LMFDB - Embedded newform 80.3.i.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("80.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 + 0.382594i) q^{4} +(-3.37360 - 3.69037i) q^{5} +(-0.473499 + 9.87810i) q^{6} +(3.22480 + 3.22480i) q^{7} +(-7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +O(q^{10})$	\(q+(-1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 + 0.382594i) q^{4} +(-3.37360 - 3.69037i) q^{5} +(-0.473499 + 9.87810i) q^{6} +(3.22480 + 3.22480i) q^{7} +(-7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +(6.38608 + 7.69532i) q^{10} +(-7.67097 + 7.67097i) q^{11} +(1.89182 - 19.6882i) q^{12} -22.2152i q^{13} +(-6.13341 - 6.75101i) q^{14} +(-18.2478 + 16.6815i) q^{15} +(15.7072 + 3.04672i) q^{16} +(-3.76038 + 3.76038i) q^{17} +(30.8651 + 1.47949i) q^{18} +(-0.809445 + 0.809445i) q^{19} +(-12.0206 - 15.9845i) q^{20} +(15.9458 - 15.9458i) q^{21} +(16.0589 - 14.5898i) q^{22} +(12.2839 - 12.2839i) q^{23} +(-5.66462 + 39.1501i) q^{24} +(-2.23764 + 24.8997i) q^{25} +(-2.12729 + 44.3794i) q^{26} +31.8948i q^{27} +(11.6063 + 14.0739i) q^{28} +(27.1574 - 27.1574i) q^{29} +(38.0512 - 31.5774i) q^{30} +25.5557 q^{31} +(-31.0867 - 7.59056i) q^{32} +(37.9308 + 37.9308i) q^{33} +(7.87223 - 7.15205i) q^{34} +(1.02151 - 22.7799i) q^{35} +(-61.5178 - 5.91119i) q^{36} -8.62466i q^{37} +(1.69454 - 1.53952i) q^{38} -109.848 q^{39} +(22.4830 + 33.0834i) q^{40} -73.4504i q^{41} +(-33.3819 + 30.3280i) q^{42} -17.5521 q^{43} +(-33.4781 + 27.6083i) q^{44} +(52.1231 + 57.0172i) q^{45} +(-25.7160 + 23.3634i) q^{46} +(17.4590 - 17.4590i) q^{47} +(15.0652 - 77.6680i) q^{48} -28.2013i q^{49} +(6.85449 - 49.5279i) q^{50} +(18.5940 + 18.5940i) q^{51} +(8.49939 - 88.4532i) q^{52} -29.3309 q^{53} +(3.05420 - 63.7165i) q^{54} +(54.1875 + 2.42991i) q^{55} +(-21.8382 - 29.2268i) q^{56} +(4.00248 + 4.00248i) q^{57} +(-56.8532 + 51.6520i) q^{58} +(72.6508 + 72.6508i) q^{59} +(-79.0390 + 59.4386i) q^{60} +(19.7110 + 19.7110i) q^{61} +(-51.0529 - 2.44718i) q^{62} +(-49.8241 - 49.8241i) q^{63} +(61.3753 + 18.1405i) q^{64} +(-81.9821 + 74.9451i) q^{65} +(-72.1424 - 79.4068i) q^{66} +14.0319 q^{67} +(-16.4113 + 13.5339i) q^{68} +(-60.7406 - 60.7406i) q^{69} +(-4.22205 + 45.4098i) q^{70} +91.3292i q^{71} +(122.328 + 17.6997i) q^{72} +(-42.7665 + 42.7665i) q^{73} +(-0.825884 + 17.2295i) q^{74} +(123.122 + 11.0645i) q^{75} +(-3.53262 + 2.91325i) q^{76} -49.4747 q^{77} +(219.444 + 10.5188i) q^{78} -46.7110i q^{79} +(-41.7464 - 68.2439i) q^{80} +18.6585 q^{81} +(-7.03350 + 146.732i) q^{82} +82.9430i q^{83} +(69.5913 - 57.3898i) q^{84} +(26.5632 + 1.19117i) q^{85} +(35.0639 + 1.68076i) q^{86} +(-134.286 - 134.286i) q^{87} +(69.5231 - 51.9475i) q^{88} +131.145 q^{89} +(-98.6667 - 118.895i) q^{90} +(71.6395 - 71.6395i) q^{91} +(53.6102 - 44.2106i) q^{92} -126.366i q^{93} +(-36.5499 + 33.2062i) q^{94} +(5.71789 + 0.256406i) q^{95} +(-37.5332 + 153.715i) q^{96} +(-30.5363 + 30.5363i) q^{97} +(-2.70051 + 56.3379i) q^{98} +(118.519 - 118.519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	$ 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.99771	−	0.0957584i	−0.998853	−	0.0478792i
$2$	−1.99771	−	0.0957584i	−0.998853	−	0.0478792i
$3$		−	4.94472i		−	1.64824i	−0.566415	−	0.824120i	$-0.691670\pi$
$3$		−	4.94472i		−	1.64824i	0.566415	−	0.824120i	$-0.308330\pi$
$4$	3.98166	+	0.382594i	0.995415	+	0.0956486i
$5$	−3.37360	−	3.69037i	−0.674720	−	0.738074i
$5$	−3.37360	−	3.69037i	−0.674720	−	0.738074i
$6$	−0.473499	+	9.87810i	−0.0789165	+	1.64635i
$7$	3.22480	+	3.22480i	0.460686	+	0.460686i	0.898880	−	0.438194i	$-0.144382\pi$
$7$	3.22480	+	3.22480i	0.460686	+	0.460686i	−0.438194	+	0.898880i	$0.644382\pi$
$8$	−7.91755	−	1.14559i	−0.989694	−	0.143199i
$9$	−15.4503			−1.71670
$10$	6.38608	+	7.69532i	0.638608	+	0.769532i
$11$	−7.67097	+	7.67097i	−0.697361	+	0.697361i	−0.963841	−	0.266480i	$-0.914139\pi$
$11$	−7.67097	+	7.67097i	−0.697361	+	0.697361i	0.266480	+	0.963841i	$0.414139\pi$
$12$	1.89182	−	19.6882i	0.157652	−	1.64068i
$13$		−	22.2152i		−	1.70886i	−0.519568	−	0.854429i	$-0.673907\pi$
$13$		−	22.2152i		−	1.70886i	0.519568	−	0.854429i	$-0.326093\pi$
$14$	−6.13341	−	6.75101i	−0.438101	−	0.482215i
$15$	−18.2478	+	16.6815i	−1.21652	+	1.11210i
$16$	15.7072	+	3.04672i	0.981703	+	0.190420i
$17$	−3.76038	+	3.76038i	−0.221199	+	0.221199i	−0.809003	−	0.587804i	$-0.799993\pi$
$17$	−3.76038	+	3.76038i	−0.221199	+	0.221199i	0.587804	+	0.809003i	$0.299993\pi$
$18$	30.8651	+	1.47949i	1.71473	+	0.0821941i
$19$	−0.809445	+	0.809445i	−0.0426024	+	0.0426024i	−0.728087	−	0.685485i	$-0.759590\pi$
$19$	−0.809445	+	0.809445i	−0.0426024	+	0.0426024i	0.685485	+	0.728087i	$0.259590\pi$
$20$	−12.0206	−	15.9845i	−0.601031	−	0.799226i
$21$	15.9458	−	15.9458i	0.759322	−	0.759322i
$22$	16.0589	−	14.5898i	0.729950	−	0.663172i
$23$	12.2839	−	12.2839i	0.534083	−	0.534083i	−0.387701	−	0.921785i	$-0.626731\pi$
$23$	12.2839	−	12.2839i	0.534083	−	0.534083i	0.921785	+	0.387701i	$0.126731\pi$
$24$	−5.66462	+	39.1501i	−0.236026	+	1.63125i
$25$	−2.23764	+	24.8997i	−0.0895055	+	0.995986i
$26$	−2.12729	+	44.3794i	−0.0818188	+	1.70690i
$27$			31.8948i			1.18129i
$28$	11.6063	+	14.0739i	0.414510	+	0.502638i
$29$	27.1574	−	27.1574i	0.936464	−	0.936464i	−0.0616350	−	0.998099i	$-0.519631\pi$
$29$	27.1574	−	27.1574i	0.936464	−	0.936464i	0.998099	+	0.0616350i	$0.0196315\pi$
$30$	38.0512	−	31.5774i	1.26837	−	1.05258i
$31$	25.5557			0.824379			0.412189	−	0.911098i	$-0.364764\pi$
$31$	25.5557			0.824379			0.412189	+	0.911098i	$0.364764\pi$
$32$	−31.0867	−	7.59056i	−0.971460	−	0.237205i
$33$	37.9308	+	37.9308i	1.14942	+	1.14942i
$34$	7.87223	−	7.15205i	0.231536	−	0.210354i
$35$	1.02151	−	22.7799i	0.0291861	−	0.650855i
$36$	−61.5178	−	5.91119i	−1.70883	−	0.164200i
$37$		−	8.62466i		−	0.233099i	−0.993185	−	0.116550i	$-0.962817\pi$
$37$		−	8.62466i		−	0.233099i	0.993185	−	0.116550i	$-0.0371834\pi$
$38$	1.69454	−	1.53952i	0.0445933	−	0.0405137i
$39$	−109.848			−2.81661
$40$	22.4830	+	33.0834i	0.562075	+	0.827086i
$41$		−	73.4504i		−	1.79147i	−0.444585	−	0.895737i	$-0.646649\pi$
$41$		−	73.4504i		−	1.79147i	0.444585	−	0.895737i	$-0.353351\pi$
$42$	−33.3819	+	30.3280i	−0.794807	+	0.722095i
$43$	−17.5521			−0.408188			−0.204094	−	0.978951i	$-0.565425\pi$
$43$	−17.5521			−0.408188			−0.204094	+	0.978951i	$0.565425\pi$
$44$	−33.4781	+	27.6083i	−0.760865	+	0.627462i
$45$	52.1231	+	57.0172i	1.15829	+	1.26705i
$46$	−25.7160	+	23.3634i	−0.559042	+	0.507899i
$47$	17.4590	−	17.4590i	0.371469	−	0.371469i	−0.496543	−	0.868012i	$-0.665398\pi$
$47$	17.4590	−	17.4590i	0.371469	−	0.371469i	0.868012	+	0.496543i	$0.165398\pi$
$48$	15.0652	−	77.6680i	0.313858	−	1.61808i
$49$		−	28.2013i		−	0.575536i
$50$	6.85449	−	49.5279i	0.137090	−	0.990559i
$51$	18.5940	+	18.5940i	0.364589	+	0.364589i
$52$	8.49939	−	88.4532i	0.163450	−	1.70102i
$53$	−29.3309			−0.553413			−0.276707	−	0.960954i	$-0.589243\pi$
$53$	−29.3309			−0.553413			−0.276707	+	0.960954i	$0.589243\pi$
$54$	3.05420	−	63.7165i	0.0565592	−	1.17993i
$55$	54.1875	+	2.42991i	0.985227	+	0.0441803i
$56$	−21.8382	−	29.2268i	−0.389969	−	0.521908i
$57$	4.00248	+	4.00248i	0.0702190	+	0.0702190i
$58$	−56.8532	+	51.6520i	−0.980227	+	0.890553i
$59$	72.6508	+	72.6508i	1.23137	+	1.23137i	0.963438	+	0.267931i	$0.0863398\pi$
$59$	72.6508	+	72.6508i	1.23137	+	1.23137i	0.267931	+	0.963438i	$0.413660\pi$
$60$	−79.0390	+	59.4386i	−1.31732	+	0.990644i
$61$	19.7110	+	19.7110i	0.323132	+	0.323132i	0.849967	−	0.526835i	$-0.176622\pi$
$61$	19.7110	+	19.7110i	0.323132	+	0.323132i	−0.526835	+	0.849967i	$0.676622\pi$
$62$	−51.0529	−	2.44718i	−0.823433	−	0.0394706i
$63$	−49.8241	−	49.8241i	−0.790859	−	0.790859i
$64$	61.3753	+	18.1405i	0.958988	+	0.283446i
$65$	−81.9821	+	74.9451i	−1.26126	+	1.15300i
$66$	−72.1424	−	79.4068i	−1.09307	−	1.20313i
$67$	14.0319			0.209431			0.104716	−	0.994502i	$-0.466607\pi$
$67$	14.0319			0.209431			0.104716	+	0.994502i	$0.466607\pi$
$68$	−16.4113	+	13.5339i	−0.241342	+	0.199027i
$69$	−60.7406	−	60.7406i	−0.880298	−	0.880298i
$70$	−4.22205	+	45.4098i	−0.0603150	+	0.648711i
$71$			91.3292i			1.28633i	0.765729	+	0.643163i	$0.222378\pi$
$71$			91.3292i			1.28633i	−0.765729	+	0.643163i	$0.777622\pi$
$72$	122.328	+	17.6997i	1.69900	+	0.245829i
$73$	−42.7665	+	42.7665i	−0.585843	+	0.585843i	−0.936503	−	0.350660i	$-0.885957\pi$
$73$	−42.7665	+	42.7665i	−0.585843	+	0.585843i	0.350660	+	0.936503i	$0.385957\pi$
$74$	−0.825884	+	17.2295i	−0.0111606	+	0.232832i
$75$	123.122	+	11.0645i	1.64163	+	0.147527i
$76$	−3.53262	+	2.91325i	−0.0464819	+	0.0383322i
$77$	−49.4747			−0.642529
$78$	219.444	+	10.5188i	2.81338	+	0.134857i
$79$		−	46.7110i		−	0.591278i	−0.955300	−	0.295639i	$-0.904467\pi$
$79$		−	46.7110i		−	0.591278i	0.955300	−	0.295639i	$-0.0955326\pi$
$80$	−41.7464	−	68.2439i	−0.521830	−	0.853049i
$81$	18.6585			0.230352
$82$	−7.03350	+	146.732i	−0.0857744	+	1.78942i
$83$			82.9430i			0.999313i	0.866224	+	0.499656i	$0.166540\pi$
