LMFDB - Embedded newform 66.3.g.a.59.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(5,66)] 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("66.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.g (of order $10$, degree $4$, 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:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	66.59
Dual form			66.3.g.a.47.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831254 + 1.14412i) q^{2} +(2.91405 + 0.712977i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(2.69884 + 3.71463i) q^{5} +(-3.23805 + 2.74136i) q^{6} +(-1.21805 - 3.74878i) q^{7} +(2.68999 + 0.874032i) q^{8} +(7.98333 + 4.15530i) q^{9} -6.49342 q^{10} +(-6.59206 + 8.80595i) q^{11} +(-0.444816 - 5.98349i) q^{12} +(2.32832 + 1.69162i) q^{13} +(5.30157 + 1.72258i) q^{14} +(5.21609 + 12.7488i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(-12.4551 - 17.1429i) q^{17} +(-11.3903 + 5.67980i) q^{18} +(7.91916 - 24.3727i) q^{19} +(5.39768 - 7.42927i) q^{20} +(-0.876664 - 11.7925i) q^{21} +(-4.59542 - 14.8621i) q^{22} -20.3867i q^{23} +(7.21560 + 4.46487i) q^{24} +(1.21065 - 3.72600i) q^{25} +(-3.87085 + 1.25772i) q^{26} +(20.3011 + 17.8007i) q^{27} +(-6.37780 + 4.63374i) q^{28} +(-23.0338 + 7.48412i) q^{29} +(-18.9221 - 4.62966i) q^{30} +(-31.0742 - 22.5767i) q^{31} -5.65685i q^{32} +(-25.4880 + 20.9610i) q^{33} +29.9669 q^{34} +(10.6380 - 14.6420i) q^{35} +(2.96988 - 17.7533i) q^{36} +(20.6249 + 63.4769i) q^{37} +(21.3025 + 29.3204i) q^{38} +(5.57874 + 6.58951i) q^{39} +(4.01315 + 12.3512i) q^{40} +(36.7962 + 11.9558i) q^{41} +(14.2209 + 8.79959i) q^{42} -32.3233 q^{43} +(20.8240 + 7.09646i) q^{44} +(6.11031 + 40.8696i) q^{45} +(23.3248 + 16.9465i) q^{46} +(5.00094 + 1.62490i) q^{47} +(-11.1064 + 4.54409i) q^{48} +(27.0722 - 19.6691i) q^{49} +(3.25665 + 4.48239i) q^{50} +(-24.0721 - 58.8355i) q^{51} +(1.77868 - 5.47421i) q^{52} +(-31.3981 + 43.2158i) q^{53} +(-37.2415 + 8.43014i) q^{54} +(-50.5018 - 0.721219i) q^{55} -11.1488i q^{56} +(40.4539 - 65.3769i) q^{57} +(10.5841 - 32.5747i) q^{58} +(-37.3900 + 12.1488i) q^{59} +(21.0260 - 17.8008i) q^{60} +(-66.2994 + 48.1693i) q^{61} +(51.6610 - 16.7857i) q^{62} +(5.85318 - 34.9891i) q^{63} +(6.47214 + 4.70228i) q^{64} +13.2143i q^{65} +(-2.79492 - 46.5853i) q^{66} +113.002 q^{67} +(-24.9101 + 34.2859i) q^{68} +(14.5352 - 59.4077i) q^{69} +(7.90932 + 24.3424i) q^{70} +(-62.5261 - 86.0597i) q^{71} +(17.8432 + 18.1554i) q^{72} +(30.2057 + 92.9635i) q^{73} +(-89.7699 - 29.1680i) q^{74} +(6.18445 - 9.99458i) q^{75} -51.2539 q^{76} +(41.0410 + 13.9860i) q^{77} +(-12.1766 + 0.905212i) q^{78} +(42.6778 + 31.0072i) q^{79} +(-17.4673 - 5.67546i) q^{80} +(46.4670 + 66.3462i) q^{81} +(-44.2659 + 32.1611i) q^{82} +(-30.0965 - 41.4243i) q^{83} +(-21.8889 + 8.95571i) q^{84} +(30.0655 - 92.5320i) q^{85} +(26.8688 - 36.9818i) q^{86} +(-72.4575 + 5.38653i) q^{87} +(-25.4293 + 17.9263i) q^{88} +0.204051i q^{89} +(-51.8391 - 26.9821i) q^{90} +(3.50551 - 10.7888i) q^{91} +(-38.7777 + 12.5996i) q^{92} +(-74.4549 - 87.9447i) q^{93} +(-6.01614 + 4.37098i) q^{94} +(111.908 - 36.3611i) q^{95} +(4.03321 - 16.4843i) q^{96} +(-5.42715 - 3.94306i) q^{97} +47.3239i q^{98} +(-89.2179 + 42.9088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i
$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i
$3$	2.91405	+	0.712977i	0.971349	+	0.237659i
$3$	2.91405	+	0.712977i	0.971349	+	0.237659i
$4$	−0.618034	−	1.90211i	−0.154508	−	0.475528i
$5$	2.69884	+	3.71463i	0.539768	+	0.742927i	0.988580	−	0.150699i	$-0.0481526\pi$
$5$	2.69884	+	3.71463i	0.539768	+	0.742927i	−0.448812	+	0.893626i	$0.648153\pi$
$6$	−3.23805	+	2.74136i	−0.539674	+	0.456894i
$7$	−1.21805	−	3.74878i	−0.174007	−	0.535539i	0.825579	−	0.564286i	$-0.190848\pi$
$7$	−1.21805	−	3.74878i	−0.174007	−	0.535539i	−0.999587	+	0.0287465i	$0.990848\pi$
$8$	2.68999	+	0.874032i	0.336249	+	0.109254i
$9$	7.98333	+	4.15530i	0.887036	+	0.461700i
$10$	−6.49342			−0.649342
$11$	−6.59206	+	8.80595i	−0.599278	+	0.800541i
$11$	−6.59206	+	8.80595i	−0.599278	+	0.800541i
$12$	−0.444816	−	5.98349i	−0.0370680	−	0.498624i
$13$	2.32832	+	1.69162i	0.179102	+	0.130125i	0.673724	−	0.738983i	$-0.264694\pi$
$13$	2.32832	+	1.69162i	0.179102	+	0.130125i	−0.494622	+	0.869108i	$0.664694\pi$
$14$	5.30157	+	1.72258i	0.378684	+	0.123042i
$15$	5.21609	+	12.7488i	0.347740	+	0.849922i
$16$	−3.23607	+	2.35114i	−0.202254	+	0.146946i
$17$	−12.4551	−	17.1429i	−0.732651	−	1.00841i	−0.999008	−	0.0445331i	$-0.985820\pi$
$17$	−12.4551	−	17.1429i	−0.732651	−	1.00841i	0.266357	−	0.963874i	$-0.414180\pi$
$18$	−11.3903	+	5.67980i	−0.632797	+	0.315544i
$19$	7.91916	−	24.3727i	0.416798	−	1.28277i	−0.493835	−	0.869556i	$-0.664405\pi$
$19$	7.91916	−	24.3727i	0.416798	−	1.28277i	0.910633	−	0.413216i	$-0.135595\pi$
$20$	5.39768	−	7.42927i	0.269884	−	0.371463i
$21$	−0.876664	−	11.7925i	−0.0417459	−	0.561550i
$22$	−4.59542	−	14.8621i	−0.208883	−	0.675550i
$23$		−	20.3867i		−	0.886376i	−0.896429	−	0.443188i	$-0.853847\pi$
$23$		−	20.3867i		−	0.886376i	0.896429	−	0.443188i	$-0.146153\pi$
$24$	7.21560	+	4.46487i	0.300650	+	0.186036i
$25$	1.21065	−	3.72600i	0.0484261	−	0.149040i
$26$	−3.87085	+	1.25772i	−0.148879	+	0.0483737i
$27$	20.3011	+	17.8007i	0.751894	+	0.659284i
$28$	−6.37780	+	4.63374i	−0.227779	+	0.165491i
$29$	−23.0338	+	7.48412i	−0.794268	+	0.258073i	−0.677920	−	0.735135i	$-0.737119\pi$
$29$	−23.0338	+	7.48412i	−0.794268	+	0.258073i	−0.116347	+	0.993209i	$0.537119\pi$
$30$	−18.9221	−	4.62966i	−0.630737	−	0.154322i
$31$	−31.0742	−	22.5767i	−1.00239	−	0.728281i	−0.0397926	−	0.999208i	$-0.512670\pi$
$31$	−31.0742	−	22.5767i	−1.00239	−	0.728281i	−0.962600	+	0.270927i	$0.912670\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−25.4880	+	20.9610i	−0.772364	+	0.635181i
$34$	29.9669			0.881381
$35$	10.6380	−	14.6420i	0.303943	−	0.418342i
$36$	2.96988	−	17.7533i	0.0824966	−	0.493147i
$37$	20.6249	+	63.4769i	0.557429	+	1.71559i	0.689440	+	0.724343i	$0.257857\pi$
$37$	20.6249	+	63.4769i	0.557429	+	1.71559i	−0.132010	+	0.991248i	$0.542143\pi$
$38$	21.3025	+	29.3204i	0.560592	+	0.771588i
$39$	5.57874	+	6.58951i	0.143045	+	0.168962i
$40$	4.01315	+	12.3512i	0.100329	+	0.308780i
$41$	36.7962	+	11.9558i	0.897469	+	0.291605i	0.721192	−	0.692735i	$-0.243595\pi$
$41$	36.7962	+	11.9558i	0.897469	+	0.291605i	0.176277	+	0.984341i	$0.443595\pi$
$42$	14.2209	+	8.79959i	0.338592	+	0.209514i
$43$	−32.3233			−0.751704			−0.375852	−	0.926680i	$-0.622650\pi$
$43$	−32.3233			−0.751704			−0.375852	+	0.926680i	$0.622650\pi$
$44$	20.8240	+	7.09646i	0.473273	+	0.161283i
$45$	6.11031	+	40.8696i	0.135785	+	0.908214i
$46$	23.3248	+	16.9465i	0.507062	+	0.368402i
$47$	5.00094	+	1.62490i	0.106403	+	0.0345724i	0.361735	−	0.932281i	$-0.382185\pi$
$47$	5.00094	+	1.62490i	0.106403	+	0.0345724i	−0.255332	+	0.966854i	$0.582185\pi$
$48$	−11.1064	+	4.54409i	−0.231383	+	0.0946685i
$49$	27.0722	−	19.6691i	0.552493	−	0.401410i
$50$	3.25665	+	4.48239i	0.0651330	+	0.0896478i
$51$	−24.0721	−	58.8355i	−0.472002	−	1.15364i
$52$	1.77868	−	5.47421i	0.0342054	−	0.105273i
$53$	−31.3981	+	43.2158i	−0.592417	+	0.815392i	−0.994988	−	0.0999971i	$-0.968117\pi$
$53$	−31.3981	+	43.2158i	−0.592417	+	0.815392i	0.402571	+	0.915389i	$0.368117\pi$
$54$	−37.2415	+	8.43014i	−0.689658	+	0.156114i
$55$	−50.5018	−	0.721219i	−0.918215	−	0.0131131i
$56$		−	11.1488i		−	0.199086i
$57$	40.4539	−	65.3769i	0.709718	−	1.14696i
$58$	10.5841	−	32.5747i	0.182485	−	0.561632i
$59$	−37.3900	+	12.1488i	−0.633729	+	0.205911i	−0.608226	−	0.793764i	$-0.708119\pi$
$59$	−37.3900	+	12.1488i	−0.633729	+	0.205911i	−0.0255029	+	0.999675i	$0.508119\pi$
$60$	21.0260	−	17.8008i	0.350433	−	0.296680i
$61$	−66.2994	+	48.1693i	−1.08687	+	0.789661i	−0.978869	−	0.204490i	$-0.934447\pi$
$61$	−66.2994	+	48.1693i	−1.08687	+	0.789661i	−0.108006	+	0.994150i	$0.534447\pi$
$62$	51.6610	−	16.7857i	0.833243	−	0.270737i
$63$	5.85318	−	34.9891i	0.0929076	−	0.555382i
$64$	6.47214	+	4.70228i	0.101127	+	0.0734732i
$65$			13.2143i			0.203297i
$66$	−2.79492	−	46.5853i	−0.0423473	−	0.705838i
$67$	113.002			1.68660			0.843299	−	0.537445i	$-0.180610\pi$
$67$	113.002			1.68660			0.843299	+	0.537445i	$0.180610\pi$
$68$	−24.9101	+	34.2859i	−0.366326	+	0.504204i
$69$	14.5352	−	59.4077i	0.210655	−	0.860981i
$70$	7.90932	+	24.3424i	0.112990	+	0.347748i
$71$	−62.5261	−	86.0597i	−0.880649	−	1.21211i	−0.976241	−	0.216688i	$-0.930474\pi$
$71$	−62.5261	−	86.0597i	−0.880649	−	1.21211i	0.0955922	−	0.995421i	$-0.469526\pi$
$72$	17.8432	+	18.1554i	0.247823	+	0.252158i
$73$	30.2057	+	92.9635i	0.413776	+	1.27347i	0.913341	+	0.407196i	$0.133493\pi$
$73$	30.2057	+	92.9635i	0.413776	+	1.27347i	−0.499565	+	0.866277i	$0.666507\pi$
$74$	−89.7699	−	29.1680i	−1.21311	−	0.394162i
$75$	6.18445	−	9.99458i	0.0824594	−	0.133261i
$76$	−51.2539			−0.674393
$77$	41.0410	+	13.9860i	0.533000	+	0.181637i
$78$	−12.1766	+	0.905212i	−0.156110	+	0.0116053i
$79$	42.6778	+	31.0072i	0.540225	+	0.392497i	0.824169	−	0.566344i	$-0.191643\pi$
