LMFDB - Embedded newform 176.4.m.e.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [176,4,Mod(49,176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(176, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("176.49"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	176.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3843361610$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 60 x^{14} - 83 x^{13} + 1685 x^{12} - 14618 x^{11} + 106543 x^{10} - 521269 x^{9} + \cdots + 2025 $ x^16 - 4x^15 + 60x^14 - 83x^13 + 1685x^12 - 14618x^11 + 106543x^10 - 521269x^9 + 3907139x^8 - 15948298x^7 + 37290102x^6 - 37052438x^5 + 40742731x^4 + 4262985x^3 + 9787185x^2 + 227475*x + 2025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			49.1
Root			$-5.58272 + 4.05608i$ of defining polynomial
Character	$\chi$	$=$	176.49
Dual form			176.4.m.e.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.04830 - 3.66781i) q^{3} +(2.49068 - 7.66551i) q^{5} +(-20.6812 + 15.0258i) q^{7} +(3.68910 + 11.3539i) q^{9} +(-8.40596 - 35.5013i) q^{11} +(11.6665 + 35.9057i) q^{13} +(-40.6893 + 29.5625i) q^{15} +(-12.5673 + 38.6783i) q^{17} +(92.8556 + 67.4635i) q^{19} +159.517 q^{21} -40.3517 q^{23} +(48.5705 + 35.2886i) q^{25} +(-29.0434 + 89.3864i) q^{27} +(-77.0648 + 55.9909i) q^{29} +(67.2604 + 207.006i) q^{31} +(-87.7760 + 210.053i) q^{33} +(63.6701 + 195.957i) q^{35} +(-205.488 + 149.296i) q^{37} +(72.7993 - 224.053i) q^{39} +(-299.830 - 217.839i) q^{41} +453.237 q^{43} +96.2217 q^{45} +(-246.505 - 179.096i) q^{47} +(95.9460 - 295.292i) q^{49} +(205.308 - 149.165i) q^{51} +(81.3303 + 250.309i) q^{53} +(-293.072 - 23.9861i) q^{55} +(-221.320 - 681.153i) q^{57} +(-21.4573 + 15.5897i) q^{59} +(81.1994 - 249.906i) q^{61} +(-246.896 - 179.381i) q^{63} +304.293 q^{65} -956.232 q^{67} +(203.708 + 148.002i) q^{69} +(125.329 - 385.722i) q^{71} +(-451.297 + 327.886i) q^{73} +(-115.767 - 356.295i) q^{75} +(707.280 + 607.904i) q^{77} +(286.804 + 882.691i) q^{79} +(735.243 - 534.186i) q^{81} +(115.095 - 354.225i) q^{83} +(265.187 + 192.670i) q^{85} +594.411 q^{87} -1382.64 q^{89} +(-780.789 - 567.276i) q^{91} +(419.708 - 1291.73i) q^{93} +(748.416 - 543.756i) q^{95} +(-302.720 - 931.677i) q^{97} +(372.067 - 226.408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - q^{5} + 13 q^{7} + 7 q^{9} - 83 q^{11} + 69 q^{13} - 93 q^{15} - 217 q^{17} - 126 q^{19} + 34 q^{21} + 92 q^{23} + 307 q^{25} - 158 q^{27} - 553 q^{29} - 205 q^{31} - 198 q^{33} - 7 q^{35}+ \cdots + 3265 q^{99}+O(q^{100}) $ 16 * q + q^3 - q^5 + 13 * q^7 + 7 * q^9 - 83 * q^11 + 69 * q^13 - 93 * q^15 - 217 * q^17 - 126 * q^19 + 34 * q^21 + 92 * q^23 + 307 * q^25 - 158 * q^27 - 553 * q^29 - 205 * q^31 - 198 * q^33 - 7 * q^35 + 127 * q^37 + 629 * q^39 - 553 * q^41 - 70 * q^43 - 1132 * q^45 - 779 * q^47 + 847 * q^49 + 2176 * q^51 + 1401 * q^53 + 385 * q^55 - 488 * q^57 - 1354 * q^59 - 1623 * q^61 - 256 * q^63 + 1674 * q^65 + 1658 * q^67 + 5470 * q^69 - 1985 * q^71 - 1245 * q^73 - 4114 * q^75 - 2645 * q^77 + 2007 * q^79 + 1966 * q^81 + 2946 * q^83 - 1543 * q^85 + 262 * q^87 - 6410 * q^89 - 3937 * q^91 + 2221 * q^93 + 8359 * q^95 + 6566 * q^97 + 3265 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−5.04830	−	3.66781i	−0.971547	−	0.705870i	−0.0157431	−	0.999876i	$-0.505011\pi$
$3$	−5.04830	−	3.66781i	−0.971547	−	0.705870i	−0.955804	+	0.294006i	$0.905011\pi$
$4$		0			0
$5$	2.49068	−	7.66551i	0.222773	−	0.685624i	−0.775737	−	0.631056i	$-0.782622\pi$
$5$	2.49068	−	7.66551i	0.222773	−	0.685624i	0.998510	−	0.0545681i	$-0.0173782\pi$
$6$		0			0
$7$	−20.6812	+	15.0258i	−1.11668	+	0.811317i	−0.983703	−	0.179802i	$-0.942454\pi$
$7$	−20.6812	+	15.0258i	−1.11668	+	0.811317i	−0.132979	+	0.991119i	$0.542454\pi$
$8$		0			0
$9$	3.68910	+	11.3539i	0.136633	+	0.420514i
$10$		0			0
$11$	−8.40596	−	35.5013i	−0.230408	−	0.973094i
$11$	−8.40596	−	35.5013i	−0.230408	−	0.973094i
$12$		0			0
$13$	11.6665	+	35.9057i	0.248900	+	0.766035i	0.994971	+	0.100168i	$0.0319380\pi$
$13$	11.6665	+	35.9057i	0.248900	+	0.766035i	−0.746071	+	0.665867i	$0.768062\pi$
$14$		0			0
$15$	−40.6893	+	29.5625i	−0.700395	+	0.508867i
$16$		0			0
$17$	−12.5673	+	38.6783i	−0.179296	+	0.551815i	−0.999804	−	0.0198201i	$-0.993691\pi$
$17$	−12.5673	+	38.6783i	−0.179296	+	0.551815i	0.820508	+	0.571635i	$0.193691\pi$
$18$		0			0
$19$	92.8556	+	67.4635i	1.12119	+	0.814589i	0.984388	−	0.176010i	$-0.0563190\pi$
$19$	92.8556	+	67.4635i	1.12119	+	0.814589i	0.136798	+	0.990599i	$0.456319\pi$
$20$		0			0
$21$	159.517			1.65759
$22$		0			0
$23$	−40.3517			−0.365823			−0.182911	−	0.983129i	$-0.558552\pi$
$23$	−40.3517			−0.365823			−0.182911	+	0.983129i	$0.558552\pi$
$24$		0			0
$25$	48.5705	+	35.2886i	0.388564	+	0.282309i
$26$		0			0
$27$	−29.0434	+	89.3864i	−0.207015	+	0.637127i
$28$		0			0
$29$	−77.0648	+	55.9909i	−0.493468	+	0.358526i	−0.806517	−	0.591211i	$-0.798650\pi$
$29$	−77.0648	+	55.9909i	−0.493468	+	0.358526i	0.313048	+	0.949737i	$0.398650\pi$
$30$		0			0
$31$	67.2604	+	207.006i	0.389688	+	1.19934i	0.933022	+	0.359819i	$0.117162\pi$
$31$	67.2604	+	207.006i	0.389688	+	1.19934i	−0.543334	+	0.839516i	$0.682838\pi$
$32$		0			0
$33$	−87.7760	+	210.053i	−0.463025	+	1.10804i
$34$		0			0
$35$	63.6701	+	195.957i	0.307492	+	0.946363i
$36$		0			0
$37$	−205.488	+	149.296i	−0.913028	+	0.663354i	−0.941779	−	0.336233i	$-0.890847\pi$
$37$	−205.488	+	149.296i	−0.913028	+	0.663354i	0.0287508	+	0.999587i	$0.490847\pi$
$38$		0			0
$39$	72.7993	−	224.053i	0.298903	−	0.919929i
$40$		0			0
$41$	−299.830	−	217.839i	−1.14209	−	0.829774i	−0.154677	−	0.987965i	$-0.549434\pi$
$41$	−299.830	−	217.839i	−1.14209	−	0.829774i	−0.987409	+	0.158191i	$0.949434\pi$
$42$		0			0
$43$	453.237			1.60740			0.803698	−	0.595038i	$-0.202863\pi$
$43$	453.237			1.60740			0.803698	+	0.595038i	$0.202863\pi$
$44$		0			0
$45$	96.2217			0.318753
$46$		0			0
$47$	−246.505	−	179.096i	−0.765030	−	0.555827i	0.135419	−	0.990788i	$-0.456762\pi$
$47$	−246.505	−	179.096i	−0.765030	−	0.555827i	−0.900449	+	0.434961i	$0.856762\pi$
$48$		0			0
$49$	95.9460	−	295.292i	0.279726	−	0.860908i
$50$		0			0
$51$	205.308	−	149.165i	0.563704	−	0.409555i
$52$		0			0
$53$	81.3303	+	250.309i	0.210785	+	0.648728i	0.999426	+	0.0338748i	$0.0107848\pi$
$53$	81.3303	+	250.309i	0.210785	+	0.648728i	−0.788642	+	0.614853i	$0.789215\pi$
$54$		0			0
$55$	−293.072	−	23.9861i	−0.718505	−	0.0588052i
$56$		0			0
$57$	−221.320	−	681.153i	−0.514290	−	1.58282i
$58$		0			0
$59$	−21.4573	+	15.5897i	−0.0473476	+	0.0344000i	−0.611207	−	0.791471i	$-0.709316\pi$
$59$	−21.4573	+	15.5897i	−0.0473476	+	0.0344000i	0.563860	+	0.825871i	$0.309316\pi$
$60$		0			0
$61$	81.1994	−	249.906i	0.170435	−	0.524544i	−0.828961	−	0.559307i	$-0.811067\pi$
