LMFDB - Embedded newform 465.2.k.b.32.9

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			32.9
Character	$\chi$	$=$	465.32
Dual form			465.2.k.b.218.9

$q$-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} +(-1.58066 - 0.708168i) 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} +(-0.000875632 + 0.00195445i) q^{12} +(0.606001 - 0.606001i) q^{13} +3.33937 q^{14} +(2.39491 + 3.04375i) q^{15} +4.00247 q^{16} +(-0.560255 + 0.560255i) q^{17} +(-4.23706 - 0.241832i) 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} +(-1.57116 - 4.95292i) q^{27} +(-0.00206388 + 0.00206388i) q^{28} -0.216767 q^{29} +(-5.44034 - 0.649033i) q^{30} -1.00000 q^{31} +(-0.00494590 + 0.00494590i) q^{32} +(0.346031 - 0.772356i) 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} +(-5.27841 - 2.36483i) q^{42} +(4.14486 - 4.14486i) q^{43} +0.000604176 q^{44} +(-1.63007 - 6.50714i) q^{45} -6.85833 q^{46} +(-6.37862 + 6.37862i) q^{47} +(-6.32656 - 2.83442i) 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} +(1.03472 - 2.30955i) q^{57} +(0.216834 - 0.216834i) q^{58} +9.51422 q^{59} +(0.00376351 - 0.00296125i) q^{60} +3.65071 q^{61} +(1.00031 - 1.00031i) q^{62} +(0.403534 - 7.07017i) 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} +(0.483365 - 8.46887i) q^{72} +(1.94880 - 1.94880i) q^{73} -10.4692 q^{74} +(-1.58220 - 8.51450i) q^{75} +0.00180664 q^{76} +(0.815601 - 0.815601i) q^{77} +(0.858567 - 1.91636i) 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} +(0.342636 + 0.153508i) q^{87} +(0.976954 - 0.976954i) q^{88} +12.2175 q^{89} +(8.13972 + 4.87858i) q^{90} -2.02303 q^{91} +(0.00423877 - 0.00423877i) q^{92} +(1.58066 + 0.708168i) 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 $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

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

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	$-0.916723\pi$
$2$	−1.00031	+	1.00031i	−0.707325	+	0.707325i	0.258647	+	0.965972i	$0.416723\pi$
$3$	−1.58066	−	0.708168i	−0.912597	−	0.408861i
$3$	−1.58066	−	0.708168i	−0.912597	−	0.408861i
$4$		−	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	0.317405	−	0.948290i	$-0.397189\pi$
$7$	−1.66917	−	1.66917i	−0.630886	−	0.630886i	−0.948290	+	0.317405i	$0.897189\pi$
$8$	−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	$0.976531\pi$
$12$	−0.000875632		0.00195445i	−0.000252773		0.000564201i
$13$	0.606001	−	0.606001i	0.168074	−	0.168074i	−0.618058	−	0.786132i	$-0.712080\pi$
$13$	0.606001	−	0.606001i	0.168074	−	0.168074i	0.786132	+	0.618058i	$0.212080\pi$
$14$	3.33937			0.892483
$15$	2.39491	+	3.04375i	0.618364	+	0.785892i
$16$	4.00247			1.00062
$17$	−0.560255	+	0.560255i	−0.135882	+	0.135882i	−0.771776	−	0.635894i	$-0.780631\pi$
$17$	−0.560255	+	0.560255i	−0.135882	+	0.135882i	0.635894	+	0.771776i	$0.280631\pi$
$18$	−4.23706	−	0.241832i	−0.998684	−	0.0570004i
$19$			1.46112i			0.335205i	0.985855	+	0.167602i	$0.0536025\pi$
$19$			1.46112i			0.335205i	−0.985855	+	0.167602i	$0.946397\pi$
$20$	−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	$-0.0813276\pi$
$23$	3.42811	+	3.42811i	0.714810	+	0.714810i	−0.252728	+	0.967537i	$0.581328\pi$
$24$	1.74445	+	4.57625i	0.356084	+	0.934123i
$25$	2.84354	+	4.11270i	0.568708	+	0.822540i
$26$			1.21238i			0.237767i
$27$	−1.57116	−	4.95292i	−0.302370	−	0.953190i
$28$	−0.00206388	+	0.00206388i	−0.000390037	+	0.000390037i
$29$	−0.216767			−0.0402527			−0.0201263	−	0.999797i	$-0.506407\pi$
$29$	−0.216767			−0.0402527			−0.0201263	+	0.999797i	$0.506407\pi$
$30$	−5.44034	−	0.649033i	−0.993266	−	0.118497i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.00494590	+	0.00494590i	−0.000874319	+	0.000874319i
$33$	0.346031	−	0.772356i	0.0602362	−	0.134450i
$34$		−	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	0.991372	−	0.131076i	$-0.0418433\pi$
$37$	5.23298	+	5.23298i	0.860296	+	0.860296i	−0.131076	+	0.991372i	$0.541843\pi$
$38$	−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	$0.812454\pi$
$42$	−5.27841	−	2.36483i	−0.814477	−	0.364902i
$43$	4.14486	−	4.14486i	0.632084	−	0.632084i	−0.316506	−	0.948591i	$-0.602510\pi$
$43$	4.14486	−	4.14486i	0.632084	−	0.632084i	0.948591	+	0.316506i	$0.102510\pi$
$44$	0.000604176	0		9.10829e−5	0
$45$	−1.63007	−	6.50714i	−0.242996	−	0.970027i
$46$	−6.85833			−1.01121
$47$	−6.37862	+	6.37862i	−0.930418	+	0.930418i	−0.997732	−	0.0673142i	$-0.978557\pi$
$47$	−6.37862	+	6.37862i	−0.930418	+	0.930418i	0.0673142	+	0.997732i	$0.478557\pi$
$48$	−6.32656	−	2.83442i	−0.913160	−	0.409114i
$49$		−	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	$-0.0150151\pi$
$53$	6.92873	+	6.92873i	0.951734	+	0.951734i	−0.0471539	+	0.998888i	$0.515015\pi$
$54$	6.52610	+	3.38280i	0.888090	+	0.460341i
$55$	0.507381	−	0.967652i	0.0684152	−	0.130478i
$56$			6.67460i			0.891931i
$57$	1.03472	−	2.30955i	0.137052	−	0.305907i
$58$	0.216834	−	0.216834i	0.0284717	−	0.0284717i
$59$	9.51422			1.23865			0.619323	−	0.785136i	$-0.287407\pi$
$59$	9.51422			1.23865			0.619323	+	0.785136i	$0.287407\pi$
$60$	0.00376351	−	0.00296125i	0.000485868	−	0.000382296i
$61$	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
$63$	0.403534	−	7.07017i	0.0508404	−	0.890757i
$64$			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	0.356104	−	0.934446i	$-0.384105\pi$
$67$	−4.73394	−	4.73394i	−0.578342	−	0.578342i	−0.934446	+	0.356104i	$0.884105\pi$
$68$	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	$-0.00163530\pi$
$72$	0.483365	−	8.46887i	0.0569652	−	0.998066i
$73$	1.94880	−	1.94880i	0.228090	−	0.228090i	−0.583804	−	0.811895i	$-0.698436\pi$
$73$	1.94880	−	1.94880i	0.228090	−	0.228090i	0.811895	+	0.583804i	$0.198436\pi$
$74$	−10.4692			−1.21702
$75$	−1.58220	−	8.51450i	−0.182696	−	0.983169i
$76$	0.00180664			0.000207236
$77$	0.815601	−	0.815601i	0.0929464	−	0.0929464i
$78$	0.858567	−	1.91636i	0.0972135	−	0.216985i
