LMFDB - Embedded newform 28.4.f.a.3.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [28,4,Mod(3,28)] 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("28.3"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	28.f (of order $6$, degree $2$, 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:	$1.65205348016$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.8
Root			$0.448398 - 2.79266i$ of defining polynomial
Character	$\chi$	$=$	28.3
Dual form			28.4.f.a.19.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19431 + 1.78465i) q^{2} +(2.11164 - 3.65747i) q^{3} +(1.63002 + 7.83218i) q^{4} +(1.03358 - 0.596737i) q^{5} +(11.1609 - 4.25709i) q^{6} +(-16.7651 - 7.86959i) q^{7} +(-10.4009 + 20.0953i) q^{8} +(4.58193 + 7.93614i) q^{9} +(3.33297 + 0.535152i) q^{10} +(-29.6160 - 17.0988i) q^{11} +(32.0880 + 10.5770i) q^{12} -56.1127i q^{13} +(-22.7434 - 47.1883i) q^{14} -5.04038i q^{15} +(-58.6860 + 25.5333i) q^{16} +(19.4520 + 11.2306i) q^{17} +(-4.10906 + 25.5916i) q^{18} +(53.4022 + 92.4953i) q^{19} +(6.35851 + 7.12248i) q^{20} +(-64.1848 + 44.7002i) q^{21} +(-34.4714 - 90.3744i) q^{22} +(51.2640 - 29.5973i) q^{23} +(51.5349 + 80.4752i) q^{24} +(-61.7878 + 107.020i) q^{25} +(100.142 - 123.129i) q^{26} +152.730 q^{27} +(34.3085 - 144.135i) q^{28} +211.906 q^{29} +(8.99533 - 11.0602i) q^{30} +(-54.1933 + 93.8656i) q^{31} +(-174.344 - 48.7062i) q^{32} +(-125.077 + 72.2131i) q^{33} +(22.6411 + 59.3587i) q^{34} +(-22.0242 + 1.87053i) q^{35} +(-54.6886 + 48.8226i) q^{36} +(-81.0013 - 140.298i) q^{37} +(-47.8909 + 298.268i) q^{38} +(-205.231 - 118.490i) q^{39} +(1.24141 + 26.9767i) q^{40} -414.943i q^{41} +(-220.616 - 16.4613i) q^{42} +258.254i q^{43} +(85.6461 - 259.829i) q^{44} +(9.47158 + 5.46842i) q^{45} +(165.310 + 26.5428i) q^{46} +(-304.267 - 527.006i) q^{47} +(-30.5366 + 268.560i) q^{48} +(219.139 + 263.870i) q^{49} +(-326.575 + 124.565i) q^{50} +(82.1515 - 47.4302i) q^{51} +(439.485 - 91.4651i) q^{52} +(-112.165 + 194.275i) q^{53} +(335.138 + 272.571i) q^{54} -40.8140 q^{55} +(332.515 - 255.049i) q^{56} +451.065 q^{57} +(464.988 + 378.179i) q^{58} +(42.9260 - 74.3501i) q^{59} +(39.4772 - 8.21595i) q^{60} +(-312.035 + 180.154i) q^{61} +(-286.435 + 109.254i) q^{62} +(-14.3625 - 169.108i) q^{63} +(-295.641 - 418.020i) q^{64} +(-33.4846 - 57.9969i) q^{65} +(-403.333 - 64.7605i) q^{66} +(580.112 + 334.928i) q^{67} +(-56.2531 + 170.658i) q^{68} -249.996i q^{69} +(-51.6662 - 35.2010i) q^{70} +133.439i q^{71} +(-207.135 + 9.53195i) q^{72} +(-675.475 - 389.985i) q^{73} +(72.6417 - 452.418i) q^{74} +(260.947 + 451.974i) q^{75} +(-637.393 + 569.025i) q^{76} +(361.955 + 519.730i) q^{77} +(-238.877 - 626.270i) q^{78} +(-729.310 + 421.067i) q^{79} +(-45.4200 + 61.4108i) q^{80} +(198.800 - 344.331i) q^{81} +(740.529 - 910.514i) q^{82} +432.711 q^{83} +(-454.723 - 429.844i) q^{84} +26.8070 q^{85} +(-460.894 + 566.690i) q^{86} +(447.470 - 775.040i) q^{87} +(651.640 - 417.298i) q^{88} +(-439.022 + 253.470i) q^{89} +(11.0244 + 28.9029i) q^{90} +(-441.584 + 940.737i) q^{91} +(315.373 + 353.265i) q^{92} +(228.874 + 396.421i) q^{93} +(272.865 - 1699.43i) q^{94} +(110.391 + 63.7342i) q^{95} +(-546.293 + 534.807i) q^{96} +372.919i q^{97} +(9.94400 + 970.100i) q^{98} -313.382i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29}+ \cdots - 4900 q^{98}+O(q^{100}) $ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.19431	+	1.78465i	0.775807	+	0.630970i
$2$	2.19431	+	1.78465i	0.775807	+	0.630970i
$3$	2.11164	−	3.65747i	0.406386	−	0.703881i	−0.588096	−	0.808791i	$-0.700122\pi$
$3$	2.11164	−	3.65747i	0.406386	−	0.703881i	0.994482	+	0.104910i	$0.0334556\pi$
$4$	1.63002	+	7.83218i	0.203753	+	0.979022i
$5$	1.03358	−	0.596737i	0.0924461	−	0.0533738i	−0.453064	−	0.891478i	$-0.649669\pi$
$5$	1.03358	−	0.596737i	0.0924461	−	0.0533738i	0.545510	+	0.838104i	$0.316336\pi$
$6$	11.1609	−	4.25709i	0.759405	−	0.289658i
$7$	−16.7651	−	7.86959i	−0.905232	−	0.424918i
$7$	−16.7651	−	7.86959i	−0.905232	−	0.424918i
$8$	−10.4009	+	20.0953i	−0.459661	+	0.888095i
$9$	4.58193	+	7.93614i	0.169701	+	0.293931i
$10$	3.33297	+	0.535152i	0.105398	+	0.0169230i
$11$	−29.6160	−	17.0988i	−0.811778	−	0.468680i	0.0357948	−	0.999359i	$-0.488604\pi$
$11$	−29.6160	−	17.0988i	−0.811778	−	0.468680i	−0.847573	+	0.530679i	$0.821937\pi$
$12$	32.0880	+	10.5770i	0.771917	+	0.254443i
$13$		−	56.1127i		−	1.19714i	−0.801069	−	0.598572i	$-0.795735\pi$
$13$		−	56.1127i		−	1.19714i	0.801069	−	0.598572i	$-0.204265\pi$
$14$	−22.7434	−	47.1883i	−0.434174	−	0.900829i
$15$		−	5.04038i		−	0.0867614i
$16$	−58.6860	+	25.5333i	−0.916969	+	0.398958i
$17$	19.4520	+	11.2306i	0.277518	+	0.160225i	0.632299	−	0.774724i	$-0.282111\pi$
$17$	19.4520	+	11.2306i	0.277518	+	0.160225i	−0.354781	+	0.934949i	$0.615445\pi$
$18$	−4.10906	+	25.5916i	−0.0538064	+	0.335110i
$19$	53.4022	+	92.4953i	0.644806	+	1.11684i	0.984346	+	0.176245i	$0.0563950\pi$
$19$	53.4022	+	92.4953i	0.644806	+	1.11684i	−0.339541	+	0.940591i	$0.610272\pi$
$20$	6.35851	+	7.12248i	0.0710903	+	0.0796317i
$21$	−64.1848	+	44.7002i	−0.666965	+	0.464495i
$22$	−34.4714	−	90.3744i	−0.334060	−	0.875813i
$23$	51.2640	−	29.5973i	0.464752	−	0.268325i	−0.249288	−	0.968429i	$-0.580197\pi$
$23$	51.2640	−	29.5973i	0.464752	−	0.268325i	0.714040	+	0.700105i	$0.246863\pi$
$24$	51.5349	+	80.4752i	0.438313	+	0.684455i
$25$	−61.7878	+	107.020i	−0.494302	+	0.856157i
$26$	100.142	−	123.129i	0.755362	−	0.928753i
$27$	152.730			1.08863
$28$	34.3085	−	144.135i	0.231561	−	0.972820i
$29$	211.906			1.35689			0.678447	−	0.734649i	$-0.262653\pi$
$29$	211.906			1.35689			0.678447	+	0.734649i	$0.262653\pi$
$30$	8.99533	−	11.0602i	0.0547439	−	0.0673101i
$31$	−54.1933	+	93.8656i	−0.313981	+	0.543831i	−0.979220	−	0.202799i	$-0.934996\pi$
$31$	−54.1933	+	93.8656i	−0.313981	+	0.543831i	0.665239	+	0.746630i	$0.268329\pi$
$32$	−174.344	−	48.7062i	−0.963122	−	0.269066i
$33$	−125.077	+	72.2131i	−0.659790	+	0.380930i
$34$	22.6411	+	59.3587i	0.114203	+	0.299410i
$35$	−22.0242	+	1.87053i	−0.106365	+	0.00903362i
$36$	−54.6886	+	48.8226i	−0.253188	+	0.226031i
$37$	−81.0013	−	140.298i	−0.359906	−	0.623376i	0.628038	−	0.778182i	$-0.283858\pi$
$37$	−81.0013	−	140.298i	−0.359906	−	0.623376i	−0.987945	+	0.154806i	$0.950525\pi$
$38$	−47.8909	+	298.268i	−0.204446	+	1.27330i
$39$	−205.231	−	118.490i	−0.842646	−	0.486502i
$40$	1.24141	+	26.9767i	0.00490711	+	0.106635i
$41$		−	414.943i		−	1.58056i	−0.612743	−	0.790282i	$-0.709934\pi$
$41$		−	414.943i		−	1.58056i	0.612743	−	0.790282i	$-0.290066\pi$
$42$	−220.616	−	16.4613i	−0.810518	−	0.0604770i
$43$			258.254i			0.915892i	0.888980	+	0.457946i	$0.151415\pi$
$43$			258.254i			0.915892i	−0.888980	+	0.457946i	$0.848585\pi$
$44$	85.6461	−	259.829i	0.293446	−	0.890244i
$45$	9.47158	+	5.46842i	0.0313765	+	0.0181152i
$46$	165.310	+	26.5428i	0.529862	+	0.0850764i
$47$	−304.267	−	527.006i	−0.944295	−	1.63557i	−0.757156	−	0.653234i	$-0.773412\pi$
$47$	−304.267	−	527.006i	−0.944295	−	1.63557i	−0.187139	−	0.982333i	$-0.559922\pi$
$48$	−30.5366	+	268.560i	−0.0918247	+	0.807568i
$49$	219.139	+	263.870i	0.638889	+	0.769299i
$50$	−326.575	+	124.565i	−0.923693	+	0.352322i
$51$	82.1515	−	47.4302i	0.225559	−	0.130227i
$52$	439.485	−	91.4651i	1.17203	−	0.243922i
$53$	−112.165	+	194.275i	−0.290698	+	0.503503i	−0.973975	−	0.226656i	$-0.927221\pi$
$53$	−112.165	+	194.275i	−0.290698	+	0.503503i	0.683277	+	0.730159i	$0.260554\pi$
$54$	335.138	+	272.571i	0.844565	+	0.686892i
$55$	−40.8140			−0.100061
$56$	332.515	−	255.049i	0.793467	−	0.608613i
$57$	451.065			1.04816
$58$	464.988	+	378.179i	1.05269	+	0.856160i
$59$	42.9260	−	74.3501i	0.0947203	−	0.164060i	−0.814772	−	0.579782i	$-0.803138\pi$
$59$	42.9260	−	74.3501i	0.0947203	−	0.164060i	0.909492	+	0.415722i	$0.136471\pi$
$60$	39.4772	−	8.21595i	0.0849413	−	0.0176779i
$61$	−312.035	+	180.154i	−0.654951	+	0.378136i	−0.790351	−	0.612655i	$-0.790102\pi$
$61$	−312.035	+	180.154i	−0.654951	+	0.378136i	0.135399	+	0.990791i	$0.456768\pi$
$62$	−286.435	+	109.254i	−0.586730	+	0.223795i
$63$	−14.3625	−	169.108i	−0.0287223	−	0.338185i
$64$	−295.641	−	418.020i	−0.577424	−	0.816445i
$65$	−33.4846	−	57.9969i	−0.0638961	−	0.110671i
$66$	−403.333	−	64.7605i	−0.752225	−	0.120780i
$67$	580.112	+	334.928i	1.05779	+	0.610715i	0.924820	−	0.380405i	$-0.124215\pi$
$67$	580.112	+	334.928i	1.05779	+	0.610715i	0.132970	+	0.991120i	$0.457549\pi$
$68$	−56.2531	+	170.658i	−0.100319	+	0.304343i
$69$		−	249.996i		−	0.436173i
$70$	−51.6662	−	35.2010i	−0.0882184	−	0.0601046i
$71$			133.439i			0.223047i	0.993762	+	0.111523i	$0.0355730\pi$
$71$			133.439i			0.223047i	−0.993762	+	0.111523i	$0.964427\pi$
$72$	−207.135	+	9.53195i	−0.339044	+	0.0156021i
$73$	−675.475	−	389.985i	−1.08299	−	0.625265i	−0.151289	−	0.988490i	$-0.548342\pi$
$73$	−675.475	−	389.985i	−1.08299	−	0.625265i	−0.931702	+	0.363225i	$0.881676\pi$
$74$	72.6417	−	452.418i	0.114114	−	0.710710i
$75$	260.947	+	451.974i	0.401755	+	0.695860i
