LMFDB - Embedded newform 561.2.m.d.460.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (of order $5$, 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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			460.2
Character	$\chi$	$=$	561.460
Dual form			561.2.m.d.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.532612 + 1.63921i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.785303 - 0.570556i) q^{4} +(-1.21172 - 3.72929i) q^{5} +(-0.532612 - 1.63921i) q^{6} +(2.86209 + 2.07943i) q^{7} +(-1.43527 + 1.04278i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.532612 + 1.63921i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.785303 - 0.570556i) q^{4} +(-1.21172 - 3.72929i) q^{5} +(-0.532612 - 1.63921i) q^{6} +(2.86209 + 2.07943i) q^{7} +(-1.43527 + 1.04278i) q^{8} +(0.309017 - 0.951057i) q^{9} +6.75848 q^{10} +(-2.46710 + 2.21662i) q^{11} +0.970688 q^{12} +(-0.761945 + 2.34502i) q^{13} +(-4.93301 + 3.58404i) q^{14} +(3.17233 + 2.30483i) q^{15} +(-1.54482 - 4.75447i) q^{16} +(0.309017 + 0.951057i) q^{17} +(1.39440 + 1.01309i) q^{18} +(-2.19471 + 1.59455i) q^{19} +(-1.17620 + 3.61998i) q^{20} -3.53774 q^{21} +(-2.31950 - 5.22470i) q^{22} -5.32848 q^{23} +(0.548224 - 1.68726i) q^{24} +(-8.39428 + 6.09880i) q^{25} +(-3.43817 - 2.49798i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.06118 - 3.26597i) q^{28} +(2.69281 + 1.95644i) q^{29} +(-5.46772 + 3.97253i) q^{30} +(-2.40792 + 7.41080i) q^{31} +5.06818 q^{32} +(0.693031 - 3.24341i) q^{33} -1.72357 q^{34} +(4.28675 - 13.1933i) q^{35} +(-0.785303 + 0.570556i) q^{36} +(-9.20481 - 6.68769i) q^{37} +(-1.44488 - 4.44687i) q^{38} +(-0.761945 - 2.34502i) q^{39} +(5.62799 + 4.08898i) q^{40} +(-10.0681 + 7.31492i) q^{41} +(1.88424 - 5.79910i) q^{42} +5.23509 q^{43} +(3.20213 - 0.333099i) q^{44} -3.92121 q^{45} +(2.83801 - 8.73450i) q^{46} +(7.29965 - 5.30350i) q^{47} +(4.04439 + 2.93842i) q^{48} +(1.70441 + 5.24564i) q^{49} +(-5.52633 - 17.0083i) q^{50} +(-0.809017 - 0.587785i) q^{51} +(1.93633 - 1.40682i) q^{52} +(1.24305 - 3.82572i) q^{53} -1.72357 q^{54} +(11.2559 + 6.51463i) q^{55} -6.27626 q^{56} +(0.838305 - 2.58004i) q^{57} +(-4.64124 + 3.37206i) q^{58} +(2.04218 + 1.48373i) q^{59} +(-1.17620 - 3.61998i) q^{60} +(0.855712 + 2.63361i) q^{61} +(-10.8654 - 7.89416i) q^{62} +(2.86209 - 2.07943i) q^{63} +(0.390264 - 1.20111i) q^{64} +9.66855 q^{65} +(4.94752 + 2.86350i) q^{66} +5.19206 q^{67} +(0.299959 - 0.923179i) q^{68} +(4.31083 - 3.13200i) q^{69} +(19.3434 + 14.0538i) q^{70} +(2.41474 + 7.43181i) q^{71} +(0.548224 + 1.68726i) q^{72} +(-2.98945 - 2.17196i) q^{73} +(15.8651 - 11.5267i) q^{74} +(3.20633 - 9.86807i) q^{75} +2.63329 q^{76} +(-11.6704 + 1.21400i) q^{77} +4.24981 q^{78} +(-0.126666 + 0.389836i) q^{79} +(-15.8589 + 11.5222i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-6.62829 - 20.3998i) q^{82} +(0.899162 + 2.76734i) q^{83} +(2.77820 + 2.01848i) q^{84} +(3.17233 - 2.30483i) q^{85} +(-2.78827 + 8.58142i) q^{86} -3.32849 q^{87} +(1.22950 - 5.75410i) q^{88} -13.6350 q^{89} +(2.08848 - 6.42769i) q^{90} +(-7.05707 + 5.12726i) q^{91} +(4.18447 + 3.04019i) q^{92} +(-2.40792 - 7.41080i) q^{93} +(4.80568 + 14.7904i) q^{94} +(8.60593 + 6.25257i) q^{95} +(-4.10025 + 2.97900i) q^{96} +(-4.72231 + 14.5338i) q^{97} -9.50651 q^{98} +(1.34575 + 3.03133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.532612	+	1.63921i	−0.376614	+	1.15910i	0.565770	+	0.824563i	$0.308579\pi$
$2$	−0.532612	+	1.63921i	−0.376614	+	1.15910i	−0.942384	+	0.334534i	$0.891421\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.785303	−	0.570556i	−0.392652	−	0.285278i
$5$	−1.21172	−	3.72929i	−0.541898	−	1.66779i	−0.728253	−	0.685309i	$-0.759667\pi$
$5$	−1.21172	−	3.72929i	−0.541898	−	1.66779i	0.186355	−	0.982483i	$-0.440333\pi$
$6$	−0.532612	−	1.63921i	−0.217438	−	0.669205i
$7$	2.86209	+	2.07943i	1.08177	+	0.785951i	0.977990	−	0.208650i	$-0.0669068\pi$
$7$	2.86209	+	2.07943i	1.08177	+	0.785951i	0.103778	+	0.994600i	$0.466907\pi$
$8$	−1.43527	+	1.04278i	−0.507444	+	0.368680i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	6.75848			2.13722
$11$	−2.46710	+	2.21662i	−0.743859	+	0.668336i
$11$	−2.46710	+	2.21662i	−0.743859	+	0.668336i
$12$	0.970688			0.280214
$13$	−0.761945	+	2.34502i	−0.211325	+	0.650393i	0.788069	+	0.615587i	$0.211081\pi$
$13$	−0.761945	+	2.34502i	−0.211325	+	0.650393i	−0.999394	+	0.0348054i	$0.988919\pi$
$14$	−4.93301	+	3.58404i	−1.31840	+	0.957875i
$15$	3.17233	+	2.30483i	0.819091	+	0.595105i
$16$	−1.54482	−	4.75447i	−0.386205	−	1.18862i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	1.39440	+	1.01309i	0.328662	+	0.238787i
$19$	−2.19471	+	1.59455i	−0.503501	+	0.365815i	−0.810353	−	0.585942i	$-0.800724\pi$
$19$	−2.19471	+	1.59455i	−0.503501	+	0.365815i	0.306852	+	0.951757i	$0.400724\pi$
$20$	−1.17620	+	3.61998i	−0.263007	+	0.809453i
$21$	−3.53774			−0.771998
$22$	−2.31950	−	5.22470i	−0.494519	−	1.11391i
$23$	−5.32848			−1.11106			−0.555532	−	0.831495i	$-0.687485\pi$
$23$	−5.32848			−1.11106			−0.555532	+	0.831495i	$0.687485\pi$
$24$	0.548224	−	1.68726i	0.111906	−	0.344410i
$25$	−8.39428	+	6.09880i	−1.67886	+	1.21976i
$26$	−3.43817	−	2.49798i	−0.674280	−	0.489893i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.06118	−	3.26597i	−0.200544	−	0.617210i
$29$	2.69281	+	1.95644i	0.500042	+	0.363302i	0.809033	−	0.587763i	$-0.199991\pi$
$29$	2.69281	+	1.95644i	0.500042	+	0.363302i	−0.308991	+	0.951065i	$0.599991\pi$
$30$	−5.46772	+	3.97253i	−0.998265	+	0.725282i
$31$	−2.40792	+	7.41080i	−0.432474	+	1.33102i	0.463178	+	0.886265i	$0.346709\pi$
$31$	−2.40792	+	7.41080i	−0.432474	+	1.33102i	−0.895653	+	0.444754i	$0.853291\pi$
$32$	5.06818			0.895937
$33$	0.693031	−	3.24341i	0.120641	−	0.564605i
$34$	−1.72357			−0.295590
$35$	4.28675	−	13.1933i	0.724594	−	2.23007i
$36$	−0.785303	+	0.570556i	−0.130884	+	0.0950927i
$37$	−9.20481	−	6.68769i	−1.51326	−	1.09945i	−0.964704	−	0.263336i	$-0.915177\pi$
$37$	−9.20481	−	6.68769i	−1.51326	−	1.09945i	−0.548557	−	0.836113i	$-0.684823\pi$
$38$	−1.44488	−	4.44687i	−0.234390	−	0.721378i
$39$	−0.761945	−	2.34502i	−0.122009	−	0.375504i
$40$	5.62799	+	4.08898i	0.889864	+	0.646524i
$41$	−10.0681	+	7.31492i	−1.57238	+	1.14240i	−0.647541	+	0.762031i	$0.724203\pi$
$41$	−10.0681	+	7.31492i	−1.57238	+	1.14240i	−0.924835	+	0.380368i	$0.875797\pi$
$42$	1.88424	−	5.79910i	0.290745	−	0.894821i
$43$	5.23509			0.798344			0.399172	−	0.916876i	$-0.369298\pi$
$43$	5.23509			0.798344			0.399172	+	0.916876i	$0.369298\pi$
$44$	3.20213	−	0.333099i	0.482739	−	0.0502165i
$45$	−3.92121			−0.584540
$46$	2.83801	−	8.73450i	0.418442	−	1.28783i
$47$	7.29965	−	5.30350i	1.06476	−	0.773595i	0.0897991	−	0.995960i	$-0.471377\pi$
$47$	7.29965	−	5.30350i	1.06476	−	0.773595i	0.974964	+	0.222364i	$0.0713775\pi$
$48$	4.04439	+	2.93842i	0.583757	+	0.424125i
$49$	1.70441	+	5.24564i	0.243488	+	0.749378i
$50$	−5.52633	−	17.0083i	−0.781541	−	2.40534i
$51$	−0.809017	−	0.587785i	−0.113285	−	0.0823064i
$52$	1.93633	−	1.40682i	0.268520	−	0.195091i
$53$	1.24305	−	3.82572i	0.170746	−	0.525504i	−0.828667	−	0.559742i	$-0.810900\pi$
$53$	1.24305	−	3.82572i	0.170746	−	0.525504i	0.999414	+	0.0342379i	$0.0109004\pi$
$54$	−1.72357			−0.234548
$55$	11.2559	+	6.51463i	1.51774	+	0.878432i
$56$	−6.27626			−0.838701
$57$	0.838305	−	2.58004i	0.111036	−	0.341734i
$58$	−4.64124	+	3.37206i	−0.609425	+	0.442773i
$59$	2.04218	+	1.48373i	0.265869	+	0.193165i	0.712730	−	0.701438i	$-0.247458\pi$
$59$	2.04218	+	1.48373i	0.265869	+	0.193165i	−0.446862	+	0.894603i	$0.647458\pi$
$60$	−1.17620	−	3.61998i	−0.151847	−	0.467338i
$61$	0.855712	+	2.63361i	0.109563	+	0.337199i	0.990774	−	0.135523i	$-0.0432715\pi$
$61$	0.855712	+	2.63361i	0.109563	+	0.337199i	−0.881212	+	0.472722i	$0.843271\pi$
$62$	−10.8654	−	7.89416i	−1.37991	−	1.00256i
$63$	2.86209	−	2.07943i	0.360590	−	0.261984i
$64$	0.390264	−	1.20111i	0.0487830	−	0.150139i
$65$	9.66855			1.19924
$66$	4.94752	+	2.86350i	0.608997	+	0.352473i
$67$	5.19206			0.634311			0.317156	−	0.948373i	$-0.397272\pi$
$67$	5.19206			0.634311			0.317156	+	0.948373i	$0.397272\pi$
$68$	0.299959	−	0.923179i	0.0363754	−	0.111952i
$69$	4.31083	−	3.13200i	0.518963	−	0.377048i
$70$	19.3434	+	14.0538i	2.31198	+	1.67975i
$71$	2.41474	+	7.43181i	0.286577	+	0.881994i	0.985921	+	0.167209i	$0.0534754\pi$
$71$	2.41474	+	7.43181i	0.286577	+	0.881994i	−0.699344	+	0.714785i	$0.746525\pi$
$72$	0.548224	+	1.68726i	0.0646088	+	0.198845i
$73$	−2.98945	−	2.17196i	−0.349889	−	0.254209i	0.398934	−	0.916980i	$-0.369380\pi$
$73$	−2.98945	−	2.17196i	−0.349889	−	0.254209i	−0.748822	+	0.662771i	$0.769380\pi$
$74$	15.8651	−	11.5267i	1.84428	−	1.33995i
$75$	3.20633	−	9.86807i	0.370235	−	1.13947i
$76$	2.63329			0.302060
