LMFDB - Embedded newform 175.2.x.a.73.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			73.18
Character	$\chi$	$=$	175.73
Dual form			175.2.x.a.12.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.48322 - 0.953219i) q^{2} +(-1.59480 - 0.0835800i) q^{3} +(3.77146 - 3.39584i) q^{4} +(-1.20602 - 1.88296i) q^{5} +(-4.03991 + 1.31265i) q^{6} +(0.777975 + 2.52879i) q^{7} +(3.71326 - 7.28769i) q^{8} +(-0.447157 - 0.0469981i) q^{9} +O(q^{10})$	\(q+(2.48322 - 0.953219i) q^{2} +(-1.59480 - 0.0835800i) q^{3} +(3.77146 - 3.39584i) q^{4} +(-1.20602 - 1.88296i) q^{5} +(-4.03991 + 1.31265i) q^{6} +(0.777975 + 2.52879i) q^{7} +(3.71326 - 7.28769i) q^{8} +(-0.447157 - 0.0469981i) q^{9} +(-4.78967 - 3.52620i) q^{10} +(0.454141 + 4.32086i) q^{11} +(-6.29856 + 5.10048i) q^{12} +(3.44108 - 0.545014i) q^{13} +(4.34237 + 5.53795i) q^{14} +(1.76598 + 3.10374i) q^{15} +(1.21312 - 11.5421i) q^{16} +(0.608257 + 0.936633i) q^{17} +(-1.15519 + 0.309532i) q^{18} +(-2.20351 + 2.44725i) q^{19} +(-10.9427 - 3.00606i) q^{20} +(-1.02936 - 4.09794i) q^{21} +(5.24646 + 10.2967i) q^{22} +(-1.36876 - 3.56575i) q^{23} +(-6.53103 + 11.3121i) q^{24} +(-2.09105 + 4.54175i) q^{25} +(8.02545 - 4.63349i) q^{26} +(5.44119 + 0.861799i) q^{27} +(11.5215 + 6.89534i) q^{28} +(-6.66539 - 2.16572i) q^{29} +(7.34386 + 6.02391i) q^{30} +(-0.293918 + 1.38278i) q^{31} +(-3.75583 - 14.0170i) q^{32} +(-0.363127 - 6.92887i) q^{33} +(2.40325 + 1.74606i) q^{34} +(3.82334 - 4.51465i) q^{35} +(-1.84604 + 1.34122i) q^{36} +(-0.792854 - 0.979093i) q^{37} +(-3.13904 + 8.17748i) q^{38} +(-5.53340 + 0.581584i) q^{39} +(-18.2007 + 1.79716i) q^{40} +(-2.49483 + 3.43383i) q^{41} +(-6.46235 - 9.19487i) q^{42} +(-0.933537 - 0.933537i) q^{43} +(16.3857 + 14.7538i) q^{44} +(0.450784 + 0.898658i) q^{45} +(-6.79787 - 7.54980i) q^{46} +(-6.91457 - 4.49037i) q^{47} +(-2.89938 + 18.3060i) q^{48} +(-5.78951 + 3.93466i) q^{49} +(-0.863254 + 13.2714i) q^{50} +(-0.891766 - 1.54458i) q^{51} +(11.1271 - 13.7409i) q^{52} +(0.564893 - 10.7788i) q^{53} +(14.3331 - 3.04660i) q^{54} +(7.58829 - 6.06615i) q^{55} +(21.3178 + 3.72041i) q^{56} +(3.71871 - 3.71871i) q^{57} +(-18.6160 + 0.975625i) q^{58} +(10.6963 - 4.76231i) q^{59} +(17.2001 + 5.70866i) q^{60} +(1.08030 - 2.42639i) q^{61} +(0.588225 + 3.71391i) q^{62} +(-0.229029 - 1.16733i) q^{63} +(-9.04452 - 12.4487i) q^{64} +(-5.17624 - 5.82211i) q^{65} +(-7.50646 - 16.8598i) q^{66} +(9.39294 - 6.09985i) q^{67} +(5.47468 + 1.46694i) q^{68} +(1.88488 + 5.80106i) q^{69} +(5.19075 - 14.8553i) q^{70} +(-3.75418 + 11.5542i) q^{71} +(-2.00292 + 3.08423i) q^{72} +(2.59496 + 2.10136i) q^{73} +(-2.90212 - 1.67554i) q^{74} +(3.71441 - 7.06843i) q^{75} +16.7125i q^{76} +(-10.5732 + 4.50994i) q^{77} +(-13.1863 + 6.71874i) q^{78} +(0.143730 + 0.676195i) q^{79} +(-23.1963 + 11.6357i) q^{80} +(-7.28620 - 1.54873i) q^{81} +(-2.92201 + 10.9051i) q^{82} +(-2.77341 - 1.41312i) q^{83} +(-17.7981 - 11.9597i) q^{84} +(1.03007 - 2.27492i) q^{85} +(-3.20804 - 1.42831i) q^{86} +(10.4490 + 4.01098i) q^{87} +(33.1754 + 12.7349i) q^{88} +(-9.11987 - 4.06043i) q^{89} +(1.97601 + 1.80187i) q^{90} +(4.05530 + 8.27775i) q^{91} +(-17.2709 - 8.79998i) q^{92} +(0.584314 - 2.18069i) q^{93} +(-21.4507 - 4.55949i) q^{94} +(7.26553 + 1.19770i) q^{95} +(4.81827 + 22.6682i) q^{96} +(1.61466 - 0.822712i) q^{97} +(-10.6260 + 15.2893i) q^{98} -1.95345i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{20}\right)$

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 $

$2$	2.48322	−	0.953219i	1.75590	−	0.674027i	0.756093	−	0.654465i	$-0.227106\pi$
$2$	2.48322	−	0.953219i	1.75590	−	0.674027i	0.999809	−	0.0195628i	$-0.00622745\pi$
$3$	−1.59480	−	0.0835800i	−0.920759	−	0.0482550i	−0.413937	−	0.910305i	$-0.635847\pi$
$3$	−1.59480	−	0.0835800i	−0.920759	−	0.0482550i	−0.506822	+	0.862051i	$0.669180\pi$
$4$	3.77146	−	3.39584i	1.88573	−	1.69792i
$5$	−1.20602	−	1.88296i	−0.539347	−	0.842084i
$5$	−1.20602	−	1.88296i	−0.539347	−	0.842084i
$6$	−4.03991	+	1.31265i	−1.64929	+	0.535886i
$7$	0.777975	+	2.52879i	0.294047	+	0.955791i
$7$	0.777975	+	2.52879i	0.294047	+	0.955791i
$8$	3.71326	−	7.28769i	1.31284	−	2.57659i
$9$	−0.447157	−	0.0469981i	−0.149052	−	0.0156660i
$10$	−4.78967	−	3.52620i	−1.51463	−	1.11508i
$11$	0.454141	+	4.32086i	0.136929	+	1.30279i	0.819969	+	0.572408i	$0.193991\pi$
$11$	0.454141	+	4.32086i	0.136929	+	1.30279i	−0.683041	+	0.730380i	$0.739343\pi$
$12$	−6.29856	+	5.10048i	−1.81824	+	1.47238i
$13$	3.44108	−	0.545014i	0.954385	−	0.151160i	0.340227	−	0.940343i	$-0.389496\pi$
$13$	3.44108	−	0.545014i	0.954385	−	0.151160i	0.614157	+	0.789184i	$0.289496\pi$
$14$	4.34237	+	5.53795i	1.16055	+	1.48008i
$15$	1.76598	+	3.10374i	0.455974	+	0.801383i
$16$	1.21312	−	11.5421i	0.303281	−	2.88552i
$17$	0.608257	+	0.936633i	0.147524	+	0.227167i	0.904705	−	0.426038i	$-0.140091\pi$
$17$	0.608257	+	0.936633i	0.147524	+	0.227167i	−0.757182	+	0.653205i	$0.773424\pi$
$18$	−1.15519	+	0.309532i	−0.272281	+	0.0729574i
$19$	−2.20351	+	2.44725i	−0.505520	+	0.561437i	−0.940845	−	0.338836i	$-0.889967\pi$
$19$	−2.20351	+	2.44725i	−0.505520	+	0.561437i	0.435325	+	0.900273i	$0.356633\pi$
$20$	−10.9427	−	3.00606i	−2.44685	−	0.672176i
$21$	−1.02936	−	4.09794i	−0.224625	−	0.894243i
$22$	5.24646	+	10.2967i	1.11855	+	2.19527i
$23$	−1.36876	−	3.56575i	−0.285407	−	0.743509i	−0.999074	−	0.0430248i	$-0.986301\pi$
$23$	−1.36876	−	3.56575i	−0.285407	−	0.743509i	0.713667	−	0.700485i	$-0.247033\pi$
$24$	−6.53103	+	11.3121i	−1.33314	+	2.30907i
$25$	−2.09105	+	4.54175i	−0.418210	+	0.908350i
$26$	8.02545	−	4.63349i	1.57392	−	0.908703i
$27$	5.44119	+	0.861799i	1.04716	+	0.165853i
$28$	11.5215	+	6.89534i	2.17735	+	1.30310i
$29$	−6.66539	−	2.16572i	−1.23773	−	0.402164i	−0.384222	−	0.923241i	$-0.625530\pi$
$29$	−6.66539	−	2.16572i	−1.23773	−	0.402164i	−0.853510	+	0.521077i	$0.825530\pi$
$30$	7.34386	+	6.02391i	1.34080	+	1.09981i
$31$	−0.293918	+	1.38278i	−0.0527893	+	0.248354i	−0.996628	−	0.0820524i	$-0.973853\pi$
$31$	−0.293918	+	1.38278i	−0.0527893	+	0.248354i	0.943839	+	0.330407i	$0.107186\pi$
$32$	−3.75583	−	14.0170i	−0.663944	−	2.47787i
$33$	−0.363127	−	6.92887i	−0.0632123	−	1.20616i
$34$	2.40325	+	1.74606i	0.412154	+	0.299448i
$35$	3.82334	−	4.51465i	0.646263	−	0.763115i
$36$	−1.84604	+	1.34122i	−0.307673	+	0.223537i
$37$	−0.792854	−	0.979093i	−0.130344	−	0.160962i	0.707795	−	0.706418i	$-0.249690\pi$
$37$	−0.792854	−	0.979093i	−0.130344	−	0.160962i	−0.838140	+	0.545456i	$0.816357\pi$
$38$	−3.13904	+	8.17748i	−0.509220	+	1.32656i
$39$	−5.53340	+	0.581584i	−0.886053	+	0.0931279i
$40$	−18.2007	+	1.79716i	−2.87778	+	0.284156i
$41$	−2.49483	+	3.43383i	−0.389627	+	0.536275i	−0.958103	−	0.286425i	$-0.907533\pi$
$41$	−2.49483	+	3.43383i	−0.389627	+	0.536275i	0.568476	+	0.822700i	$0.307533\pi$
$42$	−6.46235	−	9.19487i	−0.997163	−	1.41880i
$43$	−0.933537	−	0.933537i	−0.142363	−	0.142363i	0.632333	−	0.774696i	$-0.282097\pi$
$43$	−0.933537	−	0.933537i	−0.142363	−	0.142363i	−0.774696	+	0.632333i	$0.782097\pi$
$44$	16.3857	+	14.7538i	2.47024	+	2.22422i
$45$	0.450784	+	0.898658i	0.0671988	+	0.133964i
$46$	−6.79787	−	7.54980i	−1.00229	−	1.11316i
$47$	−6.91457	−	4.49037i	−1.00859	−	0.654988i	−0.0691196	−	0.997608i	$-0.522019\pi$
$47$	−6.91457	−	4.49037i	−1.00859	−	0.654988i	−0.939474	+	0.342620i	$0.888686\pi$
$48$	−2.89938	+	18.3060i	−0.418489	+	2.64224i
$49$	−5.78951	+	3.93466i	−0.827073	+	0.562094i
$50$	−0.863254	+	13.2714i	−0.122083	+	1.87686i
$51$	−0.891766	−	1.54458i	−0.124872	−	0.216285i
$52$	11.1271	−	13.7409i	1.54306	−	1.90552i
$53$	0.564893	−	10.7788i	0.0775940	−	1.48058i	−0.631449	−	0.775417i	$-0.717540\pi$
$53$	0.564893	−	10.7788i	0.0775940	−	1.48058i	0.709043	−	0.705165i	$-0.249127\pi$
$54$	14.3331	−	3.04660i	1.95049	−	0.414590i
$55$	7.58829	−	6.06615i	1.02320	−	0.817960i
$56$	21.3178	+	3.72041i	2.84872	+	0.497161i
$57$	3.71871	−	3.71871i	0.492555	−	0.492555i
$58$	−18.6160	+	0.975625i	−2.44440	+	0.128106i
$59$	10.6963	−	4.76231i	1.39254	−	0.620000i	0.432957	−	0.901415i	$-0.357470\pi$
$59$	10.6963	−	4.76231i	1.39254	−	0.620000i	0.959586	+	0.281415i	$0.0908037\pi$
$60$	17.2001	+	5.70866i	2.22053	+	0.736985i
$61$	1.08030	−	2.42639i	0.138318	−	0.310668i	−0.831084	−	0.556148i	$-0.812279\pi$
$61$	1.08030	−	2.42639i	0.138318	−	0.310668i	0.969402	+	0.245480i	$0.0789456\pi$
$62$	0.588225	+	3.71391i	0.0747047	+	0.471667i
$63$	−0.229029	−	1.16733i	−0.0288549	−	0.147070i
$64$	−9.04452	−	12.4487i	−1.13056	−	1.55609i
$65$	−5.17624	−	5.82211i	−0.642033	−	0.722144i
$66$	−7.50646	−	16.8598i	−0.923981	−	2.07529i
$67$	9.39294	−	6.09985i	1.14753	−	0.745215i	0.176531	−	0.984295i	$-0.443512\pi$
$67$	9.39294	−	6.09985i	1.14753	−	0.745215i	0.971000	+	0.239080i	$0.0768458\pi$
$68$	5.47468	+	1.46694i	0.663902	+	0.177892i
$69$	1.88488	+	5.80106i	0.226913	+	0.698366i
$70$	5.19075	−	14.8553i	0.620414	−	1.77555i
$71$	−3.75418	+	11.5542i	−0.445539	+	1.37123i	0.436353	+	0.899776i	$0.356270\pi$
$71$	−3.75418	+	11.5542i	−0.445539	+	1.37123i	−0.881892	+	0.471452i	$0.843730\pi$
$72$	−2.00292	+	3.08423i	−0.236047	+	0.363480i
$73$	2.59496	+	2.10136i	0.303718	+	0.245946i	0.769047	−	0.639192i	$-0.220731\pi$
$73$	2.59496	+	2.10136i	0.303718	+	0.245946i	−0.465330	+	0.885137i	$0.654064\pi$
$74$	−2.90212	−	1.67554i	−0.337365	−	0.194778i
$75$	3.71441	−	7.06843i	0.428903	−	0.816191i
$76$			16.7125i			1.91705i
$77$	−10.5732	+	4.50994i	−1.20493	+	0.513956i
