LMFDB - Embedded newform 252.2.be.a.179.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(107,252)]

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([3, 3, 2]))

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

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

chi := DirichletCharacter("252.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.be (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.2
Character	$\chi$	$=$	252.179
Dual form			252.2.be.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40272 + 0.179921i) q^{2} +(1.93526 - 0.504757i) q^{4} +(-0.604694 + 0.349120i) q^{5} +(-1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +O(q^{10})$	\(q+(-1.40272 + 0.179921i) q^{2} +(1.93526 - 0.504757i) q^{4} +(-0.604694 + 0.349120i) q^{5} +(-1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +(0.785403 - 0.598515i) q^{10} +(-1.27599 + 2.21008i) q^{11} +1.88088 q^{13} +(1.20312 - 3.54295i) q^{14} +(3.49044 - 1.95367i) q^{16} +(3.44095 + 1.98663i) q^{17} +(-6.11257 + 3.52909i) q^{19} +(-0.994017 + 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} +(2.01328 + 3.48710i) q^{23} +(-2.25623 + 3.90791i) q^{25} +(-2.63835 + 0.338409i) q^{26} +(-1.05019 + 5.18624i) q^{28} +1.86081i q^{29} +(-0.815018 - 0.470551i) q^{31} +(-4.54461 + 3.36846i) q^{32} +(-5.18413 - 2.16759i) q^{34} +(-0.126755 - 1.84302i) q^{35} +(3.74996 + 6.49512i) q^{37} +(7.93928 - 6.05012i) q^{38} +(1.21785 - 1.55472i) q^{40} -10.6065i q^{41} -3.97212i q^{43} +(-1.35382 + 4.92114i) q^{44} +(-3.45147 - 4.52920i) q^{46} +(4.45219 + 7.71142i) q^{47} +(-4.29698 - 5.52593i) q^{49} +(2.46175 - 5.88765i) q^{50} +(3.63998 - 0.949386i) q^{52} +(0.458798 + 0.264887i) q^{53} -1.78190i q^{55} +(0.540009 - 7.46381i) q^{56} +(-0.334798 - 2.61020i) q^{58} +(6.65037 - 11.5188i) q^{59} +(-5.18413 - 8.97918i) q^{61} +(1.22791 + 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} +(-1.13735 + 0.656652i) q^{65} +(2.35819 + 1.36150i) q^{67} +(7.66189 + 2.10780i) q^{68} +(0.509399 + 2.56243i) q^{70} +3.51310 q^{71} +(1.37535 - 2.38218i) q^{73} +(-6.42876 - 8.43615i) q^{74} +(-10.0481 + 9.91507i) q^{76} +(-3.76921 - 5.60191i) q^{77} +(11.7206 - 6.76690i) q^{79} +(-1.42858 + 2.39995i) q^{80} +(1.90833 + 14.8780i) q^{82} -17.1516 q^{83} -2.77429 q^{85} +(0.714666 + 5.57178i) q^{86} +(1.01361 - 7.14657i) q^{88} +(-10.2797 + 5.93499i) q^{89} +(-2.18660 + 4.47020i) q^{91} +(5.65635 + 5.73222i) q^{92} +(-7.63263 - 10.0159i) q^{94} +(2.46415 - 4.26804i) q^{95} +10.8682 q^{97} +(7.02170 + 6.97823i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) $ 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.40272	+	0.179921i	−0.991874	+	0.127223i
$2$	−1.40272	+	0.179921i	−0.991874	+	0.127223i
$3$		0			0
$3$		0			0
$4$	1.93526	−	0.504757i	0.967629	−	0.252379i
$5$	−0.604694	+	0.349120i	−0.270427	+	0.156131i	−0.629082	−	0.777339i	$-0.716569\pi$
$5$	−0.604694	+	0.349120i	−0.270427	+	0.156131i	0.358655	+	0.933470i	$0.383236\pi$
$6$		0			0
$7$	−1.16254	+	2.37666i	−0.439400	+	0.898291i
$7$	−1.16254	+	2.37666i	−0.439400	+	0.898291i
$8$	−2.62381	+	1.05623i	−0.927657	+	0.373433i
$9$		0			0
$10$	0.785403	−	0.598515i	0.248366	−	0.189267i
$11$	−1.27599	+	2.21008i	−0.384726	+	0.666365i	−0.991731	−	0.128333i	$-0.959037\pi$
$11$	−1.27599	+	2.21008i	−0.384726	+	0.666365i	0.607005	+	0.794698i	$0.292371\pi$
$12$		0			0
$13$	1.88088			0.521661			0.260831	−	0.965385i	$-0.416004\pi$
$13$	1.88088			0.521661			0.260831	+	0.965385i	$0.416004\pi$
$14$	1.20312	−	3.54295i	0.321546	−	0.946894i
$15$		0			0
$16$	3.49044	−	1.95367i	0.872610	−	0.488418i
$17$	3.44095	+	1.98663i	0.834553	+	0.481829i	0.855409	−	0.517953i	$-0.173306\pi$
$17$	3.44095	+	1.98663i	0.834553	+	0.481829i	−0.0208563	+	0.999782i	$0.506639\pi$
$18$		0			0
$19$	−6.11257	+	3.52909i	−1.40232	+	0.809630i	−0.994630	−	0.103491i	$-0.966999\pi$
$19$	−6.11257	+	3.52909i	−1.40232	+	0.809630i	−0.407689	+	0.913121i	$0.633665\pi$
$20$	−0.994017	+	0.980861i	−0.222269	+	0.219327i
$21$		0			0
$22$	1.39222	−	3.32971i	0.296823	−	0.709896i
$23$	2.01328	+	3.48710i	0.419798	+	0.727111i	0.995919	−	0.0902534i	$-0.0287677\pi$
$23$	2.01328	+	3.48710i	0.419798	+	0.727111i	−0.576121	+	0.817364i	$0.695434\pi$
$24$		0			0
$25$	−2.25623	+	3.90791i	−0.451246	+	0.781581i
$26$	−2.63835	+	0.338409i	−0.517422	+	0.0663674i
$27$		0			0
$28$	−1.05019	+	5.18624i	−0.198467	+	0.980108i
$29$			1.86081i			0.345544i	0.984962	+	0.172772i	$0.0552724\pi$
$29$			1.86081i			0.345544i	−0.984962	+	0.172772i	$0.944728\pi$
$30$		0			0
$31$	−0.815018	−	0.470551i	−0.146382	−	0.0845134i	0.425020	−	0.905184i	$-0.360267\pi$
$31$	−0.815018	−	0.470551i	−0.146382	−	0.0845134i	−0.571402	+	0.820670i	$0.693600\pi$
$32$	−4.54461	+	3.36846i	−0.803381	+	0.595465i
$33$		0			0
$34$	−5.18413	−	2.16759i	−0.889071	−	0.371739i
$35$	−0.126755	−	1.84302i	−0.0214255	−	0.311527i
$36$		0			0
$37$	3.74996	+	6.49512i	0.616490	+	1.06779i	0.990121	+	0.140214i	$0.0447792\pi$
$37$	3.74996	+	6.49512i	0.616490	+	1.06779i	−0.373631	+	0.927577i	$0.621888\pi$
$38$	7.93928	−	6.05012i	1.28792	−	0.981458i
$39$		0			0
$40$	1.21785	−	1.55472i	0.192559	−	0.245823i
$41$		−	10.6065i		−	1.65646i	−0.560392	−	0.828228i	$-0.689349\pi$
$41$		−	10.6065i		−	1.65646i	0.560392	−	0.828228i	$-0.310651\pi$
$42$		0			0
$43$		−	3.97212i		−	0.605743i	−0.953031	−	0.302871i	$-0.902055\pi$
$43$		−	3.97212i		−	0.605743i	0.953031	−	0.302871i	$-0.0979452\pi$
$44$	−1.35382	+	4.92114i	−0.204096	+	0.741890i
$45$		0			0
$46$	−3.45147	−	4.52920i	−0.508892	−	0.667795i
$47$	4.45219	+	7.71142i	0.649418	+	1.12483i	0.983262	+	0.182197i	$0.0583209\pi$
$47$	4.45219	+	7.71142i	0.649418	+	1.12483i	−0.333844	+	0.942628i	$0.608346\pi$
$48$		0			0
$49$	−4.29698	−	5.52593i	−0.613855	−	0.789419i
$50$	2.46175	−	5.88765i	0.348144	−	0.832639i
$51$		0			0
$52$	3.63998	−	0.949386i	0.504774	−	0.131656i
$53$	0.458798	+	0.264887i	0.0630207	+	0.0363850i	0.531179	−	0.847259i	$-0.321749\pi$
$53$	0.458798	+	0.264887i	0.0630207	+	0.0363850i	−0.468159	+	0.883644i	$0.655082\pi$
$54$		0			0
$55$		−	1.78190i		−	0.240271i
$56$	0.540009	−	7.46381i	0.0721617	−	0.997393i
$57$		0			0
$58$	−0.334798	−	2.61020i	−0.0439612	−	0.342736i
$59$	6.65037	−	11.5188i	0.865804	−	1.49962i	−0.000442051	−	1.00000i	$-0.500141\pi$
$59$	6.65037	−	11.5188i	0.865804	−	1.49962i	0.866246	−	0.499617i	$-0.166526\pi$
$60$		0			0
$61$	−5.18413	−	8.97918i	−0.663760	−	1.14967i	−0.979620	−	0.200860i	$-0.935626\pi$
$61$	−5.18413	−	8.97918i	−0.663760	−	1.14967i	0.315860	−	0.948806i	$-0.397707\pi$
$62$	1.22791	+	0.513413i	0.155944	+	0.0652036i
$63$		0			0
$64$	5.76877	−	5.54268i	0.721096	−	0.692835i
$65$	−1.13735	+	0.656652i	−0.141071	+	0.0814476i
$66$		0			0
$67$	2.35819	+	1.36150i	0.288098	+	0.166334i	0.637084	−	0.770794i	$-0.280140\pi$
$67$	2.35819	+	1.36150i	0.288098	+	0.166334i	−0.348986	+	0.937128i	$0.613474\pi$
$68$	7.66189	+	2.10780i	0.929140	+	0.255608i
$69$		0			0
$70$	0.509399	+	2.56243i	0.0608848	+	0.306269i
$71$	3.51310			0.416928			0.208464	−	0.978030i	$-0.433154\pi$
$71$	3.51310			0.416928			0.208464	+	0.978030i	$0.433154\pi$
$72$		0			0
$73$	1.37535	−	2.38218i	0.160973	−	0.278813i	−0.774245	−	0.632886i	$-0.781870\pi$
$73$	1.37535	−	2.38218i	0.160973	−	0.278813i	0.935218	+	0.354073i	$0.115203\pi$
$74$	−6.42876	−	8.43615i	−0.747328	−	0.980683i
$75$		0			0
$76$	−10.0481	+	9.91507i	−1.15259	+	1.13734i
$77$	−3.76921	−	5.60191i	−0.429541	−	0.638397i
$78$		0			0
