LMFDB - Embedded newform 80.3.t.a.77.17

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			77.17
Character	$\chi$	$=$	80.77
Dual form			80.3.t.a.53.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46337 - 1.36329i) q^{2} +1.90859 q^{3} +(0.282885 - 3.98998i) q^{4} +(4.97175 + 0.530759i) q^{5} +(2.79297 - 2.60196i) q^{6} +(-8.62025 + 8.62025i) q^{7} +(-5.02554 - 6.22446i) q^{8} -5.35728 q^{9} +O(q^{10})$	\(q+(1.46337 - 1.36329i) q^{2} +1.90859 q^{3} +(0.282885 - 3.98998i) q^{4} +(4.97175 + 0.530759i) q^{5} +(2.79297 - 2.60196i) q^{6} +(-8.62025 + 8.62025i) q^{7} +(-5.02554 - 6.22446i) q^{8} -5.35728 q^{9} +(7.99907 - 6.00124i) q^{10} +(6.35145 - 6.35145i) q^{11} +(0.539911 - 7.61525i) q^{12} +6.65056 q^{13} +(-0.862693 + 24.3665i) q^{14} +(9.48903 + 1.01300i) q^{15} +(-15.8400 - 2.25741i) q^{16} +(-5.36508 - 5.36508i) q^{17} +(-7.83967 + 7.30353i) q^{18} +(-18.1009 + 18.1009i) q^{19} +(3.52415 - 19.6871i) q^{20} +(-16.4525 + 16.4525i) q^{21} +(0.635637 - 17.9534i) q^{22} +(16.1730 + 16.1730i) q^{23} +(-9.59170 - 11.8800i) q^{24} +(24.4366 + 5.27760i) q^{25} +(9.73220 - 9.06663i) q^{26} -27.4022 q^{27} +(31.9561 + 36.8332i) q^{28} +(12.4816 - 12.4816i) q^{29} +(15.2670 - 11.4539i) q^{30} -18.5625 q^{31} +(-26.2572 + 18.2910i) q^{32} +(12.1223 - 12.1223i) q^{33} +(-15.1652 - 0.536924i) q^{34} +(-47.4330 + 38.2825i) q^{35} +(-1.51549 + 21.3755i) q^{36} +49.8083 q^{37} +(-1.81149 + 51.1649i) q^{38} +12.6932 q^{39} +(-21.6820 - 33.6138i) q^{40} -62.1433i q^{41} +(-1.64653 + 46.5056i) q^{42} -32.2720i q^{43} +(-23.5455 - 27.1389i) q^{44} +(-26.6351 - 2.84343i) q^{45} +(45.7154 + 1.61855i) q^{46} +(13.2635 + 13.2635i) q^{47} +(-30.2320 - 4.30847i) q^{48} -99.6175i q^{49} +(42.9546 - 25.5911i) q^{50} +(-10.2397 - 10.2397i) q^{51} +(1.88134 - 26.5356i) q^{52} +64.2436i q^{53} +(-40.0994 + 37.3571i) q^{54} +(34.9489 - 28.2067i) q^{55} +(96.9779 + 10.3350i) q^{56} +(-34.5471 + 34.5471i) q^{57} +(1.24913 - 35.2812i) q^{58} +(2.55993 + 2.55993i) q^{59} +(6.72616 - 37.5745i) q^{60} +(-52.5270 - 52.5270i) q^{61} +(-27.1638 + 25.3061i) q^{62} +(46.1811 - 46.1811i) q^{63} +(-13.4879 + 62.5626i) q^{64} +(33.0649 + 3.52984i) q^{65} +(1.21317 - 34.2656i) q^{66} -72.2222i q^{67} +(-22.9243 + 19.8889i) q^{68} +(30.8676 + 30.8676i) q^{69} +(-17.2218 + 120.686i) q^{70} +24.3819i q^{71} +(26.9232 + 33.3462i) q^{72} +(1.39841 + 1.39841i) q^{73} +(72.8878 - 67.9031i) q^{74} +(46.6394 + 10.0728i) q^{75} +(67.1017 + 77.3426i) q^{76} +109.502i q^{77} +(18.5748 - 17.3045i) q^{78} -90.0709i q^{79} +(-77.5541 - 19.6305i) q^{80} -4.08398 q^{81} +(-84.7193 - 90.9385i) q^{82} +3.78386 q^{83} +(60.9912 + 70.2995i) q^{84} +(-23.8263 - 29.5214i) q^{85} +(-43.9960 - 47.2257i) q^{86} +(23.8222 - 23.8222i) q^{87} +(-71.4538 - 7.61491i) q^{88} -61.3939 q^{89} +(-42.8533 + 32.1503i) q^{90} +(-57.3295 + 57.3295i) q^{91} +(69.1050 - 59.9548i) q^{92} -35.4283 q^{93} +(37.4913 + 1.32738i) q^{94} +(-99.6001 + 80.3857i) q^{95} +(-50.1142 + 34.9101i) q^{96} +(103.182 + 103.182i) q^{97} +(-135.807 - 145.777i) q^{98} +(-34.0265 + 34.0265i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.46337	−	1.36329i	0.731683	−	0.681645i
$2$	1.46337	−	1.36329i	0.731683	−	0.681645i
$3$	1.90859			0.636197			0.318098	−	0.948058i	$-0.396956\pi$
$3$	1.90859			0.636197			0.318098	+	0.948058i	$0.396956\pi$
$4$	0.282885	−	3.98998i	0.0707212	−	0.997496i
$5$	4.97175	+	0.530759i	0.994350	+	0.106152i
$5$	4.97175	+	0.530759i	0.994350	+	0.106152i
$6$	2.79297	−	2.60196i	0.465495	−	0.433660i
$7$	−8.62025	+	8.62025i	−1.23146	+	1.23146i	−0.268063	+	0.963401i	$0.586384\pi$
$7$	−8.62025	+	8.62025i	−1.23146	+	1.23146i	−0.963401	+	0.268063i	$0.913616\pi$
$8$	−5.02554	−	6.22446i	−0.628192	−	0.778058i
$9$	−5.35728			−0.595254
$10$	7.99907	−	6.00124i	0.799907	−	0.600124i
$11$	6.35145	−	6.35145i	0.577404	−	0.577404i	−0.356783	−	0.934187i	$-0.616126\pi$
$11$	6.35145	−	6.35145i	0.577404	−	0.577404i	0.934187	+	0.356783i	$0.116126\pi$
$12$	0.539911	−	7.61525i	0.0449926	−	0.634604i
$13$	6.65056			0.511581			0.255791	−	0.966732i	$-0.417664\pi$
$13$	6.65056			0.511581			0.255791	+	0.966732i	$0.417664\pi$
$14$	−0.862693	+	24.3665i	−0.0616209	+	1.74046i
$15$	9.48903	+	1.01300i	0.632602	+	0.0675334i
$16$	−15.8400	−	2.25741i	−0.989997	−	0.141088i
$17$	−5.36508	−	5.36508i	−0.315593	−	0.315593i	0.531479	−	0.847072i	$-0.321637\pi$
$17$	−5.36508	−	5.36508i	−0.315593	−	0.315593i	−0.847072	+	0.531479i	$0.821637\pi$
$18$	−7.83967	+	7.30353i	−0.435537	+	0.405751i
$19$	−18.1009	+	18.1009i	−0.952677	+	0.952677i	−0.998930	−	0.0462531i	$-0.985272\pi$
$19$	−18.1009	+	18.1009i	−0.952677	+	0.952677i	0.0462531	+	0.998930i	$0.485272\pi$
$20$	3.52415	−	19.6871i	0.176208	−	0.984353i
$21$	−16.4525	+	16.4525i	−0.783454	+	0.783454i
$22$	0.635637	−	17.9534i	0.0288926	−	0.816062i
$23$	16.1730	+	16.1730i	0.703172	+	0.703172i	0.965090	−	0.261918i	$-0.0843549\pi$
$23$	16.1730	+	16.1730i	0.703172	+	0.703172i	−0.261918	+	0.965090i	$0.584355\pi$
$24$	−9.59170	−	11.8800i	−0.399654	−	0.494998i
$25$	24.4366	+	5.27760i	0.977464	+	0.211104i
$26$	9.73220	−	9.06663i	0.374316	−	0.348717i
$27$	−27.4022			−1.01490
$28$	31.9561	+	36.8332i	1.14129	+	1.31547i
$29$	12.4816	−	12.4816i	0.430400	−	0.430400i	−0.458365	−	0.888764i	$-0.651565\pi$
$29$	12.4816	−	12.4816i	0.430400	−	0.430400i	0.888764	+	0.458365i	$0.151565\pi$
$30$	15.2670	−	11.4539i	0.508898	−	0.381797i
$31$	−18.5625			−0.598792			−0.299396	−	0.954129i	$-0.596785\pi$
$31$	−18.5625			−0.598792			−0.299396	+	0.954129i	$0.596785\pi$
$32$	−26.2572	+	18.2910i	−0.820536	+	0.571594i
$33$	12.1223	−	12.1223i	0.367343	−	0.367343i
$34$	−15.1652	−	0.536924i	−0.446036	−	0.0157919i
$35$	−47.4330	+	38.2825i	−1.35523	+	1.09378i
$36$	−1.51549	+	21.3755i	−0.0420970	+	0.593763i
$37$	49.8083			1.34617			0.673085	−	0.739565i	$-0.264969\pi$
$37$	49.8083			1.34617			0.673085	+	0.739565i	$0.264969\pi$
$38$	−1.81149	+	51.1649i	−0.0476707	+	1.34644i
$39$	12.6932			0.325466
$40$	−21.6820	−	33.6138i	−0.542051	−	0.840346i
$41$		−	62.1433i		−	1.51569i	−0.652434	−	0.757846i	$-0.726252\pi$
$41$		−	62.1433i		−	1.51569i	0.652434	−	0.757846i	$-0.273748\pi$
$42$	−1.64653	+	46.5056i	−0.0392030	+	1.10728i
$43$		−	32.2720i		−	0.750511i	−0.926921	−	0.375255i	$-0.877555\pi$
$43$		−	32.2720i		−	0.750511i	0.926921	−	0.375255i	$-0.122445\pi$
$44$	−23.5455	−	27.1389i	−0.535124	−	0.616793i
$45$	−26.6351	−	2.84343i	−0.591890	−	0.0631872i
$46$	45.7154	+	1.61855i	0.993813	+	0.0351859i
$47$	13.2635	+	13.2635i	0.282202	+	0.282202i	0.833986	−	0.551785i	$-0.186053\pi$
$47$	13.2635	+	13.2635i	0.282202	+	0.282202i	−0.551785	+	0.833986i	$0.686053\pi$
$48$	−30.2320	−	4.30847i	−0.629833	−	0.0897598i
$49$		−	99.6175i		−	2.03301i
$50$	42.9546	−	25.5911i	0.859092	−	0.511821i
$51$	−10.2397	−	10.2397i	−0.200779	−	0.200779i
$52$	1.88134	−	26.5356i	0.0361796	−	0.510300i
$53$			64.2436i			1.21214i	0.795410	+	0.606071i	$0.207255\pi$
$53$			64.2436i			1.21214i	−0.795410	+	0.606071i	$0.792745\pi$
$54$	−40.0994	+	37.3571i	−0.742582	+	0.691798i
$55$	34.9489	−	28.2067i	0.635435	−	0.512850i
$56$	96.9779	+	10.3350i	1.73175	+	0.184554i
$57$	−34.5471	+	34.5471i	−0.606090	+	0.606090i
$58$	1.24913	−	35.2812i	0.0215367	−	0.608296i
$59$	2.55993	+	2.55993i	0.0433887	+	0.0433887i	0.728468	−	0.685080i	$-0.240233\pi$
$59$	2.55993	+	2.55993i	0.0433887	+	0.0433887i	−0.685080	+	0.728468i	$0.740233\pi$
$60$	6.72616	−	37.5745i	0.112103	−	0.626242i
$61$	−52.5270	−	52.5270i	−0.861098	−	0.861098i	0.130367	−	0.991466i	$-0.458384\pi$
$61$	−52.5270	−	52.5270i	−0.861098	−	0.861098i	−0.991466	+	0.130367i	$0.958384\pi$
$62$	−27.1638	+	25.3061i	−0.438126	+	0.408163i
$63$	46.1811	−	46.1811i	0.733034	−	0.733034i
$64$	−13.4879	+	62.5626i	−0.210749	+	0.977540i
$65$	33.0649	+	3.52984i	0.508691	+	0.0543053i
$66$	1.21317	−	34.2656i	0.0183814	−	0.519176i
$67$		−	72.2222i		−	1.07794i	−0.842324	−	0.538972i	$-0.818813\pi$
$67$		−	72.2222i		−	1.07794i	0.842324	−	0.538972i	$-0.181187\pi$
$68$	−22.9243	+	19.8889i	−0.337122	+	0.292484i
$69$	30.8676	+	30.8676i	0.447356	+	0.447356i
$70$	−17.2218	+	120.686i	−0.246026	+	1.72409i
$71$			24.3819i			0.343407i	0.985149	+	0.171703i	$0.0549270\pi$
$71$			24.3819i			0.343407i	−0.985149	+	0.171703i	$0.945073\pi$
$72$	26.9232	+	33.3462i	0.373934	+	0.463142i
$73$	1.39841	+	1.39841i	0.0191563	+	0.0191563i	0.716620	−	0.697464i	$-0.245688\pi$
$73$	1.39841	+	1.39841i	0.0191563	+	0.0191563i	−0.697464	+	0.716620i	$0.745688\pi$
$74$	72.8878	−	67.9031i	0.984970	−	0.917609i
$75$	46.6394	+	10.0728i	0.621859	+	0.134304i
$76$	67.1017	+	77.3426i	0.882917	+	1.01767i
$77$			109.502i			1.42211i
$78$	18.5748	−	17.3045i	0.238138	−	0.221852i
$79$		−	90.0709i		−	1.14014i	−0.821597	−	0.570069i	$-0.806917\pi$
