LMFDB - Embedded newform 80.3.t.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(53,80)]

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, 1, 3]))

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

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

chi := DirichletCharacter("80.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.t (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			53.2
Character	$\chi$	$=$	80.53
Dual form			80.3.t.a.77.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94569 + 0.462923i) q^{2} +4.38426 q^{3} +(3.57140 - 1.80141i) q^{4} +(1.54952 - 4.75384i) q^{5} +(-8.53040 + 2.02957i) q^{6} +(-3.84157 - 3.84157i) q^{7} +(-6.11493 + 5.15826i) q^{8} +10.2217 q^{9} +O(q^{10})$	\(q+(-1.94569 + 0.462923i) q^{2} +4.38426 q^{3} +(3.57140 - 1.80141i) q^{4} +(1.54952 - 4.75384i) q^{5} +(-8.53040 + 2.02957i) q^{6} +(-3.84157 - 3.84157i) q^{7} +(-6.11493 + 5.15826i) q^{8} +10.2217 q^{9} +(-0.814216 + 9.96680i) q^{10} +(1.14088 + 1.14088i) q^{11} +(15.6580 - 7.89784i) q^{12} +9.68938 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} +(-19.8883 + 4.73186i) q^{18} +(24.3373 + 24.3373i) q^{19} +(-3.02965 - 19.7692i) q^{20} +(-16.8424 - 16.8424i) q^{21} +(-2.74794 - 1.69166i) 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} +5.35627 q^{27} +(-20.6400 - 6.79956i) q^{28} +(-21.4101 - 21.4101i) q^{29} +(-3.56973 + 43.6970i) q^{30} +42.4278 q^{31} +(-12.5467 + 29.4377i) q^{32} +(5.00192 + 5.00192i) q^{33} +(18.7511 - 30.4593i) q^{34} +(-24.2148 + 12.3096i) q^{35} +(36.5058 - 18.4135i) q^{36} -37.4340 q^{37} +(-58.6191 - 36.0865i) q^{38} +42.4807 q^{39} +(15.0464 + 37.0622i) q^{40} -2.23637i q^{41} +(40.5668 + 24.9733i) q^{42} +37.4392i q^{43} +(6.12974 + 2.01936i) q^{44} +(15.8387 - 48.5924i) q^{45} +(35.5911 - 57.8143i) q^{46} +(17.4520 - 17.4520i) q^{47} +(41.6937 - 56.4127i) q^{48} -19.4847i q^{49} +(46.1189 + 19.3144i) q^{50} +(-55.4434 + 55.4434i) q^{51} +(34.6047 - 17.4545i) q^{52} -32.3677i 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} +(51.5687 + 31.7462i) q^{58} +(-21.2720 + 21.2720i) q^{59} +(-13.2828 - 86.6732i) q^{60} +(-52.5704 + 52.5704i) q^{61} +(-82.5512 + 19.6408i) 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} -82.6126i q^{67} +(-22.3834 + 67.9446i) q^{68} +(-105.236 + 105.236i) q^{69} +(41.4160 - 35.1602i) q^{70} +14.2246i q^{71} +(-62.5050 + 52.7263i) q^{72} +(-10.2704 + 10.2704i) q^{73} +(72.8348 - 17.3291i) q^{74} +(-88.5532 - 64.5903i) q^{75} +(130.760 + 43.0769i) q^{76} -8.76554i q^{77} +(-82.6542 + 19.6653i) q^{78} +55.6719i q^{79} +(-46.4325 - 65.1462i) q^{80} -68.5121 q^{81} +(1.03527 + 4.35129i) q^{82} +38.4377 q^{83} +(-90.4911 - 29.8110i) q^{84} +(40.5219 + 79.7123i) q^{85} +(-17.3315 - 72.8450i) q^{86} +(-93.8675 - 93.8675i) q^{87} +(-12.8614 - 1.09144i) q^{88} +138.133 q^{89} +(-8.32268 + 101.878i) q^{90} +(-37.2224 - 37.2224i) q^{91} +(-42.4855 + 128.965i) q^{92} +186.014 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} +(9.01994 + 37.9112i) q^{98} +(11.6618 + 11.6618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} - 4 q^{3} - 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^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9	\( 44 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} + 108 q^{9} - 10 q^{10} - 4 q^{11} - 44 q^{12} - 4 q^{13} - 4 q^{15} + 24 q^{16} - 4 q^{17} - 42 q^{18} - 32 q^{19} - 44 q^{20} - 4 q^{21} + 16 q^{22} - 36 q^{24} - 52 q^{26} - 40 q^{27} - 104 q^{28} - 160 q^{30} - 8 q^{31} - 12 q^{32} - 4 q^{33} + 88 q^{34} - 4 q^{35} - 116 q^{36} - 4 q^{37} - 68 q^{38} - 72 q^{39} + 200 q^{40} + 244 q^{42} + 168 q^{44} - 70 q^{45} + 108 q^{46} - 4 q^{47} - 4 q^{48} + 206 q^{50} - 100 q^{51} + 264 q^{52} - 228 q^{54} - 172 q^{56} - 36 q^{57} + 332 q^{58} - 64 q^{59} + 364 q^{60} - 36 q^{61} + 84 q^{62} - 200 q^{63} + 176 q^{64} - 4 q^{65} + 276 q^{66} + 440 q^{68} + 60 q^{69} + 472 q^{70} - 288 q^{72} - 48 q^{73} - 284 q^{74} - 324 q^{75} + 252 q^{76} - 132 q^{78} - 588 q^{80} + 100 q^{81} - 388 q^{82} + 156 q^{83} - 288 q^{84} - 52 q^{85} + 20 q^{86} - 36 q^{87} + 160 q^{88} - 554 q^{90} + 188 q^{91} - 352 q^{92} - 40 q^{93} + 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 818 q^{98} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9 - 10 * q^10 - 4 * q^11 - 44 * q^12 - 4 * q^13 - 4 * q^15 + 24 * q^16 - 4 * q^17 - 42 * q^18 - 32 * q^19 - 44 * q^20 - 4 * q^21 + 16 * q^22 - 36 * q^24 - 52 * q^26 - 40 * q^27 - 104 * q^28 - 160 * q^30 - 8 * q^31 - 12 * q^32 - 4 * q^33 + 88 * q^34 - 4 * q^35 - 116 * q^36 - 4 * q^37 - 68 * q^38 - 72 * q^39 + 200 * q^40 + 244 * q^42 + 168 * q^44 - 70 * q^45 + 108 * q^46 - 4 * q^47 - 4 * q^48 + 206 * q^50 - 100 * q^51 + 264 * q^52 - 228 * q^54 - 172 * q^56 - 36 * q^57 + 332 * q^58 - 64 * q^59 + 364 * q^60 - 36 * q^61 + 84 * q^62 - 200 * q^63 + 176 * q^64 - 4 * q^65 + 276 * q^66 + 440 * q^68 + 60 * q^69 + 472 * q^70 - 288 * q^72 - 48 * q^73 - 284 * q^74 - 324 * q^75 + 252 * q^76 - 132 * q^78 - 588 * q^80 + 100 * q^81 - 388 * q^82 + 156 * q^83 - 288 * q^84 - 52 * q^85 + 20 * q^86 - 36 * q^87 + 160 * q^88 - 554 * q^90 + 188 * q^91 - 352 * q^92 - 40 * q^93 + 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 818 * q^98 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.94569	+	0.462923i	−0.972844	+	0.231462i
$2$	−1.94569	+	0.462923i	−0.972844	+	0.231462i
$3$	4.38426			1.46142			0.730709	−	0.682689i	$-0.239189\pi$
$3$	4.38426			1.46142			0.730709	+	0.682689i	$0.239189\pi$
$4$	3.57140	−	1.80141i	0.892851	−	0.450352i
$5$	1.54952	−	4.75384i	0.309904	−	0.950768i
$5$	1.54952	−	4.75384i	0.309904	−	0.950768i
$6$	−8.53040	+	2.02957i	−1.42173	+	0.338262i
$7$	−3.84157	−	3.84157i	−0.548795	−	0.548795i	0.377297	−	0.926092i	$-0.376854\pi$
$7$	−3.84157	−	3.84157i	−0.548795	−	0.548795i	−0.926092	+	0.377297i	$0.876854\pi$
$8$	−6.11493	+	5.15826i	−0.764366	+	0.644783i
$9$	10.2217			1.13575
$10$	−0.814216	+	9.96680i	−0.0814216	+	0.996680i
$11$	1.14088	+	1.14088i	0.103716	+	0.103716i	0.757061	−	0.653344i	$-0.226635\pi$
$11$	1.14088	+	1.14088i	0.103716	+	0.103716i	−0.653344	+	0.757061i	$0.726635\pi$
$12$	15.6580	−	7.89784i	1.30483	−	0.658153i
$13$	9.68938			0.745337			0.372668	−	0.927965i	$-0.378443\pi$
$13$	9.68938			0.745337			0.372668	+	0.927965i	$0.378443\pi$
$14$	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	$0.426311\pi$
$18$	−19.8883	+	4.73186i	−1.10490	+	0.262881i
$19$	24.3373	+	24.3373i	1.28091	+	1.28091i	0.940150	+	0.340760i	$0.110684\pi$
$19$	24.3373	+	24.3373i	1.28091	+	1.28091i	0.340760	+	0.940150i	$0.389316\pi$
$20$	−3.02965	−	19.7692i	−0.151483	−	0.988460i
$21$	−16.8424	−	16.8424i	−0.802020	−	0.802020i
$22$	−2.74794	−	1.69166i	−0.124906	−	0.0768936i
$23$	−24.0032	+	24.0032i	−1.04362	+	1.04362i	−0.0446119	+	0.999004i	$0.514205\pi$
$23$	−24.0032	+	24.0032i	−1.04362	+	1.04362i	−0.999004	+	0.0446119i	$0.985795\pi$
$24$	−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
$27$	5.35627			0.198381
$28$	−20.6400	−	6.79956i	−0.737143	−	0.242841i
$29$	−21.4101	−	21.4101i	−0.738280	−	0.738280i	0.233965	−	0.972245i	$-0.424830\pi$
$29$	−21.4101	−	21.4101i	−0.738280	−	0.738280i	−0.972245	+	0.233965i	$0.924830\pi$
$30$	−3.56973	+	43.6970i	−0.118991	+	1.45657i
$31$	42.4278			1.36864			0.684319	−	0.729183i	$-0.260100\pi$
$31$	42.4278			1.36864			0.684319	+	0.729183i	$0.260100\pi$
$32$	−12.5467	+	29.4377i	−0.392085	+	0.919929i
$33$	5.00192	+	5.00192i	0.151573	+	0.151573i
$34$	18.7511	−	30.4593i	0.551502	−	0.895863i
$35$	−24.2148	+	12.3096i	−0.691850	+	0.351703i
$36$	36.5058	−	18.4135i	1.01405	−	0.511485i
$37$	−37.4340			−1.01173			−0.505865	−	0.862613i	$-0.668826\pi$
$37$	−37.4340			−1.01173			−0.505865	+	0.862613i	$0.668826\pi$
$38$	−58.6191	−	36.0865i	−1.54261	−	0.949644i
$39$	42.4807			1.08925
$40$	15.0464	+	37.0622i	0.376159	+	0.926555i
$41$		−	2.23637i		−	0.0545457i	−0.999628	−	0.0272728i	$-0.991318\pi$
$41$		−	2.23637i		−	0.0545457i	0.999628	−	0.0272728i	$-0.00868229\pi$
$42$	40.5668	+	24.9733i	0.965877	+	0.594603i