$79$		−	8.96053i		−	1.00814i	−0.863663	−	0.504069i	$-0.831836\pi$
$79$		−	8.96053i		−	1.00814i	0.863663	−	0.504069i	$-0.168164\pi$
$80$	−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	$-0.258548\pi$
$83$	−0.345948	−	0.345948i	−0.0379727	−	0.0379727i	−0.725838	+	0.687865i	$0.758548\pi$
$84$	0.00472388	−	0.00180073i	0.000515417	−	0.000196475i
$85$	1.69126	−	0.527742i	0.183443	−	0.0572417i
$86$			8.29227i			0.894179i
$87$	0.342636	+	0.153508i	0.0367344	+	0.0164578i
$88$	0.976954	−	0.976954i	0.104144	−	0.104144i
$89$	12.2175			1.29505			0.647525	−	0.762044i	$-0.275804\pi$
$89$	12.2175			1.29505			0.647525	+	0.762044i	$0.275804\pi$
$90$	8.13972	+	4.87858i	0.858002	+	0.514247i
$91$	−2.02303			−0.212071
$92$	0.00423877	−	0.00423877i	0.000441922	−	0.000441922i
$93$	1.58066	+	0.708168i	0.163907	+	0.0734337i
$94$		−	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	0.636113	−	0.771596i	$-0.280541\pi$
$97$	−1.33436	−	1.33436i	−0.135484	−	0.135484i	−0.771596	+	0.636113i	$0.780541\pi$
$98$	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	$-0.235491\pi$
$102$	−0.793755	+	1.77170i	−0.0785935	+	0.175424i
$103$	−3.23911	+	3.23911i	−0.319159	+	0.319159i	−0.848444	−	0.529285i	$-0.822460\pi$
$103$	−3.23911	+	3.23911i	−0.319159	+	0.319159i	0.529285	+	0.848444i	$0.322460\pi$
$104$	−2.42325			−0.237620
$105$	1.08301	−	9.07803i	0.105691	−	0.885925i
$106$	−13.8617			−1.34637
$107$	5.66961	−	5.66961i	0.548102	−	0.548102i	−0.377790	−	0.925891i	$-0.623316\pi$
$107$	5.66961	−	5.66961i	0.548102	−	0.548102i	0.925891	+	0.377790i	$0.123316\pi$
$108$	−0.00612416	+	0.00194270i	−0.000589298	+	0.000186937i
$109$			14.9745i			1.43430i	0.696921	+	0.717148i	$0.254553\pi$
$109$			14.9745i			1.43430i	−0.696921	+	0.717148i	$0.745447\pi$
$110$	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	$-0.262853\pi$
$113$	−0.606854	−	0.606854i	−0.0570880	−	0.0570880i	−0.735074	+	0.677986i	$0.762853\pi$
$114$	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
$117$	2.56687	+	0.146505i	0.237307	+	0.0135444i
$118$	−9.51716	+	9.51716i	−0.876126	+	0.876126i
$119$	1.87032			0.171452
$120$	1.29726	−	10.8740i	0.118423	−	0.992652i
$121$	10.7612			0.978295
$122$	−3.65184	+	3.65184i	−0.330622	+	0.330622i
$123$	5.03954	−	11.2485i	0.454400	−	1.01424i
$124$			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	0.947934	−	0.318468i	$-0.103168\pi$
$127$	7.09372	+	7.09372i	0.629466	+	0.629466i	−0.318468	+	0.947934i	$0.603168\pi$
$128$	−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	$-0.200637\pi$
$132$	−0.000954999	0	0.000427858i	−8.31220e−5	0	3.72403e-5i
$133$	2.43886	−	2.43886i	0.211476	−	0.211476i
$134$	9.47080			0.818153
$135$	−2.03156	+	11.4400i	−0.174849	+	0.984595i
$136$	2.24033			0.192107
$137$	−12.2568	+	12.2568i	−1.04717	+	1.04717i	−0.0483356	+	0.998831i	$0.515392\pi$
$137$	−12.2568	+	12.2568i	−1.04717	+	1.04717i	−0.998831	+	0.0483356i	$0.984608\pi$
$138$	10.8407	+	4.85686i	0.922823	+	0.413443i
$139$		−	1.52125i		−	0.129031i	−0.997917	−	0.0645155i	$-0.979450\pi$
$139$		−	1.52125i		−	0.129031i	0.997917	−	0.0645155i	$-0.0205502\pi$
$140$	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
$147$	−1.01110	+	2.25682i	−0.0833940	+	0.186139i
$148$	0.00647044	−	0.00647044i	0.000531867	−	0.000531867i
$149$	19.3963			1.58900			0.794502	−	0.607261i	$-0.207732\pi$
$149$	19.3963			1.58900			0.794502	+	0.607261i	$0.207732\pi$
$150$	10.0998	+	6.93444i	0.824646	+	0.566195i
$151$	−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
$153$	−2.37310	−	0.135446i	−0.191854	−	0.0109502i
$154$			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	0.939578	+	0.342336i	$0.111218\pi$
$157$	16.0623	+	16.0623i	1.28191	+	1.28191i	0.342336	+	0.939578i	$0.388782\pi$
$158$	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
$162$	−7.91998	−	9.96866i	−0.622252	−	0.783212i
$163$	3.67219	−	3.67219i	0.287628	−	0.287628i	−0.548514	−	0.836142i	$-0.684806\pi$
$163$	3.67219	−	3.67219i	0.287628	−	0.287628i	0.836142	+	0.548514i	$0.184806\pi$
$164$	0.00879913			0.000687096
$165$	−1.48726	+	1.17022i	−0.115783	+	0.0911016i
$166$	0.692110			0.0537181
$167$	−14.2829	+	14.2829i	−1.10524	+	1.10524i	−0.111477	+	0.993767i	$0.535558\pi$
$167$	−14.2829	+	14.2829i	−1.10524	+	1.10524i	−0.993767	+	0.111477i	$0.964442\pi$
$168$	4.72674	−	10.5503i	0.364676	−	0.813973i
$169$			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	$-0.312608\pi$
$173$	−3.63506	−	3.63506i	−0.276369	−	0.276369i	−0.831658	+	0.555289i	$0.812608\pi$
$174$	−0.496297	+	0.189187i	−0.0376242	+	0.0143422i
$175$	2.11844	−	11.6111i	0.160139	−	0.877718i
$176$			1.95572i			0.147418i
$177$	−15.0388	−	6.73767i	−1.13038	−	0.506434i
$178$	−12.2212	+	12.2212i	−0.916021	+	0.916021i
$179$	20.8745			1.56023			0.780116	−	0.625635i	$-0.215160\pi$
$179$	20.8745			1.56023			0.780116	+	0.625635i	$0.215160\pi$
$180$	−0.00804591	+	0.00201554i	−0.000599707	+	0.000150229i
$181$	−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
$183$	−5.77054	−	2.58532i	−0.426571	−	0.191112i
$184$		−	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	$0.656229\pi$
$192$	5.66184	−	12.6375i	0.408608	−	0.912032i
$193$	−5.95019	+	5.95019i	−0.428304	+	0.428304i	−0.888050	−	0.459746i	$-0.847940\pi$
$193$	−5.95019	+	5.95019i	−0.428304	+	0.428304i	0.459746	+	0.888050i	$0.347940\pi$
$194$	2.66954			0.191662
$195$	3.29583	+	0.393193i	0.236019	+	0.0281571i
$196$	−0.00176539			−0.000126100
$197$	−15.7539	+	15.7539i	−1.12242	+	1.12242i	−0.131046	+	0.991376i	$0.541833\pi$
$197$	−15.7539	+	15.7539i	−1.12242	+	1.12242i	−0.991376	+	0.131046i	$0.958167\pi$
$198$	0.118166	−	2.07034i	0.00839769	−	0.147133i
$199$			4.09660i			0.290400i	0.989402	+	0.145200i	$0.0463826\pi$
$199$			4.09660i			0.290400i	−0.989402	+	0.145200i	$0.953617\pi$
$200$	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
$207$	−0.828771	+	14.5206i	−0.0576035	+	1.00925i
