LMFDB - Embedded newform 465.2.k.b.218.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(32,465)] 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("465.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,-4,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.22
Character	$\chi$	$=$	465.218
Dual form			465.2.k.b.32.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00031 + 1.00031i) q^{2} +(0.708168 - 1.58066i) q^{3} +0.00123647i q^{4} +(1.98035 - 1.03838i) q^{5} +(2.28954 - 0.872765i) q^{6} +(-1.66917 + 1.66917i) q^{7} +(1.99938 - 1.99938i) q^{8} +(-1.99699 - 2.23875i) q^{9} +(3.01966 + 0.942258i) q^{10} +0.488628i q^{11} +(0.00195445 + 0.000875632i) q^{12} +(0.606001 + 0.606001i) q^{13} -3.33937 q^{14} +(-0.238909 - 3.86561i) q^{15} +4.00247 q^{16} +(0.560255 + 0.560255i) q^{17} +(0.241832 - 4.23706i) q^{18} -1.46112i q^{19} +(0.00128393 + 0.00244865i) q^{20} +(1.45634 + 3.82044i) q^{21} +(-0.488779 + 0.488779i) q^{22} +(-3.42811 + 3.42811i) q^{23} +(-1.74445 - 4.57625i) q^{24} +(2.84354 - 4.11270i) q^{25} +1.21238i q^{26} +(-4.95292 + 1.57116i) q^{27} +(-0.00206388 - 0.00206388i) q^{28} +0.216767 q^{29} +(3.62782 - 4.10578i) q^{30} -1.00000 q^{31} +(0.00494590 + 0.00494590i) q^{32} +(0.772356 + 0.346031i) q^{33} +1.12086i q^{34} +(-1.57230 + 5.03875i) q^{35} +(0.00276816 - 0.00246923i) q^{36} +(5.23298 - 5.23298i) q^{37} +(1.46158 - 1.46158i) q^{38} +(1.38703 - 0.528733i) q^{39} +(1.88335 - 6.03558i) q^{40} +7.11630i q^{41} +(-2.36483 + 5.27841i) q^{42} +(4.14486 + 4.14486i) q^{43} -0.000604176 q^{44} +(-6.27941 - 2.35987i) q^{45} -6.85833 q^{46} +(6.37862 + 6.37862i) q^{47} +(2.83442 - 6.32656i) q^{48} +1.42776i q^{49} +(6.95839 - 1.26955i) q^{50} +(1.28233 - 0.488820i) q^{51} +(-0.000749304 + 0.000749304i) q^{52} +(-6.92873 + 6.92873i) q^{53} +(-6.52610 - 3.38280i) q^{54} +(0.507381 + 0.967652i) q^{55} +6.67460i q^{56} +(-2.30955 - 1.03472i) q^{57} +(0.216834 + 0.216834i) q^{58} -9.51422 q^{59} +(0.00477972 - 0.000295405i) q^{60} +3.65071 q^{61} +(-1.00031 - 1.00031i) q^{62} +(7.07017 + 0.403534i) q^{63} -7.99505i q^{64} +(1.82935 + 0.570833i) q^{65} +(0.426457 + 1.11873i) q^{66} +(-4.73394 + 4.73394i) q^{67} +(-0.000692741 + 0.000692741i) q^{68} +(2.99101 + 7.84636i) q^{69} +(-6.61310 + 3.46753i) q^{70} -0.0865773i q^{71} +(-8.46887 - 0.483365i) q^{72} +(1.94880 + 1.94880i) q^{73} +10.4692 q^{74} +(-4.48709 - 7.40716i) q^{75} +0.00180664 q^{76} +(-0.815601 - 0.815601i) q^{77} +(1.91636 + 0.858567i) q^{78} +8.96053i q^{79} +(7.92628 - 4.15608i) q^{80} +(-1.02402 + 8.94155i) q^{81} +(-7.11850 + 7.11850i) q^{82} +(0.345948 - 0.345948i) q^{83} +(-0.00472388 + 0.00180073i) q^{84} +(1.69126 + 0.527742i) q^{85} +8.29227i q^{86} +(0.153508 - 0.342636i) q^{87} +(0.976954 + 0.976954i) q^{88} -12.2175 q^{89} +(-3.92076 - 8.64195i) q^{90} -2.02303 q^{91} +(-0.00423877 - 0.00423877i) q^{92} +(-0.708168 + 1.58066i) q^{93} +12.7612i q^{94} +(-1.51720 - 2.89353i) q^{95} +(0.0113203 - 0.00431527i) q^{96} +(-1.33436 + 1.33436i) q^{97} +(-1.42821 + 1.42821i) q^{98} +(1.09392 - 0.975787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40}+ \cdots + 56 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.00031	+	1.00031i	0.707325	+	0.707325i	0.965972	−	0.258647i	$-0.0832765\pi$
$2$	1.00031	+	1.00031i	0.707325	+	0.707325i	−0.258647	+	0.965972i	$0.583277\pi$
$3$	0.708168	−	1.58066i	0.408861	−	0.912597i
$3$	0.708168	−	1.58066i	0.408861	−	0.912597i
$4$			0.00123647i			0.000618237i
$5$	1.98035	−	1.03838i	0.885638	−	0.464377i
$5$	1.98035	−	1.03838i	0.885638	−	0.464377i
$6$	2.28954	−	0.872765i	0.934701	−	0.356305i
$7$	−1.66917	+	1.66917i	−0.630886	+	0.630886i	−0.948290	−	0.317405i	$-0.897189\pi$
$7$	−1.66917	+	1.66917i	−0.630886	+	0.630886i	0.317405	+	0.948290i	$0.397189\pi$
$8$	1.99938	−	1.99938i	0.706888	−	0.706888i
$9$	−1.99699	−	2.23875i	−0.665665	−	0.746251i
$10$	3.01966	+	0.942258i	0.954900	+	0.297968i
$11$			0.488628i			0.147327i	0.997283	+	0.0736634i	$0.0234691\pi$
$11$			0.488628i			0.147327i	−0.997283	+	0.0736634i	$0.976531\pi$
$12$	0.00195445		0.000875632i	0.000564201		0.000252773i
$13$	0.606001	+	0.606001i	0.168074	+	0.168074i	0.786132	−	0.618058i	$-0.212080\pi$
$13$	0.606001	+	0.606001i	0.168074	+	0.168074i	−0.618058	+	0.786132i	$0.712080\pi$
$14$	−3.33937			−0.892483
$15$	−0.238909	−	3.86561i	−0.0616860	−	0.998096i
$16$	4.00247			1.00062
$17$	0.560255	+	0.560255i	0.135882	+	0.135882i	0.771776	−	0.635894i	$-0.219369\pi$
$17$	0.560255	+	0.560255i	0.135882	+	0.135882i	−0.635894	+	0.771776i	$0.719369\pi$
$18$	0.241832	−	4.23706i	0.0570004	−	0.998684i
$19$		−	1.46112i		−	0.335205i	−0.985855	−	0.167602i	$-0.946397\pi$
$19$		−	1.46112i		−	0.335205i	0.985855	−	0.167602i	$-0.0536025\pi$
$20$	0.00128393	+	0.00244865i	0.000287095	+	0.000547534i
$21$	1.45634	+	3.82044i	0.317799	+	0.833689i
$22$	−0.488779	+	0.488779i	−0.104208	+	0.104208i
$23$	−3.42811	+	3.42811i	−0.714810	+	0.714810i	−0.967537	−	0.252728i	$-0.918672\pi$
$23$	−3.42811	+	3.42811i	−0.714810	+	0.714810i	0.252728	+	0.967537i	$0.418672\pi$
$24$	−1.74445	−	4.57625i	−0.356084	−	0.934123i
$25$	2.84354	−	4.11270i	0.568708	−	0.822540i
$26$			1.21238i			0.237767i
$27$	−4.95292	+	1.57116i	−0.953190	+	0.302370i
$28$	−0.00206388	−	0.00206388i	−0.000390037	−	0.000390037i
$29$	0.216767			0.0402527			0.0201263	−	0.999797i	$-0.493593\pi$
$29$	0.216767			0.0402527			0.0201263	+	0.999797i	$0.493593\pi$
$30$	3.62782	−	4.10578i	0.662346	−	0.749610i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.00494590	+	0.00494590i	0.000874319	+	0.000874319i
$33$	0.772356	+	0.346031i	0.134450	+	0.0602362i
$34$			1.12086i			0.192225i
$35$	−1.57230	+	5.03875i	−0.265767	+	0.851705i
$36$	0.00276816	−	0.00246923i	0.000461360	−	0.000411539i
$37$	5.23298	−	5.23298i	0.860296	−	0.860296i	−0.131076	−	0.991372i	$-0.541843\pi$
$37$	5.23298	−	5.23298i	0.860296	−	0.860296i	0.991372	+	0.131076i	$0.0418433\pi$
$38$	1.46158	−	1.46158i	0.237099	−	0.237099i
$39$	1.38703	−	0.528733i	0.222103	−	0.0846650i
$40$	1.88335	−	6.03558i	0.297784	−	0.954309i
$41$			7.11630i			1.11138i	0.831390	+	0.555690i	$0.187546\pi$
$41$			7.11630i			1.11138i	−0.831390	+	0.555690i	$0.812454\pi$
$42$	−2.36483	+	5.27841i	−0.364902	+	0.814477i
$43$	4.14486	+	4.14486i	0.632084	+	0.632084i	0.948591	−	0.316506i	$-0.102510\pi$
$43$	4.14486	+	4.14486i	0.632084	+	0.632084i	−0.316506	+	0.948591i	$0.602510\pi$
$44$	−0.000604176	0		−9.10829e−5	0
$45$	−6.27941	−	2.35987i	−0.936080	−	0.351788i
$46$	−6.85833			−1.01121
$47$	6.37862	+	6.37862i	0.930418	+	0.930418i	0.997732	−	0.0673142i	$-0.0214430\pi$
$47$	6.37862	+	6.37862i	0.930418	+	0.930418i	−0.0673142	+	0.997732i	$0.521443\pi$
$48$	2.83442	−	6.32656i	0.409114	−	0.913160i
$49$			1.42776i			0.203966i
$50$	6.95839	−	1.26955i	0.984065	−	0.179542i
$51$	1.28233	−	0.488820i	0.179562	−	0.0684485i
$52$	−0.000749304	0	0.000749304i	−0.000103910	0	0.000103910i
$53$	−6.92873	+	6.92873i	−0.951734	+	0.951734i	−0.998888	−	0.0471539i	$-0.984985\pi$
$53$	−6.92873	+	6.92873i	−0.951734	+	0.951734i	0.0471539	+	0.998888i	$0.484985\pi$
$54$	−6.52610	−	3.38280i	−0.888090	−	0.460341i
$55$	0.507381	+	0.967652i	0.0684152	+	0.130478i
$56$			6.67460i			0.891931i
$57$	−2.30955	−	1.03472i	−0.305907	−	0.137052i
$58$	0.216834	+	0.216834i	0.0284717	+	0.0284717i
$59$	−9.51422			−1.23865			−0.619323	−	0.785136i	$-0.712593\pi$
$59$	−9.51422			−1.23865			−0.619323	+	0.785136i	$0.712593\pi$
$60$	0.00477972		0.000295405i	0.000617060		3.81366e-5i
$61$	3.65071			0.467425			0.233713	−	0.972306i	$-0.424912\pi$
$61$	3.65071			0.467425			0.233713	+	0.972306i	$0.424912\pi$
$62$	−1.00031	−	1.00031i	−0.127039	−	0.127039i
$63$	7.07017	+	0.403534i	0.890757	+	0.0508404i
$64$		−	7.99505i		−	0.999381i
$65$	1.82935	+	0.570833i	0.226903	+	0.0708031i
$66$	0.426457	+	1.11873i	0.0524933	+	0.137707i
$67$	−4.73394	+	4.73394i	−0.578342	+	0.578342i	−0.934446	−	0.356104i	$-0.884105\pi$
$67$	−4.73394	+	4.73394i	−0.578342	+	0.578342i	0.356104	+	0.934446i	$0.384105\pi$
$68$	−0.000692741	0	0.000692741i	−8.40072e−5	0	8.40072e-5i
$69$	2.99101	+	7.84636i	0.360075	+	0.944591i
$70$	−6.61310	+	3.46753i	−0.790416	+	0.414449i
$71$		−	0.0865773i		−	0.0102748i	−0.999987	−	0.00513742i	$-0.998365\pi$
$71$		−	0.0865773i		−	0.0102748i	0.999987	−	0.00513742i	$-0.00163530\pi$
$72$	−8.46887	−	0.483365i	−0.998066	−	0.0569652i
$73$	1.94880	+	1.94880i	0.228090	+	0.228090i	0.811895	−	0.583804i	$-0.198436\pi$
$73$	1.94880	+	1.94880i	0.228090	+	0.228090i	−0.583804	+	0.811895i	$0.698436\pi$
$74$	10.4692			1.21702
$75$	−4.48709	−	7.40716i	−0.518124	−	0.855305i
$76$	0.00180664			0.000207236
$77$	−0.815601	−	0.815601i	−0.0929464	−	0.0929464i
