LMFDB - Embedded newform 448.3.o.b.95.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,3,Mod(95,448)] 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("448.95"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 34 x^{18} + 755 x^{16} - 9698 x^{14} + 89921 x^{12} - 522048 x^{10} + 2189920 x^{8} + \cdots + 7311616 $ x^20 - 34x^18 + 755x^16 - 9698x^14 + 89921x^12 - 522048x^10 + 2189920x^8 - 5640416x^6 + 10423552x^4 - 10729472*x^2 + 7311616
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.1
Root			$1.31764 - 0.760743i$ of defining polynomial
Character	$\chi$	$=$	448.95
Dual form			448.3.o.b.415.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.75361 + 4.76940i) q^{3} +(4.79340 - 2.76747i) q^{5} +(-4.79446 + 5.10031i) q^{7} +(-10.6648 - 18.4719i) q^{9} +(7.54807 - 13.0736i) q^{11} -11.8687i q^{13} +30.4821i q^{15} +(2.62597 - 4.54831i) q^{17} +(-14.5507 - 25.2026i) q^{19} +(-11.1233 - 36.9110i) q^{21} +(4.42361 - 2.55397i) q^{23} +(2.81777 - 4.88051i) q^{25} +67.9015 q^{27} +28.2517i q^{29} +(-41.5036 - 23.9621i) q^{31} +(41.5689 + 71.9995i) q^{33} +(-8.86681 + 37.7163i) q^{35} +(27.0470 - 15.6156i) q^{37} +(56.6065 + 32.6818i) q^{39} +10.3413 q^{41} +47.2232 q^{43} +(-102.241 - 59.0288i) q^{45} +(14.4460 - 8.34039i) q^{47} +(-3.02629 - 48.9065i) q^{49} +(14.4618 + 25.0486i) q^{51} +(-16.1897 - 9.34712i) q^{53} -83.5562i q^{55} +160.268 q^{57} +(34.4268 - 59.6290i) q^{59} +(18.4819 - 10.6705i) q^{61} +(145.344 + 34.1693i) q^{63} +(-32.8462 - 56.8913i) q^{65} +(9.93291 - 17.2043i) q^{67} +28.1306i q^{69} +127.543i q^{71} +(-9.54079 + 16.5251i) q^{73} +(15.5181 + 26.8781i) q^{75} +(30.4907 + 101.179i) q^{77} +(3.20338 - 1.84947i) q^{79} +(-90.9915 + 157.602i) q^{81} +5.08000 q^{83} -29.0692i q^{85} +(-134.744 - 77.7943i) q^{87} +(-51.5261 - 89.2458i) q^{89} +(60.5340 + 56.9040i) q^{91} +(228.570 - 131.965i) q^{93} +(-139.495 - 80.5372i) q^{95} -62.3085 q^{97} -321.994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) $ 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.75361	+	4.76940i	−0.917871	+	1.58980i	−0.115228	+	0.993339i	$0.536760\pi$
$3$	−2.75361	+	4.76940i	−0.917871	+	1.58980i	−0.802643	+	0.596460i	$0.796573\pi$
$4$		0			0
$5$	4.79340	−	2.76747i	0.958679	−	0.553494i	0.0629130	−	0.998019i	$-0.479961\pi$
$5$	4.79340	−	2.76747i	0.958679	−	0.553494i	0.895766	+	0.444525i	$0.146628\pi$
$6$		0			0
$7$	−4.79446	+	5.10031i	−0.684923	+	0.728615i
$7$	−4.79446	+	5.10031i	−0.684923	+	0.728615i
$8$		0			0
$9$	−10.6648	−	18.4719i	−1.18497	−	2.05243i
$10$		0			0
$11$	7.54807	−	13.0736i	0.686188	−	1.18851i	−0.286873	−	0.957969i	$-0.592616\pi$
$11$	7.54807	−	13.0736i	0.686188	−	1.18851i	0.973062	−	0.230545i	$-0.0740508\pi$
$12$		0			0
$13$		−	11.8687i		−	0.912976i	−0.889730	−	0.456488i	$-0.849107\pi$
$13$		−	11.8687i		−	0.912976i	0.889730	−	0.456488i	$-0.150893\pi$
$14$		0			0
$15$			30.4821i			2.03214i
$16$		0			0
$17$	2.62597	−	4.54831i	0.154469	−	0.267548i	−0.778397	−	0.627773i	$-0.783967\pi$
$17$	2.62597	−	4.54831i	0.154469	−	0.267548i	0.932865	+	0.360225i	$0.117300\pi$
$18$		0			0
$19$	−14.5507	−	25.2026i	−0.765826	−	1.32645i	−0.939809	−	0.341702i	$-0.888997\pi$
$19$	−14.5507	−	25.2026i	−0.765826	−	1.32645i	0.173982	−	0.984749i	$-0.444337\pi$
$20$		0			0
$21$	−11.1233	−	36.9110i	−0.529681	−	1.75766i
$22$		0			0
$23$	4.42361	−	2.55397i	0.192331	−	0.111042i	−0.400742	−	0.916191i	$-0.631248\pi$
$23$	4.42361	−	2.55397i	0.192331	−	0.111042i	0.593073	+	0.805149i	$0.297914\pi$
$24$		0			0
$25$	2.81777	−	4.88051i	0.112711	−	0.195221i
$26$		0			0
$27$	67.9015			2.51487
$28$		0			0
$29$			28.2517i			0.974197i	0.873347	+	0.487099i	$0.161945\pi$
$29$			28.2517i			0.974197i	−0.873347	+	0.487099i	$0.838055\pi$
$30$		0			0
$31$	−41.5036	−	23.9621i	−1.33883	−	0.772971i	−0.352192	−	0.935928i	$-0.614564\pi$
$31$	−41.5036	−	23.9621i	−1.33883	−	0.772971i	−0.986633	+	0.162957i	$0.947897\pi$
$32$		0			0
$33$	41.5689	+	71.9995i	1.25966	+	2.18180i
$34$		0			0
$35$	−8.86681	+	37.7163i	−0.253337	+	1.07761i
$36$		0			0
$37$	27.0470	−	15.6156i	0.730999	−	0.422042i	−0.0877887	−	0.996139i	$-0.527980\pi$
$37$	27.0470	−	15.6156i	0.730999	−	0.422042i	0.818787	+	0.574097i	$0.194647\pi$
$38$		0			0
$39$	56.6065	+	32.6818i	1.45145	+	0.837994i
$40$		0			0
$41$	10.3413			0.252227			0.126113	−	0.992016i	$-0.459750\pi$
$41$	10.3413			0.252227			0.126113	+	0.992016i	$0.459750\pi$
$42$		0			0
$43$	47.2232			1.09821			0.549107	−	0.835752i	$-0.314968\pi$
$43$	47.2232			1.09821			0.549107	+	0.835752i	$0.314968\pi$
$44$		0			0
$45$	−102.241	−	59.0288i	−2.27202	−	1.31175i
$46$		0			0
$47$	14.4460	−	8.34039i	0.307361	−	0.177455i	−0.338384	−	0.941008i	$-0.609880\pi$
$47$	14.4460	−	8.34039i	0.307361	−	0.177455i	0.645745	+	0.763553i	$0.276547\pi$
$48$		0			0
$49$	−3.02629	−	48.9065i	−0.0617611	−	0.998091i
$50$		0			0
$51$	14.4618	+	25.0486i	0.283565	+	0.491149i
$52$		0			0
$53$	−16.1897	−	9.34712i	−0.305466	−	0.176361i	0.339430	−	0.940631i	$-0.389766\pi$
$53$	−16.1897	−	9.34712i	−0.305466	−	0.176361i	−0.644896	+	0.764271i	$0.723099\pi$
$54$		0			0
$55$		−	83.5562i		−	1.51920i
$56$		0			0
$57$	160.268			2.81172
$58$		0			0
$59$	34.4268	−	59.6290i	0.583506	−	1.01066i	−0.411554	−	0.911385i	$-0.635014\pi$
$59$	34.4268	−	59.6290i	0.583506	−	1.01066i	0.995060	−	0.0992764i	$-0.0316528\pi$
$60$		0			0
$61$	18.4819	−	10.6705i	0.302981	−	0.174926i	−0.340800	−	0.940136i	$-0.610698\pi$
$61$	18.4819	−	10.6705i	0.302981	−	0.174926i	0.643781	+	0.765209i	$0.277365\pi$
$62$		0			0
$63$	145.344	+	34.1693i	2.30705	+	0.542369i
$64$		0			0
$65$	−32.8462	−	56.8913i	−0.505327	−	0.875251i
$66$		0			0
$67$	9.93291	−	17.2043i	0.148252	−	0.256781i	−0.782329	−	0.622865i	$-0.785969\pi$
$67$	9.93291	−	17.2043i	0.148252	−	0.256781i	0.930582	+	0.366084i	$0.119302\pi$
$68$		0			0
$69$			28.1306i			0.407690i
$70$		0			0
$71$			127.543i			1.79638i	0.439606	+	0.898191i	$0.355118\pi$
$71$			127.543i			1.79638i	−0.439606	+	0.898191i	$0.644882\pi$
$72$		0			0
$73$	−9.54079	+	16.5251i	−0.130696	+	0.226372i	−0.923945	−	0.382525i	$-0.875054\pi$
$73$	−9.54079	+	16.5251i	−0.130696	+	0.226372i	0.793249	+	0.608897i	$0.208388\pi$
$74$		0			0
$75$	15.5181	+	26.8781i	0.206908	+	0.358374i
$76$		0			0
$77$	30.4907	+	101.179i	0.395983	+	1.31401i
$78$		0			0
$79$	3.20338	−	1.84947i	0.0405492	−	0.0234111i	−0.479588	−	0.877494i	$-0.659214\pi$