$78$	−13.1863	+	6.71874i	−1.49305	+	0.760747i
$79$	0.143730	+	0.676195i	0.0161708	+	0.0760778i	0.985493	−	0.169715i	$-0.0542849\pi$
$79$	0.143730	+	0.676195i	0.0161708	+	0.0760778i	−0.969322	+	0.245793i	$0.920952\pi$
$80$	−23.1963	+	11.6357i	−2.59342	+	1.30091i
$81$	−7.28620	−	1.54873i	−0.809578	−	0.172081i
$82$	−2.92201	+	10.9051i	−0.322682	+	1.20426i
$83$	−2.77341	−	1.41312i	−0.304421	−	0.155110i	0.295106	−	0.955464i	$-0.404645\pi$
$83$	−2.77341	−	1.41312i	−0.304421	−	0.155110i	−0.599528	+	0.800354i	$0.704645\pi$
$84$	−17.7981	−	11.9597i	−1.94194	−	1.30491i
$85$	1.03007	−	2.27492i	0.111727	−	0.246749i
$86$	−3.20804	−	1.42831i	−0.345932	−	0.154019i
$87$	10.4490	+	4.01098i	1.12025	+	0.430023i
$88$	33.1754	+	12.7349i	3.53651	+	1.35754i
$89$	−9.11987	−	4.06043i	−0.966705	−	0.430405i	−0.138211	−	0.990403i	$-0.544135\pi$
$89$	−9.11987	−	4.06043i	−0.966705	−	0.430405i	−0.828494	+	0.559998i	$0.810802\pi$
$90$	1.97601	+	1.80187i	0.208290	+	0.189934i
$91$	4.05530	+	8.27775i	0.425111	+	0.867744i
$92$	−17.2709	−	8.79998i	−1.80062	−	0.917462i
$93$	0.584314	−	2.18069i	0.0605906	−	0.226127i
$94$	−21.4507	−	4.55949i	−2.21247	−	0.470275i
$95$	7.26553	+	1.19770i	0.745428	+	0.122881i
$96$	4.81827	+	22.6682i	0.491763	+	2.31356i
$97$	1.61466	−	0.822712i	0.163944	−	0.0835337i	−0.370093	−	0.928995i	$-0.620674\pi$
$97$	1.61466	−	0.822712i	0.163944	−	0.0835337i	0.534037	+	0.845461i	$0.320674\pi$
$98$	−10.6260	+	15.2893i	−1.07339	+	1.54445i
$99$		−	1.95345i		−	0.196329i
$100$	7.53675	+	24.2299i	0.753675	+	2.42299i
$101$	−8.56638	−	4.94580i	−0.852387	−	0.492126i	0.00906846	−	0.999959i	$-0.497113\pi$
$101$	−8.56638	−	4.94580i	−0.852387	−	0.492126i	−0.861456	+	0.507833i	$0.830447\pi$
$102$	−3.68678	−	2.98549i	−0.365045	−	0.295608i
$103$	−1.22728	+	1.88985i	−0.120928	+	0.186212i	−0.893950	−	0.448166i	$-0.852077\pi$
$103$	−1.22728	+	1.88985i	−0.120928	+	0.186212i	0.773023	+	0.634379i	$0.218744\pi$
$104$	8.80576	−	27.1013i	0.863476	−	2.65750i
$105$	−6.47481	+	6.88042i	−0.631877	+	0.671460i
$106$	−8.87180	−	27.3046i	−0.861705	−	2.65206i
$107$	12.7056	+	3.40446i	1.22830	+	0.329122i	0.813917	−	0.580981i	$-0.197331\pi$
$107$	12.7056	+	3.40446i	1.22830	+	0.329122i	0.414383	+	0.910103i	$0.363997\pi$
$108$	23.4478	−	15.2272i	2.25626	−	1.46523i
$109$	2.15369	+	4.83726i	0.206286	+	0.463326i	0.986827	−	0.161779i	$-0.0517231\pi$
$109$	2.15369	+	4.83726i	0.206286	+	0.463326i	−0.780541	+	0.625104i	$0.785056\pi$
$110$	13.0610	−	22.2969i	1.24532	−	2.12593i
$111$	1.18261	+	1.62773i	0.112249	+	0.154497i
$112$	30.1312	−	5.91172i	2.84713	−	0.558605i
$113$	0.487520	+	3.07808i	0.0458620	+	0.289561i	0.999950	−	0.00996409i	$-0.00317172\pi$
$113$	0.487520	+	3.07808i	0.0458620	+	0.289561i	−0.954088	+	0.299525i	$0.903172\pi$
$114$	5.68962	−	12.7791i	0.532882	−	1.19687i
$115$	−5.06340	+	6.87767i	−0.472164	+	0.641346i
$116$	−32.4927	+	14.4667i	−3.01687	+	1.34320i
$117$	−1.56432	+	0.0819825i	−0.144621	+	0.00757929i
$118$	22.0218	−	22.0218i	2.02727	−	2.02727i
$119$	−1.89534	+	2.26683i	−0.173745	+	0.207800i
$120$	29.1767	−	1.34490i	2.66345	−	0.122772i
$121$	−7.70396	+	1.63753i	−0.700360	+	0.148866i
$122$	0.369738	−	7.05502i	0.0334745	−	0.638732i
$123$	4.26576	−	5.26777i	0.384630	−	0.474979i
$124$	3.58719	+	6.21320i	0.322139	+	0.557962i
$125$	11.0738	−	1.54007i	0.990467	−	0.137748i
$126$	−1.68145	−	2.68042i	−0.149795	−	0.238791i
$127$	−2.40328	+	15.1737i	−0.213257	+	1.34645i	0.616072	+	0.787689i	$0.288723\pi$
$127$	−2.40328	+	15.1737i	−0.213257	+	1.34645i	−0.829329	+	0.558760i	$0.811277\pi$
$128$	−9.98525	−	6.48450i	−0.882580	−	0.573154i
$129$	1.41078	+	1.56683i	0.124212	+	0.137952i
$130$	−18.4035	−	9.52350i	−1.61409	−	0.835266i
$131$	−0.912564	−	0.821676i	−0.0797311	−	0.0717902i	0.628302	−	0.777970i	$-0.283750\pi$
$131$	−0.912564	−	0.821676i	−0.0797311	−	0.0717902i	−0.708033	+	0.706180i	$0.750417\pi$
$132$	−24.8989	−	24.8989i	−2.16717	−	2.16717i
$133$	−7.90284	−	3.66831i	−0.685263	−	0.318083i
$134$	17.5103	−	24.1008i	1.51266	−	2.08199i
$135$	−4.93943	−	11.2849i	−0.425118	−	0.971246i
$136$	9.08452	−	0.954821i	0.778991	−	0.0818752i
$137$	−0.740584	+	1.92929i	−0.0632723	+	0.164830i	−0.961572	−	0.274554i	$-0.911470\pi$
$137$	−0.740584	+	1.92929i	−0.0632723	+	0.164830i	0.898299	+	0.439384i	$0.144803\pi$
$138$	10.2102	+	12.6086i	0.869154	+	1.07332i
$139$	−16.2625	+	11.8154i	−1.37937	+	1.00217i	−0.382426	+	0.923986i	$0.624911\pi$
$139$	−16.2625	+	11.8154i	−1.37937	+	1.00217i	−0.996939	+	0.0781815i	$0.975089\pi$
$140$	−0.911429	−	30.0103i	−0.0770298	−	2.53633i
$141$	10.6521	+	7.73918i	0.897066	+	0.651756i
$142$	1.69120	+	32.2701i	0.141923	+	2.70805i
$143$	3.91766	+	14.6209i	0.327612	+	1.22266i
$144$	−1.08491	+	5.10411i	−0.0904094	+	0.425343i
$145$	3.96062	+	15.1625i	0.328912	+	1.25918i
$146$	8.44692	+	2.74457i	0.699072	+	0.227142i
$147$	9.56198	−	5.79112i	0.788659	−	0.477643i
$148$	−6.31506	−	1.00021i	−0.519095	−	0.0822166i
$149$	15.9985	−	9.23671i	1.31064	−	0.756701i	0.328442	−	0.944524i	$-0.393477\pi$
$149$	15.9985	−	9.23671i	1.31064	−	0.756701i	0.982203	+	0.187823i	$0.0601432\pi$
$150$	2.48594	−	21.0931i	0.202976	−	1.72224i
$151$	6.91634	−	11.9795i	0.562844	−	0.974874i	−0.434403	−	0.900719i	$-0.643040\pi$
$151$	6.91634	−	11.9795i	0.562844	−	0.974874i	0.997247	−	0.0741557i	$-0.0236262\pi$
$152$	9.65257	+	25.1458i	0.782927	+	2.03959i
$153$	−0.227967	−	0.447409i	−0.0184300	−	0.0361709i
$154$	−21.9567	+	21.2778i	−1.76932	+	1.71461i
$155$	2.95818	−	1.11422i	0.237607	−	0.0894960i
$156$	−18.8940	+	20.9840i	−1.51273	+	1.68006i
$157$	10.2032	−	2.73394i	0.814304	−	0.218192i	0.172450	−	0.985018i	$-0.444832\pi$
$157$	10.2032	−	2.73394i	0.814304	−	0.218192i	0.641855	+	0.766826i	$0.278165\pi$
$158$	1.00147	+	1.54213i	0.0796730	+	0.122686i
$159$	−1.80179	+	17.1428i	−0.142891	+	1.35952i
$160$	−21.8637	+	23.9768i	−1.72848	+	1.89553i
$161$	7.95214	−	6.23536i	0.626717	−	0.491416i
$162$	−19.5695	+	3.09951i	−1.53753	+	0.243520i
$163$	−0.336549	+	0.272532i	−0.0263606	+	0.0213464i	−0.642410	−	0.766361i	$-0.722065\pi$
$163$	−0.336549	+	0.272532i	−0.0263606	+	0.0213464i	0.616050	+	0.787707i	$0.288732\pi$
$164$	2.25161	+	21.4226i	0.175821	+	1.67283i
$165$	−12.6088	+	9.04009i	−0.981596	+	0.703770i
$166$	−8.23401	−	0.865429i	−0.639083	−	0.0671703i
$167$	6.74343	−	13.2347i	0.521823	−	1.02413i	−0.468252	−	0.883595i	$-0.655116\pi$
$167$	6.74343	−	13.2347i	0.521823	−	1.02413i	0.990075	−	0.140540i	$-0.0448838\pi$
$168$	−33.6868	−	7.71506i	−2.59899	−	0.595230i
$169$	−0.819726	+	0.266345i	−0.0630558	+	0.0204881i
$170$	0.389403	−	6.63100i	0.0298659	−	0.508575i
$171$	1.10033	−	0.990744i	0.0841445	−	0.0757641i
$172$	−6.69094	−	0.350657i	−0.510180	−	0.0267374i
$173$	−9.23654	+	3.54558i	−0.702241	+	0.269565i	−0.683177	−	0.730253i	$-0.739402\pi$
$173$	−9.23654	+	3.54558i	−0.702241	+	0.269565i	−0.0190644	+	0.999818i	$0.506069\pi$
$174$	29.7704			2.25689
$175$	−13.1119	−	1.75445i	−0.991166	−	0.132624i
$176$	50.4227			3.80075
$177$	−17.4566	+	6.70094i	−1.31212	+	0.503674i
$178$	−26.5171	−	1.38970i	−1.98754	−	0.104163i
$179$	0.859937	−	0.774290i	0.0642747	−	0.0578732i	−0.636367	−	0.771386i	$-0.719564\pi$
$179$	0.859937	−	0.774290i	0.0642747	−	0.0578732i	0.700642	+	0.713513i	$0.252897\pi$
$180$	4.75181	+	1.85847i	0.354179	+	0.138522i
$181$	14.9384	−	4.85377i	1.11036	−	0.360778i	0.304279	−	0.952583i	$-0.401584\pi$
$181$	14.9384	−	4.85377i	1.11036	−	0.360778i	0.806081	+	0.591805i	$0.201584\pi$
$182$	17.9607	+	16.6899i	1.33134	+	1.23714i
$183$	−1.92566	+	3.77932i	−0.142349	+	0.279376i
$184$	−31.0686	−	3.26545i	−2.29041	−	0.240732i
$185$	−0.887395	+	2.67371i	−0.0652426	+	0.196575i
$186$	−0.627695	−	5.97211i	−0.0460248	−	0.437897i
$187$	−3.77083	+	3.05356i	−0.275750	+	0.223298i
$188$	−41.3266	+	6.54550i	−3.01406	+	0.477379i
$189$	2.05380	+	14.4301i	0.149392	+	1.04963i
$190$	19.1836	−	3.95150i	1.39172	−	0.286672i
$191$	−0.265828	+	2.52919i	−0.0192347	+	0.183005i	−0.999921	−	0.0125823i	$-0.995995\pi$
$191$	−0.265828	+	2.52919i	−0.0192347	+	0.183005i	0.980686	+	0.195588i	$0.0626615\pi$
$192$	13.3838	+	20.6092i	0.965889	+	1.48734i
$193$	−14.3278	+	3.83911i	−1.03133	+	0.276345i	−0.734518	−	0.678589i	$-0.762592\pi$
$193$	−14.3278	+	3.83911i	−1.03133	+	0.276345i	−0.296817	+	0.954934i	$0.595925\pi$
$194$	3.22534	−	3.58210i	0.231566	−	0.257180i
$195$	7.76846	+	9.71775i	0.556311	+	0.695902i
$196$	−8.47345	+	34.4997i	−0.605246	+	2.46426i
$197$	−0.772721	−	1.51655i	−0.0550541	−	0.108050i	0.861840	−	0.507180i	$-0.169312\pi$
$197$	−0.772721	−	1.51655i	−0.0550541	−	0.108050i	−0.916894	+	0.399130i	$0.869312\pi$
$198$	−1.86206	−	4.85084i	−0.132331	−	0.344734i
$199$	1.87071	−	3.24016i	0.132611	−	0.229689i	−0.792071	−	0.610429i	$-0.790997\pi$
$199$	1.87071	−	3.24016i	0.132611	−	0.229689i	0.924682	+	0.380740i	$0.124331\pi$
$200$	25.3343	+	32.1037i	1.79140	+	2.27007i
$201$	−15.4897	+	8.94299i	−1.09256	+	0.630790i
$202$	−25.9866	−	4.11588i	−1.82841	−	0.289592i
$203$	0.291129	−	18.5402i	0.0204332	−	1.30127i
$204$	−8.60842	−	2.79705i	−0.602710	−	0.195832i
$205$	9.47456	+	0.556390i	0.661732	+	0.0388600i
$206$	−1.24617	+	5.86278i	−0.0868249	+	0.408479i
$207$	0.444468	+	1.65878i	0.0308927	+	0.115293i
$208$	−2.11614	−	40.3784i	−0.146728	−	2.79974i
$209$	−11.5749	−	8.40967i	−0.800654	−	0.581709i
$210$	−9.51983	+	23.2575i	−0.656931	+	1.60492i
$211$	−9.23159	+	6.70715i	−0.635529	+	0.461739i	−0.858311	−	0.513129i	$-0.828486\pi$
