LMFDB - Embedded newform 672.3.bh.d.481.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,3,Mod(481,672)] 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("672.481"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	672.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,24,0,0,0,12,0,24,0,12,0,0,0,0,0,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3106737650$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 120 x^{14} - 700 x^{13} + 5060 x^{12} - 21624 x^{11} + 95002 x^{10} - 292520 x^{9} + \cdots + 76783 $ x^16 - 8x^15 + 120x^14 - 700x^13 + 5060x^12 - 21624x^11 + 95002x^10 - 292520x^9 + 820115x^8 - 1736320x^7 + 3049290x^6 - 4089680x^5 + 4223014x^4 - 3175248x^3 + 1657766x^2 - 534268*x + 76783
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			481.6
Root			$0.500000 + 4.68078i$ of defining polynomial
Character	$\chi$	$=$	672.481
Dual form			672.3.bh.d.577.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} +(1.77068 + 1.02231i) q^{5} +(-6.69221 - 2.05287i) q^{7} +(1.50000 - 2.59808i) q^{9} +(6.13527 + 10.6266i) q^{11} -16.5743i q^{13} +3.54137 q^{15} +(5.61550 - 3.24211i) q^{17} +(11.2051 + 6.46927i) q^{19} +(-11.8162 + 2.71632i) q^{21} +(13.4273 - 23.2568i) q^{23} +(-10.4098 - 18.0303i) q^{25} -5.19615i q^{27} +38.4413 q^{29} +(6.60865 - 3.81551i) q^{31} +(18.4058 + 10.6266i) q^{33} +(-9.75114 - 10.4765i) q^{35} +(26.9315 - 46.6467i) q^{37} +(-14.3538 - 24.8615i) q^{39} -6.44781i q^{41} -13.8206 q^{43} +(5.31205 - 3.06692i) q^{45} +(24.4111 + 14.0938i) q^{47} +(40.5715 + 27.4765i) q^{49} +(5.61550 - 9.72633i) q^{51} +(-34.4114 - 59.6024i) q^{53} +25.0885i q^{55} +22.4102 q^{57} +(-62.8802 + 36.3039i) q^{59} +(-21.4925 - 12.4087i) q^{61} +(-15.3718 + 14.3076i) q^{63} +(16.9440 - 29.3479i) q^{65} +(35.3422 + 61.2144i) q^{67} -46.5135i q^{69} -12.5498 q^{71} +(93.9800 - 54.2594i) q^{73} +(-31.2294 - 18.0303i) q^{75} +(-19.2435 - 83.7104i) q^{77} +(-48.8779 + 84.6590i) q^{79} +(-4.50000 - 7.79423i) q^{81} -83.3264i q^{83} +13.2577 q^{85} +(57.6619 - 33.2911i) q^{87} +(51.6473 + 29.8186i) q^{89} +(-34.0249 + 110.919i) q^{91} +(6.60865 - 11.4465i) q^{93} +(13.2271 + 22.9101i) q^{95} +147.707i q^{97} +36.8116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{3} + 12 q^{7} + 24 q^{9} + 12 q^{11} + 48 q^{17} - 36 q^{19} + 24 q^{21} - 48 q^{23} + 20 q^{25} + 64 q^{29} + 60 q^{31} + 36 q^{33} - 36 q^{37} - 12 q^{39} - 72 q^{43} + 72 q^{47} - 40 q^{49}+ \cdots + 72 q^{99}+O(q^{100}) $ 16 * q + 24 * q^3 + 12 * q^7 + 24 * q^9 + 12 * q^11 + 48 * q^17 - 36 * q^19 + 24 * q^21 - 48 * q^23 + 20 * q^25 + 64 * q^29 + 60 * q^31 + 36 * q^33 - 36 * q^37 - 12 * q^39 - 72 * q^43 + 72 * q^47 - 40 * q^49 + 48 * q^51 + 56 * q^53 - 72 * q^57 + 36 * q^59 + 72 * q^61 + 36 * q^63 + 120 * q^65 - 12 * q^67 - 240 * q^71 + 156 * q^73 + 60 * q^75 + 224 * q^77 - 84 * q^79 - 72 * q^81 + 800 * q^85 + 96 * q^87 + 192 * q^89 - 300 * q^91 + 60 * q^93 + 48 * q^95 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	1.77068	+	1.02231i	0.354137	+	0.204461i	0.666506	−	0.745500i	$-0.267789\pi$
$5$	1.77068	+	1.02231i	0.354137	+	0.204461i	−0.312369	+	0.949961i	$0.601122\pi$
$6$		0			0
$7$	−6.69221	−	2.05287i	−0.956031	−	0.293267i
$7$	−6.69221	−	2.05287i	−0.956031	−	0.293267i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	6.13527	+	10.6266i	0.557752	+	0.966055i	0.997684	+	0.0680235i	$0.0216693\pi$
$11$	6.13527	+	10.6266i	0.557752	+	0.966055i	−0.439932	+	0.898031i	$0.644997\pi$
$12$		0			0
$13$		−	16.5743i		−	1.27495i	−0.770472	−	0.637474i	$-0.779979\pi$
$13$		−	16.5743i		−	1.27495i	0.770472	−	0.637474i	$-0.220021\pi$
$14$		0			0
$15$	3.54137			0.236091
$16$		0			0
$17$	5.61550	−	3.24211i	0.330323	−	0.190712i	−0.325661	−	0.945487i	$-0.605587\pi$
$17$	5.61550	−	3.24211i	0.330323	−	0.190712i	0.655985	+	0.754774i	$0.272254\pi$
$18$		0			0
$19$	11.2051	+	6.46927i	0.589742	+	0.340488i	0.764996	−	0.644035i	$-0.222741\pi$
$19$	11.2051	+	6.46927i	0.589742	+	0.340488i	−0.175253	+	0.984523i	$0.556074\pi$
$20$		0			0
$21$	−11.8162	+	2.71632i	−0.562674	+	0.129349i
$22$		0			0
$23$	13.4273	−	23.2568i	0.583795	−	1.01116i	−0.411229	−	0.911532i	$-0.634900\pi$
$23$	13.4273	−	23.2568i	0.583795	−	1.01116i	0.995024	−	0.0996313i	$-0.0317663\pi$
$24$		0			0
$25$	−10.4098	−	18.0303i	−0.416391	−	0.721211i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	38.4413			1.32556			0.662780	−	0.748814i	$-0.269376\pi$
$29$	38.4413			1.32556			0.662780	+	0.748814i	$0.269376\pi$
$30$		0			0
$31$	6.60865	−	3.81551i	0.213182	−	0.123081i	−0.389607	−	0.920981i	$-0.627389\pi$
$31$	6.60865	−	3.81551i	0.213182	−	0.123081i	0.602789	+	0.797900i	$0.294056\pi$
$32$		0			0
$33$	18.4058	+	10.6266i	0.557752	+	0.322018i
$34$		0			0
$35$	−9.75114	−	10.4765i	−0.278604	−	0.299328i
$36$		0			0
$37$	26.9315	−	46.6467i	0.727877	−	1.26072i	−0.229901	−	0.973214i	$-0.573840\pi$
$37$	26.9315	−	46.6467i	0.727877	−	1.26072i	0.957779	−	0.287507i	$-0.0928263\pi$
$38$		0			0
$39$	−14.3538	−	24.8615i	−0.368046	−	0.637474i
$40$		0			0
$41$		−	6.44781i		−	0.157264i	−0.996904	−	0.0786319i	$-0.974945\pi$
$41$		−	6.44781i		−	0.157264i	0.996904	−	0.0786319i	$-0.0250552\pi$
$42$		0			0
$43$	−13.8206			−0.321408			−0.160704	−	0.987003i	$-0.551377\pi$
$43$	−13.8206			−0.321408			−0.160704	+	0.987003i	$0.551377\pi$
$44$		0			0
$45$	5.31205	−	3.06692i	0.118046	−	0.0681537i
$46$		0			0
$47$	24.4111	+	14.0938i	0.519386	+	0.299868i	0.736683	−	0.676238i	$-0.236391\pi$
$47$	24.4111	+	14.0938i	0.519386	+	0.299868i	−0.217297	+	0.976105i	$0.569724\pi$
$48$		0			0
$49$	40.5715	+	27.4765i	0.827989	+	0.560745i
$50$		0			0
$51$	5.61550	−	9.72633i	0.110108	−	0.190712i
$52$		0			0
$53$	−34.4114	−	59.6024i	−0.649272	−	1.12457i	−0.983297	−	0.182008i	$-0.941740\pi$
$53$	−34.4114	−	59.6024i	−0.649272	−	1.12457i	0.334025	−	0.942564i	$-0.391593\pi$
$54$		0			0
$55$			25.0885i			0.456154i
$56$		0			0
$57$	22.4102			0.393162
$58$		0			0
$59$	−62.8802	+	36.3039i	−1.06577	+	0.615321i	−0.927022	−	0.375007i	$-0.877640\pi$
$59$	−62.8802	+	36.3039i	−1.06577	+	0.615321i	−0.138745	+	0.990328i	$0.544307\pi$
$60$		0			0
$61$	−21.4925	−	12.4087i	−0.352337	−	0.203422i	0.313377	−	0.949629i	$-0.398540\pi$
$61$	−21.4925	−	12.4087i	−0.352337	−	0.203422i	−0.665714	+	0.746207i	$0.731873\pi$
$62$		0			0
$63$	−15.3718	+	14.3076i	−0.243997	+	0.227104i
$64$		0			0
$65$	16.9440	−	29.3479i	0.260677	−	0.451506i
$66$		0			0
$67$	35.3422	+	61.2144i	0.527495	+	0.913648i	0.999486	+	0.0320451i	$0.0102020\pi$
