LMFDB - Embedded newform 80.3.t.a.53.17

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			53.17
Character	$\chi$	$=$	80.53
Dual form			80.3.t.a.77.17

$q$-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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.46337	+	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	−0.963401	−	0.268063i	$-0.913616\pi$
$7$	−8.62025	−	8.62025i	−1.23146	−	1.23146i	−0.268063	−	0.963401i	$-0.586384\pi$
$8$	−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	0.934187	−	0.356783i	$-0.116126\pi$
$11$	6.35145	+	6.35145i	0.577404	+	0.577404i	−0.356783	+	0.934187i	$0.616126\pi$
$12$	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	−0.847072	−	0.531479i	$-0.821637\pi$
$17$	−5.36508	+	5.36508i	−0.315593	+	0.315593i	0.531479	+	0.847072i	$0.321637\pi$
$18$	−7.83967	−	7.30353i	−0.435537	−	0.405751i
$19$	−18.1009	−	18.1009i	−0.952677	−	0.952677i	0.0462531	−	0.998930i	$-0.485272\pi$
$19$	−18.1009	−	18.1009i	−0.952677	−	0.952677i	−0.998930	+	0.0462531i	$0.985272\pi$
$20$	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	−0.261918	−	0.965090i	$-0.584355\pi$
$23$	16.1730	−	16.1730i	0.703172	−	0.703172i	0.965090	+	0.261918i	$0.0843549\pi$
$24$	−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	0.888764	−	0.458365i	$-0.151565\pi$
$29$	12.4816	+	12.4816i	0.430400	+	0.430400i	−0.458365	+	0.888764i	$0.651565\pi$
$30$	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	$0.273748\pi$
$41$			62.1433i			1.51569i	−0.652434	+	0.757846i	$0.726252\pi$
$42$	−1.64653	−	46.5056i	−0.0392030	−	1.10728i
$43$			32.2720i			0.750511i	0.926921	+	0.375255i	$0.122445\pi$
$43$			32.2720i			0.750511i	−0.926921	+	0.375255i	$0.877555\pi$
$44$	−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	−0.551785	−	0.833986i	$-0.686053\pi$
$47$	13.2635	−	13.2635i	0.282202	−	0.282202i	0.833986	+	0.551785i	$0.186053\pi$
$48$	−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	$-0.792745\pi$
$53$		−	64.2436i		−	1.21214i	0.795410	−	0.606071i	$-0.207255\pi$
$54$	−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	−0.685080	−	0.728468i	$-0.740233\pi$
$59$	2.55993	−	2.55993i	0.0433887	−	0.0433887i	0.728468	+	0.685080i	$0.240233\pi$
$60$	6.72616	+	37.5745i	0.112103	+	0.626242i
$61$	−52.5270	+	52.5270i	−0.861098	+	0.861098i	−0.991466	−	0.130367i	$-0.958384\pi$
$61$	−52.5270	+	52.5270i	−0.861098	+	0.861098i	0.130367	+	0.991466i	$0.458384\pi$
$62$	−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	$0.181187\pi$
$67$			72.2222i			1.07794i	−0.842324	+	0.538972i	$0.818813\pi$
$68$	−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	$-0.945073\pi$
$71$		−	24.3819i		−	0.343407i	0.985149	−	0.171703i	$-0.0549270\pi$
$72$	26.9232	−	33.3462i	0.373934	−	0.463142i
$73$	1.39841	−	1.39841i	0.0191563	−	0.0191563i	−0.697464	−	0.716620i	$-0.745688\pi$
$73$	1.39841	−	1.39841i	0.0191563	−	0.0191563i	0.716620	+	0.697464i	$0.245688\pi$
$74$	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	$0.193083\pi$
$79$			90.0709i			1.14014i	−0.821597	+	0.570069i	$0.806917\pi$
$80$	−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	0.0659075	−	0.997826i	$-0.479006\pi$
$97$	103.182	−	103.182i	1.06373	−	1.06373i	0.997826	−	0.0659075i	$-0.0209942\pi$
$98$	−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	0.0839323	−	0.996471i	$-0.473252\pi$
$101$	−92.1665	−	92.1665i	−0.912539	−	0.912539i	−0.996471	+	0.0839323i	$0.973252\pi$
