LMFDB - Embedded newform 1680.2.dx.h.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(31,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.dx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6,0,0,0,-2,0,-6,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 328 x^{8} - 658 x^{7} + 1045 x^{6} - 1270 x^{5} + 1183 x^{4} + \cdots + 13 $ x^12 - 6x^11 + 35x^10 - 120x^9 + 328x^8 - 658x^7 + 1045x^6 - 1270x^5 + 1183x^4 - 810x^3 + 376x^2 - 104*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 - 0.189815i$ of defining polynomial
Character	$\chi$	$=$	1680.31
Dual form			1680.2.dx.h.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-1.57301 + 2.12736i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.62387 - 0.937541i) q^{11} -4.52565i q^{13} +1.00000i q^{15} +(2.57799 + 1.48840i) q^{17} +(2.83434 + 4.90922i) q^{19} +(1.05584 + 2.42594i) q^{21} +(5.18469 - 2.99338i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -7.45204 q^{29} +(4.48735 - 7.77232i) q^{31} +(-1.62387 + 0.937541i) q^{33} +(0.298587 - 2.62885i) q^{35} +(-3.86348 - 6.69175i) q^{37} +(-3.91933 - 2.26282i) q^{39} -11.3805i q^{41} +2.86693i q^{43} +(0.866025 + 0.500000i) q^{45} +(-3.60713 - 6.24774i) q^{47} +(-2.05129 - 6.69270i) q^{49} +(2.57799 - 1.48840i) q^{51} +(4.11168 - 7.12164i) q^{53} +1.87508 q^{55} +5.66868 q^{57} +(-5.23100 + 9.06036i) q^{59} +(6.12735 - 3.53762i) q^{61} +(2.62885 + 0.298587i) q^{63} +(2.26282 + 3.91933i) q^{65} +(7.40170 + 4.27337i) q^{67} -5.98676i q^{69} -0.634344i q^{71} +(-0.999540 - 0.577085i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(4.54884 - 1.97979i) q^{77} +(6.36997 - 3.67770i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.14602 q^{83} -2.97680 q^{85} +(-3.72602 + 6.45366i) q^{87} +(8.82148 - 5.09309i) q^{89} +(9.62766 + 7.11888i) q^{91} +(-4.48735 - 7.77232i) q^{93} +(-4.90922 - 2.83434i) q^{95} +13.3613i q^{97} +1.87508i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 2 q^{7} - 6 q^{9} + 10 q^{19} - 4 q^{21} + 12 q^{23} + 6 q^{25} - 12 q^{27} + 8 q^{29} - 2 q^{31} - 4 q^{35} - 10 q^{37} + 6 q^{39} + 2 q^{49} + 16 q^{53} + 20 q^{57} + 24 q^{61} - 2 q^{63}+ \cdots + 24 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 - 2 * q^7 - 6 * q^9 + 10 * q^19 - 4 * q^21 + 12 * q^23 + 6 * q^25 - 12 * q^27 + 8 * q^29 - 2 * q^31 - 4 * q^35 - 10 * q^37 + 6 * q^39 + 2 * q^49 + 16 * q^53 + 20 * q^57 + 24 * q^61 - 2 * q^63 + 4 * q^65 - 6 * q^67 + 30 * q^73 - 6 * q^75 + 36 * q^77 + 42 * q^79 - 6 * q^81 - 64 * q^83 - 8 * q^85 + 4 * q^87 + 14 * q^91 + 2 * q^93 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$	$-1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	−1.57301	+	2.12736i	−0.594541	+	0.804065i
$7$	−1.57301	+	2.12736i	−0.594541	+	0.804065i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.62387	−	0.937541i	−0.489615	−	0.282679i	0.234800	−	0.972044i	$-0.424557\pi$
$11$	−1.62387	−	0.937541i	−0.489615	−	0.282679i	−0.724415	+	0.689364i	$0.757890\pi$
$12$		0			0
$13$		−	4.52565i		−	1.25519i	−0.778541	−	0.627594i	$-0.784040\pi$
$13$		−	4.52565i		−	1.25519i	0.778541	−	0.627594i	$-0.215960\pi$
$14$		0			0
$15$			1.00000i			0.258199i
$16$		0			0
$17$	2.57799	+	1.48840i	0.625254	+	0.360991i	0.778912	−	0.627134i	$-0.215772\pi$
$17$	2.57799	+	1.48840i	0.625254	+	0.360991i	−0.153658	+	0.988124i	$0.549105\pi$
$18$		0			0
$19$	2.83434	+	4.90922i	0.650242	+	1.12625i	0.983064	+	0.183262i	$0.0586658\pi$
$19$	2.83434	+	4.90922i	0.650242	+	1.12625i	−0.332822	+	0.942990i	$0.608001\pi$
$20$		0			0
$21$	1.05584	+	2.42594i	0.230403	+	0.529384i
$22$		0			0
$23$	5.18469	−	2.99338i	1.08108	−	0.624163i	0.149894	−	0.988702i	$-0.452107\pi$
$23$	5.18469	−	2.99338i	1.08108	−	0.624163i	0.931188	+	0.364539i	$0.118773\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−7.45204			−1.38381			−0.691905	−	0.721989i	$-0.743228\pi$
$29$	−7.45204			−1.38381			−0.691905	+	0.721989i	$0.743228\pi$
$30$		0			0
$31$	4.48735	−	7.77232i	0.805952	−	1.39595i	−0.109694	−	0.993965i	$-0.534987\pi$
$31$	4.48735	−	7.77232i	0.805952	−	1.39595i	0.915646	−	0.401985i	$-0.131680\pi$
$32$		0			0
$33$	−1.62387	+	0.937541i	−0.282679	+	0.163205i
$34$		0			0
$35$	0.298587	−	2.62885i	0.0504703	−	0.444357i
$36$		0			0
$37$	−3.86348	−	6.69175i	−0.635153	−	1.10012i	−0.986483	−	0.163865i	$-0.947604\pi$
$37$	−3.86348	−	6.69175i	−0.635153	−	1.10012i	0.351330	−	0.936252i	$-0.385730\pi$
$38$		0			0
$39$	−3.91933	−	2.26282i	−0.627594	−	0.362342i
$40$		0			0
$41$		−	11.3805i		−	1.77734i	−0.458549	−	0.888669i	$-0.651631\pi$
$41$		−	11.3805i		−	1.77734i	0.458549	−	0.888669i	$-0.348369\pi$
$42$		0			0
$43$			2.86693i			0.437203i	0.975814	+	0.218601i	$0.0701494\pi$
$43$			2.86693i			0.437203i	−0.975814	+	0.218601i	$0.929851\pi$
$44$		0			0
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$		0			0
$47$	−3.60713	−	6.24774i	−0.526154	−	0.911326i	−0.999536	−	0.0304686i	$-0.990300\pi$
$47$	−3.60713	−	6.24774i	−0.526154	−	0.911326i	0.473381	−	0.880858i	$-0.343033\pi$
$48$		0			0
$49$	−2.05129	−	6.69270i	−0.293042	−	0.956100i
$50$		0			0
$51$	2.57799	−	1.48840i	0.360991	−	0.208418i
$52$		0			0
$53$	4.11168	−	7.12164i	0.564783	−	0.978233i	−0.432287	−	0.901736i	$-0.642293\pi$
$53$	4.11168	−	7.12164i	0.564783	−	0.978233i	0.997070	−	0.0764966i	$-0.0243734\pi$
$54$		0			0
$55$	1.87508			0.252836
$56$		0			0
$57$	5.66868			0.750835
$58$		0			0
$59$	−5.23100	+	9.06036i	−0.681018	+	1.17956i	0.293652	+	0.955912i	$0.405129\pi$
$59$	−5.23100	+	9.06036i	−0.681018	+	1.17956i	−0.974670	+	0.223646i	$0.928204\pi$
$60$		0			0
$61$	6.12735	−	3.53762i	0.784526	−	0.452946i	−0.0535057	−	0.998568i	$-0.517040\pi$
$61$	6.12735	−	3.53762i	0.784526	−	0.452946i	0.838032	+	0.545621i	$0.183706\pi$
$62$		0			0
$63$	2.62885	+	0.298587i	0.331204	+	0.0376184i
$64$		0			0
$65$	2.26282	+	3.91933i	0.280669	+	0.486132i
$66$		0			0
$67$	7.40170	+	4.27337i	0.904261	+	0.522076i	0.878580	−	0.477595i	$-0.158491\pi$
$67$	7.40170	+	4.27337i	0.904261	+	0.522076i	0.0256811	+	0.999670i	$0.491825\pi$
$68$		0			0
$69$		−	5.98676i		−	0.720722i
$70$		0			0
$71$		−	0.634344i		−	0.0752828i	−0.999291	−	0.0376414i	$-0.988016\pi$
$71$		−	0.634344i		−	0.0752828i	0.999291	−	0.0376414i	$-0.0119845\pi$
$72$		0			0
$73$	−0.999540	−	0.577085i	−0.116987	−	0.0675427i	0.440365	−	0.897819i	$-0.354849\pi$
$73$	−0.999540	−	0.577085i	−0.116987	−	0.0675427i	−0.557352	+	0.830276i	$0.688183\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	4.54884	−	1.97979i	0.518389	−	0.225618i