$67$	35.3422	+	61.2144i	0.527495	+	0.913648i	−0.471991	+	0.881603i	$0.656465\pi$
$68$		0			0
$69$		−	46.5135i		−	0.674109i
$70$		0			0
$71$	−12.5498			−0.176758			−0.0883788	−	0.996087i	$-0.528169\pi$
$71$	−12.5498			−0.176758			−0.0883788	+	0.996087i	$0.528169\pi$
$72$		0			0
$73$	93.9800	−	54.2594i	1.28740	−	0.743279i	0.309208	−	0.950994i	$-0.399936\pi$
$73$	93.9800	−	54.2594i	1.28740	−	0.743279i	0.978189	+	0.207715i	$0.0666028\pi$
$74$		0			0
$75$	−31.2294	−	18.0303i	−0.416391	−	0.240404i
$76$		0			0
$77$	−19.2435	−	83.7104i	−0.249916	−	1.08715i
$78$		0			0
$79$	−48.8779	+	84.6590i	−0.618708	+	1.07163i	0.371014	+	0.928627i	$0.379010\pi$
$79$	−48.8779	+	84.6590i	−0.618708	+	1.07163i	−0.989722	+	0.143006i	$0.954323\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	83.3264i		−	1.00393i	−0.864887	−	0.501966i	$-0.832610\pi$
$83$		−	83.3264i		−	1.00393i	0.864887	−	0.501966i	$-0.167390\pi$
$84$		0			0
$85$	13.2577			0.155973
$86$		0			0
$87$	57.6619	−	33.2911i	0.662780	−	0.382656i
$88$		0			0
$89$	51.6473	+	29.8186i	0.580306	+	0.335040i	0.761255	−	0.648453i	$-0.224584\pi$
$89$	51.6473	+	29.8186i	0.580306	+	0.335040i	−0.180949	+	0.983493i	$0.557917\pi$
$90$		0			0
$91$	−34.0249	+	110.919i	−0.373900	+	1.21889i
$92$		0			0
$93$	6.60865	−	11.4465i	0.0710608	−	0.123081i
$94$		0			0
$95$	13.2271	+	22.9101i	0.139233	+	0.241159i
$96$		0			0
$97$			147.707i			1.52275i	0.648312	+	0.761375i	$0.275475\pi$
$97$			147.707i			1.52275i	−0.648312	+	0.761375i	$0.724525\pi$
$98$		0			0
$99$	36.8116			0.371835
$100$		0			0
$101$	89.0062	−	51.3878i	0.881250	−	0.508790i	0.0101796	−	0.999948i	$-0.496760\pi$
$101$	89.0062	−	51.3878i	0.881250	−	0.508790i	0.871070	+	0.491158i	$0.163426\pi$
$102$		0			0
$103$	−98.4243	−	56.8253i	−0.955576	−	0.551702i	−0.0607674	−	0.998152i	$-0.519355\pi$
$103$	−98.4243	−	56.8253i	−0.955576	−	0.551702i	−0.894809	+	0.446450i	$0.852688\pi$
$104$		0			0
$105$	−23.6996	−	7.26997i	−0.225710	−	0.0692378i
$106$		0			0
$107$	97.1996	−	168.355i	0.908408	−	1.57341i	0.0921308	−	0.995747i	$-0.470632\pi$
$107$	97.1996	−	168.355i	0.908408	−	1.57341i	0.816277	−	0.577661i	$-0.196034\pi$
$108$		0			0
$109$	−64.4077	−	111.557i	−0.590896	−	1.02346i	−0.994112	−	0.108358i	$-0.965441\pi$
$109$	−64.4077	−	111.557i	−0.590896	−	1.02346i	0.403216	−	0.915105i	$-0.367892\pi$
$110$		0			0
$111$		−	93.2933i		−	0.840480i
$112$		0			0
$113$	−22.5876			−0.199890			−0.0999451	−	0.994993i	$-0.531867\pi$
$113$	−22.5876			−0.199890			−0.0999451	+	0.994993i	$0.531867\pi$
$114$		0			0
$115$	47.5510	−	27.4536i	0.413487	−	0.238727i
$116$		0			0
$117$	−43.0614	−	24.8615i	−0.368046	−	0.212491i
$118$		0			0
$119$	−44.2357	+	10.1690i	−0.371729	+	0.0854538i
$120$		0			0
$121$	−14.7831	+	25.6051i	−0.122174	+	0.211612i
$122$		0			0
$123$	−5.58397	−	9.67172i	−0.0453981	−	0.0786319i
$124$		0			0
$125$		−	93.6832i		−	0.749465i
$126$		0			0
$127$	8.72204			0.0686775			0.0343387	−	0.999410i	$-0.489067\pi$
$127$	8.72204			0.0686775			0.0343387	+	0.999410i	$0.489067\pi$
$128$		0			0
$129$	−20.7308	+	11.9690i	−0.160704	+	0.0927826i
$130$		0			0
$131$	−99.9492	−	57.7057i	−0.762971	−	0.440501i	0.0673905	−	0.997727i	$-0.478533\pi$
$131$	−99.9492	−	57.7057i	−0.762971	−	0.440501i	−0.830361	+	0.557225i	$0.811866\pi$
$132$		0			0
$133$	−61.7064	−	66.2964i	−0.463958	−	0.498469i
$134$		0			0
$135$	5.31205	−	9.20075i	0.0393485	−	0.0681537i
$136$		0			0
$137$	102.088	+	176.821i	0.745167	+	1.29067i	0.950117	+	0.311895i	$0.100964\pi$
$137$	102.088	+	176.821i	0.745167	+	1.29067i	−0.204949	+	0.978773i	$0.565703\pi$
$138$		0			0
$139$			189.134i			1.36068i	0.732898	+	0.680338i	$0.238167\pi$
$139$			189.134i			1.36068i	−0.732898	+	0.680338i	$0.761833\pi$
$140$		0			0
$141$	48.8223			0.346257
$142$		0			0
$143$	176.129	−	101.688i	1.23167	−	0.711105i
$144$		0			0
$145$	68.0674	+	39.2987i	0.469430	+	0.271026i
$146$		0			0
$147$	84.6525	+	6.07882i	0.575867	+	0.0413525i
$148$		0			0
$149$	−107.003	+	185.335i	−0.718143	+	1.24386i	0.243591	+	0.969878i	$0.421675\pi$
$149$	−107.003	+	185.335i	−0.718143	+	1.24386i	−0.961735	+	0.273983i	$0.911659\pi$
$150$		0			0
$151$	131.942	+	228.530i	0.873787	+	1.51344i	0.858050	+	0.513567i	$0.171676\pi$
$151$	131.942	+	228.530i	0.873787	+	1.51344i	0.0157369	+	0.999876i	$0.494991\pi$
$152$		0			0
$153$		−	19.4527i		−	0.127142i
$154$		0			0
$155$	15.6025			0.100661
$156$		0			0
$157$	−22.9344	+	13.2412i	−0.146079	+	0.0843386i	−0.571258	−	0.820771i	$-0.693544\pi$
$157$	−22.9344	+	13.2412i	−0.146079	+	0.0843386i	0.425179	+	0.905109i	$0.360211\pi$
$158$		0			0
$159$	−103.234	−	59.6024i	−0.649272	−	0.374858i
$160$		0			0
$161$	−137.601	+	128.075i	−0.854667	+	0.795495i
$162$		0			0
$163$	−13.7906	+	23.8860i	−0.0846047	+	0.146540i	−0.905223	−	0.424937i	$-0.860296\pi$
$163$	−13.7906	+	23.8860i	−0.0846047	+	0.146540i	0.820618	+	0.571477i	$0.193629\pi$
$164$		0			0
$165$	21.7273	+	37.6327i	0.131680	+	0.228077i
$166$		0			0
$167$			113.557i			0.679980i	0.940429	+	0.339990i	$0.110424\pi$
$167$			113.557i			0.679980i	−0.940429	+	0.339990i	$0.889576\pi$
$168$		0			0
$169$	−105.708			−0.625494
$170$		0			0
$171$	33.6153	−	19.4078i	0.196581	−	0.113496i
$172$		0			0
$173$	−22.0339	−	12.7213i	−0.127364	−	0.0735334i	0.434965	−	0.900448i	$-0.356761\pi$
$173$	−22.0339	−	12.7213i	−0.127364	−	0.0735334i	−0.562328	+	0.826914i	$0.690094\pi$
$174$		0			0
$175$	32.6507	+	142.032i	0.186575	+	0.811614i
$176$		0			0
$177$	−62.8802	+	108.912i	−0.355256	+	0.615321i
$178$		0			0
$179$	−67.9229	−	117.646i	−0.379457	−	0.657239i	0.611526	−	0.791224i	$-0.290556\pi$
$179$	−67.9229	−	117.646i	−0.379457	−	0.657239i	−0.990983	+	0.133985i	$0.957223\pi$
$180$		0			0
$181$			237.390i			1.31155i	0.754957	+	0.655774i	$0.227658\pi$
$181$			237.390i			1.31155i	−0.754957	+	0.655774i	$0.772342\pi$
$182$		0			0
$183$	−42.9851			−0.234891
$184$		0			0
$185$	95.3743	−	55.0644i	0.515537	−	0.297645i
$186$		0			0
$187$	68.9052	+	39.7824i	0.368477	+	0.212740i
$188$		0			0
$189$	−10.6670	+	34.7738i	−0.0564393	+	0.183988i
$190$		0			0
$191$	106.028	−	183.645i	0.555118	−	0.961492i	−0.442776	−	0.896632i	$-0.646006\pi$
$191$	106.028	−	183.645i	0.555118	−	0.961492i	0.997894	−	0.0648604i	$-0.0206602\pi$
$192$		0			0
$193$	1.03965	+	1.80072i	0.00538677	+	0.00933015i	0.868706	−	0.495328i	$-0.164952\pi$
$193$	1.03965	+	1.80072i	0.00538677	+	0.00933015i	−0.863319	+	0.504658i	$0.831619\pi$
$194$		0			0
$195$		−	58.6958i		−	0.301004i
$196$		0			0
$197$	−297.578			−1.51055			−0.755274	−	0.655409i	$-0.772496\pi$
