LMFDB - Embedded newform 288.2.bf.a.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	288.59
Dual form			288.2.bf.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33971 + 0.452974i) q^{2} +(0.679302 + 1.59328i) q^{3} +(1.58963 - 1.21370i) q^{4} +(-2.26044 - 2.94587i) q^{5} +(-1.63178 - 1.82683i) q^{6} +(3.12162 + 0.836436i) q^{7} +(-1.57986 + 2.34607i) q^{8} +(-2.07710 + 2.16464i) q^{9} +O(q^{10})$	\(q+(-1.33971 + 0.452974i) q^{2} +(0.679302 + 1.59328i) q^{3} +(1.58963 - 1.21370i) q^{4} +(-2.26044 - 2.94587i) q^{5} +(-1.63178 - 1.82683i) q^{6} +(3.12162 + 0.836436i) q^{7} +(-1.57986 + 2.34607i) q^{8} +(-2.07710 + 2.16464i) q^{9} +(4.36273 + 2.92268i) q^{10} +(3.54236 - 0.466360i) q^{11} +(3.01361 + 1.70826i) q^{12} +(0.516010 - 3.91948i) q^{13} +(-4.56094 + 0.293433i) q^{14} +(3.15807 - 5.60266i) q^{15} +(1.05385 - 3.85868i) q^{16} +5.24229 q^{17} +(1.80218 - 3.84085i) q^{18} +(1.75861 + 4.24565i) q^{19} +(-7.16868 - 1.93933i) q^{20} +(0.787846 + 5.54181i) q^{21} +(-4.53447 + 2.22938i) q^{22} +(-0.277647 - 1.03619i) q^{23} +(-4.81115 - 0.923476i) q^{24} +(-2.27443 + 8.48829i) q^{25} +(1.08412 + 5.48470i) q^{26} +(-4.85986 - 1.83895i) q^{27} +(5.97741 - 2.45910i) q^{28} +(3.54092 + 2.71704i) q^{29} +(-1.69304 + 8.93644i) q^{30} +(4.01166 + 2.31613i) q^{31} +(0.336036 + 5.64686i) q^{32} +(3.14938 + 5.32718i) q^{33} +(-7.02313 + 2.37462i) q^{34} +(-4.59222 - 11.0866i) q^{35} +(-0.674581 + 5.96196i) q^{36} +(-6.64812 - 2.75374i) q^{37} +(-4.27918 - 4.89132i) q^{38} +(6.59537 - 1.84037i) q^{39} +(10.4824 - 0.649090i) q^{40} +(2.68188 - 0.718607i) q^{41} +(-3.56578 - 7.06753i) q^{42} +(-0.632622 - 4.80524i) q^{43} +(5.06501 - 5.04071i) q^{44} +(11.0719 + 1.22580i) q^{45} +(0.841333 + 1.26243i) q^{46} +(-4.22270 + 2.43797i) q^{47} +(6.86385 - 0.942138i) q^{48} +(2.98271 + 1.72207i) q^{49} +(-0.797902 - 12.4021i) q^{50} +(3.56110 + 8.35244i) q^{51} +(-3.93683 - 6.85681i) q^{52} +(1.94961 + 0.807553i) q^{53} +(7.34379 + 0.262272i) q^{54} +(-9.38113 - 9.38113i) q^{55} +(-6.89406 + 6.00208i) q^{56} +(-5.56989 + 5.68603i) q^{57} +(-5.97454 - 2.03610i) q^{58} +(-5.14661 + 3.94913i) q^{59} +(-1.77980 - 12.7391i) q^{60} +(7.64946 - 9.96896i) q^{61} +(-6.42359 - 1.28576i) q^{62} +(-8.29449 + 5.01983i) q^{63} +(-3.00807 - 7.41293i) q^{64} +(-12.7127 + 7.33967i) q^{65} +(-6.63231 - 5.71027i) q^{66} +(0.994715 - 7.55561i) q^{67} +(8.33329 - 6.36258i) q^{68} +(1.46234 - 1.14626i) q^{69} +(11.1742 + 12.7726i) q^{70} +(-3.32494 - 3.32494i) q^{71} +(-1.79687 - 8.29284i) q^{72} +(-10.1954 + 10.1954i) q^{73} +(10.1539 + 0.677783i) q^{74} +(-15.0693 + 2.14231i) q^{75} +(7.94849 + 4.61458i) q^{76} +(11.4480 + 1.50715i) q^{77} +(-8.00223 + 5.45308i) q^{78} +(1.24672 + 2.15938i) q^{79} +(-13.7493 + 5.61784i) q^{80} +(-0.371341 - 8.99234i) q^{81} +(-3.26742 + 2.17754i) q^{82} +(-4.89714 - 3.75771i) q^{83} +(7.97851 + 7.85322i) q^{84} +(-11.8499 - 15.4431i) q^{85} +(3.02417 + 6.15105i) q^{86} +(-1.92366 + 7.48738i) q^{87} +(-4.50232 + 9.04740i) q^{88} +(2.67909 - 2.67909i) q^{89} +(-15.3884 + 3.37306i) q^{90} +(4.88918 - 11.8035i) q^{91} +(-1.69899 - 1.31018i) q^{92} +(-0.965122 + 7.96506i) q^{93} +(4.55284 - 5.17894i) q^{94} +(8.53189 - 14.7777i) q^{95} +(-8.76878 + 4.37133i) q^{96} +(-2.46934 - 4.27703i) q^{97} +(-4.77601 - 0.955978i) q^{98} +(-6.34832 + 8.63661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.33971	+	0.452974i	−0.947316	+	0.320301i
$2$	−1.33971	+	0.452974i	−0.947316	+	0.320301i
$3$	0.679302	+	1.59328i	0.392195	+	0.919882i
$3$	0.679302	+	1.59328i	0.392195	+	0.919882i
$4$	1.58963	−	1.21370i	0.794815	−	0.606852i
$5$	−2.26044	−	2.94587i	−1.01090	−	1.31743i	−0.947608	−	0.319436i	$-0.896506\pi$
$5$	−2.26044	−	2.94587i	−1.01090	−	1.31743i	−0.0632930	−	0.997995i	$-0.520160\pi$
$6$	−1.63178	−	1.82683i	−0.666172	−	0.745798i
$7$	3.12162	+	0.836436i	1.17986	+	0.316143i	0.794872	−	0.606778i	$-0.207538\pi$
$7$	3.12162	+	0.836436i	1.17986	+	0.316143i	0.384990	+	0.922921i	$0.374205\pi$
$8$	−1.57986	+	2.34607i	−0.558566	+	0.829460i
$9$	−2.07710	+	2.16464i	−0.692365	+	0.721547i
$10$	4.36273	+	2.92268i	1.37962	+	0.924232i
$11$	3.54236	−	0.466360i	1.06806	−	0.140613i	0.424058	−	0.905635i	$-0.360605\pi$
$11$	3.54236	−	0.466360i	1.06806	−	0.140613i	0.644004	+	0.765022i	$0.277272\pi$
$12$	3.01361	+	1.70826i	0.869955	+	0.493131i
$13$	0.516010	−	3.91948i	0.143115	−	1.08707i	−0.757618	−	0.652698i	$-0.773637\pi$
$13$	0.516010	−	3.91948i	0.143115	−	1.08707i	0.900734	−	0.434372i	$-0.143030\pi$
$14$	−4.56094	+	0.293433i	−1.21896	+	0.0784233i
$15$	3.15807	−	5.60266i	0.815411	−	1.44660i
$16$	1.05385	−	3.85868i	0.263461	−	0.964670i
$17$	5.24229			1.27144			0.635721	−	0.771919i	$-0.280703\pi$
$17$	5.24229			1.27144			0.635721	+	0.771919i	$0.280703\pi$
$18$	1.80218	−	3.84085i	0.424777	−	0.905298i
$19$	1.75861	+	4.24565i	0.403452	+	0.974019i	0.986822	+	0.161812i	$0.0517338\pi$
$19$	1.75861	+	4.24565i	0.403452	+	0.974019i	−0.583370	+	0.812207i	$0.698266\pi$
$20$	−7.16868	−	1.93933i	−1.60296	−	0.433647i
$21$	0.787846	+	5.54181i	0.171922	+	1.20932i
$22$	−4.53447	+	2.22938i	−0.966753	+	0.475306i
$23$	−0.277647	−	1.03619i	−0.0578933	−	0.216061i	0.930919	−	0.365226i	$-0.119008\pi$
$23$	−0.277647	−	1.03619i	−0.0578933	−	0.216061i	−0.988812	+	0.149165i	$0.952342\pi$
$24$	−4.81115	−	0.923476i	−0.982072	−	0.188504i
$25$	−2.27443	+	8.48829i	−0.454886	+	1.69766i
$26$	1.08412	+	5.48470i	0.212614	+	1.07564i
$27$	−4.85986	−	1.83895i	−0.935281	−	0.353907i
$28$	5.97741	−	2.45910i	1.12962	−	0.464726i
$29$	3.54092	+	2.71704i	0.657532	+	0.504542i	0.882797	−	0.469755i	$-0.155658\pi$
$29$	3.54092	+	2.71704i	0.657532	+	0.504542i	−0.225264	+	0.974298i	$0.572325\pi$
$30$	−1.69304	+	8.93644i	−0.309105	+	1.63156i
$31$	4.01166	+	2.31613i	0.720515	+	0.415989i	0.814942	−	0.579542i	$-0.196769\pi$
$31$	4.01166	+	2.31613i	0.720515	+	0.415989i	−0.0944273	+	0.995532i	$0.530102\pi$
$32$	0.336036	+	5.64686i	0.0594034	+	0.998234i
$33$	3.14938	+	5.32718i	0.548236	+	0.927343i
$34$	−7.02313	+	2.37462i	−1.20446	+	0.407244i
$35$	−4.59222	−	11.0866i	−0.776226	−	1.87398i
$36$	−0.674581	+	5.96196i	−0.112430	+	0.993660i
$37$	−6.64812	−	2.75374i	−1.09294	−	0.452712i	−0.237912	−	0.971287i	$-0.576463\pi$
$37$	−6.64812	−	2.75374i	−1.09294	−	0.452712i	−0.855032	+	0.518575i	$0.826463\pi$
$38$	−4.27918	−	4.89132i	−0.694175	−	0.793477i
$39$	6.59537	−	1.84037i	1.05610	−	0.294694i
$40$	10.4824	−	0.649090i	1.65741	−	0.102630i
$41$	2.68188	−	0.718607i	0.418839	−	0.112228i	−0.0432433	−	0.999065i	$-0.513769\pi$
$41$	2.68188	−	0.718607i	0.418839	−	0.112228i	0.462082	+	0.886837i	$0.347102\pi$
$42$	−3.56578	−	7.06753i	−0.550212	−	1.09054i
$43$	−0.632622	−	4.80524i	−0.0964739	−	0.732792i	−0.969495	−	0.245110i	$-0.921176\pi$
$43$	−0.632622	−	4.80524i	−0.0964739	−	0.732792i	0.873021	−	0.487682i	$-0.162157\pi$
$44$	5.06501	−	5.04071i	0.763580	−	0.759916i
$45$	11.0719	+	1.22580i	1.65050	+	0.182732i
$46$	0.841333	+	1.26243i	0.124048	+	0.186135i
$47$	−4.22270	+	2.43797i	−0.615943	+	0.355615i	−0.775288	−	0.631608i	$-0.782395\pi$
$47$	−4.22270	+	2.43797i	−0.615943	+	0.355615i	0.159345	+	0.987223i	$0.449062\pi$
$48$	6.86385	−	0.942138i	0.990711	−	0.135986i
$49$	2.98271	+	1.72207i	0.426102	+	0.246010i
$50$	−0.797902	−	12.4021i	−0.112840	−	1.75392i
$51$	3.56110	+	8.35244i	0.498653	+	1.16958i
$52$	−3.93683	−	6.85681i	−0.545940	−	0.950869i
$53$	1.94961	+	0.807553i	0.267799	+	0.110926i	0.512542	−	0.858662i	$-0.328704\pi$
$53$	1.94961	+	0.807553i	0.267799	+	0.110926i	−0.244743	+	0.969588i	$0.578704\pi$
$54$	7.34379	+	0.262272i	0.999363	+	0.0356907i
$55$	−9.38113	−	9.38113i	−1.26495	−	1.26495i
$56$	−6.89406	+	6.00208i	−0.921258	+	0.802062i
$57$	−5.56989	+	5.68603i	−0.737750	+	0.753134i
$58$	−5.97454	−	2.03610i	−0.784496	−	0.267353i
$59$	−5.14661	+	3.94913i	−0.670031	+	0.514133i	−0.886837	−	0.462082i	$-0.847103\pi$
$59$	−5.14661	+	3.94913i	−0.670031	+	0.514133i	0.216806	+	0.976215i	$0.430436\pi$
$60$	−1.77980	−	12.7391i	−0.229771	−	1.64461i
$61$	7.64946	−	9.96896i	0.979412	−	1.27640i	0.0184171	−	0.999830i	$-0.494137\pi$
$61$	7.64946	−	9.96896i	0.979412	−	1.27640i	0.960995	−	0.276565i	$-0.0891960\pi$
$62$	−6.42359	−	1.28576i	−0.815797	−	0.163292i
$63$	−8.29449	+	5.01983i	−1.04501	+	0.632439i
$64$	−3.00807	−	7.41293i	−0.376009	−	0.926616i
$65$	−12.7127	+	7.33967i	−1.57681	+	0.910375i
$66$	−6.63231	−	5.71027i	−0.816381	−	0.702886i
$67$	0.994715	−	7.55561i	0.121524	−	0.923065i	−0.816707	−	0.577053i	$-0.804203\pi$
$67$	0.994715	−	7.55561i	0.121524	−	0.923065i	0.938230	−	0.346011i	$-0.112464\pi$
$68$	8.33329	−	6.36258i	1.01056	−	0.771577i
$69$	1.46234	−	1.14626i	0.176045	−	0.137993i
$70$	11.1742	+	12.7726i	1.33557	+	1.52662i
$71$	−3.32494	−	3.32494i	−0.394598	−	0.394598i	0.481725	−	0.876323i	$-0.340011\pi$
$71$	−3.32494	−	3.32494i	−0.394598	−	0.394598i	−0.876323	+	0.481725i	$0.840011\pi$
$72$	−1.79687	−	8.29284i	−0.211763	−	0.977321i
$73$	−10.1954	+	10.1954i	−1.19328	+	1.19328i	−0.217138	+	0.976141i	$0.569672\pi$
$73$	−10.1954	+	10.1954i	−1.19328	+	1.19328i	−0.976141	+	0.217138i	$0.930328\pi$
$74$	10.1539	+	0.677783i	1.18037	+	0.0787907i
$75$	−15.0693	+	2.14231i	−1.74005	+	0.247372i
$76$	7.94849	+	4.61458i	0.911754	+	0.529329i
$77$	11.4480	+	1.50715i	1.30462	+	0.171756i
$78$	−8.00223	+	5.45308i	−0.906074	+	0.617440i
