LMFDB - Embedded newform 252.2.l.b.205.5

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			205.5
Root			$1.13119 + 1.31165i$ of defining polynomial
Character	$\chi$	$=$	252.205
Dual form			252.2.l.b.193.5

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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	0.999995	+	0.00302796i	$0.000963830\pi$
$13$	1.81222	+	3.13886i	0.502620	+	0.870563i	−0.497375	+	0.867535i	$0.665703\pi$
$14$		0			0
$15$	−1.73004	−	2.00604i	−0.446694	−	0.517957i
$16$		0			0
$17$	0.301057	+	0.521446i	0.0730170	+	0.126469i	0.900222	−	0.435431i	$-0.143404\pi$
$17$	0.301057	+	0.521446i	0.0730170	+	0.126469i	−0.827205	+	0.561900i	$0.810071\pi$
$18$		0			0
$19$	0.846884	−	1.46685i	0.194289	−	0.336518i	−0.752379	−	0.658731i	$-0.771094\pi$
$19$	0.846884	−	1.46685i	0.194289	−	0.336518i	0.946667	+	0.322213i	$0.104427\pi$
$20$		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	0.140977	−	0.990013i	$-0.454976\pi$
$29$	4.99671	−	8.65455i	0.927865	−	1.60711i	0.786888	−	0.617096i	$-0.211691\pi$
$30$		0			0
$31$	1.65421	−	2.86517i	0.297104	−	0.514599i	−0.678368	−	0.734722i	$-0.737312\pi$
$31$	1.65421	−	2.86517i	0.297104	−	0.514599i	0.975472	+	0.220123i	$0.0706458\pi$
$32$		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	−0.236649	−	0.971595i	$-0.576049\pi$
$37$	4.39846	−	7.61835i	0.723102	−	1.25245i	0.959751	−	0.280854i	$-0.0906177\pi$
$38$		0			0
$39$	−2.06712	+	5.92763i	−0.331004	+	0.949181i
$40$		0			0
$41$	3.51718	+	6.09194i	0.549291	+	0.951401i	0.998323	+	0.0578850i	$0.0184357\pi$
$41$	3.51718	+	6.09194i	0.549291	+	0.951401i	−0.449032	+	0.893516i	$0.648231\pi$
$42$		0			0
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	−0.794198	−	0.607659i	$-0.792109\pi$
$43$	0.846884	−	1.46685i	0.129149	−	0.223692i	0.923347	+	0.383967i	$0.125442\pi$
$44$		0			0
$45$	0.674220	−	4.53841i	0.100507	−	0.676546i
$46$		0			0
$47$	−4.23200	−	7.33004i	−0.617301	−	1.06920i	−0.989976	−	0.141235i	$-0.954893\pi$
$47$	−4.23200	−	7.33004i	−0.617301	−	1.06920i	0.372675	−	0.927962i	$-0.378441\pi$
$48$		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	−0.998349	−	0.0574350i	$-0.981708\pi$
$53$	−3.99616	−	6.92155i	−0.548915	−	0.950748i	0.449434	−	0.893313i	$-0.351626\pi$
$54$		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	−0.870239	−	0.492629i	$-0.836036\pi$
$59$	−0.0652138	+	0.112954i	−0.00849011	+	0.0147053i	0.861749	+	0.507335i	$0.169369\pi$
$60$		0			0
$61$	2.38343	+	4.12822i	0.305166	+	0.528564i	0.977298	−	0.211868i	$-0.0679546\pi$
$61$	2.38343	+	4.12822i	0.305166	+	0.528564i	−0.672132	+	0.740431i	$0.734621\pi$
$62$		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	−0.789339	−	0.613957i	$-0.789577\pi$
$67$	1.12166	−	1.94278i	0.137033	−	0.237348i	0.926372	+	0.376609i	$0.122910\pi$
$68$		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	0.703394	−	0.710800i	$-0.251667\pi$
$73$	−2.25454	−	3.90498i	−0.263874	−	0.457044i	−0.967268	+	0.253757i	$0.918334\pi$