$78$	1.91636	+	0.858567i	0.216985	+	0.0972135i
$79$			8.96053i			1.00814i	0.863663	+	0.504069i	$0.168164\pi$
$79$			8.96053i			1.00814i	−0.863663	+	0.504069i	$0.831836\pi$
$80$	7.92628	−	4.15608i	0.886185	−	0.464664i
$81$	−1.02402	+	8.94155i	−0.113780	+	0.993506i
$82$	−7.11850	+	7.11850i	−0.786107	+	0.786107i
$83$	0.345948	−	0.345948i	0.0379727	−	0.0379727i	−0.687865	−	0.725838i	$-0.741452\pi$
$83$	0.345948	−	0.345948i	0.0379727	−	0.0379727i	0.725838	+	0.687865i	$0.241452\pi$
$84$	−0.00472388	+	0.00180073i	−0.000515417	+	0.000196475i
$85$	1.69126	+	0.527742i	0.183443	+	0.0572417i
$86$			8.29227i			0.894179i
$87$	0.153508	−	0.342636i	0.0164578	−	0.0367344i
$88$	0.976954	+	0.976954i	0.104144	+	0.104144i
$89$	−12.2175			−1.29505			−0.647525	−	0.762044i	$-0.724196\pi$
$89$	−12.2175			−1.29505			−0.647525	+	0.762044i	$0.724196\pi$
$90$	−3.92076	−	8.64195i	−0.413284	−	0.910942i
$91$	−2.02303			−0.212071
$92$	−0.00423877	−	0.00423877i	−0.000441922	−	0.000441922i
$93$	−0.708168	+	1.58066i	−0.0734337	+	0.163907i
$94$			12.7612i			1.31622i
$95$	−1.51720	−	2.89353i	−0.155661	−	0.296870i
$96$	0.0113203	−	0.00431527i	0.00115538	−	0.000440425i
$97$	−1.33436	+	1.33436i	−0.135484	+	0.135484i	−0.771596	−	0.636113i	$-0.780541\pi$
$97$	−1.33436	+	1.33436i	−0.135484	+	0.135484i	0.636113	+	0.771596i	$0.280541\pi$
$98$	−1.42821	+	1.42821i	−0.144271	+	0.144271i
$99$	1.09392	−	0.975787i	0.109943	−	0.0980703i
$100$	0.00508525	+	0.00351596i	0.000508525	+	0.000351596i
$101$		−	13.5503i		−	1.34830i	−0.738593	−	0.674152i	$-0.764509\pi$
$101$		−	13.5503i		−	1.34830i	0.738593	−	0.674152i	$-0.235491\pi$
$102$	1.77170	+	0.793755i	0.175424	+	0.0785935i
$103$	−3.23911	−	3.23911i	−0.319159	−	0.319159i	0.529285	−	0.848444i	$-0.322460\pi$
$103$	−3.23911	−	3.23911i	−0.319159	−	0.319159i	−0.848444	+	0.529285i	$0.822460\pi$
$104$	2.42325			0.237620
$105$	6.85112	+	6.05357i	0.668601	+	0.590767i
$106$	−13.8617			−1.34637
$107$	−5.66961	−	5.66961i	−0.548102	−	0.548102i	0.377790	−	0.925891i	$-0.376684\pi$
$107$	−5.66961	−	5.66961i	−0.548102	−	0.548102i	−0.925891	+	0.377790i	$0.876684\pi$
$108$	−0.00194270	−	0.00612416i	−0.000186937	−	0.000589298i
$109$		−	14.9745i		−	1.43430i	−0.696921	−	0.717148i	$-0.745447\pi$
$109$		−	14.9745i		−	1.43430i	0.696921	−	0.717148i	$-0.254553\pi$
$110$	−0.460414	+	1.47549i	−0.0438987	+	0.140682i
$111$	−4.56575	−	11.9774i	−0.433361	−	1.13684i
$112$	−6.68079	+	6.68079i	−0.631276	+	0.631276i
$113$	0.606854	−	0.606854i	0.0570880	−	0.0570880i	−0.677986	−	0.735074i	$-0.737147\pi$
$113$	0.606854	−	0.606854i	0.0570880	−	0.0570880i	0.735074	+	0.677986i	$0.237147\pi$
$114$	−1.27522	−	3.34530i	−0.119435	−	0.313316i
$115$	−3.22917	+	10.3485i	−0.301121	+	0.965004i
$116$		0	0.000268027i		0	2.48857e-5i
$117$	0.146505	−	2.56687i	0.0135444	−	0.237307i
$118$	−9.51716	−	9.51716i	−0.876126	−	0.876126i
$119$	−1.87032			−0.171452
$120$	−8.20649	−	7.25115i	−0.749147	−	0.661937i
$121$	10.7612			0.978295
$122$	3.65184	+	3.65184i	0.330622	+	0.330622i
$123$	11.2485	+	5.03954i	1.01424	+	0.454400i
$124$		−	0.00123647i		−	0.000111039i
$125$	1.36065	−	11.0972i	0.121701	−	0.992567i
$126$	6.66870	+	7.47601i	0.594095	+	0.666016i
$127$	7.09372	−	7.09372i	0.629466	−	0.629466i	−0.318468	−	0.947934i	$-0.603168\pi$
$127$	7.09372	−	7.09372i	0.629466	−	0.629466i	0.947934	+	0.318468i	$0.103168\pi$
$128$	8.00741	−	8.00741i	0.707762	−	0.707762i
$129$	9.48688	−	3.61637i	0.835273	−	0.318403i
$130$	1.25891	+	2.40092i	0.110413	+	0.210575i
$131$		−	13.4920i		−	1.17881i	−0.807839	−	0.589403i	$-0.799363\pi$
$131$		−	13.4920i		−	1.17881i	0.807839	−	0.589403i	$-0.200637\pi$
$132$	−0.000427858	0	0.000954999i	−3.72403e−5	0	8.31220e-5i
$133$	2.43886	+	2.43886i	0.211476	+	0.211476i
$134$	−9.47080			−0.818153
$135$	−8.17704	+	8.25446i	−0.703767	+	0.710430i
$136$	2.24033			0.192107
$137$	12.2568	+	12.2568i	1.04717	+	1.04717i	0.998831	+	0.0483356i	$0.0153917\pi$
$137$	12.2568	+	12.2568i	1.04717	+	1.04717i	0.0483356	+	0.998831i	$0.484608\pi$
$138$	−4.85686	+	10.8407i	−0.413443	+	0.922823i
$139$			1.52125i			0.129031i	0.997917	+	0.0645155i	$0.0205502\pi$
$139$			1.52125i			0.129031i	−0.997917	+	0.0645155i	$0.979450\pi$
$140$	−0.00623029	−	0.00194411i	−0.000526556	−	0.000164307i
$141$	14.5996	−	5.56532i	1.22951	−	0.468684i
$142$	0.0866040	−	0.0866040i	0.00726765	−	0.00726765i
$143$	−0.296109	+	0.296109i	−0.0247619	+	0.0247619i
$144$	−7.99291	−	8.96054i	−0.666076	−	0.746712i
$145$	0.429274	−	0.225086i	0.0356493	−	0.0186924i
$146$			3.89881i			0.322668i
$147$	2.25682	+	1.01110i	0.186139	+	0.0833940i
$148$	0.00647044	+	0.00647044i	0.000531867	+	0.000531867i
$149$	−19.3963			−1.58900			−0.794502	−	0.607261i	$-0.792268\pi$
$149$	−19.3963			−1.58900			−0.794502	+	0.607261i	$0.792268\pi$
$150$	2.92098	−	11.8979i	0.238497	−	0.971462i
$151$	−18.4786			−1.50376			−0.751882	−	0.659298i	$-0.770854\pi$
$151$	−18.4786			−1.50376			−0.751882	+	0.659298i	$0.770854\pi$
$152$	−2.92134	−	2.92134i	−0.236952	−	0.236952i
$153$	0.135446	−	2.37310i	0.0109502	−	0.191854i
$154$		−	1.63171i		−	0.131487i
$155$	−1.98035	+	1.03838i	−0.159065	+	0.0834046i
$156$	0.000653764		0.00171503i	5.23430e−5		0.000137312i
$157$	16.0623	−	16.0623i	1.28191	−	1.28191i	0.342336	−	0.939578i	$-0.388782\pi$
$157$	16.0623	−	16.0623i	1.28191	−	1.28191i	0.939578	−	0.342336i	$-0.111218\pi$
$158$	−8.96330	+	8.96330i	−0.713082	+	0.713082i
$159$	6.04528	+	15.8587i	0.479422	+	1.25768i
$160$	0.0149303	+	0.00465887i	0.00118034	+	0.000368316i
$161$		−	11.4442i		−	0.901927i
$162$	−9.96866	+	7.91998i	−0.783212	+	0.622252i
$163$	3.67219	+	3.67219i	0.287628	+	0.287628i	0.836142	−	0.548514i	$-0.184806\pi$
$163$	3.67219	+	3.67219i	0.287628	+	0.287628i	−0.548514	+	0.836142i	$0.684806\pi$
$164$	−0.00879913			−0.000687096
$165$	1.88884	−	0.116737i	0.147046	−	0.00908800i
$166$	0.692110			0.0537181
$167$	14.2829	+	14.2829i	1.10524	+	1.10524i	0.993767	+	0.111477i	$0.0355581\pi$
$167$	14.2829	+	14.2829i	1.10524	+	1.10524i	0.111477	+	0.993767i	$0.464442\pi$
$168$	10.5503	+	4.72674i	0.813973	+	0.364676i
$169$		−	12.2655i		−	0.943502i
$170$	1.16387	+	2.21968i	0.0892650	+	0.170242i
$171$	−3.27110	+	2.91786i	−0.250147	+	0.223134i
$172$	−0.00512501	+	0.00512501i	−0.000390778	+	0.000390778i
$173$	3.63506	−	3.63506i	0.276369	−	0.276369i	−0.555289	−	0.831658i	$-0.687392\pi$
$173$	3.63506	−	3.63506i	0.276369	−	0.276369i	0.831658	+	0.555289i	$0.187392\pi$
$174$	0.496297	−	0.189187i	0.0376242	−	0.0143422i
$175$	2.11844	+	11.6111i	0.160139	+	0.877718i
$176$			1.95572i			0.147418i
$177$	−6.73767	+	15.0388i	−0.506434	+	1.13038i
$178$	−12.2212	−	12.2212i	−0.916021	−	0.916021i
$179$	−20.8745			−1.56023			−0.780116	−	0.625635i	$-0.784840\pi$
$179$	−20.8745			−1.56023			−0.780116	+	0.625635i	$0.784840\pi$
$180$	0.00291792	−	0.00776433i	0.000217489	−	0.000578719i
$181$	−19.2211			−1.42870			−0.714348	−	0.699791i	$-0.753277\pi$
$181$	−19.2211			−1.42870			−0.714348	+	0.699791i	$0.753277\pi$
$182$	−2.02366	−	2.02366i	−0.150004	−	0.150004i
$183$	2.58532	−	5.77054i	0.191112	−	0.426571i
$184$			13.7082i			1.01058i
$185$	4.92929	−	15.7969i	0.362409	−	1.16141i
$186$	−2.28954	+	0.872765i	−0.167877	+	0.0639942i
$187$	−0.273756	+	0.273756i	−0.0200190	+	0.0200190i
$188$	−0.00788700	+	0.00788700i	−0.000575219	+	0.000575219i
$189$	5.64472	−	10.8898i	0.410593	−	0.792115i
$190$	1.37676	−	4.41210i	0.0998804	−	0.320087i
$191$			24.3776i			1.76390i	0.471339	+	0.881952i	$0.343771\pi$
$191$			24.3776i			1.76390i	−0.471339	+	0.881952i	$0.656229\pi$
$192$	−12.6375	−	5.66184i	−0.912032	−	0.408608i
$193$	−5.95019	−	5.95019i	−0.428304	−	0.428304i	0.459746	−	0.888050i	$-0.347940\pi$
$193$	−5.95019	−	5.95019i	−0.428304	−	0.428304i	−0.888050	+	0.459746i	$0.847940\pi$
$194$	−2.66954			−0.191662
$195$	2.19778	−	2.48734i	0.157386	−	0.178122i
$196$	−0.00176539			−0.000126100
$197$	15.7539	+	15.7539i	1.12242	+	1.12242i	0.991376	+	0.131046i	$0.0418334\pi$
$197$	15.7539	+	15.7539i	1.12242	+	1.12242i	0.131046	+	0.991376i	$0.458167\pi$
$198$	2.07034	+	0.118166i	0.147133	+	0.00839769i
$199$		−	4.09660i		−	0.290400i	−0.989402	−	0.145200i	$-0.953617\pi$
$199$		−	4.09660i		−	0.290400i	0.989402	−	0.145200i	$-0.0463826\pi$
$200$	−2.53753	−	13.9082i	−0.179431	−	0.983456i
$201$	4.13034	+	10.8352i	0.291332	+	0.764255i
$202$	13.5545	−	13.5545i	0.953689	−	0.953689i
$203$	−0.361821	+	0.361821i	−0.0253948	+	0.0253948i
$204$	0.000604413		0.00158557i	4.23174e−5		0.000111012i
$205$	7.38942	+	14.0927i	0.516099	+	0.984280i
$206$		−	6.48022i		−	0.451499i
$207$	14.5206	+	0.828771i	1.00925	+	0.0576035i
$208$	2.42550	+	2.42550i	0.168178	+	0.168178i
$209$	0.713946			0.0493847
$210$	0.797803	+	12.9087i	0.0550537	+	0.890783i