$77$	−11.6704	+	1.21400i	−1.32996	+	0.138348i
$78$	4.24981			0.481196
$79$	−0.126666	+	0.389836i	−0.0142510	+	0.0438600i	−0.957929	−	0.287005i	$-0.907340\pi$
$79$	−0.126666	+	0.389836i	−0.0142510	+	0.0438600i	0.943678	+	0.330865i	$0.107340\pi$
$80$	−15.8589	+	11.5222i	−1.77308	+	1.28822i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−6.62829	−	20.3998i	−0.731972	−	2.25278i
$83$	0.899162	+	2.76734i	0.0986959	+	0.303755i	0.988199	−	0.153174i	$-0.0489495\pi$
$83$	0.899162	+	2.76734i	0.0986959	+	0.303755i	−0.889503	+	0.456929i	$0.848949\pi$
$84$	2.77820	+	2.01848i	0.303126	+	0.220234i
$85$	3.17233	−	2.30483i	0.344087	−	0.249994i
$86$	−2.78827	+	8.58142i	−0.300667	+	0.925358i
$87$	−3.32849			−0.356852
$88$	1.22950	−	5.75410i	0.131065	−	0.613389i
$89$	−13.6350			−1.44530			−0.722651	−	0.691213i	$-0.757077\pi$
$89$	−13.6350			−1.44530			−0.722651	+	0.691213i	$0.757077\pi$
$90$	2.08848	−	6.42769i	0.220146	−	0.677538i
$91$	−7.05707	+	5.12726i	−0.739782	+	0.537483i
$92$	4.18447	+	3.04019i	0.436261	+	0.316962i
$93$	−2.40792	−	7.41080i	−0.249689	−	0.768464i
$94$	4.80568	+	14.7904i	0.495668	+	1.52551i
$95$	8.60593	+	6.25257i	0.882949	+	0.641500i
$96$	−4.10025	+	2.97900i	−0.418480	+	0.304043i
$97$	−4.72231	+	14.5338i	−0.479478	+	1.47568i	0.360343	+	0.932820i	$0.382660\pi$
$97$	−4.72231	+	14.5338i	−0.479478	+	1.47568i	−0.839821	+	0.542863i	$0.817340\pi$
$98$	−9.50651			−0.960302
$99$	1.34575	+	3.03133i	0.135253	+	0.304660i
$100$	10.0718			1.00718
$101$	−1.84444	+	5.67659i	−0.183528	+	0.564842i	−0.999920	−	0.0126568i	$-0.995971\pi$
$101$	−1.84444	+	5.67659i	−0.183528	+	0.564842i	0.816392	+	0.577499i	$0.195971\pi$
$102$	1.39440	−	1.01309i	0.138066	−	0.100311i
$103$	−6.19750	−	4.50275i	−0.610658	−	0.443669i	0.238988	−	0.971023i	$-0.423184\pi$
$103$	−6.19750	−	4.50275i	−0.610658	−	0.443669i	−0.849646	+	0.527354i	$0.823184\pi$
$104$	−1.35176	−	4.16028i	−0.132551	−	0.407949i
$105$	4.28675	+	13.1933i	0.418344	+	1.28753i
$106$	5.60910	+	4.07525i	0.544804	+	0.395824i
$107$	−7.09324	+	5.15354i	−0.685729	+	0.498212i	−0.875253	−	0.483664i	$-0.839306\pi$
$107$	−7.09324	+	5.15354i	−0.685729	+	0.498212i	0.189524	+	0.981876i	$0.439306\pi$
$108$	0.299959	−	0.923179i	0.0288636	−	0.0888330i
$109$	9.34840			0.895415			0.447707	−	0.894180i	$-0.352241\pi$
$109$	9.34840			0.895415			0.447707	+	0.894180i	$0.352241\pi$
$110$	−16.6739	+	14.9810i	−1.58979	+	1.42838i
$111$	11.3778			1.07993
$112$	5.46517	−	16.8201i	0.516410	−	1.58935i
$113$	5.65367	−	4.10763i	0.531853	−	0.386414i	−0.289198	−	0.957269i	$-0.593388\pi$
$113$	5.65367	−	4.10763i	0.531853	−	0.386414i	0.821050	+	0.570856i	$0.193388\pi$
$114$	3.78273	+	2.74832i	0.354286	+	0.257403i
$115$	6.45663	+	19.8715i	0.602084	+	1.85302i
$116$	−0.998412	−	3.07280i	−0.0927003	−	0.285302i
$117$	1.99480	+	1.44930i	0.184419	+	0.133988i
$118$	−3.51983	+	2.55731i	−0.324027	+	0.235419i
$119$	−1.09322	+	3.36459i	−0.100215	+	0.308431i
$120$	−6.95658			−0.635046
$121$	1.17319	−	10.9373i	0.106653	−	0.994296i
$122$	−4.77280			−0.432109
$123$	3.84568	−	11.8358i	0.346753	−	1.06720i
$124$	6.11922	−	4.44588i	0.549523	−	0.399251i
$125$	17.0541	+	12.3906i	1.52537	+	1.10824i
$126$	1.88424	+	5.79910i	0.167862	+	0.516625i
$127$	1.88910	+	5.81405i	0.167631	+	0.515914i	0.999221	−	0.0394763i	$-0.0125690\pi$
$127$	1.88910	+	5.81405i	0.167631	+	0.515914i	−0.831590	+	0.555390i	$0.812569\pi$
$128$	9.96151	+	7.23746i	0.880481	+	0.639707i
$129$	−4.23528	+	3.07711i	−0.372895	+	0.270924i
$130$	−5.14959	+	15.8488i	−0.451648	+	1.39003i
$131$	4.29186			0.374981			0.187491	−	0.982266i	$-0.439965\pi$
$131$	4.29186			0.374981			0.187491	+	0.982266i	$0.439965\pi$
$132$	−2.39479	+	2.15165i	−0.208439	+	0.187277i
$133$	−9.59722			−0.832184
$134$	−2.76535	+	8.51089i	−0.238890	+	0.735228i
$135$	3.17233	−	2.30483i	0.273030	−	0.198368i
$136$	−1.43527	−	1.04278i	−0.123073	−	0.0894180i
$137$	3.12389	+	9.61433i	0.266892	+	0.821408i	0.991252	+	0.131986i	$0.0421354\pi$
$137$	3.12389	+	9.61433i	0.266892	+	0.821408i	−0.724360	+	0.689422i	$0.757865\pi$
$138$	2.83801	+	8.73450i	0.241587	+	0.743530i
$139$	−7.94833	−	5.77480i	−0.674168	−	0.489812i	0.197250	−	0.980353i	$-0.436799\pi$
$139$	−7.94833	−	5.77480i	−0.674168	−	0.489812i	−0.871418	+	0.490541i	$0.836799\pi$
$140$	−10.8939	+	7.91488i	−0.920703	+	0.668930i
$141$	−2.78822	+	8.58125i	−0.234810	+	0.722671i
$142$	−13.4684			−1.13025
$143$	−3.31823	−	7.47436i	−0.277485	−	0.625037i
$144$	−4.99914			−0.416595
$145$	4.03321	−	12.4129i	0.334940	−	1.03084i
$146$	5.15252	−	3.74352i	0.426426	−	0.309816i
$147$	−4.46221	−	3.24199i	−0.368037	−	0.267394i
$148$	3.41287	+	10.5037i	0.280536	+	0.863401i
$149$	0.662251	+	2.03820i	0.0542537	+	0.166976i	0.974512	−	0.224336i	$-0.0720214\pi$
$149$	0.662251	+	2.03820i	0.0542537	+	0.166976i	−0.920258	+	0.391312i	$0.872021\pi$
$150$	14.4681	+	10.5117i	1.18132	+	0.858277i
$151$	−13.4434	+	9.76719i	−1.09401	+	0.794843i	−0.980071	−	0.198645i	$-0.936346\pi$
$151$	−13.4434	+	9.76719i	−1.09401	+	0.794843i	−0.113936	+	0.993488i	$0.536346\pi$
$152$	1.48723	−	4.57722i	0.120630	−	0.371261i
$153$	1.00000			0.0808452
$154$	4.22578	−	19.7768i	0.340523	−	1.59366i
$155$	30.5548			2.45422
$156$	−0.739611	+	2.27629i	−0.0592162	+	0.182249i
$157$	19.9462	−	14.4918i	1.59188	−	1.15657i	0.690684	−	0.723156i	$-0.257309\pi$
$157$	19.9462	−	14.4918i	1.59188	−	1.15657i	0.901196	−	0.433412i	$-0.142691\pi$
$158$	−0.571561	−	0.415263i	−0.0454709	−	0.0330366i
$159$	1.24305	+	3.82572i	0.0985805	+	0.303400i
$160$	−6.14122	−	18.9007i	−0.485506	−	1.49424i
$161$	−15.2506	−	11.0802i	−1.20191	−	0.873242i
$162$	1.39440	−	1.01309i	0.109554	−	0.0795957i
$163$	6.72536	−	20.6985i	0.526771	−	1.62123i	−0.234016	−	0.972233i	$-0.575187\pi$
$163$	6.72536	−	20.6985i	0.526771	−	1.62123i	0.760787	−	0.649001i	$-0.224813\pi$
$164$	12.0801			0.943297
$165$	−12.9354	+	1.34559i	−1.00702	+	0.104754i
$166$	−5.01515			−0.389251
$167$	4.26806	−	13.1358i	0.330273	−	1.01647i	−0.638731	−	0.769430i	$-0.720540\pi$
$167$	4.26806	−	13.1358i	0.330273	−	1.01647i	0.969004	−	0.247045i	$-0.0794595\pi$
$168$	5.07760	−	3.68910i	0.391746	−	0.284620i
$169$	5.59864	+	4.06765i	0.430665	+	0.312896i
$170$	2.08848	+	6.42769i	0.160179	+	0.492982i
$171$	0.838305	+	2.58004i	0.0641068	+	0.197300i
$172$	−4.11113	−	2.98691i	−0.313471	−	0.227750i
$173$	2.99549	−	2.17635i	0.227743	−	0.165465i	−0.468062	−	0.883695i	$-0.655048\pi$
$173$	2.99549	−	2.17635i	0.227743	−	0.165465i	0.695805	+	0.718231i	$0.255048\pi$
$174$	1.77280	−	5.45610i	0.134395	−	0.413626i
$175$	−36.7072			−2.77481
$176$	14.3501	+	8.30547i	1.08168	+	0.626049i
$177$	−2.52427			−0.189736
$178$	7.26214	−	22.3506i	0.544320	−	1.67525i
$179$	10.0057	−	7.26955i	0.747860	−	0.543352i	−0.147303	−	0.989091i	$-0.547059\pi$
$179$	10.0057	−	7.26955i	0.747860	−	0.543352i	0.895163	+	0.445739i	$0.147059\pi$
$180$	3.07934	+	2.23727i	0.229521	+	0.166756i
$181$	0.236776	+	0.728721i	0.0175994	+	0.0541654i	0.959471	−	0.281809i	$-0.0909344\pi$
$181$	0.236776	+	0.728721i	0.0175994	+	0.0541654i	−0.941871	+	0.335974i	$0.890934\pi$
$182$	−4.64598	−	14.2989i	−0.344383	−	1.05990i
$183$	−2.24028	−	1.62766i	−0.165606	−	0.120320i
$184$	7.64779	−	5.55645i	0.563803	−	0.409627i
$185$	−13.7867	+	42.4311i	−1.01362	+	3.11959i
$186$	13.4304			0.984761
$187$	−2.87051	−	1.66138i	−0.209912	−	0.121492i
$188$	−8.75838			−0.638771
$189$	−1.09322	+	3.36459i	−0.0795202	+	0.244738i
$190$	−14.8329	+	10.7767i	−1.07609	+	0.781827i
$191$	21.4253	+	15.5664i	1.55028	+	1.12635i	0.943450	+	0.331516i	$0.107560\pi$
$191$	21.4253	+	15.5664i	1.55028	+	1.12635i	0.606833	+	0.794830i	$0.292440\pi$
$192$	0.390264	+	1.20111i	0.0281649	+	0.0866826i
$193$	3.55431	+	10.9390i	0.255845	+	0.787410i	0.993662	+	0.112409i	$0.0358567\pi$
$193$	3.55431	+	10.9390i	0.255845	+	0.787410i	−0.737817	+	0.675001i	$0.764143\pi$
$194$	−21.3088	−	15.4817i	−1.52988	−	1.11152i
$195$	−7.82202	+	5.68303i	−0.560147	+	0.406970i
$196$	1.65445	−	5.09188i	0.118175	−	0.363706i
$197$	11.2723			0.803119			0.401559	−	0.915833i	$-0.368468\pi$
$197$	11.2723			0.803119			0.401559	+	0.915833i	$0.368468\pi$
$198$	−5.68575	+	0.591455i	−0.404069	+	0.0420329i
$199$	19.2614			1.36540			0.682702	−	0.730697i	$-0.260805\pi$
$199$	19.2614			1.36540			0.682702	+	0.730697i	$0.260805\pi$
$200$	5.68832	−	17.5068i	0.402225	−	1.23792i
$201$	−4.20047	+	3.05182i	−0.296278	+	0.215259i
$202$	−8.32276	−	6.04684i	−0.585587	−	0.425454i
$203$	3.63878	+	11.1990i	0.255392	+	0.786017i
$204$	0.299959	+	0.923179i	0.0210013	+	0.0646355i
$205$	39.4792	+	28.6833i	2.75735	+	2.00333i
$206$	10.6818	−	7.76079i	0.744237	−	0.540720i
$207$	−1.64659	+	5.06768i	−0.114446	+	0.352228i
$208$	12.3264			0.854682
$209$	1.88006	−	8.79876i	0.130047	−	0.608623i
$210$	−23.9097			−1.64993
$211$	2.82711	−	8.70096i	0.194626	−	0.598999i	−0.805354	−	0.592794i	$-0.798025\pi$