$76$	−637.393	+	569.025i	−0.962026	+	0.858838i
$77$	361.955	+	519.730i	0.535697	+	0.769204i
$78$	−238.877	−	626.270i	−0.346763	−	0.909117i
$79$	−729.310	+	421.067i	−1.03866	+	0.599668i	−0.919452	−	0.393202i	$-0.871367\pi$
$79$	−729.310	+	421.067i	−1.03866	+	0.599668i	−0.119203	+	0.992870i	$0.538034\pi$
$80$	−45.4200	+	61.4108i	−0.0634764	+	0.0858242i
$81$	198.800	−	344.331i	0.272702	−	0.472333i
$82$	740.529	−	910.514i	0.997289	−	1.22621i
$83$	432.711			0.572243			0.286122	−	0.958193i	$-0.407634\pi$
$83$	432.711			0.572243			0.286122	+	0.958193i	$0.407634\pi$
$84$	−454.723	−	429.844i	−0.590647	−	0.558331i
$85$	26.8070			0.0342073
$86$	−460.894	+	566.690i	−0.577901	+	0.710555i
$87$	447.470	−	775.040i	0.551423	−	0.955092i
$88$	651.640	−	417.298i	0.789375	−	0.505502i
$89$	−439.022	+	253.470i	−0.522879	+	0.301884i	−0.738112	−	0.674678i	$-0.764282\pi$
$89$	−439.022	+	253.470i	−0.522879	+	0.301884i	0.215233	+	0.976563i	$0.430949\pi$
$90$	11.0244	+	28.9029i	0.0129119	+	0.0338515i
$91$	−441.584	+	940.737i	−0.508688	+	1.08369i
$92$	315.373	+	353.265i	0.357390	+	0.400330i
$93$	228.874	+	396.421i	0.255195	+	0.442010i
$94$	272.865	−	1699.43i	0.299403	−	1.86471i
$95$	110.391	+	63.7342i	0.119220	+	0.0688315i
$96$	−546.293	+	534.807i	−0.580789	+	0.568578i
$97$			372.919i			0.390352i	0.980768	+	0.195176i	$0.0625278\pi$
$97$			372.919i			0.390352i	−0.980768	+	0.195176i	$0.937472\pi$
$98$	9.94400	+	970.100i	0.0102500	+	0.999947i
$99$		−	313.382i		−	0.318143i
$100$	−938.912	−	309.489i	−0.938912	−	0.309489i
$101$	−426.861	−	246.449i	−0.420538	−	0.242798i	0.274770	−	0.961510i	$-0.411398\pi$
$101$	−426.861	−	246.449i	−0.420538	−	0.242798i	−0.695307	+	0.718713i	$0.744732\pi$
$102$	264.913	+	42.5352i	0.257159	+	0.0412903i
$103$	−253.633	−	439.305i	−0.242633	−	0.420252i	0.718831	−	0.695185i	$-0.244678\pi$
$103$	−253.633	−	439.305i	−0.242633	−	0.420252i	−0.961463	+	0.274933i	$0.911344\pi$
$104$	1127.60	+	583.625i	1.06318	+	0.550280i
$105$	−39.6658	+	84.5026i	−0.0368665	+	0.0785392i
$106$	−592.837	+	226.125i	−0.543221	+	0.207200i
$107$	928.131	−	535.857i	0.838559	−	0.484142i	−0.0182153	−	0.999834i	$-0.505798\pi$
$107$	928.131	−	535.857i	0.838559	−	0.484142i	0.856774	+	0.515692i	$0.172465\pi$
$108$	248.954	+	1196.21i	0.221811	+	1.06579i
$109$	398.763	−	690.678i	0.350409	−	0.606926i	−0.635912	−	0.771761i	$-0.719376\pi$
$109$	398.763	−	690.678i	0.350409	−	0.606926i	0.986321	+	0.164835i	$0.0527093\pi$
$110$	−89.5587	−	72.8388i	−0.0776280	−	0.0631355i
$111$	−684.183			−0.585043
$112$	1184.82	+	33.7665i	0.999594	+	0.0284878i
$113$	592.933			0.493615			0.246807	−	0.969065i	$-0.420618\pi$
$113$	592.933			0.493615			0.246807	+	0.969065i	$0.420618\pi$
$114$	989.779	+	804.996i	0.813169	+	0.661357i
$115$	35.3236	−	61.1823i	0.0286430	−	0.0496111i
$116$	345.412	+	1659.69i	0.276471	+	1.32843i
$117$	445.319	−	257.105i	0.351878	−	0.203157i
$118$	226.882	−	86.5393i	0.177002	−	0.0675135i
$119$	−237.735	−	341.363i	−0.183136	−	0.262964i
$120$	101.288	+	52.4247i	0.0770523	+	0.0398808i
$121$	−80.7617	−	139.883i	−0.0606775	−	0.105096i
$122$	−1006.22	−	161.561i	−0.746709	−	0.119894i
$123$	−1517.64	−	876.210i	−1.11253	−	0.642319i
$124$	−823.509	−	271.449i	−0.596397	−	0.196587i
$125$			296.669i			0.212279i
$126$	270.284	−	396.709i	0.191102	−	0.280489i
$127$		−	510.787i		−	0.356890i	−0.983950	−	0.178445i	$-0.942893\pi$
$127$		−	510.787i		−	0.356890i	0.983950	−	0.178445i	$-0.0571066\pi$
$128$	97.2911	−	1444.88i	0.0671828	−	0.997741i
$129$	944.556	+	545.340i	0.644679	+	0.372205i
$130$	30.0288	−	187.022i	0.0202593	−	0.126176i
$131$	314.812	+	545.270i	0.209963	+	0.363667i	0.951703	−	0.307021i	$-0.0993322\pi$
$131$	314.812	+	545.270i	0.209963	+	0.363667i	−0.741739	+	0.670688i	$0.765999\pi$
$132$	−769.464	−	861.915i	−0.507373	−	0.568334i
$133$	−167.394	−	1970.95i	−0.109135	−	1.28499i
$134$	675.217	+	1770.23i	0.435298	+	1.14123i
$135$	157.859	−	91.1399i	0.100639	−	0.0581042i
$136$	−428.002	+	274.085i	−0.269860	+	0.172813i
$137$	−491.951	+	852.084i	−0.306790	+	0.531375i	−0.977658	−	0.210201i	$-0.932588\pi$
$137$	−491.951	+	852.084i	−0.306790	+	0.531375i	0.670868	+	0.741576i	$0.265922\pi$
$138$	446.156	−	548.569i	0.275212	−	0.338386i
$139$	−1920.76			−1.17206			−0.586032	−	0.810288i	$-0.699311\pi$
$139$	−1920.76			−1.17206			−0.586032	+	0.810288i	$0.699311\pi$
$140$	−50.5502	−	169.448i	−0.0305162	−	0.102293i
$141$	−2570.01			−1.53499
$142$	−238.143	+	292.807i	−0.140736	+	0.173041i
$143$	−959.461	+	1661.83i	−0.561078	+	0.971815i
$144$	−471.531	−	348.749i	−0.272877	−	0.201822i
$145$	219.022	−	126.452i	0.125440	−	0.0724226i
$146$	−786.214	−	2061.24i	−0.445668	−	1.16842i
$147$	1427.84	−	244.297i	0.801130	−	0.137070i
$148$	966.808	−	863.107i	0.536967	−	0.479371i
$149$	44.5907	+	77.2334i	0.0245169	+	0.0424645i	0.878024	−	0.478617i	$-0.158862\pi$
$149$	44.5907	+	77.2334i	0.0245169	+	0.0424645i	−0.853507	+	0.521082i	$0.825529\pi$
$150$	−234.017	+	1457.47i	−0.127383	+	0.793348i
$151$	1878.47	+	1084.53i	1.01237	+	0.584491i	0.911884	−	0.410448i	$-0.134628\pi$
$151$	1878.47	+	1084.53i	1.01237	+	0.584491i	0.100484	+	0.994939i	$0.467961\pi$
$152$	−2414.15	+	111.094i	−1.28825	+	0.0592825i
$153$			205.832i			0.108762i
$154$	−133.294	+	1786.41i	−0.0697474	+	0.934762i
$155$			129.357i			0.0670334i
$156$	593.504	−	1800.54i	0.304605	−	0.924096i
$157$	2158.33	+	1246.11i	1.09716	+	0.633444i	0.935473	−	0.353398i	$-0.114974\pi$
$157$	2158.33	+	1246.11i	1.09716	+	0.633444i	0.161685	+	0.986842i	$0.448307\pi$
$158$	−2351.79	−	377.612i	−1.18417	−	0.190134i
$159$	473.703	+	820.477i	0.236271	+	0.409233i
$160$	−209.263	+	53.6956i	−0.103398	+	0.0265313i
$161$	−1092.37	+	92.7754i	−0.534724	+	0.0454144i
$162$	1050.74	−	400.782i	0.509592	−	0.194373i
$163$	998.625	−	576.557i	0.479867	−	0.277051i	−0.240494	−	0.970651i	$-0.577309\pi$
$163$	998.625	−	576.557i	0.479867	−	0.277051i	0.720361	+	0.693599i	$0.243976\pi$
$164$	3249.90	−	676.367i	1.54741	−	0.322045i
$165$	−86.1845	+	149.276i	−0.0406634	+	0.0704310i
$166$	949.504	+	772.239i	0.443951	+	0.361069i
$167$	3471.09			1.60839			0.804194	−	0.594367i	$-0.202597\pi$
$167$	3471.09			1.60839			0.804194	+	0.594367i	$0.202597\pi$
$168$	−230.682	−	1754.74i	−0.105937	−	0.805838i
$169$	−951.638			−0.433153
$170$	58.8229	+	47.8411i	0.0265383	+	0.0215838i
$171$	−489.371	+	847.615i	−0.218849	+	0.379057i
$172$	−2022.69	+	420.960i	−0.896679	+	0.186616i
$173$	2483.27	−	1433.72i	1.09133	−	0.630079i	0.157399	−	0.987535i	$-0.449689\pi$
$173$	2483.27	−	1433.72i	1.09133	−	0.630079i	0.933930	+	0.357456i	$0.116356\pi$
$174$	2365.07	−	902.103i	1.03043	−	0.393036i
$175$	1878.08	−	1307.95i	0.811255	−	0.564982i
$176$	2174.63	+	247.267i	0.931359	+	0.105900i
$177$	−181.289	−	314.002i	−0.0769859	−	0.133344i
$178$	−1415.71	−	227.311i	−0.596134	−	0.0957171i
$179$	−1478.02	−	853.337i	−0.617166	−	0.356321i	0.158599	−	0.987343i	$-0.449302\pi$
$179$	−1478.02	−	853.337i	−0.617166	−	0.356321i	−0.775765	+	0.631022i	$0.782636\pi$
$180$	−27.3907	+	83.0968i	−0.0113421	+	0.0344093i
$181$			4153.44i			1.70565i	0.522197	+	0.852825i	$0.325113\pi$
$181$			4153.44i			1.70565i	−0.522197	+	0.852825i	$0.674887\pi$
$182$	−2647.86	+	1276.20i	−1.07842	+	0.519769i
$183$			1521.68i			0.614677i
$184$	61.5722	+	1338.00i	0.0246694	+	0.536082i
$185$	−167.443	−	96.6730i	−0.0665439	−	0.0384192i
$186$	−205.253	+	1278.33i	−0.0809134	+	0.503935i
$187$	−384.061	−	665.213i	−0.150189	−	0.260135i
$188$	3631.64	−	3242.10i	1.40885	−	1.25774i
$189$	−2560.54	−	1201.93i	−0.985461	−	0.462578i
$190$	128.489	+	336.862i	0.0490608	+	0.128624i
$191$	−3079.88	+	1778.17i	−1.16677	+	0.673633i	−0.952916	−	0.303233i	$-0.901934\pi$
$191$	−3079.88	+	1778.17i	−1.16677	+	0.673633i	−0.213851	+	0.976866i	$0.568601\pi$
$192$	−2153.18	+	198.591i	−0.809336	+	0.0746460i
$193$	−380.619	+	659.252i	−0.141956	+	0.245876i	−0.928233	−	0.371999i	$-0.878673\pi$
$193$	−380.619	+	659.252i	−0.141956	+	0.245876i	0.786277	+	0.617874i	$0.212006\pi$
$194$	−665.531	+	818.301i	−0.246301	+	0.302838i
$195$	−282.830			−0.103866
$196$	−1709.47	+	2146.45i	−0.622985	+	0.782234i
$197$	−954.802			−0.345314			−0.172657	−	0.984982i	$-0.555235\pi$
$197$	−954.802			−0.345314			−0.172657	+	0.984982i	$0.555235\pi$
$198$	559.279	−	687.659i	0.200739	−	0.246817i
$199$	−137.500	+	238.157i	−0.0489805	+	0.0848367i	−0.889476	−	0.456982i	$-0.848931\pi$
$199$	−137.500	+	238.157i	−0.0489805	+	0.0848367i	0.840496	+	0.541818i	$0.182264\pi$
$200$	−1507.94	−	2354.75i	−0.533137	−	0.832529i
$201$	2449.98	−	1414.49i	0.859742	−	0.496372i
$202$	−496.843	−	1302.59i	−0.173058	−	0.453711i
$203$	−3552.63	−	1667.61i	−1.22830	−	0.576569i
$204$	505.391	+	566.113i	0.173453	+	0.194293i
$205$	−247.612	−	428.876i	−0.0843607	−	0.146117i
$206$	227.457	−	1416.62i	0.0769305	−	0.479129i
$207$	469.777	+	271.226i	0.157738	+	0.0910700i
$208$	1432.74	+	3293.03i	0.477610	+	1.09774i
$209$		−	3652.46i		−	1.20883i
$210$	−237.847	+	114.636i	−0.0781572	+	0.0376696i
$211$		−	5361.25i		−	1.74921i	−0.484835	−	0.874605i	$-0.661121\pi$
