LMFDB - Embedded newform 666.2.k.a.175.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.19
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.67441 + 0.443112i) q^{3} -1.00000 q^{4} -4.41362i q^{5} +(0.443112 - 1.67441i) q^{6} +(1.98016 - 3.42973i) q^{7} +1.00000i q^{8} +(2.60730 + 1.48390i) q^{9} -4.41362 q^{10} +(-0.0240994 - 0.0417415i) q^{11} +(-1.67441 - 0.443112i) q^{12} +5.39546i q^{13} +(-3.42973 - 1.98016i) q^{14} +(1.95573 - 7.39021i) q^{15} +1.00000 q^{16} +(-5.31505 - 3.06865i) q^{17} +(1.48390 - 2.60730i) q^{18} +(-0.908762 + 0.524674i) q^{19} +4.41362i q^{20} +(4.83535 - 4.86535i) q^{21} +(-0.0417415 + 0.0240994i) q^{22} +(4.81699 + 2.78109i) q^{23} +(-0.443112 + 1.67441i) q^{24} -14.4800 q^{25} +5.39546 q^{26} +(3.70816 + 3.63999i) q^{27} +(-1.98016 + 3.42973i) q^{28} +(-3.42495 + 1.97740i) q^{29} +(-7.39021 - 1.95573i) q^{30} +(5.20190 + 3.00332i) q^{31} -1.00000i q^{32} +(-0.0218562 - 0.0805711i) q^{33} +(-3.06865 + 5.31505i) q^{34} +(-15.1375 - 8.73966i) q^{35} +(-2.60730 - 1.48390i) q^{36} +(5.48149 + 2.63690i) q^{37} +(0.524674 + 0.908762i) q^{38} +(-2.39079 + 9.03421i) q^{39} +4.41362 q^{40} +4.79219 q^{41} +(-4.86535 - 4.83535i) q^{42} +(-2.18070 + 1.25903i) q^{43} +(0.0240994 + 0.0417415i) q^{44} +(6.54938 - 11.5076i) q^{45} +(2.78109 - 4.81699i) q^{46} +(-2.90046 - 5.02374i) q^{47} +(1.67441 + 0.443112i) q^{48} +(-4.34205 - 7.52065i) q^{49} +14.4800i q^{50} +(-7.53982 - 7.49334i) q^{51} -5.39546i q^{52} +(4.35744 - 7.54731i) q^{53} +(3.63999 - 3.70816i) q^{54} +(-0.184231 + 0.106366i) q^{55} +(3.42973 + 1.98016i) q^{56} +(-1.75413 + 0.475836i) q^{57} +(1.97740 + 3.42495i) q^{58} +(2.01654 - 1.16425i) q^{59} +(-1.95573 + 7.39021i) q^{60} +(3.21374 + 1.85545i) q^{61} +(3.00332 - 5.20190i) q^{62} +(10.2523 - 6.00400i) q^{63} -1.00000 q^{64} +23.8135 q^{65} +(-0.0805711 + 0.0218562i) q^{66} +10.6630 q^{67} +(5.31505 + 3.06865i) q^{68} +(6.83329 + 6.79116i) q^{69} +(-8.73966 + 15.1375i) q^{70} +(-4.73531 - 8.20180i) q^{71} +(-1.48390 + 2.60730i) q^{72} -10.4334 q^{73} +(2.63690 - 5.48149i) q^{74} +(-24.2455 - 6.41627i) q^{75} +(0.908762 - 0.524674i) q^{76} -0.190883 q^{77} +(9.03421 + 2.39079i) q^{78} +(-6.04185 - 3.48826i) q^{79} -4.41362i q^{80} +(4.59607 + 7.73797i) q^{81} -4.79219i q^{82} +2.00537 q^{83} +(-4.83535 + 4.86535i) q^{84} +(-13.5438 + 23.4586i) q^{85} +(1.25903 + 2.18070i) q^{86} +(-6.61098 + 1.79334i) q^{87} +(0.0417415 - 0.0240994i) q^{88} +(7.63221 + 4.40646i) q^{89} +(-11.5076 - 6.54938i) q^{90} +(18.5050 + 10.6839i) q^{91} +(-4.81699 - 2.78109i) q^{92} +(7.37931 + 7.33381i) q^{93} +(-5.02374 + 2.90046i) q^{94} +(2.31571 + 4.01093i) q^{95} +(0.443112 - 1.67441i) q^{96} +(-3.70760 + 2.14058i) q^{97} +(-7.52065 + 4.34205i) q^{98} +(-0.000894313 - 0.144594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.67441	+	0.443112i	0.966722	+	0.255831i
$3$	1.67441	+	0.443112i	0.966722	+	0.255831i
$4$	−1.00000			−0.500000
$5$		−	4.41362i		−	1.97383i	−0.161242	−	0.986915i	$-0.551550\pi$
$5$		−	4.41362i		−	1.97383i	0.161242	−	0.986915i	$-0.448450\pi$
$6$	0.443112	−	1.67441i	0.180900	−	0.683575i
$7$	1.98016	−	3.42973i	0.748429	−	1.29632i	−0.200146	−	0.979766i	$-0.564142\pi$
$7$	1.98016	−	3.42973i	0.748429	−	1.29632i	0.948575	−	0.316551i	$-0.102525\pi$
$8$			1.00000i			0.353553i
$9$	2.60730	+	1.48390i	0.869101	+	0.494634i
$10$	−4.41362			−1.39571
$11$	−0.0240994	−	0.0417415i	−0.00726626	−	0.0125855i	0.862369	−	0.506280i	$-0.168980\pi$
$11$	−0.0240994	−	0.0417415i	−0.00726626	−	0.0125855i	−0.869636	+	0.493694i	$0.835646\pi$
$12$	−1.67441	−	0.443112i	−0.483361	−	0.127915i
$13$			5.39546i			1.49643i	0.663456	+	0.748215i	$0.269089\pi$
$13$			5.39546i			1.49643i	−0.663456	+	0.748215i	$0.730911\pi$
$14$	−3.42973	−	1.98016i	−0.916635	−	0.529219i
$15$	1.95573	−	7.39021i	0.504966	−	1.90814i
$16$	1.00000			0.250000
$17$	−5.31505	−	3.06865i	−1.28909	−	0.744256i	−0.310597	−	0.950542i	$-0.600529\pi$
$17$	−5.31505	−	3.06865i	−1.28909	−	0.744256i	−0.978492	+	0.206286i	$0.933862\pi$
$18$	1.48390	−	2.60730i	0.349759	−	0.614547i
$19$	−0.908762	+	0.524674i	−0.208484	+	0.120368i	−0.600607	−	0.799545i	$-0.705074\pi$
$19$	−0.908762	+	0.524674i	−0.208484	+	0.120368i	0.392123	+	0.919913i	$0.371741\pi$
$20$			4.41362i			0.986915i
$21$	4.83535	−	4.86535i	1.05516	−	1.06171i
$22$	−0.0417415	+	0.0240994i	−0.00889931	+	0.00513802i
$23$	4.81699	+	2.78109i	1.00441	+	0.579898i	0.909551	−	0.415593i	$-0.136426\pi$
$23$	4.81699	+	2.78109i	1.00441	+	0.579898i	0.0948616	+	0.995490i	$0.469759\pi$
$24$	−0.443112	+	1.67441i	−0.0904498	+	0.341788i
$25$	−14.4800			−2.89600
$26$	5.39546			1.05814
$27$	3.70816	+	3.63999i	0.713636	+	0.700516i
$28$	−1.98016	+	3.42973i	−0.374215	+	0.648159i
$29$	−3.42495	+	1.97740i	−0.635997	+	0.367193i	−0.783071	−	0.621932i	$-0.786348\pi$
$29$	−3.42495	+	1.97740i	−0.635997	+	0.367193i	0.147074	+	0.989126i	$0.453015\pi$
$30$	−7.39021	−	1.95573i	−1.34926	−	0.357065i
$31$	5.20190	+	3.00332i	0.934288	+	0.539412i	0.888165	−	0.459524i	$-0.151980\pi$
$31$	5.20190	+	3.00332i	0.934288	+	0.539412i	0.0461231	+	0.998936i	$0.485313\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.0218562	−	0.0805711i	−0.00380468	−	0.0140256i
$34$	−3.06865	+	5.31505i	−0.526268	+	0.911524i
$35$	−15.1375	−	8.73966i	−2.55871	−	1.47727i
$36$	−2.60730	−	1.48390i	−0.434551	−	0.247317i
$37$	5.48149	+	2.63690i	0.901152	+	0.433504i
$37$	5.48149	+	2.63690i	0.901152	+	0.433504i
$38$	0.524674	+	0.908762i	0.0851133	+	0.147421i
$39$	−2.39079	+	9.03421i	−0.382833	+	1.44663i
$40$	4.41362			0.697854
$41$	4.79219			0.748414			0.374207	−	0.927345i	$-0.377915\pi$
$41$	4.79219			0.748414			0.374207	+	0.927345i	$0.377915\pi$
$42$	−4.86535	−	4.83535i	−0.750740	−	0.746111i
$43$	−2.18070	+	1.25903i	−0.332554	+	0.192000i	−0.656975	−	0.753913i	$-0.728164\pi$
$43$	−2.18070	+	1.25903i	−0.332554	+	0.192000i	0.324420	+	0.945913i	$0.394831\pi$
$44$	0.0240994	+	0.0417415i	0.00363313	+	0.00629276i
$45$	6.54938	−	11.5076i	0.976324	−	1.71546i
$46$	2.78109	−	4.81699i	0.410050	−	0.710227i
$47$	−2.90046	−	5.02374i	−0.423076	−	0.732788i	0.573163	−	0.819441i	$-0.305716\pi$
$47$	−2.90046	−	5.02374i	−0.423076	−	0.732788i	−0.996239	+	0.0866530i	$0.972383\pi$
$48$	1.67441	+	0.443112i	0.241680	+	0.0639577i
$49$	−4.34205	−	7.52065i	−0.620292	−	1.07438i
$50$			14.4800i			2.04778i
$51$	−7.53982	−	7.49334i	−1.05579	−	1.04928i
$52$		−	5.39546i		−	0.748215i
$53$	4.35744	−	7.54731i	0.598541	−	1.03670i	−0.394496	−	0.918898i	$-0.629081\pi$
$53$	4.35744	−	7.54731i	0.598541	−	1.03670i	0.993037	−	0.117806i	$-0.0375860\pi$
$54$	3.63999	−	3.70816i	0.495340	−	0.504617i
$55$	−0.184231	+	0.106366i	−0.0248417	+	0.0143424i
$56$	3.42973	+	1.98016i	0.458317	+	0.264610i
$57$	−1.75413	+	0.475836i	−0.232340	+	0.0630261i
$58$	1.97740	+	3.42495i	0.259645	+	0.449718i
$59$	2.01654	−	1.16425i	0.262531	−	0.151573i	−0.362957	−	0.931806i	$-0.618233\pi$
$59$	2.01654	−	1.16425i	0.262531	−	0.151573i	0.625489	+	0.780233i	$0.284900\pi$
$60$	−1.95573	+	7.39021i	−0.252483	+	0.954072i
$61$	3.21374	+	1.85545i	0.411477	+	0.237566i	0.691424	−	0.722449i	$-0.256984\pi$
$61$	3.21374	+	1.85545i	0.411477	+	0.237566i	−0.279947	+	0.960015i	$0.590317\pi$
$62$	3.00332	−	5.20190i	0.381422	−	0.660642i
$63$	10.2523	−	6.00400i	1.29166	−	0.756432i
$64$	−1.00000			−0.125000
$65$	23.8135			2.95370
$66$	−0.0805711	+	0.0218562i	−0.00991762	+	0.00269032i
$67$	10.6630			1.30269			0.651345	−	0.758782i	$-0.274205\pi$
$67$	10.6630			1.30269			0.651345	+	0.758782i	$0.274205\pi$
$68$	5.31505	+	3.06865i	0.644544	+	0.372128i
$69$	6.83329	+	6.79116i	0.822631	+	0.817559i
$70$	−8.73966	+	15.1375i	−1.04459	+	1.80928i
$71$	−4.73531	−	8.20180i	−0.561978	−	0.973375i	−0.997324	−	0.0731115i	$-0.976707\pi$
$71$	−4.73531	−	8.20180i	−0.561978	−	0.973375i	0.435345	−	0.900263i	$-0.356626\pi$
$72$	−1.48390	+	2.60730i	−0.174880	+	0.307274i
$73$	−10.4334			−1.22114			−0.610569	−	0.791963i	$-0.709059\pi$
$73$	−10.4334			−1.22114			−0.610569	+	0.791963i	$0.709059\pi$
$74$	2.63690	−	5.48149i	0.306534	−	0.637210i
$75$	−24.2455	−	6.41627i	−2.79963	−	0.740887i
$76$	0.908762	−	0.524674i	0.104242	−	0.0601842i
$77$	−0.190883			−0.0217531
$78$	9.03421	+	2.39079i	1.02292	+	0.270704i
$79$	−6.04185	−	3.48826i	−0.679761	−	0.392460i	0.120004	−	0.992773i	$-0.461709\pi$
$79$	−6.04185	−	3.48826i	−0.679761	−	0.392460i	−0.799765	+	0.600313i	$0.795043\pi$
$80$		−	4.41362i		−	0.493457i
$81$	4.59607	+	7.73797i	0.510674	+	0.859774i
$82$		−	4.79219i		−	0.529209i
$83$	2.00537			0.220118			0.110059	−	0.993925i	$-0.464896\pi$
$83$	2.00537			0.220118			0.110059	+	0.993925i	$0.464896\pi$
$84$	−4.83535	+	4.86535i	−0.527580	+	0.530853i