$83$			82.9430i			0.999313i	−0.866224	+	0.499656i	$0.833460\pi$
$84$	69.5913	−	57.3898i	0.828468	−	0.683212i
$85$	26.5632	+	1.19117i	0.312508	+	0.0140137i
$86$	35.0639	+	1.68076i	0.407720	+	0.0195437i
$87$	−134.286	−	134.286i	−1.54352	−	1.54352i
$88$	69.5231	−	51.9475i	0.790035	−	0.590313i
$89$	131.145			1.47354			0.736768	−	0.676146i	$-0.236351\pi$
$89$	131.145			1.47354			0.736768	+	0.676146i	$0.236351\pi$
$90$	−98.6667	−	118.895i	−1.09630	−	1.32105i
$91$	71.6395	−	71.6395i	0.787247	−	0.787247i
$92$	53.6102	−	44.2106i	0.582719	−	0.480550i
$93$		−	126.366i		−	1.35877i
$94$	−36.5499	+	33.2062i	−0.388828	+	0.353257i
$95$	5.71789	+	0.256406i	0.0601884	+	0.00269901i
$96$	−37.5332	+	153.715i	−0.390971	+	1.60120i
$97$	−30.5363	+	30.5363i	−0.314807	+	0.314807i	−0.846769	−	0.531962i	$-0.821455\pi$
$97$	−30.5363	+	30.5363i	−0.314807	+	0.314807i	0.531962	+	0.846769i	$0.321455\pi$
$98$	−2.70051	+	56.3379i	−0.0275562	+	0.574876i
$99$	118.519	−	118.519i	1.19716	−	1.19716i
$100$	−18.4360	+	98.2859i	−0.184360	+	0.982859i
$101$	22.0905	−	22.0905i	0.218718	−	0.218718i	−0.589240	−	0.807958i	$-0.700573\pi$
$101$	22.0905	−	22.0905i	0.218718	−	0.218718i	0.807958	+	0.589240i	$0.200573\pi$
$102$	−35.3649	−	38.9260i	−0.346715	−	0.381627i
$103$	5.06551	−	5.06551i	0.0491797	−	0.0491797i	−0.682089	−	0.731269i	$-0.738928\pi$
$103$	5.06551	−	5.06551i	0.0491797	−	0.0491797i	0.731269	+	0.682089i	$0.238928\pi$
$104$	−25.4494	+	175.890i	−0.244706	+	1.69125i
$105$	−112.640	−	5.05110i	−1.07276	−	0.0481057i
$106$	58.5945	+	2.80868i	0.552779	+	0.0264970i
$107$		−	54.6933i		−	0.511153i	−0.966789	−	0.255576i	$-0.917735\pi$
$107$		−	54.6933i		−	0.511153i	0.966789	−	0.255576i	$-0.0822652\pi$
$108$	−12.2028	+	126.994i	−0.112989	+	1.17587i
$109$	−81.8934	+	81.8934i	−0.751316	+	0.751316i	−0.974725	−	0.223409i	$-0.928281\pi$
$109$	−81.8934	+	81.8934i	−0.751316	+	0.751316i	0.223409	+	0.974725i	$0.428281\pi$
$110$	−108.018	−	10.0432i	−0.981982	−	0.0913015i
$111$	−42.6466			−0.384203
$112$	40.8277	+	60.4778i	0.364533	+	0.539981i
$113$	−19.1764	−	19.1764i	−0.169703	−	0.169703i	0.617146	−	0.786849i	$-0.288289\pi$
$113$	−19.1764	−	19.1764i	−0.169703	−	0.169703i	−0.786849	+	0.617146i	$0.788289\pi$
$114$	−7.61251	−	8.37905i	−0.0667764	−	0.0735005i
$115$	−86.7732	−	3.89115i	−0.754550	−	0.0338361i
$116$	118.522	−	97.7415i	1.02174	−	0.842599i
$117$			343.230i			2.93359i
$118$	−138.178	−	152.092i	−1.17100	−	1.28891i
$119$	−24.2530			−0.203807
$120$	163.588	−	111.172i	1.36324	−	0.926435i
$121$			3.31247i			0.0273758i
$122$	−37.4894	−	41.2644i	−0.307290	−	0.338233i
$123$	−363.192			−2.95278
$124$	101.754	+	9.77749i	0.820599	+	0.0788507i
$125$	99.4378	−	75.7438i	0.795502	−	0.605950i
$126$	94.7628	+	104.305i	0.752086	+	0.827817i
$127$	100.021	−	100.021i	0.787565	−	0.787565i	−0.193529	−	0.981094i	$-0.561993\pi$
$127$	100.021	−	100.021i	0.787565	−	0.787565i	0.981094	+	0.193529i	$0.0619935\pi$
$128$	−120.873	−	42.1166i	−0.944317	−	0.329036i
$129$			86.7901i			0.672792i
$130$	170.953	−	141.868i	1.31502	−	1.09129i
$131$	−48.8021	−	48.8021i	−0.372535	−	0.372535i	0.495865	−	0.868400i	$-0.334851\pi$
$131$	−48.8021	−	48.8021i	−0.372535	−	0.372535i	−0.868400	+	0.495865i	$0.834851\pi$
$132$	136.515	+	165.540i	1.03421	+	1.25409i
$133$	−5.22060			−0.0392526
$134$	−28.0316	−	1.34367i	−0.209191	−	0.0100274i
$135$	117.704	−	107.600i	0.871879	−	0.797040i
$136$	34.0809	−	25.4652i	0.250595	−	0.187244i
$137$	116.195	+	116.195i	0.848135	+	0.848135i	0.989900	−	0.141765i	$-0.0452778\pi$
$137$	116.195	+	116.195i	0.848135	+	0.848135i	−0.141765	+	0.989900i	$0.545278\pi$
$138$	115.525	+	127.158i	0.837141	+	0.921437i
$139$	−25.5977	−	25.5977i	−0.184156	−	0.184156i	0.609008	−	0.793164i	$-0.291568\pi$
$139$	−25.5977	−	25.5977i	−0.184156	−	0.184156i	−0.793164	+	0.609008i	$0.791568\pi$
$140$	12.7828	−	90.3110i	0.0913056	−	0.645079i
$141$	−86.3301	−	86.3301i	−0.612270	−	0.612270i
$142$	8.74554	−	182.449i	0.0615883	−	1.28485i
$143$	170.412	+	170.412i	1.19169	+	1.19169i
$144$	−242.681	−	47.0727i	−1.68529	−	0.326894i
$145$	−191.839	−	8.60260i	−1.32303	−	0.0593283i
$146$	89.5303	−	81.3397i	0.613221	−	0.557122i
$147$	−139.448			−0.948623
$148$	3.29975	−	34.3405i	0.0222956	−	0.232030i
$149$	−11.6294	−	11.6294i	−0.0780497	−	0.0780497i	0.667004	−	0.745054i	$-0.267576\pi$
$149$	−11.6294	−	11.6294i	−0.0780497	−	0.0780497i	−0.745054	+	0.667004i	$0.767576\pi$
$150$	−244.902	−	33.8936i	−1.63268	−	0.225957i
$151$			84.9872i			0.562829i	0.959586	+	0.281414i	$0.0908036\pi$
$151$			84.9872i			0.562829i	−0.959586	+	0.281414i	$0.909196\pi$
$152$	7.33611	−	5.48153i	0.0482639	−	0.0360627i
$153$	58.0989	−	58.0989i	0.379732	−	0.379732i
$154$	98.8360	+	4.73762i	0.641792	+	0.0307638i
$155$	−86.2149	−	94.3101i	−0.556225	−	0.608452i
$156$	−437.376	−	42.0271i	−2.80370	−	0.269405i
$157$	128.249			0.816874			0.408437	−	0.912787i	$-0.366074\pi$
$157$	128.249			0.816874			0.408437	+	0.912787i	$0.366074\pi$
$158$	−4.47297	+	93.3148i	−0.0283099	+	0.590600i
$159$			145.033i			0.912158i
$160$	76.8622	+	140.329i	0.480389	+	0.877056i
$161$	79.2265			0.492090
$162$	−37.2743	−	1.78671i	−0.230088	−	0.0110291i
$163$			82.0115i			0.503138i	0.967839	+	0.251569i	$0.0809466\pi$
$163$			82.0115i			0.503138i	−0.967839	+	0.251569i	$0.919053\pi$
$164$	28.1017	−	292.455i	0.171352	−	1.78326i
$165$	12.0153	−	267.942i	0.0728197	−	1.62389i
$166$	7.94249	−	165.696i	0.0478463	−	0.998167i
$167$	131.169	+	131.169i	0.785444	+	0.785444i	0.980744	−	0.195299i	$-0.0625678\pi$
$167$	131.169	+	131.169i	0.785444	+	0.785444i	−0.195299	+	0.980744i	$0.562568\pi$
$168$	−144.519	+	107.984i	−0.860230	+	0.642762i
$169$	−324.513			−1.92020
$170$	−52.9514	−	4.92325i	−0.311479	−	0.0289603i
$171$	12.5061	−	12.5061i	0.0731354	−	0.0731354i
$172$	−69.8864	−	6.71533i	−0.406316	−	0.0390426i
$173$			58.5238i			0.338288i	0.985591	+	0.169144i	$0.0541003\pi$
$173$			58.5238i			0.338288i	−0.985591	+	0.169144i	$0.945900\pi$
$174$	255.405	+	281.123i	1.46784	+	1.61565i
$175$	−87.5124	+	73.0806i	−0.500071	+	0.417603i
$176$	−143.861	+	97.1185i	−0.817393	+	0.551809i
$177$	359.238	−	359.238i	2.02959	−	2.02959i
$178$	−261.988	−	12.5582i	−1.47185	−	0.0705517i
$179$	114.264	−	114.264i	0.638347	−	0.638347i	−0.311801	−	0.950147i	$-0.600932\pi$
$179$	114.264	−	114.264i	0.638347	−	0.638347i	0.950147	+	0.311801i	$0.100932\pi$
$180$	185.722	+	246.965i	1.03179	+	1.37203i
$181$	74.0068	−	74.0068i	0.408878	−	0.408878i	−0.472470	−	0.881347i	$-0.656637\pi$
$181$	74.0068	−	74.0068i	0.408878	−	0.408878i	0.881347	+	0.472470i	$0.156637\pi$
$182$	−149.975	+	136.255i	−0.824037	+	0.748652i
$183$	97.4656	−	97.4656i	0.532599	−	0.532599i
$184$	−111.331	+	83.1863i	−0.605059	+	0.452099i
$185$	−31.8282	+	29.0962i	−0.172044	+	0.157277i
$186$	−12.1006	+	252.442i	−0.0650571	+	1.35722i
$187$		−	57.6915i		−	0.308511i
$188$	76.1957	−	62.8362i	0.405296	−	0.334235i
$189$	−102.855	+	102.855i	−0.544204	+	0.544204i
$190$	−11.3981	−	1.05976i	−0.0599901	−	0.00557769i
$191$	92.5178			0.484387			0.242193	−	0.970228i	$-0.422133\pi$
$191$	92.5178			0.484387			0.242193	+	0.970228i	$0.422133\pi$
$192$	89.6998	−	303.484i	0.467187	−	1.58064i
$193$	52.8692	+	52.8692i	0.273934	+	0.273934i	0.830682	−	0.556748i	$-0.187951\pi$
$193$	52.8692	+	52.8692i	0.273934	+	0.273934i	−0.556748	+	0.830682i	$0.687951\pi$
$194$	63.9266	−	58.0784i	0.329519	−	0.299373i
$195$	370.582	+	405.379i	1.90042	+	2.07887i
$196$	10.7897	−	112.288i	0.0550493	−	0.572898i
$197$			99.4134i			0.504637i	0.967644	+	0.252318i	$0.0811930\pi$
$197$			99.4134i			0.504637i	−0.967644	+	0.252318i	$0.918807\pi$
$198$	−248.114	+	225.416i	−1.25310	+	1.13847i
$199$	265.168			1.33250			0.666252	−	0.745727i	$-0.267898\pi$
$199$	265.168			1.33250			0.666252	+	0.745727i	$0.267898\pi$
$200$	46.2414	−	194.581i	0.231207	−	0.972905i
$201$		−	69.3838i		−	0.345193i
$202$	−46.2457	+	42.0150i	−0.228939	+	0.207995i
$203$	175.155			0.862832
$204$	66.9212	+	81.1491i	0.328045	+	0.397790i
$205$	−271.059	+	247.792i	−1.32224	+	1.20874i
$206$	−10.6045	+	9.63433i	−0.0514779	+	0.0467686i
$207$	−189.790	+	189.790i	−0.916860	+	0.916860i
$208$	67.6834	−	348.939i	0.325401	−	1.67759i
$209$		−	12.4185i		−	0.0594184i
$210$	224.539	+	20.8769i	1.06923	+	0.0994137i
$211$	−226.573	−	226.573i	−1.07380	−	1.07380i	−0.997050	−	0.0767547i	$-0.975544\pi$
$211$	−226.573	−	226.573i	−1.07380	−	1.07380i	−0.0767547	−	0.997050i	$-0.524456\pi$
$212$	−116.786	−	11.2218i	−0.550876	−	0.0529332i
$213$	451.597			2.12017
$214$	−5.23735	+	109.261i	−0.0244736	+	0.510566i
$215$	59.2137	+	64.7736i	0.275413	+	0.301273i
$216$	36.5384	−	252.529i	0.169159	−	1.16912i
$217$	82.4122	+	82.4122i	0.379780	+	0.379780i
$218$	171.441	−	155.757i	0.786427	−	0.714482i
$219$	211.469	+	211.469i	0.965610	+	0.965610i
$220$	214.827	+	30.4069i	0.976484	+	0.138213i
$221$	83.5374	+	83.5374i	0.377997	+	0.377997i
$222$	85.1953	+	4.08377i	0.383763	+	0.0183954i
$223$	−238.888	−	238.888i	−1.07125	−	1.07125i	−0.997259	−	0.0739871i	$-0.976428\pi$
$223$	−238.888	−	238.888i	−1.07125	−	1.07125i	−0.0739871	−	0.997259i	$-0.523572\pi$
