LMFDB - Embedded newform 54.4.e.a.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,4,Mod(7,54)] 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("54.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18610314031$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	54.13
Dual form			54.4.e.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.347296 + 1.96962i) q^{2} +(-4.52643 + 2.55175i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(-5.66862 - 4.75653i) q^{5} +(-6.59798 - 8.02911i) q^{6} +(-11.1935 - 4.07412i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(13.9771 - 23.1006i) q^{9} +(7.39985 - 12.8169i) q^{10} +(-46.3308 + 38.8761i) q^{11} +(13.5228 - 15.7840i) q^{12} +(2.09014 - 11.8538i) q^{13} +(4.13696 - 23.4619i) q^{14} +(37.7961 + 7.06523i) q^{15} +(12.2567 - 10.2846i) q^{16} +(-52.1248 + 90.2827i) q^{17} +(50.3536 + 19.5068i) q^{18} +(22.8348 + 39.5511i) q^{19} +(27.8143 + 10.1236i) q^{20} +(61.0629 - 10.1219i) q^{21} +(-92.6616 - 77.7523i) q^{22} +(-13.0410 + 4.74653i) q^{23} +(35.7848 + 21.1530i) q^{24} +(-12.1974 - 69.1750i) q^{25} +24.0732 q^{26} +(-4.31954 + 140.230i) q^{27} +47.6477 q^{28} +(29.4992 + 167.298i) q^{29} +(-0.789345 + 76.8975i) q^{30} +(19.5480 - 7.11491i) q^{31} +(24.5134 + 20.5692i) q^{32} +(110.511 - 294.195i) q^{33} +(-195.925 - 71.3109i) q^{34} +(44.0732 + 76.3370i) q^{35} +(-20.9334 + 105.952i) q^{36} +(156.422 - 270.931i) q^{37} +(-69.9700 + 58.7118i) q^{38} +(20.7870 + 58.9887i) q^{39} +(-10.2798 + 58.2995i) q^{40} +(59.6415 - 338.244i) q^{41} +(41.1432 + 116.755i) q^{42} +(-308.776 + 259.094i) q^{43} +(120.961 - 209.511i) q^{44} +(-189.110 + 64.4659i) q^{45} +(-13.8779 - 24.0373i) q^{46} +(-81.8198 - 29.7800i) q^{47} +(-29.2354 + 77.8286i) q^{48} +(-154.056 - 129.269i) q^{49} +(132.012 - 48.0485i) q^{50} +(5.56017 - 541.668i) q^{51} +(8.36055 + 47.4150i) q^{52} -753.474 q^{53} +(-277.699 + 40.1934i) q^{54} +447.547 q^{55} +(16.5479 + 93.8476i) q^{56} +(-204.285 - 120.757i) q^{57} +(-319.268 + 116.204i) q^{58} +(263.901 + 221.440i) q^{59} +(-151.733 + 25.1515i) q^{60} +(669.676 + 243.742i) q^{61} +(20.8026 + 36.0311i) q^{62} +(-250.568 + 201.633i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-68.2310 + 57.2526i) q^{65} +(617.831 + 115.491i) q^{66} +(-2.10545 + 11.9406i) q^{67} +(72.4110 - 410.663i) q^{68} +(46.9172 - 54.7622i) q^{69} +(-135.048 + 113.319i) q^{70} +(212.776 - 368.538i) q^{71} +(-215.954 - 4.43397i) q^{72} +(294.170 + 509.518i) q^{73} +(587.955 + 213.998i) q^{74} +(231.728 + 281.991i) q^{75} +(-139.940 - 117.424i) q^{76} +(676.991 - 246.405i) q^{77} +(-108.966 + 61.4289i) q^{78} +(167.873 + 952.056i) q^{79} -118.398 q^{80} +(-338.279 - 645.762i) q^{81} +686.924 q^{82} +(55.6100 + 315.380i) q^{83} +(-215.674 + 121.585i) q^{84} +(724.908 - 263.845i) q^{85} +(-617.552 - 518.188i) q^{86} +(-560.430 - 681.990i) q^{87} +(454.665 + 165.485i) q^{88} +(-49.8431 - 86.3309i) q^{89} +(-192.650 - 350.085i) q^{90} +(-71.6896 + 124.170i) q^{91} +(42.5245 - 35.6823i) q^{92} +(-70.3274 + 82.0868i) q^{93} +(30.2394 - 171.496i) q^{94} +(58.6842 - 332.815i) q^{95} +(-163.446 - 30.5530i) q^{96} +(-1273.09 + 1068.25i) q^{97} +(201.106 - 348.326i) q^{98} +(250.491 + 1613.65i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{5} - 18 q^{6} - 33 q^{7} - 96 q^{8} + 54 q^{9} + 30 q^{10} - 12 q^{11} - 36 q^{12} + 60 q^{13} - 66 q^{14} + 81 q^{15} + 102 q^{17} + 108 q^{18} + 171 q^{19} + 96 q^{20} + 126 q^{21} - 24 q^{22}+ \cdots - 4014 q^{99}+O(q^{100}) $ 24 * q - 12 * q^5 - 18 * q^6 - 33 * q^7 - 96 * q^8 + 54 * q^9 + 30 * q^10 - 12 * q^11 - 36 * q^12 + 60 * q^13 - 66 * q^14 + 81 * q^15 + 102 * q^17 + 108 * q^18 + 171 * q^19 + 96 * q^20 + 126 * q^21 - 24 * q^22 - 708 * q^23 + 864 * q^25 - 468 * q^26 - 702 * q^27 - 336 * q^28 - 381 * q^29 - 18 * q^30 + 909 * q^31 - 819 * q^33 - 48 * q^34 + 624 * q^35 + 468 * q^36 + 555 * q^37 + 66 * q^38 + 333 * q^39 - 96 * q^40 + 618 * q^41 + 1332 * q^42 - 1161 * q^43 + 132 * q^44 - 909 * q^45 + 348 * q^46 - 378 * q^47 + 579 * q^49 + 36 * q^50 - 810 * q^51 + 240 * q^52 - 1794 * q^53 - 486 * q^54 - 3906 * q^55 - 264 * q^56 - 1485 * q^57 + 444 * q^58 + 1038 * q^59 - 324 * q^60 + 324 * q^61 + 744 * q^62 + 3096 * q^63 - 768 * q^64 + 5718 * q^65 + 2610 * q^66 - 576 * q^67 + 1056 * q^68 + 4455 * q^69 - 1038 * q^70 + 120 * q^71 - 864 * q^72 + 3036 * q^73 - 1110 * q^74 - 5355 * q^75 + 132 * q^76 - 3804 * q^77 - 468 * q^78 - 2991 * q^79 - 480 * q^80 + 1458 * q^81 - 3408 * q^82 + 513 * q^83 - 612 * q^84 - 2925 * q^85 - 2322 * q^86 - 7092 * q^87 + 480 * q^88 + 1065 * q^89 - 252 * q^90 + 2859 * q^91 + 1884 * q^92 + 9918 * q^93 - 828 * q^94 + 6357 * q^95 + 576 * q^96 - 2055 * q^97 + 1356 * q^98 - 4014 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.347296	+	1.96962i	0.122788	+	0.696364i
$2$	0.347296	+	1.96962i	0.122788	+	0.696364i
$3$	−4.52643	+	2.55175i	−0.871112	+	0.491084i
$3$	−4.52643	+	2.55175i	−0.871112	+	0.491084i
$4$	−3.75877	+	1.36808i	−0.469846	+	0.171010i
$5$	−5.66862	−	4.75653i	−0.507016	−	0.425437i	0.353061	−	0.935600i	$-0.385141\pi$
$5$	−5.66862	−	4.75653i	−0.507016	−	0.425437i	−0.860078	+	0.510163i	$0.829585\pi$
$6$	−6.59798	−	8.02911i	−0.448936	−	0.546312i
$7$	−11.1935	−	4.07412i	−0.604394	−	0.219982i	0.0216544	−	0.999766i	$-0.493107\pi$
$7$	−11.1935	−	4.07412i	−0.604394	−	0.219982i	−0.626049	+	0.779784i	$0.715329\pi$
$8$	−4.00000	−	6.92820i	−0.176777	−	0.306186i
$9$	13.9771	−	23.1006i	0.517672	−	0.855579i
$10$	7.39985	−	12.8169i	0.234004	−	0.405307i
$11$	−46.3308	+	38.8761i	−1.26993	+	1.06560i	−0.275383	+	0.961335i	$0.588805\pi$
$11$	−46.3308	+	38.8761i	−1.26993	+	1.06560i	−0.994550	+	0.104265i	$0.966751\pi$
$12$	13.5228	−	15.7840i	0.325308	−	0.379703i
$13$	2.09014	−	11.8538i	0.0445923	−	0.252895i	−0.954360	−	0.298659i	$-0.903461\pi$
$13$	2.09014	−	11.8538i	0.0445923	−	0.252895i	0.998952	+	0.0457631i	$0.0145719\pi$
$14$	4.13696	−	23.4619i	0.0789750	−	0.447890i
$15$	37.7961	+	7.06523i	0.650594	+	0.121616i
$16$	12.2567	−	10.2846i	0.191511	−	0.160697i
$17$	−52.1248	+	90.2827i	−0.743654	+	1.28805i	0.207167	+	0.978305i	$0.433576\pi$
$17$	−52.1248	+	90.2827i	−0.743654	+	1.28805i	−0.950821	+	0.309740i	$0.899758\pi$
$18$	50.3536	+	19.5068i	0.659359	+	0.255434i
$19$	22.8348	+	39.5511i	0.275720	+	0.477560i	0.970316	−	0.241839i	$-0.0777506\pi$
$19$	22.8348	+	39.5511i	0.275720	+	0.477560i	−0.694597	+	0.719399i	$0.744417\pi$
$20$	27.8143	+	10.1236i	0.310974	+	0.113185i
$21$	61.0629	−	10.1219i	0.634525	−	0.105180i
$22$	−92.6616	−	77.7523i	−0.897978	−	0.753493i
$23$	−13.0410	+	4.74653i	−0.118228	+	0.0430313i	−0.400457	−	0.916316i	$-0.631148\pi$
$23$	−13.0410	+	4.74653i	−0.118228	+	0.0430313i	0.282229	+	0.959347i	$0.408926\pi$
$24$	35.7848	+	21.1530i	0.304356	+	0.179910i
$25$	−12.1974	−	69.1750i	−0.0975794	−	0.553400i
$26$	24.0732			0.181583
$27$	−4.31954	+	140.230i	−0.0307888	+	0.999526i
$28$	47.6477			0.321592
$29$	29.4992	+	167.298i	0.188892	+	1.07126i	0.920852	+	0.389912i	$0.127495\pi$
$29$	29.4992	+	167.298i	0.188892	+	1.07126i	−0.731960	+	0.681347i	$0.761394\pi$
$30$	−0.789345	+	76.8975i	−0.00480380	+	0.467983i
$31$	19.5480	−	7.11491i	0.113256	−	0.0412218i	−0.284771	−	0.958596i	$-0.591917\pi$
$31$	19.5480	−	7.11491i	0.113256	−	0.0412218i	0.398026	+	0.917374i	$0.369695\pi$
$32$	24.5134	+	20.5692i	0.135419	+	0.113630i
$33$	110.511	−	294.195i	0.582954	−	1.55190i
$34$	−195.925	−	71.3109i	−0.988261	−	0.359698i
$35$	44.0732	+	76.3370i	0.212849	+	0.368666i
$36$	−20.9334	+	105.952i	−0.0969137	+	0.490518i
$37$	156.422	−	270.931i	0.695017	−	1.20381i	−0.275158	−	0.961399i	$-0.588730\pi$
$37$	156.422	−	270.931i	0.695017	−	1.20381i	0.970175	−	0.242406i	$-0.0779367\pi$
$38$	−69.9700	+	58.7118i	−0.298701	+	0.250640i
$39$	20.7870	+	58.9887i	0.0853481	+	0.242199i
$40$	−10.2798	+	58.2995i	−0.0406343	+	0.230449i
$41$	59.6415	−	338.244i	0.227181	−	1.28841i	−0.631289	−	0.775548i	$-0.717474\pi$
$41$	59.6415	−	338.244i	0.227181	−	1.28841i	0.858471	−	0.512863i	$-0.171415\pi$
$42$	41.1432	+	116.755i	0.151156	+	0.428945i
$43$	−308.776	+	259.094i	−1.09507	+	0.918871i	−0.997084	−	0.0763170i	$-0.975684\pi$
$43$	−308.776	+	259.094i	−1.09507	+	0.918871i	−0.0979842	+	0.995188i	$0.531239\pi$
$44$	120.961	−	209.511i	0.414445	−	0.717839i
$45$	−189.110	+	64.4659i	−0.626463	+	0.213556i
$46$	−13.8779	−	24.0373i	−0.0444824	−	0.0770458i
$47$	−81.8198	−	29.7800i	−0.253929	−	0.0924225i	0.211920	−	0.977287i	$-0.432029\pi$
$47$	−81.8198	−	29.7800i	−0.253929	−	0.0924225i	−0.465848	+	0.884865i	$0.654251\pi$
$48$	−29.2354	+	77.8286i	−0.0879119	+	0.234033i
$49$	−154.056	−	129.269i	−0.449144	−	0.376876i
$50$	132.012	−	48.0485i	0.373387	−	0.135902i
$51$	5.56017	−	541.668i	0.0152663	−	1.48723i
$52$	8.36055	+	47.4150i	0.0222961	+	0.126448i
$53$	−753.474			−1.95278			−0.976392	−	0.216006i	$-0.930697\pi$
$53$	−753.474			−1.95278			−0.976392	+	0.216006i	$0.930697\pi$
$54$	−277.699	+	40.1934i	−0.699815	+	0.101289i
$55$	447.547			1.09722
$56$	16.5479	+	93.8476i	0.0394875	+	0.223945i
$57$	−204.285	−	120.757i	−0.474705	−	0.280607i
$58$	−319.268	+	116.204i	−0.722793	+	0.263075i
$59$	263.901	+	221.440i	0.582323	+	0.488627i	0.885709	−	0.464241i	$-0.153673\pi$
$59$	263.901	+	221.440i	0.582323	+	0.488627i	−0.303386	+	0.952868i	$0.598117\pi$
$60$	−151.733	+	25.1515i	−0.326477	+	0.0541174i
$61$	669.676	+	243.742i	1.40563	+	0.511606i	0.929843	−	0.367957i	$-0.119943\pi$
$61$	669.676	+	243.742i	1.40563	+	0.511606i	0.475783	+	0.879563i	$0.342165\pi$