$85$	−13.5438	+	23.4586i	−1.46903	+	2.54444i
$86$	1.25903	+	2.18070i	0.135765	+	0.235151i
$87$	−6.61098	+	1.79334i	−0.708772	+	0.192266i
$88$	0.0417415	−	0.0240994i	0.00444966	−	0.00256901i
$89$	7.63221	+	4.40646i	0.809013	+	0.467084i	0.846613	−	0.532209i	$-0.178638\pi$
$89$	7.63221	+	4.40646i	0.809013	+	0.467084i	−0.0376001	+	0.999293i	$0.511971\pi$
$90$	−11.5076	−	6.54938i	−1.21301	−	0.690365i
$91$	18.5050	+	10.6839i	1.93985	+	1.11997i
$92$	−4.81699	−	2.78109i	−0.502206	−	0.289949i
$93$	7.37931	+	7.33381i	0.765199	+	0.760481i
$94$	−5.02374	+	2.90046i	−0.518160	+	0.299160i
$95$	2.31571	+	4.01093i	0.237587	+	0.411512i
$96$	0.443112	−	1.67441i	0.0452249	−	0.170894i
$97$	−3.70760	+	2.14058i	−0.376449	+	0.217343i	−0.676272	−	0.736652i	$-0.736406\pi$
$97$	−3.70760	+	2.14058i	−0.376449	+	0.217343i	0.299823	+	0.953995i	$0.403072\pi$
$98$	−7.52065	+	4.34205i	−0.759700	+	0.438613i
$99$	−0.000894313	−	0.144594i	−8.98818e−5	−	0.0145322i
$100$	14.4800			1.44800
$101$	3.74777	+	6.49133i	0.372917	+	0.645911i	0.990013	−	0.140977i	$-0.0450243\pi$
$101$	3.74777	+	6.49133i	0.372917	+	0.645911i	−0.617096	+	0.786888i	$0.711691\pi$
$102$	−7.49334	+	7.53982i	−0.741951	+	0.746554i
$103$	−7.86814	−	4.54267i	−0.775271	−	0.447603i	0.0594807	−	0.998229i	$-0.481056\pi$
$103$	−7.86814	−	4.54267i	−0.775271	−	0.447603i	−0.834752	+	0.550627i	$0.814389\pi$
$104$	−5.39546			−0.529068
$105$	−21.4738	−	21.3414i	−2.09563	−	2.08271i
$106$	−7.54731	−	4.35744i	−0.733060	−	0.423232i
$107$	6.25397	+	10.8322i	0.604594	+	1.04719i	0.992116	+	0.125327i	$0.0399979\pi$
$107$	6.25397	+	10.8322i	0.604594	+	1.04719i	−0.387522	+	0.921861i	$0.626669\pi$
$108$	−3.70816	−	3.63999i	−0.356818	−	0.350258i
$109$	0.932171	+	0.538189i	0.0892858	+	0.0515492i	0.543978	−	0.839099i	$-0.316917\pi$
$109$	0.932171	+	0.538189i	0.0892858	+	0.0515492i	−0.454692	+	0.890649i	$0.650251\pi$
$110$	0.106366	+	0.184231i	0.0101416	+	0.0175657i
$111$	8.00983	+	6.84417i	0.760259	+	0.649620i
$112$	1.98016	−	3.42973i	0.187107	−	0.324079i
$113$	3.36897	−	1.94507i	0.316926	−	0.182977i	−0.333096	−	0.942893i	$-0.608093\pi$
$113$	3.36897	−	1.94507i	0.316926	−	0.182977i	0.650021	+	0.759916i	$0.274760\pi$
$114$	0.475836	+	1.75413i	0.0445662	+	0.164289i
$115$	12.2747	−	21.2604i	1.14462	−	1.98254i
$116$	3.42495	−	1.97740i	0.317999	−	0.183597i
$117$	−8.00633	+	14.0676i	−0.740186	+	1.30055i
$118$	−1.16425	−	2.01654i	−0.107178	−	0.185638i
$119$	−21.0493	+	12.1528i	−1.92958	+	1.11405i
$120$	7.39021	+	1.95573i	0.674631	+	0.178533i
$121$	5.49884	−	9.52427i	0.499894	−	0.865843i
$122$	1.85545	−	3.21374i	0.167985	−	0.290958i
$123$	8.02409	+	2.12348i	0.723508	+	0.191467i
$124$	−5.20190	−	3.00332i	−0.467144	−	0.269706i
$125$			41.8412i			3.74239i
$126$	−6.00400	−	10.2523i	−0.534878	−	0.913344i
$127$	−6.36870	+	11.0309i	−0.565131	+	0.978835i	0.431907	+	0.901918i	$0.357841\pi$
$127$	−6.36870	+	11.0309i	−0.565131	+	0.978835i	−0.997038	+	0.0769166i	$0.975492\pi$
$128$			1.00000i			0.0883883i
$129$	−4.20928	+	1.14184i	−0.370607	+	0.100533i
$130$		−	23.8135i		−	2.08858i
$131$	−10.6553	+	6.15186i	−0.930961	+	0.537491i	−0.887116	−	0.461547i	$-0.847294\pi$
$131$	−10.6553	+	6.15186i	−0.930961	+	0.537491i	−0.0438459	+	0.999038i	$0.513961\pi$
$132$	0.0218562	+	0.0805711i	0.00190234	+	0.00701282i
$133$			4.15575i			0.360349i
$134$		−	10.6630i		−	0.921141i
$135$	16.0655	−	16.3664i	1.38270	−	1.40860i
$136$	3.06865	−	5.31505i	0.263134	−	0.455762i
$137$	2.76565	+	4.79025i	0.236286	+	0.409259i	0.959645	−	0.281213i	$-0.0907366\pi$
$137$	2.76565	+	4.79025i	0.236286	+	0.409259i	−0.723360	+	0.690471i	$0.757403\pi$
$138$	6.79116	−	6.83329i	0.578102	−	0.581688i
$139$	−2.35037	−	4.07096i	−0.199356	−	0.345294i	0.748964	−	0.662611i	$-0.230552\pi$
$139$	−2.35037	−	4.07096i	−0.199356	−	0.345294i	−0.948320	+	0.317316i	$0.897218\pi$
$140$	15.1375	+	8.73966i	1.27935	+	0.738636i
$141$	−2.63048	−	9.69704i	−0.221527	−	0.816638i
$142$	−8.20180	+	4.73531i	−0.688280	+	0.397379i
$143$	0.225214	−	0.130027i	0.0188334	−	0.0108734i
$144$	2.60730	+	1.48390i	0.217275	+	0.123659i
$145$	8.72747	+	15.1164i	0.724777	+	1.25535i
$146$			10.4334i			0.863475i
$147$	−3.93788	−	14.5167i	−0.324791	−	1.19731i
$148$	−5.48149	−	2.63690i	−0.450576	−	0.216752i
$149$	7.07493	−	12.2541i	0.579601	−	1.00390i	−0.415924	−	0.909399i	$-0.636542\pi$
$149$	7.07493	−	12.2541i	0.579601	−	1.00390i	0.995525	−	0.0944984i	$-0.0301247\pi$
$150$	−6.41627	+	24.2455i	−0.523886	+	1.97964i
$151$	−2.53024	+	4.38251i	−0.205908	+	0.356643i	−0.950422	−	0.310964i	$-0.899348\pi$
$151$	−2.53024	+	4.38251i	−0.205908	+	0.356643i	0.744514	+	0.667607i	$0.232682\pi$
$152$	−0.524674	−	0.908762i	−0.0425567	−	0.0737103i
$153$	−9.30438	−	15.8879i	−0.752214	−	1.28446i
$154$			0.190883i			0.0153818i
$155$	13.2555	−	22.9592i	1.06471	−	1.84413i
$156$	2.39079	−	9.03421i	0.191416	−	0.723316i
$157$	7.51560	+	13.0174i	0.599811	+	1.03890i	0.992849	+	0.119380i	$0.0380907\pi$
$157$	7.51560	+	13.0174i	0.599811	+	1.03890i	−0.393038	+	0.919522i	$0.628576\pi$
$158$	−3.48826	+	6.04185i	−0.277511	+	0.480664i
$159$	10.6405	−	10.7065i	0.843843	−	0.849078i
$160$	−4.41362			−0.348927
$161$	19.0768	−	11.0140i	1.50346	−	0.868025i
$162$	7.73797	−	4.59607i	0.607952	−	0.361101i
$163$	−8.80880	−	5.08576i	−0.689959	−	0.398348i	0.113638	−	0.993522i	$-0.463750\pi$
$163$	−8.80880	−	5.08576i	−0.689959	−	0.398348i	−0.803597	+	0.595174i	$0.797083\pi$
$164$	−4.79219			−0.374207
$165$	−0.355610	+	0.0964651i	−0.0276842	+	0.00750980i
$166$		−	2.00537i		−	0.155647i
$167$			19.2843i			1.49226i	0.665799	+	0.746131i	$0.268091\pi$
$167$			19.2843i			1.49226i	−0.665799	+	0.746131i	$0.731909\pi$
$168$	4.86535	+	4.83535i	0.375370	+	0.373056i
$169$	−16.1109			−1.23930
$170$	23.4586	+	13.5438i	1.79919	+	1.03876i
$171$	−3.14798	+	0.0194703i	−0.240732	+	0.00148893i
$172$	2.18070	−	1.25903i	0.166277	−	0.0960001i
$173$	0.730095			0.0555081			0.0277541	−	0.999615i	$-0.491164\pi$
$173$	0.730095			0.0555081			0.0277541	+	0.999615i	$0.491164\pi$
$174$	1.79334	+	6.61098i	0.135953	+	0.501177i
$175$	−28.6727	+	49.6626i	−2.16745	+	3.75414i
$176$	−0.0240994	−	0.0417415i	−0.00181656	−	0.00314638i
$177$	3.89241	−	1.05588i	0.292572	−	0.0793649i
$178$	4.40646	−	7.63221i	0.330278	−	0.572058i
$179$		−	12.9827i		−	0.970371i	−0.874411	−	0.485185i	$-0.838752\pi$
$179$		−	12.9827i		−	0.970371i	0.874411	−	0.485185i	$-0.161248\pi$
$180$	−6.54938	+	11.5076i	−0.488162	+	0.857729i
$181$	−5.12818	−	8.88228i	−0.381175	−	0.660214i	0.610056	−	0.792359i	$-0.291147\pi$
$181$	−5.12818	−	8.88228i	−0.381175	−	0.660214i	−0.991230	+	0.132144i	$0.957814\pi$
$182$	10.6839	−	18.5050i	0.791940	−	1.37168i
$183$	4.55895	+	4.53084i	0.337007	+	0.334929i
$184$	−2.78109	+	4.81699i	−0.205025	+	0.355113i
$185$	11.6383	−	24.1932i	0.855663	−	1.77872i
$186$	7.33381	−	7.37931i	0.537741	−	0.541077i
$187$			0.295811i			0.0216318i
$188$	2.90046	+	5.02374i	0.211538	+	0.366394i
$189$	19.8269	−	5.51026i	1.44220	−	0.400812i
$190$	4.01093	−	2.31571i	0.290983	−	0.167999i
$191$	−9.47690	+	5.47149i	−0.685724	+	0.395903i	−0.802008	−	0.597313i	$-0.796235\pi$
$191$	−9.47690	+	5.47149i	−0.685724	+	0.395903i	0.116284	+	0.993216i	$0.462902\pi$
$192$	−1.67441	−	0.443112i	−0.120840	−	0.0319788i
$193$	16.2249	+	9.36743i	1.16789	+	0.674282i	0.953182	−	0.302396i	$-0.0977865\pi$
$193$	16.2249	+	9.36743i	1.16789	+	0.674282i	0.214709	+	0.976678i	$0.431120\pi$
$194$	2.14058	+	3.70760i	0.153685	+	0.266190i
$195$	39.8735	+	10.5520i	2.85540	+	0.755647i
$196$	4.34205	+	7.52065i	0.310146	+	0.537189i
$197$	3.54437	−	6.13904i	0.252526	−	0.437388i	−0.711694	−	0.702489i	$-0.752072\pi$
$197$	3.54437	−	6.13904i	0.252526	−	0.437388i	0.964221	+	0.265101i	$0.0854053\pi$
$198$	−0.144594		0.000894313i	−0.0102758		6.35561e-5i
$199$			21.1169i			1.49694i	0.663171	+	0.748468i	$0.269210\pi$
$199$			21.1169i			1.49694i	−0.663171	+	0.748468i	$0.730790\pi$
$200$		−	14.4800i		−	1.02389i
$201$	17.8542	+	4.72489i	1.25934	+	0.333268i
$202$	6.49133	−	3.74777i	0.456728	−	0.263692i
$203$			15.6622i			1.09927i
$204$	7.53982	+	7.49334i	0.527893	+	0.524638i
$205$		−	21.1509i		−	1.47724i
$206$	−4.54267	+	7.86814i	−0.316503	+	0.548199i
$207$	8.43249	+	14.3991i	0.586099	+	1.00081i
$208$			5.39546i			0.374108i
$209$	0.0438013	+	0.0252887i	0.00302980	+	0.00174926i
$210$	−21.3414	+	21.4738i	−1.47270	+	1.48183i
$211$	1.50425	−	2.60544i	0.103557	−	0.179366i	−0.809591	−	0.586995i	$-0.800311\pi$
$211$	1.50425	−	2.60544i	0.103557	−	0.179366i	0.913148	+	0.407629i	$0.133644\pi$
$212$	−4.35744	+	7.54731i	−0.299270	+	0.518352i
$213$	−4.29454	−	15.8315i	−0.294257	−	1.08475i
$214$	10.8322	−	6.25397i	0.740473	−	0.427512i
