LMFDB - Embedded newform 336.3.bh.e.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(145,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.3.bh.e.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-1.24264 + 0.717439i) q^{5} +(-1.74264 + 6.77962i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.24264 + 0.717439i) q^{5} +(-1.74264 + 6.77962i) q^{7} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{11} -21.3280i q^{13} +2.48528 q^{15} +(-7.75736 - 4.47871i) q^{17} +(6.25736 - 3.61269i) q^{19} +(8.48528 - 8.66025i) q^{21} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} -5.19615i q^{27} -33.9411 q^{29} +(-38.2279 - 22.0709i) q^{31} +(-9.00000 + 5.19615i) q^{33} +(-2.69848 - 9.67487i) q^{35} +(13.9853 + 24.2232i) q^{37} +(-18.4706 + 31.9920i) q^{39} -54.8313i q^{41} +1.48528 q^{43} +(-3.72792 - 2.15232i) q^{45} +(37.2426 - 21.5020i) q^{47} +(-42.9264 - 23.6289i) q^{49} +(7.75736 + 13.4361i) q^{51} +(42.7279 - 74.0069i) q^{53} +8.60927i q^{55} -12.5147 q^{57} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} +(-20.2279 + 5.64191i) q^{63} +(15.3015 + 26.5030i) q^{65} +(2.19848 - 3.80789i) q^{67} +64.8754i q^{69} -137.397 q^{71} +(68.3528 + 39.4635i) q^{73} +(34.4117 - 19.8676i) q^{75} +(30.0000 + 29.3939i) q^{77} +(49.1690 + 85.1633i) q^{79} +(-4.50000 + 7.79423i) q^{81} -110.401i q^{83} +12.8528 q^{85} +(50.9117 + 29.3939i) q^{87} +(-18.0000 + 10.3923i) q^{89} +(144.595 + 37.1670i) q^{91} +(38.2279 + 66.2127i) q^{93} +(-5.18377 + 8.97855i) q^{95} -10.9867i q^{97} +18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 12 * q^5 + 10 * q^7 + 6 * q^9	$ 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9} + 12 q^{11} - 24 q^{15} - 48 q^{17} + 42 q^{19} - 24 q^{23} + 22 q^{25} - 102 q^{31} - 36 q^{33} + 108 q^{35} + 22 q^{37} - 6 q^{39} - 28 q^{43} + 36 q^{45} + 132 q^{47} - 2 q^{49} + 48 q^{51} + 120 q^{53} - 84 q^{57} + 24 q^{59} - 72 q^{61} - 30 q^{63} + 180 q^{65} - 110 q^{67} - 312 q^{71} - 66 q^{73} - 66 q^{75} + 120 q^{77} + 10 q^{79} - 18 q^{81} - 288 q^{85} - 72 q^{89} + 222 q^{91} + 102 q^{93} + 132 q^{95} + 72 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 12 * q^5 + 10 * q^7 + 6 * q^9 + 12 * q^11 - 24 * q^15 - 48 * q^17 + 42 * q^19 - 24 * q^23 + 22 * q^25 - 102 * q^31 - 36 * q^33 + 108 * q^35 + 22 * q^37 - 6 * q^39 - 28 * q^43 + 36 * q^45 + 132 * q^47 - 2 * q^49 + 48 * q^51 + 120 * q^53 - 84 * q^57 + 24 * q^59 - 72 * q^61 - 30 * q^63 + 180 * q^65 - 110 * q^67 - 312 * q^71 - 66 * q^73 - 66 * q^75 + 120 * q^77 + 10 * q^79 - 18 * q^81 - 288 * q^85 - 72 * q^89 + 222 * q^91 + 102 * q^93 + 132 * q^95 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		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
$5$	−1.24264	+	0.717439i	−0.248528	+	0.143488i	−0.619090	−	0.785320i	$-0.712498\pi$
$5$	−1.24264	+	0.717439i	−0.248528	+	0.143488i	0.370562	+	0.928808i	$0.379165\pi$
$6$		0			0
$7$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$7$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	−	5.19615i	0.272727	−	0.472377i	−0.696832	−	0.717234i	$-0.745408\pi$
$11$	3.00000	−	5.19615i	0.272727	−	0.472377i	0.969559	+	0.244857i	$0.0787410\pi$
$12$		0			0
$13$		−	21.3280i		−	1.64061i	−0.571924	−	0.820306i	$-0.693803\pi$
$13$		−	21.3280i		−	1.64061i	0.571924	−	0.820306i	$-0.306197\pi$
$14$		0			0
$15$	2.48528			0.165685
$16$		0			0
$17$	−7.75736	−	4.47871i	−0.456315	−	0.263454i	0.254178	−	0.967157i	$-0.418195\pi$
$17$	−7.75736	−	4.47871i	−0.456315	−	0.263454i	−0.710494	+	0.703704i	$0.751528\pi$
$18$		0			0
$19$	6.25736	−	3.61269i	0.329335	−	0.190141i	−0.326211	−	0.945297i	$-0.605772\pi$
$19$	6.25736	−	3.61269i	0.329335	−	0.190141i	0.655546	+	0.755156i	$0.272439\pi$
$20$		0			0
$21$	8.48528	−	8.66025i	0.404061	−	0.412393i
$22$		0			0
$23$	−18.7279	−	32.4377i	−0.814257	−	1.41034i	−0.909860	−	0.414916i	$-0.863811\pi$
$23$	−18.7279	−	32.4377i	−0.814257	−	1.41034i	0.0956024	−	0.995420i	$-0.469522\pi$
$24$		0			0
$25$	−11.4706	+	19.8676i	−0.458823	+	0.794704i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−33.9411			−1.17038			−0.585192	−	0.810895i	$-0.698981\pi$
$29$	−33.9411			−1.17038			−0.585192	+	0.810895i	$0.698981\pi$
$30$		0			0
$31$	−38.2279	−	22.0709i	−1.23316	−	0.711965i	−0.265472	−	0.964119i	$-0.585528\pi$
$31$	−38.2279	−	22.0709i	−1.23316	−	0.711965i	−0.967687	+	0.252154i	$0.918861\pi$
$32$		0			0
$33$	−9.00000	+	5.19615i	−0.272727	+	0.157459i
$34$		0			0
$35$	−2.69848	−	9.67487i	−0.0770996	−	0.276425i
$36$		0			0
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	0.990768	−	0.135566i	$-0.0432853\pi$
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	−0.612788	+	0.790248i	$0.709952\pi$
$38$		0			0
$39$	−18.4706	+	31.9920i	−0.473604	+	0.820306i
$40$		0			0
$41$		−	54.8313i		−	1.33735i	−0.743556	−	0.668674i	$-0.766862\pi$
$41$		−	54.8313i		−	1.33735i	0.743556	−	0.668674i	$-0.233138\pi$
$42$		0			0
$43$	1.48528			0.0345414			0.0172707	−	0.999851i	$-0.494502\pi$
$43$	1.48528			0.0345414			0.0172707	+	0.999851i	$0.494502\pi$
$44$		0			0
$45$	−3.72792	−	2.15232i	−0.0828427	−	0.0478293i
$46$		0			0
$47$	37.2426	−	21.5020i	0.792397	−	0.457490i	−0.0484090	−	0.998828i	$-0.515415\pi$
$47$	37.2426	−	21.5020i	0.792397	−	0.457490i	0.840806	+	0.541337i	$0.182082\pi$
$48$		0			0
$49$	−42.9264	−	23.6289i	−0.876049	−	0.482222i
$50$		0			0
$51$	7.75736	+	13.4361i	0.152105	+	0.263454i
$52$		0			0
$53$	42.7279	−	74.0069i	0.806187	−	1.39636i	−0.109299	−	0.994009i	$-0.534861\pi$
$53$	42.7279	−	74.0069i	0.806187	−	1.39636i	0.915487	−	0.402348i	$-0.131806\pi$
$54$		0			0
$55$			8.60927i			0.156532i
$56$		0			0
$57$	−12.5147			−0.219556
$58$		0			0
$59$	35.6985	+	20.6105i	0.605059	+	0.349331i	0.771029	−	0.636800i	$-0.219742\pi$
$59$	35.6985	+	20.6105i	0.605059	+	0.349331i	−0.165970	+	0.986131i	$0.553076\pi$
$60$		0			0
$61$	−1.02944	+	0.594346i	−0.0168760	+	0.00974337i	−0.508414	−	0.861113i	$-0.669768\pi$
$61$	−1.02944	+	0.594346i	−0.0168760	+	0.00974337i	0.491538	+	0.870856i	$0.336435\pi$
$62$		0			0
$63$	−20.2279	+	5.64191i	−0.321078	+	0.0895542i
$64$		0			0
$65$	15.3015	+	26.5030i	0.235408	+	0.407738i
$66$		0			0
$67$	2.19848	−	3.80789i	0.0328132	−	0.0568341i	−0.849152	−	0.528148i	$-0.822887\pi$
$67$	2.19848	−	3.80789i	0.0328132	−	0.0568341i	0.881966	+	0.471314i	$0.156220\pi$
$68$		0			0
$69$			64.8754i			0.940224i
$70$		0			0
$71$	−137.397			−1.93517			−0.967584	−	0.252548i	$-0.918731\pi$
$71$	−137.397			−1.93517			−0.967584	+	0.252548i	$0.918731\pi$
$72$		0			0
$73$	68.3528	+	39.4635i	0.936340	+	0.540596i	0.888811	−	0.458274i	$-0.151532\pi$
$73$	68.3528	+	39.4635i	0.936340	+	0.540596i	0.0475288	+	0.998870i	$0.484865\pi$
$74$		0			0