$79$	1.24672	+	2.15938i	0.140267	+	0.242949i	0.927597	−	0.373582i	$-0.121871\pi$
$79$	1.24672	+	2.15938i	0.140267	+	0.242949i	−0.787330	+	0.616531i	$0.788537\pi$
$80$	−13.7493	+	5.61784i	−1.53722	+	0.628093i
$81$	−0.371341	−	8.99234i	−0.0412601	−	0.999148i
$82$	−3.26742	+	2.17754i	−0.360826	+	0.240469i
$83$	−4.89714	−	3.75771i	−0.537531	−	0.412462i	0.303999	−	0.952672i	$-0.401678\pi$
$83$	−4.89714	−	3.75771i	−0.537531	−	0.412462i	−0.841530	+	0.540210i	$0.818345\pi$
$84$	7.97851	+	7.85322i	0.870526	+	0.856857i
$85$	−11.8499	−	15.4431i	−1.28530	−	1.67504i
$86$	3.02417	+	6.15105i	0.326105	+	0.663285i
$87$	−1.92366	+	7.48738i	−0.206238	+	0.802731i
$88$	−4.50232	+	9.04740i	−0.479949	+	0.964456i
$89$	2.67909	−	2.67909i	0.283983	−	0.283983i	−0.550712	−	0.834695i	$-0.685644\pi$
$89$	2.67909	−	2.67909i	0.283983	−	0.283983i	0.834695	+	0.550712i	$0.185644\pi$
$90$	−15.3884	+	3.37306i	−1.62208	+	0.355552i
$91$	4.88918	−	11.8035i	0.512526	−	1.23735i
$92$	−1.69899	−	1.31018i	−0.177131	−	0.136596i
$93$	−0.965122	+	7.96506i	−0.100079	+	0.825938i
$94$	4.55284	−	5.17894i	0.469589	−	0.534167i
$95$	8.53189	−	14.7777i	0.875353	−	1.51616i
$96$	−8.76878	+	4.37133i	−0.894960	+	0.446147i
$97$	−2.46934	−	4.27703i	−0.250724	−	0.434266i	0.713002	−	0.701162i	$-0.247335\pi$
$97$	−2.46934	−	4.27703i	−0.250724	−	0.434266i	−0.963725	+	0.266896i	$0.914002\pi$
$98$	−4.77601	−	0.955978i	−0.482450	−	0.0965684i
$99$	−6.34832	+	8.63661i	−0.638030	+	0.868012i
$100$	6.68677	+	16.2537i	0.668677	+	1.62537i
$101$	−7.12634	+	0.938201i	−0.709098	+	0.0933545i	−0.476444	−	0.879205i	$-0.658074\pi$
$101$	−7.12634	+	0.938201i	−0.709098	+	0.0933545i	−0.232654	+	0.972560i	$0.574741\pi$
$102$	−8.55426	−	9.57674i	−0.846998	−	0.948239i
$103$	2.03704	+	7.60234i	0.200716	+	0.749081i	0.990713	+	0.135971i	$0.0434153\pi$
$103$	2.03704	+	7.60234i	0.200716	+	0.749081i	−0.789997	+	0.613110i	$0.789918\pi$
$104$	8.38015	+	7.40284i	0.821742	+	0.725908i
$105$	14.5446	−	14.8478i	1.41940	−	1.44900i
$106$	−2.97770	−	0.198765i	−0.289220	−	0.0193057i
$107$	4.00430	−	9.66723i	0.387110	−	0.934566i	−0.603439	−	0.797409i	$-0.706203\pi$
$107$	4.00430	−	9.66723i	0.387110	−	0.934566i	0.990549	−	0.137157i	$-0.0437966\pi$
$108$	−9.95733	+	2.97517i	−0.958144	+	0.286286i
$109$	−10.3891	+	4.30331i	−0.995097	+	0.412183i	−0.819997	−	0.572368i	$-0.806025\pi$
$109$	−10.3891	+	4.30331i	−0.995097	+	0.412183i	−0.175100	+	0.984551i	$0.556025\pi$
$110$	16.8174	+	8.31856i	1.60347	+	0.793144i
$111$	−0.128597	−	12.4630i	−0.0122059	−	1.18293i
$112$	6.51724	−	11.1639i	0.615822	−	1.05489i
$113$	−8.60134	+	14.8980i	−0.809146	+	1.40148i	0.104309	+	0.994545i	$0.466737\pi$
$113$	−8.60134	+	14.8980i	−0.809146	+	1.40148i	−0.913456	+	0.406938i	$0.866597\pi$
$114$	4.88640	−	10.1406i	0.457653	−	0.949757i
$115$	−2.42488	+	3.16016i	−0.226121	+	0.294687i
$116$	8.92644	+	0.0214644i	0.828799	+	0.00199292i
$117$	7.41247	+	9.25812i	0.685284	+	0.855914i
$118$	5.10609	−	7.62195i	0.470054	−	0.701658i
$119$	16.3644	+	4.38484i	1.50012	+	0.401957i
$120$	8.15490	+	16.2605i	0.744437	+	1.48437i
$121$	1.70563	−	0.457022i	0.155057	−	0.0415474i
$122$	−5.73235	+	16.8205i	−0.518983	+	1.52286i
$123$	2.96675	+	3.78484i	0.267503	+	0.341267i
$124$	9.18815	−	1.18717i	0.825120	−	0.106611i
$125$	12.9939	−	5.38226i	1.16221	−	0.481404i
$126$	8.83833	−	10.4823i	0.787381	−	0.933836i
$127$		−	2.20403i		−	0.195576i	−0.995207	−	0.0977882i	$-0.968823\pi$
$127$		−	2.20403i		−	0.195576i	0.995207	−	0.0977882i	$-0.0311768\pi$
$128$	7.38780	+	8.56858i	0.652995	+	0.757362i
$129$	7.22636	−	4.27215i	0.636245	−	0.376142i
$130$	13.7066	−	15.5915i	1.20215	−	1.36747i
$131$	18.4954	+	2.43497i	1.61595	+	0.212744i	0.883620	−	0.468204i	$-0.155099\pi$
$131$	18.4954	+	2.43497i	1.61595	+	0.212744i	0.732332	+	0.680948i	$0.238432\pi$
$132$	11.4720	+	4.64583i	0.998506	+	0.404367i
$133$	1.93849	+	14.7243i	0.168088	+	1.27676i
$134$	2.08987	+	10.5729i	0.180537	+	0.913358i
$135$	5.56812	+	18.4734i	0.479228	+	1.58993i
$136$	−8.28209	+	12.2988i	−0.710183	+	1.05461i
$137$	1.77162	−	6.61179i	0.151360	−	0.564883i	−0.848030	−	0.529949i	$-0.822211\pi$
$137$	1.77162	−	6.61179i	0.151360	−	0.564883i	0.999390	−	0.0349343i	$-0.0111222\pi$
$138$	−1.43988	+	2.19805i	−0.122571	+	0.187110i
$139$	−2.89296	+	2.21985i	−0.245378	+	0.188285i	−0.724127	−	0.689667i	$-0.757757\pi$
$139$	−2.89296	+	2.21985i	−0.245378	+	0.188285i	0.478749	+	0.877952i	$0.341090\pi$
$140$	−20.7558	−	12.0500i	−1.75418	−	1.01841i
$141$	−6.75287	−	5.07182i	−0.568694	−	0.427125i
$142$	5.96056	+	2.94834i	0.500199	+	0.247419i
$143$		−	14.1249i		−	1.18118i
$144$	6.16372	+	10.2960i	0.513643	+	0.858004i
$145$		−	16.5728i		−	1.37630i
$146$	9.04058	−	18.2771i	0.748204	−	1.51262i
$147$	−0.717579	+	5.92211i	−0.0591849	+	0.488447i
$148$	−13.9103	+	3.69142i	−1.14342	+	0.303433i
$149$	−10.8658	+	8.33759i	−0.890157	+	0.683042i	−0.949017	−	0.315224i	$-0.897920\pi$
$149$	−10.8658	+	8.33759i	−0.890157	+	0.683042i	0.0588597	+	0.998266i	$0.481254\pi$
$150$	19.2180	−	9.69605i	1.56914	−	0.791679i
$151$	−5.40484	+	20.1712i	−0.439840	+	1.64151i	0.289372	+	0.957217i	$0.406554\pi$
$151$	−5.40484	+	20.1712i	−0.439840	+	1.64151i	−0.729212	+	0.684288i	$0.760113\pi$
$152$	−12.7389	−	2.58173i	−1.03326	−	0.209406i
$153$	−10.8887	+	11.3477i	−0.880302	+	0.917405i
$154$	−16.0196	+	3.16649i	−1.29090	+	0.255163i
$155$	−2.24511	−	17.0533i	−0.180331	−	1.36975i
$156$	8.25054	−	10.9303i	0.660572	−	0.875127i
$157$	−10.2086	−	1.34399i	−0.814738	−	0.107262i	−0.288370	−	0.957519i	$-0.593113\pi$
$157$	−10.2086	−	1.34399i	−0.814738	−	0.107262i	−0.526368	+	0.850257i	$0.676447\pi$
$158$	−2.64838	−	2.32820i	−0.210694	−	0.185222i
$159$	0.0377119	+	3.65484i	0.00299074	+	0.289848i
$160$	15.8753	−	13.7543i	1.25505	−	1.08738i
$161$		−	3.46683i		−	0.273224i
$162$	4.57078	+	11.8789i	0.359114	+	0.933294i
$163$	−12.0677	+	4.99859i	−0.945213	+	0.391520i	−0.801430	−	0.598089i	$-0.795927\pi$
$163$	−12.0677	+	4.99859i	−0.945213	+	0.391520i	−0.143784	+	0.989609i	$0.545927\pi$
$164$	3.39102	−	4.39733i	0.264794	−	0.343374i
$165$	8.57417	−	21.3194i	0.667498	−	1.65971i
$166$	8.26288	+	2.81595i	0.641324	+	0.218560i
$167$	5.18514	−	1.38935i	0.401238	−	0.107511i	−0.0525561	−	0.998618i	$-0.516737\pi$
$167$	5.18514	−	1.38935i	0.401238	−	0.107511i	0.453794	+	0.891107i	$0.350070\pi$
$168$	−14.2462	−	6.90696i	−1.09912	−	0.532884i
$169$	−2.53906	−	0.680339i	−0.195312	−	0.0523337i
$170$	22.8707	+	15.3215i	1.75410	+	1.17511i
$171$	−12.8431	−	5.01187i	−0.982136	−	0.383267i
$172$	−6.83777	−	6.87073i	−0.521375	−	0.523889i
$173$	−4.82272	+	6.28509i	−0.366665	+	0.477847i	−0.939854	−	0.341576i	$-0.889039\pi$
$173$	−4.82272	+	6.28509i	−0.366665	+	0.477847i	0.573189	+	0.819423i	$0.305706\pi$
$174$	−0.814443	−	10.9023i	−0.0617427	−	0.826498i
$175$	−14.1998	+	24.5948i	−1.07341	+	1.85919i
$176$	1.93356	−	14.1603i	0.145748	−	1.06737i
$177$	−9.78818	−	5.51734i	−0.735725	−	0.414709i
$178$	−2.37564	+	4.80275i	−0.178062	+	0.359982i
$179$	−17.6401	+	7.30675i	−1.31848	+	0.546132i	−0.927347	−	0.374202i	$-0.877917\pi$
$179$	−17.6401	+	7.30675i	−1.31848	+	0.546132i	−0.391132	+	0.920334i	$0.627917\pi$
$180$	19.0880	−	11.4894i	1.42273	−	0.856372i
$181$	−6.46998	+	15.6199i	−0.480910	+	1.16102i	0.478267	+	0.878214i	$0.341265\pi$
$181$	−6.46998	+	15.6199i	−0.480910	+	1.16102i	−0.959177	+	0.282805i	$0.908735\pi$
$182$	−1.20338	+	18.0279i	−0.0892007	+	1.33632i
$183$	21.0797	+	5.41580i	1.55825	+	0.400347i
$184$	2.86962	+	0.985662i	0.211551	+	0.0726639i
$185$	6.91554	+	25.8091i	0.508441	+	1.89753i
$186$	−2.31498	−	11.1080i	−0.169743	−	0.814479i
$187$	18.5701	−	2.44479i	1.35798	−	0.178781i
$188$	−3.75354	+	9.00058i	−0.273755	+	0.656435i
$189$	−13.6325	−	9.80548i	−0.991616	−	0.713244i
$190$	−4.73634	+	23.6625i	−0.343610	+	1.71665i
$191$	1.24027	+	2.14820i	0.0897425	+	0.155439i	0.907402	−	0.420263i	$-0.138062\pi$
$191$	1.24027	+	2.14820i	0.0897425	+	0.155439i	−0.817660	+	0.575702i	$0.804729\pi$
$192$	9.76750	−	9.82833i	0.704908	−	0.709298i
$193$	−5.65854	+	9.80089i	−0.407311	+	0.705483i	−0.994587	−	0.103903i	$-0.966867\pi$
$193$	−5.65854	+	9.80089i	−0.407311	+	0.705483i	0.587276	+	0.809386i	$0.300200\pi$
$194$	5.24558	+	4.61142i	0.376610	+	0.331080i
$195$	−20.3299	−	15.2690i	−1.45586	−	1.09344i
$196$	6.83149	−	0.882676i	0.487963	−	0.0630483i
$197$	3.97340	−	9.59264i	0.283093	−	0.683448i	−0.716811	−	0.697267i	$-0.754399\pi$
$197$	3.97340	−	9.59264i	0.283093	−	0.683448i	0.999905	+	0.0138197i	$0.00439908\pi$
$198$	4.59273	−	14.4461i	0.326391	−	1.02664i
$199$	11.9966	−	11.9966i	0.850417	−	0.850417i	−0.139767	−	0.990184i	$-0.544635\pi$
$199$	11.9966	−	11.9966i	0.850417	−	0.850417i	0.990184	+	0.139767i	$0.0446354\pi$
$200$	−16.3208	−	18.7463i	−1.15406	−	1.32556i
$201$	12.7139	−	3.54768i	0.896771	−	0.250234i
$202$	9.12223	−	4.48496i	0.641838	−	0.315561i
$203$	8.78077	+	11.4433i	0.616290	+	0.803164i
$204$	15.7982	+	8.95517i	1.10610	+	0.626987i
$205$	−8.17915	−	6.27609i	−0.571257	−	0.438341i
$206$	−6.17270	−	9.26218i	−0.430072	−	0.645327i
$207$	2.81968	+	1.55126i	0.195981	+	0.107820i
$208$	−14.5802	−	6.12165i	−1.01096	−	0.424460i
$209$	8.20961	+	14.2195i	0.567871	+	0.983581i
$210$	−12.7598	+	26.4801i	−0.880508	+	1.82730i
$211$	−1.59946	−	0.210572i	−0.110111	−	0.0144964i	0.0752693	−	0.997163i	$-0.476018\pi$
