LMFDB - Embedded newform 160.4.n.d.127.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,4,Mod(63,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, 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("160.63"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 22x^{5} + 532x^{4} - 636x^{3} + 450x^{2} + 2160x + 5184 $ x^8 - 2x^7 + 2x^6 + 22x^5 + 532x^4 - 636x^3 + 450x^2 + 2160*x + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$3.63424 + 3.63424i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.4.n.d.63.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.50577 - 4.50577i) q^{3} +(-6.30193 - 9.23502i) q^{5} +(-19.0427 + 19.0427i) q^{7} +13.6039i q^{9} +24.0624i q^{11} +(35.4262 - 35.4262i) q^{13} +(-13.2158 + 70.0059i) q^{15} +(51.7286 + 51.7286i) q^{17} +68.8524 q^{19} +171.604 q^{21} +(-63.6865 - 63.6865i) q^{23} +(-45.5714 + 116.397i) q^{25} +(-60.3599 + 60.3599i) q^{27} +276.882i q^{29} +165.440i q^{31} +(108.419 - 108.419i) q^{33} +(295.866 + 55.8541i) q^{35} +(-245.210 - 245.210i) q^{37} -319.244 q^{39} +255.156 q^{41} +(-10.3009 - 10.3009i) q^{43} +(125.632 - 85.7306i) q^{45} +(-352.011 + 352.011i) q^{47} -382.250i q^{49} -466.154i q^{51} +(-275.902 + 275.902i) q^{53} +(222.217 - 151.639i) q^{55} +(-310.233 - 310.233i) q^{57} +245.936 q^{59} -1.64423 q^{61} +(-259.054 - 259.054i) q^{63} +(-550.415 - 103.908i) q^{65} +(544.329 - 544.329i) q^{67} +573.913i q^{69} +127.897i q^{71} +(-786.990 + 786.990i) q^{73} +(729.791 - 319.124i) q^{75} +(-458.213 - 458.213i) q^{77} -111.627 q^{79} +911.239 q^{81} +(-650.682 - 650.682i) q^{83} +(151.725 - 803.705i) q^{85} +(1247.56 - 1247.56i) q^{87} +467.584i q^{89} +1349.22i q^{91} +(745.433 - 745.433i) q^{93} +(-433.903 - 635.854i) q^{95} +(695.729 + 695.729i) q^{97} -327.341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 14 q^{5} - 10 q^{7} - 32 q^{13} - 22 q^{15} + 44 q^{17} - 80 q^{19} + 236 q^{21} - 230 q^{23} - 44 q^{25} - 80 q^{27} - 260 q^{33} + 866 q^{35} - 292 q^{37} - 1068 q^{39} + 932 q^{41} - 458 q^{43}+ \cdots - 1844 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 14 * q^5 - 10 * q^7 - 32 * q^13 - 22 * q^15 + 44 * q^17 - 80 * q^19 + 236 * q^21 - 230 * q^23 - 44 * q^25 - 80 * q^27 - 260 * q^33 + 866 * q^35 - 292 * q^37 - 1068 * q^39 + 932 * q^41 - 458 * q^43 - 110 * q^45 + 766 * q^47 - 892 * q^53 + 920 * q^55 - 1064 * q^57 - 16 * q^59 + 2564 * q^61 - 798 * q^63 - 888 * q^65 + 194 * q^67 - 1744 * q^73 + 4918 * q^75 - 1516 * q^77 - 3216 * q^79 + 4828 * q^81 - 3762 * q^83 - 920 * q^85 + 3904 * q^87 - 2420 * q^93 + 1544 * q^95 - 680 * q^97 - 1844 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−4.50577	−	4.50577i	−0.867135	−	0.867135i	0.125019	−	0.992154i	$-0.460101\pi$
$3$	−4.50577	−	4.50577i	−0.867135	−	0.867135i	−0.992154	+	0.125019i	$0.960101\pi$
$4$		0			0
$5$	−6.30193	−	9.23502i	−0.563662	−	0.826006i
$5$	−6.30193	−	9.23502i	−0.563662	−	0.826006i
$6$		0			0
$7$	−19.0427	+	19.0427i	−1.02821	+	1.02821i	−0.0286199	+	0.999590i	$0.509111\pi$
$7$	−19.0427	+	19.0427i	−1.02821	+	1.02821i	−0.999590	+	0.0286199i	$0.990889\pi$
$8$		0			0
$9$			13.6039i			0.503847i
$10$		0			0
$11$			24.0624i			0.659553i	0.944059	+	0.329776i	$0.106973\pi$
$11$			24.0624i			0.659553i	−0.944059	+	0.329776i	$0.893027\pi$
$12$		0			0
$13$	35.4262	−	35.4262i	0.755805	−	0.755805i	−0.219751	−	0.975556i	$-0.570525\pi$
$13$	35.4262	−	35.4262i	0.755805	−	0.755805i	0.975556	+	0.219751i	$0.0705245\pi$
$14$		0			0
$15$	−13.2158	+	70.0059i	−0.227488	+	1.20503i
$16$		0			0
$17$	51.7286	+	51.7286i	0.738002	+	0.738002i	0.972191	−	0.234189i	$-0.0752435\pi$
$17$	51.7286	+	51.7286i	0.738002	+	0.738002i	−0.234189	+	0.972191i	$0.575244\pi$
$18$		0			0
$19$	68.8524			0.831359			0.415680	−	0.909511i	$-0.363544\pi$
$19$	68.8524			0.831359			0.415680	+	0.909511i	$0.363544\pi$
$20$		0			0
$21$	171.604			1.78319
$22$		0			0
$23$	−63.6865	−	63.6865i	−0.577372	−	0.577372i	0.356807	−	0.934178i	$-0.383865\pi$
$23$	−63.6865	−	63.6865i	−0.577372	−	0.577372i	−0.934178	+	0.356807i	$0.883865\pi$
$24$		0			0
$25$	−45.5714	+	116.397i	−0.364571	+	0.931176i
$26$		0			0
$27$	−60.3599	+	60.3599i	−0.430232	+	0.430232i
$28$		0			0
$29$			276.882i			1.77295i	0.462774	+	0.886476i	$0.346854\pi$
$29$			276.882i			1.77295i	−0.462774	+	0.886476i	$0.653146\pi$
$30$		0			0
$31$			165.440i			0.958512i	0.877675	+	0.479256i	$0.159093\pi$
$31$			165.440i			0.958512i	−0.877675	+	0.479256i	$0.840907\pi$
$32$		0			0
$33$	108.419	−	108.419i	0.571921	−	0.571921i
$34$		0			0
$35$	295.866	+	55.8541i	1.42887	+	0.269745i
$36$		0			0
$37$	−245.210	−	245.210i	−1.08952	−	1.08952i	−0.995578	−	0.0939428i	$-0.970053\pi$
$37$	−245.210	−	245.210i	−1.08952	−	1.08952i	−0.0939428	−	0.995578i	$-0.529947\pi$
$38$		0			0
$39$	−319.244			−1.31077
$40$		0			0
$41$	255.156			0.971918			0.485959	−	0.873982i	$-0.338470\pi$
$41$	255.156			0.971918			0.485959	+	0.873982i	$0.338470\pi$
$42$		0			0
$43$	−10.3009	−	10.3009i	−0.0365318	−	0.0365318i	0.688605	−	0.725137i	$-0.258223\pi$
$43$	−10.3009	−	10.3009i	−0.0365318	−	0.0365318i	−0.725137	+	0.688605i	$0.758223\pi$
$44$		0			0
$45$	125.632	−	85.7306i	0.416180	−	0.283999i
$46$		0			0
$47$	−352.011	+	352.011i	−1.09247	+	1.09247i	−0.0972053	+	0.995264i	$0.530990\pi$
$47$	−352.011	+	352.011i	−1.09247	+	1.09247i	−0.995264	+	0.0972053i	$0.969010\pi$
$48$		0			0
$49$		−	382.250i		−	1.11443i
$50$		0			0
$51$		−	466.154i		−	1.27989i
$52$		0			0
$53$	−275.902	+	275.902i	−0.715057	+	0.715057i	−0.967589	−	0.252532i	$-0.918737\pi$
$53$	−275.902	+	275.902i	−0.715057	+	0.715057i	0.252532	+	0.967589i	$0.418737\pi$
$54$		0			0
$55$	222.217	−	151.639i	0.544794	−	0.371765i
$56$		0			0
$57$	−310.233	−	310.233i	−0.720901	−	0.720901i
$58$		0			0
$59$	245.936			0.542680			0.271340	−	0.962484i	$-0.412533\pi$
$59$	245.936			0.542680			0.271340	+	0.962484i	$0.412533\pi$
$60$		0			0
$61$	−1.64423			−0.00345119			−0.00172559	−	0.999999i	$-0.500549\pi$
$61$	−1.64423			−0.00345119			−0.00172559	+	0.999999i	$0.500549\pi$
$62$		0			0
$63$	−259.054	−	259.054i	−0.518060	−	0.518060i
$64$		0			0
$65$	−550.415	−	103.908i	−1.05032	−	0.198281i
$66$		0			0
$67$	544.329	−	544.329i	0.992542	−	0.992542i	−0.00743015	−	0.999972i	$-0.502365\pi$
$67$	544.329	−	544.329i	0.992542	−	0.992542i	0.999972	+	0.00743015i	$0.00236511\pi$