$197$	−297.578			−1.51055			−0.755274	+	0.655409i	$0.772496\pi$
$198$		0			0
$199$	−220.767	+	127.460i	−1.10938	+	0.640501i	−0.938669	−	0.344820i	$-0.887940\pi$
$199$	−220.767	+	127.460i	−1.10938	+	0.640501i	−0.170711	+	0.985321i	$0.554607\pi$
$200$		0			0
$201$	106.027	+	61.2144i	0.527495	+	0.304549i
$202$		0			0
$203$	−257.257	−	78.9149i	−1.26728	−	0.388743i
$204$		0			0
$205$	6.59164	−	11.4170i	0.0321543	−	0.0556929i
$206$		0			0
$207$	−40.2819	−	69.7703i	−0.194598	−	0.337054i
$208$		0			0
$209$			158.763i			0.759631i
$210$		0			0
$211$	188.235			0.892110			0.446055	−	0.895005i	$-0.352829\pi$
$211$	188.235			0.892110			0.446055	+	0.895005i	$0.352829\pi$
$212$		0			0
$213$	−18.8247	+	10.8684i	−0.0883788	+	0.0510255i
$214$		0			0
$215$	−24.4719	−	14.1288i	−0.113823	−	0.0657155i
$216$		0			0
$217$	−52.0593	+	11.9675i	−0.239904	+	0.0551497i
$218$		0			0
$219$	93.9800	−	162.778i	0.429132	−	0.743279i
$220$		0			0
$221$	−53.7358	−	93.0731i	−0.243148	−	0.421145i
$222$		0			0
$223$			91.4723i			0.410190i	0.978742	+	0.205095i	$0.0657503\pi$
$223$			91.4723i			0.410190i	−0.978742	+	0.205095i	$0.934250\pi$
$224$		0			0
$225$	−62.4587			−0.277594
$226$		0			0
$227$	−46.8480	+	27.0477i	−0.206379	+	0.119153i	−0.599627	−	0.800279i	$-0.704685\pi$
$227$	−46.8480	+	27.0477i	−0.206379	+	0.119153i	0.393249	+	0.919432i	$0.371351\pi$
$228$		0			0
$229$	−181.400	−	104.731i	−0.792138	−	0.457341i	0.0485765	−	0.998819i	$-0.484532\pi$
$229$	−181.400	−	104.731i	−0.792138	−	0.457341i	−0.840715	+	0.541478i	$0.817865\pi$
$230$		0			0
$231$	−101.361	−	108.900i	−0.438791	−	0.471430i
$232$		0			0
$233$	−38.0063	+	65.8289i	−0.163117	+	0.282527i	−0.935985	−	0.352040i	$-0.885488\pi$
$233$	−38.0063	+	65.8289i	−0.163117	+	0.282527i	0.772868	+	0.634567i	$0.218822\pi$
$234$		0			0
$235$	28.8163	+	49.9113i	0.122623	+	0.212388i
$236$		0			0
$237$			169.318i			0.714422i
$238$		0			0
$239$	142.401			0.595820			0.297910	−	0.954594i	$-0.403710\pi$
$239$	142.401			0.595820			0.297910	+	0.954594i	$0.403710\pi$
$240$		0			0
$241$	−327.326	+	188.982i	−1.35820	+	0.784156i	−0.989381	−	0.145346i	$-0.953570\pi$
$241$	−327.326	+	188.982i	−1.35820	+	0.784156i	−0.368817	+	0.929502i	$0.620237\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	43.7499	+	90.1286i	0.178571	+	0.367872i
$246$		0			0
$247$	107.224	−	185.717i	0.434105	−	0.751891i
$248$		0			0
$249$	−72.1628	−	124.990i	−0.289810	−	0.501966i
$250$		0			0
$251$			76.3113i			0.304029i	0.988378	+	0.152015i	$0.0485761\pi$
$251$			76.3113i			0.304029i	−0.988378	+	0.152015i	$0.951424\pi$
$252$		0			0
$253$	329.520			1.30245
$254$		0			0
$255$	19.8866	−	11.4815i	0.0779865	−	0.0450255i
$256$		0			0
$257$	−38.5195	−	22.2393i	−0.149881	−	0.0865341i	0.423184	−	0.906044i	$-0.360912\pi$
$257$	−38.5195	−	22.2393i	−0.149881	−	0.0865341i	−0.573065	+	0.819510i	$0.694246\pi$
$258$		0			0
$259$	−275.991	+	256.883i	−1.06560	+	0.991825i
$260$		0			0
$261$	57.6619	−	99.8733i	0.220927	−	0.382656i
$262$		0			0
$263$	194.459	+	336.814i	0.739390	+	1.28066i	0.952770	+	0.303691i	$0.0982191\pi$
$263$	194.459	+	336.814i	0.739390	+	1.28066i	−0.213381	+	0.976969i	$0.568448\pi$
$264$		0			0
$265$		−	140.716i		−	0.531004i
$266$		0			0
$267$	103.295			0.386871
$268$		0			0
$269$	−98.9666	+	57.1384i	−0.367905	+	0.212410i	−0.672543	−	0.740058i	$-0.734798\pi$
$269$	−98.9666	+	57.1384i	−0.367905	+	0.212410i	0.304638	+	0.952468i	$0.401465\pi$
$270$		0			0
$271$	−355.967	−	205.518i	−1.31353	−	0.758367i	−0.330851	−	0.943683i	$-0.607336\pi$
$271$	−355.967	−	205.518i	−1.31353	−	0.758367i	−0.982679	+	0.185316i	$0.940669\pi$
$272$		0			0
$273$	45.0212	+	195.845i	0.164913	+	0.717381i
$274$		0			0
$275$	127.734	−	221.241i	0.464486	−	0.804514i
$276$		0			0
$277$	45.3175	+	78.4922i	0.163601	+	0.283365i	0.936158	−	0.351581i	$-0.114356\pi$
$277$	45.3175	+	78.4922i	0.163601	+	0.283365i	−0.772557	+	0.634946i	$0.781022\pi$
$278$		0			0
$279$		−	22.8930i		−	0.0820539i
$280$		0			0
$281$	67.3105			0.239539			0.119770	−	0.992802i	$-0.461784\pi$
$281$	67.3105			0.239539			0.119770	+	0.992802i	$0.461784\pi$
$282$		0			0
$283$	−223.431	+	128.998i	−0.789508	+	0.455823i	−0.839789	−	0.542912i	$-0.817322\pi$
$283$	−223.431	+	128.998i	−0.789508	+	0.455823i	0.0502810	+	0.998735i	$0.483988\pi$
$284$		0			0
$285$	39.6814	+	22.9101i	0.139233	+	0.0803862i
$286$		0			0
$287$	−13.2365	+	43.1502i	−0.0461203	+	0.150349i
$288$		0			0
$289$	−123.477	+	213.869i	−0.427258	+	0.740032i
$290$		0			0
$291$	127.918	+	221.560i	0.439580	+	0.761375i
$292$		0			0
$293$			440.320i			1.50280i	0.659848	+	0.751399i	$0.270621\pi$
$293$			440.320i			1.50280i	−0.659848	+	0.751399i	$0.729379\pi$
$294$		0			0
$295$	−148.455			−0.503237
$296$		0			0
$297$	55.2174	−	31.8798i	0.185917	−	0.107339i
$298$		0			0
$299$	−385.465	−	222.548i	−1.28918	−	0.744309i
$300$		0			0
$301$	92.4901	+	28.3718i	0.307276	+	0.0942585i
$302$		0			0
$303$	89.0062	−	154.163i	0.293750	−	0.508790i
$304$		0			0
$305$	−25.3710	−	43.9439i	−0.0831836	−	0.144078i
$306$		0			0
$307$			465.462i			1.51616i	0.652160	+	0.758082i	$0.273863\pi$
$307$			465.462i			1.51616i	−0.652160	+	0.758082i	$0.726137\pi$
$308$		0			0
$309$	−196.849			−0.637051
$310$		0			0
$311$	222.189	−	128.281i	0.714434	−	0.412478i	−0.0982668	−	0.995160i	$-0.531330\pi$
$311$	222.189	−	128.281i	0.714434	−	0.412478i	0.812701	+	0.582682i	$0.197997\pi$
$312$		0			0
$313$	85.1309	+	49.1504i	0.271984	+	0.157030i	0.629789	−	0.776766i	$-0.283141\pi$
$313$	85.1309	+	49.1504i	0.271984	+	0.157030i	−0.357805	+	0.933796i	$0.616475\pi$
$314$		0			0
$315$	−41.8454	+	9.61950i	−0.132842	+	0.0305381i
$316$		0			0
$317$	145.846	−	252.613i	0.460083	−	0.796887i	−0.538882	−	0.842381i	$-0.681153\pi$
$317$	145.846	−	252.613i	0.460083	−	0.796887i	0.998965	+	0.0454947i	$0.0144864\pi$
$318$		0			0
$319$	235.848	+	408.500i	0.739334	+	1.28056i
$320$		0			0
$321$		−	336.709i		−	1.04894i
$322$		0			0
$323$	83.8963			0.259741
$324$		0			0
$325$	−298.840	+	172.535i	−0.919507	+	0.530878i
$326$		0			0
$327$	−193.223	−	111.557i	−0.590896	−	0.341154i
$328$		0			0
$329$	−134.432	−	144.432i	−0.408608	−	0.439002i
$330$		0			0
$331$	143.715	−	248.922i	0.434184	−	0.752029i	−0.563044	−	0.826427i	$-0.690370\pi$
$331$	143.715	−	248.922i	0.434184	−	0.752029i	0.997229	+	0.0743973i	$0.0237033\pi$
$332$		0			0
$333$	−80.7944	−	139.940i	−0.242626	−	0.420240i
$334$		0			0
$335$			144.522i			0.431409i
$336$		0			0
$337$	294.785			0.874731			0.437366	−	0.899284i	$-0.355912\pi$