$211$	−9.23159	+	6.70715i	−0.635529	+	0.461739i	0.222782	+	0.974868i	$0.428486\pi$
$212$	−34.4726	−	42.5701i	−2.36759	−	2.92373i
$213$	6.95287	−	18.1128i	0.476403	−	1.24107i
$214$	34.7961	−	3.65722i	2.37861	−	0.250002i
$215$	−0.631949	+	2.88367i	−0.0430985	+	0.196665i
$216$	26.4851	−	36.4536i	1.80208	−	2.48035i
$217$	−3.72541	+	0.332509i	−0.252897	+	0.0225722i
$218$	9.95905	+	9.95905i	0.674512	+	0.674512i
$219$	−3.96282	−	3.56814i	−0.267783	−	0.241113i
$220$	8.01927	−	48.6469i	0.540659	−	3.27977i
$221$	2.60354	+	2.89152i	0.175133	+	0.194505i
$222$	4.48827	+	2.91471i	0.301233	+	0.195623i
$223$	−3.79101	+	23.9355i	−0.253865	+	1.60284i	0.450348	+	0.892853i	$0.351300\pi$
$223$	−3.79101	+	23.9355i	−0.253865	+	1.60284i	−0.704214	+	0.709988i	$0.748700\pi$
$224$	32.5240	−	20.4025i	2.17310	−	1.36320i
$225$	1.14848	−	1.93260i	0.0765655	−	0.128840i
$226$	4.14470	+	7.17883i	0.275701	+	0.477529i
$227$	6.98614	−	8.62716i	0.463686	−	0.572605i	−0.490643	−	0.871361i	$-0.663238\pi$
$227$	6.98614	−	8.62716i	0.463686	−	0.572605i	0.954330	+	0.298756i	$0.0965715\pi$
$228$	1.39683	−	26.6531i	0.0925073	−	1.76514i
$229$	20.1173	−	4.27606i	1.32939	−	0.282570i	0.512162	−	0.858889i	$-0.328845\pi$
$229$	20.1173	−	4.27606i	1.32939	−	0.282570i	0.817225	+	0.576319i	$0.195511\pi$
$230$	−6.01760	+	21.9053i	−0.396789	+	1.44439i
$231$	17.2391	−	6.30876i	1.13425	−	0.415086i
$232$	−40.5334	+	40.5334i	−2.66115	+	2.66115i
$233$	27.5753	−	1.44516i	1.80652	−	0.0946754i	0.880937	−	0.473233i	$-0.156913\pi$
$233$	27.5753	−	1.44516i	1.80652	−	0.0946754i	0.925578	+	0.378558i	$0.123580\pi$
$234$	−3.80640	+	1.69472i	−0.248832	+	0.110787i
$235$	−0.116096	+	18.4353i	−0.00757327	+	1.20259i
$236$	24.1687	−	54.2839i	1.57325	−	3.53358i
$237$	−0.172704	−	1.09041i	−0.0112183	−	0.0708297i
$238$	−2.54575	+	7.43570i	−0.165017	+	0.481985i
$239$	−0.279352	−	0.384496i	−0.0180698	−	0.0248710i	0.799887	−	0.600151i	$-0.204893\pi$
$239$	−0.279352	−	0.384496i	−0.0180698	−	0.0248710i	−0.817956	+	0.575280i	$0.804893\pi$
$240$	37.9660	−	16.6179i	2.45070	−	1.07268i
$241$	0.659276	+	1.48076i	0.0424677	+	0.0953840i	0.933534	−	0.358490i	$-0.116708\pi$
$241$	0.659276	+	1.48076i	0.0424677	+	0.0953840i	−0.891066	+	0.453874i	$0.850042\pi$
$242$	−17.5697	+	11.4099i	−1.12942	+	0.733456i
$243$	−4.47328	−	1.19861i	−0.286961	−	0.0768910i
$244$	−4.16533	−	12.8196i	−0.266658	−	0.820689i
$245$	14.3910	+	6.15613i	0.919410	+	0.393301i
$246$	5.57147	−	17.1472i	0.355224	−	1.09327i
$247$	−6.24868	+	9.62213i	−0.397594	+	0.612241i
$248$	8.98586	+	7.27661i	0.570603	+	0.462065i
$249$	4.30493	+	2.48545i	0.272814	+	0.157509i
$250$	26.0306	−	14.3800i	1.64632	−	0.909474i
$251$		−	1.15026i		−	0.0726039i	−0.999341	−	0.0363020i	$-0.988442\pi$
$251$		−	1.15026i		−	0.0726039i	0.999341	−	0.0363020i	$-0.0115578\pi$
$252$	−4.82784	−	3.62479i	−0.304125	−	0.228340i
$253$	14.7855	−	7.53358i	0.929555	−	0.473632i
$254$	8.49600	+	39.9705i	0.533086	+	2.50797i
$255$	−1.83290	+	3.54195i	−0.114781	+	0.221805i
$256$	−0.874307	−	0.185840i	−0.0546442	−	0.0116150i
$257$	3.00155	−	11.2019i	0.187231	−	0.698757i	−0.806911	−	0.590674i	$-0.798862\pi$
$257$	3.00155	−	11.2019i	0.187231	−	0.698757i	0.994142	−	0.108083i	$-0.0344712\pi$
$258$	4.99681	+	2.54600i	0.311088	+	0.158507i
$259$	1.85910	−	2.76667i	0.115519	−	0.171912i
$260$	−39.2930	−	4.38020i	−2.43685	−	0.271649i
$261$	2.87869	+	1.28168i	0.178187	+	0.0793338i
$262$	−3.04933	−	1.17053i	−0.188388	−	0.0723156i
$263$	−17.3733	−	6.66898i	−1.07128	−	0.411227i	−0.242127	−	0.970245i	$-0.577845\pi$
$263$	−17.3733	−	6.66898i	−1.07128	−	0.411227i	−0.829156	+	0.559018i	$0.811178\pi$
$264$	−51.8439	−	23.0824i	−3.19077	−	1.42062i
$265$	−20.9773	+	11.9357i	−1.28862	+	0.733207i
$266$	−23.1212	−	1.57609i	−1.41765	−	0.0966362i
$267$	14.2050	+	7.23782i	0.869333	+	0.442947i
$268$	14.7110	−	54.9023i	0.898619	−	3.35369i
$269$	−25.9910	−	5.52456i	−1.58470	−	0.336838i	−0.670439	−	0.741964i	$-0.733894\pi$
$269$	−25.9910	−	5.52456i	−1.58470	−	0.336838i	−0.914261	+	0.405126i	$0.867228\pi$
$270$	−23.0226	−	23.3144i	−1.40111	−	1.41887i
$271$	−2.66564	−	12.5409i	−0.161926	−	0.761802i	−0.981900	−	0.189401i	$-0.939345\pi$
$271$	−2.66564	−	12.5409i	−0.161926	−	0.761802i	0.819974	−	0.572401i	$-0.193988\pi$
$272$	11.5486	−	5.88430i	0.700236	−	0.356788i
$273$	−5.77554	−	13.5403i	−0.349552	−	0.819497i
$274$			5.49678i			0.332073i
$275$	−20.5739	−	6.97254i	−1.24065	−	0.420460i
$276$	26.8082	+	15.4777i	1.61367	+	0.931650i
$277$	−3.80597	−	3.08201i	−0.228679	−	0.185180i	0.508133	−	0.861279i	$-0.330336\pi$
$277$	−3.80597	−	3.08201i	−0.228679	−	0.185180i	−0.736811	+	0.676099i	$0.763669\pi$
$278$	−29.1207	+	44.8419i	−1.74654	+	2.68944i
$279$	0.196416	−	0.604506i	0.0117591	−	0.0361908i
$280$	−18.7043	−	44.6274i	−1.11779	−	2.66700i
$281$	6.26329	+	19.2764i	0.373637	+	1.14994i	0.944394	+	0.328816i	$0.106650\pi$
$281$	6.26329	+	19.2764i	0.373637	+	1.14994i	−0.570757	+	0.821119i	$0.693350\pi$
$282$	33.8285	+	9.06433i	2.01446	+	0.539773i
$283$	−2.72189	+	1.76761i	−0.161799	+	0.105074i	−0.622999	−	0.782223i	$-0.714086\pi$
$283$	−2.72189	+	1.76761i	−0.161799	+	0.105074i	0.461200	+	0.887296i	$0.347419\pi$
$284$	25.0774	+	56.3247i	1.48807	+	3.34226i
$285$	−11.4870	−	2.51734i	−0.680430	−	0.149114i
$286$	23.6654	+	32.5726i	1.39936	+	1.92606i
$287$	−10.6243	−	3.63745i	−0.627135	−	0.214712i
$288$	1.02068	+	6.44431i	0.0601440	+	0.379734i
$289$	6.40722	−	14.3908i	0.376895	−	0.846520i
$290$	24.2883	+	33.8766i	1.42626	+	1.98930i
$291$	−2.64383	+	1.17711i	−0.154984	+	0.0690034i
$292$	16.9227	−	0.886881i	0.990326	−	0.0519008i
$293$	15.0886	−	15.0886i	0.881488	−	0.881488i	−0.112198	−	0.993686i	$-0.535789\pi$
$293$	15.0886	−	15.0886i	0.881488	−	0.881488i	0.993686	+	0.112198i	$0.0357891\pi$
$294$	18.2243	−	23.4953i	1.06286	−	1.37027i
$295$	−21.8672	−	14.3973i	−1.27316	−	0.838243i
$296$	−10.0794	+	2.14244i	−0.585854	+	0.124527i
$297$	−1.25265	+	23.9020i	−0.0726861	+	1.38693i
$298$	30.9231	−	38.1868i	1.79133	−	2.21210i
$299$	−6.65340	−	11.5240i	−0.384776	−	0.666452i
$300$	−9.99448	−	39.2719i	−0.577032	−	2.26736i
$301$	1.63445	−	3.08698i	0.0942079	−	0.177931i
$302$	5.75576	−	36.3404i	0.331207	−	2.09116i
$303$	13.2483	+	8.60356i	0.761096	+	0.494262i
$304$	25.5732	+	28.4019i	1.46672	+	1.62896i
$305$	−5.87165	+	0.892111i	−0.336210	+	0.0510821i
$306$	−0.992570	−	0.893714i	−0.0567414	−	0.0510902i
$307$	14.5065	+	14.5065i	0.827930	+	0.827930i	0.987230	−	0.159300i	$-0.0509239\pi$
$307$	14.5065	+	14.5065i	0.827930	+	0.827930i	−0.159300	+	0.987230i	$0.550924\pi$
$308$	−24.5615	+	52.9141i	−1.39952	+	3.01506i
$309$	2.11523	−	2.91136i	0.120331	−	0.165621i
$310$	6.28372	−	5.58664i	0.356891	−	0.317300i
$311$	9.08931	−	0.955325i	0.515408	−	0.0541715i	0.156746	−	0.987639i	$-0.449900\pi$
$311$	9.08931	−	0.955325i	0.515408	−	0.0541715i	0.358662	+	0.933467i	$0.383233\pi$
$312$	−16.3086	+	42.4853i	−0.923291	+	2.40526i
$313$	4.42649	+	5.46626i	0.250200	+	0.308971i	0.886736	−	0.462275i	$-0.152967\pi$
$313$	4.42649	+	5.46626i	0.250200	+	0.308971i	−0.636536	+	0.771247i	$0.719633\pi$
$314$	22.7308	−	16.5149i	1.28277	−	0.931987i
$315$	−1.92182	+	1.83907i	−0.108282	+	0.103620i
$316$	2.83832	+	2.06216i	0.159668	+	0.116006i
$317$	−1.24258	−	23.7098i	−0.0697900	−	1.33167i	−0.779155	−	0.626831i	$-0.784352\pi$
$317$	−1.24258	−	23.7098i	−0.0697900	−	1.33167i	0.709365	−	0.704841i	$-0.248982\pi$
$318$	11.8666	+	44.2869i	0.665448	+	2.48349i
$319$	6.33073	−	29.7838i	0.354453	−	1.66757i
$320$	−12.5325	+	32.0438i	−0.700591	+	1.79130i
$321$	−19.9784	−	6.49139i	−1.11509	−	0.362314i
$322$	13.8033	−	23.0639i	0.769225	−	1.28530i
$323$	−3.63248	−	0.575328i	−0.202116	−	0.0320121i
$324$	−32.7389	+	18.9018i	−1.81883	+	1.05010i
$325$	−4.72016	+	16.7682i	−0.261827	+	0.930132i
$326$	−0.575943	+	0.997562i	−0.0318985	+	0.0552499i
$327$	−3.03041	−	7.89448i	−0.167582	−	0.436566i
$328$	15.7608	+	30.9323i	0.870243	+	1.70795i
$329$	5.97583	−	20.9789i	0.329458	−	1.15660i
$330$	−22.6933	+	34.4675i	−1.24923	+	1.89737i
$331$	−4.68293	+	5.20092i	−0.257397	+	0.285869i	−0.857968	−	0.513703i	$-0.828273\pi$
$331$	−4.68293	+	5.20092i	−0.257397	+	0.285869i	0.600571	+	0.799572i	$0.294940\pi$
$332$	−15.2586	+	4.08852i	−0.837423	+	0.224387i
$333$	0.308515	+	0.475071i	0.0169065	+	0.0260337i
$334$	4.12983	−	39.2927i	0.225974	−	2.15000i
$335$	−22.8138	−	10.3300i	−1.24645	−	0.564388i
$336$	−48.5475	+	6.90966i	−2.64848	+	0.376953i
$337$	6.25421	−	0.990569i	0.340688	−	0.0539597i	0.0162539	−	0.999868i	$-0.494826\pi$
$337$	6.25421	−	0.990569i	0.340688	−	0.0539597i	0.324435	+	0.945908i	$0.394826\pi$
$338$	−1.78167	+	1.44277i	−0.0969103	+	0.0784764i
$339$	−0.520231	−	4.94967i	−0.0282551	−	0.268829i
$340$	−3.84037	−	12.0777i	−0.208274	−	0.655007i
$341$	−6.10827	−	0.642005i	−0.330781	−	0.0347665i
$342$	1.78797	−	3.50909i	0.0966824	−	0.189750i
$343$	−14.4540	−	11.5794i	−0.780443	−	0.625227i
$344$	−10.2698	+	3.33686i	−0.553710	+	0.179911i
$345$	8.64995	−	10.5453i	0.465698	−	0.567741i
$346$	−19.5566	+	17.6089i	−1.05137	+	0.946659i
$347$	7.97978	+	0.418203i	0.428377	+	0.0224503i	0.265307	−	0.964164i	$-0.414527\pi$
$347$	7.97978	+	0.418203i	0.428377	+	0.0224503i	0.163071	+	0.986614i	$0.447860\pi$
$348$	53.0286	−	20.3558i	2.84263	−	1.09118i
$349$	0.150068			0.00803295			0.00401647	−	0.999992i	$-0.498722\pi$
$349$	0.150068			0.00803295			0.00401647	+	0.999992i	$0.498722\pi$
$350$	−34.2321	+	8.14182i	−1.82978	+	0.435199i
$351$	19.1933			1.02446
