LMFDB - Embedded newform 252.2.be.a.107.13

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			107.13
Character	$\chi$	$=$	252.107
Dual form			252.2.be.a.179.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.857177 + 1.12483i) q^{2} +(-0.530496 + 1.92836i) q^{4} +(0.604694 + 0.349120i) q^{5} +(1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +O(q^{10})$	\(q+(0.857177 + 1.12483i) q^{2} +(-0.530496 + 1.92836i) q^{4} +(0.604694 + 0.349120i) q^{5} +(1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +(0.125628 + 0.979437i) q^{10} +(-1.27599 - 2.21008i) q^{11} +1.88088 q^{13} +(-1.67683 + 3.34488i) q^{14} +(-3.43715 - 2.04597i) q^{16} +(-3.44095 + 1.98663i) q^{17} +(6.11257 + 3.52909i) q^{19} +(-0.994017 + 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} +(2.01328 - 3.48710i) q^{23} +(-2.25623 - 3.90791i) q^{25} +(1.61224 + 2.11567i) q^{26} +(-5.19977 + 0.980998i) q^{28} +1.86081i q^{29} +(0.815018 - 0.470551i) q^{31} +(-0.644865 - 5.61998i) q^{32} +(-5.18413 - 2.16759i) q^{34} +(-0.126755 + 1.84302i) q^{35} +(3.74996 - 6.49512i) q^{37} +(1.26991 + 9.90067i) q^{38} +(-1.95535 - 0.277331i) q^{40} -10.6065i q^{41} -3.97212i q^{43} +(4.93874 - 1.28813i) q^{44} +(5.64814 - 0.724461i) q^{46} +(4.45219 - 7.71142i) q^{47} +(-4.29698 + 5.52593i) q^{49} +(2.46175 - 5.88765i) q^{50} +(-0.997797 + 3.62701i) q^{52} +(-0.458798 + 0.264887i) q^{53} -1.78190i q^{55} +(-5.56058 - 5.00799i) q^{56} +(-2.09310 + 1.59504i) q^{58} +(6.65037 + 11.5188i) q^{59} +(-5.18413 + 8.97918i) q^{61} +(1.22791 + 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} +(1.13735 + 0.656652i) q^{65} +(-2.35819 + 1.36150i) q^{67} +(-2.00553 - 7.68929i) q^{68} +(-2.18174 + 1.43721i) q^{70} +3.51310 q^{71} +(1.37535 + 2.38218i) q^{73} +(10.5203 - 1.34939i) q^{74} +(-10.0481 + 9.91507i) q^{76} +(3.76921 - 5.60191i) q^{77} +(-11.7206 - 6.76690i) q^{79} +(-1.36413 - 2.43717i) q^{80} +(11.9305 - 9.09164i) q^{82} -17.1516 q^{83} -2.77429 q^{85} +(4.46797 - 3.40481i) q^{86} +(5.68231 + 4.45110i) q^{88} +(10.2797 + 5.93499i) q^{89} +(2.18660 + 4.47020i) q^{91} +(5.65635 + 5.73222i) q^{92} +(12.4904 - 1.60208i) q^{94} +(2.46415 + 4.26804i) q^{95} +10.8682 q^{97} +(-9.89902 - 0.0966841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.857177	+	1.12483i	0.606116	+	0.795377i
$2$	0.857177	+	1.12483i	0.606116	+	0.795377i
$3$		0			0
$3$		0			0
$4$	−0.530496	+	1.92836i	−0.265248	+	0.964180i
$5$	0.604694	+	0.349120i	0.270427	+	0.156131i	0.629082	−	0.777339i	$-0.283431\pi$
$5$	0.604694	+	0.349120i	0.270427	+	0.156131i	−0.358655	+	0.933470i	$0.616764\pi$
$6$		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
$10$	0.125628	+	0.979437i	0.0397270	+	0.309725i
$11$	−1.27599	−	2.21008i	−0.384726	−	0.666365i	0.607005	−	0.794698i	$-0.292371\pi$
$11$	−1.27599	−	2.21008i	−0.384726	−	0.666365i	−0.991731	+	0.128333i	$0.959037\pi$
$12$		0			0
$13$	1.88088			0.521661			0.260831	−	0.965385i	$-0.416004\pi$
$13$	1.88088			0.521661			0.260831	+	0.965385i	$0.416004\pi$
$14$	−1.67683	+	3.34488i	−0.448153	+	0.893957i
$15$		0			0
$16$	−3.43715	−	2.04597i	−0.859287	−	0.511494i
$17$	−3.44095	+	1.98663i	−0.834553	+	0.481829i	−0.855409	−	0.517953i	$-0.826694\pi$
$17$	−3.44095	+	1.98663i	−0.834553	+	0.481829i	0.0208563	+	0.999782i	$0.493361\pi$
$18$		0			0
$19$	6.11257	+	3.52909i	1.40232	+	0.809630i	0.994630	−	0.103491i	$-0.0330013\pi$
$19$	6.11257	+	3.52909i	1.40232	+	0.809630i	0.407689	+	0.913121i	$0.366335\pi$
$20$	−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	−0.576121	−	0.817364i	$-0.695434\pi$
$23$	2.01328	−	3.48710i	0.419798	−	0.727111i	0.995919	+	0.0902534i	$0.0287677\pi$
$24$		0			0
$25$	−2.25623	−	3.90791i	−0.451246	−	0.781581i
$26$	1.61224	+	2.11567i	0.316187	+	0.414917i
$27$		0			0
$28$	−5.19977	+	0.980998i	−0.982665	+	0.185391i
$29$			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	$-0.639733\pi$