$337$	294.785			0.874731			0.437366	+	0.899284i	$0.355912\pi$
$338$		0			0
$339$	−33.8814	+	19.5614i	−0.0999451	+	0.0577033i
$340$		0			0
$341$	81.0917	+	46.8183i	0.237806	+	0.137297i
$342$		0			0
$343$	−215.107	−	267.166i	−0.627135	−	0.778911i
$344$		0			0
$345$	47.5510	−	82.3608i	0.137829	−	0.238727i
$346$		0			0
$347$	−36.6378	−	63.4585i	−0.105584	−	0.182878i	0.808392	−	0.588644i	$-0.200338\pi$
$347$	−36.6378	−	63.4585i	−0.105584	−	0.182878i	−0.913977	+	0.405766i	$0.867005\pi$
$348$		0			0
$349$		−	101.957i		−	0.292140i	−0.989274	−	0.146070i	$-0.953338\pi$
$349$		−	101.957i		−	0.292140i	0.989274	−	0.146070i	$-0.0466624\pi$
$350$		0			0
$351$	−86.1228			−0.245364
$352$		0			0
$353$	−65.5939	+	37.8706i	−0.185818	+	0.107282i	−0.590023	−	0.807386i	$-0.700882\pi$
$353$	−65.5939	+	37.8706i	−0.185818	+	0.107282i	0.404205	+	0.914668i	$0.367548\pi$
$354$		0			0
$355$	−22.2217	−	12.8297i	−0.0625964	−	0.0361400i
$356$		0			0
$357$	−57.5470	+	53.5628i	−0.161196	+	0.150036i
$358$		0			0
$359$	−62.3384	+	107.973i	−0.173645	+	0.300761i	−0.939691	−	0.342024i	$-0.888888\pi$
$359$	−62.3384	+	107.973i	−0.173645	+	0.300761i	0.766047	+	0.642785i	$0.222221\pi$
$360$		0			0
$361$	−96.7970	−	167.657i	−0.268136	−	0.464425i
$362$		0			0
$363$			51.2102i			0.141075i
$364$		0			0
$365$	221.879			0.607887
$366$		0			0
$367$	422.961	−	244.196i	1.15248	−	0.665385i	0.202991	−	0.979181i	$-0.434934\pi$
$367$	422.961	−	244.196i	1.15248	−	0.665385i	0.949491	+	0.313795i	$0.101601\pi$
$368$		0			0
$369$	−16.7519	−	9.67172i	−0.0453981	−	0.0262106i
$370$		0			0
$371$	107.933	+	469.514i	0.290924	+	1.26554i
$372$		0			0
$373$	−248.879	+	431.071i	−0.667236	+	1.15569i	0.311438	+	0.950267i	$0.399190\pi$
$373$	−248.879	+	431.071i	−0.667236	+	1.15569i	−0.978674	+	0.205421i	$0.934144\pi$
$374$		0			0
$375$	−81.1320	−	140.525i	−0.216352	−	0.374733i
$376$		0			0
$377$		−	637.138i		−	1.69002i
$378$		0			0
$379$	699.265			1.84503			0.922514	−	0.385964i	$-0.126131\pi$
$379$	699.265			1.84503			0.922514	+	0.385964i	$0.126131\pi$
$380$		0			0
$381$	13.0831	−	7.55351i	0.0343387	−	0.0198255i
$382$		0			0
$383$	−572.153	−	330.333i	−1.49387	−	0.862487i	−0.493896	−	0.869521i	$-0.664428\pi$
$383$	−572.153	−	330.333i	−1.49387	−	0.862487i	−0.999975	+	0.00703401i	$0.997761\pi$
$384$		0			0
$385$	51.5034	−	167.897i	0.133775	−	0.436097i
$386$		0			0
$387$	−20.7308	+	35.9069i	−0.0535681	+	0.0927826i
$388$		0			0
$389$	207.214	+	358.906i	0.532685	+	0.922637i	0.999272	+	0.0381615i	$0.0121501\pi$
$389$	207.214	+	358.906i	0.532685	+	0.922637i	−0.466587	+	0.884475i	$0.654517\pi$
$390$		0			0
$391$		−	174.131i		−	0.445348i
$392$		0			0
$393$	−199.898			−0.508647
$394$		0			0
$395$	−173.095	+	99.9363i	−0.438214	+	0.253003i
$396$		0			0
$397$	11.7266	+	6.77035i	0.0295380	+	0.0170538i	0.514696	−	0.857373i	$-0.327905\pi$
$397$	11.7266	+	6.77035i	0.0295380	+	0.0170538i	−0.485158	+	0.874426i	$0.661238\pi$
$398$		0			0
$399$	−149.974	−	46.0052i	−0.375875	−	0.115301i
$400$		0			0
$401$	203.149	−	351.864i	0.506605	−	0.877466i	−0.493365	−	0.869822i	$-0.664233\pi$
$401$	203.149	−	351.864i	0.506605	−	0.877466i	0.999971	−	0.00764415i	$-0.00243323\pi$
$402$		0			0
$403$	−63.2395	−	109.534i	−0.156922	−	0.271797i
$404$		0			0
$405$		−	18.4015i		−	0.0454358i
$406$		0			0
$407$	660.927			1.62390
$408$		0			0
$409$	459.724	−	265.422i	1.12402	−	0.648953i	0.181596	−	0.983373i	$-0.441874\pi$
$409$	459.724	−	265.422i	1.12402	−	0.648953i	0.942424	+	0.334420i	$0.108540\pi$
$410$		0			0
$411$	306.264	+	176.821i	0.745167	+	0.430223i
$412$		0			0
$413$	495.335	−	113.869i	1.19936	−	0.275711i
$414$		0			0
$415$	85.1850	−	147.545i	0.205265	−	0.355530i
$416$		0			0
$417$	163.795	+	283.701i	0.392793	+	0.680338i
$418$		0			0
$419$		−	781.472i		−	1.86509i	−0.361055	−	0.932545i	$-0.617583\pi$
$419$		−	781.472i		−	1.86509i	0.361055	−	0.932545i	$-0.382417\pi$
$420$		0			0
$421$	620.648			1.47422			0.737112	−	0.675771i	$-0.236189\pi$
$421$	620.648			1.47422			0.737112	+	0.675771i	$0.236189\pi$
$422$		0			0
$423$	73.2334	−	42.2813i	0.173129	−	0.0999559i
$424$		0			0
$425$	−116.912	−	67.4993i	−0.275088	−	0.158822i
$426$		0			0
$427$	118.359	+	127.163i	0.277188	+	0.297806i
$428$		0			0
$429$	176.129	−	305.064i	0.410557	−	0.711105i
$430$		0			0
$431$	399.782	+	692.443i	0.927569	+	1.60660i	0.787376	+	0.616473i	$0.211439\pi$
$431$	399.782	+	692.443i	0.927569	+	1.60660i	0.140193	+	0.990124i	$0.455228\pi$
$432$		0			0
$433$		−	299.556i		−	0.691814i	−0.938269	−	0.345907i	$-0.887571\pi$
$433$		−	299.556i		−	0.691814i	0.938269	−	0.345907i	$-0.112429\pi$
$434$		0			0
$435$	136.135			0.312953
$436$		0			0
$437$	300.909	−	173.730i	0.688578	−	0.397551i
$438$		0			0
$439$	−208.614	−	120.444i	−0.475204	−	0.274359i	0.243212	−	0.969973i	$-0.421799\pi$
$439$	−208.614	−	120.444i	−0.475204	−	0.274359i	−0.718416	+	0.695614i	$0.755132\pi$
$440$		0			0
$441$	132.243	−	64.1930i	0.299871	−	0.145562i
$442$		0			0
$443$	67.6910	−	117.244i	0.152801	−	0.264660i	−0.779455	−	0.626458i	$-0.784504\pi$
$443$	67.6910	−	117.244i	0.152801	−	0.264660i	0.932256	+	0.361799i	$0.117837\pi$
$444$		0			0
$445$	60.9673	+	105.599i	0.137005	+	0.237300i
$446$		0			0
$447$			370.671i			0.829241i
$448$		0			0
$449$	−865.136			−1.92681			−0.963404	−	0.268055i	$-0.913619\pi$
$449$	−865.136			−1.92681			−0.963404	+	0.268055i	$0.913619\pi$
$450$		0			0
$451$	68.5184	−	39.5591i	0.151925	−	0.0877142i
$452$		0			0
$453$	395.825	+	228.530i	0.873787	+	0.504481i
$454$		0			0
$455$	−173.640	+	161.619i	−0.381627	+	0.355206i
$456$		0			0
$457$	375.026	−	649.564i	0.820626	−	1.42137i	−0.0845906	−	0.996416i	$-0.526958\pi$
$457$	375.026	−	649.564i	0.820626	−	1.42137i	0.905217	−	0.424950i	$-0.139708\pi$
$458$		0			0
$459$	−16.8465	−	29.1790i	−0.0367026	−	0.0635708i
$460$		0			0
$461$		−	493.466i		−	1.07042i	−0.844717	−	0.535212i	$-0.820232\pi$
$461$		−	493.466i		−	1.07042i	0.844717	−	0.535212i	$-0.179768\pi$
$462$		0			0
$463$	−279.584			−0.603853			−0.301927	−	0.953331i	$-0.597630\pi$
$463$	−279.584			−0.603853			−0.301927	+	0.953331i	$0.597630\pi$
$464$		0			0
$465$	23.4037	−	13.5121i	0.0503305	−	0.0290583i
$466$		0			0
$467$	−712.016	−	411.083i	−1.52466	−	0.880263i	−0.999573	−	0.0292136i	$-0.990700\pi$
$467$	−712.016	−	411.083i	−1.52466	−	0.880263i	−0.525086	−	0.851049i	$-0.675967\pi$
$468$		0			0
$469$	−110.852	−	482.213i	−0.236358	−	1.02817i
$470$		0			0
$471$	−22.9344	+	39.7235i	−0.0486929	+	0.0843386i
$472$		0			0
