LMFDB - Embedded newform 80.3.i.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(13,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("80.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.462923 + 1.94569i) q^{2} +4.38426i q^{3} +(-3.57140 - 1.80141i) q^{4} +(-4.75384 - 1.54952i) q^{5} +(-8.53040 - 2.02957i) q^{6} +(3.84157 + 3.84157i) q^{7} +(5.15826 - 6.11493i) q^{8} -10.2217 q^{9} +O(q^{10})$	\(q+(-0.462923 + 1.94569i) q^{2} +4.38426i q^{3} +(-3.57140 - 1.80141i) q^{4} +(-4.75384 - 1.54952i) q^{5} +(-8.53040 - 2.02957i) q^{6} +(3.84157 + 3.84157i) q^{7} +(5.15826 - 6.11493i) q^{8} -10.2217 q^{9} +(5.21554 - 8.53218i) q^{10} +(1.14088 - 1.14088i) q^{11} +(7.89784 - 15.6580i) q^{12} +9.68938i q^{13} +(-9.25284 + 5.69614i) q^{14} +(6.79348 - 20.8421i) q^{15} +(9.50986 + 12.8671i) q^{16} +(-12.6460 + 12.6460i) q^{17} +(4.73186 - 19.8883i) q^{18} +(-24.3373 + 24.3373i) q^{19} +(14.1866 + 14.0976i) q^{20} +(-16.8424 + 16.8424i) q^{21} +(1.69166 + 2.74794i) q^{22} +(24.0032 - 24.0032i) q^{23} +(26.8094 + 22.6152i) q^{24} +(20.1980 + 14.7323i) q^{25} +(-18.8525 - 4.48544i) q^{26} -5.35627i q^{27} +(-6.79956 - 20.6400i) q^{28} +(21.4101 - 21.4101i) q^{29} +(37.4073 + 22.8663i) q^{30} +42.4278 q^{31} +(-29.4377 + 12.5467i) q^{32} +(5.00192 + 5.00192i) q^{33} +(-18.7511 - 30.4593i) q^{34} +(-12.3096 - 24.2148i) q^{35} +(36.5058 + 18.4135i) q^{36} +37.4340i q^{37} +(-36.0865 - 58.6191i) q^{38} -42.4807 q^{39} +(-33.9967 + 21.0766i) q^{40} +2.23637i q^{41} +(-24.9733 - 40.5668i) q^{42} +37.4392 q^{43} +(-6.12974 + 2.01936i) q^{44} +(48.5924 + 15.8387i) q^{45} +(35.5911 + 57.8143i) q^{46} +(17.4520 - 17.4520i) q^{47} +(-56.4127 + 41.6937i) q^{48} -19.4847i q^{49} +(-38.0146 + 32.4791i) q^{50} +(-55.4434 - 55.4434i) q^{51} +(17.4545 - 34.6047i) q^{52} -32.3677 q^{53} +(10.4216 + 2.47954i) q^{54} +(-7.19138 + 3.65575i) q^{55} +(43.3067 - 3.67508i) q^{56} +(-106.701 - 106.701i) q^{57} +(31.7462 + 51.5687i) q^{58} +(21.2720 + 21.2720i) q^{59} +(-61.8073 + 62.1976i) q^{60} +(-52.5704 - 52.5704i) q^{61} +(-19.6408 + 82.5512i) q^{62} +(-39.2674 - 39.2674i) q^{63} +(-10.7846 - 63.0848i) q^{64} +(15.0139 - 46.0618i) q^{65} +(-12.0477 + 7.41667i) q^{66} +82.6126 q^{67} +(67.9446 - 22.3834i) q^{68} +(105.236 + 105.236i) q^{69} +(52.8128 - 12.7411i) q^{70} -14.2246i q^{71} +(-52.7263 + 62.5050i) q^{72} +(10.2704 - 10.2704i) q^{73} +(-72.8348 - 17.3291i) q^{74} +(-64.5903 + 88.5532i) q^{75} +(130.760 - 43.0769i) q^{76} +8.76554 q^{77} +(19.6653 - 82.6542i) q^{78} +55.6719i q^{79} +(-25.2705 - 75.9039i) q^{80} -68.5121 q^{81} +(-4.35129 - 1.03527i) q^{82} +38.4377i q^{83} +(90.4911 - 29.8110i) q^{84} +(79.7123 - 40.5219i) q^{85} +(-17.3315 + 72.8450i) q^{86} +(93.8675 + 93.8675i) q^{87} +(-1.09144 - 12.8614i) q^{88} -138.133 q^{89} +(-53.3117 + 87.2135i) q^{90} +(-37.2224 + 37.2224i) q^{91} +(-128.965 + 42.4855i) q^{92} +186.014i q^{93} +(25.8772 + 42.0351i) q^{94} +(153.407 - 77.9845i) q^{95} +(-55.0081 - 129.063i) q^{96} +(113.344 - 113.344i) q^{97} +(37.9112 + 9.01994i) q^{98} +(-11.6618 + 11.6618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.462923	+	1.94569i	−0.231462	+	0.972844i
$2$	−0.462923	+	1.94569i	−0.231462	+	0.972844i
$3$			4.38426i			1.46142i	0.682689	+	0.730709i	$0.260811\pi$
$3$			4.38426i			1.46142i	−0.682689	+	0.730709i	$0.739189\pi$
$4$	−3.57140	−	1.80141i	−0.892851	−	0.450352i
$5$	−4.75384	−	1.54952i	−0.950768	−	0.309904i
$5$	−4.75384	−	1.54952i	−0.950768	−	0.309904i
$6$	−8.53040	−	2.02957i	−1.42173	−	0.338262i
$7$	3.84157	+	3.84157i	0.548795	+	0.548795i	0.926092	−	0.377297i	$-0.123146\pi$
$7$	3.84157	+	3.84157i	0.548795	+	0.548795i	−0.377297	+	0.926092i	$0.623146\pi$
$8$	5.15826	−	6.11493i	0.644783	−	0.764366i
$9$	−10.2217			−1.13575
$10$	5.21554	−	8.53218i	0.521554	−	0.853218i
$11$	1.14088	−	1.14088i	0.103716	−	0.103716i	−0.653344	−	0.757061i	$-0.726635\pi$
$11$	1.14088	−	1.14088i	0.103716	−	0.103716i	0.757061	+	0.653344i	$0.226635\pi$
$12$	7.89784	−	15.6580i	0.658153	−	1.30483i
$13$			9.68938i			0.745337i	0.927965	+	0.372668i	$0.121557\pi$
$13$			9.68938i			0.745337i	−0.927965	+	0.372668i	$0.878443\pi$
$14$	−9.25284	+	5.69614i	−0.660917	+	0.406867i
$15$	6.79348	−	20.8421i	0.452899	−	1.38947i
$16$	9.50986	+	12.8671i	0.594366	+	0.804195i
$17$	−12.6460	+	12.6460i	−0.743883	+	0.743883i	−0.973323	−	0.229440i	$-0.926311\pi$
$17$	−12.6460	+	12.6460i	−0.743883	+	0.743883i	0.229440	+	0.973323i	$0.426311\pi$
$18$	4.73186	−	19.8883i	0.262881	−	1.10490i
$19$	−24.3373	+	24.3373i	−1.28091	+	1.28091i	−0.340760	+	0.940150i	$0.610684\pi$
$19$	−24.3373	+	24.3373i	−1.28091	+	1.28091i	−0.940150	+	0.340760i	$0.889316\pi$
$20$	14.1866	+	14.0976i	0.709329	+	0.704878i
$21$	−16.8424	+	16.8424i	−0.802020	+	0.802020i
$22$	1.69166	+	2.74794i	0.0768936	+	0.124906i
$23$	24.0032	−	24.0032i	1.04362	−	1.04362i	0.0446119	−	0.999004i	$-0.485795\pi$
$23$	24.0032	−	24.0032i	1.04362	−	1.04362i	0.999004	−	0.0446119i	$-0.0142051\pi$
$24$	26.8094	+	22.6152i	1.11706	+	0.942298i
$25$	20.1980	+	14.7323i	0.807920	+	0.589293i
$26$	−18.8525	−	4.48544i	−0.725097	−	0.172517i
$27$		−	5.35627i		−	0.198381i
$28$	−6.79956	−	20.6400i	−0.242841	−	0.737143i
$29$	21.4101	−	21.4101i	0.738280	−	0.738280i	−0.233965	−	0.972245i	$-0.575170\pi$
$29$	21.4101	−	21.4101i	0.738280	−	0.738280i	0.972245	+	0.233965i	$0.0751701\pi$
$30$	37.4073	+	22.8663i	1.24691	+	0.762209i
$31$	42.4278			1.36864			0.684319	−	0.729183i	$-0.260100\pi$
$31$	42.4278			1.36864			0.684319	+	0.729183i	$0.260100\pi$
$32$	−29.4377	+	12.5467i	−0.919929	+	0.392085i
$33$	5.00192	+	5.00192i	0.151573	+	0.151573i
$34$	−18.7511	−	30.4593i	−0.551502	−	0.895863i
$35$	−12.3096	−	24.2148i	−0.351703	−	0.691850i
$36$	36.5058	+	18.4135i	1.01405	+	0.511485i
$37$			37.4340i			1.01173i	0.862613	+	0.505865i	$0.168826\pi$
$37$			37.4340i			1.01173i	−0.862613	+	0.505865i	$0.831174\pi$
$38$	−36.0865	−	58.6191i	−0.949644	−	1.54261i
$39$	−42.4807			−1.08925
$40$	−33.9967	+	21.0766i	−0.849919	+	0.526914i
$41$			2.23637i			0.0545457i	0.999628	+	0.0272728i	$0.00868229\pi$
$41$			2.23637i			0.0545457i	−0.999628	+	0.0272728i	$0.991318\pi$
$42$	−24.9733	−	40.5668i	−0.594603	−	0.965877i
$43$	37.4392			0.870679			0.435339	−	0.900266i	$-0.356628\pi$
$43$	37.4392			0.870679			0.435339	+	0.900266i	$0.356628\pi$
$44$	−6.12974	+	2.01936i	−0.139312	+	0.0458944i
$45$	48.5924	+	15.8387i	1.07983	+	0.351971i
$46$	35.5911	+	57.8143i	0.773719	+	1.25683i
$47$	17.4520	−	17.4520i	0.371319	−	0.371319i	−0.496638	−	0.867958i	$-0.665432\pi$
$47$	17.4520	−	17.4520i	0.371319	−	0.371319i	0.867958	+	0.496638i	$0.165432\pi$
$48$	−56.4127	+	41.6937i	−1.17527	+	0.868618i
$49$		−	19.4847i		−	0.397648i
$50$	−38.0146	+	32.4791i	−0.760292	+	0.649581i
$51$	−55.4434	−	55.4434i	−1.08712	−	1.08712i
$52$	17.4545	−	34.6047i	0.335664	−	0.665475i
$53$	−32.3677			−0.610712			−0.305356	−	0.952238i	$-0.598775\pi$
$53$	−32.3677			−0.610712			−0.305356	+	0.952238i	$0.598775\pi$
$54$	10.4216	+	2.47954i	0.192993	+	0.0459175i
$55$	−7.19138	+	3.65575i	−0.130752	+	0.0664682i
$56$	43.3067	−	3.67508i	0.773334	−	0.0656264i
$57$	−106.701	−	106.701i	−1.87195	−	1.87195i
$58$	31.7462	+	51.5687i	0.547348	+	0.889115i
$59$	21.2720	+	21.2720i	0.360543	+	0.360543i	0.864013	−	0.503470i	$-0.167944\pi$
$59$	21.2720	+	21.2720i	0.360543	+	0.360543i	−0.503470	+	0.864013i	$0.667944\pi$
$60$	−61.8073	+	62.1976i	−1.03012	+	1.03663i
$61$	−52.5704	−	52.5704i	−0.861809	−	0.861809i	0.129739	−	0.991548i	$-0.458586\pi$
$61$	−52.5704	−	52.5704i	−0.861809	−	0.861809i	−0.991548	+	0.129739i	$0.958586\pi$
$62$	−19.6408	+	82.5512i	−0.316787	+	1.33147i
$63$	−39.2674	−	39.2674i	−0.623291	−	0.623291i
$64$	−10.7846	−	63.0848i	−0.168510	−	0.985700i
$65$	15.0139	−	46.0618i	0.230983	−	0.708642i
$66$	−12.0477	+	7.41667i	−0.182540	+	0.112374i
$67$	82.6126			1.23302			0.616512	−	0.787346i	$-0.288545\pi$
$67$	82.6126			1.23302			0.616512	+	0.787346i	$0.288545\pi$
$68$	67.9446	−	22.3834i	0.999186	−	0.329168i
$69$	105.236	+	105.236i	1.52516	+	1.52516i
$70$	52.8128	−	12.7411i	0.754468	−	0.182016i
$71$		−	14.2246i		−	0.200347i	−0.994970	−	0.100174i	$-0.968060\pi$
$71$		−	14.2246i		−	0.200347i	0.994970	−	0.100174i	$-0.0319398\pi$
$72$	−52.7263	+	62.5050i	−0.732309	+	0.868125i
$73$	10.2704	−	10.2704i	0.140690	−	0.140690i	−0.633254	−	0.773944i	$-0.718281\pi$
$73$	10.2704	−	10.2704i	0.140690	−	0.140690i	0.773944	+	0.633254i	$0.218281\pi$
$74$	−72.8348	−	17.3291i	−0.984255	−	0.234176i
$75$	−64.5903	+	88.5532i	−0.861204	+	1.18071i
$76$	130.760	−	43.0769i	1.72052	−	0.566802i
$77$	8.76554			0.113838
$78$	19.6653	−	82.6542i	0.252119	−	1.05967i
$79$			55.6719i			0.704707i	0.935867	+	0.352354i	$0.114619\pi$
$79$			55.6719i			0.704707i	−0.935867	+	0.352354i	$0.885381\pi$
