LMFDB - Embedded newform 288.2.bf.a.11.43

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			11.43
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38102 - 0.304622i) q^{2} +(0.418469 + 1.68074i) q^{3} +(1.81441 - 0.841375i) q^{4} +(0.534666 + 4.06119i) q^{5} +(1.08990 + 2.19365i) q^{6} +(-1.15445 - 4.30845i) q^{7} +(2.24943 - 1.71466i) q^{8} +(-2.64977 + 1.40667i) q^{9} +O(q^{10})$	\(q+(1.38102 - 0.304622i) q^{2} +(0.418469 + 1.68074i) q^{3} +(1.81441 - 0.841375i) q^{4} +(0.534666 + 4.06119i) q^{5} +(1.08990 + 2.19365i) q^{6} +(-1.15445 - 4.30845i) q^{7} +(2.24943 - 1.71466i) q^{8} +(-2.64977 + 1.40667i) q^{9} +(1.97551 + 5.44570i) q^{10} +(-1.66994 + 1.28139i) q^{11} +(2.17341 + 2.69746i) q^{12} +(1.27782 - 1.66528i) q^{13} +(-2.90675 - 5.59837i) q^{14} +(-6.60207 + 2.59812i) q^{15} +(2.58418 - 3.05320i) q^{16} -2.44036 q^{17} +(-3.23087 + 2.74982i) q^{18} +(3.81763 - 1.58131i) q^{19} +(4.38709 + 6.91882i) q^{20} +(6.75828 - 3.74327i) q^{21} +(-1.91587 + 2.27832i) q^{22} +(1.17961 + 0.316074i) q^{23} +(3.82322 + 3.06317i) q^{24} +(-11.3778 + 3.04867i) q^{25} +(1.25740 - 2.68903i) q^{26} +(-3.47310 - 3.86492i) q^{27} +(-5.71966 - 6.84597i) q^{28} +(-0.104663 - 0.0137791i) q^{29} +(-8.32612 + 5.59918i) q^{30} +(6.01303 - 3.47163i) q^{31} +(2.63872 - 5.00371i) q^{32} +(-2.85250 - 2.27051i) q^{33} +(-3.37017 + 0.743386i) q^{34} +(16.8802 - 6.99201i) q^{35} +(-3.62423 + 4.78173i) q^{36} +(-1.33791 + 3.23000i) q^{37} +(4.79050 - 3.34675i) q^{38} +(3.33363 + 1.45081i) q^{39} +(8.16627 + 8.21860i) q^{40} +(2.21215 - 8.25586i) q^{41} +(8.19301 - 7.22824i) q^{42} +(-1.12558 - 1.46689i) q^{43} +(-1.95183 + 3.73001i) q^{44} +(-7.12952 - 10.0091i) q^{45} +(1.72534 + 0.0771704i) q^{46} +(0.235013 + 0.135685i) q^{47} +(6.21303 + 3.06566i) q^{48} +(-11.1678 + 6.44773i) q^{49} +(-14.7842 + 7.67619i) q^{50} +(-1.02121 - 4.10160i) q^{51} +(0.917358 - 4.09663i) q^{52} +(-1.39716 + 3.37305i) q^{53} +(-5.97374 - 4.27953i) q^{54} +(-6.09683 - 6.09683i) q^{55} +(-9.98437 - 7.71207i) q^{56} +(4.25533 + 5.75470i) q^{57} +(-0.148738 + 0.0128534i) q^{58} +(-10.9495 + 1.44153i) q^{59} +(-9.79287 + 10.2689i) q^{60} +(-0.404733 + 3.07425i) q^{61} +(7.24656 - 6.62607i) q^{62} +(9.11959 + 9.79246i) q^{63} +(2.11987 - 7.71402i) q^{64} +(7.44625 + 4.29909i) q^{65} +(-4.63099 - 2.26668i) q^{66} +(-8.66829 + 11.2967i) q^{67} +(-4.42781 + 2.05325i) q^{68} +(-0.0376102 + 2.11488i) q^{69} +(21.1819 - 14.7981i) q^{70} +(1.42724 + 1.42724i) q^{71} +(-3.54850 + 7.70767i) q^{72} +(-3.46821 + 3.46821i) q^{73} +(-0.863748 + 4.86824i) q^{74} +(-9.88528 - 17.8473i) q^{75} +(5.59627 - 6.08120i) q^{76} +(7.44865 + 5.71555i) q^{77} +(5.04575 + 0.988092i) q^{78} +(4.60186 - 7.97066i) q^{79} +(13.7813 + 8.86240i) q^{80} +(5.04253 - 7.45472i) q^{81} +(0.540103 - 12.0753i) q^{82} +(-3.51986 - 0.463399i) q^{83} +(9.11280 - 12.4781i) q^{84} +(-1.30478 - 9.91076i) q^{85} +(-2.00129 - 1.68292i) q^{86} +(-0.0206390 - 0.181677i) q^{87} +(-1.55926 + 5.74578i) q^{88} +(-8.58494 + 8.58494i) q^{89} +(-12.8950 - 11.6509i) q^{90} +(-8.64996 - 3.58293i) q^{91} +(2.40623 - 0.419002i) q^{92} +(8.35117 + 8.65357i) q^{93} +(0.365890 + 0.115793i) q^{94} +(8.46317 + 14.6586i) q^{95} +(9.51416 + 2.34110i) q^{96} +(1.28048 - 2.21785i) q^{97} +(-13.4588 + 12.3064i) q^{98} +(2.62245 - 5.74444i) 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.38102	−	0.304622i	0.976526	−	0.215400i
$2$	1.38102	−	0.304622i	0.976526	−	0.215400i
$3$	0.418469	+	1.68074i	0.241603	+	0.970375i
$3$	0.418469	+	1.68074i	0.241603	+	0.970375i
$4$	1.81441	−	0.841375i	0.907206	−	0.420687i
$5$	0.534666	+	4.06119i	0.239110	+	1.81622i	0.517422	+	0.855730i	$0.326892\pi$
$5$	0.534666	+	4.06119i	0.239110	+	1.81622i	−0.278312	+	0.960491i	$0.589775\pi$
$6$	1.08990	+	2.19365i	0.444951	+	0.895555i
$7$	−1.15445	−	4.30845i	−0.436339	−	1.62844i	−0.737841	−	0.674975i	$-0.764155\pi$
$7$	−1.15445	−	4.30845i	−0.436339	−	1.62844i	0.301502	−	0.953466i	$-0.402512\pi$
$8$	2.24943	−	1.71466i	0.795294	−	0.606224i
$9$	−2.64977	+	1.40667i	−0.883256	+	0.468891i
$10$	1.97551	+	5.44570i	0.624711	+	1.72208i
$11$	−1.66994	+	1.28139i	−0.503506	+	0.386353i	−0.829051	−	0.559173i	$-0.811119\pi$
$11$	−1.66994	+	1.28139i	−0.503506	+	0.386353i	0.325545	+	0.945526i	$0.394452\pi$
$12$	2.17341	+	2.69746i	0.627408	+	0.778690i
$13$	1.27782	−	1.66528i	0.354403	−	0.461867i	−0.581798	−	0.813334i	$-0.697650\pi$
$13$	1.27782	−	1.66528i	0.354403	−	0.461867i	0.936200	+	0.351467i	$0.114317\pi$
$14$	−2.90675	−	5.59837i	−0.776863	−	1.49623i
$15$	−6.60207	+	2.59812i	−1.70465	+	0.670831i
$16$	2.58418	−	3.05320i	0.646044	−	0.763300i
$17$	−2.44036			−0.591873			−0.295937	−	0.955208i	$-0.595632\pi$
$17$	−2.44036			−0.591873			−0.295937	+	0.955208i	$0.595632\pi$
$18$	−3.23087	+	2.74982i	−0.761523	+	0.648138i
$19$	3.81763	−	1.58131i	0.875823	−	0.362778i	0.100948	−	0.994892i	$-0.467813\pi$
$19$	3.81763	−	1.58131i	0.875823	−	0.362778i	0.774876	+	0.632114i	$0.217813\pi$
$20$	4.38709	+	6.91882i	0.980983	+	1.54710i
$21$	6.75828	−	3.74327i	1.47478	−	0.816849i
$22$	−1.91587	+	2.27832i	−0.408466	+	0.485739i
$23$	1.17961	+	0.316074i	0.245965	+	0.0659061i	0.379695	−	0.925112i	$-0.376029\pi$
$23$	1.17961	+	0.316074i	0.245965	+	0.0659061i	−0.133730	+	0.991018i	$0.542696\pi$
$24$	3.82322	+	3.06317i	0.780410	+	0.625268i
$25$	−11.3778	+	3.04867i	−2.27556	+	0.609734i
$26$	1.25740	−	2.68903i	0.246597	−	0.527363i
$27$	−3.47310	−	3.86492i	−0.668398	−	0.743804i
$28$	−5.71966	−	6.84597i	−1.08091	−	1.29377i
$29$	−0.104663	−	0.0137791i	−0.0194354	−	0.00255871i	0.120802	−	0.992677i	$-0.461453\pi$
$29$	−0.104663	−	0.0137791i	−0.0194354	−	0.00255871i	−0.140238	+	0.990118i	$0.544787\pi$
$30$	−8.32612	+	5.59918i	−1.52013	+	1.02226i
$31$	6.01303	−	3.47163i	1.07997	−	0.623523i	0.149084	−	0.988825i	$-0.452368\pi$
$31$	6.01303	−	3.47163i	1.07997	−	0.623523i	0.930889	+	0.365302i	$0.119034\pi$
$32$	2.63872	−	5.00371i	0.466464	−	0.884540i
$33$	−2.85250	−	2.27051i	−0.496556	−	0.395245i
$34$	−3.37017	+	0.743386i	−0.577980	+	0.127490i
$35$	16.8802	−	6.99201i	2.85327	−	1.18186i
$36$	−3.62423	+	4.78173i	−0.604038	+	0.796956i
$37$	−1.33791	+	3.23000i	−0.219951	+	0.531009i	−0.994883	−	0.101036i	$-0.967784\pi$
$37$	−1.33791	+	3.23000i	−0.219951	+	0.531009i	0.774932	+	0.632045i	$0.217784\pi$
$38$	4.79050	−	3.34675i	0.777122	−	0.542914i
$39$	3.33363	+	1.45081i	0.533809	+	0.232315i
$40$	8.16627	+	8.21860i	1.29120	+	1.29947i
$41$	2.21215	−	8.25586i	0.345480	−	1.28935i	−0.546571	−	0.837413i	$-0.684067\pi$
$41$	2.21215	−	8.25586i	0.345480	−	1.28935i	0.892050	−	0.451936i	$-0.149266\pi$
$42$	8.19301	−	7.22824i	1.26421	−	1.11534i
$43$	−1.12558	−	1.46689i	−0.171650	−	0.223698i	0.699604	−	0.714530i	$-0.253360\pi$
$43$	−1.12558	−	1.46689i	−0.171650	−	0.223698i	−0.871254	+	0.490832i	$0.836693\pi$
$44$	−1.95183	+	3.73001i	−0.294249	+	0.562321i
$45$	−7.12952	−	10.0091i	−1.06281	−	1.49207i
$46$	1.72534	+	0.0771704i	0.254387	+	0.0113782i
$47$	0.235013	+	0.135685i	0.0342802	+	0.0197917i	0.517042	−	0.855960i	$-0.327033\pi$
$47$	0.235013	+	0.135685i	0.0342802	+	0.0197917i	−0.482762	+	0.875752i	$0.660366\pi$
$48$	6.21303	+	3.06566i	0.896774	+	0.442489i
$49$	−11.1678	+	6.44773i	−1.59540	+	0.921105i
$50$	−14.7842	+	7.67619i	−2.09081	+	1.08558i
$51$	−1.02121	−	4.10160i	−0.142999	−	0.574339i
$52$	0.917358	−	4.09663i	0.127215	−	0.568101i
$53$	−1.39716	+	3.37305i	−0.191915	+	0.463324i	−0.990321	−	0.138796i	$-0.955677\pi$
$53$	−1.39716	+	3.37305i	−0.191915	+	0.463324i	0.798406	+	0.602119i	$0.205677\pi$
$54$	−5.97374	−	4.27953i	−0.812923	−	0.582371i
$55$	−6.09683	−	6.09683i	−0.822097	−	0.822097i
$56$	−9.98437	−	7.71207i	−1.33422	−	1.03057i
$57$	4.25533	+	5.75470i	0.563632	+	0.762229i
$58$	−0.148738	+	0.0128534i	−0.0195303	+	0.00168773i
$59$	−10.9495	+	1.44153i	−1.42551	+	0.187671i	−0.803483	−	0.595328i	$-0.797022\pi$
$59$	−10.9495	+	1.44153i	−1.42551	+	0.187671i	−0.622023	+	0.782999i	$0.713689\pi$
$60$	−9.79287	+	10.2689i	−1.26425	+	1.32571i
$61$	−0.404733	+	3.07425i	−0.0518207	+	0.393617i	0.945804	+	0.324737i	$0.105276\pi$
$61$	−0.404733	+	3.07425i	−0.0518207	+	0.393617i	−0.997625	+	0.0688801i	$0.978057\pi$
$62$	7.24656	−	6.62607i	0.920315	−	0.841512i
$63$	9.11959	+	9.79246i	1.14896	+	1.23373i
$64$	2.11987	−	7.71402i	0.264984	−	0.964253i
$65$	7.44625	+	4.29909i	0.923593	+	0.533237i
$66$	−4.63099	−	2.26668i	−0.570036	−	0.279009i
$67$	−8.66829	+	11.2967i	−1.05900	+	1.38012i	−0.138055	+	0.990425i	$0.544085\pi$
$67$	−8.66829	+	11.2967i	−1.05900	+	1.38012i	−0.920945	+	0.389691i	$0.872582\pi$
$68$	−4.42781	+	2.05325i	−0.536951	+	0.248994i
$69$	−0.0376102	+	2.11488i	−0.00452773	+	0.254601i
$70$	21.1819	−	14.7981i	2.53172	−	1.76872i
$71$	1.42724	+	1.42724i	0.169382	+	0.169382i	0.786708	−	0.617326i	$-0.211784\pi$
$71$	1.42724	+	1.42724i	0.169382	+	0.169382i	−0.617326	+	0.786708i	$0.711784\pi$
$72$	−3.54850	+	7.70767i	−0.418194	+	0.908358i
$73$	−3.46821	+	3.46821i	−0.405923	+	0.405923i	−0.880314	−	0.474391i	$-0.842668\pi$
$73$	−3.46821	+	3.46821i	−0.405923	+	0.405923i	0.474391	+	0.880314i	$0.342668\pi$
$74$	−0.863748	+	4.86824i	−0.100409	+	0.565922i
$75$	−9.88528	−	17.8473i	−1.14145	−	2.06083i
$76$	5.59627	−	6.08120i	0.641936	−	0.697562i
$77$	7.44865	+	5.71555i	0.848853	+	0.651348i
$78$	5.04575	+	0.988092i	0.571319	+	0.111879i