$215$	5.55688	+	9.62479i	0.378976	+	0.656405i
$216$	−3.63999	+	3.70816i	−0.247670	+	0.252309i
$217$	20.6012	−	11.8941i	1.39850	−	0.807423i
$218$	0.538189	−	0.932171i	0.0364508	−	0.0631346i
$219$	−17.4698	−	4.62317i	−1.18050	−	0.312405i
$220$	0.184231	−	0.106366i	0.0124208	−	0.00717118i
$221$	16.5567	−	28.6771i	1.11373	−	1.92903i
$222$	6.84417	−	8.00983i	0.459351	−	0.537584i
$223$	3.63463	+	6.29537i	0.243393	+	0.421569i	0.961679	−	0.274179i	$-0.0884061\pi$
$223$	3.63463	+	6.29537i	0.243393	+	0.421569i	−0.718285	+	0.695749i	$0.755073\pi$
$224$	−3.42973	−	1.98016i	−0.229159	−	0.132305i
$225$	−37.7538	−	21.4869i	−2.51692	−	1.43246i
$226$	−1.94507	−	3.36897i	−0.129384	−	0.224100i
$227$	−14.7626	−	8.52318i	−0.979827	−	0.565703i	−0.0776089	−	0.996984i	$-0.524729\pi$
$227$	−14.7626	−	8.52318i	−0.979827	−	0.565703i	−0.902218	+	0.431281i	$0.858062\pi$
$228$	1.75413	−	0.475836i	0.116170	−	0.0315130i
$229$	9.61903			0.635643			0.317822	−	0.948150i	$-0.397049\pi$
$229$	9.61903			0.635643			0.317822	+	0.948150i	$0.397049\pi$
$230$	−21.2604	−	12.2747i	−1.40187	−	0.809368i
$231$	−0.319616	−	0.0845824i	−0.0210292	−	0.00556511i
$232$	−1.97740	−	3.42495i	−0.129822	−	0.224859i
$233$	−11.8465			−0.776087			−0.388044	−	0.921641i	$-0.626849\pi$
$233$	−11.8465			−0.776087			−0.388044	+	0.921641i	$0.626849\pi$
$234$	14.0676	+	8.00633i	0.919627	+	0.523390i
$235$	−22.1729	+	12.8015i	−1.44640	+	0.835079i
$236$	−2.01654	+	1.16425i	−0.131266	+	0.0757863i
$237$	−8.57084	−	8.51800i	−0.556736	−	0.553303i
$238$	12.1528	+	21.0493i	0.787749	+	1.36442i
$239$	−6.27782	+	3.62450i	−0.406079	+	0.234450i	−0.689103	−	0.724663i	$-0.741995\pi$
$239$	−6.27782	+	3.62450i	−0.406079	+	0.234450i	0.283025	+	0.959113i	$0.408662\pi$
$240$	1.95573	−	7.39021i	0.126242	−	0.477036i
$241$	13.2575	+	7.65425i	0.853994	+	0.493053i	0.861996	−	0.506915i	$-0.169214\pi$
$241$	13.2575	+	7.65425i	0.853994	+	0.493053i	−0.00800270	+	0.999968i	$0.502547\pi$
$242$	−9.52427	−	5.49884i	−0.612243	−	0.353479i
$243$	4.26692	+	14.9931i	0.273723	+	0.961809i
$244$	−3.21374	−	1.85545i	−0.205739	−	0.118783i
$245$	−33.1933	+	19.1641i	−2.12064	+	1.22435i
$246$	2.12348	−	8.02409i	0.135388	−	0.511597i
$247$	−2.83085	−	4.90318i	−0.180123	−	0.311982i
$248$	−3.00332	+	5.20190i	−0.190711	+	0.330321i
$249$	3.35782	+	0.888605i	0.212793	+	0.0563130i
$250$	41.8412			2.64627
$251$		−	7.23696i		−	0.456793i	−0.973568	−	0.228396i	$-0.926652\pi$
$251$		−	7.23696i		−	0.456793i	0.973568	−	0.228396i	$-0.0733482\pi$
$252$	−10.2523	+	6.00400i	−0.645832	+	0.378216i
$253$		−	0.268091i		−	0.0168547i
$254$	11.0309	+	6.36870i	0.692141	+	0.399608i
$255$	−33.0727	+	33.2779i	−2.07109	+	2.08394i
$256$	1.00000			0.0625000
$257$	−11.4423	+	6.60624i	−0.713754	+	0.412086i	−0.812449	−	0.583032i	$-0.801866\pi$
$257$	−11.4423	+	6.60624i	−0.713754	+	0.412086i	0.0986956	+	0.995118i	$0.468533\pi$
$258$	1.14184	+	4.20928i	0.0710877	+	0.262059i
$259$	19.8981	−	13.5786i	1.23641	−	0.843731i
$260$	−23.8135			−1.47685
$261$	−11.8642	+	0.0733797i	−0.734372	+	0.00454209i
$262$	6.15186	+	10.6553i	0.380063	+	0.658289i
$263$	0.282291	−	0.488942i	0.0174068	−	0.0301495i	−0.857191	−	0.514999i	$-0.827792\pi$
$263$	0.282291	−	0.488942i	0.0174068	−	0.0301495i	0.874598	+	0.484850i	$0.161126\pi$
$264$	0.0805711	−	0.0218562i	0.00495881	−	0.00134516i
$265$	−33.3110	−	19.2321i	−2.04628	−	1.18142i
$266$	4.15575			0.254805
$267$	10.8269	+	10.7601i	0.662596	+	0.658510i
$268$	−10.6630			−0.651345
$269$	1.45048			0.0884373			0.0442187	−	0.999022i	$-0.485920\pi$
$269$	1.45048			0.0884373			0.0442187	+	0.999022i	$0.485920\pi$
$270$	−16.3664	−	16.0655i	−0.996028	−	0.977717i
$271$	4.28623	−	7.42397i	0.260370	−	0.450974i	−0.705970	−	0.708241i	$-0.749489\pi$
$271$	4.28623	−	7.42397i	0.260370	−	0.450974i	0.966340	+	0.257267i	$0.0828221\pi$
$272$	−5.31505	−	3.06865i	−0.322272	−	0.186064i
$273$	26.2508	+	26.0889i	1.58877	+	1.57897i
$274$	4.79025	−	2.76565i	0.289389	−	0.167079i
$275$	0.348960	+	0.604417i	0.0210431	+	0.0364477i
$276$	−6.83329	−	6.79116i	−0.411316	−	0.408780i
$277$	−20.4460	−	11.8045i	−1.22848	−	0.709265i	−0.261770	−	0.965130i	$-0.584306\pi$
$277$	−20.4460	−	11.8045i	−1.22848	−	0.709265i	−0.966712	+	0.255865i	$0.917640\pi$
$278$	−4.07096	+	2.35037i	−0.244160	+	0.140966i
$279$	9.10630	+	15.5497i	0.545180	+	0.930934i
$280$	8.73966	−	15.1375i	0.522294	−	0.904641i
$281$		−	28.3282i		−	1.68992i	−0.534830	−	0.844960i	$-0.679624\pi$
$281$		−	28.3282i		−	1.68992i	0.534830	−	0.844960i	$-0.320376\pi$
$282$	−9.69704	+	2.63048i	−0.577450	+	0.156643i
$283$		−	16.4783i		−	0.979535i	−0.871853	−	0.489767i	$-0.837082\pi$
$283$		−	16.4783i		−	0.979535i	0.871853	−	0.489767i	$-0.162918\pi$
$284$	4.73531	+	8.20180i	0.280989	+	0.486687i
$285$	2.10016	+	7.74206i	0.124403	+	0.458600i
$286$	−0.130027	−	0.225214i	−0.00768869	−	0.0133172i
$287$	9.48929	−	16.4359i	0.560135	−	0.970182i
$288$	1.48390	−	2.60730i	0.0874398	−	0.153637i
$289$	10.3332	+	17.8976i	0.607834	+	1.05280i
$290$	15.1164	−	8.72747i	0.887667	−	0.512495i
$291$	−7.15656	+	1.94133i	−0.419525	+	0.113803i
$292$	10.4334			0.610569
$293$	−18.9457			−1.10682			−0.553411	−	0.832909i	$-0.686674\pi$
$293$	−18.9457			−1.10682			−0.553411	+	0.832909i	$0.686674\pi$
$294$	−14.5167	+	3.93788i	−0.846629	+	0.229662i
$295$	−5.13856	−	8.90025i	−0.299179	−	0.518192i
$296$	−2.63690	+	5.48149i	−0.153267	+	0.318605i
$297$	0.0625738	−	0.242506i	0.00363090	−	0.0140716i
$298$	−12.2541	−	7.07493i	−0.709863	−	0.409839i
$299$	−15.0053	+	25.9899i	−0.867777	+	1.50303i
$300$	24.2455	+	6.41627i	1.39981	+	0.370443i
$301$			9.97231i			0.574794i
$302$	4.38251	+	2.53024i	0.252185	+	0.145599i
$303$	3.39892	+	12.5298i	0.195263	+	0.719820i
$304$	−0.908762	+	0.524674i	−0.0521211	+	0.0300921i
$305$	8.18926	−	14.1842i	0.468916	−	0.812186i
$306$	−15.8879	+	9.30438i	−0.908251	+	0.531896i
$307$	5.17608			0.295414			0.147707	−	0.989031i	$-0.452811\pi$
$307$	5.17608			0.295414			0.147707	+	0.989031i	$0.452811\pi$
$308$	0.190883			0.0108766
$309$	−11.1616	−	11.0928i	−0.634961	−	0.631046i
$310$	−22.9592	−	13.2555i	−1.30399	−	0.752861i
$311$	−4.03486	+	2.32953i	−0.228796	+	0.132095i	−0.610017	−	0.792389i	$-0.708837\pi$
$311$	−4.03486	+	2.32953i	−0.228796	+	0.132095i	0.381220	+	0.924484i	$0.375504\pi$
$312$	−9.03421	−	2.39079i	−0.511461	−	0.135352i
$313$			8.08143i			0.456790i	0.973569	+	0.228395i	$0.0733477\pi$
$313$			8.08143i			0.456790i	−0.973569	+	0.228395i	$0.926652\pi$
$314$	13.0174	−	7.51560i	0.734615	−	0.424130i
$315$	−26.4993	−	45.2496i	−1.49307	−	2.54952i
$316$	6.04185	+	3.48826i	0.339880	+	0.196230i
$317$	−5.12630			−0.287922			−0.143961	−	0.989583i	$-0.545984\pi$
$317$	−5.12630			−0.287922			−0.143961	+	0.989583i	$0.545984\pi$
$318$	−10.7065	−	10.6405i	−0.600389	−	0.596687i
$319$	0.165079	+	0.0953083i	0.00924264	+	0.00533624i
$320$			4.41362i			0.246729i
$321$	5.67184	+	20.9087i	0.316571	+	1.16701i
$322$	−11.0140	−	19.0768i	−0.613786	−	1.06311i
$323$	6.44015			0.358340
$324$	−4.59607	−	7.73797i	−0.255337	−	0.429887i
$325$		−	78.1263i		−	4.33367i
$326$	−5.08576	+	8.80880i	−0.281674	+	0.487874i
$327$	1.32236	+	1.31421i	0.0731266	+	0.0726757i
$328$			4.79219i			0.264604i
$329$	−22.9735			−1.26657
$330$	0.0964651	+	0.355610i	0.00531023	+	0.0195757i
$331$			4.27485i			0.234967i	0.993075	+	0.117484i	$0.0374827\pi$
$331$			4.27485i			0.234967i	−0.993075	+	0.117484i	$0.962517\pi$
$332$	−2.00537			−0.110059
$333$	10.3790	+	15.0092i	0.568766	+	0.822499i
$334$	19.2843			1.05519
$335$		−	47.0623i		−	2.57129i
$336$	4.83535	−	4.86535i	0.263790	−	0.265427i
$337$	19.8340			1.08042			0.540212	−	0.841529i	$-0.318344\pi$
$337$	19.8340			1.08042			0.540212	+	0.841529i	$0.318344\pi$
$338$			16.1109i			0.876320i
$339$	6.50292	−	1.76402i	0.353190	−	0.0958086i
$340$	13.5438	−	23.4586i	0.734517	−	1.27222i
$341$		−	0.289513i		−	0.0156780i
$342$	0.0194703	+	3.14798i	0.00105283	+	0.170223i
$343$	−6.66954			−0.360121
$344$	−1.25903	−	2.18070i	−0.0678823	−	0.117576i
$345$	29.9736	−	30.1595i	1.61372	−	1.62373i
$346$		−	0.730095i		−	0.0392502i
$347$	−15.7626	−	9.10054i	−0.846181	−	0.488543i	0.0131797	−	0.999913i	$-0.495805\pi$
$347$	−15.7626	−	9.10054i	−0.846181	−	0.488543i	−0.859360	+	0.511371i	$0.829138\pi$
$348$	6.61098	−	1.79334i	0.354386	−	0.0961330i
$349$	−0.117144			−0.00627055			−0.00313527	−	0.999995i	$-0.500998\pi$
$349$	−0.117144			−0.00627055			−0.00313527	+	0.999995i	$0.500998\pi$
$350$	49.6626	+	28.6727i	2.65458	+	1.53262i
$351$	−19.6394	+	20.0072i	−1.04827	+	1.06791i
$352$	−0.0417415	+	0.0240994i	−0.00222483	+	0.00128450i
$353$			10.8262i			0.576220i	0.957597	+	0.288110i	$0.0930269\pi$
