LMFDB - Embedded newform 160.2.u.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	160.43
Dual form			160.2.u.a.67.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30208 - 0.551886i) q^{2} +(-0.577765 + 1.39485i) q^{3} +(1.39084 - 1.43720i) q^{4} +(0.315793 + 2.21366i) q^{5} +(0.0174990 + 2.13507i) q^{6} -1.62907i q^{7} +(1.01782 - 2.63895i) q^{8} +(0.509534 + 0.509534i) q^{9} +O(q^{10})$	\(q+(1.30208 - 0.551886i) q^{2} +(-0.577765 + 1.39485i) q^{3} +(1.39084 - 1.43720i) q^{4} +(0.315793 + 2.21366i) q^{5} +(0.0174990 + 2.13507i) q^{6} -1.62907i q^{7} +(1.01782 - 2.63895i) q^{8} +(0.509534 + 0.509534i) q^{9} +(1.63288 + 2.70808i) q^{10} +(0.655490 - 1.58249i) q^{11} +(1.20110 + 2.77038i) q^{12} +(-1.77030 + 4.27389i) q^{13} +(-0.899059 - 2.12118i) q^{14} +(-3.27017 - 0.838489i) q^{15} +(-0.131110 - 3.99785i) q^{16} +(-3.79340 - 3.79340i) q^{17} +(0.944661 + 0.382251i) q^{18} +(-1.31761 - 3.18099i) q^{19} +(3.62069 + 2.62499i) q^{20} +(2.27230 + 0.941216i) q^{21} +(-0.0198531 - 2.42229i) q^{22} -6.56332i q^{23} +(3.09287 + 2.94439i) q^{24} +(-4.80055 + 1.39811i) q^{25} +(0.0536180 + 6.54197i) q^{26} +(-5.18965 + 2.14962i) q^{27} +(-2.34130 - 2.26577i) q^{28} +(0.0280276 + 0.0676646i) q^{29} +(-4.72078 + 0.712976i) q^{30} +5.64355i q^{31} +(-2.37707 - 5.13318i) q^{32} +(1.82862 + 1.82862i) q^{33} +(-7.03285 - 2.84580i) q^{34} +(3.60619 - 0.514447i) q^{35} +(1.44099 - 0.0236223i) q^{36} +(1.57710 + 3.80745i) q^{37} +(-3.47118 - 3.41474i) q^{38} +(-4.93861 - 4.93861i) q^{39} +(6.16314 + 1.41975i) q^{40} +(5.30956 - 5.30956i) q^{41} +(3.47817 - 0.0285071i) q^{42} +(1.86599 - 0.772917i) q^{43} +(-1.36268 - 3.14307i) q^{44} +(-0.967026 + 1.28884i) q^{45} +(-3.62220 - 8.54599i) q^{46} +(-9.10229 + 9.10229i) q^{47} +(5.65214 + 2.12694i) q^{48} +4.34615 q^{49} +(-5.47912 + 4.46982i) q^{50} +(7.48290 - 3.09952i) q^{51} +(3.68024 + 8.48860i) q^{52} +(1.32771 + 3.20538i) q^{53} +(-5.57101 + 5.66309i) q^{54} +(3.71010 + 0.951290i) q^{55} +(-4.29902 - 1.65810i) q^{56} +5.19825 q^{57} +(0.0738375 + 0.0726370i) q^{58} +(0.973697 - 2.35071i) q^{59} +(-5.75337 + 3.53369i) q^{60} +(7.38048 - 3.05710i) q^{61} +(3.11460 + 7.34837i) q^{62} +(0.830064 - 0.830064i) q^{63} +(-5.92808 - 5.37195i) q^{64} +(-10.0200 - 2.56918i) q^{65} +(3.39020 + 1.37182i) q^{66} +(8.89195 + 3.68317i) q^{67} +(-10.7279 + 0.175864i) q^{68} +(9.15482 + 3.79205i) q^{69} +(4.41165 - 2.66006i) q^{70} +(-6.21992 + 6.21992i) q^{71} +(1.86325 - 0.826019i) q^{72} +0.0521227 q^{73} +(4.15480 + 4.08724i) q^{74} +(0.823432 - 7.50381i) q^{75} +(-6.40431 - 2.53058i) q^{76} +(-2.57799 - 1.06784i) q^{77} +(-9.15603 - 3.70493i) q^{78} -0.0281168i q^{79} +(8.80846 - 1.55272i) q^{80} -6.31898i q^{81} +(3.98322 - 9.84377i) q^{82} +(-5.43842 - 2.25267i) q^{83} +(4.51313 - 1.95667i) q^{84} +(7.19935 - 9.59521i) q^{85} +(2.00311 - 2.03621i) q^{86} -0.110575 q^{87} +(-3.50894 - 3.34050i) q^{88} +(10.7926 - 10.7926i) q^{89} +(-0.547856 + 2.21187i) q^{90} +(6.96245 + 2.88394i) q^{91} +(-9.43283 - 9.12855i) q^{92} +(-7.87189 - 3.26064i) q^{93} +(-6.82851 + 16.8754i) q^{94} +(6.62552 - 3.92126i) q^{95} +(8.53339 - 0.349886i) q^{96} +(-10.6737 + 10.6737i) q^{97} +(5.65904 - 2.39858i) q^{98} +(1.14033 - 0.472340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	1.30208	−	0.551886i	0.920712	−	0.390242i
$2$	1.30208	−	0.551886i	0.920712	−	0.390242i
$3$	−0.577765	+	1.39485i	−0.333573	+	0.805315i	0.664731	+	0.747083i	$0.268546\pi$
$3$	−0.577765	+	1.39485i	−0.333573	+	0.805315i	−0.998303	+	0.0582321i	$0.981454\pi$
$4$	1.39084	−	1.43720i	0.695422	−	0.718602i
$5$	0.315793	+	2.21366i	0.141227	+	0.989977i
$5$	0.315793	+	2.21366i	0.141227	+	0.989977i
$6$	0.0174990	+	2.13507i	0.00714395	+	0.871638i
$7$		−	1.62907i		−	0.615729i	−0.951430	−	0.307864i	$-0.900386\pi$
$7$		−	1.62907i		−	0.615729i	0.951430	−	0.307864i	$-0.0996143\pi$
$8$	1.01782	−	2.63895i	0.359854	−	0.933009i
$9$	0.509534	+	0.509534i	0.169845	+	0.169845i
$10$	1.63288	+	2.70808i	0.516360	+	0.856371i
$11$	0.655490	−	1.58249i	0.197638	−	0.477140i	−0.793727	−	0.608274i	$-0.791862\pi$
$11$	0.655490	−	1.58249i	0.197638	−	0.477140i	0.991365	+	0.131135i	$0.0418620\pi$
$12$	1.20110	+	2.77038i	0.346728	+	0.799740i
$13$	−1.77030	+	4.27389i	−0.490994	+	1.18536i	0.463221	+	0.886243i	$0.346694\pi$
$13$	−1.77030	+	4.27389i	−0.490994	+	1.18536i	−0.954215	+	0.299122i	$0.903306\pi$
$14$	−0.899059	−	2.12118i	−0.240284	−	0.566909i
$15$	−3.27017	−	0.838489i	−0.844353	−	0.216497i
$16$	−0.131110	−	3.99785i	−0.0327774	−	0.999463i
$17$	−3.79340	−	3.79340i	−0.920034	−	0.920034i	0.0769971	−	0.997031i	$-0.475467\pi$
$17$	−3.79340	−	3.79340i	−0.920034	−	0.920034i	−0.997031	+	0.0769971i	$0.975467\pi$
$18$	0.944661	+	0.382251i	0.222659	+	0.0900975i
$19$	−1.31761	−	3.18099i	−0.302280	−	0.729768i	−0.999911	−	0.0133114i	$-0.995763\pi$
$19$	−1.31761	−	3.18099i	−0.302280	−	0.729768i	0.697632	−	0.716457i	$-0.254237\pi$
$20$	3.62069	+	2.62499i	0.809612	+	0.586966i
$21$	2.27230	+	0.941216i	0.495856	+	0.205390i
$22$	−0.0198531	−	2.42229i	−0.00423270	−	0.516435i
$23$		−	6.56332i		−	1.36855i	−0.729226	−	0.684273i	$-0.760120\pi$
$23$		−	6.56332i		−	1.36855i	0.729226	−	0.684273i	$-0.239880\pi$
$24$	3.09287	+	2.94439i	0.631329	+	0.601022i
$25$	−4.80055	+	1.39811i	−0.960110	+	0.279623i
$26$	0.0536180	+	6.54197i	0.0105154	+	1.28299i
$27$	−5.18965	+	2.14962i	−0.998749	+	0.413696i
$28$	−2.34130	−	2.26577i	−0.442464	−	0.428191i
$29$	0.0280276	+	0.0676646i	0.00520460	+	0.0125650i	0.926460	−	0.376392i	$-0.122835\pi$
$29$	0.0280276	+	0.0676646i	0.00520460	+	0.0125650i	−0.921256	+	0.388957i	$0.872835\pi$
$30$	−4.72078	+	0.712976i	−0.861893	+	0.130171i
$31$			5.64355i			1.01361i	0.862060	+	0.506806i	$0.169174\pi$
$31$			5.64355i			1.01361i	−0.862060	+	0.506806i	$0.830826\pi$
$32$	−2.37707	−	5.13318i	−0.420211	−	0.907426i
$33$	1.82862	+	1.82862i	0.318321	+	0.318321i
$34$	−7.03285	−	2.84580i	−1.20612	−	0.488050i
$35$	3.60619	−	0.514447i	0.609558	−	0.0869575i
$36$	1.44099	−	0.0236223i	0.240164	−	0.00393704i
$37$	1.57710	+	3.80745i	0.259273	+	0.625941i	0.998891	−	0.0470861i	$-0.0149935\pi$
$37$	1.57710	+	3.80745i	0.259273	+	0.625941i	−0.739617	+	0.673028i	$0.764994\pi$
$38$	−3.47118	−	3.41474i	−0.563099	−	0.553944i
$39$	−4.93861	−	4.93861i	−0.790810	−	0.790810i
$40$	6.16314	+	1.41975i	0.974478	+	0.224482i
$41$	5.30956	−	5.30956i	0.829215	−	0.829215i	−0.158194	−	0.987408i	$-0.550567\pi$
$41$	5.30956	−	5.30956i	0.829215	−	0.829215i	0.987408	+	0.158194i	$0.0505670\pi$
$42$	3.47817	−	0.0285071i	0.536693	−	0.00439873i
$43$	1.86599	−	0.772917i	0.284560	−	0.117869i	−0.235838	−	0.971792i	$-0.575783\pi$
$43$	1.86599	−	0.772917i	0.284560	−	0.117869i	0.520398	+	0.853924i	$0.325783\pi$
$44$	−1.36268	−	3.14307i	−0.205432	−	0.473836i
$45$	−0.967026	+	1.28884i	−0.144156	+	0.192129i
$46$	−3.62220	−	8.54599i	−0.534065	−	1.26004i
$47$	−9.10229	+	9.10229i	−1.32771	+	1.32771i	−0.420337	+	0.907368i	$0.638088\pi$
$47$	−9.10229	+	9.10229i	−1.32771	+	1.32771i	−0.907368	+	0.420337i	$0.861912\pi$
$48$	5.65214	+	2.12694i	0.815816	+	0.306997i
$49$	4.34615			0.620878
$50$	−5.47912	+	4.46982i	−0.774864	+	0.632128i
$51$	7.48290	−	3.09952i	1.04782	−	0.434019i
$52$	3.68024	+	8.48860i	0.510357	+	1.17716i
$53$	1.32771	+	3.20538i	0.182375	+	0.440293i	0.988455	−	0.151514i	$-0.0484149\pi$
$53$	1.32771	+	3.20538i	0.182375	+	0.440293i	−0.806080	+	0.591807i	$0.798415\pi$
$54$	−5.57101	+	5.66309i	−0.758119	+	0.770649i
$55$	3.71010	+	0.951290i	0.500269	+	0.128272i
$56$	−4.29902	−	1.65810i	−0.574480	−	0.221573i
$57$	5.19825			0.688526
$58$	0.0738375	+	0.0726370i	0.00969533	+	0.00953770i
$59$	0.973697	−	2.35071i	0.126764	−	0.306037i	−0.847737	−	0.530416i	$-0.822036\pi$
$59$	0.973697	−	2.35071i	0.126764	−	0.306037i	0.974502	+	0.224380i	$0.0720356\pi$
$60$	−5.75337	+	3.53369i	−0.742757	+	0.456197i
$61$	7.38048	−	3.05710i	0.944974	−	0.391421i	0.143635	−	0.989631i	$-0.454121\pi$
$61$	7.38048	−	3.05710i	0.944974	−	0.391421i	0.801340	+	0.598210i	$0.204121\pi$
$62$	3.11460	+	7.34837i	0.395554	+	0.933244i
$63$	0.830064	−	0.830064i	0.104578	−	0.104578i
$64$	−5.92808	−	5.37195i	−0.741010	−	0.671494i
$65$	−10.0200	−	2.56918i	−1.24283	−	0.318668i
$66$	3.39020	+	1.37182i	0.417305	+	0.168860i
$67$	8.89195	+	3.68317i	1.08633	+	0.449971i	0.852724	−	0.522362i	$-0.174949\pi$
$67$	8.89195	+	3.68317i	1.08633	+	0.449971i	0.233601	+	0.972333i	$0.424949\pi$
$68$	−10.7279	+	0.175864i	−1.30095	+	0.0213266i
$69$	9.15482	+	3.79205i	1.10211	+	0.456509i
$70$	4.41165	−	2.66006i	0.527293	−	0.317938i
$71$	−6.21992	+	6.21992i	−0.738169	+	0.738169i	−0.972224	−	0.234054i	$-0.924801\pi$
$71$	−6.21992	+	6.21992i	−0.738169	+	0.738169i	0.234054	+	0.972224i	$0.424801\pi$
$72$	1.86325	−	0.826019i	0.219586	−	0.0973472i
$73$	0.0521227			0.00610050			0.00305025	−	0.999995i	$-0.499029\pi$
$73$	0.0521227			0.00610050			0.00305025	+	0.999995i	$0.499029\pi$
$74$	4.15480	+	4.08724i	0.482985	+	0.475132i
$75$	0.823432	−	7.50381i	0.0950818	−	0.866466i
$76$	−6.40431	−	2.53058i	−0.734625	−	0.290278i
$77$	−2.57799	−	1.06784i	−0.293789	−	0.121691i
$78$	−9.15603	−	3.70493i	−1.03672	−	0.419501i
