LMFDB - Embedded newform 80.3.i.a.13.19

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			13.19
Character	$\chi$	$=$	80.13
Dual form			80.3.i.a.37.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83264 + 0.800895i) q^{2} +3.83124i q^{3} +(2.71713 + 2.93550i) q^{4} +(0.146974 - 4.99784i) q^{5} +(-3.06842 + 7.02129i) q^{6} +(-1.69668 - 1.69668i) q^{7} +(2.62850 + 7.55586i) q^{8} -5.67842 q^{9} +O(q^{10})$	\(q+(1.83264 + 0.800895i) q^{2} +3.83124i q^{3} +(2.71713 + 2.93550i) q^{4} +(0.146974 - 4.99784i) q^{5} +(-3.06842 + 7.02129i) q^{6} +(-1.69668 - 1.69668i) q^{7} +(2.62850 + 7.55586i) q^{8} -5.67842 q^{9} +(4.27210 - 9.04153i) q^{10} +(-6.09580 + 6.09580i) q^{11} +(-11.2466 + 10.4100i) q^{12} -14.9024i q^{13} +(-1.75054 - 4.46825i) q^{14} +(19.1479 + 0.563095i) q^{15} +(-1.23437 + 15.9523i) q^{16} +(10.0145 - 10.0145i) q^{17} +(-10.4065 - 4.54782i) q^{18} +(4.15403 - 4.15403i) q^{19} +(15.0705 - 13.1484i) q^{20} +(6.50038 - 6.50038i) q^{21} +(-16.0535 + 6.28931i) q^{22} +(31.1044 - 31.1044i) q^{23} +(-28.9483 + 10.0704i) q^{24} +(-24.9568 - 1.46911i) q^{25} +(11.9353 - 27.3107i) q^{26} +12.7258i q^{27} +(0.370503 - 9.59069i) q^{28} +(-38.9751 + 38.9751i) q^{29} +(34.6403 + 16.3674i) q^{30} -15.2616 q^{31} +(-15.0383 + 28.2462i) q^{32} +(-23.3545 - 23.3545i) q^{33} +(26.3735 - 10.3324i) q^{34} +(-8.72908 + 8.23034i) q^{35} +(-15.4290 - 16.6690i) q^{36} -10.0034i q^{37} +(10.9398 - 4.28590i) q^{38} +57.0947 q^{39} +(38.1493 - 12.0263i) q^{40} +17.1555i q^{41} +(17.1190 - 6.70672i) q^{42} -41.2482 q^{43} +(-34.4574 - 1.33114i) q^{44} +(-0.834582 + 28.3798i) q^{45} +(81.9145 - 32.0918i) q^{46} +(-35.1314 + 35.1314i) q^{47} +(-61.1172 - 4.72915i) q^{48} -43.2426i q^{49} +(-44.5602 - 22.6801i) q^{50} +(38.3679 + 38.3679i) q^{51} +(43.7461 - 40.4918i) q^{52} -5.40107 q^{53} +(-10.1920 + 23.3218i) q^{54} +(29.5699 + 31.3618i) q^{55} +(8.36014 - 17.2795i) q^{56} +(15.9151 + 15.9151i) q^{57} +(-102.642 + 40.2123i) q^{58} +(13.6188 + 13.6188i) q^{59} +(50.3745 + 57.7388i) q^{60} +(55.0109 + 55.0109i) q^{61} +(-27.9690 - 12.2229i) q^{62} +(9.63443 + 9.63443i) q^{63} +(-50.1820 + 39.7211i) q^{64} +(-74.4798 - 2.19027i) q^{65} +(-24.0959 - 61.5049i) q^{66} -67.6058 q^{67} +(56.6082 + 2.18686i) q^{68} +(119.168 + 119.168i) q^{69} +(-22.5889 + 8.09218i) q^{70} +68.8740i q^{71} +(-14.9257 - 42.9053i) q^{72} +(84.8652 - 84.8652i) q^{73} +(8.01170 - 18.3327i) q^{74} +(5.62851 - 95.6155i) q^{75} +(23.4812 + 0.907115i) q^{76} +20.6852 q^{77} +(104.634 + 45.7269i) q^{78} -89.5060i q^{79} +(79.5457 + 8.51374i) q^{80} -99.8613 q^{81} +(-13.7397 + 31.4398i) q^{82} +128.441i q^{83} +(36.7443 + 1.41949i) q^{84} +(-48.5789 - 51.5226i) q^{85} +(-75.5931 - 33.0355i) q^{86} +(-149.323 - 149.323i) q^{87} +(-62.0818 - 30.0362i) q^{88} -43.6449 q^{89} +(-24.2588 + 51.3416i) q^{90} +(-25.2845 + 25.2845i) q^{91} +(175.822 + 6.79226i) q^{92} -58.4708i q^{93} +(-92.5197 + 36.2466i) q^{94} +(-20.1507 - 21.3717i) q^{95} +(-108.218 - 57.6153i) q^{96} +(50.0681 - 50.0681i) q^{97} +(34.6328 - 79.2481i) q^{98} +(34.6145 - 34.6145i) 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 $

$2$	1.83264	+	0.800895i	0.916320	+	0.400448i
$2$	1.83264	+	0.800895i	0.916320	+	0.400448i
$3$			3.83124i			1.27708i	0.769588	+	0.638540i	$0.220461\pi$
$3$			3.83124i			1.27708i	−0.769588	+	0.638540i	$0.779539\pi$
$4$	2.71713	+	2.93550i	0.679284	+	0.733876i
$5$	0.146974	−	4.99784i	0.0293949	−	0.999568i
$5$	0.146974	−	4.99784i	0.0293949	−	0.999568i
$6$	−3.06842	+	7.02129i	−0.511404	+	1.17021i
$7$	−1.69668	−	1.69668i	−0.242382	−	0.242382i	0.575453	−	0.817835i	$-0.304826\pi$
$7$	−1.69668	−	1.69668i	−0.242382	−	0.242382i	−0.817835	+	0.575453i	$0.804826\pi$
$8$	2.62850	+	7.55586i	0.328562	+	0.944482i
$9$	−5.67842			−0.630935
$10$	4.27210	−	9.04153i	0.427210	−	0.904153i
$11$	−6.09580	+	6.09580i	−0.554164	+	0.554164i	−0.927640	−	0.373476i	$-0.878166\pi$
$11$	−6.09580	+	6.09580i	−0.554164	+	0.554164i	0.373476	+	0.927640i	$0.378166\pi$
$12$	−11.2466	+	10.4100i	−0.937219	+	0.867500i
$13$		−	14.9024i		−	1.14634i	−0.819437	−	0.573169i	$-0.805714\pi$
$13$		−	14.9024i		−	1.14634i	0.819437	−	0.573169i	$-0.194286\pi$
$14$	−1.75054	−	4.46825i	−0.125038	−	0.319161i
$15$	19.1479	+	0.563095i	1.27653	+	0.0375396i
$16$	−1.23437	+	15.9523i	−0.0771478	+	0.997020i
$17$	10.0145	−	10.0145i	0.589087	−	0.589087i	−0.348297	−	0.937384i	$-0.613240\pi$
$17$	10.0145	−	10.0145i	0.589087	−	0.589087i	0.937384	+	0.348297i	$0.113240\pi$
$18$	−10.4065	−	4.54782i	−0.578139	−	0.252657i
$19$	4.15403	−	4.15403i	0.218633	−	0.218633i	−0.589289	−	0.807922i	$-0.700592\pi$
$19$	4.15403	−	4.15403i	0.218633	−	0.218633i	0.807922	+	0.589289i	$0.200592\pi$
$20$	15.0705	−	13.1484i	0.753526	−	0.657418i
$21$	6.50038	−	6.50038i	0.309542	−	0.309542i
$22$	−16.0535	+	6.28931i	−0.729705	+	0.285878i
$23$	31.1044	−	31.1044i	1.35237	−	1.35237i	0.469356	−	0.883009i	$-0.344486\pi$
$23$	31.1044	−	31.1044i	1.35237	−	1.35237i	0.883009	−	0.469356i	$-0.155514\pi$
$24$	−28.9483	+	10.0704i	−1.20618	+	0.419600i
$25$	−24.9568	−	1.46911i	−0.998272	−	0.0587644i
$26$	11.9353	−	27.3107i	0.459049	−	1.05041i
$27$			12.7258i			0.471325i
$28$	0.370503	−	9.59069i	0.0132322	−	0.342525i
$29$	−38.9751	+	38.9751i	−1.34397	+	1.34397i	−0.451901	+	0.892068i	$0.649254\pi$
$29$	−38.9751	+	38.9751i	−1.34397	+	1.34397i	−0.892068	+	0.451901i	$0.850746\pi$
$30$	34.6403	+	16.3674i	1.15468	+	0.545581i
$31$	−15.2616			−0.492309			−0.246154	−	0.969231i	$-0.579167\pi$
$31$	−15.2616			−0.492309			−0.246154	+	0.969231i	$0.579167\pi$
$32$	−15.0383	+	28.2462i	−0.469946	+	0.882695i
$33$	−23.3545	−	23.3545i	−0.707712	−	0.707712i
$34$	26.3735	−	10.3324i	0.775690	−	0.303893i
$35$	−8.72908	+	8.23034i	−0.249402	+	0.235153i
$36$	−15.4290	−	16.6690i	−0.428584	−	0.463028i
$37$		−	10.0034i		−	0.270363i	−0.990821	−	0.135181i	$-0.956838\pi$
$37$		−	10.0034i		−	0.270363i	0.990821	−	0.135181i	$-0.0431617\pi$
$38$	10.9398	−	4.28590i	0.287889	−	0.112787i
$39$	57.0947			1.46397
$40$	38.1493	−	12.0263i	0.953732	−	0.300657i
$41$			17.1555i			0.418427i	0.977870	+	0.209213i	$0.0670903\pi$
$41$			17.1555i			0.418427i	−0.977870	+	0.209213i	$0.932910\pi$
$42$	17.1190	−	6.70672i	0.407594	−	0.159684i
$43$	−41.2482			−0.959261			−0.479630	−	0.877471i	$-0.659229\pi$
$43$	−41.2482			−0.959261			−0.479630	+	0.877471i	$0.659229\pi$
$44$	−34.4574	−	1.33114i	−0.783122	−	0.0302531i
$45$	−0.834582	+	28.3798i	−0.0185463	+	0.630663i
$46$	81.9145	−	32.0918i	1.78075	−	0.697648i
$47$	−35.1314	+	35.1314i	−0.747476	+	0.747476i	−0.974004	−	0.226529i	$-0.927262\pi$
$47$	−35.1314	+	35.1314i	−0.747476	+	0.747476i	0.226529	+	0.974004i	$0.427262\pi$
$48$	−61.1172	−	4.72915i	−1.27327	−	0.0985240i
$49$		−	43.2426i		−	0.882502i
$50$	−44.5602	−	22.6801i	−0.891204	−	0.453602i
$51$	38.3679	+	38.3679i	0.752311	+	0.752311i
$52$	43.7461	−	40.4918i	0.841271	−	0.778689i
$53$	−5.40107			−0.101907			−0.0509535	−	0.998701i	$-0.516226\pi$
$53$	−5.40107			−0.101907			−0.0509535	+	0.998701i	$0.516226\pi$
$54$	−10.1920	+	23.3218i	−0.188741	+	0.431885i
$55$	29.5699	+	31.3618i	0.537635	+	0.570214i
$56$	8.36014	−	17.2795i	0.149288	−	0.308563i
$57$	15.9151	+	15.9151i	0.279212	+	0.279212i
$58$	−102.642	+	40.2123i	−1.76969	+	0.693316i
$59$	13.6188	+	13.6188i	0.230827	+	0.230827i	0.813038	−	0.582211i	$-0.197812\pi$
$59$	13.6188	+	13.6188i	0.230827	+	0.230827i	−0.582211	+	0.813038i	$0.697812\pi$
$60$	50.3745	+	57.7388i	0.839576	+	0.962314i
$61$	55.0109	+	55.0109i	0.901818	+	0.901818i	0.995593	−	0.0937755i	$-0.0298936\pi$
$61$	55.0109	+	55.0109i	0.901818	+	0.901818i	−0.0937755	+	0.995593i	$0.529894\pi$
$62$	−27.9690	−	12.2229i	−0.451112	−	0.197144i
$63$	9.63443	+	9.63443i	0.152928	+	0.152928i
$64$	−50.1820	+	39.7211i	−0.784094	+	0.620642i
$65$	−74.4798	−	2.19027i	−1.14584	−	0.0336965i
$66$	−24.0959	−	61.5049i	−0.365089	−	0.931892i
$67$	−67.6058			−1.00904			−0.504521	−	0.863400i	$-0.668331\pi$
$67$	−67.6058			−1.00904			−0.504521	+	0.863400i	$0.668331\pi$
$68$	56.6082	+	2.18686i	0.832473	+	0.0321597i
$69$	119.168	+	119.168i	1.72708	+	1.72708i
$70$	−22.5889	+	8.09218i	−0.322699	+	0.115603i
$71$			68.8740i			0.970057i	0.874498	+	0.485028i	$0.161191\pi$
$71$			68.8740i			0.970057i	−0.874498	+	0.485028i	$0.838809\pi$
$72$	−14.9257	−	42.9053i	−0.207301	−	0.595907i
$73$	84.8652	−	84.8652i	1.16254	−	1.16254i	0.178619	−	0.983918i	$-0.442837\pi$
$73$	84.8652	−	84.8652i	1.16254	−	1.16254i	0.983918	−	0.178619i	$-0.0571630\pi$
$74$	8.01170	−	18.3327i	0.108266	−	0.247739i
$75$	5.62851	−	95.6155i	0.0750468	−	1.27487i
$76$	23.4812	+	0.907115i	0.308964	+	0.0119357i
$77$	20.6852			0.268639
$78$	104.634	+	45.7269i	1.34146	+	0.586242i
$79$		−	89.5060i		−	1.13299i	−0.824066	−	0.566494i	$-0.808300\pi$