$79$	3.20338	−	1.84947i	0.0405492	−	0.0234111i	0.520138	+	0.854083i	$0.325881\pi$
$80$		0			0
$81$	−90.9915	+	157.602i	−1.12335	+	1.94570i
$82$		0			0
$83$	5.08000			0.0612048			0.0306024	−	0.999532i	$-0.490257\pi$
$83$	5.08000			0.0612048			0.0306024	+	0.999532i	$0.490257\pi$
$84$		0			0
$85$		−	29.0692i		−	0.341990i
$86$		0			0
$87$	−134.744	−	77.7943i	−1.54878	−	0.894187i
$88$		0			0
$89$	−51.5261	−	89.2458i	−0.578945	−	1.00276i	−0.995601	−	0.0936979i	$-0.970131\pi$
$89$	−51.5261	−	89.2458i	−0.578945	−	1.00276i	0.416656	−	0.909064i	$-0.363202\pi$
$90$		0			0
$91$	60.5340	+	56.9040i	0.665209	+	0.625318i
$92$		0			0
$93$	228.570	−	131.965i	2.45774	−	1.41898i
$94$		0			0
$95$	−139.495	−	80.5372i	−1.46836	−	0.847760i
$96$		0			0
$97$	−62.3085			−0.642355			−0.321178	−	0.947019i	$-0.604079\pi$
$97$	−62.3085			−0.642355			−0.321178	+	0.947019i	$0.604079\pi$
$98$		0			0
$99$	−321.994			−3.25246
$100$		0			0
$101$	−3.96546	−	2.28946i	−0.0392620	−	0.0226679i	0.480241	−	0.877137i	$-0.340549\pi$
$101$	−3.96546	−	2.28946i	−0.0392620	−	0.0226679i	−0.519503	+	0.854469i	$0.673883\pi$
$102$		0			0
$103$	−174.134	+	100.536i	−1.69062	+	0.976082i	−0.736611	+	0.676317i	$0.763575\pi$
$103$	−174.134	+	100.536i	−1.69062	+	0.976082i	−0.954013	+	0.299765i	$0.903092\pi$
$104$		0			0
$105$	−155.468	−	146.145i	−1.48065	−	1.39186i
$106$		0			0
$107$	−86.9183	−	150.547i	−0.812321	−	1.40698i	−0.911236	−	0.411885i	$-0.864871\pi$
$107$	−86.9183	−	150.547i	−0.812321	−	1.40698i	0.0989153	−	0.995096i	$-0.468463\pi$
$108$		0			0
$109$	−97.9049	−	56.5254i	−0.898210	−	0.518582i	−0.0215911	−	0.999767i	$-0.506873\pi$
$109$	−97.9049	−	56.5254i	−0.898210	−	0.518582i	−0.876619	+	0.481185i	$0.840207\pi$
$110$		0			0
$111$			171.997i			1.54952i
$112$		0			0
$113$	110.448			0.977415			0.488708	−	0.872448i	$-0.337468\pi$
$113$	110.448			0.977415			0.488708	+	0.872448i	$0.337468\pi$
$114$		0			0
$115$	14.1361	−	24.4844i	0.122922	−	0.212908i
$116$		0			0
$117$	−219.237	+	126.577i	−1.87382	+	1.08185i
$118$		0			0
$119$	10.6077	+	35.2000i	0.0891403	+	0.295798i
$120$		0			0
$121$	−53.4468	−	92.5726i	−0.441709	−	0.765063i
$122$		0			0
$123$	−28.4759	+	49.3217i	−0.231511	+	0.400990i
$124$		0			0
$125$			107.181i			0.857449i
$126$		0			0
$127$		−	126.454i		−	0.995697i	−0.867264	−	0.497849i	$-0.834124\pi$
$127$		−	126.454i		−	0.995697i	0.867264	−	0.497849i	$-0.165876\pi$
$128$		0			0
$129$	−130.034	+	225.226i	−1.00802	+	1.74594i
$130$		0			0
$131$	−11.1981	−	19.3957i	−0.0854816	−	0.148058i	0.820115	−	0.572199i	$-0.193910\pi$
$131$	−11.1981	−	19.3957i	−0.0854816	−	0.148058i	−0.905596	+	0.424141i	$0.860576\pi$
$132$		0			0
$133$	198.304	+	46.6196i	1.49100	+	0.350523i
$134$		0			0
$135$	325.479	−	187.915i	2.41095	−	1.39196i
$136$		0			0
$137$	84.0808	−	145.632i	0.613729	−	1.06301i	−0.376877	−	0.926263i	$-0.623002\pi$
$137$	84.0808	−	145.632i	0.613729	−	1.06301i	0.990606	−	0.136746i	$-0.0436645\pi$
$138$		0			0
$139$	−41.4804			−0.298420			−0.149210	−	0.988806i	$-0.547673\pi$
$139$	−41.4804			−0.298420			−0.149210	+	0.988806i	$0.547673\pi$
$140$		0			0
$141$			91.8649i			0.651524i
$142$		0			0
$143$	−155.167	−	89.5857i	−1.08508	−	0.626474i
$144$		0			0
$145$	78.1857	+	135.422i	0.539212	+	0.933943i
$146$		0			0
$147$	241.588	+	120.236i	1.64345	+	0.817931i
$148$		0			0
$149$	−136.931	+	79.0574i	−0.919002	+	0.530586i	−0.883317	−	0.468777i	$-0.844695\pi$
$149$	−136.931	+	79.0574i	−0.919002	+	0.530586i	−0.0356857	+	0.999363i	$0.511362\pi$
$150$		0			0
$151$	72.2919	+	41.7378i	0.478755	+	0.276409i	0.719897	−	0.694081i	$-0.244189\pi$
$151$	72.2919	+	41.7378i	0.478755	+	0.276409i	−0.241143	+	0.970490i	$0.577522\pi$
$152$		0			0
$153$	−112.021			−0.732166
$154$		0			0
$155$	−265.257			−1.71134
$156$		0			0
$157$	26.4511	+	15.2716i	0.168478	+	0.0972711i	0.581868	−	0.813283i	$-0.302322\pi$
$157$	26.4511	+	15.2716i	0.168478	+	0.0972711i	−0.413390	+	0.910554i	$0.635655\pi$
$158$		0			0
$159$	89.1603	−	51.4767i	0.560756	−	0.323753i
$160$		0			0
$161$	−8.18277	+	34.8067i	−0.0508247	+	0.216191i
$162$		0			0
$163$	12.8470	+	22.2516i	0.0788157	+	0.136513i	0.902739	−	0.430188i	$-0.141553\pi$
$163$	12.8470	+	22.2516i	0.0788157	+	0.136513i	−0.823924	+	0.566701i	$0.808219\pi$
$164$		0			0
$165$	398.513	+	230.081i	2.41523	+	1.39443i
$166$		0			0
$167$		−	300.278i		−	1.79807i	−0.437872	−	0.899037i	$-0.644268\pi$
$167$		−	300.278i		−	1.79807i	0.437872	−	0.899037i	$-0.355732\pi$
$168$		0			0
$169$	28.1342			0.166474
$170$		0			0
$171$	−310.360	+	537.559i	−1.81497	+	3.14362i
$172$		0			0
$173$	142.145	−	82.0674i	0.821647	−	0.474378i	−0.0293370	−	0.999570i	$-0.509340\pi$
$173$	142.145	−	82.0674i	0.821647	−	0.474378i	0.850984	+	0.525191i	$0.176006\pi$
$174$		0			0
$175$	11.3825	+	37.7709i	0.0650426	+	0.215834i
$176$		0			0
$177$	189.596	+	328.391i	1.07117	+	1.85531i
$178$		0			0
$179$	73.2978	−	126.955i	0.409485	−	0.709248i	−0.585347	−	0.810783i	$-0.699042\pi$
$179$	73.2978	−	126.955i	0.409485	−	0.709248i	0.994832	+	0.101534i	$0.0323752\pi$
$180$		0			0
$181$			72.4205i			0.400113i	0.979784	+	0.200057i	$0.0641126\pi$
$181$			72.4205i			0.400113i	−0.979784	+	0.200057i	$0.935887\pi$
$182$		0			0
$183$			117.530i			0.642239i
$184$		0			0
$185$	86.4312	−	149.703i	0.467196	−	0.809206i
$186$		0			0
$187$	−39.6420	−	68.6620i	−0.211989	−	0.367177i
$188$		0			0
$189$	−325.551	+	346.318i	−1.72249	+	1.83237i
$190$		0			0
$191$	161.562	−	93.2777i	0.845872	−	0.488365i	−0.0133836	−	0.999910i	$-0.504260\pi$
$191$	161.562	−	93.2777i	0.845872	−	0.488365i	0.859256	+	0.511546i	$0.170927\pi$
$192$		0			0
$193$	−10.6056	+	18.3694i	−0.0549511	+	0.0951781i	−0.892192	−	0.451655i	$-0.850834\pi$
$193$	−10.6056	+	18.3694i	−0.0549511	+	0.0951781i	0.837241	+	0.546834i	$0.184167\pi$
$194$		0			0
$195$	361.783			1.85530
$196$		0			0
$197$		−	15.0736i		−	0.0765156i	−0.999268	−	0.0382578i	$-0.987819\pi$
$197$		−	15.0736i		−	0.0765156i	0.999268	−	0.0382578i	$-0.0121808\pi$
$198$		0			0
$199$	6.56821	+	3.79216i	0.0330061	+	0.0190561i	0.516412	−	0.856340i	$-0.327267\pi$
$199$	6.56821	+	3.79216i	0.0330061	+	0.0190561i	−0.483406	+	0.875396i	$0.660601\pi$
$200$		0			0
$201$	54.7028	+	94.7480i	0.272153	+	0.471383i
$202$		0			0
$203$	−144.092	−	135.452i	−0.709815	−	0.667250i
$204$		0			0
$205$	49.5699	−	28.6192i	0.241804	−	0.139606i