$211$		−	5361.25i		−	1.74921i	0.484835	−	0.874605i	$-0.338879\pi$
$212$	−1704.42	−	561.820i	−0.552172	−	0.182009i
$213$	488.050	+	281.776i	0.156998	+	0.0906430i
$214$	2992.93	+	480.554i	0.956039	+	0.153505i
$215$	154.110	+	266.926i	0.0488846	+	0.0846707i
$216$	−1588.54	+	3069.16i	−0.500400	+	0.966805i
$217$	1647.24	−	1147.19i	0.515309	−	0.358877i
$218$	2107.63	−	803.910i	0.654802	−	0.249760i
$219$	−2852.72	+	1647.02i	−0.880224	+	0.508198i
$220$	−66.5278	−	319.662i	−0.0203877	−	0.0979620i
$221$	630.182	−	1091.51i	0.191813	−	0.332229i
$222$	−1501.31	−	1221.03i	−0.453881	−	0.369145i
$223$	−2056.85			−0.617653			−0.308826	−	0.951118i	$-0.599936\pi$
$223$	−2056.85			−0.617653			−0.308826	+	0.951118i	$0.599936\pi$
$224$	2539.60	+	2188.58i	0.757517	+	0.652815i
$225$	−1132.43			−0.335535
$226$	1301.08	+	1058.18i	0.382950	+	0.311456i
$227$	1283.13	−	2222.44i	0.375173	−	0.649818i	−0.615180	−	0.788387i	$-0.710917\pi$
$227$	1283.13	−	2222.44i	0.375173	−	0.649818i	0.990353	+	0.138568i	$0.0442501\pi$
$228$	735.248	+	3532.83i	0.213566	+	1.02617i
$229$	804.017	−	464.200i	0.232013	−	0.133953i	−0.379487	−	0.925197i	$-0.623900\pi$
$229$	804.017	−	464.200i	0.232013	−	0.133953i	0.611500	+	0.791244i	$0.290566\pi$
$230$	186.700	−	71.2128i	0.0535246	−	0.0204158i
$231$	2665.22	−	226.358i	0.759127	−	0.0644731i
$232$	−2204.02	+	4258.31i	−0.623711	+	1.20505i
$233$	1097.14	+	1900.31i	0.308481	+	0.534305i	0.978030	−	0.208463i	$-0.0668459\pi$
$233$	1097.14	+	1900.31i	0.308481	+	0.534305i	−0.669549	+	0.742768i	$0.733513\pi$
$234$	1436.01	+	230.571i	0.401175	+	0.0644140i
$235$	−628.968	−	363.135i	−0.174593	−	0.100801i
$236$	652.294	+	215.012i	0.179918	+	0.0593055i
$237$			3556.57i			0.974786i
$238$	87.5483	−	1173.33i	0.0238442	−	0.319562i
$239$			2314.74i			0.626479i	0.949674	+	0.313239i	$0.101414\pi$
$239$			2314.74i			0.626479i	−0.949674	+	0.313239i	$0.898586\pi$
$240$	128.698	+	295.800i	0.0346141	+	0.0795575i
$241$	228.740	+	132.063i	0.0611388	+	0.0352985i	0.530258	−	0.847836i	$-0.322095\pi$
$241$	228.740	+	132.063i	0.0611388	+	0.0352985i	−0.469119	+	0.883135i	$0.655428\pi$
$242$	72.4268	−	451.080i	0.0192387	−	0.119820i
$243$	1222.27	+	2117.04i	0.322670	+	0.558881i
$244$	−1919.62	−	2150.26i	−0.503652	−	0.564166i
$245$	383.958	+	141.962i	0.100123	+	0.0370188i
$246$	−1766.45	−	4631.14i	−0.457824	−	1.20029i
$247$	5190.17	−	2996.54i	1.33701	−	0.771925i
$248$	−1322.59	−	2065.32i	−0.338649	−	0.528823i
$249$	913.731	−	1582.63i	0.232552	−	0.402791i
$250$	−529.451	+	650.984i	−0.133942	+	0.164687i
$251$	−2249.39			−0.565659			−0.282830	−	0.959170i	$-0.591273\pi$
$251$	−2249.39			−0.565659			−0.282830	+	0.959170i	$0.591273\pi$
$252$	1301.08	−	388.140i	0.325238	−	0.0970260i
$253$	−2024.31			−0.503034
$254$	911.578	−	1120.83i	0.225187	−	0.276878i
$255$	56.6067	−	98.0457i	0.0139014	−	0.0240779i
$256$	2792.10	−	2996.90i	0.681666	−	0.731664i
$257$	−6237.24	+	3601.07i	−1.51388	+	0.874042i	−0.514017	+	0.857780i	$0.671843\pi$
$257$	−6237.24	+	3601.07i	−1.51388	+	0.874042i	−0.999868	+	0.0162619i	$0.994823\pi$
$258$	1099.41	+	2882.35i	0.265296	+	0.695533i
$259$	253.906	+	2989.57i	0.0609149	+	0.717231i
$260$	399.662	−	356.793i	0.0953307	−	0.0851053i
$261$	970.939	+	1681.72i	0.230267	+	0.398834i
$262$	−282.322	+	1758.32i	−0.0665722	+	0.414616i
$263$	3065.98	+	1770.14i	0.718845	+	0.415026i	0.814328	−	0.580406i	$-0.197106\pi$
$263$	3065.98	+	1770.14i	0.718845	+	0.415026i	−0.0954822	+	0.995431i	$0.530439\pi$
$264$	−150.227	−	3264.54i	−0.0350222	−	0.761055i
$265$			267.731i			0.0620626i
$266$	3150.15	−	4623.62i	0.726120	−	1.06576i
$267$			2140.95i			0.490726i
$268$	−1677.62	+	5089.48i	−0.382376	+	1.16004i
$269$	−3374.92	−	1948.51i	−0.764954	−	0.441646i	0.0661178	−	0.997812i	$-0.478939\pi$
$269$	−3374.92	−	1948.51i	−0.764954	−	0.441646i	−0.831071	+	0.556166i	$0.812272\pi$
$270$	509.045	+	81.7339i	0.114739	+	0.0184228i
$271$	−546.539	−	946.634i	−0.122509	−	0.212192i	0.798248	−	0.602329i	$-0.205761\pi$
$271$	−546.539	−	946.634i	−0.122509	−	0.212192i	−0.920756	+	0.390138i	$0.872427\pi$
$272$	−1428.32	−	162.407i	−0.318399	−	0.0362036i
$273$	2508.25	+	3601.58i	0.556067	+	0.798453i
$274$	−2600.17	+	991.777i	−0.573292	+	0.218670i
$275$	3659.82	−	2113.00i	0.802528	−	0.463340i
$276$	1958.01	−	407.499i	0.427023	−	0.0888716i
$277$	443.394	−	767.981i	0.0961768	−	0.166583i	−0.813922	−	0.580974i	$-0.802672\pi$
$277$	443.394	−	767.981i	0.0961768	−	0.166583i	0.910099	+	0.414391i	$0.136005\pi$
$278$	−4214.75	−	3427.89i	−0.909295	−	0.739537i
$279$	−993.241			−0.213132
$280$	191.483	−	462.037i	0.0408690	−	0.0986143i
$281$	7748.61			1.64499			0.822497	−	0.568769i	$-0.192580\pi$
$281$	7748.61			1.64499			0.822497	+	0.568769i	$0.192580\pi$
$282$	−5639.41	−	4586.58i	−1.19086	−	0.968535i
$283$	−453.400	+	785.312i	−0.0952362	+	0.164954i	−0.909707	−	0.415250i	$-0.863694\pi$
$283$	−453.400	+	785.312i	−0.0952362	+	0.164954i	0.814471	+	0.580204i	$0.197027\pi$
$284$	−1045.12	+	217.509i	−0.218368	+	0.0454464i
$285$	466.212	−	269.168i	0.0968983	−	0.0559442i
$286$	−5071.16	+	1934.28i	−1.04847	+	0.399918i
$287$	−3265.43	+	6956.57i	−0.671611	+	1.43078i
$288$	−412.292	−	1606.78i	−0.0843560	−	0.328752i
$289$	−2204.25	−	3817.87i	−0.448656	−	0.777094i
$290$	706.275	+	113.402i	0.143013	+	0.0229627i
$291$	1363.94	+	787.471i	0.274761	+	0.158634i
$292$	1953.40	−	5926.12i	0.391486	−	1.18767i
$293$		−	2063.79i		−	0.411495i	−0.978605	−	0.205748i	$-0.934037\pi$
$293$		−	2063.79i		−	0.411495i	0.978605	−	0.205748i	$-0.0659626\pi$
$294$	3569.11	+	2012.13i	0.708009	+	0.399150i
$295$		−	102.462i		−	0.0202223i
$296$	3661.83	−	168.510i	0.719052	−	0.0330893i
$297$	−4523.26	−	2611.51i	−0.883725	−	0.510219i
$298$	−39.9888	+	249.053i	−0.00777346	+	0.0484137i
$299$	−1660.79	−	2876.56i	−0.321223	−	0.556375i
$300$	−3114.59	+	2780.52i	−0.599404	+	0.535111i
$301$	2032.35	−	4329.66i	0.389179	−	0.829095i
$302$	2186.43	+	5732.22i	0.416606	+	1.09223i
$303$	−1802.76	+	1040.82i	−0.341801	+	0.197339i
$304$	−5495.67	−	4064.65i	−1.03684	−	0.766854i
$305$	−215.009	+	372.406i	−0.0403651	+	0.0699145i
$306$	−367.339	+	451.660i	−0.0686254	+	0.0843781i
$307$	4283.78			0.796379			0.398189	−	0.917303i	$-0.369639\pi$
$307$	4283.78			0.796379			0.398189	+	0.917303i	$0.369639\pi$
$308$	−3480.62	+	3682.07i	−0.643918	+	0.681187i
$309$	−2142.33			−0.394410
$310$	−230.857	+	283.849i	−0.0422961	+	0.0520050i
$311$	1950.58	−	3378.51i	0.355650	−	0.616005i	−0.631579	−	0.775312i	$-0.717593\pi$
$311$	1950.58	−	3378.51i	0.355650	−	0.616005i	0.987229	+	0.159307i	$0.0509260\pi$
$312$	4515.68	−	2891.76i	0.819391	−	0.524724i
$313$	−8158.28	+	4710.19i	−1.47327	+	0.850593i	−0.999547	−	0.0300815i	$-0.990423\pi$
$313$	−8158.28	+	4710.19i	−1.47327	+	0.850593i	−0.473722	+	0.880674i	$0.657090\pi$
$314$	2512.18	+	6586.24i	0.451498	+	1.18370i
$315$	−115.758	−	166.216i	−0.0207055	−	0.0297309i
$316$	−4486.67	−	5025.73i	−0.798717	−	0.894682i
$317$	460.618	+	797.814i	0.0816116	+	0.141355i	0.903942	−	0.427654i	$-0.140660\pi$
$317$	460.618	+	797.814i	0.0816116	+	0.141355i	−0.822331	+	0.569010i	$0.807327\pi$
$318$	−424.815	+	2645.78i	−0.0749133	+	0.466566i
$319$	−6275.81	−	3623.34i	−1.10150	−	0.635950i
$320$	−555.016	−	255.636i	−0.0969573	−	0.0446578i
$321$		−	4526.15i		−	0.786994i
$322$	−2562.57	−	1745.92i	−0.443498	−	0.302162i
$323$			2398.96i			0.413257i
$324$	3020.91	+	995.765i	0.517988	+	0.170742i
$325$	6005.16	+	3467.08i	1.02494	+	0.591751i
$326$	3220.25	+	517.054i	0.547096	+	0.0878435i
$327$	−1684.09	−	2916.93i	−0.284802	−	0.493292i
$328$	8338.39	+	4315.79i	1.40369	+	0.726524i
$329$	953.751	+	11229.8i	0.159824	+	1.88182i
$330$	−455.522	+	173.749i	−0.0759868	+	0.0289835i
$331$	−2745.37	+	1585.04i	−0.455889	+	0.263208i	−0.710314	−	0.703885i	$-0.751447\pi$
$331$	−2745.37	+	1585.04i	−0.455889	+	0.263208i	0.254425	+	0.967092i	$0.418114\pi$
$332$	705.330	+	3389.07i	0.116596	+	0.560239i
$333$	742.286	−	1285.68i	0.122153	−	0.211576i
$334$	7616.65	+	6194.69i	1.24780	+	1.01484i
$335$	799.455			0.130385
$336$	2625.41	−	4262.13i	0.426273	−	0.692018i
$337$	11402.9			1.84320			0.921598	−	0.388145i	$-0.126884\pi$
$337$	11402.9			1.84320			0.921598	+	0.388145i	$0.126884\pi$
$338$	−2088.19	−	1698.34i	−0.336043	−	0.273307i
$339$	1252.06	−	2168.64i	0.200598	−	0.347446i
$340$	43.6960	+	209.957i	0.00696985	+	0.0334897i
$341$	3209.98	−	1853.28i	0.509766	−	0.294313i
$342$	−2586.53	+	986.576i	−0.408958	+	0.155988i
$343$	−1597.35	−	6148.34i	−0.251454	−	0.967869i
$344$	−5189.69	−	2686.08i	−0.813399	−	0.421000i
$345$	−149.182	−	258.390i	−0.0232802	−	0.0403225i
$346$	8007.77	+	1285.75i	1.24422	+	0.199776i
$347$	1629.30	+	940.675i	0.252061	+	0.145528i	0.620708	−	0.784042i	$-0.286845\pi$
$347$	1629.30	+	940.675i	0.252061	+	0.145528i	−0.368647	+	0.929570i	$0.620179\pi$
$348$	6799.64	+	2241.33i	1.04741	+	0.345252i
$349$		−	827.050i		−	0.126851i	−0.997987	−	0.0634255i	$-0.979797\pi$
$349$		−	827.050i		−	0.126851i	0.997987	−	0.0634255i	$-0.0202025\pi$
