LMFDB - Embedded newform 27.2.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,2,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$0.215596085457$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 + 0.258654i$ of defining polynomial
Character	$\chi$	$=$	27.16
Dual form			27.2.e.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62143 - 1.36054i) q^{2} +(-0.986166 - 1.42389i) q^{3} +(0.430663 + 2.44241i) q^{4} +(2.52129 + 0.917674i) q^{5} +(-0.338267 + 3.65046i) q^{6} +(0.168844 - 0.957561i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-1.05495 + 2.80839i) q^{9} +O(q^{10})$	\(q+(-1.62143 - 1.36054i) q^{2} +(-0.986166 - 1.42389i) q^{3} +(0.430663 + 2.44241i) q^{4} +(2.52129 + 0.917674i) q^{5} +(-0.338267 + 3.65046i) q^{6} +(0.168844 - 0.957561i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-1.05495 + 2.80839i) q^{9} +(-2.83955 - 4.91825i) q^{10} +(0.297791 - 0.108387i) q^{11} +(3.05303 - 3.02185i) q^{12} +(-1.15981 + 0.973200i) q^{13} +(-1.57657 + 1.32290i) q^{14} +(-1.17974 - 4.49503i) q^{15} +(2.63991 - 0.960847i) q^{16} +(-0.587342 - 1.01731i) q^{17} +(5.53146 - 3.11830i) q^{18} +(-3.11040 + 5.38737i) q^{19} +(-1.15551 + 6.55323i) q^{20} +(-1.52997 + 0.703898i) q^{21} +(-0.630310 - 0.229414i) q^{22} +(0.375556 + 2.12988i) q^{23} +(-1.75413 + 0.144396i) q^{24} +(1.68454 + 1.41350i) q^{25} +3.20463 q^{26} +(5.03922 - 1.26740i) q^{27} +2.41147 q^{28} +(-3.37436 - 2.83142i) q^{29} +(-4.20280 + 8.89344i) q^{30} +(-1.50609 - 8.54146i) q^{31} +(-7.49746 - 2.72885i) q^{32} +(-0.448003 - 0.317135i) q^{33} +(-0.431752 + 2.44859i) q^{34} +(1.30443 - 2.25934i) q^{35} +(-7.31359 - 1.36716i) q^{36} +(2.23332 + 3.86823i) q^{37} +(12.3730 - 4.50341i) q^{38} +(2.52950 + 0.691717i) q^{39} +(2.08861 - 1.75255i) q^{40} +(4.47767 - 3.75721i) q^{41} +(3.43842 + 0.940269i) q^{42} +(-5.25381 + 1.91223i) q^{43} +(0.392973 + 0.680649i) q^{44} +(-5.23703 + 6.11267i) q^{45} +(2.28885 - 3.96441i) q^{46} +(-0.429965 + 2.43845i) q^{47} +(-3.97153 - 2.81139i) q^{48} +(5.68943 + 2.07078i) q^{49} +(-0.808243 - 4.58377i) q^{50} +(-0.869320 + 1.83955i) q^{51} +(-2.87645 - 2.41362i) q^{52} -10.8920 q^{53} +(-9.89507 - 4.80105i) q^{54} +0.850279 q^{55} +(-0.756896 - 0.635111i) q^{56} +(10.7384 - 0.883963i) q^{57} +(1.61901 + 9.18189i) q^{58} +(1.62023 + 0.589715i) q^{59} +(10.4706 - 4.81725i) q^{60} +(0.176214 - 0.999361i) q^{61} +(-9.17898 + 15.8985i) q^{62} +(2.51109 + 1.48436i) q^{63} +(5.63455 + 9.75933i) q^{64} +(-3.81731 + 1.38939i) q^{65} +(0.294929 + 1.12374i) q^{66} +(0.656156 - 0.550580i) q^{67} +(2.23174 - 1.87265i) q^{68} +(2.66237 - 2.63517i) q^{69} +(-5.18896 + 1.88863i) q^{70} +(4.79788 + 8.31018i) q^{71} +(1.93547 + 2.35530i) q^{72} +(7.62091 - 13.1998i) q^{73} +(1.64171 - 9.31057i) q^{74} +(0.351434 - 3.79256i) q^{75} +(-14.4977 - 5.27674i) q^{76} +(-0.0535070 - 0.303453i) q^{77} +(-3.16030 - 4.56306i) q^{78} +(-8.59024 - 7.20807i) q^{79} +7.53771 q^{80} +(-6.77415 - 5.92544i) q^{81} -12.3721 q^{82} +(3.58886 + 3.01141i) q^{83} +(-2.37811 - 3.43369i) q^{84} +(-0.547303 - 3.10391i) q^{85} +(11.1203 + 4.04747i) q^{86} +(-0.703969 + 7.59698i) q^{87} +(0.0559194 - 0.317135i) q^{88} +(7.74976 - 13.4230i) q^{89} +(16.8080 - 2.78607i) q^{90} +(0.736071 + 1.27491i) q^{91} +(-5.04032 + 1.83453i) q^{92} +(-10.6769 + 10.5678i) q^{93} +(4.01476 - 3.36879i) q^{94} +(-12.7861 + 10.7288i) q^{95} +(3.50815 + 13.3667i) q^{96} +(5.21481 - 1.89804i) q^{97} +(-6.40762 - 11.0983i) q^{98} +(-0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−1.62143	−	1.36054i	−1.14652	−	0.962046i	−0.146889	−	0.989153i	$-0.546926\pi$
$2$	−1.62143	−	1.36054i	−1.14652	−	0.962046i	−0.999633	+	0.0271067i	$0.991371\pi$
$3$	−0.986166	−	1.42389i	−0.569363	−	0.822086i
$3$	−0.986166	−	1.42389i	−0.569363	−	0.822086i
$4$	0.430663	+	2.44241i	0.215332	+	1.22121i
$5$	2.52129	+	0.917674i	1.12755	+	0.410396i	0.837404	−	0.546585i	$-0.184072\pi$
$5$	2.52129	+	0.917674i	1.12755	+	0.410396i	0.290150	+	0.956981i	$0.406295\pi$
$6$	−0.338267	+	3.65046i	−0.138097	+	1.49029i
$7$	0.168844	−	0.957561i	0.0638170	−	0.361924i	−0.936130	−	0.351653i	$-0.885620\pi$
$7$	0.168844	−	0.957561i	0.0638170	−	0.361924i	0.999947	−	0.0102706i	$-0.00326930\pi$
$8$	0.508086	−	0.880031i	0.179636	−	0.311138i
$9$	−1.05495	+	2.80839i	−0.351651	+	0.936131i
$10$	−2.83955	−	4.91825i	−0.897945	−	1.55529i
$11$	0.297791	−	0.108387i	0.0897872	−	0.0326799i	−0.296736	−	0.954960i	$-0.595898\pi$
$11$	0.297791	−	0.108387i	0.0897872	−	0.0326799i	0.386523	+	0.922280i	$0.373676\pi$
$12$	3.05303	−	3.02185i	0.881335	−	0.872332i
$13$	−1.15981	+	0.973200i	−0.321675	+	0.269917i	−0.789297	−	0.614011i	$-0.789555\pi$
$13$	−1.15981	+	0.973200i	−0.321675	+	0.269917i	0.467623	+	0.883928i	$0.345111\pi$
$14$	−1.57657	+	1.32290i	−0.421355	+	0.353559i
$15$	−1.17974	−	4.49503i	−0.304607	−	1.16061i
$16$	2.63991	−	0.960847i	0.659977	−	0.240212i
$17$	−0.587342	−	1.01731i	−0.142451	−	0.246733i	0.785968	−	0.618267i	$-0.212165\pi$
$17$	−0.587342	−	1.01731i	−0.142451	−	0.246733i	−0.928419	+	0.371534i	$0.878832\pi$
$18$	5.53146	−	3.11830i	1.30378	−	0.734991i
$19$	−3.11040	+	5.38737i	−0.713575	+	1.23595i	0.249931	+	0.968264i	$0.419592\pi$
$19$	−3.11040	+	5.38737i	−0.713575	+	1.23595i	−0.963507	+	0.267685i	$0.913741\pi$
$20$	−1.15551	+	6.55323i	−0.258380	+	1.46535i
$21$	−1.52997	+	0.703898i	−0.333868	+	0.153603i
$22$	−0.630310	−	0.229414i	−0.134383	−	0.0489113i
$23$	0.375556	+	2.12988i	0.0783089	+	0.444112i	0.998601	+	0.0528796i	$0.0168399\pi$
$23$	0.375556	+	2.12988i	0.0783089	+	0.444112i	−0.920292	+	0.391232i	$0.872049\pi$
$24$	−1.75413	+	0.144396i	−0.358060	+	0.0294747i
$25$	1.68454	+	1.41350i	0.336909	+	0.282700i
$26$	3.20463			0.628480
$27$	5.03922	−	1.26740i	0.969797	−	0.243912i
$28$	2.41147			0.455726
$29$	−3.37436	−	2.83142i	−0.626602	−	0.525782i	0.273269	−	0.961938i	$-0.411895\pi$
$29$	−3.37436	−	2.83142i	−0.626602	−	0.525782i	−0.899871	+	0.436156i	$0.856340\pi$
$30$	−4.20280	+	8.89344i	−0.767322	+	1.62371i
$31$	−1.50609	−	8.54146i	−0.270502	−	1.53409i	−0.752897	−	0.658138i	$-0.771344\pi$
$31$	−1.50609	−	8.54146i	−0.270502	−	1.53409i	0.482395	−	0.875954i	$-0.339767\pi$
$32$	−7.49746	−	2.72885i	−1.32538	−	0.482398i
$33$	−0.448003	−	0.317135i	−0.0779872	−	0.0552061i
$34$	−0.431752	+	2.44859i	−0.0740449	+	0.419930i
$35$	1.30443	−	2.25934i	0.220489	−	0.381899i
$36$	−7.31359	−	1.36716i	−1.21893	−	0.227859i
$37$	2.23332	+	3.86823i	0.367156	+	0.635933i	0.989120	−	0.147113i	$-0.0469982\pi$
$37$	2.23332	+	3.86823i	0.367156	+	0.635933i	−0.621964	+	0.783046i	$0.713665\pi$
$38$	12.3730	−	4.50341i	2.00717	−	0.730550i
$39$	2.52950	+	0.691717i	0.405045	+	0.110763i
$40$	2.08861	−	1.75255i	0.330239	−	0.277103i
$41$	4.47767	−	3.75721i	0.699295	−	0.586778i	−0.222278	−	0.974983i	$-0.571349\pi$
$41$	4.47767	−	3.75721i	0.699295	−	0.586778i	0.921573	+	0.388205i	$0.126905\pi$
$42$	3.43842	+	0.940269i	0.530560	+	0.145087i
$43$	−5.25381	+	1.91223i	−0.801199	+	0.291613i	−0.709983	−	0.704219i	$-0.751298\pi$
$43$	−5.25381	+	1.91223i	−0.801199	+	0.291613i	−0.0912158	+	0.995831i	$0.529075\pi$
$44$	0.392973	+	0.680649i	0.0592429	+	0.102612i
$45$	−5.23703	+	6.11267i	−0.780690	+	0.911223i
$46$	2.28885	−	3.96441i	0.337473	−	0.584521i
$47$	−0.429965	+	2.43845i	−0.0627168	+	0.355685i	0.937258	+	0.348636i	$0.113355\pi$
$47$	−0.429965	+	2.43845i	−0.0627168	+	0.355685i	−0.999975	+	0.00704911i	$0.997756\pi$
$48$	−3.97153	−	2.81139i	−0.573241	−	0.405790i
$49$	5.68943	+	2.07078i	0.812776	+	0.295826i
$50$	−0.808243	−	4.58377i	−0.114303	−	0.648243i
$51$	−0.869320	+	1.83955i	−0.121729	+	0.257588i
$52$	−2.87645	−	2.41362i	−0.398891	−	0.334710i
$53$	−10.8920			−1.49613			−0.748063	−	0.663628i	$-0.769016\pi$
$53$	−10.8920			−1.49613			−0.748063	+	0.663628i	$0.769016\pi$
$54$	−9.89507	−	4.80105i	−1.34655	−	0.653340i
$55$	0.850279			0.114652
$56$	−0.756896	−	0.635111i	−0.101145	−	0.0848703i
$57$	10.7384	−	0.883963i	1.42234	−	0.117084i
$58$	1.61901	+	9.18189i	0.212587	+	1.20564i
$59$	1.62023	+	0.589715i	0.210936	+	0.0767743i	0.445327	−	0.895368i	$-0.353087\pi$
$59$	1.62023	+	0.589715i	0.210936	+	0.0767743i	−0.234391	+	0.972142i	$0.575310\pi$
$60$	10.4706	−	4.81725i	1.35175	−	0.621905i
$61$	0.176214	−	0.999361i	0.0225619	−	0.127955i	−0.971446	−	0.237259i	$-0.923751\pi$
$61$	0.176214	−	0.999361i	0.0225619	−	0.127955i	0.994008	+	0.109304i	$0.0348621\pi$
$62$	−9.17898	+	15.8985i	−1.16573	+	2.01911i
$63$	2.51109	+	1.48436i	0.316367	+	0.187012i
$64$	5.63455	+	9.75933i	0.704319	+	1.21992i
$65$	−3.81731	+	1.38939i	−0.473478	+	0.172332i
$66$	0.294929	+	1.12374i	0.0363033	+	0.138322i
$67$	0.656156	−	0.550580i	0.0801622	−	0.0672641i	−0.601826	−	0.798627i	$-0.705560\pi$
$67$	0.656156	−	0.550580i	0.0801622	−	0.0672641i	0.681988	+	0.731363i	$0.261116\pi$
$68$	2.23174	−	1.87265i	0.270638	−	0.227092i
$69$	2.66237	−	2.63517i	0.320512	−	0.317238i
$70$	−5.18896	+	1.88863i	−0.620200	+	0.225734i
$71$	4.79788	+	8.31018i	0.569404	+	0.986237i	0.996625	+	0.0820894i	$0.0261593\pi$
$71$	4.79788	+	8.31018i	0.569404	+	0.986237i	−0.427221	+	0.904147i	$0.640507\pi$
$72$	1.93547	+	2.35530i	0.228097	+	0.277574i
$73$	7.62091	−	13.1998i	0.891960	−	1.54492i	0.0544385	−	0.998517i	$-0.482663\pi$
$73$	7.62091	−	13.1998i	0.891960	−	1.54492i	0.837522	−	0.546404i	$-0.184004\pi$
$74$	1.64171	−	9.31057i	0.190844	−	1.08233i