$79$		−	90.0709i		−	1.14014i	0.821597	−	0.570069i	$-0.193083\pi$
$80$	−77.5541	−	19.6305i	−0.969427	−	0.245381i
$81$	−4.08398			−0.0504195
$82$	−84.7193	−	90.9385i	−1.03316	−	1.10901i
$83$	3.78386			0.0455886			0.0227943	−	0.999740i	$-0.492744\pi$
$83$	3.78386			0.0455886			0.0227943	+	0.999740i	$0.492744\pi$
$84$	60.9912	+	70.2995i	0.726085	+	0.836899i
$85$	−23.8263	−	29.5214i	−0.280309	−	0.347311i
$86$	−43.9960	−	47.2257i	−0.511582	−	0.549136i
$87$	23.8222	−	23.8222i	0.273819	−	0.273819i
$88$	−71.4538	−	7.61491i	−0.811975	−	0.0865331i
$89$	−61.3939			−0.689819			−0.344910	−	0.938636i	$-0.612090\pi$
$89$	−61.3939			−0.689819			−0.344910	+	0.938636i	$0.612090\pi$
$90$	−42.8533	+	32.1503i	−0.476148	+	0.357226i
$91$	−57.3295	+	57.3295i	−0.629994	+	0.629994i
$92$	69.1050	−	59.9548i	0.751141	−	0.651683i
$93$	−35.4283			−0.380949
$94$	37.4913	+	1.32738i	0.398843	+	0.0141210i
$95$	−99.6001	+	80.3857i	−1.04842	+	0.846166i
$96$	−50.1142	+	34.9101i	−0.522023	+	0.363646i
$97$	103.182	+	103.182i	1.06373	+	1.06373i	0.997826	+	0.0659075i	$0.0209942\pi$
$97$	103.182	+	103.182i	1.06373	+	1.06373i	0.0659075	+	0.997826i	$0.479006\pi$
$98$	−135.807	−	145.777i	−1.38579	−	1.48752i
$99$	−34.0265	+	34.0265i	−0.343702	+	0.343702i
$100$	27.9703	−	96.0087i	0.279703	−	0.960087i
$101$	−92.1665	+	92.1665i	−0.912539	+	0.912539i	−0.996471	−	0.0839323i	$-0.973252\pi$
$101$	−92.1665	+	92.1665i	−0.912539	+	0.912539i	0.0839323	+	0.996471i	$0.473252\pi$
$102$	−28.9442	−	1.02477i	−0.283767	−	0.0100467i
$103$	73.2115	+	73.2115i	0.710791	+	0.710791i	0.966701	−	0.255909i	$-0.0823749\pi$
$103$	73.2115	+	73.2115i	0.710791	+	0.710791i	−0.255909	+	0.966701i	$0.582375\pi$
$104$	−33.4226	−	41.3962i	−0.321371	−	0.398040i
$105$	−90.5302	+	73.0655i	−0.862192	+	0.695862i
$106$	87.5826	+	94.0119i	0.826251	+	0.886905i
$107$	17.7853			0.166218			0.0831089	−	0.996540i	$-0.473515\pi$
$107$	17.7853			0.166218			0.0831089	+	0.996540i	$0.473515\pi$
$108$	−7.75165	+	109.334i	−0.0717746	+	1.01235i
$109$	−9.64065	+	9.64065i	−0.0884463	+	0.0884463i	−0.749946	−	0.661499i	$-0.769920\pi$
$109$	−9.64065	+	9.64065i	−0.0884463	+	0.0884463i	0.661499	+	0.749946i	$0.269920\pi$
$110$	12.6891	−	88.9223i	0.115356	−	0.808384i
$111$	95.0636			0.856429
$112$	156.004	−	117.085i	1.39289	−	1.04540i
$113$	−62.4937	+	62.4937i	−0.553042	+	0.553042i	−0.927317	−	0.374276i	$-0.877891\pi$
$113$	−62.4937	+	62.4937i	−0.553042	+	0.553042i	0.374276	+	0.927317i	$0.377891\pi$
$114$	−3.45739	+	97.6528i	−0.0303280	+	0.856604i
$115$	71.8240	+	88.9919i	0.624556	+	0.773842i
$116$	−46.2705	−	53.3322i	−0.398884	−	0.459760i
$117$	−35.6289			−0.304521
$118$	7.23605	+	0.256192i	0.0613225	+	0.00217112i
$119$	92.4967			0.777283
$120$	−41.3821	−	64.1550i	−0.344851	−	0.534625i
$121$			40.3182i			0.333208i
$122$	−148.476	−	5.25677i	−1.21701	−	0.0430883i
$123$		−	118.606i		−	0.964278i
$124$	−5.25106	+	74.0642i	−0.0423472	+	0.597292i
$125$	118.691	+	39.2089i	0.949532	+	0.313671i
$126$	4.62169	−	130.538i	0.0366801	−	1.03602i
$127$	−50.6008	−	50.6008i	−0.398432	−	0.398432i	0.479248	−	0.877680i	$-0.340909\pi$
$127$	−50.6008	−	50.6008i	−0.398432	−	0.398432i	−0.877680	+	0.479248i	$0.840909\pi$
$128$	65.5531	+	109.940i	0.512134	+	0.858906i
$129$		−	61.5939i		−	0.477472i
$130$	53.1983	−	39.9116i	0.409218	−	0.307012i
$131$	−22.0987	−	22.0987i	−0.168693	−	0.168693i	0.617712	−	0.786404i	$-0.288060\pi$
$131$	−22.0987	−	22.0987i	−0.168693	−	0.168693i	−0.786404	+	0.617712i	$0.788060\pi$
$132$	−44.9386	−	51.7971i	−0.340444	−	0.392402i
$133$		−	312.068i		−	2.34637i
$134$	−98.4598	−	105.688i	−0.734775	−	0.788714i
$135$	−136.237	−	14.5440i	−1.00916	−	0.107733i
$136$	−6.43233	+	60.3572i	−0.0472966	+	0.443803i
$137$	102.317	−	102.317i	0.746841	−	0.746841i	−0.227043	−	0.973885i	$-0.572906\pi$
$137$	102.317	−	102.317i	0.746841	−	0.746841i	0.973885	+	0.227043i	$0.0729059\pi$
$138$	87.2520	+	3.08915i	0.632261	+	0.0223851i
$139$	83.0087	+	83.0087i	0.597185	+	0.597185i	0.939562	−	0.342378i	$-0.111232\pi$
$139$	83.0087	+	83.0087i	0.597185	+	0.597185i	−0.342378	+	0.939562i	$0.611232\pi$
$140$	139.328	+	200.086i	0.995202	+	1.42919i
$141$	25.3145	+	25.3145i	0.179536	+	0.179536i
$142$	33.2395	+	35.6796i	0.234081	+	0.251265i
$143$	42.2407	−	42.2407i	0.295389	−	0.295389i
$144$	84.8591	+	12.0936i	0.589299	+	0.0839832i
$145$	68.6800	−	55.4306i	0.473656	−	0.382280i
$146$	3.95283	+	0.139950i	0.0270742	+	0.000958559i
$147$		−	190.129i		−	1.29339i
$148$	14.0900	−	198.734i	0.0952027	−	1.34280i
$149$	134.149	+	134.149i	0.900331	+	0.900331i	0.995465	−	0.0951332i	$-0.0303277\pi$
$149$	134.149	+	134.149i	0.900331	+	0.900331i	−0.0951332	+	0.995465i	$0.530328\pi$
$150$	81.9827	−	48.8429i	0.546551	−	0.325619i
$151$		−	48.5859i		−	0.321761i	−0.986974	−	0.160881i	$-0.948567\pi$
$151$		−	48.5859i		−	0.321761i	0.986974	−	0.160881i	$-0.0514334\pi$
$152$	203.635	+	21.7016i	1.33970	+	0.142774i
$153$	28.7423	+	28.7423i	0.187858	+	0.187858i
$154$	149.283	+	160.242i	0.969371	+	1.04053i
$155$	−92.2883	−	9.85223i	−0.595408	−	0.0635628i
$156$	3.59071	−	50.6456i	0.0230174	−	0.324651i
$157$			140.992i			0.898038i	0.893522	+	0.449019i	$0.148226\pi$
$157$			140.992i			0.898038i	−0.893522	+	0.449019i	$0.851774\pi$
$158$	−122.793	−	131.807i	−0.777169	−	0.834220i
$159$			122.615i			0.771162i
$160$	−140.252	+	77.0021i	−0.876576	+	0.481263i
$161$	−278.830			−1.73186
$162$	−5.97636	+	5.56765i	−0.0368911	+	0.0343682i
$163$	98.2045			0.602482			0.301241	−	0.953548i	$-0.402599\pi$
$163$	98.2045			0.602482			0.301241	+	0.953548i	$0.402599\pi$
$164$	−247.951	−	17.5794i	−1.51190	−	0.107191i
$165$	66.7031	−	53.8351i	0.404261	−	0.326273i
$166$	5.53717	−	5.15849i	0.0333564	−	0.0310752i
$167$	−9.58867	+	9.58867i	−0.0574172	+	0.0574172i	−0.735232	−	0.677815i	$-0.762927\pi$
$167$	−9.58867	+	9.58867i	−0.0574172	+	0.0574172i	0.677815	+	0.735232i	$0.262927\pi$
$168$	185.091	+	19.7254i	1.10173	+	0.117413i
$169$	−124.770			−0.738285
$170$	−75.1128	−	10.7185i	−0.441840	−	0.0630502i
$171$	96.9714	−	96.9714i	0.567084	−	0.567084i
$172$	−128.765	−	9.12924i	−0.748631	−	0.0530770i
$173$	−172.905			−0.999452			−0.499726	−	0.866184i	$-0.666566\pi$
$173$	−172.905			−0.999452			−0.499726	+	0.866184i	$0.666566\pi$
$174$	2.38407	−	67.3373i	0.0137016	−	0.386996i
$175$	−256.144	+	165.155i	−1.46368	+	0.943744i
$176$	−114.944	+	86.2688i	−0.653094	+	0.490164i
$177$	4.88586	+	4.88586i	0.0276037	+	0.0276037i
$178$	−89.8418	+	83.6977i	−0.504729	+	0.470212i
$179$	47.1828	−	47.1828i	0.263591	−	0.263591i	−0.562920	−	0.826511i	$-0.690322\pi$
$179$	47.1828	−	47.1828i	0.263591	−	0.263591i	0.826511	+	0.562920i	$0.190322\pi$
$180$	−18.8799	+	105.469i	−0.104888	+	0.585940i
$181$	50.7180	−	50.7180i	0.280210	−	0.280210i	−0.552983	−	0.833193i	$-0.686511\pi$
$181$	50.7180	−	50.7180i	0.280210	−	0.280210i	0.833193	+	0.552983i	$0.186511\pi$
$182$	−5.73739	+	162.051i	−0.0315241	+	0.890388i
$183$	−100.253	−	100.253i	−0.547828	−	0.547828i
$184$	19.3902	−	181.946i	0.105381	−	0.988837i
$185$	247.634	+	26.4362i	1.33856	+	0.142898i
$186$	−51.8446	+	48.2990i	−0.278734	+	0.259672i
$187$	−68.1521			−0.364450
$188$	56.6731	−	49.1690i	0.301453	−	0.261537i
$189$	236.214	−	236.214i	1.24981	−	1.24981i
$190$	−36.1625	+	253.418i	−0.190329	+	1.33378i
$191$	330.128			1.72842			0.864210	−	0.503132i	$-0.167819\pi$
$191$	330.128			1.72842			0.864210	+	0.503132i	$0.167819\pi$
$192$	−25.7429	+	119.406i	−0.134078	+	0.621908i
$193$	−150.560	+	150.560i	−0.780103	+	0.780103i	−0.979848	−	0.199745i	$-0.935989\pi$
$193$	−150.560	+	150.560i	−0.780103	+	0.780103i	0.199745	+	0.979848i	$0.435989\pi$
$194$	291.660	+	10.3262i	1.50340	+	0.0532279i
$195$	63.1074	+	6.73702i	0.323627	+	0.0345488i
$196$	−397.472	−	28.1802i	−2.02792	−	0.143777i
$197$	−257.794			−1.30860			−0.654299	−	0.756236i	$-0.727036\pi$
$197$	−257.794			−1.30860			−0.654299	+	0.756236i	$0.727036\pi$
$198$	−3.40529	+	96.1812i	−0.0171984	+	0.485764i
$199$	−328.501			−1.65076			−0.825378	−	0.564580i	$-0.809038\pi$
$199$	−328.501			−1.65076			−0.825378	+	0.564580i	$0.809038\pi$
$200$	−89.9568	−	178.627i	−0.449784	−	0.893137i
$201$		−	137.843i		−	0.685785i
$202$	−9.22379	+	260.523i	−0.0456623	+	1.28972i
$203$			215.189i			1.06004i
$204$	−43.7531	+	37.9598i	−0.214476	+	0.186077i
$205$	32.9831	−	308.961i	0.160893	−	1.50713i
$206$	206.944	+	7.32682i	1.00458	+	0.0355671i
$207$	−86.6431	−	86.6431i	−0.418566	−	0.418566i
$208$	−105.344	−	15.0130i	−0.506464	−	0.0721781i
$209$			229.933i			1.10016i
$210$	−32.8694	+	230.340i	−0.156521	+	1.09686i
$211$	51.3916	+	51.3916i	0.243562	+	0.243562i	0.818322	−	0.574760i	$-0.194905\pi$
$211$	51.3916	+	51.3916i	0.243562	+	0.243562i	−0.574760	+	0.818322i	$0.694905\pi$
$212$	256.331	+	18.1735i	1.20911	+	0.0857242i
$213$			46.5350i			0.218474i