$78$		0			0
$79$	6.36997	−	3.67770i	0.716677	−	0.413774i	−0.0968512	−	0.995299i	$-0.530877\pi$
$79$	6.36997	−	3.67770i	0.716677	−	0.413774i	0.813528	+	0.581525i	$0.197544\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−8.14602			−0.894141			−0.447071	−	0.894499i	$-0.647533\pi$
$83$	−8.14602			−0.894141			−0.447071	+	0.894499i	$0.647533\pi$
$84$		0			0
$85$	−2.97680			−0.322880
$86$		0			0
$87$	−3.72602	+	6.45366i	−0.399471	+	0.691905i
$88$		0			0
$89$	8.82148	−	5.09309i	0.935075	−	0.539866i	0.0466622	−	0.998911i	$-0.485142\pi$
$89$	8.82148	−	5.09309i	0.935075	−	0.539866i	0.888413	+	0.459045i	$0.151808\pi$
$90$		0			0
$91$	9.62766	+	7.11888i	1.00925	+	0.746261i
$92$		0			0
$93$	−4.48735	−	7.77232i	−0.465317	−	0.805952i
$94$		0			0
$95$	−4.90922	−	2.83434i	−0.503675	−	0.290797i
$96$		0			0
$97$			13.3613i			1.35664i	0.734769	+	0.678318i	$0.237291\pi$
$97$			13.3613i			1.35664i	−0.734769	+	0.678318i	$0.762709\pi$
$98$		0			0
$99$			1.87508i			0.188453i
$100$		0			0
$101$	−10.9074	−	6.29739i	−1.08533	−	0.626614i	−0.152999	−	0.988226i	$-0.548893\pi$
$101$	−10.9074	−	6.29739i	−1.08533	−	0.626614i	−0.932328	+	0.361612i	$0.882226\pi$
$102$		0			0
$103$	−1.10619	−	1.91597i	−0.108996	−	0.188786i	0.806368	−	0.591414i	$-0.201430\pi$
$103$	−1.10619	−	1.91597i	−0.108996	−	0.188786i	−0.915364	+	0.402628i	$0.868097\pi$
$104$		0			0
$105$	−2.12736	−	1.57301i	−0.207609	−	0.153510i
$106$		0			0
$107$	2.54219	−	1.46774i	0.245763	−	0.141891i	−0.372060	−	0.928209i	$-0.621348\pi$
$107$	2.54219	−	1.46774i	0.245763	−	0.141891i	0.617823	+	0.786318i	$0.288015\pi$
$108$		0			0
$109$	7.27466	−	12.6001i	0.696786	−	1.20687i	−0.272789	−	0.962074i	$-0.587946\pi$
$109$	7.27466	−	12.6001i	0.696786	−	1.20687i	0.969575	−	0.244794i	$-0.0787205\pi$
$110$		0			0
$111$	−7.72697			−0.733411
$112$		0			0
$113$	5.54080			0.521235			0.260617	−	0.965442i	$-0.416074\pi$
$113$	5.54080			0.521235			0.260617	+	0.965442i	$0.416074\pi$
$114$		0			0
$115$	−2.99338	+	5.18469i	−0.279134	+	0.483475i
$116$		0			0
$117$	−3.91933	+	2.26282i	−0.362342	+	0.209198i
$118$		0			0
$119$	−7.22156	+	3.14303i	−0.661999	+	0.288121i
$120$		0			0
$121$	−3.74203	−	6.48139i	−0.340185	−	0.589217i
$122$		0			0
$123$	−9.85582	−	5.69026i	−0.888669	−	0.513073i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			9.92226i			0.880458i	0.897886	+	0.440229i	$0.145103\pi$
$127$			9.92226i			0.880458i	−0.897886	+	0.440229i	$0.854897\pi$
$128$		0			0
$129$	2.48283	+	1.43346i	0.218601	+	0.126209i
$130$		0			0
$131$	−7.71881	−	13.3694i	−0.674396	−	1.16809i	−0.976645	−	0.214859i	$-0.931071\pi$
$131$	−7.71881	−	13.3694i	−0.674396	−	1.16809i	0.302249	−	0.953229i	$-0.402263\pi$
$132$		0			0
$133$	−14.9021	−	1.69259i	−1.29218	−	0.146766i
$134$		0			0
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$		0			0
$137$	−0.0825367	+	0.142958i	−0.00705158	+	0.0122137i	−0.869530	−	0.493881i	$-0.835578\pi$
$137$	−0.0825367	+	0.142958i	−0.00705158	+	0.0122137i	0.862478	+	0.506094i	$0.168911\pi$
$138$		0			0
$139$	−12.8666			−1.09133			−0.545667	−	0.838002i	$-0.683724\pi$
$139$	−12.8666			−1.09133			−0.545667	+	0.838002i	$0.683724\pi$
$140$		0			0
$141$	−7.21427			−0.607551
$142$		0			0
$143$	−4.24298	+	7.34906i	−0.354816	+	0.614559i
$144$		0			0
$145$	6.45366	−	3.72602i	0.535947	−	0.309429i
$146$		0			0
$147$	−6.82169	−	1.56988i	−0.562644	−	0.129481i
$148$		0			0
$149$	−9.38749	−	16.2596i	−0.769053	−	1.33204i	−0.938077	−	0.346428i	$-0.887395\pi$
$149$	−9.38749	−	16.2596i	−0.769053	−	1.33204i	0.169023	−	0.985612i	$-0.445939\pi$
$150$		0			0
$151$	8.81002	+	5.08647i	0.716949	+	0.413931i	0.813629	−	0.581385i	$-0.197489\pi$
$151$	8.81002	+	5.08647i	0.716949	+	0.413931i	−0.0966795	+	0.995316i	$0.530822\pi$
$152$		0			0
$153$		−	2.97680i		−	0.240660i
$154$		0			0
$155$			8.97471i			0.720866i
$156$		0			0
$157$	16.8074	+	9.70377i	1.34138	+	0.774445i	0.987010	−	0.160660i	$-0.0513624\pi$
$157$	16.8074	+	9.70377i	1.34138	+	0.774445i	0.354369	+	0.935106i	$0.384696\pi$
$158$		0			0
$159$	−4.11168	−	7.12164i	−0.326078	−	0.564783i
$160$		0			0
$161$	−1.78757	+	15.7383i	−0.140880	+	1.24035i
$162$		0			0
$163$	11.1093	−	6.41397i	0.870149	−	0.502381i	0.00275097	−	0.999996i	$-0.499124\pi$
$163$	11.1093	−	6.41397i	0.870149	−	0.502381i	0.867398	+	0.497616i	$0.165791\pi$
$164$		0			0
$165$	0.937541	−	1.62387i	0.0729875	−	0.126418i
$166$		0			0
$167$	5.24370			0.405770			0.202885	−	0.979203i	$-0.434968\pi$
$167$	5.24370			0.405770			0.202885	+	0.979203i	$0.434968\pi$
$168$		0			0
$169$	−7.48148			−0.575498
$170$		0			0
$171$	2.83434	−	4.90922i	0.216747	−	0.375417i
$172$		0			0
$173$	−11.0691	+	6.39077i	−0.841571	+	0.485881i	−0.857798	−	0.513987i	$-0.828168\pi$
$173$	−11.0691	+	6.39077i	−0.841571	+	0.485881i	0.0162270	+	0.999868i	$0.494835\pi$
$174$		0			0
$175$	1.05584	+	2.42594i	0.0798141	+	0.183384i
$176$		0			0
$177$	5.23100	+	9.06036i	0.393186	+	0.681018i
$178$		0			0
$179$	15.1207	+	8.72995i	1.13018	+	0.652507i	0.943979	−	0.330005i	$-0.107050\pi$
$179$	15.1207	+	8.72995i	1.13018	+	0.652507i	0.186197	+	0.982512i	$0.440384\pi$
$180$		0			0
$181$			9.94777i			0.739412i	0.929149	+	0.369706i	$0.120542\pi$
$181$			9.94777i			0.739412i	−0.929149	+	0.369706i	$0.879458\pi$
$182$		0			0
$183$		−	7.07525i		−	0.523018i
$184$		0			0
$185$	6.69175	+	3.86348i	0.491987	+	0.284049i
$186$		0			0
$187$	−2.79088	−	4.83394i	−0.204089	−	0.353493i
$188$		0			0
$189$	1.57301	−	2.12736i	0.114419	−	0.154742i
$190$		0			0
$191$	−9.88439	+	5.70676i	−0.715210	+	0.412926i	−0.812987	−	0.582282i	$-0.802160\pi$
$191$	−9.88439	+	5.70676i	−0.715210	+	0.412926i	0.0977774	+	0.995208i	$0.468827\pi$
$192$		0			0
$193$	6.59852	−	11.4290i	0.474972	−	0.822675i	−0.524617	−	0.851338i	$-0.675792\pi$
$193$	6.59852	−	11.4290i	0.474972	−	0.822675i	0.999589	+	0.0286628i	$0.00912491\pi$
$194$		0			0
$195$	4.52565			0.324088
$196$		0			0
$197$	0.0103779			0.000739396			0.000369698	−	1.00000i	$-0.499882\pi$
$197$	0.0103779			0.000739396			0.000369698		1.00000i	$0.499882\pi$
$198$		0			0
$199$	−9.19370	+	15.9240i	−0.651724	+	1.12882i	0.330980	+	0.943638i	$0.392621\pi$
$199$	−9.19370	+	15.9240i	−0.651724	+	1.12882i	−0.982704	+	0.185182i	$0.940713\pi$
$200$		0			0
$201$	7.40170	−	4.27337i	0.522076	−	0.301420i
$202$		0			0
$203$	11.7221	−	15.8532i	0.822732	−	1.11267i
$204$		0			0