$75$	0.351434	−	3.79256i	0.0405802	−	0.437927i
$76$	−14.4977	−	5.27674i	−1.66300	−	0.605284i
$77$	−0.0535070	−	0.303453i	−0.00609768	−	0.0345817i
$78$	−3.16030	−	4.56306i	−0.357833	−	0.516664i
$79$	−8.59024	−	7.20807i	−0.966478	−	0.810971i	0.0155168	−	0.999880i	$-0.495061\pi$
$79$	−8.59024	−	7.20807i	−0.966478	−	0.810971i	−0.981995	+	0.188908i	$0.939505\pi$
$80$	7.53771			0.842741
$81$	−6.77415	−	5.92544i	−0.752684	−	0.658382i
$82$	−12.3721			−1.36626
$83$	3.58886	+	3.01141i	0.393929	+	0.330546i	0.818141	−	0.575017i	$-0.195005\pi$
$83$	3.58886	+	3.01141i	0.393929	+	0.330546i	−0.424212	+	0.905563i	$0.639449\pi$
$84$	−2.37811	−	3.43369i	−0.259474	−	0.374646i
$85$	−0.547303	−	3.10391i	−0.0593633	−	0.336666i
$86$	11.1203	+	4.04747i	1.19914	+	0.436450i
$87$	−0.703969	+	7.59698i	−0.0754734	+	0.814482i
$88$	0.0559194	−	0.317135i	0.00596103	−	0.0338067i
$89$	7.74976	−	13.4230i	0.821473	−	1.42283i	−0.0831130	−	0.996540i	$-0.526486\pi$
$89$	7.74976	−	13.4230i	0.821473	−	1.42283i	0.904586	−	0.426292i	$-0.140180\pi$
$90$	16.8080	−	2.78607i	1.77172	−	0.293677i
$91$	0.736071	+	1.27491i	0.0771612	+	0.133647i
$92$	−5.04032	+	1.83453i	−0.525490	+	0.191263i
$93$	−10.6769	+	10.5678i	−1.10714	+	1.09583i
$94$	4.01476	−	3.36879i	0.414091	−	0.347464i
$95$	−12.7861	+	10.7288i	−1.31182	+	1.10075i
$96$	3.50815	+	13.3667i	0.358049	+	1.36423i
$97$	5.21481	−	1.89804i	0.529484	−	0.192716i	−0.0634241	−	0.997987i	$-0.520202\pi$
$97$	5.21481	−	1.89804i	0.529484	−	0.192716i	0.592908	+	0.805270i	$0.297980\pi$
$98$	−6.40762	−	11.0983i	−0.647267	−	1.12110i
$99$	−0.00976156	+	0.950656i	−0.000981074	+	0.0955445i
$100$	−2.72688	+	4.72309i	−0.272688	+	0.472309i
$101$	−1.76063	+	9.98501i	−0.175189	+	0.993546i	0.762737	+	0.646709i	$0.223855\pi$
$101$	−1.76063	+	9.98501i	−0.175189	+	0.993546i	−0.937926	+	0.346836i	$0.887256\pi$
$102$	3.91231	−	1.79995i	0.387377	−	0.178221i
$103$	9.25906	+	3.37002i	0.912323	+	0.332058i	0.755180	−	0.655518i	$-0.227549\pi$
$103$	9.25906	+	3.37002i	0.912323	+	0.332058i	0.157143	+	0.987576i	$0.449772\pi$
$104$	0.267160	+	1.51514i	0.0261972	+	0.148572i
$105$	−4.50345	+	0.370714i	−0.439492	+	0.0361780i
$106$	17.6605	+	14.8189i	1.71534	+	1.43934i
$107$	5.17080			0.499880			0.249940	−	0.968261i	$-0.419589\pi$
$107$	5.17080			0.499880			0.249940	+	0.968261i	$0.419589\pi$
$108$	5.26573	+	11.7620i	0.506695	+	1.13180i
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$	−1.37867	−	1.15684i	−0.131451	−	0.110300i
$111$	3.30552	−	6.99473i	0.313746	−	0.663911i
$112$	−0.474338	−	2.69010i	−0.0448207	−	0.254191i
$113$	−9.74991	−	3.54868i	−0.917195	−	0.333832i	−0.160073	−	0.987105i	$-0.551173\pi$
$113$	−9.74991	−	3.54868i	−0.917195	−	0.333832i	−0.757122	+	0.653274i	$0.773395\pi$
$114$	−18.6142	−	13.1768i	−1.74338	−	1.23412i
$115$	−1.00765	+	5.71469i	−0.0939642	+	0.532898i
$116$	5.46229	−	9.46096i	0.507161	−	0.878428i
$117$	−1.50958	−	4.28390i	−0.139561	−	0.396046i
$118$	−1.82475	−	3.16056i	−0.167982	−	0.290953i
$119$	−1.07330	+	0.390650i	−0.0983894	+	0.0358108i
$120$	−4.55517	−	1.24565i	−0.415828	−	0.113712i
$121$	−8.34956	+	7.00611i	−0.759051	+	0.636919i
$122$	−1.64539	+	1.38064i	−0.148966	+	0.124998i
$123$	−9.76560	−	2.67050i	−0.880535	−	0.240790i
$124$	20.2132	−	7.35699i	1.81520	−	0.660677i
$125$	−3.75766	−	6.50846i	−0.336095	−	0.582134i
$126$	−2.05201	−	5.82321i	−0.182808	−	0.518773i
$127$	−2.61372	+	4.52709i	−0.231930	+	0.401714i	−0.958376	−	0.285509i	$-0.907837\pi$
$127$	−2.61372	+	4.52709i	−0.231930	+	0.401714i	0.726446	+	0.687223i	$0.241171\pi$
$128$	1.37098	−	7.77522i	0.121179	−	0.687239i
$129$	7.90395	+	5.59510i	0.695904	+	0.492621i
$130$	8.07980	+	2.94081i	0.708645	+	0.257926i
$131$	−1.25622	−	7.12440i	−0.109757	−	0.622461i	−0.989213	−	0.146482i	$-0.953205\pi$
$131$	−1.25622	−	7.12440i	−0.109757	−	0.622461i	0.879457	−	0.475979i	$-0.157906\pi$
$132$	0.581636	−	1.23079i	0.0506249	−	0.107126i
$133$	4.63357	+	3.88802i	0.401781	+	0.337134i
$134$	−1.81300			−0.156619
$135$	13.8684	+	1.42887i	1.19360	+	0.122977i
$136$	−1.19368			−0.102357
$137$	8.61748	+	7.23092i	0.736241	+	0.617779i	0.931825	−	0.362907i	$-0.118216\pi$
$137$	8.61748	+	7.23092i	0.736241	+	0.617779i	−0.195584	+	0.980687i	$0.562660\pi$
$138$	−7.90210	+	0.650482i	−0.672671	+	0.0553727i
$139$	1.62885	+	9.23766i	0.138157	+	0.783528i	0.972609	+	0.232447i	$0.0746733\pi$
$139$	1.62885	+	9.23766i	0.138157	+	0.783528i	−0.834452	+	0.551081i	$0.814216\pi$
$140$	6.08002	+	2.21295i	0.513855	+	0.187028i
$141$	3.89612	−	1.79249i	0.328112	−	0.150955i
$142$	3.52690	−	20.0021i	0.295971	−	1.67854i
$143$	−0.239900	+	0.415518i	−0.0200614	+	0.0347474i
$144$	−0.0865360	+	8.42754i	−0.00721133	+	0.702295i
$145$	−5.90940	−	10.2354i	−0.490749	−	0.850003i
$146$	−30.3156	+	11.0340i	−2.50894	+	0.913179i
$147$	−2.66215	−	10.1433i	−0.219570	−	0.836605i
$148$	−8.48600	+	7.12060i	−0.697545	+	0.585310i
$149$	14.5941	−	12.2459i	1.19560	−	1.00322i	0.195851	−	0.980634i	$-0.437253\pi$
$149$	14.5941	−	12.2459i	1.19560	−	1.00322i	0.999745	−	0.0225899i	$-0.00719121\pi$
$150$	−5.72975	+	5.67121i	−0.467832	+	0.463053i
$151$	−3.77193	+	1.37287i	−0.306955	+	0.111723i	−0.490905	−	0.871213i	$-0.663334\pi$
$151$	−3.77193	+	1.37287i	−0.306955	+	0.111723i	0.183950	+	0.982936i	$0.441112\pi$
$152$	3.16070	+	5.47450i	0.256367	+	0.444041i
$153$	3.47661	−	0.576279i	0.281068	−	0.0465894i
$154$	−0.326102	+	0.564825i	−0.0262780	+	0.0455149i
$155$	4.04099	−	22.9176i	0.324580	−	1.84078i
$156$	−0.600093	+	6.47599i	−0.0480459	+	0.518494i
$157$	−6.83713	−	2.48851i	−0.545662	−	0.198605i	0.0544560	−	0.998516i	$-0.482658\pi$
$157$	−6.83713	−	2.48851i	−0.545662	−	0.198605i	−0.600118	+	0.799911i	$0.704880\pi$
$158$	4.12159	+	23.3747i	0.327896	+	1.85959i
$159$	10.7413	+	15.5090i	0.851839	+	1.22994i
$160$	−16.3991	−	13.7604i	−1.29646	−	1.08786i
$161$	2.10290			0.165732
$162$	2.92200	+	18.8242i	0.229574	+	1.47897i
$163$	12.4492			0.975094			0.487547	−	0.873097i	$-0.337892\pi$
$163$	12.4492			0.975094			0.487547	+	0.873097i	$0.337892\pi$
$164$	11.1050	+	9.31823i	0.867157	+	0.727632i
$165$	−0.838517	−	1.21071i	−0.0652785	−	0.0942535i
$166$	−1.72194	−	9.76558i	−0.133648	−	0.757956i
$167$	2.19126	+	0.797553i	0.169565	+	0.0617165i	0.425408	−	0.905002i	$-0.360131\pi$
$167$	2.19126	+	0.797553i	0.169565	+	0.0617165i	−0.255843	+	0.966718i	$0.582353\pi$
$168$	−0.157906	+	1.70407i	−0.0121827	+	0.131472i
$169$	−1.85937	+	10.5450i	−0.143029	+	0.811157i
$170$	−3.33558	+	5.77739i	−0.255827	+	0.443106i
$171$	−11.8485	−	14.4187i	−0.906081	−	1.10262i
$172$	−6.93308	−	12.0085i	−0.528643	−	0.915636i
$173$	3.36623	−	1.22521i	0.255930	−	0.0931509i	−0.210869	−	0.977514i	$-0.567629\pi$
$173$	3.36623	−	1.22521i	0.255930	−	0.0931509i	0.466799	+	0.884363i	$0.345407\pi$
$174$	11.4774	−	11.3602i	0.870101	−	0.861213i
$175$	1.63794	−	1.37439i	0.123816	−	0.103894i
$176$	0.681996	−	0.572262i	0.0514074	−	0.0431359i
$177$	−0.758123	−	2.88859i	−0.0569840	−	0.217120i
$178$	−30.8281	+	11.2205i	−2.31067	+	0.841014i
$179$	9.99785	+	17.3168i	0.747275	+	1.29432i	0.949124	+	0.314901i	$0.101971\pi$
$179$	9.99785	+	17.3168i	0.747275	+	1.29432i	−0.201850	+	0.979416i	$0.564695\pi$
$180$	−17.1851	−	10.1585i	−1.28090	−	0.757168i
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	−0.988241	−	0.152907i	$-0.951136\pi$
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	0.626542	+	0.779388i	$0.284470\pi$
$182$	0.541082	−	3.06863i	0.0401077	−	0.227462i
$183$	−1.59676	+	0.734626i	−0.118036	+	0.0543051i
$184$	2.06518	+	0.751664i	0.152247	+	0.0554134i
$185$	2.08108	+	11.8024i	0.153004	+	0.867728i
$186$	31.6897	−	2.60862i	2.32360	−	0.191274i
$187$	−0.285168	−	0.239284i	−0.0208535	−	0.0174982i
$188$	−6.14088			−0.447869
$189$	−0.362776	−	5.03935i	−0.0263881	−	0.366559i
$190$	35.3286			2.56301
$191$	−13.6023	−	11.4137i	−0.984227	−	0.825864i	0.000494763	−	1.00000i	$-0.499843\pi$
$191$	−13.6023	−	11.4137i	−0.984227	−	0.825864i	−0.984722	+	0.174135i	$0.944287\pi$
$192$	8.33965	−	17.6473i	0.601862	−	1.27359i
$193$	1.83795	+	10.4235i	0.132299	+	0.750303i	0.976703	+	0.214596i	$0.0688435\pi$
$193$	1.83795	+	10.4235i	0.132299	+	0.750303i	−0.844404	+	0.535706i	$0.820045\pi$
$194$	−11.0378	−	4.01743i	−0.792467	−	0.288434i
$195$	5.74284	+	4.06528i	0.411253	+	0.291120i
$196$	−2.60748	+	14.7878i	−0.186249	+	1.05627i
$197$	−7.07945	+	12.2620i	−0.504390	+	0.873628i	0.495597	+	0.868552i	$0.334949\pi$
$197$	−7.07945	+	12.2620i	−0.504390	+	0.873628i	−0.999987	+	0.00507615i	$0.998384\pi$
$198$	1.30923	−	1.52814i	0.0930431	−	0.108600i
$199$	−3.77010	−	6.53000i	−0.267255	−	0.462899i	0.700897	−	0.713263i	$-0.252783\pi$
$199$	−3.77010	−	6.53000i	−0.267255	−	0.462899i	−0.968152	+	0.250363i	$0.919450\pi$
$200$	2.09982	−	0.764271i	0.148479	−	0.0540421i
$201$	−1.43105	−	0.391333i	−0.100938	−	0.0276025i
$202$	16.4397	−	13.7946i	1.15669	−	0.970582i
$203$	−3.28100	+	2.75308i	−0.230281	+	0.193229i
$204$	−4.86732	−	1.33101i	−0.340780	−	0.0931896i
$205$	14.7374	−	5.36397i	1.02930	−	0.374636i
$206$	−10.4278	−	18.0616i	−0.726543	−	1.25841i
$207$	−6.37775	−	1.19222i	−0.443284	−	0.0828648i
$208$	−2.12670	+	3.68356i	−0.147460	+	0.255409i
$209$	−0.342328	+	1.94144i	−0.0236793	+	0.134292i
$210$	7.80639	+	5.52604i	0.538692	+	0.381333i
$211$	−4.89922	−	1.78317i	−0.337276	−	0.122758i	0.167829	−	0.985816i	$-0.446324\pi$