$206$		0			0
$207$	−94.3535	−	54.4750i	−0.455814	−	0.263164i
$208$		0			0
$209$	−439.319			−2.10201
$210$		0			0
$211$	220.505			1.04505			0.522524	−	0.852624i	$-0.324990\pi$
$211$	220.505			1.04505			0.522524	+	0.852624i	$0.324990\pi$
$212$		0			0
$213$	−608.304	−	351.204i	−2.85589	−	1.64885i
$214$		0			0
$215$	226.359	−	130.689i	1.05283	−	0.607854i
$216$		0			0
$217$	321.201	−	96.7957i	1.48019	−	0.446063i
$218$		0			0
$219$	−52.5433	−	91.0077i	−0.239924	−	0.415560i
$220$		0			0
$221$	−53.9825	−	31.1668i	−0.244265	−	0.141026i
$222$		0			0
$223$			223.596i			1.00267i	0.865252	+	0.501337i	$0.167158\pi$
$223$			223.596i			1.00267i	−0.865252	+	0.501337i	$0.832842\pi$
$224$		0			0
$225$	−120.203			−0.534236
$226$		0			0
$227$	5.82995	−	10.0978i	0.0256826	−	0.0444836i	−0.852898	−	0.522077i	$-0.825157\pi$
$227$	5.82995	−	10.0978i	0.0256826	−	0.0444836i	0.878581	+	0.477593i	$0.158491\pi$
$228$		0			0
$229$	174.370	−	100.673i	0.761441	−	0.439618i	−0.0683717	−	0.997660i	$-0.521780\pi$
$229$	174.370	−	100.673i	0.761441	−	0.439618i	0.829813	+	0.558042i	$0.188447\pi$
$230$		0			0
$231$	−566.520	−	133.184i	−2.45247	−	0.576556i
$232$		0			0
$233$	92.5278	+	160.263i	0.397115	+	0.687824i	0.993369	−	0.114973i	$-0.0366780\pi$
$233$	92.5278	+	160.263i	0.397115	+	0.687824i	−0.596253	+	0.802796i	$0.703345\pi$
$234$		0			0
$235$	46.1636	−	79.9576i	0.196441	−	0.340245i
$236$		0			0
$237$			20.3709i			0.0859533i
$238$		0			0
$239$		−	20.4580i		−	0.0855985i	−0.999084	−	0.0427993i	$-0.986372\pi$
$239$		−	20.4580i		−	0.0855985i	0.999084	−	0.0427993i	$-0.0136276\pi$
$240$		0			0
$241$	202.142	−	350.120i	0.838762	−	1.45278i	−0.0521674	−	0.998638i	$-0.516613\pi$
$241$	202.142	−	350.120i	0.838762	−	1.45278i	0.890930	−	0.454141i	$-0.150054\pi$
$242$		0			0
$243$	−195.554	−	338.709i	−0.804749	−	1.39387i
$244$		0			0
$245$	−149.853	−	226.053i	−0.611646	−	0.922665i
$246$		0			0
$247$	−299.121	+	172.698i	−1.21102	+	0.699181i
$248$		0			0
$249$	−13.9884	+	24.2285i	−0.0561781	+	0.0973034i
$250$		0			0
$251$	−180.653			−0.719735			−0.359868	−	0.933003i	$-0.617178\pi$
$251$	−180.653			−0.719735			−0.359868	+	0.933003i	$0.617178\pi$
$252$		0			0
$253$		−	77.1103i		−	0.304784i
$254$		0			0
$255$	138.642	+	80.0452i	0.543696	+	0.313903i
$256$		0			0
$257$	−119.512	−	207.001i	−0.465027	−	0.805450i	0.534176	−	0.845373i	$-0.320622\pi$
$257$	−119.512	−	207.001i	−0.465027	−	0.805450i	−0.999203	+	0.0399235i	$0.987289\pi$
$258$		0			0
$259$	−50.0314	+	212.816i	−0.193171	+	0.821683i
$260$		0			0
$261$	521.863	−	301.298i	1.99948	−	1.15440i
$262$		0			0
$263$	269.493	+	155.592i	1.02469	+	0.591604i	0.915459	−	0.402412i	$-0.131828\pi$
$263$	269.493	+	155.592i	1.02469	+	0.591604i	0.109230	+	0.994016i	$0.465161\pi$
$264$		0			0
$265$	−103.471			−0.390458
$266$		0			0
$267$	567.532			2.12559
$268$		0			0
$269$	−197.013	−	113.746i	−0.732391	−	0.422846i	0.0869052	−	0.996217i	$-0.472302\pi$
$269$	−197.013	−	113.746i	−0.732391	−	0.422846i	−0.819296	+	0.573370i	$0.805636\pi$
$270$		0			0
$271$	−355.387	+	205.183i	−1.31139	+	0.757132i	−0.982327	−	0.187175i	$-0.940067\pi$
$271$	−355.387	+	205.183i	−1.31139	+	0.757132i	−0.329065	+	0.944307i	$0.606734\pi$
$272$		0			0
$273$	−438.085	+	132.019i	−1.60471	+	0.483586i
$274$		0			0
$275$	−42.5374	−	73.6769i	−0.154681	−	0.267916i
$276$		0			0
$277$	333.624	+	192.618i	1.20442	+	0.695372i	0.961535	−	0.274683i	$-0.0885730\pi$
$277$	333.624	+	192.618i	1.20442	+	0.695372i	0.242885	+	0.970055i	$0.421906\pi$
$278$		0			0
$279$			1022.20i			3.66380i
$280$		0			0
$281$	−498.190			−1.77292			−0.886459	−	0.462808i	$-0.846842\pi$
$281$	−498.190			−1.77292			−0.886459	+	0.462808i	$0.846842\pi$
$282$		0			0
$283$	−139.441	+	241.519i	−0.492724	+	0.853423i	−0.999965	−	0.00838102i	$-0.997332\pi$
$283$	−139.441	+	241.519i	−0.492724	+	0.853423i	0.507241	+	0.861804i	$0.330666\pi$
$284$		0			0
$285$	768.228	−	443.537i	2.69554	−	1.55627i
$286$		0			0
$287$	−49.5809	+	52.7438i	−0.172756	+	0.183776i
$288$		0			0
$289$	130.709	+	226.394i	0.452279	+	0.783370i
$290$		0			0
$291$	171.573	−	297.174i	0.589599	−	1.02122i
$292$		0			0
$293$			558.513i			1.90619i	0.302676	+	0.953093i	$0.402120\pi$
$293$			558.513i			1.90619i	−0.302676	+	0.953093i	$0.597880\pi$
$294$		0			0
$295$		−	381.101i		−	1.29187i
$296$		0			0
$297$	512.525	−	887.720i	1.72567	−	2.98896i
$298$		0			0
$299$	−30.3123	−	52.5024i	−0.101379	−	0.175593i
$300$		0			0
$301$	−226.410	+	240.853i	−0.752191	+	0.800175i
$302$		0			0
$303$	21.8387	−	12.6086i	0.0720749	−	0.0416125i
$304$		0			0
$305$	59.0606	−	102.296i	0.193641	−	0.335397i
$306$		0			0
$307$	156.861			0.510948			0.255474	−	0.966816i	$-0.417768\pi$
$307$	156.861			0.510948			0.255474	+	0.966816i	$0.417768\pi$
$308$		0			0
$309$		−	1107.35i		−	3.58367i
$310$		0			0
$311$	1.92734	+	1.11275i	0.00619724	+	0.00357798i	0.503095	−	0.864231i	$-0.332194\pi$
$311$	1.92734	+	1.11275i	0.00619724	+	0.00357798i	−0.496898	+	0.867809i	$0.665528\pi$
$312$		0			0
$313$	−38.7116	−	67.0505i	−0.123679	−	0.214219i	0.797537	−	0.603271i	$-0.206136\pi$
$313$	−38.7116	−	67.0505i	−0.123679	−	0.214219i	−0.921216	+	0.389052i	$0.872803\pi$
$314$		0			0
$315$	791.255	−	238.449i	2.51192	−	0.756980i
$316$		0			0
$317$	−417.406	+	240.989i	−1.31674	+	0.760219i	−0.983202	−	0.182518i	$-0.941575\pi$
$317$	−417.406	+	240.989i	−1.31674	+	0.760219i	−0.333536	+	0.942737i	$0.608242\pi$
$318$		0			0
$319$	369.353	+	213.246i	1.15785	+	0.668483i
$320$		0			0
$321$	957.357			2.98242
$322$		0			0
$323$	−152.839			−0.473185
$324$		0			0
$325$	−57.9253	−	33.4432i	−0.178232	−	0.102902i
$326$		0			0
$327$	539.184	−	311.298i	1.64888	−	0.951982i
$328$		0			0
$329$	−26.7221	+	113.667i	−0.0812223	+	0.345491i
$330$		0			0
$331$	−203.579	−	352.609i	−0.615042	−	1.06528i	−0.990377	−	0.138395i	$-0.955806\pi$
$331$	−203.579	−	352.609i	−0.615042	−	1.06528i	0.375335	−	0.926889i	$-0.377528\pi$
$332$		0			0
$333$	−576.899	−	333.073i	−1.73243	−	1.00022i
$334$		0			0
$335$		−	109.956i		−	0.328227i
$336$		0			0
$337$	152.439			0.452341			0.226170	−	0.974088i	$-0.427379\pi$
$337$	152.439			0.452341			0.226170	+	0.974088i	$0.427379\pi$
$338$		0			0
$339$	−304.131	+	526.770i	−0.897141	+	1.55389i
$340$		0			0
$341$	−626.544	+	361.735i	−1.83737	+	1.06081i
$342$		0			0
$343$	263.947	+	219.045i	0.769526	+	0.638615i
$344$		0			0