$79$	42.6778	+	31.0072i	0.540225	+	0.392497i	−0.283943	+	0.958841i	$0.591643\pi$
$80$	−17.4673	−	5.67546i	−0.218341	−	0.0709432i
$81$	46.4670	+	66.3462i	0.573667	+	0.819089i
$82$	−44.2659	+	32.1611i	−0.539828	+	0.392208i
$83$	−30.0965	−	41.4243i	−0.362608	−	0.499088i	0.588265	−	0.808668i	$-0.299811\pi$
$83$	−30.0965	−	41.4243i	−0.362608	−	0.499088i	−0.950873	+	0.309581i	$0.899811\pi$
$84$	−21.8889	+	8.95571i	−0.260583	+	0.106616i
$85$	30.0655	−	92.5320i	0.353712	−	1.08861i
$86$	26.8688	−	36.9818i	0.312428	−	0.430021i
$87$	−72.4575	+	5.38653i	−0.832844	+	0.0619141i
$88$	−25.4293	+	17.9263i	−0.288969	+	0.203708i
$89$			0.204051i			0.00229271i	0.999999	+	0.00114636i	$0.000364896\pi$
$89$			0.204051i			0.00229271i	−0.999999	+	0.00114636i	$0.999635\pi$
$90$	−51.8391	−	26.9821i	−0.575990	−	0.299801i
$91$	3.50551	−	10.7888i	0.0385220	−	0.118559i
$92$	−38.7777	+	12.5996i	−0.421497	+	0.136953i
$93$	−74.4549	−	87.9447i	−0.800590	−	0.945642i
$94$	−6.01614	+	4.37098i	−0.0640015	+	0.0464998i
$95$	111.908	−	36.3611i	1.17798	−	0.382749i
$96$	4.03321	−	16.4843i	0.0420126	−	0.171712i
$97$	−5.42715	−	3.94306i	−0.0559500	−	0.0406501i	0.559459	−	0.828858i	$-0.311009\pi$
$97$	−5.42715	−	3.94306i	−0.0559500	−	0.0406501i	−0.615409	+	0.788208i	$0.711009\pi$
$98$			47.3239i			0.482897i
$99$	−89.2179	+	42.9088i	−0.901191	+	0.433423i
$100$	−7.83551			−0.0783551
$101$	−64.8408	+	89.2457i	−0.641988	+	0.883621i	−0.998720	−	0.0505860i	$-0.983891\pi$
$101$	−64.8408	+	89.2457i	−0.641988	+	0.883621i	0.356732	+	0.934207i	$0.383891\pi$
$102$	87.3250	+	21.3658i	0.856128	+	0.209468i
$103$	−3.87811	−	11.9356i	−0.0376515	−	0.115880i	0.930464	−	0.366383i	$-0.119404\pi$
$103$	−3.87811	−	11.9356i	−0.0376515	−	0.115880i	−0.968116	+	0.250503i	$0.919404\pi$
$104$	4.78464	+	6.58549i	0.0460061	+	0.0633220i
$105$	41.4390	−	35.0827i	0.394657	−	0.334121i
$106$	−23.3444	−	71.8465i	−0.220230	−	0.677797i
$107$	198.719	+	64.5678i	1.85719	+	0.603437i	0.995358	+	0.0962404i	$0.0306818\pi$
$107$	198.719	+	64.5678i	1.85719	+	0.603437i	0.861830	+	0.507197i	$0.169318\pi$
$108$	21.3121	−	49.6165i	0.197334	−	0.459412i
$109$	26.1304			0.239728			0.119864	−	0.992790i	$-0.461754\pi$
$109$	26.1304			0.239728			0.119864	+	0.992790i	$0.461754\pi$
$110$	42.8050	−	57.1807i	0.389136	−	0.519825i
$111$	14.8443	+	199.680i	0.133732	+	1.79892i
$112$	12.7556	+	9.26748i	0.113889	+	0.0827454i
$113$	−34.4231	−	11.1848i	−0.304630	−	0.0989801i	0.152713	−	0.988271i	$-0.451199\pi$
$113$	−34.4231	−	11.1848i	−0.304630	−	0.0989801i	−0.457343	+	0.889290i	$0.651199\pi$
$114$	41.1717	+	100.629i	0.361155	+	0.882711i
$115$	75.7290	−	55.0203i	0.658513	−	0.478438i
$116$	28.4713	+	39.1874i	0.245442	+	0.337822i
$117$	11.5585	+	23.1797i	0.0987910	+	0.198117i
$118$	17.1809	−	52.8775i	0.145601	−	0.448114i
$119$	−49.0941	+	67.5722i	−0.412555	+	0.567834i
$120$	2.88837	+	38.8533i	0.0240698	+	0.323778i
$121$	−34.0896	−	116.099i	−0.281732	−	0.959493i
$122$		−	115.896i		−	0.949963i
$123$	98.7016	+	61.0747i	0.802452	+	0.496542i
$124$	−23.7385	+	73.0597i	−0.191440	+	0.589191i
$125$	126.278	−	41.0304i	1.01023	−	0.328243i
$126$	35.1663	+	35.7816i	0.279098	+	0.283981i
$127$	−124.005	+	90.0948i	−0.976416	+	0.709408i	−0.956905	−	0.290402i	$-0.906211\pi$
$127$	−124.005	+	90.0948i	−0.976416	+	0.709408i	−0.0195112	+	0.999810i	$0.506211\pi$
$128$	−10.7600	+	3.49613i	−0.0840623	+	0.0273135i
$129$	−94.1915	−	23.0458i	−0.730167	−	0.178649i
$130$	−15.1188	−	10.9844i	−0.116298	−	0.0844956i
$131$		−	8.46829i		−	0.0646434i	−0.999478	−	0.0323217i	$-0.989710\pi$
$131$		−	8.46829i		−	0.0646434i	0.999478	−	0.0323217i	$-0.0102901\pi$
$132$	55.6226	+	35.5265i	0.421383	+	0.269140i
$133$	−101.014			−0.759501
$134$	−93.9334	+	129.288i	−0.700995	+	0.964837i
$135$	−11.3334	+	123.452i	−0.0839511	+	0.914463i
$136$	−18.5206	−	57.0005i	−0.136181	−	0.419121i
$137$	20.7205	+	28.5194i	0.151245	+	0.208171i	0.877916	−	0.478815i	$-0.158934\pi$
$137$	20.7205	+	28.5194i	0.151245	+	0.208171i	−0.726671	+	0.686986i	$0.758934\pi$
$138$	55.8872	+	66.0129i	0.404980	+	0.478355i
$139$	−37.4498	−	115.259i	−0.269423	−	0.829199i	−0.990641	−	0.136491i	$-0.956417\pi$
$139$	−37.4498	−	115.259i	−0.269423	−	0.829199i	0.721218	−	0.692708i	$-0.243583\pi$
$140$	−34.4253	−	11.1855i	−0.245895	−	0.0798962i
$141$	13.4145	+	8.30061i	0.0951380	+	0.0588695i
$142$	150.438			1.05942
$143$	−30.2448	+	9.35180i	−0.211502	+	0.0653972i
$144$	−35.6043	+	5.32310i	−0.247252	+	0.0369660i
$145$	−89.9652	−	65.3636i	−0.620450	−	0.450783i
$146$	−131.470	−	42.7173i	−0.900481	−	0.292584i
$147$	92.9131	−	38.0148i	0.632062	−	0.258604i
$148$	107.993	−	78.4617i	0.729685	−	0.530147i
$149$	8.74853	+	12.0413i	0.0587149	+	0.0808142i	0.837365	−	0.546645i	$-0.184095\pi$
$149$	8.74853	+	12.0413i	0.0587149	+	0.0808142i	−0.778650	+	0.627459i	$0.784095\pi$
$150$	6.29418	+	15.3838i	0.0419612	+	0.102559i
$151$	−80.0796	+	246.460i	−0.530328	+	1.63218i	0.223203	+	0.974772i	$0.428349\pi$
$151$	−80.0796	+	246.460i	−0.530328	+	1.63218i	−0.753532	+	0.657411i	$0.771651\pi$
$152$	42.6050	−	58.6407i	0.280296	−	0.385794i
$153$	−28.1989	−	188.612i	−0.184306	−	1.23276i
$154$	−50.1172	+	35.3300i	−0.325437	+	0.229416i
$155$		−	176.360i		−	1.13781i
$156$	9.08614	−	14.6839i	0.0582445	−	0.0941278i
$157$	56.5318	−	173.987i	0.360075	−	1.10820i	−0.592933	−	0.805252i	$-0.702030\pi$
$157$	56.5318	−	173.987i	0.360075	−	1.10820i	0.953008	−	0.302945i	$-0.0979698\pi$
$158$	−70.9522	+	23.0538i	−0.449065	+	0.145910i
$159$	−122.307	+	103.547i	−0.769228	+	0.651236i
$160$	21.0131	−	15.2669i	0.131332	−	0.0954184i
$161$	−76.4250	+	24.8320i	−0.474690	+	0.154236i
$162$	−114.534	−	1.98658i	−0.707000	−	0.0122629i
$163$	70.2069	+	51.0083i	0.430717	+	0.312934i	0.781936	−	0.623359i	$-0.214233\pi$
$163$	70.2069	+	51.0083i	0.430717	+	0.312934i	−0.351218	+	0.936294i	$0.614233\pi$
$164$		−	77.3797i		−	0.471827i
$165$	−146.650	−	38.1083i	−0.888790	−	0.230959i
$166$	72.4123			0.436218
$167$	52.4902	−	72.2466i	0.314313	−	0.432614i	−0.622407	−	0.782693i	$-0.713845\pi$
$167$	52.4902	−	72.2466i	0.314313	−	0.432614i	0.936720	+	0.350079i	$0.113845\pi$
$168$	7.94884	−	32.4881i	0.0473145	−	0.193382i
$169$	−49.6644	−	152.851i	−0.293872	−	0.904445i
$170$	80.8760	+	111.316i	0.475741	+	0.654801i
$171$	164.497	−	161.668i	0.961970	−	0.945430i
$172$	19.9769	+	61.4825i	0.116145	+	0.357456i
$173$	225.229	+	73.1814i	1.30190	+	0.423014i	0.876243	−	0.481869i	$-0.160042\pi$
$173$	225.229	+	73.1814i	1.30190	+	0.423014i	0.425660	+	0.904883i	$0.360042\pi$
$174$	54.0677	−	87.3778i	0.310734	−	0.502171i
$175$	−15.4426			−0.0882434
$176$	0.628303	−	43.9955i	0.00356990	−	0.249975i
$177$	−117.618	+	8.74379i	−0.664509	+	0.0493999i
$178$	−0.233460	−	0.169618i	−0.00131157	−	0.000952912i
$179$	−310.471	−	100.878i	−1.73447	−	0.563564i	−0.740389	−	0.672179i	$-0.765358\pi$
$179$	−310.471	−	100.878i	−1.73447	−	0.563564i	−0.994084	+	0.108615i	$0.965358\pi$
$180$	73.9623	−	36.8813i	0.410901	−	0.204896i
$181$	−99.3656	+	72.1933i	−0.548981	+	0.398858i	−0.827410	−	0.561599i	$-0.810186\pi$
$181$	−99.3656	+	72.1933i	−0.548981	+	0.398858i	0.278428	+	0.960457i	$0.410186\pi$
$182$	9.42979	+	12.9790i	0.0518120	+	0.0713131i
$183$	−227.543	+	93.0976i	−1.24340	+	0.508730i
$184$	17.8186	−	54.8400i	0.0968402	−	0.298043i
$185$	−180.130	+	247.928i	−0.973677	+	1.34015i
$186$	162.510	−	12.0811i	0.873712	−	0.0649522i
$187$	233.064	+	3.32841i	1.24633	+	0.0177990i
$188$		−	10.5166i		−	0.0559394i
$189$	42.0029	−	97.7866i	0.222237	−	0.517389i
$190$	−51.4224	+	158.262i	−0.270644	+	0.832957i
$191$	0.746211	−	0.242459i	0.00390686	−	0.00126942i	−0.307063	−	0.951689i	$-0.599346\pi$
$191$	0.746211	−	0.242459i	0.00390686	−	0.00126942i	0.310970	+	0.950420i	$0.399346\pi$
$192$	15.5075	+	18.3172i	0.0807681	+	0.0954018i
$193$	123.450	−	89.6916i	0.639637	−	0.464723i	−0.220089	−	0.975480i	$-0.570635\pi$
$193$	123.450	−	89.6916i	0.639637	−	0.464723i	0.859725	+	0.510757i	$0.170635\pi$
$194$	9.02268	−	2.93165i	0.0465087	−	0.0151116i
$195$	−9.42149	+	38.5070i	−0.0483153	+	0.197472i
$196$	−54.1443	−	39.3382i	−0.276247	−	0.200705i
$197$		−	149.172i		−	0.757217i	−0.925557	−	0.378609i	$-0.876403\pi$
$197$		−	149.172i		−	0.757217i	0.925557	−	0.378609i	$-0.123597\pi$
$198$	25.0697	−	137.744i	0.126615	−	0.695679i
$199$	−47.0772			−0.236569			−0.118284	−	0.992980i	$-0.537739\pi$
$199$	−47.0772			−0.236569			−0.118284	+	0.992980i	$0.537739\pi$
$200$	6.51330	−	8.96478i	0.0325665	−	0.0448239i
$201$	329.293	+	80.5679i	1.63827	+	0.400835i
$202$	−48.2089	−	148.372i	−0.238658	−	0.734513i
$203$	56.1126	+	77.2324i	0.276417	+	0.380455i
$204$	−97.0343	+	82.1502i	−0.475658	+	0.402697i
$205$	54.8956	+	168.951i	0.267784	+	0.824153i
$206$	16.8795	+	5.48448i	0.0819392	+	0.0266237i
$207$	84.7126	−	162.753i	0.409240	−	0.786248i
$208$	−11.5119			−0.0553454
$209$	162.421	+	230.402i	0.777134	+	1.10240i
$210$	5.69255	+	76.5740i	0.0271074	+	0.364638i
$211$	−66.2986	−	48.1688i	−0.314212	−	0.228288i	0.419490	−	0.907760i	$-0.362209\pi$