$353$			10.8262i			0.576220i	−0.957597	+	0.288110i	$0.906973\pi$
$354$	−1.05588	−	3.89241i	−0.0561195	−	0.206879i
$355$	−36.1996	+	20.8999i	−1.92128	+	1.10925i
$356$	−7.63221	−	4.40646i	−0.404506	−	0.233542i
$357$	−40.6302	+	11.0216i	−2.15038	+	0.583325i
$358$	−12.9827			−0.686156
$359$	−24.9160			−1.31502			−0.657509	−	0.753447i	$-0.728390\pi$
$359$	−24.9160			−1.31502			−0.657509	+	0.753447i	$0.728390\pi$
$360$	11.5076	+	6.54938i	0.606506	+	0.345183i
$361$	−8.94943	+	15.5009i	−0.471023	+	0.815836i
$362$	−8.88228	+	5.12818i	−0.466842	+	0.269531i
$363$	13.4276	−	13.5109i	0.704768	−	0.709140i
$364$	−18.5050	−	10.6839i	−0.969924	−	0.559986i
$365$			46.0491i			2.41032i
$366$	4.53084	−	4.55895i	0.236831	−	0.238300i
$367$	4.48554	−	7.76919i	0.234143	−	0.405548i	−0.724880	−	0.688875i	$-0.758105\pi$
$367$	4.48554	−	7.76919i	0.234143	−	0.405548i	0.959023	+	0.283327i	$0.0914381\pi$
$368$	4.81699	+	2.78109i	0.251103	+	0.144974i
$369$	12.4947	+	7.11114i	0.650448	+	0.370191i
$370$	−24.1932	−	11.6383i	−1.25774	−	0.605045i
$371$	−17.2568	−	29.8897i	−0.895931	−	1.55180i
$372$	−7.37931	−	7.33381i	−0.382599	−	0.380240i
$373$	29.0842			1.50592			0.752961	−	0.658065i	$-0.228625\pi$
$373$	29.0842			1.50592			0.752961	+	0.658065i	$0.228625\pi$
$374$	0.295811			0.0152960
$375$	−18.5403	+	70.0593i	−0.957418	+	3.61785i
$376$	5.02374	−	2.90046i	0.259080	−	0.149580i
$377$	−10.6690	−	18.4792i	−0.549479	−	0.951726i
$378$	−5.51026	−	19.8269i	−0.283417	−	1.01979i
$379$	11.8465	−	20.5188i	0.608514	−	1.05398i	−0.382971	−	0.923760i	$-0.625099\pi$
$379$	11.8465	−	20.5188i	0.608514	−	1.05398i	0.991485	−	0.130217i	$-0.0415675\pi$
$380$	−2.31571	−	4.01093i	−0.118793	−	0.205756i
$381$	−15.5517	+	15.6482i	−0.796740	+	0.801683i
$382$	5.47149	+	9.47690i	0.279946	+	0.484880i
$383$			12.2836i			0.627664i	0.949478	+	0.313832i	$0.101613\pi$
$383$			12.2836i			0.627664i	−0.949478	+	0.313832i	$0.898387\pi$
$384$	−0.443112	+	1.67441i	−0.0226125	+	0.0854469i
$385$			0.842484i			0.0429369i
$386$	9.36743	−	16.2249i	0.476789	−	0.825824i
$387$	−7.55403	+	0.0467217i	−0.383993	+	0.00237500i
$388$	3.70760	−	2.14058i	0.188225	−	0.108672i
$389$	−17.5956	−	10.1588i	−0.892132	−	0.515073i	−0.0174927	−	0.999847i	$-0.505568\pi$
$389$	−17.5956	−	10.1588i	−0.892132	−	0.515073i	−0.874639	+	0.484774i	$0.838902\pi$
$390$	10.5520	−	39.8735i	0.534323	−	2.01908i
$391$	−17.0684	−	29.5633i	−0.863185	−	1.49508i
$392$	7.52065	−	4.34205i	0.379850	−	0.219306i
$393$	−20.5674	+	5.57924i	−1.03749	+	0.281435i
$394$	−6.13904	−	3.54437i	−0.309280	−	0.178563i
$395$	−15.3959	+	26.6664i	−0.774650	+	1.34173i
$396$	0.000894313		0.144594i	4.49409e−5		0.00726612i
$397$	15.6329			0.784590			0.392295	−	0.919839i	$-0.371681\pi$
$397$	15.6329			0.784590			0.392295	+	0.919839i	$0.371681\pi$
$398$	21.1169			1.05849
$399$	−1.84146	+	6.95843i	−0.0921883	+	0.348357i
$400$	−14.4800			−0.724001
$401$	12.2359	+	7.06440i	0.611032	+	0.352780i	0.773369	−	0.633956i	$-0.218570\pi$
$401$	12.2359	+	7.06440i	0.611032	+	0.352780i	−0.162337	+	0.986735i	$0.551903\pi$
$402$	4.72489	−	17.8542i	0.235656	−	0.890487i
$403$	−16.2043	+	28.0666i	−0.807192	+	1.39810i
$404$	−3.74777	−	6.49133i	−0.186458	−	0.322956i
$405$	34.1524	−	20.2853i	1.69705	−	1.00798i
$406$	15.6622			0.777303
$407$	−0.0220328	−	0.292353i	−0.00109212	−	0.0144914i
$408$	7.49334	−	7.53982i	0.370975	−	0.373277i
$409$	3.38525	−	1.95447i	0.167390	−	0.0966425i	−0.413965	−	0.910293i	$-0.635856\pi$
$409$	3.38525	−	1.95447i	0.167390	−	0.0966425i	0.581354	+	0.813650i	$0.302523\pi$
$410$	−21.1509			−1.04457
$411$	2.50822	+	9.24634i	0.123721	+	0.456088i
$412$	7.86814	+	4.54267i	0.387636	+	0.223801i
$413$		−	9.22160i		−	0.453765i
$414$	14.3991	−	8.43249i	0.707677	−	0.414434i
$415$		−	8.85095i		−	0.434476i
$416$	5.39546			0.264534
$417$	−2.13160	−	7.85794i	−0.104385	−	0.384805i
$418$	0.0252887	−	0.0438013i	0.00123691	−	0.00214239i
$419$	−7.46433	−	12.9286i	−0.364657	−	0.631604i	0.624064	−	0.781373i	$-0.285480\pi$
$419$	−7.46433	−	12.9286i	−0.364657	−	0.631604i	−0.988721	+	0.149769i	$0.952147\pi$
$420$	21.4738	+	21.3414i	1.04781	+	1.04135i
$421$	7.68983	−	4.43973i	0.374779	−	0.216379i	−0.300765	−	0.953698i	$-0.597242\pi$
$421$	7.68983	−	4.43973i	0.374779	−	0.216379i	0.675544	+	0.737319i	$0.263909\pi$
$422$	−2.60544	−	1.50425i	−0.126831	−	0.0732257i
$423$	−0.107634	−	17.4024i	−0.00523334	−	0.846135i
$424$	7.54731	+	4.35744i	0.366530	+	0.211616i
$425$	76.9620	+	44.4340i	3.73321	+	2.15537i
$426$	−15.8315	+	4.29454i	−0.767037	+	0.208071i
$427$	12.7274	−	7.34818i	0.615923	−	0.355603i
$428$	−6.25397	−	10.8322i	−0.302297	−	0.523594i
$429$	0.434718	−	0.117924i	0.0209884	−	0.00569344i
$430$	9.62479	−	5.55688i	0.464149	−	0.267976i
$431$	−28.6566	+	16.5449i	−1.38034	+	0.796940i	−0.992200	−	0.124659i	$-0.960216\pi$
$431$	−28.6566	+	16.5449i	−1.38034	+	0.796940i	−0.388142	+	0.921600i	$0.626883\pi$
$432$	3.70816	+	3.63999i	0.178409	+	0.175129i
$433$	−12.5598			−0.603587			−0.301794	−	0.953373i	$-0.597585\pi$
$433$	−12.5598			−0.603587			−0.301794	+	0.953373i	$0.597585\pi$
$434$	−11.8941	−	20.6012i	−0.570934	−	0.988887i
$435$	7.91511	+	29.1783i	0.379500	+	1.39899i
$436$	−0.932171	−	0.538189i	−0.0446429	−	0.0257746i
$437$	−5.83666			−0.279206
$438$	−4.62317	+	17.4698i	−0.220903	+	0.834740i
$439$	22.0708	+	12.7426i	1.05338	+	0.608171i	0.923594	−	0.383371i	$-0.125237\pi$
$439$	22.0708	+	12.7426i	1.05338	+	0.608171i	0.129788	+	0.991542i	$0.458570\pi$
$440$	−0.106366	−	0.184231i	−0.00507079	−	0.00878286i
$441$	−0.161130	−	26.0518i	−0.00767287	−	1.24056i
$442$	−28.6771	−	16.5567i	−1.36403	−	0.787524i
$443$	8.16738	+	14.1463i	0.388044	+	0.672111i	0.992186	−	0.124765i	$-0.0398176\pi$
$443$	8.16738	+	14.1463i	0.388044	+	0.672111i	−0.604143	+	0.796876i	$0.706484\pi$
$444$	−8.00983	−	6.84417i	−0.380130	−	0.324810i
$445$	19.4484	−	33.6857i	0.921944	−	1.59685i
$446$	6.29537	−	3.63463i	0.298095	−	0.172105i
$447$	17.2763	−	17.3835i	0.817140	−	0.822210i
$448$	−1.98016	+	3.42973i	−0.0935536	+	0.162040i
$449$	−6.47858	+	3.74041i	−0.305743	+	0.176521i	−0.645020	−	0.764166i	$-0.723151\pi$
$449$	−6.47858	+	3.74041i	−0.305743	+	0.176521i	0.339277	+	0.940687i	$0.389818\pi$
$450$	−21.4869	+	37.7538i	−1.01290	+	1.77973i
$451$	−0.115489	−	0.200033i	−0.00543817	−	0.00941918i
$452$	−3.36897	+	1.94507i	−0.158463	+	0.0914886i
$453$	−6.17861	+	6.21694i	−0.290296	+	0.292097i
$454$	−8.52318	+	14.7626i	−0.400013	+	0.692842i
$455$	47.1544	−	81.6739i	2.21063	−	3.82893i
$456$	−0.475836	−	1.75413i	−0.0222831	−	0.0821446i
$457$	−33.2159	−	19.1772i	−1.55377	−	0.897071i	−0.997830	−	0.0658502i	$-0.979024\pi$
$457$	−33.2159	−	19.1772i	−1.55377	−	0.897071i	−0.555943	−	0.831221i	$-0.687643\pi$
$458$		−	9.61903i		−	0.449468i
$459$	−8.53923	−	30.7258i	−0.398577	−	1.43416i
$460$	−12.2747	+	21.2604i	−0.572310	+	0.991270i
$461$			29.1926i			1.35964i	0.733381	+	0.679818i	$0.237941\pi$
$461$			29.1926i			1.35964i	−0.733381	+	0.679818i	$0.762059\pi$
$462$	−0.0845824	+	0.319616i	−0.00393513	+	0.0148699i
$463$			35.7048i			1.65934i	0.558254	+	0.829670i	$0.311472\pi$
$463$			35.7048i			1.65934i	−0.558254	+	0.829670i	$0.688528\pi$
$464$	−3.42495	+	1.97740i	−0.158999	+	0.0917983i
$465$	32.3686	−	32.5694i	1.50106	−	1.51037i
$466$			11.8465i			0.548777i
$467$			6.41563i			0.296880i	0.988921	+	0.148440i	$0.0474252\pi$
$467$			6.41563i			0.296880i	−0.988921	+	0.148440i	$0.952575\pi$
$468$	8.00633	−	14.0676i	0.370093	−	0.650275i
$469$	21.1144	−	36.5712i	0.974971	−	1.68870i
$470$	12.8015	+	22.1729i	0.590490	+	1.02276i
$471$	6.81604	+	25.1267i	0.314067	+	1.15778i
$472$	1.16425	+	2.01654i	0.0535890	+	0.0928189i
$473$	0.105107	+	0.0606838i	0.00483285	+	0.00279025i
$474$	−8.51800	+	8.57084i	−0.391245	+	0.393672i
$475$	13.1589	−	7.59729i	0.603771	−	0.348587i
$476$	21.0493	−	12.1528i	0.964792	−	0.557023i
$477$	22.5607	−	13.2121i	1.03298	−	0.604941i
$478$	3.62450	+	6.27782i	0.165781	+	0.287141i
$479$			27.4742i			1.25533i	0.778485	+	0.627663i	$0.215988\pi$
$479$			27.4742i			1.25533i	−0.778485	+	0.627663i	$0.784012\pi$
$480$	−7.39021	−	1.95573i	−0.337315	−	0.0892663i
$481$	−14.2273	+	29.5751i	−0.648708	+	1.34851i
$482$	7.65425	−	13.2575i	0.348641	−	0.603865i
$483$	36.8228	−	9.98880i	1.67550	−	0.454506i
$484$	−5.49884	+	9.52427i	−0.249947	+	0.432921i
$485$	9.44771	+	16.3639i	0.428998	+	0.743047i
$486$	14.9931	−	4.26692i	0.680101	−	0.193551i
$487$			16.4828i			0.746905i	0.927649	+	0.373453i	$0.121826\pi$
$487$			16.4828i			0.746905i	−0.927649	+	0.373453i	$0.878174\pi$
$488$	−1.85545	+	3.21374i	−0.0839924	+	0.145479i
$489$	−12.4960	−	12.4189i	−0.565088	−	0.561604i
$490$	19.1641	+	33.1933i	0.865747	+	1.49952i
