LMFDB - Embedded newform 228.2.c.a.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(191,228)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("228.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41330 - 0.0507215i) q^{2} +(-0.756793 - 1.55797i) q^{3} +(1.99485 + 0.143370i) q^{4} +0.762708i q^{5} +(0.990556 + 2.24027i) q^{6} +3.87706i q^{7} +(-2.81206 - 0.303807i) q^{8} +(-1.85453 + 2.35812i) q^{9} +O(q^{10})$	\(q+(-1.41330 - 0.0507215i) q^{2} +(-0.756793 - 1.55797i) q^{3} +(1.99485 + 0.143370i) q^{4} +0.762708i q^{5} +(0.990556 + 2.24027i) q^{6} +3.87706i q^{7} +(-2.81206 - 0.303807i) q^{8} +(-1.85453 + 2.35812i) q^{9} +(0.0386857 - 1.07794i) q^{10} +5.11004 q^{11} +(-1.28633 - 3.21642i) q^{12} -0.587034 q^{13} +(0.196650 - 5.47947i) q^{14} +(1.18828 - 0.577212i) q^{15} +(3.95889 + 0.572003i) q^{16} +1.64637i q^{17} +(2.74062 - 3.23867i) q^{18} -1.00000i q^{19} +(-0.109349 + 1.52149i) q^{20} +(6.04034 - 2.93413i) q^{21} +(-7.22203 - 0.259189i) q^{22} +4.13228 q^{23} +(1.65483 + 4.61102i) q^{24} +4.41828 q^{25} +(0.829657 + 0.0297752i) q^{26} +(5.07737 + 1.10469i) q^{27} +(-0.555853 + 7.73417i) q^{28} +0.844401i q^{29} +(-1.70867 + 0.755505i) q^{30} +8.95324i q^{31} +(-5.56610 - 1.00921i) q^{32} +(-3.86724 - 7.96127i) q^{33} +(0.0835061 - 2.32682i) q^{34} -2.95707 q^{35} +(-4.03760 + 4.43822i) q^{36} -1.82868 q^{37} +(-0.0507215 + 1.41330i) q^{38} +(0.444263 + 0.914580i) q^{39} +(0.231716 - 2.14478i) q^{40} -4.99332i q^{41} +(-8.68566 + 3.84045i) q^{42} -8.79674i q^{43} +(10.1938 + 0.732624i) q^{44} +(-1.79856 - 1.41446i) q^{45} +(-5.84017 - 0.209595i) q^{46} -10.6216 q^{47} +(-2.10490 - 6.60071i) q^{48} -8.03161 q^{49} +(-6.24437 - 0.224101i) q^{50} +(2.56499 - 1.24596i) q^{51} +(-1.17105 - 0.0841628i) q^{52} +10.3008i q^{53} +(-7.11983 - 1.81879i) q^{54} +3.89747i q^{55} +(1.17788 - 10.9025i) q^{56} +(-1.55797 + 0.756793i) q^{57} +(0.0428293 - 1.19340i) q^{58} +7.90462 q^{59} +(2.45319 - 0.981092i) q^{60} +3.61610 q^{61} +(0.454122 - 12.6537i) q^{62} +(-9.14257 - 7.19012i) q^{63} +(7.81540 + 1.70865i) q^{64} -0.447736i q^{65} +(5.06178 + 11.4479i) q^{66} +8.43168i q^{67} +(-0.236039 + 3.28426i) q^{68} +(-3.12728 - 6.43796i) q^{69} +(4.17923 + 0.149987i) q^{70} -5.12574 q^{71} +(5.93147 - 6.06776i) q^{72} -7.37979 q^{73} +(2.58448 + 0.0927532i) q^{74} +(-3.34372 - 6.88353i) q^{75} +(0.143370 - 1.99485i) q^{76} +19.8119i q^{77} +(-0.581490 - 1.31511i) q^{78} -13.4309i q^{79} +(-0.436272 + 3.01948i) q^{80} +(-2.12144 - 8.74640i) q^{81} +(-0.253269 + 7.05708i) q^{82} -6.07788 q^{83} +(12.4703 - 4.98717i) q^{84} -1.25570 q^{85} +(-0.446183 + 12.4325i) q^{86} +(1.31555 - 0.639037i) q^{87} +(-14.3697 - 1.55246i) q^{88} +9.06338i q^{89} +(2.47016 + 2.09029i) q^{90} -2.27597i q^{91} +(8.24330 + 0.592443i) q^{92} +(13.9489 - 6.77575i) q^{93} +(15.0116 + 0.538745i) q^{94} +0.762708 q^{95} +(2.64006 + 9.43558i) q^{96} -4.70298 q^{97} +(11.3511 + 0.407375i) q^{98} +(-9.47671 + 12.0501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6}+O(q^{10}) $ 36 * q - 6 * q^6	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.41330	−	0.0507215i	−0.999357	−	0.0358655i
$2$	−1.41330	−	0.0507215i	−0.999357	−	0.0358655i
$3$	−0.756793	−	1.55797i	−0.436935	−	0.899493i
$3$	−0.756793	−	1.55797i	−0.436935	−	0.899493i
$4$	1.99485	+	0.143370i	0.997427	+	0.0716848i
$5$			0.762708i			0.341093i	0.985350	+	0.170547i	$0.0545534\pi$
$5$			0.762708i			0.341093i	−0.985350	+	0.170547i	$0.945447\pi$
$6$	0.990556	+	2.24027i	0.404393	+	0.914585i
$7$			3.87706i			1.46539i	0.680556	+	0.732696i	$0.261738\pi$
$7$			3.87706i			1.46539i	−0.680556	+	0.732696i	$0.738262\pi$
$8$	−2.81206	−	0.303807i	−0.994215	−	0.107412i
$9$	−1.85453	+	2.35812i	−0.618176	+	0.786039i
$10$	0.0386857	−	1.07794i	0.0122335	−	0.340874i
$11$	5.11004			1.54073			0.770367	−	0.637601i	$-0.220073\pi$
$11$	5.11004			1.54073			0.770367	+	0.637601i	$0.220073\pi$
$12$	−1.28633	−	3.21642i	−0.371330	−	0.928501i
$13$	−0.587034			−0.162814			−0.0814070	−	0.996681i	$-0.525941\pi$
$13$	−0.587034			−0.162814			−0.0814070	+	0.996681i	$0.525941\pi$
$14$	0.196650	−	5.47947i	0.0525570	−	1.46445i
$15$	1.18828	−	0.577212i	0.306811	−	0.149036i
$16$	3.95889	+	0.572003i	0.989723	+	0.143001i
$17$			1.64637i			0.399303i	0.979867	+	0.199651i	$0.0639809\pi$
$17$			1.64637i			0.399303i	−0.979867	+	0.199651i	$0.936019\pi$
$18$	2.74062	−	3.23867i	0.645970	−	0.763363i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.109349	+	1.52149i	−0.0244512	+	0.340216i
$21$	6.04034	−	2.93413i	1.31811	−	0.640280i
$22$	−7.22203	−	0.259189i	−1.53974	−	0.0552592i
$23$	4.13228			0.861640			0.430820	−	0.902438i	$-0.358224\pi$
$23$	4.13228			0.861640			0.430820	+	0.902438i	$0.358224\pi$
$24$	1.65483	+	4.61102i	0.337790	+	0.941221i
$25$	4.41828			0.883655
$26$	0.829657	+	0.0297752i	0.162709	+	0.00583940i
$27$	5.07737	+	1.10469i	0.977140	+	0.212598i
$28$	−0.555853	+	7.73417i	−0.105046	+	1.46162i
$29$			0.844401i			0.156801i	0.996922	+	0.0784007i	$0.0249813\pi$
$29$			0.844401i			0.156801i	−0.996922	+	0.0784007i	$0.975019\pi$
$30$	−1.70867	+	0.755505i	−0.311959	+	0.137936i
$31$			8.95324i			1.60805i	0.594596	+	0.804025i	$0.297312\pi$
$31$			8.95324i			1.60805i	−0.594596	+	0.804025i	$0.702688\pi$
$32$	−5.56610	−	1.00921i	−0.983957	−	0.178406i
$33$	−3.86724	−	7.96127i	−0.673200	−	1.38588i
$34$	0.0835061	−	2.32682i	0.0143212	−	0.399046i
$35$	−2.95707			−0.499835
$36$	−4.03760	+	4.43822i	−0.672933	+	0.739703i
$37$	−1.82868			−0.300633			−0.150316	−	0.988638i	$-0.548029\pi$
$37$	−1.82868			−0.300633			−0.150316	+	0.988638i	$0.548029\pi$
$38$	−0.0507215	+	1.41330i	−0.00822811	+	0.229268i
$39$	0.444263	+	0.914580i	0.0711390	+	0.146450i
$40$	0.231716	−	2.14478i	0.0366375	−	0.339120i
$41$		−	4.99332i		−	0.779826i	−0.920852	−	0.389913i	$-0.872505\pi$
$41$		−	4.99332i		−	0.779826i	0.920852	−	0.389913i	$-0.127495\pi$
$42$	−8.68566	+	3.84045i	−1.34023	+	0.592594i
$43$		−	8.79674i		−	1.34149i	−0.741688	−	0.670745i	$-0.765975\pi$
$43$		−	8.79674i		−	1.34149i	0.741688	−	0.670745i	$-0.234025\pi$
$44$	10.1938	+	0.732624i	1.53677	+	0.110447i
$45$	−1.79856	−	1.41446i	−0.268113	−	0.210856i
$46$	−5.84017	−	0.209595i	−0.861085	−	0.0309031i
$47$	−10.6216			−1.54933			−0.774663	−	0.632374i	$-0.782081\pi$
$47$	−10.6216			−1.54933			−0.774663	+	0.632374i	$0.782081\pi$
$48$	−2.10490	−	6.60071i	−0.303816	−	0.952731i
$49$	−8.03161			−1.14737
$50$	−6.24437	−	0.224101i	−0.883087	−	0.0316927i
$51$	2.56499	−	1.24596i	0.359170	−	0.174469i
$52$	−1.17105	−	0.0841628i	−0.162395	−	0.0116713i
$53$			10.3008i			1.41493i	0.706750	+	0.707463i	$0.250161\pi$
$53$			10.3008i			1.41493i	−0.706750	+	0.707463i	$0.749839\pi$
$54$	−7.11983	−	1.81879i	−0.968886	−	0.247507i
$55$			3.89747i			0.525534i
$56$	1.17788	−	10.9025i	0.157401	−	1.45691i
$57$	−1.55797	+	0.756793i	−0.206358	+	0.100240i
$58$	0.0428293	−	1.19340i	0.00562376	−	0.156700i
$59$	7.90462			1.02909			0.514547	−	0.857462i	$-0.327960\pi$
$59$	7.90462			1.02909			0.514547	+	0.857462i	$0.327960\pi$
$60$	2.45319	−	0.981092i	0.316706	−	0.126658i
$61$	3.61610			0.462994			0.231497	−	0.972836i	$-0.425638\pi$
$61$	3.61610			0.462994			0.231497	+	0.972836i	$0.425638\pi$
$62$	0.454122	−	12.6537i	0.0576735	−	1.60702i
$63$	−9.14257	−	7.19012i	−1.15186	−	0.905870i
$64$	7.81540	+	1.70865i	0.976925	+	0.213581i
$65$		−	0.447736i		−	0.0555348i
$66$	5.06178	+	11.4479i	0.623062	+	1.40913i
$67$			8.43168i			1.03009i	0.857162	+	0.515047i	$0.172225\pi$
$67$			8.43168i			1.03009i	−0.857162	+	0.515047i	$0.827775\pi$
$68$	−0.236039	+	3.28426i	−0.0286239	+	0.398275i
$69$	−3.12728	−	6.43796i	−0.376480	−	0.775039i
$70$	4.17923	+	0.149987i	0.499514	+	0.0179268i
$71$	−5.12574			−0.608313			−0.304156	−	0.952622i	$-0.598375\pi$
$71$	−5.12574			−0.608313			−0.304156	+	0.952622i	$0.598375\pi$
$72$	5.93147	−	6.06776i	0.699030	−	0.715092i
$73$	−7.37979			−0.863739			−0.431869	−	0.901936i	$-0.642146\pi$
$73$	−7.37979			−0.863739			−0.431869	+	0.901936i	$0.642146\pi$
$74$	2.58448	+	0.0927532i	0.300439	+	0.0107823i
$75$	−3.34372	−	6.88353i	−0.386100	−	0.794842i
$76$	0.143370	−	1.99485i	0.0164456	−	0.228826i
$77$			19.8119i			2.25778i
