LMFDB - Embedded newform 560.3.v.b.447.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,3,Mod(223,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.223"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			447.22
Character	$\chi$	$=$	560.447
Dual form			560.3.v.b.223.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09571 - 1.09571i) q^{3} +(-0.913268 + 4.91589i) q^{5} +(-0.925122 + 6.93860i) q^{7} +6.59885i q^{9} -4.54485i q^{11} +(-14.2356 - 14.2356i) q^{13} +(4.38570 + 6.38705i) q^{15} +(-13.7331 + 13.7331i) q^{17} +3.69805i q^{19} +(6.58901 + 8.61634i) q^{21} +(-25.9196 - 25.9196i) q^{23} +(-23.3319 - 8.97904i) q^{25} +(17.0918 + 17.0918i) q^{27} -42.9655i q^{29} -10.8529 q^{31} +(-4.97983 - 4.97983i) q^{33} +(-33.2645 - 10.8846i) q^{35} +(-36.7375 - 36.7375i) q^{37} -31.1960 q^{39} +30.7016i q^{41} +(47.4558 + 47.4558i) q^{43} +(-32.4392 - 6.02651i) q^{45} +(39.0656 + 39.0656i) q^{47} +(-47.2883 - 12.8381i) q^{49} +30.0949i q^{51} +(-17.0697 + 17.0697i) q^{53} +(22.3420 + 4.15067i) q^{55} +(4.05198 + 4.05198i) q^{57} +93.6633i q^{59} +51.6120i q^{61} +(-45.7868 - 6.10474i) q^{63} +(82.9812 - 56.9795i) q^{65} +(-54.9566 + 54.9566i) q^{67} -56.8005 q^{69} -50.1559i q^{71} +(1.87062 + 1.87062i) q^{73} +(-35.4033 + 15.7265i) q^{75} +(31.5349 + 4.20454i) q^{77} +103.203 q^{79} -21.9344 q^{81} +(51.9509 - 51.9509i) q^{83} +(-54.9682 - 80.0521i) q^{85} +(-47.0776 - 47.0776i) q^{87} -67.4648 q^{89} +(111.944 - 85.6052i) q^{91} +(-11.8917 + 11.8917i) q^{93} +(-18.1792 - 3.37731i) q^{95} +(-25.1837 + 25.1837i) q^{97} +29.9908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) $ 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$3$	1.09571	−	1.09571i	0.365236	−	0.365236i	−0.500500	−	0.865736i	$-0.666851\pi$
$3$	1.09571	−	1.09571i	0.365236	−	0.365236i	0.865736	+	0.500500i	$0.166851\pi$
$4$		0			0
$5$	−0.913268	+	4.91589i	−0.182654	+	0.983177i
$5$	−0.913268	+	4.91589i	−0.182654	+	0.983177i
$6$		0			0
$7$	−0.925122	+	6.93860i	−0.132160	+	0.991228i
$7$	−0.925122	+	6.93860i	−0.132160	+	0.991228i
$8$		0			0
$9$			6.59885i			0.733205i
$10$		0			0
$11$		−	4.54485i		−	0.413169i	−0.978429	−	0.206584i	$-0.933765\pi$
$11$		−	4.54485i		−	0.413169i	0.978429	−	0.206584i	$-0.0662348\pi$
$12$		0			0
$13$	−14.2356	−	14.2356i	−1.09504	−	1.09504i	−0.994981	−	0.100061i	$-0.968096\pi$
$13$	−14.2356	−	14.2356i	−1.09504	−	1.09504i	−0.100061	−	0.994981i	$-0.531904\pi$
$14$		0			0
$15$	4.38570	+	6.38705i	0.292380	+	0.425803i
$16$		0			0
$17$	−13.7331	+	13.7331i	−0.807827	+	0.807827i	−0.984305	−	0.176477i	$-0.943530\pi$
$17$	−13.7331	+	13.7331i	−0.807827	+	0.807827i	0.176477	+	0.984305i	$0.443530\pi$
$18$		0			0
$19$			3.69805i			0.194634i	0.995253	+	0.0973170i	$0.0310261\pi$
$19$			3.69805i			0.194634i	−0.995253	+	0.0973170i	$0.968974\pi$
$20$		0			0
$21$	6.58901	+	8.61634i	0.313763	+	0.410302i
$22$		0			0
$23$	−25.9196	−	25.9196i	−1.12694	−	1.12694i	−0.990672	−	0.136265i	$-0.956490\pi$
$23$	−25.9196	−	25.9196i	−1.12694	−	1.12694i	−0.136265	−	0.990672i	$-0.543510\pi$
$24$		0			0
$25$	−23.3319	−	8.97904i	−0.933275	−	0.359162i
$26$		0			0
$27$	17.0918	+	17.0918i	0.633029	+	0.633029i
$28$		0			0
$29$		−	42.9655i		−	1.48157i	−0.671743	−	0.740784i	$-0.734454\pi$
$29$		−	42.9655i		−	1.48157i	0.671743	−	0.740784i	$-0.265546\pi$
$30$		0			0
$31$	−10.8529			−0.350095			−0.175047	−	0.984560i	$-0.556008\pi$
$31$	−10.8529			−0.350095			−0.175047	+	0.984560i	$0.556008\pi$
$32$		0			0
$33$	−4.97983	−	4.97983i	−0.150904	−	0.150904i
$34$		0			0
$35$	−33.2645	−	10.8846i	−0.950414	−	0.310988i
$36$		0			0
$37$	−36.7375	−	36.7375i	−0.992905	−	0.992905i	0.00707017	−	0.999975i	$-0.497749\pi$
$37$	−36.7375	−	36.7375i	−0.992905	−	0.992905i	−0.999975	+	0.00707017i	$0.997749\pi$
$38$		0			0
$39$	−31.1960			−0.799898
$40$		0			0
$41$			30.7016i			0.748819i	0.927263	+	0.374410i	$0.122155\pi$
$41$			30.7016i			0.748819i	−0.927263	+	0.374410i	$0.877845\pi$
$42$		0			0
$43$	47.4558	+	47.4558i	1.10362	+	1.10362i	0.993970	+	0.109655i	$0.0349745\pi$
$43$	47.4558	+	47.4558i	1.10362	+	1.10362i	0.109655	+	0.993970i	$0.465026\pi$
$44$		0			0
$45$	−32.4392	−	6.02651i	−0.720871	−	0.133923i
$46$		0			0
$47$	39.0656	+	39.0656i	0.831183	+	0.831183i	0.987679	−	0.156496i	$-0.0500197\pi$
$47$	39.0656	+	39.0656i	0.831183	+	0.831183i	−0.156496	+	0.987679i	$0.550020\pi$
$48$		0			0
$49$	−47.2883	−	12.8381i	−0.965067	−	0.262002i
$50$		0			0
$51$			30.0949i			0.590095i
$52$		0			0
$53$	−17.0697	+	17.0697i	−0.322069	+	0.322069i	−0.849561	−	0.527491i	$-0.823133\pi$
$53$	−17.0697	+	17.0697i	−0.322069	+	0.322069i	0.527491	+	0.849561i	$0.323133\pi$
$54$		0			0
$55$	22.3420	+	4.15067i	0.406218	+	0.0754667i
$56$		0			0
$57$	4.05198	+	4.05198i	0.0710874	+	0.0710874i
$58$		0			0
$59$			93.6633i			1.58751i	0.608235	+	0.793757i	$0.291878\pi$
$59$			93.6633i			1.58751i	−0.608235	+	0.793757i	$0.708122\pi$
$60$		0			0
$61$			51.6120i			0.846099i	0.906107	+	0.423049i	$0.139040\pi$
$61$			51.6120i			0.846099i	−0.906107	+	0.423049i	$0.860960\pi$
$62$		0			0
$63$	−45.7868	−	6.10474i	−0.726774	−	0.0969006i
$64$		0			0
$65$	82.9812	−	56.9795i	1.27663	−	0.876608i
$66$		0			0
$67$	−54.9566	+	54.9566i	−0.820247	+	0.820247i	−0.986143	−	0.165896i	$-0.946948\pi$
$67$	−54.9566	+	54.9566i	−0.820247	+	0.820247i	0.165896	+	0.986143i	$0.446948\pi$
$68$		0			0
$69$	−56.8005			−0.823196
$70$		0			0
$71$		−	50.1559i		−	0.706421i	−0.935544	−	0.353211i	$-0.885090\pi$
$71$		−	50.1559i		−	0.706421i	0.935544	−	0.353211i	$-0.114910\pi$
$72$		0			0
$73$	1.87062	+	1.87062i	0.0256250	+	0.0256250i	0.719803	−	0.694178i	$-0.244232\pi$
$73$	1.87062	+	1.87062i	0.0256250	+	0.0256250i	−0.694178	+	0.719803i	$0.744232\pi$
$74$		0			0
$75$	−35.4033	+	15.7265i	−0.472045	+	0.209687i
$76$		0			0
$77$	31.5349	+	4.20454i	0.409544	+	0.0546045i
$78$		0			0
$79$	103.203			1.30637			0.653185	−	0.757198i	$-0.273432\pi$
$79$	103.203			1.30637			0.653185	+	0.757198i	$0.273432\pi$
$80$		0			0
$81$	−21.9344			−0.270795
$82$		0			0
$83$	51.9509	−	51.9509i	0.625915	−	0.625915i	−0.321123	−	0.947038i	$-0.604060\pi$
$83$	51.9509	−	51.9509i	0.625915	−	0.625915i	0.947038	+	0.321123i	$0.104060\pi$
$84$		0			0