$350$	6455.34	+	481.666i	0.985864	+	0.0735604i
$351$		−	8570.11i		−	1.30324i
$352$	4330.54	+	4423.55i	0.655735	+	0.669818i
$353$	−7054.69	−	4073.03i	−1.06369	−	0.614123i	−0.137241	−	0.990538i	$-0.543823\pi$
$353$	−7054.69	−	4073.03i	−1.06369	−	0.614123i	−0.926451	+	0.376415i	$0.877157\pi$
$354$	162.579	−	1012.56i	0.0244096	−	0.152025i
$355$	79.6281	+	137.920i	0.0119048	+	0.0206198i
$356$	−2700.84	−	3025.34i	−0.402090	−	0.450401i
$357$	−1750.54	+	148.674i	−0.259519	+	0.0220411i
$358$	−1720.34	−	4510.25i	−0.253974	−	0.665849i
$359$	−2220.38	+	1281.94i	−0.326427	+	0.188463i	−0.654254	−	0.756275i	$-0.727017\pi$
$359$	−2220.38	+	1281.94i	−0.326427	+	0.188463i	0.327827	+	0.944738i	$0.393684\pi$
$360$	−208.403	+	133.457i	−0.0305105	+	0.0195384i
$361$	−2274.09	+	3938.84i	−0.331549	+	0.574259i
$362$	−7412.45	+	9113.95i	−1.07621	+	1.32326i
$363$	−682.159			−0.0986338
$364$	−8087.81	−	1925.14i	−1.16461	−	0.277211i
$365$	−930.875			−0.133491
$366$	−2715.67	+	3339.04i	−0.387843	+	0.476871i
$367$	−2738.05	+	4742.45i	−0.389442	+	0.674533i	−0.992375	−	0.123259i	$-0.960665\pi$
$367$	−2738.05	+	4742.45i	−0.389442	+	0.674533i	0.602933	+	0.797792i	$0.293999\pi$
$368$	−2252.77	+	3045.89i	−0.319113	+	0.431462i
$369$	3293.04	−	1901.24i	0.464577	−	0.268224i
$370$	−194.894	−	510.958i	−0.0273839	−	0.0717931i
$371$	3409.32	−	2374.35i	0.477097	−	0.332264i
$372$	−2731.77	+	2438.76i	−0.380741	+	0.339902i
$373$	−1993.55	−	3452.93i	−0.276735	−	0.479319i	0.693836	−	0.720133i	$-0.255919\pi$
$373$	−1993.55	−	3452.93i	−0.276735	−	0.479319i	−0.970571	+	0.240814i	$0.922586\pi$
$374$	344.425	−	2145.10i	0.0476197	−	0.296579i
$375$	1085.06	+	626.458i	0.149419	+	0.0862671i
$376$	13755.0	−	632.976i	1.88659	−	0.0868171i
$377$		−	11890.6i		−	1.62440i
$378$	−3473.61	−	7207.08i	−0.472655	−	0.980668i
$379$			12140.4i			1.64542i	0.568464	+	0.822708i	$0.307538\pi$
$379$			12140.4i			1.64542i	−0.568464	+	0.822708i	$0.692462\pi$
$380$	−319.238	+	968.489i	−0.0430962	+	0.130743i
$381$	−1868.19	−	1078.60i	−0.251208	−	0.145035i
$382$	−9931.65	−	1594.66i	−1.33023	−	0.213586i
$383$	−8.80269	−	15.2467i	−0.00117440	−	0.00203413i	0.865438	−	0.501017i	$-0.167040\pi$
$383$	−8.80269	−	15.2467i	−0.00117440	−	0.00203413i	−0.866612	+	0.498983i	$0.833707\pi$
$384$	−5079.17	−	3406.91i	−0.674988	−	0.452756i
$385$	684.251	+	321.189i	0.0905784	+	0.0425177i
$386$	−2011.73	+	767.332i	−0.265271	+	0.101182i
$387$	−2049.54	+	1183.30i	−0.269209	+	0.155428i
$388$	−2920.77	+	607.867i	−0.382163	+	0.0795355i
$389$	−2946.39	+	5103.30i	−0.384031	+	0.665161i	−0.991634	−	0.129080i	$-0.958798\pi$
$389$	−2946.39	+	5103.30i	−0.384031	+	0.665161i	0.607603	+	0.794241i	$0.292131\pi$
$390$	−620.617	−	504.753i	−0.0805799	−	0.0655363i
$391$	1329.59			0.171969
$392$	−7581.78	+	1659.17i	−0.976882	+	0.213777i
$393$	2659.08			0.341305
$394$	−2095.13	−	1703.99i	−0.267897	−	0.217883i
$395$	−502.533	+	870.413i	−0.0640131	+	0.110874i
$396$	2454.47	−	510.821i	0.311469	−	0.0648225i
$397$	−3729.04	+	2152.96i	−0.471423	+	0.272176i	−0.716835	−	0.697242i	$-0.754410\pi$
$397$	−3729.04	+	2152.96i	−0.471423	+	0.272176i	0.245412	+	0.969419i	$0.421077\pi$
$398$	−726.746	+	277.201i	−0.0915288	+	0.0349117i
$399$	−7562.17	−	3549.70i	−0.948827	−	0.445382i
$400$	893.519	−	7858.20i	0.111690	−	0.982275i
$401$	763.591	+	1322.58i	0.0950921	+	0.164704i	0.909647	−	0.415382i	$-0.136352\pi$
$401$	763.591	+	1322.58i	0.0950921	+	0.164704i	−0.814555	+	0.580086i	$0.803019\pi$
$402$	7900.40	+	1268.51i	0.980190	+	0.157382i
$403$	5267.05	+	3040.94i	0.651044	+	0.375880i
$404$	1234.43	−	3744.97i	0.152018	−	0.461186i
$405$		−	474.524i		−	0.0582205i
$406$	−4819.47	−	9999.48i	−0.589129	−	1.22233i
$407$			5540.10i			0.674724i
$408$	98.6705	+	2144.18i	0.0119728	+	0.260178i
$409$	6137.85	+	3543.69i	0.742047	+	0.428421i	0.822813	−	0.568312i	$-0.192403\pi$
$409$	6137.85	+	3543.69i	0.742047	+	0.428421i	−0.0807660	+	0.996733i	$0.525737\pi$
$410$	222.057	−	1382.99i	0.0267479	−	0.166588i
$411$	2077.65	+	3598.59i	0.249350	+	0.431887i
$412$	3027.29	−	2702.57i	0.361999	−	0.323171i
$413$	−1304.77	+	908.678i	−0.155456	+	0.108264i
$414$	546.794	+	1433.54i	0.0649117	+	0.170181i
$415$	447.241	−	258.215i	0.0529017	−	0.0305428i
$416$	−2733.04	+	9782.90i	−0.322111	+	1.15300i
$417$	−4055.96	+	7025.13i	−0.476310	+	0.824993i
$418$	6518.37	−	8014.63i	0.762736	−	0.937820i
$419$	16580.0			1.93314			0.966569	−	0.256406i	$-0.0825382\pi$
$419$	16580.0			1.93314			0.966569	+	0.256406i	$0.0825382\pi$
$420$	−726.496	−	172.928i	−0.0844033	−	0.0200905i
$421$	−6613.72			−0.765637			−0.382818	−	0.923824i	$-0.625046\pi$
$421$	−6613.72			−0.765637			−0.382818	+	0.923824i	$0.625046\pi$
$422$	9567.97	−	11764.3i	1.10370	−	1.35705i
$423$	2788.26	−	4829.41i	0.320496	−	0.555116i
$424$	−2737.39	−	4274.62i	−0.313536	−	0.489608i
$425$	−2403.80	+	1387.83i	−0.274356	+	0.158400i
$426$	568.062	+	1489.30i	0.0646073	+	0.169383i
$427$	6649.05	−	564.708i	0.753560	−	0.0640003i
$428$	5709.80	+	6395.83i	0.644845	+	0.722322i
$429$	4052.07	+	7018.40i	0.456028	+	0.789864i
$430$	−138.205	+	860.752i	−0.0154996	+	0.0965329i
$431$	−9840.60	−	5681.47i	−1.09978	−	0.634958i	−0.163617	−	0.986524i	$-0.552316\pi$
$431$	−9840.60	−	5681.47i	−1.09978	−	0.634958i	−0.936163	+	0.351566i	$0.885649\pi$
$432$	−8963.14	+	3899.71i	−0.998239	+	0.434317i
$433$		−	5830.20i		−	0.647071i	−0.946216	−	0.323535i	$-0.895129\pi$
$433$		−	5830.20i		−	0.647071i	0.946216	−	0.323535i	$-0.104871\pi$
$434$	5661.90	+	422.464i	0.626221	+	0.0467256i
$435$		−	1068.09i		−	0.117726i
$436$	6059.51	+	1997.36i	0.665591	+	0.219395i
$437$	5475.23	+	3161.12i	0.599349	+	0.346034i
$438$	−9199.12	−	1477.04i	−1.00354	−	0.161132i
$439$	3140.33	+	5439.20i	0.341411	+	0.591342i	0.984695	−	0.174286i	$-0.0557618\pi$
$439$	3140.33	+	5439.20i	0.341411	+	0.591342i	−0.643284	+	0.765628i	$0.722428\pi$
$440$	424.504	−	820.168i	0.0459941	−	0.0888636i
$441$	−1090.03	+	2948.15i	−0.117701	+	0.318340i
$442$	3330.78	−	1270.45i	0.358436	−	0.136718i
$443$	4211.87	−	2431.72i	0.451720	−	0.260801i	−0.256836	−	0.966455i	$-0.582680\pi$
$443$	4211.87	−	2431.72i	0.451720	−	0.260801i	0.708556	+	0.705654i	$0.249347\pi$
$444$	−1115.24	−	5358.65i	−0.119204	−	0.572771i
$445$	−302.509	+	523.962i	−0.0322254	+	0.0558161i
$446$	−4513.36	−	3670.76i	−0.479179	−	0.389720i
$447$	376.639			0.0398533
$448$	1666.81	+	9334.73i	0.175780	+	0.984429i
$449$	6326.57			0.664965			0.332483	−	0.943109i	$-0.392114\pi$
$449$	6326.57			0.664965			0.332483	+	0.943109i	$0.392114\pi$
$450$	−2484.91	−	2021.00i	−0.260310	−	0.211713i
$451$	−7095.02	+	12288.9i	−0.740780	+	1.28307i
$452$	966.496	+	4643.96i	0.100576	+	0.483260i
$453$	7933.31	−	4580.30i	0.822824	−	0.475058i
$454$	6781.88	−	2586.80i	0.701078	−	0.267411i
$455$	104.960	+	1235.84i	0.0108145	+	0.127334i
$456$	−4691.50	+	9064.29i	−0.481798	+	0.930865i
$457$	−8550.00	−	14809.0i	−0.875168	−	1.51584i	−0.856583	−	0.516009i	$-0.827417\pi$
$457$	−8550.00	−	14809.0i	−0.875168	−	1.51584i	−0.0185851	−	0.999827i	$-0.505916\pi$
$458$	2592.70	+	416.293i	0.264517	+	0.0424718i
$459$	2970.92	+	1715.26i	0.302114	+	0.174426i
$460$	536.769	+	176.932i	0.0544065	+	0.0179337i
$461$			15378.2i			1.55365i	0.629717	+	0.776825i	$0.283171\pi$
$461$			15378.2i			1.55365i	−0.629717	+	0.776825i	$0.716829\pi$
$462$	6252.29	+	4259.79i	0.629617	+	0.428968i
$463$		−	2225.59i		−	0.223395i	−0.993742	−	0.111697i	$-0.964371\pi$
$463$		−	2225.59i		−	0.223395i	0.993742	−	0.111697i	$-0.0356287\pi$
$464$	−12435.9	+	5410.66i	−1.24423	+	0.541344i
$465$	473.118	+	273.155i	0.0471835	+	0.0272414i
$466$	−983.913	+	6127.88i	−0.0978088	+	0.609160i
$467$	−6133.89	−	10624.2i	−0.607800	−	1.05274i	−0.991602	−	0.129325i	$-0.958719\pi$
$467$	−6133.89	−	10624.2i	−0.607800	−	1.05274i	0.383802	−	0.923415i	$-0.374615\pi$
$468$	2739.57	+	3068.73i	0.270591	+	0.303103i
$469$	−7089.90	−	10180.4i	−0.698041	−	1.00231i
$470$	−732.083	−	1919.32i	−0.0718478	−	0.188365i
$471$	9115.26	−	5262.70i	0.891738	−	0.514845i
$472$	1047.62	+	1635.92i	0.102162	+	0.159533i
$473$	4415.83	−	7648.45i	0.429261	−	0.743501i
$474$	−6347.25	+	7804.24i	−0.615061	+	0.756246i
$475$	−13198.4			−1.27492
$476$	2286.10	−	2418.41i	0.220133	−	0.232874i
$477$	−2055.72			−0.197327
$478$	−4131.02	+	5079.28i	−0.395289	+	0.486027i
$479$	1770.66	−	3066.87i	0.168901	−	0.292545i	−0.769133	−	0.639089i	$-0.779312\pi$
$479$	1770.66	−	3066.87i	0.168901	−	0.292545i	0.938034	+	0.346544i	$0.112645\pi$
$480$	−245.498	+	878.759i	−0.0233446	+	0.0835618i
$481$	−7872.53	+	4545.21i	−0.746271	+	0.430860i
$482$	266.241	+	698.010i	0.0251596	+	0.0659616i
$483$	−1967.36	+	4191.21i	−0.185338	+	0.394838i
$484$	963.948	−	860.554i	0.0905286	−	0.0808183i
$485$	222.534	+	385.441i	0.0208346	+	0.0360865i
$486$	−1096.13	+	6826.78i	−0.102308	+	0.637179i
$487$	−12479.1	−	7204.80i	−1.16115	−	0.670392i	−0.209573	−	0.977793i	$-0.567207\pi$
$487$	−12479.1	−	7204.80i	−1.16115	−	0.670392i	−0.951580	+	0.307401i	$0.900541\pi$
$488$	−374.780	−	8144.21i	−0.0347653	−	0.755473i