$345$	77.8505	+	134.841i	0.225654	+	0.390844i
$346$		0			0
$347$	78.8246	−	136.528i	0.227160	−	0.393453i	−0.729805	−	0.683655i	$-0.760389\pi$
$347$	78.8246	−	136.528i	0.227160	−	0.393453i	0.956965	+	0.290202i	$0.0937226\pi$
$348$		0			0
$349$		−	638.146i		−	1.82850i	−0.405153	−	0.914249i	$-0.632782\pi$
$349$		−	638.146i		−	1.82850i	0.405153	−	0.914249i	$-0.367218\pi$
$350$		0			0
$351$		−	805.902i		−	2.29602i
$352$		0			0
$353$	−121.308	+	210.111i	−0.343647	+	0.595215i	−0.985107	−	0.171942i	$-0.944996\pi$
$353$	−121.308	+	210.111i	−0.343647	+	0.595215i	0.641460	+	0.767157i	$0.278329\pi$
$354$		0			0
$355$	352.972	+	611.365i	0.994286	+	1.72215i
$356$		0			0
$357$	−197.092	−	46.3348i	−0.552079	−	0.129789i
$358$		0			0
$359$	−267.399	+	154.383i	−0.744843	+	0.430036i	−0.823828	−	0.566840i	$-0.808166\pi$
$359$	−267.399	+	154.383i	−0.744843	+	0.430036i	0.0789843	+	0.996876i	$0.474832\pi$
$360$		0			0
$361$	−242.946	+	420.795i	−0.672980	+	1.16564i
$362$		0			0
$363$	588.687			1.62173
$364$		0			0
$365$			105.615i			0.289357i
$366$		0			0
$367$	359.908	+	207.793i	0.980676	+	0.566194i	0.902474	−	0.430744i	$-0.141749\pi$
$367$	359.908	+	207.793i	0.980676	+	0.566194i	0.0782019	+	0.996938i	$0.475082\pi$
$368$		0			0
$369$	−110.287	−	191.023i	−0.298882	−	0.517679i
$370$		0			0
$371$	125.294	−	37.7580i	0.337720	−	0.101774i
$372$		0			0
$373$	−40.2824	+	23.2570i	−0.107996	+	0.0623513i	−0.553025	−	0.833165i	$-0.686527\pi$
$373$	−40.2824	+	23.2570i	−0.107996	+	0.0623513i	0.445029	+	0.895516i	$0.353193\pi$
$374$		0			0
$375$	−511.189	−	295.135i	−1.36317	−	0.787027i
$376$		0			0
$377$	335.311			0.889419
$378$		0			0
$379$	206.049			0.543664			0.271832	−	0.962345i	$-0.412371\pi$
$379$	206.049			0.543664			0.271832	+	0.962345i	$0.412371\pi$
$380$		0			0
$381$	603.107	+	348.204i	1.58296	+	0.913921i
$382$		0			0
$383$	357.877	−	206.620i	0.934404	−	0.539478i	0.0462024	−	0.998932i	$-0.485288\pi$
$383$	357.877	−	206.620i	0.934404	−	0.539478i	0.888202	+	0.459454i	$0.151955\pi$
$384$		0			0
$385$	426.163	+	400.607i	1.10692	+	1.04054i
$386$		0			0
$387$	−503.624	−	872.302i	−1.30135	−	2.25401i
$388$		0			0
$389$	140.809	+	81.2961i	0.361977	+	0.208988i	0.669948	−	0.742408i	$-0.266317\pi$
$389$	140.809	+	81.2961i	0.361977	+	0.208988i	−0.307971	+	0.951396i	$0.599650\pi$
$390$		0			0
$391$		−	26.8266i		−	0.0686103i
$392$		0			0
$393$	123.341			0.313844
$394$		0			0
$395$	10.2367	−	17.7305i	0.0259158	−	0.0448874i
$396$		0			0
$397$	−119.975	+	69.2674i	−0.302203	+	0.174477i	−0.643432	−	0.765503i	$-0.722490\pi$
$397$	−119.975	+	69.2674i	−0.302203	+	0.174477i	0.341229	+	0.939980i	$0.389157\pi$
$398$		0			0
$399$	−768.399	+	817.416i	−1.92581	+	2.04866i
$400$		0			0
$401$	232.520	+	402.736i	0.579850	+	1.00433i	0.995496	+	0.0948029i	$0.0302221\pi$
$401$	232.520	+	402.736i	0.579850	+	1.00433i	−0.415646	+	0.909526i	$0.636445\pi$
$402$		0			0
$403$	−284.399	+	492.593i	−0.705704	+	1.22232i
$404$		0			0
$405$			1007.26i			2.48707i
$406$		0			0
$407$		−	471.470i		−	1.15840i
$408$		0			0
$409$	−210.416	+	364.451i	−0.514464	+	0.891078i	0.485395	+	0.874295i	$0.338676\pi$
$409$	−210.416	+	364.451i	−0.514464	+	0.891078i	−0.999859	+	0.0167832i	$0.994657\pi$
$410$		0			0
$411$	463.052	+	802.030i	1.12665	+	1.95141i
$412$		0			0
$413$	139.068	+	461.477i	0.336727	+	1.11738i
$414$		0			0
$415$	24.3505	−	14.0587i	0.0586758	−	0.0338765i
$416$		0			0
$417$	114.221	−	197.837i	0.273911	−	0.474428i
$418$		0			0
$419$	233.514			0.557313			0.278657	−	0.960391i	$-0.410111\pi$
$419$	233.514			0.557313			0.278657	+	0.960391i	$0.410111\pi$
$420$		0			0
$421$		−	599.421i		−	1.42380i	−0.702280	−	0.711901i	$-0.747834\pi$
$421$		−	599.421i		−	1.42380i	0.702280	−	0.711901i	$-0.252166\pi$
$422$		0			0
$423$	−308.126	−	177.897i	−0.728430	−	0.420560i
$424$		0			0
$425$	−14.7987	−	25.6322i	−0.0348206	−	0.0603110i
$426$		0			0
$427$	−34.1877	+	145.423i	−0.0800648	+	0.340568i
$428$		0			0
$429$	854.540	−	493.369i	1.99193	−	1.15004i
$430$		0			0
$431$	365.445	+	210.990i	0.847900	+	0.489535i	0.859942	−	0.510392i	$-0.170500\pi$
$431$	365.445	+	210.990i	0.847900	+	0.489535i	−0.0120420	+	0.999927i	$0.503833\pi$
$432$		0			0
$433$	−459.611			−1.06146			−0.530729	−	0.847542i	$-0.678082\pi$
$433$	−459.611			−1.06146			−0.530729	+	0.847542i	$0.678082\pi$
$434$		0			0
$435$	−861.173			−1.97971
$436$		0			0
$437$	−128.733	−	74.3242i	−0.294584	−	0.170078i
$438$		0			0
$439$	331.615	−	191.458i	0.755386	−	0.436122i	−0.0722505	−	0.997387i	$-0.523018\pi$
$439$	331.615	−	191.458i	0.755386	−	0.436122i	0.827637	+	0.561264i	$0.189685\pi$
$440$		0			0
$441$	−871.121	+	577.477i	−1.97533	+	1.30947i
$442$		0			0
$443$	−243.261	−	421.340i	−0.549121	−	0.951106i	−0.998335	−	0.0576815i	$-0.981629\pi$
$443$	−243.261	−	421.340i	−0.549121	−	0.951106i	0.449214	−	0.893424i	$-0.351704\pi$
$444$		0			0
$445$	−493.970	−	285.194i	−1.11005	−	0.640885i
$446$		0			0
$447$		−	870.773i		−	1.94804i
$448$		0			0
$449$	−552.028			−1.22946			−0.614730	−	0.788738i	$-0.710735\pi$
$449$	−552.028			−1.22946			−0.614730	+	0.788738i	$0.710735\pi$
$450$		0			0
$451$	78.0568	−	135.198i	0.173075	−	0.299775i
$452$		0			0
$453$	−398.128	+	229.859i	−0.878870	+	0.507416i
$454$		0			0
$455$	447.643	+	105.237i	0.983832	+	0.231291i
$456$		0			0
$457$	275.133	+	476.545i	0.602042	+	1.04277i	0.992511	+	0.122152i	$0.0389794\pi$
$457$	275.133	+	476.545i	0.602042	+	1.04277i	−0.390469	+	0.920616i	$0.627687\pi$
$458$		0			0
$459$	178.307	−	308.837i	0.388469	−	0.672848i
$460$		0			0
$461$		−	3.42045i		−	0.00741963i	−0.999993	−	0.00370982i	$-0.998819\pi$
$461$		−	3.42045i		−	0.00741963i	0.999993	−	0.00370982i	$-0.00118087\pi$
$462$		0			0
$463$		−	194.634i		−	0.420376i	−0.977661	−	0.210188i	$-0.932592\pi$
$463$		−	194.634i		−	0.420376i	0.977661	−	0.210188i	$-0.0674076\pi$
$464$		0			0
$465$	730.416	−	1265.12i	1.57079	−	2.72068i
$466$		0			0
$467$	−259.821	−	450.024i	−0.556363	−	0.963649i	−0.997796	−	0.0663545i	$-0.978863\pi$
$467$	−259.821	−	450.024i	−0.556363	−	0.963649i	0.441433	−	0.897294i	$-0.354470\pi$
$468$		0			0
$469$	40.1243	+	133.146i	0.0855529	+	0.283894i
$470$		0			0
$471$	−145.672	+	84.1039i	−0.309283	+	0.178565i
$472$		0			0
$473$	356.444	−	617.379i	0.753581	−	1.30524i
$474$		0			0
$475$	−164.002			−0.345267
$476$		0			0
$477$			398.739i			0.835932i
$478$		0			0
