LMFDB - Embedded newform 320.4.n.k.63.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,4,Mod(63,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.63"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	320.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.8806112018$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.2
Root			$-1.13579 - 1.64620i$ of defining polynomial
Character	$\chi$	$=$	320.63
Dual form			320.4.n.k.127.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.02923 + 4.02923i) q^{3} +(-10.9349 - 2.32970i) q^{5} +(-14.4440 - 14.4440i) q^{7} -5.46937i q^{9} -47.0607i q^{11} +(8.79525 + 8.79525i) q^{13} +(53.4462 - 34.6724i) q^{15} +(-26.4898 + 26.4898i) q^{17} +49.8054 q^{19} +116.396 q^{21} +(-41.2762 + 41.2762i) q^{23} +(114.145 + 50.9501i) q^{25} +(-86.7518 - 86.7518i) q^{27} +247.406i q^{29} -62.3240i q^{31} +(189.618 + 189.618i) q^{33} +(124.294 + 191.594i) q^{35} +(73.2182 - 73.2182i) q^{37} -70.8761 q^{39} +118.624 q^{41} +(-245.335 + 245.335i) q^{43} +(-12.7420 + 59.8071i) q^{45} +(125.525 + 125.525i) q^{47} +74.2578i q^{49} -213.467i q^{51} +(326.574 + 326.574i) q^{53} +(-109.637 + 514.605i) q^{55} +(-200.677 + 200.677i) q^{57} +365.123 q^{59} +268.160 q^{61} +(-78.9995 + 78.9995i) q^{63} +(-75.6851 - 116.666i) q^{65} +(112.617 + 112.617i) q^{67} -332.623i q^{69} -559.873i q^{71} +(215.825 + 215.825i) q^{73} +(-665.206 + 254.627i) q^{75} +(-679.744 + 679.744i) q^{77} +1172.36 q^{79} +846.759 q^{81} +(592.561 - 592.561i) q^{83} +(351.377 - 227.951i) q^{85} +(-996.857 - 996.857i) q^{87} +552.071i q^{89} -254.077i q^{91} +(251.118 + 251.118i) q^{93} +(-544.618 - 116.032i) q^{95} +(460.651 - 460.651i) q^{97} -257.392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 116 q^{13} - 332 q^{17} + 144 q^{21} + 340 q^{25} + 80 q^{33} - 508 q^{37} - 656 q^{41} - 1180 q^{45} + 644 q^{53} - 960 q^{57} + 896 q^{61} - 2740 q^{65} + 1436 q^{73} - 3120 q^{77} + 5988 q^{81}+ \cdots - 4772 q^{97}+O(q^{100}) $ 12 * q - 116 * q^13 - 332 * q^17 + 144 * q^21 + 340 * q^25 + 80 * q^33 - 508 * q^37 - 656 * q^41 - 1180 * q^45 + 644 * q^53 - 960 * q^57 + 896 * q^61 - 2740 * q^65 + 1436 * q^73 - 3120 * q^77 + 5988 * q^81 - 500 * q^85 + 3280 * q^93 - 4772 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−4.02923	+	4.02923i	−0.775425	+	0.775425i	−0.979049	−	0.203624i	$-0.934728\pi$
$3$	−4.02923	+	4.02923i	−0.775425	+	0.775425i	0.203624	+	0.979049i	$0.434728\pi$
$4$		0			0
$5$	−10.9349	−	2.32970i	−0.978049	−	0.208375i
$5$	−10.9349	−	2.32970i	−0.978049	−	0.208375i
$6$		0			0
$7$	−14.4440	−	14.4440i	−0.779902	−	0.779902i	0.199912	−	0.979814i	$-0.435934\pi$
$7$	−14.4440	−	14.4440i	−0.779902	−	0.779902i	−0.979814	+	0.199912i	$0.935934\pi$
$8$		0			0
$9$		−	5.46937i		−	0.202569i
$10$		0			0
$11$		−	47.0607i		−	1.28994i	−0.764209	−	0.644969i	$-0.776870\pi$
$11$		−	47.0607i		−	1.28994i	0.764209	−	0.644969i	$-0.223130\pi$
$12$		0			0
$13$	8.79525	+	8.79525i	0.187643	+	0.187643i	0.794676	−	0.607033i	$-0.207640\pi$
$13$	8.79525	+	8.79525i	0.187643	+	0.187643i	−0.607033	+	0.794676i	$0.707640\pi$
$14$		0			0
$15$	53.4462	−	34.6724i	0.919983	−	0.596825i
$16$		0			0
$17$	−26.4898	+	26.4898i	−0.377925	+	0.377925i	−0.870353	−	0.492428i	$-0.836109\pi$
$17$	−26.4898	+	26.4898i	−0.377925	+	0.377925i	0.492428	+	0.870353i	$0.336109\pi$
$18$		0			0
$19$	49.8054			0.601376			0.300688	−	0.953723i	$-0.402784\pi$
$19$	49.8054			0.601376			0.300688	+	0.953723i	$0.402784\pi$
$20$		0			0
$21$	116.396			1.20951
$22$		0			0
$23$	−41.2762	+	41.2762i	−0.374204	+	0.374204i	−0.869006	−	0.494802i	$-0.835241\pi$
$23$	−41.2762	+	41.2762i	−0.374204	+	0.374204i	0.494802	+	0.869006i	$0.335241\pi$
$24$		0			0
$25$	114.145	+	50.9501i	0.913160	+	0.407601i
$26$		0			0
$27$	−86.7518	−	86.7518i	−0.618348	−	0.618348i
$28$		0			0
$29$			247.406i			1.58421i	0.610382	+	0.792107i	$0.291016\pi$
$29$			247.406i			1.58421i	−0.610382	+	0.792107i	$0.708984\pi$
$30$		0			0
$31$		−	62.3240i		−	0.361088i	−0.983567	−	0.180544i	$-0.942214\pi$
$31$		−	62.3240i		−	0.361088i	0.983567	−	0.180544i	$-0.0577858\pi$
$32$		0			0
$33$	189.618	+	189.618i	1.00025	+	1.00025i
$34$		0			0
$35$	124.294	+	191.594i	0.600271	+	0.925294i
$36$		0			0
$37$	73.2182	−	73.2182i	0.325324	−	0.325324i	−0.525481	−	0.850805i	$-0.676115\pi$
$37$	73.2182	−	73.2182i	0.325324	−	0.325324i	0.850805	+	0.525481i	$0.176115\pi$
$38$		0			0
$39$	−70.8761			−0.291007
$40$		0			0
$41$	118.624			0.451854			0.225927	−	0.974144i	$-0.427459\pi$
$41$	118.624			0.451854			0.225927	+	0.974144i	$0.427459\pi$
$42$		0			0
$43$	−245.335	+	245.335i	−0.870076	+	0.870076i	−0.992480	−	0.122404i	$-0.960940\pi$
$43$	−245.335	+	245.335i	−0.870076	+	0.870076i	0.122404	+	0.992480i	$0.460940\pi$
$44$		0			0
$45$	−12.7420	+	59.8071i	−0.0422103	+	0.198123i
$46$		0			0
$47$	125.525	+	125.525i	0.389567	+	0.389567i	0.874533	−	0.484966i	$-0.161168\pi$
$47$	125.525	+	125.525i	0.389567	+	0.389567i	−0.484966	+	0.874533i	$0.661168\pi$
$48$		0			0
$49$			74.2578i			0.216495i
$50$		0			0
$51$		−	213.467i		−	0.586105i
$52$		0			0
$53$	326.574	+	326.574i	0.846385	+	0.846385i	0.989680	−	0.143295i	$-0.0457699\pi$
$53$	326.574	+	326.574i	0.846385	+	0.846385i	−0.143295	+	0.989680i	$0.545770\pi$
$54$		0			0
$55$	−109.637	+	514.605i	−0.268790	+	1.26162i
$56$		0			0
$57$	−200.677	+	200.677i	−0.466322	+	0.466322i
$58$		0			0
$59$	365.123			0.805677			0.402839	−	0.915271i	$-0.368024\pi$
$59$	365.123			0.805677			0.402839	+	0.915271i	$0.368024\pi$
$60$		0			0
$61$	268.160			0.562858			0.281429	−	0.959582i	$-0.409192\pi$
$61$	268.160			0.562858			0.281429	+	0.959582i	$0.409192\pi$
$62$		0			0
$63$	−78.9995	+	78.9995i	−0.157984	+	0.157984i
$64$		0			0
$65$	−75.6851	−	116.666i	−0.144424	−	0.222624i
$66$		0			0
$67$	112.617	+	112.617i	0.205349	+	0.205349i	0.802287	−	0.596938i	$-0.203616\pi$
$67$	112.617	+	112.617i	0.205349	+	0.205349i	−0.596938	+	0.802287i	$0.703616\pi$
$68$		0			0
$69$		−	332.623i		−	0.580334i
$70$		0			0
$71$		−	559.873i		−	0.935841i	−0.883771	−	0.467921i	$-0.845003\pi$
$71$		−	559.873i		−	0.935841i	0.883771	−	0.467921i	$-0.154997\pi$
$72$		0			0
$73$	215.825	+	215.825i	0.346033	+	0.346033i	0.858629	−	0.512597i	$-0.171316\pi$
$73$	215.825	+	215.825i	0.346033	+	0.346033i	−0.512597	+	0.858629i	$0.671316\pi$
$74$		0			0
