LMFDB - Embedded newform 375.3.p.a.14.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(14,375)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("375.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([25, 43])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.p (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$1960$
Relative dimension:	$98$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			14.19
Character	$\chi$	$=$	375.14
Dual form			375.3.p.a.134.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15116 - 2.44634i) q^{2} +(-2.86760 - 0.881397i) q^{3} +(-2.10970 + 2.55019i) q^{4} +(-4.99959 + 0.0638640i) q^{5} +(1.14487 + 8.02975i) q^{6} +(-1.66437 - 0.540787i) q^{7} +(-1.80761 - 0.464116i) q^{8} +(7.44628 + 5.05499i) q^{9} +(5.91156 + 12.1572i) q^{10} +(1.28139 - 0.602977i) q^{11} +(8.29752 - 5.45345i) q^{12} +(-2.29817 + 18.1919i) q^{13} +(0.593008 + 4.69414i) q^{14} +(14.3931 + 4.22349i) q^{15} +(3.42619 + 17.9607i) q^{16} +(-8.58302 - 10.3751i) q^{17} +(3.79437 - 24.0352i) q^{18} +(-0.311515 - 4.95138i) q^{19} +(10.3848 - 12.8847i) q^{20} +(4.29610 + 3.01773i) q^{21} +(-2.95017 - 2.44059i) q^{22} +(-5.10963 - 2.80905i) q^{23} +(4.77444 + 2.92412i) q^{24} +(24.9918 - 0.638588i) q^{25} +(47.1491 - 15.3197i) q^{26} +(-16.8975 - 21.0588i) q^{27} +(4.89044 - 3.10357i) q^{28} +(17.9014 - 11.3605i) q^{29} +(-6.23669 - 40.0724i) q^{30} +(2.18766 + 2.64442i) q^{31} +(33.9546 - 24.6695i) q^{32} +(-4.20598 + 0.599682i) q^{33} +(-15.5005 + 32.9403i) q^{34} +(8.35571 + 2.59742i) q^{35} +(-28.6006 + 8.32491i) q^{36} +(-29.6731 + 5.66046i) q^{37} +(-11.7541 + 6.46190i) q^{38} +(22.6246 - 50.1416i) q^{39} +(9.06696 + 2.20495i) q^{40} +(11.0141 + 20.0345i) q^{41} +(2.43689 - 13.9836i) q^{42} +(16.9230 - 23.2926i) q^{43} +(-1.16565 + 4.53989i) q^{44} +(-37.5512 - 24.7974i) q^{45} +(-0.989871 + 15.7335i) q^{46} +(58.7279 - 15.0788i) q^{47} +(6.00559 - 54.5241i) q^{48} +(-37.1642 - 27.0013i) q^{49} +(-30.3318 - 60.4034i) q^{50} +(15.4681 + 37.3167i) q^{51} +(-41.5444 - 44.2403i) q^{52} +(-89.0003 - 35.2377i) q^{53} +(-32.0653 + 65.5790i) q^{54} +(-6.36792 + 3.09647i) q^{55} +(2.75755 + 1.74999i) q^{56} +(-3.47084 + 14.4732i) q^{57} +(-48.3990 - 30.7150i) q^{58} +(-3.15782 + 3.36274i) q^{59} +(-41.1359 + 27.7949i) q^{60} +(100.743 + 55.3838i) q^{61} +(3.95081 - 8.39589i) q^{62} +(-9.65969 - 12.4402i) q^{63} +(-35.3454 - 19.4313i) q^{64} +(10.3281 - 91.0989i) q^{65} +(6.30878 + 9.59891i) q^{66} +(38.7695 + 24.6039i) q^{67} +44.5661 q^{68} +(12.1765 + 12.5588i) q^{69} +(-3.26458 - 23.4309i) q^{70} +(1.01657 + 3.95929i) q^{71} +(-11.1139 - 12.5934i) q^{72} +(63.3036 + 67.4114i) q^{73} +(48.0059 + 66.0744i) q^{74} +(-72.2295 - 20.1965i) q^{75} +(13.2842 + 9.65152i) q^{76} +(-2.45879 + 0.310617i) q^{77} +(-148.708 + 2.37362i) q^{78} +(2.42640 - 38.5665i) q^{79} +(-18.2766 - 89.5775i) q^{80} +(29.8941 + 75.2818i) q^{81} +(36.3322 - 50.0070i) q^{82} +(1.00440 + 15.9645i) q^{83} +(-16.7593 + 4.58937i) q^{84} +(43.5742 + 51.3231i) q^{85} +(-76.4625 - 14.5860i) q^{86} +(-61.3471 + 16.7993i) q^{87} +(-2.59611 + 0.495234i) q^{88} +(68.4996 + 72.9447i) q^{89} +(-17.4353 + 120.409i) q^{90} +(13.6630 - 29.0353i) q^{91} +(17.9434 - 7.10430i) q^{92} +(-3.94254 - 9.51134i) q^{93} +(-104.493 - 126.310i) q^{94} +(1.87366 + 24.7350i) q^{95} +(-119.112 + 40.8147i) q^{96} +(102.117 - 64.8056i) q^{97} +(-23.2725 + 121.999i) q^{98} +(12.5896 + 1.98749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) $ 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{43}{50}\right)$	$-1$

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 $

$2$	−1.15116	−	2.44634i	−0.575579	−	1.22317i	−0.954631	−	0.297793i	$-0.903750\pi$
$2$	−1.15116	−	2.44634i	−0.575579	−	1.22317i	0.379051	−	0.925376i	$-0.376250\pi$
$3$	−2.86760	−	0.881397i	−0.955867	−	0.293799i
$3$	−2.86760	−	0.881397i	−0.955867	−	0.293799i
$4$	−2.10970	+	2.55019i	−0.527426	+	0.637548i
$5$	−4.99959	+	0.0638640i	−0.999918	+	0.0127728i
$5$	−4.99959	+	0.0638640i	−0.999918	+	0.0127728i
$6$	1.14487	+	8.02975i	0.190812	+	1.33829i
$7$	−1.66437	−	0.540787i	−0.237767	−	0.0772552i	0.187710	−	0.982225i	$-0.439894\pi$
$7$	−1.66437	−	0.540787i	−0.237767	−	0.0772552i	−0.425477	+	0.904969i	$0.639894\pi$
$8$	−1.80761	−	0.464116i	−0.225951	−	0.0580145i
$9$	7.44628	+	5.05499i	0.827364	+	0.561666i
$10$	5.91156	+	12.1572i	0.591156	+	1.21572i
$11$	1.28139	−	0.602977i	0.116490	−	0.0548160i	−0.366651	−	0.930358i	$-0.619496\pi$
$11$	1.28139	−	0.602977i	0.116490	−	0.0548160i	0.483141	+	0.875542i	$0.339496\pi$
$12$	8.29752	−	5.45345i	0.691460	−	0.454454i
$13$	−2.29817	+	18.1919i	−0.176783	+	1.39938i	0.614977	+	0.788545i	$0.289165\pi$
$13$	−2.29817	+	18.1919i	−0.176783	+	1.39938i	−0.791759	+	0.610833i	$0.790835\pi$
$14$	0.593008	+	4.69414i	0.0423577	+	0.335296i
$15$	14.3931	+	4.22349i	0.959542	+	0.281566i
$16$	3.42619	+	17.9607i	0.214137	+	1.12255i
$17$	−8.58302	−	10.3751i	−0.504883	−	0.610299i	0.455071	−	0.890455i	$-0.349614\pi$
$17$	−8.58302	−	10.3751i	−0.504883	−	0.610299i	−0.959955	+	0.280156i	$0.909614\pi$
$18$	3.79437	−	24.0352i	0.210798	−	1.33529i
$19$	−0.311515	−	4.95138i	−0.0163955	−	0.260599i	−0.997682	−	0.0680465i	$-0.978323\pi$
$19$	−0.311515	−	4.95138i	−0.0163955	−	0.260599i	0.981287	−	0.192553i	$-0.0616766\pi$
$20$	10.3848	−	12.8847i	0.519239	−	0.644233i
$21$	4.29610	+	3.01773i	0.204576	+	0.143702i
$22$	−2.95017	−	2.44059i	−0.134099	−	0.110936i
$23$	−5.10963	−	2.80905i	−0.222158	−	0.122132i	0.366789	−	0.930304i	$-0.380457\pi$
$23$	−5.10963	−	2.80905i	−0.222158	−	0.122132i	−0.588947	+	0.808172i	$0.700457\pi$
$24$	4.77444	+	2.92412i	0.198935	+	0.121838i
$25$	24.9918	−	0.638588i	0.999674	−	0.0255435i
$26$	47.1491	−	15.3197i	1.81343	−	0.589218i
$27$	−16.8975	−	21.0588i	−0.625833	−	0.779957i
$28$	4.89044	−	3.10357i	0.174658	−	0.110842i
$29$	17.9014	−	11.3605i	0.617288	−	0.391743i	−0.190099	−	0.981765i	$-0.560881\pi$
$29$	17.9014	−	11.3605i	0.617288	−	0.391743i	0.807387	+	0.590022i	$0.200881\pi$
$30$	−6.23669	−	40.0724i	−0.207890	−	1.33575i
$31$	2.18766	+	2.64442i	0.0705695	+	0.0853039i	0.804617	−	0.593795i	$-0.202371\pi$
$31$	2.18766	+	2.64442i	0.0705695	+	0.0853039i	−0.734047	+	0.679099i	$0.762371\pi$
$32$	33.9546	−	24.6695i	1.06108	−	0.770921i
$33$	−4.20598	+	0.599682i	−0.127454	+	0.0181722i
$34$	−15.5005	+	32.9403i	−0.455898	+	0.968833i
$35$	8.35571	+	2.59742i	0.238735	+	0.0742120i
$36$	−28.6006	+	8.32491i	−0.794462	+	0.231247i
$37$	−29.6731	+	5.66046i	−0.801977	+	0.152985i	−0.572046	−	0.820222i	$-0.693850\pi$
$37$	−29.6731	+	5.66046i	−0.801977	+	0.152985i	−0.229931	+	0.973207i	$0.573850\pi$
$38$	−11.7541	+	6.46190i	−0.309320	+	0.170050i
$39$	22.6246	−	50.1416i	0.580117	−	1.28568i
$40$	9.06696	+	2.20495i	0.226674	+	0.0551237i
$41$	11.0141	+	20.0345i	0.268636	+	0.488646i	0.975876	−	0.218327i	$-0.0700600\pi$
$41$	11.0141	+	20.0345i	0.268636	+	0.488646i	−0.707240	+	0.706974i	$0.750060\pi$
$42$	2.43689	−	13.9836i	0.0580213	−	0.332943i
$43$	16.9230	−	23.2926i	0.393559	−	0.541687i	−0.565554	−	0.824711i	$-0.691338\pi$
$43$	16.9230	−	23.2926i	0.393559	−	0.541687i	0.959113	+	0.283024i	$0.0913376\pi$
$44$	−1.16565	+	4.53989i	−0.0264920	+	0.103179i
$45$	−37.5512	−	24.7974i	−0.834471	−	0.551052i
$46$	−0.989871	+	15.7335i	−0.0215189	+	0.342034i
$47$	58.7279	−	15.0788i	1.24953	−	0.320825i	0.434727	−	0.900562i	$-0.356845\pi$
$47$	58.7279	−	15.0788i	1.24953	−	0.320825i	0.814803	+	0.579737i	$0.196845\pi$
$48$	6.00559	−	54.5241i	0.125116	−	1.13592i
$49$	−37.1642	−	27.0013i	−0.758452	−	0.551048i
$50$	−30.3318	−	60.4034i	−0.606636	−	1.20807i
$51$	15.4681	+	37.3167i	0.303296	+	0.731699i
$52$	−41.5444	−	44.2403i	−0.798931	−	0.850776i
$53$	−89.0003	−	35.2377i	−1.67925	−	0.664862i	−0.681495	−	0.731823i	$-0.738670\pi$
$53$	−89.0003	−	35.2377i	−1.67925	−	0.664862i	−0.997756	+	0.0669603i	$0.978670\pi$
$54$	−32.0653	+	65.5790i	−0.593802	+	1.21443i
$55$	−6.36792	+	3.09647i	−0.115780	+	0.0562995i
$56$	2.75755	+	1.74999i	0.0492419	+	0.0312499i
$57$	−3.47084	+	14.4732i	−0.0608919	+	0.253915i
$58$	−48.3990	−	30.7150i	−0.834466	−	0.529568i
$59$	−3.15782	+	3.36274i	−0.0535224	+	0.0569955i	−0.755173	−	0.655526i	$-0.772447\pi$
$59$	−3.15782	+	3.36274i	−0.0535224	+	0.0569955i	0.701650	+	0.712522i	$0.252447\pi$
$60$	−41.1359	+	27.7949i	−0.685599	+	0.463249i
$61$	100.743	+	55.3838i	1.65152	+	0.907932i	0.987011	+	0.160653i	$0.0513600\pi$
$61$	100.743	+	55.3838i	1.65152	+	0.907932i	0.664511	+	0.747279i	$0.268640\pi$
$62$	3.95081	−	8.39589i	0.0637227	−	0.135418i
$63$	−9.65969	−	12.4402i	−0.153328	−	0.197464i
$64$	−35.3454	−	19.4313i	−0.552271	−	0.303614i
$65$	10.3281	−	91.0989i	0.158894	−	1.40152i
$66$	6.30878	+	9.59891i	0.0955875	+	0.145438i
$67$	38.7695	+	24.6039i	0.578649	+	0.367222i	0.792710	−	0.609598i	$-0.208669\pi$
$67$	38.7695	+	24.6039i	0.578649	+	0.367222i	−0.214061	+	0.976820i	$0.568669\pi$
$68$	44.5661			0.655384
$69$	12.1765	+	12.5588i	0.176471	+	0.182012i
$70$	−3.26458	−	23.4309i	−0.0466369	−	0.334727i
$71$	1.01657	+	3.95929i	0.0143179	+	0.0557647i	0.975341	−	0.220704i	$-0.0708356\pi$
$71$	1.01657	+	3.95929i	0.0143179	+	0.0557647i	−0.961023	+	0.276469i	$0.910836\pi$
$72$	−11.1139	−	12.5934i	−0.154359	−	0.174908i
$73$	63.3036	+	67.4114i	0.867172	+	0.923444i	0.997685	−	0.0680022i	$-0.0216625\pi$
$73$	63.3036	+	67.4114i	0.867172	+	0.923444i	−0.130513	+	0.991447i	$0.541662\pi$