$79$		−	89.5060i		−	1.13299i	0.824066	−	0.566494i	$-0.191700\pi$
$80$	79.5457	+	8.51374i	0.994321	+	0.106422i
$81$	−99.8613			−1.23286
$82$	−13.7397	+	31.4398i	−0.167558	+	0.383412i
$83$			128.441i			1.54748i	0.633504	+	0.773740i	$0.281616\pi$
$83$			128.441i			1.54748i	−0.633504	+	0.773740i	$0.718384\pi$
$84$	36.7443	+	1.41949i	0.437432	+	0.0168986i
$85$	−48.5789	−	51.5226i	−0.571516	−	0.606148i
$86$	−75.5931	−	33.0355i	−0.878990	−	0.384134i
$87$	−149.323	−	149.323i	−1.71636	−	1.71636i
$88$	−62.0818	−	30.0362i	−0.705475	−	0.341321i
$89$	−43.6449			−0.490392			−0.245196	−	0.969474i	$-0.578852\pi$
$89$	−43.6449			−0.490392			−0.245196	+	0.969474i	$0.578852\pi$
$90$	−24.2588	+	51.3416i	−0.269542	+	0.570462i
$91$	−25.2845	+	25.2845i	−0.277852	+	0.277852i
$92$	175.822	+	6.79226i	1.91111	+	0.0738289i
$93$		−	58.4708i		−	0.628718i
$94$	−92.5197	+	36.2466i	−0.984252	+	0.385602i
$95$	−20.1507	−	21.3717i	−0.212112	−	0.224966i
$96$	−108.218	−	57.6153i	−1.12727	−	0.600159i
$97$	50.0681	−	50.0681i	0.516166	−	0.516166i	−0.400243	−	0.916409i	$-0.631074\pi$
$97$	50.0681	−	50.0681i	0.516166	−	0.516166i	0.916409	+	0.400243i	$0.131074\pi$
$98$	34.6328	−	79.2481i	0.353396	−	0.808654i
$99$	34.6145	−	34.6145i	0.349642	−	0.349642i
$100$	−63.4984	−	77.2525i	−0.634984	−	0.772525i
$101$	72.5051	−	72.5051i	0.717872	−	0.717872i	−0.250297	−	0.968169i	$-0.580528\pi$
$101$	72.5051	−	72.5051i	0.717872	−	0.717872i	0.968169	+	0.250297i	$0.0805282\pi$
$102$	39.5858	+	101.043i	0.388096	+	0.990619i
$103$	35.2795	−	35.2795i	0.342520	−	0.342520i	−0.514794	−	0.857314i	$-0.672132\pi$
$103$	35.2795	−	35.2795i	0.342520	−	0.342520i	0.857314	+	0.514794i	$0.172132\pi$
$104$	112.600	−	39.1709i	1.08270	−	0.376643i
$105$	−31.5324	−	33.4432i	−0.300309	−	0.318507i
$106$	−9.89821	−	4.32569i	−0.0933794	−	0.0408084i
$107$		−	82.1016i		−	0.767304i	−0.923478	−	0.383652i	$-0.874666\pi$
$107$		−	82.1016i		−	0.767304i	0.923478	−	0.383652i	$-0.125334\pi$
$108$	−37.3566	+	34.5777i	−0.345894	+	0.320163i
$109$	21.7299	−	21.7299i	0.199357	−	0.199357i	−0.600367	−	0.799724i	$-0.704979\pi$
$109$	21.7299	−	21.7299i	0.199357	−	0.199357i	0.799724	+	0.600367i	$0.204979\pi$
$110$	29.0735	+	81.1572i	0.264304	+	0.737793i
$111$	38.3256			0.345275
$112$	29.1602	−	24.9716i	0.260359	−	0.222961i
$113$	126.862	+	126.862i	1.12267	+	1.12267i	0.991339	+	0.131331i	$0.0419249\pi$
$113$	126.862	+	126.862i	1.12267	+	1.12267i	0.131331	+	0.991339i	$0.458075\pi$
$114$	16.4203	+	41.9130i	0.144038	+	0.367658i
$115$	−150.883	−	160.026i	−1.31203	−	1.39153i
$116$	−220.312	−	8.51098i	−1.89924	−	0.0733706i
$117$			84.6221i			0.723266i
$118$	14.0511	+	35.8656i	0.119077	+	0.303946i
$119$	−33.9826			−0.285568
$120$	46.0756	+	146.159i	0.383963	+	1.21799i
$121$			46.6824i			0.385805i
$122$	56.7572	+	144.873i	0.465223	+	1.18748i
$123$	−65.7268			−0.534364
$124$	−41.4678	−	44.8004i	−0.334417	−	0.361294i
$125$	−11.0104	+	124.514i	−0.0880830	+	0.996113i
$126$	9.94027	+	25.3726i	0.0788911	+	0.201370i
$127$	12.9872	−	12.9872i	0.102261	−	0.102261i	−0.654125	−	0.756386i	$-0.726963\pi$
$127$	12.9872	−	12.9872i	0.102261	−	0.102261i	0.756386	+	0.654125i	$0.226963\pi$
$128$	−123.778	+	32.6039i	−0.967015	+	0.254718i
$129$		−	158.032i		−	1.22505i
$130$	−134.740	−	63.6645i	−1.03647	−	0.489727i
$131$	79.1439	+	79.1439i	0.604152	+	0.604152i	0.941412	−	0.337260i	$-0.109500\pi$
$131$	79.1439	+	79.1439i	0.604152	+	0.604152i	−0.337260	+	0.941412i	$0.609500\pi$
$132$	5.09991	−	132.014i	0.0386357	−	1.00011i
$133$	−14.0961			−0.105986
$134$	−123.897	−	54.1451i	−0.924604	−	0.404068i
$135$	63.6014	+	1.87036i	0.471122	+	0.0138545i
$136$	101.991	+	49.3450i	0.749934	+	0.362831i
$137$	156.302	+	156.302i	1.14089	+	1.14089i	0.988288	+	0.152600i	$0.0487646\pi$
$137$	156.302	+	156.302i	1.14089	+	1.14089i	0.152600	+	0.988288i	$0.451235\pi$
$138$	122.951	+	313.834i	0.890952	+	2.27416i
$139$	−10.6258	−	10.6258i	−0.0764446	−	0.0764446i	0.667851	−	0.744295i	$-0.267214\pi$
$139$	−10.6258	−	10.6258i	−0.0764446	−	0.0764446i	−0.744295	+	0.667851i	$0.767214\pi$
$140$	−47.8783	−	3.26130i	−0.341988	−	0.0232950i
$141$	−134.597	−	134.597i	−0.954587	−	0.954587i
$142$	−55.1609	+	126.221i	−0.388457	+	0.888882i
$143$	90.8421	+	90.8421i	0.635259	+	0.635259i
$144$	7.00924	−	90.5839i	0.0486753	−	0.629055i
$145$	189.063	+	200.520i	1.30388	+	1.38289i
$146$	223.496	−	87.5592i	1.53079	−	0.599721i
$147$	165.673			1.12703
$148$	29.3651	−	27.1807i	0.198413	−	0.183653i
$149$	−59.6091	−	59.6091i	−0.400061	−	0.400061i	0.478193	−	0.878255i	$-0.341292\pi$
$149$	−59.6091	−	59.6091i	−0.400061	−	0.400061i	−0.878255	+	0.478193i	$0.841292\pi$
$150$	86.8931	−	170.721i	0.579287	−	1.13814i
$151$			3.55134i			0.0235188i	0.999931	+	0.0117594i	$0.00374322\pi$
$151$			3.55134i			0.0235188i	−0.999931	+	0.0117594i	$0.996257\pi$
$152$	42.3061	+	20.4684i	0.278330	+	0.134661i
$153$	−56.8664	+	56.8664i	−0.371676	+	0.371676i
$154$	37.9085	+	16.5667i	0.246159	+	0.107576i
$155$	−2.24306	+	76.2749i	−0.0144714	+	0.492096i
$156$	155.134	+	167.602i	0.994449	+	1.07437i
$157$	2.28360			0.0145453			0.00727263	−	0.999974i	$-0.497685\pi$
$157$	2.28360			0.0145453			0.00727263	+	0.999974i	$0.497685\pi$
$158$	71.6849	−	164.032i	0.453702	−	1.03818i
$159$		−	20.6928i		−	0.130143i
$160$	138.960	+	79.3104i	0.868500	+	0.495690i
$161$	−105.548			−0.655579
$162$	−183.010	−	79.9784i	−1.12969	−	0.493694i
$163$		−	116.769i		−	0.716375i	−0.933650	−	0.358188i	$-0.883395\pi$
$163$		−	116.769i		−	0.716375i	0.933650	−	0.358188i	$-0.116605\pi$
$164$	−50.3600	+	46.6138i	−0.307073	+	0.284230i
$165$	−120.155	+	113.289i	−0.728209	+	0.686603i
$166$	−102.868	+	235.386i	−0.619684	+	1.41799i
$167$	−20.9709	−	20.9709i	−0.125574	−	0.125574i	0.641527	−	0.767101i	$-0.278301\pi$
$167$	−20.9709	−	20.9709i	−0.125574	−	0.125574i	−0.767101	+	0.641527i	$0.778301\pi$
$168$	66.2021	+	32.0297i	0.394060	+	0.190653i
$169$	−53.0817			−0.314093
$170$	−47.7633	−	133.329i	−0.280961	−	0.784288i
$171$	−23.5883	+	23.5883i	−0.137944	+	0.137944i
$172$	−112.077	−	121.084i	−0.651610	−	0.703978i
$173$		−	242.412i		−	1.40122i	−0.713543	−	0.700612i	$-0.752910\pi$
$173$		−	242.412i		−	1.40122i	0.713543	−	0.700612i	$-0.247090\pi$
$174$	−154.063	−	393.247i	−0.885421	−	2.26004i
$175$	39.8510	+	44.8362i	0.227720	+	0.256207i
$176$	−89.7177	−	104.767i	−0.509760	−	0.595265i
$177$	−52.1770	+	52.1770i	−0.294785	+	0.294785i
$178$	−79.9853	−	34.9550i	−0.449356	−	0.196376i
$179$	−177.009	+	177.009i	−0.988880	+	0.988880i	−0.999939	−	0.0110592i	$-0.996480\pi$
$179$	−177.009	+	177.009i	−0.988880	+	0.988880i	0.0110592	+	0.999939i	$0.496480\pi$
$180$	−85.5768	+	74.6619i	−0.475426	+	0.414788i
$181$	−24.0528	+	24.0528i	−0.132888	+	0.132888i	−0.770422	−	0.637534i	$-0.779955\pi$
$181$	−24.0528	+	24.0528i	−0.132888	+	0.132888i	0.637534	+	0.770422i	$0.279955\pi$
$182$	−66.5877	+	26.0872i	−0.365867	+	0.143336i
$183$	−210.760	+	210.760i	−1.15169	+	1.15169i
$184$	316.778	+	153.263i	1.72162	+	0.832949i
$185$	−49.9955	−	1.47025i	−0.270246	−	0.00794729i
$186$	46.8290	−	107.156i	0.251769	−	0.576107i
$187$			122.092i			0.652901i
$188$	−198.585	−	7.67163i	−1.05630	−	0.0408065i
$189$	21.5915	−	21.5915i	0.114241	−	0.114241i
$190$	−19.8124	−	55.3052i	−0.104276	−	0.291080i
$191$	−23.7935			−0.124573			−0.0622867	−	0.998058i	$-0.519839\pi$
$191$	−23.7935			−0.124573			−0.0622867	+	0.998058i	$0.519839\pi$
$192$	−152.181	−	192.259i	−0.792610	−	1.00135i
$193$	72.7930	+	72.7930i	0.377166	+	0.377166i	0.870079	−	0.492913i	$-0.164068\pi$
$193$	72.7930	+	72.7930i	0.377166	+	0.377166i	−0.492913	+	0.870079i	$0.664068\pi$
$194$	131.856	−	51.6574i	0.679670	−	0.266275i
$195$	8.39146	−	285.350i	0.0430331	−	1.46333i
$196$	126.939	−	117.496i	0.647647	−	0.599469i
$197$		−	211.841i		−	1.07533i	−0.843157	−	0.537667i	$-0.819306\pi$
$197$		−	211.841i		−	1.07533i	0.843157	−	0.537667i	$-0.180694\pi$
$198$	91.1585	−	35.7133i	0.460396	−	0.180370i
$199$	106.366			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$199$	106.366			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$200$	−54.4985	−	192.432i	−0.272492	−	0.962158i
$201$		−	259.014i		−	1.28863i
$202$	190.945	−	74.8067i	0.945271	−	0.370330i
$203$	132.256			0.651508
$204$	−8.37838	+	216.880i	−0.0410705	+	1.06314i
$205$	85.7404	+	2.52142i	0.418246	+	0.0122996i
$206$	92.9099	−	36.3995i	0.451019	−	0.176696i
$207$	−176.624	+	176.624i	−0.853255	+	0.853255i
$208$	237.728	+	18.3950i	1.14292	+	0.0884375i
$209$			50.6443i			0.242317i
$210$	−31.0031	−	86.5435i	−0.147634	−	0.412112i
$211$	−5.13143	−	5.13143i	−0.0243196	−	0.0243196i	0.694842	−	0.719162i	$-0.255474\pi$
$211$	−5.13143	−	5.13143i	−0.0243196	−	0.0243196i	−0.719162	+	0.694842i	$0.755474\pi$
$212$	−14.6754	−	15.8549i	−0.0692237	−	0.0747871i
$213$	−263.873			−1.23884