$352$	58.8597	−	22.5941i	3.13723	−	1.20427i
$353$	−15.7183	−	0.823760i	−0.836600	−	0.0438443i	−0.370777	−	0.928722i	$-0.620908\pi$
$353$	−15.7183	−	0.823760i	−0.836600	−	0.0438443i	−0.465823	+	0.884878i	$0.654242\pi$
$354$	−36.9610	+	33.2798i	−1.96445	+	1.76880i
$355$	26.2836	−	6.86556i	1.39499	−	0.364386i
$356$	−48.1838	+	15.6559i	−2.55374	+	0.829760i
$357$	3.21215	−	3.45673i	0.170005	−	0.182950i
$358$	1.39734	−	2.74244i	0.0738519	−	0.144942i
$359$	−17.0677	−	1.79389i	−0.900798	−	0.0946777i	−0.357204	−	0.934026i	$-0.616270\pi$
$359$	−17.0677	−	1.79389i	−0.900798	−	0.0946777i	−0.543594	+	0.839349i	$0.682937\pi$
$360$	8.22302	+	0.0517844i	0.433391	+	0.00272928i
$361$	0.852483	+	8.11084i	0.0448675	+	0.426886i
$362$	32.4686	−	26.2925i	1.70651	−	1.38190i
$363$	12.4232	−	1.96764i	0.652047	−	0.103274i
$364$	43.4043	+	17.4481i	2.27501	+	0.914529i
$365$	0.827201	−	7.42048i	0.0432977	−	0.388406i
$366$	−1.17932	+	11.2205i	−0.0616440	+	0.586503i
$367$	−8.47789	−	13.0548i	−0.442542	−	0.681456i	0.545066	−	0.838393i	$-0.316505\pi$
$367$	−8.47789	−	13.0548i	−0.442542	−	0.681456i	−0.987609	+	0.156938i	$0.949838\pi$
$368$	−42.8166	+	11.4727i	−2.23197	+	0.598055i
$369$	1.27696	−	1.41821i	0.0664761	−	0.0738292i
$370$	0.345035	+	7.48529i	0.0179375	+	0.389142i
$371$	27.6967	−	6.95714i	1.43794	−	0.361197i
$372$	−5.20156	−	10.2086i	−0.269688	−	0.529293i
$373$	5.50704	+	14.3463i	0.285144	+	0.742825i	0.999091	+	0.0426256i	$0.0135723\pi$
$373$	5.50704	+	14.3463i	0.285144	+	0.742825i	−0.713947	+	0.700199i	$0.753094\pi$
$374$	−6.45309	+	11.1771i	−0.333681	+	0.577953i
$375$	−17.7892	+	1.53056i	−0.918629	+	0.0790379i
$376$	−58.4001	+	33.7173i	−3.01176	+	1.73884i
$377$	−24.1165	−	3.81968i	−1.24206	−	0.196724i
$378$	18.8550	+	33.8753i	0.969798	+	1.74236i
$379$	−18.8555	−	6.12653i	−0.968543	−	0.314699i	−0.218315	−	0.975878i	$-0.570056\pi$
$379$	−18.8555	−	6.12653i	−0.968543	−	0.314699i	−0.750228	+	0.661180i	$0.770056\pi$
$380$	31.4689	−	20.1555i	1.61432	−	1.03396i
$381$	5.10098	−	23.9982i	0.261331	−	1.22947i
$382$	1.75076	+	6.53392i	0.0895766	+	0.334304i
$383$	1.31296	+	25.0527i	0.0670890	+	1.28013i	0.800079	+	0.599895i	$0.204791\pi$
$383$	1.31296	+	25.0527i	0.0670890	+	1.28013i	−0.732990	+	0.680240i	$0.761876\pi$
$384$	15.3825	+	11.1761i	0.784986	+	0.570326i
$385$	21.2435	+	14.4698i	1.08267	+	0.737452i
$386$	−31.9195	+	23.1908i	−1.62466	+	1.18038i
$387$	0.373563	+	0.461312i	0.0189893	+	0.0234498i
$388$	3.29584	−	8.58597i	0.167321	−	0.435886i
$389$	−16.8814	+	1.77431i	−0.855922	+	0.0899610i	−0.522316	−	0.852752i	$-0.674932\pi$
$389$	−16.8814	+	1.77431i	−0.855922	+	0.0899610i	−0.333605	+	0.942713i	$0.608265\pi$
$390$	28.5539	+	16.7263i	1.44589	+	0.846967i
$391$	2.50724	−	3.45092i	0.126796	−	0.174520i
$392$	7.17661	+	56.8026i	0.362474	+	2.86897i
$393$	1.38668	+	1.38668i	0.0699489	+	0.0699489i
$394$	−3.36444	−	3.02936i	−0.169498	−	0.152617i
$395$	1.09990	−	1.08614i	0.0553422	−	0.0546496i
$396$	−6.63360	−	7.36736i	−0.333351	−	0.370224i
$397$	−19.1858	−	12.4594i	−0.962907	−	0.625319i	−0.0354988	−	0.999370i	$-0.511302\pi$
$397$	−19.1858	−	12.4594i	−0.962907	−	0.625319i	−0.927408	+	0.374051i	$0.877969\pi$
$398$	1.55680	−	9.82923i	0.0780351	−	0.492695i
$399$	12.2969	+	6.51075i	0.615614	+	0.325945i
$400$	49.8846	+	29.6448i	2.49423	+	1.48224i
$401$	−7.39250	−	12.8042i	−0.369164	−	0.639410i	0.620271	−	0.784387i	$-0.287023\pi$
$401$	−7.39250	−	12.8042i	−0.369164	−	0.639410i	−0.989435	+	0.144977i	$0.953689\pi$
$402$	−29.9397	+	36.9725i	−1.49326	+	1.84402i
$403$	−0.257765	+	4.91844i	−0.0128402	+	0.245005i
$404$	−49.1030	+	10.4372i	−2.44296	+	0.519268i
$405$	5.87109	+	15.5874i	0.291737	+	0.774544i
$406$	−16.9499	−	46.3169i	−0.841212	−	2.29867i
$407$	3.87046	−	3.87046i	0.191851	−	0.191851i
$408$	−14.5678	+	0.763467i	−0.721214	+	0.0377972i
$409$	20.1025	−	8.95022i	0.994006	−	0.442560i	0.155726	−	0.987800i	$-0.450228\pi$
$409$	20.1025	−	8.95022i	0.994006	−	0.442560i	0.838280	+	0.545240i	$0.183562\pi$
$410$	24.0578	−	7.64969i	1.18813	−	0.377791i
$411$	1.34233	−	3.01493i	0.0662125	−	0.148716i
$412$	1.78898	+	11.2952i	0.0881366	+	0.556472i
$413$	20.3643	+	23.3438i	1.00206	+	1.14867i
$414$	2.68489	+	3.69544i	0.131955	+	0.181621i
$415$	0.683929	+	6.92646i	0.0335727	+	0.340007i
$416$	−20.5636	−	46.1866i	−1.00821	−	2.26448i
$417$	26.9230	−	17.4840i	1.31842	−	0.856194i
$418$	−36.7593	−	9.84963i	−1.79796	−	0.481761i
$419$	2.95836	+	9.10490i	0.144525	+	0.444803i	0.996950	−	0.0780473i	$-0.0248685\pi$
$419$	2.95836	+	9.10490i	0.144525	+	0.444803i	−0.852424	+	0.522851i	$0.824869\pi$
$420$	−1.05471	+	47.9367i	−0.0514647	+	2.33907i
$421$	1.12621	−	3.46612i	0.0548881	−	0.168928i	−0.919854	−	0.392260i	$-0.871693\pi$
$421$	1.12621	−	3.46612i	0.0548881	−	0.168928i	0.974742	+	0.223332i	$0.0716933\pi$
$422$	−16.5307	+	25.4550i	−0.804702	+	1.23913i
$423$	2.88086	+	2.33288i	0.140072	+	0.113428i
$424$	−76.4550	−	44.1413i	−3.71298	−	2.14369i
$425$	−5.52585	+	0.804004i	−0.268043	+	0.0389999i
$426$		−	51.6058i		−	2.50031i
$427$	6.97627	+	0.844174i	0.337605	+	0.0408524i
$428$	59.4799	−	30.3065i	2.87507	−	1.46492i
$429$	−5.02588	−	23.6449i	−0.242652	−	1.14159i
$430$	1.17950	+	7.76317i	0.0568806	+	0.374373i
$431$	35.5765	+	7.56203i	1.71366	+	0.364250i	0.957119	−	0.289695i	$-0.0935537\pi$
$431$	35.5765	+	7.56203i	1.71366	+	0.364250i	0.756542	+	0.653945i	$0.226887\pi$
$432$	16.5478	−	61.7572i	0.796156	−	2.97129i
$433$	−18.5582	−	9.45585i	−0.891848	−	0.454419i	−0.0528804	−	0.998601i	$-0.516840\pi$
$433$	−18.5582	−	9.45585i	−0.891848	−	0.454419i	−0.838967	+	0.544182i	$0.816840\pi$
$434$	−8.93406	+	4.37682i	−0.428848	+	0.210094i
$435$	−5.04912	−	24.5123i	−0.242087	−	1.17527i
$436$	24.5491	+	10.9300i	1.17569	+	0.523451i
$437$	11.7423	+	4.50746i	0.561713	+	0.215621i
$438$	−13.2418	−	5.08304i	−0.632716	−	0.242877i
$439$	24.4942	+	10.9055i	1.16905	+	0.520493i	0.897103	−	0.441821i	$-0.145667\pi$
$439$	24.4942	+	10.9055i	1.16905	+	0.520493i	0.271943	+	0.962313i	$0.412334\pi$
$440$	−16.0309	−	77.8264i	−0.764245	−	3.71023i
$441$	2.77374	−	1.48732i	0.132083	−	0.0708246i
$442$	9.22142	+	4.69855i	0.438618	+	0.223487i
$443$	−6.84732	+	25.5545i	−0.325326	+	1.21413i	0.588658	+	0.808382i	$0.299657\pi$
$443$	−6.84732	+	25.5545i	−0.325326	+	1.21413i	−0.913984	+	0.405751i	$0.867010\pi$
$444$	9.98768	+	2.12295i	0.473994	+	0.100751i
$445$	3.35310	+	22.0693i	0.158952	+	1.04618i
$446$	13.4019	+	63.0508i	0.634597	+	2.98554i
$447$	−26.2864	+	13.3936i	−1.24330	+	0.633494i
$448$	24.4437	−	32.5564i	1.15486	−	1.53815i
$449$		−	13.0427i		−	0.615523i	−0.951463	−	0.307762i	$-0.900420\pi$
$449$		−	13.0427i		−	0.615523i	0.951463	−	0.307762i	$-0.0995799\pi$
$450$	1.00974	−	5.89383i	0.0475996	−	0.277838i
$451$	−15.9701	−	9.22035i	−0.752004	−	0.434170i
$452$	12.2913	+	9.95332i	0.578135	+	0.468165i
$453$	−12.0314	+	18.5268i	−0.565286	+	0.870465i
$454$	9.12454	−	28.0825i	0.428236	−	1.31798i
$455$	10.6959	−	17.6191i	0.501431	−	0.825994i
$456$	−13.2922	−	40.9093i	−0.622467	−	1.91576i
$457$	−21.8433	−	5.85290i	−1.02179	−	0.273787i	−0.291241	−	0.956650i	$-0.594068\pi$
$457$	−21.8433	−	5.85290i	−1.02179	−	0.273787i	−0.730547	+	0.682863i	$0.760735\pi$
$458$	45.8796	−	29.7946i	2.14381	−	1.39221i
$459$	2.50245	+	5.62059i	0.116804	+	0.262347i
$460$	4.25905	+	43.1334i	0.198579	+	2.01110i
$461$	22.7733	+	31.3447i	1.06066	+	1.45987i	0.879190	+	0.476470i	$0.158084\pi$
$461$	22.7733	+	31.3447i	1.06066	+	1.45987i	0.181466	+	0.983397i	$0.441916\pi$
$462$	36.7949	−	32.0987i	1.71185	−	1.49337i
$463$	−6.18068	−	39.0233i	−0.287240	−	1.81356i	−0.535122	−	0.844775i	$-0.679735\pi$
$463$	−6.18068	−	39.0233i	−0.287240	−	1.81356i	0.247882	−	0.968790i	$-0.420265\pi$
$464$	−33.0828	+	74.3052i	−1.53583	+	3.44953i
$465$	−4.81084	+	1.52971i	−0.223097	+	0.0709386i
$466$	67.0979	−	29.8739i	3.10825	−	1.38388i
$467$	−28.9027	+	1.51473i	−1.33746	+	0.0700932i	−0.707597	−	0.706616i	$-0.750221\pi$
$467$	−28.9027	+	1.51473i	−1.33746	+	0.0700932i	−0.629860	+	0.776709i	$0.716888\pi$
$468$	−5.62138	+	5.62138i	−0.259848	+	0.259848i
$469$	22.7327	+	19.0072i	1.04970	+	0.877671i
$470$	17.2846	+	45.8896i	0.797278	+	2.11673i
$471$	−16.5006	+	3.50731i	−0.760307	+	0.161608i
$472$	5.01203	−	95.6352i	0.230697	−	4.40197i
$473$	3.60972	−	4.45764i	0.165975	−	0.204962i
$474$	−1.46826	−	2.54310i	−0.0674394	−	0.116809i
$475$	−6.50714	−	15.1251i	−0.298568	−	0.693988i
$476$	0.549595	+	14.9855i	0.0251906	+	0.686860i
$477$	−0.759179	+	4.79327i	−0.0347604	+	0.219469i
$478$	−1.06020	−	0.688503i	−0.0484925	−	0.0314914i
$479$	21.7197	+	24.1221i	0.992398	+	1.10217i	0.994767	+	0.102172i	$0.0325792\pi$
$479$	21.7197	+	24.1221i	0.992398	+	1.10217i	−0.00236919	+	0.999997i	$0.500754\pi$
$480$	36.8723	−	36.4108i	1.68298	−	1.66192i
$481$	−3.26190	−	2.93702i	−0.148730	−	0.133917i
$482$	3.04861	+	3.04861i	0.138861	+	0.138861i
$483$	−13.2032	+	9.27953i	−0.600769	+	0.422233i
$484$	−23.4944	+	32.3373i	−1.06793	+	1.46988i
$485$	−3.49644	−	2.04814i	−0.158765	−	0.0930011i
$486$	−12.2507	+	1.28760i	−0.555702	+	0.0584067i
$487$	−0.872054	+	2.27178i	−0.0395166	+	0.102944i	−0.951919	−	0.306351i	$-0.900892\pi$
$487$	−0.872054	+	2.27178i	−0.0395166	+	0.102944i	0.912402	+	0.409295i	$0.134225\pi$
$488$	−13.6714	−	16.8827i	−0.618873	−	0.764245i
$489$	0.559508	−	0.406506i	0.0253018	−	0.0183828i
$490$	41.6043	+	1.56922i	1.87949	+	0.0708901i
$491$	−7.70103	−	5.59512i	−0.347543	−	0.252504i	0.400295	−	0.916386i	$-0.368908\pi$