$102$	−28.9442	+	1.02477i	−0.283767	+	0.0100467i
$103$	73.2115	−	73.2115i	0.710791	−	0.710791i	−0.255909	−	0.966701i	$-0.582375\pi$
$103$	73.2115	−	73.2115i	0.710791	−	0.710791i	0.966701	+	0.255909i	$0.0823749\pi$
$104$	−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	0.661499	−	0.749946i	$-0.269920\pi$
$109$	−9.64065	−	9.64065i	−0.0884463	−	0.0884463i	−0.749946	+	0.661499i	$0.769920\pi$
$110$	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	0.374276	−	0.927317i	$-0.377891\pi$
$113$	−62.4937	−	62.4937i	−0.553042	−	0.553042i	−0.927317	+	0.374276i	$0.877891\pi$
$114$	−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	−0.877680	−	0.479248i	$-0.840909\pi$
$127$	−50.6008	+	50.6008i	−0.398432	+	0.398432i	0.479248	+	0.877680i	$0.340909\pi$
$128$	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	−0.786404	−	0.617712i	$-0.788060\pi$
$131$	−22.0987	+	22.0987i	−0.168693	+	0.168693i	0.617712	+	0.786404i	$0.288060\pi$
$132$	−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	0.973885	−	0.227043i	$-0.0729059\pi$
$137$	102.317	+	102.317i	0.746841	+	0.746841i	−0.227043	+	0.973885i	$0.572906\pi$
$138$	87.2520	−	3.08915i	0.632261	−	0.0223851i
$139$	83.0087	−	83.0087i	0.597185	−	0.597185i	−0.342378	−	0.939562i	$-0.611232\pi$
$139$	83.0087	−	83.0087i	0.597185	−	0.597185i	0.939562	+	0.342378i	$0.111232\pi$
$140$	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	−0.0951332	−	0.995465i	$-0.530328\pi$
$149$	134.149	−	134.149i	0.900331	−	0.900331i	0.995465	+	0.0951332i	$0.0303277\pi$
$150$	81.9827	+	48.8429i	0.546551	+	0.325619i
$151$			48.5859i			0.321761i	0.986974	+	0.160881i	$0.0514334\pi$
$151$			48.5859i			0.321761i	−0.986974	+	0.160881i	$0.948567\pi$
$152$	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	$-0.851774\pi$
$157$		−	140.992i		−	0.898038i	0.893522	−	0.449019i	$-0.148226\pi$
$158$	−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	0.677815	−	0.735232i	$-0.262927\pi$
$167$	−9.58867	−	9.58867i	−0.0574172	−	0.0574172i	−0.735232	+	0.677815i	$0.762927\pi$
$168$	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	0.826511	−	0.562920i	$-0.190322\pi$
$179$	47.1828	+	47.1828i	0.263591	+	0.263591i	−0.562920	+	0.826511i	$0.690322\pi$
$180$	−18.8799	−	105.469i	−0.104888	−	0.585940i
$181$	50.7180	+	50.7180i	0.280210	+	0.280210i	0.833193	−	0.552983i	$-0.186511\pi$
$181$	50.7180	+	50.7180i	0.280210	+	0.280210i	−0.552983	+	0.833193i	$0.686511\pi$
$182$	−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	0.199745	−	0.979848i	$-0.435989\pi$
$193$	−150.560	−	150.560i	−0.780103	−	0.780103i	−0.979848	+	0.199745i	$0.935989\pi$
$194$	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	−0.574760	−	0.818322i	$-0.694905\pi$
$211$	51.3916	−	51.3916i	0.243562	−	0.243562i	0.818322	+	0.574760i	$0.194905\pi$
$212$	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	0.0982168	−	0.995165i	$-0.468686\pi$
$223$	−200.019	−	200.019i	−0.896948	−	0.896948i	−0.995165	+	0.0982168i	$0.968686\pi$
$224$	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	$-0.966602\pi$
$227$		−	47.5480i		−	0.209462i	0.994501	−	0.104731i	$-0.0333982\pi$
$228$	128.070	−	147.615i	0.561709	−	0.647436i
$229$	−65.5550	+	65.5550i	−0.286266	+	0.286266i	−0.835602	−	0.549336i	$-0.814881\pi$
$229$	−65.5550	+	65.5550i	−0.286266	+	0.286266i	0.549336	+	0.835602i	$0.314881\pi$