$62$	20.8026	+	36.0311i	0.0426118	+	0.0738058i
$63$	−250.568	+	201.633i	−0.501090	+	0.403229i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−68.2310	+	57.2526i	−0.130200	+	0.109251i
$66$	617.831	+	115.491i	1.15227	+	0.215394i
$67$	−2.10545	+	11.9406i	−0.00383912	+	0.0217727i	−0.986667	−	0.162751i	$-0.947963\pi$
$67$	−2.10545	+	11.9406i	−0.00383912	+	0.0217727i	0.982828	+	0.184524i	$0.0590743\pi$
$68$	72.4110	−	410.663i	0.129134	−	0.732356i
$69$	46.9172	−	54.7622i	0.0818575	−	0.0955449i
$70$	−135.048	+	113.319i	−0.230591	+	0.193488i
$71$	212.776	−	368.538i	0.355660	−	0.616020i	−0.631571	−	0.775318i	$-0.717590\pi$
$71$	212.776	−	368.538i	0.355660	−	0.616020i	0.987231	+	0.159298i	$0.0509229\pi$
$72$	−215.954	−	4.43397i	−0.353479	−	0.00725762i
$73$	294.170	+	509.518i	0.471644	+	0.816912i	0.999474	−	0.0324386i	$-0.0103273\pi$
$73$	294.170	+	509.518i	0.471644	+	0.816912i	−0.527830	+	0.849350i	$0.676994\pi$
$74$	587.955	+	213.998i	0.923627	+	0.336173i
$75$	231.728	+	281.991i	0.356769	+	0.434154i
$76$	−139.940	−	117.424i	−0.211213	−	0.177229i
$77$	676.991	−	246.405i	1.00195	−	0.364681i
$78$	−108.966	+	61.4289i	−0.158179	+	0.0891725i
$79$	167.873	+	952.056i	0.239079	+	1.35588i	0.833852	+	0.551988i	$0.186131\pi$
$79$	167.873	+	952.056i	0.239079	+	1.35588i	−0.594773	+	0.803893i	$0.702758\pi$
$80$	−118.398			−0.165466
$81$	−338.279	−	645.762i	−0.464031	−	0.885819i
$82$	686.924			0.925098
$83$	55.6100	+	315.380i	0.0735420	+	0.417078i	0.999246	+	0.0388285i	$0.0123626\pi$
$83$	55.6100	+	315.380i	0.0735420	+	0.417078i	−0.925704	+	0.378249i	$0.876526\pi$
$84$	−215.674	+	121.585i	−0.280142	+	0.157929i
$85$	724.908	−	263.845i	0.925027	−	0.336682i
$86$	−617.552	−	518.188i	−0.774330	−	0.649740i
$87$	−560.430	−	681.990i	−0.690625	−	0.840425i
$88$	454.665	+	165.485i	0.550766	+	0.200463i
$89$	−49.8431	−	86.3309i	−0.0593636	−	0.102821i	0.834816	−	0.550529i	$-0.185574\pi$
$89$	−49.8431	−	86.3309i	−0.0593636	−	0.102821i	−0.894180	+	0.447708i	$0.852240\pi$
$90$	−192.650	−	350.085i	−0.225635	−	0.410025i
$91$	−71.6896	+	124.170i	−0.0825837	+	0.143039i
$92$	42.5245	−	35.6823i	0.0481900	−	0.0404362i
$93$	−70.3274	+	82.0868i	−0.0784152	+	0.0915270i
$94$	30.2394	−	171.496i	0.0331804	−	0.188175i
$95$	58.6842	−	332.815i	0.0633776	−	0.359432i
$96$	−163.446	−	30.5530i	−0.173767	−	0.0324823i
$97$	−1273.09	+	1068.25i	−1.33260	+	1.11818i	−0.349138	+	0.937071i	$0.613526\pi$
$97$	−1273.09	+	1068.25i	−1.33260	+	1.11818i	−0.983462	+	0.181113i	$0.942030\pi$
$98$	201.106	−	348.326i	0.207294	−	0.359044i
$99$	250.491	+	1613.65i	0.254296	+	1.63816i
$100$	140.484	+	243.326i	0.140484	+	0.243326i
$101$	231.684	+	84.3259i	0.228251	+	0.0830767i	0.453614	−	0.891198i	$-0.350134\pi$
$101$	231.684	+	84.3259i	0.228251	+	0.0830767i	−0.225363	+	0.974275i	$0.572357\pi$
$102$	1068.81	−	177.168i	1.03753	−	0.171983i
$103$	−814.444	−	683.400i	−0.779122	−	0.653761i	0.163906	−	0.986476i	$-0.447591\pi$
$103$	−814.444	−	683.400i	−0.779122	−	0.653761i	−0.943027	+	0.332715i	$0.892035\pi$
$104$	−90.4858	+	32.9341i	−0.0853160	+	0.0310525i
$105$	−394.287	−	233.070i	−0.366462	−	0.216622i
$106$	−261.679	−	1484.05i	−0.239778	−	1.35985i
$107$	−1532.32			−1.38444			−0.692219	−	0.721688i	$-0.743367\pi$
$107$	−1532.32			−1.38444			−0.692219	+	0.721688i	$0.743367\pi$
$108$	−175.609	−	533.000i	−0.156463	−	0.474889i
$109$	−767.656			−0.674570			−0.337285	−	0.941403i	$-0.609509\pi$
$109$	−767.656			−0.674570			−0.337285	+	0.941403i	$0.609509\pi$
$110$	155.431	+	881.496i	0.134726	+	0.764066i
$111$	−16.6856	+	1625.50i	−0.0142678	+	1.38996i
$112$	−179.097	+	65.1858i	−0.151099	+	0.0549954i
$113$	524.906	+	440.448i	0.436982	+	0.366672i	0.834579	−	0.550889i	$-0.185711\pi$
$113$	524.906	+	440.448i	0.436982	+	0.366672i	−0.397596	+	0.917560i	$0.630156\pi$
$114$	166.897	−	444.301i	0.137117	−	0.365023i
$115$	96.5014	+	35.1236i	0.0782505	+	0.0284808i
$116$	−339.758	−	588.479i	−0.271946	−	0.471025i
$117$	−244.615	−	213.965i	−0.193288	−	0.169069i
$118$	−344.499	+	596.690i	−0.268760	+	0.465506i
$119$	951.283	−	798.221i	0.732806	−	0.614898i
$120$	−102.235	−	290.120i	−0.0777728	−	0.220702i
$121$	404.061	−	2291.55i	0.303577	−	1.72167i
$122$	−247.502	+	1403.65i	−0.183670	+	1.04165i
$123$	593.151	+	1683.23i	0.434818	+	1.23391i
$124$	−63.7428	+	53.4866i	−0.0461635	+	0.0387358i
$125$	−722.382	+	1251.20i	−0.516894	+	0.895287i
$126$	−484.162	−	423.497i	−0.342322	−	0.299429i
$127$	−1337.64	−	2316.86i	−0.934617	−	1.61880i	−0.775316	−	0.631574i	$-0.782409\pi$
$127$	−1337.64	−	2316.86i	−0.934617	−	1.61880i	−0.159301	−	0.987230i	$-0.550924\pi$
$128$	−120.281	−	43.7786i	−0.0830579	−	0.0302306i
$129$	736.511	−	1960.69i	0.502683	−	1.33821i
$130$	−136.462	−	114.505i	−0.0920654	−	0.0772521i
$131$	890.773	−	324.215i	0.594101	−	0.216235i	−0.0274312	−	0.999624i	$-0.508733\pi$
$131$	890.773	−	324.215i	0.594101	−	0.216235i	0.621532	+	0.783389i	$0.286510\pi$
$132$	−12.9030	+	1257.00i	−0.00850802	+	0.828846i
$133$	−94.4669	−	535.749i	−0.0615889	−	0.349288i
$134$	−24.2495			−0.0156331
$135$	691.493	−	774.362i	0.440846	−	0.493677i
$136$	833.996			0.525843
$137$	−202.017	−	1145.69i	−0.125981	−	0.714476i	−0.980720	−	0.195417i	$-0.937394\pi$
$137$	−202.017	−	1145.69i	−0.125981	−	0.714476i	0.854739	−	0.519058i	$-0.173717\pi$
$138$	124.155	+	73.3901i	0.0765851	+	0.0452709i
$139$	−679.027	+	247.146i	−0.414348	+	0.150810i	−0.540778	−	0.841165i	$-0.681870\pi$
$139$	−679.027	+	247.146i	−0.414348	+	0.150810i	0.126430	+	0.991975i	$0.459648\pi$
$140$	−270.096	−	226.638i	−0.163052	−	0.136817i
$141$	446.343	−	73.9867i	0.266587	−	0.0441901i
$142$	799.775	+	291.094i	0.472645	+	0.172029i
$143$	363.991	+	630.450i	0.212856	+	0.368678i
$144$	−66.2670	−	426.887i	−0.0383490	−	0.247041i
$145$	628.540	−	1088.66i	0.359982	−	0.623508i
$146$	−901.390	+	756.356i	−0.510956	+	0.428743i
$147$	1027.19	+	192.012i	0.576333	+	0.107734i
$148$	−217.299	+	1232.37i	−0.120688	+	0.684458i
$149$	−209.269	+	1186.83i	−0.115061	+	0.652541i	0.871660	+	0.490112i	$0.163044\pi$
$149$	−209.269	+	1186.83i	−0.115061	+	0.652541i	−0.986720	+	0.162429i	$0.948067\pi$
$150$	−474.936	+	554.350i	−0.258522	+	0.301750i
$151$	−539.880	+	453.013i	−0.290959	+	0.244144i	−0.776569	−	0.630032i	$-0.783042\pi$
$151$	−539.880	+	453.013i	−0.290959	+	0.244144i	0.485610	+	0.874175i	$0.338597\pi$
$152$	182.679	−	316.409i	0.0974816	−	0.168843i
$153$	1357.03	+	2466.01i	0.717056	+	1.30304i
$154$	720.439	+	1247.84i	0.376978	+	0.652945i
$155$	−144.653	−	52.6492i	−0.0749599	−	0.0272832i
$156$	−158.835	−	193.287i	−0.0815189	−	0.0992008i
$157$	2277.87	+	1911.36i	1.15792	+	0.971613i	0.999875	−	0.0158184i	$-0.00503538\pi$
$157$	2277.87	+	1911.36i	1.15792	+	0.971613i	0.158048	+	0.987431i	$0.449480\pi$
$158$	−1816.88	+	661.291i	−0.914832	+	0.332971i
$159$	3410.55	−	1922.68i	1.70109	−	0.958982i
$160$	−41.1191	−	233.198i	−0.0203172	−	0.115224i
$161$	165.313			0.0809222
$162$	1154.42	−	890.550i	0.559875	−	0.431902i
$163$	−3208.52			−1.54179			−0.770893	−	0.636965i	$-0.780189\pi$
$163$	−3208.52			−1.54179			−0.770893	+	0.636965i	$0.780189\pi$
$164$	238.566	+	1352.98i	0.113591	+	0.644205i
$165$	−2025.79	+	1142.03i	−0.955804	+	0.538829i
$166$	−601.864	+	219.061i	−0.281408	+	0.102424i
$167$	782.322	+	656.446i	0.362503	+	0.304176i	0.805787	−	0.592205i	$-0.201742\pi$
$167$	782.322	+	656.446i	0.362503	+	0.304176i	−0.443285	+	0.896381i	$0.646187\pi$
$168$	−314.378	−	382.569i	−0.144374	−	0.175689i
$169$	1928.36	+	701.866i	0.877725	+	0.319466i
$170$	771.431	+	1336.16i	0.348036	+	0.602816i
$171$	1232.82	+	25.3123i	0.551323	+	0.0113197i
$172$	806.157	−	1396.31i	0.357377	−	0.618996i
$173$	−1264.45	+	1061.00i	−0.555688	+	0.466278i	−0.876862	−	0.480743i	$-0.840367\pi$
$173$	−1264.45	+	1061.00i	−0.555688	+	0.466278i	0.321174	+	0.947020i	$0.395923\pi$
$174$	1148.62	−	1340.68i	0.500442	−	0.584120i
$175$	−145.295	+	824.007i	−0.0627614	+	0.355938i
$176$	−168.037	+	952.987i	−0.0719676	+	0.408148i
$177$	−1759.59	−	328.921i	−0.747225	−	0.139679i
$178$	152.728	−	128.154i	0.0643116	−	0.0539639i
$179$	1562.73	−	2706.74i	0.652538	−	1.13023i	−0.329967	−	0.943992i	$-0.607038\pi$
$179$	1562.73	−	2706.74i	0.652538	−	1.13023i	0.982505	−	0.186236i	$-0.0596290\pi$
$180$	622.627	−	501.030i	0.257821	−	0.207470i
$181$	383.688	+	664.567i	0.157565	+	0.272911i	0.933990	−	0.357299i	$-0.116302\pi$
$181$	383.688	+	664.567i	0.157565	+	0.272911i	−0.776425	+	0.630210i	$0.782969\pi$
$182$	−269.465	−	98.0772i	−0.109748	−	0.0399448i
$183$	−3653.21	+	605.563i	−1.47570	+	0.244615i
$184$	85.0489	+	71.3645i	0.0340755	+	0.0285927i
$185$	−2175.39	+	791.777i	−0.864529	+	0.314663i
$186$	−186.104	−	110.009i	−0.0733645	−	0.0433671i
$187$	−1094.86	−	6209.28i	−0.428152	−	2.42817i
$188$	348.283			0.135113
$189$	619.663	−	1552.07i	0.238486	−	0.597335i
$190$	675.898			0.258078
$191$	−825.200	−	4679.94i	−0.312615	−	1.77293i	−0.585294	−	0.810821i	$-0.699021\pi$
$191$	−825.200	−	4679.94i	−0.312615	−	1.77293i	0.272680	−	0.962105i	$-0.412090\pi$
$192$	3.41345	−	332.536i	0.00128305	−	0.124993i
$193$	1130.48	−	411.462i	0.421627	−	0.153460i	−0.122489	−	0.992470i	$-0.539088\pi$
$193$	1130.48	−	411.462i	0.421627	−	0.153460i	0.544115	+	0.839010i	$0.316865\pi$
$194$	−2546.17	−	2136.49i	−0.942291	−	0.790676i
$195$	162.748	−	433.258i	0.0597675	−	0.159109i
$196$	755.912	+	275.130i	0.275478	+	0.100266i
$197$	2397.51	+	4152.62i	0.867085	+	1.50184i	0.864962	+	0.501838i	$0.167343\pi$
$197$	2397.51	+	4152.62i	0.867085	+	1.50184i	0.00212390	+	0.999998i	$0.499324\pi$