$68$		0			0
$69$			573.913i			1.00132i
$70$		0			0
$71$			127.897i			0.213782i	0.994271	+	0.106891i	$0.0340896\pi$
$71$			127.897i			0.213782i	−0.994271	+	0.106891i	$0.965910\pi$
$72$		0			0
$73$	−786.990	+	786.990i	−1.26178	+	1.26178i	−0.311556	+	0.950228i	$0.600850\pi$
$73$	−786.990	+	786.990i	−1.26178	+	1.26178i	−0.950228	+	0.311556i	$0.899150\pi$
$74$		0			0
$75$	729.791	−	319.124i	1.12359	−	0.491323i
$76$		0			0
$77$	−458.213	−	458.213i	−0.678159	−	0.678159i
$78$		0			0
$79$	−111.627			−0.158975			−0.0794876	−	0.996836i	$-0.525328\pi$
$79$	−111.627			−0.158975			−0.0794876	+	0.996836i	$0.525328\pi$
$80$		0			0
$81$	911.239			1.24999
$82$		0			0
$83$	−650.682	−	650.682i	−0.860502	−	0.860502i	0.130894	−	0.991396i	$-0.458215\pi$
$83$	−650.682	−	650.682i	−0.860502	−	0.860502i	−0.991396	+	0.130894i	$0.958215\pi$
$84$		0			0
$85$	151.725	−	803.705i	0.193610	−	1.02558i
$86$		0			0
$87$	1247.56	−	1247.56i	1.53739	−	1.53739i
$88$		0			0
$89$			467.584i			0.556897i	0.960451	+	0.278448i	$0.0898201\pi$
$89$			467.584i			0.556897i	−0.960451	+	0.278448i	$0.910180\pi$
$90$		0			0
$91$			1349.22i			1.55425i
$92$		0			0
$93$	745.433	−	745.433i	0.831159	−	0.831159i
$94$		0			0
$95$	−433.903	−	635.854i	−0.468605	−	0.686708i
$96$		0			0
$97$	695.729	+	695.729i	0.728253	+	0.728253i	0.970272	−	0.242018i	$-0.0778094\pi$
$97$	695.729	+	695.729i	0.728253	+	0.728253i	−0.242018	+	0.970272i	$0.577809\pi$
$98$		0			0
$99$	−327.341			−0.332313
$100$		0			0
$101$	−1250.06			−1.23154			−0.615770	−	0.787926i	$-0.711155\pi$
$101$	−1250.06			−1.23154			−0.615770	+	0.787926i	$0.711155\pi$
$102$		0			0
$103$	323.304	+	323.304i	0.309283	+	0.309283i	0.844631	−	0.535348i	$-0.179820\pi$
$103$	323.304	+	323.304i	0.309283	+	0.309283i	−0.535348	+	0.844631i	$0.679820\pi$
$104$		0			0
$105$	−1081.44	−	1584.77i	−1.00512	−	1.47293i
$106$		0			0
$107$	−694.477	+	694.477i	−0.627454	+	0.627454i	−0.947427	−	0.319973i	$-0.896326\pi$
$107$	−694.477	+	694.477i	−0.627454	+	0.627454i	0.319973	+	0.947427i	$0.396326\pi$
$108$		0			0
$109$		−	110.318i		−	0.0969411i	−0.998825	−	0.0484705i	$-0.984565\pi$
$109$		−	110.318i		−	0.0969411i	0.998825	−	0.0484705i	$-0.0154347\pi$
$110$		0			0
$111$			2209.72i			1.88952i
$112$		0			0
$113$	−640.630	+	640.630i	−0.533322	+	0.533322i	−0.921559	−	0.388237i	$-0.873084\pi$
$113$	−640.630	+	640.630i	−0.533322	+	0.533322i	0.388237	+	0.921559i	$0.373084\pi$
$114$		0			0
$115$	−186.798	+	989.494i	−0.151470	+	0.802354i
$116$		0			0
$117$	481.933	+	481.933i	0.380810	+	0.380810i
$118$		0			0
$119$	−1970.11			−1.51764
$120$		0			0
$121$	752.002			0.564990
$122$		0			0
$123$	−1149.67	−	1149.67i	−0.842784	−	0.842784i
$124$		0			0
$125$	1362.12	−	312.673i	0.974651	−	0.223730i
$126$		0			0
$127$	1688.98	−	1688.98i	1.18010	−	1.18010i	0.200378	−	0.979719i	$-0.435783\pi$
$127$	1688.98	−	1688.98i	1.18010	−	1.18010i	0.979719	−	0.200378i	$-0.0642172\pi$
$128$		0			0
$129$			92.8266i			0.0633561i
$130$		0			0
$131$			447.782i			0.298648i	0.988788	+	0.149324i	$0.0477097\pi$
$131$			447.782i			0.298648i	−0.988788	+	0.149324i	$0.952290\pi$
$132$		0			0
$133$	−1311.14	+	1311.14i	−0.854812	+	0.854812i
$134$		0			0
$135$	937.809	+	177.041i	0.597879	+	0.112869i
$136$		0			0
$137$	402.750	+	402.750i	0.251163	+	0.251163i	0.821447	−	0.570285i	$-0.193167\pi$
$137$	402.750	+	402.750i	0.251163	+	0.251163i	−0.570285	+	0.821447i	$0.693167\pi$
$138$		0			0
$139$	−1826.99			−1.11484			−0.557422	−	0.830229i	$-0.688209\pi$
$139$	−1826.99			−1.11484			−0.557422	+	0.830229i	$0.688209\pi$
$140$		0			0
$141$	3172.16			1.89464
$142$		0			0
$143$	852.439	+	852.439i	0.498493	+	0.498493i
$144$		0			0
$145$	2557.01	−	1744.89i	1.46447	−	0.999345i
$146$		0			0
$147$	−1722.33	+	1722.33i	−0.966364	+	0.966364i
$148$		0			0
$149$			2424.72i			1.33316i	0.745435	+	0.666579i	$0.232242\pi$
$149$			2424.72i			1.33316i	−0.745435	+	0.666579i	$0.767758\pi$
$150$		0			0
$151$			2496.98i			1.34570i	0.739778	+	0.672851i	$0.234931\pi$
$151$			2496.98i			1.34570i	−0.739778	+	0.672851i	$0.765069\pi$
$152$		0			0
$153$	−703.709	+	703.709i	−0.371840	+	0.371840i
$154$		0			0
$155$	1527.84	−	1042.59i	0.791736	−	0.540276i
$156$		0			0
$157$	573.265	+	573.265i	0.291411	+	0.291411i	0.837638	−	0.546226i	$-0.183936\pi$
$157$	573.265	+	573.265i	0.291411	+	0.291411i	−0.546226	+	0.837638i	$0.683936\pi$
$158$		0			0
$159$	2486.30			1.24010
$160$		0			0
$161$	2425.53			1.18732
$162$		0			0
$163$	1863.90	+	1863.90i	0.895658	+	0.895658i	0.995049	−	0.0993905i	$-0.0316893\pi$
$163$	1863.90	+	1863.90i	0.895658	+	0.895658i	−0.0993905	+	0.995049i	$0.531689\pi$
$164$		0			0
$165$	−1684.51	−	318.005i	−0.794780	−	0.150040i
$166$		0			0
$167$	1005.91	−	1005.91i	0.466105	−	0.466105i	−0.434545	−	0.900650i	$-0.643091\pi$
$167$	1005.91	−	1005.91i	0.466105	−	0.466105i	0.900650	+	0.434545i	$0.143091\pi$
$168$		0			0
$169$		−	313.033i		−	0.142482i
$170$		0			0
$171$			936.659i			0.418878i
$172$		0			0
$173$	−1498.38	+	1498.38i	−0.658495	+	0.658495i	−0.955024	−	0.296529i	$-0.904171\pi$
$173$	−1498.38	+	1498.38i	−0.658495	+	0.658495i	0.296529	+	0.955024i	$0.404171\pi$
$174$		0			0
$175$	−1348.71	−	3084.32i	−0.582589	−	1.33230i
$176$		0			0
$177$	−1108.13	−	1108.13i	−0.470577	−	0.470577i
$178$		0			0
$179$	−2761.65			−1.15316			−0.576578	−	0.817042i	$-0.695612\pi$
$179$	−2761.65			−1.15316			−0.576578	+	0.817042i	$0.695612\pi$
$180$		0			0
$181$	375.460			0.154186			0.0770932	−	0.997024i	$-0.475436\pi$
$181$	375.460			0.154186			0.0770932	+	0.997024i	$0.475436\pi$
$182$		0			0
$183$	7.40852	+	7.40852i	0.00299264	+	0.00299264i
$184$		0			0
$185$	−719.224	+	3809.81i	−0.285829	+	1.51407i
$186$		0			0
$187$	−1244.71	+	1244.71i	−0.486751	+	0.486751i
$188$		0			0
$189$		−	2298.83i		−	0.884738i
$190$		0			0
$191$		−	1955.48i		−	0.740802i	−0.928872	−	0.370401i	$-0.879220\pi$
$191$		−	1955.48i		−	0.740802i	0.928872	−	0.370401i	$-0.120780\pi$
$192$		0			0
$193$	2668.92	−	2668.92i	0.995404	−	0.995404i	−0.00458525	−	0.999989i	$-0.501460\pi$
$193$	2668.92	−	2668.92i	0.995404	−	0.995404i	0.999989	+	0.00458525i	$0.00145954\pi$
$194$		0			0
$195$	2011.86	+	2948.23i	0.738831	+	1.08270i
$196$		0			0
$197$	−1985.98	−	1985.98i	−0.718249	−	0.718249i	0.249998	−	0.968246i	$-0.419570\pi$
$197$	−1985.98	−	1985.98i	−0.718249	−	0.718249i	−0.968246	+	0.249998i	$0.919570\pi$
