LMFDB - Embedded newform 527.2.h.c.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [527,2,Mod(35,527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(527, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("527.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 527 = 17 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	527.h (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:	$4.20811618652$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	527.35
Dual form			527.2.h.c.256.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.682226 + 2.09968i) q^{2} +(0.165718 - 0.510029i) q^{3} +(-2.32517 + 1.68934i) q^{4} -1.12759 q^{5} +1.18395 q^{6} +(3.62195 - 2.63150i) q^{7} +(-1.56117 - 1.13426i) q^{8} +(2.19438 + 1.59431i) q^{9} +O(q^{10})$	\(q+(0.682226 + 2.09968i) q^{2} +(0.165718 - 0.510029i) q^{3} +(-2.32517 + 1.68934i) q^{4} -1.12759 q^{5} +1.18395 q^{6} +(3.62195 - 2.63150i) q^{7} +(-1.56117 - 1.13426i) q^{8} +(2.19438 + 1.59431i) q^{9} +(-0.769269 - 2.36757i) q^{10} +(2.14895 - 1.56130i) q^{11} +(0.476286 + 1.46586i) q^{12} +(-0.216982 + 0.667801i) q^{13} +(7.99629 + 5.80964i) q^{14} +(-0.186862 + 0.575102i) q^{15} +(-0.459774 + 1.41504i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.85048 + 5.69518i) q^{18} +(1.14876 + 3.53550i) q^{19} +(2.62183 - 1.90487i) q^{20} +(-0.741917 - 2.28339i) q^{21} +(4.74430 + 3.44694i) q^{22} +(-1.21353 - 0.881683i) q^{23} +(-0.837218 + 0.608274i) q^{24} -3.72855 q^{25} -1.55020 q^{26} +(2.47836 - 1.80064i) q^{27} +(-3.97617 + 12.2374i) q^{28} +(-0.910935 - 2.80357i) q^{29} -1.33501 q^{30} +(-1.23741 + 5.42852i) q^{31} -7.14421 q^{32} +(-0.440189 - 1.35476i) q^{33} +(0.682226 - 2.09968i) q^{34} +(-4.08407 + 2.96725i) q^{35} -7.79565 q^{36} +5.35310 q^{37} +(-6.63970 + 4.82403i) q^{38} +(0.304640 + 0.221334i) q^{39} +(1.76036 + 1.27897i) q^{40} +(-3.35422 - 10.3232i) q^{41} +(4.28822 - 3.11557i) q^{42} +(2.95842 + 9.10509i) q^{43} +(-2.35911 + 7.26060i) q^{44} +(-2.47436 - 1.79773i) q^{45} +(1.02334 - 3.14953i) q^{46} +(-0.145101 + 0.446575i) q^{47} +(0.645517 + 0.468996i) q^{48} +(4.03061 - 12.4049i) q^{49} +(-2.54371 - 7.82874i) q^{50} +(-0.433856 + 0.315215i) q^{51} +(-0.623621 - 1.91931i) q^{52} +(4.57063 + 3.32076i) q^{53} +(5.47156 + 3.97532i) q^{54} +(-2.42313 + 1.76051i) q^{55} -8.63928 q^{56} +1.99358 q^{57} +(5.26512 - 3.82534i) q^{58} +(-0.228100 + 0.702019i) q^{59} +(-0.537054 - 1.65288i) q^{60} +3.92569 q^{61} +(-12.2423 + 1.10532i) q^{62} +12.1434 q^{63} +(-3.95442 - 12.1705i) q^{64} +(0.244666 - 0.753004i) q^{65} +(2.54426 - 1.84851i) q^{66} -3.17807 q^{67} +2.87407 q^{68} +(-0.650788 + 0.472825i) q^{69} +(-9.01651 - 6.55088i) q^{70} +(-1.40097 - 1.01787i) q^{71} +(-1.61745 - 4.97799i) q^{72} +(0.389369 - 0.282893i) q^{73} +(3.65202 + 11.2398i) q^{74} +(-0.617889 + 1.90167i) q^{75} +(-8.64371 - 6.28002i) q^{76} +(3.67482 - 11.3099i) q^{77} +(-0.256896 + 0.790645i) q^{78} +(-12.4776 - 9.06554i) q^{79} +(0.518435 - 1.59558i) q^{80} +(2.00687 + 6.17653i) q^{81} +(19.3871 - 14.0856i) q^{82} +(-4.35277 - 13.3964i) q^{83} +(5.58249 + 4.05592i) q^{84} +(0.912237 + 0.662779i) q^{85} +(-17.0994 + 12.4235i) q^{86} -1.58086 q^{87} -5.12580 q^{88} +(7.32575 - 5.32247i) q^{89} +(2.08657 - 6.42181i) q^{90} +(0.971422 + 2.98973i) q^{91} +4.31113 q^{92} +(2.56364 + 1.53072i) q^{93} -1.03665 q^{94} +(-1.29532 - 3.98659i) q^{95} +(-1.18393 + 3.64375i) q^{96} +(-14.0423 + 10.2023i) q^{97} +28.7961 q^{98} +7.20483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/527\mathbb{Z}\right)^\times$.

$n$	$156$	$375$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.682226	+	2.09968i	0.482407	+	1.48469i	0.835702	+	0.549183i	$0.185061\pi$
$2$	0.682226	+	2.09968i	0.482407	+	1.48469i	−0.353295	+	0.935512i	$0.614939\pi$
$3$	0.165718	−	0.510029i	0.0956775	−	0.294465i	−0.891752	−	0.452524i	$-0.850524\pi$
$3$	0.165718	−	0.510029i	0.0956775	−	0.294465i	0.987430	+	0.158059i	$0.0505236\pi$
$4$	−2.32517	+	1.68934i	−1.16259	+	0.844668i
$5$	−1.12759			−0.504272			−0.252136	−	0.967692i	$-0.581133\pi$
$5$	−1.12759			−0.504272			−0.252136	+	0.967692i	$0.581133\pi$
$6$	1.18395			0.483346
$7$	3.62195	−	2.63150i	1.36897	−	0.994614i	0.371152	−	0.928572i	$-0.378963\pi$
$7$	3.62195	−	2.63150i	1.36897	−	0.994614i	0.997817	−	0.0660418i	$-0.0210371\pi$
$8$	−1.56117	−	1.13426i	−0.551957	−	0.401020i
$9$	2.19438	+	1.59431i	0.731461	+	0.531438i
$10$	−0.769269	−	2.36757i	−0.243264	−	0.748691i
$11$	2.14895	−	1.56130i	0.647933	−	0.470751i	−0.214633	−	0.976695i	$-0.568856\pi$
$11$	2.14895	−	1.56130i	0.647933	−	0.470751i	0.862567	+	0.505944i	$0.168856\pi$
$12$	0.476286	+	1.46586i	0.137492	+	0.423157i
$13$	−0.216982	+	0.667801i	−0.0601799	+	0.185215i	−0.976627	−	0.214941i	$-0.931044\pi$
$13$	−0.216982	+	0.667801i	−0.0601799	+	0.185215i	0.916447	+	0.400156i	$0.131044\pi$
$14$	7.99629	+	5.80964i	2.13710	+	1.55269i
$15$	−0.186862	+	0.575102i	−0.0482475	+	0.148491i
$16$	−0.459774	+	1.41504i	−0.114943	+	0.353760i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−1.85048	+	5.69518i	−0.436161	+	1.34237i
$19$	1.14876	+	3.53550i	0.263542	+	0.811100i	0.992026	+	0.126037i	$0.0402257\pi$
$19$	1.14876	+	3.53550i	0.263542	+	0.811100i	−0.728483	+	0.685064i	$0.759774\pi$
$20$	2.62183	−	1.90487i	0.586260	−	0.425943i
$21$	−0.741917	−	2.28339i	−0.161900	−	0.498276i
$22$	4.74430	+	3.44694i	1.01149	+	0.734890i
$23$	−1.21353	−	0.881683i	−0.253039	−	0.183844i	0.454034	−	0.890985i	$-0.349985\pi$
$23$	−1.21353	−	0.881683i	−0.253039	−	0.183844i	−0.707073	+	0.707141i	$0.749985\pi$
$24$	−0.837218	+	0.608274i	−0.170896	+	0.124163i
$25$	−3.72855			−0.745709
$26$	−1.55020			−0.304019
$27$	2.47836	−	1.80064i	0.476961	−	0.346533i
$28$	−3.97617	+	12.2374i	−0.751425	+	2.31265i
$29$	−0.910935	−	2.80357i	−0.169156	−	0.520610i	0.830162	−	0.557522i	$-0.188248\pi$
$29$	−0.910935	−	2.80357i	−0.169156	−	0.520610i	−0.999319	+	0.0369123i	$0.988248\pi$
$30$	−1.33501			−0.243738
$31$	−1.23741	+	5.42852i	−0.222245	+	0.974991i
$31$	−1.23741	+	5.42852i	−0.222245	+	0.974991i
$32$	−7.14421			−1.26293
$33$	−0.440189	−	1.35476i	−0.0766271	−	0.235834i
$34$	0.682226	−	2.09968i	0.117001	−	0.360091i
$35$	−4.08407	+	2.96725i	−0.690333	+	0.501556i
$36$	−7.79565			−1.29928
$37$	5.35310			0.880043			0.440022	−	0.897987i	$-0.354971\pi$
$37$	5.35310			0.880043			0.440022	+	0.897987i	$0.354971\pi$
$38$	−6.63970	+	4.82403i	−1.07710	+	0.782560i
$39$	0.304640	+	0.221334i	0.0487814	+	0.0354418i
$40$	1.76036	+	1.27897i	0.278337	+	0.202223i
$41$	−3.35422	−	10.3232i	−0.523842	−	1.61222i	−0.766595	−	0.642131i	$-0.778051\pi$
$41$	−3.35422	−	10.3232i	−0.523842	−	1.61222i	0.242753	−	0.970088i	$-0.421949\pi$
$42$	4.28822	−	3.11557i	0.661686	−	0.480743i
$43$	2.95842	+	9.10509i	0.451155	+	1.38851i	0.875590	+	0.483055i	$0.160473\pi$
$43$	2.95842	+	9.10509i	0.451155	+	1.38851i	−0.424435	+	0.905459i	$0.639527\pi$
$44$	−2.35911	+	7.26060i	−0.355650	+	1.09458i
$45$	−2.47436	−	1.79773i	−0.368856	−	0.267989i
$46$	1.02334	−	3.14953i	0.150884	−	0.464373i
$47$	−0.145101	+	0.446575i	−0.0211652	+	0.0651397i	−0.961081	−	0.276266i	$-0.910903\pi$
$47$	−0.145101	+	0.446575i	−0.0211652	+	0.0651397i	0.939916	+	0.341406i	$0.110903\pi$
$48$	0.645517	+	0.468996i	0.0931724	+	0.0676937i
$49$	4.03061	−	12.4049i	0.575801	−	1.77213i
$50$	−2.54371	−	7.82874i	−0.359735	−	1.10715i
$51$	−0.433856	+	0.315215i	−0.0607520	+	0.0441389i
$52$	−0.623621	−	1.91931i	−0.0864807	−	0.266160i
$53$	4.57063	+	3.32076i	0.627824	+	0.456141i	0.855646	−	0.517562i	$-0.173160\pi$
$53$	4.57063	+	3.32076i	0.627824	+	0.456141i	−0.227822	+	0.973703i	$0.573160\pi$
$54$	5.47156	+	3.97532i	0.744585	+	0.540973i
$55$	−2.42313	+	1.76051i	−0.326735	+	0.237387i
$56$	−8.63928			−1.15447
$57$	1.99358			0.264056
$58$	5.26512	−	3.82534i	0.691344	−	0.502291i
$59$	−0.228100	+	0.702019i	−0.0296961	+	0.0913951i	−0.964806	−	0.262963i	$-0.915300\pi$
$59$	−0.228100	+	0.702019i	−0.0296961	+	0.0913951i	0.935110	+	0.354358i	$0.115300\pi$
$60$	−0.537054	−	1.65288i	−0.0693334	−	0.213386i
$61$	3.92569			0.502633			0.251317	−	0.967905i	$-0.419136\pi$
$61$	3.92569			0.502633			0.251317	+	0.967905i	$0.419136\pi$
$62$	−12.2423	+	1.10532i	−1.55478	+	0.140376i
$63$	12.1434			1.52992
$64$	−3.95442	−	12.1705i	−0.494303	−	1.52131i
$65$	0.244666	−	0.753004i	0.0303471	−	0.0933987i
$66$	2.54426	−	1.84851i	0.313176	−	0.227536i
$67$	−3.17807			−0.388263			−0.194131	−	0.980976i	$-0.562189\pi$
$67$	−3.17807			−0.388263			−0.194131	+	0.980976i	$0.562189\pi$
$68$	2.87407			0.348532
$69$	−0.650788	+	0.472825i	−0.0783457	+	0.0569215i
$70$	−9.01651	−	6.55088i	−1.07768	−	0.782980i
$71$	−1.40097	−	1.01787i	−0.166265	−	0.120798i	0.501541	−	0.865134i	$-0.332766\pi$
$71$	−1.40097	−	1.01787i	−0.166265	−	0.120798i	−0.667806	+	0.744335i	$0.732766\pi$