$491$	6.75748	−	11.7043i	0.304961	−	0.528208i	−0.672292	−	0.740286i	$-0.734690\pi$
$491$	6.75748	−	11.7043i	0.304961	−	0.528208i	0.977253	+	0.212079i	$0.0680233\pi$
$492$	−8.02409	−	2.12348i	−0.361754	−	0.0957336i
$493$	24.2717			1.09314
$494$	−4.90318	+	2.83085i	−0.220605	+	0.127366i
$495$	−0.638182	+	0.00394716i	−0.0286842	+	0.000177411i
$496$	5.20190	+	3.00332i	0.233572	+	0.134853i
$497$	−37.5067			−1.68240
$498$	0.888605	−	3.35782i	0.0398193	−	0.150468i
$499$			23.1679i			1.03714i	0.855035	+	0.518570i	$0.173535\pi$
$499$			23.1679i			1.03714i	−0.855035	+	0.518570i	$0.826465\pi$
$500$		−	41.8412i		−	1.87119i
$501$	−8.54509	+	32.2898i	−0.381767	+	1.44260i
$502$	−7.23696			−0.323001
$503$	8.63382	+	4.98474i	0.384963	+	0.222259i	0.679975	−	0.733235i	$-0.261990\pi$
$503$	8.63382	+	4.98474i	0.384963	+	0.222259i	−0.295012	+	0.955493i	$0.595324\pi$
$504$	6.00400	+	10.2523i	0.267439	+	0.456672i
$505$	28.6502	−	16.5412i	1.27492	−	0.736074i
$506$	−0.268091			−0.0119181
$507$	−26.9763	−	7.13895i	−1.19806	−	0.317052i
$508$	6.36870	−	11.0309i	0.282565	−	0.489417i
$509$	3.45080	+	5.97696i	0.152954	+	0.264924i	0.932312	−	0.361655i	$-0.117788\pi$
$509$	3.45080	+	5.97696i	0.152954	+	0.264924i	−0.779358	+	0.626579i	$0.784455\pi$
$510$	33.2779	+	33.0727i	1.47357	+	1.46448i
$511$	−20.6598	+	35.7838i	−0.913935	+	1.58298i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.27964	−	1.36231i	−0.233102	−	0.0601473i
$514$	6.60624	+	11.4423i	0.291389	+	0.504700i
$515$	−20.0496	+	34.7270i	−0.883492	+	1.53025i
$516$	4.20928	−	1.14184i	0.185303	−	0.0502666i
$517$	−0.139799	+	0.242139i	−0.00614835	+	0.0106493i
$518$	−13.5786	−	19.8981i	−0.596608	−	0.874272i
$519$	1.22248	+	0.323514i	0.0536609	+	0.0142007i
$520$			23.8135i			1.04429i
$521$	15.6166	+	27.0487i	0.684174	+	1.18502i	0.973696	+	0.227853i	$0.0731705\pi$
$521$	15.6166	+	27.0487i	0.684174	+	1.18502i	−0.289521	+	0.957172i	$0.593496\pi$
$522$	0.0733797	+	11.8642i	0.00321174	+	0.519280i
$523$	20.3465	−	11.7471i	0.889691	−	0.513663i	0.0158497	−	0.999874i	$-0.494955\pi$
$523$	20.3465	−	11.7471i	0.889691	−	0.513663i	0.873841	+	0.486211i	$0.161621\pi$
$524$	10.6553	−	6.15186i	0.465481	−	0.268745i
$525$	−70.0160	+	70.4504i	−3.05575	+	3.07471i
$526$	−0.488942	−	0.282291i	−0.0213189	−	0.0123085i
$527$	−18.4322	−	31.9256i	−0.802921	−	1.39070i
$528$	−0.0218562	−	0.0805711i	−0.000951171	−	0.00350641i
$529$	3.96894	+	6.87441i	0.172563	+	0.298888i
$530$	−19.2321	+	33.3110i	−0.835389	+	1.44694i
$531$	6.98537	−	0.0432045i	0.303139	−	0.00187492i
$532$		−	4.15575i		−	0.180174i
$533$			25.8560i			1.11995i
$534$	10.7601	−	10.8269i	0.465637	−	0.468526i
$535$	47.8091	−	27.6026i	2.06697	−	1.19337i
$536$			10.6630i			0.460571i
$537$	5.75278	−	21.7383i	0.248251	−	0.938078i
$538$		−	1.45048i		−	0.0625346i
$539$	−0.209282	+	0.362487i	−0.00901441	+	0.0156134i
$540$	−16.0655	+	16.3664i	−0.691350	+	0.704298i
$541$		−	22.9964i		−	0.988693i	−0.869265	−	0.494347i	$-0.835407\pi$
$541$		−	22.9964i		−	0.988693i	0.869265	−	0.494347i	$-0.164593\pi$
$542$	−7.42397	−	4.28623i	−0.318887	−	0.184109i
$543$	−4.65085	−	17.1449i	−0.199587	−	0.735760i
$544$	−3.06865	+	5.31505i	−0.131567	+	0.227881i
$545$	2.37536	−	4.11425i	0.101749	−	0.176235i
$546$	26.0889	−	26.2508i	1.11650	−	1.12343i
$547$	−34.9494	+	20.1780i	−1.49433	+	0.862750i	−0.999979	−	0.00651414i	$-0.997926\pi$
$547$	−34.9494	+	20.1780i	−1.49433	+	0.862750i	−0.494348	+	0.869264i	$0.664593\pi$
$548$	−2.76565	−	4.79025i	−0.118143	−	0.204629i
$549$	5.62588	+	9.60661i	0.240107	+	0.410000i
$550$	0.604417	−	0.348960i	0.0257724	−	0.0148797i
$551$	2.07498	−	3.59396i	0.0883969	−	0.153108i
$552$	−6.79116	+	6.83329i	−0.289051	+	0.290844i
$553$	−23.9276	+	13.8146i	−1.01751	+	0.587457i
$554$	−11.8045	+	20.4460i	−0.501526	+	0.868669i
$555$	30.2076	−	35.3523i	1.28224	−	1.50062i
$556$	2.35037	+	4.07096i	0.0996779	+	0.172647i
$557$	−26.1474	−	15.0962i	−1.10790	−	0.639646i	−0.169614	−	0.985510i	$-0.554252\pi$
$557$	−26.1474	−	15.0962i	−1.10790	−	0.639646i	−0.938284	+	0.345865i	$0.887586\pi$
$558$	15.5497	−	9.10630i	0.658270	−	0.385500i
$559$	−6.79304	−	11.7659i	−0.287315	−	0.497644i
$560$	−15.1375	−	8.73966i	−0.639677	−	0.369318i
$561$	−0.131077	+	0.495309i	−0.00553408	+	0.0209119i
$562$	−28.3282			−1.19495
$563$	−34.1183	−	19.6982i	−1.43791	−	0.830181i	−0.440210	−	0.897895i	$-0.645096\pi$
$563$	−34.1183	−	19.6982i	−1.43791	−	0.830181i	−0.997705	+	0.0677142i	$0.978429\pi$
$564$	2.63048	+	9.69704i	0.110763	+	0.408319i
$565$	−8.58481	−	14.8693i	−0.361166	−	0.625557i
$566$	−16.4783			−0.692636
$567$	35.6401	−	0.440885i	1.49674	−	0.0185154i
$568$	8.20180	−	4.73531i	0.344140	−	0.198689i
$569$	13.2786	−	7.66638i	0.556666	−	0.321391i	−0.195140	−	0.980775i	$-0.562516\pi$
$569$	13.2786	−	7.66638i	0.556666	−	0.321391i	0.751806	+	0.659384i	$0.229183\pi$
$570$	7.74206	−	2.10016i	0.324279	−	0.0879660i
$571$	−4.21009	−	7.29210i	−0.176187	−	0.305165i	0.764384	−	0.644761i	$-0.223043\pi$
$571$	−4.21009	−	7.29210i	−0.176187	−	0.305165i	−0.940571	+	0.339596i	$0.889710\pi$
$572$	−0.225214	+	0.130027i	−0.00941668	+	0.00543672i
$573$	−18.2927	+	4.96220i	−0.764189	+	0.207299i
$574$	−16.4359	−	9.48929i	−0.686022	−	0.396075i
$575$	−69.7501	−	40.2703i	−2.90878	−	1.67939i
$576$	−2.60730	−	1.48390i	−0.108638	−	0.0618293i
$577$	−17.9520	−	10.3646i	−0.747350	−	0.431483i	0.0773853	−	0.997001i	$-0.475343\pi$
$577$	−17.9520	−	10.3646i	−0.747350	−	0.431483i	−0.824736	+	0.565518i	$0.808676\pi$
$578$	17.8976	−	10.3332i	0.744441	−	0.429803i
$579$	23.0163	+	22.8743i	0.956523	+	0.950626i
$580$	−8.72747	−	15.1164i	−0.362388	−	0.627675i
$581$	3.97096	−	6.87790i	0.164743	−	0.285343i
$582$	1.94133	+	7.15656i	0.0804709	+	0.296649i
$583$	−0.420048			−0.0173966
$584$		−	10.4334i		−	0.431738i
$585$	62.0890	+	35.3369i	2.56706	+	1.46100i
$586$			18.9457i			0.782641i
$587$	−15.5892	−	9.00043i	−0.643435	−	0.371487i	0.142501	−	0.989795i	$-0.454485\pi$
$587$	−15.5892	−	9.00043i	−0.643435	−	0.371487i	−0.785937	+	0.618307i	$0.787819\pi$
$588$	3.93788	+	14.5167i	0.162396	+	0.598657i
$589$	−6.30305			−0.259713
$590$	−8.90025	+	5.13856i	−0.366417	+	0.211551i
$591$	8.65502	−	8.70871i	0.356020	−	0.358229i
$592$	5.48149	+	2.63690i	0.225288	+	0.108376i
$593$	−20.3794			−0.836884			−0.418442	−	0.908244i	$-0.637424\pi$
$593$	−20.3794			−0.836884			−0.418442	+	0.908244i	$0.637424\pi$
$594$	−0.242506	−	0.0625738i	−0.00995014	−	0.00256744i
$595$	53.6378	+	92.9034i	2.19894	+	3.80867i
$596$	−7.07493	+	12.2541i	−0.289800	+	0.501949i
$597$	−9.35714	+	35.3583i	−0.382962	+	1.44712i
$598$	25.9899	+	15.0053i	1.06280	+	0.613611i
$599$	18.5047			0.756080			0.378040	−	0.925789i	$-0.376598\pi$
$599$	18.5047			0.756080			0.378040	+	0.925789i	$0.376598\pi$
$600$	6.41627	−	24.2455i	0.261943	−	0.989819i
$601$	12.5323			0.511201			0.255601	−	0.966782i	$-0.417727\pi$
$601$	12.5323			0.511201			0.255601	+	0.966782i	$0.417727\pi$
$602$	9.97231			0.406441
$603$	27.8016	+	15.8228i	1.13217	+	0.644355i
$604$	2.53024	−	4.38251i	0.102954	−	0.178322i
$605$	−42.0365	−	24.2698i	−1.70903	−	0.986706i
$606$	12.5298	−	3.39892i	0.508989	−	0.138072i
$607$	−0.350174	+	0.202173i	−0.0142131	+	0.00820595i	−0.507090	−	0.861893i	$-0.669279\pi$
$607$	−0.350174	+	0.202173i	−0.0142131	+	0.00820595i	0.492877	+	0.870099i	$0.335945\pi$
$608$	0.524674	+	0.908762i	0.0212783	+	0.0368552i
$609$	−6.94012	+	26.2250i	−0.281228	+	1.06269i
$610$	−14.1842	−	8.18926i	−0.574302	−	0.331574i
$611$	27.1054	−	15.6493i	1.09657	−	0.633103i
$612$	9.30438	+	15.8879i	0.376107	+	0.642231i
$613$	−15.2659	+	26.4412i	−0.616582	+	1.06795i	0.373523	+	0.927621i	$0.378150\pi$
$613$	−15.2659	+	26.4412i	−0.616582	+	1.06795i	−0.990105	+	0.140330i	$0.955184\pi$
$614$		−	5.17608i		−	0.208890i
$615$	9.37221	−	35.4153i	0.377924	−	1.42808i
$616$		−	0.190883i		−	0.00769089i
$617$	−19.3887	−	33.5822i	−0.780559	−	1.35197i	−0.931617	−	0.363443i	$-0.881601\pi$
$617$	−19.3887	−	33.5822i	−0.780559	−	1.35197i	0.151058	−	0.988525i	$-0.451732\pi$
$618$	−11.0928	+	11.1616i	−0.446217	+	0.448985i
$619$	−18.6738	−	32.3439i	−0.750563	−	1.30001i	−0.947550	−	0.319607i	$-0.896449\pi$
$619$	−18.6738	−	32.3439i	−0.750563	−	1.30001i	0.196987	−	0.980406i	$-0.436884\pi$
$620$	−13.2555	+	22.9592i	−0.532353	+	0.922063i
$621$	7.73905	+	27.8465i	0.310557	+	1.11744i
$622$	2.32953	+	4.03486i	0.0934056	+	0.161783i
$623$	30.2260	−	17.4510i	1.21098	−	0.699158i
$624$	−2.39079	+	9.03421i	−0.0957082	+	0.361658i
$625$	112.271			4.49083
$626$	8.08143			0.322999
$627$	0.0621357	+	0.0617525i	0.00248146	+	0.00246616i
$628$	−7.51560	−	13.0174i	−0.299905	−	0.519451i
$629$	−21.0427	−	30.8360i	−0.839027	−	1.22951i