$43$			37.4392i			0.870679i	0.900266	+	0.435339i	$0.143372\pi$
$43$			37.4392i			0.870679i	−0.900266	+	0.435339i	$0.856628\pi$
$44$	6.12974	+	2.01936i	0.139312	+	0.0458944i
$45$	15.8387	−	48.5924i	0.351971	−	1.07983i
$46$	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	$0.165432\pi$
$48$	41.6937	−	56.4127i	0.868618	−	1.17527i
$49$		−	19.4847i		−	0.397648i
$50$	46.1189	+	19.3144i	0.922378	+	0.386288i
$51$	−55.4434	+	55.4434i	−1.08712	+	1.08712i
$52$	34.6047	−	17.4545i	0.665475	−	0.335664i
$53$		−	32.3677i		−	0.610712i	−0.952238	−	0.305356i	$-0.901225\pi$
$53$		−	32.3677i		−	0.610712i	0.952238	−	0.305356i	$-0.0987754\pi$
$54$	−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
$58$	51.5687	+	31.7462i	0.889115	+	0.547348i
$59$	−21.2720	+	21.2720i	−0.360543	+	0.360543i	−0.864013	−	0.503470i	$-0.832056\pi$
$59$	−21.2720	+	21.2720i	−0.360543	+	0.360543i	0.503470	+	0.864013i	$0.332056\pi$
$60$	−13.2828	−	86.6732i	−0.221379	−	1.44455i
$61$	−52.5704	+	52.5704i	−0.861809	+	0.861809i	−0.991548	−	0.129739i	$-0.958586\pi$
$61$	−52.5704	+	52.5704i	−0.861809	+	0.861809i	0.129739	+	0.991548i	$0.458586\pi$
$62$	−82.5512	+	19.6408i	−1.33147	+	0.316787i
$63$	−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
$67$		−	82.6126i		−	1.23302i	−0.787346	−	0.616512i	$-0.788545\pi$
$67$		−	82.6126i		−	1.23302i	0.787346	−	0.616512i	$-0.211455\pi$
$68$	−22.3834	+	67.9446i	−0.329168	+	0.999186i
$69$	−105.236	+	105.236i	−1.52516	+	1.52516i
$70$	41.4160	−	35.1602i	0.591657	−	0.502289i
$71$			14.2246i			0.200347i	0.994970	+	0.100174i	$0.0319398\pi$
$71$			14.2246i			0.200347i	−0.994970	+	0.100174i	$0.968060\pi$
$72$	−62.5050	+	52.7263i	−0.868125	+	0.732309i
$73$	−10.2704	+	10.2704i	−0.140690	+	0.140690i	−0.773944	−	0.633254i	$-0.781719\pi$
$73$	−10.2704	+	10.2704i	−0.140690	+	0.140690i	0.633254	+	0.773944i	$0.281719\pi$
$74$	72.8348	−	17.3291i	0.984255	−	0.234176i
$75$	−88.5532	−	64.5903i	−1.18071	−	0.861204i
$76$	130.760	+	43.0769i	1.72052	+	0.566802i
$77$		−	8.76554i		−	0.113838i
$78$	−82.6542	+	19.6653i	−1.05967	+	0.252119i
$79$			55.6719i			0.704707i	0.935867	+	0.352354i	$0.114619\pi$
$79$			55.6719i			0.704707i	−0.935867	+	0.352354i	$0.885381\pi$
$80$	−46.4325	−	65.1462i	−0.580406	−	0.814327i
$81$	−68.5121			−0.845828
$82$	1.03527	+	4.35129i	0.0126252	+	0.0530645i
$83$	38.4377			0.463105			0.231553	−	0.972822i	$-0.425619\pi$
$83$	38.4377			0.463105			0.231553	+	0.972822i	$0.425619\pi$
$84$	−90.4911	−	29.8110i	−1.07728	−	0.354893i
$85$	40.5219	+	79.7123i	0.476728	+	0.937792i
$86$	−17.3315	−	72.8450i	−0.201529	−	0.847035i
$87$	−93.8675	−	93.8675i	−1.07894	−	1.07894i
$88$	−12.8614	−	1.09144i	−0.146152	−	0.0124027i
$89$	138.133			1.55206			0.776030	−	0.630696i	$-0.217231\pi$
$89$	138.133			1.55206			0.776030	+	0.630696i	$0.217231\pi$
$90$	−8.32268	+	101.878i	−0.0924742	+	1.13197i
$91$	−37.2224	−	37.2224i	−0.409037	−	0.409037i
$92$	−42.4855	+	128.965i	−0.461799	+	1.40179i
$93$	186.014			2.00015
$94$	−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	$-0.0595323\pi$
$98$	9.01994	+	37.9112i	0.0920402	+	0.386849i
$99$	11.6618	+	11.6618i	0.117795	+	0.117795i
$100$	−98.6741	−	16.2303i	−0.986741	−	0.162303i
$101$	13.3073	+	13.3073i	0.131755	+	0.131755i	0.769909	−	0.638154i	$-0.220302\pi$
$101$	13.3073	+	13.3073i	0.131755	+	0.131755i	−0.638154	+	0.769909i	$0.720302\pi$
$102$	82.2095	−	133.542i	0.805975	−	1.30923i
$103$	37.4630	−	37.4630i	0.363718	−	0.363718i	−0.501462	−	0.865180i	$-0.667204\pi$
$103$	37.4630	−	37.4630i	0.363718	−	0.363718i	0.865180	+	0.501462i	$0.167204\pi$
$104$	−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
$107$	6.15039			0.0574803			0.0287401	−	0.999587i	$-0.490850\pi$
$107$	6.15039			0.0574803			0.0287401	+	0.999587i	$0.490850\pi$
$108$	19.1294	−	9.64884i	0.177124	−	0.0893411i
$109$	−115.185	−	115.185i	−1.05674	−	1.05674i	−0.998290	−	0.0584506i	$-0.981384\pi$
$109$	−115.185	−	115.185i	−1.05674	−	1.05674i	−0.0584506	−	0.998290i	$-0.518616\pi$
$110$	−12.2999	+	10.4420i	−0.111817	+	0.0949273i
$111$	−164.120			−1.47856
$112$	−85.9626	+	12.8971i	−0.767523	+	0.115153i
$113$	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
$115$	76.9139	+	151.301i	0.668817	+	1.31566i
$116$	−115.033	−	37.8958i	−0.991660	−	0.326688i
$117$	99.0420			0.846513
$118$	31.5414	−	51.2361i	0.267300	−	0.434204i
$119$	97.1610			0.816479
$120$	65.9672	+	162.490i	0.549726	+	1.35408i
$121$		−	118.397i		−	0.978486i
$122$	77.9495	−	126.622i	0.638930	−	1.03788i
$123$		−	9.80484i		−	0.0797141i
$124$	151.527	−	76.4297i	1.22199	−	0.616369i
$125$	−101.332	+	73.1900i	−0.810658	+	0.585520i
$126$	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	$0.397615\pi$
$128$	8.21989	+	127.736i	0.0642179	+	0.997936i
$129$			164.143i			1.27243i
$130$	−7.88925	+	96.5721i	−0.0606865	+	0.742862i
$131$	−18.5843	+	18.5843i	−0.141865	+	0.141865i	−0.774472	−	0.632608i	$-0.781985\pi$
$131$	−18.5843	+	18.5843i	−0.141865	+	0.141865i	0.632608	+	0.774472i	$0.281985\pi$
$132$	26.8744	+	8.85337i	0.203594	+	0.0670710i
$133$		−	186.987i		−	1.40591i
$134$	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	0.333249	−	0.942839i	$-0.391855\pi$
$137$	−83.5138	−	83.5138i	−0.609590	−	0.609590i	−0.942839	+	0.333249i	$0.891855\pi$
$138$	156.040	−	253.473i	1.13073	−	1.83676i
$139$	0.886367	−	0.886367i	0.00637674	−	0.00637674i	−0.703911	−	0.710288i	$-0.748565\pi$
$139$	0.886367	−	0.886367i	0.00637674	−	0.00637674i	0.710288	+	0.703911i	$0.248565\pi$
$140$	−64.3061	+	87.5833i	−0.459329	+	0.625595i
$141$	76.5141	−	76.5141i	0.542653	−	0.542653i
$142$	−6.58492	−	27.6767i	−0.0463727	−	0.194907i
$143$	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
$147$		−	85.4261i		−	0.581130i
$148$	−133.692	+	67.4339i	−0.903323	+	0.455634i
$149$	126.231	−	126.231i	0.847186	−	0.847186i	−0.142595	−	0.989781i	$-0.545545\pi$
$149$	126.231	−	126.231i	0.847186	−	0.847186i	0.989781	+	0.142595i	$0.0455446\pi$
$150$	202.197	+	84.6792i	1.34798	+	0.564528i
$151$			85.8641i			0.568636i	0.958730	+	0.284318i	$0.0917672\pi$
$151$			85.8641i			0.568636i	−0.958730	+	0.284318i	$0.908233\pi$
$152$	−274.359	−	23.2826i	−1.80499	−	0.153175i
$153$	−129.264	+	129.264i	−0.844862	+	0.844862i
$154$	4.05777	+	17.0550i	0.0263492	+	0.110747i
$155$	65.7426	−	201.695i	0.424146	−	1.30126i
$156$	151.716	−	76.5251i	0.972538	−	0.490546i
$157$			222.987i			1.42030i	0.704052	+	0.710148i	$0.251372\pi$
$157$			222.987i			1.42030i	−0.704052	+	0.710148i	$0.748628\pi$
$158$	−25.7718	−	108.320i	−0.163113	−	0.685570i
$159$		−	141.908i		−	0.892506i
$160$	120.501	+	105.259i	0.753130	+	0.657872i
$161$	184.420			1.14546
$162$	133.303	−	31.7158i	0.822859	−	0.195777i
$163$	114.176			0.700465			0.350233	−	0.936663i	$-0.386103\pi$
$163$	114.176			0.700465			0.350233	+	0.936663i	$0.386103\pi$
$164$	−4.02862	−	7.98699i	−0.0245648	−	0.0487012i
$165$	31.5289	−	16.0277i	0.191084	−	0.0971379i
$166$	−74.7878	+	17.7937i	−0.450529	+	0.107191i
$167$	−83.1357	−	83.1357i	−0.497818	−	0.497818i	0.412940	−	0.910758i	$-0.364502\pi$
$167$	−83.1357	−	83.1357i	−0.497818	−	0.497818i	−0.910758	+	0.412940i	$0.864502\pi$
$168$	189.868	+	16.1125i	1.13016	+	0.0959077i
$169$	−75.1159			−0.444473
$170$	−115.744	−	136.337i	−0.680845	−	0.801981i
$171$	248.769	+	248.769i	1.45479	+	1.45479i
$172$	67.4433	+	133.710i	0.392112	+	0.777387i
$173$	31.8309			0.183993			0.0919967	−	0.995759i	$-0.470675\pi$
$173$	31.8309			0.183993			0.0919967	+	0.995759i	$0.470675\pi$
$174$	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
$178$	−268.764	+	63.9451i	−1.50991	+	0.359242i
$179$	−197.541	−	197.541i	−1.10358	−	1.10358i	−0.993975	−	0.109605i	$-0.965041\pi$
$179$	−197.541	−	197.541i	−1.10358	−	1.10358i	−0.109605	−	0.993975i	$-0.534959\pi$
$180$	−30.9682	−	202.075i	−0.172046	−	1.12264i
$181$	85.6404	+	85.6404i	0.473151	+	0.473151i	0.902933	−	0.429782i	$-0.141409\pi$
$181$	85.6404	+	85.6404i	0.473151	+	0.473151i	−0.429782	+	0.902933i	$0.641409\pi$
$182$	89.6543	+	55.1921i	0.492606	+	0.303253i
$183$	−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
$187$	−28.8552			−0.154306