$211$	−66.2986	−	48.1688i	−0.314212	−	0.228288i	−0.733701	+	0.679472i	$0.762209\pi$
$212$	101.606	+	33.0139i	0.479275	+	0.155726i
$213$	−120.845	−	295.362i	−0.567348	−	1.38667i
$214$	−239.060	+	173.687i	−1.11710	+	0.811621i
$215$	−87.2353	−	120.069i	−0.405746	−	0.558461i
$216$	39.0516	+	65.6275i	0.180795	+	0.303831i
$217$	−46.7851	+	143.990i	−0.215599	+	0.663547i
$218$	−21.7210	+	29.8963i	−0.0996374	+	0.137139i
$219$	21.7398	+	292.436i	0.0992687	+	1.33532i
$220$	29.8400	+	96.5059i	0.135636	+	0.438663i
$221$		−	60.9835i		−	0.275944i
$222$	−240.797	−	149.001i	−1.08467	−	0.671175i
$223$	−88.8289	+	273.387i	−0.398336	+	1.22595i	0.527997	+	0.849246i	$0.322943\pi$
$223$	−88.8289	+	273.387i	−0.398336	+	1.22595i	−0.926333	+	0.376706i	$0.877057\pi$
$224$	−21.2063	+	6.89034i	−0.0946709	+	0.0307604i
$225$	25.1477	−	24.7153i	0.111768	−	0.109846i
$226$	41.4111	−	30.0869i	0.183235	−	0.133128i
$227$	126.162	−	40.9926i	0.555780	−	0.180584i	−0.0176413	−	0.999844i	$-0.505616\pi$
$227$	126.162	−	40.9926i	0.555780	−	0.180584i	0.573422	+	0.819260i	$0.305616\pi$
$228$	−149.356	−	36.5429i	−0.655071	−	0.160276i
$229$	103.037	+	74.8604i	0.449941	+	0.326901i	0.789573	−	0.613657i	$-0.210302\pi$
$229$	103.037	+	74.8604i	0.449941	+	0.326901i	−0.339631	+	0.940559i	$0.610302\pi$
$230$			132.379i			0.575561i
$231$	109.624	+	70.0173i	0.474561	+	0.303105i
$232$	−68.5021			−0.295267
$233$	−54.1379	+	74.5145i	−0.232352	+	0.319805i	−0.909233	−	0.416287i	$-0.863331\pi$
$233$	−54.1379	+	74.5145i	−0.232352	+	0.319805i	0.676881	+	0.736092i	$0.263331\pi$
$234$	−36.1285	−	6.04378i	−0.154395	−	0.0258281i
$235$	7.46082	+	22.9620i	0.0317482	+	0.0977108i
$236$	46.2166	+	63.6117i	0.195833	+	0.269541i
$237$	102.258	+	120.785i	0.431467	+	0.509641i
$238$	−36.5013	−	112.339i	−0.153367	−	0.472014i
$239$	6.96567	+	2.26328i	0.0291451	+	0.00946981i	0.323553	−	0.946210i	$-0.395123\pi$
$239$	6.96567	+	2.26328i	0.0291451	+	0.00946981i	−0.294408	+	0.955680i	$0.595123\pi$
$240$	−46.8539	−	28.9923i	−0.195225	−	0.120801i
$241$	333.266			1.38285			0.691424	−	0.722449i	$-0.256984\pi$
$241$	333.266			1.38285			0.691424	+	0.722449i	$0.256984\pi$
$242$	161.168	+	57.5048i	0.665984	+	0.237623i
$243$	88.1036	+	226.466i	0.362566	+	0.931958i
$244$	132.599	+	96.3386i	0.543437	+	0.394830i
$245$	146.127	+	47.4795i	0.596436	+	0.193794i
$246$	−151.923	+	62.1582i	−0.617573	+	0.252676i
$247$	59.6677	−	43.3511i	0.241570	−	0.175511i
$248$	−63.8566	−	87.8910i	−0.257486	−	0.354399i
$249$	−58.1680	−	142.170i	−0.233606	−	0.570965i
$250$	−58.0257	+	178.585i	−0.232103	+	0.714339i
$251$	70.2370	−	96.6729i	0.279828	−	0.385151i	−0.645849	−	0.763466i	$-0.723496\pi$
$251$	70.2370	−	96.6729i	0.279828	−	0.385151i	0.925677	+	0.378315i	$0.123496\pi$
$252$	−70.1706	+	10.4910i	−0.278455	+	0.0416310i
$253$	179.524	+	134.390i	0.709581	+	0.531186i
$254$		−	216.768i		−	0.853419i
$255$	153.585	−	248.207i	0.602296	−	0.973359i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−200.581	+	65.1727i	−0.780471	+	0.253590i	−0.672041	−	0.740514i	$-0.734582\pi$
$257$	−200.581	+	65.1727i	−0.780471	+	0.253590i	−0.108430	+	0.994104i	$0.534582\pi$
$258$	104.664	−	88.6097i	0.405675	−	0.343449i
$259$	212.838	−	154.636i	0.821770	−	0.597051i
$260$	25.1351	−	8.16688i	0.0966733	−	0.0314111i
$261$	−214.985	−	35.9640i	−0.823697	−	0.137793i
$262$	9.68876	+	7.03930i	0.0369800	+	0.0268676i
$263$			156.325i			0.594392i	0.954816	+	0.297196i	$0.0960515\pi$
$263$			156.325i			0.594392i	−0.954816	+	0.297196i	$0.903948\pi$
$264$	−86.8831	+	34.1075i	−0.329103	+	0.129195i
$265$	−245.269			−0.925544
$266$	83.9679	−	115.572i	0.315669	−	0.434481i
$267$	−0.145484	+	0.594615i	−0.000544884	+	0.00222702i
$268$	−69.8391	−	214.943i	−0.260594	−	0.802025i
$269$	−207.312	−	285.340i	−0.770675	−	1.06074i	−0.996250	−	0.0865172i	$-0.972426\pi$
$269$	−207.312	−	285.340i	−0.770675	−	1.06074i	0.225576	−	0.974226i	$-0.427574\pi$
$270$	−131.824	−	115.587i	−0.488236	−	0.428101i
$271$	−2.82994	−	8.70965i	−0.0104426	−	0.0321389i	0.945699	−	0.325042i	$-0.105379\pi$
$271$	−2.82994	−	8.70965i	−0.0104426	−	0.0321389i	−0.956142	+	0.292903i	$0.905379\pi$
$272$	80.6109	+	26.1921i	0.296364	+	0.0962944i
$273$	17.9074	−	28.9398i	0.0655949	−	0.106007i
$274$	−49.8537			−0.181948
$275$	24.8303	+	35.2230i	0.0902921	+	0.128084i
$276$	−121.983	+	9.06831i	−0.441969	+	0.0328562i
$277$	−274.791	−	199.648i	−0.992027	−	0.720750i	−0.0316627	−	0.999499i	$-0.510080\pi$
$277$	−274.791	−	199.648i	−0.992027	−	0.720750i	−0.960364	+	0.278749i	$0.910080\pi$
$278$	163.000	+	52.9620i	0.586332	+	0.190511i
$279$	−154.262	−	309.360i	−0.552911	−	1.10882i
$280$	41.4137	−	30.0888i	0.147906	−	0.107460i
$281$	−217.518	−	299.388i	−0.774085	−	1.06544i	−0.995910	−	0.0903498i	$-0.971201\pi$
$281$	−217.518	−	299.388i	−0.774085	−	1.06544i	0.221825	−	0.975086i	$-0.428799\pi$
$282$	−20.6477	+	8.44787i	−0.0732189	+	0.0299570i
$283$	−32.1078	+	98.8177i	−0.113455	+	0.349179i	−0.991622	−	0.129176i	$-0.958767\pi$
$283$	−32.1078	+	98.8177i	−0.113455	+	0.349179i	0.878166	+	0.478355i	$0.158767\pi$
$284$	−125.052	+	172.119i	−0.440324	+	0.606054i
$285$	352.030	−	26.1701i	1.23519	−	0.0918249i
$286$	14.4415	−	42.3775i	0.0504947	−	0.148173i
$287$		−	152.504i		−	0.531371i
$288$	23.5059	−	45.1605i	0.0816178	−	0.156807i
$289$	−49.4454	+	152.177i	−0.171091	+	0.526565i
$290$	149.568	−	48.5976i	0.515751	−	0.167578i
$291$	−13.0037	−	15.3597i	−0.0446861	−	0.0527824i
$292$	158.159	−	114.909i	0.541640	−	0.393525i
$293$	153.484	−	49.8701i	0.523838	−	0.170205i	−0.0351486	−	0.999382i	$-0.511190\pi$
$293$	153.484	−	49.8701i	0.523838	−	0.170205i	0.558986	+	0.829177i	$0.311190\pi$
$294$	−33.7409	+	137.904i	−0.114765	+	0.469061i
$295$	−146.038	−	106.103i	−0.495044	−	0.359670i
$296$			188.779i			0.637768i
$297$	−290.578	+	61.4280i	−0.978377	+	0.206828i
$298$	−21.0490			−0.0706342
$299$	34.4866	−	47.4667i	0.115340	−	0.158751i
$300$	−22.8330	−	5.58654i	−0.0761101	−	0.0186218i
$301$	39.3714	+	121.173i	0.130802	+	0.402567i
$302$	−215.414	−	296.491i	−0.713290	−	0.981760i
$303$	−252.579	+	213.836i	−0.833595	+	0.705730i
$304$	31.6766	+	97.4907i	0.104199	+	0.320693i
$305$	−357.863	−	116.277i	−1.17332	−	0.381235i
$306$	239.236	+	124.522i	0.781817	+	0.406933i
$307$	94.9339			0.309231			0.154615	−	0.987975i	$-0.450586\pi$
$307$	94.9339			0.309231			0.154615	+	0.987975i	$0.450586\pi$
$308$	1.23829	−	86.7085i	0.00402042	−	0.281521i
$309$	−2.79118	−	37.5459i	−0.00903294	−	0.121508i
$310$	201.778	+	146.600i	0.650895	+	0.472903i
$311$	−194.971	−	63.3499i	−0.626916	−	0.203697i	−0.0217078	−	0.999764i	$-0.506910\pi$
$311$	−194.971	−	63.3499i	−0.626916	−	0.203697i	−0.605209	+	0.796067i	$0.706910\pi$
$312$	9.24734	+	22.6017i	0.0296389	+	0.0724415i
$313$	−25.9469	+	18.8515i	−0.0828975	+	0.0602286i	−0.628462	−	0.777840i	$-0.716315\pi$
$313$	−25.9469	+	18.8515i	−0.0828975	+	0.0602286i	0.545565	+	0.838069i	$0.316315\pi$
$314$	152.070	+	209.307i	0.484300	+	0.666581i
$315$	145.768	−	72.6875i	0.462757	−	0.230754i
$316$	32.6029	−	100.342i	0.103174	−	0.317537i
$317$	−49.9314	+	68.7247i	−0.157512	+	0.216797i	−0.880478	−	0.474087i	$-0.842778\pi$
$317$	−49.9314	+	68.7247i	−0.157512	+	0.216797i	0.722966	+	0.690884i	$0.242778\pi$
$318$	−16.8016	−	226.008i	−0.0528351	−	0.710717i
$319$	85.9350	−	252.170i	0.269389	−	0.790502i
$320$			36.7323i			0.114789i
$321$	533.041	+	329.836i	1.66057	+	1.02753i
$322$	35.1177	−	108.081i	0.109061	−	0.335656i
$323$	−516.452	+	167.806i	−1.59892	+	0.519522i
$324$	97.4798	−	129.390i	0.300864	−	0.399351i
$325$	9.12179	−	6.62737i	0.0280670	−	0.0203919i
$326$	−116.720	+	37.9245i	−0.358035	+	0.116333i
$327$	76.1450	+	18.6304i	0.232859	+	0.0569736i
$328$	88.5318	+	64.3222i	0.269914	+	0.196104i
$329$		−	20.7266i		−	0.0629989i
$330$	165.504	−	136.108i	0.501528	−	0.412449i
$331$	−525.606			−1.58793			−0.793967	−	0.607961i	$-0.791988\pi$
$331$	−525.606			−1.58793			−0.793967	+	0.607961i	$0.791988\pi$
$332$	−60.1930	+	82.8485i	−0.181304	+	0.249544i
$333$	−99.1101	+	592.459i	−0.297628	+	1.77916i
$334$	39.0263	+	120.111i	0.116845	+	0.359612i
$335$	304.974	+	419.761i	0.910371	+	1.25302i
$336$	30.5629	+	36.1003i	0.0909610	+	0.107441i
$337$	50.2893	+	154.774i	0.149226	+	0.459271i	0.997530	−	0.0702382i	$-0.0223759\pi$
$337$	50.2893	+	154.774i	0.149226	+	0.459271i	−0.848304	+	0.529510i	$0.822376\pi$
$338$	216.164	+	70.2360i	0.639539	+	0.207799i
$339$	−92.3361	−	57.1358i	−0.272378	−	0.168542i
$340$	−194.588			−0.572317
$341$	403.652	−	124.811i	1.18373	−	0.366014i
$342$	48.2299	+	322.592i	0.141023	+	0.943252i
$343$	−262.966	−	191.056i	−0.766666	−	0.557015i
$344$	−86.9494	−	28.2516i	−0.252760	−	0.0821267i
$345$	259.906	−	106.339i	0.753351	−	0.308228i
$346$	−270.951	+	196.858i	−0.783096	+	0.568953i
$347$	228.036	+	313.865i	0.657164	+	0.904509i	0.999383	−	0.0351112i	$-0.0111785\pi$
$347$	228.036	+	313.865i	0.657164	+	0.904509i	−0.342219	+	0.939620i	$0.611179\pi$
$348$	55.0270	+	134.493i	0.158123	+	0.386475i
$349$	108.871	−	335.069i	0.311950	−	0.960084i	−0.665042	−	0.746806i	$-0.731586\pi$