$61$	81.1994	−	249.906i	0.170435	−	0.524544i	0.999396	+	0.0347624i	$0.0110674\pi$
$62$		0			0
$63$	−246.896	−	179.381i	−0.493746	−	0.358728i
$64$		0			0
$65$	304.293			0.580660
$66$		0			0
$67$	−956.232			−1.74362			−0.871808	−	0.489847i	$-0.837053\pi$
$67$	−956.232			−1.74362			−0.871808	+	0.489847i	$0.837053\pi$
$68$		0			0
$69$	203.708	+	148.002i	0.355414	+	0.258223i
$70$		0			0
$71$	125.329	−	385.722i	0.209490	−	0.644744i	−0.790009	−	0.613095i	$-0.789924\pi$
$71$	125.329	−	385.722i	0.209490	−	0.644744i	0.999499	−	0.0316489i	$-0.0100758\pi$
$72$		0			0
$73$	−451.297	+	327.886i	−0.723566	+	0.525702i	−0.887522	−	0.460766i	$-0.847575\pi$
$73$	−451.297	+	327.886i	−0.723566	+	0.525702i	0.163955	+	0.986468i	$0.447575\pi$
$74$		0			0
$75$	−115.767	−	356.295i	−0.178235	−	0.548552i
$76$		0			0
$77$	707.280	+	607.904i	1.04678	+	0.899702i
$78$		0			0
$79$	286.804	+	882.691i	0.408455	+	1.25709i	0.917976	+	0.396637i	$0.129823\pi$
$79$	286.804	+	882.691i	0.408455	+	1.25709i	−0.509521	+	0.860458i	$0.670177\pi$
$80$		0			0
$81$	735.243	−	534.186i	1.00856	−	0.732765i
$82$		0			0
$83$	115.095	−	354.225i	0.152208	−	0.468449i	−0.845659	−	0.533723i	$-0.820792\pi$
$83$	115.095	−	354.225i	0.152208	−	0.468449i	0.997867	+	0.0652746i	$0.0207923\pi$
$84$		0			0
$85$	265.187	+	192.670i	0.338395	+	0.245859i
$86$		0			0
$87$	594.411			0.732500
$88$		0			0
$89$	−1382.64			−1.64673			−0.823366	−	0.567511i	$-0.807906\pi$
$89$	−1382.64			−1.64673			−0.823366	+	0.567511i	$0.807906\pi$
$90$		0			0
$91$	−780.789	−	567.276i	−0.899438	−	0.653480i
$92$		0			0
$93$	419.708	−	1291.73i	0.467975	−	1.44028i
$94$		0			0
$95$	748.416	−	543.756i	0.808272	−	0.587244i
$96$		0			0
$97$	−302.720	−	931.677i	−0.316872	−	0.975232i	−0.974977	−	0.222306i	$-0.928642\pi$
$97$	−302.720	−	931.677i	−0.316872	−	0.975232i	0.658105	−	0.752926i	$-0.271358\pi$
$98$		0			0
$99$	372.067	−	226.408i	0.377719	−	0.229847i
$100$		0			0
$101$	569.259	+	1752.00i	0.560825	+	1.72604i	0.680041	+	0.733174i	$0.261962\pi$
$101$	569.259	+	1752.00i	0.560825	+	1.72604i	−0.119216	+	0.992868i	$0.538038\pi$
$102$		0			0
$103$	−826.760	+	600.677i	−0.790904	+	0.574625i	−0.908232	−	0.418468i	$-0.862567\pi$
$103$	−826.760	+	600.677i	−0.790904	+	0.574625i	0.117328	+	0.993093i	$0.462567\pi$
$104$		0			0
$105$	397.305	−	1222.78i	0.369266	−	1.13649i
$106$		0			0
$107$	−1052.81	−	764.910i	−0.951203	−	0.691090i	−0.000112216	−	1.00000i	$-0.500036\pi$
$107$	−1052.81	−	764.910i	−0.951203	−	0.691090i	−0.951091	+	0.308910i	$0.900036\pi$
$108$		0			0
$109$	−529.422			−0.465224			−0.232612	−	0.972570i	$-0.574727\pi$
$109$	−529.422			−0.465224			−0.232612	+	0.972570i	$0.574727\pi$
$110$		0			0
$111$	1584.96			1.35529
$112$		0			0
$113$	617.494	+	448.635i	0.514061	+	0.373487i	0.814362	−	0.580357i	$-0.197087\pi$
$113$	617.494	+	448.635i	0.514061	+	0.373487i	−0.300301	+	0.953845i	$0.597087\pi$
$114$		0			0
$115$	−100.503	+	309.317i	−0.0814953	+	0.250817i
$116$		0			0
$117$	−364.631	+	264.920i	−0.288121	+	0.209332i
$118$		0			0
$119$	−321.264	−	988.748i	−0.247481	−	0.761667i
$120$		0			0
$121$	−1189.68	+	596.845i	−0.893824	+	0.448418i
$122$		0			0
$123$	714.640	+	2199.44i	0.523877	+	1.61233i
$124$		0			0
$125$	1206.56	−	876.619i	0.863346	−	0.627257i
$126$		0			0
$127$	−478.822	+	1473.66i	−0.334556	+	1.02966i	0.632384	+	0.774655i	$0.282076\pi$
$127$	−478.822	+	1473.66i	−0.334556	+	1.02966i	−0.966940	+	0.255003i	$0.917924\pi$
$128$		0			0
$129$	−2288.08	−	1662.39i	−1.56166	−	1.13461i
$130$		0			0
$131$	−224.401			−0.149664			−0.0748322	−	0.997196i	$-0.523842\pi$
$131$	−224.401			−0.149664			−0.0748322	+	0.997196i	$0.523842\pi$
$132$		0			0
$133$	−2934.06			−1.91290
$134$		0			0
$135$	612.855	+	445.265i	0.390712	+	0.283869i
$136$		0			0
$137$	−645.535	+	1986.75i	−0.402568	+	1.23898i	0.520341	+	0.853958i	$0.325805\pi$
$137$	−645.535	+	1986.75i	−0.402568	+	1.23898i	−0.922909	+	0.385018i	$0.874195\pi$
$138$		0			0
$139$	1357.75	−	986.463i	0.828510	−	0.601947i	−0.0906277	−	0.995885i	$-0.528887\pi$
$139$	1357.75	−	986.463i	0.828510	−	0.601947i	0.919137	+	0.393937i	$0.128887\pi$
$140$		0			0
$141$	587.541	+	1808.26i	0.350921	+	1.08002i
$142$		0			0
$143$	1176.63	−	715.996i	0.688075	−	0.418704i
$144$		0			0
$145$	237.255	+	730.196i	0.135883	+	0.418204i
$146$		0			0
$147$	−1567.44	+	1138.81i	−0.879456	+	0.638962i
$148$		0			0
$149$	361.318	−	1112.02i	0.198660	−	0.611412i	−0.801254	−	0.598324i	$-0.795834\pi$
$149$	361.318	−	1112.02i	0.198660	−	0.611412i	0.999914	−	0.0130885i	$-0.00416632\pi$
$150$		0			0
$151$	−1538.93	−	1118.10i	−0.829381	−	0.602580i	0.0900033	−	0.995941i	$-0.471312\pi$
$151$	−1538.93	−	1118.10i	−0.829381	−	0.602580i	−0.919384	+	0.393361i	$0.871312\pi$
$152$		0			0
$153$	−485.511			−0.256544
$154$		0			0
$155$	1754.33			0.909105
$156$		0			0
$157$	2778.77	+	2018.90i	1.41255	+	1.02628i	0.992946	+	0.118570i	$0.0378309\pi$
$157$	2778.77	+	2018.90i	1.41255	+	1.02628i	0.419604	+	0.907707i	$0.362169\pi$
$158$		0			0
$159$	507.505	−	1561.94i	0.253131	−	0.779056i
$160$		0			0
$161$	834.524	−	606.317i	0.408507	−	0.296798i
$162$		0			0
$163$	971.234	+	2989.15i	0.466705	+	1.43637i	0.856825	+	0.515607i	$0.172433\pi$
$163$	971.234	+	2989.15i	0.466705	+	1.43637i	−0.390120	+	0.920764i	$0.627567\pi$
$164$		0			0
$165$	1391.54	+	1196.02i	0.656553	+	0.564303i
$166$		0			0
$167$	1063.30	+	3272.51i	0.492700	+	1.51637i	0.820511	+	0.571631i	$0.193689\pi$
$167$	1063.30	+	3272.51i	0.492700	+	1.51637i	−0.327811	+	0.944743i	$0.606311\pi$
$168$		0			0
$169$	624.297	−	453.578i	0.284159	−	0.206454i
$170$		0			0
$171$	−423.420	+	1303.15i	−0.189355	+	0.582775i
$172$		0			0
$173$	3235.74	+	2350.91i	1.42202	+	1.03316i	0.991434	+	0.130605i	$0.0416920\pi$
$173$	3235.74	+	2350.91i	1.42202	+	1.03316i	0.430583	+	0.902551i	$0.358308\pi$
$174$		0			0
$175$	−1534.74			−0.662944
$176$		0			0
$177$	165.503			0.0702823
$178$		0			0
$179$	−1799.22	−	1307.21i	−0.751285	−	0.545841i	0.144940	−	0.989440i	$-0.453701\pi$
$179$	−1799.22	−	1307.21i	−0.751285	−	0.545841i	−0.896225	+	0.443600i	$0.853701\pi$
$180$		0			0
$181$	279.277	−	859.526i	0.114688	−	0.352973i	−0.877194	−	0.480136i	$-0.840587\pi$
$181$	279.277	−	859.526i	0.114688	−	0.352973i	0.991882	+	0.127163i	$0.0405872\pi$
$182$		0			0
$183$	−1326.53	+	963.778i	−0.535845	+	0.389314i
$184$		0			0
$185$	632.625	+	1947.02i	0.251413	+	0.773771i
$186$		0			0
$187$	1478.77	+	121.028i	0.578279	+	0.0473286i
$188$		0			0
$189$	−742.448	−	2285.02i	−0.285742	−	0.879422i
$190$		0			0
$191$	−2255.20	+	1638.50i	−0.854349	+	0.620721i	−0.926342	−	0.376685i	$-0.877064\pi$
$191$	−2255.20	+	1638.50i	−0.854349	+	0.620721i	0.0719930	+	0.997405i	$0.477064\pi$
$192$		0			0
$193$	307.424	−	946.155i	0.114657	−	0.352879i	−0.877218	−	0.480092i	$-0.840603\pi$
