LMFDB - Embedded newform 252.2.l.b.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(193,252)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("252.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.5
Root			$1.13119 - 1.31165i$ of defining polynomial
Character	$\chi$	$=$	252.193
Dual form			252.2.l.b.205.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13119 - 1.31165i) q^{3} -1.52940 q^{5} +(2.53654 - 0.752299i) q^{7} +(-0.440838 - 2.96743i) q^{9} +O(q^{10})$	\(q+(1.13119 - 1.31165i) q^{3} -1.52940 q^{5} +(2.53654 - 0.752299i) q^{7} +(-0.440838 - 2.96743i) q^{9} +0.835636 q^{11} +(1.81222 - 3.13886i) q^{13} +(-1.73004 + 2.00604i) q^{15} +(0.301057 - 0.521446i) q^{17} +(0.846884 + 1.46685i) q^{19} +(1.88255 - 4.17804i) q^{21} -6.14405 q^{23} -2.66092 q^{25} +(-4.39090 - 2.77849i) q^{27} +(4.99671 + 8.65455i) q^{29} +(1.65421 + 2.86517i) q^{31} +(0.945260 - 1.09606i) q^{33} +(-3.87940 + 1.15057i) q^{35} +(4.39846 + 7.61835i) q^{37} +(-2.06712 - 5.92763i) q^{39} +(3.51718 - 6.09194i) q^{41} +(0.846884 + 1.46685i) q^{43} +(0.674220 + 4.53841i) q^{45} +(-4.23200 + 7.33004i) q^{47} +(5.86809 - 3.81648i) q^{49} +(-0.343402 - 0.984732i) q^{51} +(-3.99616 + 6.92155i) q^{53} -1.27803 q^{55} +(2.88197 + 0.548462i) q^{57} +(-0.0652138 - 0.112954i) q^{59} +(2.38343 - 4.12822i) q^{61} +(-3.35060 - 7.19538i) q^{63} +(-2.77162 + 4.80059i) q^{65} +(1.12166 + 1.94278i) q^{67} +(-6.95006 + 8.05882i) q^{69} -9.39130 q^{71} +(-2.25454 + 3.90498i) q^{73} +(-3.01000 + 3.49019i) q^{75} +(2.11963 - 0.628648i) q^{77} +(-7.87120 + 13.6333i) q^{79} +(-8.61132 + 2.61632i) q^{81} +(-3.16210 - 5.47692i) q^{83} +(-0.460438 + 0.797501i) q^{85} +(17.0039 + 3.23598i) q^{87} +(-0.531180 - 0.920030i) q^{89} +(2.23542 - 9.32519i) q^{91} +(5.62930 + 1.07130i) q^{93} +(-1.29523 - 2.24340i) q^{95} +(-7.76364 - 13.4470i) q^{97} +(-0.368380 - 2.47969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.13119	−	1.31165i	0.653090	−	0.757280i
$3$	1.13119	−	1.31165i	0.653090	−	0.757280i
$4$		0			0
$5$	−1.52940			−0.683970			−0.341985	−	0.939705i	$-0.611099\pi$
$5$	−1.52940			−0.683970			−0.341985	+	0.939705i	$0.611099\pi$
$6$		0			0
$7$	2.53654	−	0.752299i	0.958723	−	0.284342i
$7$	2.53654	−	0.752299i	0.958723	−	0.284342i
$8$		0			0
$9$	−0.440838	−	2.96743i	−0.146946	−	0.989145i
$10$		0			0
$11$	0.835636			0.251954			0.125977	−	0.992033i	$-0.459793\pi$
$11$	0.835636			0.251954			0.125977	+	0.992033i	$0.459793\pi$
$12$		0			0
$13$	1.81222	−	3.13886i	0.502620	−	0.870563i	−0.497375	−	0.867535i	$-0.665703\pi$
$13$	1.81222	−	3.13886i	0.502620	−	0.870563i	0.999995	−	0.00302796i	$-0.000963830\pi$
$14$		0			0
$15$	−1.73004	+	2.00604i	−0.446694	+	0.517957i
$16$		0			0
$17$	0.301057	−	0.521446i	0.0730170	−	0.126469i	−0.827205	−	0.561900i	$-0.810071\pi$
$17$	0.301057	−	0.521446i	0.0730170	−	0.126469i	0.900222	+	0.435431i	$0.143404\pi$
$18$		0			0
$19$	0.846884	+	1.46685i	0.194289	+	0.336518i	0.946667	−	0.322213i	$-0.104427\pi$
$19$	0.846884	+	1.46685i	0.194289	+	0.336518i	−0.752379	+	0.658731i	$0.771094\pi$
$20$		0			0
$21$	1.88255	−	4.17804i	0.410806	−	0.911723i
$22$		0			0
$23$	−6.14405			−1.28112			−0.640561	−	0.767907i	$-0.721298\pi$
$23$	−6.14405			−1.28112			−0.640561	+	0.767907i	$0.721298\pi$
$24$		0			0
$25$	−2.66092			−0.532184
$26$		0			0
$27$	−4.39090	−	2.77849i	−0.845028	−	0.534721i
$28$		0			0
$29$	4.99671	+	8.65455i	0.927865	+	1.60711i	0.786888	+	0.617096i	$0.211691\pi$
$29$	4.99671	+	8.65455i	0.927865	+	1.60711i	0.140977	+	0.990013i	$0.454976\pi$
$30$		0			0
$31$	1.65421	+	2.86517i	0.297104	+	0.514599i	0.975472	−	0.220123i	$-0.0706458\pi$
$31$	1.65421	+	2.86517i	0.297104	+	0.514599i	−0.678368	+	0.734722i	$0.737312\pi$
$32$		0			0
$33$	0.945260	−	1.09606i	0.164549	−	0.190800i
$34$		0			0
$35$	−3.87940	+	1.15057i	−0.655738	+	0.194482i
$36$		0			0
$37$	4.39846	+	7.61835i	0.723102	+	1.25245i	0.959751	+	0.280854i	$0.0906177\pi$
$37$	4.39846	+	7.61835i	0.723102	+	1.25245i	−0.236649	+	0.971595i	$0.576049\pi$
$38$		0			0
$39$	−2.06712	−	5.92763i	−0.331004	−	0.949181i
$40$		0			0
$41$	3.51718	−	6.09194i	0.549291	−	0.951401i	−0.449032	−	0.893516i	$-0.648231\pi$
$41$	3.51718	−	6.09194i	0.549291	−	0.951401i	0.998323	−	0.0578850i	$-0.0184357\pi$
$42$		0			0
$43$	0.846884	+	1.46685i	0.129149	+	0.223692i	0.923347	−	0.383967i	$-0.125442\pi$
$43$	0.846884	+	1.46685i	0.129149	+	0.223692i	−0.794198	+	0.607659i	$0.792109\pi$
$44$		0			0
$45$	0.674220	+	4.53841i	0.100507	+	0.676546i
$46$		0			0
$47$	−4.23200	+	7.33004i	−0.617301	+	1.06920i	0.372675	+	0.927962i	$0.378441\pi$
$47$	−4.23200	+	7.33004i	−0.617301	+	1.06920i	−0.989976	+	0.141235i	$0.954893\pi$
$48$		0			0
$49$	5.86809	−	3.81648i	0.838299	−	0.545211i
$50$		0			0
$51$	−0.343402	−	0.984732i	−0.0480859	−	0.137890i
$52$		0			0
$53$	−3.99616	+	6.92155i	−0.548915	+	0.950748i	0.449434	+	0.893313i	$0.351626\pi$
$53$	−3.99616	+	6.92155i	−0.548915	+	0.950748i	−0.998349	+	0.0574350i	$0.981708\pi$
$54$		0			0
$55$	−1.27803			−0.172329
$56$		0			0
$57$	2.88197	+	0.548462i	0.381726	+	0.0726456i
$58$		0			0
$59$	−0.0652138	−	0.112954i	−0.00849011	−	0.0147053i	0.861749	−	0.507335i	$-0.169369\pi$
$59$	−0.0652138	−	0.112954i	−0.00849011	−	0.0147053i	−0.870239	+	0.492629i	$0.836036\pi$
$60$		0			0
$61$	2.38343	−	4.12822i	0.305166	−	0.528564i	−0.672132	−	0.740431i	$-0.734621\pi$
$61$	2.38343	−	4.12822i	0.305166	−	0.528564i	0.977298	+	0.211868i	$0.0679546\pi$
$62$		0			0
$63$	−3.35060	−	7.19538i	−0.422136	−	0.906532i
$64$		0			0
$65$	−2.77162	+	4.80059i	−0.343777	+	0.595440i
$66$		0			0
$67$	1.12166	+	1.94278i	0.137033	+	0.237348i	0.926372	−	0.376609i	$-0.122910\pi$
$67$	1.12166	+	1.94278i	0.137033	+	0.237348i	−0.789339	+	0.613957i	$0.789577\pi$
$68$		0			0
$69$	−6.95006	+	8.05882i	−0.836689	+	0.970168i
$70$		0			0
$71$	−9.39130			−1.11454			−0.557271	−	0.830331i	$-0.688152\pi$
$71$	−9.39130			−1.11454			−0.557271	+	0.830331i	$0.688152\pi$
$72$		0			0
$73$	−2.25454	+	3.90498i	−0.263874	+	0.457044i	−0.967268	−	0.253757i	$-0.918334\pi$
$73$	−2.25454	+	3.90498i	−0.263874	+	0.457044i	0.703394	+	0.710800i	$0.251667\pi$
$74$		0			0
$75$	−3.01000	+	3.49019i	−0.347565	+	0.403013i
$76$		0			0
$77$	2.11963	−	0.628648i	0.241554	−	0.0716411i
$78$		0			0
$79$	−7.87120	+	13.6333i	−0.885580	+	1.53387i	−0.0405317	+	0.999178i	$0.512905\pi$
$79$	−7.87120	+	13.6333i	−0.885580	+	1.53387i	−0.845048	+	0.534691i	$0.820428\pi$
$80$		0			0
$81$	−8.61132	+	2.61632i	−0.956814	+	0.290702i
$82$		0			0
$83$	−3.16210	−	5.47692i	−0.347085	−	0.601170i	0.638645	−	0.769502i	$-0.279495\pi$
$83$	−3.16210	−	5.47692i	−0.347085	−	0.601170i	−0.985730	+	0.168332i	$0.946162\pi$
$84$		0			0
$85$	−0.460438	+	0.797501i	−0.0499415	+	0.0865011i