$75$	−665.206	+	254.627i	−1.02415	+	0.392023i
$76$		0			0
$77$	−679.744	+	679.744i	−1.00603	+	1.00603i
$78$		0			0
$79$	1172.36			1.66963			0.834816	−	0.550528i	$-0.185574\pi$
$79$	1172.36			1.66963			0.834816	+	0.550528i	$0.185574\pi$
$80$		0			0
$81$	846.759			1.16153
$82$		0			0
$83$	592.561	−	592.561i	0.783639	−	0.783639i	−0.196804	−	0.980443i	$-0.563056\pi$
$83$	592.561	−	592.561i	0.783639	−	0.783639i	0.980443	+	0.196804i	$0.0630562\pi$
$84$		0			0
$85$	351.377	−	227.951i	0.448379	−	0.290879i
$86$		0			0
$87$	−996.857	−	996.857i	−1.22844	−	1.22844i
$88$		0			0
$89$			552.071i			0.657522i	0.944413	+	0.328761i	$0.106631\pi$
$89$			552.071i			0.657522i	−0.944413	+	0.328761i	$0.893369\pi$
$90$		0			0
$91$		−	254.077i		−	0.292687i
$92$		0			0
$93$	251.118	+	251.118i	0.279997	+	0.279997i
$94$		0			0
$95$	−544.618	−	116.032i	−0.588175	−	0.125311i
$96$		0			0
$97$	460.651	−	460.651i	0.482186	−	0.482186i	−0.423643	−	0.905829i	$-0.639249\pi$
$97$	460.651	−	460.651i	0.482186	−	0.482186i	0.905829	+	0.423643i	$0.139249\pi$
$98$		0			0
$99$	−257.392			−0.261302
$100$		0			0
$101$	5.97644			0.00588790			0.00294395	−	0.999996i	$-0.499063\pi$
$101$	5.97644			0.00588790			0.00294395	+	0.999996i	$0.499063\pi$
$102$		0			0
$103$	−137.824	+	137.824i	−0.131847	+	0.131847i	−0.769951	−	0.638104i	$-0.779719\pi$
$103$	−137.824	+	137.824i	−0.131847	+	0.131847i	0.638104	+	0.769951i	$0.279719\pi$
$104$		0			0
$105$	−1272.78	−	271.168i	−1.18296	−	0.252032i
$106$		0			0
$107$	−723.943	−	723.943i	−0.654077	−	0.654077i	0.299895	−	0.953972i	$-0.403048\pi$
$107$	−723.943	−	723.943i	−0.654077	−	0.654077i	−0.953972	+	0.299895i	$0.903048\pi$
$108$		0			0
$109$		−	896.758i		−	0.788017i	−0.919107	−	0.394009i	$-0.871088\pi$
$109$		−	896.758i		−	0.788017i	0.919107	−	0.394009i	$-0.128912\pi$
$110$		0			0
$111$			590.026i			0.504530i
$112$		0			0
$113$	−525.727	−	525.727i	−0.437665	−	0.437665i	0.453560	−	0.891226i	$-0.350154\pi$
$113$	−525.727	−	525.727i	−0.437665	−	0.437665i	−0.891226	+	0.453560i	$0.850154\pi$
$114$		0			0
$115$	547.513	−	355.191i	0.443964	−	0.288015i
$116$		0			0
$117$	48.1045	−	48.1045i	0.0380108	−	0.0380108i
$118$		0			0
$119$	765.237			0.589488
$120$		0			0
$121$	−883.705			−0.663941
$122$		0			0
$123$	−477.965	+	477.965i	−0.350379	+	0.350379i
$124$		0			0
$125$	−1129.47	−	823.059i	−0.808182	−	0.588933i
$126$		0			0
$127$	−75.4237	−	75.4237i	−0.0526990	−	0.0526990i	0.680266	−	0.732965i	$-0.261864\pi$
$127$	−75.4237	−	75.4237i	−0.0526990	−	0.0526990i	−0.732965	+	0.680266i	$0.761864\pi$
$128$		0			0
$129$		−	1977.02i		−	1.34936i
$130$		0			0
$131$			1374.47i			0.916701i	0.888771	+	0.458351i	$0.151560\pi$
$131$			1374.47i			0.916701i	−0.888771	+	0.458351i	$0.848440\pi$
$132$		0			0
$133$	−719.389	−	719.389i	−0.469014	−	0.469014i
$134$		0			0
$135$	746.519	+	1150.73i	0.475927	+	0.733623i
$136$		0			0
$137$	−2002.37	+	2002.37i	−1.24871	+	1.24871i	−0.292424	+	0.956289i	$0.594462\pi$
$137$	−2002.37	+	2002.37i	−1.24871	+	1.24871i	−0.956289	+	0.292424i	$0.905538\pi$
$138$		0			0
$139$	2575.00			1.57129			0.785643	−	0.618679i	$-0.212332\pi$
$139$	2575.00			1.57129			0.785643	+	0.618679i	$0.212332\pi$
$140$		0			0
$141$	−1011.53			−0.604160
$142$		0			0
$143$	413.910	−	413.910i	0.242048	−	0.242048i
$144$		0			0
$145$	576.382	−	2705.37i	0.330110	−	1.54944i
$146$		0			0
$147$	−299.202	−	299.202i	−0.167876	−	0.167876i
$148$		0			0
$149$		−	1322.91i		−	0.727364i	−0.931523	−	0.363682i	$-0.881519\pi$
$149$		−	1322.91i		−	0.727364i	0.931523	−	0.363682i	$-0.118481\pi$
$150$		0			0
$151$		−	57.2419i		−	0.0308495i	−0.999881	−	0.0154248i	$-0.995090\pi$
$151$		−	57.2419i		−	0.0308495i	0.999881	−	0.0154248i	$-0.00491005\pi$
$152$		0			0
$153$	144.882	+	144.882i	0.0765559	+	0.0765559i
$154$		0			0
$155$	−145.196	+	681.508i	−0.0752415	+	0.353162i
$156$		0			0
$157$	−1622.22	+	1622.22i	−0.824634	+	0.824634i	−0.986769	−	0.162134i	$-0.948162\pi$
$157$	−1622.22	+	1622.22i	−0.824634	+	0.824634i	0.162134	+	0.986769i	$0.448162\pi$
$158$		0			0
$159$	−2631.68			−1.31262
$160$		0			0
$161$	1192.39			0.583685
$162$		0			0
$163$	−1696.16	+	1696.16i	−0.815052	+	0.815052i	−0.985386	−	0.170334i	$-0.945515\pi$
$163$	−1696.16	+	1696.16i	−0.815052	+	0.815052i	0.170334	+	0.985386i	$0.445515\pi$
$164$		0			0
$165$	−1631.71	−	2515.21i	−0.769868	−	1.18672i
$166$		0			0
$167$	2015.29	+	2015.29i	0.933819	+	0.933819i	0.997942	−	0.0641235i	$-0.0204251\pi$
$167$	2015.29	+	2015.29i	0.933819	+	0.933819i	−0.0641235	+	0.997942i	$0.520425\pi$
$168$		0			0
$169$		−	2042.29i		−	0.929580i
$170$		0			0
$171$		−	272.404i		−	0.121820i
$172$		0			0
$173$	−317.896	−	317.896i	−0.139706	−	0.139706i	0.633795	−	0.773501i	$-0.281496\pi$
$173$	−317.896	−	317.896i	−0.139706	−	0.139706i	−0.773501	+	0.633795i	$0.781496\pi$
$174$		0			0
$175$	−912.786	−	2384.63i	−0.394287	−	1.03006i
$176$		0			0
$177$	−1471.16	+	1471.16i	−0.624743	+	0.624743i
$178$		0			0
$179$	−3518.04			−1.46900			−0.734499	−	0.678610i	$-0.762583\pi$
$179$	−3518.04			−1.46900			−0.734499	+	0.678610i	$0.762583\pi$
$180$		0			0
$181$	4769.86			1.95879			0.979395	−	0.201955i	$-0.0647294\pi$
$181$	4769.86			1.95879			0.979395	+	0.201955i	$0.0647294\pi$
$182$		0			0
$183$	−1080.48	+	1080.48i	−0.436455	+	0.436455i
$184$		0			0
$185$	−971.212	+	630.059i	−0.385972	+	0.250394i
$186$		0			0
$187$	1246.63	+	1246.63i	0.487499	+	0.487499i
$188$		0			0
$189$			2506.09i			0.964502i
$190$		0			0
$191$			1728.42i			0.654787i	0.944888	+	0.327393i	$0.106170\pi$
$191$			1728.42i			0.654787i	−0.944888	+	0.327393i	$0.893830\pi$
$192$		0			0
$193$	1439.32	+	1439.32i	0.536813	+	0.536813i	0.922591	−	0.385779i	$-0.126067\pi$
$193$	1439.32	+	1439.32i	0.536813	+	0.536813i	−0.385779	+	0.922591i	$0.626067\pi$
$194$		0			0
$195$	775.025	+	165.120i	0.284619	+	0.0606384i
$196$		0			0
$197$	658.673	−	658.673i	0.238216	−	0.238216i	−0.577895	−	0.816111i	$-0.696126\pi$
$197$	658.673	−	658.673i	0.238216	−	0.238216i	0.816111	+	0.577895i	$0.196126\pi$
$198$		0			0
$199$	−658.733			−0.234655			−0.117327	−	0.993093i	$-0.537433\pi$
$199$	−658.733			−0.234655			−0.117327	+	0.993093i	$0.537433\pi$
$200$		0			0
$201$	−907.523			−0.318466
$202$		0			0
$203$	3573.53	−	3573.53i	1.23553	−	1.23553i
$204$		0			0
$205$	−1297.15	−	276.359i	−0.441935	−	0.0941549i
$206$		0			0