$214$	26.0264	−	24.2465i	0.121619	−	0.113301i
$215$	17.1286	−	160.448i	0.0796681	−	0.746270i
$216$	137.711	+	170.564i	0.637549	+	0.789647i
$217$	160.014	−	160.014i	0.737390	−	0.737390i
$218$	−0.964812	+	27.2508i	−0.00442574	+	0.125004i
$219$	2.66900	+	2.66900i	0.0121872	+	0.0121872i
$220$	−102.658	−	147.425i	−0.466627	−	0.670113i
$221$	−35.6808	−	35.6808i	−0.161451	−	0.161451i
$222$	139.113	−	129.599i	0.626635	−	0.583780i
$223$	−200.019	+	200.019i	−0.896948	+	0.896948i	−0.995165	−	0.0982168i	$-0.968686\pi$
$223$	−200.019	+	200.019i	−0.896948	+	0.896948i	0.0982168	+	0.995165i	$0.468686\pi$
$224$	68.6702	−	384.017i	0.306563	−	1.71436i
$225$	−130.914	−	28.2736i	−0.581839	−	0.125660i
$226$	−6.25421	+	176.648i	−0.0276735	+	0.781629i
$227$			47.5480i			0.209462i	0.994501	+	0.104731i	$0.0333982\pi$
$227$			47.5480i			0.209462i	−0.994501	+	0.104731i	$0.966602\pi$
$228$	128.070	+	147.615i	0.561709	+	0.647436i
$229$	−65.5550	−	65.5550i	−0.286266	−	0.286266i	0.549336	−	0.835602i	$-0.314881\pi$
$229$	−65.5550	−	65.5550i	−0.286266	−	0.286266i	−0.835602	+	0.549336i	$0.814881\pi$
$230$	226.427	+	32.3109i	0.984463	+	0.140482i
$231$			208.995i			0.904739i
$232$	−140.418	−	14.9645i	−0.605250	−	0.0645021i
$233$	201.087	+	201.087i	0.863035	+	0.863035i	0.991689	−	0.128655i	$-0.0410659\pi$
$233$	201.087	+	201.087i	0.863035	+	0.863035i	−0.128655	+	0.991689i	$0.541066\pi$
$234$	−52.1382	+	48.5725i	−0.222813	+	0.207575i
$235$	58.9030	+	72.9824i	0.250651	+	0.310563i
$236$	10.9383	−	9.48993i	0.0463486	−	0.0402116i
$237$		−	171.908i		−	0.725352i
$238$	135.357	−	126.100i	0.568725	−	0.529831i
$239$		−	245.088i		−	1.02547i	−0.858546	−	0.512737i	$-0.828632\pi$
$239$		−	245.088i		−	1.02547i	0.858546	−	0.512737i	$-0.171368\pi$
$240$	−148.019	−	37.4665i	−0.616746	−	0.156111i
$241$	462.483			1.91902			0.959508	−	0.281682i	$-0.0908922\pi$
$241$	462.483			1.91902			0.959508	+	0.281682i	$0.0908922\pi$
$242$	54.9653	+	59.0003i	0.227130	+	0.243803i
$243$	238.825			0.982819
$244$	−224.441	+	194.723i	−0.919840	+	0.798044i
$245$	52.8729	−	495.273i	0.215808	−	2.02152i
$246$	−161.695	−	173.564i	−0.657295	−	0.705546i
$247$	−120.381	+	120.381i	−0.487372	+	0.487372i
$248$	93.2868	+	115.542i	0.376156	+	0.465895i
$249$	7.22183			0.0290033
$250$	227.142	−	104.434i	0.908569	−	0.417735i
$251$	−53.5564	+	53.5564i	−0.213372	+	0.213372i	−0.805698	−	0.592326i	$-0.798210\pi$
$251$	−53.5564	+	53.5564i	−0.213372	+	0.213372i	0.592326	+	0.805698i	$0.298210\pi$
$252$	−171.198	−	197.326i	−0.679357	−	0.783039i
$253$	205.444			0.812030
$254$	−143.031	−	5.06400i	−0.563115	−	0.0199370i
$255$	−45.4746	−	56.3443i	−0.178332	−	0.220958i
$256$	245.808	+	71.5146i	0.960188	+	0.279354i
$257$	128.524	+	128.524i	0.500092	+	0.500092i	0.911466	−	0.411374i	$-0.134951\pi$
$257$	128.524	+	128.524i	0.500092	+	0.500092i	−0.411374	+	0.911466i	$0.634951\pi$
$258$	−83.9704	−	90.1345i	−0.325467	−	0.349359i
$259$	−429.360	+	429.360i	−1.65776	+	1.65776i
$260$	23.4376	−	130.930i	0.0901445	−	0.503577i
$261$	−66.8674	+	66.8674i	−0.256197	+	0.256197i
$262$	−62.4655	−	2.21159i	−0.238418	−	0.00844117i
$263$	−351.385	−	351.385i	−1.33606	−	1.33606i	−0.899836	−	0.436228i	$-0.856314\pi$
$263$	−351.385	−	351.385i	−1.33606	−	1.33606i	−0.436228	−	0.899836i	$-0.643686\pi$
$264$	−136.376	−	14.5338i	−0.516576	−	0.0550521i
$265$	−34.0979	+	319.403i	−0.128671	+	1.20529i
$266$	−425.439	−	456.670i	−1.59939	−	1.71680i
$267$	−117.176			−0.438861
$268$	−288.166	−	20.4306i	−1.07524	−	0.0762335i
$269$	−45.4562	+	45.4562i	−0.168982	+	0.168982i	−0.786532	−	0.617550i	$-0.788125\pi$
$269$	−45.4562	+	45.4562i	−0.168982	+	0.168982i	0.617550	+	0.786532i	$0.288125\pi$
$270$	−219.192	+	164.447i	−0.811822	+	0.609063i
$271$	43.2087			0.159442			0.0797209	−	0.996817i	$-0.474597\pi$
$271$	43.2087			0.159442			0.0797209	+	0.996817i	$0.474597\pi$
$272$	72.8714	+	97.0938i	0.267910	+	0.356963i
$273$	−109.418	+	109.418i	−0.400800	+	0.400800i
$274$	10.2397	−	289.216i	0.0373710	−	1.05553i
$275$	188.728	−	121.687i	0.686284	−	0.442499i
$276$	131.893	−	114.429i	0.477873	−	0.414598i
$277$	−53.1202			−0.191770			−0.0958849	−	0.995392i	$-0.530568\pi$
$277$	−53.1202			−0.191770			−0.0958849	+	0.995392i	$0.530568\pi$
$278$	234.637	+	8.30730i	0.844018	+	0.0298824i
$279$	99.4448			0.356433
$280$	476.664	+	102.855i	1.70237	+	0.367340i
$281$		−	146.320i		−	0.520712i	−0.965513	−	0.260356i	$-0.916160\pi$
$281$		−	146.320i		−	0.520712i	0.965513	−	0.260356i	$-0.0838399\pi$
$282$	71.5555	+	2.53342i	0.253743	+	0.00898375i
$283$		−	87.7034i		−	0.309906i	−0.987922	−	0.154953i	$-0.950477\pi$
$283$		−	87.7034i		−	0.309906i	0.987922	−	0.154953i	$-0.0495226\pi$
$284$	97.2833	+	6.89726i	0.342547	+	0.0242861i
$285$	−190.096	+	153.423i	−0.667003	+	0.538328i
$286$	4.22734	−	119.400i	0.0147809	−	0.417482i
$287$	535.691	+	535.691i	1.86652	+	1.86652i
$288$	140.667	−	97.9901i	0.488427	−	0.340244i
$289$		−	231.432i		−	0.800802i
$290$	24.9361	−	174.746i	0.0859867	−	0.602573i
$291$	196.932	+	196.932i	0.676744	+	0.676744i
$292$	5.97523	−	5.18405i	0.0204631	−	0.0177536i
$293$			257.077i			0.877395i	0.898635	+	0.438697i	$0.144560\pi$
$293$			257.077i			0.877395i	−0.898635	+	0.438697i	$0.855440\pi$
$294$	−259.201	−	278.228i	−0.881635	−	0.946355i
$295$	11.3686	+	14.0861i	0.0385378	+	0.0477493i
$296$	−250.313	−	310.030i	−0.845653	−	1.04740i
$297$	−174.044	+	174.044i	−0.586005	+	0.586005i
$298$	379.194	+	13.4253i	1.27246	+	0.0450515i
$299$	107.559	+	107.559i	0.359730	+	0.359730i
$300$	53.3838	−	183.241i	0.177946	−	0.610804i
$301$	278.192	+	278.192i	0.924227	+	0.924227i
$302$	−66.2367	−	71.0990i	−0.219327	−	0.235427i
$303$	−175.908	+	175.908i	−0.580555	+	0.580555i
$304$	327.578	−	245.856i	1.07756	−	0.808736i
$305$	−233.272	−	289.030i	−0.764826	−	0.947640i
$306$	81.2445	+	2.87645i	0.265505	+	0.00940017i
$307$		−	601.105i		−	1.95800i	−0.203870	−	0.978998i	$-0.565352\pi$
$307$		−	601.105i		−	1.95800i	0.203870	−	0.978998i	$-0.434648\pi$
$308$	436.912	+	30.9765i	1.41855	+	0.100573i
$309$	139.731	+	139.731i	0.452203	+	0.452203i
$310$	−148.483	+	111.398i	−0.478978	+	0.359349i
$311$			7.34424i			0.0236149i	0.999930	+	0.0118075i	$0.00375852\pi$
$311$			7.34424i			0.0236149i	−0.999930	+	0.0118075i	$0.996241\pi$
$312$	−63.7901	−	79.0083i	−0.204455	−	0.253232i
$313$	−170.573	−	170.573i	−0.544962	−	0.544962i	0.380017	−	0.924979i	$-0.375918\pi$
$313$	−170.573	−	170.573i	−0.544962	−	0.544962i	−0.924979	+	0.380017i	$0.875918\pi$
$314$	192.213	+	206.323i	0.612143	+	0.657079i
$315$	254.112	−	205.090i	0.806705	−	0.651079i
$316$	−359.381	−	25.4797i	−1.13728	−	0.0806319i
$317$			266.389i			0.840345i	0.907444	+	0.420172i	$0.138030\pi$
$317$			266.389i			0.840345i	−0.907444	+	0.420172i	$0.861970\pi$
$318$	167.159	+	179.430i	0.525658	+	0.564246i
$319$		−	158.552i		−	0.497029i
$320$	−100.264	+	303.887i	−0.313326	+	0.949646i
$321$	33.9449			0.105747
$322$	−408.031	+	380.126i	−1.26718	+	1.18052i
$323$	194.225			0.601316
$324$	−1.15530	+	16.2950i	−0.00356573	+	0.0502933i
$325$	162.517	+	35.0990i	0.500052	+	0.107997i
$326$	143.709	−	133.881i	0.440826	−	0.410678i
$327$	−18.4000	+	18.4000i	−0.0562693	+	0.0562693i
$328$	−386.809	+	312.304i	−1.17930	+	0.952146i
$329$	−228.669			−0.695043
$330$	24.2184	−	169.716i	0.0733890	−	0.514291i
$331$	−66.9868	+	66.9868i	−0.202377	+	0.202377i	−0.801018	−	0.598641i	$-0.795708\pi$
$331$	−66.9868	+	66.9868i	−0.202377	+	0.202377i	0.598641	+	0.801018i	$0.295708\pi$
$332$	1.07039	−	15.0975i	0.00322408	−	0.0454745i
$333$	−266.837			−0.801312
$334$	−0.959611	+	27.1039i	−0.00287309	+	0.0811494i
$335$	38.3326	−	359.071i	0.114426	−	1.07185i
$336$	297.747	−	223.467i	0.886153	−	0.665081i
$337$	−167.759	−	167.759i	−0.497801	−	0.497801i	0.412952	−	0.910753i	$-0.364498\pi$
$337$	−167.759	−	167.759i	−0.497801	−	0.497801i	−0.910753	+	0.412952i	$0.864498\pi$
$338$	−182.584	+	170.098i	−0.540191	+	0.503248i
$339$	−119.275	+	119.275i	−0.351843	+	0.351843i
$340$	−124.530	+	86.7153i	−0.366265	+	0.255045i
$341$	−117.899	+	117.899i	−0.345745	+	0.345745i
$342$	9.70466	−	274.105i	0.0283762	−	0.801476i
$343$	436.335	+	436.335i	1.27211	+	1.27211i
$344$	−200.876	+	162.184i	−0.583941	+	0.471465i
$345$	137.083	+	169.849i	0.397341	+	0.492316i
$346$	−253.024	+	235.720i	−0.731283	+	0.681271i
$347$	−575.495			−1.65849			−0.829243	−	0.558888i	$-0.811228\pi$
$347$	−575.495			−1.65849			−0.829243	+	0.558888i	$0.811228\pi$
$348$	−88.3114	−	101.789i	−0.253768	−	0.292498i
$349$	−218.302	+	218.302i	−0.625508	+	0.625508i	−0.946935	−	0.321426i	$-0.895838\pi$
$349$	−218.302	+	218.302i	−0.625508	+	0.625508i	0.321426	+	0.946935i	$0.395838\pi$
$350$	−149.678	+	590.881i	−0.427651	+	1.68823i
$351$	−182.240			−0.519201
$352$	−50.5966	+	282.946i	−0.143740	+	0.803823i