$79$		−	0.0281168i		−	0.00316338i	−0.999999	−	0.00158169i	$-0.999497\pi$
$79$		−	0.0281168i		−	0.00316338i	0.999999	−	0.00158169i	$-0.000503468\pi$
$80$	8.80846	−	1.55272i	0.984816	−	0.173600i
$81$		−	6.31898i		−	0.702109i
$82$	3.98322	−	9.84377i	0.439873	−	1.08706i
$83$	−5.43842	−	2.25267i	−0.596944	−	0.247263i	0.0636906	−	0.997970i	$-0.479713\pi$
$83$	−5.43842	−	2.25267i	−0.596944	−	0.247263i	−0.660635	+	0.750707i	$0.729713\pi$
$84$	4.51313	−	1.95667i	0.492423	−	0.213490i
$85$	7.19935	−	9.59521i	0.780879	−	1.04075i
$86$	2.00311	−	2.03621i	0.216001	−	0.219571i
$87$	−0.110575			−0.0118549
$88$	−3.50894	−	3.34050i	−0.374055	−	0.356098i
$89$	10.7926	−	10.7926i	1.14401	−	1.14401i	0.156301	−	0.987709i	$-0.450043\pi$
$89$	10.7926	−	10.7926i	1.14401	−	1.14401i	0.987709	−	0.156301i	$-0.0499570\pi$
$90$	−0.547856	+	2.21187i	−0.0577491	+	0.233151i
$91$	6.96245	+	2.88394i	0.729863	+	0.302319i
$92$	−9.43283	−	9.12855i	−0.983440	−	0.951717i
$93$	−7.87189	−	3.26064i	−0.816277	−	0.338113i
$94$	−6.82851	+	16.8754i	−0.704307	+	1.74056i
$95$	6.62552	−	3.92126i	0.679764	−	0.402313i
$96$	8.53339	−	0.349886i	0.870935	−	0.0357101i
$97$	−10.6737	+	10.6737i	−1.08375	+	1.08375i	−0.0875919	+	0.996156i	$0.527917\pi$
$97$	−10.6737	+	10.6737i	−1.08375	+	1.08375i	−0.996156	+	0.0875919i	$0.972083\pi$
$98$	5.65904	−	2.39858i	0.571650	−	0.242293i
$99$	1.14033	−	0.472340i	0.114607	−	0.0474719i
$100$	−4.66744	+	8.84393i	−0.466744	+	0.884393i
$101$	−5.72517	+	13.8218i	−0.569676	+	1.37532i	0.332153	+	0.943226i	$0.392225\pi$
$101$	−5.72517	+	13.8218i	−0.569676	+	1.37532i	−0.901829	+	0.432094i	$0.857775\pi$
$102$	8.03278	−	8.16554i	0.795364	−	0.808509i
$103$	15.2263			1.50029			0.750145	−	0.661273i	$-0.229984\pi$
$103$	15.2263			1.50029			0.750145	+	0.661273i	$0.229984\pi$
$104$	9.47672	+	9.02180i	0.929269	+	0.884660i
$105$	−1.36595	+	5.32731i	−0.133303	+	0.519893i
$106$	3.49779	+	3.44092i	0.339736	+	0.334212i
$107$	1.34151	+	3.23870i	0.129689	+	0.313097i	0.975364	−	0.220601i	$-0.0708019\pi$
$107$	1.34151	+	3.23870i	0.129689	+	0.313097i	−0.845675	+	0.533698i	$0.820802\pi$
$108$	−4.12855	+	10.4484i	−0.397270	+	1.00540i
$109$	−9.18917	+	3.80628i	−0.880162	+	0.364575i	−0.776560	−	0.630044i	$-0.783037\pi$
$109$	−9.18917	+	3.80628i	−0.880162	+	0.364575i	−0.103603	+	0.994619i	$0.533037\pi$
$110$	5.35586	−	0.808892i	0.510661	−	0.0771248i
$111$	−6.22201			−0.590567
$112$	−6.51276	+	0.213586i	−0.615398	+	0.0201820i
$113$	−2.24936	+	2.24936i	−0.211602	+	0.211602i	−0.804948	−	0.593346i	$-0.797807\pi$
$113$	−2.24936	+	2.24936i	−0.211602	+	0.211602i	0.593346	+	0.804948i	$0.297807\pi$
$114$	6.76856	−	2.86884i	0.633934	−	0.268692i
$115$	14.5289	−	2.07265i	1.35483	−	0.193276i
$116$	0.136230	+	0.0538295i	0.0126486	+	0.00499795i
$117$	−3.07972	+	1.27566i	−0.284721	+	0.117935i
$118$	−0.0294908	−	3.59819i	−0.00271485	−	0.331240i
$119$	−6.17969	+	6.17969i	−0.566492	+	0.566492i
$120$	−5.54117	+	7.77636i	−0.505838	+	0.709881i
$121$	5.70356	+	5.70356i	0.518505	+	0.518505i
$122$	7.92284	−	8.05378i	0.717300	−	0.729155i
$123$	4.33835	+	10.4737i	0.391176	+	0.944382i
$124$	8.11093	+	7.84929i	0.728383	+	0.704887i
$125$	−4.61092	−	10.1853i	−0.412414	−	0.910997i
$126$	0.622712	−	1.53891i	0.0554756	−	0.137097i
$127$	0.145197	+	0.145197i	0.0128842	+	0.0128842i	0.713520	−	0.700635i	$-0.247100\pi$
$127$	0.145197	+	0.145197i	0.0128842	+	0.0128842i	−0.700635	+	0.713520i	$0.747100\pi$
$128$	−10.6836	−	3.72311i	−0.944302	−	0.329079i
$129$			3.04933i			0.268479i
$130$	−14.4647	+	2.18460i	−1.26864	+	0.191602i
$131$	0.427434	+	1.03192i	0.0373451	+	0.0901590i	0.941452	−	0.337148i	$-0.109462\pi$
$131$	0.427434	+	1.03192i	0.0373451	+	0.0901590i	−0.904107	+	0.427307i	$0.859462\pi$
$132$	5.17142	−	0.0847756i	0.450114	−	0.00737877i
$133$	−5.18203	+	2.14647i	−0.449339	+	0.186122i
$134$	13.6108	−	0.111554i	1.17579	−	0.00963678i
$135$	−6.39739	−	10.8093i	−0.550599	−	0.930314i
$136$	−13.8716	+	6.14957i	−1.18948	+	0.527322i
$137$		−	22.3945i		−	1.91329i	−0.291255	−	0.956646i	$-0.594073\pi$
$137$		−	22.3945i		−	1.91329i	0.291255	−	0.956646i	$-0.405927\pi$
$138$	14.0131	−	0.114852i	1.19288	−	0.00977682i
$139$	−13.3940	−	5.54799i	−1.13607	−	0.470575i	−0.266229	−	0.963910i	$-0.585778\pi$
$139$	−13.3940	−	5.54799i	−1.13607	−	0.470575i	−0.869839	+	0.493335i	$0.835778\pi$
$140$	4.27628	−	5.89835i	0.361412	−	0.498501i
$141$	−7.43732	−	17.9553i	−0.626335	−	1.51211i
$142$	−4.66617	+	11.5316i	−0.391576	+	0.967706i
$143$	5.60299	+	5.60299i	0.468546	+	0.468546i
$144$	1.97024	−	2.10385i	0.164186	−	0.175321i
$145$	−0.140935	+	0.0834115i	−0.0117040	+	0.00692695i
$146$	0.0678681	−	0.0287658i	0.00561680	−	0.00238067i
$147$	−2.51105	+	6.06221i	−0.207108	+	0.500002i
$148$	7.66558	+	3.02896i	0.630107	+	0.248979i
$149$	−2.51173	+	6.06385i	−0.205769	+	0.496770i	−0.992749	−	0.120209i	$-0.961644\pi$
$149$	−2.51173	+	6.06385i	−0.205769	+	0.496770i	0.786980	+	0.616979i	$0.211644\pi$
$150$	−3.06907	−	10.2250i	−0.250589	−	0.834870i
$151$	−1.60182	−	1.60182i	−0.130355	−	0.130355i	0.638919	−	0.769274i	$-0.279382\pi$
$151$	−1.60182	−	1.60182i	−0.130355	−	0.130355i	−0.769274	+	0.638919i	$0.779382\pi$
$152$	−9.73554	+	0.239421i	−0.789657	+	0.0194196i
$153$		−	3.86573i		−	0.312526i
$154$	−3.94608	+	0.0323421i	−0.317984	+	0.00260620i
$155$	−12.4929	+	1.78219i	−1.00345	+	0.143149i
$156$	−13.9666	+	0.228956i	−1.11822	+	0.0183312i
$157$	−1.42831	+	3.44825i	−0.113992	+	0.275200i	−0.970571	−	0.240815i	$-0.922585\pi$
$157$	−1.42831	+	3.44825i	−0.113992	+	0.275200i	0.856579	+	0.516015i	$0.172585\pi$
$158$	−0.0155173	−	0.0366104i	−0.00123449	−	0.00291257i
$159$	−5.23812			−0.415410
$160$	10.6124	−	6.88305i	0.838986	−	0.544153i
$161$	−10.6921			−0.842654
$162$	−3.48736	−	8.22784i	−0.273993	−	0.646440i
$163$	−5.77413	+	13.9400i	−0.452264	+	1.09186i	0.519195	+	0.854656i	$0.326232\pi$
$163$	−5.77413	+	13.9400i	−0.452264	+	1.09186i	−0.971459	+	0.237207i	$0.923768\pi$
$164$	−0.246154	−	15.0157i	−0.0192214	−	1.17253i
$165$	−3.47047	+	4.62539i	−0.270175	+	0.360086i
$166$	−8.32450	+	0.0682276i	−0.646106	+	0.00529549i
$167$		−	9.61910i		−	0.744348i	−0.928163	−	0.372174i	$-0.878612\pi$
$167$		−	9.61910i		−	0.744348i	0.928163	−	0.372174i	$-0.121388\pi$
$168$	4.79661	−	5.03848i	0.370067	−	0.388727i
$169$	−5.93979	−	5.93979i	−0.456907	−	0.456907i
$170$	4.07870	−	16.4670i	0.312822	−	1.26296i
$171$	0.949455	−	2.29219i	0.0726066	−	0.175288i
$172$	1.48446	−	3.75681i	0.113189	−	0.286454i
$173$	5.76667	−	13.9220i	0.438432	−	1.05847i	−0.538059	−	0.842907i	$-0.680842\pi$
$173$	5.76667	−	13.9220i	0.438432	−	1.05847i	0.976491	−	0.215560i	$-0.0691577\pi$
$174$	−0.143978	+	0.0610249i	−0.0109150	+	0.00462629i
$175$	2.27762	+	7.82041i	0.172172	+	0.591167i
$176$	−6.41251	−	2.41307i	−0.483361	−	0.181892i
$177$	2.71632	+	2.71632i	0.204171	+	0.204171i
$178$	8.09656	−	20.0091i	0.606863	−	1.49975i
$179$	3.54880	+	8.56757i	0.265250	+	0.640370i	0.999248	−	0.0387816i	$-0.0123477\pi$
$179$	3.54880	+	8.56757i	0.265250	+	0.640370i	−0.733998	+	0.679152i	$0.762348\pi$
$180$	0.507345	+	3.18239i	0.0378153	+	0.237201i
$181$	−4.63172	−	1.91852i	−0.344273	−	0.142602i	0.203846	−	0.979003i	$-0.434656\pi$
$181$	−4.63172	−	1.91852i	−0.344273	−	0.142602i	−0.548119	+	0.836400i	$0.684656\pi$
$182$	10.6573	−	0.0873473i	0.789972	−	0.00647461i
$183$			12.0609i			0.891569i
$184$	−17.3202	−	6.68029i	−1.27687	−	0.492477i
$185$	−7.93036	+	4.69352i	−0.583051	+	0.345075i
$186$	−12.0494	+	0.0987566i	−0.883502	+	0.00724119i
$187$	−8.48956	+	3.51649i	−0.620818	+	0.257151i
$188$	0.421987	+	25.7417i	0.0307765	+	1.87741i
$189$	3.50188	+	8.45429i	0.254724	+	0.614959i
$190$	6.46289	−	8.76234i	0.468867	−	0.635687i
$191$			18.3995i			1.33134i	0.746245	+	0.665672i	$0.231855\pi$
$191$			18.3995i			1.33134i	−0.746245	+	0.665672i	$0.768145\pi$
$192$	10.9181	−	5.16504i	0.787945	−	0.372755i
$193$	13.1501	+	13.1501i	0.946568	+	0.946568i	0.998643	−	0.0520750i	$-0.0165835\pi$
$193$	13.1501	+	13.1501i	0.946568	+	0.946568i	−0.0520750	+	0.998643i	$0.516583\pi$
$194$	−8.00737	+	19.7887i	−0.574896	+	1.42074i
$195$	9.37280	−	12.4920i	0.671200	−	0.894568i
$196$	6.04481	−	6.24630i	0.431772	−	0.446164i
$197$	−8.99511	−	21.7161i	−0.640875	−	1.54721i	−0.825501	−	0.564400i	$-0.809107\pi$
$197$	−8.99511	−	21.7161i	−0.640875	−	1.54721i	0.184626	−	0.982809i	$-0.440893\pi$
$198$	1.22413	−	1.24436i	0.0869948	−	0.0884326i
$199$	−4.07321	−	4.07321i	−0.288742	−	0.288742i	0.547841	−	0.836583i	$-0.315450\pi$
$199$	−4.07321	−	4.07321i	−0.288742	−	0.288742i	−0.836583	+	0.547841i	$0.815450\pi$
$200$	−1.19655	+	14.0914i	−0.0846091	+	0.996414i
$201$	−10.2749	+	10.2749i	−0.724736	+	0.724736i
$202$	0.173401	+	21.1568i	0.0122004	+	1.48858i
$203$	0.110230	−	0.0456588i	0.00773664	−	0.00320462i
$204$	5.95290	−	15.0654i	0.416787	−	1.05479i
$205$	13.4303	+	10.0768i	0.938011	+	0.703796i
$206$	19.8259	−	8.40318i	1.38134	−	0.585477i
$207$	3.34423	−	3.34423i	0.232440	−	0.232440i
$208$	17.3185	+	6.51706i	1.20082	+	0.451877i
$209$	−5.89757			−0.407943
$210$	1.16148	+	7.69046i	0.0801501	+	0.530692i
$211$	−20.7530	+	8.59618i	−1.42870	+	0.591785i	−0.957029	−	0.289992i	$-0.906347\pi$
$211$	−20.7530	+	8.59618i	−1.42870	+	0.591785i	−0.471667	+	0.881777i	$0.656347\pi$