$72$	−1.61745	−	4.97799i	−0.190618	−	0.586662i
$73$	0.389369	−	0.282893i	0.0455722	−	0.0331101i	−0.564766	−	0.825251i	$-0.691034\pi$
$73$	0.389369	−	0.282893i	0.0455722	−	0.0331101i	0.610338	+	0.792141i	$0.291034\pi$
$74$	3.65202	+	11.2398i	0.424539	+	1.30660i
$75$	−0.617889	+	1.90167i	−0.0713476	+	0.219585i
$76$	−8.64371	−	6.28002i	−0.991502	−	0.720368i
$77$	3.67482	−	11.3099i	0.418785	−	1.28889i
$78$	−0.256896	+	0.790645i	−0.0290877	+	0.0895229i
$79$	−12.4776	−	9.06554i	−1.40385	−	1.01995i	−0.994182	−	0.107716i	$-0.965646\pi$
$79$	−12.4776	−	9.06554i	−1.40385	−	1.01995i	−0.409663	−	0.912237i	$-0.634354\pi$
$80$	0.518435	−	1.59558i	0.0579628	−	0.178391i
$81$	2.00687	+	6.17653i	0.222986	+	0.686281i
$82$	19.3871	−	14.0856i	2.14095	−	1.55549i
$83$	−4.35277	−	13.3964i	−0.477778	−	1.47045i	−0.842174	−	0.539206i	$-0.818724\pi$
$83$	−4.35277	−	13.3964i	−0.477778	−	1.47045i	0.364395	−	0.931244i	$-0.381276\pi$
$84$	5.58249	+	4.05592i	0.609100	+	0.442537i
$85$	0.912237	+	0.662779i	0.0989460	+	0.0718885i
$86$	−17.0994	+	12.4235i	−1.84388	+	1.33966i
$87$	−1.58086			−0.169486
$88$	−5.12580			−0.546412
$89$	7.32575	−	5.32247i	0.776528	−	0.564180i	−0.127407	−	0.991851i	$-0.540665\pi$
$89$	7.32575	−	5.32247i	0.776528	−	0.564180i	0.903935	+	0.427670i	$0.140665\pi$
$90$	2.08657	−	6.42181i	0.219944	−	0.676918i
$91$	0.971422	+	2.98973i	0.101833	+	0.313409i
$92$	4.31113			0.449466
$93$	2.56364	+	1.53072i	0.265837	+	0.158728i
$94$	−1.03665			−0.106923
$95$	−1.29532	−	3.98659i	−0.132897	−	0.409016i
$96$	−1.18393	+	3.64375i	−0.120834	+	0.371889i
$97$	−14.0423	+	10.2023i	−1.42578	+	1.03589i	−0.434999	+	0.900431i	$0.643251\pi$
$97$	−14.0423	+	10.2023i	−1.42578	+	1.03589i	−0.990783	+	0.135460i	$0.956749\pi$
$98$	28.7961			2.90885
$99$	7.20483			0.724113
$100$	8.66951	−	6.29877i	0.866951	−	0.629877i
$101$	−16.0626	−	11.6702i	−1.59829	−	1.16122i	−0.890694	−	0.454602i	$-0.849781\pi$
$101$	−16.0626	−	11.6702i	−1.59829	−	1.16122i	−0.707592	−	0.706621i	$-0.750219\pi$
$102$	−0.957837	−	0.695910i	−0.0948400	−	0.0689053i
$103$	1.34649	+	4.14407i	0.132674	+	0.408327i	0.995221	−	0.0976490i	$-0.0311323\pi$
$103$	1.34649	+	4.14407i	0.132674	+	0.408327i	−0.862547	+	0.505976i	$0.831132\pi$
$104$	1.09620	−	0.796438i	0.107492	−	0.0780972i
$105$	0.836577	+	2.57472i	0.0816415	+	0.251267i
$106$	−3.85431	+	11.8623i	−0.374364	+	1.15217i
$107$	−2.64037	−	1.91834i	−0.255255	−	0.185453i	0.452798	−	0.891613i	$-0.350426\pi$
$107$	−2.64037	−	1.91834i	−0.255255	−	0.185453i	−0.708052	+	0.706160i	$0.750426\pi$
$108$	−2.72074	+	8.37358i	−0.261803	+	0.805748i
$109$	1.14117	−	3.51215i	0.109304	−	0.336403i	−0.881412	−	0.472347i	$-0.843407\pi$
$109$	1.14117	−	3.51215i	0.109304	−	0.336403i	0.990717	+	0.135944i	$0.0434068\pi$
$110$	−5.34962	−	3.88672i	−0.510066	−	0.370585i
$111$	0.887106	−	2.73023i	0.0842004	−	0.259142i
$112$	2.05840	+	6.33509i	0.194500	+	0.598610i
$113$	−13.1324	+	9.54124i	−1.23539	+	0.897564i	−0.997282	−	0.0736744i	$-0.976527\pi$
$113$	−13.1324	+	9.54124i	−1.23539	+	0.897564i	−0.238109	+	0.971239i	$0.576527\pi$
$114$	1.36007	+	4.18587i	0.127382	+	0.392042i
$115$	1.36836	+	0.994174i	0.127601	+	0.0927072i
$116$	6.85425	+	4.97990i	0.636401	+	0.462373i
$117$	−1.54083	+	1.11948i	−0.142449	+	0.103496i
$118$	−1.62963			−0.150019
$119$	−4.47698			−0.410404
$120$	0.944036	−	0.685882i	0.0861783	−	0.0626122i
$121$	−1.21887	+	3.75129i	−0.110806	+	0.341026i
$122$	2.67821	+	8.24268i	0.242474	+	0.746257i
$123$	−5.82100			−0.524862
$124$	−6.29341	−	14.7126i	−0.565165	−	1.32123i
$125$	9.84220			0.880313
$126$	8.28454	+	25.4972i	0.738045	+	2.27147i
$127$	−0.283221	+	0.871666i	−0.0251318	+	0.0773478i	−0.962836	−	0.270087i	$-0.912947\pi$
$127$	−0.283221	+	0.871666i	−0.0251318	+	0.0773478i	0.937704	+	0.347435i	$0.112947\pi$
$128$	11.2966	−	8.20748i	0.998490	−	0.725445i
$129$	5.13412			0.452034
$130$	1.74798			0.153308
$131$	−3.35260	+	2.43581i	−0.292918	+	0.212817i	−0.724532	−	0.689241i	$-0.757944\pi$
$131$	−3.35260	+	2.43581i	−0.292918	+	0.212817i	0.431614	+	0.902058i	$0.357944\pi$
$132$	3.31217	+	2.40643i	0.288287	+	0.209453i
$133$	13.4644	+	9.78247i	1.16751	+	0.848248i
$134$	−2.16816	−	6.67291i	−0.187301	−	0.576452i
$135$	−2.79457	+	2.03038i	−0.240518	+	0.174747i
$136$	0.596314	+	1.83527i	0.0511335	+	0.157373i
$137$	1.05626	−	3.25082i	0.0902421	−	0.277736i	−0.895742	−	0.444573i	$-0.853355\pi$
$137$	1.05626	−	3.25082i	0.0902421	−	0.277736i	0.985985	+	0.166837i	$0.0533553\pi$
$138$	−1.43676	−	1.04387i	−0.122305	−	0.0888601i
$139$	3.77170	−	11.6081i	0.319911	−	0.984586i	−0.653774	−	0.756690i	$-0.726815\pi$
$139$	3.77170	−	11.6081i	0.319911	−	0.984586i	0.973685	−	0.227896i	$-0.0731846\pi$
$140$	4.48348	−	13.7987i	0.378923	−	1.16620i
$141$	0.203720	+	0.148011i	0.0171563	+	0.0124648i
$142$	1.18141	−	3.63600i	0.0991416	−	0.305126i
$143$	0.576358	+	1.77385i	0.0481975	+	0.148337i
$144$	−3.26493	+	2.37211i	−0.272078	+	0.197676i
$145$	1.02716	+	3.16127i	0.0853009	+	0.262529i
$146$	0.859621	+	0.624551i	0.0711427	+	0.0516882i
$147$	−5.65893	−	4.11145i	−0.466741	−	0.339107i
$148$	−12.4469	+	9.04318i	−1.02313	+	0.743345i
$149$	−7.03728			−0.576516			−0.288258	−	0.957553i	$-0.593076\pi$
$149$	−7.03728			−0.576516			−0.288258	+	0.957553i	$0.593076\pi$
$150$	−4.41442			−0.360436
$151$	−0.619535	+	0.450118i	−0.0504170	+	0.0366301i	−0.612708	−	0.790309i	$-0.709920\pi$
$151$	−0.619535	+	0.450118i	−0.0504170	+	0.0366301i	0.562291	+	0.826939i	$0.309920\pi$
$152$	2.21677	−	6.82251i	0.179803	−	0.553378i
$153$	−0.838180	−	2.57965i	−0.0677629	−	0.208553i
$154$	26.2543			2.11563
$155$	1.39528	−	6.12113i	0.112072	−	0.491661i
$156$	−1.08225			−0.0866491
$157$	−5.25247	−	16.1654i	−0.419193	−	1.29014i	−0.908446	−	0.418001i	$-0.862731\pi$
$157$	−5.25247	−	16.1654i	−0.419193	−	1.29014i	0.489254	−	0.872142i	$-0.337269\pi$
$158$	10.5221	−	32.3838i	0.837095	−	2.57631i
$159$	2.45112	−	1.78084i	0.194386	−	0.141230i
$160$	8.05573			0.636861
$161$	−6.71550			−0.529256
$162$	−11.5996	+	8.42757i	−0.911347	+	0.662133i
$163$	0.457003	+	0.332032i	0.0357952	+	0.0260068i	0.605539	−	0.795816i	$-0.292958\pi$
$163$	0.457003	+	0.332032i	0.0357952	+	0.0260068i	−0.569744	+	0.821822i	$0.692958\pi$
$164$	25.2386	+	18.3369i	1.97080	+	1.43187i
$165$	0.496352	+	1.52761i	0.0386409	+	0.118925i
$166$	25.1586	−	18.2788i	1.95269	−	1.41871i
$167$	−6.19308	−	19.0603i	−0.479235	−	1.47493i	−0.840160	−	0.542339i	$-0.817539\pi$
$167$	−6.19308	−	19.0603i	−0.479235	−	1.47493i	0.360925	−	0.932595i	$-0.382461\pi$
$168$	−1.43169	+	4.40628i	−0.110457	+	0.339952i
$169$	10.1183	+	7.35141i	0.778334	+	0.565493i
$170$	−0.769269	+	2.36757i	−0.0590003	+	0.181584i
$171$	−3.11589	+	9.58973i	−0.238278	+	0.733345i
$172$	−22.2604	−	16.1731i	−1.69734	−	1.23319i
$173$	−0.135542	+	0.417156i	−0.0103051	+	0.0317158i	−0.956077	−	0.293116i	$-0.905308\pi$
$173$	−0.135542	+	0.417156i	−0.0103051	+	0.0317158i	0.945772	+	0.324832i	$0.105308\pi$
$174$	−1.07850	−	3.31929i	−0.0817611	−	0.251635i
$175$	−13.5046	+	9.81168i	−1.02085	+	0.741693i
$176$	1.22127	+	3.75870i	0.0920570	+	0.283322i
$177$	0.320249	+	0.232675i	0.0240714	+	0.0174889i
$178$	16.1733	+	11.7506i	1.21224	+	0.880743i
$179$	−3.28167	+	2.38427i	−0.245283	+	0.178209i	−0.703634	−	0.710563i	$-0.748440\pi$
$179$	−3.28167	+	2.38427i	−0.245283	+	0.178209i	0.458351	+	0.888771i	$0.348440\pi$
$180$	8.79028			0.655189
$181$	17.5299			1.30299			0.651493	−	0.758655i	$-0.274143\pi$
$181$	17.5299			1.30299			0.651493	+	0.758655i	$0.274143\pi$
$182$	−5.61474	+	4.07934i	−0.416192	+	0.302381i
$183$	0.650559	−	2.00221i	0.0480907	−	0.148008i
$184$	0.894475	+	2.75291i	0.0659416	+	0.202947i
$185$	−6.03608			−0.443782
$186$	−1.46503	+	6.42711i	−0.107421	+	0.471258i
$187$	−2.65625			−0.194244
$188$	−0.417031	−	1.28349i	−0.0304151	−	0.0936080i
$189$	4.23813	−	13.0436i	0.308279	−	0.948785i
$190$	7.48684	−	5.43951i	0.543153	−	0.394624i
$191$	14.6299			1.05858			0.529289	−	0.848441i	$-0.322459\pi$
$191$	14.6299			1.05858			0.529289	+	0.848441i	$0.322459\pi$
$192$	−6.86260			−0.495266
$193$	−11.7075	+	8.50598i	−0.842723	+	0.612274i	−0.923130	−	0.384488i	$-0.874378\pi$
$193$	−11.7075	+	8.50598i	−0.842723	+	0.612274i	0.0804073	+	0.996762i	$0.474378\pi$
$194$	−31.0017	−	22.5240i	−2.22579	−	1.61713i
$195$	−0.343508	−	0.249573i	−0.0245991	−	0.0178723i
$196$	11.5843	+	35.6527i	0.827447	+	2.54662i
$197$	18.4444	−	13.4007i	1.31411	−	0.954759i	0.314127	−	0.949381i	$-0.398288\pi$
$197$	18.4444	−	13.4007i	1.31411	−	0.954759i	0.999986	−	0.00537771i	$-0.00171179\pi$
$198$	4.91533	+	15.1278i	0.349317	+	1.07509i
$199$	−2.91571	+	8.97364i	−0.206689	+	0.636124i	0.792950	+	0.609286i	$0.208544\pi$
$199$	−2.91571	+	8.97364i	−0.206689	+	0.636124i	−0.999640	+	0.0268383i	$0.991456\pi$
$200$	5.82089	+	4.22913i	0.411599	+	0.299044i