$75$	34.4117	−	19.8676i	0.458823	−	0.264901i
$76$		0			0
$77$	30.0000	+	29.3939i	0.389610	+	0.381739i
$78$		0			0
$79$	49.1690	+	85.1633i	0.622393	+	1.07802i	0.989039	+	0.147656i	$0.0471728\pi$
$79$	49.1690	+	85.1633i	0.622393	+	1.07802i	−0.366646	+	0.930361i	$0.619494\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	110.401i		−	1.33013i	−0.746784	−	0.665067i	$-0.768403\pi$
$83$		−	110.401i		−	1.33013i	0.746784	−	0.665067i	$-0.231597\pi$
$84$		0			0
$85$	12.8528			0.151210
$86$		0			0
$87$	50.9117	+	29.3939i	0.585192	+	0.337861i
$88$		0			0
$89$	−18.0000	+	10.3923i	−0.202247	+	0.116767i	−0.597703	−	0.801717i	$-0.703920\pi$
$89$	−18.0000	+	10.3923i	−0.202247	+	0.116767i	0.395456	+	0.918485i	$0.370587\pi$
$90$		0			0
$91$	144.595	+	37.1670i	1.58896	+	0.408428i
$92$		0			0
$93$	38.2279	+	66.2127i	0.411053	+	0.711965i
$94$		0			0
$95$	−5.18377	+	8.97855i	−0.0545660	+	0.0945110i
$96$		0			0
$97$		−	10.9867i		−	0.113264i	−0.998395	−	0.0566322i	$-0.981964\pi$
$97$		−	10.9867i		−	0.113264i	0.998395	−	0.0566322i	$-0.0180362\pi$
$98$		0			0
$99$	18.0000			0.181818
$100$		0			0
$101$	−92.8234	−	53.5916i	−0.919043	−	0.530610i	−0.0357136	−	0.999362i	$-0.511370\pi$
$101$	−92.8234	−	53.5916i	−0.919043	−	0.530610i	−0.883330	+	0.468752i	$0.844704\pi$
$102$		0			0
$103$	−91.1102	+	52.6025i	−0.884565	+	0.510704i	−0.872161	−	0.489219i	$-0.837282\pi$
$103$	−91.1102	+	52.6025i	−0.884565	+	0.510704i	−0.0124040	+	0.999923i	$0.503948\pi$
$104$		0			0
$105$	−4.33095	+	16.8493i	−0.0412472	+	0.160469i
$106$		0			0
$107$	59.2721	+	102.662i	0.553945	+	0.959460i	0.997985	+	0.0634534i	$0.0202114\pi$
$107$	59.2721	+	102.662i	0.553945	+	0.959460i	−0.444040	+	0.896007i	$0.646455\pi$
$108$		0			0
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	0.490496	+	0.871444i	$0.336816\pi$
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	−0.999940	+	0.0109400i	$0.996518\pi$
$110$		0			0
$111$		−	48.4464i		−	0.436454i
$112$		0			0
$113$	101.397			0.897318			0.448659	−	0.893703i	$-0.351902\pi$
$113$	101.397			0.897318			0.448659	+	0.893703i	$0.351902\pi$
$114$		0			0
$115$	46.5442	+	26.8723i	0.404732	+	0.233672i
$116$		0			0
$117$	55.4117	−	31.9920i	0.473604	−	0.273435i
$118$		0			0
$119$	43.8823	−	44.7871i	0.368758	−	0.376362i
$120$		0			0
$121$	42.5000	+	73.6122i	0.351240	+	0.608365i
$122$		0			0
$123$	−47.4853	+	82.2469i	−0.386059	+	0.668674i
$124$		0			0
$125$		−	68.7897i		−	0.550317i
$126$		0			0
$127$	−82.5736			−0.650186			−0.325093	−	0.945682i	$-0.605396\pi$
$127$	−82.5736			−0.650186			−0.325093	+	0.945682i	$0.605396\pi$
$128$		0			0
$129$	−2.22792	−	1.28629i	−0.0172707	−	0.00997125i
$130$		0			0
$131$	52.4558	−	30.2854i	0.400426	−	0.231186i	−0.286242	−	0.958157i	$-0.592406\pi$
$131$	52.4558	−	30.2854i	0.400426	−	0.231186i	0.686668	+	0.726971i	$0.259073\pi$
$132$		0			0
$133$	13.5883	+	48.7181i	0.102168	+	0.366302i
$134$		0			0
$135$	3.72792	+	6.45695i	0.0276142	+	0.0478293i
$136$		0			0
$137$	−33.5147	+	58.0492i	−0.244633	+	0.423717i	−0.962028	−	0.272949i	$-0.912001\pi$
$137$	−33.5147	+	58.0492i	−0.244633	+	0.423717i	0.717395	+	0.696666i	$0.245334\pi$
$138$		0			0
$139$		−	91.5525i		−	0.658651i	−0.944216	−	0.329326i	$-0.893179\pi$
$139$		−	91.5525i		−	0.658651i	0.944216	−	0.329326i	$-0.106821\pi$
$140$		0			0
$141$	−74.4853			−0.528264
$142$		0			0
$143$	−110.823	−	63.9839i	−0.774989	−	0.447440i
$144$		0			0
$145$	42.1766	−	24.3507i	0.290873	−	0.167936i
$146$		0			0
$147$	43.9264	+	72.6187i	0.298819	+	0.494005i
$148$		0			0
$149$	−40.5442	−	70.2245i	−0.272108	−	0.471306i	0.697293	−	0.716786i	$-0.254388\pi$
$149$	−40.5442	−	70.2245i	−0.272108	−	0.471306i	−0.969402	+	0.245480i	$0.921054\pi$
$150$		0			0
$151$	−25.6030	+	44.3457i	−0.169556	+	0.293680i	−0.938264	−	0.345920i	$-0.887567\pi$
$151$	−25.6030	+	44.3457i	−0.169556	+	0.293680i	0.768708	+	0.639600i	$0.220900\pi$
$152$		0			0
$153$		−	26.8723i		−	0.175636i
$154$		0			0
$155$	63.3381			0.408633
$156$		0			0
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.917513	−	0.397705i	$-0.130193\pi$
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.114334	+	0.993442i	$0.463527\pi$
$158$		0			0
$159$	−128.184	+	74.0069i	−0.806187	+	0.465452i
$160$		0			0
$161$	252.551	−	70.4409i	1.56864	−	0.437521i
$162$		0			0
$163$	41.9706	+	72.6951i	0.257488	+	0.445982i	0.965568	−	0.260149i	$-0.0837718\pi$
$163$	41.9706	+	72.6951i	0.257488	+	0.445982i	−0.708080	+	0.706132i	$0.750439\pi$
$164$		0			0
$165$	7.45584	−	12.9139i	0.0451869	−	0.0782661i
$166$		0			0
$167$			127.620i			0.764190i	0.924123	+	0.382095i	$0.124797\pi$
$167$			127.620i			0.764190i	−0.924123	+	0.382095i	$0.875203\pi$
$168$		0			0
$169$	−285.882			−1.69161
$170$		0			0
$171$	18.7721	+	10.8381i	0.109778	+	0.0633805i
$172$		0			0
$173$	−123.816	+	71.4853i	−0.715701	+	0.413210i	−0.813168	−	0.582029i	$-0.802259\pi$
$173$	−123.816	+	71.4853i	−0.715701	+	0.413210i	0.0974675	+	0.995239i	$0.468926\pi$
$174$		0			0
$175$	−114.706	−	112.388i	−0.655461	−	0.642218i
$176$		0			0
$177$	−35.6985	−	61.8316i	−0.201686	−	0.349331i
$178$		0			0
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	−0.526670	−	0.850070i	$-0.676560\pi$
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	0.999517	+	0.0310748i	$0.00989300\pi$
$180$		0			0
$181$		−	209.969i		−	1.16005i	−0.814600	−	0.580024i	$-0.803043\pi$
$181$		−	209.969i		−	1.16005i	0.814600	−	0.580024i	$-0.196957\pi$
$182$		0			0
$183$	2.05887			0.0112507
$184$		0			0
$185$	−34.7574	−	20.0672i	−0.187878	−	0.108471i
$186$		0			0
$187$	−46.5442	+	26.8723i	−0.248899	+	0.143702i
$188$		0			0
$189$	35.2279	+	9.05503i	0.186391	+	0.0479102i
$190$		0			0
$191$	33.3015	+	57.6799i	0.174353	+	0.301989i	0.939937	−	0.341347i	$-0.110883\pi$
$191$	33.3015	+	57.6799i	0.174353	+	0.301989i	−0.765584	+	0.643336i	$0.777550\pi$
$192$		0			0
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	−0.853060	−	0.521813i	$-0.825256\pi$
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	0.878433	+	0.477865i	$0.158589\pi$
$194$		0			0
$195$		−	53.0060i		−	0.271826i
$196$		0			0
$197$	−267.161			−1.35615			−0.678075	−	0.734993i	$-0.737185\pi$
$197$	−267.161			−1.35615			−0.678075	+	0.734993i	$0.737185\pi$
$198$		0			0
$199$	113.397	+	65.4698i	0.569834	+	0.328994i	0.757083	−	0.653319i	$-0.226624\pi$
$199$	113.397	+	65.4698i	0.569834	+	0.328994i	−0.187249	+	0.982312i	$0.559957\pi$
$200$		0			0
$201$	−6.59545	+	3.80789i	−0.0328132	+	0.0189447i
$202$		0			0
$203$	59.1472	−	230.108i	0.291365	−	1.13354i
$204$		0			0
$205$	39.3381	+	68.1356i	0.191893	+	0.332369i
$206$		0			0
$207$	56.1838	−	97.3131i	0.271419	−	0.470112i
$208$		0			0
$209$		−	43.3523i		−	0.207427i
$210$		0			0