$198$	−3091.27	+	1053.79i	−1.10953	+	0.378229i
$199$	−1731.13	+	2998.40i	−0.616666	+	1.06810i	0.373424	+	0.927661i	$0.378184\pi$
$199$	−1731.13	+	2998.40i	−0.616666	+	1.06810i	−0.990090	+	0.140436i	$0.955150\pi$
$200$	−430.469	+	361.206i	−0.152194	+	0.127706i
$201$	−20.9392	−	59.4207i	−0.00734795	−	0.0208518i
$202$	−85.6268	+	485.614i	−0.0298252	+	0.169147i
$203$	351.392	−	1992.84i	0.121492	−	0.689016i
$204$	720.146	+	2043.61i	0.247158	+	0.701380i
$205$	−1946.95	+	1633.69i	−0.663322	+	0.556594i
$206$	1063.18	−	1841.48i	0.359589	−	0.622826i
$207$	−72.6279	+	367.598i	−0.0243864	+	0.123429i
$208$	−96.2930	−	166.784i	−0.0320996	−	0.0555981i
$209$	−2595.55	−	944.703i	−0.859033	−	0.312663i
$210$	322.125	−	857.539i	0.105851	−	0.281790i
$211$	534.632	+	448.609i	0.174434	+	0.146368i	0.725825	−	0.687879i	$-0.241458\pi$
$211$	534.632	+	448.609i	0.174434	+	0.146368i	−0.551391	+	0.834247i	$0.685903\pi$
$212$	2832.13	−	1030.81i	0.917508	−	0.333946i
$213$	−22.6969	+	2211.11i	−0.00730124	+	0.711282i
$214$	−532.169	−	3018.08i	−0.169992	−	0.964073i
$215$	2982.72			0.946139
$216$	988.817	−	530.992i	0.311484	−	0.167266i
$217$	−247.799			−0.0775192
$218$	−266.604	−	1511.99i	−0.0828290	−	0.469746i
$219$	−2631.70	−	1555.65i	−0.812028	−	0.480004i
$220$	−1682.23	+	612.280i	−0.515526	+	0.187636i
$221$	961.242	+	806.578i	0.292580	+	0.245504i
$222$	−3207.41	+	531.666i	−0.969671	+	0.160735i
$223$	4731.65	+	1722.18i	1.42087	+	0.517155i	0.934301	−	0.356486i	$-0.116025\pi$
$223$	4731.65	+	1722.18i	1.42087	+	0.517155i	0.486571	+	0.873641i	$0.338247\pi$
$224$	−190.591	−	330.113i	−0.0568499	−	0.0984669i
$225$	−1768.47	−	685.101i	−0.523992	−	0.202993i
$226$	−685.216	+	1186.83i	−0.201681	+	0.349322i
$227$	2703.98	−	2268.91i	0.790616	−	0.663405i	−0.155282	−	0.987870i	$-0.549629\pi$
$227$	2703.98	−	2268.91i	0.790616	−	0.663405i	0.945898	+	0.324465i	$0.105184\pi$
$228$	933.064	+	174.418i	0.271025	+	0.0506628i
$229$	−810.900	+	4598.84i	−0.233999	+	1.32708i	0.610712	+	0.791853i	$0.290883\pi$
$229$	−810.900	+	4598.84i	−0.233999	+	1.32708i	−0.844711	+	0.535222i	$0.820228\pi$
$230$	−35.6655	+	202.269i	−0.0102248	+	0.0579879i
$231$	−2435.59	+	2842.85i	−0.693724	+	0.809721i
$232$	1041.08	−	873.570i	0.294613	−	0.247210i
$233$	−1467.22	+	2541.30i	−0.412535	+	0.714532i	−0.995166	−	0.0982048i	$-0.968690\pi$
$233$	−1467.22	+	2541.30i	−0.412535	+	0.714532i	0.582631	+	0.812737i	$0.302023\pi$
$234$	336.475	−	556.107i	0.0940003	−	0.155358i
$235$	322.156	+	557.990i	0.0894260	+	0.154890i
$236$	−1294.89	−	471.302i	−0.357162	−	0.129996i
$237$	−3189.27	−	3881.04i	−0.874117	−	1.06372i
$238$	1902.57	+	1596.44i	0.518172	+	0.434798i
$239$	−2843.49	+	1034.94i	−0.769581	+	0.280104i	−0.696821	−	0.717245i	$-0.745403\pi$
$239$	−2843.49	+	1034.94i	−0.769581	+	0.280104i	−0.0727596	+	0.997350i	$0.523181\pi$
$240$	535.919	−	302.121i	0.144139	−	0.0812576i
$241$	−381.399	−	2163.02i	−0.101942	−	0.578144i	−0.992398	−	0.123073i	$-0.960725\pi$
$241$	−381.399	−	2163.02i	−0.101942	−	0.578144i	0.890455	−	0.455071i	$-0.150386\pi$
$242$	4653.79			1.23619
$243$	3179.02	+	2059.79i	0.839235	+	0.543769i
$244$	−2850.62			−0.747918
$245$	258.416	+	1465.55i	0.0673860	+	0.382165i
$246$	−3109.31	+	1752.86i	−0.805864	+	0.454301i
$247$	516.557	−	188.011i	0.133068	−	0.0484327i
$248$	−127.486	−	106.973i	−0.0326425	−	0.0273903i
$249$	−1056.49	−	1285.64i	−0.268884	−	0.327206i
$250$	−2715.27	−	988.276i	−0.686914	−	0.250016i
$251$	−1984.26	−	3436.84i	−0.498985	−	0.864268i	0.501014	−	0.865439i	$-0.332961\pi$
$251$	−1984.26	−	3436.84i	−0.498985	−	0.864268i	−0.999999	+	0.00117126i	$0.999627\pi$
$252$	665.978	−	1100.69i	0.166479	−	0.275147i
$253$	419.673	−	726.894i	0.104287	−	0.180630i
$254$	4098.77	−	3439.27i	1.01252	−	0.849603i
$255$	−2607.98	+	3044.06i	−0.640463	+	0.747555i
$256$	44.4539	−	252.111i	0.0108530	−	0.0615505i
$257$	613.781	−	3480.92i	0.148975	−	0.844880i	−0.815114	−	0.579301i	$-0.803326\pi$
$257$	613.781	−	3480.92i	0.148975	−	0.844880i	0.964089	−	0.265579i	$-0.0855631\pi$
$258$	4117.59	+	769.703i	0.993605	+	0.185735i
$259$	−2854.72	+	2395.40i	−0.684879	+	0.574682i
$260$	178.138	−	308.545i	0.0424911	−	0.0735967i
$261$	4277.01	+	1656.90i	1.01433	+	0.392949i
$262$	947.941	+	1641.88i	0.223527	+	0.387160i
$263$	185.627	+	67.5627i	0.0435219	+	0.0158407i	0.363689	−	0.931520i	$-0.381517\pi$
$263$	185.627	+	67.5627i	0.0435219	+	0.0158407i	−0.320167	+	0.947361i	$0.603739\pi$
$264$	−2480.28	+	411.137i	−0.578223	+	0.0958475i
$265$	4271.15	+	3583.92i	0.990094	+	0.830787i
$266$	1022.41	−	372.127i	0.235669	−	0.0857766i
$267$	445.906	+	263.583i	0.102206	+	0.0604159i
$268$	−8.42178	−	47.7623i	−0.00191956	−	0.0108864i
$269$	5218.25			1.18276			0.591380	−	0.806393i	$-0.298583\pi$
$269$	5218.25			1.18276			0.591380	+	0.806393i	$0.298583\pi$
$270$	1765.35	+	1093.04i	0.397910	+	0.246372i
$271$	4679.73			1.04898			0.524490	−	0.851417i	$-0.324256\pi$
$271$	4679.73			1.04898			0.524490	+	0.851417i	$0.324256\pi$
$272$	289.644	+	1642.65i	0.0645671	+	0.366178i
$273$	7.64716	−	744.981i	0.00169534	−	0.165159i
$274$	2186.42	−	795.790i	0.482066	−	0.175458i
$275$	3254.38	+	2730.75i	0.713623	+	0.598800i
$276$	−101.432	+	270.025i	−0.0221213	+	0.0588899i
$277$	4097.74	+	1491.45i	0.888842	+	0.323512i	0.745773	−	0.666201i	$-0.232081\pi$
$277$	4097.74	+	1491.45i	0.888842	+	0.323512i	0.143069	+	0.989713i	$0.454303\pi$
$278$	−722.606	−	1251.59i	−0.155896	−	0.270019i
$279$	108.867	−	551.018i	0.0233609	−	0.118239i
$280$	352.586	−	610.696i	0.0752537	−	0.130343i
$281$	−2704.01	+	2268.94i	−0.574049	+	0.481685i	−0.882987	−	0.469398i	$-0.844471\pi$
$281$	−2704.01	+	2268.94i	−0.574049	+	0.481685i	0.308938	+	0.951082i	$0.400027\pi$
$282$	300.739	+	853.428i	0.0635061	+	0.180216i
$283$	−128.070	+	726.321i	−0.0269010	+	0.152563i	−0.995299	−	0.0968450i	$-0.969125\pi$
$283$	−128.070	+	726.321i	−0.0269010	+	0.152563i	0.968399	+	0.249408i	$0.0802360\pi$
$284$	−295.585	+	1676.35i	−0.0617596	+	0.350256i
$285$	583.630	+	1656.21i	0.121303	+	0.344230i
$286$	−1115.33	+	935.875i	−0.230598	+	0.193495i
$287$	−2045.64	+	3543.16i	−0.420734	+	0.728732i
$288$	817.789	−	278.777i	0.167322	−	0.0570385i
$289$	−2977.48	−	5157.15i	−0.606042	−	1.04969i
$290$	2362.54	+	859.894i	0.478390	+	0.174120i
$291$	3036.64	−	8083.93i	0.611721	−	1.62848i
$292$	−1802.78	−	1512.71i	−0.361300	−	0.303167i
$293$	−4406.96	+	1604.00i	−0.878694	+	0.319818i	−0.741683	−	0.670751i	$-0.765972\pi$
$293$	−4406.96	+	1604.00i	−0.878694	+	0.319818i	−0.137011	+	0.990569i	$0.543750\pi$
$294$	−21.4521	+	2089.85i	−0.00425548	+	0.414566i
$295$	−442.671	−	2510.51i	−0.0873671	−	0.495484i
$296$	−2502.75			−0.491451
$297$	−5251.46	−	6664.87i	−1.02599	−	1.30214i
$298$	−2410.27			−0.468534
$299$	29.0068	+	164.506i	0.00561039	+	0.0318181i
$300$	−1256.80	−	742.918i	−0.241871	−	0.142975i
$301$	4511.88	−	1642.19i	0.863987	−	0.314466i
$302$	−1079.76	−	906.026i	−0.205739	−	0.172636i
$303$	−1263.88	+	209.503i	−0.239630	+	0.0397216i
$304$	686.647	+	249.919i	0.129546	+	0.0471508i
$305$	−2636.77	−	4567.01i	−0.495019	−	0.857398i
$306$	−4385.80	+	3529.27i	−0.819345	+	0.659330i
$307$	−1929.12	+	3341.33i	−0.358634	+	0.621172i	−0.987733	−	0.156153i	$-0.950091\pi$
$307$	−1929.12	+	3341.33i	−0.358634	+	0.621172i	0.629099	+	0.777325i	$0.283424\pi$
$308$	−2207.55	+	1852.36i	−0.408399	+	0.342688i
$309$	5430.39	+	1015.10i	0.999754	+	0.186884i
$310$	53.4614	−	303.195i	0.00979486	−	0.0555494i
$311$	−809.595	+	4591.44i	−0.147614	+	0.837160i	0.817617	+	0.575762i	$0.195295\pi$
$311$	−809.595	+	4591.44i	−0.147614	+	0.837160i	−0.965231	+	0.261398i	$0.915817\pi$
$312$	325.538	−	379.971i	0.0590704	−	0.0689475i
$313$	1018.62	−	854.721i	0.183948	−	0.154350i	−0.546164	−	0.837678i	$-0.683912\pi$
$313$	1018.62	−	854.721i	0.183948	−	0.154350i	0.730112	+	0.683328i	$0.239468\pi$
$314$	−2973.55	+	5150.34i	−0.534418	+	0.925639i
$315$	2379.45	+	48.8548i	0.425609	+	0.00873860i
$316$	−1933.49	−	3348.90i	−0.344200	−	0.596171i
$317$	−3291.09	−	1197.86i	−0.583110	−	0.212235i	0.0335863	−	0.999436i	$-0.489307\pi$
$317$	−3291.09	−	1197.86i	−0.583110	−	0.212235i	−0.616696	+	0.787201i	$0.711529\pi$
$318$	4971.40	+	6049.73i	0.876674	+	1.06683i
$319$	−7870.64	−	6604.25i	−1.38141	−	1.15914i
$320$	445.030	−	161.978i	0.0777435	−	0.0282963i
$321$	6935.93	−	3910.09i	1.20600	−	0.679876i
$322$	57.4125	+	325.603i	0.00993626	+	0.0563513i
$323$	−4761.04			−0.820159
$324$	2154.97	+	1964.48i	0.369507	+	0.336845i
$325$	−845.478			−0.144304
$326$	−1114.31	−	6319.56i	−0.189312	−	1.07364i
$327$	3474.74	−	1958.87i	0.587626	−	0.331271i
$328$	−2581.99	+	939.767i	−0.434654	+	0.158201i
$329$	794.526	+	666.687i	0.133142	+	0.111719i
$330$	−2952.91	−	3593.41i	−0.492582	−	0.599426i
$331$	−842.078	−	306.491i	−0.139833	−	0.0508951i	0.271155	−	0.962536i	$-0.412594\pi$
$331$	−842.078	−	306.491i	−0.139833	−	0.0508951i	−0.410989	+	0.911640i	$0.634816\pi$
$332$	−640.490	−	1109.36i	−0.105878	−	0.183386i
$333$	−4072.35	−	7400.29i	−0.670160	−	1.21782i
$334$	−1021.25	+	1768.86i	−0.167306	+	0.289783i
$335$	68.7307	−	57.6719i	0.0112094	−	0.00940583i
$336$	644.331	−	752.069i	0.104616	−	0.122109i
$337$	1035.27	−	5871.30i	0.167343	−	0.949051i	−0.779272	−	0.626686i	$-0.784411\pi$
$337$	1035.27	−	5871.30i	0.167343	−	0.949051i	0.946615	−	0.322365i	$-0.104478\pi$
$338$	−712.694	+	4041.89i	−0.114691	+	0.650443i
$339$	−3499.86	−	654.230i	−0.560727	−	0.104817i
$340$	−2363.80	+	1983.47i	−0.377045	+	0.316378i
$341$	−629.076	+	1089.59i	−0.0999014	+	0.173034i
$342$	378.299	+	2436.98i	0.0598131	+	0.385311i