$201$	−0.526664	+	1.62091i	−0.0371480	+	0.114330i
$202$	13.5452	−	41.6879i	0.953038	−	2.93315i
$203$	−10.6770	−	7.75726i	−0.749375	−	0.544453i
$204$	0.476286	−	1.46586i	0.0333467	−	0.102631i
$205$	3.78218	+	11.6404i	0.264159	+	0.812998i
$206$	−7.78260	+	5.65439i	−0.542239	+	0.393960i
$207$	−1.25728	−	3.86950i	−0.0873868	−	0.268949i
$208$	−0.845202	−	0.614075i	−0.0586042	−	0.0425784i
$209$	7.98862	+	5.80407i	0.552584	+	0.401476i
$210$	−4.83534	+	3.51308i	−0.333670	+	0.242425i
$211$	7.84331			0.539955			0.269978	−	0.962867i	$-0.412984\pi$
$211$	7.84331			0.539955			0.269978	+	0.962867i	$0.412984\pi$
$212$	−16.2374			−1.11519
$213$	−0.751307	+	0.545857i	−0.0514787	+	0.0374015i
$214$	2.22657	−	6.85267i	0.152205	−	0.468439i
$215$	−3.33588	−	10.2668i	−0.227505	−	0.700189i
$216$	−5.91153			−0.402229
$217$	9.80333	+	22.9181i	0.665493	+	1.55578i
$218$	8.15292			0.552185
$219$	−0.0797580	−	0.245470i	−0.00538954	−	0.0165873i
$220$	2.66011	−	8.18696i	0.179344	−	0.551965i
$221$	0.568066	−	0.412724i	0.0382122	−	0.0277628i
$222$	6.33781			0.425366
$223$	−15.2404			−1.02057			−0.510287	−	0.860004i	$-0.670461\pi$
$223$	−15.2404			−1.02057			−0.510287	+	0.860004i	$0.670461\pi$
$224$	−25.8760	+	18.8000i	−1.72891	+	1.25613i
$225$	−8.18186	−	5.94447i	−0.545458	−	0.396298i
$226$	−28.9928	−	21.0645i	−1.92857	−	1.40119i
$227$	−0.659246	−	2.02895i	−0.0437557	−	0.134666i	0.926792	−	0.375575i	$-0.122555\pi$
$227$	−0.659246	−	2.02895i	−0.0437557	−	0.134666i	−0.970548	+	0.240908i	$0.922555\pi$
$228$	−4.63541	+	3.36782i	−0.306988	+	0.223040i
$229$	−3.09196	−	9.51608i	−0.204323	−	0.628840i	−0.999741	−	0.0227790i	$-0.992749\pi$
$229$	−3.09196	−	9.51608i	−0.204323	−	0.628840i	0.795418	−	0.606061i	$-0.207251\pi$
$230$	−1.15391	+	3.55137i	−0.0760866	+	0.234170i
$231$	−5.15941	−	3.74853i	−0.339464	−	0.246635i
$232$	−1.75784	+	5.41008i	−0.115408	+	0.355189i
$233$	−5.81202	+	17.8876i	−0.380758	+	1.17185i	0.558753	+	0.829334i	$0.311280\pi$
$233$	−5.81202	+	17.8876i	−0.380758	+	1.17185i	−0.939511	+	0.342519i	$0.888720\pi$
$234$	−3.40173	−	2.47150i	−0.222378	−	0.161567i
$235$	0.163614	−	0.503552i	0.0106730	−	0.0328481i
$236$	−0.655575	−	2.01765i	−0.0426743	−	0.131338i
$237$	−6.69146	+	4.86163i	−0.434657	+	0.315797i
$238$	−3.05431	−	9.40020i	−0.197982	−	0.609325i
$239$	3.36574	+	2.44535i	0.217711	+	0.158177i	0.691296	−	0.722572i	$-0.257040\pi$
$239$	3.36574	+	2.44535i	0.217711	+	0.158177i	−0.473584	+	0.880748i	$0.657040\pi$
$240$	−0.727877	−	0.528833i	−0.0469842	−	0.0341361i
$241$	−15.8174	+	11.4920i	−1.01889	+	0.740266i	−0.966055	−	0.258337i	$-0.916825\pi$
$241$	−15.8174	+	11.4920i	−1.01889	+	0.740266i	−0.0528341	+	0.998603i	$0.516825\pi$
$242$	−8.70803			−0.559773
$243$	12.6731			0.812977
$244$	−9.12791	+	6.63181i	−0.584354	+	0.424558i
$245$	−4.54486	+	13.9877i	−0.290361	+	0.893638i
$246$	−3.97124	−	12.2222i	−0.253197	−	0.779260i
$247$	−2.61027			−0.166088
$248$	8.08913	−	7.07130i	0.513661	−	0.449028i
$249$	−7.55390			−0.478709
$250$	6.71460	+	20.6654i	0.424669	+	1.30700i
$251$	−5.20041	+	16.0052i	−0.328247	+	1.01024i	0.641707	+	0.766950i	$0.278227\pi$
$251$	−5.20041	+	16.0052i	−0.328247	+	1.01024i	−0.969954	+	0.243290i	$0.921773\pi$
$252$	−28.2355	+	20.5143i	−1.77867	+	1.29228i
$253$	−3.98440			−0.250497
$254$	−2.02344			−0.126962
$255$	0.489211	−	0.355432i	0.0306356	−	0.0222580i
$256$	4.23427	+	3.07638i	0.264642	+	0.192274i
$257$	−5.18496	−	3.76710i	−0.323429	−	0.234985i	0.414208	−	0.910182i	$-0.364059\pi$
$257$	−5.18496	−	3.76710i	−0.323429	−	0.234985i	−0.737637	+	0.675197i	$0.764059\pi$
$258$	3.50263	+	10.7800i	0.218064	+	0.671133i
$259$	19.3886	−	14.0867i	1.20475	−	0.875304i
$260$	0.703187	+	2.16419i	0.0436098	+	0.134217i
$261$	2.47083	−	7.60442i	0.152940	−	0.470702i
$262$	−7.40164	−	5.37760i	−0.457275	−	0.332229i
$263$	−2.32672	+	7.16091i	−0.143472	+	0.441561i	−0.996811	−	0.0797948i	$-0.974573\pi$
$263$	−2.32672	+	7.16091i	−0.143472	+	0.441561i	0.853340	+	0.521356i	$0.174573\pi$
$264$	−0.849439	+	2.61430i	−0.0522793	+	0.160899i
$265$	−5.15378	−	3.74444i	−0.316594	−	0.230019i
$266$	−11.3542	+	34.9448i	−0.696173	+	2.14260i
$267$	−1.50060	−	4.61837i	−0.0918352	−	0.282640i
$268$	7.38956	−	5.36883i	0.451389	−	0.327953i
$269$	3.84969	+	11.8481i	0.234719	+	0.722392i	0.997158	+	0.0753322i	$0.0240017\pi$
$269$	3.84969	+	11.8481i	0.234719	+	0.722392i	−0.762439	+	0.647060i	$0.775998\pi$
$270$	−6.16966	−	4.48252i	−0.375474	−	0.272797i
$271$	7.69085	+	5.58773i	0.467186	+	0.339430i	0.796344	−	0.604845i	$-0.206765\pi$
$271$	7.69085	+	5.58773i	0.467186	+	0.339430i	−0.329158	+	0.944275i	$0.606765\pi$
$272$	1.20370	−	0.874542i	0.0729852	−	0.0530269i
$273$	1.68583			0.102031
$274$	7.54628			0.455887
$275$	−8.01247	+	5.82140i	−0.483170	+	0.351043i
$276$	0.714433	−	2.19880i	0.0430038	−	0.132352i
$277$	6.12044	+	18.8368i	0.367742	+	1.13179i	0.948246	+	0.317536i	$0.102855\pi$
$277$	6.12044	+	18.8368i	0.367742	+	1.13179i	−0.580505	+	0.814257i	$0.697145\pi$
$278$	26.9464			1.61614
$279$	−11.3701	+	9.93944i	−0.680711	+	0.595059i
$280$	9.74154			0.582168
$281$	7.70531	+	23.7145i	0.459661	+	1.41469i	0.865575	+	0.500779i	$0.166953\pi$
$281$	7.70531	+	23.7145i	0.459661	+	1.41469i	−0.405915	+	0.913911i	$0.633047\pi$
$282$	−0.171793	+	0.528724i	−0.0102301	+	0.0314850i
$283$	−16.2879	+	11.8339i	−0.968217	+	0.703451i	−0.955045	−	0.296462i	$-0.904193\pi$
$283$	−16.2879	+	11.8339i	−0.968217	+	0.703451i	−0.0131726	+	0.999913i	$0.504193\pi$
$284$	4.97702			0.295332
$285$	−2.24793			−0.133156
$286$	−3.33130	+	2.42033i	−0.196984	+	0.143117i
$287$	−39.3144	−	28.5636i	−2.32066	−	1.68606i
$288$	−15.6772	−	11.3901i	−0.923785	−	0.671169i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−5.93689	+	4.31340i	−0.348626	+	0.253292i
$291$	2.87642	+	8.85270i	0.168619	+	0.518955i
$292$	−0.427448	+	1.31555i	−0.0250145	+	0.0769867i
$293$	9.67350	+	7.02821i	0.565132	+	0.410592i	0.833333	−	0.552771i	$-0.186429\pi$
$293$	9.67350	+	7.02821i	0.565132	+	0.410592i	−0.268202	+	0.963363i	$0.586429\pi$
$294$	4.77205	−	14.6869i	0.278312	−	0.856555i
$295$	0.257202	−	0.791588i	0.0149749	−	0.0460880i
$296$	−8.35709	−	6.07178i	−0.485746	−	0.352915i
$297$	2.51454	−	7.73896i	0.145909	−	0.449060i
$298$	−4.80102	−	14.7760i	−0.278115	−	0.855951i
$299$	0.852103	−	0.619089i	0.0492784	−	0.0358028i
$300$	−1.77586	−	5.46552i	−0.102529	−	0.315552i
$301$	34.6753	+	25.1931i	1.99865	+	1.45211i
$302$	−1.36777	−	0.993740i	−0.0787061	−	0.0571833i
$303$	−8.61398	+	6.25842i	−0.494860	+	0.359537i
$304$	−5.53104			−0.317227
$305$	−4.42656			−0.253464
$306$	4.84461	−	3.51981i	0.276948	−	0.201214i
$307$	8.14084	−	25.0549i	0.464622	−	1.42996i	−0.394835	−	0.918752i	$-0.629198\pi$
$307$	8.14084	−	25.0549i	0.464622	−	1.42996i	0.859457	−	0.511208i	$-0.170802\pi$
$308$	10.5617	+	32.5056i	0.601809	+	1.85218i
$309$	2.33673			0.132932
$310$	13.8043	−	1.24635i	0.784031	−	0.0707879i
$311$	−22.8954			−1.29828			−0.649138	−	0.760670i	$-0.724870\pi$
$311$	−22.8954			−1.29828			−0.649138	+	0.760670i	$0.724870\pi$
$312$	−0.224545	−	0.691079i	−0.0127124	−	0.0391247i
$313$	8.99360	−	27.6794i	0.508348	−	1.56453i	−0.286720	−	0.958014i	$-0.592565\pi$
$313$	8.99360	−	27.6794i	0.508348	−	1.56453i	0.795068	−	0.606520i	$-0.207435\pi$
$314$	30.3588	−	22.0570i	1.71325	−	1.24475i
$315$	−13.6927			−0.771498
$316$	44.3274			2.49361
$317$	−3.00131	+	2.18058i	−0.168570	+	0.122474i	−0.668872	−	0.743378i	$-0.733223\pi$
$317$	−3.00131	+	2.18058i	−0.168570	+	0.122474i	0.500301	+	0.865851i	$0.333223\pi$
$318$	5.41141	+	3.93162i	0.303457	+	0.220474i
$319$	−6.33478	−	4.60249i	−0.354680	−	0.257690i
$320$	4.45896	+	13.7233i	0.249263	+	0.767153i
$321$	−1.41597	+	1.02876i	−0.0790317	+	0.0574199i
$322$	−4.58149	−	14.1004i	−0.255316	−	0.785783i
$323$	1.14876	−	3.53550i	0.0639184	−	0.196721i
$324$	−15.1006	−	10.9712i	−0.838920	−	0.609511i
$325$	0.809027	−	2.48993i	0.0448767	−	0.138116i
$326$	−0.385381	+	1.18608i	−0.0213443	+	0.0656909i
$327$	−1.60219	−	1.16406i	−0.0886011	−	0.0643725i
$328$	−6.47268	+	19.9209i	−0.357394	+	1.09995i
$329$	0.649614	+	1.99931i	0.0358144	+	0.110225i
$330$	−2.86887	+	2.08436i	−0.157926	+	0.114740i
$331$	−8.64445	−	26.6049i	−0.475142	−	1.46234i	−0.845766	−	0.533554i	$-0.820856\pi$
$331$	−8.64445	−	26.6049i	−0.475142	−	1.46234i	0.370624	−	0.928783i	$-0.379144\pi$
$332$	32.7520	+	23.7957i	1.79750	+	1.30596i
$333$	11.7467	+	8.53451i	0.643718	+	0.467688i
$334$	35.7955	−	26.0069i	1.95864	−	1.42304i
$335$	3.58355			0.195790
$336$	3.57219			0.194879
$337$	−21.4090	+	15.5545i	−1.16622	+	0.847310i	−0.990552	−	0.137139i	$-0.956209\pi$
$337$	−21.4090	+	15.5545i	−1.16622	+	0.847310i	−0.175671	+	0.984449i	$0.556209\pi$
$338$	−8.53257	+	26.2606i	−0.464111	+	1.42839i
$339$	2.69003	+	8.27905i	0.146102	+	0.449656i
$340$	−3.24077			−0.175755
$341$	5.81645	+	13.5976i	0.314978	+	0.736351i