$74$	48.0059	+	66.0744i	0.648728	+	0.892898i
$75$	−72.2295	−	20.1965i	−0.963060	−	0.269287i
$76$	13.2842	+	9.65152i	0.174792	+	0.126994i
$77$	−2.45879	+	0.310617i	−0.0319323	+	0.00403399i
$78$	−148.708	+	2.37362i	−1.90651	+	0.0304310i
$79$	2.42640	−	38.5665i	0.0307139	−	0.488183i	−0.952360	−	0.304975i	$-0.901352\pi$
$79$	2.42640	−	38.5665i	0.0307139	−	0.488183i	0.983074	−	0.183208i	$-0.0586482\pi$
$80$	−18.2766	−	89.5775i	−0.228458	−	1.11972i
$81$	29.8941	+	75.2818i	0.369063	+	0.929404i
$82$	36.3322	−	50.0070i	0.443076	−	0.609841i
$83$	1.00440	+	15.9645i	0.0121012	+	0.192343i	0.999433	+	0.0336731i	$0.0107205\pi$
$83$	1.00440	+	15.9645i	0.0121012	+	0.192343i	−0.987332	+	0.158670i	$0.949279\pi$
$84$	−16.7593	+	4.58937i	−0.199515	+	0.0546354i
$85$	43.5742	+	51.3231i	0.512637	+	0.603801i
$86$	−76.4625	−	14.5860i	−0.889099	−	0.169605i
$87$	−61.3471	+	16.7993i	−0.705139	+	0.193096i
$88$	−2.59611	+	0.495234i	−0.0295012	+	0.00562766i
$89$	68.4996	+	72.9447i	0.769659	+	0.819603i	0.987704	−	0.156335i	$-0.0499681\pi$
$89$	68.4996	+	72.9447i	0.769659	+	0.819603i	−0.218045	+	0.975939i	$0.569968\pi$
$90$	−17.4353	+	120.409i	−0.193726	+	1.33787i
$91$	13.6630	−	29.0353i	0.150142	−	0.319069i
$92$	17.9434	−	7.10430i	0.195037	−	0.0772207i
$93$	−3.94254	−	9.51134i	−0.0423929	−	0.102272i
$94$	−104.493	−	126.310i	−1.11163	−	1.34373i
$95$	1.87366	+	24.7350i	0.0197227	+	0.260368i
$96$	−119.112	+	40.8147i	−1.24075	+	0.425153i
$97$	102.117	−	64.8056i	1.05276	−	0.668099i	0.107426	−	0.994213i	$-0.465739\pi$
$97$	102.117	−	64.8056i	1.05276	−	0.668099i	0.945331	+	0.326114i	$0.105739\pi$
$98$	−23.2725	+	121.999i	−0.237475	+	1.24489i
$99$	12.5896	+	1.98749i	0.127168	+	0.0200757i
$100$	−51.0968	+	65.0812i	−0.510968	+	0.650812i
$101$	61.2835	+	19.9122i	0.606767	+	0.197151i	0.596256	−	0.802794i	$-0.296654\pi$
$101$	61.2835	+	19.9122i	0.606767	+	0.197151i	0.0105109	+	0.999945i	$0.496654\pi$
$102$	73.4829	−	80.7976i	0.720421	−	0.792133i
$103$	57.5609	+	47.6185i	0.558844	+	0.462316i	0.873455	−	0.486905i	$-0.161874\pi$
$103$	57.5609	+	47.6185i	0.558844	+	0.462316i	−0.314611	+	0.949221i	$0.601874\pi$
$104$	12.5974	−	31.8173i	0.121128	−	0.305936i
$105$	−21.6715	−	14.8131i	−0.206395	−	0.141077i
$106$	16.2502	+	258.289i	0.153303	+	2.43669i
$107$	55.0446	+	169.410i	0.514435	+	1.58327i	0.784307	+	0.620373i	$0.213019\pi$
$107$	55.0446	+	169.410i	0.514435	+	1.58327i	−0.269872	+	0.962896i	$0.586981\pi$
$108$	89.3528	+	1.33602i	0.827341	+	0.0123705i
$109$	−5.18676	−	27.1899i	−0.0475850	−	0.249449i	0.950544	−	0.310589i	$-0.100526\pi$
$109$	−5.18676	−	27.1899i	−0.0475850	−	0.249449i	−0.998129	+	0.0611401i	$0.980526\pi$
$110$	14.9055	+	12.0136i	0.135505	+	0.109214i
$111$	90.0799	+	9.92191i	0.811530	+	0.0893865i
$112$	4.01047	−	31.7461i	0.0358078	−	0.283448i
$113$	−0.444437	−	0.417354i	−0.00393307	−	0.00369340i	0.682578	−	0.730813i	$-0.260859\pi$
$113$	−0.444437	−	0.417354i	−0.00393307	−	0.00369340i	−0.686511	+	0.727119i	$0.740859\pi$
$114$	39.4017	−	8.17007i	0.345629	−	0.0716673i
$115$	25.7255	+	13.7178i	0.223700	+	0.119285i
$116$	−8.79496	+	69.6193i	−0.0758187	+	0.600166i
$117$	−109.073	+	123.845i	−0.932247	+	1.05850i
$118$	11.8615	+	3.85405i	0.100522	+	0.0326614i
$119$	8.67461	+	21.9096i	0.0728959	+	0.184114i
$120$	−24.0570	−	14.3145i	−0.200475	−	0.119288i
$121$	−75.8499	+	91.6868i	−0.626859	+	0.757742i
$122$	19.5165	−	310.207i	0.159972	−	2.54268i
$123$	−13.9256	−	67.1587i	−0.113216	−	0.546006i
$124$	−11.3591			−0.0916055
$125$	−124.908	+	4.78876i	−0.999266	+	0.0383100i
$126$	−19.3132	+	37.9515i	−0.153279	+	0.301203i
$127$	149.299	−	70.2546i	1.17558	−	0.553186i	0.264086	−	0.964499i	$-0.414930\pi$
$127$	149.299	−	70.2546i	1.17558	−	0.553186i	0.911494	+	0.411313i	$0.134930\pi$
$128$	3.69400	−	58.7145i	0.0288594	−	0.458707i
$129$	−69.0585	+	51.8778i	−0.535337	+	0.402154i
$130$	−234.748	+	79.6033i	−1.80575	+	0.612333i
$131$	50.9259	+	128.624i	0.388748	+	0.981865i	0.983975	+	0.178307i	$0.0570621\pi$
$131$	50.9259	+	128.624i	0.388748	+	0.981865i	−0.595227	+	0.803557i	$0.702938\pi$
$132$	7.34406	−	11.9912i	0.0556368	−	0.0908425i
$133$	−2.15917	+	8.40939i	−0.0162343	+	0.0632285i
$134$	15.5595	−	123.166i	0.116116	−	0.919151i
$135$	85.8255	+	104.206i	0.635744	+	0.771900i
$136$	10.6995	+	22.7376i	0.0786729	+	0.167189i
$137$	120.067	+	112.750i	0.876398	+	0.822992i	0.985260	−	0.171064i	$-0.0547206\pi$
$137$	120.067	+	112.750i	0.876398	+	0.822992i	−0.108862	+	0.994057i	$0.534721\pi$
$138$	16.7061	−	44.2451i	0.121058	−	0.320616i
$139$	42.2904	−	5.34252i	0.304248	−	0.0384354i	0.0282727	−	0.999600i	$-0.490999\pi$
$139$	42.2904	−	5.34252i	0.304248	−	0.0384354i	0.275975	+	0.961165i	$0.410999\pi$
$140$	−24.2520	+	15.8289i	−0.173228	+	0.113063i
$141$	−181.699	−	8.52275i	−1.28864	−	0.0604450i
$142$	8.51553	−	7.04466i	0.0599685	−	0.0496103i
$143$	8.02444	+	24.6967i	0.0561150	+	0.172704i
$144$	−65.2790	+	151.060i	−0.453326	+	1.04903i
$145$	−88.7740	+	57.9414i	−0.612234	+	0.399596i
$146$	92.0387	−	232.463i	0.630402	−	1.59221i
$147$	82.7731	+	110.185i	0.563082	+	0.749561i
$148$	48.1663	−	87.6141i	0.325448	−	0.591987i
$149$	−81.3228	−	26.4234i	−0.545790	−	0.177338i	0.0231272	−	0.999733i	$-0.492638\pi$
$149$	−81.3228	−	26.4234i	−0.545790	−	0.177338i	−0.568918	+	0.822394i	$0.692638\pi$
$150$	33.7401	+	199.947i	0.224934	+	1.33298i
$151$	−55.4208	−	170.568i	−0.367025	−	1.12959i	−0.948703	−	0.316168i	$-0.897604\pi$
$151$	−55.4208	−	170.568i	−0.367025	−	1.12959i	0.581678	−	0.813419i	$-0.302396\pi$
$152$	−1.73492	+	9.09475i	−0.0114139	+	0.0598339i
$153$	−11.4655	−	120.643i	−0.0749381	−	0.788515i
$154$	3.59033	+	5.65746i	0.0233138	+	0.0367367i
$155$	−11.1063	−	13.0813i	−0.0716533	−	0.0843956i
$156$	80.1396	+	163.481i	0.513715	+	1.04795i
$157$	23.5013	+	32.3467i	0.149690	+	0.206030i	0.877276	−	0.479986i	$-0.159358\pi$
$157$	23.5013	+	32.3467i	0.149690	+	0.206030i	−0.727587	+	0.686016i	$0.759358\pi$
$158$	−97.1398	+	38.4604i	−0.614809	+	0.243420i
$159$	224.159	+	179.492i	1.40980	+	1.12888i
$160$	−168.184	+	125.506i	−1.05115	+	0.784411i
$161$	6.98523	+	7.43851i	0.0433865	+	0.0462019i
$162$	149.752	−	159.792i	0.924393	−	0.986372i
$163$	85.5190	+	155.559i	0.524657	+	0.954347i	0.997324	+	0.0731060i	$0.0232911\pi$
$163$	85.5190	+	155.559i	0.524657	+	0.954347i	−0.472668	+	0.881241i	$0.656709\pi$
$164$	−74.3282	−	14.1789i	−0.453221	−	0.0864565i
$165$	20.9899	−	3.26678i	0.127211	−	0.0197986i
$166$	37.8982	−	20.8347i	0.228303	−	0.125510i
$167$	1.20565	+	19.1633i	0.00721948	+	0.114750i	0.999986	−	0.00531153i	$-0.00169072\pi$
$167$	1.20565	+	19.1633i	0.00721948	+	0.114750i	−0.992766	+	0.120062i	$0.961691\pi$
$168$	−6.36511	−	7.44877i	−0.0378875	−	0.0443379i
$169$	−161.974	−	41.5878i	−0.958424	−	0.246082i
$170$	75.3927	−	165.678i	0.443486	−	0.974577i
$171$	22.7096	−	38.4441i	0.132805	−	0.224819i
$172$	23.6979	+	92.2974i	0.137779	+	0.536613i
$173$	−57.7813	+	7.29947i	−0.333996	+	0.0421935i	−0.290543	−	0.956862i	$-0.593836\pi$
$173$	−57.7813	+	7.29947i	−0.333996	+	0.0421935i	−0.0434530	+	0.999055i	$0.513836\pi$
$174$	111.717	+	130.737i	0.642052	+	0.751363i
$175$	−41.9410	−	12.4524i	−0.239663	−	0.0711566i
$176$	15.2202	+	20.9488i	0.0864783	+	0.119027i
$177$	12.0193	−	6.85969i	0.0679055	−	0.0387553i
$178$	99.5934	−	251.544i	0.559513	−	1.41317i
$179$	80.8420	+	314.859i	0.451631	+	1.75899i	0.631578	+	0.775312i	$0.282407\pi$
$179$	80.8420	+	314.859i	0.451631	+	1.75899i	−0.179947	+	0.983676i	$0.557593\pi$
$180$	142.460	−	43.4477i	0.791444	−	0.241376i
$181$	33.2945	−	52.4637i	0.183947	−	0.289854i	−0.739823	−	0.672801i	$-0.765091\pi$
$181$	33.2945	−	52.4637i	0.183947	−	0.289854i	0.923770	+	0.382947i	$0.125091\pi$
$182$	−86.7583			−0.476694
$183$	−240.075	−	247.613i	−1.31189	−	1.35308i
$184$	7.93251	+	7.44912i	0.0431115	+	0.0404844i
$185$	147.992	−	30.1950i	0.799957	−	0.163216i
$186$	−18.7295	+	20.5938i	−0.100696	+	0.110720i
$187$	−17.2541	−	8.11918i	−0.0922681	−	0.0434181i
$188$	−85.4447	+	181.579i	−0.454493	+	0.965847i
$189$	16.7353	+	44.1876i	0.0885468	+	0.233797i
$190$	58.3533	−	33.0575i	0.307122	−	0.173987i
$191$	−8.28007	+	8.81738i	−0.0433512	+	0.0461643i	−0.750279	−	0.661122i	$-0.770081\pi$
$191$	−8.28007	+	8.81738i	−0.0433512	+	0.0461643i	0.706928	+	0.707286i	$0.250081\pi$
$192$	84.2297	+	86.8744i	0.438696	+	0.452471i
$193$		−	230.202i		−	1.19276i	−0.802703	−	0.596379i	$-0.796606\pi$
$193$		−	230.202i		−	1.19276i	0.802703	−	0.596379i	$-0.203394\pi$
$194$	−276.090	−	175.212i	−1.42314	−	0.903154i
$195$	−109.911	+	252.132i	−0.563648	+	1.29299i
$196$	147.264	−	37.8110i	0.751347	−	0.192913i
$197$	−330.247	−	130.754i	−1.67638	−	0.663727i	−0.678873	−	0.734256i	$-0.737531\pi$
$197$	−330.247	−	130.754i	−1.67638	−	0.663727i	−0.997510	+	0.0705287i	$0.977531\pi$
$198$	−9.63059	−	33.0864i	−0.0486394	−	0.167103i
$199$	−82.7318	+	60.1082i	−0.415738	+	0.302051i	−0.775921	−	0.630831i	$-0.782714\pi$
$199$	−82.7318	+	60.1082i	−0.415738	+	0.302051i	0.360183	+	0.932882i	$0.382714\pi$
$200$	−45.4719	−	10.4448i	−0.227360	−	0.0522239i
$201$	−89.4897	−	104.725i	−0.445222	−	0.521022i
$202$	−21.8350	−	172.842i	−0.108094	−	0.855654i
$203$	−35.9381	+	9.22734i	−0.177035	+	0.0454549i
$204$	−127.798	−	39.2804i	−0.626460	−	0.192551i
$205$	−56.3453	−	99.4609i	−0.274855	−	0.485175i
$206$	50.2292	−	195.630i	0.243831	−	0.949660i