$79$	11.7206	−	6.76690i	1.31867	−	0.761335i	0.335157	−	0.942162i	$-0.391211\pi$
$79$	11.7206	−	6.76690i	1.31867	−	0.761335i	0.983515	+	0.180827i	$0.0578775\pi$
$80$	−1.42858	+	2.39995i	−0.159720	+	0.268323i
$81$		0			0
$82$	1.90833	+	14.8780i	0.210739	+	1.64300i
$83$	−17.1516			−1.88264			−0.941319	−	0.337520i	$-0.890412\pi$
$83$	−17.1516			−1.88264			−0.941319	+	0.337520i	$0.890412\pi$
$84$		0			0
$85$	−2.77429			−0.300914
$86$	0.714666	+	5.57178i	0.0770645	+	0.600820i
$87$		0			0
$88$	1.01361	−	7.14657i	0.108051	−	0.761827i
$89$	−10.2797	+	5.93499i	−1.08965	+	0.629107i	−0.933482	−	0.358624i	$-0.883246\pi$
$89$	−10.2797	+	5.93499i	−1.08965	+	0.629107i	−0.156164	+	0.987731i	$0.549913\pi$
$90$		0			0
$91$	−2.18660	+	4.47020i	−0.229218	+	0.468604i
$92$	5.65635	+	5.73222i	0.589715	+	0.597625i
$93$		0			0
$94$	−7.63263	−	10.0159i	−0.787245	−	1.03306i
$95$	2.46415	−	4.26804i	0.252817	−	0.437892i
$96$		0			0
$97$	10.8682			1.10350			0.551748	−	0.834011i	$-0.313961\pi$
$97$	10.8682			1.10350			0.551748	+	0.834011i	$0.313961\pi$
$98$	7.02170	+	6.97823i	0.709299	+	0.704908i
$99$		0			0
$100$	−2.39384	+	8.70165i	−0.239384	+	0.870165i
$101$	9.18549	+	5.30325i	0.913990	+	0.527693i	0.881713	−	0.471786i	$-0.156391\pi$
$101$	9.18549	+	5.30325i	0.913990	+	0.527693i	0.0322775	+	0.999479i	$0.489724\pi$
$102$		0			0
$103$	11.4970	−	6.63779i	1.13283	−	0.654041i	0.188187	−	0.982133i	$-0.439739\pi$
$103$	11.4970	−	6.63779i	1.13283	−	0.654041i	0.944646	+	0.328092i	$0.106406\pi$
$104$	−4.93507	+	1.98663i	−0.483923	+	0.194805i
$105$		0			0
$106$	−0.691224	−	0.289016i	−0.0671377	−	0.0280717i
$107$	−4.80599	−	8.32422i	−0.464613	−	0.804733i	0.534571	−	0.845123i	$-0.320473\pi$
$107$	−4.80599	−	8.32422i	−0.464613	−	0.804733i	−0.999184	+	0.0403906i	$0.987140\pi$
$108$		0			0
$109$	−7.11203	+	12.3184i	−0.681209	+	1.17989i	0.293403	+	0.955989i	$0.405212\pi$
$109$	−7.11203	+	12.3184i	−0.681209	+	1.17989i	−0.974612	+	0.223899i	$0.928121\pi$
$110$	0.320600	+	2.49951i	0.0305680	+	0.238319i
$111$		0			0
$112$	0.585411	+	10.5668i	0.0553161	+	0.998469i
$113$			12.1039i			1.13864i	0.822117	+	0.569319i	$0.192793\pi$
$113$			12.1039i			1.13864i	−0.822117	+	0.569319i	$0.807207\pi$
$114$		0			0
$115$	−2.43483	−	1.40575i	−0.227049	−	0.131087i
$116$	0.939258	+	3.60115i	0.0872079	+	0.334358i
$117$		0			0
$118$	−7.25615	+	17.3542i	−0.667983	+	1.59758i
$119$	−8.72179	+	5.86840i	−0.799526	+	0.537955i
$120$		0			0
$121$	2.24369	+	3.88619i	0.203972	+	0.353290i
$122$	8.88743	+	11.6626i	0.804630	+	1.05588i
$123$		0			0
$124$	−1.81478	−	0.499251i	−0.162972	−	0.0448340i
$125$		−	6.64198i		−	0.594077i
$126$		0			0
$127$			0.582584i			0.0516960i	0.999666	+	0.0258480i	$0.00822859\pi$
$127$			0.582584i			0.0516960i	−0.999666	+	0.0258480i	$0.991771\pi$
$128$	−7.09474	+	8.81276i	−0.627092	+	0.778945i
$129$		0			0
$130$	1.47725	−	1.12573i	0.129563	−	0.0987333i
$131$	−5.44621	−	9.43310i	−0.475837	−	0.824174i	0.523780	−	0.851854i	$-0.324522\pi$
$131$	−5.44621	−	9.43310i	−0.475837	−	0.824174i	−0.999617	+	0.0276796i	$0.991188\pi$
$132$		0			0
$133$	−1.28131	−	18.6302i	−0.111104	−	1.61544i
$134$	−3.55284	−	1.48552i	−0.306919	−	0.128329i
$135$		0			0
$136$	−11.1267	−	1.57813i	−0.954109	−	0.135323i
$137$	11.5198	+	6.65096i	0.984203	+	0.568230i	0.903536	−	0.428511i	$-0.140962\pi$
$137$	11.5198	+	6.65096i	0.984203	+	0.568230i	0.0806665	+	0.996741i	$0.474295\pi$
$138$		0			0
$139$		−	0.840795i		−	0.0713153i	−0.999364	−	0.0356577i	$-0.988647\pi$
$139$		−	0.840795i		−	0.0713153i	0.999364	−	0.0356577i	$-0.0113526\pi$
$140$	−1.17558	−	3.50273i	−0.0993546	−	0.296035i
$141$		0			0
$142$	−4.92790	+	0.632079i	−0.413540	+	0.0530429i
$143$	−2.39998	+	4.15689i	−0.200697	+	0.347617i
$144$		0			0
$145$	−0.649646	−	1.12522i	−0.0539502	−	0.0934445i
$146$	−1.50063	+	3.58899i	−0.124193	+	0.297027i
$147$		0			0
$148$	10.5356	+	10.6769i	0.866021	+	0.877637i
$149$	−4.89898	+	2.82843i	−0.401340	+	0.231714i	−0.687062	−	0.726599i	$-0.741100\pi$
$149$	−4.89898	+	2.82843i	−0.401340	+	0.231714i	0.285722	+	0.958313i	$0.407767\pi$
$150$		0			0
$151$	14.7077	+	8.49147i	1.19689	+	0.691026i	0.959861	−	0.280476i	$-0.0904925\pi$
$151$	14.7077	+	8.49147i	1.19689	+	0.691026i	0.237031	+	0.971502i	$0.423826\pi$
$152$	12.3107	−	15.7159i	0.998530	−	1.27473i
$153$		0			0
$154$	6.29505	+	7.17976i	0.507270	+	0.578562i
$155$	0.657115			0.0527807
$156$		0			0
$157$	0.987461	−	1.71033i	0.0788079	−	0.136499i	−0.823928	−	0.566695i	$-0.808222\pi$
$157$	0.987461	−	1.71033i	0.0788079	−	0.136499i	0.902736	+	0.430195i	$0.141555\pi$
$158$	−15.2232	+	11.6009i	−1.21110	+	0.922914i
$159$		0			0
$160$	1.57210	−	3.62350i	0.124286	−	0.286463i
$161$	−10.6282	+	0.730962i	−0.837617	+	0.0576079i
$162$		0			0
$163$	−2.43483	+	1.40575i	−0.190711	+	0.110107i	−0.592315	−	0.805706i	$-0.701786\pi$
$163$	−2.43483	+	1.40575i	−0.190711	+	0.110107i	0.401604	+	0.915813i	$0.368453\pi$
$164$	−5.35370	−	20.5263i	−0.418054	−	1.60283i
$165$		0			0
$166$	24.0590	−	3.08593i	1.86734	−	0.239515i
$167$	2.40833			0.186362			0.0931810	−	0.995649i	$-0.470296\pi$
$167$	2.40833			0.186362			0.0931810	+	0.995649i	$0.470296\pi$
$168$		0			0
$169$	−9.46230			−0.727869
$170$	3.89156	−	0.499153i	0.298469	−	0.0382833i
$171$		0			0
$172$	−2.00496	−	7.68707i	−0.152876	−	0.586134i
$173$	−4.05322	+	2.34013i	−0.308161	+	0.177917i	−0.646103	−	0.763250i	$-0.723602\pi$
$173$	−4.05322	+	2.34013i	−0.308161	+	0.177917i	0.337942	+	0.941167i	$0.390269\pi$
$174$		0			0
$175$	−6.66478	−	9.90539i	−0.503810	−	0.748777i
$176$	−0.136000	+	10.2070i	−0.0102514	+	0.769384i
$177$		0			0
$178$	13.3517	−	10.1747i	1.00075	−	0.762623i
$179$	6.59544	−	11.4236i	0.492966	−	0.853843i	−0.507001	−	0.861946i	$-0.669246\pi$
$179$	6.59544	−	11.4236i	0.492966	−	0.853843i	0.999967	+	0.00810267i	$0.00257919\pi$
$180$		0			0
$181$	17.6801			1.31415			0.657075	−	0.753825i	$-0.271793\pi$
$181$	17.6801			1.31415			0.657075	+	0.753825i	$0.271793\pi$
$182$	2.26291	−	6.66386i	0.167738	−	0.493958i
$183$		0			0
$184$	−8.96563	−	7.02302i	−0.660955	−	0.517744i
$185$	−4.53515	−	2.61837i	−0.333431	−	0.192507i
$186$		0			0
$187$	−8.78124	+	5.06985i	−0.642148	+	0.370744i
$188$	12.5085	+	12.6763i	0.912278	+	0.924514i
$189$		0			0
$190$	−2.68862	+	6.43023i	−0.195053	+	0.466498i
$191$	10.6220	+	18.3978i	0.768581	+	1.33122i	0.938332	+	0.345734i	$0.112370\pi$
$191$	10.6220	+	18.3978i	0.768581	+	1.33122i	−0.169752	+	0.985487i	$0.554297\pi$
$192$		0			0
$193$	−2.08382	+	3.60927i	−0.149996	+	0.259801i	−0.931226	−	0.364443i	$-0.881260\pi$
$193$	−2.08382	+	3.60927i	−0.149996	+	0.259801i	0.781230	+	0.624244i	$0.214593\pi$
$194$	−15.2450	+	1.95541i	−1.09453	+	0.140390i
$195$		0			0
$196$	−11.1050	−	8.52517i	−0.793216	−	0.608941i
$197$		−	8.04744i		−	0.573356i	−0.958027	−	0.286678i	$-0.907449\pi$
$197$		−	8.04744i		−	0.573356i	0.958027	−	0.286678i	$-0.0925510\pi$
$198$		0			0
$199$	−1.31955	−	0.761843i	−0.0935405	−	0.0540056i	0.452500	−	0.891764i	$-0.350532\pi$
$199$	−1.31955	−	0.761843i	−0.0935405	−	0.0540056i	−0.546041	+	0.837759i	$0.683866\pi$
$200$	1.79229	−	12.6367i	0.126734	−	0.893549i
$201$		0			0
$202$	−13.8389	−	5.78632i	−0.973698	−	0.407124i
$203$	−4.42251	−	2.16327i	−0.310399	−	0.151832i
$204$		0			0
$205$	3.70294	+	6.41368i	0.258624	+	0.447951i
$206$	−14.9328	+	11.3795i	−1.04042	+	0.792849i
$207$		0			0
$208$	6.56509	−	3.67461i	0.455207	−	0.254789i
$209$		−	18.0124i		−	1.24594i
$210$		0			0
$211$			19.2878i			1.32783i	0.747809	+	0.663914i	$0.231106\pi$