$79$	4.60186	−	7.97066i	0.517750	−	0.896770i	−0.482037	−	0.876151i	$-0.660103\pi$
$79$	4.60186	−	7.97066i	0.517750	−	0.896770i	0.999787	−	0.0206189i	$-0.00656367\pi$
$80$	13.7813	+	8.86240i	1.54080	+	0.990846i
$81$	5.04253	−	7.45472i	0.560282	−	0.828302i
$82$	0.540103	−	12.0753i	0.0596443	−	1.33350i
$83$	−3.51986	−	0.463399i	−0.386355	−	0.0508646i	−0.0651531	−	0.997875i	$-0.520754\pi$
$83$	−3.51986	−	0.463399i	−0.386355	−	0.0508646i	−0.321202	+	0.947011i	$0.604087\pi$
$84$	9.11280	−	12.4781i	0.994288	−	1.36147i
$85$	−1.30478	−	9.91076i	−0.141523	−	1.07497i
$86$	−2.00129	−	1.68292i	−0.215805	−	0.181474i
$87$	−0.0206390	−	0.181677i	−0.00221273	−	0.0194778i
$88$	−1.55926	+	5.74578i	−0.166218	+	0.612502i
$89$	−8.58494	+	8.58494i	−0.910002	+	0.910002i	−0.996272	−	0.0862695i	$-0.972505\pi$
$89$	−8.58494	+	8.58494i	−0.910002	+	0.910002i	0.0862695	+	0.996272i	$0.472505\pi$
$90$	−12.8950	−	11.6509i	−1.35925	−	1.22812i
$91$	−8.64996	−	3.58293i	−0.906762	−	0.375593i
$92$	2.40623	−	0.419002i	0.250867	−	0.0436839i
$93$	8.35117	+	8.65357i	0.865976	+	0.897334i
$94$	0.365890	+	0.115793i	0.0377386	+	0.0119431i
$95$	8.46317	+	14.6586i	0.868303	+	1.50394i
$96$	9.51416	+	2.34110i	0.971035	+	0.238937i
$97$	1.28048	−	2.21785i	0.130013	−	0.225188i	−0.793669	−	0.608350i	$-0.791832\pi$
$97$	1.28048	−	2.21785i	0.130013	−	0.225188i	0.923681	+	0.383162i	$0.125165\pi$
$98$	−13.4588	+	12.3064i	−1.35954	+	1.24313i
$99$	2.62245	−	5.74444i	0.263566	−	0.577338i
$100$	−18.0789	+	15.1045i	−1.80789	+	1.51045i
$101$	9.72422	−	7.46166i	0.967596	−	0.742463i	0.00132784	−	0.999999i	$-0.499577\pi$
$101$	9.72422	−	7.46166i	0.967596	−	0.742463i	0.966269	+	0.257536i	$0.0829107\pi$
$102$	−2.65975	−	5.35330i	−0.263354	−	0.530055i
$103$	−1.69233	−	0.453458i	−0.166750	−	0.0446805i	0.174478	−	0.984661i	$-0.444176\pi$
$103$	−1.69233	−	0.453458i	−0.166750	−	0.0446805i	−0.341228	+	0.939981i	$0.610843\pi$
$104$	0.0189630	−	5.93696i	0.00185948	−	0.582167i
$105$	18.8156	+	25.4453i	1.83621	+	2.48320i
$106$	−0.902000	+	5.08384i	−0.0876100	+	0.493786i
$107$	−8.84387	−	3.66325i	−0.854970	−	0.354140i	−0.0882315	−	0.996100i	$-0.528122\pi$
$107$	−8.84387	−	3.66325i	−0.854970	−	0.354140i	−0.766738	+	0.641960i	$0.778122\pi$
$108$	−9.55347	−	4.09037i	−0.919283	−	0.393596i
$109$	6.04419	+	14.5920i	0.578928	+	1.39766i	0.893776	+	0.448514i	$0.148046\pi$
$109$	6.04419	+	14.5920i	0.578928	+	1.39766i	−0.314848	+	0.949142i	$0.601954\pi$
$110$	−10.2770	−	6.56260i	−0.979878	−	0.625719i
$111$	−5.98867	−	0.897023i	−0.568419	−	0.0851417i
$112$	−16.1378	−	7.60904i	−1.52488	−	0.718986i
$113$	3.95812	+	6.85566i	0.372349	+	0.644927i	0.989926	−	0.141583i	$-0.0452193\pi$
$113$	3.95812	+	6.85566i	0.372349	+	0.644927i	−0.617578	+	0.786510i	$0.711886\pi$
$114$	7.62969	+	6.65107i	0.714586	+	0.622930i
$115$	−0.652944	+	4.95960i	−0.0608873	+	0.462485i
$116$	−0.201494	+	0.0630596i	−0.0187083	+	0.00585493i
$117$	−1.04341	+	6.21009i	−0.0964630	+	0.574123i
$118$	−14.6823	+	5.32624i	−1.35162	+	0.490320i
$119$	2.81726	+	10.5141i	0.258258	+	0.963830i
$120$	−10.3960	+	17.1646i	−0.949020	+	1.56691i
$121$	−1.70027	+	6.34550i	−0.154570	+	0.576864i
$122$	0.377541	+	4.36888i	0.0341809	+	0.395540i
$123$	14.8017	+	0.263227i	1.33462	+	0.0237344i
$124$	7.98918	−	11.3582i	0.717449	−	1.01999i
$125$	−10.6268	−	25.6553i	−0.950487	−	2.29468i
$126$	15.5773	+	10.7455i	1.38774	+	0.957286i
$127$		−	13.6176i		−	1.20837i	−0.796845	−	0.604183i	$-0.793499\pi$
$127$		−	13.6176i		−	1.20837i	0.796845	−	0.604183i	$-0.206501\pi$
$128$	0.577721	−	11.2989i	0.0510638	−	0.998695i
$129$	1.99444	−	2.50566i	0.175600	−	0.220611i
$130$	11.5930	+	3.66883i	1.01677	+	0.321778i
$131$	3.51542	+	2.69748i	0.307144	+	0.235680i	0.750819	−	0.660508i	$-0.229659\pi$
$131$	3.51542	+	2.69748i	0.307144	+	0.235680i	−0.443675	+	0.896188i	$0.646326\pi$
$132$	−7.08596	−	1.71962i	−0.616753	−	0.149674i
$133$	−11.2202	−	14.6225i	−0.972918	−	1.26793i
$134$	−8.52982	+	18.2415i	−0.736864	+	1.57583i
$135$	13.8392	−	16.1714i	1.19109	−	1.39181i
$136$	−5.48941	+	4.18439i	−0.470713	+	0.358808i
$137$	2.10306	−	0.563514i	0.179677	−	0.0481443i	−0.167859	−	0.985811i	$-0.553685\pi$
$137$	2.10306	−	0.563514i	0.179677	−	0.0481443i	0.347536	+	0.937667i	$0.387019\pi$
$138$	0.592297	+	2.93214i	0.0504197	+	0.249600i
$139$	13.0293	−	1.71534i	1.10513	−	0.145493i	0.444191	−	0.895932i	$-0.353491\pi$
$139$	13.0293	−	1.71534i	1.10513	−	0.145493i	0.660939	+	0.750439i	$0.270158\pi$
$140$	24.7447	−	26.8890i	2.09131	−	2.27253i
$141$	−0.129705	+	0.451776i	−0.0109232	+	0.0380464i
$142$	2.40580	+	1.53627i	0.201891	+	0.128921i
$143$			4.41830i			0.369477i
$144$	−2.55261	+	11.7254i	−0.212717	+	0.977114i
$145$		−	0.432423i		−	0.0359107i
$146$	−3.73316	+	5.84615i	−0.308959	+	0.483831i
$147$	−15.5103	−	16.0720i	−1.27927	−	1.32559i
$148$	0.290123	+	6.98624i	0.0238479	+	0.574265i
$149$	−2.71317	+	0.357195i	−0.222271	+	0.0292626i	−0.240839	−	0.970565i	$-0.577423\pi$
$149$	−2.71317	+	0.357195i	−0.222271	+	0.0292626i	0.0185679	+	0.999828i	$0.494089\pi$
$150$	−19.0884	−	21.6362i	−1.55856	−	1.76659i
$151$	−1.68542	+	0.451608i	−0.137158	+	0.0367513i	−0.326745	−	0.945113i	$-0.605952\pi$
$151$	−1.68542	+	0.451608i	−0.137158	+	0.0367513i	0.189587	+	0.981864i	$0.439285\pi$
$152$	5.87607	−	10.1030i	0.476612	−	0.819460i
$153$	6.46638	−	3.43279i	0.522776	−	0.277524i
$154$	12.0278	+	5.62425i	0.969227	+	0.453215i
$155$	17.3139	+	22.5639i	1.39069	+	1.81238i
$156$	7.26926	−	0.172475i	0.582006	−	0.0138090i
$157$	6.69383	+	5.13636i	0.534226	+	0.409926i	0.840332	−	0.542071i	$-0.182360\pi$
$157$	6.69383	+	5.13636i	0.534226	+	0.409926i	−0.306107	+	0.951997i	$0.599026\pi$
$158$	3.92721	−	12.4094i	0.312432	−	0.987242i
$159$	−6.25388	−	0.936749i	−0.495965	−	0.0742890i
$160$	21.7319	+	8.04103i	1.71806	+	0.635699i
$161$		−	5.44716i		−	0.429296i
$162$	4.69295	−	11.8312i	0.368713	−	0.929543i
$163$	0.190189	+	0.459157i	0.0148967	+	0.0359639i	0.931153	−	0.364629i	$-0.118804\pi$
$163$	0.190189	+	0.459157i	0.0148967	+	0.0359639i	−0.916256	+	0.400593i	$0.868804\pi$
$164$	−2.93252	−	16.8408i	−0.228991	−	1.31504i
$165$	7.69585	−	12.7985i	0.599121	−	0.996363i
$166$	−5.00215	+	0.432266i	−0.388242	+	0.0335503i
$167$	−3.25733	+	12.1565i	−0.252060	+	0.940700i	0.717643	+	0.696411i	$0.245221\pi$
$167$	−3.25733	+	12.1565i	−0.252060	+	0.940700i	−0.969703	+	0.244288i	$0.921446\pi$
$168$	8.78383	−	20.0084i	0.677687	−	1.54368i
$169$	2.22429	+	8.30118i	0.171100	+	0.638552i
$170$	−4.82095	−	13.2895i	−0.369750	−	1.01926i
$171$	−7.89143	+	9.56026i	−0.603473	+	0.731092i
$172$	−3.27647	−	1.71450i	−0.249829	−	0.130730i
$173$	0.0798614	−	0.606607i	0.00607175	−	0.0461195i	−0.988141	−	0.153551i	$-0.950929\pi$
$173$	0.0798614	−	0.606607i	0.00607175	−	0.0461195i	0.994213	+	0.107431i	$0.0342625\pi$
$174$	−0.0838455	−	0.244611i	−0.00635631	−	0.0185439i
$175$	26.2701	+	45.5011i	1.98583	+	3.43956i
$176$	−0.403079	+	8.41000i	−0.0303833	+	0.633927i
$177$	−7.00487	−	17.8001i	−0.526519	−	1.33793i
$178$	−9.24079	+	14.4711i	−0.692626	+	1.08466i
$179$	3.91965	+	9.46287i	0.292968	+	0.707288i	1.00000		0.000106127i	$3.37814e-5\pi$
$179$	3.91965	+	9.46287i	0.292968	+	0.707288i	−0.707032	+	0.707182i	$0.749966\pi$
$180$	−21.3573	−	12.1621i	−1.59188	−	0.906506i
$181$	18.9049	+	7.83068i	1.40519	+	0.582050i	0.951094	−	0.308901i	$-0.0999613\pi$
$181$	18.9049	+	7.83068i	1.40519	+	0.582050i	0.454099	+	0.890951i	$0.349961\pi$
$182$	−13.0372	−	2.31312i	−0.966379	−	0.171460i
$183$	−5.33638	+	0.606228i	−0.394477	+	0.0448137i
$184$	3.19540	−	1.31164i	0.235568	−	0.0966952i
$185$	−13.8330	−	3.70654i	−1.01702	−	0.272510i
$186$	14.1692	+	9.40678i	1.03893	+	0.689738i
$187$	4.07525	−	3.12705i	0.298012	−	0.228672i
$188$	0.540573	+	0.0484541i	0.0394253	+	0.00353388i
$189$	−12.6423	+	19.4255i	−0.919592	+	1.41300i
$190$	16.1531	+	17.6658i	1.17187	+	1.28161i
$191$	0.881036	−	1.52600i	0.0637495	−	0.110417i	−0.832389	−	0.554192i	$-0.813027\pi$
$191$	0.881036	−	1.52600i	0.0637495	−	0.110417i	0.896139	+	0.443774i	$0.146361\pi$
$192$	13.8524	+	0.334875i	0.999708	+	0.0241675i
$193$	−4.03369	−	6.98656i	−0.290351	−	0.502904i	0.683541	−	0.729912i	$-0.260439\pi$
$193$	−4.03369	−	6.98656i	−0.290351	−	0.502904i	−0.973893	+	0.227008i	$0.927106\pi$
$194$	1.09275	−	3.45295i	0.0784551	−	0.247907i
$195$	−4.10963	+	14.3142i	−0.294297	+	1.02506i
$196$	−14.8380	+	21.0951i	−1.05986	+	1.50680i
$197$	−16.4773	−	6.82511i	−1.17396	−	0.486269i	−0.291458	−	0.956584i	$-0.594140\pi$
$197$	−16.4773	−	6.82511i	−1.17396	−	0.486269i	−0.882499	+	0.470315i	$0.844140\pi$
$198$	1.87177	−	8.73203i	0.133021	−	0.620558i
$199$	−3.50596	+	3.50596i	−0.248531	+	0.248531i	−0.820368	−	0.571837i	$-0.806231\pi$
$199$	−3.50596	+	3.50596i	−0.248531	+	0.248531i	0.571837	+	0.820368i	$0.306231\pi$
$200$	−20.3661	+	26.3668i	−1.44010	+	1.86442i
$201$	−22.6143	−	9.84180i	−1.59509	−	0.694187i
$202$	11.1563	−	13.2669i	0.784956	−	0.933455i
$203$	0.0614607	+	0.466841i	0.00431370	+	0.0327658i
$204$	−5.30389	−	6.58277i	−0.371346	−	0.460886i
$205$	34.7114	+	4.56984i	2.42435	+	0.319172i
$206$	−2.47526	−	0.110713i	−0.172460	−	0.00771373i
$207$	−3.57029	+	0.821798i	−0.248153	+	0.0571189i
$208$	−1.78234	−	8.20482i	−0.123583	−	0.568902i
$209$	−4.34893	+	7.53256i	−0.300821	+	0.521038i
$210$	33.7358	+	29.4087i	2.32799	+	2.02939i
$211$	−8.30094	−	6.36954i	−0.571461	−	0.438497i	0.282179	−	0.959362i	$-0.408943\pi$