$489$		−	4869.92i		−	0.450359i
$490$	589.172	+	996.741i	0.0543186	+	0.0918942i
$491$		−	12333.7i		−	1.13363i	−0.823846	−	0.566814i	$-0.808176\pi$
$491$		−	12333.7i		−	1.13363i	0.823846	−	0.566814i	$-0.191824\pi$
$492$	4388.84	−	13314.7i	0.402163	−	1.22007i
$493$	4122.00	+	2379.84i	0.376563	+	0.217409i
$494$	16736.6	+	2687.29i	1.52433	+	0.244751i
$495$	−187.007	−	323.906i	−0.0169805	−	0.0294111i
$496$	783.694	−	6892.33i	0.0709454	−	0.623941i
$497$	1050.11	−	2237.12i	0.0947766	−	0.201909i
$498$	4829.46	−	1842.09i	0.434564	−	0.165755i
$499$	−3342.44	+	1929.76i	−0.299856	+	0.173122i	−0.642378	−	0.766388i	$-0.722052\pi$
$499$	−3342.44	+	1929.76i	−0.299856	+	0.173122i	0.342522	+	0.939510i	$0.388719\pi$
$500$	−2323.56	+	483.577i	−0.207826	+	0.0432525i
$501$	7329.69	−	12695.4i	0.653626	−	1.13211i
$502$	−4935.87	−	4014.39i	−0.438842	−	0.356914i
$503$	−21123.7			−1.87248			−0.936242	−	0.351355i	$-0.885721\pi$
$503$	−21123.7			−1.87248			−0.936242	+	0.351355i	$0.885721\pi$
$504$	3547.67	+	1470.27i	0.313543	+	0.129942i
$505$	−588.260			−0.0518361
$506$	−4441.98	−	3612.70i	−0.390257	−	0.317399i
$507$	−2009.52	+	3480.59i	−0.176027	+	0.304888i
$508$	4000.58	−	832.596i	0.349403	−	0.0727174i
$509$	15427.0	−	8906.80i	1.34340	−	0.775613i	0.356096	−	0.934449i	$-0.384108\pi$
$509$	15427.0	−	8906.80i	1.34340	−	0.775613i	0.987305	+	0.158837i	$0.0507743\pi$
$510$	299.190	−	114.120i	0.0259772	−	0.00990844i
$511$	8255.39	+	11853.9i	0.714671	+	1.02619i
$512$	11475.2	−	1593.19i	0.990499	−	0.137519i
$513$	8156.14	+	14126.8i	0.701954	+	1.21582i
$514$	−20113.1	−	3229.43i	−1.72598	−	0.277129i
$515$	−524.299	−	302.704i	−0.0448609	−	0.0259005i
$516$	−2731.55	+	8286.85i	−0.233042	+	0.706993i
$517$			20810.4i			1.77029i
$518$	−4778.20	+	7013.19i	−0.405293	+	0.594868i
$519$		−	12110.0i		−	1.02422i
$520$	1513.74	−	69.6590i	0.127657	−	0.00587452i
$521$	−6584.35	−	3801.48i	−0.553677	−	0.319665i	0.196927	−	0.980418i	$-0.436904\pi$
$521$	−6584.35	−	3801.48i	−0.553677	−	0.319665i	−0.750604	+	0.660753i	$0.770237\pi$
$522$	−870.735	+	5423.00i	−0.0730097	+	0.454710i
$523$	866.244	+	1500.38i	0.0724248	+	0.125443i	0.899964	−	0.435965i	$-0.143593\pi$
$523$	866.244	+	1500.38i	0.0724248	+	0.125443i	−0.827539	+	0.561409i	$0.810260\pi$
$524$	−3757.50	+	3354.46i	−0.313258	+	0.279657i
$525$	−817.963	−	9630.96i	−0.0679978	−	0.800628i
$526$	3568.63	+	9355.96i	0.295816	+	0.775550i
$527$	−2108.34	+	1217.25i	−0.174271	+	0.100615i
$528$	5496.42	−	7431.52i	0.453032	−	0.612529i
$529$	−4331.50	+	7502.38i	−0.356004	+	0.616617i
$530$	−477.807	+	587.486i	−0.0391596	+	0.0481486i
$531$	786.737			0.0642966
$532$	15164.0	−	4523.76i	1.23579	−	0.368665i
$533$	−23283.6			−1.89216
$534$	−3820.85	+	4697.91i	−0.309634	+	0.380709i
$535$	639.531	−	1107.70i	0.0516810	−	0.0895141i
$536$	−12764.2	+	8173.95i	−1.02860	+	0.658696i
$537$	−6242.11	+	3603.88i	−0.501615	+	0.289607i
$538$	−3928.22	−	10298.7i	−0.314791	−	0.825295i
$539$	−1978.17	−	11561.8i	−0.158081	−	0.923935i
$540$	971.137	+	1087.82i	0.0773909	+	0.0866894i
$541$	−2721.01	−	4712.93i	−0.216239	−	0.374537i	0.737416	−	0.675439i	$-0.236046\pi$
$541$	−2721.01	−	4712.93i	−0.216239	−	0.374537i	−0.953655	+	0.300902i	$0.902712\pi$
$542$	490.135	−	3052.59i	0.0388433	−	0.241919i
$543$	15191.1	+	8770.58i	1.20057	+	0.693152i
$544$	−2844.34	−	2905.42i	−0.224173	−	0.228987i
$545$		−	951.827i		−	0.0748106i
$546$	−923.688	+	12379.4i	−0.0723996	+	0.970307i
$547$			4559.51i			0.356399i	0.983994	+	0.178200i	$0.0570273\pi$
$547$			4559.51i			0.356399i	−0.983994	+	0.178200i	$0.942973\pi$
$548$	−7475.56	−	2464.13i	−0.582738	−	0.192085i
$549$	−2859.45	−	1650.90i	−0.222292	−	0.128340i
$550$	11801.7	+	1894.93i	0.914960	+	0.146909i
$551$	11316.2	+	19600.3i	0.874933	+	1.51543i
$552$	5023.73	+	2600.19i	0.387363	+	0.200492i
$553$	15540.6	−	1319.87i	1.19503	−	0.101495i
$554$	2343.53	−	893.886i	0.179724	−	0.0685516i
$555$	−707.158	+	408.278i	−0.0540850	+	0.0312260i
$556$	−3130.89	−	15043.7i	−0.238812	−	1.14748i
$557$	6808.62	−	11792.9i	0.517936	−	0.897092i	−0.481846	−	0.876256i	$-0.660034\pi$
$557$	6808.62	−	11792.9i	0.517936	−	0.897092i	0.999783	−	0.0208366i	$-0.00663298\pi$
$558$	−2179.48	−	1772.59i	−0.165349	−	0.134480i
$559$	14491.3			1.09645
$560$	1244.75	−	672.123i	0.0939291	−	0.0507186i
$561$	−3244.00			−0.244138
$562$	17002.9	+	13828.6i	1.27620	+	1.03794i
$563$	10859.4	−	18809.0i	0.812912	−	1.40800i	−0.0979055	−	0.995196i	$-0.531214\pi$
$563$	10859.4	−	18809.0i	0.812912	−	1.40800i	0.910818	−	0.412809i	$-0.135452\pi$
$564$	−4189.18	−	20128.8i	−0.312759	−	1.50279i
$565$	612.844	−	353.825i	0.0456328	−	0.0263461i
$566$	−2396.41	+	914.059i	−0.177966	+	0.0678812i
$567$	−6042.64	+	4208.28i	−0.447561	+	0.311695i
$568$	−2681.50	−	1387.89i	−0.198086	−	0.102526i
$569$	8176.19	+	14161.6i	0.602397	+	1.04338i	0.992457	+	0.122592i	$0.0391208\pi$
$569$	8176.19	+	14161.6i	0.602397	+	1.04338i	−0.390060	+	0.920789i	$0.627546\pi$
$570$	1503.39	+	241.389i	0.110474	+	0.0177380i
$571$	8594.29	+	4961.91i	0.629877	+	0.363660i	0.780704	−	0.624901i	$-0.214860\pi$
$571$	8594.29	+	4961.91i	0.629877	+	0.363660i	−0.150828	+	0.988560i	$0.548194\pi$
$572$	−14579.7	−	4805.83i	−1.06575	−	0.351297i
$573$			15019.4i			1.09502i
$574$	−19580.4	+	9437.23i	−1.42382	+	0.686241i
$575$			7315.01i			0.530534i
$576$	1962.86	−	4261.59i	0.141989	−	0.308275i
$577$	6086.87	+	3514.26i	0.439168	+	0.253554i	0.703245	−	0.710948i	$-0.251734\pi$
$577$	6086.87	+	3514.26i	0.439168	+	0.253554i	−0.264077	+	0.964502i	$0.585067\pi$
$578$	1976.76	−	12311.4i	0.142253	−	0.885964i
$579$	1607.46	+	2784.21i	0.115378	+	0.199841i
$580$	1347.41	+	1509.30i	0.0964621	+	0.108052i
$581$	−7254.46	−	3405.26i	−0.518013	−	0.243157i
$582$	1587.55	+	4162.12i	0.113069	+	0.296435i
$583$	6643.73	−	3835.76i	0.471964	−	0.272489i
$584$	14862.4	−	9517.64i	1.05310	−	0.674388i
$585$	306.848	−	531.476i	0.0216865	−	0.0375621i
$586$	3683.16	−	4528.61i	0.259641	−	0.319241i
$587$	−8277.57			−0.582030			−0.291015	−	0.956718i	$-0.593993\pi$
$587$	−8277.57			−0.582030			−0.291015	+	0.956718i	$0.593993\pi$
$588$	4240.79	+	10784.9i	0.297427	+	0.756396i
$589$	−11576.2			−0.809827
$590$	182.860	−	224.834i	0.0127597	−	0.0156886i
$591$	−2016.20	+	3492.16i	−0.140331	+	0.243060i
$592$	8335.93	+	6165.33i	0.578724	+	0.428030i
$593$	10422.0	−	6017.16i	0.721722	−	0.416687i	−0.0936639	−	0.995604i	$-0.529858\pi$
$593$	10422.0	−	6017.16i	0.721722	−	0.416687i	0.815386	+	0.578917i	$0.196525\pi$
$594$	−5264.82	−	13802.9i	−0.363667	−	0.953435i
$595$	−449.422	−	210.960i	−0.0309656	−	0.0145353i
$596$	−532.222	+	475.135i	−0.0365783	+	0.0326549i
$597$	580.702	+	1005.80i	0.0398099	+	0.0689528i
$598$	1489.39	−	9276.01i	0.101849	−	0.634321i
$599$	17523.6	+	10117.3i	1.19532	+	0.690118i	0.959508	−	0.281681i	$-0.0908921\pi$
$599$	17523.6	+	10117.3i	1.19532	+	0.690118i	0.235811	+	0.971799i	$0.424225\pi$
$600$	−11796.7	+	542.857i	−0.802660	+	0.0369368i
$601$			11846.7i			0.804052i	0.915628	+	0.402026i	$0.131694\pi$
$601$			11846.7i			0.804052i	−0.915628	+	0.402026i	$0.868306\pi$
$602$	12186.6	−	5873.59i	0.825062	−	0.397657i
$603$			6138.47i			0.414557i
$604$	−5432.32	+	16480.3i	−0.365957	+	1.11022i
$605$	−166.947	−	96.3871i	−0.0112188	−	0.00647718i
$606$	−5813.32	−	933.406i	−0.389687	−	0.0625694i
$607$	−7756.88	−	13435.3i	−0.518686	−	0.898390i	−0.999764	−	0.0217125i	$-0.993088\pi$
$607$	−7756.88	−	13435.3i	−0.518686	−	0.898390i	0.481079	−	0.876678i	$-0.340245\pi$
$608$	−4805.24	−	18727.0i	−0.320523	−	1.24914i
$609$	−13601.1	+	9472.24i	−0.905001	+	0.630270i
$610$	−1136.41	+	433.460i	−0.0754295	+	0.0287709i
$611$	−29571.7	+	17073.2i	−1.95801	+	1.13046i
$612$	−1612.11	+	335.512i	−0.106480	+	0.0221605i
$613$	1721.81	−	2982.27i	0.113447	−	0.196497i	−0.803711	−	0.595020i	$-0.797144\pi$
$613$	1721.81	−	2982.27i	0.113447	−	0.196497i	0.917158	+	0.398524i	$0.130477\pi$
$614$	9399.96	+	7645.06i	0.617836	+	0.502491i
$615$	−2091.47			−0.137132
$616$	−14208.8	+	1867.92i	−0.929364	+	0.122176i
$617$	−7010.85			−0.457449			−0.228725	−	0.973491i	$-0.573456\pi$
$617$	−7010.85			−0.457449			−0.228725	+	0.973491i	$0.573456\pi$
$618$	−4700.94	−	3823.31i	−0.305986	−	0.248861i
$619$	7448.93	−	12901.9i	0.483680	−	0.837758i	−0.516144	−	0.856502i	$-0.672633\pi$
$619$	7448.93	−	12901.9i	0.483680	−	0.837758i	0.999824	+	0.0187433i	$0.00596652\pi$
$620$	−1013.14	+	210.855i	−0.0656272	+	0.0136583i
$621$	7829.57	−	4520.40i	0.505942	−	0.292106i
$622$	10309.6	−	3932.39i	0.664597	−	0.253496i
$623$	9354.96	−	794.523i	0.601603	−	0.0510945i
$624$	15069.6	+	1713.49i	0.966775	+	0.109927i
$625$	−7546.44	−	13070.8i	−0.482972	−	0.836533i
$626$	−26307.9	−	4224.08i	−1.67967	−	0.269694i
$627$	−13358.8	−	7712.68i	−0.850873	−	0.491252i
$628$	−6241.65	+	18935.7i	−0.396607	+	1.20321i
$629$		−	3638.79i		−	0.230664i
$630$	42.6290	−	571.319i	0.00269584	−	0.0361300i
$631$			3172.41i			0.200145i	0.994980	+	0.100073i	$0.0319075\pi$
$631$			3172.41i			0.200145i	−0.994980	+	0.100073i	$0.968093\pi$