$193$	307.424	−	946.155i	0.114657	−	0.352879i	0.991875	+	0.127213i	$0.0406032\pi$
$194$		0			0
$195$	−1536.16	−	1116.09i	−0.564138	−	0.409870i
$196$		0			0
$197$	−2774.75			−1.00352			−0.501758	−	0.865008i	$-0.667313\pi$
$197$	−2774.75			−1.00352			−0.501758	+	0.865008i	$0.667313\pi$
$198$		0			0
$199$	−2875.77			−1.02441			−0.512206	−	0.858863i	$-0.671172\pi$
$199$	−2875.77			−1.02441			−0.512206	+	0.858863i	$0.671172\pi$
$200$		0			0
$201$	4827.35	+	3507.27i	1.69400	+	1.23077i
$202$		0			0
$203$	752.488	−	2315.92i	0.260169	−	0.800718i
$204$		0			0
$205$	−2416.63	+	1755.78i	−0.823339	+	0.598191i
$206$		0			0
$207$	−148.862	−	458.149i	−0.0499836	−	0.153834i
$208$		0			0
$209$	1614.50	−	3863.59i	0.534341	−	1.27871i
$210$		0			0
$211$	−558.952	−	1720.28i	−0.182369	−	0.561274i	0.817524	−	0.575894i	$-0.195346\pi$
$211$	−558.952	−	1720.28i	−0.182369	−	0.561274i	−0.999893	+	0.0146202i	$0.995346\pi$
$212$		0			0
$213$	−2047.45	+	1487.56i	−0.658635	+	0.478526i
$214$		0			0
$215$	1128.87	−	3474.29i	0.358084	−	1.10207i
$216$		0			0
$217$	−4501.46	−	3270.50i	−1.40820	−	1.02312i
$218$		0			0
$219$	3480.91			1.07406
$220$		0			0
$221$	−1535.39			−0.467336
$222$		0			0
$223$	1838.84	+	1336.00i	0.552188	+	0.401188i	0.828592	−	0.559854i	$-0.189143\pi$
$223$	1838.84	+	1336.00i	0.552188	+	0.401188i	−0.276404	+	0.961042i	$0.589143\pi$
$224$		0			0
$225$	−221.481	+	681.648i	−0.0656239	+	0.201970i
$226$		0			0
$227$	2998.36	−	2178.43i	0.876687	−	0.636950i	−0.0556860	−	0.998448i	$-0.517735\pi$
$227$	2998.36	−	2178.43i	0.876687	−	0.636950i	0.932373	+	0.361498i	$0.117735\pi$
$228$		0			0
$229$	−915.357	−	2817.18i	−0.264142	−	0.812945i	−0.991890	−	0.127101i	$-0.959433\pi$
$229$	−915.357	−	2817.18i	−0.264142	−	0.812945i	0.727748	−	0.685845i	$-0.240567\pi$
$230$		0			0
$231$	−1340.89	−	5663.05i	−0.381923	−	1.61299i
$232$		0			0
$233$	−1107.83	−	3409.56i	−0.311487	−	0.958659i	−0.977176	−	0.212430i	$-0.931862\pi$
$233$	−1107.83	−	3409.56i	−0.311487	−	0.958659i	0.665689	−	0.746229i	$-0.268138\pi$
$234$		0			0
$235$	−1986.83	+	1443.51i	−0.551516	+	0.400700i
$236$		0			0
$237$	1789.67	−	5508.03i	0.490512	−	1.50964i
$238$		0			0
$239$	1397.58	+	1015.40i	0.378251	+	0.274815i	0.760624	−	0.649193i	$-0.224893\pi$
$239$	1397.58	+	1015.40i	0.378251	+	0.274815i	−0.382373	+	0.924008i	$0.624893\pi$
$240$		0			0
$241$	1906.29			0.509524			0.254762	−	0.967004i	$-0.418003\pi$
$241$	1906.29			0.509524			0.254762	+	0.967004i	$0.418003\pi$
$242$		0			0
$243$	−3133.39			−0.827189
$244$		0			0
$245$	−2024.59	−	1470.95i	−0.527944	−	0.383574i
$246$		0			0
$247$	−1339.03	+	4121.11i	−0.344941	+	1.06162i
$248$		0			0
$249$	−1880.26	+	1366.09i	−0.478541	+	0.347681i
$250$		0			0
$251$	381.729	+	1174.84i	0.0959940	+	0.295439i	0.987511	−	0.157547i	$-0.0503586\pi$
$251$	381.729	+	1174.84i	0.0959940	+	0.295439i	−0.891517	+	0.452986i	$0.850359\pi$
$252$		0			0
$253$	339.195	+	1432.54i	0.0842886	+	0.355980i
$254$		0			0
$255$	−632.070	−	1945.31i	−0.155223	−	0.477726i
$256$		0			0
$257$	−3535.53	+	2568.71i	−0.858134	+	0.623471i	−0.927377	−	0.374129i	$-0.877942\pi$
$257$	−3535.53	+	2568.71i	−0.858134	+	0.623471i	0.0692428	+	0.997600i	$0.477942\pi$
$258$		0			0
$259$	2006.46	−	6175.24i	0.481372	−	1.48151i
$260$		0			0
$261$	−920.015	−	668.430i	−0.218190	−	0.158524i
$262$		0			0
$263$	−2475.73			−0.580455			−0.290228	−	0.956958i	$-0.593731\pi$
$263$	−2475.73			−0.580455			−0.290228	+	0.956958i	$0.593731\pi$
$264$		0			0
$265$	2121.31			0.491741
$266$		0			0
$267$	6979.97	+	5071.24i	1.59988	+	1.16238i
$268$		0			0
$269$	2154.61	−	6631.19i	0.488359	−	1.50301i	−0.338697	−	0.940895i	$-0.609986\pi$
$269$	2154.61	−	6631.19i	0.488359	−	1.50301i	0.827056	−	0.562119i	$-0.190014\pi$
$270$		0			0
$271$	850.107	−	617.639i	0.190555	−	0.138446i	−0.488418	−	0.872610i	$-0.662426\pi$
$271$	850.107	−	617.639i	0.190555	−	0.138446i	0.678972	+	0.734164i	$0.262426\pi$
$272$		0			0
$273$	1861.00	+	5727.57i	0.412574	+	1.26977i
$274$		0			0
$275$	844.507	−	2020.95i	0.185184	−	0.443156i
$276$		0			0
$277$	−494.952	−	1523.30i	−0.107360	−	0.330421i	0.882917	−	0.469529i	$-0.155576\pi$
$277$	−494.952	−	1523.30i	−0.107360	−	0.330421i	−0.990277	+	0.139109i	$0.955576\pi$
$278$		0			0
$279$	−2102.19	+	1527.33i	−0.451094	+	0.327739i
$280$		0			0
$281$	240.109	−	738.979i	0.0509740	−	0.156882i	−0.922329	−	0.386405i	$-0.873717\pi$
$281$	240.109	−	738.979i	0.0509740	−	0.156882i	0.973303	+	0.229523i	$0.0737167\pi$
$282$		0			0
$283$	−40.3274	−	29.2996i	−0.00847072	−	0.00615434i	0.583542	−	0.812083i	$-0.301666\pi$
$283$	−40.3274	−	29.2996i	−0.00847072	−	0.00615434i	−0.592013	+	0.805929i	$0.701666\pi$
$284$		0			0
$285$	−5772.62			−1.19979
$286$		0			0
$287$	9474.05			1.94856
$288$		0			0
$289$	2636.63	+	1915.62i	0.536664	+	0.389909i
$290$		0			0
$291$	−1888.99	+	5813.71i	−0.380531	+	1.17115i
$292$		0			0
$293$	5155.11	−	3745.41i	1.02787	−	0.746788i	0.0599854	−	0.998199i	$-0.480895\pi$
$293$	5155.11	−	3745.41i	1.02787	−	0.746788i	0.967880	+	0.251411i	$0.0808946\pi$
$294$		0			0
$295$	66.0595	+	203.310i	0.0130377	+	0.0401260i
$296$		0			0
$297$	3417.47	+	279.699i	0.667682	+	0.0546457i
$298$		0			0
$299$	−470.762	−	1448.86i	−0.0910532	−	0.280233i
$300$		0			0
$301$	−9373.50	+	6810.25i	−1.79495	+	1.30411i
$302$		0			0
$303$	3552.20	−	10932.5i	0.673494	−	2.07280i
$304$		0			0
$305$	−1713.42	−	1244.87i	−0.321672	−	0.233708i
$306$		0			0
$307$	−7352.11			−1.36680			−0.683399	−	0.730045i	$-0.739499\pi$
$307$	−7352.11			−1.36680			−0.683399	+	0.730045i	$0.739499\pi$
$308$		0			0
$309$	6376.90			1.17401
$310$		0			0
$311$	−561.112	−	407.672i	−0.102308	−	0.0743310i	0.535455	−	0.844564i	$-0.320140\pi$
$311$	−561.112	−	407.672i	−0.102308	−	0.0743310i	−0.637763	+	0.770233i	$0.720140\pi$
$312$		0			0
$313$	−822.015	+	2529.90i	−0.148444	+	0.456864i	−0.997438	−	0.0715389i	$-0.977209\pi$
$313$	−822.015	+	2529.90i	−0.148444	+	0.456864i	0.848994	+	0.528403i	$0.177209\pi$
$314$		0			0
$315$	−1989.98	+	1445.81i	−0.355946	+	0.258610i
$316$		0			0
$317$	−2069.34	−	6368.77i	−0.366642	−	1.12841i	−0.948946	−	0.315438i	$-0.897849\pi$
$317$	−2069.34	−	6368.77i	−0.366642	−	1.12841i	0.582304	−	0.812971i	$-0.302151\pi$
$318$		0			0
$319$	2635.55	+	2265.24i	0.462579	+	0.397584i
$320$		0			0
$321$	2509.35	+	7722.99i	0.436319	+	1.34285i
$322$		0			0
$323$	−3776.32	+	2743.66i	−0.650526	+	0.472635i
$324$		0			0
$325$	−700.414	+	2155.65i	−0.119545	+	0.367920i
$326$		0			0
$327$	2672.69	+	1941.82i	0.451987	+	0.328388i
$328$		0			0
$329$	7789.09			1.30525
$330$		0			0
$331$	−9026.82			−1.49897			−0.749485	−	0.662021i	$-0.769699\pi$
$331$	−9026.82			−1.49897			−0.749485	+	0.662021i	$0.769699\pi$
$332$		0			0
$333$	−2453.16	−	1782.32i	−0.403700	−	0.293305i
$334$		0			0
$335$	−2381.66	+	7330.01i	−0.388430	+	1.19547i