$224$	−75.7705	−	124.727i	−0.338261	−	0.556815i
$225$	34.5721	−	384.707i	0.153654	−	1.70981i
$226$	36.4725	+	40.1451i	0.161383	+	0.177633i
$227$	−442.991			−1.95150			−0.975751	−	0.218884i	$-0.929758\pi$
$227$	−442.991			−1.95150			−0.975751	+	0.218884i	$0.929758\pi$
$228$	14.4052	+	17.4678i	0.0631807	+	0.0766134i
$229$	−218.763	−	218.763i	−0.955297	−	0.955297i	0.0437454	−	0.999043i	$-0.486071\pi$
$229$	−218.763	−	218.763i	−0.955297	−	0.955297i	−0.999043	+	0.0437454i	$0.986071\pi$
$230$	172.975	+	16.0826i	0.752064	+	0.0699245i
$231$			244.639i			1.05904i
$232$	−246.132	+	183.909i	−1.06091	+	0.792712i
$233$	181.998	−	181.998i	0.781108	−	0.781108i	−0.198910	−	0.980018i	$-0.563740\pi$
$233$	181.998	−	181.998i	0.781108	−	0.781108i	0.980018	+	0.198910i	$0.0637401\pi$
$234$	32.8672	−	685.673i	0.140458	−	2.93023i
$235$	−123.330	−	5.53046i	−0.524809	−	0.0235339i
$236$	261.475	+	317.066i	1.10794	+	1.34350i
$237$	−230.973			−0.974569
$238$	48.4503	+	2.32243i	0.203573	+	0.00975810i
$239$			41.3149i			0.172866i	0.996258	+	0.0864328i	$0.0275468\pi$
$239$			41.3149i			0.172866i	−0.996258	+	0.0864328i	$0.972453\pi$
$240$	−337.447	+	206.425i	−1.40603	+	0.860102i
$241$	223.654			0.928023			0.464012	−	0.885829i	$-0.346410\pi$
$241$	223.654			0.928023			0.464012	+	0.885829i	$0.346410\pi$
$242$	0.317197	−	6.61734i	0.00131073	−	0.0273444i
$243$			194.792i			0.801614i
$244$	70.9414	+	86.0240i	0.290743	+	0.352557i
$245$	−104.073	+	95.1399i	−0.424788	+	0.388326i
$246$	725.551	+	34.7787i	2.94939	+	0.141377i
$247$	17.9819	+	17.9819i	0.0728014	+	0.0728014i
$248$	−202.339	−	29.2764i	−0.815883	−	0.118050i
$249$	410.130			1.64711
$250$	−205.901	+	141.792i	−0.823603	+	0.567167i
$251$	−329.376	+	329.376i	−1.31226	+	1.31226i	−0.392507	+	0.919749i	$0.628392\pi$
$251$	−329.376	+	329.376i	−1.31226	+	1.31226i	−0.919749	+	0.392507i	$0.871608\pi$
$252$	−179.320	−	217.445i	−0.711588	−	0.862877i
$253$			188.459i			0.744898i
$254$	−209.390	+	190.234i	−0.824370	+	0.748954i
$255$	5.88999	−	131.348i	0.0230980	−	0.515089i
$256$	237.435	+	95.7112i	0.927480	+	0.373872i
$257$	−102.275	+	102.275i	−0.397958	+	0.397958i	−0.877512	−	0.479555i	$-0.840798\pi$
$257$	−102.275	+	102.275i	−0.397958	+	0.397958i	0.479555	+	0.877512i	$0.340798\pi$
$258$	8.31089	−	173.381i	0.0322127	−	0.672020i
$259$	27.8128	−	27.8128i	0.107386	−	0.107386i
$260$	−355.098	+	267.040i	−1.36576	+	1.02708i
$261$	−419.590	+	419.590i	−1.60762	+	1.60762i
$262$	92.8191	+	102.165i	0.354271	+	0.389945i
$263$	−149.290	+	149.290i	−0.567642	+	0.567642i	−0.931467	−	0.363826i	$-0.881470\pi$
$263$	−149.290	+	149.290i	−0.567642	+	0.567642i	0.363826	+	0.931467i	$0.381470\pi$
$264$	−256.866	−	343.772i	−0.972977	−	1.30217i
$265$	98.9508	+	108.242i	0.373399	+	0.408460i
$266$	10.4292	+	0.499917i	0.0392076	+	0.00187939i
$267$		−	648.474i		−	2.42874i
$268$	55.8702	+	5.36852i	0.208471	+	0.0200318i
$269$	169.168	−	169.168i	0.628876	−	0.628876i	−0.318909	−	0.947785i	$-0.603316\pi$
$269$	169.168	−	169.168i	0.628876	−	0.628876i	0.947785	+	0.318909i	$0.103316\pi$
$270$	−245.441	+	203.683i	−0.909040	+	0.754381i
$271$	−389.998			−1.43911			−0.719554	−	0.694437i	$-0.755654\pi$
$271$	−389.998			−1.43911			−0.719554	+	0.694437i	$0.755654\pi$
$272$	−70.5221	+	47.6084i	−0.259272	+	0.175031i
$273$	−354.237	−	354.237i	−1.29757	−	1.29757i
$274$	−220.996	−	243.249i	−0.806554	−	0.887770i
$275$	−173.840	−	208.169i	−0.632144	−	0.756979i
$276$	−218.609	−	265.087i	−0.792063	−	0.960461i
$277$		−	290.668i		−	1.04934i	−0.851305	−	0.524671i	$-0.824188\pi$
$277$		−	290.668i		−	1.04934i	0.851305	−	0.524671i	$-0.175812\pi$
$278$	48.6854	+	53.5878i	0.175127	+	0.192762i
$279$	−394.843			−1.41521
$280$	−34.1843	+	179.191i	−0.122087	+	0.639967i
$281$		−	235.390i		−	0.837688i	−0.908058	−	0.418844i	$-0.862435\pi$
$281$		−	235.390i		−	0.837688i	0.908058	−	0.418844i	$-0.137565\pi$
$282$	164.195	+	180.729i	0.582253	+	0.640883i
$283$	468.675			1.65609			0.828047	−	0.560659i	$-0.189452\pi$
$283$	468.675			1.65609			0.828047	+	0.560659i	$0.189452\pi$
$284$	−34.9420	+	363.642i	−0.123035	+	1.28043i
$285$	1.26786	−	28.2734i	0.00444862	−	0.0992049i
$286$	−324.114	−	356.751i	−1.13327	−	1.24738i
$287$	236.863	−	236.863i	0.825307	−	0.825307i
$288$	480.298	+	117.276i	1.66770	+	0.407209i
$289$			260.719i			0.902142i
$290$	382.415	+	35.5557i	1.31867	+	0.122606i
$291$	150.993	+	150.993i	0.518878	+	0.518878i
$292$	−186.644	+	153.920i	−0.639192	+	0.527122i
$293$	179.844			0.613801			0.306901	−	0.951742i	$-0.400708\pi$
$293$	179.844			0.613801			0.306901	+	0.951742i	$0.400708\pi$
$294$	278.575	+	13.3533i	0.947535	+	0.0454193i
$295$	23.0134	−	513.203i	0.0780116	−	1.73967i
$296$	−9.88032	+	68.2862i	−0.0333795	+	0.230697i
$297$	−244.664	−	244.664i	−0.823785	−	0.823785i
$298$	22.1185	+	24.3457i	0.0742232	+	0.0816971i
$299$	−272.889	−	272.889i	−0.912673	−	0.912673i
$300$	485.996	+	91.1608i	1.61999	+	0.303869i
$301$	−56.6020	−	56.6020i	−0.188047	−	0.188047i
$302$	8.13824	−	169.779i	0.0269478	−	0.562183i
$303$	−109.231	−	109.231i	−0.360500	−	0.360500i
$304$	−15.1803	+	10.2480i	−0.0499352	+	0.0337105i
$305$	6.24382	−	139.238i	0.0204715	−	0.456519i
$306$	−121.628	+	110.501i	−0.397477	+	0.361115i
$307$	110.106			0.358653			0.179326	−	0.983790i	$-0.442608\pi$
$307$	110.106			0.358653			0.179326	+	0.983790i	$0.442608\pi$
$308$	−196.992	−	18.9288i	−0.639583	−	0.0614570i
$309$	−25.0475	−	25.0475i	−0.0810599	−	0.0810599i
$310$	163.201	+	196.660i	0.526455	+	0.634386i
$311$		−	53.7610i		−	0.172865i	−0.996258	−	0.0864325i	$-0.972453\pi$
$311$		−	53.7610i		−	0.172865i	0.996258	−	0.0864325i	$-0.0275467\pi$
$312$	869.725	+	125.840i	2.78758	+	0.403335i
$313$	−165.965	+	165.965i	−0.530241	+	0.530241i	−0.920644	−	0.390403i	$-0.872336\pi$
$313$	−165.965	+	165.965i	−0.530241	+	0.530241i	0.390403	+	0.920644i	$0.372336\pi$
$314$	−256.204	−	12.2809i	−0.815937	−	0.0391113i
$315$	−15.7827	+	351.956i	−0.0501037	+	1.11732i
$316$	17.8714	−	185.987i	0.0565549	−	0.588567i
$317$	−40.4315			−0.127544			−0.0637721	−	0.997964i	$-0.520313\pi$
$317$	−40.4315			−0.127544			−0.0637721	+	0.997964i	$0.520313\pi$
$318$	13.8882	−	289.734i	0.0436734	−	0.911112i
$319$			416.648i			1.30611i
$320$	−140.110	−	287.696i	−0.437845	−	0.899050i
$321$	−270.443			−0.842503
$322$	−158.271	−	7.58660i	−0.491525	−	0.0235609i
$323$		−	6.08764i		−	0.0188472i
$324$	74.2920	+	7.13865i	0.229296	+	0.0220329i
$325$	553.150	+	49.7094i	1.70200	+	0.152952i
$326$	7.85330	−	163.835i	0.0240899	−	0.502561i
$327$	404.940	+	404.940i	1.23835	+	1.23835i
$328$	−84.1440	+	581.548i	−0.256537	+	1.77301i
$329$	112.604			0.342261
$330$	−49.6607	+	534.119i	−0.150487	+	1.61854i
$331$	−107.944	+	107.944i	−0.326116	+	0.326116i	−0.851107	−	0.524992i	$-0.824068\pi$
$331$	−107.944	+	107.944i	−0.326116	+	0.326116i	0.524992	+	0.851107i	$0.324068\pi$
$332$	−31.7335	+	330.251i	−0.0955829	+	0.994731i
$333$			133.253i			0.400160i
$334$	−249.477	−	274.598i	−0.746937	−	0.822150i
$335$	−47.3380	−	51.7828i	−0.141307	−	0.154576i
$336$	299.046	−	201.882i	0.890018	−	0.600838i
$337$	−119.972	+	119.972i	−0.356000	+	0.356000i	−0.862336	−	0.506336i	$-0.830999\pi$
$337$	−119.972	+	119.972i	−0.356000	+	0.356000i	0.506336	+	0.862336i	$0.330999\pi$
$338$	648.282	+	31.0749i	1.91799	+	0.0919375i
$339$	−94.8219	+	94.8219i	−0.279711	+	0.279711i
$340$	105.310	+	14.9058i	0.309735	+	0.0438405i
$341$	−196.037	+	196.037i	−0.574889	+	0.574889i
$342$	−26.1812	+	23.7860i	−0.0765532	+	0.0695498i
$343$	248.959	−	248.959i	0.725828	−	0.725828i
$344$	138.969	+	20.1075i	0.403981	+	0.0584519i
$345$	−19.2406	+	429.070i	−0.0557700	+	1.24368i
$346$	5.60415	−	116.913i	0.0161970	−	0.337900i
$347$			165.996i			0.478375i	0.970973	+	0.239188i	$0.0768811\pi$
$347$			165.996i			0.478375i	−0.970973	+	0.239188i	$0.923119\pi$
$348$	−483.304	−	586.058i	−1.38881	−	1.68408i
$349$	201.279	−	201.279i	0.576730	−	0.576730i	−0.357271	−	0.934001i	$-0.616293\pi$
$349$	201.279	−	201.279i	0.576730	−	0.576730i	0.934001	+	0.357271i	$0.116293\pi$
$350$	181.822	−	137.613i	0.519492	−	0.393181i
$351$	708.548			2.01866
$352$	296.692	−	180.238i	0.842875	−	0.512040i
$353$	−5.16188	−	5.16188i	−0.0146229	−	0.0146229i	0.699758	−	0.714380i	$-0.253291\pi$
$353$	−5.16188	−	5.16188i	−0.0146229	−	0.0146229i	−0.714380	+	0.699758i	$0.753291\pi$
$354$	−752.052	+	683.252i	−2.12444	+	1.93009i
$355$	337.038	−	308.108i	0.949403	−	0.867910i
$356$	522.173	+	50.1752i	1.46678	+	0.140942i
$357$			119.924i			0.335922i
$358$	−239.208	+	217.324i	−0.668178	+	0.607051i
$359$	−81.8547			−0.228008			−0.114004	−	0.993480i	$-0.536368\pi$
$359$	−81.8547			−0.228008			−0.114004	+	0.993480i	$0.536368\pi$
$360$	−347.369	−	511.148i	−0.964913	−	1.41986i
$361$			359.690i			0.996370i
$362$	−154.931	+	140.757i	−0.427985	+	0.388832i
$363$	16.3792			0.0451218
$364$	312.653	−	257.835i	0.858937	−	0.708339i
$365$	302.102	+	13.5471i	0.827676	+	0.0371152i
$366$	−204.041	+	185.375i	−0.557489	+	0.506488i