$230$	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	−0.128655	−	0.991689i	$-0.541066\pi$
$233$	201.087	−	201.087i	0.863035	−	0.863035i	0.991689	+	0.128655i	$0.0410659\pi$
$234$	−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	$0.171368\pi$
$239$			245.088i			1.02547i	−0.858546	+	0.512737i	$0.828632\pi$
$240$	−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	0.592326	−	0.805698i	$-0.298210\pi$
$251$	−53.5564	−	53.5564i	−0.213372	−	0.213372i	−0.805698	+	0.592326i	$0.798210\pi$
$252$	−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	−0.411374	−	0.911466i	$-0.634951\pi$
$257$	128.524	−	128.524i	0.500092	−	0.500092i	0.911466	+	0.411374i	$0.134951\pi$
$258$	−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	−0.436228	+	0.899836i	$0.643686\pi$
$263$	−351.385	+	351.385i	−1.33606	+	1.33606i	−0.899836	+	0.436228i	$0.856314\pi$
$264$	−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	0.617550	−	0.786532i	$-0.288125\pi$
$269$	−45.4562	−	45.4562i	−0.168982	−	0.168982i	−0.786532	+	0.617550i	$0.788125\pi$
$270$	−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	$0.0838399\pi$
$281$			146.320i			0.520712i	−0.965513	+	0.260356i	$0.916160\pi$
$282$	71.5555	−	2.53342i	0.253743	−	0.00898375i
$283$			87.7034i			0.309906i	0.987922	+	0.154953i	$0.0495226\pi$
$283$			87.7034i			0.309906i	−0.987922	+	0.154953i	$0.950477\pi$
$284$	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	$-0.855440\pi$
$293$		−	257.077i		−	0.877395i	0.898635	−	0.438697i	$-0.144560\pi$
$294$	−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	$0.434648\pi$
$307$			601.105i			1.95800i	−0.203870	+	0.978998i	$0.565352\pi$
$308$	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	$-0.996241\pi$
$311$		−	7.34424i		−	0.0236149i	0.999930	−	0.0118075i	$-0.00375852\pi$
$312$	−63.7901	+	79.0083i	−0.204455	+	0.253232i
$313$	−170.573	+	170.573i	−0.544962	+	0.544962i	−0.924979	−	0.380017i	$-0.875918\pi$
$313$	−170.573	+	170.573i	−0.544962	+	0.544962i	0.380017	+	0.924979i	$0.375918\pi$
$314$	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	$-0.861970\pi$
$317$		−	266.389i		−	0.840345i	0.907444	−	0.420172i	$-0.138030\pi$
$318$	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	0.598641	−	0.801018i	$-0.295708\pi$
$331$	−66.9868	−	66.9868i	−0.202377	−	0.202377i	−0.801018	+	0.598641i	$0.795708\pi$
$332$	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	−0.910753	−	0.412952i	$-0.864498\pi$
$337$	−167.759	+	167.759i	−0.497801	+	0.497801i	0.412952	+	0.910753i	$0.364498\pi$
$338$	−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	0.321426	−	0.946935i	$-0.395838\pi$
$349$	−218.302	−	218.302i	−0.625508	−	0.625508i	−0.946935	+	0.321426i	$0.895838\pi$
$350$	−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	0.926418	−	0.376498i	$-0.122872\pi$
$353$	194.122	+	194.122i	0.549920	+	0.549920i	−0.376498	+	0.926418i	$0.622872\pi$
$354$	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	−0.986062	−	0.166376i	$-0.946793\pi$
$367$	−300.825	+	300.825i	−0.819686	+	0.819686i	0.166376	+	0.986062i	$0.446793\pi$
$368$	−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	$-0.968661\pi$
$373$		−	73.3291i		−	0.196593i	0.995157	−	0.0982963i	$-0.0313393\pi$
$374$	−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	−0.572883	−	0.819637i	$-0.694175\pi$
$379$	93.5200	−	93.5200i	0.246755	−	0.246755i	0.819637	+	0.572883i	$0.194175\pi$