$188$	30.8900	−	93.7663i	0.164308	−	0.498757i
$189$	−20.5765	−	20.5765i	−0.108870	−	0.108870i
$190$	−262.381	+	222.749i	−1.38095	+	1.17236i
$191$	6.70134			0.0350856			0.0175428	−	0.999846i	$-0.494416\pi$
$191$	6.70134			0.0350856			0.0175428	+	0.999846i	$0.494416\pi$
$192$	47.2826	−	276.580i	0.246263	−	1.44052i
$193$	−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
$195$	65.8247	−	201.947i	0.337562	−	1.03562i
$196$	−35.1000	−	69.5879i	−0.179081	−	0.355040i
$197$	54.1842			0.275047			0.137523	−	0.990499i	$-0.456086\pi$
$197$	54.1842			0.275047			0.137523	+	0.990499i	$0.456086\pi$
$198$	−28.0886	−	17.2916i	−0.141862	−	0.0873315i
$199$	−82.2399			−0.413266			−0.206633	−	0.978419i	$-0.566251\pi$
$199$	−82.2399			−0.413266			−0.206633	+	0.978419i	$0.566251\pi$
$200$	199.502	−	14.0995i	0.997512	−	0.0704976i
$201$		−	362.195i		−	1.80196i
$202$	−32.0521	−	19.7316i	−0.158674	−	0.0976812i
$203$			164.497i			0.810329i
$204$	−98.1345	+	297.887i	−0.481052	+	1.46023i
$205$	−10.6314	−	3.46530i	−0.0518603	−	0.0169039i
$206$	−55.5488	+	90.2338i	−0.269654	+	0.438028i
$207$	−245.353	+	245.353i	−1.18528	+	1.18528i
$208$	92.1446	−	124.674i	0.443003	−	0.599396i
$209$			55.5319i			0.265703i
$210$	181.578	−	154.152i	0.864658	−	0.734055i
$211$	−75.9246	+	75.9246i	−0.359832	+	0.359832i	−0.863751	−	0.503919i	$-0.831891\pi$
$211$	−75.9246	+	75.9246i	−0.359832	+	0.359832i	0.503919	+	0.863751i	$0.331891\pi$
$212$	−58.3075	−	115.598i	−0.275035	−	0.545275i
$213$			62.3645i			0.292791i
$214$	−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
$218$	277.435	+	170.792i	1.27264	+	0.783449i
$219$	−45.0280	+	45.0280i	−0.205607	+	0.205607i
$220$	19.0978	−	26.0108i	0.0868083	−	0.118231i
$221$	−122.532	+	122.532i	−0.554444	+	0.554444i
$222$	319.327	−	75.9750i	1.43841	−	0.342230i
$223$	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
$227$		−	98.3454i		−	0.433240i	−0.976256	−	0.216620i	$-0.930497\pi$
$227$		−	98.3454i		−	0.433240i	0.976256	−	0.216620i	$-0.0695032\pi$
$228$	573.284	+	188.860i	2.51440	+	0.828335i
$229$	−176.947	+	176.947i	−0.772695	+	0.772695i	−0.978577	−	0.205882i	$-0.933994\pi$
$229$	−176.947	+	176.947i	−0.772695	+	0.772695i	0.205882	+	0.978577i	$0.433994\pi$
$230$	−219.691	−	258.779i	−0.955178	−	1.12512i
$231$		−	38.4304i		−	0.166365i
$232$	241.360	+	20.4822i	1.04035	+	0.0882855i
$233$	177.619	−	177.619i	0.762312	−	0.762312i	−0.214427	−	0.976740i	$-0.568789\pi$
$233$	177.619	−	177.619i	0.762312	−	0.762312i	0.976740	+	0.214427i	$0.0687885\pi$
$234$	−192.705	+	45.8488i	−0.823525	+	0.195935i
$235$	−55.9218	−	110.006i	−0.237965	−	0.468112i
$236$	−37.6514	+	114.291i	−0.159540	+	0.484282i
$237$			244.080i			1.02987i
$238$	−189.045	+	44.9781i	−0.794307	+	0.188983i
$239$		−	232.519i		−	0.972881i	−0.873714	−	0.486440i	$-0.838295\pi$
$239$		−	232.519i		−	0.972881i	0.873714	−	0.486440i	$-0.161705\pi$
$240$	−203.572	−	285.618i	−0.848217	−	1.19007i
$241$	146.374			0.607362			0.303681	−	0.952774i	$-0.401784\pi$
$241$	146.374			0.607362			0.303681	+	0.952774i	$0.401784\pi$
$242$	54.8086	+	230.363i	0.226482	+	0.951914i
$243$	−348.581			−1.43449
$244$	−93.0494	+	282.451i	−0.381350	+	1.15759i
$245$	−92.6273	−	30.1919i	−0.378071	−	0.123232i
$246$	4.53889	+	19.0772i	0.0184508	+	0.0775494i
$247$	235.813	+	235.813i	0.954710	+	0.954710i
$248$	−259.443	+	218.854i	−1.04614	+	0.882474i
$249$	168.521			0.676791
$250$	163.280	−	189.314i	0.653118	−	0.757256i
$251$	172.155	+	172.155i	0.685878	+	0.685878i	0.961318	−	0.275440i	$-0.0888236\pi$
$251$	172.155	+	172.155i	0.685878	+	0.685878i	−0.275440	+	0.961318i	$0.588824\pi$
$252$	−210.976	−	69.5031i	−0.837207	−	0.275806i
$253$	−54.7695			−0.216480
$254$	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	$0.185067\pi$
$258$	−75.9856	−	319.371i	−0.294518	−	1.23787i
$259$	143.805	+	143.805i	0.555232	+	0.555232i
$260$	−29.3554	−	191.551i	−0.112906	−	0.736736i
$261$	−218.848	−	218.848i	−0.838498	−	0.838498i
$262$	27.5561	−	44.7623i	0.105176	−	0.170849i
$263$	141.657	−	141.657i	0.538620	−	0.538620i	−0.384504	−	0.923123i	$-0.625627\pi$
$263$	141.657	−	141.657i	0.538620	−	0.538620i	0.923123	+	0.384504i	$0.125627\pi$
$264$	−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
$267$	605.612			2.26821
$268$	−148.819	−	295.043i	−0.555295	−	1.10091i
$269$	−51.7648	−	51.7648i	−0.192434	−	0.192434i	0.604313	−	0.796747i	$-0.293448\pi$
$269$	−51.7648	−	51.7648i	−0.192434	−	0.192434i	−0.796747	+	0.604313i	$0.793448\pi$
$270$	−4.36116	+	53.3849i	−0.0161525	+	0.197722i
$271$	−92.2487			−0.340401			−0.170201	−	0.985409i	$-0.554442\pi$
$271$	−92.2487			−0.340401			−0.170201	+	0.985409i	$0.554442\pi$
$272$	42.4559	+	282.979i	0.156088	+	1.04037i
$273$	−163.193	−	163.193i	−0.597775	−	0.597775i
$274$	201.152	+	123.831i	0.734132	+	0.451939i
$275$	−6.23568	−	39.8513i	−0.0226752	−	0.144914i
$276$	−186.267	+	565.414i	−0.674882	+	2.04860i
$277$	169.623			0.612357			0.306179	−	0.951974i	$-0.400949\pi$
$277$	169.623			0.612357			0.306179	+	0.951974i	$0.400949\pi$
$278$	−1.31427	+	2.13491i	−0.00472761	+	0.00767955i
$279$	433.684			1.55442
$280$	84.5753	−	200.179i	0.302054	−	0.714923i
$281$		−	194.385i		−	0.691761i	−0.938278	−	0.345881i	$-0.887580\pi$
$281$		−	194.385i		−	0.691761i	0.938278	−	0.345881i	$-0.112420\pi$
$282$	−113.452	+	184.293i	−0.402313	+	0.653520i
$283$		−	523.679i		−	1.85046i	−0.379410	−	0.925229i	$-0.623873\pi$
$283$		−	523.679i		−	1.85046i	0.379410	−	0.925229i	$-0.376127\pi$
$284$	25.6244	+	50.8020i	0.0902267	+	0.178880i
$285$	672.574	−	341.904i	2.35991	−	1.19966i
$286$	−26.6258	−	16.3911i	−0.0930973	−	0.0573116i
$287$	−8.59118	+	8.59118i	−0.0299344	+	0.0299344i
$288$	−128.249	+	300.904i	−0.445309	+	1.04480i
$289$		−	30.8432i		−	0.106724i
$290$	230.823	−	195.958i	0.795941	−	0.675717i
$291$	496.931	−	496.931i	1.70767	−	1.70767i
$292$	−18.1786	+	55.1809i	−0.0622553	+	0.188976i
$293$			272.325i			0.929435i	0.885459	+	0.464718i	$0.153844\pi$
$293$			272.325i			0.929435i	−0.885459	+	0.464718i	$0.846156\pi$
$294$	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
$298$	−187.171	+	304.041i	−0.628089	+	1.02027i
$299$	−232.576	+	232.576i	−0.777846	+	0.777846i
$300$	−432.613	−	71.1576i	−1.44204	−	0.237192i
$301$	143.825	−	143.825i	0.477824	−	0.477824i
$302$	−39.7485	−	167.065i	−0.131617	−	0.553194i
$303$	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
$307$			112.655i			0.366954i	0.983024	+	0.183477i	$0.0587353\pi$
$307$			112.655i			0.366954i	−0.983024	+	0.183477i	$0.941265\pi$
$308$	−15.7903	−	31.3053i	−0.0512673	−	0.101641i
$309$	164.247	−	164.247i	0.531545	−	0.531545i
$310$	−34.5454	+	422.869i	−0.111437	+	1.36409i
$311$		−	254.031i		−	0.816820i	−0.912799	−	0.408410i	$-0.866083\pi$
$311$		−	254.031i		−	0.816820i	0.912799	−	0.408410i	$-0.133917\pi$
$312$	−259.766	+	219.127i	−0.832585	+	0.702330i
$313$	22.4916	−	22.4916i	0.0718580	−	0.0718580i	−0.670264	−	0.742122i	$-0.733819\pi$
$313$	22.4916	−	22.4916i	0.0718580	−	0.0718580i	0.742122	+	0.670264i	$0.233819\pi$
$314$	−103.226	−	433.862i	−0.328744	−	1.38173i
$315$	−247.516	+	125.825i	−0.785766	+	0.399445i
$316$	100.288	+	198.827i	0.317366	+	0.629199i
$317$			379.973i			1.19865i	0.800504	+	0.599327i	$0.204565\pi$
$317$			379.973i			1.19865i	−0.800504	+	0.599327i	$0.795435\pi$
$318$	65.6927	+	276.110i	0.206581	+	0.868269i
$319$		−	48.8528i		−	0.153144i
$320$	−283.184	−	149.019i	−0.884950	−	0.465686i
$321$	26.9649			0.0840028
$322$	−358.823	+	85.3721i	−1.11436	+	0.265131i
$323$	−615.539			−1.90569
$324$	−244.684	+	123.418i	−0.755199	+	0.380920i
$325$	−195.706	−	142.747i	−0.602172	−	0.439222i
$326$	−222.151	+	52.8546i	−0.681444	+	0.162131i
$327$	−505.000	−	505.000i	−1.54434	−	1.54434i
$328$	11.5358	+	13.6753i	0.0351701	+	0.0416929i
$329$	−134.086			−0.407556
$330$	−53.9257	+	45.7804i	−0.163411	+	0.138729i
$331$	−56.7172	−	56.7172i	−0.171351	−	0.171351i	0.616222	−	0.787573i	$-0.288663\pi$
$331$	−56.7172	−	56.7172i	−0.171351	−	0.171351i	−0.787573	+	0.616222i	$0.788663\pi$
$332$	137.277	−	69.2420i	0.413484	−	0.208560i
$333$	−382.639			−1.14907