$208$	2.42550	−	2.42550i	0.168178	−	0.168178i
$209$	−0.713946			−0.0493847
$210$	7.99749	+	10.1642i	0.551879	+	0.701395i
$211$	−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
$213$	−0.0613113	+	0.136850i	−0.00420098	+	0.00937677i
$214$			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
$222$	16.5483	+	7.41395i	1.11065	+	0.497592i
$223$	3.30852	−	3.30852i	0.221555	−	0.221555i	−0.587598	−	0.809153i	$-0.699926\pi$
$223$	3.30852	−	3.30852i	0.221555	−	0.221555i	0.809153	+	0.587598i	$0.199926\pi$
$224$	0.0165111			0.00110319
$225$	−3.52878	+	14.5790i	−0.235252	+	0.971934i
$226$	1.21408			0.0807596
$227$	−4.51141	+	4.51141i	−0.299433	+	0.299433i	−0.840792	−	0.541359i	$-0.817910\pi$
$227$	−4.51141	+	4.51141i	−0.299433	+	0.299433i	0.541359	+	0.840792i	$0.317910\pi$
$228$	−0.00285569	−	0.00127941i	−0.000189123	−	8.47308e-5i
$229$			23.0217i			1.52132i	0.649151	+	0.760660i	$0.275124\pi$
$229$			23.0217i			1.52132i	−0.649151	+	0.760660i	$0.724876\pi$
$230$	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	0.937618	+	0.347666i	$0.113026\pi$
$233$	19.6190	+	19.6190i	1.28528	+	1.28528i	0.347666	+	0.937618i	$0.386974\pi$
$234$	−2.71421	+	2.42111i	−0.177433	+	0.158273i
$235$	19.2553	−	6.00845i	1.25608	−	0.391948i
$236$		−	0.0117641i		−	0.000765777i
$237$	−6.34556	+	14.1636i	−0.412189	+	0.920023i
$238$	−1.87090	+	1.87090i	−0.121272	+	0.121272i
$239$	−8.66511			−0.560499			−0.280250	−	0.959927i	$-0.590417\pi$
$239$	−8.66511			−0.560499			−0.280250	+	0.959927i	$0.590417\pi$
$240$	9.58557	+	12.1825i	0.618746	+	0.786377i
$241$	−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
$243$	7.95076	−	13.4084i	0.510042	−	0.860150i
$244$		−	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	$-0.0674731\pi$
$252$	−0.00874208		0.000498959i	−0.000550699		3.14315e-5i
$253$	−1.67507	+	1.67507i	−0.105311	+	0.105311i
$254$	−14.1918			−0.890474
$255$	−3.04704	−	0.363512i	−0.190813	−	0.0227640i
$256$	0.0296754			0.00185471
$257$	4.13272	−	4.13272i	0.257792	−	0.257792i	−0.566364	−	0.824155i	$-0.691650\pi$
$257$	4.13272	−	4.13272i	0.257792	−	0.257792i	0.824155	+	0.566364i	$0.191650\pi$
$258$	5.87233	−	13.1073i	0.365595	−	0.816024i
$259$		−	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	$-0.279849\pi$
$263$	−2.14753	−	2.14753i	−0.132423	−	0.132423i	−0.770211	+	0.637789i	$0.779849\pi$
$264$	−2.23608	+	0.852387i	−0.137621	+	0.0524608i
$265$	−6.52663	−	20.9159i	−0.400928	−	1.28485i
$266$			4.87923i			0.299165i
$267$	−19.3117	−	8.65203i	−1.18186	−	0.529496i
$268$	−0.00585339	+	0.00585339i	−0.000357553	+	0.000357553i
$269$	−16.1691			−0.985846			−0.492923	−	0.870073i	$-0.664072\pi$
$269$	−16.1691			−0.985846			−0.492923	+	0.870073i	$0.664072\pi$
$270$	−9.41131	−	13.4757i	−0.572754	−	0.820104i
$271$	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
$273$	3.19773	+	1.43265i	0.193536	+	0.0867078i
$274$		−	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	0.999344	−	0.0362031i	$-0.0115263\pi$
$277$	16.0299	+	16.0299i	0.963141	+	0.963141i	−0.0362031	+	0.999344i	$0.511526\pi$
$278$	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	$-0.299481\pi$
$282$	−9.03707	+	20.1711i	−0.538150	+	1.20117i
$283$	−7.86447	+	7.86447i	−0.467494	+	0.467494i	−0.901102	−	0.433608i	$-0.857240\pi$
$283$	−7.86447	+	7.86447i	−0.467494	+	0.467494i	0.433608	+	0.901102i	$0.357240\pi$
$284$	−0.000107051	0		−6.35228e−6	0
$285$	−4.44729	+	3.49927i	−0.263435	+	0.207279i
$286$	−0.592401			−0.0350294
$287$	11.8783	−	11.8783i	0.701154	−	0.701154i
$288$	−0.0209496	−	0.00119571i	−0.00123447	−	7.04577e-5i
$289$			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	$-0.397082\pi$
$293$	−10.7917	−	10.7917i	−0.630460	−	0.630460i	−0.948183	+	0.317723i	$0.897082\pi$
$294$	−1.24610	−	3.26892i	−0.0726742	−	0.190648i
$295$	−18.8415	−	9.87936i	−1.09699	−	0.575199i
$296$		−	20.9254i		−	1.21627i
$297$	2.42014	−	0.767714i	0.140431	−	0.0445473i
$298$	−19.4023	+	19.4023i	−1.12394	+	1.12394i
$299$	4.15487			0.240282
$300$	−0.0105280	+	0.00195635i	−0.000607832	+	0.000112950i
$301$	−13.8369			−0.797546
$302$	18.4843	−	18.4843i	1.06365	−	1.06365i
$303$	−9.59588	+	21.4184i	−0.551269	+	1.23046i
$304$			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	0.970754	−	0.240076i	$-0.0771723\pi$
$307$	12.8025	+	12.8025i	0.730678	+	0.730678i	−0.240076	+	0.970754i	$0.577172\pi$
$308$	−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	$-0.210536\pi$
$312$	3.83035	+	1.71607i	0.216851	+	0.0971534i
$313$	15.5220	−	15.5220i	0.877353	−	0.877353i	−0.115907	−	0.993260i	$-0.536977\pi$
$313$	15.5220	−	15.5220i	0.877353	−	0.877353i	0.993260	+	0.115907i	$0.0369774\pi$
$314$	−32.1346			−1.81346
$315$	−8.14065	+	13.5824i	−0.458674	+	0.765279i
$316$	−0.0110795			−0.000623268
$317$	13.7279	−	13.7279i	0.771035	−	0.771035i	−0.207252	−	0.978288i	$-0.566452\pi$
$317$	13.7279	−	13.7279i	0.771035	−	0.771035i	0.978288	+	0.207252i	$0.0664521\pi$
$318$	21.9107	+	9.81644i	1.22869	+	0.550479i
$319$		−	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
$327$	10.6045	−	23.6696i	0.586428	−	1.30893i
$328$	14.2282	−	14.2282i	0.785621	−	0.785621i
$329$	21.2940			1.17397
$330$	0.317135	−	2.65830i	0.0174577	−	0.146335i
$331$	−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
$333$	−1.26511	+	22.1656i	−0.0693277	+	1.21467i
$334$		−	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	0.999898	+	0.0142748i	$0.00454395\pi$
$337$	18.6177	+	18.6177i	1.01417	+	1.01417i	0.0142748	+	0.999898i	$0.495456\pi$
$338$	−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
$342$	0.353347	−	6.19087i	0.0191068	−	0.334764i
$343$	−14.0673	+	14.0673i	−0.759565	+	0.759565i
$344$	−16.5743			−0.893626
$345$	−2.22427	+	18.6443i	−0.119750	+	1.00378i
$346$	7.27238			0.390965
$347$	21.7272	−	21.7272i	1.16637	−	1.16637i	0.183322	−	0.983053i	$-0.441315\pi$
$347$	21.7272	−	21.7272i	1.16637	−	1.16637i	0.983053	−	0.183322i	$-0.0586850\pi$