$630$	−45.2496	+	26.4993i	−1.80279	+	1.05576i
$631$	−31.2521	−	18.0434i	−1.24412	−	0.718296i	−0.274193	−	0.961675i	$-0.588411\pi$
$631$	−31.2521	−	18.0434i	−1.24412	−	0.718296i	−0.969931	+	0.243379i	$0.921744\pi$
$632$	3.48826	−	6.04185i	0.138756	−	0.240332i
$633$	3.67323	−	3.69602i	0.145998	−	0.146904i
$634$			5.12630i			0.203592i
$635$	48.6862	+	28.1090i	1.93205	+	1.11547i
$636$	−10.6405	+	10.7065i	−0.421922	+	0.424539i
$637$	40.5773	−	23.4273i	1.60773	−	0.928224i
$638$	0.0953083	−	0.165079i	0.00377329	−	0.00653553i
$639$	−0.175724	−	28.4113i	−0.00695154	−	1.12394i
$640$	4.41362			0.174464
$641$	−0.451545			−0.0178350			−0.00891748	−	0.999960i	$-0.502839\pi$
$641$	−0.451545			−0.0178350			−0.00891748	+	0.999960i	$0.502839\pi$
$642$	20.9087	−	5.67184i	0.825202	−	0.223850i
$643$	−30.3165	−	17.5032i	−1.19557	−	0.690260i	−0.236002	−	0.971752i	$-0.575837\pi$
$643$	−30.3165	−	17.5032i	−1.19557	−	0.690260i	−0.959564	+	0.281492i	$0.909171\pi$
$644$	−19.0768	+	11.0140i	−0.751732	+	0.434012i
$645$	5.03963	+	18.5782i	0.198435	+	0.731515i
$646$		−	6.44015i		−	0.253384i
$647$	12.3197	−	7.11279i	0.484338	−	0.279632i	−0.237885	−	0.971293i	$-0.576454\pi$
$647$	12.3197	−	7.11279i	0.484338	−	0.279632i	0.722222	+	0.691661i	$0.243121\pi$
$648$	−7.73797	+	4.59607i	−0.303976	+	0.180551i
$649$	−0.0971951	−	0.0561156i	−0.00381524	−	0.00220273i
$650$	−78.1263			−3.06437
$651$	39.7652	−	10.7870i	1.55852	−	0.422774i
$652$	8.80880	+	5.08576i	0.344979	+	0.199174i
$653$			0.764978i			0.0299359i	0.999888	+	0.0149680i	$0.00476463\pi$
$653$			0.764978i			0.0299359i	−0.999888	+	0.0149680i	$0.995235\pi$
$654$	1.31421	−	1.32236i	0.0513895	−	0.0517083i
$655$	27.1520	+	47.0286i	1.06092	+	1.83756i
$656$	4.79219			0.187103
$657$	−27.2031	−	15.4822i	−1.06129	−	0.604017i
$658$			22.9735i			0.895599i
$659$	−4.18973	+	7.25683i	−0.163209	+	0.282686i	−0.936018	−	0.351953i	$-0.885518\pi$
$659$	−4.18973	+	7.25683i	−0.163209	+	0.282686i	0.772809	+	0.634639i	$0.218851\pi$
$660$	0.355610	−	0.0964651i	0.0138421	−	0.00375490i
$661$			18.0336i			0.701425i	0.936483	+	0.350713i	$0.114061\pi$
$661$			18.0336i			0.701425i	−0.936483	+	0.350713i	$0.885939\pi$
$662$	4.27485			0.166147
$663$	40.4300	−	40.6808i	1.57017	−	1.57991i
$664$			2.00537i			0.0778236i
$665$	18.3419			0.711267
$666$	15.0092	−	10.3790i	0.581595	−	0.402178i
$667$	−21.9973			−0.851738
$668$		−	19.2843i		−	0.746131i
$669$	3.29632	+	12.1516i	0.127443	+	0.469808i
$670$	−47.0623			−1.81818
$671$		−	0.178862i		−	0.00690488i
$672$	−4.86535	−	4.83535i	−0.187685	−	0.186528i
$673$	0.621990	−	1.07732i	0.0239759	−	0.0415275i	−0.853788	−	0.520620i	$-0.825701\pi$
$673$	0.621990	−	1.07732i	0.0239759	−	0.0415275i	0.877764	+	0.479092i	$0.159034\pi$
$674$		−	19.8340i		−	0.763976i
$675$	−53.6943	−	52.7071i	−2.06669	−	2.02870i
$676$	16.1109			0.619652
$677$	20.6829	+	35.8238i	0.794907	+	1.37682i	0.922898	+	0.385043i	$0.125814\pi$
$677$	20.6829	+	35.8238i	0.794907	+	1.37682i	−0.127992	+	0.991775i	$0.540853\pi$
$678$	−1.76402	−	6.50292i	−0.0677469	−	0.249743i
$679$			16.9548i			0.650664i
$680$	−23.4586	−	13.5438i	−0.899596	−	0.519382i
$681$	−20.9419	−	20.8128i	−0.802495	−	0.797547i
$682$	−0.289513			−0.0110860
$683$	−2.14957	−	1.24105i	−0.0822509	−	0.0474876i	0.458310	−	0.888792i	$-0.348455\pi$
$683$	−2.14957	−	1.24105i	−0.0822509	−	0.0474876i	−0.540561	+	0.841305i	$0.681788\pi$
$684$	3.14798	−	0.0194703i	0.120366	−	0.000744464i
$685$	21.1423	−	12.2065i	0.807807	−	0.466387i
$686$			6.66954i			0.254644i
$687$	16.1062	+	4.26231i	0.614490	+	0.162617i
$688$	−2.18070	+	1.25903i	−0.0831385	+	0.0480001i
$689$	40.7212	+	23.5104i	1.55135	+	0.895675i
$690$	−30.1595	−	29.9736i	−1.14815	−	1.14107i
$691$	−25.4740			−0.969075			−0.484538	−	0.874770i	$-0.661012\pi$
$691$	−25.4740			−0.969075			−0.484538	+	0.874770i	$0.661012\pi$
$692$	−0.730095			−0.0277541
$693$	−0.497689	−	0.283251i	−0.0189057	−	0.0107598i
$694$	−9.10054	+	15.7626i	−0.345452	+	0.598340i
$695$	−17.9677	+	10.3736i	−0.681552	+	0.393494i
$696$	−1.79334	−	6.61098i	−0.0679763	−	0.250589i
$697$	−25.4707	−	14.7055i	−0.964772	−	0.557012i
$698$			0.117144i			0.00443395i
$699$	−19.8358	−	5.24931i	−0.750260	−	0.198547i
$700$	28.6727	−	49.6626i	1.08373	−	1.87707i
$701$	26.2285	+	15.1430i	0.990636	+	0.571944i	0.905464	−	0.424422i	$-0.139523\pi$
$701$	26.2285	+	15.1430i	0.990636	+	0.571944i	0.0851717	+	0.996366i	$0.472856\pi$
$702$	20.0072	+	19.6394i	0.755124	+	0.741242i
$703$	−6.36488	+	0.479680i	−0.240056	+	0.0180915i
$704$	0.0240994	+	0.0417415i	0.000908282	+	0.00157319i
$705$	−42.7990	+	11.6099i	−1.61190	+	0.437256i
$706$	10.8262			0.407449
$707$	29.6847			1.11641
$708$	−3.89241	+	1.05588i	−0.146286	+	0.0396825i
$709$	44.2939	−	25.5731i	1.66349	−	0.960419i	0.692467	−	0.721450i	$-0.256524\pi$
$709$	44.2939	−	25.5731i	1.66349	−	0.960419i	0.971027	−	0.238969i	$-0.0768094\pi$
$710$	20.8999	+	36.1996i	0.784358	+	1.35855i
$711$	−10.5767	−	18.0605i	−0.396657	−	0.677321i
$712$	−4.40646	+	7.63221i	−0.165139	+	0.286029i
$713$	16.7050	+	28.9339i	0.625607	+	1.08358i
$714$	11.0216	+	40.6302i	0.412473	+	1.52055i
$715$	−0.573892	−	0.994009i	−0.0214623	−	0.0371738i
$716$			12.9827i			0.485185i
$717$	−12.1177	+	3.28713i	−0.452544	+	0.122760i
$718$			24.9160i			0.929858i
$719$	−10.4029	+	18.0183i	−0.387962	+	0.671969i	−0.992175	−	0.124853i	$-0.960154\pi$
$719$	−10.4029	+	18.0183i	−0.387962	+	0.671969i	0.604214	+	0.796822i	$0.293487\pi$
$720$	6.54938	−	11.5076i	0.244081	−	0.428864i
$721$	−31.1603	+	17.9904i	−1.16047	+	0.669998i
$722$	15.5009	+	8.94943i	0.576883	+	0.333063i
$723$	18.8069	+	18.6909i	0.699436	+	0.695123i
$724$	5.12818	+	8.88228i	0.190587	+	0.330107i
$725$	49.5934	−	28.6327i	1.84185	−	1.06339i
$726$	−13.5109	−	13.4276i	−0.501438	−	0.498346i
$727$	−16.4271	−	9.48419i	−0.609247	−	0.351749i	0.163424	−	0.986556i	$-0.447746\pi$
$727$	−16.4271	−	9.48419i	−0.609247	−	0.351749i	−0.772671	+	0.634807i	$0.781080\pi$
$728$	−10.6839	+	18.5050i	−0.395970	+	0.685840i
$729$	0.500950	+	26.9954i	0.0185537	+	0.999828i
$730$	46.0491			1.70435
$731$	15.4541			0.571589
$732$	−4.55895	−	4.53084i	−0.168504	−	0.167465i
$733$	2.64923			0.0978514			0.0489257	−	0.998802i	$-0.484420\pi$
$733$	2.64923			0.0978514			0.0489257	+	0.998802i	$0.484420\pi$
$734$	−7.76919	−	4.48554i	−0.286766	−	0.165564i
$735$	−64.0710	+	17.3803i	−2.36329	+	0.641082i
$736$	2.78109	−	4.81699i	0.102512	−	0.177557i
$737$	−0.256972	−	0.445088i	−0.00946568	−	0.0163950i
$738$	7.11114	−	12.4947i	0.261765	−	0.459936i
$739$	16.8227			0.618835			0.309417	−	0.950926i	$-0.399866\pi$
$739$	16.8227			0.618835			0.309417	+	0.950926i	$0.399866\pi$
$740$	−11.6383	+	24.1932i	−0.427832	+	0.889360i
$741$	−2.56735	−	9.46433i	−0.0943141	−	0.347681i
$742$	−29.8897	+	17.2568i	−1.09729	+	0.633519i
$743$	−11.2198			−0.411615			−0.205808	−	0.978592i	$-0.565982\pi$
$743$	−11.2198			−0.411615			−0.205808	+	0.978592i	$0.565982\pi$
$744$	−7.33381	+	7.37931i	−0.268870	+	0.270539i
$745$	−54.0851	−	31.2260i	−1.98152	−	1.14403i
$746$		−	29.0842i		−	1.06485i
$747$	5.22862	+	2.97578i	0.191305	+	0.108878i
$748$		−	0.295811i		−	0.0108159i
$749$	49.5354			1.80998
$750$	70.0593	+	18.5403i	2.55821	+	0.676997i
$751$	−15.5049	+	26.8553i	−0.565782	+	0.979963i	0.431195	+	0.902259i	$0.358092\pi$
$751$	−15.5049	+	26.8553i	−0.565782	+	0.979963i	−0.996976	+	0.0777039i	$0.975241\pi$
$752$	−2.90046	−	5.02374i	−0.105769	−	0.183197i
$753$	3.20678	−	12.1176i	0.116862	−	0.441591i
$754$	−18.4792	+	10.6690i	−0.672972	+	0.388540i
$755$	19.3427	+	11.1675i	0.703954	+	0.406428i
$756$	−19.8269	+	5.51026i	−0.721099	+	0.200406i
$757$	16.6038	+	9.58623i	0.603477	+	0.348417i	0.770408	−	0.637551i	$-0.220053\pi$
$757$	16.6038	+	9.58623i	0.603477	+	0.348417i	−0.166931	+	0.985969i	$0.553386\pi$
$758$	−20.5188	−	11.8465i	−0.745275	−	0.430285i
$759$	0.118794	−	0.448895i	0.00431196	−	0.0162938i
$760$	−4.01093	+	2.31571i	−0.145492	+	0.0839996i
$761$	−22.8229	−	39.5305i	−0.827331	−	1.43298i	−0.900125	−	0.435632i	$-0.856525\pi$
$761$	−22.8229	−	39.5305i	−0.827331	−	1.43298i	0.0727939	−	0.997347i	$-0.476808\pi$
$762$	15.6482	+	15.5517i	0.566875	+	0.563380i
$763$	3.69169	−	2.13140i	0.133648	−	0.0771618i
$764$	9.47690	−	5.47149i	0.342862	−	0.197952i
$765$	−70.1231	+	41.0660i	−2.53531	+	1.48474i
$766$	12.2836			0.443826
$767$	6.28167	+	10.8802i	0.226818	+	0.392860i
$768$	1.67441	+	0.443112i	0.0604201	+	0.0159894i
$769$	33.4493	+	19.3120i	1.20621	+	0.696408i	0.961930	−	0.273295i	$-0.0881137\pi$
$769$	33.4493	+	19.3120i	1.20621	+	0.696408i	0.244284	+	0.969704i	$0.421447\pi$
$770$	0.842484			0.0303610
$771$	−22.0865	+	5.99132i	−0.795425	+	0.215772i