$205$	5.69026	+	9.85582i	0.397425	+	0.688360i
$206$		0			0
$207$	−5.18469	−	2.99338i	−0.360361	−	0.208054i
$208$		0			0
$209$		−	10.6292i		−	0.735240i
$210$		0			0
$211$			16.5593i			1.13999i	0.821649	+	0.569994i	$0.193054\pi$
$211$			16.5593i			1.13999i	−0.821649	+	0.569994i	$0.806946\pi$
$212$		0			0
$213$	−0.549358	−	0.317172i	−0.0376414	−	0.0217323i
$214$		0			0
$215$	−1.43346	−	2.48283i	−0.0977615	−	0.169328i
$216$		0			0
$217$	9.47586	+	21.7721i	0.643263	+	1.47799i
$218$		0			0
$219$	−0.999540	+	0.577085i	−0.0675427	+	0.0389958i
$220$		0			0
$221$	6.73598	−	11.6671i	0.453111	−	0.784812i
$222$		0			0
$223$	29.2181			1.95659			0.978294	−	0.207220i	$-0.0664416\pi$
$223$	29.2181			1.95659			0.978294	+	0.207220i	$0.0664416\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	8.86152	−	15.3486i	0.588160	−	1.01872i	−0.406314	−	0.913734i	$-0.633186\pi$
$227$	8.86152	−	15.3486i	0.588160	−	1.01872i	0.994473	−	0.104989i	$-0.0334807\pi$
$228$		0			0
$229$	−22.2460	+	12.8437i	−1.47005	+	0.848737i	−0.999435	−	0.0335996i	$-0.989303\pi$
$229$	−22.2460	+	12.8437i	−1.47005	+	0.848737i	−0.470620	+	0.882336i	$0.655970\pi$
$230$		0			0
$231$	0.559874	−	4.92931i	0.0368370	−	0.324325i
$232$		0			0
$233$	3.98378	+	6.90011i	0.260986	+	0.452041i	0.966504	−	0.256651i	$-0.0826190\pi$
$233$	3.98378	+	6.90011i	0.260986	+	0.452041i	−0.705518	+	0.708692i	$0.749286\pi$
$234$		0			0
$235$	6.24774	+	3.60713i	0.407557	+	0.235303i
$236$		0			0
$237$		−	7.35540i		−	0.477785i
$238$		0			0
$239$		−	11.1738i		−	0.722776i	−0.932416	−	0.361388i	$-0.882303\pi$
$239$		−	11.1738i		−	0.722776i	0.932416	−	0.361388i	$-0.117697\pi$
$240$		0			0
$241$	2.80307	+	1.61835i	0.180561	+	0.104247i	0.587556	−	0.809183i	$-0.300090\pi$
$241$	2.80307	+	1.61835i	0.180561	+	0.104247i	−0.406995	+	0.913430i	$0.633423\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	5.12282	+	4.77040i	0.327285	+	0.304770i
$246$		0			0
$247$	22.2174	−	12.8272i	1.41366	−	0.816176i
$248$		0			0
$249$	−4.07301	+	7.05466i	−0.258116	+	0.447071i
$250$		0			0
$251$	−23.0777			−1.45665			−0.728325	−	0.685232i	$-0.759701\pi$
$251$	−23.0777			−1.45665			−0.728325	+	0.685232i	$0.759701\pi$
$252$		0			0
$253$	−11.2257			−0.705752
$254$		0			0
$255$	−1.48840	+	2.57799i	−0.0932073	+	0.161440i
$256$		0			0
$257$	−11.6825	+	6.74492i	−0.728737	+	0.420737i	−0.817960	−	0.575275i	$-0.804895\pi$
$257$	−11.6825	+	6.74492i	−0.728737	+	0.420737i	0.0892228	+	0.996012i	$0.471562\pi$
$258$		0			0
$259$	20.3130	+	2.30717i	1.26219	+	0.143360i
$260$		0			0
$261$	3.72602	+	6.45366i	0.230635	+	0.399471i
$262$		0			0
$263$	−10.6311	−	6.13786i	−0.655541	−	0.378477i	0.135035	−	0.990841i	$-0.456885\pi$
$263$	−10.6311	−	6.13786i	−0.655541	−	0.378477i	−0.790576	+	0.612364i	$0.790219\pi$
$264$		0			0
$265$			8.22336i			0.505157i
$266$		0			0
$267$		−	10.1862i		−	0.623384i
$268$		0			0
$269$	−14.3635	−	8.29279i	−0.875760	−	0.505620i	−0.00650214	−	0.999979i	$-0.502070\pi$
$269$	−14.3635	−	8.29279i	−0.875760	−	0.505620i	−0.869258	+	0.494358i	$0.835403\pi$
$270$		0			0
$271$	−2.61765	−	4.53390i	−0.159011	−	0.275415i	0.775501	−	0.631346i	$-0.217497\pi$
$271$	−2.61765	−	4.53390i	−0.159011	−	0.275415i	−0.934512	+	0.355931i	$0.884164\pi$
$272$		0			0
$273$	10.9790	−	4.77836i	0.664477	−	0.289200i
$274$		0			0
$275$	−1.62387	+	0.937541i	−0.0979230	+	0.0565359i
$276$		0			0
$277$	−8.59955	+	14.8949i	−0.516697	+	0.894945i	0.483115	+	0.875557i	$0.339505\pi$
$277$	−8.59955	+	14.8949i	−0.516697	+	0.894945i	−0.999812	+	0.0193884i	$0.993828\pi$
$278$		0			0
$279$	−8.97471			−0.537302
$280$		0			0
$281$	−0.275724			−0.0164483			−0.00822417	−	0.999966i	$-0.502618\pi$
$281$	−0.275724			−0.0164483			−0.00822417	+	0.999966i	$0.502618\pi$
$282$		0			0
$283$	−7.95480	+	13.7781i	−0.472864	+	0.819024i	−0.999518	−	0.0310560i	$-0.990113\pi$
$283$	−7.95480	+	13.7781i	−0.472864	+	0.819024i	0.526654	+	0.850080i	$0.323446\pi$
$284$		0			0
$285$	−4.90922	+	2.83434i	−0.290797	+	0.167892i
$286$		0			0
$287$	24.2104	+	17.9016i	1.42910	+	1.05670i
$288$		0			0
$289$	−4.06932	−	7.04827i	−0.239372	−	0.414604i
$290$		0			0
$291$	11.5712	+	6.68066i	0.678318	+	0.391627i
$292$		0			0
$293$			17.0929i			0.998581i	0.866435	+	0.499290i	$0.166406\pi$
$293$			17.0929i			0.998581i	−0.866435	+	0.499290i	$0.833594\pi$
$294$		0			0
$295$		−	10.4620i		−	0.609121i
$296$		0			0
$297$	1.62387	+	0.937541i	0.0942264	+	0.0544017i
$298$		0			0
$299$	−13.5470	−	23.4641i	−0.783443	−	1.35696i
$300$		0			0
$301$	−6.09898	−	4.50970i	−0.351539	−	0.259935i
$302$		0			0
$303$	−10.9074	+	6.29739i	−0.626614	+	0.361776i
$304$		0			0
$305$	−3.53762	+	6.12735i	−0.202564	+	0.350851i
$306$		0			0
$307$	−18.8394			−1.07522			−0.537612	−	0.843192i	$-0.680674\pi$
$307$	−18.8394			−1.07522			−0.537612	+	0.843192i	$0.680674\pi$
$308$		0			0
$309$	−2.21237			−0.125857
$310$		0			0
$311$	−10.0004	+	17.3212i	−0.567069	+	0.982192i	0.429785	+	0.902931i	$0.358589\pi$
$311$	−10.0004	+	17.3212i	−0.567069	+	0.982192i	−0.996854	+	0.0792610i	$0.974744\pi$
$312$		0			0
$313$	23.3223	−	13.4651i	1.31825	−	0.761093i	0.334805	−	0.942288i	$-0.391330\pi$
$313$	23.3223	−	13.4651i	1.31825	−	0.761093i	0.983447	+	0.181194i	$0.0579963\pi$
$314$		0			0
$315$	−2.42594	+	1.05584i	−0.136686	+	0.0594899i
$316$		0			0
$317$	17.4094	+	30.1539i	0.977808	+	1.69361i	0.670340	+	0.742054i	$0.266148\pi$
$317$	17.4094	+	30.1539i	0.977808	+	1.69361i	0.307468	+	0.951559i	$0.400518\pi$
$318$		0			0
$319$	12.1011	+	6.98660i	0.677534	+	0.391174i
$320$		0			0
$321$		−	2.93547i		−	0.163842i
$322$		0			0
$323$			16.8745i			0.938925i
$324$		0			0
$325$	−3.91933	−	2.26282i	−0.217405	−	0.125519i
$326$		0			0
$327$	−7.27466	−	12.6001i	−0.402289	−	0.696786i
$328$		0			0
$329$	18.9652	+	2.15408i	1.04559	+	0.118758i
$330$		0			0
$331$	18.4194	−	10.6345i	1.01242	−	0.584523i	0.100523	−	0.994935i	$-0.467948\pi$
$331$	18.4194	−	10.6345i	1.01242	−	0.584523i	0.911900	+	0.410412i	$0.134615\pi$
$332$		0			0
$333$	−3.86348	+	6.69175i	−0.211718	+	0.366706i
$334$		0			0
$335$	−8.54674			−0.466959
$336$		0			0
$337$	19.3575			1.05447			0.527234	−	0.849720i	$-0.323229\pi$
$337$	19.3575			1.05447			0.527234	+	0.849720i	$0.323229\pi$
$338$		0			0
$339$	2.77040	−	4.79847i	0.150467	−	0.260617i
$340$		0			0
$341$	−14.5737	+	8.41416i	−0.789213	+	0.455652i
$342$		0			0
$343$	17.4645	+	6.16384i	0.942992	+	0.332816i
$344$		0			0
$345$	2.99338	+	5.18469i	0.161158	+	0.279134i