$348$	0.000189808	0	0.000423661i	1.01748e−5	0	2.27106e-5i
$349$			2.53205i			0.135537i	0.997701	+	0.0677687i	$0.0215880\pi$
$349$			2.53205i			0.135537i	−0.997701	+	0.0677687i	$0.978412\pi$
$350$	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	$-0.181166\pi$
$353$	5.70119	+	5.70119i	0.303444	+	0.303444i	−0.538916	+	0.842360i	$0.681166\pi$
$354$	21.7832	−	8.30368i	1.15776	−	0.441336i
$355$	−0.0899000	+	0.171453i	−0.00477140	+	0.00909978i
$356$		−	0.0151066i		−	0.000800648i
$357$	−2.95635	−	1.32450i	−0.156466	−	0.0701000i
$358$	−20.8809	+	20.8809i	−1.10359	+	1.10359i
$359$	16.7850			0.885877			0.442938	−	0.896552i	$-0.353936\pi$
$359$	16.7850			0.885877			0.442938	+	0.896552i	$0.353936\pi$
$360$	−9.75113	+	16.2694i	−0.513930	+	0.857472i
$361$	16.8651			0.887638
$362$	19.2271	−	19.2271i	1.01055	−	1.01055i
$363$	−17.0099	−	7.62077i	−0.892788	−	0.399987i
$364$			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	−0.919299	−	0.393560i	$-0.871243\pi$
$367$	−25.1508	−	25.1508i	−1.31286	−	1.31286i	−0.393560	−	0.919299i	$-0.628757\pi$
$368$	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
$372$	0.000875632	−	0.00195445i	4.53994e−5	−	0.000101334i
$373$	−1.28708	+	1.28708i	−0.0666427	+	0.0666427i	−0.739643	−	0.673000i	$-0.765005\pi$
$373$	−1.28708	+	1.28708i	−0.0666427	+	0.0666427i	0.673000	+	0.739643i	$0.265005\pi$
$374$	0.547682			0.0283200
$375$	−5.70797	+	18.5046i	−0.294759	+	0.955572i
$376$	25.5066			1.31540
$377$	−0.131361	+	0.131361i	−0.00676544	+	0.00676544i
$378$	−5.24669	−	16.5396i	−0.269861	−	0.850706i
$379$		−	26.9785i		−	1.38579i	−0.721038	−	0.692896i	$-0.756335\pi$
$379$		−	26.9785i		−	1.38579i	0.721038	−	0.692896i	$-0.243665\pi$
$380$	−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	$-0.141097\pi$
$383$	9.28532	+	9.28532i	0.474458	+	0.474458i	−0.428896	+	0.903354i	$0.641097\pi$
$384$	6.98643	+	18.3276i	0.356525	+	0.935277i
$385$	−2.46208	+	0.768270i	−0.125479	+	0.0391547i
$386$		−	11.9041i		−	0.605901i
$387$	17.5566	+	1.00205i	0.892450	+	0.0509370i
$388$	−0.00164990	+	0.00164990i	−8.37611e−5	+	8.37611e-5i
$389$	5.45183			0.276419			0.138209	−	0.990403i	$-0.455865\pi$
$389$	5.45183			0.276419			0.138209	+	0.990403i	$0.455865\pi$
$390$	−3.69016	+	2.90354i	−0.186859	+	0.147026i
$391$	−3.84123			−0.194259
$392$	−2.85465	+	2.85465i	−0.144181	+	0.144181i
$393$	−9.55464	+	21.3264i	−0.481968	+	1.07577i
$394$		−	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	0.949245	−	0.314538i	$-0.101850\pi$
$397$	12.6464	+	12.6464i	0.634706	+	0.634706i	−0.314538	+	0.949245i	$0.601850\pi$
$398$	−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	$0.802950\pi$
$402$	−14.9701	−	6.70692i	−0.746643	−	0.334511i
$403$	−0.606001	+	0.606001i	−0.0301870	+	0.0301870i
$404$	−0.0167546			−0.000833571
$405$	11.3126	−	16.6440i	0.562130	−	0.827049i
$406$	−0.723865			−0.0359248
$407$	−2.55698	+	2.55698i	−0.126745	+	0.126745i
$408$	−3.54120	−	1.58653i	−0.175316	−	0.0785449i
$409$		−	20.9451i		−	1.03567i	−0.855480	−	0.517835i	$-0.826738\pi$
$409$		−	20.9451i		−	1.03567i	0.855480	−	0.517835i	$-0.173262\pi$
$410$	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
$417$	−1.07730	+	2.40459i	−0.0527558	+	0.117753i
$418$	0.714167	−	0.714167i	0.0349310	−	0.0349310i
$419$	−8.76420			−0.428159			−0.214080	−	0.976816i	$-0.568675\pi$
$419$	−8.76420			−0.428159			−0.214080	+	0.976816i	$0.568675\pi$
$420$	−0.0112248	−	0.00133911i	−0.000547712	−	6.53420e-5i
$421$	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
$423$	−27.0182	−	1.54208i	−1.31367	−	0.0749785i
$424$		−	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	$-0.0180456\pi$
$432$	−6.28854	−	19.8239i	−0.302557	−	0.953779i
$433$	16.6004	−	16.6004i	0.797762	−	0.797762i	−0.184980	−	0.982742i	$-0.559222\pi$
$433$	16.6004	−	16.6004i	0.797762	−	0.797762i	0.982742	+	0.184980i	$0.0592221\pi$
$434$	−3.33937			−0.160295
$435$	−0.519139	−	0.659784i	−0.0248908	−	0.0316342i
$436$	0.0185156			0.000886735
$437$	−5.00889	+	5.00889i	−0.239608	+	0.239608i
$438$	2.76102	−	6.16271i	0.131927	−	0.294466i
$439$			11.3213i			0.540337i	0.962813	+	0.270169i	$0.0870795\pi$
$439$			11.3213i			0.540337i	−0.962813	+	0.270169i	$0.912921\pi$
$440$	−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	$-0.251318\pi$
$443$	−0.123239	−	0.123239i	−0.00585525	−	0.00585525i	−0.710028	+	0.704173i	$0.751318\pi$
$444$	−0.0148098	+	0.00564543i	−0.000702840	+	0.000267920i
$445$	−24.1948	−	12.6864i	−1.14694	−	0.601391i
$446$			6.61909i			0.313423i
$447$	−30.6590	−	13.7358i	−1.45012	−	0.649682i
$448$	13.3451	−	13.3451i	0.630495	−	0.630495i
$449$	5.58480			0.263563			0.131782	−	0.991279i	$-0.457930\pi$
$449$	5.58480			0.263563			0.131782	+	0.991279i	$0.457930\pi$
$450$	−11.0537	−	18.1134i	−0.521074	−	0.853873i
$451$	−3.47722			−0.163736
$452$	−0.000750360	0	0.000750360i	−3.52940e−5	0	3.52940e-5i
$453$	29.2084	+	13.0859i	1.37233	+	0.614831i
$454$		−	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	0.116808	−	0.993155i	$-0.462734\pi$
$457$	−18.7342	−	18.7342i	−0.876347	−	0.876347i	−0.993155	+	0.116808i	$0.962734\pi$
$458$	−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	$0.986640\pi$
$462$	1.15552	−	2.57918i	0.0537598	−	0.119994i
$463$	−28.8896	+	28.8896i	−1.34261	+	1.34261i	−0.449162	+	0.893450i	$0.648277\pi$
$463$	−28.8896	+	28.8896i	−1.34261	+	1.34261i	−0.893450	+	0.449162i	$0.851723\pi$
$464$	−0.867605			−0.0402775
$465$	−2.39491	−	3.04375i	−0.111061	−	0.141150i
$466$	−39.2502			−1.81823
$467$	1.77213	−	1.77213i	0.0820043	−	0.0820043i	−0.664915	−	0.746919i	$-0.731532\pi$
$467$	1.77213	−	1.77213i	0.0820043	−	0.0820043i	0.746919	+	0.664915i	$0.231532\pi$
$468$	0.000181150	−	0.00317386i	8.37366e−6	−	0.000146712i
$469$			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
$477$	−1.67507	+	29.3483i	−0.0766962	+	1.34377i