$74$		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	−0.845048	−	0.534691i	$-0.820428\pi$
$79$	−7.87120	−	13.6333i	−0.885580	−	1.53387i	−0.0405317	−	0.999178i	$-0.512905\pi$
$80$		0			0
$81$	−8.61132	−	2.61632i	−0.956814	−	0.290702i
$82$		0			0
$83$	−3.16210	+	5.47692i	−0.347085	+	0.601170i	−0.985730	−	0.168332i	$-0.946162\pi$
$83$	−3.16210	+	5.47692i	−0.347085	+	0.601170i	0.638645	+	0.769502i	$0.279495\pi$
$84$		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	−0.892804	−	0.450445i	$-0.851265\pi$
$89$	−0.531180	+	0.920030i	−0.0563049	+	0.0975230i	0.836499	+	0.547968i	$0.184599\pi$
$90$		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	0.138742	+	0.990329i	$0.455694\pi$
$97$	−7.76364	+	13.4470i	−0.788279	+	1.36534i	−0.927021	+	0.375010i	$0.877639\pi$
$98$		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	0.490393	+	0.871501i	$0.336853\pi$
$107$	−5.27078	+	9.12926i	−0.509546	+	0.882559i	−0.999939	+	0.0110578i	$0.996480\pi$
$108$		0			0
$109$	6.30442	+	10.9196i	0.603854	+	1.04591i	0.992231	+	0.124406i	$0.0397025\pi$
$109$	6.30442	+	10.9196i	0.603854	+	1.04591i	−0.388377	+	0.921501i	$0.626964\pi$
$110$		0			0
$111$	14.9681	−	2.84854i	1.42071	−	0.270372i
$112$		0			0
$113$	7.76452	+	13.4485i	0.730424	+	1.26513i	0.956702	+	0.291069i	$0.0940110\pi$
$113$	7.76452	+	13.4485i	0.730424	+	1.26513i	−0.226278	+	0.974063i	$0.572656\pi$
$114$		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	−0.998490	−	0.0549357i	$-0.982505\pi$
$139$	−6.44692	−	11.1664i	−0.546821	−	0.947121i	0.451669	−	0.892185i	$-0.350829\pi$
$140$		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	−0.922684	−	0.385556i	$-0.874010\pi$
$157$	−1.59683	+	2.76579i	−0.127441	+	0.220734i	0.795244	+	0.606290i	$0.207343\pi$
$158$		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	−0.774600	−	0.632451i	$-0.782049\pi$
$163$	2.04809	−	3.54740i	0.160419	−	0.277854i	0.935019	+	0.354598i	$0.115382\pi$
$164$		0			0
$165$	−1.44568	−	1.67632i	−0.112546	−	0.130501i
$166$		0			0
$167$	8.24859	+	14.2870i	0.638295	+	1.10556i	0.985807	+	0.167883i	$0.0536932\pi$
$167$	8.24859	+	14.2870i	0.638295	+	1.10556i	−0.347512	+	0.937676i	$0.612973\pi$
$168$		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	0.999895	−	0.0144987i	$-0.00461525\pi$
$173$	6.41063	+	11.1035i	0.487391	+	0.844186i	−0.512504	+	0.858685i	$0.671282\pi$
$174$		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	−0.842732	−	0.538333i	$-0.819054\pi$
$179$	−11.8750	−	20.5680i	−0.887576	−	1.53733i	−0.0448441	−	0.998994i	$-0.514279\pi$
$180$		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	0.992591	−	0.121500i	$-0.0387703\pi$
$191$	5.40475	+	9.36130i	0.391074	+	0.677360i	−0.601517	+	0.798860i	$0.705437\pi$
$192$		0			0
$193$	−0.375130	+	0.649745i	−0.0270025	+	0.0467696i	−0.879211	−	0.476433i	$-0.841930\pi$
$193$	−0.375130	+	0.649745i	−0.0270025	+	0.0467696i	0.852208	+	0.523203i	$0.175263\pi$