$473$	−84.7929	−	146.866i	−0.179266	−	0.310498i
$474$		0			0
$475$		−	269.375i		−	0.567105i
$476$		0			0
$477$	−206.469			−0.432848
$478$		0			0
$479$	491.761	−	283.918i	1.02664	−	0.592732i	0.110621	−	0.993863i	$-0.464716\pi$
$479$	491.761	−	283.918i	1.02664	−	0.592732i	0.916021	+	0.401131i	$0.131383\pi$
$480$		0			0
$481$	−773.137	−	446.371i	−1.60735	−	0.928006i
$482$		0			0
$483$	−95.4862	+	311.278i	−0.197694	+	0.644469i
$484$		0			0
$485$	−151.001	+	261.542i	−0.311343	+	0.539262i
$486$		0			0
$487$	14.7365	+	25.5243i	0.0302597	+	0.0524113i	0.880759	−	0.473565i	$-0.157033\pi$
$487$	14.7365	+	25.5243i	0.0302597	+	0.0524113i	−0.850499	+	0.525977i	$0.823700\pi$
$488$		0			0
$489$			47.7719i			0.0976931i
$490$		0			0
$491$	−139.613			−0.284344			−0.142172	−	0.989842i	$-0.545409\pi$
$491$	−139.613			−0.284344			−0.142172	+	0.989842i	$0.545409\pi$
$492$		0			0
$493$	215.867	−	124.631i	0.437864	−	0.252801i
$494$		0			0
$495$	65.1818	+	37.6327i	0.131680	+	0.0760257i
$496$		0			0
$497$	83.9859	+	25.7631i	0.168986	+	0.0518372i
$498$		0			0
$499$	300.617	−	520.684i	0.602439	−	1.04346i	−0.390011	−	0.920810i	$-0.627529\pi$
$499$	300.617	−	520.684i	0.602439	−	1.04346i	0.992451	−	0.122645i	$-0.0391377\pi$
$500$		0			0
$501$	98.3429	+	170.335i	0.196293	+	0.339990i
$502$		0			0
$503$			630.250i			1.25298i	0.779429	+	0.626491i	$0.215509\pi$
$503$			630.250i			1.25298i	−0.779429	+	0.626491i	$0.784491\pi$
$504$		0			0
$505$	210.136			0.416111
$506$		0			0
$507$	−158.563	+	91.5462i	−0.312747	+	0.180565i
$508$		0			0
$509$	30.2755	+	17.4796i	0.0594803	+	0.0343410i	0.529445	−	0.848344i	$-0.322400\pi$
$509$	30.2755	+	17.4796i	0.0594803	+	0.0343410i	−0.469965	+	0.882685i	$0.655733\pi$
$510$		0			0
$511$	−740.322	+	170.187i	−1.44877	+	0.333046i
$512$		0			0
$513$	33.6153	−	58.2234i	0.0655269	−	0.113496i
$514$		0			0
$515$	−116.186	−	201.239i	−0.225603	−	0.390756i
$516$		0			0
$517$			345.877i			0.669007i
$518$		0			0
$519$	−44.0678			−0.0849090
$520$		0			0
$521$	432.482	−	249.693i	0.830099	−	0.479258i	−0.0237873	−	0.999717i	$-0.507572\pi$
$521$	432.482	−	249.693i	0.830099	−	0.479258i	0.853887	+	0.520459i	$0.174239\pi$
$522$		0			0
$523$	−659.230	−	380.606i	−1.26048	−	0.727737i	−0.287310	−	0.957838i	$-0.592761\pi$
$523$	−659.230	−	380.606i	−1.26048	−	0.727737i	−0.973167	+	0.230101i	$0.926094\pi$
$524$		0			0
$525$	171.980	+	184.772i	0.327580	+	0.351947i
$526$		0			0
$527$	24.7406	−	42.8519i	0.0469461	−	0.0813130i
$528$		0			0
$529$	−96.0845	−	166.423i	−0.181634	−	0.314600i
$530$		0			0
$531$			217.824i			0.410214i
$532$		0			0
$533$	−106.868			−0.200503
$534$		0			0
$535$	344.220	−	198.735i	0.643401	−	0.371468i
$536$		0			0
$537$	−203.769	−	117.646i	−0.379457	−	0.219080i
$538$		0			0
$539$	−43.0648	+	599.712i	−0.0798976	+	1.11264i
$540$		0			0
$541$	176.568	−	305.825i	0.326373	−	0.565295i	−0.655416	−	0.755268i	$-0.727507\pi$
$541$	176.568	−	305.825i	0.326373	−	0.565295i	0.981789	+	0.189973i	$0.0608400\pi$
$542$		0			0
$543$	205.586	+	356.085i	0.378611	+	0.655774i
$544$		0			0
$545$		−	263.377i		−	0.483261i
$546$		0			0
$547$	71.1385			0.130052			0.0650260	−	0.997884i	$-0.479287\pi$
$547$	71.1385			0.130052			0.0650260	+	0.997884i	$0.479287\pi$
$548$		0			0
$549$	−64.4776	+	37.2262i	−0.117446	+	0.0678072i
$550$		0			0
$551$	430.739	+	248.687i	0.781740	+	0.451338i
$552$		0			0
$553$	500.895	−	466.216i	0.905778	−	0.843067i
$554$		0			0
$555$	95.3743	−	165.193i	0.171846	−	0.297645i
$556$		0			0
$557$	207.721	+	359.783i	0.372928	+	0.645930i	0.990015	−	0.140965i	$-0.0450206\pi$
$557$	207.721	+	359.783i	0.372928	+	0.645930i	−0.617087	+	0.786895i	$0.711687\pi$
$558$		0			0
$559$			229.067i			0.409779i
$560$		0			0
$561$	137.810			0.245651
$562$		0			0
$563$	−509.087	+	293.921i	−0.904239	+	0.522063i	−0.878573	−	0.477608i	$-0.841504\pi$
$563$	−509.087	+	293.921i	−0.904239	+	0.522063i	−0.0256661	+	0.999671i	$0.508171\pi$
$564$		0			0
$565$	−39.9955	−	23.0914i	−0.0707885	−	0.0408698i
$566$		0			0
$567$	14.1144	+	61.3986i	0.0248932	+	0.108287i
$568$		0			0
$569$	244.661	−	423.765i	0.429984	−	0.744753i	−0.566888	−	0.823795i	$-0.691853\pi$
$569$	244.661	−	423.765i	0.429984	−	0.744753i	0.996871	+	0.0790417i	$0.0251860\pi$
$570$		0			0
$571$	176.937	+	306.464i	0.309872	+	0.536714i	0.978334	−	0.207032i	$-0.0663804\pi$
$571$	176.937	+	306.464i	0.309872	+	0.536714i	−0.668462	+	0.743746i	$0.733047\pi$
$572$		0			0
$573$		−	367.290i		−	0.640995i
$574$		0			0
$575$	−559.101			−0.972350
$576$		0			0
$577$	−551.570	+	318.449i	−0.955927	+	0.551905i	−0.894917	−	0.446233i	$-0.852765\pi$
$577$	−551.570	+	318.449i	−0.955927	+	0.551905i	−0.0610097	+	0.998137i	$0.519432\pi$
$578$		0			0
$579$	3.11894	+	1.80072i	0.00538677	+	0.00311005i
$580$		0			0
$581$	−171.058	+	557.638i	−0.294420	+	0.959790i
$582$		0			0
$583$	422.247	−	731.353i	0.724266	−	1.25447i
$584$		0			0
$585$	−50.8321	−	88.0437i	−0.0868924	−	0.150502i
$586$		0			0
$587$			831.051i			1.41576i	0.706333	+	0.707880i	$0.250348\pi$
$587$			831.051i			1.41576i	−0.706333	+	0.707880i	$0.749652\pi$
$588$		0			0
$589$	98.7342			0.167630
$590$		0			0
$591$	−446.367	+	257.710i	−0.755274	+	0.436058i
$592$		0			0
$593$	996.763	+	575.481i	1.68088	+	0.970457i	0.961077	+	0.276281i	$0.0891019\pi$
$593$	996.763	+	575.481i	1.68088	+	0.970457i	0.719805	+	0.694177i	$0.244231\pi$
$594$		0			0
$595$	−88.7234	−	27.2163i	−0.149115	−	0.0457417i
$596$		0			0
$597$	−220.767	+	382.379i	−0.369793	+	0.640501i
$598$		0			0
$599$	244.474	+	423.442i	0.408138	+	0.706915i	0.994681	−	0.103003i	$-0.0328450\pi$
$599$	244.474	+	423.442i	0.408138	+	0.706915i	−0.586543	+	0.809918i	$0.699512\pi$
$600$		0			0
$601$			995.313i			1.65609i	0.560659	+	0.828047i	$0.310548\pi$
$601$			995.313i			1.65609i	−0.560659	+	0.828047i	$0.689452\pi$
$602$		0			0
$603$	212.053			0.351663
$604$		0			0
$605$	−52.3524	+	30.2257i	−0.0865329	+	0.0499598i
$606$		0			0
$607$	−452.616	−	261.318i	−0.745660	−	0.430507i	0.0784634	−	0.996917i	$-0.474999\pi$
$607$	−452.616	−	261.318i	−0.745660	−	0.430507i	−0.824124	+	0.566410i	$0.808332\pi$
$608$		0			0
$609$	−454.228	+	104.419i	−0.745859	+	0.171460i
$610$		0			0
$611$	233.595	−	404.598i	0.382316	−	0.662191i
$612$		0			0
$613$	137.094	+	237.454i	0.223645	+	0.387364i	0.955912	−	0.293653i	$-0.0948711\pi$
$613$	137.094	+	237.454i	0.223645	+	0.387364i	−0.732267	+	0.681018i	$0.761538\pi$
$614$		0			0
$615$		−	22.8341i		−	0.0371286i
$616$		0			0
$617$	−101.665			−0.164773			−0.0823867	−	0.996600i	$-0.526254\pi$