$491$	−7.70103	−	5.59512i	−0.347543	−	0.252504i	−0.747837	+	0.663882i	$0.768908\pi$
$492$	−1.80037	−	34.3530i	−0.0811668	−	1.54875i
$493$	−2.02579	−	7.56034i	−0.0912369	−	0.340501i
$494$	−6.34486	+	29.8502i	−0.285469	+	1.34302i
$495$	−3.67826	+	2.35589i	−0.165325	+	0.105889i
$496$	15.6036	+	5.06991i	0.700622	+	0.227646i
$497$	−32.1387	−	0.504659i	−1.44162	−	0.0226370i
$498$	13.0593	+	2.06839i	0.585200	+	0.0926866i
$499$	−16.4913	+	9.52128i	−0.738254	+	0.426231i	−0.821434	−	0.570303i	$-0.806826\pi$
$499$	−16.4913	+	9.52128i	−0.738254	+	0.426231i	0.0831803	+	0.996535i	$0.473492\pi$
$500$	36.5345	−	43.4131i	1.63387	−	1.94149i
$501$	−11.8606	+	20.5432i	−0.529893	+	0.917801i
$502$	−1.09645	−	2.85635i	−0.0489370	−	0.127485i
$503$	7.08444	+	13.9040i	0.315880	+	0.619949i	0.993289	−	0.115657i	$-0.0368974\pi$
$503$	7.08444	+	13.9040i	0.315880	+	0.619949i	−0.677409	+	0.735606i	$0.736897\pi$
$504$	−9.35757	−	2.66551i	−0.416820	−	0.118731i
$505$	1.01846	+	22.0948i	0.0453210	+	0.983208i
$506$	29.5344	−	32.8013i	1.31297	−	1.45820i
$507$	1.32956	−	0.356255i	0.0590479	−	0.0158218i
$508$	42.4637	+	65.3883i	1.88402	+	2.90114i
$509$	−4.05994	+	38.6278i	−0.179954	+	1.71214i	0.416199	+	0.909274i	$0.363362\pi$
$509$	−4.05994	+	38.6278i	−0.179954	+	1.71214i	−0.596152	+	0.802871i	$0.703305\pi$
$510$	−1.17524	+	10.5426i	−0.0520405	+	0.466834i
$511$	−3.29507	+	8.19691i	−0.145765	+	0.362610i
$512$	21.1707	−	3.35311i	0.935621	−	0.148188i
$513$	−14.0988	+	11.4169i	−0.622475	+	0.504071i
$514$	−3.22438	−	30.6780i	−0.142221	−	1.35315i
$515$	5.03863	+	0.0317307i	0.222028	+	0.00139822i
$516$	10.6414	+	1.11846i	0.468462	+	0.0492374i
$517$	16.2621	−	31.9162i	0.715206	−	1.40367i
$518$	1.97931	−	8.64237i	0.0869657	−	0.379724i
$519$	15.0268	−	4.88250i	0.659603	−	0.214318i
$520$	−61.6505	+	16.1038i	−2.70355	+	0.706198i
$521$	−23.5910	+	21.2415i	−1.03354	+	0.930605i	−0.997634	−	0.0687502i	$-0.978099\pi$
$521$	−23.5910	+	21.2415i	−1.03354	+	0.930605i	−0.0359076	+	0.999355i	$0.511432\pi$
$522$	8.37015	+	0.438661i	0.366351	+	0.0191997i
$523$	−3.62732	+	1.39240i	−0.158612	+	0.0608853i	−0.436378	−	0.899763i	$-0.643739\pi$
$523$	−3.62732	+	1.39240i	−0.158612	+	0.0608853i	0.277767	+	0.960649i	$0.410406\pi$
$524$	−6.23198			−0.272245
$525$	20.7642	+	3.89389i	0.906226	+	0.169943i
$526$	−49.4987			−2.15825
$527$	−1.47393	+	0.565790i	−0.0642056	+	0.0246462i
$528$	−80.4142	−	4.21433i	−3.49958	−	0.183405i
$529$	6.25130	−	5.62869i	0.271795	−	0.244726i
$530$	−40.7138	+	49.6350i	−1.76850	+	2.15601i
$531$	−5.00676	+	1.62679i	−0.217275	+	0.0705969i
$532$	−42.2623	+	13.0019i	−1.83230	+	0.563703i
$533$	−6.71342	+	13.1758i	−0.290790	+	0.570708i
$534$	42.1734	+	4.43260i	1.82502	+	0.191818i
$535$	−8.91274	−	28.0300i	−0.385331	−	1.21184i
$536$	−9.57534	−	91.1032i	−0.413592	−	3.93506i
$537$	−1.43614	+	1.16297i	−0.0619742	+	0.0501857i
$538$	−69.8075	+	11.0564i	−3.00962	+	0.476676i
$539$	−19.6304	−	23.2288i	−0.845540	−	1.00053i
$540$	−56.9505	−	25.7869i	−2.45076	−	1.10969i
$541$	−1.74839	+	16.6348i	−0.0751691	+	0.715187i	0.890424	+	0.455131i	$0.150408\pi$
$541$	−1.74839	+	16.6348i	−0.0751691	+	0.715187i	−0.965594	+	0.260056i	$0.916259\pi$
$542$	−18.5735	−	28.6007i	−0.797802	−	1.22851i
$543$	−24.2294	+	6.49226i	−1.03978	+	0.278609i
$544$	10.8442	−	12.0438i	0.464943	−	0.516372i
$545$	6.51097	−	9.88912i	0.278899	−	0.423603i
$546$	−27.2488	−	28.1182i	−1.16614	−	1.20335i
$547$	−2.84903	−	5.59154i	−0.121816	−	0.239077i	0.822044	−	0.569425i	$-0.192834\pi$
$547$	−2.84903	−	5.59154i	−0.121816	−	0.239077i	−0.943859	+	0.330348i	$0.892834\pi$
$548$	3.75847	+	9.79114i	0.160554	+	0.418257i
$549$	−0.597100	+	1.03421i	−0.0254836	+	0.0441389i
$550$	−57.7359	+	2.29708i	−2.46187	+	0.0979479i
$551$	19.9873	−	11.5397i	0.851488	−	0.491607i
$552$	49.2754	+	7.80446i	2.09730	+	0.332180i
$553$	−1.59813	+	0.889524i	−0.0679595	+	0.0378264i
$554$	−12.3889	−	4.02539i	−0.526354	−	0.171023i
$555$	1.63869	−	4.18987i	0.0695585	−	0.177850i
$556$	−21.2102	+	99.7861i	−0.899512	+	4.23187i
$557$	−2.80497	−	10.4683i	−0.118850	−	0.443555i	0.880696	−	0.473682i	$-0.157075\pi$
$557$	−2.80497	−	10.4683i	−0.118850	−	0.443555i	−0.999546	+	0.0301270i	$0.990409\pi$
$558$	−0.0884825	−	1.68835i	−0.00374576	−	0.0714734i
$559$	−3.72117	−	2.70359i	−0.157389	−	0.114350i
$560$	−47.4703	−	49.6062i	−2.00599	−	2.09624i
$561$	6.26894	−	4.55465i	0.264675	−	0.192298i
$562$	33.9278	+	41.8973i	1.43116	+	1.76733i
$563$	−11.6296	+	30.2962i	−0.490130	+	1.27683i	0.436108	+	0.899894i	$0.356357\pi$
$563$	−11.6296	+	30.2962i	−0.490130	+	1.27683i	−0.926238	+	0.376938i	$0.876977\pi$
$564$	66.4549	−	6.98469i	2.79826	−	0.294109i
$565$	5.20793	−	4.63019i	0.219099	−	0.194794i
$566$	−5.07412	+	6.98393i	−0.213281	+	0.293556i
$567$	−1.75207	−	19.6301i	−0.0735802	−	0.824387i
$568$	70.2630	+	70.2630i	2.94817	+	2.94817i
$569$	8.39615	+	7.55992i	0.351985	+	0.316928i	0.826088	−	0.563541i	$-0.190561\pi$
$569$	8.39615	+	7.55992i	0.351985	+	0.316928i	−0.474104	+	0.880469i	$0.657228\pi$
$570$	−30.9243	+	4.69849i	−1.29528	+	0.196798i
$571$	16.6756	+	18.5201i	0.697851	+	0.775042i	0.983033	−	0.183431i	$-0.0587205\pi$
$571$	16.6756	+	18.5201i	0.697851	+	0.775042i	−0.285181	+	0.958474i	$0.592054\pi$
$572$	64.4257	+	41.8385i	2.69377	+	1.74936i
$573$	0.635333	−	4.01133i	0.0265414	−	0.167576i
$574$	−29.8499	+	1.09475i	−1.24591	+	0.0456938i
$575$	19.0569	+	1.23958i	0.794727	+	0.0516940i
$576$	3.45926	+	5.99161i	0.144136	+	0.249650i
$577$	−7.95269	+	9.82076i	−0.331075	+	0.408844i	−0.915316	−	0.402737i	$-0.868059\pi$
$577$	−7.95269	+	9.82076i	−0.331075	+	0.408844i	0.584241	+	0.811580i	$0.301392\pi$
$578$	2.19290	−	41.8431i	0.0912128	−	1.74044i
$579$	23.1708	−	4.92511i	0.962946	−	0.204681i
$580$	66.4269	+	43.7353i	2.75823	+	1.81601i
$581$	1.41584	−	8.11274i	0.0587391	−	0.336573i
$582$	−5.44317	+	5.44317i	−0.225627	+	0.225627i
$583$	46.8302	−	2.45427i	1.93951	−	0.101645i
$584$	24.9499	−	11.1084i	1.03243	−	0.459668i
$585$	2.04096	+	2.84667i	0.0843835	+	0.117695i
$586$	23.0856	−	51.8512i	0.953659	−	2.14195i
$587$	2.46271	+	15.5490i	0.101647	+	0.641775i	0.984933	+	0.172939i	$0.0553263\pi$
$587$	2.46271	+	15.5490i	0.101647	+	0.641775i	−0.883285	+	0.468836i	$0.844674\pi$
$588$	16.3970	−	54.3120i	0.676199	−	2.23979i
$589$	−2.73635	−	3.76626i	−0.112749	−	0.155186i
$590$	−68.0247	−	14.9074i	−2.80053	−	0.613730i
$591$	1.10558	+	2.48318i	0.0454777	+	0.102145i
$592$	−12.2626	+	7.96343i	−0.503990	+	0.327295i
$593$	40.5367	+	10.8618i	1.66464	+	0.446040i	0.963659	−	0.267135i	$-0.0860771\pi$
$593$	40.5367	+	10.8618i	1.66464	+	0.446040i	0.700986	+	0.713175i	$0.252744\pi$
$594$	19.6732	+	60.5479i	0.807202	+	2.48431i
$595$	6.55415	+	0.835005i	0.268694	+	0.0342319i
$596$	28.9712	−	89.1641i	1.18671	−	3.65231i
$597$	−3.25422	+	5.01106i	−0.133186	+	0.205089i
$598$	−27.5068	−	22.2746i	−1.12484	−	0.910874i
$599$	−33.2602	−	19.2028i	−1.35898	−	0.784606i	−0.369491	−	0.929234i	$-0.620468\pi$
$599$	−33.2602	−	19.2028i	−1.35898	−	0.784606i	−0.989486	+	0.144629i	$0.953801\pi$
$600$	−37.7199	−	53.3164i	−1.53991	−	2.17663i
$601$		−	29.1068i		−	1.18729i	−0.804726	−	0.593646i	$-0.797688\pi$
$601$		−	29.1068i		−	1.18729i	0.804726	−	0.593646i	$-0.202312\pi$
$602$	1.11612	−	9.22364i	0.0454897	−	0.375927i
$603$	−4.48681	+	2.28614i	−0.182717	+	0.0930989i
$604$	−14.5956	−	68.6669i	−0.593886	−	2.79402i
$605$	12.3745	+	12.5313i	0.503095	+	0.509472i
$606$	41.0996	+	8.73598i	1.66956	+	0.354875i
$607$	−6.03345	+	22.5172i	−0.244890	+	0.913943i	0.728548	+	0.684995i	$0.240195\pi$
$607$	−6.03345	+	22.5172i	−0.244890	+	0.913943i	−0.973438	+	0.228949i	$0.926471\pi$
$608$	42.5790	+	21.6951i	1.72681	+	0.879852i
$609$	−2.01388	+	29.5436i	−0.0816067	+	1.19717i
$610$	−13.7302	+	7.81227i	−0.555920	+	0.316310i
$611$	−26.2409	−	11.6832i	−1.06159	−	0.472652i
$612$	−2.37910	−	0.913250i	−0.0961694	−	0.0369160i
$613$	32.4858	+	12.4701i	1.31209	+	0.503664i	0.911012	−	0.412381i	$-0.135303\pi$
$613$	32.4858	+	12.4701i	1.31209	+	0.503664i	0.401077	+	0.916044i	$0.368636\pi$
$614$	49.8507	+	22.1950i	2.01181	+	0.895716i
$615$	−15.0636	−	1.67922i	−0.607421	−	0.0677126i
$616$	−6.39408	+	93.8010i	−0.257625	+	3.77935i
$617$	−13.1594	−	6.70505i	−0.529777	−	0.269935i	0.168575	−	0.985689i	$-0.446083\pi$
$617$	−13.1594	−	6.70505i	−0.529777	−	0.269935i	−0.698353	+	0.715754i	$0.746083\pi$
$618$	2.47741	−	9.24582i	0.0996560	−	0.371921i
$619$	19.5416	+	4.15370i	0.785444	+	0.166951i	0.583140	−	0.812371i	$-0.301824\pi$
$619$	19.5416	+	4.15370i	0.785444	+	0.166951i	0.202304	+	0.979323i	$0.435157\pi$
$620$	7.37297	−	14.2477i	0.296106	−	0.572203i
$621$	−4.37473	−	20.5815i	−0.175552	−	0.825907i
$622$	21.6601	−	11.0364i	0.868492	−	0.442519i
$623$	3.17292	−	26.2211i	0.127121	−	1.05053i
$624$			64.5725i			2.58497i
$625$	−16.2550	−	18.9941i	−0.650201	−	0.759762i
$626$	16.2025	+	9.35452i	0.647582	+	0.373882i
$627$	17.7568	+	14.3792i	0.709139	+	0.574250i
$628$	29.1970	−	44.9594i	1.16509	−	1.79408i
$629$	0.434793	−	1.33815i	0.0173363	−	0.0533557i
$630$	−3.01926	+	6.39872i	−0.120290	+	0.254931i
$631$	−11.4151	−	35.1322i	−0.454430	−	1.39859i	−0.871803	−	0.489856i	$-0.837049\pi$
$631$	−11.4151	−	35.1322i	−0.454430	−	1.39859i	0.417373	−	0.908735i	$-0.362951\pi$
$632$	5.46161	+	1.46343i	0.217251	+	0.0582122i
$633$	15.2831	−	9.92499i	0.607451	−	0.394483i
$634$	−25.6862	−	57.6921i	−1.02013	−	2.29124i
$635$	31.4698	−	13.7745i	1.24884	−	0.546623i
$636$	51.4190	+	70.7722i	2.03890	+	2.80630i