$194$		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	0.746945	−	0.664886i	$-0.231520\pi$
$199$	−2.85430	−	4.94379i	−0.202336	−	0.350456i	−0.949281	+	0.314430i	$0.898187\pi$
$200$		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	0.944575	−	0.328295i	$-0.106474\pi$
$211$	2.73050	+	4.72937i	0.187976	+	0.325583i	−0.756600	+	0.653878i	$0.773141\pi$
$212$		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	0.389318	+	0.921103i	$0.372711\pi$
$223$	−9.00530	+	15.5976i	−0.603040	+	1.04450i	−0.992358	+	0.123392i	$0.960623\pi$
$224$		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	−0.951784	−	0.306768i	$-0.900752\pi$
$233$	−3.20892	+	5.55801i	−0.210223	+	0.364117i	0.741561	+	0.670885i	$0.234086\pi$
$234$		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	0.780646	−	0.624974i	$-0.214890\pi$
$239$	−2.33317	−	4.04118i	−0.150920	−	0.261402i	−0.931566	+	0.363572i	$0.881557\pi$
$240$		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	0.720427	−	0.693531i	$-0.243946\pi$
$269$	−3.94288	−	6.82927i	−0.240402	−	0.416388i	−0.960829	+	0.277143i	$0.910612\pi$
$270$		0			0
$271$	12.7947	−	22.1610i	0.777220	−	1.34618i	−0.156318	−	0.987707i	$-0.549963\pi$
$271$	12.7947	−	22.1610i	0.777220	−	1.34618i	0.933538	−	0.358478i	$-0.116704\pi$
$272$		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	−0.882016	−	0.471219i	$-0.843814\pi$
$281$	−0.551848	+	0.955828i	−0.0329205	+	0.0570199i	0.849096	+	0.528239i	$0.177147\pi$
$282$		0			0
$283$	−1.45369	+	2.51786i	−0.0864128	+	0.149671i	−0.905992	−	0.423294i	$-0.860874\pi$
$283$	−1.45369	+	2.51786i	−0.0864128	+	0.149671i	0.819580	+	0.572965i	$0.194207\pi$
$284$		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	−0.958295	−	0.285782i	$-0.907747\pi$
$293$	−12.4381	−	21.5434i	−0.726642	−	1.25858i	0.231653	−	0.972798i	$-0.425587\pi$
$294$		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	0.468790	+	0.883310i	$0.344690\pi$
$311$	−9.35677	+	16.2064i	−0.530574	+	0.918981i	−0.999364	+	0.0356711i	$0.988643\pi$
$312$		0			0
$313$	9.65797	+	16.7281i	0.545901	+	0.945527i	0.998550	+	0.0538387i	$0.0171457\pi$
$313$	9.65797	+	16.7281i	0.545901	+	0.945527i	−0.452649	+	0.891689i	$0.649521\pi$
$314$		0			0
$315$	5.12442	−	11.0046i	0.288729	−	0.620041i
$316$		0			0
$317$	0.897542	+	1.55459i	0.0504110	+	0.0873144i	0.890130	−	0.455707i	$-0.150614\pi$
$317$	0.897542	+	1.55459i	0.0504110	+	0.0873144i	−0.839719	+	0.543021i	$0.817280\pi$
$318$		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	0.992249	−	0.124262i	$-0.0396563\pi$
$331$	7.06833	+	12.2427i	0.388511	+	0.672920i	−0.603739	+	0.797182i	$0.706323\pi$
$332$		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	0.774746	−	0.632273i	$-0.217878\pi$
$337$	−2.94072	−	5.09348i	−0.160191	−	0.277459i	−0.934937	+	0.354813i	$0.884544\pi$
$338$		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	−0.768099	−	0.640331i	$-0.778797\pi$
$347$	3.17593	−	5.50087i	0.170493	−	0.295302i	0.938592	+	0.345028i	$0.112131\pi$