$212$	6.45342	+	2.54999i	0.443223	+	0.175134i
$213$	−5.08219	−	12.2695i	−0.348226	−	0.840692i
$214$	3.53415	+	3.47669i	0.241590	+	0.237662i
$215$	2.30024	+	3.88657i	0.156875	+	0.265062i
$216$	0.390605	+	15.8832i	0.0265773	+	1.08071i
$217$	9.19371			0.624110
$218$	−9.86443	+	10.0275i	−0.668103	+	0.679146i
$219$	−0.0301146	+	0.0727031i	−0.00203496	+	0.00491282i
$220$	6.52736	−	4.00907i	0.440075	−	0.270291i
$221$	22.9280	−	9.49711i	1.54231	−	0.638845i
$222$	−8.10157	+	3.43384i	−0.543742	+	0.230464i
$223$	12.0426	−	12.0426i	0.806431	−	0.806431i	−0.177661	−	0.984092i	$-0.556853\pi$
$223$	12.0426	−	12.0426i	0.806431	−	0.806431i	0.984092	+	0.177661i	$0.0568529\pi$
$224$	−8.36228	+	3.87241i	−0.558729	+	0.258736i
$225$	−3.15843	−	1.73366i	−0.210562	−	0.115577i
$226$	−1.68747	+	4.17025i	−0.112249	+	0.277401i
$227$	13.7092	+	5.67855i	0.909914	+	0.376899i	0.788024	−	0.615645i	$-0.211104\pi$
$227$	13.7092	+	5.67855i	0.909914	+	0.376899i	0.121890	+	0.992544i	$0.461104\pi$
$228$	7.22996	−	7.47095i	0.478816	−	0.494776i
$229$	21.1045	+	8.74177i	1.39462	+	0.577672i	0.948351	−	0.317224i	$-0.102751\pi$
$229$	21.1045	+	8.74177i	1.39462	+	0.577672i	0.446274	+	0.894897i	$0.352751\pi$
$230$	17.7740	−	10.7171i	1.17198	−	0.706663i
$231$	2.97894	−	2.97894i	0.196000	−	0.196000i
$232$	0.207090	−	0.00509286i	0.0135962	−	0.000334362i
$233$	−1.43825			−0.0942232			−0.0471116	−	0.998890i	$-0.515002\pi$
$233$	−1.43825			−0.0942232			−0.0471116	+	0.998890i	$0.515002\pi$
$234$	−3.30604	+	3.36068i	−0.216122	+	0.219694i
$235$	−23.0238	−	17.2749i	−1.50191	−	1.12689i
$236$	−2.02419	−	4.66887i	−0.131764	−	0.303918i
$237$	0.0392186	+	0.0162449i	0.00254752	+	0.00105522i
$238$	−4.63599	+	11.4570i	−0.300507	+	0.742645i
$239$		−	19.2161i		−	1.24299i	−0.783420	−	0.621493i	$-0.786527\pi$
$239$		−	19.2161i		−	1.24299i	0.783420	−	0.621493i	$-0.213473\pi$
$240$	−2.92341	+	13.1836i	−0.188705	+	0.850996i
$241$		−	0.910269i		−	0.0586356i	−0.999570	−	0.0293178i	$-0.990667\pi$
$241$		−	0.910269i		−	0.0586356i	0.999570	−	0.0293178i	$-0.00933348\pi$
$242$	10.5742	+	4.27879i	0.679737	+	0.275051i
$243$	−6.75495	−	2.79799i	−0.433330	−	0.179491i
$244$	5.87143	−	14.8592i	0.375880	−	0.951263i
$245$	1.37248	+	9.62087i	0.0876846	+	0.614655i
$246$	11.4292	+	11.2434i	0.728699	+	0.716851i
$247$	15.9278			1.01346
$248$	14.8930	+	5.74412i	0.945708	+	0.364752i
$249$	6.28426	−	6.28426i	0.398249	−	0.398249i
$250$	−11.6249	−	10.7173i	−0.735224	−	0.677824i
$251$	−20.5181	−	8.49886i	−1.29509	−	0.536443i	−0.374591	−	0.927190i	$-0.622217\pi$
$251$	−20.5181	−	8.49886i	−1.29509	−	0.536443i	−0.920498	+	0.390747i	$0.872217\pi$
$252$	−0.0384822	−	2.34746i	−0.00242415	−	0.147876i
$253$	−10.3864	−	4.30219i	−0.652988	−	0.270476i
$254$	0.269192	+	0.108927i	0.0168906	+	0.00683467i
$255$	9.22432	+	15.5858i	0.577649	+	0.976019i
$256$	−15.9656	+	1.04831i	−0.997851	+	0.0655196i
$257$	17.6500	−	17.6500i	1.10098	−	1.10098i	0.106686	−	0.994293i	$-0.465976\pi$
$257$	17.6500	−	17.6500i	1.10098	−	1.10098i	0.994293	−	0.106686i	$-0.0340239\pi$
$258$	1.68288	+	3.97048i	0.104772	+	0.247191i
$259$	6.20259	−	2.56920i	0.385410	−	0.159642i
$260$	−17.6287	+	10.8274i	−1.09328	+	0.671488i
$261$	−0.0201964	+	0.0487585i	−0.00125013	+	0.00301807i
$262$	1.12605	+	1.10775i	0.0695679	+	0.0684368i
$263$	19.3451			1.19287			0.596434	−	0.802662i	$-0.296584\pi$
$263$	19.3451			1.19287			0.596434	+	0.802662i	$0.296584\pi$
$264$	6.68683	−	2.96442i	0.411546	−	0.182447i
$265$	−6.67632	+	3.95133i	−0.410123	+	0.242728i
$266$	−5.56284	+	5.65477i	−0.341079	+	0.346716i
$267$	8.81842	+	21.2896i	0.539679	+	1.30290i
$268$	17.6608	−	7.65684i	1.07880	−	0.467716i
$269$	−4.94280	+	2.04738i	−0.301368	+	0.124831i	−0.528243	−	0.849093i	$-0.677149\pi$
$269$	−4.94280	+	2.04738i	−0.301368	+	0.124831i	0.226875	+	0.973924i	$0.427149\pi$
$270$	−14.2954	−	10.5439i	−0.869992	−	0.641684i
$271$	27.8402			1.69117			0.845585	−	0.533840i	$-0.179252\pi$
$271$	27.8402			1.69117			0.845585	+	0.533840i	$0.179252\pi$
$272$	−14.6681	+	15.6628i	−0.889383	+	0.949696i
$273$	−8.04531	+	8.04531i	−0.486925	+	0.486925i
$274$	−12.3592	−	29.1595i	−0.746647	−	1.76159i
$275$	−0.934207	+	8.51329i	−0.0563348	+	0.513371i
$276$	18.1829	−	7.88320i	1.09448	−	0.474513i
$277$	2.30553	−	0.954983i	0.138526	−	0.0573793i	−0.312343	−	0.949969i	$-0.601114\pi$
$277$	2.30553	−	0.954983i	0.138526	−	0.0573793i	0.450869	+	0.892590i	$0.351114\pi$
$278$	−20.5020	+	0.168035i	−1.22963	+	0.0100781i
$279$	−2.87558	+	2.87558i	−0.172157	+	0.172157i
$280$	2.31286	−	10.0402i	0.138220	−	0.600014i
$281$	3.64042	+	3.64042i	0.217169	+	0.217169i	0.807304	−	0.590135i	$-0.200926\pi$
$281$	3.64042	+	3.64042i	0.217169	+	0.217169i	−0.590135	+	0.807304i	$0.700926\pi$
$282$	−19.5933	−	19.2747i	−1.16676	−	1.14779i
$283$	−9.64194	−	23.2777i	−0.573154	−	1.38372i	−0.898856	−	0.438243i	$-0.855601\pi$
$283$	−9.64194	−	23.2777i	−0.573154	−	1.38372i	0.325703	−	0.945472i	$-0.394399\pi$
$284$	0.288359	+	17.5902i	0.0171109	+	1.04379i
$285$	1.64157	+	11.5072i	0.0972383	+	0.681625i
$286$	10.3878	+	4.20335i	0.614242	+	0.248549i
$287$	−8.64963	−	8.64963i	−0.510571	−	0.510571i
$288$	1.40433	−	3.82673i	0.0827509	−	0.225492i
$289$			11.7797i			0.692926i
$290$	−0.137476	+	0.186389i	−0.00807286	+	0.0109451i
$291$	−8.72128	−	21.0550i	−0.511250	−	1.23427i
$292$	0.0724944	−	0.0749109i	0.00424242	−	0.00438383i
$293$	11.5685	−	4.79184i	0.675840	−	0.279942i	−0.0182467	−	0.999834i	$-0.505808\pi$
$293$	11.5685	−	4.79184i	0.675840	−	0.279942i	0.694087	+	0.719891i	$0.255808\pi$
$294$	0.0760533	+	9.27931i	0.00443552	+	0.541181i
$295$	5.51115	+	1.41309i	0.320872	+	0.0822734i
$296$	11.6529	−	0.286572i	0.677309	−	0.0166567i
$297$			9.62165i			0.558305i
$298$	0.0760739	+	9.28182i	0.00440684	+	0.537682i
$299$	28.0509	+	11.6191i	1.62223	+	0.671948i
$300$	−9.63924	−	11.6201i	−0.556522	−	0.670885i
$301$	−1.25913	−	3.03981i	−0.0725752	−	0.175212i
$302$	−2.96973	−	1.20168i	−0.170889	−	0.0691492i
$303$	−15.9715	−	15.9715i	−0.917537	−	0.917537i
$304$	−12.5444	+	5.68466i	−0.719468	+	0.326037i
$305$	9.09807	+	15.3724i	0.520954	+	0.880224i
$306$	−2.13344	−	5.03351i	−0.121961	−	0.287746i
$307$	6.02470	−	14.5449i	0.343848	−	0.830122i	−0.653472	−	0.756951i	$-0.726688\pi$
$307$	6.02470	−	14.5449i	0.343848	−	0.830122i	0.997319	−	0.0731709i	$-0.0233119\pi$
$308$	−5.12027	+	2.21990i	−0.291755	+	0.126490i
$309$	−8.79721	+	21.2383i	−0.500456	+	1.20821i
$310$	−15.2832	+	9.21521i	−0.868028	+	0.523389i
$311$	−11.2299	−	11.2299i	−0.636791	−	0.636791i	0.312972	−	0.949762i	$-0.398675\pi$
$311$	−11.2299	−	11.2299i	−0.636791	−	0.636791i	−0.949762	+	0.312972i	$0.898675\pi$
$312$	−18.0593	+	8.00610i	−1.02241	+	0.453256i
$313$			2.97140i			0.167953i	0.996468	+	0.0839767i	$0.0267621\pi$
$313$			2.97140i			0.167953i	−0.996468	+	0.0839767i	$0.973238\pi$
$314$	0.0432600	+	5.27818i	0.00244130	+	0.297865i
$315$	2.09961	+	1.57535i	0.118299	+	0.0887609i
$316$	−0.0404095	−	0.0391060i	−0.00227321	−	0.00219989i
$317$	−5.69520	+	13.7494i	−0.319874	+	0.772244i	0.679386	+	0.733781i	$0.262246\pi$
$317$	−5.69520	+	13.7494i	−0.319874	+	0.772244i	−0.999260	+	0.0384633i	$0.987754\pi$
$318$	−6.82047	+	2.89084i	−0.382473	+	0.162110i
$319$	0.125451			0.00702389
$320$	10.0196	−	14.8192i	0.560113	−	0.828416i
$321$	−5.29257			−0.295402
$322$	−13.9220	+	5.90081i	−0.775841	+	0.328839i
$323$	−7.06854	+	17.0650i	−0.393304	+	0.949519i
$324$	−9.08166	−	8.78871i	−0.504537	−	0.488262i
$325$	2.52304	−	22.9921i	0.139953	−	1.27537i
$326$	0.174884	+	21.3377i	0.00968591	+	1.18178i
$327$		−	15.0166i		−	0.830420i
$328$	−8.60747	−	19.4158i	−0.475268	−	1.07206i
$329$	14.8282	+	14.8282i	0.817506	+	0.817506i
$330$	−1.96615	+	7.93795i	−0.108233	+	0.436970i
$331$	−3.30562	+	7.98047i	−0.181693	+	0.438647i	−0.988316	−	0.152421i	$-0.951293\pi$
$331$	−3.30562	+	7.98047i	−0.181693	+	0.438647i	0.806622	+	0.591067i	$0.201293\pi$
$332$	−10.8015	+	4.68301i	−0.592811	+	0.257014i
$333$	−1.13644	+	2.74361i	−0.0622766	+	0.150349i
$334$	−5.30865	−	12.5249i	−0.290476	−	0.685330i
$335$	−5.34525	+	20.8468i	−0.292042	+	1.13898i
$336$	3.46492	−	9.20771i	0.189027	−	0.502322i
$337$	6.39165	+	6.39165i	0.348176	+	0.348176i	0.859430	−	0.511254i	$-0.170819\pi$
$337$	6.39165	+	6.39165i	0.348176	+	0.348176i	−0.511254	+	0.859430i	$0.670819\pi$
$338$	−11.0122	−	4.45602i	−0.598984	−	0.242375i
$339$	−1.83792	−	4.43712i	−0.0998219	−	0.240991i
$340$	−3.77710	−	23.6924i	−0.204842	−	1.28490i
$341$	8.93088	+	3.69929i	0.483634	+	0.200328i
$342$	−0.0287566	−	3.50861i	−0.00155498	−	0.189724i
$343$		−	18.4836i		−	0.998021i
$344$	−0.140446	−	5.71093i	−0.00757232	−	0.307913i
$345$	−5.50327	+	21.4631i	−0.296286	+	1.15554i
$346$	−0.174658	−	21.3101i	−0.00938966	−	1.14564i
$347$	3.70776	−	1.53581i	0.199043	−	0.0824464i	−0.280935	−	0.959727i	$-0.590645\pi$
$347$	3.70776	−	1.53581i	0.199043	−	0.0824464i	0.479978	+	0.877280i	$0.340645\pi$
$348$	−0.153793	+	0.158919i	−0.00824416	+	0.00851896i
$349$	−5.15522	−	12.4458i	−0.275953	−	0.666209i	0.723763	−	0.690049i	$-0.242411\pi$
$349$	−5.15522	−	12.4458i	−0.275953	−	0.666209i	−0.999716	+	0.0238396i	$0.992411\pi$