$637$	−17.7777	+	16.6949i	−0.704380	+	0.661474i
$638$	−12.6698	−	79.9942i	−0.501604	−	3.16700i
$639$	2.22173	−	4.99009i	0.0878904	−	0.197405i
$640$	−0.167653	+	26.6222i	−0.00662706	+	1.05233i
$641$	−32.7423	+	14.5778i	−1.29324	+	0.575789i	−0.933939	−	0.357431i	$-0.883653\pi$
$641$	−32.7423	+	14.5778i	−1.29324	+	0.575789i	−0.359304	+	0.933220i	$0.616986\pi$
$642$	−55.7985	+	2.92428i	−2.20219	+	0.115412i
$643$	−13.0287	+	13.0287i	−0.513801	+	0.513801i	−0.915689	−	0.401888i	$-0.868354\pi$
$643$	−13.0287	+	13.0287i	−0.513801	+	0.513801i	0.401888	+	0.915689i	$0.368354\pi$
$644$	8.81692	−	50.5207i	0.347435	−	1.99079i
$645$	1.24885	−	4.54606i	0.0491734	−	0.179001i
$646$	−9.56865	+	2.03388i	−0.376473	+	0.0800219i
$647$	−2.56118	+	48.8702i	−0.100690	+	1.92129i	0.222465	+	0.974941i	$0.428590\pi$
$647$	−2.56118	+	48.8702i	−0.100690	+	1.92129i	−0.323155	+	0.946346i	$0.604744\pi$
$648$	−38.3423	+	47.3488i	−1.50623	+	1.86003i
$649$	25.4349	+	44.0546i	0.998408	+	1.72929i
$650$	4.26257	+	46.1384i	0.167192	+	1.80970i
$651$	5.96908	−	0.218916i	0.233947	−	0.00858001i
$652$	−0.343807	+	2.17071i	−0.0134645	+	0.0850117i
$653$	−13.7471	−	8.92747i	−0.537965	−	0.349359i	0.246884	−	0.969045i	$-0.420593\pi$
$653$	−13.7471	−	8.92747i	−0.537965	−	0.349359i	−0.784850	+	0.619686i	$0.787260\pi$
$654$	−15.0503	−	16.7151i	−0.588515	−	0.653612i
$655$	−0.446614	+	2.70927i	−0.0174506	+	0.105860i
$656$	36.6071	+	32.9612i	1.42927	+	1.28692i
$657$	−1.06160	−	1.06160i	−0.0414168	−	0.0414168i
$658$	−5.15814	−	57.7914i	−0.201085	−	2.25294i
$659$	−20.7257	+	28.5265i	−0.807359	+	1.11123i	0.184367	+	0.982858i	$0.440977\pi$
$659$	−20.7257	+	28.5265i	−0.807359	+	1.11123i	−0.991725	+	0.128377i	$0.959023\pi$
$660$	−16.8551	+	76.9119i	−0.656082	+	2.99379i
$661$	23.3836	−	2.45771i	0.909516	−	0.0955940i	0.361798	−	0.932257i	$-0.382163\pi$
$661$	23.3836	−	2.45771i	0.909516	−	0.0955940i	0.547719	+	0.836663i	$0.315496\pi$
$662$	−6.67113	+	17.3789i	−0.259281	+	0.675450i
$663$	−3.91046	−	4.82901i	−0.151870	−	0.187543i
$664$	−20.5968	+	14.9645i	−0.799312	+	0.580734i
$665$	2.62368	+	19.3047i	0.101742	+	0.748606i
$666$	1.21896	+	0.885624i	0.0472336	+	0.0343172i
$667$	1.40094	+	26.7314i	0.0542444	+	1.03505i
$668$	−19.5104	−	72.8139i	−0.754882	−	2.81726i
$669$	8.04645	−	37.8556i	0.311094	−	1.46358i
$670$	−66.4984	−	3.90509i	−2.56906	−	0.150867i
$671$	10.9747	+	3.56590i	0.423674	+	0.137660i
$672$	−53.5745	+	29.8197i	−2.06668	+	1.15032i
$673$	33.6594	+	5.33113i	1.29747	+	0.205500i	0.766696	−	0.642011i	$-0.221900\pi$
$673$	33.6594	+	5.33113i	1.29747	+	0.205500i	0.530779	+	0.847510i	$0.321900\pi$
$674$	14.5863	−	8.42143i	0.561845	−	0.324381i
$675$	−15.2919	+	22.9105i	−0.588584	+	0.881824i
$676$	−2.18710	+	3.78817i	−0.0841193	+	0.145699i
$677$	−1.98714	−	5.17668i	−0.0763720	−	0.198956i	0.890079	−	0.455806i	$-0.150649\pi$
$677$	−1.98714	−	5.17668i	−0.0763720	−	0.198956i	−0.966451	+	0.256850i	$0.917315\pi$
$678$	−6.00997	−	11.7952i	−0.230811	−	0.452993i
$679$	3.33663	+	3.44309i	0.128048	+	0.132134i
$680$	−12.7540	−	15.9542i	−0.489092	−	0.611816i
$681$	−11.8626	+	13.1747i	−0.454575	+	0.504856i
$682$	−15.7801	+	4.22828i	−0.604253	+	0.161909i
$683$	6.27477	+	9.66229i	0.240097	+	0.369717i	0.938092	−	0.346385i	$-0.112591\pi$
$683$	6.27477	+	9.66229i	0.240097	+	0.369717i	−0.697995	+	0.716103i	$0.745924\pi$
$684$	0.785455	−	7.47311i	0.0300326	−	0.285741i
$685$	4.52592	−	0.932264i	0.172926	−	0.0356200i
$686$	−46.9301	−	14.9763i	−1.79180	−	0.571797i
$687$	−32.4405	+	5.13807i	−1.23768	+	0.196030i
$688$	−11.9075	+	9.64247i	−0.453968	+	0.367616i
$689$	−3.93075	−	37.3986i	−0.149750	−	1.42477i
$690$	11.4277	−	34.4316i	0.435046	−	1.31079i
$691$	−4.13006	−	0.434087i	−0.157115	−	0.0165134i	0.0256444	−	0.999671i	$-0.491836\pi$
$691$	−4.13006	−	0.434087i	−0.157115	−	0.0165134i	−0.182759	+	0.983158i	$0.558503\pi$
$692$	−22.7951	+	44.7378i	−0.866538	+	1.70068i
$693$	4.93985	−	1.51973i	0.187649	−	0.0577299i
$694$	20.2142	−	6.56799i	0.767320	−	0.249317i
$695$	41.8607	+	16.3720i	1.58787	+	0.621025i
$696$	68.0306	−	61.2550i	2.57869	−	2.32187i
$697$	−4.73374	−	0.248085i	−0.179303	−	0.00939688i
$698$	0.372651	−	0.143047i	0.0141051	−	0.00541443i
$699$	−44.0979			−1.66793
$700$	−55.4089	+	37.9091i	−2.09426	+	1.43283i
$701$	3.61903			0.136689			0.0683445	−	0.997662i	$-0.478228\pi$
$701$	3.61903			0.136689			0.0683445	+	0.997662i	$0.478228\pi$
$702$	47.6611	−	18.2954i	1.79885	−	0.690515i
$703$	4.14315	+	0.217133i	0.156262	+	0.00818933i
$704$	49.6817	−	44.7336i	1.87245	−	1.68596i
$705$	1.72597	−	29.3910i	0.0650039	−	1.10693i
$706$	−39.8172	+	12.9374i	−1.49854	+	0.486905i
$707$	5.84245	−	25.5103i	0.219728	−	0.959412i
$708$	−43.0814	+	84.5521i	−1.61910	+	3.17766i
$709$	40.6832	+	4.27598i	1.52789	+	0.160588i	0.830871	−	0.556465i	$-0.187842\pi$
$709$	40.6832	+	4.27598i	1.52789	+	0.160588i	0.697019	+	0.717052i	$0.254509\pi$
$710$	58.7236	−	42.1027i	2.20386	−	1.58009i
$711$	−0.0324899	−	0.309120i	−0.00121847	−	0.0115929i
$712$	−63.4557	+	51.3854i	−2.37810	+	1.92575i
$713$	5.33294	−	0.844655i	0.199720	−	0.0316326i
$714$	4.68145	−	11.6457i	0.175199	−	0.435829i
$715$	22.8058	−	25.0099i	0.852888	−	0.935316i
$716$	0.613852	−	5.84042i	0.0229407	−	0.218267i
$717$	0.413376	+	0.636543i	0.0154378	+	0.0237721i
$718$	−44.0928	+	11.8146i	−1.64553	+	0.440918i
$719$	−1.79333	+	1.99169i	−0.0668797	+	0.0742775i	−0.775656	−	0.631156i	$-0.782581\pi$
$719$	−1.79333	+	1.99169i	−0.0668797	+	0.0742775i	0.708776	+	0.705433i	$0.249248\pi$
$720$	10.9192	−	4.11280i	0.406936	−	0.153275i
$721$	−5.73382	−	1.63328i	−0.213539	−	0.0608265i
$722$	9.84830	+	19.3284i	0.366516	+	0.719328i
$723$	−0.927653	−	2.41662i	−0.0344998	−	0.0898750i
$724$	39.8569	−	69.0342i	1.48127	−	2.56563i
$725$	23.7738	−	25.7439i	0.882937	−	0.956106i
$726$	28.9739	−	16.7281i	1.07532	−	0.620837i
$727$	12.6022	+	1.99600i	0.467391	+	0.0740274i	0.385688	−	0.922629i	$-0.373964\pi$
$727$	12.6022	+	1.99600i	0.467391	+	0.0740274i	0.0817027	+	0.996657i	$0.473964\pi$
$728$	75.3841	+	1.18372i	2.79392	+	0.0438717i
$729$	28.2870	+	9.19101i	1.04767	+	0.340408i
$730$	−5.01921	−	19.2152i	−0.185769	−	0.711186i
$731$	0.306552	−	1.44221i	0.0113382	−	0.0533421i
$732$	5.57142	+	20.7928i	0.205926	+	0.768525i
$733$	−0.329353	−	6.28443i	−0.0121649	−	0.232121i	−0.997945	−	0.0640790i	$-0.979589\pi$
$733$	−0.329353	−	6.28443i	−0.0121649	−	0.232121i	0.985780	−	0.168042i	$-0.0537443\pi$
$734$	−33.4966	−	24.3367i	−1.23638	−	0.898283i
$735$	−22.4363	−	11.0206i	−0.827577	−	0.406502i
$736$	−44.8401	+	32.5782i	−1.65283	+	1.20085i
$737$	30.6223	+	37.8154i	1.12799	+	1.39295i
$738$	1.81912	−	4.73896i	0.0669626	−	0.174443i
$739$	−41.9630	+	4.41048i	−1.54363	+	0.162242i	−0.837737	−	0.546074i	$-0.816122\pi$
$739$	−41.9630	+	4.41048i	−1.54363	+	0.162242i	−0.705895	+	0.708316i	$0.749455\pi$
$740$	5.73272	+	13.0973i	0.210739	+	0.481465i
$741$	10.7696	−	14.8231i	0.395632	−	0.544541i
$742$	62.1454	−	43.6772i	2.28143	−	1.60344i
$743$	−1.76402	−	1.76402i	−0.0647155	−	0.0647155i	0.674008	−	0.738724i	$-0.264571\pi$
$743$	−1.76402	−	1.76402i	−0.0647155	−	0.0647155i	−0.738724	+	0.674008i	$0.764571\pi$
$744$	−13.7225	−	12.3558i	−0.503091	−	0.452985i
$745$	−36.6867	−	18.9848i	−1.34410	−	0.695548i
$746$	27.3504	+	30.3757i	1.00137	+	1.11213i
$747$	1.17374	+	0.762234i	0.0429448	+	0.0278887i
$748$	−3.85215	+	24.3215i	−0.140849	+	0.889282i
$749$	1.27550	+	34.7784i	0.0466058	+	1.27078i
$750$	−42.7155	+	20.7577i	−1.55975	+	0.757964i
$751$	1.91456	+	3.31611i	0.0698632	+	0.121007i	0.898841	−	0.438275i	$-0.144410\pi$
$751$	1.91456	+	3.31611i	0.0698632	+	0.121007i	−0.828978	+	0.559282i	$0.811077\pi$
$752$	−60.2165	+	74.3612i	−2.19587	+	2.71167i
$753$	−0.0961390	+	1.83444i	−0.00350350	+	0.0668508i
$754$	−63.5276	+	13.5032i	−2.31354	+	0.491758i
$755$	−30.8980	+	1.42425i	−1.12449	+	0.0518336i
$756$	56.7480	+	47.4480i	2.06390	+	1.72567i
$757$	5.57353	−	5.57353i	0.202573	−	0.202573i	−0.598528	−	0.801102i	$-0.704248\pi$
$757$	5.57353	−	5.57353i	0.202573	−	0.202573i	0.801102	+	0.598528i	$0.204248\pi$
$758$	−52.6623	+	2.75991i	−1.91278	+	0.100245i
$759$	−24.2096	+	10.7788i	−0.878752	+	0.391245i
$760$	35.7073	−	48.5016i	1.29524	−	1.75934i
$761$	−4.61190	+	10.3585i	−0.167181	+	0.375495i	−0.977635	−	0.210307i	$-0.932554\pi$
$761$	−4.61190	+	10.3585i	−0.167181	+	0.375495i	0.810454	+	0.585802i	$0.199220\pi$
$762$	−10.2087	−	64.4552i	−0.369822	−	2.33496i
$763$	−10.5569	+	9.20948i	−0.382185	+	0.333406i
$764$	7.58615	+	10.4414i	0.274457	+	0.377758i
$765$	−0.567521	+	0.968834i	−0.0205188	+	0.0350283i
$766$	27.1411	+	60.9599i	0.980647	+	2.20257i
$767$	34.2114	−	22.2171i	1.23530	−	0.802215i
$768$	1.37881	+	0.369452i	0.0497536	+	0.0133315i
$769$	6.63510	+	20.4207i	0.239268	+	0.736390i	0.996527	+	0.0832755i	$0.0265381\pi$
$769$	6.63510	+	20.4207i	0.239268	+	0.736390i	−0.757259	+	0.653115i	$0.773462\pi$
$770$	66.5452	+	15.6821i	2.39812	+	0.565144i
$771$	−5.72313	+	17.6140i	−0.206113	+	0.634352i
$772$	−40.9996	+	63.1339i	−1.47561	+	2.27224i
$773$	−9.26025	−	7.49880i	−0.333068	−	0.269713i	0.448168	−	0.893950i	$-0.352077\pi$
$773$	−9.26025	−	7.49880i	−0.333068	−	0.269713i	−0.781235	+	0.624237i	$0.785410\pi$
$774$	1.36737	+	0.789452i	0.0491491	+	0.0283763i
$775$	−5.66564	−	4.22636i	−0.203516	−	0.151815i
$776$		−	14.8221i		−	0.532083i
$777$	−3.19613	+	4.25690i	−0.114660	+	0.152716i
$778$	−40.2290	+	20.4977i	−1.44228	+	0.734877i