$214$	65.7547	−	150.463i	0.307265	−	0.703096i
$215$	−6.06243	+	206.152i	−0.0281974	+	0.958846i
$216$	−96.1542	+	33.4497i	−0.445158	+	0.154860i
$217$	25.8939	+	25.8939i	0.119327	+	0.119327i
$218$	57.2264	−	22.4197i	0.262507	−	0.102843i
$219$	325.139	+	325.139i	1.48465	+	1.48465i
$220$	−11.7172	+	172.017i	−0.0532598	+	0.781894i
$221$	−149.240	−	149.240i	−0.675293	−	0.675293i
$222$	70.2369	+	30.6948i	0.316383	+	0.138265i
$223$	−116.577	−	116.577i	−0.522765	−	0.522765i	0.395640	−	0.918406i	$-0.370523\pi$
$223$	−116.577	−	116.577i	−0.522765	−	0.522765i	−0.918406	+	0.395640i	$0.870523\pi$
$224$	73.4398	−	22.4096i	0.327856	−	0.100043i
$225$	141.715	+	8.34222i	0.629845	+	0.0370765i
$226$	130.889	+	334.094i	0.579154	+	1.47829i
$227$	256.557			1.13021			0.565104	−	0.825020i	$-0.308836\pi$
$227$	256.557			1.13021			0.565104	+	0.825020i	$0.308836\pi$
$228$	−3.47538	+	89.9623i	−0.0152429	+	0.394572i
$229$	15.0848	+	15.0848i	0.0658724	+	0.0658724i	0.739275	−	0.673403i	$-0.235168\pi$
$229$	15.0848	+	15.0848i	0.0658724	+	0.0658724i	−0.673403	+	0.739275i	$0.735168\pi$
$230$	−148.350	−	414.112i	−0.645001	−	1.80049i
$231$			79.2500i			0.343074i
$232$	−396.936	−	192.045i	−1.71093	−	0.827778i
$233$	106.551	−	106.551i	0.457298	−	0.457298i	−0.440469	−	0.897768i	$-0.645188\pi$
$233$	106.551	−	106.551i	0.457298	−	0.457298i	0.897768	+	0.440469i	$0.145188\pi$
$234$	−67.7734	+	155.082i	−0.289630	+	0.662743i
$235$	170.417	+	180.744i	0.725181	+	0.769125i
$236$	−2.97394	+	76.9822i	−0.0126014	+	0.326196i
$237$	342.919			1.44692
$238$	−62.2779	−	27.2165i	−0.261672	−	0.114355i
$239$			8.02920i			0.0335950i	0.999859	+	0.0167975i	$0.00534706\pi$
$239$			8.02920i			0.0335950i	−0.999859	+	0.0167975i	$0.994653\pi$
$240$	−32.6182	+	304.759i	−0.135909	+	1.26983i
$241$	9.19588			0.0381572			0.0190786	−	0.999818i	$-0.493927\pi$
$241$	9.19588			0.0381572			0.0190786	+	0.999818i	$0.493927\pi$
$242$	−37.3877	+	85.5521i	−0.154495	+	0.353521i
$243$		−	268.061i		−	1.10313i
$244$	−12.0127	+	310.957i	−0.0492324	+	1.27441i
$245$	−216.119	−	6.35555i	−0.882120	−	0.0259410i
$246$	−120.454	−	52.6403i	−0.489649	−	0.213985i
$247$	−61.9051	−	61.9051i	−0.250628	−	0.250628i
$248$	−40.1150	−	115.314i	−0.161754	−	0.464977i
$249$	−492.088			−1.97626
$250$	−119.901	+	219.371i	−0.479603	+	0.877485i
$251$	326.061	−	326.061i	1.29905	−	1.29905i	0.370024	−	0.929022i	$-0.379349\pi$
$251$	326.061	−	326.061i	1.29905	−	1.29905i	0.929022	−	0.370024i	$-0.120651\pi$
$252$	−2.10387	+	54.4600i	−0.00834869	+	0.216111i
$253$			379.212i			1.49886i
$254$	34.2021	−	13.3994i	0.134654	−	0.0527537i
$255$	197.396	−	186.117i	0.774100	−	0.729872i
$256$	−252.953	−	39.3820i	−0.988096	−	0.153836i
$257$	−185.092	+	185.092i	−0.720204	+	0.720204i	−0.968647	−	0.248443i	$-0.920081\pi$
$257$	−185.092	+	185.092i	−0.720204	+	0.720204i	0.248443	+	0.968647i	$0.420081\pi$
$258$	126.567	−	289.616i	0.490570	−	1.12254i
$259$	−16.9726	+	16.9726i	−0.0655312	+	0.0655312i
$260$	−195.942	−	224.587i	−0.753624	−	0.863797i
$261$	221.317	−	221.317i	0.847958	−	0.847958i
$262$	81.6563	+	208.428i	0.311665	+	0.795527i
$263$	−202.165	+	202.165i	−0.768689	+	0.768689i	−0.977876	−	0.209187i	$-0.932918\pi$
$263$	−202.165	+	202.165i	−0.768689	+	0.768689i	0.209187	+	0.977876i	$0.432918\pi$
$264$	115.076	−	237.850i	0.435894	−	0.900949i
$265$	−0.793819	+	26.9937i	−0.00299554	+	0.101863i
$266$	−25.8331	−	11.2895i	−0.0971167	−	0.0424417i
$267$		−	167.214i		−	0.626270i
$268$	−183.694	−	198.457i	−0.685425	−	0.740511i
$269$	−135.481	+	135.481i	−0.503647	+	0.503647i	−0.912569	−	0.408922i	$-0.865905\pi$
$269$	−135.481	+	135.481i	−0.503647	+	0.503647i	0.408922	+	0.912569i	$0.365905\pi$
$270$	115.060	+	54.3658i	0.426150	+	0.201355i
$271$	−276.220			−1.01926			−0.509632	−	0.860393i	$-0.670218\pi$
$271$	−276.220			−1.01926			−0.509632	+	0.860393i	$0.670218\pi$
$272$	147.393	+	172.116i	0.541884	+	0.632778i
$273$	−96.8712	−	96.8712i	−0.354840	−	0.354840i
$274$	161.263	+	411.626i	0.588552	+	1.50228i
$275$	161.087	−	143.176i	0.585771	−	0.520641i
$276$	−26.0228	+	673.616i	−0.0942855	+	2.44064i
$277$		−	184.706i		−	0.666808i	−0.942784	−	0.333404i	$-0.891803\pi$
$277$		−	184.706i		−	0.666808i	0.942784	−	0.333404i	$-0.108197\pi$
$278$	−10.9631	−	27.9834i	−0.0394356	−	0.100660i
$279$	86.6616			0.310615
$280$	−85.1317	−	44.3223i	−0.304042	−	0.158294i
$281$			173.967i			0.619100i	0.950883	+	0.309550i	$0.100178\pi$
$281$			173.967i			0.619100i	−0.950883	+	0.309550i	$0.899822\pi$
$282$	−138.869	−	354.465i	−0.492445	−	1.25697i
$283$	33.1982			0.117308			0.0586541	−	0.998278i	$-0.481319\pi$
$283$	33.1982			0.117308			0.0586541	+	0.998278i	$0.481319\pi$
$284$	−202.180	+	187.140i	−0.711901	+	0.658943i
$285$	81.8803	−	77.2020i	0.287299	−	0.270884i
$286$	93.7258	+	239.236i	0.327713	+	0.836489i
$287$	29.1073	−	29.1073i	0.101419	−	0.101419i
$288$	85.3936	−	160.394i	0.296506	−	0.556924i
$289$			88.4206i			0.305954i
$290$	185.889	+	518.900i	0.640997	+	1.78931i
$291$	191.823	+	191.823i	0.659185	+	0.659185i
$292$	479.712	+	18.5320i	1.64285	+	0.0634658i
$293$	−194.502			−0.663829			−0.331915	−	0.943309i	$-0.607695\pi$
$293$	−194.502			−0.663829			−0.331915	+	0.943309i	$0.607695\pi$
$294$	303.619	+	132.687i	1.03272	+	0.451315i
$295$	70.0662	−	66.0630i	0.237513	−	0.223942i
$296$	75.5845	−	26.2940i	0.255353	−	0.0888310i
$297$	−77.5738	−	77.5738i	−0.261191	−	0.261191i
$298$	−61.5014	−	156.983i	−0.206380	−	0.526788i
$299$	−463.530	−	463.530i	−1.55027	−	1.55027i
$300$	295.973	−	243.278i	0.986577	−	0.810926i
$301$	69.9848	+	69.9848i	0.232508	+	0.232508i
$302$	−2.84425	+	6.50832i	−0.00941804	+	0.0215507i
$303$	277.785	+	277.785i	0.916781	+	0.916781i
$304$	61.1388	+	71.3940i	0.201115	+	0.234849i
$305$	283.021	−	266.850i	0.927937	−	0.874919i
$306$	−149.760	+	58.6716i	−0.489410	+	0.191737i
$307$	−517.509			−1.68570			−0.842849	−	0.538150i	$-0.819123\pi$
$307$	−517.509			−1.68570			−0.842849	+	0.538150i	$0.819123\pi$
$308$	56.2044	+	60.7215i	0.182482	+	0.197148i
$309$	135.164	+	135.164i	0.437426	+	0.437426i
$310$	−65.1989	+	137.988i	−0.210319	+	0.445122i
$311$		−	482.841i		−	1.55254i	−0.630399	−	0.776271i	$-0.717109\pi$
$311$		−	482.841i		−	1.55254i	0.630399	−	0.776271i	$-0.282891\pi$
$312$	150.073	+	431.400i	0.481004	+	1.38269i
$313$	96.1945	−	96.1945i	0.307331	−	0.307331i	−0.536543	−	0.843873i	$-0.680270\pi$
$313$	96.1945	−	96.1945i	0.307331	−	0.307331i	0.843873	+	0.536543i	$0.180270\pi$
$314$	4.18502	+	1.82893i	0.0133281	+	0.00582461i
$315$	49.5674	−	46.7353i	0.157357	−	0.148366i
$316$	262.745	−	243.200i	0.831472	−	0.769619i
$317$	−344.707			−1.08740			−0.543702	−	0.839278i	$-0.682978\pi$
$317$	−344.707			−1.08740			−0.543702	+	0.839278i	$0.682978\pi$
$318$	16.5728	−	37.9225i	0.0521156	−	0.119253i
$319$		−	475.169i		−	1.48956i
$320$	191.144	+	256.640i	0.597326	+	0.801999i
$321$	314.551			0.979910
$322$	−193.432	−	84.5330i	−0.600720	−	0.262525i
$323$		−	83.2009i		−	0.257588i
$324$	−271.337	−	293.143i	−0.837459	−	0.904763i
$325$	−21.8933	+	371.916i	−0.0673639	+	1.14436i
$326$	93.5199	−	213.996i	0.286871	−	0.656429i
$327$	83.2525	+	83.2525i	0.254595	+	0.254595i
$328$	−129.624	+	45.0931i	−0.395196	+	0.137479i
$329$	119.213			0.362350
$330$	−310.933	+	111.388i	−0.942221	+	0.337538i
$331$	−204.460	+	204.460i	−0.617704	+	0.617704i	−0.944942	−	0.327238i	$-0.893882\pi$
$331$	−204.460	+	204.460i	−0.617704	+	0.617704i	0.327238	+	0.944942i	$0.393882\pi$
$332$	−377.038	+	348.991i	−1.13566	+	1.05118i
$333$			56.8037i			0.170582i
$334$	−21.6366	−	55.2276i	−0.0647803	−	0.165352i
$335$	−9.93632	+	337.883i	−0.0296606	+	1.00861i
$336$	95.6722	+	111.720i	0.284739	+	0.332500i
$337$	−200.716	+	200.716i	−0.595598	+	0.595598i	−0.939138	−	0.343540i	$-0.888374\pi$
$337$	−200.716	+	200.716i	−0.595598	+	0.595598i	0.343540	+	0.939138i	$0.388374\pi$
$338$	−97.2797	−	42.5129i	−0.287810	−	0.125778i
$339$	−486.038	+	486.038i	−1.43374	+	1.43374i
$340$	19.2495	−	282.597i	0.0566162	−	0.831168i
$341$	93.0315	−	93.0315i	0.272820	−	0.272820i
$342$	−62.1207	+	24.3371i	−0.181639	+	0.0711612i
$343$	−156.506	+	156.506i	−0.456285	+	0.456285i
$344$	−108.421	−	311.666i	−0.315177	−	0.906005i
$345$	613.100	−	578.070i	1.77710	−	1.67557i
$346$	194.146	−	444.253i	0.561117	−	1.28397i
$347$			187.616i			0.540681i	0.962765	+	0.270341i	$0.0871363\pi$
$347$			187.616i			0.540681i	−0.962765	+	0.270341i	$0.912864\pi$
$348$	32.6076	−	844.069i	0.0937001	−	2.42549i
$349$	316.337	−	316.337i	0.906409	−	0.906409i	−0.0895710	−	0.995980i	$-0.528550\pi$
$349$	316.337	−	316.337i	0.906409	−	0.906409i	0.995980	+	0.0895710i	$0.0285496\pi$
$350$	37.1234	+	114.085i	0.106067	+	0.325957i
$351$	189.645			0.540299
$352$	−80.5131	−	263.854i	−0.228730	−	0.749585i
$353$	−284.733	−	284.733i	−0.806610	−	0.806610i	0.177509	−	0.984119i	$-0.443196\pi$