$343$	3240.67	+	5613.01i	0.510146	+	0.883598i
$344$	3030.16	+	1102.89i	0.474928	+	0.172860i
$345$	−526.434	+	87.2627i	−0.0821514	+	0.0136176i
$346$	−2528.89	−	2121.99i	−0.392931	−	0.329708i
$347$	−7751.93	+	2821.47i	−1.19927	+	0.436497i	−0.862968	−	0.505259i	$-0.831397\pi$
$347$	−7751.93	+	2821.47i	−1.19927	+	0.436497i	−0.336298	+	0.941756i	$0.609175\pi$
$348$	3039.54	+	1796.73i	0.468209	+	0.276767i
$349$	333.247	+	1889.94i	0.0511127	+	0.289874i	0.999640	−	0.0268201i	$-0.00853811\pi$
$349$	333.247	+	1889.94i	0.0511127	+	0.289874i	−0.948528	+	0.316694i	$0.897427\pi$
$350$	−1673.44			−0.255569
$351$	1653.22	+	344.302i	0.251403	+	0.0523575i
$352$	−1935.38			−0.293057
$353$	549.740	+	3117.73i	0.0828887	+	0.470085i	0.997792	+	0.0664125i	$0.0211553\pi$
$353$	549.740	+	3117.73i	0.0828887	+	0.470085i	−0.914904	+	0.403672i	$0.867734\pi$
$354$	36.7478	−	3579.95i	0.00551730	−	0.537492i
$355$	−2959.11	+	1077.03i	−0.442403	+	0.161022i
$356$	305.457	+	256.308i	0.0454752	+	0.0381582i
$357$	−2269.06	+	6040.53i	−0.336390	+	0.895514i
$358$	5873.96	+	2137.95i	0.867174	+	0.315626i
$359$	244.067	+	422.736i	0.0358812	+	0.0621480i	0.883408	−	0.468604i	$-0.155243\pi$
$359$	244.067	+	422.736i	0.0358812	+	0.0621480i	−0.847527	+	0.530752i	$0.821910\pi$
$360$	1203.07	+	1052.33i	0.176132	+	0.154063i
$361$	2386.64	−	4133.78i	0.347957	−	0.602680i
$362$	−1175.69	+	986.519i	−0.170698	+	0.143233i
$363$	4018.49	+	11403.6i	0.581037	+	1.64885i
$364$	99.5901	−	564.804i	0.0143405	−	0.0813290i
$365$	756.001	−	4287.49i	0.108413	−	0.614843i
$366$	−2461.47	−	6985.11i	−0.351539	−	0.997588i
$367$	2096.30	−	1759.01i	0.298164	−	0.250189i	−0.481416	−	0.876492i	$-0.659877\pi$
$367$	2096.30	−	1759.01i	0.298164	−	0.250189i	0.779580	+	0.626303i	$0.215433\pi$
$368$	−111.023	+	192.298i	−0.0157269	+	0.0272398i
$369$	−6980.03	−	6105.44i	−0.984731	−	0.861346i
$370$	−2315.00	−	4009.70i	−0.325273	−	0.563390i
$371$	8434.04	+	3069.74i	1.18025	+	0.429576i
$372$	152.043	−	404.759i	0.0211910	−	0.0564134i
$373$	−104.296	−	87.5151i	−0.0144779	−	0.0121484i	0.635520	−	0.772084i	$-0.280786\pi$
$373$	−104.296	−	87.5151i	−0.0144779	−	0.0121484i	−0.649998	+	0.759936i	$0.725230\pi$
$374$	11849.7	−	4312.92i	1.63832	−	0.596299i
$375$	77.0567	−	7506.82i	0.0106112	−	1.03373i
$376$	120.958	+	685.984i	0.0165902	+	0.0940876i
$377$	2044.77			0.279340
$378$	3272.18	+	681.470i	0.445246	+	0.0927276i
$379$	839.393			0.113764			0.0568822	−	0.998381i	$-0.481884\pi$
$379$	839.393			0.113764			0.0568822	+	0.998381i	$0.481884\pi$
$380$	234.737	+	1331.26i	0.0316888	+	0.179716i
$381$	11966.8	+	7073.78i	1.60913	+	0.951183i
$382$	8931.10	−	3250.65i	1.19622	−	0.435387i
$383$	−384.276	−	322.446i	−0.0512678	−	0.0430188i	0.616794	−	0.787125i	$-0.288431\pi$
$383$	−384.276	−	322.446i	−0.0512678	−	0.0430188i	−0.668062	+	0.744106i	$0.732876\pi$
$384$	656.154	−	108.765i	0.0871985	−	0.0144542i
$385$	−5009.64	−	1823.36i	−0.663155	−	0.241369i
$386$	1203.03	+	2083.72i	0.158634	+	0.274763i
$387$	1669.43	+	10754.3i	0.219281	+	1.41259i
$388$	3323.79	−	5756.97i	0.434897	−	0.753263i
$389$	−2189.47	+	1837.18i	−0.285374	+	0.239457i	−0.774226	−	0.632910i	$-0.781860\pi$
$389$	−2189.47	+	1837.18i	−0.285374	+	0.239457i	0.488852	+	0.872367i	$0.337416\pi$
$390$	909.874	+	170.083i	0.118137	+	0.0220833i
$391$	251.229	−	1424.79i	0.0324941	−	0.184283i
$392$	−279.374	+	1584.41i	−0.0359962	+	0.204145i
$393$	−3204.71	+	3740.57i	−0.411339	+	0.480119i
$394$	−7346.41	+	6164.37i	−0.939357	+	0.788214i
$395$	3576.88	−	6195.33i	0.455626	−	0.789167i
$396$	−3149.14	−	5722.64i	−0.399622	−	0.726196i
$397$	−1449.95	−	2511.38i	−0.183301	−	0.317487i	0.759701	−	0.650272i	$-0.225345\pi$
$397$	−1449.95	−	2511.38i	−0.183301	−	0.317487i	−0.943003	+	0.332785i	$0.892012\pi$
$398$	−6506.92	−	2368.33i	−0.819504	−	0.298275i
$399$	1794.69	+	2183.97i	0.225181	+	0.274024i
$400$	−860.938	−	722.413i	−0.107617	−	0.0903016i
$401$	8600.41	−	3130.29i	1.07103	−	0.389824i	0.254469	−	0.967081i	$-0.418099\pi$
$401$	8600.41	−	3130.29i	1.07103	−	0.389824i	0.816562	+	0.577257i	$0.195877\pi$
$402$	109.764	−	61.8788i	0.0136182	−	0.00767720i
$403$	−43.4803	−	246.589i	−0.00537446	−	0.0304801i
$404$	−986.210			−0.121450
$405$	−1154.02	+	5269.61i	−0.141589	+	0.646541i
$406$	4047.17			0.494724
$407$	3285.60	+	18633.5i	0.400150	+	2.26936i
$408$	−3775.03	+	2128.15i	−0.458068	+	0.258233i
$409$	−14107.1	+	5134.57i	−1.70551	+	0.620753i	−0.996433	−	0.0843820i	$-0.973108\pi$
$409$	−14107.1	+	5134.57i	−1.70551	+	0.620753i	−0.709073	+	0.705135i	$0.750886\pi$
$410$	−3893.91	−	3267.38i	−0.469040	−	0.393571i
$411$	3837.94	+	4670.41i	0.460612	+	0.560521i
$412$	3996.25	+	1454.52i	0.477867	+	0.173929i
$413$	−2051.82	−	3553.86i	−0.244464	−	0.423424i
$414$	−749.251	−	15.3836i	−0.0889460	−	0.00182624i
$415$	1184.88	−	2052.28i	0.140153	−	0.242753i
$416$	295.059	−	247.584i	0.0347751	−	0.0291798i
$417$	2442.92	−	2851.40i	0.286883	−	0.334852i
$418$	959.277	−	5440.33i	0.112248	−	0.636591i
$419$	1176.74	−	6673.65i	0.137202	−	0.778112i	−0.836099	−	0.548579i	$-0.815169\pi$
$419$	1176.74	−	6673.65i	0.137202	−	0.778112i	0.973301	−	0.229533i	$-0.0737199\pi$
$420$	1800.89	+	336.642i	0.209225	+	0.0391106i
$421$	−3081.29	+	2585.51i	−0.356705	+	0.299311i	−0.803476	−	0.595338i	$-0.797018\pi$
$421$	−3081.29	+	2585.51i	−0.356705	+	0.299311i	0.446771	+	0.894648i	$0.352574\pi$
$422$	−697.912	+	1208.82i	−0.0805067	+	0.139442i
$423$	−1831.54	+	1473.85i	−0.210526	+	0.169411i
$424$	3013.89	+	5220.22i	0.345207	+	0.597916i
$425$	6881.10	+	2504.52i	0.785370	+	0.285851i
$426$	−4362.93	+	723.207i	−0.496208	+	0.0822524i
$427$	−6503.01	−	5456.67i	−0.737008	−	0.618424i
$428$	5759.63	−	2096.34i	0.650473	−	0.236753i
$429$	−3256.33	−	1924.88i	−0.366473	−	0.216629i
$430$	1035.89	+	5874.82i	0.116174	+	0.658858i
$431$	−9048.23			−1.01122			−0.505612	−	0.862761i	$-0.668733\pi$
$431$	−9048.23			−1.01122			−0.505612	+	0.862761i	$0.668733\pi$
$432$	1389.26	+	1763.18i	0.154724	+	0.196368i
$433$	7204.53			0.799602			0.399801	−	0.916602i	$-0.369079\pi$
$433$	7204.53			0.799602			0.399801	+	0.916602i	$0.369079\pi$
$434$	−86.0596	−	488.068i	−0.00951842	−	0.0539816i
$435$	−67.0467	+	6531.64i	−0.00738998	+	0.719927i
$436$	2885.44	−	1050.22i	0.316944	−	0.115358i
$437$	−485.520	−	407.399i	−0.0531477	−	0.0445962i
$438$	2150.05	−	5723.72i	0.234551	−	0.624406i
$439$	2182.85	+	794.494i	0.237316	+	0.0863761i	0.457941	−	0.888983i	$-0.348587\pi$
$439$	2182.85	+	794.494i	0.237316	+	0.0863761i	−0.220624	+	0.975359i	$0.570809\pi$
$440$	−1790.19	−	3100.70i	−0.193963	−	0.335954i
$441$	−5139.46	+	1751.99i	−0.554957	+	0.189180i
$442$	−1254.81	+	2173.40i	−0.135035	+	0.233887i
$443$	6112.27	−	5128.80i	0.655536	−	0.550060i	−0.253209	−	0.967412i	$-0.581486\pi$
$443$	6112.27	−	5128.80i	0.655536	−	0.550060i	0.908745	+	0.417351i	$0.137042\pi$
$444$	−2161.10	−	6132.71i	−0.230994	−	0.655508i
$445$	−128.094	+	726.457i	−0.0136455	+	0.0773873i
$446$	−1748.75	+	9917.63i	−0.185663	+	1.05294i
$447$	−2081.24	−	5906.09i	−0.220222	−	0.624941i
$448$	584.004	−	490.037i	0.0615883	−	0.0516788i
$449$	−1253.26	+	2170.70i	−0.131726	+	0.228155i	−0.924342	−	0.381565i	$-0.875385\pi$
$449$	−1253.26	+	2170.70i	−0.131726	+	0.228155i	0.792616	+	0.609721i	$0.208718\pi$
$450$	735.202	−	3721.14i	0.0770173	−	0.389814i
$451$	10386.4	+	17989.7i	1.08442	+	1.87828i
$452$	−2575.57	−	937.431i	−0.268019	−	0.0975509i
$453$	1287.75	−	3428.17i	0.133563	−	0.355562i
$454$	5407.97	+	4537.83i	0.559050	+	0.469098i
$455$	997.000	−	362.878i	0.102725	−	0.0373890i
$456$	−19.4864	+	1898.35i	−0.00200117	+	0.194953i
$457$	1951.37	+	11066.8i	0.199740	+	1.13278i	0.905505	+	0.424337i	$0.139493\pi$
$457$	1951.37	+	11066.8i	0.199740	+	1.13278i	−0.705764	+	0.708447i	$0.749396\pi$
$458$	−9339.58			−0.952860
$459$	−12435.2	−	7699.42i	−1.26454	−	0.782958i
$460$	−410.779			−0.0416362
$461$	−1632.42	−	9257.91i	−0.164923	−	0.935323i	−0.949144	−	0.314842i	$-0.898049\pi$
$461$	−1632.42	−	9257.91i	−0.164923	−	0.935323i	0.784222	−	0.620481i	$-0.213063\pi$
$462$	−6445.19	−	3809.87i	−0.649042	−	0.383660i
$463$	1847.54	−	672.448i	0.185448	−	0.0674974i	−0.247627	−	0.968855i	$-0.579651\pi$
$463$	1847.54	−	672.448i	0.185448	−	0.0674974i	0.433075	+	0.901358i	$0.357429\pi$
$464$	2082.16	+	1747.14i	0.208323	+	0.174804i
$465$	789.108	−	130.804i	0.0786968	−	0.0130449i
$466$	−5514.94	−	2007.27i	−0.548229	−	0.199539i
$467$	−7125.38	−	12341.5i	−0.706046	−	1.22291i	−0.966313	−	0.257370i	$-0.917144\pi$
$467$	−7125.38	−	12341.5i	−0.706046	−	1.22291i	0.260267	−	0.965537i	$-0.416189\pi$
$468$	1212.17	+	469.593i	0.119728	+	0.0463823i
$469$	72.2146	−	125.079i	0.00710994	−	0.0123148i
$470$	−987.142	+	828.310i	−0.0968797	+	0.0812917i
$471$	−15187.9	−	2839.09i	−1.48582	−	0.277746i
$472$	478.573	−	2714.12i	0.0466697	−	0.264677i
$473$	4233.27	−	24008.0i	0.411513	−	2.33381i
$474$	6536.54	−	7629.52i	0.633404	−	0.739315i
$475$	2457.42	−	2062.02i	0.237377	−	0.199183i
$476$	−2483.62	+	4301.76i	−0.239153	+	0.414225i
$477$	−10531.4	+	17405.7i	−1.01090	+	1.67076i
$478$	−3025.97	−	5241.14i	−0.289550	−	0.501515i
$479$	2777.79	+	1011.03i	0.264970	+	0.0964411i	0.471089	−	0.882086i	$-0.343861\pi$
$479$	2777.79	+	1011.03i	0.264970	+	0.0964411i	−0.206119	+	0.978527i	$0.566083\pi$
$480$	781.185	+	950.628i	0.0742835	+	0.0903959i
$481$	−2884.61	−	2420.47i	−0.273444	−	0.229447i
$482$	4127.87	−	1502.42i	0.390081	−	0.141978i
$483$	−748.277	+	421.837i	−0.0704923	+	0.0397396i
$484$	1616.24	+	9166.18i	0.151789	+	0.860836i
$485$	12297.8			1.15137