$78$	−0.581490	−	1.31511i	−0.0658408	−	0.148907i
$79$		−	13.4309i		−	1.51110i	−0.655093	−	0.755549i	$-0.727370\pi$
$79$		−	13.4309i		−	1.51110i	0.655093	−	0.755549i	$-0.272630\pi$
$80$	−0.436272	+	3.01948i	−0.0487766	+	0.337588i
$81$	−2.12144	−	8.74640i	−0.235716	−	0.971822i
$82$	−0.253269	+	7.05708i	−0.0279688	+	0.779325i
$83$	−6.07788			−0.667134			−0.333567	−	0.942726i	$-0.608252\pi$
$83$	−6.07788			−0.667134			−0.333567	+	0.942726i	$0.608252\pi$
$84$	12.4703	−	4.98717i	1.36062	−	0.544144i
$85$	−1.25570			−0.136199
$86$	−0.446183	+	12.4325i	−0.0481132	+	1.34063i
$87$	1.31555	−	0.639037i	0.141042	−	0.0685119i
$88$	−14.3697	−	1.55246i	−1.53182	−	0.165493i
$89$			9.06338i			0.960716i	0.877073	+	0.480358i	$0.159493\pi$
$89$			9.06338i			0.960716i	−0.877073	+	0.480358i	$0.840507\pi$
$90$	2.47016	+	2.09029i	0.260378	+	0.220336i
$91$		−	2.27597i		−	0.238586i
$92$	8.24330	+	0.592443i	0.859423	+	0.0617665i
$93$	13.9489	−	6.77575i	1.44643	−	0.702613i
$94$	15.0116	+	0.538745i	1.54833	+	0.0555673i
$95$	0.762708			0.0782522
$96$	2.64006	+	9.43558i	0.269450	+	0.963014i
$97$	−4.70298			−0.477515			−0.238758	−	0.971079i	$-0.576740\pi$
$97$	−4.70298			−0.477515			−0.238758	+	0.971079i	$0.576740\pi$
$98$	11.3511	+	0.407375i	1.14663	+	0.0411511i
$99$	−9.47671	+	12.0501i	−0.952445	+	1.21108i
$100$	8.81382	+	0.633447i	0.881382	+	0.0633447i
$101$		−	8.33215i		−	0.829080i	−0.910031	−	0.414540i	$-0.863943\pi$
$101$		−	8.33215i		−	0.829080i	0.910031	−	0.414540i	$-0.136057\pi$
$102$	−3.68830	+	1.63082i	−0.365196	+	0.161475i
$103$			2.15168i			0.212011i	0.994366	+	0.106006i	$0.0338061\pi$
$103$			2.15168i			0.212011i	−0.994366	+	0.106006i	$0.966194\pi$
$104$	1.65078	+	0.178345i	0.161872	+	0.0174882i
$105$	2.23789	+	4.60702i	0.218395	+	0.449599i
$106$	0.522473	−	14.5582i	0.0507470	−	1.41402i
$107$	10.5723			1.02207			0.511033	−	0.859561i	$-0.329263\pi$
$107$	10.5723			1.02207			0.511033	+	0.859561i	$0.329263\pi$
$108$	9.97023	+	2.93164i	0.959386	+	0.282097i
$109$	13.0704			1.25192			0.625960	−	0.779855i	$-0.284707\pi$
$109$	13.0704			1.25192			0.625960	+	0.779855i	$0.284707\pi$
$110$	0.197685	−	5.50830i	0.0188485	−	0.525196i
$111$	1.38393	+	2.84902i	0.131357	+	0.270417i
$112$	−2.21769	+	15.3489i	−0.209552	+	1.45033i
$113$		−	3.59199i		−	0.337906i	−0.985624	−	0.168953i	$-0.945961\pi$
$113$		−	3.59199i		−	0.337906i	0.985624	−	0.168953i	$-0.0540386\pi$
$114$	2.24027	−	0.990556i	0.209820	−	0.0927740i
$115$			3.15172i			0.293900i
$116$	−0.121061	+	1.68446i	−0.0112403	+	0.156398i
$117$	1.08867	−	1.38430i	0.100648	−	0.127978i
$118$	−11.1716	−	0.400934i	−1.02843	−	0.0369089i
$119$	−6.38306			−0.585135
$120$	−3.51687	+	1.26215i	−0.321044	+	0.115218i
$121$	15.1125			1.37386
$122$	−5.11065	−	0.183414i	−0.462696	−	0.0166055i
$123$	−7.77944	+	3.77891i	−0.701449	+	0.340733i
$124$	−1.28362	+	17.8604i	−0.115273	+	1.60391i
$125$			7.18340i			0.642503i
$126$	12.5565	+	10.6256i	1.11862	+	0.946599i
$127$		−	10.8930i		−	0.966598i	−0.875455	−	0.483299i	$-0.839438\pi$
$127$		−	10.8930i		−	0.966598i	0.875455	−	0.483299i	$-0.160562\pi$
$128$	−10.9589	−	2.81125i	−0.968637	−	0.248481i
$129$	−13.7050	+	6.65731i	−1.20666	+	0.586143i
$130$	−0.0227098	+	0.632786i	−0.00199178	+	0.0554990i
$131$	−8.00545			−0.699439			−0.349720	−	0.936854i	$-0.613723\pi$
$131$	−8.00545			−0.699439			−0.349720	+	0.936854i	$0.613723\pi$
$132$	−6.57318	−	16.4360i	−0.572122	−	1.43057i
$133$	3.87706			0.336184
$134$	0.427667	−	11.9165i	0.0369448	−	1.02943i
$135$	−0.842556	+	3.87255i	−0.0725157	+	0.333296i
$136$	0.500177	−	4.62969i	0.0428899	−	0.396992i
$137$		−	20.8200i		−	1.77878i	−0.457154	−	0.889388i	$-0.651131\pi$
$137$		−	20.8200i		−	1.77878i	0.457154	−	0.889388i	$-0.348869\pi$
$138$	4.09325	+	9.25741i	0.348441	+	0.788043i
$139$		−	16.7117i		−	1.41747i	−0.705477	−	0.708733i	$-0.749267\pi$
$139$		−	16.7117i		−	1.41747i	0.705477	−	0.708733i	$-0.250733\pi$
$140$	−5.89892	−	0.423954i	−0.498550	−	0.0358306i
$141$	8.03839	+	16.5482i	0.676954	+	1.39361i
$142$	7.24422	+	0.259985i	0.607922	+	0.0218174i
$143$	−2.99976			−0.250853
$144$	−8.69073	+	8.27473i	−0.724227	+	0.689561i
$145$	−0.644032			−0.0534839
$146$	10.4299	+	0.374314i	0.863183	+	0.0309784i
$147$	6.07826	+	12.5130i	0.501327	+	1.03205i
$148$	−3.64795	−	0.262177i	−0.299859	−	0.0215508i
$149$			4.00704i			0.328269i	0.986438	+	0.164135i	$0.0524832\pi$
$149$			4.00704i			0.328269i	−0.986438	+	0.164135i	$0.947517\pi$
$150$	4.37655	+	9.89812i	0.357344	+	0.808178i
$151$		−	12.0050i		−	0.976951i	−0.872578	−	0.488476i	$-0.837553\pi$
$151$		−	12.0050i		−	0.976951i	0.872578	−	0.488476i	$-0.162447\pi$
$152$	−0.303807	+	2.81206i	−0.0246420	+	0.228088i
$153$	−3.88233	−	3.05323i	−0.313868	−	0.246839i
$154$	1.00489	−	28.0003i	0.0809763	−	2.25633i
$155$	−6.82871			−0.548495
$156$	0.755117	+	1.88815i	0.0604578	+	0.151173i
$157$	4.28650			0.342100			0.171050	−	0.985262i	$-0.445284\pi$
$157$	4.28650			0.342100			0.171050	+	0.985262i	$0.445284\pi$
$158$	−0.681236	+	18.9820i	−0.0541962	+	1.51012i
$159$	16.0484	−	7.79559i	1.27272	−	0.618230i
$160$	0.769736	−	4.24531i	0.0608530	−	0.335621i
$161$			16.0211i			1.26264i
$162$	2.55461	+	12.4689i	0.200709	+	0.979651i
$163$		−	13.6584i		−	1.06981i	−0.844913	−	0.534904i	$-0.820348\pi$
$163$		−	13.6584i		−	1.06981i	0.844913	−	0.534904i	$-0.179652\pi$
$164$	0.715891	−	9.96096i	0.0559017	−	0.777820i
$165$	6.07213	−	2.94958i	0.472715	−	0.229624i
$166$	8.58989	+	0.308279i	0.666705	+	0.0239271i
$167$	13.2030			1.02168			0.510838	−	0.859677i	$-0.329335\pi$
$167$	13.2030			1.02168			0.510838	+	0.859677i	$0.329335\pi$
$168$	−17.8772	+	6.41587i	−1.37926	+	0.494995i
$169$	−12.6554			−0.973492
$170$	1.77468	+	0.0636908i	0.136112	+	0.00488486i
$171$	2.35812	+	1.85453i	0.180330	+	0.141819i
$172$	1.26118	−	17.5482i	0.0961645	−	1.33804i
$173$		−	21.5437i		−	1.63794i	−0.573837	−	0.818970i	$-0.694546\pi$
$173$		−	21.5437i		−	1.63794i	0.573837	−	0.818970i	$-0.305454\pi$
$174$	−1.89168	+	0.836426i	−0.143408	+	0.0634093i
$175$			17.1299i			1.29490i
$176$	20.2301	+	2.92296i	1.52490	+	0.220326i
$177$	−5.98216	−	12.3151i	−0.449646	−	0.925663i
$178$	0.459708	−	12.8093i	0.0344565	−	0.960098i
$179$	−18.3784			−1.37367			−0.686834	−	0.726814i	$-0.741000\pi$
$179$	−18.3784			−1.37367			−0.686834	+	0.726814i	$0.741000\pi$
$180$	−3.38507	−	3.07951i	−0.252308	−	0.229533i
$181$	0.662077			0.0492118			0.0246059	−	0.999697i	$-0.492167\pi$
$181$	0.662077			0.0492118			0.0246059	+	0.999697i	$0.492167\pi$
$182$	−0.115440	+	3.21663i	−0.00855701	+	0.238433i
$183$	−2.73664	−	5.63377i	−0.202298	−	0.416460i
$184$	−11.6202	−	1.25541i	−0.856655	−	0.0925504i
$185$		−	1.39475i		−	0.102544i
$186$	−20.0577	+	8.86869i	−1.47070	+	0.650284i
$187$			8.41299i			0.615219i
$188$	−21.1886	−	1.52282i	−1.54534	−	0.111063i
$189$	−4.28295	+	19.6853i	−0.311539	+	1.43189i
$190$	−1.07794	−	0.0386857i	−0.0782019	−	0.00280655i
$191$	14.0483			1.01650			0.508250	−	0.861210i	$-0.330293\pi$
$191$	14.0483			1.01650			0.508250	+	0.861210i	$0.330293\pi$
$192$	−3.25262	−	13.4692i	−0.234738	−	0.972059i
$193$	2.46211			0.177227			0.0886134	−	0.996066i	$-0.471756\pi$
$193$	2.46211			0.177227			0.0886134	+	0.996066i	$0.471756\pi$
$194$	6.64674	+	0.238542i	0.477208	+	0.0171263i
$195$	−0.697558	+	0.338843i	−0.0499531	+	0.0242651i
$196$	−16.0219	−	1.15149i	−1.14442	−	0.0822492i
$197$		−	20.5990i		−	1.46762i	−0.679357	−	0.733808i	$-0.737741\pi$
$197$		−	20.5990i		−	1.46762i	0.679357	−	0.733808i	$-0.262259\pi$
$198$	14.0047	−	16.5497i	0.995269	−	1.17614i
$199$			12.8363i			0.909940i	0.890507	+	0.454970i	$0.150350\pi$
$199$			12.8363i			0.909940i	−0.890507	+	0.454970i	$0.849650\pi$
$200$	−12.4245	−	1.34230i	−0.878543	−	0.0949151i
$201$	13.1363	−	6.38103i	0.926562	−	0.450084i
$202$	−0.422619	+	11.7759i	−0.0297354	+	0.828546i
$203$	−3.27380			−0.229775
$204$	5.29541	−	2.11776i	0.370753	−	0.148273i
$205$	3.80845			0.265994
$206$	0.109136	−	3.04098i	0.00760388	−	0.211875i
$207$	−7.66343	+	9.74440i	−0.532645	+	0.677283i
$208$	−2.32400	−	0.335785i	−0.161141	−	0.0232825i
$209$		−	5.11004i		−	0.353469i
$210$	−2.92914	−	6.62462i	−0.202130	−	0.457142i