$198$		0			0
$199$	−2555.09			−0.910179			−0.455090	−	0.890446i	$-0.650393\pi$
$199$	−2555.09			−0.910179			−0.455090	+	0.890446i	$0.650393\pi$
$200$		0			0
$201$	−4905.24			−1.72134
$202$		0			0
$203$	−5272.58	−	5272.58i	−1.82297	−	1.82297i
$204$		0			0
$205$	−1607.97	−	2356.37i	−0.547833	−	0.802810i
$206$		0			0
$207$	866.382	−	866.382i	0.290907	−	0.290907i
$208$		0			0
$209$			1656.75i			0.548325i
$210$		0			0
$211$		−	4962.05i		−	1.61896i	−0.587145	−	0.809482i	$-0.699748\pi$
$211$		−	4962.05i		−	1.61896i	0.587145	−	0.809482i	$-0.300252\pi$
$212$		0			0
$213$	576.272	−	576.272i	0.185378	−	0.185378i
$214$		0			0
$215$	−30.2134	+	160.044i	−0.00958390	+	0.0507671i
$216$		0			0
$217$	−3150.42	−	3150.42i	−0.985552	−	0.985552i
$218$		0			0
$219$	7091.99			2.18827
$220$		0			0
$221$	3665.10			1.11557
$222$		0			0
$223$	406.248	+	406.248i	0.121993	+	0.121993i	0.765467	−	0.643475i	$-0.222508\pi$
$223$	406.248	+	406.248i	0.121993	+	0.121993i	−0.643475	+	0.765467i	$0.722508\pi$
$224$		0			0
$225$	−1583.45	−	619.946i	−0.469170	−	0.183688i
$226$		0			0
$227$	−1741.25	+	1741.25i	−0.509123	+	0.509123i	−0.914257	−	0.405134i	$-0.867225\pi$
$227$	−1741.25	+	1741.25i	−0.509123	+	0.509123i	0.405134	+	0.914257i	$0.367225\pi$
$228$		0			0
$229$		−	2752.03i		−	0.794146i	−0.917787	−	0.397073i	$-0.870026\pi$
$229$		−	2752.03i		−	0.794146i	0.917787	−	0.397073i	$-0.129974\pi$
$230$		0			0
$231$			4129.20i			1.17611i
$232$		0			0
$233$	−1429.30	+	1429.30i	−0.401875	+	0.401875i	−0.878893	−	0.477018i	$-0.841717\pi$
$233$	−1429.30	+	1429.30i	−0.401875	+	0.401875i	0.477018	+	0.878893i	$0.341717\pi$
$234$		0			0
$235$	5469.18	+	1032.48i	1.51817	+	0.286603i
$236$		0			0
$237$	502.966	+	502.966i	0.137853	+	0.137853i
$238$		0			0
$239$	−652.750			−0.176665			−0.0883324	−	0.996091i	$-0.528154\pi$
$239$	−652.750			−0.176665			−0.0883324	+	0.996091i	$0.528154\pi$
$240$		0			0
$241$	−2698.72			−0.721328			−0.360664	−	0.932696i	$-0.617450\pi$
$241$	−2698.72			−0.721328			−0.360664	+	0.932696i	$0.617450\pi$
$242$		0			0
$243$	−2476.11	−	2476.11i	−0.653674	−	0.653674i
$244$		0			0
$245$	−3530.09	+	2408.92i	−0.920528	+	0.628163i
$246$		0			0
$247$	2439.18	−	2439.18i	0.628345	−	0.628345i
$248$		0			0
$249$			5863.65i			1.49234i
$250$		0			0
$251$		−	5353.49i		−	1.34625i	−0.739528	−	0.673126i	$-0.764951\pi$
$251$		−	5353.49i		−	1.34625i	0.739528	−	0.673126i	$-0.235049\pi$
$252$		0			0
$253$	1532.45	−	1532.45i	0.380807	−	0.380807i
$254$		0			0
$255$	−4304.94	+	2937.67i	−1.05720	+	0.721428i
$256$		0			0
$257$	835.937	+	835.937i	0.202896	+	0.202896i	0.801240	−	0.598343i	$-0.204174\pi$
$257$	835.937	+	835.937i	0.202896	+	0.202896i	−0.598343	+	0.801240i	$0.704174\pi$
$258$		0			0
$259$	9338.93			2.24051
$260$		0			0
$261$	−3766.66			−0.893296
$262$		0			0
$263$	−1135.76	−	1135.76i	−0.266289	−	0.266289i	0.561314	−	0.827603i	$-0.310296\pi$
$263$	−1135.76	−	1135.76i	−0.266289	−	0.266289i	−0.827603	+	0.561314i	$0.810296\pi$
$264$		0			0
$265$	4286.67	+	809.246i	0.993691	+	0.187591i
$266$		0			0
$267$	2106.83	−	2106.83i	0.482905	−	0.482905i
$268$		0			0
$269$			188.749i			0.0427814i	0.999771	+	0.0213907i	$0.00680940\pi$
$269$			188.749i			0.0427814i	−0.999771	+	0.0213907i	$0.993191\pi$
$270$		0			0
$271$		−	6368.79i		−	1.42759i	−0.700356	−	0.713794i	$-0.746975\pi$
$271$		−	6368.79i		−	1.42759i	0.700356	−	0.713794i	$-0.253025\pi$
$272$		0			0
$273$	6079.28	−	6079.28i	1.34775	−	1.34775i
$274$		0			0
$275$	−2800.79	−	1096.56i	−0.614159	−	0.240454i
$276$		0			0
$277$	1045.45	+	1045.45i	0.226769	+	0.226769i	0.811341	−	0.584573i	$-0.198738\pi$
$277$	1045.45	+	1045.45i	0.226769	+	0.226769i	−0.584573	+	0.811341i	$0.698738\pi$
$278$		0			0
$279$	−2250.62			−0.482943
$280$		0			0
$281$	−1076.19			−0.228470			−0.114235	−	0.993454i	$-0.536442\pi$
$281$	−1076.19			−0.228470			−0.114235	+	0.993454i	$0.536442\pi$
$282$		0			0
$283$	4873.91	+	4873.91i	1.02376	+	1.02376i	0.999711	+	0.0240482i	$0.00765550\pi$
$283$	4873.91	+	4873.91i	1.02376	+	1.02376i	0.0240482	+	0.999711i	$0.492344\pi$
$284$		0			0
$285$	−909.943	+	4820.07i	−0.189124	+	1.00181i
$286$		0			0
$287$	−4858.86	+	4858.86i	−0.999336	+	0.999336i
$288$		0			0
$289$			438.699i			0.0892934i
$290$		0			0
$291$		−	6269.59i		−	1.26299i
$292$		0			0
$293$	−1143.86	+	1143.86i	−0.228072	+	0.228072i	−0.811887	−	0.583815i	$-0.801559\pi$
$293$	−1143.86	+	1143.86i	−0.228072	+	0.228072i	0.583815	+	0.811887i	$0.301559\pi$
$294$		0			0
$295$	−1549.87	−	2271.22i	−0.305888	−	0.448257i
$296$		0			0
$297$	−1452.40	−	1452.40i	−0.283761	−	0.283761i
$298$		0			0
$299$	−4512.34			−0.872760
$300$		0			0
$301$	392.313			0.0751248
$302$		0			0
$303$	5632.47	+	5632.47i	1.06791	+	1.06791i
$304$		0			0
$305$	10.3618	+	15.1845i	0.00194530	+	0.00285070i
$306$		0			0
$307$	−5265.16	+	5265.16i	−0.978822	+	0.978822i	−0.999780	−	0.0209582i	$-0.993328\pi$
$307$	−5265.16	+	5265.16i	−0.978822	+	0.978822i	0.0209582	+	0.999780i	$0.493328\pi$
$308$		0			0
$309$		−	2913.47i		−	0.536380i
$310$		0			0
$311$			6997.16i			1.27580i	0.770121	+	0.637898i	$0.220196\pi$
$311$			6997.16i			1.27580i	−0.770121	+	0.637898i	$0.779804\pi$
$312$		0			0
$313$	−2468.13	+	2468.13i	−0.445708	+	0.445708i	−0.893925	−	0.448217i	$-0.852059\pi$
$313$	−2468.13	+	2468.13i	−0.445708	+	0.445708i	0.448217	+	0.893925i	$0.352059\pi$
$314$		0			0
$315$	−759.831	+	4024.92i	−0.135910	+	0.719932i
$316$		0			0
$317$	2339.88	+	2339.88i	0.414577	+	0.414577i	0.883329	−	0.468753i	$-0.155296\pi$
$317$	2339.88	+	2339.88i	0.414577	+	0.414577i	−0.468753	+	0.883329i	$0.655296\pi$
$318$		0			0
$319$	−6662.43			−1.16936
$320$		0			0
$321$	6258.30			1.08818
$322$		0			0
$323$	3561.64	+	3561.64i	0.613545	+	0.613545i
$324$		0			0
$325$	2509.08	+	5737.92i	0.428243	+	0.979332i
$326$		0			0
$327$	−497.069	+	497.069i	−0.0840610	+	0.0840610i
$328$		0			0
$329$		−	13406.5i		−	2.24658i
$330$		0			0
$331$			8050.09i			1.33678i	0.743812	+	0.668388i	$0.233016\pi$
$331$			8050.09i			1.33678i	−0.743812	+	0.668388i	$0.766984\pi$
$332$		0			0
$333$	3335.80	−	3335.80i	0.548951	−	0.548951i
$334$		0			0
$335$	−8457.21	−	1596.57i	−1.37930	−	0.260388i
$336$		0			0
$337$	872.819	+	872.819i	0.141085	+	0.141085i	0.774122	−	0.633037i	$-0.218192\pi$
$337$	872.819	+	872.819i	0.141085	+	0.141085i	−0.633037	+	0.774122i	$0.718192\pi$