$85$	−54.9682	−	80.0521i	−0.646685	−	0.941790i
$86$		0			0
$87$	−47.0776	−	47.0776i	−0.541122	−	0.541122i
$88$		0			0
$89$	−67.4648			−0.758031			−0.379016	−	0.925390i	$-0.623737\pi$
$89$	−67.4648			−0.758031			−0.379016	+	0.925390i	$0.623737\pi$
$90$		0			0
$91$	111.944	−	85.6052i	1.23016	−	0.940716i
$92$		0			0
$93$	−11.8917	+	11.8917i	−0.127867	+	0.127867i
$94$		0			0
$95$	−18.1792	−	3.37731i	−0.191360	−	0.0355506i
$96$		0			0
$97$	−25.1837	+	25.1837i	−0.259626	+	0.259626i	−0.824902	−	0.565276i	$-0.808770\pi$
$97$	−25.1837	+	25.1837i	−0.259626	+	0.259626i	0.565276	+	0.824902i	$0.308770\pi$
$98$		0			0
$99$	29.9908			0.302937
$100$		0			0
$101$			49.5625i			0.490717i	0.969432	+	0.245359i	$0.0789057\pi$
$101$			49.5625i			0.490717i	−0.969432	+	0.245359i	$0.921094\pi$
$102$		0			0
$103$	−143.158	+	143.158i	−1.38988	+	1.38988i	−0.564336	+	0.825545i	$0.690868\pi$
$103$	−143.158	+	143.158i	−1.38988	+	1.38988i	−0.825545	+	0.564336i	$0.809132\pi$
$104$		0			0
$105$	−48.3745	+	24.5218i	−0.460709	+	0.233541i
$106$		0			0
$107$	−8.90840	+	8.90840i	−0.0832561	+	0.0832561i	−0.747508	−	0.664252i	$-0.768750\pi$
$107$	−8.90840	+	8.90840i	−0.0832561	+	0.0832561i	0.664252	+	0.747508i	$0.268750\pi$
$108$		0			0
$109$			157.196i			1.44217i	0.692847	+	0.721084i	$0.256356\pi$
$109$			157.196i			1.44217i	−0.692847	+	0.721084i	$0.743644\pi$
$110$		0			0
$111$	−80.5071			−0.725289
$112$		0			0
$113$	−42.3161	+	42.3161i	−0.374479	+	0.374479i	−0.869105	−	0.494627i	$-0.835305\pi$
$113$	−42.3161	+	42.3161i	−0.374479	+	0.374479i	0.494627	+	0.869105i	$0.335305\pi$
$114$		0			0
$115$	151.089	−	103.746i	1.31382	−	0.902140i
$116$		0			0
$117$	93.9383	−	93.9383i	0.802891	−	0.802891i
$118$		0			0
$119$	−82.5835	−	107.993i	−0.693979	−	0.907504i
$120$		0			0
$121$	100.344			0.829292
$122$		0			0
$123$	33.6400	+	33.6400i	0.273496	+	0.273496i
$124$		0			0
$125$	65.4482	−	106.497i	0.523586	−	0.851973i
$126$		0			0
$127$	−1.97227	+	1.97227i	−0.0155297	+	0.0155297i	−0.714829	−	0.699299i	$-0.753495\pi$
$127$	−1.97227	+	1.97227i	−0.0155297	+	0.0155297i	0.699299	+	0.714829i	$0.253495\pi$
$128$		0			0
$129$	103.996			0.806167
$130$		0			0
$131$	43.5183			0.332201			0.166101	−	0.986109i	$-0.446882\pi$
$131$	43.5183			0.332201			0.166101	+	0.986109i	$0.446882\pi$
$132$		0			0
$133$	−25.6593	−	3.42114i	−0.192927	−	0.0257229i
$134$		0			0
$135$	−99.6306	+	68.4119i	−0.738005	+	0.506755i
$136$		0			0
$137$	−112.904	−	112.904i	−0.824119	−	0.824119i	0.162577	−	0.986696i	$-0.448019\pi$
$137$	−112.904	−	112.904i	−0.824119	−	0.824119i	−0.986696	+	0.162577i	$0.948019\pi$
$138$		0			0
$139$		−	190.110i		−	1.36770i	−0.729622	−	0.683851i	$-0.760304\pi$
$139$		−	190.110i		−	1.36770i	0.729622	−	0.683851i	$-0.239696\pi$
$140$		0			0
$141$	85.6090			0.607156
$142$		0			0
$143$	−64.6985	+	64.6985i	−0.452437	+	0.452437i
$144$		0			0
$145$	211.213	+	39.2390i	1.45664	+	0.270614i
$146$		0			0
$147$	−65.8810	+	37.7474i	−0.448170	+	0.256785i
$148$		0			0
$149$			32.5745i			0.218621i	0.994008	+	0.109310i	$0.0348643\pi$
$149$			32.5745i			0.218621i	−0.994008	+	0.109310i	$0.965136\pi$
$150$		0			0
$151$		−	14.8749i		−	0.0985092i	−0.998786	−	0.0492546i	$-0.984315\pi$
$151$		−	14.8749i		−	0.0985092i	0.998786	−	0.0492546i	$-0.0156846\pi$
$152$		0			0
$153$	−90.6224	−	90.6224i	−0.592303	−	0.592303i
$154$		0			0
$155$	9.91164	−	53.3518i	0.0639461	−	0.344205i
$156$		0			0
$157$	62.4968	−	62.4968i	0.398069	−	0.398069i	−0.479482	−	0.877551i	$-0.659176\pi$
$157$	62.4968	−	62.4968i	0.398069	−	0.398069i	0.877551	+	0.479482i	$0.159176\pi$
$158$		0			0
$159$			37.4068i			0.235263i
$160$		0			0
$161$	203.824	−	155.867i	1.26599	−	0.968116i
$162$		0			0
$163$	−20.9465	−	20.9465i	−0.128506	−	0.128506i	0.639928	−	0.768435i	$-0.278964\pi$
$163$	−20.9465	−	20.9465i	−0.128506	−	0.128506i	−0.768435	+	0.639928i	$0.778964\pi$
$164$		0			0
$165$	29.0282	−	19.9324i	0.175929	−	0.120802i
$166$		0			0
$167$	−116.009	−	116.009i	−0.694665	−	0.694665i	0.268589	−	0.963255i	$-0.413443\pi$
$167$	−116.009	−	116.009i	−0.694665	−	0.694665i	−0.963255	+	0.268589i	$0.913443\pi$
$168$		0			0
$169$			236.302i			1.39824i
$170$		0			0
$171$	−24.4029			−0.142707
$172$		0			0
$173$	80.4110	+	80.4110i	0.464804	+	0.464804i	0.900226	−	0.435423i	$-0.143401\pi$
$173$	80.4110	+	80.4110i	0.464804	+	0.464804i	−0.435423	+	0.900226i	$0.643401\pi$
$174$		0			0
$175$	83.8868	−	153.584i	0.479353	−	0.877622i
$176$		0			0
$177$	102.628	+	102.628i	0.579817	+	0.579817i
$178$		0			0
$179$	278.980			1.55855			0.779275	−	0.626682i	$-0.215588\pi$
$179$	278.980			1.55855			0.779275	+	0.626682i	$0.215588\pi$
$180$		0			0
$181$			184.138i			1.01734i	0.860962	+	0.508668i	$0.169862\pi$
$181$			184.138i			1.01734i	−0.860962	+	0.508668i	$0.830138\pi$
$182$		0			0
$183$	56.5517	+	56.5517i	0.309026	+	0.309026i
$184$		0			0
$185$	214.148	−	147.046i	1.15756	−	0.794844i
$186$		0			0
$187$	62.4148	+	62.4148i	0.333769	+	0.333769i
$188$		0			0
$189$	−134.405	+	102.781i	−0.711138	+	0.543815i
$190$		0			0
$191$		−	344.531i		−	1.80383i	−0.431917	−	0.901913i	$-0.642163\pi$
$191$		−	344.531i		−	1.80383i	0.431917	−	0.901913i	$-0.357837\pi$
$192$		0			0
$193$	−185.239	+	185.239i	−0.959789	+	0.959789i	−0.999222	−	0.0394328i	$-0.987445\pi$
$193$	−185.239	+	185.239i	−0.959789	+	0.959789i	0.0394328	+	0.999222i	$0.487445\pi$
$194$		0			0
$195$	28.4903	−	153.356i	0.146104	−	0.786442i
$196$		0			0
$197$	70.0929	+	70.0929i	0.355801	+	0.355801i	0.862263	−	0.506461i	$-0.169047\pi$
$197$	70.0929	+	70.0929i	0.355801	+	0.355801i	−0.506461	+	0.862263i	$0.669047\pi$
$198$		0			0
$199$			290.020i			1.45739i	0.684841	+	0.728693i	$0.259872\pi$
$199$			290.020i			1.45739i	−0.684841	+	0.728693i	$0.740128\pi$
$200$		0			0
$201$			120.433i			0.599168i
$202$		0			0
$203$	298.120	+	39.7483i	1.46857	+	0.195804i
$204$		0			0
$205$	−150.926	−	28.0388i	−0.736222	−	0.136775i
$206$		0			0
$207$	171.039	−	171.039i	0.826276	−	0.826276i
$208$		0			0
$209$	16.8071			0.0804167
$210$		0			0
$211$			70.4202i			0.333745i	0.985978	+	0.166873i	$0.0533668\pi$
$211$			70.4202i			0.333745i	−0.985978	+	0.166873i	$0.946633\pi$
$212$		0			0
$213$	−54.9562	−	54.9562i	−0.258010	−	0.258010i
$214$		0			0