$31$	0.815018	−	0.470551i	0.146382	−	0.0845134i	0.571402	+	0.820670i	$0.306400\pi$
$32$	−0.644865	−	5.61998i	−0.113997	−	0.993481i
$33$		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	−0.373631	−	0.927577i	$-0.621888\pi$
$37$	3.74996	−	6.49512i	0.616490	−	1.06779i	0.990121	−	0.140214i	$-0.0447792\pi$
$38$	1.26991	+	9.90067i	0.206007	+	1.60610i
$39$		0			0
$40$	−1.95535	−	0.277331i	−0.309168	−	0.0438499i
$41$		−	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	$-0.0979452\pi$
$44$	4.93874	−	1.28813i	0.744544	−	0.194193i
$45$		0			0
$46$	5.64814	−	0.724461i	0.832773	−	0.106816i
$47$	4.45219	−	7.71142i	0.649418	−	1.12483i	−0.333844	−	0.942628i	$-0.608346\pi$
$47$	4.45219	−	7.71142i	0.649418	−	1.12483i	0.983262	−	0.182197i	$-0.0583209\pi$
$48$		0			0
$49$	−4.29698	+	5.52593i	−0.613855	+	0.789419i
$50$	2.46175	−	5.88765i	0.348144	−	0.832639i
$51$		0			0
$52$	−0.997797	+	3.62701i	−0.138370	+	0.502976i
$53$	−0.458798	+	0.264887i	−0.0630207	+	0.0363850i	−0.531179	−	0.847259i	$-0.678251\pi$
$53$	−0.458798	+	0.264887i	−0.0630207	+	0.0363850i	0.468159	+	0.883644i	$0.344918\pi$
$54$		0			0
$55$		−	1.78190i		−	0.240271i
$56$	−5.56058	−	5.00799i	−0.743064	−	0.669220i
$57$		0			0
$58$	−2.09310	+	1.59504i	−0.274838	+	0.209440i
$59$	6.65037	+	11.5188i	0.865804	+	1.49962i	0.866246	+	0.499617i	$0.166526\pi$
$59$	6.65037	+	11.5188i	0.865804	+	1.49962i	−0.000442051		1.00000i	$0.500141\pi$
$60$		0			0
$61$	−5.18413	+	8.97918i	−0.663760	+	1.14967i	0.315860	+	0.948806i	$0.397707\pi$
$61$	−5.18413	+	8.97918i	−0.663760	+	1.14967i	−0.979620	+	0.200860i	$0.935626\pi$
$62$	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	$-0.719860\pi$
$67$	−2.35819	+	1.36150i	−0.288098	+	0.166334i	0.348986	+	0.937128i	$0.386526\pi$
$68$	−2.00553	−	7.68929i	−0.243207	−	0.932463i
$69$		0			0
$70$	−2.18174	+	1.43721i	−0.260767	+	0.171780i
$71$	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	0.935218	−	0.354073i	$-0.115203\pi$
$73$	1.37535	+	2.38218i	0.160973	+	0.278813i	−0.774245	+	0.632886i	$0.781870\pi$
$74$	10.5203	−	1.34939i	1.22296	−	0.156863i
$75$		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	$-0.608789\pi$
$79$	−11.7206	−	6.76690i	−1.31867	−	0.761335i	−0.983515	+	0.180827i	$0.942123\pi$
$80$	−1.36413	−	2.43717i	−0.152514	−	0.272483i
$81$		0			0
$82$	11.9305	−	9.09164i	1.31751	−	1.00400i
$83$	−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
$86$	4.46797	−	3.40481i	0.481793	−	0.367150i
$87$		0			0
$88$	5.68231	+	4.45110i	0.605736	+	0.474489i
$89$	10.2797	+	5.93499i	1.08965	+	0.629107i	0.933482	−	0.358624i	$-0.116754\pi$
$89$	10.2797	+	5.93499i	1.08965	+	0.629107i	0.156164	+	0.987731i	$0.450087\pi$
$90$		0			0
$91$	2.18660	+	4.47020i	0.229218	+	0.468604i
$92$	5.65635	+	5.73222i	0.589715	+	0.597625i
$93$		0			0
$94$	12.4904	−	1.60208i	1.28828	−	0.165242i
$95$	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	$0.313961\pi$
$98$	−9.89902	−	0.0966841i	−0.999952	−	0.00976657i
$99$		0			0
$100$	8.73277	−	2.27770i	0.873277	−	0.227770i
$101$	−9.18549	+	5.30325i	−0.913990	+	0.527693i	−0.881713	−	0.471786i	$-0.843609\pi$
$101$	−9.18549	+	5.30325i	−0.913990	+	0.527693i	−0.0322775	+	0.999479i	$0.510276\pi$
$102$		0			0
$103$	−11.4970	−	6.63779i	−1.13283	−	0.654041i	−0.188187	−	0.982133i	$-0.560261\pi$
$103$	−11.4970	−	6.63779i	−1.13283	−	0.654041i	−0.944646	+	0.328092i	$0.893594\pi$
$104$	−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	−0.999184	−	0.0403906i	$-0.987140\pi$
$107$	−4.80599	+	8.32422i	−0.464613	+	0.804733i	0.534571	+	0.845123i	$0.320473\pi$
$108$		0			0
$109$	−7.11203	−	12.3184i	−0.681209	−	1.17989i	−0.974612	−	0.223899i	$-0.928121\pi$
$109$	−7.11203	−	12.3184i	−0.681209	−	1.17989i	0.293403	−	0.955989i	$-0.405212\pi$
$110$	2.00434	−	1.52740i	0.191106	−	0.145632i
$111$		0			0
$112$	0.866741	−	10.5475i	0.0818993	−	0.996641i
$113$			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