$211$	−8.30094	−	6.36954i	−0.571461	−	0.438497i	−0.853639	+	0.520865i	$0.825610\pi$
$212$	0.302971	+	7.29563i	0.0208081	+	0.501066i
$213$	−1.80156	+	2.99607i	−0.123441	+	0.205287i
$214$	−13.3294	−	2.36498i	−0.911182	−	0.161666i
$215$	5.35551	−	5.35551i	0.365243	−	0.365243i
$216$	−14.4395	−	2.73868i	−0.982485	−	0.186343i
$217$	−21.8990	−	21.8990i	−1.48660	−	1.48660i
$218$	12.7921	+	18.3105i	0.866393	+	1.24015i
$219$	−7.28050	−	4.37782i	−0.491970	−	0.295826i
$220$	−16.1919	−	5.93244i	−1.09166	−	0.399965i
$221$	−3.11833	+	4.06389i	−0.209762	+	0.273367i
$222$	−8.54370	+	0.585474i	−0.573415	+	0.0392944i
$223$	−0.272576	−	0.157372i	−0.0182530	−	0.0105384i	0.490846	−	0.871247i	$-0.336688\pi$
$223$	−0.272576	−	0.157372i	−0.0182530	−	0.0105384i	−0.509099	+	0.860708i	$0.670021\pi$
$224$	−24.6045	−	5.59227i	−1.64396	−	0.373649i
$225$	25.8600	−	24.0831i	1.72400	−	1.60554i
$226$	7.55461	+	8.26205i	0.502525	+	0.549584i
$227$	2.53480	−	19.2537i	0.168240	−	1.27791i	−0.673968	−	0.738761i	$-0.735411\pi$
$227$	2.53480	−	19.2537i	0.168240	−	1.27791i	0.842208	−	0.539152i	$-0.181255\pi$
$228$	12.5628	+	6.86107i	0.831990	+	0.454385i
$229$	0.741709	−	0.0976479i	0.0490135	−	0.00645275i	−0.105980	−	0.994368i	$-0.533798\pi$
$229$	0.741709	−	0.0976479i	0.0490135	−	0.00645275i	0.154993	+	0.987916i	$0.450464\pi$
$230$	0.609076	+	7.04819i	0.0401613	+	0.464744i
$231$	−6.48932	+	14.9110i	−0.426966	+	0.981073i
$232$	−0.259058	+	0.148466i	−0.0170080	+	0.00974726i
$233$	−1.04654	−	1.04654i	−0.0685611	−	0.0685611i	0.671995	−	0.740556i	$-0.265438\pi$
$233$	−1.04654	−	1.04654i	−0.0685611	−	0.0685611i	−0.740556	+	0.671995i	$0.765438\pi$
$234$	0.450766	+	8.89408i	0.0294675	+	0.581424i
$235$	−0.425389	+	1.02698i	−0.0277493	+	0.0669928i
$236$	−18.6541	+	11.8282i	−1.21428	+	0.769949i
$237$	15.3223	+	4.39906i	0.995293	+	0.285750i
$238$	7.09352	+	13.6620i	0.459804	+	0.885577i
$239$	−15.9651	+	9.21746i	−1.03270	+	0.596228i	−0.917756	−	0.397145i	$-0.870001\pi$
$239$	−15.9651	+	9.21746i	−1.03270	+	0.596228i	−0.114941	+	0.993372i	$0.536668\pi$
$240$	−9.12833	+	26.8714i	−0.589231	+	1.73454i
$241$	19.7627	+	11.4100i	1.27303	+	0.734983i	0.975557	−	0.219748i	$-0.0705236\pi$
$241$	19.7627	+	11.4100i	1.27303	+	0.734983i	0.297471	+	0.954731i	$0.403857\pi$
$242$	−0.415126	+	9.28118i	−0.0266853	+	0.596617i
$243$	14.6396	+	5.35562i	0.939130	+	0.343563i
$244$	1.85225	+	5.91849i	0.118578	+	0.378892i
$245$	−32.1565	−	41.9072i	−2.05441	−	2.67735i
$246$	20.5215	−	4.14539i	1.30840	−	0.264300i
$247$	2.24489	−	8.37806i	0.142839	−	0.533083i
$248$	7.57324	−	18.1195i	0.480901	−	1.15059i
$249$	−0.694102	−	6.10989i	−0.0439869	−	0.387199i
$250$	−22.4909	−	32.1932i	−1.42245	−	2.03608i
$251$	0.772923	−	1.86600i	0.0487865	−	0.117781i	−0.897607	−	0.440796i	$-0.854696\pi$
$251$	0.772923	−	1.86600i	0.0487865	−	0.117781i	0.946394	+	0.323015i	$0.104696\pi$
$252$	24.7858	+	10.0945i	1.56136	+	0.635897i
$253$	−2.37488	+	0.983709i	−0.149308	+	0.0618453i
$254$	−4.14822	−	18.8061i	−0.260282	−	1.18000i
$255$	16.1114	−	6.34034i	1.00893	−	0.397047i
$256$	−2.64406	−	15.7800i	−0.165254	−	0.986251i
$257$	0.536990	−	0.310031i	0.0334965	−	0.0193392i	−0.483158	−	0.875533i	$-0.660510\pi$
$257$	0.536990	−	0.310031i	0.0334965	−	0.0193392i	0.516655	+	0.856194i	$0.327177\pi$
$258$	1.99107	−	4.06790i	0.123959	−	0.253257i
$259$	15.4608	+	2.03546i	0.960690	+	0.126477i
$260$	17.1277	+	1.53524i	1.06222	+	0.0952114i
$261$	0.296714	−	0.110715i	0.0183662	−	0.00685308i
$262$	5.67657	+	2.65439i	0.350699	+	0.163989i
$263$	10.7644	−	2.88431i	0.663760	−	0.177854i	0.0888177	−	0.996048i	$-0.471691\pi$
$263$	10.7644	−	2.88431i	0.663760	−	0.177854i	0.574942	+	0.818194i	$0.305024\pi$
$264$	−10.3097	−	0.216285i	−0.634515	−	0.0133114i
$265$	−14.4456	−	3.87069i	−0.887387	−	0.237775i
$266$	−19.9497	−	16.7760i	−1.22319	−	1.02860i
$267$	−18.0216	−	10.8365i	−1.10290	−	0.663184i
$268$	−6.22305	+	27.7902i	−0.380134	+	1.69756i
$269$	25.9642	−	10.7547i	1.58307	−	0.655728i	0.594171	−	0.804339i	$-0.297480\pi$
$269$	25.9642	−	10.7547i	1.58307	−	0.655728i	0.988896	+	0.148611i	$0.0474802\pi$
$270$	14.1861	−	26.5486i	0.863336	−	1.61570i
$271$	−17.0512			−1.03578			−0.517892	−	0.855446i	$-0.673283\pi$
$271$	−17.0512			−1.03578			−0.517892	+	0.855446i	$0.673283\pi$
$272$	−6.30631	+	7.45090i	−0.382376	+	0.451777i
$273$	2.40223	−	16.0377i	0.145390	−	0.970644i
$274$	2.73271	−	1.41886i	0.165089	−	0.0857165i
$275$	15.0937	−	19.6705i	0.910184	−	1.18618i
$276$	1.71116	+	3.86890i	0.103000	+	0.232880i
$277$	−24.7226	+	18.9703i	−1.48544	+	1.13982i	−0.528721	+	0.848796i	$0.677328\pi$
$277$	−24.7226	+	18.9703i	−1.48544	+	1.13982i	−0.956717	+	0.291020i	$0.906005\pi$
$278$	17.4711	−	6.33791i	1.04785	−	0.380123i
$279$	−11.0497	+	17.6574i	−0.661528	+	1.05712i
$280$	25.9819	−	44.6719i	1.55272	−	2.66965i
$281$	4.09769	+	15.2928i	0.244447	+	0.912290i	0.973660	+	0.228003i	$0.0732197\pi$
$281$	4.09769	+	15.2928i	0.244447	+	0.912290i	−0.729213	+	0.684287i	$0.760114\pi$
$282$	−0.0415043	+	0.663421i	−0.00247155	+	0.0395061i
$283$	−3.47266	−	26.3775i	−0.206428	−	1.56798i	−0.710112	−	0.704089i	$-0.751356\pi$
$283$	−3.47266	−	26.3775i	−0.206428	−	1.56798i	0.503684	−	0.863888i	$-0.331978\pi$
$284$	3.79043	+	1.38875i	0.224921	+	0.0824073i
$285$	−21.0958	+	20.3586i	−1.24961	+	1.20594i
$286$	1.34591	+	6.10175i	0.0795854	+	0.360804i
$287$	−38.1238			−2.25037
$288$	0.0466067	+	16.9705i	0.00274633	+	0.999996i
$289$	−11.0447			−0.649686
$290$	−0.131725	−	0.597183i	−0.00773517	−	0.0350678i
$291$	4.26346	+	1.22404i	0.249929	+	0.0717548i
$292$	−3.37470	+	9.21083i	−0.197489	+	0.539023i
$293$	−3.74476	−	28.4443i	−0.218771	−	1.66173i	−0.650334	−	0.759649i	$-0.725371\pi$
$293$	−3.74476	−	28.4443i	−0.218771	−	1.66173i	0.431562	−	0.902083i	$-0.357962\pi$
$294$	−26.3159	−	17.4709i	−1.53477	−	1.01892i
$295$	−11.7087	−	43.6974i	−0.681706	−	2.54416i
$296$	2.52882	+	9.55973i	0.146985	+	0.555648i
$297$	10.7523	+	2.00379i	0.623913	+	0.116272i
$298$	−3.63812	+	1.31978i	−0.210751	+	0.0764529i
$299$	2.03367	−	1.56049i	0.117610	−	0.0902457i
$300$	−32.9523	−	24.0652i	−1.90250	−	1.38940i
$301$	−5.02059	+	6.54296i	−0.289382	+	0.377130i
$302$	−2.19003	+	1.13709i	−0.126022	+	0.0654325i
$303$	16.6104	+	13.2214i	0.954242	+	0.759550i
$304$	5.03736	−	15.7424i	0.288912	−	0.902886i
$305$	−12.7015			−0.727287
$306$	7.88447	−	6.71053i	0.450725	−	0.383616i
$307$	−10.0004	+	4.14229i	−0.570752	+	0.236413i	−0.649345	−	0.760494i	$-0.724957\pi$
$307$	−10.0004	+	4.14229i	−0.570752	+	0.236413i	0.0785936	+	0.996907i	$0.474957\pi$
$308$	18.3238	+	4.10325i	1.04410	+	0.233805i
$309$	0.0539576	−	3.03412i	0.00306954	−	0.172605i
$310$	30.7843	+	25.8870i	1.74843	+	1.47028i
$311$	6.25476	+	1.67596i	0.354675	+	0.0950348i	0.431757	−	0.901990i	$-0.357894\pi$
$311$	6.25476	+	1.67596i	0.354675	+	0.0950348i	−0.0770824	+	0.997025i	$0.524560\pi$
$312$	9.98642	−	2.45256i	0.565370	−	0.138849i
$313$	12.7141	−	3.40674i	0.718645	−	0.192560i	0.119078	−	0.992885i	$-0.462006\pi$
$313$	12.7141	−	3.40674i	0.718645	−	0.192560i	0.599567	+	0.800324i	$0.295339\pi$
$314$	10.8089	+	5.05431i	0.609983	+	0.285231i
$315$	−34.8931	+	42.2721i	−1.96600	+	2.38177i
$316$	1.64336	−	18.3340i	0.0924462	−	1.03137i
$317$	23.0047	+	3.02862i	1.29207	+	0.170104i	0.745047	−	0.667012i	$-0.232427\pi$
$317$	23.0047	+	3.02862i	1.29207	+	0.170104i	0.547025	+	0.837116i	$0.315760\pi$
$318$	−8.92206	+	0.611402i	−0.500325	+	0.0342857i
$319$	0.192437	−	0.111103i	0.0107744	−	0.00622059i
$320$	32.4616	+	4.48479i	1.81466	+	0.250707i
$321$	2.45608	−	16.3972i	0.137085	−	0.915203i
$322$	−1.65932	−	7.52262i	−0.0924705	−	0.419219i
$323$	−9.31637	+	3.85897i	−0.518377	+	0.214719i
$324$	2.87702	−	17.7686i	0.159834	−	0.987144i
$325$	−9.46184	+	22.8429i	−0.524849	+	1.26710i
$326$	0.402523	+	0.576167i	0.0222937	+	0.0319109i
$327$	−21.9960	+	16.2650i	−1.21638	+	0.899455i
$328$	−9.17992	−	22.3641i	−0.506877	−	1.23485i
$329$	0.313282	−	1.16918i	0.0172718	−	0.0644592i
$330$	6.72938	−	20.0193i	0.370440	−	1.10203i
$331$	8.75860	+	11.4144i	0.481416	+	0.627394i	0.969408	−	0.245454i	$-0.0789371\pi$
$331$	8.75860	+	11.4144i	0.481416	+	0.627394i	−0.487992	+	0.872848i	$0.662270\pi$
$332$	−6.77637	+	2.12073i	−0.371902	+	0.116390i
$333$	−0.998409	−	10.4408i	−0.0547125	−	0.572150i
$334$	−0.795285	+	17.7806i	−0.0435161	+	0.972911i
$335$	−50.5129	−	29.1636i	−2.75981	−	1.59338i
$336$	6.03562	−	30.3076i	0.329270	−	1.65342i
$337$	25.7080	−	14.8425i	1.40041	−	0.808525i	0.405972	−	0.913885i	$-0.366933\pi$
$337$	25.7080	−	14.8425i	1.40041	−	0.808525i	0.994434	+	0.105360i	$0.0335996\pi$
$338$	5.60050	+	10.7865i	0.304627	+	0.586708i
$339$	−9.86623	+	9.52145i	−0.535860	+	0.517134i
$340$	−10.7061	−	16.8844i	−0.580618	−	0.915685i
$341$	−5.59290	+	13.5024i	−0.302872	+	0.731198i
$342$	−7.98592	+	15.6068i	−0.431829	+	0.843918i
$343$	18.5943	+	18.5943i	1.00400	+	1.00400i
$344$	−5.04714	−	1.36967i	−0.272123	−	0.0738476i
$345$	−8.60903	+	0.978011i	−0.463495	+	0.0526544i
$346$	−0.0744959	−	0.862062i	−0.00400493	−	0.0463448i
$347$	−17.5858	+	2.31521i	−0.944055	+	0.124287i	−0.586811	−	0.809724i	$-0.699617\pi$
$347$	−17.5858	+	2.31521i	−0.944055	+	0.124287i	−0.357244	+	0.934011i	$0.616284\pi$
$348$	−0.190306	−	0.312271i	−0.0102015	−	0.0167395i
$349$	3.22334	−	24.4837i	0.172541	−	1.31058i	−0.657744	−	0.753242i	$-0.728489\pi$