$334$	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	$0.245385\pi$
$338$	146.152	−	34.7729i	0.432403	−	0.102878i
$339$	321.220	+	321.220i	0.947552	+	0.947552i
$340$	288.315	+	211.689i	0.847984	+	0.622613i
$341$	48.4050	+	48.4050i	0.141950	+	0.141950i
$342$	−599.187	−	368.865i	−1.75201	−	1.07855i
$343$	−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
$347$	−512.927			−1.47817			−0.739087	−	0.673610i	$-0.764743\pi$
$347$	−512.927			−1.47817			−0.739087	+	0.673610i	$0.764743\pi$
$348$	−504.332	−	166.145i	−1.44923	−	0.477428i
$349$	−335.325	−	335.325i	−0.960817	−	0.960817i	0.0384442	−	0.999261i	$-0.487760\pi$
$349$	−335.325	−	335.325i	−0.960817	−	0.960817i	−0.999261	+	0.0384442i	$0.987760\pi$
$350$	−102.971	−	251.366i	−0.294204	−	0.718190i
$351$	51.8990			0.147860
$352$	−47.8993	+	19.2706i	−0.136077	+	0.0547460i
$353$	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
$355$	67.6217	+	22.0413i	0.190484	+	0.0620883i
$356$	493.330	−	248.834i	1.38576	−	0.698973i
$357$	425.979			1.19322
$358$	475.799	+	292.907i	1.32905	+	0.818175i
$359$	−55.6486			−0.155010			−0.0775050	−	0.996992i	$-0.524695\pi$
$359$	−55.6486			−0.155010			−0.0775050	+	0.996992i	$0.524695\pi$
$360$	153.800	+	378.839i	0.427221	+	1.05233i
$361$			823.608i			2.28146i
$362$	−206.274	−	126.985i	−0.569819	−	0.350786i
$363$		−	519.082i		−	1.42998i
$364$	−199.989	−	65.8835i	−0.549420	−	0.180999i
$365$	32.9096	+	64.7380i	0.0901634	+	0.177364i
$366$	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	$0.133750\pi$
$368$	80.5848	+	537.118i	0.218980	+	1.45956i
$369$		−	22.8596i		−	0.0619500i
$370$	30.4793	−	373.097i	0.0823766	−	1.00837i
$371$	−124.343	+	124.343i	−0.335156	+	0.335156i
$372$	664.332	−	335.088i	1.78584	−	0.900773i
$373$		−	16.1719i		−	0.0433562i	−0.999765	−	0.0216781i	$-0.993099\pi$
$373$		−	16.1719i		−	0.0433562i	0.999765	−	0.0216781i	$-0.00690090\pi$
$374$	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
$378$	49.5607	+	30.5101i	0.131113	+	0.0807145i
$379$	−467.798	+	467.798i	−1.23430	+	1.23430i	−0.271998	+	0.962298i	$0.587684\pi$
$379$	−467.798	+	467.798i	−1.23430	+	1.23430i	−0.962298	+	0.271998i	$0.912316\pi$
$380$	407.395	−	554.862i	1.07209	−	1.46016i
$381$	−352.222	+	352.222i	−0.924466	+	0.924466i
$382$	−13.0387	+	3.10221i	−0.0341328	+	0.00812096i
$383$	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
$387$			382.692i			0.988869i
$388$	200.619	−	608.978i	0.517060	−	1.56953i
$389$	356.792	−	356.792i	0.917202	−	0.917202i	−0.0796230	−	0.996825i	$-0.525372\pi$
$389$	356.792	−	356.792i	0.917202	−	0.917202i	0.996825	+	0.0796230i	$0.0253716\pi$
$390$	−34.5885	+	423.397i	−0.0886884	+	1.08563i
$391$		−	607.089i		−	1.55266i
$392$	100.507	+	119.148i	0.256396	+	0.303948i
$393$	−81.4783	+	81.4783i	−0.207324	+	0.207324i
$394$	−105.426	+	25.0831i	−0.267578	+	0.0636628i
$395$	264.655	+	86.2646i	0.670013	+	0.218391i
$396$	62.6564	+	20.6413i	0.158223	+	0.0521244i
$397$		−	287.234i		−	0.723511i	−0.932273	−	0.361755i	$-0.882178\pi$
$397$		−	287.234i		−	0.723511i	0.932273	−	0.361755i	$-0.117822\pi$
$398$	160.013	−	38.0708i	0.402043	−	0.0956552i
$399$		−	819.797i		−	2.05463i
$400$	−381.642	+	119.788i	−0.954106	+	0.299469i
$401$	178.508			0.445157			0.222579	−	0.974915i	$-0.428553\pi$
$401$	178.508			0.445157			0.222579	+	0.974915i	$0.428553\pi$
$402$	167.668	+	704.718i	0.417085	+	1.75303i
$403$	411.099			1.02010
$404$	71.4976	+	23.5539i	0.176974	+	0.0583017i
$405$	−106.161	+	325.695i	−0.262125	+	0.804186i
$406$	−76.1494	−	320.060i	−0.187560	−	0.788324i
$407$	−42.7077	−	42.7077i	−0.104933	−	0.104933i
$408$	53.0405	−	625.024i	0.130001	−	1.53192i
$409$	−60.0556			−0.146835			−0.0734176	−	0.997301i	$-0.523391\pi$
$409$	−60.0556			−0.146835			−0.0734176	+	0.997301i	$0.523391\pi$
$410$	22.2895	+	1.82089i	0.0543646	+	0.00444120i
$411$	−366.146	−	366.146i	−0.890866	−	0.890866i
$412$	66.3094	−	201.282i	0.160945	−	0.488548i
$413$	163.436			0.395728
$414$	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
$418$	−25.7070	−	108.048i	−0.0615000	−	0.258488i
$419$	258.872	+	258.872i	0.617833	+	0.617833i	0.944975	−	0.327142i	$-0.106086\pi$
$419$	258.872	+	258.872i	0.617833	+	0.617833i	−0.327142	+	0.944975i	$0.606086\pi$
$420$	−281.934	+	383.988i	−0.671272	+	0.914256i
$421$	429.322	+	429.322i	1.01977	+	1.01977i	0.999801	+	0.0199654i	$0.00635560\pi$
$421$	429.322	+	429.322i	1.01977	+	1.01977i	0.0199654	+	0.999801i	$0.493644\pi$
$422$	112.578	−	182.873i	0.266773	−	0.433348i
$423$	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
$427$	403.905			0.945914
$428$	21.9655	−	11.0794i	0.0513213	−	0.0258864i
$429$	48.4655	+	48.4655i	0.112973	+	0.112973i
$430$	−373.149	−	30.4836i	−0.867788	−	0.0708921i
$431$	−412.636			−0.957392			−0.478696	−	0.877981i	$-0.658890\pi$
$431$	−412.636			−0.957392			−0.478696	+	0.877981i	$0.658890\pi$
$432$	50.9374	−	68.9198i	0.117911	−	0.159537i
$433$	−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
$435$	−591.680	+	300.782i	−1.36018	+	0.691452i
$436$	−618.866	−	203.877i	−1.41942	−	0.467607i
$437$	−1168.34			−2.67356
$438$	66.7660	−	108.455i	0.152434	−	0.247614i
$439$	−190.193			−0.433241			−0.216621	−	0.976256i	$-0.569503\pi$
$439$	−190.193			−0.433241			−0.216621	+	0.976256i	$0.569503\pi$
$440$	−25.1174	+	59.4497i	−0.0570851	+	0.135113i
$441$		−	199.167i		−	0.451626i
$442$	181.686	−	295.132i	0.411055	−	0.667719i
$443$			255.432i			0.576595i	0.957541	+	0.288298i	$0.0930892\pi$
$443$			255.432i			0.576595i	−0.957541	+	0.288298i	$0.906911\pi$
$444$	−586.139	+	295.647i	−1.32013	+	0.665872i
$445$	214.040	−	656.664i	0.480989	−	1.47565i
$446$	−248.179	−	152.782i	−0.556456	−	0.342560i
$447$	553.428	−	553.428i	1.23809	−	1.23809i
$448$	−283.774	+	200.915i	−0.633425	+	0.448470i
$449$			569.939i			1.26935i	0.772778	+	0.634676i	$0.218867\pi$
$449$			569.939i			1.26935i	−0.772778	+	0.634676i	$0.781133\pi$
$450$	471.414	+	197.426i	1.04759	+	0.438724i
$451$	2.55144	−	2.55144i	0.00565729	−	0.00565729i
$452$	393.648	+	129.682i	0.870904	+	0.286907i
$453$			376.450i			0.831016i
$454$	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	0.948337	−	0.317265i	$-0.102764\pi$
$457$	288.400	+	288.400i	0.631072	+	0.631072i	−0.317265	+	0.948337i	$0.602764\pi$
$458$	262.371	−	426.197i	0.572863	−	0.930561i
$459$	−67.7355	+	67.7355i	−0.147572	+	0.147572i
$460$	547.245	+	401.802i	1.18966	+	0.873483i
$461$	−184.673	+	184.673i	−0.400593	+	0.400593i	−0.878442	−	0.477849i	$-0.841417\pi$
$461$	−184.673	+	184.673i	−0.400593	+	0.400593i	0.477849	+	0.878442i	$0.341417\pi$
$462$	17.7903	+	74.7735i	0.0385072	+	0.161847i
$463$	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
$467$			360.961i			0.772937i	0.922303	+	0.386468i	$0.126305\pi$
$467$			360.961i			0.772937i	−0.922303	+	0.386468i	$0.873695\pi$
$468$	353.719	−	178.415i	0.755810	−	0.381229i
$469$	−317.362	+	317.362i	−0.676677	+	0.676677i
$470$	159.731	+	188.150i	0.339853	+	0.400320i
$471$			977.631i			2.07565i
$472$	20.3501	−	239.804i	0.0431147	−	0.508059i
$473$	−42.7137	+	42.7137i	−0.0903037	+	0.0903037i
$474$	−112.990	−	474.903i	−0.238376	−	1.00191i
$475$	−133.020	−	850.109i	−0.280041	−	1.78970i
$476$	347.001	−	175.027i	0.728994	−	0.367703i
$477$		−	330.853i		−	0.693613i
$478$	107.638	+	452.408i	0.225185	+	0.946461i
$479$			111.130i			0.232005i	0.993249	+	0.116003i	$0.0370081\pi$
$479$			111.130i			0.232005i	−0.993249	+	0.116003i	$0.962992\pi$
$480$	528.307	+	461.484i	1.10064	+	0.961426i
$481$	−362.712			−0.754079
$482$	−284.798	+	67.7600i	−0.590868	+	0.140581i
$483$	808.543			1.67400
$484$	−213.281	−	422.843i	−0.440663	−	0.873642i
$485$	−363.192	−	714.450i	−0.748850	−	1.47309i
$486$	678.230	−	161.366i	1.39553	−	0.332029i
$487$	467.586	+	467.586i	0.960135	+	0.960135i	0.999235	−	0.0391007i	$-0.0124493\pi$
$487$	467.586	+	467.586i	0.960135	+	0.960135i	−0.0391007	+	0.999235i	$0.512449\pi$
$488$	50.2921	−	592.636i	0.103058	−	1.21442i
$489$	500.576			1.02367
$490$	194.200	+	15.8648i	0.396327	+	0.0323771i
$491$	333.638	+	333.638i	0.679507	+	0.679507i	0.959889	−	0.280382i	$-0.0904610\pi$