$207$	225.755	+	225.755i	0.0758022	+	0.0758022i
$208$		0			0
$209$		−	2343.87i		−	0.775738i
$210$		0			0
$211$		−	5821.53i		−	1.89939i	−0.313182	−	0.949693i	$-0.601395\pi$
$211$		−	5821.53i		−	1.89939i	0.313182	−	0.949693i	$-0.398605\pi$
$212$		0			0
$213$	2255.86	+	2255.86i	0.725675	+	0.725675i
$214$		0			0
$215$	3254.28	−	2111.16i	1.03228	−	0.669675i
$216$		0			0
$217$	−900.208	+	900.208i	−0.281613	+	0.281613i
$218$		0			0
$219$	−1739.22			−0.536645
$220$		0			0
$221$	−465.969			−0.141830
$222$		0			0
$223$	2315.57	−	2315.57i	0.695347	−	0.695347i	−0.268056	−	0.963403i	$-0.586381\pi$
$223$	2315.57	−	2315.57i	0.695347	−	0.695347i	0.963403	+	0.268056i	$0.0863814\pi$
$224$		0			0
$225$	278.665	−	624.301i	0.0825674	−	0.184978i
$226$		0			0
$227$	2970.19	+	2970.19i	0.868450	+	0.868450i	0.992301	−	0.123851i	$-0.0395243\pi$
$227$	2970.19	+	2970.19i	0.868450	+	0.868450i	−0.123851	+	0.992301i	$0.539524\pi$
$228$		0			0
$229$		−	4981.25i		−	1.43742i	−0.695308	−	0.718712i	$-0.744732\pi$
$229$		−	4981.25i		−	1.43742i	0.695308	−	0.718712i	$-0.255268\pi$
$230$		0			0
$231$		−	5477.69i		−	1.56020i
$232$		0			0
$233$	1649.04	+	1649.04i	0.463659	+	0.463659i	0.899853	−	0.436194i	$-0.143674\pi$
$233$	1649.04	+	1649.04i	0.463659	+	0.463659i	−0.436194	+	0.899853i	$0.643674\pi$
$234$		0			0
$235$	−1080.17	−	1665.04i	−0.299840	−	0.462191i
$236$		0			0
$237$	−4723.71	+	4723.71i	−1.29468	+	1.29468i
$238$		0			0
$239$	−3574.98			−0.967558			−0.483779	−	0.875190i	$-0.660736\pi$
$239$	−3574.98			−0.967558			−0.483779	+	0.875190i	$0.660736\pi$
$240$		0			0
$241$	5135.22			1.37257			0.686283	−	0.727334i	$-0.259241\pi$
$241$	5135.22			1.37257			0.686283	+	0.727334i	$0.259241\pi$
$242$		0			0
$243$	−1069.49	+	1069.49i	−0.282336	+	0.282336i
$244$		0			0
$245$	172.998	−	812.003i	0.0451121	−	0.211743i
$246$		0			0
$247$	438.051	+	438.051i	0.112844	+	0.112844i
$248$		0			0
$249$			4775.13i			1.21531i
$250$		0			0
$251$			6648.06i			1.67180i	0.548882	+	0.835900i	$0.315054\pi$
$251$			6648.06i			1.67180i	−0.548882	+	0.835900i	$0.684946\pi$
$252$		0			0
$253$	1942.49	+	1942.49i	0.482700	+	0.482700i
$254$		0			0
$255$	−497.313	+	2334.24i	−0.122129	+	0.573239i
$256$		0			0
$257$	−448.260	+	448.260i	−0.108800	+	0.108800i	−0.759411	−	0.650611i	$-0.774513\pi$
$257$	−448.260	+	448.260i	−0.108800	+	0.108800i	0.650611	+	0.759411i	$0.274513\pi$
$258$		0			0
$259$	−2115.13			−0.507442
$260$		0			0
$261$	1353.16			0.320913
$262$		0			0
$263$	−145.529	+	145.529i	−0.0341205	+	0.0341205i	−0.723961	−	0.689841i	$-0.757681\pi$
$263$	−145.529	+	145.529i	−0.0341205	+	0.0341205i	0.689841	+	0.723961i	$0.257681\pi$
$264$		0			0
$265$	−2810.24	−	4331.88i	−0.651441	−	1.00417i
$266$		0			0
$267$	−2224.42	−	2224.42i	−0.509859	−	0.509859i
$268$		0			0
$269$			2764.90i			0.626687i	0.949640	+	0.313344i	$0.101449\pi$
$269$			2764.90i			0.626687i	−0.949640	+	0.313344i	$0.898551\pi$
$270$		0			0
$271$			6372.29i			1.42837i	0.699955	+	0.714187i	$0.253203\pi$
$271$			6372.29i			1.42837i	−0.699955	+	0.714187i	$0.746797\pi$
$272$		0			0
$273$	1023.73	+	1023.73i	0.226957	+	0.226957i
$274$		0			0
$275$	2397.75	−	5371.74i	0.525780	−	1.17792i
$276$		0			0
$277$	387.343	−	387.343i	0.0840187	−	0.0840187i	−0.663848	−	0.747867i	$-0.731078\pi$
$277$	387.343	−	387.343i	0.0840187	−	0.0840187i	0.747867	+	0.663848i	$0.231078\pi$
$278$		0			0
$279$	−340.873			−0.0731453
$280$		0			0
$281$	5284.49			1.12187			0.560936	−	0.827859i	$-0.310441\pi$
$281$	5284.49			1.12187			0.560936	+	0.827859i	$0.310441\pi$
$282$		0			0
$283$	341.577	−	341.577i	0.0717479	−	0.0717479i	−0.670322	−	0.742070i	$-0.733844\pi$
$283$	341.577	−	341.577i	0.0717479	−	0.0717479i	0.742070	+	0.670322i	$0.233844\pi$
$284$		0			0
$285$	2661.91	−	1726.87i	0.553256	−	0.358916i
$286$		0			0
$287$	−1713.41	−	1713.41i	−0.352402	−	0.352402i
$288$		0			0
$289$			3509.58i			0.714346i
$290$		0			0
$291$			3712.13i			0.747798i
$292$		0			0
$293$	6655.74	+	6655.74i	1.32707	+	1.32707i	0.907912	+	0.419161i	$0.137676\pi$
$293$	6655.74	+	6655.74i	1.32707	+	1.32707i	0.419161	+	0.907912i	$0.362324\pi$
$294$		0			0
$295$	−3992.59	−	850.626i	−0.787992	−	0.167883i
$296$		0			0
$297$	−4082.60	+	4082.60i	−0.797631	+	0.797631i
$298$		0			0
$299$	−726.069			−0.140434
$300$		0			0
$301$	7087.24			1.35715
$302$		0			0
$303$	−24.0804	+	24.0804i	−0.00456563	+	0.00456563i
$304$		0			0
$305$	−2932.31	−	624.732i	−0.550503	−	0.117285i
$306$		0			0
$307$	535.672	+	535.672i	0.0995844	+	0.0995844i	0.755144	−	0.655559i	$-0.227567\pi$
$307$	535.672	+	535.672i	0.0995844	+	0.0995844i	−0.655559	+	0.755144i	$0.727567\pi$
$308$		0			0
$309$		−	1110.65i		−	0.204475i
$310$		0			0
$311$			3579.61i			0.652672i	0.945254	+	0.326336i	$0.105814\pi$
$311$			3579.61i			0.652672i	−0.945254	+	0.326336i	$0.894186\pi$
$312$		0			0
$313$	6740.52	+	6740.52i	1.21724	+	1.21724i	0.968594	+	0.248648i	$0.0799861\pi$
$313$	6740.52	+	6740.52i	1.21724	+	1.21724i	0.248648	+	0.968594i	$0.420014\pi$
$314$		0			0
$315$	1047.90	−	679.809i	0.187436	−	0.121596i
$316$		0			0
$317$	−4163.19	+	4163.19i	−0.737628	+	0.737628i	−0.972118	−	0.234490i	$-0.924658\pi$
$317$	−4163.19	+	4163.19i	−0.737628	+	0.737628i	0.234490	+	0.972118i	$0.424658\pi$
$318$		0			0
$319$	11643.1			2.04354
$320$		0			0
$321$	5833.86			1.01438
$322$		0			0
$323$	−1319.33	+	1319.33i	−0.227275	+	0.227275i
$324$		0			0
$325$	555.815	+	1452.05i	0.0948648	+	0.247832i
$326$		0			0
$327$	3613.24	+	3613.24i	0.611049	+	0.611049i
$328$		0			0
$329$		−	3626.15i		−	0.607648i
$330$		0			0
$331$			8821.65i			1.46490i	0.680821	+	0.732450i	$0.261623\pi$
$331$			8821.65i			1.46490i	−0.680821	+	0.732450i	$0.738377\pi$
$332$		0			0
$333$	−400.457	−	400.457i	−0.0659007	−	0.0659007i
$334$		0			0
$335$	−969.099	−	1493.83i	−0.158052	−	0.243631i
$336$		0			0
$337$	3165.30	−	3165.30i	0.511647	−	0.511647i	−0.403384	−	0.915031i	$-0.632166\pi$
$337$	3165.30	−	3165.30i	0.511647	−	0.511647i	0.915031	+	0.403384i	$0.132166\pi$
$338$		0			0
$339$	4236.55			0.678754
$340$		0			0
$341$	−2933.01			−0.465781
$342$		0			0
$343$	−3881.71	+	3881.71i	−0.611057	+	0.611057i
$344$		0			0
$345$	−774.910	+	3637.20i	−0.120927	+	0.567595i
$346$		0			0
$347$	−856.765	−	856.765i	−0.132546	−	0.132546i	0.637721	−	0.770267i	$-0.279877\pi$
$347$	−856.765	−	856.765i	−0.132546	−	0.132546i	−0.770267	+	0.637721i	$0.779877\pi$