$478$	8.66779	−	8.66779i	0.396455	−	0.396455i
$479$	−36.3824			−1.66236			−0.831178	−	0.556007i	$-0.812333\pi$
$479$	−36.3824			−1.66236			−0.831178	+	0.556007i	$0.812333\pi$
$480$	−0.0268990	−	0.00320906i	−0.00122777	−	0.000146473i
$481$	6.34237			0.289187
$482$	19.4827	−	19.4827i	0.887414	−	0.887414i
$483$	−8.10440	+	18.0894i	−0.368763	+	0.823095i
$484$		−	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	0.212250	−	0.977215i	$-0.431921\pi$
$487$	−16.8813	−	16.8813i	−0.764966	−	0.764966i	−0.977215	+	0.212250i	$0.931921\pi$
$488$	−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	$-0.0269869\pi$
$492$	−0.0139085	−	0.00623126i	−0.000627042	−	0.000280927i
$493$	0.121445	−	0.121445i	0.00546961	−	0.00546961i
$494$	−1.77143			−0.0797005
$495$	3.17957	−	0.796497i	0.142911	−	0.0357999i
$496$	−4.00247			−0.179716
$497$	−0.144512	+	0.144512i	−0.00648224	+	0.00648224i
$498$	−1.09399	−	0.490130i	−0.0490230	−	0.0219633i
$499$		−	6.14567i		−	0.275118i	−0.990494	−	0.137559i	$-0.956074\pi$
$499$		−	6.14567i		−	0.275118i	0.990494	−	0.137559i	$-0.0439257\pi$
$500$	−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	$-0.147852\pi$
$503$	10.0046	+	10.0046i	0.446084	+	0.446084i	−0.447966	+	0.894050i	$0.647852\pi$
$504$	−14.9428	+	13.3291i	−0.665604	+	0.593727i
$505$	−14.0703	+	26.8342i	−0.626121	+	1.19411i
$506$		−	3.35117i		−	0.148978i
$507$	8.68606	−	19.3877i	0.385761	−	0.861037i
$508$	0.00877120	−	0.00877120i	0.000389159	−	0.000389159i
$509$	8.38449			0.371636			0.185818	−	0.982584i	$-0.440506\pi$
$509$	8.38449			0.371636			0.185818	+	0.982584i	$0.440506\pi$
$510$	3.41160	−	2.68436i	0.151068	−	0.118865i
$511$	−6.50576			−0.287798
$512$	15.9851	−	15.9851i	0.706450	−	0.706450i
$513$	7.23684	−	2.29566i	0.319514	−	0.101356i
$514$			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	$0.879490\pi$
$522$	0.918455	+	0.0524213i	0.0401997	+	0.00229442i
$523$	7.41293	−	7.41293i	0.324145	−	0.324145i	−0.526210	−	0.850355i	$-0.676387\pi$
$523$	7.41293	−	7.41293i	0.324145	−	0.324145i	0.850355	+	0.526210i	$0.176387\pi$
$524$	−0.0166826			−0.000728781
$525$	−11.5712	+	16.8531i	−0.505007	+	0.735528i
$526$	4.29640			0.187332
$527$	0.560255	−	0.560255i	0.0244051	−	0.0244051i
$528$	1.38498	−	3.09133i	0.0602735	−	0.134533i
$529$			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
$537$	−32.9955	−	14.7826i	−1.42386	−	0.637918i
$538$	16.1741	−	16.1741i	0.697314	−	0.697314i
$539$	0.697646			0.0300497
$540$	0.0141452	+	0.00251198i	0.000608713	+	0.000108098i
$541$	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
$543$	30.3821	+	13.6118i	1.30382	+	0.584138i
$544$		−	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	0.736946	−	0.675951i	$-0.236267\pi$
$547$	1.42656	+	1.42656i	0.0609951	+	0.0609951i	−0.675951	+	0.736946i	$0.736267\pi$
$548$	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
$552$	−9.70771	+	21.6680i	−0.413187	+	0.922253i
$553$	−14.9566	+	14.9566i	−0.636020	+	0.636020i
$554$	−32.0696			−1.36251
$555$	−3.39532	+	28.4604i	−0.144123	+	1.20808i
$556$	−0.00188099			−7.97718e−5
$557$	15.6580	−	15.6580i	0.663449	−	0.663449i	−0.292742	−	0.956191i	$-0.594568\pi$
$557$	15.6580	−	15.6580i	0.663449	−	0.663449i	0.956191	+	0.292742i	$0.0945678\pi$
$558$	4.23706	+	0.241832i	0.179369	+	0.0102376i
$559$		−	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	$-0.0195686\pi$
$563$	22.2250	+	22.2250i	0.936673	+	0.936673i	−0.0614379	+	0.998111i	$0.519569\pi$
$564$	−0.00688137	−	0.0180520i	−0.000289758	−	0.000760127i
$565$	0.571637	+	1.83193i	0.0240489	+	0.0770697i
$566$		−	15.7338i		−	0.661341i
$567$	16.6342	−	13.2157i	0.698571	−	0.555006i
$568$	−0.173101	+	0.173101i	−0.00726315	+	0.00726315i
$569$	−36.0307			−1.51048			−0.755242	−	0.655446i	$-0.772481\pi$
$569$	−36.0307			−1.51048			−0.755242	+	0.655446i	$0.772481\pi$
$570$	0.948317	−	7.94901i	0.0397206	−	0.332948i
$571$	−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
$573$	17.2635	−	38.5328i	0.721192	−	1.60973i
$574$			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	0.722301	−	0.691579i	$-0.243085\pi$
$577$	0.737957	+	0.737957i	0.0307216	+	0.0307216i	−0.691579	+	0.722301i	$0.743085\pi$
$578$	−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
$582$	−4.21965	−	1.89049i	−0.174910	−	0.0783632i
$583$	−3.38557	+	3.38557i	−0.140216	+	0.140216i
$584$	−7.79281			−0.322469
$585$	−4.93115	−	2.95551i	−0.203878	−	0.122195i
$586$	21.5901			0.891881
$587$	−3.85573	+	3.85573i	−0.159143	+	0.159143i	−0.782187	−	0.623044i	$-0.785896\pi$
$587$	−3.85573	+	3.85573i	−0.159143	+	0.159143i	0.623044	+	0.782187i	$0.285896\pi$
$588$	0.00279049	+	0.00125020i	0.000115078	+	5.15572e-5i
$589$		−	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	0.989001	+	0.147910i	$0.0472546\pi$
$593$	27.6856	+	27.6856i	1.13691	+	1.13691i	0.147910	+	0.989001i	$0.452745\pi$
$594$	−1.65293	+	3.18884i	−0.0678207	+	0.130840i
$595$	−3.70388	−	1.94210i	−0.151844	−	0.0796183i
$596$		−	0.0239830i		−	0.000982382i
$597$	2.90108	−	6.47535i	0.118733	−	0.265018i
$598$	−4.15616	+	4.15616i	−0.169958	+	0.169958i
$599$	43.2024			1.76520			0.882600	−	0.470124i	$-0.155791\pi$
$599$	43.2024			1.76520			0.882600	+	0.470124i	$0.155791\pi$
$600$	−13.8603	+	20.1871i	−0.565845	+	0.824137i
$601$	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
$603$	1.14446	−	20.0518i	0.0466062	−	0.816571i
$604$			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	0.945566	−	0.325429i	$-0.105509\pi$
$607$	15.2786	+	15.2786i	0.620137	+	0.620137i	−0.325429	+	0.945566i	$0.605509\pi$
$608$	−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
$612$	−0.000167475		0.00293428i	−6.76979e−6		0.000118611i
$613$	−4.86567	+	4.86567i	−0.196523	+	0.196523i	−0.798507	−	0.601985i	$-0.794377\pi$
$613$	−4.86567	+	4.86567i	−0.196523	+	0.196523i	0.601985	+	0.798507i	$0.294377\pi$
$614$	−25.6130			−1.03365
$615$	−21.6602	+	17.0429i	−0.873424	+	0.687237i