$380$	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	0.595764	−	0.803159i	$-0.296849\pi$
$383$	−79.4324	−	79.4324i	−0.207395	−	0.207395i	−0.803159	+	0.595764i	$0.796849\pi$
$384$	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	−0.821343	−	0.570434i	$-0.806775\pi$
$389$	−97.6035	+	97.6035i	−0.250909	+	0.250909i	0.570434	+	0.821343i	$0.306775\pi$
$390$	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	$0.123114\pi$
$397$			299.500i			0.754407i	−0.926130	+	0.377204i	$0.876886\pi$
$398$	−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	0.512311	−	0.858800i	$-0.328790\pi$
$419$	−145.179	−	145.179i	−0.346489	−	0.346489i	−0.858800	+	0.512311i	$0.828790\pi$
$420$	265.921	−	381.883i	0.633145	−	0.909246i
$421$	−19.6145	−	19.6145i	−0.0465904	−	0.0465904i	0.683428	−	0.730018i	$-0.260488\pi$
$421$	−19.6145	−	19.6145i	−0.0465904	−	0.0465904i	−0.730018	+	0.683428i	$0.760488\pi$
$422$	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	0.997485	−	0.0708779i	$-0.0225801\pi$
$433$	401.221	+	401.221i	0.926607	+	0.926607i	−0.0708779	+	0.997485i	$0.522580\pi$
$434$	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	$0.190578\pi$
$443$			499.336i			1.12717i	−0.826058	+	0.563585i	$0.809422\pi$
$444$	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	$0.339413\pi$
$449$			786.125i			1.75083i	−0.483368	+	0.875417i	$0.660587\pi$
$450$	−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	0.995387	−	0.0959440i	$-0.0305870\pi$
$457$	411.045	+	411.045i	0.899443	+	0.899443i	−0.0959440	+	0.995387i	$0.530587\pi$
$458$	−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	0.200821	−	0.979628i	$-0.435639\pi$
$461$	544.187	−	544.187i	1.18045	−	1.18045i	0.979628	−	0.200821i	$-0.0643610\pi$
$462$	284.920	−	305.836i	0.616711	−	0.661983i
$463$	109.453	+	109.453i	0.236400	+	0.236400i	0.815358	−	0.578957i	$-0.196540\pi$
$463$	109.453	+	109.453i	0.236400	+	0.236400i	−0.578957	+	0.815358i	$0.696540\pi$
$464$	−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	$-0.835085\pi$
$467$		−	462.541i		−	0.990452i	0.868764	−	0.495226i	$-0.164915\pi$
$468$	−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	$-0.957636\pi$
$479$		−	127.125i		−	0.265397i	0.991156	−	0.132698i	$-0.0423642\pi$
$480$	−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	0.205299	−	0.978699i	$-0.434183\pi$
$487$	−376.646	−	376.646i	−0.773401	−	0.773401i	−0.978699	+	0.205299i	$0.934183\pi$
$488$	−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	−0.990800	−	0.135334i	$-0.956789\pi$
$491$	−552.932	−	552.932i	−1.12613	−	1.12613i	−0.135334	−	0.990800i	$-0.543211\pi$
$492$	−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	0.945261	−	0.326314i	$-0.105807\pi$
$499$	308.855	+	308.855i	0.618947	+	0.618947i	−0.326314	+	0.945261i	$0.605807\pi$
$500$	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	−0.961650	−	0.274281i	$-0.911560\pi$
$503$	−345.746	+	345.746i	−0.687368	+	0.687368i	0.274281	+	0.961650i	$0.411560\pi$
$504$	−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	0.843762	−	0.536717i	$-0.180336\pi$
$509$	156.286	+	156.286i	0.307046	+	0.307046i	−0.536717	+	0.843762i	$0.680336\pi$
$510$	−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	$0.153651\pi$
$521$			483.674i			0.928358i	−0.885741	+	0.464179i	$0.846349\pi$
$522$	−6.69192	−	189.011i	−0.0128198	−	0.362090i
$523$		−	114.482i		−	0.218895i	−0.993993	−	0.109448i	$-0.965092\pi$