$211$			1.23795i			0.0852242i	0.999092	+	0.0426121i	$0.0135680\pi$
$211$			1.23795i			0.0852242i	−0.999092	+	0.0426121i	$0.986432\pi$
$212$	−1.47682	+	20.5486i	−0.101429	+	1.41129i
$213$	3.87912	+	7.98573i	0.265793	+	0.547173i
$214$	−14.9419	−	0.536244i	−1.02141	−	0.0366569i
$215$	6.70934			0.457573
$216$	−13.9423	−	4.64900i	−0.948651	−	0.316324i
$217$	−34.7123			−2.35642
$218$	−18.4725	−	0.662951i	−1.25111	−	0.0449007i
$219$	5.58497	+	11.4975i	0.377397	+	0.776927i
$220$	−0.558778	+	7.77488i	−0.0376728	+	0.524182i
$221$		−	0.966473i		−	0.0650120i
$222$	−1.81141	−	4.09673i	−0.121574	−	0.274954i
$223$			20.5448i			1.37578i	0.725816	+	0.687889i	$0.241463\pi$
$223$			20.5448i			1.37578i	−0.725816	+	0.687889i	$0.758537\pi$
$224$	3.91279	−	21.5801i	0.261434	−	1.44188i
$225$	−8.19382	+	10.4188i	−0.546255	+	0.694588i
$226$	−0.182191	+	5.07657i	−0.0121192	+	0.337689i
$227$	25.6172			1.70027			0.850137	−	0.526562i	$-0.176519\pi$
$227$	25.6172			1.70027			0.850137	+	0.526562i	$0.176519\pi$
$228$	−3.21642	+	1.28633i	−0.213013	+	0.0851891i
$229$	−18.7952			−1.24202			−0.621012	−	0.783801i	$-0.713278\pi$
$229$	−18.7952			−1.24202			−0.621012	+	0.783801i	$0.713278\pi$
$230$	0.159860	−	4.45434i	0.0105409	−	0.293711i
$231$	30.8664	−	14.9935i	2.03086	−	0.986502i
$232$	0.256535	−	2.37451i	0.0168423	−	0.155894i
$233$			13.5571i			0.888153i	0.895989	+	0.444077i	$0.146468\pi$
$233$			13.5571i			0.888153i	−0.895989	+	0.444077i	$0.853532\pi$
$234$	−1.60884	+	1.90121i	−0.105173	+	0.124286i
$235$		−	8.10122i		−	0.528465i
$236$	15.7686	+	1.13328i	1.02645	+	0.0737704i
$237$	−20.9250	+	10.1644i	−1.35922	+	0.660251i
$238$	9.02121	+	0.323758i	0.584758	+	0.0209861i
$239$	−11.3716			−0.735569			−0.367785	−	0.929911i	$-0.619884\pi$
$239$	−11.3716			−0.735569			−0.367785	+	0.929911i	$0.619884\pi$
$240$	5.03442	−	1.60542i	0.324970	−	0.103630i
$241$	−12.0622			−0.776992			−0.388496	−	0.921450i	$-0.627005\pi$
$241$	−12.0622			−0.776992			−0.388496	+	0.921450i	$0.627005\pi$
$242$	−21.3585	−	0.766527i	−1.37298	−	0.0492742i
$243$	−12.0211	+	9.92435i	−0.771155	+	0.636648i
$244$	7.21359	+	0.518439i	0.461803	+	0.0331896i
$245$		−	6.12577i		−	0.391361i
$246$	11.1864	−	4.94617i	0.713218	−	0.315356i
$247$			0.587034i			0.0373521i
$248$	2.72006	−	25.1771i	0.172724	−	1.59875i
$249$	4.59970	+	9.46915i	0.291494	+	0.600083i
$250$	0.364352	−	10.1523i	0.0230437	−	0.642089i
$251$	−0.536967			−0.0338931			−0.0169465	−	0.999856i	$-0.505395\pi$
$251$	−0.536967			−0.0338931			−0.0169465	+	0.999856i	$0.505395\pi$
$252$	−17.2073	−	15.6540i	−1.08395	−	0.986110i
$253$	21.1161			1.32756
$254$	−0.552509	+	15.3951i	−0.0346675	+	0.965976i
$255$	0.950303	+	1.95634i	0.0595103	+	0.122511i
$256$	15.3456	+	4.52900i	0.959102	+	0.283062i
$257$		−	19.8858i		−	1.24044i	−0.784427	−	0.620221i	$-0.787043\pi$
$257$		−	19.8858i		−	1.24044i	0.784427	−	0.620221i	$-0.212957\pi$
$258$	19.7070	−	8.71366i	1.22691	−	0.542489i
$259$		−	7.08990i		−	0.440545i
$260$	0.0641917	−	0.893167i	0.00398100	−	0.0553919i
$261$	−1.99120	−	1.56597i	−0.123252	−	0.0969309i
$262$	11.3141	+	0.406048i	0.698989	+	0.0250857i
$263$	13.4752			0.830919			0.415459	−	0.909612i	$-0.363621\pi$
$263$	13.4752			0.830919			0.415459	+	0.909612i	$0.363621\pi$
$264$	8.45623	+	23.5625i	0.520445	+	1.45017i
$265$	−7.85652			−0.482622
$266$	−5.47947	−	0.196650i	−0.335968	−	0.0120574i
$267$	14.1205	−	6.85910i	0.864158	−	0.419770i
$268$	−1.20885	+	16.8200i	−0.0738421	+	1.02744i
$269$		−	14.5106i		−	0.884728i	−0.896836	−	0.442364i	$-0.854140\pi$
$269$		−	14.5106i		−	0.884728i	0.896836	−	0.442364i	$-0.145860\pi$
$270$	1.38721	−	5.43035i	0.0844229	−	0.330481i
$271$		−	1.76652i		−	0.107308i	−0.998560	−	0.0536541i	$-0.982913\pi$
$271$		−	1.76652i		−	0.107308i	0.998560	−	0.0536541i	$-0.0170868\pi$
$272$	−0.941727	+	6.51778i	−0.0571006	+	0.395199i
$273$	−3.54588	+	1.72244i	−0.214607	+	0.104247i
$274$	−1.05602	+	29.4250i	−0.0637966	+	1.77763i
$275$	22.5776			1.36148
$276$	−5.31546	−	13.2911i	−0.319953	−	0.800033i
$277$	4.01710			0.241364			0.120682	−	0.992691i	$-0.461492\pi$
$277$	4.01710			0.241364			0.120682	+	0.992691i	$0.461492\pi$
$278$	−0.847640	+	23.6187i	−0.0508381	+	1.41655i
$279$	−21.1128	−	16.6041i	−1.26399	−	0.994058i
$280$	8.31546	+	0.898377i	0.496944	+	0.0536883i
$281$			21.6108i			1.28919i	0.764524	+	0.644596i	$0.222974\pi$
$281$			21.6108i			1.28919i	−0.764524	+	0.644596i	$0.777026\pi$
$282$	−10.5213	−	23.7953i	−0.626536	−	1.41699i
$283$			17.6039i			1.04644i	0.852198	+	0.523220i	$0.175269\pi$
$283$			17.6039i			1.04644i	−0.852198	+	0.523220i	$0.824731\pi$
$284$	−10.2251	−	0.734875i	−0.606748	−	0.0436068i
$285$	−0.577212	−	1.18828i	−0.0341911	−	0.0703873i
$286$	4.23958	+	0.152152i	0.250692	+	0.00899696i
$287$	19.3594			1.14275
$288$	12.7023	−	11.2539i	0.748493	−	0.663143i
$289$	14.2895			0.840557
$290$	0.910212	+	0.0326662i	0.0534495	+	0.00191823i
$291$	3.55918	+	7.32709i	0.208643	+	0.429522i
$292$	−14.7216	−	1.05804i	−0.861517	−	0.0619170i
$293$			11.6431i			0.680199i	0.940390	+	0.340099i	$0.110461\pi$
$293$			11.6431i			0.680199i	−0.940390	+	0.340099i	$0.889539\pi$
$294$	−7.95575	−	17.9929i	−0.463989	−	1.04937i
$295$			6.02892i			0.351017i
$296$	5.14236	+	0.555565i	0.298894	+	0.0322915i
$297$	25.9455	+	5.64501i	1.50551	+	0.327557i
$298$	0.203243	−	5.66316i	0.0117735	−	0.328058i
$299$	−2.42579			−0.140287
$300$	−5.68335	−	14.2110i	−0.328128	−	0.820475i
$301$	34.1055			1.96581
$302$	−0.608910	+	16.9667i	−0.0350388	+	0.976322i
$303$	−12.9812	+	6.30571i	−0.745752	+	0.362254i
$304$	0.572003	−	3.95889i	0.0328066	−	0.227058i
$305$			2.75803i			0.157924i
$306$	5.33204	+	4.51207i	0.304813	+	0.257938i
$307$		−	5.09802i		−	0.290960i	−0.989361	−	0.145480i	$-0.953527\pi$
$307$		−	5.09802i		−	0.290960i	0.989361	−	0.145480i	$-0.0464726\pi$
$308$	−2.84043	+	39.5219i	−0.161848	+	2.25197i
$309$	3.35225	−	1.62837i	0.190703	−	0.0926350i
$310$	9.65104	+	0.346362i	0.548142	+	0.0196721i
$311$	−12.0774			−0.684849			−0.342424	−	0.939545i	$-0.611248\pi$
$311$	−12.0774			−0.684849			−0.342424	+	0.939545i	$0.611248\pi$
$312$	−0.971440	−	2.70683i	−0.0549970	−	0.153244i
$313$	21.0857			1.19184			0.595918	−	0.803045i	$-0.296788\pi$
$313$	21.0857			1.19184			0.595918	+	0.803045i	$0.296788\pi$
$314$	−6.05813	−	0.217418i	−0.341880	−	0.0122696i
$315$	5.48397	−	6.97311i	0.308986	−	0.392890i
$316$	1.92559	−	26.7927i	0.108323	−	1.50721i
$317$		−	9.77428i		−	0.548978i	−0.961590	−	0.274489i	$-0.911491\pi$
$317$		−	9.77428i		−	0.548978i	0.961590	−	0.274489i	$-0.0885087\pi$
$318$	−23.0766	+	10.2035i	−1.29407	+	0.572186i
$319$			4.31492i			0.241589i
$320$	−1.30320	+	5.96087i	−0.0728511	+	0.333223i
$321$	−8.00107	−	16.4714i	−0.446576	−	0.919342i
$322$	0.812613	−	22.6427i	0.0452852	−	1.26183i
$323$	1.64637			0.0916063
$324$	−2.97800	−	17.7519i	−0.165445	−	0.986219i
$325$	−2.59368			−0.143871
$326$	−0.692774	+	19.3035i	−0.0383692	+	1.06912i
$327$	−9.89160	−	20.3633i	−0.547007	−	1.12609i
$328$	−1.51701	+	14.0415i	−0.0837626	+	0.775315i
$329$		−	41.1808i		−	2.27037i
$330$	−8.73137	+	3.86066i	−0.480646	+	0.212522i
$331$			1.42855i			0.0785204i	0.999229	+	0.0392602i	$0.0125001\pi$
$331$			1.42855i			0.0785204i	−0.999229	+	0.0392602i	$0.987500\pi$
$332$	−12.1245	−	0.871384i	−0.665418	−	0.0478234i
$333$	3.39134	−	4.31224i	0.185844	−	0.236309i
$334$	−18.6598	−	0.669674i	−1.02102	−	0.0366429i
$335$	−6.43091			−0.351358
$336$	25.5914	−	8.16082i	1.39612	−	0.445209i
$337$	0.0498717			0.00271668			0.00135834	−	0.999999i	$-0.499568\pi$
$337$	0.0498717			0.00271668			0.00135834	+	0.999999i	$0.499568\pi$
$338$	17.8859	+	0.641900i	0.972865	+	0.0349147i
$339$	−5.59621	+	2.71839i	−0.303944	+	0.147643i
$340$	−2.50493	−	0.180029i	−0.135849	−	0.00976344i
$341$			45.7514i			2.47758i
$342$	−3.23867	−	2.74062i	−0.175127	−	0.148196i
$343$		−	3.99960i		−	0.215958i
$344$	−2.67251	+	24.7370i	−0.144092	+	1.33373i
$345$	4.91028	−	2.38520i	0.264361	−	0.128415i
$346$	−1.09273	+	30.4478i	−0.0587455	+	1.63689i
$347$	−11.2205			−0.602346			−0.301173	−	0.953569i	$-0.597378\pi$
$347$	−11.2205			−0.602346			−0.301173	+	0.953569i	$0.597378\pi$
$348$	2.71595	−	1.08618i	0.145590	−	0.0582251i