$211$	2.82711	−	8.70096i	0.194626	−	0.598999i	0.999981	−	0.00620493i	$-0.00197510\pi$
$212$	−3.15896	+	2.29512i	−0.216959	+	0.157630i
$213$	−6.32188	−	4.59311i	−0.433168	−	0.314715i
$214$	−4.66980	−	14.3722i	−0.319221	−	0.982460i
$215$	−6.34347	−	19.5232i	−0.432621	−	1.33147i
$216$	−1.43527	−	1.04278i	−0.0976576	−	0.0709524i
$217$	−22.3019	+	16.2033i	−1.51395	+	1.09995i
$218$	−4.97907	+	15.3240i	−0.337225	+	1.03787i
$219$	3.69516			0.249696
$220$	−5.12231	−	11.5381i	−0.345346	−	0.777896i
$221$	−2.46570			−0.165861
$222$	−6.05994	+	18.6506i	−0.406716	+	1.25174i
$223$	−2.37046	+	1.72224i	−0.158737	+	0.115330i	−0.664319	−	0.747450i	$-0.731278\pi$
$223$	−2.37046	+	1.72224i	−0.158737	+	0.115330i	0.505581	+	0.862779i	$0.331278\pi$
$224$	14.5056	+	10.5389i	0.969196	+	0.704162i
$225$	3.20633	+	9.86807i	0.213755	+	0.657872i
$226$	3.72207	+	11.4553i	0.247588	+	0.761998i
$227$	−1.74773	−	1.26980i	−0.116001	−	0.0842798i	0.528272	−	0.849075i	$-0.322840\pi$
$227$	−1.74773	−	1.26980i	−0.116001	−	0.0842798i	−0.644273	+	0.764795i	$0.722840\pi$
$228$	−2.13038	+	1.54781i	−0.141088	+	0.102506i
$229$	2.19924	−	6.76857i	0.145330	−	0.447279i	−0.851723	−	0.523992i	$-0.824442\pi$
$229$	2.19924	−	6.76857i	0.145330	−	0.447279i	0.997053	+	0.0767122i	$0.0244423\pi$
$230$	−36.0124			−2.37459
$231$	8.72796	−	7.84182i	0.574258	−	0.515954i
$232$	−5.90505			−0.387685
$233$	−6.22331	+	19.1534i	−0.407703	+	1.25478i	0.510914	+	0.859632i	$0.329307\pi$
$233$	−6.22331	+	19.1534i	−0.407703	+	1.25478i	−0.918617	+	0.395149i	$0.870693\pi$
$234$	−3.43817	+	2.49798i	−0.224760	+	0.163298i
$235$	−28.6235	−	20.7962i	−1.86719	−	1.35659i
$236$	−0.757178	−	2.33035i	−0.0492881	−	0.151693i
$237$	−0.126666	−	0.389836i	−0.00822781	−	0.0253226i
$238$	−4.93301	−	3.58404i	−0.319760	−	0.232319i
$239$	11.0960	−	8.06168i	0.717738	−	0.521467i	−0.167923	−	0.985800i	$-0.553706\pi$
$239$	11.0960	−	8.06168i	0.717738	−	0.521467i	0.885661	+	0.464333i	$0.153706\pi$
$240$	6.05757	−	18.6433i	0.391014	−	1.20342i
$241$	−7.20215			−0.463931			−0.231966	−	0.972724i	$-0.574516\pi$
$241$	−7.20215			−0.463931			−0.231966	+	0.972724i	$0.574516\pi$
$242$	17.3036	+	7.74842i	1.11232	+	0.498087i
$243$	1.00000			0.0641500
$244$	0.830629	−	2.55641i	0.0531756	−	0.163658i
$245$	17.4973	−	12.7125i	1.11786	−	0.812173i
$246$	17.3531	+	12.6078i	1.10639	+	0.803842i
$247$	−2.06701	−	6.36161i	−0.131521	−	0.404779i
$248$	−4.27186	−	13.1474i	−0.271263	−	0.834862i
$249$	−2.35404	−	1.71031i	−0.149181	−	0.108386i
$250$	−29.3940	+	21.3560i	−1.85904	+	1.35067i
$251$	−6.41180	+	19.7335i	−0.404709	+	1.24557i	0.516428	+	0.856330i	$0.327261\pi$
$251$	−6.41180	+	19.7335i	−0.404709	+	1.24557i	−0.921138	+	0.389237i	$0.872739\pi$
$252$	−3.43404			−0.216324
$253$	13.1459	−	11.8112i	0.826475	−	0.742564i
$254$	−10.5366			−0.661126
$255$	−1.21172	+	3.72929i	−0.0758809	+	0.233537i
$256$	−15.1259	+	10.9896i	−0.945368	+	0.686850i
$257$	7.40738	+	5.38178i	0.462060	+	0.335706i	0.794339	−	0.607475i	$-0.207818\pi$
$257$	7.40738	+	5.38178i	0.462060	+	0.335706i	−0.332279	+	0.943181i	$0.607818\pi$
$258$	−2.78827	−	8.58142i	−0.173590	−	0.534256i
$259$	−12.4384	−	38.2815i	−0.772886	−	2.37870i
$260$	−7.59274	−	5.51645i	−0.470882	−	0.342116i
$261$	2.69281	−	1.95644i	0.166681	−	0.121101i
$262$	−2.28589	+	7.03526i	−0.141223	+	0.434640i
$263$	−24.0341			−1.48201			−0.741004	−	0.671501i	$-0.765650\pi$
$263$	−24.0341			−1.48201			−0.741004	+	0.671501i	$0.765650\pi$
$264$	2.38749	+	5.37785i	0.146940	+	0.330983i
$265$	−15.7735			−0.968958
$266$	5.11159	−	15.7319i	0.313412	−	0.964583i
$267$	11.0309	−	8.01443i	0.675081	−	0.490475i
$268$	−4.07734	−	2.96236i	−0.249063	−	0.180955i
$269$	−3.35871	−	10.3370i	−0.204784	−	0.630261i	−0.999722	−	0.0235700i	$-0.992497\pi$
$269$	−3.35871	−	10.3370i	−0.204784	−	0.630261i	0.794938	−	0.606691i	$-0.207503\pi$
$270$	2.08848	+	6.42769i	0.127101	+	0.391177i
$271$	19.5269	+	14.1871i	1.18617	+	0.861806i	0.992855	−	0.119330i	$-0.0380747\pi$
$271$	19.5269	+	14.1871i	1.18617	+	0.861806i	0.193319	+	0.981136i	$0.438075\pi$
$272$	4.04439	−	2.93842i	0.245227	−	0.178168i
$273$	2.69556	−	8.29608i	0.163143	−	0.502102i
$274$	−17.4237			−1.05261
$275$	7.19082	−	33.6533i	0.433623	−	2.02937i
$276$	−5.17229			−0.311335
$277$	0.0307632	−	0.0946795i	0.00184838	−	0.00568874i	−0.950128	−	0.311860i	$-0.899048\pi$
$277$	0.0307632	−	0.0946795i	0.00184838	−	0.00568874i	0.951976	+	0.306171i	$0.0990480\pi$
$278$	13.6995	−	9.95326i	0.821641	−	0.596957i
$279$	6.30401	+	4.58013i	0.377411	+	0.274205i
$280$	7.60508	+	23.4060i	0.454491	+	1.39878i
$281$	−9.97664	−	30.7050i	−0.595157	−	1.83170i	−0.553945	−	0.832553i	$-0.686878\pi$
$281$	−9.97664	−	30.7050i	−0.595157	−	1.83170i	−0.0412119	−	0.999150i	$-0.513122\pi$
$282$	−12.5814	−	9.14095i	−0.749214	−	0.544336i
$283$	1.71076	−	1.24294i	0.101694	−	0.0738850i	−0.535776	−	0.844360i	$-0.679981\pi$
$283$	1.71076	−	1.24294i	0.101694	−	0.0738850i	0.637470	+	0.770475i	$0.279981\pi$
$284$	2.34396	−	7.21397i	0.139089	−	0.428071i
$285$	−10.6375			−0.630112
$286$	14.0194	−	1.45835i	0.828983	−	0.0862342i
$287$	−44.0267			−2.59882
$288$	1.56615	−	4.82013i	0.0922865	−	0.284029i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	18.1993	+	13.2226i	1.06870	+	0.776455i
$291$	−4.72231	−	14.5338i	−0.276827	−	0.851986i
$292$	1.10840	+	3.41130i	0.0648641	+	0.199631i
$293$	−4.33030	−	3.14614i	−0.252979	−	0.183800i	0.454067	−	0.890967i	$-0.349973\pi$
$293$	−4.33030	−	3.14614i	−0.252979	−	0.183800i	−0.707046	+	0.707168i	$0.749973\pi$
$294$	7.69093	−	5.58778i	0.448544	−	0.325886i
$295$	3.05871	−	9.41375i	0.178085	−	0.548089i
$296$	20.1852			1.17324
$297$	−2.87051	−	1.66138i	−0.166564	−	0.0964031i
$298$	−3.69376			−0.213974
$299$	4.06000	−	12.4954i	0.234796	−	0.722628i
$300$	−8.14823	+	5.92004i	−0.470438	+	0.341794i
$301$	14.9833	+	10.8860i	0.863623	+	0.627459i
$302$	−8.85038	−	27.2387i	−0.509282	−	1.56741i
$303$	−1.84444	−	5.67659i	−0.105960	−	0.326112i
$304$	10.9717	+	7.97138i	0.629268	+	0.457190i
$305$	8.78462	−	6.38240i	0.503006	−	0.365455i
$306$	−0.532612	+	1.63921i	−0.0304474	+	0.0937075i
$307$	−25.0667			−1.43063			−0.715315	−	0.698802i	$-0.753717\pi$
$307$	−25.0667			−1.43063			−0.715315	+	0.698802i	$0.753717\pi$
$308$	9.85744	+	5.70525i	0.561680	+	0.325087i
$309$	7.66053			0.435792
$310$	−16.2738	+	50.0857i	−0.924292	+	2.84468i
$311$	−19.4903	+	14.1605i	−1.10519	+	0.802969i	−0.981900	−	0.189401i	$-0.939345\pi$
$311$	−19.4903	+	14.1605i	−1.10519	+	0.802969i	−0.123293	+	0.992370i	$0.539345\pi$
$312$	3.53895	+	2.57120i	0.200353	+	0.145565i
$313$	1.80664	+	5.56025i	0.102117	+	0.314284i	0.989043	−	0.147628i	$-0.0471637\pi$
$313$	1.80664	+	5.56025i	0.102117	+	0.314284i	−0.886926	+	0.461912i	$0.847164\pi$
$314$	13.1315	+	40.4145i	0.741052	+	2.28072i
$315$	−11.2229	−	8.15389i	−0.632337	−	0.459420i
$316$	0.321894	−	0.233870i	0.0181080	−	0.0131562i
$317$	−5.70032	+	17.5438i	−0.320162	+	0.985357i	0.653415	+	0.757000i	$0.273336\pi$
$317$	−5.70032	+	17.5438i	−0.320162	+	0.985357i	−0.973577	+	0.228358i	$0.926664\pi$
$318$	−6.93323			−0.388796
$319$	−10.9801	+	1.14220i	−0.614769	+	0.0639507i
$320$	−4.95218			−0.276835
$321$	2.70938	−	8.33860i	0.151223	−	0.465416i
$322$	26.2854	−	19.0975i	1.46483	−	1.06426i
$323$	−2.19471	−	1.59455i	−0.122117	−	0.0887232i
$324$	0.299959	+	0.923179i	0.0166644	+	0.0512877i
$325$	−7.90586	−	24.3317i	−0.438538	−	1.34968i
$326$	30.3473	+	22.0486i	1.68078	+	1.22116i
$327$	−7.56302	+	5.49485i	−0.418236	+	0.303866i
$328$	6.82258	−	20.9977i	0.376714	−	1.15941i
$329$	31.9205			1.75983
$330$	4.68383	−	21.9205i	0.257837	−	1.20668i
$331$	16.3791			0.900274			0.450137	−	0.892959i	$-0.351375\pi$
$331$	16.3791			0.900274			0.450137	+	0.892959i	$0.351375\pi$
$332$	0.872806	−	2.68622i	0.0479015	−	0.147426i
$333$	−9.20481	+	6.68769i	−0.504420	+	0.366483i
$334$	19.2590	+	13.9925i	1.05381	+	0.765636i
$335$	−6.29133	−	19.3627i	−0.343732	−	1.05790i
$336$	5.46517	+	16.8201i	0.298149	+	0.917609i
$337$	−8.23673	−	5.98434i	−0.448683	−	0.325988i	0.340392	−	0.940283i	$-0.389440\pi$
$337$	−8.23673	−	5.98434i	−0.448683	−	0.325988i	−0.789076	+	0.614296i	$0.789440\pi$
$338$	−9.64964	+	7.01088i	−0.524871	+	0.381341i
$339$	−2.15951	+	6.64629i	−0.117289	+	0.360977i
$340$	−3.80627			−0.206424
$341$	−10.4864	−	23.6206i	−0.567868	−	1.27913i
$342$	−4.67572			−0.252834
$343$	1.62278	−	4.99441i	0.0876220	−	0.269673i
$344$	−7.51376	+	5.45907i	−0.405115	+	0.294333i
$345$	−16.9037	−	12.2812i	−0.910063	−	0.661199i
$346$	1.97206	+	6.06938i	0.106019	+	0.326292i
$347$	−4.60285	−	14.1661i	−0.247094	−	0.760477i	−0.995285	−	0.0969939i	$-0.969077\pi$
$347$	−4.60285	−	14.1661i	−0.247094	−	0.760477i	0.748191	−	0.663484i	$-0.230923\pi$
$348$	2.61388	+	1.89909i	0.140119	+	0.101802i