$779$	−2.90606	−	13.6720i	−0.104121	−	0.489849i
$780$	62.2984	+	10.2697i	2.23064	+	0.367713i
$781$	−51.6289	−	10.9741i	−1.84743	−	0.392683i
$782$	2.93654	−	10.9593i	0.105011	−	0.391905i
$783$	−34.4012	−	17.5283i	−1.22940	−	0.626410i
$784$	38.3908	+	71.5963i	1.37110	+	2.55701i
$785$	−17.4531	−	15.9150i	−0.622929	−	0.568031i
$786$	4.76525	+	2.12163i	0.169971	+	0.0756759i
$787$	−20.4254	−	7.84058i	−0.728088	−	0.279487i	−0.0340447	−	0.999420i	$-0.510839\pi$
$787$	−20.4254	−	7.84058i	−0.728088	−	0.279487i	−0.694043	+	0.719934i	$0.744172\pi$
$788$	−8.06426	−	3.09558i	−0.287277	−	0.110275i
$789$	27.1496	+	12.0878i	0.966550	+	0.430336i
$790$	1.69598	−	3.74557i	0.0603402	−	0.133261i
$791$	−7.40452	+	3.62750i	−0.263274	+	0.128979i
$792$	−14.2361	−	7.25367i	−0.505859	−	0.257748i
$793$	2.39498	−	8.93819i	0.0850483	−	0.317405i
$794$	−59.5191	−	12.6512i	−2.11225	−	0.448973i
$795$	34.4522	−	17.2819i	1.22189	−	0.612924i
$796$	−3.94777	−	18.5728i	−0.139925	−	0.658295i
$797$	46.2744	−	23.5780i	1.63912	−	0.835175i	0.641438	−	0.767175i	$-0.278338\pi$
$797$	46.2744	−	23.5780i	1.63912	−	0.835175i	0.997685	−	0.0679998i	$-0.0216617\pi$
$798$	36.7420	+	4.44602i	1.30065	+	0.157387i
$799$		−	9.20772i		−	0.325746i
$800$	71.5152	+	12.2521i	2.52844	+	0.433177i
$801$	3.88719	+	2.24427i	0.137347	+	0.0792973i
$802$	−30.5624	−	24.7489i	−1.07920	−	0.873915i
$803$	−7.90120	+	12.1668i	−0.278827	+	0.429357i
$804$	−28.0499	+	86.3288i	−0.989244	+	3.04458i
$805$	−21.3313	−	7.45359i	−0.751831	−	0.262705i
$806$	4.04826	+	12.4593i	0.142594	+	0.438859i
$807$	40.9888	+	10.9829i	1.44287	+	0.386617i
$808$	−67.8528	+	44.0641i	−2.38705	+	1.55017i
$809$	−0.666119	−	1.49613i	−0.0234195	−	0.0526011i	0.901457	−	0.432869i	$-0.142499\pi$
$809$	−0.666119	−	1.49613i	−0.0234195	−	0.0526011i	−0.924877	+	0.380268i	$0.875832\pi$
$810$	29.4374	+	33.1105i	1.03432	+	1.16338i
$811$	−26.0483	−	35.8524i	−0.914678	−	1.25895i	−0.965544	−	0.260241i	$-0.916198\pi$
$811$	−26.0483	−	35.8524i	−0.914678	−	1.25895i	0.0508656	−	0.998706i	$-0.483802\pi$
$812$	−61.8616	−	70.9124i	−2.17092	−	2.48854i
$813$	3.20300	+	20.2230i	0.112334	+	0.709250i
$814$	5.92180	−	13.3006i	0.207559	−	0.466185i
$815$	0.919050	+	0.305029i	0.0321929	+	0.0106847i
$816$	−18.9095	+	8.41907i	−0.661966	+	0.294726i
$817$	4.34166	−	0.227537i	0.151895	−	0.00796050i
$818$	41.3875	−	41.3875i	1.44708	−	1.44708i
$819$	−1.42432	−	3.89205i	−0.0497697	−	0.135999i
$820$	37.6224	−	30.0757i	1.31383	−	1.05029i
$821$	−16.6366	+	3.53622i	−0.580621	+	0.123415i	−0.488854	−	0.872366i	$-0.662585\pi$
$821$	−16.6366	+	3.53622i	−0.580621	+	0.123415i	−0.0917672	+	0.995780i	$0.529252\pi$
$822$	0.459421	−	8.76628i	0.0160241	−	0.305759i
$823$	9.80693	−	12.1105i	0.341848	−	0.422147i	−0.577009	−	0.816738i	$-0.695780\pi$
$823$	9.80693	−	12.1105i	0.341848	−	0.422147i	0.918857	+	0.394591i	$0.129114\pi$
$824$	9.21542	+	15.9616i	0.321034	+	0.556048i
$825$	32.2285	+	12.8394i	1.12205	+	0.447010i
$826$	72.8208	+	38.5560i	2.53376	+	1.34153i
$827$	4.99312	−	31.5253i	0.173628	−	1.09624i	−0.734825	−	0.678256i	$-0.762736\pi$
$827$	4.99312	−	31.5253i	0.173628	−	1.09624i	0.908453	−	0.417986i	$-0.137264\pi$
$828$	7.30925	+	4.74668i	0.254014	+	0.164959i
$829$	21.2285	+	23.5766i	0.737295	+	0.818849i	0.988838	−	0.148997i	$-0.0476045\pi$
$829$	21.2285	+	23.5766i	0.737295	+	0.818849i	−0.251542	+	0.967846i	$0.580938\pi$
$830$	8.30078	+	16.5480i	0.288124	+	0.574389i
$831$	5.81217	+	5.23331i	0.201622	+	0.181541i
$832$	−37.9077	−	37.9077i	−1.31421	−	1.31421i
$833$	−7.20685	−	3.02937i	−0.249702	−	0.104961i
$834$	50.1896	−	69.0800i	1.73792	−	2.39205i
$835$	−33.0531	+	3.26371i	−1.14385	+	0.112945i
$836$	−72.2123	+	7.58982i	−2.49751	+	0.262499i
$837$	−2.79094	+	7.27065i	−0.0964691	+	0.251311i
$838$	16.0252	+	19.7895i	0.553582	+	0.683617i
$839$	3.11816	−	2.26548i	0.107651	−	0.0782130i	−0.532657	−	0.846331i	$-0.678807\pi$
$839$	3.11816	−	2.26548i	0.107651	−	0.0782130i	0.640308	+	0.768118i	$0.278807\pi$
$840$	26.0997	+	72.7352i	0.900524	+	2.50960i
$841$	16.2756	+	11.8249i	0.561228	+	0.407756i
$842$	−0.507342	−	9.68066i	−0.0174842	−	0.333618i
$843$	−8.37759	−	31.2656i	−0.288539	−	1.07684i
$844$	−12.0402	+	56.6448i	−0.414441	+	1.94979i
$845$	1.49012	+	1.22229i	0.0512616	+	0.0420481i
$846$	9.37755	+	3.04695i	0.322407	+	0.104756i
$847$	−10.1344	−	18.2077i	−0.348224	−	0.625625i
$848$	−123.725	−	19.5960i	−4.24872	−	0.672931i
$849$	4.48861	−	2.59150i	0.154049	−	0.0889400i
$850$	−12.9555	+	7.26387i	−0.444370	+	0.249149i
$851$	−2.40597	+	4.16726i	−0.0824756	+	0.142852i
$852$	−35.2858	−	91.9228i	−1.20887	−	3.14922i
$853$	−23.1639	−	45.4618i	−0.793118	−	1.55658i	−0.830329	−	0.557274i	$-0.811847\pi$
$853$	−23.1639	−	45.4618i	−0.793118	−	1.55658i	0.0372113	−	0.999307i	$-0.488153\pi$
$854$	18.1283	−	4.55364i	0.620337	−	0.155822i
$855$	−3.19255	−	0.877025i	−0.109183	−	0.0299936i
$856$	71.9901	−	79.9531i	2.46057	−	2.73274i
$857$	−18.1604	+	4.86606i	−0.620347	+	0.166222i	−0.555286	−	0.831660i	$-0.687391\pi$
$857$	−18.1604	+	4.86606i	−0.620347	+	0.166222i	−0.0650616	+	0.997881i	$0.520724\pi$
$858$	−35.0191	−	53.9248i	−1.19553	−	1.84096i
$859$	3.38363	−	32.1931i	0.115448	−	1.09841i	−0.771399	−	0.636352i	$-0.780443\pi$
$859$	3.38363	−	32.1931i	0.115448	−	1.09841i	0.886847	−	0.462063i	$-0.152891\pi$
$860$	7.40911	+	13.0217i	0.252649	+	0.444035i
$861$	16.6397	+	6.68899i	0.567080	+	0.227960i
$862$	95.5526	−	15.1340i	3.25454	−	0.515468i
$863$	−0.0938981	+	0.0760372i	−0.00319633	+	0.00258834i	−0.630917	−	0.775850i	$-0.717321\pi$
$863$	−0.0938981	+	0.0760372i	−0.00319633	+	0.00258834i	0.627721	+	0.778438i	$0.283988\pi$
$864$	−8.35639	−	79.5057i	−0.284290	−	2.70484i
$865$	17.8156	+	13.1160i	0.605748	+	0.445957i
$866$	−55.0975	−	5.79098i	−1.87229	−	0.196785i
$867$	−11.4210	+	22.4150i	−0.387879	+	0.761255i
$868$	−12.9211	+	13.9049i	−0.438571	+	0.471965i
$869$	−2.85647	+	0.928123i	−0.0968991	+	0.0314844i
$870$	−35.9036	−	56.0564i	−1.21725	−	1.90049i
$871$	28.9974	−	26.1094i	0.982539	−	0.884682i
$872$	43.2497	+	2.26662i	1.46462	+	0.0767575i
$873$	−0.760674	+	0.291996i	−0.0257449	+	0.00988255i
$874$	33.4554			1.13165
$875$	12.5096	+	26.8050i	0.422902	+	0.906175i
$876$	−27.0625			−0.914356
$877$	16.2662	−	6.24399i	0.549269	−	0.210845i	−0.0678763	−	0.997694i	$-0.521622\pi$
$877$	16.2662	−	6.24399i	0.549269	−	0.210845i	0.617146	+	0.786849i	$0.288289\pi$
$878$	71.2199	+	3.73248i	2.40356	+	0.125965i
$879$	−25.3245	+	22.8023i	−0.854174	+	0.769102i
$880$	−60.8106	−	94.9437i	−2.04992	−	3.20055i
$881$	−33.0502	+	10.7387i	−1.11349	+	0.361795i	−0.807280	−	0.590169i	$-0.799061\pi$
$881$	−33.0502	+	10.7387i	−1.11349	+	0.361795i	−0.306211	+	0.951964i	$0.599061\pi$
$882$	5.47008	−	6.33732i	0.184187	−	0.213389i
$883$	−0.00259144	+	0.00508600i	−8.72090e−5	+	0.000171157i	−0.891050	−	0.453905i	$-0.850031\pi$
$883$	−0.00259144	+	0.00508600i	−8.72090e−5	+	0.000171157i	0.890963	+	0.454076i	$0.150031\pi$
$884$	19.6383	+	2.06407i	0.660508	+	0.0694222i
$885$	33.6705	+	24.7885i	1.13182	+	0.833256i
$886$	7.35567	+	69.9845i	0.247119	+	2.35118i
$887$	−30.9601	+	25.0710i	−1.03954	+	0.841802i	−0.987623	−	0.156849i	$-0.949866\pi$
$887$	−30.9601	+	25.0710i	−1.03954	+	0.841802i	−0.0519166	+	0.998651i	$0.516533\pi$
$888$	16.2537	−	2.57434i	0.545439	−	0.0863891i
$889$	−40.2408	+	5.72739i	−1.34963	+	0.192090i
$890$	29.3633	+	51.6066i	0.984261	+	1.72986i
$891$	3.38289	−	32.1860i	0.113331	−	1.07827i
$892$	66.9836	+	103.146i	2.24278	+	3.45357i
$893$	26.2254	−	7.02707i	0.877599	−	0.235152i
$894$	−52.5078	+	58.3159i	−1.75612	+	1.95037i
$895$	−2.49505	−	0.685416i	−0.0834004	−	0.0229109i
$896$	8.62963	−	30.2953i	0.288296	−	1.01210i
$897$	9.64768	+	18.9346i	0.322127	+	0.632209i
$898$	−12.4326	−	32.3879i	−0.414880	−	1.08080i
$899$	4.95379	−	8.58021i	0.165218	−	0.286166i
$900$	−2.23135	−	11.1888i	−0.0743784	−	0.372960i
$901$	10.4394	−	6.02718i	0.347786	−	0.200795i
$902$	−48.4463	−	7.67314i	−1.61309	−	0.255488i
$903$	−2.86463	+	4.78652i	−0.0953289	+	0.159285i
$904$	24.2424	+	7.87682i	0.806289	+	0.261979i
$905$	−27.1554	−	22.2746i	−0.902675	−	0.740432i
$906$	−12.2166	+	57.4747i	−0.405870	+	1.90947i
$907$	−6.18223	−	23.0724i	−0.205278	−	0.766107i	−0.989365	−	0.145456i	$-0.953535\pi$
$907$	−6.18223	−	23.0724i	−0.205278	−	0.766107i	0.784087	−	0.620651i	$-0.213132\pi$
$908$	−2.94851	−	56.2609i	−0.0978496	−	1.86708i
$909$	3.59808	+	2.61416i	0.119341	+	0.0867061i
$910$	9.76544	−	53.9475i	0.323721	−	1.78834i
$911$	−11.7738	+	8.55418i	−0.390084	+	0.283413i	−0.765490	−	0.643448i	$-0.777503\pi$
$911$	−11.7738	+	8.55418i	−0.390084	+	0.283413i	0.375406	+	0.926861i	$0.377503\pi$
$912$	−38.4104	−	47.4329i	−1.27190	−	1.57066i
$913$	4.84639	−	12.6253i	0.160392	−	0.417836i
$914$	−59.8209	+	6.28743i	−1.97870	+	0.207970i
$915$	9.43868	−	0.931988i	0.312033	−	0.0308106i
$916$	61.3508	−	84.4421i	2.02709	−	2.79005i
$917$	1.36789	−	2.94692i	0.0451718	−	0.0973159i
$918$	11.5718	+	11.5718i	0.381926	+	0.381926i
$919$	5.35896	+	4.82523i	0.176776	+	0.159170i	0.752769	−	0.658285i	$-0.228718\pi$
$919$	5.35896	+	4.82523i	0.176776	+	0.159170i	−0.575993	+	0.817455i	$0.695384\pi$
$920$	31.3206	+	62.4391i	1.03261	+	2.05856i
$921$	−21.9225	−	24.3475i	−0.722372	−	0.802276i
$922$	86.4293	+	56.1279i	2.84640	+	1.84847i
$923$	−6.62125	+	41.8049i	−0.217941	+	1.37603i
$924$	43.5932	−	82.3346i	1.43411	−	2.70861i
$925$	6.10470	−	1.55361i	0.200721	−	0.0510825i
$926$	−52.5457	−	91.0118i	−1.72676	−	2.99083i