$491$	333.638	+	333.638i	0.679507	+	0.679507i	−0.280382	+	0.959889i	$0.590461\pi$
$492$	−17.6625	−	35.0170i	−0.0358994	−	0.0711728i
$493$	541.505			1.09839
$494$	−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
$498$	−327.889	+	78.0122i	−0.658412	+	0.156651i
$499$	−173.095	−	173.095i	−0.346884	−	0.346884i	0.512064	−	0.858947i	$-0.328881\pi$
$499$	−173.095	−	173.095i	−0.346884	−	0.346884i	−0.858947	+	0.512064i	$0.828881\pi$
$500$	−230.053	+	443.932i	−0.460107	+	0.887864i
$501$	−364.488	−	364.488i	−0.727521	−	0.727521i
$502$	−414.656	−	255.266i	−0.826007	−	0.508498i
$503$	618.020	−	618.020i	1.22867	−	1.22867i	0.264201	−	0.964468i	$-0.414892\pi$
$503$	618.020	−	618.020i	1.22867	−	1.22867i	0.964468	−	0.264201i	$-0.0851083\pi$
$504$	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
$507$	−329.327			−0.649561
$508$	−142.198	+	431.640i	−0.279917	+	0.849685i
$509$	−519.035	−	519.035i	−1.01972	−	1.01972i	−0.999802	−	0.0199135i	$-0.993661\pi$
$509$	−519.035	−	519.035i	−1.01972	−	1.01972i	−0.0199135	−	0.999802i	$-0.506339\pi$
$510$	−507.450	−	597.736i	−0.995000	−	1.17203i
$511$	78.9088			0.154420
$512$	259.461	+	441.389i	0.506759	+	0.862088i
$513$	130.357	+	130.357i	0.254108	+	0.254108i
$514$	−109.174	+	177.343i	−0.212401	+	0.345026i
$515$	−120.044	−	236.143i	−0.233094	−	0.458529i
$516$	295.689	+	586.221i	0.573040	+	1.13609i
$517$	39.8213			0.0770238
$518$	−346.371	−	213.229i	−0.668669	−	0.411639i
$519$	139.555			0.268891
$520$	145.790	+	359.110i	0.280365	+	0.690596i
$521$			687.482i			1.31954i	0.751467	+	0.659771i	$0.229347\pi$
$521$			687.482i			1.31954i	−0.751467	+	0.659771i	$0.770653\pi$
$522$	527.120	+	324.500i	1.00981	+	0.621648i
$523$			472.937i			0.904277i	0.891948	+	0.452139i	$0.149339\pi$
$523$			472.937i			0.904277i	−0.891948	+	0.452139i	$0.850661\pi$
$524$	−32.8941	+	99.8499i	−0.0627750	+	0.190553i
$525$	92.0550	+	588.311i	0.175343	+	1.12059i
$526$	−210.044	+	341.197i	−0.399323	+	0.648663i
$527$	−536.542	+	536.542i	−1.01811	+	1.01811i
$528$	111.928	−	16.7927i	0.211984	−	0.0318044i
$529$		−	623.305i		−	1.17827i
$530$	322.603	+	26.3543i	0.608684	+	0.0497251i
$531$	−217.436	+	217.436i	−0.409485	+	0.409485i
$532$	−336.839	−	667.805i	−0.633157	−	1.25527i
$533$		−	21.6691i		−	0.0406549i
$534$	−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
$538$	124.681	+	76.7551i	0.231750	+	0.142667i
$539$	22.2298	−	22.2298i	0.0412426	−	0.0412426i
$540$	−16.2276	−	105.889i	−0.0300512	−	0.196091i
$541$	91.9662	−	91.9662i	0.169993	−	0.169993i	−0.616983	−	0.786976i	$-0.711645\pi$
$541$	91.9662	−	91.9662i	0.169993	−	0.169993i	0.786976	+	0.616983i	$0.211645\pi$
$542$	179.487	−	42.7041i	0.331157	−	0.0787898i
$543$	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
$547$		−	238.842i		−	0.436640i	−0.975877	−	0.218320i	$-0.929942\pi$
$547$		−	238.842i		−	0.436640i	0.975877	−	0.218320i	$-0.0700577\pi$
$548$	−448.704	−	147.819i	−0.818803	−	0.269743i
$549$	−537.359	+	537.359i	−0.978796	+	0.978796i
$550$	30.5808	+	74.6516i	0.0556014	+	0.135730i
$551$		−	1042.13i		−	1.89134i
$552$	100.675	−	1186.35i	0.182383	−	2.14918i
$553$	213.867	−	213.867i	0.386740	−	0.386740i
$554$	−330.033	+	78.5224i	−0.595728	+	0.141737i
$555$	−254.307	+	780.201i	−0.458211	+	1.40577i
$556$	1.56887	−	4.76229i	0.00282170	−	0.00856526i
$557$		−	181.535i		−	0.325915i	−0.986633	−	0.162958i	$-0.947897\pi$
$557$		−	181.535i		−	0.325915i	0.986633	−	0.162958i	$-0.0521034\pi$
$558$	−843.814	+	200.762i	−1.51221	+	0.359789i
$559$			362.763i			0.648949i
$560$	−71.8898	+	428.637i	−0.128375	+	0.765423i
$561$	−126.509			−0.225505
$562$	89.9853	+	378.213i	0.160116	+	0.672976i
$563$	−759.434			−1.34891			−0.674453	−	0.738318i	$-0.735621\pi$
$563$	−759.434			−1.34891			−0.674453	+	0.738318i	$0.735621\pi$
$564$	135.430	−	411.096i	0.240123	−	0.728893i
$565$	461.826	−	234.770i	0.817392	−	0.415523i
$566$	242.423	+	1018.92i	0.428310	+	1.80021i
$567$	263.194	+	263.194i	0.464186	+	0.464186i
$568$	−73.3745	−	86.9827i	−0.129180	−	0.153138i
$569$	1063.33			1.86878			0.934388	−	0.356258i	$-0.115947\pi$
$569$	1063.33			1.86878			0.934388	+	0.356258i	$0.115947\pi$
$570$	−1150.34	+	976.589i	−2.01815	+	1.71331i
$571$	342.578	+	342.578i	0.599962	+	0.599962i	0.940302	−	0.340341i	$-0.110542\pi$
$571$	342.578	+	342.578i	0.599962	+	0.599962i	−0.340341	+	0.940302i	$0.610542\pi$
$572$	59.3934	+	19.5663i	0.103835	+	0.0342068i
$573$	29.3804			0.0512747
$574$	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	$0.0565895\pi$
$578$	14.2780	+	60.0113i	0.0247025	+	0.103826i
$579$	−882.484	−	882.484i	−1.52415	−	1.52415i
$580$	−358.396	+	488.126i	−0.617924	+	0.841597i
$581$	−147.661	−	147.661i	−0.254150	−	0.254150i
$582$	−736.832	+	1196.91i	−1.26603	+	2.05655i
$583$	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
$587$	236.253			0.402476			0.201238	−	0.979542i	$-0.435504\pi$
$587$	236.253			0.402476			0.201238	+	0.979542i	$0.435504\pi$
$588$	−153.887	−	305.091i	−0.261713	−	0.518862i
$589$	1032.58	+	1032.58i	1.75310	+	1.75310i
$590$	−194.694	−	229.334i	−0.329990	−	0.388702i
$591$	237.558			0.401959
$592$	−355.992	+	481.667i	−0.601337	+	0.813627i
$593$	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
$595$	150.553	−	461.888i	0.253030	−	0.776282i
$596$	223.428	−	678.214i	0.374879	−	1.13794i
$597$	−360.561			−0.603955
$598$	344.855	−	560.185i	0.576681	−	0.936764i
$599$	−100.435			−0.167670			−0.0838352	−	0.996480i	$-0.526717\pi$
$599$	−100.435			−0.167670			−0.0838352	+	0.996480i	$0.526717\pi$
$600$	874.670	−	61.8159i	1.45778	−	0.103026i
$601$		−	189.816i		−	0.315834i	−0.987452	−	0.157917i	$-0.949522\pi$
$601$		−	189.816i		−	0.315834i	0.987452	−	0.157917i	$-0.0504778\pi$
$602$	−213.259	+	346.419i	−0.354251	+	0.575447i
$603$		−	844.442i		−	1.40040i
$604$	154.676	+	306.655i	0.256086	+	0.507708i
$605$	−562.839	−	183.458i	−0.930313	−	0.303236i
$606$	−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	$0.141088\pi$
$608$	−1021.79	+	411.081i	−1.68057	+	0.676120i
$609$			721.196i			1.18423i
$610$	−481.155	−	566.762i	−0.788778	−	0.929118i
$611$	169.099	−	169.099i	0.276758	−	0.276758i
$612$	−228.796	+	694.510i	−0.373850	+	1.13482i
$613$		−	194.536i		−	0.317351i	−0.987331	−	0.158676i	$-0.949278\pi$
$613$		−	194.536i		−	0.317351i	0.987331	−	0.158676i	$-0.0507224\pi$
$614$	−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	0.631087	−	0.775712i	$-0.282609\pi$
$617$	−89.2331	−	89.2331i	−0.144624	−	0.144624i	−0.775712	+	0.631087i	$0.782609\pi$
$618$	−243.540	+	395.608i	−0.394078	+	0.640143i
$619$	98.7690	−	98.7690i	0.159562	−	0.159562i	−0.622811	−	0.782373i	$-0.714009\pi$
$619$	98.7690	−	98.7690i	0.159562	−	0.159562i	0.782373	+	0.622811i	$0.214009\pi$
$620$	−128.541	−	838.763i	−0.207325	−	1.35284i
$621$	−128.568	+	128.568i	−0.207033	+	0.207033i
$622$	117.597	+	494.265i	0.189062	+	0.794638i
$623$	−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
$627$			243.466i			0.388303i
$628$	401.690	+	796.375i	0.639634	+	1.26811i
$629$	473.390	−	473.390i	0.752608	−	0.752608i
$630$	423.342	−	359.398i	0.671971	−	0.570473i
$631$			361.528i			0.572945i	0.958089	+	0.286472i	$0.0924827\pi$
$631$			361.528i			0.572945i	−0.958089	+	0.286472i	$0.907517\pi$
$632$	−287.170	−	340.429i	−0.454383	−	0.538654i
$633$	−332.873	+	332.873i	−0.525866	+	0.525866i
$634$	−175.898	−	739.310i	−0.277442	−	1.16610i
$635$	257.428	+	506.398i	0.405399	+	0.797477i
$636$	−255.635	−	506.812i	−0.401942	−	0.796875i
$637$		−	188.795i		−	0.296382i
$638$	22.6151	+	95.0523i	0.0354469	+	0.148985i
$639$			145.400i			0.227543i
$640$	619.972	+	158.853i	0.968707	+	0.248208i
$641$	−225.925			−0.352458			−0.176229	−	0.984349i	$-0.556390\pi$
$641$	−225.925			−0.352458			−0.176229	+	0.984349i	$0.556390\pi$
$642$	−52.4653	+	12.4827i	−0.0817216	+	0.0194434i
$643$	1219.79			1.89703			0.948515	−	0.316731i	$-0.102585\pi$
$643$	1219.79			1.89703			0.948515	+	0.316731i	$0.102585\pi$
$644$	658.637	−	332.215i	1.02273	−	0.515862i
$645$	780.310	+	254.343i	1.20978	+	0.394330i
$646$	1197.65	−	284.947i	1.85394	−	0.441095i