$211$			19.2878i			1.32783i	−0.747809	+	0.663914i	$0.768894\pi$
$212$	1.02160	+	0.281043i	0.0701635	+	0.0193021i
$213$		0			0
$214$	8.23917	+	10.8119i	0.563218	+	0.739084i
$215$	1.38675	+	2.40192i	0.0945753	+	0.163809i
$216$		0			0
$217$	2.06583	−	1.38998i	0.140238	−	0.0943580i
$218$	7.75986	−	18.5589i	0.525564	−	1.25697i
$219$		0			0
$220$	−0.899425	−	3.44843i	−0.0606393	−	0.232493i
$221$	6.47200	+	3.73661i	0.435354	+	0.251352i
$222$		0			0
$223$		−	18.1390i		−	1.21468i	−0.794443	−	0.607338i	$-0.792237\pi$
$223$		−	18.1390i		−	1.21468i	0.794443	−	0.607338i	$-0.207763\pi$
$224$	−2.72235	−	14.7170i	−0.181895	−	0.983318i
$225$		0			0
$226$	−2.17774	−	16.9784i	−0.144861	−	1.12938i
$227$	−4.78909	+	8.29495i	−0.317863	+	0.550555i	−0.980042	−	0.198791i	$-0.936299\pi$
$227$	−4.78909	+	8.29495i	−0.317863	+	0.550555i	0.662179	+	0.749346i	$0.269632\pi$
$228$		0			0
$229$	−2.42163	−	4.19438i	−0.160026	−	0.277173i	0.774852	−	0.632143i	$-0.217824\pi$
$229$	−2.42163	−	4.19438i	−0.160026	−	0.277173i	−0.934878	+	0.354970i	$0.884491\pi$
$230$	3.66832	+	1.53380i	0.241882	+	0.101136i
$231$		0			0
$232$	−1.96544	−	4.88242i	−0.129037	−	0.320546i
$233$	18.7348	−	10.8165i	1.22736	−	0.708615i	0.260881	−	0.965371i	$-0.415987\pi$
$233$	18.7348	−	10.8165i	1.22736	−	0.708615i	0.966476	+	0.256755i	$0.0826535\pi$
$234$		0			0
$235$	−5.38442	−	3.10870i	−0.351241	−	0.202789i
$236$	7.05599	−	25.6486i	0.459306	−	1.66958i
$237$		0			0
$238$	11.1784	−	9.80097i	0.724588	−	0.635302i
$239$	20.5549			1.32958			0.664792	−	0.747028i	$-0.268520\pi$
$239$	20.5549			1.32958			0.664792	+	0.747028i	$0.268520\pi$
$240$		0			0
$241$	−5.37528	+	9.31025i	−0.346252	+	0.599726i	−0.985580	−	0.169208i	$-0.945879\pi$
$241$	−5.37528	+	9.31025i	−0.346252	+	0.599726i	0.639328	+	0.768934i	$0.279212\pi$
$242$	−3.84648	−	5.04755i	−0.247261	−	0.324469i
$243$		0			0
$244$	−14.5649	−	14.7603i	−0.932424	−	0.944930i
$245$	4.52757	+	1.84133i	0.289256	+	0.117639i
$246$		0			0
$247$	−11.4970	+	6.63779i	−0.731536	+	0.422353i
$248$	2.63546	+	0.373793i	0.167352	+	0.0237359i
$249$		0			0
$250$	1.19503	+	9.31685i	0.0755803	+	0.589249i
$251$	19.4316			1.22651			0.613257	−	0.789884i	$-0.289859\pi$
$251$	19.4316			1.22651			0.613257	+	0.789884i	$0.289859\pi$
$252$		0			0
$253$	−10.2757			−0.646028
$254$	−0.104819	−	0.817203i	−0.00657692	−	0.0512759i
$255$		0			0
$256$	8.36634	−	13.6383i	0.522897	−	0.852396i
$257$	7.56621	−	4.36835i	0.471967	−	0.272490i	−0.245096	−	0.969499i	$-0.578819\pi$
$257$	7.56621	−	4.36835i	0.471967	−	0.272490i	0.717063	+	0.697009i	$0.245486\pi$
$258$		0			0
$259$	−19.7962	+	1.36150i	−1.23007	+	0.0845994i
$260$	−1.86962	+	1.84488i	−0.115949	+	0.114414i
$261$		0			0
$262$	9.33672	+	12.2521i	0.576825	+	0.756940i
$263$	−10.9040	+	18.8862i	−0.672368	+	1.16458i	0.304863	+	0.952396i	$0.401389\pi$
$263$	−10.9040	+	18.8862i	−0.672368	+	1.16458i	−0.977231	+	0.212179i	$0.931944\pi$
$264$		0			0
$265$	−0.369910			−0.0227234
$266$	5.14928	+	25.9025i	0.315723	+	1.58818i
$267$		0			0
$268$	5.25092	+	1.44454i	0.320751	+	0.0882393i
$269$	−12.7340	−	7.35200i	−0.776408	−	0.448259i	0.0587478	−	0.998273i	$-0.481289\pi$
$269$	−12.7340	−	7.35200i	−0.776408	−	0.448259i	−0.835156	+	0.550014i	$0.814623\pi$
$270$		0			0
$271$	−4.49275	+	2.59389i	−0.272915	+	0.157568i	−0.630212	−	0.776423i	$-0.717032\pi$
$271$	−4.49275	+	2.59389i	−0.272915	+	0.157568i	0.357296	+	0.933991i	$0.383699\pi$
$272$	15.8916	+	0.211743i	0.963573	+	0.0128388i
$273$		0			0
$274$	−17.3557	−	7.25680i	−1.04850	−	0.438399i
$275$	−5.75786	−	9.97291i	−0.347212	−	0.601389i
$276$		0			0
$277$	−11.8627	+	20.5469i	−0.712763	+	1.23454i	0.251053	+	0.967973i	$0.419223\pi$
$277$	−11.8627	+	20.5469i	−0.712763	+	1.23454i	−0.963816	+	0.266568i	$0.914110\pi$
$278$	0.151276	+	1.17940i	0.00907296	+	0.0707358i
$279$		0			0
$280$	2.27922	+	4.70184i	0.136210	+	0.280989i
$281$			4.12400i			0.246017i	0.992406	+	0.123009i	$0.0392542\pi$
$281$			4.12400i			0.246017i	−0.992406	+	0.123009i	$0.960746\pi$
$282$		0			0
$283$	−6.11257	−	3.52909i	−0.363355	−	0.209783i	0.307197	−	0.951646i	$-0.400609\pi$
$283$	−6.11257	−	3.52909i	−0.363355	−	0.209783i	−0.670551	+	0.741863i	$0.733942\pi$
$284$	6.79875	−	1.77326i	0.403432	−	0.105224i
$285$		0			0
$286$	2.61860	−	6.26277i	0.154841	−	0.370325i
$287$	25.2080	+	12.3305i	1.48798	+	0.727847i
$288$		0			0
$289$	−0.606584	−	1.05063i	−0.0356814	−	0.0618020i
$290$	1.11372	+	1.46149i	0.0654001	+	0.0858215i
$291$		0			0
$292$	1.45924	−	5.30436i	0.0853955	−	0.310414i
$293$			15.9675i			0.932830i	0.884566	+	0.466415i	$0.154455\pi$
$293$			15.9675i			0.932830i	−0.884566	+	0.466415i	$0.845545\pi$
$294$		0			0
$295$			9.28711i			0.540716i
$296$	−16.6995	−	13.0812i	−0.970639	−	0.760327i
$297$		0			0
$298$	6.36301	−	4.84892i	0.368599	−	0.280891i
$299$	3.78673	+	6.55881i	0.218992	+	0.379306i
$300$		0			0
$301$	9.44036	+	4.61776i	0.544133	+	0.266163i
$302$	−22.1585	−	9.26495i	−1.27508	−	0.533138i
$303$		0			0
$304$	−14.4409	+	24.2600i	−0.828241	+	1.39141i
$305$	6.26962	+	3.61977i	0.358997	+	0.207267i
$306$		0			0
$307$			5.53450i			0.315871i	0.987449	+	0.157935i	$0.0504838\pi$
$307$			5.53450i			0.315871i	−0.987449	+	0.157935i	$0.949516\pi$
$308$	−10.1220	−	8.93860i	−0.576754	−	0.509324i
$309$		0			0
$310$	−0.921749	+	0.118229i	−0.0523518	+	0.00671493i
$311$	−5.24440	+	9.08357i	−0.297383	+	0.515082i	−0.975536	−	0.219838i	$-0.929447\pi$
$311$	−5.24440	+	9.08357i	−0.297383	+	0.515082i	0.678154	+	0.734920i	$0.262780\pi$
$312$		0			0
$313$	−1.13158	−	1.95996i	−0.0639609	−	0.110784i	0.832272	−	0.554368i	$-0.187040\pi$
$313$	−1.13158	−	1.95996i	−0.0639609	−	0.110784i	−0.896233	+	0.443584i	$0.853707\pi$
$314$	−1.07741	+	2.57678i	−0.0608017	+	0.145416i
$315$		0			0
$316$	19.2668	−	19.0117i	1.08384	−	1.06949i
$317$	8.23233	−	4.75294i	0.462374	−	0.266952i	−0.250668	−	0.968073i	$-0.580650\pi$
$317$	8.23233	−	4.75294i	0.462374	−	0.266952i	0.713042	+	0.701122i	$0.247317\pi$
$318$		0			0
$319$	−4.11255	−	2.37438i	−0.230258	−	0.132940i
$320$	−1.55328	+	5.36562i	−0.0868309	+	0.299947i
$321$		0			0
$322$	14.7768	−	2.93756i	0.823481	−	0.163704i
$323$	−28.0441			−1.56041
$324$		0			0
$325$	−4.24369	+	7.35029i	−0.235398	+	0.407721i
$326$	3.16247	−	2.40996i	0.175153	−	0.133475i
$327$		0			0
$328$	11.2029	+	27.8294i	0.618574	+	1.53662i
$329$	−23.5032	+	1.61646i	−1.29578	+	0.0891182i
$330$		0			0
$331$	−8.60924	+	4.97055i	−0.473207	+	0.273206i	−0.717581	−	0.696475i	$-0.754751\pi$
$331$	−8.60924	+	4.97055i	−0.473207	+	0.273206i	0.244374	+	0.969681i	$0.421417\pi$
$332$	−33.1928	+	8.65742i	−1.82169	+	0.475137i
$333$		0			0
$334$	−3.37821	+	0.433308i	−0.184848	+	0.0237095i
$335$	−1.90131			−0.103879
$336$		0			0
$337$	10.6441			0.579822			0.289911	−	0.957054i	$-0.406374\pi$
$337$	10.6441			0.579822			0.289911	+	0.957054i	$0.406374\pi$
$338$	13.2730	−	1.70246i	0.721955	−	0.0926018i
$339$		0			0
$340$	−5.36897	+	1.40034i	−0.291173	+	0.0759443i
$341$	2.07991	−	1.20084i	0.112634	−	0.0650290i
$342$		0			0
$343$	18.1287	−	3.78831i	0.978856	−	0.204549i
$344$	4.19546	+	10.4221i	0.226204	+	0.561922i
$345$		0			0
$346$	5.26451	−	4.01181i	0.283022	−	0.215676i
$347$	8.77440	−	15.1977i	0.471035	−	0.815856i	−0.528416	−	0.848985i	$-0.677214\pi$
$347$	8.77440	−	15.1977i	0.471035	−	0.815856i	0.999451	+	0.0331294i	$0.0105473\pi$
$348$		0			0
$349$	29.0703			1.55610			0.778049	−	0.628204i	$-0.216210\pi$
$349$	29.0703			1.55610			0.778049	+	0.628204i	$0.216210\pi$