$338$		0			0
$339$	5773.06			0.924925
$340$		0			0
$341$	−3980.88			−0.632189
$342$		0			0
$343$	747.435	+	747.435i	0.117661	+	0.117661i
$344$		0			0
$345$	5300.10	−	3616.76i	0.827095	−	0.564405i
$346$		0			0
$347$	−2135.83	+	2135.83i	−0.330425	+	0.330425i	−0.852748	−	0.522323i	$-0.825066\pi$
$347$	−2135.83	+	2135.83i	−0.330425	+	0.330425i	0.522323	+	0.852748i	$0.325066\pi$
$348$		0			0
$349$		−	5750.76i		−	0.882038i	−0.897498	−	0.441019i	$-0.854617\pi$
$349$		−	5750.76i		−	0.882038i	0.897498	−	0.441019i	$-0.145383\pi$
$350$		0			0
$351$			4276.64i			0.650343i
$352$		0			0
$353$	−4490.90	+	4490.90i	−0.677128	+	0.677128i	−0.959349	−	0.282221i	$-0.908929\pi$
$353$	−4490.90	+	4490.90i	−0.677128	+	0.677128i	0.282221	+	0.959349i	$0.408929\pi$
$354$		0			0
$355$	1181.13	−	805.996i	0.176585	−	0.120501i
$356$		0			0
$357$	8876.84	+	8876.84i	1.31600	+	1.31600i
$358$		0			0
$359$	4519.92			0.664491			0.332245	−	0.943193i	$-0.392194\pi$
$359$	4519.92			0.664491			0.332245	+	0.943193i	$0.392194\pi$
$360$		0			0
$361$	−2118.34			−0.308842
$362$		0			0
$363$	−3388.35	−	3388.35i	−0.489923	−	0.489923i
$364$		0			0
$365$	12227.4	+	2308.32i	1.75346	+	0.331021i
$366$		0			0
$367$	1807.81	−	1807.81i	0.257131	−	0.257131i	−0.566756	−	0.823886i	$-0.691802\pi$
$367$	1807.81	−	1807.81i	0.257131	−	0.257131i	0.823886	+	0.566756i	$0.191802\pi$
$368$		0			0
$369$			3471.10i			0.489698i
$370$		0			0
$371$		−	10507.8i		−	1.47046i
$372$		0			0
$373$	3871.38	−	3871.38i	0.537406	−	0.537406i	−0.385360	−	0.922766i	$-0.625923\pi$
$373$	3871.38	−	3871.38i	0.537406	−	0.537406i	0.922766	+	0.385360i	$0.125923\pi$
$374$		0			0
$375$	−7546.21	−	4728.55i	−1.03916	−	0.651150i
$376$		0			0
$377$	9808.87	+	9808.87i	1.34001	+	1.34001i
$378$		0			0
$379$	−9766.74			−1.32370			−0.661852	−	0.749635i	$-0.730229\pi$
$379$	−9766.74			−1.32370			−0.661852	+	0.749635i	$0.730229\pi$
$380$		0			0
$381$	−15220.3			−2.04661
$382$		0			0
$383$	9798.07	+	9798.07i	1.30720	+	1.30720i	0.923427	+	0.383774i	$0.125376\pi$
$383$	9798.07	+	9798.07i	1.30720	+	1.30720i	0.383774	+	0.923427i	$0.374624\pi$
$384$		0			0
$385$	−1343.98	+	7119.24i	−0.177911	+	0.942415i
$386$		0			0
$387$	140.132	−	140.132i	0.0184064	−	0.0184064i
$388$		0			0
$389$			3097.02i			0.403664i	0.979420	+	0.201832i	$0.0646895\pi$
$389$			3097.02i			0.403664i	−0.979420	+	0.201832i	$0.935310\pi$
$390$		0			0
$391$		−	6588.82i		−	0.852203i
$392$		0			0
$393$	2017.60	−	2017.60i	0.258968	−	0.258968i
$394$		0			0
$395$	703.467	+	1030.88i	0.0896082	+	0.131314i
$396$		0			0
$397$	−4297.58	−	4297.58i	−0.543298	−	0.543298i	0.381197	−	0.924494i	$-0.375512\pi$
$397$	−4297.58	−	4297.58i	−0.543298	−	0.543298i	−0.924494	+	0.381197i	$0.875512\pi$
$398$		0			0
$399$	11815.4			1.48248
$400$		0			0
$401$	−13709.1			−1.70723			−0.853615	−	0.520905i	$-0.825595\pi$
$401$	−13709.1			−1.70723			−0.853615	+	0.520905i	$0.825595\pi$
$402$		0			0
$403$	5860.91	+	5860.91i	0.724448	+	0.724448i
$404$		0			0
$405$	−5742.57	−	8415.32i	−0.704569	−	1.03249i
$406$		0			0
$407$	5900.33	−	5900.33i	0.718596	−	0.718596i
$408$		0			0
$409$			4992.59i			0.603588i	0.953373	+	0.301794i	$0.0975855\pi$
$409$			4992.59i			0.603588i	−0.953373	+	0.301794i	$0.902414\pi$
$410$		0			0
$411$		−	3629.40i		−	0.435584i
$412$		0			0
$413$	−4683.29	+	4683.29i	−0.557989	+	0.557989i
$414$		0			0
$415$	−1908.51	+	10109.6i	−0.225748	+	1.19581i
$416$		0			0
$417$	8231.99	+	8231.99i	0.966721	+	0.966721i
$418$		0			0
$419$	6897.24			0.804182			0.402091	−	0.915600i	$-0.368284\pi$
$419$	6897.24			0.804182			0.402091	+	0.915600i	$0.368284\pi$
$420$		0			0
$421$	4086.33			0.473053			0.236527	−	0.971625i	$-0.423991\pi$
$421$	4086.33			0.473053			0.236527	+	0.971625i	$0.423991\pi$
$422$		0			0
$423$	−4788.71	−	4788.71i	−0.550437	−	0.550437i
$424$		0			0
$425$	−8378.40	+	3663.71i	−0.956263	+	0.418155i
$426$		0			0
$427$	31.3106	−	31.3106i	0.00354854	−	0.00354854i
$428$		0			0
$429$		−	7681.78i		−	0.864522i
$430$		0			0
$431$		−	3100.64i		−	0.346526i	−0.984876	−	0.173263i	$-0.944569\pi$
$431$		−	3100.64i		−	0.346526i	0.984876	−	0.173263i	$-0.0554311\pi$
$432$		0			0
$433$	4730.61	−	4730.61i	0.525031	−	0.525031i	−0.394055	−	0.919087i	$-0.628928\pi$
$433$	4730.61	−	4730.61i	0.525031	−	0.525031i	0.919087	+	0.394055i	$0.128928\pi$
$434$		0			0
$435$	−19383.3	−	3659.22i	−2.13646	−	0.403325i
$436$		0			0
$437$	−4384.97	−	4384.97i	−0.480003	−	0.480003i
$438$		0			0
$439$	2151.92			0.233953			0.116977	−	0.993135i	$-0.462680\pi$
$439$	2151.92			0.233953			0.116977	+	0.993135i	$0.462680\pi$
$440$		0			0
$441$	5200.08			0.561503
$442$		0			0
$443$	658.583	+	658.583i	0.0706326	+	0.0706326i	0.741541	−	0.670908i	$-0.234095\pi$
$443$	658.583	+	658.583i	0.0706326	+	0.0706326i	−0.670908	+	0.741541i	$0.734095\pi$
$444$		0			0
$445$	4318.15	−	2946.68i	0.460000	−	0.313901i
$446$		0			0
$447$	10925.2	−	10925.2i	1.15603	−	1.15603i
$448$		0			0
$449$		−	12825.5i		−	1.34805i	−0.738709	−	0.674025i	$-0.764564\pi$
$449$		−	12825.5i		−	1.34805i	0.738709	−	0.674025i	$-0.235436\pi$
$450$		0			0
$451$			6139.65i			0.641031i
$452$		0			0
$453$	11250.8	−	11250.8i	1.16691	−	1.16691i
$454$		0			0
$455$	12460.1	−	8502.71i	1.28382	−	0.876073i
$456$		0			0
$457$	−12267.0	−	12267.0i	−1.25564	−	1.25564i	−0.953154	−	0.302485i	$-0.902184\pi$
$457$	−12267.0	−	12267.0i	−1.25564	−	1.25564i	−0.302485	−	0.953154i	$-0.597816\pi$
$458$		0			0
$459$	−6244.67			−0.635024
$460$		0			0
$461$	−3613.51			−0.365072			−0.182536	−	0.983199i	$-0.558431\pi$
$461$	−3613.51			−0.365072			−0.182536	+	0.983199i	$0.558431\pi$
$462$		0			0
$463$	−6123.47	−	6123.47i	−0.614647	−	0.614647i	0.329506	−	0.944153i	$-0.393118\pi$
$463$	−6123.47	−	6123.47i	−0.614647	−	0.614647i	−0.944153	+	0.329506i	$0.893118\pi$
$464$		0			0
$465$	−11581.8	−	2186.43i	−1.15504	−	0.218050i
$466$		0			0
$467$	25.8320	−	25.8320i	0.00255966	−	0.00255966i	−0.705826	−	0.708385i	$-0.749424\pi$
$467$	25.8320	−	25.8320i	0.00255966	−	0.00255966i	0.708385	+	0.705826i	$0.249424\pi$
$468$		0			0
$469$			20731.0i			2.04108i
$470$		0			0
$471$		−	5166.00i		−	0.505386i
$472$		0			0
$473$	247.863	−	247.863i	0.0240947	−	0.0240947i
$474$		0			0
$475$	−3137.70	+	8014.21i	−0.303089	+	0.774142i
$476$		0			0
$477$	−3753.33	−	3753.33i	−0.360279	−	0.360279i