$349$	3.22334	−	24.4837i	0.172541	−	1.31058i	0.830285	−	0.557339i	$-0.188178\pi$
$350$	50.1400	+	54.8354i	2.68010	+	2.93107i
$351$	−10.8742	+	0.845035i	−0.580420	+	0.0451047i
$352$	2.00521	+	11.7371i	0.106878	+	0.625591i
$353$	13.6879	+	7.90273i	0.728535	+	0.420620i	0.817886	−	0.575380i	$-0.195146\pi$
$353$	13.6879	+	7.90273i	0.728535	+	0.420620i	−0.0893509	+	0.996000i	$0.528479\pi$
$354$	−15.0961	−	22.4483i	−0.802350	−	1.19311i
$355$	−5.03319	+	6.55938i	−0.267134	+	0.348136i
$356$	−8.35346	+	22.7998i	−0.442733	+	1.20839i
$357$	−16.4926	+	9.13492i	−0.872881	+	0.483471i
$358$	8.29569	+	11.8744i	0.438441	+	0.627580i
$359$	−20.2525	−	20.2525i	−1.06888	−	1.06888i	−0.997445	−	0.0714401i	$-0.977241\pi$
$359$	−20.2525	−	20.2525i	−1.06888	−	1.06888i	−0.0714401	−	0.997445i	$-0.522759\pi$
$360$	−33.1996	−	10.2901i	−1.74977	−	0.542336i
$361$	−1.36132	+	1.36132i	−0.0716482	+	0.0716482i
$362$	28.4934	+	5.05544i	1.49758	+	0.265708i
$363$	−11.3766	−	0.202318i	−0.597119	−	0.0106189i
$364$	−18.7092	+	0.776949i	−0.980627	+	0.0407232i
$365$	−15.9394	−	12.2307i	−0.834307	−	0.640186i
$366$	−7.18496	+	2.46279i	−0.375564	+	0.128732i
$367$	−1.53847	+	2.66471i	−0.0803075	+	0.139097i	−0.903382	−	0.428837i	$-0.858924\pi$
$367$	−1.53847	+	2.66471i	−0.0803075	+	0.139097i	0.823075	+	0.567933i	$0.192257\pi$
$368$	4.01335	−	2.78478i	0.209210	−	0.145167i
$369$	5.75162	+	24.9879i	0.299417	+	1.30082i
$370$	−20.2327	−	0.904962i	−1.05185	−	0.0470467i
$371$	16.1455	+	2.12560i	0.838235	+	0.110356i
$372$	22.4334	+	8.67468i	1.16312	+	0.449761i
$373$	−0.129874	−	0.986491i	−0.00672462	−	0.0510786i	0.987754	−	0.156022i	$-0.0498671\pi$
$373$	−0.129874	−	0.986491i	−0.00672462	−	0.0510786i	−0.994478	+	0.104944i	$0.966534\pi$
$374$	4.67542	−	5.55991i	0.241760	−	0.287496i
$375$	38.6729	−	28.5968i	1.99706	−	1.47673i
$376$	0.761300	−	0.0977543i	0.0392610	−	0.00504129i
$377$	−0.156686	+	0.156686i	−0.00806973	+	0.00806973i
$378$	−11.5418	+	30.6780i	−0.593645	+	1.57791i
$379$	15.3573	+	6.36119i	0.788850	+	0.326753i	0.740481	−	0.672077i	$-0.234598\pi$
$379$	15.3573	+	6.36119i	0.788850	+	0.326753i	0.0483691	+	0.998830i	$0.484598\pi$
$380$	27.6891	+	19.4761i	1.42042	+	0.999103i
$381$	22.8876	−	5.69854i	1.17257	−	0.291945i
$382$	0.751873	−	2.37581i	0.0384691	−	0.121557i
$383$	16.5787	+	28.7152i	0.847132	+	1.46728i	0.883756	+	0.467947i	$0.155006\pi$
$383$	16.5787	+	28.7152i	0.847132	+	1.46728i	−0.0366241	+	0.999329i	$0.511660\pi$
$384$	19.2323	−	3.75726i	0.981446	−	0.191737i
$385$	−19.2294	+	33.3063i	−0.980022	+	1.69745i
$386$	−7.69885	−	8.41980i	−0.391861	−	0.428557i
$387$	5.04597	+	2.30358i	0.256501	+	0.117098i
$388$	0.457267	−	5.10145i	0.0232142	−	0.258987i
$389$	−0.996678	+	0.764778i	−0.0505336	+	0.0387758i	−0.633719	−	0.773563i	$-0.718473\pi$
$389$	−0.996678	+	0.764778i	−0.0505336	+	0.0387758i	0.583186	+	0.812339i	$0.301806\pi$
$390$	−1.31504	+	21.0201i	−0.0665896	+	1.06439i
$391$	−2.87866	−	0.771334i	−0.145580	−	0.0390081i
$392$	−14.0655	+	33.6527i	−0.710416	+	1.69972i
$393$	−3.06266	+	7.03732i	−0.154491	+	0.354986i
$394$	−24.8345	−	4.40625i	−1.25114	−	0.221984i
$395$	34.8309	+	14.4274i	1.75253	+	0.725922i
$396$	−0.0750235	−	12.6293i	−0.00377007	−	0.634644i
$397$	−13.9665	−	33.7182i	−0.700961	−	1.69227i	−0.721438	−	0.692479i	$-0.756519\pi$
$397$	−13.9665	−	33.7182i	−0.700961	−	1.69227i	0.0204776	−	0.999790i	$-0.493481\pi$
$398$	−3.77380	+	5.90978i	−0.189163	+	0.296231i
$399$	19.8813	−	24.9774i	0.995309	−	1.25043i
$400$	−20.0940	+	42.6170i	−1.00470	+	2.13085i
$401$	13.9873	+	24.2267i	0.698492	+	1.20982i	0.968989	+	0.247103i	$0.0794786\pi$
$401$	13.9873	+	24.2267i	0.698492	+	1.20982i	−0.270497	+	0.962721i	$0.587188\pi$
$402$	−34.2287	−	6.70289i	−1.70717	−	0.334310i
$403$	1.90231	−	14.4495i	0.0947610	−	0.719782i
$404$	11.3657	−	21.7202i	0.565464	−	1.08062i
$405$	32.9711	+	16.4929i	1.63835	+	0.819540i
$406$	0.227088	+	0.625992i	0.0112702	+	0.0310675i
$407$	−1.90466	−	7.10829i	−0.0944106	−	0.352345i
$408$	−9.33001	−	7.47523i	−0.461904	−	0.370079i
$409$	3.77493	−	14.0882i	0.186658	−	0.696618i	−0.807611	−	0.589715i	$-0.799240\pi$
$409$	3.77493	−	14.0882i	0.186658	−	0.696618i	0.994269	−	0.106903i	$-0.0340934\pi$
$410$	49.3291	−	4.26282i	2.43619	−	0.210526i
$411$	1.82719	+	3.29889i	0.0901285	+	0.162722i
$412$	−3.45210	+	0.601123i	−0.170073	+	0.0296152i
$413$	18.8514	+	45.5113i	0.927616	+	2.23946i
$414$	−4.68030	+	2.22250i	−0.230024	+	0.109230i
$415$		−	14.5426i		−	0.713869i
$416$	−4.96081	−	10.7880i	−0.243224	−	0.528928i
$417$	8.33539	+	21.1810i	0.408186	+	1.03724i
$418$	−3.71136	+	11.7274i	−0.181528	+	0.573604i
$419$	−16.5106	−	12.6690i	−0.806595	−	0.618922i	0.120939	−	0.992660i	$-0.461409\pi$
$419$	−16.5106	−	12.6690i	−0.806595	−	0.618922i	−0.927534	+	0.373738i	$0.878076\pi$
$420$	55.5482	+	30.3372i	2.71048	+	1.48031i
$421$	2.56568	+	3.34366i	0.125044	+	0.162960i	0.851680	−	0.524062i	$-0.175584\pi$
$421$	2.56568	+	3.34366i	0.125044	+	0.162960i	−0.726636	+	0.687022i	$0.758917\pi$
$422$	−13.4040	−	6.26779i	−0.652498	−	0.305111i
$423$	−0.813595	−	0.0289465i	−0.0395584	−	0.00140743i
$424$	2.64082	+	9.98309i	0.128249	+	0.484822i
$425$	27.7659	−	7.43985i	1.34684	−	0.360886i
$426$	−1.57531	+	4.68641i	−0.0763242	+	0.227057i
$427$	13.7125	−	1.80528i	0.663594	−	0.0873638i
$428$	−19.1286	+	0.794367i	−0.924615	+	0.0383972i
$429$	−7.42602	+	1.84892i	−0.358531	+	0.0892669i
$430$	5.76464	−	9.02745i	0.277996	−	0.435342i
$431$		−	10.2644i		−	0.494417i	−0.968962	−	0.247208i	$-0.920487\pi$
$431$		−	10.2644i		−	0.494417i	0.968962	−	0.247208i	$-0.0795133\pi$
$432$	−20.7755	+	0.616433i	−0.999560	+	0.0296582i
$433$		−	27.7533i		−	1.33374i	−0.745176	−	0.666868i	$-0.767634\pi$
$433$		−	27.7533i		−	1.33374i	0.745176	−	0.666868i	$-0.232366\pi$
$434$	−36.9138	−	23.5720i	−1.77192	−	1.13149i
$435$	0.726789	−	0.180955i	0.0348469	−	0.00867615i
$436$	23.2439	+	21.3904i	1.11318	+	1.02441i
$437$	5.00310	−	0.658671i	0.239331	−	0.0315085i
$438$	−11.3881	−	3.82804i	−0.544143	−	0.182911i
$439$	9.38793	−	2.51549i	0.448062	−	0.120058i	−0.0277307	−	0.999615i	$-0.508828\pi$
$439$	9.38793	−	2.51549i	0.448062	−	0.120058i	0.475792	+	0.879558i	$0.342161\pi$
$440$	−24.1684	−	3.26040i	−1.15218	−	0.155433i
$441$	20.5222	−	32.7944i	0.977248	−	1.56164i
$442$	−3.06852	+	6.56220i	−0.145954	+	0.312132i
$443$	−3.89799	−	5.07996i	−0.185199	−	0.241356i	0.691522	−	0.722356i	$-0.256941\pi$
$443$	−3.89799	−	5.07996i	−0.185199	−	0.241356i	−0.876721	+	0.480999i	$0.840274\pi$
$444$	−11.6206	+	3.41114i	−0.551491	+	0.161886i
$445$	−39.4552	−	30.2750i	−1.87036	−	1.43517i
$446$	−0.424370	−	0.134300i	−0.0200945	−	0.00635930i
$447$	−1.73573	−	4.41065i	−0.0820971	−	0.208617i
$448$	−35.6827	−	0.227948i	−1.68585	−	0.0107695i
$449$		−	32.8062i		−	1.54822i	−0.633050	−	0.774111i	$-0.718197\pi$
$449$		−	32.8062i		−	1.54822i	0.633050	−	0.774111i	$-0.281803\pi$
$450$	28.3769	−	41.1367i	1.33770	−	1.93920i
$451$	6.88481	+	16.6214i	0.324193	+	0.782672i
$452$	12.9498	+	9.10873i	0.609109	+	0.428439i
$453$	−1.46433	−	2.64377i	−0.0688004	−	0.124215i
$454$	−2.36450	−	27.3618i	−0.110971	−	1.28415i
$455$	9.92613	−	37.0448i	0.465344	−	1.73669i
$456$	19.4394	+	5.64835i	0.910335	+	0.264508i
$457$	−2.85175	−	10.6429i	−0.133399	−	0.497852i	0.866600	−	0.499003i	$-0.166300\pi$
$457$	−2.85175	−	10.6429i	−0.133399	−	0.497852i	−0.999999	+	0.00115080i	$0.999634\pi$
$458$	0.994567	−	0.360794i	0.0464731	−	0.0168588i
$459$	8.47560	+	9.43178i	0.395607	+	0.440238i
$460$	2.98818	+	9.54813i	0.139324	+	0.445184i
$461$	−1.52205	+	11.5611i	−0.0708889	+	0.538455i	0.918746	+	0.394849i	$0.129203\pi$
$461$	−1.52205	+	11.5611i	−0.0708889	+	0.538455i	−0.989635	+	0.143606i	$0.954130\pi$
$462$	−4.41964	+	22.5692i	−0.205620	+	1.05001i
$463$	−4.92407	−	8.52874i	−0.228841	−	0.396364i	0.728624	−	0.684914i	$-0.240160\pi$
$463$	−4.92407	−	8.52874i	−0.228841	−	0.396364i	−0.957465	+	0.288550i	$0.906827\pi$
$464$	−0.312537	+	0.283948i	−0.0145092	+	0.0131820i
$465$	−30.6788	+	38.5425i	−1.42269	+	1.78736i
$466$	−1.76409	−	1.12649i	−0.0817197	−	0.0521836i
$467$	11.5830	+	27.9637i	0.535995	+	1.29401i	0.927497	+	0.373830i	$0.121956\pi$
$467$	11.5830	+	27.9637i	0.535995	+	1.29401i	−0.391502	+	0.920177i	$0.628044\pi$
$468$	3.33184	+	12.1455i	0.154015	+	0.561428i
$469$	58.6785	+	24.3054i	2.70952	+	1.12232i
$470$	−0.274629	+	1.54786i	−0.0126677	+	0.0713975i
$471$	−5.83171	+	13.4000i	−0.268711	+	0.617439i
$472$	−22.1584	+	22.0173i	−1.01993	+	1.01343i
$473$	3.75931	+	1.00730i	0.172853	+	0.0463159i
$474$	22.5005	+	1.40765i	1.03348	+	0.0646556i
$475$	−38.6153	+	29.6305i	−1.77179	+	1.35954i
$476$	13.9580	+	16.7066i	0.639764	+	0.765747i
$477$	−1.04262	−	10.9031i	−0.0477385	−	0.499221i
$478$	−19.2402	+	17.5928i	−0.880028	+	0.804675i
$479$	13.1111	−	22.7091i	0.599062	−	1.03761i	−0.393898	−	0.919154i	$-0.628874\pi$
$479$	13.1111	−	22.7091i	0.599062	−	1.03761i	0.992960	−	0.118452i	$-0.0377931\pi$
$480$	−4.42075	+	39.8906i	−0.201779	+	1.82075i
$481$	3.66927	+	6.35536i	0.167304	+	0.289779i
$482$	30.7683	+	9.73725i	1.40146	+	0.443519i
$483$	9.15525	−	2.27947i	0.416579	−	0.103719i
$484$	2.25395	+	12.9439i	0.102452	+	0.588360i
$485$	9.69174	+	4.01445i	0.440079	+	0.182287i
$486$	21.8489	+	2.93666i	0.991088	+	0.133209i
$487$	30.2492	−	30.2492i	1.37072	−	1.37072i	0.511354	−	0.859370i	$-0.329144\pi$
$487$	30.2492	−	30.2492i	1.37072	−	1.37072i	0.859370	−	0.511354i	$-0.170856\pi$