$616$	−3.26140			−0.131405
$617$	−16.5719	+	16.5719i	−0.667160	+	0.667160i	−0.957058	−	0.289897i	$-0.906379\pi$
$617$	−16.5719	+	16.5719i	−0.667160	+	0.667160i	0.289897	+	0.957058i	$0.406379\pi$
$618$	−4.58909	+	10.2431i	−0.184600	+	0.412036i
$619$			22.9117i			0.920899i	0.887686	+	0.460450i	$0.152312\pi$
$619$			22.9117i			0.920899i	−0.887686	+	0.460450i	$0.847688\pi$
$620$	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
$627$	1.12851	+	0.505594i	0.0450683	+	0.0201915i
$628$	0.0198607	−	0.0198607i	0.000792527	−	0.000792527i
$629$	−5.86360			−0.233797
$630$	−5.44339	−	21.7297i	−0.216870	−	0.865733i
$631$	−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
$633$	1.49386	+	0.669278i	0.0593756	+	0.0266014i
$634$			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	$-0.0161160\pi$
$642$	8.03256	−	17.9290i	0.317020	−	0.707602i
$643$	27.8538	−	27.8538i	1.09845	−	1.09845i	0.103856	−	0.994592i	$-0.466882\pi$
$643$	27.8538	−	27.8538i	1.09845	−	1.09845i	0.994592	−	0.103856i	$-0.0331181\pi$
$644$	−0.0141504			−0.000557605
$645$	22.5425	+	2.68932i	0.887608	+	0.105892i
$646$	1.63771			0.0644349
$647$	8.41427	−	8.41427i	0.330799	−	0.330799i	−0.522091	−	0.852890i	$-0.674848\pi$
$647$	8.41427	−	8.41427i	0.330799	−	0.330799i	0.852890	+	0.522091i	$0.174848\pi$
$648$	19.9250	−	15.8302i	0.782727	−	0.621867i
$649$			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	$-0.390221\pi$
$653$	−15.4098	−	15.4098i	−0.603031	−	0.603031i	−0.941116	+	0.338085i	$0.890221\pi$
$654$	13.0692	+	34.2847i	0.511046	+	1.34064i
$655$	−14.0099	+	26.7189i	−0.547410	+	1.04399i
$656$			28.4828i			1.11207i
$657$	8.25464	+	0.471138i	0.322044	+	0.0183808i
$658$	−21.3005	+	21.3005i	−0.830382	+	0.830382i
$659$	−1.48765			−0.0579506			−0.0289753	−	0.999580i	$-0.509224\pi$
$659$	−1.48765			−0.0579506			−0.0289753	+	0.999580i	$0.509224\pi$
$660$	0.00144695	+	0.00183896i	5.63224e−5	+	7.15813e-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
$663$	0.480868	−	1.07332i	0.0186754	−	0.0416842i
$664$			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
$672$	−0.0260984	−	0.0116926i	−0.00100677	−	0.000451052i
$673$	9.80668	−	9.80668i	0.378020	−	0.378020i	−0.492367	−	0.870387i	$-0.663868\pi$
$673$	9.80668	−	9.80668i	0.378020	−	0.378020i	0.870387	+	0.492367i	$0.163868\pi$
$674$	−37.2470			−1.43470
$675$	15.9022	−	20.5456i	0.612076	−	0.790799i
$676$	0.0151660			0.000583308
$677$	25.2317	−	25.2317i	0.969733	−	0.969733i	−0.0298219	−	0.999555i	$-0.509494\pi$
$677$	25.2317	−	25.2317i	0.969733	−	0.969733i	0.999555	+	0.0298219i	$0.00949402\pi$
$678$	−1.91906	−	0.859776i	−0.0737010	−	0.0330195i
$679$			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	0.971331	+	0.237731i	$0.0764036\pi$
$683$	31.5979	+	31.5979i	1.20906	+	1.20906i	0.237731	+	0.971331i	$0.423596\pi$
$684$	0.00360786	+	0.00404463i	0.000137950	+	0.000154650i
$685$	36.9998	−	11.5455i	1.41369	−	0.441130i
$686$		−	28.1434i		−	1.07452i
$687$	16.3033	−	36.3896i	0.622009	−	1.38835i
$688$	16.5897	−	16.5897i	0.632475	−	0.632475i
$689$	8.39763			0.319924
$690$	−16.4251	−	20.8750i	−0.625294	−	0.794699i
$691$	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
$693$	3.45468	+	0.197178i	0.131233	+	0.00749016i
$694$			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	$0.944437\pi$
$702$	6.00481	−	1.90484i	0.226637	−	0.0718936i
$703$	−7.64603	+	7.64603i	−0.288375	+	0.288375i
$704$	−3.90660			−0.147236
$705$	−34.6912	−	4.13865i	−1.30654	−	0.155871i
$706$	−11.4059			−0.429267
$707$	−22.6177	+	22.6177i	−0.850625	+	0.850625i
$708$	−0.00833096	+	0.0185951i	−0.000313097	+	0.000698846i
$709$		−	37.0608i		−	1.39185i	−0.718115	−	0.695924i	$-0.754995\pi$
$709$		−	37.0608i		−	1.39185i	0.718115	−	0.695924i	$-0.245005\pi$
$710$	−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
$717$	13.6966	+	6.13636i	0.511510	+	0.229167i
$718$	−16.7902	+	16.7902i	−0.626603	+	0.626603i
$719$	−22.4294			−0.836477			−0.418238	−	0.908337i	$-0.637352\pi$
$719$	−22.4294			−0.836477			−0.418238	+	0.908337i	$0.637352\pi$
$720$	−6.52430	−	26.0446i	−0.243146	−	0.970627i
$721$	10.8132			0.402706
$722$	−16.8703	+	16.8703i	−0.627849	+	0.627849i
$723$	30.7861	+	13.7928i	1.14495	+	0.512959i
$724$			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	0.955087	−	0.296325i	$-0.0957610\pi$
$727$	17.7622	+	17.7622i	0.658763	+	0.658763i	−0.296325	+	0.955087i	$0.595761\pi$
$728$	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
$732$	−0.00319668	+	0.00713513i	−0.000118153	+	0.000263722i
$733$	14.5129	−	14.5129i	0.536046	−	0.536046i	−0.386319	−	0.922365i	$-0.626254\pi$
$733$	14.5129	−	14.5129i	0.536046	−	0.536046i	0.922365	+	0.386319i	$0.126254\pi$
$734$	50.3171			1.85724
$735$	4.34575	−	3.41937i	0.160296	−	0.126125i
$736$	−0.0339101			−0.00124994
$737$	2.31313	−	2.31313i	0.0852054	−	0.0852054i
$738$	1.72095	−	30.1522i	0.0633491	−	1.10992i
$739$			32.9388i			1.21167i	0.795589	+	0.605837i	$0.207162\pi$
$739$			32.9388i			1.21167i	−0.795589	+	0.605837i	$0.792838\pi$
$740$	−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	$-0.275612\pi$
$743$	−3.09833	−	3.09833i	−0.113667	−	0.113667i	−0.761652	+	0.647986i	$0.775612\pi$
$744$	−1.74445	−	4.57625i	−0.0639547	−	0.167773i
$745$	−38.4113	−	20.1407i	−1.40728	−	0.737897i
$746$		−	2.57496i		−	0.0942761i
$747$	0.0836355	−	1.46535i	0.00306006	−	0.0536143i
$748$	−0.000338493	0	0.000338493i	−1.23765e−5	0	1.23765e-5i
$749$	−18.9270			−0.691579
$750$	−12.8005	−	24.2200i	−0.467410	−	0.884390i
$751$	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
$753$	−4.72092	+	10.5373i	−0.172040	+	0.384001i
$754$		−	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	0.204233	−	0.978922i	$-0.434530\pi$
$757$	−21.3145	−	21.3145i	−0.774689	−	0.774689i	−0.978922	+	0.204233i	$0.934530\pi$
$758$	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	$0.916209\pi$