$772$	−16.2249	−	9.36743i	−0.583945	−	0.337141i
$773$	−22.4902	−	38.9543i	−0.808918	−	1.40109i	−0.913614	−	0.406583i	$-0.866720\pi$
$773$	−22.4902	−	38.9543i	−0.808918	−	1.40109i	0.104696	−	0.994504i	$-0.466613\pi$
$774$	0.0467217	+	7.55403i	0.00167938	+	0.271524i
$775$	−75.3236	−	43.4881i	−2.70570	−	1.56214i
$776$	−2.14058	−	3.70760i	−0.0768424	−	0.133095i
$777$	39.3344	−	13.9190i	1.41111	−	0.499343i
$778$	−10.1588	+	17.5956i	−0.364211	+	0.630833i
$779$	−4.35496	+	2.51434i	−0.156033	+	0.0900854i
$780$	−39.8735	−	10.5520i	−1.42770	−	0.377823i
$781$	−0.228237	+	0.395318i	−0.00816696	+	0.0141456i
$782$	−29.5633	+	17.0684i	−1.05718	+	0.610364i
$783$	−19.8980	−	5.13428i	−0.711096	−	0.183484i
$784$	−4.34205	−	7.52065i	−0.155073	−	0.268595i
$785$	57.4539	−	33.1710i	2.05062	−	1.18392i
$786$	5.57924	+	20.5674i	0.199005	+	0.733614i
$787$	4.10761	−	7.11459i	0.146420	−	0.253608i	−0.783482	−	0.621415i	$-0.786558\pi$
$787$	4.10761	−	7.11459i	0.146420	−	0.253608i	0.929902	+	0.367807i	$0.119891\pi$
$788$	−3.54437	+	6.13904i	−0.126263	+	0.218694i
$789$	0.689327	−	0.693603i	0.0245407	−	0.0246929i
$790$	26.6664	+	15.3959i	0.948748	+	0.547760i
$791$		−	15.4062i		−	0.547782i
$792$	0.144594		0.000894313i	0.00513792		3.17780e-5i
$793$	−10.0110	+	17.3396i	−0.355502	+	0.615747i
$794$		−	15.6329i		−	0.554789i
$795$	−47.2543	−	46.9629i	−1.67594	−	1.66560i
$796$		−	21.1169i		−	0.748468i
$797$	−30.4557	+	17.5836i	−1.07880	+	0.622843i	−0.930571	−	0.366111i	$-0.880689\pi$
$797$	−30.4557	+	17.5836i	−1.07880	+	0.622843i	−0.148224	+	0.988954i	$0.547356\pi$
$798$	6.95843	+	1.84146i	0.246326	+	0.0651870i
$799$			35.6019i			1.25951i
$800$			14.4800i			0.511946i
$801$	13.3607	+	22.8144i	0.472078	+	0.806108i
$802$	7.06440	−	12.2359i	0.249453	−	0.432065i
$803$	0.251439	+	0.435506i	0.00887310	+	0.0153687i
$804$	−17.8542	−	4.72489i	−0.629669	−	0.166634i
$805$	−48.6116	−	84.1977i	−1.71333	−	2.96758i
$806$	28.0666	+	16.2043i	0.988604	+	0.570771i
$807$	2.42870	+	0.642725i	0.0854943	+	0.0226250i
$808$	−6.49133	+	3.74777i	−0.228364	+	0.131846i
$809$	−6.40072	+	3.69546i	−0.225037	+	0.129925i	−0.608281	−	0.793722i	$-0.708140\pi$
$809$	−6.40072	+	3.69546i	−0.225037	+	0.129925i	0.383243	+	0.923647i	$0.374807\pi$
$810$	−20.2853	−	34.1524i	−0.712752	−	1.19999i
$811$	0.612209	+	1.06038i	0.0214976	+	0.0372349i	0.876574	−	0.481267i	$-0.159823\pi$
$811$	0.612209	+	1.06038i	0.0214976	+	0.0372349i	−0.855076	+	0.518502i	$0.826490\pi$
$812$		−	15.6622i		−	0.549636i
$813$	10.4666	−	10.5315i	0.367078	−	0.369356i
$814$	−0.292353	+	0.0220328i	−0.0102470	+	0.000772248i
$815$	−22.4466	+	38.8787i	−0.786271	+	1.36186i
$816$	−7.53982	−	7.49334i	−0.263947	−	0.262319i
$817$	1.32116	−	2.28832i	0.0462215	−	0.0800580i
$818$	−1.95447	−	3.38525i	−0.0683365	−	0.118362i
$819$	32.3943	+	55.3156i	1.13195	+	1.93288i
$820$			21.1509i			0.738621i
$821$	−3.31641	+	5.74418i	−0.115743	+	0.200473i	−0.918077	−	0.396403i	$-0.870258\pi$
$821$	−3.31641	+	5.74418i	−0.115743	+	0.200473i	0.802333	+	0.596876i	$0.203592\pi$
$822$	9.24634	−	2.50822i	0.322503	−	0.0874842i
$823$	−26.1879	−	45.3587i	−0.912852	−	1.58111i	−0.810017	−	0.586407i	$-0.800542\pi$
$823$	−26.1879	−	45.3587i	−0.912852	−	1.58111i	−0.102835	−	0.994698i	$-0.532791\pi$
$824$	4.54267	−	7.86814i	0.158252	−	0.274100i
$825$	0.316479	+	1.16667i	0.0110184	+	0.0406183i
$826$	−9.22160			−0.320861
$827$	−1.34886	+	0.778762i	−0.0469043	+	0.0270802i	−0.523269	−	0.852168i	$-0.675288\pi$
$827$	−1.34886	+	0.778762i	−0.0469043	+	0.0270802i	0.476364	+	0.879248i	$0.341954\pi$
$828$	−8.43249	−	14.3991i	−0.293049	−	0.500403i
$829$	33.8766	+	19.5587i	1.17658	+	0.679301i	0.955222	−	0.295891i	$-0.0956164\pi$
$829$	33.8766	+	19.5587i	1.17658	+	0.679301i	0.221362	+	0.975192i	$0.428950\pi$
$830$	−8.85095			−0.307221
$831$	−29.0043	−	28.8255i	−1.00615	−	0.999945i
$832$		−	5.39546i		−	0.187054i
$833$			53.2968i			1.84663i
$834$	−7.85794	+	2.13160i	−0.272098	+	0.0738111i
$835$	85.1134			2.94547
$836$	−0.0438013	−	0.0252887i	−0.00151490	−	0.000874628i
$837$	8.35744	+	30.0716i	0.288875	+	1.03943i
$838$	−12.9286	+	7.46433i	−0.446611	+	0.257851i
$839$	42.8108			1.47799			0.738996	−	0.673710i	$-0.235300\pi$
$839$	42.8108			1.47799			0.738996	+	0.673710i	$0.235300\pi$
$840$	21.3414	−	21.4738i	0.736348	−	0.740917i
$841$	−6.67981	+	11.5698i	−0.230338	+	0.398958i
$842$	−4.43973	−	7.68983i	−0.153003	−	0.265009i
$843$	12.5526	−	47.4331i	0.432333	−	1.63368i
$844$	−1.50425	+	2.60544i	−0.0517784	+	0.0896828i
$845$			71.1076i			2.44617i
$846$	−17.4024	+	0.107634i	−0.598308	+	0.00370053i
$847$	−21.7771	−	37.7191i	−0.748271	−	1.29604i
$848$	4.35744	−	7.54731i	0.149635	−	0.259176i
$849$	7.30174	−	27.5915i	0.250595	−	0.946938i
$850$	44.4340	−	76.9620i	1.52408	−	2.63978i
$851$	19.0708	+	27.9465i	0.653740	+	0.957993i
$852$	4.29454	+	15.8315i	0.147129	+	0.542377i
$853$			11.3953i			0.390168i	0.980787	+	0.195084i	$0.0624980\pi$
$853$			11.3953i			0.390168i	−0.980787	+	0.195084i	$0.937502\pi$
$854$	−7.34818	−	12.7274i	−0.251450	−	0.435523i
$855$	0.0859343	+	13.8940i	0.00293889	+	0.475164i
$856$	−10.8322	+	6.25397i	−0.370237	+	0.213756i
$857$	−18.2218	+	10.5204i	−0.622445	+	0.359369i	−0.777820	−	0.628487i	$-0.783675\pi$
$857$	−18.2218	+	10.5204i	−0.622445	+	0.359369i	0.155375	+	0.987856i	$0.450341\pi$
$858$	−0.117924	−	0.434718i	−0.00402587	−	0.0148410i
$859$	21.5673	+	12.4519i	0.735866	+	0.424852i	0.820564	−	0.571554i	$-0.193659\pi$
$859$	21.5673	+	12.4519i	0.735866	+	0.424852i	−0.0846984	+	0.996407i	$0.526993\pi$
$860$	−5.55688	−	9.62479i	−0.189488	−	0.328203i
$861$	23.1719	−	23.3157i	0.789697	−	0.794596i
$862$	16.5449	+	28.6566i	0.563522	+	0.976049i
$863$	13.1340	−	22.7487i	0.447085	−	0.774374i	−0.551110	−	0.834433i	$-0.685795\pi$
$863$	13.1340	−	22.7487i	0.447085	−	0.774374i	0.998195	+	0.0600585i	$0.0191287\pi$
$864$	3.63999	−	3.70816i	0.123835	−	0.126154i
$865$		−	3.22236i		−	0.109564i
$866$			12.5598i			0.426801i
$867$	9.37135	+	34.5466i	0.318268	+	1.17327i
$868$	−20.6012	+	11.8941i	−0.699249	+	0.403711i
$869$			0.336261i			0.0114069i
$870$	29.1783	−	7.91511i	0.989239	−	0.268347i
$871$			57.5316i			1.94939i
$872$	−0.538189	+	0.932171i	−0.0182254	+	0.0315673i
$873$	−12.8432	+	0.0794354i	−0.434678	+	0.00268848i
$874$			5.83666i			0.197428i
$875$	143.504	+	82.8521i	4.85132	+	2.80091i
$876$	17.4698	+	4.62317i	0.590250	+	0.156202i
$877$	4.79203	−	8.30003i	0.161815	−	0.280272i	−0.773704	−	0.633547i	$-0.781598\pi$
$877$	4.79203	−	8.30003i	0.161815	−	0.280272i	0.935520	+	0.353274i	$0.114932\pi$
$878$	12.7426	−	22.0708i	0.430042	−	0.744854i
$879$	−31.7229	−	8.39508i	−1.06999	−	0.283159i
$880$	−0.184231	+	0.106366i	−0.00621042	+	0.00358559i
$881$	26.9060	+	46.6025i	0.906485	+	1.57008i	0.818912	+	0.573919i	$0.194578\pi$
$881$	26.9060	+	46.6025i	0.906485	+	1.57008i	0.0875725	+	0.996158i	$0.472089\pi$
$882$	−26.0518	+	0.161130i	−0.877209	+	0.00542554i
$883$	45.0704	−	26.0214i	1.51674	−	0.875690i	0.516933	−	0.856026i	$-0.327074\pi$
$883$	45.0704	−	26.0214i	1.51674	−	0.875690i	0.999807	−	0.0196644i	$-0.00625979\pi$
$884$	−16.5567	+	28.6771i	−0.556864	+	0.964516i
$885$	−4.66026	−	17.1796i	−0.156653	−	0.577487i
$886$	14.1463	−	8.16738i	0.475255	−	0.274388i
$887$	−17.6252	+	30.5277i	−0.591796	+	1.02502i	0.402194	+	0.915554i	$0.368248\pi$
$887$	−17.6252	+	30.5277i	−0.591796	+	1.02502i	−0.993990	+	0.109467i	$0.965086\pi$
$888$	−6.84417	+	8.00983i	−0.229675	+	0.268792i
$889$	25.2220	+	43.6859i	0.845920	+	1.46518i
$890$	−33.6857	−	19.4484i	−1.12915	−	0.651913i
$891$	0.212232	−	0.378327i	0.00711002	−	0.0126744i
$892$	−3.63463	−	6.29537i	−0.121697	−	0.210785i
$893$	5.27165	+	3.04359i	0.176409	+	0.101850i
$894$	−17.3835	−	17.2763i	−0.581390	−	0.577805i
$895$	−57.3006			−1.91535
$896$	3.42973	+	1.98016i	0.114579	+	0.0661524i
$897$	−36.6414	+	36.8687i	−1.22342	+	1.23101i
$898$	3.74041	+	6.47858i	0.124819	+	0.216193i
$899$	−23.7550			−0.792273
$900$	37.7538	+	21.4869i	1.25846	+	0.716231i
$901$	−46.3201	+	26.7429i	−1.54315	+	0.890935i
$902$	−0.200033	+	0.115489i	−0.00666037	+	0.00384537i
$903$	−4.41885	+	16.6977i	−0.147050	+	0.555666i
$904$	1.94507	+	3.36897i	0.0646922	+	0.112050i
$905$	−39.2030	+	22.6338i	−1.30315	+	0.752375i
$906$	6.21694	+	6.17861i	0.206544	+	0.205270i
$907$	−35.5891	−	20.5474i	−1.18172	−	0.682265i	−0.225306	−	0.974288i	$-0.572338\pi$
$907$	−35.5891	−	20.5474i	−1.18172	−	0.682265i	−0.956411	+	0.292023i	$0.905671\pi$
$908$	14.7626	+	8.52318i	0.489913	+	0.282852i
$909$	0.139077	+	22.4862i	0.00461289	+	0.745820i
$910$	−81.6739	−	47.1544i	−2.70746	−	1.56315i
$911$	21.9174	−	12.6540i	0.726155	−	0.419246i	−0.0908592	−	0.995864i	$-0.528961\pi$