$350$	11.1310	+	12.6954i	0.594978	+	0.678597i
$351$		0			0
$352$	−1.64568	−	14.3421i	−0.0877153	−	0.764436i
$353$	9.73945	+	5.62308i	0.518379	+	0.299286i	0.736271	−	0.676687i	$-0.236585\pi$
$353$	9.73945	+	5.62308i	0.518379	+	0.299286i	−0.217892	+	0.975973i	$0.569918\pi$
$354$		0			0
$355$	−2.12435	+	1.22649i	−0.112749	+	0.0650955i
$356$	−16.8981	+	16.6745i	−0.895599	+	0.883745i
$357$		0			0
$358$	−7.19622	+	17.2108i	−0.380332	+	0.909621i
$359$	−14.5218	−	25.1525i	−0.766431	−	1.32750i	−0.939486	−	0.342586i	$-0.888697\pi$
$359$	−14.5218	−	25.1525i	−0.766431	−	1.32750i	0.173055	−	0.984912i	$-0.444636\pi$
$360$		0			0
$361$	15.4090	−	26.6892i	0.811001	−	1.40469i
$362$	−24.8002	+	3.18101i	−1.30347	+	0.167190i
$363$		0			0
$364$	−1.97527	+	9.75468i	−0.103532	+	0.511284i
$365$			1.92065i			0.100532i
$366$		0			0
$367$	20.8594	+	12.0432i	1.08885	+	0.628649i	0.933271	−	0.359174i	$-0.116941\pi$
$367$	20.8594	+	12.0432i	1.08885	+	0.628649i	0.155582	+	0.987823i	$0.450275\pi$
$368$	13.8399	+	8.23824i	0.721453	+	0.429448i
$369$		0			0
$370$	6.83266	+	2.85688i	0.355213	+	0.148522i
$371$	−1.16292	+	0.782462i	−0.0603757	+	0.0406234i
$372$		0			0
$373$	−6.69734	−	11.6001i	−0.346775	−	0.600632i	0.638900	−	0.769290i	$-0.279390\pi$
$373$	−6.69734	−	11.6001i	−0.346775	−	0.600632i	−0.985675	+	0.168658i	$0.946057\pi$
$374$	11.4055	−	8.69152i	0.589763	−	0.449428i
$375$		0			0
$376$	−19.8267	−	15.5308i	−1.02248	−	0.800939i
$377$			3.49996i			0.180257i
$378$		0			0
$379$		−	12.9558i		−	0.665493i	−0.943016	−	0.332746i	$-0.892025\pi$
$379$		−	12.9558i		−	0.665493i	0.943016	−	0.332746i	$-0.107975\pi$
$380$	2.61445	−	9.50356i	0.134118	−	0.487522i
$381$		0			0
$382$	−18.2099	−	23.8959i	−0.931698	−	1.22262i
$383$	1.26675	+	2.19407i	0.0647277	+	0.112112i	0.896573	−	0.442896i	$-0.146049\pi$
$383$	1.26675	+	2.19407i	0.0647277	+	0.112112i	−0.831845	+	0.555007i	$0.812715\pi$
$384$		0			0
$385$	4.23496	+	2.07153i	0.215833	+	0.105575i
$386$	2.27363	−	5.43773i	0.115725	−	0.276773i
$387$		0			0
$388$	21.0327	−	5.48579i	1.06777	−	0.278499i
$389$	−13.2543	−	7.65235i	−0.672018	−	0.387990i	0.124823	−	0.992179i	$-0.460164\pi$
$389$	−13.2543	−	7.65235i	−0.672018	−	0.387990i	−0.796841	+	0.604189i	$0.793497\pi$
$390$		0			0
$391$			15.9986i			0.809083i
$392$	17.1111	+	9.96042i	0.864242	+	0.503077i
$393$		0			0
$394$	1.44790	+	11.2883i	0.0729442	+	0.568697i
$395$	−4.72492	+	8.18380i	−0.237736	+	0.411772i
$396$		0			0
$397$	−6.55329	−	11.3506i	−0.328900	−	0.569672i	0.653394	−	0.757018i	$-0.273345\pi$
$397$	−6.55329	−	11.3506i	−0.328900	−	0.569672i	−0.982294	+	0.187346i	$0.940011\pi$
$398$	1.98803	+	0.831239i	0.0996511	+	0.0416663i
$399$		0			0
$400$	−0.240478	+	18.0482i	−0.0120239	+	0.902412i
$401$	−1.00499	+	0.580229i	−0.0501866	+	0.0289753i	−0.524883	−	0.851174i	$-0.675891\pi$
$401$	−1.00499	+	0.580229i	−0.0501866	+	0.0289753i	0.474697	+	0.880149i	$0.342558\pi$
$402$		0			0
$403$	−1.53295	−	0.885048i	−0.0763616	−	0.0440874i
$404$	20.4531	+	5.62670i	1.01758	+	0.279939i
$405$		0			0
$406$	6.59276	+	2.23877i	0.327193	+	0.111108i
$407$	−19.1397			−0.948718
$408$		0			0
$409$	−3.59404	+	6.22507i	−0.177714	+	0.307810i	−0.941097	−	0.338136i	$-0.890204\pi$
$409$	−3.59404	+	6.22507i	−0.177714	+	0.307810i	0.763383	+	0.645946i	$0.223537\pi$
$410$	−6.34815	−	8.33037i	−0.313513	−	0.411408i
$411$		0			0
$412$	18.8992	−	18.6490i	0.931095	−	0.918771i
$413$	19.6448	+	29.1967i	0.966658	+	1.43668i
$414$		0			0
$415$	10.3715	−	5.98798i	0.509116	−	0.293938i
$416$	−8.54785	+	6.33565i	−0.419093	+	0.310631i
$417$		0			0
$418$	3.24080	+	25.2664i	0.158513	+	1.23582i
$419$	−16.1127			−0.787155			−0.393578	−	0.919291i	$-0.628763\pi$
$419$	−16.1127			−0.787155			−0.393578	+	0.919291i	$0.628763\pi$
$420$		0			0
$421$	5.49992			0.268050			0.134025	−	0.990978i	$-0.457210\pi$
$421$	5.49992			0.268050			0.134025	+	0.990978i	$0.457210\pi$
$422$	−3.47028	−	27.0554i	−0.168930	−	1.31704i
$423$		0			0
$424$	−1.48358	−	0.210419i	−0.0720490	−	0.0102189i
$425$	−15.5271	+	8.96460i	−0.753177	+	0.434847i
$426$		0			0
$427$	27.3672	−	1.88220i	1.32439	−	0.0910862i
$428$	−13.5025	−	13.6836i	−0.652670	−	0.661424i
$429$		0			0
$430$	−2.37737	−	3.11971i	−0.114647	−	0.150446i
$431$	6.70530	−	11.6139i	0.322983	−	0.559423i	−0.658119	−	0.752914i	$-0.728648\pi$
$431$	6.70530	−	11.6139i	0.322983	−	0.559423i	0.981102	+	0.193491i	$0.0619811\pi$
$432$		0			0
$433$	−31.6801			−1.52245			−0.761224	−	0.648489i	$-0.775401\pi$
$433$	−31.6801			−1.52245			−0.761224	+	0.648489i	$0.775401\pi$
$434$	−2.64770	+	2.32144i	−0.127094	+	0.111433i
$435$		0			0
$436$	−7.54580	+	27.4291i	−0.361378	+	1.31362i
$437$	−24.6126	−	14.2101i	−1.17738	−	0.679761i
$438$		0			0
$439$	−16.8712	+	9.74059i	−0.805218	+	0.464893i	−0.845292	−	0.534304i	$-0.820574\pi$
$439$	−16.8712	+	9.74059i	−0.805218	+	0.464893i	0.0400745	+	0.999197i	$0.487240\pi$
$440$	1.88209	+	4.67536i	0.0897250	+	0.222889i
$441$		0			0
$442$	−9.75071	−	4.07698i	−0.463794	−	0.193922i
$443$	−3.44127	−	5.96046i	−0.163500	−	0.283190i	0.772622	−	0.634867i	$-0.218945\pi$
$443$	−3.44127	−	5.96046i	−0.163500	−	0.283190i	−0.936121	+	0.351677i	$0.885612\pi$
$444$		0			0
$445$	4.14404	−	7.17770i	0.196447	−	0.340255i
$446$	3.26358	+	25.4440i	0.154535	+	1.20481i
$447$		0			0
$448$	6.46659	+	20.1540i	0.305518	+	0.952186i
$449$		−	19.3255i		−	0.912025i	−0.889973	−	0.456012i	$-0.849277\pi$
$449$		−	19.3255i		−	0.912025i	0.889973	−	0.456012i	$-0.150723\pi$
$450$		0			0
$451$	23.4412	+	13.5338i	1.10380	+	0.637281i
$452$	6.10952	+	23.4241i	0.287368	+	1.10178i
$453$		0			0
$454$	5.22533	−	12.4972i	0.245237	−	0.586521i
$455$	−0.238411	−	3.46649i	−0.0111769	−	0.162511i
$456$		0			0
$457$	−2.41849	−	4.18896i	−0.113132	−	0.195951i	0.803899	−	0.594766i	$-0.202755\pi$
$457$	−2.41849	−	4.18896i	−0.113132	−	0.195951i	−0.917032	+	0.398814i	$0.869422\pi$
$458$	4.15153	+	5.44785i	0.193988	+	0.254562i
$459$		0			0
$460$	−5.42159	−	1.49149i	−0.252783	−	0.0695411i
$461$			26.3490i			1.22720i	0.789618	+	0.613599i	$0.210279\pi$
$461$			26.3490i			1.22720i	−0.789618	+	0.613599i	$0.789721\pi$
$462$		0			0
$463$		−	38.1024i		−	1.77077i	−0.464858	−	0.885385i	$-0.653895\pi$
$463$		−	38.1024i		−	1.77077i	0.464858	−	0.885385i	$-0.346105\pi$
$464$	3.63541	+	6.49505i	0.168770	+	0.301525i
$465$		0			0
$466$	−24.3336	+	18.5434i	−1.12723	+	0.859006i
$467$	−3.19220	−	5.52905i	−0.147717	−	0.255854i	0.782666	−	0.622442i	$-0.213859\pi$
$467$	−3.19220	−	5.52905i	−0.147717	−	0.255854i	−0.930383	+	0.366588i	$0.880526\pi$
$468$		0			0
$469$	−5.97731	+	4.02179i	−0.276007	+	0.185709i
$470$	8.11216	+	3.39187i	0.374186	+	0.156455i
$471$		0			0
$472$	−5.28287	+	37.2474i	−0.243164	+	1.71445i
$473$	8.77871	+	5.06839i	0.403646	+	0.233045i
$474$		0			0
$475$		−	31.8498i		−	1.46137i
$476$	−13.9168	+	15.7593i	−0.637875	+	0.722324i
$477$		0			0
$478$	−28.8328	+	3.69825i	−1.31878	+	0.169154i
$479$	10.5205	−	18.2220i	0.480693	−	0.832585i	−0.519061	−	0.854737i	$-0.673718\pi$
$479$	10.5205	−	18.2220i	0.480693	−	0.832585i	0.999755	+	0.0221516i	$0.00705165\pi$
$480$		0			0
$481$	7.05321	+	12.2165i	0.321599	+	0.557026i
$482$	5.86491	−	14.0268i	0.267139	−	0.638904i
$483$		0			0
$484$	6.30370	+	6.38825i	0.286532	+	0.290375i
$485$	−6.57192	+	3.79430i	−0.298415	+	0.172290i
$486$		0			0
$487$	−13.6690	−	7.89181i	−0.619402	−	0.357612i	0.157234	−	0.987561i	$-0.449742\pi$
$487$	−13.6690	−	7.89181i	−0.619402	−	0.357612i	−0.776636	+	0.629949i	$0.783076\pi$