$211$	−4.89922	−	1.78317i	−0.337276	−	0.122758i	−0.505106	+	0.863058i	$0.668546\pi$
$212$	−4.69077	−	26.6027i	−0.322163	−	1.82708i
$213$	7.10131	−	15.0269i	0.486573	−	1.02963i
$214$	−8.38408	−	7.03508i	−0.573124	−	0.480908i
$215$	−15.0012			−1.02307
$216$	1.44500	−	5.07862i	0.0983199	−	0.345556i
$217$	−8.43326			−0.572487
$218$	11.8537	+	9.94643i	0.802833	+	0.673657i
$219$	−26.3106	+	2.16583i	−1.77791	+	0.146353i
$220$	0.366184	+	2.07673i	0.0246881	+	0.140013i
$221$	1.67125	+	0.608285i	0.112420	+	0.0409177i
$222$	−14.8763	+	6.84416i	−0.998430	+	0.459350i
$223$	3.07250	−	17.4250i	0.205750	−	1.16686i	−0.690506	−	0.723326i	$-0.742612\pi$
$223$	3.07250	−	17.4250i	0.205750	−	1.16686i	0.896256	−	0.443537i	$-0.146277\pi$
$224$	−3.87894	+	6.71853i	−0.259173	+	0.448901i
$225$	−5.74677	+	3.23969i	−0.383118	+	0.215979i
$226$	10.9807	+	19.0191i	0.730423	+	1.26513i
$227$	14.8208	−	5.39434i	0.983692	−	0.358035i	0.200418	−	0.979711i	$-0.435770\pi$
$227$	14.8208	−	5.39434i	0.983692	−	0.358035i	0.783275	+	0.621676i	$0.213548\pi$
$228$	6.78365	+	25.8470i	0.449258	+	1.71176i
$229$	−1.35350	+	1.13572i	−0.0894415	+	0.0750504i	−0.686412	−	0.727213i	$-0.740815\pi$
$229$	−1.35350	+	1.13572i	−0.0894415	+	0.0750504i	0.596971	+	0.802263i	$0.296371\pi$
$230$	9.40889	−	7.89500i	0.620404	−	0.520581i
$231$	−0.379318	+	0.375443i	−0.0249573	+	0.0247024i
$232$	−4.20620	+	1.53093i	−0.276151	+	0.100511i
$233$	6.94920	+	12.0364i	0.455257	+	0.788529i	0.998703	−	0.0509157i	$-0.0162140\pi$
$233$	6.94920	+	12.0364i	0.455257	+	0.788529i	−0.543446	+	0.839444i	$0.682881\pi$
$234$	−3.38073	+	8.99987i	−0.221005	+	0.588340i
$235$	−3.32177	+	5.75347i	−0.216688	+	0.375315i
$236$	−0.742554	+	4.21123i	−0.0483362	+	0.274128i
$237$	−1.79212	+	19.3400i	−0.116411	+	1.25627i
$238$	2.27177	+	0.826858i	0.147257	+	0.0535973i
$239$	−3.44391	−	19.5314i	−0.222768	−	1.26338i	−0.866906	−	0.498471i	$-0.833895\pi$
$239$	−3.44391	−	19.5314i	−0.222768	−	1.26338i	0.644138	−	0.764909i	$-0.277216\pi$
$240$	−7.43343	−	10.7329i	−0.479826	−	0.692806i
$241$	14.8419	+	12.4538i	0.956050	+	0.802221i	0.980306	−	0.197485i	$-0.0632773\pi$
$241$	14.8419	+	12.4538i	0.956050	+	0.802221i	−0.0242563	+	0.999706i	$0.507722\pi$
$242$	23.0703			1.48301
$243$	−1.75676	+	15.4892i	−0.112696	+	0.993629i
$244$	2.51674			0.161118
$245$	12.4444	+	10.4421i	0.795043	+	0.667120i
$246$	12.2009	+	17.6165i	0.777901	+	1.12319i
$247$	−1.63550	−	9.27540i	−0.104065	−	0.590179i
$248$	−8.28198	−	3.01439i	−0.525906	−	0.191414i
$249$	0.748720	−	8.07992i	0.0474482	−	0.512044i
$250$	−2.76224	+	15.6654i	−0.174699	+	0.990769i
$251$	2.73786	−	4.74212i	0.172812	−	0.299320i	−0.766590	−	0.642137i	$-0.778048\pi$
$251$	2.73786	−	4.74212i	0.172812	−	0.299320i	0.939402	+	0.342818i	$0.111381\pi$
$252$	−2.54399	+	6.77237i	−0.160256	+	0.426619i
$253$	0.342689	+	0.593554i	0.0215447	+	0.0373164i
$254$	10.3972	−	3.78428i	0.652380	−	0.237447i
$255$	−3.87991	+	3.84027i	−0.242969	+	0.240487i
$256$	4.46383	−	3.74560i	0.278989	−	0.234100i
$257$	−8.85943	+	7.43395i	−0.552636	+	0.463717i	−0.875833	−	0.482615i	$-0.839687\pi$
$257$	−8.85943	+	7.43395i	−0.552636	+	0.463717i	0.323196	+	0.946332i	$0.395243\pi$
$258$	−5.20333	−	19.8257i	−0.323945	−	1.23429i
$259$	4.08115	−	1.48542i	0.253590	−	0.0922993i
$260$	−5.03743	−	8.72508i	−0.312408	−	0.541107i
$261$	11.5115	−	6.48951i	0.712546	−	0.401691i
$262$	−7.65614	+	13.2608i	−0.472998	+	0.819257i
$263$	1.12488	−	6.37952i	0.0693632	−	0.393378i	−0.930285	−	0.366839i	$-0.880440\pi$
$263$	1.12488	−	6.37952i	0.0693632	−	0.393378i	0.999648	−	0.0265395i	$-0.00844878\pi$
$264$	−0.506712	+	0.233124i	−0.0311860	+	0.0143478i
$265$	−27.4618	−	9.99526i	−1.68696	−	0.614004i
$266$	−2.22318	−	12.6083i	−0.136312	−	0.773064i
$267$	−26.7554	+	2.20245i	−1.63741	+	0.134788i
$268$	1.62733	+	1.36549i	0.0994048	+	0.0834106i
$269$	−13.8387			−0.843758			−0.421879	−	0.906652i	$-0.638629\pi$
$269$	−13.8387			−0.843758			−0.421879	+	0.906652i	$0.638629\pi$
$270$	−20.5425	−	21.1853i	−1.25018	−	1.28929i
$271$	1.94536			0.118172			0.0590860	−	0.998253i	$-0.481181\pi$
$271$	1.94536			0.118172			0.0590860	+	0.998253i	$0.481181\pi$
$272$	−2.52800	−	2.12125i	−0.153283	−	0.128619i
$273$	1.08945	−	2.30536i	0.0659366	−	0.139527i
$274$	−4.13466	−	23.4488i	−0.249784	−	1.41660i
$275$	0.654846	+	0.238344i	0.0394887	+	0.0143727i
$276$	7.58277	+	5.36774i	0.456429	+	0.323100i
$277$	2.16586	−	12.2832i	0.130134	−	0.738026i	−0.847991	−	0.530010i	$-0.822188\pi$
$277$	2.16586	−	12.2832i	0.130134	−	0.738026i	0.978125	−	0.208016i	$-0.0667007\pi$
$278$	9.92713	−	17.1943i	0.595390	−	1.03125i
$279$	25.5766	+	4.78114i	1.53123	+	0.286239i
$280$	−1.32553	−	2.29588i	−0.0792154	−	0.137205i
$281$	−9.16752	+	3.33670i	−0.546888	+	0.199051i	−0.600663	−	0.799502i	$-0.705097\pi$
$281$	−9.16752	+	3.33670i	−0.546888	+	0.199051i	0.0537751	+	0.998553i	$0.482875\pi$
$282$	−8.75602	−	2.39442i	−0.521414	−	0.142585i
$283$	20.3547	−	17.0797i	1.20996	−	1.01528i	0.210676	−	0.977556i	$-0.432433\pi$
$283$	20.3547	−	17.0797i	1.20996	−	1.01528i	0.999288	−	0.0377246i	$-0.0120110\pi$
$284$	−18.2306	+	15.2973i	−1.08179	+	0.907728i
$285$	27.8858	+	7.62565i	1.65181	+	0.451704i
$286$	0.954309	−	0.347340i	0.0564295	−	0.0205386i
$287$	−2.84173	−	4.92202i	−0.167742	−	0.290538i
$288$	15.5732	−	18.1770i	0.917657	−	1.07109i
$289$	7.81006	−	13.5274i	0.459415	−	0.795730i
$290$	−4.34397	+	24.6359i	−0.255087	+	1.44667i
$291$	−7.84527	−	5.55356i	−0.459898	−	0.325556i
$292$	35.5214	+	12.9287i	2.07873	+	0.756598i
$293$	2.12849	+	12.0712i	0.124347	+	0.705210i	0.981693	+	0.190469i	$0.0610008\pi$
$293$	2.12849	+	12.0712i	0.124347	+	0.705210i	−0.857346	+	0.514741i	$0.827888\pi$
$294$	−9.48386	+	20.0686i	−0.553110	+	1.17042i
$295$	3.54389	+	2.97368i	0.206334	+	0.173134i
$296$	4.53888			0.263817
$297$	1.36326	−	0.923606i	0.0791044	−	0.0535930i
$298$	−40.3243			−2.33592
$299$	−2.50838	−	2.10478i	−0.145063	−	0.121723i
$300$	9.41434	−	0.774967i	0.543537	−	0.0447427i
$301$	0.944004	+	5.35371i	0.0544115	+	0.308583i
$302$	7.98375	+	2.90585i	0.459413	+	0.167213i
$303$	15.9539	−	7.33993i	0.916526	−	0.421668i
$304$	−3.03473	+	17.2108i	−0.174053	+	0.987106i
$305$	1.36137	−	2.35797i	0.0779521	−	0.135017i
$306$	−6.42113	−	3.79567i	−0.367071	−	0.216984i
$307$	13.2370	+	22.9271i	0.755475	+	1.30852i	0.945138	+	0.326671i	$0.105927\pi$
$307$	13.2370	+	22.9271i	0.755475	+	1.30852i	−0.189663	+	0.981849i	$0.560740\pi$
$308$	0.718114	−	0.261372i	0.0409184	−	0.0148931i
$309$	−4.33242	−	16.5073i	−0.246463	−	0.939070i
$310$	−37.7324	+	31.6613i	−2.14306	+	1.79824i
$311$	−13.5280	+	11.3513i	−0.767100	+	0.643673i	−0.939964	−	0.341272i	$-0.889142\pi$
$311$	−13.5280	+	11.3513i	−0.767100	+	0.643673i	0.172865	+	0.984946i	$0.444698\pi$
$312$	1.89394	−	1.87459i	0.107223	−	0.106128i
$313$	−9.06541	+	3.29954i	−0.512407	+	0.186501i	−0.585266	−	0.810841i	$-0.699010\pi$
$313$	−9.06541	+	3.29954i	−0.512407	+	0.186501i	0.0728589	+	0.997342i	$0.476788\pi$
$314$	7.70019	+	13.3371i	0.434547	+	0.752657i
$315$	4.96901	+	6.04686i	0.279972	+	0.340702i
$316$	13.9056	−	24.0852i	0.782250	−	1.35490i
$317$	−0.644320	+	3.65412i	−0.0361886	+	0.205236i	−0.997541	−	0.0700850i	$-0.977673\pi$
$317$	−0.644320	+	3.65412i	−0.0361886	+	0.205236i	0.961352	+	0.275321i	$0.0887841\pi$
$318$	3.68439	−	39.7606i	0.206610	−	2.22967i
$319$	−1.31174	−	0.477435i	−0.0734434	−	0.0267312i
$320$	5.25044	+	29.7767i	0.293509	+	1.66457i
$321$	−5.09927	−	7.36268i	−0.284614	−	0.410945i
$322$	−3.40971	−	2.86108i	−0.190016	−	0.159442i
$323$	7.30748			0.406599
$324$	11.5550	−	19.0972i	0.641944	−	1.06095i
$325$	−3.32937			−0.184680
$326$	−20.1854	−	16.9376i	−1.11797	−	0.938085i
$327$	7.20952	+	10.4096i	0.398687	+	0.575652i
$328$	−1.03142	−	5.84948i	−0.0569507	−	0.322983i
$329$	2.26237	+	0.823435i	0.124728	+	0.0453974i
$330$	−0.287622	+	3.10391i	−0.0158330	+	0.170865i
$331$	−0.245329	+	1.39133i	−0.0134845	+	0.0764745i	−0.990807	−	0.135280i	$-0.956807\pi$
$331$	−0.245329	+	1.39133i	−0.0134845	+	0.0764745i	0.977323	+	0.211755i	$0.0679177\pi$
$332$	−5.80953	+	10.0624i	−0.318839	+	0.552246i
$333$	−13.2196	+	2.19126i	−0.724427	+	0.120080i
$334$	−2.46786	−	4.27446i	−0.135035	−	0.233888i
$335$	2.15961	−	0.786034i	0.117992	−	0.0429456i
$336$	−3.36265	+	3.32830i	−0.183447	+	0.181573i
$337$	−9.95097	+	8.34986i	−0.542064	+	0.454846i	−0.872243	−	0.489073i	$-0.837335\pi$
$337$	−9.95097	+	8.34986i	−0.542064	+	0.454846i	0.330179	+	0.943918i	$0.392891\pi$
$338$	17.3618	−	14.5683i	0.944356	−	0.792409i
$339$	4.56209	+	17.3824i	0.247779	+	0.944084i
$340$	7.34533	−	2.67348i	0.398356	−	0.144990i
$341$	−1.37428	−	2.38033i	−0.0744215	−	0.128902i
$342$	−0.405587	+	39.4992i	−0.0219316	+	2.13587i
$343$	6.34669	−	10.9928i	0.342689	−	0.593555i
$344$	−0.986567	+	5.59510i	−0.0531921	+	0.301667i
$345$	9.13083	−	4.20084i	0.491587	−	0.226166i
$346$	−7.12504	−	2.59330i	−0.383045	−	0.139417i
$347$	−0.833591	−	4.72753i	−0.0447495	−	0.253787i	0.954224	−	0.299094i	$-0.0966845\pi$
$347$	−0.833591	−	4.72753i	−0.0447495	−	0.253787i	−0.998973	+	0.0453070i	$0.985573\pi$
$348$	−18.8581	+	1.55236i	−1.01090	+	0.0832152i
$349$	−17.2954	−	14.5126i	−0.925803	−	0.776841i	0.0492565	−	0.998786i	$-0.484315\pi$
$349$	−17.2954	−	14.5126i	−0.925803	−	0.776841i	−0.975059	+	0.221946i	$0.928759\pi$
$350$	−4.52571			−0.241909
$351$	−4.61112	+	6.37412i	−0.246123	+	0.340225i
$352$	−2.52845			−0.134767