$86$		0			0
$87$	17.0039	+	3.23598i	1.82301	+	0.346934i
$88$		0			0
$89$	−0.531180	−	0.920030i	−0.0563049	−	0.0975230i	0.836499	−	0.547968i	$-0.184599\pi$
$89$	−0.531180	−	0.920030i	−0.0563049	−	0.0975230i	−0.892804	+	0.450445i	$0.851265\pi$
$90$		0			0
$91$	2.23542	−	9.32519i	0.234335	−	0.977545i
$92$		0			0
$93$	5.62930	+	1.07130i	0.583732	+	0.111089i
$94$		0			0
$95$	−1.29523	−	2.24340i	−0.132888	−	0.230168i
$96$		0			0
$97$	−7.76364	−	13.4470i	−0.788279	−	1.36534i	−0.927021	−	0.375010i	$-0.877639\pi$
$97$	−7.76364	−	13.4470i	−0.788279	−	1.36534i	0.138742	−	0.990329i	$-0.455694\pi$
$98$		0			0
$99$	−0.368380	−	2.47969i	−0.0370236	−	0.249219i
$100$		0			0
$101$	19.5151			1.94183			0.970914	−	0.239427i	$-0.0769597\pi$
$101$	19.5151			1.94183			0.970914	+	0.239427i	$0.0769597\pi$
$102$		0			0
$103$	−1.82354			−0.179679			−0.0898394	−	0.995956i	$-0.528635\pi$
$103$	−1.82354			−0.179679			−0.0898394	+	0.995956i	$0.528635\pi$
$104$		0			0
$105$	−2.87918	+	6.38991i	−0.280979	+	0.623591i
$106$		0			0
$107$	−5.27078	−	9.12926i	−0.509546	−	0.882559i	−0.999939	−	0.0110578i	$-0.996480\pi$
$107$	−5.27078	−	9.12926i	−0.509546	−	0.882559i	0.490393	−	0.871501i	$-0.336853\pi$
$108$		0			0
$109$	6.30442	−	10.9196i	0.603854	−	1.04591i	−0.388377	−	0.921501i	$-0.626964\pi$
$109$	6.30442	−	10.9196i	0.603854	−	1.04591i	0.992231	−	0.124406i	$-0.0397025\pi$
$110$		0			0
$111$	14.9681	+	2.84854i	1.42071	+	0.270372i
$112$		0			0
$113$	7.76452	−	13.4485i	0.730424	−	1.26513i	−0.226278	−	0.974063i	$-0.572656\pi$
$113$	7.76452	−	13.4485i	0.730424	−	1.26513i	0.956702	−	0.291069i	$-0.0940110\pi$
$114$		0			0
$115$	9.39673			0.876250
$116$		0			0
$117$	−10.1133	−	3.99392i	−0.934971	−	0.369238i
$118$		0			0
$119$	0.371360	−	1.54915i	0.0340425	−	0.142011i
$120$		0			0
$121$	−10.3017			−0.936519
$122$		0			0
$123$	−4.01189	−	11.5044i	−0.361740	−	1.03732i
$124$		0			0
$125$	11.7166			1.04797
$126$		0			0
$127$	−10.8966			−0.966919			−0.483460	−	0.875367i	$-0.660620\pi$
$127$	−10.8966			−0.966919			−0.483460	+	0.875367i	$0.660620\pi$
$128$		0			0
$129$	2.88197	+	0.548462i	0.253743	+	0.0482894i
$130$		0			0
$131$	19.4618			1.70038			0.850191	−	0.526474i	$-0.176486\pi$
$131$	19.4618			1.70038			0.850191	+	0.526474i	$0.176486\pi$
$132$		0			0
$133$	3.25166	+	3.08361i	0.281955	+	0.267383i
$134$		0			0
$135$	6.71546	+	4.24944i	0.577974	+	0.365734i
$136$		0			0
$137$	12.2767			1.04887			0.524433	−	0.851452i	$-0.324277\pi$
$137$	12.2767			1.04887			0.524433	+	0.851452i	$0.324277\pi$
$138$		0			0
$139$	−6.44692	+	11.1664i	−0.546821	+	0.947121i	0.451669	+	0.892185i	$0.350829\pi$
$139$	−6.44692	+	11.1664i	−0.546821	+	0.947121i	−0.998490	+	0.0549357i	$0.982505\pi$
$140$		0			0
$141$	4.82725	+	13.8425i	0.406528	+	1.16575i
$142$		0			0
$143$	1.51436	−	2.62295i	0.126637	−	0.219342i
$144$		0			0
$145$	−7.64198	−	13.2363i	−0.634632	−	1.09922i
$146$		0			0
$147$	1.63203	−	12.0140i	0.134608	−	0.990899i
$148$		0			0
$149$	−18.0653			−1.47997			−0.739986	−	0.672623i	$-0.765168\pi$
$149$	−18.0653			−1.47997			−0.739986	+	0.672623i	$0.765168\pi$
$150$		0			0
$151$	8.59782			0.699681			0.349840	−	0.936809i	$-0.386236\pi$
$151$	8.59782			0.699681			0.349840	+	0.936809i	$0.386236\pi$
$152$		0			0
$153$	−1.68007	−	0.663493i	−0.135826	−	0.0536402i
$154$		0			0
$155$	−2.52995	−	4.38200i	−0.203210	−	0.351971i
$156$		0			0
$157$	−1.59683	−	2.76579i	−0.127441	−	0.220734i	0.795244	−	0.606290i	$-0.207343\pi$
$157$	−1.59683	−	2.76579i	−0.127441	−	0.220734i	−0.922684	+	0.385556i	$0.874010\pi$
$158$		0			0
$159$	4.55824	+	13.0711i	0.361492	+	1.03661i
$160$		0			0
$161$	−15.5846	+	4.62216i	−1.22824	+	0.364277i
$162$		0			0
$163$	2.04809	+	3.54740i	0.160419	+	0.277854i	0.935019	−	0.354598i	$-0.115382\pi$
$163$	2.04809	+	3.54740i	0.160419	+	0.277854i	−0.774600	+	0.632451i	$0.782049\pi$
$164$		0			0
$165$	−1.44568	+	1.67632i	−0.112546	+	0.130501i
$166$		0			0
$167$	8.24859	−	14.2870i	0.638295	−	1.10556i	−0.347512	−	0.937676i	$-0.612973\pi$
$167$	8.24859	−	14.2870i	0.638295	−	1.10556i	0.985807	−	0.167883i	$-0.0536932\pi$
$168$		0			0
$169$	−0.0682984	−	0.118296i	−0.00525372	−	0.00909971i
$170$		0			0
$171$	3.97943	−	3.15971i	0.304315	−	0.241629i
$172$		0			0
$173$	6.41063	−	11.1035i	0.487391	−	0.844186i	−0.512504	−	0.858685i	$-0.671282\pi$
$173$	6.41063	−	11.1035i	0.487391	−	0.844186i	0.999895	+	0.0144987i	$0.00461525\pi$
$174$		0			0
$175$	−6.74954	+	2.00181i	−0.510217	+	0.151322i
$176$		0			0
$177$	−0.221924	−	0.0422340i	−0.0166808	−	0.00317450i
$178$		0			0
$179$	−11.8750	+	20.5680i	−0.887576	+	1.53733i	−0.0448441	+	0.998994i	$0.514279\pi$
$179$	−11.8750	+	20.5680i	−0.887576	+	1.53733i	−0.842732	+	0.538333i	$0.819054\pi$
$180$		0			0
$181$	−16.0244			−1.19108			−0.595542	−	0.803324i	$-0.703063\pi$
$181$	−16.0244			−1.19108			−0.595542	+	0.803324i	$0.703063\pi$
$182$		0			0
$183$	−2.71867	−	7.79599i	−0.200970	−	0.576296i
$184$		0			0
$185$	−6.72702	−	11.6515i	−0.494580	−	0.856638i
$186$		0			0
$187$	0.251574	−	0.435739i	0.0183969	−	0.0318644i
$188$		0			0
$189$	−13.2280	−	3.74450i	−0.962192	−	0.272372i
$190$		0			0
$191$	5.40475	−	9.36130i	0.391074	−	0.677360i	−0.601517	−	0.798860i	$-0.705437\pi$
$191$	5.40475	−	9.36130i	0.391074	−	0.677360i	0.992591	+	0.121500i	$0.0387703\pi$
$192$		0			0
$193$	−0.375130	−	0.649745i	−0.0270025	−	0.0467696i	0.852208	−	0.523203i	$-0.175263\pi$
$193$	−0.375130	−	0.649745i	−0.0270025	−	0.0467696i	−0.879211	+	0.476433i	$0.841930\pi$
$194$		0			0
$195$	3.16146	+	9.06574i	0.226397	+	0.649211i
$196$		0			0
$197$	10.3186			0.735169			0.367584	−	0.929990i	$-0.380185\pi$
$197$	10.3186			0.735169			0.367584	+	0.929990i	$0.380185\pi$
$198$		0			0
$199$	−2.85430	+	4.94379i	−0.202336	+	0.350456i	−0.949281	−	0.314430i	$-0.898187\pi$
$199$	−2.85430	+	4.94379i	−0.202336	+	0.350456i	0.746945	+	0.664886i	$0.231520\pi$
$200$		0			0
$201$	3.81704	+	0.726415i	0.269234	+	0.0512373i
$202$		0			0
$203$	19.1852	+	18.1936i	1.34653	+	1.27694i
$204$		0			0
$205$	−5.37919	+	9.31704i	−0.375699	+	0.650730i
$206$		0			0
$207$	2.70853	+	18.2321i	0.188256	+	1.26722i
$208$		0			0
$209$	0.707687	+	1.22575i	0.0489517	+	0.0847869i
$210$		0			0
$211$	2.73050	−	4.72937i	0.187976	−	0.325583i	−0.756600	−	0.653878i	$-0.773141\pi$
$211$	2.73050	−	4.72937i	0.187976	−	0.325583i	0.944575	+	0.328295i	$0.106474\pi$
$212$		0			0
$213$	−10.6233	+	12.3181i	−0.727897	+	0.844020i
$214$		0			0
$215$	−1.29523	−	2.24340i	−0.0883338	−	0.152999i
$216$		0			0
$217$	6.35143	+	6.02316i	0.431163	+	0.408879i
$218$		0			0
$219$	2.57166	+	7.37443i	0.173776	+	0.498318i
$220$		0			0
$221$	−1.09116	−	1.88995i	−0.0733996	−	0.127132i
$222$		0			0
$223$	−9.00530	−	15.5976i	−0.603040	−	1.04450i	−0.992358	−	0.123392i	$-0.960623\pi$