$215$	−276.627	+	189.948i	−1.28664	+	0.883478i
$216$		0			0
$217$	10.0403	−	75.3042i	0.0462686	−	0.347024i
$218$		0			0
$219$	4.09932			0.0187183
$220$		0			0
$221$	390.995			1.76921
$222$		0			0
$223$	107.981	−	107.981i	0.484219	−	0.484219i	−0.422257	−	0.906476i	$-0.638762\pi$
$223$	107.981	−	107.981i	0.484219	−	0.484219i	0.906476	+	0.422257i	$0.138762\pi$
$224$		0			0
$225$	59.2513	−	153.964i	0.263339	−	0.684282i
$226$		0			0
$227$	−132.415	−	132.415i	−0.583326	−	0.583326i	0.352490	−	0.935816i	$-0.385335\pi$
$227$	−132.415	−	132.415i	−0.583326	−	0.583326i	−0.935816	+	0.352490i	$0.885335\pi$
$228$		0			0
$229$	394.112			1.72101			0.860507	−	0.509439i	$-0.170147\pi$
$229$	394.112			1.72101			0.860507	+	0.509439i	$0.170147\pi$
$230$		0			0
$231$	39.1600	−	29.9461i	0.169524	−	0.129637i
$232$		0			0
$233$	−224.060	+	224.060i	−0.961629	+	0.961629i	−0.999291	−	0.0376612i	$-0.988009\pi$
$233$	−224.060	+	224.060i	−0.961629	+	0.961629i	0.0376612	+	0.999291i	$0.488009\pi$
$234$		0			0
$235$	−227.719	+	156.365i	−0.969019	+	0.665382i
$236$		0			0
$237$	113.081	−	113.081i	0.477134	−	0.477134i
$238$		0			0
$239$	−174.806			−0.731404			−0.365702	−	0.930732i	$-0.619171\pi$
$239$	−174.806			−0.731404			−0.365702	+	0.930732i	$0.619171\pi$
$240$		0			0
$241$			219.930i			0.912571i	0.889833	+	0.456286i	$0.150820\pi$
$241$			219.930i			0.912571i	−0.889833	+	0.456286i	$0.849180\pi$
$242$		0			0
$243$	−177.860	+	177.860i	−0.731933	+	0.731933i
$244$		0			0
$245$	106.298	−	220.739i	0.433867	−	0.900977i
$246$		0			0
$247$	52.6438	−	52.6438i	0.213133	−	0.213133i
$248$		0			0
$249$		−	113.846i		−	0.457213i
$250$		0			0
$251$	455.701			1.81554			0.907770	−	0.419468i	$-0.137784\pi$
$251$	455.701			1.81554			0.907770	+	0.419468i	$0.137784\pi$
$252$		0			0
$253$	−117.801	+	117.801i	−0.465615	+	0.465615i
$254$		0			0
$255$	−147.943	−	27.4847i	−0.580168	−	0.107783i
$256$		0			0
$257$	108.826	−	108.826i	0.423449	−	0.423449i	−0.462940	−	0.886389i	$-0.653206\pi$
$257$	108.826	−	108.826i	0.423449	−	0.423449i	0.886389	+	0.462940i	$0.153206\pi$
$258$		0			0
$259$	288.893	−	220.920i	1.11542	−	0.852973i
$260$		0			0
$261$	283.523			1.08629
$262$		0			0
$263$	76.9969	+	76.9969i	0.292764	+	0.292764i	0.838171	−	0.545407i	$-0.183625\pi$
$263$	76.9969	+	76.9969i	0.292764	+	0.292764i	−0.545407	+	0.838171i	$0.683625\pi$
$264$		0			0
$265$	−68.3234	−	99.5018i	−0.257824	−	0.375479i
$266$		0			0
$267$	−73.9217	+	73.9217i	−0.276860	+	0.276860i
$268$		0			0
$269$	−279.111			−1.03759			−0.518795	−	0.854899i	$-0.673619\pi$
$269$	−279.111			−1.03759			−0.518795	+	0.854899i	$0.673619\pi$
$270$		0			0
$271$	−79.9263			−0.294931			−0.147466	−	0.989067i	$-0.547112\pi$
$271$	−79.9263			−0.294931			−0.147466	+	0.989067i	$0.547112\pi$
$272$		0			0
$273$	28.8601	−	216.457i	0.105715	−	0.792882i
$274$		0			0
$275$	−40.8084	+	106.040i	−0.148394	+	0.385600i
$276$		0			0
$277$	−58.7715	−	58.7715i	−0.212172	−	0.212172i	0.593018	−	0.805189i	$-0.297936\pi$
$277$	−58.7715	−	58.7715i	−0.212172	−	0.212172i	−0.805189	+	0.593018i	$0.797936\pi$
$278$		0			0
$279$		−	71.6169i		−	0.256691i
$280$		0			0
$281$	45.3999			0.161565			0.0807827	−	0.996732i	$-0.474258\pi$
$281$	45.3999			0.161565			0.0807827	+	0.996732i	$0.474258\pi$
$282$		0			0
$283$	59.0957	−	59.0957i	0.208819	−	0.208819i	−0.594946	−	0.803765i	$-0.702827\pi$
$283$	59.0957	−	59.0957i	0.208819	−	0.208819i	0.803765	+	0.594946i	$0.202827\pi$
$284$		0			0
$285$	−23.6196	+	16.2185i	−0.0828759	+	0.0569071i
$286$		0			0
$287$	−213.026	−	28.4027i	−0.742251	−	0.0989641i
$288$		0			0
$289$		−	88.1940i		−	0.305170i
$290$		0			0
$291$			55.1880i			0.189650i
$292$		0			0
$293$	−403.678	−	403.678i	−1.37774	−	1.37774i	−0.848426	−	0.529315i	$-0.822449\pi$
$293$	−403.678	−	403.678i	−1.37774	−	1.37774i	−0.529315	−	0.848426i	$-0.677551\pi$
$294$		0			0
$295$	−460.438	−	85.5397i	−1.56081	−	0.289965i
$296$		0			0
$297$	77.6797	−	77.6797i	0.261548	−	0.261548i
$298$		0			0
$299$			737.959i			2.46809i
$300$		0			0
$301$	−373.180	+	285.375i	−1.23980	+	0.948088i
$302$		0			0
$303$	54.3060	+	54.3060i	0.179228	+	0.179228i
$304$		0			0
$305$	−253.719	−	47.1356i	−0.831865	−	0.154543i
$306$		0			0
$307$	−68.7863	−	68.7863i	−0.224060	−	0.224060i	0.586146	−	0.810206i	$-0.300645\pi$
$307$	−68.7863	−	68.7863i	−0.224060	−	0.224060i	−0.810206	+	0.586146i	$0.800645\pi$
$308$		0			0
$309$			313.718i			1.01527i
$310$		0			0
$311$	−24.2261			−0.0778973			−0.0389487	−	0.999241i	$-0.512401\pi$
$311$	−24.2261			−0.0778973			−0.0389487	+	0.999241i	$0.512401\pi$
$312$		0			0
$313$	122.813	+	122.813i	0.392374	+	0.392374i	0.875533	−	0.483159i	$-0.160511\pi$
$313$	122.813	+	122.813i	0.392374	+	0.392374i	−0.483159	+	0.875533i	$0.660511\pi$
$314$		0			0
$315$	71.8258	−	219.507i	0.228018	−	0.696848i
$316$		0			0
$317$	−192.472	−	192.472i	−0.607166	−	0.607166i	0.335039	−	0.942204i	$-0.391251\pi$
$317$	−192.472	−	192.472i	−0.607166	−	0.607166i	−0.942204	+	0.335039i	$0.891251\pi$
$318$		0			0
$319$	−195.272			−0.612137
$320$		0			0
$321$			19.5220i			0.0608163i
$322$		0			0
$323$	−50.7855	−	50.7855i	−0.157231	−	0.157231i
$324$		0			0
$325$	204.321	+	459.964i	0.628679	+	1.41527i
$326$		0			0
$327$	172.241	+	172.241i	0.526732	+	0.526732i
$328$		0			0
$329$	−307.201	+	234.920i	−0.933741	+	0.714043i
$330$		0			0
$331$			340.784i			1.02956i	0.857322	+	0.514780i	$0.172126\pi$
$331$			340.784i			1.02956i	−0.857322	+	0.514780i	$0.827874\pi$
$332$		0			0
$333$	242.425	−	242.425i	0.728003	−	0.728003i
$334$		0			0
$335$	−219.970	−	320.350i	−0.656627	−	0.956269i
$336$		0			0
$337$	−316.775	−	316.775i	−0.939985	−	0.939985i	0.0583132	−	0.998298i	$-0.481428\pi$
$337$	−316.775	−	316.775i	−0.939985	−	0.939985i	−0.998298	+	0.0583132i	$0.981428\pi$
$338$		0			0
$339$			92.7321i			0.273546i
$340$		0			0
$341$			49.3250i			0.144648i
$342$		0			0
$343$	132.826	−	316.238i	0.387247	−	0.921976i
$344$		0			0
$345$	51.8741	−	279.225i	0.150360	−	0.809348i
$346$		0			0
$347$	140.058	−	140.058i	0.403624	−	0.403624i	−0.475884	−	0.879508i	$-0.657872\pi$
$347$	140.058	−	140.058i	0.403624	−	0.403624i	0.879508	+	0.475884i	$0.157872\pi$
$348$		0			0
$349$	−223.623			−0.640753			−0.320376	−	0.947290i	$-0.603809\pi$