$353$	−284.733	−	284.733i	−0.806610	−	0.806610i	−0.984119	+	0.177509i	$0.943196\pi$
$354$	−137.410	+	53.8333i	−0.388163	+	0.152071i
$355$	344.221	+	10.1227i	0.969637	+	0.0285147i
$356$	−118.589	−	128.120i	−0.333115	−	0.359887i
$357$		−	130.196i		−	0.364694i
$358$	−466.161	+	182.628i	−1.30212	+	0.510135i
$359$	425.478			1.18518			0.592588	−	0.805506i	$-0.298106\pi$
$359$	425.478			1.18518			0.592588	+	0.805506i	$0.298106\pi$
$360$	−216.628	+	68.2903i	−0.601744	+	0.189695i
$361$			326.488i			0.904399i
$362$	−63.3439	+	24.8163i	−0.174983	+	0.0685534i
$363$	−178.852			−0.492704
$364$	−142.924	−	5.52138i	−0.392649	−	0.0151686i
$365$	−411.670	−	436.616i	−1.12786	−	1.19621i
$366$	−555.044	+	217.450i	−1.51651	+	0.594127i
$367$	−203.918	+	203.918i	−0.555635	+	0.555635i	−0.928062	−	0.372427i	$-0.878526\pi$
$367$	−203.918	+	203.918i	−0.555635	+	0.555635i	0.372427	+	0.928062i	$0.378526\pi$
$368$	457.793	+	534.581i	1.24400	+	1.45267i
$369$		−	97.4160i		−	0.264000i
$370$	−90.4463	−	42.7356i	−0.244449	−	0.115502i
$371$	9.16386	+	9.16386i	0.0247004	+	0.0247004i
$372$	171.641	−	158.873i	0.461401	−	0.427078i
$373$	601.037			1.61136			0.805680	−	0.592351i	$-0.201800\pi$
$373$	601.037			1.61136			0.805680	+	0.592351i	$0.201800\pi$
$374$	−97.7833	+	223.751i	−0.261453	+	0.598266i
$375$	−477.044	−	42.1834i	−1.27212	−	0.112489i
$376$	−357.790	−	173.105i	−0.951570	−	0.460386i
$377$	580.823	+	580.823i	1.54064	+	1.54064i
$378$	56.8620	−	22.2769i	0.150429	−	0.0589337i
$379$	−300.652	−	300.652i	−0.793276	−	0.793276i	0.188750	−	0.982025i	$-0.439557\pi$
$379$	−300.652	−	300.652i	−0.793276	−	0.793276i	−0.982025	+	0.188750i	$0.939557\pi$
$380$	7.98476	−	117.222i	0.0210125	−	0.308479i
$381$	49.7570	+	49.7570i	0.130596	+	0.130596i
$382$	−43.6049	−	19.0561i	−0.114149	−	0.0498851i
$383$	−135.792	−	135.792i	−0.354547	−	0.354547i	0.507251	−	0.861798i	$-0.330662\pi$
$383$	−135.792	−	135.792i	−0.354547	−	0.354547i	−0.861798	+	0.507251i	$0.830662\pi$
$384$	−124.913	−	474.223i	−0.325296	−	1.23496i
$385$	3.04019	−	103.381i	0.00789661	−	0.268523i
$386$	75.1038	+	191.703i	0.194569	+	0.496640i
$387$	234.225			0.605232
$388$	283.017	+	10.9334i	0.729424	+	0.0281787i
$389$	428.756	+	428.756i	1.10220	+	1.10220i	0.994145	+	0.108054i	$0.0344620\pi$
$389$	428.756	+	428.756i	1.10220	+	1.10220i	0.108054	+	0.994145i	$0.465538\pi$
$390$	243.914	−	516.224i	0.625421	−	1.32365i
$391$		−	622.988i		−	1.59332i
$392$	326.735	−	113.663i	0.833507	−	0.289957i
$393$	−303.219	+	303.219i	−0.771551	+	0.771551i
$394$	169.662	−	388.228i	0.430615	−	0.985351i
$395$	−447.337	−	13.1551i	−1.13250	−	0.0333040i
$396$	195.663	+	7.55876i	0.494099	+	0.0190878i
$397$	194.112			0.488947			0.244474	−	0.969656i	$-0.421385\pi$
$397$	194.112			0.488947			0.244474	+	0.969656i	$0.421385\pi$
$398$	194.930	+	85.1880i	0.489775	+	0.214040i
$399$		−	54.0055i		−	0.135352i
$400$	54.2415	−	396.305i	0.135604	−	0.990763i
$401$	−285.335			−0.711560			−0.355780	−	0.934570i	$-0.615785\pi$
$401$	−285.335			−0.711560			−0.355780	+	0.934570i	$0.615785\pi$
$402$	207.443	−	474.679i	0.516028	−	1.18079i
$403$			227.434i			0.564353i
$404$	409.845	+	15.8329i	1.01447	+	0.0391904i
$405$	−14.6771	+	499.091i	−0.0362397	+	1.23232i
$406$	242.378	+	105.923i	0.596990	+	0.260895i
$407$	60.9789	+	60.9789i	0.149825	+	0.149825i
$408$	−189.052	+	390.752i	−0.463364	+	0.957726i
$409$	−219.624			−0.536978			−0.268489	−	0.963283i	$-0.586524\pi$
$409$	−219.624			−0.536978			−0.268489	+	0.963283i	$0.586524\pi$
$410$	155.112	+	73.2899i	0.378321	+	0.178756i
$411$	−598.830	+	598.830i	−1.45701	+	1.45701i
$412$	199.422	+	7.70398i	0.484035	+	0.0186990i
$413$		−	46.2134i		−	0.111897i
$414$	−465.145	+	182.231i	−1.12354	+	0.440171i
$415$	641.926	+	18.8775i	1.54681	+	0.0454880i
$416$	420.937	+	224.107i	1.01187	+	0.538718i
$417$	40.7100	−	40.7100i	0.0976259	−	0.0976259i
$418$	−40.5608	+	92.8128i	−0.0970354	+	0.222040i
$419$	92.3158	−	92.3158i	0.220324	−	0.220324i	−0.588311	−	0.808635i	$-0.700207\pi$
$419$	92.3158	−	92.3158i	0.220324	−	0.220324i	0.808635	+	0.588311i	$0.200207\pi$
$420$	12.4948	−	183.433i	0.0297496	−	0.436746i
$421$	−203.067	+	203.067i	−0.482345	+	0.482345i	−0.905880	−	0.423535i	$-0.860789\pi$
$421$	−203.067	+	203.067i	−0.482345	+	0.482345i	0.423535	+	0.905880i	$0.360789\pi$
$422$	−5.29432	−	13.5138i	−0.0125458	−	0.0320232i
$423$	199.491	−	199.491i	0.471609	−	0.471609i
$424$	−14.1967	−	40.8097i	−0.0334828	−	0.0962494i
$425$	−264.642	+	235.217i	−0.622686	+	0.553451i
$426$	−483.584	−	211.335i	−1.13517	−	0.496091i
$427$		−	186.671i		−	0.437169i
$428$	241.009	−	223.081i	0.563106	−	0.521217i
$429$	−348.038	+	348.038i	−0.811278	+	0.811278i
$430$	−176.216	+	372.947i	−0.409805	+	0.867318i
$431$	−468.188			−1.08628			−0.543142	−	0.839641i	$-0.682765\pi$
$431$	−468.188			−1.08628			−0.543142	+	0.839641i	$0.682765\pi$
$432$	−203.006	−	15.7083i	−0.469921	−	0.0363617i
$433$	55.1786	+	55.1786i	0.127433	+	0.127433i	0.767947	−	0.640514i	$-0.221278\pi$
$433$	55.1786	+	55.1786i	0.127433	+	0.127433i	−0.640514	+	0.767947i	$0.721278\pi$
$434$	26.7159	+	68.1926i	0.0615574	+	0.157126i
$435$	−768.239	+	724.346i	−1.76607	+	1.66516i
$436$	122.831	+	4.74515i	0.281723	+	0.0108834i
$437$		−	258.417i		−	0.591344i
$438$	335.461	+	856.266i	0.765892	+	1.95494i
$439$	40.4072			0.0920437			0.0460219	−	0.998940i	$-0.485346\pi$
$439$	40.4072			0.0920437			0.0460219	+	0.998940i	$0.485346\pi$
$440$	−159.241	+	305.860i	−0.361911	+	0.695137i
$441$			245.550i			0.556802i
$442$	−153.977	−	393.028i	−0.348365	−	0.889204i
$443$	551.916			1.24586			0.622930	−	0.782277i	$-0.285942\pi$
$443$	551.916			1.24586			0.622930	+	0.782277i	$0.285942\pi$
$444$	104.136	+	112.505i	0.234540	+	0.253389i
$445$	−6.41468	+	218.130i	−0.0144150	+	0.490180i
$446$	−120.277	−	307.009i	−0.269680	−	0.688360i
$447$	228.377	−	228.377i	0.510911	−	0.510911i
$448$	152.536	+	17.7488i	0.340483	+	0.0396178i
$449$			161.753i			0.360252i	0.983644	+	0.180126i	$0.0576506\pi$
$449$			161.753i			0.360252i	−0.983644	+	0.180126i	$0.942349\pi$
$450$	253.032	+	128.787i	0.562292	+	0.286194i
$451$	−104.576	−	104.576i	−0.231877	−	0.231877i
$452$	−27.7027	+	717.103i	−0.0612892	+	1.58651i
$453$	−13.6060			−0.0300354
$454$	470.177	+	205.475i	1.03563	+	0.452589i
$455$	122.652	+	130.084i	0.269565	+	0.285900i
$456$	−78.4195	+	162.085i	−0.171973	+	0.355450i
$457$	−397.309	−	397.309i	−0.869384	−	0.869384i	0.123020	−	0.992404i	$-0.460742\pi$
$457$	−397.309	−	397.309i	−0.869384	−	0.869384i	−0.992404	+	0.123020i	$0.960742\pi$
$458$	15.5636	+	39.7263i	0.0339817	+	0.0867386i
$459$	127.442	+	127.442i	0.277651	+	0.277651i
$460$	59.7879	−	877.731i	0.129974	−	1.90811i
$461$	426.786	+	426.786i	0.925784	+	0.925784i	0.997430	−	0.0716461i	$-0.0228252\pi$
$461$	426.786	+	426.786i	0.925784	+	0.925784i	−0.0716461	+	0.997430i	$0.522825\pi$
$462$	−63.4709	+	145.237i	−0.137383	+	0.314365i
$463$	33.0173	+	33.0173i	0.0713118	+	0.0713118i	0.741863	−	0.670551i	$-0.233942\pi$
$463$	33.0173	+	33.0173i	0.0713118	+	0.0713118i	−0.670551	+	0.741863i	$0.733942\pi$
$464$	−573.634	−	669.853i	−1.23628	−	1.44365i
$465$	−292.228	−	8.59371i	−0.628447	−	0.0184811i
$466$	280.605	−	109.933i	0.602156	−	0.235908i
$467$	771.151			1.65129			0.825644	−	0.564192i	$-0.190812\pi$
$467$	771.151			1.65129			0.825644	+	0.564192i	$0.190812\pi$
$468$	−248.409	+	229.930i	−0.530787	+	0.491303i
$469$	114.705	+	114.705i	0.244574	+	0.244574i
$470$	167.557	+	467.726i	0.356503	+	0.995161i
$471$			8.74904i			0.0185755i
$472$	−67.1048	+	138.699i	−0.142171	+	0.293853i
$473$	251.441	−	251.441i	0.531588	−	0.531588i
$474$	628.447	+	274.642i	1.32584	+	0.579414i
$475$	−109.774	+	97.5686i	−0.231103	+	0.205408i
$476$	−92.3354	−	99.7561i	−0.193982	−	0.209572i
$477$	30.6695			0.0642967
$478$	−6.43055	+	14.7146i	−0.0134530	+	0.0307837i
$479$		−	210.902i		−	0.440295i	−0.975467	−	0.220148i	$-0.929346\pi$
$479$		−	210.902i		−	0.440295i	0.975467	−	0.220148i	$-0.0706539\pi$
$480$	−303.857	+	532.389i	−0.633036	+	1.10914i
$481$	−149.075			−0.309928
$482$	16.8527	+	7.36493i	0.0349642	+	0.0152799i
$483$		−	404.381i		−	0.837227i
$484$	−137.036	+	126.842i	−0.283133	+	0.262071i
$485$	−242.873	−	257.591i	−0.500770	−	0.531115i
$486$	214.689	−	491.259i	0.441746	−	1.01082i
$487$	196.542	+	196.542i	0.403578	+	0.403578i	0.879492	−	0.475914i	$-0.157883\pi$
$487$	196.542	+	196.542i	0.403578	+	0.403578i	−0.475914	+	0.879492i	$0.657883\pi$
$488$	−271.059	+	560.250i	−0.555448	+	1.14805i
$489$	447.371			0.914869
$490$	−390.979	−	184.736i	−0.797916	−	0.377013i
$491$	391.245	−	391.245i	0.796833	−	0.796833i	−0.185762	−	0.982595i	$-0.559475\pi$
$491$	391.245	−	391.245i	0.796833	−	0.796833i	0.982595	+	0.185762i	$0.0594753\pi$
$492$	−178.589	−	192.941i	−0.362985	−	0.392157i