$336$		0			0
$337$	−4699.31	+	3414.25i	−0.759607	+	0.551887i	−0.898790	−	0.438380i	$-0.855553\pi$
$337$	−4699.31	+	3414.25i	−0.759607	+	0.551887i	0.139182	+	0.990267i	$0.455553\pi$
$338$		0			0
$339$	−1471.79	−	4529.70i	−0.235801	−	0.725721i
$340$		0			0
$341$	6783.59	−	4127.91i	1.07728	−	0.655540i
$342$		0			0
$343$	−256.830	−	790.442i	−0.0404301	−	0.124431i
$344$		0			0
$345$	1641.88	−	1192.90i	0.256220	−	0.186155i
$346$		0			0
$347$	−1823.61	+	5612.49i	−0.282122	+	0.868283i	0.705124	+	0.709084i	$0.250891\pi$
$347$	−1823.61	+	5612.49i	−0.282122	+	0.868283i	−0.987246	+	0.159199i	$0.949109\pi$
$348$		0			0
$349$	−980.631	−	712.470i	−0.150407	−	0.109277i	0.510037	−	0.860153i	$-0.329632\pi$
$349$	−980.631	−	712.470i	−0.150407	−	0.109277i	−0.660444	+	0.750876i	$0.729632\pi$
$350$		0			0
$351$	−3548.32			−0.539587
$352$		0			0
$353$	5188.71			0.782344			0.391172	−	0.920318i	$-0.372070\pi$
$353$	5188.71			0.782344			0.391172	+	0.920318i	$0.372070\pi$
$354$		0			0
$355$	−2644.61	−	1921.42i	−0.395383	−	0.287263i
$356$		0			0
$357$	−2004.70	+	6169.83i	−0.297199	+	0.914684i
$358$		0			0
$359$	−4183.88	+	3039.77i	−0.615089	+	0.446888i	−0.851203	−	0.524837i	$-0.824126\pi$
$359$	−4183.88	+	3039.77i	−0.615089	+	0.446888i	0.236114	+	0.971725i	$0.424126\pi$
$360$		0			0
$361$	1951.29	+	6005.44i	0.284485	+	0.875556i
$362$		0			0
$363$	8194.98	+	1350.46i	1.18492	+	0.195264i
$364$		0			0
$365$	1389.38	+	4276.08i	0.199243	+	0.613206i
$366$		0			0
$367$	2971.21	−	2158.71i	0.422605	−	0.307040i	−0.356080	−	0.934455i	$-0.615887\pi$
$367$	2971.21	−	2158.71i	0.422605	−	0.307040i	0.778685	+	0.627415i	$0.215887\pi$
$368$		0			0
$369$	1367.22	−	4207.86i	0.192885	−	0.593639i
$370$		0			0
$371$	−5443.10	−	3954.65i	−0.761703	−	0.553410i
$372$		0			0
$373$	−3048.06			−0.423116			−0.211558	−	0.977365i	$-0.567854\pi$
$373$	−3048.06			−0.423116			−0.211558	+	0.977365i	$0.567854\pi$
$374$		0			0
$375$	−9306.36			−1.28154
$376$		0			0
$377$	−2909.47	−	2113.85i	−0.397467	−	0.288777i
$378$		0			0
$379$	3388.05	−	10427.3i	0.459188	−	1.41324i	−0.406959	−	0.913446i	$-0.633411\pi$
$379$	3388.05	−	10427.3i	0.459188	−	1.41324i	0.866147	−	0.499789i	$-0.166589\pi$
$380$		0			0
$381$	7822.35	−	5683.27i	1.05184	−	0.764207i
$382$		0			0
$383$	2676.41	+	8237.15i	0.357071	+	1.09895i	0.954799	+	0.297253i	$0.0960703\pi$
$383$	2676.41	+	8237.15i	0.357071	+	1.09895i	−0.597728	+	0.801699i	$0.703930\pi$
$384$		0			0
$385$	6421.50	−	3907.57i	0.850051	−	0.517269i
$386$		0			0
$387$	1672.04	+	5146.01i	0.219624	+	0.675933i
$388$		0			0
$389$	−9796.55	+	7117.61i	−1.27688	+	0.927704i	−0.999454	−	0.0330439i	$-0.989480\pi$
$389$	−9796.55	+	7117.61i	−1.27688	+	0.927704i	−0.277422	+	0.960748i	$0.589480\pi$
$390$		0			0
$391$	507.114	−	1560.73i	0.0655904	−	0.201866i
$392$		0			0
$393$	1132.85	+	823.061i	0.145406	+	0.105644i
$394$		0			0
$395$	7480.61			0.952887
$396$		0			0
$397$	−9791.79			−1.23787			−0.618937	−	0.785441i	$-0.712436\pi$
$397$	−9791.79			−1.23787			−0.618937	+	0.785441i	$0.712436\pi$
$398$		0			0
$399$	14812.0	+	10761.6i	1.85847	+	1.35026i
$400$		0			0
$401$	−4003.09	+	12320.2i	−0.498515	+	1.53427i	0.312890	+	0.949789i	$0.398703\pi$
$401$	−4003.09	+	12320.2i	−0.498515	+	1.53427i	−0.811406	+	0.584483i	$0.801297\pi$
$402$		0			0
$403$	−6648.01	+	4830.06i	−0.821739	+	0.597029i
$404$		0			0
$405$	−2263.55	−	6966.50i	−0.277721	−	0.854736i
$406$		0			0
$407$	7027.52	+	6040.11i	0.855875	+	0.735620i
$408$		0			0
$409$	521.166	+	1603.99i	0.0630074	+	0.193917i	0.977605	−	0.210449i	$-0.0674924\pi$
$409$	521.166	+	1603.99i	0.0630074	+	0.193917i	−0.914598	+	0.404365i	$0.867492\pi$
$410$		0			0
$411$	10545.9	−	7662.03i	1.26567	−	0.919563i
$412$		0			0
$413$	209.517	−	644.827i	0.0249629	−	0.0768278i
$414$		0			0
$415$	−2428.65	−	1764.52i	−0.287272	−	0.208715i
$416$		0			0
$417$	−10472.5			−1.22983
$418$		0			0
$419$	491.088			0.0572583			0.0286291	−	0.999590i	$-0.490886\pi$
$419$	491.088			0.0572583			0.0286291	+	0.999590i	$0.490886\pi$
$420$		0			0
$421$	6535.69	+	4748.46i	0.756603	+	0.549705i	0.897867	−	0.440268i	$-0.145116\pi$
$421$	6535.69	+	4748.46i	0.756603	+	0.549705i	−0.141263	+	0.989972i	$0.545116\pi$
$422$		0			0
$423$	1124.06	−	3459.49i	0.129205	−	0.397651i
$424$		0			0
$425$	−1975.30	+	1435.14i	−0.225450	+	0.163799i
$426$		0			0
$427$	2075.73	+	6388.45i	0.235250	+	0.724025i
$428$		0			0
$429$	−8566.12	−	701.085i	−0.964047	−	0.0789013i
$430$		0			0
$431$	−1926.20	−	5928.25i	−0.215272	−	0.662538i	−0.999134	−	0.0416034i	$-0.986753\pi$
$431$	−1926.20	−	5928.25i	−0.215272	−	0.662538i	0.783863	−	0.620934i	$-0.213247\pi$
$432$		0			0
$433$	8248.93	−	5993.20i	0.915516	−	0.665161i	−0.0268877	−	0.999638i	$-0.508560\pi$
$433$	8248.93	−	5993.20i	0.915516	−	0.665161i	0.942404	+	0.334477i	$0.108560\pi$
$434$		0			0
$435$	1480.48	−	4556.46i	0.163181	−	0.502220i
$436$		0			0
$437$	−3746.89	−	2722.27i	−0.410155	−	0.297995i
$438$		0			0
$439$	−1418.48			−0.154215			−0.0771073	−	0.997023i	$-0.524568\pi$
$439$	−1418.48			−0.154215			−0.0771073	+	0.997023i	$0.524568\pi$
$440$		0			0
$441$	3706.66			0.400244
$442$		0			0
$443$	7867.23	+	5715.88i	0.843755	+	0.613024i	0.923417	−	0.383798i	$-0.125384\pi$
$443$	7867.23	+	5715.88i	0.843755	+	0.613024i	−0.0796618	+	0.996822i	$0.525384\pi$
$444$		0			0
$445$	−3443.70	+	10598.6i	−0.366847	+	1.12904i
$446$		0			0
$447$	−5902.73	+	4288.58i	−0.624585	+	0.453787i
$448$		0			0
$449$	318.529	+	980.332i	0.0334796	+	0.103039i	0.966400	−	0.257044i	$-0.0827484\pi$
$449$	318.529	+	980.332i	0.0334796	+	0.103039i	−0.932920	+	0.360083i	$0.882748\pi$
$450$		0			0
$451$	−5213.20	+	12475.5i	−0.544302	+	1.30254i
$452$		0			0
$453$	3668.02	+	11289.0i	0.380439	+	1.17087i
$454$		0			0
$455$	−6293.15	+	4572.24i	−0.648412	+	0.471099i
$456$		0			0
$457$	−2057.79	+	6333.23i	−0.210633	+	0.648263i	0.788801	+	0.614648i	$0.210702\pi$
$457$	−2057.79	+	6333.23i	−0.210633	+	0.648263i	−0.999435	+	0.0336149i	$0.989298\pi$
$458$		0			0
$459$	−3092.31	−	2246.70i	−0.314459	−	0.228468i
$460$		0			0
$461$	6709.39			0.677847			0.338924	−	0.940814i	$-0.389937\pi$
$461$	6709.39			0.677847			0.338924	+	0.940814i	$0.389937\pi$
$462$		0			0
$463$	10505.3			1.05448			0.527240	−	0.849716i	$-0.323227\pi$
$463$	10505.3			1.05448			0.527240	+	0.849716i	$0.323227\pi$
$464$		0			0
$465$	−8856.40	−	6434.55i	−0.883238	−	0.641710i
$466$		0			0
$467$	621.845	−	1913.84i	0.0616179	−	0.189640i	−0.915509	−	0.402298i	$-0.868212\pi$
$467$	621.845	−	1913.84i	0.0616179	−	0.189640i	0.977127	+	0.212657i	$0.0682117\pi$
$468$		0			0
$469$	19776.1	−	14368.1i	1.94706	−	1.41463i
$470$		0			0
$471$	−6623.17	−	20384.0i	−0.647939	−	1.99415i
$472$		0			0
$473$	−3809.89	−	16090.5i	−0.370358	−	1.56415i
$474$		0			0
$475$	2129.36	+	6553.48i	0.205687	+	0.633041i