$223$	−9.00530	−	15.5976i	−0.603040	−	1.04450i	0.389318	−	0.921103i	$-0.372711\pi$
$224$		0			0
$225$	1.17304	+	7.89611i	0.0782024	+	0.526407i
$226$		0			0
$227$	−18.1740			−1.20625			−0.603125	−	0.797647i	$-0.706078\pi$
$227$	−18.1740			−1.20625			−0.603125	+	0.797647i	$0.706078\pi$
$228$		0			0
$229$	−15.4278			−1.01950			−0.509750	−	0.860323i	$-0.670262\pi$
$229$	−15.4278			−1.01950			−0.509750	+	0.860323i	$0.670262\pi$
$230$		0			0
$231$	1.57313	−	3.49132i	0.103504	−	0.229712i
$232$		0			0
$233$	−3.20892	−	5.55801i	−0.210223	−	0.364117i	0.741561	−	0.670885i	$-0.234086\pi$
$233$	−3.20892	−	5.55801i	−0.210223	−	0.364117i	−0.951784	+	0.306768i	$0.900752\pi$
$234$		0			0
$235$	6.47244	−	11.2106i	0.422216	−	0.731299i
$236$		0			0
$237$	8.97832	+	25.7461i	0.583205	+	1.67239i
$238$		0			0
$239$	−2.33317	+	4.04118i	−0.150920	+	0.261402i	−0.931566	−	0.363572i	$-0.881557\pi$
$239$	−2.33317	+	4.04118i	−0.150920	+	0.261402i	0.780646	+	0.624974i	$0.214890\pi$
$240$		0			0
$241$	−18.8572			−1.21470			−0.607348	−	0.794436i	$-0.707767\pi$
$241$	−18.8572			−1.21470			−0.607348	+	0.794436i	$0.707767\pi$
$242$		0			0
$243$	−6.30932	+	14.2546i	−0.404743	+	0.914430i
$244$		0			0
$245$	−8.97469	+	5.83693i	−0.573372	+	0.372908i
$246$		0			0
$247$	6.13897			0.390613
$248$		0			0
$249$	−10.7607	−	2.04785i	−0.681932	−	0.129777i
$250$		0			0
$251$	15.7016			0.991074			0.495537	−	0.868587i	$-0.334971\pi$
$251$	15.7016			0.991074			0.495537	+	0.868587i	$0.334971\pi$
$252$		0			0
$253$	−5.13419			−0.322784
$254$		0			0
$255$	0.525200	+	1.50605i	0.0328893	+	0.0943127i
$256$		0			0
$257$	9.21785			0.574993			0.287497	−	0.957782i	$-0.407177\pi$
$257$	9.21785			0.574993			0.287497	+	0.957782i	$0.407177\pi$
$258$		0			0
$259$	16.8881	+	16.0153i	1.04938	+	0.995143i
$260$		0			0
$261$	23.4791	−	18.6426i	1.45332	−	1.15395i
$262$		0			0
$263$	0.482621			0.0297597			0.0148799	−	0.999889i	$-0.495263\pi$
$263$	0.482621			0.0297597			0.0148799	+	0.999889i	$0.495263\pi$
$264$		0			0
$265$	6.11174	−	10.5859i	0.375442	−	0.650284i
$266$		0			0
$267$	−1.80762	−	0.344004i	−0.110624	−	0.0210527i
$268$		0			0
$269$	−3.94288	+	6.82927i	−0.240402	+	0.416388i	−0.960829	−	0.277143i	$-0.910612\pi$
$269$	−3.94288	+	6.82927i	−0.240402	+	0.416388i	0.720427	+	0.693531i	$0.243946\pi$
$270$		0			0
$271$	12.7947	+	22.1610i	0.777220	+	1.34618i	0.933538	+	0.358478i	$0.116704\pi$
$271$	12.7947	+	22.1610i	0.777220	+	1.34618i	−0.156318	+	0.987707i	$0.549963\pi$
$272$		0			0
$273$	−9.70268	−	13.4806i	−0.587233	−	0.815883i
$274$		0			0
$275$	−2.22356			−0.134086
$276$		0			0
$277$	8.36931			0.502863			0.251432	−	0.967875i	$-0.419099\pi$
$277$	8.36931			0.502863			0.251432	+	0.967875i	$0.419099\pi$
$278$		0			0
$279$	7.77296	−	6.17182i	0.465355	−	0.369497i
$280$		0			0
$281$	−0.551848	−	0.955828i	−0.0329205	−	0.0570199i	0.849096	−	0.528239i	$-0.177147\pi$
$281$	−0.551848	−	0.955828i	−0.0329205	−	0.0570199i	−0.882016	+	0.471219i	$0.843814\pi$
$282$		0			0
$283$	−1.45369	−	2.51786i	−0.0864128	−	0.149671i	0.819580	−	0.572965i	$-0.194207\pi$
$283$	−1.45369	−	2.51786i	−0.0864128	−	0.149671i	−0.905992	+	0.423294i	$0.860874\pi$
$284$		0			0
$285$	−4.40770	−	0.838820i	−0.261089	−	0.0496874i
$286$		0			0
$287$	4.33852	−	18.0984i	0.256095	−	1.06832i
$288$		0			0
$289$	8.31873	+	14.4085i	0.489337	+	0.847557i
$290$		0			0
$291$	−26.4199	−	5.02792i	−1.54876	−	0.294742i
$292$		0			0
$293$	−12.4381	+	21.5434i	−0.726642	+	1.25858i	0.231653	+	0.972798i	$0.425587\pi$
$293$	−12.4381	+	21.5434i	−0.726642	+	1.25858i	−0.958295	+	0.285782i	$0.907747\pi$
$294$		0			0
$295$	0.0997383	+	0.172752i	0.00580699	+	0.0100580i
$296$		0			0
$297$	−3.66919	−	2.32181i	−0.212908	−	0.134725i
$298$		0			0
$299$	−11.1344	+	19.2853i	−0.643918	+	1.11530i
$300$		0			0
$301$	3.25166	+	3.08361i	0.187423	+	0.177736i
$302$		0			0
$303$	22.0752	−	25.5970i	1.26819	−	1.47051i
$304$		0			0
$305$	−3.64522	+	6.31371i	−0.208725	+	0.361522i
$306$		0			0
$307$	−23.7968			−1.35816			−0.679078	−	0.734066i	$-0.737620\pi$
$307$	−23.7968			−1.35816			−0.679078	+	0.734066i	$0.737620\pi$
$308$		0			0
$309$	−2.06276	+	2.39184i	−0.117346	+	0.136067i
$310$		0			0
$311$	−9.35677	−	16.2064i	−0.530574	−	0.918981i	−0.999364	−	0.0356711i	$-0.988643\pi$
$311$	−9.35677	−	16.2064i	−0.530574	−	0.918981i	0.468790	−	0.883310i	$-0.344690\pi$
$312$		0			0
$313$	9.65797	−	16.7281i	0.545901	−	0.945527i	−0.452649	−	0.891689i	$-0.649521\pi$
$313$	9.65797	−	16.7281i	0.545901	−	0.945527i	0.998550	−	0.0538387i	$-0.0171457\pi$
$314$		0			0
$315$	5.12442	+	11.0046i	0.288729	+	0.620041i
$316$		0			0
$317$	0.897542	−	1.55459i	0.0504110	−	0.0873144i	−0.839719	−	0.543021i	$-0.817280\pi$
$317$	0.897542	−	1.55459i	0.0504110	−	0.0873144i	0.890130	+	0.455707i	$0.150614\pi$
$318$		0			0
$319$	4.17543	+	7.23205i	0.233779	+	0.404917i
$320$		0			0
$321$	−17.9366	−	3.41348i	−1.00112	−	0.190522i
$322$		0			0
$323$	1.01984			0.0567455
$324$		0			0
$325$	−4.82218	+	8.35226i	−0.267487	+	0.463300i
$326$		0			0
$327$	−7.19117	−	20.6213i	−0.397673	−	1.14036i
$328$		0			0
$329$	−5.22027	+	21.7767i	−0.287803	+	1.20059i
$330$		0			0
$331$	7.06833	−	12.2427i	0.388511	−	0.672920i	−0.603739	−	0.797182i	$-0.706323\pi$
$331$	7.06833	−	12.2427i	0.388511	−	0.672920i	0.992249	+	0.124262i	$0.0396563\pi$
$332$		0			0
$333$	20.6679	−	16.4106i	1.13260	−	0.899295i
$334$		0			0
$335$	−1.71547	−	2.97129i	−0.0937264	−	0.162339i
$336$		0			0
$337$	−2.94072	+	5.09348i	−0.160191	+	0.277459i	−0.934937	−	0.354813i	$-0.884544\pi$
$337$	−2.94072	+	5.09348i	−0.160191	+	0.277459i	0.774746	+	0.632273i	$0.217878\pi$
$338$		0			0
$339$	−8.85663	−	25.3971i	−0.481026	−	1.37938i
$340$		0			0
$341$	1.38231	+	2.39424i	0.0748565	+	0.129655i
$342$		0			0
$343$	12.0135	−	14.0952i	0.648670	−	0.761070i
$344$		0			0
$345$	10.6294	−	12.3252i	0.572270	−	0.663567i
$346$		0			0
$347$	3.17593	+	5.50087i	0.170493	+	0.295302i	0.938592	−	0.345028i	$-0.112131\pi$
$347$	3.17593	+	5.50087i	0.170493	+	0.295302i	−0.768099	+	0.640331i	$0.778797\pi$
$348$		0			0
$349$	10.4321	+	18.0689i	0.558416	+	0.967205i	0.997629	+	0.0688222i	$0.0219241\pi$
$349$	10.4321	+	18.0689i	0.558416	+	0.967205i	−0.439213	+	0.898383i	$0.644743\pi$
$350$		0			0
$351$	−16.6786	+	8.74717i	−0.890237	+	0.466889i
$352$		0			0
$353$	−2.14229			−0.114023			−0.0570114	−	0.998374i	$-0.518157\pi$
$353$	−2.14229			−0.114023			−0.0570114	+	0.998374i	$0.518157\pi$
$354$		0			0
$355$	14.3631			0.762314
$356$		0			0
$357$	−1.61187	−	2.23947i	−0.0853090	−	0.118526i
$358$		0			0
$359$	−10.6198	−	18.3940i	−0.560492	−	0.970800i	−0.997454	−	0.0713198i	$-0.977279\pi$
$359$	−10.6198	−	18.3940i	−0.560492	−	0.970800i	0.436962	−	0.899480i	$-0.356054\pi$