$349$	−223.623			−0.640753			−0.320376	+	0.947290i	$0.603809\pi$
$350$		0			0
$351$		−	486.622i		−	1.38639i
$352$		0			0
$353$	−138.290	−	138.290i	−0.391757	−	0.391757i	0.483556	−	0.875313i	$-0.339345\pi$
$353$	−138.290	−	138.290i	−0.391757	−	0.391757i	−0.875313	+	0.483556i	$0.839345\pi$
$354$		0			0
$355$	246.561	+	45.8058i	0.694537	+	0.129030i
$356$		0			0
$357$	−208.816	−	27.8414i	−0.584919	−	0.0779871i
$358$		0			0
$359$	15.5564			0.0433326			0.0216663	−	0.999765i	$-0.493103\pi$
$359$	15.5564			0.0433326			0.0216663	+	0.999765i	$0.493103\pi$
$360$		0			0
$361$	347.324			0.962118
$362$		0			0
$363$	109.948	−	109.948i	0.302887	−	0.302887i
$364$		0			0
$365$	−10.9042	+	7.48740i	−0.0298744	+	0.0205134i
$366$		0			0
$367$	216.007	+	216.007i	0.588575	+	0.588575i	0.937245	−	0.348671i	$-0.113367\pi$
$367$	216.007	+	216.007i	0.588575	+	0.588575i	−0.348671	+	0.937245i	$0.613367\pi$
$368$		0			0
$369$	−202.595			−0.549038
$370$		0			0
$371$	−102.648	−	134.231i	−0.276680	−	0.361809i
$372$		0			0
$373$	−146.833	+	146.833i	−0.393655	+	0.393655i	−0.875988	−	0.482333i	$-0.839790\pi$
$373$	−146.833	+	146.833i	−0.393655	+	0.393655i	0.482333	+	0.875988i	$0.339790\pi$
$374$		0			0
$375$	−44.9771	−	188.401i	−0.119939	−	0.502404i
$376$		0			0
$377$	−611.637	+	611.637i	−1.62238	+	1.62238i
$378$		0			0
$379$	122.426			0.323024			0.161512	−	0.986871i	$-0.448363\pi$
$379$	122.426			0.323024			0.161512	+	0.986871i	$0.448363\pi$
$380$		0			0
$381$			4.32207i			0.0113440i
$382$		0			0
$383$	−456.717	+	456.717i	−1.19247	+	1.19247i	−0.216101	+	0.976371i	$0.569334\pi$
$383$	−456.717	+	456.717i	−1.19247	+	1.19247i	−0.976371	+	0.216101i	$0.930666\pi$
$384$		0			0
$385$	−49.4689	+	151.182i	−0.128491	+	0.392681i
$386$		0			0
$387$	−313.154	+	313.154i	−0.809183	+	0.809183i
$388$		0			0
$389$		−	30.6460i		−	0.0787815i	−0.999224	−	0.0393907i	$-0.987458\pi$
$389$		−	30.6460i		−	0.0787815i	0.999224	−	0.0393907i	$-0.0125417\pi$
$390$		0			0
$391$	711.910			1.82074
$392$		0			0
$393$	47.6834	−	47.6834i	0.121332	−	0.121332i
$394$		0			0
$395$	−94.2522	+	507.336i	−0.238613	+	1.28439i
$396$		0			0
$397$	−304.980	+	304.980i	−0.768212	+	0.768212i	−0.977792	−	0.209580i	$-0.932790\pi$
$397$	−304.980	+	304.980i	−0.768212	+	0.768212i	0.209580	+	0.977792i	$0.432790\pi$
$398$		0			0
$399$	−31.8636	+	24.3665i	−0.0798588	+	0.0610689i
$400$		0			0
$401$	16.6464			0.0415123			0.0207561	−	0.999785i	$-0.493393\pi$
$401$	16.6464			0.0415123			0.0207561	+	0.999785i	$0.493393\pi$
$402$		0			0
$403$	154.498	+	154.498i	0.383369	+	0.383369i
$404$		0			0
$405$	20.0320	−	107.827i	0.0494617	−	0.266240i
$406$		0			0
$407$	−166.966	+	166.966i	−0.410237	+	0.410237i
$408$		0			0
$409$	−341.288			−0.834446			−0.417223	−	0.908804i	$-0.636997\pi$
$409$	−341.288			−0.834446			−0.417223	+	0.908804i	$0.636997\pi$
$410$		0			0
$411$	−247.420			−0.601996
$412$		0			0
$413$	−649.892	−	86.6500i	−1.57359	−	0.209806i
$414$		0			0
$415$	207.940	+	302.830i	0.501060	+	0.729711i
$416$		0			0
$417$	−208.306	−	208.306i	−0.499534	−	0.499534i
$418$		0			0
$419$		−	252.786i		−	0.603307i	−0.953418	−	0.301653i	$-0.902461\pi$
$419$		−	252.786i		−	0.603307i	0.953418	−	0.301653i	$-0.0975385\pi$
$420$		0			0
$421$	283.059			0.672349			0.336175	−	0.941800i	$-0.390867\pi$
$421$	283.059			0.672349			0.336175	+	0.941800i	$0.390867\pi$
$422$		0			0
$423$	−257.788	+	257.788i	−0.609428	+	0.609428i
$424$		0			0
$425$	443.728	−	197.108i	1.04407	−	0.463785i
$426$		0			0
$427$	−358.115	−	47.7474i	−0.838677	−	0.111821i
$428$		0			0
$429$			141.781i			0.330493i
$430$		0			0
$431$		−	12.1303i		−	0.0281444i	−0.999901	−	0.0140722i	$-0.995521\pi$
$431$		−	12.1303i		−	0.0281444i	0.999901	−	0.0140722i	$-0.00447948\pi$
$432$		0			0
$433$	215.703	+	215.703i	0.498160	+	0.498160i	0.910865	−	0.412705i	$-0.135416\pi$
$433$	215.703	+	215.703i	0.498160	+	0.498160i	−0.412705	+	0.910865i	$0.635416\pi$
$434$		0			0
$435$	274.423	−	188.434i	0.630857	−	0.433181i
$436$		0			0
$437$	95.8518	−	95.8518i	0.219340	−	0.219340i
$438$		0			0
$439$			698.492i			1.59110i	0.605890	+	0.795548i	$0.292817\pi$
$439$			698.492i			1.59110i	−0.605890	+	0.795548i	$0.707183\pi$
$440$		0			0
$441$	84.7166	−	312.048i	0.192101	−	0.707593i
$442$		0			0
$443$	−244.732	−	244.732i	−0.552443	−	0.552443i	0.374702	−	0.927145i	$-0.377745\pi$
$443$	−244.732	−	244.732i	−0.552443	−	0.552443i	−0.927145	+	0.374702i	$0.877745\pi$
$444$		0			0
$445$	61.6134	−	331.649i	0.138457	−	0.745279i
$446$		0			0
$447$	35.6922	+	35.6922i	0.0798482	+	0.0798482i
$448$		0			0
$449$		−	581.130i		−	1.29428i	−0.762373	−	0.647138i	$-0.775966\pi$
$449$		−	581.130i		−	1.29428i	0.762373	−	0.647138i	$-0.224034\pi$
$450$		0			0
$451$	139.534			0.309389
$452$		0			0
$453$	−16.2985	−	16.2985i	−0.0359791	−	0.0359791i
$454$		0			0
$455$	318.590	+	628.486i	0.700198	+	1.38129i
$456$		0			0
$457$	7.06448	+	7.06448i	0.0154584	+	0.0154584i	0.714794	−	0.699335i	$-0.246521\pi$
$457$	7.06448	+	7.06448i	0.0154584	+	0.0154584i	−0.699335	+	0.714794i	$0.746521\pi$
$458$		0			0
$459$	−469.445			−1.02276
$460$		0			0
$461$		−	245.800i		−	0.533188i	−0.963809	−	0.266594i	$-0.914102\pi$
$461$		−	245.800i		−	0.533188i	0.963809	−	0.266594i	$-0.0858983\pi$
$462$		0			0
$463$	409.210	+	409.210i	0.883823	+	0.883823i	0.993921	−	0.110098i	$-0.0351165\pi$
$463$	409.210	+	409.210i	0.883823	+	0.883823i	−0.110098	+	0.993921i	$0.535116\pi$
$464$		0			0
$465$	−47.5978	−	69.3183i	−0.102361	−	0.149072i
$466$		0			0
$467$	−150.989	−	150.989i	−0.323316	−	0.323316i	0.526722	−	0.850038i	$-0.323421\pi$
$467$	−150.989	−	150.989i	−0.323316	−	0.323316i	−0.850038	+	0.526722i	$0.823421\pi$
$468$		0			0
$469$	−330.480	−	432.163i	−0.704648	−	0.921456i
$470$		0			0
$471$		−	136.957i		−	0.290778i
$472$		0			0
$473$	215.680	−	215.680i	0.455983	−	0.455983i
$474$		0			0
$475$	33.2049	−	86.2824i	0.0699051	−	0.181647i
$476$		0			0
$477$	−112.640	−	112.640i	−0.236143	−	0.236143i
$478$		0			0
$479$		−	718.590i		−	1.50019i	−0.661332	−	0.750094i	$-0.730008\pi$
$479$		−	718.590i		−	1.50019i	0.661332	−	0.750094i	$-0.269992\pi$
$480$		0			0
$481$			1045.96i			2.17455i
$482$		0			0
$483$	52.5474	−	394.116i	0.108794	−	0.815975i