$488$	23.0862	+	18.0840i	1.04506	+	0.818626i
$489$		0			0
$490$	−6.68222	−	1.76828i	−0.301872	−	0.0798825i
$491$	18.8204			0.849351			0.424675	−	0.905346i	$-0.360388\pi$
$491$	18.8204			0.849351			0.424675	+	0.905346i	$0.360388\pi$
$492$		0			0
$493$	−3.69675	+	6.40295i	−0.166493	+	0.288375i
$494$	14.9328	−	11.3795i	0.671859	−	0.511989i
$495$		0			0
$496$	−3.76407	−	0.0501532i	−0.169012	−	0.00225194i
$497$	−4.08413	+	8.34943i	−0.183198	+	0.374523i
$498$		0			0
$499$	6.97921	−	4.02945i	0.312432	−	0.180383i	−0.335582	−	0.942011i	$-0.608933\pi$
$499$	6.97921	−	4.02945i	0.312432	−	0.180383i	0.648014	+	0.761628i	$0.275600\pi$
$500$	−3.35259	−	12.8539i	−0.149932	−	0.574846i
$501$		0			0
$502$	−27.2572	+	3.49615i	−1.21655	+	0.156041i
$503$	0.823898			0.0367358			0.0183679	−	0.999831i	$-0.494153\pi$
$503$	0.823898			0.0367358			0.0183679	+	0.999831i	$0.494153\pi$
$504$		0			0
$505$	−7.40588			−0.329557
$506$	14.4140	−	1.84881i	0.640779	−	0.0821897i
$507$		0			0
$508$	0.294064	+	1.12745i	0.0130470	+	0.0500225i
$509$	33.8626	−	19.5506i	1.50093	−	0.866563i	0.500932	−	0.865487i	$-0.332991\pi$
$509$	33.8626	−	19.5506i	1.50093	−	0.866563i	0.999999	−	0.00107666i	$-0.000342710\pi$
$510$		0			0
$511$	4.06272	+	6.03813i	0.179724	+	0.267111i
$512$	−9.28184	+	20.6361i	−0.410203	+	0.911994i
$513$		0			0
$514$	−9.82733	+	7.48890i	−0.433465	+	0.330321i
$515$	−4.63477	+	8.02766i	−0.204232	+	0.353741i
$516$		0			0
$517$	−22.7238			−0.999392
$518$	27.5235	−	5.47154i	1.20932	−	0.240406i
$519$		0			0
$520$	2.29063	−	2.92423i	0.100451	−	0.128236i
$521$	−0.453045	−	0.261566i	−0.0198483	−	0.0114594i	0.490043	−	0.871698i	$-0.336981\pi$
$521$	−0.453045	−	0.261566i	−0.0198483	−	0.0114594i	−0.509891	+	0.860239i	$0.670314\pi$
$522$		0			0
$523$	32.5034	−	18.7658i	1.42127	−	0.820573i	0.424865	−	0.905257i	$-0.360321\pi$
$523$	32.5034	−	18.7658i	1.42127	−	0.820573i	0.996408	+	0.0846840i	$0.0269881\pi$
$524$	−15.3012	−	15.5065i	−0.668438	−	0.677403i
$525$		0			0
$526$	11.8972	−	28.4540i	0.518743	−	1.24065i
$527$	−1.86962	−	3.23828i	−0.0814421	−	0.141062i
$528$		0			0
$529$	3.39342	−	5.87757i	0.147540	−	0.255546i
$530$	0.518880	−	0.0665544i	0.0225387	−	0.00289094i
$531$		0			0
$532$	−11.8834	−	35.4075i	−0.515210	−	1.53511i
$533$		−	19.9495i		−	0.864109i
$534$		0			0
$535$	5.81230	+	3.35574i	0.251288	+	0.145081i
$536$	−7.62549	−	1.08154i	−0.329371	−	0.0467153i
$537$		0			0
$538$	19.1851	+	8.02169i	0.827128	+	0.345840i
$539$	17.6957	−	2.44564i	0.762207	−	0.105341i
$540$		0			0
$541$	−11.1770	−	19.3592i	−0.480538	−	0.832317i	0.519212	−	0.854645i	$-0.326225\pi$
$541$	−11.1770	−	19.3592i	−0.480538	−	0.832317i	−0.999751	+	0.0223286i	$0.992892\pi$
$542$	5.83539	−	4.44685i	0.250651	−	0.191009i
$543$		0			0
$544$	−22.3297	+	2.56222i	−0.957376	+	0.109854i
$545$		−	9.93181i		−	0.425432i
$546$		0			0
$547$			8.09960i			0.346314i	0.984894	+	0.173157i	$0.0553968\pi$
$547$			8.09960i			0.346314i	−0.984894	+	0.173157i	$0.944603\pi$
$548$	25.6509	+	7.05661i	1.09575	+	0.301444i
$549$		0			0
$550$	9.87101	+	12.9533i	0.420901	+	0.552329i
$551$	−6.56698	−	11.3743i	−0.279763	−	0.484563i
$552$		0			0
$553$	2.45686	+	35.7227i	0.104476	+	1.51908i
$554$	12.9433	−	30.9559i	0.549909	−	1.31519i
$555$		0			0
$556$	−0.424398	−	1.62716i	−0.0179985	−	0.0690067i
$557$	−27.3598	−	15.7962i	−1.15927	−	0.669307i	−0.208144	−	0.978098i	$-0.566742\pi$
$557$	−27.3598	−	15.7962i	−1.15927	−	0.669307i	−0.951130	+	0.308791i	$0.900076\pi$
$558$		0			0
$559$		−	7.47107i		−	0.315992i
$560$	−4.04308	−	6.18530i	−0.170851	−	0.261377i
$561$		0			0
$562$	−0.741992	−	5.78482i	−0.0312991	−	0.244018i
$563$	−4.17946	+	7.23904i	−0.176143	+	0.305089i	−0.940556	−	0.339638i	$-0.889696\pi$
$563$	−4.17946	+	7.23904i	−0.176143	+	0.305089i	0.764413	+	0.644727i	$0.223029\pi$
$564$		0			0
$565$	−4.22571	−	7.31914i	−0.177777	−	0.307919i
$566$	9.20919	+	3.85056i	0.387091	+	0.161851i
$567$		0			0
$568$	−9.21771	+	3.71063i	−0.386766	+	0.155695i
$569$	11.2838	−	6.51469i	0.473041	−	0.273110i	−0.244471	−	0.969657i	$-0.578614\pi$
$569$	11.2838	−	6.51469i	0.473041	−	0.273110i	0.717512	+	0.696546i	$0.245281\pi$
$570$		0			0
$571$	−12.4590	−	7.19319i	−0.521392	−	0.301026i	0.216112	−	0.976369i	$-0.430662\pi$
$571$	−12.4590	−	7.19319i	−0.521392	−	0.301026i	−0.737504	+	0.675343i	$0.763996\pi$
$572$	−2.54636	+	9.25606i	−0.106469	+	0.387015i
$573$		0			0
$574$	−37.5783	−	12.7608i	−1.56849	−	0.532627i
$575$	−18.1697			−0.757728
$576$		0			0
$577$	12.8808	−	22.3102i	0.536235	−	0.928786i	−0.462868	−	0.886427i	$-0.653180\pi$
$577$	12.8808	−	22.3102i	0.536235	−	0.928786i	0.999102	−	0.0423583i	$-0.0134871\pi$
$578$	1.03990	+	1.36461i	0.0432541	+	0.0567603i
$579$		0			0
$580$	−1.82520	−	1.84968i	−0.0757871	−	0.0768037i
$581$	19.9395	−	40.7635i	0.827231	−	1.69116i
$582$		0			0
$583$	−1.17084	+	0.675987i	−0.0484914	+	0.0279965i
$584$	−1.09254	+	7.70308i	−0.0452098	+	0.318756i
$585$		0			0
$586$	−2.87288	−	22.3979i	−0.118678	−	0.925250i
$587$	33.3927			1.37826			0.689131	−	0.724637i	$-0.257992\pi$
$587$	33.3927			1.37826			0.689131	+	0.724637i	$0.257992\pi$
$588$		0			0
$589$	6.64247			0.273698
$590$	−1.67094	−	13.0272i	−0.0687916	−	0.536323i
$591$		0			0
$592$	25.7783	+	15.3446i	1.05948	+	0.630661i
$593$	−25.5907	+	14.7748i	−1.05089	+	0.606729i	−0.922897	−	0.385046i	$-0.874185\pi$
$593$	−25.5907	+	14.7748i	−1.05089	+	0.606729i	−0.127989	+	0.991776i	$0.540852\pi$
$594$		0			0
$595$	3.22524	−	6.59354i	0.132222	−	0.270309i
$596$	−8.05312	+	7.94653i	−0.329868	+	0.325503i
$597$		0			0
$598$	−6.49179	−	8.51887i	−0.265469	−	0.348363i
$599$	−2.99964	+	5.19553i	−0.122562	+	0.212284i	−0.920777	−	0.390089i	$-0.872444\pi$
$599$	−2.99964	+	5.19553i	−0.122562	+	0.212284i	0.798215	+	0.602372i	$0.205778\pi$
$600$		0			0
$601$	−5.44843			−0.222246			−0.111123	−	0.993807i	$-0.535445\pi$
$601$	−5.44843			−0.222246			−0.111123	+	0.993807i	$0.535445\pi$
$602$	−14.0730	−	4.77892i	−0.573574	−	0.194774i
$603$		0			0
$604$	32.7492	+	9.00938i	1.33255	+	0.366586i
$605$	−2.71349	−	1.56663i	−0.110319	−	0.0636928i
$606$		0			0
$607$	−3.76460	+	2.17350i	−0.152801	+	0.0882195i	−0.574451	−	0.818539i	$-0.694784\pi$
$607$	−3.76460	+	2.17350i	−0.152801	+	0.0882195i	0.421650	+	0.906759i	$0.361451\pi$
$608$	15.8916	−	36.6283i	0.644491	−	1.48547i
$609$		0			0
$610$	−9.44580	−	3.94949i	−0.382449	−	0.159910i
$611$	8.37402	+	14.5042i	0.338776	+	0.586778i
$612$		0			0
$613$	7.48103	−	12.9575i	0.302156	−	0.523350i	−0.674468	−	0.738304i	$-0.735627\pi$
$613$	7.48103	−	12.9575i	0.302156	−	0.523350i	0.976624	+	0.214954i	$0.0689603\pi$
$614$	−0.995771	−	7.76337i	−0.0401861	−	0.313304i
$615$		0			0
$616$	15.8066	+	10.7172i	0.636865	+	0.431809i
$617$			21.4967i			0.865425i	0.901532	+	0.432713i	$0.142443\pi$
$617$			21.4967i			0.865425i	−0.901532	+	0.432713i	$0.857557\pi$
$618$		0			0
$619$	−12.4590	−	7.19319i	−0.500769	−	0.289119i	0.228262	−	0.973600i	$-0.426696\pi$
$619$	−12.4590	−	7.19319i	−0.500769	−	0.289119i	−0.729031	+	0.684481i	$0.760029\pi$
$620$	1.27169	−	0.331684i	0.0510721	−	0.0133207i
$621$		0			0
$622$	5.72212	−	13.6853i	0.229436	−	0.548731i
$623$	−2.15482	−	31.3310i	−0.0863309	−	1.25525i
$624$		0			0
$625$	−8.96230	−	15.5232i	−0.358492	−	0.620927i
$626$	1.93994	+	2.54569i	0.0775354	+	0.101746i
$627$		0			0
$628$	1.04769	−	3.80836i	0.0418073	−	0.151970i
$629$			29.7992i			1.18817i
$630$		0			0
$631$			15.8983i			0.632900i	0.948609	+	0.316450i	$0.102491\pi$