$211$	−0.945083			−0.0650622			−0.0325311	−	0.999471i	$-0.510357\pi$
$211$	−0.945083			−0.0650622			−0.0325311	+	0.999471i	$0.510357\pi$
$212$	−0.00856719	−	0.00856719i	−0.000588397	−	0.000588397i
$213$	−0.136850	−	0.0613113i	−0.00937677	−	0.00420098i
$214$		−	11.3427i		−	0.775372i
$215$	12.5122	+	3.90432i	0.853323	+	0.266272i
$216$	−6.76143	+	13.0441i	−0.460057	+	0.887541i
$217$	1.66917	−	1.66917i	0.113310	−	0.113310i
$218$	14.9791	−	14.9791i	1.01451	−	1.01451i
$219$	4.46049	−	1.70032i	0.301412	−	0.114897i
$220$	−0.00119648		0.000627363i	−8.06665e−5		4.22968e-5i
$221$			0.679030i			0.0456765i
$222$	7.41395	−	16.5483i	0.497592	−	1.11065i
$223$	3.30852	+	3.30852i	0.221555	+	0.221555i	0.809153	−	0.587598i	$-0.199926\pi$
$223$	3.30852	+	3.30852i	0.221555	+	0.221555i	−0.587598	+	0.809153i	$0.699926\pi$
$224$	−0.0165111			−0.00110319
$225$	−14.8858	+	1.84705i	−0.992390	+	0.123137i
$226$	1.21408			0.0807596
$227$	4.51141	+	4.51141i	0.299433	+	0.299433i	0.840792	−	0.541359i	$-0.182090\pi$
$227$	4.51141	+	4.51141i	0.299433	+	0.299433i	−0.541359	+	0.840792i	$0.682090\pi$
$228$	0.00127941	−	0.00285569i	8.47308e−5	−	0.000189123i
$229$		−	23.0217i		−	1.52132i	−0.649151	−	0.760660i	$-0.724876\pi$
$229$		−	23.0217i		−	1.52132i	0.649151	−	0.760660i	$-0.275124\pi$
$230$	−13.5819	+	7.12155i	−0.895562	+	0.469581i
$231$	−1.86677	+	0.711608i	−0.122825	+	0.0468204i
$232$	0.433400	−	0.433400i	0.0284541	−	0.0284541i
$233$	−19.6190	+	19.6190i	−1.28528	+	1.28528i	−0.347666	+	0.937618i	$0.613026\pi$
$233$	−19.6190	+	19.6190i	−1.28528	+	1.28528i	−0.937618	+	0.347666i	$0.886974\pi$
$234$	2.71421	−	2.42111i	0.177433	−	0.158273i
$235$	19.2553	+	6.00845i	1.25608	+	0.391948i
$236$		−	0.0117641i		−	0.000765777i
$237$	14.1636	+	6.34556i	0.920023	+	0.412189i
$238$	−1.87090	−	1.87090i	−0.121272	−	0.121272i
$239$	8.66511			0.560499			0.280250	−	0.959927i	$-0.409583\pi$
$239$	8.66511			0.560499			0.280250	+	0.959927i	$0.409583\pi$
$240$	−0.956225	−	15.4720i	−0.0617241	−	0.998712i
$241$	−19.4767			−1.25460			−0.627302	−	0.778776i	$-0.715841\pi$
$241$	−19.4767			−1.25460			−0.627302	+	0.778776i	$0.715841\pi$
$242$	10.7646	+	10.7646i	0.691973	+	0.691973i
$243$	13.4084	+	7.95076i	0.860150	+	0.510042i
$244$			0.00451401i			0.000288980i
$245$	1.48256	+	2.82747i	0.0947173	+	0.180640i
$246$	6.21086	+	16.2931i	0.395990	+	1.03881i
$247$	0.885442	−	0.885442i	0.0563394	−	0.0563394i
$248$	−1.99938	+	1.99938i	−0.126961	+	0.126961i
$249$	−0.301838	−	0.791817i	−0.0191282	−	0.0501794i
$250$	12.4617	−	9.73959i	0.788150	−	0.615986i
$251$		−	6.66638i		−	0.420778i	−0.977618	−	0.210389i	$-0.932527\pi$
$251$		−	6.66638i		−	0.420778i	0.977618	−	0.210389i	$-0.0674731\pi$
$252$	−0.000498959		0.00874208i	−3.14315e−5		0.000550699i
$253$	−1.67507	−	1.67507i	−0.105311	−	0.105311i
$254$	14.1918			0.890474
$255$	2.03188	−	2.29958i	0.127241	−	0.144005i
$256$	0.0296754			0.00185471
$257$	−4.13272	−	4.13272i	−0.257792	−	0.257792i	0.566364	−	0.824155i	$-0.308350\pi$
$257$	−4.13272	−	4.13272i	−0.257792	−	0.257792i	−0.824155	+	0.566364i	$0.808350\pi$
$258$	13.1073	+	5.87233i	0.816024	+	0.365595i
$259$			17.4694i			1.08550i
$260$	−0.000705820		0.00226194i	−4.37731e−5		0.000140280i
$261$	−0.432883	−	0.485288i	−0.0267948	−	0.0300386i
$262$	13.4962	−	13.4962i	0.833799	−	0.833799i
$263$	2.14753	−	2.14753i	0.132423	−	0.132423i	−0.637789	−	0.770211i	$-0.720151\pi$
$263$	2.14753	−	2.14753i	0.132423	−	0.132423i	0.770211	+	0.637789i	$0.220151\pi$
$264$	2.23608	−	0.852387i	0.137621	−	0.0524608i
$265$	−6.52663	+	20.9159i	−0.400928	+	1.28485i
$266$			4.87923i			0.299165i
$267$	−8.65203	+	19.3117i	−0.529496	+	1.18186i
$268$	−0.00585339	−	0.00585339i	−0.000357553	−	0.000357553i
$269$	16.1691			0.985846			0.492923	−	0.870073i	$-0.335928\pi$
$269$	16.1691			0.985846			0.492923	+	0.870073i	$0.335928\pi$
$270$	−16.4366	+	0.0774414i	−1.00030	+	0.00471293i
$271$	27.6629			1.68040			0.840200	−	0.542277i	$-0.182438\pi$
$271$	27.6629			1.68040			0.840200	+	0.542277i	$0.182438\pi$
$272$	2.24241	+	2.24241i	0.135966	+	0.135966i
$273$	−1.43265	+	3.19773i	−0.0867078	+	0.193536i
$274$			24.5211i			1.48138i
$275$	2.00958	+	1.38943i	0.121182	+	0.0837860i
$276$	−0.00970183	+	0.00369830i	−0.000583981	+	0.000222612i
$277$	16.0299	−	16.0299i	0.963141	−	0.963141i	−0.0362031	−	0.999344i	$-0.511526\pi$
$277$	16.0299	−	16.0299i	0.963141	−	0.963141i	0.999344	+	0.0362031i	$0.0115263\pi$
$278$	−1.52172	+	1.52172i	−0.0912669	+	0.0912669i
$279$	1.99699	+	2.23875i	0.119557	+	0.134031i
$280$	6.93076	+	13.2180i	0.414192	+	0.789928i
$281$		−	27.0910i		−	1.61611i	−0.589104	−	0.808057i	$-0.700519\pi$
$281$		−	27.0910i		−	1.61611i	0.589104	−	0.808057i	$-0.299481\pi$
$282$	20.1711	+	9.03707i	1.20117	+	0.538150i
$283$	−7.86447	−	7.86447i	−0.467494	−	0.467494i	0.433608	−	0.901102i	$-0.357240\pi$
$283$	−7.86447	−	7.86447i	−0.467494	−	0.467494i	−0.901102	+	0.433608i	$0.857240\pi$
$284$	0.000107051	0		6.35228e−6	0
$285$	−5.64813	+	0.349075i	−0.334567	+	0.0206774i
$286$	−0.592401			−0.0350294
$287$	−11.8783	−	11.8783i	−0.701154	−	0.701154i
$288$	0.00119571	−	0.0209496i	7.04577e−5	−	0.00123447i
$289$		−	16.3722i		−	0.963072i
$290$	0.654563	+	0.204251i	0.0384372	+	0.0119940i
$291$	1.16422	+	3.05412i	0.0682479	+	0.179036i
$292$	−0.00240965	+	0.00240965i	−0.000141014	+	0.000141014i
$293$	10.7917	−	10.7917i	0.630460	−	0.630460i	−0.317723	−	0.948183i	$-0.602918\pi$
$293$	10.7917	−	10.7917i	0.630460	−	0.630460i	0.948183	+	0.317723i	$0.102918\pi$
$294$	1.24610	+	3.26892i	0.0726742	+	0.190648i
$295$	−18.8415	+	9.87936i	−1.09699	+	0.575199i
$296$		−	20.9254i		−	1.21627i
$297$	−0.767714	−	2.42014i	−0.0445473	−	0.140431i
$298$	−19.4023	−	19.4023i	−1.12394	−	1.12394i
$299$	−4.15487			−0.240282
$300$	0.00915877	−	0.00554817i	0.000528782	−	0.000320324i
$301$	−13.8369			−0.797546
$302$	−18.4843	−	18.4843i	−1.06365	−	1.06365i
$303$	−21.4184	−	9.59588i	−1.23046	−	0.551269i
$304$		−	5.84811i		−	0.335412i
$305$	7.22967	−	3.79082i	0.413970	−	0.217062i
$306$	2.50932	−	2.23835i	0.143448	−	0.127958i
$307$	12.8025	−	12.8025i	0.730678	−	0.730678i	−0.240076	−	0.970754i	$-0.577172\pi$
$307$	12.8025	−	12.8025i	0.730678	−	0.730678i	0.970754	+	0.240076i	$0.0771723\pi$
$308$	0.00100847	−	0.00100847i	5.74629e−5	−	5.74629e-5i
$309$	−7.41378	+	2.82611i	−0.421755	+	0.160772i
$310$	−3.01966	−	0.942258i	−0.171505	−	0.0535167i
$311$		−	21.6644i		−	1.22847i	−0.789121	−	0.614237i	$-0.789464\pi$
$311$		−	21.6644i		−	1.22847i	0.789121	−	0.614237i	$-0.210536\pi$
$312$	1.71607	−	3.83035i	0.0971534	−	0.216851i
$313$	15.5220	+	15.5220i	0.877353	+	0.877353i	0.993260	−	0.115907i	$-0.0369774\pi$
$313$	15.5220	+	15.5220i	0.877353	+	0.877353i	−0.115907	+	0.993260i	$0.536977\pi$
$314$	32.1346			1.81346
$315$	14.4204	−	6.54238i	0.812497	−	0.368621i
$316$	−0.0110795			−0.000623268
$317$	−13.7279	−	13.7279i	−0.771035	−	0.771035i	0.207252	−	0.978288i	$-0.433548\pi$
$317$	−13.7279	−	13.7279i	−0.771035	−	0.771035i	−0.978288	+	0.207252i	$0.933548\pi$
$318$	−9.81644	+	21.9107i	−0.550479	+	1.22869i
$319$			0.105919i			0.00593030i
$320$	−8.30189	−	15.8330i	−0.464090	−	0.885089i
$321$	−12.9768	+	4.94671i	−0.724293	+	0.276098i
$322$	11.4477	−	11.4477i	0.637956	−	0.637956i
$323$	0.818603	−	0.818603i	0.0455483	−	0.0455483i
$324$	−0.0110560	−	0.00126618i	−0.000614222	−	7.03433e-5i
$325$	4.21549	−	0.769111i	0.233833	−	0.0426626i
$326$			7.34665i			0.406893i
$327$	−23.6696	−	10.6045i	−1.30893	−	0.586428i
$328$	14.2282	+	14.2282i	0.785621	+	0.785621i
$329$	−21.2940			−1.17397
$330$	2.00620	+	1.77265i	0.110438	+	0.0975814i
$331$	−16.4734			−0.905461			−0.452731	−	0.891647i	$-0.649550\pi$
$331$	−16.4734			−0.905461			−0.452731	+	0.891647i	$0.649550\pi$
$332$	0.000427756	0	0.000427756i	2.34762e−5	0	2.34762e-5i
$333$	−22.1656	−	1.26511i	−1.21467	−	0.0693277i
$334$			28.5746i			1.56353i
$335$	−4.45921	+	14.2905i	−0.243633	+	0.780771i
$336$	5.82896	+	15.2912i	0.317996	+	0.834204i
$337$	18.6177	−	18.6177i	1.01417	−	1.01417i	0.0142748	−	0.999898i	$-0.495456\pi$
$337$	18.6177	−	18.6177i	1.01417	−	1.01417i	0.999898	−	0.0142748i	$-0.00454395\pi$
$338$	12.2693	−	12.2693i	0.667363	−	0.667363i
$339$	−0.529477	−	1.38899i	−0.0287573	−	0.0754394i
$340$	−0.000652540		0.00209120i	−3.53889e−5		0.000113411i
$341$		−	0.488628i		−	0.0264607i
$342$	−6.19087	−	0.353347i	−0.334764	−	0.0191068i
$343$	−14.0673	−	14.0673i	−0.759565	−	0.759565i
$344$	16.5743			0.893626
$345$	14.0707	+	12.4327i	0.757542	+	0.669355i
$346$	7.27238			0.390965
$347$	−21.7272	−	21.7272i	−1.16637	−	1.16637i	−0.983053	−	0.183322i	$-0.941315\pi$
$347$	−21.7272	−	21.7272i	−1.16637	−	1.16637i	−0.183322	−	0.983053i	$-0.558685\pi$