$80$	−25.2705	−	75.9039i	−0.315882	−	0.948799i
$81$	−68.5121			−0.845828
$82$	−4.35129	−	1.03527i	−0.0530645	−	0.0126252i
$83$			38.4377i			0.463105i	0.972822	+	0.231553i	$0.0743805\pi$
$83$			38.4377i			0.463105i	−0.972822	+	0.231553i	$0.925619\pi$
$84$	90.4911	−	29.8110i	1.07728	−	0.354893i
$85$	79.7123	−	40.5219i	0.937792	−	0.476728i
$86$	−17.3315	+	72.8450i	−0.201529	+	0.847035i
$87$	93.8675	+	93.8675i	1.07894	+	1.07894i
$88$	−1.09144	−	12.8614i	−0.0124027	−	0.146152i
$89$	−138.133			−1.55206			−0.776030	−	0.630696i	$-0.782769\pi$
$89$	−138.133			−1.55206			−0.776030	+	0.630696i	$0.782769\pi$
$90$	−53.3117	+	87.2135i	−0.592353	+	0.969038i
$91$	−37.2224	+	37.2224i	−0.409037	+	0.409037i
$92$	−128.965	+	42.4855i	−1.40179	+	0.461799i
$93$			186.014i			2.00015i
$94$	25.8772	+	42.0351i	0.275290	+	0.447182i
$95$	153.407	−	77.9845i	1.61481	−	0.820890i
$96$	−55.0081	−	129.063i	−0.573001	−	1.34440i
$97$	113.344	−	113.344i	1.16850	−	1.16850i	0.185938	−	0.982562i	$-0.440468\pi$
$97$	113.344	−	113.344i	1.16850	−	1.16850i	0.982562	−	0.185938i	$-0.0595323\pi$
$98$	37.9112	+	9.01994i	0.386849	+	0.0920402i
$99$	−11.6618	+	11.6618i	−0.117795	+	0.117795i
$100$	−45.5963	−	88.9999i	−0.455963	−	0.889999i
$101$	13.3073	−	13.3073i	0.131755	−	0.131755i	−0.638154	−	0.769909i	$-0.720302\pi$
$101$	13.3073	−	13.3073i	0.131755	−	0.131755i	0.769909	+	0.638154i	$0.220302\pi$
$102$	133.542	−	82.2095i	1.30923	−	0.805975i
$103$	−37.4630	+	37.4630i	−0.363718	+	0.363718i	−0.865180	−	0.501462i	$-0.832796\pi$
$103$	−37.4630	+	37.4630i	−0.363718	+	0.363718i	0.501462	+	0.865180i	$0.332796\pi$
$104$	59.2498	+	49.9804i	0.569710	+	0.480581i
$105$	106.164	−	53.9685i	1.01108	−	0.513986i
$106$	14.9838	−	62.9775i	0.141356	−	0.594127i
$107$		−	6.15039i		−	0.0574803i	−0.999587	−	0.0287401i	$-0.990850\pi$
$107$		−	6.15039i		−	0.0574803i	0.999587	−	0.0287401i	$-0.00914953\pi$
$108$	−9.64884	+	19.1294i	−0.0893411	+	0.177124i
$109$	115.185	−	115.185i	1.05674	−	1.05674i	0.0584506	−	0.998290i	$-0.481384\pi$
$109$	115.185	−	115.185i	1.05674	−	1.05674i	0.998290	−	0.0584506i	$-0.0186160\pi$
$110$	−3.78389	−	15.6845i	−0.0343990	−	0.142587i
$111$	−164.120			−1.47856
$112$	−12.8971	+	85.9626i	−0.115153	+	0.767523i
$113$	73.2667	+	73.2667i	0.648378	+	0.648378i	0.952601	−	0.304223i	$-0.0983967\pi$
$113$	73.2667	+	73.2667i	0.648378	+	0.648378i	−0.304223	+	0.952601i	$0.598397\pi$
$114$	257.001	−	158.212i	2.25440	−	1.38783i
$115$	−151.301	+	76.9139i	−1.31566	+	0.668817i
$116$	−115.033	+	37.8958i	−0.991660	+	0.326688i
$117$		−	99.0420i		−	0.846513i
$118$	−51.2361	+	31.5414i	−0.434204	+	0.267300i
$119$	−97.1610			−0.816479
$120$	−92.4050	−	149.050i	−0.770042	−	1.24209i
$121$			118.397i			0.978486i
$122$	126.622	−	77.9495i	1.03788	−	0.638930i
$123$	−9.80484			−0.0797141
$124$	−151.527	−	76.4297i	−1.22199	−	0.616369i
$125$	−73.1900	−	101.332i	−0.585520	−	0.810658i
$126$	94.5798	−	58.2243i	0.750633	−	0.462097i
$127$	−80.3378	+	80.3378i	−0.632581	+	0.632581i	−0.948715	−	0.316133i	$-0.897615\pi$
$127$	−80.3378	+	80.3378i	−0.632581	+	0.632581i	0.316133	+	0.948715i	$0.397615\pi$
$128$	127.736	+	8.21989i	0.997936	+	0.0642179i
$129$			164.143i			1.27243i
$130$	82.6716	+	50.5354i	0.635935	+	0.388734i
$131$	−18.5843	−	18.5843i	−0.141865	−	0.141865i	0.632608	−	0.774472i	$-0.281985\pi$
$131$	−18.5843	−	18.5843i	−0.141865	−	0.141865i	−0.774472	+	0.632608i	$0.781985\pi$
$132$	−8.85337	−	26.8744i	−0.0670710	−	0.203594i
$133$	−186.987			−1.40591
$134$	−38.2433	+	160.738i	−0.285398	+	1.19954i
$135$	−8.29964	+	25.4629i	−0.0614788	+	0.188614i
$136$	12.0980	+	142.561i	0.0889556	+	1.04824i
$137$	83.5138	+	83.5138i	0.609590	+	0.609590i	0.942839	−	0.333249i	$-0.108145\pi$
$137$	83.5138	+	83.5138i	0.609590	+	0.609590i	−0.333249	+	0.942839i	$0.608145\pi$
$138$	−253.473	+	156.040i	−1.83676	+	1.13073i
$139$	−0.886367	−	0.886367i	−0.00637674	−	0.00637674i	0.703911	−	0.710288i	$-0.251435\pi$
$139$	−0.886367	−	0.886367i	−0.00637674	−	0.00637674i	−0.710288	+	0.703911i	$0.751435\pi$
$140$	0.341939	+	108.655i	0.00244242	+	0.776110i
$141$	76.5141	+	76.5141i	0.542653	+	0.542653i
$142$	27.6767	+	6.58492i	0.194907	+	0.0463727i
$143$	11.0544	+	11.0544i	0.0773037	+	0.0773037i
$144$	−97.2070	−	131.524i	−0.675048	−	0.913360i
$145$	−134.956	+	68.6049i	−0.930729	+	0.473137i
$146$	15.2286	+	24.7374i	0.104305	+	0.169434i
$147$	85.4261			0.581130
$148$	67.4339	−	133.692i	0.455634	−	0.903323i
$149$	−126.231	−	126.231i	−0.847186	−	0.847186i	0.142595	−	0.989781i	$-0.454455\pi$
$149$	−126.231	−	126.231i	−0.847186	−	0.847186i	−0.989781	+	0.142595i	$0.954455\pi$
$150$	−142.397	−	166.666i	−0.949310	−	1.11111i
$151$		−	85.8641i		−	0.568636i	−0.958730	−	0.284318i	$-0.908233\pi$
$151$		−	85.8641i		−	0.568636i	0.958730	−	0.284318i	$-0.0917672\pi$
$152$	23.2826	+	274.359i	0.153175	+	1.80499i
$153$	129.264	−	129.264i	0.844862	−	0.844862i
$154$	−4.05777	+	17.0550i	−0.0263492	+	0.110747i
$155$	−201.695	−	65.7426i	−1.30126	−	0.424146i
$156$	151.716	+	76.5251i	0.972538	+	0.490546i
$157$	−222.987			−1.42030			−0.710148	−	0.704052i	$-0.751372\pi$
$157$	−222.987			−1.42030			−0.710148	+	0.704052i	$0.751372\pi$
$158$	−108.320	−	25.7718i	−0.685570	−	0.163113i
$159$		−	141.908i		−	0.892506i
$160$	159.384	−	14.0309i	0.996148	−	0.0876930i
$161$	184.420			1.14546
$162$	31.7158	−	133.303i	0.195777	−	0.822859i
$163$			114.176i			0.700465i	0.936663	+	0.350233i	$0.113897\pi$
$163$			114.176i			0.700465i	−0.936663	+	0.350233i	$0.886103\pi$
$164$	4.02862	−	7.98699i	0.0245648	−	0.0487012i
$165$	−16.0277	−	31.5289i	−0.0971379	−	0.191084i
$166$	−74.7878	−	17.7937i	−0.450529	−	0.107191i
$167$	83.1357	+	83.1357i	0.497818	+	0.497818i	0.910758	−	0.412940i	$-0.135498\pi$
$167$	83.1357	+	83.1357i	0.497818	+	0.497818i	−0.412940	+	0.910758i	$0.635498\pi$
$168$	16.1125	+	189.868i	0.0959077	+	1.13016i
$169$	75.1159			0.444473
$170$	41.9423	+	173.854i	0.246719	+	1.02267i
$171$	248.769	−	248.769i	1.45479	−	1.45479i
$172$	−133.710	−	67.4433i	−0.777387	−	0.392112i
$173$			31.8309i			0.183993i	0.995759	+	0.0919967i	$0.0293249\pi$
$173$			31.8309i			0.183993i	−0.995759	+	0.0919967i	$0.970675\pi$
$174$	−226.090	+	139.183i	−1.29937	+	0.799905i
$175$	20.9967	+	134.187i	0.119981	+	0.766783i
$176$	25.5295	+	3.83023i	0.145054	+	0.0217627i
$177$	−93.2620	+	93.2620i	−0.526904	+	0.526904i
$178$	63.9451	−	268.764i	0.359242	−	1.50991i
$179$	197.541	−	197.541i	1.10358	−	1.10358i	0.109605	−	0.993975i	$-0.465041\pi$
$179$	197.541	−	197.541i	1.10358	−	1.10358i	0.993975	−	0.109605i	$-0.0349586\pi$
$180$	−145.011	−	144.101i	−0.805616	−	0.800562i
$181$	85.6404	−	85.6404i	0.473151	−	0.473151i	−0.429782	−	0.902933i	$-0.641409\pi$
$181$	85.6404	−	85.6404i	0.473151	−	0.473151i	0.902933	+	0.429782i	$0.141409\pi$
$182$	−55.1921	−	89.6543i	−0.303253	−	0.492606i
$183$	230.482	−	230.482i	1.25946	−	1.25946i
$184$	−22.9629	−	270.592i	−0.124798	−	1.47061i
$185$	58.0046	−	177.955i	0.313538	−	0.961920i
$186$	−361.926	−	86.1103i	−1.94584	−	0.462959i
$187$			28.8552i			0.154306i
$188$	−93.7663	+	30.8900i	−0.498757	+	0.164308i
$189$	20.5765	−	20.5765i	0.108870	−	0.108870i
$190$	80.7181	+	334.582i	0.424832	+	1.76096i
$191$	6.70134			0.0350856			0.0175428	−	0.999846i	$-0.494416\pi$
$191$	6.70134			0.0350856			0.0175428	+	0.999846i	$0.494416\pi$
$192$	276.580	−	47.2826i	1.44052	−	0.246263i
$193$	−201.285	−	201.285i	−1.04293	−	1.04293i	−0.999036	−	0.0438900i	$-0.986025\pi$
$193$	−201.285	−	201.285i	−1.04293	−	1.04293i	−0.0438900	−	0.999036i	$-0.513975\pi$
$194$	168.063	+	273.003i	0.866305	+	1.40723i
$195$	201.947	+	65.8247i	1.03562	+	0.337562i
$196$	−35.1000	+	69.5879i	−0.179081	+	0.355040i
$197$		−	54.1842i		−	0.275047i	−0.990499	−	0.137523i	$-0.956086\pi$
$197$		−	54.1842i		−	0.275047i	0.990499	−	0.137523i	$-0.0439142\pi$
$198$	−17.2916	−	28.0886i	−0.0873315	−	0.141862i
$199$	82.2399			0.413266			0.206633	−	0.978419i	$-0.433749\pi$
$199$	82.2399			0.413266			0.206633	+	0.978419i	$0.433749\pi$
$200$	194.274	−	47.5160i	0.971368	−	0.237580i
$201$			362.195i			1.80196i
$202$	19.7316	+	32.0521i	0.0976812	+	0.158674i
$203$	164.497			0.810329
$204$	98.1345	+	297.887i	0.481052	+	1.46023i
$205$	3.46530	−	10.6314i	0.0169039	−	0.0518603i
$206$	−55.5488	−	90.2338i	−0.269654	−	0.438028i
$207$	−245.353	+	245.353i	−1.18528	+	1.18528i
$208$	−124.674	+	92.1446i	−0.599396	+	0.443003i
$209$			55.5319i			0.265703i
$210$	55.8602	+	231.545i	0.266001	+	1.10259i
$211$	−75.9246	−	75.9246i	−0.359832	−	0.359832i	0.503919	−	0.863751i	$-0.331891\pi$
$211$	−75.9246	−	75.9246i	−0.359832	−	0.359832i	−0.863751	+	0.503919i	$0.831891\pi$
$212$	115.598	+	58.3075i	0.545275	+	0.275035i
$213$	62.3645			0.292791
$214$	11.9667	+	2.84716i	0.0559194	+	0.0133045i