$484$		0			0
$485$	−100.801	−	146.800i	−0.207837	−	0.302680i
$486$		0			0
$487$	24.7273	−	24.7273i	0.0507747	−	0.0507747i	−0.681264	−	0.732038i	$-0.738569\pi$
$487$	24.7273	−	24.7273i	0.0507747	−	0.0507747i	0.732038	+	0.681264i	$0.238569\pi$
$488$		0			0
$489$	−45.9026			−0.0938703
$490$		0			0
$491$			565.961i			1.15267i	0.817213	+	0.576336i	$0.195518\pi$
$491$			565.961i			1.15267i	−0.817213	+	0.576336i	$0.804482\pi$
$492$		0			0
$493$	590.048	+	590.048i	1.19685	+	1.19685i
$494$		0			0
$495$	−27.3896	+	147.431i	−0.0553326	+	0.297841i
$496$		0			0
$497$	348.012	+	46.4003i	0.700225	+	0.0933608i
$498$		0			0
$499$	357.067			0.715566			0.357783	−	0.933805i	$-0.383533\pi$
$499$	357.067			0.715566			0.357783	+	0.933805i	$0.383533\pi$
$500$		0			0
$501$	−254.224			−0.507434
$502$		0			0
$503$	−247.987	+	247.987i	−0.493017	+	0.493017i	−0.909255	−	0.416239i	$-0.863348\pi$
$503$	−247.987	+	247.987i	−0.493017	+	0.493017i	0.416239	+	0.909255i	$0.363348\pi$
$504$		0			0
$505$	−243.643	−	45.2638i	−0.482462	−	0.0896313i
$506$		0			0
$507$	258.918	+	258.918i	0.510686	+	0.510686i
$508$		0			0
$509$	778.236			1.52895			0.764475	−	0.644653i	$-0.222998\pi$
$509$	778.236			1.52895			0.764475	+	0.644653i	$0.222998\pi$
$510$		0			0
$511$	−14.7101	+	11.2490i	−0.0287868	+	0.0220136i
$512$		0			0
$513$	−63.2062	+	63.2062i	−0.123209	+	0.123209i
$514$		0			0
$515$	−573.006	−	834.489i	−1.11263	−	1.62037i
$516$		0			0
$517$	177.547	−	177.547i	0.343419	−	0.343419i
$518$		0			0
$519$	176.214			0.339526
$520$		0			0
$521$		−	447.349i		−	0.858634i	−0.903154	−	0.429317i	$-0.858754\pi$
$521$		−	447.349i		−	0.858634i	0.903154	−	0.429317i	$-0.141246\pi$
$522$		0			0
$523$	−201.809	+	201.809i	−0.385868	+	0.385868i	−0.873211	−	0.487343i	$-0.837966\pi$
$523$	−201.809	+	201.809i	−0.385868	+	0.385868i	0.487343	+	0.873211i	$0.337966\pi$
$524$		0			0
$525$	−76.3677	−	260.199i	−0.145462	−	0.495616i
$526$		0			0
$527$	149.044	−	149.044i	0.282816	−	0.282816i
$528$		0			0
$529$			814.647i			1.53998i
$530$		0			0
$531$	−618.070			−1.16397
$532$		0			0
$533$	437.054	−	437.054i	0.819989	−	0.819989i
$534$		0			0
$535$	−35.6569	−	51.9285i	−0.0666485	−	0.0970625i
$536$		0			0
$537$	305.681	−	305.681i	0.569239	−	0.569239i
$538$		0			0
$539$	−58.3473	+	214.918i	−0.108251	+	0.398735i
$540$		0			0
$541$	−903.984			−1.67095			−0.835475	−	0.549529i	$-0.814807\pi$
$541$	−903.984			−1.67095			−0.835475	+	0.549529i	$0.814807\pi$
$542$		0			0
$543$	201.761	+	201.761i	0.371568	+	0.371568i
$544$		0			0
$545$	−772.760	−	143.562i	−1.41791	−	0.263417i
$546$		0			0
$547$	559.251	−	559.251i	1.02240	−	1.02240i	0.0226529	−	0.999743i	$-0.492789\pi$
$547$	559.251	−	559.251i	1.02240	−	1.02240i	0.999743	−	0.0226529i	$-0.00721124\pi$
$548$		0			0
$549$	−340.580			−0.620364
$550$		0			0
$551$	158.888			0.288364
$552$		0			0
$553$	−95.4756	+	716.086i	−0.172650	+	1.29491i
$554$		0			0
$555$	73.5245	−	395.764i	0.132477	−	0.713088i
$556$		0			0
$557$	354.107	+	354.107i	0.635739	+	0.635739i	0.949502	−	0.313762i	$-0.101590\pi$
$557$	354.107	+	354.107i	0.635739	+	0.635739i	−0.313762	+	0.949502i	$0.601590\pi$
$558$		0			0
$559$		−	1351.12i		−	2.41703i
$560$		0			0
$561$	136.777			0.243809
$562$		0			0
$563$	−69.7893	+	69.7893i	−0.123960	+	0.123960i	−0.766365	−	0.642405i	$-0.777937\pi$
$563$	−69.7893	+	69.7893i	−0.123960	+	0.123960i	0.642405	+	0.766365i	$0.277937\pi$
$564$		0			0
$565$	−169.375	−	246.667i	−0.299779	−	0.436579i
$566$		0			0
$567$	20.2920	−	152.194i	0.0357884	−	0.268420i
$568$		0			0
$569$		−	80.2029i		−	0.140954i	−0.997513	−	0.0704771i	$-0.977548\pi$
$569$		−	80.2029i		−	0.140954i	0.997513	−	0.0704771i	$-0.0224522\pi$
$570$		0			0
$571$			173.604i			0.304035i	0.988378	+	0.152017i	$0.0485770\pi$
$571$			173.604i			0.304035i	−0.988378	+	0.152017i	$0.951423\pi$
$572$		0			0
$573$	−377.505	−	377.505i	−0.658822	−	0.658822i
$574$		0			0
$575$	372.019	+	837.485i	0.646990	+	1.45650i
$576$		0			0
$577$	518.091	−	518.091i	0.897904	−	0.897904i	−0.0973463	−	0.995251i	$-0.531035\pi$
$577$	518.091	−	518.091i	0.897904	−	0.897904i	0.995251	+	0.0973463i	$0.0310354\pi$
$578$		0			0
$579$			405.936i			0.701099i
$580$		0			0
$581$	312.406	+	408.528i	0.537704	+	0.703146i
$582$		0			0
$583$	77.5792	+	77.5792i	0.133069	+	0.133069i
$584$		0			0
$585$	375.999	+	547.581i	0.642733	+	0.936035i
$586$		0			0
$587$	−145.339	−	145.339i	−0.247596	−	0.247596i	0.572387	−	0.819983i	$-0.306017\pi$
$587$	−145.339	−	145.339i	−0.247596	−	0.247596i	−0.819983	+	0.572387i	$0.806017\pi$
$588$		0			0
$589$		−	40.1347i		−	0.0681404i
$590$		0			0
$591$	153.603			0.259903
$592$		0			0
$593$	−58.2193	−	58.2193i	−0.0981775	−	0.0981775i	0.656312	−	0.754490i	$-0.272115\pi$
$593$	−58.2193	−	58.2193i	−0.0981775	−	0.0981775i	−0.754490	+	0.656312i	$0.772115\pi$
$594$		0			0
$595$	606.302	−	307.344i	1.01899	−	0.516545i
$596$		0			0
$597$	317.777	+	317.777i	0.532290	+	0.532290i
$598$		0			0
$599$	−625.366			−1.04402			−0.522008	−	0.852941i	$-0.674817\pi$
$599$	−625.366			−1.04402			−0.522008	+	0.852941i	$0.674817\pi$
$600$		0			0
$601$			433.587i			0.721443i	0.932674	+	0.360721i	$0.117469\pi$
$601$			433.587i			0.721443i	−0.932674	+	0.360721i	$0.882531\pi$
$602$		0			0
$603$	−362.650	−	362.650i	−0.601410	−	0.601410i
$604$		0			0
$605$	−91.6412	+	493.281i	−0.151473	+	0.815341i
$606$		0			0
$607$	−138.847	−	138.847i	−0.228744	−	0.228744i	0.583424	−	0.812168i	$-0.301713\pi$
$607$	−138.847	−	138.847i	−0.228744	−	0.228744i	−0.812168	+	0.583424i	$0.801713\pi$
$608$		0			0
$609$	370.205	−	283.100i	0.607890	−	0.464861i
$610$		0			0
$611$		−	1112.24i		−	1.82036i
$612$		0			0
$613$	−185.617	+	185.617i	−0.302800	+	0.302800i	−0.842108	−	0.539308i	$-0.818686\pi$
$613$	−185.617	+	185.617i	−0.302800	+	0.302800i	0.539308	+	0.842108i	$0.318686\pi$
$614$		0			0
$615$	−196.093	+	134.648i	−0.318850	+	0.218940i
$616$		0			0
$617$	660.890	+	660.890i	1.07113	+	1.07113i	0.997268	+	0.0738659i	$0.0235337\pi$
$617$	660.890	+	660.890i	1.07113	+	1.07113i	0.0738659	+	0.997268i	$0.476466\pi$
$618$		0			0
$619$			192.450i			0.310905i	0.987843	+	0.155452i	$0.0496836\pi$
$619$			192.450i			0.310905i	−0.987843	+	0.155452i	$0.950316\pi$