$476$		0			0
$477$	−2541.95	+	1846.83i	−0.243999	+	0.177276i
$478$		0			0
$479$	231.706	−	713.117i	0.0221021	−	0.0680233i	−0.939397	−	0.342831i	$-0.888614\pi$
$479$	231.706	−	713.117i	0.0221021	−	0.0680233i	0.961499	+	0.274808i	$0.0886142\pi$
$480$		0			0
$481$	−7757.89	−	5636.44i	−0.735404	−	0.534303i
$482$		0			0
$483$	−6436.78			−0.606385
$484$		0			0
$485$	−7895.76			−0.739233
$486$		0			0
$487$	−3667.54	−	2664.62i	−0.341257	−	0.247938i	0.403935	−	0.914788i	$-0.367642\pi$
$487$	−3667.54	−	2664.62i	−0.341257	−	0.247938i	−0.745192	+	0.666850i	$0.767642\pi$
$488$		0			0
$489$	6060.55	−	18652.4i	0.560465	−	1.72493i
$490$		0			0
$491$	8443.43	−	6134.51i	0.776062	−	0.563842i	−0.127732	−	0.991809i	$-0.540770\pi$
$491$	8443.43	−	6134.51i	0.776062	−	0.563842i	0.903795	+	0.427966i	$0.140770\pi$
$492$		0			0
$493$	−1197.13	−	3684.39i	−0.109363	−	0.336585i
$494$		0			0
$495$	−808.836	−	3415.99i	−0.0734434	−	0.310177i
$496$		0			0
$497$	3203.83	+	9860.38i	0.289158	+	0.889937i
$498$		0			0
$499$	10737.8	−	7801.48i	0.963308	−	0.699884i	0.00939148	−	0.999956i	$-0.497011\pi$
$499$	10737.8	−	7801.48i	0.963308	−	0.699884i	0.953917	+	0.300072i	$0.0970106\pi$
$500$		0			0
$501$	6635.06	−	20420.6i	0.591682	−	1.82101i
$502$		0			0
$503$	−10559.2	−	7671.67i	−0.936003	−	0.680046i	0.0114525	−	0.999934i	$-0.496354\pi$
$503$	−10559.2	−	7671.67i	−0.936003	−	0.680046i	−0.947455	+	0.319889i	$0.896354\pi$
$504$		0			0
$505$	14847.8			1.30835
$506$		0			0
$507$	−4815.28			−0.421803
$508$		0			0
$509$	−4751.24	−	3451.98i	−0.413742	−	0.300602i	0.361373	−	0.932421i	$-0.382308\pi$
$509$	−4751.24	−	3451.98i	−0.413742	−	0.300602i	−0.775115	+	0.631820i	$0.782308\pi$
$510$		0			0
$511$	4406.62	−	13562.2i	0.381483	−	1.17408i
$512$		0			0
$513$	−8727.17	+	6340.66i	−0.751099	+	0.545705i
$514$		0			0
$515$	2545.30	+	7833.63i	0.217785	+	0.670274i
$516$		0			0
$517$	−4286.03	+	10256.7i	−0.364603	+	0.872514i
$518$		0			0
$519$	−7712.35	−	23736.2i	−0.652282	−	2.00752i
$520$		0			0
$521$	−320.304	+	232.715i	−0.0269343	+	0.0195689i	−0.601171	−	0.799120i	$-0.705299\pi$
$521$	−320.304	+	232.715i	−0.0269343	+	0.0195689i	0.574237	+	0.818689i	$0.305299\pi$
$522$		0			0
$523$	2112.41	−	6501.32i	0.176614	−	0.543562i	−0.823090	−	0.567912i	$-0.807752\pi$
$523$	2112.41	−	6501.32i	0.176614	−	0.543562i	0.999704	+	0.0243497i	$0.00775151\pi$
$524$		0			0
$525$	7747.82	+	5629.12i	0.644081	+	0.467952i
$526$		0			0
$527$	−8851.92			−0.731681
$528$		0			0
$529$	−10538.7			−0.866174
$530$		0			0
$531$	−256.162	−	186.112i	−0.0209350	−	0.0152101i
$532$		0			0
$533$	4323.71	−	13307.0i	0.351371	−	1.08141i
$534$		0			0
$535$	−8485.62	+	6165.17i	−0.685730	+	0.498212i
$536$		0			0
$537$	4288.42	+	13198.4i	0.344616	+	1.06062i
$538$		0			0
$539$	−11289.7	−	923.996i	−0.902196	−	0.0738392i
$540$		0			0
$541$	2401.08	+	7389.77i	0.190814	+	0.587266i	1.00000		0.000286877i	$-9.13158e-5\pi$
$541$	2401.08	+	7389.77i	0.190814	+	0.587266i	−0.809186	+	0.587553i	$0.800091\pi$
$542$		0			0
$543$	−4562.45	+	3314.82i	−0.360578	+	0.261975i
$544$		0			0
$545$	−1318.62	+	4058.29i	−0.103639	+	0.318969i
$546$		0			0
$547$	−5997.01	−	4357.08i	−0.468763	−	0.340577i	0.328196	−	0.944610i	$-0.393559\pi$
$547$	−5997.01	−	4357.08i	−0.468763	−	0.340577i	−0.796959	+	0.604033i	$0.793559\pi$
$548$		0			0
$549$	3136.96			0.243866
$550$		0			0
$551$	−10933.2			−0.845321
$552$		0			0
$553$	−19194.6	−	13945.7i	−1.47602	−	1.07239i
$554$		0			0
$555$	3947.61	−	12149.5i	0.301922	−	0.929220i
$556$		0			0
$557$	−47.9436	+	34.8330i	−0.00364710	+	0.00264977i	−0.589607	−	0.807690i	$-0.700717\pi$
$557$	−47.9436	+	34.8330i	−0.00364710	+	0.00264977i	0.585960	+	0.810340i	$0.300717\pi$
$558$		0			0
$559$	5287.68	+	16273.8i	0.400080	+	1.23132i
$560$		0			0
$561$	−7021.36	−	6034.82i	−0.528417	−	0.454172i
$562$		0			0
$563$	−135.140	−	415.918i	−0.0101163	−	0.0311347i	0.945871	−	0.324543i	$-0.105210\pi$
$563$	−135.140	−	415.918i	−0.0101163	−	0.0311347i	−0.955987	+	0.293408i	$0.905210\pi$
$564$		0			0
$565$	4976.99	−	3616.00i	0.370591	−	0.269250i
$566$		0			0
$567$	−7179.18	+	22095.2i	−0.531741	+	1.63653i
$568$		0			0
$569$	1674.80	+	1216.81i	0.123394	+	0.0896509i	0.647770	−	0.761836i	$-0.275702\pi$
$569$	1674.80	+	1216.81i	0.123394	+	0.0896509i	−0.524377	+	0.851486i	$0.675702\pi$
$570$		0			0
$571$	14131.1			1.03567			0.517837	−	0.855479i	$-0.326737\pi$
$571$	14131.1			1.03567			0.517837	+	0.855479i	$0.326737\pi$
$572$		0			0
$573$	17394.6			1.26819
$574$		0			0
$575$	−1959.91	−	1423.96i	−0.142146	−	0.103275i
$576$		0			0
$577$	7964.66	−	24512.7i	0.574650	−	1.76859i	−0.0627179	−	0.998031i	$-0.519977\pi$
$577$	7964.66	−	24512.7i	0.574650	−	1.76859i	0.637368	−	0.770560i	$-0.280023\pi$
$578$		0			0
$579$	−5022.29	+	3648.90i	−0.360482	+	0.261906i
$580$		0			0
$581$	2942.21	+	9055.20i	0.210092	+	0.646597i
$582$		0			0
$583$	8202.63	−	4991.42i	0.582707	−	0.354586i
$584$		0			0
$585$	1122.57	+	3454.91i	0.0793375	+	0.244176i
$586$		0			0
$587$	−3858.76	+	2803.56i	−0.271326	+	0.197130i	−0.715125	−	0.698996i	$-0.753630\pi$
$587$	−3858.76	+	2803.56i	−0.271326	+	0.197130i	0.443799	+	0.896126i	$0.353630\pi$
$588$		0			0
$589$	−7719.87	+	23759.3i	−0.540054	+	1.66211i
$590$		0			0
$591$	14007.8	+	10177.2i	0.974963	+	0.708352i
$592$		0			0
$593$	3093.70			0.214238			0.107119	−	0.994246i	$-0.465837\pi$
$593$	3093.70			0.214238			0.107119	+	0.994246i	$0.465837\pi$
$594$		0			0
$595$	−8379.42			−0.577349
$596$		0			0
$597$	14517.8	+	10547.8i	0.995264	+	0.723101i
$598$		0			0
$599$	−5510.74	+	16960.3i	−0.375898	+	1.15689i	0.566973	+	0.823736i	$0.308114\pi$
$599$	−5510.74	+	16960.3i	−0.375898	+	1.15689i	−0.942871	+	0.333158i	$0.891886\pi$
$600$		0			0
$601$	14244.7	−	10349.3i	0.966808	−	0.702427i	0.0120861	−	0.999927i	$-0.496153\pi$
$601$	14244.7	−	10349.3i	0.966808	−	0.702427i	0.954722	+	0.297500i	$0.0961528\pi$
$602$		0			0
$603$	−3527.64	−	10857.0i	−0.238236	−	0.733216i
$604$		0			0
$605$	1612.01	+	10606.0i	0.108327	+	0.712722i
$606$		0			0
$607$	3474.45	+	10693.3i	0.232329	+	0.715034i	0.997465	+	0.0711653i	$0.0226718\pi$
$607$	3474.45	+	10693.3i	0.232329	+	0.715034i	−0.765136	+	0.643869i	$0.777328\pi$
$608$		0			0
$609$	−12293.1	+	8931.49i	−0.817969	+	0.594289i
$610$		0			0
$611$	3554.74	−	10940.4i	0.235367	−	0.724385i
$612$		0			0
$613$	−1103.15	−	801.483i	−0.0726846	−	0.0528085i	0.550850	−	0.834605i	$-0.314304\pi$
$613$	−1103.15	−	801.483i	−0.0726846	−	0.0528085i	−0.623534	+	0.781796i	$0.714304\pi$
$614$		0			0
$615$	18639.7			1.22216
$616$		0			0
$617$	−9137.98			−0.596242			−0.298121	−	0.954528i	$-0.596360\pi$
$617$	−9137.98			−0.596242			−0.298121	+	0.954528i	$0.596360\pi$
$618$		0			0
$619$	5464.94	+	3970.51i	0.354854	+	0.257816i	0.750902	−	0.660413i	$-0.229619\pi$