$631$			15.8983i			0.632900i	−0.948609	+	0.316450i	$0.897509\pi$
$632$	−23.6053	+	30.1347i	−0.938968	+	1.19869i
$633$		0			0
$634$	−10.6925	+	8.14822i	−0.424654	+	0.323607i
$635$	−0.203392	−	0.352285i	−0.00807136	−	0.0139800i
$636$		0			0
$637$	−8.08209	−	10.3936i	−0.320224	−	0.411809i
$638$	6.19596	+	2.59066i	0.245300	+	0.102565i
$639$		0			0
$640$	1.21343	−	7.80593i	0.0479651	−	0.308557i
$641$	−1.35619	−	0.782995i	−0.0535661	−	0.0309264i	0.472978	−	0.881074i	$-0.343179\pi$
$641$	−1.35619	−	0.782995i	−0.0535661	−	0.0309264i	−0.526544	+	0.850148i	$0.676512\pi$
$642$		0			0
$643$			33.5314i			1.32235i	0.750232	+	0.661174i	$0.229942\pi$
$643$			33.5314i			1.32235i	−0.750232	+	0.661174i	$0.770058\pi$
$644$	−20.1993	+	6.77924i	−0.795963	+	0.267140i
$645$		0			0
$646$	39.3380	−	5.04570i	1.54773	−	0.198521i
$647$	−8.65921	+	14.9982i	−0.340429	+	0.589640i	−0.984512	−	0.175315i	$-0.943906\pi$
$647$	−8.65921	+	14.9982i	−0.340429	+	0.589640i	0.644084	+	0.764955i	$0.277239\pi$
$648$		0			0
$649$	16.9716	+	29.3957i	0.666195	+	1.15388i
$650$	4.63025	−	11.0739i	0.181613	−	0.434356i
$651$		0			0
$652$	−4.00247	+	3.94949i	−0.156749	+	0.154674i
$653$	−23.4648	+	13.5474i	−0.918247	+	0.530150i	−0.883075	−	0.469231i	$-0.844531\pi$
$653$	−23.4648	+	13.5474i	−0.918247	+	0.530150i	−0.0351715	+	0.999381i	$0.511198\pi$
$654$		0			0
$655$	6.58657	+	3.80276i	0.257359	+	0.148586i
$656$	−20.7216	−	37.0213i	−0.809042	−	1.44544i
$657$		0			0
$658$	32.6777	−	6.49616i	1.27391	−	0.253247i
$659$	10.9749			0.427521			0.213761	−	0.976886i	$-0.431429\pi$
$659$	10.9749			0.427521			0.213761	+	0.976886i	$0.431429\pi$
$660$		0			0
$661$	−1.44036	+	2.49478i	−0.0560235	+	0.0970355i	−0.892677	−	0.450697i	$-0.851176\pi$
$661$	−1.44036	+	2.49478i	−0.0560235	+	0.0970355i	0.836654	+	0.547732i	$0.184509\pi$
$662$	11.1821	−	8.52128i	0.434603	−	0.331189i
$663$		0			0
$664$	45.0027	−	18.1160i	1.74644	−	0.703038i
$665$	7.27898	+	10.8182i	0.282267	+	0.419513i
$666$		0			0
$667$	−6.48884	+	3.74633i	−0.251249	+	0.145059i
$668$	4.66073	−	1.21562i	0.180329	−	0.0470338i
$669$		0			0
$670$	2.66700	−	0.342084i	0.103035	−	0.0132159i
$671$	26.4596			1.02146
$672$		0			0
$673$	9.09255			0.350492			0.175246	−	0.984525i	$-0.443928\pi$
$673$	9.09255			0.350492			0.175246	+	0.984525i	$0.443928\pi$
$674$	−14.9307	+	1.91510i	−0.575111	+	0.0737668i
$675$		0			0
$676$	−18.3120	+	4.77617i	−0.704307	+	0.183699i
$677$	13.8282	−	7.98374i	0.531463	−	0.306840i	−0.210149	−	0.977669i	$-0.567395\pi$
$677$	13.8282	−	7.98374i	0.531463	−	0.306840i	0.741612	+	0.670829i	$0.234062\pi$
$678$		0			0
$679$	−12.6347	+	25.8299i	−0.484877	+	0.991261i
$680$	7.27922	−	2.93028i	0.279145	−	0.112371i
$681$		0			0
$682$	−2.70148	+	2.05866i	−0.103445	+	0.0788302i
$683$	−22.2769	+	38.5848i	−0.852404	+	1.47641i	0.0266295	+	0.999645i	$0.491523\pi$
$683$	−22.2769	+	38.5848i	−0.852404	+	1.47641i	−0.879033	+	0.476761i	$0.841811\pi$
$684$		0			0
$685$	−9.28793			−0.354874
$686$	−24.7479	+	8.57566i	−0.944879	+	0.327420i
$687$		0			0
$688$	−7.76021	−	13.8644i	−0.295855	−	0.528577i
$689$	0.862942	+	0.498220i	0.0328755	+	0.0189807i
$690$		0			0
$691$	−12.1180	+	6.99631i	−0.460989	+	0.266152i	−0.712460	−	0.701713i	$-0.752419\pi$
$691$	−12.1180	+	6.99631i	−0.460989	+	0.266152i	0.251471	+	0.967865i	$0.419086\pi$
$692$	−6.66283	+	6.57465i	−0.253283	+	0.249931i
$693$		0			0
$694$	−9.57366	+	22.8969i	−0.363411	+	0.869153i
$695$	0.293538	+	0.508424i	0.0111345	+	0.0192856i
$696$		0			0
$697$	21.0712	−	36.4964i	0.798128	−	1.38240i
$698$	−40.7775	+	5.23035i	−1.54345	+	0.197972i
$699$		0			0
$700$	−17.8979	−	15.8054i	−0.676476	−	0.597388i
$701$		−	14.4059i		−	0.544104i	−0.962283	−	0.272052i	$-0.912298\pi$
$701$		−	14.4059i		−	0.544104i	0.962283	−	0.272052i	$-0.0877022\pi$
$702$		0			0
$703$	−45.8438	−	26.4679i	−1.72903	−	0.998257i
$704$	4.88888	+	19.8219i	0.184256	+	0.747065i
$705$		0			0
$706$	−14.6735	−	6.13528i	−0.552243	−	0.230904i
$707$	−23.2825	+	15.6655i	−0.875629	+	0.589161i
$708$		0			0
$709$	22.0939	+	38.2677i	0.829753	+	1.43717i	0.898232	+	0.439522i	$0.144852\pi$
$709$	22.0939	+	38.2677i	0.829753	+	1.43717i	−0.0684783	+	0.997653i	$0.521814\pi$
$710$	2.75920	−	2.10264i	0.103551	−	0.0789108i
$711$		0			0
$712$	20.7033	−	26.4300i	0.775889	−	0.990505i
$713$		−	3.78940i		−	0.141914i
$714$		0			0
$715$		−	3.35153i		−	0.125340i
$716$	6.99771	−	25.4368i	0.261517	−	0.950617i
$717$		0			0
$718$	24.8955	+	32.6692i	0.929092	+	1.21920i
$719$	6.06830	+	10.5106i	0.226309	+	0.391979i	0.956711	−	0.291038i	$-0.0940006\pi$
$719$	6.06830	+	10.5106i	0.226309	+	0.391979i	−0.730402	+	0.683017i	$0.760667\pi$
$720$		0			0
$721$	2.40998	+	35.0411i	0.0897525	+	1.30500i
$722$	−16.8126	+	40.2099i	−0.625701	+	1.49646i
$723$		0			0
$724$	34.2155	−	8.92415i	1.27161	−	0.331664i
$725$	−7.27187	−	4.19842i	−0.270071	−	0.155925i
$726$		0			0
$727$			27.8081i			1.03134i	0.856786	+	0.515672i	$0.172458\pi$
$727$			27.8081i			1.03134i	−0.856786	+	0.515672i	$0.827542\pi$
$728$	1.01569	−	14.0385i	0.0376440	−	0.520301i
$729$		0			0
$730$	−0.345565	−	2.69414i	−0.0127899	−	0.0997147i
$731$	7.89114	−	13.6679i	0.291864	−	0.505524i
$732$		0			0
$733$	19.8313	+	34.3488i	0.732486	+	1.26870i	0.955818	+	0.293961i	$0.0949734\pi$
$733$	19.8313	+	34.3488i	0.732486	+	1.26870i	−0.223331	+	0.974743i	$0.571693\pi$
$734$	−31.4268	−	13.1402i	−1.15998	−	0.485014i
$735$		0			0
$736$	−20.8957	−	9.06587i	−0.770227	−	0.334173i
$737$	−6.01805	+	3.47452i	−0.221678	+	0.127986i
$738$		0			0
$739$	28.2813	+	16.3282i	1.04034	+	0.600643i	0.919931	−	0.392080i	$-0.128244\pi$
$739$	28.2813	+	16.3282i	1.04034	+	0.600643i	0.120414	+	0.992724i	$0.461578\pi$
$740$	−10.0983	−	2.77807i	−0.371222	−	0.102124i
$741$		0			0
$742$	1.49047	−	1.30681i	0.0547169	−	0.0479745i
$743$	−33.8538			−1.24198			−0.620988	−	0.783820i	$-0.713268\pi$
$743$	−33.8538			−1.24198			−0.620988	+	0.783820i	$0.713268\pi$
$744$		0			0
$745$	1.97492	−	3.42066i	0.0723555	−	0.125323i
$746$	11.4816	+	15.0668i	0.420371	+	0.551633i
$747$		0			0
$748$	−14.4349	+	14.2439i	−0.527793	+	0.520807i
$749$	25.3710	−	1.74491i	0.927036	−	0.0637577i
$750$		0			0
$751$	−25.7744	+	14.8808i	−0.940520	+	0.543010i	−0.890123	−	0.455720i	$-0.849382\pi$
$751$	−25.7744	+	14.8808i	−0.940520	+	0.543010i	−0.0503969	+	0.998729i	$0.516049\pi$
$752$	30.6057	+	18.2181i	1.11607	+	0.664347i
$753$		0			0
$754$	−0.629714	−	4.90946i	−0.0229328	−	0.178792i
$755$	−11.8582			−0.431563
$756$		0			0
$757$	21.4183			0.778460			0.389230	−	0.921141i	$-0.372741\pi$
$757$	21.4183			0.778460			0.389230	+	0.921141i	$0.372741\pi$
$758$	2.33101	+	18.1733i	0.0846661	+	0.660085i
$759$		0			0
$760$	−1.95746	+	13.8012i	−0.0710044	+	0.500624i
$761$	37.9234	−	21.8951i	1.37472	−	0.793696i	0.383203	−	0.923664i	$-0.374821\pi$
$761$	37.9234	−	21.8951i	1.37472	−	0.793696i	0.991518	+	0.129969i	$0.0414877\pi$
$762$		0			0
$763$	−21.0085	−	31.2235i	−0.760560	−	1.13037i
$764$	29.8427	+	30.2430i	1.07967	+	1.09415i
$765$		0			0
$766$	−2.17165	−	2.84975i	−0.0784649	−	0.102966i
$767$	12.5085	−	21.6654i	0.451657	−	0.782292i
$768$		0			0
$769$	−53.6687			−1.93534			−0.967672	−	0.252212i	$-0.918842\pi$
$769$	−53.6687			−1.93534			−0.967672	+	0.252212i	$0.918842\pi$
$770$	−6.31318	−	2.14383i	−0.227511	−	0.0772582i
$771$		0			0
$772$	−2.21091	+	8.03669i	−0.0795724	+	0.289247i
$773$	37.6921	+	21.7615i	1.35569	+	0.782708i	0.989040	−	0.147650i	$-0.0471710\pi$