$479$	302.357	+	174.566i	0.631225	+	0.364438i	0.781227	−	0.624248i	$-0.214594\pi$
$479$	302.357	+	174.566i	0.631225	+	0.364438i	−0.150001	+	0.988686i	$0.547928\pi$
$480$		0			0
$481$	−185.336	−	321.012i	−0.385315	−	0.667384i
$482$		0			0
$483$	−143.475	−	134.871i	−0.297049	−	0.279236i
$484$		0			0
$485$	−298.669	+	172.437i	−0.615813	+	0.355540i
$486$		0			0
$487$	460.337	+	265.776i	0.945250	+	0.545740i	0.891602	−	0.452820i	$-0.149582\pi$
$487$	460.337	+	265.776i	0.945250	+	0.545740i	0.0536479	+	0.998560i	$0.482915\pi$
$488$		0			0
$489$	−141.502			−0.289370
$490$		0			0
$491$	−338.337			−0.689077			−0.344539	−	0.938772i	$-0.611965\pi$
$491$	−338.337			−0.689077			−0.344539	+	0.938772i	$0.611965\pi$
$492$		0			0
$493$	128.498	+	74.1882i	0.260644	+	0.150483i
$494$		0			0
$495$	−1543.44	+	891.107i	−3.11807	+	1.80022i
$496$		0			0
$497$	−650.509	−	611.500i	−1.30887	−	1.23038i
$498$		0			0
$499$	261.677	+	453.237i	0.524402	+	0.908291i	0.999596	+	0.0284100i	$0.00904439\pi$
$499$	261.677	+	453.237i	0.524402	+	0.908291i	−0.475194	+	0.879881i	$0.657622\pi$
$500$		0			0
$501$	1432.15	+	826.851i	2.85858	+	1.65040i
$502$		0			0
$503$			302.320i			0.601035i	0.953776	+	0.300517i	$0.0971593\pi$
$503$			302.320i			0.601035i	−0.953776	+	0.300517i	$0.902841\pi$
$504$		0			0
$505$	−25.3440			−0.0501862
$506$		0			0
$507$	−77.4706	+	134.183i	−0.152802	+	0.264661i
$508$		0			0
$509$	82.4340	−	47.5933i	0.161953	−	0.0935036i	−0.416833	−	0.908983i	$-0.636860\pi$
$509$	82.4340	−	47.5933i	0.161953	−	0.0935036i	0.578786	+	0.815480i	$0.303527\pi$
$510$		0			0
$511$	−38.5403	−	127.890i	−0.0754214	−	0.250274i
$512$		0			0
$513$	−988.014	−	1711.29i	−1.92595	−	3.33585i
$514$		0			0
$515$	−556.463	+	963.822i	−1.08051	+	1.87150i
$516$		0			0
$517$		−	251.816i		−	0.487071i
$518$		0			0
$519$			903.928i			1.74167i
$520$		0			0
$521$	−361.975	+	626.958i	−0.694769	+	1.20337i	0.275490	+	0.961304i	$0.411160\pi$
$521$	−361.975	+	626.958i	−0.694769	+	1.20337i	−0.970259	+	0.242071i	$0.922173\pi$
$522$		0			0
$523$	−469.684	−	813.517i	−0.898058	−	1.55548i	−0.829974	−	0.557802i	$-0.811645\pi$
$523$	−469.684	−	813.517i	−0.898058	−	1.55548i	−0.0680840	−	0.997680i	$-0.521689\pi$
$524$		0			0
$525$	−211.487	−	49.7190i	−0.402833	−	0.0947028i
$526$		0			0
$527$	−217.974	+	125.848i	−0.413613	+	0.238800i
$528$		0			0
$529$	−251.454	+	435.532i	−0.475339	+	0.823312i
$530$		0			0
$531$	−1468.62			−2.76576
$532$		0			0
$533$		−	122.738i		−	0.230277i
$534$		0			0
$535$	−833.268	−	481.087i	−1.55751	−	0.899229i
$536$		0			0
$537$	403.667	+	699.172i	0.751708	+	1.30200i
$538$		0			0
$539$	−662.228	−	329.585i	−1.22862	−	0.611475i
$540$		0			0
$541$	593.877	−	342.875i	1.09774	−	0.633780i	0.162113	−	0.986772i	$-0.448169\pi$
$541$	593.877	−	342.875i	1.09774	−	0.633780i	0.935626	+	0.352992i	$0.114836\pi$
$542$		0			0
$543$	−345.402	−	199.418i	−0.636100	−	0.367252i
$544$		0			0
$545$	−625.729			−1.14813
$546$		0			0
$547$	589.026			1.07683			0.538415	−	0.842680i	$-0.319023\pi$
$547$	589.026			1.07683			0.538415	+	0.842680i	$0.319023\pi$
$548$		0			0
$549$	−394.209	−	227.597i	−0.718050	−	0.414566i
$550$		0			0
$551$	712.015	−	411.082i	1.29222	−	0.746066i
$552$		0			0
$553$	−5.92561	+	25.2055i	−0.0107154	+	0.0455795i
$554$		0			0
$555$	475.996	+	824.449i	0.857650	+	1.48549i
$556$		0			0
$557$	120.475	+	69.5566i	0.216294	+	0.124877i	0.604233	−	0.796808i	$-0.293480\pi$
$557$	120.475	+	69.5566i	0.216294	+	0.124877i	−0.387939	+	0.921685i	$0.626813\pi$
$558$		0			0
$559$		−	560.477i		−	1.00264i
$560$		0			0
$561$	436.635			0.778316
$562$		0			0
$563$	−240.961	+	417.357i	−0.427995	+	0.741309i	−0.996695	−	0.0812362i	$-0.974113\pi$
$563$	−240.961	+	417.357i	−0.427995	+	0.741309i	0.568700	+	0.822545i	$0.307447\pi$
$564$		0			0
$565$	529.421	−	305.661i	0.937028	−	0.540993i
$566$		0			0
$567$	−367.563	−	1219.70i	−0.648259	−	2.15115i
$568$		0			0
$569$	−127.991	−	221.686i	−0.224940	−	0.389607i	0.731362	−	0.681990i	$-0.238885\pi$
$569$	−127.991	−	221.686i	−0.224940	−	0.389607i	−0.956301	+	0.292383i	$0.905552\pi$
$570$		0			0
$571$	−254.168	+	440.233i	−0.445129	+	0.770985i	−0.998061	−	0.0622407i	$-0.980175\pi$
$571$	−254.168	+	440.233i	−0.445129	+	0.770985i	0.552933	+	0.833226i	$0.313509\pi$
$572$		0			0
$573$			1027.40i			1.79302i
$574$		0			0
$575$		−	28.7860i		−	0.0500626i
$576$		0			0
$577$	−23.0495	+	39.9228i	−0.0399471	+	0.0691904i	−0.885308	−	0.465006i	$-0.846052\pi$
$577$	−23.0495	+	39.9228i	−0.0399471	+	0.0691904i	0.845361	+	0.534196i	$0.179386\pi$
$578$		0			0
$579$	−58.4072	−	101.164i	−0.100876	−	0.174722i
$580$		0			0
$581$	−24.3559	+	25.9096i	−0.0419206	+	0.0445948i
$582$		0			0
$583$	−244.402	+	141.106i	−0.419214	+	0.242033i
$584$		0			0
$585$	−700.595	+	1213.47i	−1.19760	+	2.07430i
$586$		0			0
$587$	604.834			1.03038			0.515191	−	0.857075i	$-0.327721\pi$
$587$	604.834			1.03038			0.515191	+	0.857075i	$0.327721\pi$
$588$		0			0
$589$			1394.66i			2.36785i
$590$		0			0
$591$	71.8919	+	41.5068i	0.121644	+	0.0702314i
$592$		0			0
$593$	531.026	+	919.765i	0.895491	+	1.55104i	0.833195	+	0.552979i	$0.186509\pi$
$593$	531.026	+	919.765i	0.895491	+	1.55104i	0.0622963	+	0.998058i	$0.480158\pi$
$594$		0			0
$595$	148.262	+	139.371i	0.249179	+	0.234237i
$596$		0			0
$597$	−36.1726	+	20.8843i	−0.0605906	+	0.0349820i
$598$		0			0
$599$	−335.212	−	193.535i	−0.559619	−	0.323096i	0.193373	−	0.981125i	$-0.438057\pi$
$599$	−335.212	−	193.535i	−0.559619	−	0.323096i	−0.752993	+	0.658029i	$0.771390\pi$
$600$		0			0
$601$	−429.568			−0.714756			−0.357378	−	0.933960i	$-0.616329\pi$
$601$	−429.568			−0.714756			−0.357378	+	0.933960i	$0.616329\pi$
$602$		0			0
$603$	−423.729			−0.702701
$604$		0			0
$605$	−512.384	−	295.825i	−0.846915	−	0.488967i
$606$		0			0
$607$	19.7842	−	11.4224i	0.0325934	−	0.0188178i	−0.483615	−	0.875281i	$-0.660676\pi$
$607$	19.7842	−	11.4224i	0.0325934	−	0.0188178i	0.516208	+	0.856463i	$0.327343\pi$
$608$		0			0
$609$	1042.80	−	314.253i	1.71231	−	0.516014i
$610$		0			0
$611$	−98.9896	−	171.455i	−0.162012	−	0.280614i
$612$		0			0
$613$	−409.020	−	236.148i	−0.667243	−	0.385233i	0.127788	−	0.991802i	$-0.459212\pi$
$613$	−409.020	−	236.148i	−0.667243	−	0.385233i	−0.795031	+	0.606568i	$0.792546\pi$
$614$		0			0
$615$			315.225i			0.512560i
$616$		0			0
$617$	622.191			1.00841			0.504207	−	0.863583i	$-0.331785\pi$