$350$	7.28163	+	8.92584i	0.389219	+	0.477106i
$351$		−	25.9855i		−	1.38700i
$352$	−9.68137	+	0.396956i	−0.516019	+	0.0211578i
$353$	10.4376	+	10.4376i	0.555535	+	0.555535i	0.928033	−	0.372498i	$-0.121499\pi$
$353$	10.4376	+	10.4376i	0.555535	+	0.555535i	−0.372498	+	0.928033i	$0.621499\pi$
$354$	5.03597	+	2.03777i	0.267659	+	0.108306i
$355$	−15.7330	−	11.8046i	−0.835020	−	0.626521i
$356$	−0.500349	−	30.5219i	−0.0265184	−	1.61766i
$357$	−5.04932	−	12.1901i	−0.267238	−	0.645170i
$358$	9.34917	+	9.19716i	0.494119	+	0.486085i
$359$	3.03708	+	3.03708i	0.160291	+	0.160291i	0.782696	−	0.622405i	$-0.213844\pi$
$359$	3.03708	+	3.03708i	0.160291	+	0.160291i	−0.622405	+	0.782696i	$0.713844\pi$
$360$	2.41692	+	3.86374i	0.127383	+	0.203637i
$361$	5.05245	−	5.05245i	0.265918	−	0.265918i
$362$	−7.08969	+	0.0581071i	−0.372626	+	0.00305404i
$363$	−11.2509	+	4.66028i	−0.590519	+	0.244601i
$364$	13.8285	−	5.99535i	0.724810	−	0.314242i
$365$	0.0164600	+	0.115382i	0.000861554	+	0.00603935i
$366$	6.65626	+	15.7043i	0.347928	+	0.820879i
$367$	−7.17018	+	7.17018i	−0.374280	+	0.374280i	−0.869034	−	0.494753i	$-0.835258\pi$
$367$	−7.17018	+	7.17018i	−0.374280	+	0.374280i	0.494753	+	0.869034i	$0.335258\pi$
$368$	−26.2392	+	0.860514i	−1.36781	+	0.0448574i
$369$	5.41081			0.281675
$370$	−7.73570	+	10.4880i	−0.402160	+	0.545246i
$371$	5.22177	−	2.16293i	0.271101	−	0.112294i
$372$	−15.6348	+	6.77846i	−0.810625	+	0.351447i
$373$	−12.7084	−	30.6808i	−0.658017	−	1.58859i	−0.800862	−	0.598849i	$-0.795625\pi$
$373$	−12.7084	−	30.6808i	−0.658017	−	1.58859i	0.142845	−	0.989745i	$-0.454375\pi$
$374$	−9.11342	+	9.26404i	−0.471244	+	0.479032i
$375$	16.8709	−	0.546854i	0.871209	−	0.0282394i
$376$	14.7559	+	33.2850i	0.760980	+	1.71654i
$377$	−0.338809			−0.0174495
$378$	9.22554	+	9.07555i	0.474511	+	0.466796i
$379$	4.86962	−	11.7563i	0.250136	−	0.603881i	−0.748079	−	0.663610i	$-0.769024\pi$
$379$	4.86962	−	11.7563i	0.250136	−	0.603881i	0.998215	+	0.0597288i	$0.0190236\pi$
$380$	3.57940	−	14.9761i	0.183620	−	0.768257i
$381$	−0.286418	+	0.118638i	−0.0146736	+	0.00607802i
$382$	10.1544	+	23.9577i	0.519547	+	1.22578i
$383$	−10.8475	+	10.8475i	−0.554280	+	0.554280i	−0.927673	−	0.373393i	$-0.878194\pi$
$383$	−10.8475	+	10.8475i	−0.554280	+	0.554280i	0.373393	+	0.927673i	$0.378194\pi$
$384$	11.3657	−	12.7509i	0.580006	−	0.650689i
$385$	1.54971	−	6.04399i	0.0789807	−	0.308030i
$386$	24.3800	+	9.86521i	1.24091	+	0.502126i
$387$	1.34461	+	0.556956i	0.0683504	+	0.0283117i
$388$	0.494837	+	30.1857i	0.0251216	+	1.53245i
$389$	−8.53599	−	3.53572i	−0.432792	−	0.179268i	0.155642	−	0.987813i	$-0.450255\pi$
$389$	−8.53599	−	3.53572i	−0.432792	−	0.179268i	−0.588434	+	0.808545i	$0.700255\pi$
$390$	5.31003	−	21.4383i	0.268884	−	1.08557i
$391$	−24.8973	+	24.8973i	−1.25911	+	1.25911i
$392$	4.42360	−	11.4692i	0.223426	−	0.579284i
$393$	−1.68632			−0.0850637
$394$	−23.6972	−	23.3119i	−1.19385	−	1.17444i
$395$	0.0622409	−	0.00887908i	0.00313168	−	0.000446755i
$396$	0.907171	−	2.29584i	0.0455870	−	0.115370i
$397$	2.67158	+	1.10660i	0.134083	+	0.0555388i	0.448716	−	0.893674i	$-0.351882\pi$
$397$	2.67158	+	1.10660i	0.134083	+	0.0555388i	−0.314633	+	0.949213i	$0.601882\pi$
$398$	−7.55161	−	3.05571i	−0.378528	−	0.153169i
$399$		−	8.46830i		−	0.423945i
$400$	6.21885	+	19.0086i	0.310942	+	0.950429i
$401$		−	6.73952i		−	0.336556i	−0.985740	−	0.168278i	$-0.946179\pi$
$401$		−	6.73952i		−	0.336556i	0.985740	−	0.168278i	$-0.0538206\pi$
$402$	−7.70821	+	19.0494i	−0.384451	+	0.950096i
$403$	−24.1199	−	9.99080i	−1.20150	−	0.497677i
$404$	11.9019	+	27.4522i	0.592142	+	1.36580i
$405$	13.9881	−	1.99549i	0.695072	−	0.0991566i
$406$	0.118330	−	0.120286i	0.00587264	−	0.00596970i
$407$	7.05904			0.349904
$408$	−0.563209	−	22.9017i	−0.0278830	−	1.13380i
$409$	−13.4165	+	13.4165i	−0.663404	+	0.663404i	−0.956181	−	0.292777i	$-0.905421\pi$
$409$	−13.4165	+	13.4165i	−0.663404	+	0.663404i	0.292777	+	0.956181i	$0.405421\pi$
$410$	23.0486	+	5.70889i	1.13829	+	0.281942i
$411$	31.2369	+	12.9387i	1.54080	+	0.638221i
$412$	21.1774	−	21.8833i	1.04333	−	1.07811i
$413$	−3.82946	−	1.58622i	−0.188436	−	0.0780526i
$414$	2.50884	−	6.20011i	0.123303	−	0.304719i
$415$	3.26922	−	12.7502i	0.160480	−	0.625882i
$416$	26.1468	−	1.07207i	1.28195	−	0.0525627i
$417$	15.4772	−	15.4772i	0.757922	−	0.757922i
$418$	−7.67913	+	3.25479i	−0.375598	+	0.159197i
$419$	−17.5932	+	7.28736i	−0.859486	+	0.356011i	−0.768507	−	0.639842i	$-0.779000\pi$
$419$	−17.5932	+	7.28736i	−0.859486	+	0.356011i	−0.0909796	+	0.995853i	$0.529000\pi$
$420$	5.75661	+	9.37261i	0.280894	+	0.457337i
$421$	−3.71850	+	8.97726i	−0.181229	+	0.437525i	−0.988220	−	0.153038i	$-0.951094\pi$
$421$	−3.71850	+	8.97726i	−0.181229	+	0.437525i	0.806992	+	0.590563i	$0.201094\pi$
$422$	−22.2780	+	22.6462i	−1.08448	+	1.10240i
$423$	−9.27585			−0.451007
$424$	9.81019	−	0.241256i	0.476425	−	0.0117164i
$425$	23.5140	+	12.9068i	1.14060	+	0.626071i
$426$	−13.3888	−	13.1711i	−0.648690	−	0.638143i
$427$	−4.98021	−	12.0233i	−0.241009	−	0.581848i
$428$	6.52050	+	2.57649i	0.315180	+	0.124540i
$429$	−11.0525	+	4.57810i	−0.533621	+	0.221033i
$430$	5.14005	+	3.79117i	0.247875	+	0.182827i
$431$	13.0730			0.629705			0.314852	−	0.949141i	$-0.398045\pi$
$431$	13.0730			0.629705			0.314852	+	0.949141i	$0.398045\pi$
$432$	9.27429	+	20.4656i	0.446210	+	0.984653i
$433$	−9.90796	+	9.90796i	−0.476146	+	0.476146i	−0.903897	−	0.427751i	$-0.859306\pi$
$433$	−9.90796	+	9.90796i	−0.476146	+	0.476146i	0.427751	+	0.903897i	$0.359306\pi$
$434$	11.9710	−	5.07388i	0.574625	−	0.243554i
$435$	−0.0349189	−	0.244775i	−0.00167423	−	0.0117361i
$436$	−7.31029	+	18.5006i	−0.350100	+	0.886020i
$437$	−20.8778	+	8.64788i	−0.998722	+	0.413684i
$438$	0.000912096		0.111285i	4.35816e−5		0.00531742i
$439$	−13.9180	+	13.9180i	−0.664270	+	0.664270i	−0.956384	−	0.292113i	$-0.905642\pi$
$439$	−13.9180	+	13.9180i	−0.664270	+	0.664270i	0.292113	+	0.956384i	$0.405642\pi$
$440$	6.28662	−	8.82250i	0.299703	−	0.420596i
$441$	2.21451	+	2.21451i	0.105453	+	0.105453i
$442$	24.6129	−	25.0197i	1.17072	−	1.19007i
$443$	−1.52373	−	3.67860i	−0.0723944	−	0.174775i	0.883540	−	0.468355i	$-0.155153\pi$
$443$	−1.52373	−	3.67860i	−0.0723944	−	0.174775i	−0.955935	+	0.293580i	$0.905153\pi$
$444$	−8.65384	+	8.94229i	−0.410693	+	0.424382i
$445$	27.2993	+	20.4828i	1.29411	+	0.970979i
$446$	9.03432	−	22.3266i	0.427787	−	1.05719i
$447$	−7.00695	−	7.00695i	−0.331417	−	0.331417i
$448$	−8.75126	+	9.65723i	−0.413458	+	0.456261i
$449$		−	38.3156i		−	1.80823i	−0.427292	−	0.904113i	$-0.640533\pi$
$449$		−	38.3156i		−	1.80823i	0.427292	−	0.904113i	$-0.359467\pi$
$450$	−5.06932	−	0.514272i	−0.238970	−	0.0242430i
$451$	−4.92198	−	11.8827i	−0.231767	−	0.559535i
$452$	0.104282	+	6.36131i	0.00490499	+	0.299211i
$453$	3.15978	−	1.30882i	0.148459	−	0.0614938i
$454$	20.9845	−	0.171989i	0.984850	−	0.00807184i
$455$	−4.18536	+	16.3232i	−0.196213	+	0.765244i
$456$	5.29089	−	13.7179i	0.247769	−	0.642400i
$457$			15.2274i			0.712308i	0.934427	+	0.356154i	$0.115912\pi$
$457$			15.2274i			0.712308i	−0.934427	+	0.356154i	$0.884088\pi$
$458$	32.3043	−	0.264766i	1.50948	−	0.0123717i
$459$	27.8408	+	11.5320i	1.29950	+	0.538270i
$460$	17.2286	−	23.7638i	0.803290	−	1.10799i
$461$	1.54964	+	3.74117i	0.0721741	+	0.174244i	0.955850	−	0.293856i	$-0.0949387\pi$
$461$	1.54964	+	3.74117i	0.0721741	+	0.174244i	−0.883675	+	0.468100i	$0.844939\pi$
$462$	2.23479	−	5.52286i	0.103972	−	0.256947i
$463$	1.77902	+	1.77902i	0.0826781	+	0.0826781i	0.747236	−	0.664558i	$-0.231380\pi$
$463$	1.77902	+	1.77902i	0.0826781	+	0.0826781i	−0.664558	+	0.747236i	$0.731380\pi$
$464$	0.266838	−	0.120922i	0.0123877	−	0.00561365i
$465$	4.73206	−	18.4553i	0.219444	−	0.855846i
$466$	−1.87273	+	0.793753i	−0.0867524	+	0.0367699i
$467$	−5.50705	+	13.2952i	−0.254836	+	0.615228i	−0.998582	−	0.0532341i	$-0.983047\pi$
$467$	−5.50705	+	13.2952i	−0.254836	+	0.615228i	0.743746	+	0.668462i	$0.233047\pi$
$468$	−2.45003	+	6.20044i	−0.113252	+	0.286615i
$469$	6.00012	−	14.4856i	0.277060	−	0.668882i
$470$	−39.5127	−	9.78686i	−1.82258	−	0.451434i
$471$	−3.98456	−	3.98456i	−0.183599	−	0.183599i
$472$	−5.21235	−	4.96214i	−0.239918	−	0.228401i
$473$		−	3.45955i		−	0.159070i
$474$	0.0600312		0.000492016i	0.00275732		2.25990e-5i
$475$	10.7726	+	13.4283i	0.494282	+	0.616133i
$476$	0.286494	+	17.4765i	0.0131314	+	0.801033i
$477$	−0.956735	+	2.30976i	−0.0438059	+	0.105757i
$478$	−10.6051	−	25.0210i	−0.485066	−	1.14443i
$479$	−37.1038			−1.69532			−0.847658	−	0.530544i	$-0.821988\pi$
$479$	−37.1038			−1.69532			−0.847658	+	0.530544i	$0.821988\pi$
$480$	3.46931	+	18.7795i	0.158352	+	0.857163i
$481$	−19.0646			−0.869271
$482$	−0.502365	−	1.18525i	−0.0228821	−	0.0539865i
$483$	6.17750	−	14.9138i	0.281086	−	0.678602i
$484$	16.1299	−	0.264420i	0.733178	−	0.0120191i
$485$	−26.9985	−	20.2572i	−1.22594	−	0.919832i
$486$	−10.3397	+	0.0847441i	−0.469018	+	0.00384407i
$487$			23.7418i			1.07584i	0.842995	+	0.537922i	$0.180791\pi$
$487$			23.7418i			1.07584i	−0.842995	+	0.537922i	$0.819209\pi$
$488$	−0.555501	−	22.5883i	−0.0251463	−	1.02252i
$489$	−16.1080	−	16.1080i	−0.728431	−	0.728431i