$211$	23.0883			0.109423			0.0547116	−	0.998502i	$-0.482576\pi$
$211$	23.0883			0.109423			0.0547116	+	0.998502i	$0.482576\pi$
$212$		0			0
$213$	206.095	+	118.989i	0.967584	+	0.558635i
$214$		0			0
$215$	−1.84567	+	1.06560i	−0.00858452	+	0.00495627i
$216$		0			0
$217$	216.250	−	220.709i	0.996543	−	1.01709i
$218$		0			0
$219$	−68.3528	−	118.391i	−0.312113	−	0.540596i
$220$		0			0
$221$	−95.5219	+	165.449i	−0.432226	+	0.748637i
$222$		0			0
$223$		−	228.631i		−	1.02525i	−0.858613	−	0.512625i	$-0.828673\pi$
$223$		−	228.631i		−	1.02525i	0.858613	−	0.512625i	$-0.171327\pi$
$224$		0			0
$225$	−68.8234			−0.305882
$226$		0			0
$227$	−56.8234	−	32.8070i	−0.250323	−	0.144524i	0.369589	−	0.929195i	$-0.379498\pi$
$227$	−56.8234	−	32.8070i	−0.250323	−	0.144524i	−0.619912	+	0.784671i	$0.712832\pi$
$228$		0			0
$229$	80.9558	−	46.7399i	0.353519	−	0.204104i	−0.312715	−	0.949847i	$-0.601239\pi$
$229$	80.9558	−	46.7399i	0.353519	−	0.204104i	0.666234	+	0.745743i	$0.267905\pi$
$230$		0			0
$231$	−19.5442	−	70.0716i	−0.0846067	−	0.303340i
$232$		0			0
$233$	118.757	+	205.694i	0.509688	+	0.882806i	0.999937	+	0.0112234i	$0.00357259\pi$
$233$	118.757	+	205.694i	0.509688	+	0.882806i	−0.490249	+	0.871583i	$0.663094\pi$
$234$		0			0
$235$	−30.8528	+	53.4386i	−0.131289	+	0.227398i
$236$		0			0
$237$		−	170.327i		−	0.718678i
$238$		0			0
$239$	−366.853			−1.53495			−0.767475	−	0.641079i	$-0.778487\pi$
$239$	−366.853			−1.53495			−0.767475	+	0.641079i	$0.778487\pi$
$240$		0			0
$241$	−364.617	−	210.512i	−1.51293	−	0.873493i	−0.999885	−	0.0151343i	$-0.995182\pi$
$241$	−364.617	−	210.512i	−1.51293	−	0.873493i	−0.513049	−	0.858359i	$-0.671484\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	70.2944	−	1.43488i	0.286916	−	0.00585664i
$246$		0			0
$247$	−77.0513	−	133.457i	−0.311949	−	0.540311i
$248$		0			0
$249$	−95.6102	+	165.602i	−0.383977	+	0.665067i
$250$		0			0
$251$			146.621i			0.584148i	0.956396	+	0.292074i	$0.0943454\pi$
$251$			146.621i			0.584148i	−0.956396	+	0.292074i	$0.905655\pi$
$252$		0			0
$253$	−224.735			−0.888281
$254$		0			0
$255$	−19.2792	−	11.1309i	−0.0756048	−	0.0436504i
$256$		0			0
$257$	21.7279	−	12.5446i	0.0845444	−	0.0488118i	−0.457132	−	0.889399i	$-0.651123\pi$
$257$	21.7279	−	12.5446i	0.0845444	−	0.0488118i	0.541676	+	0.840587i	$0.317790\pi$
$258$		0			0
$259$	−188.595	+	52.6025i	−0.728168	+	0.203098i
$260$		0			0
$261$	−50.9117	−	88.1816i	−0.195064	−	0.337861i
$262$		0			0
$263$	−45.3381	+	78.5279i	−0.172388	+	0.298585i	−0.939254	−	0.343222i	$-0.888482\pi$
$263$	−45.3381	+	78.5279i	−0.172388	+	0.298585i	0.766866	+	0.641807i	$0.221815\pi$
$264$		0			0
$265$			122.619i			0.462712i
$266$		0			0
$267$	36.0000			0.134831
$268$		0			0
$269$	−59.2355	−	34.1996i	−0.220206	−	0.127136i	0.385839	−	0.922566i	$-0.373912\pi$
$269$	−59.2355	−	34.1996i	−0.220206	−	0.127136i	−0.606046	+	0.795430i	$0.707245\pi$
$270$		0			0
$271$	106.971	−	61.7595i	0.394725	−	0.227895i	−0.289480	−	0.957184i	$-0.593482\pi$
$271$	106.971	−	61.7595i	0.394725	−	0.227895i	0.684206	+	0.729289i	$0.260149\pi$
$272$		0			0
$273$	−184.706	−	180.974i	−0.676577	−	0.662908i
$274$		0			0
$275$	68.8234	+	119.206i	0.250267	+	0.433475i
$276$		0			0
$277$	136.441	−	236.323i	0.492567	−	0.853151i	−0.507396	−	0.861713i	$-0.669392\pi$
$277$	136.441	−	236.323i	0.492567	−	0.853151i	0.999963	+	0.00856145i	$0.00272523\pi$
$278$		0			0
$279$		−	132.425i		−	0.474643i
$280$		0			0
$281$	133.103			0.473675			0.236837	−	0.971549i	$-0.423889\pi$
$281$	133.103			0.473675			0.236837	+	0.971549i	$0.423889\pi$
$282$		0			0
$283$	111.507	+	64.3787i	0.394018	+	0.227486i	0.683900	−	0.729576i	$-0.260283\pi$
$283$	111.507	+	64.3787i	0.394018	+	0.227486i	−0.289882	+	0.957063i	$0.593616\pi$
$284$		0			0
$285$	15.5513	−	8.97855i	0.0545660	−	0.0315037i
$286$		0			0
$287$	371.735	+	95.5512i	1.29524	+	0.332931i
$288$		0			0
$289$	−104.382	−	180.795i	−0.361184	−	0.625589i
$290$		0			0
$291$	−9.51472	+	16.4800i	−0.0326966	+	0.0566322i
$292$		0			0
$293$		−	308.984i		−	1.05455i	−0.849694	−	0.527276i	$-0.823213\pi$
$293$		−	308.984i		−	1.05455i	0.849694	−	0.527276i	$-0.176787\pi$
$294$		0			0
$295$	−59.1472			−0.200499
$296$		0			0
$297$	−27.0000	−	15.5885i	−0.0909091	−	0.0524864i
$298$		0			0
$299$	−691.831	+	399.429i	−2.31381	+	1.33588i
$300$		0			0
$301$	−2.58831	+	10.0696i	−0.00859904	+	0.0334539i
$302$		0			0
$303$	92.8234	+	160.775i	0.306348	+	0.530610i
$304$		0			0
$305$	0.852814	−	1.47712i	0.00279611	−	0.00484301i
$306$		0			0
$307$		−	606.090i		−	1.97423i	−0.160003	−	0.987117i	$-0.551150\pi$
$307$		−	606.090i		−	1.97423i	0.160003	−	0.987117i	$-0.448850\pi$
$308$		0			0
$309$	182.220			0.589710
$310$		0			0
$311$	176.044	+	101.639i	0.566057	+	0.326813i	0.755573	−	0.655064i	$-0.227359\pi$
$311$	176.044	+	101.639i	0.566057	+	0.326813i	−0.189516	+	0.981878i	$0.560692\pi$
$312$		0			0
$313$	−351.294	+	202.820i	−1.12234	+	0.647986i	−0.941999	−	0.335617i	$-0.891055\pi$
$313$	−351.294	+	202.820i	−1.12234	+	0.647986i	−0.180346	+	0.983603i	$0.557722\pi$
$314$		0			0
$315$	21.0883	−	21.5232i	0.0669470	−	0.0683275i
$316$		0			0
$317$	13.0294	+	22.5676i	0.0411023	+	0.0711913i	0.885845	−	0.463982i	$-0.153580\pi$
$317$	13.0294	+	22.5676i	0.0411023	+	0.0711913i	−0.844742	+	0.535173i	$0.820246\pi$
$318$		0			0
$319$	−101.823	+	176.363i	−0.319196	+	0.552863i
$320$		0			0
$321$		−	205.325i		−	0.639640i
$322$		0			0
$323$	−64.7208			−0.200374
$324$		0			0
$325$	423.735	+	244.644i	1.30380	+	0.752750i
$326$		0			0
$327$	166.588	−	96.1798i	0.509444	−	0.294128i
$328$		0			0
$329$	80.8751	+	289.961i	0.245821	+	0.881341i
$330$		0			0
$331$	−54.3162	−	94.0785i	−0.164097	−	0.284225i	0.772237	−	0.635335i	$-0.219138\pi$
$331$	−54.3162	−	94.0785i	−0.164097	−	0.284225i	−0.936334	+	0.351110i	$0.885804\pi$
$332$		0			0
$333$	−41.9558	+	72.6697i	−0.125994	+	0.218227i
$334$		0			0
$335$			6.30911i			0.0188332i
$336$		0			0
$337$	441.735			1.31079			0.655393	−	0.755288i	$-0.272503\pi$
$337$	441.735			1.31079			0.655393	+	0.755288i	$0.272503\pi$
$338$		0			0
$339$	−152.095	−	87.8124i	−0.448659	−	0.259033i
$340$		0			0
$341$	−229.368	+	132.425i	−0.672632	+	0.388344i
$342$		0			0
$343$	235.000	−	249.848i	0.685131	−	0.728420i
$344$		0			0
$345$	−46.5442	−	80.6168i	−0.134911	−	0.233672i
$346$		0			0
$347$	17.0955	−	29.6102i	0.0492664	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$347$	17.0955	−	29.6102i	0.0492664	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$348$		0			0
$349$			221.787i			0.635493i	0.948176	+	0.317746i	$0.102926\pi$
$349$			221.787i			0.635493i	−0.948176	+	0.317746i	$0.897074\pi$
$350$		0			0
$351$	−110.823			−0.315736
$352$		0			0
$353$	387.448	+	223.693i	1.09759	+	0.633692i	0.935586	−	0.353099i	$-0.114872\pi$