$488$	4.36088	+	7.60929i	0.197408	+	0.344456i
$489$	−0.692134	+	0.511801i	−0.0312994	+	0.0231444i
$490$	−57.1745	−	48.0790i	−2.58288	−	2.17199i
$491$	4.42448	+	33.6073i	0.199674	+	1.51668i	0.738497	+	0.674257i	$0.235536\pi$
$491$	4.42448	+	33.6073i	0.199674	+	1.51668i	−0.538823	+	0.842419i	$0.681131\pi$
$492$	27.0778	−	11.9761i	1.22076	−	0.539926i
$493$	0.255414	+	0.0336259i	0.0115033	+	0.00151444i
$494$	0.548097	−	12.2541i	0.0246600	−	0.551337i
$495$	24.7314	+	7.57893i	1.11160	+	0.340648i
$496$	4.93917	−	27.3303i	0.221775	−	1.22717i
$497$	4.50151	−	7.79684i	0.201920	−	0.349736i
$498$	−2.81977	−	8.22642i	−0.126357	−	0.368635i
$499$	22.2416	+	17.0666i	0.995669	+	0.764004i	0.971823	−	0.235712i	$-0.0757421\pi$
$499$	22.2416	+	17.0666i	0.995669	+	0.764004i	0.0238462	+	0.999716i	$0.492409\pi$
$500$	−40.8670	−	37.6081i	−1.82763	−	1.68189i
$501$	−21.7950	−	0.387594i	−0.973730	−	0.0173164i
$502$	0.498995	−	2.81243i	0.0222712	−	0.125525i
$503$	−19.6062	+	19.6062i	−0.874195	+	0.874195i	−0.992926	−	0.118731i	$-0.962117\pi$
$503$	−19.6062	+	19.6062i	−0.874195	+	0.874195i	0.118731	+	0.992926i	$0.462117\pi$
$504$	37.3046	+	6.39043i	1.66168	+	0.284652i
$505$	35.5025	+	35.5025i	1.57984	+	1.57984i
$506$	−2.98009	+	2.08196i	−0.132481	+	0.0925544i
$507$	−13.0213	+	7.21224i	−0.578297	+	0.320307i
$508$	−11.4575	−	24.7079i	−0.508345	−	1.09624i
$509$	6.70678	−	8.74045i	0.297273	−	0.387413i	−0.620706	−	0.784044i	$-0.713154\pi$
$509$	6.70678	−	8.74045i	0.297273	−	0.387413i	0.917978	+	0.396630i	$0.129820\pi$
$510$	20.3187	−	13.6640i	0.899727	−	0.605051i
$511$	18.9465	+	10.9387i	0.838142	+	0.483902i
$512$	−8.45843	−	20.9870i	−0.373813	−	0.927504i
$513$	−19.3706	−	9.26276i	−0.855234	−	0.408961i
$514$	0.647150	−	0.591737i	0.0285445	−	0.0261004i
$515$	0.936749	−	7.11532i	0.0412781	−	0.313538i
$516$	1.51053	−	6.22436i	0.0664972	−	0.274012i
$517$	−0.566323	+	0.0745579i	−0.0249069	+	0.00327905i
$518$	21.9717	−	1.89871i	0.965382	−	0.0834244i
$519$	1.05297	−	0.119620i	0.0462202	−	0.00525075i
$520$	24.1213	−	3.09728i	1.05779	−	0.135825i
$521$	21.5211	+	21.5211i	0.942855	+	0.942855i	0.998453	−	0.0555986i	$-0.0177067\pi$
$521$	21.5211	+	21.5211i	0.942855	+	0.942855i	−0.0555986	+	0.998453i	$0.517707\pi$
$522$	0.376041	−	0.243285i	0.0164589	−	0.0106483i
$523$	−8.83559	+	21.3310i	−0.386354	+	0.932740i	0.604352	+	0.796717i	$0.293432\pi$
$523$	−8.83559	+	21.3310i	−0.386354	+	0.932740i	−0.990706	+	0.136023i	$0.956568\pi$
$524$	8.64801	+	1.93655i	0.377790	+	0.0845985i
$525$	−65.4823	+	63.1940i	−2.85788	+	2.75801i
$526$	13.9872	−	7.26234i	0.609869	−	0.316653i
$527$	−14.6739	+	8.47201i	−0.639207	+	0.369046i
$528$	−14.3037	+	2.84185i	−0.622488	+	0.123676i
$529$	−18.6270	−	10.7543i	−0.809870	−	0.467579i
$530$	−21.1287	−	0.945039i	−0.917773	−	0.0410499i
$531$	26.9859	−	19.2221i	1.17109	−	0.834170i
$532$	−32.6611	−	17.0908i	−1.41604	−	0.740980i
$533$	−10.9216	−	14.2333i	−0.473068	−	0.616514i
$534$	−28.1891	−	9.47564i	−1.21986	−	0.410051i
$535$	10.1487	−	37.8753i	0.438765	−	1.63749i
$536$	−0.128639	+	40.2744i	−0.00555636	+	1.73959i
$537$	−14.2644	+	10.5478i	−0.615553	+	0.455172i
$538$	32.5809	−	22.7617i	1.40466	−	0.981328i
$539$	10.3875	−	25.0776i	0.447421	−	1.08017i
$540$	11.5039	−	40.9855i	0.495048	−	1.76373i
$541$	22.5194	−	9.32784i	0.968184	−	0.401035i	0.158148	−	0.987415i	$-0.449448\pi$
$541$	22.5194	−	9.32784i	0.968184	−	0.401035i	0.810036	+	0.586380i	$0.199448\pi$
$542$	−23.5479	+	5.19415i	−1.01147	+	0.223108i
$543$	−5.25020	+	35.0512i	−0.225308	+	1.50419i
$544$	−6.43942	+	12.2108i	−0.276088	+	0.523536i
$545$	−56.0291	+	32.3484i	−2.40002	+	1.38565i
$546$	−1.56790	−	22.8800i	−0.0671000	−	0.979176i
$547$	24.7444	+	3.25766i	1.05799	+	0.139288i	0.639391	−	0.768881i	$-0.279186\pi$
$547$	24.7444	+	3.25766i	1.05799	+	0.139288i	0.418604	+	0.908169i	$0.362520\pi$
$548$	3.34170	−	2.79191i	0.142750	−	0.119265i
$549$	−3.25202	−	8.71538i	−0.138793	−	0.371963i
$550$	14.8526	−	31.7631i	0.633316	−	1.35438i
$551$	−0.421352	+	0.112901i	−0.0179502	+	0.00480974i
$552$	3.54170	+	4.82176i	0.150745	+	0.205228i
$553$	−39.6538	−	10.6252i	−1.68625	−	0.451829i
$554$	−28.3635	+	33.7294i	−1.20505	+	1.43302i
$555$	0.441047	−	24.8007i	0.0187214	−	1.05273i
$556$	22.1972	−	14.0748i	0.941373	−	0.596907i
$557$	−20.1813	+	8.35937i	−0.855110	+	0.354198i	−0.766793	−	0.641894i	$-0.778149\pi$
$557$	−20.1813	+	8.35937i	−0.855110	+	0.354198i	−0.0883167	+	0.996092i	$0.528149\pi$
$558$	−9.88098	+	27.7511i	−0.418295	+	1.17480i
$559$	−3.88108			−0.164152
$560$	22.2734	−	69.6072i	0.941224	−	2.94144i
$561$	6.96112	+	5.54086i	0.293899	+	0.233935i
$562$	10.3175	+	19.8713i	0.435217	+	0.838221i
$563$	1.96734	−	2.56389i	0.0829137	−	0.108055i	−0.750055	−	0.661376i	$-0.769973\pi$
$563$	1.96734	−	2.56389i	0.0829137	−	0.108055i	0.832968	+	0.553321i	$0.186640\pi$
$564$	0.144774	+	0.928838i	0.00609610	+	0.0391111i
$565$	−25.7259	+	19.7402i	−1.08230	+	0.830476i
$566$	−12.8309	−	35.3699i	−0.539325	−	1.48671i
$567$	−37.9396	−	13.1194i	−1.59331	−	0.550964i
$568$	5.65770	+	0.763242i	0.237392	+	0.0320249i
$569$	9.11593	+	34.0211i	0.382160	+	1.42624i	0.842596	+	0.538546i	$0.181026\pi$
$569$	9.11593	+	34.0211i	0.382160	+	1.42624i	−0.460436	+	0.887693i	$0.652307\pi$
$570$	−22.9319	+	34.5417i	−0.960514	+	1.44679i
$571$	2.52129	+	19.1511i	0.105513	+	0.801448i	0.959610	+	0.281334i	$0.0907770\pi$
$571$	2.52129	+	19.1511i	0.105513	+	0.801448i	−0.854097	+	0.520114i	$0.825890\pi$
$572$	3.71745	+	8.01662i	0.155434	+	0.335192i
$573$	2.93349	+	0.842208i	0.122548	+	0.0351838i
$574$	−52.6495	+	11.6133i	−2.19755	+	0.484731i
$575$	−14.3849			−0.599893
$576$	5.23395	+	23.4223i	0.218081	+	0.975931i
$577$	30.9084			1.28673			0.643367	−	0.765558i	$-0.277537\pi$
$577$	30.9084			1.28673			0.643367	+	0.765558i	$0.277537\pi$
$578$	−15.2529	+	3.36444i	−0.634435	+	0.139942i
$579$	10.0546	−	9.70324i	0.417855	−	0.403253i
$580$	−0.363829	−	0.784592i	−0.0151072	−	0.0325784i
$581$	2.06696	+	15.7001i	0.0857520	+	0.651351i
$582$	6.26078	+	0.391681i	0.259518	+	0.0162357i
$583$	−1.98901	−	7.42309i	−0.0823764	−	0.307433i
$584$	−1.85469	+	13.7483i	−0.0767477	+	0.568909i
$585$	−25.7782	−	0.917151i	−1.06580	−	0.0379195i
$586$	−13.8363	−	38.1413i	−0.571573	−	1.57560i
$587$	34.1352	−	26.1929i	1.40891	−	1.08110i	0.424458	−	0.905448i	$-0.360465\pi$
$587$	34.1352	−	26.1929i	1.40891	−	1.08110i	0.984453	−	0.175647i	$-0.0562018\pi$
$588$	−41.6647	−	16.1112i	−1.71822	−	0.664414i
$589$	17.4658	−	22.7619i	0.719665	−	0.937886i
$590$	−29.4810	−	56.7801i	−1.21372	−	2.33760i
$591$	4.57600	−	30.5501i	0.188232	−	1.25666i
$592$	6.40445	+	12.4318i	0.263221	+	0.510944i
$593$	−23.3812			−0.960152			−0.480076	−	0.877227i	$-0.659391\pi$
$593$	−23.3812			−0.960152			−0.480076	+	0.877227i	$0.659391\pi$
$594$	15.4595	−	0.508130i	0.634312	−	0.0208488i
$595$	−41.1937	+	17.0630i	−1.68878	+	0.699514i
$596$	−4.62227	+	2.93089i	−0.189335	+	0.120054i
$597$	−7.35974	−	4.42547i	−0.301214	−	0.181122i
$598$	2.33318	−	2.77457i	0.0954107	−	0.113461i
$599$	−5.56286	−	1.49057i	−0.227292	−	0.0609028i	0.143375	−	0.989668i	$-0.454204\pi$
$599$	−5.56286	−	1.49057i	−0.227292	−	0.0609028i	−0.370668	+	0.928766i	$0.620871\pi$
$600$	−52.8384	−	23.1964i	−2.15712	−	0.946991i
$601$	−19.9474	+	5.34490i	−0.813672	+	0.218023i	−0.641578	−	0.767058i	$-0.721720\pi$
$601$	−19.9474	+	5.34490i	−0.813672	+	0.218023i	−0.172094	+	0.985081i	$0.555053\pi$
$602$	−4.94039	+	10.5653i	−0.201355	+	0.430610i
$603$	7.07812	−	42.1272i	0.288244	−	1.71555i
$604$	−2.67808	+	2.23748i	−0.108970	+	0.0910416i
$605$	−26.6794	−	3.51241i	−1.08467	−	0.142800i
$606$	26.9667	+	13.1991i	1.09545	+	0.536177i
$607$	−24.2585	+	14.0057i	−0.984623	+	0.568473i	−0.903663	−	0.428245i	$-0.859132\pi$
$607$	−24.2585	+	14.0057i	−0.984623	+	0.568473i	−0.0809606	+	0.996717i	$0.525799\pi$
$608$	2.16120	−	23.2749i	0.0876484	−	0.943924i
$609$	−0.758918	+	0.298658i	−0.0307529	+	0.0121022i
$610$	−17.5410	+	3.86916i	−0.710215	+	0.156658i
$611$	0.526258	−	0.217983i	0.0212901	−	0.00881866i
$612$	8.84441	−	11.6691i	0.357514	−	0.471697i
$613$	14.0542	−	33.9298i	0.567643	−	1.37041i	−0.335894	−	0.941900i	$-0.609038\pi$
$613$	14.0542	−	33.9298i	0.567643	−	1.37041i	0.903537	−	0.428511i	$-0.140962\pi$
$614$	−12.5489	+	8.76691i	−0.506431	+	0.353804i
$615$	6.84494	+	60.2532i	0.276014	+	2.42964i
$616$	26.5555	+	0.0848198i	1.06995	+	0.00341749i
$617$	10.6493	−	39.7436i	0.428723	−	1.60002i	−0.326932	−	0.945048i	$-0.606015\pi$
$617$	10.6493	−	39.7436i	0.428723	−	1.60002i	0.755655	−	0.654969i	$-0.227319\pi$
$618$	−0.849742	−	4.20660i	−0.0341816	−	0.169214i
$619$	2.10556	+	2.74402i	0.0846297	+	0.110292i	0.833749	−	0.552143i	$-0.186190\pi$
$619$	2.10556	+	2.74402i	0.0846297	+	0.110292i	−0.749120	+	0.662435i	$0.769523\pi$
$620$	50.3993	+	26.3728i	2.02408	+	1.05916i
$621$	−2.87528	−	5.65684i	−0.115381	−	0.227001i
$622$	9.14845	+	0.409189i	0.366820	+	0.0164070i
$623$	46.8986	+	27.0769i	1.87895	+	1.08481i
$624$	13.0443	−	6.42911i	0.522190	−	0.257370i
$625$	47.5040	−	27.4265i	1.90016	−	1.09706i
$626$	16.5207	−	8.57777i	0.660298	−	0.342836i
$627$	−14.4802	−	4.15727i	−0.578282	−	0.166025i
$628$	16.4670	+	3.68744i	0.657103	+	0.147145i
$629$	3.26498	−	7.88236i	0.130183	−	0.314290i
$630$	−35.3110	+	69.0077i	−1.40682	+	2.74933i
$631$	−28.1453	−	28.1453i	−1.12045	−	1.12045i	−0.991674	−	0.128775i	$-0.958896\pi$