$348$		0			0
$349$		−	3731.17i		−	0.572278i	−0.958188	−	0.286139i	$-0.907628\pi$
$349$		−	3731.17i		−	0.572278i	0.958188	−	0.286139i	$-0.0923720\pi$
$350$		0			0
$351$		−	1526.01i		−	0.232058i
$352$		0			0
$353$	−1774.39	−	1774.39i	−0.267539	−	0.267539i	0.560569	−	0.828108i	$-0.310583\pi$
$353$	−1774.39	−	1774.39i	−0.267539	−	0.267539i	−0.828108	+	0.560569i	$0.810583\pi$
$354$		0			0
$355$	−1304.34	+	6122.17i	−0.195005	+	0.915298i
$356$		0			0
$357$	−3083.31	+	3083.31i	−0.457104	+	0.457104i
$358$		0			0
$359$	−10477.6			−1.54036			−0.770178	−	0.637829i	$-0.779832\pi$
$359$	−10477.6			−1.54036			−0.770178	+	0.637829i	$0.779832\pi$
$360$		0			0
$361$	−4378.42			−0.638347
$362$		0			0
$363$	3560.65	−	3560.65i	0.514837	−	0.514837i
$364$		0			0
$365$	−1857.22	−	2862.83i	−0.266333	−	0.410541i
$366$		0			0
$367$	−5250.87	−	5250.87i	−0.746848	−	0.746848i	0.227038	−	0.973886i	$-0.427096\pi$
$367$	−5250.87	−	5250.87i	−0.746848	−	0.746848i	−0.973886	+	0.227038i	$0.927096\pi$
$368$		0			0
$369$		−	648.801i		−	0.0915317i
$370$		0			0
$371$		−	9434.06i		−	1.32019i
$372$		0			0
$373$	−3349.09	−	3349.09i	−0.464904	−	0.464904i	0.435355	−	0.900259i	$-0.356623\pi$
$373$	−3349.09	−	3349.09i	−0.464904	−	0.464904i	−0.900259	+	0.435355i	$0.856623\pi$
$374$		0			0
$375$	7867.18	−	1234.59i	1.08336	−	0.170011i
$376$		0			0
$377$	−2176.00	+	2176.00i	−0.297267	+	0.297267i
$378$		0			0
$379$	−1701.61			−0.230622			−0.115311	−	0.993329i	$-0.536787\pi$
$379$	−1701.61			−0.230622			−0.115311	+	0.993329i	$0.536787\pi$
$380$		0			0
$381$	607.798			0.0817282
$382$		0			0
$383$	5674.07	−	5674.07i	0.757001	−	0.757001i	−0.218775	−	0.975775i	$-0.570206\pi$
$383$	5674.07	−	5674.07i	0.757001	−	0.757001i	0.975775	+	0.218775i	$0.0702060\pi$
$384$		0			0
$385$	9016.54	−	5849.35i	1.19357	−	0.774312i
$386$		0			0
$387$	1341.83	+	1341.83i	0.176251	+	0.176251i
$388$		0			0
$389$			2301.42i			0.299965i	0.988689	+	0.149983i	$0.0479218\pi$
$389$			2301.42i			0.299965i	−0.988689	+	0.149983i	$0.952078\pi$
$390$		0			0
$391$		−	2186.80i		−	0.282842i
$392$		0			0
$393$	−5538.05	−	5538.05i	−0.710833	−	0.710833i
$394$		0			0
$395$	−12819.7	−	2731.25i	−1.63298	−	0.347909i
$396$		0			0
$397$	7499.18	−	7499.18i	0.948043	−	0.948043i	−0.0506721	−	0.998715i	$-0.516136\pi$
$397$	7499.18	−	7499.18i	0.948043	−	0.948043i	0.998715	+	0.0506721i	$0.0161363\pi$
$398$		0			0
$399$	5797.16			0.727371
$400$		0			0
$401$	−9495.99			−1.18256			−0.591280	−	0.806466i	$-0.701377\pi$
$401$	−9495.99			−1.18256			−0.591280	+	0.806466i	$0.701377\pi$
$402$		0			0
$403$	548.155	−	548.155i	0.0677557	−	0.0677557i
$404$		0			0
$405$	−9259.24	−	1972.69i	−1.13604	−	0.242034i
$406$		0			0
$407$	−3445.70	−	3445.70i	−0.419648	−	0.419648i
$408$		0			0
$409$		−	10456.4i		−	1.26415i	−0.774909	−	0.632073i	$-0.782204\pi$
$409$		−	10456.4i		−	1.26415i	0.774909	−	0.632073i	$-0.217796\pi$
$410$		0			0
$411$		−	16136.0i		−	1.93657i
$412$		0			0
$413$	−5273.83	−	5273.83i	−0.628349	−	0.628349i
$414$		0			0
$415$	−7860.10	+	5099.12i	−0.929728	+	0.603147i
$416$		0			0
$417$	−10375.3	+	10375.3i	−1.21842	+	1.21842i
$418$		0			0
$419$	8542.91			0.996058			0.498029	−	0.867160i	$-0.334057\pi$
$419$	8542.91			0.996058			0.498029	+	0.867160i	$0.334057\pi$
$420$		0			0
$421$	3112.71			0.360342			0.180171	−	0.983635i	$-0.442335\pi$
$421$	3112.71			0.360342			0.180171	+	0.983635i	$0.442335\pi$
$422$		0			0
$423$	686.540	−	686.540i	0.0789142	−	0.0789142i
$424$		0			0
$425$	−4373.34	+	1674.02i	−0.499148	+	0.191063i
$426$		0			0
$427$	−3873.30	−	3873.30i	−0.438974	−	0.438974i
$428$		0			0
$429$			3335.48i			0.375381i
$430$		0			0
$431$		−	1474.93i		−	0.164837i	−0.996598	−	0.0824187i	$-0.973736\pi$
$431$		−	1474.93i		−	0.164837i	0.996598	−	0.0824187i	$-0.0262645\pi$
$432$		0			0
$433$	−6196.57	−	6196.57i	−0.687733	−	0.687733i	0.273998	−	0.961730i	$-0.411654\pi$
$433$	−6196.57	−	6196.57i	−0.687733	−	0.687733i	−0.961730	+	0.273998i	$0.911654\pi$
$434$		0			0
$435$	8578.17	+	13222.9i	0.945499	+	1.45745i
$436$		0			0
$437$	−2055.78	+	2055.78i	−0.225037	+	0.225037i
$438$		0			0
$439$	−4661.49			−0.506790			−0.253395	−	0.967363i	$-0.581547\pi$
$439$	−4661.49			−0.506790			−0.253395	+	0.967363i	$0.581547\pi$
$440$		0			0
$441$	406.144			0.0438553
$442$		0			0
$443$	−5250.61	+	5250.61i	−0.563124	+	0.563124i	−0.930194	−	0.367069i	$-0.880361\pi$
$443$	−5250.61	+	5250.61i	−0.563124	+	0.563124i	0.367069	+	0.930194i	$0.380361\pi$
$444$		0			0
$445$	1286.16	−	6036.85i	0.137011	−	0.643088i
$446$		0			0
$447$	5330.32	+	5330.32i	0.564017	+	0.564017i
$448$		0			0
$449$			2992.06i			0.314485i	0.987560	+	0.157243i	$0.0502605\pi$
$449$			2992.06i			0.314485i	−0.987560	+	0.157243i	$0.949740\pi$
$450$		0			0
$451$		−	5582.54i		−	0.582864i
$452$		0			0
$453$	230.641	+	230.641i	0.0239215	+	0.0239215i
$454$		0			0
$455$	−591.923	+	2778.31i	−0.0609885	+	0.286262i
$456$		0			0
$457$	13147.8	−	13147.8i	1.34579	−	1.34579i	0.455619	−	0.890175i	$-0.349418\pi$
$457$	13147.8	−	13147.8i	1.34579	−	1.34579i	0.890175	−	0.455619i	$-0.150582\pi$
$458$		0			0
$459$	4596.08			0.467378
$460$		0			0
$461$	−3239.67			−0.327302			−0.163651	−	0.986518i	$-0.552327\pi$
$461$	−3239.67			−0.327302			−0.163651	+	0.986518i	$0.552327\pi$
$462$		0			0
$463$	−1552.82	+	1552.82i	−0.155865	+	0.155865i	−0.780732	−	0.624867i	$-0.785153\pi$
$463$	−1552.82	+	1552.82i	−0.155865	+	0.155865i	0.624867	+	0.780732i	$0.285153\pi$
$464$		0			0
$465$	−2160.92	−	3330.98i	−0.215506	−	0.332195i
$466$		0			0
$467$	−6322.16	−	6322.16i	−0.626456	−	0.626456i	0.320719	−	0.947174i	$-0.396076\pi$
$467$	−6322.16	−	6322.16i	−0.626456	−	0.626456i	−0.947174	+	0.320719i	$0.896076\pi$
$468$		0			0
$469$		−	3253.29i		−	0.320305i
$470$		0			0
$471$		−	13072.6i		−	1.27888i
$472$		0			0
$473$	11545.6	+	11545.6i	1.12234	+	1.12234i
$474$		0			0
$475$	5685.04	+	2537.59i	0.549152	+	0.245121i
$476$		0			0
$477$	1786.15	−	1786.15i	0.171451	−	0.171451i
$478$		0			0
$479$	7141.64			0.681232			0.340616	−	0.940203i	$-0.389364\pi$
$479$	7141.64			0.681232			0.340616	+	0.940203i	$0.389364\pi$
$480$		0			0
$481$	1287.94			0.122090
$482$		0			0
$483$	−4804.40	+	4804.40i	−0.452604	+	0.452604i
$484$		0			0
$485$	−6110.36	+	3964.00i	−0.572076	+	0.371126i
$486$		0			0