$478$		0			0
$479$	−4039.99			−0.385370			−0.192685	−	0.981261i	$-0.561719\pi$
$479$	−4039.99			−0.385370			−0.192685	+	0.981261i	$0.561719\pi$
$480$		0			0
$481$	−17373.7			−1.64693
$482$		0			0
$483$	−10928.9	−	10928.9i	−1.02957	−	1.02957i
$484$		0			0
$485$	2040.64	−	10809.5i	0.191053	−	1.01203i
$486$		0			0
$487$	−2976.53	+	2976.53i	−0.276960	+	0.276960i	−0.831894	−	0.554934i	$-0.812743\pi$
$487$	−2976.53	+	2976.53i	−0.276960	+	0.276960i	0.554934	+	0.831894i	$0.312743\pi$
$488$		0			0
$489$		−	16796.6i		−	1.55331i
$490$		0			0
$491$			5036.72i			0.462941i	0.972842	+	0.231470i	$0.0743536\pi$
$491$			5036.72i			0.462941i	−0.972842	+	0.231470i	$0.925646\pi$
$492$		0			0
$493$	−14322.7	+	14322.7i	−1.30844	+	1.30844i
$494$		0			0
$495$	2062.88	+	3023.00i	0.187312	+	0.274493i
$496$		0			0
$497$	−2435.50	−	2435.50i	−0.219813	−	0.219813i
$498$		0			0
$499$	1212.29			0.108756			0.0543781	−	0.998520i	$-0.482682\pi$
$499$	1212.29			0.108756			0.0543781	+	0.998520i	$0.482682\pi$
$500$		0			0
$501$	−9064.77			−0.808351
$502$		0			0
$503$	6638.76	+	6638.76i	0.588485	+	0.588485i	0.937221	−	0.348736i	$-0.113389\pi$
$503$	6638.76	+	6638.76i	0.588485	+	0.588485i	−0.348736	+	0.937221i	$0.613389\pi$
$504$		0			0
$505$	7877.78	+	11544.3i	0.694172	+	1.01726i
$506$		0			0
$507$	−1410.45	+	1410.45i	−0.123551	+	0.123551i
$508$		0			0
$509$			9412.97i			0.819690i	0.912155	+	0.409845i	$0.134417\pi$
$509$			9412.97i			0.819690i	−0.912155	+	0.409845i	$0.865583\pi$
$510$		0			0
$511$		−	29972.9i		−	2.59476i
$512$		0			0
$513$	−4155.92	+	4155.92i	−0.357677	+	0.357677i
$514$		0			0
$515$	948.283	−	5023.17i	0.0811385	−	0.429800i
$516$		0			0
$517$	−8470.22	−	8470.22i	−0.720541	−	0.720541i
$518$		0			0
$519$	13502.7			1.14201
$520$		0			0
$521$	19248.8			1.61863			0.809316	−	0.587374i	$-0.199838\pi$
$521$	19248.8			1.61863			0.809316	+	0.587374i	$0.199838\pi$
$522$		0			0
$523$	261.022	+	261.022i	0.0218235	+	0.0218235i	0.717934	−	0.696111i	$-0.245088\pi$
$523$	261.022	+	261.022i	0.0218235	+	0.0218235i	−0.696111	+	0.717934i	$0.745088\pi$
$524$		0			0
$525$	−7820.23	+	19974.2i	−0.650101	+	1.66047i
$526$		0			0
$527$	−8557.97	+	8557.97i	−0.707384	+	0.707384i
$528$		0			0
$529$		−	4055.07i		−	0.333284i
$530$		0			0
$531$			3345.68i			0.273427i
$532$		0			0
$533$	9039.20	−	9039.20i	0.734580	−	0.734580i
$534$		0			0
$535$	10790.1	+	2036.97i	0.871953	+	0.164609i
$536$		0			0
$537$	12443.3	+	12443.3i	0.999943	+	0.999943i
$538$		0			0
$539$	9197.85			0.735027
$540$		0			0
$541$	10923.4			0.868081			0.434040	−	0.900893i	$-0.357088\pi$
$541$	10923.4			0.868081			0.434040	+	0.900893i	$0.357088\pi$
$542$		0			0
$543$	−1691.74	−	1691.74i	−0.133700	−	0.133700i
$544$		0			0
$545$	−1018.79	+	695.218i	−0.0800739	+	0.0546420i
$546$		0			0
$547$	−5573.10	+	5573.10i	−0.435628	+	0.435628i	−0.890538	−	0.454909i	$-0.849672\pi$
$547$	−5573.10	+	5573.10i	−0.435628	+	0.435628i	0.454909	+	0.890538i	$0.349672\pi$
$548$		0			0
$549$		−	22.3679i		−	0.00173887i
$550$		0			0
$551$			19064.0i			1.47396i
$552$		0			0
$553$	2125.69	−	2125.69i	0.163460	−	0.163460i
$554$		0			0
$555$	20406.8	−	13925.5i	1.56076	−	1.06505i
$556$		0			0
$557$	−5747.58	−	5747.58i	−0.437222	−	0.437222i	0.453854	−	0.891076i	$-0.350049\pi$
$557$	−5747.58	−	5747.58i	−0.437222	−	0.437222i	−0.891076	+	0.453854i	$0.850049\pi$
$558$		0			0
$559$	−729.842			−0.0552219
$560$		0			0
$561$	11216.8			0.844158
$562$		0			0
$563$	3286.45	+	3286.45i	0.246016	+	0.246016i	0.819334	−	0.573317i	$-0.194344\pi$
$563$	3286.45	+	3286.45i	0.246016	+	0.246016i	−0.573317	+	0.819334i	$0.694344\pi$
$564$		0			0
$565$	9953.44	+	1879.03i	0.741141	+	0.139914i
$566$		0			0
$567$	−17352.5	+	17352.5i	−1.28525	+	1.28525i
$568$		0			0
$569$		−	6597.28i		−	0.486067i	−0.970018	−	0.243034i	$-0.921857\pi$
$569$		−	6597.28i		−	0.486067i	0.970018	−	0.243034i	$-0.0781426\pi$
$570$		0			0
$571$		−	17436.9i		−	1.27796i	−0.769225	−	0.638978i	$-0.779358\pi$
$571$		−	17436.9i		−	1.27796i	0.769225	−	0.638978i	$-0.220642\pi$
$572$		0			0
$573$	−8810.92	+	8810.92i	−0.642376	+	0.642376i
$574$		0			0
$575$	10315.2	−	4510.63i	0.748127	−	0.327141i
$576$		0			0
$577$	1224.90	+	1224.90i	0.0883764	+	0.0883764i	0.749913	−	0.661537i	$-0.230095\pi$
$577$	1224.90	+	1224.90i	0.0883764	+	0.0883764i	−0.661537	+	0.749913i	$0.730095\pi$
$578$		0			0
$579$	−24051.1			−1.72630
$580$		0			0
$581$	24781.5			1.76955
$582$		0			0
$583$	−6638.85	−	6638.85i	−0.471617	−	0.471617i
$584$		0			0
$585$	1413.56	−	7487.77i	0.0999032	−	0.529199i
$586$		0			0
$587$	9031.37	−	9031.37i	0.635033	−	0.635033i	−0.314293	−	0.949326i	$-0.601767\pi$
$587$	9031.37	−	9031.37i	0.635033	−	0.635033i	0.949326	+	0.314293i	$0.101767\pi$
$588$		0			0
$589$			11390.9i			0.796868i
$590$		0			0
$591$			17896.7i			1.24564i
$592$		0			0
$593$	5309.82	−	5309.82i	0.367703	−	0.367703i	−0.498936	−	0.866639i	$-0.666276\pi$
$593$	5309.82	−	5309.82i	0.367703	−	0.367703i	0.866639	+	0.498936i	$0.166276\pi$
$594$		0			0
$595$	12415.5	+	18194.0i	0.855437	+	1.25358i
$596$		0			0
$597$	11512.7	+	11512.7i	0.789249	+	0.789249i
$598$		0			0
$599$	−10472.4			−0.714339			−0.357169	−	0.934040i	$-0.616258\pi$
$599$	−10472.4			−0.714339			−0.357169	+	0.934040i	$0.616258\pi$
$600$		0			0
$601$	16729.2			1.13544			0.567718	−	0.823223i	$-0.307826\pi$
$601$	16729.2			1.13544			0.567718	+	0.823223i	$0.307826\pi$
$602$		0			0
$603$	7404.97	+	7404.97i	0.500089	+	0.500089i
$604$		0			0
$605$	−4739.06	−	6944.76i	−0.318463	−	0.466685i
$606$		0			0
$607$	−5258.02	+	5258.02i	−0.351592	+	0.351592i	−0.860702	−	0.509110i	$-0.829975\pi$
$607$	−5258.02	+	5258.02i	−0.351592	+	0.351592i	0.509110	+	0.860702i	$0.329975\pi$
$608$		0			0
$609$			47514.0i			3.16152i
$610$		0			0
$611$			24940.8i			1.65139i
$612$		0			0
$613$	6137.40	−	6137.40i	0.404384	−	0.404384i	−0.475391	−	0.879775i	$-0.657693\pi$
$613$	6137.40	−	6137.40i	0.404384	−	0.404384i	0.879775	+	0.475391i	$0.157693\pi$
$614$		0			0
$615$	−3372.10	+	17862.4i	−0.221099	+	1.17119i
$616$		0			0
$617$	−18906.7	−	18906.7i	−1.23364	−	1.23364i	−0.962556	−	0.271084i	$-0.912618\pi$
$617$	−18906.7	−	18906.7i	−1.23364	−	1.23364i	−0.271084	−	0.962556i	$-0.587382\pi$
$618$		0			0
$619$	−13550.3			−0.879859			−0.439929	−	0.898032i	$-0.644997\pi$
$619$	−13550.3			−0.879859			−0.439929	+	0.898032i	$0.644997\pi$