$348$		0			0
$349$	10.4321	−	18.0689i	0.558416	−	0.967205i	−0.439213	−	0.898383i	$-0.644743\pi$
$349$	10.4321	−	18.0689i	0.558416	−	0.967205i	0.997629	−	0.0688222i	$-0.0219241\pi$
$350$		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	0.436962	+	0.899480i	$0.356054\pi$
$359$	−10.6198	+	18.3940i	−0.560492	+	0.970800i	−0.997454	+	0.0713198i	$0.977279\pi$
$360$		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	−0.988596	−	0.150590i	$-0.951883\pi$
$397$	−7.25033	+	12.5579i	−0.363884	+	0.630265i	0.624713	+	0.780855i	$0.285216\pi$
$398$		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	−0.977559	−	0.210663i	$-0.932438\pi$
$409$	−6.19535	+	10.7307i	−0.306340	+	0.530597i	0.671219	+	0.741259i	$0.265771\pi$
$410$		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	−0.947646	−	0.319323i	$-0.896545\pi$
$419$	−15.3596	−	26.6036i	−0.750365	−	1.29967i	0.197281	−	0.980347i	$-0.436789\pi$
$420$		0			0
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	−0.927801	−	0.373076i	$-0.878303\pi$
$421$	−2.88912	+	5.00410i	−0.140807	+	0.243885i	0.786994	+	0.616961i	$0.211636\pi$
$422$		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	0.860917	−	0.508746i	$-0.169891\pi$
$431$	−0.210278	−	0.364212i	−0.0101287	−	0.0175435i	−0.871045	+	0.491203i	$0.836557\pi$
$432$		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	0.827849	−	0.560951i	$-0.189564\pi$
$439$	−1.50590	−	2.60830i	−0.0718729	−	0.124488i	−0.899722	+	0.436463i	$0.856231\pi$
$440$		0			0
$441$	−13.9120	+	15.7307i	−0.662477	+	0.749082i
$442$		0			0
$443$	9.22141	+	15.9719i	0.438122	+	0.758850i	0.997545	−	0.0700326i	$-0.0223103\pi$
$443$	9.22141	+	15.9719i	0.438122	+	0.758850i	−0.559422	+	0.828883i	$0.688977\pi$
$444$		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	0.684403	−	0.729103i	$-0.260063\pi$
$457$	−6.18283	−	10.7090i	−0.289220	−	0.500944i	−0.973624	+	0.228159i	$0.926729\pi$
$458$		0			0
$459$	−2.77074	−	1.45313i	−0.129327	−	0.0678263i
$460$		0			0
$461$	−16.3651	+	28.3453i	−0.762201	+	1.32017i	0.179513	+	0.983756i	$0.442548\pi$
$461$	−16.3651	+	28.3453i	−0.762201	+	1.32017i	−0.941714	+	0.336415i	$0.890786\pi$
$462$		0			0
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	0.998164	−	0.0605719i	$-0.0192924\pi$
$463$	9.61023	+	16.6454i	0.446625	+	0.773577i	−0.551539	+	0.834149i	$0.685959\pi$
$464$		0			0
$465$	−8.60948	+	1.63845i	−0.399255	+	0.0759815i
$466$		0			0
$467$	1.50855	−	2.61289i	0.0698075	−	0.120910i	−0.829009	−	0.559235i	$-0.811095\pi$
$467$	1.50855	−	2.61289i	0.0698075	−	0.120910i	0.898816	+	0.438325i	$0.144428\pi$
$468$		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	−0.753025	−	0.657992i	$-0.771406\pi$
$487$	−20.8841	−	36.1724i	−0.946350	−	1.63913i	−0.193326	−	0.981135i	$-0.561927\pi$
$488$		0			0
$489$	6.96970	−	1.32639i	0.315181	−	0.0599815i
$490$		0			0
$491$	−13.9879	−	24.2278i	−0.631265	−	1.09338i	−0.987293	−	0.158908i	$-0.949203\pi$