$617$	−101.665			−0.164773			−0.0823867	+	0.996600i	$0.526254\pi$
$618$		0			0
$619$	179.409	−	103.582i	0.289837	−	0.167337i	−0.348031	−	0.937483i	$-0.613150\pi$
$619$	179.409	−	103.582i	0.289837	−	0.167337i	0.637868	+	0.770145i	$0.279816\pi$
$620$		0			0
$621$	−120.846	−	69.7703i	−0.194598	−	0.112351i
$622$		0			0
$623$	−284.421	−	305.577i	−0.456534	−	0.490493i
$624$		0			0
$625$	−164.472	+	284.874i	−0.263155	+	0.455798i
$626$		0			0
$627$	137.493	+	238.144i	0.219287	+	0.379816i
$628$		0			0
$629$		−	349.259i		−	0.555261i
$630$		0			0
$631$	−500.062			−0.792492			−0.396246	−	0.918144i	$-0.629687\pi$
$631$	−500.062			−0.792492			−0.396246	+	0.918144i	$0.629687\pi$
$632$		0			0
$633$	282.353	−	163.017i	0.446055	−	0.257530i
$634$		0			0
$635$	15.4440	+	8.91659i	0.0243212	+	0.0140419i
$636$		0			0
$637$	455.404	−	672.445i	0.714921	−	1.05564i
$638$		0			0
$639$	−18.8247	+	32.6053i	−0.0294596	+	0.0510255i
$640$		0			0
$641$	262.210	+	454.162i	0.409065	+	0.708521i	0.994785	−	0.101992i	$-0.0325218\pi$
$641$	262.210	+	454.162i	0.409065	+	0.708521i	−0.585721	+	0.810513i	$0.699188\pi$
$642$		0			0
$643$		−	879.365i		−	1.36760i	−0.729671	−	0.683798i	$-0.760327\pi$
$643$		−	879.365i		−	1.36760i	0.729671	−	0.683798i	$-0.239673\pi$
$644$		0			0
$645$	−48.9437			−0.0758817
$646$		0			0
$647$	79.5097	−	45.9049i	0.122890	−	0.0709504i	−0.437295	−	0.899318i	$-0.644063\pi$
$647$	79.5097	−	45.9049i	0.122890	−	0.0709504i	0.560185	+	0.828368i	$0.310730\pi$
$648$		0			0
$649$	−771.575	−	445.469i	−1.18887	−	0.686393i
$650$		0			0
$651$	−67.7247	+	63.0359i	−0.104032	+	0.0968293i
$652$		0			0
$653$	−126.457	+	219.031i	−0.193656	+	0.335422i	−0.946459	−	0.322824i	$-0.895368\pi$
$653$	−126.457	+	219.031i	−0.193656	+	0.335422i	0.752803	+	0.658246i	$0.228701\pi$
$654$		0			0
$655$	−117.986	−	204.357i	−0.180131	−	0.311996i
$656$		0			0
$657$		−	325.556i		−	0.495519i
$658$		0			0
$659$	575.427			0.873182			0.436591	−	0.899660i	$-0.356186\pi$
$659$	575.427			0.873182			0.436591	+	0.899660i	$0.356186\pi$
$660$		0			0
$661$	−791.756	+	457.120i	−1.19782	+	0.691559i	−0.960068	−	0.279768i	$-0.909742\pi$
$661$	−791.756	+	457.120i	−1.19782	+	0.691559i	−0.237748	+	0.971327i	$0.576409\pi$
$662$		0			0
$663$	−161.207	−	93.0731i	−0.243148	−	0.140382i
$664$		0			0
$665$	−41.4874	−	180.473i	−0.0623871	−	0.271388i
$666$		0			0
$667$	516.162	−	894.019i	0.773856	−	1.34036i
$668$		0			0
$669$	79.2173	+	137.208i	0.118412	+	0.205095i
$670$		0			0
$671$		−	304.524i		−	0.453835i
$672$		0			0
$673$	80.8779			0.120175			0.0600876	−	0.998193i	$-0.480862\pi$
$673$	80.8779			0.120175			0.0600876	+	0.998193i	$0.480862\pi$
$674$		0			0
$675$	−93.6881	+	54.0908i	−0.138797	+	0.0801346i
$676$		0			0
$677$	−773.940	−	446.835i	−1.14319	−	0.660022i	−0.195972	−	0.980609i	$-0.562786\pi$
$677$	−773.940	−	446.835i	−1.14319	−	0.660022i	−0.947219	+	0.320588i	$0.896120\pi$
$678$		0			0
$679$	303.223	−	988.485i	0.446572	−	1.45580i
$680$		0			0
$681$	−46.8480	+	81.1431i	−0.0687929	+	0.119153i
$682$		0			0
$683$	−1.31596	−	2.27931i	−0.00192673	−	0.00333720i	0.865060	−	0.501668i	$-0.167280\pi$
$683$	−1.31596	−	2.27931i	−0.00192673	−	0.00333720i	−0.866987	+	0.498330i	$0.833947\pi$
$684$		0			0
$685$			417.460i			0.609431i
$686$		0			0
$687$	−362.799			−0.528092
$688$		0			0
$689$	−987.869	+	570.347i	−1.43377	+	0.827789i
$690$		0			0
$691$	645.194	+	372.503i	0.933711	+	0.539078i	0.887983	−	0.459876i	$-0.152106\pi$
$691$	645.194	+	372.503i	0.933711	+	0.539078i	0.0457278	+	0.998954i	$0.485439\pi$
$692$		0			0
$693$	−246.351	−	75.5695i	−0.355485	−	0.109047i
$694$		0			0
$695$	−193.353	+	334.897i	−0.278205	+	0.481866i
$696$		0			0
$697$	−20.9045	−	36.2077i	−0.0299921	−	0.0519479i
$698$		0			0
$699$			131.658i			0.188352i
$700$		0			0
$701$	361.857			0.516202			0.258101	−	0.966118i	$-0.416903\pi$
$701$	361.857			0.516202			0.258101	+	0.966118i	$0.416903\pi$
$702$		0			0
$703$	603.540	−	348.454i	0.858520	−	0.495667i
$704$		0			0
$705$	86.4489	+	49.9113i	0.122623	+	0.0707962i
$706$		0			0
$707$	−701.141	+	161.180i	−0.991713	+	0.227977i
$708$		0			0
$709$	−93.3275	+	161.648i	−0.131633	+	0.227994i	−0.924306	−	0.381652i	$-0.875355\pi$
$709$	−93.3275	+	161.648i	−0.131633	+	0.227994i	0.792673	+	0.609646i	$0.208689\pi$
$710$		0			0
$711$	146.634	+	253.977i	0.206236	+	0.357211i
$712$		0			0
$713$		−	204.928i		−	0.287416i
$714$		0			0
$715$	415.825			0.581573
$716$		0			0
$717$	213.601	−	123.323i	0.297910	−	0.171998i
$718$		0			0
$719$	390.952	+	225.716i	0.543744	+	0.313931i	0.746595	−	0.665279i	$-0.231687\pi$
$719$	390.952	+	225.716i	0.543744	+	0.313931i	−0.202851	+	0.979210i	$0.565021\pi$
$720$		0			0
$721$	542.022	+	582.339i	0.751764	+	0.807683i
$722$		0			0
$723$	−327.326	+	566.945i	−0.452733	+	0.784156i
$724$		0			0
$725$	−400.165	−	693.107i	−0.551952	−	0.956009i
$726$		0			0
$727$		−	245.173i		−	0.337239i	−0.985681	−	0.168620i	$-0.946069\pi$
$727$		−	245.173i		−	0.337239i	0.985681	−	0.168620i	$-0.0539309\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−77.6093	+	44.8078i	−0.106169	+	0.0612965i
$732$		0			0
$733$	125.959	+	72.7222i	0.171840	+	0.0992117i	0.583453	−	0.812147i	$-0.301701\pi$
$733$	125.959	+	72.7222i	0.171840	+	0.0992117i	−0.411613	+	0.911359i	$0.635035\pi$
$734$		0			0
$735$	143.678	+	97.3044i	0.195481	+	0.132387i
$736$		0			0
$737$	−433.668	+	751.134i	−0.588423	+	1.01918i
$738$		0			0
$739$	−239.497	−	414.822i	−0.324083	−	0.561328i	0.657243	−	0.753678i	$-0.271722\pi$
$739$	−239.497	−	414.822i	−0.324083	−	0.561328i	−0.981326	+	0.192350i	$0.938389\pi$
$740$		0			0
$741$		−	371.434i		−	0.501261i
$742$		0			0
$743$	−717.987			−0.966335			−0.483167	−	0.875528i	$-0.660514\pi$
$743$	−717.987			−0.966335			−0.483167	+	0.875528i	$0.660514\pi$
$744$		0			0
$745$	−378.938	+	218.780i	−0.508642	+	0.293665i
$746$		0			0
$747$	−216.488	−	124.990i	−0.289810	−	0.167322i
$748$		0			0
$749$	−996.091	+	927.127i	−1.32989	+	1.23782i
$750$		0			0
$751$	96.6403	−	167.386i	0.128682	−	0.222884i	−0.794484	−	0.607285i	$-0.792259\pi$
$751$	96.6403	−	167.386i	0.128682	−	0.222884i	0.923166	+	0.384401i	$0.125592\pi$
$752$		0			0
$753$	66.0875	+	114.467i	0.0877656	+	0.152015i
$754$		0			0
$755$			539.539i			0.714621i
$756$		0			0
$757$	220.503			0.291285			0.145643	−	0.989337i	$-0.453475\pi$
$757$	220.503			0.291285			0.145643	+	0.989337i	$0.453475\pi$
$758$		0			0
$759$	494.281	−	285.373i	0.651226	−	0.375986i
$760$		0			0
$761$	1034.04	+	597.004i	1.35879	+	0.784500i	0.989461	−	0.144798i	$-0.0462532\pi$