$348$	0.000423661	0	0.000189808i	2.27106e−5	0	1.01748e-5i
$349$		−	2.53205i		−	0.135537i	−0.997701	−	0.0677687i	$-0.978412\pi$
$349$		−	2.53205i		−	0.135537i	0.997701	−	0.0677687i	$-0.0215880\pi$
$350$	−9.49562	+	13.7338i	−0.507562	+	0.734102i
$351$	−3.95360	−	2.04935i	−0.211028	−	0.109386i
$352$	−0.00241670	+	0.00241670i	−0.000128811	+	0.000128811i
$353$	−5.70119	+	5.70119i	−0.303444	+	0.303444i	−0.842360	−	0.538916i	$-0.818834\pi$
$353$	−5.70119	+	5.70119i	−0.303444	+	0.303444i	0.538916	+	0.842360i	$0.318834\pi$
$354$	−21.7832	+	8.30368i	−1.15776	+	0.441336i
$355$	−0.0899000	−	0.171453i	−0.00477140	−	0.00909978i
$356$		−	0.0151066i		−	0.000800648i
$357$	−1.32450	+	2.95635i	−0.0701000	+	0.156466i
$358$	−20.8809	−	20.8809i	−1.10359	−	1.10359i
$359$	−16.7850			−0.885877			−0.442938	−	0.896552i	$-0.646064\pi$
$359$	−16.7850			−0.885877			−0.442938	+	0.896552i	$0.646064\pi$
$360$	−17.2732	+	7.83667i	−0.910378	+	0.413029i
$361$	16.8651			0.887638
$362$	−19.2271	−	19.2271i	−1.01055	−	1.01055i
$363$	7.62077	−	17.0099i	0.399987	−	0.892788i
$364$		−	0.00250143i		−	0.000131110i
$365$	5.88290	+	1.83571i	0.307925	+	0.0960855i
$366$	8.35844	−	3.18621i	0.436903	−	0.166546i
$367$	−25.1508	+	25.1508i	−1.31286	+	1.31286i	−0.393560	+	0.919299i	$0.628757\pi$
$367$	−25.1508	+	25.1508i	−1.31286	+	1.31286i	−0.919299	+	0.393560i	$0.871243\pi$
$368$	−13.7209	+	13.7209i	−0.715252	+	0.715252i
$369$	15.9316	−	14.2112i	0.829368	−	0.739807i
$370$	20.7326	−	10.8710i	1.07784	−	0.565155i
$371$		−	23.1304i		−	1.20087i
$372$	−0.00195445		0.000875632i	−0.000101334		4.53994e-5i
$373$	−1.28708	−	1.28708i	−0.0666427	−	0.0666427i	0.673000	−	0.739643i	$-0.265005\pi$
$373$	−1.28708	−	1.28708i	−0.0666427	−	0.0666427i	−0.739643	+	0.673000i	$0.765005\pi$
$374$	−0.547682			−0.0283200
$375$	−16.5774	−	10.0094i	−0.856054	−	0.516886i
$376$	25.5066			1.31540
$377$	0.131361	+	0.131361i	0.00676544	+	0.00676544i
$378$	16.5396	−	5.24669i	0.850706	−	0.269861i
$379$			26.9785i			1.38579i	0.721038	+	0.692896i	$0.243665\pi$
$379$			26.9785i			1.38579i	−0.721038	+	0.692896i	$0.756335\pi$
$380$	0.00357778	−	0.00187598i	0.000183536	−	9.62357e-5i
$381$	−6.18924	−	16.2363i	−0.317084	−	0.831812i
$382$	−24.3852	+	24.3852i	−1.24765	+	1.24765i
$383$	−9.28532	+	9.28532i	−0.474458	+	0.474458i	−0.903354	−	0.428896i	$-0.858903\pi$
$383$	−9.28532	+	9.28532i	−0.474458	+	0.474458i	0.428896	+	0.903354i	$0.358903\pi$
$384$	−6.98643	−	18.3276i	−0.356525	−	0.935277i
$385$	−2.46208	−	0.768270i	−0.125479	−	0.0391547i
$386$		−	11.9041i		−	0.605901i
$387$	1.00205	−	17.5566i	0.0509370	−	0.892450i
$388$	−0.00164990	−	0.00164990i	−8.37611e−5	−	8.37611e-5i
$389$	−5.45183			−0.276419			−0.138209	−	0.990403i	$-0.544135\pi$
$389$	−5.45183			−0.276419			−0.138209	+	0.990403i	$0.544135\pi$
$390$	4.68657	−	0.289647i	0.237314	−	0.0146669i
$391$	−3.84123			−0.194259
$392$	2.85465	+	2.85465i	0.144181	+	0.144181i
$393$	−21.3264	−	9.55464i	−1.07577	−	0.481968i
$394$			31.5176i			1.58783i
$395$	9.30442	+	17.7449i	0.468156	+	0.892845i
$396$	0.00120654	+	0.00135260i	6.06307e−5	+	6.79707e-5i
$397$	12.6464	−	12.6464i	0.634706	−	0.634706i	−0.314538	−	0.949245i	$-0.601850\pi$
$397$	12.6464	−	12.6464i	0.634706	−	0.634706i	0.949245	+	0.314538i	$0.101850\pi$
$398$	4.09787	−	4.09787i	0.205408	−	0.205408i
$399$	5.58214	−	2.12789i	0.279457	−	0.106528i
$400$	11.3812	−	16.4610i	0.569059	−	0.823048i
$401$			23.2395i			1.16053i	0.814429	+	0.580264i	$0.197050\pi$
$401$			23.2395i			1.16053i	−0.814429	+	0.580264i	$0.802950\pi$
$402$	−6.70692	+	14.9701i	−0.334511	+	0.746643i
$403$	−0.606001	−	0.606001i	−0.0301870	−	0.0301870i
$404$	0.0167546			0.000833571
$405$	7.25680	+	18.7707i	0.360593	+	0.932723i
$406$	−0.723865			−0.0359248
$407$	2.55698	+	2.55698i	0.126745	+	0.126745i
$408$	1.58653	−	3.54120i	0.0785449	−	0.175316i
$409$			20.9451i			1.03567i	0.855480	+	0.517835i	$0.173262\pi$
$409$			20.9451i			1.03567i	−0.855480	+	0.517835i	$0.826738\pi$
$410$	−6.70540	+	21.4888i	−0.331156	+	1.06126i
$411$	28.0537	−	10.6940i	1.38379	−	0.527495i
$412$	0.00400508	−	0.00400508i	0.000197316	−	0.000197316i
$413$	15.8808	−	15.8808i	0.781444	−	0.781444i
$414$	13.6961	+	15.3541i	0.673125	+	0.754613i
$415$	0.325872	−	1.04432i	0.0159964	−	0.0512637i
$416$			0.00599443i			0.000293901i
$417$	2.40459	+	1.07730i	0.117753	+	0.0527558i
$418$	0.714167	+	0.714167i	0.0349310	+	0.0349310i
$419$	8.76420			0.428159			0.214080	−	0.976816i	$-0.431325\pi$
$419$	8.76420			0.428159			0.214080	+	0.976816i	$0.431325\pi$
$420$	−0.00748508	+	0.00847124i	−0.000365234	+	0.000413354i
$421$	6.41350			0.312575			0.156287	−	0.987712i	$-0.450047\pi$
$421$	6.41350			0.312575			0.156287	+	0.987712i	$0.450047\pi$
$422$	−0.945375	−	0.945375i	−0.0460202	−	0.0460202i
$423$	1.54208	−	27.0182i	0.0749785	−	1.31367i
$424$			27.7063i			1.34554i
$425$	3.89727	−	0.711052i	0.189045	−	0.0344911i
$426$	−0.0755616	−	0.198222i	−0.00366097	−	0.00960389i
$427$	−6.09364	+	6.09364i	−0.294892	+	0.294892i
$428$	0.00701032	−	0.00701032i	0.000338857	−	0.000338857i
$429$	0.258354	+	0.677744i	0.0124734	+	0.0327218i
$430$	8.61052	+	16.4216i	0.415236	+	0.791918i
$431$		−	2.35265i		−	0.113323i	−0.998393	−	0.0566616i	$-0.981954\pi$
$431$		−	2.35265i		−	0.113323i	0.998393	−	0.0566616i	$-0.0180456\pi$
$432$	−19.8239	+	6.28854i	−0.953779	+	0.302557i
$433$	16.6004	+	16.6004i	0.797762	+	0.797762i	0.982742	−	0.184980i	$-0.0592221\pi$
$433$	16.6004	+	16.6004i	0.797762	+	0.797762i	−0.184980	+	0.982742i	$0.559222\pi$
$434$	3.33937			0.160295
$435$	−0.0517876	−	0.837937i	−0.00248302	−	0.0401760i
$436$	0.0185156			0.000886735
$437$	5.00889	+	5.00889i	0.239608	+	0.239608i
$438$	6.16271	+	2.76102i	0.294466	+	0.131927i
$439$		−	11.3213i		−	0.540337i	−0.962813	−	0.270169i	$-0.912921\pi$
$439$		−	11.3213i		−	0.540337i	0.962813	−	0.270169i	$-0.0870795\pi$
$440$	2.94915	+	0.920258i	0.140595	+	0.0438716i
$441$	3.19641	−	2.85124i	0.152210	−	0.135773i
$442$	−0.679240	+	0.679240i	−0.0323082	+	0.0323082i
$443$	0.123239	−	0.123239i	0.00585525	−	0.00585525i	−0.704173	−	0.710028i	$-0.748682\pi$
$443$	0.123239	−	0.123239i	0.00585525	−	0.00585525i	0.710028	+	0.704173i	$0.248682\pi$
$444$	0.0148098	−	0.00564543i	0.000702840	−	0.000267920i
$445$	−24.1948	+	12.6864i	−1.14694	+	0.601391i
$446$			6.61909i			0.313423i
$447$	−13.7358	+	30.6590i	−0.649682	+	1.45012i
$448$	13.3451	+	13.3451i	0.630495	+	0.630495i
$449$	−5.58480			−0.263563			−0.131782	−	0.991279i	$-0.542070\pi$
$449$	−5.58480			−0.263563			−0.131782	+	0.991279i	$0.542070\pi$
$450$	−16.7381	−	13.0428i	−0.789040	−	0.614844i
$451$	−3.47722			−0.163736
$452$	0.000750360	0	0.000750360i	3.52940e−5	0	3.52940e-5i
$453$	−13.0859	+	29.2084i	−0.614831	+	1.37233i
$454$			9.02561i			0.423593i
$455$	−4.00630	+	2.10067i	−0.187818	+	0.0984811i
$456$	−6.68647	+	2.54886i	−0.313123	+	0.119361i
$457$	−18.7342	+	18.7342i	−0.876347	+	0.876347i	−0.993155	−	0.116808i	$-0.962734\pi$
$457$	−18.7342	+	18.7342i	−0.876347	+	0.876347i	0.116808	+	0.993155i	$0.462734\pi$
$458$	23.0289	−	23.0289i	1.07607	−	1.07607i
$459$	−3.65515	−	1.89465i	−0.170608	−	0.0884346i
$460$	−0.0127957	−	0.00399278i	−0.000596601	−	0.000186164i
$461$			1.80178i			0.0839173i	0.999119	+	0.0419587i	$0.0133598\pi$
$461$			1.80178i			0.0839173i	−0.999119	+	0.0419587i	$0.986640\pi$
$462$	−2.57918	−	1.15552i	−0.119994	−	0.0537598i
$463$	−28.8896	−	28.8896i	−1.34261	−	1.34261i	−0.893450	−	0.449162i	$-0.851723\pi$
$463$	−28.8896	−	28.8896i	−1.34261	−	1.34261i	−0.449162	−	0.893450i	$-0.648277\pi$
$464$	0.867605			0.0402775
$465$	0.238909	+	3.86561i	0.0110791	+	0.179263i
$466$	−39.2502			−1.81823
$467$	−1.77213	−	1.77213i	−0.0820043	−	0.0820043i	0.664915	−	0.746919i	$-0.268468\pi$
$467$	−1.77213	−	1.77213i	−0.0820043	−	0.0820043i	−0.746919	+	0.664915i	$0.768468\pi$
$468$	0.00317386		0.000181150i	0.000146712		8.37366e-6i
$469$		−	15.8035i		−	0.729736i
$470$	13.2509	+	25.2716i	0.611220	+	1.16569i
$471$	−14.0143	−	36.7640i	−0.645745	−	1.69399i
$472$	−19.0226	+	19.0226i	−0.875584	+	0.875584i
$473$	−2.02529	+	2.02529i	−0.0931230	+	0.0931230i
$474$	7.82043	+	20.5155i	0.359204	+	0.942307i
$475$	−6.00916	−	4.15477i	−0.275719	−	0.190634i
$476$		−	0.00231260i		−	0.000105998i
$477$	29.3483	+	1.67507i	1.34377	+	0.0766962i
$478$	8.66779	+	8.66779i	0.396455	+	0.396455i
$479$	36.3824			1.66236			0.831178	−	0.556007i	$-0.187667\pi$
$479$	36.3824			1.66236			0.831178	+	0.556007i	$0.187667\pi$
$480$	0.0179373	−	0.0203005i	0.000818721	−	0.000926587i
$481$	6.34237			0.289187
$482$	−19.4827	−	19.4827i	−0.887414	−	0.887414i
$483$	−18.0894	−	8.10440i	−0.823095	−	0.368763i
$484$			0.0133060i			0.000604818i