$620$		0			0
$621$		−	886.023i		−	1.42677i
$622$		0			0
$623$	62.4131	−	468.111i	0.100182	−	0.751382i
$624$		0			0
$625$	463.754	+	418.996i	0.742006	+	0.670393i
$626$		0			0
$627$	18.4157	−	18.4157i	0.0293711	−	0.0293711i
$628$		0			0
$629$	1009.04			1.60419
$630$		0			0
$631$			165.195i			0.261799i	0.991396	+	0.130899i	$0.0417865\pi$
$631$			165.195i			0.261799i	−0.991396	+	0.130899i	$0.958213\pi$
$632$		0			0
$633$	77.1600	+	77.1600i	0.121896	+	0.121896i
$634$		0			0
$635$	−7.89426	−	11.4967i	−0.0124319	−	0.0181050i
$636$		0			0
$637$	490.418	+	855.933i	0.769887	+	1.34369i
$638$		0			0
$639$	330.971			0.517952
$640$		0			0
$641$	29.4047			0.0458731			0.0229366	−	0.999737i	$-0.492698\pi$
$641$	29.4047			0.0458731			0.0229366	+	0.999737i	$0.492698\pi$
$642$		0			0
$643$	293.272	−	293.272i	0.456100	−	0.456100i	−0.441273	−	0.897373i	$-0.645473\pi$
$643$	293.272	−	293.272i	0.456100	−	0.456100i	0.897373	+	0.441273i	$0.145473\pi$
$644$		0			0
$645$	−94.9757	+	511.230i	−0.147249	+	0.792605i
$646$		0			0
$647$	204.997	+	204.997i	0.316842	+	0.316842i	0.847553	−	0.530711i	$-0.178075\pi$
$647$	204.997	+	204.997i	0.316842	+	0.316842i	−0.530711	+	0.847553i	$0.678075\pi$
$648$		0			0
$649$	425.686			0.655911
$650$		0			0
$651$	−71.5102	−	93.5126i	−0.109847	−	0.143645i
$652$		0			0
$653$	381.175	−	381.175i	0.583728	−	0.583728i	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	381.175	−	381.175i	0.583728	−	0.583728i	0.935926	+	0.352197i	$0.114565\pi$
$654$		0			0
$655$	−39.7439	+	213.931i	−0.0606777	+	0.326613i
$656$		0			0
$657$	−12.3440	+	12.3440i	−0.0187884	+	0.0187884i
$658$		0			0
$659$	447.923			0.679700			0.339850	−	0.940480i	$-0.389624\pi$
$659$	447.923			0.679700			0.339850	+	0.940480i	$0.389624\pi$
$660$		0			0
$661$		−	600.074i		−	0.907828i	−0.891045	−	0.453914i	$-0.850027\pi$
$661$		−	600.074i		−	0.907828i	0.891045	−	0.453914i	$-0.149973\pi$
$662$		0			0
$663$	428.417	−	428.417i	0.646179	−	0.646179i
$664$		0			0
$665$	40.2517	−	123.014i	0.0605289	−	0.184983i
$666$		0			0
$667$	−1113.65	+	1113.65i	−1.66963	+	1.66963i
$668$		0			0
$669$		−	236.631i		−	0.353709i
$670$		0			0
$671$	234.569			0.349581
$672$		0			0
$673$	−355.777	+	355.777i	−0.528643	+	0.528643i	−0.920168	−	0.391525i	$-0.871948\pi$
$673$	−355.777	+	355.777i	−0.528643	+	0.528643i	0.391525	+	0.920168i	$0.371948\pi$
$674$		0			0
$675$	−245.316	−	552.251i	−0.363431	−	0.818150i
$676$		0			0
$677$	32.1048	−	32.1048i	0.0474221	−	0.0474221i	−0.682998	−	0.730420i	$-0.739324\pi$
$677$	32.1048	−	32.1048i	0.0474221	−	0.0474221i	0.730420	+	0.682998i	$0.239324\pi$
$678$		0			0
$679$	−151.442	−	198.038i	−0.223037	−	0.291661i
$680$		0			0
$681$	−290.176			−0.426103
$682$		0			0
$683$	−222.741	−	222.741i	−0.326122	−	0.326122i	0.524988	−	0.851110i	$-0.324070\pi$
$683$	−222.741	−	222.741i	−0.326122	−	0.326122i	−0.851110	+	0.524988i	$0.824070\pi$
$684$		0			0
$685$	658.136	−	451.913i	0.960783	−	0.659726i
$686$		0			0
$687$	431.832	−	431.832i	0.628576	−	0.628576i
$688$		0			0
$689$	485.993			0.705360
$690$		0			0
$691$	−945.754			−1.36867			−0.684337	−	0.729166i	$-0.739908\pi$
$691$	−945.754			−1.36867			−0.684337	+	0.729166i	$0.739908\pi$
$692$		0			0
$693$	−27.7451	+	208.094i	−0.0400363	+	0.300280i
$694$		0			0
$695$	934.561	+	173.622i	1.34469	+	0.249815i
$696$		0			0
$697$	−421.627	−	421.627i	−0.604917	−	0.604917i
$698$		0			0
$699$			491.008i			0.702443i
$700$		0			0
$701$	232.770			0.332054			0.166027	−	0.986121i	$-0.446906\pi$
$701$	232.770			0.332054			0.166027	+	0.986121i	$0.446906\pi$
$702$		0			0
$703$	135.857	−	135.857i	0.193253	−	0.193253i
$704$		0			0
$705$	−78.1839	+	420.844i	−0.110899	+	0.596942i
$706$		0			0
$707$	−343.894	−	45.8513i	−0.486413	−	0.0648533i
$708$		0			0
$709$			499.525i			0.704549i	0.935897	+	0.352274i	$0.114592\pi$
$709$			499.525i			0.704549i	−0.935897	+	0.352274i	$0.885408\pi$
$710$		0			0
$711$			681.023i			0.957838i
$712$		0			0
$713$	281.303	+	281.303i	0.394535	+	0.394535i
$714$		0			0
$715$	−258.963	−	377.138i	−0.362187	−	0.527465i
$716$		0			0
$717$	−191.536	+	191.536i	−0.267135	+	0.267135i
$718$		0			0
$719$		−	1290.46i		−	1.79480i	−0.441222	−	0.897398i	$-0.645455\pi$
$719$		−	1290.46i		−	1.79480i	0.441222	−	0.897398i	$-0.354545\pi$
$720$		0			0
$721$	−860.876	−	1125.75i	−1.19400	−	1.56138i
$722$		0			0
$723$	240.979	+	240.979i	0.333304	+	0.333304i
$724$		0			0
$725$	−385.789	+	1002.47i	−0.532123	+	1.38271i
$726$		0			0
$727$	863.661	+	863.661i	1.18798	+	1.18798i	0.977625	+	0.210355i	$0.0674619\pi$
$727$	863.661	+	863.661i	1.18798	+	1.18798i	0.210355	+	0.977625i	$0.432538\pi$
$728$		0			0
$729$			192.355i			0.263861i
$730$		0			0
$731$	−1303.43			−1.78308
$732$		0			0
$733$	526.267	+	526.267i	0.717963	+	0.717963i	0.968188	−	0.250225i	$-0.0805045\pi$
$733$	526.267	+	526.267i	0.717963	+	0.717963i	−0.250225	+	0.968188i	$0.580504\pi$
$734$		0			0
$735$	−125.395	−	358.337i	−0.170605	−	0.487533i
$736$		0			0
$737$	249.770	+	249.770i	0.338900	+	0.338900i
$738$		0			0
$739$	1016.79			1.37590			0.687952	−	0.725756i	$-0.258510\pi$
$739$	1016.79			1.37590			0.687952	+	0.725756i	$0.258510\pi$
$740$		0			0
$741$		−	115.364i		−	0.155687i
$742$		0			0
$743$	−365.633	−	365.633i	−0.492104	−	0.492104i	0.416865	−	0.908969i	$-0.363129\pi$
$743$	−365.633	−	365.633i	−0.492104	−	0.492104i	−0.908969	+	0.416865i	$0.863129\pi$
$744$		0			0
$745$	−160.133	−	29.7493i	−0.214943	−	0.0399319i
$746$		0			0
$747$	342.816	+	342.816i	0.458924	+	0.458924i
$748$		0			0
$749$	−53.5705	−	70.0532i	−0.0715227	−	0.0935290i
$750$		0			0
$751$			413.171i			0.550161i	0.961421	+	0.275081i	$0.0887046\pi$
$751$			413.171i			0.550161i	−0.961421	+	0.275081i	$0.911295\pi$
$752$		0			0
$753$	499.315	−	499.315i	0.663101	−	0.663101i
$754$		0			0
$755$	73.1233	+	13.5848i	0.0968521	+	0.0179931i
$756$		0			0
$757$	−979.929	−	979.929i	−1.29449	−	1.29449i	−0.931980	−	0.362511i	$-0.881920\pi$
$757$	−979.929	−	979.929i	−1.29449	−	1.29449i	−0.362511	−	0.931980i	$-0.618080\pi$
$758$		0			0
$759$			258.150i			0.340119i
$760$		0			0
$761$		−	355.292i		−	0.466876i	−0.972372	−	0.233438i	$-0.925002\pi$
$761$		−	355.292i		−	0.466876i	0.972372	−	0.233438i	$-0.0749975\pi$