$493$			780.630i			1.58343i
$494$	−63.8702	−	163.029i	−0.129292	−	0.330019i
$495$	−167.910	−	178.085i	−0.339213	−	0.359768i
$496$	18.8384	−	243.458i	0.0379806	−	0.490842i
$497$	116.857	−	116.857i	0.235124	−	0.235124i
$498$	−901.819	−	394.111i	−1.81088	−	0.791387i
$499$	−240.105	+	240.105i	−0.481173	+	0.481173i	−0.905506	−	0.424333i	$-0.860509\pi$
$499$	−240.105	+	240.105i	−0.481173	+	0.481173i	0.424333	+	0.905506i	$0.360509\pi$
$500$	−395.428	+	306.001i	−0.790857	+	0.612001i
$501$	80.3446	−	80.3446i	0.160368	−	0.160368i
$502$	858.692	−	336.411i	1.71054	−	0.670142i
$503$	459.843	−	459.843i	0.914200	−	0.914200i	−0.0823992	−	0.996599i	$-0.526258\pi$
$503$	459.843	−	459.843i	0.914200	−	0.914200i	0.996599	+	0.0823992i	$0.0262582\pi$
$504$	−47.4724	+	98.1205i	−0.0941912	+	0.194684i
$505$	−351.713	−	373.025i	−0.696460	−	0.738664i
$506$	−303.709	+	694.960i	−0.600216	+	1.37344i
$507$		−	203.369i		−	0.401122i
$508$	73.4117	+	2.83600i	0.144511	+	0.00558268i
$509$	348.808	−	348.808i	0.685281	−	0.685281i	−0.275904	−	0.961185i	$-0.588977\pi$
$509$	348.808	−	348.808i	0.685281	−	0.685281i	0.961185	+	0.275904i	$0.0889772\pi$
$510$	510.815	−	182.993i	1.00160	−	0.358810i
$511$	−287.978			−0.563557
$512$	−432.030	−	274.761i	−0.843809	−	0.536644i
$513$	52.8633	+	52.8633i	0.103047	+	0.103047i
$514$	−487.447	+	190.968i	−0.948341	+	0.371533i
$515$	−171.136	−	181.507i	−0.332304	−	0.352440i
$516$	463.903	−	429.394i	0.899037	−	0.832159i
$517$		−	428.308i		−	0.828448i
$518$	−44.6979	+	17.5114i	−0.0862893	+	0.0338057i
$519$	928.738			1.78948
$520$	−179.221	−	568.516i	−0.344655	−	1.09330i
$521$		−	54.0067i		−	0.103660i	−0.998656	−	0.0518298i	$-0.983495\pi$
$521$		−	54.0067i		−	0.103660i	0.998656	−	0.0518298i	$-0.0165053\pi$
$522$	582.846	−	228.343i	1.11656	−	0.437438i
$523$	−367.680			−0.703022			−0.351511	−	0.936184i	$-0.614332\pi$
$523$	−367.680			−0.703022			−0.351511	+	0.936184i	$0.614332\pi$
$524$	−17.2826	+	447.372i	−0.0329821	+	0.853763i
$525$	−171.778	+	152.679i	−0.327197	+	0.290817i
$526$	−532.409	+	208.583i	−1.01218	+	0.396545i
$527$	−152.837	+	152.837i	−0.290013	+	0.290013i
$528$	401.386	−	343.730i	0.760201	−	0.651004i
$529$		−	1405.97i		−	2.65778i
$530$	−23.0739	+	48.8339i	−0.0435356	+	0.0921395i
$531$	−77.3333	−	77.3333i	−0.145637	−	0.145637i
$532$	−38.3010	−	41.3791i	−0.0719943	−	0.0777803i
$533$	255.658			0.479659
$534$	133.921	−	306.443i	0.250788	−	0.573863i
$535$	−410.330	−	12.0668i	−0.766973	−	0.0225548i
$536$	−177.702	−	510.820i	−0.331533	−	0.953022i
$537$	−678.166	−	678.166i	−1.26288	−	1.26288i
$538$	−356.794	+	139.782i	−0.663185	+	0.259817i
$539$	263.598	+	263.598i	0.489050	+	0.489050i
$540$	167.323	+	191.784i	0.309858	+	0.355156i
$541$	−39.4092	−	39.4092i	−0.0728451	−	0.0728451i	0.669746	−	0.742591i	$-0.266403\pi$
$541$	−39.4092	−	39.4092i	−0.0728451	−	0.0728451i	−0.742591	+	0.669746i	$0.766403\pi$
$542$	−506.212	−	221.224i	−0.933971	−	0.408161i
$543$	−92.1521	−	92.1521i	−0.169709	−	0.169709i
$544$	132.271	+	433.472i	0.243145	+	0.796823i
$545$	−105.409	−	111.796i	−0.193411	−	0.205131i
$546$	−99.9463	−	255.114i	−0.183052	−	0.467241i
$547$	428.552			0.783459			0.391730	−	0.920080i	$-0.371877\pi$
$547$	428.552			0.783459			0.391730	+	0.920080i	$0.371877\pi$
$548$	−34.1316	+	883.517i	−0.0622839	+	1.61226i
$549$	−312.375	−	312.375i	−0.568989	−	0.568989i
$550$	409.884	−	133.377i	0.745243	−	0.242503i
$551$			323.808i			0.587673i
$552$	−587.186	+	1213.65i	−1.06374	+	2.19865i
$553$	−151.863	+	151.863i	−0.274616	+	0.274616i
$554$	147.930	−	338.499i	0.267022	−	0.611009i
$555$	5.63288	−	191.545i	0.0101493	−	0.345126i
$556$	2.32035	−	60.0638i	0.00417330	−	0.108028i
$557$	−816.333			−1.46559			−0.732794	−	0.680450i	$-0.761784\pi$
$557$	−816.333			−1.46559			−0.732794	+	0.680450i	$0.761784\pi$
$558$	158.820	+	69.4069i	0.284623	+	0.124385i
$559$			614.698i			1.09964i
$560$	−120.518	−	149.408i	−0.215211	−	0.266800i
$561$	−467.766			−0.833807
$562$	−139.330	+	318.819i	−0.247917	+	0.567294i
$563$		−	242.788i		−	0.431240i	−0.976477	−	0.215620i	$-0.930823\pi$
$563$		−	242.788i		−	0.431240i	0.976477	−	0.215620i	$-0.0691772\pi$
$564$	29.3919	−	760.827i	0.0521132	−	1.34898i
$565$	652.679	−	615.389i	1.15518	−	1.08918i
$566$	60.8404	+	26.5883i	0.107492	+	0.0469758i
$567$	169.432	+	169.432i	0.298822	+	0.298822i
$568$	−520.402	+	181.035i	−0.916201	+	0.318724i
$569$	310.112			0.545011			0.272506	−	0.962154i	$-0.412148\pi$
$569$	310.112			0.545011			0.272506	+	0.962154i	$0.412148\pi$
$570$	211.888	−	75.9060i	0.371733	−	0.133168i
$571$	403.169	−	403.169i	0.706075	−	0.706075i	−0.259632	−	0.965708i	$-0.583601\pi$
$571$	403.169	−	403.169i	0.706075	−	0.706075i	0.965708	+	0.259632i	$0.0836014\pi$
$572$	−19.8372	+	513.497i	−0.0346804	+	0.897723i
$573$		−	91.1587i		−	0.159090i
$574$	76.6551	−	30.0313i	0.133545	−	0.0523193i
$575$	−821.962	+	730.570i	−1.42950	+	1.27056i
$576$	284.955	−	225.553i	0.494713	−	0.391585i
$577$	−47.9244	+	47.9244i	−0.0830580	+	0.0830580i	−0.747415	−	0.664357i	$-0.768705\pi$
$577$	−47.9244	+	47.9244i	−0.0830580	+	0.0830580i	0.664357	+	0.747415i	$0.268705\pi$
$578$	−70.8156	+	162.043i	−0.122518	+	0.280351i
$579$	−278.888	+	278.888i	−0.481671	+	0.481671i
$580$	−74.9168	+	1099.83i	−0.129167	+	1.89627i
$581$	217.922	−	217.922i	0.375081	−	0.375081i
$582$	197.912	+	505.172i	0.340055	+	0.867993i
$583$	32.9238	−	32.9238i	0.0564732	−	0.0564732i
$584$	864.298	+	418.162i	1.47996	+	0.716031i
$585$	422.928	+	12.4373i	0.722953	+	0.0212603i
$586$	−356.452	−	155.776i	−0.608280	−	0.265829i
$587$		−	466.709i		−	0.795075i	−0.917586	−	0.397538i	$-0.869865\pi$
$587$		−	466.709i		−	0.795075i	0.917586	−	0.397538i	$-0.130135\pi$
$588$	450.155	+	486.333i	0.765570	+	0.827097i
$589$	−63.3971	+	63.3971i	−0.107635	+	0.107635i
$590$	181.316	−	64.9540i	0.307315	−	0.110091i
$591$	811.614			1.37329
$592$	159.578	+	12.3479i	0.269557	+	0.0208579i
$593$	−214.674	−	214.674i	−0.362013	−	0.362013i	0.502541	−	0.864554i	$-0.332399\pi$
$593$	−214.674	−	214.674i	−0.362013	−	0.362013i	−0.864554	+	0.502541i	$0.832399\pi$
$594$	−80.0364	−	204.293i	−0.134741	−	0.343928i
$595$	−4.99458	+	169.840i	−0.00839425	+	0.285445i
$596$	13.0168	−	336.949i	0.0218403	−	0.565350i
$597$			407.514i			0.682603i
$598$	−478.245	−	1220.72i	−0.799741	−	2.04134i
$599$	−1167.57			−1.94920			−0.974600	−	0.223954i	$-0.928104\pi$
$599$	−1167.57			−1.94920			−0.974600	+	0.223954i	$0.928104\pi$
$600$	737.252	−	208.797i	1.22875	−	0.347995i
$601$			82.0258i			0.136482i	0.997669	+	0.0682411i	$0.0217387\pi$
$601$			82.0258i			0.136482i	−0.997669	+	0.0682411i	$0.978261\pi$
$602$	72.2065	+	184.307i	0.119944	+	0.306159i
$603$	383.894			0.636640
$604$	−10.4250	+	9.64946i	−0.0172599	+	0.0159759i
$605$	233.311	+	6.86112i	0.385639	+	0.0113407i
$606$	286.603	+	731.556i	0.472942	+	1.20719i
$607$	419.964	−	419.964i	0.691869	−	0.691869i	−0.270774	−	0.962643i	$-0.587280\pi$
$607$	419.964	−	419.964i	0.691869	−	0.691869i	0.962643	+	0.270774i	$0.0872796\pi$
$608$	54.8663	+	179.805i	0.0902407	+	0.295732i
$609$			506.706i			0.832029i
$610$	732.394	−	262.371i	1.20065	−	0.430116i
$611$	523.542	+	523.542i	0.856861	+	0.856861i
$612$	−321.445	−	12.4179i	−0.525237	−	0.0202907i
$613$	−725.219			−1.18307			−0.591533	−	0.806281i	$-0.701477\pi$
$613$	−725.219			−1.18307			−0.591533	+	0.806281i	$0.701477\pi$
$614$	−948.408	−	414.471i	−1.54464	−	0.675034i
$615$	−9.66016	+	328.492i	−0.0157076	+	0.534134i
$616$	54.3709	+	156.294i	0.0882645	+	0.253725i
$617$	−321.786	−	321.786i	−0.521534	−	0.521534i	0.396501	−	0.918034i	$-0.370224\pi$
$617$	−321.786	−	321.786i	−0.521534	−	0.521534i	−0.918034	+	0.396501i	$0.870224\pi$
$618$	139.455	+	355.960i	0.225656	+	0.575988i
$619$	161.377	+	161.377i	0.260706	+	0.260706i	0.825341	−	0.564635i	$-0.190983\pi$
$619$	161.377	+	161.377i	0.260706	+	0.260706i	−0.564635	+	0.825341i	$0.690983\pi$
$620$	−230.000	+	200.665i	−0.370968	+	0.323653i
$621$	395.828	+	395.828i	0.637404	+	0.637404i
$622$	386.705	−	884.873i	0.621712	−	1.42262i
$623$	74.0512	+	74.0512i	0.118862	+	0.118862i
$624$	−70.4757	+	910.793i	−0.112942	+	1.45960i
$625$	620.683	+	73.3285i	0.993094	+	0.117326i
$626$	253.332	−	99.2481i	0.404683	−	0.158543i
$627$	−194.031			−0.309459
$628$	6.20486	+	6.70353i	0.00988035	+	0.0106744i
$629$	−100.179	−	100.179i	−0.159267	−	0.159267i
$630$	128.269	−	45.9508i	0.203602	−	0.0729377i
$631$			620.361i			0.983140i	0.870838	+	0.491570i	$0.163577\pi$
$631$			620.361i			0.983140i	−0.870838	+	0.491570i	$0.836423\pi$
$632$	676.295	−	235.266i	1.07009	−	0.372257i
$633$	19.6598	−	19.6598i	0.0310581	−	0.0310581i
$634$	−631.724	−	276.074i	−0.996410	−	0.435448i
$635$	−62.9990	−	66.8165i	−0.0992110	−	0.105223i
$636$	60.7438	−	56.2251i	0.0955092	−	0.0884043i
$637$	−644.419			−1.01165