$491$	−13.9879	−	24.2278i	−0.631265	−	1.09338i	0.356028	−	0.934475i	$-0.384131\pi$
$492$		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	−0.994755	−	0.102286i	$-0.967384\pi$
$521$	−13.3748	−	23.1658i	−0.585960	−	1.01491i	0.408795	−	0.912626i	$-0.365949\pi$
$522$		0			0
$523$	−10.6131	+	18.3824i	−0.464079	+	0.803808i	−0.999159	−	0.0409928i	$-0.986948\pi$
$523$	−10.6131	+	18.3824i	−0.464079	+	0.803808i	0.535081	+	0.844801i	$0.320281\pi$
$524$		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	−0.561939	−	0.827178i	$-0.689945\pi$
$541$	10.1269	−	17.5402i	0.435388	−	0.754114i	0.997327	+	0.0730646i	$0.0232779\pi$
$542$		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	−0.172327	+	0.985040i	$0.555129\pi$
$547$	−21.9668	+	38.0476i	−0.939233	+	1.62680i	−0.766906	+	0.641760i	$0.778205\pi$
$548$		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	0.756079	−	0.654480i	$-0.227113\pi$
$557$	−4.45483	−	7.71599i	−0.188757	−	0.326937i	−0.944836	+	0.327544i	$0.893779\pi$
$558$		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	−0.394124	−	0.919057i	$-0.628952\pi$
$563$	14.2096	−	24.6118i	0.598865	−	1.03726i	0.992989	−	0.118207i	$-0.0377146\pi$
$564$		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	0.941820	−	0.336117i	$-0.109114\pi$
$569$	4.28948	+	7.42959i	0.179824	+	0.311465i	−0.761996	+	0.647582i	$0.775780\pi$
$570$		0			0
$571$	−9.68861	+	16.7812i	−0.405456	+	0.702270i	−0.994374	−	0.105922i	$-0.966221\pi$
$571$	−9.68861	+	16.7812i	−0.405456	+	0.702270i	0.588919	+	0.808192i	$0.299554\pi$
$572$		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	0.877934	−	0.478781i	$-0.158921\pi$
$577$	0.584441	+	1.01228i	0.0243306	+	0.0421418i	−0.853604	+	0.520923i	$0.825588\pi$
$578$		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	0.341372	+	0.939928i	$0.389108\pi$
$587$	−15.5863	+	26.9963i	−0.643316	+	1.11426i	−0.984688	+	0.174327i	$0.944225\pi$
$588$		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	0.365062	+	0.930983i	$0.381048\pi$
$593$	−15.1887	+	26.3075i	−0.623724	+	1.08032i	−0.988786	+	0.149338i	$0.952286\pi$
$594$		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	−0.781675	−	0.623685i	$-0.785635\pi$
$599$	3.65379	−	6.32855i	0.149290	−	0.258577i	0.930965	+	0.365108i	$0.118968\pi$
$600$		0			0
$601$	4.61461	−	7.99274i	0.188234	−	0.326031i	−0.756428	−	0.654077i	$-0.773057\pi$
$601$	4.61461	−	7.99274i	0.188234	−	0.326031i	0.944661	+	0.328047i	$0.106390\pi$
$602$		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	0.857979	−	0.513686i	$-0.171720\pi$
$613$	−0.393059	−	0.680797i	−0.0158755	−	0.0274972i	−0.873854	+	0.486188i	$0.838387\pi$
$614$		0			0
$615$	6.13580	−	17.5949i	0.247419	−	0.709495i
$616$		0			0
$617$	23.7960	+	41.2159i	0.957991	+	1.65929i	0.727370	+	0.686246i	$0.240743\pi$
$617$	23.7960	+	41.2159i	0.957991	+	1.65929i	0.230621	+	0.973044i	$0.425924\pi$
$618$		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	0.833780	−	0.552097i	$-0.186172\pi$