$215$	−177.980	−	58.0127i	−0.827814	−	0.269826i
$216$	−32.7532	−	27.6291i	−0.151635	−	0.127912i
$217$	162.989	+	162.989i	0.751102	+	0.751102i
$218$	170.792	+	277.435i	0.783449	+	1.27264i
$219$	45.0280	+	45.0280i	0.205607	+	0.205607i
$220$	32.2688	−	0.101550i	0.146677	−	0.000461591i
$221$	−122.532	−	122.532i	−0.554444	−	0.554444i
$222$	75.9750	−	319.327i	0.342230	−	1.43841i
$223$	103.038	+	103.038i	0.462056	+	0.462056i	0.899329	−	0.437273i	$-0.144056\pi$
$223$	103.038	+	103.038i	0.462056	+	0.462056i	−0.437273	+	0.899329i	$0.644056\pi$
$224$	−161.286	−	64.8879i	−0.720027	−	0.289678i
$225$	−206.458	−	150.589i	−0.917591	−	0.669286i
$226$	−176.471	+	108.637i	−0.780846	+	0.480696i
$227$	98.3454			0.433240			0.216620	−	0.976256i	$-0.430497\pi$
$227$	98.3454			0.433240			0.216620	+	0.976256i	$0.430497\pi$
$228$	188.860	+	573.284i	0.828335	+	2.51440i
$229$	176.947	+	176.947i	0.772695	+	0.772695i	0.978577	−	0.205882i	$-0.0660061\pi$
$229$	176.947	+	176.947i	0.772695	+	0.772695i	−0.205882	+	0.978577i	$0.566006\pi$
$230$	−79.6099	−	329.989i	−0.346130	−	1.43473i
$231$			38.4304i			0.166365i
$232$	−20.4822	−	241.360i	−0.0882855	−	1.04035i
$233$	−177.619	+	177.619i	−0.762312	+	0.762312i	−0.976740	−	0.214427i	$-0.931211\pi$
$233$	−177.619	+	177.619i	−0.762312	+	0.762312i	0.214427	+	0.976740i	$0.431211\pi$
$234$	192.705	+	45.8488i	0.823525	+	0.195935i
$235$	−110.006	+	55.9218i	−0.468112	+	0.237965i
$236$	−37.6514	−	114.291i	−0.159540	−	0.484282i
$237$	−244.080			−1.02987
$238$	44.9781	−	189.045i	0.188983	−	0.794307i
$239$		−	232.519i		−	0.972881i	−0.873714	−	0.486440i	$-0.838295\pi$
$239$		−	232.519i		−	0.972881i	0.873714	−	0.486440i	$-0.161705\pi$
$240$	332.782	−	110.792i	1.38659	−	0.461635i
$241$	146.374			0.607362			0.303681	−	0.952774i	$-0.401784\pi$
$241$	146.374			0.607362			0.303681	+	0.952774i	$0.401784\pi$
$242$	−230.363	−	54.8086i	−0.951914	−	0.226482i
$243$		−	348.581i		−	1.43449i
$244$	93.0494	+	282.451i	0.381350	+	1.15759i
$245$	−30.1919	+	92.6273i	−0.123232	+	0.378071i
$246$	4.53889	−	19.0772i	0.0184508	−	0.0775494i
$247$	−235.813	−	235.813i	−0.954710	−	0.954710i
$248$	218.854	−	259.443i	0.882474	−	1.04614i
$249$	−168.521			−0.676791
$250$	231.042	−	95.4959i	0.924169	−	0.381984i
$251$	172.155	−	172.155i	0.685878	−	0.685878i	−0.275440	−	0.961318i	$-0.588824\pi$
$251$	172.155	−	172.155i	0.685878	−	0.685878i	0.961318	+	0.275440i	$0.0888236\pi$
$252$	69.5031	+	210.976i	0.275806	+	0.837207i
$253$		−	54.7695i		−	0.216480i
$254$	−119.122	−	193.503i	−0.468985	−	0.761821i
$255$	177.658	+	349.479i	0.696700	+	1.37051i
$256$	−75.1252	+	244.729i	−0.293458	+	0.955972i
$257$	73.6289	−	73.6289i	0.286494	−	0.286494i	−0.549198	−	0.835692i	$-0.685067\pi$
$257$	73.6289	−	73.6289i	0.286494	−	0.286494i	0.835692	+	0.549198i	$0.185067\pi$
$258$	−319.371	−	75.9856i	−1.23787	−	0.294518i
$259$	−143.805	+	143.805i	−0.555232	+	0.555232i
$260$	−136.597	+	137.459i	−0.525372	+	0.528689i
$261$	−218.848	+	218.848i	−0.838498	+	0.838498i
$262$	44.7623	−	27.5561i	0.170849	−	0.105176i
$263$	−141.657	+	141.657i	−0.538620	+	0.538620i	−0.923123	−	0.384504i	$-0.874373\pi$
$263$	−141.657	+	141.657i	−0.538620	+	0.538620i	0.384504	+	0.923123i	$0.374373\pi$
$264$	56.3875	−	4.78514i	0.213589	−	0.0181255i
$265$	153.871	+	50.1544i	0.580645	+	0.189262i
$266$	86.5604	−	363.818i	0.325415	−	1.36774i
$267$		−	605.612i		−	2.26821i
$268$	−295.043	−	148.819i	−1.10091	−	0.555295i
$269$	51.7648	−	51.7648i	0.192434	−	0.192434i	−0.604313	−	0.796747i	$-0.706552\pi$
$269$	51.7648	−	51.7648i	0.192434	−	0.192434i	0.796747	+	0.604313i	$0.206552\pi$
$270$	−45.7007	−	27.9359i	−0.169262	−	0.103466i
$271$	−92.2487			−0.340401			−0.170201	−	0.985409i	$-0.554442\pi$
$271$	−92.2487			−0.340401			−0.170201	+	0.985409i	$0.554442\pi$
$272$	−282.979	−	42.4559i	−1.04037	−	0.156088i
$273$	−163.193	−	163.193i	−0.597775	−	0.597775i
$274$	−201.152	+	123.831i	−0.734132	+	0.451939i
$275$	39.8513	−	6.23568i	0.144914	−	0.0226752i
$276$	−186.267	−	565.414i	−0.674882	−	2.04860i
$277$		−	169.623i		−	0.612357i	−0.951974	−	0.306179i	$-0.900949\pi$
$277$		−	169.623i		−	0.612357i	0.951974	−	0.306179i	$-0.0990505\pi$
$278$	2.13491	−	1.31427i	0.00767955	−	0.00472761i
$279$	−433.684			−1.55442
$280$	−211.568	−	49.6338i	−0.755599	−	0.177263i
$281$			194.385i			0.691761i	0.938278	+	0.345881i	$0.112420\pi$
$281$			194.385i			0.691761i	−0.938278	+	0.345881i	$0.887580\pi$
$282$	−184.293	+	113.452i	−0.653520	+	0.402313i
$283$	−523.679			−1.85046			−0.925229	−	0.379410i	$-0.876127\pi$
$283$	−523.679			−1.85046			−0.925229	+	0.379410i	$0.876127\pi$
$284$	−25.6244	+	50.8020i	−0.0902267	+	0.178880i
$285$	341.904	+	672.574i	1.19966	+	2.35991i
$286$	−26.6258	+	16.3911i	−0.0930973	+	0.0573116i
$287$	−8.59118	+	8.59118i	−0.0299344	+	0.0299344i
$288$	300.904	−	128.249i	1.04480	−	0.445309i
$289$		−	30.8432i		−	0.106724i
$290$	−71.0097	−	294.340i	−0.244861	−	1.01497i
$291$	496.931	+	496.931i	1.70767	+	1.70767i
$292$	−55.1809	+	18.1786i	−0.188976	+	0.0622553i
$293$	272.325			0.929435			0.464718	−	0.885459i	$-0.346156\pi$
$293$	272.325			0.929435			0.464718	+	0.885459i	$0.346156\pi$
$294$	−39.5457	+	166.213i	−0.134509	+	0.565349i
$295$	−68.1624	−	134.085i	−0.231059	−	0.454526i
$296$	228.906	+	193.094i	0.773331	+	0.652346i
$297$	−6.11087	−	6.11087i	−0.0205753	−	0.0205753i
$298$	304.041	−	187.171i	1.02027	−	0.628089i
$299$	232.576	+	232.576i	0.777846	+	0.777846i
$300$	390.198	−	199.906i	1.30066	−	0.666352i
$301$	143.825	+	143.825i	0.477824	+	0.477824i
$302$	167.065	+	39.7485i	0.553194	+	0.131617i
$303$	58.3426	+	58.3426i	0.192550	+	0.192550i
$304$	−544.595	−	81.7065i	−1.79143	−	0.268771i
$305$	168.452	+	331.370i	0.552303	+	1.08646i
$306$	191.668	+	311.346i	0.626366	+	1.01747i
$307$	−112.655			−0.366954			−0.183477	−	0.983024i	$-0.558735\pi$
$307$	−112.655			−0.366954			−0.183477	+	0.983024i	$0.558735\pi$
$308$	−31.3053	−	15.7903i	−0.101641	−	0.0512673i
$309$	−164.247	−	164.247i	−0.531545	−	0.531545i
$310$	221.284	−	362.002i	0.713819	−	1.16775i
$311$			254.031i			0.816820i	0.912799	+	0.408410i	$0.133917\pi$
$311$			254.031i			0.816820i	−0.912799	+	0.408410i	$0.866083\pi$
$312$	−219.127	+	259.766i	−0.702330	+	0.832585i
$313$	−22.4916	+	22.4916i	−0.0718580	+	0.0718580i	−0.742122	−	0.670264i	$-0.766181\pi$
$313$	−22.4916	+	22.4916i	−0.0718580	+	0.0718580i	0.670264	+	0.742122i	$0.266181\pi$
$314$	103.226	−	433.862i	0.328744	−	1.38173i
$315$	125.825	+	247.516i	0.399445	+	0.785766i
$316$	100.288	−	198.827i	0.317366	−	0.629199i
$317$	−379.973			−1.19865			−0.599327	−	0.800504i	$-0.704565\pi$
$317$	−379.973			−1.19865			−0.599327	+	0.800504i	$0.704565\pi$
$318$	276.110	+	65.6927i	0.868269	+	0.206581i
$319$		−	48.8528i		−	0.153144i
$320$	−46.4826	+	316.606i	−0.145258	+	0.989394i
$321$	26.9649			0.0840028
$322$	−85.3721	+	358.823i	−0.265131	+	1.11436i
$323$		−	615.539i		−	1.90569i
$324$	244.684	+	123.418i	0.755199	+	0.380920i
$325$	−142.747	+	195.706i	−0.439222	+	0.602172i
$326$	−222.151	−	52.8546i	−0.681444	−	0.162131i
$327$	505.000	+	505.000i	1.54434	+	1.54434i
$328$	13.6753	+	11.5358i	0.0416929	+	0.0351701i
$329$	134.086			0.407556
$330$	68.7650	−	16.5896i	0.208379	−	0.0502714i
$331$	−56.7172	+	56.7172i	−0.171351	+	0.171351i	−0.787573	−	0.616222i	$-0.788663\pi$
$331$	−56.7172	+	56.7172i	−0.171351	+	0.171351i	0.616222	+	0.787573i	$0.288663\pi$
$332$	69.2420	−	137.277i	0.208560	−	0.413484i
$333$		−	382.639i		−	1.14907i
$334$	−200.241	+	123.271i	−0.599525	+	0.369074i
$335$	−392.727	−	128.010i	−1.17232	−	0.382118i
$336$	−376.882	−	56.5443i	−1.12167	−	0.168287i
$337$	6.90955	−	6.90955i	0.0205031	−	0.0205031i	−0.696781	−	0.717284i	$-0.745385\pi$
$337$	6.90955	−	6.90955i	0.0205031	−	0.0205031i	0.717284	+	0.696781i	$0.245385\pi$
$338$	−34.7729	+	146.152i	−0.102878	+	0.432403i
$339$	−321.220	+	321.220i	−0.947552	+	0.947552i
$340$	−357.681	+	1.12562i	−1.05200	+	0.00331066i
$341$	48.4050	−	48.4050i	0.141950	−	0.141950i
$342$	368.865	+	599.187i	1.07855	+	1.75201i
$343$	263.089	−	263.089i	0.767022	−	0.767022i
$344$	193.121	−	228.938i	0.561399	−	0.665517i
$345$	−337.210	−	663.341i	−0.977421	−	1.92273i
$346$	−61.9329	−	14.7352i	−0.178997	−	0.0425874i
$347$			512.927i			1.47817i	0.673610	+	0.739087i	$0.264743\pi$
$347$			512.927i			1.47817i	−0.673610	+	0.739087i	$0.735257\pi$
$348$	−166.145	−	504.332i	−0.477428	−	1.44923i
$349$	335.325	−	335.325i	0.960817	−	0.960817i	−0.0384442	−	0.999261i	$-0.512240\pi$
$349$	335.325	−	335.325i	0.960817	−	0.960817i	0.999261	+	0.0384442i	$0.0122402\pi$
$350$	−270.806	−	21.2652i	−0.773732	−	0.0607578i
$351$	51.8990			0.147860
$352$	−19.2706	+	47.8993i	−0.0547460	+	0.136077i
$353$	304.970	+	304.970i	0.863938	+	0.863938i	0.991793	−	0.127855i	$-0.0408092\pi$