$342$	−22.2611			−1.20374
$343$	−8.36071	−	25.7316i	−0.451436	−	1.38938i
$344$	5.70890	−	17.5702i	0.307804	−	0.947322i
$345$	0.733820	−	0.533152i	0.0395076	−	0.0287039i
$346$	−0.968363			−0.0520595
$347$	−25.9849			−1.39494			−0.697470	−	0.716613i	$-0.745691\pi$
$347$	−25.9849			−1.39494			−0.697470	+	0.716613i	$0.745691\pi$
$348$	3.67577	−	2.67060i	0.197042	−	0.143159i
$349$	−12.2069	−	8.86886i	−0.653422	−	0.474739i	0.211013	−	0.977483i	$-0.432324\pi$
$349$	−12.2069	−	8.86886i	−0.653422	−	0.474739i	−0.864435	+	0.502744i	$0.832324\pi$
$350$	−29.8145	−	21.6615i	−1.59365	−	1.15786i
$351$	0.664708	+	2.04576i	0.0354795	+	0.109195i
$352$	−15.3526	+	11.1543i	−0.818295	+	0.594526i
$353$	−6.30356	−	19.4004i	−0.335505	−	1.03258i	−0.966473	−	0.256769i	$-0.917342\pi$
$353$	−6.30356	−	19.4004i	−0.335505	−	1.03258i	0.630968	−	0.775809i	$-0.282658\pi$
$354$	−0.270059	+	0.831157i	−0.0143535	+	0.0441755i
$355$	1.57972	+	1.14773i	0.0838427	+	0.0609153i
$356$	−8.04219	+	24.7513i	−0.426235	+	1.31182i
$357$	−0.741917	+	2.28339i	−0.0392664	+	0.120850i
$358$	−7.24503	−	5.26382i	−0.382912	−	0.278202i
$359$	−8.15935	+	25.1119i	−0.430634	+	1.32536i	0.466861	+	0.884331i	$0.345385\pi$
$359$	−8.15935	+	25.1119i	−0.430634	+	1.32536i	−0.897495	+	0.441024i	$0.854615\pi$
$360$	1.82381	+	5.61312i	0.0961233	+	0.295837i
$361$	4.19117	−	3.04506i	0.220588	−	0.160266i
$362$	11.9593	+	36.8071i	0.628569	+	1.93454i
$363$	1.71127	+	1.24331i	0.0898186	+	0.0652570i
$364$	−7.30938	−	5.31058i	−0.383116	−	0.278350i
$365$	−0.439047	+	0.318987i	−0.0229808	+	0.0166965i
$366$	4.64783			0.242946
$367$	18.9882			0.991178			0.495589	−	0.868557i	$-0.334952\pi$
$367$	18.9882			0.991178			0.495589	+	0.868557i	$0.334952\pi$
$368$	1.80556	−	1.31182i	0.0941216	−	0.0683833i
$369$	9.09802	−	28.0008i	0.473624	−	1.45767i
$370$	−4.11797	−	12.6738i	−0.214083	−	0.658880i
$371$	25.2932			1.31316
$372$	−8.54680	+	0.771666i	−0.443131	+	0.0400090i
$373$	29.3391			1.51912			0.759561	−	0.650436i	$-0.225414\pi$
$373$	29.3391			1.51912			0.759561	+	0.650436i	$0.225414\pi$
$374$	−1.81216	−	5.57726i	−0.0937047	−	0.288393i
$375$	1.63103	−	5.01980i	0.0842262	−	0.259222i
$376$	0.733058	−	0.532598i	0.0378046	−	0.0274666i
$377$	2.06988			0.106604
$378$	30.2788			1.55737
$379$	11.7383	−	8.52834i	0.602954	−	0.438072i	−0.243972	−	0.969782i	$-0.578451\pi$
$379$	11.7383	−	8.52834i	0.602954	−	0.438072i	0.846926	+	0.531711i	$0.178451\pi$
$380$	9.74654	+	7.08127i	0.499987	+	0.363262i
$381$	0.397640	+	0.288902i	0.0203717	+	0.0148009i
$382$	9.98087	+	30.7179i	0.510666	+	1.57167i
$383$	−5.12273	+	3.72188i	−0.261759	+	0.190179i	−0.710922	−	0.703271i	$-0.751722\pi$
$383$	−5.12273	+	3.72188i	−0.261759	+	0.190179i	0.449163	+	0.893450i	$0.351722\pi$
$384$	−2.31399	−	7.12173i	−0.118085	−	0.363429i
$385$	−4.14368	+	12.7529i	−0.211182	+	0.649950i
$386$	−25.8469	−	18.7789i	−1.31557	−	0.955821i
$387$	−8.02445	+	24.6967i	−0.407906	+	1.25541i
$388$	15.4156	−	47.4444i	0.782610	−	2.40862i
$389$	30.1387	+	21.8971i	1.52809	+	1.11022i	0.957287	+	0.289140i	$0.0933695\pi$
$389$	30.1387	+	21.8971i	1.52809	+	1.11022i	0.570807	+	0.821084i	$0.306631\pi$
$390$	0.289673	−	0.891521i	0.0146681	−	0.0451439i
$391$	0.463528	+	1.42659i	0.0234416	+	0.0721459i
$392$	−20.3628	+	14.7945i	−1.02848	+	0.747234i
$393$	0.686744	+	2.11358i	0.0346416	+	0.106616i
$394$	40.7204	+	29.5851i	2.05146	+	1.49047i
$395$	14.0696	+	10.2222i	0.707920	+	0.514334i
$396$	−16.7525	+	12.1714i	−0.841844	+	0.611635i
$397$	12.7855			0.641684			0.320842	−	0.947133i	$-0.396034\pi$
$397$	12.7855			0.641684			0.320842	+	0.947133i	$0.396034\pi$
$398$	−20.8309			−1.04416
$399$	7.22064	−	5.24610i	0.361484	−	0.262634i
$400$	1.71429	−	5.27604i	0.0857144	−	0.263802i
$401$	−6.43063	−	19.7914i	−0.321130	−	0.988338i	−0.973157	−	0.230142i	$-0.926081\pi$
$401$	−6.43063	−	19.7914i	−0.321130	−	0.988338i	0.652027	−	0.758196i	$-0.273919\pi$
$402$	−3.76268			−0.187665
$403$	−3.35668	−	2.00423i	−0.167208	−	0.0998379i
$404$	57.0631			2.83899
$405$	−2.26293	−	6.96457i	−0.112446	−	0.346072i
$406$	9.00364	−	27.7104i	0.446843	−	1.37524i
$407$	11.5035	−	8.35781i	0.570209	−	0.414281i
$408$	1.03486			0.0512331
$409$	36.1890			1.78943			0.894714	−	0.446639i	$-0.147379\pi$
$409$	36.1890			1.78943			0.894714	+	0.446639i	$0.147379\pi$
$410$	−21.8607	+	15.8827i	−1.07962	+	0.784391i
$411$	−1.48297	−	1.07744i	−0.0731496	−	0.0531463i
$412$	−10.1316	−	7.36100i	−0.499146	−	0.362651i
$413$	1.02120	+	3.14292i	0.0502498	+	0.154653i
$414$	7.26695	−	5.27975i	0.357151	−	0.259485i
$415$	4.90813	+	15.1057i	0.240930	+	0.741508i
$416$	1.55016	−	4.77091i	0.0760031	−	0.233913i
$417$	−5.29542	−	3.84735i	−0.259318	−	0.188405i
$418$	−6.73662	+	20.7332i	−0.329499	+	1.01409i
$419$	0.311622	−	0.959074i	0.0152237	−	0.0468538i	−0.943156	−	0.332350i	$-0.892158\pi$
$419$	0.311622	−	0.959074i	0.0152237	−	0.0468538i	0.958380	+	0.285496i	$0.0921584\pi$
$420$	−6.29475	−	4.57340i	−0.307152	−	0.223159i
$421$	7.70903	−	23.7259i	0.375715	−	1.15633i	−0.567280	−	0.823525i	$-0.692004\pi$
$421$	7.70903	−	23.7259i	0.375715	−	1.15633i	0.942995	−	0.332807i	$-0.107996\pi$
$422$	5.35091	+	16.4684i	0.260478	+	0.801669i
$423$	−1.03039	+	0.748621i	−0.0500992	+	0.0363992i
$424$	−3.36894	−	10.3685i	−0.163610	−	0.503540i
$425$	3.01646	+	2.19158i	0.146320	+	0.106307i
$426$	−1.65868	−	1.20510i	−0.0803635	−	0.0583875i
$427$	14.2187	−	10.3305i	0.688089	−	0.499926i
$428$	9.38005			0.453402
$429$	1.00023			0.0482914
$430$	19.2811	−	14.0085i	0.929817	−	0.675552i
$431$	−3.72418	+	11.4619i	−0.179388	+	0.552098i	−0.999807	−	0.0196646i	$-0.993740\pi$
$431$	−3.72418	+	11.4619i	−0.179388	+	0.552098i	0.820419	+	0.571763i	$0.193740\pi$
$432$	1.40848	+	4.33487i	0.0677657	+	0.208561i
$433$	−22.8428			−1.09775			−0.548877	−	0.835903i	$-0.684945\pi$
$433$	−22.8428			−1.09775			−0.548877	+	0.835903i	$0.684945\pi$
$434$	−41.4324	+	36.2191i	−1.98882	+	1.73857i
$435$	1.78256			0.0854670
$436$	3.27980	+	10.0942i	0.157074	+	0.483423i
$437$	1.72314	−	5.30329i	0.0824291	−	0.253691i
$438$	0.460994	−	0.334932i	0.0220271	−	0.0160037i
$439$	14.5495			0.694412			0.347206	−	0.937789i	$-0.387130\pi$
$439$	14.5495			0.694412			0.347206	+	0.937789i	$0.387130\pi$
$440$	5.77978			0.275540
$441$	28.6221	−	20.7952i	1.36296	−	0.990245i
$442$	1.25414	+	0.911183i	0.0596531	+	0.0433405i
$443$	26.1761	+	19.0181i	1.24366	+	0.903575i	0.997837	−	0.0657387i	$-0.0209404\pi$
$443$	26.1761	+	19.0181i	1.24366	+	0.903575i	0.245827	+	0.969314i	$0.420940\pi$
$444$	2.54961	+	7.84688i	0.120999	+	0.372396i
$445$	−8.26042	+	6.00155i	−0.391582	+	0.284501i
$446$	−10.3974	−	32.0000i	−0.492332	−	1.51524i
$447$	−1.16621	+	3.58921i	−0.0551597	+	0.169764i
$448$	−46.3493	−	33.6747i	−2.18980	−	1.59098i
$449$	−2.50923	+	7.72260i	−0.118418	+	0.364452i	−0.992645	−	0.121066i	$-0.961369\pi$
$449$	−2.50923	+	7.72260i	−0.118418	+	0.364452i	0.874227	+	0.485518i	$0.161369\pi$
$450$	6.89958	−	21.2347i	0.325250	−	1.00102i
$451$	−23.3258	−	16.9472i	−1.09837	−	0.798011i
$452$	14.4167	−	44.3700i	0.678104	−	2.08699i
$453$	0.126905	+	0.390573i	0.00596252	+	0.0183507i
$454$	3.81038	−	2.76841i	0.178830	−	0.129928i
$455$	−1.09536	−	3.37118i	−0.0513514	−	0.158043i
$456$	−3.11231	−	2.26123i	−0.145747	−	0.105892i
$457$	17.7321	+	12.8831i	0.829474	+	0.602648i	0.919410	−	0.393300i	$-0.128666\pi$
$457$	17.7321	+	12.8831i	0.829474	+	0.602648i	−0.0899368	+	0.995947i	$0.528666\pi$
$458$	17.8713	−	12.9842i	0.835069	−	0.606713i
$459$	−3.06343			−0.142989
$460$	−4.86117			−0.226653
$461$	28.1055	−	20.4198i	1.30900	−	0.951046i	0.309003	−	0.951061i	$-0.400005\pi$
$461$	28.1055	−	20.4198i	1.30900	−	0.951046i	1.00000		1.46920e-5i	$4.67660e-6\pi$
$462$	4.35081	−	13.3904i	0.202418	−	0.622979i
$463$	9.52943	+	29.3286i	0.442870	+	1.36301i	0.884803	+	0.465966i	$0.154293\pi$
$463$	9.52943	+	29.3286i	0.442870	+	1.36301i	−0.441933	+	0.897048i	$0.645707\pi$
$464$	4.38598			0.203614
$465$	−2.89073	−	1.72602i	−0.134054	−	0.0800422i
$466$	−41.5232			−1.92352
$467$	1.08354	+	3.33481i	0.0501405	+	0.154317i	0.972992	−	0.230840i	$-0.0741474\pi$
$467$	1.08354	+	3.33481i	0.0501405	+	0.154317i	−0.922851	+	0.385157i	$0.874147\pi$
$468$	1.69151	−	5.20595i	0.0781903	−	0.240645i
$469$	−11.5108	+	8.36309i	−0.531520	+	0.386172i
$470$	1.16892			0.0539182
$471$	−9.11527			−0.420009
$472$	1.15237	−	0.837247i	0.0530422	−	0.0385374i
$473$	20.5733	+	14.9474i	0.945963	+	0.687282i
$474$	−14.7729	−	10.7332i	−0.678543	−	0.492991i
$475$	−4.28319	−	13.1823i	−0.196526	−	0.604845i
$476$	10.4097	−	7.56312i	0.477130	−	0.346655i
$477$	4.73539	+	14.5740i	0.216819	+	0.667299i
$478$	−2.83825	+	8.73524i	−0.129819	+	0.399540i
$479$	−19.0462	−	13.8379i	−0.870243	−	0.632268i	0.0604092	−	0.998174i	$-0.480759\pi$
$479$	−19.0462	−	13.8379i	−0.870243	−	0.632268i	−0.930652	+	0.365905i	$0.880759\pi$