$207$	−23.8480	−	46.7461i	−0.115208	−	0.225827i
$208$	−334.614	+	21.0521i	−1.60872	+	0.101212i
$209$	−3.38474	−	6.15682i	−0.0161949	−	0.0294585i
$210$	−11.2904	+	70.0679i	−0.0537639	+	0.333657i
$211$	63.8226	−	334.570i	0.302477	−	1.58564i	−0.428698	−	0.903448i	$-0.641028\pi$
$211$	63.8226	−	334.570i	0.302477	−	1.58564i	0.731175	−	0.682190i	$-0.238972\pi$
$212$	277.627	−	152.627i	1.30956	−	0.719938i
$213$	0.574583	−	12.2497i	0.00269757	−	0.0575102i
$214$	351.068	−	329.675i	1.64051	−	1.54054i
$215$	−83.1207	+	117.534i	−0.386608	+	0.546670i
$216$	20.7704	+	45.9086i	0.0961591	+	0.212540i
$217$	−2.21100	−	5.58435i	−0.0101889	−	0.0257343i
$218$	−60.5450	+	43.9885i	−0.277729	+	0.201782i
$219$	−122.113	−	249.105i	−0.557594	−	1.13746i
$220$	5.53782	−	22.7721i	0.0251719	−	0.103509i
$221$	208.468	−	132.298i	0.943294	−	0.598633i
$222$	−79.4239	−	231.787i	−0.357765	−	1.04409i
$223$	−57.1666	−	10.9051i	−0.256353	−	0.0489019i	0.0576029	−	0.998340i	$-0.481654\pi$
$223$	−57.1666	−	10.9051i	−0.256353	−	0.0489019i	−0.313956	+	0.949438i	$0.601654\pi$
$224$	−69.8540	+	22.6969i	−0.311848	+	0.101326i
$225$	189.324	+	121.579i	0.841441	+	0.540349i
$226$	−0.509371	+	1.56768i	−0.00225386	+	0.00693666i
$227$	279.952	+	153.905i	1.23327	+	0.677995i	0.958931	−	0.283639i	$-0.0915416\pi$
$227$	279.952	+	153.905i	1.23327	+	0.677995i	0.274337	+	0.961634i	$0.411542\pi$
$228$	−29.5869	−	39.3854i	−0.129767	−	0.172743i
$229$	−328.855	−	130.203i	−1.43605	−	0.568571i	−0.484149	−	0.874986i	$-0.660871\pi$
$229$	−328.855	−	130.203i	−1.43605	−	0.568571i	−0.951898	+	0.306414i	$0.900871\pi$
$230$	3.94414	−	78.7245i	0.0171484	−	0.342281i
$231$	7.32461	+	1.27644i	0.0317082	+	0.00552573i
$232$	−37.6313	+	12.2272i	−0.162204	+	0.0527033i
$233$	−13.5109	−	16.3319i	−0.0579867	−	0.0700939i	0.740722	−	0.671811i	$-0.234483\pi$
$233$	−13.5109	−	16.3319i	−0.0579867	−	0.0700939i	−0.798709	+	0.601717i	$0.794483\pi$
$234$	428.526	+	124.264i	1.83131	+	0.531043i
$235$	−292.653	+	79.1383i	−1.24533	+	0.336759i
$236$	−1.91356	−	15.1474i	−0.00810832	−	0.0641840i
$237$	−40.9503	+	108.455i	−0.172786	+	0.457615i
$238$	43.6123	−	46.4424i	0.183245	−	0.195136i
$239$	−247.703	+	116.560i	−1.03641	+	0.487699i	−0.867241	−	0.497888i	$-0.834109\pi$
$239$	−247.703	+	116.560i	−1.03641	+	0.487699i	−0.169171	+	0.985587i	$0.554109\pi$
$240$	−26.5434	+	272.982i	−0.110597	+	1.13742i
$241$	55.8531	+	7.05589i	0.231756	+	0.0292775i	0.240353	−	0.970686i	$-0.422737\pi$
$241$	55.8531	+	7.05589i	0.231756	+	0.0292775i	−0.00859762	+	0.999963i	$0.502737\pi$
$242$	311.612	+	80.0084i	1.28765	+	0.330613i
$243$	−19.3712	−	242.227i	−0.0797167	−	0.996818i
$244$	−353.777	+	140.070i	−1.44991	+	0.574058i
$245$	187.530	+	132.622i	0.765429	+	0.541315i
$246$	−148.262	+	111.377i	−0.602692	+	0.452752i
$247$	90.7911	+	5.71209i	0.367575	+	0.0231259i
$248$	−2.72711	−	5.79541i	−0.0109964	−	0.0233686i
$249$	11.1908	−	46.6650i	0.0449431	−	0.187410i
$250$	155.504	+	300.055i	0.622017	+	1.20022i
$251$		−	313.736i		−	1.24995i	−0.780647	−	0.624973i	$-0.785110\pi$
$251$		−	313.736i		−	1.24995i	0.780647	−	0.624973i	$-0.214890\pi$
$252$	52.1040	+	1.61112i	0.206762	+	0.00639332i
$253$	−8.24122	−	0.518494i	−0.0325740	−	0.00204938i
$254$	−343.733	−	284.361i	−1.35328	−	1.11953i
$255$	−79.7174	−	185.580i	−0.312617	−	0.727766i
$256$	−297.896	+	117.945i	−1.16366	+	0.460724i
$257$	−93.9320	+	289.093i	−0.365494	+	1.12488i	0.584177	+	0.811626i	$0.301417\pi$
$257$	−93.9320	+	289.093i	−0.365494	+	1.12488i	−0.949671	+	0.313249i	$0.898583\pi$
$258$	206.408	+	109.221i	0.800031	+	0.423336i
$259$	52.4482	+	6.62575i	0.202503	+	0.0255820i
$260$	210.531	+	218.530i	0.809733	+	0.840502i
$261$	190.726	+	5.89747i	0.730751	+	0.0225957i
$262$	256.034	−	272.649i	0.977231	−	1.04065i
$263$	359.430	+	45.4065i	1.36665	+	0.172648i	0.774192	−	0.632951i	$-0.218157\pi$
$263$	359.430	+	45.4065i	1.36665	+	0.172648i	0.592460	+	0.805600i	$0.298157\pi$
$264$	7.88110	+	0.868069i	0.0298526	+	0.00328814i
$265$	447.216	+	170.490i	1.68761	+	0.643359i
$266$	23.0578	−	4.39850i	0.0866833	−	0.0165357i
$267$	−132.136	−	269.552i	−0.494893	−	1.00956i
$268$	−144.537	+	46.9628i	−0.539316	+	0.175234i
$269$	−374.361	+	23.5528i	−1.39167	+	0.0875568i	−0.740850	−	0.671671i	$-0.765577\pi$
$269$	−374.361	+	23.5528i	−1.39167	+	0.0875568i	−0.650825	+	0.759228i	$0.725577\pi$
$270$	156.125	−	329.916i	0.578242	−	1.22191i
$271$	355.689	+	140.827i	1.31251	+	0.519658i	0.917030	−	0.398818i	$-0.130579\pi$
$271$	355.689	+	140.827i	1.31251	+	0.519658i	0.395477	+	0.918476i	$0.370579\pi$
$272$	156.937	−	189.704i	0.576974	−	0.697442i
$273$	−64.7715	+	71.2191i	−0.237258	+	0.260876i
$274$	137.609	−	423.516i	0.502222	−	1.54568i
$275$	31.6393	−	15.8878i	0.115052	−	0.0577737i
$276$	−57.7163	+	4.55702i	−0.209117	+	0.0165110i
$277$	−233.261	−	44.4969i	−0.842096	−	0.160638i	−0.251754	−	0.967791i	$-0.581007\pi$
$277$	−233.261	−	44.4969i	−0.842096	−	0.160638i	−0.590342	+	0.807153i	$0.701007\pi$
$278$	−61.7526	−	97.3066i	−0.222132	−	0.350024i
$279$	2.92236	+	30.7497i	0.0104744	+	0.110214i
$280$	−13.8984	−	8.57314i	−0.0496370	−	0.0306184i
$281$	48.0619	−	39.7602i	0.171039	−	0.141496i	−0.547966	−	0.836500i	$-0.684598\pi$
$281$	48.0619	−	39.7602i	0.171039	−	0.141496i	0.719005	+	0.695005i	$0.244598\pi$
$282$	188.315	+	454.307i	0.667782	+	1.61102i
$283$	−21.4984	−	54.2988i	−0.0759662	−	0.191869i	0.886831	−	0.462094i	$-0.152902\pi$
$283$	−21.4984	−	54.2988i	−0.0759662	−	0.191869i	−0.962797	+	0.270225i	$0.912902\pi$
$284$	−12.2416	−	5.76047i	−0.0431043	−	0.0202834i
$285$	16.4285	−	72.5816i	0.0576437	−	0.254672i
$286$	51.1790	−	48.0603i	0.178948	−	0.168043i
$287$	−7.49708	−	39.3011i	−0.0261222	−	0.136938i
$288$	377.540	−	12.0554i	1.31090	−	0.0418589i
$289$	20.1790	−	105.782i	0.0698235	−	0.366027i
$290$	243.937	+	150.471i	0.841162	+	0.518867i
$291$	−349.951	+	95.8308i	−1.20258	+	0.329315i
$292$	−305.464	+	19.2182i	−1.04611	+	0.0658156i
$293$	236.325	+	171.700i	0.806571	+	0.586008i	0.912834	−	0.408330i	$-0.133889\pi$
$293$	236.325	+	171.700i	0.806571	+	0.586008i	−0.106264	+	0.994338i	$0.533889\pi$
$294$	174.266	−	329.332i	0.592741	−	1.12018i
$295$	15.5731	−	17.0140i	0.0527900	−	0.0576745i
$296$	56.2646	+	3.53987i	0.190083	+	0.0119590i
$297$	−34.3503	−	16.7958i	−0.115657	−	0.0565515i
$298$	28.9750	+	229.360i	0.0972314	+	0.769666i
$299$	62.8447	−	86.4984i	0.210183	−	0.289292i
$300$	203.888	−	141.590i	0.679626	−	0.471968i
$301$	−40.7625	+	29.6157i	−0.135424	+	0.0983910i
$302$	−353.468	+	331.929i	−1.17042	+	1.09910i
$303$	−158.186	−	111.115i	−0.522066	−	0.366718i
$304$	87.8631	−	22.5594i	0.289023	−	0.0742086i
$305$	−507.210	−	270.463i	−1.66298	−	0.886763i
$306$	−281.934	+	166.928i	−0.921354	+	0.545515i
$307$			589.619i			1.92058i	0.278999	+	0.960291i	$0.409997\pi$
$307$			589.619i			1.92058i	−0.278999	+	0.960291i	$0.590003\pi$
$308$	4.39518	−	6.92570i	0.0142701	−	0.0224860i
$309$	−123.091	−	187.285i	−0.398353	−	0.606100i
$310$	−19.2162	+	42.2283i	−0.0619878	+	0.136220i
$311$	157.178	−	285.905i	0.505394	−	0.919309i	−0.493380	−	0.869814i	$-0.664239\pi$
$311$	157.178	−	285.905i	0.505394	−	0.919309i	0.998774	−	0.0494952i	$-0.0157613\pi$
$312$	−64.1679	+	80.1361i	−0.205666	+	0.256846i
$313$	211.760	+	99.6467i	0.676550	+	0.318360i	0.733180	−	0.680035i	$-0.238035\pi$
$313$	211.760	+	99.6467i	0.676550	+	0.318360i	−0.0566297	+	0.998395i	$0.518035\pi$
$314$	52.0773	−	94.7282i	0.165851	−	0.301682i
$315$	49.0890	+	61.5791i	0.155838	+	0.195489i
$316$	93.2330	+	87.5516i	0.295041	+	0.277062i
$317$	−166.488	+	262.343i	−0.525198	+	0.827580i	−0.998580	−	0.0532772i	$-0.983033\pi$
$317$	−166.488	+	262.343i	−0.525198	+	0.827580i	0.473381	+	0.880858i	$0.343033\pi$
$318$	181.056	−	754.993i	0.569359	−	2.37419i
$319$	16.0885	−	25.3514i	0.0504341	−	0.0794715i
$320$	177.953	+	94.8911i	0.556104	+	0.296535i
$321$	−8.52855	−	534.316i	−0.0265687	−	1.66454i
$322$	10.1560	−	25.6511i	0.0315404	−	0.0796619i
$323$	−48.6973	+	45.7298i	−0.150766	+	0.141578i
$324$	−255.051	−	82.5865i	−0.787193	−	0.254897i
$325$	−45.8185	+	456.117i	−0.140980	+	1.40344i
$326$	282.103	−	388.281i	0.865345	−	1.19105i
$327$	−9.09159	+	82.5415i	−0.0278030	+	0.252421i
$328$	−10.6108	−	41.3264i	−0.0323500	−	0.125995i
$329$	−105.899	−	6.66262i	−0.321883	−	0.0202511i
$330$	−32.1543	−	47.5877i	−0.0974374	−	0.144205i
$331$	293.752	+	75.4226i	0.887467	+	0.227863i	0.664791	−	0.747029i	$-0.268521\pi$
$331$	293.752	+	75.4226i	0.887467	+	0.227863i	0.222677	+	0.974892i	$0.428521\pi$
$332$	−42.8314	−	31.1189i	−0.129010	−	0.0937315i
$333$	−249.568	−	107.848i	−0.749454	−	0.323869i
$334$	45.4920	−	25.0094i	0.136204	−	0.0748785i
$335$	−195.403	−	120.533i	−0.583292	−	0.359801i
$336$	−39.4814	+	87.5005i	−0.117504	+	0.260418i
$337$	−290.552	−	528.511i	−0.862171	−	1.56828i	−0.822283	−	0.569079i	$-0.807300\pi$
$337$	−290.552	−	528.511i	−0.862171	−	1.56828i	−0.0398876	−	0.999204i	$-0.512700\pi$
$338$	84.7198	+	444.116i	0.250650	+	1.31395i
$339$	0.906614	+	1.58853i	0.00267438	+	0.00468593i
$340$	−222.812	+	2.84617i	−0.655330	+	0.00837108i
$341$	4.39776	+	2.06943i	0.0128967	+	0.00606871i
$342$	−120.189	−	11.3001i	−0.351431	−	0.0330411i
$343$	97.6562	+	134.412i	0.284712	+	0.391872i
$344$	−41.4007	+	34.2496i	−0.120351	+	0.0995629i
$345$	−61.6796	−	62.0114i	−0.178782	−	0.179743i
$346$	84.3724	+	132.950i	0.243851	+	0.384248i