$211$	−1.59946	−	0.210572i	−0.110111	−	0.0144964i	−0.185380	+	0.982667i	$0.559352\pi$
$212$	4.07928	−	1.08253i	0.280166	−	0.0743487i
$213$	3.03893	−	7.55621i	0.208224	−	0.517743i
$214$	−0.985585	+	14.7651i	−0.0673732	+	1.00932i
$215$	−12.7256	+	12.7256i	−0.867878	+	0.867878i
$216$	11.9922	−	8.49627i	0.815967	−	0.578098i
$217$	10.5856	+	10.5856i	0.718596	+	0.718596i
$218$	11.9691	−	10.4712i	0.810649	−	0.709198i
$219$	−23.1699	−	9.31837i	−1.56567	−	0.629677i
$220$	−26.2984	−	3.52661i	−1.77304	−	0.237764i
$221$	2.70507	−	20.5471i	0.181963	−	1.38214i
$222$	5.81767	+	16.6385i	0.390457	+	1.11670i
$223$	−5.19834	+	3.00126i	−0.348107	+	0.200980i	−0.663851	−	0.747865i	$-0.731079\pi$
$223$	−5.19834	+	3.00126i	−0.348107	+	0.200980i	0.315744	+	0.948844i	$0.397746\pi$
$224$	−3.67426	+	17.9084i	−0.245497	+	1.19656i
$225$	−13.6499	−	22.5543i	−0.909993	−	1.50362i
$226$	4.77490	−	23.8551i	0.317621	−	1.58682i
$227$	−10.4554	+	13.6258i	−0.693951	+	0.904374i	−0.998847	−	0.0480115i	$-0.984712\pi$
$227$	−10.4554	+	13.6258i	−0.693951	+	0.904374i	0.304896	+	0.952386i	$0.401378\pi$
$228$	−1.95290	+	15.7989i	−0.129334	+	1.04631i
$229$	13.0911	−	10.0452i	0.865085	−	0.663803i	−0.0777830	−	0.996970i	$-0.524784\pi$
$229$	13.0911	−	10.0452i	0.865085	−	0.663803i	0.942868	+	0.333168i	$0.108117\pi$
$230$	1.81715	−	5.33210i	0.119820	−	0.351588i
$231$	5.37532	+	19.2637i	0.353670	+	1.26746i
$232$	−11.9685	+	4.01468i	−0.785773	+	0.263577i
$233$	3.82586	+	3.82586i	0.250640	+	0.250640i	0.821233	−	0.570593i	$-0.193287\pi$
$233$	3.82586	+	3.82586i	0.250640	+	0.250640i	−0.570593	+	0.821233i	$0.693287\pi$
$234$	−14.1242	−	9.04552i	−0.923330	−	0.591324i
$235$	16.7271	+	6.92859i	1.09116	+	0.451972i
$236$	−3.38812	+	12.5241i	−0.220548	+	0.815250i
$237$	−2.59360	+	3.45324i	−0.168473	+	0.224312i
$238$	−23.9098	+	1.53826i	−1.54984	+	0.0997106i
$239$	−13.4526	−	7.76688i	−0.870179	−	0.502398i	−0.00277108	−	0.999996i	$-0.500882\pi$
$239$	−13.4526	−	7.76688i	−0.870179	−	0.502398i	−0.867408	+	0.497598i	$0.834215\pi$
$240$	−18.2907	−	18.0903i	−1.18066	−	1.16773i
$241$	22.2318	−	12.8356i	1.43208	−	0.826811i	0.434799	−	0.900528i	$-0.356820\pi$
$241$	22.2318	−	12.8356i	1.43208	−	0.826811i	0.997279	+	0.0737172i	$0.0234862\pi$
$242$	−2.07802	+	1.38488i	−0.133580	+	0.0890234i
$243$	14.0751	−	6.70017i	0.902917	−	0.429816i
$244$	0.0604299	−	25.1311i	0.00386863	−	1.60886i
$245$	−1.66926	−	12.6793i	−0.106645	−	0.810051i
$246$	−5.68901	−	3.72671i	−0.362718	−	0.237607i
$247$	17.5482	−	4.70203i	1.11657	−	0.299183i
$248$	−11.7717	+	5.75245i	−0.747502	+	0.365281i
$249$	2.66045	−	10.3552i	0.168599	−	0.656231i
$250$	−14.9700	+	13.0966i	−0.946788	+	0.828299i
$251$	27.7645	+	11.5004i	1.75248	+	0.725901i	0.997539	+	0.0701069i	$0.0223340\pi$
$251$	27.7645	+	11.5004i	1.75248	+	0.725901i	0.754940	+	0.655794i	$0.227666\pi$
$252$	−7.09258	+	18.0467i	−0.446791	+	1.13684i
$253$	−1.46676	−	3.54108i	−0.0922146	−	0.222626i
$254$	0.998370	+	2.95276i	0.0626433	+	0.185273i
$255$	16.5555	−	29.3707i	1.03675	−	1.83927i
$256$	−13.7788	−	8.13290i	−0.861176	−	0.508306i
$257$	−5.35214	−	3.09006i	−0.333857	−	0.192753i	0.323695	−	0.946161i	$-0.395075\pi$
$257$	−5.35214	−	3.09006i	−0.333857	−	0.192753i	−0.657552	+	0.753409i	$0.728408\pi$
$258$	−7.74603	+	8.99679i	−0.482247	+	0.560115i
$259$	−18.4496	−	14.1569i	−1.14640	−	0.879664i
$260$	−11.3003	+	27.0968i	−0.700813	+	1.68047i
$261$	−13.2363	+	2.02126i	−0.819304	+	0.125113i
$262$	−25.8814	+	5.11579i	−1.59896	+	0.316055i
$263$	4.87792	−	18.2047i	0.300786	−	1.12255i	−0.635727	−	0.771914i	$-0.719300\pi$
$263$	4.87792	−	18.2047i	0.300786	−	1.12255i	0.936513	−	0.350633i	$-0.114034\pi$
$264$	−17.4735	−	1.02755i	−1.07542	−	0.0632416i
$265$	−2.02803	−	7.56870i	−0.124581	−	0.464942i
$266$	−9.26671	−	18.8481i	−0.568178	−	1.15565i
$267$	6.08846	+	2.44863i	0.372608	+	0.149854i
$268$	−7.58904	−	13.2179i	−0.463575	−	0.807412i
$269$	7.05869	+	17.0412i	0.430376	+	1.03902i	0.979166	+	0.203059i	$0.0650884\pi$
$269$	7.05869	+	17.0412i	0.430376	+	1.03902i	−0.548791	+	0.835960i	$0.684912\pi$
$270$	−15.8276	−	22.2267i	−0.963237	−	1.35267i
$271$	3.68342			0.223752			0.111876	−	0.993722i	$-0.464314\pi$
$271$	3.68342			0.223752			0.111876	+	0.993722i	$0.464314\pi$
$272$	5.52456	−	20.2283i	0.334976	−	1.22652i
$273$	22.1276	−	0.228320i	1.33922	−	0.0138185i
$274$	0.621510	+	9.66036i	0.0375468	+	0.583603i
$275$	−4.09825	+	31.1293i	−0.247134	+	1.87717i
$276$	0.933362	−	3.59697i	0.0561818	−	0.216512i
$277$	−18.0672	+	2.37859i	−1.08555	+	0.142916i	−0.652004	−	0.758215i	$-0.726072\pi$
$277$	−18.0672	+	2.37859i	−1.08555	+	0.142916i	−0.433547	+	0.901131i	$0.642738\pi$
$278$	2.87019	−	4.28438i	0.172143	−	0.256960i
$279$	−13.3462	+	3.87297i	−0.799016	+	0.231869i
$280$	33.2650	+	6.74163i	1.98796	+	0.402890i
$281$	−7.86422	−	2.10721i	−0.469140	−	0.125706i	0.0165012	−	0.999864i	$-0.494747\pi$
$281$	−7.86422	−	2.10721i	−0.469140	−	0.125706i	−0.485641	+	0.874158i	$0.661414\pi$
$282$	11.3443	+	3.73589i	0.675541	+	0.222469i
$283$	9.45302	+	12.3194i	0.561924	+	0.732314i	0.984765	−	0.173890i	$-0.0556338\pi$
$283$	9.45302	+	12.3194i	0.561924	+	0.732314i	−0.422841	+	0.906204i	$0.638967\pi$
$284$	−9.32092	−	1.24993i	−0.553095	−	0.0741698i
$285$	29.3407	+	3.55520i	1.73799	+	0.210592i
$286$	6.39819	+	18.9232i	0.378333	+	1.11895i
$287$	8.97288			0.529652
$288$	−12.9214	−	11.0017i	−0.761402	−	0.648280i
$289$	10.4816			0.616563
$290$	7.50704	+	22.2027i	0.440829	+	1.30379i
$291$	5.13708	−	6.83975i	0.301141	−	0.400953i
$292$	−3.83271	+	28.5811i	−0.224292	+	1.67258i
$293$	−15.3009	−	19.9405i	−0.893888	−	1.16494i	−0.985590	−	0.169151i	$-0.945897\pi$
$293$	−15.3009	−	19.9405i	−0.893888	−	1.16494i	0.0917021	−	0.995786i	$-0.470769\pi$
$294$	−1.72121	−	8.25893i	−0.100383	−	0.481671i
$295$	23.2672	+	6.23443i	1.35467	+	0.362983i
$296$	16.9636	−	11.2464i	0.985988	−	0.653684i
$297$	−18.0730	−	4.24779i	−1.04870	−	0.246482i
$298$	10.7802	−	16.0918i	0.624481	−	0.932174i
$299$	−4.20460	+	0.553547i	−0.243159	+	0.0320124i
$300$	−21.3544	+	21.6951i	−1.23290	+	1.25257i
$301$	2.04447	−	15.5293i	0.117841	−	0.895093i
$302$	−1.89609	−	29.4717i	−0.109108	−	1.69590i
$303$	−6.33576	−	10.7170i	−0.363980	−	0.615673i
$304$	18.2359	−	2.31164i	1.04590	−	0.132582i
$305$	−46.6584			−2.67165
$306$	9.44752	−	20.1349i	0.540079	−	1.15103i
$307$	−2.05721	−	4.96655i	−0.117411	−	0.283456i	0.854238	−	0.519882i	$-0.174024\pi$
$307$	−2.05721	−	4.96655i	−0.117411	−	0.283456i	−0.971650	+	0.236426i	$0.924024\pi$
$308$	20.0273	−	11.4986i	1.14116	−	0.655196i
$309$	−10.7289	+	8.40987i	−0.610346	+	0.478421i
$310$	10.7325	+	21.8294i	0.609564	+	1.23983i
$311$	−3.60350	−	13.4484i	−0.204336	−	0.762591i	−0.989651	−	0.143495i	$-0.954166\pi$
$311$	−3.60350	−	13.4484i	−0.204336	−	0.762591i	0.785316	−	0.619096i	$-0.212501\pi$
$312$	−6.10215	+	18.3807i	−0.345466	+	1.04060i
$313$	1.53697	−	5.73604i	0.0868746	−	0.324220i	−0.908788	−	0.417258i	$-0.862991\pi$
$313$	1.53697	−	5.73604i	0.0868746	−	0.324220i	0.995663	+	0.0930379i	$0.0296578\pi$
$314$	14.2854	−	2.82369i	0.806170	−	0.159350i
$315$	33.5370	+	13.0874i	1.88959	+	0.737392i
$316$	4.60267	+	1.91947i	0.258920	+	0.107978i
$317$	−5.42414	−	4.16209i	−0.304650	−	0.233766i	0.445110	−	0.895476i	$-0.353165\pi$
$317$	−5.42414	−	4.16209i	−0.304650	−	0.233766i	−0.749760	+	0.661710i	$0.769831\pi$
$318$	−1.70607	−	4.87934i	−0.0956717	−	0.273620i
$319$	13.8103	+	7.97340i	0.773230	+	0.446424i
$320$	−15.0379	+	25.6179i	−0.840645	+	1.43208i
$321$	18.1228	−	0.186996i	1.01151	−	0.0104371i
$322$	1.57038	+	4.64454i	0.0875140	+	0.258830i
$323$	9.21911	+	22.2569i	0.512965	+	1.23841i
$324$	−11.5043	−	13.8438i	−0.639129	−	0.769099i
$325$	32.0961	+	13.2946i	1.78037	+	0.737454i
$326$	13.9029	−	12.1630i	0.770011	−	0.673646i
$327$	−13.9137	−	13.6295i	−0.769432	−	0.753716i
$328$	−2.55110	+	7.42717i	−0.140861	+	0.410097i
$329$	−15.2209	+	4.07842i	−0.839153	+	0.224850i
$330$	−1.82974	+	32.4456i	−0.100724	+	1.78607i
$331$	−0.773833	−	5.87785i	−0.0425337	−	0.323076i	−0.999463	−	0.0327558i	$-0.989572\pi$
$331$	−0.773833	−	5.87785i	−0.0425337	−	0.323076i	0.956930	−	0.290320i	$-0.0937617\pi$
$332$	−12.3454	−	0.0296855i	−0.677541	−	0.00162921i
$333$	19.7696	−	8.67101i	1.08337	−	0.475168i
$334$	−6.31722	+	4.21006i	−0.345663	+	0.230364i
$335$	−24.5063	+	14.1487i	−1.33892	+	0.773027i
$336$	22.2144	+	2.80017i	1.21189	+	0.152762i
$337$	−1.32272	−	0.763672i	−0.0720531	−	0.0415999i	0.463541	−	0.886076i	$-0.346579\pi$
$337$	−1.32272	−	0.763672i	−0.0720531	−	0.0415999i	−0.535594	+	0.844476i	$0.679912\pi$
$338$	3.70977	−	0.238672i	0.201785	−	0.0129821i
$339$	−29.5796	−	3.58414i	−1.60654	−	0.194664i
$340$	−37.5803	−	10.1665i	−2.03808	−	0.551357i
$341$	15.2909	+	6.33369i	0.828048	+	0.342989i
$342$	19.4762	+	0.896856i	1.05315	+	0.0484964i
$343$	−8.12580	−	8.12580i	−0.438752	−	0.438752i
$344$	12.2729	+	6.10744i	0.661709	+	0.329291i
$345$	−6.68225	−	1.71681i	−0.359760	−	0.0924298i
$346$	3.61405	−	10.6048i	0.194293	−	0.570115i
$347$	−1.48985	+	1.14320i	−0.0799794	+	0.0613704i	−0.647977	−	0.761660i	$-0.724385\pi$
$347$	−1.48985	+	1.14320i	−0.0799794	+	0.0613704i	0.567998	+	0.823030i	$0.307718\pi$
$348$	6.02955	+	14.2369i	0.323218	+	0.763179i
$349$	−21.4418	+	27.9435i	−1.14775	+	1.49578i	−0.309168	+	0.951007i	$0.600051\pi$