$486$	−2952.94	+	6976.80i	−0.275613	+	0.651181i
$487$	4304.17			0.400494			0.200247	−	0.979745i	$-0.435826\pi$
$487$	4304.17			0.400494			0.200247	+	0.979745i	$0.435826\pi$
$488$	−990.008	−	5614.62i	−0.0918352	−	0.520823i
$489$	14523.2	−	8187.35i	1.34307	−	0.757147i
$490$	−2796.82	+	1017.96i	−0.257852	+	0.0938504i
$491$	−2624.29	−	2202.04i	−0.241207	−	0.202396i	0.514168	−	0.857689i	$-0.328101\pi$
$491$	−2624.29	−	2202.04i	−0.241207	−	0.202396i	−0.755375	+	0.655293i	$0.772545\pi$
$492$	−4532.31	−	5515.39i	−0.415309	−	0.505392i
$493$	−16641.8	−	6057.12i	−1.52030	−	0.553345i
$494$	549.709	+	952.123i	0.0500659	+	0.0867167i
$495$	6255.43	−	10338.6i	0.568001	−	0.938761i
$496$	166.421	−	288.249i	0.0150655	−	0.0260943i
$497$	−3883.18	+	3258.38i	−0.350472	+	0.294081i
$498$	2165.31	−	2527.37i	0.194839	−	0.227418i
$499$	−2427.85	+	13769.0i	−0.217806	+	1.23524i	0.658163	+	0.752875i	$0.271334\pi$
$499$	−2427.85	+	13769.0i	−0.217806	+	1.23524i	−0.875970	+	0.482366i	$0.839777\pi$
$500$	1003.52	−	5691.26i	0.0897577	−	0.509041i
$501$	−5216.22	−	975.068i	−0.465156	−	0.0869518i
$502$	6080.12	−	5101.83i	0.540576	−	0.453597i
$503$	−80.5977	+	139.599i	−0.00714448	+	0.0123746i	−0.869576	−	0.493800i	$-0.835608\pi$
$503$	−80.5977	+	139.599i	−0.00714448	+	0.0123746i	0.862431	+	0.506175i	$0.168941\pi$
$504$	2399.23	+	929.455i	0.212044	+	0.0821453i
$505$	−912.226	−	1580.02i	−0.0803832	−	0.139228i
$506$	1577.45	+	574.146i	0.138590	+	0.0504425i
$507$	−10519.6	+	1743.75i	−0.921481	+	0.152747i
$508$	8197.53	+	6878.55i	0.715958	+	0.600760i
$509$	−2690.05	+	979.096i	−0.234252	+	0.0852607i	−0.456479	−	0.889734i	$-0.650890\pi$
$509$	−2690.05	+	979.096i	−0.234252	+	0.0852607i	0.222227	+	0.974995i	$0.428667\pi$
$510$	−6901.37	−	4079.53i	−0.599211	−	0.354205i
$511$	−1216.97	−	6901.79i	−0.105354	−	0.597490i
$512$	512.000			0.0441942
$513$	−5644.87	+	3031.28i	−0.485823	+	0.260885i
$514$	7069.25			0.606636
$515$	1366.16	+	7747.86i	0.116893	+	0.662935i
$516$	−85.9931	+	8377.39i	−0.00733650	+	0.714717i
$517$	4948.51	−	1801.11i	0.420958	−	0.153216i
$518$	−5709.44	−	4790.79i	−0.484283	−	0.406362i
$519$	3016.03	−	8029.07i	0.255085	−	0.679070i
$520$	669.581	+	243.708i	0.0564675	+	0.0205525i
$521$	6324.76	+	10954.8i	0.531848	+	0.921187i	0.999309	+	0.0371736i	$0.0118354\pi$
$521$	6324.76	+	10954.8i	0.531848	+	0.921187i	−0.467461	+	0.884014i	$0.654831\pi$
$522$	−1778.07	+	8999.51i	−0.149088	+	0.754593i
$523$	7489.19	−	12971.7i	0.626155	−	1.08453i	−0.362161	−	0.932116i	$-0.617961\pi$
$523$	7489.19	−	12971.7i	0.626155	−	1.08453i	0.988316	−	0.152417i	$-0.0487058\pi$
$524$	−2904.66	+	2437.30i	−0.242158	+	0.203195i
$525$	−1444.99	−	4100.57i	−0.120123	−	0.340883i
$526$	−68.6050	+	389.078i	−0.00568692	+	0.0322521i
$527$	−376.584	+	2135.71i	−0.0311276	+	0.176533i
$528$	−1671.18	−	4742.42i	−0.137744	−	0.390885i
$529$	−9172.92	+	7697.00i	−0.753918	+	0.632613i
$530$	−5575.59	+	9657.21i	−0.456959	+	0.791476i
$531$	8803.99	−	3001.20i	0.719511	−	0.245275i
$532$	1088.03	+	1884.52i	0.0886691	+	0.153579i
$533$	−3884.80	−	1413.95i	−0.315703	−	0.114906i
$534$	−364.296	+	969.806i	−0.0295218	+	0.0785910i
$535$	8686.13	+	7288.52i	0.701933	+	0.588991i
$536$	91.1485	−	33.1753i	0.00734518	−	0.00267343i
$537$	−166.698	+	16239.6i	−0.0133958	+	1.30501i
$538$	1812.28	+	10278.0i	0.145229	+	0.823632i
$539$	12163.0			0.971982
$540$	−1539.77	+	3856.67i	−0.122706	+	0.307342i
$541$	6564.59			0.521689			0.260844	−	0.965381i	$-0.415999\pi$
$541$	6564.59			0.521689			0.260844	+	0.965381i	$0.415999\pi$
$542$	1625.25	+	9217.28i	0.128802	+	0.730472i
$543$	−3432.54	−	2029.04i	−0.271279	−	0.160358i
$544$	−3134.80	+	1140.97i	−0.247065	+	0.0899244i
$545$	4351.55	+	3651.38i	0.342018	+	0.286987i
$546$	1469.98	−	243.667i	0.115219	−	0.0190989i
$547$	−5715.92	−	2080.43i	−0.446792	−	0.162619i	0.108819	−	0.994062i	$-0.465293\pi$
$547$	−5715.92	−	2080.43i	−0.446792	−	0.162619i	−0.555611	+	0.831443i	$0.687515\pi$
$548$	2326.74	+	4030.02i	0.181374	+	0.314150i
$549$	14990.8	−	12063.1i	1.16537	−	0.937780i
$550$	−4248.29	+	7358.25i	−0.329359	+	0.570467i
$551$	−5943.22	+	4986.96i	−0.459510	+	0.385574i
$552$	−567.072	−	106.003i	−0.0437250	−	0.00817353i
$553$	1999.69	−	11340.8i	0.153771	−	0.872080i
$554$	−1514.46	+	8588.95i	−0.116143	+	0.658681i
$555$	7826.33	−	9134.97i	0.598575	−	0.698663i
$556$	2214.19	−	1857.93i	0.168890	−	0.141715i
$557$	10541.0	−	18257.6i	0.801863	−	1.38887i	−0.116525	−	0.993188i	$-0.537176\pi$
$557$	10541.0	−	18257.6i	0.801863	−	1.38887i	0.918389	−	0.395680i	$-0.129491\pi$
$558$	1123.10	+	23.0595i	0.0852056	+	0.00174944i
$559$	2425.85	+	4201.70i	0.183547	+	0.317912i
$560$	1325.29	+	482.366i	0.100007	+	0.0363994i
$561$	20800.4	+	25312.1i	1.56540	+	1.90495i
$562$	−5408.02	−	4537.87i	−0.405914	−	0.340602i
$563$	−11759.2	+	4280.00i	−0.880269	+	0.320392i	−0.742318	−	0.670047i	$-0.766274\pi$
$563$	−11759.2	+	4280.00i	−0.880269	+	0.320392i	−0.137951	+	0.990439i	$0.544052\pi$
$564$	−1576.48	+	888.732i	−0.117698	+	0.0663517i
$565$	−880.482	−	4993.46i	−0.0655614	−	0.371817i
$566$	−1475.05			−0.109542
$567$	1155.63	+	8606.55i	0.0855940	+	0.637462i
$568$	−3404.41			−0.251489
$569$	−1170.85	−	6640.20i	−0.0862644	−	0.489230i	−0.997077	−	0.0764088i	$-0.975655\pi$
$569$	−1170.85	−	6640.20i	−0.0862644	−	0.489230i	0.910812	−	0.412821i	$-0.135457\pi$
$570$	−3059.40	+	1724.72i	−0.224815	+	0.126738i
$571$	−20826.8	+	7580.35i	−1.52640	+	0.555565i	−0.962737	−	0.270438i	$-0.912832\pi$
$571$	−20826.8	+	7580.35i	−1.52640	+	0.555565i	−0.563665	+	0.826003i	$0.690609\pi$
$572$	−2230.66	−	1871.75i	−0.163057	−	0.136821i
$573$	15677.3	+	19077.7i	1.14298	+	1.39090i
$574$	−7689.11	−	2798.61i	−0.559124	−	0.203504i
$575$	487.408	+	844.216i	0.0353501	+	0.0612282i
$576$	833.098	+	1513.91i	0.0602646	+	0.109513i
$577$	−4751.88	+	8230.49i	−0.342848	+	0.593830i	−0.984960	−	0.172781i	$-0.944725\pi$
$577$	−4751.88	+	8230.49i	−0.342848	+	0.593830i	0.642113	+	0.766610i	$0.278058\pi$
$578$	9123.54	−	7655.56i	0.656555	−	0.550915i
$579$	−4067.10	+	4747.16i	−0.291922	+	0.340735i
$580$	−873.159	+	4951.93i	−0.0625103	+	0.354513i
$581$	662.422	−	3756.78i	0.0473010	−	0.268257i
$582$	16976.9	+	3173.49i	1.20913	+	0.226023i
$583$	34909.0	−	29292.1i	2.47990	−	2.08089i
$584$	2353.36	−	4076.14i	0.166751	−	0.288822i
$585$	368.897	+	2376.41i	0.0260718	+	0.167953i
$586$	−4689.79	−	8122.95i	−0.330603	−	0.572621i
$587$	−7375.59	−	2684.50i	−0.518609	−	0.188758i	0.0694363	−	0.997586i	$-0.477880\pi$
$587$	−7375.59	−	2684.50i	−0.518609	−	0.188758i	−0.588045	+	0.808828i	$0.700102\pi$
$588$	−4123.65	+	683.544i	−0.289211	+	0.0479403i
$589$	727.779	+	610.679i	0.0509127	+	0.0427209i
$590$	4791.01	−	1743.78i	0.334309	−	0.121679i
$591$	−21448.6	−	12678.7i	−1.49286	−	0.882455i
$592$	−869.197	−	4929.46i	−0.0603442	−	0.342229i
$593$	−11931.9			−0.826277			−0.413139	−	0.910668i	$-0.635568\pi$
$593$	−11931.9			−0.826277			−0.413139	+	0.910668i	$0.635568\pi$
$594$	11303.4	−	12658.0i	0.780783	−	0.874353i
$595$	−9189.22			−0.633145
$596$	−837.078	−	4747.30i	−0.0575303	−	0.326270i
$597$	184.660	−	17989.5i	0.0126594	−	1.23327i
$598$	−313.939	+	114.264i	−0.0214681	+	0.00781375i
$599$	15419.1	+	12938.1i	1.05176	+	0.882533i	0.993278	−	0.115755i	$-0.0369288\pi$
$599$	15419.1	+	12938.1i	1.05176	+	0.882533i	0.0584842	+	0.998288i	$0.481373\pi$
$600$	1026.78	−	2733.43i	0.0698635	−	0.185986i
$601$	1748.24	+	636.306i	0.118656	+	0.0431871i	0.400666	−	0.916224i	$-0.368779\pi$
$601$	1748.24	+	636.306i	0.118656	+	0.0431871i	−0.282010	+	0.959411i	$0.591001\pi$
$602$	4801.44	+	8316.34i	0.325070	+	0.563037i
$603$	246.407	+	215.532i	0.0166409	+	0.0145558i
$604$	1409.53	−	2441.37i	0.0949550	−	0.164467i
$605$	−13190.3	+	11068.0i	−0.886382	+	0.743763i
$606$	−851.581	−	2416.60i	−0.0570843	−	0.161993i
$607$	2233.48	−	12666.7i	0.149348	−	0.846993i	−0.814425	−	0.580269i	$-0.802948\pi$
$607$	2233.48	−	12666.7i	0.149348	−	0.846993i	0.963773	−	0.266724i	$-0.0859413\pi$
$608$	−253.775	+	1439.23i	−0.0169275	+	0.0960006i
$609$	3494.69	+	9917.13i	0.232532	+	0.659873i
$610$	8079.52	−	6779.52i	0.536279	−	0.449992i
$611$	−524.019	+	907.628i	−0.0346965	+	0.0600961i
$612$	−8474.48	−	7412.64i	−0.559739	−	0.489605i
$613$	−13134.7	−	22749.9i	−0.865422	−	1.49896i	−0.866627	−	0.498956i	$-0.833717\pi$
$613$	−13134.7	−	22749.9i	−0.865422	−	1.49896i	0.00120540	−	0.999999i	$-0.499616\pi$
$614$	−7251.11	−	2639.19i	−0.476598	−	0.173467i
$615$	4643.99	−	12362.9i	0.304494	−	0.810603i
$616$	−4415.11	−	3704.71i	−0.288782	−	0.242317i
$617$	−6412.47	+	2333.95i	−0.418406	+	0.152287i	−0.542639	−	0.839966i	$-0.682575\pi$
$617$	−6412.47	+	2333.95i	−0.418406	+	0.152287i	0.124234	+	0.992253i	$0.460353\pi$
$618$	−113.410	+	11048.3i	−0.00738190	+	0.719140i
$619$	3289.67	+	18656.6i	0.213607	+	1.21143i	0.883307	+	0.468795i	$0.155312\pi$
$619$	3289.67	+	18656.6i	0.213607	+	1.21143i	−0.669700	+	0.742632i	$0.733577\pi$
$620$	615.744			0.0398853
$621$	−609.273	−	1849.24i	−0.0393709	−	0.119496i
$622$	−9324.54			−0.601093
$623$	206.199	+	1169.41i	0.0132604	+	0.0752032i
$624$	861.455	+	509.222i	0.0552657	+	0.0326686i
$625$	1795.53	−	653.519i	0.114914	−	0.0418252i
$626$	2037.23	+	1709.44i	0.130071	+	0.109142i
$627$	14159.2	−	2347.06i	0.901858	−	0.149494i
$628$	−11176.9	−	4068.06i	−0.710202	−	0.258492i
$629$	16306.9	+	28244.4i	1.03370	+	1.79043i
$630$	730.150	+	4703.57i	0.0461744	+	0.297452i
$631$	−2944.48	+	5099.98i	−0.185765	+	0.321755i	−0.943834	−	0.330420i	$-0.892810\pi$
$631$	−2944.48	+	5099.98i	−0.185765	+	0.321755i	0.758069	+	0.652174i	$0.226143\pi$