$349$	108.871	−	335.069i	0.311950	−	0.960084i	0.976992	−	0.213277i	$-0.0684138\pi$
$350$	12.8367	−	17.6682i	0.0366763	−	0.0504806i
$351$	17.1556	+	75.7875i	0.0488762	+	0.215919i
$352$	49.8140	+	37.2903i	0.141517	+	0.105938i
$353$			91.0351i			0.257890i	0.991652	+	0.128945i	$0.0411590\pi$
$353$			91.0351i			0.257890i	−0.991652	+	0.128945i	$0.958841\pi$
$354$	87.7665	−	141.838i	0.247928	−	0.400672i
$355$	150.933	−	464.523i	0.425162	−	1.30852i
$356$	0.388129	−	0.126111i	0.00109025	−	0.000354243i
$357$	−191.240	+	161.906i	−0.535686	+	0.453517i
$358$	373.497	−	271.361i	1.04329	−	0.757992i
$359$	119.155	−	38.7157i	0.331907	−	0.107843i	−0.138323	−	0.990387i	$-0.544171\pi$
$359$	119.155	−	38.7157i	0.331907	−	0.107843i	0.470230	+	0.882544i	$0.344171\pi$
$360$	−19.2847	+	115.280i	−0.0535685	+	0.320221i
$361$	−239.258	−	173.831i	−0.662766	−	0.481528i
$362$		−	173.697i		−	0.479827i
$363$	−16.5630	−	362.622i	−0.0456280	−	0.998959i
$364$	−22.6881			−0.0623300
$365$	−263.805	+	363.097i	−0.722754	+	0.994785i
$366$	82.6309	−	337.725i	0.225767	−	0.922746i
$367$	42.9214	+	132.098i	0.116952	+	0.359941i	0.992349	−	0.123463i	$-0.0394001\pi$
$367$	42.9214	+	132.098i	0.116952	+	0.359941i	−0.875397	+	0.483404i	$0.839400\pi$
$368$	47.9319	+	65.9726i	0.130250	+	0.179273i
$369$	244.076	+	248.346i	0.661453	+	0.673026i
$370$	−133.926	−	412.182i	−0.361962	−	1.11401i
$371$	200.251	+	65.0654i	0.539759	+	0.175378i
$372$	−121.265	+	195.974i	−0.325982	+	0.526813i
$373$	−464.536			−1.24540			−0.622702	−	0.782459i	$-0.713965\pi$
$373$	−464.536			−1.24540			−0.622702	+	0.782459i	$0.713965\pi$
$374$	−197.544	+	263.887i	−0.528192	+	0.705581i
$375$	397.235	−	29.5307i	1.05929	−	0.0787484i
$376$	12.0323	+	8.74197i	0.0320008	+	0.0232499i
$377$	−66.2903	−	21.5390i	−0.175836	−	0.0571327i
$378$	76.9648	+	129.342i	0.203611	+	0.342174i
$379$	332.654	−	241.687i	0.877714	−	0.637697i	−0.0549316	−	0.998490i	$-0.517494\pi$
$379$	332.654	−	241.687i	0.877714	−	0.637697i	0.932646	+	0.360793i	$0.117494\pi$
$380$	−138.326	−	190.389i	−0.364016	−	0.501025i
$381$	−425.591	+	174.128i	−1.11704	+	0.457028i
$382$	−0.342888	+	1.05530i	−0.000897614	+	0.00276257i
$383$	222.081	−	305.668i	0.579846	−	0.798090i	−0.413832	−	0.910353i	$-0.635810\pi$
$383$	222.081	−	305.668i	0.579846	−	0.798090i	0.993678	+	0.112263i	$0.0358100\pi$
$384$	−33.8477	+	2.51626i	−0.0881451	+	0.00655275i
$385$	58.8101	+	190.198i	0.152753	+	0.494022i
$386$			215.798i			0.559063i
$387$	−258.047	−	134.313i	−0.666789	−	0.347062i
$388$	−4.14598	+	12.7600i	−0.0106855	+	0.0328866i
$389$	712.696	−	231.569i	1.83212	−	0.595293i	0.833007	−	0.553262i	$-0.186617\pi$
$389$	712.696	−	231.569i	1.83212	−	0.595293i	0.999116	−	0.0420308i	$-0.0133828\pi$
$390$	−36.2251	−	42.7884i	−0.0928849	−	0.109714i
$391$	−349.487	+	253.917i	−0.893829	+	0.649405i
$392$	90.0154	−	29.2478i	0.229631	−	0.0746116i
$393$	6.03770	−	24.6770i	0.0153631	−	0.0627913i
$394$	170.671	+	124.000i	0.433175	+	0.314720i
$395$			242.216i			0.613205i
$396$	136.757	+	143.183i	0.345346	+	0.361574i
$397$	583.694			1.47026			0.735131	−	0.677925i	$-0.237121\pi$
$397$	583.694			1.47026			0.735131	+	0.677925i	$0.237121\pi$
$398$	39.1331	−	53.8621i	0.0983244	−	0.135332i
$399$	−294.358	−	72.0204i	−0.737740	−	0.180502i
$400$	4.84261	+	14.9040i	0.0121065	+	0.0372600i
$401$	77.5802	+	106.780i	0.193467	+	0.266284i	0.894719	−	0.446629i	$-0.147375\pi$
$401$	77.5802	+	106.780i	0.193467	+	0.266284i	−0.701253	+	0.712913i	$0.747375\pi$
$402$	−365.906	+	309.779i	−0.910213	+	0.770596i
$403$	−34.1593	−	105.132i	−0.0847626	−	0.260872i
$404$	209.829	+	68.1777i	0.519379	+	0.168757i
$405$	−121.045	+	351.666i	−0.298876	+	0.868310i
$406$	−135.007			−0.332530
$407$	−694.935	−	236.821i	−1.70746	−	0.581871i
$408$	−13.3298	−	179.307i	−0.0326710	−	0.439478i
$409$	185.166	+	134.531i	0.452728	+	0.328926i	0.790672	−	0.612240i	$-0.209731\pi$
$409$	185.166	+	134.531i	0.452728	+	0.328926i	−0.337944	+	0.941166i	$0.609731\pi$
$410$	−238.933	−	77.6341i	−0.582764	−	0.189352i
$411$	40.0469	+	97.8801i	0.0974378	+	0.238151i
$412$	−20.3060	+	14.7532i	−0.0492865	+	0.0358088i
$413$	91.0859	+	125.369i	0.220547	+	0.303557i
$414$	115.792	+	232.211i	0.279691	+	0.560896i
$415$	72.6504	−	223.595i	0.175061	−	0.538783i
$416$	9.56927	−	13.1710i	0.0230031	−	0.0316610i
$417$	−26.9536	−	362.570i	−0.0646370	−	0.869472i
$418$	−398.621	−	5.69273i	−0.953638	−	0.0136190i
$419$		−	332.727i		−	0.794098i	−0.917797	−	0.397049i	$-0.870034\pi$
$419$		−	332.727i		−	0.794098i	0.917797	−	0.397049i	$-0.129966\pi$
$420$	−92.3420	−	57.1394i	−0.219862	−	0.136046i
$421$	−0.615775	+	1.89516i	−0.00146265	+	0.00450157i	−0.951785	−	0.306765i	$-0.900753\pi$
$421$	−0.615775	+	1.89516i	−0.00146265	+	0.00450157i	0.950323	+	0.311267i	$0.100753\pi$
$422$	110.222	−	35.8133i	0.261190	−	0.0848656i
$423$	33.1722	+	33.7525i	0.0784213	+	0.0797933i
$424$	−122.233	+	88.8072i	−0.288284	+	0.209451i
$425$	−78.9534	+	25.6535i	−0.185773	+	0.0603612i
$426$	438.383	+	107.259i	1.02907	+	0.251781i
$427$	261.332	+	189.869i	0.612019	+	0.444657i
$428$		−	417.891i		−	0.976382i
$429$	−94.8023	+	5.68774i	−0.220984	+	0.0132581i
$430$	209.889			0.488113
$431$	−151.788	+	208.918i	−0.352175	+	0.484728i	−0.947948	−	0.318425i	$-0.896846\pi$
$431$	−151.788	+	208.918i	−0.352175	+	0.484728i	0.595773	+	0.803153i	$0.296846\pi$
$432$	−107.548	−	9.87329i	−0.248953	−	0.0228548i
$433$	181.466	+	558.494i	0.419089	+	1.28982i	0.908542	+	0.417794i	$0.137197\pi$
$433$	181.466	+	558.494i	0.419089	+	1.28982i	−0.489453	+	0.872030i	$0.662803\pi$
$434$	−125.852	−	173.220i	−0.289981	−	0.399124i
$435$	−215.560	−	254.616i	−0.495540	−	0.585323i
$436$	−16.1494	−	49.7029i	−0.0370400	−	0.113997i
$437$	−496.877	−	161.445i	−1.13702	−	0.369440i
$438$	−352.654	−	218.215i	−0.805146	−	0.498209i
$439$	157.315			0.358349			0.179175	−	0.983817i	$-0.442657\pi$
$439$	157.315			0.358349			0.179175	+	0.983817i	$0.442657\pi$
$440$	−135.219	−	46.0803i	−0.307316	−	0.104728i
$441$	297.857	−	44.5318i	0.675412	−	0.100979i
$442$	69.7726	+	50.6928i	0.157857	+	0.114690i
$443$	123.544	+	40.1417i	0.278879	+	0.0906134i	0.445117	−	0.895472i	$-0.353162\pi$
$443$	123.544	+	40.1417i	0.278879	+	0.0906134i	−0.166238	+	0.986086i	$0.553162\pi$
$444$	370.639	−	151.644i	0.834772	−	0.341541i
$445$	−0.757976	+	0.550702i	−0.00170332	+	0.00123753i
$446$	−238.949	−	328.885i	−0.535761	−	0.737411i
$447$	16.9084	+	41.3264i	0.0378264	+	0.0924529i
$448$	9.74441	−	29.9902i	0.0217509	−	0.0669424i
$449$	317.127	−	436.489i	0.706297	−	0.972135i	−0.293572	−	0.955937i	$-0.594844\pi$
$449$	317.127	−	436.489i	0.706297	−	0.972135i	0.999869	−	0.0161977i	$-0.00515611\pi$
$450$	7.37321	+	49.3167i	0.0163849	+	0.109593i
$451$	−347.845	+	245.212i	−0.771275	+	0.543708i
$452$			72.3893i			0.160153i
$453$	−409.076	+	661.100i	−0.903037	+	1.45938i
$454$	−57.9722	+	178.420i	−0.127692	+	0.392996i
$455$	49.5374	−	16.0957i	0.108873	−	0.0353751i
$456$	165.962	−	140.505i	0.363953	−	0.308126i
$457$	−112.957	+	82.0679i	−0.247170	+	0.179580i	−0.704472	−	0.709732i	$-0.748816\pi$
$457$	−112.957	+	82.0679i	−0.247170	+	0.179580i	0.457301	+	0.889312i	$0.348816\pi$
$458$	−171.299	+	55.6584i	−0.374015	+	0.121525i
$459$	52.3033	−	569.730i	0.113951	−	1.24124i
$460$	−151.458	−	110.041i	−0.329256	−	0.239219i
$461$		−	384.562i		−	0.834191i	−0.908863	−	0.417096i	$-0.863048\pi$
$461$		−	384.562i		−	0.834191i	0.908863	−	0.417096i	$-0.136952\pi$
$462$	−171.233	+	67.2208i	−0.370635	+	0.145500i
$463$	154.535			0.333770			0.166885	−	0.985976i	$-0.446629\pi$
$463$	154.535			0.333770			0.166885	+	0.985976i	$0.446629\pi$
$464$	56.9426	−	78.3748i	0.122721	−	0.168911i
$465$	125.741	−	513.921i	0.270410	−	1.10521i
$466$	−40.2513	−	123.881i	−0.0863763	−	0.265839i
$467$	−38.6742	−	53.2305i	−0.0828141	−	0.113984i	0.765600	−	0.643317i	$-0.222442\pi$
$467$	−38.6742	−	53.2305i	−0.0828141	−	0.113984i	−0.848414	+	0.529333i	$0.822442\pi$
$468$	36.9467	−	36.3115i	0.0789460	−	0.0775886i
$469$	−137.642	−	423.619i	−0.293480	−	0.903240i
$470$	−32.4732	−	10.5512i	−0.0690919	−	0.0224493i
$471$	288.785	−	466.700i	0.613131	−	0.990870i
$472$	−111.197			−0.235588
$473$	213.077	−	284.637i	0.450479	−	0.601770i
$474$	−223.195	+	16.5924i	−0.470875	+	0.0350051i
$475$	−81.2253	−	59.0136i	−0.171001	−	0.124239i
$476$	158.872	+	51.6206i	0.333764	+	0.108447i
$477$	−430.235	+	214.537i	−0.901961	+	0.449763i
$478$	−8.37972	+	6.08822i	−0.0175308	+	0.0127369i
$479$	267.689	+	368.442i	0.558850	+	0.769191i	0.991180	−	0.132525i	$-0.0423084\pi$
$479$	267.689	+	368.442i	0.558850	+	0.769191i	−0.432330	+	0.901716i	$0.642308\pi$
$480$	72.1183	−	29.5067i	0.150246	−	0.0614722i
$481$	−59.3577	+	182.684i	−0.123405	+	0.379801i
$482$	−277.029	+	381.298i	−0.574749	+	0.791074i
$483$	−240.411	+	17.8723i	−0.497745	+	0.0370026i
$484$	−199.764	+	136.595i	−0.412736	+	0.282222i
$485$		−	30.8016i		−	0.0635084i
$486$	−332.341	−	87.4492i	−0.683830	−	0.179937i
$487$	206.411	−	635.269i	0.423843	−	1.30445i	−0.480255	−	0.877129i	$-0.659456\pi$