$349$	−21.4418	+	27.9435i	−1.14775	+	1.49578i	−0.838584	+	0.544772i	$0.816616\pi$
$350$	7.88280	−	39.3820i	0.421353	−	2.10506i
$351$	−9.71549	+	18.0992i	−0.518575	+	0.966065i
$352$	3.82384	+	19.8465i	0.203811	+	1.05782i
$353$	8.77512	−	5.06632i	0.467052	−	0.269653i	−0.247953	−	0.968772i	$-0.579758\pi$
$353$	8.77512	−	5.06632i	0.467052	−	0.269653i	0.715005	+	0.699119i	$0.246424\pi$
$354$	15.6125	+	2.95783i	0.829795	+	0.157207i
$355$	−2.27899	+	17.3107i	−0.120956	+	0.918755i
$356$	1.00714	−	7.51038i	0.0533783	−	0.398050i
$357$	4.13012	+	29.0518i	0.218589	+	1.53758i
$358$	20.3227	−	17.7794i	1.07409	−	0.939670i
$359$	−20.6337	−	20.6337i	−1.08901	−	1.08901i	−0.995631	−	0.0933741i	$-0.970235\pi$
$359$	−20.6337	−	20.6337i	−1.08901	−	1.08901i	−0.0933741	−	0.995631i	$-0.529765\pi$
$360$	−20.3679	+	24.0388i	−1.07348	+	1.26696i
$361$	−1.49781	+	1.49781i	−0.0788321	+	0.0788321i
$362$	1.59247	−	23.8568i	0.0836983	−	1.25389i
$363$	1.88680	+	2.40709i	0.0990314	+	0.126339i
$364$	−6.55400	−	24.6973i	−0.343523	−	1.29449i
$365$	53.0803	+	6.98815i	2.77835	+	0.365777i
$366$	−30.6938	+	2.29295i	−1.60439	+	0.119854i
$367$	−0.414329	−	0.717639i	−0.0216278	−	0.0374604i	0.855009	−	0.518613i	$-0.173552\pi$
$367$	−0.414329	−	0.717639i	−0.0216278	−	0.0374604i	−0.876637	+	0.481153i	$0.840218\pi$
$368$	−4.29093	−	0.0206359i	−0.223680	−	0.00107572i
$369$	−4.01499	+	7.29792i	−0.209012	+	0.379915i
$370$	−20.9557	−	31.4441i	−1.08943	−	1.63470i
$371$	5.41046	+	4.15159i	0.280897	+	0.215540i
$372$	8.13303	+	13.8329i	0.421678	+	0.717201i
$373$	−8.00553	−	10.4330i	−0.414511	−	0.540201i	0.538704	−	0.842495i	$-0.318914\pi$
$373$	−8.00553	−	10.4330i	−0.414511	−	0.540201i	−0.953215	+	0.302294i	$0.902247\pi$
$374$	−23.7710	+	11.6871i	−1.22917	+	0.604323i
$375$	17.4023	+	17.0468i	0.898650	+	0.880294i
$376$	0.951623	−	13.7584i	0.0490762	−	0.709535i
$377$	12.4766	−	12.4766i	0.642575	−	0.642575i
$378$	22.7051	+	6.96132i	1.16783	+	0.358052i
$379$	−2.17541	+	5.25191i	−0.111743	+	0.269772i	−0.969851	−	0.243697i	$-0.921640\pi$
$379$	−2.17541	+	5.25191i	−0.111743	+	0.269772i	0.858108	+	0.513469i	$0.171640\pi$
$380$	−4.37317	−	33.8462i	−0.224339	−	1.73627i
$381$	3.51165	−	1.49721i	0.179907	−	0.0767042i
$382$	−2.63467	−	2.31616i	−0.134802	−	0.118505i
$383$	−8.97726	+	15.5491i	−0.458716	+	0.794520i	−0.998893	−	0.0470314i	$-0.985024\pi$
$383$	−8.97726	+	15.5491i	−0.458716	+	0.794520i	0.540177	+	0.841551i	$0.318357\pi$
$384$	−8.63361	+	17.5915i	−0.440582	+	0.897712i
$385$	−21.4376	−	37.1311i	−1.09256	−	1.89237i
$386$	3.14125	−	15.6935i	0.159885	−	0.798778i
$387$	11.7156	+	8.61154i	0.595539	+	0.437749i
$388$	−9.11638	−	3.80184i	−0.462814	−	0.193009i
$389$	25.7015	−	3.38367i	1.30312	−	0.171559i	0.553178	−	0.833063i	$-0.313415\pi$
$389$	25.7015	−	3.38367i	1.30312	−	0.171559i	0.749942	+	0.661504i	$0.230082\pi$
$390$	34.1526	+	11.2471i	1.72939	+	0.569520i
$391$	−1.45550	−	5.43201i	−0.0736080	−	0.274709i
$392$	−8.75236	+	4.27701i	−0.442061	+	0.216022i
$393$	8.68439	+	31.1225i	0.438070	+	1.56992i
$394$	−0.977981	+	14.6512i	−0.0492700	+	0.738116i
$395$	3.54311	−	8.55382i	0.178273	−	0.430389i
$396$	0.390813	+	21.4340i	0.0196391	+	1.07710i
$397$	−10.5467	+	4.36858i	−0.529322	+	0.219253i	−0.631306	−	0.775533i	$-0.717481\pi$
$397$	−10.5467	+	4.36858i	−0.529322	+	0.219253i	0.101984	+	0.994786i	$0.467481\pi$
$398$	−10.6378	+	21.5061i	−0.533224	+	1.07800i
$399$	−22.1431	+	13.0908i	−1.10854	+	0.655359i
$400$	30.3567	+	17.7217i	1.51784	+	0.886083i
$401$	11.6527	−	20.1831i	0.581909	−	1.00790i	−0.413344	−	0.910575i	$-0.635639\pi$
$401$	11.6527	−	20.1831i	0.581909	−	1.00790i	0.995253	−	0.0973210i	$-0.0310273\pi$
$402$	−15.4259	+	10.5119i	−0.769376	+	0.524287i
$403$	11.1481	−	14.5285i	0.555326	−	0.723715i
$404$	−10.1896	+	10.1407i	−0.506949	+	0.504517i
$405$	−25.6508	+	21.4206i	−1.27460	+	1.06440i
$406$	−16.9472	−	11.3532i	−0.841075	−	0.563452i
$407$	−24.8343	−	6.65432i	−1.23099	−	0.329842i
$408$	−25.2214	−	4.84113i	−1.24865	−	0.239672i
$409$	29.1645	−	7.81459i	1.44209	−	0.386407i	0.548825	−	0.835937i	$-0.315075\pi$
$409$	29.1645	−	7.81459i	1.44209	−	0.386407i	0.893265	+	0.449531i	$0.148409\pi$
$410$	13.8006	+	4.70317i	0.681562	+	0.232273i
$411$	11.7379	−	1.66871i	0.578988	−	0.0823113i
$412$	12.4651	+	9.61254i	0.614113	+	0.473576i
$413$	−19.3689	+	8.02288i	−0.953083	+	0.394780i
$414$	−4.48023	−	0.800998i	−0.220191	−	0.0393669i
$415$			22.9204i			1.12512i
$416$	22.3062	+	1.59675i	1.09365	+	0.0782870i
$417$	−5.50204	−	3.10136i	−0.269436	−	0.151874i
$418$	−17.4395	−	15.3312i	−0.852995	−	0.749872i
$419$	34.0794	+	4.48664i	1.66489	+	0.219187i	0.903341	−	0.428923i	$-0.141107\pi$
$419$	34.0794	+	4.48664i	1.66489	+	0.219187i	0.761547	+	0.648110i	$0.224440\pi$
$420$	5.09958	−	41.2554i	0.248834	−	2.01306i
$421$	−2.50855	−	19.0543i	−0.122259	−	0.928649i	−0.937124	−	0.348998i	$-0.886522\pi$
$421$	−2.50855	−	19.0543i	−0.122259	−	0.928649i	0.814865	−	0.579651i	$-0.196811\pi$
$422$	2.23819	−	0.442406i	0.108953	−	0.0215360i
$423$	3.49361	−	14.2045i	0.169865	−	0.690648i
$424$	−4.97468	+	3.29808i	−0.241592	+	0.160169i
$425$	−11.9232	+	44.4981i	−0.578361	+	2.15847i
$426$	−0.648511	+	11.4997i	−0.0314204	+	0.557161i
$427$	32.2171	−	24.7210i	1.55909	−	1.19634i
$428$	−5.36780	−	20.2273i	−0.259463	−	0.977726i
$429$	22.5049	−	9.59506i	1.08655	−	0.463254i
$430$	11.2842	−	22.8129i	0.544172	−	1.10014i
$431$		−	17.0564i		−	0.821579i	−0.911730	−	0.410789i	$-0.865253\pi$
$431$		−	17.0564i		−	0.821579i	0.911730	−	0.410789i	$-0.134747\pi$
$432$	−12.2175	+	16.8147i	−0.587814	+	0.808996i
$433$			5.27234i			0.253373i	0.991943	+	0.126686i	$0.0404342\pi$
$433$			5.27234i			0.253373i	−0.991943	+	0.126686i	$0.959566\pi$
$434$	−18.9766	−	9.38658i	−0.910904	−	0.450570i
$435$	26.4051	−	11.2579i	1.26603	−	0.539777i
$436$	−11.2919	+	19.4500i	−0.540784	+	0.931486i
$437$	3.91103	−	3.00104i	0.187090	−	0.143559i
$438$	35.2618	+	1.98855i	1.68487	+	0.0950166i
$439$	−3.17725	+	11.8576i	−0.151642	+	0.565935i	0.847728	+	0.530431i	$0.177970\pi$
$439$	−3.17725	+	11.8576i	−0.151642	+	0.565935i	−0.999370	+	0.0355032i	$0.988697\pi$
$440$	36.8297	−	7.18788i	1.75579	−	0.342669i
$441$	−9.92304	+	2.87960i	−0.472526	+	0.137124i
$442$	5.68327	+	28.7524i	0.270326	+	1.36761i
$443$	−1.46990	−	11.1650i	−0.0698372	−	0.530466i	−0.990227	−	0.139464i	$-0.955462\pi$
$443$	−1.46990	−	11.1650i	−0.0698372	−	0.530466i	0.920390	−	0.391002i	$-0.127871\pi$
$444$	−15.3308	−	19.6554i	−0.727566	−	0.932804i
$445$	−13.9482	−	1.83631i	−0.661207	−	0.0870495i
$446$	5.60476	−	6.37553i	0.265393	−	0.301890i
$447$	−20.6653	−	11.6485i	−0.977433	−	0.550954i
$448$	−3.18962	−	25.6564i	−0.150695	−	1.21215i
$449$			0.904922i			0.0427059i	0.999772	+	0.0213530i	$0.00679737\pi$
$449$			0.904922i			0.0427059i	−0.999772	+	0.0213530i	$0.993203\pi$
$450$	28.5034	+	24.0332i	1.34366	+	1.13293i
$451$	9.16505	−	3.79629i	0.431565	−	0.178760i
$452$	4.40877	+	34.1217i	0.207371	+	1.60495i
$453$	−35.8099	+	5.09087i	−1.68249	+	0.239190i
$454$	7.83509	−	22.9906i	0.367719	−	1.07900i
$455$	−45.8234	+	12.2783i	−2.14823	+	0.575617i
$456$	−4.54016	−	22.0505i	−0.212613	−	1.03261i
$457$	28.4932	+	7.63472i	1.33285	+	0.357137i	0.853778	−	0.520637i	$-0.174305\pi$
$457$	28.4932	+	7.63472i	1.33285	+	0.357137i	0.479075	+	0.877774i	$0.340972\pi$
$458$	−12.9881	+	19.3875i	−0.606892	+	0.905918i
$459$	−25.4768	−	9.64033i	−1.18915	−	0.449972i
$460$	−0.0191563	+	7.96657i	−0.000893167	+	0.371443i
$461$	−11.7459	+	15.3075i	−0.547060	+	0.712942i	−0.982288	−	0.187378i	$-0.940001\pi$
$461$	−11.7459	+	15.3075i	−0.547060	+	0.712942i	0.435228	+	0.900320i	$0.356668\pi$
$462$	−15.9273	−	23.3728i	−0.741004	−	1.08740i
$463$	10.3612	−	17.9461i	0.481526	−	0.834028i	−0.518249	−	0.855230i	$-0.673416\pi$
$463$	10.3612	−	17.9461i	0.481526	−	0.834028i	0.999775	+	0.0212019i	$0.00674927\pi$
$464$	14.2158	−	10.7999i	0.659951	−	0.501374i
$465$	25.6456	−	15.1614i	1.18929	−	0.703095i
$466$	−6.85854	−	3.39252i	−0.317716	−	0.157155i
$467$	−18.0328	+	7.46944i	−0.834459	+	0.345644i	−0.758667	−	0.651479i	$-0.774149\pi$
$467$	−18.0328	+	7.46944i	−0.834459	+	0.345644i	−0.0757929	+	0.997124i	$0.524149\pi$
$468$	23.0197	+	5.72044i	1.06409	+	0.264427i
$469$	9.42490	−	22.7537i	0.435202	−	1.05067i
$470$	−25.5479	−	1.70535i	−1.17844	−	0.0786618i
$471$	−4.79339	−	17.1782i	−0.220868	−	0.791530i
$472$	−1.13400	−	18.3134i	−0.0521966	−	0.842941i
$473$	−4.48195	−	16.7268i	−0.206080	−	0.769101i
$474$	1.91044	−	5.80117i	0.0877493	−	0.266457i
$475$	−40.0381	+	5.27112i	−1.83708	+	0.241856i
$476$	31.3353	−	12.8913i	1.43625	−	0.590872i
$477$	−5.79758	+	2.54283i	−0.265453	+	0.116428i
$478$	21.5408	+	4.31166i	0.985253	+	0.197211i
$479$	1.65705	+	2.87010i	0.0757127	+	0.131138i	0.901396	−	0.432996i	$-0.142543\pi$
$479$	1.65705	+	2.87010i	0.0757127	+	0.131138i	−0.825683	+	0.564134i	$0.809210\pi$
$480$	32.6987	+	15.9505i	1.49248	+	0.728038i
$481$	−14.2237	+	24.6362i	−0.648547	+	1.12332i
$482$	−23.9700	+	27.2663i	−1.09180	+	1.24195i
$483$	5.52364	−	2.35503i	0.251334	−	0.107157i
$484$	2.15663	−	2.79662i	0.0980285	−	0.127119i
$485$	−7.01774	+	16.9423i	−0.318659	+	0.769311i
$486$	−15.8215	+	15.3519i	−0.717677	+	0.696376i
$487$	14.7459	−	14.7459i	0.668199	−	0.668199i	−0.289100	−	0.957299i	$-0.593356\pi$