$487$	3827.76	+	3827.76i	0.356165	+	0.356165i	0.862397	−	0.506232i	$-0.168962\pi$
$487$	3827.76	+	3827.76i	0.356165	+	0.356165i	−0.506232	+	0.862397i	$0.668962\pi$
$488$		0			0
$489$		−	13668.4i		−	1.26402i
$490$		0			0
$491$			14943.2i			1.37348i	0.726904	+	0.686739i	$0.240959\pi$
$491$			14943.2i			1.37348i	−0.726904	+	0.686739i	$0.759041\pi$
$492$		0			0
$493$	−6553.74	−	6553.74i	−0.598713	−	0.598713i
$494$		0			0
$495$	2814.56	+	599.646i	0.255566	+	0.0544486i
$496$		0			0
$497$	−8086.80	+	8086.80i	−0.729865	+	0.729865i
$498$		0			0
$499$	−2324.51			−0.208535			−0.104268	−	0.994549i	$-0.533250\pi$
$499$	−2324.51			−0.208535			−0.104268	+	0.994549i	$0.533250\pi$
$500$		0			0
$501$	−16240.1			−1.44821
$502$		0			0
$503$	−4791.06	+	4791.06i	−0.424697	+	0.424697i	−0.886817	−	0.462120i	$-0.847089\pi$
$503$	−4791.06	+	4791.06i	−0.424697	+	0.424697i	0.462120	+	0.886817i	$0.347089\pi$
$504$		0			0
$505$	−65.3519	−	13.9233i	−0.00575865	−	0.00122689i
$506$		0			0
$507$	8228.84	+	8228.84i	0.720820	+	0.720820i
$508$		0			0
$509$		−	3391.52i		−	0.295337i	−0.989037	−	0.147668i	$-0.952823\pi$
$509$		−	3391.52i		−	0.295337i	0.989037	−	0.147668i	$-0.0471768\pi$
$510$		0			0
$511$		−	6234.74i		−	0.539743i
$512$		0			0
$513$	−4320.71	−	4320.71i	−0.371860	−	0.371860i
$514$		0			0
$515$	1828.19	−	1186.01i	0.156426	−	0.101479i
$516$		0			0
$517$	5907.27	−	5907.27i	0.502517	−	0.502517i
$518$		0			0
$519$	2561.75			0.216664
$520$		0			0
$521$	−10835.4			−0.911146			−0.455573	−	0.890198i	$-0.650566\pi$
$521$	−10835.4			−0.911146			−0.455573	+	0.890198i	$0.650566\pi$
$522$		0			0
$523$	−1210.80	+	1210.80i	−0.101233	+	0.101233i	−0.755909	−	0.654676i	$-0.772805\pi$
$523$	−1210.80	+	1210.80i	−0.101233	+	0.101233i	0.654676	+	0.755909i	$0.272805\pi$
$524$		0			0
$525$	13286.1	+	5930.41i	1.10448	+	0.492998i
$526$		0			0
$527$	1650.95	+	1650.95i	0.136464	+	0.136464i
$528$		0			0
$529$			8759.55i			0.719943i
$530$		0			0
$531$		−	1996.99i		−	0.163205i
$532$		0			0
$533$	1043.33	+	1043.33i	0.0847874	+	0.0847874i
$534$		0			0
$535$	6229.69	+	9602.83i	0.503426	+	0.776012i
$536$		0			0
$537$	14175.0	−	14175.0i	1.13910	−	1.13910i
$538$		0			0
$539$	3494.62			0.279265
$540$		0			0
$541$	7014.81			0.557468			0.278734	−	0.960368i	$-0.410085\pi$
$541$	7014.81			0.557468			0.278734	+	0.960368i	$0.410085\pi$
$542$		0			0
$543$	−19218.9	+	19218.9i	−1.51890	+	1.51890i
$544$		0			0
$545$	−2089.18	+	9805.98i	−0.164203	+	0.770719i
$546$		0			0
$547$	−10104.9	−	10104.9i	−0.789860	−	0.789860i	0.191611	−	0.981471i	$-0.438629\pi$
$547$	−10104.9	−	10104.9i	−0.789860	−	0.789860i	−0.981471	+	0.191611i	$0.938629\pi$
$548$		0			0
$549$		−	1466.67i		−	0.114018i
$550$		0			0
$551$			12322.2i			0.952708i
$552$		0			0
$553$	−16933.6	−	16933.6i	−1.30215	−	1.30215i
$554$		0			0
$555$	1374.58	−	6451.89i	0.105131	−	0.493455i
$556$		0			0
$557$	−1950.22	+	1950.22i	−0.148355	+	0.148355i	−0.777383	−	0.629028i	$-0.783453\pi$
$557$	−1950.22	+	1950.22i	−0.148355	+	0.148355i	0.629028	+	0.777383i	$0.283453\pi$
$558$		0			0
$559$	−4315.57			−0.326528
$560$		0			0
$561$	−10045.9			−0.756039
$562$		0			0
$563$	−4425.60	+	4425.60i	−0.331291	+	0.331291i	−0.853077	−	0.521786i	$-0.825266\pi$
$563$	−4425.60	+	4425.60i	−0.331291	+	0.331291i	0.521786	+	0.853077i	$0.325266\pi$
$564$		0			0
$565$	4523.99	+	6973.56i	0.336860	+	0.519257i
$566$		0			0
$567$	−12230.6	−	12230.6i	−0.905884	−	0.905884i
$568$		0			0
$569$			14666.9i			1.08061i	0.841469	+	0.540305i	$0.181691\pi$
$569$			14666.9i			1.08061i	−0.841469	+	0.540305i	$0.818309\pi$
$570$		0			0
$571$		−	664.054i		−	0.0486686i	−0.999704	−	0.0243343i	$-0.992253\pi$
$571$		−	664.054i		−	0.0486686i	0.999704	−	0.0243343i	$-0.00774662\pi$
$572$		0			0
$573$	−6964.21	−	6964.21i	−0.507738	−	0.507738i
$574$		0			0
$575$	−6814.50	+	2608.45i	−0.494234	+	0.189182i
$576$		0			0
$577$	583.058	−	583.058i	0.0420676	−	0.0420676i	−0.685760	−	0.727828i	$-0.740530\pi$
$577$	583.058	−	583.058i	0.0420676	−	0.0420676i	0.727828	+	0.685760i	$0.240530\pi$
$578$		0			0
$579$	−11598.7			−0.832516
$580$		0			0
$581$	−17117.9			−1.22232
$582$		0			0
$583$	15368.8	−	15368.8i	1.09178	−	1.09178i
$584$		0			0
$585$	−638.088	+	413.950i	−0.0450969	+	0.0292559i
$586$		0			0
$587$	6911.99	+	6911.99i	0.486011	+	0.486011i	0.907045	−	0.421034i	$-0.138333\pi$
$587$	6911.99	+	6911.99i	0.486011	+	0.486011i	−0.421034	+	0.907045i	$0.638333\pi$
$588$		0			0
$589$		−	3104.07i		−	0.217150i
$590$		0			0
$591$			5307.89i			0.369437i
$592$		0			0
$593$	−11384.8	−	11384.8i	−0.788396	−	0.788396i	0.192835	−	0.981231i	$-0.438232\pi$
$593$	−11384.8	−	11384.8i	−0.788396	−	0.788396i	−0.981231	+	0.192835i	$0.938232\pi$
$594$		0			0
$595$	−8367.80	−	1782.77i	−0.576549	−	0.122834i
$596$		0			0
$597$	2654.19	−	2654.19i	0.181957	−	0.181957i
$598$		0			0
$599$	25321.6			1.72723			0.863616	−	0.504151i	$-0.168194\pi$
$599$	25321.6			1.72723			0.863616	+	0.504151i	$0.168194\pi$
$600$		0			0
$601$	27777.8			1.88533			0.942663	−	0.333746i	$-0.108313\pi$
$601$	27777.8			1.88533			0.942663	+	0.333746i	$0.108313\pi$
$602$		0			0
$603$	615.947	−	615.947i	0.0415975	−	0.0415975i
$604$		0			0
$605$	9663.25	+	2058.77i	0.649367	+	0.138348i
$606$		0			0
$607$	−19575.7	−	19575.7i	−1.30898	−	1.30898i	−0.922150	−	0.386833i	$-0.873569\pi$
$607$	−19575.7	−	19575.7i	−1.30898	−	1.30898i	−0.386833	−	0.922150i	$-0.626431\pi$
$608$		0			0
$609$			28797.2i			1.91613i
$610$		0			0
$611$			2208.04i			0.146199i
$612$		0			0
$613$	12841.3	+	12841.3i	0.846091	+	0.846091i	0.989643	−	0.143552i	$-0.0458525\pi$
$613$	12841.3	+	12841.3i	0.846091	+	0.846091i	−0.143552	+	0.989643i	$0.545853\pi$
$614$		0			0
$615$	6340.02	−	4112.99i	0.415698	−	0.269678i
$616$		0			0
$617$	15254.6	−	15254.6i	0.995346	−	0.995346i	−0.00464336	−	0.999989i	$-0.501478\pi$
$617$	15254.6	−	15254.6i	0.995346	−	0.995346i	0.999989	+	0.00464336i	$0.00147803\pi$
$618$		0			0
$619$	13042.3			0.846874			0.423437	−	0.905926i	$-0.360824\pi$
$619$	13042.3			0.846874			0.423437	+	0.905926i	$0.360824\pi$
$620$		0			0
$621$	7161.58			0.462776
$622$		0			0
$623$	7974.11	−	7974.11i	0.512803	−	0.512803i
$624$		0			0
$625$	10433.2	+	11631.4i	0.667723	+	0.744410i
$626$		0			0
$627$	9444.01	+	9444.01i	0.601527	+	0.601527i
$628$		0			0
$629$			3879.07i			0.245896i
$630$		0			0
$631$			6843.39i			0.431745i	0.976422	+	0.215872i	$0.0692595\pi$