$620$		0			0
$621$	7688.21			0.496807
$622$		0			0
$623$	−8904.08	−	8904.08i	−0.572607	−	0.572607i
$624$		0			0
$625$	−11471.5	−	10608.7i	−0.734176	−	0.678959i
$626$		0			0
$627$	7464.94	−	7464.94i	0.475472	−	0.475472i
$628$		0			0
$629$		−	25368.7i		−	1.60814i
$630$		0			0
$631$		−	5665.10i		−	0.357407i	−0.983903	−	0.178704i	$-0.942810\pi$
$631$		−	5665.10i		−	0.357407i	0.983903	−	0.178704i	$-0.0571903\pi$
$632$		0			0
$633$	−22357.8	+	22357.8i	−1.40386	+	1.40386i
$634$		0			0
$635$	−26241.5	−	4953.93i	−1.63994	−	0.309591i
$636$		0			0
$637$	−13541.7	−	13541.7i	−0.842294	−	0.842294i
$638$		0			0
$639$	−1739.89			−0.107713
$640$		0			0
$641$	−836.036			−0.0515155			−0.0257578	−	0.999668i	$-0.508200\pi$
$641$	−836.036			−0.0515155			−0.0257578	+	0.999668i	$0.508200\pi$
$642$		0			0
$643$	4378.78	+	4378.78i	0.268557	+	0.268557i	0.828519	−	0.559962i	$-0.189184\pi$
$643$	4378.78	+	4378.78i	0.268557	+	0.268557i	−0.559962	+	0.828519i	$0.689184\pi$
$644$		0			0
$645$	857.256	−	584.987i	0.0523325	−	0.0357114i
$646$		0			0
$647$	−14469.2	+	14469.2i	−0.879201	+	0.879201i	−0.993452	−	0.114251i	$-0.963553\pi$
$647$	−14469.2	+	14469.2i	−0.879201	+	0.879201i	0.114251	+	0.993452i	$0.463553\pi$
$648$		0			0
$649$			5917.80i			0.357926i
$650$		0			0
$651$			28390.2i			1.70921i
$652$		0			0
$653$	6716.28	−	6716.28i	0.402494	−	0.402494i	−0.476617	−	0.879111i	$-0.658137\pi$
$653$	6716.28	−	6716.28i	0.402494	−	0.402494i	0.879111	+	0.476617i	$0.158137\pi$
$654$		0			0
$655$	4135.28	−	2821.89i	0.246685	−	0.168336i
$656$		0			0
$657$	−10706.1	−	10706.1i	−0.635745	−	0.635745i
$658$		0			0
$659$	19429.3			1.14850			0.574248	−	0.818682i	$-0.305295\pi$
$659$	19429.3			1.14850			0.574248	+	0.818682i	$0.305295\pi$
$660$		0			0
$661$	−1931.93			−0.113681			−0.0568406	−	0.998383i	$-0.518103\pi$
$661$	−1931.93			−0.113681			−0.0568406	+	0.998383i	$0.518103\pi$
$662$		0			0
$663$	−16514.1	−	16514.1i	−0.967351	−	0.967351i
$664$		0			0
$665$	20371.1	+	3845.69i	1.18790	+	0.224255i
$666$		0			0
$667$	17633.6	−	17633.6i	1.02365	−	1.02365i
$668$		0			0
$669$		−	3660.92i		−	0.211568i
$670$		0			0
$671$		−	39.5641i		−	0.00227624i
$672$		0			0
$673$	5530.06	−	5530.06i	0.316743	−	0.316743i	−0.530772	−	0.847515i	$-0.678098\pi$
$673$	5530.06	−	5530.06i	0.316743	−	0.316743i	0.847515	+	0.530772i	$0.178098\pi$
$674$		0			0
$675$	−4275.02	−	9776.39i	−0.243771	−	0.557472i
$676$		0			0
$677$	17641.4	+	17641.4i	1.00150	+	1.00150i	0.999999	+	0.00150001i	$0.000477467\pi$
$677$	17641.4	+	17641.4i	1.00150	+	1.00150i	0.00150001	+	0.999999i	$0.499523\pi$
$678$		0			0
$679$	−26497.2			−1.49760
$680$		0			0
$681$	15691.4			0.882957
$682$		0			0
$683$	−5334.23	−	5334.23i	−0.298841	−	0.298841i	0.541719	−	0.840560i	$-0.317774\pi$
$683$	−5334.23	−	5334.23i	−0.298841	−	0.298841i	−0.840560	+	0.541719i	$0.817774\pi$
$684$		0			0
$685$	1181.31	−	6257.51i	0.0658910	−	0.349033i
$686$		0			0
$687$	−12400.0	+	12400.0i	−0.688632	+	0.688632i
$688$		0			0
$689$			19548.3i			1.08089i
$690$		0			0
$691$			9565.00i			0.526584i	0.964716	+	0.263292i	$0.0848083\pi$
$691$			9565.00i			0.526584i	−0.964716	+	0.263292i	$0.915192\pi$
$692$		0			0
$693$	6233.47	−	6233.47i	0.341688	−	0.341688i
$694$		0			0
$695$	11513.6	+	16872.3i	0.628395	+	0.920868i
$696$		0			0
$697$	13198.9	+	13198.9i	0.717277	+	0.717277i
$698$		0			0
$699$	12880.2			0.696960
$700$		0			0
$701$	834.888			0.0449833			0.0224916	−	0.999747i	$-0.492840\pi$
$701$	834.888			0.0449833			0.0224916	+	0.999747i	$0.492840\pi$
$702$		0			0
$703$	−16883.3	−	16883.3i	−0.905783	−	0.905783i
$704$		0			0
$705$	−19990.7	−	29295.0i	−1.06793	−	1.56498i
$706$		0			0
$707$	23804.5	−	23804.5i	1.26628	−	1.26628i
$708$		0			0
$709$			14997.9i			0.794442i	0.917723	+	0.397221i	$0.130025\pi$
$709$			14997.9i			0.794442i	−0.917723	+	0.397221i	$0.869975\pi$
$710$		0			0
$711$		−	1518.56i		−	0.0800991i
$712$		0			0
$713$	10536.3	−	10536.3i	0.553418	−	0.553418i
$714$		0			0
$715$	2500.28	−	13244.3i	0.130777	−	0.692740i
$716$		0			0
$717$	2941.14	+	2941.14i	0.153192	+	0.153192i
$718$		0			0
$719$	28170.8			1.46119			0.730593	−	0.682813i	$-0.239244\pi$
$719$	28170.8			1.46119			0.730593	+	0.682813i	$0.239244\pi$
$720$		0			0
$721$	−12313.2			−0.636016
$722$		0			0
$723$	12159.8	+	12159.8i	0.625489	+	0.625489i
$724$		0			0
$725$	−32228.2	−	12617.9i	−1.65093	−	0.646367i
$726$		0			0
$727$	23410.6	−	23410.6i	1.19429	−	1.19429i	0.218442	−	0.975850i	$-0.429903\pi$
$727$	23410.6	−	23410.6i	1.19429	−	1.19429i	0.975850	−	0.218442i	$-0.0700974\pi$
$728$		0			0
$729$		−	2289.88i		−	0.116338i
$730$		0			0
$731$		−	1065.70i		−	0.0539211i
$732$		0			0
$733$	−22255.1	+	22255.1i	−1.12143	+	1.12143i	−0.129908	+	0.991526i	$0.541468\pi$
$733$	−22255.1	+	22255.1i	−1.12143	+	1.12143i	−0.991526	+	0.129908i	$0.958532\pi$
$734$		0			0
$735$	26759.8	+	5051.76i	1.34292	+	0.253520i
$736$		0			0
$737$	13097.8	+	13097.8i	0.654634	+	0.654634i
$738$		0			0
$739$	−31299.7			−1.55802			−0.779010	−	0.627011i	$-0.784278\pi$
$739$	−31299.7			−1.55802			−0.779010	+	0.627011i	$0.784278\pi$
$740$		0			0
$741$	−21980.8			−1.08972
$742$		0			0
$743$	6394.92	+	6394.92i	0.315756	+	0.315756i	0.847135	−	0.531378i	$-0.178326\pi$
$743$	6394.92	+	6394.92i	0.315756	+	0.315756i	−0.531378	+	0.847135i	$0.678326\pi$
$744$		0			0
$745$	22392.3	−	15280.4i	1.10120	−	0.751450i
$746$		0			0
$747$	8851.79	−	8851.79i	0.433561	−	0.433561i
$748$		0			0
$749$		−	26449.5i		−	1.29031i
$750$		0			0
$751$			35567.0i			1.72817i	0.503344	+	0.864086i	$0.332103\pi$
$751$			35567.0i			1.72817i	−0.503344	+	0.864086i	$0.667897\pi$
$752$		0			0
$753$	−24121.6	+	24121.6i	−1.16738	+	1.16738i
$754$		0			0
$755$	23059.6	−	15735.8i	1.11156	−	0.758521i
$756$		0			0
$757$	17860.9	+	17860.9i	0.857550	+	0.857550i	0.991049	−	0.133499i	$-0.0426212\pi$
$757$	17860.9	+	17860.9i	0.857550	+	0.857550i	−0.133499	+	0.991049i	$0.542621\pi$
$758$		0			0
$759$	−13809.7			−0.660422
$760$		0			0
$761$	−1174.25			−0.0559350			−0.0279675	−	0.999609i	$-0.508903\pi$
$761$	−1174.25			−0.0559350			−0.0279675	+	0.999609i	$0.508903\pi$
$762$		0			0
$763$	2100.76	+	2100.76i	0.0996758	+	0.0996758i
$764$		0			0
$765$	10933.5	+	2064.04i	0.516734	+	0.0975499i
$766$		0			0
$767$	8712.57	−	8712.57i	0.410160	−	0.410160i
$768$		0			0