$643$	−1.55289	−	2.68968i	−0.0612399	−	0.106071i	−0.895020	+	0.446026i	$0.852839\pi$
$644$		0			0
$645$	−4.40770	+	0.838820i	−0.173553	+	0.0330285i
$646$		0			0
$647$	23.3556	+	40.4532i	0.918205	+	1.59038i	0.802140	+	0.597137i	$0.203695\pi$
$647$	23.3556	+	40.4532i	0.918205	+	1.59038i	0.116066	+	0.993242i	$0.462972\pi$
$648$		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	−0.655587	−	0.755120i	$-0.727579\pi$
$659$	8.37284	−	14.5022i	0.326160	−	0.564925i	0.981746	+	0.190195i	$0.0609120\pi$
$660$		0			0
$661$	−6.28870	+	10.8924i	−0.244602	+	0.423664i	−0.962020	−	0.272980i	$-0.911991\pi$
$661$	−6.28870	+	10.8924i	−0.244602	+	0.423664i	0.717417	+	0.696644i	$0.245324\pi$
$662$		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	0.115792	−	0.993273i	$-0.463059\pi$
$673$	23.8175	−	41.2531i	0.918096	−	1.59019i	0.802304	−	0.596916i	$-0.203607\pi$
$674$		0			0
$675$	11.6838	−	7.39336i	0.449711	−	0.284570i
$676$		0			0
$677$	4.54664	+	7.87500i	0.174741	+	0.302661i	0.940072	−	0.340977i	$-0.110758\pi$
$677$	4.54664	+	7.87500i	0.174741	+	0.302661i	−0.765330	+	0.643638i	$0.777424\pi$
$678$		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	0.908552	−	0.417773i	$-0.137189\pi$
$683$	2.41674	+	4.18592i	0.0924741	+	0.160170i	−0.816078	+	0.577942i	$0.803856\pi$
$684$		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	0.950175	−	0.311718i	$-0.100904\pi$
$691$	5.39228	+	9.33969i	0.205132	+	0.355299i	−0.745043	+	0.667017i	$0.767571\pi$
$692$		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	0.999921	+	0.0126076i	$0.00401324\pi$
$709$	13.6032	+	23.5614i	0.510879	+	0.884868i	−0.489042	+	0.872260i	$0.662653\pi$
$710$		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	0.459878	+	0.887982i	$0.347893\pi$
$719$	−14.4549	+	25.0366i	−0.539076	+	0.933707i	−0.998954	+	0.0457252i	$0.985440\pi$
$720$		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	−0.775208	−	0.631706i	$-0.782355\pi$
$727$	4.29978	−	7.44744i	0.159470	−	0.276210i	0.934678	+	0.355496i	$0.115688\pi$
$728$		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	0.958807	−	0.284059i	$-0.0916811\pi$
$739$	6.34491	+	10.9897i	0.233401	+	0.404263i	−0.725405	+	0.688322i	$0.758348\pi$
$740$		0			0
$741$	6.94431	+	8.05216i	0.255106	+	0.295804i
$742$		0			0
$743$	−5.04492	−	8.73806i	−0.185080	−	0.320568i	0.758523	−	0.651646i	$-0.225921\pi$
$743$	−5.04492	−	8.73806i	−0.185080	−	0.320568i	−0.943604	+	0.331078i	$0.892588\pi$
$744$		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	0.827581	−	0.561346i	$-0.189716\pi$
$769$	−2.00631	−	3.47503i	−0.0723493	−	0.125313i	−0.899931	+	0.436033i	$0.856383\pi$
$770$		0			0
$771$	10.4271	+	12.0906i	0.375523	+	0.435431i
$772$		0			0
$773$	−13.6861	−	23.7051i	−0.492256	−	0.852612i	0.507704	−	0.861531i	$-0.330494\pi$
$773$	−13.6861	−	23.7051i	−0.492256	−	0.852612i	−0.999960	+	0.00891927i	$0.997161\pi$
$774$		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	−0.728208	−	0.685356i	$-0.759647\pi$