$116$	−3.58831	−	0.987153i	−0.333167	−	0.0916548i
$117$		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
$122$	−14.5438	+	1.86546i	−1.31673	+	0.168891i
$123$		0			0
$124$	0.475028	+	1.82127i	0.0426588	+	0.163555i
$125$		−	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	$0.991771\pi$
$128$	11.1794	+	1.73784i	0.988132	+	0.153605i
$129$		0			0
$130$	0.236290	+	1.84220i	0.0207240	+	0.161572i
$131$	−5.44621	+	9.43310i	−0.475837	+	0.824174i	−0.999617	−	0.0276796i	$-0.991188\pi$
$131$	−5.44621	+	9.43310i	−0.475837	+	0.824174i	0.523780	+	0.851854i	$0.324522\pi$
$132$		0			0
$133$	−1.28131	+	18.6302i	−0.111104	+	1.61544i
$134$	−3.55284	−	1.48552i	−0.306919	−	0.128329i
$135$		0			0
$136$	6.93006	−	8.84697i	0.594248	−	0.758621i
$137$	−11.5198	+	6.65096i	−0.984203	+	0.568230i	−0.903536	−	0.428511i	$-0.859038\pi$
$137$	−11.5198	+	6.65096i	−0.984203	+	0.568230i	−0.0806665	+	0.996741i	$0.525705\pi$
$138$		0			0
$139$		−	0.840795i		−	0.0713153i	−0.999364	−	0.0356577i	$-0.988647\pi$
$139$		−	0.840795i		−	0.0713153i	0.999364	−	0.0356577i	$-0.0113526\pi$
$140$	−3.48676	−	1.22214i	−0.294685	−	0.103290i
$141$		0			0
$142$	3.01135	+	3.95165i	0.252707	+	0.331615i
$143$	−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	$-0.258900\pi$
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	−0.285722	+	0.958313i	$0.592233\pi$
$150$		0			0
$151$	−14.7077	+	8.49147i	−1.19689	+	0.691026i	−0.959861	−	0.280476i	$-0.909508\pi$
$151$	−14.7077	+	8.49147i	−1.19689	+	0.691026i	−0.237031	+	0.971502i	$0.576174\pi$
$152$	−19.7658	−	2.80342i	−1.60321	−	0.227387i
$153$		0			0
$154$	9.53209	−	0.562100i	0.768118	−	0.0452953i
$155$	0.657115			0.0527807
$156$		0			0
$157$	0.987461	+	1.71033i	0.0788079	+	0.136499i	0.902736	−	0.430195i	$-0.141555\pi$
$157$	0.987461	+	1.71033i	0.0788079	+	0.136499i	−0.823928	+	0.566695i	$0.808222\pi$
$158$	−2.43501	−	18.9841i	−0.193719	−	1.51030i
$159$		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	$-0.298214\pi$
$163$	2.43483	+	1.40575i	0.190711	+	0.110107i	−0.401604	+	0.915813i	$0.631547\pi$
$164$	20.4531	+	5.62670i	1.59712	+	0.439371i
$165$		0			0
$166$	−14.7020	−	19.2927i	−1.14110	−	1.49741i
$167$	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
$170$	−2.37806	−	3.12061i	−0.182389	−	0.239340i
$171$		0			0
$172$	7.65968	+	2.10719i	0.584045	+	0.160672i
$173$	4.05322	+	2.34013i	0.308161	+	0.177917i	0.646103	−	0.763250i	$-0.276398\pi$
$173$	4.05322	+	2.34013i	0.308161	+	0.177917i	−0.337942	+	0.941167i	$0.609731\pi$
$174$		0			0
$175$	6.66478	−	9.90539i	0.503810	−	0.748777i
$176$	−0.136000	+	10.2070i	−0.0102514	+	0.769384i
$177$		0			0
$178$	2.13565	+	16.6503i	0.160074	+	1.24799i
$179$	6.59544	+	11.4236i	0.492966	+	0.853843i	0.999967	−	0.00810267i	$-0.00257919\pi$
$179$	6.59544	+	11.4236i	0.492966	+	0.853843i	−0.507001	+	0.861946i	$0.669246\pi$
$180$		0			0
$181$	17.6801			1.31415			0.657075	−	0.753825i	$-0.271793\pi$
$181$	17.6801			1.31415			0.657075	+	0.753825i	$0.271793\pi$
$182$	−3.15392	+	6.29131i	−0.233784	+	0.466343i
$183$		0			0
$184$	−1.59929	+	11.2760i	−0.117901	+	0.831276i
$185$	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	−0.169752	−	0.985487i	$-0.554297\pi$
$191$	10.6220	−	18.3978i	0.768581	−	1.33122i	0.938332	−	0.345734i	$-0.112370\pi$
$192$		0			0
$193$	−2.08382	−	3.60927i	−0.149996	−	0.259801i	0.781230	−	0.624244i	$-0.214593\pi$
$193$	−2.08382	−	3.60927i	−0.149996	−	0.259801i	−0.931226	+	0.364443i	$0.881260\pi$
$194$	9.31595	+	12.2249i	0.668846	+	0.877695i
$195$		0			0
$196$	−8.37646	−	11.2176i	−0.598319	−	0.801258i
$197$		−	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	$-0.649468\pi$
$199$	1.31955	−	0.761843i	0.0935405	−	0.0540056i	0.546041	+	0.837759i	$0.316134\pi$
$200$	10.0476	+	7.87052i	0.710470	+	0.556529i
$201$		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
$206$	−2.38855	−	18.6219i	−0.166418	−	1.29745i