$353$	387.448	+	223.693i	1.09759	+	0.633692i	0.162000	+	0.986791i	$0.448206\pi$
$354$		0			0
$355$	170.735	−	98.5739i	0.480944	−	0.277673i
$356$		0			0
$357$	−104.610	+	29.1776i	−0.293026	+	0.0817299i
$358$		0			0
$359$	145.882	+	252.675i	0.406357	+	0.703831i	0.994478	−	0.104941i	$-0.0334655\pi$
$359$	145.882	+	252.675i	0.406357	+	0.703831i	−0.588121	+	0.808773i	$0.700132\pi$
$360$		0			0
$361$	−154.397	+	267.423i	−0.427692	+	0.740785i
$362$		0			0
$363$		−	147.224i		−	0.405577i
$364$		0			0
$365$	−113.251			−0.310276
$366$		0			0
$367$	363.169	+	209.676i	0.989561	+	0.571324i	0.905143	−	0.425107i	$-0.139763\pi$
$367$	363.169	+	209.676i	0.989561	+	0.571324i	0.0844183	+	0.996430i	$0.473097\pi$
$368$		0			0
$369$	142.456	−	82.2469i	0.386059	−	0.222891i
$370$		0			0
$371$	427.279	+	418.646i	1.15170	+	1.12843i
$372$		0			0
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	0.844225	−	0.535988i	$-0.180061\pi$
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	−0.886292	+	0.463127i	$0.846728\pi$
$374$		0			0
$375$	−59.5736	+	103.184i	−0.158863	+	0.275159i
$376$		0			0
$377$			723.895i			1.92015i
$378$		0			0
$379$	−206.779			−0.545590			−0.272795	−	0.962072i	$-0.587948\pi$
$379$	−206.779			−0.545590			−0.272795	+	0.962072i	$0.587948\pi$
$380$		0			0
$381$	123.860	+	71.5108i	0.325093	+	0.187692i
$382$		0			0
$383$	431.772	−	249.283i	1.12734	−	0.650871i	0.184076	−	0.982912i	$-0.441071\pi$
$383$	431.772	−	249.283i	1.12734	−	0.650871i	0.943265	+	0.332041i	$0.107737\pi$
$384$		0			0
$385$	−58.3675	−	15.0029i	−0.151604	−	0.0389685i
$386$		0			0
$387$	2.22792	+	3.85887i	0.00575690	+	0.00997125i
$388$		0			0
$389$	324.213	−	561.554i	0.833453	−	1.44358i	−0.0618308	−	0.998087i	$-0.519694\pi$
$389$	324.213	−	561.554i	0.833453	−	1.44358i	0.895284	−	0.445496i	$-0.146973\pi$
$390$		0			0
$391$			335.508i			0.858077i
$392$		0			0
$393$	−104.912			−0.266951
$394$		0			0
$395$	−122.199	−	70.5516i	−0.309364	−	0.178612i
$396$		0			0
$397$	65.6026	−	37.8757i	0.165246	−	0.0954047i	−0.415096	−	0.909777i	$-0.636252\pi$
$397$	65.6026	−	37.8757i	0.165246	−	0.0954047i	0.580342	+	0.814373i	$0.302919\pi$
$398$		0			0
$399$	21.8087	−	84.8450i	0.0546583	−	0.212644i
$400$		0			0
$401$	282.125	+	488.655i	0.703553	+	1.21859i	0.967211	+	0.253974i	$0.0817377\pi$
$401$	282.125	+	488.655i	0.703553	+	1.21859i	−0.263658	+	0.964616i	$0.584929\pi$
$402$		0			0
$403$	−470.727	+	815.324i	−1.16806	+	2.02314i
$404$		0			0
$405$		−	12.9139i		−	0.0318862i
$406$		0			0
$407$	167.823			0.412342
$408$		0			0
$409$	−309.559	−	178.724i	−0.756868	−	0.436978i	0.0713023	−	0.997455i	$-0.477284\pi$
$409$	−309.559	−	178.724i	−0.756868	−	0.436978i	−0.828170	+	0.560477i	$0.810618\pi$
$410$		0			0
$411$	100.544	−	58.0492i	0.244633	−	0.141239i
$412$		0			0
$413$	−201.941	+	206.105i	−0.488962	+	0.499044i
$414$		0			0
$415$	79.2061	+	137.189i	0.190858	+	0.330576i
$416$		0			0
$417$	−79.2868	+	137.329i	−0.190136	+	0.329326i
$418$		0			0
$419$			502.175i			1.19851i	0.800559	+	0.599254i	$0.204536\pi$
$419$			502.175i			1.19851i	−0.800559	+	0.599254i	$0.795464\pi$
$420$		0			0
$421$	33.7939			0.0802706			0.0401353	−	0.999194i	$-0.487221\pi$
$421$	33.7939			0.0802706			0.0401353	+	0.999194i	$0.487221\pi$
$422$		0			0
$423$	111.728	+	64.5061i	0.264132	+	0.152497i
$424$		0			0
$425$	177.963	−	102.747i	0.418735	−	0.241757i
$426$		0			0
$427$	−2.23550	−	8.01492i	−0.00523536	−	0.0187703i
$428$		0			0
$429$	110.823	+	191.952i	0.258330	+	0.447440i
$430$		0			0
$431$	251.860	−	436.234i	0.584362	−	1.01214i	−0.410593	−	0.911819i	$-0.634678\pi$
$431$	251.860	−	436.234i	0.584362	−	1.01214i	0.994955	−	0.100326i	$-0.0319884\pi$
$432$		0			0
$433$		−	837.548i		−	1.93429i	−0.254224	−	0.967145i	$-0.581820\pi$
$433$		−	837.548i		−	1.93429i	0.254224	−	0.967145i	$-0.418180\pi$
$434$		0			0
$435$	−84.3532			−0.193916
$436$		0			0
$437$	−234.375	−	135.316i	−0.536326	−	0.309648i
$438$		0			0
$439$	164.558	−	95.0079i	0.374848	−	0.216419i	−0.300726	−	0.953711i	$-0.597229\pi$
$439$	164.558	−	95.0079i	0.374848	−	0.216419i	0.675575	+	0.737292i	$0.263896\pi$
$440$		0			0
$441$	−3.00000	−	146.969i	−0.00680272	−	0.333264i
$442$		0			0
$443$	−84.7279	−	146.753i	−0.191259	−	0.331271i	0.754408	−	0.656405i	$-0.227924\pi$
$443$	−84.7279	−	146.753i	−0.191259	−	0.331271i	−0.945668	+	0.325134i	$0.894591\pi$
$444$		0			0
$445$	14.9117	−	25.8278i	0.0335094	−	0.0580400i
$446$		0			0
$447$			140.449i			0.314204i
$448$		0			0
$449$	18.1035			0.0403195			0.0201598	−	0.999797i	$-0.493583\pi$
$449$	18.1035			0.0403195			0.0201598	+	0.999797i	$0.493583\pi$
$450$		0			0
$451$	−284.912	−	164.494i	−0.631733	−	0.364731i
$452$		0			0
$453$	76.8091	−	44.3457i	0.169556	−	0.0978935i
$454$		0			0
$455$	−206.345	+	57.5532i	−0.453506	+	0.126491i
$456$		0			0
$457$	164.412	+	284.769i	0.359763	+	0.623128i	0.987921	−	0.154958i	$-0.0495242\pi$
$457$	164.412	+	284.769i	0.359763	+	0.623128i	−0.628158	+	0.778086i	$0.716191\pi$
$458$		0			0
$459$	−23.2721	+	40.3084i	−0.0507017	+	0.0878179i
$460$		0			0
$461$			794.331i			1.72306i	0.507706	+	0.861530i	$0.330494\pi$
$461$			794.331i			1.72306i	−0.507706	+	0.861530i	$0.669506\pi$
$462$		0			0
$463$	403.396			0.871266			0.435633	−	0.900124i	$-0.356525\pi$
$463$	403.396			0.871266			0.435633	+	0.900124i	$0.356525\pi$
$464$		0			0
$465$	−95.0071	−	54.8524i	−0.204316	−	0.117962i
$466$		0			0
$467$	2.44870	−	1.41376i	0.00524347	−	0.00302732i	−0.497376	−	0.867535i	$-0.665703\pi$
$467$	2.44870	−	1.41376i	0.00524347	−	0.00302732i	0.502619	+	0.864508i	$0.332370\pi$
$468$		0			0
$469$	21.9848	+	21.5407i	0.0468760	+	0.0459289i
$470$		0			0
$471$	−162.000	−	280.592i	−0.343949	−	0.595737i
$472$		0			0
$473$	4.45584	−	7.71775i	0.00942039	−	0.0163166i
$474$		0			0
$475$			165.758i			0.348965i
$476$		0			0
$477$	256.368			0.537458
$478$		0			0
$479$	−328.669	−	189.757i	−0.686157	−	0.396153i	0.116014	−	0.993248i	$-0.462988\pi$
$479$	−328.669	−	189.757i	−0.686157	−	0.396153i	−0.802171	+	0.597095i	$0.796322\pi$
$480$		0			0
$481$	516.632	−	298.278i	1.07408	−	0.620120i
$482$		0			0
$483$	−439.831	−	113.055i	−0.910622	−	0.234067i
$484$		0			0
$485$	7.88225	+	13.6525i	0.0162521	+	0.0281494i
$486$		0			0
$487$	287.757	−	498.410i	0.590877	−	1.02343i	−0.403238	−	0.915095i	$-0.632115\pi$
$487$	287.757	−	498.410i	0.590877	−	1.02343i	0.994115	−	0.108333i	$-0.0345513\pi$
$488$		0			0
$489$		−	145.390i		−	0.297322i
$490$		0			0
$491$	−238.441			−0.485623			−0.242811	−	0.970074i	$-0.578070\pi$
$491$	−238.441			−0.485623			−0.242811	+	0.970074i	$0.578070\pi$
$492$		0			0
$493$	263.294	+	152.013i	0.534064	+	0.308342i
$494$		0			0
$495$	−22.3675	+	12.9139i	−0.0451869	+	0.0260887i