$632$	5924.54	−	4971.28i	0.372889	−	0.312891i
$633$	−3564.71	−	666.353i	−0.223830	−	0.0418407i
$634$	1216.34	−	6898.19i	0.0761938	−	0.432117i
$635$	−3437.66	+	19495.9i	−0.214833	+	1.21838i
$636$	−10189.1	+	11892.8i	−0.635257	+	0.741478i
$637$	−1854.32	+	1555.96i	−0.115339	+	0.0967806i
$638$	10274.4	−	17795.8i	0.637566	−	1.10430i
$639$	−5539.47	−	10066.4i	−0.342939	−	0.623191i
$640$	473.591	+	820.283i	0.0292505	+	0.0506633i
$641$	−6633.97	−	2414.57i	−0.408777	−	0.148783i	0.129443	−	0.991587i	$-0.458681\pi$
$641$	−6633.97	−	2414.57i	−0.408777	−	0.148783i	−0.538220	+	0.842804i	$0.680903\pi$
$642$	10110.2	+	12303.2i	0.621523	+	0.756335i
$643$	−9885.05	−	8294.54i	−0.606265	−	0.508717i	0.287188	−	0.957874i	$-0.407280\pi$
$643$	−9885.05	−	8294.54i	−0.606265	−	0.508717i	−0.893452	+	0.449158i	$0.851724\pi$
$644$	−621.373	+	226.161i	−0.0380210	+	0.0138385i
$645$	−13501.1	+	7611.16i	−0.824193	+	0.464634i
$646$	−1653.49	−	9377.42i	−0.100706	−	0.571130i
$647$	−23050.1			−1.40061			−0.700305	−	0.713844i	$-0.746953\pi$
$647$	−23050.1			−1.40061			−0.700305	+	0.713844i	$0.746953\pi$
$648$	−3120.86	+	4926.71i	−0.189196	+	0.298672i
$649$	−20835.5			−1.26019
$650$	−293.632	−	1665.27i	−0.0177187	−	0.100488i
$651$	1121.64	−	632.320i	0.0675279	−	0.0380685i
$652$	12060.1	−	4389.52i	0.724402	−	0.263661i
$653$	−4397.76	−	3690.16i	−0.263549	−	0.221144i	0.501431	−	0.865197i	$-0.332807\pi$
$653$	−4397.76	−	3690.16i	−0.263549	−	0.221144i	−0.764981	+	0.644053i	$0.777251\pi$
$654$	5064.98	+	6163.60i	0.302838	+	0.368526i
$655$	−6591.59	−	2399.14i	−0.393213	−	0.143118i
$656$	−2747.69	−	4759.15i	−0.163536	−	0.283252i
$657$	15881.8	+	326.086i	0.943090	+	0.0193635i
$658$	−1037.18	+	1796.45i	−0.0614491	+	0.106433i
$659$	20829.1	−	17477.7i	1.23124	−	1.03313i	0.233084	−	0.972457i	$-0.425118\pi$
$659$	20829.1	−	17477.7i	1.23124	−	1.03313i	0.998157	−	0.0606773i	$-0.0193260\pi$
$660$	6052.10	−	7064.07i	0.356936	−	0.416619i
$661$	−4738.68	+	26874.4i	−0.278840	+	1.58138i	0.447653	+	0.894207i	$0.352260\pi$
$661$	−4738.68	+	26874.4i	−0.278840	+	1.58138i	−0.726493	+	0.687174i	$0.758851\pi$
$662$	311.220	−	1765.01i	0.0182717	−	0.103624i
$663$	−6409.18	−	1198.07i	−0.375433	−	0.0701797i
$664$	1962.58	−	1646.80i	0.114703	−	0.0962472i
$665$	−2012.81	+	3486.29i	−0.117374	+	0.203297i
$666$	13161.4	−	10591.0i	0.765758	−	0.616208i
$667$	−1178.79	−	2041.72i	−0.0684300	−	0.118524i
$668$	−3838.64	−	1397.15i	−0.222338	−	0.0809243i
$669$	−25812.0	+	4278.66i	−1.49171	+	0.247268i
$670$	137.461	+	115.344i	0.00792626	+	0.00665092i
$671$	−40502.3	+	14741.6i	−2.33022	+	0.848130i
$672$	1705.06	+	1007.89i	0.0978782	+	0.0578576i
$673$	888.691	+	5040.02i	0.0509012	+	0.288675i	0.999624	−	0.0274354i	$-0.00873406\pi$
$673$	888.691	+	5040.02i	0.0509012	+	0.288675i	−0.948722	+	0.316111i	$0.897623\pi$
$674$	11923.8			0.681433
$675$	9753.08	−	1411.64i	0.556142	−	0.0804946i
$676$	−8208.48			−0.467028
$677$	−433.103	−	2456.25i	−0.0245871	−	0.139441i	0.970043	−	0.242933i	$-0.0781094\pi$
$677$	−433.103	−	2456.25i	−0.0245871	−	0.139441i	−0.994630	+	0.103492i	$0.966998\pi$
$678$	73.0922	−	7120.60i	0.00414025	−	0.403341i
$679$	18602.5	−	6770.75i	1.05140	−	0.382677i
$680$	−4727.60	−	3966.93i	−0.266611	−	0.223713i
$681$	−6449.70	+	17170.0i	−0.362927	+	0.966160i
$682$	−2364.55	−	860.627i	−0.132762	−	0.0483213i
$683$	1280.87	+	2218.53i	0.0717586	+	0.124289i	0.899672	−	0.436566i	$-0.143806\pi$
$683$	1280.87	+	2218.53i	0.0717586	+	0.124289i	−0.827914	+	0.560856i	$0.810472\pi$
$684$	−4668.52	+	1591.46i	−0.260973	+	0.0889632i
$685$	−4304.37	+	7455.39i	−0.240090	+	0.415848i
$686$	−9930.00	+	8332.26i	−0.552666	+	0.463742i
$687$	−8064.62	−	22885.6i	−0.447867	−	1.27094i
$688$	−1119.90	+	6351.28i	−0.0620579	+	0.351948i
$689$	−1574.86	+	8931.49i	−0.0870791	+	0.493850i
$690$	−354.703	−	1006.57i	−0.0195700	−	0.0555352i
$691$	16748.0	−	14053.2i	0.922032	−	0.773677i	−0.0523374	−	0.998629i	$-0.516667\pi$
$691$	16748.0	−	14053.2i	0.922032	−	0.773677i	0.974370	+	0.224952i	$0.0722227\pi$
$692$	3301.23	−	5717.90i	0.181350	−	0.314107i
$693$	3770.30	−	19083.0i	0.206669	−	1.04603i
$694$	−8249.43	−	14288.4i	−0.451216	−	0.781529i
$695$	5024.70	+	1828.84i	0.274241	+	0.0998157i
$696$	−2483.24	+	6610.73i	−0.135240	+	0.360027i
$697$	27428.8	+	23015.5i	1.49059	+	1.25075i
$698$	−3606.72	+	1312.74i	−0.195582	+	0.0711861i
$699$	156.509	−	15247.0i	0.00846882	−	0.825027i
$700$	−581.179	−	3296.03i	−0.0313807	−	0.177969i
$701$	−6799.85			−0.366372			−0.183186	−	0.983078i	$-0.558641\pi$
$701$	−6799.85			−0.366372			−0.183186	+	0.983078i	$0.558641\pi$
$702$	−103.985	+	3375.78i	−0.00559071	+	0.181497i
$703$	14287.5			0.766519
$704$	−672.149	−	3811.95i	−0.0359838	−	0.204074i
$705$	−2882.07	−	1703.64i	−0.153964	−	0.0910112i
$706$	−5949.81	+	2165.55i	−0.317173	+	0.115441i
$707$	−2249.81	−	1887.81i	−0.119678	−	0.100422i
$708$	7063.89	−	1170.92i	0.374968	−	0.0621554i
$709$	−11713.5	−	4263.38i	−0.620468	−	0.225832i	0.0126095	−	0.999920i	$-0.495986\pi$
$709$	−11713.5	−	4263.38i	−0.620468	−	0.225832i	−0.633077	+	0.774089i	$0.718208\pi$
$710$	−3149.02	−	5454.26i	−0.166451	−	0.288302i
$711$	24339.5	+	9429.05i	1.28383	+	0.497352i
$712$	−398.745	+	690.647i	−0.0209882	+	0.0363527i
$713$	−221.155	+	185.571i	−0.0116161	+	0.00974710i
$714$	−12685.6	−	2371.31i	−0.664909	−	0.124292i
$715$	935.435	−	5305.11i	0.0489277	−	0.277483i
$716$	−2170.93	+	12311.9i	−0.113312	+	0.642624i
$717$	10229.9	−	11940.5i	0.532836	−	0.621931i
$718$	−747.863	+	627.532i	−0.0388719	+	0.0326174i
$719$	784.462	−	1358.73i	0.0406892	−	0.0704757i	−0.844964	−	0.534824i	$-0.820378\pi$
$719$	784.462	−	1358.73i	0.0406892	−	0.0704757i	0.885653	+	0.464348i	$0.153711\pi$
$720$	−1654.86	+	2735.06i	−0.0856570	+	0.141569i
$721$	6332.26	+	10967.8i	0.327081	+	0.566522i
$722$	8970.83	+	3265.12i	0.462410	+	0.168303i
$723$	7245.87	+	8817.54i	0.372720	+	0.453565i
$724$	−2351.38	−	1973.04i	−0.120702	−	0.101281i
$725$	11213.1	−	4081.22i	0.574403	−	0.209066i
$726$	−21065.1	+	11875.3i	−1.07686	+	0.607072i
$727$	2390.05	+	13554.7i	0.121929	+	0.691492i	0.983085	+	0.183151i	$0.0586298\pi$
$727$	2390.05	+	13554.7i	0.121929	+	0.691492i	−0.861156	+	0.508341i	$0.830259\pi$
$728$	1147.03			0.0583955
$729$	−19645.7	−	1211.46i	−0.998104	−	0.0615483i
$730$	8707.27			0.441466
$731$	−7296.83	−	41382.4i	−0.369197	−	2.09382i
$732$	12903.1	−	7274.06i	0.651520	−	0.367291i
$733$	34358.7	−	12505.6i	1.73133	−	0.630154i	0.732610	−	0.680648i	$-0.238302\pi$
$733$	34358.7	−	12505.6i	1.73133	−	0.630154i	0.998724	+	0.0504942i	$0.0160797\pi$
$734$	4192.60	+	3518.01i	0.210834	+	0.176910i
$735$	−4909.41	−	5974.29i	−0.246376	−	0.299816i
$736$	−417.312	−	151.889i	−0.0208999	−	0.00760694i
$737$	−366.656	−	635.068i	−0.0183256	−	0.0317409i
$738$	9601.23	−	15868.4i	0.478897	−	0.791494i
$739$	−8065.87	+	13970.5i	−0.401499	+	0.695417i	−0.993907	−	0.110221i	$-0.964844\pi$
$739$	−8065.87	+	13970.5i	−0.401499	+	0.695417i	0.592408	+	0.805638i	$0.298177\pi$
$740$	7093.58	−	5952.22i	0.352385	−	0.295686i
$741$	−1858.40	+	2169.14i	−0.0921324	+	0.107538i
$742$	−3117.09	+	17677.9i	−0.154221	+	0.874632i
$743$	−3481.71	+	19745.7i	−0.171913	+	0.974967i	0.769734	+	0.638365i	$0.220389\pi$
$743$	−3481.71	+	19745.7i	−0.171913	+	0.974967i	−0.941647	+	0.336602i	$0.890722\pi$
$744$	850.024	+	158.895i	0.0418863	+	0.00782981i
$745$	6831.45	−	5732.26i	0.335953	−	0.281898i
$746$	136.149	−	235.818i	0.00668201	−	0.0115736i
$747$	8062.75	+	3123.49i	0.394914	+	0.152988i
$748$	12610.1	+	21841.4i	0.616407	+	1.06765i
$749$	17152.1	+	6242.84i	0.836746	+	0.304551i
$750$	14812.3	−	2455.32i	0.721158	−	0.119541i
$751$	13793.4	+	11574.0i	0.670210	+	0.562373i	0.913127	−	0.407674i	$-0.133660\pi$
$751$	13793.4	+	11574.0i	0.670210	+	0.562373i	−0.242918	+	0.970047i	$0.578105\pi$
$752$	−1309.12	+	476.480i	−0.0634822	+	0.0231056i
$753$	17751.6	+	10493.3i	0.859101	+	0.507830i
$754$	710.142	+	4027.41i	0.0342995	+	0.194522i
$755$	5215.14			0.251389
$756$	−205.816	+	6681.61i	−0.00990140	+	0.321439i
$757$	−33197.8			−1.59392			−0.796959	−	0.604034i	$-0.793559\pi$
$757$	−33197.8			−1.59392			−0.796959	+	0.604034i	$0.793559\pi$
$758$	291.518	+	1653.28i	0.0139689	+	0.0792215i
$759$	−44.7666	+	4361.14i	−0.00214088	+	0.208563i
$760$	−2540.54	+	924.683i	−0.121257	+	0.0441339i
$761$	12058.7	+	10118.4i	0.574412	+	0.481989i	0.883107	−	0.469172i	$-0.155448\pi$
$761$	12058.7	+	10118.4i	0.574412	+	0.481989i	−0.308695	+	0.951161i	$0.599892\pi$
$762$	−9776.61	+	26026.7i	−0.464789	+	1.23733i
$763$	8592.79	+	3127.52i	0.407706	+	0.148393i
$764$	9504.28	+	16461.9i	0.450069	+	0.779542i
$765$	4037.16	−	20433.6i	0.190802	−	0.965725i
$766$	501.636	−	868.860i	0.0236617	−	0.0409833i
$767$	3176.48	−	2665.38i	0.149539	−	0.125478i
$768$	442.106	+	1254.60i	0.0207723	+	0.0589471i
$769$	1156.79	−	6560.48i	0.0542456	−	0.307642i	−0.945598	−	0.325338i	$-0.894522\pi$
$769$	1156.79	−	6560.48i	0.0542456	−	0.307642i	0.999843	+	0.0176957i	$0.00563302\pi$
$770$	1851.49	−	10500.3i	0.0866532	−	0.491435i
$771$	6104.21	+	17322.4i	0.285133	+	0.809144i
$772$	−3686.31	+	3093.18i	−0.171857	+	0.144205i
$773$	−5109.26	+	8849.49i	−0.237732	+	0.411765i	−0.960063	−	0.279783i	$-0.909737\pi$
$773$	−5109.26	+	8849.49i	−0.237732	+	0.411765i	0.722331	+	0.691548i	$0.243071\pi$
$774$	−20602.1	+	7023.06i	−0.956753	+	0.326148i
$775$	−730.610	−	1265.45i	−0.0338636	−	0.0586534i
$776$	12493.4	+	4547.21i	0.577945	+	0.210355i
$777$	6809.25	−	18127.1i	0.314389	−	0.836946i
$778$	−4378.94	−	3674.37i	−0.201790	−	0.169322i