$347$	121.483	+	191.427i	0.350096	+	0.551663i	0.973050	−	0.230596i	$-0.0740674\pi$
$347$	121.483	+	191.427i	0.350096	+	0.551663i	−0.622954	+	0.782259i	$0.714067\pi$
$348$	86.5827	−	191.889i	0.248801	−	0.551404i
$349$	104.629	+	322.014i	0.299796	+	0.922678i	0.981568	+	0.191113i	$0.0612096\pi$
$349$	104.629	+	322.014i	0.299796	+	0.922678i	−0.681772	+	0.731565i	$0.738790\pi$
$350$	17.8180	+	116.937i	0.0509085	+	0.334104i
$351$	421.934	−	259.001i	1.20209	−	0.737895i
$352$	28.6340	−	52.0851i	0.0813466	−	0.147969i
$353$	114.779	−	138.744i	0.325154	−	0.393044i	−0.582453	−	0.812864i	$-0.697907\pi$
$353$	114.779	−	138.744i	0.325154	−	0.393044i	0.907607	+	0.419821i	$0.137907\pi$
$354$	−30.6172	−	21.5066i	−0.0864893	−	0.0607531i
$355$	−5.33531	−	19.7299i	−0.0150290	−	0.0555773i
$356$	−330.537	+	20.7956i	−0.928474	+	0.0584147i
$357$	−5.56429	−	70.4737i	−0.0155862	−	0.197405i
$358$	677.189	−	560.220i	1.89159	−	1.56486i
$359$	320.182	−	61.0780i	0.891872	−	0.170134i	0.278977	−	0.960298i	$-0.410005\pi$
$359$	320.182	−	61.0780i	0.891872	−	0.170134i	0.612895	+	0.790164i	$0.290005\pi$
$360$	56.3691	+	62.2521i	0.156581	+	0.172922i
$361$	333.734	−	42.1604i	0.924472	−	0.116788i
$362$	−166.671	−	21.0554i	−0.460417	−	0.0581642i
$363$	298.320	−	196.067i	0.821818	−	0.540130i
$364$	45.2207	+	96.0989i	0.124233	+	0.264008i
$365$	−320.797	−	332.987i	−0.878896	−	0.912293i
$366$	−329.381	+	872.347i	−0.899948	+	2.38346i
$367$	−120.670	+	469.978i	−0.328800	+	1.28059i	0.562355	+	0.826896i	$0.309895\pi$
$367$	−120.670	+	469.978i	−0.328800	+	1.28059i	−0.891156	+	0.453698i	$0.850105\pi$
$368$	32.9459	−	101.397i	0.0895269	−	0.275536i
$369$	−19.2605	+	204.858i	−0.0521966	+	0.555172i
$370$	−244.230	−	327.279i	−0.660080	−	0.884539i
$371$	129.073	+	106.779i	0.347907	+	0.287813i
$372$	32.5733	+	10.0119i	0.0875627	+	0.0269136i
$373$	−543.818	+	255.901i	−1.45796	+	0.686063i	−0.981204	−	0.192974i	$-0.938187\pi$
$373$	−543.818	+	255.901i	−1.45796	+	0.686063i	−0.476754	+	0.879037i	$0.658187\pi$
$374$			51.5559i			0.137850i
$375$	362.408	+	96.3616i	0.966421	+	0.256964i
$376$	−113.156			−0.300946
$377$	165.530	+	351.769i	0.439071	+	0.933073i
$378$	88.8328	−	91.8073i	0.235007	−	0.242876i
$379$	56.8816	−	68.7580i	0.150083	−	0.181419i	−0.690114	−	0.723701i	$-0.742439\pi$
$379$	56.8816	−	68.7580i	0.150083	−	0.181419i	0.840197	+	0.542282i	$0.182439\pi$
$380$	−67.0319	−	47.4053i	−0.176400	−	0.124751i
$381$	−490.051	+	69.8708i	−1.28622	+	0.183388i
$382$	31.1020	+	10.1056i	0.0814188	+	0.0264546i
$383$	223.054	+	57.2706i	0.582387	+	0.149532i	0.528379	−	0.849009i	$-0.322800\pi$
$383$	223.054	+	57.2706i	0.582387	+	0.149532i	0.0540086	+	0.998540i	$0.482800\pi$
$384$	−62.3437	+	165.114i	−0.162353	+	0.429984i
$385$	12.2731	−	1.70999i	0.0318782	−	0.00444153i
$386$	−563.152	+	264.999i	−1.45894	+	0.686527i
$387$	243.757	−	87.8970i	0.629864	−	0.227124i
$388$	−50.1704	+	397.140i	−0.129305	+	1.02356i
$389$	30.4884	+	241.340i	0.0783763	+	0.620412i	0.981560	+	0.191157i	$0.0612239\pi$
$389$	30.4884	+	241.340i	0.0783763	+	0.620412i	−0.903183	+	0.429255i	$0.858776\pi$
$390$	743.326	−	21.3642i	1.90596	−	0.0547799i
$391$	14.7120	+	77.1230i	0.0376266	+	0.197245i
$392$	54.6466	+	66.0564i	0.139405	+	0.168511i
$393$	−32.6662	−	413.729i	−0.0831202	−	1.05275i
$394$	60.2984	+	958.415i	0.153042	+	2.43253i
$395$	−9.66799	+	192.972i	−0.0244759	+	0.488536i
$396$	−31.6289	+	27.9130i	−0.0798709	+	0.0704873i
$397$	339.123	+	280.547i	0.854213	+	0.706667i	0.957639	−	0.287970i	$-0.0929805\pi$
$397$	339.123	+	280.547i	0.854213	+	0.706667i	−0.103426	+	0.994637i	$0.532980\pi$
$398$	242.282	+	133.196i	0.608750	+	0.334663i
$399$	13.6036	−	22.2117i	0.0340944	−	0.0556684i
$400$	97.0964	+	446.684i	0.242741	+	1.11671i
$401$	57.9144	−	18.8175i	0.144425	−	0.0469265i	−0.235912	−	0.971774i	$-0.575808\pi$
$401$	57.9144	−	18.8175i	0.144425	−	0.0469265i	0.380337	+	0.924848i	$0.375808\pi$
$402$	−153.177	+	339.478i	−0.381037	+	0.844471i
$403$	−53.1347	+	33.7203i	−0.131848	+	0.0836732i
$404$	−180.070	+	114.276i	−0.445718	+	0.282861i
$405$	−154.266	−	374.469i	−0.380904	−	0.924615i
$406$	63.9437	+	77.2946i	0.157497	+	0.190381i
$407$	−34.6098	+	25.1455i	−0.0850363	+	0.0617825i
$408$	−10.6411	−	74.6330i	−0.0260810	−	0.182924i
$409$	−68.6570	+	145.903i	−0.167865	+	0.356732i	−0.971005	−	0.239059i	$-0.923161\pi$
$409$	−68.6570	+	145.903i	−0.167865	+	0.356732i	0.803140	+	0.595791i	$0.203161\pi$
$410$	−178.453	+	252.335i	−0.435250	+	0.615451i
$411$	−244.925	−	429.148i	−0.595926	−	1.04416i
$412$	−242.873	+	46.3305i	−0.589497	+	0.112453i
$413$	7.07430	−	3.88913i	0.0171291	−	0.00941678i
$414$	−86.9038	+	112.153i	−0.209913	+	0.270900i
$415$	−6.04114	−	79.7517i	−0.0145570	−	0.192173i
$416$	370.751	+	674.394i	0.891230	+	1.62114i
$417$	−125.981	−	21.9545i	−0.302113	−	0.0526486i
$418$	−11.1653	+	15.3677i	−0.0267112	+	0.0367648i
$419$	68.5537	−	266.999i	0.163613	−	0.637229i	−0.832873	−	0.553464i	$-0.813306\pi$
$419$	68.5537	−	266.999i	0.163613	−	0.637229i	0.996486	−	0.0837649i	$-0.0266945\pi$
$420$	83.4966	−	24.0153i	0.198801	−	0.0571793i
$421$	−27.4031	+	435.561i	−0.0650906	+	1.03459i	0.820957	+	0.570991i	$0.193441\pi$
$421$	−27.4031	+	435.561i	−0.0650906	+	1.03459i	−0.886047	+	0.463595i	$0.846559\pi$
$422$	−891.940	+	229.011i	−2.11360	+	0.542681i
$423$	513.527	+	184.589i	1.21401	+	0.436380i
$424$	144.524	+	105.003i	0.340857	+	0.247647i
$425$	−221.131	−	253.812i	−0.520308	−	0.597204i
$426$	−30.6283	+	12.6957i	−0.0718974	+	0.0298021i
$427$	−137.722	−	146.660i	−0.322535	−	0.343465i
$428$	−548.155	−	217.030i	−1.28074	−	0.507080i
$429$	−1.24330	−	77.8930i	−0.00289813	−	0.181569i
$430$	383.213	+	68.0409i	0.891193	+	0.158235i
$431$	−239.362	−	151.904i	−0.555365	−	0.352445i	0.228337	−	0.973582i	$-0.426671\pi$
$431$	−239.362	−	151.904i	−0.555365	−	0.352445i	−0.783702	+	0.621137i	$0.786671\pi$
$432$	320.338	−	375.643i	0.741523	−	0.869544i
$433$	36.4124	+	23.1080i	0.0840934	+	0.0533673i	0.577209	−	0.816597i	$-0.304142\pi$
$433$	36.4124	+	23.1080i	0.0840934	+	0.0533673i	−0.493115	+	0.869964i	$0.664142\pi$
$434$	−11.1160	+	11.8373i	−0.0256129	+	0.0272749i
$435$	305.638	−	87.9076i	0.702616	−	0.202086i
$436$	80.2821	+	44.1355i	0.184133	+	0.101228i
$437$	−12.3169	+	26.1748i	−0.0281852	+	0.0598966i
$438$	−468.823	+	585.489i	−1.07037	+	1.33673i
$439$	−295.324	−	162.356i	−0.672720	−	0.369831i	0.108491	−	0.994097i	$-0.465398\pi$
$439$	−295.324	−	162.356i	−0.672720	−	0.369831i	−0.781212	+	0.624266i	$0.785398\pi$
$440$	12.9478	−	2.64176i	0.0294269	−	0.00600401i
$441$	−140.243	−	388.924i	−0.318011	−	0.881914i
$442$	−563.625	−	357.687i	−1.27517	−	0.809247i
$443$	−149.756			−0.338049			−0.169024	−	0.985612i	$-0.554062\pi$
$443$	−149.756			−0.338049			−0.169024	+	0.985612i	$0.554062\pi$
$444$	−215.345	+	208.789i	−0.485010	+	0.470245i
$445$	−347.129	−	360.319i	−0.780065	−	0.809706i
$446$	39.1303	+	152.402i	0.0877361	+	0.341709i
$447$	209.912	+	147.449i	0.469601	+	0.329864i
$448$	48.3196	+	51.4551i	0.107856	+	0.114855i
$449$	−370.432	−	509.856i	−0.825015	−	1.13554i	−0.988830	−	0.149045i	$-0.952380\pi$
$449$	−370.432	−	509.856i	−0.825015	−	1.13554i	0.163815	−	0.986491i	$-0.447620\pi$
$450$	79.4797	−	603.107i	0.176622	−	1.34024i
$451$	26.1936	+	19.0308i	0.0580790	+	0.0421969i
$452$	2.00196	−	0.252907i	0.00442912	−	0.000559528i
$453$	8.58685	+	537.968i	0.0189555	+	1.18757i
$454$	54.2341	−	862.026i	0.119458	−	1.89873i
$455$	−66.4549	+	146.037i	−0.146055	+	0.320960i
$456$	12.9911	−	24.5510i	0.0284894	−	0.0538399i
$457$	−152.947	+	210.513i	−0.334676	+	0.460642i	−0.942877	−	0.333141i	$-0.891891\pi$
$457$	−152.947	+	210.513i	−0.334676	+	0.460642i	0.608201	+	0.793783i	$0.291891\pi$
$458$	60.0441	+	954.374i	0.131101	+	2.08379i
$459$	−73.4557	+	356.061i	−0.160034	+	0.775733i
$460$	−89.2561	+	36.6645i	−0.194035	+	0.0797055i
$461$	−58.3220	−	11.1255i	−0.126512	−	0.0241334i	0.123736	−	0.992315i	$-0.460512\pi$
$461$	−58.3220	−	11.1255i	−0.126512	−	0.0241334i	−0.250248	+	0.968182i	$0.580512\pi$
$462$	−5.30917	−	19.3878i	−0.0114917	−	0.0419650i
$463$	714.119	−	136.226i	1.54237	−	0.294224i	0.655127	−	0.755518i	$-0.272615\pi$
$463$	714.119	−	136.226i	1.54237	−	0.294224i	0.887247	+	0.461295i	$0.152615\pi$
$464$	265.377	+	282.598i	0.571934	+	0.609048i
$465$	20.3185	+	47.3010i	0.0436957	+	0.101723i
$466$	−24.4001	+	51.8528i	−0.0523607	+	0.111272i
$467$	−334.093	+	132.277i	−0.715403	+	0.283248i	−0.697493	−	0.716591i	$-0.745701\pi$
$467$	−334.093	+	132.277i	−0.715403	+	0.283248i	−0.0179100	+	0.999840i	$0.505701\pi$
$468$	−85.7168	−	539.433i	−0.183156	−	1.15263i
$469$	−51.2213	−	61.9160i	−0.109214	−	0.132017i
$470$	530.489	+	624.826i	1.12870	+	1.32942i
$471$	−38.8819	−	113.471i	−0.0825519	−	0.240916i
$472$	7.26881	−	4.61293i	0.0154000	−	0.00977315i
$473$	7.64015	−	40.0510i	0.0161525	−	0.0846745i
$474$	312.457	−	24.6702i	0.659192	−	0.0520469i
$475$	−10.9472	−	123.545i	−0.0230468	−	0.260095i
$476$	−74.1745	−	24.1007i	−0.155829	−	0.0506318i
$477$	−484.594	−	712.286i	−1.01592	−	1.49326i
$478$	570.290	+	471.785i	1.19308	+	0.986998i
$479$	−284.065	+	717.465i	−0.593037	+	1.49784i	0.254484	+	0.967077i	$0.418094\pi$
$479$	−284.065	+	717.465i	−0.593037	+	1.49784i	−0.847521	+	0.530762i	$0.821906\pi$
$480$	592.905	−	211.664i	1.23522	−	0.440966i
$481$	−34.7805	−	552.820i	−0.0723087	−	1.14931i
$482$	−47.0347	−	144.758i	−0.0975824	−	0.300328i