$631$	−28.1453	−	28.1453i	−1.12045	−	1.12045i	−0.128775	−	0.991674i	$-0.541104\pi$
$632$	−3.31541	−	25.8201i	−0.131880	−	1.02707i
$633$	7.23184	−	16.6172i	0.287440	−	0.660473i
$634$	32.6924	−	2.82515i	1.29838	−	0.112201i
$635$	55.3037	−	7.28087i	2.19466	−	0.288933i
$636$	−12.1353	+	3.56221i	−0.481195	+	0.141251i
$637$	−3.53310	+	26.8366i	−0.139987	+	1.06330i
$638$	0.231914	−	0.212056i	0.00918155	−	0.00839537i
$639$	−5.78950	−	1.77419i	−0.229029	−	0.0701858i
$640$	46.1961	−	3.69493i	1.82606	−	0.146055i
$641$	−4.09680	−	2.36529i	−0.161814	−	0.0934234i	0.416906	−	0.908949i	$-0.363114\pi$
$641$	−4.09680	−	2.36529i	−0.161814	−	0.0934234i	−0.578720	+	0.815526i	$0.696448\pi$
$642$	−1.60305	−	23.3930i	−0.0632674	−	0.923247i
$643$	−11.8671	+	15.4655i	−0.467994	+	0.609901i	−0.966400	−	0.257042i	$-0.917252\pi$
$643$	−11.8671	+	15.4655i	−0.467994	+	0.609901i	0.498406	+	0.866943i	$0.333919\pi$
$644$	−4.58310	−	9.88339i	−0.180600	−	0.389460i
$645$	11.2423	+	6.76010i	0.442666	+	0.266179i
$646$	−11.6905	+	8.16726i	−0.459958	+	0.321337i
$647$	−1.61023	−	1.61023i	−0.0633045	−	0.0633045i	0.674746	−	0.738050i	$-0.264253\pi$
$647$	−1.61023	−	1.61023i	−0.0633045	−	0.0633045i	−0.738050	+	0.674746i	$0.764253\pi$
$648$	−1.43949	−	25.4151i	−0.0565485	−	0.998400i
$649$	16.4379	−	16.4379i	0.645243	−	0.645243i
$650$	−6.10851	+	34.4287i	−0.239596	+	1.35041i
$651$	27.6425	−	45.9706i	1.08340	−	1.80173i
$652$	0.731404	+	0.673079i	0.0286440	+	0.0263598i
$653$	17.8914	+	13.7285i	0.700143	+	0.537239i	0.896363	−	0.443321i	$-0.146200\pi$
$653$	17.8914	+	13.7285i	0.700143	+	0.537239i	−0.196220	+	0.980560i	$0.562867\pi$
$654$	−25.4221	+	29.1626i	−0.994084	+	1.14035i
$655$	−9.07541	+	15.7191i	−0.354605	+	0.614195i
$656$	−19.4902	−	28.0887i	−0.760965	−	1.09668i
$657$	4.31131	−	14.0686i	0.168200	−	0.548868i
$658$	0.0764886	−	1.71009i	0.00298183	−	0.0666664i
$659$	−34.8338	−	4.58595i	−1.35693	−	0.178643i	−0.583288	−	0.812265i	$-0.698234\pi$
$659$	−34.8338	−	4.58595i	−1.35693	−	0.178643i	−0.773643	+	0.633622i	$0.781567\pi$
$660$	3.19508	−	29.6969i	0.124368	−	1.15595i
$661$	5.24801	+	39.8626i	0.204124	+	1.55048i	0.720098	+	0.693872i	$0.244097\pi$
$661$	5.24801	+	39.8626i	0.204124	+	1.55048i	−0.515974	+	0.856604i	$0.672570\pi$
$662$	15.5729	+	13.0955i	0.605256	+	0.508969i
$663$	−8.13526	−	3.54049i	−0.315947	−	0.137501i
$664$	−8.71226	+	4.99299i	−0.338101	+	0.193766i
$665$	53.3857	−	53.3857i	2.07021	−	2.07021i
$666$	−4.55930	−	14.1147i	−0.176669	−	0.546934i
$667$	−0.119105	−	0.0493351i	−0.00461178	−	0.00191026i
$668$	4.31805	+	24.7976i	0.167071	+	0.959446i
$669$	0.150436	−	0.523983i	0.00581620	−	0.0202584i
$670$	−78.6430	−	24.8881i	−3.03824	−	0.961512i
$671$	−3.26343	−	5.65243i	−0.125983	−	0.218210i
$672$	−0.897078	−	43.6939i	−0.0346055	−	1.68553i
$673$	0.476414	−	0.825173i	0.0183644	−	0.0318081i	−0.856697	−	0.515820i	$-0.827487\pi$
$673$	0.476414	−	0.825173i	0.0183644	−	0.0318081i	0.875062	+	0.484012i	$0.160821\pi$
$674$	30.9819	−	28.3290i	1.19338	−	1.09119i
$675$	51.2991	+	33.3859i	1.97450	+	1.28502i
$676$	11.0202	+	13.1903i	0.423853	+	0.507319i
$677$	−39.7624	+	30.5108i	−1.52819	+	1.17262i	−0.600302	+	0.799774i	$0.704953\pi$
$677$	−39.7624	+	30.5108i	−1.52819	+	1.17262i	−0.927892	+	0.372850i	$0.878381\pi$
$678$	−10.7250	+	16.1547i	−0.411891	+	0.620419i
$679$	−11.0337	−	2.95648i	−0.423435	−	0.113459i
$680$	−19.9286	−	20.0563i	−0.764227	−	0.769125i
$681$	33.4212	−	3.79674i	1.28070	−	0.145492i
$682$	−3.61074	+	20.3508i	−0.138262	+	0.779273i
$683$	−32.1596	−	13.3209i	−1.23055	−	0.509712i	−0.329803	−	0.944050i	$-0.606982\pi$
$683$	−32.1596	−	13.3209i	−1.23055	−	0.509712i	−0.900750	+	0.434338i	$0.856982\pi$
$684$	−6.27453	+	23.9859i	−0.239913	+	0.917124i
$685$	3.41298	+	8.23966i	0.130403	+	0.314821i
$686$	31.3433	+	20.0148i	1.19669	+	0.764169i
$687$	0.474503	+	1.20576i	0.0181034	+	0.0460025i
$688$	−7.38741	−	0.354068i	−0.281642	−	0.0134987i
$689$	3.83176	+	6.63681i	0.145979	+	0.252842i
$690$	−11.5913	+	3.97315i	−0.441273	+	0.151255i
$691$	0.248259	−	1.88571i	0.00944422	−	0.0717360i	−0.986074	−	0.166309i	$-0.946815\pi$
$691$	0.248259	−	1.88571i	0.00944422	−	0.0717360i	0.995518	+	0.0945728i	$0.0301485\pi$
$692$	−0.365483	−	1.16783i	−0.0138936	−	0.0443942i
$693$	−27.7771	−	4.66705i	−1.05517	−	0.177287i
$694$	−23.5810	+	8.55436i	−0.895123	+	0.324719i
$695$	13.9326	+	51.9973i	0.528495	+	1.97237i
$696$	−0.357940	−	0.373280i	−0.0135677	−	0.0141492i
$697$	−5.39844	+	20.1472i	−0.204480	+	0.763131i
$698$	−3.00678	−	34.7942i	−0.113808	−	1.31698i
$699$	1.32102	−	2.19690i	0.0499654	−	0.0830946i
$700$	85.9483	+	60.4548i	3.24854	+	2.28498i
$701$	4.44608	+	10.7338i	0.167926	+	0.405409i	0.985331	−	0.170654i	$-0.0545881\pi$
$701$	4.44608	+	10.7338i	0.167926	+	0.405409i	−0.817405	+	0.576064i	$0.804588\pi$
$702$	−14.7600	+	4.47952i	−0.557080	+	0.169068i
$703$			14.4466i			0.544864i
$704$	6.34461	+	15.5983i	0.239121	+	0.587884i
$705$	−1.90410	−	0.285209i	−0.0717125	−	0.0107416i
$706$	21.3106	+	6.74416i	0.802035	+	0.253820i
$707$	−43.3743	−	33.2822i	−1.63126	−	1.25171i
$708$	−27.6862	−	26.4029i	−1.04051	−	0.992281i
$709$	14.6294	+	19.0654i	0.549418	+	0.716015i	0.982692	−	0.185247i	$-0.0593086\pi$
$709$	14.6294	+	19.0654i	0.549418	+	0.716015i	−0.433274	+	0.901262i	$0.642642\pi$
$710$	−4.95279	+	10.5918i	−0.185875	+	0.397504i
$711$	−0.981743	+	27.5937i	−0.0368182	+	1.03485i
$712$	−4.59096	+	34.0315i	−0.172054	+	1.27538i
$713$	8.19030	−	2.19458i	0.306729	−	0.0821878i
$714$	−19.9939	+	17.6395i	−0.748251	+	0.660141i
$715$	−17.9436	+	2.36232i	−0.671052	+	0.0883457i
$716$	15.0737	+	13.8716i	0.563330	+	0.518408i
$717$	−22.1730	−	22.9760i	−0.828068	−	0.858053i
$718$	−34.1383	−	21.7997i	−1.27403	−	0.813556i
$719$		−	30.4270i		−	1.13474i	−0.823464	−	0.567368i	$-0.807962\pi$
$719$		−	30.4270i		−	1.13474i	0.823464	−	0.567368i	$-0.192038\pi$
$720$	−48.9838	−	4.09748i	−1.82552	−	0.152704i
$721$			7.81479i			0.291038i
$722$	−1.46531	+	2.29469i	−0.0545333	+	0.0853994i
$723$	−10.9072	+	37.9907i	−0.405641	+	1.41289i
$724$	40.8899	−	1.69806i	1.51966	−	0.0631080i
$725$	1.23284	−	0.162306i	0.0457865	−	0.00602790i
$726$	−15.7730	+	3.18617i	−0.585389	+	0.118250i
$727$	−2.98535	+	0.799922i	−0.110721	+	0.0296675i	−0.313754	−	0.949504i	$-0.601587\pi$
$727$	−2.98535	+	0.799922i	−0.110721	+	0.0296675i	0.203033	+	0.979172i	$0.434920\pi$
$728$	−25.6010	+	6.77220i	−0.948836	+	0.250994i
$729$	−2.87518	+	26.8465i	−0.106488	+	0.994314i
$730$	−25.7383	−	12.0354i	−0.952619	−	0.445449i
$731$	2.74682	+	3.57973i	0.101595	+	0.132401i
$732$	−9.17232	+	5.58984i	−0.339019	+	0.206607i
$733$	2.28536	+	1.75362i	0.0844119	+	0.0647715i	0.650105	−	0.759844i	$-0.274725\pi$
$733$	2.28536	+	1.75362i	0.0844119	+	0.0647715i	−0.565693	+	0.824616i	$0.691391\pi$
$734$	−1.31292	+	4.14866i	−0.0484609	+	0.153130i
$735$	56.9786	−	71.5836i	2.10169	−	2.64040i
$736$	4.69419	−	5.06838i	0.173030	−	0.186823i
$737$		−	29.9723i		−	1.10404i
$738$	15.5549	+	32.7566i	0.572585	+	1.20579i
$739$	−16.6740	−	40.2546i	−0.613363	−	1.48079i	−0.859284	−	0.511498i	$-0.829091\pi$
$739$	−16.6740	−	40.2546i	−0.613363	−	1.48079i	0.245922	−	0.969290i	$-0.420909\pi$
$740$	−28.2174	+	4.91355i	−1.03729	+	0.180626i
$741$	15.0207	+	0.267123i	0.551801	+	0.00981301i
$742$	22.9448	−	1.98279i	0.842329	−	0.0727906i
$743$	7.74812	−	28.9164i	0.284251	−	1.06084i	−0.665134	−	0.746724i	$-0.731626\pi$
$743$	7.74812	−	28.9164i	0.284251	−	1.06084i	0.949385	−	0.314115i	$-0.101708\pi$
$744$	33.6233	+	5.14619i	1.23269	+	0.188668i
$745$	−2.90128	−	10.8277i	−0.106295	−	0.396697i
$746$	−0.479865	−	1.32280i	−0.0175691	−	0.0484311i
$747$	9.97867	−	3.72340i	0.365101	−	0.136232i
$748$	4.76316	−	9.10256i	0.174158	−	0.332823i
$749$	−5.57317	+	42.3324i	−0.203639	+	1.54679i
$750$	44.6966	−	51.2732i	1.63209	−	1.87223i
$751$	−24.9664	−	43.2431i	−0.911038	−	1.57796i	−0.812600	−	0.582822i	$-0.801949\pi$
$751$	−24.9664	−	43.2431i	−0.911038	−	1.57796i	−0.0984385	−	0.995143i	$-0.531385\pi$
$752$	1.02159	−	0.366909i	0.0372535	−	0.0133798i
$753$	3.45970	+	0.518218i	0.126079	+	0.0188849i
$754$	−0.168656	+	0.264116i	−0.00614208	+	0.00961852i
$755$	−2.73521	−	6.60338i	−0.0995444	−	0.240321i
$756$	−6.59420	+	45.8827i	−0.239829	+	1.66874i
$757$	−16.5369	−	6.84980i	−0.601043	−	0.248960i	0.0613506	−	0.998116i	$-0.480459\pi$
$757$	−16.5369	−	6.84980i	−0.601043	−	0.248960i	−0.662393	+	0.749156i	$0.730459\pi$
$758$	23.1464	+	4.10675i	0.840715	+	0.149164i
$759$	−2.64717	−	3.57991i	−0.0960863	−	0.129942i
$760$	44.1719	+	18.4621i	1.60228	+	0.669692i
$761$	−37.9644	−	10.1725i	−1.37621	−	0.368754i	−0.506467	−	0.862259i	$-0.669049\pi$
$761$	−37.9644	−	10.1725i	−1.37621	−	0.368754i	−0.869743	+	0.493505i	$0.835715\pi$
$762$	29.8723	−	14.8418i	1.08216	−	0.537663i
$763$	55.8910	−	42.8867i	2.02339	−	1.55260i
$764$	0.314624	−	3.51007i	0.0113827	−	0.126990i
$765$	17.3986	+	24.4258i	0.629047	+	0.883117i
$766$	31.6427	+	34.6059i	1.14330	+	1.25036i
$767$	−11.5909	+	20.0761i	−0.418524	+	0.724905i
$768$	25.4156	−	11.0474i	0.917108	−	0.398640i
$769$	7.53261	+	13.0469i	0.271633	+	0.470482i	0.969280	−	0.245959i	$-0.0791030\pi$
$769$	7.53261	+	13.0469i	0.271633	+	0.470482i	−0.697647	+	0.716441i	$0.745770\pi$
$770$	−16.4103	+	51.8543i	−0.591387	+	1.86870i
$771$	0.745795	+	0.772801i	0.0268592	+	0.0278318i
$772$	−13.1971	−	9.28264i	−0.474974	−	0.334090i