$207$		0			0
$208$	−6.46485	−	3.84823i	−0.448257	−	0.266826i
$209$		−	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	$0.768894\pi$
$212$	−0.267407	−	1.02525i	−0.0183656	−	0.0704144i
$213$		0			0
$214$	−13.4829	+	1.72939i	−0.921675	+	0.118219i
$215$	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
$220$	3.43614	+	0.945289i	0.231664	+	0.0637314i
$221$	−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	$-0.207763\pi$
$224$	12.6071	−	8.06609i	0.842345	−	0.538939i
$225$		0			0
$226$	−13.6148	+	10.3752i	−0.905646	+	0.690146i
$227$	−4.78909	−	8.29495i	−0.317863	−	0.550555i	0.662179	−	0.749346i	$-0.269632\pi$
$227$	−4.78909	−	8.29495i	−0.317863	−	0.550555i	−0.980042	+	0.198791i	$0.936299\pi$
$228$		0			0
$229$	−2.42163	+	4.19438i	−0.160026	+	0.277173i	−0.934878	−	0.354970i	$-0.884491\pi$
$229$	−2.42163	+	4.19438i	−0.160026	+	0.277173i	0.774852	+	0.632143i	$0.217824\pi$
$230$	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	$-0.584013\pi$
$233$	−18.7348	−	10.8165i	−1.22736	−	0.708615i	−0.966476	+	0.256755i	$0.917347\pi$
$234$		0			0
$235$	5.38442	−	3.10870i	0.351241	−	0.202789i
$236$	−25.7403	+	6.71364i	−1.67555	+	0.437021i
$237$		0			0
$238$	−0.875152	−	14.8408i	−0.0567277	−	0.961987i
$239$	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	0.639328	−	0.768934i	$-0.279212\pi$
$241$	−5.37528	−	9.31025i	−0.346252	−	0.599726i	−0.985580	+	0.169208i	$0.945879\pi$
$242$	6.29455	−	0.807373i	0.404629	−	0.0518999i
$243$		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
$248$	−1.64144	+	2.09548i	−0.104232	+	0.133063i
$249$		0			0
$250$	7.47112	−	5.69335i	0.472515	−	0.360079i
$251$	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
$254$	−0.655309	+	0.499378i	−0.0411178	+	0.0313337i
$255$		0			0
$256$	7.62798	+	14.0646i	0.476748	+	0.879040i
$257$	−7.56621	−	4.36835i	−0.471967	−	0.272490i	0.245096	−	0.969499i	$-0.421181\pi$
$257$	−7.56621	−	4.36835i	−0.471967	−	0.272490i	−0.717063	+	0.697009i	$0.754514\pi$
$258$		0			0
$259$	19.7962	+	1.36150i	1.23007	+	0.0845994i
$260$	−1.86962	+	1.84488i	−0.115949	+	0.114414i
$261$		0			0
$262$	−15.2790	+	1.95977i	−0.943941	+	0.121075i
$263$	−10.9040	−	18.8862i	−0.672368	−	1.16458i	−0.977231	−	0.212179i	$-0.931944\pi$
$263$	−10.9040	−	18.8862i	−0.672368	−	1.16458i	0.304863	−	0.952396i	$-0.401389\pi$
$264$		0			0
$265$	−0.369910			−0.0227234
$266$	−22.0542	+	14.5281i	−1.35223	+	0.890776i
$267$		0			0
$268$	−1.37445	−	5.26970i	−0.0839581	−	0.321898i
$269$	12.7340	−	7.35200i	0.776408	−	0.448259i	−0.0587478	−	0.998273i	$-0.518711\pi$
$269$	12.7340	−	7.35200i	0.776408	−	0.448259i	0.835156	+	0.550014i	$0.185377\pi$
$270$		0			0
$271$	4.49275	+	2.59389i	0.272915	+	0.157568i	0.630212	−	0.776423i	$-0.282968\pi$
$271$	4.49275	+	2.59389i	0.272915	+	0.157568i	−0.357296	+	0.933991i	$0.616301\pi$
$272$	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	−0.963816	−	0.266568i	$-0.914110\pi$
$277$	−11.8627	−	20.5469i	−0.712763	−	1.23454i	0.251053	−	0.967973i	$-0.419223\pi$
$278$	0.945754	−	0.720710i	0.0567225	−	0.0432253i
$279$		0			0
$280$	−1.61406	−	4.96961i	−0.0964586	−	0.296991i
$281$			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	$-0.599391\pi$
$283$	6.11257	−	3.52909i	0.363355	−	0.209783i	0.670551	+	0.741863i	$0.266058\pi$
$284$	−1.86368	+	6.77452i	−0.110589	+	0.401994i
$285$		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
$290$	−1.82255	+	0.233770i	−0.107024	+	0.0137274i
$291$		0			0
$292$	−5.32333	+	1.38844i	−0.311524	+	0.0812523i
$293$			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
$296$	−2.97887	+	21.0028i	−0.173143	+	1.22076i
$297$		0			0
$298$	1.01778	+	7.93499i	0.0589587	+	0.459662i
$299$	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
$304$	−13.7894	−	24.6362i	−0.790875	−	1.41298i
$305$	−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	$0.949516\pi$
$308$	8.80295	+	10.2402i	0.501595	+	0.583489i