$632$	−875.960	−	19035.2i	−0.0551326	−	1.19807i
$633$	−19608.6	−	11321.0i	−1.23124	−	0.710854i
$634$	−413.081	+	2572.70i	−0.0258762	+	0.161159i
$635$	−304.806	−	527.939i	−0.0190486	−	0.0329931i
$636$	−5653.98	+	5047.52i	−0.352507	+	0.314697i
$637$	14806.4	−	12296.5i	0.920961	−	0.764842i
$638$	−7304.68	−	19150.9i	−0.453284	−	1.18839i
$639$	−1058.99	+	611.409i	−0.0655604	+	0.0378513i
$640$	−761.657	−	1551.46i	−0.0470424	−	0.0958231i
$641$	880.382	−	1524.87i	0.0542480	−	0.0939603i	−0.837626	−	0.546244i	$-0.816057\pi$
$641$	880.382	−	1524.87i	0.0542480	−	0.0939603i	0.891874	+	0.452284i	$0.149391\pi$
$642$	8077.61	−	9931.79i	0.496570	−	0.610555i
$643$	−11358.8			−0.696651			−0.348325	−	0.937374i	$-0.613250\pi$
$643$	−11358.8			−0.696651			−0.348325	+	0.937374i	$0.613250\pi$
$644$	−2507.22	−	8404.38i	−0.153413	−	0.514253i
$645$	1301.70			0.0794641
$646$	−4281.32	+	5264.08i	−0.260753	+	0.320607i
$647$	−11317.1	+	19601.8i	−0.687667	+	1.19107i	0.284924	+	0.958550i	$0.408032\pi$
$647$	−11317.1	+	19601.8i	−0.687667	+	1.19107i	−0.972591	+	0.232523i	$0.925302\pi$
$648$	4851.73	+	7576.30i	0.294126	+	0.459298i
$649$	−2542.60	+	1467.97i	−0.153784	+	0.0887870i
$650$	6989.67	+	18325.0i	0.421781	+	1.10579i
$651$	−717.425	−	8447.19i	−0.0431922	−	0.508559i
$652$	6143.48	+	6881.61i	0.369014	+	0.413351i
$653$	6027.89	+	10440.6i	0.361240	+	0.625686i	0.988165	−	0.153393i	$-0.0490202\pi$
$653$	6027.89	+	10440.6i	0.361240	+	0.625686i	−0.626925	+	0.779079i	$0.715687\pi$
$654$	1510.29	−	9406.17i	0.0903010	−	0.562401i
$655$	650.765	+	375.720i	0.0388206	+	0.0224131i
$656$	10594.9	+	24351.3i	0.630578	+	1.44933i
$657$		−	7147.55i		−	0.424433i
$658$	−17948.4	+	26343.8i	−1.06338	+	1.56077i
$659$		−	28180.2i		−	1.66577i	−0.553443	−	0.832887i	$-0.686686\pi$
$659$		−	28180.2i		−	1.66577i	0.553443	−	0.832887i	$-0.313314\pi$
$660$	−1309.64	−	431.689i	−0.0772388	−	0.0254598i
$661$	12273.4	+	7086.03i	0.722207	+	0.416966i	0.815564	−	0.578666i	$-0.196427\pi$
$661$	12273.4	+	7086.03i	0.722207	+	0.416966i	−0.0933574	+	0.995633i	$0.529760\pi$
$662$	−8852.96	−	1421.46i	−0.519758	−	0.0834541i
$663$	−2661.44	−	4609.74i	−0.155900	−	0.270027i
$664$	−4500.60	+	8695.45i	−0.263038	+	0.508206i
$665$	−1349.15	−	1937.24i	−0.0786736	−	0.112967i
$666$	3923.30	−	1496.46i	0.228265	−	0.0870668i
$667$	10863.2	−	6271.84i	0.630619	−	0.364088i
$668$	5657.96	+	27186.2i	0.327714	+	1.57465i
$669$	−4343.32	+	7522.85i	−0.251005	+	0.434754i
$670$	1754.26	+	1426.75i	0.101153	+	0.0822689i
$671$	12321.7			0.708900
$672$	13367.4	−	4667.00i	0.767348	−	0.267907i
$673$	20823.6			1.19271			0.596353	−	0.802722i	$-0.296616\pi$
$673$	20823.6			1.19271			0.596353	+	0.802722i	$0.296616\pi$
$674$	25021.6	+	20350.3i	1.42996	+	1.16300i
$675$	−9436.87	+	16345.1i	−0.538112	+	0.932037i
$676$	−1551.19	−	7453.40i	−0.0882563	−	0.424067i
$677$	7961.97	−	4596.84i	0.451999	−	0.260962i	−0.256675	−	0.966498i	$-0.582627\pi$
$677$	7961.97	−	4596.84i	0.451999	−	0.260962i	0.708674	+	0.705536i	$0.249294\pi$
$678$	6617.69	−	2524.17i	0.374854	−	0.142980i
$679$	2934.72	−	6252.03i	0.165868	−	0.353359i
$680$	−278.818	+	538.693i	−0.0157238	+	0.0303793i
$681$	−5419.02	−	9386.01i	−0.304930	−	0.528154i
$682$	10351.2	+	1662.02i	0.581183	+	0.0933166i
$683$	−6425.91	−	3710.00i	−0.360001	−	0.207847i	0.309080	−	0.951036i	$-0.399979\pi$
$683$	−6425.91	−	3710.00i	−0.360001	−	0.207847i	−0.669081	+	0.743189i	$0.733312\pi$
$684$	−7436.36	−	2451.21i	−0.415696	−	0.137024i
$685$			1174.26i			0.0654981i
$686$	7467.58	−	16342.1i	0.415617	−	0.909540i
$687$		−	3920.89i		−	0.217746i
$688$	−6594.07	−	15155.9i	−0.365402	−	0.839845i
$689$	10901.3	+	6293.86i	0.602766	+	0.348007i
$690$	133.786	−	833.227i	0.00738135	−	0.0459716i
$691$	−13698.2	−	23726.1i	−0.754133	−	1.30620i	−0.945804	−	0.324737i	$-0.894724\pi$
$691$	−13698.2	−	23726.1i	−0.754133	−	1.30620i	0.191672	−	0.981459i	$-0.438609\pi$
$692$	15276.9	+	17112.4i	0.839223	+	0.940054i
$693$	−2466.19	+	5253.90i	−0.135185	+	0.287993i
$694$	1896.41	+	4971.87i	0.103727	+	0.271944i
$695$	−1985.26	+	1146.19i	−0.108353	+	0.0625575i
$696$	10920.5	+	17053.2i	0.594745	+	0.928734i
$697$	4660.07	−	8071.48i	0.253246	−	0.438636i
$698$	1476.00	−	1814.81i	0.0800392	−	0.0984119i
$699$	9267.08			0.501450
$700$	13305.4	+	12577.5i	0.718426	+	0.679120i
$701$	−14947.5			−0.805362			−0.402681	−	0.915340i	$-0.631922\pi$
$701$	−14947.5			−0.805362			−0.402681	+	0.915340i	$0.631922\pi$
$702$	15294.7	−	18805.5i	0.822308	−	1.01107i
$703$	8651.30	−	14984.5i	0.464139	−	0.803913i
$704$	1608.07	+	17435.2i	0.0860885	+	0.933399i
$705$	−2656.31	+	1533.62i	−0.141904	+	0.0819284i
$706$	−8211.26	−	21527.7i	−0.437726	−	1.14760i
$707$	5216.94	+	7490.97i	0.277515	+	0.398482i
$708$	2163.81	−	1931.72i	0.114860	−	0.102540i
$709$	−1150.36	−	1992.49i	−0.0609348	−	0.105542i	0.833949	−	0.551842i	$-0.186075\pi$
$709$	−1150.36	−	1992.49i	−0.0609348	−	0.105542i	−0.894884	+	0.446300i	$0.852742\pi$
$710$	−71.4102	+	444.748i	−0.00377462	+	0.0235086i
$711$	−6683.30	−	3858.60i	−0.352522	−	0.203529i
$712$	−527.301	−	11458.6i	−0.0277548	−	0.603131i
$713$			6415.91i			0.336995i
$714$	−4106.56	−	2797.86i	−0.215244	−	0.146649i
$715$			2290.18i			0.119787i
$716$	4274.27	−	12967.1i	0.223097	−	0.676820i
$717$	8466.11	+	4887.91i	0.440966	+	0.254592i
$718$	−7160.03	−	1149.64i	−0.372158	−	0.0597550i
$719$	14069.6	+	24369.3i	0.729775	+	1.26401i	0.956978	+	0.290161i	$0.0937087\pi$
$719$	14069.6	+	24369.3i	0.729775	+	1.26401i	−0.227202	+	0.973848i	$0.572958\pi$
$720$	−695.477	−	79.0793i	−0.0359984	−	0.00409321i
$721$	795.034	+	9360.99i	0.0410661	+	0.483525i
$722$	−12019.5	+	4584.59i	−0.619558	+	0.236317i
$723$	966.034	−	557.740i	0.0496918	−	0.0286896i
$724$	−32530.5	+	6770.21i	−1.66987	+	0.347532i
$725$	−13093.2	+	22678.1i	−0.670716	+	1.16171i
$726$	−1496.87	−	1217.42i	−0.0765208	−	0.0622350i
$727$	−9987.58			−0.509517			−0.254758	−	0.967005i	$-0.581996\pi$
$727$	−9987.58			−0.509517			−0.254758	+	0.967005i	$0.581996\pi$
$728$	−14311.5	−	18658.3i	−0.728597	−	0.949894i
$729$	21059.2			1.06992
$730$	−2042.63	−	1661.29i	−0.103563	−	0.0842289i
$731$	−2900.36	+	5023.57i	−0.146749	+	0.254177i
$732$	−11918.1	+	2480.38i	−0.601782	+	0.125242i
$733$	−25711.7	+	14844.7i	−1.29561	+	0.748022i	−0.979643	−	0.200748i	$-0.935663\pi$
$733$	−25711.7	+	14844.7i	−1.29561	+	0.748022i	−0.315969	+	0.948770i	$0.602330\pi$
$734$	−14471.8	+	5519.94i	−0.727742	+	0.277581i
$735$	1330.00	−	1104.54i	0.0667454	−	0.0554309i
$736$	−10379.1	+	2663.23i	−0.519809	+	0.133380i
$737$	−11453.7	−	19838.4i	−0.572461	−	0.991531i
$738$	10619.0	+	1705.03i	0.529664	+	0.0850445i
$739$	−11937.0	−	6891.81i	−0.594193	−	0.343057i	0.172561	−	0.984999i	$-0.444796\pi$
$739$	−11937.0	−	6891.81i	−0.594193	−	0.343057i	−0.766754	+	0.641942i	$0.778129\pi$
$740$	484.225	−	1469.02i	0.0240547	−	0.0729760i
$741$		−	25310.5i		−	1.25480i
$742$	11718.5	+	874.378i	0.579784	+	0.0432607i
$743$			33130.8i			1.63587i	0.575311	+	0.817935i	$0.304881\pi$
$743$			33130.8i			1.63587i	−0.575311	+	0.817935i	$0.695119\pi$
$744$	−10346.7	+	476.134i	−0.509850	+	0.0234622i
$745$	92.1761	+	53.2179i	0.00453298	+	0.00261712i
$746$	1787.81	−	11134.6i	0.0877431	−	0.546471i
$747$	1982.65	+	3434.06i	0.0971105	+	0.168200i
$748$	4584.04	−	4092.35i	0.224076	−	0.200042i
$749$	−19777.2	+	1679.69i	−0.964811	+	0.0819420i
$750$	1262.95	+	3311.10i	0.0614883	+	0.161206i
$751$	14825.3	−	8559.37i	0.720348	−	0.415893i	−0.0945328	−	0.995522i	$-0.530136\pi$
$751$	14825.3	−	8559.37i	0.720348	−	0.415893i	0.814881	+	0.579629i	$0.196802\pi$
$752$	31312.4	+	23158.9i	1.51841	+	1.12303i
$753$	−4749.91	+	8227.09i	−0.229876	+	0.398157i
$754$	21220.6	−	26091.7i	1.02495	−	1.26022i
$755$	2588.73			0.124786
$756$	5239.95	−	22013.8i	0.252083	−	1.05904i
$757$	21689.4			1.04137			0.520683	−	0.853750i	$-0.325677\pi$
$757$	21689.4			1.04137			0.520683	+	0.853750i	$0.325677\pi$
$758$	−21666.5	+	26639.9i	−1.03821	+	1.27653i
$759$	−4274.63	+	7403.87i	−0.204426	+	0.354076i
$760$	−2428.92	+	1555.44i	−0.115929	+	0.0742391i
$761$	−8593.87	+	4961.67i	−0.409366	+	0.236347i	−0.690517	−	0.723316i	$-0.742617\pi$
$761$	−8593.87	+	4961.67i	−0.409366	+	0.236347i	0.281151	+	0.959663i	$0.409284\pi$
$762$	−2174.47	−	5700.86i	−0.103376	−	0.271024i
$763$	−12120.7	+	8441.20i	−0.575095	+	0.400514i
$764$	−18947.2	−	21223.7i	−0.897234	−	1.00504i
$765$	122.828	+	212.744i	0.00580503	+	0.0100546i
$766$	7.89422	−	49.1658i	0.000372363	−	0.00231910i
$767$	−4171.99	−	2408.70i	−0.196404	−	0.113394i
$768$	−5065.14	−	16540.4i	−0.237985	−	0.777149i
$769$		−	39574.3i		−	1.85577i	−0.372869	−	0.927884i	$-0.621626\pi$
$769$		−	39574.3i		−	1.85577i	0.372869	−	0.927884i	$-0.378374\pi$
$770$	928.250	+	1925.94i	0.0434439	+	0.0901378i
$771$			30416.7i			1.42079i
$772$	−5783.80	−	1906.48i	−0.269642	−	0.0888805i
$773$	−2247.09	−	1297.36i	−0.104557	−	0.0603658i	0.446810	−	0.894629i	$-0.352560\pi$
$773$	−2247.09	−	1297.36i	−0.104557	−	0.0603658i	−0.551366	+	0.834263i	$0.685893\pi$