$353$	194.122	−	194.122i	0.549920	−	0.549920i	−0.376498	−	0.926418i	$-0.622872\pi$
$353$	194.122	−	194.122i	0.549920	−	0.549920i	0.926418	+	0.376498i	$0.122872\pi$
$354$	13.8107	+	0.488965i	0.0390131	+	0.00138126i
$355$	−12.9409	+	121.221i	−0.0364532	+	0.341466i
$356$	−17.3674	+	244.961i	−0.0487848	+	0.688092i
$357$	176.538			0.494505
$358$	4.72194	−	133.370i	0.0131898	−	0.372541i
$359$	545.851			1.52048			0.760238	−	0.649644i	$-0.225082\pi$
$359$	545.851			1.52048			0.760238	+	0.649644i	$0.225082\pi$
$360$	116.157	+	180.079i	0.322658	+	0.500219i
$361$		−	294.282i		−	0.815186i
$362$	5.07573	−	143.362i	0.0140213	−	0.396028i
$363$			76.9509i			0.211986i
$364$	212.526	+	244.961i	0.583863	+	0.672971i
$365$	6.21033	+	7.69477i	0.0170146	+	0.0210816i
$366$	−283.379	−	10.0330i	−0.774261	−	0.0274126i
$367$	−300.825	−	300.825i	−0.819686	−	0.819686i	0.166376	−	0.986062i	$-0.446793\pi$
$367$	−300.825	−	300.825i	−0.819686	−	0.819686i	−0.986062	+	0.166376i	$0.946793\pi$
$368$	−219.670	−	292.688i	−0.596929	−	0.795348i
$369$			332.919i			0.902221i
$370$	398.420	−	298.911i	1.07681	−	0.807868i
$371$	−553.796	−	553.796i	−1.49271	−	1.49271i
$372$	−10.0221	+	141.358i	−0.0269412	+	0.379995i
$373$			73.3291i			0.196593i	0.995157	+	0.0982963i	$0.0313393\pi$
$373$			73.3291i			0.196593i	−0.995157	+	0.0982963i	$0.968661\pi$
$374$	−99.7315	+	92.9110i	−0.266662	+	0.248425i
$375$	226.533	+	74.8336i	0.604089	+	0.199556i
$376$	15.9019	−	149.214i	0.0422923	−	0.396846i
$377$	83.0095	−	83.0095i	0.220184	−	0.220184i
$378$	23.6397	−	667.695i	0.0625388	−	1.76639i
$379$	93.5200	+	93.5200i	0.246755	+	0.246755i	0.819637	−	0.572883i	$-0.194175\pi$
$379$	93.5200	+	93.5200i	0.246755	+	0.246755i	−0.572883	+	0.819637i	$0.694175\pi$
$380$	292.562	+	420.143i	0.769901	+	1.10564i
$381$	−96.5762	−	96.5762i	−0.253481	−	0.253481i
$382$	483.099	−	450.060i	1.26466	−	1.17817i
$383$	−79.4324	+	79.4324i	−0.207395	+	0.207395i	−0.803159	−	0.595764i	$-0.796849\pi$
$383$	−79.4324	+	79.4324i	−0.207395	+	0.207395i	0.595764	+	0.803159i	$0.296849\pi$
$384$	125.114	+	209.830i	0.325818	+	0.546433i
$385$	−58.1193	+	544.417i	−0.150959	+	1.41407i
$386$	−15.0677	+	425.581i	−0.0390354	+	1.10254i
$387$			172.890i			0.446744i
$388$	440.884	−	382.506i	1.13630	−	0.985841i
$389$	−97.6035	−	97.6035i	−0.250909	−	0.250909i	0.570434	−	0.821343i	$-0.306775\pi$
$389$	−97.6035	−	97.6035i	−0.250909	−	0.250909i	−0.821343	+	0.570434i	$0.806775\pi$
$390$	101.534	−	76.1748i	0.260343	−	0.195320i
$391$		−	173.539i		−	0.443833i
$392$	−620.065	+	500.631i	−1.58180	+	1.27712i
$393$	−42.1774	−	42.1774i	−0.107322	−	0.107322i
$394$	−377.247	+	351.448i	−0.957480	+	0.891999i
$395$	47.8059	−	447.810i	0.121028	−	1.13370i
$396$	126.140	+	145.391i	0.318535	+	0.367149i
$397$		−	299.500i		−	0.754407i	−0.926130	−	0.377204i	$-0.876886\pi$
$397$		−	299.500i		−	0.754407i	0.926130	−	0.377204i	$-0.123114\pi$
$398$	−480.717	+	447.841i	−1.20783	+	1.12523i
$399$		−	595.610i		−	1.49276i
$400$	−375.161	−	138.760i	−0.937902	−	0.346901i
$401$	−90.9226			−0.226740			−0.113370	−	0.993553i	$-0.536164\pi$
$401$	−90.9226			−0.226740			−0.113370	+	0.993553i	$0.536164\pi$
$402$	−187.919	−	201.714i	−0.467461	−	0.501777i
$403$	−123.451			−0.306331
$404$	341.670	+	393.815i	0.845718	+	0.974790i
$405$	−20.3045	−	2.16761i	−0.0501346	−	0.00535212i
$406$	293.365	+	314.900i	0.722573	+	0.775616i
$407$	316.355	−	316.355i	0.777284	−	0.777284i
$408$	−12.2767	+	115.197i	−0.0300899	+	0.282346i
$409$	−657.734			−1.60815			−0.804076	−	0.594526i	$-0.797340\pi$
$409$	−657.734			−1.60815			−0.804076	+	0.594526i	$0.797340\pi$
$410$	−372.937	−	497.089i	−0.909602	−	1.21241i
$411$	195.282	−	195.282i	0.475138	−	0.475138i
$412$	312.823	−	271.402i	0.759280	−	0.658744i
$413$	−44.1345			−0.106863
$414$	−244.910	−	8.67103i	−0.591571	−	0.0209445i
$415$	18.8124	+	2.00832i	0.0453310	+	0.00483931i
$416$	−174.625	+	121.645i	−0.419771	+	0.292417i
$417$	158.430	+	158.430i	0.379927	+	0.379927i
$418$	313.466	+	336.477i	0.749918	+	0.804968i
$419$	−145.179	+	145.179i	−0.346489	+	0.346489i	−0.858800	−	0.512311i	$-0.828790\pi$
$419$	−145.179	+	145.179i	−0.346489	+	0.346489i	0.512311	+	0.858800i	$0.328790\pi$
$420$	265.921	+	381.883i	0.633145	+	0.909246i
$421$	−19.6145	+	19.6145i	−0.0465904	+	0.0465904i	−0.730018	−	0.683428i	$-0.760488\pi$
$421$	−19.6145	+	19.6145i	−0.0465904	+	0.0465904i	0.683428	+	0.730018i	$0.260488\pi$
$422$	145.266	+	5.14315i	0.344233	+	0.0121875i
$423$	−71.0562	−	71.0562i	−0.167982	−	0.167982i
$424$	399.882	−	322.859i	0.943118	−	0.761459i
$425$	−102.790	−	159.419i	−0.241858	−	0.375104i
$426$	63.4407	+	68.0978i	0.148922	+	0.159854i
$427$	905.592			2.12082
$428$	5.03119	−	70.9631i	0.0117551	−	0.165802i
$429$	80.6201	−	80.6201i	0.187926	−	0.187926i
$430$	−193.672	−	258.146i	−0.450399	−	0.600339i
$431$	184.193			0.427362			0.213681	−	0.976903i	$-0.431455\pi$
$431$	184.193			0.427362			0.213681	+	0.976903i	$0.431455\pi$
$432$	434.049	+	61.8580i	1.00474	+	0.143190i
$433$	401.221	−	401.221i	0.926607	−	0.926607i	−0.0708779	−	0.997485i	$-0.522580\pi$
$433$	401.221	−	401.221i	0.926607	−	0.926607i	0.997485	+	0.0708779i	$0.0225801\pi$
$434$	16.0138	−	452.304i	0.0368981	−	1.04217i
$435$	131.082	−	105.794i	0.301338	−	0.243205i
$436$	35.7388	+	41.1932i	0.0819698	+	0.0944799i
$437$	−585.489			−1.33979
$438$	7.54433	+	0.267106i	0.0172245	+	0.000609832i
$439$	705.526			1.60712			0.803561	−	0.595223i	$-0.202936\pi$
$439$	705.526			1.60712			0.803561	+	0.595223i	$0.202936\pi$
$440$	−351.209	−	75.7842i	−0.798202	−	0.172237i
$441$			533.679i			1.21016i
$442$	−100.857	−	3.57084i	−0.228184	−	0.00807883i
$443$		−	499.336i		−	1.12717i	−0.826058	−	0.563585i	$-0.809422\pi$
$443$		−	499.336i		−	1.12717i	0.826058	−	0.563585i	$-0.190578\pi$
$444$	26.8920	−	379.302i	0.0605676	−	0.854284i
$445$	−305.235	−	32.5854i	−0.685922	−	0.0732256i
$446$	−20.0174	+	565.386i	−0.0448822	+	1.26768i
$447$	256.036	+	256.036i	0.572788	+	0.572788i
$448$	−423.036	−	655.574i	−0.944277	−	1.46334i
$449$		−	786.125i		−	1.75083i	−0.483368	−	0.875417i	$-0.660587\pi$
$449$		−	786.125i		−	1.75083i	0.483368	−	0.875417i	$-0.339413\pi$
$450$	−230.120	+	137.099i	−0.511378	+	0.304664i
$451$	−394.700	−	394.700i	−0.875167	−	0.875167i
$452$	231.670	+	267.027i	0.512545	+	0.590769i
$453$		−	92.7306i		−	0.204703i
$454$	64.8217	+	69.5801i	0.142779	+	0.153260i
$455$	−315.456	+	254.600i	−0.693310	+	0.559560i
$456$	388.655	+	41.4194i	0.852314	+	0.0908321i
$457$	411.045	−	411.045i	0.899443	−	0.899443i	−0.0959440	−	0.995387i	$-0.530587\pi$
$457$	411.045	−	411.045i	0.899443	−	0.899443i	0.995387	+	0.0959440i	$0.0305870\pi$
$458$	−185.301	−	6.56058i	−0.404588	−	0.0143244i
$459$	147.015	+	147.015i	0.320294	+	0.320294i
$460$	375.394	−	261.402i	0.816074	−	0.568266i
$461$	544.187	+	544.187i	1.18045	+	1.18045i	0.979628	+	0.200821i	$0.0643610\pi$
$461$	544.187	+	544.187i	1.18045	+	1.18045i	0.200821	+	0.979628i	$0.435639\pi$
$462$	284.920	+	305.836i	0.616711	+	0.661983i
$463$	109.453	−	109.453i	0.236400	−	0.236400i	−0.578957	−	0.815358i	$-0.696540\pi$
$463$	109.453	−	109.453i	0.236400	−	0.236400i	0.815358	+	0.578957i	$0.196540\pi$
$464$	−225.884	+	169.532i	−0.486819	+	0.365370i
$465$	−176.141	−	18.8039i	−0.378797	−	0.0404384i
$466$	568.404	+	20.1243i	1.21975	+	0.0431852i
$467$			462.541i			0.990452i	0.868764	+	0.495226i	$0.164915\pi$
$467$			462.541i			0.990452i	−0.868764	+	0.495226i	$0.835085\pi$
$468$	−10.0789	+	142.159i	−0.0215361	+	0.303758i
$469$	622.574	+	622.574i	1.32745	+	1.32745i
$470$	185.693	+	26.4982i	0.395091	+	0.0563792i
$471$			269.096i			0.571329i
$472$	3.06917	−	28.7993i	0.00650248	−	0.0610154i
$473$	−204.974	−	204.974i	−0.433348	−	0.433348i
$474$	−234.361	−	251.565i	−0.494432	−	0.530728i
$475$	−537.852	+	346.794i	−1.13232	+	0.730093i
$476$	26.1659	−	369.060i	0.0549704	−	0.775337i
$477$		−	344.171i		−	0.721533i
$478$	−334.126	−	358.654i	−0.699009	−	0.750322i
$479$			127.125i			0.265397i	0.991156	+	0.132698i	$0.0423642\pi$
$479$			127.125i			0.265397i	−0.991156	+	0.132698i	$0.957636\pi$
$480$	−267.684	+	146.966i	−0.557675	+	0.306178i
$481$	331.253			0.688675
$482$	676.782	−	630.498i	1.40411	−	1.30809i
$483$	−532.172			−1.10181
$484$	160.869	+	11.4054i	0.332374	+	0.0235649i
$485$	458.231	+	567.761i	0.944806	+	1.17064i
$486$	349.488	−	325.587i	0.719112	−	0.669933i
$487$	−376.646	+	376.646i	−0.773401	+	0.773401i	−0.978699	−	0.205299i	$-0.934183\pi$
$487$	−376.646	+	376.646i	−0.773401	+	0.773401i	0.205299	+	0.978699i	$0.434183\pi$
$488$	−62.9760	+	590.929i	−0.129049	+	1.21092i
$489$	187.432			0.383297
$490$	−597.828	−	796.847i	−1.22006	−	1.62622i
$491$	−552.932	+	552.932i	−1.12613	+	1.12613i	−0.135334	+	0.990800i	$0.543211\pi$
$491$	−552.932	+	552.932i	−1.12613	+	1.12613i	−0.990800	+	0.135334i	$0.956789\pi$