$762$		0			0
$763$	−1090.72	−	145.426i	−1.42952	−	0.190597i
$764$		0			0
$765$	528.252	−	362.727i	0.690525	−	0.474153i
$766$		0			0
$767$	1333.35	−	1333.35i	1.73840	−	1.73840i
$768$		0			0
$769$	−22.1176			−0.0287615			−0.0143807	−	0.999897i	$-0.504578\pi$
$769$	−22.1176			−0.0287615			−0.0143807	+	0.999897i	$0.504578\pi$
$770$		0			0
$771$		−	238.484i		−	0.309318i
$772$		0			0
$773$	36.3262	+	36.3262i	0.0469938	+	0.0469938i	0.730213	−	0.683219i	$-0.239421\pi$
$773$	36.3262	+	36.3262i	0.0469938	+	0.0469938i	−0.683219	+	0.730213i	$0.739421\pi$
$774$		0			0
$775$	253.220	+	97.4490i	0.326735	+	0.125741i
$776$		0			0
$777$	74.4789	−	558.606i	0.0958544	−	0.718927i
$778$		0			0
$779$	−113.536			−0.145746
$780$		0			0
$781$	−227.951			−0.291871
$782$		0			0
$783$	734.357	−	734.357i	0.937876	−	0.937876i
$784$		0			0
$785$	250.151	+	364.304i	0.318664	+	0.464081i
$786$		0			0
$787$	−534.112	−	534.112i	−0.678668	−	0.678668i	0.281031	−	0.959699i	$-0.409324\pi$
$787$	−534.112	−	534.112i	−0.678668	−	0.678668i	−0.959699	+	0.281031i	$0.909324\pi$
$788$		0			0
$789$	168.732			0.213856
$790$		0			0
$791$	−254.467	−	332.762i	−0.321703	−	0.420685i
$792$		0			0
$793$	734.726	−	734.726i	0.926514	−	0.926514i
$794$		0			0
$795$	−183.887	−	34.1624i	−0.231305	−	0.0429716i
$796$		0			0
$797$	410.638	−	410.638i	0.515229	−	0.515229i	−0.400895	−	0.916124i	$-0.631301\pi$
$797$	410.638	−	410.638i	0.515229	−	0.515229i	0.916124	+	0.400895i	$0.131301\pi$
$798$		0			0
$799$	−1072.98			−1.34290
$800$		0			0
$801$		−	445.190i		−	0.555792i
$802$		0			0
$803$	8.50171	−	8.50171i	0.0105874	−	0.0105874i
$804$		0			0
$805$	580.077	+	1144.32i	0.720592	+	1.42152i
$806$		0			0
$807$	−305.825	+	305.825i	−0.378965	+	0.378965i
$808$		0			0
$809$		−	841.822i		−	1.04057i	−0.853992	−	0.520286i	$-0.825825\pi$
$809$		−	841.822i		−	1.04057i	0.853992	−	0.520286i	$-0.174175\pi$
$810$		0			0
$811$	−907.084			−1.11848			−0.559238	−	0.829007i	$-0.688906\pi$
$811$	−907.084			−1.11848			−0.559238	+	0.829007i	$0.688906\pi$
$812$		0			0
$813$	−87.5759	+	87.5759i	−0.107719	+	0.107719i
$814$		0			0
$815$	122.101	−	83.8410i	0.149817	−	0.102872i
$816$		0			0
$817$	−175.494	+	175.494i	−0.214803	+	0.214803i
$818$		0			0
$819$	564.896	+	738.704i	0.689738	+	0.901959i
$820$		0			0
$821$	−241.482			−0.294131			−0.147066	−	0.989127i	$-0.546983\pi$
$821$	−241.482			−0.294131			−0.147066	+	0.989127i	$0.546983\pi$
$822$		0			0
$823$	811.704	+	811.704i	0.986274	+	0.986274i	0.999907	−	0.0136330i	$-0.00433966\pi$
$823$	811.704	+	811.704i	0.986274	+	0.986274i	−0.0136330	+	0.999907i	$0.504340\pi$
$824$		0			0
$825$	71.4748	+	160.903i	0.0866361	+	0.195034i
$826$		0			0
$827$	−383.505	+	383.505i	−0.463731	+	0.463731i	−0.899876	−	0.436145i	$-0.856343\pi$
$827$	−383.505	+	383.505i	−0.463731	+	0.463731i	0.436145	+	0.899876i	$0.356343\pi$
$828$		0			0
$829$	383.372			0.462452			0.231226	−	0.972900i	$-0.425726\pi$
$829$	383.372			0.462452			0.231226	+	0.972900i	$0.425726\pi$
$830$		0			0
$831$	−128.793			−0.154985
$832$		0			0
$833$	825.720	−	473.107i	0.991260	−	0.567955i
$834$		0			0
$835$	676.235	−	464.340i	0.809862	−	0.556096i
$836$		0			0
$837$	−185.496	−	185.496i	−0.221620	−	0.221620i
$838$		0			0
$839$			212.492i			0.253268i	0.991949	+	0.126634i	$0.0404174\pi$
$839$			212.492i			0.253268i	−0.991949	+	0.126634i	$0.959583\pi$
$840$		0			0
$841$	−1005.03			−1.19505
$842$		0			0
$843$	49.7450	−	49.7450i	0.0590095	−	0.0590095i
$844$		0			0
$845$	−1161.63	−	215.807i	−1.37471	−	0.255393i
$846$		0			0
$847$	−92.8307	+	696.249i	−0.109599	+	0.822018i
$848$		0			0
$849$		−	129.503i		−	0.152536i
$850$		0			0
$851$			1904.44i			2.23788i
$852$		0			0
$853$	−55.2759	−	55.2759i	−0.0648018	−	0.0648018i	0.673963	−	0.738765i	$-0.264591\pi$
$853$	−55.2759	−	55.2759i	−0.0648018	−	0.0648018i	−0.738765	+	0.673963i	$0.764591\pi$
$854$		0			0
$855$	22.2863	−	119.962i	0.0260659	−	0.140306i
$856$		0			0
$857$	−145.511	+	145.511i	−0.169791	+	0.169791i	−0.786887	−	0.617097i	$-0.788309\pi$
$857$	−145.511	+	145.511i	−0.169791	+	0.169791i	0.617097	+	0.786887i	$0.288309\pi$
$858$		0			0
$859$		−	603.378i		−	0.702419i	−0.936297	−	0.351209i	$-0.885771\pi$
$859$		−	603.378i		−	0.702419i	0.936297	−	0.351209i	$-0.114229\pi$
$860$		0			0
$861$	−264.535	+	202.293i	−0.307242	+	0.234952i
$862$		0			0
$863$	−418.474	−	418.474i	−0.484906	−	0.484906i	0.421789	−	0.906694i	$-0.361402\pi$
$863$	−418.474	−	418.474i	−0.484906	−	0.484906i	−0.906694	+	0.421789i	$0.861402\pi$
$864$		0			0
$865$	−468.728	+	321.855i	−0.541882	+	0.372086i
$866$		0			0
$867$	−96.6349	−	96.6349i	−0.111459	−	0.111459i
$868$		0			0
$869$		−	469.044i		−	0.539751i
$870$		0			0
$871$	1564.67			1.79641
$872$		0			0
$873$	−166.184	−	166.184i	−0.190359	−	0.190359i
$874$		0			0
$875$	678.390	+	552.641i	0.775303	+	0.631590i
$876$		0			0
$877$	1090.80	+	1090.80i	1.24378	+	1.24378i	0.958419	+	0.285366i	$0.0921153\pi$
$877$	1090.80	+	1090.80i	1.24378	+	1.24378i	0.285366	+	0.958419i	$0.407885\pi$
$878$		0			0
$879$	−884.626			−1.00640
$880$		0			0
$881$			418.536i			0.475069i	0.971379	+	0.237534i	$0.0763393\pi$
$881$			418.536i			0.475069i	−0.971379	+	0.237534i	$0.923661\pi$
$882$		0			0
$883$	−323.810	−	323.810i	−0.366716	−	0.366716i	0.499562	−	0.866278i	$-0.333494\pi$
$883$	−323.810	−	323.810i	−0.366716	−	0.366716i	−0.866278	+	0.499562i	$0.833494\pi$
$884$		0			0
$885$	−598.233	+	410.779i	−0.675969	+	0.464158i
$886$		0			0
$887$	956.213	+	956.213i	1.07803	+	1.07803i	0.996686	+	0.0813440i	$0.0259212\pi$
$887$	956.213	+	956.213i	1.07803	+	1.07803i	0.0813440	+	0.996686i	$0.474079\pi$
$888$		0			0
$889$	−11.8602	−	15.5094i	−0.0133411	−	0.0174459i
$890$		0			0
$891$			99.6887i			0.111884i
$892$		0			0
$893$	−144.466	+	144.466i	−0.161777	+	0.161777i
$894$		0			0
$895$	−254.784	+	1371.44i	−0.284675	+	1.53233i
$896$		0			0
$897$	808.587	+	808.587i	0.901435	+	0.901435i
$898$		0			0
$899$			466.302i			0.518689i
$900$		0			0
$901$		−	468.838i		−	0.520353i
$902$		0			0
$903$	−96.2085	+	721.583i	−0.106543	+	0.799095i
$904$		0			0
$905$	−905.201	−	168.167i	−1.00022	−	0.185820i
$906$		0			0
$907$	1079.01	−	1079.01i	1.18965	−	1.18965i	0.212484	−	0.977165i	$-0.431845\pi$