$638$	380.560	−	870.813i	0.596490	−	1.36491i
$639$		−	391.096i		−	0.612043i
$640$	144.757	+	623.414i	0.226183	+	0.974085i
$641$	890.879			1.38983			0.694914	−	0.719093i	$-0.255443\pi$
$641$	890.879			1.38983			0.694914	+	0.719093i	$0.255443\pi$
$642$	576.459	+	251.922i	0.897911	+	0.392402i
$643$		−	304.169i		−	0.473047i	−0.971626	−	0.236523i	$-0.923992\pi$
$643$		−	304.169i		−	0.473047i	0.971626	−	0.236523i	$-0.0760080\pi$
$644$	−286.788	−	309.837i	−0.445324	−	0.481113i
$645$	−789.818	−	23.2266i	−1.22452	−	0.0360103i
$646$	66.6352	−	152.477i	0.103150	−	0.236033i
$647$	71.6597	+	71.6597i	0.110757	+	0.110757i	0.760313	−	0.649556i	$-0.225045\pi$
$647$	71.6597	+	71.6597i	0.110757	+	0.110757i	−0.649556	+	0.760313i	$0.725045\pi$
$648$	−262.485	−	754.538i	−0.405070	−	1.16441i
$649$	−166.035			−0.255832
$650$	−337.988	+	664.054i	−0.519982	+	1.02162i
$651$	−99.2060	+	99.2060i	−0.152390	+	0.152390i
$652$	342.776	−	317.278i	0.525731	−	0.486622i
$653$		−	304.063i		−	0.465640i	−0.972520	−	0.232820i	$-0.925205\pi$
$653$		−	304.063i		−	0.465640i	0.972520	−	0.232820i	$-0.0747953\pi$
$654$	85.8953	+	219.248i	0.131338	+	0.335242i
$655$	407.181	−	383.916i	0.621650	−	0.586132i
$656$	−273.670	−	21.1761i	−0.417179	−	0.0322807i
$657$	−481.900	+	481.900i	−0.733486	+	0.733486i
$658$	218.475	+	95.4771i	0.332028	+	0.145102i
$659$	560.205	−	560.205i	0.850083	−	0.850083i	−0.140060	−	0.990143i	$-0.544730\pi$
$659$	560.205	−	560.205i	0.850083	−	0.850083i	0.990143	+	0.140060i	$0.0447296\pi$
$660$	−659.038	−	44.8913i	−0.998542	−	0.0680171i
$661$	−863.183	+	863.183i	−1.30588	+	1.30588i	−0.381511	+	0.924364i	$0.624596\pi$
$661$	−863.183	+	863.183i	−1.30588	+	1.30588i	−0.924364	+	0.381511i	$0.875404\pi$
$662$	−538.452	+	210.950i	−0.813372	+	0.318656i
$663$	571.774	−	571.774i	0.862404	−	0.862404i
$664$	−970.480	+	337.606i	−1.46157	+	0.508443i
$665$	−2.07176	+	70.4500i	−0.00311544	+	0.105940i
$666$	−45.4938	+	104.101i	−0.0683090	+	0.156307i
$667$			2424.59i			3.63507i
$668$	4.57941	−	118.541i	0.00685540	−	0.177456i
$669$	446.634	−	446.634i	0.667614	−	0.667614i
$670$	−288.818	+	611.259i	−0.431072	+	0.912327i
$671$	−670.671			−0.999509
$672$	85.8567	+	281.366i	0.127763	+	0.418699i
$673$	720.376	+	720.376i	1.07040	+	1.07040i	0.997327	+	0.0730683i	$0.0232791\pi$
$673$	720.376	+	720.376i	1.07040	+	1.07040i	0.0730683	+	0.997327i	$0.476721\pi$
$674$	−528.594	+	207.088i	−0.784264	+	0.307252i
$675$	18.6956	−	317.595i	0.0276971	−	0.470511i
$676$	−144.230	−	155.822i	−0.213358	−	0.230505i
$677$			110.173i			0.162738i	0.996684	+	0.0813688i	$0.0259292\pi$
$677$			110.173i			0.162738i	−0.996684	+	0.0813688i	$0.974071\pi$
$678$	−1280.00	+	501.467i	−1.88790	+	0.739626i
$679$	−169.899			−0.250219
$680$	261.608	−	502.482i	0.384718	−	0.738944i
$681$			982.933i			1.44337i
$682$	245.002	−	95.9848i	0.359240	−	0.140740i
$683$	−537.997			−0.787697			−0.393849	−	0.919175i	$-0.628857\pi$
$683$	−537.997			−0.787697			−0.393849	+	0.919175i	$0.628857\pi$
$684$	−133.336	−	5.15098i	−0.194936	−	0.00753067i
$685$	804.143	−	758.198i	1.17393	−	1.10686i
$686$	−412.163	+	161.474i	−0.600821	+	0.235385i
$687$	−57.7934	+	57.7934i	−0.0841244	+	0.0841244i
$688$	50.9154	−	658.005i	0.0740049	−	0.956402i
$689$			80.4890i			0.116820i
$690$	1586.56	−	568.366i	2.29937	−	0.823719i
$691$	−433.458	−	433.458i	−0.627290	−	0.627290i	0.320095	−	0.947385i	$-0.396285\pi$
$691$	−433.458	−	433.458i	−0.627290	−	0.627290i	−0.947385	+	0.320095i	$0.896285\pi$
$692$	711.601	−	658.665i	1.02832	−	0.951828i
$693$	−117.459			−0.169494
$694$	−150.261	+	343.833i	−0.216514	+	0.495437i
$695$	−54.6678	+	51.5443i	−0.0786587	+	0.0741645i
$696$	735.769	−	1520.76i	1.05714	−	2.18500i
$697$	171.803	+	171.803i	0.246490	+	0.246490i
$698$	833.084	−	326.379i	1.19353	−	0.467591i
$699$	408.221	+	408.221i	0.584007	+	0.584007i
$700$	−23.3363	+	238.809i	−0.0333376	+	0.341155i
$701$	−390.739	−	390.739i	−0.557402	−	0.557402i	0.371165	−	0.928567i	$-0.378958\pi$
$701$	−390.739	−	390.739i	−0.557402	−	0.557402i	−0.928567	+	0.371165i	$0.878958\pi$
$702$	347.550	+	151.886i	0.495086	+	0.216361i
$703$	−41.5546	−	41.5546i	−0.0591103	−	0.0591103i
$704$	63.7677	−	548.031i	0.0905791	−	0.778454i
$705$	−692.475	+	652.911i	−0.982234	+	0.926115i
$706$	−293.772	−	749.855i	−0.416108	−	1.06212i
$707$	−246.035			−0.347999
$708$	−294.937	−	11.3939i	−0.416578	−	0.0160930i
$709$	340.829	+	340.829i	0.480718	+	0.480718i	0.905361	−	0.424643i	$-0.139600\pi$
$709$	340.829	+	340.829i	0.480718	+	0.480718i	−0.424643	+	0.905361i	$0.639600\pi$
$710$	622.726	+	294.236i	0.877079	+	0.414418i
$711$			508.252i			0.714842i
$712$	−114.720	−	329.774i	−0.161124	−	0.463166i
$713$	−474.702	+	474.702i	−0.665782	+	0.665782i
$714$	104.273	−	238.602i	0.146041	−	0.334176i
$715$	467.366	−	440.663i	0.653658	−	0.616312i
$716$	−1000.57	−	38.6535i	−1.39744	−	0.0539854i
$717$	−30.7618			−0.0429035
$718$	779.748	+	340.764i	1.08600	+	0.474601i
$719$			1185.79i			1.64922i	0.565702	+	0.824609i	$0.308605\pi$
$719$			1185.79i			1.64922i	−0.565702	+	0.824609i	$0.691395\pi$
$720$	−451.694	−	48.3446i	−0.627352	−	0.0671453i
$721$	−119.716			−0.166041
$722$	−261.483	+	598.335i	−0.362164	+	0.828719i
$723$			35.2316i			0.0487298i
$724$	−135.962	−	5.25241i	−0.187793	−	0.00725470i
$725$	1029.95	−	915.435i	1.42062	−	1.26267i
$726$	−327.771	−	143.241i	−0.451475	−	0.197302i
$727$	−493.648	−	493.648i	−0.679021	−	0.679021i	0.280758	−	0.959779i	$-0.409414\pi$
$727$	−493.648	−	493.648i	−0.679021	−	0.679021i	−0.959779	+	0.280758i	$0.909414\pi$
$728$	−257.507	−	124.586i	−0.353718	−	0.171135i
$729$	128.254			0.175932
$730$	−404.759	−	1129.86i	−0.554464	−	1.54776i
$731$	−413.079	+	413.079i	−0.565088	+	0.565088i
$732$	−1191.35	−	46.0236i	−1.62753	−	0.0628738i
$733$		−	864.330i		−	1.17917i	−0.807707	−	0.589584i	$-0.799292\pi$
$733$		−	864.330i		−	1.17917i	0.807707	−	0.589584i	$-0.200708\pi$
$734$	−537.025	+	210.391i	−0.731642	+	0.286637i
$735$	24.3497	−	828.006i	0.0331288	−	1.12654i
$736$	410.826	+	1346.34i	0.558187	+	1.82926i
$737$	412.111	−	412.111i	0.559174	−	0.559174i
$738$	78.0200	−	178.528i	0.105718	−	0.241908i
$739$	667.334	−	667.334i	0.903023	−	0.903023i	−0.0926732	−	0.995697i	$-0.529541\pi$
$739$	667.334	−	667.334i	0.903023	−	0.903023i	0.995697	+	0.0926732i	$0.0295412\pi$
$740$	−131.529	−	150.757i	−0.177741	−	0.203726i
$741$	237.173	−	237.173i	0.320072	−	0.320072i
$742$	9.45476	+	24.1334i	0.0127423	+	0.0325247i
$743$	87.5208	−	87.5208i	0.117794	−	0.117794i	−0.645753	−	0.763547i	$-0.723456\pi$
$743$	87.5208	−	87.5208i	0.117794	−	0.117794i	0.763547	+	0.645753i	$0.223456\pi$
$744$	441.797	−	153.690i	0.593813	−	0.206573i
$745$	−306.678	+	289.156i	−0.411648	+	0.388129i
$746$	1101.48	+	481.368i	1.47652	+	0.645265i
$747$		−	729.341i		−	0.976360i
$748$	−358.403	+	331.742i	−0.479148	+	0.443505i
$749$	−139.300	+	139.300i	−0.185981	+	0.185981i
$750$	−840.465	−	459.369i	−1.12062	−	0.612492i
$751$	809.874			1.07839			0.539197	−	0.842180i	$-0.318728\pi$
$751$	809.874			1.07839			0.539197	+	0.842180i	$0.318728\pi$
$752$	−517.062	−	603.791i	−0.687582	−	0.802914i
$753$	1249.22	+	1249.22i	1.65899	+	1.65899i
$754$	599.261	+	1529.62i	0.794775	+	2.02867i
$755$	17.7490	+	0.521956i	0.0235086	+	0.000691332i
$756$	122.049	+	4.71494i	0.161441	+	0.00623669i
$757$			1268.47i			1.67565i	0.545937	+	0.837827i	$0.316174\pi$
$757$			1268.47i			1.67565i	−0.545937	+	0.837827i	$0.683826\pi$
$758$	−310.195	−	791.776i	−0.409229	−	1.04456i
$759$	−1452.85			−1.91417
$760$	108.516	−	208.431i	0.142784	−	0.274251i
$761$			332.602i			0.437059i	0.975830	+	0.218529i	$0.0701259\pi$
$761$			332.602i			0.437059i	−0.975830	+	0.218529i	$0.929874\pi$
$762$	51.3365	+	131.037i	0.0673707	+	0.171964i
$763$	−73.7372			−0.0966411
$764$	−64.6502	−	69.8460i	−0.0846206	−	0.0914214i
$765$	275.851	+	292.567i	0.360590	+	0.382440i
$766$	−140.102	−	357.612i	−0.182901	−	0.466856i
$767$	202.953	−	202.953i	0.264606	−	0.264606i
$768$	150.882	−	969.123i	0.196461	−	1.26188i
$769$			519.527i			0.675588i	0.941220	+	0.337794i	$0.109681\pi$
$769$			519.527i			0.675588i	−0.941220	+	0.337794i	$0.890319\pi$
$770$	88.3691	−	187.026i	0.114765	−	0.242891i
$771$	−709.134	−	709.134i	−0.919759	−	0.919759i
$772$	−15.8958	+	411.473i	−0.0205904	+	0.532996i
$773$	−895.057			−1.15790			−0.578950	−	0.815363i	$-0.696537\pi$
$773$	−895.057			−1.15790			−0.578950	+	0.815363i	$0.696537\pi$
$774$	429.249	+	187.589i	0.554586	+	0.242364i
$775$	380.880	+	22.4209i	0.491458	+	0.0289302i
$776$	509.911	+	246.704i	0.657102	+	0.317917i
$777$	−65.0260	−	65.0260i	−0.0836886	−	0.0836886i
$778$	442.366	+	1129.14i	0.568594	+	1.45134i
$779$	71.2645	+	71.2645i	0.0914820	+	0.0914820i
$780$	860.448	−	750.702i	1.10314	−	0.962438i
$781$	−419.842	−	419.842i	−0.537570	−	0.537570i