$492$	−473.237	−	33.5519i	−0.961863	−	0.0681949i
$493$	−133.929			−0.271662
$494$	−12.0474	+	340.275i	−0.0243875	+	0.688816i
$495$	−187.231	+	151.111i	−0.378245	+	0.305276i
$496$	294.030	+	41.9033i	0.592802	+	0.0844824i
$497$	−210.178	−	210.178i	−0.422893	−	0.422893i
$498$	10.5682	−	9.84544i	0.0212213	−	0.0197700i
$499$	308.855	−	308.855i	0.618947	−	0.618947i	−0.326314	−	0.945261i	$-0.605807\pi$
$499$	308.855	−	308.855i	0.618947	−	0.618947i	0.945261	+	0.326314i	$0.105807\pi$
$500$	190.019	−	462.486i	0.380037	−	0.924971i
$501$	−18.3009	+	18.3009i	−0.0365286	+	0.0365286i
$502$	−5.35979	+	151.385i	−0.0106769	+	0.301565i
$503$	−345.746	−	345.746i	−0.687368	−	0.687368i	0.274281	−	0.961650i	$-0.411560\pi$
$503$	−345.746	−	345.746i	−0.687368	−	0.687368i	−0.961650	+	0.274281i	$0.911560\pi$
$504$	−519.538	−	55.3677i	−1.03083	−	0.109857i
$505$	−507.147	+	409.310i	−1.00425	+	0.810516i
$506$	300.639	−	280.079i	0.594149	−	0.553516i
$507$	−238.135			−0.469694
$508$	−216.211	+	187.582i	−0.425612	+	0.369256i
$509$	156.286	−	156.286i	0.307046	−	0.307046i	−0.536717	−	0.843762i	$-0.680336\pi$
$509$	156.286	−	156.286i	0.307046	−	0.307046i	0.843762	+	0.536717i	$0.180336\pi$
$510$	−143.360	−	20.4573i	−0.281097	−	0.0401124i
$511$	−24.1093			−0.0471807
$512$	457.203	−	230.456i	0.892974	−	0.450109i
$513$	496.003	−	496.003i	0.966867	−	0.966867i
$514$	363.292	+	12.8623i	0.706794	+	0.0250240i
$515$	325.132	+	402.847i	0.631324	+	0.782227i
$516$	−245.759	−	17.4240i	−0.476277	−	0.0337674i
$517$	168.485			0.325889
$518$	−42.9693	+	1213.65i	−0.0829522	+	2.34296i
$519$	−330.005			−0.635848
$520$	−144.198	−	223.551i	−0.277303	−	0.429905i
$521$		−	483.674i		−	0.928358i	−0.885741	−	0.464179i	$-0.846349\pi$
$521$		−	483.674i		−	0.928358i	0.885741	−	0.464179i	$-0.153651\pi$
$522$	−6.69192	+	189.011i	−0.0128198	+	0.362090i
$523$			114.482i			0.218895i	0.993993	+	0.109448i	$0.0349082\pi$
$523$			114.482i			0.218895i	−0.993993	+	0.109448i	$0.965092\pi$
$524$	−94.4250	+	81.9222i	−0.180200	+	0.156340i
$525$	−488.874	+	315.214i	−0.931188	+	0.600407i
$526$	−993.244	−	35.1657i	−1.88830	−	0.0668550i
$527$	99.5895	+	99.5895i	0.188974	+	0.188974i
$528$	−219.382	+	164.652i	−0.415496	+	0.311841i
$529$		−	5.87038i		−	0.0110971i
$530$	385.541	+	513.889i	0.727436	+	0.969602i
$531$	−13.7143	−	13.7143i	−0.0258273	−	0.0258273i
$532$	−1245.15	−	88.2792i	−2.34050	−	0.165938i
$533$		−	413.288i		−	0.775399i
$534$	−171.471	+	159.745i	−0.321107	+	0.299147i
$535$	88.4241	+	9.43971i	0.165279	+	0.0176443i
$536$	−449.545	+	362.956i	−0.838703	+	0.677156i
$537$	90.0527	−	90.0527i	0.167696	−	0.167696i
$538$	−4.54914	+	128.489i	−0.00845565	+	0.238827i
$539$	−632.715	−	632.715i	−1.17387	−	1.17387i
$540$	−96.5694	+	539.468i	−0.178832	+	0.999015i
$541$	−575.569	−	575.569i	−1.06390	−	1.06390i	−0.997814	−	0.0660852i	$-0.978949\pi$
$541$	−575.569	−	575.569i	−1.06390	−	1.06390i	−0.0660852	−	0.997814i	$-0.521051\pi$
$542$	63.2302	−	58.9060i	0.116661	−	0.108683i
$543$	96.7998	−	96.7998i	0.178269	−	0.178269i
$544$	239.005	+	42.7390i	0.439347	+	0.0785644i
$545$	−53.0478	+	42.8140i	−0.0973353	+	0.0785579i
$546$	−10.9503	+	309.288i	−0.0200555	+	0.566462i
$547$			1053.61i			1.92616i	0.269219	+	0.963079i	$0.413234\pi$
$547$			1053.61i			1.92616i	−0.269219	+	0.963079i	$0.586766\pi$
$548$	−379.300	−	437.188i	−0.692154	−	0.797789i
$549$	281.402	+	281.402i	0.512572	+	0.512572i
$550$	110.284	−	435.364i	0.200515	−	0.791572i
$551$			451.855i			0.820063i
$552$	37.0079	−	347.260i	0.0670433	−	0.629095i
$553$	776.434	+	776.434i	1.40404	+	1.40404i
$554$	−77.7344	+	72.4182i	−0.140315	+	0.130719i
$555$	472.632	+	50.4559i	0.851590	+	0.0909115i
$556$	354.685	−	307.722i	0.637923	−	0.553456i
$557$			680.234i			1.22125i	0.791922	+	0.610623i	$0.209081\pi$
$557$			680.234i			1.22125i	−0.791922	+	0.610623i	$0.790919\pi$
$558$	145.524	−	135.572i	0.260796	−	0.242961i
$559$		−	214.626i		−	0.383947i
$560$	837.756	−	499.316i	1.49599	−	0.891637i
$561$	−130.074			−0.231862
$562$	−199.476	−	214.120i	−0.354940	−	0.380996i
$563$	−408.818			−0.726142			−0.363071	−	0.931761i	$-0.618272\pi$
$563$	−408.818			−0.726142			−0.363071	+	0.931761i	$0.618272\pi$
$564$	108.166	−	93.8435i	0.191783	−	0.166389i
$565$	−343.872	+	277.534i	−0.608623	+	0.491211i
$566$	−119.565	−	128.342i	−0.211246	−	0.226753i
$567$	35.2049	−	35.2049i	0.0620898	−	0.0620898i
$568$	151.764	−	122.532i	0.267190	−	0.215725i
$569$	324.426			0.570169			0.285084	−	0.958502i	$-0.407978\pi$
$569$	324.426			0.570169			0.285084	+	0.958502i	$0.407978\pi$
$570$	−69.0194	+	483.670i	−0.121087	+	0.848545i
$571$	−124.307	+	124.307i	−0.217700	+	0.217700i	−0.807528	−	0.589829i	$-0.799195\pi$
$571$	−124.307	+	124.307i	−0.217700	+	0.217700i	0.589829	+	0.807528i	$0.299195\pi$
$572$	−156.590	−	180.489i	−0.273759	−	0.315540i
$573$	630.079			1.09962
$574$	1514.21	+	53.6106i	2.63800	+	0.0933983i
$575$	309.858	+	480.567i	0.538883	+	0.835768i
$576$	72.2586	−	335.165i	0.125449	−	0.581884i
$577$	−303.425	−	303.425i	−0.525866	−	0.525866i	0.393471	−	0.919337i	$-0.371274\pi$
$577$	−303.425	−	303.425i	−0.525866	−	0.525866i	−0.919337	+	0.393471i	$0.871274\pi$
$578$	−315.508	−	338.670i	−0.545862	−	0.585934i
$579$	−287.357	+	287.357i	−0.496299	+	0.496299i
$580$	−201.739	−	289.713i	−0.347825	−	0.499505i
$581$	−32.6178	+	32.6178i	−0.0561408	+	0.0561408i
$582$	556.660	+	19.7085i	0.956461	+	0.0338634i
$583$	408.040	+	408.040i	0.699897	+	0.699897i
$584$	1.67659	−	15.7321i	0.00287088	−	0.0269386i
$585$	−177.138	−	18.9104i	−0.302800	−	0.0323254i
$586$	350.470	+	376.197i	0.598071	+	0.641975i
$587$	279.206			0.475649			0.237824	−	0.971308i	$-0.423566\pi$
$587$	279.206			0.475649			0.237824	+	0.971308i	$0.423566\pi$
$588$	−758.611	−	53.7846i	−1.29016	−	0.0914703i
$589$	335.998	−	335.998i	0.570455	−	0.570455i
$590$	35.8399	+	5.11432i	0.0607455	+	0.00866834i
$591$	−492.023			−0.832526
$592$	−788.961	−	112.438i	−1.33270	−	0.189929i
$593$	−383.903	+	383.903i	−0.647392	+	0.647392i	−0.952362	−	0.304970i	$-0.901354\pi$
$593$	−383.903	+	383.903i	−0.647392	+	0.647392i	0.304970	+	0.952362i	$0.401354\pi$
$594$	−17.4178	+	491.961i	−0.0293230	+	0.828217i
$595$	459.870	+	49.0935i	0.772892	+	0.0825100i
$596$	573.203	−	497.305i	0.961750	−	0.834405i
$597$	−626.973			−1.05021
$598$	304.033	+	10.7643i	0.508416	+	0.0180004i
$599$	−169.873			−0.283594			−0.141797	−	0.989896i	$-0.545288\pi$
$599$	−169.873			−0.283594			−0.141797	+	0.989896i	$0.545288\pi$
$600$	−171.691	−	340.927i	−0.286151	−	0.568211i
$601$			283.673i			0.472002i	0.971753	+	0.236001i	$0.0758369\pi$
$601$			283.673i			0.472002i	−0.971753	+	0.236001i	$0.924163\pi$
$602$	786.354	+	27.8408i	1.30624	+	0.0462472i
$603$			386.915i			0.641650i
$604$	−193.857	−	13.7442i	−0.320955	−	0.0227553i
$605$	−21.3992	+	200.452i	−0.0353706	+	0.331325i
$606$	−17.6044	+	497.231i	−0.0290502	+	0.820514i
$607$	438.351	+	438.351i	0.722160	+	0.722160i	0.969045	−	0.246885i	$-0.0794069\pi$
$607$	438.351	+	438.351i	0.722160	+	0.722160i	−0.246885	+	0.969045i	$0.579407\pi$
$608$	144.194	−	806.360i	0.237161	−	1.32625i
$609$			410.707i			0.674396i
$610$	−735.394	−	104.940i	−1.20556	−	0.172033i
$611$	88.2095	+	88.2095i	0.144369	+	0.144369i
$612$	122.812	−	106.550i	0.200673	−	0.174102i
$613$		−	165.499i		−	0.269981i	−0.990847	−	0.134991i	$-0.956900\pi$
$613$		−	165.499i		−	0.269981i	0.990847	−	0.134991i	$-0.0431005\pi$
$614$	−819.480	−	879.637i	−1.33466	−	1.43263i
$615$	62.9513	−	589.680i	0.102360	−	0.958830i
$616$	681.592	−	550.307i	1.10648	−	0.893356i
$617$	219.108	−	219.108i	0.355118	−	0.355118i	−0.506892	−	0.862010i	$-0.669206\pi$
$617$	219.108	−	219.108i	0.355118	−	0.355118i	0.862010	+	0.506892i	$0.169206\pi$
$618$	394.971	+	13.9839i	0.639111	+	0.0226277i
$619$	−365.140	−	365.140i	−0.589888	−	0.589888i	0.347713	−	0.937601i	$-0.386958\pi$
$619$	−365.140	−	365.140i	−0.589888	−	0.589888i	−0.937601	+	0.347713i	$0.886958\pi$
$620$	−65.4172	+	365.442i	−0.105512	+	0.589422i
$621$	−443.174	−	443.174i	−0.713646	−	0.713646i
$622$	10.0123	+	10.7473i	0.0160970	+	0.0172786i
$623$	529.231	−	529.231i	0.849488	−	0.849488i
$624$	−201.060	−	28.6537i	−0.322211	−	0.0459195i
$625$	569.294	+	257.933i	0.910870	+	0.412693i
$626$	−482.152	−	17.0705i	−0.770211	−	0.0272692i
$627$			438.849i			0.699918i
$628$	562.556	+	39.8845i	0.895789	+	0.0635103i
$629$	−267.225	−	267.225i	−0.424842	−	0.424842i
$630$	92.2622	−	646.550i	0.146448	−	1.02627i
$631$		−	1113.61i		−	1.76484i	−0.470463	−	0.882420i	$-0.655913\pi$
$631$		−	1113.61i		−	1.76484i	0.470463	−	0.882420i	$-0.344087\pi$
$632$	−560.643	+	452.655i	−0.887093	+	0.716226i
$633$	98.0856	+	98.0856i	0.154953	+	0.154953i
$634$	363.166	+	389.825i	0.572816	+	0.614866i
$635$	−224.718	−	278.431i	−0.353886	−	0.438475i
$636$	489.231	+	34.6858i	0.769231	+	0.0545374i