$487$	206.411	−	635.269i	0.423843	−	1.30445i	0.904098	−	0.427325i	$-0.140544\pi$
$488$	−220.446	+	71.6274i	−0.451734	+	0.146777i
$489$	168.218	+	198.696i	0.344005	+	0.406332i
$490$	−175.791	+	127.720i	−0.358757	+	0.260652i
$491$	102.588	−	33.3327i	0.208936	−	0.0678874i	−0.202679	−	0.979245i	$-0.564965\pi$
$491$	102.588	−	33.3327i	0.208936	−	0.0678874i	0.411615	+	0.911358i	$0.364965\pi$
$492$	55.1700	−	225.488i	0.112134	−	0.458309i
$493$	415.187	+	301.651i	0.842164	+	0.611868i
$494$			104.303i			0.211140i
$495$	−400.175	−	215.608i	−0.808435	−	0.435571i
$496$	153.639			0.309756
$497$	−246.459	+	339.221i	−0.495893	+	0.682538i
$498$	211.013	+	51.6283i	0.423720	+	0.103671i
$499$	283.711	+	873.173i	0.568559	+	1.74984i	0.657132	+	0.753775i	$0.271769\pi$
$499$	283.711	+	873.173i	0.568559	+	1.74984i	−0.0885733	+	0.996070i	$0.528231\pi$
$500$	−156.089	−	214.838i	−0.312178	−	0.429676i
$501$	204.469	−	173.106i	0.408122	−	0.345520i
$502$	52.2209	+	160.719i	0.104026	+	0.320158i
$503$	335.272	+	108.936i	0.666545	+	0.216573i	0.622695	−	0.782465i	$-0.286038\pi$
$503$	335.272	+	108.936i	0.666545	+	0.216573i	0.0438496	+	0.999038i	$0.486038\pi$
$504$	46.3266	−	89.0045i	0.0919178	−	0.176596i
$505$	−506.510			−1.00299
$506$	−302.989	+	93.6853i	−0.598792	+	0.185149i
$507$	−35.7448	−	480.825i	−0.0705026	−	0.948373i
$508$	248.010	+	180.190i	0.488208	+	0.354704i
$509$	810.098	+	263.217i	1.59155	+	0.517125i	0.964998	−	0.262256i	$-0.0844664\pi$
$509$	810.098	+	263.217i	1.59155	+	0.517125i	0.626550	+	0.779381i	$0.284466\pi$
$510$	156.310	+	382.043i	0.306491	+	0.749105i
$511$	311.707	−	226.469i	0.609995	−	0.443187i
$512$	13.3001	+	18.3060i	0.0259767	+	0.0357538i
$513$	594.617	−	353.827i	1.15910	−	0.689721i
$514$	92.1681	−	283.664i	0.179315	−	0.551876i
$515$	33.8700	−	46.6180i	0.0657669	−	0.0905204i
$516$	14.3779	+	193.406i	0.0278641	+	0.374818i
$517$	−47.2753	+	33.3266i	−0.0914416	+	0.0644615i
$518$			372.055i			0.718253i
$519$	604.152	+	373.837i	1.16407	+	0.720303i
$520$	−11.5497	+	35.5463i	−0.0222110	+	0.0683583i
$521$	57.8334	−	18.7912i	0.111005	−	0.0360676i	−0.252988	−	0.967469i	$-0.581413\pi$
$521$	57.8334	−	18.7912i	0.111005	−	0.0360676i	0.363993	+	0.931402i	$0.381413\pi$
$522$	219.854	−	216.074i	0.421177	−	0.413935i
$523$	62.1420	−	45.1488i	0.118818	−	0.0863266i	−0.526789	−	0.849996i	$-0.676604\pi$
$523$	62.1420	−	45.1488i	0.118818	−	0.0863266i	0.645607	+	0.763669i	$0.276604\pi$
$524$	−16.1076	+	5.23369i	−0.0307398	+	0.00998796i
$525$	−45.0004	−	11.0102i	−0.0857151	−	0.0209718i
$526$	−178.855	−	129.946i	−0.340029	−	0.247045i
$527$			813.897i			1.54440i
$528$	33.1987	−	127.757i	0.0628763	−	0.241964i
$529$	113.384			0.214337
$530$	203.881	−	280.618i	0.384681	−	0.529468i
$531$	−348.978	−	58.3792i	−0.657210	−	0.109942i
$532$	62.4298	+	192.139i	0.117349	+	0.361164i
$533$	65.4487	+	90.0823i	0.122793	+	0.169010i
$534$	−0.559378	−	0.660727i	−0.00104752	−	0.00123732i
$535$	296.466	+	912.427i	0.554141	+	1.70547i
$536$	303.975	+	98.7674i	0.567117	+	0.184268i
$537$	−832.802	−	515.322i	−1.55084	−	0.959631i
$538$	498.792			0.927123
$539$	−5.25623	+	368.056i	−0.00975182	+	0.682849i
$540$	241.825	−	54.7404i	0.447824	−	0.101371i
$541$	−80.8758	−	58.7597i	−0.149493	−	0.108613i	0.510525	−	0.859863i	$-0.329451\pi$
$541$	−80.8758	−	58.7597i	−0.149493	−	0.108613i	−0.660018	+	0.751250i	$0.729451\pi$
$542$	12.3173	+	4.00213i	0.0227257	+	0.00738401i
$543$	−341.028	+	139.529i	−0.628045	+	0.256960i
$544$	−96.9751	+	70.4565i	−0.178263	+	0.129516i
$545$	70.5216	+	97.0647i	0.129398	+	0.178100i
$546$	18.2251	+	44.5446i	0.0333793	+	0.0815835i
$547$	−149.118	+	458.939i	−0.272611	+	0.839011i	0.717230	+	0.696836i	$0.245410\pi$
$547$	−149.118	+	458.939i	−0.272611	+	0.839011i	−0.989842	+	0.142175i	$0.954590\pi$
$548$	41.4411	−	57.0388i	0.0756224	−	0.104085i
$549$	−729.447	+	109.058i	−1.32868	+	0.198648i
$550$	−60.9397	−	0.870284i	−0.110799	−	0.00158233i
$551$			620.662i			1.12643i
$552$	91.0239	−	147.102i	0.164898	−	0.266489i
$553$	64.2555	−	197.758i	0.116194	−	0.357609i
$554$	456.843	−	148.437i	0.824626	−	0.267937i
$555$	−701.675	+	594.044i	−1.26428	+	1.07035i
$556$	−196.090	+	142.468i	−0.352679	+	0.256237i
$557$	−714.569	+	232.178i	−1.28289	+	0.416836i	−0.869597	−	0.493763i	$-0.835621\pi$
$557$	−714.569	+	232.178i	−1.28289	+	0.416836i	−0.413292	+	0.910598i	$0.635621\pi$
$558$	482.176	+	80.6614i	0.864116	+	0.144554i
$559$	−75.2589	−	54.6788i	−0.134631	−	0.0978154i
$560$			72.3938i			0.129275i
$561$	676.787	+	175.869i	1.20639	+	0.313492i
$562$	523.349			0.931225
$563$	384.041	−	528.587i	0.682133	−	0.938875i	−0.317824	−	0.948150i	$-0.602952\pi$
$563$	384.041	−	528.587i	0.682133	−	0.938875i	0.999957	+	0.00927437i	$0.00295217\pi$
$564$	7.49810	−	30.6459i	0.0132945	−	0.0543366i
$565$	−51.3553	−	158.055i	−0.0908943	−	0.279744i
$566$	−86.3699	−	118.878i	−0.152597	−	0.210032i
$567$	192.118	−	255.007i	0.338832	−	0.449749i
$568$	−92.9757	−	286.150i	−0.163690	−	0.503785i
$569$	−926.914	−	301.172i	−1.62902	−	0.529301i	−0.654976	−	0.755650i	$-0.727321\pi$
$569$	−926.914	−	301.172i	−1.62902	−	0.529301i	−0.974046	+	0.226349i	$0.927321\pi$
$570$	−262.684	+	424.519i	−0.460850	+	0.744771i
$571$	−1011.22			−1.77097			−0.885483	−	0.464672i	$-0.846172\pi$
$571$	−1011.22			−1.77097			−0.885483	+	0.464672i	$0.846172\pi$
$572$	36.4805	+	51.7493i	0.0637771	+	0.0904707i
$573$	2.34736	−	0.174504i	0.00409662	−	0.000304545i
$574$	174.483	+	126.769i	0.303977	+	0.220852i
$575$	−75.9608	−	24.6812i	−0.132106	−	0.0429238i
$576$	32.1298	+	64.4335i	0.0557809	+	0.111864i
$577$	453.280	−	329.327i	0.785581	−	0.570758i	−0.121068	−	0.992644i	$-0.538632\pi$
$577$	453.280	−	329.327i	0.785581	−	0.570758i	0.906649	+	0.421886i	$0.138632\pi$
$578$	−133.008	−	183.070i	−0.230117	−	0.316729i
$579$	423.687	−	173.348i	0.731756	−	0.299393i
$580$	−68.7273	+	211.521i	−0.118495	+	0.364691i
$581$	−118.631	+	163.282i	−0.204185	+	0.281036i
$582$	28.3827	−	2.10999i	0.0487675	−	0.00362540i
$583$	−173.578	−	561.371i	−0.297732	−	0.962900i
$584$			276.472i			0.473411i
$585$	−54.9093	+	105.494i	−0.0938620	+	0.180332i
$586$	−70.5270	+	217.060i	−0.120353	+	0.370409i
$587$	−546.181	+	177.465i	−0.930462	+	0.302325i	−0.734751	−	0.678336i	$-0.762701\pi$
$587$	−546.181	+	177.465i	−0.930462	+	0.302325i	−0.195710	+	0.980662i	$0.562701\pi$
$588$	−129.732	−	153.237i	−0.220632	−	0.260607i
$589$	−796.336	+	578.572i	−1.35201	+	0.982295i
$590$	242.789	−	78.8870i	0.411507	−	0.133707i
$591$	106.356	−	434.694i	0.179960	−	0.735522i
$592$	−215.987	−	156.923i	−0.364842	−	0.265073i
$593$		−	1123.87i		−	1.89523i	−0.319408	−	0.947617i	$-0.603484\pi$
$593$		−	1123.87i		−	1.89523i	0.319408	−	0.947617i	$-0.396516\pi$
$594$	171.263	−	383.519i	0.288321	−	0.645655i
$595$	−383.503			−0.644543
$596$	17.4971	−	24.0826i	0.0293575	−	0.0404071i
$597$	−137.185	−	33.5650i	−0.229791	−	0.0562228i
$598$	25.6406	+	78.9137i	0.0428773	+	0.131963i
$599$	10.7658	+	14.8178i	0.0179729	+	0.0247376i	0.817909	−	0.575348i	$-0.195133\pi$
$599$	10.7658	+	14.8178i	0.0179729	+	0.0247376i	−0.799936	+	0.600085i	$0.795133\pi$
$600$	25.3717	−	21.4800i	0.0422862	−	0.0357999i
$601$	−239.072	−	735.787i	−0.397790	−	1.22427i	−0.926767	−	0.375636i	$-0.877424\pi$
$601$	−239.072	−	735.787i	−0.397790	−	1.22427i	0.528977	−	0.848636i	$-0.322576\pi$
$602$	−171.364	−	55.6796i	−0.284658	−	0.0924910i
$603$	902.132	+	469.557i	1.49607	+	0.778702i
$604$	518.286			0.858089
$605$	339.262	−	439.962i	0.560763	−	0.727210i
$606$	−34.6972	−	466.734i	−0.0572562	−	0.770188i
$607$	439.788	+	319.525i	0.724527	+	0.526400i	0.887827	−	0.460177i	$-0.152214\pi$
$607$	439.788	+	319.525i	0.724527	+	0.526400i	−0.163300	+	0.986576i	$0.552214\pi$
$608$	−137.873	−	44.7975i	−0.226764	−	0.0736801i
$609$	108.450	+	265.066i	0.178078	+	0.435247i
$610$	430.510	−	312.783i	0.705753	−	0.512760i
$611$	8.89507	+	12.2430i	0.0145582	+	0.0200377i
$612$	−341.334	+	170.206i	−0.557735	+	0.278115i
$613$	283.814	−	873.490i	0.462992	−	1.42494i	−0.398498	−	0.917169i	$-0.630469\pi$
$613$	283.814	−	873.490i	0.462992	−	1.42494i	0.861490	−	0.507774i	$-0.169531\pi$
$614$	−78.9142	+	108.616i	−0.128525	+	0.176899i
$615$	39.5099	+	531.471i	0.0642437	+	0.864181i
$616$	98.1758	+	73.4935i	0.159376	+	0.119308i
$617$			487.529i			0.790160i	0.918647	+	0.395080i	$0.129283\pi$
$617$			487.529i			0.790160i	−0.918647	+	0.395080i	$0.870717\pi$
$618$	45.2773	+	28.0167i	0.0732642	+	0.0453345i
$619$	−12.1975	+	37.5402i	−0.0197052	+	0.0606465i	−0.960426	−	0.278537i	$-0.910151\pi$
$619$	−12.1975	+	37.5402i	−0.0197052	+	0.0606465i	0.940720	+	0.339183i	$0.110151\pi$
$620$	−335.457	+	108.997i	−0.541059	+	0.175801i
$621$	362.896	−	413.873i	0.584374	−	0.666461i
$622$	234.550	−	170.411i	0.377091	−	0.273973i
$623$	0.764943	−	0.248545i	0.00122784	−	0.000398948i
$624$	−33.5461	−	8.20769i	−0.0537597	−	0.0131533i
$625$	413.980	+	300.774i	0.662368	+	0.481238i
$626$		−	45.3569i		−	0.0724551i
$627$	309.031	+	787.204i	0.492872	+	1.25551i
$628$	−365.881			−0.582613