$480$	1.33498	−	4.10865i	0.0609333	−	0.187533i
$481$	−1.16152	+	3.57480i	−0.0529609	+	0.162997i
$482$	−34.9206	−	25.3713i	−1.59059	−	1.15563i
$483$	−1.11288	+	3.42510i	−0.0506379	+	0.155847i
$484$	−3.50311	−	10.7815i	−0.159232	−	0.490066i
$485$	15.8339	−	11.5040i	0.718982	−	0.522371i
$486$	8.64589	+	26.6093i	0.392186	+	1.20702i
$487$	−4.25612	−	3.09225i	−0.192863	−	0.140123i	0.487163	−	0.873311i	$-0.338032\pi$
$487$	−4.25612	−	3.09225i	−0.192863	−	0.140123i	−0.680026	+	0.733188i	$0.738032\pi$
$488$	−6.12867	−	4.45274i	−0.277432	−	0.201566i
$489$	0.245080	−	0.178061i	0.0110829	−	0.00805219i
$490$	−32.4702			−1.46685
$491$	14.1928			0.640512			0.320256	−	0.947331i	$-0.396231\pi$
$491$	14.1928			0.640512			0.320256	+	0.947331i	$0.396231\pi$
$492$	13.5348	−	9.83363i	0.610197	−	0.443334i
$493$	−0.910935	+	2.80357i	−0.0410264	+	0.126266i
$494$	−1.78080	−	5.48073i	−0.0801218	−	0.246590i
$495$	−8.12408			−0.365150
$496$	−7.11263	−	4.24687i	−0.319367	−	0.190690i
$497$	−7.75277			−0.347759
$498$	−5.15347	−	15.8607i	−0.230932	−	0.710737i
$499$	−12.2561	+	37.7204i	−0.548658	+	1.68860i	0.163472	+	0.986548i	$0.447731\pi$
$499$	−12.2561	+	37.7204i	−0.548658	+	1.68860i	−0.712130	+	0.702048i	$0.752269\pi$
$500$	−22.8848	+	16.6268i	−1.02344	+	0.743572i
$501$	−10.7476			−0.480169
$502$	−37.1536			−1.65825
$503$	−4.58999	+	3.33483i	−0.204658	+	0.148693i	−0.685393	−	0.728173i	$-0.740370\pi$
$503$	−4.58999	+	3.33483i	−0.204658	+	0.148693i	0.480736	+	0.876866i	$0.340370\pi$
$504$	−18.9579	−	13.7737i	−0.844452	−	0.613530i
$505$	18.1120	+	13.1591i	0.805972	+	0.585573i
$506$	−2.71826	−	8.36594i	−0.120841	−	0.371911i
$507$	5.42622	−	3.94238i	0.240987	−	0.175087i
$508$	−0.813998	−	2.50523i	−0.0361153	−	0.111152i
$509$	6.32468	−	19.4654i	0.280337	−	0.862787i	−0.707421	−	0.706792i	$-0.750142\pi$
$509$	6.32468	−	19.4654i	0.280337	−	0.862787i	0.987758	−	0.155995i	$-0.0498584\pi$
$510$	1.08005	+	0.784699i	0.0478252	+	0.0347470i
$511$	0.665841	−	2.04925i	0.0294551	−	0.0906534i
$512$	5.05918	−	15.5706i	0.223586	−	0.688128i
$513$	9.21319	+	6.69378i	0.406772	+	0.295537i
$514$	4.37236	−	13.4568i	0.192857	−	0.593552i
$515$	−1.51829	−	4.67280i	−0.0669037	−	0.205908i
$516$	−11.9377	+	8.67326i	−0.525529	+	0.381819i
$517$	0.385425	+	1.18622i	0.0169510	+	0.0521697i
$518$	42.8049	+	31.0996i	1.88074	+	1.36644i
$519$	0.190300	+	0.138261i	0.00835323	+	0.00606898i
$520$	−1.23606	+	0.898053i	−0.0542050	+	0.0393822i
$521$	36.4774			1.59810			0.799052	−	0.601262i	$-0.205335\pi$
$521$	36.4774			1.59810			0.799052	+	0.601262i	$0.205335\pi$
$522$	17.6525			0.772628
$523$	−29.3222	+	21.3038i	−1.28217	+	0.931552i	−0.999616	−	0.0276997i	$-0.991182\pi$
$523$	−29.3222	+	21.3038i	−1.28217	+	0.931552i	−0.282554	+	0.959251i	$0.591182\pi$
$524$	3.68048	−	11.3273i	0.160782	−	0.494837i
$525$	2.76627	+	8.51371i	0.120730	+	0.371569i
$526$	−16.6229			−0.724795
$527$	4.19189	−	3.66443i	0.182601	−	0.159625i
$528$	2.11943			0.0922363
$529$	−6.41210	−	19.7344i	−0.278787	−	0.858017i
$530$	4.34607	−	13.3758i	0.188781	−	0.581009i
$531$	−1.61978	+	1.17684i	−0.0702923	+	0.0510704i
$532$	−47.8330			−2.07382
$533$	7.62168			0.330131
$534$	8.67334	−	6.30155i	0.375332	−	0.272695i
$535$	2.97725	+	2.16310i	0.128718	+	0.0935190i
$536$	4.96150	+	3.60474i	0.214304	+	0.155701i
$537$	0.672214	+	2.06886i	0.0290082	+	0.0892779i
$538$	−22.2508	+	16.1662i	−0.959302	+	0.696974i
$539$	−10.7063	−	32.9506i	−0.461153	−	1.41928i
$540$	3.06787	−	9.44194i	0.132020	−	0.406317i
$541$	−7.47858	−	5.43351i	−0.321529	−	0.233605i	0.415298	−	0.909685i	$-0.363677\pi$
$541$	−7.47858	−	5.43351i	−0.321529	−	0.233605i	−0.736828	+	0.676080i	$0.763677\pi$
$542$	−6.48552	+	19.9604i	−0.278577	+	0.857372i
$543$	2.90502	−	8.94074i	0.124667	−	0.383684i
$544$	5.77979	+	4.19926i	0.247806	+	0.180042i
$545$	−1.28677	+	3.96026i	−0.0551190	+	0.169639i
$546$	1.15012	+	3.53970i	0.0492205	+	0.151485i
$547$	1.50241	−	1.09156i	0.0642382	−	0.0466718i	−0.555203	−	0.831715i	$-0.687359\pi$
$547$	1.50241	−	1.09156i	0.0642382	−	0.0466718i	0.619441	+	0.785043i	$0.287359\pi$
$548$	3.03575	+	9.34309i	0.129681	+	0.399117i
$549$	8.61447	+	6.25878i	0.367657	+	0.267118i
$550$	−17.6894	−	12.8521i	−0.754277	−	0.548014i
$551$	8.86559	−	6.44123i	0.377687	−	0.274406i
$552$	1.55230			0.0660701
$553$	−69.0494			−2.93628
$554$	−35.3756	+	25.7019i	−1.50297	+	1.09197i
$555$	−1.00029	+	3.07857i	−0.0424599	+	0.130678i
$556$	10.8401	+	33.3625i	0.459724	+	1.41488i
$557$	5.45451			0.231115			0.115557	−	0.993301i	$-0.463135\pi$
$557$	5.45451			0.231115			0.115557	+	0.993301i	$0.463135\pi$
$558$	−28.6266	−	17.0926i	−1.21186	−	0.723587i
$559$	−6.72231			−0.284324
$560$	−2.32102	−	7.14337i	−0.0980811	−	0.301863i
$561$	−0.440189	+	1.35476i	−0.0185848	+	0.0571982i
$562$	−44.5360	+	32.3573i	−1.87864	+	1.36491i
$563$	−9.14022			−0.385214			−0.192607	−	0.981276i	$-0.561694\pi$
$563$	−9.14022			−0.385214			−0.192607	+	0.981276i	$0.561694\pi$
$564$	−0.723726			−0.0304743
$565$	14.8079	−	10.7586i	0.622974	−	0.452617i
$566$	−35.9594	−	26.1260i	−1.51148	−	1.09816i
$567$	23.5223	+	17.0900i	0.987845	+	0.717712i
$568$	1.03263	+	3.17812i	0.0433284	+	0.133351i
$569$	−13.2174	+	9.60300i	−0.554102	+	0.402579i	−0.829296	−	0.558810i	$-0.811258\pi$
$569$	−13.2174	+	9.60300i	−0.554102	+	0.402579i	0.275193	+	0.961389i	$0.411258\pi$
$570$	−1.53360	−	4.71993i	−0.0642354	−	0.197696i
$571$	7.18976	−	22.1278i	0.300882	−	0.926020i	−0.680300	−	0.732934i	$-0.738150\pi$
$571$	7.18976	−	22.1278i	0.300882	−	0.926020i	0.981182	−	0.193086i	$-0.0618497\pi$
$572$	−4.33676	−	3.15084i	−0.181329	−	0.131743i
$573$	2.42444	−	7.46164i	0.101282	−	0.311715i
$574$	33.1530	−	102.034i	1.38378	−	4.25884i
$575$	4.52471	+	3.28740i	0.188693	+	0.137094i
$576$	10.7260	−	33.0112i	0.446917	−	1.37547i
$577$	2.02069	+	6.21905i	0.0841225	+	0.258903i	0.984267	−	0.176690i	$-0.0565389\pi$
$577$	2.02069	+	6.21905i	0.0841225	+	0.258903i	−0.900144	+	0.435592i	$0.856539\pi$
$578$	−1.78609	+	1.29767i	−0.0742916	+	0.0539760i
$579$	2.39815	+	7.38074i	0.0996637	+	0.306733i
$580$	−7.72877	−	5.61528i	−0.320920	−	0.233162i
$581$	−51.0183	−	37.0669i	−2.11659	−	1.53780i
$582$	−16.6254	+	12.0791i	−0.689147	+	0.500694i
$583$	15.0068			0.621517
$584$	−0.928744			−0.0384317
$585$	1.73742	−	1.26231i	0.0718333	−	0.0521899i
$586$	−8.15744	+	25.1060i	−0.336981	+	1.03712i
$587$	1.38431	+	4.26046i	0.0571365	+	0.175848i	0.975552	−	0.219770i	$-0.0705305\pi$
$587$	1.38431	+	4.26046i	0.0571365	+	0.175848i	−0.918415	+	0.395618i	$0.870531\pi$
$588$	20.1036			0.829059
$589$	−20.6140	+	1.86118i	−0.849386	+	0.0766886i
$590$	1.83755			0.0756506
$591$	−3.77815	−	11.6279i	−0.155412	−	0.478309i
$592$	−2.46121	+	7.57483i	−0.101155	+	0.311324i
$593$	−13.4164	+	9.74756i	−0.550944	+	0.400284i	−0.828134	−	0.560531i	$-0.810597\pi$
$593$	−13.4164	+	9.74756i	−0.550944	+	0.400284i	0.277189	+	0.960815i	$0.410597\pi$
$594$	17.9648			0.737105
$595$	5.04818			0.206955
$596$	16.3629	−	11.8883i	0.670250	−	0.486965i
$597$	4.09363	+	2.97419i	0.167541	+	0.121726i
$598$	1.88121	+	1.36678i	0.0769285	+	0.0558918i
$599$	6.59488	+	20.2970i	0.269460	+	0.829312i	0.990632	+	0.136556i	$0.0436034\pi$
$599$	6.59488	+	20.2970i	0.269460	+	0.829312i	−0.721173	+	0.692755i	$0.756397\pi$
$600$	3.12161	−	2.26798i	0.127439	−	0.0925898i
$601$	−1.51916	−	4.67550i	−0.0619679	−	0.190718i	0.915280	−	0.402819i	$-0.131969\pi$
$601$	−1.51916	−	4.67550i	−0.0619679	−	0.190718i	−0.977248	+	0.212101i	$0.931969\pi$
$602$	−29.2409	+	89.9943i	−1.19177	+	3.66789i
$603$	−6.97390	−	5.06684i	−0.283999	−	0.206338i
$604$	0.680124	−	2.09321i	0.0276738	−	0.0851713i
$605$	1.37438	−	4.22990i	0.0558764	−	0.171970i
$606$	−19.0173	−	13.8169i	−0.772526	−	0.561273i
$607$	−3.14833	+	9.68956i	−0.127787	+	0.393287i	−0.994399	−	0.105696i	$-0.966293\pi$
$607$	−3.14833	+	9.68956i	−0.127787	+	0.393287i	0.866612	+	0.498983i	$0.166293\pi$
$608$	−8.20695	−	25.2584i	−0.332836	−	1.02436i
$609$	−5.72579	+	4.16003i	−0.232021	+	0.168573i
$610$	−3.01991	−	9.29434i	−0.122273	−	0.376317i
$611$	−0.266739	−	0.193797i	−0.0107911	−	0.00784020i
$612$	6.30682	+	4.58217i	0.254938	+	0.185223i
$613$	−4.97125	+	3.61182i	−0.200787	+	0.145880i	−0.683635	−	0.729824i	$-0.739602\pi$
$613$	−4.97125	+	3.61182i	−0.200787	+	0.145880i	0.482849	+	0.875704i	$0.339602\pi$
$614$	58.1611			2.34719
$615$	6.56369			0.264674
$616$	−18.5654	+	13.4885i	−0.748021	+	0.543469i
$617$	−3.29328	+	10.1357i	−0.132583	+	0.408047i	−0.995206	−	0.0977990i	$-0.968820\pi$
$617$	−3.29328	+	10.1357i	−0.132583	+	0.408047i	0.862624	+	0.505846i	$0.168820\pi$
$618$	1.59418	+	4.90638i	0.0641273	+	0.197364i
$619$	34.0212			1.36743			0.683714	−	0.729750i	$-0.260364\pi$
$619$	34.0212			1.36743			0.683714	+	0.729750i	$0.260364\pi$
$620$	7.09637	+	16.5898i	0.284997	+	0.666262i