$773$	37.6921	+	21.7615i	1.35569	+	0.782708i	0.366651	+	0.930359i	$0.380504\pi$
$774$		0			0
$775$	3.67774	−	2.12334i	0.132108	−	0.0762727i
$776$	−28.5161	+	11.4793i	−1.02367	+	0.412082i
$777$		0			0
$778$	19.9689	+	8.34941i	0.715918	+	0.299341i
$779$	37.4313	+	64.8329i	1.34112	+	2.32288i
$780$		0			0
$781$	−4.48268	+	7.76424i	−0.160403	+	0.277826i
$782$	−2.87848	−	22.4416i	−0.102934	−	0.802508i
$783$		0			0
$784$	−25.7942	−	10.8931i	−0.921222	−	0.389038i
$785$			1.37897i			0.0492175i
$786$		0			0
$787$	−9.79031	−	5.65244i	−0.348987	−	0.201488i	0.315252	−	0.949008i	$-0.397911\pi$
$787$	−9.79031	−	5.65244i	−0.348987	−	0.201488i	−0.664239	+	0.747520i	$0.731244\pi$
$788$	−4.06200	−	15.5739i	−0.144703	−	0.554796i
$789$		0			0
$790$	5.15531	−	12.3297i	0.183418	−	0.438671i
$791$	−28.7668	−	14.0713i	−1.02283	−	0.500318i
$792$		0			0
$793$	−9.75071	−	16.8887i	−0.346258	−	0.599736i
$794$	11.2347	+	14.7427i	0.398703	+	0.523199i
$795$		0			0
$796$	−2.93822	−	0.808309i	−0.104142	−	0.0286498i
$797$			52.0507i			1.84373i	0.387511	+	0.921865i	$0.373335\pi$
$797$			52.0507i			1.84373i	−0.387511	+	0.921865i	$0.626665\pi$
$798$		0			0
$799$			35.3794i			1.25163i
$800$	−2.90993	−	25.3599i	−0.102881	−	0.896609i
$801$		0			0
$802$	1.30532	−	0.994718i	0.0460925	−	0.0351247i
$803$	3.50988	+	6.07929i	0.123861	+	0.214533i
$804$		0			0
$805$	6.17159	−	4.15251i	0.217520	−	0.146357i
$806$	2.30954	+	0.965667i	0.0813500	+	0.0340142i
$807$		0			0
$808$	−29.7024	−	4.21275i	−1.04493	−	0.148204i
$809$	11.0507	+	6.38012i	0.388521	+	0.224313i	0.681519	−	0.731800i	$-0.261320\pi$
$809$	11.0507	+	6.38012i	0.388521	+	0.224313i	−0.292998	+	0.956113i	$0.594653\pi$
$810$		0			0
$811$			37.2617i			1.30843i	0.756307	+	0.654217i	$0.227002\pi$
$811$			37.2617i			1.30843i	−0.756307	+	0.654217i	$0.772998\pi$
$812$	−9.65062	−	1.95420i	−0.338670	−	0.0685790i
$813$		0			0
$814$	26.8476	−	3.44362i	0.941009	−	0.120699i
$815$	0.981552	−	1.70010i	0.0343823	−	0.0595519i
$816$		0			0
$817$	14.0180	+	24.2799i	0.490427	+	0.849445i
$818$	3.92143	−	9.37868i	0.137109	−	0.327918i
$819$		0			0
$820$	10.4035	+	10.5430i	0.363306	+	0.368179i
$821$	−34.1392	+	19.7103i	−1.19147	+	0.687893i	−0.958639	−	0.284625i	$-0.908131\pi$
$821$	−34.1392	+	19.7103i	−1.19147	+	0.687893i	−0.232827	+	0.972518i	$0.574798\pi$
$822$		0			0
$823$	−43.1751	−	24.9272i	−1.50499	−	0.868907i	−0.999983	−	0.00579133i	$-0.998157\pi$
$823$	−43.1751	−	24.9272i	−1.50499	−	0.868907i	−0.505007	−	0.863115i	$-0.668510\pi$
$824$	−23.1549	+	29.5597i	−0.806640	+	1.02976i
$825$		0			0
$826$	−32.8093	−	37.4204i	−1.14158	−	1.30202i
$827$	48.4688			1.68542			0.842712	−	0.538364i	$-0.180957\pi$
$827$	48.4688			1.68542			0.842712	+	0.538364i	$0.180957\pi$
$828$		0			0
$829$	4.30870	−	7.46288i	0.149647	−	0.259197i	−0.781450	−	0.623968i	$-0.785520\pi$
$829$	4.30870	−	7.46288i	0.149647	−	0.259197i	0.931097	+	0.364771i	$0.118853\pi$
$830$	−13.4710	+	10.2655i	−0.467584	+	0.356321i
$831$		0			0
$832$	10.8503	−	10.4251i	0.376168	−	0.361425i
$833$	−3.80770	−	27.5510i	−0.131929	−	0.954585i
$834$		0			0
$835$	−1.45630	+	0.840795i	−0.0503973	+	0.0290969i
$836$	−9.09188	−	34.8586i	−0.314449	−	1.20561i
$837$		0			0
$838$	22.6016	−	2.89900i	0.780759	−	0.100144i
$839$	−35.7594			−1.23455			−0.617275	−	0.786747i	$-0.711763\pi$
$839$	−35.7594			−1.23455			−0.617275	+	0.786747i	$0.711763\pi$
$840$		0			0
$841$	25.5374			0.880599
$842$	−7.71486	+	0.989550i	−0.265872	+	0.0341021i
$843$		0			0
$844$	9.73566	+	37.3269i	0.335115	+	1.28484i
$845$	5.72179	−	3.30348i	0.196836	−	0.113643i
$846$		0			0
$847$	−11.8445	+	0.814618i	−0.406982	+	0.0279906i
$848$	2.11891	+	0.0282327i	0.0727636	+	0.000969516i
$849$		0			0
$850$	20.1673	−	15.3685i	0.691734	−	0.527135i
$851$	−15.0994	+	26.1530i	−0.517602	+	0.896513i
$852$		0			0
$853$	−13.3666			−0.457664			−0.228832	−	0.973466i	$-0.573491\pi$
$853$	−13.3666			−0.457664			−0.228832	+	0.973466i	$0.573491\pi$
$854$	−38.0499	+	7.56413i	−1.30204	+	0.258839i
$855$		0			0
$856$	21.4023	+	16.7650i	0.731515	+	0.573015i
$857$	−8.60210	−	4.96642i	−0.293842	−	0.169650i	0.345831	−	0.938297i	$-0.387597\pi$
$857$	−8.60210	−	4.96642i	−0.293842	−	0.169650i	−0.639673	+	0.768647i	$0.720930\pi$
$858$		0			0
$859$	25.8761	−	14.9395i	0.882879	−	0.509731i	0.0112727	−	0.999936i	$-0.496412\pi$
$859$	25.8761	−	14.9395i	0.882879	−	0.509731i	0.871607	+	0.490206i	$0.163078\pi$
$860$	3.89610	+	3.94835i	0.132856	+	0.134638i
$861$		0			0
$862$	−7.31608	+	17.4975i	−0.249187	+	0.595968i
$863$	−1.78179	−	3.08616i	−0.0606530	−	0.105054i	0.834104	−	0.551606i	$-0.185985\pi$
$863$	−1.78179	−	3.08616i	−0.0606530	−	0.105054i	−0.894757	+	0.446552i	$0.852652\pi$
$864$		0			0
$865$	1.63397	−	2.83012i	0.0555567	−	0.0962271i
$866$	44.4384	−	5.69990i	1.51008	−	0.193691i
$867$		0			0
$868$	3.29631	−	3.73271i	0.111884	−	0.126697i
$869$			34.5380i			1.17162i
$870$		0			0
$871$	4.43546	+	2.56081i	0.150290	+	0.0867698i
$872$	5.64960	−	39.8331i	0.191320	−	1.34892i
$873$		0			0
$874$	37.0813	+	15.5045i	1.25430	+	0.524448i
$875$	15.7857	+	7.72160i	0.533654	+	0.261038i
$876$		0			0
$877$	4.34706	+	7.52933i	0.146790	+	0.254247i	0.930039	−	0.367460i	$-0.119773\pi$
$877$	4.34706	+	7.52933i	0.146790	+	0.254247i	−0.783249	+	0.621708i	$0.786439\pi$
$878$	21.9131	−	16.6988i	0.739530	−	0.563558i
$879$		0			0
$880$	−3.48124	−	6.21960i	−0.117353	−	0.209663i
$881$		−	48.2017i		−	1.62396i	−0.583688	−	0.811978i	$-0.698391\pi$
$881$		−	48.2017i		−	1.62396i	0.583688	−	0.811978i	$-0.301609\pi$
$882$		0			0
$883$		−	6.60661i		−	0.222330i	−0.993802	−	0.111165i	$-0.964542\pi$
$883$		−	6.60661i		−	0.222330i	0.993802	−	0.111165i	$-0.0354582\pi$
$884$	14.4111	+	3.96451i	0.484697	+	0.133341i
$885$		0			0
$886$	5.89956	+	7.74171i	0.198199	+	0.260088i
$887$	−24.0596	−	41.6725i	−0.807844	−	1.39923i	−0.914354	−	0.404915i	$-0.867301\pi$
$887$	−24.0596	−	41.6725i	−0.807844	−	1.39923i	0.106511	−	0.994312i	$-0.466032\pi$
$888$		0			0
$889$	−1.38460	−	0.677280i	−0.0464380	−	0.0227152i
$890$	−4.52153	+	10.8139i	−0.151562	+	0.362483i
$891$		0			0
$892$	−9.15579	−	35.1036i	−0.306559	−	1.17536i
$893$	−54.4286	−	31.4244i	−1.82138	−	1.05158i
$894$		0			0
$895$			9.21040i			0.307870i
$896$	−12.6969	−	27.1070i	−0.424175	−	0.905580i
$897$		0			0
$898$	3.47705	+	27.1082i	0.116031	+	0.904614i
$899$	0.875606	−	1.51659i	0.0292031	−	0.0505813i
$900$		0			0
$901$	1.05247	+	1.82293i	0.0350627	+	0.0607305i
$902$	−35.3165	−	14.7666i	−1.17591	−	0.491674i
$903$		0			0
$904$	−12.7844	−	31.7583i	−0.425204	−	1.05627i
$905$	−10.6910	+	6.17247i	−0.355382	+	0.205180i
$906$		0			0
$907$	6.95656	+	4.01637i	0.230989	+	0.133361i	0.611028	−	0.791609i	$-0.290756\pi$
$907$	6.95656	+	4.01637i	0.230989	+	0.133361i	−0.380039	+	0.924970i	$0.624090\pi$
$908$	−5.08119	+	18.4702i	−0.168625	+	0.612955i
$909$		0			0
$910$	0.958116	+	4.81962i	0.0317612	+	0.159769i
$911$	55.0200			1.82289			0.911446	−	0.411419i	$-0.134967\pi$
$911$	55.0200			1.82289			0.911446	+	0.411419i	$0.134967\pi$
$912$		0			0
$913$	21.8853	−	37.9065i	0.724299	−	1.25452i
$914$	4.14616	+	5.44080i	0.137143	+	0.179966i
$915$		0			0
$916$	−6.80362	−	6.89488i	−0.224798	−	0.227813i
$917$	28.7507	−	1.97736i	0.949432	−	0.0652980i
$918$		0			0
$919$	−14.7985	+	8.54390i	−0.488156	+	0.281837i	−0.723809	−	0.690000i	$-0.757610\pi$
$919$	−14.7985	+	8.54390i	−0.488156	+	0.281837i	0.235653	+	0.971837i	$0.424277\pi$
$920$	7.87334	+	1.11669i	0.259576	+	0.0368162i
$921$		0			0