$774$	−6609.12	−	1061.18i	−0.306925	−	0.0492809i
$775$	−6696.97	−	11599.5i	−0.310403	−	0.537634i
$776$	−7493.91	−	3878.70i	−0.346670	−	0.179430i
$777$	11470.4	+	5384.25i	0.529600	+	0.248596i
$778$	−15572.9	+	5939.96i	−0.717631	+	0.273725i
$779$	38380.3	−	22158.9i	1.76523	−	1.01916i
$780$	−461.019	−	2215.17i	−0.0211630	−	0.101687i
$781$	2281.65	−	3951.93i	0.104538	−	0.181064i
$782$	2917.53	+	2372.85i	0.133415	+	0.108508i
$783$	32364.5			1.47715
$784$	−19597.9	−	9890.12i	−0.892759	−	0.450534i
$785$	2974.41			0.135237
$786$	5834.85	+	4745.53i	0.264787	+	0.215353i
$787$	−8417.03	+	14578.7i	−0.381239	+	0.660325i	−0.991240	−	0.132076i	$-0.957836\pi$
$787$	−8417.03	+	14578.7i	−0.381239	+	0.660325i	0.610001	+	0.792401i	$0.291169\pi$
$788$	−1556.35	−	7478.18i	−0.0703588	−	0.338070i
$789$	12948.5	−	7475.82i	0.584257	−	0.337321i
$790$	−2656.10	+	1013.11i	−0.119620	+	0.0456264i
$791$	−9940.61	−	4666.15i	−0.446836	−	0.209746i
$792$	6297.51	+	3259.47i	0.282541	+	0.146238i
$793$	10108.9	+	17509.2i	0.452684	+	0.784071i
$794$	−12025.0	−	1930.77i	−0.537469	−	0.0862977i
$795$	979.219	+	565.352i	0.0436847	+	0.0252214i
$796$	−2089.42	−	688.723i	−0.0930369	−	0.0306672i
$797$		−	1595.10i		−	0.0708927i	−0.999372	−	0.0354464i	$-0.988715\pi$
$797$		−	1595.10i		−	0.0708927i	0.999372	−	0.0354464i	$-0.0112853\pi$
$798$	−10258.8	−	21285.0i	−0.455084	−	0.944212i
$799$		−	13668.4i		−	0.605200i
$800$	15984.8	−	15648.7i	0.706436	−	0.691583i
$801$	−4023.14	−	2322.76i	−0.177467	−	0.102460i
$802$	−684.786	+	4264.90i	−0.0301504	+	0.187779i
$803$	13336.6	+	23099.6i	0.586099	+	1.01515i
$804$	15072.1	+	16883.0i	0.661134	+	0.740569i
$805$	−1073.68	+	747.747i	−0.0470092	+	0.0327386i
$806$	6130.55	+	16072.6i	0.267915	+	0.702400i
$807$	−14253.2	+	8229.12i	−0.621732	+	0.358957i
$808$	9392.21	−	6014.61i	0.408932	−	0.261873i
$809$	−10018.8	+	17353.0i	−0.435403	+	0.754140i	−0.997328	−	0.0730482i	$-0.976727\pi$
$809$	−10018.8	+	17353.0i	−0.435403	+	0.754140i	0.561926	+	0.827188i	$0.310061\pi$
$810$	846.861	−	1041.26i	0.0367354	−	0.0451679i
$811$	16147.8			0.699167			0.349583	−	0.936905i	$-0.386323\pi$
$811$	16147.8			0.699167			0.349583	+	0.936905i	$0.386323\pi$
$812$	7270.17	−	30543.1i	0.314203	−	1.32001i
$813$	−4616.38			−0.199143
$814$	−9887.17	+	12156.7i	−0.425731	+	0.523456i
$815$	688.105	−	1191.83i	0.0295746	−	0.0512247i
$816$	−3610.10	+	4881.09i	−0.154876	+	0.209402i
$817$	−23887.3	+	13791.3i	−1.02290	+	0.590572i
$818$	7144.11	+	18729.9i	0.305364	+	0.800582i
$819$	−9489.13	+	805.918i	−0.404856	+	0.0343847i
$820$	2955.42	−	2638.42i	0.125863	−	0.112363i
$821$	7626.13	+	13208.9i	0.324183	+	0.561501i	0.981347	−	0.192247i	$-0.0615774\pi$
$821$	7626.13	+	13208.9i	0.324183	+	0.561501i	−0.657164	+	0.753748i	$0.728244\pi$
$822$	−1863.23	+	11604.3i	−0.0790603	+	0.492393i
$823$	−1161.51	−	670.600i	−0.0491954	−	0.0284030i	0.475201	−	0.879878i	$-0.342375\pi$
$823$	−1161.51	−	670.600i	−0.0491954	−	0.0284030i	−0.524396	+	0.851475i	$0.675709\pi$
$824$	11466.0	−	527.640i	0.484753	−	0.0223073i
$825$		−	17847.6i		−	0.753179i
$826$	−4484.74	−	334.630i	−0.188915	−	0.0140959i
$827$		−	12566.7i		−	0.528400i	−0.964468	−	0.264200i	$-0.914892\pi$
$827$		−	12566.7i		−	0.528400i	0.964468	−	0.264200i	$-0.0851079\pi$
$828$	−1358.54	+	4121.48i	−0.0570200	+	0.172985i
$829$	−11202.2	−	6467.57i	−0.469321	−	0.270963i	0.246634	−	0.969109i	$-0.420675\pi$
$829$	−11202.2	−	6467.57i	−0.469321	−	0.270963i	−0.715955	+	0.698146i	$0.754009\pi$
$830$	1442.21	+	231.566i	0.0603131	+	0.00968407i
$831$	−1872.58	−	3243.40i	−0.0781697	−	0.135394i
$832$	−23456.2	+	16589.2i	−0.977402	+	0.691259i
$833$	1299.28	+	7593.87i	0.0540423	+	0.315861i
$834$	−21437.5	+	8176.85i	−0.890071	+	0.339498i
$835$	3587.64	−	2071.33i	0.148689	−	0.0858458i
$836$	28606.7	−	5953.59i	1.18347	−	0.246303i
$837$	−8276.96	+	14336.1i	−0.341809	+	0.592030i
$838$	36381.7	+	29589.5i	1.49974	+	1.21975i
$839$	−15886.4			−0.653706			−0.326853	−	0.945075i	$-0.605988\pi$
$839$	−15886.4			−0.653706			−0.326853	+	0.945075i	$0.605988\pi$
$840$	−1285.54	−	1676.00i	−0.0528041	−	0.0688423i
$841$	20515.1			0.841163
$842$	−14512.6	−	11803.2i	−0.593986	−	0.483094i
$843$	16362.3	−	28340.3i	0.668502	−	1.15788i
$844$	41990.2	−	8738.97i	1.71252	−	0.356407i
$845$	−983.593	+	567.878i	−0.0400433	+	0.0231190i
$846$	14737.1	−	5621.16i	0.598905	−	0.228439i
$847$	253.155	+	2980.73i	0.0102698	+	0.120920i
$848$	1622.02	−	14265.1i	0.0656845	−	0.577673i
$849$	1914.84	+	3316.60i	0.0774053	+	0.134070i
$850$	−7751.49	−	1244.60i	−0.312793	−	0.0502230i
$851$	−8304.91	−	4794.84i	−0.334534	−	0.193143i
$852$	−1411.38	+	4281.79i	−0.0567526	+	0.172174i
$853$		−	2788.43i		−	0.111928i	−0.998433	−	0.0559638i	$-0.982177\pi$
$853$		−	2788.43i		−	0.111928i	0.998433	−	0.0559638i	$-0.0178231\pi$
$854$	15597.9	+	10627.1i	0.624999	+	0.425822i
$855$			1168.10i			0.0467232i
$856$	1114.76	+	24224.5i	0.0445113	+	0.967261i
$857$	−5676.87	−	3277.55i	−0.226276	−	0.130640i	0.382577	−	0.923924i	$-0.375037\pi$
$857$	−5676.87	−	3277.55i	−0.226276	−	0.130640i	−0.608853	+	0.793283i	$0.708370\pi$
$858$	−3633.89	+	22632.1i	−0.144591	+	0.900522i
$859$	10190.7	+	17650.9i	0.404777	+	0.701095i	0.994296	−	0.106660i	$-0.0340157\pi$
$859$	10190.7	+	17650.9i	0.404777	+	0.701095i	−0.589518	+	0.807755i	$0.700682\pi$
$860$	−1839.41	+	1642.11i	−0.0729341	+	0.0651111i
$861$	18548.0	+	26633.0i	0.734164	+	1.05418i
$862$	−11453.9	−	30029.0i	−0.452577	−	1.18653i
$863$	−29681.7	+	17136.7i	−1.17077	+	0.675945i	−0.953862	−	0.300246i	$-0.902931\pi$
$863$	−29681.7	+	17136.7i	−1.17077	+	0.675945i	−0.216910	+	0.976192i	$0.569598\pi$
$864$	−26627.6	−	7438.91i	−1.04848	−	0.292913i
$865$	1711.11	−	2963.72i	0.0672594	−	0.116497i
$866$	10404.9	−	12793.3i	0.408282	−	0.502002i
$867$	−18618.3			−0.729309
$868$	11670.0	+	11031.5i	0.456344	+	0.431377i
$869$	28799.0			1.12421
$870$	1906.16	−	2343.72i	0.0742817	−	0.0913327i
$871$	18793.7	−	32551.7i	0.731114	−	1.26633i
$872$	9731.86	+	15197.0i	0.377938	+	0.590176i
$873$	−2959.54	+	1708.69i	−0.114737	+	0.0662433i
$874$	6372.85	+	16707.9i	0.246642	+	0.646627i
$875$	2334.66	−	4973.69i	0.0902011	−	0.192162i
$876$	−17549.8	−	19658.3i	−0.676885	−	0.758212i
$877$	−17002.8	−	29449.7i	−0.654669	−	1.13392i	−0.981977	−	0.189002i	$-0.939475\pi$
$877$	−17002.8	−	29449.7i	−0.654669	−	1.13392i	0.327308	−	0.944918i	$-0.393858\pi$
$878$	−2816.23	+	17539.7i	−0.108250	+	0.674187i
$879$	−7548.27	−	4358.00i	−0.289644	−	0.167226i
$880$	2395.21	−	1042.12i	0.0917529	−	0.0399201i
$881$			3501.55i			0.133905i	0.997756	+	0.0669525i	$0.0213276\pi$
$881$			3501.55i			0.133905i	−0.997756	+	0.0669525i	$0.978672\pi$
$882$	−7653.29	+	4523.85i	−0.292176	+	0.172705i
$883$		−	19090.8i		−	0.727583i	−0.931480	−	0.363791i	$-0.881482\pi$
$883$		−	19090.8i		−	0.727583i	0.931480	−	0.363791i	$-0.118518\pi$
$884$	9576.09	+	3156.51i	0.364342	+	0.120096i
$885$	−374.753	−	216.364i	−0.0142341	−	0.00821806i
$886$	13581.9	+	2180.76i	0.515005	+	0.0826909i
$887$	−18192.2	−	31509.9i	−0.688653	−	1.19278i	−0.972274	−	0.233845i	$-0.924869\pi$
$887$	−18192.2	−	31509.9i	−0.688653	−	1.19278i	0.283621	−	0.958937i	$-0.408464\pi$
$888$	7116.15	−	13748.9i	0.268922	−	0.519574i
$889$	−4019.69	+	8563.41i	−0.151649	+	0.323068i
$890$	−1598.89	+	609.862i	−0.0602190	+	0.0229692i
$891$	−11775.3	+	6798.47i	−0.442746	+	0.255620i
$892$	−3352.71	−	16109.6i	−0.125849	−	0.604696i
$893$	32497.0	−	56286.5i	1.21777	−	2.10925i
$894$	826.464	+	672.170i	0.0309184	+	0.0251462i
$895$	−2036.87			−0.0760728
$896$	−13001.7	+	23458.0i	−0.484774	+	0.874639i
$897$	−14027.9			−0.522162
$898$	13882.5	+	11290.7i	0.515885	+	0.419573i
$899$	−11483.9	+	19890.7i	−0.426039	+	0.737921i
$900$	−1845.89	−	8869.40i	−0.0683663	−	0.328496i
$901$	−4363.66	+	2519.36i	−0.161348	+	0.0931543i
$902$	−37500.2	+	14303.6i	−1.38428	+	0.528003i
$903$	−11544.0	−	16576.0i	−0.425427	−	0.610868i
$904$	−6167.06	+	11915.2i	−0.226895	+	0.438377i
$905$	2478.51	+	4292.91i	0.0910370	+	0.157681i
$906$	25582.4	+	4107.59i	0.938100	+	0.150624i
$907$	25756.4	+	14870.5i	0.942918	+	0.544394i	0.890874	−	0.454251i	$-0.150093\pi$
$907$	25756.4	+	14870.5i	0.942918	+	0.544394i	0.0520440	+	0.998645i	$0.483426\pi$
$908$	19498.1	+	6427.05i	0.712629	+	0.234900i
$909$		−	4516.85i		−	0.164812i
$910$	−1975.22	+	2899.13i	−0.0719538	+	0.105610i
$911$		−	29434.3i		−	1.07047i	−0.844702	−	0.535236i	$-0.820223\pi$
$911$		−	29434.3i		−	1.07047i	0.844702	−	0.535236i	$-0.179777\pi$
$912$	−26471.2	+	11517.2i	−0.961130	+	0.418171i
$913$	−12815.2	−	7398.84i	−0.464535	−	0.268199i
$914$	7667.61	−	47754.4i	0.277486	−	1.72820i
$915$	908.043	+	1572.78i	0.0328076	+	0.0568245i
$916$	4946.26	+	5540.55i	0.178416	+	0.199853i
$917$	−986.805	−	11619.0i	−0.0355367	−	0.418421i
$918$	3457.98	+	9065.87i	0.124325	+	0.325946i
$919$	−38082.9	+	21987.2i	−1.36696	+	0.789216i	−0.990539	−	0.137231i	$-0.956180\pi$
$919$	−38082.9	+	21987.2i	−1.36696	+	0.789216i	−0.376424	+	0.926448i	$0.622846\pi$
$920$	862.077	+	1346.19i	0.0308933	+	0.0482420i