$349$	0.301202	−	0.218836i	0.0161230	−	0.0117140i	−0.579695	−	0.814834i	$-0.696828\pi$
$349$	0.301202	−	0.218836i	0.0161230	−	0.0117140i	0.595818	+	0.803120i	$0.296828\pi$
$350$	19.5507	−	60.1709i	1.04503	−	3.21627i
$351$	−2.46570			−0.131610
$352$	−12.5037	+	11.2342i	−0.666451	+	0.598787i
$353$	28.2820			1.50530			0.752648	−	0.658423i	$-0.228776\pi$
$353$	28.2820			1.50530			0.752648	+	0.658423i	$0.228776\pi$
$354$	1.34446	−	4.13781i	0.0714570	−	0.219922i
$355$	24.7894	−	18.0106i	1.31569	−	0.955902i
$356$	10.7076	+	7.77951i	0.567500	+	0.412313i
$357$	−1.09322	−	3.36459i	−0.0578594	−	0.178073i
$358$	6.58719	+	20.2733i	0.348144	+	1.07148i
$359$	7.06116	+	5.13023i	0.372674	+	0.270763i	0.758319	−	0.651884i	$-0.226021\pi$
$359$	7.06116	+	5.13023i	0.372674	+	0.270763i	−0.385645	+	0.922647i	$0.626021\pi$
$360$	5.62799	−	4.08898i	0.296621	−	0.215508i
$361$	−3.59716	+	11.0709i	−0.189324	+	0.582680i
$362$	−1.32064			−0.0694112
$363$	5.47963	+	9.53801i	0.287606	+	0.500616i
$364$	8.46733			0.443809
$365$	−4.47751	+	13.7803i	−0.234363	+	0.721296i
$366$	3.86128	−	2.80538i	0.201832	−	0.146640i
$367$	−14.4058	−	10.4664i	−0.751975	−	0.546342i	0.144463	−	0.989510i	$-0.453854\pi$
$367$	−14.4058	−	10.4664i	−0.751975	−	0.546342i	−0.896438	+	0.443168i	$0.853854\pi$
$368$	8.23153	+	25.3341i	0.429098	+	1.32063i
$369$	3.84568	+	11.8358i	0.200198	+	0.616146i
$370$	−62.2105	−	45.1986i	−3.23417	−	2.34976i
$371$	11.5131	−	8.36473i	0.597728	−	0.434275i
$372$	−2.33734	+	7.19358i	−0.121185	+	0.372970i
$373$	25.7087			1.33115			0.665574	−	0.746332i	$-0.268187\pi$
$373$	25.7087			1.33115			0.665574	+	0.746332i	$0.268187\pi$
$374$	4.25222	−	3.82050i	0.219877	−	0.197553i
$375$	−21.0801			−1.08857
$376$	−4.94655	+	15.2239i	−0.255099	+	0.785113i
$377$	−6.63967	+	4.82400i	−0.341960	+	0.248449i
$378$	−4.93301	−	3.58404i	−0.253727	−	0.184343i
$379$	0.996554	+	3.06708i	0.0511895	+	0.157545i	0.973383	−	0.229183i	$-0.0736053\pi$
$379$	0.996554	+	3.06708i	0.0511895	+	0.157545i	−0.922194	+	0.386728i	$0.873605\pi$
$380$	−3.19082	−	9.82033i	−0.163686	−	0.503772i
$381$	−4.94573	−	3.59328i	−0.253377	−	0.184089i
$382$	−36.9280	+	26.8298i	−1.88940	+	1.37273i
$383$	−7.55553	+	23.2535i	−0.386070	+	1.18820i	0.549632	+	0.835407i	$0.314768\pi$
$383$	−7.55553	+	23.2535i	−0.386070	+	1.18820i	−0.935701	+	0.352793i	$0.885232\pi$
$384$	−12.3131			−0.628350
$385$	18.6686	+	42.0513i	0.951441	+	2.14313i
$386$	−19.8245			−1.00904
$387$	1.61773	−	4.97887i	0.0822339	−	0.253090i
$388$	12.0008	−	8.71909i	0.609248	−	0.442645i
$389$	2.24174	+	1.62872i	0.113661	+	0.0825795i	0.643164	−	0.765729i	$-0.277621\pi$
$389$	2.24174	+	1.62872i	0.113661	+	0.0825795i	−0.529503	+	0.848308i	$0.677621\pi$
$390$	−5.14959	−	15.8488i	−0.260759	−	0.802535i
$391$	−1.64659	−	5.06768i	−0.0832716	−	0.256284i
$392$	−7.91636	−	5.75157i	−0.399837	−	0.290498i
$393$	−3.47219	+	2.52269i	−0.175149	+	0.127253i
$394$	−6.00377	+	18.4777i	−0.302465	+	0.930893i
$395$	1.60730			0.0808720
$396$	0.672717	−	3.14834i	0.0338053	−	0.158210i
$397$	−25.5164			−1.28063			−0.640316	−	0.768112i	$-0.721197\pi$
$397$	−25.5164			−1.28063			−0.640316	+	0.768112i	$0.721197\pi$
$398$	−10.2589	+	31.5735i	−0.514230	+	1.58264i
$399$	7.76431	−	5.64110i	0.388702	−	0.282408i
$400$	41.9642	+	30.4888i	2.09821	+	1.52444i
$401$	−0.0305965	−	0.0941665i	−0.00152792	−	0.00470245i	0.950290	−	0.311367i	$-0.100787\pi$
$401$	−0.0305965	−	0.0941665i	−0.00152792	−	0.00470245i	−0.951818	+	0.306665i	$0.900787\pi$
$402$	−2.76535	−	8.51089i	−0.137923	−	0.424484i
$403$	−15.5438	−	11.2932i	−0.774292	−	0.562556i
$404$	4.68726	−	3.40549i	0.233200	−	0.169429i
$405$	−1.21172	+	3.72929i	−0.0602109	+	0.185310i
$406$	−20.2956			−1.00725
$407$	37.5333	−	3.90436i	1.86046	−	0.193532i
$408$	1.77409			0.0878305
$409$	−10.6569	+	32.7987i	−0.526952	+	1.62179i	0.233471	+	0.972364i	$0.424992\pi$
$409$	−10.6569	+	32.7987i	−0.526952	+	1.62179i	−0.760423	+	0.649428i	$0.775008\pi$
$410$	−68.0452	+	49.4377i	−3.36051	+	2.44155i
$411$	−8.17844	−	5.94199i	−0.403413	−	0.293097i
$412$	2.29785	+	7.07205i	0.113207	+	0.348415i
$413$	2.75959	+	8.49313i	0.135790	+	0.417920i
$414$	−7.43001	−	5.39822i	−0.365165	−	0.265308i
$415$	9.23068	−	6.70648i	0.453116	−	0.329208i
$416$	−3.86167	+	11.8850i	−0.189334	+	0.582711i
$417$	9.82467			0.481116
$418$	13.4217	+	7.76814i	0.656476	+	0.379952i
$419$	−13.4576			−0.657447			−0.328724	−	0.944426i	$-0.606618\pi$
$419$	−13.4576			−0.657447			−0.328724	+	0.944426i	$0.606618\pi$
$420$	4.16110	−	12.8066i	0.203041	−	0.624896i
$421$	−8.07877	+	5.86957i	−0.393735	+	0.286065i	−0.766984	−	0.641666i	$-0.778244\pi$
$421$	−8.07877	+	5.86957i	−0.393735	+	0.286065i	0.373249	+	0.927731i	$0.378244\pi$
$422$	12.7570	+	9.26847i	0.620999	+	0.451182i
$423$	−2.78822	−	8.58125i	−0.135568	−	0.417235i
$424$	2.20529	+	6.78718i	0.107098	+	0.329614i
$425$	−8.39428	−	6.09880i	−0.407183	−	0.295835i
$426$	10.8962	−	7.91654i	0.527922	−	0.383558i
$427$	−3.02728	+	9.31702i	−0.146501	+	0.450882i
$428$	8.51073			0.411382
$429$	7.07782	+	4.09647i	0.341721	+	0.197780i
$430$	35.3812			1.70624
$431$	−1.19208	+	3.66883i	−0.0574202	+	0.176721i	−0.975653	−	0.219320i	$-0.929616\pi$
$431$	−1.19208	+	3.66883i	−0.0574202	+	0.176721i	0.918233	+	0.396041i	$0.129616\pi$
$432$	4.04439	−	2.93842i	0.194586	−	0.141375i
$433$	−8.40593	−	6.10727i	−0.403963	−	0.293496i	0.367190	−	0.930146i	$-0.380320\pi$
$433$	−8.40593	−	6.10727i	−0.403963	−	0.293496i	−0.771153	+	0.636649i	$0.780320\pi$
$434$	−14.6824	−	45.1876i	−0.704775	−	2.16908i
$435$	4.03321	+	12.4129i	0.193377	+	0.595155i
$436$	−7.34133	−	5.33379i	−0.351586	−	0.255442i
$437$	11.6945	−	8.49652i	0.559422	−	0.406444i
$438$	−1.96809	+	6.05715i	−0.0940389	+	0.289422i
$439$	−15.9156			−0.759608			−0.379804	−	0.925067i	$-0.624009\pi$
$439$	−15.9156			−0.759608			−0.379804	+	0.925067i	$0.624009\pi$
$440$	−22.9485	+	2.38720i	−1.09403	+	0.113805i
$441$	5.51560			0.262647
$442$	1.31326	−	4.04181i	0.0624656	−	0.192249i
$443$	−2.17757	+	1.58210i	−0.103460	+	0.0751678i	−0.638312	−	0.769778i	$-0.720367\pi$
$443$	−2.17757	+	1.58210i	−0.103460	+	0.0751678i	0.534853	+	0.844945i	$0.320367\pi$
$444$	−8.93500	−	6.49166i	−0.424036	−	0.308080i
$445$	16.5218	+	50.8488i	0.783207	+	2.41046i
$446$	−1.56058	−	4.80296i	−0.0738955	−	0.227427i
$447$	−1.73380	−	1.25968i	−0.0820057	−	0.0595807i
$448$	3.61460	−	2.62616i	0.170774	−	0.124074i
$449$	−1.88622	+	5.80520i	−0.0890164	+	0.273964i	−0.985648	−	0.168813i	$-0.946007\pi$
$449$	−1.88622	+	5.80520i	−0.0890164	+	0.273964i	0.896632	+	0.442777i	$0.146007\pi$
$450$	−17.8836			−0.843040
$451$	8.62469	−	40.3639i	0.406121	−	1.90066i
$452$	−6.78348			−0.319068
$453$	5.13492	−	15.8036i	0.241259	−	0.742520i
$454$	3.01234	−	2.18859i	0.141376	−	0.102716i
$455$	27.6723	+	20.1051i	1.29730	+	0.942541i
$456$	1.48723	+	4.57722i	0.0696458	+	0.214348i
$457$	−9.87933	−	30.4055i	−0.462136	−	1.42231i	−0.862549	−	0.505973i	$-0.831134\pi$
$457$	−9.87933	−	30.4055i	−0.462136	−	1.42231i	0.400414	−	0.916335i	$-0.368866\pi$
$458$	9.92377	+	7.21004i	0.463707	+	0.336903i
$459$	−0.809017	+	0.587785i	−0.0377617	+	0.0274355i
$460$	6.26737	−	19.2890i	0.292218	−	0.899354i
$461$	−19.9035			−0.927000			−0.463500	−	0.886097i	$-0.653407\pi$
$461$	−19.9035			−0.927000			−0.463500	+	0.886097i	$0.653407\pi$
$462$	8.20579	+	18.4836i	0.381768	+	0.859936i
$463$	15.0596			0.699878			0.349939	−	0.936772i	$-0.386202\pi$
$463$	15.0596			0.699878			0.349939	+	0.936772i	$0.386202\pi$
$464$	5.14192	−	15.8252i	0.238708	−	0.734667i
$465$	−24.7193	+	17.9597i	−1.14633	+	0.832859i
$466$	−28.0818	−	20.4026i	−1.30087	−	0.945134i
$467$	−5.36353	−	16.5072i	−0.248194	−	0.763864i	−0.995095	−	0.0989278i	$-0.968459\pi$
$467$	−5.36353	−	16.5072i	−0.248194	−	0.763864i	0.746900	−	0.664936i	$-0.231541\pi$
$468$	−0.739611	−	2.27629i	−0.0341885	−	0.105221i
$469$	14.8602	+	10.7965i	0.686178	+	0.498538i
$470$	49.3345	−	35.8436i	2.27563	−	1.65334i
$471$	−7.61877	+	23.4482i	−0.351054	+	1.08043i
$472$	−4.47828			−0.206130
$473$	−12.9155	+	11.6042i	−0.593856	+	0.533562i
$474$	0.706488			0.0324501
$475$	8.69817	−	26.7702i	0.399100	−	1.22830i
$476$	2.77820	−	2.01848i	0.127338	−	0.0925168i
$477$	−3.25436	−	2.36443i	−0.149007	−	0.108260i
$478$	7.30496	+	22.4824i	0.334121	+	1.02832i
$479$	11.5874	+	35.6624i	0.529443	+	1.62946i	0.755359	+	0.655311i	$0.227462\pi$
$479$	11.5874	+	35.6624i	0.529443	+	1.62946i	−0.225916	+	0.974147i	$0.572538\pi$
$480$	16.0779	+	11.6813i	0.733854	+	0.533176i
$481$	22.6963	−	16.4899i	1.03486	−	0.751873i
$482$	3.83595	−	11.8058i	0.174723	−	0.537742i
$483$	18.8508			0.857739
$484$	−7.16163	+	7.91970i	−0.325529	+	0.359986i
$485$	59.9229			2.72096
$486$	−0.532612	+	1.63921i	−0.0241598	+	0.0743561i