$490$	7.09671	+	11.7697i	0.320597	+	0.531702i
$491$	−11.3630	+	27.4326i	−0.512803	+	1.23802i	0.429443	+	0.903094i	$0.358710\pi$
$491$	−11.3630	+	27.4326i	−0.512803	+	1.23802i	−0.942246	+	0.334922i	$0.891290\pi$
$492$	21.0868	+	8.33219i	0.950667	+	0.375644i
$493$	0.150359	−	0.362999i	0.00677183	−	0.0163486i
$494$	20.7393	−	8.79031i	0.933104	−	0.395495i
$495$	1.40571	+	2.37514i	0.0631818	+	0.106754i
$496$	22.5621	−	0.739924i	1.01307	−	0.0332236i
$497$	10.1327	+	10.1327i	0.454512	+	0.454512i
$498$	4.71443	−	11.6508i	0.211259	−	0.522086i
$499$	−2.83491	−	6.84409i	−0.126908	−	0.306383i	0.847636	−	0.530578i	$-0.178025\pi$
$499$	−2.83491	−	6.84409i	−0.126908	−	0.306383i	−0.974544	+	0.224194i	$0.928025\pi$
$500$	−21.0514	−	7.53925i	−0.941445	−	0.337166i
$501$	13.4172	+	5.55757i	0.599435	+	0.248294i
$502$	−31.4066	+	0.257409i	−1.40175	+	0.0114887i
$503$		−	5.30346i		−	0.236470i	−0.992986	−	0.118235i	$-0.962276\pi$
$503$		−	5.30346i		−	0.236470i	0.992986	−	0.118235i	$-0.0377236\pi$
$504$	−1.34564	−	3.03535i	−0.0599395	−	0.135205i
$505$	−32.4047	−	8.30874i	−1.44199	−	0.369734i
$506$	−15.8983	+	0.130302i	−0.706765	+	0.00579265i
$507$	11.7169	−	4.85330i	0.520366	−	0.215543i
$508$	0.410625	−	0.00673143i	0.0182186	−	0.000298659i
$509$	−7.86417	−	18.9858i	−0.348573	−	0.841530i	−0.996789	−	0.0800732i	$-0.974485\pi$
$509$	−7.86417	−	18.9858i	−0.348573	−	0.841530i	0.648216	−	0.761457i	$-0.275515\pi$
$510$	20.6124	+	15.2032i	0.912732	+	0.673209i
$511$		−	0.0849112i		−	0.00375625i
$512$	−20.2100	+	10.1762i	−0.893165	+	0.449729i
$513$	13.6759	+	13.6759i	0.603804	+	0.603804i
$514$	13.2410	−	32.7226i	0.584036	−	1.44333i
$515$	4.80835	+	33.7058i	0.211881	+	1.48525i
$516$	4.38251	+	4.24114i	0.192929	+	0.186706i
$517$	8.43785	+	20.3708i	0.371096	+	0.895905i
$518$	6.65839	−	6.76843i	0.292553	−	0.297388i
$519$	16.0872	+	16.0872i	0.706151	+	0.706151i
$520$	−16.9785	+	23.8272i	−0.744556	+	1.04489i
$521$	−0.493748	+	0.493748i	−0.0216315	+	0.0216315i	−0.717840	−	0.696208i	$-0.754869\pi$
$521$	−0.493748	+	0.493748i	−0.0216315	+	0.0216315i	0.696208	+	0.717840i	$0.254869\pi$
$522$	0.000611698		0.0746337i	2.67733e−5		0.00326663i
$523$	16.3810	−	6.78525i	0.716293	−	0.296698i	0.00538717	−	0.999985i	$-0.498285\pi$
$523$	16.3810	−	6.78525i	0.716293	−	0.296698i	0.710906	+	0.703287i	$0.248285\pi$
$524$	2.07757	+	0.820925i	0.0907590	+	0.0358623i
$525$	−12.2242	−	1.34143i	−0.533508	−	0.0585446i
$526$	25.1889	−	10.6763i	1.09829	−	0.465508i
$527$	21.4082	−	21.4082i	0.932557	−	0.932557i
$528$	7.07079	−	7.55029i	0.307717	−	0.328584i
$529$	−20.0771			−0.872919
$530$	−6.51245	+	8.82954i	−0.282883	+	0.383531i
$531$	1.69390	−	0.701636i	0.0735090	−	0.0304484i
$532$	−4.12248	+	10.4330i	−0.178732	+	0.452330i
$533$	13.2930	+	32.0921i	0.575782	+	1.39006i
$534$	23.2317	+	22.8540i	1.00534	+	0.988990i
$535$	−6.74573	+	3.99241i	−0.291643	+	0.172607i
$536$	18.7701	−	19.7166i	0.810745	−	0.851627i
$537$	−14.0008			−0.604180
$538$	−5.30602	+	5.39372i	−0.228759	+	0.232540i
$539$	2.84886	−	6.87775i	0.122709	−	0.296246i
$540$	−24.4329	−	5.83966i	−1.05142	−	0.251299i
$541$	−5.54416	+	2.29647i	−0.238362	+	0.0987329i	−0.498667	−	0.866794i	$-0.666177\pi$
$541$	−5.54416	+	2.29647i	−0.238362	+	0.0987329i	0.260305	+	0.965526i	$0.416177\pi$
$542$	36.2502	−	15.3646i	1.55708	−	0.659967i
$543$	5.35208	−	5.35208i	0.229680	−	0.229680i
$544$	−10.4550	+	28.4894i	−0.448254	+	1.22147i
$545$	−11.3277	−	19.1397i	−0.485224	−	0.819853i
$546$	−6.03557	+	14.9158i	−0.258299	+	0.638336i
$547$	−29.1895	−	12.0907i	−1.24805	−	0.516960i	−0.341830	−	0.939762i	$-0.611047\pi$
$547$	−29.1895	−	12.0907i	−1.24805	−	0.516960i	−0.906222	+	0.422801i	$0.861047\pi$
$548$	−32.1855	−	31.1472i	−1.37489	−	1.33054i
$549$	5.31830	+	2.20291i	0.226980	+	0.0940181i
$550$	3.48195	+	11.6006i	0.148471	+	0.494651i
$551$	0.178311	−	0.178311i	0.00759630	−	0.00759630i
$552$	19.3250	−	20.2995i	0.822527	−	0.864002i
$553$	−0.0458041			−0.00194779
$554$	2.47495	−	2.51586i	0.105151	−	0.106889i
$555$	−1.96487	−	13.7734i	−0.0834039	−	0.584648i
$556$	−26.6026	+	11.5336i	−1.12820	+	0.489133i
$557$	16.8053	+	6.96098i	0.712064	+	0.294946i	0.709158	−	0.705049i	$-0.249075\pi$
$557$	16.8053	+	6.96098i	0.712064	+	0.294946i	0.00290537	+	0.999996i	$0.499075\pi$
$558$	−2.15725	+	5.33124i	−0.0913238	+	0.225689i
$559$			9.34332i			0.395181i
$560$	−2.52949	−	14.3496i	−0.106890	−	0.606380i
$561$		−	13.8733i		−	0.585733i
$562$	6.74923	+	2.73104i	0.284699	+	0.115202i
$563$	40.2435	+	16.6694i	1.69606	+	0.702532i	0.999882	−	0.0153364i	$-0.00488193\pi$
$563$	40.2435	+	16.6694i	1.69606	+	0.702532i	0.696179	+	0.717868i	$0.254882\pi$
$564$	−36.1495	−	14.2840i	−1.52217	−	0.601466i
$565$	−5.68965	−	4.26898i	−0.239365	−	0.179598i
$566$	−25.4012	−	24.9883i	−1.06769	−	1.05033i
$567$	−10.2940			−0.432309
$568$	10.0833	+	22.7448i	0.423085	+	0.954351i
$569$	5.68501	−	5.68501i	0.238328	−	0.238328i	−0.577830	−	0.816157i	$-0.696100\pi$
$569$	5.68501	−	5.68501i	0.238328	−	0.238328i	0.816157	+	0.577830i	$0.196100\pi$
$570$	8.48810	+	14.0773i	0.355527	+	0.589634i
$571$	33.3349	+	13.8078i	1.39502	+	0.577837i	0.948455	−	0.316912i	$-0.102646\pi$
$571$	33.3349	+	13.8078i	1.39502	+	0.577837i	0.446568	+	0.894750i	$0.352646\pi$
$572$	15.8455	−	0.259757i	0.662534	−	0.0108610i
$573$	−25.6645	−	10.6306i	−1.07215	−	0.444099i
$574$	−16.0361	−	6.48893i	−0.669336	−	0.270843i
$575$	9.17627	+	31.5075i	0.382677	+	1.31396i
$576$	−0.283365	−	5.75775i	−0.0118069	−	0.239906i
$577$	10.9487	−	10.9487i	0.455799	−	0.455799i	−0.441475	−	0.897274i	$-0.645544\pi$
$577$	10.9487	−	10.9487i	0.455799	−	0.455799i	0.897274	+	0.441475i	$0.145544\pi$
$578$	6.50108	+	15.3382i	0.270409	+	0.637985i
$579$	−25.9401	+	10.7448i	−1.07803	+	0.446537i
$580$	−0.0761396	+	0.318565i	−0.00316153	+	0.0132277i
$581$	−3.66974	+	8.85955i	−0.152247	+	0.367556i
$582$	−22.9758	−	22.6023i	−0.952378	−	0.936894i
$583$	5.94279			0.246125
$584$	0.0530516	−	0.137549i	0.00219529	−	0.00569181i
$585$	−3.79644	−	6.41461i	−0.156963	−	0.265211i
$586$	12.4186	−	12.6239i	0.513009	−	0.521487i
$587$	−10.5329	−	25.4287i	−0.434739	−	1.04955i	−0.977740	−	0.209821i	$-0.932712\pi$
$587$	−10.5329	−	25.4287i	−0.434739	−	1.04955i	0.543001	−	0.839732i	$-0.317288\pi$
$588$	5.22015	+	12.0405i	0.215275	+	0.496541i
$589$	17.9520	−	7.43598i	0.739701	−	0.306394i
$590$	7.95585	−	1.20157i	0.327537	−	0.0494677i
$591$	35.4877			1.45977
$592$	15.0149	−	6.80420i	0.617107	−	0.279651i
$593$	−4.01024	+	4.01024i	−0.164681	+	0.164681i	−0.784637	−	0.619956i	$-0.787151\pi$
$593$	−4.01024	+	4.01024i	−0.164681	+	0.164681i	0.619956	+	0.784637i	$0.287151\pi$
$594$	5.31006	+	12.5282i	0.217874	+	0.514038i
$595$	−15.6312	−	11.7282i	−0.640818	−	0.480810i
$596$	5.22156	+	12.0437i	0.213884	+	0.493330i
$597$	8.03486	−	3.32815i	0.328845	−	0.136212i
$598$	42.9370	−	0.351912i	1.75583	−	0.0143908i
$599$	2.63772	−	2.63772i	0.107774	−	0.107774i	−0.651163	−	0.758938i	$-0.725719\pi$
$599$	2.63772	−	2.63772i	0.107774	−	0.107774i	0.758938	+	0.651163i	$0.225719\pi$
$600$	−18.9641	−	9.81054i	−0.774204	−	0.400513i
$601$	−21.8230	−	21.8230i	−0.890180	−	0.890180i	0.104360	−	0.994540i	$-0.466721\pi$
$601$	−21.8230	−	21.8230i	−0.890180	−	0.890180i	−0.994540	+	0.104360i	$0.966721\pi$
$602$	−3.31713	−	3.26319i	−0.135196	−	0.132998i
$603$	2.65405	+	6.40745i	0.108081	+	0.260932i
$604$	−4.53003	+	0.0742614i	−0.184324	+	0.00302165i
$605$	−10.8246	+	14.4269i	−0.440081	+	0.586535i
$606$	−29.6106	−	11.9818i	−1.20285	−	0.486726i
$607$	−5.66846	−	5.66846i	−0.230076	−	0.230076i	0.582648	−	0.812724i	$-0.302016\pi$
$607$	−5.66846	−	5.66846i	−0.230076	−	0.230076i	−0.812724	+	0.582648i	$0.802016\pi$
$608$	−13.1965	+	14.3250i	−0.535189	+	0.580954i
$609$			0.180134i			0.00729941i
$610$	20.3303	+	14.9951i	0.823149	+	0.607134i
$611$	−22.7884	−	55.0160i	−0.921919	−	2.22571i
$612$	−5.55584	−	5.37663i	−0.224582	−	0.217337i
$613$	14.9201	−	6.18013i	0.602619	−	0.249613i	−0.0604501	−	0.998171i	$-0.519254\pi$
$613$	14.9201	−	6.18013i	0.602619	−	0.249613i	0.663069	+	0.748558i	$0.269254\pi$
$614$	−0.182473	−	22.2636i	−0.00736401	−	0.898487i
$615$	−21.8152	+	12.9111i	−0.879673	+	0.520628i
$616$	−5.44189	+	5.71630i	−0.219260	+	0.230316i
$617$			0.245646i			0.00988934i	0.999988	+	0.00494467i	$0.00157394\pi$
$617$			0.245646i			0.00988934i	−0.999988	+	0.00494467i	$0.998426\pi$
$618$	0.266445	+	32.5092i	0.0107180	+	1.30771i
$619$	28.5608	+	11.8303i	1.14796	+	0.475499i	0.873848	−	0.486200i	$-0.161617\pi$
$619$	28.5608	+	11.8303i	1.14796	+	0.475499i	0.274109	+	0.961699i	$0.411617\pi$
$620$	−14.8143	+	20.4336i	−0.594955	+	0.820632i
$621$	14.1087	+	34.0613i	0.566162	+	1.36683i
$622$	−20.8199	−	8.42466i	−0.834804	−	0.337798i
$623$	−17.5818	−	17.5818i	−0.704400	−	0.704400i
$624$	−19.0963	+	20.3913i	−0.764464	+	0.816306i
$625$	21.0906	−	13.4234i	0.843622	−	0.536937i
$626$	1.63987	+	3.86901i	0.0655426	+	0.154637i
$627$	3.40741	−	8.22620i	0.136079	−	0.328523i
$628$	2.96928	+	6.84875i	0.118487	+	0.273295i
$629$	8.46062	−	20.4257i	0.337347	−	0.814428i
$630$	3.60328	+	0.892493i	0.143558	+	0.0355578i
$631$	−2.65113	−	2.65113i	−0.105540	−	0.105540i	0.652365	−	0.757905i	$-0.273777\pi$