$617$	622.191			1.00841			0.504207	+	0.863583i	$0.331785\pi$
$618$		0			0
$619$	219.754	−	380.625i	0.355014	−	0.614903i	−0.632106	−	0.774882i	$-0.717809\pi$
$619$	219.754	−	380.625i	0.355014	−	0.614903i	0.987120	+	0.159979i	$0.0511426\pi$
$620$		0			0
$621$	300.370	−	173.418i	0.483687	−	0.279257i
$622$		0			0
$623$	702.221	+	165.087i	1.12716	+	0.264987i
$624$		0			0
$625$	367.065	+	635.774i	0.587303	+	1.01724i
$626$		0			0
$627$	1209.71	−	2095.29i	1.92937	−	3.34177i
$628$		0			0
$629$		−	164.024i		−	0.260770i
$630$		0			0
$631$			817.228i			1.29513i	0.762010	+	0.647565i	$0.224213\pi$
$631$			817.228i			1.29513i	−0.762010	+	0.647565i	$0.775787\pi$
$632$		0			0
$633$	−607.186	+	1051.68i	−0.959220	+	1.66142i
$634$		0			0
$635$	−349.956	−	606.142i	−0.551112	−	0.954554i
$636$		0			0
$637$	−580.456	+	35.9181i	−0.911233	+	0.0563864i
$638$		0			0
$639$	2355.97	−	1360.22i	3.68696	−	2.12867i
$640$		0			0
$641$	192.818	−	333.970i	0.300808	−	0.521014i	−0.675511	−	0.737350i	$-0.736077\pi$
$641$	192.818	−	333.970i	0.300808	−	0.521014i	0.976319	+	0.216335i	$0.0694104\pi$
$642$		0			0
$643$	1235.25			1.92107			0.960537	−	0.278151i	$-0.0897216\pi$
$643$	1235.25			1.92107			0.960537	+	0.278151i	$0.0897216\pi$
$644$		0			0
$645$			1439.46i			2.23173i
$646$		0			0
$647$	−331.418	−	191.345i	−0.512239	−	0.295741i	0.221515	−	0.975157i	$-0.428900\pi$
$647$	−331.418	−	191.345i	−0.512239	−	0.295741i	−0.733753	+	0.679416i	$0.762233\pi$
$648$		0			0
$649$	−519.713	−	900.169i	−0.800790	−	1.38701i
$650$		0			0
$651$	−422.807	+	1798.47i	−0.649473	+	2.76263i
$652$		0			0
$653$	−921.585	+	532.077i	−1.41131	+	0.814820i	−0.995512	−	0.0946374i	$-0.969831\pi$
$653$	−921.585	+	532.077i	−1.41131	+	0.814820i	−0.415798	+	0.909457i	$0.636498\pi$
$654$		0			0
$655$	−107.354	−	61.9807i	−0.163899	−	0.0946271i
$656$		0			0
$657$	407.001			0.619484
$658$		0			0
$659$	604.104			0.916698			0.458349	−	0.888772i	$-0.348441\pi$
$659$	604.104			0.916698			0.458349	+	0.888772i	$0.348441\pi$
$660$		0			0
$661$	161.954	+	93.5041i	0.245014	+	0.141459i	0.617479	−	0.786587i	$-0.288154\pi$
$661$	161.954	+	93.5041i	0.245014	+	0.141459i	−0.372465	+	0.928046i	$0.621487\pi$
$662$		0			0
$663$	297.294	−	171.643i	0.448407	−	0.258888i
$664$		0			0
$665$	1079.57	−	325.333i	1.62341	−	0.489222i
$666$		0			0
$667$	72.1541	+	124.975i	0.108177	+	0.187368i
$668$		0			0
$669$	−1066.42	−	615.698i	−1.59405	−	0.920326i
$670$		0			0
$671$		−	322.167i		−	0.480130i
$672$		0			0
$673$	253.646			0.376889			0.188445	−	0.982084i	$-0.439655\pi$
$673$	253.646			0.376889			0.188445	+	0.982084i	$0.439655\pi$
$674$		0			0
$675$	191.330	−	331.394i	0.283453	−	0.490954i
$676$		0			0
$677$	−51.4995	+	29.7333i	−0.0760702	+	0.0439191i	−0.537553	−	0.843230i	$-0.680651\pi$
$677$	−51.4995	+	29.7333i	−0.0760702	+	0.0439191i	0.461482	+	0.887149i	$0.347318\pi$
$678$		0			0
$679$	298.736	−	317.792i	0.439964	−	0.468030i
$680$		0			0
$681$	32.1069	+	55.6107i	0.0471466	+	0.0816604i
$682$		0			0
$683$	−333.120	+	576.981i	−0.487731	+	0.844774i	−0.999900	−	0.0141100i	$-0.995509\pi$
$683$	−333.120	+	576.981i	−0.487731	+	0.844774i	0.512170	+	0.858884i	$0.328842\pi$
$684$		0			0
$685$		−	930.764i		−	1.35878i
$686$		0			0
$687$			1108.85i			1.61405i
$688$		0			0
$689$	−110.938	+	192.150i	−0.161013	+	0.278883i
$690$		0			0
$691$	103.065	+	178.515i	0.149154	+	0.258342i	0.930915	−	0.365236i	$-0.119012\pi$
$691$	103.065	+	178.515i	0.149154	+	0.258342i	−0.781761	+	0.623578i	$0.785678\pi$
$692$		0			0
$693$	1543.79	−	1642.27i	2.22769	−	2.36979i
$694$		0			0
$695$	−198.832	+	114.796i	−0.286089	+	0.165174i
$696$		0			0
$697$	27.1559	−	47.0354i	0.0389611	−	0.0674827i
$698$		0			0
$699$	−1019.14			−1.45800
$700$		0			0
$701$			54.9968i			0.0784548i	0.999230	+	0.0392274i	$0.0124897\pi$
$701$			54.9968i			0.0784548i	−0.999230	+	0.0392274i	$0.987510\pi$
$702$		0			0
$703$	−787.104	−	454.435i	−1.11964	−	0.646422i
$704$		0			0
$705$	254.233	+	440.345i	0.360614	+	0.624602i
$706$		0			0
$707$	30.6892	−	9.24835i	0.0434077	−	0.0130811i
$708$		0			0
$709$	−807.852	+	466.414i	−1.13943	+	0.657847i	−0.946288	−	0.323324i	$-0.895200\pi$
$709$	−807.852	+	466.414i	−1.13943	+	0.657847i	−0.193137	+	0.981172i	$0.561866\pi$
$710$		0			0
$711$	−68.3266	−	39.4484i	−0.0960994	−	0.0554830i
$712$		0			0
$713$	−244.794			−0.343330
$714$		0			0
$715$	−991.703			−1.38700
$716$		0			0
$717$	97.5725	+	56.3335i	0.136084	+	0.0785684i
$718$		0			0
$719$	−156.465	+	90.3352i	−0.217615	+	0.125640i	−0.604845	−	0.796343i	$-0.706765\pi$
$719$	−156.465	+	90.3352i	−0.217615	+	0.125640i	0.387231	+	0.921983i	$0.373432\pi$
$720$		0			0
$721$	322.113	−	1370.16i	0.446759	−	1.90036i
$722$		0			0
$723$	1113.24	+	1928.19i	1.53975	+	2.66693i
$724$		0			0
$725$	137.883	+	79.6067i	0.190183	+	0.109802i
$726$		0			0
$727$			70.5863i			0.0970925i	0.998821	+	0.0485463i	$0.0154588\pi$
$727$			70.5863i			0.0970925i	−0.998821	+	0.0485463i	$0.984541\pi$
$728$		0			0
$729$	516.073			0.707918
$730$		0			0
$731$	124.007	−	214.786i	0.169640	−	0.293825i
$732$		0			0
$733$	282.839	−	163.297i	0.385865	−	0.222779i	−0.294502	−	0.955651i	$-0.595154\pi$
$733$	282.839	−	163.297i	0.385865	−	0.222779i	0.680367	+	0.732872i	$0.261820\pi$
$734$		0			0
$735$	1490.77	−	92.2479i	2.02826	−	0.125507i
$736$		0			0
$737$	−149.949	−	259.719i	−0.203458	−	0.352400i
$738$		0			0
$739$	−8.32520	+	14.4197i	−0.0112655	+	0.0195124i	−0.871603	−	0.490212i	$-0.836919\pi$
$739$	−8.32520	+	14.4197i	−0.0112655	+	0.0195124i	0.860338	+	0.509724i	$0.170253\pi$
$740$		0			0
$741$		−	1902.17i		−	2.56703i
$742$		0			0
$743$			152.185i			0.204825i	0.994742	+	0.102413i	$0.0326562\pi$
$743$			152.185i			0.204825i	−0.994742	+	0.102413i	$0.967344\pi$
$744$		0			0
$745$	−437.577	+	757.906i	−0.587352	+	1.01732i
$746$		0			0
$747$	−54.1770	−	93.8374i	−0.0725261	−	0.125619i
$748$		0			0
$749$	1184.56	+	278.481i	1.58152	+	0.371804i
$750$		0			0
$751$	−1077.99	+	622.377i	−1.43540	+	0.828731i	−0.997526	−	0.0703024i	$-0.977604\pi$
$751$	−1077.99	+	622.377i	−1.43540	+	0.828731i	−0.437879	+	0.899034i	$0.644270\pi$
$752$		0			0
$753$	497.450	−	861.608i	0.660624	−	1.14423i
$754$		0			0
$755$	462.032			0.611963
$756$		0			0
$757$			93.6659i			0.123733i	0.998084	+	0.0618665i	$0.0197053\pi$
$757$			93.6659i			0.123733i	−0.998084	+	0.0618665i	$0.980295\pi$
$758$		0			0