$309$		0			0
$310$	0.563264	+	0.739144i	0.0319912	+	0.0419806i
$311$	−5.24440	−	9.08357i	−0.297383	−	0.515082i	0.678154	−	0.734920i	$-0.262780\pi$
$311$	−5.24440	−	9.08357i	−0.297383	−	0.515082i	−0.975536	+	0.219838i	$0.929447\pi$
$312$		0			0
$313$	−1.13158	+	1.95996i	−0.0639609	+	0.110784i	−0.896233	−	0.443584i	$-0.853707\pi$
$313$	−1.13158	+	1.95996i	−0.0639609	+	0.110784i	0.832272	+	0.554368i	$0.187040\pi$
$314$	−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	$-0.419350\pi$
$317$	−8.23233	−	4.75294i	−0.462374	−	0.266952i	−0.713042	+	0.701122i	$0.752683\pi$
$318$		0			0
$319$	4.11255	−	2.37438i	0.230258	−	0.132940i
$320$	5.42340	−	1.33763i	0.303177	−	0.0747758i
$321$		0			0
$322$	8.28801	+	12.5815i	0.461873	+	0.701138i
$323$	−28.0441			−1.56041
$324$		0			0
$325$	−4.24369	−	7.35029i	−0.235398	−	0.407721i
$326$	0.505848	+	3.94376i	0.0280163	+	0.218425i
$327$		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	$-0.245249\pi$
$331$	8.60924	+	4.97055i	0.473207	+	0.273206i	−0.244374	+	0.969681i	$0.578583\pi$
$332$	9.09887	−	33.0745i	0.499366	−	1.81520i
$333$		0			0
$334$	2.06436	+	2.70896i	0.112957	+	0.148228i
$335$	−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	$0.406374\pi$
$338$	−8.11087	−	10.6435i	−0.441173	−	0.578930i
$339$		0			0
$340$	1.47175	−	5.34984i	0.0798169	−	0.290136i
$341$	−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
$346$	0.842076	+	6.56510i	0.0452703	+	0.352942i
$347$	8.77440	+	15.1977i	0.471035	+	0.815856i	0.999451	−	0.0331294i	$-0.0105473\pi$
$347$	8.77440	+	15.1977i	0.471035	+	0.815856i	−0.528416	+	0.848985i	$0.677214\pi$
$348$		0			0
$349$	29.0703			1.55610			0.778049	−	0.628204i	$-0.216210\pi$
$349$	29.0703			1.55610			0.778049	+	0.628204i	$0.216210\pi$
$350$	16.8548	−	0.993915i	0.900927	−	0.0531270i
$351$		0			0
$352$	−11.5978	+	8.59625i	−0.618163	+	0.458182i
$353$	−9.73945	+	5.62308i	−0.518379	+	0.299286i	−0.736271	−	0.676687i	$-0.763415\pi$
$353$	−9.73945	+	5.62308i	−0.518379	+	0.299286i	0.217892	+	0.975973i	$0.430082\pi$
$354$		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	0.173055	+	0.984912i	$0.444636\pi$
$359$	−14.5218	+	25.1525i	−0.766431	+	1.32750i	−0.939486	+	0.342586i	$0.888697\pi$
$360$		0			0
$361$	15.4090	+	26.6892i	0.811001	+	1.40469i
$362$	15.1550	+	19.8871i	0.796527	+	1.04524i
$363$		0			0
$364$	−9.78013	+	1.84514i	−0.512618	+	0.0967114i
$365$			1.92065i			0.100532i
$366$		0			0
$367$	−20.8594	+	12.0432i	−1.08885	+	0.628649i	−0.933271	−	0.359174i	$-0.883059\pi$
$367$	−20.8594	+	12.0432i	−1.08885	+	0.628649i	−0.155582	+	0.987823i	$0.549725\pi$
$368$	−14.0545	+	7.86657i	−0.732639	+	0.410073i
$369$		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	−0.985675	−	0.168658i	$-0.946057\pi$
$373$	−6.69734	+	11.6001i	−0.346775	+	0.600632i	0.638900	+	0.769290i	$0.279390\pi$
$374$	1.82434	+	14.2232i	0.0943345	+	0.735463i
$375$		0			0
$376$	−3.53670	+	24.9358i	−0.182391	+	1.28597i
$377$			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	$-0.107975\pi$
$380$	−9.53755	+	2.48760i	−0.489266	+	0.127611i
$381$		0			0
$382$	29.7994	−	3.82223i	1.52467	−	0.195563i
$383$	1.26675	−	2.19407i	0.0647277	−	0.112112i	−0.831845	−	0.555007i	$-0.812715\pi$
$383$	1.26675	−	2.19407i	0.0647277	−	0.112112i	0.896573	+	0.442896i	$0.146049\pi$
$384$		0			0
$385$	4.23496	−	2.07153i	0.215833	−	0.105575i
$386$	2.27363	−	5.43773i	0.115725	−	0.276773i
$387$		0			0
$388$	−5.76553	+	20.9578i	−0.292700	+	1.06397i
$389$	13.2543	−	7.65235i	0.672018	−	0.387990i	−0.124823	−	0.992179i	$-0.539836\pi$
$389$	13.2543	−	7.65235i	0.672018	−	0.387990i	0.796841	+	0.604189i	$0.206503\pi$
$390$		0			0
$391$			15.9986i			0.809083i
$392$	5.43783	−	19.0376i	0.274652	−	0.961544i
$393$		0			0
$394$	9.05202	−	6.89808i	0.456034	−	0.347520i
$395$	−4.72492	−	8.18380i	−0.237736	−	0.411772i
$396$		0			0
$397$	−6.55329	+	11.3506i	−0.328900	+	0.569672i	−0.982294	−	0.187346i	$-0.940011\pi$