$631$	−2.65113	−	2.65113i	−0.105540	−	0.105540i	−0.757905	+	0.652365i	$0.773777\pi$
$632$	−0.0741987	−	0.0286178i	−0.00295146	−	0.00113836i
$633$		−	33.9138i		−	1.34795i
$634$	0.172493	+	21.0460i	0.00685058	+	0.835843i
$635$	−0.275565	+	0.367270i	−0.0109355	+	0.0145747i
$636$	−7.28540	+	7.52824i	−0.288885	+	0.298514i
$637$	−7.69400	+	18.5750i	−0.304847	+	0.735967i
$638$	0.163347	−	0.0692345i	0.00646698	−	0.00274102i
$639$	−6.33853			−0.250748
$640$	4.86789	−	24.8255i	0.192420	−	0.981313i
$641$	−27.3236			−1.07922			−0.539608	−	0.841916i	$-0.681427\pi$
$641$	−27.3236			−1.07922			−0.539608	+	0.841916i	$0.681427\pi$
$642$	−6.89137	+	2.92089i	−0.271980	+	0.115279i
$643$	−16.5094	+	39.8572i	−0.651067	+	1.57182i	0.160164	+	0.987090i	$0.448798\pi$
$643$	−16.5094	+	39.8572i	−0.651067	+	1.57182i	−0.811231	+	0.584725i	$0.801202\pi$
$644$	−14.8710	+	15.3667i	−0.586000	+	0.605532i
$645$	−6.75017	+	0.962957i	−0.265788	+	0.0379164i
$646$	0.214088	+	26.1210i	0.00842318	+	1.02772i
$647$		−	3.21338i		−	0.126331i	−0.998003	−	0.0631655i	$-0.979880\pi$
$647$		−	3.21338i		−	0.126331i	0.998003	−	0.0631655i	$-0.0201196\pi$
$648$	−16.6755	−	6.43159i	−0.655074	−	0.252657i
$649$	−3.08174	−	3.08174i	−0.120969	−	0.120969i
$650$	−9.40382	−	31.3301i	−0.368848	−	1.22887i
$651$	−5.31180	+	12.8238i	−0.208186	+	0.502605i
$652$	12.0037	+	27.6869i	0.470100	+	1.08430i
$653$	1.22388	−	2.95471i	0.0478942	−	0.115627i	−0.898122	−	0.439747i	$-0.855068\pi$
$653$	1.22388	−	2.95471i	0.0478942	−	0.115627i	0.946016	+	0.324120i	$0.105068\pi$
$654$	−8.28746	−	19.5529i	−0.324065	−	0.764578i
$655$	−2.14933	+	1.27206i	−0.0839812	+	0.0497036i
$656$	−21.9230	−	20.5307i	−0.855949	−	0.801590i
$657$	0.0265583	+	0.0265583i	0.00103614	+	0.00103614i
$658$	27.4911	+	11.1241i	1.07171	+	0.433662i
$659$	14.1751	+	34.2218i	0.552185	+	1.33309i	0.915834	+	0.401557i	$0.131531\pi$
$659$	14.1751	+	34.2218i	0.552185	+	1.33309i	−0.363648	+	0.931536i	$0.618469\pi$
$660$	1.82076	+	11.4210i	0.0708730	+	0.444561i
$661$	−35.0402	−	14.5141i	−1.36290	−	0.564533i	−0.423049	−	0.906107i	$-0.639040\pi$
$661$	−35.0402	−	14.5141i	−1.36290	−	0.564533i	−0.939855	+	0.341574i	$0.889040\pi$
$662$	0.100119	+	12.2156i	0.00389123	+	0.474772i
$663$			37.4682i			1.45514i
$664$	−11.4800	+	12.0589i	−0.445511	+	0.467976i
$665$	−6.38799	−	10.7934i	−0.247716	−	0.418550i
$666$	0.0344199	+	4.19960i	0.00133375	+	0.162731i
$667$	0.444105	−	0.183954i	0.0171958	−	0.00712273i
$668$	−13.8246	−	13.3787i	−0.534890	−	0.517636i
$669$	9.83979	+	23.7553i	0.380428	+	0.918435i
$670$	4.54512	+	30.0943i	0.175593	+	1.16264i
$671$		−	13.6835i		−	0.528244i
$672$	−0.569988	−	13.9014i	−0.0219878	−	0.536260i
$673$	6.94891	+	6.94891i	0.267861	+	0.267861i	0.828238	−	0.560377i	$-0.189344\pi$
$673$	6.94891	+	6.94891i	0.267861	+	0.267861i	−0.560377	+	0.828238i	$0.689344\pi$
$674$	11.8499	+	4.79500i	0.456442	+	0.184697i
$675$	21.9078	−	17.5751i	0.843230	−	0.676466i
$676$	−16.7980	+	0.275372i	−0.646077	+	0.0105912i
$677$	2.03140	+	4.90424i	0.0780731	+	0.188485i	0.958097	−	0.286445i	$-0.0924735\pi$
$677$	2.03140	+	4.90424i	0.0780731	+	0.188485i	−0.880024	+	0.474930i	$0.842473\pi$
$678$	−4.84190	−	4.76318i	−0.185952	−	0.182929i
$679$	17.3881	+	17.3881i	0.667295	+	0.667295i
$680$	−17.9936	−	28.7649i	−0.690023	−	1.10308i
$681$	−15.8414	+	15.8414i	−0.607044	+	0.607044i
$682$	13.6703	−	0.112042i	0.523464	−	0.00429032i
$683$	17.3992	−	7.20700i	0.665763	−	0.275768i	−0.0240982	−	0.999710i	$-0.507671\pi$
$683$	17.3992	−	7.20700i	0.665763	−	0.275768i	0.689861	+	0.723941i	$0.257671\pi$
$684$	−1.97380	−	4.55263i	−0.0754700	−	0.174074i
$685$	49.5737	−	7.07202i	1.89411	−	0.270208i
$686$	−10.2009	−	24.0672i	−0.389470	−	0.918890i
$687$	−24.3869	+	24.3869i	−0.930417	+	0.930417i
$688$	−3.33466	−	7.35860i	−0.127133	−	0.280544i
$689$	−16.0499			−0.611452
$690$	4.67949	+	30.9840i	0.178145	+	1.17954i
$691$	39.1646	−	16.2225i	1.48989	−	0.617134i	0.518599	−	0.855017i	$-0.326454\pi$
$691$	39.1646	−	16.2225i	1.48989	−	0.617134i	0.971294	+	0.237883i	$0.0764536\pi$
$692$	−11.9882	−	27.6511i	−0.455722	−	1.05114i
$693$	−0.769472	−	1.85767i	−0.0292298	−	0.0705671i
$694$	3.98023	−	4.04601i	0.151087	−	0.153585i
$695$	8.05161	−	31.4018i	0.305415	−	1.19114i
$696$	−0.112546	+	0.291802i	−0.00426604	+	0.0110607i
$697$	−40.2826			−1.52581
$698$	−13.5812	−	13.3604i	−0.514056	−	0.505698i
$699$	0.830973	−	2.00615i	0.0314303	−	0.0758794i
$700$	14.4073	+	7.60356i	0.544546	+	0.287388i
$701$	−0.646576	+	0.267821i	−0.0244208	+	0.0101154i	−0.394860	−	0.918741i	$-0.629207\pi$
$701$	−0.646576	+	0.267821i	−0.0244208	+	0.0101154i	0.370440	+	0.928857i	$0.379207\pi$
$702$	−14.3410	−	33.8353i	−0.541268	−	1.27703i
$703$	10.0335	−	10.0335i	0.378419	−	0.378419i
$704$	−12.3869	+	5.85988i	−0.466848	+	0.220853i
$705$	37.3982	−	22.1338i	1.40850	−	0.833608i
$706$	19.3509	+	7.83023i	0.728281	+	0.294695i
$707$	22.5166	+	9.32668i	0.846824	+	0.350766i
$708$	7.68187	−	0.125930i	0.288702	−	0.00473273i
$709$	−39.6656	−	16.4300i	−1.48967	−	0.617043i	−0.518427	−	0.855122i	$-0.673482\pi$
$709$	−39.6656	−	16.4300i	−1.48967	−	0.617043i	−0.971246	+	0.238079i	$0.923482\pi$
$710$	−27.0004	−	6.68772i	−1.01331	−	0.250986i
$711$	0.0143265	−	0.0143265i	0.000537284	−	0.000537284i
$712$	−17.4961	−	39.4659i	−0.655695	−	1.47905i
$713$	37.0404			1.38717
$714$	−13.3022	−	13.0859i	−0.497822	−	0.489728i
$715$	−10.6337	+	14.1725i	−0.397678	+	0.530021i
$716$	17.2492	+	6.81580i	0.644632	+	0.254718i
$717$	26.8035	+	11.1024i	1.00100	+	0.414626i
$718$	5.63066	+	2.27841i	0.210134	+	0.0850295i
$719$		−	38.6667i		−	1.44203i	−0.692921	−	0.721013i	$-0.743677\pi$
$719$		−	38.6667i		−	1.44203i	0.692921	−	0.721013i	$-0.256323\pi$
$720$	5.27938	+	3.69705i	0.196751	+	0.137781i
$721$		−	24.8046i		−	0.923772i
$722$	3.79033	−	9.36709i	0.141062	−	0.348607i
$723$	1.26969	+	0.525921i	0.0472201	+	0.0195592i
$724$	−9.19930	+	3.98836i	−0.341889	+	0.148226i
$725$	−0.229151	−	0.285642i	−0.00851045	−	0.0106085i
$726$	−12.0777	+	12.2773i	−0.448244	+	0.455653i
$727$	−20.0126			−0.742227			−0.371113	−	0.928588i	$-0.621024\pi$
$727$	−20.0126			−0.742227			−0.371113	+	0.928588i	$0.621024\pi$
$728$	14.6971	−	15.4382i	0.544711	−	0.572178i
$729$	21.2101	−	21.2101i	0.785560	−	0.785560i
$730$	0.0851098	+	0.141153i	0.00315005	+	0.00522429i
$731$	−10.0104	−	4.14645i	−0.370248	−	0.153362i
$732$	17.3340	+	16.7749i	0.640684	+	0.620017i
$733$	−15.4469	−	6.39832i	−0.570544	−	0.236327i	0.0787113	−	0.996897i	$-0.474919\pi$
$733$	−15.4469	−	6.39832i	−0.570544	−	0.236327i	−0.649256	+	0.760570i	$0.724919\pi$
$734$	−5.37905	+	13.2933i	−0.198544	+	0.490665i
$735$	−14.2126	−	3.64420i	−0.524240	−	0.134418i
$736$	−33.6907	+	15.6015i	−1.24186	+	0.575079i
$737$	11.6572	−	11.6572i	0.429398	−	0.429398i
$738$	7.04532	−	2.98615i	0.259342	−	0.109922i
$739$	18.5989	−	7.70390i	0.684170	−	0.283392i	−0.0133989	−	0.999910i	$-0.504265\pi$
$739$	18.5989	−	7.70390i	0.684170	−	0.283392i	0.697569	+	0.716518i	$0.254265\pi$
$740$	−4.28434	+	17.9255i	−0.157495	+	0.658954i
$741$	−9.20249	+	22.2168i	−0.338062	+	0.816154i
$742$	5.60549	−	5.69814i	0.205784	−	0.209185i
$743$	−5.76884			−0.211638			−0.105819	−	0.994385i	$-0.533746\pi$
$743$	−5.76884			−0.211638			−0.105819	+	0.994385i	$0.533746\pi$
$744$	−16.6168	+	17.4547i	−0.609203	+	0.639922i
$745$	−14.2165	−	3.64518i	−0.520851	−	0.133549i
$746$	−33.4798	−	32.9354i	−1.22578	−	1.20585i
$747$	−1.62325	−	3.91887i	−0.0593916	−	0.143384i
$748$	−6.75374	+	17.0921i	−0.246941	+	0.624950i
$749$	5.27605	−	2.18541i	0.192783	−	0.0798532i
$750$	21.6655	−	10.0229i	0.791113	−	0.365983i
$751$	−15.7136			−0.573399			−0.286699	−	0.958021i	$-0.592558\pi$
$751$	−15.7136			−0.573399			−0.286699	+	0.958021i	$0.592558\pi$
$752$	37.5830	+	35.1962i	1.37051	+	1.28347i
$753$	23.7092	−	23.7092i	0.864012	−	0.864012i
$754$	−0.441157	+	0.186984i	−0.0160660	+	0.00680955i
$755$	3.04004	−	4.05173i	0.110639	−	0.147458i
$756$	17.0211	+	6.72567i	0.619051	+	0.244610i
$757$	10.9605	−	4.53997i	0.398365	−	0.165008i	−0.174502	−	0.984657i	$-0.555831\pi$
$757$	10.9605	−	4.53997i	0.398365	−	0.165008i	0.572866	+	0.819649i	$0.305831\pi$
$758$	−0.147489	−	17.9952i	−0.00535702	−	0.653614i
$759$	12.0018	−	12.0018i	0.435638	−	0.435638i
$760$	−3.60441	−	21.4755i	−0.130746	−	0.779000i
$761$	31.8451	+	31.8451i	1.15439	+	1.15439i	0.985664	+	0.168722i	$0.0539640\pi$
$761$	31.8451	+	31.8451i	1.15439	+	1.15439i	0.168722	+	0.985664i	$0.446036\pi$
$762$	−0.307466	+	0.312547i	−0.0111383	+	0.0113224i
$763$	6.20067	+	14.9698i	0.224479	+	0.541941i
$764$	26.4439	+	25.5909i	0.956706	+	0.925845i
$765$	8.55740	−	1.22077i	0.309394	−	0.0441371i
$766$	−8.13774	+	20.1109i	−0.294029	+	0.726636i
$767$	8.32295	+	8.32295i	0.300524	+	0.300524i
$768$	7.76213	−	22.8753i	0.280092	−	0.825440i
$769$			38.8732i			1.40180i	0.713258	+	0.700902i	$0.247219\pi$
$769$			38.8732i			1.40180i	−0.713258	+	0.700902i	$0.752781\pi$
$770$	−1.31774	−	8.72505i	−0.0474880	−	0.314429i
$771$	14.4215	+	34.8167i	0.519379	+	1.25389i
$772$	37.1892	−	0.609647i	1.33847	−	0.0219417i
$773$	6.94877	−	2.87828i	0.249930	−	0.103524i	−0.254202	−	0.967151i	$-0.581813\pi$
$773$	6.94877	−	2.87828i	0.249930	−	0.103524i	0.504132	+	0.863627i	$0.331813\pi$