$911$	21.9174	−	12.6540i	0.726155	−	0.419246i	0.817014	+	0.576618i	$0.195628\pi$
$912$	−1.75413	+	0.475836i	−0.0580850	+	0.0157565i
$913$	−0.0483284	−	0.0837072i	−0.00159944	−	0.00277031i
$914$	−19.1772	+	33.2159i	−0.634325	+	1.09868i
$915$	19.9974	−	20.1215i	0.661093	−	0.665195i
$916$	−9.61903			−0.317822
$917$			48.7266i			1.60910i
$918$	−30.7258	+	8.53923i	−1.01410	+	0.281837i
$919$		−	16.9641i		−	0.559593i	−0.960059	−	0.279796i	$-0.909733\pi$
$919$		−	16.9641i		−	0.559593i	0.960059	−	0.279796i	$-0.0902670\pi$
$920$	21.2604	+	12.2747i	0.700933	+	0.404684i
$921$	8.66688	+	2.29358i	0.285584	+	0.0755761i
$922$	29.1926			0.961408
$923$	44.2525	−	25.5492i	1.45659	−	0.840961i
$924$	0.319616	+	0.0845824i	0.0105146	+	0.00278256i
$925$	−79.3721	−	38.1824i	−2.60974	−	1.25543i
$926$	35.7048			1.17333
$927$	−13.7738	−	23.5197i	−0.452389	−	0.772488i
$928$	1.97740	+	3.42495i	0.0649112	+	0.112430i
$929$	−6.89696	+	11.9459i	−0.226282	+	0.391932i	−0.956703	−	0.291065i	$-0.905990\pi$
$929$	−6.89696	+	11.9459i	−0.226282	+	0.391932i	0.730421	+	0.682997i	$0.239324\pi$
$930$	−32.5694	−	32.3686i	−1.06799	−	1.06141i
$931$	7.89177	+	4.55632i	0.258642	+	0.149327i
$932$	11.8465			0.388044
$933$	−7.78826	+	2.11269i	−0.254976	+	0.0691665i
$934$	6.41563			0.209926
$935$	1.30559			0.0426975
$936$	−14.0676	−	8.00633i	−0.459814	−	0.261695i
$937$	−12.5296	+	21.7019i	−0.409324	+	0.708971i	−0.994814	−	0.101709i	$-0.967569\pi$
$937$	−12.5296	+	21.7019i	−0.409324	+	0.708971i	0.585490	+	0.810680i	$0.300902\pi$
$938$	−36.5712	−	21.1144i	−1.19409	−	0.689409i
$939$	−3.58098	+	13.5316i	−0.116861	+	0.441588i
$940$	22.1729	−	12.8015i	0.723200	−	0.417540i
$941$	−4.31985	−	7.48220i	−0.140823	−	0.243913i	0.786984	−	0.616974i	$-0.211642\pi$
$941$	−4.31985	−	7.48220i	−0.140823	−	0.243913i	−0.927807	+	0.373061i	$0.878308\pi$
$942$	25.1267	−	6.81604i	0.818674	−	0.222079i
$943$	23.0839	+	13.3275i	0.751716	+	0.434004i
$944$	2.01654	−	1.16425i	0.0656329	−	0.0378932i
$945$	−24.3202	−	87.5085i	−0.791135	−	2.84665i
$946$	0.0606838	−	0.105107i	0.00197300	−	0.00341734i
$947$		−	60.2244i		−	1.95703i	−0.206179	−	0.978514i	$-0.566103\pi$
$947$		−	60.2244i		−	1.95703i	0.206179	−	0.978514i	$-0.433897\pi$
$948$	8.57084	+	8.51800i	0.278368	+	0.276652i
$949$		−	56.2930i		−	1.82735i
$950$	−7.59729	−	13.1589i	−0.246489	−	0.426931i
$951$	−8.58354	−	2.27153i	−0.278340	−	0.0736593i
$952$	−12.1528	−	21.0493i	−0.393875	−	0.682211i
$953$	25.0450	−	43.3791i	0.811286	−	1.40519i	−0.100679	−	0.994919i	$-0.532102\pi$
$953$	25.0450	−	43.3791i	0.811286	−	1.40519i	0.911965	−	0.410269i	$-0.134565\pi$
$954$	−13.2121	−	22.5607i	−0.427758	−	0.730428i
$955$	24.1491	+	41.8274i	0.781445	+	1.35350i
$956$	6.27782	−	3.62450i	0.203039	−	0.117225i
$957$	0.234178	+	0.232734i	0.00756989	+	0.00752321i
$958$	27.4742			0.887650
$959$	21.9057			0.707372
$960$	−1.95573	+	7.39021i	−0.0631208	+	0.238518i
$961$	2.53982	+	4.39910i	0.0819298	+	0.141907i
$962$	29.5751	+	14.2273i	0.953541	+	0.458706i
$963$	0.232080	+	37.5231i	0.00747868	+	1.20916i
$964$	−13.2575	−	7.65425i	−0.426997	−	0.246527i
$965$	41.3442	−	71.6103i	1.33092	−	2.30522i
$966$	−9.98880	−	36.8228i	−0.321384	−	1.18476i
$967$		−	51.3310i		−	1.65069i	−0.564626	−	0.825347i	$-0.690980\pi$
$967$		−	51.3310i		−	1.65069i	0.564626	−	0.825347i	$-0.309020\pi$
$968$	9.52427	+	5.49884i	0.306122	+	0.176739i
$969$	10.7835	+	2.85371i	0.346415	+	0.0916743i
$970$	16.3639	−	9.44771i	0.525414	−	0.303348i
$971$	−9.14048	+	15.8318i	−0.293332	+	0.508066i	−0.974595	−	0.223972i	$-0.928097\pi$
$971$	−9.14048	+	15.8318i	−0.293332	+	0.508066i	0.681264	+	0.732038i	$0.261431\pi$
$972$	−4.26692	−	14.9931i	−0.136861	−	0.480904i
$973$	−18.6164			−0.596815
$974$	16.4828			0.528142
$975$	34.6187	−	130.816i	1.10869	−	4.18945i
$976$	3.21374	+	1.85545i	0.102869	+	0.0593916i
$977$	−32.9328	+	19.0137i	−1.05361	+	0.608303i	−0.923658	−	0.383217i	$-0.874816\pi$
$977$	−32.9328	+	19.0137i	−1.05361	+	0.608303i	−0.129954	+	0.991520i	$0.541483\pi$
$978$	−12.4189	+	12.4960i	−0.397114	+	0.399578i
$979$		−	0.424773i		−	0.0135758i
$980$	33.1933	−	19.1641i	1.06032	−	0.612176i
$981$	1.63183	+	2.78647i	0.0521004	+	0.0889652i
$982$	−11.7043	−	6.75748i	−0.373499	−	0.215640i
$983$	−38.1698			−1.21743			−0.608715	−	0.793389i	$-0.708315\pi$
$983$	−38.1698			−1.21743			−0.608715	+	0.793389i	$0.708315\pi$
$984$	−2.12348	+	8.02409i	−0.0676939	+	0.255799i
$985$	−27.0954	−	15.6435i	−0.863330	−	0.498444i
$986$		−	24.2717i		−	0.772969i
$987$	−38.4670	−	10.1798i	−1.22442	−	0.324027i
$988$	2.83085	+	4.90318i	0.0900615	+	0.155991i
$989$	−14.0059			−0.445362
$990$	0.00394716	+	0.638182i	0.000125449	+	0.0202828i
$991$		−	37.4725i		−	1.19035i	−0.803595	−	0.595176i	$-0.797082\pi$
$991$		−	37.4725i		−	1.19035i	0.803595	−	0.595176i	$-0.202918\pi$
$992$	3.00332	−	5.20190i	0.0953554	−	0.165160i
$993$	−1.89424	+	7.15786i	−0.0601118	+	0.227148i
$994$			37.5067i			1.18964i
$995$	93.2019			2.95470
$996$	−3.35782	−	0.888605i	−0.106397	−	0.0281565i
$997$		−	13.7497i		−	0.435457i	−0.976009	−	0.217729i	$-0.930135\pi$
$997$		−	13.7497i		−	0.435457i	0.976009	−	0.217729i	$-0.0698648\pi$
$998$	23.1679			0.733368
$999$	10.7280	+	29.7306i	0.339418	+	0.940636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.19	✓	76
3.2	odd	2		1998.2.k.a.1063.20		76
9.2	odd	6		1998.2.t.a.397.20		76
9.7	even	3		666.2.t.a.619.8	yes	76
37.11	even	6		666.2.t.a.85.8	yes	76
111.11	odd	6		1998.2.t.a.307.20		76
333.11	odd	6		1998.2.k.a.1639.19		76
333.196	even	6	inner	666.2.k.a.529.38	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.19	✓	76	1.1	even	1	trivial
666.2.k.a.529.38	yes	76	333.196	even	6	inner
666.2.t.a.85.8	yes	76	37.11	even	6
666.2.t.a.619.8	yes	76	9.7	even	3
1998.2.k.a.1063.20		76	3.2	odd	2
1998.2.k.a.1639.19		76	333.11	odd	6
1998.2.t.a.307.20		76	111.11	odd	6
1998.2.t.a.397.20		76	9.2	odd	6

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.67441 + 0.443112i) q^{3} -1.00000 q^{4} -4.41362i q^{5} +(0.443112 - 1.67441i) q^{6} +(1.98016 - 3.42973i) q^{7} +1.00000i q^{8} +(2.60730 + 1.48390i) q^{9} -4.41362 q^{10} +(-0.0240994 - 0.0417415i) q^{11} +(-1.67441 - 0.443112i) q^{12} +5.39546i q^{13} +(-3.42973 - 1.98016i) q^{14} +(1.95573 - 7.39021i) q^{15} +1.00000 q^{16} +(-5.31505 - 3.06865i) q^{17} +(1.48390 - 2.60730i) q^{18} +(-0.908762 + 0.524674i) q^{19} +4.41362i q^{20} +(4.83535 - 4.86535i) q^{21} +(-0.0417415 + 0.0240994i) q^{22} +(4.81699 + 2.78109i) q^{23} +(-0.443112 + 1.67441i) q^{24} -14.4800 q^{25} +5.39546 q^{26} +(3.70816 + 3.63999i) q^{27} +(-1.98016 + 3.42973i) q^{28} +(-3.42495 + 1.97740i) q^{29} +(-7.39021 - 1.95573i) q^{30} +(5.20190 + 3.00332i) q^{31} -1.00000i q^{32} +(-0.0218562 - 0.0805711i) q^{33} +(-3.06865 + 5.31505i) q^{34} +(-15.1375 - 8.73966i) q^{35} +(-2.60730 - 1.48390i) q^{36} +(5.48149 + 2.63690i) q^{37} +(0.524674 + 0.908762i) q^{38} +(-2.39079 + 9.03421i) q^{39} +4.41362 q^{40} +4.79219 q^{41} +(-4.86535 - 4.83535i) q^{42} +(-2.18070 + 1.25903i) q^{43} +(0.0240994 + 0.0417415i) q^{44} +(6.54938 - 11.5076i) q^{45} +(2.78109 - 4.81699i) q^{46} +(-2.90046 - 5.02374i) q^{47} +(1.67441 + 0.443112i) q^{48} +(-4.34205 - 7.52065i) q^{49} +14.4800i q^{50} +(-7.53982 - 7.49334i) q^{51} -5.39546i q^{52} +(4.35744 - 7.54731i) q^{53} +(3.63999 - 3.70816i) q^{54} +(-0.184231 + 0.106366i) q^{55} +(3.42973 + 1.98016i) q^{56} +(-1.75413 + 0.475836i) q^{57} +(1.97740 + 3.42495i) q^{58} +(2.01654 - 1.16425i) q^{59} +(-1.95573 + 7.39021i) q^{60} +(3.21374 + 1.85545i) q^{61} +(3.00332 - 5.20190i) q^{62} +(10.2523 - 6.00400i) q^{63} -1.00000 q^{64} +23.8135 q^{65} +(-0.0805711 + 0.0218562i) q^{66} +10.6630 q^{67} +(5.31505 + 3.06865i) q^{68} +(6.83329 + 6.79116i) q^{69} +(-8.73966 + 15.1375i) q^{70} +(-4.73531 - 8.20180i) q^{71} +(-1.48390 + 2.60730i) q^{72} -10.4334 q^{73} +(2.63690 - 5.48149i) q^{74} +(-24.2455 - 6.41627i) q^{75} +(0.908762 - 0.524674i) q^{76} -0.190883 q^{77} +(9.03421 + 2.39079i) q^{78} +(-6.04185 - 3.48826i) q^{79} -4.41362i q^{80} +(4.59607 + 7.73797i) q^{81} -4.79219i q^{82} +2.00537 q^{83} +(-4.83535 + 4.86535i) q^{84} +(-13.5438 + 23.4586i) q^{85} +(1.25903 + 2.18070i) q^{86} +(-6.61098 + 1.79334i) q^{87} +(0.0417415 - 0.0240994i) q^{88} +(7.63221 + 4.40646i) q^{89} +(-11.5076 - 6.54938i) q^{90} +(18.5050 + 10.6839i) q^{91} +(-4.81699 - 2.78109i) q^{92} +(7.37931 + 7.33381i) q^{93} +(-5.02374 + 2.90046i) q^{94} +(2.31571 + 4.01093i) q^{95} +(0.443112 - 1.67441i) q^{96} +(-3.70760 + 2.14058i) q^{97} +(-7.52065 + 4.34205i) q^{98} +(-0.000894313 - 0.144594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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