$360$		0			0
$361$	8.06557	−	13.9700i	0.424504	−	0.735262i
$362$		0			0
$363$	−11.6531	+	13.5122i	−0.611632	+	0.709207i
$364$		0			0
$365$	3.44811	−	5.97230i	0.180482	−	0.312605i
$366$		0			0
$367$	−32.4107			−1.69182			−0.845912	−	0.533323i	$-0.820943\pi$
$367$	−32.4107			−1.69182			−0.845912	+	0.533323i	$0.820943\pi$
$368$		0			0
$369$	−19.6279	−	7.75144i	−1.02179	−	0.403524i
$370$		0			0
$371$	−4.92935	+	20.5631i	−0.255919	+	1.06758i
$372$		0			0
$373$	33.6202			1.74079			0.870393	−	0.492358i	$-0.163865\pi$
$373$	33.6202			1.74079			0.870393	+	0.492358i	$0.163865\pi$
$374$		0			0
$375$	13.2537	−	15.3681i	0.684418	−	0.793606i
$376$		0			0
$377$	36.2206			1.86545
$378$		0			0
$379$	28.2829			1.45279			0.726396	−	0.687276i	$-0.241194\pi$
$379$	28.2829			1.45279			0.726396	+	0.687276i	$0.241194\pi$
$380$		0			0
$381$	−12.3261	+	14.2925i	−0.631485	+	0.732229i
$382$		0			0
$383$	−10.1895			−0.520657			−0.260329	−	0.965520i	$-0.583831\pi$
$383$	−10.1895			−0.520657			−0.260329	+	0.965520i	$0.583831\pi$
$384$		0			0
$385$	−3.24177	+	0.961457i	−0.165216	+	0.0490004i
$386$		0			0
$387$	3.97943	−	3.15971i	0.202286	−	0.160617i
$388$		0			0
$389$	10.4505			0.529861			0.264931	−	0.964267i	$-0.414651\pi$
$389$	10.4505			0.529861			0.264931	+	0.964267i	$0.414651\pi$
$390$		0			0
$391$	−1.84971	+	3.20379i	−0.0935437	+	0.162022i
$392$		0			0
$393$	22.0149	−	25.5270i	1.11050	−	1.28767i
$394$		0			0
$395$	12.0383	−	20.8509i	0.605710	−	1.04912i
$396$		0			0
$397$	−7.25033	−	12.5579i	−0.363884	−	0.630265i	0.624713	−	0.780855i	$-0.285216\pi$
$397$	−7.25033	−	12.5579i	−0.363884	−	0.630265i	−0.988596	+	0.150590i	$0.951883\pi$
$398$		0			0
$399$	7.72284	−	0.776904i	0.386626	−	0.0388938i
$400$		0			0
$401$	−25.4142			−1.26913			−0.634563	−	0.772871i	$-0.718820\pi$
$401$	−25.4142			−1.26913			−0.634563	+	0.772871i	$0.718820\pi$
$402$		0			0
$403$	11.9912			0.597322
$404$		0			0
$405$	13.1702	−	4.00141i	0.654432	−	0.198831i
$406$		0			0
$407$	3.67551	+	6.36617i	0.182188	+	0.315559i
$408$		0			0
$409$	−6.19535	−	10.7307i	−0.306340	−	0.530597i	0.671219	−	0.741259i	$-0.265771\pi$
$409$	−6.19535	−	10.7307i	−0.306340	−	0.530597i	−0.977559	+	0.210663i	$0.932438\pi$
$410$		0			0
$411$	13.8872	−	16.1026i	0.685004	−	0.794285i
$412$		0			0
$413$	−0.250392	−	0.237451i	−0.0123210	−	0.0116842i
$414$		0			0
$415$	4.83613	+	8.37642i	0.237396	+	0.411182i
$416$		0			0
$417$	7.35371	+	21.0874i	0.360113	+	1.03265i
$418$		0			0
$419$	−15.3596	+	26.6036i	−0.750365	+	1.29967i	0.197281	+	0.980347i	$0.436789\pi$
$419$	−15.3596	+	26.6036i	−0.750365	+	1.29967i	−0.947646	+	0.319323i	$0.896545\pi$
$420$		0			0
$421$	−2.88912	−	5.00410i	−0.140807	−	0.243885i	0.786994	−	0.616961i	$-0.211636\pi$
$421$	−2.88912	−	5.00410i	−0.140807	−	0.243885i	−0.927801	+	0.373076i	$0.878303\pi$
$422$		0			0
$423$	23.6170	+	9.32682i	1.14830	+	0.453486i
$424$		0			0
$425$	−0.801089	+	1.38753i	−0.0388585	+	0.0673049i
$426$		0			0
$427$	2.94001	−	12.2644i	0.142277	−	0.593518i
$428$		0			0
$429$	−1.72736	−	4.95334i	−0.0833977	−	0.239150i
$430$		0			0
$431$	−0.210278	+	0.364212i	−0.0101287	+	0.0175435i	−0.871045	−	0.491203i	$-0.836557\pi$
$431$	−0.210278	+	0.364212i	−0.0101287	+	0.0175435i	0.860917	+	0.508746i	$0.169891\pi$
$432$		0			0
$433$	30.8208			1.48115			0.740576	−	0.671972i	$-0.234553\pi$
$433$	30.8208			1.48115			0.740576	+	0.671972i	$0.234553\pi$
$434$		0			0
$435$	−26.0059	−	4.94913i	−1.24689	−	0.237293i
$436$		0			0
$437$	−5.20330	−	9.01237i	−0.248907	−	0.431120i
$438$		0			0
$439$	−1.50590	+	2.60830i	−0.0718729	+	0.124488i	−0.899722	−	0.436463i	$-0.856231\pi$
$439$	−1.50590	+	2.60830i	−0.0718729	+	0.124488i	0.827849	+	0.560951i	$0.189564\pi$
$440$		0			0
$441$	−13.9120	−	15.7307i	−0.662477	−	0.749082i
$442$		0			0
$443$	9.22141	−	15.9719i	0.438122	−	0.758850i	−0.559422	−	0.828883i	$-0.688977\pi$
$443$	9.22141	−	15.9719i	0.438122	−	0.758850i	0.997545	+	0.0700326i	$0.0223103\pi$
$444$		0			0
$445$	0.812388	+	1.40710i	0.0385109	+	0.0667028i
$446$		0			0
$447$	−20.4353	+	23.6954i	−0.966555	+	1.12075i
$448$		0			0
$449$	−6.80998			−0.321383			−0.160691	−	0.987005i	$-0.551372\pi$
$449$	−6.80998			−0.321383			−0.160691	+	0.987005i	$0.551372\pi$
$450$		0			0
$451$	2.93908	−	5.09064i	0.138396	−	0.239709i
$452$		0			0
$453$	9.72573	−	11.2773i	0.456955	−	0.529854i
$454$		0			0
$455$	−3.41886	+	14.2620i	−0.160278	+	0.668612i
$456$		0			0
$457$	−6.18283	+	10.7090i	−0.289220	+	0.500944i	−0.973624	−	0.228159i	$-0.926729\pi$
$457$	−6.18283	+	10.7090i	−0.289220	+	0.500944i	0.684403	+	0.729103i	$0.260063\pi$
$458$		0			0
$459$	−2.77074	+	1.45313i	−0.129327	+	0.0678263i
$460$		0			0
$461$	−16.3651	−	28.3453i	−0.762201	−	1.32017i	−0.941714	−	0.336415i	$-0.890786\pi$
$461$	−16.3651	−	28.3453i	−0.762201	−	1.32017i	0.179513	−	0.983756i	$-0.442548\pi$
$462$		0			0
$463$	9.61023	−	16.6454i	0.446625	−	0.773577i	−0.551539	−	0.834149i	$-0.685959\pi$
$463$	9.61023	−	16.6454i	0.446625	−	0.773577i	0.998164	+	0.0605719i	$0.0192924\pi$
$464$		0			0
$465$	−8.60948	−	1.63845i	−0.399255	−	0.0759815i
$466$		0			0
$467$	1.50855	+	2.61289i	0.0698075	+	0.120910i	0.898816	−	0.438325i	$-0.144428\pi$
$467$	1.50855	+	2.61289i	0.0698075	+	0.120910i	−0.829009	+	0.559235i	$0.811095\pi$
$468$		0			0
$469$	4.30669	+	4.08411i	0.198864	+	0.188587i
$470$		0			0
$471$	−5.43405	−	1.03414i	−0.250388	−	0.0476509i
$472$		0			0
$473$	0.707687	+	1.22575i	0.0325395	+	0.0563600i
$474$		0			0
$475$	−2.25349	−	3.90316i	−0.103397	−	0.179089i
$476$		0			0
$477$	22.3009	+	8.80705i	1.02109	+	0.403247i
$478$		0			0
$479$	−25.8972			−1.18327			−0.591635	−	0.806206i	$-0.701518\pi$
$479$	−25.8972			−1.18327			−0.591635	+	0.806206i	$0.701518\pi$
$480$		0			0
$481$	31.8839			1.45378
$482$		0			0
$483$	−11.5665	+	25.6701i	−0.526293	+	1.16803i
$484$		0			0
$485$	11.8738	+	20.5659i	0.539159	+	0.933851i
$486$		0			0
$487$	−20.8841	+	36.1724i	−0.946350	+	1.63913i	−0.193326	+	0.981135i	$0.561927\pi$
$487$	−20.8841	+	36.1724i	−0.946350	+	1.63913i	−0.753025	+	0.657992i	$0.771406\pi$
$488$		0			0
$489$	6.96970	+	1.32639i	0.315181	+	0.0599815i
$490$		0			0
$491$	−13.9879	+	24.2278i	−0.631265	+	1.09338i	0.356028	+	0.934475i	$0.384131\pi$
$491$	−13.9879	+	24.2278i	−0.631265	+	1.09338i	−0.987293	+	0.158908i	$0.949203\pi$
$492$		0			0
$493$	6.01717			0.271000
$494$		0			0
$495$	0.563402	+	3.79246i	0.0253231	+	0.170458i
$496$		0			0
$497$	−23.8214	+	7.06506i	−1.06854	+	0.316911i
$498$		0			0
$499$	−24.9497			−1.11690			−0.558450	−	0.829538i	$-0.688604\pi$
$499$	−24.9497			−1.11690			−0.558450	+	0.829538i	$0.688604\pi$
$500$		0			0
$501$	−9.40879	−	26.9805i	−0.420354	−	1.20540i
$502$		0			0