$759$	367.769	+	212.332i	0.484545	+	0.279752i
$760$		0			0
$761$	173.538	+	300.576i	0.228039	+	0.394975i	0.957227	−	0.289338i	$-0.0934353\pi$
$761$	173.538	+	300.576i	0.228039	+	0.394975i	−0.729188	+	0.684314i	$0.760102\pi$
$762$		0			0
$763$	757.698	−	228.336i	0.993052	−	0.299261i
$764$		0			0
$765$	−536.963	+	310.016i	−0.701912	+	0.405249i
$766$		0			0
$767$	−707.719	−	408.602i	−0.922710	−	0.532727i
$768$		0			0
$769$	578.300			0.752016			0.376008	−	0.926617i	$-0.377297\pi$
$769$	578.300			0.752016			0.376008	+	0.926617i	$0.377297\pi$
$770$		0			0
$771$	1316.36			1.70734
$772$		0			0
$773$	−29.6112	−	17.0960i	−0.0383068	−	0.0221164i	0.480724	−	0.876872i	$-0.340374\pi$
$773$	−29.6112	−	17.0960i	−0.0383068	−	0.0221164i	−0.519031	+	0.854755i	$0.673707\pi$
$774$		0			0
$775$	−233.895	+	135.039i	−0.301800	+	0.174244i
$776$		0			0
$777$	−877.237	−	824.632i	−1.12901	−	1.06130i
$778$		0			0
$779$	−150.473	−	260.627i	−0.193162	−	0.334566i
$780$		0			0
$781$	1667.45	+	962.705i	2.13502	+	1.23266i
$782$		0			0
$783$			1918.33i			2.44998i
$784$		0			0
$785$	169.054			0.215356
$786$		0			0
$787$	307.280	−	532.225i	0.390445	−	0.676271i	−0.602063	−	0.798449i	$-0.705654\pi$
$787$	307.280	−	532.225i	0.390445	−	0.676271i	0.992508	+	0.122178i	$0.0389877\pi$
$788$		0			0
$789$	−1484.16	+	856.880i	−1.88106	+	1.08603i
$790$		0			0
$791$	−529.538	+	563.319i	−0.669454	+	0.712160i
$792$		0			0
$793$	−126.645	−	219.356i	−0.159704	−	0.276615i
$794$		0			0
$795$	284.920	−	493.496i	0.358390	−	0.620750i
$796$		0			0
$797$		−	1042.48i		−	1.30800i	−0.756494	−	0.654001i	$-0.773089\pi$
$797$		−	1042.48i		−	1.30800i	0.756494	−	0.654001i	$-0.226911\pi$
$798$		0			0
$799$		−	87.6065i		−	0.109645i
$800$		0			0
$801$	−1099.03	+	1903.57i	−1.37207	+	2.37649i
$802$		0			0
$803$	144.029	+	249.466i	0.179364	+	0.310667i
$804$		0			0
$805$	57.1031	+	189.488i	0.0709356	+	0.235389i
$806$		0			0
$807$	1085.00	−	626.423i	1.34448	−	0.776236i
$808$		0			0
$809$	367.854	−	637.143i	0.454703	−	0.787568i	−0.543968	−	0.839106i	$-0.683079\pi$
$809$	367.854	−	637.143i	0.454703	−	0.787568i	0.998671	+	0.0515376i	$0.0164122\pi$
$810$		0			0
$811$	−479.569			−0.591331			−0.295665	−	0.955292i	$-0.595541\pi$
$811$	−479.569			−0.591331			−0.295665	+	0.955292i	$0.595541\pi$
$812$		0			0
$813$		−	2259.98i		−	2.77980i
$814$		0			0
$815$	123.161	+	71.1071i	0.151118	+	0.0872480i
$816$		0			0
$817$	−687.130	−	1190.14i	−0.841041	−	1.45673i
$818$		0			0
$819$	405.545	−	1725.05i	0.495170	−	2.10628i
$820$		0			0
$821$	1089.70	−	629.138i	1.32728	−	0.766307i	0.342404	−	0.939553i	$-0.388759\pi$
$821$	1089.70	−	629.138i	1.32728	−	0.766307i	0.984879	+	0.173246i	$0.0554256\pi$
$822$		0			0
$823$	1148.55	+	663.116i	1.39557	+	0.805730i	0.993924	−	0.110067i	$-0.0351066\pi$
$823$	1148.55	+	663.116i	1.39557	+	0.805730i	0.401641	+	0.915797i	$0.368440\pi$
$824$		0			0
$825$	468.526			0.567910
$826$		0			0
$827$	−865.743			−1.04685			−0.523424	−	0.852073i	$-0.675345\pi$
$827$	−865.743			−1.04685			−0.523424	+	0.852073i	$0.675345\pi$
$828$		0			0
$829$	−634.533	−	366.348i	−0.765420	−	0.441915i	0.0658183	−	0.997832i	$-0.479034\pi$
$829$	−634.533	−	366.348i	−0.765420	−	0.441915i	−0.831238	+	0.555916i	$0.812368\pi$
$830$		0			0
$831$	−1837.34	+	1060.79i	−2.21100	+	1.27652i
$832$		0			0
$833$	−230.389	−	114.662i	−0.276577	−	0.137650i
$834$		0			0
$835$	−831.011	−	1439.35i	−0.995223	−	1.72378i
$836$		0			0
$837$	−2818.15	−	1627.06i	−3.36697	−	1.94392i
$838$		0			0
$839$		−	816.131i		−	0.972743i	−0.873752	−	0.486372i	$-0.838320\pi$
$839$		−	816.131i		−	0.972743i	0.873752	−	0.486372i	$-0.161680\pi$
$840$		0			0
$841$	42.8406			0.0509401
$842$		0			0
$843$	1371.82	−	2376.06i	1.62731	−	2.81858i
$844$		0			0
$845$	134.858	−	77.8604i	0.159596	−	0.0921425i
$846$		0			0
$847$	728.398	+	171.240i	0.859973	+	0.202173i
$848$		0			0
$849$	−767.933	−	1330.10i	−0.904514	−	1.56667i
$850$		0			0
$851$	79.7634	−	138.154i	0.0937290	−	0.162343i
$852$		0			0
$853$			211.653i			0.248127i	0.992274	+	0.124064i	$0.0395927\pi$
$853$			211.653i			0.248127i	−0.992274	+	0.124064i	$0.960407\pi$
$854$		0			0
$855$			3435.64i			4.01829i
$856$		0			0
$857$	267.510	−	463.341i	0.312147	−	0.540655i	−0.666680	−	0.745344i	$-0.732285\pi$
$857$	267.510	−	463.341i	0.312147	−	0.540655i	0.978827	+	0.204689i	$0.0656185\pi$
$858$		0			0
$859$	517.682	+	896.651i	0.602657	+	1.04383i	0.992417	+	0.122916i	$0.0392244\pi$
$859$	517.682	+	896.651i	0.602657	+	1.04383i	−0.389761	+	0.920916i	$0.627442\pi$
$860$		0			0
$861$	−115.029	−	381.707i	−0.133600	−	0.443330i
$862$		0			0
$863$	−627.407	+	362.234i	−0.727007	+	0.419738i	−0.817326	−	0.576175i	$-0.804545\pi$
$863$	−627.407	+	362.234i	−0.727007	+	0.419738i	0.0903190	+	0.995913i	$0.471211\pi$
$864$		0			0
$865$	454.238	−	786.763i	0.525131	−	0.909553i
$866$		0			0
$867$	−1439.68			−1.66053
$868$		0			0
$869$		−	55.8399i		−	0.0642576i
$870$		0			0
$871$	−204.193	−	117.891i	−0.234435	−	0.135351i
$872$		0			0
$873$	664.505	+	1150.96i	0.761174	+	1.31839i
$874$		0			0
$875$	−546.657	−	513.876i	−0.624751	−	0.587286i
$876$		0			0
$877$	460.810	−	266.049i	0.525439	−	0.303362i	−0.213718	−	0.976895i	$-0.568558\pi$
$877$	460.810	−	266.049i	0.525439	−	0.303362i	0.739157	+	0.673533i	$0.235224\pi$
$878$		0			0
$879$	−2663.77	−	1537.93i	−3.03045	−	1.74963i
$880$		0			0
$881$	−1289.53			−1.46372			−0.731858	−	0.681457i	$-0.761346\pi$
$881$	−1289.53			−1.46372			−0.731858	+	0.681457i	$0.761346\pi$
$882$		0			0
$883$	−501.393			−0.567829			−0.283915	−	0.958850i	$-0.591633\pi$
$883$	−501.393			−0.567829			−0.283915	+	0.958850i	$0.591633\pi$
$884$		0			0
$885$	1817.62	+	1049.40i	2.05381	+	1.18577i
$886$		0			0
$887$	−947.184	+	546.857i	−1.06785	+	0.616524i	−0.927594	−	0.373591i	$-0.878126\pi$
$887$	−947.184	+	546.857i	−1.06785	+	0.616524i	−0.140258	+	0.990115i	$0.544793\pi$
$888$		0			0
$889$	644.952	+	606.276i	0.725480	+	0.681976i
$890$		0			0
$891$	1373.62	+	2379.18i	1.54166	+	2.67024i
$892$		0			0
$893$	−420.399	−	242.717i	−0.470771	−	0.271800i
$894$		0			0
$895$		−	811.397i		−	0.906589i
$896$		0			0
$897$	333.873			0.372211
$898$		0			0
$899$	676.970	−	1172.55i	0.753026	−	1.30428i
$900$		0			0
$901$	−85.0273	+	49.0905i	−0.0943699	+	0.0544845i
$902$		0			0
$903$	−525.278	−	1743.05i	−0.581703	−	1.93029i
$904$		0			0
$905$	200.422	+	347.140i	0.221460	+	0.383580i