$367$	120.769	−	120.769i	0.329071	−	0.329071i	−0.523162	−	0.852233i	$-0.675248\pi$
$367$	120.769	−	120.769i	0.329071	−	0.329071i	0.852233	+	0.523162i	$0.175248\pi$
$368$	230.372	−	155.521i	0.626011	−	0.422611i
$369$			1134.83i			3.07542i
$370$	66.3696	−	55.0778i	0.179377	−	0.148859i
$371$	−94.5864	−	94.5864i	−0.254950	−	0.254950i
$372$	48.3469	−	503.147i	0.129965	−	1.35254i
$373$	−320.574			−0.859447			−0.429724	−	0.902960i	$-0.641389\pi$
$373$	−320.574			−0.859447			−0.429724	+	0.902960i	$0.641389\pi$
$374$	−5.52445	+	115.251i	−0.0147713	+	0.308157i
$375$	−374.532	−	491.692i	−0.998752	−	1.31118i
$376$	−158.234	+	118.232i	−0.420834	+	0.314447i
$377$	−603.307	−	603.307i	−1.60028	−	1.60028i
$378$	215.322	−	195.624i	0.569636	−	0.517524i
$379$	3.16506	+	3.16506i	0.00835109	+	0.00835109i	0.711270	−	0.702919i	$-0.248120\pi$
$379$	3.16506	+	3.16506i	0.00835109	+	0.00835109i	−0.702919	+	0.711270i	$0.748120\pi$
$380$	22.6686	+	3.20856i	0.0596543	+	0.00844357i
$381$	−494.575	−	494.575i	−1.29810	−	1.29810i
$382$	−184.823	−	8.85936i	−0.483831	−	0.0231921i
$383$	401.423	+	401.423i	1.04810	+	1.04810i	0.998783	+	0.0493197i	$0.0157053\pi$
$383$	401.423	+	401.423i	1.04810	+	1.04810i	0.0493197	+	0.998783i	$0.484295\pi$
$384$	−208.255	+	597.681i	−0.542331	+	1.55646i
$385$	166.908	+	182.580i	0.433527	+	0.474234i
$386$	−100.554	−	110.680i	−0.260504	−	0.286735i
$387$	271.184			0.700735
$388$	−133.268	+	109.902i	−0.343474	+	0.283253i
$389$	−179.440	−	179.440i	−0.461286	−	0.461286i	0.437791	−	0.899077i	$-0.355761\pi$
$389$	−179.440	−	179.440i	−0.461286	−	0.461286i	−0.899077	+	0.437791i	$0.855761\pi$
$390$	−701.496	−	845.314i	−1.79871	−	2.16747i
$391$			92.3844i			0.236277i
$392$	−32.3071	+	223.285i	−0.0824160	+	0.569605i
$393$	−241.313	+	241.313i	−0.614028	+	0.614028i
$394$	9.51967	−	198.599i	0.0241616	−	0.504058i
$395$	−172.381	+	157.584i	−0.436407	+	0.398947i
$396$	517.245	−	426.556i	1.30618	−	1.07716i
$397$	321.234			0.809154			0.404577	−	0.914504i	$-0.367419\pi$
$397$	321.234			0.809154			0.404577	+	0.914504i	$0.367419\pi$
$398$	−529.728	−	25.3921i	−1.33097	−	0.0637992i
$399$			25.8144i			0.0646978i
$400$	−111.009	+	384.288i	−0.277524	+	0.960719i
$401$	649.404			1.61946			0.809730	−	0.586802i	$-0.199613\pi$
$401$	649.404			1.61946			0.809730	+	0.586802i	$0.199613\pi$
$402$	−6.64408	+	138.608i	−0.0165276	+	0.344797i
$403$		−	567.725i		−	1.40875i
$404$	96.4086	−	79.5052i	0.238635	−	0.196795i
$405$	−62.9465	−	68.8569i	−0.155423	−	0.170017i
$406$	−349.908	−	16.7726i	−0.861842	−	0.0413117i
$407$	66.1595	+	66.1595i	0.162554	+	0.162554i
$408$	−125.918	−	168.520i	−0.308623	−	0.413040i
$409$	−20.3455			−0.0497444			−0.0248722	−	0.999691i	$-0.507918\pi$
$409$	−20.3455			−0.0497444			−0.0248722	+	0.999691i	$0.507918\pi$
$410$	565.225	−	469.060i	1.37860	−	1.14405i
$411$	574.550	−	574.550i	1.39793	−	1.39793i
$412$	22.1072	−	18.2311i	0.0536582	−	0.0442502i
$413$			468.569i			1.13455i
$414$	397.319	−	360.971i	0.959707	−	0.871910i
$415$	306.090	−	279.816i	0.737566	−	0.674256i
$416$	−168.625	+	690.596i	−0.405350	+	1.66009i
$417$	−126.573	+	126.573i	−0.303533	+	0.303533i
$418$	−1.18917	+	24.8084i	−0.00284491	+	0.0593503i
$419$	204.233	−	204.233i	0.487430	−	0.487430i	−0.420064	−	0.907494i	$-0.637992\pi$
$419$	204.233	−	204.233i	0.487430	−	0.487430i	0.907494	+	0.420064i	$0.137992\pi$
$420$	−446.563	−	63.2073i	−1.06325	−	0.150494i
$421$	−74.3563	+	74.3563i	−0.176618	+	0.176618i	−0.789880	−	0.613262i	$-0.789857\pi$
$421$	−74.3563	+	74.3563i	−0.176618	+	0.176618i	0.613262	+	0.789880i	$0.289857\pi$
$422$	430.930	+	474.322i	1.02116	+	1.12399i
$423$	−269.747	+	269.747i	−0.637699	+	0.637699i
$424$	232.229	+	33.6012i	0.547710	+	0.0792480i
$425$	−85.2178	−	102.047i	−0.200513	−	0.240110i
$426$	−902.159	−	43.2442i	−2.11774	−	0.101512i
$427$			127.128i			0.297725i
$428$	20.9254	−	217.770i	0.0488910	−	0.508809i
$429$	842.639	−	842.639i	1.96419	−	1.96419i
$430$	−112.089	−	135.069i	−0.260672	−	0.314114i
$431$	30.9498			0.0718092			0.0359046	−	0.999355i	$-0.488569\pi$
$431$	30.9498			0.0718092			0.0359046	+	0.999355i	$0.488569\pi$
$432$	−97.1747	+	500.980i	−0.224941	+	1.15968i
$433$	−68.9194	−	68.9194i	−0.159167	−	0.159167i	0.623030	−	0.782198i	$-0.285901\pi$
$433$	−68.9194	−	68.9194i	−0.159167	−	0.159167i	−0.782198	+	0.623030i	$0.785901\pi$
$434$	−156.744	−	172.527i	−0.361161	−	0.397528i
$435$	−42.5375	+	948.592i	−0.0977873	+	2.18067i
$436$	−357.404	+	294.740i	−0.819733	+	0.676009i
$437$			19.8863i			0.0455064i
$438$	−402.202	−	442.702i	−0.918270	−	1.01074i
$439$	−755.005			−1.71983			−0.859914	−	0.510439i	$-0.829483\pi$
$439$	−755.005			−1.71983			−0.859914	+	0.510439i	$0.829483\pi$
$440$	−426.249	−	81.3156i	−0.968747	−	0.184808i
$441$			435.718i			0.988022i
$442$	−158.884	−	174.883i	−0.359466	−	0.395662i
$443$	−109.778			−0.247806			−0.123903	−	0.992294i	$-0.539541\pi$
$443$	−109.778			−0.247806			−0.123903	+	0.992294i	$0.539541\pi$
$444$	−169.804	−	16.3163i	−0.382442	−	0.0367485i
$445$	−442.430	−	483.972i	−0.994224	−	1.08758i
$446$	454.352	+	500.103i	1.01873	+	1.12131i
$447$	−57.5042	+	57.5042i	−0.128645	+	0.128645i
$448$	139.424	+	256.423i	0.311213	+	0.572372i
$449$		−	491.218i		−	1.09403i	−0.837124	−	0.547013i	$-0.815765\pi$
$449$		−	491.218i		−	1.09403i	0.837124	−	0.547013i	$-0.184235\pi$
$450$	−105.904	+	765.220i	−0.235342	+	1.70049i
$451$	563.436	+	563.436i	1.24930	+	1.24930i
$452$	−69.0171	−	83.6907i	−0.152693	−	0.185156i
$453$	420.238			0.927678
$454$	884.966	+	42.4201i	1.94926	+	0.0934364i
$455$	−506.059	−	22.6931i	−1.11222	−	0.0498749i
$456$	−27.1046	−	36.2750i	−0.0594400	−	0.0795505i
$457$	468.944	+	468.944i	1.02614	+	1.02614i	0.999649	+	0.0264867i	$0.00843195\pi$
$457$	468.944	+	468.944i	1.02614	+	1.02614i	0.0264867	+	0.999649i	$0.491568\pi$
$458$	416.076	+	457.973i	0.908463	+	0.999941i
$459$	−119.937	−	119.937i	−0.261300	−	0.261300i
$460$	−344.013	−	48.6922i	−0.747854	−	0.105853i
$461$	−78.6933	−	78.6933i	−0.170701	−	0.170701i	0.616586	−	0.787287i	$-0.288515\pi$
$461$	−78.6933	−	78.6933i	−0.170701	−	0.170701i	−0.787287	+	0.616586i	$0.788515\pi$
$462$	23.4262	−	488.716i	0.0507061	−	1.05783i
$463$	−382.322	−	382.322i	−0.825749	−	0.825749i	0.161176	−	0.986926i	$-0.448471\pi$
$463$	−382.322	−	382.322i	−0.825749	−	0.825749i	−0.986926	+	0.161176i	$0.948471\pi$
$464$	509.310	−	343.827i	1.09765	−	0.741007i
$465$	−466.337	+	426.309i	−1.00288	+	0.916793i
$466$	−381.007	+	346.151i	−0.817611	+	0.742813i
$467$	−374.594			−0.802129			−0.401065	−	0.916050i	$-0.631360\pi$
$467$	−374.594			−0.802129			−0.401065	+	0.916050i	$0.631360\pi$
$468$	−131.318	+	1366.63i	−0.280594	+	2.92014i
$469$	45.2501	+	45.2501i	0.0964820	+	0.0964820i
$470$	245.848	+	22.8581i	0.523080	+	0.0486343i
$471$		−	634.157i		−	1.34640i
$472$	−491.988	−	658.444i	−1.04235	−	1.39501i
$473$	134.641	−	134.641i	0.284654	−	0.284654i
$474$	461.416	+	22.1176i	0.973451	+	0.0466616i
$475$	−18.3437	−	21.9661i	−0.0386182	−	0.0462445i
$476$	−96.5671	−	9.27906i	−0.202872	−	0.0194938i
$477$	453.171			0.950043
$478$	3.95625	−	82.5350i	0.00827667	−	0.172667i
$479$		−	450.432i		−	0.940359i	−0.882571	−	0.470179i	$-0.844189\pi$
$479$		−	450.432i		−	0.940359i	0.882571	−	0.470179i	$-0.155811\pi$
$480$	693.887	−	380.062i	1.44560	−	0.791796i
$481$	−191.598			−0.398333
$482$	−446.794	−	21.4167i	−0.926959	−	0.0444330i
$483$		−	391.753i		−	0.811082i
$484$	−1.26733	+	13.1891i	−0.00261845	+	0.0272502i
$485$	215.707	+	9.67290i	0.444757	+	0.0199441i
$486$	18.6530	−	389.137i	0.0383806	−	0.800694i
$487$	292.281	+	292.281i	0.600166	+	0.600166i	0.940357	−	0.340190i	$-0.110492\pi$
$487$	292.281	+	292.281i	0.600166	+	0.600166i	−0.340190	+	0.940357i	$0.610492\pi$
$488$	−133.482	−	178.644i	−0.273530	−	0.366074i
$489$	405.524			0.829293
$490$	217.018	−	180.096i	0.442894	−	0.367542i
$491$	434.376	−	434.376i	0.884677	−	0.884677i	−0.109329	−	0.994006i	$-0.534870\pi$
$491$	434.376	−	434.376i	0.884677	−	0.884677i	0.994006	+	0.109329i	$0.0348702\pi$
$492$	−1446.11	−	138.955i	−2.93924	−	0.282429i
$493$			204.245i			0.414289i
$494$	−34.2007	−	37.6446i	−0.0692322	−	0.0762036i
$495$	−837.212	−	37.5429i	−1.69134	−	0.0758441i
$496$	401.410	+	77.8613i	0.809295	+	0.156978i
$497$	−294.519	+	294.519i	−0.592593	+	0.592593i
$498$	−819.319	−	39.2734i	−1.64522	−	0.0788622i
$499$	−36.0616	+	36.0616i	−0.0722676	+	0.0722676i	−0.742317	−	0.670049i	$-0.766273\pi$
$499$	−36.0616	+	36.0616i	−0.0722676	+	0.0722676i	0.670049	+	0.742317i	$0.266273\pi$
$500$	424.907	−	263.542i	0.849813	−	0.527084i
$501$	648.595	−	648.595i	1.29460	−	1.29460i
$502$	689.538	−	626.456i	1.37358	−	1.24792i
$503$	−196.896	+	196.896i	−0.391444	+	0.391444i	−0.875202	−	0.483758i	$-0.839271\pi$
$503$	−196.896	+	196.896i	−0.391444	+	0.391444i	0.483758	+	0.875202i	$0.339271\pi$
$504$	337.407	+	451.563i	0.669458	+	0.895958i
$505$	−156.047	−	6.99756i	−0.309003	−	0.0138565i
$506$	18.0466	−	376.486i	0.0356651	−	0.744043i
$507$			1604.63i			3.16494i
$508$	436.516	−	359.981i	0.859284	−	0.708625i