$483$	−13.4746	−	27.4874i	−0.0278976	−	0.0569098i
$484$	−73.7982	−	386.864i	−0.152476	−	0.799305i
$485$	−506.406	+	330.523i	−1.04414	+	0.681492i
$486$	−570.269	+	326.230i	−1.17339	+	0.671255i
$487$	94.1311	−	745.124i	0.193288	−	1.53003i	−0.535056	−	0.844817i	$-0.679709\pi$
$487$	94.1311	−	745.124i	0.193288	−	1.53003i	0.728344	−	0.685212i	$-0.240291\pi$
$488$	−156.399	−	146.869i	−0.320491	−	0.300961i
$489$	−108.126	−	521.456i	−0.221116	−	1.06637i
$490$	108.562	−	611.431i	0.221555	−	1.24782i
$491$	21.4266	−	169.609i	0.0436387	−	0.345436i	−0.955145	−	0.296137i	$-0.904301\pi$
$491$	21.4266	−	169.609i	0.0436387	−	0.345436i	0.998784	−	0.0492985i	$-0.0156986\pi$
$492$	200.647	+	106.172i	0.407818	+	0.215797i
$493$	−271.514	−	88.2204i	−0.550739	−	0.178946i
$494$	−90.5412	−	228.681i	−0.183282	−	0.462917i
$495$	−63.0699	−	9.13261i	−0.127414	−	0.0184497i
$496$	−40.0004	+	48.3522i	−0.0806460	+	0.0974842i
$497$	0.449178	−	7.13948i	0.000903779	−	0.0143651i
$498$	−127.041	+	26.3423i	−0.255102	+	0.0528962i
$499$	804.274			1.61177			0.805886	−	0.592071i	$-0.201689\pi$
$499$	804.274			1.61177			0.805886	+	0.592071i	$0.201689\pi$
$500$	251.307	−	328.643i	0.502614	−	0.657286i
$501$	13.4332	−	56.0154i	0.0268127	−	0.111807i
$502$	−767.505	+	361.160i	−1.52889	+	0.719443i
$503$	16.0769	−	255.535i	0.0319620	−	0.508021i	−0.949180	−	0.314733i	$-0.898085\pi$
$503$	16.0769	−	255.535i	0.0319620	−	0.508021i	0.981142	−	0.193288i	$-0.0619151\pi$
$504$	11.6873	+	26.9703i	0.0231890	+	0.0535125i
$505$	−307.664	−	95.6391i	−0.609236	−	0.189384i
$506$	8.21855	+	20.7577i	0.0162422	+	0.0410231i
$507$	427.821	+	262.020i	0.843828	+	0.516806i
$508$	−135.813	+	528.957i	−0.267349	+	1.04125i
$509$	−86.9624	+	688.378i	−0.170849	+	1.35241i	0.640548	+	0.767918i	$0.278707\pi$
$509$	−86.9624	+	688.378i	−0.170849	+	1.35241i	−0.811397	+	0.584495i	$0.801293\pi$
$510$	−362.224	+	408.648i	−0.710244	+	0.801270i
$511$	−68.9053	−	146.431i	−0.134844	−	0.286558i
$512$	459.917	+	431.891i	0.898275	+	0.843537i
$513$	−99.0065	+	90.2261i	−0.192995	+	0.175879i
$514$	815.350	−	103.003i	1.58628	−	0.200394i
$515$	−290.822	−	234.397i	−0.564703	−	0.455140i
$516$	13.3944	−	285.559i	0.0259582	−	0.553410i
$517$	66.1613	−	54.7333i	0.127971	−	0.105867i
$518$	−44.1674	−	135.933i	−0.0852652	−	0.262419i
$519$	172.127	+	29.9963i	0.331652	+	0.0577963i
$520$	−60.9497	+	159.878i	−0.117211	+	0.307458i
$521$	−132.372	+	334.333i	−0.254072	+	0.641714i	−0.999696	−	0.0246537i	$-0.992152\pi$
$521$	−132.372	+	334.333i	−0.254072	+	0.641714i	0.745624	+	0.666367i	$0.232152\pi$
$522$	−205.129	−	473.369i	−0.392967	−	0.906837i
$523$	−394.094	+	716.855i	−0.753526	+	1.37066i	0.169347	+	0.985556i	$0.445834\pi$
$523$	−394.094	+	716.855i	−0.753526	+	1.37066i	−0.922874	+	0.385103i	$0.874166\pi$
$524$	−435.455	−	141.488i	−0.831022	−	0.270015i
$525$	109.295	+	72.6752i	0.208180	+	0.138429i
$526$	−302.681	−	931.556i	−0.575439	−	1.77102i
$527$	8.65941	−	45.3942i	0.0164315	−	0.0861371i
$528$	−25.1812	−	73.4878i	−0.0476917	−	0.139181i
$529$	−265.235	−	417.943i	−0.501389	−	0.790063i
$530$	−97.7395	−	1290.30i	−0.184414	−	2.43453i
$531$	−40.5126	+	9.07711i	−0.0762949	+	0.0170944i
$532$	−16.8904	−	23.2476i	−0.0317488	−	0.0436985i
$533$	−389.778	+	154.324i	−0.731291	+	0.289539i
$534$	−507.304	+	633.547i	−0.950008	+	1.18642i
$535$	−286.020	−	843.465i	−0.534616	−	1.57657i
$536$	−58.6611	−	62.4678i	−0.109442	−	0.116544i
$537$	45.6931	−	974.144i	0.0850896	−	1.81405i
$538$	488.566	+	888.699i	0.908116	+	1.65186i
$539$	−63.9030	−	12.1901i	−0.118558	−	0.0226162i
$540$	−446.813	−	0.973110i	−0.827431	−	0.00180206i
$541$	−127.766	+	70.2401i	−0.236167	+	0.129834i	−0.595443	−	0.803397i	$-0.703024\pi$
$541$	−127.766	+	70.2401i	−0.236167	+	0.129834i	0.359276	+	0.933231i	$0.383024\pi$
$542$	−64.9437	−	1032.25i	−0.119822	−	1.90452i
$543$	−141.717	+	121.099i	−0.260988	+	0.223019i
$544$	−547.381	−	140.544i	−1.00622	−	0.258352i
$545$	27.6681	+	135.607i	0.0507672	+	0.248821i
$546$	248.788	+	76.4685i	0.455656	+	0.140052i
$547$	82.1178	+	319.828i	0.150124	+	0.584694i	0.998472	+	0.0552557i	$0.0175974\pi$
$547$	82.1178	+	319.828i	0.150124	+	0.584694i	−0.848348	+	0.529439i	$0.822403\pi$
$548$	−540.839	+	68.3238i	−0.986932	+	0.124679i
$549$	470.194	+	921.658i	0.856455	+	1.67879i
$550$	−75.2887	−	59.1109i	−0.136888	−	0.107474i
$551$	−61.8270	−	85.0975i	−0.112209	−	0.154442i
$552$	−16.1816	−	28.3528i	−0.0293146	−	0.0513638i
$553$	−24.8947	+	62.8767i	−0.0450175	+	0.113701i
$554$	159.666	+	621.857i	0.288205	+	1.12249i
$555$	−450.996	−	43.8526i	−0.812606	−	0.0790137i
$556$	−75.5958	+	119.120i	−0.135964	+	0.214244i
$557$	554.432			0.995390			0.497695	−	0.867352i	$-0.334180\pi$
$557$	554.432			0.995390			0.497695	+	0.867352i	$0.334180\pi$
$558$	71.8600	−	42.5468i	0.128781	−	0.0762488i
$559$	384.844	+	361.393i	0.688451	+	0.646499i
$560$	−18.0233	+	158.974i	−0.0321844	+	0.283882i
$561$	42.3217	+	38.4903i	0.0754398	+	0.0686102i
$562$	−152.594	−	71.8052i	−0.271519	−	0.127767i
$563$	283.726	−	602.947i	0.503953	−	1.07095i	−0.477390	−	0.878691i	$-0.658417\pi$
$563$	283.726	−	602.947i	0.503953	−	1.07095i	0.981343	−	0.192263i	$-0.0615828\pi$
$564$	405.065	−	445.386i	0.718200	−	0.789692i
$565$	2.24866	+	2.05822i	0.00397993	+	0.00364286i
$566$	−108.085	+	115.099i	−0.190963	+	0.203355i
$567$	−9.04344	−	141.463i	−0.0159496	−	0.249494i
$568$		−	7.62867i		−	0.0134308i
$569$	181.247	+	115.023i	0.318536	+	0.202149i	0.685476	−	0.728096i	$-0.259594\pi$
$569$	181.247	+	115.023i	0.318536	+	0.202149i	−0.366939	+	0.930245i	$0.619594\pi$
$570$	−196.471	+	43.3634i	−0.344685	+	0.0760761i
$571$	958.897	−	246.203i	1.67933	−	0.431178i	0.715697	−	0.698411i	$-0.246109\pi$
$571$	958.897	−	246.203i	1.67933	−	0.431178i	0.963632	+	0.267232i	$0.0861092\pi$
$572$	−79.9105	−	31.6388i	−0.139704	−	0.0553126i
$573$	31.5156	−	17.9867i	0.0550010	−	0.0313904i
$574$	−87.5134	+	63.5822i	−0.152462	+	0.110770i
$575$	−129.493	−	66.9403i	−0.225205	−	0.116418i
$576$	−164.966	−	323.361i	−0.286400	−	0.561391i
$577$	114.925	+	909.723i	0.199176	+	1.57664i	0.701951	+	0.712225i	$0.252312\pi$
$577$	114.925	+	909.723i	0.199176	+	1.57664i	−0.502775	+	0.864417i	$0.667688\pi$
$578$	−282.007	+	72.4072i	−0.487902	+	0.125272i
$579$	−202.900	+	660.128i	−0.350431	+	1.14012i
$580$	39.5251	−	348.630i	0.0681467	−	0.601086i
$581$	6.96168	−	27.1139i	0.0119822	−	0.0466677i
$582$	637.284	+	745.783i	1.09499	+	1.28141i
$583$	−135.292	+	8.51183i	−0.232061	+	0.0146000i
$584$	−83.1415	−	151.234i	−0.142366	−	0.258962i
$585$	537.411	−	626.139i	0.918651	−	1.07032i
$586$	147.989	−	775.786i	0.252541	−	1.32387i
$587$	827.490	−	454.916i	1.40969	−	0.774985i	0.418601	−	0.908170i	$-0.362520\pi$
$587$	827.490	−	454.916i	1.40969	−	0.774985i	0.991091	+	0.133185i	$0.0425204\pi$
$588$	−455.621	−	21.3713i	−0.774865	−	0.0363458i
$589$	12.4121	−	11.6557i	0.0210731	−	0.0197890i
$590$	−59.5490	−	18.5111i	−0.100930	−	0.0313748i
$591$	831.772	+	666.030i	1.40740	+	1.12695i
$592$	−203.332	−	513.558i	−0.343466	−	0.867496i
$593$	631.503	−	458.814i	1.06493	−	0.773717i	0.0899358	−	0.995948i	$-0.471334\pi$
$593$	631.503	−	458.814i	1.06493	−	0.773717i	0.974994	+	0.222231i	$0.0713338\pi$
$594$	−1.54556	+	103.367i	−0.00260195	+	0.174018i
$595$	−44.7687	−	108.985i	−0.0752416	−	0.183168i
$596$	238.952	−	151.643i	0.400926	−	0.254435i
$597$	290.221	−	99.4467i	0.486132	−	0.166577i
$598$	−283.948	−	54.1661i	−0.474830	−	0.0905787i
$599$	1110.27	−	360.749i	1.85354	−	0.602252i	0.857384	−	0.514678i	$-0.172088\pi$
$599$	1110.27	−	360.749i	1.85354	−	0.602252i	0.996158	−	0.0875747i	$-0.0279117\pi$
$600$	121.189	+	70.0303i	0.201982	+	0.116717i
$601$	234.910	−	722.978i	0.390865	−	1.20296i	−0.541270	−	0.840849i	$-0.682056\pi$
$601$	234.910	−	722.978i	0.390865	−	1.20296i	0.932135	−	0.362110i	$-0.117944\pi$
$602$	119.374	+	65.6264i	0.198296	+	0.109014i
$603$	164.316	+	379.187i	0.272498	+	0.628834i
$604$	551.902	+	218.514i	0.913745	+	0.361777i
$605$	373.363	−	463.241i	0.617129	−	0.765687i
$606$	−89.7285	+	514.888i	−0.148067	+	0.849650i
$607$	−844.320	+	274.336i	−1.39097	+	0.451954i	−0.906260	−	0.422720i	$-0.861075\pi$
$607$	−844.320	+	274.336i	−1.39097	+	0.451954i	−0.484712	+	0.874674i	$0.661075\pi$
$608$	−132.725	−	160.437i	−0.218298	−	0.263877i
$609$	111.189	+	5.21543i	0.182577	+	0.00856393i
$610$	−77.7637	+	1552.15i	−0.127482	+	2.54451i
$611$	139.345	+	1103.03i	0.228060	+	1.80528i
$612$	331.851	+	225.281i	0.542241	+	0.368107i
$613$	162.859	−	173.427i	0.265675	−	0.282916i	−0.582274	−	0.812993i	$-0.697837\pi$
$613$	162.859	−	173.427i	0.265675	−	0.282916i	0.847950	+	0.530077i	$0.177837\pi$
$614$	1442.41	−	678.745i	2.34920	−	1.10545i
$615$	73.9112	+	334.877i	0.120181	+	0.544515i
$616$	4.58870	+	0.579687i	0.00744918	+	0.000941051i
$617$	448.208	+	115.080i	0.726431	+	0.186516i	0.593757	−	0.804644i	$-0.297644\pi$
$617$	448.208	+	115.080i	0.726431	+	0.186516i	0.132673	+	0.991160i	$0.457644\pi$
$618$	−316.465	+	516.717i	−0.512080	+	0.836111i
$619$	−234.368	+	92.7929i	−0.378624	+	0.149908i	−0.549725	−	0.835346i	$-0.685267\pi$
$619$	−234.368	+	92.7929i	−0.378624	+	0.149908i	0.171101	+	0.985253i	$0.445267\pi$
$620$	56.7908	−	0.725436i	0.0915981	−	0.00117006i
$621$	27.1848	+	155.069i	0.0437758	+	0.249708i
$622$	−880.357	−	55.3874i	−1.41536	−	0.0890472i
$623$	−74.5612	−	158.451i	−0.119681	−	0.254335i
$624$	978.095	+	234.559i	1.56746	+	0.375896i