$353$	304.970	+	304.970i	0.863938	+	0.863938i	−0.127855	+	0.991793i	$0.540809\pi$
$354$	−138.286	−	224.632i	−0.390638	−	0.634554i
$355$	−22.0413	+	67.6217i	−0.0620883	+	0.190484i
$356$	493.330	+	248.834i	1.38576	+	0.698973i
$357$		−	425.979i		−	1.19322i
$358$	292.907	+	475.799i	0.818175	+	1.32905i
$359$	55.6486			0.155010			0.0775050	−	0.996992i	$-0.475305\pi$
$359$	55.6486			0.155010			0.0775050	+	0.996992i	$0.475305\pi$
$360$	347.505	−	215.438i	0.965291	−	0.598440i
$361$		−	823.608i		−	2.28146i
$362$	126.985	+	206.274i	0.350786	+	0.569819i
$363$	−519.082			−1.42998
$364$	199.989	−	65.8835i	0.549420	−	0.180999i
$365$	−64.7380	+	32.9096i	−0.177364	+	0.0901634i
$366$	341.751	+	555.142i	0.933745	+	1.51678i
$367$	185.365	−	185.365i	0.505081	−	0.505081i	−0.407931	−	0.913013i	$-0.633750\pi$
$367$	185.365	−	185.365i	0.505081	−	0.505081i	0.913013	+	0.407931i	$0.133750\pi$
$368$	537.118	+	80.5848i	1.45956	+	0.218980i
$369$		−	22.8596i		−	0.0619500i
$370$	319.393	+	195.238i	0.863226	+	0.527671i
$371$	−124.343	−	124.343i	−0.335156	−	0.335156i
$372$	335.088	−	664.332i	0.900773	−	1.78584i
$373$	−16.1719			−0.0433562			−0.0216781	−	0.999765i	$-0.506901\pi$
$373$	−16.1719			−0.0433562			−0.0216781	+	0.999765i	$0.506901\pi$
$374$	−56.1432	−	13.3577i	−0.150116	−	0.0357159i
$375$	444.267	−	320.884i	1.18471	−	0.855690i
$376$	−16.6957	−	196.740i	−0.0444034	−	0.523244i
$377$	207.451	+	207.451i	0.550267	+	0.550267i
$378$	30.5101	+	49.5607i	0.0807145	+	0.131113i
$379$	467.798	+	467.798i	1.23430	+	1.23430i	0.962298	+	0.271998i	$0.0876843\pi$
$379$	467.798	+	467.798i	1.23430	+	1.23430i	0.271998	+	0.962298i	$0.412316\pi$
$380$	−688.359	+	2.16627i	−1.81147	+	0.00570070i
$381$	−352.222	−	352.222i	−0.924466	−	0.924466i
$382$	−3.10221	+	13.0387i	−0.00812096	+	0.0341328i
$383$	138.301	+	138.301i	0.361100	+	0.361100i	0.864218	−	0.503118i	$-0.167814\pi$
$383$	138.301	+	138.301i	0.361100	+	0.361100i	−0.503118	+	0.864218i	$0.667814\pi$
$384$	−36.0381	+	560.027i	−0.0938492	+	1.45840i
$385$	−41.6700	−	13.5824i	−0.108234	−	0.0352789i
$386$	484.817	−	298.458i	1.25600	−	0.773207i
$387$	−382.692			−0.988869
$388$	−608.978	+	200.619i	−1.56953	+	0.517060i
$389$	−356.792	−	356.792i	−0.917202	−	0.917202i	0.0796230	−	0.996825i	$-0.474628\pi$
$389$	−356.792	−	356.792i	−0.917202	−	0.917202i	−0.996825	+	0.0796230i	$0.974628\pi$
$390$	−221.560	+	362.453i	−0.568103	+	0.929367i
$391$			607.089i			1.55266i
$392$	−119.148	−	100.507i	−0.303948	−	0.256396i
$393$	81.4783	−	81.4783i	0.207324	−	0.207324i
$394$	105.426	+	25.0831i	0.267578	+	0.0636628i
$395$	86.2646	−	264.655i	0.218391	−	0.670013i
$396$	62.6564	−	20.6413i	0.158223	−	0.0521244i
$397$	287.234			0.723511			0.361755	−	0.932273i	$-0.382178\pi$
$397$	287.234			0.723511			0.361755	+	0.932273i	$0.382178\pi$
$398$	−38.0708	+	160.013i	−0.0956552	+	0.402043i
$399$		−	819.797i		−	2.05463i
$400$	2.51758	+	399.992i	0.00629394	+	0.999980i
$401$	178.508			0.445157			0.222579	−	0.974915i	$-0.428553\pi$
$401$	178.508			0.445157			0.222579	+	0.974915i	$0.428553\pi$
$402$	−704.718	−	167.668i	−1.75303	−	0.417085i
$403$			411.099i			1.02010i
$404$	−71.4976	+	23.5539i	−0.176974	+	0.0583017i
$405$	325.695	+	106.161i	0.804186	+	0.262125i
$406$	−76.1494	+	320.060i	−0.187560	+	0.788324i
$407$	42.7077	+	42.7077i	0.104933	+	0.104933i
$408$	−625.024	+	53.0405i	−1.53192	+	0.130001i
$409$	60.0556			0.146835			0.0734176	−	0.997301i	$-0.476609\pi$
$409$	60.0556			0.146835			0.0734176	+	0.997301i	$0.476609\pi$
$410$	19.0811	+	11.6639i	0.0465394	+	0.0284485i
$411$	−366.146	+	366.146i	−0.890866	+	0.890866i
$412$	201.282	−	66.3094i	0.488548	−	0.160945i
$413$			163.436i			0.395728i
$414$	−363.801	−	590.961i	−0.878747	−	1.42744i
$415$	59.5599	−	182.727i	0.143518	−	0.440306i
$416$	−121.570	−	285.233i	−0.292236	−	0.685657i
$417$	3.88606	−	3.88606i	0.00931909	−	0.00931909i
$418$	−108.048	−	25.7070i	−0.258488	−	0.0615000i
$419$	−258.872	+	258.872i	−0.617833	+	0.617833i	−0.944975	−	0.327142i	$-0.893914\pi$
$419$	−258.872	+	258.872i	−0.617833	+	0.617833i	0.327142	+	0.944975i	$0.393914\pi$
$420$	−476.373	+	1.49915i	−1.13422	+	0.00356940i
$421$	429.322	−	429.322i	1.01977	−	1.01977i	0.0199654	−	0.999801i	$-0.493644\pi$
$421$	429.322	−	429.322i	1.01977	−	1.01977i	0.999801	−	0.0199654i	$-0.00635560\pi$
$422$	182.873	−	112.578i	0.433348	−	0.266773i
$423$	−178.389	+	178.389i	−0.421724	+	0.421724i
$424$	−166.961	+	197.926i	−0.393777	+	0.466807i
$425$	−441.729	+	69.1189i	−1.03936	+	0.162633i
$426$	−28.8700	+	121.342i	−0.0677699	+	0.284840i
$427$		−	403.905i		−	0.945914i
$428$	−11.0794	+	21.9655i	−0.0258864	+	0.0513213i
$429$	−48.4655	+	48.4655i	−0.112973	+	0.112973i
$430$	195.266	−	319.438i	0.454106	−	0.742879i
$431$	−412.636			−0.957392			−0.478696	−	0.877981i	$-0.658890\pi$
$431$	−412.636			−0.957392			−0.478696	+	0.877981i	$0.658890\pi$
$432$	68.9198	−	50.9374i	0.159537	−	0.117911i
$433$	−203.596	−	203.596i	−0.470200	−	0.470200i	0.431780	−	0.901979i	$-0.357886\pi$
$433$	−203.596	−	203.596i	−0.470200	−	0.470200i	−0.901979	+	0.431780i	$0.857886\pi$
$434$	−392.577	+	241.675i	−0.904556	+	0.556854i
$435$	−300.782	−	591.680i	−0.691452	−	1.36018i
$436$	−618.866	+	203.877i	−1.41942	+	0.467607i
$437$			1168.34i			2.67356i
$438$	−108.455	+	66.7660i	−0.247614	+	0.152434i
$439$	190.193			0.433241			0.216621	−	0.976256i	$-0.430497\pi$
$439$	190.193			0.433241			0.216621	+	0.976256i	$0.430497\pi$
$440$	−14.7404	+	62.8321i	−0.0335009	+	0.142800i
$441$			199.167i			0.451626i
$442$	295.132	−	181.686i	0.667719	−	0.411055i
$443$	255.432			0.576595			0.288298	−	0.957541i	$-0.406911\pi$
$443$	255.432			0.576595			0.288298	+	0.957541i	$0.406911\pi$
$444$	586.139	+	295.647i	1.32013	+	0.665872i
$445$	656.664	+	214.040i	1.47565	+	0.480989i
$446$	−248.179	+	152.782i	−0.556456	+	0.342560i
$447$	553.428	−	553.428i	1.23809	−	1.23809i
$448$	200.915	−	283.774i	0.448470	−	0.633425i
$449$			569.939i			1.26935i	0.772778	+	0.634676i	$0.218867\pi$
$449$			569.939i			1.26935i	−0.772778	+	0.634676i	$0.781133\pi$
$450$	388.574	−	331.991i	0.863498	−	0.737759i
$451$	2.55144	+	2.55144i	0.00565729	+	0.00565729i
$452$	−129.682	−	393.648i	−0.286907	−	0.870904i
$453$	376.450			0.831016
$454$	−45.5264	+	191.350i	−0.100278	+	0.421475i
$455$	234.626	−	119.273i	0.515662	−	0.262137i
$456$	−1202.86	+	102.077i	−2.63785	+	0.223852i
$457$	−288.400	−	288.400i	−0.631072	−	0.631072i	0.317265	−	0.948337i	$-0.397236\pi$
$457$	−288.400	−	288.400i	−0.631072	−	0.631072i	−0.948337	+	0.317265i	$0.897236\pi$
$458$	−426.197	+	262.371i	−0.930561	+	0.572863i
$459$	67.7355	+	67.7355i	0.147572	+	0.147572i
$460$	678.909	−	2.13653i	1.47589	−	0.00464462i
$461$	−184.673	−	184.673i	−0.400593	−	0.400593i	0.477849	−	0.878442i	$-0.341417\pi$
$461$	−184.673	−	184.673i	−0.400593	−	0.400593i	−0.878442	+	0.477849i	$0.841417\pi$
$462$	−74.7735	−	17.7903i	−0.161847	−	0.0385072i
$463$	232.357	+	232.357i	0.501850	+	0.501850i	0.912013	−	0.410162i	$-0.134528\pi$
$463$	232.357	+	232.357i	0.501850	+	0.501850i	−0.410162	+	0.912013i	$0.634528\pi$
$464$	479.094	+	71.8792i	1.03253	+	0.154912i
$465$	288.232	−	884.282i	0.619855	−	1.90168i
$466$	−263.367	−	427.815i	−0.565165	−	0.918057i
$467$	−360.961			−0.772937			−0.386468	−	0.922303i	$-0.626305\pi$
$467$	−360.961			−0.772937			−0.386468	+	0.922303i	$0.626305\pi$
$468$	−178.415	+	353.719i	−0.381229	+	0.755810i
$469$	317.362	+	317.362i	0.676677	+	0.676677i
$470$	−57.8820	−	239.925i	−0.123153	−	0.510479i
$471$		−	977.631i		−	2.07565i
$472$	239.804	−	20.3501i	0.508059	−	0.0431147i
$473$	42.7137	−	42.7137i	0.0903037	−	0.0903037i
$474$	112.990	−	474.903i	0.238376	−	1.00191i
$475$	−850.109	+	133.020i	−1.78970	+	0.280041i
$476$	347.001	+	175.027i	0.728994	+	0.367703i
$477$	330.853			0.693613
$478$	452.408	+	107.638i	0.946461	+	0.225185i
$479$			111.130i			0.232005i	0.993249	+	0.116003i	$0.0370081\pi$
$479$			111.130i			0.232005i	−0.993249	+	0.116003i	$0.962992\pi$
$480$	61.5150	+	698.779i	0.128156	+	1.45579i
$481$	−362.712			−0.754079
$482$	−67.7600	+	284.798i	−0.140581	+	0.590868i
$483$			808.543i			1.67400i
$484$	213.281	−	422.843i	0.440663	−	0.873642i
$485$	−714.450	+	363.192i	−1.47309	+	0.748850i
$486$	678.230	+	161.366i	1.39553	+	0.332029i
$487$	−467.586	−	467.586i	−0.960135	−	0.960135i	0.0391007	−	0.999235i	$-0.487551\pi$
$487$	−467.586	−	467.586i	−0.960135	−	0.960135i	−0.999235	+	0.0391007i	$0.987551\pi$
$488$	−592.636	+	50.2921i	−1.21442	+	0.103058i
$489$	−500.576			−1.02367
$490$	−166.247	−	101.623i	−0.339280	−	0.207395i
$491$	333.638	−	333.638i	0.679507	−	0.679507i	−0.280382	−	0.959889i	$-0.590461\pi$
$491$	333.638	−	333.638i	0.679507	−	0.679507i	0.959889	+	0.280382i	$0.0904610\pi$
$492$	35.0170	+	17.6625i	0.0711728	+	0.0358994i