$509$	−459.143	+	459.143i	−0.902049	+	0.902049i	−0.995613	−	0.0935638i	$-0.970174\pi$
$509$	−459.143	+	459.143i	−0.902049	+	0.902049i	0.0935638	+	0.995613i	$0.470174\pi$
$510$	−24.3441	+	261.830i	−0.0477336	+	0.513392i
$511$	−275.827			−0.539780
$512$	−465.160	−	213.939i	−0.908516	−	0.417850i
$513$	−25.8171	−	25.8171i	−0.0503257	−	0.0503257i
$514$	214.109	−	194.522i	0.416555	−	0.378447i
$515$	−35.7826	−	1.60459i	−0.0694807	−	0.00311571i
$516$	−33.2054	+	345.569i	−0.0643516	+	0.669707i
$517$			267.855i			0.518096i
$518$	−58.2252	+	52.8986i	−0.112404	+	0.102121i
$519$	289.384			0.557580
$520$	734.954	−	499.464i	1.41337	−	0.960507i
$521$		−	726.368i		−	1.39418i	−0.716984	−	0.697090i	$-0.754478\pi$
$521$		−	726.368i		−	1.39418i	0.716984	−	0.697090i	$-0.245522\pi$
$522$	878.397	−	798.038i	1.68275	−	1.52881i
$523$	542.697			1.03766			0.518831	−	0.854877i	$-0.326367\pi$
$523$	542.697			1.03766			0.518831	+	0.854877i	$0.326367\pi$
$524$	−175.642	−	212.985i	−0.335195	−	0.406460i
$525$	361.363	+	432.725i	0.688311	+	0.824237i
$526$	312.533	−	283.941i	0.594169	−	0.539812i
$527$	−96.0993	+	96.0993i	−0.182352	+	0.182352i
$528$	480.224	+	711.353i	0.909515	+	1.34726i
$529$			227.211i			0.429510i
$530$	−187.309	−	225.711i	−0.353414	−	0.425869i
$531$	−1122.47	−	1122.47i	−2.11389	−	2.11389i
$532$	−20.7867	−	1.99737i	−0.0390727	−	0.00375446i
$533$	−1631.71			−3.06137
$534$	−62.0968	+	1295.46i	−0.116286	+	2.42596i
$535$	−201.839	+	184.513i	−0.377268	+	0.344885i
$536$	−111.098	−	16.0748i	−0.207273	−	0.0299902i
$537$	−565.004	−	565.004i	−1.05215	−	1.05215i
$538$	−354.147	+	321.748i	−0.658265	+	0.598045i
$539$	216.331	+	216.331i	0.401357	+	0.401357i
$540$	509.823	−	383.395i	0.944117	−	0.709992i
$541$	727.376	+	727.376i	1.34450	+	1.34450i	0.891519	+	0.452983i	$0.149640\pi$
$541$	727.376	+	727.376i	1.34450	+	1.34450i	0.452983	+	0.891519i	$0.350360\pi$
$542$	779.102	+	37.3456i	1.43746	+	0.0689033i
$543$	−365.943	−	365.943i	−0.673929	−	0.673929i
$544$	145.441	−	88.3545i	0.267355	−	0.162416i
$545$	578.493	+	25.9412i	1.06145	+	0.0475985i
$546$	673.741	+	741.584i	1.23396	+	1.35821i
$547$	511.401			0.934920			0.467460	−	0.884014i	$-0.345169\pi$
$547$	511.401			0.934920			0.467460	+	0.884014i	$0.345169\pi$
$548$	418.192	+	507.102i	0.763124	+	0.925369i
$549$	−304.541	−	304.541i	−0.554720	−	0.554720i
$550$	327.347	+	432.508i	0.595176	+	0.786378i
$551$			43.9649i			0.0797911i
$552$	411.333	+	550.500i	0.745168	+	0.997283i
$553$	150.634	−	150.634i	0.272394	−	0.272394i
$554$	−27.8339	+	580.669i	−0.0502417	+	1.04814i
$555$	143.872	+	157.382i	0.259230	+	0.283570i
$556$	−92.1277	−	111.715i	−0.165697	−	0.200926i
$557$	−804.398			−1.44416			−0.722081	−	0.691809i	$-0.756814\pi$
$557$	−804.398			−1.44416			−0.722081	+	0.691809i	$0.756814\pi$
$558$	788.781	+	37.8096i	1.41359	+	0.0677591i
$559$			389.922i			0.697535i
$560$	85.4492	−	354.697i	0.152588	−	0.633388i
$561$	−285.269			−0.508500
$562$	−22.5406	+	470.241i	−0.0401079	+	0.836728i
$563$			695.151i			1.23473i	0.786678	+	0.617363i	$0.211799\pi$
$563$			695.151i			1.23473i	−0.786678	+	0.617363i	$0.788201\pi$
$564$	−310.708	−	376.766i	−0.550900	−	0.668026i
$565$	−6.07446	+	135.461i	−0.0107513	+	0.239755i
$566$	−936.274	−	44.8795i	−1.65419	−	0.0792925i
$567$	60.1701	+	60.1701i	0.106120	+	0.106120i
$568$	104.626	−	723.103i	0.184200	−	1.27307i
$569$	−277.088			−0.486974			−0.243487	−	0.969904i	$-0.578291\pi$
$569$	−277.088			−0.486974			−0.243487	+	0.969904i	$0.578291\pi$
$570$	−5.24022	+	56.3605i	−0.00919337	+	0.0988781i
$571$	−569.098	+	569.098i	−0.996669	+	0.996669i	−0.999994	−	0.00332578i	$-0.998941\pi$
$571$	−569.098	+	569.098i	−0.996669	+	0.996669i	0.00332578	+	0.999994i	$0.498941\pi$
$572$	613.323	+	743.720i	1.07224	+	1.30021i
$573$		−	457.475i		−	0.798386i
$574$	−495.865	+	450.501i	−0.863876	+	0.784846i
$575$	278.378	+	333.352i	0.484136	+	0.579743i
$576$	−948.265	−	280.276i	−1.64629	−	0.486590i
$577$	687.894	−	687.894i	1.19219	−	1.19219i	0.215740	−	0.976451i	$-0.430784\pi$
$577$	687.894	−	687.894i	1.19219	−	1.19219i	0.976451	−	0.215740i	$-0.0692163\pi$
$578$	24.9660	−	520.840i	0.0431939	−	0.901107i
$579$	261.424	−	261.424i	0.451509	−	0.451509i
$580$	−760.548	−	107.649i	−1.31129	−	0.185602i
$581$	−267.475	+	267.475i	−0.460370	+	0.460370i
$582$	−287.182	−	316.099i	−0.493439	−	0.543126i
$583$	224.996	−	224.996i	0.385929	−	0.385929i
$584$	387.599	−	289.613i	0.663697	−	0.495913i
$585$	1266.65	−	1157.92i	2.16521	−	1.97935i
$586$	−359.275	−	17.2216i	−0.613097	−	0.0293883i
$587$		−	78.2483i		−	0.133302i	−0.997776	−	0.0666510i	$-0.978769\pi$
$587$		−	78.2483i		−	0.133302i	0.997776	−	0.0666510i	$-0.0212314\pi$
$588$	−555.233	−	53.3518i	−0.944273	−	0.0907344i
$589$	−20.6860	+	20.6860i	−0.0351205	+	0.0351205i
$590$	−95.1175	+	1023.02i	−0.161216	+	1.73394i
$591$	491.572			0.831763
$592$	26.2770	−	135.470i	0.0443868	−	0.228834i
$593$	−296.118	−	296.118i	−0.499355	−	0.499355i	0.411882	−	0.911237i	$-0.364872\pi$
$593$	−296.118	−	296.118i	−0.499355	−	0.499355i	−0.911237	+	0.411882i	$0.864872\pi$
$594$	465.339	+	512.196i	0.783398	+	0.862283i
$595$	81.8199	+	89.5024i	0.137512	+	0.150424i
$596$	−41.8550	−	50.7537i	−0.0702265	−	0.0851572i
$597$		−	1311.18i		−	2.19629i
$598$	519.021	+	571.284i	0.867928	+	0.955324i
$599$	−48.2788			−0.0805990			−0.0402995	−	0.999188i	$-0.512831\pi$
$599$	−48.2788			−0.0805990			−0.0402995	+	0.999188i	$0.512831\pi$
$600$	−962.149	−	228.651i	−1.60358	−	0.381085i
$601$		−	592.230i		−	0.985408i	−0.870197	−	0.492704i	$-0.836008\pi$
$601$		−	592.230i		−	0.985408i	0.870197	−	0.492704i	$-0.163992\pi$
$602$	107.654	+	118.494i	0.178827	+	0.196834i
$603$	−216.796			−0.359530
$604$	−32.5156	+	338.390i	−0.0538338	+	0.560248i
$605$	12.2242	−	11.1749i	0.0202053	−	0.0184710i
$606$	207.752	+	228.672i	0.342826	+	0.377347i
$607$	−289.382	+	289.382i	−0.476741	+	0.476741i	−0.904088	−	0.427346i	$-0.859448\pi$
$607$	−289.382	+	289.382i	−0.476741	+	0.476741i	0.427346	+	0.904088i	$0.359448\pi$
$608$	31.3071	−	19.0188i	0.0514920	−	0.0312810i
$609$		−	866.092i		−	1.42215i
$610$	−25.8066	+	277.559i	−0.0423058	+	0.455015i
$611$	−387.855	−	387.855i	−0.634787	−	0.634787i
$612$	253.559	−	209.102i	0.414311	−	0.341670i
$613$	719.493			1.17373			0.586863	−	0.809687i	$-0.300363\pi$
$613$	719.493			1.17373			0.586863	+	0.809687i	$0.300363\pi$
$614$	−219.960	−	10.5436i	−0.358241	−	0.0171720i
$615$	1225.26	+	1340.31i	1.99230	+	2.17937i
$616$	391.719	+	56.6777i	0.635907	+	0.0920093i
$617$	370.007	+	370.007i	0.599687	+	0.599687i	0.940229	−	0.340542i	$-0.110611\pi$
$617$	370.007	+	370.007i	0.599687	+	0.599687i	−0.340542	+	0.940229i	$0.610611\pi$
$618$	47.6391	+	52.4361i	0.0770859	+	0.0848481i
$619$	524.739	+	524.739i	0.847721	+	0.847721i	0.989848	−	0.142127i	$-0.0453942\pi$
$619$	524.739	+	524.739i	0.847721	+	0.847721i	−0.142127	+	0.989848i	$0.545394\pi$
$620$	−307.196	−	408.496i	−0.495477	−	0.658865i
$621$	391.793	+	391.793i	0.630907	+	0.630907i
$622$	−5.14807	+	107.399i	−0.00827665	+	0.172667i
$623$	422.916	+	422.916i	0.678837	+	0.678837i
$624$	−1725.41	−	334.676i	−2.76507	−	0.536339i
$625$	−614.986	−	111.433i	−0.983978	−	0.178292i
$626$	347.443	−	315.658i	0.555020	−	0.504245i
$627$	−61.4058			−0.0979359
$628$	510.645	+	49.0674i	0.813129	+	0.0781328i
$629$	32.4320	+	32.4320i	0.0515612	+	0.0515612i
$630$	65.2319	−	701.593i	0.103543	−	1.11364i
$631$		−	481.853i		−	0.763634i	−0.924238	−	0.381817i	$-0.875298\pi$
$631$		−	481.853i		−	0.763634i	0.924238	−	0.381817i	$-0.124702\pi$
$632$	−53.5116	+	369.837i	−0.0846702	+	0.585184i
$633$	−1120.34	+	1120.34i	−1.76989	+	1.76989i
$634$	80.7703	+	3.87166i	0.127398	+	0.00610672i
$635$	−706.544	−	31.6833i	−1.11267	−	0.0498950i
$636$	−55.4889	+	577.473i	−0.0872467	+	0.907976i
$637$	−626.496			−0.983510
$638$	39.8975	−	832.340i	0.0625353	−	1.30461i
$639$		−	1411.06i		−	2.20823i
$640$	252.350	+	588.149i	0.394297	+	0.918983i
$641$	602.798			0.940403			0.470202	−	0.882559i	$-0.344181\pi$
$641$	602.798			0.940403			0.470202	+	0.882559i	$0.344181\pi$
$642$	540.266	+	25.8972i	0.841536	+	0.0403384i
$643$			1220.05i			1.89744i	0.316118	+	0.948720i	$0.397621\pi$
$643$			1220.05i			1.89744i	−0.316118	+	0.948720i	$0.602379\pi$
$644$	315.453	+	30.3116i	0.489834	+	0.0470677i
$645$	320.288	−	292.795i	0.496570	−	0.453946i
$646$	−0.582943	+	12.1613i	−0.000902389	+	0.0188256i
$647$	−674.538	−	674.538i	−1.04256	−	1.04256i	−0.999053	−	0.0435096i	$-0.986146\pi$
$647$	−674.538	−	674.538i	−1.04256	−	1.04256i	−0.0435096	−	0.999053i	$-0.513854\pi$
$648$	−147.730	−	21.3750i	−0.227978	−	0.0329861i
$649$	−1114.60			−1.71742
$650$	−1100.27	−	152.274i	−1.69272	−	0.234267i
$651$	407.506	−	407.506i	0.625969	−	0.625969i
$652$	−31.3772	+	326.542i	−0.0481245	+	0.500831i
$653$		−	1069.12i		−	1.63724i	−0.574336	−	0.818620i	$-0.694740\pi$
$653$		−	1069.12i		−	1.63724i	0.574336	−	0.818620i	$-0.305260\pi$
$654$	−770.175	−	847.728i	−1.17764	−	1.29622i
$655$	−15.4589	+	344.737i	−0.0236014	+	0.526315i
$656$	223.783	−	1153.70i	0.341133	−	1.75869i