$787$	6.43636	−	11.1481i	0.229432	−	0.397387i	0.957640	+	0.287969i	$0.0929799\pi$
$788$		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	0.669477	−	0.742833i	$-0.266518\pi$
$797$	−8.71139	−	15.0886i	−0.308573	−	0.534465i	−0.978050	+	0.208368i	$0.933185\pi$
$798$		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	0.807604	−	0.589725i	$-0.200764\pi$
$809$	−3.04097	−	5.26712i	−0.106915	−	0.185182i	−0.914519	+	0.404543i	$0.867431\pi$
$810$		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	0.938427	−	0.345478i	$-0.112283\pi$
$821$	4.87162	+	8.43789i	0.170021	+	0.294484i	−0.768406	+	0.639962i	$0.778950\pi$
$822$		0			0
$823$	−5.38983	+	9.33546i	−0.187878	+	0.325414i	−0.944542	−	0.328389i	$-0.893494\pi$
$823$	−5.38983	+	9.33546i	−0.187878	+	0.325414i	0.756665	+	0.653803i	$0.226827\pi$
$824$		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	0.878651	+	0.477465i	$0.158444\pi$
$829$	24.5548	+	42.5301i	0.852822	+	1.47713i	−0.0258286	+	0.999666i	$0.508222\pi$
$830$		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	−0.995652	−	0.0931549i	$-0.970305\pi$
$839$	−12.0830	+	20.9284i	−0.417151	+	0.722527i	0.578500	+	0.815682i	$0.303638\pi$
$840$		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	−0.815561	−	0.578672i	$-0.803571\pi$
$853$	2.72681	−	4.72297i	0.0933641	−	0.161711i	0.908925	+	0.416960i	$0.136905\pi$
$854$		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	−0.0664116	−	0.997792i	$-0.521155\pi$
$863$	24.4095	−	42.2784i	0.830908	−	1.43917i	0.897319	−	0.441382i	$-0.145512\pi$
$864$		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	−0.168776	−	0.985654i	$-0.553981\pi$
$911$	23.2170	−	40.2130i	0.769214	−	1.33232i	0.937990	−	0.346663i	$-0.112685\pi$
$912$		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	−0.909112	−	0.416553i	$-0.863238\pi$
$919$	−2.84387	+	4.92572i	−0.0938106	+	0.162485i	0.815301	+	0.579037i	$0.196571\pi$
$920$		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	−0.927938	−	0.372734i	$-0.878420\pi$
$929$	−23.9803	−	41.5350i	−0.786767	−	1.36272i	0.141172	−	0.989985i	$-0.454913\pi$
$930$		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	−0.885779	−	0.464107i	$-0.846375\pi$
$941$	−1.25651	+	2.17634i	−0.0409611	+	0.0709468i	0.844818	+	0.535054i	$0.179709\pi$
$942$		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	0.723497	−	0.690328i	$-0.242534\pi$
$947$	−7.26537	−	12.5840i	−0.236093	−	0.408925i	−0.959590	+	0.281403i	$0.909200\pi$
$948$		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	0.966035	−	0.258410i	$-0.0831986\pi$
$967$	8.06111	+	13.9623i	0.259228	+	0.448996i	−0.706807	+	0.707406i	$0.749865\pi$
$968$		0			0
$969$	1.15363	+	1.33767i	0.0370599	+	0.0429722i
$970$		0			0
$971$	8.60100	−	14.8974i	0.276019	−	0.478079i	−0.694373	−	0.719616i	$-0.744318\pi$
$971$	8.60100	−	14.8974i	0.276019	−	0.478079i	0.970392	+	0.241537i	$0.0776514\pi$
$972$		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	0.340806	+	0.940133i	$0.389300\pi$