$761$	1034.04	+	597.004i	1.35879	+	0.784500i	0.369332	+	0.929298i	$0.379587\pi$
$762$		0			0
$763$	202.017	+	878.787i	0.264767	+	1.15175i
$764$		0			0
$765$	19.8866	−	34.4445i	0.0259955	−	0.0450255i
$766$		0			0
$767$	601.713	+	1042.20i	0.784502	+	1.35880i
$768$		0			0
$769$			1394.14i			1.81293i	0.422279	+	0.906466i	$0.361230\pi$
$769$			1394.14i			1.81293i	−0.422279	+	0.906466i	$0.638770\pi$
$770$		0			0
$771$	−77.0390			−0.0999209
$772$		0			0
$773$	−5.10280	+	2.94610i	−0.00660129	+	0.00381126i	−0.503297	−	0.864113i	$-0.667880\pi$
$773$	−5.10280	+	2.94610i	−0.00660129	+	0.00381126i	0.496696	+	0.867925i	$0.334546\pi$
$774$		0			0
$775$	−137.589	−	79.4372i	−0.177535	−	0.102500i
$776$		0			0
$777$	−191.519	+	624.339i	−0.246485	+	0.803525i
$778$		0			0
$779$	41.7127	−	72.2485i	0.0535464	−	0.0927451i
$780$		0			0
$781$	−76.9964	−	133.362i	−0.0985869	−	0.170757i
$782$		0			0
$783$		−	199.747i		−	0.255104i
$784$		0			0
$785$	−54.1460			−0.0689758
$786$		0			0
$787$	−1231.26	+	710.870i	−1.56450	+	0.903265i	−0.567709	+	0.823229i	$0.692170\pi$
$787$	−1231.26	+	710.870i	−1.56450	+	0.903265i	−0.996792	+	0.0800358i	$0.974497\pi$
$788$		0			0
$789$	583.378	+	336.814i	0.739390	+	0.426887i
$790$		0			0
$791$	151.161	+	46.3694i	0.191101	+	0.0586212i
$792$		0			0
$793$	−205.666	+	356.225i	−0.259352	+	0.449211i
$794$		0			0
$795$	−121.864	−	211.074i	−0.153288	−	0.265502i
$796$		0			0
$797$		−	671.028i		−	0.841942i	−0.907074	−	0.420971i	$-0.861689\pi$
$797$		−	671.028i		−	0.841942i	0.907074	−	0.420971i	$-0.138311\pi$
$798$		0			0
$799$	182.774			0.228754
$800$		0			0
$801$	154.942	−	89.4557i	0.193435	−	0.111680i
$802$		0			0
$803$	1153.19	+	665.792i	1.43610	+	0.829131i
$804$		0			0
$805$	−374.580	+	86.1093i	−0.465317	+	0.106968i
$806$		0			0
$807$	−98.9666	+	171.415i	−0.122635	+	0.212410i
$808$		0			0
$809$	−348.851	−	604.228i	−0.431213	−	0.746882i	0.565765	−	0.824566i	$-0.308581\pi$
$809$	−348.851	−	604.228i	−0.431213	−	0.746882i	−0.996978	+	0.0776841i	$0.975247\pi$
$810$		0			0
$811$		−	1045.25i		−	1.28884i	−0.764671	−	0.644421i	$-0.777099\pi$
$811$		−	1045.25i		−	1.28884i	0.764671	−	0.644421i	$-0.222901\pi$
$812$		0			0
$813$	−711.934			−0.875687
$814$		0			0
$815$	−48.8375	+	28.1963i	−0.0599233	+	0.0345967i
$816$		0			0
$817$	−154.861	−	89.4089i	−0.189548	−	0.109436i
$818$		0			0
$819$	237.139	+	254.778i	0.289546	+	0.311084i
$820$		0			0
$821$	194.315	−	336.563i	0.236680	−	0.409942i	−0.723079	−	0.690765i	$-0.757274\pi$
$821$	194.315	−	336.563i	0.236680	−	0.409942i	0.959760	+	0.280823i	$0.0906072\pi$
$822$		0			0
$823$	127.219	+	220.351i	0.154580	+	0.267741i	0.932906	−	0.360120i	$-0.117264\pi$
$823$	127.219	+	220.351i	0.154580	+	0.267741i	−0.778326	+	0.627860i	$0.783931\pi$
$824$		0			0
$825$		−	442.482i		−	0.536342i
$826$		0			0
$827$	1009.61			1.22081			0.610406	−	0.792088i	$-0.291006\pi$
$827$	1009.61			1.22081			0.610406	+	0.792088i	$0.291006\pi$
$828$		0			0
$829$	−692.786	+	399.980i	−0.835689	+	0.482485i	−0.855797	−	0.517313i	$-0.826932\pi$
$829$	−692.786	+	399.980i	−0.835689	+	0.482485i	0.0201076	+	0.999798i	$0.493599\pi$
$830$		0			0
$831$	135.952	+	78.4922i	0.163601	+	0.0944551i
$832$		0			0
$833$	316.911	+	22.7571i	0.380445	+	0.0273194i
$834$		0			0
$835$	−116.090	+	201.073i	−0.139029	+	0.240806i
$836$		0			0
$837$	−19.8260	−	34.3396i	−0.0236869	−	0.0410270i
$838$		0			0
$839$			557.928i			0.664992i	0.943105	+	0.332496i	$0.107891\pi$
$839$			557.928i			0.664992i	−0.943105	+	0.332496i	$0.892109\pi$
$840$		0			0
$841$	636.731			0.757112
$842$		0			0
$843$	100.966	−	58.2926i	0.119770	−	0.0691490i
$844$		0			0
$845$	−187.176	−	108.066i	−0.221510	−	0.127889i
$846$		0			0
$847$	151.496	−	141.007i	0.178861	−	0.166478i
$848$		0			0
$849$	−223.431	+	386.994i	−0.263169	+	0.455823i
$850$		0			0
$851$	−723.233	−	1252.68i	−0.849863	−	1.47201i
$852$		0			0
$853$			1050.40i			1.23142i	0.787974	+	0.615709i	$0.211130\pi$
$853$			1050.40i			1.23142i	−0.787974	+	0.615709i	$0.788870\pi$
$854$		0			0
$855$	79.3628			0.0928220
$856$		0			0
$857$	−832.914	+	480.883i	−0.971895	+	0.561124i	−0.899813	−	0.436275i	$-0.856298\pi$
$857$	−832.914	+	480.883i	−0.971895	+	0.561124i	−0.0720816	+	0.997399i	$0.522964\pi$
$858$		0			0
$859$	−1398.37	−	807.348i	−1.62790	−	0.939870i	−0.984718	−	0.174159i	$-0.944279\pi$
$859$	−1398.37	−	807.348i	−1.62790	−	0.939870i	−0.643185	−	0.765711i	$-0.722387\pi$
$860$		0			0
$861$	17.5143	+	76.1884i	0.0203419	+	0.0884883i
$862$		0			0
$863$	589.299	−	1020.70i	0.682849	−	1.18273i	−0.291259	−	0.956644i	$-0.594074\pi$
$863$	589.299	−	1020.70i	0.682849	−	1.18273i	0.974108	−	0.226085i	$-0.0725927\pi$
$864$		0			0
$865$	−26.0100	−	45.0507i	−0.0300694	−	0.0520818i
$866$		0			0
$867$			427.738i			0.493355i
$868$		0			0
$869$	−1199.52			−1.38034
$870$		0			0
$871$	1014.59	−	585.773i	1.16485	−	0.672529i
$872$		0			0
$873$	383.753	+	221.560i	0.439580	+	0.253792i
$874$		0			0
$875$	−192.319	+	626.948i	−0.219794	+	0.716512i
$876$		0			0
$877$	266.040	−	460.794i	0.303352	−	0.525421i	−0.673541	−	0.739150i	$-0.735228\pi$
$877$	266.040	−	460.794i	0.303352	−	0.525421i	0.976893	+	0.213729i	$0.0685609\pi$
$878$		0			0
$879$	381.328	+	660.480i	0.433820	+	0.751399i
$880$		0			0
$881$			1103.22i			1.25224i	0.779729	+	0.626118i	$0.215357\pi$
$881$			1103.22i			1.25224i	−0.779729	+	0.626118i	$0.784643\pi$
$882$		0			0
$883$	213.506			0.241796			0.120898	−	0.992665i	$-0.461423\pi$
$883$	213.506			0.241796			0.120898	+	0.992665i	$0.461423\pi$
$884$		0			0
$885$	−222.682	+	128.566i	−0.251618	+	0.145272i
$886$		0			0
$887$	−1380.19	−	796.856i	−1.55603	−	0.898372i	−0.997631	−	0.0687962i	$-0.978084\pi$
$887$	−1380.19	−	796.856i	−1.55603	−	0.898372i	−0.558395	−	0.829575i	$-0.688582\pi$
$888$		0			0
$889$	−58.3698	−	17.9052i	−0.0656578	−	0.0201409i
$890$		0			0
$891$	55.2174	−	95.6394i	0.0619724	−	0.107339i
$892$		0			0
$893$	182.353	+	315.845i	0.204203	+	0.353689i
$894$		0			0
$895$		−	277.752i		−	0.310337i
$896$		0			0
$897$	−770.930			−0.859454
$898$		0			0
$899$	254.045	−	146.673i	0.282586	−	0.163151i
$900$		0			0
$901$	−386.475	−	223.131i	−0.428940	−	0.247648i
$902$		0			0
$903$	163.306	−	37.5411i	0.180848	−	0.0415738i
$904$		0			0
$905$	−242.685	+	420.343i	−0.268161	+	0.464468i
$906$		0			0
$907$	−865.834	−	1499.67i	−0.954613	−	1.65344i	−0.735252	−	0.677794i	$-0.762936\pi$
$907$	−865.834	−	1499.67i	−0.954613	−	1.65344i	−0.219360	−	0.975644i	$-0.570397\pi$
$908$		0			0
$909$		−	308.327i		−	0.339193i