$487$	14.7459	−	14.7459i	0.668199	−	0.668199i	0.957299	+	0.289100i	$0.0933559\pi$
$488$	11.3028	+	33.6957i	0.511653	+	1.52533i
$489$	−16.1618	−	15.8317i	−0.730861	−	0.715932i
$490$	7.97971	+	16.2304i	0.360487	+	0.733216i
$491$	−16.9981	−	22.1524i	−0.767116	−	0.999725i	−0.999632	−	0.0271321i	$-0.991363\pi$
$491$	−16.9981	−	22.1524i	−0.767116	−	0.999725i	0.232516	−	0.972593i	$-0.425304\pi$
$492$	9.30971	+	2.41573i	0.419714	+	0.108910i
$493$	18.5625	+	14.2435i	0.836014	+	0.641496i
$494$	−21.3796	+	14.2482i	−0.961912	+	0.641058i
$495$	39.7923	−	0.821267i	1.78853	−	0.0369132i
$496$	13.1649	−	13.0389i	0.591120	−	0.585462i
$497$	−7.59811	−	13.1603i	−0.340822	−	0.590321i
$498$	1.12639	+	15.0780i	0.0504746	+	0.675660i
$499$	24.8424	+	3.27056i	1.11210	+	0.146410i	0.664114	−	0.747631i	$-0.268809\pi$
$499$	24.8424	+	3.27056i	1.11210	+	0.146410i	0.447984	+	0.894042i	$0.352142\pi$
$500$	14.1231	−	24.3266i	0.631603	−	1.08792i
$501$	5.73591	+	7.31760i	0.256261	+	0.326926i
$502$	−42.4057	−	2.83062i	−1.89266	−	0.126337i
$503$	9.78430	−	9.78430i	0.436260	−	0.436260i	−0.454491	−	0.890751i	$-0.650179\pi$
$503$	9.78430	−	9.78430i	0.436260	−	0.436260i	0.890751	+	0.454491i	$0.150179\pi$
$504$	1.32729	−	27.3901i	0.0591221	−	1.22005i
$505$	18.8725	+	18.8725i	0.839816	+	0.839816i
$506$	3.56905	+	4.07960i	0.158664	+	0.181360i
$507$	−0.640817	−	4.50759i	−0.0284597	−	0.200189i
$508$	−2.67505	−	3.50360i	−0.118686	−	0.155447i
$509$	−1.80288	+	13.6943i	−0.0799114	+	0.606988i	0.903895	+	0.427754i	$0.140695\pi$
$509$	−1.80288	+	13.6943i	−0.0799114	+	0.606988i	−0.983807	+	0.179234i	$0.942638\pi$
$510$	−8.87537	+	46.8474i	−0.393008	+	2.07444i
$511$	−40.3539	+	23.2983i	−1.78515	+	1.03066i
$512$	22.1436	+	4.65426i	0.978617	+	0.205691i
$513$	−0.739020	−	23.8673i	−0.0326285	−	1.05377i
$514$	8.57001	+	1.71540i	0.378007	+	0.0756628i
$515$	17.7909	−	23.1855i	0.783959	−	1.02168i
$516$	6.30210	−	15.5618i	0.277435	−	0.685070i
$517$	−13.8213	+	10.6055i	−0.607861	+	0.466428i
$518$	31.1297	+	10.6089i	1.36776	+	0.466127i
$519$	−13.2900	−	3.41448i	−0.583367	−	0.149879i
$520$	2.86492	−	41.4205i	0.125635	−	1.81641i
$521$	−16.3725	−	16.3725i	−0.717293	−	0.717293i	0.250757	−	0.968050i	$-0.419320\pi$
$521$	−16.3725	−	16.3725i	−0.717293	−	0.717293i	−0.968050	+	0.250757i	$0.919320\pi$
$522$	16.8171	−	8.70357i	0.736066	−	0.380945i
$523$	41.7082	+	17.2761i	1.82377	+	0.755431i	0.973348	+	0.229332i	$0.0736540\pi$
$523$	41.7082	+	17.2761i	1.82377	+	0.755431i	0.850423	+	0.526099i	$0.176346\pi$
$524$	32.3562	−	18.5773i	1.41349	−	0.811551i
$525$	−48.8325	−	5.91701i	−2.13122	−	0.258239i
$526$	1.71124	+	26.5985i	0.0746137	+	1.15975i
$527$	21.0303	+	12.1418i	0.916092	+	0.528906i
$528$	23.8748	−	6.53841i	1.03902	−	0.284548i
$529$	18.9220	−	10.9246i	0.822695	−	0.474983i
$530$	6.14539	+	9.22120i	0.266939	+	0.400543i
$531$	2.14155	−	19.3433i	0.0929353	−	0.839427i
$532$	20.9524	+	21.0534i	0.908400	+	0.912780i
$533$	−1.43269	−	10.8824i	−0.0620569	−	0.471369i
$534$	−9.26592	−	0.522541i	−0.400976	−	0.0226126i
$535$	−37.5298	+	10.0561i	−1.62256	+	0.434763i
$536$	16.1545	+	14.2705i	0.697766	+	0.616391i
$537$	−23.6246	−	23.1421i	−1.01948	−	0.998655i
$538$	−17.1758	−	19.6328i	−0.740500	−	0.846430i
$539$	11.3689	+	4.70917i	0.489695	+	0.202838i
$540$	31.2724	+	22.6077i	1.34575	+	0.972882i
$541$	7.30422	+	17.6340i	0.314033	+	0.758143i	0.999547	+	0.0300837i	$0.00957737\pi$
$541$	7.30422	+	17.6340i	0.314033	+	0.758143i	−0.685514	+	0.728059i	$0.740423\pi$
$542$	−4.93471	+	1.66849i	−0.211964	+	0.0716679i
$543$	−29.2820	+	0.302141i	−1.25661	+	0.0129661i
$544$	1.76160	+	29.6025i	0.0755279	+	1.26920i
$545$	36.1610	+	20.8776i	1.54897	+	0.894296i
$546$	−29.5411	+	10.3291i	−1.26424	+	0.442045i
$547$	10.3410	+	7.93494i	0.442150	+	0.339274i	0.805723	−	0.592292i	$-0.201777\pi$
$547$	10.3410	+	7.93494i	0.442150	+	0.339274i	−0.363573	+	0.931566i	$0.618443\pi$
$548$	−5.20853	−	12.6605i	−0.222497	−	0.540831i
$549$	5.69057	+	37.2648i	0.242868	+	1.59042i
$550$	−8.61029	−	43.5605i	−0.367144	−	1.85743i
$551$	−5.30853	+	19.8117i	−0.226151	+	0.844007i
$552$	0.378902	+	5.24168i	0.0161271	+	0.223101i
$553$	2.08560	+	7.78356i	0.0886887	+	0.330991i
$554$	23.1273	−	11.3706i	0.982584	−	0.483089i
$555$	−36.4235	+	28.5506i	−1.54609	+	1.21191i
$556$	−1.90450	+	7.03994i	−0.0807688	+	0.298560i
$557$	6.37288	+	15.3855i	0.270028	+	0.651904i	0.999484	−	0.0321230i	$-0.0102268\pi$
$557$	6.37288	+	15.3855i	0.270028	+	0.651904i	−0.729456	+	0.684027i	$0.760227\pi$
$558$	16.1256	−	11.2341i	0.682653	−	0.475578i
$559$	−19.1605			−0.810403
$560$	−47.6191	+	6.03634i	−2.01227	+	0.255082i
$561$	16.5099	+	27.9266i	0.697050	+	1.17906i
$562$	11.4903	−	0.739239i	0.484688	−	0.0311829i
$563$	−1.22004	+	9.26709i	−0.0514184	+	0.390561i	0.946314	+	0.323250i	$0.104775\pi$
$563$	−1.22004	+	9.26709i	−0.0514184	+	0.390561i	−0.997732	+	0.0673114i	$0.978558\pi$
$564$	−16.8903	+	0.133662i	−0.711208	+	0.00562817i
$565$	63.3303	−	8.33759i	2.66432	−	0.350765i
$566$	−18.2447	−	12.2224i	−0.766880	−	0.513748i
$567$	6.36232	−	28.3813i	0.267193	−	1.19190i
$568$	13.0535	−	2.54759i	0.547712	−	0.106895i
$569$	−22.8162	−	6.11359i	−0.956506	−	0.256295i	−0.253385	−	0.967366i	$-0.581544\pi$
$569$	−22.8162	−	6.11359i	−0.956506	−	0.256295i	−0.703121	+	0.711071i	$0.748211\pi$
$570$	−40.9184	+	8.52764i	−1.71388	+	0.357184i
$571$	−7.23289	−	9.42609i	−0.302687	−	0.394469i	0.617102	−	0.786883i	$-0.288307\pi$
$571$	−7.23289	−	9.42609i	−0.302687	−	0.394469i	−0.919789	+	0.392414i	$0.871640\pi$
$572$	−17.1434	−	22.4533i	−0.716802	−	0.938820i
$573$	−2.58018	+	3.43537i	−0.107789	+	0.143515i
$574$	−12.0210	+	4.06448i	−0.501748	+	0.169648i
$575$	9.42699			0.393132
$576$	22.2944	+	8.88597i	0.928933	+	0.370249i
$577$	−24.4322			−1.01713			−0.508563	−	0.861025i	$-0.669823\pi$
$577$	−24.4322			−1.01713			−0.508563	+	0.861025i	$0.669823\pi$
$578$	−14.0422	+	4.74787i	−0.584080	+	0.197485i
$579$	−19.4594	−	2.35789i	−0.808707	−	0.0979907i
$580$	−20.1145	−	26.3446i	−0.835208	−	1.09390i
$581$	−12.1439	−	15.8263i	−0.503815	−	0.656585i
$582$	−3.78395	+	11.4902i	−0.156850	+	0.476285i
$583$	7.28281	+	1.95142i	0.301623	+	0.0808197i
$584$	−7.81176	−	40.0264i	−0.323253	−	1.65630i
$585$	10.5177	−	42.7636i	0.434854	−	1.76806i
$586$	29.5313	+	19.7835i	1.21992	+	0.817251i
$587$	−26.9887	+	3.55313i	−1.11394	+	0.146653i	−0.664955	−	0.746884i	$-0.731549\pi$
$587$	−26.9887	+	3.55313i	−1.11394	+	0.146653i	−0.448989	+	0.893537i	$0.648216\pi$
$588$	6.04700	+	10.2849i	0.249374	+	0.424141i
$589$	−2.77856	+	21.1052i	−0.114489	+	0.869627i
$590$	−33.9953	+	2.18712i	−1.39956	+	0.0900425i
$591$	17.9829	−	0.185554i	0.739719	−	0.00763266i
$592$	−17.6319	+	22.7509i	−0.724666	+	0.935058i
$593$	−33.9207			−1.39296			−0.696479	−	0.717577i	$-0.745251\pi$
$593$	−33.9207			−1.39296			−0.696479	+	0.717577i	$0.745251\pi$
$594$	26.1366	−	2.49579i	1.07240	−	0.102404i
$595$	−24.0737	−	58.1191i	−0.986926	−	2.38265i
$596$	−7.15317	+	26.4415i	−0.293005	+	1.08309i
$597$	27.2633	+	10.9647i	1.11581	+	0.448754i
$598$	5.38220	−	2.64617i	0.220094	−	0.108210i
$599$	−2.25144	−	8.40249i	−0.0919914	−	0.343316i	0.904555	−	0.426357i	$-0.140203\pi$
$599$	−2.25144	−	8.40249i	−0.0919914	−	0.343316i	−0.996546	+	0.0830410i	$0.973537\pi$
$600$	18.7814	−	38.7381i	0.766747	−	1.58148i
$601$	−10.3186	+	38.5097i	−0.420906	+	1.57084i	0.351797	+	0.936076i	$0.385571\pi$
$601$	−10.3186	+	38.5097i	−0.420906	+	1.57084i	−0.772703	+	0.634767i	$0.781096\pi$
$602$	4.29537	+	21.7308i	0.175066	+	0.885680i
$603$	14.2891	+	17.8469i	0.581896	+	0.726783i
$604$	15.8901	+	38.6245i	0.646559	+	1.57161i
$605$	−5.20180	−	3.99148i	−0.211483	−	0.162277i
$606$	13.3426	+	11.4876i	0.542005	+	0.466654i
$607$	−20.5619	−	11.8714i	−0.834580	−	0.481845i	0.0208382	−	0.999783i	$-0.493367\pi$
$607$	−20.5619	−	11.8714i	−0.834580	−	0.481845i	−0.855418	+	0.517938i	$0.826700\pi$
$608$	−23.3836	+	11.3573i	−0.948332	+	0.460599i
$609$	−12.2676	+	21.7637i	−0.497110	+	0.881911i
$610$	62.5086	−	21.1350i	2.53090	−	0.855732i
$611$	7.37665	+	17.8088i	0.298427	+	0.720467i
$612$	−3.53635	+	31.2543i	−0.142948	+	1.26338i
$613$	−18.6581	−	7.72844i	−0.753594	−	0.312149i	−0.0273869	−	0.999625i	$-0.508719\pi$
$613$	−18.6581	−	7.72844i	−0.753594	−	0.312149i	−0.726207	+	0.687476i	$0.758719\pi$
$614$	5.00578	+	5.72186i	0.202017	+	0.230915i
$615$	4.44346	−	17.2951i	0.179177	−	0.697404i
$616$	−21.6221	+	24.4766i	−0.871180	+	0.986192i
$617$	7.25796	−	1.94476i	0.292194	−	0.0782933i	−0.109744	−	0.993960i	$-0.535003\pi$
$617$	7.25796	−	1.94476i	0.292194	−	0.0782933i	0.401939	+	0.915667i	$0.368337\pi$
$618$	10.5641	−	16.1267i	0.424952	−	0.648710i
$619$	−1.86154	−	14.1398i	−0.0748218	−	0.568328i	−0.987260	−	0.159114i	$-0.949136\pi$
$619$	−1.86154	−	14.1398i	−0.0748218	−	0.568328i	0.912438	−	0.409214i	$-0.134197\pi$
$620$	−24.2665	−	24.3835i	−0.974567	−	0.979266i
$621$	−0.556185	+	5.54633i	−0.0223189	+	0.222566i
$622$	10.9194	+	16.3847i	0.437829	+	0.656965i
$623$	10.6040	−	6.12222i	0.424840	−	0.245281i
$624$	−0.150881	−	27.3889i	−0.00604009	−	1.09643i
$625$	−7.17548	−	4.14277i	−0.287019	−	0.165711i
$626$	0.539189	+	8.38082i	0.0215503	+	0.334965i
$627$	−17.0788	+	22.7395i	−0.682062	+	0.908130i
$628$	−17.8592	+	10.2538i	−0.712658	+	0.409172i
$629$	−34.8513	−	14.4359i	−1.38961	−	0.575597i
$630$	−50.8580	−	2.34194i	−2.02623	−	0.0933053i