$647$	406.190	+	406.190i	0.627806	+	0.627806i	0.947516	−	0.319710i	$-0.103585\pi$
$647$	406.190	+	406.190i	0.627806	+	0.627806i	−0.319710	+	0.947516i	$0.603585\pi$
$648$	418.946	−	353.403i	0.646522	−	0.545376i
$649$	−48.5377			−0.0747885
$650$	446.864	+	187.144i	0.687483	+	0.287914i
$651$	−714.586	−	714.586i	−1.09767	−	1.09767i
$652$	407.768	−	205.677i	0.625411	−	0.315456i
$653$	−652.961			−0.999940			−0.499970	−	0.866043i	$-0.666656\pi$
$653$	−652.961			−0.999940			−0.499970	+	0.866043i	$0.666656\pi$
$654$	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
$658$	260.890	−	62.0715i	0.396489	−	0.0943336i
$659$	565.772	+	565.772i	0.858532	+	0.858532i	0.991165	−	0.132634i	$-0.0423434\pi$
$659$	565.772	+	565.772i	0.858532	+	0.858532i	−0.132634	+	0.991165i	$0.542343\pi$
$660$	83.7298	−	114.038i	0.126863	−	0.172785i
$661$	−304.268	−	304.268i	−0.460315	−	0.460315i	0.438443	−	0.898759i	$-0.355530\pi$
$661$	−304.268	−	304.268i	−0.460315	−	0.460315i	−0.898759	+	0.438443i	$0.855530\pi$
$662$	136.610	+	84.0983i	0.206359	+	0.127037i
$663$	−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
$667$	1027.82			1.54096
$668$	−446.672	−	147.150i	−0.668671	−	0.220284i
$669$	451.747	+	451.747i	0.675257	+	0.675257i
$670$	823.383	+	67.2645i	1.22893	+	0.100395i
$671$	−119.953			−0.178768
$672$	707.120	−	284.485i	1.05226	−	0.423341i
$673$	−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
$675$	−108.186	−	78.9103i	−0.160276	−	0.116904i
$676$	−268.269	+	135.314i	−0.396848	+	0.200169i
$677$	796.004			1.17578			0.587890	−	0.808941i	$-0.299959\pi$
$677$	796.004			1.17578			0.587890	+	0.808941i	$0.299959\pi$
$678$	−773.695	−	476.294i	−1.14114	−	0.702499i
$679$	−870.840			−1.28253
$680$	−658.966	−	278.412i	−0.969067	−	0.409430i
$681$		−	431.172i		−	0.633145i
$682$	−116.589	−	71.7733i	−0.170952	−	0.105239i
$683$			949.934i			1.39083i	0.718610	+	0.695413i	$0.244778\pi$
$683$			949.934i			1.39083i	−0.718610	+	0.695413i	$0.755222\pi$
$684$	1336.59	+	440.320i	1.95408	+	0.643742i
$685$	−526.417	+	267.605i	−0.768492	+	0.390664i
$686$	390.099	−	633.678i	0.568657	−	0.923729i
$687$	−775.782	+	775.782i	−1.12923	+	1.12923i
$688$	481.734	+	356.041i	0.700195	+	0.517502i
$689$		−	313.623i		−	0.455186i
$690$	−963.182	−	1134.55i	−1.39592	−	1.64428i
$691$	−882.517	+	882.517i	−1.27716	+	1.27716i	−0.334908	+	0.942251i	$0.608705\pi$
$691$	−882.517	+	882.517i	−1.27716	+	1.27716i	−0.942251	+	0.334908i	$0.891295\pi$
$692$	113.681	−	57.3404i	0.164279	−	0.0828618i
$693$		−	89.5988i		−	0.129291i
$694$	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
$698$	807.668	+	497.208i	1.15712	+	0.712333i
$699$	778.726	−	778.726i	1.11406	−	1.11406i
$700$	316.714	+	441.413i	0.452448	+	0.630590i
$701$	−42.7867	+	42.7867i	−0.0610367	+	0.0610367i	−0.736966	−	0.675930i	$-0.763742\pi$
$701$	−42.7867	+	42.7867i	−0.0610367	+	0.0610367i	0.675930	+	0.736966i	$0.263742\pi$
$702$	−100.979	+	24.0252i	−0.143845	+	0.0342240i
$703$	−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
$707$		−	102.242i		−	0.144613i
$708$	−165.073	+	501.079i	−0.233155	+	0.707739i
$709$	−239.953	+	239.953i	−0.338439	+	0.338439i	−0.855780	−	0.517341i	$-0.826922\pi$
$709$	−239.953	+	239.953i	−0.338439	+	0.338439i	0.517341	+	0.855780i	$0.326922\pi$
$710$	−141.774	−	11.5819i	−0.199682	−	0.0163126i
$711$			569.062i			0.800368i
$712$	−844.675	+	712.528i	−1.18634	+	1.00074i
$713$	−1018.40	+	1018.40i	−1.42833	+	1.42833i
$714$	−828.822	+	197.195i	−1.16081	+	0.276184i
$715$	69.6800	−	35.4220i	0.0974546	−	0.0495412i
$716$	−1061.35	−	349.647i	−1.48233	−	0.488333i
$717$		−	1019.42i		−	1.42179i
$718$	108.275	−	25.7610i	0.150801	−	0.0358788i
$719$			840.915i			1.16956i	0.811191	+	0.584781i	$0.198819\pi$
$719$			840.915i			1.16956i	−0.811191	+	0.584781i	$0.801181\pi$
$720$	−474.619	−	665.905i	−0.659194	−	0.924868i
$721$	−287.833			−0.399214
$722$	−381.267	−	1602.48i	−0.528071	−	2.21951i
$723$	641.742			0.887610
$724$	460.130	+	151.583i	0.635538	+	0.209369i
$725$	117.021	+	747.862i	0.161408	+	1.03153i
$726$	240.295	+	1009.97i	0.330985	+	1.39115i
$727$	−8.90967	−	8.90967i	−0.0122554	−	0.0122554i	0.700953	−	0.713208i	$-0.252758\pi$
$727$	−8.90967	−	8.90967i	−0.0122554	−	0.0122554i	−0.713208	+	0.700953i	$0.752758\pi$
$728$	419.615	+	35.6092i	0.576394	+	0.0489138i
$729$	−911.660			−1.25056
$730$	−94.0006	−	110.725i	−0.128768	−	0.151678i
$731$	−473.456	−	473.456i	−0.647683	−	0.647683i
$732$	−407.952	+	1238.34i	−0.557312	+	1.69172i
$733$	65.3306			0.0891277			0.0445639	−	0.999007i	$-0.485810\pi$
$733$	65.3306			0.0891277			0.0445639	+	0.999007i	$0.485810\pi$
$734$	−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
$738$	10.5822	+	44.4776i	0.0143390	+	0.0602677i
$739$	−254.204	−	254.204i	−0.343984	−	0.343984i	0.513879	−	0.857863i	$-0.328208\pi$
$739$	−254.204	−	254.204i	−0.343984	−	0.343984i	−0.857863	+	0.513879i	$0.828208\pi$
$740$	113.412	+	740.040i	0.153259	+	1.00005i
$741$	1033.87	+	1033.87i	1.39523	+	1.39523i
$742$	184.371	−	299.493i	0.248479	−	0.403630i
$743$	−6.53981	+	6.53981i	−0.00880189	+	0.00880189i	−0.711494	−	0.702692i	$-0.751981\pi$
$743$	−6.53981	+	6.53981i	−0.00880189	+	0.00880189i	0.702692	+	0.711494i	$0.251981\pi$
$744$	−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
$747$	392.899			0.525969
$748$	−103.054	+	51.9800i	−0.137772	+	0.0694919i
$749$	−23.6271	−	23.6271i	−0.0315449	−	0.0315449i
$750$	715.860	−	830.001i	0.954479	−	1.10667i
$751$	−512.529			−0.682462			−0.341231	−	0.939979i	$-0.610844\pi$
$751$	−512.529			−0.682462			−0.341231	+	0.939979i	$0.610844\pi$
$752$	−58.5908	−	390.523i	−0.0779133	−	0.519312i
$753$	754.774	+	754.774i	1.00236	+	1.00236i
$754$	499.668	+	307.601i	0.662690	+	0.407959i
$755$	408.184	+	133.048i	0.540641	+	0.176222i
$756$	−110.554	−	36.4203i	−0.146235	−	0.0481750i
$757$	−109.439			−0.144570			−0.0722849	−	0.997384i	$-0.523029\pi$
$757$	−109.439			−0.144570			−0.0722849	+	0.997384i	$0.523029\pi$
$758$	693.635	−	1126.74i	0.915085	−	1.48647i
$759$	−240.124			−0.316369
$760$	−535.806	+	1268.18i	−0.705007	+	1.66866i
$761$		−	737.899i		−	0.969644i	−0.874613	−	0.484822i	$-0.838884\pi$
$761$		−	737.899i		−	0.969644i	0.874613	−	0.484822i	$-0.161116\pi$
$762$	522.262	−	848.365i	0.685383	−	1.11334i
$763$			884.980i			1.15987i
$764$	23.9332	−	12.0719i	0.0313262	−	0.0158009i
$765$	414.203	+	814.796i	0.541442	+	1.06509i
$766$	−333.114	−	205.069i	−0.434875	−	0.267714i
$767$	−206.113	+	206.113i	−0.268726	+	0.268726i
$768$	−329.368	−	1072.95i	−0.428865	−	1.39708i
$769$			1218.07i			1.58396i	0.610545	+	0.791981i	$0.290950\pi$
$769$			1218.07i			1.58396i	−0.610545	+	0.791981i	$0.709050\pi$
$770$	87.3644	+	7.13704i	0.113460	+	0.00926889i
$771$	322.808	−	322.808i	0.418687	−	0.418687i
$772$	−1081.47	−	356.273i	−1.40086	−	0.461494i
$773$		−	1341.89i		−	1.73595i	−0.496612	−	0.867973i	$-0.665423\pi$
$773$		−	1341.89i		−	1.73595i	0.496612	−	0.867973i	$-0.334577\pi$
$774$	−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
$778$	−529.038	+	859.372i	−0.679998	+	1.10459i
$779$	54.4273	−	54.4273i	0.0698681	−	0.0698681i
$780$	−128.702	−	839.810i	−0.165002	−	1.07668i
$781$	−16.2286	+	16.2286i	−0.0207793	+	0.0207793i
$782$	281.035	+	1181.21i	0.359380	+	1.51049i
$783$	−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
$787$		−	1158.29i		−	1.47178i	−0.677099	−	0.735892i	$-0.736763\pi$
$787$		−	1158.29i		−	1.47178i	0.677099	−	0.735892i	$-0.263237\pi$
$788$	193.514	−	97.6079i	0.245576	−	0.123868i
$789$	621.060	−	621.060i	0.787149	−	0.787149i
$790$	−554.870	−	45.3290i	−0.702368	−	0.0573784i
$791$		−	562.918i		−	0.711654i
$792$	−131.465	−	11.1564i	−0.165991	−	0.0140863i
$793$	−509.374	+	509.374i	−0.642338	+	0.642338i
$794$	132.967	+	558.867i	0.167465	+	0.703863i
$795$	−674.610	−	219.890i	−0.848566	−	0.276591i
$796$	−293.712	+	148.148i	−0.368985	+	0.186115i
$797$			67.0596i			0.0841400i	0.999115	+	0.0420700i	$0.0133952\pi$
$797$			67.0596i			0.0841400i	−0.999115	+	0.0420700i	$0.986605\pi$
$798$	379.503	+	1595.07i	0.475568	+	1.99883i
$799$			441.396i			0.552436i
$800$	687.105	−	409.740i	0.858881	−	0.512175i
