.418505\pi$
$991$	−22.3880	+	38.7772i	−0.711179	+	1.23180i	−0.964415	+	0.264394i	$0.914828\pi$
$992$	8.87711	−	29.1879i	0.281848	−	0.926716i
$993$	−0.674245	+	0.674245i	−0.0213965	+	0.0213965i
$994$	−29.1296	−	46.3343i	−0.923934	−	1.46963i
$995$	−15.7330	+	12.2302i	−0.498771	+	0.387722i
$996$	−2.68570	−	13.5224i	−0.0850996	−	0.428472i
$997$	−29.8147	−	17.2135i	−0.944242	−	0.545159i	−0.0529547	−	0.998597i	$-0.516864\pi$
$997$	−29.8147	−	17.2135i	−0.944242	−	0.545159i	−0.891288	+	0.453438i	$0.850197\pi$
$998$	−5.54226	−	56.3550i	−0.175437	−	1.78389i
$999$	−4.19049	+	2.41938i	−0.132581	+	0.0765459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cz.c.213.79	yes	360
5.2	odd	4		560.2.ch.c.437.56	yes	360
7.5	odd	6	inner	560.2.cz.c.453.20	yes	360
16.13	even	4		560.2.ch.c.493.64	yes	360
35.12	even	12		560.2.ch.c.117.64	✓	360
80.77	odd	4	inner	560.2.cz.c.157.20	yes	360
112.61	odd	12		560.2.ch.c.173.56	yes	360
560.397	even	12	inner	560.2.cz.c.397.79	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.64	✓	360	35.12	even	12
560.2.ch.c.173.56	yes	360	112.61	odd	12
560.2.ch.c.437.56	yes	360	5.2	odd	4
560.2.ch.c.493.64	yes	360	16.13	even	4
560.2.cz.c.157.20	yes	360	80.77	odd	4	inner
560.2.cz.c.213.79	yes	360	1.1	even	1	trivial
560.2.cz.c.397.79	yes	360	560.397	even	12	inner
560.2.cz.c.453.20	yes	360	7.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32364 - 0.497965i) q^{2} +(-0.623698 - 0.360092i) q^{3} +(1.50406 - 1.31826i) q^{4} +(0.842714 - 2.07119i) q^{5} +(-1.00487 - 0.166053i) q^{6} +(-2.59227 + 0.529295i) q^{7} +(1.33439 - 2.49387i) q^{8} +(-1.24067 - 2.14890i) q^{9} +(0.0840704 - 3.16116i) q^{10} +(-3.86774 + 1.03636i) q^{11} +(-1.41277 + 0.280593i) q^{12} -1.30220i q^{13} +(-3.16767 + 1.99146i) q^{14} +(-1.27142 + 0.988343i) q^{15} +(0.524399 - 3.96548i) q^{16} +(2.97541 - 0.797258i) q^{17} +(-2.71228 - 2.22657i) q^{18} +(3.10711 + 0.832549i) q^{19} +(-1.46287 - 4.22611i) q^{20} +(1.80739 + 0.603335i) q^{21} +(-4.60343 + 3.29776i) q^{22} +(1.57212 + 0.421249i) q^{23} +(-1.73028 + 1.07492i) q^{24} +(-3.57967 - 3.49084i) q^{25} +(-0.648449 - 1.72364i) q^{26} +3.94757i q^{27} +(-3.20118 + 4.21336i) q^{28} +(1.22355 + 1.22355i) q^{29} +(-1.19074 + 1.94134i) q^{30} +(4.67056 + 2.69655i) q^{31} +(-1.28055 - 5.51001i) q^{32} +(2.78548 + 0.746367i) q^{33} +(3.54137 - 2.53693i) q^{34} +(-1.08827 + 5.81512i) q^{35} +(-4.69884 - 1.59656i) q^{36} +(0.612879 + 1.06154i) q^{37} +(4.52729 - 0.445238i) q^{38} +(-0.468911 + 0.812178i) q^{39} +(-4.04077 - 4.86540i) q^{40} +5.53618 q^{41} +(2.69277 - 0.101416i) q^{42} -6.24099i q^{43} +(-4.45113 + 6.65741i) q^{44} +(-5.49631 + 0.758753i) q^{45} +(2.29070 - 0.225279i) q^{46} +(2.48511 - 9.27457i) q^{47} +(-1.75500 + 2.28443i) q^{48} +(6.43969 - 2.74415i) q^{49} +(-6.47652 - 2.83808i) q^{50} +(-2.14284 - 0.574172i) q^{51} +(-1.71663 - 1.95859i) q^{52} +(-4.64563 - 2.68216i) q^{53} +(1.96575 + 5.22517i) q^{54} +(-1.11290 + 8.88417i) q^{55} +(-2.13911 + 7.17107i) q^{56} +(-1.63811 - 1.63811i) q^{57} +(2.22883 + 1.01026i) q^{58} +(8.86473 - 2.37530i) q^{59} +(-0.609401 + 3.16258i) q^{60} +(-1.26482 + 4.72039i) q^{61} +(7.52494 + 1.24349i) q^{62} +(4.35354 + 4.91384i) q^{63} +(-4.43879 - 6.65561i) q^{64} +(-2.69710 - 1.09738i) q^{65} +(4.05865 - 0.399149i) q^{66} +(-7.00704 - 4.04552i) q^{67} +(3.42420 - 5.12147i) q^{68} +(-0.828841 - 0.828841i) q^{69} +(1.45525 + 8.23907i) q^{70} +14.6273i q^{71} +(-7.01462 + 0.226587i) q^{72} +(-6.30257 + 1.68877i) q^{73} +(1.33984 + 1.09990i) q^{74} +(0.975606 + 3.46624i) q^{75} +(5.77080 - 2.84377i) q^{76} +(9.47766 - 4.73368i) q^{77} +(-0.216234 + 1.30853i) q^{78} +(10.0365 - 5.79459i) q^{79} +(-7.77134 - 4.42789i) q^{80} +(-2.30051 + 3.98461i) q^{81} +(7.32792 - 2.75682i) q^{82} +9.57150i q^{83} +(3.51377 - 1.47515i) q^{84} +(0.856142 - 6.83450i) q^{85} +(-3.10779 - 8.26084i) q^{86} +(-0.322536 - 1.20372i) q^{87} +(-2.57654 + 11.0285i) q^{88} +(14.0247 - 8.09717i) q^{89} +(-6.89732 + 3.74129i) q^{90} +(0.689246 + 3.37564i) q^{91} +(2.91988 - 1.43888i) q^{92} +(-1.94201 - 3.36366i) q^{93} +(-1.32901 - 13.5137i) q^{94} +(4.34278 - 5.73383i) q^{95} +(-1.18543 + 3.89770i) q^{96} +(-0.176114 - 0.176114i) q^{97} +(7.15737 - 6.83901i) q^{98} +(7.02560 + 7.02560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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