$346$		0			0
$347$	−20.7161	−	11.9604i	−1.11210	−	0.642070i	−0.172726	−	0.984970i	$-0.555258\pi$
$347$	−20.7161	−	11.9604i	−1.11210	−	0.642070i	−0.939372	+	0.342900i	$0.888591\pi$
$348$		0			0
$349$		−	22.7648i		−	1.21857i	−0.792950	−	0.609286i	$-0.791456\pi$
$349$		−	22.7648i		−	1.21857i	0.792950	−	0.609286i	$-0.208544\pi$
$350$		0			0
$351$			4.52565i			0.241561i
$352$		0			0
$353$	11.1738	+	6.45121i	0.594723	+	0.343363i	0.766963	−	0.641692i	$-0.221767\pi$
$353$	11.1738	+	6.45121i	0.594723	+	0.343363i	−0.172240	+	0.985055i	$0.555100\pi$
$354$		0			0
$355$	0.317172	+	0.549358i	0.0168337	+	0.0291569i
$356$		0			0
$357$	−0.888834	+	7.82557i	−0.0470421	+	0.414173i
$358$		0			0
$359$	20.7774	−	11.9958i	1.09659	−	0.633116i	0.161266	−	0.986911i	$-0.448442\pi$
$359$	20.7774	−	11.9958i	1.09659	−	0.633116i	0.935323	+	0.353795i	$0.115109\pi$
$360$		0			0
$361$	−6.56696	+	11.3743i	−0.345629	+	0.598647i
$362$		0			0
$363$	−7.48407			−0.392812
$364$		0			0
$365$	1.15417			0.0604120
$366$		0			0
$367$	−1.92425	+	3.33290i	−0.100445	+	0.173976i	−0.911868	−	0.410483i	$-0.865360\pi$
$367$	−1.92425	+	3.33290i	−0.100445	+	0.173976i	0.811423	+	0.584459i	$0.198693\pi$
$368$		0			0
$369$	−9.85582	+	5.69026i	−0.513073	+	0.296223i
$370$		0			0
$371$	8.68256	+	19.9494i	0.450776	+	1.03572i
$372$		0			0
$373$	−8.57170	−	14.8466i	−0.443826	−	0.768728i	0.554144	−	0.832421i	$-0.313046\pi$
$373$	−8.57170	−	14.8466i	−0.443826	−	0.768728i	−0.997970	+	0.0636924i	$0.979712\pi$
$374$		0			0
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$		0			0
$377$			33.7253i			1.73694i
$378$		0			0
$379$		−	10.5714i		−	0.543014i	−0.962436	−	0.271507i	$-0.912478\pi$
$379$		−	10.5714i		−	0.543014i	0.962436	−	0.271507i	$-0.0875220\pi$
$380$		0			0
$381$	8.59293	+	4.96113i	0.440229	+	0.254166i
$382$		0			0
$383$	−4.13461	−	7.16135i	−0.211269	−	0.365928i	0.740843	−	0.671678i	$-0.234426\pi$
$383$	−4.13461	−	7.16135i	−0.211269	−	0.365928i	−0.952112	+	0.305750i	$0.901093\pi$
$384$		0			0
$385$	−2.94952	+	3.98897i	−0.150321	+	0.203297i
$386$		0			0
$387$	2.48283	−	1.43346i	0.126209	−	0.0728671i
$388$		0			0
$389$	−5.86397	+	10.1567i	−0.297315	+	0.514965i	−0.975521	−	0.219907i	$-0.929425\pi$
$389$	−5.86397	+	10.1567i	−0.297315	+	0.514965i	0.678206	+	0.734872i	$0.262758\pi$
$390$		0			0
$391$	17.8214			0.901268
$392$		0			0
$393$	−15.4376			−0.778725
$394$		0			0
$395$	−3.67770	+	6.36997i	−0.185045	+	0.320508i
$396$		0			0
$397$	5.82047	−	3.36045i	0.292121	−	0.168656i	−0.346777	−	0.937948i	$-0.612724\pi$
$397$	5.82047	−	3.36045i	0.292121	−	0.168656i	0.638898	+	0.769291i	$0.279391\pi$
$398$		0			0
$399$	−8.91688	+	12.0593i	−0.446402	+	0.603720i
$400$		0			0
$401$	2.05829	+	3.56506i	0.102786	+	0.178031i	0.912832	−	0.408336i	$-0.133891\pi$
$401$	2.05829	+	3.56506i	0.102786	+	0.178031i	−0.810045	+	0.586367i	$0.800558\pi$
$402$		0			0
$403$	−35.1748	−	20.3082i	−1.75218	−	1.01162i
$404$		0			0
$405$		−	1.00000i		−	0.0496904i
$406$		0			0
$407$			14.4887i			0.718178i
$408$		0			0
$409$	−3.43444	−	1.98288i	−0.169822	−	0.0980469i	0.412680	−	0.910876i	$-0.364593\pi$
$409$	−3.43444	−	1.98288i	−0.169822	−	0.0980469i	−0.582502	+	0.812829i	$0.697926\pi$
$410$		0			0
$411$	0.0825367	+	0.142958i	0.00407123	+	0.00705158i
$412$		0			0
$413$	−11.0462	−	25.3802i	−0.543549	−	1.24888i
$414$		0			0
$415$	7.05466	−	4.07301i	0.346299	−	0.199936i
$416$		0			0
$417$	−6.43332	+	11.1428i	−0.315041	+	0.545667i
$418$		0			0
$419$	6.92874			0.338491			0.169246	−	0.985574i	$-0.445867\pi$
$419$	6.92874			0.338491			0.169246	+	0.985574i	$0.445867\pi$
$420$		0			0
$421$	33.2661			1.62129			0.810645	−	0.585538i	$-0.199117\pi$
$421$	33.2661			1.62129			0.810645	+	0.585538i	$0.199117\pi$
$422$		0			0
$423$	−3.60713	+	6.24774i	−0.175385	+	0.303775i
$424$		0			0
$425$	2.57799	−	1.48840i	0.125051	−	0.0721981i
$426$		0			0
$427$	−2.11257	+	18.5998i	−0.102235	+	0.900106i
$428$		0			0
$429$	4.24298	+	7.34906i	0.204853	+	0.354816i
$430$		0			0
$431$	−24.1032	−	13.9160i	−1.16101	−	0.670310i	−0.209465	−	0.977816i	$-0.567172\pi$
$431$	−24.1032	−	13.9160i	−1.16101	−	0.670310i	−0.951546	+	0.307506i	$0.900506\pi$
$432$		0			0
$433$			33.4797i			1.60893i	0.593998	+	0.804467i	$0.297549\pi$
$433$			33.4797i			1.60893i	−0.593998	+	0.804467i	$0.702451\pi$
$434$		0			0
$435$		−	7.45204i		−	0.357298i
$436$		0			0
$437$	29.3903	+	16.9685i	1.40593	+	0.811714i
$438$		0			0
$439$	−1.36991	−	2.37276i	−0.0653823	−	0.113245i	0.831481	−	0.555553i	$-0.187493\pi$
$439$	−1.36991	−	2.37276i	−0.0653823	−	0.113245i	−0.896864	+	0.442307i	$0.854160\pi$
$440$		0			0
$441$	−4.77040	+	5.12282i	−0.227162	+	0.243944i
$442$		0			0
$443$	23.3468	−	13.4793i	1.10924	−	0.640419i	0.170606	−	0.985339i	$-0.445428\pi$
$443$	23.3468	−	13.4793i	1.10924	−	0.640419i	0.938632	+	0.344921i	$0.112094\pi$
$444$		0			0
$445$	−5.09309	+	8.82148i	−0.241435	+	0.418178i
$446$		0			0
$447$	−18.7750			−0.888026
$448$		0			0
$449$	−28.8273			−1.36045			−0.680223	−	0.733005i	$-0.738117\pi$
$449$	−28.8273			−1.36045			−0.680223	+	0.733005i	$0.738117\pi$
$450$		0			0
$451$	−10.6697	+	18.4805i	−0.502417	+	0.870211i
$452$		0			0
$453$	8.81002	−	5.08647i	0.413931	−	0.238983i
$454$		0			0
$455$	−11.8972	−	1.35130i	−0.557751	−	0.0633498i
$456$		0			0
$457$	8.04242	+	13.9299i	0.376208	+	0.651612i	0.990507	−	0.137462i	$-0.0438944\pi$
$457$	8.04242	+	13.9299i	0.376208	+	0.651612i	−0.614299	+	0.789074i	$0.710561\pi$
$458$		0			0
$459$	−2.57799	−	1.48840i	−0.120330	−	0.0694727i
$460$		0			0
$461$		−	4.99187i		−	0.232494i	−0.993220	−	0.116247i	$-0.962914\pi$
$461$		−	4.99187i		−	0.232494i	0.993220	−	0.116247i	$-0.0370865\pi$
$462$		0			0
$463$			31.6923i			1.47287i	0.676509	+	0.736434i	$0.263492\pi$
$463$			31.6923i			1.47287i	−0.676509	+	0.736434i	$0.736508\pi$
$464$		0			0
$465$	7.77232	+	4.48735i	0.360433	+	0.208096i
$466$		0			0
$467$	13.6091	+	23.5716i	0.629752	+	1.09076i	0.987601	+	0.156983i	$0.0501767\pi$
$467$	13.6091	+	23.5716i	0.629752	+	1.09076i	−0.357850	+	0.933779i	$0.616490\pi$
$468$		0			0
$469$	−20.7339	+	9.02400i	−0.957403	+	0.416690i
$470$		0			0
$471$	16.8074	−	9.70377i	0.774445	−	0.447126i
$472$		0			0
$473$	2.68786	−	4.65552i	0.123588	−	0.214061i
$474$		0			0
$475$	5.66868			0.260097
$476$		0			0
$477$	−8.22336			−0.376522
$478$		0			0
$479$	0.465259	−	0.805852i	0.0212582	−	0.0368203i	−0.855201	−	0.518297i	$-0.826566\pi$