$631$	22.2267	+	22.2267i	0.884829	+	0.884829i	0.994021	−	0.109192i	$-0.0348262\pi$
$631$	22.2267	+	22.2267i	0.884829	+	0.884829i	−0.109192	+	0.994021i	$0.534826\pi$
$632$	−7.03569	−	0.486636i	−0.279865	−	0.0193573i
$633$	−0.751013	−	2.69143i	−0.0298501	−	0.106975i
$634$	9.15208	+	3.11899i	0.363475	+	0.123871i
$635$	−6.49279	+	4.98209i	−0.257659	+	0.197708i
$636$	4.49585	+	5.76408i	0.178272	+	0.228561i
$637$	8.28873	−	10.8021i	0.328412	−	0.427994i
$638$	−22.1135	−	4.42630i	−0.875483	−	0.175239i
$639$	14.1035	−	0.291081i	0.557927	−	0.0115150i
$640$	8.54219	−	41.1322i	0.337660	−	1.62589i
$641$	−17.1218	+	9.88528i	−0.676271	+	0.390445i	−0.798449	−	0.602063i	$-0.794346\pi$
$641$	−17.1218	+	9.88528i	−0.676271	+	0.390445i	0.122178	+	0.992508i	$0.461012\pi$
$642$	−24.1945	+	8.45965i	−0.954880	+	0.333876i
$643$	3.63445	−	27.6064i	0.143329	−	1.08869i	−0.756980	−	0.653438i	$-0.773326\pi$
$643$	3.63445	−	27.6064i	0.143329	−	1.08869i	0.900309	−	0.435252i	$-0.143341\pi$
$644$	−4.20771	−	5.51098i	−0.165807	−	0.217163i
$645$	−28.9200	−	11.6309i	−1.13872	−	0.457967i
$646$	−22.4327	−	25.6417i	−0.882603	−	1.00886i
$647$	15.5379	+	15.5379i	0.610857	+	0.610857i	0.943169	−	0.332312i	$-0.107829\pi$
$647$	15.5379	+	15.5379i	0.610857	+	0.610857i	−0.332312	+	0.943169i	$0.607829\pi$
$648$	21.6833	+	13.3355i	0.851800	+	0.523866i
$649$	−16.3894	+	16.3894i	−0.643341	+	0.643341i
$650$	−49.0215	−	3.27224i	−1.92278	−	0.128348i
$651$	−9.67500	+	24.0566i	−0.379193	+	0.942853i
$652$	−13.1163	+	22.5925i	−0.513675	+	0.884790i
$653$	−41.4758	−	5.46039i	−1.62307	−	0.213682i	−0.736556	−	0.676377i	$-0.763549\pi$
$653$	−41.4758	−	5.46039i	−1.62307	−	0.213682i	−0.886517	+	0.462696i	$0.846882\pi$
$654$	24.8142	+	11.9570i	0.970311	+	0.467557i
$655$	−34.6347	−	59.9891i	−1.35329	−	2.34397i
$656$	0.0534100	−	11.1058i	0.00208531	−	0.433609i
$657$	−0.892550	−	43.2461i	−0.0348217	−	1.68719i
$658$	18.5441	−	12.3585i	0.722923	−	0.481786i
$659$	−0.600445	−	0.460738i	−0.0233900	−	0.0179478i	0.597000	−	0.802241i	$-0.296359\pi$
$659$	−0.600445	−	0.460738i	−0.0233900	−	0.0179478i	−0.620390	+	0.784293i	$0.713026\pi$
$660$	−12.2457	−	44.2965i	−0.476664	−	1.72424i
$661$	5.45852	+	7.11368i	0.212312	+	0.276690i	0.887354	−	0.461089i	$-0.152541\pi$
$661$	5.45852	+	7.11368i	0.212312	+	0.276690i	−0.675042	+	0.737779i	$0.735875\pi$
$662$	3.69922	+	7.52407i	0.143774	+	0.292431i
$663$	34.5748	−	9.64773i	1.34278	−	0.374687i
$664$	16.5527	−	5.55237i	0.642367	−	0.215474i
$665$	38.9939	−	38.9939i	1.51212	−	1.51212i
$666$	−22.5578	+	20.5717i	−0.874097	+	0.797139i
$667$	1.83225	−	4.42345i	0.0709451	−	0.171277i
$668$	6.55618	−	8.50178i	0.253666	−	0.328944i
$669$	−8.31311	−	6.24366i	−0.321403	−	0.241394i
$670$	26.4223	−	30.0559i	1.02078	−	1.16116i
$671$	22.4480	−	38.8810i	0.866595	−	1.50099i
$672$	−31.0291	+	6.31111i	−1.19697	+	0.243456i
$673$	14.1170	+	24.4514i	0.544171	+	0.942532i	0.998659	+	0.0517790i	$0.0164891\pi$
$673$	14.1170	+	24.4514i	0.544171	+	0.942532i	−0.454487	+	0.890753i	$0.650178\pi$
$674$	2.11798	+	0.423940i	0.0815815	+	0.0163296i
$675$	26.6630	−	37.0693i	1.02626	−	1.42680i
$676$	−4.86189	+	2.00018i	−0.186996	+	0.0769300i
$677$	30.6797	−	4.03906i	1.17912	−	0.155234i	0.484617	−	0.874726i	$-0.338959\pi$
$677$	30.6797	−	4.03906i	1.17912	−	0.155234i	0.694500	+	0.719493i	$0.255626\pi$
$678$	41.2515	−	8.59707i	1.58425	−	0.330168i
$679$	−4.13089	−	15.4167i	−0.158529	−	0.591639i
$680$	54.9517	−	3.40272i	2.10730	−	0.130488i
$681$	−28.8121	−	7.40242i	−1.10408	−	0.283661i
$682$	−23.3543	−	1.55892i	−0.894282	−	0.0596942i
$683$	4.92844	−	11.8983i	0.188581	−	0.455276i	−0.801105	−	0.598523i	$-0.795754\pi$
$683$	4.92844	−	11.8983i	0.188581	−	0.455276i	0.989687	+	0.143247i	$0.0457544\pi$
$684$	−26.4987	+	7.62070i	−1.01320	+	0.291385i
$685$	−23.4821	+	9.72660i	−0.897205	+	0.371634i
$686$	14.5670	+	7.20542i	0.556169	+	0.275104i
$687$	24.8976	+	14.0341i	0.949902	+	0.535435i
$688$	−19.2086	−	2.62289i	−0.732320	−	0.0999969i
$689$	4.17121	−	7.22474i	0.158910	−	0.275241i
$690$	9.72993	−	0.726865i	0.370412	−	0.0276713i
$691$	−14.9331	+	19.4612i	−0.568082	+	0.740339i	−0.985742	−	0.168265i	$-0.946184\pi$
$691$	−14.9331	+	19.4612i	−0.568082	+	0.740339i	0.417660	+	0.908603i	$0.362850\pi$
$692$	−0.0380990	+	15.8443i	−0.00144831	+	0.602311i
$693$	−27.0410	+	21.6503i	−1.02720	+	0.822425i
$694$	1.47812	−	2.20642i	0.0561088	−	0.0837546i
$695$	13.0788	+	3.50444i	0.496105	+	0.132931i
$696$	−14.5268	−	16.3421i	−0.550636	−	0.619444i
$697$	14.0592	−	3.76715i	0.532529	−	0.142691i
$698$	16.0680	−	47.1486i	0.608185	−	1.78460i
$699$	−3.49676	+	8.69459i	−0.132260	+	0.328860i
$700$	7.27836	+	56.3310i	0.275096	+	2.12911i
$701$	6.58666	−	2.72828i	0.248775	−	0.103046i	−0.254812	−	0.966991i	$-0.582014\pi$
$701$	6.58666	−	2.72828i	0.248775	−	0.103046i	0.503586	+	0.863945i	$0.332014\pi$
$702$	4.81744	−	28.6485i	0.181822	−	1.08127i
$703$		−	33.0683i		−	1.24720i
$704$	−14.1128	−	24.8564i	−0.531895	−	0.936811i
$705$	0.323558	+	31.3576i	0.0121859	+	1.18100i
$706$	−9.46118	+	10.7623i	−0.356076	+	0.405044i
$707$	−23.0305	−	3.03202i	−0.866151	−	0.114031i
$708$	−22.2560	+	3.10942i	−0.836432	+	0.116859i
$709$	3.20416	+	24.3380i	0.120335	+	0.914033i	0.939996	+	0.341185i	$0.110828\pi$
$709$	3.20416	+	24.3380i	0.120335	+	0.914033i	−0.819662	+	0.572848i	$0.805839\pi$
$710$	−4.78810	−	24.2236i	−0.179694	−	0.909094i
$711$	−7.26383	−	1.78654i	−0.272415	−	0.0670005i
$712$	2.05274	+	10.5179i	0.0769295	+	0.394176i
$713$	1.28613	−	4.79991i	0.0481660	−	0.179758i
$714$	−18.6928	−	37.0500i	−0.699562	−	1.38656i
$715$	−41.6100	+	31.9285i	−1.55612	+	1.19406i
$716$	−19.1729	+	33.0248i	−0.716526	+	1.23420i
$717$	3.23643	−	26.7099i	0.120867	−	0.997500i
$718$	36.9896	+	18.2966i	1.38044	+	0.682823i
$719$			28.2223i			1.05251i	0.850326	+	0.526257i	$0.176405\pi$
$719$			28.2223i			1.05251i	−0.850326	+	0.526257i	$0.823595\pi$
$720$	16.3980	−	41.4311i	0.611119	−	1.54405i
$721$			25.4355i			0.947267i
$722$	1.32816	−	2.68509i	0.0494289	−	0.0999288i
$723$	35.5528	+	26.7024i	1.32222	+	0.993071i
$724$	8.67308	+	32.6825i	0.322333	+	1.21464i
$725$	−31.1166	+	23.8766i	−1.15564	+	0.886756i
$726$	−3.61811	−	2.37012i	−0.134281	−	0.0879636i
$727$	8.65868	−	32.3146i	0.321133	−	1.19848i	−0.597010	−	0.802234i	$-0.703645\pi$
$727$	8.65868	−	32.3146i	0.321133	−	1.19848i	0.918143	−	0.396250i	$-0.129688\pi$
$728$	19.9677	+	30.1183i	0.740051	+	1.11626i
$729$	20.2365	+	17.8741i	0.749500	+	0.662005i
$730$	−74.2775	+	14.6819i	−2.74913	+	0.543401i
$731$	−3.31638	−	25.1904i	−0.122661	−	0.931702i
$732$	40.0820	−	16.9754i	1.48147	−	0.627427i
$733$	−11.8560	−	1.56087i	−0.437910	−	0.0576519i	−0.0916516	−	0.995791i	$-0.529215\pi$
$733$	−11.8560	−	1.56087i	−0.437910	−	0.0576519i	−0.346258	+	0.938139i	$0.612548\pi$
$734$	0.880151	+	0.773746i	0.0324870	+	0.0285595i
$735$	19.0678	−	11.2727i	0.703326	−	0.415799i
$736$	5.75793	−	1.91603i	0.212240	−	0.0706258i
$737$		−	27.2286i		−	1.00298i
$738$	2.07315	−	11.5958i	0.0763137	−	0.426846i
$739$	−29.0727	+	12.0423i	−1.06946	+	0.442984i	−0.846799	−	0.531913i	$-0.821474\pi$
$739$	−29.0727	+	12.0423i	−1.06946	+	0.442984i	−0.222659	+	0.974896i	$0.571474\pi$
$740$	42.3178	+	32.6336i	1.55563	+	1.19963i
$741$	19.4122	+	24.7652i	0.713125	+	0.909771i
$742$	−9.12900	−	3.11112i	−0.335136	−	0.114213i
$743$	7.14318	−	1.91401i	0.262058	−	0.0702181i	−0.125398	−	0.992107i	$-0.540021\pi$
$743$	7.14318	−	1.91401i	0.262058	−	0.0702181i	0.387456	+	0.921888i	$0.373354\pi$
$744$	−17.1618	−	14.8479i	−0.629182	−	0.544352i
$745$	49.1228	+	13.1624i	1.79972	+	0.482234i
$746$	15.4509	+	10.3509i	0.565699	+	0.378973i
$747$	18.3059	−	2.79543i	0.669779	−	0.102279i
$748$	26.5523	−	26.4249i	0.970847	−	0.966189i
$749$	20.5859	−	26.8281i	0.752193	−	0.980277i
$750$	−31.0357	−	14.9550i	−1.13326	−	0.546078i
$751$	−13.1491	+	22.7749i	−0.479816	+	0.831066i	−0.999732	−	0.0231513i	$-0.992630\pi$
$751$	−13.1491	+	22.7749i	−0.479816	+	0.831066i	0.519916	+	0.854218i	$0.325963\pi$
$752$	4.95729	+	18.8633i	0.180774	+	0.687873i
$753$	0.537058	+	52.0489i	0.0195715	+	1.89677i
$754$	−11.0634	+	22.3665i	−0.402905	+	0.814539i
$755$	71.6389	−	29.6738i	2.60720	−	1.07994i
$756$	−33.5715	+	0.958704i	−1.22098	+	0.0348677i
$757$	15.9960	−	38.6177i	0.581384	−	1.40359i	−0.310174	−	0.950680i	$-0.600387\pi$
$757$	15.9960	−	38.6177i	0.581384	−	1.40359i	0.891558	−	0.452906i	$-0.149613\pi$
$758$	0.535438	−	8.02142i	0.0194480	−	0.291351i
$759$	4.64556	−	4.74243i	0.168623	−	0.172139i
$760$	21.1902	+	43.3631i	0.768649	+	1.57294i
$761$	−2.13532	−	7.96910i	−0.0774051	−	0.288880i	0.916363	−	0.400349i	$-0.131111\pi$
$761$	−2.13532	−	7.96910i	−0.0774051	−	0.288880i	−0.993768	+	0.111469i	$0.964444\pi$
$762$	−4.02639	+	3.59650i	−0.145861	+	0.130288i
$763$	−36.0303	+	4.74348i	−1.30439	+	0.171726i
$764$	4.57885	+	1.90953i	0.165657	+	0.0690845i
$765$	58.0421	+	6.42600i	2.09852	+	0.232333i
$766$	4.98358	−	24.8976i	0.180064	−	0.899589i
$767$	12.8229	+	22.2098i	0.463006	+	0.801951i
$768$	3.59802	−	27.4782i	0.129833	−	0.991536i
$769$	20.6607	−	35.7854i	0.745045	−	1.29046i	−0.205129	−	0.978735i	$-0.565761\pi$
$769$	20.6607	−	35.7854i	0.745045	−	1.29046i	0.950174	−	0.311721i	$-0.100905\pi$
$770$	45.5395	+	40.0341i	1.64113	+	1.44273i
$771$	1.28761	−	10.6266i	0.0463723	−	0.382706i