$629$	831.295	−	1144.18i	1.32161	−	1.81905i
$630$	−38.0072	+	227.199i	−0.0603288	+	0.360633i
$631$	−137.350	−	422.721i	−0.217671	−	0.669922i	−0.998953	−	0.0457441i	$-0.985434\pi$
$631$	−137.350	−	422.721i	−0.217671	−	0.669922i	0.781282	−	0.624178i	$-0.214566\pi$
$632$	87.7017	+	120.711i	0.138769	+	0.190999i
$633$	−158.854	−	187.635i	−0.250954	−	0.296422i
$634$	−37.1238	−	114.255i	−0.0585549	−	0.180213i
$635$	−669.338	−	217.481i	−1.05408	−	0.342490i
$636$	272.547	+	168.647i	0.428534	+	0.265168i
$637$	96.3054			0.151186
$638$	217.080	+	307.938i	0.340250	+	0.482661i
$639$	−141.562	−	946.857i	−0.221537	−	1.48178i
$640$	−42.0263	−	30.5339i	−0.0656661	−	0.0477092i
$641$	−152.272	−	49.4761i	−0.237554	−	0.0771859i	0.187821	−	0.982203i	$-0.439858\pi$
$641$	−152.272	−	49.4761i	−0.237554	−	0.0771859i	−0.425374	+	0.905017i	$0.639858\pi$
$642$	−820.465	+	335.688i	−1.27798	+	0.522878i
$643$	−573.656	+	416.785i	−0.892155	+	0.648188i	−0.936439	−	0.350831i	$-0.885899\pi$
$643$	−573.656	+	416.785i	−0.892155	+	0.648188i	0.0442842	+	0.999019i	$0.485899\pi$
$644$	94.4665	+	130.022i	0.146687	+	0.201898i
$645$	−168.601	−	412.084i	−0.261397	−	0.638890i
$646$	237.313	−	730.374i	0.367357	−	1.13061i
$647$	200.757	−	276.318i	0.310289	−	0.427076i	−0.625182	−	0.780479i	$-0.714975\pi$
$647$	200.757	−	276.318i	0.310289	−	0.427076i	0.935471	+	0.353402i	$0.114975\pi$
$648$	67.0072	+	219.085i	0.103406	+	0.338093i
$649$	139.496	−	409.340i	0.214940	−	0.630724i
$650$			15.9455i			0.0245315i
$651$	−238.995	+	386.236i	−0.367120	+	0.593296i
$652$	53.6333	−	165.066i	0.0822597	−	0.253169i
$653$	−145.700	+	47.3409i	−0.223124	+	0.0724975i	−0.418446	−	0.908242i	$-0.637425\pi$
$653$	−145.700	+	47.3409i	−0.223124	+	0.0724975i	0.195321	+	0.980739i	$0.437425\pi$
$654$	−84.6113	+	71.6327i	−0.129375	+	0.109530i
$655$	31.4566	−	22.8546i	0.0480253	−	0.0348925i
$656$	−147.185	+	47.8233i	−0.224367	+	0.0729013i
$657$	−145.149	+	867.672i	−0.220927	+	1.32066i
$658$	23.7138	+	17.2291i	0.0360392	+	0.0261840i
$659$			771.163i			1.17020i	0.810961	+	0.585101i	$0.198945\pi$
$659$			771.163i			1.17020i	−0.810961	+	0.585101i	$0.801055\pi$
$660$	18.1486	+	302.498i	0.0274979	+	0.458330i
$661$	164.339			0.248621			0.124311	−	0.992243i	$-0.460328\pi$
$661$	164.339			0.248621			0.124311	+	0.992243i	$0.460328\pi$
$662$	436.912	−	601.358i	0.659988	−	0.908396i
$663$	43.4799	−	177.709i	0.0655805	−	0.268037i
$664$	−44.7532	−	137.736i	−0.0673995	−	0.207434i
$665$	−272.619	−	375.229i	−0.409954	−	0.564253i
$666$	−595.460	−	605.878i	−0.894085	−	0.909727i
$667$	152.576	+	469.582i	0.228750	+	0.704020i
$668$	−169.862	−	55.1915i	−0.254284	−	0.0826220i
$669$	−453.770	+	733.330i	−0.678282	+	1.09616i
$670$	−733.770			−1.09518
$671$	12.8724	−	901.364i	0.0191840	−	1.34331i
$672$	−66.7087	+	4.95916i	−0.0992689	+	0.00737970i
$673$	−464.711	−	337.632i	−0.690507	−	0.501683i	0.186320	−	0.982489i	$-0.440344\pi$
$673$	−464.711	−	337.632i	−0.690507	−	0.501683i	−0.876827	+	0.480806i	$0.840344\pi$
$674$	−218.884	−	71.1198i	−0.324754	−	0.105519i
$675$	90.9030	−	54.0918i	0.134671	−	0.0801359i
$676$	−260.046	+	188.935i	−0.384684	+	0.279489i
$677$	37.2310	+	51.2441i	0.0549941	+	0.0756929i	0.835628	−	0.549295i	$-0.185104\pi$
$677$	37.2310	+	51.2441i	0.0549941	+	0.0756929i	−0.780634	+	0.624988i	$0.785104\pi$
$678$	142.125	−	58.1495i	0.209624	−	0.0857662i
$679$	−8.17109	+	25.1480i	−0.0120340	+	0.0370368i
$680$	161.752	−	222.632i	0.237871	−	0.327401i
$681$	396.869	−	29.5035i	0.582774	−	0.0433237i
$682$	−192.738	+	565.577i	−0.282608	+	0.829292i
$683$			446.726i			0.654064i	0.945013	+	0.327032i	$0.106049\pi$
$683$			446.726i			0.654064i	−0.945013	+	0.327032i	$0.893951\pi$
$684$	−409.176	−	212.975i	−0.598211	−	0.311367i
$685$	−50.0176	+	153.938i	−0.0730185	+	0.224728i
$686$	437.183	−	142.050i	0.637294	−	0.207069i
$687$	246.879	+	291.609i	0.359359	+	0.424468i
$688$	104.600	−	75.9966i	0.152035	−	0.110460i
$689$	−146.210	+	47.5064i	−0.212206	+	0.0689498i
$690$	−94.3833	+	385.759i	−0.136787	+	0.559071i
$691$	−572.022	−	415.598i	−0.827818	−	0.601445i	0.0911232	−	0.995840i	$-0.470954\pi$
$691$	−572.022	−	415.598i	−0.827818	−	0.601445i	−0.918941	+	0.394395i	$0.870954\pi$
$692$		−	473.640i		−	0.684451i
$693$	269.528	+	282.193i	0.388929	+	0.407204i
$694$	−548.655			−0.790570
$695$	327.073	−	450.177i	0.470608	−	0.647737i
$696$	−199.618	−	48.8404i	−0.286808	−	0.0701730i
$697$	−253.342	−	779.705i	−0.363474	−	1.11866i
$698$	292.861	+	403.089i	0.419572	+	0.577491i
$699$	−210.888	+	178.539i	−0.301699	+	0.255421i
$700$	9.54405	+	29.3736i	0.0136344	+	0.0419622i
$701$	372.055	+	120.888i	0.530750	+	0.172451i	0.562118	−	0.827057i	$-0.309987\pi$
$701$	372.055	+	120.888i	0.530750	+	0.172451i	−0.0313686	+	0.999508i	$0.509987\pi$
$702$	−100.971	−	43.3706i	−0.143833	−	0.0617815i
$703$	1710.43			2.43305
$704$	−84.0728	+	25.9956i	−0.119422	+	0.0369256i
$705$	5.36975	+	72.2318i	0.00761667	+	0.102456i
$706$	−104.155	−	75.6733i	−0.147529	−	0.107186i
$707$	413.542	+	134.368i	0.584924	+	0.190053i
$708$	89.3236	+	218.319i	0.126163	+	0.308360i
$709$	−152.381	+	110.711i	−0.214923	+	0.156151i	−0.690038	−	0.723773i	$-0.742406\pi$
$709$	−152.381	+	110.711i	−0.214923	+	0.156151i	0.475115	+	0.879924i	$0.342406\pi$
$710$	406.008	+	558.822i	0.571842	+	0.787073i
$711$	211.867	+	424.880i	0.297984	+	0.597581i
$712$	−0.178347	+	0.548897i	−0.000250488	+	0.000770922i
$713$	−460.264	+	633.498i	−0.645531	+	0.888497i
$714$	−26.2709	−	353.387i	−0.0367940	−	0.494939i
$715$	−116.364	−	87.1093i	−0.162747	−	0.121831i
$716$			652.896i			0.911866i
$717$	18.6846	+	11.5617i	0.0260594	+	0.0161251i
$718$	−54.7523	+	168.510i	−0.0762566	+	0.234694i
$719$	−368.415	+	119.705i	−0.512400	+	0.166489i	−0.553793	−	0.832654i	$-0.686820\pi$
$719$	−368.415	+	119.705i	−0.512400	+	0.166489i	0.0413936	+	0.999143i	$0.486820\pi$
$720$	−115.864	−	117.891i	−0.160922	−	0.163737i
$721$	−40.0201	+	29.0763i	−0.0555064	+	0.0403278i
$722$	397.769	−	129.243i	0.550927	−	0.179007i
$723$	971.153	+	237.611i	1.34323	+	0.328646i
$724$	198.731	+	144.387i	0.274491	+	0.199429i
$725$			94.8846i			0.130875i
$726$	428.652	+	282.481i	0.590430	+	0.389092i
$727$	919.762			1.26515			0.632573	−	0.774500i	$-0.281999\pi$
$727$	919.762			1.26515			0.632573	+	0.774500i	$0.281999\pi$
$728$	18.8596	−	25.9580i	0.0259060	−	0.0356566i
$729$	95.2730	+	722.748i	0.130690	+	0.991423i
$730$	−196.138	−	603.651i	−0.268682	−	0.826919i
$731$	402.588	+	554.115i	0.550737	+	0.758024i
$732$	317.711	+	375.275i	0.434032	+	0.512671i
$733$	150.925	+	464.500i	0.205901	+	0.633697i	0.999675	+	0.0254851i	$0.00811305\pi$
$733$	150.925	+	464.500i	0.205901	+	0.633697i	−0.793774	+	0.608212i	$0.791887\pi$
$734$	−186.815	−	60.7000i	−0.254517	−	0.0826976i
$735$	391.969	+	242.543i	0.533291	+	0.329990i
$736$	−115.324			−0.156691
$737$	−744.916	+	995.091i	−1.01074	+	1.35019i
$738$	−487.028	+	72.8143i	−0.659930	+	0.0986643i
$739$	86.4708	+	62.8247i	0.117011	+	0.0850132i	0.644752	−	0.764392i	$-0.276961\pi$
$739$	86.4708	+	62.8247i	0.117011	+	0.0850132i	−0.527741	+	0.849405i	$0.676961\pi$
$740$	582.913	+	189.400i	0.787721	+	0.255946i
$741$	204.783	−	83.7855i	0.276360	−	0.113071i
$742$	−240.902	+	175.025i	−0.324666	+	0.235883i
$743$	−332.635	−	457.833i	−0.447692	−	0.616195i	0.524208	−	0.851590i	$-0.324362\pi$
$743$	−332.635	−	457.833i	−0.447692	−	0.616195i	−0.971900	+	0.235395i	$0.924362\pi$
$744$	−123.417	−	301.647i	−0.165883	−	0.405439i
$745$	−21.1182	+	64.9952i	−0.0283466	+	0.0872418i
$746$	386.147	−	531.486i	0.517624	−	0.712448i
$747$	−68.1399	−	455.763i	−0.0912181	−	0.610125i
$748$	−137.711	−	445.372i	−0.184105	−	0.595417i
$749$		−	823.600i		−	1.09960i
$750$	−296.416	+	479.033i	−0.395222	+	0.638711i
$751$	−114.219	+	351.528i	−0.152089	+	0.468080i	−0.997854	−	0.0654740i	$-0.979144\pi$
$751$	−114.219	+	351.528i	−0.152089	+	0.468080i	0.845766	+	0.533554i	$0.179144\pi$
$752$	−20.0038	+	6.49962i	−0.0266008	+	0.00864311i
$753$	273.599	−	231.632i	0.363346	−	0.307612i
$754$	79.7474	−	57.9399i	0.105766	−	0.0768433i
$755$	−1131.63	+	367.689i	−1.49885	+	0.487005i
$756$	−211.960	−	19.4588i	−0.280371	−	0.0257391i
$757$	−873.731	−	634.803i	−1.15420	−	0.838577i	−0.165169	−	0.986265i	$-0.552817\pi$
$757$	−873.731	−	634.803i	−1.15420	−	0.838577i	−0.989034	+	0.147688i	$0.952817\pi$
$758$			581.500i			0.767150i
$759$	427.324	+	519.615i	0.563009	+	0.684605i
$760$	332.813			0.437912
$761$	−524.818	+	722.350i	−0.689643	+	0.949212i	−0.999999	−	0.00140845i	$-0.999552\pi$
$761$	−524.818	+	722.350i	−0.689643	+	0.949212i	0.310356	+	0.950620i	$0.399552\pi$
$762$	154.551	−	631.673i	0.202823	−	0.828967i
$763$	−31.8281	−	97.9568i	−0.0417144	−	0.128384i
$764$	−0.922368	−	1.26953i	−0.00120729	−	0.00166169i
$765$	624.521	−	613.782i	0.816367	−	0.802330i
$766$	165.116	+	508.176i	0.215557	+	0.663415i
$767$	−107.607	−	34.9637i	−0.140296	−	0.0455850i
$768$	25.2571	−	40.8176i	0.0328869	−	0.0531479i
$769$	367.017			0.477265			0.238633	−	0.971110i	$-0.423301\pi$
$769$	367.017			0.477265			0.238633	+	0.971110i	$0.423301\pi$