$479$	0.465259	−	0.805852i	0.0212582	−	0.0368203i	0.876459	+	0.481477i	$0.159899\pi$
$480$		0			0
$481$	−30.2845	+	17.4848i	−1.38085	+	0.797237i
$482$		0			0
$483$	12.7360	+	9.41723i	0.579507	+	0.428499i
$484$		0			0
$485$	−6.68066	−	11.5712i	−0.303353	−	0.525423i
$486$		0			0
$487$	−7.58152	−	4.37719i	−0.343551	−	0.198350i	0.318290	−	0.947993i	$-0.396891\pi$
$487$	−7.58152	−	4.37719i	−0.343551	−	0.198350i	−0.661841	+	0.749644i	$0.730225\pi$
$488$		0			0
$489$		−	12.8279i		−	0.580099i
$490$		0			0
$491$		−	26.6319i		−	1.20188i	−0.799293	−	0.600941i	$-0.794793\pi$
$491$		−	26.6319i		−	1.20188i	0.799293	−	0.600941i	$-0.205207\pi$
$492$		0			0
$493$	−19.2113	−	11.0916i	−0.865232	−	0.499542i
$494$		0			0
$495$	−0.937541	−	1.62387i	−0.0421393	−	0.0729875i
$496$		0			0
$497$	1.34948	+	0.997828i	0.0605323	+	0.0447587i
$498$		0			0
$499$	10.2300	−	5.90631i	0.457959	−	0.264403i	−0.253226	−	0.967407i	$-0.581492\pi$
$499$	10.2300	−	5.90631i	0.457959	−	0.264403i	0.711186	+	0.703004i	$0.248158\pi$
$500$		0			0
$501$	2.62185	−	4.54118i	0.117136	−	0.202885i
$502$		0			0
$503$	−29.1214			−1.29846			−0.649230	−	0.760592i	$-0.724909\pi$
$503$	−29.1214			−1.29846			−0.649230	+	0.760592i	$0.724909\pi$
$504$		0			0
$505$	12.5948			0.560461
$506$		0			0
$507$	−3.74074	+	6.47915i	−0.166132	+	0.287749i
$508$		0			0
$509$	11.3952	−	6.57904i	0.505085	−	0.291611i	−0.225726	−	0.974191i	$-0.572475\pi$
$509$	11.3952	−	6.57904i	0.505085	−	0.291611i	0.730811	+	0.682580i	$0.239142\pi$
$510$		0			0
$511$	2.79995	−	1.21862i	0.123862	−	0.0539085i
$512$		0			0
$513$	−2.83434	−	4.90922i	−0.125139	−	0.216747i
$514$		0			0
$515$	1.91597	+	1.10619i	0.0844278	+	0.0487444i
$516$		0			0
$517$			13.5273i			0.594932i
$518$		0			0
$519$			12.7815i			0.561047i
$520$		0			0
$521$	11.7230	+	6.76830i	0.513596	+	0.296525i	0.734311	−	0.678814i	$-0.237506\pi$
$521$	11.7230	+	6.76830i	0.513596	+	0.296525i	−0.220715	+	0.975338i	$0.570839\pi$
$522$		0			0
$523$	1.11008	+	1.92272i	0.0485406	+	0.0840748i	0.889275	−	0.457373i	$-0.151210\pi$
$523$	1.11008	+	1.92272i	0.0485406	+	0.0840748i	−0.840734	+	0.541448i	$0.817876\pi$
$524$		0			0
$525$	2.62885	+	0.298587i	0.114732	+	0.0130314i
$526$		0			0
$527$	23.1367	−	13.3580i	1.00785	−	0.581882i
$528$		0			0
$529$	6.42067	−	11.1209i	0.279160	−	0.483519i
$530$		0			0
$531$	10.4620			0.454012
$532$		0			0
$533$	−51.5042			−2.23089
$534$		0			0
$535$	−1.46774	+	2.54219i	−0.0634557	+	0.109909i
$536$		0			0
$537$	15.1207	−	8.72995i	0.652507	−	0.376725i
$538$		0			0
$539$	−2.94365	+	12.7912i	−0.126792	+	0.550957i
$540$		0			0
$541$	−8.26130	−	14.3090i	−0.355181	−	0.615192i	0.631968	−	0.774995i	$-0.282247\pi$
$541$	−8.26130	−	14.3090i	−0.355181	−	0.615192i	−0.987149	+	0.159803i	$0.948914\pi$
$542$		0			0
$543$	8.61502	+	4.97388i	0.369706	+	0.213450i
$544$		0			0
$545$			14.5493i			0.623224i
$546$		0			0
$547$		−	12.9826i		−	0.555097i	−0.960712	−	0.277548i	$-0.910478\pi$
$547$		−	12.9826i		−	0.555097i	0.960712	−	0.277548i	$-0.0895219\pi$
$548$		0			0
$549$	−6.12735	−	3.53762i	−0.261509	−	0.150982i
$550$		0			0
$551$	−21.1216	−	36.5837i	−0.899811	−	1.55852i
$552$		0			0
$553$	−2.19622	+	19.3362i	−0.0933930	+	0.822261i
$554$		0			0
$555$	6.69175	−	3.86348i	0.284049	−	0.163996i
$556$		0			0
$557$	−6.06010	+	10.4964i	−0.256775	+	0.444747i	−0.965376	−	0.260862i	$-0.915993\pi$
$557$	−6.06010	+	10.4964i	−0.256775	+	0.444747i	0.708601	+	0.705609i	$0.249326\pi$
$558$		0			0
$559$	12.9747			0.548772
$560$		0			0
$561$	−5.58175			−0.235662
$562$		0			0
$563$	6.92368	−	11.9922i	0.291798	−	0.505410i	−0.682437	−	0.730945i	$-0.739080\pi$
$563$	6.92368	−	11.9922i	0.291798	−	0.505410i	0.974235	+	0.225535i	$0.0724130\pi$
$564$		0			0
$565$	−4.79847	+	2.77040i	−0.201873	+	0.116552i
$566$		0			0
$567$	−1.05584	−	2.42594i	−0.0443411	−	0.101880i
$568$		0			0
$569$	3.18848	+	5.52260i	0.133668	+	0.231520i	0.925088	−	0.379753i	$-0.123991\pi$
$569$	3.18848	+	5.52260i	0.133668	+	0.231520i	−0.791420	+	0.611273i	$0.790658\pi$
$570$		0			0
$571$	8.96399	+	5.17536i	0.375131	+	0.216582i	0.675698	−	0.737179i	$-0.263842\pi$
$571$	8.96399	+	5.17536i	0.375131	+	0.216582i	−0.300567	+	0.953761i	$0.597176\pi$
$572$		0			0
$573$			11.4135i			0.476806i
$574$		0			0
$575$		−	5.98676i		−	0.249665i
$576$		0			0
$577$	−4.35151	−	2.51234i	−0.181156	−	0.104590i	0.406680	−	0.913571i	$-0.366686\pi$
$577$	−4.35151	−	2.51234i	−0.181156	−	0.104590i	−0.587835	+	0.808980i	$0.700020\pi$
$578$		0			0
$579$	−6.59852	−	11.4290i	−0.274225	−	0.474972i
$580$		0			0
$581$	12.8137	−	17.3295i	0.531604	−	0.718948i
$582$		0			0
$583$	−13.3537	+	7.70974i	−0.553052	+	0.319305i
$584$		0			0
$585$	2.26282	−	3.91933i	0.0935562	−	0.162044i
$586$		0			0
$587$	20.2367			0.835259			0.417629	−	0.908618i	$-0.362861\pi$
$587$	20.2367			0.835259			0.417629	+	0.908618i	$0.362861\pi$
$588$		0			0
$589$	50.8747			2.09626
$590$		0			0
$591$	0.00518896	−	0.00898754i	0.000213445	−	0.000369698i
$592$		0			0
$593$	19.6222	−	11.3289i	0.805787	−	0.465221i	−0.0397037	−	0.999211i	$-0.512641\pi$
$593$	19.6222	−	11.3289i	0.805787	−	0.465221i	0.845491	+	0.533990i	$0.179308\pi$
$594$		0			0
$595$	4.68254	−	6.33272i	0.191965	−	0.259616i
$596$		0			0
$597$	9.19370	+	15.9240i	0.376273	+	0.651724i
$598$		0			0
$599$	4.88840	+	2.82232i	0.199735	+	0.115317i	0.596532	−	0.802590i	$-0.296545\pi$
$599$	4.88840	+	2.82232i	0.199735	+	0.115317i	−0.396797	+	0.917906i	$0.629878\pi$
$600$		0			0
$601$			1.39017i			0.0567064i	0.999598	+	0.0283532i	$0.00902631\pi$
$601$			1.39017i			0.0567064i	−0.999598	+	0.0283532i	$0.990974\pi$
$602$		0			0
$603$		−	8.54674i		−	0.348050i
$604$		0			0
$605$	6.48139	+	3.74203i	0.263506	+	0.152135i
$606$		0			0
$607$	−11.9793	−	20.7488i	−0.486225	−	0.842167i	0.513649	−	0.858000i	$-0.328293\pi$
$607$	−11.9793	−	20.7488i	−0.486225	−	0.842167i	−0.999875	+	0.0158335i	$0.994960\pi$
$608$		0			0
$609$	−7.86817	−	18.0782i	−0.318834	−	0.732567i
$610$		0			0
$611$	−28.2751	+	16.3246i	−1.14389	+	0.660423i
$612$		0			0
$613$	−6.96316	+	12.0605i	−0.281239	+	0.487121i	−0.971690	−	0.236258i	$-0.924079\pi$
$613$	−6.96316	+	12.0605i	−0.281239	+	0.487121i	0.690451	+	0.723379i	$0.257412\pi$
$614$		0			0
$615$	11.3805			0.458907
$616$		0			0
$617$	23.5607			0.948519			0.474259	−	0.880385i	$-0.342716\pi$
$617$	23.5607			0.948519			0.474259	+	0.880385i	$0.342716\pi$
$618$		0			0
$619$	−21.3824	+	37.0354i	−0.859431	+	1.48858i	0.0130411	+	0.999915i	$0.495849\pi$