$619$	5464.94	+	3970.51i	0.354854	+	0.257816i	−0.396049	+	0.918229i	$0.629619\pi$
$620$		0			0
$621$	1171.95	−	3606.90i	0.0757308	−	0.233075i
$622$		0			0
$623$	28594.6	−	20775.2i	1.83888	−	1.33602i
$624$		0			0
$625$	−1395.54	−	4295.02i	−0.0893144	−	0.274882i
$626$		0			0
$627$	−22321.4	+	13582.9i	−1.42174	+	0.865149i
$628$		0			0
$629$	−3192.07	−	9824.17i	−0.202347	−	0.622759i
$630$		0			0
$631$	7248.74	−	5266.52i	0.457318	−	0.332261i	−0.335160	−	0.942161i	$-0.608790\pi$
$631$	7248.74	−	5266.52i	0.457318	−	0.332261i	0.792478	+	0.609900i	$0.208790\pi$
$632$		0			0
$633$	−3487.89	+	10734.6i	−0.219007	+	0.674033i
$634$		0			0
$635$	10103.8	+	7340.83i	0.631428	+	0.458759i
$636$		0			0
$637$	11722.0			0.729109
$638$		0			0
$639$	4841.80			0.299748
$640$		0			0
$641$	−1501.34	−	1090.78i	−0.0925104	−	0.0672127i	0.540569	−	0.841300i	$-0.318209\pi$
$641$	−1501.34	−	1090.78i	−0.0925104	−	0.0672127i	−0.633079	+	0.774087i	$0.718209\pi$
$642$		0			0
$643$	5860.06	−	18035.4i	0.359407	−	1.10614i	−0.594004	−	0.804462i	$-0.702454\pi$
$643$	5860.06	−	18035.4i	0.359407	−	1.10614i	0.953410	−	0.301677i	$-0.0975465\pi$
$644$		0			0
$645$	−18441.9	+	13398.8i	−1.12581	+	0.817951i
$646$		0			0
$647$	152.657	+	469.831i	0.00927601	+	0.0285486i	0.955587	−	0.294708i	$-0.0952223\pi$
$647$	152.657	+	469.831i	0.00927601	+	0.0285486i	−0.946311	+	0.323257i	$0.895222\pi$
$648$		0			0
$649$	733.823	+	630.716i	0.0443837	+	0.0381476i
$650$		0			0
$651$	10729.2	+	33021.0i	0.645943	+	1.98801i
$652$		0			0
$653$	−4903.00	+	3562.24i	−0.293828	+	0.213478i	−0.724926	−	0.688827i	$-0.758126\pi$
$653$	−4903.00	+	3562.24i	−0.293828	+	0.213478i	0.431099	+	0.902305i	$0.358126\pi$
$654$		0			0
$655$	−558.911	+	1720.15i	−0.0333412	+	0.102614i
$656$		0			0
$657$	−5387.67	−	3914.37i	−0.319928	−	0.232442i
$658$		0			0
$659$	22461.7			1.32774			0.663872	−	0.747846i	$-0.268912\pi$
$659$	22461.7			1.32774			0.663872	+	0.747846i	$0.268912\pi$
$660$		0			0
$661$	−10681.4			−0.628531			−0.314265	−	0.949335i	$-0.601758\pi$
$661$	−10681.4			−0.628531			−0.314265	+	0.949335i	$0.601758\pi$
$662$		0			0
$663$	7751.10	+	5631.50i	0.454039	+	0.329878i
$664$		0			0
$665$	−7307.79	+	22491.1i	−0.426142	+	1.31153i
$666$		0			0
$667$	3109.70	−	2259.33i	0.180522	−	0.131157i
$668$		0			0
$669$	−4382.85	−	13489.0i	−0.253290	−	0.779546i
$670$		0			0
$671$	−9554.54	−	781.980i	−0.549700	−	0.0449896i
$672$		0			0
$673$	−7718.25	−	23754.3i	−0.442075	−	1.36057i	−0.885659	−	0.464336i	$-0.846293\pi$
$673$	−7718.25	−	23754.3i	−0.442075	−	1.36057i	0.443584	−	0.896233i	$-0.353707\pi$
$674$		0			0
$675$	−4564.97	+	3316.65i	−0.260305	+	0.189123i
$676$		0			0
$677$	−7753.17	+	23861.8i	−0.440146	+	1.35463i	0.447575	+	0.894247i	$0.352288\pi$
$677$	−7753.17	+	23861.8i	−0.440146	+	1.35463i	−0.887720	+	0.460383i	$0.847712\pi$
$678$		0			0
$679$	20259.8	+	14719.6i	1.14507	+	0.831940i
$680$		0			0
$681$	−23126.7			−1.30135
$682$		0			0
$683$	−28044.5			−1.57114			−0.785572	−	0.618770i	$-0.787631\pi$
$683$	−28044.5			−1.57114			−0.785572	+	0.618770i	$0.787631\pi$
$684$		0			0
$685$	13621.7	+	9896.71i	0.759791	+	0.552020i
$686$		0			0
$687$	−5711.87	+	17579.3i	−0.317207	+	0.976264i
$688$		0			0
$689$	−8038.68	+	5840.45i	−0.444484	+	0.322937i
$690$		0			0
$691$	3174.31	+	9769.53i	0.174756	+	0.537844i	0.999622	−	0.0274839i	$-0.00874949\pi$
$691$	3174.31	+	9769.53i	0.174756	+	0.537844i	−0.824866	+	0.565328i	$0.808749\pi$
$692$		0			0
$693$	−4292.84	+	10273.0i	−0.235312	+	0.563116i
$694$		0			0
$695$	−4180.03	−	12864.8i	−0.228140	−	0.702144i
$696$		0			0
$697$	12193.7	−	8859.23i	0.662653	−	0.481445i
$698$		0			0
$699$	−6912.92	+	21275.8i	−0.374064	+	1.15125i
$700$		0			0
$701$	11238.8	+	8165.43i	0.605538	+	0.439949i	0.847840	−	0.530252i	$-0.177903\pi$
$701$	11238.8	+	8165.43i	0.605538	+	0.439949i	−0.242302	+	0.970201i	$0.577903\pi$
$702$		0			0
$703$	−29152.8			−1.56404
$704$		0			0
$705$	15324.6			0.818666
$706$		0			0
$707$	−38098.1	−	27679.9i	−2.02663	−	1.47243i
$708$		0			0
$709$	−5357.41	+	16488.4i	−0.283782	+	0.873392i	0.702979	+	0.711211i	$0.251853\pi$
$709$	−5357.41	+	16488.4i	−0.283782	+	0.873392i	−0.986761	+	0.162181i	$0.948147\pi$
$710$		0			0
$711$	−8963.93	+	6512.68i	−0.472818	+	0.343522i
$712$		0			0
$713$	−2714.07	−	8353.06i	−0.142557	−	0.438744i
$714$		0			0
$715$	−2557.88	−	10802.8i	−0.133789	−	0.565037i
$716$		0			0
$717$	−3331.11	−	10252.1i	−0.173504	−	0.533992i
$718$		0			0
$719$	27655.7	−	20093.0i	1.43447	−	1.04220i	0.445306	−	0.895378i	$-0.353095\pi$
$719$	27655.7	−	20093.0i	1.43447	−	1.04220i	0.989163	−	0.146824i	$-0.0469051\pi$
$720$		0			0
$721$	8072.78	−	24845.5i	0.416985	−	1.28335i
$722$		0			0
$723$	−9623.56	−	6991.92i	−0.495026	−	0.359658i
$724$		0			0
$725$	−5718.92			−0.292959
$726$		0			0
$727$	12623.5			0.643987			0.321994	−	0.946742i	$-0.395647\pi$
$727$	12623.5			0.643987			0.321994	+	0.946742i	$0.395647\pi$
$728$		0			0
$729$	−4033.27	−	2930.34i	−0.204911	−	0.148877i
$730$		0			0
$731$	−5695.98	+	17530.4i	−0.288199	+	0.886985i
$732$		0			0
$733$	12958.5	−	9414.91i	0.652979	−	0.474417i	−0.211305	−	0.977420i	$-0.567771\pi$
$733$	12958.5	−	9414.91i	0.652979	−	0.474417i	0.864285	+	0.503003i	$0.167771\pi$
$734$		0			0
$735$	4825.58	+	14851.6i	0.242169	+	0.745320i
$736$		0			0
$737$	8038.05	+	33947.4i	0.401744	+	1.69670i
$738$		0			0
$739$	4254.96	+	13095.4i	0.211801	+	0.651858i	0.999365	+	0.0356245i	$0.0113420\pi$
$739$	4254.96	+	13095.4i	0.211801	+	0.651858i	−0.787564	+	0.616233i	$0.788658\pi$
$740$		0			0
$741$	21875.3	−	15893.3i	1.08449	−	0.787929i
$742$		0			0
$743$	3829.04	−	11784.6i	0.189063	−	0.581876i	−0.810932	−	0.585141i	$-0.801039\pi$
$743$	3829.04	−	11784.6i	0.189063	−	0.581876i	0.999995	+	0.00326492i	$0.00103926\pi$
$744$		0			0
$745$	−7624.29	−	5539.37i	−0.374943	−	0.272412i
$746$		0			0
$747$	4446.43			0.217786
$748$		0			0
$749$	33266.7			1.62288
$750$		0			0
$751$	−24133.2	−	17533.8i	−1.17261	−	0.851954i	−0.181295	−	0.983429i	$-0.558029\pi$
$751$	−24133.2	−	17533.8i	−1.17261	−	0.851954i	−0.991320	+	0.131475i	$0.958029\pi$
$752$		0			0
$753$	2382.00	−	7331.06i	0.115279	−	0.354792i
$754$		0			0
$755$	−12403.8	+	9011.88i	−0.597907	+	0.434405i
$756$		0			0
$757$	4742.52	+	14596.0i	0.227701	+	0.700792i	0.998006	+	0.0631163i	$0.0201039\pi$
$757$	4742.52	+	14596.0i	0.227701	+	0.700792i	−0.770305	+	0.637675i	$0.779896\pi$
$758$		0			0
$759$	3541.91	−	8475.99i	0.169385	−	0.405348i
$760$		0			0
$761$	−2584.42	−	7954.03i	−0.123108	−	0.378888i	0.870444	−	0.492268i	$-0.163832\pi$
$761$	−2584.42	−	7954.03i	−0.123108	−	0.378888i	−0.993552	+	0.113381i	$0.963832\pi$
$762$		0			0
$763$	10949.1	−	7954.99i	0.519508	−	0.377444i
$764$		0			0
$765$	−1209.25	+	3721.69i	−0.0571510	+	0.175893i
$766$		0			0