$782$	498.948	−	1141.71i	0.638041	−	1.45999i
$783$	−495.989	−	495.989i	−0.633447	−	0.633447i
$784$	689.819	+	53.3771i	0.879872	+	0.0680831i
$785$	0.335631	−	11.4131i	0.000427556	−	0.0145390i
$786$	−798.539	+	312.845i	−1.01595	+	0.398022i
$787$	−58.1451			−0.0738820			−0.0369410	−	0.999317i	$-0.511761\pi$
$787$	−58.1451			−0.0738820			−0.0369410	+	0.999317i	$0.511761\pi$
$788$	621.860	−	575.600i	0.789162	−	0.730457i
$789$	−774.544	−	774.544i	−0.981678	−	0.981678i
$790$	−809.271	−	382.378i	−1.02439	−	0.484023i
$791$		−	430.486i		−	0.544230i
$792$	352.526	+	170.558i	0.445109	+	0.215351i
$793$	819.795	−	819.795i	1.03379	−	1.03379i
$794$	355.737	+	155.463i	0.448032	+	0.195798i
$795$	−103.419	−	3.04131i	−0.130087	−	0.00382555i
$796$	289.011	+	312.238i	0.363079	+	0.392258i
$797$	−238.679			−0.299472			−0.149736	−	0.988726i	$-0.547842\pi$
$797$	−238.679			−0.299472			−0.149736	+	0.988726i	$0.547842\pi$
$798$	43.2528	−	98.9727i	0.0542015	−	0.124026i
$799$			703.644i			0.880656i
$800$	416.804	−	682.843i	0.521005	−	0.853554i
$801$	247.834			0.309406
$802$	−522.917	−	228.524i	−0.652016	−	0.284942i
$803$			1034.64i			1.28847i
$804$	760.337	−	703.776i	0.945693	−	0.875343i
$805$	−15.5129	+	527.513i	−0.0192707	+	0.655295i
$806$	−182.151	+	416.805i	−0.225994	+	0.517128i
$807$	−519.060	−	519.060i	−0.643197	−	0.643197i
$808$	738.418	+	357.259i	0.913883	+	0.442152i
$809$	612.464			0.757062			0.378531	−	0.925589i	$-0.376429\pi$
$809$	612.464			0.757062			0.378531	+	0.925589i	$0.376429\pi$
$810$	−426.617	+	902.899i	−0.526688	+	1.11469i
$811$	618.905	−	618.905i	0.763138	−	0.763138i	−0.213750	−	0.976888i	$-0.568568\pi$
$811$	618.905	−	618.905i	0.763138	−	0.763138i	0.976888	+	0.213750i	$0.0685679\pi$
$812$	359.358	+	388.239i	0.442559	+	0.478126i
$813$		−	1058.27i		−	1.30168i
$814$	62.9146	+	160.590i	0.0772907	+	0.197285i
$815$	−583.594	−	17.1621i	−0.716066	−	0.0210578i
$816$	−659.416	+	564.697i	−0.808108	+	0.692030i
$817$	−171.346	+	171.346i	−0.209726	+	0.209726i
$818$	−402.492	−	175.896i	−0.492044	−	0.215032i
$819$	143.576	−	143.576i	0.175307	−	0.175307i
$820$	225.566	+	258.542i	0.275081	+	0.315295i
$821$	67.0385	−	67.0385i	0.0816547	−	0.0816547i	−0.665100	−	0.746755i	$-0.731611\pi$
$821$	67.0385	−	67.0385i	0.0816547	−	0.0816547i	0.746755	+	0.665100i	$0.231611\pi$
$822$	−1577.04	+	617.839i	−1.91854	+	0.751629i
$823$	−720.633	+	720.633i	−0.875617	+	0.875617i	−0.993078	−	0.117461i	$-0.962525\pi$
$823$	−720.633	+	720.633i	−0.875617	+	0.875617i	0.117461	+	0.993078i	$0.462525\pi$
$824$	359.299	+	173.835i	0.436043	+	0.210965i
$825$	548.543	+	617.164i	0.664901	+	0.748077i
$826$	37.0121	−	84.6925i	0.0448088	−	0.102533i
$827$		−	1189.91i		−	1.43883i	−0.694582	−	0.719413i	$-0.744411\pi$
$827$		−	1189.91i		−	1.43883i	0.694582	−	0.719413i	$-0.255589\pi$
$828$	−998.390	−	38.5693i	−1.20579	−	0.0465813i
$829$	−77.7453	+	77.7453i	−0.0937821	+	0.0937821i	−0.752441	−	0.658659i	$-0.771124\pi$
$829$	−77.7453	+	77.7453i	−0.0937821	+	0.0937821i	0.658659	+	0.752441i	$0.271124\pi$
$830$	1161.30	+	548.711i	1.39916	+	0.661098i
$831$	707.653			0.851567
$832$	591.940	+	747.833i	0.711466	+	0.898837i
$833$	−433.052	−	433.052i	−0.519870	−	0.519870i
$834$	107.211	−	42.0023i	0.128551	−	0.0503625i
$835$	−107.891	+	101.727i	−0.129211	+	0.121829i
$836$	−148.667	+	137.607i	−0.177831	+	0.164602i
$837$		−	194.216i		−	0.232038i
$838$	243.117	−	95.2463i	0.290116	−	0.113659i
$839$	−1281.90			−1.52789			−0.763947	−	0.645279i	$-0.776741\pi$
$839$	−1281.90			−1.52789			−0.763947	+	0.645279i	$0.776741\pi$
$840$	169.809	−	326.160i	0.202154	−	0.388286i
$841$		−	2197.12i		−	2.61251i
$842$	−534.785	+	209.514i	−0.635136	+	0.248828i
$843$	−666.511			−0.790641
$844$	1.12055	−	29.0061i	0.00132767	−	0.0343674i
$845$	−7.80165	+	265.294i	−0.00923273	+	0.313957i
$846$	525.365	−	205.823i	0.620999	−	0.243290i
$847$	79.2049	−	79.2049i	0.0935123	−	0.0935123i
$848$	6.66689	−	86.1596i	0.00786190	−	0.101603i
$849$			127.191i			0.149812i
$850$	−673.377	+	219.118i	−0.792208	+	0.257785i
$851$	−311.151	−	311.151i	−0.365629	−	0.365629i
$852$	−716.979	−	774.600i	−0.841524	−	0.909155i
$853$	−62.5726			−0.0733559			−0.0366779	−	0.999327i	$-0.511678\pi$
$853$	−62.5726			−0.0733559			−0.0366779	+	0.999327i	$0.511678\pi$
$854$	149.504	−	342.101i	0.175063	−	0.400587i
$855$	114.424	+	121.358i	0.133829	+	0.141939i
$856$	620.348	−	215.804i	0.724706	−	0.252107i
$857$	1102.12	+	1102.12i	1.28602	+	1.28602i	0.937183	+	0.348838i	$0.113423\pi$
$857$	1102.12	+	1102.12i	1.28602	+	1.28602i	0.348838	+	0.937183i	$0.386577\pi$
$858$	−916.570	+	359.086i	−1.06826	+	0.418516i
$859$	−677.212	−	677.212i	−0.788373	−	0.788373i	0.192855	−	0.981227i	$-0.438225\pi$
$859$	−677.212	−	677.212i	−0.788373	−	0.788373i	−0.981227	+	0.192855i	$0.938225\pi$
$860$	−621.632	+	542.346i	−0.722828	+	0.630635i
$861$	111.517	+	111.517i	0.129520	+	0.129520i
$862$	−858.020	−	374.970i	−0.995383	−	0.435000i
$863$	−448.822	−	448.822i	−0.520072	−	0.520072i	0.397521	−	0.917593i	$-0.369871\pi$
$863$	−448.822	−	448.822i	−0.520072	−	0.520072i	−0.917593	+	0.397521i	$0.869871\pi$
$864$	−359.456	−	191.374i	−0.416036	−	0.221497i
$865$	−1211.53	−	35.6283i	−1.40062	−	0.0411888i
$866$	56.9302	+	145.315i	0.0657393	+	0.167800i
$867$	−338.761			−0.390728
$868$	−5.65445	+	146.369i	−0.00651435	+	0.168628i
$869$	545.611	+	545.611i	0.627860	+	0.627860i
$870$	−1988.03	+	712.186i	−2.28509	+	0.818605i
$871$			1007.49i			1.15670i
$872$	221.305	+	107.071i	0.253790	+	0.122788i
$873$	−284.307	+	284.307i	−0.325667	+	0.325667i
$874$	206.965	−	473.586i	0.236802	−	0.541860i
$875$	229.941	−	192.579i	0.262790	−	0.220090i
$876$	−71.0006	+	1837.89i	−0.0810509	+	2.09805i
$877$	834.366			0.951387			0.475693	−	0.879611i	$-0.342197\pi$
$877$	834.366			0.951387			0.475693	+	0.879611i	$0.342197\pi$
$878$	74.0518	+	32.3619i	0.0843415	+	0.0368587i
$879$		−	745.184i		−	0.847764i
$880$	−536.793	+	432.997i	−0.609992	+	0.492042i
$881$	678.979			0.770691			0.385346	−	0.922772i	$-0.374082\pi$
$881$	678.979			0.770691			0.385346	+	0.922772i	$0.374082\pi$
$882$	−196.659	+	450.004i	−0.222970	+	0.510208i
$883$			708.993i			0.802937i	0.915873	+	0.401468i	$0.131500\pi$
$883$			708.993i			0.802937i	−0.915873	+	0.401468i	$0.868500\pi$
$884$	32.5894	−	843.598i	0.0368659	−	0.954297i
$885$	253.103	+	268.441i	0.285993	+	0.303323i
$886$	1011.46	+	442.027i	1.14161	+	0.498902i
$887$	472.922	+	472.922i	0.533170	+	0.533170i	0.921514	−	0.388344i	$-0.126953\pi$
$887$	472.922	+	472.922i	0.533170	+	0.533170i	−0.388344	+	0.921514i	$0.626953\pi$
$888$	100.739	+	289.583i	0.113444	+	0.326106i
$889$	−44.0700			−0.0495726
$890$	−186.455	+	394.616i	−0.209500	+	0.443389i
$891$	608.735	−	608.735i	0.683204	−	0.683204i
$892$	25.4568	−	658.966i	0.0285390	−	0.738751i
$893$			291.874i			0.326846i
$894$	601.439	−	235.627i	0.672750	−	0.263565i
$895$	858.649	+	910.681i	0.959384	+	1.01752i
$896$	265.329	+	154.693i	0.296126	+	0.172648i
$897$	1775.90	−	1775.90i	1.97982	−	1.97982i
$898$	−129.547	+	296.435i	−0.144262	+	0.330106i
$899$	594.822	−	594.822i	0.661648	−	0.661648i
$900$	360.570	+	438.672i	0.400634	+	0.487414i
$901$	−54.0889	+	54.0889i	−0.0600321	+	0.0600321i
$902$	−107.896	−	275.406i	−0.119619	−	0.305328i
$903$	−268.129	+	268.129i	−0.296931	+	0.296931i
$904$	−625.093	+	1292.00i	−0.691475	+	1.42921i
$905$	116.677	+	123.747i	0.128925	+	0.136737i
$906$	−24.9350	−	10.8970i	−0.0275220	−	0.0120276i
$907$		−	27.0583i		−	0.0298328i	−0.999889	−	0.0149164i	$-0.995252\pi$
$907$		−	27.0583i		−	0.0298328i	0.999889	−	0.0149164i	$-0.00474821\pi$
$908$	697.100	+	753.125i	0.767732	+	0.829432i
$909$	−411.714	+	411.714i	−0.452931	+	0.452931i
$910$	120.593	+	336.629i	0.132520	+	0.369922i
$911$	−51.9221			−0.0569946			−0.0284973	−	0.999594i	$-0.509072\pi$
$911$	−51.9221			−0.0569946			−0.0284973	+	0.999594i	$0.509072\pi$
$912$	−273.528	+	234.238i	−0.299921	+	0.256840i
$913$	−782.949	−	782.949i	−0.857557	−	0.857557i
$914$	−409.921	−	1046.33i	−0.448491	−	1.14478i
$915$	1022.37	+	1084.32i	1.11734	+	1.18505i
$916$	−3.29406	+	85.2688i	−0.00359613	+	0.0930882i
$917$		−	268.563i		−	0.292871i
$918$	131.488	+	335.623i	0.143233	+	0.365602i
$919$	365.843			0.398089			0.199044	−	0.979990i	$-0.436216\pi$
$919$	365.843			0.398089			0.199044	+	0.979990i	$0.436216\pi$
$920$	812.540	−	1560.68i	0.883196	−	1.69639i
$921$		−	1982.70i		−	2.15277i
$922$	440.334	+	1123.96i	0.477586	+	1.21904i
$923$	1026.39			1.11201
$924$	−232.639	+	215.333i	−0.251773	+	0.233044i
$925$	−14.6961	+	249.654i	−0.0158877	+	0.269896i
$926$	34.0655	+	86.9523i	0.0367878	+	0.0939010i
$927$	−200.332	+	200.332i	−0.216108	+	0.216108i
$928$	−514.782	−	1687.02i	−0.554722	−	1.81791i
$929$			1736.63i			1.86936i	0.355491	+	0.934680i	$0.384314\pi$
$929$			1736.63i			1.86936i	−0.355491	+	0.934680i	$0.615686\pi$