$637$		−	662.511i		−	1.04005i
$638$	−216.153	−	232.020i	−0.338797	−	0.363668i
$639$		−	130.621i		−	0.204414i
$640$	267.562	+	581.387i	0.418066	+	0.908417i
$641$	279.808			0.436518			0.218259	−	0.975891i	$-0.429962\pi$
$641$	279.808			0.436518			0.218259	+	0.975891i	$0.429962\pi$
$642$	49.6738	−	46.2767i	0.0773735	−	0.0720820i
$643$	68.4686			0.106483			0.0532415	−	0.998582i	$-0.483045\pi$
$643$	68.4686			0.106483			0.0532415	+	0.998582i	$0.483045\pi$
$644$	−78.8767	+	1112.53i	−0.122479	+	1.72753i
$645$	32.6915	−	306.230i	0.0506846	−	0.474775i
$646$	284.223	−	264.785i	0.439973	−	0.409884i
$647$	−60.8229	+	60.8229i	−0.0940075	+	0.0940075i	−0.752547	−	0.658539i	$-0.771175\pi$
$647$	−60.8229	+	60.8229i	−0.0940075	+	0.0940075i	0.658539	+	0.752547i	$0.271175\pi$
$648$	20.5242	+	25.4206i	0.0316732	+	0.0392293i
$649$	32.5186			0.0501057
$650$	285.672	−	170.195i	0.439495	−	0.261838i
$651$	305.401	−	305.401i	0.469125	−	0.469125i
$652$	27.7805	−	391.834i	0.0426082	−	0.600973i
$653$	815.643			1.24907			0.624536	−	0.780996i	$-0.285288\pi$
$653$	815.643			1.24907			0.624536	+	0.780996i	$0.285288\pi$
$654$	−1.84143	+	52.0106i	−0.00281564	+	0.0795269i
$655$	−98.1403	−	121.598i	−0.149832	−	0.185646i
$656$	−140.283	+	984.347i	−0.213846	+	1.50053i
$657$	−7.49169	−	7.49169i	−0.0114029	−	0.0114029i
$658$	−334.627	+	311.742i	−0.508551	+	0.473772i
$659$	765.294	−	765.294i	1.16130	−	1.16130i	0.177103	−	0.984192i	$-0.443327\pi$
$659$	765.294	−	765.294i	1.16130	−	1.16130i	0.984192	−	0.177103i	$-0.0566727\pi$
$660$	−195.932	−	281.374i	−0.296866	−	0.426324i
$661$	423.035	−	423.035i	0.639993	−	0.639993i	−0.310561	−	0.950553i	$-0.600517\pi$
$661$	423.035	−	423.035i	0.639993	−	0.639993i	0.950553	+	0.310561i	$0.100517\pi$
$662$	−6.70387	+	189.349i	−0.0101267	+	0.286025i
$663$	−68.1000	−	68.1000i	−0.102715	−	0.102715i
$664$	−19.0159	−	23.5525i	−0.0286384	−	0.0354706i
$665$	165.633	−	1551.52i	0.249072	−	2.33312i
$666$	−390.480	+	363.776i	−0.586307	+	0.546210i
$667$	403.729			0.605290
$668$	35.5462	+	40.9712i	0.0532128	+	0.0613341i
$669$	−381.755	+	381.755i	−0.570636	+	0.570636i
$670$	−433.423	−	577.711i	−0.646900	−	0.862255i
$671$	−667.245			−0.994404
$672$	131.063	−	732.930i	0.195035	−	1.09067i
$673$	−372.278	+	372.278i	−0.553162	+	0.553162i	−0.927352	−	0.374190i	$-0.877921\pi$
$673$	−372.278	+	372.278i	−0.553162	+	0.553162i	0.374190	+	0.927352i	$0.377921\pi$
$674$	−474.197	−	16.7889i	−0.703557	−	0.0249094i
$675$	−669.616	−	144.618i	−0.992023	−	0.214249i
$676$	−35.2955	+	497.831i	−0.0522123	+	0.736436i
$677$	244.469			0.361106			0.180553	−	0.983565i	$-0.442211\pi$
$677$	244.469			0.361106			0.180553	+	0.983565i	$0.442211\pi$
$678$	−11.9367	+	337.149i	−0.0176058	+	0.497270i
$679$	−1778.91			−2.61990
$680$	−64.0151	+	296.667i	−0.0941398	+	0.436275i
$681$			90.7496i			0.133259i
$682$	−11.7990	+	333.260i	−0.0173006	+	0.488651i
$683$			434.494i			0.636155i	0.948065	+	0.318077i	$0.103037\pi$
$683$			434.494i			0.636155i	−0.948065	+	0.318077i	$0.896963\pi$
$684$	−359.483	−	414.346i	−0.525559	−	0.605769i
$685$	563.002	−	454.390i	0.821900	−	0.663343i
$686$	1233.37	+	43.6673i	1.79791	+	0.0636550i
$687$	−125.118	−	125.118i	−0.182122	−	0.182122i
$688$	−72.8511	+	511.186i	−0.105888	+	0.743003i
$689$			427.256i			0.620110i
$690$	432.155	+	61.6683i	0.626312	+	0.0893743i
$691$	−140.105	−	140.105i	−0.202756	−	0.202756i	0.598424	−	0.801180i	$-0.295794\pi$
$691$	−140.105	−	140.105i	−0.202756	−	0.202756i	−0.801180	+	0.598424i	$0.795794\pi$
$692$	−48.9122	+	689.889i	−0.0706824	+	0.996950i
$693$		−	586.634i		−	0.846514i
$694$	−842.160	+	784.566i	−1.21349	+	1.13050i
$695$	368.641	+	456.756i	0.530419	+	0.657203i
$696$	−268.000	−	28.5611i	−0.385058	−	0.0410360i
$697$	−333.404	+	333.404i	−0.478342	+	0.478342i
$698$	−21.8472	+	617.066i	−0.0312996	+	0.884048i
$699$	383.793	+	383.793i	0.549060	+	0.549060i
$700$	586.508	+	1068.73i	0.837868	+	1.52676i
$701$	333.050	+	333.050i	0.475106	+	0.475106i	0.903563	−	0.428456i	$-0.140942\pi$
$701$	333.050	+	333.050i	0.475106	+	0.475106i	−0.428456	+	0.903563i	$0.640942\pi$
$702$	−266.684	+	248.445i	−0.379891	+	0.353911i
$703$	−901.572	+	901.572i	−1.28246	+	1.28246i
$704$	311.695	+	483.031i	0.442749	+	0.686123i
$705$	112.422	+	139.294i	0.159463	+	0.197579i
$706$	19.4272	−	548.715i	0.0275173	−	0.777217i
$707$		−	1589.00i		−	2.24752i
$708$	20.8767	−	18.1124i	0.0294868	−	0.0255825i
$709$	−588.688	−	588.688i	−0.830308	−	0.830308i	0.157251	−	0.987559i	$-0.449737\pi$
$709$	−588.688	−	588.688i	−0.830308	−	0.830308i	−0.987559	+	0.157251i	$0.949737\pi$
$710$	146.321	+	195.032i	0.206087	+	0.274693i
$711$			482.535i			0.678671i
$712$	308.537	+	382.144i	0.433339	+	0.536719i
$713$	−300.211	−	300.211i	−0.421054	−	0.421054i
$714$	258.340	−	240.673i	0.361821	−	0.337077i
$715$	232.430	−	187.590i	0.325076	−	0.262364i
$716$	−174.911	−	201.606i	−0.244290	−	0.281573i
$717$		−	467.773i		−	0.652403i
$718$	798.780	−	744.153i	1.11251	−	1.03642i
$719$			837.132i			1.16430i	0.813081	+	0.582150i	$0.197788\pi$
$719$			837.132i			1.16430i	−0.813081	+	0.582150i	$0.802212\pi$
$720$	415.479	+	105.166i	0.577055	+	0.146064i
$721$	−1262.20			−1.75063
$722$	−401.191	−	430.642i	−0.555667	−	0.596458i
$723$	882.690			1.22087
$724$	−188.017	−	216.711i	−0.259691	−	0.299325i
$725$	370.880	−	239.135i	0.511559	−	0.329841i
$726$	104.906	+	112.607i	0.144499	+	0.155107i
$727$	−115.757	+	115.757i	−0.159225	+	0.159225i	−0.782223	−	0.622998i	$-0.785914\pi$
$727$	−115.757	+	115.757i	−0.159225	+	0.159225i	0.622998	+	0.782223i	$0.285914\pi$
$728$	644.957	+	68.7337i	0.885930	+	0.0944145i
$729$	492.575			0.675686
$730$	19.5782	+	2.79379i	0.0268195	+	0.00382712i
$731$	−173.142	+	173.142i	−0.236856	+	0.236856i
$732$	−428.366	+	371.646i	−0.585199	+	0.507713i
$733$	−123.197			−0.168073			−0.0840363	−	0.996463i	$-0.526781\pi$
$733$	−123.197			−0.168073			−0.0840363	+	0.996463i	$0.526781\pi$
$734$	−850.329	−	30.1058i	−1.15849	−	0.0410161i
$735$	100.913	−	945.273i	0.137296	−	1.28609i
$736$	−720.476	−	128.836i	−0.978908	−	0.175049i
$737$	−458.716	−	458.716i	−0.622410	−	0.622410i
$738$	453.865	+	487.183i	0.614994	+	0.660140i
$739$	641.523	−	641.523i	0.868096	−	0.868096i	−0.124166	−	0.992262i	$-0.539625\pi$
$739$	641.523	−	641.523i	0.868096	−	0.868096i	0.992262	+	0.124166i	$0.0396254\pi$
$740$	175.532	−	980.578i	0.237205	−	1.32511i
$741$	−229.758	+	229.758i	−0.310064	+	0.310064i
$742$	−1565.39	−	55.4225i	−2.10969	−	0.0746934i
$743$	−84.7652	−	84.7652i	−0.114085	−	0.114085i	0.647760	−	0.761845i	$-0.275706\pi$
$743$	−84.7652	−	84.7652i	−0.114085	−	0.114085i	−0.761845	+	0.647760i	$0.775706\pi$
$744$	178.046	+	220.522i	0.239309	+	0.296401i
$745$	595.756	+	738.158i	0.799673	+	0.990816i
$746$	99.9687	+	107.307i	0.134006	+	0.143844i
$747$	−20.2712			−0.0271368
$748$	−19.2792	+	271.926i	−0.0257743	+	0.363537i
$749$	−153.314	+	153.314i	−0.204691	+	0.204691i
$750$	433.521	−	199.321i	0.578028	−	0.265762i
$751$	137.548			0.183153			0.0915766	−	0.995798i	$-0.470809\pi$
$751$	137.548			0.183153			0.0915766	+	0.995798i	$0.470809\pi$
$752$	−180.152	−	240.034i	−0.239563	−	0.319194i
$753$	−102.217	+	102.217i	−0.135747	+	0.135747i
$754$	8.30738	−	234.639i	0.0110178	−	0.311193i
$755$	25.7874	−	241.557i	0.0341555	−	0.319943i
$756$	−875.667	−	1009.31i	−1.15829	−	1.33507i
$757$	857.792			1.13315			0.566574	−	0.824011i	$-0.308269\pi$
$757$	857.792			1.13315			0.566574	+	0.824011i	$0.308269\pi$
$758$	264.349	+	9.35925i	0.348745	+	0.0123473i
$759$	392.108			0.516611
$760$	1000.90	+	215.976i	1.31698	+	0.284179i
$761$			353.070i			0.463956i	0.972721	+	0.231978i	$0.0745197\pi$
$761$			353.070i			0.463956i	−0.972721	+	0.231978i	$0.925480\pi$
$762$	−272.988	−	9.66511i	−0.358252	−	0.0126839i
$763$		−	166.210i		−	0.217837i
$764$	93.3882	−	1317.21i	0.122236	−	1.72409i
$765$	127.644	+	158.155i	0.166855	+	0.206738i
$766$	−7.94940	+	224.528i	−0.0103778	+	0.293118i
$767$	17.0250	+	17.0250i	0.0221968	+	0.0221968i
$768$	469.147	+	136.492i	0.610869	+	0.177724i
$769$			401.035i			0.521503i	0.965406	+	0.260751i	$0.0839703\pi$
$769$			401.035i			0.521503i	−0.965406	+	0.260751i	$0.916030\pi$
$770$	657.149	+	875.916i	0.853440	+	1.13755i
$771$	245.299	+	245.299i	0.318157	+	0.318157i
$772$	558.141	+	643.323i	0.722980	+	0.833320i
$773$			396.076i			0.512388i	0.966625	+	0.256194i	$0.0824686\pi$
$773$			396.076i			0.512388i	−0.966625	+	0.256194i	$0.917531\pi$
$774$	235.699	+	253.001i	0.304521	+	0.326875i
$775$	−453.605	−	97.9657i	−0.585297	−	0.126407i
$776$	123.708	−	1160.80i	0.159417	−	1.49588i
$777$	−819.472	+	819.472i	−1.05466	+	1.05466i
$778$	−275.892	−	9.76792i	−0.354617	−	0.0125552i
$779$	1124.85	+	1124.85i	1.44396	+	1.44396i
$780$	44.7327	−	249.892i	0.0573496	−	0.320374i