$767$	−810.089	−	588.564i	−0.0381364	−	0.0277077i
$768$		0			0
$769$	20316.4			0.952704			0.476352	−	0.879255i	$-0.341959\pi$
$769$	20316.4			0.952704			0.476352	+	0.879255i	$0.341959\pi$
$770$		0			0
$771$	27270.0			1.27381
$772$		0			0
$773$	−11806.9	−	8578.18i	−0.549370	−	0.399141i	0.278183	−	0.960528i	$-0.410268\pi$
$773$	−11806.9	−	8578.18i	−0.549370	−	0.399141i	−0.827553	+	0.561387i	$0.810268\pi$
$774$		0			0
$775$	−4038.08	+	12427.9i	−0.187164	+	0.576031i
$776$		0			0
$777$	−32778.8	+	23815.2i	−1.51343	+	1.09957i
$778$		0			0
$779$	−13144.7	−	40455.1i	−0.604566	−	1.86066i
$780$		0			0
$781$	−14747.1	−	1206.96i	−0.675665	−	0.0552990i
$782$		0			0
$783$	−2766.60	−	8514.71i	−0.126271	−	0.388622i
$784$		0			0
$785$	22396.9	−	16272.3i	1.01832	−	0.739851i
$786$		0			0
$787$	−3590.44	+	11050.2i	−0.162624	+	0.500506i	−0.998853	−	0.0478741i	$-0.984755\pi$
$787$	−3590.44	+	11050.2i	−0.162624	+	0.500506i	0.836229	+	0.548380i	$0.184755\pi$
$788$		0			0
$789$	12498.2	+	9080.48i	0.563939	+	0.409726i
$790$		0			0
$791$	−19511.6			−0.877059
$792$		0			0
$793$	9920.37			0.444240
$794$		0			0
$795$	−10709.0	−	7780.57i	−0.477749	−	0.347105i
$796$		0			0
$797$	4142.39	−	12749.0i	0.184104	−	0.566614i	−0.815828	−	0.578295i	$-0.803718\pi$
$797$	4142.39	−	12749.0i	0.184104	−	0.566614i	0.999932	+	0.0116808i	$0.00371821\pi$
$798$		0			0
$799$	10025.0	−	7283.62i	0.443880	−	0.322498i
$800$		0			0
$801$	−5100.69	−	15698.3i	−0.224999	−	0.692475i
$802$		0			0
$803$	15434.0	+	13265.4i	0.678273	+	0.582972i
$804$		0			0
$805$	−2569.20	−	7907.19i	−0.112488	−	0.346201i
$806$		0			0
$807$	−35199.0	+	25573.6i	−1.53540	+	1.11553i
$808$		0			0
$809$	−3096.50	+	9530.05i	−0.134570	+	0.414164i	−0.995523	−	0.0945207i	$-0.969868\pi$
$809$	−3096.50	+	9530.05i	−0.134570	+	0.414164i	0.860953	+	0.508685i	$0.169868\pi$
$810$		0			0
$811$	20665.2	+	15014.2i	0.894764	+	0.650084i	0.937116	−	0.349018i	$-0.113485\pi$
$811$	20665.2	+	15014.2i	0.894764	+	0.650084i	−0.0423515	+	0.999103i	$0.513485\pi$
$812$		0			0
$813$	−6556.98			−0.282858
$814$		0			0
$815$	25332.4			1.08878
$816$		0			0
$817$	42085.6	+	30577.0i	1.80219	+	1.30937i
$818$		0			0
$819$	3560.38	−	10957.7i	0.151905	−	0.467514i
$820$		0			0
$821$	−24127.9	+	17530.0i	−1.02566	+	0.745188i	−0.967436	−	0.253115i	$-0.918545\pi$
$821$	−24127.9	+	17530.0i	−1.02566	+	0.745188i	−0.0582277	+	0.998303i	$0.518545\pi$
$822$		0			0
$823$	−5383.82	−	16569.7i	−0.228029	−	0.701802i	−0.997970	−	0.0636868i	$-0.979714\pi$
$823$	−5383.82	−	16569.7i	−0.228029	−	0.701802i	0.769940	−	0.638116i	$-0.220286\pi$
$824$		0			0
$825$	−11675.8	+	7104.88i	−0.492726	+	0.299831i
$826$		0			0
$827$	340.676	+	1048.49i	0.0143246	+	0.0440866i	0.957963	−	0.286891i	$-0.0926216\pi$
$827$	340.676	+	1048.49i	0.0143246	+	0.0440866i	−0.943639	+	0.330977i	$0.892622\pi$
$828$		0			0
$829$	26540.6	−	19282.9i	1.11193	−	0.807867i	0.128967	−	0.991649i	$-0.458834\pi$
$829$	26540.6	−	19282.9i	1.11193	−	0.807867i	0.982967	+	0.183782i	$0.0588339\pi$
$830$		0			0
$831$	−3088.52	+	9505.49i	−0.128929	+	0.396801i
$832$		0			0
$833$	10215.6	+	7422.05i	0.424908	+	0.308714i
$834$		0			0
$835$	27733.8			1.14942
$836$		0			0
$837$	−20457.0			−0.844800
$838$		0			0
$839$	−12498.1	−	9080.43i	−0.514283	−	0.373649i	0.300163	−	0.953888i	$-0.402959\pi$
$839$	−12498.1	−	9080.43i	−0.514283	−	0.373649i	−0.814446	+	0.580239i	$0.802959\pi$
$840$		0			0
$841$	−4732.60	+	14565.5i	−0.194047	+	0.597214i
$842$		0			0
$843$	−3922.58	+	2849.92i	−0.160262	+	0.116437i
$844$		0			0
$845$	−1921.99	−	5915.27i	−0.0782467	−	0.240818i
$846$		0			0
$847$	15636.0	−	30219.4i	0.634308	−	1.22591i
$848$		0			0
$849$	96.1198	+	295.826i	0.00388554	+	0.0119585i
$850$		0			0
$851$	8291.80	−	6024.35i	0.334006	−	0.242670i
$852$		0			0
$853$	3454.47	−	10631.8i	0.138662	−	0.426758i	−0.857480	−	0.514518i	$-0.827971\pi$
$853$	3454.47	−	10631.8i	0.138662	−	0.426758i	0.996142	+	0.0877602i	$0.0279709\pi$
$854$		0			0
$855$	8934.73	+	6491.46i	0.357381	+	0.259653i
$856$		0			0
$857$	−10846.6			−0.432338			−0.216169	−	0.976356i	$-0.569356\pi$
$857$	−10846.6			−0.432338			−0.216169	+	0.976356i	$0.569356\pi$
$858$		0			0
$859$	18632.5			0.740086			0.370043	−	0.929015i	$-0.379343\pi$
$859$	18632.5			0.740086			0.370043	+	0.929015i	$0.379343\pi$
$860$		0			0
$861$	−47827.9	−	34749.0i	−1.89311	−	1.37543i
$862$		0			0
$863$	−11305.0	+	34793.1i	−0.445916	+	1.37239i	0.435560	+	0.900160i	$0.356550\pi$
$863$	−11305.0	+	34793.1i	−0.445916	+	1.37239i	−0.881476	+	0.472229i	$0.843450\pi$
$864$		0			0
$865$	26080.1	−	18948.3i	1.02514	−	0.744810i
$866$		0			0
$867$	−6284.37	−	19341.3i	−0.246169	−	0.757630i
$868$		0			0
$869$	28925.8	−	17601.8i	1.12916	−	0.687110i
$870$		0			0
$871$	−11155.9	−	34334.2i	−0.433986	−	1.33567i
$872$		0			0
$873$	9461.40	−	6874.11i	0.366804	−	0.266499i
$874$		0			0
$875$	−11781.3	+	36259.1i	−0.455178	+	1.40089i
$876$		0			0
$877$	2220.08	+	1612.98i	0.0854809	+	0.0621055i	0.629705	−	0.776834i	$-0.283176\pi$
$877$	2220.08	+	1612.98i	0.0854809	+	0.0621055i	−0.544224	+	0.838940i	$0.683176\pi$
$878$		0			0
$879$	−39762.0			−1.52575
$880$		0			0
$881$	−43965.1			−1.68130			−0.840649	−	0.541581i	$-0.817826\pi$
$881$	−43965.1			−1.68130			−0.840649	+	0.541581i	$0.817826\pi$
$882$		0			0
$883$	−20983.0	−	15245.1i	−0.799701	−	0.581017i	0.111126	−	0.993806i	$-0.464554\pi$
$883$	−20983.0	−	15245.1i	−0.799701	−	0.581017i	−0.910826	+	0.412790i	$0.864554\pi$
$884$		0			0
$885$	412.214	−	1268.67i	0.0156570	−	0.0481873i
$886$		0			0
$887$	10218.8	−	7424.37i	0.386824	−	0.281044i	−0.377329	−	0.926079i	$-0.623157\pi$
$887$	10218.8	−	7424.37i	0.386824	−	0.281044i	0.764153	+	0.645035i	$0.223157\pi$
$888$		0			0
$889$	−12240.3	−	37671.9i	−0.461786	−	1.42123i
$890$		0			0
$891$	−25144.7	−	21611.7i	−0.945431	−	0.812593i
$892$		0			0
$893$	−10806.9	−	33260.2i	−0.404971	−	1.24637i
$894$		0			0
$895$	−14501.7	+	10536.1i	−0.541607	+	0.393501i
$896$		0			0
$897$	−2937.58	+	9040.94i	−0.109346	+	0.336531i
$898$		0			0
$899$	−16773.9	−	12186.9i	−0.622291	−	0.452121i
$900$		0			0
$901$	−10703.6			−0.395771
$902$		0			0
$903$	72299.0			2.66441
$904$		0			0
$905$	−5893.12	−	4281.60i	−0.216457	−	0.157266i
$906$		0			0
$907$	11927.2	−	36708.2i	0.436644	−	1.34385i	−0.454748	−	0.890620i	$-0.650271\pi$
$907$	11927.2	−	36708.2i	0.436644	−	1.34385i	0.891392	−	0.453233i	$-0.149729\pi$
$908$		0			0
$909$	−17791.9	+	12926.6i	−0.649198	+	0.471670i
$910$		0			0
$911$	−2605.83	−	8019.92i	−0.0947695	−	0.291671i	0.892424	−	0.451198i	$-0.149003\pi$
$911$	−2605.83	−	8019.92i	−0.0947695	−	0.291671i	−0.987194	+	0.159527i	$0.949003\pi$
$912$		0			0
$913$	−13542.9	−	1108.40i	−0.490915	−	0.0401784i
$914$		0			0
$915$	4083.90	+	12569.0i	0.147552	+	0.454117i
$916$		0			0