$353$	−22.7565	−	19.0950i	−1.21121	−	1.01632i	−0.999237	−	0.0390490i	$-0.987567\pi$
$353$	−22.7565	−	19.0950i	−1.21121	−	1.01632i	−0.211972	−	0.977276i	$-0.567988\pi$
$354$	−2.70080	+	5.71509i	−0.143546	+	0.303754i
$355$	4.47081	+	25.3552i	0.237286	+	1.34572i
$356$	36.1220	+	13.1473i	1.91446	+	0.696807i
$357$	1.61470	+	1.14302i	0.0854589	+	0.0604952i
$358$	7.34937	−	41.6804i	0.388427	−	2.20288i
$359$	−6.70991	+	11.6219i	−0.354136	+	0.613381i	−0.986970	−	0.160906i	$-0.948558\pi$
$359$	−6.70991	+	11.6219i	−0.354136	+	0.613381i	0.632834	+	0.774288i	$0.281892\pi$
$360$	2.71848	+	7.71451i	0.143276	+	0.406590i
$361$	−9.84920	−	17.0593i	−0.518379	−	0.897858i
$362$	19.3573	−	7.04550i	1.01740	−	0.370303i
$363$	18.2100	+	4.97970i	0.955778	+	0.261366i
$364$	−2.79686	+	2.34685i	−0.146595	+	0.123008i
$365$	31.3276	−	26.2870i	1.63976	−	1.37592i
$366$	3.58852	+	0.981314i	0.187575	+	0.0512941i
$367$	7.47054	−	2.71905i	0.389959	−	0.141933i	−0.139597	−	0.990208i	$-0.544581\pi$
$367$	7.47054	−	2.71905i	0.389959	−	0.141933i	0.529556	+	0.848275i	$0.322359\pi$
$368$	3.03793	+	5.26184i	0.158363	+	0.274293i
$369$	5.82801	+	16.5387i	0.303394	+	0.860973i
$370$	12.6833	−	21.9681i	0.659372	−	1.14207i
$371$	−1.83904	+	10.4297i	−0.0954782	+	0.541484i
$372$	−30.4091	−	21.5262i	−1.57664	−	1.11608i
$373$	10.7318	+	3.90604i	0.555670	+	0.202247i	0.604564	−	0.796557i	$-0.293347\pi$
$373$	10.7318	+	3.90604i	0.555670	+	0.202247i	−0.0488939	+	0.998804i	$0.515570\pi$
$374$	0.136823	+	0.775963i	0.00707496	+	0.0401241i
$375$	−5.56168	+	11.7689i	−0.287204	+	0.607745i
$376$	1.92745	+	1.61733i	0.0994009	+	0.0834072i
$377$	6.66917			0.343480
$378$	−6.26801	+	8.66451i	−0.322392	+	0.445654i
$379$	−24.1705			−1.24155			−0.620777	−	0.783987i	$-0.713183\pi$
$379$	−24.1705			−1.24155			−0.620777	+	0.783987i	$0.713183\pi$
$380$	−31.7106	−	26.6084i	−1.62672	−	1.36498i
$381$	9.02366	−	0.742807i	0.462296	−	0.0380551i
$382$	6.52637	+	37.0129i	0.333918	+	1.89374i
$383$	−8.87378	−	3.22979i	−0.453429	−	0.165035i	0.105202	−	0.994451i	$-0.466451\pi$
$383$	−8.87378	−	3.22979i	−0.453429	−	0.165035i	−0.558631	+	0.829416i	$0.688673\pi$
$384$	−12.4231	+	5.71553i	−0.633964	+	0.291669i
$385$	0.143564	−	0.814194i	0.00731672	−	0.0414952i
$386$	11.2015	−	19.4016i	0.570143	−	0.987516i
$387$	0.172220	−	16.7721i	0.00875442	−	0.852573i
$388$	6.88162	+	11.9193i	0.349361	+	0.605111i
$389$	2.39406	−	0.871367i	0.121384	−	0.0441801i	−0.280614	−	0.959821i	$-0.590538\pi$
$389$	2.39406	−	0.871367i	0.121384	−	0.0441801i	0.401998	+	0.915641i	$0.368316\pi$
$390$	−3.78063	−	14.4049i	−0.191439	−	0.729420i
$391$	1.94617	−	1.63303i	0.0984218	−	0.0825857i
$392$	4.71308	−	3.95474i	0.238046	−	0.199745i
$393$	−8.90554	+	8.81457i	−0.449225	+	0.444636i
$394$	28.1617	−	10.2500i	1.41876	−	0.516388i
$395$	−15.0438	−	26.0567i	−0.756937	−	1.31105i
$396$	−2.32610	+	0.385571i	−0.116891	+	0.0193757i
$397$	−1.83759	+	3.18279i	−0.0922258	+	0.159740i	−0.908447	−	0.417999i	$-0.862731\pi$
$397$	−1.83759	+	3.18279i	−0.0922258	+	0.159740i	0.816222	+	0.577739i	$0.196065\pi$
$398$	−2.77138	+	15.7173i	−0.138917	+	0.787836i
$399$	0.966669	−	10.4319i	0.0483940	−	0.522251i
$400$	5.80519	+	2.11292i	0.290260	+	0.105646i
$401$	2.80420	+	15.9034i	0.140035	+	0.794177i	0.971220	+	0.238182i	$0.0765516\pi$
$401$	2.80420	+	15.9034i	0.140035	+	0.794177i	−0.831186	+	0.555995i	$0.812337\pi$
$402$	1.78791	+	2.58151i	0.0891731	+	0.128754i
$403$	10.0593	+	8.44078i	0.501091	+	0.420465i
$404$	−25.1458			−1.25105
$405$	−11.6420	−	21.1562i	−0.578494	−	1.05126i
$406$	9.06558			0.449917
$407$	1.08433	+	0.909859i	0.0537481	+	0.0451000i
$408$	1.17717	+	1.69968i	0.0582785	+	0.0841465i
$409$	1.59443	+	9.04248i	0.0788396	+	0.447122i	0.998517	+	0.0544462i	$0.0173393\pi$
$409$	1.59443	+	9.04248i	0.0788396	+	0.447122i	−0.919677	+	0.392676i	$0.871550\pi$
$410$	−31.1935	−	11.3535i	−1.54054	−	0.560710i
$411$	1.79780	−	19.4013i	0.0886792	−	0.956994i
$412$	−4.24345	+	24.0658i	−0.209060	+	1.18564i
$413$	0.838253	−	1.45190i	0.0412477	−	0.0714432i
$414$	8.71900	+	10.6103i	0.428515	+	0.521466i
$415$	6.28506	+	10.8860i	0.308522	+	0.534375i
$416$	11.3514	−	4.13157i	0.556548	−	0.202567i
$417$	11.5471	−	11.4292i	0.565466	−	0.559689i
$418$	3.19646	−	2.68215i	0.156344	−	0.131188i
$419$	−5.34613	+	4.48594i	−0.261176	+	0.219152i	−0.763967	−	0.645256i	$-0.776751\pi$
$419$	−5.34613	+	4.48594i	−0.261176	+	0.219152i	0.502791	+	0.864408i	$0.332306\pi$
$420$	−2.84491	−	10.8396i	−0.138817	−	0.528920i
$421$	−28.9525	+	10.5379i	−1.41106	+	0.513584i	−0.931441	−	0.363894i	$-0.881447\pi$
$421$	−28.9525	+	10.5379i	−1.41106	+	0.513584i	−0.479619	+	0.877477i	$0.659225\pi$
$422$	5.51765	+	9.55686i	0.268595	+	0.465221i
$423$	−6.39454	−	3.77996i	−0.310913	−	0.183788i
$424$	−5.53405	+	9.58526i	−0.268757	+	0.465502i
$425$	0.448559	−	2.54390i	0.0217583	−	0.123397i
$426$	−31.9589	+	14.7034i	−1.54842	+	0.712383i
$427$	−0.927196	−	0.337472i	−0.0448702	−	0.0163314i
$428$	2.22687	+	12.6292i	0.107640	+	0.610457i
$429$	0.828236	−	0.0681784i	0.0399876	−	0.00329169i
$430$	24.3233	+	20.4097i	1.17297	+	0.984242i
$431$	27.8971			1.34376			0.671879	−	0.740661i	$-0.265487\pi$
$431$	27.8971			1.34376			0.671879	+	0.740661i	$0.265487\pi$
$432$	12.0853	−	8.18774i	0.581453	−	0.393933i
$433$	19.1706			0.921278			0.460639	−	0.887588i	$-0.347620\pi$
$433$	19.1706			0.921278			0.460639	+	0.887588i	$0.347620\pi$
$434$	13.6739	+	11.4738i	0.656369	+	0.550759i
$435$	−8.74646	+	18.5082i	−0.419361	+	0.887398i
$436$	−3.14843	−	17.8556i	−0.150782	−	0.855130i
$437$	−12.6426	−	4.60154i	−0.604778	−	0.220121i
$438$	45.6075	+	32.2849i	2.17921	+	1.54263i
$439$	−4.12397	+	23.3882i	−0.196826	+	1.11626i	0.712968	+	0.701197i	$0.247351\pi$
$439$	−4.12397	+	23.3882i	−0.196826	+	1.11626i	−0.909794	+	0.415060i	$0.863761\pi$
$440$	0.432015	−	0.748272i	0.0205955	−	0.0356725i
$441$	−11.8177	+	13.7936i	−0.562746	+	0.656838i
$442$	−1.88221	−	3.26009i	−0.0895278	−	0.155067i
$443$	−21.9496	+	7.98900i	−1.04286	+	0.379569i	−0.805962	−	0.591967i	$-0.798352\pi$
$443$	−21.9496	+	7.98900i	−1.04286	+	0.379569i	−0.236894	+	0.971536i	$0.576129\pi$
$444$	18.5076	+	5.06108i	0.878332	+	0.240188i
$445$	31.8573	−	26.7314i	1.51018	−	1.26719i
$446$	−28.6892	+	24.0731i	−1.35847	+	1.13989i
$447$	−31.8291	−	8.70396i	−1.50546	−	0.411683i
$448$	10.2965	−	3.74762i	0.486464	−	0.177059i
$449$	−2.40953	−	4.17343i	−0.113713	−	0.196956i	0.803552	−	0.595235i	$-0.202941\pi$
$449$	−2.40953	−	4.17343i	−0.113713	−	0.196956i	−0.917264	+	0.398279i	$0.869608\pi$
$450$	13.7257	+	2.56579i	0.647035	+	0.120953i
$451$	0.926176	−	1.60418i	0.0436119	−	0.0755380i
$452$	4.46841	−	25.3416i	0.210176	−	1.19197i
$453$	5.67457	+	4.01695i	0.266615	+	0.188733i
$454$	−31.3701	−	11.4178i	−1.47227	−	0.535863i
$455$	0.685893	+	3.88989i	0.0321552	+	0.182361i
$456$	4.67813	−	9.89928i	0.219074	−	0.463576i
$457$	−3.74872	−	3.14555i	−0.175358	−	0.147142i	0.550885	−	0.834581i	$-0.314290\pi$
$457$	−3.74872	−	3.14555i	−0.175358	−	0.147142i	−0.726242	+	0.687439i	$0.758735\pi$
$458$	3.73978			0.174749
$459$	−4.24908	−	4.38203i	−0.198330	−	0.204535i
$460$	−14.3916			−0.671012
$461$	21.4419	+	17.9919i	0.998650	+	0.837967i	0.986797	−	0.161963i	$-0.0517824\pi$
$461$	21.4419	+	17.9919i	0.998650	+	0.837967i	0.0118535	+	0.999930i	$0.496227\pi$
$462$	1.12584	−	0.0926768i	0.0523789	−	0.00431171i
$463$	−4.77104	−	27.0579i	−0.221729	−	1.25749i	−0.868840	−	0.495093i	$-0.835134\pi$
$463$	−4.77104	−	27.0579i	−0.221729	−	1.25749i	0.647111	−	0.762396i	$-0.275977\pi$
$464$	−11.6285	−	4.23245i	−0.539842	−	0.196486i
$465$	−36.6173	+	16.8466i	−1.69809	+	0.781243i
$466$	5.10832	−	28.9707i	0.236639	−	1.34204i
$467$	10.6232	−	18.4000i	0.491585	−	0.851450i	−0.508368	−	0.861140i	$-0.669751\pi$
$467$	10.6232	−	18.4000i	0.491585	−	0.851450i	0.999953	+	0.00968963i	$0.00308435\pi$
$468$	9.81292	−	5.53194i	0.453602	−	0.255714i
$469$	−0.416426	−	0.721272i	−0.0192288	−	0.0333052i
$470$	13.2138	−	4.80944i	0.609508	−	0.221843i
$471$	3.19917	+	12.1894i	0.147410	+	0.561659i
$472$	1.34218	−	1.12623i	0.0617790	−	0.0518387i
$473$	−1.35728	+	1.13889i	−0.0624076	+	0.0523662i
$474$	29.2186	−	28.9201i	1.34205	−	1.32834i
$475$	−12.8547	+	4.67871i	−0.589812	+	0.214674i
$476$	−1.41636	−	2.45321i	−0.0649188	−	0.112443i
$477$	11.4905	−	30.5889i	0.526113	−	1.40057i
$478$	−20.9892	+	36.3543i	−0.960022	+	1.66281i
$479$	−7.23745	+	41.0456i	−0.330688	+	1.87542i	0.135560	+	0.990769i	$0.456717\pi$
$479$	−7.23745	+	41.0456i	−0.330688	+	1.87542i	−0.466248	+	0.884654i	$0.654394\pi$
$480$	−3.42122	+	36.9206i	−0.156157	+	1.68519i
$481$	−6.35480	−	2.31296i	−0.289754	−	0.105462i
$482$	−7.12113	−	40.3859i	−0.324358	−	1.83953i
$483$	−2.07381	−	2.99431i	−0.0943618	−	0.136246i
$484$	−20.7077	−	17.3758i	−0.941258	−	0.789809i
$485$	14.8898			0.676112
$486$	23.9220	−	22.7244i	1.08513	−	1.03080i
$487$	4.02801			0.182527			0.0912634	−	0.995827i	$-0.470909\pi$
$487$	4.02801			0.182527			0.0912634	+	0.995827i	$0.470909\pi$
$488$	−0.789937	−	0.662836i	−0.0357588	−	0.0300052i
$489$	−12.2769	−	17.7263i	−0.555183	−	0.801611i
$490$	−5.97081	−	33.8622i	−0.269734	−	1.52974i
$491$	36.2922	+	13.2093i	1.63784	+	0.596126i	0.986660	−	0.162793i	$-0.0520504\pi$
$491$	36.2922	+	13.2093i	1.63784	+	0.596126i	0.651184	+	0.758920i	$0.274273\pi$
$492$	2.31677	−	25.0017i	0.104448	−	1.12716i