$487$	0.333613	−	0.242384i	0.0151174	−	0.0109835i	−0.580201	−	0.814473i	$-0.697026\pi$
$487$	0.333613	−	0.242384i	0.0151174	−	0.0109835i	0.595318	+	0.803490i	$0.297026\pi$
$488$	−3.97446	−	2.88761i	−0.179915	−	0.130716i
$489$	6.72536	+	20.6985i	0.304131	+	0.936020i
$490$	11.5192	+	35.4526i	0.520386	+	1.60158i
$491$	17.9352	+	13.0307i	0.809402	+	0.588065i	0.913657	−	0.406485i	$-0.133246\pi$
$491$	17.9352	+	13.0307i	0.809402	+	0.588065i	−0.104255	+	0.994551i	$0.533246\pi$
$492$	−9.77301	+	7.10050i	−0.440601	+	0.320115i
$493$	−1.02856	+	3.16559i	−0.0463241	+	0.142571i
$494$	11.5289			0.518711
$495$	9.67403	−	8.69184i	0.434815	−	0.390669i
$496$	38.9542			1.74910
$497$	−8.54273	+	26.2918i	−0.383194	+	1.17935i
$498$	4.05734	−	2.94783i	0.181814	−	0.132096i
$499$	−20.4634	−	14.8675i	−0.916065	−	0.665561i	0.0264761	−	0.999649i	$-0.491571\pi$
$499$	−20.4634	−	14.8675i	−0.916065	−	0.665561i	−0.942542	+	0.334089i	$0.891571\pi$
$500$	−6.32316	−	19.4607i	−0.282780	−	0.870308i
$501$	4.26806	+	13.1358i	0.190683	+	0.586862i
$502$	−28.9324	−	21.0206i	−1.29131	−	0.938195i
$503$	17.4512	−	12.6791i	0.778112	−	0.565331i	−0.126300	−	0.991992i	$-0.540310\pi$
$503$	17.4512	−	12.6791i	0.778112	−	0.565331i	0.904412	+	0.426661i	$0.140310\pi$
$504$	−1.93947	+	5.96908i	−0.0863910	+	0.265884i
$505$	23.4046			1.04149
$506$	12.3594	+	27.8397i	0.549442	+	1.23762i
$507$	−6.92030			−0.307341
$508$	1.83373	−	5.64363i	0.0813585	−	0.250396i
$509$	−18.1476	+	13.1850i	−0.804377	+	0.584414i	−0.912195	−	0.409756i	$-0.865614\pi$
$509$	−18.1476	+	13.1850i	−0.804377	+	0.584414i	0.107818	+	0.994171i	$0.465614\pi$
$510$	−5.46772	−	3.97253i	−0.242115	−	0.175907i
$511$	−4.03963	−	12.4327i	−0.178703	−	0.549990i
$512$	−2.34813	−	7.22681i	−0.103774	−	0.319383i
$513$	−2.19471	−	1.59455i	−0.0968988	−	0.0704011i
$514$	−12.7671	+	9.27586i	−0.563134	+	0.409141i
$515$	−9.28243	+	28.5684i	−0.409033	+	1.25887i
$516$	5.08164			0.223707
$517$	−6.25312	+	29.2648i	−0.275012	+	1.28707i
$518$	69.3764			3.04822
$519$	−1.14417	+	3.52140i	−0.0502236	+	0.154572i
$520$	−13.8770	+	10.0822i	−0.608545	+	0.442134i
$521$	6.69836	+	4.86664i	0.293460	+	0.213211i	0.724767	−	0.688994i	$-0.241947\pi$
$521$	6.69836	+	4.86664i	0.293460	+	0.213211i	−0.431307	+	0.902205i	$0.641947\pi$
$522$	1.77280	+	5.45610i	0.0775932	+	0.238807i
$523$	0.141912	+	0.436760i	0.00620538	+	0.0190982i	0.954111	−	0.299452i	$-0.0968040\pi$
$523$	0.141912	+	0.436760i	0.00620538	+	0.0190982i	−0.947906	+	0.318551i	$0.896804\pi$
$524$	−3.37041	−	2.44875i	−0.147237	−	0.106974i
$525$	29.6968	−	21.5760i	1.29607	−	0.941653i
$526$	12.8009	−	39.3970i	0.558144	−	1.71779i
$527$	−7.79218			−0.339433
$528$	−16.4913	+	1.71549i	−0.717691	+	0.0746572i
$529$	5.39265			0.234463
$530$	8.40115	−	25.8561i	0.364923	−	1.12312i
$531$	2.04218	−	1.48373i	0.0886229	−	0.0643883i
$532$	7.53673	+	5.47575i	0.326759	+	0.237404i
$533$	−9.48231	−	29.1835i	−0.410724	−	1.26408i
$534$	7.26214	+	22.3506i	0.314264	+	0.967204i
$535$	27.8141	+	20.2081i	1.20251	+	0.873674i
$536$	−7.45200	+	5.41420i	−0.321877	+	0.233858i
$537$	−3.82183	+	11.7624i	−0.164924	+	0.507584i
$538$	18.7335			0.807658
$539$	−15.8326	−	9.16350i	−0.681957	−	0.394700i
$540$	−3.80627			−0.163796
$541$	−4.90502	+	15.0961i	−0.210883	+	0.649032i	0.788537	+	0.614987i	$0.210839\pi$
$541$	−4.90502	+	15.0961i	−0.210883	+	0.649032i	−0.999420	+	0.0340450i	$0.989161\pi$
$542$	−33.6559	+	24.4525i	−1.44565	+	1.05032i
$543$	−0.619888	−	0.450375i	−0.0266019	−	0.0193274i
$544$	1.56615	+	4.82013i	0.0671483	+	0.206661i
$545$	−11.3277	−	34.8630i	−0.485224	−	1.49336i
$546$	12.1633	+	8.83719i	0.520543	+	0.378197i
$547$	−28.0887	+	20.4076i	−1.20098	+	0.872566i	−0.994381	−	0.105858i	$-0.966241\pi$
$547$	−28.0887	+	20.4076i	−1.20098	+	0.872566i	−0.206603	+	0.978425i	$0.566241\pi$
$548$	3.03232	−	9.33252i	0.129534	−	0.398666i
$549$	2.76914			0.118184
$550$	51.3350	+	29.7114i	2.18893	+	1.26690i
$551$	−9.02958			−0.384673
$552$	−2.92120	+	8.99052i	−0.124334	+	0.382662i
$553$	−1.17317	+	0.852355i	−0.0498881	+	0.0362458i
$554$	0.138815	+	0.100855i	0.00589767	+	0.00428491i
$555$	−13.7867	−	42.4311i	−0.585212	−	1.80110i
$556$	2.94700	+	9.06994i	0.124981	+	0.384651i
$557$	−2.42973	−	1.76530i	−0.102951	−	0.0747982i	0.535119	−	0.844777i	$-0.320267\pi$
$557$	−2.42973	−	1.76530i	−0.102951	−	0.0747982i	−0.638070	+	0.769979i	$0.720267\pi$
$558$	−10.8654	+	7.89416i	−0.459968	+	0.334187i
$559$	−3.98885	+	12.2764i	−0.168710	+	0.519237i
$560$	−69.3492			−2.93054
$561$	3.29882	−	0.343157i	0.139276	−	0.0144881i
$562$	55.6456			2.34727
$563$	−0.0860134	+	0.264722i	−0.00362503	+	0.0111567i	−0.952853	−	0.303433i	$-0.901867\pi$
$563$	−0.0860134	+	0.264722i	−0.00362503	+	0.0111567i	0.949228	+	0.314590i	$0.101867\pi$
$564$	7.08568	−	5.14805i	0.298361	−	0.216772i
$565$	−22.1693	−	16.1069i	−0.932668	−	0.677623i
$566$	1.12627	+	3.46630i	0.0473406	+	0.145699i
$567$	−1.09322	−	3.36459i	−0.0459110	−	0.141299i
$568$	−11.2156	−	8.14859i	−0.470595	−	0.341907i
$569$	25.8265	−	18.7641i	1.08270	−	0.786630i	0.104551	−	0.994520i	$-0.466659\pi$
$569$	25.8265	−	18.7641i	1.08270	−	0.786630i	0.978152	+	0.207890i	$0.0666595\pi$
$570$	5.66566	−	17.4371i	0.237309	−	0.730361i
$571$	−14.5506			−0.608925			−0.304463	−	0.952524i	$-0.598477\pi$
$571$	−14.5506			−0.608925			−0.304463	+	0.952524i	$0.598477\pi$
$572$	−1.65872	+	7.76287i	−0.0693546	+	0.324582i
$573$	−26.4832			−1.10635
$574$	23.4492	−	72.1691i	0.978749	−	3.01228i
$575$	44.7287	−	32.4973i	1.86532	−	1.35523i
$576$	−1.02173	−	0.742327i	−0.0425719	−	0.0309303i
$577$	−11.5535	−	35.5580i	−0.480978	−	1.48030i	−0.837722	−	0.546097i	$-0.816113\pi$
$577$	−11.5535	−	35.5580i	−0.480978	−	1.48030i	0.356744	−	0.934202i	$-0.383887\pi$
$578$	−0.532612	−	1.63921i	−0.0221537	−	0.0681822i
$579$	−9.30531	−	6.76070i	−0.386715	−	0.280965i
$580$	−10.2496	+	7.44675i	−0.425590	+	0.309209i
$581$	−3.18100	+	9.79012i	−0.131970	+	0.406162i
$582$	26.3391			1.09179
$583$	5.41344	+	12.1938i	0.224202	+	0.505017i
$584$	6.55555			0.271270
$585$	2.98775	−	9.19534i	0.123528	−	0.380180i
$586$	7.46356	−	5.42259i	0.308317	−	0.224005i
$587$	−5.27082	−	3.82947i	−0.217550	−	0.158059i	0.473673	−	0.880701i	$-0.342928\pi$
$587$	−5.27082	−	3.82947i	−0.217550	−	0.158059i	−0.691223	+	0.722641i	$0.742928\pi$
$588$	1.65445	+	5.09188i	0.0682285	+	0.209986i
$589$	−6.53222	−	20.1041i	−0.269156	−	0.828376i
$590$	13.8020	+	10.0277i	0.568220	+	0.412836i
$591$	−9.11949	+	6.62570i	−0.375126	+	0.272545i
$592$	−17.5766	+	54.0952i	−0.722394	+	2.22330i
$593$	40.0335			1.64398			0.821989	−	0.569504i	$-0.192865\pi$
$593$	40.0335			1.64398			0.821989	+	0.569504i	$0.192865\pi$
$594$	4.25222	−	3.82050i	0.174471	−	0.156757i
$595$	13.8722			0.568706
$596$	0.642839	−	1.97846i	0.0263317	−	0.0810407i
$597$	−15.5828	+	11.3216i	−0.637762	+	0.463361i
$598$	18.3202	+	13.3104i	0.749169	+	0.544303i
$599$	4.40242	+	13.5492i	0.179878	+	0.553607i	0.999823	−	0.0188356i	$-0.00599590\pi$
$599$	4.40242	+	13.5492i	0.179878	+	0.553607i	−0.819945	+	0.572443i	$0.805996\pi$
$600$	5.68832	+	17.5068i	0.232225	+	0.714714i
$601$	−16.3437	−	11.8744i	−0.666674	−	0.484367i	0.202236	−	0.979337i	$-0.435179\pi$
$601$	−16.3437	−	11.8744i	−0.666674	−	0.484367i	−0.868910	+	0.494970i	$0.835179\pi$
$602$	−25.8248	+	18.7628i	−1.05254	+	0.764714i
$603$	1.60444	−	4.93794i	0.0653377	−	0.201089i
$604$	16.1299			0.656315
$605$	−42.2098	+	8.87775i	−1.71607	+	0.360932i
$606$	10.2875			0.417901
$607$	−8.96369	+	27.5874i	−0.363825	+	1.11974i	0.586888	+	0.809668i	$0.300353\pi$
$607$	−8.96369	+	27.5874i	−0.363825	+	1.11974i	−0.950714	+	0.310071i	$0.899647\pi$
$608$	−11.1232	+	8.08147i	−0.451105	+	0.327747i
$609$	−9.52645	−	6.92137i	−0.386031	−	0.280468i
$610$	5.78331	+	17.7992i	0.234159	+	0.720668i
$611$	6.87492	+	21.1588i	0.278129	+	0.855994i
$612$	−0.785303	−	0.570556i	−0.0317440	−	0.0230634i
$613$	−13.2245	+	9.60814i	−0.534131	+	0.388069i	−0.821901	−	0.569631i	$-0.807086\pi$
$613$	−13.2245	+	9.60814i	−0.534131	+	0.388069i	0.287770	+	0.957700i	$0.407086\pi$
$614$	13.3508	−	41.0896i	0.538795	−	1.65824i
$615$	−48.7990			−1.96777
$616$	15.4842	−	13.9121i	0.623876	−	0.560534i
$617$	35.1554			1.41530			0.707652	−	0.706561i	$-0.249754\pi$
$617$	35.1554			1.41530			0.707652	+	0.706561i	$0.249754\pi$
$618$	−4.08009	+	12.5572i	−0.164125	+	0.505126i
$619$	−11.7244	+	8.51829i	−0.471244	+	0.342379i	−0.797926	−	0.602755i	$-0.794069\pi$
$619$	−11.7244	+	8.51829i	−0.471244	+	0.342379i	0.326682	+	0.945134i	$0.394069\pi$
$620$	−23.9948	−	17.4332i	−0.963653	−	0.700135i
$621$	−1.64659	−	5.06768i	−0.0660754	−	0.203359i
$622$	−12.8313	−	39.4907i	−0.514489	−	1.58343i
$623$	−39.0245	−	28.3529i	−1.56348	−	1.13594i
$624$	−9.97227	+	7.24528i	−0.399210	+	0.290043i
$625$	9.51151	−	29.2734i	0.380460	−	1.17094i
$626$	−10.0767			−0.402744