$485$	−1.25692	+	4.02806i	−0.0570739	+	0.182905i
$486$	5.45933	+	21.3658i	0.247640	+	0.969171i
$487$	−16.8813	+	16.8813i	−0.764966	+	0.764966i	−0.977215	−	0.212250i	$-0.931921\pi$
$487$	−16.8813	+	16.8813i	−0.764966	+	0.764966i	0.212250	+	0.977215i	$0.431921\pi$
$488$	7.29916	−	7.29916i	0.330417	−	0.330417i
$489$	8.40502	−	3.20397i	0.380088	−	0.144888i
$490$	−1.34532	+	4.31136i	−0.0607755	+	0.194767i
$491$		−	3.75278i		−	0.169361i	−0.996408	−	0.0846803i	$-0.973013\pi$
$491$		−	3.75278i		−	0.169361i	0.996408	−	0.0846803i	$-0.0269869\pi$
$492$	−0.00623126	+	0.0139085i	−0.000280927	+	0.000627042i
$493$	0.121445	+	0.121445i	0.00546961	+	0.00546961i
$494$	1.77143			0.0797005
$495$	1.15310	−	3.06830i	0.0518279	−	0.137910i
$496$	−4.00247			−0.179716
$497$	0.144512	+	0.144512i	0.00648224	+	0.00648224i
$498$	0.490130	−	1.09399i	0.0219633	−	0.0490230i
$499$			6.14567i			0.275118i	0.990494	+	0.137559i	$0.0439257\pi$
$499$			6.14567i			0.275118i	−0.990494	+	0.137559i	$0.956074\pi$
$500$	0.0137214	+	0.00168241i	0.000613642	+	7.52399e-5i
$501$	32.6912	−	12.4618i	1.46053	−	0.556750i
$502$	6.66844	−	6.66844i	0.297627	−	0.297627i
$503$	−10.0046	+	10.0046i	−0.446084	+	0.446084i	−0.894050	−	0.447966i	$-0.852148\pi$
$503$	−10.0046	+	10.0046i	−0.446084	+	0.446084i	0.447966	+	0.894050i	$0.352148\pi$
$504$	14.9428	−	13.3291i	0.665604	−	0.593727i
$505$	−14.0703	−	26.8342i	−0.626121	−	1.19411i
$506$		−	3.35117i		−	0.148978i
$507$	−19.3877	−	8.68606i	−0.861037	−	0.385761i
$508$	0.00877120	+	0.00877120i	0.000389159	+	0.000389159i
$509$	−8.38449			−0.371636			−0.185818	−	0.982584i	$-0.559494\pi$
$509$	−8.38449			−0.371636			−0.185818	+	0.982584i	$0.559494\pi$
$510$	4.33279	−	0.267782i	0.191859	−	0.0118576i
$511$	−6.50576			−0.287798
$512$	−15.9851	−	15.9851i	−0.706450	−	0.706450i
$513$	2.29566	+	7.23684i	0.101356	+	0.319514i
$514$		−	8.26799i		−	0.364685i
$515$	−9.77798	−	3.05114i	−0.430869	−	0.134449i
$516$	0.00447154	+	0.0117303i	0.000196849	+	0.000516397i
$517$	−3.11677	+	3.11677i	−0.137076	+	0.137076i
$518$	−17.4748	+	17.4748i	−0.767799	+	0.767799i
$519$	−3.17158	−	8.32005i	−0.139217	−	0.365210i
$520$	4.79888	−	2.51625i	0.210445	−	0.110345i
$521$			16.8731i			0.739225i	0.929186	+	0.369613i	$0.120510\pi$
$521$			16.8731i			0.739225i	−0.929186	+	0.369613i	$0.879490\pi$
$522$	0.0524213	−	0.918455i	0.00229442	−	0.0401997i
$523$	7.41293	+	7.41293i	0.324145	+	0.324145i	0.850355	−	0.526210i	$-0.176387\pi$
$523$	7.41293	+	7.41293i	0.324145	+	0.324145i	−0.526210	+	0.850355i	$0.676387\pi$
$524$	0.0166826			0.000728781
$525$	19.8535	+	4.87409i	0.866477	+	0.212723i
$526$	4.29640			0.187332
$527$	−0.560255	−	0.560255i	−0.0244051	−	0.0244051i
$528$	3.09133	+	1.38498i	0.134533	+	0.0602735i
$529$		−	0.503846i		−	0.0219063i
$530$	−27.4510	+	14.3937i	−1.19240	+	0.625224i
$531$	18.9999	+	21.3000i	0.824523	+	0.924341i
$532$	−0.00301559	+	0.00301559i	−0.000130742	+	0.000130742i
$533$	−4.31249	+	4.31249i	−0.186794	+	0.186794i
$534$	−27.9724	+	10.6630i	−1.21048	+	0.461432i
$535$	−17.1150	−	5.34059i	−0.739945	−	0.230894i
$536$			18.9299i			0.817647i
$537$	−14.7826	+	32.9955i	−0.637918	+	1.42386i
$538$	16.1741	+	16.1741i	0.697314	+	0.697314i
$539$	−0.697646			−0.0300497
$540$	−0.0102064	−	0.0101107i	−0.000439215	−	0.000435095i
$541$	5.37201			0.230961			0.115480	−	0.993310i	$-0.463159\pi$
$541$	5.37201			0.230961			0.115480	+	0.993310i	$0.463159\pi$
$542$	27.6714	+	27.6714i	1.18859	+	1.18859i
$543$	−13.6118	+	30.3821i	−0.584138	+	1.30382i
$544$			0.00554193i			0.000237608i
$545$	−15.5492	−	29.6547i	−0.666054	−	1.27027i
$546$	−4.63181	+	1.76563i	−0.198223	+	0.0755621i
$547$	1.42656	−	1.42656i	0.0609951	−	0.0609951i	−0.675951	−	0.736946i	$-0.736267\pi$
$547$	1.42656	−	1.42656i	0.0609951	−	0.0609951i	0.736946	+	0.675951i	$0.236267\pi$
$548$	−0.0151552	+	0.0151552i	−0.000647397	+	0.000647397i
$549$	−7.29045	−	8.17303i	−0.311149	−	0.348817i
$550$	0.620338	+	3.40006i	0.0264513	+	0.144979i
$551$		−	0.316724i		−	0.0134929i
$552$	21.6680	+	9.70771i	0.922253	+	0.413187i
$553$	−14.9566	−	14.9566i	−0.636020	−	0.636020i
$554$	32.0696			1.36251
$555$	−21.4788	−	18.9784i	−0.911726	−	0.805589i
$556$	−0.00188099			−7.97718e−5
$557$	−15.6580	−	15.6580i	−0.663449	−	0.663449i	0.292742	−	0.956191i	$-0.405432\pi$
$557$	−15.6580	−	15.6580i	−0.663449	−	0.663449i	−0.956191	+	0.292742i	$0.905432\pi$
$558$	−0.241832	+	4.23706i	−0.0102376	+	0.179369i
$559$			5.02357i			0.212474i
$560$	−6.29309	+	20.1675i	−0.265931	+	0.852231i
$561$	0.238851	+	0.626582i	0.0100843	+	0.0264543i
$562$	27.0994	−	27.0994i	1.14312	−	1.14312i
$563$	−22.2250	+	22.2250i	−0.936673	+	0.936673i	−0.998111	−	0.0614379i	$-0.980431\pi$
$563$	−22.2250	+	22.2250i	−0.936673	+	0.936673i	0.0614379	+	0.998111i	$0.480431\pi$
$564$	0.00688137	+	0.0180520i	0.000289758	+	0.000760127i
$565$	0.571637	−	1.83193i	0.0240489	−	0.0770697i
$566$		−	15.7338i		−	0.661341i
$567$	−13.2157	−	16.6342i	−0.555006	−	0.698571i
$568$	−0.173101	−	0.173101i	−0.00726315	−	0.00726315i
$569$	36.0307			1.51048			0.755242	−	0.655446i	$-0.227519\pi$
$569$	36.0307			1.51048			0.755242	+	0.655446i	$0.227519\pi$
$570$	−5.99906	−	5.30070i	−0.251273	−	0.222022i
$571$	−35.3321			−1.47860			−0.739302	−	0.673374i	$-0.764844\pi$
$571$	−35.3321			−1.47860			−0.739302	+	0.673374i	$0.764844\pi$
$572$	−0.000366131	0	0.000366131i	−1.53087e−5	0	1.53087e-5i
$573$	38.5328	+	17.2635i	1.60973	+	0.721192i
$574$		−	23.7639i		−	0.991888i
$575$	4.35081	+	23.8467i	0.181441	+	0.994477i
$576$	−17.8989	+	15.9661i	−0.745789	+	0.665253i
$577$	0.737957	−	0.737957i	0.0307216	−	0.0307216i	−0.691579	−	0.722301i	$-0.743085\pi$
$577$	0.737957	−	0.737957i	0.0307216	−	0.0307216i	0.722301	+	0.691579i	$0.243085\pi$
$578$	16.3773	−	16.3773i	0.681205	−	0.681205i
$579$	−13.6190	+	5.19151i	−0.565986	+	0.215752i
$580$	0.000278314	0	0.000530786i	1.15563e−5	0	2.20397e-5i
$581$			1.15489i			0.0479129i
$582$	−1.89049	+	4.21965i	−0.0783632	+	0.174910i
$583$	−3.38557	−	3.38557i	−0.140216	−	0.140216i
$584$	7.79281			0.322469
$585$	−2.37525	−	5.23541i	−0.0982044	−	0.216458i
$586$	21.5901			0.891881
$587$	3.85573	+	3.85573i	0.159143	+	0.159143i	0.782187	−	0.623044i	$-0.214104\pi$
$587$	3.85573	+	3.85573i	0.159143	+	0.159143i	−0.623044	+	0.782187i	$0.714104\pi$
$588$	−0.00125020	+	0.00279049i	−5.15572e−5	+	0.000115078i
$589$			1.46112i			0.0602046i
$590$	−28.7297	−	8.96486i	−1.18278	−	0.369077i
$591$	36.0581	−	13.7452i	1.48323	−	0.565404i
$592$	20.9448	−	20.9448i	0.860827	−	0.860827i
$593$	−27.6856	+	27.6856i	−1.13691	+	1.13691i	−0.147910	+	0.989001i	$0.547255\pi$
$593$	−27.6856	+	27.6856i	−1.13691	+	1.13691i	−0.989001	+	0.147910i	$0.952745\pi$
$594$	1.65293	−	3.18884i	0.0678207	−	0.130840i
$595$	−3.70388	+	1.94210i	−0.151844	+	0.0796183i
$596$		−	0.0239830i		−	0.000982382i
$597$	−6.47535	−	2.90108i	−0.265018	−	0.118733i
$598$	−4.15616	−	4.15616i	−0.169958	−	0.169958i
$599$	−43.2024			−1.76520			−0.882600	−	0.470124i	$-0.844209\pi$
$599$	−43.2024			−1.76520			−0.882600	+	0.470124i	$0.844209\pi$
$600$	−23.7811	−	5.83835i	−0.970861	−	0.238349i
$601$	13.9160			0.567646			0.283823	−	0.958877i	$-0.408397\pi$
$601$	13.9160			0.567646			0.283823	+	0.958877i	$0.408397\pi$
$602$	−13.8412	−	13.8412i	−0.564125	−	0.564125i
$603$	20.0518	+	1.14446i	0.816571	+	0.0466062i
$604$		−	0.0228483i		−	0.000929683i
$605$	21.3110	−	11.1742i	0.866415	−	0.454298i
$606$	−11.8262	−	31.0239i	−0.480407	−	1.26026i
$607$	15.2786	−	15.2786i	0.620137	−	0.620137i	−0.325429	−	0.945566i	$-0.605509\pi$
$607$	15.2786	−	15.2786i	0.620137	−	0.620137i	0.945566	+	0.325429i	$0.105509\pi$
$608$	0.00722657	−	0.00722657i	0.000293076	−	0.000293076i
$609$	0.315687	+	0.828147i	0.0127923	+	0.0335582i
$610$	11.0239	+	3.43991i	0.446344	+	0.139278i
$611$			7.73090i			0.312759i
$612$	0.00293428		0.000167475i	0.000118611		6.76979e-6i
$613$	−4.86567	−	4.86567i	−0.196523	−	0.196523i	0.601985	−	0.798507i	$-0.294377\pi$
$613$	−4.86567	−	4.86567i	−0.196523	−	0.196523i	−0.798507	+	0.601985i	$0.794377\pi$
$614$	25.6130			1.03365
$615$	27.5088	−	1.70015i	1.10926	−	0.0685565i
$616$	−3.26140			−0.131405
$617$	16.5719	+	16.5719i	0.667160	+	0.667160i	0.957058	−	0.289897i	$-0.0936212\pi$
$617$	16.5719	+	16.5719i	0.667160	+	0.667160i	−0.289897	+	0.957058i	$0.593621\pi$
$618$	−10.2431	−	4.58909i	−0.412036	−	0.184600i
$619$		−	22.9117i		−	0.920899i	−0.887686	−	0.460450i	$-0.847688\pi$
$619$		−	22.9117i		−	0.920899i	0.887686	−	0.460450i	$-0.152312\pi$
$620$	−0.00128393	−	0.00244865i	−5.15638e−5	−	9.83400e-5i
$621$	11.5930	−	22.3653i	0.465213	−	0.897487i
$622$	21.6711	−	21.6711i	0.868931	−	0.868931i
$623$	20.3930	−	20.3930i	0.817028	−	0.817028i