$657$	660.755	−	660.755i	1.00572	−	1.00572i
$658$	−224.949	−	10.7828i	−0.341869	−	0.0163872i
$659$	392.851	−	392.851i	0.596131	−	0.596131i	−0.343149	−	0.939281i	$-0.611494\pi$
$659$	392.851	−	392.851i	0.596131	−	0.596131i	0.939281	+	0.343149i	$0.111494\pi$
$660$	150.354	−	1062.26i	0.227809	−	1.60948i
$661$	−251.961	+	251.961i	−0.381182	+	0.381182i	−0.871528	−	0.490346i	$-0.836871\pi$
$661$	−251.961	+	251.961i	−0.381182	+	0.381182i	0.490346	+	0.871528i	$0.336871\pi$
$662$	225.978	−	205.305i	0.341356	−	0.310128i
$663$	413.069	−	413.069i	0.623031	−	0.623031i
$664$	95.0185	−	656.705i	0.143100	−	0.989014i
$665$	17.6122	+	19.2659i	0.0264845	+	0.0289713i
$666$	12.7601	−	266.201i	0.0191594	−	0.399702i
$667$		−	667.200i		−	1.00030i
$668$	472.087	+	572.456i	0.706717	+	0.856970i
$669$	−1181.23	+	1181.23i	−1.76567	+	1.76567i
$670$	89.6087	+	107.980i	0.133744	+	0.161164i
$671$	−302.406			−0.450679
$672$	−616.738	+	374.664i	−0.917765	+	0.557536i
$673$	−54.2702	−	54.2702i	−0.0806392	−	0.0806392i	0.665637	−	0.746276i	$-0.268160\pi$
$673$	−54.2702	−	54.2702i	−0.0806392	−	0.0806392i	−0.746276	+	0.665637i	$0.768160\pi$
$674$	251.157	−	228.180i	0.372637	−	0.338547i
$675$	−794.170	−	71.3690i	−1.17655	−	0.105732i
$676$	−1292.10	−	124.157i	−1.91139	−	0.183664i
$677$			862.549i			1.27408i	0.770832	+	0.637038i	$0.219841\pi$
$677$			862.549i			1.27408i	−0.770832	+	0.637038i	$0.780159\pi$
$678$	198.506	−	180.346i	0.292782	−	0.265998i
$679$	−196.947			−0.290054
$680$	−208.951	−	39.8617i	−0.307281	−	0.0586201i
$681$			2190.47i			3.21654i
$682$	410.397	−	372.853i	0.601755	−	0.546705i
$683$	−887.581			−1.29953			−0.649766	−	0.760134i	$-0.725133\pi$
$683$	−887.581			−1.29953			−0.649766	+	0.760134i	$0.725133\pi$
$684$	54.5800	−	45.0105i	0.0797954	−	0.0658048i
$685$	36.8067	−	820.794i	0.0537323	−	1.19824i
$686$	−521.187	+	473.507i	−0.759748	+	0.690243i
$687$	−1081.72	+	1081.72i	−1.57456	+	1.57456i
$688$	−275.695	−	53.4763i	−0.400719	−	0.0777272i
$689$			651.591i			0.945705i
$690$	79.5242	−	855.312i	0.115252	−	1.23958i
$691$	810.243	+	810.243i	1.17257	+	1.17257i	0.981596	+	0.190969i	$0.0611631\pi$
$691$	810.243	+	810.243i	1.17257	+	1.17257i	0.190969	+	0.981596i	$0.438837\pi$
$692$	−22.3909	+	233.022i	−0.0323568	+	0.336737i
$693$	764.398			1.10303
$694$	15.8955	−	331.612i	0.0229042	−	0.477826i
$695$	−8.10851	+	180.821i	−0.0116669	+	0.260174i
$696$	909.380	+	1217.05i	1.30658	+	1.74864i
$697$	276.202	+	276.202i	0.396272	+	0.396272i
$698$	−421.370	+	382.821i	−0.603682	+	0.548455i
$699$	−899.930	−	899.930i	−1.28745	−	1.28745i
$700$	−376.405	+	257.500i	−0.537721	+	0.367857i
$701$	768.186	+	768.186i	1.09584	+	1.09584i	0.994891	+	0.100952i	$0.0321889\pi$
$701$	768.186	+	768.186i	1.09584	+	1.09584i	0.100952	+	0.994891i	$0.467811\pi$
$702$	−1415.47	−	67.8495i	−2.01634	−	0.0966517i
$703$	6.98119	+	6.98119i	0.00993057	+	0.00993057i
$704$	−609.963	+	331.652i	−0.866425	+	0.471097i
$705$	−27.3466	+	609.833i	−0.0387895	+	0.865011i
$706$	9.81763	+	10.8062i	0.0139060	+	0.0153063i
$707$	142.475			0.201521
$708$	1567.81	−	1292.92i	2.21441	−	1.82616i
$709$	587.694	+	587.694i	0.828906	+	0.828906i	0.987365	−	0.158459i	$-0.0506527\pi$
$709$	587.694	+	587.694i	0.828906	+	0.828906i	−0.158459	+	0.987365i	$0.550653\pi$
$710$	−702.807	+	583.235i	−0.989869	+	0.821458i
$711$			721.697i			1.01505i
$712$	−1038.34	−	150.238i	−1.45835	−	0.211008i
$713$	313.925	−	313.925i	0.440287	−	0.440287i
$714$	11.4838	−	239.573i	0.0160837	−	0.335537i
$715$	53.9809	−	1203.78i	0.0754978	−	1.68361i
$716$	498.677	−	411.244i	0.696477	−	0.574363i
$717$	204.291			0.284924
$718$	163.522	+	7.83828i	0.227746	+	0.0109168i
$719$			735.293i			1.02266i	0.859384	+	0.511330i	$0.170847\pi$
$719$			735.293i			1.02266i	−0.859384	+	0.511330i	$0.829153\pi$
$720$	644.994	+	1054.39i	0.895825	+	1.46443i
$721$	32.6705			0.0453128
$722$	34.4433	−	718.554i	0.0477054	−	0.995227i
$723$		−	1105.90i		−	1.52961i
$724$	322.985	−	266.355i	0.446111	−	0.367894i
$725$	615.443	+	736.980i	0.848886	+	1.01652i
$726$	−32.7209	−	1.56845i	−0.0450701	−	0.00216040i
$727$	282.639	+	282.639i	0.388775	+	0.388775i	0.874250	−	0.485475i	$-0.161353\pi$
$727$	282.639	+	282.639i	0.388775	+	0.388775i	−0.485475	+	0.874250i	$0.661353\pi$
$728$	−649.279	+	485.140i	−0.891867	+	0.666401i
$729$	1131.12			1.55160
$730$	−602.213	−	55.9918i	−0.824949	−	0.0767011i
$731$	66.0025	−	66.0025i	0.0902907	−	0.0902907i
$732$	425.365	−	350.785i	0.581100	−	0.479215i
$733$		−	1241.78i		−	1.69410i	−0.531513	−	0.847050i	$-0.678376\pi$
$733$		−	1241.78i		−	1.69410i	0.531513	−	0.847050i	$-0.321624\pi$
$734$	−252.826	+	229.697i	−0.344450	+	0.312938i
$735$	470.440	+	514.613i	0.640055	+	0.700153i
$736$	−475.108	+	288.625i	−0.645528	+	0.392153i
$737$	−107.638	+	107.638i	−0.146049	+	0.146049i
$738$	108.669	−	2267.06i	0.147249	−	3.07189i
$739$	−682.480	+	682.480i	−0.923518	+	0.923518i	−0.997276	−	0.0737578i	$-0.976501\pi$
$739$	−682.480	+	682.480i	−0.923518	+	0.923518i	0.0737578	+	0.997276i	$0.476501\pi$
$740$	−137.861	+	103.674i	−0.186299	+	0.140100i
$741$	88.9157	−	88.9157i	0.119994	−	0.119994i
$742$	179.898	+	198.013i	0.242451	+	0.266864i
$743$	603.646	−	603.646i	0.812444	−	0.812444i	−0.172556	−	0.985000i	$-0.555203\pi$
$743$	603.646	−	603.646i	0.812444	−	0.812444i	0.985000	+	0.172556i	$0.0552025\pi$
$744$	−144.764	+	1000.51i	−0.194575	+	1.34477i
$745$	−3.68382	+	82.1497i	−0.00494472	+	0.110268i
$746$	640.412	+	30.6977i	0.858462	+	0.0411497i
$747$		−	1281.49i		−	1.71552i
$748$	22.0725	−	229.708i	0.0295086	−	0.307096i
$749$	176.375	−	176.375i	0.235481	−	0.235481i
$750$	701.121	+	1018.12i	0.934828	+	1.35750i
$751$	849.499			1.13116			0.565578	−	0.824695i	$-0.308653\pi$
$751$	849.499			1.13116			0.565578	+	0.824695i	$0.308653\pi$
$752$	327.426	−	221.040i	0.435407	−	0.293937i
$753$	1628.67	+	1628.67i	2.16291	+	2.16291i
$754$	1147.46	+	1263.00i	1.52183	+	1.67507i
$755$	313.634	−	286.713i	0.415409	−	0.379752i
$756$	−448.883	+	370.180i	−0.593761	+	0.489656i
$757$		−	410.039i		−	0.541663i	−0.962627	−	0.270832i	$-0.912701\pi$
$757$		−	410.039i		−	0.541663i	0.962627	−	0.270832i	$-0.0872986\pi$
$758$	−6.01978	−	6.62595i	−0.00794167	−	0.00874135i
$759$	931.878			1.22777
$760$	−44.9780	−	8.58046i	−0.0591816	−	0.0112901i
$761$		−	582.295i		−	0.765171i	−0.923920	−	0.382585i	$-0.875034\pi$
$761$		−	582.295i		−	0.765171i	0.923920	−	0.382585i	$-0.124966\pi$
$762$	940.656	+	1035.38i	1.23446	+	1.35876i
$763$	−528.180			−0.692242
$764$	368.375	+	35.3968i	0.482166	+	0.0463309i
$765$	−410.409	−	18.4039i	−0.536482	−	0.0240573i
$766$	−763.486	−	840.366i	−0.996718	−	1.09708i
$767$	1613.95	−	1613.95i	2.10423	−	2.10423i
$768$	473.265	−	1174.05i	0.616231	−	1.52871i
$769$		−	1386.11i		−	1.80249i	−0.433311	−	0.901245i	$-0.642655\pi$
$769$		−	1386.11i		−	1.80249i	0.433311	−	0.901245i	$-0.357345\pi$
$770$	−315.950	−	380.724i	−0.410324	−	0.494447i
$771$	505.722	+	505.722i	0.655930	+	0.655930i
$772$	190.280	+	230.735i	0.246476	+	0.298879i
$773$	−1124.50			−1.45473			−0.727363	−	0.686253i	$-0.759254\pi$
$773$	−1124.50			−1.45473			−0.727363	+	0.686253i	$0.759254\pi$
$774$	−541.747	−	25.9682i	−0.699931	−	0.0335506i
$775$	−57.1845	+	636.329i	−0.0737864	+	0.821070i
$776$	276.755	−	206.791i	0.356642	−	0.266483i
$777$	−137.527	−	137.527i	−0.176997	−	0.176997i
$778$	341.286	+	375.652i	0.438671	+	0.482843i
$779$	59.4541	+	59.4541i	0.0763210	+	0.0763210i
$780$	1320.44	+	1755.86i	1.69287	+	2.25111i
$781$	−700.583	−	700.583i	−0.897033	−	0.897033i
$782$	8.84659	−	184.557i	0.0113128	−	0.236006i
$783$	866.182	+	866.182i	1.10623	+	1.10623i
$784$	85.9215	−	442.964i	0.109594	−	0.565006i
$785$	−432.662	−	473.287i	−0.551161	−	0.602913i
$786$	505.180	−	458.964i	0.642723	−	0.583924i
$787$	−785.121			−0.997612			−0.498806	−	0.866714i	$-0.666228\pi$
$787$	−785.121			−0.997612			−0.498806	+	0.866714i	$0.666228\pi$
$788$	−38.0350	+	395.831i	−0.0482678	+	0.502323i
$789$	738.196	+	738.196i	0.935610	+	0.935610i
$790$	359.456	−	298.300i	0.455008	−	0.377595i
$791$		−	123.680i		−	0.156359i
$792$	−1074.15	+	802.603i	−1.35625	+	1.01339i
$793$	437.884	−	437.884i	0.552186	−	0.552186i
$794$	−641.731	−	30.7609i	−0.808226	−	0.0387416i
$795$	535.226	−	489.284i	0.673240	−	0.615452i
$796$	1055.81	+	101.452i	1.32639	+	0.127452i
$797$	−58.6173			−0.0735474			−0.0367737	−	0.999324i	$-0.511708\pi$
$797$	−58.6173			−0.0735474			−0.0367737	+	0.999324i	$0.511708\pi$
$798$	2.47195	−	51.5696i	0.00309768	−	0.0646236i
$799$			131.305i			0.164337i
$800$	258.563	−	757.064i	0.323204	−	0.946329i
$801$	−2026.22			−2.52961
$802$	−1297.32	−	62.1859i	−1.61760	−	0.0775385i
$803$		−	656.122i		−	0.817088i
$804$	26.5458	−	276.263i	0.0330172	−	0.343610i
$805$	−267.278	−	292.375i	−0.332023	−	0.363198i
$806$	−54.3644	+	1134.15i	−0.0674497	+	1.40713i
$807$	−836.488	−	836.488i	−1.03654	−	1.03654i
$808$	−200.209	+	149.596i	−0.247784	+	0.185144i
$809$	−361.896			−0.447337			−0.223669	−	0.974665i	$-0.571803\pi$
$809$	−361.896			−0.447337			−0.223669	+	0.974665i	$0.571803\pi$