$770$	−266.496	−	90.8172i	−0.346099	−	0.117944i
$771$	−630.969	+	46.9065i	−0.818377	+	0.0608386i
$772$	−246.900	−	179.383i	−0.319818	−	0.232362i
$773$	912.078	+	296.352i	1.17992	+	0.383379i	0.832337	−	0.554270i	$-0.187003\pi$
$773$	912.078	+	296.352i	1.17992	+	0.383379i	0.347583	+	0.937649i	$0.387003\pi$
$774$	368.173	−	183.590i	0.475676	−	0.237196i
$775$	−121.741	+	88.4499i	−0.157085	+	0.114129i
$776$	−11.1526	−	15.3503i	−0.0143720	−	0.0197813i
$777$	730.473	−	298.868i	0.940120	−	0.384643i
$778$	−327.488	+	1007.90i	−0.420936	+	1.29551i
$779$	582.790	−	802.142i	0.748126	−	1.02971i
$780$	79.0675	−	5.87792i	0.101369	−	0.00753579i
$781$	1170.01	+	16.7090i	1.49810	+	0.0213944i
$782$		−	610.926i		−	0.781235i
$783$	−600.834	−	258.080i	−0.767349	−	0.329604i
$784$	−41.3626	+	127.301i	−0.0527584	+	0.162374i
$785$	798.868	−	259.568i	1.01767	−	0.330660i
$786$	23.2146	+	27.4207i	0.0295352	+	0.0348864i
$787$	1063.12	−	772.402i	1.35085	−	0.981452i	0.351884	−	0.936044i	$-0.385541\pi$
$787$	1063.12	−	772.402i	1.35085	−	0.981452i	0.998969	−	0.0454078i	$-0.0144587\pi$
$788$	−283.742	+	92.1933i	−0.360078	+	0.116997i
$789$	−111.456	+	455.539i	−0.141263	+	0.577362i
$790$	−277.125	−	201.343i	−0.350791	−	0.254865i
$791$			142.668i			0.180364i
$792$	−277.499	+	37.4452i	−0.350378	+	0.0472793i
$793$	−235.851			−0.297416
$794$	−485.198	+	667.818i	−0.611081	+	0.841080i
$795$	−714.726	−	174.871i	−0.899026	−	0.219964i
$796$	29.0953	+	89.5462i	0.0365519	+	0.112495i
$797$	85.5042	+	117.686i	0.107283	+	0.147662i	0.859282	−	0.511502i	$-0.170911\pi$
$797$	85.5042	+	117.686i	0.107283	+	0.147662i	−0.752000	+	0.659163i	$0.770911\pi$
$798$	327.087	−	276.915i	0.409883	−	0.347011i
$799$	−34.4314	−	105.969i	−0.0430932	−	0.132627i
$800$	−21.0775	−	6.84848i	−0.0263468	−	0.00856060i
$801$	−0.847894	+	1.62901i	−0.00105854	+	0.00203372i
$802$	−186.658			−0.232741
$803$	−1017.75	−	346.831i	−1.26743	−	0.431919i
$804$	−50.2651	−	676.146i	−0.0625188	−	0.840978i
$805$	−298.501	−	216.873i	−0.370808	−	0.269408i
$806$	148.679	+	48.3086i	0.184465	+	0.0599362i
$807$	−400.674	−	979.302i	−0.496499	−	1.21351i
$808$	−252.425	+	183.397i	−0.312407	+	0.226977i
$809$	561.827	+	773.289i	0.694471	+	0.955857i	0.999993	+	0.00367243i	$0.00116897\pi$
$809$	561.827	+	773.289i	0.694471	+	0.955857i	−0.305522	+	0.952185i	$0.598831\pi$
$810$	−301.730	−	430.814i	−0.372506	−	0.531869i
$811$	−283.845	+	873.586i	−0.349994	+	1.07717i	0.608861	+	0.793277i	$0.291627\pi$
$811$	−283.845	+	873.586i	−0.349994	+	1.07717i	−0.958855	+	0.283895i	$0.908373\pi$
$812$	112.225	−	154.465i	0.138208	−	0.190228i
$813$	−2.03678	−	27.3980i	−0.00250527	−	0.0336999i
$814$	848.620	−	598.232i	1.04253	−	0.734929i
$815$			398.456i			0.488903i
$816$	216.229	+	133.799i	0.264987	+	0.163969i
$817$	−255.973	+	787.804i	−0.313309	+	0.964264i
$818$	−307.840	+	100.023i	−0.376332	+	0.122278i
$819$	72.8164	−	71.5644i	0.0889089	−	0.0873802i
$820$	287.437	−	208.835i	0.350533	−	0.254677i
$821$	−160.409	+	52.1199i	−0.195382	+	0.0634835i	−0.405073	−	0.914284i	$-0.632754\pi$
$821$	−160.409	+	52.1199i	−0.195382	+	0.0634835i	0.209691	+	0.977768i	$0.432754\pi$
$822$	−145.276	−	35.5446i	−0.176735	−	0.0432416i
$823$	−314.340	−	228.382i	−0.381945	−	0.277499i	0.380202	−	0.924903i	$-0.375854\pi$
$823$	−314.340	−	228.382i	−0.381945	−	0.277499i	−0.762147	+	0.647404i	$0.775854\pi$
$824$		−	35.4963i		−	0.0430780i
$825$	47.2435	+	120.345i	0.0572649	+	0.145873i
$826$	−219.153			−0.265318
$827$	37.4915	−	51.6026i	0.0453343	−	0.0623973i	−0.785748	−	0.618547i	$-0.787722\pi$
$827$	37.4915	−	51.6026i	0.0453343	−	0.0623973i	0.831082	+	0.556149i	$0.187722\pi$
$828$	−361.931	−	60.5459i	−0.437114	−	0.0731231i
$829$	−0.864811	−	2.66162i	−0.00104320	−	0.00321063i	0.950534	−	0.310622i	$-0.100537\pi$
$829$	−0.864811	−	2.66162i	−0.00104320	−	0.00321063i	−0.951577	+	0.307411i	$0.900537\pi$
$830$	195.429	+	268.985i	0.235457	+	0.324078i
$831$	−658.410	−	777.702i	−0.792311	−	0.935863i
$832$	7.11471	+	21.8968i	0.00855134	+	0.0263183i
$833$	−674.371	−	219.116i	−0.809569	−	0.263045i
$834$	437.230	+	270.549i	0.524256	+	0.324400i
$835$	410.033			0.491057
$836$	337.868	−	451.339i	0.404149	−	0.539879i
$837$	−228.961	−	1011.47i	−0.273549	−	1.20845i
$838$	380.681	+	276.581i	0.454273	+	0.330048i
$839$	−802.306	−	260.685i	−0.956265	−	0.310709i	−0.211006	−	0.977485i	$-0.567674\pi$
$839$	−802.306	−	260.685i	−0.956265	−	0.310709i	−0.745259	+	0.666775i	$0.767674\pi$
$840$	142.134	−	58.1532i	0.169207	−	0.0692300i
$841$	−205.841	+	149.552i	−0.244757	+	0.177827i
$842$	−1.65643	−	2.27988i	−0.00196726	−	0.00270770i
$843$	−420.400	−	1027.51i	−0.498695	−	1.21888i
$844$	−50.6476	+	155.877i	−0.0600091	+	0.184689i
$845$	433.750	−	597.006i	0.513314	−	0.706516i
$846$	−66.1916	+	9.89612i	−0.0782406	+	0.0116975i
$847$	−393.705	+	269.208i	−0.464823	+	0.317838i
$848$		−	213.670i		−	0.251970i
$849$	−164.019	+	265.067i	−0.193190	+	0.312211i
$850$	36.2795	−	111.657i	0.0426818	−	0.131361i
$851$	1294.08	−	420.473i	1.52066	−	0.494092i
$852$	−487.125	+	412.405i	−0.571743	+	0.484043i
$853$	−763.381	+	554.629i	−0.894936	+	0.650209i	−0.937160	−	0.348899i	$-0.886556\pi$
$853$	−763.381	+	554.629i	−0.894936	+	0.650209i	0.0422240	+	0.999108i	$0.486556\pi$
$854$	−434.466	+	141.167i	−0.508743	+	0.165301i
$855$	1044.49	+	174.729i	1.22163	+	0.204361i
$856$	478.119	+	347.374i	0.558550	+	0.405811i
$857$		−	1114.14i		−	1.30004i	−0.759915	−	0.650022i	$-0.774760\pi$
$857$		−	1114.14i		−	1.30004i	0.759915	−	0.650022i	$-0.225240\pi$
$858$	72.2973	−	113.193i	0.0842626	−	0.131927i
$859$	−1415.22			−1.64752			−0.823762	−	0.566936i	$-0.808129\pi$
$859$	−1415.22			−1.64752			−0.823762	+	0.566936i	$0.808129\pi$
$860$	−174.471	+	240.138i	−0.202873	+	0.279231i
$861$	108.732	−	444.402i	0.126285	−	0.516147i
$862$	−112.853	−	347.327i	−0.130921	−	0.402932i
$863$	−626.826	−	862.753i	−0.726334	−	0.999713i	−0.999290	−	0.0376866i	$-0.988001\pi$
$863$	−626.826	−	862.753i	−0.726334	−	0.999713i	0.272955	−	0.962027i	$-0.411999\pi$
$864$	100.696	−	114.841i	0.116546	−	0.132917i
$865$	336.016	+	1034.15i	0.388457	+	1.19555i
$866$	−789.829	−	256.631i	−0.912043	−	0.296341i
$867$	−252.585	+	408.198i	−0.291332	+	0.470817i
$868$	302.799			0.348847
$869$	−554.383	+	171.417i	−0.637955	+	0.197258i
$870$	470.497	−	34.9770i	0.540801	−	0.0402034i
$871$	263.105	+	191.157i	0.302072	+	0.219468i
$872$	70.2905	+	22.8388i	0.0806084	+	0.0261912i
$873$	−26.9421	−	54.0301i	−0.0308616	−	0.0618902i
$874$	597.744	−	434.287i	0.683918	−	0.496895i
$875$	−307.627	−	423.413i	−0.351574	−	0.483900i
$876$	542.810	−	222.087i	0.619646	−	0.253524i
$877$	−434.882	+	1338.43i	−0.495875	+	1.52615i	0.319714	+	0.947514i	$0.396413\pi$
$877$	−434.882	+	1338.43i	−0.495875	+	1.52615i	−0.815589	+	0.578632i	$0.803587\pi$
$878$	−130.769	+	179.988i	−0.148940	+	0.204998i
$879$	482.817	−	35.8929i	0.549280	−	0.0408337i
$880$	165.123	−	116.403i	0.187640	−	0.132276i
$881$			1591.58i			1.80656i	0.429056	+	0.903278i	$0.358846\pi$
$881$			1591.58i			1.80656i	−0.429056	+	0.903278i	$0.641154\pi$
$882$	−196.645	+	377.802i	−0.222953	+	0.428347i
$883$	−227.572	+	700.394i	−0.257726	+	0.793198i	0.735555	+	0.677465i	$0.236922\pi$
$883$	−227.572	+	700.394i	−0.257726	+	0.793198i	−0.993280	+	0.115733i	$0.963078\pi$
$884$	−115.998	+	37.6899i	−0.131219	+	0.0426356i
$885$	−349.912	−	413.310i	−0.395381	−	0.467017i
$886$	−148.623	+	107.981i	−0.167746	+	0.121875i
$887$	636.902	−	206.942i	0.718041	−	0.233306i	0.0728672	−	0.997342i	$-0.476785\pi$
$887$	636.902	−	206.942i	0.718041	−	0.233306i	0.645174	+	0.764036i	$0.276785\pi$
$888$	−134.595	+	550.111i	−0.151571	+	0.619495i
$889$	488.789	+	355.126i	0.549819	+	0.399467i
$890$		−	1.32499i		−	0.00148875i
$891$	−890.555	−	28.1716i	−0.999500	−	0.0316180i
$892$	574.913			0.644521
$893$	79.2065	−	109.018i	0.0886971	−	0.122081i
$894$	−61.3377	−	15.0075i	−0.0686104	−	0.0167869i
$895$	−463.185	−	1425.54i	−0.517526	−	1.59278i
$896$	26.2124	+	36.0783i	0.0292549	+	0.0402659i
$897$	134.338	−	113.732i	0.149764	−	0.126791i
$898$	235.783	+	725.666i	0.262565	+	0.808091i
$899$	884.722	+	287.464i	0.984118	+	0.319759i
$900$	−62.5534	−	32.5589i	−0.0695038	−	0.0361765i
$901$	1131.91			1.25628
$902$	8.59451	−	601.811i	0.00952828	−	0.667196i
$903$	28.3366	+	381.174i	0.0313806	+	0.422119i
$904$	−82.8222	−	60.1739i	−0.0916175	−	0.0665640i
$905$	−536.344	−	174.269i	−0.592645	−	0.192562i
$906$	−416.334	−	1017.57i	−0.459529	−	1.12315i
$907$	−90.6956	+	65.8942i	−0.0999951	+	0.0726507i	−0.636659	−	0.771145i	$-0.719684\pi$
$907$	−90.6956	+	65.8942i	−0.0999951	+	0.0726507i	0.536664	+	0.843796i	$0.319684\pi$
$908$	−155.945	−	214.640i	−0.171746	−	0.236388i
$909$	−888.488	+	443.045i	−0.977434	+	0.487398i
$910$	−22.7627	+	70.0564i	−0.0250140	+	0.0769851i
$911$	−230.856	+	317.746i	−0.253409	+	0.348788i	−0.916702	−	0.399572i	$-0.869159\pi$
$911$	−230.856	+	317.746i	−0.253409	+	0.348788i	0.663292	+	0.748360i	$0.269159\pi$
$912$	22.7985	+	306.677i	0.0249984	+	0.336269i