$772$	2.90038	+	22.4476i	0.104387	+	0.807906i
$773$	−7.60476	+	18.3595i	−0.273524	+	0.660346i	−0.999629	−	0.0272380i	$-0.991329\pi$
$773$	−7.60476	+	18.3595i	−0.273524	+	0.660346i	0.726105	+	0.687584i	$0.241329\pi$
$774$	−19.5963	−	6.23007i	−0.704375	−	0.223935i
$775$	−28.7842	+	28.7842i	−1.03396	+	1.03396i
$776$	13.9354	+	0.963867i	0.500252	+	0.0346008i
$777$	10.0230	−	39.0122i	0.359574	−	1.39955i
$778$	−32.8998	+	16.1753i	−1.17952	+	0.579911i
$779$	7.76732	+	10.1226i	0.278293	+	0.362679i
$780$	−50.8492	+	0.402397i	−1.82069	+	0.0144081i
$781$	−13.3288	−	10.2275i	−0.476941	−	0.365969i
$782$	4.41051	+	6.61800i	0.157719	+	0.236659i
$783$	−12.2119	−	19.7160i	−0.436416	−	0.704594i
$784$	9.78823	−	9.69453i	0.349580	−	0.346233i
$785$	19.1168	+	33.1113i	0.682308	+	1.18179i
$786$	−25.7322	−	37.7612i	−0.917838	−	1.34690i
$787$	6.56214	+	0.863922i	0.233915	+	0.0307955i	0.246572	−	0.969124i	$-0.420696\pi$
$787$	6.56214	+	0.863922i	0.233915	+	0.0307955i	−0.0126572	+	0.999920i	$0.504029\pi$
$788$	−5.32639	−	20.0713i	−0.189745	−	0.715010i
$789$	32.3187	−	4.59456i	1.15058	−	0.163571i
$790$	−0.872071	+	13.0645i	−0.0310269	+	0.464816i
$791$	−39.3113	+	39.3113i	−1.39775	+	1.39775i
$792$	−10.2326	−	28.5382i	−0.363600	−	1.01406i
$793$	−35.1260	−	35.1260i	−1.24736	−	1.24736i
$794$	12.1506	−	10.6300i	0.431209	−	0.377244i
$795$	10.6814	−	8.37266i	0.378832	−	0.296948i
$796$	4.50983	−	33.6305i	0.159847	−	1.19200i
$797$	−2.33303	+	17.7212i	−0.0826403	+	0.627715i	0.899135	+	0.437671i	$0.144197\pi$
$797$	−2.33303	+	17.7212i	−0.0826403	+	0.627715i	−0.981775	+	0.190044i	$0.939137\pi$
$798$	23.7355	−	27.5680i	0.840226	−	0.975898i
$799$	−22.1366	+	12.7806i	−0.783136	+	0.452144i
$800$	−48.6965	−	9.99103i	−1.72168	−	0.353236i
$801$	0.234540	+	11.3640i	0.00828705	+	0.401527i
$802$	−6.46882	+	32.3178i	−0.228422	+	1.14118i
$803$	−31.3610	+	40.8704i	−1.10670	+	1.44229i
$804$	15.9046	−	21.0704i	0.560912	−	0.743097i
$805$	−10.2128	+	7.83657i	−0.359954	+	0.276203i
$806$	−8.35416	+	24.5137i	−0.294263	+	0.863458i
$807$	−22.3564	+	22.8226i	−0.786983	+	0.803393i
$808$	9.05756	−	18.2011i	0.318644	−	0.640313i
$809$	2.22883	+	2.22883i	0.0783613	+	0.0783613i	0.745201	−	0.666840i	$-0.232353\pi$
$809$	2.22883	+	2.22883i	0.0783613	+	0.0783613i	−0.666840	+	0.745201i	$0.732353\pi$
$810$	24.6616	−	40.3164i	0.866521	−	1.41658i
$811$	31.8099	+	13.1761i	1.11700	+	0.462675i	0.863342	−	0.504620i	$-0.168367\pi$
$811$	31.8099	+	13.1761i	1.11700	+	0.462675i	0.253655	+	0.967295i	$0.418367\pi$
$812$	27.8470	+	7.53339i	0.977238	+	0.264370i
$813$	2.50216	+	5.86873i	0.0877545	+	0.205825i
$814$	36.2849	−	2.33443i	1.27178	−	0.0818216i
$815$	42.0035	+	24.2507i	1.47132	+	0.849466i
$816$	35.9822	−	4.93896i	1.25963	−	0.172898i
$817$	19.2888	−	11.1364i	0.674830	−	0.389614i
$818$	−35.5320	+	23.6800i	−1.24235	+	0.827952i
$819$	15.3951	+	35.1004i	0.537949	+	1.22651i
$820$	−20.6191	−	0.0495805i	−0.720052	−	0.00173142i
$821$	−6.62258	−	50.3035i	−0.231130	−	1.75560i	−0.576462	−	0.817124i	$-0.695567\pi$
$821$	−6.62258	−	50.3035i	−0.231130	−	1.75560i	0.345332	−	0.938481i	$-0.387766\pi$
$822$	−14.9695	+	7.55254i	−0.522121	+	0.263425i
$823$	−3.81284	+	1.02165i	−0.132907	+	0.0356124i	−0.324659	−	0.945831i	$-0.605250\pi$
$823$	−3.81284	+	1.02165i	−0.132907	+	0.0356124i	0.191752	+	0.981443i	$0.438583\pi$
$824$	−21.0539	−	7.23161i	−0.733446	−	0.251925i
$825$	−52.3817	+	14.6165i	−1.82370	+	0.508882i
$826$	22.3146	−	19.5219i	0.776423	−	0.679255i
$827$	−29.6367	−	12.2759i	−1.03057	−	0.426876i	−0.197651	−	0.980272i	$-0.563331\pi$
$827$	−29.6367	−	12.2759i	−1.03057	−	0.426876i	−0.832918	+	0.553397i	$0.813331\pi$
$828$	6.36502	−	0.956323i	0.221200	−	0.0332345i
$829$	7.49211	+	18.0875i	0.260212	+	0.628206i	0.998951	−	0.0457845i	$-0.0145787\pi$
$829$	7.49211	+	18.0875i	0.260212	+	0.628206i	−0.738740	+	0.673991i	$0.764579\pi$
$830$	−10.3823	−	30.7066i	−0.360376	−	1.06584i
$831$	−16.0628	−	27.1703i	−0.557214	−	0.942528i
$832$	−30.6071	+	7.96494i	−1.06111	+	0.276135i
$833$	15.6362	+	9.02758i	0.541763	+	0.312787i
$834$	8.77596	+	1.66263i	0.303887	+	0.0575722i
$835$	−15.8136	−	12.1342i	−0.547251	−	0.419920i
$836$	30.3085	+	12.6396i	1.04824	+	0.437151i
$837$	−15.2368	−	18.6333i	−0.526662	−	0.644062i
$838$	−47.6887	+	9.42629i	−1.64738	+	0.325626i
$839$	−13.9693	+	52.1341i	−0.482273	+	1.79987i	0.109765	+	0.993958i	$0.464990\pi$
$839$	−13.9693	+	52.1341i	−0.482273	+	1.79987i	−0.592038	+	0.805910i	$0.701677\pi$
$840$	11.8556	+	57.5801i	0.409059	+	1.98670i
$841$	−2.34996	−	8.77019i	−0.0810333	−	0.302420i
$842$	11.9918	+	24.3909i	0.413265	+	0.840565i
$843$	−1.98480	−	13.9614i	−0.0683602	−	0.480855i
$844$	−2.79811	+	1.60653i	−0.0963151	+	0.0552992i
$845$	3.73521	+	9.01759i	0.128495	+	0.310215i
$846$	1.75387	+	20.6124i	0.0602992	+	0.708669i
$847$	5.70659			0.196081
$848$	5.17067	−	6.67187i	0.177562	−	0.229113i
$849$	−13.2069	+	23.4299i	−0.453258	+	0.804114i
$850$	−4.18283	−	65.0153i	−0.143470	−	2.23001i
$851$	−1.00757	+	7.65329i	−0.0345392	+	0.262351i
$852$	−4.34023	−	15.6999i	−0.148694	−	0.537871i
$853$	−31.1412	+	4.09981i	−1.06625	+	0.140375i	−0.643176	−	0.765719i	$-0.722383\pi$
$853$	−31.1412	+	4.09981i	−1.06625	+	0.140375i	−0.423077	+	0.906094i	$0.639050\pi$
$854$	−31.9635	+	47.7125i	−1.09377	+	1.63269i
$855$	14.2668	+	49.1631i	0.487914	+	1.68134i
$856$	16.3537	+	24.6672i	0.558959	+	0.843109i
$857$	28.9748	+	7.76378i	0.989762	+	0.265206i	0.717150	−	0.696918i	$-0.245446\pi$
$857$	28.9748	+	7.76378i	0.989762	+	0.265206i	0.272611	+	0.962124i	$0.412113\pi$
$858$	−25.8037	+	23.0487i	−0.880923	+	0.786869i
$859$	8.11603	+	10.5770i	0.276915	+	0.360883i	0.911019	−	0.412365i	$-0.135297\pi$
$859$	8.11603	+	10.5770i	0.276915	+	0.360883i	−0.634103	+	0.773248i	$0.718631\pi$
$860$	−4.78387	+	35.6741i	−0.163129	+	1.21648i
$861$	6.09530	+	14.2963i	0.207727	+	0.487217i
$862$	7.72611	+	22.8506i	0.263152	+	0.778295i
$863$	19.7853			0.673499			0.336750	−	0.941594i	$-0.390672\pi$
$863$	19.7853			0.673499			0.336750	+	0.941594i	$0.390672\pi$
$864$	8.75124	−	28.0609i	0.297723	−	0.954652i
$865$	29.4165			1.00019
$866$	−2.38823	−	7.06340i	−0.0811555	−	0.240024i
$867$	7.12015	+	16.7001i	0.241813	+	0.567165i
$868$	29.6749	+	3.97939i	1.00723	+	0.135069i
$869$	5.42337	+	7.06787i	0.183975	+	0.239761i
$870$	−30.2756	+	27.0432i	−1.02644	+	0.916849i
$871$	−29.1008	−	7.79754i	−0.986043	−	0.264210i
$872$	6.31751	−	31.1722i	0.213938	−	1.05562i
$873$	14.3873	+	3.53856i	0.486936	+	0.119762i
$874$	−3.88025	+	5.79211i	−0.131251	+	0.195921i
$875$	45.0640	−	5.93279i	1.52344	−	0.200565i
$876$	−48.1413	+	13.3086i	−1.62654	+	0.449656i
$877$	−1.67886	+	12.7522i	−0.0566911	+	0.430611i	0.939439	+	0.342717i	$0.111347\pi$
$877$	−1.67886	+	12.7522i	−0.0566911	+	0.430611i	−0.996130	+	0.0878945i	$0.971986\pi$
$878$	−1.11462	−	17.3250i	−0.0376167	−	0.584690i
$879$	21.3769	−	37.9243i	0.721026	−	1.27915i
$880$	−46.0851	+	26.3125i	−1.55353	+	0.886995i
$881$	4.03208			0.135844			0.0679222	−	0.997691i	$-0.478363\pi$
$881$	4.03208			0.135844			0.0679222	+	0.997691i	$0.478363\pi$
$882$	11.9896	−	8.35269i	0.403710	−	0.281250i
$883$	−20.8136	−	50.2484i	−0.700433	−	1.69099i	−0.722625	−	0.691241i	$-0.757064\pi$
$883$	−20.8136	−	50.2484i	−0.700433	−	1.69099i	0.0221919	−	0.999754i	$-0.492936\pi$
$884$	−20.6380	−	35.9454i	−0.694131	−	1.20897i
$885$	5.87227	+	41.3063i	0.197394	+	1.38850i
$886$	7.02670	+	14.2920i	0.236066	+	0.480150i
$887$	−3.89637	−	14.5415i	−0.130827	−	0.488254i	0.869153	−	0.494543i	$-0.164665\pi$
$887$	−3.89637	−	14.5415i	−0.130827	−	0.488254i	−0.999980	+	0.00628923i	$0.997998\pi$
$888$	29.4421	+	19.3881i	0.988012	+	0.650620i
$889$	1.84353	−	6.88016i	0.0618301	−	0.230753i
$890$	19.5183	−	3.85804i	0.654254	−	0.129322i
$891$	−5.50909	−	31.6809i	−0.184562	−	1.06135i
$892$	−4.62079	+	11.0801i	−0.154716	+	0.370991i
$893$	−17.7768	−	13.6406i	−0.594879	−	0.456467i
$894$	32.9619	+	6.24472i	1.10241	+	0.208855i
$895$	61.3990	+	35.4487i	2.05234	+	1.18492i
$896$	15.8948	+	32.9273i	0.531009	+	1.10002i
$897$	−3.73815	−	6.32310i	−0.124813	−	0.211122i
$898$	−0.409906	−	1.21233i	−0.0136787	−	0.0404560i
$899$	7.91193	+	19.1011i	0.263878	+	0.637057i
$900$	−49.0726	−	19.2861i	−1.63575	−	0.642870i
$901$	10.2204	+	4.23342i	0.340491	+	0.141036i
$902$	−10.5589	+	9.23744i	−0.351572	+	0.307573i
$903$	26.1313	−	7.29166i	0.869596	−	0.242651i
$904$	−21.3627	−	43.7161i	−0.710513	−	1.45397i
$905$	60.6392	−	16.2482i	2.01572	−	0.540109i
$906$	45.6687	−	23.0412i	1.51724	−	0.765493i
$907$	3.52336	+	26.7625i	0.116991	+	0.888636i	0.944805	+	0.327633i	$0.106251\pi$
$907$	3.52336	+	26.7625i	0.116991	+	0.888636i	−0.827814	+	0.561003i	$0.810416\pi$
$908$	−0.0825968	+	34.3497i	−0.00274107	+	1.13994i
$909$	12.7712	−	17.3747i	0.423595	−	0.576283i
$910$	55.8281	−	37.2061i	1.85068	−	1.23337i
$911$	43.2008	−	24.9420i	1.43131	−	0.826366i	0.434087	−	0.900871i	$-0.357071\pi$
$911$	43.2008	−	24.9420i	1.43131	−	0.826366i	0.997221	+	0.0745050i	$0.0237377\pi$
$912$	16.0708	+	27.4846i	0.532157	+	0.910107i
$913$	−19.0999	−	11.0273i	−0.632114	−	0.364951i
$914$	−41.6308	+	2.67836i	−1.37702	+	0.0885924i
$915$	−31.6952	−	74.3400i	−1.04781	−	2.45760i
$916$	8.61816	−	31.8568i	0.284752	−	1.05258i
$917$	55.6990	+	23.0713i	1.83934	+	0.761880i
$918$	38.4982	+	1.37490i	1.27063	+	0.0453786i