$349$	−13.0436			−0.698207			−0.349104	−	0.937084i	$-0.613514\pi$
$349$	−13.0436			−0.698207			−0.349104	+	0.937084i	$0.613514\pi$
$350$	0.868855	−	24.2098i	0.0464422	−	1.29407i
$351$	−2.98059	−	0.648491i	−0.159092	−	0.0346139i
$352$	−28.4430	−	5.15713i	−1.51602	−	0.274876i
$353$		−	20.2748i		−	1.07912i	−0.841947	−	0.539560i	$-0.818590\pi$
$353$		−	20.2748i		−	1.07912i	0.841947	−	0.539560i	$-0.181410\pi$
$354$	7.82996	+	17.7085i	0.416158	+	0.941194i
$355$		−	3.90944i		−	0.207492i
$356$	−1.29941	+	18.0801i	−0.0688688	+	0.958244i
$357$	4.83066	+	9.94461i	0.255666	+	0.526325i
$358$	25.9743	+	0.932180i	1.37278	+	0.0492673i
$359$	−5.33549			−0.281597			−0.140798	−	0.990038i	$-0.544967\pi$
$359$	−5.33549			−0.281597			−0.140798	+	0.990038i	$0.544967\pi$
$360$	4.62793	+	4.52398i	0.243913	+	0.238435i
$361$	−1.00000			−0.0526316
$362$	−0.935716	−	0.0335815i	−0.0491802	−	0.00176501i
$363$	−11.4370	−	23.5448i	−0.600288	−	1.23578i
$364$	0.326304	−	4.54022i	0.0171030	−	0.237972i
$365$		−	5.62862i		−	0.294616i
$366$	3.58195	+	8.10103i	0.187231	+	0.423448i
$367$			14.9149i			0.778551i	0.921121	+	0.389276i	$0.127275\pi$
$367$			14.9149i			0.778551i	−0.921121	+	0.389276i	$0.872725\pi$
$368$	16.3592	+	2.36368i	0.852784	+	0.123215i
$369$	11.7749	+	9.26027i	0.612974	+	0.482070i
$370$	−0.0707436	+	1.97120i	−0.00367779	+	0.102478i
$371$	−39.9369			−2.07342
$372$	28.7974	−	11.5168i	1.49308	−	0.597118i
$373$	−9.47842			−0.490774			−0.245387	−	0.969425i	$-0.578915\pi$
$373$	−9.47842			−0.490774			−0.245387	+	0.969425i	$0.578915\pi$
$374$	0.426719	−	11.8901i	0.0220651	−	0.614823i
$375$	11.1915	−	5.43634i	0.577927	−	0.280732i
$376$	29.8687	+	3.22693i	1.54036	+	0.166416i
$377$		−	0.495692i		−	0.0255294i
$378$	7.05158	−	27.6040i	0.362694	−	1.41980i
$379$		−	5.01719i		−	0.257716i	−0.991663	−	0.128858i	$-0.958869\pi$
$379$		−	5.01719i		−	0.257716i	0.991663	−	0.128858i	$-0.0411311\pi$
$380$	1.52149	+	0.109349i	0.0780509	+	0.00560950i
$381$	−16.9710	+	8.24375i	−0.869448	+	0.422340i
$382$	−19.8545	−	0.712551i	−1.01585	−	0.0364573i
$383$	−20.5573			−1.05043			−0.525215	−	0.850970i	$-0.676015\pi$
$383$	−20.5573			−1.05043			−0.525215	+	0.850970i	$0.676015\pi$
$384$	3.91376	+	19.2011i	0.199723	+	0.979852i
$385$	−15.1107			−0.770114
$386$	−3.47971	−	0.124882i	−0.177113	−	0.00635633i
$387$	20.7437	+	16.3138i	1.05446	+	0.829277i
$388$	−9.38176	−	0.674264i	−0.476287	−	0.0342306i
$389$		−	19.0560i		−	0.966179i	−0.875571	−	0.483089i	$-0.839515\pi$
$389$		−	19.0560i		−	0.966179i	0.875571	−	0.483089i	$-0.160485\pi$
$390$	1.00305	−	0.443507i	0.0507913	−	0.0224579i
$391$			6.80325i			0.344055i
$392$	22.5854	+	2.44006i	1.14073	+	0.123241i
$393$	6.05847	+	12.4722i	0.305609	+	0.629141i
$394$	−1.04481	+	29.1126i	−0.0526367	+	1.46667i
$395$	10.2439			0.515425
$396$	−20.6323	+	22.6795i	−1.03681	+	1.13969i
$397$	35.2791			1.77061			0.885304	−	0.465012i	$-0.153950\pi$
$397$	35.2791			1.77061			0.885304	+	0.465012i	$0.153950\pi$
$398$	0.651075	−	18.1416i	0.0326355	−	0.909355i
$399$	−2.93413	−	6.04034i	−0.146890	−	0.302395i
$400$	17.4915	+	2.52727i	0.874574	+	0.126363i
$401$			18.4215i			0.919928i	0.887938	+	0.459964i	$0.152138\pi$
$401$			18.4215i			0.919928i	−0.887938	+	0.459964i	$0.847862\pi$
$402$	−18.8892	+	8.35205i	−0.942109	+	0.416562i
$403$		−	5.25586i		−	0.261813i
$404$	1.19458	−	16.6214i	0.0594324	−	0.826947i
$405$	6.67095	−	1.61804i	0.331482	−	0.0804012i
$406$	4.62687	+	0.166052i	0.229628	+	0.00824101i
$407$	−9.34461			−0.463195
$408$	−7.59144	+	2.72445i	−0.375832	+	0.134881i
$409$	−5.91166			−0.292313			−0.146156	−	0.989261i	$-0.546690\pi$
$409$	−5.91166			−0.292313			−0.146156	+	0.989261i	$0.546690\pi$
$410$	−5.38250	−	0.193170i	−0.265823	−	0.00953999i
$411$	−32.4369	+	15.7565i	−1.60000	+	0.777208i
$412$	−0.308485	+	4.29229i	−0.0151980	+	0.211466i
$413$			30.6467i			1.50802i
$414$	11.3250	−	13.3831i	0.556594	−	0.657743i
$415$		−	4.63565i		−	0.227555i
$416$	3.26749	+	0.592443i	0.160202	+	0.0290469i
$417$	−26.0363	+	12.6473i	−1.27500	+	0.619340i
$418$	−0.259189	+	7.22203i	−0.0126773	+	0.353241i
$419$	−34.7614			−1.69821			−0.849104	−	0.528226i	$-0.822857\pi$
$419$	−34.7614			−1.69821			−0.849104	+	0.528226i	$0.822857\pi$
$420$	3.80375	+	9.51117i	0.185604	+	0.464098i
$421$	17.4241			0.849198			0.424599	−	0.905381i	$-0.360415\pi$
$421$	17.4241			0.849198			0.424599	+	0.905381i	$0.360415\pi$
$422$	0.0627908	−	1.74960i	0.00305661	−	0.0851693i
$423$	19.6982	−	25.0471i	0.957757	−	1.21783i
$424$	3.12946	−	28.9666i	0.151980	−	1.40674i
$425$			7.27410i			0.352846i
$426$	−5.07733	−	11.4830i	−0.245997	−	0.556354i
$427$			14.0198i			0.678467i
$428$	21.0903	+	1.51575i	1.01944	+	0.0732666i
$429$	2.27020	+	4.67354i	0.109606	+	0.225641i
$430$	−9.48234	−	0.340308i	−0.457279	−	0.0164111i
$431$	26.1850			1.26129			0.630644	−	0.776072i	$-0.282791\pi$
$431$	26.1850			1.26129			0.630644	+	0.776072i	$0.282791\pi$
$432$	19.4689	+	7.27762i	0.936696	+	0.350145i
$433$	−33.3944			−1.60483			−0.802417	−	0.596764i	$-0.796453\pi$
$433$	−33.3944			−1.60483			−0.802417	+	0.596764i	$0.796453\pi$
$434$	49.0590	+	1.76066i	2.35491	+	0.0845142i
$435$	0.487399	+	1.00338i	0.0233690	+	0.0481084i
$436$	26.0736	+	1.87390i	1.24870	+	0.0897436i
$437$		−	4.13228i		−	0.197674i
$438$	−7.31009	−	16.5327i	−0.349290	−	0.789963i
$439$		−	11.6628i		−	0.556636i	−0.960489	−	0.278318i	$-0.910223\pi$
$439$		−	11.6628i		−	0.556636i	0.960489	−	0.278318i	$-0.0897770\pi$
$440$	1.18408	−	10.9599i	0.0564487	−	0.522494i
$441$	14.8948	−	18.9395i	0.709278	−	0.901880i
$442$	−0.0490209	+	1.36592i	−0.00233169	+	0.0649702i
$443$	22.5598			1.07185			0.535924	−	0.844266i	$-0.319963\pi$
$443$	22.5598			1.07185			0.535924	+	0.844266i	$0.319963\pi$
$444$	2.35228	+	5.88180i	0.111634	+	0.279138i
$445$	−6.91271			−0.327694
$446$	1.04206	−	29.0360i	0.0493430	−	1.37489i
$447$	6.24284	−	3.03250i	0.295276	−	0.143432i
$448$	−6.62453	+	30.3008i	−0.312980	+	1.43158i
$449$		−	5.11285i		−	0.241290i	−0.992696	−	0.120645i	$-0.961504\pi$
$449$		−	5.11285i		−	0.241290i	0.992696	−	0.120645i	$-0.0384963\pi$
$450$	12.1088	−	14.3094i	0.570815	−	0.674549i
$451$		−	25.5161i		−	1.20151i
$452$	0.514982	−	7.16550i	0.0242227	−	0.337037i
$453$	−18.7034	+	9.08528i	−0.878761	+	0.426864i
$454$	−36.2049	−	1.29934i	−1.69918	−	0.0609811i
$455$	1.73590			0.0813802
$456$	4.61102	−	1.65483i	0.215931	−	0.0774944i
$457$	20.6806			0.967398			0.483699	−	0.875235i	$-0.339293\pi$
$457$	20.6806			0.967398			0.483699	+	0.875235i	$0.339293\pi$
$458$	26.5634	+	0.953322i	1.24122	+	0.0445458i
$459$	−1.81872	+	8.35921i	−0.0848908	+	0.390174i
$460$	−0.451861	+	6.28723i	−0.0210681	+	0.293144i
$461$			2.97037i			0.138344i	0.997605	+	0.0691720i	$0.0220357\pi$
$461$			2.97037i			0.138344i	−0.997605	+	0.0691720i	$0.977964\pi$
$462$	−44.3840	+	19.6248i	−2.06493	+	0.913029i
$463$			19.0211i			0.883984i	0.897019	+	0.441992i	$0.145728\pi$
$463$			19.0211i			0.883984i	−0.897019	+	0.441992i	$0.854272\pi$
$464$	−0.483000	+	3.34289i	−0.0224227	+	0.155190i
$465$	5.16792	+	10.6389i	0.239657	+	0.493368i
$466$	0.687634	−	19.1603i	0.0318541	−	0.887582i
$467$	9.90799			0.458487			0.229243	−	0.973369i	$-0.426375\pi$
$467$	9.90799			0.458487			0.229243	+	0.973369i	$0.426375\pi$
$468$	2.37021	−	2.60539i	0.109563	−	0.120434i
$469$	−32.6901			−1.50949
$470$	−0.410906	+	11.4495i	−0.0189537	+	0.528125i
$471$	−3.24400	−	6.67824i	−0.149475	−	0.307717i
$472$	−22.2283	−	2.40148i	−1.02314	−	0.110537i
$473$		−	44.9517i		−	2.06688i
$474$	30.0889	−	13.3041i	1.38203	−	0.611077i
$475$		−	4.41828i		−	0.202724i
$476$	−12.7333	−	0.915138i	−0.583629	−	0.0419453i
$477$	−24.2906	−	19.1032i	−1.11219	−	0.874674i
$478$	16.0716	+	0.576785i	0.735096	+	0.0263815i
$479$	3.29331			0.150475			0.0752376	−	0.997166i	$-0.476028\pi$
$479$	3.29331			0.150475			0.0752376	+	0.997166i	$0.476028\pi$
$480$	−7.19659	+	2.01360i	−0.328478	+	0.0919077i
$481$	1.07350			0.0489472
$482$	17.0475	+	0.611810i	0.776492	+	0.0278672i
$483$	24.9604	−	12.1247i	1.13574	−	0.551691i
$484$	30.1472	+	2.16667i	1.37033	+	0.0984850i
$485$		−	3.58700i		−	0.162877i
$486$	17.4929	−	13.4164i	0.793492	−	0.608580i
$487$		−	3.51432i		−	0.159249i	−0.996825	−	0.0796246i	$-0.974628\pi$