$523$		−	114.482i		−	0.218895i	0.993993	−	0.109448i	$-0.0349082\pi$
$524$	−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	−0.0660852	+	0.997814i	$0.521051\pi$
$541$	−575.569	+	575.569i	−1.06390	+	1.06390i	−0.997814	+	0.0660852i	$0.978949\pi$
$542$	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	$-0.586766\pi$
$547$		−	1053.61i		−	1.92616i	0.269219	−	0.963079i	$-0.413234\pi$
$548$	−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	$-0.790919\pi$
$557$		−	680.234i		−	1.22125i	0.791922	−	0.610623i	$-0.209081\pi$
$558$	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	0.589829	−	0.807528i	$-0.299195\pi$
$571$	−124.307	−	124.307i	−0.217700	−	0.217700i	−0.807528	+	0.589829i	$0.799195\pi$
$572$	−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	−0.919337	−	0.393471i	$-0.871274\pi$
$577$	−303.425	+	303.425i	−0.525866	+	0.525866i	0.393471	+	0.919337i	$0.371274\pi$
$578$	−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	0.304970	−	0.952362i	$-0.401354\pi$
$593$	−383.903	−	383.903i	−0.647392	−	0.647392i	−0.952362	+	0.304970i	$0.901354\pi$
$594$	−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	$-0.924163\pi$
$601$		−	283.673i		−	0.472002i	0.971753	−	0.236001i	$-0.0758369\pi$
$602$	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	−0.246885	−	0.969045i	$-0.579407\pi$
$607$	438.351	−	438.351i	0.722160	−	0.722160i	0.969045	+	0.246885i	$0.0794069\pi$
$608$	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	$0.0431005\pi$
$613$			165.499i			0.269981i	−0.990847	+	0.134991i	$0.956900\pi$
$614$	−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	0.862010	−	0.506892i	$-0.169206\pi$
$617$	219.108	+	219.108i	0.355118	+	0.355118i	−0.506892	+	0.862010i	$0.669206\pi$
$618$	394.971	−	13.9839i	0.639111	−	0.0226277i
$619$	−365.140	+	365.140i	−0.589888	+	0.589888i	−0.937601	−	0.347713i	$-0.886958\pi$
$619$	−365.140	+	365.140i	−0.589888	+	0.589888i	0.347713	+	0.937601i	$0.386958\pi$
$620$	−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	$0.344087\pi$
$631$			1113.61i			1.76484i	−0.470463	+	0.882420i	$0.655913\pi$
$632$	−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	0.658539	−	0.752547i	$-0.271175\pi$
$647$	−60.8229	−	60.8229i	−0.0940075	−	0.0940075i	−0.752547	+	0.658539i	$0.771175\pi$
$648$	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	0.984192	+	0.177103i	$0.0566727\pi$
$659$	765.294	+	765.294i	1.16130	+	1.16130i	0.177103	+	0.984192i	$0.443327\pi$
$660$	−195.932	+	281.374i	−0.296866	+	0.426324i
$661$	423.035	+	423.035i	0.639993	+	0.639993i	0.950553	−	0.310561i	$-0.100517\pi$
$661$	423.035	+	423.035i	0.639993	+	0.639993i	−0.310561	+	0.950553i	$0.600517\pi$
$662$	−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	0.374190	−	0.927352i	$-0.377921\pi$
$673$	−372.278	−	372.278i	−0.553162	−	0.553162i	−0.927352	+	0.374190i	$0.877921\pi$
$674$	−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	$-0.896963\pi$
$683$		−	434.494i		−	0.636155i	0.948065	−	0.318077i	$-0.103037\pi$
$684$	−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	−0.801180	−	0.598424i	$-0.795794\pi$
$691$	−140.105	+	140.105i	−0.202756	+	0.202756i	0.598424	+	0.801180i	$0.295794\pi$
$692$	−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	−0.428456	−	0.903563i	$-0.640942\pi$
$701$	333.050	−	333.050i	0.475106	−	0.475106i	0.903563	+	0.428456i	$0.140942\pi$