$919$	−12.8383	−	12.8383i	−0.423495	−	0.423495i	0.462910	−	0.886405i	$-0.346805\pi$
$919$	−12.8383	−	12.8383i	−0.423495	−	0.423495i	−0.886405	+	0.462910i	$0.846805\pi$
$920$	−3.58298	−	10.6815i	−0.118127	−	0.352160i
$921$	6.51564	−	6.65151i	0.214698	−	0.219175i
$922$	8.80212	−	25.8282i	0.289882	−	0.850605i
$923$	−14.7478	+	11.3164i	−0.485429	+	0.372482i
$924$	31.9252	+	24.0981i	1.05026	+	0.792768i
$925$	38.4953	−	50.1680i	1.26572	−	1.64951i
$926$	−5.75186	+	28.7359i	−0.189018	+	0.944321i
$927$	−20.6875	−	11.3813i	−0.679466	−	0.373812i
$928$	−14.1529	+	20.9081i	−0.464592	+	0.686343i
$929$	38.5154	−	22.2369i	1.26365	−	0.729569i	0.289871	−	0.957066i	$-0.406388\pi$
$929$	38.5154	−	22.2369i	1.26365	−	0.729569i	0.973779	+	0.227497i	$0.0730542\pi$
$930$	−27.4899	+	31.9287i	−0.901428	+	1.04698i
$931$	−2.06589	+	15.6920i	−0.0677068	+	0.514284i
$932$	10.7252	+	1.43824i	0.351314	+	0.0471111i
$933$	18.9793	−	14.8769i	0.621354	−	0.487049i
$934$	20.7752	−	18.1753i	0.679786	−	0.594712i
$935$	−49.1786	−	49.1786i	−1.60831	−	1.60831i
$936$	−33.4309	+	2.76361i	−1.09272	+	0.0903315i
$937$	−5.72001	+	5.72001i	−0.186864	+	0.186864i	−0.794339	−	0.607475i	$-0.792183\pi$
$937$	−5.72001	+	5.72001i	−0.186864	+	0.186864i	0.607475	+	0.794339i	$0.292183\pi$
$938$	−2.31977	+	34.7526i	−0.0757431	+	1.13471i
$939$	10.1832	−	1.44768i	0.332316	−	0.0472434i
$940$	34.9992	−	9.28786i	1.14155	−	0.302936i
$941$	−36.6456	−	4.82448i	−1.19461	−	0.157274i	−0.493127	−	0.869957i	$-0.664146\pi$
$941$	−36.6456	−	4.82448i	−1.19461	−	0.157274i	−0.701485	+	0.712684i	$0.747479\pi$
$942$	14.2030	+	20.8425i	0.462759	+	0.679085i
$943$	−1.48923	−	2.57942i	−0.0484960	−	0.0839975i
$944$	9.81470	+	24.0209i	0.319441	+	0.781813i
$945$	1.92979	+	62.3242i	0.0627761	+	2.02741i
$946$	13.5813	+	20.3789i	0.441567	+	0.662574i
$947$	13.6697	+	10.4891i	0.444205	+	0.340850i	0.806522	−	0.591205i	$-0.201347\pi$
$947$	13.6697	+	10.4891i	0.444205	+	0.340850i	−0.362317	+	0.932055i	$0.618014\pi$
$948$	0.0683512	+	8.63724i	0.00221994	+	0.280525i
$949$	34.6997	+	45.2216i	1.12640	+	1.46795i
$950$	51.2517	−	25.1980i	1.66282	−	0.817530i
$951$	2.94675	−	11.4695i	0.0955550	−	0.371924i
$952$	−36.1407	+	31.4646i	−1.17133	+	1.01977i
$953$	28.8567	−	28.8567i	0.934759	−	0.934759i	−0.0632396	−	0.997998i	$-0.520143\pi$
$953$	28.8567	−	28.8567i	0.934759	−	0.934759i	0.997998	+	0.0632396i	$0.0201432\pi$
$954$	6.61522	−	6.03280i	0.214176	−	0.195319i
$955$	3.52477	−	8.50955i	0.114059	−	0.275363i
$956$	−30.8114	+	3.98105i	−0.996512	+	0.128756i
$957$	−3.32248	+	27.4201i	−0.107401	+	0.886366i
$958$	−3.52005	−	3.09449i	−0.113728	−	0.0999786i
$959$	11.0607	−	19.1576i	0.357168	−	0.618632i
$960$	−51.0318	−	6.55737i	−1.64704	−	0.211638i
$961$	−4.77107	−	8.26374i	−0.153906	−	0.266572i
$962$	7.89608	−	39.4483i	0.254580	−	1.27187i
$963$	12.6088	+	28.7476i	0.406312	+	0.926379i
$964$	19.7618	−	47.3866i	0.636485	−	1.52622i
$965$	41.6629	−	5.48503i	1.34118	−	0.176569i
$966$	−6.33329	+	5.65711i	−0.203770	+	0.182014i
$967$	−0.0797515	−	0.297637i	−0.00256464	−	0.00957135i	0.964632	−	0.263602i	$-0.0849104\pi$
$967$	−0.0797515	−	0.297637i	−0.00256464	−	0.00957135i	−0.967196	+	0.254030i	$0.918244\pi$
$968$	−1.62245	+	4.72355i	−0.0521476	+	0.151821i
$969$	−29.1990	+	29.8078i	−0.938006	+	0.957565i
$970$	1.72729	−	25.8766i	0.0554599	−	0.830848i
$971$	14.2728	−	34.4576i	0.458036	−	1.10580i	−0.511155	−	0.859488i	$-0.670782\pi$
$971$	14.2728	−	34.4576i	0.458036	−	1.10580i	0.969191	−	0.246309i	$-0.0792177\pi$
$972$	14.2421	−	27.7338i	0.456817	−	0.889561i
$973$	−10.8875	+	4.50975i	−0.349037	+	0.144576i
$974$	−13.0757	+	26.4346i	−0.418971	+	0.847021i
$975$	0.620846	+	60.1692i	0.0198830	+	1.92696i
$976$	−30.4057	−	40.0225i	−0.973263	−	1.28109i
$977$	−25.7160	+	44.5415i	−0.822729	+	1.42501i	0.0809138	+	0.996721i	$0.474216\pi$
$977$	−25.7160	+	44.5415i	−0.822729	+	1.42501i	−0.903643	+	0.428287i	$0.859117\pi$
$978$	28.8234	+	13.8889i	0.921669	+	0.444119i
$979$	8.24088	−	10.7397i	0.263380	−	0.343243i
$980$	−18.0424	−	18.1294i	−0.576344	−	0.579123i
$981$	12.2641	−	31.4271i	0.391562	−	1.00339i
$982$	32.8070	+	21.9780i	1.04691	+	0.701347i
$983$	50.5133	+	13.5350i	1.61112	+	0.431699i	0.948377	−	0.317144i	$-0.102724\pi$
$983$	50.5133	+	13.5350i	1.61112	+	0.431699i	0.662747	+	0.748843i	$0.269391\pi$
$984$	−13.5665	+	0.980677i	−0.432486	+	0.0312629i
$985$	−37.2403	+	9.97851i	−1.18657	+	0.317942i
$986$	−31.3203	−	10.6738i	−0.997441	−	0.339923i
$987$	−16.8376	−	21.4806i	−0.535948	−	0.683737i
$988$	22.1883	−	28.7728i	0.705903	−	0.915385i
$989$	−4.80350	+	1.98968i	−0.152742	+	0.0632680i
$990$	−52.9380	+	19.1251i	−1.68248	+	0.607836i
$991$			29.5159i			0.937603i	0.883303	+	0.468802i	$0.155314\pi$
$991$			29.5159i			0.937603i	−0.883303	+	0.468802i	$0.844686\pi$
$992$	−11.7308	+	23.4316i	−0.372454	+	0.743954i
$993$	8.83940	−	5.22577i	0.280510	−	0.165835i
$994$	16.1405	+	14.1892i	0.511946	+	0.450055i
$995$	−62.4581	−	8.22276i	−1.98005	−	0.260679i
$996$	−8.33896	−	19.6899i	−0.264230	−	0.623897i
$997$	1.58486	+	12.0382i	0.0501931	+	0.381254i	0.998043	+	0.0625363i	$0.0199189\pi$
$997$	1.58486	+	12.0382i	0.0501931	+	0.381254i	−0.947850	+	0.318718i	$0.896748\pi$
$998$	−34.7630	+	6.87135i	−1.10040	+	0.217509i
$999$	27.2449	+	25.6084i	0.861991	+	0.810214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.59.4	✓	368
3.2	odd	2		864.2.bn.a.827.43		368
9.2	odd	6	inner	288.2.bf.a.155.13	yes	368
9.7	even	3		864.2.bn.a.251.34		368
32.19	odd	8	inner	288.2.bf.a.275.13	yes	368
96.83	even	8		864.2.bn.a.179.34		368
288.83	even	24	inner	288.2.bf.a.83.4	yes	368
288.115	odd	24		864.2.bn.a.467.43		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.4	✓	368	1.1	even	1	trivial
288.2.bf.a.83.4	yes	368	288.83	even	24	inner
288.2.bf.a.155.13	yes	368	9.2	odd	6	inner
288.2.bf.a.275.13	yes	368	32.19	odd	8	inner
864.2.bn.a.179.34		368	96.83	even	8
864.2.bn.a.251.34		368	9.7	even	3
864.2.bn.a.467.43		368	288.115	odd	24
864.2.bn.a.827.43		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33971 + 0.452974i) q^{2} +(0.679302 + 1.59328i) q^{3} +(1.58963 - 1.21370i) q^{4} +(-2.26044 - 2.94587i) q^{5} +(-1.63178 - 1.82683i) q^{6} +(3.12162 + 0.836436i) q^{7} +(-1.57986 + 2.34607i) q^{8} +(-2.07710 + 2.16464i) q^{9} +O(q^{10})\)	\(q+(-1.33971 + 0.452974i) q^{2} +(0.679302 + 1.59328i) q^{3} +(1.58963 - 1.21370i) q^{4} +(-2.26044 - 2.94587i) q^{5} +(-1.63178 - 1.82683i) q^{6} +(3.12162 + 0.836436i) q^{7} +(-1.57986 + 2.34607i) q^{8} +(-2.07710 + 2.16464i) q^{9} +(4.36273 + 2.92268i) q^{10} +(3.54236 - 0.466360i) q^{11} +(3.01361 + 1.70826i) q^{12} +(0.516010 - 3.91948i) q^{13} +(-4.56094 + 0.293433i) q^{14} +(3.15807 - 5.60266i) q^{15} +(1.05385 - 3.85868i) q^{16} +5.24229 q^{17} +(1.80218 - 3.84085i) q^{18} +(1.75861 + 4.24565i) q^{19} +(-7.16868 - 1.93933i) q^{20} +(0.787846 + 5.54181i) q^{21} +(-4.53447 + 2.22938i) q^{22} +(-0.277647 - 1.03619i) q^{23} +(-4.81115 - 0.923476i) q^{24} +(-2.27443 + 8.48829i) q^{25} +(1.08412 + 5.48470i) q^{26} +(-4.85986 - 1.83895i) q^{27} +(5.97741 - 2.45910i) q^{28} +(3.54092 + 2.71704i) q^{29} +(-1.69304 + 8.93644i) q^{30} +(4.01166 + 2.31613i) q^{31} +(0.336036 + 5.64686i) q^{32} +(3.14938 + 5.32718i) q^{33} +(-7.02313 + 2.37462i) q^{34} +(-4.59222 - 11.0866i) q^{35} +(-0.674581 + 5.96196i) q^{36} +(-6.64812 - 2.75374i) q^{37} +(-4.27918 - 4.89132i) q^{38} +(6.59537 - 1.84037i) q^{39} +(10.4824 - 0.649090i) q^{40} +(2.68188 - 0.718607i) q^{41} +(-3.56578 - 7.06753i) q^{42} +(-0.632622 - 4.80524i) q^{43} +(5.06501 - 5.04071i) q^{44} +(11.0719 + 1.22580i) q^{45} +(0.841333 + 1.26243i) q^{46} +(-4.22270 + 2.43797i) q^{47} +(6.86385 - 0.942138i) q^{48} +(2.98271 + 1.72207i) q^{49} +(-0.797902 - 12.4021i) q^{50} +(3.56110 + 8.35244i) q^{51} +(-3.93683 - 6.85681i) q^{52} +(1.94961 + 0.807553i) q^{53} +(7.34379 + 0.262272i) q^{54} +(-9.38113 - 9.38113i) q^{55} +(-6.89406 + 6.00208i) q^{56} +(-5.56989 + 5.68603i) q^{57} +(-5.97454 - 2.03610i) q^{58} +(-5.14661 + 3.94913i) q^{59} +(-1.77980 - 12.7391i) q^{60} +(7.64946 - 9.96896i) q^{61} +(-6.42359 - 1.28576i) q^{62} +(-8.29449 + 5.01983i) q^{63} +(-3.00807 - 7.41293i) q^{64} +(-12.7127 + 7.33967i) q^{65} +(-6.63231 - 5.71027i) q^{66} +(0.994715 - 7.55561i) q^{67} +(8.33329 - 6.36258i) q^{68} +(1.46234 - 1.14626i) q^{69} +(11.1742 + 12.7726i) q^{70} +(-3.32494 - 3.32494i) q^{71} +(-1.79687 - 8.29284i) q^{72} +(-10.1954 + 10.1954i) q^{73} +(10.1539 + 0.677783i) q^{74} +(-15.0693 + 2.14231i) q^{75} +(7.94849 + 4.61458i) q^{76} +(11.4480 + 1.50715i) q^{77} +(-8.00223 + 5.45308i) q^{78} +(1.24672 + 2.15938i) q^{79} +(-13.7493 + 5.61784i) q^{80} +(-0.371341 - 8.99234i) q^{81} +(-3.26742 + 2.17754i) q^{82} +(-4.89714 - 3.75771i) q^{83} +(7.97851 + 7.85322i) q^{84} +(-11.8499 - 15.4431i) q^{85} +(3.02417 + 6.15105i) q^{86} +(-1.92366 + 7.48738i) q^{87} +(-4.50232 + 9.04740i) q^{88} +(2.67909 - 2.67909i) q^{89} +(-15.3884 + 3.37306i) q^{90} +(4.88918 - 11.8035i) q^{91} +(-1.69899 - 1.31018i) q^{92} +(-0.965122 + 7.96506i) q^{93} +(4.55284 - 5.17894i) q^{94} +(8.53189 - 14.7777i) q^{95} +(-8.76878 + 4.37133i) q^{96} +(-2.46934 - 4.27703i) q^{97} +(-4.77601 - 0.955978i) q^{98} +(-6.34832 + 8.63661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

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