$769$			17440.1i			0.817822i	0.912574	+	0.408911i	$0.134091\pi$
$769$			17440.1i			0.817822i	−0.912574	+	0.408911i	$0.865909\pi$
$770$		0			0
$771$		−	7533.08i		−	0.351877i
$772$		0			0
$773$	−21388.2	+	21388.2i	−0.995188	+	0.995188i	−0.999988	−	0.00480031i	$-0.998472\pi$
$773$	−21388.2	+	21388.2i	−0.995188	+	0.995188i	0.00480031	+	0.999988i	$0.498472\pi$
$774$		0			0
$775$	−19256.7	−	7539.32i	−0.892543	−	0.349446i
$776$		0			0
$777$	−42079.0	−	42079.0i	−1.94283	−	1.94283i
$778$		0			0
$779$	17568.1			0.808013
$780$		0			0
$781$	−3077.50			−0.141001
$782$		0			0
$783$	−16712.5	−	16712.5i	−0.762781	−	0.762781i
$784$		0			0
$785$	1681.44	−	8906.80i	0.0764500	−	0.404965i
$786$		0			0
$787$	22085.8	−	22085.8i	1.00035	−	1.00035i	0.000346279	−	1.00000i	$-0.499890\pi$
$787$	22085.8	−	22085.8i	1.00035	−	1.00035i	1.00000		0.000346279i	$-0.000110224\pi$
$788$		0			0
$789$			10234.9i			0.461816i
$790$		0			0
$791$		−	24398.7i		−	1.09673i
$792$		0			0
$793$	−58.2489	+	58.2489i	−0.00260842	+	0.00260842i
$794$		0			0
$795$	−15668.5	−	22961.0i	−0.698998	−	1.02433i
$796$		0			0
$797$	−332.495	−	332.495i	−0.0147774	−	0.0147774i	0.699679	−	0.714457i	$-0.253326\pi$
$797$	−332.495	−	332.495i	−0.0147774	−	0.0147774i	−0.714457	+	0.699679i	$0.753326\pi$
$798$		0			0
$799$	−36418.1			−1.61249
$800$		0			0
$801$	−6360.95			−0.280591
$802$		0			0
$803$	−18936.8	−	18936.8i	−0.832213	−	0.832213i
$804$		0			0
$805$	−15285.5	−	22399.8i	−0.669246	−	0.980732i
$806$		0			0
$807$	850.457	−	850.457i	0.0370973	−	0.0370973i
$808$		0			0
$809$		−	35130.2i		−	1.52672i	−0.645976	−	0.763358i	$-0.723549\pi$
$809$		−	35130.2i		−	1.52672i	0.645976	−	0.763358i	$-0.276451\pi$
$810$		0			0
$811$			20353.7i			0.881278i	0.897684	+	0.440639i	$0.145248\pi$
$811$			20353.7i			0.881278i	−0.897684	+	0.440639i	$0.854752\pi$
$812$		0			0
$813$	−28696.3	+	28696.3i	−1.23791	+	1.23791i
$814$		0			0
$815$	5467.01	−	28959.4i	0.234971	−	1.24467i
$816$		0			0
$817$	−709.240	−	709.240i	−0.0303711	−	0.0303711i
$818$		0			0
$819$	−18354.6			−0.783105
$820$		0			0
$821$	35961.9			1.52872			0.764360	−	0.644790i	$-0.223055\pi$
$821$	35961.9			1.52872			0.764360	+	0.644790i	$0.223055\pi$
$822$		0			0
$823$	20475.6	+	20475.6i	0.867236	+	0.867236i	0.992166	−	0.124930i	$-0.0398706\pi$
$823$	20475.6	+	20475.6i	0.867236	+	0.867236i	−0.124930	+	0.992166i	$0.539871\pi$
$824$		0			0
$825$	7678.87	+	17560.5i	0.324053	+	0.741065i
$826$		0			0
$827$	−14505.7	+	14505.7i	−0.609930	+	0.609930i	−0.942928	−	0.332998i	$-0.891940\pi$
$827$	−14505.7	+	14505.7i	−0.609930	+	0.609930i	0.332998	+	0.942928i	$0.391940\pi$
$828$		0			0
$829$		−	12556.2i		−	0.526051i	−0.964789	−	0.263026i	$-0.915280\pi$
$829$		−	12556.2i		−	0.526051i	0.964789	−	0.263026i	$-0.0847204\pi$
$830$		0			0
$831$		−	9421.10i		−	0.393278i
$832$		0			0
$833$	19773.3	−	19773.3i	0.822453	−	0.822453i
$834$		0			0
$835$	−15628.7	−	2950.42i	−0.647730	−	0.122280i
$836$		0			0
$837$	−9985.93	−	9985.93i	−0.412383	−	0.412383i
$838$		0			0
$839$	42777.2			1.76023			0.880116	−	0.474759i	$-0.157465\pi$
$839$	42777.2			1.76023			0.880116	+	0.474759i	$0.157465\pi$
$840$		0			0
$841$	−52274.4			−2.14336
$842$		0			0
$843$	4849.06	+	4849.06i	0.198115	+	0.198115i
$844$		0			0
$845$	−2890.86	+	1972.71i	−0.117691	+	0.0803116i
$846$		0			0
$847$	−14320.2	+	14320.2i	−0.580929	+	0.580929i
$848$		0			0
$849$		−	43921.4i		−	1.77547i
$850$		0			0
$851$			31233.1i			1.25812i
$852$		0			0
$853$	19721.7	−	19721.7i	0.791628	−	0.791628i	−0.190131	−	0.981759i	$-0.560891\pi$
$853$	19721.7	−	19721.7i	0.791628	−	0.791628i	0.981759	+	0.190131i	$0.0608912\pi$
$854$		0			0
$855$	8650.07	−	5902.76i	0.345995	−	0.236105i
$856$		0			0
$857$	−3410.56	−	3410.56i	−0.135942	−	0.135942i	0.635861	−	0.771804i	$-0.280645\pi$
$857$	−3410.56	−	3410.56i	−0.135942	−	0.135942i	−0.771804	+	0.635861i	$0.780645\pi$
$858$		0			0
$859$	−23192.7			−0.921217			−0.460609	−	0.887603i	$-0.652369\pi$
$859$	−23192.7			−0.921217			−0.460609	+	0.887603i	$0.652369\pi$
$860$		0			0
$861$	43785.8			1.73312
$862$		0			0
$863$	15477.6	+	15477.6i	0.610502	+	0.610502i	0.943077	−	0.332575i	$-0.107917\pi$
$863$	15477.6	+	15477.6i	0.610502	+	0.610502i	−0.332575	+	0.943077i	$0.607917\pi$
$864$		0			0
$865$	23280.2	+	4394.89i	0.915089	+	0.172752i
$866$		0			0
$867$	1976.67	−	1976.67i	0.0774295	−	0.0774295i
$868$		0			0
$869$		−	2686.02i		−	0.104853i
$870$		0			0
$871$		−	38567.0i		−	1.50034i
$872$		0			0
$873$	−9464.60	+	9464.60i	−0.366928	+	0.366928i
$874$		0			0
$875$	−19984.3	+	31892.5i	−0.772104	+	1.23219i
$876$		0			0
$877$	−26716.5	−	26716.5i	−1.02868	−	1.02868i	−0.999576	−	0.0291035i	$-0.990735\pi$
$877$	−26716.5	−	26716.5i	−1.02868	−	1.02868i	−0.0291035	−	0.999576i	$-0.509265\pi$
$878$		0			0
$879$	10307.9			0.395538
$880$		0			0
$881$	−2792.61			−0.106794			−0.0533970	−	0.998573i	$-0.517005\pi$
$881$	−2792.61			−0.106794			−0.0533970	+	0.998573i	$0.517005\pi$
$882$		0			0
$883$	19487.1	+	19487.1i	0.742687	+	0.742687i	0.973094	−	0.230407i	$-0.0740058\pi$
$883$	19487.1	+	19487.1i	0.742687	+	0.742687i	−0.230407	+	0.973094i	$0.574006\pi$
$884$		0			0
$885$	−3250.25	+	17217.0i	−0.123453	+	0.653945i
$886$		0			0
$887$	−8117.18	+	8117.18i	−0.307270	+	0.307270i	−0.843849	−	0.536580i	$-0.819716\pi$
$887$	−8117.18	+	8117.18i	−0.307270	+	0.307270i	0.536580	+	0.843849i	$0.319716\pi$
$888$		0			0
$889$			64325.4i			2.42678i
$890$		0			0
$891$			21926.6i			0.824431i
$892$		0			0
$893$	−24236.8	+	24236.8i	−0.908235	+	0.908235i
$894$		0			0
$895$	17403.7	+	25503.9i	0.649990	+	0.952514i
$896$		0			0
$897$	20331.6	+	20331.6i	0.756801	+	0.756801i
$898$		0			0
$899$	−45807.2			−1.69940
$900$		0			0
$901$	−28544.0			−1.05543
$902$		0			0
$903$	−1767.67	−	1767.67i	−0.0651433	−	0.0651433i
$904$		0			0
$905$	−2366.12	−	3467.38i	−0.0869089	−	0.127359i
$906$		0			0
$907$	1356.62	−	1356.62i	0.0496645	−	0.0496645i	−0.681838	−	0.731503i	$-0.738819\pi$
$907$	1356.62	−	1356.62i	0.0496645	−	0.0496645i	0.731503	+	0.681838i	$0.238819\pi$
$908$		0			0
$909$		−	17005.6i		−	0.620507i
$910$		0			0
$911$			5974.65i			0.217288i	0.994081	+	0.108644i	$0.0346508\pi$
$911$			5974.65i			0.217288i	−0.994081	+	0.108644i	$0.965349\pi$
$912$		0			0
$913$	15657.0	−	15657.0i	0.567546	−	0.567546i
$914$		0			0
$915$	21.7299	−	115.106i	0.000785102	−	0.00415878i