$493$	−0.898521	+	5.09577i	−0.0404674	+	0.229502i
$494$	−9.96769	+	17.2645i	−0.448468	+	0.776769i
$495$	−0.897004	+	2.38792i	−0.0403173	+	0.107329i
$496$	−12.1830	−	21.1015i	−0.547032	−	0.947487i
$497$	8.76759	−	3.19114i	0.393280	−	0.143142i
$498$	−12.2070	+	12.0823i	−0.547011	+	0.541423i
$499$	−3.11922	+	2.61734i	−0.139636	+	0.117168i	−0.709930	−	0.704272i	$-0.751274\pi$
$499$	−3.11922	+	2.61734i	−0.139636	+	0.117168i	0.570295	+	0.821440i	$0.306829\pi$
$500$	14.2781	−	11.9807i	0.638534	−	0.535794i
$501$	−1.02531	−	3.90664i	−0.0458076	−	0.174536i
$502$	−10.8911	+	3.96403i	−0.486093	+	0.176923i
$503$	1.71297	+	2.96695i	0.0763775	+	0.132290i	0.901684	−	0.432395i	$-0.142331\pi$
$503$	1.71297	+	2.96695i	0.0763775	+	0.132290i	−0.825307	+	0.564684i	$0.808998\pi$
$504$	2.58213	−	1.45565i	0.115017	−	0.0648398i
$505$	−13.6020	+	23.5594i	−0.605282	+	1.04838i
$506$	0.251909	−	1.42865i	0.0111987	−	0.0635111i
$507$	16.8487	−	7.75161i	0.748276	−	0.344261i
$508$	−12.1827	−	4.43412i	−0.540518	−	0.196732i
$509$	−2.12952	−	12.0771i	−0.0943893	−	0.535308i	−0.994933	−	0.100542i	$-0.967942\pi$
$509$	−2.12952	−	12.0771i	−0.0943893	−	0.535308i	0.900543	−	0.434766i	$-0.143169\pi$
$510$	11.5158	−	0.947957i	0.509930	−	0.0419762i
$511$	−11.3529	−	9.52619i	−0.502222	−	0.421414i
$512$	−28.1241			−1.24292
$513$	−8.84601	+	31.0903i	−0.390561	+	1.37267i
$514$	24.4791			1.07973
$515$	20.2522	+	16.9936i	0.892418	+	0.748827i
$516$	−10.2616	+	21.7143i	−0.451742	+	0.955920i
$517$	0.136257	+	0.772750i	0.00599257	+	0.0339855i
$518$	−8.63825	−	3.14407i	−0.379543	−	0.138142i
$519$	−5.06423	−	3.58490i	−0.222295	−	0.157360i
$520$	−0.716818	+	4.06528i	−0.0314345	+	0.178274i
$521$	−7.04117	+	12.1957i	−0.308479	+	0.534302i	−0.978030	−	0.208465i	$-0.933153\pi$
$521$	−7.04117	+	12.1957i	−0.308479	+	0.534302i	0.669551	+	0.742766i	$0.266487\pi$
$522$	−27.4943	−	5.13962i	−1.20339	−	0.224955i
$523$	−4.88956	−	8.46897i	−0.213806	−	0.370322i	0.739097	−	0.673599i	$-0.235253\pi$
$523$	−4.88956	−	8.46897i	−0.213806	−	0.370322i	−0.952902	+	0.303277i	$0.901919\pi$
$524$	16.8597	−	6.13643i	0.736520	−	0.268071i
$525$	−3.57227	−	0.976870i	−0.155906	−	0.0426341i
$526$	−10.5035	+	8.81348i	−0.457974	+	0.384286i
$527$	−7.80469	+	6.54892i	−0.339978	+	0.285275i
$528$	−1.48740	−	0.406744i	−0.0647309	−	0.0177013i
$529$	17.2176	−	6.26668i	0.748590	−	0.272464i
$530$	30.9283	+	53.5694i	1.34344	+	2.32691i
$531$	−3.36541	+	3.92812i	−0.146047	+	0.170466i
$532$	−7.50065	+	12.9915i	−0.325195	+	0.563254i
$533$	−1.53675	+	8.71534i	−0.0665640	+	0.377503i
$534$	46.3785	+	32.8307i	2.00699	+	1.42072i
$535$	13.0371	+	4.74511i	0.563642	+	0.205149i
$536$	−0.151144	−	0.857180i	−0.00652843	−	0.0370245i
$537$	14.7977	−	31.3131i	0.638569	−	1.35126i
$538$	22.4384	+	18.8280i	0.967387	+	0.811734i
$539$	1.91871			0.0826445
$540$	2.48272	+	34.4877i	0.106839	+	1.48411i
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$	−3.15426	−	2.64674i	−0.135487	−	0.113687i
$543$	16.8001	−	1.38294i	0.720959	−	0.0593477i
$544$	1.62750	+	9.22999i	0.0697783	+	0.395732i
$545$	−18.4323	−	6.70879i	−0.789551	−	0.287373i
$546$	−4.90300	+	2.25573i	−0.209829	+	0.0965365i
$547$	0.192798	−	1.09341i	0.00824343	−	0.0467508i	−0.980409	−	0.196975i	$-0.936888\pi$
$547$	0.192798	−	1.09341i	0.00824343	−	0.0467508i	0.988652	+	0.150224i	$0.0479994\pi$
$548$	−13.9497	+	24.1615i	−0.595900	+	1.03213i
$549$	2.62070	+	1.54916i	0.111849	+	0.0661164i
$550$	−0.737508	−	1.27740i	−0.0314474	−	0.0544686i
$551$	25.7495	−	9.37206i	1.09697	−	0.399263i
$552$	−0.966321	−	3.68186i	−0.0411293	−	0.156711i
$553$	−8.35257	+	7.00864i	−0.355188	+	0.298038i
$554$	−20.2236	+	16.9696i	−0.859216	+	0.720968i
$555$	14.7531	−	14.6023i	0.626232	−	0.619835i
$556$	−21.8607	+	7.95664i	−0.927100	+	0.337437i
$557$	−17.5201	−	30.3458i	−0.742352	−	1.28579i	−0.951422	−	0.307890i	$-0.900377\pi$
$557$	−17.5201	−	30.3458i	−0.742352	−	1.28579i	0.209070	−	0.977901i	$-0.432956\pi$
$558$	−34.9657	−	42.5503i	−1.48022	−	1.80130i
$559$	4.23247	−	7.33084i	0.179014	−	0.310062i
$560$	1.27269	−	7.21781i	0.0537812	−	0.305008i
$561$	−0.0594925	+	0.642022i	−0.00251178	+	0.0271062i
$562$	19.4042	+	7.06254i	0.818516	+	0.297915i
$563$	−6.73255	−	38.1822i	−0.283743	−	1.60919i	−0.709741	−	0.704463i	$-0.751188\pi$
$563$	−6.73255	−	38.1822i	−0.283743	−	1.60919i	0.425998	−	0.904724i	$-0.359923\pi$
$564$	6.05593	+	8.74396i	0.255001	+	0.368187i
$565$	−21.3258	−	17.8945i	−0.897183	−	0.752826i
$566$	−56.2413			−2.36400
$567$	−6.81774	+	5.48619i	−0.286318	+	0.230398i
$568$	9.75095			0.409141
$569$	−26.0213	−	21.8344i	−1.09087	−	0.915347i	−0.0940904	−	0.995564i	$-0.529994\pi$
$569$	−26.0213	−	21.8344i	−1.09087	−	0.915347i	−0.996777	+	0.0802169i	$0.974439\pi$
$570$	−34.8399	−	50.3042i	−1.45928	−	2.10701i
$571$	1.75191	+	9.93559i	0.0733153	+	0.415792i	0.999272	+	0.0381610i	$0.0121500\pi$
$571$	1.75191	+	9.93559i	0.0733153	+	0.415792i	−0.925956	+	0.377631i	$0.876739\pi$
$572$	−1.11818	−	0.406986i	−0.0467536	−	0.0170169i
$573$	−2.83775	+	30.6240i	−0.118549	+	1.27934i
$574$	−2.08894	+	11.8470i	−0.0871908	+	0.494484i
$575$	−2.37795	+	4.11873i	−0.0991674	+	0.171763i
$576$	−33.3522	+	5.52842i	−1.38968	+	0.230351i
$577$	6.06615	+	10.5069i	0.252537	+	0.437407i	0.964224	−	0.265090i	$-0.0854017\pi$
$577$	6.06615	+	10.5069i	0.252537	+	0.437407i	−0.711687	+	0.702497i	$0.752068\pi$
$578$	−31.0680	+	11.3078i	−1.29226	+	0.470344i
$579$	13.0295	−	12.8964i	0.541487	−	0.535956i
$580$	22.4541	−	18.8412i	0.932355	−	0.782339i
$581$	3.48957	−	2.92810i	0.144772	−	0.121478i
$582$	5.16470	+	19.6785i	0.214084	+	0.815700i
$583$	−3.24352	+	1.18055i	−0.134333	+	0.0488932i
$584$	−7.74416	−	13.4133i	−0.320456	−	0.555046i
$585$	0.125131	−	12.1862i	0.00517353	−	0.503839i
$586$	12.9722	−	22.4685i	0.535877	−	0.928167i
$587$	5.51319	−	31.2669i	0.227554	−	1.29052i	−0.630189	−	0.776442i	$-0.717023\pi$
$587$	5.51319	−	31.2669i	0.227554	−	1.29052i	0.857743	−	0.514079i	$-0.171866\pi$
$588$	23.6276	−	10.8704i	0.974387	−	0.448288i
$589$	50.7006	+	18.4535i	2.08908	+	0.760363i
$590$	−1.70036	−	9.64321i	−0.0700027	−	0.397005i
$591$	24.4412	−	2.01195i	1.00538	−	0.0827605i
$592$	9.61254	+	8.06588i	0.395073	+	0.331506i
$593$	13.4906			0.553993			0.276996	−	0.960871i	$-0.410661\pi$
$593$	13.4906			0.553993			0.276996	+	0.960871i	$0.410661\pi$
$594$	−3.46703	−	0.357210i	−0.142254	−	0.0146565i
$595$	−3.06459			−0.125636
$596$	36.1947	+	30.3710i	1.48259	+	1.24404i
$597$	−5.58009	+	11.8079i	−0.228378	+	0.483265i
$598$	1.20352	+	6.82550i	0.0492156	+	0.279115i
$599$	39.8715	+	14.5120i	1.62911	+	0.592946i	0.985086	−	0.172063i	$-0.0550432\pi$
$599$	39.8715	+	14.5120i	1.62911	+	0.592946i	0.644020	+	0.765009i	$0.277265\pi$
$600$	−3.15901	−	2.23622i	−0.128966	−	0.0912933i
$601$	−3.43906	+	19.5039i	−0.140282	+	0.795579i	0.830753	+	0.556641i	$0.187910\pi$
$601$	−3.43906	+	19.5039i	−0.140282	+	0.795579i	−0.971035	+	0.238938i	$0.923201\pi$
$602$	5.75330	−	9.96501i	0.234487	−	0.406144i
$603$	0.854034	+	2.42358i	0.0347789	+	0.0986958i
$604$	−4.97755	−	8.62136i	−0.202533	−	0.350798i
$605$	−27.4810	+	10.0022i	−1.11726	+	0.406649i
$606$	−35.8543	−	9.80470i	−1.45648	−	0.398289i
$607$	−27.5769	+	23.1397i	−1.11931	+	0.939213i	−0.998569	−	0.0534715i	$-0.982971\pi$
$607$	−27.5769	+	23.1397i	−1.11931	+	0.939213i	−0.120741	+	0.992684i	$0.538527\pi$
$608$	38.0215	−	31.9038i	1.54197	−	1.29387i
$609$	7.15571	+	1.95680i	0.289964	+	0.0792934i
$610$	−5.41548	+	1.97107i	−0.219266	+	0.0798064i
$611$	−1.87442	−	3.24659i	−0.0758310	−	0.131343i
$612$	2.90476	+	8.24315i	0.117418	+	0.333209i
$613$	−13.2314	+	22.9175i	−0.534411	+	0.925627i	0.464780	+	0.885426i	$0.346133\pi$
$613$	−13.2314	+	22.9175i	−0.534411	+	0.925627i	−0.999192	+	0.0402013i	$0.987200\pi$
$614$	9.73045	−	55.1841i	0.392689	−	2.22705i
$615$	−22.1712	−	15.6947i	−0.894031	−	0.632872i
$616$	−0.294234	−	0.107093i	−0.0118550	−	0.00431488i
$617$	8.52903	+	48.3705i	0.343366	+	1.94732i	0.319425	+	0.947611i	$0.396510\pi$
$617$	8.52903	+	48.3705i	0.343366	+	1.94732i	0.0239406	+	0.999713i	$0.492379\pi$
$618$	−15.4342	+	32.6599i	−0.620853	+	1.31377i
$619$	−18.5430	−	15.5595i	−0.745307	−	0.625387i	0.188950	−	0.981987i	$-0.439492\pi$
$619$	−18.5430	−	15.5595i	−0.745307	−	0.625387i	−0.934257	+	0.356600i	$0.883936\pi$
$620$	57.7145			2.31787
$621$	4.59193	+	10.2570i	0.184268	+	0.411598i
$622$	37.3785			1.49874
$623$	−11.5448	−	9.68725i	−0.462533	−	0.388111i
$624$	7.34229	−	0.604400i	0.293927	−	0.0241954i
$625$	−5.41077	−	30.6860i	−0.216431	−	1.22744i
$626$	19.1881	+	6.98388i	0.766909	+	0.279132i
$627$	3.10199	−	1.42714i	0.123882	−	0.0569945i
$628$	3.13347	−	17.7708i	0.125039	−	0.709132i
$629$	2.62345	−	4.54395i	0.104604	−	0.181179i
$630$	0.170094	−	16.5651i	0.00677671	−	0.659968i
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	0.634393	−	0.773010i	$-0.281250\pi$
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	−0.986643	+	0.162895i	$0.947917\pi$
$632$	−10.7079	+	3.89736i	−0.425938	+	0.155029i
$633$	2.29240	+	8.73447i	0.0911147	+	0.347164i
$634$	6.01629	−	5.04827i	0.238937	−	0.200492i
$635$	−10.7443	+	9.01555i	−0.426375	+	0.357771i
$636$	−33.2535	+	32.9138i	−1.31859	+	1.30512i
$637$	−8.61398	+	3.13523i	−0.341298	+	0.124222i
$638$	1.47732	+	2.55880i	0.0584878	+	0.101304i
$639$	−28.3998	+	4.70751i	−1.12348	+	0.186226i
$640$	10.5917	−	18.3454i	0.418676	−	0.725167i