$927$	0.637608	−	0.787380i	0.0209418	−	0.0258610i
$928$	−5.32267	+	101.563i	−0.174725	+	3.33396i
$929$	−21.5074	+	4.57153i	−0.705633	+	0.149987i	−0.546732	−	0.837307i	$-0.684128\pi$
$929$	−21.5074	+	4.57153i	−0.705633	+	0.149987i	−0.158901	+	0.987295i	$0.550795\pi$
$930$	−10.4882	+	8.38439i	−0.343922	+	0.274935i
$931$	3.12817	−	22.8384i	0.102521	−	0.748500i
$932$	99.0915	−	99.0915i	3.24585	−	3.24585i
$933$	−14.5755	+	0.763870i	−0.477181	+	0.0250080i
$934$	−70.3279	+	31.3120i	−2.30120	+	1.02456i
$935$	10.2974	+	3.41767i	0.336761	+	0.111770i
$936$	−5.21127	+	11.7047i	−0.170336	+	0.382580i
$937$	−5.11236	−	32.2782i	−0.167014	−	1.05448i	−0.918698	−	0.394960i	$-0.870758\pi$
$937$	−5.11236	−	32.2782i	−0.167014	−	1.05448i	0.751685	−	0.659523i	$-0.229242\pi$
$938$	74.5683	+	25.5299i	2.43474	+	0.833580i
$939$	−6.60251	−	9.08758i	−0.215465	−	0.296562i
$940$	62.1655	+	69.9223i	2.02761	+	2.28061i
$941$	−5.96355	−	13.3944i	−0.194406	−	0.436644i	0.789871	−	0.613273i	$-0.210147\pi$
$941$	−5.96355	−	13.3944i	−0.194406	−	0.436644i	−0.984277	+	0.176629i	$0.943481\pi$
$942$	−37.6314	+	24.4381i	−1.22610	+	0.796236i
$943$	15.6590	+	4.19582i	0.509927	+	0.136635i
$944$	−41.9911	−	129.235i	−1.36669	−	4.20625i
$945$	24.6942	−	21.2701i	0.803304	−	0.691916i
$946$	4.71463	−	14.5102i	0.153286	−	0.471766i
$947$	3.31715	−	5.10796i	0.107793	−	0.165986i	−0.780658	−	0.624959i	$-0.785116\pi$
$947$	3.31715	−	5.10796i	0.107793	−	0.165986i	0.888450	+	0.458973i	$0.151782\pi$
$948$	−4.35420	−	3.52597i	−0.141418	−	0.114518i
$949$	10.0748	+	5.81666i	0.327040	+	0.188817i
$950$	−30.5762	−	31.3563i	−0.992023	−	1.01733i
$951$			37.9162i			1.22952i
$952$	9.48206	+	22.2300i	0.307315	+	0.720477i
$953$	15.7088	−	8.00402i	0.508857	−	0.259276i	−0.180659	−	0.983546i	$-0.557823\pi$
$953$	15.7088	−	8.00402i	0.508857	−	0.259276i	0.689516	+	0.724270i	$0.257823\pi$
$954$	2.68383	+	12.6264i	0.0868921	+	0.408795i
$955$	5.08294	−	2.54970i	0.164480	−	0.0825062i
$956$	−2.35925	−	0.501475i	−0.0763037	−	0.0162189i
$957$	−12.5856	+	46.9701i	−0.406835	+	1.51833i
$958$	76.9284	+	39.1970i	2.48544	+	1.26640i
$959$	−5.45491	−	0.371841i	−0.176148	−	0.0120074i
$960$	22.6652	−	50.0560i	0.731515	−	1.61555i
$961$	26.4942	+	11.7960i	0.854652	+	0.380516i
$962$	−10.8996	−	4.18398i	−0.351418	−	0.134897i
$963$	−5.52141	−	2.11947i	−0.177925	−	0.0682990i
$964$	7.51485	+	3.34583i	0.242037	+	0.107762i
$965$	24.5084	+	22.3485i	0.788953	+	0.719424i
$966$	−23.9411	+	35.6287i	−0.770294	+	1.14633i
$967$	−25.9882	−	13.2416i	−0.835723	−	0.425822i	−0.0168922	−	0.999857i	$-0.505377\pi$
$967$	−25.9882	−	13.2416i	−0.835723	−	0.425822i	−0.818831	+	0.574035i	$0.805377\pi$
$968$	−16.6731	+	62.2247i	−0.535892	+	1.99998i
$969$	5.74499	+	1.22114i	0.184556	+	0.0392285i
$970$	−10.6347	−	1.75310i	−0.341461	−	0.0562886i
$971$	−8.05025	−	37.8735i	−0.258345	−	1.21542i	−0.895634	−	0.444792i	$-0.853278\pi$
$971$	−8.05025	−	37.8735i	−0.258345	−	1.21542i	0.637289	−	0.770625i	$-0.280056\pi$
$972$	−20.9411	+	10.6700i	−0.671687	+	0.342242i
$973$	−42.5304	−	31.9322i	−1.36346	−	1.02370i
$974$			6.47259i			0.207395i
$975$	8.92920	−	26.3474i	0.285963	−	0.843793i
$976$	−26.6951	−	15.4124i	−0.854489	−	0.493339i
$977$	20.8912	+	16.9174i	0.668370	+	0.541235i	0.902349	−	0.431006i	$-0.141841\pi$
$977$	20.8912	+	16.9174i	0.668370	+	0.541235i	−0.233979	+	0.972242i	$0.575175\pi$
$978$	1.00189	−	1.54278i	0.0320369	−	0.0493326i
$979$	13.4028	−	41.2497i	0.428357	−	1.31835i
$980$	75.1805	−	25.6521i	2.40155	−	0.819425i
$981$	−0.735695	−	2.26424i	−0.0234889	−	0.0722915i
$982$	−24.4567	−	6.55316i	−0.780445	−	0.209120i
$983$	−11.2700	+	7.31880i	−0.359456	+	0.233434i	−0.711714	−	0.702469i	$-0.752081\pi$
$983$	−11.2700	+	7.31880i	−0.359456	+	0.233434i	0.352258	+	0.935903i	$0.385414\pi$
$984$	−22.5500	−	50.6481i	−0.718868	−	1.61460i
$985$	−1.92369	+	3.28399i	−0.0612937	+	0.104637i
$986$	−12.2371	−	16.8430i	−0.389710	−	0.536389i
$987$	−11.2837	+	32.9577i	−0.359164	+	1.04905i
$988$	9.10854	+	57.5090i	0.289781	+	1.82961i
$989$	−2.05097	+	4.60654i	−0.0652169	+	0.146480i
$990$	−6.88824	+	9.35638i	−0.218923	+	0.297365i
$991$	−26.3524	+	11.7328i	−0.837110	+	0.372706i	−0.780090	−	0.625667i	$-0.784827\pi$
$991$	−26.3524	+	11.7328i	−0.837110	+	0.372706i	−0.0570205	+	0.998373i	$0.518160\pi$
$992$	20.4863	−	1.07364i	0.650439	−	0.0340881i
$993$	7.90304	−	7.90304i	0.250796	−	0.250796i
$994$	−80.2884	+	29.3820i	−2.54659	+	0.931941i
$995$	−8.35719	+	0.385225i	−0.264941	+	0.0122125i
$996$	24.6761	−	5.24507i	0.781893	−	0.166196i
$997$	3.14320	−	59.9757i	0.0995460	−	1.89945i	−0.258906	−	0.965902i	$-0.583362\pi$
$997$	3.14320	−	59.9757i	0.0995460	−	1.89945i	0.358452	−	0.933548i	$-0.383305\pi$
$998$	−31.8758	+	39.3633i	−1.00901	+	1.24602i
$999$	−3.47028	−	6.01071i	−0.109795	−	0.190170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.73.18	yes	288
5.2	odd	4		875.2.bb.b.157.18		288
5.3	odd	4		875.2.bb.a.157.1		288
5.4	even	2		875.2.bb.c.843.1		288
7.5	odd	6	inner	175.2.x.a.173.1	yes	288
25.9	even	10		875.2.bb.a.668.1		288
25.12	odd	20	inner	175.2.x.a.87.1	yes	288
25.13	odd	20		875.2.bb.c.332.18		288
25.16	even	5		875.2.bb.b.668.18		288
35.12	even	12		875.2.bb.b.782.18		288
35.19	odd	6		875.2.bb.c.593.18		288
35.33	even	12		875.2.bb.a.782.1		288
175.12	even	60	inner	175.2.x.a.12.18	✓	288
175.138	even	60		875.2.bb.c.82.1		288
175.159	odd	30		875.2.bb.a.418.1		288
175.166	odd	30		875.2.bb.b.418.18		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.12.18	✓	288	175.12	even	60	inner
175.2.x.a.73.18	yes	288	1.1	even	1	trivial
175.2.x.a.87.1	yes	288	25.12	odd	20	inner
175.2.x.a.173.1	yes	288	7.5	odd	6	inner
875.2.bb.a.157.1		288	5.3	odd	4
875.2.bb.a.418.1		288	175.159	odd	30
875.2.bb.a.668.1		288	25.9	even	10
875.2.bb.a.782.1		288	35.33	even	12
875.2.bb.b.157.18		288	5.2	odd	4
875.2.bb.b.418.18		288	175.166	odd	30
875.2.bb.b.668.18		288	25.16	even	5
875.2.bb.b.782.18		288	35.12	even	12
875.2.bb.c.82.1		288	175.138	even	60
875.2.bb.c.332.18		288	25.13	odd	20
875.2.bb.c.593.18		288	35.19	odd	6
875.2.bb.c.843.1		288	5.4	even	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.48322 - 0.953219i) q^{2} +(-1.59480 - 0.0835800i) q^{3} +(3.77146 - 3.39584i) q^{4} +(-1.20602 - 1.88296i) q^{5} +(-4.03991 + 1.31265i) q^{6} +(0.777975 + 2.52879i) q^{7} +(3.71326 - 7.28769i) q^{8} +(-0.447157 - 0.0469981i) q^{9} +O(q^{10})\)	\(q+(2.48322 - 0.953219i) q^{2} +(-1.59480 - 0.0835800i) q^{3} +(3.77146 - 3.39584i) q^{4} +(-1.20602 - 1.88296i) q^{5} +(-4.03991 + 1.31265i) q^{6} +(0.777975 + 2.52879i) q^{7} +(3.71326 - 7.28769i) q^{8} +(-0.447157 - 0.0469981i) q^{9} +(-4.78967 - 3.52620i) q^{10} +(0.454141 + 4.32086i) q^{11} +(-6.29856 + 5.10048i) q^{12} +(3.44108 - 0.545014i) q^{13} +(4.34237 + 5.53795i) q^{14} +(1.76598 + 3.10374i) q^{15} +(1.21312 - 11.5421i) q^{16} +(0.608257 + 0.936633i) q^{17} +(-1.15519 + 0.309532i) q^{18} +(-2.20351 + 2.44725i) q^{19} +(-10.9427 - 3.00606i) q^{20} +(-1.02936 - 4.09794i) q^{21} +(5.24646 + 10.2967i) q^{22} +(-1.36876 - 3.56575i) q^{23} +(-6.53103 + 11.3121i) q^{24} +(-2.09105 + 4.54175i) q^{25} +(8.02545 - 4.63349i) q^{26} +(5.44119 + 0.861799i) q^{27} +(11.5215 + 6.89534i) q^{28} +(-6.66539 - 2.16572i) q^{29} +(7.34386 + 6.02391i) q^{30} +(-0.293918 + 1.38278i) q^{31} +(-3.75583 - 14.0170i) q^{32} +(-0.363127 - 6.92887i) q^{33} +(2.40325 + 1.74606i) q^{34} +(3.82334 - 4.51465i) q^{35} +(-1.84604 + 1.34122i) q^{36} +(-0.792854 - 0.979093i) q^{37} +(-3.13904 + 8.17748i) q^{38} +(-5.53340 + 0.581584i) q^{39} +(-18.2007 + 1.79716i) q^{40} +(-2.49483 + 3.43383i) q^{41} +(-6.46235 - 9.19487i) q^{42} +(-0.933537 - 0.933537i) q^{43} +(16.3857 + 14.7538i) q^{44} +(0.450784 + 0.898658i) q^{45} +(-6.79787 - 7.54980i) q^{46} +(-6.91457 - 4.49037i) q^{47} +(-2.89938 + 18.3060i) q^{48} +(-5.78951 + 3.93466i) q^{49} +(-0.863254 + 13.2714i) q^{50} +(-0.891766 - 1.54458i) q^{51} +(11.1271 - 13.7409i) q^{52} +(0.564893 - 10.7788i) q^{53} +(14.3331 - 3.04660i) q^{54} +(7.58829 - 6.06615i) q^{55} +(21.3178 + 3.72041i) q^{56} +(3.71871 - 3.71871i) q^{57} +(-18.6160 + 0.975625i) q^{58} +(10.6963 - 4.76231i) q^{59} +(17.2001 + 5.70866i) q^{60} +(1.08030 - 2.42639i) q^{61} +(0.588225 + 3.71391i) q^{62} +(-0.229029 - 1.16733i) q^{63} +(-9.04452 - 12.4487i) q^{64} +(-5.17624 - 5.82211i) q^{65} +(-7.50646 - 16.8598i) q^{66} +(9.39294 - 6.09985i) q^{67} +(5.47468 + 1.46694i) q^{68} +(1.88488 + 5.80106i) q^{69} +(5.19075 - 14.8553i) q^{70} +(-3.75418 + 11.5542i) q^{71} +(-2.00292 + 3.08423i) q^{72} +(2.59496 + 2.10136i) q^{73} +(-2.90212 - 1.67554i) q^{74} +(3.71441 - 7.06843i) q^{75} +16.7125i q^{76} +(-10.5732 + 4.50994i) q^{77} +(-13.1863 + 6.71874i) q^{78} +(0.143730 + 0.676195i) q^{79} +(-23.1963 + 11.6357i) q^{80} +(-7.28620 - 1.54873i) q^{81} +(-2.92201 + 10.9051i) q^{82} +(-2.77341 - 1.41312i) q^{83} +(-17.7981 - 11.9597i) q^{84} +(1.03007 - 2.27492i) q^{85} +(-3.20804 - 1.42831i) q^{86} +(10.4490 + 4.01098i) q^{87} +(33.1754 + 12.7349i) q^{88} +(-9.11987 - 4.06043i) q^{89} +(1.97601 + 1.80187i) q^{90} +(4.05530 + 8.27775i) q^{91} +(-17.2709 - 8.79998i) q^{92} +(0.584314 - 2.18069i) q^{93} +(-21.4507 - 4.55949i) q^{94} +(7.26553 + 1.19770i) q^{95} +(4.81827 + 22.6682i) q^{96} +(1.61466 - 0.822712i) q^{97} +(-10.6260 + 15.2893i) q^{98} -1.95345i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

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