$493$			541.505i			1.09839i
$494$	567.983	−	349.656i	1.14976	−	0.707805i
$495$	73.5082	−	37.3680i	0.148501	−	0.0754909i
$496$	403.482	+	545.923i	0.813472	+	1.10065i
$497$	54.6449	−	54.6449i	0.109950	−	0.109950i
$498$	78.0122	−	327.889i	0.156651	−	0.658412i
$499$	173.095	−	173.095i	0.346884	−	0.346884i	−0.512064	−	0.858947i	$-0.671119\pi$
$499$	173.095	−	173.095i	0.346884	−	0.346884i	0.858947	+	0.512064i	$0.171119\pi$
$500$	78.8504	+	493.743i	0.157701	+	0.987487i
$501$	−364.488	+	364.488i	−0.727521	+	0.727521i
$502$	255.266	+	414.656i	0.508498	+	0.826007i
$503$	−618.020	+	618.020i	−1.22867	+	1.22867i	−0.264201	+	0.964468i	$0.585108\pi$
$503$	−618.020	+	618.020i	−1.22867	+	1.22867i	−0.964468	+	0.264201i	$0.914892\pi$
$504$	−442.668	+	37.5656i	−0.878310	+	0.0745349i
$505$	−83.8807	+	42.6409i	−0.166100	+	0.0844374i
$506$	106.564	+	25.3541i	0.210602	+	0.0501069i
$507$			329.327i			0.649561i
$508$	431.640	−	142.198i	0.849685	−	0.279917i
$509$	519.035	−	519.035i	1.01972	−	1.01972i	0.0199135	−	0.999802i	$-0.493661\pi$
$509$	519.035	−	519.035i	1.01972	−	1.01972i	0.999802	−	0.0199135i	$-0.00633909\pi$
$510$	−762.220	+	183.886i	−1.49455	+	0.360560i
$511$	78.9088			0.154420
$512$	−441.389	−	259.461i	−0.862088	−	0.506759i
$513$	130.357	+	130.357i	0.254108	+	0.254108i
$514$	109.174	+	177.343i	0.212401	+	0.345026i
$515$	236.143	−	120.044i	0.458529	−	0.233094i
$516$	295.689	−	586.221i	0.573040	−	1.13609i
$517$		−	39.8213i		−	0.0770238i
$518$	−213.229	−	346.371i	−0.411639	−	0.668669i
$519$	−139.555			−0.268891
$520$	−204.219	−	329.407i	−0.392728	−	0.633476i
$521$		−	687.482i		−	1.31954i	−0.751467	−	0.659771i	$-0.770653\pi$
$521$		−	687.482i		−	1.31954i	0.751467	−	0.659771i	$-0.229347\pi$
$522$	−324.500	−	527.120i	−0.621648	−	1.00981i
$523$	472.937			0.904277			0.452139	−	0.891948i	$-0.350661\pi$
$523$	472.937			0.904277			0.452139	+	0.891948i	$0.350661\pi$
$524$	32.8941	+	99.8499i	0.0627750	+	0.190553i
$525$	−588.311	+	92.0550i	−1.12059	+	0.175343i
$526$	−210.044	−	341.197i	−0.399323	−	0.648663i
$527$	−536.542	+	536.542i	−1.01811	+	1.01811i
$528$	−16.7927	+	111.928i	−0.0318044	+	0.211984i
$529$		−	623.305i		−	1.17827i
$530$	−168.815	+	276.167i	−0.318519	+	0.521070i
$531$	−217.436	−	217.436i	−0.409485	−	0.409485i
$532$	667.805	+	336.839i	1.25527	+	0.633157i
$533$	−21.6691			−0.0406549
$534$	1178.33	+	280.352i	2.20661	+	0.525003i
$535$	−9.53014	+	29.2380i	−0.0178133	+	0.0546504i
$536$	426.137	−	505.170i	0.795033	−	0.942481i
$537$	866.070	+	866.070i	1.61279	+	1.61279i
$538$	76.7551	+	124.681i	0.142667	+	0.231750i
$539$	−22.2298	−	22.2298i	−0.0412426	−	0.0412426i
$540$	75.5104	−	75.9872i	0.139834	−	0.140717i
$541$	91.9662	+	91.9662i	0.169993	+	0.169993i	0.786976	−	0.616983i	$-0.211645\pi$
$541$	91.9662	+	91.9662i	0.169993	+	0.169993i	−0.616983	+	0.786976i	$0.711645\pi$
$542$	42.7041	−	179.487i	0.0787898	−	0.331157i
$543$	375.469	+	375.469i	0.691472	+	0.691472i
$544$	213.604	−	530.936i	0.392654	−	0.975985i
$545$	−726.051	+	369.089i	−1.33220	+	0.677228i
$546$	393.067	−	241.976i	0.719904	−	0.443180i
$547$	238.842			0.436640			0.218320	−	0.975877i	$-0.429942\pi$
$547$	238.842			0.436640			0.218320	+	0.975877i	$0.429942\pi$
$548$	−147.819	−	448.704i	−0.269743	−	0.818803i
$549$	537.359	+	537.359i	0.978796	+	0.978796i
$550$	−6.31542	+	80.4249i	−0.0114826	+	0.146227i
$551$			1042.13i			1.89134i
$552$	1186.35	−	100.675i	2.14918	−	0.182383i
$553$	−213.867	+	213.867i	−0.386740	+	0.386740i
$554$	330.033	+	78.5224i	0.595728	+	0.141737i
$555$	780.201	+	254.307i	1.40577	+	0.458211i
$556$	1.56887	+	4.76229i	0.00282170	+	0.00856526i
$557$	181.535			0.325915			0.162958	−	0.986633i	$-0.447897\pi$
$557$	181.535			0.325915			0.162958	+	0.986633i	$0.447897\pi$
$558$	200.762	−	843.814i	0.359789	−	1.51221i
$559$			362.763i			0.648949i
$560$	194.511	−	388.668i	0.347342	−	0.694050i
$561$	−126.509			−0.225505
$562$	−378.213	−	89.9853i	−0.672976	−	0.160116i
$563$		−	759.434i		−	1.34891i	−0.738318	−	0.674453i	$-0.764379\pi$
$563$		−	759.434i		−	1.34891i	0.738318	−	0.674453i	$-0.235621\pi$
$564$	−135.430	−	411.096i	−0.240123	−	0.728893i
$565$	−234.770	−	461.826i	−0.415523	−	0.817392i
$566$	242.423	−	1018.92i	0.428310	−	1.80021i
$567$	−263.194	−	263.194i	−0.464186	−	0.464186i
$568$	−86.9827	−	73.3745i	−0.153138	−	0.129180i
$569$	−1063.33			−1.86878			−0.934388	−	0.356258i	$-0.884053\pi$
$569$	−1063.33			−1.86878			−0.934388	+	0.356258i	$0.884053\pi$
$570$	−1466.90	+	353.889i	−2.57350	+	0.620857i
$571$	342.578	−	342.578i	0.599962	−	0.599962i	−0.340341	−	0.940302i	$-0.610542\pi$
$571$	342.578	−	342.578i	0.599962	−	0.599962i	0.940302	+	0.340341i	$0.110542\pi$
$572$	−19.5663	−	59.3934i	−0.0342068	−	0.103835i
$573$			29.3804i			0.0512747i
$574$	−12.7387	−	20.6928i	−0.0221929	−	0.0360502i
$575$	838.438	−	131.193i	1.45815	−	0.228162i
$576$	110.237	+	644.834i	0.191384	+	1.11950i
$577$	465.865	−	465.865i	0.807392	−	0.807392i	−0.176846	−	0.984239i	$-0.556590\pi$
$577$	465.865	−	465.865i	0.807392	−	0.807392i	0.984239	+	0.176846i	$0.0565895\pi$
$578$	60.0113	+	14.2780i	0.103826	+	0.0247025i
$579$	882.484	−	882.484i	1.52415	−	1.52415i
$580$	605.567	−	1.90572i	1.04408	−	0.00328572i
$581$	−147.661	+	147.661i	−0.254150	+	0.254150i
$582$	−1196.91	+	736.832i	−2.05655	+	1.26603i
$583$	−36.9277	+	36.9277i	−0.0633409	+	0.0633409i
$584$	−9.82529	−	115.780i	−0.0168241	−	0.198254i
$585$	−153.467	+	470.830i	−0.262337	+	0.804837i
$586$	−126.065	+	529.859i	−0.215129	+	0.904196i
$587$		−	236.253i		−	0.402476i	−0.979542	−	0.201238i	$-0.935504\pi$
$587$		−	236.253i		−	0.402476i	0.979542	−	0.201238i	$-0.0644964\pi$
$588$	−305.091	−	153.887i	−0.518862	−	0.261713i
$589$	−1032.58	+	1032.58i	−1.75310	+	1.75310i
$590$	292.442	−	70.5517i	0.495664	−	0.119579i
$591$	237.558			0.401959
$592$	−481.667	+	355.992i	−0.813627	+	0.601337i
$593$	208.498	+	208.498i	0.351599	+	0.351599i	0.860704	−	0.509106i	$-0.170024\pi$
$593$	208.498	+	208.498i	0.351599	+	0.351599i	−0.509106	+	0.860704i	$0.670024\pi$
$594$	14.7187	−	9.06099i	0.0247790	−	0.0152542i
$595$	461.888	+	150.553i	0.776282	+	0.253030i
$596$	223.428	+	678.214i	0.374879	+	1.13794i
$597$			360.561i			0.603955i
$598$	−560.185	+	344.855i	−0.936764	+	0.576681i
$599$	100.435			0.167670			0.0838352	−	0.996480i	$-0.473283\pi$
$599$	100.435			0.167670			0.0838352	+	0.996480i	$0.473283\pi$
$600$	208.322	+	851.745i	0.347204	+	1.41958i
$601$			189.816i			0.315834i	0.987452	+	0.157917i	$0.0504778\pi$
$601$			189.816i			0.315834i	−0.987452	+	0.157917i	$0.949522\pi$
$602$	−346.419	+	213.259i	−0.575447	+	0.354251i
$603$	−844.442			−1.40040
$604$	−154.676	+	306.655i	−0.256086	+	0.507708i
$605$	183.458	−	562.839i	0.303236	−	0.930313i
$606$	−140.525	+	86.5084i	−0.231889	+	0.142753i
$607$	288.020	−	288.020i	0.474498	−	0.474498i	−0.428869	−	0.903367i	$-0.641088\pi$
$607$	288.020	−	288.020i	0.474498	−	0.474498i	0.903367	+	0.428869i	$0.141088\pi$
$608$	411.081	−	1021.79i	0.676120	−	1.68057i
$609$			721.196i			1.18423i
$610$	−722.723	+	174.357i	−1.18479	+	0.285831i
$611$	169.099	+	169.099i	0.276758	+	0.276758i
$612$	−694.510	+	228.796i	−1.13482	+	0.373850i
$613$	−194.536			−0.317351			−0.158676	−	0.987331i	$-0.550722\pi$
$613$	−194.536			−0.317351			−0.158676	+	0.987331i	$0.550722\pi$
$614$	52.1505	−	219.191i	0.0849357	−	0.356989i
$615$	46.6106	+	15.1928i	0.0757896	+	0.0247037i
$616$	45.2150	−	53.6006i	0.0734009	−	0.0870140i
$617$	89.2331	+	89.2331i	0.144624	+	0.144624i	0.775712	−	0.631087i	$-0.217391\pi$
$617$	89.2331	+	89.2331i	0.144624	+	0.144624i	−0.631087	+	0.775712i	$0.717391\pi$
$618$	395.608	−	243.540i	0.640143	−	0.394078i
$619$	−98.7690	−	98.7690i	−0.159562	−	0.159562i	0.622811	−	0.782373i	$-0.285991\pi$
$619$	−98.7690	−	98.7690i	−0.159562	−	0.159562i	−0.782373	+	0.622811i	$0.785991\pi$
$620$	601.905	+	598.128i	0.970814	+	0.964723i
$621$	−128.568	−	128.568i	−0.207033	−	0.207033i
$622$	−494.265	−	117.597i	−0.794638	−	0.189062i
$623$	−530.648	−	530.648i	−0.851763	−	0.851763i
$624$	−403.986	−	546.604i	−0.647413	−	0.875969i
$625$	190.917	+	595.126i	0.305468	+	0.952202i
$626$	−33.3497	−	54.1734i	−0.0532743	−	0.0865390i
$627$	−243.466			−0.388303
$628$	796.375	+	401.690i	1.26811	+	0.639634i
$629$	−473.390	−	473.390i	−0.752608	−	0.752608i
$630$	−539.837	+	130.236i	−0.856884	+	0.206723i
$631$		−	361.528i		−	0.572945i	−0.958089	−	0.286472i	$-0.907517\pi$
$631$		−	361.528i		−	0.572945i	0.958089	−	0.286472i	$-0.0924827\pi$
$632$	340.429	+	287.170i	0.538654	+	0.454383i
$633$	332.873	−	332.873i	0.525866	−	0.525866i
$634$	175.898	−	739.310i	0.277442	−	1.16610i
$635$	506.398	−	257.428i	0.797477	−	0.405399i
$636$	−255.635	+	506.812i	−0.401942	+	0.796875i
$637$	188.795			0.296382