$910$		0			0
$911$	−478.767			−0.525540			−0.262770	−	0.964858i	$-0.584636\pi$
$911$	−478.767			−0.525540			−0.262770	+	0.964858i	$0.584636\pi$
$912$		0			0
$913$	885.476	−	511.230i	0.969853	−	0.559945i
$914$		0			0
$915$	−76.1130	−	43.9439i	−0.0831836	−	0.0480261i
$916$		0			0
$917$	550.419	+	591.361i	0.600239	+	0.644887i
$918$		0			0
$919$	−795.127	+	1377.20i	−0.865209	+	1.49859i	0.00163103	+	0.999999i	$0.499481\pi$
$919$	−795.127	+	1377.20i	−0.865209	+	1.49859i	−0.866840	+	0.498587i	$0.833853\pi$
$920$		0			0
$921$	403.102	+	698.193i	0.437679	+	0.758082i
$922$		0			0
$923$			208.004i			0.225357i
$924$		0			0
$925$	−1121.40			−1.21233
$926$		0			0
$927$	−295.273	+	170.476i	−0.318525	+	0.183901i
$928$		0			0
$929$	−748.214	−	431.982i	−0.805397	−	0.464996i	0.0399577	−	0.999201i	$-0.487278\pi$
$929$	−748.214	−	431.982i	−0.805397	−	0.464996i	−0.845355	+	0.534205i	$0.820611\pi$
$930$		0			0
$931$	276.855	+	570.345i	0.297373	+	0.612615i
$932$		0			0
$933$	222.189	−	384.842i	0.238145	−	0.412478i
$934$		0			0
$935$	81.3396	+	140.884i	0.0869942	+	0.150678i
$936$		0			0
$937$			1187.54i			1.26739i	0.773584	+	0.633694i	$0.218462\pi$
$937$			1187.54i			1.26739i	−0.773584	+	0.633694i	$0.781538\pi$
$938$		0			0
$939$	170.262			0.181322
$940$		0			0
$941$	1140.58	−	658.512i	1.21209	−	0.699800i	0.248876	−	0.968535i	$-0.419939\pi$
$941$	1140.58	−	658.512i	1.21209	−	0.699800i	0.963214	+	0.268735i	$0.0866056\pi$
$942$		0			0
$943$	−149.955	−	86.5767i	−0.159019	−	0.0918099i
$944$		0			0
$945$	−54.4373	+	50.6684i	−0.0576056	+	0.0536174i
$946$		0			0
$947$	−217.972	+	377.539i	−0.230172	+	0.398669i	−0.957858	−	0.287241i	$-0.907262\pi$
$947$	−217.972	+	377.539i	−0.230172	+	0.398669i	0.727687	+	0.685909i	$0.240595\pi$
$948$		0			0
$949$	−899.313	−	1557.66i	−0.947643	−	1.64137i
$950$		0			0
$951$		−	505.226i		−	0.531258i
$952$		0			0
$953$	1318.53			1.38355			0.691777	−	0.722112i	$-0.256828\pi$
$953$	1318.53			1.38355			0.691777	+	0.722112i	$0.256828\pi$
$954$		0			0
$955$	375.483	−	216.785i	0.393175	−	0.227000i
$956$		0			0
$957$	707.543	+	408.500i	0.739334	+	0.426855i
$958$		0			0
$959$	−320.203	−	1392.90i	−0.333892	−	1.45245i
$960$		0			0
$961$	−451.384	+	781.820i	−0.469702	+	0.813548i
$962$		0			0
$963$	−291.599	−	505.064i	−0.302803	−	0.524469i
$964$		0			0
$965$			4.25134i			0.00440554i
$966$		0			0
$967$	706.981			0.731107			0.365554	−	0.930790i	$-0.380880\pi$
$967$	706.981			0.731107			0.365554	+	0.930790i	$0.380880\pi$
$968$		0			0
$969$	125.845	−	72.6564i	0.129870	−	0.0749808i
$970$		0			0
$971$	548.877	+	316.894i	0.565269	+	0.326358i	0.755258	−	0.655428i	$-0.227512\pi$
$971$	548.877	+	316.894i	0.565269	+	0.326358i	−0.189988	+	0.981786i	$0.560845\pi$
$972$		0			0
$973$	388.267	−	1265.73i	0.399042	−	1.30085i
$974$		0			0
$975$	−298.840	+	517.606i	−0.306502	+	0.530878i
$976$		0			0
$977$	664.402	+	1150.78i	0.680043	+	1.17787i	0.974967	+	0.222349i	$0.0713724\pi$
$977$	664.402	+	1150.78i	0.680043	+	1.17787i	−0.294924	+	0.955521i	$0.595294\pi$
$978$		0			0
$979$			731.780i			0.747477i
$980$		0			0
$981$	−386.446			−0.393931
$982$		0			0
$983$	−307.260	+	177.397i	−0.312574	+	0.180465i	−0.648078	−	0.761574i	$-0.724427\pi$
$983$	−307.260	+	177.397i	−0.312574	+	0.180465i	0.335504	+	0.942039i	$0.391094\pi$
$984$		0			0
$985$	−526.917	−	304.215i	−0.534941	−	0.308848i
$986$		0			0
$987$	−326.729	−	100.226i	−0.331033	−	0.101546i
$988$		0			0
$989$	−185.573	+	321.421i	−0.187637	+	0.324996i
$990$		0			0
$991$	286.950	+	497.011i	0.289556	+	0.501525i	0.973704	−	0.227818i	$-0.0731592\pi$
$991$	286.950	+	497.011i	0.289556	+	0.501525i	−0.684148	+	0.729343i	$0.739826\pi$
$992$		0			0
$993$		−	497.843i		−	0.501353i
$994$		0			0
$995$	−521.211			−0.523830
$996$		0			0
$997$	923.961	−	533.449i	0.926741	−	0.535054i	0.0409617	−	0.999161i	$-0.486958\pi$
$997$	923.961	−	533.449i	0.926741	−	0.535054i	0.885779	+	0.464106i	$0.153624\pi$
$998$		0			0
$999$	−242.383	−	139.940i	−0.242626	−	0.140080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bh.d.481.6	yes	16
4.3	odd	2		672.3.bh.b.481.6	✓	16
7.3	odd	6	inner	672.3.bh.d.577.6	yes	16
28.3	even	6		672.3.bh.b.577.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.3.bh.b.481.6	✓	16	4.3	odd	2
672.3.bh.b.577.6	yes	16	28.3	even	6
672.3.bh.d.481.6	yes	16	1.1	even	1	trivial
672.3.bh.d.577.6	yes	16	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(1.77068 + 1.02231i) q^{5} +(-6.69221 - 2.05287i) q^{7} +(1.50000 - 2.59808i) q^{9} +(6.13527 + 10.6266i) q^{11} -16.5743i q^{13} +3.54137 q^{15} +(5.61550 - 3.24211i) q^{17} +(11.2051 + 6.46927i) q^{19} +(-11.8162 + 2.71632i) q^{21} +(13.4273 - 23.2568i) q^{23} +(-10.4098 - 18.0303i) q^{25} -5.19615i q^{27} +38.4413 q^{29} +(6.60865 - 3.81551i) q^{31} +(18.4058 + 10.6266i) q^{33} +(-9.75114 - 10.4765i) q^{35} +(26.9315 - 46.6467i) q^{37} +(-14.3538 - 24.8615i) q^{39} -6.44781i q^{41} -13.8206 q^{43} +(5.31205 - 3.06692i) q^{45} +(24.4111 + 14.0938i) q^{47} +(40.5715 + 27.4765i) q^{49} +(5.61550 - 9.72633i) q^{51} +(-34.4114 - 59.6024i) q^{53} +25.0885i q^{55} +22.4102 q^{57} +(-62.8802 + 36.3039i) q^{59} +(-21.4925 - 12.4087i) q^{61} +(-15.3718 + 14.3076i) q^{63} +(16.9440 - 29.3479i) q^{65} +(35.3422 + 61.2144i) q^{67} -46.5135i q^{69} -12.5498 q^{71} +(93.9800 - 54.2594i) q^{73} +(-31.2294 - 18.0303i) q^{75} +(-19.2435 - 83.7104i) q^{77} +(-48.8779 + 84.6590i) q^{79} +(-4.50000 - 7.79423i) q^{81} -83.3264i q^{83} +13.2577 q^{85} +(57.6619 - 33.2911i) q^{87} +(51.6473 + 29.8186i) q^{89} +(-34.0249 + 110.919i) q^{91} +(6.60865 - 11.4465i) q^{93} +(13.2271 + 22.9101i) q^{95} +147.707i q^{97} +36.8116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{3} + 12 q^{7} + 24 q^{9} + 12 q^{11} + 48 q^{17} - 36 q^{19} + 24 q^{21} - 48 q^{23} + 20 q^{25} + 64 q^{29} + 60 q^{31} + 36 q^{33} - 36 q^{37} - 12 q^{39} - 72 q^{43} + 72 q^{47} - 40 q^{49}+ \cdots + 72 q^{99}+O(q^{100}) \) 16 * q + 24 * q^3 + 12 * q^7 + 24 * q^9 + 12 * q^11 + 48 * q^17 - 36 * q^19 + 24 * q^21 - 48 * q^23 + 20 * q^25 + 64 * q^29 + 60 * q^31 + 36 * q^33 - 36 * q^37 - 12 * q^39 - 72 * q^43 + 72 * q^47 - 40 * q^49 + 48 * q^51 + 56 * q^53 - 72 * q^57 + 36 * q^59 + 72 * q^61 + 36 * q^63 + 120 * q^65 - 12 * q^67 - 240 * q^71 + 156 * q^73 + 60 * q^75 + 224 * q^77 - 84 * q^79 - 72 * q^81 + 800 * q^85 + 96 * q^87 + 192 * q^89 - 300 * q^91 + 60 * q^93 + 48 * q^95 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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