$487$		−	3.51432i		−	0.159249i	0.996825	−	0.0796246i	$-0.0253722\pi$
$488$	−10.1687	−	1.09860i	−0.460315	−	0.0497311i
$489$	−21.2793	+	10.3366i	−0.962285	+	0.467436i
$490$	−0.310708	+	8.65758i	−0.0140364	+	0.391109i
$491$	−27.3945			−1.23630			−0.618149	−	0.786061i	$-0.712117\pi$
$491$	−27.3945			−1.23630			−0.618149	+	0.786061i	$0.712117\pi$
$492$	−16.0606	+	6.42305i	−0.724069	+	0.289573i
$493$	−1.39019			−0.0626112
$494$	0.0297752	−	0.829657i	0.00133965	−	0.0373280i
$495$	−9.19069	−	7.22797i	−0.413091	−	0.324873i
$496$	−5.12128	+	35.4449i	−0.229952	+	1.59152i
$497$		−	19.8728i		−	0.891417i
$498$	−6.02048	−	13.6161i	−0.269784	−	0.610151i
$499$			22.7931i			1.02036i	0.860068	+	0.510179i	$0.170421\pi$
$499$			22.7931i			1.02036i	−0.860068	+	0.510179i	$0.829579\pi$
$500$	−1.02988	+	14.3298i	−0.0460577	+	0.640850i
$501$	−9.99191	−	20.5698i	−0.446406	−	0.918991i
$502$	0.758898	+	0.0272358i	0.0338713	+	0.00121559i
$503$	−11.0608			−0.493177			−0.246588	−	0.969120i	$-0.579310\pi$
$503$	−11.0608			−0.493177			−0.246588	+	0.969120i	$0.579310\pi$
$504$	23.5251	+	22.9967i	1.04789	+	1.02435i
$505$	6.35500			0.282794
$506$	−29.8435	−	1.07104i	−1.32670	−	0.0476135i
$507$	9.57751	+	19.7167i	0.425352	+	0.875649i
$508$	1.56173	−	21.7300i	0.0692904	−	0.964111i
$509$		−	16.9182i		−	0.749887i	−0.927048	−	0.374944i	$-0.877662\pi$
$509$		−	16.9182i		−	0.749887i	0.927048	−	0.374944i	$-0.122338\pi$
$510$	−1.24384	−	2.81310i	−0.0550781	−	0.124566i
$511$		−	28.6119i		−	1.26572i
$512$	−21.4583	−	7.17920i	−0.948332	−	0.317279i
$513$	1.10469	−	5.07737i	0.0487733	−	0.224171i
$514$	−1.00864	+	28.1047i	−0.0444891	+	1.23964i
$515$	−1.64110			−0.0723156
$516$	−28.2940	+	11.3155i	−1.24557	+	0.498136i
$517$	−54.2770			−2.38710
$518$	−0.359610	+	10.0202i	−0.0158004	+	0.440261i
$519$	−33.5644	+	16.3041i	−1.47332	+	0.715672i
$520$	−0.136025	+	1.25906i	−0.00596509	+	0.0552135i
$521$			32.2873i			1.41453i	0.706948	+	0.707265i	$0.250071\pi$
$521$			32.2873i			1.41453i	−0.706948	+	0.707265i	$0.749929\pi$
$522$	2.73474	+	2.31418i	0.119696	+	0.101289i
$523$		−	16.7639i		−	0.733034i	−0.930411	−	0.366517i	$-0.880550\pi$
$523$		−	16.7639i		−	0.733034i	0.930411	−	0.366517i	$-0.119450\pi$
$524$	−15.9697	−	1.14774i	−0.697640	−	0.0501392i
$525$	26.6879	−	12.9638i	1.16475	−	0.565787i
$526$	−19.0446	−	0.683484i	−0.830384	−	0.0298013i
$527$	−14.7403			−0.642098
$528$	−10.7561	−	33.7299i	−0.468099	−	1.46790i
$529$	−5.92427			−0.257577
$530$	11.1036	+	0.398494i	0.482312	+	0.0173095i
$531$	−14.6593	+	18.6400i	−0.636161	+	0.808908i
$532$	7.73417	+	0.555853i	0.335319	+	0.0240993i
$533$			2.93125i			0.126967i
$534$	−20.3044	+	8.97778i	−0.878657	+	0.388507i
$535$			8.06361i			0.348620i
$536$	2.56160	−	23.7104i	0.110644	−	1.02413i
$537$	13.9087	+	28.6330i	0.600203	+	1.23560i
$538$	−0.736000	+	20.5079i	−0.0317312	+	0.884159i
$539$	−41.0418			−1.76780
$540$	−2.23598	+	7.60438i	−0.0962214	+	0.327240i
$541$	−3.18983			−0.137141			−0.0685707	−	0.997646i	$-0.521844\pi$
$541$	−3.18983			−0.137141			−0.0685707	+	0.997646i	$0.521844\pi$
$542$	−0.0896003	+	2.49662i	−0.00384866	+	0.107239i
$543$	−0.501055	−	1.03150i	−0.0215023	−	0.0442657i
$544$	1.66154	−	9.16384i	0.0712378	−	0.392897i
$545$			9.96892i			0.427022i
$546$	5.09877	−	2.25447i	0.218207	−	0.0964825i
$547$		−	37.9635i		−	1.62320i	−0.584211	−	0.811602i	$-0.698596\pi$
$547$		−	37.9635i		−	1.62320i	0.584211	−	0.811602i	$-0.301404\pi$
$548$	2.98496	−	41.5329i	0.127511	−	1.77420i
$549$	−6.70616	+	8.52719i	−0.286212	+	0.363932i
$550$	−31.9089	−	1.14517i	−1.36060	−	0.0488301i
$551$	0.844401			0.0359727
$552$	6.83821	+	19.0540i	0.291054	+	0.810994i
$553$	52.0725			2.21435
$554$	−5.67739	−	0.203753i	−0.241209	−	0.00865665i
$555$	−2.17297	+	1.05554i	−0.0922375	+	0.0448050i
$556$	2.39595	−	33.3374i	0.101611	−	1.41382i
$557$		−	3.37117i		−	0.142841i	−0.997446	−	0.0714204i	$-0.977247\pi$
$557$		−	3.37117i		−	0.142841i	0.997446	−	0.0714204i	$-0.0227532\pi$
$558$	28.9966	+	24.5374i	1.22753	+	1.03875i
$559$			5.16398i			0.218413i
$560$	−11.7067	−	1.69145i	−0.494698	−	0.0714769i
$561$	13.1072	−	6.36689i	0.553385	−	0.268810i
$562$	1.09613	−	30.5426i	0.0462375	−	1.28836i
$563$	26.3977			1.11253			0.556265	−	0.831005i	$-0.312234\pi$
$563$	26.3977			1.11253			0.556265	+	0.831005i	$0.312234\pi$
$564$	13.6629	+	34.1637i	0.575312	+	1.43855i
$565$	2.73964			0.115258
$566$	0.892893	−	24.8796i	0.0375311	−	1.04577i
$567$	33.9103	−	8.22497i	1.42410	−	0.345416i
$568$	14.4139	+	1.55723i	0.604794	+	0.0653401i
$569$			27.7716i			1.16425i	0.813101	+	0.582123i	$0.197778\pi$
$569$			27.7716i			1.16425i	−0.813101	+	0.582123i	$0.802222\pi$
$570$	0.755505	+	1.70867i	0.0316446	+	0.0715683i
$571$			0.846452i			0.0354229i	0.999843	+	0.0177115i	$0.00563803\pi$
$571$			0.846452i			0.0354229i	−0.999843	+	0.0177115i	$0.994362\pi$
$572$	−5.98410	−	0.430075i	−0.250208	−	0.0179823i
$573$	−10.6317	−	21.8868i	−0.444144	−	0.914335i
$574$	−27.3608	−	0.981938i	−1.14202	−	0.0409853i
$575$	18.2575			0.761392
$576$	−18.5231	+	15.2609i	−0.771795	+	0.635871i
$577$	18.5211			0.771045			0.385523	−	0.922698i	$-0.374021\pi$
$577$	18.5211			0.771045			0.385523	+	0.922698i	$0.374021\pi$
$578$	−20.1954	−	0.724783i	−0.840017	−	0.0301470i
$579$	−1.86331	−	3.83589i	−0.0774365	−	0.159414i
$580$	−1.28475	−	0.0923346i	−0.0533463	−	0.00383399i
$581$		−	23.5643i		−	0.977613i
$582$	−4.65856	−	10.5359i	−0.193104	−	0.436728i
$583$			52.6376i			2.18003i
$584$	20.7524	+	2.24203i	0.858742	+	0.0927758i
$585$	1.05581	+	0.830339i	0.0436525	+	0.0343303i
$586$	0.590556	−	16.4553i	0.0243956	−	0.679761i
$587$	38.1358			1.57403			0.787017	−	0.616931i	$-0.211624\pi$
$587$	38.1358			1.57403			0.787017	+	0.616931i	$0.211624\pi$
$588$	10.3313	+	25.8330i	0.426054	+	1.06534i
$589$	8.95324			0.368912
$590$	0.305795	−	8.52069i	0.0125894	−	0.350791i
$591$	−32.0925	+	15.5891i	−1.32011	+	0.641252i
$592$	−7.23954	−	1.04601i	−0.297543	−	0.0429907i
$593$			6.09379i			0.250242i	0.992142	+	0.125121i	$0.0399319\pi$
$593$			6.09379i			0.250242i	−0.992142	+	0.125121i	$0.960068\pi$
$594$	−36.3826	−	9.29411i	−1.49280	−	0.381342i
$595$		−	4.86842i		−	0.199586i
$596$	−0.574487	+	7.99346i	−0.0235319	+	0.327425i
$597$	19.9985	−	9.71441i	0.818485	−	0.397584i
$598$	3.42837	+	0.123039i	0.140197	+	0.00503146i
$599$	37.7702			1.54325			0.771625	−	0.636078i	$-0.219444\pi$
$599$	37.7702			1.54325			0.771625	+	0.636078i	$0.219444\pi$
$600$	7.31149	+	20.3728i	0.298490	+	0.831715i
$601$	−21.2157			−0.865405			−0.432702	−	0.901537i	$-0.642440\pi$
$601$	−21.2157			−0.865405			−0.432702	+	0.901537i	$0.642440\pi$
$602$	−48.2014	−	1.72988i	−1.96454	−	0.0705046i
$603$	−19.8829	−	15.6368i	−0.809694	−	0.636780i
$604$	1.72115	−	23.9482i	0.0700326	−	0.974438i
$605$			11.5264i			0.468615i
$606$	18.6662	−	8.25346i	0.758264	−	0.335274i
$607$			17.2749i			0.701168i	0.936531	+	0.350584i	$0.114017\pi$
$607$			17.2749i			0.701168i	−0.936531	+	0.350584i	$0.885983\pi$
$608$	−1.00921	+	5.56610i	−0.0409291	+	0.225735i
$609$	2.47758	+	5.10047i	0.100397	+	0.206681i
$610$	0.139891	−	3.89793i	0.00566403	−	0.157823i
$611$	6.23527			0.252252
$612$	−7.30694	−	6.64737i	−0.295365	−	0.268704i
$613$	−28.0989			−1.13490			−0.567452	−	0.823406i	$-0.692071\pi$
$613$	−28.0989			−1.13490			−0.567452	+	0.823406i	$0.692071\pi$
$614$	−0.258579	+	7.20506i	−0.0104354	+	0.290772i
$615$	−2.88221	−	5.93344i	−0.116222	−	0.239260i
$616$	6.01900	−	55.7124i	0.242512	−	2.24472i
$617$			43.2071i			1.73945i	0.493535	+	0.869726i	$0.335704\pi$
$617$			43.2071i			1.73945i	−0.493535	+	0.869726i	$0.664296\pi$
$618$	−4.82034	+	2.13136i	−0.193902	+	0.0857358i
$619$		−	4.54698i		−	0.182759i	−0.995816	−	0.0913793i	$-0.970872\pi$
$619$		−	4.54698i		−	0.182759i	0.995816	−	0.0913793i	$-0.0291276\pi$
$620$	−13.6223	−	0.979030i	−0.547084	−	0.0393188i
$621$	20.9811	+	4.56489i	0.841942	+	0.183183i
$622$	17.0691	+	0.612585i	0.684408	+	0.0245624i
$623$	−35.1393			−1.40783
$624$	1.23565	+	3.87484i	0.0494654	+	0.155118i
$625$	16.6125			0.664502
$626$	−29.8005	−	1.06950i	−1.19107	−	0.0427458i
$627$	−7.96127	+	3.86724i	−0.317943	+	0.154443i
$628$	8.55095	+	0.614554i	0.341220	+	0.0245234i