$810$	119.155	+	143.583i	0.147105	+	0.177264i
$811$	88.5414	−	88.5414i	0.109176	−	0.109176i	−0.650409	−	0.759584i	$-0.725402\pi$
$811$	88.5414	−	88.5414i	0.109176	−	0.109176i	0.759584	+	0.650409i	$0.225402\pi$
$812$	697.407	+	67.0133i	0.858876	+	0.0825287i
$813$			1928.43i			2.37200i
$814$	−125.832	−	138.503i	−0.154585	−	0.170151i
$815$	302.653	−	276.674i	0.371353	−	0.339477i
$816$	235.410	+	348.712i	0.288493	+	0.427343i
$817$	14.2074	−	14.2074i	0.0173898	−	0.0173898i
$818$	40.6443	+	1.94825i	0.0496873	+	0.00238172i
$819$	−1106.85	+	1106.85i	−1.35147	+	1.35147i
$820$	−1174.07	+	882.920i	−1.43179	+	1.07673i
$821$	−74.7330	+	74.7330i	−0.0910268	+	0.0910268i	−0.751154	−	0.660127i	$-0.770502\pi$
$821$	−74.7330	+	74.7330i	−0.0910268	+	0.0910268i	0.660127	+	0.751154i	$0.270502\pi$
$822$	−1202.80	+	1092.76i	−1.46326	+	1.32940i
$823$	481.562	−	481.562i	0.585131	−	0.585131i	−0.351178	−	0.936309i	$-0.614219\pi$
$823$	481.562	−	481.562i	0.585131	−	0.585131i	0.936309	+	0.351178i	$0.114219\pi$
$824$	−45.9094	+	34.3034i	−0.0557153	+	0.0416304i
$825$	−1029.34	+	859.589i	−1.24768	+	1.04193i
$826$	44.8694	−	936.063i	0.0543213	−	1.13325i
$827$			1232.64i			1.49049i	0.666789	+	0.745246i	$0.267668\pi$
$827$			1232.64i			1.49049i	−0.666789	+	0.745246i	$0.732332\pi$
$828$	−828.292	+	683.067i	−1.00035	+	0.824960i
$829$	−503.806	+	503.806i	−0.607727	+	0.607727i	−0.942352	−	0.334624i	$-0.891391\pi$
$829$	−503.806	+	503.806i	−0.607727	+	0.607727i	0.334624	+	0.942352i	$0.391391\pi$
$830$	−638.273	+	529.680i	−0.769003	+	0.638169i
$831$	−1437.27			−1.72957
$832$	402.994	−	1363.46i	0.484368	−	1.63877i
$833$	106.048	+	106.048i	0.127308	+	0.127308i
$834$	264.977	−	240.736i	0.317718	−	0.288652i
$835$	41.5502	−	926.575i	0.0497607	−	1.10967i
$836$	4.75123	−	49.4461i	0.00568329	−	0.0591460i
$837$			815.096i			0.973830i
$838$	−427.555	+	388.441i	−0.510209	+	0.463534i
$839$	949.352			1.13153			0.565764	−	0.824567i	$-0.308581\pi$
$839$	949.352			1.13153			0.565764	+	0.824567i	$0.308581\pi$
$840$	886.049	+	169.032i	1.05482	+	0.201228i
$841$		−	634.054i		−	0.753929i
$842$	155.662	−	141.422i	0.184872	−	0.167959i
$843$	−1163.94			−1.38071
$844$	−815.450	−	988.821i	−0.966174	−	1.17159i
$845$	1094.78	+	1197.57i	1.29559	+	1.41725i
$846$	564.706	−	513.044i	0.667501	−	0.606436i
$847$	−10.6821	+	10.6821i	−0.0126116	+	0.0126116i
$848$	−460.708	−	89.3631i	−0.543287	−	0.105381i
$849$		−	2317.47i		−	2.72964i
$850$	160.468	+	212.019i	0.188786	+	0.249435i
$851$	−105.945	−	105.945i	−0.124494	−	0.124494i
$852$	1798.11	+	172.779i	2.11045	+	0.202792i
$853$	−331.721			−0.388887			−0.194444	−	0.980914i	$-0.562290\pi$
$853$	−331.721			−0.388887			−0.194444	+	0.980914i	$0.562290\pi$
$854$	12.1736	−	253.965i	0.0142548	−	0.297383i
$855$	−88.3430	−	3.96154i	−0.103325	−	0.00463338i
$856$	−62.6561	+	433.037i	−0.0731964	+	0.505885i
$857$	207.103	+	207.103i	0.241660	+	0.241660i	0.817537	−	0.575876i	$-0.195339\pi$
$857$	207.103	+	207.103i	0.241660	+	0.241660i	−0.575876	+	0.817537i	$0.695339\pi$
$858$	−1764.03	+	1602.65i	−2.05598	+	1.86790i
$859$	−315.715	−	315.715i	−0.367538	−	0.367538i	0.499041	−	0.866579i	$-0.333686\pi$
$859$	−315.715	−	315.715i	−0.367538	−	0.367538i	−0.866579	+	0.499041i	$0.833686\pi$
$860$	210.987	+	280.561i	0.245334	+	0.326234i
$861$	−1171.22	−	1171.22i	−1.36030	−	1.36030i
$862$	−61.8285	−	2.96370i	−0.0717268	−	0.00343817i
$863$	278.969	+	278.969i	0.323255	+	0.323255i	0.850014	−	0.526760i	$-0.176593\pi$
$863$	278.969	+	278.969i	0.323255	+	0.323255i	−0.526760	+	0.850014i	$0.676593\pi$
$864$	242.099	−	991.505i	0.280208	−	1.14758i
$865$	215.974	−	197.436i	0.249681	−	0.228250i
$866$	131.081	+	144.280i	0.151364	+	0.166606i
$867$	1289.18			1.48695
$868$	296.607	+	359.668i	0.341713	+	0.414364i
$869$	358.318	+	358.318i	0.412334	+	0.412334i
$870$	175.813	−	1890.94i	0.202084	−	2.17349i
$871$		−	311.720i		−	0.357888i
$872$	742.212	−	554.579i	0.851160	−	0.635985i
$873$	471.794	−	471.794i	0.540428	−	0.540428i
$874$	1.90428	−	39.7270i	0.00217881	−	0.0454543i
$875$	564.926	+	76.4085i	0.645630	+	0.0873240i
$876$	761.090	+	922.903i	0.868824	+	1.05354i
$877$	−1338.50			−1.52623			−0.763114	−	0.646263i	$-0.776331\pi$
$877$	−1338.50			−1.52623			−0.763114	+	0.646263i	$0.776331\pi$
$878$	1508.28	+	72.2981i	1.71786	+	0.0823440i
$879$		−	889.277i		−	1.01169i
$880$	843.733	+	203.261i	0.958787	+	0.230979i
$881$	−138.825			−0.157576			−0.0787881	−	0.996891i	$-0.525105\pi$
$881$	−138.825			−0.157576			−0.0787881	+	0.996891i	$0.525105\pi$
$882$	41.7236	−	870.436i	0.0473057	−	0.986889i
$883$			212.516i			0.240675i	0.992733	+	0.120337i	$0.0383976\pi$
$883$			212.516i			0.240675i	−0.992733	+	0.120337i	$0.961602\pi$
$884$	300.657	+	364.579i	0.340109	+	0.412419i
$885$	−2537.64	−	113.795i	−2.86740	−	0.128582i
$886$	219.304	+	10.5122i	0.247522	+	0.0118648i
$887$	368.959	+	368.959i	0.415963	+	0.415963i	0.883810	−	0.467847i	$-0.154970\pi$
$887$	368.959	+	368.959i	0.415963	+	0.415963i	−0.467847	+	0.883810i	$0.654970\pi$
$888$	337.656	+	48.8554i	0.380244	+	0.0550174i
$889$	645.095			0.725641
$890$	837.500	+	1009.20i	0.941011	+	1.13393i
$891$	−143.129	+	143.129i	−0.160639	+	0.160639i
$892$	−859.773	−	1042.57i	−0.963872	−	1.16880i
$893$			28.2643i			0.0316509i
$894$	120.383	−	109.370i	0.134657	−	0.122338i
$895$	−807.158	−	36.1951i	−0.901852	−	0.0404415i
$896$	−253.973	−	525.608i	−0.283452	−	0.586616i
$897$	−1349.36	+	1349.36i	−1.50430	+	1.50430i
$898$	−47.0383	+	981.309i	−0.0523811	+	1.09277i
$899$	694.029	−	694.029i	0.772001	−	0.772001i
$900$	284.841	−	1518.54i	0.316490	−	1.68727i
$901$	110.295	−	110.295i	0.122414	−	0.122414i
$902$	−1071.63	−	1179.53i	−1.18806	−	1.30769i
$903$	−279.881	+	279.881i	−0.309946	+	0.309946i
$904$	129.862	+	173.798i	0.143652	+	0.192255i
$905$	−522.782	−	23.4430i	−0.577660	−	0.0259038i
$906$	−839.512	−	40.2413i	−0.926614	−	0.0444165i
$907$			783.206i			0.863513i	0.901990	+	0.431756i	$0.142106\pi$
$907$			783.206i			0.863513i	−0.901990	+	0.431756i	$0.857894\pi$
$908$	−1763.84	−	169.486i	−1.94255	−	0.186658i
$909$	−341.304	+	341.304i	−0.375472	+	0.375472i
$910$	1008.78	+	93.7935i	1.10855	+	0.103070i
$911$	−1463.16			−1.60610			−0.803052	−	0.595909i	$-0.796792\pi$
$911$	−1463.16			−1.60610			−0.803052	+	0.595909i	$0.796792\pi$
$912$	50.6735	+	75.0624i	0.0555630	+	0.0823052i
$913$	−636.253	−	636.253i	−0.696882	−	0.696882i
$914$	−891.907	−	981.718i	−0.975828	−	1.07409i
$915$	−688.494	−	30.8740i	−0.752453	−	0.0337420i
$916$	−787.343	−	954.738i	−0.859545	−	1.04229i
$917$		−	314.754i		−	0.343244i
$918$	228.113	+	251.083i	0.248489	+	0.273511i
$919$	−1217.73			−1.32506			−0.662529	−	0.749036i	$-0.730517\pi$
$919$	−1217.73			−1.32506			−0.662529	+	0.749036i	$0.730517\pi$
$920$	682.574	+	130.215i	0.741928	+	0.141538i
$921$		−	544.445i		−	0.591146i
$922$	149.670	+	164.742i	0.162332	+	0.178678i
$923$	2028.89			2.19815
$924$	−93.5974	+	974.069i	−0.101296	+	1.05419i
$925$	214.751	+	19.2989i	0.232163	+	0.0208636i
$926$	727.156	+	800.378i	0.785266	+	0.864339i
$927$	−78.2635	+	78.2635i	−0.0844266	+	0.0844266i
$928$	−1050.38	+	638.095i	−1.13187	+	0.687603i
$929$			169.265i			0.182201i	0.995842	+	0.0911004i	$0.0290384\pi$
$929$			169.265i			0.182201i	−0.995842	+	0.0911004i	$0.970962\pi$
$930$	972.428	−	806.984i	1.04562	−	0.867724i
$931$	22.8274	+	22.8274i	0.0245192	+	0.0245192i
$932$	794.286	−	655.023i	0.852238	−	0.702815i
$933$	−265.833			−0.284923
$934$	748.330	+	35.8706i	0.801209	+	0.0384053i
$935$	−212.903	+	194.628i	−0.227704	+	0.208159i
$936$	393.201	−	2717.54i	0.420086	−	2.90336i
$937$	457.486	+	457.486i	0.488245	+	0.488245i	0.907752	−	0.419507i	$-0.137797\pi$
$937$	457.486	+	457.486i	0.488245	+	0.488245i	−0.419507	+	0.907752i	$0.637797\pi$
$938$	−86.0633	−	94.7294i	−0.0917519	−	0.100991i
$939$	820.653	+	820.653i	0.873965	+	0.873965i
$940$	−488.943	−	69.2058i	−0.520152	−	0.0736232i
$941$	−206.539	−	206.539i	−0.219489	−	0.219489i	0.588794	−	0.808283i	$-0.299603\pi$
$941$	−206.539	−	206.539i	−0.219489	−	0.219489i	−0.808283	+	0.588794i	$0.799603\pi$
$942$	−60.7258	+	1266.86i	−0.0644648	+	1.34486i
$943$	−902.259	−	902.259i	−0.956797	−	0.956797i
$944$	919.796	+	1362.49i	0.974361	+	1.44332i
$945$	726.561	+	32.5810i	0.768848	+	0.0344772i
$946$	−281.867	+	256.081i	−0.297957	+	0.270699i
$947$	952.719			1.00604			0.503019	−	0.864275i	$-0.332222\pi$
$947$	952.719			1.00604			0.503019	+	0.864275i	$0.332222\pi$
$948$	−919.655	−	88.3689i	−0.970100	−	0.0932161i
$949$	950.065	+	950.065i	1.00112	+	1.00112i
$950$	34.5418	+	45.6385i	0.0363598	+	0.0480405i
$951$			199.923i			0.210224i
$952$	192.024	+	27.7839i	0.201706	+	0.0291848i
$953$	830.106	−	830.106i	0.871045	−	0.871045i	−0.121542	−	0.992586i	$-0.538784\pi$
$953$	830.106	−	830.106i	0.871045	−	0.871045i	0.992586	+	0.121542i	$0.0387838\pi$
$954$	−905.302	−	43.3949i	−0.948954	−	0.0454873i
$955$	−312.118	−	341.425i	−0.326825	−	0.357513i
$956$	−15.8068	+	164.502i	−0.0165344	+	0.172073i
$957$	2060.21			2.15278
$958$	−43.1326	+	899.830i	−0.0450236	+	0.939280i