$631$			6843.39i			0.431745i	−0.976422	+	0.215872i	$0.930740\pi$
$632$		0			0
$633$	23456.3	+	23456.3i	1.47283	+	1.47283i
$634$		0			0
$635$	649.038	+	1000.47i	0.0405611	+	0.0625233i
$636$		0			0
$637$	−653.116	+	653.116i	−0.0406239	+	0.0406239i
$638$		0			0
$639$	−3062.15			−0.189573
$640$		0			0
$641$	−2449.97			−0.150964			−0.0754820	−	0.997147i	$-0.524050\pi$
$641$	−2449.97			−0.150964			−0.0754820	+	0.997147i	$0.524050\pi$
$642$		0			0
$643$	22279.7	−	22279.7i	1.36645	−	1.36645i	0.500999	−	0.865448i	$-0.332966\pi$
$643$	22279.7	−	22279.7i	1.36645	−	1.36645i	0.865448	−	0.500999i	$-0.167034\pi$
$644$		0			0
$645$	−4605.87	+	21618.6i	−0.281172	+	1.31974i
$646$		0			0
$647$	5040.77	+	5040.77i	0.306295	+	0.306295i	0.843471	−	0.537175i	$-0.180509\pi$
$647$	5040.77	+	5040.77i	0.306295	+	0.306295i	−0.537175	+	0.843471i	$0.680509\pi$
$648$		0			0
$649$		−	17182.9i		−	1.03927i
$650$		0			0
$651$		−	7254.29i		−	0.436740i
$652$		0			0
$653$	4532.72	+	4532.72i	0.271637	+	0.271637i	0.829759	−	0.558122i	$-0.188478\pi$
$653$	4532.72	+	4532.72i	0.271637	+	0.271637i	−0.558122	+	0.829759i	$0.688478\pi$
$654$		0			0
$655$	3202.10	−	15029.7i	0.191017	−	0.896579i
$656$		0			0
$657$	1180.43	−	1180.43i	0.0700956	−	0.0700956i
$658$		0			0
$659$	−12951.7			−0.765595			−0.382797	−	0.923832i	$-0.625039\pi$
$659$	−12951.7			−0.765595			−0.382797	+	0.923832i	$0.625039\pi$
$660$		0			0
$661$	−6827.08			−0.401729			−0.200864	−	0.979619i	$-0.564375\pi$
$661$	−6827.08			−0.401729			−0.200864	+	0.979619i	$0.564375\pi$
$662$		0			0
$663$	1877.49	−	1877.49i	0.109979	−	0.109979i
$664$		0			0
$665$	6190.50	+	9542.42i	0.360988	+	0.556450i
$666$		0			0
$667$	−10212.0	−	10212.0i	−0.592819	−	0.592819i
$668$		0			0
$669$			18660.0i			1.07838i
$670$		0			0
$671$		−	12619.8i		−	0.726052i
$672$		0			0
$673$	9731.89	+	9731.89i	0.557410	+	0.557410i	0.928569	−	0.371159i	$-0.121040\pi$
$673$	9731.89	+	9731.89i	0.557410	+	0.557410i	−0.371159	+	0.928569i	$0.621040\pi$
$674$		0			0
$675$	−5482.27	−	14322.3i	−0.312611	−	0.816690i
$676$		0			0
$677$	7885.88	−	7885.88i	0.447679	−	0.447679i	−0.446903	−	0.894582i	$-0.647473\pi$
$677$	7885.88	−	7885.88i	0.447679	−	0.447679i	0.894582	+	0.446903i	$0.147473\pi$
$678$		0			0
$679$	−13307.3			−0.752115
$680$		0			0
$681$	−23935.1			−1.34684
$682$		0			0
$683$	15861.8	−	15861.8i	0.888629	−	0.888629i	−0.105763	−	0.994391i	$-0.533728\pi$
$683$	15861.8	−	15861.8i	0.888629	−	0.888629i	0.994391	+	0.105763i	$0.0337284\pi$
$684$		0			0
$685$	26560.6	−	17230.8i	1.48150	−	0.961102i
$686$		0			0
$687$	20070.6	+	20070.6i	1.11462	+	1.11462i
$688$		0			0
$689$			5744.60i			0.317637i
$690$		0			0
$691$			30100.7i			1.65714i	0.559883	+	0.828572i	$0.310846\pi$
$691$			30100.7i			1.65714i	−0.559883	+	0.828572i	$0.689154\pi$
$692$		0			0
$693$	3717.77	+	3717.77i	0.203790	+	0.203790i
$694$		0			0
$695$	−28157.5	−	5998.98i	−1.53680	−	0.327416i
$696$		0			0
$697$	−3142.34	+	3142.34i	−0.170767	+	0.170767i
$698$		0			0
$699$	−13288.8			−0.719066
$700$		0			0
$701$	20267.4			1.09199			0.545997	−	0.837787i	$-0.316151\pi$
$701$	20267.4			1.09199			0.545997	+	0.837787i	$0.316151\pi$
$702$		0			0
$703$	3646.66	−	3646.66i	0.195642	−	0.195642i
$704$		0			0
$705$	11061.0	+	2356.57i	0.590898	+	0.125892i
$706$		0			0
$707$	−86.3236	−	86.3236i	−0.00459199	−	0.00459199i
$708$		0			0
$709$			18499.1i			0.979900i	0.871750	+	0.489950i	$0.162985\pi$
$709$			18499.1i			0.979900i	−0.871750	+	0.489950i	$0.837015\pi$
$710$		0			0
$711$		−	6412.08i		−	0.338216i
$712$		0			0
$713$	2572.50	+	2572.50i	0.135120	+	0.135120i
$714$		0			0
$715$	−5490.36	+	3561.79i	−0.287172	+	0.186298i
$716$		0			0
$717$	14404.4	−	14404.4i	0.750269	−	0.750269i
$718$		0			0
$719$	−25990.9			−1.34812			−0.674060	−	0.738676i	$-0.735451\pi$
$719$	−25990.9			−1.34812			−0.674060	+	0.738676i	$0.735451\pi$
$720$		0			0
$721$	3981.47			0.205656
$722$		0			0
$723$	−20691.0	+	20691.0i	−1.06432	+	1.06432i
$724$		0			0
$725$	−12605.4	+	28240.2i	−0.645727	+	1.44664i
$726$		0			0
$727$	23543.5	+	23543.5i	1.20107	+	1.20107i	0.973841	+	0.227232i	$0.0729675\pi$
$727$	23543.5	+	23543.5i	1.20107	+	1.20107i	0.227232	+	0.973841i	$0.427033\pi$
$728$		0			0
$729$			14244.1i			0.723674i
$730$		0			0
$731$		−	12997.8i		−	0.657646i
$732$		0			0
$733$	−16546.7	−	16546.7i	−0.833789	−	0.833789i	0.154244	−	0.988033i	$-0.450706\pi$
$733$	−16546.7	−	16546.7i	−0.833789	−	0.833789i	−0.988033	+	0.154244i	$0.950706\pi$
$734$		0			0
$735$	2574.70	+	3968.80i	0.129210	+	0.199172i
$736$		0			0
$737$	5299.85	−	5299.85i	0.264888	−	0.264888i
$738$		0			0
$739$	8124.95			0.404440			0.202220	−	0.979340i	$-0.435184\pi$
$739$	8124.95			0.404440			0.202220	+	0.979340i	$0.435184\pi$
$740$		0			0
$741$	−3530.01			−0.175004
$742$		0			0
$743$	−5222.62	+	5222.62i	−0.257873	+	0.257873i	−0.824188	−	0.566316i	$-0.808368\pi$
$743$	−5222.62	+	5222.62i	−0.257873	+	0.257873i	0.566316	+	0.824188i	$0.308368\pi$
$744$		0			0
$745$	−3081.99	+	14465.9i	−0.151564	+	0.711398i
$746$		0			0
$747$	−3240.94	−	3240.94i	−0.158741	−	0.158741i
$748$		0			0
$749$			20913.3i			1.02023i
$750$		0			0
$751$			27086.9i			1.31613i	0.752961	+	0.658066i	$0.228625\pi$
$751$			27086.9i			1.31613i	−0.752961	+	0.658066i	$0.771375\pi$
$752$		0			0
$753$	−26786.5	−	26786.5i	−1.29636	−	1.29636i
$754$		0			0
$755$	−133.356	+	625.936i	−0.00642826	+	0.0301724i
$756$		0			0
$757$	11094.6	−	11094.6i	0.532684	−	0.532684i	−0.388686	−	0.921370i	$-0.627071\pi$
$757$	11094.6	−	11094.6i	0.532684	−	0.532684i	0.921370	+	0.388686i	$0.127071\pi$
$758$		0			0
$759$	−15653.4			−0.748595
$760$		0			0
$761$	−8006.53			−0.381388			−0.190694	−	0.981649i	$-0.561074\pi$
$761$	−8006.53			−0.381388			−0.190694	+	0.981649i	$0.561074\pi$
$762$		0			0
$763$	−12952.8	+	12952.8i	−0.614576	+	0.614576i
$764$		0			0
$765$	−1246.75	−	1921.81i	−0.0589231	−	0.0908277i
$766$		0			0
$767$	3211.35	+	3211.35i	0.151180	+	0.151180i
$768$		0			0
$769$			5515.54i			0.258642i	0.991603	+	0.129321i	$0.0412797\pi$
$769$			5515.54i			0.258642i	−0.991603	+	0.129321i	$0.958720\pi$
$770$		0			0
$771$		−	3612.28i		−	0.168733i
$772$		0			0
$773$	−7904.07	−	7904.07i	−0.367774	−	0.367774i	0.498891	−	0.866665i	$-0.333741\pi$
$773$	−7904.07	−	7904.07i	−0.367774	−	0.367774i	−0.866665	+	0.498891i	$0.833741\pi$