$627$	3.65078	+	8.22342i	0.145798	+	0.328412i
$628$	−23.9322			−0.954998
$629$	3.51592	−	10.8209i	0.140189	−	0.431458i
$630$	19.3434	−	14.0538i	0.770659	−	0.559916i
$631$	3.63729	+	2.64265i	0.144798	+	0.105202i	0.657826	−	0.753170i	$-0.271476\pi$
$631$	3.63729	+	2.64265i	0.144798	+	0.105202i	−0.513028	+	0.858372i	$0.671476\pi$
$632$	−0.224716	−	0.691605i	−0.00893872	−	0.0275106i
$633$	2.82711	+	8.70096i	0.112368	+	0.345832i
$634$	−25.7219	−	18.6881i	−1.02155	−	0.742198i
$635$	19.3933	−	14.0900i	0.769598	−	0.559145i
$636$	1.20662	−	3.71359i	0.0478455	−	0.147253i
$637$	−13.5998			−0.538845
$638$	3.97584	−	18.6071i	0.157405	−	0.736661i
$639$	7.81427			0.309128
$640$	14.9200	−	45.9192i	0.589766	−	1.81511i
$641$	6.92728	−	5.03297i	0.273611	−	0.198790i	−0.442515	−	0.896761i	$-0.645914\pi$
$641$	6.92728	−	5.03297i	0.273611	−	0.198790i	0.716126	+	0.697971i	$0.245914\pi$
$642$	12.2257	+	8.88248i	0.482509	+	0.350564i
$643$	−4.49966	−	13.8485i	−0.177449	−	0.546132i	0.822288	−	0.569072i	$-0.192697\pi$
$643$	−4.49966	−	13.8485i	−0.177449	−	0.546132i	−0.999737	+	0.0229397i	$0.992697\pi$
$644$	5.65446	+	17.4026i	0.222817	+	0.685760i
$645$	16.6074	+	12.0660i	0.653917	+	0.475098i
$646$	3.78273	−	2.74832i	0.148830	−	0.108131i
$647$	11.3455	−	34.9178i	0.446037	−	1.37276i	−0.435306	−	0.900283i	$-0.643360\pi$
$647$	11.3455	−	34.9178i	0.446037	−	1.37276i	0.881343	−	0.472478i	$-0.156640\pi$
$648$	1.77409			0.0696928
$649$	−8.32712	+	0.866221i	−0.326868	+	0.0340022i
$650$	44.0956			1.72957
$651$	8.51858	−	26.2175i	0.333869	−	1.02754i
$652$	−17.0911	+	12.4174i	−0.669340	+	0.486304i
$653$	−28.8762	−	20.9798i	−1.13001	−	0.821002i	−0.144315	−	0.989532i	$-0.546098\pi$
$653$	−28.8762	−	20.9798i	−1.13001	−	0.821002i	−0.985696	+	0.168530i	$0.946098\pi$
$654$	−4.97907	−	15.3240i	−0.194697	−	0.599216i
$655$	−5.20053	−	16.0056i	−0.203202	−	0.625390i
$656$	50.3320	+	36.5683i	1.96513	+	1.42775i
$657$	−2.98945	+	2.17196i	−0.116630	+	0.0847363i
$658$	−17.0012	+	52.3245i	−0.662778	+	2.03982i
$659$	6.79564			0.264720			0.132360	−	0.991202i	$-0.457744\pi$
$659$	6.79564			0.264720			0.132360	+	0.991202i	$0.457744\pi$
$660$	10.9259	+	6.32367i	0.425292	+	0.246149i
$661$	−20.0185			−0.778628			−0.389314	−	0.921105i	$-0.627288\pi$
$661$	−20.0185			−0.778628			−0.389314	+	0.921105i	$0.627288\pi$
$662$	−8.72368	+	26.8487i	−0.339055	+	1.04351i
$663$	1.99480	−	1.44930i	0.0774715	−	0.0562863i
$664$	−4.17627	−	3.03424i	−0.162071	−	0.117751i
$665$	11.6292	+	35.7909i	0.450959	+	1.38791i
$666$	−6.05994	−	18.6506i	−0.234818	−	0.722695i
$667$	−14.3486	−	10.4248i	−0.555579	−	0.403652i
$668$	−10.8464	+	7.88038i	−0.419660	+	0.304901i
$669$	0.905434	−	2.78664i	0.0350061	−	0.107738i
$670$	35.0904			1.35566
$671$	−7.94884	−	4.60060i	−0.306862	−	0.177604i
$672$	−17.9299			−0.691661
$673$	1.27890	−	3.93605i	0.0492980	−	0.151724i	−0.923377	−	0.383894i	$-0.874583\pi$
$673$	1.27890	−	3.93605i	0.0492980	−	0.151724i	0.972675	+	0.232170i	$0.0745827\pi$
$674$	14.1966	−	10.3144i	0.546832	−	0.397296i
$675$	−8.39428	−	6.09880i	−0.323096	−	0.234743i
$676$	−2.07581	−	6.38868i	−0.0798388	−	0.245718i
$677$	−5.49015	−	16.8969i	−0.211004	−	0.649402i	−0.999413	−	0.0342516i	$-0.989095\pi$
$677$	−5.49015	−	16.8969i	−0.211004	−	0.649402i	0.788410	−	0.615151i	$-0.210905\pi$
$678$	−9.74449	−	7.07979i	−0.374235	−	0.271898i
$679$	−43.7377	+	31.7773i	−1.67850	+	1.21950i
$680$	−2.14970	+	6.61610i	−0.0824373	+	0.253716i
$681$	2.16032			0.0827836
$682$	44.3044	−	4.60872i	1.69650	−	0.176477i
$683$	−20.7562			−0.794215			−0.397108	−	0.917772i	$-0.629986\pi$
$683$	−20.7562			−0.794215			−0.397108	+	0.917772i	$0.629986\pi$
$684$	0.813733	−	2.50441i	0.0311138	−	0.0957586i
$685$	32.0694	−	23.2998i	1.22531	−	0.890239i
$686$	7.32258	+	5.32017i	0.279577	+	0.203125i
$687$	2.19924	+	6.76857i	0.0839063	+	0.258237i
$688$	−8.08727	−	24.8901i	−0.308324	−	0.948925i
$689$	8.02428	+	5.82998i	0.305701	+	0.222105i
$690$	29.1346	−	21.1675i	1.10914	−	0.805835i
$691$	−8.61764	+	26.5224i	−0.327831	+	1.00896i	0.642316	+	0.766440i	$0.277974\pi$
$691$	−8.61764	+	26.5224i	−0.327831	+	1.00896i	−0.970147	+	0.242519i	$0.922026\pi$
$692$	−3.59409			−0.136627
$693$	−2.45176	+	11.4743i	−0.0931348	+	0.435874i
$694$	25.6728			0.974526
$695$	−11.9048	+	36.6391i	−0.451574	+	1.38980i
$696$	4.77728	−	3.47090i	0.181082	−	0.131564i
$697$	−10.0681	−	7.31492i	−0.381357	−	0.277072i
$698$	0.198294	+	0.610288i	0.00750556	+	0.0230997i
$699$	−6.22331	−	19.1534i	−0.235387	−	0.724448i
$700$	28.8263	+	20.9435i	1.08953	+	0.791592i
$701$	−30.5422	+	22.1902i	−1.15356	+	0.838112i	−0.988950	−	0.148246i	$-0.952637\pi$
$701$	−30.5422	+	22.1902i	−1.15356	+	0.838112i	−0.164612	+	0.986358i	$0.552637\pi$
$702$	1.31326	−	4.04181i	0.0495659	−	0.152548i
$703$	30.8657			1.16412
$704$	1.69958	+	3.82833i	0.0640554	+	0.144286i
$705$	35.3805			1.33251
$706$	−15.0633	+	46.3601i	−0.566915	+	1.74479i
$707$	−17.0830	+	12.4115i	−0.642473	+	0.466784i
$708$	1.98232	+	1.44024i	0.0745000	+	0.0541275i
$709$	−9.78855	−	30.1261i	−0.367617	−	1.13141i	−0.948326	−	0.317297i	$-0.897225\pi$
$709$	−9.78855	−	30.1261i	−0.367617	−	1.13141i	0.580709	−	0.814111i	$-0.302775\pi$
$710$	16.3200	+	50.2277i	0.612478	+	1.88501i
$711$	0.331615	+	0.240932i	0.0124365	+	0.00903566i
$712$	19.5698	−	14.2183i	0.733410	−	0.532854i
$713$	12.8305	−	39.4883i	0.480507	−	1.47885i
$714$	6.09754			0.228195
$715$	−23.8533	+	21.4315i	−0.892063	+	0.801493i
$716$	−12.0052			−0.448655
$717$	−4.23828	+	13.0441i	−0.158281	+	0.487140i
$718$	−12.1704	+	8.84231i	−0.454195	+	0.329992i
$719$	31.8702	+	23.1551i	1.18856	+	0.863538i	0.993111	−	0.117176i	$-0.0373843\pi$
$719$	31.8702	+	23.1551i	1.18856	+	0.863538i	0.195447	+	0.980714i	$0.437384\pi$
$720$	6.05757	+	18.6433i	0.225752	+	0.694794i
$721$	−8.37466	−	25.7745i	−0.311889	−	0.959894i
$722$	−16.2317	−	11.7930i	−0.604081	−	0.438890i
$723$	5.82666	−	4.23332i	0.216696	−	0.157439i
$724$	0.229836	−	0.707361i	0.00854177	−	0.0262889i
$725$	−34.5361			−1.28264
$726$	−18.5533	+	3.90221i	−0.688579	+	0.144825i
$727$	5.85323			0.217084			0.108542	−	0.994092i	$-0.465382\pi$
$727$	5.85323			0.217084			0.108542	+	0.994092i	$0.465382\pi$
$728$	4.78217	−	14.7180i	0.177239	−	0.545485i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−20.2041	−	14.6792i	−0.747788	−	0.543300i
$731$	1.61773	+	4.97887i	0.0598340	+	0.184150i
$732$	0.830629	+	2.55641i	0.0307009	+	0.0944878i
$733$	40.4882	+	29.4164i	1.49546	+	1.08652i	0.972144	+	0.234383i	$0.0753070\pi$
$733$	40.4882	+	29.4164i	1.49546	+	1.08652i	0.523321	+	0.852136i	$0.324693\pi$
$734$	24.8293	−	18.0396i	0.916467	−	0.665853i
$735$	−6.68336	+	20.5693i	−0.246520	+	0.758709i
$736$	−27.0057			−0.995443
$737$	−12.8093	+	11.5088i	−0.471838	+	0.423933i
$738$	−21.4496			−0.789571
$739$	3.29672	−	10.1463i	0.121272	−	0.373236i	−0.871932	−	0.489628i	$-0.837133\pi$
$739$	3.29672	−	10.1463i	0.121272	−	0.373236i	0.993203	+	0.116392i	$0.0371328\pi$
$740$	35.0360	−	25.4552i	1.28795	−	0.935751i
$741$	5.41151	+	3.93169i	0.198797	+	0.144434i
$742$	7.57956	+	23.3275i	0.278254	+	0.856379i
$743$	10.7969	+	33.2294i	0.396099	+	1.21907i	0.928102	+	0.372326i	$0.121440\pi$
$743$	10.7969	+	33.2294i	0.396099	+	1.21907i	−0.532003	+	0.846743i	$0.678560\pi$
$744$	11.1839	+	8.12556i	0.410021	+	0.297897i
$745$	6.79858	−	4.93946i	0.249081	−	0.180968i
$746$	−13.6928	+	42.1421i	−0.501328	+	1.54293i
$747$	2.90975			0.106462
$748$	1.30631	+	2.94247i	0.0477634	+	0.107587i
$749$	−31.0179			−1.13337
$750$	11.2275	−	34.5547i	0.409970	−	1.26176i
$751$	8.88499	−	6.45532i	0.324218	−	0.235558i	−0.413755	−	0.910388i	$-0.635783\pi$
$751$	8.88499	−	6.45532i	0.324218	−	0.235558i	0.737973	+	0.674830i	$0.235783\pi$
$752$	−36.4920	−	26.5130i	−1.33072	−	0.966828i
$753$	−6.41180	−	19.7335i	−0.233659	−	0.719129i
$754$	−4.37119	−	13.4531i	−0.159189	−	0.489934i
$755$	52.7144	+	38.2992i	1.91847	+	1.39385i
$756$	2.77820	−	2.01848i	0.101042	−	0.0734114i
$757$	−3.74760	+	11.5339i	−0.136209	+	0.419208i	−0.995776	−	0.0918148i	$-0.970733\pi$
$757$	−3.74760	+	11.5339i	−0.136209	+	0.419208i	0.859567	+	0.511023i	$0.170733\pi$
$758$	−5.55836			−0.201889
$759$	−3.69280	+	17.2824i	−0.134040	+	0.627312i
$760$	−18.8719			−0.684556
$761$	−9.82609	+	30.2416i	−0.356195	+	1.09626i	0.599118	+	0.800661i	$0.295518\pi$
$761$	−9.82609	+	30.2416i	−0.356195	+	1.09626i	−0.955313	+	0.295596i	$0.904482\pi$
$762$	8.52430	−	6.19327i	0.308803	−	0.224358i
$763$	26.7560	+	19.4394i	0.968632	+	0.703752i
$764$	−7.94387	−	24.4487i	−0.287399	−	0.884523i
$765$	−1.21172	−	3.72929i	−0.0438099	−	0.134833i
$766$	−34.0933	−	24.7702i	−1.23184	−	0.894984i
$767$	−5.03540	+	3.65844i	−0.181818	+	0.132098i
$768$	5.77757	−	17.7815i	0.208480	−	0.641636i
$769$	−23.9278			−0.862860			−0.431430	−	0.902146i	$-0.641991\pi$