$503$	34.1966			1.52475			0.762376	−	0.647135i	$-0.224033\pi$
$503$	34.1966			1.52475			0.762376	+	0.647135i	$0.224033\pi$
$504$		0			0
$505$	−29.8465			−1.32815
$506$		0			0
$507$	−0.232421	−	0.0442316i	−0.0103222	−	0.00196440i
$508$		0			0
$509$	13.6868			0.606659			0.303329	−	0.952886i	$-0.401902\pi$
$509$	13.6868			0.606659			0.303329	+	0.952886i	$0.401902\pi$
$510$		0			0
$511$	−2.78103	+	11.6012i	−0.123026	+	0.513209i
$512$		0			0
$513$	0.357043	−	8.79383i	0.0157638	−	0.388257i
$514$		0			0
$515$	2.78893			0.122895
$516$		0			0
$517$	−3.53641	+	6.12525i	−0.155531	+	0.269388i
$518$		0			0
$519$	−7.31231	−	20.9686i	−0.320975	−	0.920422i
$520$		0			0
$521$	−13.3748	+	23.1658i	−0.585960	+	1.01491i	0.408795	+	0.912626i	$0.365949\pi$
$521$	−13.3748	+	23.1658i	−0.585960	+	1.01491i	−0.994755	+	0.102286i	$0.967384\pi$
$522$		0			0
$523$	−10.6131	−	18.3824i	−0.464079	−	0.803808i	0.535081	−	0.844801i	$-0.320281\pi$
$523$	−10.6131	−	18.3824i	−0.464079	−	0.803808i	−0.999159	+	0.0409928i	$0.986948\pi$
$524$		0			0
$525$	−5.00932	+	11.1174i	−0.218625	+	0.485205i
$526$		0			0
$527$	1.99204			0.0867746
$528$		0			0
$529$	14.7493			0.641275
$530$		0			0
$531$	−0.306434	+	0.243312i	−0.0132981	+	0.0105588i
$532$		0			0
$533$	−12.7478	−	22.0799i	−0.552170	−	0.956386i
$534$		0			0
$535$	8.06116	+	13.9623i	0.348514	+	0.603644i
$536$		0			0
$537$	13.5452	+	38.8420i	0.584520	+	1.67616i
$538$		0			0
$539$	4.90359	−	3.18918i	0.211213	−	0.137368i
$540$		0			0
$541$	10.1269	+	17.5402i	0.435388	+	0.754114i	0.997327	−	0.0730646i	$-0.0232779\pi$
$541$	10.1269	+	17.5402i	0.435388	+	0.754114i	−0.561939	+	0.827178i	$0.689945\pi$
$542$		0			0
$543$	−18.1266	+	21.0184i	−0.777885	+	0.901984i
$544$		0			0
$545$	−9.64201	+	16.7005i	−0.413019	+	0.715369i
$546$		0			0
$547$	−21.9668	−	38.0476i	−0.939233	−	1.62680i	−0.766906	−	0.641760i	$-0.778205\pi$
$547$	−21.9668	−	38.0476i	−0.939233	−	1.62680i	−0.172327	−	0.985040i	$-0.555129\pi$
$548$		0			0
$549$	−13.3009	−	5.25278i	−0.567669	−	0.224183i
$550$		0			0
$551$	−8.46326	+	14.6588i	−0.360547	+	0.624486i
$552$		0			0
$553$	−9.70931	+	40.5030i	−0.412882	+	1.72236i
$554$		0			0
$555$	−22.8922	−	4.35658i	−0.971721	−	0.184926i
$556$		0			0
$557$	−4.45483	+	7.71599i	−0.188757	+	0.326937i	−0.944836	−	0.327544i	$-0.893779\pi$
$557$	−4.45483	+	7.71599i	−0.188757	+	0.326937i	0.756079	+	0.654480i	$0.227113\pi$
$558$		0			0
$559$	6.13897			0.259651
$560$		0			0
$561$	−0.286959	−	0.822878i	−0.0121154	−	0.0347419i
$562$		0			0
$563$	14.2096	+	24.6118i	0.598865	+	1.03726i	0.992989	+	0.118207i	$0.0377146\pi$
$563$	14.2096	+	24.6118i	0.598865	+	1.03726i	−0.394124	+	0.919057i	$0.628952\pi$
$564$		0			0
$565$	−11.8751	+	20.5683i	−0.499589	+	0.865313i
$566$		0			0
$567$	−19.8747	+	13.1147i	−0.834660	+	0.550765i
$568$		0			0
$569$	4.28948	−	7.42959i	0.179824	−	0.311465i	−0.761996	−	0.647582i	$-0.775780\pi$
$569$	4.28948	−	7.42959i	0.179824	−	0.311465i	0.941820	+	0.336117i	$0.109114\pi$
$570$		0			0
$571$	−9.68861	−	16.7812i	−0.405456	−	0.702270i	0.588919	−	0.808192i	$-0.299554\pi$
$571$	−9.68861	−	16.7812i	−0.405456	−	0.702270i	−0.994374	+	0.105922i	$0.966221\pi$
$572$		0			0
$573$	−6.16495	−	17.6785i	−0.257545	−	0.738530i
$574$		0			0
$575$	16.3488			0.681793
$576$		0			0
$577$	0.584441	−	1.01228i	0.0243306	−	0.0421418i	−0.853604	−	0.520923i	$-0.825588\pi$
$577$	0.584441	−	1.01228i	0.0243306	−	0.0421418i	0.877934	+	0.478781i	$0.158921\pi$
$578$		0			0
$579$	−1.27658	−	0.242943i	−0.0530528	−	0.0100964i
$580$		0			0
$581$	−12.1411	−	11.5136i	−0.503697	−	0.477664i
$582$		0			0
$583$	−3.33934	+	5.78390i	−0.138301	+	0.239545i
$584$		0			0
$585$	15.4673	+	6.10832i	0.639493	+	0.252548i
$586$		0			0
$587$	−15.5863	−	26.9963i	−0.643316	−	1.11426i	−0.984688	−	0.174327i	$-0.944225\pi$
$587$	−15.5863	−	26.9963i	−0.643316	−	1.11426i	0.341372	−	0.939928i	$-0.389108\pi$
$588$		0			0
$589$	−2.80184	+	4.85293i	−0.115448	+	0.199962i
$590$		0			0
$591$	11.6722	−	13.5343i	0.480132	−	0.556729i
$592$		0			0
$593$	−15.1887	−	26.3075i	−0.623724	−	1.08032i	−0.988786	−	0.149338i	$-0.952286\pi$
$593$	−15.1887	−	26.3075i	−0.623724	−	1.08032i	0.365062	−	0.930983i	$-0.381048\pi$
$594$		0			0
$595$	−0.567960	+	2.36928i	−0.0232841	+	0.0971311i
$596$		0			0
$597$	3.25577	+	9.33617i	0.133250	+	0.382104i
$598$		0			0
$599$	3.65379	+	6.32855i	0.149290	+	0.258577i	0.930965	−	0.365108i	$-0.118968\pi$
$599$	3.65379	+	6.32855i	0.149290	+	0.258577i	−0.781675	+	0.623685i	$0.785635\pi$
$600$		0			0
$601$	4.61461	+	7.99274i	0.188234	+	0.326031i	0.944661	−	0.328047i	$-0.106390\pi$
$601$	4.61461	+	7.99274i	0.188234	+	0.326031i	−0.756428	+	0.654077i	$0.773057\pi$
$602$		0			0
$603$	5.27059	−	4.18491i	0.214635	−	0.170423i
$604$		0			0
$605$	15.7555			0.640552
$606$		0			0
$607$	−17.0674			−0.692744			−0.346372	−	0.938097i	$-0.612587\pi$
$607$	−17.0674			−0.692744			−0.346372	+	0.938097i	$0.612587\pi$
$608$		0			0
$609$	45.5656	−	4.58382i	1.84641	−	0.185746i
$610$		0			0
$611$	15.3387	+	26.5673i	0.620536	+	1.07480i
$612$		0			0
$613$	−0.393059	+	0.680797i	−0.0158755	+	0.0274972i	−0.873854	−	0.486188i	$-0.838387\pi$
$613$	−0.393059	+	0.680797i	−0.0158755	+	0.0274972i	0.857979	+	0.513686i	$0.171720\pi$
$614$		0			0
$615$	6.13580	+	17.5949i	0.247419	+	0.709495i
$616$		0			0
$617$	23.7960	−	41.2159i	0.957991	−	1.65929i	0.230621	−	0.973044i	$-0.425924\pi$
$617$	23.7960	−	41.2159i	0.957991	−	1.65929i	0.727370	−	0.686246i	$-0.240743\pi$
$618$		0			0
$619$	18.9743			0.762643			0.381321	−	0.924443i	$-0.375469\pi$
$619$	18.9743			0.762643			0.381321	+	0.924443i	$0.375469\pi$
$620$		0			0
$621$	26.9779	+	17.0712i	1.08258	+	0.685044i
$622$		0			0
$623$	−2.03950	−	1.93409i	−0.0817107	−	0.0774876i
$624$		0			0
$625$	−4.61488			−0.184595
$626$		0			0
$627$	2.40828	+	0.458315i	0.0961773	+	0.0183033i
$628$		0			0
$629$	5.29674			0.211195
$630$		0			0
$631$	0.300343			0.0119565			0.00597823	−	0.999982i	$-0.498097\pi$
$631$	0.300343			0.0119565			0.00597823	+	0.999982i	$0.498097\pi$
$632$		0			0
$633$	−3.11456	−	8.93125i	−0.123793	−	0.354985i
$634$		0			0
$635$	16.6653			0.661344
$636$		0			0
$637$	−1.34510	−	25.3354i	−0.0532946	−	1.00383i
$638$		0			0
$639$	4.14004	+	27.8680i	0.163778	+	1.10244i
$640$		0			0
$641$	28.1096			1.11026			0.555131	−	0.831763i	$-0.312668\pi$
$641$	28.1096			1.11026			0.555131	+	0.831763i	$0.312668\pi$
$642$		0			0
$643$	−1.55289	+	2.68968i	−0.0612399	+	0.106071i	−0.895020	−	0.446026i	$-0.852839\pi$
$643$	−1.55289	+	2.68968i	−0.0612399	+	0.106071i	0.833780	+	0.552097i	$0.186172\pi$
$644$		0			0
$645$	−4.40770	−	0.838820i	−0.173553	−	0.0330285i
$646$		0			0
$647$	23.3556	−	40.4532i	0.918205	−	1.59038i	0.116066	−	0.993242i	$-0.462972\pi$