$774$		0			0
$775$	3175.42	−	7113.98i	0.147180	−	0.329731i
$776$		0			0
$777$	8522.33	−	8522.33i	0.393484	−	0.393484i
$778$		0			0
$779$	5908.13			0.271734
$780$		0			0
$781$	−26348.0			−1.20718
$782$		0			0
$783$	21463.0	−	21463.0i	0.979596	−	0.979596i
$784$		0			0
$785$	21518.2	−	13959.6i	0.978366	−	0.634700i
$786$		0			0
$787$	27606.7	+	27606.7i	1.25041	+	1.25041i	0.955537	+	0.294870i	$0.0952765\pi$
$787$	27606.7	+	27606.7i	1.25041	+	1.25041i	0.294870	+	0.955537i	$0.404724\pi$
$788$		0			0
$789$		−	1172.74i		−	0.0529158i
$790$		0			0
$791$			15187.2i			0.682673i
$792$		0			0
$793$	2358.53	+	2358.53i	0.105617	+	0.105617i
$794$		0			0
$795$	28777.2	+	6131.03i	1.28380	+	0.273516i
$796$		0			0
$797$	19000.5	−	19000.5i	0.844456	−	0.844456i	−0.144979	−	0.989435i	$-0.546311\pi$
$797$	19000.5	−	19000.5i	0.844456	−	0.844456i	0.989435	+	0.144979i	$0.0463113\pi$
$798$		0			0
$799$	−6650.24			−0.294454
$800$		0			0
$801$	3019.48			0.133194
$802$		0			0
$803$	10156.9	−	10156.9i	0.446361	−	0.446361i
$804$		0			0
$805$	−13038.7	−	2777.90i	−0.570872	−	0.121625i
$806$		0			0
$807$	−11140.4	−	11140.4i	−0.485949	−	0.485949i
$808$		0			0
$809$		−	33025.1i		−	1.43523i	−0.696440	−	0.717615i	$-0.745234\pi$
$809$		−	33025.1i		−	1.43523i	0.696440	−	0.717615i	$-0.254766\pi$
$810$		0			0
$811$			19125.0i			0.828075i	0.910260	+	0.414037i	$0.135882\pi$
$811$			19125.0i			0.828075i	−0.910260	+	0.414037i	$0.864118\pi$
$812$		0			0
$813$	−25675.4	−	25675.4i	−1.10760	−	1.10760i
$814$		0			0
$815$	22498.9	−	14595.8i	0.966997	−	0.627325i
$816$		0			0
$817$	−12219.0	+	12219.0i	−0.523243	+	0.523243i
$818$		0			0
$819$	−1389.64			−0.0592894
$820$		0			0
$821$	−8022.85			−0.341047			−0.170523	−	0.985354i	$-0.554546\pi$
$821$	−8022.85			−0.341047			−0.170523	+	0.985354i	$0.554546\pi$
$822$		0			0
$823$	−941.682	+	941.682i	−0.0398845	+	0.0398845i	−0.726768	−	0.686883i	$-0.758978\pi$
$823$	−941.682	+	941.682i	−0.0398845	+	0.0398845i	0.686883	+	0.726768i	$0.258978\pi$
$824$		0			0
$825$	11982.9	+	31305.0i	0.505686	+	1.32109i
$826$		0			0
$827$	413.194	+	413.194i	0.0173739	+	0.0173739i	0.715740	−	0.698366i	$-0.246089\pi$
$827$	413.194	+	413.194i	0.0173739	+	0.0173739i	−0.698366	+	0.715740i	$0.746089\pi$
$828$		0			0
$829$			13830.1i			0.579418i	0.957115	+	0.289709i	$0.0935585\pi$
$829$			13830.1i			0.579418i	−0.957115	+	0.289709i	$0.906441\pi$
$830$		0			0
$831$			3121.39i			0.130301i
$832$		0			0
$833$	−1967.07	−	1967.07i	−0.0818188	−	0.0818188i
$834$		0			0
$835$	−17342.0	−	26732.0i	−0.718736	−	1.10790i
$836$		0			0
$837$	−5406.72	+	5406.72i	−0.223278	+	0.223278i
$838$		0			0
$839$	29230.2			1.20279			0.601393	−	0.798954i	$-0.294613\pi$
$839$	29230.2			1.20279			0.601393	+	0.798954i	$0.294613\pi$
$840$		0			0
$841$	−36820.9			−1.50973
$842$		0			0
$843$	−21292.4	+	21292.4i	−0.869929	+	0.869929i
$844$		0			0
$845$	−4757.91	+	22332.2i	−0.193701	+	0.909175i
$846$		0			0
$847$	12764.2	+	12764.2i	0.517809	+	0.517809i
$848$		0			0
$849$			2752.59i			0.111270i
$850$		0			0
$851$			6044.34i			0.243475i
$852$		0			0
$853$	20858.3	+	20858.3i	0.837251	+	0.837251i	0.988496	−	0.151245i	$-0.0483283\pi$
$853$	20858.3	+	20858.3i	0.837251	+	0.837251i	−0.151245	+	0.988496i	$0.548328\pi$
$854$		0			0
$855$	−634.619	+	2978.72i	−0.0253842	+	0.119146i
$856$		0			0
$857$	24905.5	−	24905.5i	0.992714	−	0.992714i	−0.00725972	−	0.999974i	$-0.502311\pi$
$857$	24905.5	−	24905.5i	0.992714	−	0.992714i	0.999974	+	0.00725972i	$0.00231086\pi$
$858$		0			0
$859$	−26939.2			−1.07003			−0.535013	−	0.844844i	$-0.679693\pi$
$859$	−26939.2			−1.07003			−0.535013	+	0.844844i	$0.679693\pi$
$860$		0			0
$861$	13807.4			0.546523
$862$		0			0
$863$	−17233.1	+	17233.1i	−0.679747	+	0.679747i	−0.959943	−	0.280196i	$-0.909601\pi$
$863$	−17233.1	+	17233.1i	−0.679747	+	0.679747i	0.280196	+	0.959943i	$0.409601\pi$
$864$		0			0
$865$	2735.57	+	4216.77i	0.107528	+	0.165751i
$866$		0			0
$867$	−14140.9	−	14140.9i	−0.553922	−	0.553922i
$868$		0			0
$869$		−	55172.1i		−	2.15372i
$870$		0			0
$871$			1981.00i			0.0770649i
$872$		0			0
$873$	−2519.47	−	2519.47i	−0.0976760	−	0.0976760i
$874$		0			0
$875$	4425.77	+	28202.3i	0.170992	+	1.08961i
$876$		0			0
$877$	−8676.94	+	8676.94i	−0.334093	+	0.334093i	−0.854138	−	0.520046i	$-0.825915\pi$
$877$	−8676.94	+	8676.94i	−0.334093	+	0.334093i	0.520046	+	0.854138i	$0.325915\pi$
$878$		0			0
$879$	−53635.0			−2.05809
$880$		0			0
$881$	−9480.93			−0.362566			−0.181283	−	0.983431i	$-0.558025\pi$
$881$	−9480.93			−0.362566			−0.181283	+	0.983431i	$0.558025\pi$
$882$		0			0
$883$	27861.7	−	27861.7i	1.06186	−	1.06186i	0.0639013	−	0.997956i	$-0.479646\pi$
$883$	27861.7	−	27861.7i	1.06186	−	1.06186i	0.997956	−	0.0639013i	$-0.0203543\pi$
$884$		0			0
$885$	19514.4	−	12659.7i	0.741209	−	0.480848i
$886$		0			0
$887$	−27498.7	−	27498.7i	−1.04094	−	1.04094i	−0.999125	−	0.0418178i	$-0.986685\pi$
$887$	−27498.7	−	27498.7i	−1.04094	−	1.04094i	−0.0418178	−	0.999125i	$-0.513315\pi$
$888$		0			0
$889$			2178.84i			0.0822001i
$890$		0			0
$891$		−	39849.0i		−	1.49831i
$892$		0			0
$893$	6251.80	+	6251.80i	0.234276	+	0.234276i
$894$		0			0
$895$	38469.5	+	8195.97i	1.43675	+	0.306102i
$896$		0			0
$897$	2925.50	−	2925.50i	0.108896	−	0.108896i
$898$		0			0
$899$	15419.4			0.572040
$900$		0			0
$901$	−17301.8			−0.639739
$902$		0			0
$903$	−28556.1	+	28556.1i	−1.05237	+	1.05237i
$904$		0			0
$905$	−52158.0	−	11112.3i	−1.91579	−	0.408162i
$906$		0			0
$907$	1450.80	+	1450.80i	0.0531127	+	0.0531127i	0.733164	−	0.680052i	$-0.238043\pi$
$907$	1450.80	+	1450.80i	0.0531127	+	0.0531127i	−0.680052	+	0.733164i	$0.738043\pi$
$908$		0			0
$909$		−	32.6873i		−	0.00119271i
$910$		0			0
$911$		−	20370.8i		−	0.740850i	−0.928862	−	0.370425i	$-0.879212\pi$
$911$		−	20370.8i		−	0.740850i	0.928862	−	0.370425i	$-0.120788\pi$
$912$		0			0
$913$	−27886.3	−	27886.3i	−1.01085	−	1.01085i
$914$		0			0
$915$	14332.1	−	9297.75i	0.517820	−	0.335928i
$916$		0			0
$917$	19852.8	−	19852.8i	0.714937	−	0.714937i
$918$		0			0
$919$	21825.1			0.783399			0.391699	−	0.920093i	$-0.371887\pi$
$919$	21825.1			0.783399			0.391699	+	0.920093i	$0.371887\pi$
$920$		0			0
$921$	−4316.69			−0.154440
$922$		0			0
$923$	4924.22	−	4924.22i	0.175604	−	0.175604i
$924$		0			0
$925$	12088.0	−	4627.02i	0.429676	−	0.164471i
$926$		0			0