$624$	5.55156	−	2.11624i	0.222240	−	0.0847173i
$625$	−8.82856	−	23.3892i	−0.353143	−	0.935570i
$626$			31.0535i			1.24115i
$627$	0.505594	−	1.12851i	0.0201915	−	0.0450683i
$628$	0.0198607	+	0.0198607i	0.000792527	+	0.000792527i
$629$	5.86360			0.233797
$630$	20.9693	+	7.88046i	0.835435	+	0.313965i
$631$	−5.03474			−0.200430			−0.100215	−	0.994966i	$-0.531953\pi$
$631$	−5.03474			−0.200430			−0.100215	+	0.994966i	$0.531953\pi$
$632$	17.9155	+	17.9155i	0.712641	+	0.712641i
$633$	−0.669278	+	1.49386i	−0.0266014	+	0.0593756i
$634$		−	27.4643i		−	1.09075i
$635$	6.68205	−	21.4140i	0.265169	−	0.849788i
$636$	−0.0196089	+	0.00747483i	−0.000777542	+	0.000296396i
$637$	−0.865227	+	0.865227i	−0.0342815	+	0.0342815i
$638$	−0.105951	+	0.105951i	−0.00419465	+	0.00419465i
$639$	−0.193825	+	0.172894i	−0.00766760	+	0.00683959i
$640$	7.54272	−	24.1722i	0.298152	−	0.955489i
$641$		−	2.56260i		−	0.101216i	−0.998719	−	0.0506082i	$-0.983884\pi$
$641$		−	2.56260i		−	0.101216i	0.998719	−	0.0506082i	$-0.0161160\pi$
$642$	−17.9290	−	8.03256i	−0.707602	−	0.317020i
$643$	27.8538	+	27.8538i	1.09845	+	1.09845i	0.994592	+	0.103856i	$0.0331181\pi$
$643$	27.8538	+	27.8538i	1.09845	+	1.09845i	0.103856	+	0.994592i	$0.466882\pi$
$644$	0.0141504			0.000557605
$645$	15.0321	−	17.0126i	0.591890	−	0.669872i
$646$	1.63771			0.0644349
$647$	−8.41427	−	8.41427i	−0.330799	−	0.330799i	0.522091	−	0.852890i	$-0.325152\pi$
$647$	−8.41427	−	8.41427i	−0.330799	−	0.330799i	−0.852890	+	0.522091i	$0.825152\pi$
$648$	15.8302	+	19.9250i	0.621867	+	0.782727i
$649$		−	4.64891i		−	0.182486i
$650$	4.98614	+	3.44744i	0.195572	+	0.135220i
$651$	−1.45634	−	3.82044i	−0.0570785	−	0.149735i
$652$	−0.00454057	+	0.00454057i	−0.000177822	+	0.000177822i
$653$	15.4098	−	15.4098i	0.603031	−	0.603031i	−0.338085	−	0.941116i	$-0.609779\pi$
$653$	15.4098	−	15.4098i	0.603031	−	0.603031i	0.941116	+	0.338085i	$0.109779\pi$
$654$	−13.0692	−	34.2847i	−0.511046	−	1.34064i
$655$	−14.0099	−	26.7189i	−0.547410	−	1.04399i
$656$			28.4828i			1.11207i
$657$	0.471138	−	8.25464i	0.0183808	−	0.322044i
$658$	−21.3005	−	21.3005i	−0.830382	−	0.830382i
$659$	1.48765			0.0579506			0.0289753	−	0.999580i	$-0.490776\pi$
$659$	1.48765			0.0579506			0.0289753	+	0.999580i	$0.490776\pi$
$660$	0.000144343		0.00233551i	5.61854e−6		9.09095e-5i
$661$	−10.9973			−0.427747			−0.213873	−	0.976861i	$-0.568608\pi$
$661$	−10.9973			−0.427747			−0.213873	+	0.976861i	$0.568608\pi$
$662$	−16.4785	−	16.4785i	−0.640456	−	0.640456i
$663$	1.07332	+	0.480868i	0.0416842	+	0.0186754i
$664$		−	1.38336i		−	0.0536849i
$665$	7.36225	+	2.29733i	0.285496	+	0.0890865i
$666$	−20.9069	−	23.4379i	−0.810126	−	0.908201i
$667$	−0.743101	+	0.743101i	−0.0287730	+	0.0287730i
$668$	−0.0176604	+	0.0176604i	−0.000683303	+	0.000683303i
$669$	7.57265	−	2.88667i	0.292776	−	0.111605i
$670$	−18.7555	+	9.83428i	−0.724587	+	0.379931i
$671$			1.78384i			0.0688643i
$672$	−0.0116926	+	0.0260984i	−0.000451052	+	0.00100677i
$673$	9.80668	+	9.80668i	0.378020	+	0.378020i	0.870387	−	0.492367i	$-0.163868\pi$
$673$	9.80668	+	9.80668i	0.378020	+	0.378020i	−0.492367	+	0.870387i	$0.663868\pi$
$674$	37.2470			1.43470
$675$	−7.62211	+	24.8375i	−0.293375	+	0.955997i
$676$	0.0151660			0.000583308
$677$	−25.2317	−	25.2317i	−0.969733	−	0.969733i	0.0298219	−	0.999555i	$-0.490506\pi$
$677$	−25.2317	−	25.2317i	−0.969733	−	0.969733i	−0.999555	+	0.0298219i	$0.990506\pi$
$678$	0.859776	−	1.91906i	0.0330195	−	0.0737010i
$679$		−	4.45454i		−	0.170949i
$680$	4.43662	−	2.32631i	0.170137	−	0.0892099i
$681$	10.3259	−	3.93619i	0.395688	−	0.150835i
$682$	0.488779	−	0.488779i	0.0187163	−	0.0187163i
$683$	−31.5979	+	31.5979i	−1.20906	+	1.20906i	−0.237731	+	0.971331i	$0.576404\pi$
$683$	−31.5979	+	31.5979i	−1.20906	+	1.20906i	−0.971331	+	0.237731i	$0.923596\pi$
$684$	−0.00360786	−	0.00404463i	−0.000137950	−	0.000154650i
$685$	36.9998	+	11.5455i	1.41369	+	0.441130i
$686$		−	28.1434i		−	1.07452i
$687$	−36.3896	−	16.3033i	−1.38835	−	0.622009i
$688$	16.5897	+	16.5897i	0.632475	+	0.632475i
$689$	−8.39763			−0.319924
$690$	1.63852	+	26.5116i	0.0623772	+	1.00928i
$691$	23.7307			0.902758			0.451379	−	0.892332i	$-0.350932\pi$
$691$	23.7307			0.902758			0.451379	+	0.892332i	$0.350932\pi$
$692$	0.00449466	+	0.00449466i	0.000170861	+	0.000170861i
$693$	−0.197178	+	3.45468i	−0.00749016	+	0.131233i
$694$		−	43.4677i		−	1.65001i
$695$	1.57964	+	3.01261i	0.0599191	+	0.114275i
$696$	−0.378140	−	0.991980i	−0.0143333	−	0.0376009i
$697$	−3.98695	+	3.98695i	−0.151016	+	0.151016i
$698$	2.53283	−	2.53283i	0.0958690	−	0.0958690i
$699$	17.1175	+	44.9046i	0.647443	+	1.69845i
$700$	−0.0143569	+	0.00261939i	−0.000542638	+	9.90037e-5i
$701$			9.19645i			0.347345i	0.984803	+	0.173672i	$0.0555634\pi$
$701$			9.19645i			0.347345i	−0.984803	+	0.173672i	$0.944437\pi$
$702$	−1.90484	−	6.00481i	−0.0718936	−	0.226637i
$703$	−7.64603	−	7.64603i	−0.288375	−	0.288375i
$704$	3.90660			0.147236
$705$	23.1333	−	26.1812i	0.871252	−	0.986039i
$706$	−11.4059			−0.429267
$707$	22.6177	+	22.6177i	0.850625	+	0.850625i
$708$	−0.0185951	−	0.00833096i	−0.000698846	−	0.000313097i
$709$			37.0608i			1.39185i	0.718115	+	0.695924i	$0.245005\pi$
$709$			37.0608i			1.39185i	−0.718115	+	0.695924i	$0.754995\pi$
$710$	0.0815782	−	0.261434i	0.00306157	−	0.00981143i
$711$	20.0604	−	17.8941i	0.752324	−	0.671082i
$712$	−24.4274	+	24.4274i	−0.915455	+	0.915455i
$713$	3.42811	−	3.42811i	0.128384	−	0.128384i
$714$	−4.28217	+	1.63235i	−0.160256	+	0.0610891i
$715$	−0.278925	+	0.893871i	−0.0104312	+	0.0334289i
$716$		−	0.0258108i		−	0.000964593i
$717$	6.13636	−	13.6966i	0.229167	−	0.511510i
$718$	−16.7902	−	16.7902i	−0.626603	−	0.626603i
$719$	22.4294			0.836477			0.418238	−	0.908337i	$-0.362648\pi$
$719$	22.4294			0.836477			0.418238	+	0.908337i	$0.362648\pi$
$720$	−25.1332	−	9.44530i	−0.936658	−	0.352006i
$721$	10.8132			0.402706
$722$	16.8703	+	16.8703i	0.627849	+	0.627849i
$723$	−13.7928	+	30.7861i	−0.512959	+	1.14495i
$724$		−	0.0237664i		−	0.000883273i
$725$	0.616386	−	0.891498i	0.0228920	−	0.0331094i
$726$	24.6383	−	9.39203i	0.914413	−	0.348571i
$727$	17.7622	−	17.7622i	0.658763	−	0.658763i	−0.296325	−	0.955087i	$-0.595761\pi$
$727$	17.7622	−	17.7622i	0.658763	−	0.658763i	0.955087	+	0.296325i	$0.0957610\pi$
$728$	−4.04481	+	4.04481i	−0.149911	+	0.149911i
$729$	22.0629	−	15.5637i	0.817144	−	0.576433i
$730$	4.04845	+	7.72100i	0.149840	+	0.285767i
$731$			4.64435i			0.171778i
$732$	0.00713513	+	0.00319668i	0.000263722	+	0.000118153i
$733$	14.5129	+	14.5129i	0.536046	+	0.536046i	0.922365	−	0.386319i	$-0.126254\pi$
$733$	14.5129	+	14.5129i	0.536046	+	0.536046i	−0.386319	+	0.922365i	$0.626254\pi$
$734$	−50.3171			−1.85724
$735$	5.51918	−	0.341105i	0.203578	−	0.0125819i
$736$	−0.0339101			−0.00124994
$737$	−2.31313	−	2.31313i	−0.0852054	−	0.0852054i
$738$	30.1522	+	1.72095i	1.10992	+	0.0633491i
$739$		−	32.9388i		−	1.21167i	−0.795589	−	0.605837i	$-0.792838\pi$
$739$		−	32.9388i		−	1.21167i	0.795589	−	0.605837i	$-0.207162\pi$
$740$	0.0195325	+	0.00609494i	0.000718028	+	0.000224055i
$741$	−0.772544	−	2.02663i	−0.0283801	−	0.0744501i
$742$	23.1375	−	23.1375i	0.849406	−	0.849406i
$743$	3.09833	−	3.09833i	0.113667	−	0.113667i	−0.647986	−	0.761652i	$-0.724388\pi$
$743$	3.09833	−	3.09833i	0.113667	−	0.113667i	0.761652	+	0.647986i	$0.224388\pi$
$744$	1.74445	+	4.57625i	0.0639547	+	0.167773i
$745$	−38.4113	+	20.1407i	−1.40728	+	0.737897i
$746$		−	2.57496i		−	0.0942761i
$747$	−1.46535	−	0.0836355i	−0.0536143	−	0.00306006i
$748$	−0.000338493	0	0.000338493i	−1.23765e−5	0	1.23765e-5i
$749$	18.9270			0.691579
$750$	−6.57000	−	26.5951i	−0.239903	−	0.971115i
$751$	30.1178			1.09901			0.549507	−	0.835489i	$-0.314816\pi$
$751$	30.1178			1.09901			0.549507	+	0.835489i	$0.314816\pi$
$752$	25.5303	+	25.5303i	0.930992	+	0.930992i
$753$	−10.5373	−	4.72092i	−0.384001	−	0.172040i
$754$			0.262803i			0.00957073i
$755$	−36.5939	+	19.1877i	−1.33179	+	0.698314i
$756$	0.0134649	+	0.00697955i	0.000489715	+	0.000253844i
$757$	−21.3145	+	21.3145i	−0.774689	+	0.774689i	−0.978922	−	0.204233i	$-0.934530\pi$
$757$	−21.3145	+	21.3145i	−0.774689	+	0.774689i	0.204233	+	0.978922i	$0.434530\pi$
$758$	−26.9868	+	26.9868i	−0.980205	+	0.980205i
$759$	−3.83395	+	1.46149i	−0.139164	+	0.0530487i
$760$	−8.81874	−	2.75181i	−0.319889	−	0.0998187i
$761$			14.3563i			0.520417i	0.965552	+	0.260208i	$0.0837913\pi$
$761$			14.3563i			0.520417i	−0.965552	+	0.260208i	$0.916209\pi$
$762$	10.0502	−	22.4325i	0.364080	−	0.812644i
$763$	24.9949	+	24.9949i	0.904877	+	0.904877i
$764$	−0.0301423			−0.00109051
$765$	−2.19595	−	4.84020i	−0.0793946	−	0.174998i
$766$	−18.5764			−0.671192
$767$	−5.76563	−	5.76563i	−0.208185	−	0.208185i