$779$	14739.8	−	5364.86i	0.677932	−	0.246747i
$780$	−19.0021	+	1851.17i	−0.000872287	+	0.0849776i
$781$	4469.28	+	25346.6i	0.204768	+	1.16130i
$782$	2893.54			0.132318
$783$	−23587.6	+	3414.01i	−1.07657	+	0.155820i
$784$	−3217.70			−0.146579
$785$	−3820.93	−	21669.5i	−0.173726	−	0.985247i
$786$	−8480.46	−	5012.96i	−0.384845	−	0.227489i
$787$	8402.50	−	3058.26i	0.380580	−	0.138520i	−0.144644	−	0.989484i	$-0.546204\pi$
$787$	8402.50	−	3058.26i	0.380580	−	0.138520i	0.525224	+	0.850964i	$0.323981\pi$
$788$	−14692.8	−	12328.7i	−0.664226	−	0.557352i
$789$	−1012.63	+	167.856i	−0.0456915	+	0.00757392i
$790$	13444.7	+	4893.46i	0.605493	+	0.220381i
$791$	−4081.12	−	7068.70i	−0.183449	−	0.317742i
$792$	10177.7	−	8190.05i	0.456628	−	0.367450i
$793$	4288.97	−	7428.72i	0.192063	−	0.332663i
$794$	4442.89	−	3728.03i	0.198580	−	0.166628i
$795$	−28478.3	−	5323.46i	−1.27047	−	0.237489i
$796$	2404.86	−	13638.6i	0.107083	−	0.607298i
$797$	5814.54	−	32975.9i	0.258421	−	1.46558i	−0.528716	−	0.848799i	$-0.677326\pi$
$797$	5814.54	−	32975.9i	0.258421	−	1.46558i	0.787137	−	0.616779i	$-0.211563\pi$
$798$	−3678.30	+	4293.34i	−0.163171	+	0.190455i
$799$	6953.46	−	5834.64i	0.307879	−	0.258341i
$800$	1123.87	−	1946.61i	0.0496687	−	0.0860288i
$801$	−2690.96	−	55.2508i	−0.118702	−	0.00243719i
$802$	9152.36	+	15852.4i	0.402969	+	0.697963i
$803$	−33437.2	−	12170.2i	−1.46946	−	0.534839i
$804$	159.998	+	194.702i	0.00701828	+	0.00854058i
$805$	−937.095	−	786.316i	−0.0410289	−	0.0344273i
$806$	470.585	−	171.279i	0.0205653	−	0.00748516i
$807$	−23620.1	+	13315.7i	−1.03032	+	0.580835i
$808$	−342.507	−	1942.46i	−0.0149126	−	0.0845734i
$809$	18877.7			0.820399			0.410200	−	0.911996i	$-0.365459\pi$
$809$	18877.7			0.820399			0.410200	+	0.911996i	$0.365459\pi$
$810$	−10779.9	−	442.852i	−0.467613	−	0.0192101i
$811$	−11057.8			−0.478784			−0.239392	−	0.970923i	$-0.576948\pi$
$811$	−11057.8			−0.478784			−0.239392	+	0.970923i	$0.576948\pi$
$812$	1405.57	+	7971.38i	0.0607460	+	0.344508i
$813$	−21182.5	+	11941.5i	−0.913779	+	0.515138i
$814$	−35559.8	+	12942.7i	−1.53117	+	0.557300i
$815$	18187.9	+	15261.5i	0.781710	+	0.655933i
$816$	−5502.69	−	6696.25i	−0.236069	−	0.287274i
$817$	−17298.3	−	6296.07i	−0.740748	−	0.269610i
$818$	−15012.5	−	26002.4i	−0.641686	−	1.11143i
$819$	1866.39	+	3391.62i	0.0796300	+	0.144704i
$820$	5083.13	−	8804.25i	0.216477	−	0.374948i
$821$	11528.4	−	9673.49i	0.490067	−	0.411215i	−0.363984	−	0.931405i	$-0.618584\pi$
$821$	11528.4	−	9673.49i	0.490067	−	0.411215i	0.854050	+	0.520191i	$0.174139\pi$
$822$	−7866.00	+	9181.28i	−0.333769	+	0.389579i
$823$	−2003.08	+	11360.0i	−0.0848395	+	0.481148i	0.912552	+	0.408961i	$0.134109\pi$
$823$	−2003.08	+	11360.0i	−0.0848395	+	0.481148i	−0.997391	+	0.0721870i	$0.977002\pi$
$824$	−1476.96	+	8376.23i	−0.0624420	+	0.354126i
$825$	−21698.9	−	4056.18i	−0.915707	−	0.171173i
$826$	6287.14	−	5275.54i	0.264840	−	0.222227i
$827$	3374.22	−	5844.32i	0.141878	−	0.245740i	−0.786326	−	0.617812i	$-0.788019\pi$
$827$	3374.22	−	5844.32i	0.141878	−	0.245740i	0.928204	+	0.372072i	$0.121353\pi$
$828$	−229.912	−	1481.08i	−0.00964976	−	0.0621631i
$829$	−7810.47	−	13528.1i	−0.327224	−	0.566769i	0.654736	−	0.755858i	$-0.272780\pi$
$829$	−7810.47	−	13528.1i	−0.327224	−	0.566769i	−0.981960	+	0.189089i	$0.939447\pi$
$830$	4453.71	+	1621.02i	0.186253	+	0.0677907i
$831$	−22353.9	+	3705.44i	−0.933153	+	0.154681i
$832$	590.117	+	495.167i	0.0245897	+	0.0206332i
$833$	19700.9	−	7170.53i	0.819442	−	0.298252i
$834$	6464.57	+	3821.33i	0.268405	+	0.158659i
$835$	−1312.28	−	7442.29i	−0.0543870	−	0.308444i
$836$	11048.5			0.457082
$837$	913.282	+	2771.95i	0.0377152	+	0.114471i
$838$	13553.2			0.558696
$839$	6175.43	+	35022.6i	0.254111	+	1.44114i	0.798344	+	0.602202i	$0.205710\pi$
$839$	6175.43	+	35022.6i	0.254111	+	1.44114i	−0.544232	+	0.838935i	$0.683179\pi$
$840$	−37.6105	+	3663.98i	−0.00154486	+	0.150499i
$841$	−4200.37	+	1528.81i	−0.172224	+	0.0626844i
$842$	−6162.57	−	5171.01i	−0.252228	−	0.211645i
$843$	6449.77	−	17170.1i	0.263513	−	0.701508i
$844$	−2623.29	−	954.800i	−0.106988	−	0.0389403i
$845$	−7592.69	−	13150.9i	−0.309108	−	0.535391i
$846$	−3539.01	−	3095.57i	−0.143822	−	0.125801i
$847$	−13858.9	+	24004.3i	−0.562216	+	0.973787i
$848$	−9235.11	+	7749.18i	−0.373980	+	0.313806i
$849$	−1273.69	−	3614.44i	−0.0514875	−	0.146110i
$850$	−2543.15	+	14422.9i	−0.102623	+	0.582003i
$851$	−753.917	+	4275.67i	−0.0303689	+	0.172231i
$852$	−2939.67	−	8342.12i	−0.118206	−	0.335442i
$853$	13397.6	−	11241.9i	0.537779	−	0.451250i	−0.332998	−	0.942927i	$-0.608060\pi$
$853$	13397.6	−	11241.9i	0.537779	−	0.451250i	0.870778	+	0.491677i	$0.163616\pi$
$854$	8489.07	−	14703.5i	0.340152	−	0.589161i
$855$	−6867.99	−	6007.44i	−0.274714	−	0.240293i
$856$	6129.27	+	10616.2i	0.244736	+	0.423896i
$857$	−12430.2	−	4524.21i	−0.495456	−	0.180331i	0.0821930	−	0.996616i	$-0.473808\pi$
$857$	−12430.2	−	4524.21i	−0.495456	−	0.180331i	−0.577649	+	0.816285i	$0.696030\pi$
$858$	2660.35	−	7082.22i	0.105854	−	0.281798i
$859$	−26244.1	−	22021.4i	−1.04242	−	0.874693i	−0.0501419	−	0.998742i	$-0.515967\pi$
$859$	−26244.1	−	22021.4i	−1.04242	−	0.874693i	−0.992276	+	0.124050i	$0.960412\pi$
$860$	−11211.4	+	4080.60i	−0.444540	+	0.161799i
$861$	218.210	−	21257.8i	0.00863713	−	0.841423i
$862$	−3142.42	−	17821.5i	−0.124166	−	0.704181i
$863$	26527.5			1.04636			0.523179	−	0.852223i	$-0.324746\pi$
$863$	26527.5			1.04636			0.523179	+	0.852223i	$0.324746\pi$
$864$	−2990.30	+	3348.66i	−0.117745	+	0.131856i
$865$	12214.3			0.480115
$866$	2502.11	+	14190.2i	0.0981814	+	0.556814i
$867$	26637.1	+	15745.7i	1.04342	+	0.616784i
$868$	931.419	−	339.009i	0.0364221	−	0.0132566i
$869$	−44790.0	−	37583.2i	−1.74844	−	1.46712i
$870$	−12888.1	+	2136.36i	−0.502239	+	0.0832521i
$871$	137.140	+	49.9149i	0.00533503	+	0.00194179i
$872$	3070.63	+	5318.48i	0.119248	+	0.206544i
$873$	6883.05	+	44340.1i	0.266845	+	1.71900i
$874$	633.801	−	1097.78i	0.0245293	−	0.0424860i
$875$	13183.5	−	11062.3i	0.509355	−	0.427399i
$876$	12020.2	+	2246.94i	0.463614	+	0.0866634i
$877$	−1772.16	+	10050.4i	−0.0682345	+	0.386977i	0.931496	+	0.363752i	$0.118505\pi$
$877$	−1772.16	+	10050.4i	−0.0682345	+	0.386977i	−0.999730	+	0.0232250i	$0.992607\pi$
$878$	−806.750	+	4575.31i	−0.0310097	+	0.175865i
$879$	15854.8	−	18505.9i	0.608383	−	0.710111i
$880$	5485.46	−	4602.84i	0.210130	−	0.176320i
$881$	−3285.54	+	5690.72i	−0.125644	+	0.217622i	−0.921985	−	0.387227i	$-0.873433\pi$
$881$	−3285.54	+	5690.72i	−0.125644	+	0.217622i	0.796340	+	0.604849i	$0.206766\pi$
$882$	−5235.67	−	9514.29i	−0.199880	−	0.363223i
$883$	−8202.95	−	14207.9i	−0.312629	−	0.541489i	0.666302	−	0.745682i	$-0.267876\pi$
$883$	−8202.95	−	14207.9i	−0.312629	−	0.541489i	−0.978931	+	0.204193i	$0.934543\pi$
$884$	−4716.55	−	1716.68i	−0.179451	−	0.0653149i
$885$	8409.92	+	10234.1i	0.319431	+	0.388717i
$886$	12224.5	+	10257.6i	0.463534	+	0.388951i
$887$	27634.7	−	10058.2i	1.04609	−	0.380747i	0.238906	−	0.971043i	$-0.423211\pi$
$887$	27634.7	−	10058.2i	1.04609	−	0.380747i	0.807187	+	0.590296i	$0.200989\pi$
$888$	11328.5	−	6386.40i	0.428109	−	0.241344i
$889$	5533.77	+	31383.6i	0.208770	+	1.18399i
$890$	−1475.33			−0.0555653
$891$	40777.5	+	16767.7i	1.53322	+	0.630459i
$892$	−20141.2			−0.756030
$893$	−690.511	−	3916.08i	−0.0258758	−	0.146749i
$894$	10909.9	−	6150.41i	0.408146	−	0.230090i
$895$	−21733.2	+	7910.24i	−0.811689	+	0.295431i
$896$	1168.01	+	980.074i	0.0435495	+	0.0365424i
$897$	−551.075	−	670.605i	−0.0205126	−	0.0249619i
$898$	−4710.70	−	1714.55i	−0.175054	−	0.0637143i
$899$	1766.96	+	3060.47i	0.0655523	+	0.113540i
$900$	7584.56	+	155.726i	0.280910	+	0.00576763i
$901$	39274.6	−	68025.7i	1.45220	−	2.51528i
$902$	−31825.7	+	26704.9i	−1.17481	+	0.985784i
$903$	−16232.2	+	18946.4i	−0.598201	+	0.698226i
$904$	951.892	−	5398.45i	0.0350215	−	0.198617i
$905$	986.055	−	5592.20i	0.0362183	−	0.205404i
$906$	7199.41	+	1345.79i	0.264000	+	0.0493497i
$907$	−37157.2	+	31178.6i	−1.36029	+	1.14142i	−0.384402	+	0.923166i	$0.625592\pi$
$907$	−37157.2	+	31178.6i	−1.36029	+	1.14142i	−0.975892	+	0.218256i	$0.929963\pi$
$908$	−7059.60	+	12227.6i	−0.258019	+	0.446902i
$909$	5186.26	−	4173.40i	0.189238	−	0.152281i
$910$	1060.98	+	1837.68i	0.0386498	+	0.0669434i
$911$	−76.7148	−	27.9219i	−0.00278998	−	0.00101547i	0.340625	−	0.940199i	$-0.389361\pi$
$911$	−76.7148	−	27.9219i	−0.00278998	−	0.00101547i	−0.343415	+	0.939184i	$0.611584\pi$
$912$	−3745.79	+	620.910i	−0.136004	+	0.0225443i
$913$	−14837.2	−	12449.9i	−0.537831	−	0.451294i
$914$	−21119.6	+	7686.90i	−0.764304	+	0.278184i
$915$	23589.0	+	13943.9i	0.852272	+	0.503794i
$916$	−3243.60	−	18395.4i	−0.117000	−	0.663538i
$917$	−11291.8			−0.406639
$918$	10846.2	−	27166.5i	0.389954	−	0.976718i
$919$	28051.4			1.00689			0.503444	−	0.864028i	$-0.332066\pi$
$919$	28051.4			1.00689			0.503444	+	0.864028i	$0.332066\pi$
$920$	−142.662	−	809.076i	−0.00511242	−	0.0289940i
$921$	205.780	−	20046.9i	0.00736230	−	0.717230i
$922$	17667.6	−	6430.47i	0.631075	−	0.229692i
$923$	−3923.83	−	3292.49i	−0.139929	−	0.117414i
$924$	5265.59	−	14017.7i	0.187473	−	0.499078i
$925$	−20649.6	−	7515.85i	−0.734006	−	0.267156i
$926$	1966.11	+	3405.40i	0.0697735	+	0.120851i
$927$	−27170.6	+	9262.19i	−0.962674	+	0.328167i
$928$	−2718.07	+	4707.83i	−0.0961475	+	0.166532i
$929$	−24607.0	+	20647.7i	−0.869030	+	0.729203i	−0.963894	−	0.266287i	$-0.914203\pi$
$929$	−24607.0	+	20647.7i	−0.869030	+	0.729203i	0.0948634	+	0.995490i	$0.469759\pi$