$773$	18.2960	+	7.57843i	0.658060	+	0.272577i	0.686622	−	0.727015i	$-0.259093\pi$
$773$	18.2960	+	7.57843i	0.658060	+	0.272577i	−0.0285622	+	0.999592i	$0.509093\pi$
$774$	7.67029	+	1.64418i	0.275703	+	0.0590987i
$775$	−57.8312	+	57.8312i	−2.07736	+	2.07736i
$776$	−0.922519	−	7.18448i	−0.0331165	−	0.257908i
$777$	3.04881	+	26.8374i	0.109375	+	0.962787i
$778$	−1.14346	+	1.35978i	−0.0409950	+	0.0487505i
$779$	−4.60993	−	35.0159i	−0.165168	−	1.25457i
$780$	4.58708	+	29.4296i	0.164244	+	1.05375i
$781$	−4.21224	−	0.554552i	−0.150726	−	0.0198434i
$782$	−4.21044	−	0.188323i	−0.150565	−	0.00673443i
$783$	0.310249	+	0.452369i	0.0110874	+	0.0161663i
$784$	−9.17335	+	50.7596i	−0.327620	+	1.81284i
$785$	−17.2808	+	29.9312i	−0.616777	+	1.06829i
$786$	−2.08587	+	10.6516i	−0.0744004	+	0.379930i
$787$	12.3339	+	9.46412i	0.439656	+	0.337360i	0.804753	−	0.593610i	$-0.202298\pi$
$787$	12.3339	+	9.46412i	0.439656	+	0.337360i	−0.365098	+	0.930969i	$0.618964\pi$
$788$	−35.6390	+	1.48001i	−1.26959	+	0.0527231i
$789$	9.35233	+	16.8851i	0.332952	+	0.601126i
$790$	52.4969	+	9.31426i	1.86776	+	0.331387i
$791$	24.9678	−	24.9678i	0.887754	−	0.887754i
$792$	−3.95075	−	17.4183i	−0.140384	−	0.618934i
$793$	4.60233	+	4.60233i	0.163433	+	0.163433i
$794$	−29.5593	−	42.3109i	−1.04902	−	1.50156i
$795$	0.460579	−	25.8991i	0.0163351	−	0.918545i
$796$	−3.41143	+	9.31108i	−0.120915	+	0.330023i
$797$	−10.5189	+	13.7085i	−0.372599	+	0.485580i	−0.941589	−	0.336764i	$-0.890668\pi$
$797$	−10.5189	+	13.7085i	−0.372599	+	0.485580i	0.568990	+	0.822344i	$0.307334\pi$
$798$	19.8477	−	40.5504i	0.702602	−	1.43547i
$799$	−0.573516	−	0.331120i	−0.0202895	−	0.0117142i
$800$	−14.7681	+	64.9759i	−0.522132	+	2.29724i
$801$	10.6719	−	34.8243i	0.377073	−	1.23046i
$802$	26.6967	+	29.1966i	0.942692	+	1.03097i
$803$	1.34757	−	10.2358i	0.0475548	−	0.361215i
$804$	−49.3122	+	1.17001i	−1.73911	+	0.0412631i
$805$	22.1220	−	2.91241i	0.779697	−	0.102649i
$806$	−1.77451	−	20.5345i	−0.0625044	−	0.723297i
$807$	28.9411	+	39.1386i	1.01878	+	1.37774i
$808$	9.07975	−	33.4582i	0.319424	−	1.17706i
$809$	17.7176	+	17.7176i	0.622918	+	0.622918i	0.946276	−	0.323359i	$-0.104812\pi$
$809$	17.7176	+	17.7176i	0.622918	+	0.622918i	−0.323359	+	0.946276i	$0.604812\pi$
$810$	50.5578	+	12.7333i	1.77642	+	0.447402i
$811$	−1.12424	+	2.71416i	−0.0394774	+	0.0953070i	−0.942388	−	0.334521i	$-0.891426\pi$
$811$	−1.12424	+	2.71416i	−0.0394774	+	0.0953070i	0.902911	+	0.429828i	$0.141426\pi$
$812$	0.504303	+	0.795330i	0.0176976	+	0.0279106i
$813$	−7.13538	−	28.6585i	−0.250249	−	1.00510i
$814$	−4.79571	−	9.23647i	−0.168090	−	0.323738i
$815$	−1.76304	+	1.01789i	−0.0617565	+	0.0356551i
$816$	−15.1620	−	7.48130i	−0.530777	−	0.261898i
$817$	−6.61666	−	3.82013i	−0.231488	−	0.133650i
$818$	0.921659	−	20.6060i	0.0322251	−	0.720472i
$819$	27.9604	−	2.67374i	0.977015	−	0.0934282i
$820$	66.8257	−	20.9137i	2.33366	−	0.730339i
$821$	−10.7277	−	13.9806i	−0.374398	−	0.487925i	0.567713	−	0.823227i	$-0.307828\pi$
$821$	−10.7277	−	13.9806i	−0.374398	−	0.487925i	−0.942111	+	0.335302i	$0.891162\pi$
$822$	3.52829	+	3.99922i	0.123063	+	0.139489i
$823$	−9.34991	+	34.8943i	−0.325917	+	1.21634i	0.587469	+	0.809246i	$0.300124\pi$
$823$	−9.34991	+	34.8943i	−0.325917	+	1.21634i	−0.913387	+	0.407093i	$0.866542\pi$
$824$	−4.58430	+	1.88175i	−0.159702	+	0.0655537i
$825$	39.3772	+	17.1371i	1.37094	+	0.596636i
$826$	39.8978	+	57.1093i	1.38822	+	1.98709i
$827$	−5.73875	+	13.8546i	−0.199556	+	0.481771i	−0.991702	−	0.128562i	$-0.958964\pi$
$827$	−5.73875	+	13.8546i	−0.199556	+	0.481771i	0.792146	+	0.610332i	$0.208964\pi$
$828$	−5.78654	+	4.49504i	−0.201096	+	0.156213i
$829$	−10.0506	+	4.16308i	−0.349070	+	0.144590i	−0.550328	−	0.834949i	$-0.685497\pi$
$829$	−10.0506	+	4.16308i	−0.349070	+	0.144590i	0.201257	+	0.979538i	$0.435497\pi$
$830$	−4.43000	−	20.0836i	−0.153767	−	0.697112i
$831$	−42.2298	−	33.6138i	−1.46494	−	1.16605i
$832$	−10.1372	−	13.3873i	−0.351445	−	0.464121i
$833$	27.2534	−	15.7348i	0.944275	−	0.545177i
$834$	17.9635	+	26.7122i	0.622025	+	0.924968i
$835$	−51.1116	−	6.72896i	−1.76879	−	0.232865i
$836$	−1.55303	+	17.3262i	−0.0537128	+	0.599240i
$837$	−34.3014	−	11.1826i	−1.18563	−	0.386527i
$838$	−26.6607	−	12.4666i	−0.920977	−	0.430653i
$839$	20.5074	−	5.49494i	0.707994	−	0.189706i	0.113185	−	0.993574i	$-0.463895\pi$
$839$	20.5074	−	5.49494i	0.707994	−	0.189706i	0.594808	+	0.803867i	$0.297228\pi$
$840$	85.9544	+	24.9750i	2.96571	+	0.861720i
$841$	−28.0011	−	7.50287i	−0.965555	−	0.258720i
$842$	4.56180	+	3.83609i	0.157210	+	0.132200i
$843$	−23.9884	+	13.2867i	−0.826205	+	0.457618i
$844$	−20.4205	−	4.57276i	−0.702902	−	0.157401i
$845$	−32.5234	+	13.4717i	−1.11884	+	0.463439i
$846$	−1.13241	+	0.207863i	−0.0389329	+	0.00714648i
$847$	29.3021			1.00683
$848$	6.68807	+	12.9824i	0.229669	+	0.445816i
$849$	42.8804	−	16.8748i	1.47165	−	0.579141i
$850$	36.0788	−	18.7326i	1.23749	−	0.642524i
$851$	−2.59913	+	3.38725i	−0.0890970	+	0.116113i
$852$	−0.747952	+	6.95188i	−0.0256244	+	0.238168i
$853$	12.6592	−	9.71371i	0.433441	−	0.332591i	−0.368887	−	0.929474i	$-0.620261\pi$
$853$	12.6592	−	9.71371i	0.433441	−	0.332591i	0.802328	+	0.596883i	$0.203594\pi$
$854$	18.3872	−	6.67025i	0.629198	−	0.228251i
$855$	−43.0454	−	26.9371i	−1.47212	−	0.921228i
$856$	−26.1749	+	6.92402i	−0.894640	+	0.236658i
$857$	−12.0746	−	45.0630i	−0.412460	−	1.53932i	−0.789869	−	0.613276i	$-0.789851\pi$
$857$	−12.0746	−	45.0630i	−0.412460	−	1.53932i	0.377409	−	0.926047i	$-0.376815\pi$
$858$	−9.69223	+	4.81552i	−0.330887	+	0.164399i
$859$	−2.27251	−	17.2614i	−0.0775370	−	0.588952i	−0.985472	−	0.169840i	$-0.945675\pi$
$859$	−2.27251	−	17.2614i	−0.0775370	−	0.588952i	0.907935	−	0.419112i	$-0.137659\pi$
$860$	5.21110	−	14.2231i	0.177697	−	0.485003i
$861$	−15.9536	−	64.0761i	−0.543697	−	2.18371i
$862$	−3.12675	−	14.1753i	−0.106497	−	0.482811i
$863$	20.4688			0.696765			0.348382	−	0.937352i	$-0.386731\pi$
$863$	20.4688			0.696765			0.348382	+	0.937352i	$0.386731\pi$
$864$	−28.5035	+	7.17996i	−0.969708	+	0.244267i
$865$	2.50625			0.0852151
$866$	−8.45424	−	38.3277i	−0.287287	−	1.30243i
$867$	−4.62185	−	18.5632i	−0.156966	−	0.630439i
$868$	−58.1592	−	21.3086i	−1.97405	−	0.723260i
$869$	2.52869	+	19.2073i	0.0857799	+	0.651563i
$870$	0.948585	−	0.471298i	0.0321600	−	0.0159785i
$871$	7.73578	+	28.8703i	0.262117	+	0.978234i
$872$	38.6162	+	22.4599i	1.30771	+	0.760587i
$873$	−0.273171	+	7.67800i	−0.00924545	+	0.259861i
$874$	6.70872	−	2.43369i	0.226926	−	0.0823208i
$875$	−98.2664	+	75.4025i	−3.32201	+	2.54907i
$876$	−16.8932	−	1.81754i	−0.570768	−	0.0614089i
$877$	−4.93271	+	6.42844i	−0.166566	+	0.217073i	−0.869177	−	0.494501i	$-0.835351\pi$
$877$	−4.93271	+	6.42844i	−0.166566	+	0.217073i	0.702611	+	0.711574i	$0.252017\pi$
$878$	12.1986	−	6.33370i	0.411683	−	0.213752i
$879$	46.2403	−	18.1970i	1.55965	−	0.613770i
$880$	−34.3701	+	2.85956i	−1.15862	+	0.0963957i
$881$	−9.19807			−0.309891			−0.154945	−	0.987923i	$-0.549520\pi$
$881$	−9.19807			−0.309891			−0.154945	+	0.987923i	$0.549520\pi$
$882$	18.3516	−	51.5412i	0.617931	−	1.73548i
$883$	−28.4845	+	11.7987i	−0.958580	+	0.397057i	−0.806449	−	0.591304i	$-0.798614\pi$
$883$	−28.4845	+	11.7987i	−0.958580	+	0.397057i	−0.152131	+	0.988360i	$0.548614\pi$
$884$	−2.23868	+	9.99725i	−0.0752950	+	0.336244i
$885$	68.5442	−	37.9652i	2.30409	−	1.27619i
$886$	−6.93065	−	5.82809i	−0.232840	−	0.195799i
$887$	14.2354	+	3.81436i	0.477977	+	0.128074i	0.489761	−	0.871857i	$-0.337084\pi$
$887$	14.2354	+	3.81436i	0.477977	+	0.128074i	−0.0117833	+	0.999931i	$0.503751\pi$
$888$	−15.0092	+	8.25074i	−0.503675	+	0.276877i
$889$	−58.6707	+	15.7208i	−1.96775	+	0.527258i
$890$	−63.7107	−	29.7914i	−2.13559	−	0.998611i
$891$	1.13167	+	18.9104i	0.0379125	+	0.633522i
$892$	−0.626973	−	0.0561985i	−0.0209926	−	0.00188167i
$893$	1.11175	+	0.146365i	0.0372034	+	0.00489792i
$894$	−3.74065	−	5.56244i	−0.125106	−	0.186036i
$895$	−36.3348	+	20.9779i	−1.21454	+	0.701215i
$896$	−49.3479	+	10.5549i	−1.64860	+	0.352616i
$897$	3.47381	+	2.76506i	0.115987	+	0.0923226i
$898$	−9.99349	−	45.3059i	−0.333487	−	1.51188i
$899$	−0.677176	+	0.280495i	−0.0225851	+	0.00935505i
$900$	26.6578	−	65.4547i	0.888593	−	2.18182i
$901$	3.40957	−	8.23144i	0.113589	−	0.274229i
$902$	14.5713	+	20.8572i	0.485171	+	0.694468i
$903$	−13.0980	−	5.70027i	−0.435873	−	0.189693i
$904$	20.6587	+	8.63450i	0.687097	+	0.287179i
$905$	−21.6941	+	80.9634i	−0.721136	+	2.69132i
$906$	−2.82762	−	3.20503i	−0.0939413	−	0.106480i
$907$	30.3638	+	39.5709i	1.00821	+	1.31393i	0.948862	+	0.315692i	$0.102237\pi$
$907$	30.3638	+	39.5709i	1.00821	+	1.31393i	0.0593514	+	0.998237i	$0.481097\pi$
$908$	−11.6004	−	37.0668i	−0.384973	−	1.23011i
$909$	−15.2708	+	33.4505i	−0.506501	+	1.10948i
$910$	2.42349	−	54.1832i	0.0803380	−	1.79616i
$911$	−15.7261	−	9.07949i	−0.521030	−	0.300817i	0.216326	−	0.976321i	$-0.430593\pi$
$911$	−15.7261	−	9.07949i	−0.521030	−	0.300817i	−0.737356	+	0.675504i	$0.763926\pi$
$912$	28.5668	+	1.87879i	0.945941	+	0.0622129i
$913$	6.47175	−	3.73647i	0.214184	−	0.123659i
$914$	−7.18036	−	13.8293i	−0.237505	−	0.457431i
$915$	−5.31519	−	21.3479i	−0.175715	−	0.705741i
$916$	1.26361	−	0.801229i	0.0417508	−	0.0264734i
$917$	7.56358	−	18.2601i	0.249772	−	0.603002i
$918$	14.5781	+	10.4436i	0.481148	+	0.344690i