$702$	−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	−0.987559	−	0.157251i	$-0.949737\pi$
$709$	−588.688	+	588.688i	−0.830308	+	0.830308i	0.157251	+	0.987559i	$0.449737\pi$
$710$	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	$-0.802212\pi$
$719$		−	837.132i		−	1.16430i	0.813081	−	0.582150i	$-0.197788\pi$
$720$	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	0.622998	−	0.782223i	$-0.285914\pi$
$727$	−115.757	−	115.757i	−0.159225	−	0.159225i	−0.782223	+	0.622998i	$0.785914\pi$
$728$	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	0.992262	−	0.124166i	$-0.0396254\pi$
$739$	641.523	+	641.523i	0.868096	+	0.868096i	−0.124166	+	0.992262i	$0.539625\pi$
$740$	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	−0.761845	−	0.647760i	$-0.775706\pi$
$743$	−84.7652	+	84.7652i	−0.114085	+	0.114085i	0.647760	+	0.761845i	$0.275706\pi$
$744$	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	$-0.925480\pi$
$761$		−	353.070i		−	0.463956i	0.972721	−	0.231978i	$-0.0745197\pi$
$762$	−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	$-0.916030\pi$
$769$		−	401.035i		−	0.521503i	0.965406	−	0.260751i	$-0.0839703\pi$
$770$	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	$-0.917531\pi$
$773$		−	396.076i		−	0.512388i	0.966625	−	0.256194i	$-0.0824686\pi$
$774$	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	$-0.962608\pi$
$787$		−	184.472i		−	0.234399i	0.993108	−	0.117200i	$-0.0373917\pi$
$788$	−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	$-0.962566\pi$
$797$		−	187.027i		−	0.234664i	0.993093	−	0.117332i	$-0.0374341\pi$
$798$	−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	0.995702	+	0.0926166i	$0.0295231\pi$
$811$	882.626	+	882.626i	1.08832	+	1.08832i	0.0926166	+	0.995702i	$0.470477\pi$
$812$	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	0.696077	−	0.717967i	$-0.254927\pi$
$821$	−17.9719	−	17.9719i	−0.0218902	−	0.0218902i	−0.717967	+	0.696077i	$0.754927\pi$
$822$	19.5433	+	551.994i	0.0237753	+	0.671526i
$823$	36.8905	−	36.8905i	0.0448245	−	0.0448245i	−0.684339	−	0.729164i	$-0.739909\pi$
$823$	36.8905	−	36.8905i	0.0448245	−	0.0448245i	0.729164	+	0.684339i	$0.239909\pi$
$824$	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	−0.871116	−	0.491077i	$-0.836603\pi$
$829$	−1129.26	−	1129.26i	−1.36219	−	1.36219i	−0.491077	−	0.871116i	$-0.663397\pi$
$830$	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	$-0.944924\pi$
$853$		−	293.712i		−	0.344329i	0.985068	−	0.172164i	$-0.0550760\pi$
$854$	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	0.211136	−	0.977457i	$-0.432284\pi$
$857$	−656.737	−	656.737i	−0.766321	−	0.766321i	−0.977457	+	0.211136i	$0.932284\pi$
$858$	8.06826	+	227.885i	0.00940357	+	0.265601i
$859$	−1015.37	+	1015.37i	−1.18203	+	1.18203i	−0.202818	+	0.979217i	$0.565010\pi$
$859$	−1015.37	+	1015.37i	−1.18203	+	1.18203i	−0.979217	+	0.202818i	$0.934990\pi$
$860$	−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	0.899863	−	0.436174i	$-0.143667\pi$
$863$	400.164	+	400.164i	0.463689	+	0.463689i	−0.436174	+	0.899863i	$0.643667\pi$
$864$	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	$-0.901854\pi$
$877$		−	532.291i		−	0.606945i	0.952840	−	0.303472i	$-0.0981460\pi$
$878$	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	0.545876	−	0.837866i	$-0.316197\pi$
$887$	−258.995	−	258.995i	−0.291990	−	0.291990i	−0.837866	+	0.545876i	$0.816197\pi$