$801$	1411.96			1.76274
$802$	−347.321	+	82.6355i	−0.433069	+	0.103037i
$803$	−23.4346			−0.0291838
$804$	−652.461	−	1293.54i	−0.811518	−	1.60889i
$805$	285.761	−	876.701i	0.354983	−	1.08907i
$806$	−799.870	+	190.307i	−0.992395	+	0.236113i
$807$	−226.950	−	226.950i	−0.281227	−	0.281227i
$808$	−150.016	−	12.7306i	−0.185663	−	0.0157557i
$809$	−602.411			−0.744637			−0.372318	−	0.928105i	$-0.621437\pi$
$809$	−602.411			−0.744637			−0.372318	+	0.928105i	$0.621437\pi$
$810$	55.7836	−	682.846i	0.0688687	−	0.843020i
$811$	−47.6019	−	47.6019i	−0.0586953	−	0.0586953i	0.677150	−	0.735845i	$-0.263215\pi$
$811$	−47.6019	−	47.6019i	−0.0586953	−	0.0586953i	−0.735845	+	0.677150i	$0.763215\pi$
$812$	296.326	+	587.485i	0.364933	+	0.723503i
$813$	−404.442			−0.497469
$814$	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
$818$	116.849	−	27.8011i	0.142848	−	0.0339867i
$819$	−380.476	−	380.476i	−0.464562	−	0.464562i
$820$	−44.2113	+	6.77543i	−0.0539162	+	0.00826272i
$821$	569.537	+	569.537i	0.693711	+	0.693711i	0.963046	−	0.269335i	$-0.0868040\pi$
$821$	569.537	+	569.537i	0.693711	+	0.693711i	−0.269335	+	0.963046i	$0.586804\pi$
$822$	881.903	+	542.908i	1.07287	+	0.660472i
$823$	−142.304	+	142.304i	−0.172909	+	0.172909i	−0.788256	−	0.615347i	$-0.789016\pi$
$823$	−142.304	+	142.304i	−0.172909	+	0.172909i	0.615347	+	0.788256i	$0.289016\pi$
$824$	−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
$827$	−829.310			−1.00279			−0.501397	−	0.865217i	$-0.667180\pi$
$827$	−829.310			−1.00279			−0.501397	+	0.865217i	$0.667180\pi$
$828$	−434.275	+	1318.24i	−0.524486	+	1.59207i
$829$	−178.863	−	178.863i	−0.215758	−	0.215758i	0.590950	−	0.806708i	$-0.298753\pi$
$829$	−178.863	−	178.863i	−0.215758	−	0.215758i	−0.806708	+	0.590950i	$0.798753\pi$
$830$	−31.2966	+	383.101i	−0.0377068	+	0.461567i
$831$	743.671			0.894911
$832$	104.496	−	611.253i	0.125597	−	0.734679i
$833$	246.404	+	246.404i	0.295803	+	0.295803i
$834$	−5.76212	+	9.36001i	−0.00690901	+	0.0112230i
$835$	−524.034	+	266.393i	−0.627585	+	0.319034i
$836$	100.036	+	198.327i	0.119660	+	0.237233i
$837$	227.255			0.271511
$838$	−623.522	−	383.846i	−0.744060	−	0.458051i
$839$	1632.17			1.94537			0.972686	−	0.232127i	$-0.0745685\pi$
$839$	1632.17			1.94537			0.972686	+	0.232127i	$0.0745685\pi$
$840$	370.800	−	877.634i	0.441428	−	1.04480i
$841$			75.7868i			0.0901151i
$842$	−1034.07	−	636.583i	−1.22811	−	0.756037i
$843$		−	852.234i		−	1.01095i
$844$	−134.386	+	407.929i	−0.159225	+	0.483328i
$845$	−116.393	+	357.089i	−0.137744	+	0.422591i
$846$	−264.509	+	429.670i	−0.312659	+	0.507885i
$847$	−454.829	+	454.829i	−0.536988	+	0.536988i
$848$	−416.479	−	307.812i	−0.491131	−	0.362986i
$849$		−	2295.94i		−	2.70429i
$850$	−827.470	+	338.970i	−0.973494	+	0.398789i
$851$	898.534	−	898.534i	1.05586	−	1.05586i
$852$	112.344	+	222.729i	0.131859	+	0.261419i
$853$			1087.76i			1.27522i	0.770361	+	0.637608i	$0.220076\pi$
$853$			1087.76i			1.27522i	−0.770361	+	0.637608i	$0.779924\pi$
$854$	−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	0.993425	−	0.114485i	$-0.0365218\pi$
$857$	753.252	+	753.252i	0.878940	+	0.878940i	−0.114485	+	0.993425i	$0.536522\pi$
$858$	−116.734	−	71.8629i	−0.136054	−	0.0837563i
$859$	656.780	−	656.780i	0.764587	−	0.764587i	−0.212561	−	0.977148i	$-0.568180\pi$
$859$	656.780	−	656.780i	0.764587	−	0.764587i	0.977148	+	0.212561i	$0.0681804\pi$
$860$	740.143	−	113.428i	0.860631	−	0.131893i
$861$	−37.6659	+	37.6659i	−0.0437467	+	0.0437467i
$862$	802.861	−	191.019i	0.931393	−	0.221600i
$863$	−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
$867$		−	135.225i		−	0.155968i
$868$	−875.710	−	288.490i	−1.00888	−	0.332362i
$869$	−63.5150	+	63.5150i	−0.0730898	+	0.0730898i
$870$	1011.99	−	859.130i	1.16320	−	0.987505i
$871$		−	800.465i		−	0.919018i
$872$	1298.50	+	110.193i	1.48911	+	0.126368i
$873$	1158.57	−	1158.57i	1.32712	−	1.32712i
$874$	2273.23	−	540.854i	2.60095	−	0.618826i
$875$	670.439	+	108.110i	0.766216	+	0.123555i
$876$	−79.6995	+	241.927i	−0.0909811	+	0.276173i
$877$			1467.43i			1.67324i	0.547787	+	0.836618i	$0.315471\pi$
$877$			1467.43i			1.67324i	−0.547787	+	0.836618i	$0.684529\pi$
$878$	370.056	−	88.0447i	0.421476	−	0.100279i
$879$			1193.94i			1.35829i
$880$	21.3501	−	127.298i	0.0242614	−	0.144657i
$881$	−889.409			−1.00954			−0.504772	−	0.863252i	$-0.668424\pi$
$881$	−889.409			−1.00954			−0.504772	+	0.863252i	$0.668424\pi$
$882$	92.1991	+	387.517i	0.104534	+	0.439362i
$883$	−1602.95			−1.81535			−0.907674	−	0.419675i	$-0.862144\pi$
$883$	−1602.95			−1.81535			−0.907674	+	0.419675i	$0.862144\pi$
$884$	−216.881	+	658.342i	−0.245341	+	0.744730i
$885$	298.842	+	587.864i	0.337674	+	0.664253i
$886$	−118.245	−	496.990i	−0.133460	−	0.560937i
$887$	−428.954	−	428.954i	−0.483601	−	0.483601i	0.422679	−	0.906280i	$-0.361090\pi$
$887$	−428.954	−	428.954i	−0.483601	−	0.483601i	−0.906280	+	0.422679i	$0.861090\pi$
$888$	1003.58	−	846.575i	1.13016	−	0.953350i
$889$	617.246			0.694315
$890$	−112.470	+	1376.75i	−0.126371	+	1.54691i
$891$	−78.1641	−	78.1641i	−0.0877263	−	0.0877263i
$892$	553.606	+	182.378i	0.620635	+	0.204459i
$893$	849.469			0.951253
$894$	−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
$898$	−263.838	−	1108.92i	−0.293806	−	1.23488i
$899$	−908.384	−	908.384i	−1.01044	−	1.01044i
$900$	−1008.62	−	165.901i	−1.12069	−	0.184334i
$901$	409.323	+	409.323i	0.454298	+	0.454298i
$902$	−3.78318	+	6.14542i	−0.00419421	+	0.00681310i
$903$	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
$907$	−1609.72			−1.77478			−0.887388	−	0.461024i	$-0.847482\pi$
$907$	−1609.72			−1.77478			−0.887388	+	0.461024i	$0.847482\pi$
$908$	−177.160	−	351.231i	−0.195110	−	0.386819i
$909$	136.023	+	136.023i	0.149641	+	0.149641i
$910$	401.295	−	340.681i	0.440984	−	0.374375i
$911$	1117.02			1.22615			0.613074	−	0.790025i	$-0.289933\pi$
$911$	1117.02			1.22615			0.613074	+	0.790025i	$0.289933\pi$
$912$	2387.64	−	358.222i	2.61803	−	0.392788i
$913$	43.8529	+	43.8529i	0.0480316	+	0.0480316i
$914$	−694.643	−	427.629i	−0.760004	−	0.467866i
$915$	738.539	+	1452.81i	0.807146	+	1.58777i
$916$	−313.196	+	950.704i	−0.341917	+	1.03789i
$917$	142.786			0.155709
$918$	100.436	−	163.149i	0.109407	−	0.177722i
$919$	−750.127			−0.816242			−0.408121	−	0.912928i	$-0.633816\pi$
$919$	−750.127			−0.816242			−0.408121	+	0.912928i	$0.633816\pi$
$920$	−1250.77	−	528.450i	−1.35953	−	0.574402i
$921$			493.908i			0.536273i
$922$	273.827	−	444.806i	0.296993	−	0.482437i
$923$			137.828i			0.149326i
$924$	−69.2288	−	137.250i	−0.0749229	−	0.148539i
$925$	756.091	+	551.489i	0.817396	+	0.596205i
$926$	−559.657	−	344.530i	−0.604381	−	0.372063i
$927$	382.936	−	382.936i	0.413091	−	0.413091i
$928$	898.892	−	361.638i	0.968634	−	0.389696i
$929$		−	1640.80i		−	1.76620i	−0.469181	−	0.883102i	$-0.655451\pi$
$929$		−	1640.80i		−	1.76620i	0.469181	−	0.883102i	$-0.344549\pi$
$930$	−151.456	+	1853.97i	−0.162856	+	1.99351i
$931$	474.206	−	474.206i	0.509351	−	0.509351i
$932$	314.385	−	954.313i	0.337323	−	1.02394i
$933$		−	1113.74i		−	1.19372i
$934$	−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	0.926146	−	0.377166i	$-0.123101\pi$
$937$	514.395	+	514.395i	0.548980	+	0.548980i	−0.377166	+	0.926146i	$0.623101\pi$
$938$	470.573	−	764.401i	0.501677	−	0.814926i
$939$	98.6087	−	98.6087i	0.105015	−	0.105015i
$940$	−397.886	−	292.139i	−0.423282	−	0.310786i
$941$	1074.54	−	1074.54i	1.14191	−	1.14191i	0.153808	−	0.988101i	$-0.450846\pi$
$941$	1074.54	−	1074.54i	1.14191	−	1.14191i	0.988101	−	0.153808i	$-0.0491538\pi$
$942$	−452.568	−	1902.16i	−0.480433	−	2.01928i
$943$	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
$947$		−	173.864i		−	0.183595i	−0.995778	−	0.0917974i	$-0.970739\pi$
$947$		−	173.864i		−	0.183595i	0.995778	−	0.0917974i	$-0.0292612\pi$
$948$	439.687	+	871.708i	0.463805	+	0.919523i
$949$	−99.5137	+	99.5137i	−0.104862	+	0.104862i
$950$	652.350	+	1592.47i	0.686684	+	1.67628i
$951$			1665.90i			1.75174i
$952$	−594.132	+	501.182i	−0.624088	+	0.526452i