$921$	9045.81	−	15667.8i	0.323637	−	0.560556i
$922$	−27444.7	+	33744.5i	−0.980307	+	1.20533i
$923$	7487.63			0.267019
$924$	6117.25	+	20505.5i	0.217795	+	0.730066i
$925$	20019.6			0.711611
$926$	3971.90	−	4883.64i	0.140956	−	0.173311i
$927$	2324.26	−	4025.73i	0.0823502	−	0.142635i
$928$	−36944.5	−	10321.1i	−1.30685	−	0.365095i
$929$	23203.6	−	13396.6i	0.819466	−	0.473119i	−0.0307661	−	0.999527i	$-0.509795\pi$
$929$	23203.6	−	13396.6i	0.819466	−	0.473119i	0.850232	+	0.526408i	$0.176461\pi$
$930$	550.683	+	1443.74i	0.0194168	+	0.0509055i
$931$	−12704.2	+	34360.6i	−0.447222	+	1.20958i
$932$	−13095.2	+	11690.6i	−0.460243	+	0.410876i
$933$	−8237.86	−	14268.4i	−0.289063	−	0.500671i
$934$	5500.85	−	34259.7i	0.192712	−	1.20023i
$935$	−793.915	−	458.367i	−0.0277688	−	0.0160323i
$936$	534.863	+	11622.9i	0.0186779	+	0.405884i
$937$			26439.9i			0.921831i	0.887444	+	0.460915i	$0.152479\pi$
$937$			26439.9i			0.921831i	−0.887444	+	0.460915i	$0.847521\pi$
$938$	2610.93	−	34991.9i	0.0908846	−	1.21804i
$939$			39784.9i			1.38267i
$940$	1818.90	−	5518.11i	0.0631128	−	0.191469i
$941$	−33418.7	−	19294.3i	−1.15773	−	0.668413i	−0.206967	−	0.978348i	$-0.566359\pi$
$941$	−33418.7	−	19294.3i	−1.15773	−	0.668413i	−0.950758	+	0.309935i	$0.899693\pi$
$942$	29393.8	+	4719.57i	1.01667	+	0.163240i
$943$	−12281.2	−	21271.6i	−0.424104	−	0.734570i
$944$	−620.757	+	5459.36i	−0.0214025	+	0.188228i
$945$	−3363.76	+	285.686i	−0.115792	+	0.00983425i
$946$	23339.6	−	8902.36i	0.802150	−	0.305963i
$947$	24197.7	−	13970.6i	0.830328	−	0.479390i	−0.0236370	−	0.999721i	$-0.507525\pi$
$947$	24197.7	−	13970.6i	0.830328	−	0.479390i	0.853965	+	0.520331i	$0.174191\pi$
$948$	−27855.7	+	5797.30i	−0.954337	+	0.198616i
$949$	−21883.1	+	37902.7i	−0.748532	+	1.29650i
$950$	−28961.5	−	23554.6i	−0.989089	−	0.804434i
$951$	3890.64			0.132663
$952$	9332.45	−	1226.87i	0.317717	−	0.0417678i
$953$	−27352.6			−0.929735			−0.464867	−	0.885380i	$-0.653898\pi$
$953$	−27352.6			−0.929735			−0.464867	+	0.885380i	$0.653898\pi$
$954$	−4510.90	−	3668.75i	−0.153088	−	0.124508i
$955$	−2122.20	+	3675.76i	−0.0719087	+	0.124550i
$956$	−18129.5	+	3773.09i	−0.613337	+	0.127647i
$957$	−26504.5	+	15302.4i	−0.895266	+	0.516882i
$958$	9358.68	−	3569.66i	0.315621	−	0.120387i
$959$	14953.2	−	10413.8i	0.503507	−	0.350657i
$960$	−2106.98	+	1490.14i	−0.0708359	+	0.0500981i
$961$	9021.67	+	15626.0i	0.302832	+	0.524520i
$962$	−25386.4	−	4076.13i	−0.850822	−	0.136611i
$963$	8505.27	+	4910.52i	0.284609	+	0.164319i
$964$	−661.490	+	2006.80i	−0.0221008	+	0.0670484i
$965$			908.519i			0.0303070i
$966$	−11796.9	+	5685.76i	−0.392917	+	0.189375i
$967$			35591.9i			1.18362i	0.806078	+	0.591810i	$0.201586\pi$
$967$			35591.9i			1.18362i	−0.806078	+	0.591810i	$0.798414\pi$
$968$	3650.99	−	168.011i	0.121227	−	0.00557860i
$969$	8774.14	+	5065.75i	0.290883	+	0.167942i
$970$	−199.568	+	1242.93i	−0.00660593	+	0.0411422i
$971$	−11608.1	−	20105.8i	−0.383646	−	0.664495i	0.607934	−	0.793987i	$-0.291998\pi$
$971$	−11608.1	−	20105.8i	−0.383646	−	0.664495i	−0.991580	+	0.129493i	$0.958665\pi$
$972$	−14588.7	+	13023.9i	−0.481412	+	0.429775i
$973$	32201.8	+	15115.6i	1.06099	+	0.498031i
$974$	−14524.9	−	38080.4i	−0.477833	−	1.25275i
$975$	25361.5	−	14642.5i	0.833044	−	0.480958i
$976$	13712.2	−	18539.8i	0.449710	−	0.608037i
$977$	−8293.68	+	14365.1i	−0.271585	+	0.470398i	−0.969268	−	0.246008i	$-0.920881\pi$
$977$	−8293.68	+	14365.1i	−0.271585	+	0.470398i	0.697683	+	0.716406i	$0.254214\pi$
$978$	8691.13	−	10686.1i	0.284163	−	0.349392i
$979$	17336.1			0.565949
$980$	−486.008	+	3238.63i	−0.0158418	+	0.105566i
$981$	7308.43			0.237859
$982$	22011.3	−	27064.0i	0.715285	−	0.879476i
$983$	−12644.5	+	21900.9i	−0.410271	+	0.710611i	−0.994919	−	0.100676i	$-0.967899\pi$
$983$	−12644.5	+	21900.9i	−0.410271	+	0.710611i	0.584648	+	0.811287i	$0.301233\pi$
$984$	33392.6	−	21384.0i	1.08183	−	0.692782i
$985$	−986.863	+	569.766i	−0.0319229	+	0.0184307i
$986$	4797.78	+	12578.5i	0.154962	+	0.406267i
$987$	43086.6	+	20224.9i	1.38952	+	0.652246i
$988$	31929.6	+	35765.9i	1.02815	+	1.15168i
$989$	7643.62	+	13239.1i	0.245756	+	0.425662i
$990$	167.707	−	1044.49i	0.00538392	−	0.0335315i
$991$	39133.0	+	22593.5i	1.25439	+	0.724223i	0.971979	−	0.235069i	$-0.0755318\pi$
$991$	39133.0	+	22593.5i	1.25439	+	0.724223i	0.282413	+	0.959293i	$0.408865\pi$
$992$	14020.1	−	13725.3i	0.448728	−	0.439294i
$993$			13388.2i			0.427855i
$994$	6296.77	−	3034.87i	0.200927	−	0.0968411i
$995$			328.205i			0.0104571i
$996$	13884.8	+	4576.78i	0.441725	+	0.145603i
$997$	6968.90	+	4023.50i	0.221371	+	0.127809i	0.606585	−	0.795019i	$-0.292539\pi$
$997$	6968.90	+	4023.50i	0.221371	+	0.127809i	−0.385214	+	0.922827i	$0.625872\pi$
$998$	−10778.3	−	1730.60i	−0.341865	−	0.0548909i
$999$	−12371.4	−	21427.8i	−0.391804	−	0.678625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.4.f.a.3.8	yes	20
4.3	odd	2	inner	28.4.f.a.3.6	✓	20
7.2	even	3		196.4.f.d.19.6		20
7.3	odd	6		196.4.d.b.195.4		20
7.4	even	3		196.4.d.b.195.3		20
7.5	odd	6	inner	28.4.f.a.19.6	yes	20
7.6	odd	2		196.4.f.d.31.8		20
8.3	odd	2		448.4.p.h.255.8		20
8.5	even	2		448.4.p.h.255.3		20
28.3	even	6		196.4.d.b.195.1		20
28.11	odd	6		196.4.d.b.195.2		20
28.19	even	6	inner	28.4.f.a.19.8	yes	20
28.23	odd	6		196.4.f.d.19.8		20
28.27	even	2		196.4.f.d.31.6		20
56.5	odd	6		448.4.p.h.383.8		20
56.19	even	6		448.4.p.h.383.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.6	✓	20	4.3	odd	2	inner
28.4.f.a.3.8	yes	20	1.1	even	1	trivial
28.4.f.a.19.6	yes	20	7.5	odd	6	inner
28.4.f.a.19.8	yes	20	28.19	even	6	inner
196.4.d.b.195.1		20	28.3	even	6
196.4.d.b.195.2		20	28.11	odd	6
196.4.d.b.195.3		20	7.4	even	3
196.4.d.b.195.4		20	7.3	odd	6
196.4.f.d.19.6		20	7.2	even	3
196.4.f.d.19.8		20	28.23	odd	6
196.4.f.d.31.6		20	28.27	even	2
196.4.f.d.31.8		20	7.6	odd	2
448.4.p.h.255.3		20	8.5	even	2
448.4.p.h.255.8		20	8.3	odd	2
448.4.p.h.383.3		20	56.19	even	6
448.4.p.h.383.8		20	56.5	odd	6

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19431 + 1.78465i) q^{2} +(2.11164 - 3.65747i) q^{3} +(1.63002 + 7.83218i) q^{4} +(1.03358 - 0.596737i) q^{5} +(11.1609 - 4.25709i) q^{6} +(-16.7651 - 7.86959i) q^{7} +(-10.4009 + 20.0953i) q^{8} +(4.58193 + 7.93614i) q^{9} +(3.33297 + 0.535152i) q^{10} +(-29.6160 - 17.0988i) q^{11} +(32.0880 + 10.5770i) q^{12} -56.1127i q^{13} +(-22.7434 - 47.1883i) q^{14} -5.04038i q^{15} +(-58.6860 + 25.5333i) q^{16} +(19.4520 + 11.2306i) q^{17} +(-4.10906 + 25.5916i) q^{18} +(53.4022 + 92.4953i) q^{19} +(6.35851 + 7.12248i) q^{20} +(-64.1848 + 44.7002i) q^{21} +(-34.4714 - 90.3744i) q^{22} +(51.2640 - 29.5973i) q^{23} +(51.5349 + 80.4752i) q^{24} +(-61.7878 + 107.020i) q^{25} +(100.142 - 123.129i) q^{26} +152.730 q^{27} +(34.3085 - 144.135i) q^{28} +211.906 q^{29} +(8.99533 - 11.0602i) q^{30} +(-54.1933 + 93.8656i) q^{31} +(-174.344 - 48.7062i) q^{32} +(-125.077 + 72.2131i) q^{33} +(22.6411 + 59.3587i) q^{34} +(-22.0242 + 1.87053i) q^{35} +(-54.6886 + 48.8226i) q^{36} +(-81.0013 - 140.298i) q^{37} +(-47.8909 + 298.268i) q^{38} +(-205.231 - 118.490i) q^{39} +(1.24141 + 26.9767i) q^{40} -414.943i q^{41} +(-220.616 - 16.4613i) q^{42} +258.254i q^{43} +(85.6461 - 259.829i) q^{44} +(9.47158 + 5.46842i) q^{45} +(165.310 + 26.5428i) q^{46} +(-304.267 - 527.006i) q^{47} +(-30.5366 + 268.560i) q^{48} +(219.139 + 263.870i) q^{49} +(-326.575 + 124.565i) q^{50} +(82.1515 - 47.4302i) q^{51} +(439.485 - 91.4651i) q^{52} +(-112.165 + 194.275i) q^{53} +(335.138 + 272.571i) q^{54} -40.8140 q^{55} +(332.515 - 255.049i) q^{56} +451.065 q^{57} +(464.988 + 378.179i) q^{58} +(42.9260 - 74.3501i) q^{59} +(39.4772 - 8.21595i) q^{60} +(-312.035 + 180.154i) q^{61} +(-286.435 + 109.254i) q^{62} +(-14.3625 - 169.108i) q^{63} +(-295.641 - 418.020i) q^{64} +(-33.4846 - 57.9969i) q^{65} +(-403.333 - 64.7605i) q^{66} +(580.112 + 334.928i) q^{67} +(-56.2531 + 170.658i) q^{68} -249.996i q^{69} +(-51.6662 - 35.2010i) q^{70} +133.439i q^{71} +(-207.135 + 9.53195i) q^{72} +(-675.475 - 389.985i) q^{73} +(72.6417 - 452.418i) q^{74} +(260.947 + 451.974i) q^{75} +(-637.393 + 569.025i) q^{76} +(361.955 + 519.730i) q^{77} +(-238.877 - 626.270i) q^{78} +(-729.310 + 421.067i) q^{79} +(-45.4200 + 61.4108i) q^{80} +(198.800 - 344.331i) q^{81} +(740.529 - 910.514i) q^{82} +432.711 q^{83} +(-454.723 - 429.844i) q^{84} +26.8070 q^{85} +(-460.894 + 566.690i) q^{86} +(447.470 - 775.040i) q^{87} +(651.640 - 417.298i) q^{88} +(-439.022 + 253.470i) q^{89} +(11.0244 + 28.9029i) q^{90} +(-441.584 + 940.737i) q^{91} +(315.373 + 353.265i) q^{92} +(228.874 + 396.421i) q^{93} +(272.865 - 1699.43i) q^{94} +(110.391 + 63.7342i) q^{95} +(-546.293 + 534.807i) q^{96} +372.919i q^{97} +(9.94400 + 970.100i) q^{98} -313.382i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29}+ \cdots - 4900 q^{98}+O(q^{100}) \) 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Introduction

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