$930$	−528.665	−	249.793i	−0.568457	−	0.268595i
$931$	−179.631	−	179.631i	−0.192944	−	0.192944i
$932$	602.292	+	23.2674i	0.646236	+	0.0249650i
$933$	1849.88			1.98272
$934$	1413.24	+	617.611i	1.51311	+	0.661254i
$935$	610.199	+	17.9445i	0.652619	+	0.0191919i
$936$	−639.393	+	222.429i	−0.683112	+	0.237638i
$937$	−26.5779	−	26.5779i	−0.0283649	−	0.0283649i	0.692782	−	0.721147i	$-0.256385\pi$
$937$	−26.5779	−	26.5779i	−0.0283649	−	0.0283649i	−0.721147	+	0.692782i	$0.756385\pi$
$938$	118.346	+	302.080i	0.126169	+	0.322047i
$939$	368.544	+	368.544i	0.392486	+	0.392486i
$940$	−67.5284	+	991.368i	−0.0718388	+	1.05465i
$941$	770.144	+	770.144i	0.818431	+	0.818431i	0.985881	−	0.167450i	$-0.0535532\pi$
$941$	770.144	+	770.144i	0.818431	+	0.818431i	−0.167450	+	0.985881i	$0.553553\pi$
$942$	−7.00706	+	16.0338i	−0.00743850	+	0.0170211i
$943$	533.611	+	533.611i	0.565865	+	0.565865i
$944$	−234.062	+	200.441i	−0.247947	+	0.212332i
$945$	−104.738	−	111.084i	−0.110833	−	0.117550i
$946$	662.178	−	259.423i	0.699977	−	0.274231i
$947$	−585.598			−0.618372			−0.309186	−	0.951002i	$-0.600057\pi$
$947$	−585.598			−0.618372			−0.309186	+	0.951002i	$0.600057\pi$
$948$	931.757	+	1006.64i	0.982866	+	1.06186i
$949$	−1264.70	−	1264.70i	−1.33266	−	1.33266i
$950$	−279.319	+	90.8906i	−0.294020	+	0.0956743i
$951$		−	1320.66i		−	1.38870i
$952$	−89.3232	−	256.768i	−0.0938269	−	0.269714i
$953$	−1209.67	+	1209.67i	−1.26933	+	1.26933i	−0.322897	+	0.946434i	$0.604657\pi$
$953$	−1209.67	+	1209.67i	−1.26933	+	1.26933i	−0.946434	+	0.322897i	$0.895343\pi$
$954$	56.2062	+	24.5631i	0.0589164	+	0.0257475i
$955$	−3.49704	+	118.916i	−0.00366182	+	0.124520i
$956$	−23.5697	+	21.8164i	−0.0246545	+	0.0228205i
$957$	1820.49			1.90229
$958$	168.910	−	386.506i	0.176315	−	0.403451i
$959$		−	530.386i		−	0.553062i
$960$	−983.249	+	732.320i	−1.02422	+	0.762833i
$961$	−728.084			−0.757632
$962$	−273.201	−	119.394i	−0.283993	−	0.124110i
$963$			466.207i			0.484120i
$964$	24.9864	+	26.9945i	0.0259195	+	0.0280026i
$965$	374.507	−	353.109i	0.388090	−	0.365916i
$966$	323.866	−	741.084i	0.335265	−	0.767167i
$967$	265.767	+	265.767i	0.274837	+	0.274837i	0.831044	−	0.556207i	$-0.187744\pi$
$967$	265.767	+	265.767i	0.274837	+	0.274837i	−0.556207	+	0.831044i	$0.687744\pi$
$968$	−352.726	+	122.705i	−0.364386	+	0.126761i
$969$	318.763			0.328961
$970$	−238.796	−	666.587i	−0.246182	−	0.687203i
$971$	−703.377	+	703.377i	−0.724384	+	0.724384i	−0.969495	−	0.245111i	$-0.921176\pi$
$971$	−703.377	+	703.377i	−0.724384	+	0.724384i	0.245111	+	0.969495i	$0.421176\pi$
$972$	786.894	−	728.357i	0.809562	−	0.749339i
$973$			36.0571i			0.0370576i
$974$	202.782	+	517.601i	0.208195	+	0.531418i
$975$	−1424.90	−	83.8784i	−1.46144	−	0.0860291i
$976$	−945.455	+	809.647i	−0.968703	+	0.829557i
$977$	−320.028	+	320.028i	−0.327562	+	0.327562i	−0.851659	−	0.524097i	$-0.824403\pi$
$977$	−320.028	+	320.028i	−0.327562	+	0.327562i	0.524097	+	0.851659i	$0.324403\pi$
$978$	819.870	+	358.297i	0.838313	+	0.366357i
$979$	266.050	−	266.050i	0.271757	−	0.271757i
$980$	−568.569	−	651.688i	−0.580172	−	0.664988i
$981$	−123.391	+	123.391i	−0.125781	+	0.125781i
$982$	1030.36	−	403.665i	1.04924	−	0.411064i
$983$	−331.430	+	331.430i	−0.337162	+	0.337162i	−0.855298	−	0.518136i	$-0.826626\pi$
$983$	−331.430	+	331.430i	−0.337162	+	0.337162i	0.518136	+	0.855298i	$0.326626\pi$
$984$	−172.763	−	496.623i	−0.175572	−	0.504698i
$985$	−1058.75	−	31.1352i	−1.07487	−	0.0316093i
$986$	−625.203	+	1430.61i	−0.634080	+	1.45093i
$987$			456.734i			0.462750i
$988$	13.5182	−	349.927i	0.0136824	−	0.354177i
$989$	−1283.00	+	1283.00i	−1.29727	+	1.29727i
$990$	−165.091	−	460.845i	−0.166759	−	0.465499i
$991$	−1610.77			−1.62540			−0.812699	−	0.582684i	$-0.802003\pi$
$991$	−1610.77			−1.62540			−0.812699	+	0.582684i	$0.802003\pi$
$992$	229.508	−	431.082i	0.231359	−	0.434559i
$993$	−783.336	−	783.336i	−0.788858	−	0.788858i
$994$	307.747	−	120.566i	0.309604	−	0.121294i
$995$	15.6331	−	531.600i	0.0157116	−	0.534271i
$996$	−1337.07	−	1444.53i	−1.34244	−	1.45033i
$997$			513.114i			0.514658i	0.966324	+	0.257329i	$0.0828425\pi$
$997$			513.114i			0.514658i	−0.966324	+	0.257329i	$0.917158\pi$
$998$	−632.326	+	247.727i	−0.633593	+	0.248224i
$999$	127.301			0.127429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.i.a.13.19	✓	44
4.3	odd	2		320.3.i.a.273.4		44
5.2	odd	4		80.3.t.a.77.9	yes	44
5.3	odd	4		400.3.t.b.157.14		44
5.4	even	2		400.3.i.b.93.4		44
8.3	odd	2		640.3.i.a.33.19		44
8.5	even	2		640.3.i.b.33.4		44
16.3	odd	4		640.3.t.a.353.19		44
16.5	even	4		80.3.t.a.53.9	yes	44
16.11	odd	4		320.3.t.a.113.4		44
16.13	even	4		640.3.t.b.353.4		44
20.7	even	4		320.3.t.a.17.4		44
40.27	even	4		640.3.t.a.417.19		44
40.37	odd	4		640.3.t.b.417.4		44
80.27	even	4		320.3.i.a.177.19		44
80.37	odd	4	inner	80.3.i.a.37.19	yes	44
80.53	odd	4		400.3.i.b.357.4		44
80.67	even	4		640.3.i.a.97.4		44
80.69	even	4		400.3.t.b.293.14		44
80.77	odd	4		640.3.i.b.97.19		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.19	✓	44	1.1	even	1	trivial
80.3.i.a.37.19	yes	44	80.37	odd	4	inner
80.3.t.a.53.9	yes	44	16.5	even	4
80.3.t.a.77.9	yes	44	5.2	odd	4
320.3.i.a.177.19		44	80.27	even	4
320.3.i.a.273.4		44	4.3	odd	2
320.3.t.a.17.4		44	20.7	even	4
320.3.t.a.113.4		44	16.11	odd	4
400.3.i.b.93.4		44	5.4	even	2
400.3.i.b.357.4		44	80.53	odd	4
400.3.t.b.157.14		44	5.3	odd	4
400.3.t.b.293.14		44	80.69	even	4
640.3.i.a.33.19		44	8.3	odd	2
640.3.i.a.97.4		44	80.67	even	4
640.3.i.b.33.4		44	8.5	even	2
640.3.i.b.97.19		44	80.77	odd	4
640.3.t.a.353.19		44	16.3	odd	4
640.3.t.a.417.19		44	40.27	even	4
640.3.t.b.353.4		44	16.13	even	4
640.3.t.b.417.4		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)

\(f(q)\)	\(=\)	\(q+(1.83264 + 0.800895i) q^{2} +3.83124i q^{3} +(2.71713 + 2.93550i) q^{4} +(0.146974 - 4.99784i) q^{5} +(-3.06842 + 7.02129i) q^{6} +(-1.69668 - 1.69668i) q^{7} +(2.62850 + 7.55586i) q^{8} -5.67842 q^{9} +O(q^{10})\)	\(q+(1.83264 + 0.800895i) q^{2} +3.83124i q^{3} +(2.71713 + 2.93550i) q^{4} +(0.146974 - 4.99784i) q^{5} +(-3.06842 + 7.02129i) q^{6} +(-1.69668 - 1.69668i) q^{7} +(2.62850 + 7.55586i) q^{8} -5.67842 q^{9} +(4.27210 - 9.04153i) q^{10} +(-6.09580 + 6.09580i) q^{11} +(-11.2466 + 10.4100i) q^{12} -14.9024i q^{13} +(-1.75054 - 4.46825i) q^{14} +(19.1479 + 0.563095i) q^{15} +(-1.23437 + 15.9523i) q^{16} +(10.0145 - 10.0145i) q^{17} +(-10.4065 - 4.54782i) q^{18} +(4.15403 - 4.15403i) q^{19} +(15.0705 - 13.1484i) q^{20} +(6.50038 - 6.50038i) q^{21} +(-16.0535 + 6.28931i) q^{22} +(31.1044 - 31.1044i) q^{23} +(-28.9483 + 10.0704i) q^{24} +(-24.9568 - 1.46911i) q^{25} +(11.9353 - 27.3107i) q^{26} +12.7258i q^{27} +(0.370503 - 9.59069i) q^{28} +(-38.9751 + 38.9751i) q^{29} +(34.6403 + 16.3674i) q^{30} -15.2616 q^{31} +(-15.0383 + 28.2462i) q^{32} +(-23.3545 - 23.3545i) q^{33} +(26.3735 - 10.3324i) q^{34} +(-8.72908 + 8.23034i) q^{35} +(-15.4290 - 16.6690i) q^{36} -10.0034i q^{37} +(10.9398 - 4.28590i) q^{38} +57.0947 q^{39} +(38.1493 - 12.0263i) q^{40} +17.1555i q^{41} +(17.1190 - 6.70672i) q^{42} -41.2482 q^{43} +(-34.4574 - 1.33114i) q^{44} +(-0.834582 + 28.3798i) q^{45} +(81.9145 - 32.0918i) q^{46} +(-35.1314 + 35.1314i) q^{47} +(-61.1172 - 4.72915i) q^{48} -43.2426i q^{49} +(-44.5602 - 22.6801i) q^{50} +(38.3679 + 38.3679i) q^{51} +(43.7461 - 40.4918i) q^{52} -5.40107 q^{53} +(-10.1920 + 23.3218i) q^{54} +(29.5699 + 31.3618i) q^{55} +(8.36014 - 17.2795i) q^{56} +(15.9151 + 15.9151i) q^{57} +(-102.642 + 40.2123i) q^{58} +(13.6188 + 13.6188i) q^{59} +(50.3745 + 57.7388i) q^{60} +(55.0109 + 55.0109i) q^{61} +(-27.9690 - 12.2229i) q^{62} +(9.63443 + 9.63443i) q^{63} +(-50.1820 + 39.7211i) q^{64} +(-74.4798 - 2.19027i) q^{65} +(-24.0959 - 61.5049i) q^{66} -67.6058 q^{67} +(56.6082 + 2.18686i) q^{68} +(119.168 + 119.168i) q^{69} +(-22.5889 + 8.09218i) q^{70} +68.8740i q^{71} +(-14.9257 - 42.9053i) q^{72} +(84.8652 - 84.8652i) q^{73} +(8.01170 - 18.3327i) q^{74} +(5.62851 - 95.6155i) q^{75} +(23.4812 + 0.907115i) q^{76} +20.6852 q^{77} +(104.634 + 45.7269i) q^{78} -89.5060i q^{79} +(79.5457 + 8.51374i) q^{80} -99.8613 q^{81} +(-13.7397 + 31.4398i) q^{82} +128.441i q^{83} +(36.7443 + 1.41949i) q^{84} +(-48.5789 - 51.5226i) q^{85} +(-75.5931 - 33.0355i) q^{86} +(-149.323 - 149.323i) q^{87} +(-62.0818 - 30.0362i) q^{88} -43.6449 q^{89} +(-24.2588 + 51.3416i) q^{90} +(-25.2845 + 25.2845i) q^{91} +(175.822 + 6.79226i) q^{92} -58.4708i q^{93} +(-92.5197 + 36.2466i) q^{94} +(-20.1507 - 21.3717i) q^{95} +(-108.218 - 57.6153i) q^{96} +(50.0681 - 50.0681i) q^{97} +(34.6328 - 79.2481i) q^{98} +(34.6145 - 34.6145i) 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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