$647$	23.3556	−	40.4532i	0.918205	−	1.59038i	0.802140	−	0.597137i	$-0.203695\pi$
$648$		0			0
$649$	−0.0544950	−	0.0943881i	−0.00213912	−	0.00370506i
$650$		0			0
$651$	15.0849	−	1.51751i	0.591224	−	0.0594761i
$652$		0			0
$653$	−1.99753			−0.0781693			−0.0390847	−	0.999236i	$-0.512444\pi$
$653$	−1.99753			−0.0781693			−0.0390847	+	0.999236i	$0.512444\pi$
$654$		0			0
$655$	−29.7649			−1.16301
$656$		0			0
$657$	12.5817	+	4.96874i	0.490858	+	0.193849i
$658$		0			0
$659$	8.37284	+	14.5022i	0.326160	+	0.564925i	0.981746	−	0.190195i	$-0.0609120\pi$
$659$	8.37284	+	14.5022i	0.326160	+	0.564925i	−0.655587	+	0.755120i	$0.727579\pi$
$660$		0			0
$661$	−6.28870	−	10.8924i	−0.244602	−	0.423664i	0.717417	−	0.696644i	$-0.245324\pi$
$661$	−6.28870	−	10.8924i	−0.244602	−	0.423664i	−0.962020	+	0.272980i	$0.911991\pi$
$662$		0			0
$663$	−3.71326	−	0.706663i	−0.144211	−	0.0274445i
$664$		0			0
$665$	−4.97311	−	4.71608i	−0.192849	−	0.182882i
$666$		0			0
$667$	−30.7000	−	53.1740i	−1.18871	−	2.05890i
$668$		0			0
$669$	−30.6453	−	5.83204i	−1.18481	−	0.225480i
$670$		0			0
$671$	1.99168	−	3.44969i	0.0768878	−	0.133174i
$672$		0			0
$673$	23.8175	+	41.2531i	0.918096	+	1.59019i	0.802304	+	0.596916i	$0.203607\pi$
$673$	23.8175	+	41.2531i	0.918096	+	1.59019i	0.115792	+	0.993273i	$0.463059\pi$
$674$		0			0
$675$	11.6838	+	7.39336i	0.449711	+	0.284570i
$676$		0			0
$677$	4.54664	−	7.87500i	0.174741	−	0.302661i	−0.765330	−	0.643638i	$-0.777424\pi$
$677$	4.54664	−	7.87500i	0.174741	−	0.302661i	0.940072	+	0.340977i	$0.110758\pi$
$678$		0			0
$679$	−29.8090	−	28.2684i	−1.14396	−	1.08484i
$680$		0			0
$681$	−20.5582	+	23.8379i	−0.787790	+	0.913469i
$682$		0			0
$683$	2.41674	−	4.18592i	0.0924741	−	0.160170i	−0.816078	−	0.577942i	$-0.803856\pi$
$683$	2.41674	−	4.18592i	0.0924741	−	0.160170i	0.908552	+	0.417773i	$0.137189\pi$
$684$		0			0
$685$	−18.7760			−0.717393
$686$		0			0
$687$	−17.4517	+	20.2359i	−0.665825	+	0.772047i
$688$		0			0
$689$	14.4839	+	25.0868i	0.551791	+	0.955730i
$690$		0			0
$691$	5.39228	−	9.33969i	0.205132	−	0.355299i	−0.745043	−	0.667017i	$-0.767571\pi$
$691$	5.39228	−	9.33969i	0.205132	−	0.355299i	0.950175	+	0.311718i	$0.100904\pi$
$692$		0			0
$693$	−2.79988	−	6.01272i	−0.106359	−	0.228404i
$694$		0			0
$695$	9.85995	−	17.0779i	0.374009	−	0.647803i
$696$		0			0
$697$	−2.11774	−	3.66804i	−0.0802152	−	0.138937i
$698$		0			0
$699$	−10.9200	−	2.07817i	−0.413033	−	0.0786036i
$700$		0			0
$701$	−31.8393			−1.20255			−0.601276	−	0.799041i	$-0.705341\pi$
$701$	−31.8393			−1.20255			−0.601276	+	0.799041i	$0.705341\pi$
$702$		0			0
$703$	−7.44997	+	12.9037i	−0.280981	+	0.486673i
$704$		0			0
$705$	−7.38282	−	21.1708i	−0.278053	−	0.797340i
$706$		0			0
$707$	49.5010	−	14.6812i	1.86168	−	0.552144i
$708$		0			0
$709$	13.6032	−	23.5614i	0.510879	−	0.884868i	−0.489042	−	0.872260i	$-0.662653\pi$
$709$	13.6032	−	23.5614i	0.510879	−	0.884868i	0.999921	−	0.0126076i	$-0.00401324\pi$
$710$		0			0
$711$	43.9259	+	17.3472i	1.64735	+	0.650570i
$712$		0			0
$713$	−10.1635	−	17.6037i	−0.380627	−	0.659265i
$714$		0			0
$715$	−2.31607	+	4.01154i	−0.0866160	+	0.150023i
$716$		0			0
$717$	2.66134	+	7.63162i	0.0993897	+	0.285008i
$718$		0			0
$719$	−14.4549	−	25.0366i	−0.539076	−	0.933707i	−0.998954	−	0.0457252i	$-0.985440\pi$
$719$	−14.4549	−	25.0366i	−0.539076	−	0.933707i	0.459878	−	0.887982i	$-0.347893\pi$
$720$		0			0
$721$	−4.62549	+	1.37185i	−0.172262	+	0.0510902i
$722$		0			0
$723$	−21.3309	+	24.7339i	−0.793306	+	0.919865i
$724$		0			0
$725$	−13.2958	−	23.0291i	−0.493795	−	0.855278i
$726$		0			0
$727$	4.29978	+	7.44744i	0.159470	+	0.276210i	0.934678	−	0.355496i	$-0.115688\pi$
$727$	4.29978	+	7.44744i	0.159470	+	0.276210i	−0.775208	+	0.631706i	$0.782355\pi$
$728$		0			0
$729$	11.5599	+	24.4002i	0.428146	+	0.903710i
$730$		0			0
$731$	1.01984			0.0377202
$732$		0			0
$733$	−45.5506			−1.68245			−0.841225	−	0.540685i	$-0.818165\pi$
$733$	−45.5506			−1.68245			−0.841225	+	0.540685i	$0.818165\pi$
$734$		0			0
$735$	−2.49604	+	18.3743i	−0.0920678	+	0.677746i
$736$		0			0
$737$	0.937301	+	1.62345i	0.0345259	+	0.0598007i
$738$		0			0
$739$	6.34491	−	10.9897i	0.233401	−	0.404263i	−0.725405	−	0.688322i	$-0.758348\pi$
$739$	6.34491	−	10.9897i	0.233401	−	0.404263i	0.958807	+	0.284059i	$0.0916811\pi$
$740$		0			0
$741$	6.94431	−	8.05216i	0.255106	−	0.295804i
$742$		0			0
$743$	−5.04492	+	8.73806i	−0.185080	+	0.320568i	−0.943604	−	0.331078i	$-0.892588\pi$
$743$	−5.04492	+	8.73806i	−0.185080	+	0.320568i	0.758523	+	0.651646i	$0.225921\pi$
$744$		0			0
$745$	27.6292			1.01226
$746$		0			0
$747$	−14.8584	+	11.7978i	−0.543641	+	0.431657i
$748$		0			0
$749$	−20.2375	−	19.1916i	−0.739462	−	0.701244i
$750$		0			0
$751$	5.00713			0.182713			0.0913565	−	0.995818i	$-0.470880\pi$
$751$	5.00713			0.182713			0.0913565	+	0.995818i	$0.470880\pi$
$752$		0			0
$753$	17.7614	−	20.5949i	0.647261	−	0.750521i
$754$		0			0
$755$	−13.1495			−0.478561
$756$		0			0
$757$	6.83620			0.248466			0.124233	−	0.992253i	$-0.460353\pi$
$757$	6.83620			0.248466			0.124233	+	0.992253i	$0.460353\pi$
$758$		0			0
$759$	−5.80772	+	6.73424i	−0.210807	+	0.244438i
$760$		0			0
$761$	26.8753			0.974231			0.487115	−	0.873338i	$-0.338049\pi$
$761$	26.8753			0.974231			0.487115	+	0.873338i	$0.338049\pi$
$762$		0			0
$763$	7.77665	−	32.4408i	0.281534	−	1.17444i
$764$		0			0
$765$	2.56951	+	1.01475i	0.0929008	+	0.0366883i
$766$		0			0
$767$	−0.472728			−0.0170692
$768$		0			0
$769$	−2.00631	+	3.47503i	−0.0723493	+	0.125313i	−0.899931	−	0.436033i	$-0.856383\pi$
$769$	−2.00631	+	3.47503i	−0.0723493	+	0.125313i	0.827581	+	0.561346i	$0.189716\pi$
$770$		0			0
$771$	10.4271	−	12.0906i	0.375523	−	0.435431i
$772$		0			0
$773$	−13.6861	+	23.7051i	−0.492256	+	0.852612i	−0.999960	−	0.00891927i	$-0.997161\pi$
$773$	−13.6861	+	23.7051i	−0.492256	+	0.852612i	0.507704	+	0.861531i	$0.330494\pi$
$774$		0			0
$775$	−4.40171	−	7.62399i	−0.158114	−	0.273862i
$776$		0			0
$777$	40.1101	−	4.03500i	1.43894	−	0.144755i
$778$		0			0
$779$	11.9146			0.426884
$780$		0			0
$781$	−7.84771			−0.280813
$782$		0			0
$783$	2.10659	−	51.8845i	0.0752834	−	1.85420i
$784$		0			0
$785$	2.44220	+	4.23001i	0.0871658	+	0.150976i
$786$		0			0
$787$	6.43636	+	11.1481i	0.229432	+	0.397387i	0.957640	−	0.287969i	$-0.0929799\pi$
$787$	6.43636	+	11.1481i	0.229432	+	0.397387i	−0.728208	+	0.685356i	$0.759647\pi$
$788$		0			0
$789$	0.545934	−	0.633029i	0.0194358	−	0.0225364i
$790$		0			0
$791$	9.57771	−	39.9540i	0.340544	−	1.42060i
$792$		0			0
$793$	−8.63860	−	14.9625i	−0.306766	−	0.531334i
$794$		0			0
$795$	−6.97139	−	19.9910i	−0.247250	−	0.709008i
$796$		0			0
$797$	−8.71139	+	15.0886i	−0.308573	+	0.534465i	−0.978050	−	0.208368i	$-0.933185\pi$