$953$	597.594	−	597.594i	0.627066	−	0.627066i	−0.320263	−	0.947329i	$-0.603771\pi$
$953$	597.594	−	597.594i	0.627066	−	0.627066i	0.947329	+	0.320263i	$0.103771\pi$
$954$	153.160	+	643.737i	0.160545	+	0.674777i
$955$	10.3839	−	31.8571i	0.0108731	−	0.0333582i
$956$	−418.861	−	830.418i	−0.438139	−	0.868638i
$957$		−	214.183i		−	0.223807i
$958$	−51.4449	−	216.225i	−0.0537003	−	0.225705i
$959$			641.648i			0.669080i
$960$	−1241.55	−	653.339i	−1.29328	−	0.680562i
$961$	839.116			0.873170
$962$	705.724	−	167.908i	0.733601	−	0.174540i
$963$	62.8675			0.0652830
$964$	522.761	−	263.680i	0.542284	−	0.273527i
$965$	−1268.77	+	644.981i	−1.31479	+	0.668374i
$966$	−1573.17	+	374.293i	−1.62854	+	0.387467i
$967$	734.726	+	734.726i	0.759800	+	0.759800i	0.976286	−	0.216486i	$-0.0694595\pi$
$967$	734.726	+	734.726i	0.759800	+	0.759800i	−0.216486	+	0.976286i	$0.569460\pi$
$968$	610.722	+	723.987i	0.630911	+	0.747921i
$969$	−2698.68			−2.78502
$970$	1037.39	+	1221.97i	1.06948	+	1.25976i
$971$	797.762	+	797.762i	0.821588	+	0.821588i	0.986336	−	0.164748i	$-0.0526810\pi$
$971$	797.762	+	797.762i	0.821588	+	0.821588i	−0.164748	+	0.986336i	$0.552681\pi$
$972$	−1244.92	+	627.937i	−1.28079	+	0.646025i
$973$	−6.81008			−0.00699905
$974$	−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	$-0.105632\pi$
$978$	−973.965	+	231.728i	−0.995875	+	0.236941i
$979$	157.594	+	157.594i	0.160974	+	0.160974i
$980$	−385.198	+	59.0319i	−0.393059	+	0.0602367i
$981$	−1177.38	−	1177.38i	−1.20019	−	1.20019i
$982$	−803.604	−	494.707i	−0.818334	−	0.503775i
$983$	−17.3080	+	17.3080i	−0.0176073	+	0.0176073i	−0.715856	−	0.698248i	$-0.753963\pi$
$983$	−17.3080	+	17.3080i	−0.0176073	+	0.0176073i	0.698248	+	0.715856i	$0.253963\pi$
$984$	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
$987$	−587.868			−0.595611
$988$	1266.98	+	417.389i	1.28237	+	0.422458i
$989$	−898.659	−	898.659i	−0.908655	−	0.908655i
$990$	−125.726	+	106.735i	−0.126995	+	0.107813i
$991$	504.008			0.508585			0.254293	−	0.967127i	$-0.418157\pi$
$991$	504.008			0.508585			0.254293	+	0.967127i	$0.418157\pi$
$992$	−532.330	+	1248.98i	−0.536623	+	1.25905i
$993$	−248.663	−	248.663i	−0.250416	−	0.250416i
$994$	−81.0256	+	131.618i	−0.0815147	+	0.132413i
$995$	−127.432	+	390.956i	−0.128073	+	0.392920i
$996$	601.856	−	303.575i	0.604273	−	0.304794i
$997$	−1524.58			−1.52917			−0.764583	−	0.644526i	$-0.777055\pi$
$997$	−1524.58			−1.52917			−0.764583	+	0.644526i	$0.777055\pi$
$998$	416.919	+	256.659i	0.417754	+	0.257174i
$999$	−200.507			−0.200707

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.10	✓	44	16.13	even	4
80.3.i.a.37.10	yes	44	5.2	odd	4
80.3.t.a.53.2	yes	44	1.1	even	1	trivial
80.3.t.a.77.2	yes	44	80.77	odd	4	inner
320.3.i.a.177.20		44	20.7	even	4
320.3.i.a.273.3		44	16.3	odd	4
320.3.t.a.17.3		44	80.67	even	4
320.3.t.a.113.3		44	4.3	odd	2
400.3.i.b.93.13		44	80.29	even	4
400.3.i.b.357.13		44	5.3	odd	4
400.3.t.b.157.21		44	80.13	odd	4
400.3.t.b.293.21		44	5.4	even	2
640.3.i.a.33.20		44	16.11	odd	4
640.3.i.a.97.3		44	40.27	even	4
640.3.i.b.33.3		44	16.5	even	4
640.3.i.b.97.20		44	40.37	odd	4
640.3.t.a.353.20		44	8.3	odd	2
640.3.t.a.417.20		44	80.27	even	4
640.3.t.b.353.3		44	8.5	even	2
640.3.t.b.417.3		44	80.37	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.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94569 + 0.462923i) q^{2} +4.38426 q^{3} +(3.57140 - 1.80141i) q^{4} +(1.54952 - 4.75384i) q^{5} +(-8.53040 + 2.02957i) q^{6} +(-3.84157 - 3.84157i) q^{7} +(-6.11493 + 5.15826i) q^{8} +10.2217 q^{9} +O(q^{10})\)	\(q+(-1.94569 + 0.462923i) q^{2} +4.38426 q^{3} +(3.57140 - 1.80141i) q^{4} +(1.54952 - 4.75384i) q^{5} +(-8.53040 + 2.02957i) q^{6} +(-3.84157 - 3.84157i) q^{7} +(-6.11493 + 5.15826i) q^{8} +10.2217 q^{9} +(-0.814216 + 9.96680i) q^{10} +(1.14088 + 1.14088i) q^{11} +(15.6580 - 7.89784i) q^{12} +9.68938 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} +(-19.8883 + 4.73186i) q^{18} +(24.3373 + 24.3373i) q^{19} +(-3.02965 - 19.7692i) q^{20} +(-16.8424 - 16.8424i) q^{21} +(-2.74794 - 1.69166i) 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} +5.35627 q^{27} +(-20.6400 - 6.79956i) q^{28} +(-21.4101 - 21.4101i) q^{29} +(-3.56973 + 43.6970i) q^{30} +42.4278 q^{31} +(-12.5467 + 29.4377i) q^{32} +(5.00192 + 5.00192i) q^{33} +(18.7511 - 30.4593i) q^{34} +(-24.2148 + 12.3096i) q^{35} +(36.5058 - 18.4135i) q^{36} -37.4340 q^{37} +(-58.6191 - 36.0865i) q^{38} +42.4807 q^{39} +(15.0464 + 37.0622i) q^{40} -2.23637i q^{41} +(40.5668 + 24.9733i) q^{42} +37.4392i q^{43} +(6.12974 + 2.01936i) q^{44} +(15.8387 - 48.5924i) q^{45} +(35.5911 - 57.8143i) q^{46} +(17.4520 - 17.4520i) q^{47} +(41.6937 - 56.4127i) q^{48} -19.4847i q^{49} +(46.1189 + 19.3144i) q^{50} +(-55.4434 + 55.4434i) q^{51} +(34.6047 - 17.4545i) q^{52} -32.3677i 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} +(51.5687 + 31.7462i) q^{58} +(-21.2720 + 21.2720i) q^{59} +(-13.2828 - 86.6732i) q^{60} +(-52.5704 + 52.5704i) q^{61} +(-82.5512 + 19.6408i) 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} -82.6126i q^{67} +(-22.3834 + 67.9446i) q^{68} +(-105.236 + 105.236i) q^{69} +(41.4160 - 35.1602i) q^{70} +14.2246i q^{71} +(-62.5050 + 52.7263i) q^{72} +(-10.2704 + 10.2704i) q^{73} +(72.8348 - 17.3291i) q^{74} +(-88.5532 - 64.5903i) q^{75} +(130.760 + 43.0769i) q^{76} -8.76554i q^{77} +(-82.6542 + 19.6653i) q^{78} +55.6719i q^{79} +(-46.4325 - 65.1462i) q^{80} -68.5121 q^{81} +(1.03527 + 4.35129i) q^{82} +38.4377 q^{83} +(-90.4911 - 29.8110i) q^{84} +(40.5219 + 79.7123i) q^{85} +(-17.3315 - 72.8450i) q^{86} +(-93.8675 - 93.8675i) q^{87} +(-12.8614 - 1.09144i) q^{88} +138.133 q^{89} +(-8.32268 + 101.878i) q^{90} +(-37.2224 - 37.2224i) q^{91} +(-42.4855 + 128.965i) q^{92} +186.014 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} +(9.01994 + 37.9112i) q^{98} +(11.6618 + 11.6618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} + 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9	\( 44 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} + 108 q^{9} - 10 q^{10} - 4 q^{11} - 44 q^{12} - 4 q^{13} - 4 q^{15} + 24 q^{16} - 4 q^{17} - 42 q^{18} - 32 q^{19} - 44 q^{20} - 4 q^{21} + 16 q^{22} - 36 q^{24} - 52 q^{26} - 40 q^{27} - 104 q^{28} - 160 q^{30} - 8 q^{31} - 12 q^{32} - 4 q^{33} + 88 q^{34} - 4 q^{35} - 116 q^{36} - 4 q^{37} - 68 q^{38} - 72 q^{39} + 200 q^{40} + 244 q^{42} + 168 q^{44} - 70 q^{45} + 108 q^{46} - 4 q^{47} - 4 q^{48} + 206 q^{50} - 100 q^{51} + 264 q^{52} - 228 q^{54} - 172 q^{56} - 36 q^{57} + 332 q^{58} - 64 q^{59} + 364 q^{60} - 36 q^{61} + 84 q^{62} - 200 q^{63} + 176 q^{64} - 4 q^{65} + 276 q^{66} + 440 q^{68} + 60 q^{69} + 472 q^{70} - 288 q^{72} - 48 q^{73} - 284 q^{74} - 324 q^{75} + 252 q^{76} - 132 q^{78} - 588 q^{80} + 100 q^{81} - 388 q^{82} + 156 q^{83} - 288 q^{84} - 52 q^{85} + 20 q^{86} - 36 q^{87} + 160 q^{88} - 554 q^{90} + 188 q^{91} - 352 q^{92} - 40 q^{93} + 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 818 q^{98} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 + 108 * q^9 - 10 * q^10 - 4 * q^11 - 44 * q^12 - 4 * q^13 - 4 * q^15 + 24 * q^16 - 4 * q^17 - 42 * q^18 - 32 * q^19 - 44 * q^20 - 4 * q^21 + 16 * q^22 - 36 * q^24 - 52 * q^26 - 40 * q^27 - 104 * q^28 - 160 * q^30 - 8 * q^31 - 12 * q^32 - 4 * q^33 + 88 * q^34 - 4 * q^35 - 116 * q^36 - 4 * q^37 - 68 * q^38 - 72 * q^39 + 200 * q^40 + 244 * q^42 + 168 * q^44 - 70 * q^45 + 108 * q^46 - 4 * q^47 - 4 * q^48 + 206 * q^50 - 100 * q^51 + 264 * q^52 - 228 * q^54 - 172 * q^56 - 36 * q^57 + 332 * q^58 - 64 * q^59 + 364 * q^60 - 36 * q^61 + 84 * q^62 - 200 * q^63 + 176 * q^64 - 4 * q^65 + 276 * q^66 + 440 * q^68 + 60 * q^69 + 472 * q^70 - 288 * q^72 - 48 * q^73 - 284 * q^74 - 324 * q^75 + 252 * q^76 - 132 * q^78 - 588 * q^80 + 100 * q^81 - 388 * q^82 + 156 * q^83 - 288 * q^84 - 52 * q^85 + 20 * q^86 - 36 * q^87 + 160 * q^88 - 554 * q^90 + 188 * q^91 - 352 * q^92 - 40 * q^93 + 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 818 * q^98 + 92 * q^99

Introduction

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