$496$		0			0
$497$	239.434	−	931.499i	0.481758	−	1.87424i
$498$		0			0
$499$	−143.287	−	248.180i	−0.287148	−	0.497355i	0.685980	−	0.727620i	$-0.259374\pi$
$499$	−143.287	−	248.180i	−0.287148	−	0.497355i	−0.973128	+	0.230266i	$0.926040\pi$
$500$		0			0
$501$	110.522	−	191.429i	0.220603	−	0.382095i
$502$		0			0
$503$			25.4374i			0.0505714i	0.999680	+	0.0252857i	$0.00804954\pi$
$503$			25.4374i			0.0505714i	−0.999680	+	0.0252857i	$0.991950\pi$
$504$		0			0
$505$	153.795			0.304544
$506$		0			0
$507$	428.823	+	247.581i	0.845805	+	0.488326i
$508$		0			0
$509$	−697.889	+	402.926i	−1.37110	+	0.791603i	−0.991066	−	0.133370i	$-0.957420\pi$
$509$	−697.889	+	402.926i	−1.37110	+	0.791603i	−0.380031	+	0.924974i	$0.624087\pi$
$510$		0			0
$511$	−386.662	+	394.635i	−0.756677	+	0.772280i
$512$		0			0
$513$	−18.7721	−	32.5142i	−0.0365927	−	0.0633805i
$514$		0			0
$515$	75.4781	−	130.732i	0.146559	−	0.253848i
$516$		0			0
$517$		−	258.025i		−	0.499080i
$518$		0			0
$519$	247.632			0.477134
$520$		0			0
$521$	−661.706	−	382.036i	−1.27007	−	0.733274i	−0.295068	−	0.955476i	$-0.595342\pi$
$521$	−661.706	−	382.036i	−1.27007	−	0.733274i	−0.975001	+	0.222202i	$0.928676\pi$
$522$		0			0
$523$	153.096	−	88.3900i	0.292726	−	0.169006i	−0.346444	−	0.938071i	$-0.612611\pi$
$523$	153.096	−	88.3900i	0.292726	−	0.169006i	0.639171	+	0.769065i	$0.279278\pi$
$524$		0			0
$525$	74.7275	+	267.920i	0.142338	+	0.510324i
$526$		0			0
$527$	197.698	+	342.424i	0.375139	+	0.649761i
$528$		0			0
$529$	−436.970	+	756.854i	−0.826030	+	1.43073i
$530$		0			0
$531$			123.663i			0.232887i
$532$		0			0
$533$	−1169.44			−2.19407
$534$		0			0
$535$	−147.308	−	85.0482i	−0.275342	−	0.158969i
$536$		0			0
$537$	−253.919	+	146.600i	−0.472847	+	0.272998i
$538$		0			0
$539$	−251.558	+	152.166i	−0.466713	+	0.282311i
$540$		0			0
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	0.857979	−	0.513685i	$-0.171720\pi$
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	−0.873854	+	0.486189i	$0.838387\pi$
$542$		0			0
$543$	−181.838	+	314.953i	−0.334877	+	0.580024i
$544$		0			0
$545$		−	159.356i		−	0.292396i
$546$		0			0
$547$	−212.676			−0.388805			−0.194402	−	0.980922i	$-0.562277\pi$
$547$	−212.676			−0.388805			−0.194402	+	0.980922i	$0.562277\pi$
$548$		0			0
$549$	−3.08831	−	1.78304i	−0.00562534	−	0.00324779i
$550$		0			0
$551$	−212.382	+	122.619i	−0.385448	+	0.222538i
$552$		0			0
$553$	−663.058	+	184.938i	−1.19902	+	0.334427i
$554$		0			0
$555$	34.7574	+	60.2015i	0.0626259	+	0.108471i
$556$		0			0
$557$	440.823	−	763.528i	0.791424	−	1.37079i	−0.133661	−	0.991027i	$-0.542673\pi$
$557$	440.823	−	763.528i	0.791424	−	1.37079i	0.925085	−	0.379760i	$-0.123993\pi$
$558$		0			0
$559$		−	31.6780i		−	0.0566691i
$560$		0			0
$561$	93.0883			0.165933
$562$		0			0
$563$	−664.301	−	383.534i	−1.17993	−	0.681233i	−0.223932	−	0.974605i	$-0.571889\pi$
$563$	−664.301	−	383.534i	−1.17993	−	0.681233i	−0.955998	+	0.293372i	$0.905223\pi$
$564$		0			0
$565$	−126.000	+	72.7461i	−0.223009	+	0.128754i
$566$		0			0
$567$	−45.0000	−	44.0908i	−0.0793651	−	0.0777616i
$568$		0			0
$569$	14.6468	+	25.3689i	0.0257412	+	0.0445851i	0.878609	−	0.477542i	$-0.158472\pi$
$569$	14.6468	+	25.3689i	0.0257412	+	0.0445851i	−0.852868	+	0.522127i	$0.825139\pi$
$570$		0			0
$571$	482.521	−	835.752i	0.845046	−	1.46366i	−0.0405347	−	0.999178i	$-0.512906\pi$
$571$	482.521	−	835.752i	0.845046	−	1.46366i	0.885581	−	0.464485i	$-0.153761\pi$
$572$		0			0
$573$		−	115.360i		−	0.201326i
$574$		0			0
$575$	859.279			1.49440
$576$		0			0
$577$	227.883	+	131.568i	0.394944	+	0.228021i	0.684300	−	0.729201i	$-0.260108\pi$
$577$	227.883	+	131.568i	0.394944	+	0.228021i	−0.289356	+	0.957222i	$0.593441\pi$
$578$		0			0
$579$	−14.6909	+	8.48180i	−0.0253729	+	0.0146491i
$580$		0			0
$581$	748.477	+	192.389i	1.28826	+	0.331135i
$582$		0			0
$583$	−256.368	−	444.042i	−0.439738	−	0.761649i
$584$		0			0
$585$	−45.9045	+	79.5090i	−0.0784693	+	0.135913i
$586$		0			0
$587$		−	436.477i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$587$		−	436.477i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$588$		0			0
$589$	−318.941			−0.541496
$590$		0			0
$591$	400.742	+	231.369i	0.678075	+	0.391487i
$592$		0			0
$593$	603.603	−	348.490i	1.01788	−	0.587673i	0.104391	−	0.994536i	$-0.466711\pi$
$593$	603.603	−	348.490i	1.01788	−	0.587673i	0.913489	+	0.406863i	$0.133377\pi$
$594$		0			0
$595$	−22.3978	+	87.1372i	−0.0376434	+	0.146449i
$596$		0			0
$597$	−113.397	−	196.409i	−0.189945	−	0.328994i
$598$		0			0
$599$	199.206	−	345.035i	0.332564	−	0.576018i	−0.650450	−	0.759549i	$-0.725419\pi$
$599$	199.206	−	345.035i	0.332564	−	0.576018i	0.983014	+	0.183531i	$0.0587528\pi$
$600$		0			0
$601$			36.1691i			0.0601816i	0.999547	+	0.0300908i	$0.00957964\pi$
$601$			36.1691i			0.0601816i	−0.999547	+	0.0300908i	$0.990420\pi$
$602$		0			0
$603$	13.1909			0.0218755
$604$		0			0
$605$	−105.624	−	60.9823i	−0.174586	−	0.100797i
$606$		0			0
$607$	−27.3457	+	15.7880i	−0.0450505	+	0.0260099i	−0.522356	−	0.852727i	$-0.674947\pi$
$607$	−27.3457	+	15.7880i	−0.0450505	+	0.0260099i	0.477306	+	0.878737i	$0.341613\pi$
$608$		0			0
$609$	−288.000	+	293.939i	−0.472906	+	0.482658i
$610$		0			0
$611$	−458.595	−	794.310i	−0.750565	−	1.30002i
$612$		0			0
$613$	204.632	−	354.434i	0.333821	−	0.578195i	−0.649436	−	0.760416i	$-0.724995\pi$
$613$	204.632	−	354.434i	0.333821	−	0.578195i	0.983258	+	0.182220i	$0.0583285\pi$
$614$		0			0
$615$		−	136.271i		−	0.221579i
$616$		0			0
$617$	1227.38			1.98927			0.994636	−	0.103436i	$-0.0329837\pi$
$617$	1227.38			1.98927			0.994636	+	0.103436i	$0.0329837\pi$
$618$		0			0
$619$	−412.022	−	237.881i	−0.665625	−	0.384299i	0.128792	−	0.991672i	$-0.458890\pi$
$619$	−412.022	−	237.881i	−0.665625	−	0.384299i	−0.794417	+	0.607373i	$0.792223\pi$
$620$		0			0
$621$	−168.551	+	97.3131i	−0.271419	+	0.156704i
$622$		0			0
$623$	−39.0883	−	140.143i	−0.0627421	−	0.224949i
$624$		0			0
$625$	−237.412	−	411.209i	−0.379859	−	0.657935i
$626$		0			0
$627$	−37.5442	+	65.0284i	−0.0598790	+	0.103714i
$628$		0			0
$629$		−	250.544i		−	0.398322i
$630$		0			0
$631$	54.9420			0.0870713			0.0435357	−	0.999052i	$-0.486138\pi$
$631$	54.9420			0.0870713			0.0435357	+	0.999052i	$0.486138\pi$
$632$		0			0
$633$	−34.6325	−	19.9951i	−0.0547116	−	0.0315878i
$634$		0			0
$635$	102.609	−	59.2415i	0.161589	−	0.0932937i
$636$		0			0
$637$	−503.956	+	915.533i	−0.791139	+	1.43726i
$638$		0			0
$639$	−206.095	−	356.968i	−0.322528	−	0.558635i
$640$		0			0
$641$	114.551	−	198.409i	0.178707	−	0.309530i	−0.762731	−	0.646716i	$-0.776142\pi$
$641$	114.551	−	198.409i	0.178707	−	0.309530i	0.941438	+	0.337186i	$0.109475\pi$