$769$	−23.9278			−0.862860			−0.431430	+	0.902146i	$0.641991\pi$
$770$	−78.8740	+	8.20480i	−2.84242	+	0.295680i
$771$	−9.15602			−0.329746
$772$	3.45013	−	10.6184i	0.124173	−	0.382165i
$773$	−36.8758	+	26.7919i	−1.32633	+	0.963637i	−0.326502	+	0.945197i	$0.605870\pi$
$773$	−36.8758	+	26.7919i	−1.32633	+	0.963637i	−0.999830	+	0.0184400i	$0.994130\pi$
$774$	7.29979	+	5.30361i	0.262386	+	0.190634i
$775$	−24.9843	−	76.8938i	−0.897463	−	2.76211i
$776$	−8.37781	−	25.7842i	−0.300746	−	0.925600i
$777$	32.5642	+	23.6593i	1.16823	+	0.848772i
$778$	−3.86380	+	2.80722i	−0.138524	+	0.100644i
$779$	10.4326	−	32.1083i	0.373787	−	1.15040i
$780$	9.38515			0.336042
$781$	−22.4309	−	12.9825i	−0.802642	−	0.464550i
$782$	9.18399			0.328419
$783$	−1.02856	+	3.16559i	−0.0367578	+	0.113129i
$784$	22.3072	−	16.2071i	0.796686	−	0.578827i
$785$	−78.2133	−	56.8253i	−2.79155	−	2.02818i
$786$	−2.28589	−	7.03526i	−0.0815351	−	0.250939i
$787$	14.6706	+	45.1515i	0.522951	+	1.60948i	0.768333	+	0.640050i	$0.221087\pi$
$787$	14.6706	+	45.1515i	0.522951	+	1.60948i	−0.245382	+	0.969426i	$0.578913\pi$
$788$	−8.85218	−	6.43148i	−0.315346	−	0.229112i
$789$	19.4440	−	14.1269i	0.692225	−	0.502931i
$790$	−0.856066	+	2.63470i	−0.0304575	+	0.0937385i
$791$	24.7229			0.879044
$792$	−5.09254	−	2.94744i	−0.180955	−	0.104733i
$793$	−6.82788			−0.242465
$794$	13.5903	−	41.8268i	0.482303	−	1.48438i
$795$	12.7610	−	9.27142i	0.452587	−	0.328823i
$796$	−15.1260	−	10.9897i	−0.536128	−	0.389520i
$797$	−13.2571	−	40.8010i	−0.469589	−	1.44525i	−0.853118	−	0.521718i	$-0.825291\pi$
$797$	−13.2571	−	40.8010i	−0.469589	−	1.44525i	0.383529	−	0.923529i	$-0.374709\pi$
$798$	5.11159	+	15.7319i	0.180948	+	0.556902i
$799$	7.29965	+	5.30350i	0.258243	+	0.187624i
$800$	−42.5438	+	30.9099i	−1.50415	+	1.09283i
$801$	−4.21343	+	12.9676i	−0.148874	+	0.458188i
$802$	0.170655			0.00602603
$803$	12.1897	−	1.26802i	0.430165	−	0.0447475i
$804$	5.03987			0.177743
$805$	−22.8419	+	70.3000i	−0.805070	+	2.47775i
$806$	26.7908	−	19.4647i	0.943667	−	0.685614i
$807$	8.79321	+	6.38864i	0.309536	+	0.224891i
$808$	−3.27219	−	10.0708i	−0.115115	−	0.354289i
$809$	−3.36494	−	10.3562i	−0.118305	−	0.364106i	0.874317	−	0.485355i	$-0.161310\pi$
$809$	−3.36494	−	10.3562i	−0.118305	−	0.364106i	−0.992622	+	0.121250i	$0.961310\pi$
$810$	−5.46772	−	3.97253i	−0.192116	−	0.139581i
$811$	34.9433	−	25.3878i	1.22702	−	0.891486i	0.230361	−	0.973105i	$-0.426009\pi$
$811$	34.9433	−	25.3878i	1.22702	−	0.891486i	0.996664	+	0.0816196i	$0.0260092\pi$
$812$	3.53212	−	10.8708i	0.123953	−	0.381489i
$813$	−24.1366			−0.846506
$814$	−13.5906	+	63.6045i	−0.476350	+	2.22934i
$815$	−85.3402			−2.98934
$816$	−1.54482	+	4.75447i	−0.0540795	+	0.166440i
$817$	−11.4895	+	8.34762i	−0.401967	+	0.292046i
$818$	−48.0880	−	34.9380i	−1.68136	−	1.22158i
$819$	2.69556	+	8.29608i	0.0941905	+	0.289889i
$820$	−14.6377	−	45.0503i	−0.511171	−	1.57322i
$821$	−2.38274	−	1.73116i	−0.0831582	−	0.0604180i	0.545429	−	0.838157i	$-0.316367\pi$
$821$	−2.38274	−	1.73116i	−0.0831582	−	0.0604180i	−0.628588	+	0.777739i	$0.716367\pi$
$822$	14.0961	−	10.2414i	0.491658	−	0.357210i
$823$	−2.19921	+	6.76847i	−0.0766597	+	0.235934i	−0.982042	−	0.188664i	$-0.939584\pi$
$823$	−2.19921	+	6.76847i	−0.0766597	+	0.235934i	0.905382	+	0.424598i	$0.139584\pi$
$824$	13.5905			0.473446
$825$	13.9634	+	31.4528i	0.486144	+	1.09504i
$826$	−15.3918			−0.535550
$827$	3.01419	−	9.27672i	0.104814	−	0.322583i	−0.884873	−	0.465832i	$-0.845755\pi$
$827$	3.01419	−	9.27672i	0.104814	−	0.322583i	0.989687	+	0.143249i	$0.0457550\pi$
$828$	4.18447	−	3.04019i	0.145420	−	0.105654i
$829$	21.1035	+	15.3326i	0.732955	+	0.532523i	0.890497	−	0.454989i	$-0.150357\pi$
$829$	21.1035	+	15.3326i	0.732955	+	0.532523i	−0.157542	+	0.987512i	$0.550357\pi$
$830$	6.07697	+	18.7030i	0.210935	+	0.649190i
$831$	0.0307632	+	0.0946795i	0.00106716	+	0.00328439i
$832$	2.51927	+	1.83036i	0.0873400	+	0.0634563i
$833$	−4.46221	+	3.24199i	−0.154606	+	0.112328i
$834$	−5.23274	+	16.1047i	−0.181195	+	0.557661i
$835$	−54.1588			−1.87424
$836$	−6.49661	+	5.83701i	−0.224690	+	0.201877i
$837$	−7.79218			−0.269337
$838$	7.16768	−	22.0599i	0.247604	−	0.762045i
$839$	−27.4295	+	19.9287i	−0.946972	+	0.688016i	−0.950089	−	0.311980i	$-0.899008\pi$
$839$	−27.4295	+	19.9287i	−0.946972	+	0.688016i	0.00311658	+	0.999995i	$0.499008\pi$
$840$	−19.9104	−	14.4657i	−0.686973	−	0.499115i
$841$	−5.53793	−	17.0440i	−0.190963	−	0.587724i
$842$	−5.31862	−	16.3690i	−0.183292	−	0.564114i
$843$	26.1192	+	18.9767i	0.899593	+	0.653592i
$844$	−7.18453	+	5.21987i	−0.247302	+	0.179675i
$845$	8.38548	−	25.8078i	0.288469	−	0.887817i
$846$	15.5515			0.534672
$847$	26.1010	−	28.8639i	0.896842	−	0.991774i
$848$	−20.1096			−0.690565
$849$	−0.653451	+	2.01112i	−0.0224264	+	0.0690213i
$850$	14.4681	−	10.5117i	0.496253	−	0.360549i
$851$	49.0476	+	35.6352i	1.68133	+	1.22156i
$852$	2.34396	+	7.21397i	0.0803028	+	0.247147i
$853$	9.96651	+	30.6738i	0.341247	+	1.05025i	0.963562	+	0.267484i	$0.0861921\pi$
$853$	9.96651	+	30.6738i	0.341247	+	1.05025i	−0.622315	+	0.782767i	$0.713808\pi$
$854$	−13.6602	−	9.92471i	−0.467442	−	0.339617i
$855$	8.60593	−	6.25257i	0.294316	−	0.213833i
$856$	4.80668	−	14.7934i	0.164289	−	0.505629i
$857$	−32.1036			−1.09664			−0.548320	−	0.836269i	$-0.684732\pi$
$857$	−32.1036			−1.09664			−0.548320	+	0.836269i	$0.684732\pi$
$858$	−10.4847	+	9.42022i	−0.357942	+	0.321601i
$859$	−5.77012			−0.196874			−0.0984370	−	0.995143i	$-0.531384\pi$
$859$	−5.77012			−0.196874			−0.0984370	+	0.995143i	$0.531384\pi$
$860$	−6.15753	+	18.9509i	−0.209970	+	0.646222i
$861$	35.6184	−	25.8783i	1.21387	−	0.881929i
$862$	−5.37907	−	3.90813i	−0.183212	−	0.133111i
$863$	8.55257	+	26.3221i	0.291133	+	0.896015i	0.984493	+	0.175424i	$0.0561295\pi$
$863$	8.55257	+	26.3221i	0.291133	+	0.896015i	−0.693360	+	0.720591i	$0.743870\pi$
$864$	1.56615	+	4.82013i	0.0532817	+	0.163984i
$865$	−11.7459	−	8.53392i	−0.399374	−	0.290162i
$866$	14.4882	−	10.5263i	0.492329	−	0.357698i
$867$	0.309017	−	0.951057i	0.0104948	−	0.0322996i
$868$	26.7587			0.908248
$869$	−0.551623	−	1.24254i	−0.0187125	−	0.0421501i
$870$	−22.4956			−0.762671
$871$	−3.95606	+	12.1755i	−0.134046	+	0.412551i
$872$	−13.4175	+	9.74836i	−0.454373	+	0.330121i
$873$	12.3632	+	8.98237i	0.418430	+	0.304007i
$874$	7.69899	+	23.6950i	0.260422	+	0.801497i
$875$	23.0452	+	70.9258i	0.779069	+	2.39773i
$876$	−2.90182	−	2.10830i	−0.0980435	−	0.0712328i
$877$	14.2951	−	10.3860i	0.482710	−	0.350709i	−0.319664	−	0.947531i	$-0.603570\pi$
$877$	14.2951	−	10.3860i	0.482710	−	0.350709i	0.802374	+	0.596822i	$0.203570\pi$
$878$	8.47681	−	26.0889i	0.286079	−	0.880459i
$879$	5.35254			0.180537
$880$	13.5853	−	63.5796i	0.457959	−	2.14327i
$881$	−19.7348			−0.664881			−0.332441	−	0.943124i	$-0.607872\pi$
$881$	−19.7348			−0.664881			−0.332441	+	0.943124i	$0.607872\pi$
$882$	−2.93767	+	9.04123i	−0.0989166	+	0.304434i
$883$	14.2329	−	10.3408i	0.478974	−	0.347995i	−0.321955	−	0.946755i	$-0.604340\pi$
$883$	14.2329	−	10.3408i	0.478974	−	0.347995i	0.800928	+	0.598760i	$0.204340\pi$
$884$	1.93633	+	1.40682i	0.0651257	+	0.0473166i
$885$	3.05871	+	9.41375i	0.102817	+	0.316440i
$886$	−1.43359	−	4.41215i	−0.0481625	−	0.148229i
$887$	6.73611	+	4.89407i	0.226176	+	0.164327i	0.695103	−	0.718911i	$-0.255359\pi$
$887$	6.73611	+	4.89407i	0.226176	+	0.164327i	−0.468926	+	0.883237i	$0.655359\pi$
$888$	−16.3302	+	11.8646i	−0.548004	+	0.398148i
$889$	−6.68314	+	20.5686i	−0.224145	+	0.689849i
$890$	−92.1516			−3.08893
$891$	3.29882	−	0.343157i	0.110515	−	0.0114962i
$892$	2.84416			0.0952295
$893$	−7.56391	+	23.2793i	−0.253116	+	0.779012i
$894$	2.98832	−	2.17114i	0.0999442	−	0.0726137i
$895$	−39.2344	−	28.5055i	−1.31146	−	0.952833i
$896$	13.4609	+	41.4285i	0.449699	+	1.38403i
$897$	4.06000	+	12.4954i	0.135560	+	0.417209i
$898$	−8.51132	−	6.18384i	−0.284026	−	0.206357i
$899$	−20.9828	+	15.2449i	−0.699817	+	0.508447i
$900$	3.11235	−	9.57882i	0.103745	−	0.319294i
$901$	4.02260			0.134012
$902$	61.5713	+	35.6360i	2.05010	+	1.18655i
$903$	−18.5204			−0.616320
$904$	−3.83117	+	11.7911i	−0.127423	+	0.392167i
$905$	2.43071	−	1.76601i	0.0807996	−	0.0587043i
$906$	23.1706	+	16.8344i	0.769791	+	0.559286i
$907$	1.38729	+	4.26965i	0.0460643	+	0.141771i	0.971443	−	0.237272i	$-0.0762532\pi$
$907$	1.38729	+	4.26965i	0.0460643	+	0.141771i	−0.925379	+	0.379043i	$0.876253\pi$
$908$	0.648007	+	1.99436i	0.0215049	+	0.0661852i
$909$	4.82880	+	3.50833i	0.160161	+	0.116364i
$910$	−47.6950	+	34.6525i	−1.58108	+	1.14872i
$911$	0.389977	−	1.20023i	0.0129205	−	0.0397653i	−0.944388	−	0.328832i	$-0.893345\pi$
$911$	0.389977	−	1.20023i	0.0129205	−	0.0397653i	0.957309	+	0.289067i	$0.0933450\pi$
$912$	−13.5617			−0.449074
$913$	−8.35246	−	4.83420i	−0.276426	−	0.159989i