$621$	−4.59516			−0.184398
$622$	−15.6198	−	48.0728i	−0.626297	−	1.92754i
$623$	12.5274	−	38.5554i	0.501900	−	1.54469i
$624$	−0.453261	+	0.329314i	−0.0181450	+	0.0131831i
$625$	7.54480			0.301792
$626$	64.2535			2.56809
$627$	4.28410	−	3.11258i	0.171091	−	0.124305i
$628$	39.5218	+	28.7142i	1.57709	+	1.14582i
$629$	−4.33075	−	3.14647i	−0.172678	−	0.125458i
$630$	−9.34154	−	28.7503i	−0.372176	−	1.14544i
$631$	15.9058	−	11.5562i	0.633200	−	0.460046i	−0.224308	−	0.974518i	$-0.572012\pi$
$631$	15.9058	−	11.5562i	0.633200	−	0.460046i	0.857507	+	0.514472i	$0.172012\pi$
$632$	9.19708	+	28.3057i	0.365840	+	1.12594i
$633$	1.29978	−	4.00031i	0.0516616	−	0.158998i
$634$	−6.62608	−	4.81413i	−0.263155	−	0.191194i
$635$	0.319357	−	0.982879i	0.0126733	−	0.0390044i
$636$	−2.69083	+	8.28153i	−0.106698	+	0.328384i
$637$	7.40946	+	5.38329i	0.293574	+	0.213294i
$638$	5.34198	−	16.4409i	0.211491	−	0.650902i
$639$	−1.45147	−	4.46718i	−0.0574194	−	0.176719i
$640$	−12.7379	+	9.25465i	−0.503511	+	0.365822i
$641$	6.98319	+	21.4921i	0.275820	+	0.848885i	0.989001	+	0.147906i	$0.0472534\pi$
$641$	6.98319	+	21.4921i	0.275820	+	0.848885i	−0.713182	+	0.700979i	$0.752747\pi$
$642$	−3.12608	−	2.27123i	−0.123376	−	0.0896382i
$643$	−1.29500	−	0.940872i	−0.0510698	−	0.0371044i	0.561957	−	0.827166i	$-0.310048\pi$
$643$	−1.29500	−	0.940872i	−0.0510698	−	0.0371044i	−0.613027	+	0.790062i	$0.710048\pi$
$644$	15.6147	−	11.3447i	0.615305	−	0.447045i
$645$	−5.78917			−0.227948
$646$	8.20712			0.322905
$647$	−8.46173	+	6.14780i	−0.332665	+	0.241695i	−0.741560	−	0.670886i	$-0.765914\pi$
$647$	−8.46173	+	6.14780i	−0.332665	+	0.241695i	0.408896	+	0.912581i	$0.365914\pi$
$648$	3.87269	−	11.9189i	0.152134	−	0.468219i
$649$	0.605890	+	1.86474i	0.0237833	+	0.0731974i
$650$	5.77998			0.226709
$651$	13.3135	−	1.20203i	0.521796	−	0.0471114i
$652$	−1.62352			−0.0635821
$653$	6.85693	+	21.1035i	0.268332	+	0.825842i	0.990907	+	0.134549i	$0.0429587\pi$
$653$	6.85693	+	21.1035i	0.268332	+	0.825842i	−0.722574	+	0.691293i	$0.757041\pi$
$654$	1.35109	−	4.15822i	0.0528317	−	0.162599i
$655$	3.78035	−	2.74659i	0.147711	−	0.107318i
$656$	16.1500			0.630550
$657$	1.30544			0.0509303
$658$	−3.75471	+	2.72796i	−0.146374	+	0.106347i
$659$	−14.7894	−	10.7452i	−0.576115	−	0.418572i	0.261206	−	0.965283i	$-0.415880\pi$
$659$	−14.7894	−	10.7452i	−0.576115	−	0.418572i	−0.837321	+	0.546711i	$0.815880\pi$
$660$	−3.73476	−	2.71346i	−0.145375	−	0.105621i
$661$	0.487322	+	1.49982i	0.0189546	+	0.0583364i	0.960086	−	0.279703i	$-0.0902361\pi$
$661$	0.487322	+	1.49982i	0.0189546	+	0.0583364i	−0.941132	+	0.338040i	$0.890236\pi$
$662$	49.9642	−	36.3011i	1.94191	−	1.41088i
$663$	−0.116362	−	0.358126i	−0.00451913	−	0.0139084i
$664$	−8.39959	+	25.8513i	−0.325967	+	1.00322i
$665$	−15.1823	−	11.0306i	−0.588745	−	0.427748i
$666$	−9.90577	+	30.4868i	−0.383841	+	1.18134i
$667$	−1.36641	+	4.20538i	−0.0529076	+	0.162833i
$668$	46.5993	+	33.8564i	1.80298	+	1.30994i
$669$	−2.52562	+	7.77306i	−0.0976461	+	0.300524i
$670$	2.44479	+	7.52429i	0.0944505	+	0.290689i
$671$	8.43612	−	6.12920i	0.325673	−	0.236615i
$672$	5.30042	+	16.3130i	0.204468	+	0.629288i
$673$	15.5948	+	11.3303i	0.601135	+	0.436750i	0.846282	−	0.532736i	$-0.178836\pi$
$673$	15.5948	+	11.3303i	0.601135	+	0.436750i	−0.245147	+	0.969486i	$0.578836\pi$
$674$	−47.2653	−	34.3402i	−1.82059	−	1.32274i
$675$	−9.24070	+	6.71376i	−0.355675	+	0.258413i
$676$	−35.9459			−1.38253
$677$	31.8431			1.22383			0.611916	−	0.790923i	$-0.290399\pi$
$677$	31.8431			1.22383			0.611916	+	0.790923i	$0.290399\pi$
$678$	−15.5481	+	11.2964i	−0.597122	+	0.433834i
$679$	−24.0131	+	73.9048i	−0.921539	+	2.83620i
$680$	−0.672396	−	2.06942i	−0.0257852	−	0.0793587i
$681$	−1.14407			−0.0438409
$682$	−24.5824	+	21.4893i	−0.941309	+	0.822867i
$683$	−6.40619			−0.245126			−0.122563	−	0.992461i	$-0.539111\pi$
$683$	−6.40619			−0.245126			−0.122563	+	0.992461i	$0.539111\pi$
$684$	−8.95530	−	27.5616i	−0.342414	−	1.05384i
$685$	−1.19102	+	3.66559i	−0.0455066	+	0.140055i
$686$	48.3242	−	35.1096i	1.84503	−	1.34049i
$687$	−5.36587			−0.204721
$688$	−14.2443			−0.543057
$689$	−3.20935	+	2.33173i	−0.122266	+	0.0888318i
$690$	1.62008	+	1.17705i	0.0616753	+	0.0448097i
$691$	30.8892	+	22.4423i	1.17508	+	0.853747i	0.991608	−	0.129278i	$-0.0412660\pi$
$691$	30.8892	+	22.4423i	1.17508	+	0.853747i	0.183473	+	0.983025i	$0.441266\pi$
$692$	−0.389558	−	1.19894i	−0.0148088	−	0.0455767i
$693$	26.0956	−	18.9595i	0.991288	−	0.720213i
$694$	−17.7276	−	54.5598i	−0.672929	−	2.07106i
$695$	−4.25292	+	13.0891i	−0.161322	+	0.496499i
$696$	2.46799	+	1.79310i	0.0935489	+	0.0679672i
$697$	−3.35422	+	10.3232i	−0.127050	+	0.391021i
$698$	10.2938	−	31.6812i	0.389628	−	1.19915i
$699$	8.16001	+	5.92860i	0.308640	+	0.224240i
$700$	14.8253	−	45.6277i	0.560345	−	1.72456i
$701$	10.3826	+	31.9545i	0.392147	+	1.20690i	0.931161	+	0.364608i	$0.118797\pi$
$701$	10.3826	+	31.9545i	0.392147	+	1.20690i	−0.539014	+	0.842297i	$0.681203\pi$
$702$	−3.84195	+	2.79134i	−0.145005	+	0.105352i
$703$	6.14940	+	18.9259i	0.231929	+	0.713804i
$704$	−27.4997	−	19.9797i	−1.03643	−	0.753012i
$705$	−0.229712	−	0.166896i	−0.00865147	−	0.00628566i
$706$	36.4340	−	26.4709i	1.37121	−	0.996245i
$707$	−88.8879			−3.34297
$708$	−1.13770			−0.0427574
$709$	41.9900	−	30.5075i	1.57697	−	1.14573i	0.656895	−	0.753982i	$-0.271869\pi$
$709$	41.9900	−	30.5075i	1.57697	−	1.14573i	0.920071	−	0.391751i	$-0.128131\pi$
$710$	−1.33214	+	4.09991i	−0.0499944	+	0.153867i
$711$	−12.9274	−	39.7866i	−0.484817	−	1.49211i
$712$	−17.4738			−0.654858
$713$	6.28786	−	5.49668i	0.235482	−	0.205852i
$714$	−5.30053			−0.198367
$715$	−0.649894	−	2.00017i	−0.0243046	−	0.0748020i
$716$	3.60260	−	11.0877i	0.134636	−	0.414366i
$717$	1.80496	−	1.31138i	0.0674076	−	0.0489745i
$718$	−58.2934			−2.17549
$719$	25.9925			0.969358			0.484679	−	0.874692i	$-0.338936\pi$
$719$	25.9925			0.969358			0.484679	+	0.874692i	$0.338936\pi$
$720$	3.68150	−	2.67477i	0.137201	−	0.0996826i
$721$	15.7821	+	11.4663i	0.587754	+	0.427028i
$722$	9.25297	+	6.72267i	0.344360	+	0.250192i
$723$	3.24002	+	9.97177i	0.120498	+	0.370854i
$724$	−40.7600	+	29.6139i	−1.51483	+	1.10059i
$725$	3.39646	+	10.4532i	0.126141	+	0.388224i
$726$	−1.44308	+	4.44134i	−0.0535577	+	0.164834i
$727$	−4.66526	−	3.38951i	−0.173025	−	0.125710i	0.497903	−	0.867233i	$-0.334104\pi$
$727$	−4.66526	−	3.38951i	−0.173025	−	0.125710i	−0.670927	+	0.741523i	$0.734104\pi$
$728$	1.87457	−	5.76932i	0.0694760	−	0.213825i
$729$	−3.92047	+	12.0660i	−0.145202	+	0.446887i
$730$	−0.969298	−	0.704236i	−0.0358753	−	0.0260649i
$731$	2.95842	−	9.10509i	0.109421	−	0.336764i
$732$	1.86975	+	5.75451i	0.0691080	+	0.212693i
$733$	−37.8528	+	27.5017i	−1.39813	+	1.01580i	−0.403207	+	0.915109i	$0.632105\pi$
$733$	−37.8528	+	27.5017i	−1.39813	+	1.01580i	−0.994918	+	0.100689i	$0.967895\pi$
$734$	12.9543	+	39.8692i	0.478151	+	1.47160i
$735$	6.38094	+	4.63602i	0.235364	+	0.171002i
$736$	8.66973	+	6.29893i	0.319571	+	0.232182i
$737$	−6.82952	+	4.96193i	−0.251568	+	0.182775i
$738$	64.9996			2.39267
$739$	0.143651			0.00528428			0.00264214	−	0.999997i	$-0.499159\pi$
$739$	0.143651			0.00528428			0.00264214	+	0.999997i	$0.499159\pi$
$740$	14.0349	−	10.1970i	0.515934	−	0.374848i
$741$	−0.432570	+	1.33131i	−0.0158909	+	0.0489070i
$742$	17.2557	+	53.1075i	0.633475	+	1.94964i
$743$	6.43994			0.236258			0.118129	−	0.992998i	$-0.462310\pi$
$743$	6.43994			0.236258			0.118129	+	0.992998i	$0.462310\pi$
$744$	−2.26605	−	5.29753i	−0.0830774	−	0.194217i
$745$	7.93515			0.290721
$746$	20.0159	+	61.6026i	0.732834	+	2.25543i
$747$	11.8065	−	36.3366i	0.431977	−	1.32949i
$748$	6.17624	−	4.48730i	0.225826	−	0.164072i
$749$	−14.6114			−0.533890
$750$	11.6527			0.425496
$751$	10.5722	−	7.68117i	0.385786	−	0.280290i	−0.377941	−	0.925830i	$-0.623368\pi$
$751$	10.5722	−	7.68117i	0.385786	−	0.280290i	0.763726	+	0.645540i	$0.223368\pi$
$752$	−0.565207	−	0.410647i	−0.0206110	−	0.0149748i
$753$	7.30131	+	5.30471i	0.266075	+	0.193315i
$754$	1.41213	+	4.34608i	0.0514267	+	0.158275i
$755$	0.698580	−	0.507548i	0.0254239	−	0.0184716i
$756$	12.1807	+	37.4883i	0.443008	+	1.36344i
$757$	12.4042	−	38.1763i	0.450840	−	1.38754i	−0.425111	−	0.905141i	$-0.639765\pi$
$757$	12.4042	−	38.1763i	0.450840	−	1.38754i	0.875951	−	0.482400i	$-0.160235\pi$
$758$	25.9149	+	18.8283i	0.941272	+	0.683874i
$759$	−0.660288	+	2.03216i	−0.0239669	+	0.0737626i
$760$	−2.49960	+	7.69297i	−0.0906699	+	0.279053i
$761$	−19.7061	−	14.3173i	−0.714345	−	0.519002i	0.170227	−	0.985405i	$-0.445550\pi$
$761$	−19.7061	−	14.3173i	−0.714345	−	0.519002i	−0.884573	+	0.466403i	$0.845550\pi$
$762$	−0.335321	+	1.03201i	−0.0121474	+	0.0373858i
$763$	−5.10898	−	15.7238i	−0.184958	−	0.569241i
$764$	−34.0169	+	24.7147i	−1.23069	+	0.894148i