$916$		0			0
$917$	−8526.99	−	8526.99i	−0.307073	−	0.307073i
$918$		0			0
$919$	32095.3			1.15204			0.576020	−	0.817436i	$-0.304605\pi$
$919$	32095.3			1.15204			0.576020	+	0.817436i	$0.304605\pi$
$920$		0			0
$921$	47447.1			1.69754
$922$		0			0
$923$	4530.89	+	4530.89i	0.161578	+	0.161578i
$924$		0			0
$925$	39716.2	−	17367.1i	1.41174	−	0.617327i
$926$		0			0
$927$	−4398.19	+	4398.19i	−0.155831	+	0.155831i
$928$		0			0
$929$			37055.0i			1.30865i	0.756214	+	0.654324i	$0.227047\pi$
$929$			37055.0i			1.30865i	−0.756214	+	0.654324i	$0.772953\pi$
$930$		0			0
$931$		−	26318.9i		−	0.926494i
$932$		0			0
$933$	31527.5	−	31527.5i	1.10629	−	1.10629i
$934$		0			0
$935$	19339.1	+	3650.86i	0.676422	+	0.127696i
$936$		0			0
$937$	29292.7	+	29292.7i	1.02129	+	1.02129i	0.999768	+	0.0215234i	$0.00685166\pi$
$937$	29292.7	+	29292.7i	1.02129	+	1.02129i	0.0215234	+	0.999768i	$0.493148\pi$
$938$		0			0
$939$	22241.6			0.772979
$940$		0			0
$941$	24894.3			0.862412			0.431206	−	0.902254i	$-0.358088\pi$
$941$	24894.3			0.862412			0.431206	+	0.902254i	$0.358088\pi$
$942$		0			0
$943$	−16250.0	−	16250.0i	−0.561158	−	0.561158i
$944$		0			0
$945$	−21229.8	+	14487.1i	−0.730799	+	0.498693i
$946$		0			0
$947$	−1733.67	+	1733.67i	−0.0594896	+	0.0594896i	−0.736226	−	0.676736i	$-0.763394\pi$
$947$	−1733.67	+	1733.67i	−0.0594896	+	0.0594896i	0.676736	+	0.736226i	$0.263394\pi$
$948$		0			0
$949$			55760.1i			1.90732i
$950$		0			0
$951$		−	21085.9i		−	0.718988i
$952$		0			0
$953$	−26550.8	+	26550.8i	−0.902481	+	0.902481i	−0.995650	−	0.0931690i	$-0.970300\pi$
$953$	−26550.8	+	26550.8i	−0.902481	+	0.902481i	0.0931690	+	0.995650i	$0.470300\pi$
$954$		0			0
$955$	−18058.9	+	12323.3i	−0.611907	+	0.417562i
$956$		0			0
$957$	30019.3	+	30019.3i	1.01399	+	1.01399i
$958$		0			0
$959$	−15338.9			−0.516496
$960$		0			0
$961$	2420.66			0.0812548
$962$		0			0
$963$	−9447.56	−	9447.56i	−0.316141	−	0.316141i
$964$		0			0
$965$	−41466.9	−	7828.19i	−1.38328	−	0.261138i
$966$		0			0
$967$	17836.0	−	17836.0i	0.593141	−	0.593141i	−0.345338	−	0.938478i	$-0.612236\pi$
$967$	17836.0	−	17836.0i	0.593141	−	0.593141i	0.938478	+	0.345338i	$0.112236\pi$
$968$		0			0
$969$		−	32095.8i		−	1.06405i
$970$		0			0
$971$		−	15380.8i		−	0.508335i	−0.967160	−	0.254167i	$-0.918199\pi$
$971$		−	15380.8i		−	0.508335i	0.967160	−	0.254167i	$-0.0818014\pi$
$972$		0			0
$973$	34790.9	−	34790.9i	1.14629	−	1.14629i
$974$		0			0
$975$	14548.4	−	37159.1i	0.477869	−	1.22056i
$976$		0			0
$977$	15851.5	+	15851.5i	0.519074	+	0.519074i	0.917291	−	0.398217i	$-0.130371\pi$
$977$	15851.5	+	15851.5i	0.519074	+	0.519074i	−0.398217	+	0.917291i	$0.630371\pi$
$978$		0			0
$979$	−11251.2			−0.367303
$980$		0			0
$981$	1500.75			0.0488434
$982$		0			0
$983$	−19569.0	−	19569.0i	−0.634948	−	0.634948i	0.314357	−	0.949305i	$-0.398211\pi$
$983$	−19569.0	−	19569.0i	−0.634948	−	0.634948i	−0.949305	+	0.314357i	$0.898211\pi$
$984$		0			0
$985$	−5825.06	+	30856.0i	−0.188428	+	0.998127i
$986$		0			0
$987$	−60406.5	+	60406.5i	−1.94809	+	1.94809i
$988$		0			0
$989$			1312.05i			0.0421849i
$990$		0			0
$991$			57385.1i			1.83945i	0.392559	+	0.919727i	$0.371590\pi$
$991$			57385.1i			1.83945i	−0.392559	+	0.919727i	$0.628410\pi$
$992$		0			0
$993$	36271.8	−	36271.8i	1.15917	−	1.15917i
$994$		0			0
$995$	16102.0	+	23596.3i	0.513033	+	0.751813i
$996$		0			0
$997$	11684.6	+	11684.6i	0.371168	+	0.371168i	0.867902	−	0.496735i	$-0.165468\pi$
$997$	11684.6	+	11684.6i	0.371168	+	0.371168i	−0.496735	+	0.867902i	$0.665468\pi$
$998$		0			0
$999$	29601.7			0.937493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.n.d.127.1	yes	8
4.3	odd	2		160.4.n.e.127.4	yes	8
5.3	odd	4		160.4.n.e.63.4	yes	8
8.3	odd	2		320.4.n.g.127.1		8
8.5	even	2		320.4.n.h.127.4		8
20.3	even	4	inner	160.4.n.d.63.1	✓	8
40.3	even	4		320.4.n.h.63.4		8
40.13	odd	4		320.4.n.g.63.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.d.63.1	✓	8	20.3	even	4	inner
160.4.n.d.127.1	yes	8	1.1	even	1	trivial
160.4.n.e.63.4	yes	8	5.3	odd	4
160.4.n.e.127.4	yes	8	4.3	odd	2
320.4.n.g.63.1		8	40.13	odd	4
320.4.n.g.127.1		8	8.3	odd	2
320.4.n.h.63.4		8	40.3	even	4
320.4.n.h.127.4		8	8.5	even	2

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50577 - 4.50577i) q^{3} +(-6.30193 - 9.23502i) q^{5} +(-19.0427 + 19.0427i) q^{7} +13.6039i q^{9} +24.0624i q^{11} +(35.4262 - 35.4262i) q^{13} +(-13.2158 + 70.0059i) q^{15} +(51.7286 + 51.7286i) q^{17} +68.8524 q^{19} +171.604 q^{21} +(-63.6865 - 63.6865i) q^{23} +(-45.5714 + 116.397i) q^{25} +(-60.3599 + 60.3599i) q^{27} +276.882i q^{29} +165.440i q^{31} +(108.419 - 108.419i) q^{33} +(295.866 + 55.8541i) q^{35} +(-245.210 - 245.210i) q^{37} -319.244 q^{39} +255.156 q^{41} +(-10.3009 - 10.3009i) q^{43} +(125.632 - 85.7306i) q^{45} +(-352.011 + 352.011i) q^{47} -382.250i q^{49} -466.154i q^{51} +(-275.902 + 275.902i) q^{53} +(222.217 - 151.639i) q^{55} +(-310.233 - 310.233i) q^{57} +245.936 q^{59} -1.64423 q^{61} +(-259.054 - 259.054i) q^{63} +(-550.415 - 103.908i) q^{65} +(544.329 - 544.329i) q^{67} +573.913i q^{69} +127.897i q^{71} +(-786.990 + 786.990i) q^{73} +(729.791 - 319.124i) q^{75} +(-458.213 - 458.213i) q^{77} -111.627 q^{79} +911.239 q^{81} +(-650.682 - 650.682i) q^{83} +(151.725 - 803.705i) q^{85} +(1247.56 - 1247.56i) q^{87} +467.584i q^{89} +1349.22i q^{91} +(745.433 - 745.433i) q^{93} +(-433.903 - 635.854i) q^{95} +(695.729 + 695.729i) q^{97} -327.341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 14 q^{5} - 10 q^{7} - 32 q^{13} - 22 q^{15} + 44 q^{17} - 80 q^{19} + 236 q^{21} - 230 q^{23} - 44 q^{25} - 80 q^{27} - 260 q^{33} + 866 q^{35} - 292 q^{37} - 1068 q^{39} + 932 q^{41} - 458 q^{43}+ \cdots - 1844 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 14 * q^5 - 10 * q^7 - 32 * q^13 - 22 * q^15 + 44 * q^17 - 80 * q^19 + 236 * q^21 - 230 * q^23 - 44 * q^25 - 80 * q^27 - 260 * q^33 + 866 * q^35 - 292 * q^37 - 1068 * q^39 + 932 * q^41 - 458 * q^43 - 110 * q^45 + 766 * q^47 - 892 * q^53 + 920 * q^55 - 1064 * q^57 - 16 * q^59 + 2564 * q^61 - 798 * q^63 - 888 * q^65 + 194 * q^67 - 1744 * q^73 + 4918 * q^75 - 1516 * q^77 - 3216 * q^79 + 4828 * q^81 - 3762 * q^83 - 920 * q^85 + 3904 * q^87 - 2420 * q^93 + 1544 * q^95 - 680 * q^97 - 1844 * q^99

Introduction

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