$641$	6.60738	−	37.4723i	0.260976	−	1.48007i	−0.519278	−	0.854605i	$-0.673799\pi$
$641$	6.60738	−	37.4723i	0.260976	−	1.48007i	0.780254	−	0.625463i	$-0.215090\pi$
$642$	−1.74911	+	18.8758i	−0.0690319	+	0.744968i
$643$	−44.1115	−	16.0553i	−1.73959	−	0.633158i	−0.740352	−	0.672220i	$-0.765341\pi$
$643$	−44.1115	−	16.0553i	−1.73959	−	0.633158i	−0.999237	+	0.0390615i	$0.987563\pi$
$644$	0.905644	+	5.13616i	0.0356874	+	0.202393i
$645$	14.7937	+	21.3601i	0.582500	+	0.841053i
$646$	−11.8485	−	9.94211i	−0.466175	−	0.391167i
$647$	−28.2333			−1.10997			−0.554983	−	0.831862i	$-0.687275\pi$
$647$	−28.2333			−1.10997			−0.554983	+	0.831862i	$0.687275\pi$
$648$	−8.65643	+	2.95083i	−0.340057	+	0.115920i
$649$	0.546406			0.0214483
$650$	5.39834	+	4.52974i	0.211740	+	0.177671i
$651$	8.31660	+	12.0081i	0.325953	+	0.470634i
$652$	5.36140	+	30.4060i	0.209969	+	1.19079i
$653$	−33.1779	−	12.0758i	−1.29835	−	0.472562i	−0.401893	−	0.915687i	$-0.631647\pi$
$653$	−33.1779	−	12.0758i	−1.29835	−	0.472562i	−0.896460	+	0.443125i	$0.853870\pi$
$654$	2.47295	−	26.6872i	0.0967001	−	1.04355i
$655$	3.37057	−	19.1155i	0.131699	−	0.746902i
$656$	8.21052	−	14.2210i	0.320567	−	0.555239i
$657$	29.0306	+	35.3277i	1.13259	+	1.37826i
$658$	−2.54795	−	4.41318i	−0.0993295	−	0.172044i
$659$	−39.1793	+	14.2601i	−1.52621	+	0.555494i	−0.962689	−	0.270609i	$-0.912775\pi$
$659$	−39.1793	+	14.2601i	−1.52621	+	0.555494i	−0.563519	+	0.826103i	$0.690553\pi$
$660$	2.59593	−	2.56941i	0.101046	−	0.100014i
$661$	0.975874	−	0.818856i	0.0379571	−	0.0318498i	−0.623612	−	0.781734i	$-0.714335\pi$
$661$	0.975874	−	0.818856i	0.0379571	−	0.0318498i	0.661569	+	0.749884i	$0.269891\pi$
$662$	2.29075	−	1.92216i	0.0890324	−	0.0747070i
$663$	−0.781997	−	2.97956i	−0.0303702	−	0.115716i
$664$	4.47359	−	1.62825i	0.173609	−	0.0631885i
$665$	8.11461	+	14.0549i	0.314671	+	0.545027i
$666$	24.4158	+	14.4328i	0.946095	+	0.559258i
$667$	4.76334	−	8.25035i	0.184437	−	0.319455i
$668$	−1.00426	+	5.69543i	−0.0388559	+	0.220363i
$669$	−27.8413	+	12.8090i	−1.07641	+	0.495226i
$670$	−4.57108	−	1.66374i	−0.176596	−	0.0642758i
$671$	−0.0558427	−	0.316700i	−0.00215578	−	0.0122261i
$672$	13.3918	−	1.10238i	0.516598	−	0.0425252i
$673$	27.2963	+	22.9043i	1.05219	+	0.882896i	0.993323	−	0.115370i	$-0.0368053\pi$
$673$	27.2963	+	22.9043i	1.05219	+	0.882896i	0.0588715	+	0.998266i	$0.481250\pi$
$674$	27.4951			1.05907
$675$	10.2802	+	4.98793i	0.395687	+	0.191986i
$676$	−26.5561			−1.02139
$677$	13.7902	+	11.5714i	0.530002	+	0.444725i	0.868102	−	0.496386i	$-0.165340\pi$
$677$	13.7902	+	11.5714i	0.530002	+	0.444725i	−0.338100	+	0.941110i	$0.609784\pi$
$678$	16.2524	−	34.3913i	0.624169	−	1.32079i
$679$	−0.936996	−	5.31397i	−0.0359586	−	0.203931i
$680$	−3.00961	−	1.09541i	−0.115413	−	0.0420071i
$681$	−22.2968	−	15.7836i	−0.854414	−	0.604828i
$682$	−1.01023	+	5.72929i	−0.0386836	+	0.219386i
$683$	−19.8807	+	34.4344i	−0.760715	+	1.31760i	0.181768	+	0.983341i	$0.441818\pi$
$683$	−19.8807	+	34.4344i	−0.760715	+	1.31760i	−0.942483	+	0.334255i	$0.891515\pi$
$684$	30.1136	−	35.1486i	1.15142	−	1.34394i
$685$	15.0915	+	26.1393i	0.576617	+	0.998730i
$686$	−25.2468	+	9.18909i	−0.963928	+	0.350841i
$687$	2.95192	+	0.807229i	0.112623	+	0.0307977i
$688$	−12.0322	+	10.0962i	−0.458724	+	0.384915i
$689$	12.6327	−	10.6001i	0.481266	−	0.403830i
$690$	−20.5204	−	5.61149i	−0.781198	−	0.213626i
$691$	15.8251	−	5.75986i	0.602015	−	0.219115i	−0.0229909	−	0.999736i	$-0.507319\pi$
$691$	15.8251	−	5.75986i	0.602015	−	0.219115i	0.625006	+	0.780620i	$0.285097\pi$
$692$	4.44218	+	7.69408i	0.168866	+	0.292485i
$693$	0.908663	+	0.169860i	0.0345173	+	0.00645244i
$694$	−5.08038	+	8.79948i	−0.192849	+	0.334024i
$695$	−4.37036	+	24.7855i	−0.165777	+	0.940169i
$696$	6.32790	+	4.47944i	0.239859	+	0.169793i
$697$	−6.45216	−	2.34839i	−0.244393	−	0.0889518i
$698$	8.29833	+	47.0622i	0.314097	+	1.78133i
$699$	10.2854	−	21.7648i	0.389031	−	0.823220i
$700$	4.06223	+	3.40862i	0.153538	+	0.128834i
$701$	−8.96921			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$701$	−8.96921			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$702$	16.1488	−	4.06156i	0.609498	−	0.153294i
$703$	−27.7861			−1.04797
$704$	2.73570	+	2.29552i	0.103106	+	0.0865158i
$705$	11.4682	−	0.944032i	0.431916	−	0.0355543i
$706$	10.9186	+	61.9223i	0.410926	+	2.33048i
$707$	9.26398	+	3.37181i	0.348408	+	0.126810i
$708$	6.72864	−	3.09566i	0.252878	−	0.116342i
$709$	3.15026	−	17.8660i	0.118311	−	0.670973i	−0.866747	−	0.498748i	$-0.833793\pi$
$709$	3.15026	−	17.8660i	0.118311	−	0.670973i	0.985058	−	0.172225i	$-0.0550955\pi$
$710$	27.2477	−	47.1944i	1.02259	−	1.77117i
$711$	29.3054	−	16.5206i	1.09904	−	0.619572i
$712$	−7.87509	−	13.6401i	−0.295131	−	0.511183i
$713$	17.6267	−	6.41560i	0.660125	−	0.240266i
$714$	−1.06299	−	4.05019i	−0.0397814	−	0.151574i
$715$	−0.986166	+	0.827492i	−0.0368805	+	0.0309464i
$716$	−37.9890	+	31.8766i	−1.41972	+	1.19128i
$717$	−24.4144	+	24.1650i	−0.911771	+	0.902457i
$718$	26.6917	−	9.71498i	0.996125	−	0.362560i
$719$	−15.7860	−	27.3421i	−0.588718	−	1.01969i	−0.994401	−	0.105675i	$-0.966300\pi$
$719$	−15.7860	−	27.3421i	−0.588718	−	1.01969i	0.405683	−	0.914014i	$-0.367034\pi$
$720$	−7.95192	+	21.1688i	−0.296350	+	0.788916i
$721$	4.79034	−	8.29711i	0.178402	−	0.309001i
$722$	−7.24010	+	41.0606i	−0.269449	+	1.52812i
$723$	3.09636	−	33.4148i	0.115155	−	1.24271i
$724$	−22.6814	−	8.25536i	−0.842948	−	0.306808i
$725$	−1.68204	−	9.53930i	−0.0624693	−	0.354281i
$726$	−22.7511	−	32.8497i	−0.844374	−	1.21916i
$727$	29.4232	+	24.6890i	1.09125	+	0.915664i	0.996806	−	0.0798662i	$-0.0254493\pi$
$727$	29.4232	+	24.6890i	1.09125	+	0.915664i	0.0944407	+	0.995530i	$0.469894\pi$
$728$	1.49595			0.0554436
$729$	23.7874	−	12.7734i	0.881014	−	0.473090i
$730$	−86.5599			−3.20373
$731$	5.03111	+	4.22160i	0.186082	+	0.156142i
$732$	−2.48193	−	3.58358i	−0.0917346	−	0.132453i
$733$	−5.26680	−	29.8695i	−0.194534	−	1.10326i	−0.913081	−	0.407778i	$-0.866304\pi$
$733$	−5.26680	−	29.8695i	−0.194534	−	1.10326i	0.718547	−	0.695478i	$-0.244807\pi$
$734$	−15.8123	−	5.75521i	−0.583643	−	0.212429i
$735$	2.59619	−	28.0171i	0.0957618	−	1.03343i
$736$	2.99643	−	16.9936i	0.110450	−	0.626391i
$737$	0.135721	−	0.235076i	0.00499936	−	0.00865915i
$738$	13.0519	−	34.7456i	0.480448	−	1.27900i
$739$	−5.00127	−	8.66245i	−0.183975	−	0.318653i	0.759256	−	0.650792i	$-0.225563\pi$
$739$	−5.00127	−	8.66245i	−0.183975	−	0.318653i	−0.943230	+	0.332139i	$0.892230\pi$
$740$	−27.9300	+	10.1657i	−1.02673	+	0.373699i
$741$	−11.5943	+	11.4759i	−0.425928	+	0.421577i
$742$	17.1719	−	14.4089i	0.630400	−	0.528969i
$743$	27.7873	−	23.3163i	1.01942	−	0.855394i	0.0298642	−	0.999554i	$-0.490493\pi$
$743$	27.7873	−	23.3163i	1.01942	−	0.855394i	0.989554	+	0.144160i	$0.0460481\pi$
$744$	3.87523	+	14.7654i	0.142073	+	0.541324i
$745$	48.0337	−	17.4828i	1.75982	−	0.640521i
$746$	−12.0865	−	20.9344i	−0.442517	−	0.766461i
$747$	−12.2433	+	6.90205i	−0.447960	+	0.252533i
$748$	0.461619	−	0.799548i	0.0168785	−	0.0292344i
$749$	0.873058	−	4.95136i	0.0319008	−	0.180919i
$750$	25.0299	−	11.5156i	0.913964	−	0.420490i
$751$	13.6766	+	4.97788i	0.499067	+	0.181646i	0.579274	−	0.815133i	$-0.303336\pi$
$751$	13.6766	+	4.97788i	0.499067	+	0.181646i	−0.0802073	+	0.996778i	$0.525558\pi$
$752$	1.20791	+	6.85041i	0.0440480	+	0.249809i
$753$	−9.45226	+	0.778089i	−0.344460	+	0.0283551i
$754$	−10.8136	−	9.07366i	−0.393807	−	0.330443i
$755$	−10.7700			−0.391959
$756$	12.1519	−	3.05631i	0.441962	−	0.111157i
$757$	−45.5754			−1.65646			−0.828232	−	0.560385i	$-0.810653\pi$
$757$	−45.5754			−1.65646			−0.828232	+	0.560385i	$0.810653\pi$
$758$	39.1907	+	32.8849i	1.42347	+	1.19443i
$759$	0.507211	−	1.07330i	0.0184106	−	0.0389582i
$760$	2.94524	+	16.7033i	0.106835	+	0.605892i
$761$	−20.9040	−	7.60843i	−0.757769	−	0.275805i	−0.0658978	−	0.997826i	$-0.520991\pi$
$761$	−20.9040	−	7.60843i	−0.757769	−	0.275805i	−0.691871	+	0.722021i	$0.743213\pi$
$762$	−15.6418	−	11.0726i	−0.566643	−	0.401119i
$763$	−1.23436	+	7.00040i	−0.0446868	+	0.253431i
$764$	22.0189	−	38.1379i	0.796616	−	1.37978i
$765$	9.29438	+	1.73743i	0.336039	+	0.0628170i
$766$	9.99393	+	17.3100i	0.361096	+	0.625436i
$767$	−2.45307	+	0.892846i	−0.0885754	+	0.0322388i
$768$	−9.73542	−	2.66224i	−0.351297	−	0.0960654i
$769$	10.4679	−	8.78365i	0.377484	−	0.316747i	−0.434230	−	0.900802i	$-0.642979\pi$
$769$	10.4679	−	8.78365i	0.377484	−	0.316747i	0.811714	+	0.584056i	$0.198535\pi$
$770$	−1.34052	+	1.12483i	−0.0483091	+	0.0405361i
$771$	19.3220	+	5.28379i	0.695866	+	0.190291i
$772$	−24.6670	+	8.97807i	−0.887786	+	0.323128i
$773$	10.3270	+	17.8869i	0.371436	+	0.643345i	0.989787	−	0.142557i	$-0.0455323\pi$
$773$	10.3270	+	17.8869i	0.371436	+	0.643345i	−0.618351	+	0.785902i	$0.712199\pi$
$774$	−23.0983	+	26.9604i	−0.830252	+	0.969072i
$775$	9.53628	−	16.5173i	0.342553	−	0.593319i
$776$	0.979243	−	5.55356i	0.0351528	−	0.199361i
$777$	−6.13977	−	4.34626i	−0.220263	−	0.155921i
$778$	−5.06732	−	1.84436i	−0.181672	−	0.0661233i
$779$	6.31415	+	35.8093i	0.226228	+	1.28300i
$780$	−7.45585	+	15.7771i	−0.266962	+	0.564912i
$781$	2.32948	+	1.95466i	0.0833553	+	0.0699434i
$782$	−5.37736			−0.192294
$783$	−20.5927	−	9.99147i	−0.735922	−	0.357066i
$784$	17.0093			0.607474
$785$	−14.9547	−	12.5485i	−0.533757	−	0.447875i