$629$		−	3.01067i		−	0.120043i
$630$	−8.10420	+	9.57697i	−0.322879	+	0.381556i
$631$			7.74390i			0.308280i	0.988049	+	0.154140i	$0.0492606\pi$
$631$			7.74390i			0.308280i	−0.988049	+	0.154140i	$0.950739\pi$
$632$	−4.08041	+	37.7686i	−0.162310	+	1.50235i
$633$	1.92869	−	0.936874i	0.0766586	−	0.0372374i
$634$	−0.495766	+	13.8140i	−0.0196894	+	0.548625i
$635$	8.30818			0.329700
$636$	33.1318	−	13.2502i	1.31376	−	0.525405i
$637$	4.71482			0.186808
$638$	0.218859	−	6.09829i	0.00866471	−	0.241434i
$639$	9.50583	−	12.0871i	0.376045	−	0.478158i
$640$	2.14416	−	8.35842i	0.0847554	−	0.330396i
$641$		−	24.6485i		−	0.973558i	−0.873525	−	0.486779i	$-0.838172\pi$
$641$		−	24.6485i		−	0.973558i	0.873525	−	0.486779i	$-0.161828\pi$
$642$	10.4725	+	23.6849i	0.413316	+	0.934767i
$643$		−	20.1704i		−	0.795441i	−0.917507	−	0.397721i	$-0.869801\pi$
$643$		−	20.1704i		−	0.795441i	0.917507	−	0.397721i	$-0.130199\pi$
$644$	−2.29694	+	31.9598i	−0.0905121	+	1.25939i
$645$	−5.07758	−	10.4529i	−0.199930	−	0.411584i
$646$	−2.32682	−	0.0835061i	−0.0915474	−	0.00328550i
$647$	0.822458			0.0323342			0.0161671	−	0.999869i	$-0.494854\pi$
$647$	0.822458			0.0323342			0.0161671	+	0.999869i	$0.494854\pi$
$648$	3.30842	+	25.2399i	0.129967	+	0.991518i
$649$	40.3929			1.58556
$650$	3.66565	+	0.131555i	0.143779	+	0.00516002i
$651$	26.2700	+	54.0806i	1.02960	+	2.11959i
$652$	1.95820	−	27.2465i	0.0766890	−	1.06706i
$653$			28.7332i			1.12442i	0.826995	+	0.562209i	$0.190048\pi$
$653$			28.7332i			1.12442i	−0.826995	+	0.562209i	$0.809952\pi$
$654$	12.9470	+	29.2812i	0.506267	+	1.14499i
$655$		−	6.10582i		−	0.238574i
$656$	2.85620	−	19.7680i	0.111516	−	0.771812i
$657$	13.6860	−	17.4024i	0.533943	−	0.678933i
$658$	−2.08875	+	58.2009i	−0.0814279	+	2.26891i
$659$	28.7797			1.12110			0.560549	−	0.828121i	$-0.310590\pi$
$659$	28.7797			1.12110			0.560549	+	0.828121i	$0.310590\pi$
$660$	12.5359	−	5.01342i	0.487959	−	0.195147i
$661$	−3.76984			−0.146630			−0.0733149	−	0.997309i	$-0.523358\pi$
$661$	−3.76984			−0.146630			−0.0733149	+	0.997309i	$0.523358\pi$
$662$	0.0724583	−	2.01898i	0.00281617	−	0.0784699i
$663$	−1.50573	+	0.731420i	−0.0584779	+	0.0284060i
$664$	17.0914	+	1.84650i	0.663275	+	0.0716582i
$665$			2.95707i			0.114670i
$666$	−5.01171	+	5.92249i	−0.194200	+	0.229492i
$667$			3.48930i			0.135106i
$668$	26.3380	+	1.89290i	1.01905	+	0.0732387i
$669$	32.0081	−	15.5481i	1.23750	−	0.601125i
$670$	9.08883	+	0.326185i	0.351132	+	0.0126016i
$671$	18.4784			0.713351
$672$	−36.5823	+	10.2357i	−1.41119	+	0.394850i
$673$	−18.6014			−0.717033			−0.358516	−	0.933523i	$-0.616717\pi$
$673$	−18.6014			−0.717033			−0.358516	+	0.933523i	$0.616717\pi$
$674$	−0.0704838	−	0.00252956i	−0.00271493	−	9.74351e-5i
$675$	22.4332	+	4.88083i	0.863455	+	0.187863i
$676$	−25.2457	−	1.81440i	−0.970987	−	0.0697846i
$677$		−	30.9430i		−	1.18923i	−0.804009	−	0.594617i	$-0.797304\pi$
$677$		−	30.9430i		−	1.18923i	0.804009	−	0.594617i	$-0.202696\pi$
$678$	8.04702	−	3.55807i	0.309044	−	0.136647i
$679$		−	18.2337i		−	0.699746i
$680$	3.53110	+	0.381489i	0.135412	+	0.0146294i
$681$	−19.3869	−	39.9108i	−0.742908	−	1.52938i
$682$	2.32058	−	64.6606i	0.0888595	−	2.47598i
$683$	31.2070			1.19410			0.597052	−	0.802203i	$-0.296339\pi$
$683$	31.2070			1.19410			0.597052	+	0.802203i	$0.296339\pi$
$684$	4.43822	+	4.03760i	0.169700	+	0.154381i
$685$	15.8796			0.606729
$686$	−0.202865	+	5.65265i	−0.00774544	+	0.215819i
$687$	14.2241	+	29.2824i	0.542683	+	1.11719i
$688$	5.03176	−	34.8253i	0.191834	−	1.32770i
$689$		−	6.04693i		−	0.230370i
$690$	−7.06070	+	3.12196i	−0.268796	+	0.118851i
$691$		−	49.2668i		−	1.87420i	−0.349065	−	0.937099i	$-0.613501\pi$
$691$		−	49.2668i		−	1.87420i	0.349065	−	0.937099i	$-0.386499\pi$
$692$	3.08872	−	42.9766i	0.117415	−	1.63373i
$693$	−46.7189	−	36.7418i	−1.77470	−	1.39571i
$694$	15.8579	+	0.569118i	0.601959	+	0.0216034i
$695$	12.7461			0.483488
$696$	−3.89355	+	1.39734i	−0.147585	+	0.0529660i
$697$	8.22084			0.311387
$698$	18.4345	+	0.661590i	0.697758	+	0.0250415i
$699$	21.1215	−	10.2599i	0.798888	−	0.388065i
$700$	−2.45591	+	34.1717i	−0.0928247	+	1.29157i
$701$			21.9424i			0.828753i	0.910105	+	0.414377i	$0.136000\pi$
$701$			21.9424i			0.828753i	−0.910105	+	0.414377i	$0.864000\pi$
$702$	4.17958	+	1.06769i	0.157748	+	0.0402975i
$703$			1.82868i			0.0689699i
$704$	39.9370	+	8.73125i	1.50518	+	0.329072i
$705$	−12.6214	+	6.13094i	−0.475351	+	0.230905i
$706$	−1.02837	+	28.6545i	−0.0387032	+	1.07843i
$707$	32.3043			1.21493
$708$	−10.1679	−	25.4246i	−0.382134	−	0.955514i
$709$	16.0534			0.602898			0.301449	−	0.953482i	$-0.402530\pi$
$709$	16.0534			0.602898			0.301449	+	0.953482i	$0.402530\pi$
$710$	−0.198293	+	5.52523i	−0.00744179	+	0.207358i
$711$	31.6717	+	24.9080i	1.18778	+	0.934125i
$712$	2.75352	−	25.4868i	0.103192	−	0.955158i
$713$			36.9973i			1.38556i
$714$	−6.32278	−	14.2998i	−0.236624	−	0.535156i
$715$		−	2.28795i		−	0.0855643i
$716$	−36.6623	−	2.63491i	−1.37013	−	0.0984711i
$717$	8.60596	+	17.7166i	0.321396	+	0.661640i
$718$	7.54067	+	0.270624i	0.281415	+	0.0100996i
$719$	−51.9817			−1.93859			−0.969294	−	0.245904i	$-0.920915\pi$
$719$	−51.9817			−1.93859			−0.969294	+	0.245904i	$0.920915\pi$
$720$	−6.31121	−	6.62849i	−0.235205	−	0.247029i
$721$	−8.34219			−0.310679
$722$	1.41330	+	0.0507215i	0.0525977	+	0.00188766i
$723$	9.12855	+	18.7925i	0.339495	+	0.698899i
$724$	1.32075	+	0.0949218i	0.0490852	+	0.00352774i
$725$			3.73080i			0.138558i
$726$	14.9698	+	33.8560i	0.555580	+	1.25651i
$727$			11.3387i			0.420528i	0.977645	+	0.210264i	$0.0674324\pi$
$727$			11.3387i			0.420528i	−0.977645	+	0.210264i	$0.932568\pi$
$728$	−0.691454	+	6.40016i	−0.0256270	+	0.237206i
$729$	24.5593	+	11.2178i	0.909604	+	0.415475i
$730$	−0.285492	+	7.95496i	−0.0105665	+	0.294426i
$731$	14.4827			0.535660
$732$	−4.65148	−	11.6309i	−0.171924	−	0.429890i
$733$	−19.3407			−0.714364			−0.357182	−	0.934035i	$-0.616262\pi$
$733$	−19.3407			−0.714364			−0.357182	+	0.934035i	$0.616262\pi$
$734$	0.756505	−	21.0793i	0.0279231	−	0.778050i
$735$	−9.54376	+	4.63594i	−0.352027	+	0.170999i
$736$	−23.0007	−	4.17036i	−0.847816	−	0.153721i
$737$			43.0862i			1.58710i
$738$	−16.1717	−	13.6848i	−0.595290	−	0.503745i
$739$		−	3.81202i		−	0.140227i	−0.997539	−	0.0701136i	$-0.977664\pi$
$739$		−	3.81202i		−	0.140227i	0.997539	−	0.0701136i	$-0.0223362\pi$
$740$	0.199964	−	2.78232i	0.00735084	−	0.102280i
$741$	0.914580	−	0.444263i	0.0335979	−	0.0163204i
$742$	56.4430	+	2.02566i	2.07209	+	0.0743643i
$743$	−21.1840			−0.777167			−0.388583	−	0.921414i	$-0.627035\pi$
$743$	−21.1840			−0.777167			−0.388583	+	0.921414i	$0.627035\pi$
$744$	−41.2836	+	14.8161i	−1.51353	+	0.543184i
$745$	−3.05620			−0.111971
$746$	13.3959	+	0.480759i	0.490458	+	0.0176018i
$747$	11.2716	−	14.3324i	0.412407	−	0.524394i
$748$	−1.20617	+	16.7827i	−0.0441019	+	0.613636i
$749$			40.9896i			1.49773i
$750$	−16.0927	+	7.11555i	−0.587623	+	0.259823i
$751$		−	40.7496i		−	1.48697i	−0.668750	−	0.743487i	$-0.733170\pi$
$751$		−	40.7496i		−	1.48697i	0.668750	−	0.743487i	$-0.266830\pi$
$752$	−42.0499	−	6.07562i	−1.53340	−	0.221555i
$753$	0.406373	+	0.836578i	0.0148091	+	0.0304866i
$754$	−0.0251422	+	0.700563i	−0.000915626	+	0.0255130i
$755$	9.15629			0.333232
$756$	−11.3661	+	38.6552i	−0.413382	+	1.40588i
$757$	−6.39533			−0.232442			−0.116221	−	0.993223i	$-0.537078\pi$
$757$	−6.39533			−0.232442			−0.116221	+	0.993223i	$0.537078\pi$
$758$	−0.254479	+	7.09082i	−0.00924311	+	0.257550i
$759$	−15.9805	−	32.8982i	−0.580056	−	1.19413i
$760$	−2.14478	−	0.231716i	−0.0777995	−	0.00840522i
$761$			18.6783i			0.677087i	0.940951	+	0.338543i	$0.109934\pi$
$761$			18.6783i			0.677087i	−0.940951	+	0.338543i	$0.890066\pi$
$762$	24.4032	−	10.7901i	0.884036	−	0.390885i
$763$			50.6748i			1.83455i
$764$	28.0243	+	2.01410i	1.01389	+	0.0728676i
$765$	2.32873	−	2.96108i	0.0841953	−	0.107058i
$766$	29.0537	+	1.04270i	1.04975	+	0.0376742i
$767$	−4.64028			−0.167551
$768$	−4.55743	−	27.3355i	−0.164452	−	0.986385i
$769$	41.4802			1.49582			0.747908	−	0.663803i	$-0.231059\pi$
$769$	41.4802			1.49582			0.747908	+	0.663803i	$0.231059\pi$