$638$	95.0523	+	22.6151i	0.148985	+	0.0354469i
$639$			145.400i			0.227543i
$640$	−594.499	−	237.005i	−0.928904	−	0.370320i
$641$	−225.925			−0.352458			−0.176229	−	0.984349i	$-0.556390\pi$
$641$	−225.925			−0.352458			−0.176229	+	0.984349i	$0.556390\pi$
$642$	−12.4827	+	52.4653i	−0.0194434	+	0.0817216i
$643$			1219.79i			1.89703i	0.316731	+	0.948515i	$0.397415\pi$
$643$			1219.79i			1.89703i	−0.316731	+	0.948515i	$0.602585\pi$
$644$	−658.637	−	332.215i	−1.02273	−	0.515862i
$645$	254.343	−	780.310i	0.394330	−	1.20978i
$646$	1197.65	+	284.947i	1.85394	+	0.441095i
$647$	−406.190	−	406.190i	−0.627806	−	0.627806i	0.319710	−	0.947516i	$-0.396415\pi$
$647$	−406.190	−	406.190i	−0.627806	−	0.627806i	−0.947516	+	0.319710i	$0.896415\pi$
$648$	−353.403	+	418.946i	−0.545376	+	0.646522i
$649$	48.5377			0.0747885
$650$	−314.702	−	368.338i	−0.484157	−	0.566674i
$651$	−714.586	+	714.586i	−1.09767	+	1.09767i
$652$	205.677	−	407.768i	0.315456	−	0.625411i
$653$		−	652.961i		−	0.999940i	−0.866043	−	0.499970i	$-0.833344\pi$
$653$		−	652.961i		−	0.999940i	0.866043	−	0.499970i	$-0.166656\pi$
$654$	−1216.35	+	748.796i	−1.85986	+	1.14495i
$655$	59.5500	+	117.143i	0.0909161	+	0.178845i
$656$	−28.7757	+	21.2676i	−0.0438654	+	0.0324201i
$657$	−104.981	+	104.981i	−0.159788	+	0.159788i
$658$	−62.0715	+	260.890i	−0.0943336	+	0.396489i
$659$	−565.772	+	565.772i	−0.858532	+	0.858532i	−0.991165	−	0.132634i	$-0.957657\pi$
$659$	−565.772	+	565.772i	−0.858532	+	0.858532i	0.132634	+	0.991165i	$0.457657\pi$
$660$	0.445221	+	141.475i	0.000674578	+	0.214356i
$661$	−304.268	+	304.268i	−0.460315	+	0.460315i	−0.898759	−	0.438443i	$-0.855530\pi$
$661$	−304.268	+	304.268i	−0.460315	+	0.460315i	0.438443	+	0.898759i	$0.355530\pi$
$662$	−84.0983	−	136.610i	−0.127037	−	0.206359i
$663$	537.212	−	537.212i	0.810274	−	0.810274i
$664$	235.044	+	198.272i	0.353982	+	0.298602i
$665$	888.905	+	289.739i	1.33670	+	0.435698i
$666$	744.496	+	177.132i	1.11786	+	0.265965i
$667$		−	1027.82i		−	1.54096i
$668$	−147.150	−	446.672i	−0.220284	−	0.668671i
$669$	−451.747	+	451.747i	−0.675257	+	0.675257i
$670$	430.869	−	704.866i	0.643089	−	1.05204i
$671$	−119.953			−0.178768
$672$	284.485	−	707.120i	0.423341	−	1.05226i
$673$	−822.674	−	822.674i	−1.22240	−	1.22240i	−0.966777	−	0.255621i	$-0.917720\pi$
$673$	−822.674	−	822.674i	−1.22240	−	1.22240i	−0.255621	−	0.966777i	$-0.582280\pi$
$674$	10.2452	+	16.6424i	0.0152006	+	0.0246920i
$675$	78.9103	−	108.186i	0.116904	−	0.160276i
$676$	−268.269	−	135.314i	−0.396848	−	0.200169i
$677$		−	796.004i		−	1.17578i	−0.808941	−	0.587890i	$-0.799959\pi$
$677$		−	796.004i		−	1.17578i	0.808941	−	0.587890i	$-0.200041\pi$
$678$	−476.294	−	773.695i	−0.702499	−	1.14114i
$679$	870.840			1.28253
$680$	163.389	−	696.458i	0.240278	−	1.02420i
$681$			431.172i			0.633145i
$682$	71.7733	+	116.589i	0.105239	+	0.170952i
$683$	949.934			1.39083			0.695413	−	0.718610i	$-0.255222\pi$
$683$	949.934			1.39083			0.695413	+	0.718610i	$0.255222\pi$
$684$	−1336.59	+	440.320i	−1.95408	+	0.643742i
$685$	−267.605	−	526.417i	−0.390664	−	0.768492i
$686$	390.099	+	633.678i	0.568657	+	0.923729i
$687$	−775.782	+	775.782i	−1.12923	+	1.12923i
$688$	356.041	+	481.734i	0.517502	+	0.700195i
$689$		−	313.623i		−	0.455186i
$690$	1446.76	−	349.030i	2.09675	−	0.505841i
$691$	−882.517	−	882.517i	−1.27716	−	1.27716i	−0.942251	−	0.334908i	$-0.891295\pi$
$691$	−882.517	−	882.517i	−1.27716	−	1.27716i	−0.334908	−	0.942251i	$-0.608705\pi$
$692$	57.3404	−	113.681i	0.0828618	−	0.164279i
$693$	−89.5988			−0.129291
$694$	−997.995	−	237.446i	−1.43803	−	0.342141i
$695$	2.84021	+	5.58709i	0.00408663	+	0.00803898i
$696$	1058.19	−	89.7994i	1.52038	−	0.129022i
$697$	−28.2812	−	28.2812i	−0.0405756	−	0.0405756i
$698$	497.208	+	807.668i	0.712333	+	1.15712i
$699$	−778.726	−	778.726i	−1.11406	−	1.11406i
$700$	166.738	−	517.060i	0.238197	−	0.738657i
$701$	−42.7867	−	42.7867i	−0.0610367	−	0.0610367i	0.675930	−	0.736966i	$-0.263742\pi$
$701$	−42.7867	−	42.7867i	−0.0610367	−	0.0610367i	−0.736966	+	0.675930i	$0.763742\pi$
$702$	−24.0252	+	100.979i	−0.0342240	+	0.143845i
$703$	−911.042	−	911.042i	−1.29593	−	1.29593i
$704$	−84.2762	−	59.6683i	−0.119711	−	0.0847561i
$705$	−245.176	−	482.295i	−0.347767	−	0.684107i
$706$	−734.554	+	452.199i	−1.04045	+	0.640508i
$707$	102.242			0.144613
$708$	501.079	−	165.073i	0.707739	−	0.233155i
$709$	239.953	+	239.953i	0.338439	+	0.338439i	0.855780	−	0.517341i	$-0.173078\pi$
$709$	239.953	+	239.953i	0.338439	+	0.338439i	−0.517341	+	0.855780i	$0.673078\pi$
$710$	−121.367	−	74.1892i	−0.170940	−	0.104492i
$711$		−	569.062i		−	0.800368i
$712$	−712.528	+	844.675i	−1.00074	+	1.18634i
$713$	1018.40	−	1018.40i	1.42833	−	1.42833i
$714$	828.822	+	197.195i	1.16081	+	0.276184i
$715$	−35.4220	−	69.6800i	−0.0495412	−	0.0974546i
$716$	−1061.35	+	349.647i	−1.48233	+	0.488333i
$717$	1019.42			1.42179
$718$	−25.7610	+	108.275i	−0.0358788	+	0.150801i
$719$			840.915i			1.16956i	0.811191	+	0.584781i	$0.198819\pi$
$719$			840.915i			1.16956i	−0.811191	+	0.584781i	$0.801181\pi$
$720$	258.308	+	775.867i	0.358761	+	1.07759i
$721$	−287.833			−0.399214
$722$	1602.48	+	381.267i	2.21951	+	0.528071i
$723$			641.742i			0.887610i
$724$	−460.130	+	151.583i	−0.635538	+	0.209369i
$725$	747.862	−	117.021i	1.03153	−	0.161408i
$726$	240.295	−	1009.97i	0.330985	−	1.39115i
$727$	8.90967	+	8.90967i	0.0122554	+	0.0122554i	0.713208	−	0.700953i	$-0.247242\pi$
$727$	8.90967	+	8.90967i	0.0122554	+	0.0122554i	−0.700953	+	0.713208i	$0.747242\pi$
$728$	35.6092	+	419.615i	0.0489138	+	0.576394i
$729$	911.660			1.25056
$730$	−34.0632	−	141.195i	−0.0466619	−	0.193417i
$731$	−473.456	+	473.456i	−0.647683	+	0.647683i
$732$	−1238.34	+	407.952i	−1.69172	+	0.557312i
$733$			65.3306i			0.0891277i	0.999007	+	0.0445639i	$0.0141898\pi$
$733$			65.3306i			0.0891277i	−0.999007	+	0.0445639i	$0.985810\pi$
$734$	274.852	+	446.472i	0.374458	+	0.608272i
$735$	−406.102	−	132.369i	−0.552520	−	0.180094i
$736$	−405.437	+	1007.76i	−0.550866	+	1.36924i
$737$	94.2511	−	94.2511i	0.127885	−	0.127885i
$738$	44.4776	+	10.5822i	0.0602677	+	0.0143390i
$739$	254.204	−	254.204i	0.343984	−	0.343984i	−0.513879	−	0.857863i	$-0.671792\pi$
$739$	254.204	−	254.204i	0.343984	−	0.343984i	0.857863	+	0.513879i	$0.171792\pi$
$740$	−527.728	+	531.060i	−0.713146	+	0.717648i
$741$	1033.87	−	1033.87i	1.39523	−	1.39523i
$742$	299.493	−	184.371i	0.403630	−	0.248479i
$743$	6.53981	−	6.53981i	0.00880189	−	0.00880189i	−0.702692	−	0.711494i	$-0.748019\pi$
$743$	6.53981	−	6.53981i	0.00880189	−	0.00880189i	0.711494	+	0.702692i	$0.248019\pi$
$744$	1137.46	+	959.511i	1.52885	+	1.28966i
$745$	404.484	+	795.678i	0.542931	+	1.06802i
$746$	7.48633	−	31.4654i	0.0100353	−	0.0421788i
$747$		−	392.899i		−	0.525969i
$748$	51.9800	−	103.054i	0.0694919	−	0.137772i
$749$	23.6271	−	23.6271i	0.0315449	−	0.0315449i
$750$	418.679	+	1012.95i	0.558238	+	1.35060i
$751$	−512.529			−0.682462			−0.341231	−	0.939979i	$-0.610844\pi$
$751$	−512.529			−0.682462			−0.341231	+	0.939979i	$0.610844\pi$
$752$	390.523	+	58.5908i	0.519312	+	0.0779133i
$753$	754.774	+	754.774i	1.00236	+	1.00236i
$754$	−499.668	+	307.601i	−0.662690	+	0.407959i
$755$	−133.048	+	408.184i	−0.176222	+	0.540641i
$756$	−110.554	+	36.4203i	−0.146235	+	0.0481750i
$757$			109.439i			0.144570i	0.997384	+	0.0722849i	$0.0230291\pi$
$757$			109.439i			0.144570i	−0.997384	+	0.0722849i	$0.976971\pi$
$758$	−1126.74	+	693.635i	−1.48647	+	0.915085i
$759$	240.124			0.316369
$760$	314.443	−	1340.34i	0.413740	−	1.76360i
$761$			737.899i			0.969644i	0.874613	+	0.484822i	$0.161116\pi$
$761$			737.899i			0.969644i	−0.874613	+	0.484822i	$0.838884\pi$
$762$	848.365	−	522.262i	1.11334	−	0.685383i
$763$	884.980			1.15987
$764$	−23.9332	−	12.0719i	−0.0313262	−	0.0158009i
$765$	−814.796	+	414.203i	−1.06509	+	0.541442i
$766$	−333.114	+	205.069i	−0.434875	+	0.267714i
$767$	−206.113	+	206.113i	−0.268726	+	0.268726i
$768$	−1072.95	−	329.368i	−1.39708	−	0.428865i
$769$			1218.07i			1.58396i	0.610545	+	0.791981i	$0.290950\pi$
$769$			1218.07i			1.58396i	−0.610545	+	0.791981i	$0.709050\pi$
$770$	45.7170	−	74.7892i	0.0593728	−	0.0971288i
$771$	322.808	+	322.808i	0.418687	+	0.418687i
$772$	356.273	+	1081.47i	0.461494	+	1.40086i
$773$	−1341.89			−1.73595			−0.867973	−	0.496612i	$-0.834577\pi$
$773$	−1341.89			−1.73595			−0.867973	+	0.496612i	$0.834577\pi$
$774$	177.157	−	744.600i	0.228885	−	0.962016i
$775$	856.956	+	625.060i	1.10575	+	0.806529i
$776$	−108.432	−	1277.75i	−0.139732	−	1.64659i
$777$	−630.478	−	630.478i	−0.811427	−	0.811427i
$778$	859.372	−	529.038i	1.10459	−	0.679998i
$779$	−54.4273	−	54.4273i	−0.0698681	−	0.0698681i
$780$	−602.656	−	598.875i	−0.772636	−	0.767788i
$781$	−16.2286	−	16.2286i	−0.0207793	−	0.0207793i