$765$	0.945121	+	2.90878i	0.0341709	+	0.105167i
$766$	−11.3096	−	8.21691i	−0.408633	−	0.296889i
$767$	−0.419316	−	0.304651i	−0.0151406	−	0.0110003i
$768$	2.27074	−	1.64979i	0.0819382	−	0.0595316i
$769$	2.17742			0.0785196			0.0392598	−	0.999229i	$-0.487500\pi$
$769$	2.17742			0.0785196			0.0392598	+	0.999229i	$0.487500\pi$
$770$	−29.6040			−1.06685
$771$	−2.78057	+	2.02020i	−0.100140	+	0.0727558i
$772$	12.8524	−	39.5557i	0.462569	−	1.42364i
$773$	−9.98701	−	30.7369i	−0.359208	−	1.10553i	−0.953529	−	0.301300i	$-0.902579\pi$
$773$	−9.98701	−	30.7369i	−0.359208	−	1.10553i	0.594321	−	0.804228i	$-0.297421\pi$
$774$	−57.3296			−2.06067
$775$	4.61373	−	20.2405i	0.165730	−	0.727060i
$776$	33.4945			1.20238
$777$	−3.97155	−	12.2232i	−0.142479	−	0.438504i
$778$	−25.4153	+	78.2203i	−0.911183	+	2.80433i
$779$	32.6447	−	23.7177i	1.16962	−	0.849776i
$780$	1.22033			0.0436948
$781$	−4.59982			−0.164594
$782$	−2.67915	+	1.94652i	−0.0958062	+	0.0696073i
$783$	−7.30584	−	5.30800i	−0.261089	−	0.189693i
$784$	15.7003	+	11.4069i	0.560725	+	0.407390i
$785$	5.92262	+	18.2279i	0.211387	+	0.650583i
$786$	−3.96932	+	2.88388i	−0.141581	+	0.102865i
$787$	2.14526	+	6.60244i	0.0764703	+	0.235351i	0.981983	−	0.188967i	$-0.0605138\pi$
$787$	2.14526	+	6.60244i	0.0764703	+	0.235351i	−0.905513	+	0.424318i	$0.860514\pi$
$788$	−20.2483	+	62.3178i	−0.721315	+	2.21998i
$789$	3.26669	+	2.37339i	0.116297	+	0.0844949i
$790$	−11.8646	+	36.5155i	−0.422124	+	1.29916i
$791$	−22.4571	+	69.1158i	−0.798482	+	2.45747i
$792$	−11.2480	−	8.17213i	−0.399679	−	0.290384i
$793$	−0.851803	+	2.62158i	−0.0302484	+	0.0930951i
$794$	8.72258	+	26.8453i	0.309553	+	0.952705i
$795$	−2.76385	+	2.00805i	−0.0980236	+	0.0712183i
$796$	−8.37996	−	25.7909i	−0.297020	−	0.914133i
$797$	5.69147	+	4.13510i	0.201602	+	0.146473i	0.684006	−	0.729476i	$-0.260236\pi$
$797$	5.69147	+	4.13510i	0.201602	+	0.146473i	−0.482404	+	0.875949i	$0.660236\pi$
$798$	15.9412	+	11.5820i	0.564313	+	0.409998i
$799$	0.379879	−	0.275999i	0.0134392	−	0.00976413i
$800$	26.6375			0.941779
$801$	24.5612			0.867827
$802$	37.1685	−	27.0045i	1.31246	−	0.953561i
$803$	0.395053	−	1.21585i	0.0139411	−	0.0429063i
$804$	−1.51367	−	4.65860i	−0.0533830	−	0.164296i
$805$	7.57231			0.266889
$806$	1.91822	−	8.41527i	0.0675666	−	0.296415i
$807$	6.68084			0.235177
$808$	11.8395	+	36.4382i	0.416511	+	1.28189i
$809$	1.15414	−	3.55209i	0.0405775	−	0.124885i	−0.928716	−	0.370793i	$-0.879086\pi$
$809$	1.15414	−	3.55209i	0.0405775	−	0.124885i	0.969293	+	0.245908i	$0.0790861\pi$
$810$	13.0795	−	9.50282i	0.459567	−	0.333895i
$811$	−36.0075			−1.26440			−0.632198	−	0.774807i	$-0.717847\pi$
$811$	−36.0075			−1.26440			−0.632198	+	0.774807i	$0.717847\pi$
$812$	37.9304			1.33110
$813$	4.12442	−	2.99656i	0.144650	−	0.105094i
$814$	25.3967	+	18.4518i	0.890154	+	0.646735i
$815$	−0.515311	−	0.374395i	−0.0180506	−	0.0131145i
$816$	−0.246566	−	0.758851i	−0.00863152	−	0.0265651i
$817$	−28.7926	+	20.9190i	−1.00733	+	0.731865i
$818$	24.6890	+	75.9851i	0.863232	+	2.65676i
$819$	−2.63489	+	8.10937i	−0.0920706	+	0.283364i
$820$	−28.4587	−	20.6764i	−0.993821	−	0.722053i
$821$	−6.87327	+	21.1537i	−0.239879	+	0.738271i	0.756558	+	0.653927i	$0.226880\pi$
$821$	−6.87327	+	21.1537i	−0.239879	+	0.738271i	−0.996437	+	0.0843442i	$0.973120\pi$
$822$	1.25056	−	3.84882i	0.0436182	−	0.134243i
$823$	4.23829	+	3.07929i	0.147737	+	0.107337i	0.659199	−	0.751969i	$-0.270896\pi$
$823$	4.23829	+	3.07929i	0.147737	+	0.107337i	−0.511461	+	0.859306i	$0.670896\pi$
$824$	2.59834	−	7.99686i	0.0905174	−	0.278584i
$825$	1.64127	+	5.05130i	0.0571416	+	0.175864i
$826$	−5.90243	+	4.28837i	−0.205372	+	0.149211i
$827$	−4.56299	−	14.0434i	−0.158671	−	0.488339i	0.839844	−	0.542829i	$-0.182647\pi$
$827$	−4.56299	−	14.0434i	−0.158671	−	0.488339i	−0.998514	+	0.0544901i	$0.982647\pi$
$828$	9.46027	+	6.87329i	0.328767	+	0.238863i
$829$	12.8849	+	9.36143i	0.447511	+	0.325136i	0.788612	−	0.614891i	$-0.210800\pi$
$829$	12.8849	+	9.36143i	0.447511	+	0.325136i	−0.341101	+	0.940027i	$0.610800\pi$
$830$	−28.3685	+	20.6109i	−0.984686	+	0.715416i
$831$	10.6216			0.368458
$832$	8.98548			0.311516
$833$	−10.5523	+	7.66667i	−0.365615	+	0.265635i
$834$	4.46551	−	13.7434i	0.154628	−	0.475896i
$835$	6.98324	+	21.4922i	0.241665	+	0.743768i
$836$	−28.3799			−0.981541
$837$	6.70805	+	15.6820i	0.231864	+	0.542048i
$838$	2.22634			0.0769077
$839$	1.60689	+	4.94551i	0.0554761	+	0.170738i	0.974955	−	0.222401i	$-0.0713893\pi$
$839$	1.60689	+	4.94551i	0.0554761	+	0.170738i	−0.919479	+	0.393138i	$0.871389\pi$
$840$	1.61435	−	4.96846i	0.0557004	−	0.171428i
$841$	16.4313	−	11.9380i	0.566596	−	0.411656i
$842$	55.0761			1.89805
$843$	13.3720			0.460556
$844$	−18.2370	+	13.2500i	−0.627745	+	0.456083i
$845$	−11.4093	−	8.28935i	−0.392492	−	0.285162i
$846$	−2.27482	−	1.65275i	−0.0782099	−	0.0568228i
$847$	5.45684	+	16.7944i	0.187499	+	0.577063i
$848$	−6.80045	+	4.94082i	−0.233528	+	0.169668i
$849$	3.33641	+	10.2684i	0.114505	+	0.352411i
$850$	−2.54371	+	7.82874i	−0.0872486	+	0.268524i
$851$	−6.49615	−	4.71973i	−0.222685	−	0.161790i
$852$	0.824783	−	2.53842i	0.0282566	−	0.0869649i
$853$	−10.5075	+	32.3387i	−0.359769	+	1.10725i	0.593424	+	0.804890i	$0.297776\pi$
$853$	−10.5075	+	32.3387i	−0.359769	+	1.10725i	−0.953192	+	0.302364i	$0.902224\pi$
$854$	31.3910	+	22.8069i	1.07418	+	0.780435i
$855$	3.51344	−	10.8133i	0.120157	−	0.369806i
$856$	1.94618	+	5.98972i	0.0665190	+	0.204724i
$857$	18.3473	−	13.3301i	0.626731	−	0.455347i	−0.228535	−	0.973536i	$-0.573394\pi$
$857$	18.3473	−	13.3301i	0.626731	−	0.455347i	0.855266	+	0.518189i	$0.173394\pi$
$858$	0.682380	+	2.10015i	0.0232961	+	0.0716979i
$859$	−14.2876	−	10.3806i	−0.487487	−	0.354180i	0.316730	−	0.948516i	$-0.397415\pi$
$859$	−14.2876	−	10.3806i	−0.487487	−	0.354180i	−0.804217	+	0.594336i	$0.797415\pi$
$860$	25.1006	+	18.2366i	0.855922	+	0.621864i
$861$	−21.0834	+	15.3180i	−0.718520	+	0.522035i
$862$	−26.6069			−0.906235
$863$	−29.6671			−1.00988			−0.504941	−	0.863154i	$-0.668486\pi$
$863$	−29.6671			−1.00988			−0.504941	+	0.863154i	$0.668486\pi$
$864$	−17.7060	+	12.8641i	−0.602369	+	0.437647i
$865$	0.152836	−	0.470380i	0.00519657	−	0.0159934i
$866$	−15.5839	−	47.9624i	−0.529564	−	1.62983i
$867$	0.536276			0.0182129
$868$	−61.5108	−	36.7273i	−2.08781	−	1.24661i
$869$	−40.9679			−1.38974
$870$	1.21611	+	3.74279i	0.0412299	+	0.126892i
$871$	0.689583	−	2.12232i	0.0233656	−	0.0719120i
$872$	−5.76524	+	4.18869i	−0.195236	+	0.141847i
$873$	−47.0800			−1.59342
$874$	12.3108			0.416417
$875$	35.6480	−	25.8998i	1.20512	−	0.875572i
$876$	0.600132	+	0.436021i	0.0202766	+	0.0147318i
$877$	−15.7962	−	11.4766i	−0.533399	−	0.387537i	0.288229	−	0.957562i	$-0.406934\pi$
$877$	−15.7962	−	11.4766i	−0.533399	−	0.387537i	−0.821628	+	0.570025i	$0.806934\pi$
$878$	9.92608	+	30.5493i	0.334989	+	1.03099i
$879$	5.18766	−	3.76906i	0.174975	−	0.127127i
$880$	−1.37709	−	4.23826i	−0.0464218	−	0.142872i
$881$	12.4360	−	38.2741i	0.418980	−	1.28949i	−0.489663	−	0.871912i	$-0.662880\pi$
$881$	12.4360	−	38.2741i	0.418980	−	1.28949i	0.908642	−	0.417575i	$-0.137120\pi$
$882$	63.1898	+	45.9101i	2.12771	+	1.54587i
$883$	−16.6277	+	51.1749i	−0.559568	+	1.72217i	0.123998	+	0.992283i	$0.460428\pi$
$883$	−16.6277	+	51.1749i	−0.559568	+	1.72217i	−0.683565	+	0.729889i	$0.739572\pi$
$884$	−0.623621	+	1.91931i	−0.0209746	+	0.0645533i
$885$	−0.361109	−	0.262361i	−0.0121386	−	0.00881917i
$886$	−22.0737	+	67.9359i	−0.741581	+	2.28235i
$887$	−13.8982	−	42.7743i	−0.466656	−	1.43622i	−0.856887	−	0.515504i	$-0.827605\pi$
$887$	−13.8982	−	42.7743i	−0.466656	−	1.43622i	0.390231	−	0.920717i	$-0.372395\pi$
$888$	−4.48171	+	3.25615i	−0.150396	+	0.109269i
$889$	1.26798	+	3.90243i	0.0425265	+	0.130883i
$890$	−18.2368	−	13.2498i	−0.611298	−	0.444134i
$891$	13.9561	+	10.1397i	0.467547	+	0.339693i
$892$	35.4366	−	25.7462i	1.18651	−	0.862047i
$893$	−1.74555			−0.0584127
$894$	−8.33180			−0.278657
$895$	3.70036	−	2.68847i	0.123690	−	0.0898657i
$896$	19.3178	−	59.4542i	0.645363	−	1.98622i
$897$	−0.174544	−	0.537191i	−0.00582786	−	0.0179363i
$898$	−17.9268			−0.598226
$899$	16.3464	−	1.47587i	0.545184	−	0.0492231i
$900$	29.0665			0.968882
$901$	−1.74582	−	5.37310i	−0.0581619	−	0.179004i
$902$	19.6701	−	60.5384i	0.654943	−	2.01571i
$903$	18.5955	−	13.5104i	0.618821	−	0.449600i
$904$	31.3241			1.04182
$905$	−19.7665			−0.657060
$906$	−0.733500	+	0.532919i	−0.0243689	+	0.0177050i
$907$	−48.0693	−	34.9244i	−1.59612	−	1.15965i	−0.894477	−	0.447114i	$-0.852452\pi$
$907$	−48.0693	−	34.9244i	−1.59612	−	1.15965i	−0.701639	−	0.712533i	$-0.747548\pi$
$908$	4.96044	+	3.60397i	0.164618	+	0.119602i
$909$	−16.6416	−	51.2176i	−0.551967	−	1.69878i
$910$	6.33110	−	4.59982i	0.209874	−	0.152482i
$911$	−16.9380	−	52.1299i	−0.561182	−	1.72714i	−0.679033	−	0.734108i	$-0.737600\pi$