$619$	−21.3824	+	37.0354i	−0.859431	+	1.48858i	−0.872472	+	0.488664i	$0.837485\pi$
$620$		0			0
$621$	−5.18469	+	2.99338i	−0.208054	+	0.120120i
$622$		0			0
$623$	−3.04145	+	26.7779i	−0.121853	+	1.07283i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−9.20519	−	5.31462i	−0.367620	−	0.212245i
$628$		0			0
$629$		−	23.0017i		−	0.917137i
$630$		0			0
$631$			9.25893i			0.368592i	0.982871	+	0.184296i	$0.0590006\pi$
$631$			9.25893i			0.368592i	−0.982871	+	0.184296i	$0.940999\pi$
$632$		0			0
$633$	14.3407	+	8.27964i	0.569994	+	0.329086i
$634$		0			0
$635$	−4.96113	−	8.59293i	−0.196876	−	0.341000i
$636$		0			0
$637$	−30.2888	+	9.28342i	−1.20009	+	0.367823i
$638$		0			0
$639$	−0.549358	+	0.317172i	−0.0217323	+	0.0125471i
$640$		0			0
$641$	−4.56275	+	7.90292i	−0.180218	+	0.312147i	−0.941955	−	0.335740i	$-0.891014\pi$
$641$	−4.56275	+	7.90292i	−0.180218	+	0.312147i	0.761737	+	0.647887i	$0.224347\pi$
$642$		0			0
$643$	−30.0493			−1.18503			−0.592514	−	0.805560i	$-0.701864\pi$
$643$	−30.0493			−1.18503			−0.592514	+	0.805560i	$0.701864\pi$
$644$		0			0
$645$	−2.86693			−0.112885
$646$		0			0
$647$	−21.3665	+	37.0079i	−0.840005	+	1.45493i	0.0498838	+	0.998755i	$0.484115\pi$
$647$	−21.3665	+	37.0079i	−0.840005	+	1.45493i	−0.889889	+	0.456177i	$0.849218\pi$
$648$		0			0
$649$	16.9889	−	9.80856i	0.666874	−	0.385020i
$650$		0			0
$651$	23.5931	+	2.67973i	0.924688	+	0.105027i
$652$		0			0
$653$	1.86588	+	3.23180i	0.0730175	+	0.126470i	0.900222	−	0.435430i	$-0.143404\pi$
$653$	1.86588	+	3.23180i	0.0730175	+	0.126470i	−0.827205	+	0.561900i	$0.810070\pi$
$654$		0			0
$655$	13.3694	+	7.71881i	0.522385	+	0.301599i
$656$		0			0
$657$			1.15417i			0.0450284i
$658$		0			0
$659$		−	17.2197i		−	0.670784i	−0.942079	−	0.335392i	$-0.891131\pi$
$659$		−	17.2197i		−	0.670784i	0.942079	−	0.335392i	$-0.108869\pi$
$660$		0			0
$661$	−31.0073	−	17.9021i	−1.20605	−	0.696310i	−0.244152	−	0.969737i	$-0.578510\pi$
$661$	−31.0073	−	17.9021i	−1.20605	−	0.696310i	−0.961893	+	0.273426i	$0.911843\pi$
$662$		0			0
$663$	−6.73598	−	11.6671i	−0.261604	−	0.453111i
$664$		0			0
$665$	13.7519	−	5.98522i	0.533275	−	0.232097i
$666$		0			0
$667$	−38.6365	+	22.3068i	−1.49601	+	0.863723i
$668$		0			0
$669$	14.6091	−	25.3036i	0.564819	−	0.978294i
$670$		0			0
$671$	−13.2667			−0.512154
$672$		0			0
$673$	19.8440			0.764931			0.382466	−	0.923970i	$-0.375075\pi$
$673$	19.8440			0.764931			0.382466	+	0.923970i	$0.375075\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	−6.27755	+	3.62435i	−0.241266	+	0.139295i	−0.615758	−	0.787935i	$-0.711150\pi$
$677$	−6.27755	+	3.62435i	−0.241266	+	0.139295i	0.374492	+	0.927230i	$0.377817\pi$
$678$		0			0
$679$	−28.4243	−	21.0175i	−1.09082	−	0.806576i
$680$		0			0
$681$	−8.86152	−	15.3486i	−0.339574	−	0.588160i
$682$		0			0
$683$	18.0000	+	10.3923i	0.688749	+	0.397650i	0.803143	−	0.595786i	$-0.203159\pi$
$683$	18.0000	+	10.3923i	0.688749	+	0.397650i	−0.114394	+	0.993435i	$0.536493\pi$
$684$		0			0
$685$		−	0.165073i		−	0.00630713i
$686$		0			0
$687$			25.6874i			0.980037i
$688$		0			0
$689$	−32.2300	−	18.6080i	−1.22787	−	0.708909i
$690$		0			0
$691$	−5.23962	−	9.07528i	−0.199324	−	0.345240i	0.748985	−	0.662587i	$-0.230541\pi$
$691$	−5.23962	−	9.07528i	−0.199324	−	0.345240i	−0.948310	+	0.317347i	$0.897208\pi$
$692$		0			0
$693$	−3.98897	−	2.94952i	−0.151528	−	0.112043i
$694$		0			0
$695$	11.1428	−	6.43332i	0.422672	−	0.244030i
$696$		0			0
$697$	16.9388	−	29.3388i	0.641602	−	1.11129i
$698$		0			0
$699$	7.96756			0.301361
$700$		0			0
$701$	23.6132			0.891860			0.445930	−	0.895068i	$-0.352873\pi$
$701$	23.6132			0.891860			0.445930	+	0.895068i	$0.352873\pi$
$702$		0			0
$703$	21.9008	−	37.9334i	0.826006	−	1.43068i
$704$		0			0
$705$	6.24774	−	3.60713i	0.235303	−	0.135852i
$706$		0			0
$707$	30.5542	−	13.2981i	1.14911	−	0.500126i
$708$		0			0
$709$	−17.2701	−	29.9127i	−0.648593	−	1.12340i	−0.983459	−	0.181131i	$-0.942024\pi$
$709$	−17.2701	−	29.9127i	−0.648593	−	1.12340i	0.334866	−	0.942266i	$-0.391309\pi$
$710$		0			0
$711$	−6.36997	−	3.67770i	−0.238892	−	0.137925i
$712$		0			0
$713$		−	53.7294i		−	2.01218i
$714$		0			0
$715$		−	8.48596i		−	0.317357i
$716$		0			0
$717$	−9.67683	−	5.58692i	−0.361388	−	0.208647i
$718$		0			0
$719$	−2.26385	−	3.92110i	−0.0844273	−	0.146232i	0.820720	−	0.571331i	$-0.193573\pi$
$719$	−2.26385	−	3.92110i	−0.0844273	−	0.146232i	−0.905147	+	0.425099i	$0.860239\pi$
$720$		0			0
$721$	5.81599	+	0.660585i	0.216599	+	0.0246015i
$722$		0			0
$723$	2.80307	−	1.61835i	0.104247	−	0.0601871i
$724$		0			0
$725$	−3.72602	+	6.45366i	−0.138381	+	0.239683i
$726$		0			0
$727$	−13.3626			−0.495593			−0.247796	−	0.968812i	$-0.579706\pi$
$727$	−13.3626			−0.495593			−0.247796	+	0.968812i	$0.579706\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.26714	+	7.39091i	−0.157826	+	0.273363i
$732$		0			0
$733$	18.3612	−	10.6009i	0.678187	−	0.391551i	−0.120985	−	0.992654i	$-0.538605\pi$
$733$	18.3612	−	10.6009i	0.678187	−	0.391551i	0.799172	+	0.601103i	$0.205272\pi$
$734$		0			0
$735$	6.69270	−	2.05129i	0.246864	−	0.0756631i
$736$		0			0
$737$	−8.01292	−	13.8788i	−0.295160	−	0.511232i
$738$		0			0
$739$	−21.6184	−	12.4814i	−0.795244	−	0.459135i	0.0465611	−	0.998915i	$-0.485174\pi$
$739$	−21.6184	−	12.4814i	−0.795244	−	0.459135i	−0.841806	+	0.539781i	$0.818507\pi$
$740$		0			0
$741$		−	25.6544i		−	0.942439i
$742$		0			0
$743$			32.7353i			1.20094i	0.799646	+	0.600471i	$0.205020\pi$
$743$			32.7353i			1.20094i	−0.799646	+	0.600471i	$0.794980\pi$
$744$		0			0
$745$	16.2596	+	9.38749i	0.595706	+	0.343931i
$746$		0			0
$747$	4.07301	+	7.05466i	0.149024	+	0.258116i
$748$		0			0
$749$	−0.876492	+	7.71691i	−0.0320263	+	0.281970i
$750$		0			0
$751$	41.0402	−	23.6946i	1.49758	−	0.864628i	0.497583	−	0.867416i	$-0.334221\pi$
$751$	41.0402	−	23.6946i	1.49758	−	0.864628i	0.999996	+	0.00278892i	$0.000887743\pi$
$752$		0			0
$753$	−11.5388	+	19.9859i	−0.420499	+	0.728325i
$754$		0			0
$755$	−10.1729			−0.370231
$756$		0			0
$757$	25.4871			0.926344			0.463172	−	0.886268i	$-0.346711\pi$
$757$	25.4871			0.926344			0.463172	+	0.886268i	$0.346711\pi$
$758$		0			0
$759$	−5.61284	+	9.72172i	−0.203733	+	0.352876i
$760$		0			0
$761$	−19.5014	+	11.2592i	−0.706926	+	0.408144i	−0.809922	−	0.586538i	$-0.800491\pi$
$761$	−19.5014	+	11.2592i	−0.706926	+	0.408144i	0.102996	+	0.994682i	$0.467157\pi$
$762$		0			0