$768$	0.0210152	−	0.0469068i	0.000758319	−	0.00169260i
$769$		−	38.8955i		−	1.40261i	−0.712862	−	0.701304i	$-0.752601\pi$
$769$		−	38.8955i		−	1.40261i	0.712862	−	0.701304i	$-0.247399\pi$
$770$	−1.69433	−	3.23134i	−0.0610594	−	0.116450i
$771$	−9.45910	+	3.60578i	−0.340661	+	0.129859i
$772$	0.00735726	−	0.00735726i	0.000264794	−	0.000264794i
$773$	11.8920	−	11.8920i	0.427727	−	0.427727i	−0.460127	−	0.887853i	$-0.652196\pi$
$773$	11.8920	−	11.8920i	0.427727	−	0.427727i	0.887853	+	0.460127i	$0.152196\pi$
$774$	18.5643	−	16.5596i	0.667282	−	0.595223i
$775$	−2.84354	+	4.11270i	−0.102143	+	0.147732i
$776$			5.33579i			0.191544i
$777$	27.6133	+	12.3713i	0.990621	+	0.443818i
$778$	−5.45352	−	5.45352i	−0.195518	−	0.195518i
$779$	10.3978			0.372540
$780$	0.00307553	+	0.00271750i	0.000110122	+	9.73022e-5i
$781$	0.0423041			0.00151376
$782$	−3.84242	−	3.84242i	−0.137405	−	0.137405i
$783$	−1.07363	+	0.340577i	−0.0383684	+	0.0121712i
$784$			5.71459i			0.204092i
$785$	15.1302	−	48.4878i	0.540020	−	1.73060i
$786$	−11.7754	−	30.8906i	−0.420014	−	1.10183i
$787$	18.9654	−	18.9654i	0.676044	−	0.676044i	−0.283059	−	0.959103i	$-0.591349\pi$
$787$	18.9654	−	18.9654i	0.676044	−	0.676044i	0.959103	+	0.283059i	$0.0913491\pi$
$788$	−0.0194793	+	0.0194793i	−0.000693923	+	0.000693923i
$789$	−1.87371	−	4.91534i	−0.0667059	−	0.174991i
$790$	−8.44313	+	27.0577i	−0.300393	+	0.962671i
$791$			2.02588i			0.0720321i
$792$	0.236186	−	4.13813i	0.00839250	−	0.147042i
$793$	2.21233	+	2.21233i	0.0785622	+	0.0785622i
$794$	25.3007			0.897888
$795$	28.4391	+	25.1284i	1.00863	+	0.891213i
$796$	0.00506534			0.000179536
$797$	25.5972	+	25.5972i	0.906701	+	0.906701i	0.996004	−	0.0893038i	$-0.0284642\pi$
$797$	25.5972	+	25.5972i	0.906701	+	0.906701i	−0.0893038	+	0.996004i	$0.528464\pi$
$798$	7.71242	+	3.45532i	0.273017	+	0.122317i
$799$			7.14731i			0.252854i
$800$	0.0344048	−	0.00627712i	0.00121639	−	0.000221930i
$801$	24.3982	+	27.3519i	0.862069	+	0.966432i
$802$	−23.2467	+	23.2467i	−0.820870	+	0.820870i
$803$	−0.952240	+	0.952240i	−0.0336038	+	0.0336038i
$804$	−0.0133974	+	0.00510706i	−0.000472491	+	0.000180112i
$805$	−11.8834	−	22.6634i	−0.418834	−	0.798780i
$806$		−	1.21238i		−	0.0427041i
$807$	11.4504	−	25.5579i	0.403074	−	0.899680i
$808$	−27.0922	−	27.0922i	−0.953100	−	0.953100i
$809$	13.9192			0.489372			0.244686	−	0.969602i	$-0.421315\pi$
$809$	13.9192			0.489372			0.244686	+	0.969602i	$0.421315\pi$
$810$	−11.5175	+	26.0355i	−0.404682	+	0.914795i
$811$	40.5704			1.42462			0.712310	−	0.701865i	$-0.247649\pi$
$811$	40.5704			1.42462			0.712310	+	0.701865i	$0.247649\pi$
$812$	−0.000447382	0	0.000447382i	−1.57000e−5	0	1.57000e-5i
$813$	19.5900	−	43.7257i	0.687050	−	1.53353i
$814$			5.11554i			0.179299i
$815$	11.0853	+	3.45908i	0.388302	+	0.121166i
$816$	5.13249	−	1.95649i	0.179673	−	0.0684908i
$817$	6.05615	−	6.05615i	0.211878	−	0.211878i
$818$	−20.9516	+	20.9516i	−0.732556	+	0.732556i
$819$	4.03999	+	4.52907i	0.141169	+	0.158258i
$820$	−0.0174253	+	0.00913683i	−0.000608518	+	0.000319072i
$821$			22.8010i			0.795762i	0.917437	+	0.397881i	$0.130254\pi$
$821$			22.8010i			0.795762i	−0.917437	+	0.397881i	$0.869746\pi$
$822$	38.7596	+	17.3651i	1.35190	+	0.605677i
$823$	−22.5406	−	22.5406i	−0.785717	−	0.785717i	0.195072	−	0.980789i	$-0.437506\pi$
$823$	−22.5406	−	22.5406i	−0.785717	−	0.785717i	−0.980789	+	0.195072i	$0.937506\pi$
$824$	−12.9524			−0.451219
$825$	3.61935	−	2.19252i	0.126009	−	0.0763336i
$826$	31.7715			1.10547
$827$	−1.41043	−	1.41043i	−0.0490454	−	0.0490454i	0.682159	−	0.731204i	$-0.261041\pi$
$827$	−1.41043	−	1.41043i	−0.0490454	−	0.0490454i	−0.731204	+	0.682159i	$0.761041\pi$
$828$	−0.00102475	+	0.0179543i	−3.56127e−5	+	0.000623957i
$829$			33.0090i			1.14645i	0.819398	+	0.573225i	$0.194308\pi$
$829$			33.0090i			1.14645i	−0.819398	+	0.573225i	$0.805692\pi$
$830$	1.37062	−	0.718672i	0.0475748	−	0.0249455i
$831$	−13.9860	−	36.6897i	−0.485168	−	1.27275i
$832$	4.84501	−	4.84501i	0.167970	−	0.167970i
$833$	−0.799913	+	0.799913i	−0.0277153	+	0.0277153i
$834$	1.32770	+	3.48297i	0.0459744	+	0.120605i
$835$	43.1161	+	13.4540i	1.49210	+	0.465596i
$836$		0	0.000882776i		0	3.05315e-5i
$837$	4.95292	−	1.57116i	0.171198	−	0.0543073i
$838$	8.76691	+	8.76691i	0.302848	+	0.302848i
$839$	37.0786			1.28009			0.640047	−	0.768336i	$-0.278915\pi$
$839$	37.0786			1.28009			0.640047	+	0.768336i	$0.278915\pi$
$840$	25.8014	−	1.59462i	0.890233	−	0.0550196i
$841$	−28.9530			−0.998380
$842$	6.41548	+	6.41548i	0.221092	+	0.221092i
$843$	−42.8218	−	19.1850i	−1.47486	−	0.660767i
$844$		−	0.00116857i		−	4.02239e-5i
$845$	−12.7363	−	24.2900i	−0.438141	−	0.835601i
$846$	28.5691	−	25.4840i	0.982227	−	0.876159i
$847$	−17.9623	+	17.9623i	−0.617192	+	0.617192i
$848$	−27.7320	+	27.7320i	−0.952322	+	0.952322i
$849$	−18.0004	+	6.86171i	−0.617774	+	0.235493i
$850$	4.60975	+	3.18720i	0.158113	+	0.109320i
$851$			35.8784i			1.22990i
$852$	7.58098e−5	0	0.000169211i	2.59720e−6	0	5.79707e-6i
$853$	37.3086	+	37.3086i	1.27742	+	1.27742i	0.942106	+	0.335315i	$0.108843\pi$
$853$	37.3086	+	37.3086i	1.27742	+	1.27742i	0.335315	+	0.942106i	$0.391157\pi$
$854$	−12.1911			−0.417169
$855$	−3.44806	+	9.17500i	−0.117921	+	0.313778i
$856$	−22.6714			−0.774893
$857$	−4.08616	−	4.08616i	−0.139580	−	0.139580i	0.633864	−	0.773444i	$-0.281468\pi$
$857$	−4.08616	−	4.08616i	−0.139580	−	0.139580i	−0.773444	+	0.633864i	$0.781468\pi$
$858$	−0.419520	+	0.936386i	−0.0143222	+	0.0319677i
$859$			9.31165i			0.317709i	0.987302	+	0.158855i	$0.0507801\pi$
$859$			9.31165i			0.317709i	−0.987302	+	0.158855i	$0.949220\pi$
$860$	−0.00482759	+	0.0154710i	−0.000164619	+	0.000527556i
$861$	−27.1874	+	10.3638i	−0.926545	+	0.353196i
$862$	2.35338	−	2.35338i	0.0801563	−	0.0801563i
$863$	14.5615	−	14.5615i	0.495680	−	0.495680i	−0.414411	−	0.910090i	$-0.636012\pi$
$863$	14.5615	−	14.5615i	0.495680	−	0.495680i	0.910090	+	0.414411i	$0.136012\pi$
$864$	−0.0322675	−	0.0167258i	−0.00109776	−	0.000569024i
$865$	3.42411	−	10.9733i	0.116423	−	0.373102i
$866$			33.2110i			1.12855i
$867$	−25.8790	−	11.5943i	−0.878896	−	0.393763i
$868$	0.00206388	+	0.00206388i	7.00527e−5	+	7.00527e-5i
$869$	−4.37836			−0.148526
$870$	0.786392	−	0.889999i	0.0266612	−	0.0301738i
$871$	−5.73754			−0.194409
$872$	−29.9397	−	29.9397i	−1.01389	−	1.01389i
$873$	5.65201	+	0.322591i	0.191292	+	0.0109181i
$874$			10.0209i			0.338961i
$875$	16.2520	+	20.7943i	0.549417	+	0.702975i
$876$	0.00210241	+	0.00551528i	7.10337e−5	+	0.000186344i
$877$	−18.7018	+	18.7018i	−0.631515	+	0.631515i	−0.948448	−	0.316933i	$-0.897347\pi$
$877$	−18.7018	+	18.7018i	−0.631515	+	0.631515i	0.316933	+	0.948448i	$0.397347\pi$
$878$	11.3248	−	11.3248i	0.382194	−	0.382194i
$879$	−9.41574	−	24.7005i	−0.317585	−	0.833126i
$880$	2.03078	+	3.87300i	0.0684575	+	0.130559i
$881$			17.4925i			0.589338i	0.955599	+	0.294669i	$0.0952093\pi$
$881$			17.4925i			0.589338i	−0.955599	+	0.294669i	$0.904791\pi$
$882$	6.04952	+	0.345279i	0.203698	+	0.0116262i
$883$	−35.1699	−	35.1699i	−1.18356	−	1.18356i	−0.978815	−	0.204746i	$-0.934363\pi$
$883$	−35.1699	−	35.1699i	−1.18356	−	1.18356i	−0.204746	−	0.978815i	$-0.565637\pi$
$884$	−0.000839603	0		−2.82389e−5	0
$885$	2.27303	+	36.7782i	0.0764071	+	1.23629i
$886$	0.246554			0.00828313
$887$	−18.3427	−	18.3427i	−0.615887	−	0.615887i	0.328587	−	0.944474i	$-0.393428\pi$
$887$	−18.3427	−	18.3427i	−0.615887	−	0.615887i	−0.944474	+	0.328587i	$0.893428\pi$
$888$	−33.0761	−	14.8187i	−1.10996	−	0.497284i
$889$			23.6812i			0.794242i
$890$	−36.8926	−	11.5120i	−1.23664	−	0.385884i
$891$	−4.36909	−	0.500366i	−0.146370	−	0.0167629i
$892$	−0.00409090	+	0.00409090i	−0.000136974	+	0.000136974i
$893$	9.31996	−	9.31996i	0.311881	−	0.311881i
$894$	−44.4085	+	16.9284i	−1.48524	+	0.566170i
$895$	−41.3387	+	21.6756i	−1.38180	+	0.724536i
$896$			26.7314i			0.893034i
$897$	−2.94235	+	6.56745i	−0.0982422	+	0.219281i
$898$	−5.58653	−	5.58653i	−0.186425	−	0.186425i
$899$	−0.216767			−0.00722959
$900$	−0.00228384	−	0.0184060i	−7.61279e−5	−	0.000613532i
$901$	−7.76371			−0.258647
$902$	−3.47830	−	3.47830i	−0.115815	−	0.115815i
$903$	−9.79886	+	21.8715i	−0.326086	+	0.727838i
$904$		−	2.42667i		−	0.0807097i
$905$	−38.0645	+	19.9588i	−1.26531	+	0.663453i
$906$	−42.3074	+	16.1274i	−1.40557	+	0.535798i
$907$	−26.2609	+	26.2609i	−0.871980	+	0.871980i	−0.992688	−	0.120708i	$-0.961484\pi$
$907$	−26.2609	+	26.2609i	−0.871980	+	0.871980i	0.120708	+	0.992688i	$0.461484\pi$
$908$	−0.00557825	+	0.00557825i	−0.000185121	+	0.000185121i
$909$	−30.3357	+	27.0598i	−1.00617	+	0.897518i
$910$	−6.10887	−	1.90622i	−0.202507	−	0.0631906i