$930$	531.688	+	1508.81i	0.0187470	+	0.0531999i
$931$	1594.86	−	9044.93i	0.0561435	−	0.318405i
$932$	2038.24	−	11559.4i	0.0716360	−	0.406268i
$933$	−8051.63	−	22848.7i	−0.282528	−	0.801751i
$934$	21833.4	−	18320.4i	0.764895	−	0.641823i
$935$	−23328.3	+	40405.8i	−0.815954	+	1.41327i
$936$	−503.934	+	2550.60i	−0.0175979	+	0.0890696i
$937$	−4147.52	−	7183.72i	−0.144604	−	0.250461i	0.784621	−	0.619975i	$-0.212857\pi$
$937$	−4147.52	−	7183.72i	−0.144604	−	0.250461i	−0.929225	+	0.369514i	$0.879524\pi$
$938$	271.438	+	98.7955i	0.00944859	+	0.00343900i
$939$	−2429.66	+	6468.09i	−0.0844399	+	0.224790i
$940$	−1974.28	−	1656.62i	−0.0685043	−	0.0574819i
$941$	26036.6	−	9476.55i	0.901986	−	0.328296i	0.150938	−	0.988543i	$-0.451771\pi$
$941$	26036.6	−	9476.55i	0.901986	−	0.328296i	0.751048	+	0.660247i	$0.229548\pi$
$942$	317.190	−	30900.4i	0.0109709	−	1.06878i
$943$	827.701	+	4694.13i	0.0285829	+	0.162102i
$944$	5511.98			0.190042
$945$	−10895.1	+	5850.63i	−0.375045	+	0.201398i
$946$	48756.8			1.67571
$947$	6408.08	+	36342.0i	0.219889	+	1.24705i	0.872219	+	0.489116i	$0.162681\pi$
$947$	6408.08	+	36342.0i	0.219889	+	1.24705i	−0.652330	+	0.757935i	$0.726208\pi$
$948$	17297.3	+	10224.8i	0.592607	+	0.350301i
$949$	6654.56	−	2422.06i	0.227625	−	0.0828487i
$950$	4914.85	+	4124.05i	0.167851	+	0.140844i
$951$	17953.5	−	2976.01i	0.612179	−	0.101476i
$952$	−9335.37	−	3397.80i	−0.317816	−	0.115676i
$953$	18315.5	+	31723.4i	0.622559	+	1.07830i	0.989008	+	0.147865i	$0.0472402\pi$
$953$	18315.5	+	31723.4i	0.622559	+	1.07830i	−0.366449	+	0.930438i	$0.619426\pi$
$954$	−37940.1	−	14697.9i	−1.28758	−	0.498807i
$955$	−17582.6	+	30453.9i	−0.595768	+	1.03190i
$956$	9272.12	−	7780.23i	0.313684	−	0.263212i
$957$	52478.3	+	9809.78i	1.77260	+	0.331353i
$958$	−1026.63	+	5822.31i	−0.0346231	+	0.196357i
$959$	−2406.41	+	13647.4i	−0.0810291	+	0.459539i
$960$	−1601.07	+	1868.78i	−0.0538274	+	0.0628279i
$961$	−22489.7	+	18871.1i	−0.754917	+	0.633450i
$962$	3765.59	−	6522.19i	0.126203	−	0.218590i
$963$	−21417.4	+	35397.5i	−0.716685	+	1.18450i
$964$	4392.78	+	7608.52i	0.146766	+	0.254205i
$965$	−8365.40	−	3044.76i	−0.279059	−	0.101569i
$966$	−1090.73	−	1327.32i	−0.0363289	−	0.0442088i
$967$	7350.22	+	6167.57i	0.244434	+	0.205104i	0.756771	−	0.653680i	$-0.226776\pi$
$967$	7350.22	+	6167.57i	0.244434	+	0.205104i	−0.512337	+	0.858784i	$0.671220\pi$
$968$	−17492.5	+	6366.76i	−0.580818	+	0.211400i
$969$	21550.5	−	12149.0i	0.714451	−	0.402768i
$970$	4270.97	+	24221.9i	0.141374	+	0.801771i
$971$	−43330.1			−1.43206			−0.716030	−	0.698070i	$-0.754042\pi$
$971$	−43330.1			−1.43206			−0.716030	+	0.698070i	$0.754042\pi$
$972$	−14767.2	−	3393.14i	−0.487301	−	0.111970i
$973$	8607.62			0.283605
$974$	1494.82	+	8477.56i	0.0491758	+	0.278890i
$975$	3827.00	−	2157.45i	0.125705	−	0.0708653i
$976$	10714.8	−	3899.87i	0.351406	−	0.127901i
$977$	40390.4	+	33891.6i	1.32262	+	1.10981i	0.985741	+	0.168268i	$0.0538173\pi$
$977$	40390.4	+	33891.6i	1.32262	+	1.10981i	0.336884	+	0.941546i	$0.390627\pi$
$978$	21169.8	+	25761.6i	0.692162	+	0.842296i
$979$	5665.48	+	2062.07i	0.184954	+	0.0673176i
$980$	−2976.31	−	5155.13i	−0.0970151	−	0.168035i
$981$	−10729.6	+	17733.3i	−0.349206	+	0.577148i
$982$	3425.76	−	5933.60i	0.111324	−	0.192819i
$983$	15775.7	−	13237.4i	0.511868	−	0.429509i	−0.349918	−	0.936780i	$-0.613790\pi$
$983$	15775.7	−	13237.4i	0.511868	−	0.429509i	0.861786	+	0.507272i	$0.169346\pi$
$984$	9289.14	−	10842.4i	0.300942	−	0.351263i
$985$	6161.47	−	34943.4i	0.199310	−	1.13035i
$986$	6150.56	−	34881.5i	0.198655	−	1.12663i
$987$	−5297.58	−	990.279i	−0.170845	−	0.0319361i
$988$	−1684.40	+	1413.38i	−0.0542389	+	0.0455119i
$989$	2796.95	−	4844.46i	0.0899270	−	0.155758i
$990$	22535.6	+	8730.23i	0.723463	+	0.280268i
$991$	−1290.22	−	2234.73i	−0.0413574	−	0.0716332i	0.844606	−	0.535389i	$-0.179835\pi$
$991$	−1290.22	−	2234.73i	−0.0413574	−	0.0716332i	−0.885963	+	0.463756i	$0.846502\pi$
$992$	625.537	+	227.677i	0.0200210	+	0.00728705i
$993$	4593.70	−	761.461i	0.146804	−	0.0243346i
$994$	−7766.36	−	6516.75i	−0.247821	−	0.207946i
$995$	24075.1	−	8762.63i	0.767068	−	0.279190i
$996$	5729.95	+	3387.08i	0.182290	+	0.107755i
$997$	−4604.11	−	26111.2i	−0.146252	−	0.829438i	−0.966353	−	0.257219i	$-0.917194\pi$
$997$	−4604.11	−	26111.2i	−0.146252	−	0.829438i	0.820101	−	0.572219i	$-0.193917\pi$
$998$	−27962.8			−0.886922
$999$	37316.9	+	23105.3i	1.18184	+	0.731752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.4.e.a.13.1	✓	24
3.2	odd	2		162.4.e.a.91.3		24
27.2	odd	18		162.4.e.a.73.3		24
27.5	odd	18		1458.4.a.e.1.9		12
27.22	even	9		1458.4.a.h.1.4		12
27.25	even	9	inner	54.4.e.a.25.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.13.1	✓	24	1.1	even	1	trivial
54.4.e.a.25.1	yes	24	27.25	even	9	inner
162.4.e.a.73.3		24	27.2	odd	18
162.4.e.a.91.3		24	3.2	odd	2
1458.4.a.e.1.9		12	27.5	odd	18
1458.4.a.h.1.4		12	27.22	even	9

Overview	Random
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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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 + 1.96962i) q^{2} +(-4.52643 + 2.55175i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(-5.66862 - 4.75653i) q^{5} +(-6.59798 - 8.02911i) q^{6} +(-11.1935 - 4.07412i) q^{7} +(-4.00000 - 6.92820i) q^{8} +(13.9771 - 23.1006i) q^{9} +(7.39985 - 12.8169i) q^{10} +(-46.3308 + 38.8761i) q^{11} +(13.5228 - 15.7840i) q^{12} +(2.09014 - 11.8538i) q^{13} +(4.13696 - 23.4619i) q^{14} +(37.7961 + 7.06523i) q^{15} +(12.2567 - 10.2846i) q^{16} +(-52.1248 + 90.2827i) q^{17} +(50.3536 + 19.5068i) q^{18} +(22.8348 + 39.5511i) q^{19} +(27.8143 + 10.1236i) q^{20} +(61.0629 - 10.1219i) q^{21} +(-92.6616 - 77.7523i) q^{22} +(-13.0410 + 4.74653i) q^{23} +(35.7848 + 21.1530i) q^{24} +(-12.1974 - 69.1750i) q^{25} +24.0732 q^{26} +(-4.31954 + 140.230i) q^{27} +47.6477 q^{28} +(29.4992 + 167.298i) q^{29} +(-0.789345 + 76.8975i) q^{30} +(19.5480 - 7.11491i) q^{31} +(24.5134 + 20.5692i) q^{32} +(110.511 - 294.195i) q^{33} +(-195.925 - 71.3109i) q^{34} +(44.0732 + 76.3370i) q^{35} +(-20.9334 + 105.952i) q^{36} +(156.422 - 270.931i) q^{37} +(-69.9700 + 58.7118i) q^{38} +(20.7870 + 58.9887i) q^{39} +(-10.2798 + 58.2995i) q^{40} +(59.6415 - 338.244i) q^{41} +(41.1432 + 116.755i) q^{42} +(-308.776 + 259.094i) q^{43} +(120.961 - 209.511i) q^{44} +(-189.110 + 64.4659i) q^{45} +(-13.8779 - 24.0373i) q^{46} +(-81.8198 - 29.7800i) q^{47} +(-29.2354 + 77.8286i) q^{48} +(-154.056 - 129.269i) q^{49} +(132.012 - 48.0485i) q^{50} +(5.56017 - 541.668i) q^{51} +(8.36055 + 47.4150i) q^{52} -753.474 q^{53} +(-277.699 + 40.1934i) q^{54} +447.547 q^{55} +(16.5479 + 93.8476i) q^{56} +(-204.285 - 120.757i) q^{57} +(-319.268 + 116.204i) q^{58} +(263.901 + 221.440i) q^{59} +(-151.733 + 25.1515i) q^{60} +(669.676 + 243.742i) q^{61} +(20.8026 + 36.0311i) q^{62} +(-250.568 + 201.633i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-68.2310 + 57.2526i) q^{65} +(617.831 + 115.491i) q^{66} +(-2.10545 + 11.9406i) q^{67} +(72.4110 - 410.663i) q^{68} +(46.9172 - 54.7622i) q^{69} +(-135.048 + 113.319i) q^{70} +(212.776 - 368.538i) q^{71} +(-215.954 - 4.43397i) q^{72} +(294.170 + 509.518i) q^{73} +(587.955 + 213.998i) q^{74} +(231.728 + 281.991i) q^{75} +(-139.940 - 117.424i) q^{76} +(676.991 - 246.405i) q^{77} +(-108.966 + 61.4289i) q^{78} +(167.873 + 952.056i) q^{79} -118.398 q^{80} +(-338.279 - 645.762i) q^{81} +686.924 q^{82} +(55.6100 + 315.380i) q^{83} +(-215.674 + 121.585i) q^{84} +(724.908 - 263.845i) q^{85} +(-617.552 - 518.188i) q^{86} +(-560.430 - 681.990i) q^{87} +(454.665 + 165.485i) q^{88} +(-49.8431 - 86.3309i) q^{89} +(-192.650 - 350.085i) q^{90} +(-71.6896 + 124.170i) q^{91} +(42.5245 - 35.6823i) q^{92} +(-70.3274 + 82.0868i) q^{93} +(30.2394 - 171.496i) q^{94} +(58.6842 - 332.815i) q^{95} +(-163.446 - 30.5530i) q^{96} +(-1273.09 + 1068.25i) q^{97} +(201.106 - 348.326i) q^{98} +(250.491 + 1613.65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{5} - 18 q^{6} - 33 q^{7} - 96 q^{8} + 54 q^{9} + 30 q^{10} - 12 q^{11} - 36 q^{12} + 60 q^{13} - 66 q^{14} + 81 q^{15} + 102 q^{17} + 108 q^{18} + 171 q^{19} + 96 q^{20} + 126 q^{21} - 24 q^{22}+ \cdots - 4014 q^{99}+O(q^{100}) \) 24 * q - 12 * q^5 - 18 * q^6 - 33 * q^7 - 96 * q^8 + 54 * q^9 + 30 * q^10 - 12 * q^11 - 36 * q^12 + 60 * q^13 - 66 * q^14 + 81 * q^15 + 102 * q^17 + 108 * q^18 + 171 * q^19 + 96 * q^20 + 126 * q^21 - 24 * q^22 - 708 * q^23 + 864 * q^25 - 468 * q^26 - 702 * q^27 - 336 * q^28 - 381 * q^29 - 18 * q^30 + 909 * q^31 - 819 * q^33 - 48 * q^34 + 624 * q^35 + 468 * q^36 + 555 * q^37 + 66 * q^38 + 333 * q^39 - 96 * q^40 + 618 * q^41 + 1332 * q^42 - 1161 * q^43 + 132 * q^44 - 909 * q^45 + 348 * q^46 - 378 * q^47 + 579 * q^49 + 36 * q^50 - 810 * q^51 + 240 * q^52 - 1794 * q^53 - 486 * q^54 - 3906 * q^55 - 264 * q^56 - 1485 * q^57 + 444 * q^58 + 1038 * q^59 - 324 * q^60 + 324 * q^61 + 744 * q^62 + 3096 * q^63 - 768 * q^64 + 5718 * q^65 + 2610 * q^66 - 576 * q^67 + 1056 * q^68 + 4455 * q^69 - 1038 * q^70 + 120 * q^71 - 864 * q^72 + 3036 * q^73 - 1110 * q^74 - 5355 * q^75 + 132 * q^76 - 3804 * q^77 - 468 * q^78 - 2991 * q^79 - 480 * q^80 + 1458 * q^81 - 3408 * q^82 + 513 * q^83 - 612 * q^84 - 2925 * q^85 - 2322 * q^86 - 7092 * q^87 + 480 * q^88 + 1065 * q^89 - 252 * q^90 + 2859 * q^91 + 1884 * q^92 + 9918 * q^93 - 828 * q^94 + 6357 * q^95 + 576 * q^96 - 2055 * q^97 + 1356 * q^98 - 4014 * q^99

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