$922$	−4.74074	−	36.9604i	−0.156128	−	1.21723i
$923$	6.60771			0.217495
$924$		0			0
$925$	−33.8431			−1.11275
$926$	6.85542	+	53.4471i	0.225283	+	1.75638i
$927$		0			0
$928$	−6.26806	−	8.45666i	−0.205759	−	0.277604i
$929$	−24.2444	+	13.9975i	−0.795434	+	0.459244i	−0.841872	−	0.539677i	$-0.818546\pi$
$929$	−24.2444	+	13.9975i	−0.795434	+	0.459244i	0.0464382	+	0.998921i	$0.485213\pi$
$930$		0			0
$931$	45.7671	+	18.6132i	1.49996	+	0.610023i
$932$	30.7969	−	30.3893i	1.00879	−	0.995435i
$933$		0			0
$934$	5.47255	+	7.18137i	0.179067	+	0.234982i
$935$	3.53997	−	6.13141i	0.115770	−	0.200519i
$936$		0			0
$937$	−50.4480			−1.64806			−0.824031	−	0.566544i	$-0.808280\pi$
$937$	−50.4480			−1.64806			−0.824031	+	0.566544i	$0.808280\pi$
$938$	7.66090	−	6.71690i	0.250137	−	0.219314i
$939$		0			0
$940$	−11.9894	−	3.29830i	−0.391050	−	0.107579i
$941$	−20.0547	−	11.5786i	−0.653765	−	0.377451i	0.136132	−	0.990691i	$-0.456533\pi$
$941$	−20.0547	−	11.5786i	−0.653765	−	0.377451i	−0.789897	+	0.613239i	$0.789866\pi$
$942$		0			0
$943$	36.9859	−	21.3538i	1.20443	−	0.695376i
$944$	0.708823	−	53.1982i	0.0230702	−	1.73145i
$945$		0			0
$946$	−13.2260	−	5.53007i	−0.430014	−	0.179798i
$947$	−7.28937	−	12.6256i	−0.236873	−	0.410275i	0.722943	−	0.690908i	$-0.242789\pi$
$947$	−7.28937	−	12.6256i	−0.236873	−	0.410275i	−0.959815	+	0.280633i	$0.909456\pi$
$948$		0			0
$949$	2.58687	−	4.48059i	0.0839734	−	0.145446i
$950$	5.73044	+	44.6764i	0.185920	+	1.44949i
$951$		0			0
$952$	16.6860	−	24.6098i	0.540796	−	0.797607i
$953$		−	27.8728i		−	0.902889i	−0.892299	−	0.451444i	$-0.850909\pi$
$953$		−	27.8728i		−	0.902889i	0.892299	−	0.451444i	$-0.149091\pi$
$954$		0			0
$955$	−12.8461	−	7.41671i	−0.415690	−	0.239999i
$956$	39.7790	−	10.3752i	1.28654	−	0.335559i
$957$		0			0
$958$	−11.4788	+	27.4533i	−0.370863	+	0.886975i
$959$	−29.1993	+	19.6466i	−0.942895	+	0.634421i
$960$		0			0
$961$	−15.0572	−	26.0798i	−0.485715	−	0.841283i
$962$	−12.0917	−	15.8674i	−0.389852	−	0.511584i
$963$		0			0
$964$	−5.70312	+	20.7309i	−0.183685	+	0.667698i
$965$		−	2.91001i		−	0.0936764i
$966$		0			0
$967$		−	22.2042i		−	0.714038i	−0.934097	−	0.357019i	$-0.883793\pi$
$967$		−	22.2042i		−	0.714038i	0.934097	−	0.357019i	$-0.116207\pi$
$968$	−9.99172	−	7.82677i	−0.321146	−	0.251562i
$969$		0			0
$970$	8.53590	−	6.50477i	0.274071	−	0.208856i
$971$	8.09294	+	14.0174i	0.259715	+	0.449839i	0.966165	−	0.257923i	$-0.0830381\pi$
$971$	8.09294	+	14.0174i	0.259715	+	0.449839i	−0.706451	+	0.707762i	$0.749705\pi$
$972$		0			0
$973$	1.99828	+	0.977461i	0.0640619	+	0.0313360i
$974$	20.5937	+	8.61068i	0.659866	+	0.275904i
$975$		0			0
$976$	−35.6372	−	21.2132i	−1.14072	−	0.679018i
$977$	24.7828	+	14.3084i	0.792873	+	0.457766i	0.840973	−	0.541077i	$-0.181983\pi$
$977$	24.7828	+	14.3084i	0.792873	+	0.457766i	−0.0480999	+	0.998843i	$0.515317\pi$
$978$		0			0
$979$		−	30.2920i		−	0.968135i
$980$	9.69144	+	1.27813i	0.309582	+	0.0408283i
$981$		0			0
$982$	−26.3997	+	3.38617i	−0.842449	+	0.108057i
$983$	23.8922	−	41.3824i	0.762041	−	1.31989i	−0.179755	−	0.983711i	$-0.557531\pi$
$983$	23.8922	−	41.3824i	0.762041	−	1.31989i	0.941797	−	0.336183i	$-0.109136\pi$
$984$		0			0
$985$	2.80952	+	4.86624i	0.0895188	+	0.155051i
$986$	4.03348	−	9.64668i	0.128452	−	0.307213i
$987$		0			0
$988$	−18.8992	+	18.6490i	−0.601262	+	0.593304i
$989$	13.8512	−	7.99698i	0.440442	−	0.254289i
$990$		0			0
$991$	−17.7282	−	10.2354i	−0.563155	−	0.325138i	0.191256	−	0.981540i	$-0.438744\pi$
$991$	−17.7282	−	10.2354i	−0.563155	−	0.325138i	−0.754411	+	0.656403i	$0.772077\pi$
$992$	5.28897	−	0.606883i	0.167925	−	0.0192686i
$993$		0			0
$994$	4.22667	−	12.4467i	0.134062	−	0.394787i
$995$	1.06390			0.0337278
$996$		0			0
$997$	17.1746	−	29.7472i	0.543924	−	0.942104i	−0.454750	−	0.890619i	$-0.650271\pi$
$997$	17.1746	−	29.7472i	0.543924	−	0.942104i	0.998674	−	0.0514848i	$-0.0163954\pi$
$998$	−9.06490	+	6.90790i	−0.286945	+	0.218666i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.be.a.179.2	yes	32
3.2	odd	2	inner	252.2.be.a.179.15	yes	32
4.3	odd	2	inner	252.2.be.a.179.4	yes	32
7.2	even	3	inner	252.2.be.a.107.13	yes	32
7.3	odd	6		1764.2.e.h.1079.9		16
7.4	even	3		1764.2.e.i.1079.9		16
12.11	even	2	inner	252.2.be.a.179.13	yes	32
21.2	odd	6	inner	252.2.be.a.107.4	yes	32
21.11	odd	6		1764.2.e.i.1079.8		16
21.17	even	6		1764.2.e.h.1079.8		16
28.3	even	6		1764.2.e.h.1079.7		16
28.11	odd	6		1764.2.e.i.1079.7		16
28.23	odd	6	inner	252.2.be.a.107.15	yes	32
84.11	even	6		1764.2.e.i.1079.10		16
84.23	even	6	inner	252.2.be.a.107.2	✓	32
84.59	odd	6		1764.2.e.h.1079.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.2	✓	32	84.23	even	6	inner
252.2.be.a.107.4	yes	32	21.2	odd	6	inner
252.2.be.a.107.13	yes	32	7.2	even	3	inner
252.2.be.a.107.15	yes	32	28.23	odd	6	inner
252.2.be.a.179.2	yes	32	1.1	even	1	trivial
252.2.be.a.179.4	yes	32	4.3	odd	2	inner
252.2.be.a.179.13	yes	32	12.11	even	2	inner
252.2.be.a.179.15	yes	32	3.2	odd	2	inner
1764.2.e.h.1079.7		16	28.3	even	6
1764.2.e.h.1079.8		16	21.17	even	6
1764.2.e.h.1079.9		16	7.3	odd	6
1764.2.e.h.1079.10		16	84.59	odd	6
1764.2.e.i.1079.7		16	28.11	odd	6
1764.2.e.i.1079.8		16	21.11	odd	6
1764.2.e.i.1079.9		16	7.4	even	3
1764.2.e.i.1079.10		16	84.11	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40272 + 0.179921i) q^{2} +(1.93526 - 0.504757i) q^{4} +(-0.604694 + 0.349120i) q^{5} +(-1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +O(q^{10})\)	\(q+(-1.40272 + 0.179921i) q^{2} +(1.93526 - 0.504757i) q^{4} +(-0.604694 + 0.349120i) q^{5} +(-1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +(0.785403 - 0.598515i) q^{10} +(-1.27599 + 2.21008i) q^{11} +1.88088 q^{13} +(1.20312 - 3.54295i) q^{14} +(3.49044 - 1.95367i) q^{16} +(3.44095 + 1.98663i) q^{17} +(-6.11257 + 3.52909i) q^{19} +(-0.994017 + 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} +(2.01328 + 3.48710i) q^{23} +(-2.25623 + 3.90791i) q^{25} +(-2.63835 + 0.338409i) q^{26} +(-1.05019 + 5.18624i) q^{28} +1.86081i q^{29} +(-0.815018 - 0.470551i) q^{31} +(-4.54461 + 3.36846i) q^{32} +(-5.18413 - 2.16759i) q^{34} +(-0.126755 - 1.84302i) q^{35} +(3.74996 + 6.49512i) q^{37} +(7.93928 - 6.05012i) q^{38} +(1.21785 - 1.55472i) q^{40} -10.6065i q^{41} -3.97212i q^{43} +(-1.35382 + 4.92114i) q^{44} +(-3.45147 - 4.52920i) q^{46} +(4.45219 + 7.71142i) q^{47} +(-4.29698 - 5.52593i) q^{49} +(2.46175 - 5.88765i) q^{50} +(3.63998 - 0.949386i) q^{52} +(0.458798 + 0.264887i) q^{53} -1.78190i q^{55} +(0.540009 - 7.46381i) q^{56} +(-0.334798 - 2.61020i) q^{58} +(6.65037 - 11.5188i) q^{59} +(-5.18413 - 8.97918i) q^{61} +(1.22791 + 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} +(-1.13735 + 0.656652i) q^{65} +(2.35819 + 1.36150i) q^{67} +(7.66189 + 2.10780i) q^{68} +(0.509399 + 2.56243i) q^{70} +3.51310 q^{71} +(1.37535 - 2.38218i) q^{73} +(-6.42876 - 8.43615i) q^{74} +(-10.0481 + 9.91507i) q^{76} +(-3.76921 - 5.60191i) q^{77} +(11.7206 - 6.76690i) q^{79} +(-1.42858 + 2.39995i) q^{80} +(1.90833 + 14.8780i) q^{82} -17.1516 q^{83} -2.77429 q^{85} +(0.714666 + 5.57178i) q^{86} +(1.01361 - 7.14657i) q^{88} +(-10.2797 + 5.93499i) q^{89} +(-2.18660 + 4.47020i) q^{91} +(5.65635 + 5.73222i) q^{92} +(-7.63263 - 10.0159i) q^{94} +(2.46415 - 4.26804i) q^{95} +10.8682 q^{97} +(7.02170 + 6.97823i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) \) 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

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