$774$	2.05817	−	0.0168688i	0.0739795	−	0.000606336i
$775$	−7.89032	−	27.0921i	−0.283429	−	0.973178i
$776$	17.3034	+	39.0312i	0.621155	+	1.40114i
$777$			10.1361i			0.363629i
$778$	−13.0659	+	0.107088i	−0.468435	+	0.00383929i
$779$	−23.8856	−	9.89373i	−0.855789	−	0.354480i
$780$	−4.91739	−	30.8450i	−0.176071	−	1.10443i
$781$	5.76589	+	13.9201i	0.206320	+	0.498100i
$782$	−18.6779	+	46.1588i	−0.667919	+	1.65064i
$783$	−0.290907	−	0.290907i	−0.0103962	−	0.0103962i
$784$	−0.569822	−	17.3752i	−0.0203508	−	0.620544i
$785$	−8.08430	−	2.07286i	−0.288541	−	0.0739835i
$786$	−2.19573	+	0.930658i	−0.0783192	+	0.0331955i
$787$	−6.71886	+	16.2208i	−0.239501	+	0.578207i	−0.997231	−	0.0743607i	$-0.976308\pi$
$787$	−6.71886	+	16.2208i	−0.239501	+	0.578207i	0.757730	+	0.652568i	$0.226308\pi$
$788$	−43.7213	−	17.2759i	−1.55751	−	0.615429i
$789$	−11.1769	+	26.9834i	−0.397908	+	0.960634i
$790$	0.0761426	−	0.0459112i	0.00270903	−	0.00163345i
$791$	3.66436	+	3.66436i	0.130290	+	0.130290i
$792$	−0.0858282	−	3.49003i	−0.00304977	−	0.124013i
$793$			36.9554i			1.31232i
$794$	4.08933	−	0.0335162i	0.145125	−	0.00118945i
$795$	−1.65416	−	11.5954i	−0.0586670	−	0.411246i
$796$	−11.5192	+	0.188836i	−0.408288	+	0.00669312i
$797$	−7.63850	+	18.4410i	−0.270570	+	0.653213i	−0.999508	−	0.0313665i	$-0.990014\pi$
$797$	−7.63850	+	18.4410i	−0.270570	+	0.653213i	0.728938	+	0.684579i	$0.240014\pi$
$798$	−4.67354	−	11.0264i	−0.165441	−	0.390331i
$799$	69.0572			2.44307
$800$	18.5880	+	21.3187i	0.657186	+	0.753728i
$801$	10.9984			0.388608
$802$	−3.71945	−	8.77542i	−0.131338	−	0.309871i
$803$	0.0341659	−	0.0824838i	0.00120569	−	0.00291079i
$804$	0.476350	+	29.0579i	0.0167996	+	1.02479i
$805$	−3.37648	−	23.6686i	−0.119005	−	0.834208i
$806$	−36.9199	+	0.302596i	−1.30045	+	0.0106585i
$807$		−	8.07735i		−	0.284336i
$808$	30.6478	+	29.1765i	1.07818	+	1.02643i
$809$	−8.13989	−	8.13989i	−0.286183	−	0.286183i	0.549386	−	0.835569i	$-0.314862\pi$
$809$	−8.13989	−	8.13989i	−0.286183	−	0.286183i	−0.835569	+	0.549386i	$0.814862\pi$
$810$	17.1123	−	10.3181i	0.601266	−	0.362541i
$811$	−0.637153	+	1.53822i	−0.0223735	+	0.0540143i	−0.934671	−	0.355513i	$-0.884306\pi$
$811$	−0.637153	+	1.53822i	−0.0223735	+	0.0540143i	0.912298	+	0.409527i	$0.134306\pi$
$812$	0.0876918	−	0.221927i	0.00307738	−	0.00778813i
$813$	−16.0851	+	38.8328i	−0.564128	+	1.36193i
$814$	9.19146	−	3.89579i	0.322161	−	0.136547i
$815$	−32.6817	−	8.37979i	−1.14479	−	0.293531i
$816$	−13.3725	−	29.5091i	−0.468131	−	1.03303i
$817$	−4.91728	−	4.91728i	−0.172034	−	0.172034i
$818$	−10.0650	+	24.8738i	−0.351916	+	0.869692i
$819$	2.07814	+	5.01707i	0.0726161	+	0.175311i
$820$	33.1619	−	5.28675i	1.15806	−	0.184621i
$821$	5.68085	+	2.35308i	0.198263	+	0.0821232i	0.479606	−	0.877484i	$-0.340780\pi$
$821$	5.68085	+	2.35308i	0.198263	+	0.0821232i	−0.281343	+	0.959607i	$0.590780\pi$
$822$	47.8138	−	0.391882i	1.66770	−	0.0136685i
$823$			7.38031i			0.257262i	0.991693	+	0.128631i	$0.0410582\pi$
$823$			7.38031i			0.257262i	−0.991693	+	0.128631i	$0.958942\pi$
$824$	15.4976	−	40.1814i	0.539886	−	1.39978i
$825$	−11.3350	−	6.22175i	−0.394633	−	0.216614i
$826$	−5.86169	+	0.0480425i	−0.203954	+	0.00167161i
$827$	35.3291	−	14.6338i	1.22851	−	0.508867i	0.328407	−	0.944536i	$-0.393488\pi$
$827$	35.3291	−	14.6338i	1.22851	−	0.508867i	0.900107	+	0.435669i	$0.143488\pi$
$828$	−0.155040	−	9.45765i	−0.00538803	−	0.328676i
$829$	−9.04084	−	21.8265i	−0.314001	−	0.758067i	−0.999549	−	0.0300385i	$-0.990437\pi$
$829$	−9.04084	−	21.8265i	−0.314001	−	0.758067i	0.685547	−	0.728028i	$-0.259563\pi$
$830$	−2.77985	−	18.4060i	−0.0964900	−	0.638883i
$831$			3.76762i			0.130697i
$832$	33.4537	−	15.8260i	1.15980	−	0.548667i
$833$	−16.4867	−	16.4867i	−0.571229	−	0.571229i
$834$	11.6110	−	28.6943i	0.402055	−	0.993601i
$835$	21.2934	−	3.03764i	0.736888	−	0.105122i
$836$	−8.20259	+	8.47601i	−0.283693	+	0.293149i
$837$	−12.1315	−	29.2881i	−0.419326	−	1.01234i
$838$	−18.8861	+	19.1982i	−0.652409	+	0.663191i
$839$	26.3091	+	26.3091i	0.908292	+	0.908292i	0.996134	−	0.0878426i	$-0.0279972\pi$
$839$	26.3091	+	26.3091i	0.908292	+	0.908292i	−0.0878426	+	0.996134i	$0.527997\pi$
$840$	12.6682	+	9.02694i	0.437094	+	0.311459i
$841$	20.5023	−	20.5023i	0.706976	−	0.706976i
$842$	0.112624	+	13.7413i	0.00388128	+	0.473558i
$843$	−7.18114	+	2.97452i	−0.247332	+	0.102448i
$844$	−16.5097	+	41.7822i	−0.568288	+	1.43820i
$845$	11.2729	−	15.0244i	0.387800	−	0.516855i
$846$	−12.0779	+	5.11921i	−0.415248	+	0.176002i
$847$	9.29147	−	9.29147i	0.319259	−	0.319259i
$848$	12.6405	−	5.72825i	0.434078	−	0.196709i
$849$	38.0396			1.30552
$850$	37.7403	+	3.82867i	1.29448	+	0.131322i
$851$	24.9895	−	10.3510i	0.856630	−	0.354828i
$852$	−24.7023	−	9.76080i	−0.846287	−	0.334399i
$853$	10.8109	+	26.0999i	0.370159	+	0.893644i	0.993723	+	0.111871i	$0.0356843\pi$
$853$	10.8109	+	26.0999i	0.370159	+	0.893644i	−0.623563	+	0.781773i	$0.714316\pi$
$854$	−13.1201	−	12.9068i	−0.448962	−	0.441662i
$855$	5.37394	+	1.37791i	0.183785	+	0.0471235i
$856$	9.91217	−	0.243764i	0.338791	−	0.00833169i
$857$	−21.5378			−0.735717			−0.367859	−	0.929882i	$-0.619909\pi$
$857$	−21.5378			−0.735717			−0.367859	+	0.929882i	$0.619909\pi$
$858$	−11.8647	+	12.0608i	−0.405055	+	0.411749i
$859$	−6.11709	+	14.7680i	−0.208712	+	0.503876i	−0.993221	−	0.116242i	$-0.962915\pi$
$859$	−6.11709	+	14.7680i	−0.208712	+	0.503876i	0.784509	+	0.620118i	$0.212915\pi$
$860$	8.78507	+	2.09970i	0.299568	+	0.0715992i
$861$	17.0624	−	7.06746i	0.581484	−	0.240858i
$862$	17.0222	−	7.21481i	0.579777	−	0.245738i
$863$	−20.0936	+	20.0936i	−0.683994	+	0.683994i	−0.960898	−	0.276904i	$-0.910692\pi$
$863$	−20.0936	+	20.0936i	−0.683994	+	0.683994i	0.276904	+	0.960898i	$0.410692\pi$
$864$	23.3706	+	21.5296i	0.795084	+	0.732452i
$865$	32.6395	+	8.36896i	1.10978	+	0.284553i
$866$	−7.43293	+	18.3691i	−0.252581	+	0.624206i
$867$	−16.4309	−	6.80592i	−0.558024	−	0.231141i
$868$	12.7870	−	13.2132i	0.434019	−	0.448486i
$869$	−0.0444946	−	0.0184303i	−0.00150938	−	0.000625204i
$870$	−0.180555	−	0.299447i	−0.00612140	−	0.0101522i
$871$	−31.4829	+	31.4829i	−1.06676	+	1.06676i
$872$	0.691633	+	28.1238i	0.0234216	+	0.952393i
$873$	−10.8772			−0.368138
$874$	−22.4120	+	22.7824i	−0.758098	+	0.770627i
$875$	−16.5924	+	7.51150i	−0.560927	+	0.253935i
$876$	0.0626045	+	0.144400i	0.00211521	+	0.00487881i
$877$	−15.2491	−	6.31638i	−0.514925	−	0.213289i	0.110061	−	0.993925i	$-0.464895\pi$
$877$	−15.2491	−	6.31638i	−0.514925	−	0.213289i	−0.624986	+	0.780636i	$0.714895\pi$
$878$	−10.4413	+	25.8036i	−0.352375	+	0.870828i
$879$			18.9049i			0.637645i
$880$	3.31669	−	14.9571i	0.111805	−	0.504205i
$881$			37.3762i			1.25924i	0.776905	+	0.629618i	$0.216789\pi$
$881$			37.3762i			1.25924i	−0.776905	+	0.629618i	$0.783211\pi$
$882$	4.10563	+	1.66132i	0.138244	+	0.0559395i
$883$	−27.2971	−	11.3068i	−0.918620	−	0.380505i	−0.127270	−	0.991868i	$-0.540621\pi$
$883$	−27.2971	−	11.3068i	−0.918620	−	0.380505i	−0.791350	+	0.611363i	$0.790621\pi$
$884$	18.2400	−	46.1613i	0.613479	−	1.55257i
$885$	−5.15520	+	6.87078i	−0.173290	+	0.230959i
$886$	−4.01419	−	3.94892i	−0.134859	−	0.132667i
$887$	−47.8107			−1.60533			−0.802664	−	0.596432i	$-0.796585\pi$
$887$	−47.8107			−1.60533			−0.802664	+	0.596432i	$0.796585\pi$
$888$	−6.33289	+	16.4195i	−0.212518	+	0.551004i
$889$	0.236536	−	0.236536i	0.00793317	−	0.00793317i
$890$	46.8501	+	11.6043i	1.57042	+	0.388976i
$891$	−9.99974	−	4.14203i	−0.335004	−	0.138763i
$892$	−0.558300	−	34.0570i	−0.0186933	−	1.14031i
$893$	40.9475	+	16.9610i	1.37026	+	0.567578i
$894$	−12.9907	−	5.25660i	−0.434473	−	0.175807i
$895$	−17.8450	+	10.5614i	−0.596492	+	0.353029i
$896$	−6.06518	+	17.4042i	−0.202624	+	0.581434i
$897$	−32.4137	+	32.4137i	−1.08226	+	1.08226i
$898$	−21.1459	−	49.8902i	−0.705647	−	1.66486i
$899$	−0.381869	+	0.158175i	−0.0127360	+	0.00527544i
$900$	−6.88450	+	2.12806i	−0.229483	+	0.0709354i
$901$	7.12274	−	17.1958i	0.237293	−	0.572876i
$902$	−12.9667	−	12.7559i	−0.431745	−	0.424726i
$903$	4.96756			0.165310
$904$	3.64650	+	8.22540i	0.121281	+	0.273573i
$905$	2.78428	−	10.8589i	0.0925526	−	0.360962i
$906$	3.39197	−	3.44803i	0.112691	−	0.114553i
$907$	−12.4667	−	30.0974i	−0.413951	−	0.999366i	−0.984066	−	0.177802i	$-0.943101\pi$
$907$	−12.4667	−	30.0974i	−0.413951	−	0.999366i	0.570115	−	0.821565i	$-0.306899\pi$
$908$	27.2286	−	11.8050i	0.903614	−	0.391762i
$909$	−9.95984	+	4.12550i	−0.330347	+	0.136834i
$910$	3.55886	+	23.5640i	0.117975	+	0.781140i
$911$	1.88792			0.0625497			0.0312748	−	0.999511i	$-0.490043\pi$
$911$	1.88792			0.0625497			0.0312748	+	0.999511i	$0.490043\pi$
$912$	−0.681541	−	20.7818i	−0.0225681	−	0.688156i
$913$	−7.12967	+	7.12967i	−0.235958	+	0.235958i
$914$	8.40379	+	19.8274i	0.277973	+	0.655831i
$915$	−26.6988	+	3.80876i	−0.882633	+	0.125914i
$916$	41.9167	−	18.1730i	1.38497	−	0.600454i
$917$	1.68106	−	0.696318i	0.0555135	−	0.0229944i
$918$	42.6154	−	0.349276i	1.40652	−	0.0115278i
$919$	−8.49122	+	8.49122i	−0.280099	+	0.280099i	−0.833149	−	0.553049i	$-0.813464\pi$
$919$	−8.49122	+	8.49122i	−0.280099	+	0.280099i	0.553049	+	0.833149i	$0.313464\pi$