$913$	563.178	+	8.04278i	0.616843	+	0.00880918i
$914$		−	197.456i		−	0.216035i
$915$	−959.926	−	593.984i	−1.04910	−	0.649162i
$916$	78.7129	−	242.253i	0.0859311	−	0.264469i
$917$	−31.7457	+	10.3148i	−0.0346191	+	0.0112484i
$918$	608.363	+	533.431i	0.662705	+	0.581080i
$919$	158.038	−	114.821i	0.171967	−	0.124941i	−0.498473	−	0.866905i	$-0.666106\pi$
$919$	158.038	−	114.821i	0.171967	−	0.124941i	0.670440	+	0.741964i	$0.266106\pi$
$920$	251.800	−	81.8148i	0.273696	−	0.0889291i
$921$	276.642	+	67.6857i	0.300371	+	0.0734915i
$922$	439.986	+	319.669i	0.477209	+	0.346712i
$923$		−	306.145i		−	0.331685i
$924$	65.4296	−	251.790i	0.0708113	−	0.272500i
$925$	261.485			0.282686
$926$	−128.458	+	176.807i	−0.138724	+	0.190937i
$927$	18.6357	−	111.400i	0.0201033	−	0.120173i
$928$	42.3366	+	130.299i	0.0456213	+	0.140408i
$929$	−171.038	−	235.414i	−0.184110	−	0.253406i	0.706979	−	0.707235i	$-0.250058\pi$
$929$	−171.038	−	235.414i	−0.184110	−	0.253406i	−0.891089	+	0.453829i	$0.850058\pi$
$930$	483.467	+	571.062i	0.519857	+	0.614045i
$931$	−264.999	−	815.583i	−0.284639	−	0.876029i
$932$	175.194	+	56.9240i	0.187976	+	0.0610773i
$933$	−522.987	−	323.615i	−0.560544	−	0.346854i
$934$	93.0503			0.0996256
$935$	616.639	+	874.732i	0.659507	+	0.935542i
$936$	10.8326	+	72.4557i	0.0115733	+	0.0774099i
$937$	−1049.05	−	762.180i	−1.11958	−	0.813425i	−0.135438	−	0.990786i	$-0.543244\pi$
$937$	−1049.05	−	762.180i	−1.11958	−	0.813425i	−0.984146	+	0.177361i	$0.943244\pi$
$938$	599.088	+	194.656i	0.638687	+	0.207522i
$939$	−89.0512	+	36.4347i	−0.0948363	+	0.0388016i
$940$	39.0653	−	28.3826i	0.0415589	−	0.0301943i
$941$	−39.2709	−	54.0517i	−0.0417331	−	0.0574407i	0.787640	−	0.616135i	$-0.211302\pi$
$941$	−39.2709	−	54.0517i	−0.0417331	−	0.0574407i	−0.829374	+	0.558694i	$0.811302\pi$
$942$	293.908	+	718.351i	0.312005	+	0.762581i
$943$	243.739	−	750.152i	0.258472	−	0.795495i
$944$	92.4332	−	127.223i	0.0979165	−	0.134771i
$945$	476.600	−	107.885i	0.504339	−	0.114164i
$946$	148.539	+	480.392i	0.157018	+	0.507814i
$947$			488.154i			0.515474i	0.966215	+	0.257737i	$0.0829768\pi$
$947$			488.154i			0.515474i	−0.966215	+	0.257737i	$0.917023\pi$
$948$	166.548	−	269.155i	0.175683	−	0.283918i
$949$	−86.9308	+	267.545i	−0.0916025	+	0.281924i
$950$	135.038	−	43.8764i	0.142145	−	0.0461857i
$951$	−194.501	+	164.667i	−0.204523	+	0.173151i
$952$	−191.123	+	138.859i	−0.200760	+	0.145860i
$953$	962.133	−	312.616i	1.00958	−	0.328034i	0.242895	−	0.970053i	$-0.421903\pi$
$953$	962.133	−	312.616i	1.00958	−	0.328034i	0.766689	+	0.642019i	$0.221903\pi$
$954$	112.178	−	670.577i	0.117587	−	0.702911i
$955$	2.91455	+	2.11754i	0.00305188	+	0.00221732i
$956$		−	14.6483i		−	0.0153225i
$957$	430.210	−	673.565i	0.449540	−	0.703830i
$958$	−644.061			−0.672298
$959$	81.6741	−	112.415i	0.0851659	−	0.117221i
$960$	−26.1893	+	107.040i	−0.0272805	+	0.111500i
$961$	158.931	+	489.139i	0.165381	+	0.508990i
$962$	−159.672	−	219.769i	−0.165979	−	0.228450i
$963$	1318.14	+	1341.20i	1.36879	+	1.39273i
$964$	−205.970	−	633.910i	−0.213662	−	0.657583i
$965$	666.343	+	216.508i	0.690511	+	0.224361i
$966$	179.394	−	289.916i	0.185708	−	0.300120i
$967$	−96.4051			−0.0996950			−0.0498475	−	0.998757i	$-0.515874\pi$
$967$	−96.4051			−0.0996950			−0.0498475	+	0.998757i	$0.515874\pi$
$968$	9.77310	−	342.100i	0.0100962	−	0.353409i
$969$	−1624.61	+	120.774i	−1.67658	+	0.124638i
$970$	35.2408	+	25.6039i	0.0363307	+	0.0263958i
$971$	−423.770	−	137.691i	−0.436426	−	0.141803i	0.0825602	−	0.996586i	$-0.473690\pi$
$971$	−423.770	−	137.691i	−0.436426	−	0.141803i	−0.518986	+	0.854783i	$0.673690\pi$
$972$	376.312	−	307.547i	0.387153	−	0.316406i
$973$	−386.463	+	280.782i	−0.397187	+	0.288573i
$974$	555.245	+	764.230i	0.570067	+	0.784630i
$975$	31.3065	−	12.8088i	0.0321092	−	0.0131372i
$976$	101.296	−	311.758i	0.103787	−	0.319424i
$977$	−505.435	+	695.672i	−0.517334	+	0.712049i	−0.985134	−	0.171785i	$-0.945047\pi$
$977$	−505.435	+	695.672i	−0.517334	+	0.712049i	0.467801	+	0.883834i	$0.345047\pi$
$978$	−367.165	+	27.2953i	−0.375425	+	0.0279093i
$979$	−1.79687	−	1.34512i	−0.00183541	−	0.00137397i
$980$		−	307.294i		−	0.313565i
$981$	208.607	+	108.579i	0.212647	+	0.110682i
$982$	−47.1396	+	145.081i	−0.0480036	+	0.147740i
$983$	953.014	−	309.653i	0.969495	−	0.315008i	0.218883	−	0.975751i	$-0.429759\pi$
$983$	953.014	−	309.653i	0.969495	−	0.315008i	0.750612	+	0.660743i	$0.229759\pi$
$984$	212.126	+	250.559i	0.215575	+	0.254633i
$985$	554.119	−	402.591i	0.562557	−	0.408722i
$986$	−690.251	+	224.276i	−0.700052	+	0.227461i
$987$	14.7776	−	60.3983i	0.0149723	−	0.0611939i
$988$	−119.335	−	86.7023i	−0.120785	−	0.0877553i
$989$			658.963i			0.666293i
$990$	579.329	−	278.625i	0.585181	−	0.281439i
$991$	−658.024			−0.664000			−0.332000	−	0.943279i	$-0.607723\pi$
$991$	−658.024			−0.664000			−0.332000	+	0.943279i	$0.607723\pi$
$992$	−127.713	+	175.782i	−0.128743	+	0.177200i
$993$	−1531.64	−	374.745i	−1.54244	−	0.377387i
$994$	−183.241	−	563.958i	−0.184347	−	0.567362i
$995$	−127.054	−	174.875i	−0.127692	−	0.175753i
$996$	−234.474	+	198.508i	−0.235416	+	0.199305i
$997$	−226.709	−	697.738i	−0.227391	−	0.699837i	−0.998040	−	0.0625777i	$-0.980068\pi$
$997$	−226.709	−	697.738i	−0.227391	−	0.699837i	0.770649	−	0.637260i	$-0.219932\pi$
$998$	−1234.85	−	401.228i	−1.23733	−	0.402032i
$999$	−711.222	+	1655.79i	−0.711934	+	1.65745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.g.a.59.4	yes	32
3.2	odd	2	inner	66.3.g.a.59.5	yes	32
11.3	even	5	inner	66.3.g.a.47.5	yes	32
11.5	even	5		726.3.c.h.485.4		16
11.6	odd	10		726.3.c.i.485.12		16
33.5	odd	10		726.3.c.h.485.12		16
33.14	odd	10	inner	66.3.g.a.47.4	✓	32
33.17	even	10		726.3.c.i.485.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.g.a.47.4	✓	32	33.14	odd	10	inner
66.3.g.a.47.5	yes	32	11.3	even	5	inner
66.3.g.a.59.4	yes	32	1.1	even	1	trivial
66.3.g.a.59.5	yes	32	3.2	odd	2	inner
726.3.c.h.485.4		16	11.5	even	5
726.3.c.h.485.12		16	33.5	odd	10
726.3.c.i.485.4		16	33.17	even	10
726.3.c.i.485.12		16	11.6	odd	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 + 1.14412i) q^{2} +(2.91405 + 0.712977i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(2.69884 + 3.71463i) q^{5} +(-3.23805 + 2.74136i) q^{6} +(-1.21805 - 3.74878i) q^{7} +(2.68999 + 0.874032i) q^{8} +(7.98333 + 4.15530i) q^{9} -6.49342 q^{10} +(-6.59206 + 8.80595i) q^{11} +(-0.444816 - 5.98349i) q^{12} +(2.32832 + 1.69162i) q^{13} +(5.30157 + 1.72258i) q^{14} +(5.21609 + 12.7488i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(-12.4551 - 17.1429i) q^{17} +(-11.3903 + 5.67980i) q^{18} +(7.91916 - 24.3727i) q^{19} +(5.39768 - 7.42927i) q^{20} +(-0.876664 - 11.7925i) q^{21} +(-4.59542 - 14.8621i) q^{22} -20.3867i q^{23} +(7.21560 + 4.46487i) q^{24} +(1.21065 - 3.72600i) q^{25} +(-3.87085 + 1.25772i) q^{26} +(20.3011 + 17.8007i) q^{27} +(-6.37780 + 4.63374i) q^{28} +(-23.0338 + 7.48412i) q^{29} +(-18.9221 - 4.62966i) q^{30} +(-31.0742 - 22.5767i) q^{31} -5.65685i q^{32} +(-25.4880 + 20.9610i) q^{33} +29.9669 q^{34} +(10.6380 - 14.6420i) q^{35} +(2.96988 - 17.7533i) q^{36} +(20.6249 + 63.4769i) q^{37} +(21.3025 + 29.3204i) q^{38} +(5.57874 + 6.58951i) q^{39} +(4.01315 + 12.3512i) q^{40} +(36.7962 + 11.9558i) q^{41} +(14.2209 + 8.79959i) q^{42} -32.3233 q^{43} +(20.8240 + 7.09646i) q^{44} +(6.11031 + 40.8696i) q^{45} +(23.3248 + 16.9465i) q^{46} +(5.00094 + 1.62490i) q^{47} +(-11.1064 + 4.54409i) q^{48} +(27.0722 - 19.6691i) q^{49} +(3.25665 + 4.48239i) q^{50} +(-24.0721 - 58.8355i) q^{51} +(1.77868 - 5.47421i) q^{52} +(-31.3981 + 43.2158i) q^{53} +(-37.2415 + 8.43014i) q^{54} +(-50.5018 - 0.721219i) q^{55} -11.1488i q^{56} +(40.4539 - 65.3769i) q^{57} +(10.5841 - 32.5747i) q^{58} +(-37.3900 + 12.1488i) q^{59} +(21.0260 - 17.8008i) q^{60} +(-66.2994 + 48.1693i) q^{61} +(51.6610 - 16.7857i) q^{62} +(5.85318 - 34.9891i) q^{63} +(6.47214 + 4.70228i) q^{64} +13.2143i q^{65} +(-2.79492 - 46.5853i) q^{66} +113.002 q^{67} +(-24.9101 + 34.2859i) q^{68} +(14.5352 - 59.4077i) q^{69} +(7.90932 + 24.3424i) q^{70} +(-62.5261 - 86.0597i) q^{71} +(17.8432 + 18.1554i) q^{72} +(30.2057 + 92.9635i) q^{73} +(-89.7699 - 29.1680i) q^{74} +(6.18445 - 9.99458i) q^{75} -51.2539 q^{76} +(41.0410 + 13.9860i) q^{77} +(-12.1766 + 0.905212i) q^{78} +(42.6778 + 31.0072i) q^{79} +(-17.4673 - 5.67546i) q^{80} +(46.4670 + 66.3462i) q^{81} +(-44.2659 + 32.1611i) q^{82} +(-30.0965 - 41.4243i) q^{83} +(-21.8889 + 8.95571i) q^{84} +(30.0655 - 92.5320i) q^{85} +(26.8688 - 36.9818i) q^{86} +(-72.4575 + 5.38653i) q^{87} +(-25.4293 + 17.9263i) q^{88} +0.204051i q^{89} +(-51.8391 - 26.9821i) q^{90} +(3.50551 - 10.7888i) q^{91} +(-38.7777 + 12.5996i) q^{92} +(-74.4549 - 87.9447i) q^{93} +(-6.01614 + 4.37098i) q^{94} +(111.908 - 36.3611i) q^{95} +(4.03321 - 16.4843i) q^{96} +(-5.42715 - 3.94306i) q^{97} +47.3239i q^{98} +(-89.2179 + 42.9088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Introduction

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