$642$		0			0
$643$			854.640i			1.32914i	0.747224	+	0.664572i	$0.231386\pi$
$643$			854.640i			1.32914i	−0.747224	+	0.664572i	$0.768614\pi$
$644$		0			0
$645$	3.69134			0.00572301
$646$		0			0
$647$	−868.632	−	501.505i	−1.34255	−	0.775124i	−0.355372	−	0.934725i	$-0.615646\pi$
$647$	−868.632	−	501.505i	−1.34255	−	0.775124i	−0.987182	+	0.159601i	$0.948979\pi$
$648$		0			0
$649$	214.191	−	123.663i	0.330032	−	0.190544i
$650$		0			0
$651$	−515.514	+	143.786i	−0.791881	+	0.220869i
$652$		0			0
$653$	−635.382	−	1100.51i	−0.973020	−	1.68532i	−0.686321	−	0.727299i	$-0.740776\pi$
$653$	−635.382	−	1100.51i	−0.973020	−	1.68532i	−0.286698	−	0.958021i	$-0.592558\pi$
$654$		0			0
$655$	−43.4558	+	75.2677i	−0.0663448	+	0.114913i
$656$		0			0
$657$			236.781i			0.360397i
$658$		0			0
$659$	783.308			1.18863			0.594315	−	0.804232i	$-0.297423\pi$
$659$	783.308			1.18863			0.594315	+	0.804232i	$0.297423\pi$
$660$		0			0
$661$	72.5589	+	41.8919i	0.109771	+	0.0633765i	0.553881	−	0.832596i	$-0.313146\pi$
$661$	72.5589	+	41.8919i	0.109771	+	0.0633765i	−0.444109	+	0.895973i	$0.646480\pi$
$662$		0			0
$663$	286.566	−	165.449i	0.432226	−	0.249546i
$664$		0			0
$665$	−51.8377	−	50.7903i	−0.0779514	−	0.0763764i
$666$		0			0
$667$	635.647	+	1100.97i	0.952994	+	1.65063i
$668$		0			0
$669$	−198.000	+	342.946i	−0.295964	+	0.512625i
$670$		0			0
$671$			7.13215i			0.0106291i
$672$		0			0
$673$	415.676			0.617647			0.308823	−	0.951119i	$-0.400065\pi$
$673$	415.676			0.617647			0.308823	+	0.951119i	$0.400065\pi$
$674$		0			0
$675$	103.235	+	59.6028i	0.152941	+	0.0883004i
$676$		0			0
$677$	685.279	−	395.646i	1.01223	−	0.584411i	0.100386	−	0.994949i	$-0.467992\pi$
$677$	685.279	−	395.646i	1.01223	−	0.584411i	0.911844	+	0.410538i	$0.134659\pi$
$678$		0			0
$679$	74.4853	+	19.1458i	0.109698	+	0.0281970i
$680$		0			0
$681$	56.8234	+	98.4210i	0.0834411	+	0.144524i
$682$		0			0
$683$	−164.080	+	284.195i	−0.240235	+	0.416099i	−0.960781	−	0.277308i	$-0.910558\pi$
$683$	−164.080	+	284.195i	−0.240235	+	0.416099i	0.720546	+	0.693407i	$0.243891\pi$
$684$		0			0
$685$		−	96.1791i		−	0.140407i
$686$		0			0
$687$	−161.912			−0.235679
$688$		0			0
$689$	−1578.42	−	911.300i	−2.29088	−	1.32264i
$690$		0			0
$691$	−875.182	+	505.287i	−1.26654	+	0.731240i	−0.974333	−	0.225113i	$-0.927725\pi$
$691$	−875.182	+	505.287i	−1.26654	+	0.731240i	−0.292212	+	0.956353i	$0.594391\pi$
$692$		0			0
$693$	−31.3675	+	122.033i	−0.0452634	+	0.176094i
$694$		0			0
$695$	65.6833	+	113.767i	0.0945084	+	0.163693i
$696$		0			0
$697$	−245.574	+	425.346i	−0.352329	+	0.610252i
$698$		0			0
$699$		−	411.388i		−	0.588537i
$700$		0			0
$701$	−0.103464			−0.000147594			−7.37972e−5	−	1.00000i	$-0.500023\pi$
$701$	−0.103464			−0.000147594			−7.37972e−5		1.00000i	$0.500023\pi$
$702$		0			0
$703$	175.022	+	101.049i	0.248964	+	0.143740i
$704$		0			0
$705$	92.5584	−	53.4386i	0.131289	−	0.0757995i
$706$		0			0
$707$	525.088	−	535.916i	0.742699	−	0.758014i
$708$		0			0
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	−0.881286	−	0.472584i	$-0.843321\pi$
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	0.0313734	−	0.999508i	$-0.490012\pi$
$710$		0			0
$711$	−147.507	+	255.490i	−0.207464	+	0.359339i
$712$		0			0
$713$			1653.37i			2.31889i
$714$		0			0
$715$	183.618			0.256809
$716$		0			0
$717$	550.279	+	317.704i	0.767475	+	0.443102i
$718$		0			0
$719$	−850.925	+	491.282i	−1.18348	+	0.683285i	−0.956818	−	0.290688i	$-0.906116\pi$
$719$	−850.925	+	491.282i	−1.18348	+	0.683285i	−0.226666	+	0.973973i	$0.572783\pi$
$720$		0			0
$721$	−197.852	−	709.359i	−0.274414	−	0.983855i
$722$		0			0
$723$	364.617	+	631.536i	0.504312	+	0.873493i
$724$		0			0
$725$	389.324	−	674.329i	0.536998	−	0.930108i
$726$		0			0
$727$			630.440i			0.867181i	0.901110	+	0.433590i	$0.142753\pi$
$727$			630.440i			0.867181i	−0.901110	+	0.433590i	$0.857247\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−11.5219	−	6.65215i	−0.0157618	−	0.00910007i
$732$		0			0
$733$	258.486	−	149.237i	0.352641	−	0.203597i	−0.313207	−	0.949685i	$-0.601403\pi$
$733$	258.486	−	149.237i	0.352641	−	0.203597i	0.665848	+	0.746088i	$0.268070\pi$
$734$		0			0
$735$	−106.684	−	58.7244i	−0.145149	−	0.0798971i
$736$		0			0
$737$	−13.1909	−	22.8473i	−0.0178981	−	0.0310004i
$738$		0			0
$739$	172.684	−	299.097i	0.233672	−	0.404732i	−0.725214	−	0.688524i	$-0.758259\pi$
$739$	172.684	−	299.097i	0.233672	−	0.404732i	0.958886	+	0.283792i	$0.0915924\pi$
$740$		0			0
$741$			266.914i			0.360207i
$742$		0			0
$743$	−683.616			−0.920076			−0.460038	−	0.887899i	$-0.652164\pi$
$743$	−683.616			−0.920076			−0.460038	+	0.887899i	$0.652164\pi$
$744$		0			0
$745$	100.764	+	58.1759i	0.135253	+	0.0780885i
$746$		0			0
$747$	286.831	−	165.602i	0.383977	−	0.221689i
$748$		0			0
$749$	−799.301	+	222.939i	−1.06716	+	0.297648i
$750$		0			0
$751$	−289.169	−	500.855i	−0.385045	−	0.666918i	0.606730	−	0.794908i	$-0.292481\pi$
$751$	−289.169	−	500.855i	−0.385045	−	0.666918i	−0.991775	+	0.127990i	$0.959148\pi$
$752$		0			0
$753$	126.978	−	219.932i	0.168629	−	0.292074i
$754$		0			0
$755$		−	73.4744i		−	0.0973171i
$756$		0			0
$757$	1204.82			1.59158			0.795788	−	0.605576i	$-0.207057\pi$
$757$	1204.82			1.59158			0.795788	+	0.605576i	$0.207057\pi$
$758$		0			0
$759$	337.103	+	194.626i	0.444140	+	0.256425i
$760$		0			0
$761$	−202.669	+	117.011i	−0.266319	+	0.153760i	−0.627214	−	0.778847i	$-0.715805\pi$
$761$	−202.669	+	117.011i	−0.266319	+	0.153760i	0.360894	+	0.932607i	$0.382471\pi$
$762$		0			0
$763$	−555.294	−	544.075i	−0.727778	−	0.713074i
$764$		0			0
$765$	19.2792	+	33.3926i	0.0252016	+	0.0436504i
$766$		0			0
$767$	439.581	−	761.376i	0.573117	−	0.992668i
$768$		0			0
$769$			1290.16i			1.67771i	0.544358	+	0.838853i	$0.316774\pi$
$769$			1290.16i			1.67771i	−0.544358	+	0.838853i	$0.683226\pi$
$770$		0			0
$771$	−43.4558			−0.0563630
$772$		0			0
$773$	345.646	+	199.559i	0.447149	+	0.258161i	0.706625	−	0.707588i	$-0.250217\pi$
$773$	345.646	+	199.559i	0.447149	+	0.258161i	−0.259477	+	0.965749i	$0.583550\pi$
$774$		0			0
$775$	876.992	−	506.331i	1.13160	−	0.653331i
$776$		0			0
$777$	328.448	+	84.4247i	0.422713	+	0.108655i
$778$		0			0
$779$	−198.088	−	343.099i	−0.254285	−	0.440435i
$780$		0			0
$781$	−412.191	+	713.936i	−0.527773	+	0.914130i
$782$		0			0
$783$			176.363i			0.225240i
$784$		0			0
$785$	−268.410			−0.341924
$786$		0			0
$787$	1348.16	+	778.361i	1.71304	+	0.989023i	0.930401	+	0.366544i	$0.119459\pi$
$787$	1348.16	+	778.361i	1.71304	+	0.989023i	0.782637	+	0.622478i	$0.213874\pi$
$788$		0			0
$789$	136.014	−	78.5279i	0.172388	−	0.0995284i
$790$		0			0
$791$	−176.698	+	687.433i	−0.223386	+	0.869068i
$792$		0			0