$625$	624.184	−	31.9190i	0.998695	−	0.0510703i
$626$		−	632.746i		−	1.01078i
$627$	4.27948	+	20.6386i	0.00682533	+	0.0329164i
$628$	−132.071	−	8.30920i	−0.210304	−	0.0132312i
$629$	313.413	+	259.278i	0.498272	+	0.412206i
$630$	94.1341	−	190.976i	0.149419	−	0.303136i
$631$	−335.285	+	132.749i	−0.531356	+	0.210379i	−0.618454	−	0.785821i	$-0.712241\pi$
$631$	−335.285	+	132.749i	−0.531356	+	0.210379i	0.0870982	+	0.996200i	$0.472241\pi$
$632$	−22.2853	+	68.5871i	−0.0352615	+	0.108524i
$633$	−477.907	+	903.159i	−0.754987	+	1.42679i
$634$	833.433	+	105.287i	1.31456	+	0.166068i
$635$	−741.946	+	360.779i	−1.16842	+	0.568156i
$636$	−930.649	+	192.973i	−1.46328	+	0.303417i
$637$	576.616	−	614.034i	0.905205	−	0.963946i
$638$	−80.5385	−	10.1744i	−0.126236	−	0.0159473i
$639$	−12.4445	+	34.6208i	−0.0194750	+	0.0541796i
$640$	−14.7188	+	293.784i	−0.0229981	+	0.459038i
$641$	266.618	−	50.8601i	0.415941	−	0.0793450i	0.0248371	−	0.999692i	$-0.492093\pi$
$641$	266.618	−	50.8601i	0.415941	−	0.0793450i	0.391104	+	0.920347i	$0.372093\pi$
$642$	−1297.30	+	635.946i	−2.02072	+	0.990571i
$643$	503.329	−	163.542i	0.782783	−	0.254342i	0.109755	−	0.993959i	$-0.464993\pi$
$643$	503.329	−	163.542i	0.782783	−	0.254342i	0.673028	+	0.739617i	$0.264993\pi$
$644$	−33.7064	+	2.12063i	−0.0523391	+	0.00329290i
$645$	341.951	−	263.778i	0.530157	−	0.408959i
$646$	167.929	+	66.4877i	0.259952	+	0.102922i
$647$	320.099	−	386.933i	0.494744	−	0.598042i	−0.462753	−	0.886487i	$-0.653138\pi$
$647$	320.099	−	386.933i	0.494744	−	0.598042i	0.957496	+	0.288445i	$0.0931383\pi$
$648$	−19.0974	−	149.954i	−0.0294713	−	0.231411i
$649$	−2.01875	+	6.21307i	−0.00311055	+	0.00957329i
$650$	1168.56	−	412.976i	1.79779	−	0.635348i
$651$	1.41824	+	17.9625i	0.00217855	+	0.0275921i
$652$	−577.124	−	110.092i	−0.885159	−	0.168853i
$653$	−90.2116	−	142.151i	−0.138149	−	0.217689i	0.768208	−	0.640200i	$-0.221149\pi$
$653$	−90.2116	−	142.151i	−0.138149	−	0.217689i	−0.906358	+	0.422512i	$0.861149\pi$
$654$	212.390	−	72.7773i	0.324756	−	0.111280i
$655$	−262.823	−	639.817i	−0.401257	−	0.976819i
$656$	−322.098	+	266.463i	−0.491003	+	0.406193i
$657$	130.611	+	821.963i	0.198800	+	1.25109i
$658$	105.608	+	266.735i	0.160498	+	0.405373i
$659$	−181.802	−	85.5494i	−0.275875	−	0.129817i	0.282865	−	0.959160i	$-0.408715\pi$
$659$	−181.802	−	85.5494i	−0.275875	−	0.129817i	−0.558740	+	0.829343i	$0.688715\pi$
$660$	−35.9515	+	60.4202i	−0.0544720	+	0.0915457i
$661$	377.037	−	354.061i	0.570403	−	0.535644i	−0.344779	−	0.938684i	$-0.612046\pi$
$661$	377.037	−	354.061i	0.570403	−	0.535644i	0.915183	+	0.403039i	$0.132046\pi$
$662$	−153.646	−	805.439i	−0.232093	−	1.21668i
$663$	−714.410	+	195.634i	−1.07754	+	0.295074i
$664$	5.59379	−	29.3237i	0.00842439	−	0.0441622i
$665$	10.2579	−	42.1814i	0.0154254	−	0.0634307i
$666$	23.4593	+	734.678i	0.0352242	+	1.10312i
$667$	−123.382	+	7.76252i	−0.184980	+	0.0116380i
$668$	−51.4137	−	37.3542i	−0.0769666	−	0.0559195i
$669$	154.319	+	81.6581i	0.230672	+	0.122060i
$670$	−69.9253	+	616.775i	−0.104366	+	0.920559i
$671$	162.486	+	10.2228i	0.242155	+	0.0152351i
$672$	220.318	−	3.51664i	0.327855	−	0.00523310i
$673$	18.2840	+	144.733i	0.0271680	+	0.215057i	0.999854	−	0.0170666i	$-0.00543275\pi$
$673$	18.2840	+	144.733i	0.0271680	+	0.215057i	−0.972686	+	0.232123i	$0.925433\pi$
$674$	−958.446	+	1319.19i	−1.42203	+	1.95725i
$675$	−435.747	−	515.509i	−0.645552	−	0.763716i
$676$	447.773	−	325.326i	0.662387	−	0.481252i
$677$	357.830	−	336.025i	0.528553	−	0.496344i	−0.373701	−	0.927549i	$-0.621912\pi$
$677$	357.830	−	336.025i	0.528553	−	0.496344i	0.902254	+	0.431205i	$0.141912\pi$
$678$	2.84243	−	4.04653i	0.00419237	−	0.00596834i
$679$	−205.007	+	52.6369i	−0.301925	+	0.0775212i
$680$	−54.9453	−	112.996i	−0.0808020	−	0.166170i
$681$	−667.139	−	688.087i	−0.979646	−	1.01041i
$682$		−	13.1407i		−	0.0192678i
$683$	−586.824	+	924.687i	−0.859186	+	1.35386i	0.0750401	+	0.997181i	$0.476092\pi$
$683$	−586.824	+	924.687i	−0.859186	+	1.35386i	−0.934226	+	0.356680i	$0.883908\pi$
$684$	50.1293	+	139.019i	0.0732885	+	0.203245i
$685$	−607.484	−	556.036i	−0.886838	−	0.811731i
$686$	216.400	−	393.630i	0.315452	−	0.573804i
$687$	828.264	+	663.222i	1.20562	+	0.965388i
$688$	476.333	+	224.145i	0.692344	+	0.325792i
$689$	845.580	−	1538.10i	1.22726	−	2.23237i
$690$	−80.6978	+	222.274i	−0.116953	+	0.322137i
$691$	−252.879	−	237.469i	−0.365961	−	0.343660i	0.479650	−	0.877460i	$-0.340764\pi$
$691$	−252.879	−	237.469i	−0.365961	−	0.343660i	−0.845611	+	0.533800i	$0.820764\pi$
$692$	103.286	−	162.753i	0.149258	−	0.235192i
$693$	−19.8790	−	10.1162i	−0.0286854	−	0.0145977i
$694$	328.449	−	517.552i	0.473269	−	0.745753i
$695$	−211.094	+	29.4113i	−0.303732	+	0.0423184i
$696$	118.689	−	1.89446i	0.170530	−	0.00272193i
$697$	113.326	−	286.228i	0.162591	−	0.410658i
$698$	667.312	−	626.647i	0.956034	−	0.897775i
$699$	24.3490	+	58.7418i	0.0348341	+	0.0840370i
$700$	120.239	−	80.6868i	0.171770	−	0.115267i
$701$	−554.884	+	763.733i	−0.791561	+	1.08949i	0.202351	+	0.979313i	$0.435142\pi$
$701$	−554.884	+	763.733i	−0.791561	+	1.08949i	−0.993912	+	0.110177i	$0.964858\pi$
$702$	−1119.32	−	734.042i	−1.59447	−	1.04564i
$703$	37.2707	+	145.160i	0.0530166	+	0.206486i
$704$	−57.0078	−	3.58663i	−0.0809770	−	0.00509464i
$705$	908.964	+	31.0063i	1.28931	+	0.0439805i
$706$	−471.545	−	121.072i	−0.667911	−	0.171490i
$707$	−91.2301	−	66.2826i	−0.129038	−	0.0937519i
$708$	−7.86356	+	45.1234i	−0.0111067	+	0.0637336i
$709$	−358.587	+	197.135i	−0.505764	+	0.278046i	−0.714140	−	0.700002i	$-0.753182\pi$
$709$	−358.587	+	197.135i	−0.505764	+	0.278046i	0.208376	+	0.978049i	$0.433182\pi$
$710$	−42.1243	+	35.7643i	−0.0593300	+	0.0503722i
$711$	213.021	−	274.911i	0.299608	−	0.386654i
$712$	−89.9659	−	163.647i	−0.126357	−	0.229842i
$713$	−3.74982	−	19.6572i	−0.00525922	−	0.0275698i
$714$	−165.997	+	94.7385i	−0.232489	+	0.132687i
$715$	−41.6962	−	122.961i	−0.0583163	−	0.171973i
$716$	−973.504	−	458.096i	−1.35964	−	0.639799i
$717$	813.048	−	115.923i	1.13396	−	0.161678i
$718$	−517.998	−	712.963i	−0.721445	−	0.992984i
$719$	816.707	−	675.639i	1.13589	−	0.939692i	0.137187	−	0.990545i	$-0.456194\pi$
$719$	816.707	−	675.639i	1.13589	−	0.939692i	0.998706	+	0.0508531i	$0.0161940\pi$
$720$	316.721	−	759.407i	0.439890	−	1.05473i
$721$	−70.0512	−	110.383i	−0.0971584	−	0.153097i
$722$	−487.320	−	767.893i	−0.674958	−	1.06356i
$723$	−153.945	−	69.4622i	−0.212926	−	0.0960750i
$724$	63.5510	+	195.590i	0.0877777	+	0.270152i
$725$	440.133	−	295.353i	0.607080	−	0.407383i
$726$	−823.060	−	504.086i	−1.13369	−	0.694334i
$727$	−356.429	+	648.342i	−0.490274	+	0.891805i	0.509240	+	0.860625i	$0.329927\pi$
$727$	−356.429	+	648.342i	−0.490274	+	0.891805i	−0.999514	+	0.0311804i	$0.990073\pi$
$728$	−38.1730	+	46.1433i	−0.0524355	+	0.0633836i
$729$	−157.949	+	711.683i	−0.216666	+	0.976246i
$730$	−445.310	+	1168.10i	−0.610013	+	1.60014i
$731$	−386.913	+	24.3425i	−0.529293	+	0.0333003i
$732$	1137.95	−	89.8474i	1.55457	−	0.122742i
$733$	−485.362	+	401.526i	−0.662158	+	0.547785i	−0.906659	−	0.421864i	$-0.861376\pi$
$733$	−485.362	+	401.526i	−0.662158	+	0.547785i	0.244501	+	0.969649i	$0.421376\pi$
$734$	1288.63	−	245.820i	1.75563	−	0.334905i
$735$	−420.869	−	545.596i	−0.572610	−	0.742308i
$736$	−242.793	+	30.6719i	−0.329882	+	0.0416738i
$737$	64.5144	+	8.15007i	0.0875365	+	0.0110584i
$738$	523.325	−	188.707i	0.709112	−	0.255700i
$739$	72.6086	+	154.301i	0.0982525	+	0.208797i	0.947910	−	0.318537i	$-0.103192\pi$
$739$	72.6086	+	154.301i	0.0982525	+	0.208797i	−0.849658	+	0.527334i	$0.823192\pi$
$740$	−235.216	+	441.111i	−0.317860	+	0.596096i
$741$	−255.318	−	96.4030i	−0.344559	−	0.130099i
$742$	112.633	−	438.676i	0.151796	−	0.591208i
$743$	58.2482	−	179.270i	0.0783960	−	0.241278i	−0.904176	−	0.427160i	$-0.859514\pi$
$743$	58.2482	−	179.270i	0.0783960	−	0.241278i	0.982572	+	0.185882i	$0.0595141\pi$
$744$	2.71221	+	19.0226i	0.00364545	+	0.0255680i
$745$	408.268	+	126.912i	0.548011	+	0.170352i
$746$	1252.04	+	1035.78i	1.67834	+	1.38844i
$747$	−73.2212	+	123.953i	−0.0980204	+	0.165934i
$748$	57.1066	−	26.8723i	0.0763457	−	0.0359255i
$749$		−	311.728i		−	0.416192i
$750$	−181.456	−	997.499i	−0.241942	−	1.33000i
$751$	−916.418			−1.22026			−0.610132	−	0.792300i	$-0.708883\pi$
$751$	−916.418			−1.22026			−0.610132	+	0.792300i	$0.708883\pi$
$752$	472.039	+	1003.13i	0.627711	+	1.33395i
$753$	−276.526	+	899.671i	−0.367233	+	1.19478i
$754$	669.994	−	809.883i	0.888586	−	1.07412i
$755$	287.975	+	849.230i	0.381423	+	1.12481i
$756$	−147.994	−	50.5444i	−0.195759	−	0.0668577i
$757$	−176.282	−	57.2775i	−0.232869	−	0.0756638i	0.190258	−	0.981734i	$-0.439068\pi$
$757$	−176.282	−	57.2775i	−0.232869	−	0.0756638i	−0.423127	+	0.906070i	$0.639068\pi$
$758$	−233.685	−	60.0001i	−0.308291	−	0.0791558i
$759$	23.1755	+	8.75063i	0.0305343	+	0.0115292i
$760$	8.09305	−	45.5809i	0.0106488	−	0.0599748i
$761$	−1045.00	+	491.742i	−1.37320	+	0.646178i	−0.963910	−	0.266227i	$-0.914223\pi$
$761$	−1045.00	+	491.742i	−1.37320	+	0.646178i	−0.409288	+	0.912405i	$0.634223\pi$
$762$	735.055	+	1118.40i	0.964639	+	1.46771i
$763$	−6.07127	+	48.0591i	−0.00795711	+	0.0629870i
$764$	−5.01753	−	39.7178i	−0.00656745	−	0.0519867i
$765$	65.0277	+	602.433i	0.0850036	+	0.787494i
$766$	−116.668	−	611.594i	−0.152308	−	0.798425i
$767$	−53.9174	−	65.1749i	−0.0702965	−	0.0849738i