$762$	22.4325	+	10.0502i	0.812644	+	0.364080i
$763$	24.9949	−	24.9949i	0.904877	−	0.904877i
$764$	0.0301423			0.00109051
$765$	4.55891	+	2.73241i	0.164828	+	0.0987903i
$766$	−18.5764			−0.671192
$767$	5.76563	−	5.76563i	0.208185	−	0.208185i
$768$	−0.0469068	−	0.0210152i	−0.00169260	−	0.000758319i
$769$			38.8955i			1.40261i	0.712862	+	0.701304i	$0.247399\pi$
$769$			38.8955i			1.40261i	−0.712862	+	0.701304i	$0.752601\pi$
$770$	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	$-0.347804\pi$
$773$	−11.8920	−	11.8920i	−0.427727	−	0.427727i	−0.887853	+	0.460127i	$0.847804\pi$
$774$	−18.5643	+	16.5596i	−0.667282	+	0.595223i
$775$	−2.84354	−	4.11270i	−0.102143	−	0.147732i
$776$			5.33579i			0.191544i
$777$	−12.3713	+	27.6133i	−0.443818	+	0.990621i
$778$	−5.45352	+	5.45352i	−0.195518	+	0.195518i
$779$	−10.3978			−0.372540
$780$	0.000486173	−	0.00407521i	1.74078e−5	−	0.000145916i
$781$	0.0423041			0.00151376
$782$	3.84242	−	3.84242i	0.137405	−	0.137405i
$783$	0.340577	+	1.07363i	0.0121712	+	0.0383684i
$784$		−	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	0.959103	−	0.283059i	$-0.0913491\pi$
$787$	18.9654	+	18.9654i	0.676044	+	0.676044i	−0.283059	+	0.959103i	$0.591349\pi$
$788$	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
$792$	4.13813	+	0.236186i	0.147042	+	0.00839250i
$793$	2.21233	−	2.21233i	0.0785622	−	0.0785622i
$794$	−25.3007			−0.897888
$795$	−4.49558	+	37.6830i	−0.159442	+	1.33648i
$796$	0.00506534			0.000179536
$797$	−25.5972	+	25.5972i	−0.906701	+	0.906701i	−0.996004	−	0.0893038i	$-0.971536\pi$
$797$	−25.5972	+	25.5972i	−0.906701	+	0.906701i	0.0893038	+	0.996004i	$0.471536\pi$
$798$	3.45532	−	7.71242i	0.122317	−	0.273017i
$799$		−	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
$807$	25.5579	+	11.4504i	0.899680	+	0.403074i
$808$	−27.0922	+	27.0922i	−0.953100	+	0.953100i
$809$	−13.9192			−0.489372			−0.244686	−	0.969602i	$-0.578685\pi$
$809$	−13.9192			−0.489372			−0.244686	+	0.969602i	$0.578685\pi$
$810$	5.33305	+	27.9653i	0.187384	+	0.982601i
$811$	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
$813$	−43.7257	−	19.5900i	−1.53353	−	0.687050i
$814$		−	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	$0.869746\pi$
$822$	−17.3651	+	38.7596i	−0.605677	+	1.35190i
$823$	−22.5406	+	22.5406i	−0.785717	+	0.785717i	−0.980789	−	0.195072i	$-0.937506\pi$
$823$	−22.5406	+	22.5406i	−0.785717	+	0.785717i	0.195072	+	0.980789i	$0.437506\pi$
$824$	12.9524			0.451219
$825$	4.16042	−	0.773106i	0.144847	−	0.0269161i
$826$	31.7715			1.10547
$827$	1.41043	−	1.41043i	0.0490454	−	0.0490454i	−0.682159	−	0.731204i	$-0.738959\pi$
$827$	1.41043	−	1.41043i	0.0490454	−	0.0490454i	0.731204	+	0.682159i	$0.238959\pi$
$828$	0.0179543	+	0.00102475i	0.000623957	+	3.56127e-5i
$829$		−	33.0090i		−	1.14645i	−0.819398	−	0.573225i	$-0.805692\pi$
$829$		−	33.0090i		−	1.14645i	0.819398	−	0.573225i	$-0.194308\pi$
$830$	−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
$837$	1.57116	+	4.95292i	0.0543073	+	0.171198i
$838$	8.76691	−	8.76691i	0.302848	−	0.302848i
$839$	−37.0786			−1.28009			−0.640047	−	0.768336i	$-0.721085\pi$
$839$	−37.0786			−1.28009			−0.640047	+	0.768336i	$0.721085\pi$
$840$	−20.3158	+	15.9851i	−0.700961	+	0.551538i
$841$	−28.9530			−0.998380
$842$	−6.41548	+	6.41548i	−0.221092	+	0.221092i
$843$	−19.1850	+	42.8218i	−0.660767	+	1.47486i
$844$			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
$852$	0.000169211	0	7.58098e-5i	5.79707e−6	0	2.59720e-6i
$853$	37.3086	−	37.3086i	1.27742	−	1.27742i	0.335315	−	0.942106i	$-0.391157\pi$
$853$	37.3086	−	37.3086i	1.27742	−	1.27742i	0.942106	−	0.335315i	$-0.108843\pi$
$854$	12.1911			0.417169
$855$	9.50774	−	2.38173i	0.325158	−	0.0814535i
$856$	−22.6714			−0.774893
$857$	4.08616	−	4.08616i	0.139580	−	0.139580i	−0.633864	−	0.773444i	$-0.718532\pi$
$857$	4.08616	−	4.08616i	0.139580	−	0.139580i	0.773444	+	0.633864i	$0.218532\pi$
$858$	0.936386	+	0.419520i	0.0319677	+	0.0143222i
$859$		−	9.31165i		−	0.317709i	−0.987302	−	0.158855i	$-0.949220\pi$
$859$		−	9.31165i		−	0.317709i	0.987302	−	0.158855i	$-0.0507801\pi$
$860$	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	$-0.363988\pi$
$863$	−14.5615	−	14.5615i	−0.495680	−	0.495680i	−0.910090	+	0.414411i	$0.863988\pi$
$864$	0.0322675	+	0.0167258i	0.00109776	+	0.000569024i
$865$	3.42411	+	10.9733i	0.116423	+	0.373102i
$866$			33.2110i			1.12855i
$867$	11.5943	−	25.8790i	0.393763	−	0.878896i
$868$	0.00206388	−	0.00206388i	7.00527e−5	−	7.00527e-5i
$869$	4.37836			0.148526
$870$	1.17929	+	0.140689i	0.0399816	+	0.00476980i
$871$	−5.73754			−0.194409
$872$	29.9397	−	29.9397i	1.01389	−	1.01389i
$873$	0.322591	−	5.65201i	0.0109181	−	0.191292i
$874$		−	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	0.316933	−	0.948448i	$-0.397347\pi$
$877$	−18.7018	−	18.7018i	−0.631515	−	0.631515i	−0.948448	+	0.316933i	$0.897347\pi$
$878$	−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	$0.904791\pi$
$882$	−0.345279	+	6.04952i	−0.0116262	+	0.203698i
$883$	−35.1699	+	35.1699i	−1.18356	+	1.18356i	−0.204746	+	0.978815i	$0.565637\pi$
$883$	−35.1699	+	35.1699i	−1.18356	+	1.18356i	−0.978815	+	0.204746i	$0.934363\pi$
$884$	0.000839603	0		2.82389e−5	0
$885$	22.7857	+	28.9589i	0.765934	+	0.973442i
$886$	0.246554			0.00828313
$887$	18.3427	−	18.3427i	0.615887	−	0.615887i	−0.328587	−	0.944474i	$-0.606572\pi$
$887$	18.3427	−	18.3427i	0.615887	−	0.615887i	0.944474	+	0.328587i	$0.106572\pi$
$888$	−14.8187	+	33.0761i	−0.497284	+	1.10996i
$889$		−	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
$897$	−6.56745	−	2.94235i	−0.219281	−	0.0982422i
$898$	−5.58653	+	5.58653i	−0.186425	+	0.186425i
$899$	0.216767			0.00722959
$900$	0.0180266	+	0.00436324i	0.000600886	+	0.000145441i
$901$	−7.76371			−0.258647
$902$	3.47830	−	3.47830i	0.115815	−	0.115815i
$903$	21.8715	+	9.79886i	0.727838	+	0.326086i