$793$	12.6762	+	21.9558i	0.0159851	+	0.0276870i
$794$		0			0
$795$	106.191	−	183.928i	0.133573	−	0.231356i
$796$		0			0
$797$			600.232i			0.753114i	0.926393	+	0.376557i	$0.122892\pi$
$797$			600.232i			0.753114i	−0.926393	+	0.376557i	$0.877108\pi$
$798$		0			0
$799$	−385.206			−0.482110
$800$		0			0
$801$	−54.0000	−	31.1769i	−0.0674157	−	0.0389225i
$802$		0			0
$803$	410.117	−	236.781i	0.510731	−	0.294871i
$804$		0			0
$805$	−263.294	+	268.723i	−0.327073	+	0.333817i
$806$		0			0
$807$	59.2355	+	102.599i	0.0734021	+	0.127136i
$808$		0			0
$809$	114.640	−	198.562i	0.141705	−	0.245441i	−0.786434	−	0.617675i	$-0.788075\pi$
$809$	114.640	−	198.562i	0.141705	−	0.245441i	0.928139	+	0.372234i	$0.121408\pi$
$810$		0			0
$811$		−	529.955i		−	0.653459i	−0.945118	−	0.326729i	$-0.894053\pi$
$811$		−	529.955i		−	0.653459i	0.945118	−	0.326729i	$-0.105947\pi$
$812$		0			0
$813$	−213.941			−0.263150
$814$		0			0
$815$	−104.309	−	60.2226i	−0.127986	−	0.0738928i
$816$		0			0
$817$	9.29394	−	5.36586i	0.0113757	−	0.00656776i
$818$		0			0
$819$	120.331	+	431.420i	0.146924	+	0.526765i
$820$		0			0
$821$	151.669	+	262.698i	0.184737	+	0.319974i	0.943488	−	0.331407i	$-0.107523\pi$
$821$	151.669	+	262.698i	0.184737	+	0.319974i	−0.758751	+	0.651381i	$0.774190\pi$
$822$		0			0
$823$	−564.955	+	978.531i	−0.686459	+	1.18898i	0.286517	+	0.958075i	$0.407502\pi$
$823$	−564.955	+	978.531i	−0.686459	+	1.18898i	−0.972976	+	0.230906i	$0.925831\pi$
$824$		0			0
$825$		−	238.411i		−	0.288983i
$826$		0			0
$827$	161.604			0.195410			0.0977049	−	0.995215i	$-0.468850\pi$
$827$	161.604			0.195410			0.0977049	+	0.995215i	$0.468850\pi$
$828$		0			0
$829$	1325.32	+	765.175i	1.59870	+	0.923010i	0.991738	+	0.128279i	$0.0409454\pi$
$829$	1325.32	+	765.175i	1.59870	+	0.923010i	0.606962	+	0.794731i	$0.292388\pi$
$830$		0			0
$831$	−409.323	+	236.323i	−0.492567	+	0.284384i
$832$		0			0
$833$	227.169	+	375.553i	0.272711	+	0.450844i
$834$		0			0
$835$	−91.5593	−	158.585i	−0.109652	−	0.189923i
$836$		0			0
$837$	−114.684	+	198.638i	−0.137018	+	0.237322i
$838$		0			0
$839$			218.629i			0.260583i	0.991476	+	0.130291i	$0.0415913\pi$
$839$			218.629i			0.260583i	−0.991476	+	0.130291i	$0.958409\pi$
$840$		0			0
$841$	311.000			0.369798
$842$		0			0
$843$	−199.654	−	115.270i	−0.236837	−	0.136738i
$844$		0			0
$845$	355.249	−	205.103i	0.420413	−	0.242726i
$846$		0			0
$847$	−573.124	+	159.854i	−0.676652	+	0.188730i
$848$		0			0
$849$	−111.507	−	193.136i	−0.131339	−	0.227486i
$850$		0			0
$851$	523.831	−	907.301i	0.615547	−	1.06616i
$852$		0			0
$853$			762.730i			0.894174i	0.894491	+	0.447087i	$0.147539\pi$
$853$			762.730i			0.894174i	−0.894491	+	0.447087i	$0.852461\pi$
$854$		0			0
$855$	−31.1026			−0.0363773
$856$		0			0
$857$	−795.015	−	459.002i	−0.927672	−	0.535592i	−0.0415977	−	0.999134i	$-0.513245\pi$
$857$	−795.015	−	459.002i	−0.927672	−	0.535592i	−0.886075	+	0.463543i	$0.846578\pi$
$858$		0			0
$859$	761.367	−	439.575i	0.886341	−	0.511729i	0.0135969	−	0.999908i	$-0.495672\pi$
$859$	761.367	−	439.575i	0.886341	−	0.511729i	0.872744	+	0.488179i	$0.162339\pi$
$860$		0			0
$861$	−474.853	−	465.259i	−0.551513	−	0.540370i
$862$		0			0
$863$	175.294	+	303.619i	0.203122	+	0.351818i	0.949533	−	0.313668i	$-0.101558\pi$
$863$	175.294	+	303.619i	0.203122	+	0.351818i	−0.746411	+	0.665486i	$0.768224\pi$
$864$		0			0
$865$	102.573	−	177.661i	0.118581	−	0.205389i
$866$		0			0
$867$			361.591i			0.417060i
$868$		0			0
$869$	590.029			0.678974
$870$		0			0
$871$	−81.2145	−	46.8892i	−0.0932428	−	0.0538338i
$872$		0			0
$873$	28.5442	−	16.4800i	0.0326966	−	0.0188774i
$874$		0			0
$875$	466.368	+	119.876i	0.532991	+	0.137001i
$876$		0			0
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	0.865009	−	0.501756i	$-0.167313\pi$
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	−0.867038	+	0.498242i	$0.833979\pi$
$878$		0			0
$879$	−267.588	+	463.476i	−0.304423	+	0.527276i
$880$		0			0
$881$		−	488.565i		−	0.554557i	−0.960790	−	0.277279i	$-0.910567\pi$
$881$		−	488.565i		−	0.554557i	0.960790	−	0.277279i	$-0.0894325\pi$
$882$		0			0
$883$	1162.16			1.31615			0.658075	−	0.752953i	$-0.271371\pi$
$883$	1162.16			1.31615			0.658075	+	0.752953i	$0.271371\pi$
$884$		0			0
$885$	88.7208	+	51.2230i	0.100249	+	0.0578791i
$886$		0			0
$887$	−75.2801	+	43.4630i	−0.0848704	+	0.0490000i	−0.541835	−	0.840485i	$-0.682270\pi$
$887$	−75.2801	+	43.4630i	−0.0848704	+	0.0490000i	0.456964	+	0.889485i	$0.348937\pi$
$888$		0			0
$889$	143.896	−	559.817i	0.161863	−	0.629716i
$890$		0			0
$891$	27.0000	+	46.7654i	0.0303030	+	0.0524864i
$892$		0			0
$893$	155.360	−	269.092i	0.173976	−	0.301335i
$894$		0			0
$895$			242.895i			0.271391i
$896$		0			0
$897$	1383.66			1.54254
$898$		0			0
$899$	1297.50	+	749.111i	1.44327	+	0.833272i
$900$		0			0
$901$	−662.912	+	382.732i	−0.735751	+	0.424786i
$902$		0			0
$903$	12.6030	−	12.8629i	0.0139568	−	0.0142446i
$904$		0			0
$905$	150.640	+	260.915i	0.166453	+	0.288304i
$906$		0			0
$907$	−230.448	+	399.148i	−0.254077	+	0.440075i	−0.964645	−	0.263554i	$-0.915105\pi$
$907$	−230.448	+	399.148i	−0.254077	+	0.440075i	0.710567	+	0.703629i	$0.248438\pi$
$908$		0			0
$909$		−	321.550i		−	0.353740i
$910$		0			0
$911$	1184.28			1.29998			0.649988	−	0.759944i	$-0.274774\pi$
$911$	1184.28			1.29998			0.649988	+	0.759944i	$0.274774\pi$
$912$		0			0
$913$	−573.661	−	331.203i	−0.628325	−	0.362764i
$914$		0			0
$915$	−2.55844	+	1.47712i	−0.00279611	+	0.00161434i
$916$		0			0
$917$	113.912	+	408.407i	0.124222	+	0.445373i
$918$		0			0
$919$	−270.919	−	469.246i	−0.294798	−	0.510605i	0.680140	−	0.733082i	$-0.261919\pi$
$919$	−270.919	−	469.246i	−0.294798	−	0.510605i	−0.974938	+	0.222477i	$0.928586\pi$
$920$		0			0
$921$	−524.889	+	909.134i	−0.569912	+	0.987117i
$922$		0			0
$923$			2930.40i			3.17486i
$924$		0			0
$925$	−641.676			−0.693704
$926$		0			0
$927$	−273.331	−	157.807i	−0.294855	−	0.170235i
$928$		0			0
$929$	−779.610	+	450.108i	−0.839193	+	0.484508i	−0.856990	−	0.515333i	$-0.827668\pi$
$929$	−779.610	+	450.108i	−0.839193	+	0.484508i	0.0177969	+	0.999842i	$0.494335\pi$
$930$		0			0
$931$	−353.970	+	7.22538i	−0.380204	+	0.00776088i
$932$		0			0
$933$	−176.044	−	304.917i	−0.188686	−	0.326813i
$934$		0			0
$935$	38.5584	−	66.7852i	0.0412390	−	0.0714280i
$936$		0			0
$937$			233.964i			0.249695i	0.992176	+	0.124847i	$0.0398441\pi$
$937$			233.964i			0.249695i	−0.992176	+	0.124847i	$0.960156\pi$
$938$		0			0
$939$	702.588			0.748230
$940$		0			0
$941$	1132.49	+	653.845i	1.20350	+	0.694840i	0.961331	−	0.275394i	$-0.0888083\pi$
$941$	1132.49	+	653.845i	1.20350	+	0.694840i	0.242167	+	0.970234i	$0.422142\pi$
$942$		0			0
$943$	−1778.60	+	1026.88i	−1.88611	+	1.08895i