$768$	958.203	−	75.6555i	1.24766	−	0.0985098i
$769$	−36.4167	−	578.828i	−0.0473560	−	0.752702i	−0.948025	−	0.318196i	$-0.896923\pi$
$769$	−36.4167	−	578.828i	−0.0473560	−	0.752702i	0.900669	−	0.434506i	$-0.143077\pi$
$770$	−18.3115	−	28.0557i	−0.0237812	−	0.0364360i
$771$	524.165	−	746.212i	0.679851	−	0.967850i
$772$	587.060	+	485.658i	0.760440	+	0.629091i
$773$	−145.167	−	79.8060i	−0.187796	−	0.103242i	0.385082	−	0.922882i	$-0.374173\pi$
$773$	−145.167	−	79.8060i	−0.187796	−	0.103242i	−0.572878	+	0.819641i	$0.694173\pi$
$774$	−495.629	−	495.129i	−0.640348	−	0.639702i
$775$	56.3622	+	64.6919i	0.0727255	+	0.0834735i
$776$	−214.666	+	69.7492i	−0.276631	+	0.0898829i
$777$	−144.561	−	65.2277i	−0.186050	−	0.0839481i
$778$	555.303	−	352.406i	0.713757	−	0.452964i
$779$	95.7674	−	60.7759i	0.122936	−	0.0780178i
$780$	−411.106	−	812.219i	−0.527059	−	1.04131i
$781$	3.68999	+	4.46043i	0.00472470	+	0.00571118i
$782$	171.733	−	124.771i	0.219607	−	0.159554i
$783$	−541.728	−	185.017i	−0.691862	−	0.236292i
$784$	357.632	−	760.007i	0.456164	−	0.969397i
$785$	−119.562	−	160.219i	−0.152309	−	0.204101i
$786$	−974.517	+	556.181i	−1.23984	+	0.707609i
$787$	−1158.66	+	221.026i	−1.47225	+	0.280846i	−0.860192	−	0.509970i	$-0.829657\pi$
$787$	−1158.66	+	221.026i	−1.47225	+	0.280846i	−0.612054	+	0.790816i	$0.709657\pi$
$788$	1030.17	−	566.342i	1.30733	−	0.718708i
$789$	−990.679	−	447.008i	−1.25561	−	0.566550i
$790$	483.203	−	198.490i	0.611650	−	0.251253i
$791$	0.514008	+	0.934977i	0.000649821	+	0.00118202i
$792$	−21.8347	−	9.43565i	−0.0275691	−	0.0119137i
$793$	−1239.06	+	1705.42i	−1.56250	+	2.15060i
$794$	295.928	−	1152.56i	0.372705	−	1.45159i
$795$	−1132.17	−	883.073i	−1.42411	−	1.11078i
$796$	21.2521	−	337.793i	0.0266986	−	0.424362i
$797$	−1391.04	+	357.158i	−1.74534	+	0.448128i	−0.980570	−	0.196172i	$-0.937149\pi$
$797$	−1391.04	+	357.158i	−1.74534	+	0.448128i	−0.764773	+	0.644300i	$0.777149\pi$
$798$	−69.9973	−	7.70990i	−0.0877159	−	0.00966153i
$799$	−660.506	−	479.886i	−0.826666	−	0.600608i
$800$	832.835	−	638.219i	1.04104	−	0.797773i
$801$	141.332	+	889.432i	0.176445	+	1.11040i
$802$	−112.703	−	120.016i	−0.140527	−	0.149646i
$803$	121.764	+	48.2098i	0.151636	+	0.0600371i
$804$	455.867	−	7.27637i	0.566998	−	0.00905022i
$805$	−35.3983	−	36.7434i	−0.0439731	−	0.0456440i
$806$	143.658	+	91.1680i	0.178235	+	0.113112i
$807$	1094.28	+	262.420i	1.35598	+	0.325180i
$808$	−101.535	−	64.4362i	−0.125662	−	0.0797477i
$809$	80.4403	−	85.6603i	0.0994318	−	0.105884i	−0.677328	−	0.735681i	$-0.736862\pi$
$809$	80.4403	−	85.6603i	0.0994318	−	0.105884i	0.776760	+	0.629797i	$0.216862\pi$
$810$	−738.493	+	808.460i	−0.911719	+	0.998099i
$811$	1241.80	+	682.685i	1.53119	+	0.841782i	0.999985	−	0.00545883i	$-0.00173761\pi$
$811$	1241.80	+	682.685i	1.53119	+	0.841782i	0.531210	+	0.847240i	$0.321738\pi$
$812$	52.2873	−	111.116i	0.0643932	−	0.136842i
$813$	−895.851	−	717.341i	−1.10191	−	0.882338i
$814$	101.356	+	55.7207i	0.124515	+	0.0684530i
$815$	−437.495	−	772.268i	−0.536803	−	0.947568i
$816$	−617.238	+	405.672i	−0.756419	+	0.497148i
$817$	−120.602	−	76.5364i	−0.147616	−	0.0936798i
$818$	435.964			0.532963
$819$	248.511	−	147.138i	0.303432	−	0.179656i
$820$	372.516	+	66.1417i	0.454288	+	0.0806606i
$821$	215.699	+	840.093i	0.262727	+	1.02326i	0.953793	+	0.300464i	$0.0971414\pi$
$821$	215.699	+	840.093i	0.262727	+	1.02326i	−0.691066	+	0.722792i	$0.742859\pi$
$822$	−767.893	+	1093.19i	−0.934177	+	1.32991i
$823$	−572.838	−	610.011i	−0.696037	−	0.741204i	0.279715	−	0.960083i	$-0.409760\pi$
$823$	−572.838	−	610.011i	−0.696037	−	0.741204i	−0.975752	+	0.218879i	$0.929760\pi$
$824$	−81.9473	−	112.791i	−0.0994506	−	0.136882i
$825$	−104.732	+	17.6730i	−0.126948	+	0.0214219i
$826$	−17.6578	−	12.8291i	−0.0213774	−	0.0155316i
$827$	−1453.56	+	183.628i	−1.75764	+	0.222041i	−0.936980	−	0.349382i	$-0.886392\pi$
$827$	−1453.56	+	183.628i	−1.75764	+	0.222041i	−0.820656	+	0.571423i	$0.806392\pi$
$828$	169.524	+	37.8033i	0.204739	+	0.0456561i
$829$	35.9413	−	571.270i	0.0433550	−	0.689108i	−0.914987	−	0.403484i	$-0.867799\pi$
$829$	35.9413	−	571.270i	0.0433550	−	0.689108i	0.958342	−	0.285624i	$-0.0922008\pi$
$830$	−188.145	+	106.585i	−0.226681	+	0.128416i
$831$	629.679	+	333.195i	0.757737	+	0.400956i
$832$	434.722	−	598.343i	0.522502	−	0.719163i
$833$	38.8394	+	617.334i	0.0466259	+	0.741098i
$834$	91.3162	+	333.465i	0.109492	+	0.399838i
$835$	−7.25161	−	95.7317i	−0.00868457	−	0.114649i
$836$	22.8419	+	4.35732i	0.0273228	+	0.00521210i
$837$	18.7225	−	90.7536i	0.0223686	−	0.108427i
$838$	−732.086	+	139.653i	−0.873611	+	0.166650i
$839$	−160.443	−	170.854i	−0.191231	−	0.203640i	0.626207	−	0.779657i	$-0.284606\pi$
$839$	−160.443	−	170.854i	−0.191231	−	0.203640i	−0.817438	+	0.576017i	$0.804606\pi$
$840$	32.2986	+	36.8343i	0.0384508	+	0.0438504i
$841$	−166.684	+	354.221i	−0.198197	+	0.421190i
$842$	1097.07	−	434.362i	1.30294	−	0.515869i
$843$	−172.867	+	71.6549i	−0.205062	+	0.0849999i
$844$	718.570	+	868.602i	0.851387	+	1.02915i
$845$	812.459	+	197.578i	0.961489	+	0.233820i
$846$	−139.586	−	1468.75i	−0.164995	−	1.73611i
$847$	175.825	−	111.582i	0.207586	−	0.131738i
$848$	327.963	−	1719.24i	0.386749	−	2.02741i
$849$	13.7901	+	174.656i	0.0162427	+	0.205720i
$850$	−366.352	+	833.138i	−0.431002	+	0.980162i
$851$	167.519	+	54.4303i	0.196850	+	0.0639605i
$852$	30.0269	+	27.3085i	0.0352428	+	0.0320522i
$853$	−418.688	−	346.369i	−0.490842	−	0.406059i	0.358805	−	0.933413i	$-0.383184\pi$
$853$	−418.688	−	346.369i	−0.490842	−	0.406059i	−0.849646	+	0.527353i	$0.823184\pi$
$854$	−200.238	+	505.744i	−0.234471	+	0.592206i
$855$	−111.083	+	193.655i	−0.129922	+	0.226497i
$856$	−20.8735	−	331.774i	−0.0243849	−	0.387587i
$857$	−226.152	−	696.025i	−0.263888	−	0.812164i	−0.991947	−	0.126650i	$-0.959577\pi$
$857$	−226.152	−	696.025i	−0.263888	−	0.812164i	0.728059	−	0.685514i	$-0.240423\pi$
$858$	−189.121	+	92.7087i	−0.220421	+	0.108052i
$859$	−144.091	−	755.354i	−0.167743	−	0.879341i	−0.962267	−	0.272107i	$-0.912279\pi$
$859$	−144.091	−	755.354i	−0.167743	−	0.879341i	0.794524	−	0.607233i	$-0.207721\pi$
$860$	−124.374	−	459.936i	−0.144621	−	0.534809i
$861$	−13.1412	+	119.308i	−0.0152628	+	0.138569i
$862$	−96.0642	+	760.426i	−0.111443	+	0.882165i
$863$	536.509	+	503.816i	0.621679	+	0.583795i	0.930033	−	0.367476i	$-0.119778\pi$
$863$	536.509	+	503.816i	0.621679	+	0.583795i	−0.308354	+	0.951272i	$0.599778\pi$
$864$	−1093.26	−	298.192i	−1.26535	−	0.345130i
$865$	288.417	−	40.1845i	0.333430	−	0.0464561i
$866$	14.6135	−	115.678i	0.0168748	−	0.133578i
$867$	−151.101	+	285.555i	−0.174281	+	0.329360i
$868$	18.9057	+	6.14284i	0.0217808	+	0.00707701i
$869$	−20.1455	−	50.8818i	−0.0231824	−	0.0585521i
$870$	−566.889	−	646.497i	−0.651597	−	0.743101i
$871$	−536.691	+	648.747i	−0.616177	+	0.744831i
$872$	−3.24364	+	51.5561i	−0.00371977	+	0.0591240i
$873$	1087.99	+	33.6418i	1.24626	+	0.0385358i
$874$	78.2112			0.0894864
$875$	210.483	+	59.5784i	0.240552	+	0.0680896i
$876$	892.887	+	214.125i	1.01928	+	0.244435i
$877$	1366.40	−	642.978i	1.55804	−	0.733157i	0.562435	−	0.826841i	$-0.309865\pi$
$877$	1366.40	−	642.978i	1.55804	−	0.733157i	0.995602	+	0.0936845i	$0.0298645\pi$
$878$	−57.2121	+	909.360i	−0.0651618	+	1.03572i
$879$	−526.350	−	700.665i	−0.598806	−	0.797116i
$880$	−77.4326	−	103.763i	−0.0879916	−	0.117913i
$881$	−220.517	−	556.963i	−0.250303	−	0.632194i	0.749244	−	0.662295i	$-0.230417\pi$
$881$	−220.517	−	556.963i	−0.250303	−	0.632194i	−0.999547	+	0.0301006i	$0.990417\pi$
$882$	−789.997	+	790.795i	−0.895689	+	0.896593i
$883$	38.0893	−	148.348i	0.0431362	−	0.168004i	−0.943366	−	0.331755i	$-0.892359\pi$
$883$	38.0893	−	148.348i	0.0431362	−	0.168004i	0.986502	+	0.163751i	$0.0523593\pi$
$884$	−102.421	+	810.743i	−0.115860	+	0.917130i
$885$	−59.6534	+	35.0633i	−0.0674049	+	0.0396195i
$886$	172.392	+	366.353i	0.194574	+	0.413491i
$887$	796.331	+	747.805i	0.897781	+	0.843072i	0.988253	−	0.152827i	$-0.0488377\pi$
$887$	796.331	+	747.805i	0.897781	+	0.843072i	−0.0904724	+	0.995899i	$0.528838\pi$
$888$	−158.224	−	59.7424i	−0.178181	−	0.0672775i
$889$	−286.481	+	36.1910i	−0.322251	+	0.0407098i
$890$	−481.862	+	1263.98i	−0.541418	+	1.42020i
$891$	83.6991	+	78.4399i	0.0939384	+	0.0880358i
$892$	148.415	−	122.779i	0.166384	−	0.137645i
$893$	−92.9553	−	286.087i	−0.104093	−	0.320366i
$894$	119.069	−	683.253i	0.133187	−	0.764265i
$895$	−424.285	−	1569.00i	−0.474062	−	1.75308i
$896$	−37.9002	+	95.7249i	−0.0422993	+	0.106836i
$897$	−256.453	+	192.652i	−0.285901	+	0.214773i
$898$	−820.853	+	1493.13i	−0.914090	+	1.66272i
$899$	69.2041	+	22.4858i	0.0769790	+	0.0250120i
$900$	−709.467	+	226.319i	−0.788296	+	0.251465i
$901$	398.297	+	1225.83i	0.442061	+	1.36052i
$902$	16.4027	−	85.9860i	0.0181848	−	0.0953281i
$903$	142.994	−	48.9980i	0.158354	−	0.0542614i
$904$	0.609669	+	0.960684i	0.000674413	+	0.00106270i
$905$	−163.108	+	264.423i	−0.180230	+	0.292180i
$906$	1306.17	−	640.293i	1.44168	−	0.706725i
$907$	−710.759	−	978.276i	−0.783637	−	1.07858i	−0.994871	−	0.101149i	$-0.967748\pi$
$907$	−710.759	−	978.276i	−0.783637	−	1.07858i	0.211234	−	0.977436i	$-0.432252\pi$
$908$	−983.102	+	389.238i	−1.08271	+	0.428676i
$909$	355.678	+	458.060i	0.391285	+	0.503916i
$910$	433.756	−	5.54073i	0.476655	−	0.00608871i
$911$	−400.626	−	426.623i	−0.439765	−	0.468302i	0.470457	−	0.882423i	$-0.344089\pi$