$782$	−1181.21	−	281.035i	−1.51049	−	0.359380i
$783$	−114.678	−	114.678i	−0.146460	−	0.146460i
$784$	250.712	−	185.297i	0.319786	−	0.236348i
$785$	1060.04	+	345.522i	1.35037	+	0.440155i
$786$	120.813	+	196.249i	0.153706	+	0.249681i
$787$	1158.29			1.47178			0.735892	−	0.677099i	$-0.236763\pi$
$787$	1158.29			1.47178			0.735892	+	0.677099i	$0.236763\pi$
$788$	−97.6079	+	193.514i	−0.123868	+	0.245576i
$789$	−621.060	−	621.060i	−0.787149	−	0.787149i
$790$	475.003	+	290.359i	0.601269	+	0.367543i
$791$			562.918i			0.711654i
$792$	11.1564	+	131.465i	0.0140863	+	0.165991i
$793$	509.374	−	509.374i	0.642338	−	0.642338i
$794$	−132.967	+	558.867i	−0.167465	+	0.703863i
$795$	−219.890	+	674.610i	−0.276591	+	0.848566i
$796$	−293.712	−	148.148i	−0.368985	−	0.186115i
$797$	−67.0596			−0.0841400			−0.0420700	−	0.999115i	$-0.513395\pi$
$797$	−67.0596			−0.0841400			−0.0420700	+	0.999115i	$0.513395\pi$
$798$	1595.07	+	379.503i	1.99883	+	0.475568i
$799$			441.396i			0.552436i
$800$	−779.425	−	180.267i	−0.974282	−	0.225334i
$801$	1411.96			1.76274
$802$	−82.6355	+	347.321i	−0.103037	+	0.433069i
$803$		−	23.4346i		−	0.0291838i
$804$	652.461	−	1293.54i	0.811518	−	1.60889i
$805$	−876.701	−	285.761i	−1.08907	−	0.354983i
$806$	−799.870	−	190.307i	−0.992395	−	0.236113i
$807$	226.950	+	226.950i	0.281227	+	0.281227i
$808$	−12.7306	−	150.016i	−0.0157557	−	0.185663i
$809$	602.411			0.744637			0.372318	−	0.928105i	$-0.378563\pi$
$809$	602.411			0.744637			0.372318	+	0.928105i	$0.378563\pi$
$810$	−357.328	+	584.558i	−0.441145	+	0.721676i
$811$	−47.6019	+	47.6019i	−0.0586953	+	0.0586953i	−0.735845	−	0.677150i	$-0.763215\pi$
$811$	−47.6019	+	47.6019i	−0.0586953	+	0.0586953i	0.677150	+	0.735845i	$0.263215\pi$
$812$	−587.485	−	296.326i	−0.723503	−	0.364933i
$813$		−	404.442i		−	0.497469i
$814$	−102.866	+	63.3255i	−0.126371	+	0.0777955i
$815$	176.918	−	542.774i	0.217077	−	0.665980i
$816$	186.137	−	1240.65i	0.228110	−	1.52041i
$817$	−911.169	+	911.169i	−1.11526	+	1.11526i
$818$	−27.8011	+	116.849i	−0.0339867	+	0.142848i
$819$	380.476	−	380.476i	0.464562	−	0.464562i
$820$	−31.5274	+	31.7265i	−0.0384481	+	0.0386908i
$821$	569.537	−	569.537i	0.693711	−	0.693711i	−0.269335	−	0.963046i	$-0.586804\pi$
$821$	569.537	−	569.537i	0.693711	−	0.693711i	0.963046	+	0.269335i	$0.0868040\pi$
$822$	−542.908	−	881.903i	−0.660472	−	1.07287i
$823$	142.304	−	142.304i	0.172909	−	0.172909i	−0.615347	−	0.788256i	$-0.710984\pi$
$823$	142.304	−	142.304i	0.172909	−	0.172909i	0.788256	+	0.615347i	$0.210984\pi$
$824$	35.8394	+	422.327i	0.0434944	+	0.512533i
$825$	27.3388	+	174.718i	0.0331380	+	0.211780i
$826$	−317.995	−	75.6582i	−0.384982	−	0.0915959i
$827$			829.310i			1.00279i	0.865217	+	0.501397i	$0.167180\pi$
$827$			829.310i			1.00279i	−0.865217	+	0.501397i	$0.832820\pi$
$828$	1318.24	−	434.275i	1.59207	−	0.524486i
$829$	178.863	−	178.863i	0.215758	−	0.215758i	−0.590950	−	0.806708i	$-0.701247\pi$
$829$	178.863	−	178.863i	0.215758	−	0.215758i	0.806708	+	0.590950i	$0.201247\pi$
$830$	327.958	+	200.474i	0.395130	+	0.241534i
$831$	743.671			0.894911
$832$	611.253	−	104.496i	0.734679	−	0.125597i
$833$	246.404	+	246.404i	0.295803	+	0.295803i
$834$	5.76212	+	9.36001i	0.00690901	+	0.0112230i
$835$	−266.393	−	524.034i	−0.319034	−	0.627585i
$836$	100.036	−	198.327i	0.119660	−	0.237233i
$837$		−	227.255i		−	0.271511i
$838$	−383.846	−	623.522i	−0.458051	−	0.744060i
$839$	−1632.17			−1.94537			−0.972686	−	0.232127i	$-0.925432\pi$
$839$	−1632.17			−1.94537			−0.972686	+	0.232127i	$0.925432\pi$
$840$	217.607	−	927.567i	0.259056	−	1.10425i
$841$		−	75.7868i		−	0.0901151i
$842$	636.583	+	1034.07i	0.756037	+	1.22811i
$843$	−852.234			−1.01095
$844$	134.386	+	407.929i	0.159225	+	0.483328i
$845$	−357.089	−	116.393i	−0.422591	−	0.137744i
$846$	−264.509	−	429.670i	−0.312659	−	0.507885i
$847$	−454.829	+	454.829i	−0.536988	+	0.536988i
$848$	−307.812	−	416.479i	−0.362986	−	0.491131i
$849$		−	2295.94i		−	2.70429i
$850$	70.0028	−	891.464i	0.0823562	−	1.04878i
$851$	898.534	+	898.534i	1.05586	+	1.05586i
$852$	−222.729	−	112.344i	−0.261419	−	0.131859i
$853$	1087.76			1.27522			0.637608	−	0.770361i	$-0.279924\pi$
$853$	1087.76			1.27522			0.637608	+	0.770361i	$0.279924\pi$
$854$	785.873	+	186.977i	0.920227	+	0.218943i
$855$	−1568.08	+	797.135i	−1.83401	+	0.932322i
$856$	−37.6092	−	31.7253i	−0.0439360	−	0.0370623i
$857$	−753.252	−	753.252i	−0.878940	−	0.878940i	0.114485	−	0.993425i	$-0.463478\pi$
$857$	−753.252	−	753.252i	−0.878940	−	0.878940i	−0.993425	+	0.114485i	$0.963478\pi$
$858$	−71.8629	−	116.734i	−0.0837563	−	0.136054i
$859$	−656.780	−	656.780i	−0.764587	−	0.764587i	0.212561	−	0.977148i	$-0.431820\pi$
$859$	−656.780	−	656.780i	−0.764587	−	0.764587i	−0.977148	+	0.212561i	$0.931820\pi$
$860$	531.134	+	527.801i	0.617597	+	0.613722i
$861$	−37.6659	−	37.6659i	−0.0437467	−	0.0437467i
$862$	191.019	−	802.861i	0.221600	−	0.931393i
$863$	−6.97025	−	6.97025i	−0.00807676	−	0.00807676i	0.703057	−	0.711134i	$-0.251818\pi$
$863$	−6.97025	−	6.97025i	−0.00807676	−	0.00807676i	−0.711134	+	0.703057i	$0.751818\pi$
$864$	67.2037	+	157.677i	0.0777821	+	0.182496i
$865$	49.3225	−	151.319i	0.0570202	−	0.174935i
$866$	490.385	−	301.886i	0.566264	−	0.348598i
$867$	135.225			0.155968
$868$	−288.490	−	875.710i	−0.332362	−	1.00888i
$869$	63.5150	+	63.5150i	0.0730898	+	0.0730898i
$870$	1290.46	−	311.325i	1.48329	−	0.357845i
$871$			800.465i			0.919018i
$872$	−110.193	−	1298.50i	−0.126368	−	1.48911i
$873$	−1158.57	+	1158.57i	−1.32712	+	1.32712i
$874$	−2273.23	−	540.854i	−2.60095	−	0.618826i
$875$	108.110	−	670.439i	0.123555	−	0.766216i
$876$	−79.6995	−	241.927i	−0.0909811	−	0.276173i
$877$	−1467.43			−1.67324			−0.836618	−	0.547787i	$-0.815471\pi$
$877$	−1467.43			−1.67324			−0.836618	+	0.547787i	$0.815471\pi$
$878$	−88.0447	+	370.056i	−0.100279	+	0.421476i
$879$			1193.94i			1.35829i
$880$	−115.428	−	57.7667i	−0.131168	−	0.0656439i
$881$	−889.409			−1.00954			−0.504772	−	0.863252i	$-0.668424\pi$
$881$	−889.409			−1.00954			−0.504772	+	0.863252i	$0.668424\pi$
$882$	−387.517	−	92.1991i	−0.439362	−	0.104534i
$883$		−	1602.95i		−	1.81535i	−0.419675	−	0.907674i	$-0.637856\pi$
$883$		−	1602.95i		−	1.81535i	0.419675	−	0.907674i	$-0.362144\pi$
$884$	216.881	+	658.342i	0.245341	+	0.744730i
$885$	587.864	−	298.842i	0.664253	−	0.337674i
$886$	−118.245	+	496.990i	−0.133460	+	0.560937i
$887$	428.954	+	428.954i	0.483601	+	0.483601i	0.906280	−	0.422679i	$-0.138910\pi$
$887$	428.954	+	428.954i	0.483601	+	0.483601i	−0.422679	+	0.906280i	$0.638910\pi$
$888$	−846.575	+	1003.58i	−0.953350	+	1.13016i
$889$	−617.246			−0.694315
$890$	−720.440	+	1178.58i	−0.809483	+	1.32425i
$891$	−78.1641	+	78.1641i	−0.0877263	+	0.0877263i
$892$	−182.378	−	553.606i	−0.204459	−	0.620635i
$893$			849.469i			0.951253i
$894$	820.604	+	1332.99i	0.917901	+	1.49104i
$895$	−1245.17	+	632.985i	−1.39125	+	0.707245i
$896$	459.128	+	522.283i	0.512420	+	0.582905i
$897$	−1019.67	+	1019.67i	−1.13676	+	1.13676i
$898$	−1108.92	−	263.838i	−1.23488	−	0.293806i
$899$	908.384	−	908.384i	1.01044	−	1.01044i
$900$	466.072	+	909.731i	0.517857	+	1.01081i
$901$	409.323	−	409.323i	0.454298	−	0.454298i
$902$	−6.14542	+	3.78318i	−0.00681310	+	0.00419421i
$903$	−630.566	+	630.566i	−0.698302	+	0.698302i
$904$	825.950	−	70.0915i	0.913661	−	0.0775348i
$905$	−539.822	+	274.419i	−0.596488	+	0.303226i
$906$	−174.267	+	732.455i	−0.192348	+	0.808449i
$907$			1609.72i			1.77478i	0.461024	+	0.887388i	$0.347482\pi$
$907$			1609.72i			1.77478i	−0.461024	+	0.887388i	$0.652518\pi$
$908$	−351.231	−	177.160i	−0.386819	−	0.195110i
$909$	−136.023	+	136.023i	−0.149641	+	0.149641i
$910$	123.453	+	511.723i	0.135663	+	0.562333i
$911$	1117.02			1.22615			0.613074	−	0.790025i	$-0.289933\pi$
$911$	1117.02			1.22615			0.613074	+	0.790025i	$0.289933\pi$
$912$	358.222	−	2387.64i	0.392788	−	2.61803i
$913$	43.8529	+	43.8529i	0.0480316	+	0.0480316i
$914$	694.643	−	427.629i	0.760004	−	0.467866i
$915$	−1452.81	+	738.539i	−1.58777	+	0.807146i
$916$	−313.196	−	950.704i	−0.341917	−	1.03789i
$917$		−	142.786i		−	0.155709i
$918$	−163.149	+	100.436i	−0.177722	+	0.109407i
$919$	750.127			0.816242			0.408121	−	0.912928i	$-0.366184\pi$
$919$	750.127			0.816242			0.408121	+	0.912928i	$0.366184\pi$
$920$	−310.126	+	1321.93i	−0.337093	+	1.43688i
$921$		−	493.908i		−	0.536273i
$922$	444.806	−	273.827i	0.482437	−	0.296993i
$923$	137.828			0.149326
$924$	69.2288	−	137.250i	0.0749229	−	0.148539i
$925$	−551.489	+	756.091i	−0.596205	+	0.817396i
$926$	−559.657	+	344.530i	−0.604381	+	0.372063i
$927$	382.936	−	382.936i	0.413091	−	0.413091i
$928$	−361.638	+	898.892i	−0.389696	+	0.968634i
$929$		−	1640.80i		−	1.76620i	−0.469181	−	0.883102i	$-0.655451\pi$