$944$		0			0
$945$	−50.2721	+	14.0217i	−0.0531980	+	0.0148378i
$946$		0			0
$947$	−563.881	−	976.671i	−0.595440	−	1.03133i	−0.993485	−	0.113966i	$-0.963645\pi$
$947$	−563.881	−	976.671i	−0.595440	−	1.03133i	0.398045	−	0.917366i	$-0.369689\pi$
$948$		0			0
$949$	841.677	−	1457.83i	0.886909	−	1.53617i
$950$		0			0
$951$		−	45.1353i		−	0.0474609i
$952$		0			0
$953$	−91.4255			−0.0959345			−0.0479672	−	0.998849i	$-0.515274\pi$
$953$	−91.4255			−0.0959345			−0.0479672	+	0.998849i	$0.515274\pi$
$954$		0			0
$955$	−82.7636	−	47.7836i	−0.0866635	−	0.0500352i
$956$		0			0
$957$	305.470	−	176.363i	0.319196	−	0.184288i
$958$		0			0
$959$	−335.147	−	328.376i	−0.349476	−	0.342415i
$960$		0			0
$961$	493.749	+	855.199i	0.513787	+	0.889905i
$962$		0			0
$963$	−177.816	+	307.987i	−0.184648	+	0.319820i
$964$		0			0
$965$			14.0531i			0.0145628i
$966$		0			0
$967$	1098.19			1.13567			0.567834	−	0.823143i	$-0.307782\pi$
$967$	1098.19			1.13567			0.567834	+	0.823143i	$0.307782\pi$
$968$		0			0
$969$	97.0812	+	56.0498i	0.100187	+	0.0578430i
$970$		0			0
$971$	−114.405	+	66.0517i	−0.117822	+	0.0680245i	−0.557753	−	0.830007i	$-0.688336\pi$
$971$	−114.405	+	66.0517i	−0.117822	+	0.0680245i	0.439931	+	0.898032i	$0.355003\pi$
$972$		0			0
$973$	620.691	+	159.543i	0.637915	+	0.163970i
$974$		0			0
$975$	−423.735	−	733.931i	−0.434601	−	0.752750i
$976$		0			0
$977$	−224.117	+	388.182i	−0.229393	+	0.397320i	−0.957628	−	0.288007i	$-0.907007\pi$
$977$	−224.117	+	388.182i	−0.229393	+	0.397320i	0.728235	+	0.685327i	$0.240341\pi$
$978$		0			0
$979$			124.708i			0.127383i
$980$		0			0
$981$	−333.177			−0.339630
$982$		0			0
$983$	−1426.14	−	823.382i	−1.45080	−	0.837621i	−0.452276	−	0.891878i	$-0.649388\pi$
$983$	−1426.14	−	823.382i	−1.45080	−	0.837621i	−0.998527	+	0.0542567i	$0.982721\pi$
$984$		0			0
$985$	331.986	−	191.672i	0.337041	−	0.194591i
$986$		0			0
$987$	129.801	−	504.982i	0.131511	−	0.511633i
$988$		0			0
$989$	−27.8162	−	48.1791i	−0.0281256	−	0.0487150i
$990$		0			0
$991$	−314.448	+	544.640i	−0.317304	+	0.549587i	−0.979925	−	0.199369i	$-0.936111\pi$
$991$	−314.448	+	544.640i	−0.317304	+	0.549587i	0.662621	+	0.748955i	$0.269444\pi$
$992$		0			0
$993$			188.157i			0.189483i
$994$		0			0
$995$	−187.882			−0.188826
$996$		0			0
$997$	−869.645	−	502.090i	−0.872262	−	0.503601i	−0.00416289	−	0.999991i	$-0.501325\pi$
$997$	−869.645	−	502.090i	−0.872262	−	0.503601i	−0.868099	+	0.496390i	$0.834658\pi$
$998$		0			0
$999$	125.868	−	72.6697i	0.125994	−	0.0727424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.e.241.1		4
3.2	odd	2		1008.3.cg.h.577.2		4
4.3	odd	2		42.3.g.a.31.2	yes	4
7.3	odd	6		2352.3.f.e.97.2		4
7.4	even	3		2352.3.f.e.97.3		4
7.5	odd	6	inner	336.3.bh.e.145.1		4
12.11	even	2		126.3.n.a.73.1		4
20.3	even	4		1050.3.q.a.199.3		8
20.7	even	4		1050.3.q.a.199.2		8
20.19	odd	2		1050.3.p.a.451.1		4
21.5	even	6		1008.3.cg.h.145.2		4
28.3	even	6		294.3.c.a.97.2		4
28.11	odd	6		294.3.c.a.97.1		4
28.19	even	6		42.3.g.a.19.2	✓	4
28.23	odd	6		294.3.g.a.19.2		4
28.27	even	2		294.3.g.a.31.2		4
84.11	even	6		882.3.c.b.685.4		4
84.23	even	6		882.3.n.e.19.1		4
84.47	odd	6		126.3.n.a.19.1		4
84.59	odd	6		882.3.c.b.685.3		4
84.83	odd	2		882.3.n.e.325.1		4
140.19	even	6		1050.3.p.a.901.1		4
140.47	odd	12		1050.3.q.a.649.3		8
140.103	odd	12		1050.3.q.a.649.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	28.19	even	6
42.3.g.a.31.2	yes	4	4.3	odd	2
126.3.n.a.19.1		4	84.47	odd	6
126.3.n.a.73.1		4	12.11	even	2
294.3.c.a.97.1		4	28.11	odd	6
294.3.c.a.97.2		4	28.3	even	6
294.3.g.a.19.2		4	28.23	odd	6
294.3.g.a.31.2		4	28.27	even	2
336.3.bh.e.145.1		4	7.5	odd	6	inner
336.3.bh.e.241.1		4	1.1	even	1	trivial
882.3.c.b.685.3		4	84.59	odd	6
882.3.c.b.685.4		4	84.11	even	6
882.3.n.e.19.1		4	84.23	even	6
882.3.n.e.325.1		4	84.83	odd	2
1008.3.cg.h.145.2		4	21.5	even	6
1008.3.cg.h.577.2		4	3.2	odd	2
1050.3.p.a.451.1		4	20.19	odd	2
1050.3.p.a.901.1		4	140.19	even	6
1050.3.q.a.199.2		8	20.7	even	4
1050.3.q.a.199.3		8	20.3	even	4
1050.3.q.a.649.2		8	140.103	odd	12
1050.3.q.a.649.3		8	140.47	odd	12
2352.3.f.e.97.2		4	7.3	odd	6
2352.3.f.e.97.3		4	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.24264 + 0.717439i) q^{5} +(-1.74264 + 6.77962i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.24264 + 0.717439i) q^{5} +(-1.74264 + 6.77962i) q^{7} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{11} -21.3280i q^{13} +2.48528 q^{15} +(-7.75736 - 4.47871i) q^{17} +(6.25736 - 3.61269i) q^{19} +(8.48528 - 8.66025i) q^{21} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} -5.19615i q^{27} -33.9411 q^{29} +(-38.2279 - 22.0709i) q^{31} +(-9.00000 + 5.19615i) q^{33} +(-2.69848 - 9.67487i) q^{35} +(13.9853 + 24.2232i) q^{37} +(-18.4706 + 31.9920i) q^{39} -54.8313i q^{41} +1.48528 q^{43} +(-3.72792 - 2.15232i) q^{45} +(37.2426 - 21.5020i) q^{47} +(-42.9264 - 23.6289i) q^{49} +(7.75736 + 13.4361i) q^{51} +(42.7279 - 74.0069i) q^{53} +8.60927i q^{55} -12.5147 q^{57} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} +(-20.2279 + 5.64191i) q^{63} +(15.3015 + 26.5030i) q^{65} +(2.19848 - 3.80789i) q^{67} +64.8754i q^{69} -137.397 q^{71} +(68.3528 + 39.4635i) q^{73} +(34.4117 - 19.8676i) q^{75} +(30.0000 + 29.3939i) q^{77} +(49.1690 + 85.1633i) q^{79} +(-4.50000 + 7.79423i) q^{81} -110.401i q^{83} +12.8528 q^{85} +(50.9117 + 29.3939i) q^{87} +(-18.0000 + 10.3923i) q^{89} +(144.595 + 37.1670i) q^{91} +(38.2279 + 66.2127i) q^{93} +(-5.18377 + 8.97855i) q^{95} -10.9867i q^{97} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 12 * q^5 + 10 * q^7 + 6 * q^9	\( 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9} + 12 q^{11} - 24 q^{15} - 48 q^{17} + 42 q^{19} - 24 q^{23} + 22 q^{25} - 102 q^{31} - 36 q^{33} + 108 q^{35} + 22 q^{37} - 6 q^{39} - 28 q^{43} + 36 q^{45} + 132 q^{47} - 2 q^{49} + 48 q^{51} + 120 q^{53} - 84 q^{57} + 24 q^{59} - 72 q^{61} - 30 q^{63} + 180 q^{65} - 110 q^{67} - 312 q^{71} - 66 q^{73} - 66 q^{75} + 120 q^{77} + 10 q^{79} - 18 q^{81} - 288 q^{85} - 72 q^{89} + 222 q^{91} + 102 q^{93} + 132 q^{95} + 72 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 12 * q^5 + 10 * q^7 + 6 * q^9 + 12 * q^11 - 24 * q^15 - 48 * q^17 + 42 * q^19 - 24 * q^23 + 22 * q^25 - 102 * q^31 - 36 * q^33 + 108 * q^35 + 22 * q^37 - 6 * q^39 - 28 * q^43 + 36 * q^45 + 132 * q^47 - 2 * q^49 + 48 * q^51 + 120 * q^53 - 84 * q^57 + 24 * q^59 - 72 * q^61 - 30 * q^63 + 180 * q^65 - 110 * q^67 - 312 * q^71 - 66 * q^73 - 66 * q^75 + 120 * q^77 + 10 * q^79 - 18 * q^81 - 288 * q^85 - 72 * q^89 + 222 * q^91 + 102 * q^93 + 132 * q^95 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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