$914$	55.1028			1.82264
$915$	−3.35543	+	10.3269i	−0.110927	+	0.341398i
$916$	−5.58892	+	4.06059i	−0.184663	+	0.134166i
$917$	12.2837	+	8.92462i	0.405643	+	0.294717i
$918$	−0.532612	−	1.63921i	−0.0175788	−	0.0541020i
$919$	6.73742	+	20.7357i	0.222247	+	0.684006i	0.998559	+	0.0536576i	$0.0170880\pi$
$919$	6.73742	+	20.7357i	0.222247	+	0.684006i	−0.776312	+	0.630348i	$0.782912\pi$
$920$	−29.9886	−	21.7880i	−0.988695	−	0.718329i
$921$	20.2794	−	14.7338i	0.668228	−	0.485496i
$922$	10.6009	−	32.6261i	0.349121	−	1.07448i
$923$	−19.2677			−0.634203
$924$	−11.3283	+	1.17842i	−0.372674	+	0.0387670i
$925$	118.055			3.88161
$926$	−8.02092	+	24.6858i	−0.263584	+	0.811227i
$927$	−6.19750	+	4.50275i	−0.203553	+	0.147890i
$928$	13.6476	+	9.91560i	0.448006	+	0.325495i
$929$	10.6802	+	32.8703i	0.350406	+	1.07844i	0.958625	+	0.284671i	$0.0918843\pi$
$929$	10.6802	+	32.8703i	0.350406	+	1.07844i	−0.608219	+	0.793769i	$0.708116\pi$
$930$	−16.2738	−	50.0857i	−0.533640	−	1.64238i
$931$	−12.1051	−	8.79490i	−0.396730	−	0.288241i
$932$	15.8153	−	11.4905i	0.518046	−	0.376383i
$933$	7.44463	−	22.9122i	0.243726	−	0.750112i
$934$	29.9155			0.978866
$935$	−2.71752	+	12.7181i	−0.0888725	+	0.415926i
$936$	−4.37438			−0.142981
$937$	−12.2344	+	37.6537i	−0.399681	+	1.23009i	0.525575	+	0.850747i	$0.323850\pi$
$937$	−12.2344	+	37.6537i	−0.399681	+	1.23009i	−0.925256	+	0.379344i	$0.876150\pi$
$938$	−25.6125	+	18.6086i	−0.836277	+	0.607591i
$939$	−4.72983	−	3.43643i	−0.154352	−	0.112143i
$940$	10.6127	+	32.6626i	0.346149	+	1.06534i
$941$	10.4241	+	32.0820i	0.339816	+	1.04584i	0.964301	+	0.264808i	$0.0853087\pi$
$941$	10.4241	+	32.0820i	0.339816	+	1.04584i	−0.624485	+	0.781036i	$0.714691\pi$
$942$	−34.3786	−	24.9775i	−1.12012	−	0.813812i
$943$	53.6477	−	38.9774i	1.74701	−	1.26928i
$944$	3.89954	−	12.0016i	0.126919	−	0.390617i
$945$	13.8722			0.451264
$946$	−12.1428	−	27.3518i	−0.394796	−	0.889283i
$947$	42.7641			1.38965			0.694823	−	0.719181i	$-0.255483\pi$
$947$	42.7641			1.38965			0.694823	+	0.719181i	$0.255483\pi$
$948$	−0.122953	+	0.378410i	−0.00399332	+	0.0122902i
$949$	7.37110	−	5.35542i	0.239276	−	0.173844i
$950$	39.2493	+	28.5163i	1.27342	+	0.925190i
$951$	−5.70032	−	17.5438i	−0.184846	−	0.568896i
$952$	−1.93947	−	5.96908i	−0.0628587	−	0.193459i
$953$	−10.6089	−	7.70782i	−0.343656	−	0.249681i	0.402547	−	0.915399i	$-0.368125\pi$
$953$	−10.6089	−	7.70782i	−0.343656	−	0.249681i	−0.746203	+	0.665719i	$0.768125\pi$
$954$	5.60910	−	4.07525i	0.181601	−	0.131941i
$955$	32.0902	−	98.7635i	1.03841	−	3.19591i
$956$	−13.3133			−0.430584
$957$	8.21174	−	7.37801i	0.265448	−	0.238497i
$958$	−64.6298			−2.08810
$959$	−11.0515	+	34.0130i	−0.356871	+	1.09834i
$960$	4.00640	−	2.91082i	0.129306	−	0.0939463i
$961$	−24.0424	−	17.4678i	−0.775562	−	0.563479i
$962$	14.9420	+	45.9868i	0.481750	+	1.48267i
$963$	2.70938	+	8.33860i	0.0873084	+	0.268708i
$964$	5.65587	+	4.10923i	0.182163	+	0.132349i
$965$	36.4881	−	26.5101i	1.17459	−	0.853392i
$966$	−10.0401	+	30.9004i	−0.323036	+	0.994203i
$967$	3.32389			0.106889			0.0534445	−	0.998571i	$-0.482980\pi$
$967$	3.32389			0.106889			0.0534445	+	0.998571i	$0.482980\pi$
$968$	9.72135	+	16.9213i	0.312456	+	0.543871i
$969$	2.71281			0.0871481
$970$	−31.9157	+	98.2263i	−1.02475	+	3.15386i
$971$	−9.57794	+	6.95878i	−0.307371	+	0.223318i	−0.730767	−	0.682627i	$-0.760838\pi$
$971$	−9.57794	+	6.95878i	−0.307371	+	0.223318i	0.423397	+	0.905944i	$0.360838\pi$
$972$	−0.785303	−	0.570556i	−0.0251886	−	0.0183006i
$973$	−10.7405	−	33.0560i	−0.344326	−	1.05973i
$974$	0.219632	+	0.675958i	0.00703746	+	0.0216591i
$975$	20.6978	+	15.0378i	0.662861	+	0.481597i
$976$	11.1995	−	8.13690i	0.358487	−	0.260456i
$977$	15.7901	−	48.5970i	0.505170	−	1.55475i	−0.295314	−	0.955400i	$-0.595424\pi$
$977$	15.7901	−	48.5970i	0.505170	−	1.55475i	0.800484	−	0.599354i	$-0.204576\pi$
$978$	−37.5113			−1.19948
$979$	33.6388	−	30.2235i	1.07510	−	0.965948i
$980$	−20.9939			−0.670625
$981$	2.88882	−	8.89086i	0.0922328	−	0.283863i
$982$	−30.9125	+	22.4592i	−0.986457	+	0.716703i
$983$	3.18124	+	2.31131i	0.101466	+	0.0737193i	0.637361	−	0.770565i	$-0.280026\pi$
$983$	3.18124	+	2.31131i	0.101466	+	0.0737193i	−0.535895	+	0.844284i	$0.680026\pi$
$984$	6.82258	+	20.9977i	0.217496	+	0.669384i
$985$	−13.6589	−	42.0378i	−0.435209	−	1.33943i
$986$	−4.64124	−	3.37206i	−0.147807	−	0.107388i
$987$	−25.8242	+	18.7624i	−0.821995	+	0.597214i
$988$	−2.00642	+	6.17514i	−0.0638329	+	0.196457i
$989$	−27.8951			−0.887011
$990$	9.09525	+	20.4872i	0.289066	+	0.651125i
$991$	−18.9948			−0.603390			−0.301695	−	0.953405i	$-0.597552\pi$
$991$	−18.9948			−0.603390			−0.301695	+	0.953405i	$0.597552\pi$
$992$	−12.2038	+	37.5593i	−0.387470	+	1.19251i
$993$	−13.2509	+	9.62737i	−0.420506	+	0.305515i
$994$	−38.5479	−	28.0067i	−1.22266	−	0.888318i
$995$	−23.3394	−	71.8314i	−0.739910	−	2.27721i
$996$	0.872806	+	2.68622i	0.0276559	+	0.0851162i
$997$	17.4007	+	12.6423i	0.551085	+	0.400386i	0.828185	−	0.560454i	$-0.189374\pi$
$997$	17.4007	+	12.6423i	0.551085	+	0.400386i	−0.277101	+	0.960841i	$0.589374\pi$
$998$	35.2700	−	25.6251i	1.11645	−	0.811150i
$999$	3.51592	−	10.8209i	0.111239	−	0.342358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.460.2	✓	24
11.4	even	5		6171.2.a.bk.1.3		12
11.5	even	5	inner	561.2.m.d.511.2	yes	24
11.7	odd	10		6171.2.a.bl.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.460.2	✓	24	1.1	even	1	trivial
561.2.m.d.511.2	yes	24	11.5	even	5	inner
6171.2.a.bk.1.3		12	11.4	even	5
6171.2.a.bl.1.10		12	11.7	odd	10

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:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.532612 + 1.63921i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.785303 - 0.570556i) q^{4} +(-1.21172 - 3.72929i) q^{5} +(-0.532612 - 1.63921i) q^{6} +(2.86209 + 2.07943i) q^{7} +(-1.43527 + 1.04278i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.532612 + 1.63921i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.785303 - 0.570556i) q^{4} +(-1.21172 - 3.72929i) q^{5} +(-0.532612 - 1.63921i) q^{6} +(2.86209 + 2.07943i) q^{7} +(-1.43527 + 1.04278i) q^{8} +(0.309017 - 0.951057i) q^{9} +6.75848 q^{10} +(-2.46710 + 2.21662i) q^{11} +0.970688 q^{12} +(-0.761945 + 2.34502i) q^{13} +(-4.93301 + 3.58404i) q^{14} +(3.17233 + 2.30483i) q^{15} +(-1.54482 - 4.75447i) q^{16} +(0.309017 + 0.951057i) q^{17} +(1.39440 + 1.01309i) q^{18} +(-2.19471 + 1.59455i) q^{19} +(-1.17620 + 3.61998i) q^{20} -3.53774 q^{21} +(-2.31950 - 5.22470i) q^{22} -5.32848 q^{23} +(0.548224 - 1.68726i) q^{24} +(-8.39428 + 6.09880i) q^{25} +(-3.43817 - 2.49798i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.06118 - 3.26597i) q^{28} +(2.69281 + 1.95644i) q^{29} +(-5.46772 + 3.97253i) q^{30} +(-2.40792 + 7.41080i) q^{31} +5.06818 q^{32} +(0.693031 - 3.24341i) q^{33} -1.72357 q^{34} +(4.28675 - 13.1933i) q^{35} +(-0.785303 + 0.570556i) q^{36} +(-9.20481 - 6.68769i) q^{37} +(-1.44488 - 4.44687i) q^{38} +(-0.761945 - 2.34502i) q^{39} +(5.62799 + 4.08898i) q^{40} +(-10.0681 + 7.31492i) q^{41} +(1.88424 - 5.79910i) q^{42} +5.23509 q^{43} +(3.20213 - 0.333099i) q^{44} -3.92121 q^{45} +(2.83801 - 8.73450i) q^{46} +(7.29965 - 5.30350i) q^{47} +(4.04439 + 2.93842i) q^{48} +(1.70441 + 5.24564i) q^{49} +(-5.52633 - 17.0083i) q^{50} +(-0.809017 - 0.587785i) q^{51} +(1.93633 - 1.40682i) q^{52} +(1.24305 - 3.82572i) q^{53} -1.72357 q^{54} +(11.2559 + 6.51463i) q^{55} -6.27626 q^{56} +(0.838305 - 2.58004i) q^{57} +(-4.64124 + 3.37206i) q^{58} +(2.04218 + 1.48373i) q^{59} +(-1.17620 - 3.61998i) q^{60} +(0.855712 + 2.63361i) q^{61} +(-10.8654 - 7.89416i) q^{62} +(2.86209 - 2.07943i) q^{63} +(0.390264 - 1.20111i) q^{64} +9.66855 q^{65} +(4.94752 + 2.86350i) q^{66} +5.19206 q^{67} +(0.299959 - 0.923179i) q^{68} +(4.31083 - 3.13200i) q^{69} +(19.3434 + 14.0538i) q^{70} +(2.41474 + 7.43181i) q^{71} +(0.548224 + 1.68726i) q^{72} +(-2.98945 - 2.17196i) q^{73} +(15.8651 - 11.5267i) q^{74} +(3.20633 - 9.86807i) q^{75} +2.63329 q^{76} +(-11.6704 + 1.21400i) q^{77} +4.24981 q^{78} +(-0.126666 + 0.389836i) q^{79} +(-15.8589 + 11.5222i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-6.62829 - 20.3998i) q^{82} +(0.899162 + 2.76734i) q^{83} +(2.77820 + 2.01848i) q^{84} +(3.17233 - 2.30483i) q^{85} +(-2.78827 + 8.58142i) q^{86} -3.32849 q^{87} +(1.22950 - 5.75410i) q^{88} -13.6350 q^{89} +(2.08848 - 6.42769i) q^{90} +(-7.05707 + 5.12726i) q^{91} +(4.18447 + 3.04019i) q^{92} +(-2.40792 - 7.41080i) q^{93} +(4.80568 + 14.7904i) q^{94} +(8.60593 + 6.25257i) q^{95} +(-4.10025 + 2.97900i) q^{96} +(-4.72231 + 14.5338i) q^{97} -9.50651 q^{98} +(1.34575 + 3.03133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

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