$911$			11.9878i			0.397172i	0.980083	+	0.198586i	$0.0636349\pi$
$911$			11.9878i			0.397172i	−0.980083	+	0.198586i	$0.936365\pi$
$912$	−9.24389	−	4.14145i	−0.306096	−	0.137137i
$913$	0.169040	+	0.169040i	0.00559440	+	0.00559440i
$914$	−37.4799			−1.23972
$915$	−0.872186	−	14.1122i	−0.0288336	−	0.466535i
$916$	0.0284658			0.000940536
$917$	22.5205	+	22.5205i	0.743692	+	0.743692i
$918$	−1.76105	−	5.55152i	−0.0581233	−	0.183227i
$919$			26.1006i			0.860978i	0.902596	+	0.430489i	$0.141659\pi$
$919$			26.1006i			0.860978i	−0.902596	+	0.430489i	$0.858341\pi$
$920$	14.2343	+	27.1470i	0.469291	+	0.895009i
$921$	−11.1701	−	29.3028i	−0.368069	−	0.965561i
$922$	−1.80234	+	1.80234i	−0.0593569	+	0.0593569i
$923$	0.0524659	−	0.0524659i	0.00172694	−	0.00172694i
$924$	−0.000879885	−	0.00230822i	−2.89461e−5	−	7.59348e-5i
$925$	−6.64147	−	36.4018i	−0.218370	−	1.19688i
$926$		−	57.7970i		−	1.89933i
$927$	−0.783079	+	13.7201i	−0.0257197	+	0.450626i
$928$	0.00107211	+	0.00107211i	3.51937e−5	+	3.51937e-5i
$929$	15.4055			0.505437			0.252718	−	0.967540i	$-0.418675\pi$
$929$	15.4055			0.505437			0.252718	+	0.967540i	$0.418675\pi$
$930$	−3.62782	+	4.10578i	−0.118961	+	0.134634i
$931$	2.08614			0.0683705
$932$	−0.0242584	−	0.0242584i	−0.000794611	−	0.000794611i
$933$	−34.2441	−	15.3420i	−1.12110	−	0.502276i
$934$		−	3.54535i		−	0.116007i
$935$	−0.257870	+	0.826395i	−0.00843324	+	0.0270260i
$936$	−4.83922	−	5.42506i	−0.158175	−	0.177324i
$937$	−38.8342	+	38.8342i	−1.26866	+	1.26866i	−0.321874	+	0.946782i	$0.604313\pi$
$937$	−38.8342	+	38.8342i	−1.26866	+	1.26866i	−0.946782	+	0.321874i	$0.895687\pi$
$938$	15.8083	−	15.8083i	0.516161	−	0.516161i
$939$	35.5272	−	13.5428i	1.15939	−	0.441954i
$940$	−0.00742930	+	0.0238087i	−0.000242317	+	0.000776554i
$941$		−	41.2021i		−	1.34315i	−0.740937	−	0.671574i	$-0.765618\pi$
$941$		−	41.2021i		−	1.34315i	0.740937	−	0.671574i	$-0.234382\pi$
$942$	22.7567	−	50.7940i	0.741453	−	1.65496i
$943$	−24.3955	−	24.3955i	−0.794425	−	0.794425i
$944$	−38.0804			−1.23941
$945$	−0.129223	−	27.4269i	−0.00420361	−	0.892197i
$946$	−4.05184			−0.131737
$947$	16.9664	+	16.9664i	0.551332	+	0.551332i	0.926825	−	0.375493i	$-0.122527\pi$
$947$	16.9664	+	16.9664i	0.551332	+	0.551332i	−0.375493	+	0.926825i	$0.622527\pi$
$948$	−0.00784613	+	0.0175129i	−0.000254830	+	0.000568793i
$949$			2.36195i			0.0766723i
$950$	−1.85497	−	10.1671i	−0.0601832	−	0.329863i
$951$	−31.4208	+	11.9775i	−1.01889	+	0.388398i
$952$	−3.73948	+	3.73948i	−0.121197	+	0.121197i
$953$	19.9054	−	19.9054i	0.644799	−	0.644799i	−0.306932	−	0.951731i	$-0.599303\pi$
$953$	19.9054	−	19.9054i	0.644799	−	0.644799i	0.951731	+	0.306932i	$0.0993025\pi$
$954$	27.6818	+	31.0330i	0.896232	+	1.00473i
$955$	25.3132	+	48.2762i	0.819116	+	1.56218i
$956$			0.0107142i			0.000346522i
$957$	0.167422	+	0.0750081i	0.00541197	+	0.00242467i
$958$	36.3937	+	36.3937i	1.17583	+	1.17583i
$959$	−40.9172			−1.32129
$960$	−30.9057	+	1.91009i	−0.997478	+	0.0616478i
$961$	1.00000			0.0322581
$962$	6.34433	+	6.34433i	0.204550	+	0.204550i
$963$	−1.37067	+	24.0150i	−0.0441692	+	0.773873i
$964$		−	0.0240824i		−	0.000775643i
$965$	−17.9620	−	5.60488i	−0.578217	−	0.180428i
$966$	−9.98807	−	26.2019i	−0.321361	−	0.843031i
$967$	10.1993	−	10.1993i	0.327986	−	0.327986i	−0.523834	−	0.851820i	$-0.675499\pi$
$967$	10.1993	−	10.1993i	0.327986	−	0.327986i	0.851820	+	0.523834i	$0.175499\pi$
$968$	21.5158	−	21.5158i	0.691545	−	0.691545i
$969$	−0.714227	−	1.87364i	−0.0229443	−	0.0601901i
$970$	−5.28662	+	2.77200i	−0.169743	+	0.0890035i
$971$			52.2148i			1.67565i	0.545937	+	0.837826i	$0.316174\pi$
$971$			52.2148i			1.67565i	−0.545937	+	0.837826i	$0.683826\pi$
$972$	−0.00983091	+	0.0165792i	−0.000315327	+	0.000531777i
$973$	−2.53923	−	2.53923i	−0.0814038	−	0.0814038i
$974$	−33.7731			−1.08216
$975$	1.76957	−	7.20792i	0.0566715	−	0.230838i
$976$	14.6119			0.467714
$977$	16.2313	+	16.2313i	0.519287	+	0.519287i	0.917356	−	0.398069i	$-0.130319\pi$
$977$	16.2313	+	16.2313i	0.519287	+	0.519287i	−0.398069	+	0.917356i	$0.630319\pi$
$978$	11.6126	+	5.20266i	0.371329	+	0.166363i
$979$		−	5.96980i		−	0.190796i
$980$	−0.00349609	+	0.00183315i	−0.000111679	+	5.85578e-5i
$981$	−33.5242	+	29.9040i	−1.07034	+	0.954760i
$982$	3.75394	−	3.75394i	0.119793	−	0.119793i
$983$	−3.80734	+	3.80734i	−0.121435	+	0.121435i	−0.765213	−	0.643777i	$-0.777366\pi$
$983$	−3.80734	+	3.80734i	−0.121435	+	0.121435i	0.643777	+	0.765213i	$0.277366\pi$
$984$	32.5660	−	12.4140i	1.03817	−	0.395745i
$985$	47.5568	+	14.8397i	1.51529	+	0.472832i
$986$			0.242965i			0.00773758i
$987$	−15.0797	+	33.6586i	−0.479993	+	1.07136i
$988$	0.00109483	+	0.00109483i	3.48311e−5	+	3.48311e-5i
$989$	−28.4180			−0.903640
$990$	4.22270	−	1.91579i	0.134206	−	0.0608879i
$991$	26.4153			0.839111			0.419555	−	0.907730i	$-0.362186\pi$
$991$	26.4153			0.839111			0.419555	+	0.907730i	$0.362186\pi$
$992$	−0.00494590	−	0.00494590i	−0.000157032	−	0.000157032i
$993$	−11.6660	+	26.0389i	−0.370208	+	0.826321i
$994$			0.289113i			0.00917011i
$995$	−4.25382	−	8.11269i	−0.134855	−	0.257190i
$996$	0.000979061	0	0.000373215i	3.10227e−5	0	1.18258e-5i
$997$	−1.90689	+	1.90689i	−0.0603917	+	0.0603917i	−0.736658	−	0.676266i	$-0.763597\pi$
$997$	−1.90689	+	1.90689i	−0.0603917	+	0.0603917i	0.676266	+	0.736658i	$0.263597\pi$
$998$	−6.14757	+	6.14757i	−0.194598	+	0.194598i
$999$	−17.6967	+	34.1404i	−0.559898	+	1.08015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.b.218.22	yes	60
3.2	odd	2	inner	465.2.k.b.218.9	yes	60
5.2	odd	4	inner	465.2.k.b.32.9	✓	60
15.2	even	4	inner	465.2.k.b.32.22	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.9	✓	60	5.2	odd	4	inner
465.2.k.b.32.22	yes	60	15.2	even	4	inner
465.2.k.b.218.9	yes	60	3.2	odd	2	inner
465.2.k.b.218.22	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00031 + 1.00031i) q^{2} +(0.708168 - 1.58066i) q^{3} +0.00123647i q^{4} +(1.98035 - 1.03838i) q^{5} +(2.28954 - 0.872765i) q^{6} +(-1.66917 + 1.66917i) q^{7} +(1.99938 - 1.99938i) q^{8} +(-1.99699 - 2.23875i) q^{9} +(3.01966 + 0.942258i) q^{10} +0.488628i q^{11} +(0.00195445 + 0.000875632i) q^{12} +(0.606001 + 0.606001i) q^{13} -3.33937 q^{14} +(-0.238909 - 3.86561i) q^{15} +4.00247 q^{16} +(0.560255 + 0.560255i) q^{17} +(0.241832 - 4.23706i) q^{18} -1.46112i q^{19} +(0.00128393 + 0.00244865i) q^{20} +(1.45634 + 3.82044i) q^{21} +(-0.488779 + 0.488779i) q^{22} +(-3.42811 + 3.42811i) q^{23} +(-1.74445 - 4.57625i) q^{24} +(2.84354 - 4.11270i) q^{25} +1.21238i q^{26} +(-4.95292 + 1.57116i) q^{27} +(-0.00206388 - 0.00206388i) q^{28} +0.216767 q^{29} +(3.62782 - 4.10578i) q^{30} -1.00000 q^{31} +(0.00494590 + 0.00494590i) q^{32} +(0.772356 + 0.346031i) q^{33} +1.12086i q^{34} +(-1.57230 + 5.03875i) q^{35} +(0.00276816 - 0.00246923i) q^{36} +(5.23298 - 5.23298i) q^{37} +(1.46158 - 1.46158i) q^{38} +(1.38703 - 0.528733i) q^{39} +(1.88335 - 6.03558i) q^{40} +7.11630i q^{41} +(-2.36483 + 5.27841i) q^{42} +(4.14486 + 4.14486i) q^{43} -0.000604176 q^{44} +(-6.27941 - 2.35987i) q^{45} -6.85833 q^{46} +(6.37862 + 6.37862i) q^{47} +(2.83442 - 6.32656i) q^{48} +1.42776i q^{49} +(6.95839 - 1.26955i) q^{50} +(1.28233 - 0.488820i) q^{51} +(-0.000749304 + 0.000749304i) q^{52} +(-6.92873 + 6.92873i) q^{53} +(-6.52610 - 3.38280i) q^{54} +(0.507381 + 0.967652i) q^{55} +6.67460i q^{56} +(-2.30955 - 1.03472i) q^{57} +(0.216834 + 0.216834i) q^{58} -9.51422 q^{59} +(0.00477972 - 0.000295405i) q^{60} +3.65071 q^{61} +(-1.00031 - 1.00031i) q^{62} +(7.07017 + 0.403534i) q^{63} -7.99505i q^{64} +(1.82935 + 0.570833i) q^{65} +(0.426457 + 1.11873i) q^{66} +(-4.73394 + 4.73394i) q^{67} +(-0.000692741 + 0.000692741i) q^{68} +(2.99101 + 7.84636i) q^{69} +(-6.61310 + 3.46753i) q^{70} -0.0865773i q^{71} +(-8.46887 - 0.483365i) q^{72} +(1.94880 + 1.94880i) q^{73} +10.4692 q^{74} +(-4.48709 - 7.40716i) q^{75} +0.00180664 q^{76} +(-0.815601 - 0.815601i) q^{77} +(1.91636 + 0.858567i) q^{78} +8.96053i q^{79} +(7.92628 - 4.15608i) q^{80} +(-1.02402 + 8.94155i) q^{81} +(-7.11850 + 7.11850i) q^{82} +(0.345948 - 0.345948i) q^{83} +(-0.00472388 + 0.00180073i) q^{84} +(1.69126 + 0.527742i) q^{85} +8.29227i q^{86} +(0.153508 - 0.342636i) q^{87} +(0.976954 + 0.976954i) q^{88} -12.2175 q^{89} +(-3.92076 - 8.64195i) q^{90} -2.02303 q^{91} +(-0.00423877 - 0.00423877i) q^{92} +(-0.708168 + 1.58066i) q^{93} +12.7612i q^{94} +(-1.51720 - 2.89353i) q^{95} +(0.0113203 - 0.00431527i) q^{96} +(-1.33436 + 1.33436i) q^{97} +(-1.42821 + 1.42821i) q^{98} +(1.09392 - 0.975787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40}+ \cdots + 56 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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