$920$	9.31825	−	40.4507i	0.307213	−	1.33362i
$921$	16.8071	+	16.8071i	0.553812	+	0.553812i
$922$	4.08247	+	4.01609i	0.134449	+	0.132263i
$923$	−15.5721	−	37.5944i	−0.512563	−	1.23744i
$924$	−0.138105	−	8.42458i	−0.00454332	−	0.277148i
$925$	−12.8942	−	16.0729i	−0.423958	−	0.528474i
$926$	3.29825	+	1.33462i	0.108387	+	0.0438582i
$927$	7.75831	+	7.75831i	0.254816	+	0.254816i
$928$	0.280711	−	0.304715i	0.00921479	−	0.0100027i
$929$			19.7090i			0.646632i	0.946291	+	0.323316i	$0.104798\pi$
$929$			19.7090i			0.646632i	−0.946291	+	0.323316i	$0.895202\pi$
$930$	−4.02372	−	26.6420i	−0.131943	−	0.873624i
$931$	−5.72651	−	13.8250i	−0.187679	−	0.453097i
$932$	−2.00039	+	2.06707i	−0.0655249	+	0.0677090i
$933$	22.1523	−	9.17578i	0.725233	−	0.300401i
$934$	0.166795	+	20.3507i	0.00545768	+	0.665895i
$935$	−10.4652	−	17.6825i	−0.342250	−	0.578279i
$936$	0.231799	+	9.42563i	0.00757659	+	0.308086i
$937$			40.0121i			1.30714i	0.756867	+	0.653568i	$0.226729\pi$
$937$			40.0121i			1.30714i	−0.756867	+	0.653568i	$0.773271\pi$
$938$	−0.181728	−	22.1728i	−0.00593365	−	0.723968i
$939$	−4.14465	−	1.71677i	−0.135255	−	0.0560246i
$940$	−56.8500	+	9.06318i	−1.85424	+	0.295608i
$941$	−16.7669	−	40.4789i	−0.546586	−	1.31957i	−0.920003	−	0.391911i	$-0.871814\pi$
$941$	−16.7669	−	40.4789i	−0.546586	−	1.31957i	0.373417	−	0.927663i	$-0.378186\pi$
$942$	−7.38724	−	2.98920i	−0.240689	−	0.0973935i
$943$	−34.8484	−	34.8484i	−1.13482	−	1.13482i
$944$	−9.52545	−	3.58449i	−0.310027	−	0.116665i
$945$	−17.6090	+	10.4218i	−0.572821	+	0.339020i
$946$	−1.90928	−	4.50462i	−0.0620760	−	0.146458i
$947$	3.33308	−	8.04677i	0.108311	−	0.261485i	−0.860426	−	0.509575i	$-0.829803\pi$
$947$	3.33308	−	8.04677i	0.108311	−	0.261485i	0.968737	+	0.248090i	$0.0798028\pi$
$948$	0.0778941	−	0.0337710i	0.00252988	−	0.00109683i
$949$	−0.0922730	+	0.222767i	−0.00299531	+	0.00723131i
$950$	21.4378	+	11.5395i	0.695533	+	0.374392i
$951$	−15.8879	−	15.8879i	−0.515199	−	0.515199i
$952$	10.0181	+	22.5977i	0.324687	+	0.732396i
$953$		−	31.4387i		−	1.01840i	−0.860649	−	0.509199i	$-0.829942\pi$
$953$		−	31.4387i		−	1.01840i	0.860649	−	0.509199i	$-0.170058\pi$
$954$	0.0289771	+	3.53551i	0.000938168	+	0.114467i
$955$	−40.7302	+	5.81044i	−1.31800	+	0.188021i
$956$	−27.6174	−	26.7266i	−0.893212	−	0.864399i
$957$	−0.0724810	+	0.174984i	−0.00234298	+	0.00565645i
$958$	−48.3122	+	20.4771i	−1.56090	+	0.661584i
$959$	−36.4821			−1.17807
$960$	14.8815	+	22.5378i	0.480298	+	0.727405i
$961$	−0.849645			−0.0274079
$962$	−24.8237	+	10.5215i	−0.800348	+	0.339226i
$963$	−0.966681	+	2.33377i	−0.0311509	+	0.0752048i
$964$	−1.30824	−	1.26604i	−0.0421357	−	0.0407765i
$965$	−24.9572	+	33.2626i	−0.803400	+	1.07076i
$966$	−0.187101	−	22.8283i	−0.00601987	−	0.734489i
$967$		−	5.96386i		−	0.191785i	−0.995392	−	0.0958924i	$-0.969430\pi$
$967$		−	5.96386i		−	0.191785i	0.995392	−	0.0958924i	$-0.0305705\pi$
$968$	20.8566	−	9.24618i	0.670356	−	0.297183i
$969$	−19.7191	−	19.7191i	−0.633467	−	0.633467i
$970$	−46.3340	−	11.4764i	−1.48770	−	0.368486i
$971$	6.61113	−	15.9607i	0.212161	−	0.512203i	−0.781594	−	0.623788i	$-0.785593\pi$
$971$	6.61113	−	15.9607i	0.212161	−	0.512203i	0.993755	+	0.111585i	$0.0355929\pi$
$972$	−13.4164	+	5.81667i	−0.430330	+	0.186570i
$973$	−9.03805	+	21.8198i	−0.289746	+	0.699510i
$974$	13.1028	+	30.9138i	0.419840	+	0.990543i
$975$	30.6128	+	16.8033i	0.980393	+	0.538136i
$976$	−13.1895	−	29.1053i	−0.422185	−	0.931637i
$977$	5.51919	+	5.51919i	0.176575	+	0.176575i	0.789861	−	0.613286i	$-0.210153\pi$
$977$	5.51919	+	5.51919i	0.176575	+	0.176575i	−0.613286	+	0.789861i	$0.710153\pi$
$978$	−29.8638	−	12.0842i	−0.954940	−	0.386411i
$979$	−10.0047	−	24.1536i	−0.319753	−	0.771952i
$980$	15.7361	+	11.4086i	0.502670	+	0.364434i
$981$	−6.62162	−	2.74277i	−0.211412	−	0.0875698i
$982$	0.344155	+	41.9906i	0.0109824	+	1.33997i
$983$			28.5048i			0.909162i	0.890705	+	0.454581i	$0.150211\pi$
$983$			28.5048i			0.909162i	−0.890705	+	0.454581i	$0.849789\pi$
$984$	32.0552	−	0.788316i	1.02188	−	0.0251306i
$985$	45.2314	−	26.7699i	1.44119	−	0.852959i
$986$	−0.00455399	−	0.555636i	−0.000145029	−	0.0176951i
$987$	−29.2503	+	12.1159i	−0.931048	+	0.385653i
$988$	22.1530	−	22.8914i	0.704781	−	0.728273i
$989$	−5.07290	−	12.2471i	−0.161309	−	0.389434i
$990$	3.14115	+	2.31683i	0.0998323	+	0.0736338i
$991$		−	56.9957i		−	1.81053i	−0.424849	−	0.905264i	$-0.639673\pi$
$991$		−	56.9957i		−	1.81053i	0.424849	−	0.905264i	$-0.360327\pi$
$992$	28.9693	−	13.4151i	0.919778	−	0.425931i
$993$	−9.22167	−	9.22167i	−0.292641	−	0.292641i
$994$	18.7857	+	7.60150i	0.595845	+	0.241105i
$995$	7.73040	−	10.3030i	0.245070	−	0.326626i
$996$	−0.291341	−	17.7722i	−0.00923150	−	0.563133i
$997$	0.0459765	+	0.110997i	0.00145609	+	0.00351532i	0.924606	−	0.380925i	$-0.124394\pi$
$997$	0.0459765	+	0.110997i	0.00145609	+	0.00351532i	−0.923150	+	0.384440i	$0.874394\pi$
$998$	−7.46845	−	7.34702i	−0.236410	−	0.232566i
$999$	−16.3692	−	16.3692i	−0.517898	−	0.517898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.43.19	✓	88
4.3	odd	2		640.2.u.a.463.17		88
5.2	odd	4		160.2.ba.a.107.16	yes	88
5.3	odd	4		800.2.bb.b.107.7		88
5.4	even	2		800.2.v.b.43.4		88
20.7	even	4		640.2.ba.a.207.6		88
32.3	odd	8		160.2.ba.a.3.16	yes	88
32.29	even	8		640.2.ba.a.303.6		88
160.3	even	8		800.2.v.b.707.4		88
160.67	even	8	inner	160.2.u.a.67.19	yes	88
160.99	odd	8		800.2.bb.b.643.7		88
160.157	odd	8		640.2.u.a.47.17		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.19	✓	88	1.1	even	1	trivial
160.2.u.a.67.19	yes	88	160.67	even	8	inner
160.2.ba.a.3.16	yes	88	32.3	odd	8
160.2.ba.a.107.16	yes	88	5.2	odd	4
640.2.u.a.47.17		88	160.157	odd	8
640.2.u.a.463.17		88	4.3	odd	2
640.2.ba.a.207.6		88	20.7	even	4
640.2.ba.a.303.6		88	32.29	even	8
800.2.v.b.43.4		88	5.4	even	2
800.2.v.b.707.4		88	160.3	even	8
800.2.bb.b.107.7		88	5.3	odd	4
800.2.bb.b.643.7		88	160.99	odd	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30208 - 0.551886i) q^{2} +(-0.577765 + 1.39485i) q^{3} +(1.39084 - 1.43720i) q^{4} +(0.315793 + 2.21366i) q^{5} +(0.0174990 + 2.13507i) q^{6} -1.62907i q^{7} +(1.01782 - 2.63895i) q^{8} +(0.509534 + 0.509534i) q^{9} +O(q^{10})\)	\(q+(1.30208 - 0.551886i) q^{2} +(-0.577765 + 1.39485i) q^{3} +(1.39084 - 1.43720i) q^{4} +(0.315793 + 2.21366i) q^{5} +(0.0174990 + 2.13507i) q^{6} -1.62907i q^{7} +(1.01782 - 2.63895i) q^{8} +(0.509534 + 0.509534i) q^{9} +(1.63288 + 2.70808i) q^{10} +(0.655490 - 1.58249i) q^{11} +(1.20110 + 2.77038i) q^{12} +(-1.77030 + 4.27389i) q^{13} +(-0.899059 - 2.12118i) q^{14} +(-3.27017 - 0.838489i) q^{15} +(-0.131110 - 3.99785i) q^{16} +(-3.79340 - 3.79340i) q^{17} +(0.944661 + 0.382251i) q^{18} +(-1.31761 - 3.18099i) q^{19} +(3.62069 + 2.62499i) q^{20} +(2.27230 + 0.941216i) q^{21} +(-0.0198531 - 2.42229i) q^{22} -6.56332i q^{23} +(3.09287 + 2.94439i) q^{24} +(-4.80055 + 1.39811i) q^{25} +(0.0536180 + 6.54197i) q^{26} +(-5.18965 + 2.14962i) q^{27} +(-2.34130 - 2.26577i) q^{28} +(0.0280276 + 0.0676646i) q^{29} +(-4.72078 + 0.712976i) q^{30} +5.64355i q^{31} +(-2.37707 - 5.13318i) q^{32} +(1.82862 + 1.82862i) q^{33} +(-7.03285 - 2.84580i) q^{34} +(3.60619 - 0.514447i) q^{35} +(1.44099 - 0.0236223i) q^{36} +(1.57710 + 3.80745i) q^{37} +(-3.47118 - 3.41474i) q^{38} +(-4.93861 - 4.93861i) q^{39} +(6.16314 + 1.41975i) q^{40} +(5.30956 - 5.30956i) q^{41} +(3.47817 - 0.0285071i) q^{42} +(1.86599 - 0.772917i) q^{43} +(-1.36268 - 3.14307i) q^{44} +(-0.967026 + 1.28884i) q^{45} +(-3.62220 - 8.54599i) q^{46} +(-9.10229 + 9.10229i) q^{47} +(5.65214 + 2.12694i) q^{48} +4.34615 q^{49} +(-5.47912 + 4.46982i) q^{50} +(7.48290 - 3.09952i) q^{51} +(3.68024 + 8.48860i) q^{52} +(1.32771 + 3.20538i) q^{53} +(-5.57101 + 5.66309i) q^{54} +(3.71010 + 0.951290i) q^{55} +(-4.29902 - 1.65810i) q^{56} +5.19825 q^{57} +(0.0738375 + 0.0726370i) q^{58} +(0.973697 - 2.35071i) q^{59} +(-5.75337 + 3.53369i) q^{60} +(7.38048 - 3.05710i) q^{61} +(3.11460 + 7.34837i) q^{62} +(0.830064 - 0.830064i) q^{63} +(-5.92808 - 5.37195i) q^{64} +(-10.0200 - 2.56918i) q^{65} +(3.39020 + 1.37182i) q^{66} +(8.89195 + 3.68317i) q^{67} +(-10.7279 + 0.175864i) q^{68} +(9.15482 + 3.79205i) q^{69} +(4.41165 - 2.66006i) q^{70} +(-6.21992 + 6.21992i) q^{71} +(1.86325 - 0.826019i) q^{72} +0.0521227 q^{73} +(4.15480 + 4.08724i) q^{74} +(0.823432 - 7.50381i) q^{75} +(-6.40431 - 2.53058i) q^{76} +(-2.57799 - 1.06784i) q^{77} +(-9.15603 - 3.70493i) q^{78} -0.0281168i q^{79} +(8.80846 - 1.55272i) q^{80} -6.31898i q^{81} +(3.98322 - 9.84377i) q^{82} +(-5.43842 - 2.25267i) q^{83} +(4.51313 - 1.95667i) q^{84} +(7.19935 - 9.59521i) q^{85} +(2.00311 - 2.03621i) q^{86} -0.110575 q^{87} +(-3.50894 - 3.34050i) q^{88} +(10.7926 - 10.7926i) q^{89} +(-0.547856 + 2.21187i) q^{90} +(6.96245 + 2.88394i) q^{91} +(-9.43283 - 9.12855i) q^{92} +(-7.87189 - 3.26064i) q^{93} +(-6.82851 + 16.8754i) q^{94} +(6.62552 - 3.92126i) q^{95} +(8.53339 - 0.349886i) q^{96} +(-10.6737 + 10.6737i) q^{97} +(5.65904 - 2.39858i) q^{98} +(1.14033 - 0.472340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Introduction

L-functions

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