$797$	−8.71139	+	15.0886i	−0.308573	+	0.534465i	0.669477	+	0.742833i	$0.266518\pi$
$798$		0			0
$799$	2.54815	+	4.41352i	0.0901469	+	0.156139i
$800$		0			0
$801$	−2.49596	+	1.98182i	−0.0881905	+	0.0700243i
$802$		0			0
$803$	−1.88398	+	3.26315i	−0.0664842	+	0.115154i
$804$		0			0
$805$	23.8352	−	7.06915i	0.840081	−	0.249155i
$806$		0			0
$807$	4.49746	+	12.8968i	0.158318	+	0.453990i
$808$		0			0
$809$	−3.04097	+	5.26712i	−0.106915	+	0.185182i	−0.914519	−	0.404543i	$-0.867431\pi$
$809$	−3.04097	+	5.26712i	−0.106915	+	0.185182i	0.807604	+	0.589725i	$0.200764\pi$
$810$		0			0
$811$	14.6219			0.513443			0.256722	−	0.966485i	$-0.417358\pi$
$811$	14.6219			0.513443			0.256722	+	0.966485i	$0.417358\pi$
$812$		0			0
$813$	43.5405	+	8.28612i	1.52703	+	0.290607i
$814$		0			0
$815$	−3.13236	−	5.42540i	−0.109722	−	0.190044i
$816$		0			0
$817$	−1.43443	+	2.48450i	−0.0501842	+	0.0869216i
$818$		0			0
$819$	−28.6573	−	2.52255i	−1.00137	−	0.0881452i
$820$		0			0
$821$	4.87162	−	8.43789i	0.170021	−	0.294484i	−0.768406	−	0.639962i	$-0.778950\pi$
$821$	4.87162	−	8.43789i	0.170021	−	0.294484i	0.938427	+	0.345478i	$0.112283\pi$
$822$		0			0
$823$	−5.38983	−	9.33546i	−0.187878	−	0.325414i	0.756665	−	0.653803i	$-0.226827\pi$
$823$	−5.38983	−	9.33546i	−0.187878	−	0.325414i	−0.944542	+	0.328389i	$0.893494\pi$
$824$		0			0
$825$	−2.51526	+	2.91653i	−0.0875702	+	0.101541i
$826$		0			0
$827$	13.0521			0.453867			0.226933	−	0.973910i	$-0.427130\pi$
$827$	13.0521			0.453867			0.226933	+	0.973910i	$0.427130\pi$
$828$		0			0
$829$	24.5548	−	42.5301i	0.852822	−	1.47713i	−0.0258286	−	0.999666i	$-0.508222\pi$
$829$	24.5548	−	42.5301i	0.852822	−	1.47713i	0.878651	−	0.477465i	$-0.158444\pi$
$830$		0			0
$831$	9.46724	−	10.9776i	0.328415	−	0.380808i
$832$		0			0
$833$	−0.223455	−	4.20887i	−0.00774226	−	0.145829i
$834$		0			0
$835$	−12.6154	+	21.8506i	−0.436575	+	0.756170i
$836$		0			0
$837$	0.697406	−	17.1769i	0.0241059	−	0.593719i
$838$		0			0
$839$	−12.0830	−	20.9284i	−0.417151	−	0.722527i	0.578500	−	0.815682i	$-0.303638\pi$
$839$	−12.0830	−	20.9284i	−0.417151	−	0.722527i	−0.995652	+	0.0931549i	$0.970305\pi$
$840$		0			0
$841$	−35.4341	+	61.3737i	−1.22187	+	2.11633i
$842$		0			0
$843$	−1.87795	−	0.357390i	−0.0646801	−	0.0123092i
$844$		0			0
$845$	0.104456	+	0.180923i	0.00359339	+	0.00622393i
$846$		0			0
$847$	−26.1307	+	7.74997i	−0.897862	+	0.266292i
$848$		0			0
$849$	−4.94694	−	0.941443i	−0.169778	−	0.0323102i
$850$		0			0
$851$	−27.0243	−	46.8075i	−0.926382	−	1.60454i
$852$		0			0
$853$	2.72681	+	4.72297i	0.0933641	+	0.161711i	0.908925	−	0.416960i	$-0.136905\pi$
$853$	2.72681	+	4.72297i	0.0933641	+	0.161711i	−0.815561	+	0.578672i	$0.803571\pi$
$854$		0			0
$855$	−6.08616	+	4.83248i	−0.208142	+	0.165267i
$856$		0			0
$857$	32.8388			1.12175			0.560876	−	0.827900i	$-0.310464\pi$
$857$	32.8388			1.12175			0.560876	+	0.827900i	$0.310464\pi$
$858$		0			0
$859$	52.6598			1.79673			0.898365	−	0.439249i	$-0.144755\pi$
$859$	52.6598			1.79673			0.898365	+	0.439249i	$0.144755\pi$
$860$		0			0
$861$	−18.8311	−	26.1633i	−0.641762	−	0.891643i
$862$		0			0
$863$	24.4095	+	42.2784i	0.830908	+	1.43917i	0.897319	+	0.441382i	$0.145512\pi$
$863$	24.4095	+	42.2784i	0.830908	+	1.43917i	−0.0664116	+	0.997792i	$0.521155\pi$
$864$		0			0
$865$	−9.80445	+	16.9818i	−0.333361	+	0.577398i
$866$		0			0
$867$	28.3089	+	5.38740i	0.961419	+	0.182966i
$868$		0			0
$869$	−6.57746	+	11.3925i	−0.223125	+	0.386464i
$870$		0			0
$871$	8.13080			0.275502
$872$		0			0
$873$	−36.4806	+	28.9661i	−1.23468	+	0.980353i
$874$		0			0
$875$	29.7198	−	8.81442i	1.00471	−	0.297982i
$876$		0			0
$877$	−25.0745			−0.846706			−0.423353	−	0.905965i	$-0.639147\pi$
$877$	−25.0745			−0.846706			−0.423353	+	0.905965i	$0.639147\pi$
$878$		0			0
$879$	14.1876	+	40.6840i	0.478535	+	1.37224i
$880$		0			0
$881$	−16.2437			−0.547263			−0.273632	−	0.961835i	$-0.588225\pi$
$881$	−16.2437			−0.547263			−0.273632	+	0.961835i	$0.588225\pi$
$882$		0			0
$883$	29.7137			0.999945			0.499973	−	0.866041i	$-0.333343\pi$
$883$	29.7137			0.999945			0.499973	+	0.866041i	$0.333343\pi$
$884$		0			0
$885$	0.339412	+	0.0645928i	0.0114092	+	0.00217126i
$886$		0			0
$887$	−15.7471			−0.528734			−0.264367	−	0.964422i	$-0.585163\pi$
$887$	−15.7471			−0.528734			−0.264367	+	0.964422i	$0.585163\pi$
$888$		0			0
$889$	−27.6397	+	8.19752i	−0.927007	+	0.274936i
$890$		0			0
$891$	−7.19593	+	2.18629i	−0.241073	+	0.0732434i
$892$		0			0
$893$	−14.3361			−0.479738
$894$		0			0
$895$	18.1616	−	31.4568i	0.607076	−	1.05149i
$896$		0			0
$897$	12.7005	+	36.4196i	0.424057	+	1.21602i
$898$		0			0
$899$	−16.5312	+	28.6328i	−0.551345	+	0.954957i
$900$		0			0
$901$	2.40614	+	4.16756i	0.0801602	+	0.138842i
$902$		0			0
$903$	7.72284	−	0.776904i	0.257000	−	0.0258537i
$904$		0			0
$905$	24.5078			0.814666
$906$		0			0
$907$	−2.58003			−0.0856684			−0.0428342	−	0.999082i	$-0.513639\pi$
$907$	−2.58003			−0.0856684			−0.0428342	+	0.999082i	$0.513639\pi$
$908$		0			0
$909$	−8.60302	−	57.9099i	−0.285344	−	1.92075i
$910$		0			0
$911$	23.2170	+	40.2130i	0.769214	+	1.33232i	0.937990	+	0.346663i	$0.112685\pi$
$911$	23.2170	+	40.2130i	0.769214	+	1.33232i	−0.168776	+	0.985654i	$0.553981\pi$
$912$		0			0
$913$	−2.64236	−	4.57671i	−0.0874495	−	0.151467i
$914$		0			0
$915$	4.15794	+	11.9232i	0.137457	+	0.394170i
$916$		0			0
$917$	49.3656	−	14.6411i	1.63020	−	0.483490i
$918$		0			0
$919$	−2.84387	−	4.92572i	−0.0938106	−	0.162485i	0.815301	−	0.579037i	$-0.196571\pi$
$919$	−2.84387	−	4.92572i	−0.0938106	−	0.162485i	−0.909112	+	0.416553i	$0.863238\pi$
$920$		0			0
$921$	−26.9186	+	31.2130i	−0.886999	+	1.02850i
$922$		0			0
$923$	−17.0191	+	29.4780i	−0.560191	+	0.970279i
$924$		0			0
$925$	−11.7040	−	20.2718i	−0.384824	−	0.666534i
$926$		0			0
$927$	0.803886	+	5.41123i	0.0264031	+	0.177728i
$928$		0			0
$929$	−23.9803	+	41.5350i	−0.786767	+	1.36272i	0.141172	+	0.989985i	$0.454913\pi$
$929$	−23.9803	+	41.5350i	−0.786767	+	1.36272i	−0.927938	+	0.372734i	$0.878420\pi$
$930$		0			0
$931$	10.5678	+	5.37548i	0.346345	+	0.176174i
$932$		0			0
$933$	−31.8413	−	6.05967i	−1.04244	−	0.198385i
$934$		0			0
$935$	−0.384758	+	0.666421i	−0.0125829	+	0.0217943i
$936$		0			0
$937$	−25.3542			−0.828285			−0.414142	−	0.910212i	$-0.635918\pi$
$937$	−25.3542			−0.828285			−0.414142	+	0.910212i	$0.635918\pi$
$938$		0			0
$939$	−11.0164	−	31.5904i	−0.359507	−	1.03091i
$940$		0			0
$941$	−1.25651	−	2.17634i	−0.0409611	−	0.0709468i	0.844818	−	0.535054i	$-0.179709\pi$
$941$	−1.25651	−	2.17634i	−0.0409611	−	0.0709468i	−0.885779	+	0.464107i	$0.846375\pi$
$942$		0			0
$943$	−21.6097	+	37.4292i	−0.703710	+	1.21886i
$944$		0			0
$945$	20.2309	+	5.72686i	0.658111	+	0.186295i