$781$	154.860	+	154.860i	0.198285	+	0.198285i
$782$	−236.583	−	253.951i	−0.302536	−	0.324745i
$783$	−342.023	+	342.023i	−0.436811	+	0.436811i
$784$	−224.878	+	1577.94i	−0.286834	+	2.01267i
$785$	−74.8328	+	700.977i	−0.0953284	+	0.892964i
$786$	−119.221	−	4.22101i	−0.151681	−	0.00537024i
$787$			184.472i			0.234399i	0.993108	+	0.117200i	$0.0373917\pi$
$787$			184.472i			0.234399i	−0.993108	+	0.117200i	$0.962608\pi$
$788$	−72.9259	+	1028.59i	−0.0925456	+	1.30532i
$789$	−670.650	−	670.650i	−0.850000	−	0.850000i
$790$	−540.537	−	720.483i	−0.684224	−	0.912004i
$791$		−	1077.42i		−	1.36210i
$792$	382.798	+	40.7952i	0.483331	+	0.0515091i
$793$	−349.334	−	349.334i	−0.440522	−	0.440522i
$794$	−408.305	−	438.278i	−0.514238	−	0.551987i
$795$	−65.0788	+	609.609i	−0.0818602	+	0.766804i
$796$	−92.9278	+	1310.71i	−0.116743	+	1.64662i
$797$			187.027i			0.234664i	0.993093	+	0.117332i	$0.0374341\pi$
$797$			187.027i			0.234664i	−0.993093	+	0.117332i	$0.962566\pi$
$798$	−811.988	−	871.595i	−1.01753	−	1.09222i
$799$		−	142.319i		−	0.178122i
$800$	−738.168	+	308.395i	−0.922710	+	0.385494i
$801$	328.905			0.410617
$802$	−133.053	+	123.954i	−0.165902	+	0.154556i
$803$	17.7639			0.0221219
$804$	−549.990	−	38.9936i	−0.684067	−	0.0484995i
$805$	−1386.27	−	147.992i	−1.72208	−	0.183840i
$806$	−180.654	+	168.300i	−0.224137	+	0.208809i
$807$	−86.7572	+	86.7572i	−0.107506	+	0.107506i
$808$	1036.87	+	110.501i	1.28326	+	0.136758i
$809$	−356.858			−0.441110			−0.220555	−	0.975374i	$-0.570787\pi$
$809$	−356.858			−0.441110			−0.220555	+	0.975374i	$0.570787\pi$
$810$	−32.6680	+	24.5089i	−0.0403309	+	0.0302579i
$811$	882.626	−	882.626i	1.08832	−	1.08832i	0.0926166	−	0.995702i	$-0.470477\pi$
$811$	882.626	−	882.626i	1.08832	−	1.08832i	0.995702	−	0.0926166i	$-0.0295231\pi$
$812$	858.600	+	60.8736i	1.05739	+	0.0749675i
$813$	82.4677			0.101436
$814$	31.6600	−	894.226i	0.0388943	−	1.09856i
$815$	488.248	+	52.1229i	0.599078	+	0.0639545i
$816$	139.082	+	185.312i	0.170443	+	0.227098i
$817$	584.150	+	584.150i	0.714994	+	0.714994i
$818$	−962.506	+	896.682i	−1.17666	+	1.09619i
$819$	307.130	−	307.130i	0.375006	−	0.375006i
$820$	−1223.42	−	219.003i	−1.49198	−	0.267076i
$821$	−17.9719	+	17.9719i	−0.0218902	+	0.0218902i	−0.717967	−	0.696077i	$-0.754927\pi$
$821$	−17.9719	+	17.9719i	−0.0218902	+	0.0218902i	0.696077	+	0.717967i	$0.254927\pi$
$822$	19.5433	−	551.994i	0.0237753	−	0.671526i
$823$	36.8905	+	36.8905i	0.0448245	+	0.0448245i	0.729164	−	0.684339i	$-0.239909\pi$
$823$	36.8905	+	36.8905i	0.0448245	+	0.0448245i	−0.684339	+	0.729164i	$0.739909\pi$
$824$	87.7751	−	823.630i	0.106523	−	0.999551i
$825$	360.205	−	232.251i	0.436612	−	0.281517i
$826$	−64.5850	+	60.1681i	−0.0781901	+	0.0728428i
$827$	−837.787			−1.01304			−0.506522	−	0.862227i	$-0.669069\pi$
$827$	−837.787			−1.01304			−0.506522	+	0.862227i	$0.669069\pi$
$828$	−370.215	+	321.195i	−0.447119	+	0.387916i
$829$	−1129.26	+	1129.26i	−1.36219	+	1.36219i	−0.491077	+	0.871116i	$0.663397\pi$
$829$	−1129.26	+	1129.26i	−1.36219	+	1.36219i	−0.871116	+	0.491077i	$0.836603\pi$
$830$	30.2673	−	22.7078i	0.0364667	−	0.0273588i
$831$	−101.385			−0.122003
$832$	−89.7021	+	416.076i	−0.107815	+	0.500091i
$833$	−534.456	+	534.456i	−0.641604	+	0.641604i
$834$	447.826	+	15.8552i	0.536962	+	0.0190111i
$835$	−52.7618	+	42.5832i	−0.0631877	+	0.0509979i
$836$	917.430	+	65.0446i	1.09740	+	0.0778046i
$837$	508.654			0.607711
$838$	−14.5291	+	410.371i	−0.0173379	+	0.489703i
$839$	949.313			1.13148			0.565741	−	0.824583i	$-0.308590\pi$
$839$	949.313			1.13148			0.565741	+	0.824583i	$0.308590\pi$
$840$	909.757	+	196.308i	1.08304	+	0.233700i
$841$			529.420i			0.629512i
$842$	−1.96297	+	55.4436i	−0.00233132	+	0.0658475i
$843$		−	279.265i		−	0.331275i
$844$	219.590	−	190.514i	0.260177	−	0.225727i
$845$	−620.326	−	66.2229i	−0.734113	−	0.0783702i
$846$	−200.851	−	7.11113i	−0.237413	−	0.00840559i
$847$	−347.553	−	347.553i	−0.410334	−	0.410334i
$848$	145.024	−	1017.62i	0.171019	−	1.20002i
$849$		−	167.390i		−	0.197161i
$850$	−367.753	−	93.1567i	−0.432651	−	0.109596i
$851$	805.547	+	805.547i	0.946589	+	0.946589i
$852$	185.674	+	13.1640i	0.217927	+	0.0154508i
$853$			293.712i			0.344329i	0.985068	+	0.172164i	$0.0550760\pi$
$853$			293.712i			0.344329i	−0.985068	+	0.172164i	$0.944924\pi$
$854$	1325.21	−	1234.58i	1.55177	−	1.44565i
$855$	533.586	−	430.649i	0.624077	−	0.503683i
$856$	−89.3807	−	110.704i	−0.104417	−	0.129327i
$857$	−656.737	+	656.737i	−0.766321	+	0.766321i	−0.977457	−	0.211136i	$-0.932284\pi$
$857$	−656.737	+	656.737i	−0.766321	+	0.766321i	0.211136	+	0.977457i	$0.432284\pi$
$858$	8.06826	−	227.885i	0.00940357	−	0.265601i
$859$	−1015.37	−	1015.37i	−1.18203	−	1.18203i	−0.979217	−	0.202818i	$-0.934990\pi$
$859$	−1015.37	−	1015.37i	−1.18203	−	1.18203i	−0.202818	−	0.979217i	$-0.565010\pi$
$860$	−635.340	−	113.731i	−0.738767	−	0.132246i
$861$	1022.41	+	1022.41i	1.18747	+	1.18747i
$862$	269.542	−	251.109i	0.312694	−	0.291309i
$863$	400.164	−	400.164i	0.463689	−	0.463689i	−0.436174	−	0.899863i	$-0.643667\pi$
$863$	400.164	−	400.164i	0.463689	−	0.463689i	0.899863	+	0.436174i	$0.143667\pi$
$864$	719.503	−	501.214i	0.832758	−	0.580108i
$865$	−859.641	−	91.7710i	−0.993805	−	0.106094i
$866$	40.1532	−	1134.11i	0.0463663	−	1.30960i
$867$		−	441.709i		−	0.509468i
$868$	−593.187	−	683.718i	−0.683395	−	0.787693i
$869$	−572.081	−	572.081i	−0.658321	−	0.658321i
$870$	47.5929	−	333.519i	0.0547044	−	0.383355i
$871$		−	480.318i		−	0.551456i
$872$	108.457	+	11.5584i	0.124378	+	0.0132551i
$873$	−552.776	−	552.776i	−0.633191	−	0.633191i
$874$	−856.785	+	798.191i	−0.980303	+	0.913262i
$875$	−1361.14	+	685.160i	−1.55559	+	0.783040i
$876$	11.4043	−	9.89423i	0.0130186	−	0.0112948i
$877$			532.291i			0.606945i	0.952840	+	0.303472i	$0.0981460\pi$
$877$			532.291i			0.606945i	−0.952840	+	0.303472i	$0.901854\pi$
$878$	1032.44	−	961.836i	1.17590	−	1.09549i
$879$			490.654i			0.558196i
$880$	−617.263	+	367.899i	−0.701435	+	0.418067i
$881$	1748.05			1.98417			0.992083	−	0.125586i	$-0.0400812\pi$
$881$	1748.05			1.98417			0.992083	+	0.125586i	$0.0400812\pi$
$882$	727.559	+	780.968i	0.824896	+	0.885451i
$883$	−141.696			−0.160471			−0.0802354	−	0.996776i	$-0.525567\pi$
$883$	−141.696			−0.160471			−0.0802354	+	0.996776i	$0.525567\pi$
$884$	−152.459	+	132.272i	−0.172465	+	0.149629i
$885$	21.6981	+	26.8845i	0.0245176	+	0.0303780i
$886$	−680.740	−	730.712i	−0.768330	−	0.824732i
$887$	−258.995	+	258.995i	−0.291990	+	0.291990i	−0.837866	−	0.545876i	$-0.816197\pi$
$887$	−258.995	+	258.995i	−0.291990	+	0.291990i	0.545876	+	0.837866i	$0.316197\pi$
$888$	−477.746	−	591.720i	−0.538002	−	0.666351i
$889$	872.383			0.981309
$890$	−491.094	+	368.439i	−0.551791	+	0.413977i
$891$	−25.9392	+	25.9392i	−0.0291125	+	0.0291125i
$892$	741.492	+	854.657i	0.831269	+	0.958136i
$893$	−480.161			−0.537694
$894$	723.726	+	25.6235i	0.809537	+	0.0286616i
$895$	259.624	−	209.538i	0.290083	−	0.234121i
$896$	−1512.79	−	382.625i	−1.68839	−	0.427037i
$897$	205.286	+	205.286i	0.228859	+	0.228859i
$898$	−1071.72	−	1150.39i	−1.19345	−	1.28106i
$899$	−231.690	+	231.690i	−0.257720	+	0.257720i
$900$	−149.845	+	514.346i	−0.166494	+	0.571495i
$901$	344.672	−	344.672i	0.382544	−	0.382544i
$902$	−1115.68	−	39.5006i	−1.23690	−	0.0437923i
$903$	530.955	+	530.955i	0.587990	+	0.587990i
$904$	703.054	+	74.9253i	0.777715	+	0.0828820i
$905$	279.076	−	225.238i	0.308371	−	0.248882i
$906$	−126.419	−	135.699i	−0.139535	−	0.149778i
$907$	427.687			0.471540			0.235770	−	0.971809i	$-0.424239\pi$
$907$	427.687			0.471540			0.235770	+	0.971809i	$0.424239\pi$
$908$	189.716	+	13.4506i	0.208938	+	0.0148134i
$909$	493.762	−	493.762i	0.543192	−	0.543192i
$910$	−114.535	+	802.630i	−0.125862	+	0.882011i
$911$	81.2821			0.0892229			0.0446114	−	0.999004i	$-0.485795\pi$
$911$	81.2821			0.0892229			0.0446114	+	0.999004i	$0.485795\pi$
$912$	625.212	−	469.238i	0.685539	−	0.514515i
$913$	24.0330	−	24.0330i	0.0263231	−	0.0263231i
$914$	41.1364	−	1161.88i	0.0450070	−	1.27121i
$915$	−445.221	−	551.640i	−0.486580	−	0.602886i
$916$	−280.108	+	243.019i	−0.305795	+	0.265304i
$917$	380.993			0.415478
$918$	415.561	+	14.7129i	0.452680	+	0.0160271i
$919$	−314.358			−0.342065			−0.171033	−	0.985265i	$-0.554710\pi$
$919$	−314.358			−0.342065			−0.171033	+	0.985265i	$0.554710\pi$
$920$	192.973	−	894.298i	0.209753	−	0.972063i
$921$		−	1147.26i		−	1.24567i
$922$	1538.23	+	54.4609i	1.66836	+	0.0590682i
$923$			162.153i			0.175680i
$924$	833.886	+	59.1214i	0.902474	+	0.0639842i
$925$	1217.14	+	262.868i	1.31583	+	0.284182i
$926$	10.9538	−	309.387i	0.0118292	−	0.334111i
$927$	−392.215	−	392.215i	−0.423101	−	0.423101i
$928$	−99.4302	+	556.032i	−0.107145	+	0.599172i
$929$			447.538i			0.481742i	0.970557	+	0.240871i	$0.0774330\pi$