$770$	21.3560	+	0.766438i	0.769618	+	0.0276205i
$771$	−30.9814	+	15.0494i	−1.11577	+	0.541992i
$772$	4.91156	+	0.352992i	0.176771	+	0.0127045i
$773$			4.79619i			0.172507i	0.996273	+	0.0862536i	$0.0274895\pi$
$773$			4.79619i			0.172507i	−0.996273	+	0.0862536i	$0.972510\pi$
$774$	−28.4898	−	24.1085i	−1.02404	−	0.866563i
$775$			39.5579i			1.42096i
$776$	13.2251	+	1.42880i	0.474752	+	0.0512908i
$777$	−11.0458	+	5.36558i	−0.396267	+	0.192489i
$778$	−0.966549	+	26.9320i	−0.0346525	+	0.965557i
$779$	−4.99332			−0.178904
$780$	−1.44011	+	0.575934i	−0.0515641	+	0.0206217i
$781$	−26.1927			−0.937248
$782$	0.345071	−	9.61505i	0.0123397	−	0.343834i
$783$	−0.932802	+	4.28733i	−0.0333356	+	0.153217i
$784$	−31.7962	−	4.59410i	−1.13558	−	0.164075i
$785$			3.26935i			0.116688i
$786$	−7.92984	−	17.9343i	−0.282848	−	0.639697i
$787$		−	4.94761i		−	0.176363i	−0.996104	−	0.0881816i	$-0.971894\pi$
$787$		−	4.94761i		−	0.176363i	0.996104	−	0.0881816i	$-0.0281056\pi$
$788$	2.95327	−	41.0919i	0.105206	−	1.46384i
$789$	−10.1980	−	20.9940i	−0.363057	−	0.747406i
$790$	−14.4777	−	0.519584i	−0.515094	−	0.0184860i
$791$	13.9264			0.495165
$792$	30.3100	−	31.0065i	1.07702	−	1.10177i
$793$	−2.12277			−0.0753819
$794$	−49.8601	−	1.78941i	−1.76947	−	0.0635037i
$795$	5.94576	+	12.2402i	0.210874	+	0.434115i
$796$	−1.84033	+	25.6065i	−0.0652289	+	0.907599i
$797$			0.611017i			0.0216433i	0.999941	+	0.0108217i	$0.00344471\pi$
$797$			0.611017i			0.0216433i	−0.999941	+	0.0108217i	$0.996555\pi$
$798$	3.84045	+	8.68566i	0.135950	+	0.307469i
$799$		−	17.4871i		−	0.618650i
$800$	−24.5926	−	4.45899i	−0.869479	−	0.157649i
$801$	−21.3725	−	16.8083i	−0.755161	−	0.593892i
$802$	0.934368	−	26.0352i	0.0329937	−	0.919336i
$803$	−37.7110			−1.33079
$804$	27.1198	−	10.8459i	0.956443	−	0.382505i
$805$	−12.2194			−0.430678
$806$	−0.266585	+	7.42812i	−0.00939005	+	0.261644i
$807$	−22.6071	+	10.9815i	−0.795807	+	0.386568i
$808$	−2.53136	+	23.4305i	−0.0890531	+	0.824283i
$809$			22.0883i			0.776584i	0.921536	+	0.388292i	$0.126935\pi$
$809$			22.0883i			0.776584i	−0.921536	+	0.388292i	$0.873065\pi$
$810$	−9.51015	+	1.94842i	−0.334153	+	0.0684607i
$811$			3.55462i			0.124819i	0.998051	+	0.0624097i	$0.0198786\pi$
$811$			3.55462i			0.124819i	−0.998051	+	0.0624097i	$0.980121\pi$
$812$	−6.53075	−	0.469363i	−0.229184	−	0.0164714i
$813$	−2.75218	+	1.33689i	−0.0965231	+	0.0468867i
$814$	13.2068	+	0.473972i	0.462897	+	0.0166127i
$815$	10.4174			0.364905
$816$	10.8672	−	3.46543i	0.380428	−	0.121314i
$817$	−8.79674			−0.307759
$818$	8.35498	+	0.299848i	0.292125	+	0.0104839i
$819$	5.36700	+	4.22085i	0.187538	+	0.147488i
$820$	7.59730	+	0.546016i	0.265309	+	0.0190677i
$821$			3.66352i			0.127858i	0.997954	+	0.0639289i	$0.0203631\pi$
$821$			3.66352i			0.127858i	−0.997954	+	0.0639289i	$0.979637\pi$
$822$	46.6424	−	20.6234i	1.62684	−	0.719324i
$823$			23.5512i			0.820942i	0.911874	+	0.410471i	$0.134636\pi$
$823$			23.5512i			0.820942i	−0.911874	+	0.410471i	$0.865364\pi$
$824$	0.653695	−	6.05066i	0.0227725	−	0.210785i
$825$	−17.0865	−	35.1751i	−0.594877	−	1.22464i
$826$	1.55444	−	43.3131i	0.0540860	−	1.50705i
$827$	0.973110			0.0338384			0.0169192	−	0.999857i	$-0.494614\pi$
$827$	0.973110			0.0338384			0.0169192	+	0.999857i	$0.494614\pi$
$828$	−16.6845	+	18.3400i	−0.579826	+	0.637358i
$829$	−36.6213			−1.27191			−0.635955	−	0.771727i	$-0.719393\pi$
$829$	−36.6213			−1.27191			−0.635955	+	0.771727i	$0.719393\pi$
$830$	−0.235127	+	6.55158i	−0.00816138	+	0.227409i
$831$	−3.04011	−	6.25852i	−0.105460	−	0.217106i
$832$	−4.58791	−	1.00303i	−0.159057	−	0.0347740i
$833$		−	13.2230i		−	0.458149i
$834$	37.4386	−	16.5538i	1.29639	−	0.573213i
$835$			10.0700i			0.348487i
$836$	0.732624	−	10.1938i	0.0253383	−	0.352559i
$837$	−9.89056	+	45.4589i	−0.341868	+	1.57129i
$838$	49.1285	+	1.76315i	1.69711	+	0.0609070i
$839$	−43.8957			−1.51545			−0.757723	−	0.652576i	$-0.773688\pi$
$839$	−43.8957			−1.51545			−0.757723	+	0.652576i	$0.773688\pi$
$840$	−4.89344	−	13.6351i	−0.168840	−	0.470456i
$841$	28.2870			0.975413
$842$	−24.6255	−	0.883775i	−0.848652	−	0.0304569i
$843$	33.6689	−	16.3549i	1.15962	−	0.563292i
$844$	−0.177485	+	2.46954i	−0.00610928	+	0.0850049i
$845$		−	9.65237i		−	0.332052i
$846$	−29.1099	+	34.4000i	−1.00082	+	1.18270i
$847$			58.5920i			2.01325i
$848$	−5.89210	+	40.7798i	−0.202336	+	1.40038i
$849$	27.4262	−	13.3225i	0.941266	−	0.457226i
$850$	0.368953	−	10.2805i	0.0126550	−	0.352619i
$851$	−7.55661			−0.259037
$852$	6.59337	+	16.4865i	0.225885	+	0.564819i
$853$	−4.11172			−0.140783			−0.0703913	−	0.997519i	$-0.522425\pi$
$853$	−4.11172			−0.140783			−0.0703913	+	0.997519i	$0.522425\pi$
$854$	0.711106	−	19.8143i	0.0243336	−	0.678031i
$855$	−1.41446	+	1.79856i	−0.0483737	+	0.0615093i
$856$	−29.7301	−	3.21195i	−1.01615	−	0.109782i
$857$			4.47889i			0.152996i	0.997070	+	0.0764979i	$0.0243739\pi$
$857$			4.47889i			0.152996i	−0.997070	+	0.0764979i	$0.975626\pi$
$858$	−2.97143	−	6.72028i	−0.101443	−	0.229426i
$859$		−	40.8441i		−	1.39358i	−0.717273	−	0.696792i	$-0.754610\pi$
$859$		−	40.8441i		−	1.39358i	0.717273	−	0.696792i	$-0.245390\pi$
$860$	13.3842	+	0.961916i	0.456396	+	0.0328011i
$861$	−14.6511	−	30.1614i	−0.499307	−	1.02790i
$862$	−37.0074	−	1.32814i	−1.26048	−	0.0452367i
$863$	−15.5380			−0.528920			−0.264460	−	0.964397i	$-0.585194\pi$
$863$	−15.5380			−0.528920			−0.264460	+	0.964397i	$0.585194\pi$
$864$	−27.1463	−	11.2730i	−0.923535	−	0.383514i
$865$	16.4316			0.558691
$866$	47.1965	+	1.69381i	1.60380	+	0.0575581i
$867$	−10.8142	−	22.2625i	−0.367269	−	0.756076i
$868$	−69.2459	−	4.97669i	−2.35036	−	0.168920i
$869$		−	68.6325i		−	2.32820i
$870$	−0.637949	−	1.44280i	−0.0216285	−	0.0489156i
$871$		−	4.94968i		−	0.167714i
$872$	−36.7549	−	3.97088i	−1.24468	−	0.134471i
$873$	8.72181	−	11.0902i	0.295189	−	0.375346i
$874$	−0.209595	+	5.84017i	−0.00708966	+	0.197547i
$875$	−27.8505			−0.941518
$876$	9.49282	+	23.7365i	0.320733	+	0.801982i
$877$	−47.0782			−1.58972			−0.794859	−	0.606794i	$-0.792455\pi$
$877$	−47.0782			−1.58972			−0.794859	+	0.606794i	$0.792455\pi$
$878$	−0.591556	+	16.4831i	−0.0199640	+	0.556278i
$879$	18.1396	−	8.81143i	0.611834	−	0.297202i
$880$	−2.22936	+	15.4296i	−0.0751518	+	0.520133i
$881$		−	21.9573i		−	0.739760i	−0.929080	−	0.369880i	$-0.879399\pi$
$881$		−	21.9573i		−	0.739760i	0.929080	−	0.369880i	$-0.120601\pi$
$882$	−22.0116	+	26.0117i	−0.741168	+	0.875861i
$883$		−	52.0256i		−	1.75080i	−0.483399	−	0.875400i	$-0.660598\pi$
$883$		−	52.0256i		−	1.75080i	0.483399	−	0.875400i	$-0.339402\pi$
$884$	0.138563	−	1.92797i	0.00466037	−	0.0648448i
$885$	9.39286	−	4.56264i	0.315737	−	0.153371i
$886$	−31.8838	−	1.14427i	−1.07116	−	0.0384424i
$887$	−4.23989			−0.142362			−0.0711808	−	0.997463i	$-0.522677\pi$
$887$	−4.23989			−0.142362			−0.0711808	+	0.997463i	$0.522677\pi$
$888$	−3.02615	−	8.43208i	−0.101551	−	0.282962i
$889$	42.2329			1.41644
$890$	9.76976	+	0.350623i	0.327483	+	0.0117529i
$891$	−10.8407	−	44.6944i	−0.363176	−	1.49732i
$892$	−2.94549	+	40.9838i	−0.0986224	+	1.37224i
$893$			10.6216i			0.355440i
$894$	−8.97684	+	3.96919i	−0.300230	+	0.132750i
$895$		−	14.0174i		−	0.468549i
$896$	10.8994	−	42.4882i	0.364123	−	1.41943i
$897$	1.83582	+	3.77930i	0.0612962	+	0.126187i
$898$	−0.259331	+	7.22601i	−0.00865399	+	0.241135i
$899$	−7.56013			−0.252144
$900$	−17.8392	+	19.6093i	−0.594641	+	0.653643i
$901$	−16.9589			−0.564984
$902$	−1.29421	+	36.0620i	−0.0430926	+	1.20073i
$903$	−25.8108	−	53.1353i	−0.858929	−	1.76823i
$904$	−1.09127	+	10.1009i	−0.0362951	+	0.335951i
$905$			0.504972i			0.0167858i
$906$	26.8944	−	11.8916i	0.893505	−	0.395072i
$907$		−	5.68483i		−	0.188762i	−0.995536	−	0.0943808i	$-0.969913\pi$
$907$		−	5.68483i		−	0.188762i	0.995536	−	0.0943808i	$-0.0300871\pi$
$908$	51.1026	+	3.67273i	1.69590	+	0.121884i
$909$	19.6482	+	15.4522i	0.651689	+	0.512518i
$910$	−2.45335	−	0.0880473i	−0.0813278	−	0.00291874i
$911$	23.2965			0.771846			0.385923	−	0.922531i	$-0.373883\pi$
$911$	23.2965			0.771846			0.385923	+	0.922531i	$0.373883\pi$
$912$	−6.60071	+	2.10490i	−0.218571	+	0.0697001i
$913$	−31.0582			−1.02788
$914$	−29.2280	−	1.04895i	−0.966775	−	0.0346962i