$946$		0			0
$947$	−7.26537	+	12.5840i	−0.236093	+	0.408925i	−0.959590	−	0.281403i	$-0.909200\pi$
$947$	−7.26537	+	12.5840i	−0.236093	+	0.408925i	0.723497	+	0.690328i	$0.242534\pi$
$948$		0			0
$949$	8.17147	+	14.1534i	0.265257	+	0.459439i
$950$		0			0
$951$	−1.02379	−	2.93579i	−0.0331985	−	0.0951994i
$952$		0			0
$953$	−36.5564			−1.18418			−0.592089	−	0.805873i	$-0.701697\pi$
$953$	−36.5564			−1.18418			−0.592089	+	0.805873i	$0.701697\pi$
$954$		0			0
$955$	−8.26605	+	14.3172i	−0.267483	+	0.463294i
$956$		0			0
$957$	14.2091	+	2.70410i	0.459315	+	0.0874113i
$958$		0			0
$959$	31.1403	−	9.23571i	1.00557	−	0.298237i
$960$		0			0
$961$	10.0272	−	17.3676i	0.323458	−	0.560246i
$962$		0			0
$963$	−24.7669	+	19.6652i	−0.798103	+	0.633703i
$964$		0			0
$965$	0.573726	+	0.993722i	0.0184689	+	0.0319890i
$966$		0			0
$967$	8.06111	−	13.9623i	0.259228	−	0.448996i	−0.706807	−	0.707406i	$-0.749865\pi$
$967$	8.06111	−	13.9623i	0.259228	−	0.448996i	0.966035	+	0.258410i	$0.0831986\pi$
$968$		0			0
$969$	1.15363	−	1.33767i	0.0370599	−	0.0429722i
$970$		0			0
$971$	8.60100	+	14.8974i	0.276019	+	0.478079i	0.970392	−	0.241537i	$-0.0776514\pi$
$971$	8.60100	+	14.8974i	0.276019	+	0.478079i	−0.694373	+	0.719616i	$0.744318\pi$
$972$		0			0
$973$	−7.95242	+	33.1740i	−0.254943	+	1.06351i
$974$		0			0
$975$	5.50044	+	15.7730i	0.176155	+	0.505139i
$976$		0			0
$977$	−20.1225	−	34.8532i	−0.643776	−	1.11505i	−0.984583	−	0.174920i	$-0.944033\pi$
$977$	−20.1225	−	34.8532i	−0.643776	−	1.11505i	0.340806	−	0.940133i	$-0.389300\pi$
$978$		0			0
$979$	−0.443873	−	0.768810i	−0.0141862	−	0.0245713i
$980$		0			0
$981$	−35.1824	−	13.8942i	−1.12329	−	0.443607i
$982$		0			0
$983$	20.5520			0.655506			0.327753	−	0.944763i	$-0.393709\pi$
$983$	20.5520			0.655506			0.327753	+	0.944763i	$0.393709\pi$
$984$		0			0
$985$	−15.7813			−0.502834
$986$		0			0
$987$	22.6583	+	31.4806i	0.721220	+	1.00204i
$988$		0			0
$989$	−5.20330	−	9.01237i	−0.165455	−	0.286577i
$990$		0			0
$991$	−14.9872	+	25.9586i	−0.476083	+	0.824601i	−0.999625	−	0.0273998i	$-0.991277\pi$
$991$	−14.9872	+	25.9586i	−0.476083	+	0.824601i	0.523541	+	0.852000i	$0.324611\pi$
$992$		0			0
$993$	−8.06252	−	23.1199i	−0.255856	−	0.733689i
$994$		0			0
$995$	4.36537	−	7.56105i	0.138392	−	0.239701i
$996$		0			0
$997$	−12.0389			−0.381275			−0.190638	−	0.981660i	$-0.561056\pi$
$997$	−12.0389			−0.381275			−0.190638	+	0.981660i	$0.561056\pi$
$998$		0			0
$999$	1.85437	−	45.6725i	0.0586697	−	1.44501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.l.b.193.5	yes	14
3.2	odd	2		756.2.l.b.361.5		14
4.3	odd	2		1008.2.t.j.193.3		14
7.2	even	3		252.2.i.b.121.4	yes	14
7.3	odd	6		1764.2.j.h.589.7		14
7.4	even	3		1764.2.j.g.589.1		14
7.5	odd	6		1764.2.i.i.373.4		14
7.6	odd	2		1764.2.l.i.949.3		14
9.2	odd	6		756.2.i.b.613.3		14
9.4	even	3		2268.2.k.e.1621.5		14
9.5	odd	6		2268.2.k.f.1621.3		14
9.7	even	3		252.2.i.b.25.4	✓	14
12.11	even	2		3024.2.t.j.1873.5		14
21.2	odd	6		756.2.i.b.37.3		14
21.5	even	6		5292.2.i.i.1549.5		14
21.11	odd	6		5292.2.j.h.1765.3		14
21.17	even	6		5292.2.j.g.1765.5		14
21.20	even	2		5292.2.l.i.361.3		14
28.23	odd	6		1008.2.q.j.625.4		14
36.7	odd	6		1008.2.q.j.529.4		14
36.11	even	6		3024.2.q.j.2881.3		14
63.2	odd	6		756.2.l.b.289.5		14
63.11	odd	6		5292.2.j.h.3529.3		14
63.16	even	3	inner	252.2.l.b.205.5	yes	14
63.20	even	6		5292.2.i.i.2125.5		14
63.23	odd	6		2268.2.k.f.1297.3		14
63.25	even	3		1764.2.j.g.1177.1		14
63.34	odd	6		1764.2.i.i.1537.4		14
63.38	even	6		5292.2.j.g.3529.5		14
63.47	even	6		5292.2.l.i.3313.3		14
63.52	odd	6		1764.2.j.h.1177.7		14
63.58	even	3		2268.2.k.e.1297.5		14
63.61	odd	6		1764.2.l.i.961.3		14
84.23	even	6		3024.2.q.j.2305.3		14
252.79	odd	6		1008.2.t.j.961.3		14
252.191	even	6		3024.2.t.j.289.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.4	✓	14	9.7	even	3
252.2.i.b.121.4	yes	14	7.2	even	3
252.2.l.b.193.5	yes	14	1.1	even	1	trivial
252.2.l.b.205.5	yes	14	63.16	even	3	inner
756.2.i.b.37.3		14	21.2	odd	6
756.2.i.b.613.3		14	9.2	odd	6
756.2.l.b.289.5		14	63.2	odd	6
756.2.l.b.361.5		14	3.2	odd	2
1008.2.q.j.529.4		14	36.7	odd	6
1008.2.q.j.625.4		14	28.23	odd	6
1008.2.t.j.193.3		14	4.3	odd	2
1008.2.t.j.961.3		14	252.79	odd	6
1764.2.i.i.373.4		14	7.5	odd	6
1764.2.i.i.1537.4		14	63.34	odd	6
1764.2.j.g.589.1		14	7.4	even	3
1764.2.j.g.1177.1		14	63.25	even	3
1764.2.j.h.589.7		14	7.3	odd	6
1764.2.j.h.1177.7		14	63.52	odd	6
1764.2.l.i.949.3		14	7.6	odd	2
1764.2.l.i.961.3		14	63.61	odd	6
2268.2.k.e.1297.5		14	63.58	even	3
2268.2.k.e.1621.5		14	9.4	even	3
2268.2.k.f.1297.3		14	63.23	odd	6
2268.2.k.f.1621.3		14	9.5	odd	6
3024.2.q.j.2305.3		14	84.23	even	6
3024.2.q.j.2881.3		14	36.11	even	6
3024.2.t.j.289.5		14	252.191	even	6
3024.2.t.j.1873.5		14	12.11	even	2
5292.2.i.i.1549.5		14	21.5	even	6
5292.2.i.i.2125.5		14	63.20	even	6
5292.2.j.g.1765.5		14	21.17	even	6
5292.2.j.g.3529.5		14	63.38	even	6
5292.2.j.h.1765.3		14	21.11	odd	6
5292.2.j.h.3529.3		14	63.11	odd	6
5292.2.l.i.361.3		14	21.20	even	2
5292.2.l.i.3313.3		14	63.47	even	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13119 - 1.31165i) q^{3} -1.52940 q^{5} +(2.53654 - 0.752299i) q^{7} +(-0.440838 - 2.96743i) q^{9} +O(q^{10})\)	\(q+(1.13119 - 1.31165i) q^{3} -1.52940 q^{5} +(2.53654 - 0.752299i) q^{7} +(-0.440838 - 2.96743i) q^{9} +0.835636 q^{11} +(1.81222 - 3.13886i) q^{13} +(-1.73004 + 2.00604i) q^{15} +(0.301057 - 0.521446i) q^{17} +(0.846884 + 1.46685i) q^{19} +(1.88255 - 4.17804i) q^{21} -6.14405 q^{23} -2.66092 q^{25} +(-4.39090 - 2.77849i) q^{27} +(4.99671 + 8.65455i) q^{29} +(1.65421 + 2.86517i) q^{31} +(0.945260 - 1.09606i) q^{33} +(-3.87940 + 1.15057i) q^{35} +(4.39846 + 7.61835i) q^{37} +(-2.06712 - 5.92763i) q^{39} +(3.51718 - 6.09194i) q^{41} +(0.846884 + 1.46685i) q^{43} +(0.674220 + 4.53841i) q^{45} +(-4.23200 + 7.33004i) q^{47} +(5.86809 - 3.81648i) q^{49} +(-0.343402 - 0.984732i) q^{51} +(-3.99616 + 6.92155i) q^{53} -1.27803 q^{55} +(2.88197 + 0.548462i) q^{57} +(-0.0652138 - 0.112954i) q^{59} +(2.38343 - 4.12822i) q^{61} +(-3.35060 - 7.19538i) q^{63} +(-2.77162 + 4.80059i) q^{65} +(1.12166 + 1.94278i) q^{67} +(-6.95006 + 8.05882i) q^{69} -9.39130 q^{71} +(-2.25454 + 3.90498i) q^{73} +(-3.01000 + 3.49019i) q^{75} +(2.11963 - 0.628648i) q^{77} +(-7.87120 + 13.6333i) q^{79} +(-8.61132 + 2.61632i) q^{81} +(-3.16210 - 5.47692i) q^{83} +(-0.460438 + 0.797501i) q^{85} +(17.0039 + 3.23598i) q^{87} +(-0.531180 - 0.920030i) q^{89} +(2.23542 - 9.32519i) q^{91} +(5.62930 + 1.07130i) q^{93} +(-1.29523 - 2.24340i) q^{95} +(-7.76364 - 13.4470i) q^{97} +(-0.368380 - 2.47969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

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