$786$	26.4323	−	2.17584i	0.942807	−	0.0776097i
$787$	−4.28970	−	24.3281i	−0.152911	−	0.867202i	−0.960671	−	0.277690i	$-0.910431\pi$
$787$	−4.28970	−	24.3281i	−0.152911	−	0.867202i	0.807759	−	0.589512i	$-0.200680\pi$
$788$	−32.9976	−	12.0102i	−1.17549	−	0.427844i
$789$	−10.1931	+	4.68956i	−0.362884	+	0.166953i
$790$	−11.0586	+	62.7167i	−0.393449	+	2.23136i
$791$	−5.04429	+	8.73696i	−0.179354	+	0.310651i
$792$	0.831647	+	0.491606i	0.0295513	+	0.0174685i
$793$	0.768202	+	1.33057i	0.0272797	+	0.0472498i
$794$	7.30983	−	2.66056i	0.259416	−	0.0944197i
$795$	12.8497	+	48.9596i	0.455731	+	1.73642i
$796$	14.3253	−	12.0204i	0.507747	−	0.426051i
$797$	−23.4148	+	19.6473i	−0.829393	+	0.695943i	−0.955152	−	0.296117i	$-0.904308\pi$
$797$	−23.4148	+	19.6473i	−0.829393	+	0.695943i	0.125758	+	0.992061i	$0.459864\pi$
$798$	−15.7605	+	15.5995i	−0.557914	+	0.552215i
$799$	2.73319	−	0.994799i	0.0966933	−	0.0351935i
$800$	−8.77257	−	15.1945i	−0.310157	−	0.537208i
$801$	29.5214	+	35.9250i	1.04309	+	1.26935i
$802$	17.0904	−	29.6014i	0.603482	−	1.04526i
$803$	0.838750	−	4.75679i	0.0295988	−	0.167863i
$804$	0.339498	−	3.66374i	0.0119732	−	0.129210i
$805$	5.30203	+	1.92978i	0.186872	+	0.0680158i
$806$	−4.82646	−	27.3722i	−0.170005	−	0.964146i
$807$	13.6472	+	19.7048i	0.480405	+	0.693642i
$808$	7.89257	+	6.62265i	0.277660	+	0.232984i
$809$	46.8599			1.64751			0.823753	−	0.566949i	$-0.191876\pi$
$809$	46.8599			1.64751			0.823753	+	0.566949i	$0.191876\pi$
$810$	−9.90723	+	50.1426i	−0.348105	+	1.76183i
$811$	10.9984			0.386206			0.193103	−	0.981178i	$-0.438145\pi$
$811$	10.9984			0.386206			0.193103	+	0.981178i	$0.438145\pi$
$812$	−8.13717	−	6.82790i	−0.285559	−	0.239612i
$813$	−1.91845	−	2.76999i	−0.0672829	−	0.0971476i
$814$	−0.520260	−	2.95054i	−0.0182351	−	0.103416i
$815$	31.3879	+	11.4243i	1.09947	+	0.400175i
$816$	−0.527400	+	5.69151i	−0.0184627	+	0.199243i
$817$	6.03956	−	34.2521i	0.211298	−	1.19833i
$818$	9.71738	−	16.8310i	0.339760	−	0.588482i
$819$	−4.35697	+	0.722206i	−0.152245	+	0.0252359i
$820$	19.4479	+	33.6847i	0.679150	+	1.17632i
$821$	33.8133	−	12.3070i	1.18009	−	0.429518i	0.323857	−	0.946106i	$-0.395020\pi$
$821$	33.8133	−	12.3070i	1.18009	−	0.429518i	0.856234	+	0.516588i	$0.172798\pi$
$822$	−29.3112	+	29.0118i	−1.02235	+	1.01190i
$823$	−37.5259	+	31.4880i	−1.30807	+	1.09760i	−0.319383	+	0.947626i	$0.603476\pi$
$823$	−37.5259	+	31.4880i	−1.30807	+	1.09760i	−0.988689	+	0.149977i	$0.952080\pi$
$824$	7.67013	−	6.43600i	0.267202	−	0.224209i
$825$	−0.306410	−	1.16748i	−0.0106678	−	0.0406464i
$826$	−3.33453	+	1.21367i	−0.116023	+	0.0422290i
$827$	7.80533	+	13.5192i	0.271418	+	0.470109i	0.969225	−	0.246176i	$-0.0791742\pi$
$827$	7.80533	+	13.5192i	0.271418	+	0.470109i	−0.697807	+	0.716286i	$0.745841\pi$
$828$	0.165222	−	16.0905i	0.00574184	−	0.559185i
$829$	−5.73541	+	9.93401i	−0.199199	+	0.345023i	−0.948269	−	0.317468i	$-0.897167\pi$
$829$	−5.73541	+	9.93401i	−0.199199	+	0.345023i	0.749070	+	0.662491i	$0.230501\pi$
$830$	4.62012	−	26.2020i	0.160367	−	0.909485i
$831$	−19.6259	+	9.02932i	−0.680814	+	0.313224i
$832$	−16.0328	−	5.83547i	−0.555838	−	0.202308i
$833$	−1.23502	−	7.00416i	−0.0427910	−	0.242680i
$834$	−34.2727	+	2.82125i	−1.18677	+	0.0976918i
$835$	4.79290	+	4.02172i	0.165865	+	0.139177i
$836$	−4.88922			−0.169097
$837$	−18.4150	−	41.1334i	−0.636515	−	1.42178i
$838$	14.7716			0.510278
$839$	−0.517329	−	0.434090i	−0.0178602	−	0.0149865i	0.633814	−	0.773486i	$-0.281489\pi$
$839$	−0.517329	−	0.434090i	−0.0178602	−	0.0149865i	−0.651674	+	0.758499i	$0.725933\pi$
$840$	−1.96190	+	4.15153i	−0.0676921	+	0.143242i
$841$	−1.66646	−	9.45097i	−0.0574642	−	0.325895i
$842$	61.2815	+	22.3047i	2.11190	+	0.768669i
$843$	13.7918	+	9.76304i	0.475015	+	0.336257i
$844$	2.24532	−	12.7339i	0.0772872	−	0.438318i
$845$	−14.3649	+	24.8808i	−0.494168	+	0.855925i
$846$	5.22550	+	14.8290i	0.179656	+	0.509830i
$847$	5.29901	+	9.17815i	0.182076	+	0.315365i
$848$	−28.7537	+	10.4655i	−0.987408	+	0.359387i
$849$	−44.3928	−	12.1396i	−1.52356	−	0.416631i
$850$	−4.18838	+	3.51447i	−0.143660	+	0.120545i
$851$	−7.40014	+	6.20946i	−0.253674	+	0.212857i
$852$	39.7602	+	10.8728i	1.36216	+	0.372496i
$853$	−36.9823	+	13.4605i	−1.26625	+	0.460877i	−0.885862	−	0.463949i	$-0.846432\pi$
$853$	−36.9823	+	13.4605i	−1.26625	+	0.460877i	−0.380388	+	0.924827i	$0.624210\pi$
$854$	1.04424	+	1.80867i	0.0357331	+	0.0618915i
$855$	−16.6420	−	47.2267i	−0.569143	−	1.61512i
$856$	2.62721	−	4.55047i	0.0897963	−	0.155532i
$857$	5.67172	−	32.1659i	0.193742	−	1.09877i	−0.720457	−	0.693500i	$-0.756068\pi$
$857$	5.67172	−	32.1659i	0.193742	−	1.09877i	0.914199	−	0.405266i	$-0.132821\pi$
$858$	−1.43568	−	1.01630i	−0.0490134	−	0.0346959i
$859$	31.1946	+	11.3539i	1.06435	+	0.387391i	0.814060	−	0.580781i	$-0.197253\pi$
$859$	31.1946	+	11.3539i	1.06435	+	0.387391i	0.250287	+	0.968172i	$0.419475\pi$
$860$	−6.46046	−	36.6391i	−0.220300	−	1.24938i
$861$	−4.20602	+	8.90026i	−0.143341	+	0.303320i
$862$	−45.2332	−	37.9551i	−1.54065	−	1.29276i
$863$	22.6796			0.772024			0.386012	−	0.922494i	$-0.373852\pi$
$863$	22.6796			0.772024			0.386012	+	0.922494i	$0.373852\pi$
$864$	−41.2399	−	4.24897i	−1.40301	−	0.144553i
$865$	9.61158			0.326804
$866$	−31.0837	−	26.0823i	−1.05627	−	0.886312i
$867$	−26.9636	+	2.21958i	−0.915733	+	0.0753810i
$868$	−3.63190	−	20.5975i	−0.123275	−	0.699125i
$869$	−3.33935	−	1.21543i	−0.113280	−	0.0412305i
$870$	39.3628	−	18.1097i	1.33452	−	0.613978i
$871$	−0.225195	+	1.27714i	−0.00763043	+	0.0432743i
$872$	−3.71444	+	6.43360i	−0.125787	+	0.217869i
$873$	−0.170941	+	16.6476i	−0.00578549	+	0.563435i
$874$	14.2385	+	24.6618i	0.481625	+	0.834199i
$875$	−6.86670	+	2.49927i	−0.232137	+	0.0844909i
$876$	−16.6209	−	63.3287i	−0.561567	−	2.13968i
$877$	7.08113	−	5.94178i	0.239113	−	0.200640i	−0.515354	−	0.856977i	$-0.672340\pi$
$877$	7.08113	−	5.94178i	0.239113	−	0.200640i	0.754467	+	0.656338i	$0.227895\pi$
$878$	38.5072	−	32.3114i	1.29956	−	1.09046i
$879$	15.0891	−	14.9350i	0.508944	−	0.503745i
$880$	2.24466	−	0.816989i	0.0756674	−	0.0275407i
$881$	−3.89378	−	6.74422i	−0.131185	−	0.227219i	0.792949	−	0.609288i	$-0.208545\pi$
$881$	−3.89378	−	6.74422i	−0.131185	−	0.227219i	−0.924134	+	0.382070i	$0.875211\pi$
$882$	37.9282	−	6.28692i	1.27711	−	0.211692i
$883$	16.2309	−	28.1127i	0.546213	−	0.946068i	−0.452317	−	0.891857i	$-0.649402\pi$
$883$	16.2309	−	28.1127i	0.546213	−	0.946068i	0.998530	−	0.0542106i	$-0.0172642\pi$
$884$	−0.765938	+	4.34385i	−0.0257613	+	0.146099i
$885$	0.739338	−	7.97868i	0.0248526	−	0.268200i
$886$	46.4590	+	16.9097i	1.56082	+	0.568092i
$887$	−5.87759	−	33.3334i	−0.197350	−	1.11923i	−0.909032	−	0.416726i	$-0.863177\pi$
$887$	−5.87759	−	33.3334i	−0.197350	−	1.11923i	0.711682	−	0.702502i	$-0.247934\pi$
$888$	−4.47609	−	6.46289i	−0.150208	−	0.216880i
$889$	3.89365	+	3.26716i	0.130589	+	0.109577i
$890$	−88.0234			−2.95055
$891$	−2.65952	−	1.03031i	−0.0890972	−	0.0345167i
$892$	43.8822			1.46929
$893$	−11.7995	−	9.90095i	−0.394855	−	0.331323i
$894$	39.7665	+	57.4176i	1.32999	+	1.92033i
$895$	9.31630	+	52.8354i	0.311410	+	1.76609i
$896$	−7.21376	−	2.62560i	−0.240995	−	0.0877150i
$897$	−0.523306	+	5.64733i	−0.0174727	+	0.188559i
$898$	−1.77124	+	10.0452i	−0.0591069	+	0.335212i
$899$	−19.1024	+	33.0863i	−0.637101	+	1.10349i
$900$	−10.3876	−	12.6408i	−0.346253	−	0.421359i
$901$	6.39731	+	11.0805i	0.213125	+	0.369144i
$902$	−3.68428	+	1.34097i	−0.122673	+	0.0446494i
$903$	6.69218	−	6.62382i	0.222702	−	0.220427i
$904$	−8.07674	+	6.77719i	−0.268629	+	0.225406i
$905$	−20.0035	+	16.7850i	−0.664940	+	0.557951i
$906$	−3.73568	−	14.2337i	−0.124110	−	0.472882i
$907$	10.3929	−	3.78269i	0.345089	−	0.125602i	−0.163660	−	0.986517i	$-0.552330\pi$
$907$	10.3929	−	3.78269i	0.345089	−	0.125602i	0.508750	+	0.860915i	$0.330108\pi$
$908$	19.5580	+	33.8754i	0.649054	+	1.12420i
$909$	−26.1845	−	15.4782i	−0.868484	−	0.513381i
$910$	4.18022	−	7.24036i	0.138573	−	0.240016i
$911$	2.17845	−	12.3546i	0.0721751	−	0.409325i	−0.927219	−	0.374520i	$-0.877808\pi$
$911$	2.17845	−	12.3546i	0.0721751	−	0.409325i	0.999394	−	0.0348058i	$-0.0110813\pi$
$912$	27.4991	−	12.6516i	0.910586	−	0.418935i
$913$	1.39513	+	0.507785i	0.0461720	+	0.0168052i
$914$	1.79863	+	10.2005i	0.0594934	+	0.337404i
$915$	−4.70004	+	0.386897i	−0.155379	+	0.0127904i
$916$	−3.35679	−	2.81668i	−0.110912	−	0.0930659i
$917$	−7.03415			−0.232288
$918$	0.927658	+	12.8862i	0.0306173	+	0.425307i
$919$	−5.92909			−0.195583			−0.0977913	−	0.995207i	$-0.531178\pi$
$919$	−5.92909			−0.195583			−0.0977913	+	0.995207i	$0.531178\pi$
$920$	4.51713	+	3.79032i	0.148925	+	0.124963i
$921$	19.5920	−	41.4580i	0.645577	−	1.36609i
$922$	−10.2878	−	58.3452i	−0.338812	−	1.92150i
$923$	−13.6521	−	4.96897i	−0.449365	−	0.163555i
$924$	−1.08035	−	0.764763i	−0.0355408	−	0.0251588i
$925$	−1.70561	+	9.67300i	−0.0560801	+	0.318046i
$926$	−29.0775	+	50.3636i	−0.955545	+	1.65505i
$927$	−19.2322	+	22.4479i	−0.631669	+	0.737285i
$928$	17.5726	+	30.4366i	0.576848	+	0.999131i
$929$	9.42772	−	3.43141i	0.309314	−	0.112581i	−0.182699	−	0.983169i	$-0.558483\pi$
$929$	9.42772	−	3.43141i	0.309314	−	0.112581i	0.492013	+	0.870588i	$0.336261\pi$
$930$	82.2927	+	22.5037i	2.69849	+	0.737926i
$931$	−28.8525	+	24.2101i	−0.945603	+	0.793455i
$932$	−26.4050	+	22.1564i	−0.864925	+	0.725758i
$933$	29.5039	+	8.06811i	0.965913	+	0.264138i