$763$	15.3618	+	35.2958i	0.556133	+	1.27779i
$764$		0			0
$765$	1.48840	+	2.57799i	0.0538133	+	0.0932073i
$766$		0			0
$767$	41.0040	+	23.6737i	1.48057	+	0.854807i
$768$		0			0
$769$			18.6689i			0.673218i	0.941644	+	0.336609i	$0.109280\pi$
$769$			18.6689i			0.673218i	−0.941644	+	0.336609i	$0.890720\pi$
$770$		0			0
$771$			13.4898i			0.485825i
$772$		0			0
$773$	−30.6237	−	17.6806i	−1.10146	−	0.635928i	−0.164856	−	0.986318i	$-0.552716\pi$
$773$	−30.6237	−	17.6806i	−1.10146	−	0.635928i	−0.936604	+	0.350390i	$0.886049\pi$
$774$		0			0
$775$	−4.48735	−	7.77232i	−0.161190	−	0.279190i
$776$		0			0
$777$	12.1546	−	16.4380i	0.436043	−	0.589711i
$778$		0			0
$779$	55.8695	−	32.2562i	2.00173	−	1.15570i
$780$		0			0
$781$	−0.594724	+	1.03009i	−0.0212809	+	0.0368596i
$782$		0			0
$783$	7.45204			0.266314
$784$		0			0
$785$	−19.4075			−0.692685
$786$		0			0
$787$	−5.68251	+	9.84239i	−0.202559	+	0.350843i	−0.949352	−	0.314213i	$-0.898259\pi$
$787$	−5.68251	+	9.84239i	−0.202559	+	0.350843i	0.746793	+	0.665057i	$0.231593\pi$
$788$		0			0
$789$	−10.6311	+	6.13786i	−0.378477	+	0.218514i
$790$		0			0
$791$	−8.71572	+	11.7873i	−0.309895	+	0.419107i
$792$		0			0
$793$	−16.0100	−	27.7302i	−0.568533	−	0.984728i
$794$		0			0
$795$	7.12164	+	4.11168i	0.252579	+	0.145826i
$796$		0			0
$797$		−	43.3369i		−	1.53507i	−0.641006	−	0.767536i	$-0.721482\pi$
$797$		−	43.3369i		−	1.53507i	0.641006	−	0.767536i	$-0.278518\pi$
$798$		0			0
$799$		−	21.4755i		−	0.759747i
$800$		0			0
$801$	−8.82148	−	5.09309i	−0.311692	−	0.179955i
$802$		0			0
$803$	1.08208	+	1.87422i	0.0381858	+	0.0661398i
$804$		0			0
$805$	−6.32107	−	14.5235i	−0.222788	−	0.511888i
$806$		0			0
$807$	−14.3635	+	8.29279i	−0.505620	+	0.291920i
$808$		0			0
$809$	−3.16079	+	5.47464i	−0.111127	+	0.192478i	−0.916225	−	0.400664i	$-0.868779\pi$
$809$	−3.16079	+	5.47464i	−0.111127	+	0.192478i	0.805098	+	0.593142i	$0.202113\pi$
$810$		0			0
$811$	−11.9017			−0.417926			−0.208963	−	0.977924i	$-0.567009\pi$
$811$	−11.9017			−0.417926			−0.208963	+	0.977924i	$0.567009\pi$
$812$		0			0
$813$	−5.23530			−0.183610
$814$		0			0
$815$	−6.41397	+	11.1093i	−0.224671	+	0.389142i
$816$		0			0
$817$	−14.0744	+	8.12585i	−0.492400	+	0.284287i
$818$		0			0
$819$	1.35130	−	11.8972i	0.0472181	−	0.415723i
$820$		0			0
$821$	17.4032	+	30.1433i	0.607377	+	1.05201i	0.991671	+	0.128797i	$0.0411116\pi$
$821$	17.4032	+	30.1433i	0.607377	+	1.05201i	−0.384294	+	0.923211i	$0.625555\pi$
$822$		0			0
$823$	−6.60491	−	3.81335i	−0.230233	−	0.132925i	0.380447	−	0.924803i	$-0.375770\pi$
$823$	−6.60491	−	3.81335i	−0.230233	−	0.132925i	−0.610679	+	0.791878i	$0.709104\pi$
$824$		0			0
$825$			1.87508i			0.0652820i
$826$		0			0
$827$		−	16.9632i		−	0.589867i	−0.955518	−	0.294934i	$-0.904702\pi$
$827$		−	16.9632i		−	0.589867i	0.955518	−	0.294934i	$-0.0952976\pi$
$828$		0			0
$829$	−19.1415	−	11.0514i	−0.664813	−	0.383830i	0.129295	−	0.991606i	$-0.458729\pi$
$829$	−19.1415	−	11.0514i	−0.664813	−	0.383830i	−0.794109	+	0.607776i	$0.792062\pi$
$830$		0			0
$831$	8.59955	+	14.8949i	0.298315	+	0.516697i
$832$		0			0
$833$	4.67322	−	20.3068i	0.161917	−	0.703590i
$834$		0			0
$835$	−4.54118	+	2.62185i	−0.157154	+	0.0907329i
$836$		0			0
$837$	−4.48735	+	7.77232i	−0.155106	+	0.268651i
$838$		0			0
$839$	46.1447			1.59309			0.796546	−	0.604578i	$-0.206658\pi$
$839$	46.1447			1.59309			0.796546	+	0.604578i	$0.206658\pi$
$840$		0			0
$841$	26.5330			0.914930
$842$		0			0
$843$	−0.137862	+	0.238784i	−0.00474823	+	0.00822417i
$844$		0			0
$845$	6.47915	−	3.74074i	0.222890	−	0.128685i
$846$		0			0
$847$	19.6745	+	2.23464i	0.676023	+	0.0767832i
$848$		0			0
$849$	7.95480	+	13.7781i	0.273008	+	0.472864i
$850$		0			0
$851$	−40.0619	−	23.1298i	−1.37331	−	0.792878i
$852$		0			0
$853$			19.0752i			0.653123i	0.945176	+	0.326561i	$0.105890\pi$
$853$			19.0752i			0.653123i	−0.945176	+	0.326561i	$0.894110\pi$
$854$		0			0
$855$			5.66868i			0.193865i
$856$		0			0
$857$	−39.8542	−	23.0099i	−1.36139	−	0.786002i	−0.371585	−	0.928399i	$-0.621186\pi$
$857$	−39.8542	−	23.0099i	−1.36139	−	0.786002i	−0.989810	+	0.142397i	$0.954519\pi$
$858$		0			0
$859$	−26.3797	−	45.6909i	−0.900063	−	1.55895i	−0.827411	−	0.561597i	$-0.810187\pi$
$859$	−26.3797	−	45.6909i	−0.900063	−	1.55895i	−0.0726518	−	0.997357i	$-0.523146\pi$
$860$		0			0
$861$	27.6085	−	12.0160i	0.940895	−	0.409505i
$862$		0			0
$863$	−8.11689	+	4.68629i	−0.276302	+	0.159523i	−0.631748	−	0.775174i	$-0.717662\pi$
$863$	−8.11689	+	4.68629i	−0.276302	+	0.159523i	0.355446	+	0.934697i	$0.384329\pi$
$864$		0			0
$865$	6.39077	−	11.0691i	0.217293	−	0.376362i
$866$		0			0
$867$	−8.13864			−0.276403
$868$		0			0
$869$	−13.7920			−0.467861
$870$		0			0
$871$	19.3398	−	33.4975i	0.655303	−	1.13502i
$872$		0			0
$873$	11.5712	−	6.68066i	0.391627	−	0.226106i
$874$		0			0
$875$	−2.12736	−	1.57301i	−0.0719178	−	0.0531774i
$876$		0			0
$877$	9.66868	+	16.7466i	0.326488	+	0.565494i	0.981812	−	0.189854i	$-0.0608014\pi$
$877$	9.66868	+	16.7466i	0.326488	+	0.565494i	−0.655324	+	0.755348i	$0.727468\pi$
$878$		0			0
$879$	14.8029	+	8.54647i	0.499290	+	0.288265i
$880$		0			0
$881$		−	31.0888i		−	1.04741i	−0.851900	−	0.523704i	$-0.824550\pi$
$881$		−	31.0888i		−	1.04741i	0.851900	−	0.523704i	$-0.175450\pi$
$882$		0			0
$883$			9.59350i			0.322847i	0.986885	+	0.161424i	$0.0516085\pi$
$883$			9.59350i			0.322847i	−0.986885	+	0.161424i	$0.948391\pi$
$884$		0			0
$885$	−9.06036	−	5.23100i	−0.304561	−	0.175838i
$886$		0			0
$887$	−13.9328	−	24.1323i	−0.467817	−	0.810283i	0.531507	−	0.847054i	$-0.321626\pi$
$887$	−13.9328	−	24.1323i	−0.467817	−	0.810283i	−0.999324	+	0.0367714i	$0.988293\pi$
$888$		0			0
$889$	−21.1082	−	15.6078i	−0.707946	−	0.523469i
$890$		0			0
$891$	1.62387	−	0.937541i	0.0544017	−	0.0314088i
$892$		0			0
$893$	20.4477	−	35.4164i	0.684255	−	1.18517i
$894$		0			0
$895$	−17.4599			−0.583620
$896$		0			0
$897$	−27.0940			−0.904642
$898$		0			0
$899$	−33.4400	+	57.9197i	−1.11528	+	1.93173i
$900$		0			0
$901$	21.1997	−	12.2397i	0.706265	−	0.407763i
$902$		0			0
$903$	−6.95501	+	3.02702i	−0.231448	+	0.100733i
$904$		0			0
$905$	−4.97388	−	8.61502i	−0.165337	−	0.286373i
$906$		0			0
$907$	−5.52101	−	3.18756i	−0.183322	−	0.105841i	0.405530	−	0.914082i	$-0.367087\pi$
$907$	−5.52101	−	3.18756i	−0.183322	−	0.105841i	−0.588853	+	0.808240i	$0.700420\pi$
$908$		0			0
$909$			12.5948i			0.417743i
$910$		0			0