$911$	−16.9380	−	52.1299i	−0.561182	−	1.72714i	0.117851	−	0.993031i	$-0.462400\pi$
$912$	−0.916595	+	2.82099i	−0.0303515	+	0.0934123i
$913$	−30.2698	−	21.9923i	−1.00178	−	0.727839i
$914$	−14.9531	+	46.0209i	−0.494605	+	1.52224i
$915$	−0.733562	+	2.25767i	−0.0242508	+	0.0746363i
$916$	23.2652	+	16.9032i	0.768704	+	0.558496i
$917$	−5.73313	+	17.6447i	−0.189324	+	0.582681i
$918$	−2.08995	−	6.43220i	−0.0689786	−	0.212294i
$919$	35.0231	−	25.4458i	1.15530	−	0.839378i	0.166128	−	0.986104i	$-0.446874\pi$
$919$	35.0231	−	25.4458i	1.15530	−	0.839378i	0.989177	+	0.146726i	$0.0468736\pi$
$920$	−1.00860	−	3.10415i	−0.0332525	−	0.102341i
$921$	−11.4296	−	8.30412i	−0.376619	−	0.273630i
$922$	62.0493	+	45.0815i	2.04349	+	1.48468i
$923$	0.983717	−	0.714712i	0.0323794	−	0.0235250i
$924$	18.3290			0.602981
$925$	−19.9593			−0.656257
$926$	−55.0792	+	40.0174i	−1.81002	+	1.31505i
$927$	−3.65223	+	11.2404i	−0.119955	+	0.369184i
$928$	6.50791	+	20.0293i	0.213633	+	0.657494i
$929$	−28.6287			−0.939278			−0.469639	−	0.882858i	$-0.655616\pi$
$929$	−28.6287			−0.939278			−0.469639	+	0.882858i	$0.655616\pi$
$930$	1.65195	−	7.24712i	0.0541696	−	0.237643i
$931$	48.4879			1.58913
$932$	−16.7042	−	51.4101i	−0.547163	−	1.68399i
$933$	−3.79418	+	11.6773i	−0.124216	+	0.382297i
$934$	−6.26279	+	4.55019i	−0.204925	+	0.148887i
$935$	2.99515			0.0979520
$936$	3.67526			0.120130
$937$	36.1019	−	26.2295i	1.17940	−	0.856882i	0.187293	−	0.982304i	$-0.440029\pi$
$937$	36.1019	−	26.2295i	1.17940	−	0.856882i	0.992103	+	0.125423i	$0.0400286\pi$
$938$	−25.4128	−	18.4634i	−0.829756	−	0.602853i
$939$	−12.6269	−	9.17398i	−0.412063	−	0.299382i
$940$	0.470239	+	1.44725i	0.0153375	+	0.0472039i
$941$	24.4641	−	17.7742i	0.797506	−	0.579422i	−0.112675	−	0.993632i	$-0.535942\pi$
$941$	24.4641	−	17.7742i	0.797506	−	0.579422i	0.910182	+	0.414210i	$0.135942\pi$
$942$	−6.21867	−	19.1391i	−0.202615	−	0.623586i
$943$	−5.03136	+	15.4849i	−0.163844	+	0.504259i
$944$	−0.888509	−	0.645540i	−0.0289185	−	0.0210105i
$945$	−4.77887	+	14.7078i	−0.155457	+	0.478446i
$946$	−17.3490	+	53.3948i	−0.564066	+	1.73602i
$947$	−26.5438	−	19.2852i	−0.862558	−	0.626685i	0.0660215	−	0.997818i	$-0.478969\pi$
$947$	−26.5438	−	19.2852i	−0.862558	−	0.626685i	−0.928580	+	0.371133i	$0.878969\pi$
$948$	7.34587	−	22.6083i	0.238583	−	0.734282i
$949$	0.104430	+	0.321404i	0.00338995	+	0.0104332i
$950$	24.7564	−	17.9866i	0.803205	−	0.583563i
$951$	0.614786	+	1.89212i	0.0199358	+	0.0613561i
$952$	6.98932	+	5.07804i	0.226525	+	0.164580i
$953$	−30.8113	−	22.3857i	−0.998075	−	0.725144i	−0.0364007	−	0.999337i	$-0.511589\pi$
$953$	−30.8113	−	22.3857i	−0.998075	−	0.725144i	−0.961675	+	0.274193i	$0.911589\pi$
$954$	−27.3701	+	19.8856i	−0.886141	+	0.643819i
$955$	−16.4964			−0.533812
$956$	−11.9569			−0.386715
$957$	−3.39719	+	2.46820i	−0.109816	+	0.0797857i
$958$	16.0612	−	49.4314i	0.518915	−	1.59706i
$959$	−4.72883	−	14.5539i	−0.152702	−	0.469969i
$960$	7.73818			0.249749
$961$	−27.9376	−	13.4346i	−0.901214	−	0.433373i
$962$	−8.29835			−0.267550
$963$	−2.73555	−	8.41917i	−0.0881520	−	0.271304i
$964$	17.3643	−	53.4418i	0.559267	−	1.72125i
$965$	13.2012	−	9.59123i	0.424962	−	0.308753i
$966$	−7.95083			−0.255814
$967$	5.95295			0.191434			0.0957170	−	0.995409i	$-0.469486\pi$
$967$	5.95295			0.191434			0.0957170	+	0.995409i	$0.469486\pi$
$968$	6.15778	−	4.47389i	0.197918	−	0.143796i
$969$	−1.61284	−	1.17180i	−0.0518118	−	0.0376435i
$970$	34.9571	+	25.3978i	1.12240	+	0.815474i
$971$	13.2910	+	40.9055i	0.426529	+	1.31272i	0.901523	+	0.432731i	$0.142450\pi$
$971$	13.2910	+	40.9055i	0.426529	+	1.31272i	−0.474994	+	0.879989i	$0.657550\pi$
$972$	−29.4670	+	21.4091i	−0.945156	+	0.686696i
$973$	−16.8858	−	51.9692i	−0.541334	−	1.66606i
$974$	3.58909	−	11.0461i	0.115002	−	0.353939i
$975$	−1.13586	−	0.825254i	−0.0363768	−	0.0264293i
$976$	−1.80493	+	5.55500i	−0.0577744	+	0.177811i
$977$	7.34746	−	22.6132i	0.235066	−	0.723459i	−0.762046	−	0.647522i	$-0.775805\pi$
$977$	7.34746	−	22.6132i	0.235066	−	0.723459i	0.997113	−	0.0759369i	$-0.0241948\pi$
$978$	0.541070	+	0.393110i	0.0173015	+	0.0125703i
$979$	7.43268	−	22.8755i	0.237550	−	0.731103i
$980$	−13.0623	−	40.2015i	−0.417259	−	1.28419i
$981$	8.10363	−	5.88764i	0.258729	−	0.187978i
$982$	9.68270	+	29.8003i	0.308987	+	0.950966i
$983$	3.12940	+	2.27364i	0.0998123	+	0.0725179i	0.636572	−	0.771217i	$-0.280352\pi$
$983$	3.12940	+	2.27364i	0.0998123	+	0.0725179i	−0.536760	+	0.843735i	$0.680352\pi$
$984$	9.08757	+	6.60251i	0.289701	+	0.210480i
$985$	−20.7977	+	15.1104i	−0.662671	+	0.481458i
$986$	−6.50805			−0.207259
$987$	1.12736			0.0358842
$988$	6.06933	−	4.40963i	0.193091	−	0.140289i
$989$	4.43766	−	13.6577i	0.141109	−	0.434290i
$990$	−5.54246	−	17.0579i	−0.176151	−	0.542137i
$991$	60.9400			1.93582			0.967912	−	0.251289i	$-0.0808545\pi$
$991$	60.9400			1.93582			0.967912	+	0.251289i	$0.0808545\pi$
$992$	8.84030	−	38.7825i	0.280680	−	1.23135i
$993$	−15.0018			−0.476068
$994$	−5.28914	−	16.2783i	−0.167761	−	0.516316i
$995$	3.28772	−	10.1186i	0.104228	−	0.320780i
$996$	17.5641	−	12.7611i	0.556541	−	0.404350i
$997$	15.1273			0.479086			0.239543	−	0.970886i	$-0.423002\pi$
$997$	15.1273			0.479086			0.239543	+	0.970886i	$0.423002\pi$
$998$	−87.5620			−2.77173
$999$	13.2669	−	9.63898i	0.419747	−	0.304964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.35.20	✓	96
31.8	even	5	inner	527.2.h.c.256.20	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.20	✓	96	1.1	even	1	trivial
527.2.h.c.256.20	yes	96	31.8	even	5	inner

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:	\( N \)	\(=\)	\( 527 = 17 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	527.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.682226 + 2.09968i) q^{2} +(0.165718 - 0.510029i) q^{3} +(-2.32517 + 1.68934i) q^{4} -1.12759 q^{5} +1.18395 q^{6} +(3.62195 - 2.63150i) q^{7} +(-1.56117 - 1.13426i) q^{8} +(2.19438 + 1.59431i) q^{9} +O(q^{10})\)	\(q+(0.682226 + 2.09968i) q^{2} +(0.165718 - 0.510029i) q^{3} +(-2.32517 + 1.68934i) q^{4} -1.12759 q^{5} +1.18395 q^{6} +(3.62195 - 2.63150i) q^{7} +(-1.56117 - 1.13426i) q^{8} +(2.19438 + 1.59431i) q^{9} +(-0.769269 - 2.36757i) q^{10} +(2.14895 - 1.56130i) q^{11} +(0.476286 + 1.46586i) q^{12} +(-0.216982 + 0.667801i) q^{13} +(7.99629 + 5.80964i) q^{14} +(-0.186862 + 0.575102i) q^{15} +(-0.459774 + 1.41504i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.85048 + 5.69518i) q^{18} +(1.14876 + 3.53550i) q^{19} +(2.62183 - 1.90487i) q^{20} +(-0.741917 - 2.28339i) q^{21} +(4.74430 + 3.44694i) q^{22} +(-1.21353 - 0.881683i) q^{23} +(-0.837218 + 0.608274i) q^{24} -3.72855 q^{25} -1.55020 q^{26} +(2.47836 - 1.80064i) q^{27} +(-3.97617 + 12.2374i) q^{28} +(-0.910935 - 2.80357i) q^{29} -1.33501 q^{30} +(-1.23741 + 5.42852i) q^{31} -7.14421 q^{32} +(-0.440189 - 1.35476i) q^{33} +(0.682226 - 2.09968i) q^{34} +(-4.08407 + 2.96725i) q^{35} -7.79565 q^{36} +5.35310 q^{37} +(-6.63970 + 4.82403i) q^{38} +(0.304640 + 0.221334i) q^{39} +(1.76036 + 1.27897i) q^{40} +(-3.35422 - 10.3232i) q^{41} +(4.28822 - 3.11557i) q^{42} +(2.95842 + 9.10509i) q^{43} +(-2.35911 + 7.26060i) q^{44} +(-2.47436 - 1.79773i) q^{45} +(1.02334 - 3.14953i) q^{46} +(-0.145101 + 0.446575i) q^{47} +(0.645517 + 0.468996i) q^{48} +(4.03061 - 12.4049i) q^{49} +(-2.54371 - 7.82874i) q^{50} +(-0.433856 + 0.315215i) q^{51} +(-0.623621 - 1.91931i) q^{52} +(4.57063 + 3.32076i) q^{53} +(5.47156 + 3.97532i) q^{54} +(-2.42313 + 1.76051i) q^{55} -8.63928 q^{56} +1.99358 q^{57} +(5.26512 - 3.82534i) q^{58} +(-0.228100 + 0.702019i) q^{59} +(-0.537054 - 1.65288i) q^{60} +3.92569 q^{61} +(-12.2423 + 1.10532i) q^{62} +12.1434 q^{63} +(-3.95442 - 12.1705i) q^{64} +(0.244666 - 0.753004i) q^{65} +(2.54426 - 1.84851i) q^{66} -3.17807 q^{67} +2.87407 q^{68} +(-0.650788 + 0.472825i) q^{69} +(-9.01651 - 6.55088i) q^{70} +(-1.40097 - 1.01787i) q^{71} +(-1.61745 - 4.97799i) q^{72} +(0.389369 - 0.282893i) q^{73} +(3.65202 + 11.2398i) q^{74} +(-0.617889 + 1.90167i) q^{75} +(-8.64371 - 6.28002i) q^{76} +(3.67482 - 11.3099i) q^{77} +(-0.256896 + 0.790645i) q^{78} +(-12.4776 - 9.06554i) q^{79} +(0.518435 - 1.59558i) q^{80} +(2.00687 + 6.17653i) q^{81} +(19.3871 - 14.0856i) q^{82} +(-4.35277 - 13.3964i) q^{83} +(5.58249 + 4.05592i) q^{84} +(0.912237 + 0.662779i) q^{85} +(-17.0994 + 12.4235i) q^{86} -1.58086 q^{87} -5.12580 q^{88} +(7.32575 - 5.32247i) q^{89} +(2.08657 - 6.42181i) q^{90} +(0.971422 + 2.98973i) q^{91} +4.31113 q^{92} +(2.56364 + 1.53072i) q^{93} -1.03665 q^{94} +(-1.29532 - 3.98659i) q^{95} +(-1.18393 + 3.64375i) q^{96} +(-14.0423 + 10.2023i) q^{97} +28.7961 q^{98} +7.20483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

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