$959$			749.409i			0.781448i
$960$	−1422.58	+	692.807i	−1.48185	+	0.721674i
$961$	−307.904			−0.320400
$962$	382.757	+	18.3471i	0.397876	+	0.0190719i
$963$			845.027i			0.877494i
$964$	890.513	+	85.5686i	0.923768	+	0.0887641i
$965$	16.7473	−	373.467i	0.0173547	−	0.387012i
$966$	−37.5136	+	782.607i	−0.0388340	+	0.810152i
$967$	−34.0691	−	34.0691i	−0.0352318	−	0.0352318i	0.689271	−	0.724503i	$-0.257931\pi$
$967$	−34.0691	−	34.0691i	−0.0352318	−	0.0352318i	−0.724503	+	0.689271i	$0.757931\pi$
$968$	3.79473	−	26.2266i	0.00392017	−	0.0270936i
$969$	−30.1017			−0.0310647
$970$	−429.994	−	39.9794i	−0.443292	−	0.0412159i
$971$	−84.7430	+	84.7430i	−0.0872739	+	0.0872739i	−0.749396	−	0.662122i	$-0.769656\pi$
$971$	−84.7430	+	84.7430i	−0.0872739	+	0.0872739i	0.662122	+	0.749396i	$0.269656\pi$
$972$	−74.5264	+	775.596i	−0.0766732	+	0.797938i
$973$		−	165.095i		−	0.169676i
$974$	−555.903	−	611.880i	−0.570742	−	0.628213i
$975$	245.799	−	2735.17i	0.252102	−	2.80530i
$976$	249.552	+	369.660i	0.255689	+	0.378750i
$977$	28.0540	−	28.0540i	0.0287145	−	0.0287145i	−0.692604	−	0.721318i	$-0.743537\pi$
$977$	28.0540	−	28.0540i	0.0287145	−	0.0287145i	0.721318	+	0.692604i	$0.243537\pi$
$978$	−810.118	−	38.8324i	−0.828342	−	0.0397059i
$979$	−1006.01	+	1006.01i	−1.02759	+	1.02759i
$980$	−450.784	+	338.997i	−0.459984	+	0.345915i
$981$	1265.28	−	1265.28i	1.28978	−	1.28978i
$982$	−909.351	+	826.161i	−0.926020	+	0.841304i
$983$	−359.158	+	359.158i	−0.365370	+	0.365370i	−0.865785	−	0.500416i	$-0.833181\pi$
$983$	−359.158	+	359.158i	−0.365370	+	0.365370i	0.500416	+	0.865785i	$0.333181\pi$
$984$	2875.59	+	416.069i	2.92235	+	0.422834i
$985$	366.872	−	335.381i	0.372459	−	0.340489i
$986$	19.5582	−	408.021i	0.0198359	−	0.413814i
$987$		−	556.795i		−	0.564129i
$988$	64.7182	+	78.4778i	0.0655043	+	0.0794310i
$989$	−215.608	+	215.608i	−0.218006	+	0.218006i
$990$	1668.91	+	155.170i	1.68577	+	0.156737i
$991$	301.699			0.304439			0.152219	−	0.988347i	$-0.451358\pi$
$991$	301.699			0.304439			0.152219	+	0.988347i	$0.451358\pi$
$992$	−794.444	−	193.982i	−0.800851	−	0.195547i
$993$	533.755	+	533.755i	0.537517	+	0.537517i
$994$	616.564	−	560.159i	0.620286	−	0.563540i
$995$	−894.571	−	978.568i	−0.899067	−	0.983485i
$996$	1633.00	+	156.913i	1.63956	+	0.157544i
$997$		−	701.351i		−	0.703461i	−0.936101	−	0.351731i	$-0.885593\pi$
$997$		−	701.351i		−	0.703461i	0.936101	−	0.351731i	$-0.114407\pi$
$998$	75.4936	−	68.5872i	0.0756449	−	0.0687246i
$999$	275.082			0.275357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.i.a.13.1	✓	44
4.3	odd	2		320.3.i.a.273.20		44
5.2	odd	4		80.3.t.a.77.12	yes	44
5.3	odd	4		400.3.t.b.157.11		44
5.4	even	2		400.3.i.b.93.22		44
8.3	odd	2		640.3.i.a.33.3		44
8.5	even	2		640.3.i.b.33.20		44
16.3	odd	4		640.3.t.a.353.3		44
16.5	even	4		80.3.t.a.53.12	yes	44
16.11	odd	4		320.3.t.a.113.20		44
16.13	even	4		640.3.t.b.353.20		44
20.7	even	4		320.3.t.a.17.20		44
40.27	even	4		640.3.t.a.417.3		44
40.37	odd	4		640.3.t.b.417.20		44
80.27	even	4		320.3.i.a.177.3		44
80.37	odd	4	inner	80.3.i.a.37.1	yes	44
80.53	odd	4		400.3.i.b.357.22		44
80.67	even	4		640.3.i.a.97.20		44
80.69	even	4		400.3.t.b.293.11		44
80.77	odd	4		640.3.i.b.97.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.1	✓	44	1.1	even	1	trivial
80.3.i.a.37.1	yes	44	80.37	odd	4	inner
80.3.t.a.53.12	yes	44	16.5	even	4
80.3.t.a.77.12	yes	44	5.2	odd	4
320.3.i.a.177.3		44	80.27	even	4
320.3.i.a.273.20		44	4.3	odd	2
320.3.t.a.17.20		44	20.7	even	4
320.3.t.a.113.20		44	16.11	odd	4
400.3.i.b.93.22		44	5.4	even	2
400.3.i.b.357.22		44	80.53	odd	4
400.3.t.b.157.11		44	5.3	odd	4
400.3.t.b.293.11		44	80.69	even	4
640.3.i.a.33.3		44	8.3	odd	2
640.3.i.a.97.20		44	80.67	even	4
640.3.i.b.33.20		44	8.5	even	2
640.3.i.b.97.3		44	80.77	odd	4
640.3.t.a.353.3		44	16.3	odd	4
640.3.t.a.417.3		44	40.27	even	4
640.3.t.b.353.20		44	16.13	even	4
640.3.t.b.417.20		44	40.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 + 0.382594i) q^{4} +(-3.37360 - 3.69037i) q^{5} +(-0.473499 + 9.87810i) q^{6} +(3.22480 + 3.22480i) q^{7} +(-7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +O(q^{10})\)	\(q+(-1.99771 - 0.0957584i) q^{2} -4.94472i q^{3} +(3.98166 + 0.382594i) q^{4} +(-3.37360 - 3.69037i) q^{5} +(-0.473499 + 9.87810i) q^{6} +(3.22480 + 3.22480i) q^{7} +(-7.91755 - 1.14559i) q^{8} -15.4503 q^{9} +(6.38608 + 7.69532i) q^{10} +(-7.67097 + 7.67097i) q^{11} +(1.89182 - 19.6882i) q^{12} -22.2152i q^{13} +(-6.13341 - 6.75101i) q^{14} +(-18.2478 + 16.6815i) q^{15} +(15.7072 + 3.04672i) q^{16} +(-3.76038 + 3.76038i) q^{17} +(30.8651 + 1.47949i) q^{18} +(-0.809445 + 0.809445i) q^{19} +(-12.0206 - 15.9845i) q^{20} +(15.9458 - 15.9458i) q^{21} +(16.0589 - 14.5898i) q^{22} +(12.2839 - 12.2839i) q^{23} +(-5.66462 + 39.1501i) q^{24} +(-2.23764 + 24.8997i) q^{25} +(-2.12729 + 44.3794i) q^{26} +31.8948i q^{27} +(11.6063 + 14.0739i) q^{28} +(27.1574 - 27.1574i) q^{29} +(38.0512 - 31.5774i) q^{30} +25.5557 q^{31} +(-31.0867 - 7.59056i) q^{32} +(37.9308 + 37.9308i) q^{33} +(7.87223 - 7.15205i) q^{34} +(1.02151 - 22.7799i) q^{35} +(-61.5178 - 5.91119i) q^{36} -8.62466i q^{37} +(1.69454 - 1.53952i) q^{38} -109.848 q^{39} +(22.4830 + 33.0834i) q^{40} -73.4504i q^{41} +(-33.3819 + 30.3280i) q^{42} -17.5521 q^{43} +(-33.4781 + 27.6083i) q^{44} +(52.1231 + 57.0172i) q^{45} +(-25.7160 + 23.3634i) q^{46} +(17.4590 - 17.4590i) q^{47} +(15.0652 - 77.6680i) q^{48} -28.2013i q^{49} +(6.85449 - 49.5279i) q^{50} +(18.5940 + 18.5940i) q^{51} +(8.49939 - 88.4532i) q^{52} -29.3309 q^{53} +(3.05420 - 63.7165i) q^{54} +(54.1875 + 2.42991i) q^{55} +(-21.8382 - 29.2268i) q^{56} +(4.00248 + 4.00248i) q^{57} +(-56.8532 + 51.6520i) q^{58} +(72.6508 + 72.6508i) q^{59} +(-79.0390 + 59.4386i) q^{60} +(19.7110 + 19.7110i) q^{61} +(-51.0529 - 2.44718i) q^{62} +(-49.8241 - 49.8241i) q^{63} +(61.3753 + 18.1405i) q^{64} +(-81.9821 + 74.9451i) q^{65} +(-72.1424 - 79.4068i) q^{66} +14.0319 q^{67} +(-16.4113 + 13.5339i) q^{68} +(-60.7406 - 60.7406i) q^{69} +(-4.22205 + 45.4098i) q^{70} +91.3292i q^{71} +(122.328 + 17.6997i) q^{72} +(-42.7665 + 42.7665i) q^{73} +(-0.825884 + 17.2295i) q^{74} +(123.122 + 11.0645i) q^{75} +(-3.53262 + 2.91325i) q^{76} -49.4747 q^{77} +(219.444 + 10.5188i) q^{78} -46.7110i q^{79} +(-41.7464 - 68.2439i) q^{80} +18.6585 q^{81} +(-7.03350 + 146.732i) q^{82} +82.9430i q^{83} +(69.5913 - 57.3898i) q^{84} +(26.5632 + 1.19117i) q^{85} +(35.0639 + 1.68076i) q^{86} +(-134.286 - 134.286i) q^{87} +(69.5231 - 51.9475i) q^{88} +131.145 q^{89} +(-98.6667 - 118.895i) q^{90} +(71.6395 - 71.6395i) q^{91} +(53.6102 - 44.2106i) q^{92} -126.366i q^{93} +(-36.5499 + 33.2062i) q^{94} +(5.71789 + 0.256406i) q^{95} +(-37.5332 + 153.715i) q^{96} +(-30.5363 + 30.5363i) q^{97} +(-2.70051 + 56.3379i) q^{98} +(118.519 - 118.519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9	\( 44 q - 2 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{8} - 108 q^{9} + 6 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{15} + 24 q^{16} - 4 q^{17} + 22 q^{18} + 32 q^{19} + 40 q^{20} - 4 q^{21} + 92 q^{22} + 36 q^{24} - 52 q^{26} + 36 q^{28} - 28 q^{30} - 8 q^{31} - 132 q^{32} - 4 q^{33} - 88 q^{34} + 96 q^{35} - 116 q^{36} - 216 q^{38} + 72 q^{39} + 16 q^{40} + 16 q^{42} + 124 q^{43} - 168 q^{44} - 34 q^{45} + 108 q^{46} - 4 q^{47} + 340 q^{48} + 10 q^{50} - 100 q^{51} + 48 q^{52} - 4 q^{53} + 228 q^{54} - 172 q^{56} + 36 q^{57} + 16 q^{58} + 64 q^{59} + 136 q^{60} - 36 q^{61} - 356 q^{62} - 200 q^{63} - 176 q^{64} - 4 q^{65} + 276 q^{66} - 292 q^{67} - 72 q^{68} - 60 q^{69} - 92 q^{70} + 448 q^{72} + 48 q^{73} + 284 q^{74} + 96 q^{75} + 252 q^{76} + 192 q^{77} + 620 q^{78} + 4 q^{80} + 100 q^{81} - 240 q^{82} + 288 q^{84} + 48 q^{85} + 20 q^{86} + 36 q^{87} - 624 q^{88} - 578 q^{90} + 188 q^{91} - 412 q^{92} - 340 q^{94} + 380 q^{95} - 24 q^{96} - 4 q^{97} - 78 q^{98} - 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 8 * q^8 - 108 * q^9 + 6 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^15 + 24 * q^16 - 4 * q^17 + 22 * q^18 + 32 * q^19 + 40 * q^20 - 4 * q^21 + 92 * q^22 + 36 * q^24 - 52 * q^26 + 36 * q^28 - 28 * q^30 - 8 * q^31 - 132 * q^32 - 4 * q^33 - 88 * q^34 + 96 * q^35 - 116 * q^36 - 216 * q^38 + 72 * q^39 + 16 * q^40 + 16 * q^42 + 124 * q^43 - 168 * q^44 - 34 * q^45 + 108 * q^46 - 4 * q^47 + 340 * q^48 + 10 * q^50 - 100 * q^51 + 48 * q^52 - 4 * q^53 + 228 * q^54 - 172 * q^56 + 36 * q^57 + 16 * q^58 + 64 * q^59 + 136 * q^60 - 36 * q^61 - 356 * q^62 - 200 * q^63 - 176 * q^64 - 4 * q^65 + 276 * q^66 - 292 * q^67 - 72 * q^68 - 60 * q^69 - 92 * q^70 + 448 * q^72 + 48 * q^73 + 284 * q^74 + 96 * q^75 + 252 * q^76 + 192 * q^77 + 620 * q^78 + 4 * q^80 + 100 * q^81 - 240 * q^82 + 288 * q^84 + 48 * q^85 + 20 * q^86 + 36 * q^87 - 624 * q^88 - 578 * q^90 + 188 * q^91 - 412 * q^92 - 340 * q^94 + 380 * q^95 - 24 * q^96 - 4 * q^97 - 78 * q^98 - 92 * q^99

Introduction

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