$917$	4640.90	−	3371.81i	0.167128	−	0.121425i
$918$		0			0
$919$	−9889.83	+	30437.8i	−0.354989	+	1.09255i	0.601026	+	0.799229i	$0.294759\pi$
$919$	−9889.83	+	30437.8i	−0.354989	+	1.09255i	−0.956016	+	0.293316i	$0.905241\pi$
$920$		0			0
$921$	37115.7	+	26966.1i	1.32791	+	0.964781i
$922$		0			0
$923$	15311.8			0.546038
$924$		0			0
$925$	−15249.1			−0.542041
$926$		0			0
$927$	−9870.02	−	7170.99i	−0.349702	−	0.254074i
$928$		0			0
$929$	−9441.74	+	29058.7i	−0.333448	+	1.02625i	0.634033	+	0.773306i	$0.281398\pi$
$929$	−9441.74	+	29058.7i	−0.333448	+	1.02625i	−0.967481	+	0.252942i	$0.918602\pi$
$930$		0			0
$931$	28830.5	−	20946.6i	1.01491	−	0.737377i
$932$		0			0
$933$	1337.40	+	4116.10i	0.0469288	+	0.144432i
$934$		0			0
$935$	4610.87	−	11034.1i	0.161274	−	0.385938i
$936$		0			0
$937$	−15554.7	−	47872.6i	−0.542317	−	1.66908i	−0.727284	−	0.686336i	$-0.759218\pi$
$937$	−15554.7	−	47872.6i	−0.542317	−	1.66908i	0.184967	−	0.982745i	$-0.440782\pi$
$938$		0			0
$939$	13429.0	−	9756.72i	0.466707	−	0.339083i
$940$		0			0
$941$	7758.78	−	23879.1i	0.268788	−	0.827243i	−0.722009	−	0.691884i	$-0.756781\pi$
$941$	7758.78	−	23879.1i	0.268788	−	0.827243i	0.990797	−	0.135360i	$-0.0432189\pi$
$942$		0			0
$943$	12098.6	+	8790.18i	0.417801	+	0.303550i
$944$		0			0
$945$	−19365.0			−0.666609
$946$		0			0
$947$	21894.4			0.751292			0.375646	−	0.926763i	$-0.377421\pi$
$947$	21894.4			0.751292			0.375646	+	0.926763i	$0.377421\pi$
$948$		0			0
$949$	−17038.0	−	12378.9i	−0.582801	−	0.423430i
$950$		0			0
$951$	−12912.8	+	39741.4i	−0.440300	+	1.35510i
$952$		0			0
$953$	8807.21	−	6398.81i	0.299363	−	0.217500i	−0.427956	−	0.903800i	$-0.640766\pi$
$953$	8807.21	−	6398.81i	0.299363	−	0.217500i	0.727319	+	0.686299i	$0.240766\pi$
$954$		0			0
$955$	6942.96	+	21368.2i	0.235255	+	0.724042i
$956$		0			0
$957$	−4996.59	−	21102.3i	−0.168774	−	0.712791i
$958$		0			0
$959$	−16502.1	−	50788.2i	−0.555662	−	1.71015i
$960$		0			0
$961$	−14226.2	+	10335.9i	−0.477532	+	0.346948i
$962$		0			0
$963$	4800.78	−	14775.3i	0.160647	−	0.494421i
$964$		0			0
$965$	−6487.07	−	4713.13i	−0.216400	−	0.157224i
$966$		0			0
$967$	36363.5			1.20928			0.604639	−	0.796499i	$-0.293317\pi$
$967$	36363.5			1.20928			0.604639	+	0.796499i	$0.293317\pi$
$968$		0			0
$969$	29127.2			0.965635
$970$		0			0
$971$	26661.2	+	19370.5i	0.881152	+	0.640194i	0.933556	−	0.358432i	$-0.116688\pi$
$971$	26661.2	+	19370.5i	0.881152	+	0.640194i	−0.0524042	+	0.998626i	$0.516688\pi$
$972$		0			0
$973$	−13257.5	+	40802.5i	−0.436811	+	1.34437i
$974$		0			0
$975$	11442.4	−	8313.41i	0.375847	−	0.273069i
$976$		0			0
$977$	8074.40	+	24850.4i	0.264404	+	0.813752i	0.991830	+	0.127566i	$0.0407165\pi$
$977$	8074.40	+	24850.4i	0.264404	+	0.813752i	−0.727426	+	0.686186i	$0.759283\pi$
$978$		0			0
$979$	11622.4	+	49085.3i	0.379421	+	1.60242i
$980$		0			0
$981$	−1953.09	−	6011.00i	−0.0635652	−	0.195634i
$982$		0			0
$983$	−22498.9	+	16346.4i	−0.730014	+	0.530386i	−0.889568	−	0.456803i	$-0.848994\pi$
$983$	−22498.9	+	16346.4i	−0.730014	+	0.530386i	0.159554	+	0.987189i	$0.448994\pi$
$984$		0			0
$985$	−6911.00	+	21269.9i	−0.223556	+	0.688035i
$986$		0			0
$987$	−39321.7	−	28568.9i	−1.26811	−	0.921335i
$988$		0			0
$989$	−18288.9			−0.588022
$990$		0			0
$991$	−39402.4			−1.26303			−0.631513	−	0.775365i	$-0.717566\pi$
$991$	−39402.4			−1.26303			−0.631513	+	0.775365i	$0.717566\pi$
$992$		0			0
$993$	45570.2	+	33108.7i	1.45632	+	1.05808i
$994$		0			0
$995$	−7162.61	+	22044.2i	−0.228211	+	0.702361i
$996$		0			0
$997$	−31622.8	+	22975.3i	−1.00452	+	0.729824i	−0.963052	−	0.269316i	$-0.913203\pi$
$997$	−31622.8	+	22975.3i	−1.00452	+	0.729824i	−0.0414651	+	0.999140i	$0.513203\pi$
$998$		0			0
$999$	−7376.95	−	22703.9i	−0.233630	−	0.719039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.e.49.1		16
4.3	odd	2		88.4.i.a.49.4	yes	16
11.3	even	5		1936.4.a.bw.1.7		8
11.8	odd	10		1936.4.a.bv.1.7		8
11.9	even	5	inner	176.4.m.e.97.1		16
44.3	odd	10		968.4.a.n.1.2		8
44.19	even	10		968.4.a.o.1.2		8
44.31	odd	10		88.4.i.a.9.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.4.i.a.9.4	✓	16	44.31	odd	10
88.4.i.a.49.4	yes	16	4.3	odd	2
176.4.m.e.49.1		16	1.1	even	1	trivial
176.4.m.e.97.1		16	11.9	even	5	inner
968.4.a.n.1.2		8	44.3	odd	10
968.4.a.o.1.2		8	44.19	even	10
1936.4.a.bv.1.7		8	11.8	odd	10
1936.4.a.bw.1.7		8	11.3	even	5

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.04830 - 3.66781i) q^{3} +(2.49068 - 7.66551i) q^{5} +(-20.6812 + 15.0258i) q^{7} +(3.68910 + 11.3539i) q^{9} +(-8.40596 - 35.5013i) q^{11} +(11.6665 + 35.9057i) q^{13} +(-40.6893 + 29.5625i) q^{15} +(-12.5673 + 38.6783i) q^{17} +(92.8556 + 67.4635i) q^{19} +159.517 q^{21} -40.3517 q^{23} +(48.5705 + 35.2886i) q^{25} +(-29.0434 + 89.3864i) q^{27} +(-77.0648 + 55.9909i) q^{29} +(67.2604 + 207.006i) q^{31} +(-87.7760 + 210.053i) q^{33} +(63.6701 + 195.957i) q^{35} +(-205.488 + 149.296i) q^{37} +(72.7993 - 224.053i) q^{39} +(-299.830 - 217.839i) q^{41} +453.237 q^{43} +96.2217 q^{45} +(-246.505 - 179.096i) q^{47} +(95.9460 - 295.292i) q^{49} +(205.308 - 149.165i) q^{51} +(81.3303 + 250.309i) q^{53} +(-293.072 - 23.9861i) q^{55} +(-221.320 - 681.153i) q^{57} +(-21.4573 + 15.5897i) q^{59} +(81.1994 - 249.906i) q^{61} +(-246.896 - 179.381i) q^{63} +304.293 q^{65} -956.232 q^{67} +(203.708 + 148.002i) q^{69} +(125.329 - 385.722i) q^{71} +(-451.297 + 327.886i) q^{73} +(-115.767 - 356.295i) q^{75} +(707.280 + 607.904i) q^{77} +(286.804 + 882.691i) q^{79} +(735.243 - 534.186i) q^{81} +(115.095 - 354.225i) q^{83} +(265.187 + 192.670i) q^{85} +594.411 q^{87} -1382.64 q^{89} +(-780.789 - 567.276i) q^{91} +(419.708 - 1291.73i) q^{93} +(748.416 - 543.756i) q^{95} +(-302.720 - 931.677i) q^{97} +(372.067 - 226.408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - q^{5} + 13 q^{7} + 7 q^{9} - 83 q^{11} + 69 q^{13} - 93 q^{15} - 217 q^{17} - 126 q^{19} + 34 q^{21} + 92 q^{23} + 307 q^{25} - 158 q^{27} - 553 q^{29} - 205 q^{31} - 198 q^{33} - 7 q^{35}+ \cdots + 3265 q^{99}+O(q^{100}) \) 16 * q + q^3 - q^5 + 13 * q^7 + 7 * q^9 - 83 * q^11 + 69 * q^13 - 93 * q^15 - 217 * q^17 - 126 * q^19 + 34 * q^21 + 92 * q^23 + 307 * q^25 - 158 * q^27 - 553 * q^29 - 205 * q^31 - 198 * q^33 - 7 * q^35 + 127 * q^37 + 629 * q^39 - 553 * q^41 - 70 * q^43 - 1132 * q^45 - 779 * q^47 + 847 * q^49 + 2176 * q^51 + 1401 * q^53 + 385 * q^55 - 488 * q^57 - 1354 * q^59 - 1623 * q^61 - 256 * q^63 + 1674 * q^65 + 1658 * q^67 + 5470 * q^69 - 1985 * q^71 - 1245 * q^73 - 4114 * q^75 - 2645 * q^77 + 2007 * q^79 + 1966 * q^81 + 2946 * q^83 - 1543 * q^85 + 262 * q^87 - 6410 * q^89 - 3937 * q^91 + 2221 * q^93 + 8359 * q^95 + 6566 * q^97 + 3265 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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