$397$	−6.55329	+	11.3506i	−0.328900	+	0.569672i	0.653394	+	0.757018i	$0.273345\pi$
$398$	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	$-0.324109\pi$
$401$	1.00499	+	0.580229i	0.0501866	+	0.0289753i	−0.474697	+	0.880149i	$0.657442\pi$
$402$		0			0
$403$	1.53295	−	0.885048i	0.0763616	−	0.0440874i
$404$	−5.35370	−	20.5263i	−0.266357	−	1.02122i
$405$		0			0
$406$	−6.22419	−	3.12027i	−0.308901	−	0.154856i
$407$	−19.1397			−0.948718
$408$		0			0
$409$	−3.59404	−	6.22507i	−0.177714	−	0.307810i	0.763383	−	0.645946i	$-0.223537\pi$
$409$	−3.59404	−	6.22507i	−0.177714	−	0.307810i	−0.941097	+	0.338136i	$0.890204\pi$
$410$	10.3884	−	1.33247i	0.513046	−	0.0658060i
$411$		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
$416$	−1.21291	−	10.5705i	−0.0594679	−	0.518261i
$417$		0			0
$418$	20.2609	−	15.4398i	0.990993	−	0.755185i
$419$	−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	$0.457210\pi$
$422$	−21.6956	+	16.5331i	−1.05612	+	0.804817i
$423$		0			0
$424$	0.924018	−	1.17961i	0.0448743	−	0.0572868i
$425$	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
$430$	3.89044	−	0.499009i	0.187614	−	0.0240643i
$431$	6.70530	+	11.6139i	0.322983	+	0.559423i	0.981102	−	0.193491i	$-0.0619811\pi$
$431$	6.70530	+	11.6139i	0.322983	+	0.559423i	−0.658119	+	0.752914i	$0.728648\pi$
$432$		0			0
$433$	−31.6801			−1.52245			−0.761224	−	0.648489i	$-0.775401\pi$
$433$	−31.6801			−1.52245			−0.761224	+	0.648489i	$0.775401\pi$
$434$	0.207287	+	3.51517i	0.00995010	+	0.168734i
$435$		0			0
$436$	27.5272	−	7.17970i	1.31831	−	0.343845i
$437$	24.6126	−	14.2101i	1.17738	−	0.679761i
$438$		0			0
$439$	16.8712	+	9.74059i	0.805218	+	0.464893i	0.845292	−	0.534304i	$-0.179426\pi$
$439$	16.8712	+	9.74059i	0.805218	+	0.464893i	−0.0400745	+	0.999197i	$0.512760\pi$
$440$	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	−0.936121	−	0.351677i	$-0.885612\pi$
$443$	−3.44127	+	5.96046i	−0.163500	+	0.283190i	0.772622	+	0.634867i	$0.218945\pi$
$444$		0			0
$445$	4.14404	+	7.17770i	0.196447	+	0.340255i
$446$	20.4033	−	15.5483i	0.966126	−	0.736235i
$447$		0			0
$448$	19.8795	+	7.26677i	0.939218	+	0.343323i
$449$		−	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
$452$	−23.3406	−	6.42106i	−1.09785	−	0.302021i
$453$		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	−0.917032	−	0.398814i	$-0.869422\pi$
$457$	−2.41849	+	4.18896i	−0.113132	+	0.195951i	0.803899	+	0.594766i	$0.202755\pi$
$458$	−6.79374	+	0.871402i	−0.317451	+	0.0407180i
$459$		0			0
$460$	1.41913	+	5.44098i	0.0661671	+	0.253687i
$461$			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	$-0.346105\pi$
$464$	3.80717	−	6.39588i	0.176744	−	0.296921i
$465$		0			0
$466$	−3.89224	−	30.3452i	−0.180305	−	1.40571i
$467$	−3.19220	+	5.52905i	−0.147717	+	0.255854i	−0.930383	−	0.366588i	$-0.880526\pi$
$467$	−3.19220	+	5.52905i	−0.147717	+	0.255854i	0.782666	+	0.622442i	$0.213859\pi$
$468$		0			0
$469$	−5.97731	−	4.02179i	−0.276007	−	0.185709i
$470$	8.11216	+	3.39187i	0.374186	+	0.156455i
$471$		0			0
$472$	−29.6158	−	23.1988i	−1.36318	−	1.06781i
$473$	−8.77871	+	5.06839i	−0.403646	+	0.233045i
$474$		0			0
$475$		−	31.8498i		−	1.46137i
$476$	15.9433	−	13.7056i	0.730759	−	0.628195i
$477$		0			0
$478$	17.6192	+	23.1208i	0.805882	+	1.05752i
$479$	10.5205	+	18.2220i	0.480693	+	0.832585i	0.999755	−	0.0221516i	$-0.00705165\pi$
$479$	10.5205	+	18.2220i	0.480693	+	0.832585i	−0.519061	+	0.854737i	$0.673718\pi$
$480$		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	$-0.550258\pi$
$487$	13.6690	−	7.89181i	0.619402	−	0.357612i	0.776636	+	0.629949i	$0.216924\pi$
$488$	4.11813	−	29.0353i	0.186419	−	1.31437i
$489$		0			0
$490$	−5.95212	−	3.51441i	−0.268889	−	0.158765i
$491$	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
$494$	2.38855	+	18.6219i	0.107466	+	0.837841i
$495$		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	$-0.391067\pi$