$906$		0			0
$907$	−24.4674	+	42.3787i	−0.0269761	+	0.0467240i	−0.879198	−	0.476456i	$-0.841921\pi$
$907$	−24.4674	+	42.3787i	−0.0269761	+	0.0467240i	0.852222	+	0.523180i	$0.175254\pi$
$908$		0			0
$909$			97.6662i			0.107444i
$910$		0			0
$911$		−	1225.94i		−	1.34571i	−0.739776	−	0.672853i	$-0.765069\pi$
$911$		−	1225.94i		−	1.34571i	0.739776	−	0.672853i	$-0.234931\pi$
$912$		0			0
$913$	38.3442	−	66.4142i	0.0419981	−	0.0727428i
$914$		0			0
$915$	325.260	+	563.367i	0.355475	+	0.615702i
$916$		0			0
$917$	152.613	+	35.8780i	0.166426	+	0.0391254i
$918$		0			0
$919$	436.533	−	252.032i	0.475009	−	0.274246i	−0.243325	−	0.969945i	$-0.578238\pi$
$919$	436.533	−	252.032i	0.475009	−	0.274246i	0.718334	+	0.695698i	$0.244905\pi$
$920$		0			0
$921$	−431.935	+	748.133i	−0.468984	+	0.812305i
$922$		0			0
$923$	1513.77			1.64005
$924$		0			0
$925$		−	176.004i		−	0.190275i
$926$		0			0
$927$	3714.20	+	2144.40i	4.00669	+	2.31326i
$928$		0			0
$929$	−623.593	−	1080.10i	−0.671252	−	1.16264i	−0.977549	−	0.210707i	$-0.932423\pi$
$929$	−623.593	−	1080.10i	−0.671252	−	1.16264i	0.306297	−	0.951936i	$-0.400910\pi$
$930$		0			0
$931$	−1188.53	+	787.894i	−1.27662	+	0.846287i
$932$		0			0
$933$	−10.6143	+	6.12817i	−0.0113765	+	0.00656825i
$934$		0			0
$935$	−380.040	−	219.416i	−0.406460	−	0.234670i
$936$		0			0
$937$	55.7855			0.0595363			0.0297681	−	0.999557i	$-0.490523\pi$
$937$	55.7855			0.0595363			0.0297681	+	0.999557i	$0.490523\pi$
$938$		0			0
$939$	426.387			0.454087
$940$		0			0
$941$	313.904	+	181.232i	0.333585	+	0.192595i	0.657432	−	0.753514i	$-0.271643\pi$
$941$	313.904	+	181.232i	0.333585	+	0.192595i	−0.323847	+	0.946110i	$0.604976\pi$
$942$		0			0
$943$	45.7458	−	26.4114i	0.0485109	−	0.0280078i
$944$		0			0
$945$	−602.069	+	2560.99i	−0.637110	+	2.71005i
$946$		0			0
$947$	780.871	+	1352.51i	0.824573	+	1.42820i	0.902245	+	0.431224i	$0.141918\pi$
$947$	780.871	+	1352.51i	0.824573	+	1.42820i	−0.0776715	+	0.996979i	$0.524749\pi$
$948$		0			0
$949$	196.132	+	113.237i	0.206672	+	0.119322i
$950$		0			0
$951$		−	2654.37i		−	2.79113i
$952$		0			0
$953$	821.437			0.861949			0.430974	−	0.902364i	$-0.358170\pi$
$953$	821.437			0.861949			0.430974	+	0.902364i	$0.358170\pi$
$954$		0			0
$955$	516.286	−	894.234i	0.540614	−	0.936370i
$956$		0			0
$957$	−2034.11	+	1174.39i	−2.12551	+	1.22716i
$958$		0			0
$959$	339.647	+	1127.07i	0.354168	+	1.17525i
$960$		0			0
$961$	667.865	+	1156.78i	0.694968	+	1.20372i
$962$		0			0
$963$	−1853.93	+	3211.09i	−1.92516	+	3.33447i
$964$		0			0
$965$			117.402i			0.121660i
$966$		0			0
$967$			200.009i			0.206834i	0.994638	+	0.103417i	$0.0329777\pi$
$967$			200.009i			0.206834i	−0.994638	+	0.103417i	$0.967022\pi$
$968$		0			0
$969$	420.859	−	728.949i	0.434323	−	0.752269i
$970$		0			0
$971$	672.784	+	1165.30i	0.692878	+	1.20010i	0.970891	+	0.239522i	$0.0769908\pi$
$971$	672.784	+	1165.30i	0.692878	+	1.20010i	−0.278013	+	0.960577i	$0.589676\pi$
$972$		0			0
$973$	198.876	−	211.563i	0.204395	−	0.217434i
$974$		0			0
$975$	319.008	−	184.179i	0.327187	−	0.188902i
$976$		0			0
$977$	−488.959	+	846.902i	−0.500470	+	0.866840i	0.499530	+	0.866297i	$0.333506\pi$
$977$	−488.959	+	846.902i	−0.500470	+	0.866840i	−1.00000		0.000542948i	$0.999827\pi$
$978$		0			0
$979$	−1555.69			−1.58906
$980$		0			0
$981$			2411.32i			2.45802i
$982$		0			0
$983$	−246.638	−	142.397i	−0.250903	−	0.144859i	0.369274	−	0.929320i	$-0.379606\pi$
$983$	−246.638	−	142.397i	−0.250903	−	0.144859i	−0.620178	+	0.784461i	$0.712940\pi$
$984$		0			0
$985$	−41.7156	−	72.2536i	−0.0423509	−	0.0733539i
$986$		0			0
$987$	−468.539	−	440.442i	−0.474710	−	0.446244i
$988$		0			0
$989$	208.897	−	120.607i	0.211220	−	0.121948i
$990$		0			0
$991$	1119.05	+	646.081i	1.12921	+	0.651949i	0.943736	−	0.330701i	$-0.107285\pi$
$991$	1119.05	+	646.081i	1.12921	+	0.651949i	0.185472	+	0.982649i	$0.440618\pi$
$992$		0			0
$993$	2242.31			2.25812
$994$		0			0
$995$	41.9787			0.0421896
$996$		0			0
$997$	304.256	+	175.662i	0.305171	+	0.176191i	0.644764	−	0.764382i	$-0.276956\pi$
$997$	304.256	+	175.662i	0.305171	+	0.176191i	−0.339592	+	0.940573i	$0.610289\pi$
$998$		0			0
$999$	1836.53	−	1060.32i	1.83837	−	1.06138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.o.b.95.1	yes	20
4.3	odd	2	inner	448.3.o.b.95.10	yes	20
7.2	even	3		448.3.o.a.415.1	yes	20
8.3	odd	2		448.3.o.a.95.1	✓	20
8.5	even	2		448.3.o.a.95.10	yes	20
28.23	odd	6		448.3.o.a.415.10	yes	20
56.37	even	6	inner	448.3.o.b.415.10	yes	20
56.51	odd	6	inner	448.3.o.b.415.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.3.o.a.95.1	✓	20	8.3	odd	2
448.3.o.a.95.10	yes	20	8.5	even	2
448.3.o.a.415.1	yes	20	7.2	even	3
448.3.o.a.415.10	yes	20	28.23	odd	6
448.3.o.b.95.1	yes	20	1.1	even	1	trivial
448.3.o.b.95.10	yes	20	4.3	odd	2	inner
448.3.o.b.415.1	yes	20	56.51	odd	6	inner
448.3.o.b.415.10	yes	20	56.37	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75361 + 4.76940i) q^{3} +(4.79340 - 2.76747i) q^{5} +(-4.79446 + 5.10031i) q^{7} +(-10.6648 - 18.4719i) q^{9} +(7.54807 - 13.0736i) q^{11} -11.8687i q^{13} +30.4821i q^{15} +(2.62597 - 4.54831i) q^{17} +(-14.5507 - 25.2026i) q^{19} +(-11.1233 - 36.9110i) q^{21} +(4.42361 - 2.55397i) q^{23} +(2.81777 - 4.88051i) q^{25} +67.9015 q^{27} +28.2517i q^{29} +(-41.5036 - 23.9621i) q^{31} +(41.5689 + 71.9995i) q^{33} +(-8.86681 + 37.7163i) q^{35} +(27.0470 - 15.6156i) q^{37} +(56.6065 + 32.6818i) q^{39} +10.3413 q^{41} +47.2232 q^{43} +(-102.241 - 59.0288i) q^{45} +(14.4460 - 8.34039i) q^{47} +(-3.02629 - 48.9065i) q^{49} +(14.4618 + 25.0486i) q^{51} +(-16.1897 - 9.34712i) q^{53} -83.5562i q^{55} +160.268 q^{57} +(34.4268 - 59.6290i) q^{59} +(18.4819 - 10.6705i) q^{61} +(145.344 + 34.1693i) q^{63} +(-32.8462 - 56.8913i) q^{65} +(9.93291 - 17.2043i) q^{67} +28.1306i q^{69} +127.543i q^{71} +(-9.54079 + 16.5251i) q^{73} +(15.5181 + 26.8781i) q^{75} +(30.4907 + 101.179i) q^{77} +(3.20338 - 1.84947i) q^{79} +(-90.9915 + 157.602i) q^{81} +5.08000 q^{83} -29.0692i q^{85} +(-134.744 - 77.7943i) q^{87} +(-51.5261 - 89.2458i) q^{89} +(60.5340 + 56.9040i) q^{91} +(228.570 - 131.965i) q^{93} +(-139.495 - 80.5372i) q^{95} -62.3085 q^{97} -321.994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) \) 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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