$911$			48.1522i			1.59535i	0.603085	+	0.797677i	$0.293938\pi$
$911$			48.1522i			1.59535i	−0.603085	+	0.797677i	$0.706062\pi$
$912$		0			0
$913$	13.2281	+	7.63722i	0.437785	+	0.252755i
$914$		0			0
$915$	3.53762	+	6.12735i	0.116950	+	0.202564i
$916$		0			0
$917$	40.5832	+	4.60947i	1.34018	+	0.152218i
$918$		0			0
$919$	25.0624	−	14.4698i	0.826732	−	0.477314i	−0.0260007	−	0.999662i	$-0.508277\pi$
$919$	25.0624	−	14.4698i	0.826732	−	0.477314i	0.852732	+	0.522348i	$0.174944\pi$
$920$		0			0
$921$	−9.41972	+	16.3154i	−0.310390	+	0.537612i
$922$		0			0
$923$	−2.87082			−0.0944941
$924$		0			0
$925$	−7.72697			−0.254061
$926$		0			0
$927$	−1.10619	+	1.91597i	−0.0363319	+	0.0629287i
$928$		0			0
$929$	38.6977	−	22.3422i	1.26963	−	0.733022i	0.294714	−	0.955586i	$-0.404776\pi$
$929$	38.6977	−	22.3422i	1.26963	−	0.733022i	0.974918	+	0.222563i	$0.0714424\pi$
$930$		0			0
$931$	27.0419	−	29.0396i	0.886261	−	0.951735i
$932$		0			0
$933$	10.0004	+	17.3212i	0.327397	+	0.567069i
$934$		0			0
$935$	4.83394	+	2.79088i	0.158087	+	0.0912714i
$936$		0			0
$937$		−	24.9763i		−	0.815939i	−0.912996	−	0.407969i	$-0.866237\pi$
$937$		−	24.9763i		−	0.815939i	0.912996	−	0.407969i	$-0.133763\pi$
$938$		0			0
$939$		−	26.9302i		−	0.878835i
$940$		0			0
$941$	34.9238	+	20.1633i	1.13848	+	0.657303i	0.946054	−	0.324008i	$-0.105030\pi$
$941$	34.9238	+	20.1633i	1.13848	+	0.657303i	0.192428	+	0.981311i	$0.438364\pi$
$942$		0			0
$943$	−34.0662	−	59.0045i	−1.10935	−	1.92145i
$944$		0			0
$945$	−0.298587	+	2.62885i	−0.00971302	+	0.0855165i
$946$		0			0
$947$	50.8003	−	29.3295i	1.65079	−	0.953082i	0.674038	−	0.738697i	$-0.264559\pi$
$947$	50.8003	−	29.3295i	1.65079	−	0.953082i	0.976749	−	0.214385i	$-0.0687748\pi$
$948$		0			0
$949$	−2.61168	+	4.52357i	−0.0847788	+	0.146841i
$950$		0			0
$951$	34.8187			1.12908
$952$		0			0
$953$	27.1232			0.878605			0.439303	−	0.898339i	$-0.355226\pi$
$953$	27.1232			0.878605			0.439303	+	0.898339i	$0.355226\pi$
$954$		0			0
$955$	5.70676	−	9.88439i	0.184666	−	0.319851i
$956$		0			0
$957$	12.1011	−	6.98660i	0.391174	−	0.225845i
$958$		0			0
$959$	−0.174291	−	0.400459i	−0.00562816	−	0.0129315i
$960$		0			0
$961$	−24.7727	−	42.9075i	−0.799119	−	1.38411i
$962$		0			0
$963$	−2.54219	−	1.46774i	−0.0819210	−	0.0472971i
$964$		0			0
$965$			13.1970i			0.424828i
$966$		0			0
$967$			4.52047i			0.145369i	0.997355	+	0.0726843i	$0.0231566\pi$
$967$			4.52047i			0.145369i	−0.997355	+	0.0726843i	$0.976843\pi$
$968$		0			0
$969$	14.6138	+	8.43727i	0.469462	+	0.271044i
$970$		0			0
$971$	22.8215	+	39.5280i	0.732377	+	1.26851i	0.955865	+	0.293808i	$0.0949225\pi$
$971$	22.8215	+	39.5280i	0.732377	+	1.26851i	−0.223487	+	0.974707i	$0.571744\pi$
$972$		0			0
$973$	20.2393	−	27.3719i	0.648843	−	0.877504i
$974$		0			0
$975$	−3.91933	+	2.26282i	−0.125519	+	0.0724683i
$976$		0			0
$977$	−24.2171	+	41.9453i	−0.774774	+	1.34195i	0.160147	+	0.987093i	$0.448803\pi$
$977$	−24.2171	+	41.9453i	−0.774774	+	1.34195i	−0.934921	+	0.354855i	$0.884530\pi$
$978$		0			0
$979$	−19.0999			−0.610436
$980$		0			0
$981$	−14.5493			−0.464524
$982$		0			0
$983$	24.0315	−	41.6238i	0.766486	−	1.32759i	−0.172972	−	0.984927i	$-0.555337\pi$
$983$	24.0315	−	41.6238i	0.766486	−	1.32759i	0.939458	−	0.342665i	$-0.111330\pi$
$984$		0			0
$985$	−0.00898754	+	0.00518896i	−0.000286367	+	0.000165334i
$986$		0			0
$987$	11.3481	−	15.3473i	0.361214	−	0.488510i
$988$		0			0
$989$	8.58181	+	14.8641i	0.272886	+	0.472652i
$990$		0			0
$991$	−32.9328	−	19.0138i	−1.04615	−	0.603993i	−0.124578	−	0.992210i	$-0.539758\pi$
$991$	−32.9328	−	19.0138i	−1.04615	−	0.603993i	−0.921568	+	0.388217i	$0.873091\pi$
$992$		0			0
$993$		−	21.2689i		−	0.674949i
$994$		0			0
$995$		−	18.3874i		−	0.582920i
$996$		0			0
$997$	−21.7005	−	12.5288i	−0.687262	−	0.396791i	0.115323	−	0.993328i	$-0.463210\pi$
$997$	−21.7005	−	12.5288i	−0.687262	−	0.396791i	−0.802586	+	0.596537i	$0.796543\pi$
$998$		0			0
$999$	3.86348	+	6.69175i	0.122235	+	0.211718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.dx.h.31.1	yes	12
4.3	odd	2		1680.2.dx.f.31.3	✓	12
7.5	odd	6		1680.2.dx.f.271.3	yes	12
28.19	even	6	inner	1680.2.dx.h.271.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.dx.f.31.3	✓	12	4.3	odd	2
1680.2.dx.f.271.3	yes	12	7.5	odd	6
1680.2.dx.h.31.1	yes	12	1.1	even	1	trivial
1680.2.dx.h.271.1	yes	12	28.19	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.866025 + 0.500000i) q^{5} +(-1.57301 + 2.12736i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.62387 - 0.937541i) q^{11} -4.52565i q^{13} +1.00000i q^{15} +(2.57799 + 1.48840i) q^{17} +(2.83434 + 4.90922i) q^{19} +(1.05584 + 2.42594i) q^{21} +(5.18469 - 2.99338i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -7.45204 q^{29} +(4.48735 - 7.77232i) q^{31} +(-1.62387 + 0.937541i) q^{33} +(0.298587 - 2.62885i) q^{35} +(-3.86348 - 6.69175i) q^{37} +(-3.91933 - 2.26282i) q^{39} -11.3805i q^{41} +2.86693i q^{43} +(0.866025 + 0.500000i) q^{45} +(-3.60713 - 6.24774i) q^{47} +(-2.05129 - 6.69270i) q^{49} +(2.57799 - 1.48840i) q^{51} +(4.11168 - 7.12164i) q^{53} +1.87508 q^{55} +5.66868 q^{57} +(-5.23100 + 9.06036i) q^{59} +(6.12735 - 3.53762i) q^{61} +(2.62885 + 0.298587i) q^{63} +(2.26282 + 3.91933i) q^{65} +(7.40170 + 4.27337i) q^{67} -5.98676i q^{69} -0.634344i q^{71} +(-0.999540 - 0.577085i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(4.54884 - 1.97979i) q^{77} +(6.36997 - 3.67770i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.14602 q^{83} -2.97680 q^{85} +(-3.72602 + 6.45366i) q^{87} +(8.82148 - 5.09309i) q^{89} +(9.62766 + 7.11888i) q^{91} +(-4.48735 - 7.77232i) q^{93} +(-4.90922 - 2.83434i) q^{95} +13.3613i q^{97} +1.87508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 2 q^{7} - 6 q^{9} + 10 q^{19} - 4 q^{21} + 12 q^{23} + 6 q^{25} - 12 q^{27} + 8 q^{29} - 2 q^{31} - 4 q^{35} - 10 q^{37} + 6 q^{39} + 2 q^{49} + 16 q^{53} + 20 q^{57} + 24 q^{61} - 2 q^{63}+ \cdots + 24 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 - 2 * q^7 - 6 * q^9 + 10 * q^19 - 4 * q^21 + 12 * q^23 + 6 * q^25 - 12 * q^27 + 8 * q^29 - 2 * q^31 - 4 * q^35 - 10 * q^37 + 6 * q^39 + 2 * q^49 + 16 * q^53 + 20 * q^57 + 24 * q^61 - 2 * q^63 + 4 * q^65 - 6 * q^67 + 30 * q^73 - 6 * q^75 + 36 * q^77 + 42 * q^79 - 6 * q^81 - 64 * q^83 - 8 * q^85 + 4 * q^87 + 14 * q^91 + 2 * q^93 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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