$499$	−6.97921	−	4.02945i	−0.312432	−	0.180383i	−0.648014	+	0.761628i	$0.724400\pi$
$500$	12.8081	+	3.52354i	0.572797	+	0.157578i
$501$		0			0
$502$	16.6563	+	21.8573i	0.743409	+	0.975540i
$503$	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
$506$	−8.80810	−	11.5584i	−0.391568	−	0.513836i
$507$		0			0
$508$	−1.12343	−	0.309058i	−0.0498442	−	0.0137123i
$509$	−33.8626	−	19.5506i	−1.50093	−	0.866563i	−0.999999	−	0.00107666i	$-0.999657\pi$
$509$	−33.8626	−	19.5506i	−1.50093	−	0.866563i	−0.500932	−	0.865487i	$-0.667009\pi$
$510$		0			0
$511$	−4.06272	+	6.03813i	−0.179724	+	0.267111i
$512$	−9.28184	+	20.6361i	−0.410203	+	0.911994i
$513$		0			0
$514$	−1.57191	−	12.2552i	−0.0693341	−	0.540552i
$515$	−4.63477	−	8.02766i	−0.204232	−	0.353741i
$516$		0			0
$517$	−22.7238			−0.999392
$518$	15.4374	+	23.4344i	0.678278	+	1.02965i
$519$		0			0
$520$	−3.67778	−	0.521626i	−0.161281	−	0.0228748i
$521$	0.453045	−	0.261566i	0.0198483	−	0.0114594i	−0.490043	−	0.871698i	$-0.663019\pi$
$521$	0.453045	−	0.261566i	0.0198483	−	0.0114594i	0.509891	+	0.860239i	$0.329686\pi$
$522$		0			0
$523$	−32.5034	−	18.7658i	−1.42127	−	0.820573i	−0.424865	−	0.905257i	$-0.639679\pi$
$523$	−32.5034	−	18.7658i	−1.42127	−	0.820573i	−0.996408	+	0.0846840i	$0.973012\pi$
$524$	−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
$530$	−0.317078	−	0.416086i	−0.0137730	−	0.0180736i
$531$		0			0
$532$	−35.2460	−	12.3541i	−1.52811	−	0.535617i
$533$		−	19.9495i		−	0.864109i
$534$		0			0
$535$	−5.81230	+	3.35574i	−0.251288	+	0.145081i
$536$	4.74938	−	6.06310i	0.205142	−	0.261886i
$537$		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	−0.999751	−	0.0223286i	$-0.992892\pi$
$541$	−11.1770	+	19.3592i	−0.480538	+	0.832317i	0.519212	+	0.854645i	$0.326225\pi$
$542$	0.933390	+	7.27702i	0.0400925	+	0.312575i
$543$		0			0
$544$	13.3838	+	18.0569i	0.573825	+	0.774185i
$545$		−	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	$0.944603\pi$
$548$	−6.71424	−	25.7426i	−0.286818	−	1.09967i
$549$		0			0
$550$	−16.1534	+	2.07192i	−0.688781	+	0.0883468i
$551$	−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
$556$	1.62136	+	0.446038i	0.0687608	+	0.0189162i
$557$	27.3598	−	15.7962i	1.15927	−	0.669307i	0.208144	−	0.978098i	$-0.433258\pi$
$557$	27.3598	−	15.7962i	1.15927	−	0.669307i	0.951130	+	0.308791i	$0.0999244\pi$
$558$		0			0
$559$		−	7.47107i		−	0.315992i
$560$	4.20644	−	6.07538i	0.177755	−	0.256732i
$561$		0			0
$562$	−4.63881	+	3.53499i	−0.195676	+	0.149115i
$563$	−4.17946	−	7.23904i	−0.176143	−	0.305089i	0.764413	−	0.644727i	$-0.223029\pi$
$563$	−4.17946	−	7.23904i	−0.176143	−	0.305089i	−0.940556	+	0.339638i	$0.889696\pi$
$564$		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	$-0.421386\pi$
$569$	−11.2838	−	6.51469i	−0.473041	−	0.273110i	−0.717512	+	0.696546i	$0.754719\pi$
$570$		0			0
$571$	12.4590	−	7.19319i	0.521392	−	0.301026i	−0.216112	−	0.976369i	$-0.569338\pi$
$571$	12.4590	−	7.19319i	0.521392	−	0.301026i	0.737504	+	0.675343i	$0.236004\pi$
$572$	9.28917	−	2.42282i	0.388400	−	0.101303i
$573$		0			0
$574$	35.4774	+	17.7853i	1.48080	+	0.742345i
$575$	−18.1697			−0.757728
$576$		0			0
$577$	12.8808	+	22.3102i	0.536235	+	0.928786i	0.999102	+	0.0423583i	$0.0134871\pi$
$577$	12.8808	+	22.3102i	0.536235	+	0.928786i	−0.462868	+	0.886427i	$0.653180\pi$
$578$	−1.70174	+	0.218274i	−0.0707829	+	0.00907900i
$579$		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
$584$	−6.12479	−	4.79771i	−0.253446	−	0.198531i
$585$		0			0
$586$	−17.9607	+	13.6870i	−0.741951	+	0.565403i
$587$	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
$590$	−10.4464	+	7.96069i	−0.430073	+	0.327737i
$591$		0			0
$592$	−26.1780	+	14.6524i	−1.07591	+	0.602209i
$593$	25.5907	+	14.7748i	1.05089	+	0.606729i	0.922897	−	0.385046i	$-0.125815\pi$
$593$	25.5907	+	14.7748i	1.05089	+	0.606729i	0.127989	+	0.991776i	$0.459148\pi$