$919$	22.5229	+	22.5229i	0.742963	+	0.742963i	0.973147	−	0.230184i	$-0.0739327\pi$
$919$	22.5229	+	22.5229i	0.742963	+	0.742963i	−0.230184	+	0.973147i	$0.573933\pi$
$920$	7.03529	+	12.2759i	0.231947	+	0.404723i
$921$	−11.1470	−	15.0746i	−0.367305	−	0.496725i
$922$	1.41979	+	16.4297i	0.0467583	+	0.541084i
$923$	4.20050	−	0.553006i	0.138261	−	0.0182024i
$924$	0.771462	+	32.5147i	0.0253792	+	1.06965i
$925$	5.37526	−	40.8292i	0.176738	−	1.34246i
$926$	−9.39826	−	10.2783i	−0.308846	−	0.337767i
$927$	5.12214	−	1.17900i	0.168233	−	0.0387233i
$928$	−0.345122	+	0.487343i	−0.0113292	+	0.0159978i
$929$	20.8133	+	12.0166i	0.682864	+	0.394251i	0.800933	−	0.598754i	$-0.204337\pi$
$929$	20.8133	+	12.0166i	0.682864	+	0.394251i	−0.118070	+	0.993005i	$0.537671\pi$
$930$	−30.6270	+	62.5732i	−1.00430	+	2.05186i
$931$	−32.4386	+	42.2748i	−1.06313	+	1.38550i
$932$	−2.77939	−	1.01832i	−0.0910418	−	0.0333562i
$933$	−0.199425	+	11.2139i	−0.00652887	+	0.367128i
$934$	24.5146	+	35.0899i	0.802142	+	1.14818i
$935$	14.8784	+	14.8784i	0.486577	+	0.486577i
$936$	8.30113	+	15.7582i	0.271331	+	0.515074i
$937$	−35.2911	+	35.2911i	−1.15291	+	1.15291i	−0.166944	+	0.985966i	$0.553390\pi$
$937$	−35.2911	+	35.2911i	−1.15291	+	1.15291i	−0.985966	+	0.166944i	$0.946610\pi$
$938$	88.4399	+	15.6914i	2.88766	+	0.512344i
$939$	11.0463	+	19.9435i	0.360483	+	0.650832i
$940$	0.0922446	+	2.22128i	0.00300869	+	0.0724501i
$941$	18.7488	+	14.3864i	0.611193	+	0.468985i	0.867383	−	0.497642i	$-0.165801\pi$
$941$	18.7488	+	14.3864i	0.611193	+	0.468985i	−0.256190	+	0.966626i	$0.582467\pi$
$942$	−3.97177	+	20.2821i	−0.129407	+	0.660825i
$943$	5.21893	−	9.03946i	0.169952	−	0.294365i
$944$	−23.8942	+	37.1563i	−0.777690	+	1.20933i
$945$	−85.6501	−	40.9567i	−2.78620	−	1.33232i
$946$	5.49852	+	0.245936i	0.178772	+	0.00799607i
$947$	−15.5569	−	2.04810i	−0.505530	−	0.0665543i	−0.126552	−	0.991960i	$-0.540391\pi$
$947$	−15.5569	−	2.04810i	−0.505530	−	0.0665543i	−0.378978	+	0.925406i	$0.623724\pi$
$948$	31.5023	−	4.91013i	1.02315	−	0.159474i
$949$	1.34382	+	10.2073i	0.0436221	+	0.331343i
$950$	−44.3022	+	52.6833i	−1.43735	+	1.70927i
$951$	4.53642	+	39.9323i	0.147104	+	1.29489i
$952$	24.3654	+	18.8202i	0.789688	+	0.609966i
$953$	−16.8284	+	16.8284i	−0.545126	+	0.545126i	−0.925027	−	0.379901i	$-0.875958\pi$
$953$	−16.8284	+	16.8284i	−0.545126	+	0.545126i	0.379901	+	0.925027i	$0.375958\pi$
$954$	−4.76122	−	14.7398i	−0.154150	−	0.477219i
$955$	6.66844	+	2.76216i	0.215786	+	0.0893813i
$956$	−21.2119	+	30.1569i	−0.686043	+	0.975344i
$957$	0.267265	+	0.276942i	0.00863944	+	0.00895228i
$958$	11.1890	−	35.3556i	0.361499	−	1.14229i
$959$	−4.85574	−	8.41039i	−0.156800	−	0.271586i
$960$	6.04640	+	56.4362i	0.195147	+	1.82147i
$961$	8.60439	−	14.9032i	0.277561	−	0.480749i
$962$	7.00330	+	7.65911i	0.225795	+	0.246940i
$963$	28.5872	−	2.73368i	0.921210	−	0.0880917i
$964$	45.4577	+	4.07459i	1.46410	+	0.131234i
$965$	26.2171	−	20.1171i	0.843958	−	0.647592i
$966$	11.9492	−	5.93687i	0.384459	−	0.191016i
$967$	15.8865	+	4.25678i	0.510876	+	0.136889i	0.505043	−	0.863094i	$-0.331477\pi$
$967$	15.8865	+	4.25678i	0.510876	+	0.136889i	0.00583312	+	0.999983i	$0.498143\pi$
$968$	7.05574	+	17.1891i	0.226780	+	0.552480i
$969$	−10.3845	−	14.0435i	−0.333599	−	0.451143i
$970$	14.6073	+	2.59171i	0.469013	+	0.0832147i
$971$	18.7509	+	7.76689i	0.601746	+	0.249251i	0.662695	−	0.748890i	$-0.269413\pi$
$971$	18.7509	+	7.76689i	0.601746	+	0.249251i	−0.0609489	+	0.998141i	$0.519413\pi$
$972$	31.0683	−	2.60009i	0.996516	−	0.0833979i
$973$	−22.4320	−	54.1558i	−0.719138	−	1.73615i
$974$	32.5601	−	50.9893i	1.04329	−	1.63380i
$975$	−42.3525	−	6.34384i	−1.35636	−	0.203165i
$976$	8.34040	+	9.18014i	0.266970	+	0.293849i
$977$	3.19410	+	5.53235i	0.102188	+	0.176996i	0.912586	−	0.408885i	$-0.134082\pi$
$977$	3.19410	+	5.53235i	0.102188	+	0.176996i	−0.810398	+	0.585880i	$0.800749\pi$
$978$	−0.799943	+	0.917644i	−0.0255794	+	0.0293430i
$979$	3.33568	−	25.3370i	0.106609	−	0.809774i
$980$	−93.6049	−	48.9812i	−2.99010	−	1.56465i
$981$	−36.5418	−	30.1631i	−1.16669	−	0.963033i
$982$	16.3478	+	45.0644i	0.521679	+	1.43806i
$983$	−5.44936	−	20.3373i	−0.173808	−	0.648659i	−0.996752	−	0.0805364i	$-0.974337\pi$
$983$	−5.44936	−	20.3373i	−0.173808	−	0.648659i	0.822944	−	0.568122i	$-0.192330\pi$
$984$	33.7467	−	24.7877i	1.07580	−	0.790204i
$985$	18.9083	−	70.5666i	0.602467	−	2.24844i
$986$	0.362974	−	0.0313668i	0.0115595	−	0.000998921i
$987$	2.09619	+	0.0372779i	0.0667225	+	0.00118657i
$988$	−2.97593	−	17.0900i	−0.0946768	−	0.543707i
$989$	−0.864098	−	2.08612i	−0.0274767	−	0.0663347i
$990$	36.4632	+	2.93289i	1.15888	+	0.0932134i
$991$		−	23.6412i		−	0.750986i	−0.926825	−	0.375493i	$-0.877473\pi$
$991$		−	23.6412i		−	0.750986i	0.926825	−	0.375493i	$-0.122527\pi$
$992$	−1.50433	−	39.2482i	−0.0477624	−	1.24613i
$993$	−15.5195	+	19.4975i	−0.492496	+	0.618735i
$994$	3.84157	−	12.1388i	0.121847	−	0.385020i
$995$	−16.1129	−	12.3639i	−0.510813	−	0.391961i
$996$	−6.40010	−	10.5019i	−0.202795	−	0.332764i
$997$	−9.83194	−	12.8132i	−0.311381	−	0.405799i	0.611279	−	0.791416i	$-0.290656\pi$
$997$	−9.83194	−	12.8132i	−0.311381	−	0.405799i	−0.922659	+	0.385616i	$0.873989\pi$
$998$	35.9148	+	16.7939i	1.13686	+	0.531602i
$999$	17.1304	−	6.04720i	0.541982	−	0.191325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.43	✓	368
3.2	odd	2		864.2.bn.a.683.4		368
9.4	even	3		864.2.bn.a.395.19		368
9.5	odd	6	inner	288.2.bf.a.203.28	yes	368
32.3	odd	8	inner	288.2.bf.a.227.28	yes	368
96.35	even	8		864.2.bn.a.35.19		368
288.67	odd	24		864.2.bn.a.611.4		368
288.131	even	24	inner	288.2.bf.a.131.43	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.43	✓	368	1.1	even	1	trivial
288.2.bf.a.131.43	yes	368	288.131	even	24	inner
288.2.bf.a.203.28	yes	368	9.5	odd	6	inner
288.2.bf.a.227.28	yes	368	32.3	odd	8	inner
864.2.bn.a.35.19		368	96.35	even	8
864.2.bn.a.395.19		368	9.4	even	3
864.2.bn.a.611.4		368	288.67	odd	24
864.2.bn.a.683.4		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)

\(f(q)\)	\(=\)	\(q+(1.38102 - 0.304622i) q^{2} +(0.418469 + 1.68074i) q^{3} +(1.81441 - 0.841375i) q^{4} +(0.534666 + 4.06119i) q^{5} +(1.08990 + 2.19365i) q^{6} +(-1.15445 - 4.30845i) q^{7} +(2.24943 - 1.71466i) q^{8} +(-2.64977 + 1.40667i) q^{9} +O(q^{10})\)	\(q+(1.38102 - 0.304622i) q^{2} +(0.418469 + 1.68074i) q^{3} +(1.81441 - 0.841375i) q^{4} +(0.534666 + 4.06119i) q^{5} +(1.08990 + 2.19365i) q^{6} +(-1.15445 - 4.30845i) q^{7} +(2.24943 - 1.71466i) q^{8} +(-2.64977 + 1.40667i) q^{9} +(1.97551 + 5.44570i) q^{10} +(-1.66994 + 1.28139i) q^{11} +(2.17341 + 2.69746i) q^{12} +(1.27782 - 1.66528i) q^{13} +(-2.90675 - 5.59837i) q^{14} +(-6.60207 + 2.59812i) q^{15} +(2.58418 - 3.05320i) q^{16} -2.44036 q^{17} +(-3.23087 + 2.74982i) q^{18} +(3.81763 - 1.58131i) q^{19} +(4.38709 + 6.91882i) q^{20} +(6.75828 - 3.74327i) q^{21} +(-1.91587 + 2.27832i) q^{22} +(1.17961 + 0.316074i) q^{23} +(3.82322 + 3.06317i) q^{24} +(-11.3778 + 3.04867i) q^{25} +(1.25740 - 2.68903i) q^{26} +(-3.47310 - 3.86492i) q^{27} +(-5.71966 - 6.84597i) q^{28} +(-0.104663 - 0.0137791i) q^{29} +(-8.32612 + 5.59918i) q^{30} +(6.01303 - 3.47163i) q^{31} +(2.63872 - 5.00371i) q^{32} +(-2.85250 - 2.27051i) q^{33} +(-3.37017 + 0.743386i) q^{34} +(16.8802 - 6.99201i) q^{35} +(-3.62423 + 4.78173i) q^{36} +(-1.33791 + 3.23000i) q^{37} +(4.79050 - 3.34675i) q^{38} +(3.33363 + 1.45081i) q^{39} +(8.16627 + 8.21860i) q^{40} +(2.21215 - 8.25586i) q^{41} +(8.19301 - 7.22824i) q^{42} +(-1.12558 - 1.46689i) q^{43} +(-1.95183 + 3.73001i) q^{44} +(-7.12952 - 10.0091i) q^{45} +(1.72534 + 0.0771704i) q^{46} +(0.235013 + 0.135685i) q^{47} +(6.21303 + 3.06566i) q^{48} +(-11.1678 + 6.44773i) q^{49} +(-14.7842 + 7.67619i) q^{50} +(-1.02121 - 4.10160i) q^{51} +(0.917358 - 4.09663i) q^{52} +(-1.39716 + 3.37305i) q^{53} +(-5.97374 - 4.27953i) q^{54} +(-6.09683 - 6.09683i) q^{55} +(-9.98437 - 7.71207i) q^{56} +(4.25533 + 5.75470i) q^{57} +(-0.148738 + 0.0128534i) q^{58} +(-10.9495 + 1.44153i) q^{59} +(-9.79287 + 10.2689i) q^{60} +(-0.404733 + 3.07425i) q^{61} +(7.24656 - 6.62607i) q^{62} +(9.11959 + 9.79246i) q^{63} +(2.11987 - 7.71402i) q^{64} +(7.44625 + 4.29909i) q^{65} +(-4.63099 - 2.26668i) q^{66} +(-8.66829 + 11.2967i) q^{67} +(-4.42781 + 2.05325i) q^{68} +(-0.0376102 + 2.11488i) q^{69} +(21.1819 - 14.7981i) q^{70} +(1.42724 + 1.42724i) q^{71} +(-3.54850 + 7.70767i) q^{72} +(-3.46821 + 3.46821i) q^{73} +(-0.863748 + 4.86824i) q^{74} +(-9.88528 - 17.8473i) q^{75} +(5.59627 - 6.08120i) q^{76} +(7.44865 + 5.71555i) q^{77} +(5.04575 + 0.988092i) q^{78} +(4.60186 - 7.97066i) q^{79} +(13.7813 + 8.86240i) q^{80} +(5.04253 - 7.45472i) q^{81} +(0.540103 - 12.0753i) q^{82} +(-3.51986 - 0.463399i) q^{83} +(9.11280 - 12.4781i) q^{84} +(-1.30478 - 9.91076i) q^{85} +(-2.00129 - 1.68292i) q^{86} +(-0.0206390 - 0.181677i) q^{87} +(-1.55926 + 5.74578i) q^{88} +(-8.58494 + 8.58494i) q^{89} +(-12.8950 - 11.6509i) q^{90} +(-8.64996 - 3.58293i) q^{91} +(2.40623 - 0.419002i) q^{92} +(8.35117 + 8.65357i) q^{93} +(0.365890 + 0.115793i) q^{94} +(8.46317 + 14.6586i) q^{95} +(9.51416 + 2.34110i) q^{96} +(1.28048 - 2.21785i) q^{97} +(-13.4588 + 12.3064i) q^{98} +(2.62245 - 5.74444i) 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

Modular forms

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