$915$	4.29692	−	2.08726i	0.142052	−	0.0690026i
$916$	−37.4938	−	2.69467i	−1.23883	−	0.0890343i
$917$		−	31.0376i		−	1.02495i
$918$	2.99440	−	11.7219i	0.0988300	−	0.386879i
$919$			50.5761i			1.66835i	0.551497	+	0.834177i	$0.314057\pi$
$919$			50.5761i			1.66835i	−0.551497	+	0.834177i	$0.685943\pi$
$920$	0.957515	−	8.86285i	0.0315683	−	0.292199i
$921$	−7.94256	+	3.85815i	−0.261716	+	0.127130i
$922$	0.150662	−	4.19804i	0.00496177	−	0.138255i
$923$	3.00898			0.0990418
$924$	63.7235	−	25.4846i	2.09635	−	0.838382i
$925$	−8.07960			−0.265656
$926$	0.964777	−	26.8826i	0.0317045	−	0.883416i
$927$	−5.07391	−	3.99035i	−0.166649	−	0.131060i
$928$	0.852182	−	4.70002i	0.0279743	−	0.154286i
$929$		−	7.75818i		−	0.254538i	−0.991868	−	0.127269i	$-0.959379\pi$
$929$		−	7.75818i		−	0.254538i	0.991868	−	0.127269i	$-0.0406211\pi$
$930$	−6.76422	−	15.2981i	−0.221808	−	0.501646i
$931$			8.03161i			0.263225i
$932$	−1.94367	+	27.0444i	−0.0636671	+	0.885868i
$933$	9.14012	+	18.8163i	0.299234	+	0.616017i
$934$	−14.0030	−	0.502547i	−0.458192	−	0.0164439i
$935$	−6.41666			−0.209847
$936$	−3.48197	+	3.56198i	−0.113812	+	0.116427i
$937$	33.6892			1.10058			0.550289	−	0.834974i	$-0.314518\pi$
$937$	33.6892			1.10058			0.550289	+	0.834974i	$0.314518\pi$
$938$	46.2011	+	1.65809i	1.50852	+	0.0541386i
$939$	−15.9575	−	32.8509i	−0.520754	−	1.07205i
$940$	1.16147	−	16.1608i	0.0378829	−	0.527106i
$941$		−	18.8448i		−	0.614322i	−0.951657	−	0.307161i	$-0.900621\pi$
$941$		−	18.8448i		−	0.614322i	0.951657	−	0.307161i	$-0.0993791\pi$
$942$	4.24602	+	9.60292i	0.138343	+	0.312880i
$943$		−	20.6338i		−	0.671929i
$944$	31.2935	+	4.52147i	1.01852	+	0.147161i
$945$	−15.0141	−	3.26664i	−0.488409	−	0.106264i
$946$	−2.28001	+	63.5303i	−0.0741296	+	2.06555i
$947$	0.755202			0.0245408			0.0122704	−	0.999925i	$-0.496094\pi$
$947$	0.755202			0.0245408			0.0122704	+	0.999925i	$0.496094\pi$
$948$	−43.1995	+	17.2766i	−1.40305	+	0.561116i
$949$	4.33219			0.140629
$950$	−0.224101	+	6.24437i	−0.00727081	+	0.202594i
$951$	−15.2280	+	7.39711i	−0.493802	+	0.239868i
$952$	17.9496	+	1.93922i	0.581749	+	0.0628504i
$953$			33.2815i			1.07809i	0.842275	+	0.539047i	$0.181216\pi$
$953$			33.2815i			1.07809i	−0.842275	+	0.539047i	$0.818784\pi$
$954$	33.3610	+	28.2306i	1.08010	+	0.914001i
$955$			10.7148i			0.346722i
$956$	−22.6847	−	1.63035i	−0.733677	−	0.0527292i
$957$	6.72251	−	3.26550i	0.217308	−	0.105559i
$958$	−4.65445	−	0.167041i	−0.150378	−	0.00539686i
$959$	80.7205			2.60660
$960$	10.2731	−	2.48080i	0.331563	−	0.0800675i
$961$	−49.1606			−1.58582
$962$	−1.51718	−	0.0544493i	−0.0489157	−	0.00175552i
$963$	−19.6067	+	24.9308i	−0.631817	+	0.803384i
$964$	−24.0622	−	1.72935i	−0.774993	−	0.0556985i
$965$			1.87787i			0.0604509i
$966$	−35.8916	+	15.8698i	−1.15479	+	0.510602i
$967$		−	2.72533i		−	0.0876407i	−0.999039	−	0.0438203i	$-0.986047\pi$
$967$		−	2.72533i		−	0.0876407i	0.999039	−	0.0438203i	$-0.0139529\pi$
$968$	−42.4973	−	4.59127i	−1.36591	−	0.147569i
$969$	−1.24596	−	2.56499i	−0.0400260	−	0.0823992i
$970$	−0.181938	+	5.06952i	−0.00584167	+	0.162772i
$971$	−28.9519			−0.929110			−0.464555	−	0.885544i	$-0.653786\pi$
$971$	−28.9519			−0.929110			−0.464555	+	0.885544i	$0.653786\pi$
$972$	−25.4032	+	18.0742i	−0.814809	+	0.579730i
$973$	64.7922			2.07714
$974$	−0.178252	+	4.96681i	−0.00571155	+	0.159147i
$975$	1.96288	+	4.04087i	0.0628624	+	0.129411i
$976$	14.3157	+	2.06842i	0.458236	+	0.0662085i
$977$		−	31.1279i		−	0.995869i	−0.867215	−	0.497934i	$-0.834092\pi$
$977$		−	31.1279i		−	0.995869i	0.867215	−	0.497934i	$-0.165908\pi$
$978$	30.5985	−	13.5294i	0.978431	−	0.432623i
$979$			46.3142i			1.48021i
$980$	0.878250	−	12.2200i	0.0280547	−	0.390354i
$981$	−24.2395	+	30.8216i	−0.773907	+	0.984058i
$982$	38.7168	+	1.38949i	1.23550	+	0.0443404i
$983$	20.2857			0.647014			0.323507	−	0.946226i	$-0.395138\pi$
$983$	20.2857			0.647014			0.323507	+	0.946226i	$0.395138\pi$
$984$	23.0243	−	8.26310i	0.733989	−	0.263418i
$985$	15.7110			0.500594
$986$	1.96477	+	0.0705127i	0.0625709	+	0.00224558i
$987$	−64.1583	+	31.1653i	−2.04218	+	0.992003i
$988$	−0.0841628	+	1.17105i	−0.00267758	+	0.0372560i
$989$		−	36.3506i		−	1.15588i
$990$	12.6226	+	10.6815i	0.401173	+	0.339480i
$991$		−	22.3311i		−	0.709371i	−0.934986	−	0.354686i	$-0.884588\pi$
$991$		−	22.3311i		−	0.709371i	0.934986	−	0.354686i	$-0.115412\pi$
$992$	9.03575	−	49.8347i	0.286885	−	1.58225i
$993$	2.22564	−	1.08112i	0.0706286	−	0.0343083i
$994$	−1.00798	+	28.0863i	−0.0319711	+	0.890843i
$995$	−9.79034			−0.310375
$996$	7.81814	+	19.5490i	0.247727	+	0.619435i
$997$	−26.5250			−0.840055			−0.420027	−	0.907511i	$-0.637980\pi$
$997$	−26.5250			−0.840055			−0.420027	+	0.907511i	$0.637980\pi$
$998$	1.15610	−	32.2135i	0.0365956	−	1.01970i
$999$	−9.28487	−	2.02012i	−0.293760	−	0.0639138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.1	✓	36
3.2	odd	2	inner	228.2.c.a.191.36	yes	36
4.3	odd	2	inner	228.2.c.a.191.35	yes	36
12.11	even	2	inner	228.2.c.a.191.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.1	✓	36	1.1	even	1	trivial
228.2.c.a.191.2	yes	36	12.11	even	2	inner
228.2.c.a.191.35	yes	36	4.3	odd	2	inner
228.2.c.a.191.36	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41330 - 0.0507215i) q^{2} +(-0.756793 - 1.55797i) q^{3} +(1.99485 + 0.143370i) q^{4} +0.762708i q^{5} +(0.990556 + 2.24027i) q^{6} +3.87706i q^{7} +(-2.81206 - 0.303807i) q^{8} +(-1.85453 + 2.35812i) q^{9} +O(q^{10})\)	\(q+(-1.41330 - 0.0507215i) q^{2} +(-0.756793 - 1.55797i) q^{3} +(1.99485 + 0.143370i) q^{4} +0.762708i q^{5} +(0.990556 + 2.24027i) q^{6} +3.87706i q^{7} +(-2.81206 - 0.303807i) q^{8} +(-1.85453 + 2.35812i) q^{9} +(0.0386857 - 1.07794i) q^{10} +5.11004 q^{11} +(-1.28633 - 3.21642i) q^{12} -0.587034 q^{13} +(0.196650 - 5.47947i) q^{14} +(1.18828 - 0.577212i) q^{15} +(3.95889 + 0.572003i) q^{16} +1.64637i q^{17} +(2.74062 - 3.23867i) q^{18} -1.00000i q^{19} +(-0.109349 + 1.52149i) q^{20} +(6.04034 - 2.93413i) q^{21} +(-7.22203 - 0.259189i) q^{22} +4.13228 q^{23} +(1.65483 + 4.61102i) q^{24} +4.41828 q^{25} +(0.829657 + 0.0297752i) q^{26} +(5.07737 + 1.10469i) q^{27} +(-0.555853 + 7.73417i) q^{28} +0.844401i q^{29} +(-1.70867 + 0.755505i) q^{30} +8.95324i q^{31} +(-5.56610 - 1.00921i) q^{32} +(-3.86724 - 7.96127i) q^{33} +(0.0835061 - 2.32682i) q^{34} -2.95707 q^{35} +(-4.03760 + 4.43822i) q^{36} -1.82868 q^{37} +(-0.0507215 + 1.41330i) q^{38} +(0.444263 + 0.914580i) q^{39} +(0.231716 - 2.14478i) q^{40} -4.99332i q^{41} +(-8.68566 + 3.84045i) q^{42} -8.79674i q^{43} +(10.1938 + 0.732624i) q^{44} +(-1.79856 - 1.41446i) q^{45} +(-5.84017 - 0.209595i) q^{46} -10.6216 q^{47} +(-2.10490 - 6.60071i) q^{48} -8.03161 q^{49} +(-6.24437 - 0.224101i) q^{50} +(2.56499 - 1.24596i) q^{51} +(-1.17105 - 0.0841628i) q^{52} +10.3008i q^{53} +(-7.11983 - 1.81879i) q^{54} +3.89747i q^{55} +(1.17788 - 10.9025i) q^{56} +(-1.55797 + 0.756793i) q^{57} +(0.0428293 - 1.19340i) q^{58} +7.90462 q^{59} +(2.45319 - 0.981092i) q^{60} +3.61610 q^{61} +(0.454122 - 12.6537i) q^{62} +(-9.14257 - 7.19012i) q^{63} +(7.81540 + 1.70865i) q^{64} -0.447736i q^{65} +(5.06178 + 11.4479i) q^{66} +8.43168i q^{67} +(-0.236039 + 3.28426i) q^{68} +(-3.12728 - 6.43796i) q^{69} +(4.17923 + 0.149987i) q^{70} -5.12574 q^{71} +(5.93147 - 6.06776i) q^{72} -7.37979 q^{73} +(2.58448 + 0.0927532i) q^{74} +(-3.34372 - 6.88353i) q^{75} +(0.143370 - 1.99485i) q^{76} +19.8119i q^{77} +(-0.581490 - 1.31511i) q^{78} -13.4309i q^{79} +(-0.436272 + 3.01948i) q^{80} +(-2.12144 - 8.74640i) q^{81} +(-0.253269 + 7.05708i) q^{82} -6.07788 q^{83} +(12.4703 - 4.98717i) q^{84} -1.25570 q^{85} +(-0.446183 + 12.4325i) q^{86} +(1.31555 - 0.639037i) q^{87} +(-14.3697 - 1.55246i) q^{88} +9.06338i q^{89} +(2.47016 + 2.09029i) q^{90} -2.27597i q^{91} +(8.24330 + 0.592443i) q^{92} +(13.9489 - 6.77575i) q^{93} +(15.0116 + 0.538745i) q^{94} +0.762708 q^{95} +(2.64006 + 9.43558i) q^{96} -4.70298 q^{97} +(11.3511 + 0.407375i) q^{98} +(-9.47671 + 12.0501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6}+O(q^{10}) \) 36 * q - 6 * q^6	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more