$927$	753.812	+	753.812i	0.0267081	+	0.0267081i
$928$		0			0
$929$			9339.19i			0.329827i	0.986308	+	0.164913i	$0.0527345\pi$
$929$			9339.19i			0.329827i	−0.986308	+	0.164913i	$0.947266\pi$
$930$		0			0
$931$			3698.44i			0.130195i
$932$		0			0
$933$	−14423.1	−	14423.1i	−0.506099	−	0.506099i
$934$		0			0
$935$	−10727.5	−	16536.0i	−0.375216	−	0.578381i
$936$		0			0
$937$	431.639	−	431.639i	0.0150491	−	0.0150491i	−0.699542	−	0.714591i	$-0.746613\pi$
$937$	431.639	−	431.639i	0.0150491	−	0.0150491i	0.714591	+	0.699542i	$0.246613\pi$
$938$		0			0
$939$	−54318.2			−1.88776
$940$		0			0
$941$	−21225.1			−0.735300			−0.367650	−	0.929964i	$-0.619838\pi$
$941$	−21225.1			−0.735300			−0.367650	+	0.929964i	$0.619838\pi$
$942$		0			0
$943$	−4896.37	+	4896.37i	−0.169086	+	0.169086i
$944$		0			0
$945$	5838.42	−	27403.9i	0.200978	−	0.943330i
$946$		0			0
$947$	−11052.1	−	11052.1i	−0.379244	−	0.379244i	0.491585	−	0.870830i	$-0.336418\pi$
$947$	−11052.1	−	11052.1i	−0.379244	−	0.379244i	−0.870830	+	0.491585i	$0.836418\pi$
$948$		0			0
$949$			3796.47i			0.129861i
$950$		0			0
$951$		−	33548.9i		−	1.14395i
$952$		0			0
$953$	22553.2	+	22553.2i	0.766600	+	0.766600i	0.977506	−	0.210906i	$-0.0676414\pi$
$953$	22553.2	+	22553.2i	0.766600	+	0.766600i	−0.210906	+	0.977506i	$0.567641\pi$
$954$		0			0
$955$	4026.70	−	18900.2i	0.136441	−	0.640413i
$956$		0			0
$957$	−46912.7	+	46912.7i	−1.58461	+	1.58461i
$958$		0			0
$959$	57844.3			1.94775
$960$		0			0
$961$	25906.7			0.869616
$962$		0			0
$963$	−3959.51	+	3959.51i	−0.132496	+	0.132496i
$964$		0			0
$965$	−12385.7	−	19092.1i	−0.413171	−	0.636887i
$966$		0			0
$967$	−18695.9	−	18695.9i	−0.621739	−	0.621739i	0.324237	−	0.945976i	$-0.394892\pi$
$967$	−18695.9	−	18695.9i	−0.621739	−	0.621739i	−0.945976	+	0.324237i	$0.894892\pi$
$968$		0			0
$969$		−	10631.8i		−	0.352469i
$970$		0			0
$971$		−	11285.7i		−	0.372993i	−0.982456	−	0.186496i	$-0.940287\pi$
$971$		−	11285.7i		−	0.372993i	0.982456	−	0.186496i	$-0.0597133\pi$
$972$		0			0
$973$	−37193.3	−	37193.3i	−1.22545	−	1.22545i
$974$		0			0
$975$	−8090.16	−	3611.15i	−0.265736	−	0.118615i
$976$		0			0
$977$	9765.98	−	9765.98i	0.319797	−	0.319797i	−0.528892	−	0.848689i	$-0.677392\pi$
$977$	9765.98	−	9765.98i	0.319797	−	0.319797i	0.848689	+	0.528892i	$0.177392\pi$
$978$		0			0
$979$	25980.8			0.848162
$980$		0			0
$981$	−4904.70			−0.159628
$982$		0			0
$983$	33483.4	−	33483.4i	1.08642	−	1.08642i	0.0905295	−	0.995894i	$-0.471144\pi$
$983$	33483.4	−	33483.4i	1.08642	−	1.08642i	0.995894	−	0.0905295i	$-0.0288559\pi$
$984$		0			0
$985$	−8737.05	+	5668.03i	−0.282625	+	0.183349i
$986$		0			0
$987$	14610.6	+	14610.6i	0.471186	+	0.471186i
$988$		0			0
$989$		−	20253.0i		−	0.651171i
$990$		0			0
$991$		−	35651.6i		−	1.14280i	−0.820673	−	0.571398i	$-0.806401\pi$
$991$		−	35651.6i		−	1.14280i	0.820673	−	0.571398i	$-0.193599\pi$
$992$		0			0
$993$	−35544.4	−	35544.4i	−1.13592	−	1.13592i
$994$		0			0
$995$	7203.19	+	1534.65i	0.229504	+	0.0488961i
$996$		0			0
$997$	19421.9	−	19421.9i	0.616949	−	0.616949i	−0.327799	−	0.944748i	$-0.606307\pi$
$997$	19421.9	−	19421.9i	0.616949	−	0.616949i	0.944748	+	0.327799i	$0.106307\pi$
$998$		0			0
$999$	−12703.6			−0.402327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.4.n.k.63.2		12
4.3	odd	2	inner	320.4.n.k.63.5		12
5.2	odd	4	inner	320.4.n.k.127.5		12
8.3	odd	2		20.4.e.b.3.4	yes	12
8.5	even	2		20.4.e.b.3.1	✓	12
20.7	even	4	inner	320.4.n.k.127.2		12
24.5	odd	2		180.4.k.e.163.6		12
24.11	even	2		180.4.k.e.163.3		12
40.3	even	4		100.4.e.e.7.6		12
40.13	odd	4		100.4.e.e.7.3		12
40.19	odd	2		100.4.e.e.43.3		12
40.27	even	4		20.4.e.b.7.1	yes	12
40.29	even	2		100.4.e.e.43.6		12
40.37	odd	4		20.4.e.b.7.4	yes	12
120.77	even	4		180.4.k.e.127.3		12
120.107	odd	4		180.4.k.e.127.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.1	✓	12	8.5	even	2
20.4.e.b.3.4	yes	12	8.3	odd	2
20.4.e.b.7.1	yes	12	40.27	even	4
20.4.e.b.7.4	yes	12	40.37	odd	4
100.4.e.e.7.3		12	40.13	odd	4
100.4.e.e.7.6		12	40.3	even	4
100.4.e.e.43.3		12	40.19	odd	2
100.4.e.e.43.6		12	40.29	even	2
180.4.k.e.127.3		12	120.77	even	4
180.4.k.e.127.6		12	120.107	odd	4
180.4.k.e.163.3		12	24.11	even	2
180.4.k.e.163.6		12	24.5	odd	2
320.4.n.k.63.2		12	1.1	even	1	trivial
320.4.n.k.63.5		12	4.3	odd	2	inner
320.4.n.k.127.2		12	20.7	even	4	inner
320.4.n.k.127.5		12	5.2	odd	4	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	320.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.02923 + 4.02923i) q^{3} +(-10.9349 - 2.32970i) q^{5} +(-14.4440 - 14.4440i) q^{7} -5.46937i q^{9} -47.0607i q^{11} +(8.79525 + 8.79525i) q^{13} +(53.4462 - 34.6724i) q^{15} +(-26.4898 + 26.4898i) q^{17} +49.8054 q^{19} +116.396 q^{21} +(-41.2762 + 41.2762i) q^{23} +(114.145 + 50.9501i) q^{25} +(-86.7518 - 86.7518i) q^{27} +247.406i q^{29} -62.3240i q^{31} +(189.618 + 189.618i) q^{33} +(124.294 + 191.594i) q^{35} +(73.2182 - 73.2182i) q^{37} -70.8761 q^{39} +118.624 q^{41} +(-245.335 + 245.335i) q^{43} +(-12.7420 + 59.8071i) q^{45} +(125.525 + 125.525i) q^{47} +74.2578i q^{49} -213.467i q^{51} +(326.574 + 326.574i) q^{53} +(-109.637 + 514.605i) q^{55} +(-200.677 + 200.677i) q^{57} +365.123 q^{59} +268.160 q^{61} +(-78.9995 + 78.9995i) q^{63} +(-75.6851 - 116.666i) q^{65} +(112.617 + 112.617i) q^{67} -332.623i q^{69} -559.873i q^{71} +(215.825 + 215.825i) q^{73} +(-665.206 + 254.627i) q^{75} +(-679.744 + 679.744i) q^{77} +1172.36 q^{79} +846.759 q^{81} +(592.561 - 592.561i) q^{83} +(351.377 - 227.951i) q^{85} +(-996.857 - 996.857i) q^{87} +552.071i q^{89} -254.077i q^{91} +(251.118 + 251.118i) q^{93} +(-544.618 - 116.032i) q^{95} +(460.651 - 460.651i) q^{97} -257.392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 116 q^{13} - 332 q^{17} + 144 q^{21} + 340 q^{25} + 80 q^{33} - 508 q^{37} - 656 q^{41} - 1180 q^{45} + 644 q^{53} - 960 q^{57} + 896 q^{61} - 2740 q^{65} + 1436 q^{73} - 3120 q^{77} + 5988 q^{81}+ \cdots - 4772 q^{97}+O(q^{100}) \) 12 * q - 116 * q^13 - 332 * q^17 + 144 * q^21 + 340 * q^25 + 80 * q^33 - 508 * q^37 - 656 * q^41 - 1180 * q^45 + 644 * q^53 - 960 * q^57 + 896 * q^61 - 2740 * q^65 + 1436 * q^73 - 3120 * q^77 + 5988 * q^81 - 500 * q^85 + 3280 * q^93 - 4772 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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