$934$	−42.2587	+	15.3809i	−1.38275	+	0.503279i
$935$	−0.499405	−	0.864995i	−0.0163323	−	0.0282883i
$936$	−4.53696	−	0.848110i	−0.148295	−	0.0277214i
$937$	11.7671	−	20.3811i	0.384413	−	0.665823i	−0.607274	−	0.794492i	$-0.707737\pi$
$937$	11.7671	−	20.3811i	0.384413	−	0.665823i	0.991688	+	0.128669i	$0.0410705\pi$
$938$	−0.306113	+	1.73605i	−0.00999494	+	0.0566841i
$939$	13.6382	+	9.65429i	0.445066	+	0.315056i
$940$	−15.4829	−	5.63532i	−0.504997	−	0.183804i
$941$	−5.08781	−	28.8544i	−0.165858	−	0.940627i	−0.948175	−	0.317747i	$-0.897074\pi$
$941$	−5.08781	−	28.8544i	−0.165858	−	0.940627i	0.782317	−	0.622880i	$-0.214038\pi$
$942$	11.3970	−	24.1169i	0.371334	−	0.785770i
$943$	9.68405	+	8.12588i	0.315356	+	0.264615i
$944$	4.84388			0.157655
$945$	3.70981	−	13.0386i	0.120680	−	0.424144i
$946$	3.75023			0.121930
$947$	41.1074	+	34.4932i	1.33581	+	1.12088i	0.982681	+	0.185304i	$0.0593271\pi$
$947$	41.1074	+	34.4932i	1.33581	+	1.12088i	0.353130	+	0.935574i	$0.385117\pi$
$948$	−48.0080	+	3.95191i	−1.55923	+	0.128352i
$949$	4.00721	+	22.7260i	0.130079	+	0.737717i
$950$	27.2084	+	9.90307i	0.882759	+	0.321298i
$951$	5.83849	−	2.68613i	0.189326	−	0.0871036i
$952$	−0.201546	+	1.14302i	−0.00653214	+	0.0370456i
$953$	2.44828	−	4.24055i	0.0793076	−	0.137365i	−0.823644	−	0.567108i	$-0.808062\pi$
$953$	2.44828	−	4.24055i	0.0793076	−	0.137365i	0.902951	+	0.429743i	$0.141396\pi$
$954$	−60.2484	+	33.9644i	−1.95061	+	1.09964i
$955$	−23.8212	−	41.2596i	−0.770837	−	1.33513i
$956$	46.2205	−	16.8229i	1.49488	−	0.544092i
$957$	0.613778	+	2.33861i	0.0198406	+	0.0755965i
$958$	67.5792	−	56.7057i	2.18338	−	1.83208i
$959$	8.37906	−	7.03086i	0.270574	−	0.227038i
$960$	37.2211	−	36.8409i	1.20131	−	1.18904i
$961$	−41.5578	+	15.1258i	−1.34057	+	0.487929i
$962$	7.15698	+	12.3962i	0.230750	+	0.399671i
$963$	−5.45495	+	14.5216i	−0.175783	+	0.467954i
$964$	−24.0255	+	41.6134i	−0.773810	+	1.34028i
$965$	−4.93140	+	27.9674i	−0.158747	+	0.900302i
$966$	−0.711343	+	7.67657i	−0.0228871	+	0.246990i
$967$	−15.9683	−	5.81200i	−0.513507	−	0.186901i	0.0722523	−	0.997386i	$-0.476981\pi$
$967$	−15.9683	−	5.81200i	−0.513507	−	0.186901i	−0.585759	+	0.810485i	$0.699204\pi$
$968$	1.92330	+	10.9076i	0.0618172	+	0.350583i
$969$	−7.20639	−	10.4051i	−0.231503	−	0.334259i
$970$	−24.1427	−	20.2582i	−0.775177	−	0.650451i
$971$	−2.68374			−0.0861253			−0.0430627	−	0.999072i	$-0.513712\pi$
$971$	−2.68374			−0.0861253			−0.0430627	+	0.999072i	$0.513712\pi$
$972$	−38.5875	+	2.37987i	−1.23769	+	0.0763345i
$973$	9.12064			0.292394
$974$	−6.53113	−	5.48027i	−0.209271	−	0.175599i
$975$	3.28332	+	4.74068i	0.105150	+	0.151823i
$976$	−0.495044	−	2.80753i	−0.0158460	−	0.0898670i
$977$	−10.3301	−	3.75984i	−0.330488	−	0.120288i	0.171446	−	0.985193i	$-0.445156\pi$
$977$	−10.3301	−	3.75984i	−0.330488	−	0.120288i	−0.501935	+	0.864906i	$0.667378\pi$
$978$	−4.21114	+	45.4452i	−0.134657	+	1.45318i
$979$	0.852930	−	4.83721i	0.0272598	−	0.154598i
$980$	−20.1445	+	34.8914i	−0.643494	+	1.11456i
$981$	7.71239	−	20.5312i	0.246238	−	0.655511i
$982$	−40.8734	−	70.7948i	−1.30432	−	2.25915i
$983$	44.8944	−	16.3402i	1.43191	−	0.521172i	0.494431	−	0.869217i	$-0.335376\pi$
$983$	44.8944	−	16.3402i	1.43191	−	0.521172i	0.937478	+	0.348044i	$0.113154\pi$
$984$	−7.31189	+	7.23719i	−0.233094	+	0.230713i
$985$	−29.1018	+	24.4193i	−0.927260	+	0.778064i
$986$	8.38988	−	7.03994i	0.267188	−	0.224197i
$987$	−1.05859	−	4.03342i	−0.0336952	−	0.128385i
$988$	21.9500	−	7.98915i	0.698323	−	0.254169i
$989$	−6.04594	−	10.4719i	−0.192250	−	0.332986i
$990$	4.70328	−	2.65143i	0.149480	−	0.0842679i
$991$	−27.7503	+	48.0649i	−0.881517	+	1.52683i	−0.0318627	+	0.999492i	$0.510144\pi$
$991$	−27.7503	+	48.0649i	−0.881517	+	1.52683i	−0.849654	+	0.527340i	$0.823189\pi$
$992$	−12.0165	+	68.1492i	−0.381526	+	2.16374i
$993$	2.22305	−	1.02276i	0.0705462	−	0.0324564i
$994$	−18.5577	−	6.75445i	−0.588614	−	0.214238i
$995$	−3.51309	−	19.9237i	−0.111372	−	0.631624i
$996$	20.0570	−	1.65104i	0.635529	−	0.0523153i
$997$	−34.5078	−	28.9555i	−1.09287	−	0.917029i	−0.0959472	−	0.995386i	$-0.530588\pi$
$997$	−34.5078	−	28.9555i	−1.09287	−	0.917029i	−0.996925	+	0.0783575i	$0.975032\pi$
$998$	8.61859			0.272817
$999$	16.1568	+	16.6623i	0.511179	+	0.527172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.2.e.a.16.1	✓	12
3.2	odd	2		81.2.e.a.46.2		12
4.3	odd	2		432.2.u.c.97.2		12
5.2	odd	4		675.2.u.b.124.4		24
5.3	odd	4		675.2.u.b.124.1		24
5.4	even	2		675.2.l.c.151.2		12
9.2	odd	6		243.2.e.a.217.2		12
9.4	even	3		243.2.e.c.55.2		12
9.5	odd	6		243.2.e.b.55.1		12
9.7	even	3		243.2.e.d.217.1		12
27.2	odd	18		729.2.c.b.244.2		12
27.4	even	9		243.2.e.d.28.1		12
27.5	odd	18		81.2.e.a.37.2		12
27.7	even	9		729.2.a.a.1.2		6
27.11	odd	18		729.2.c.b.487.2		12
27.13	even	9		243.2.e.c.190.2		12
27.14	odd	18		243.2.e.b.190.1		12
27.16	even	9		729.2.c.e.487.5		12
27.20	odd	18		729.2.a.d.1.5		6
27.22	even	9	inner	27.2.e.a.22.1	yes	12
27.23	odd	18		243.2.e.a.28.2		12
27.25	even	9		729.2.c.e.244.5		12
108.103	odd	18		432.2.u.c.49.2		12
135.22	odd	36		675.2.u.b.49.1		24
135.49	even	18		675.2.l.c.76.2		12
135.103	odd	36		675.2.u.b.49.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.1	✓	12	1.1	even	1	trivial
27.2.e.a.22.1	yes	12	27.22	even	9	inner
81.2.e.a.37.2		12	27.5	odd	18
81.2.e.a.46.2		12	3.2	odd	2
243.2.e.a.28.2		12	27.23	odd	18
243.2.e.a.217.2		12	9.2	odd	6
243.2.e.b.55.1		12	9.5	odd	6
243.2.e.b.190.1		12	27.14	odd	18
243.2.e.c.55.2		12	9.4	even	3
243.2.e.c.190.2		12	27.13	even	9
243.2.e.d.28.1		12	27.4	even	9
243.2.e.d.217.1		12	9.7	even	3
432.2.u.c.49.2		12	108.103	odd	18
432.2.u.c.97.2		12	4.3	odd	2
675.2.l.c.76.2		12	135.49	even	18
675.2.l.c.151.2		12	5.4	even	2
675.2.u.b.49.1		24	135.22	odd	36
675.2.u.b.49.4		24	135.103	odd	36
675.2.u.b.124.1		24	5.3	odd	4
675.2.u.b.124.4		24	5.2	odd	4
729.2.a.a.1.2		6	27.7	even	9
729.2.a.d.1.5		6	27.20	odd	18
729.2.c.b.244.2		12	27.2	odd	18
729.2.c.b.487.2		12	27.11	odd	18
729.2.c.e.244.5		12	27.25	even	9
729.2.c.e.487.5		12	27.16	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62143 - 1.36054i) q^{2} +(-0.986166 - 1.42389i) q^{3} +(0.430663 + 2.44241i) q^{4} +(2.52129 + 0.917674i) q^{5} +(-0.338267 + 3.65046i) q^{6} +(0.168844 - 0.957561i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-1.05495 + 2.80839i) q^{9} +O(q^{10})\)	\(q+(-1.62143 - 1.36054i) q^{2} +(-0.986166 - 1.42389i) q^{3} +(0.430663 + 2.44241i) q^{4} +(2.52129 + 0.917674i) q^{5} +(-0.338267 + 3.65046i) q^{6} +(0.168844 - 0.957561i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-1.05495 + 2.80839i) q^{9} +(-2.83955 - 4.91825i) q^{10} +(0.297791 - 0.108387i) q^{11} +(3.05303 - 3.02185i) q^{12} +(-1.15981 + 0.973200i) q^{13} +(-1.57657 + 1.32290i) q^{14} +(-1.17974 - 4.49503i) q^{15} +(2.63991 - 0.960847i) q^{16} +(-0.587342 - 1.01731i) q^{17} +(5.53146 - 3.11830i) q^{18} +(-3.11040 + 5.38737i) q^{19} +(-1.15551 + 6.55323i) q^{20} +(-1.52997 + 0.703898i) q^{21} +(-0.630310 - 0.229414i) q^{22} +(0.375556 + 2.12988i) q^{23} +(-1.75413 + 0.144396i) q^{24} +(1.68454 + 1.41350i) q^{25} +3.20463 q^{26} +(5.03922 - 1.26740i) q^{27} +2.41147 q^{28} +(-3.37436 - 2.83142i) q^{29} +(-4.20280 + 8.89344i) q^{30} +(-1.50609 - 8.54146i) q^{31} +(-7.49746 - 2.72885i) q^{32} +(-0.448003 - 0.317135i) q^{33} +(-0.431752 + 2.44859i) q^{34} +(1.30443 - 2.25934i) q^{35} +(-7.31359 - 1.36716i) q^{36} +(2.23332 + 3.86823i) q^{37} +(12.3730 - 4.50341i) q^{38} +(2.52950 + 0.691717i) q^{39} +(2.08861 - 1.75255i) q^{40} +(4.47767 - 3.75721i) q^{41} +(3.43842 + 0.940269i) q^{42} +(-5.25381 + 1.91223i) q^{43} +(0.392973 + 0.680649i) q^{44} +(-5.23703 + 6.11267i) q^{45} +(2.28885 - 3.96441i) q^{46} +(-0.429965 + 2.43845i) q^{47} +(-3.97153 - 2.81139i) q^{48} +(5.68943 + 2.07078i) q^{49} +(-0.808243 - 4.58377i) q^{50} +(-0.869320 + 1.83955i) q^{51} +(-2.87645 - 2.41362i) q^{52} -10.8920 q^{53} +(-9.89507 - 4.80105i) q^{54} +0.850279 q^{55} +(-0.756896 - 0.635111i) q^{56} +(10.7384 - 0.883963i) q^{57} +(1.61901 + 9.18189i) q^{58} +(1.62023 + 0.589715i) q^{59} +(10.4706 - 4.81725i) q^{60} +(0.176214 - 0.999361i) q^{61} +(-9.17898 + 15.8985i) q^{62} +(2.51109 + 1.48436i) q^{63} +(5.63455 + 9.75933i) q^{64} +(-3.81731 + 1.38939i) q^{65} +(0.294929 + 1.12374i) q^{66} +(0.656156 - 0.550580i) q^{67} +(2.23174 - 1.87265i) q^{68} +(2.66237 - 2.63517i) q^{69} +(-5.18896 + 1.88863i) q^{70} +(4.79788 + 8.31018i) q^{71} +(1.93547 + 2.35530i) q^{72} +(7.62091 - 13.1998i) q^{73} +(1.64171 - 9.31057i) q^{74} +(0.351434 - 3.79256i) q^{75} +(-14.4977 - 5.27674i) q^{76} +(-0.0535070 - 0.303453i) q^{77} +(-3.16030 - 4.56306i) q^{78} +(-8.59024 - 7.20807i) q^{79} +7.53771 q^{80} +(-6.77415 - 5.92544i) q^{81} -12.3721 q^{82} +(3.58886 + 3.01141i) q^{83} +(-2.37811 - 3.43369i) q^{84} +(-0.547303 - 3.10391i) q^{85} +(11.1203 + 4.04747i) q^{86} +(-0.703969 + 7.59698i) q^{87} +(0.0559194 - 0.317135i) q^{88} +(7.74976 - 13.4230i) q^{89} +(16.8080 - 2.78607i) q^{90} +(0.736071 + 1.27491i) q^{91} +(-5.04032 + 1.83453i) q^{92} +(-10.6769 + 10.5678i) q^{93} +(4.01476 - 3.36879i) q^{94} +(-12.7861 + 10.7288i) q^{95} +(3.50815 + 13.3667i) q^{96} +(5.21481 - 1.89804i) q^{97} +(-6.40762 - 11.0983i) q^{98} +(-0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

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