$888$	−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	$-0.922567\pi$
$929$		−	447.538i		−	0.481742i	0.970557	−	0.240871i	$-0.0774330\pi$
$930$	−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	0.528809	−	0.848741i	$-0.322639\pi$
$937$	−299.777	−	299.777i	−0.319932	−	0.319932i	−0.848741	+	0.528809i	$0.822639\pi$
$938$	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	−0.0547565	+	0.998500i	$0.517438\pi$
$941$	−991.114	+	991.114i	−1.05326	+	1.05326i	−0.998500	+	0.0547565i	$0.982562\pi$
$942$	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	$-0.996278\pi$
$947$		−	22.1486i		−	0.0233882i	0.999932	−	0.0116941i	$-0.00372243\pi$
$948$	−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	0.303651	−	0.952783i	$-0.401794\pi$
$953$	1197.38	−	1197.38i	1.25643	−	1.25643i	0.952783	−	0.303651i	$-0.0982056\pi$
$954$	−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	0.999534	−	0.0305352i	$-0.00972117\pi$
$967$	937.022	+	937.022i	0.968998	+	0.968998i	−0.0305352	+	0.999534i	$0.509721\pi$
$968$	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	−0.998858	−	0.0477733i	$-0.984787\pi$
$971$	−1016.28	−	1016.28i	−1.04663	−	1.04663i	−0.0477733	−	0.998858i	$-0.515213\pi$
$972$	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	−0.938242	−	0.345980i	$-0.887546\pi$
$977$	−578.640	+	578.640i	−0.592262	+	0.592262i	0.345980	+	0.938242i	$0.387546\pi$
$978$	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	−0.959646	−	0.281209i	$-0.909265\pi$
$983$	−666.904	+	666.904i	−0.678437	+	0.678437i	0.281209	+	0.959646i	$0.409265\pi$
$984$	−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.53.17	yes	44
4.3	odd	2		320.3.t.a.113.8		44
5.2	odd	4		80.3.i.a.37.7	yes	44
5.3	odd	4		400.3.i.b.357.16		44
5.4	even	2		400.3.t.b.293.6		44
8.3	odd	2		640.3.t.a.353.15		44
8.5	even	2		640.3.t.b.353.8		44
16.3	odd	4		320.3.i.a.273.8		44
16.5	even	4		640.3.i.b.33.8		44
16.11	odd	4		640.3.i.a.33.15		44
16.13	even	4		80.3.i.a.13.7	✓	44
20.7	even	4		320.3.i.a.177.15		44
40.27	even	4		640.3.i.a.97.8		44
40.37	odd	4		640.3.i.b.97.15		44
80.13	odd	4		400.3.t.b.157.6		44
80.27	even	4		640.3.t.a.417.15		44
80.29	even	4		400.3.i.b.93.16		44
80.37	odd	4		640.3.t.b.417.8		44
80.67	even	4		320.3.t.a.17.8		44
80.77	odd	4	inner	80.3.t.a.77.17	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.7	✓	44	16.13	even	4
80.3.i.a.37.7	yes	44	5.2	odd	4
80.3.t.a.53.17	yes	44	1.1	even	1	trivial
80.3.t.a.77.17	yes	44	80.77	odd	4	inner
320.3.i.a.177.15		44	20.7	even	4
320.3.i.a.273.8		44	16.3	odd	4
320.3.t.a.17.8		44	80.67	even	4
320.3.t.a.113.8		44	4.3	odd	2
400.3.i.b.93.16		44	80.29	even	4
400.3.i.b.357.16		44	5.3	odd	4
400.3.t.b.157.6		44	80.13	odd	4
400.3.t.b.293.6		44	5.4	even	2
640.3.i.a.33.15		44	16.11	odd	4
640.3.i.a.97.8		44	40.27	even	4
640.3.i.b.33.8		44	16.5	even	4
640.3.i.b.97.15		44	40.37	odd	4
640.3.t.a.353.15		44	8.3	odd	2
640.3.t.a.417.15		44	80.27	even	4
640.3.t.b.353.8		44	8.5	even	2
640.3.t.b.417.8		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)

\(f(q)\)	\(=\)	\(q+(1.46337 + 1.36329i) q^{2} +1.90859 q^{3} +(0.282885 + 3.98998i) q^{4} +(4.97175 - 0.530759i) q^{5} +(2.79297 + 2.60196i) q^{6} +(-8.62025 - 8.62025i) q^{7} +(-5.02554 + 6.22446i) q^{8} -5.35728 q^{9} +O(q^{10})\)	\(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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