$929$			447.538i			0.481742i	−0.970557	+	0.240871i	$0.922567\pi$
$930$	−283.393	+	212.614i	−0.304724	+	0.228617i
$931$	1803.16	+	1803.16i	1.93680	+	1.93680i
$932$	859.219	−	745.450i	0.921908	−	0.799839i
$933$			14.0171i			0.0150237i
$934$	630.577	+	676.867i	0.675136	+	0.724697i
$935$	−338.835	−	36.1723i	−0.362391	−	0.0386870i
$936$	179.054	+	221.771i	0.191298	+	0.236935i
$937$	−299.777	+	299.777i	−0.319932	+	0.319932i	−0.848741	−	0.528809i	$-0.822639\pi$
$937$	−299.777	+	299.777i	−0.319932	+	0.319932i	0.528809	+	0.848741i	$0.322639\pi$
$938$	1759.80	+	62.3056i	1.87612	+	0.0664239i
$939$	−325.554	−	325.554i	−0.346703	−	0.346703i
$940$	307.861	−	214.376i	0.327512	−	0.228060i
$941$	−991.114	−	991.114i	−1.05326	−	1.05326i	−0.998500	−	0.0547565i	$-0.982562\pi$
$941$	−991.114	−	991.114i	−1.05326	−	1.05326i	−0.0547565	−	0.998500i	$-0.517438\pi$
$942$	366.856	+	393.786i	0.389443	+	0.418032i
$943$	1005.04	−	1005.04i	1.06579	−	1.06579i
$944$	−34.7704	−	46.3280i	−0.0368330	−	0.0490763i
$945$	1299.77	−	1049.02i	1.37542	−	1.11008i
$946$	−579.390	−	20.5133i	−0.612463	−	0.0216842i
$947$			22.1486i			0.0233882i	0.999932	+	0.0116941i	$0.00372243\pi$
$947$			22.1486i			0.0233882i	−0.999932	+	0.0116941i	$0.996278\pi$
$948$	−685.912	−	48.6303i	−0.723536	−	0.0512977i
$949$	9.30022	+	9.30022i	0.00980002	+	0.00980002i
$950$	−314.295	+	1240.74i	−0.330836	+	1.30604i
$951$			508.428i			0.534625i
$952$	−464.846	−	575.742i	−0.488283	−	0.604771i
$953$	1197.38	+	1197.38i	1.25643	+	1.25643i	0.952783	+	0.303651i	$0.0982056\pi$
$953$	1197.38	+	1197.38i	1.25643	+	1.25643i	0.303651	+	0.952783i	$0.401794\pi$
$954$	−469.205	−	503.648i	−0.491829	−	0.527933i
$955$	1641.31	+	175.218i	1.71865	+	0.183475i
$956$	−977.898	−	69.3317i	−1.02291	−	0.0725227i
$957$		−	302.612i		−	0.316208i
$958$	173.308	+	186.031i	0.180906	+	0.194186i
$959$			1764.00i			1.83942i
$960$	−191.363	+	579.995i	−0.199337	+	0.604162i
$961$	−616.432			−0.641449
$962$	484.744	−	451.593i	0.503892	−	0.469432i
$963$	−95.2809			−0.0989417
$964$	130.829	−	1845.30i	0.135715	−	1.91421i
$965$	−828.457	+	668.635i	−0.858505	+	0.692886i
$966$	−778.763	+	725.505i	−0.806173	+	0.751040i
$967$	937.022	−	937.022i	0.968998	−	0.968998i	−0.0305352	−	0.999534i	$-0.509721\pi$
$967$	937.022	−	937.022i	0.968998	−	0.968998i	0.999534	+	0.0305352i	$0.00972117\pi$
$968$	250.959	−	202.621i	0.259255	−	0.209319i
$969$	370.696			0.382555
$970$	1444.58	+	206.141i	1.48926	+	0.212516i
$971$	−1016.28	+	1016.28i	−1.04663	+	1.04663i	−0.0477733	+	0.998858i	$0.515213\pi$
$971$	−1016.28	+	1016.28i	−1.04663	+	1.04663i	−0.998858	+	0.0477733i	$0.984787\pi$
$972$	67.5599	−	952.908i	0.0695061	−	0.980358i
$973$	−1431.11			−1.47082
$974$	−37.6938	+	1064.65i	−0.0387000	+	1.09307i
$975$	310.178	+	66.9896i	0.318132	+	0.0687073i
$976$	713.450	+	950.600i	0.730994	+	0.973976i
$977$	−578.640	−	578.640i	−0.592262	−	0.592262i	0.345980	−	0.938242i	$-0.387546\pi$
$977$	−578.640	−	578.640i	−0.592262	−	0.592262i	−0.938242	+	0.345980i	$0.887546\pi$
$978$	274.282	−	255.524i	0.280452	−	0.261272i
$979$	−389.940	+	389.940i	−0.398305	+	0.398305i
$980$	−1961.17	−	351.067i	−2.00120	−	0.358232i
$981$	51.6477	−	51.6477i	0.0526480	−	0.0526480i
$982$	−55.3360	+	1562.95i	−0.0563503	+	1.59160i
$983$	−666.904	−	666.904i	−0.678437	−	0.678437i	0.281209	−	0.959646i	$-0.409265\pi$
$983$	−666.904	−	666.904i	−0.678437	−	0.678437i	−0.959646	+	0.281209i	$0.909265\pi$
$984$	−738.260	+	596.060i	−0.750264	+	0.605752i
$985$	−1281.69	−	136.826i	−1.30120	−	0.138910i
$986$	−195.988	+	182.585i	−0.198771	+	0.185177i
$987$	−436.435			−0.442184
$988$	446.264	+	514.371i	0.451684	+	0.520619i
$989$	521.933	−	521.933i	0.527738	−	0.527738i
$990$	−67.9793	+	476.382i	−0.0686660	+	0.481194i
$991$	573.966			0.579178			0.289589	−	0.957151i	$-0.406481\pi$
$991$	573.966			0.579178			0.289589	+	0.957151i	$0.406481\pi$
$992$	487.400	−	339.528i	0.491330	−	0.342266i
$993$	−127.850	+	127.850i	−0.128752	+	0.128752i
$994$	−594.101	−	21.0341i	−0.597687	−	0.0211610i
$995$	−1633.22	−	174.355i	−1.64143	−	0.175231i
$996$	2.04295	−	28.8150i	0.00205115	−	0.0289307i
$997$	293.423			0.294306			0.147153	−	0.989114i	$-0.452989\pi$
$997$	293.423			0.294306			0.147153	+	0.989114i	$0.452989\pi$
$998$	30.9094	−	873.026i	0.0309713	−	0.874775i
$999$	−1364.85			−1.36622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.t.a.77.17	yes	44
4.3	odd	2		320.3.t.a.17.8		44
5.2	odd	4		400.3.i.b.93.16		44
5.3	odd	4		80.3.i.a.13.7	✓	44
5.4	even	2		400.3.t.b.157.6		44
8.3	odd	2		640.3.t.a.417.15		44
8.5	even	2		640.3.t.b.417.8		44
16.3	odd	4		640.3.i.a.97.8		44
16.5	even	4		80.3.i.a.37.7	yes	44
16.11	odd	4		320.3.i.a.177.15		44
16.13	even	4		640.3.i.b.97.15		44
20.3	even	4		320.3.i.a.273.8		44
40.3	even	4		640.3.i.a.33.15		44
40.13	odd	4		640.3.i.b.33.8		44
80.3	even	4		640.3.t.a.353.15		44
80.13	odd	4		640.3.t.b.353.8		44
80.37	odd	4		400.3.t.b.293.6		44
80.43	even	4		320.3.t.a.113.8		44
80.53	odd	4	inner	80.3.t.a.53.17	yes	44
80.69	even	4		400.3.i.b.357.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.7	✓	44	5.3	odd	4
80.3.i.a.37.7	yes	44	16.5	even	4
80.3.t.a.53.17	yes	44	80.53	odd	4	inner
80.3.t.a.77.17	yes	44	1.1	even	1	trivial
320.3.i.a.177.15		44	16.11	odd	4
320.3.i.a.273.8		44	20.3	even	4
320.3.t.a.17.8		44	4.3	odd	2
320.3.t.a.113.8		44	80.43	even	4
400.3.i.b.93.16		44	5.2	odd	4
400.3.i.b.357.16		44	80.69	even	4
400.3.t.b.157.6		44	5.4	even	2
400.3.t.b.293.6		44	80.37	odd	4
640.3.i.a.33.15		44	40.3	even	4
640.3.i.a.97.8		44	16.3	odd	4
640.3.i.b.33.8		44	40.13	odd	4
640.3.i.b.97.15		44	16.13	even	4
640.3.t.a.353.15		44	80.3	even	4
640.3.t.a.417.15		44	8.3	odd	2
640.3.t.b.353.8		44	80.13	odd	4
640.3.t.b.417.8		44	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.46337 - 1.36329i) q^{2} +1.90859 q^{3} +(0.282885 - 3.98998i) q^{4} +(4.97175 + 0.530759i) q^{5} +(2.79297 - 2.60196i) q^{6} +(-8.62025 + 8.62025i) q^{7} +(-5.02554 - 6.22446i) q^{8} -5.35728 q^{9} +O(q^{10})\)	\(q+(1.46337 - 1.36329i) q^{2} +1.90859 q^{3} +(0.282885 - 3.98998i) q^{4} +(4.97175 + 0.530759i) q^{5} +(2.79297 - 2.60196i) q^{6} +(-8.62025 + 8.62025i) q^{7} +(-5.02554 - 6.22446i) q^{8} -5.35728 q^{9} +(7.99907 - 6.00124i) q^{10} +(6.35145 - 6.35145i) q^{11} +(0.539911 - 7.61525i) q^{12} +6.65056 q^{13} +(-0.862693 + 24.3665i) q^{14} +(9.48903 + 1.01300i) q^{15} +(-15.8400 - 2.25741i) q^{16} +(-5.36508 - 5.36508i) q^{17} +(-7.83967 + 7.30353i) q^{18} +(-18.1009 + 18.1009i) q^{19} +(3.52415 - 19.6871i) q^{20} +(-16.4525 + 16.4525i) q^{21} +(0.635637 - 17.9534i) q^{22} +(16.1730 + 16.1730i) q^{23} +(-9.59170 - 11.8800i) q^{24} +(24.4366 + 5.27760i) q^{25} +(9.73220 - 9.06663i) q^{26} -27.4022 q^{27} +(31.9561 + 36.8332i) q^{28} +(12.4816 - 12.4816i) q^{29} +(15.2670 - 11.4539i) q^{30} -18.5625 q^{31} +(-26.2572 + 18.2910i) q^{32} +(12.1223 - 12.1223i) q^{33} +(-15.1652 - 0.536924i) q^{34} +(-47.4330 + 38.2825i) q^{35} +(-1.51549 + 21.3755i) q^{36} +49.8083 q^{37} +(-1.81149 + 51.1649i) q^{38} +12.6932 q^{39} +(-21.6820 - 33.6138i) q^{40} -62.1433i q^{41} +(-1.64653 + 46.5056i) q^{42} -32.2720i q^{43} +(-23.5455 - 27.1389i) q^{44} +(-26.6351 - 2.84343i) q^{45} +(45.7154 + 1.61855i) q^{46} +(13.2635 + 13.2635i) q^{47} +(-30.2320 - 4.30847i) q^{48} -99.6175i q^{49} +(42.9546 - 25.5911i) q^{50} +(-10.2397 - 10.2397i) q^{51} +(1.88134 - 26.5356i) q^{52} +64.2436i q^{53} +(-40.0994 + 37.3571i) q^{54} +(34.9489 - 28.2067i) q^{55} +(96.9779 + 10.3350i) q^{56} +(-34.5471 + 34.5471i) q^{57} +(1.24913 - 35.2812i) q^{58} +(2.55993 + 2.55993i) q^{59} +(6.72616 - 37.5745i) q^{60} +(-52.5270 - 52.5270i) q^{61} +(-27.1638 + 25.3061i) q^{62} +(46.1811 - 46.1811i) q^{63} +(-13.4879 + 62.5626i) q^{64} +(33.0649 + 3.52984i) q^{65} +(1.21317 - 34.2656i) q^{66} -72.2222i q^{67} +(-22.9243 + 19.8889i) q^{68} +(30.8676 + 30.8676i) q^{69} +(-17.2218 + 120.686i) q^{70} +24.3819i q^{71} +(26.9232 + 33.3462i) q^{72} +(1.39841 + 1.39841i) q^{73} +(72.8878 - 67.9031i) q^{74} +(46.6394 + 10.0728i) q^{75} +(67.1017 + 77.3426i) q^{76} +109.502i q^{77} +(18.5748 - 17.3045i) q^{78} -90.0709i q^{79} +(-77.5541 - 19.6305i) q^{80} -4.08398 q^{81} +(-84.7193 - 90.9385i) q^{82} +3.78386 q^{83} +(60.9912 + 70.2995i) q^{84} +(-23.8263 - 29.5214i) q^{85} +(-43.9960 - 47.2257i) q^{86} +(23.8222 - 23.8222i) q^{87} +(-71.4538 - 7.61491i) q^{88} -61.3939 q^{89} +(-42.8533 + 32.1503i) q^{90} +(-57.3295 + 57.3295i) q^{91} +(69.1050 - 59.9548i) q^{92} -35.4283 q^{93} +(37.4913 + 1.32738i) q^{94} +(-99.6001 + 80.3857i) q^{95} +(-50.1142 + 34.9101i) q^{96} +(103.182 + 103.182i) q^{97} +(-135.807 - 145.777i) q^{98} +(-34.0265 + 34.0265i) 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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