$911$	−400.626	−	426.623i	−0.439765	−	0.468302i	−0.910222	+	0.414121i	$0.864089\pi$
$912$	−271.840	−	12.7509i	−0.298070	−	0.0139813i
$913$	10.9132	+	19.8511i	0.0119531	+	0.0217427i
$914$	691.053	+	131.825i	0.756075	+	0.144229i
$915$	1216.09	+	1222.63i	1.32906	+	1.33621i
$916$	1025.83	−	563.954i	1.11990	−	0.615670i
$917$	−15.2013	−	241.618i	−0.0165773	−	0.263488i
$918$	955.605	−	230.186i	1.04096	−	0.250747i
$919$	−796.711	−	204.561i	−0.866932	−	0.222590i	−0.211070	−	0.977471i	$-0.567695\pi$
$919$	−796.711	−	204.561i	−0.866932	−	0.222590i	−0.655862	+	0.754881i	$0.727695\pi$
$920$	−40.1350	−	36.7360i	−0.0436251	−	0.0399304i
$921$	519.689	−	1690.79i	0.564266	−	1.83582i
$922$	39.9211	+	155.483i	0.0432984	+	0.168636i
$923$	−74.3634	+	9.39428i	−0.0805671	+	0.0101780i
$924$	−18.7079	+	15.9862i	−0.0202467	+	0.0173011i
$925$	−737.972	+	160.414i	−0.797807	+	0.173421i
$926$	−1155.32	−	1590.16i	−1.24764	−	1.71723i
$927$	187.903	+	645.551i	0.202700	+	0.696387i
$928$	327.575	−	827.360i	0.352990	−	0.891552i
$929$	235.106	+	915.677i	0.253074	+	0.985658i	0.960367	+	0.278738i	$0.0899161\pi$
$929$	235.106	+	915.677i	0.253074	+	0.985658i	−0.707293	+	0.706920i	$0.750084\pi$
$930$	92.3244	−	104.157i	0.0992736	−	0.111997i
$931$	−122.117	+	192.425i	−0.131167	+	0.206687i
$932$	70.1535			0.0752720
$933$	−702.719	+	681.326i	−0.753182	+	0.730253i
$934$	708.188	+	665.033i	0.758232	+	0.712027i
$935$	86.7821	+	39.4907i	0.0928151	+	0.0422360i
$936$	254.640	−	173.241i	0.272051	−	0.185086i
$937$	−739.128	−	347.807i	−0.788824	−	0.371192i	−0.0112123	−	0.999937i	$-0.503569\pi$
$937$	−739.128	−	347.807i	−0.788824	−	0.371192i	−0.777612	+	0.628745i	$0.783569\pi$
$938$	−92.5034	+	196.580i	−0.0986177	+	0.209573i
$939$	−519.415	−	472.392i	−0.553158	−	0.503080i
$940$	415.592	−	913.279i	0.442119	−	0.971573i
$941$	−404.012	+	430.229i	−0.429343	+	0.457204i	−0.906868	−	0.421414i	$-0.861534\pi$
$941$	−404.012	+	430.229i	−0.429343	+	0.457204i	0.477525	+	0.878618i	$0.341534\pi$
$942$	−232.830	+	225.742i	−0.247166	+	0.239641i
$943$		−	133.308i		−	0.141366i
$944$	−71.2165	−	45.1954i	−0.0754412	−	0.0478764i
$945$	−86.4919	−	219.851i	−0.0915258	−	0.232647i
$946$	−106.773	+	27.4147i	−0.112868	+	0.0289796i
$947$	−558.220	−	221.015i	−0.589461	−	0.233384i	0.0544093	−	0.998519i	$-0.482672\pi$
$947$	−558.220	−	221.015i	−0.589461	−	0.233384i	−0.643870	+	0.765135i	$0.722672\pi$
$948$	−190.187	−	333.238i	−0.200620	−	0.351517i
$949$	−1371.83	+	996.690i	−1.44555	+	1.05025i
$950$	−289.631	+	169.001i	−0.304875	+	0.177896i
$951$	708.649	−	605.553i	0.745162	−	0.636754i
$952$	−5.51175	−	43.6300i	−0.00578965	−	0.0458298i
$953$	1374.79	−	352.985i	1.44259	−	0.370393i	0.555315	−	0.831640i	$-0.312598\pi$
$953$	1374.79	−	352.985i	1.44259	−	0.370393i	0.887272	+	0.461247i	$0.152598\pi$
$954$	−1184.65	+	2005.44i	−1.24177	+	2.10213i
$955$	40.8339	−	44.6121i	0.0427580	−	0.0467143i
$956$	225.328	−	877.596i	0.235699	−	0.917988i
$957$	−68.4800	+	58.5174i	−0.0715570	+	0.0611467i
$958$	2082.16	−	130.999i	2.17345	−	0.136742i
$959$	−138.861	−	252.588i	−0.144798	−	0.263387i
$960$	−426.662	−	428.958i	−0.444440	−	0.446831i
$961$	177.866	−	932.408i	0.185085	−	0.970248i
$962$	−1312.35	+	721.469i	−1.36419	+	0.749967i
$963$	−446.488	+	1539.72i	−0.463643	+	1.59888i
$964$	−135.827	+	127.550i	−0.140900	+	0.132314i
$965$	14.7016	+	1150.92i	0.0152348	+	1.19266i
$966$	−51.7322	+	64.6057i	−0.0535530	+	0.0668797i
$967$	390.260	+	985.685i	0.403578	+	1.01932i	0.979433	+	0.201770i	$0.0646694\pi$
$967$	390.260	+	985.685i	0.403578	+	1.01932i	−0.575855	+	0.817552i	$0.695331\pi$
$968$	179.660	−	130.531i	0.185600	−	0.134846i
$969$	179.951	−	88.2132i	0.185707	−	0.0910353i
$970$	1391.53	+	858.356i	1.43456	+	0.884903i
$971$	−1203.96	+	764.054i	−1.23991	+	0.786873i	−0.983712	−	0.179750i	$-0.942471\pi$
$971$	−1203.96	+	764.054i	−1.23991	+	0.786873i	−0.256202	+	0.966623i	$0.582471\pi$
$972$	658.592	+	461.626i	0.677564	+	0.474924i
$973$	−73.2761	−	13.9782i	−0.0753094	−	0.0143660i
$974$	−1931.18	+	627.480i	−1.98274	+	0.644230i
$975$	533.410	−	1267.58i	0.547087	−	1.30008i
$976$	−649.570	+	1999.17i	−0.665543	+	2.04833i
$977$	−212.123	−	116.615i	−0.217116	−	0.119361i	0.369485	−	0.929237i	$-0.379534\pi$
$977$	−212.123	−	116.615i	−0.217116	−	0.119361i	−0.586601	+	0.809876i	$0.699534\pi$
$978$	−1151.19	+	864.791i	−1.17708	+	0.884244i
$979$	131.759	+	52.1670i	0.134585	+	0.0532860i
$980$	−733.845	+	198.444i	−0.748821	+	0.202494i
$981$	98.8230	−	228.683i	0.100737	−	0.233112i
$982$	−439.586	+	142.830i	−0.447644	+	0.145448i
$983$	−735.234	−	888.746i	−0.747949	−	0.904115i	0.249992	−	0.968248i	$-0.419572\pi$
$983$	−735.234	−	888.746i	−0.747949	−	0.904115i	−0.997941	+	0.0641324i	$0.979572\pi$
$984$	−5.99739	+	127.860i	−0.00609491	+	0.129939i
$985$	1659.45	+	632.627i	1.68472	+	0.642261i
$986$	96.7394	+	765.771i	0.0981130	+	0.776644i
$987$	297.805	+	112.445i	0.301727	+	0.113926i
$988$	−206.109	+	219.484i	−0.208612	+	0.222150i
$989$	−151.900	+	71.4789i	−0.153590	+	0.0722739i
$990$	50.2621	+	164.803i	0.0507698	+	0.166468i
$991$	1320.64	+	166.835i	1.33263	+	0.168351i	0.759176	−	0.650886i	$-0.225602\pi$
$991$	1320.64	+	166.835i	1.33263	+	0.168351i	0.573456	+	0.819236i	$0.305602\pi$
$992$	139.518	+	35.8220i	0.140643	+	0.0361109i
$993$	−775.886	−	475.194i	−0.781355	−	0.478544i
$994$	−17.9826	+	7.11983i	−0.0180912	+	0.00716281i
$995$	409.787	−	305.800i	0.411846	−	0.307337i
$996$	95.3954	+	126.988i	0.0957785	+	0.127498i
$997$	971.444	+	61.1181i	0.974367	+	0.0613020i	0.541985	−	0.840388i	$-0.317673\pi$
$997$	971.444	+	61.1181i	0.974367	+	0.0613020i	0.432382	+	0.901690i	$0.357673\pi$
$998$	−925.847	−	1967.53i	−0.927703	−	1.97147i
$999$	620.604	+	529.234i	0.621226	+	0.529764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.p.a.14.19	✓	1960
3.2	odd	2	inner	375.3.p.a.14.80	yes	1960
125.9	even	50	inner	375.3.p.a.134.80	yes	1960
375.134	odd	50	inner	375.3.p.a.134.19	yes	1960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.p.a.14.19	✓	1960	1.1	even	1	trivial
375.3.p.a.14.80	yes	1960	3.2	odd	2	inner
375.3.p.a.134.19	yes	1960	375.134	odd	50	inner
375.3.p.a.134.80	yes	1960	125.9	even	50	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.p (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15116 - 2.44634i) q^{2} +(-2.86760 - 0.881397i) q^{3} +(-2.10970 + 2.55019i) q^{4} +(-4.99959 + 0.0638640i) q^{5} +(1.14487 + 8.02975i) q^{6} +(-1.66437 - 0.540787i) q^{7} +(-1.80761 - 0.464116i) q^{8} +(7.44628 + 5.05499i) q^{9} +(5.91156 + 12.1572i) q^{10} +(1.28139 - 0.602977i) q^{11} +(8.29752 - 5.45345i) q^{12} +(-2.29817 + 18.1919i) q^{13} +(0.593008 + 4.69414i) q^{14} +(14.3931 + 4.22349i) q^{15} +(3.42619 + 17.9607i) q^{16} +(-8.58302 - 10.3751i) q^{17} +(3.79437 - 24.0352i) q^{18} +(-0.311515 - 4.95138i) q^{19} +(10.3848 - 12.8847i) q^{20} +(4.29610 + 3.01773i) q^{21} +(-2.95017 - 2.44059i) q^{22} +(-5.10963 - 2.80905i) q^{23} +(4.77444 + 2.92412i) q^{24} +(24.9918 - 0.638588i) q^{25} +(47.1491 - 15.3197i) q^{26} +(-16.8975 - 21.0588i) q^{27} +(4.89044 - 3.10357i) q^{28} +(17.9014 - 11.3605i) q^{29} +(-6.23669 - 40.0724i) q^{30} +(2.18766 + 2.64442i) q^{31} +(33.9546 - 24.6695i) q^{32} +(-4.20598 + 0.599682i) q^{33} +(-15.5005 + 32.9403i) q^{34} +(8.35571 + 2.59742i) q^{35} +(-28.6006 + 8.32491i) q^{36} +(-29.6731 + 5.66046i) q^{37} +(-11.7541 + 6.46190i) q^{38} +(22.6246 - 50.1416i) q^{39} +(9.06696 + 2.20495i) q^{40} +(11.0141 + 20.0345i) q^{41} +(2.43689 - 13.9836i) q^{42} +(16.9230 - 23.2926i) q^{43} +(-1.16565 + 4.53989i) q^{44} +(-37.5512 - 24.7974i) q^{45} +(-0.989871 + 15.7335i) q^{46} +(58.7279 - 15.0788i) q^{47} +(6.00559 - 54.5241i) q^{48} +(-37.1642 - 27.0013i) q^{49} +(-30.3318 - 60.4034i) q^{50} +(15.4681 + 37.3167i) q^{51} +(-41.5444 - 44.2403i) q^{52} +(-89.0003 - 35.2377i) q^{53} +(-32.0653 + 65.5790i) q^{54} +(-6.36792 + 3.09647i) q^{55} +(2.75755 + 1.74999i) q^{56} +(-3.47084 + 14.4732i) q^{57} +(-48.3990 - 30.7150i) q^{58} +(-3.15782 + 3.36274i) q^{59} +(-41.1359 + 27.7949i) q^{60} +(100.743 + 55.3838i) q^{61} +(3.95081 - 8.39589i) q^{62} +(-9.65969 - 12.4402i) q^{63} +(-35.3454 - 19.4313i) q^{64} +(10.3281 - 91.0989i) q^{65} +(6.30878 + 9.59891i) q^{66} +(38.7695 + 24.6039i) q^{67} +44.5661 q^{68} +(12.1765 + 12.5588i) q^{69} +(-3.26458 - 23.4309i) q^{70} +(1.01657 + 3.95929i) q^{71} +(-11.1139 - 12.5934i) q^{72} +(63.3036 + 67.4114i) q^{73} +(48.0059 + 66.0744i) q^{74} +(-72.2295 - 20.1965i) q^{75} +(13.2842 + 9.65152i) q^{76} +(-2.45879 + 0.310617i) q^{77} +(-148.708 + 2.37362i) q^{78} +(2.42640 - 38.5665i) q^{79} +(-18.2766 - 89.5775i) q^{80} +(29.8941 + 75.2818i) q^{81} +(36.3322 - 50.0070i) q^{82} +(1.00440 + 15.9645i) q^{83} +(-16.7593 + 4.58937i) q^{84} +(43.5742 + 51.3231i) q^{85} +(-76.4625 - 14.5860i) q^{86} +(-61.3471 + 16.7993i) q^{87} +(-2.59611 + 0.495234i) q^{88} +(68.4996 + 72.9447i) q^{89} +(-17.4353 + 120.409i) q^{90} +(13.6630 - 29.0353i) q^{91} +(17.9434 - 7.10430i) q^{92} +(-3.94254 - 9.51134i) q^{93} +(-104.493 - 126.310i) q^{94} +(1.87366 + 24.7350i) q^{95} +(-119.112 + 40.8147i) q^{96} +(102.117 - 64.8056i) q^{97} +(-23.2725 + 121.999i) q^{98} +(12.5896 + 1.98749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) \) 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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