$907$	1079.01	−	1079.01i	1.18965	−	1.18965i	0.977165	−	0.212484i	$-0.0681552\pi$
$908$		0			0
$909$	−327.055			−0.359797
$910$		0			0
$911$			1165.66i			1.27954i	0.768566	+	0.639771i	$0.220971\pi$
$911$			1165.66i			1.27954i	−0.768566	+	0.639771i	$0.779029\pi$
$912$		0			0
$913$	−236.109	−	236.109i	−0.258608	−	0.258608i
$914$		0			0
$915$	−329.649	+	226.355i	−0.360272	+	0.247382i
$916$		0			0
$917$	−40.2598	+	301.956i	−0.0439038	+	0.329287i
$918$		0			0
$919$	−1616.18			−1.75863			−0.879317	−	0.476237i	$-0.842000\pi$
$919$	−1616.18			−1.75863			−0.879317	+	0.476237i	$0.842000\pi$
$920$		0			0
$921$	−150.739			−0.163669
$922$		0			0
$923$	−713.997	+	713.997i	−0.773561	+	0.773561i
$924$		0			0
$925$	527.287	+	1187.02i	0.570040	+	1.28327i
$926$		0			0
$927$	−944.676	−	944.676i	−1.01907	−	1.01907i
$928$		0			0
$929$	−1056.13			−1.13685			−0.568425	−	0.822735i	$-0.692447\pi$
$929$	−1056.13			−1.13685			−0.568425	+	0.822735i	$0.692447\pi$
$930$		0			0
$931$	47.4759	−	174.874i	0.0509945	−	0.187835i
$932$		0			0
$933$	−26.5447	+	26.5447i	−0.0284509	+	0.0284509i
$934$		0			0
$935$	−363.825	+	249.823i	−0.389118	+	0.267190i
$936$		0			0
$937$	−1214.60	+	1214.60i	−1.29626	+	1.29626i	−0.365420	+	0.930843i	$0.619075\pi$
$937$	−1214.60	+	1214.60i	−1.29626	+	1.29626i	−0.930843	+	0.365420i	$0.880925\pi$
$938$		0			0
$939$	269.134			0.286618
$940$		0			0
$941$			1456.10i			1.54740i	0.633555	+	0.773698i	$0.281595\pi$
$941$			1456.10i			1.54740i	−0.633555	+	0.773698i	$0.718405\pi$
$942$		0			0
$943$	795.772	−	795.772i	0.843873	−	0.843873i
$944$		0			0
$945$	−382.512	−	754.586i	−0.404775	−	0.798504i
$946$		0			0
$947$	95.3532	−	95.3532i	0.100690	−	0.100690i	−0.654967	−	0.755657i	$-0.727318\pi$
$947$	95.3532	−	95.3532i	0.100690	−	0.100690i	0.755657	+	0.654967i	$0.227318\pi$
$948$		0			0
$949$		−	53.2587i		−	0.0561209i
$950$		0			0
$951$	−421.785			−0.443518
$952$		0			0
$953$	257.253	−	257.253i	0.269940	−	0.269940i	−0.559136	−	0.829076i	$-0.688867\pi$
$953$	257.253	−	257.253i	0.269940	−	0.269940i	0.829076	+	0.559136i	$0.188867\pi$
$954$		0			0
$955$	1693.67	+	314.649i	1.77348	+	0.329475i
$956$		0			0
$957$	−213.961	+	213.961i	−0.223575	+	0.223575i
$958$		0			0
$959$	887.847	−	678.947i	0.925805	−	0.707974i
$960$		0			0
$961$	−843.214			−0.877434
$962$		0			0
$963$	−58.7852	−	58.7852i	−0.0610438	−	0.0610438i
$964$		0			0
$965$	−741.443	−	1079.79i	−0.768334	−	1.11895i
$966$		0			0
$967$	83.9318	−	83.9318i	0.0867961	−	0.0867961i	−0.662376	−	0.749172i	$-0.730452\pi$
$967$	83.9318	−	83.9318i	0.0867961	−	0.0867961i	0.749172	+	0.662376i	$0.230452\pi$
$968$		0			0
$969$	−111.292			−0.114853
$970$		0			0
$971$	1595.08			1.64272			0.821359	−	0.570412i	$-0.193216\pi$
$971$	1595.08			1.64272			0.821359	+	0.570412i	$0.193216\pi$
$972$		0			0
$973$	1319.10	+	175.875i	1.35570	+	0.180756i
$974$		0			0
$975$	727.862	+	280.110i	0.746525	+	0.287293i
$976$		0			0
$977$	−193.036	−	193.036i	−0.197580	−	0.197580i	0.601382	−	0.798962i	$-0.294617\pi$
$977$	−193.036	−	193.036i	−0.197580	−	0.197580i	−0.798962	+	0.601382i	$0.794617\pi$
$978$		0			0
$979$			306.617i			0.313195i
$980$		0			0
$981$	−1037.32			−1.05741
$982$		0			0
$983$	319.815	−	319.815i	0.325346	−	0.325346i	−0.525468	−	0.850814i	$-0.676110\pi$
$983$	319.815	−	319.815i	0.325346	−	0.325346i	0.850814	+	0.525468i	$0.176110\pi$
$984$		0			0
$985$	−408.582	+	280.555i	−0.414804	+	0.284828i
$986$		0			0
$987$	−79.1987	+	594.006i	−0.0802419	+	0.601830i
$988$		0			0
$989$		−	2460.07i		−	2.48743i
$990$		0			0
$991$			256.371i			0.258699i	0.991599	+	0.129349i	$0.0412889\pi$
$991$			256.371i			0.258699i	−0.991599	+	0.129349i	$0.958711\pi$
$992$		0			0
$993$	373.400	+	373.400i	0.376032	+	0.376032i
$994$		0			0
$995$	−1425.70	−	264.866i	−1.43287	−	0.266197i
$996$		0			0
$997$	−1015.44	+	1015.44i	−1.01849	+	1.01849i	−0.0186665	+	0.999826i	$0.505942\pi$
$997$	−1015.44	+	1015.44i	−1.01849	+	1.01849i	−0.999826	+	0.0186665i	$0.994058\pi$
$998$		0			0
$999$		−	1255.82i		−	1.25708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.b.447.22	yes	64
4.3	odd	2	inner	560.3.v.b.447.11	yes	64
5.3	odd	4	inner	560.3.v.b.223.21	yes	64
7.6	odd	2	inner	560.3.v.b.447.12	yes	64
20.3	even	4	inner	560.3.v.b.223.12	yes	64
28.27	even	2	inner	560.3.v.b.447.21	yes	64
35.13	even	4	inner	560.3.v.b.223.11	✓	64
140.83	odd	4	inner	560.3.v.b.223.22	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.b.223.11	✓	64	35.13	even	4	inner
560.3.v.b.223.12	yes	64	20.3	even	4	inner
560.3.v.b.223.21	yes	64	5.3	odd	4	inner
560.3.v.b.223.22	yes	64	140.83	odd	4	inner
560.3.v.b.447.11	yes	64	4.3	odd	2	inner
560.3.v.b.447.12	yes	64	7.6	odd	2	inner
560.3.v.b.447.21	yes	64	28.27	even	2	inner
560.3.v.b.447.22	yes	64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09571 - 1.09571i) q^{3} +(-0.913268 + 4.91589i) q^{5} +(-0.925122 + 6.93860i) q^{7} +6.59885i q^{9} -4.54485i q^{11} +(-14.2356 - 14.2356i) q^{13} +(4.38570 + 6.38705i) q^{15} +(-13.7331 + 13.7331i) q^{17} +3.69805i q^{19} +(6.58901 + 8.61634i) q^{21} +(-25.9196 - 25.9196i) q^{23} +(-23.3319 - 8.97904i) q^{25} +(17.0918 + 17.0918i) q^{27} -42.9655i q^{29} -10.8529 q^{31} +(-4.97983 - 4.97983i) q^{33} +(-33.2645 - 10.8846i) q^{35} +(-36.7375 - 36.7375i) q^{37} -31.1960 q^{39} +30.7016i q^{41} +(47.4558 + 47.4558i) q^{43} +(-32.4392 - 6.02651i) q^{45} +(39.0656 + 39.0656i) q^{47} +(-47.2883 - 12.8381i) q^{49} +30.0949i q^{51} +(-17.0697 + 17.0697i) q^{53} +(22.3420 + 4.15067i) q^{55} +(4.05198 + 4.05198i) q^{57} +93.6633i q^{59} +51.6120i q^{61} +(-45.7868 - 6.10474i) q^{63} +(82.9812 - 56.9795i) q^{65} +(-54.9566 + 54.9566i) q^{67} -56.8005 q^{69} -50.1559i q^{71} +(1.87062 + 1.87062i) q^{73} +(-35.4033 + 15.7265i) q^{75} +(31.5349 + 4.20454i) q^{77} +103.203 q^{79} -21.9344 q^{81} +(51.9509 - 51.9509i) q^{83} +(-54.9682 - 80.0521i) q^{85} +(-47.0776 - 47.0776i) q^{87} -67.4648 q^{89} +(111.944 - 85.6052i) q^{91} +(-11.8917 + 11.8917i) q^{93} +(-18.1792 - 3.37731i) q^{95} +(-25.1837 + 25.1837i) q^{97} +29.9908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) \) 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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