$977$	−20.1225	+	34.8532i	−0.643776	+	1.11505i	−0.984583	+	0.174920i	$0.944033\pi$
$978$		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	0.523541	−	0.852000i	$-0.324611\pi$
$991$	−14.9872	−	25.9586i	−0.476083	−	0.824601i	−0.999625	+	0.0273998i	$0.991277\pi$
$992$		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.205.5	yes	14
3.2	odd	2		756.2.l.b.289.5		14
4.3	odd	2		1008.2.t.j.961.3		14
7.2	even	3		1764.2.j.g.1177.1		14
7.3	odd	6		1764.2.i.i.1537.4		14
7.4	even	3		252.2.i.b.25.4	✓	14
7.5	odd	6		1764.2.j.h.1177.7		14
7.6	odd	2		1764.2.l.i.961.3		14
9.2	odd	6		2268.2.k.f.1297.3		14
9.4	even	3		252.2.i.b.121.4	yes	14
9.5	odd	6		756.2.i.b.37.3		14
9.7	even	3		2268.2.k.e.1297.5		14
12.11	even	2		3024.2.t.j.289.5		14
21.2	odd	6		5292.2.j.h.3529.3		14
21.5	even	6		5292.2.j.g.3529.5		14
21.11	odd	6		756.2.i.b.613.3		14
21.17	even	6		5292.2.i.i.2125.5		14
21.20	even	2		5292.2.l.i.3313.3		14
28.11	odd	6		1008.2.q.j.529.4		14
36.23	even	6		3024.2.q.j.2305.3		14
36.31	odd	6		1008.2.q.j.625.4		14
63.4	even	3	inner	252.2.l.b.193.5	yes	14
63.5	even	6		5292.2.j.g.1765.5		14
63.11	odd	6		2268.2.k.f.1621.3		14
63.13	odd	6		1764.2.i.i.373.4		14
63.23	odd	6		5292.2.j.h.1765.3		14
63.25	even	3		2268.2.k.e.1621.5		14
63.31	odd	6		1764.2.l.i.949.3		14
63.32	odd	6		756.2.l.b.361.5		14
63.40	odd	6		1764.2.j.h.589.7		14
63.41	even	6		5292.2.i.i.1549.5		14
63.58	even	3		1764.2.j.g.589.1		14
63.59	even	6		5292.2.l.i.361.3		14
84.11	even	6		3024.2.q.j.2881.3		14
252.67	odd	6		1008.2.t.j.193.3		14
252.95	even	6		3024.2.t.j.1873.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.4	✓	14	7.4	even	3
252.2.i.b.121.4	yes	14	9.4	even	3
252.2.l.b.193.5	yes	14	63.4	even	3	inner
252.2.l.b.205.5	yes	14	1.1	even	1	trivial
756.2.i.b.37.3		14	9.5	odd	6
756.2.i.b.613.3		14	21.11	odd	6
756.2.l.b.289.5		14	3.2	odd	2
756.2.l.b.361.5		14	63.32	odd	6
1008.2.q.j.529.4		14	28.11	odd	6
1008.2.q.j.625.4		14	36.31	odd	6
1008.2.t.j.193.3		14	252.67	odd	6
1008.2.t.j.961.3		14	4.3	odd	2
1764.2.i.i.373.4		14	63.13	odd	6
1764.2.i.i.1537.4		14	7.3	odd	6
1764.2.j.g.589.1		14	63.58	even	3
1764.2.j.g.1177.1		14	7.2	even	3
1764.2.j.h.589.7		14	63.40	odd	6
1764.2.j.h.1177.7		14	7.5	odd	6
1764.2.l.i.949.3		14	63.31	odd	6
1764.2.l.i.961.3		14	7.6	odd	2
2268.2.k.e.1297.5		14	9.7	even	3
2268.2.k.e.1621.5		14	63.25	even	3
2268.2.k.f.1297.3		14	9.2	odd	6
2268.2.k.f.1621.3		14	63.11	odd	6
3024.2.q.j.2305.3		14	36.23	even	6
3024.2.q.j.2881.3		14	84.11	even	6
3024.2.t.j.289.5		14	12.11	even	2
3024.2.t.j.1873.5		14	252.95	even	6
5292.2.i.i.1549.5		14	63.41	even	6
5292.2.i.i.2125.5		14	21.17	even	6
5292.2.j.g.1765.5		14	63.5	even	6
5292.2.j.g.3529.5		14	21.5	even	6
5292.2.j.h.1765.3		14	63.23	odd	6
5292.2.j.h.3529.3		14	21.2	odd	6
5292.2.l.i.361.3		14	63.59	even	6
5292.2.l.i.3313.3		14	21.20	even	2

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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