$904$			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	0.120708	−	0.992688i	$-0.461484\pi$
$907$	−26.2609	−	26.2609i	−0.871980	−	0.871980i	−0.992688	+	0.120708i	$0.961484\pi$
$908$	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	$0.936365\pi$
$912$	4.14145	−	9.24389i	0.137137	−	0.306096i
$913$	0.169040	−	0.169040i	0.00559440	−	0.00559440i
$914$	37.4799			1.23972
$915$	8.74313	+	11.1118i	0.289039	+	0.367346i
$916$	0.0284658			0.000940536
$917$	−22.5205	+	22.5205i	−0.743692	+	0.743692i
$918$	−5.55152	+	1.76105i	−0.183227	+	0.0581233i
$919$		−	26.1006i		−	0.860978i	−0.902596	−	0.430489i	$-0.858341\pi$
$919$		−	26.1006i		−	0.860978i	0.902596	−	0.430489i	$-0.141659\pi$
$920$	−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
$927$	−13.7201	−	0.783079i	−0.450626	−	0.0257197i
$928$	0.00107211	−	0.00107211i	3.51937e−5	−	3.51937e-5i
$929$	−15.4055			−0.505437			−0.252718	−	0.967540i	$-0.581325\pi$
$929$	−15.4055			−0.505437			−0.252718	+	0.967540i	$0.581325\pi$
$930$	5.44034	+	0.649033i	0.178396	+	0.0212826i
$931$	2.08614			0.0683705
$932$	0.0242584	−	0.0242584i	0.000794611	−	0.000794611i
$933$	−15.3420	+	34.2441i	−0.502276	+	1.12110i
$934$			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	−0.946782	−	0.321874i	$-0.895687\pi$
$937$	−38.8342	−	38.8342i	−1.26866	−	1.26866i	−0.321874	−	0.946782i	$-0.604313\pi$
$938$	−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	$-0.234382\pi$
$942$	50.7940	+	22.7567i	1.65496	+	0.741453i
$943$	−24.3955	+	24.3955i	−0.794425	+	0.794425i
$944$	38.0804			1.23941
$945$	22.4862	−	15.7042i	0.731477	−	0.510857i
$946$	−4.05184			−0.131737
$947$	−16.9664	+	16.9664i	−0.551332	+	0.551332i	−0.926825	−	0.375493i	$-0.877473\pi$
$947$	−16.9664	+	16.9664i	−0.551332	+	0.551332i	0.375493	+	0.926825i	$0.377473\pi$
$948$	0.0175129	+	0.00784613i	0.000568793	+	0.000254830i
$949$		−	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	$-0.400697\pi$
$953$	−19.9054	−	19.9054i	−0.644799	−	0.644799i	−0.951731	+	0.306932i	$0.900697\pi$
$954$	−27.6818	−	31.0330i	−0.896232	−	1.00473i
$955$	25.3132	−	48.2762i	0.819116	−	1.56218i
$956$			0.0107142i			0.000346522i
$957$	−0.0750081	+	0.167422i	−0.00242467	+	0.00541197i
$958$	36.3937	−	36.3937i	1.17583	−	1.17583i
$959$	40.9172			1.32129
$960$	−24.3349	+	19.1474i	−0.785405	+	0.617981i
$961$	1.00000			0.0322581
$962$	−6.34433	+	6.34433i	−0.204550	+	0.204550i
$963$	24.0150	+	1.37067i	0.773873	+	0.0441692i
$964$			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	0.851820	−	0.523834i	$-0.175499\pi$
$967$	10.1993	+	10.1993i	0.327986	+	0.327986i	−0.523834	+	0.851820i	$0.675499\pi$
$968$	−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	$0.683826\pi$
$972$	−0.0165792	−	0.00983091i	−0.000531777	−	0.000315327i
$973$	−2.53923	+	2.53923i	−0.0814038	+	0.0814038i
$974$	33.7731			1.08216
$975$	−6.11860	−	4.20098i	−0.195952	−	0.134539i
$976$	14.6119			0.467714
$977$	−16.2313	+	16.2313i	−0.519287	+	0.519287i	−0.917356	−	0.398069i	$-0.869681\pi$
$977$	−16.2313	+	16.2313i	−0.519287	+	0.519287i	0.398069	+	0.917356i	$0.369681\pi$
$978$	5.20266	−	11.6126i	0.166363	−	0.371329i
$979$			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	$-0.222634\pi$
$983$	3.80734	+	3.80734i	0.121435	+	0.121435i	−0.643777	+	0.765213i	$0.722634\pi$
$984$	−32.5660	+	12.4140i	−1.03817	+	0.395745i
$985$	47.5568	−	14.8397i	1.51529	−	0.472832i
$986$			0.242965i			0.00773758i
$987$	−33.6586	−	15.0797i	−1.07136	−	0.479993i
$988$	0.00109483	−	0.00109483i	3.48311e−5	−	3.48311e-5i
$989$	28.4180			0.903640
$990$	−2.38381	+	3.97730i	−0.0757625	+	0.126407i
$991$	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
$993$	26.0389	+	11.6660i	0.826321	+	0.370208i
$994$		−	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	0.676266	−	0.736658i	$-0.263597\pi$
$997$	−1.90689	−	1.90689i	−0.0603917	−	0.0603917i	−0.736658	+	0.676266i	$0.763597\pi$
$998$	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.32.9	✓	60
3.2	odd	2	inner	465.2.k.b.32.22	yes	60
5.3	odd	4	inner	465.2.k.b.218.22	yes	60
15.8	even	4	inner	465.2.k.b.218.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.9	✓	60	1.1	even	1	trivial
465.2.k.b.32.22	yes	60	3.2	odd	2	inner
465.2.k.b.218.9	yes	60	15.8	even	4	inner
465.2.k.b.218.22	yes	60	5.3	odd	4	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00031 + 1.00031i) q^{2} +(-1.58066 - 0.708168i) 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} +(-0.000875632 + 0.00195445i) q^{12} +(0.606001 - 0.606001i) q^{13} +3.33937 q^{14} +(2.39491 + 3.04375i) q^{15} +4.00247 q^{16} +(-0.560255 + 0.560255i) q^{17} +(-4.23706 - 0.241832i) 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} +(-1.57116 - 4.95292i) q^{27} +(-0.00206388 + 0.00206388i) q^{28} -0.216767 q^{29} +(-5.44034 - 0.649033i) q^{30} -1.00000 q^{31} +(-0.00494590 + 0.00494590i) q^{32} +(0.346031 - 0.772356i) 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} +(-5.27841 - 2.36483i) q^{42} +(4.14486 - 4.14486i) q^{43} +0.000604176 q^{44} +(-1.63007 - 6.50714i) q^{45} -6.85833 q^{46} +(-6.37862 + 6.37862i) q^{47} +(-6.32656 - 2.83442i) 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} +(1.03472 - 2.30955i) q^{57} +(0.216834 - 0.216834i) q^{58} +9.51422 q^{59} +(0.00376351 - 0.00296125i) q^{60} +3.65071 q^{61} +(1.00031 - 1.00031i) q^{62} +(0.403534 - 7.07017i) 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} +(0.483365 - 8.46887i) q^{72} +(1.94880 - 1.94880i) q^{73} -10.4692 q^{74} +(-1.58220 - 8.51450i) q^{75} +0.00180664 q^{76} +(0.815601 - 0.815601i) q^{77} +(0.858567 - 1.91636i) 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} +(0.342636 + 0.153508i) q^{87} +(0.976954 - 0.976954i) q^{88} +12.2175 q^{89} +(8.13972 + 4.87858i) q^{90} -2.02303 q^{91} +(0.00423877 - 0.00423877i) q^{92} +(1.58066 + 0.708168i) 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

Related objects

Downloads

Learn more