$929$		−	1640.80i		−	1.76620i	0.469181	−	0.883102i	$-0.344549\pi$
$930$	1587.11	+	970.165i	1.70657	+	1.04319i
$931$	474.206	+	474.206i	0.509351	+	0.509351i
$932$	954.313	−	314.385i	1.02394	−	0.337323i
$933$	−1113.74			−1.19372
$934$	167.097	−	702.318i	0.178905	−	0.751947i
$935$	44.7116	−	137.173i	0.0478199	−	0.146709i
$936$	−605.634	−	510.885i	−0.647045	−	0.545817i
$937$	−514.395	−	514.395i	−0.548980	−	0.548980i	0.377166	−	0.926146i	$-0.376899\pi$
$937$	−514.395	−	514.395i	−0.548980	−	0.548980i	−0.926146	+	0.377166i	$0.876899\pi$
$938$	−764.401	+	470.573i	−0.814926	+	0.501677i
$939$	−98.6087	−	98.6087i	−0.105015	−	0.105015i
$940$	493.615	−	1.55341i	0.525122	−	0.00165256i
$941$	1074.54	+	1074.54i	1.14191	+	1.14191i	0.988101	+	0.153808i	$0.0491538\pi$
$941$	1074.54	+	1074.54i	1.14191	+	1.14191i	0.153808	+	0.988101i	$0.450846\pi$
$942$	1902.16	+	452.568i	2.01928	+	0.480433i
$943$	53.6801	+	53.6801i	0.0569248	+	0.0569248i
$944$	−71.4156	+	476.004i	−0.0756522	+	0.504241i
$945$	−129.701	+	65.9337i	−0.137250	+	0.0697711i
$946$	63.3343	+	102.881i	0.0669496	+	0.108753i
$947$	173.864			0.183595			0.0917974	−	0.995778i	$-0.470739\pi$
$947$	173.864			0.183595			0.0917974	+	0.995778i	$0.470739\pi$
$948$	871.708	+	439.687i	0.919523	+	0.463805i
$949$	99.5137	+	99.5137i	0.104862	+	0.104862i
$950$	134.721	−	1715.63i	0.141811	−	1.80592i
$951$		−	1665.90i		−	1.75174i
$952$	−501.182	+	594.132i	−0.526452	+	0.624088i
$953$	−597.594	+	597.594i	−0.627066	+	0.627066i	−0.947329	−	0.320263i	$-0.896229\pi$
$953$	−597.594	+	597.594i	−0.627066	+	0.627066i	0.320263	+	0.947329i	$0.396229\pi$
$954$	−153.160	+	643.737i	−0.160545	+	0.674777i
$955$	−31.8571	−	10.3839i	−0.0333582	−	0.0108731i
$956$	−418.861	+	830.418i	−0.438139	+	0.868638i
$957$	214.183			0.223807
$958$	−216.225	−	51.4449i	−0.225705	−	0.0537003i
$959$			641.648i			0.669080i
$960$	−1388.08	−	203.792i	−1.44592	−	0.212283i
$961$	839.116			0.873170
$962$	167.908	−	705.724i	0.174540	−	0.733601i
$963$			62.8675i			0.0652830i
$964$	−522.761	−	263.680i	−0.542284	−	0.273527i
$965$	644.981	+	1268.77i	0.668374	+	1.31479i
$966$	−1573.17	−	374.293i	−1.62854	−	0.387467i
$967$	−734.726	−	734.726i	−0.759800	−	0.759800i	0.216486	−	0.976286i	$-0.430540\pi$
$967$	−734.726	−	734.726i	−0.759800	−	0.759800i	−0.976286	+	0.216486i	$0.930540\pi$
$968$	723.987	+	610.722i	0.747921	+	0.630911i
$969$	2698.68			2.78502
$970$	−375.923	−	1558.23i	−0.387549	−	1.60642i
$971$	797.762	−	797.762i	0.821588	−	0.821588i	−0.164748	−	0.986336i	$-0.552681\pi$
$971$	797.762	−	797.762i	0.821588	−	0.821588i	0.986336	+	0.164748i	$0.0526810\pi$
$972$	−627.937	+	1244.92i	−0.646025	+	1.28079i
$973$		−	6.81008i		−	0.00699905i
$974$	1126.23	−	693.319i	1.15630	−	0.711827i
$975$	−858.025	−	625.840i	−0.880026	−	0.641887i
$976$	176.492	−	1176.37i	0.180832	−	1.20529i
$977$	1242.00	−	1242.00i	1.27124	−	1.27124i	0.325795	−	0.945440i	$-0.394368\pi$
$977$	1242.00	−	1242.00i	1.27124	−	1.27124i	0.945440	−	0.325795i	$-0.105632\pi$
$978$	231.728	−	973.965i	0.236941	−	0.995875i
$979$	−157.594	+	157.594i	−0.160974	+	0.160974i
$980$	274.687	−	276.422i	0.280293	−	0.282063i
$981$	−1177.38	+	1177.38i	−1.20019	+	1.20019i
$982$	494.707	+	803.604i	0.503775	+	0.818334i
$983$	17.3080	−	17.3080i	0.0176073	−	0.0176073i	−0.698248	−	0.715856i	$-0.746037\pi$
$983$	17.3080	−	17.3080i	0.0176073	−	0.0176073i	0.715856	+	0.698248i	$0.246037\pi$
$984$	−50.5759	+	59.9558i	−0.0513983	+	0.0609307i
$985$	−83.9594	+	257.583i	−0.0852380	+	0.261506i
$986$	−1053.60	−	250.675i	−1.06856	−	0.254235i
$987$			587.868i			0.595611i
$988$	417.389	+	1266.98i	0.422458	+	1.28237i
$989$	898.659	−	898.659i	0.908655	−	0.908655i
$990$	38.6778	+	160.323i	0.0390685	+	0.161942i
$991$	504.008			0.508585			0.254293	−	0.967127i	$-0.418157\pi$
$991$	504.008			0.508585			0.254293	+	0.967127i	$0.418157\pi$
$992$	−1248.98	+	532.330i	−1.25905	+	0.536623i
$993$	−248.663	−	248.663i	−0.250416	−	0.250416i
$994$	81.0256	+	131.618i	0.0815147	+	0.132413i
$995$	−390.956	−	127.432i	−0.392920	−	0.128073i
$996$	601.856	+	303.575i	0.604273	+	0.304794i
$997$			1524.58i			1.52917i	0.644526	+	0.764583i	$0.277055\pi$
$997$			1524.58i			1.52917i	−0.644526	+	0.764583i	$0.722945\pi$
$998$	256.659	+	416.919i	0.257174	+	0.417754i
$999$	200.507			0.200707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.i.a.13.10	✓	44
4.3	odd	2		320.3.i.a.273.3		44
5.2	odd	4		80.3.t.a.77.2	yes	44
5.3	odd	4		400.3.t.b.157.21		44
5.4	even	2		400.3.i.b.93.13		44
8.3	odd	2		640.3.i.a.33.20		44
8.5	even	2		640.3.i.b.33.3		44
16.3	odd	4		640.3.t.a.353.20		44
16.5	even	4		80.3.t.a.53.2	yes	44
16.11	odd	4		320.3.t.a.113.3		44
16.13	even	4		640.3.t.b.353.3		44
20.7	even	4		320.3.t.a.17.3		44
40.27	even	4		640.3.t.a.417.20		44
40.37	odd	4		640.3.t.b.417.3		44
80.27	even	4		320.3.i.a.177.20		44
80.37	odd	4	inner	80.3.i.a.37.10	yes	44
80.53	odd	4		400.3.i.b.357.13		44
80.67	even	4		640.3.i.a.97.3		44
80.69	even	4		400.3.t.b.293.21		44
80.77	odd	4		640.3.i.b.97.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.10	✓	44	1.1	even	1	trivial
80.3.i.a.37.10	yes	44	80.37	odd	4	inner
80.3.t.a.53.2	yes	44	16.5	even	4
80.3.t.a.77.2	yes	44	5.2	odd	4
320.3.i.a.177.20		44	80.27	even	4
320.3.i.a.273.3		44	4.3	odd	2
320.3.t.a.17.3		44	20.7	even	4
320.3.t.a.113.3		44	16.11	odd	4
400.3.i.b.93.13		44	5.4	even	2
400.3.i.b.357.13		44	80.53	odd	4
400.3.t.b.157.21		44	5.3	odd	4
400.3.t.b.293.21		44	80.69	even	4
640.3.i.a.33.20		44	8.3	odd	2
640.3.i.a.97.3		44	80.67	even	4
640.3.i.b.33.3		44	8.5	even	2
640.3.i.b.97.20		44	80.77	odd	4
640.3.t.a.353.20		44	16.3	odd	4
640.3.t.a.417.20		44	40.27	even	4
640.3.t.b.353.3		44	16.13	even	4
640.3.t.b.417.3		44	40.37	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.462923 + 1.94569i) q^{2} +4.38426i q^{3} +(-3.57140 - 1.80141i) q^{4} +(-4.75384 - 1.54952i) q^{5} +(-8.53040 - 2.02957i) q^{6} +(3.84157 + 3.84157i) q^{7} +(5.15826 - 6.11493i) q^{8} -10.2217 q^{9} +O(q^{10})\)	\(q+(-0.462923 + 1.94569i) q^{2} +4.38426i q^{3} +(-3.57140 - 1.80141i) q^{4} +(-4.75384 - 1.54952i) q^{5} +(-8.53040 - 2.02957i) q^{6} +(3.84157 + 3.84157i) q^{7} +(5.15826 - 6.11493i) q^{8} -10.2217 q^{9} +(5.21554 - 8.53218i) q^{10} +(1.14088 - 1.14088i) q^{11} +(7.89784 - 15.6580i) q^{12} +9.68938i q^{13} +(-9.25284 + 5.69614i) q^{14} +(6.79348 - 20.8421i) q^{15} +(9.50986 + 12.8671i) q^{16} +(-12.6460 + 12.6460i) q^{17} +(4.73186 - 19.8883i) q^{18} +(-24.3373 + 24.3373i) q^{19} +(14.1866 + 14.0976i) q^{20} +(-16.8424 + 16.8424i) q^{21} +(1.69166 + 2.74794i) q^{22} +(24.0032 - 24.0032i) q^{23} +(26.8094 + 22.6152i) q^{24} +(20.1980 + 14.7323i) q^{25} +(-18.8525 - 4.48544i) q^{26} -5.35627i q^{27} +(-6.79956 - 20.6400i) q^{28} +(21.4101 - 21.4101i) q^{29} +(37.4073 + 22.8663i) q^{30} +42.4278 q^{31} +(-29.4377 + 12.5467i) q^{32} +(5.00192 + 5.00192i) q^{33} +(-18.7511 - 30.4593i) q^{34} +(-12.3096 - 24.2148i) q^{35} +(36.5058 + 18.4135i) q^{36} +37.4340i q^{37} +(-36.0865 - 58.6191i) q^{38} -42.4807 q^{39} +(-33.9967 + 21.0766i) q^{40} +2.23637i q^{41} +(-24.9733 - 40.5668i) q^{42} +37.4392 q^{43} +(-6.12974 + 2.01936i) q^{44} +(48.5924 + 15.8387i) q^{45} +(35.5911 + 57.8143i) q^{46} +(17.4520 - 17.4520i) q^{47} +(-56.4127 + 41.6937i) q^{48} -19.4847i q^{49} +(-38.0146 + 32.4791i) q^{50} +(-55.4434 - 55.4434i) q^{51} +(17.4545 - 34.6047i) q^{52} -32.3677 q^{53} +(10.4216 + 2.47954i) q^{54} +(-7.19138 + 3.65575i) q^{55} +(43.3067 - 3.67508i) q^{56} +(-106.701 - 106.701i) q^{57} +(31.7462 + 51.5687i) q^{58} +(21.2720 + 21.2720i) q^{59} +(-61.8073 + 62.1976i) q^{60} +(-52.5704 - 52.5704i) q^{61} +(-19.6408 + 82.5512i) q^{62} +(-39.2674 - 39.2674i) q^{63} +(-10.7846 - 63.0848i) q^{64} +(15.0139 - 46.0618i) q^{65} +(-12.0477 + 7.41667i) q^{66} +82.6126 q^{67} +(67.9446 - 22.3834i) q^{68} +(105.236 + 105.236i) q^{69} +(52.8128 - 12.7411i) q^{70} -14.2246i q^{71} +(-52.7263 + 62.5050i) q^{72} +(10.2704 - 10.2704i) q^{73} +(-72.8348 - 17.3291i) q^{74} +(-64.5903 + 88.5532i) q^{75} +(130.760 - 43.0769i) q^{76} +8.76554 q^{77} +(19.6653 - 82.6542i) q^{78} +55.6719i q^{79} +(-25.2705 - 75.9039i) q^{80} -68.5121 q^{81} +(-4.35129 - 1.03527i) q^{82} +38.4377i q^{83} +(90.4911 - 29.8110i) q^{84} +(79.7123 - 40.5219i) q^{85} +(-17.3315 + 72.8450i) q^{86} +(93.8675 + 93.8675i) q^{87} +(-1.09144 - 12.8614i) q^{88} -138.133 q^{89} +(-53.3117 + 87.2135i) q^{90} +(-37.2224 + 37.2224i) q^{91} +(-128.965 + 42.4855i) q^{92} +186.014i q^{93} +(25.8772 + 42.0351i) q^{94} +(153.407 - 77.9845i) q^{95} +(-55.0081 - 129.063i) q^{96} +(113.344 - 113.344i) q^{97} +(37.9112 + 9.01994i) q^{98} +(-11.6618 + 11.6618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Introduction

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