$594$		0			0
$595$	−3.22524	−	6.59354i	−0.132222	−	0.270309i
$596$	−8.05312	+	7.94653i	−0.329868	+	0.325503i
$597$		0			0
$598$	10.6235	−	1.36262i	0.434425	−	0.0557217i
$599$	−2.99964	−	5.19553i	−0.122562	−	0.212284i	0.798215	−	0.602372i	$-0.205778\pi$
$599$	−2.99964	−	5.19553i	−0.122562	−	0.212284i	−0.920777	+	0.390089i	$0.872444\pi$
$600$		0			0
$601$	−5.44843			−0.222246			−0.111123	−	0.993807i	$-0.535445\pi$
$601$	−5.44843			−0.222246			−0.111123	+	0.993807i	$0.535445\pi$
$602$	13.2863	+	6.66058i	0.541508	+	0.271465i
$603$		0			0
$604$	−8.57226	−	32.8663i	−0.348800	−	1.33731i
$605$	2.71349	−	1.56663i	0.110319	−	0.0636928i
$606$		0			0
$607$	3.76460	+	2.17350i	0.152801	+	0.0882195i	0.574451	−	0.818539i	$-0.305216\pi$
$607$	3.76460	+	2.17350i	0.152801	+	0.0882195i	−0.421650	+	0.906759i	$0.638549\pi$
$608$	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	0.976624	−	0.214954i	$-0.0689603\pi$
$613$	7.48103	+	12.9575i	0.302156	+	0.523350i	−0.674468	+	0.738304i	$0.735627\pi$
$614$	−6.22539	+	4.74405i	−0.251236	+	0.191454i
$615$		0			0
$616$	−3.97280	+	18.6795i	−0.160069	+	0.752618i
$617$			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	$-0.573304\pi$
$619$	12.4590	−	7.19319i	0.500769	−	0.289119i	0.729031	+	0.684481i	$0.239971\pi$
$620$	−0.348597	+	1.26715i	−0.0140000	+	0.0508901i
$621$		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
$626$	−3.17460	+	0.407191i	−0.126882	+	0.0162746i
$627$		0			0
$628$	−3.82198	+	0.996856i	−0.152514	+	0.0397789i
$629$			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	$0.897509\pi$
$632$	37.9000	+	5.37544i	1.50758	+	0.213823i
$633$		0			0
$634$	−1.71030	−	13.3341i	−0.0679248	−	0.529565i
$635$	−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
$640$	6.15342	+	4.95383i	0.243235	+	0.195817i
$641$	1.35619	−	0.782995i	0.0535661	−	0.0309264i	−0.472978	−	0.881074i	$-0.656821\pi$
$641$	1.35619	−	0.782995i	0.0535661	−	0.0309264i	0.526544	+	0.850148i	$0.323488\pi$
$642$		0			0
$643$			33.5314i			1.32235i	0.750232	+	0.661174i	$0.229942\pi$
$643$			33.5314i			1.32235i	−0.750232	+	0.661174i	$0.770058\pi$
$644$	−7.04776	+	20.1072i	−0.277720	+	0.792333i
$645$		0			0
$646$	−24.0387	−	31.5449i	−0.945790	−	1.24112i
$647$	−8.65921	−	14.9982i	−0.340429	−	0.589640i	0.644084	−	0.764955i	$-0.277239\pi$
$647$	−8.65921	−	14.9982i	−0.340429	−	0.589640i	−0.984512	+	0.175315i	$0.943906\pi$
$648$		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	$-0.155469\pi$
$653$	23.4648	+	13.5474i	0.918247	+	0.530150i	0.0351715	+	0.999381i	$0.488802\pi$
$654$		0			0
$655$	−6.58657	+	3.80276i	−0.257359	+	0.148586i
$656$	−21.7006	+	36.4561i	−0.847267	+	1.42337i
$657$		0			0
$658$	18.3282	+	27.8228i	0.714507	+	1.08465i
$659$	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	0.836654	−	0.547732i	$-0.184509\pi$
$661$	−1.44036	−	2.49478i	−0.0560235	−	0.0970355i	−0.892677	+	0.450697i	$0.851176\pi$
$662$	1.78861	+	13.9446i	0.0695163	+	0.541972i
$663$		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
$668$	−1.27761	+	4.64412i	−0.0494321	+	0.179687i
$669$		0			0
$670$	−1.62976	−	2.13865i	−0.0629630	−	0.0826233i
$671$	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	$0.443928\pi$
$674$	9.12390	+	11.9729i	0.351439	+	0.461177i
$675$		0			0
$676$	5.01971	−	18.2467i	0.193066	−	0.701797i
$677$	−13.8282	−	7.98374i	−0.531463	−	0.306840i	0.210149	−	0.977669i	$-0.432605\pi$
$677$	−13.8282	−	7.98374i	−0.531463	−	0.306840i	−0.741612	+	0.670829i	$0.765938\pi$
$678$		0			0
$679$	12.6347	+	25.8299i	0.484877	+	0.991261i
$680$	7.27922	−	2.93028i	0.279145	−	0.112371i
$681$		0			0
$682$	−0.432111	−	3.36888i	−0.0165464	−	0.129001i
$683$	−22.2769	−	38.5848i	−0.852404	−	1.47641i	−0.879033	−	0.476761i	$-0.841811\pi$
$683$	−22.2769	−	38.5848i	−0.852404	−	1.47641i	0.0266295	−	0.999645i	$-0.491523\pi$
$684$		0			0
$685$	−9.28793			−0.354874
$686$	−11.2783	−	23.6390i	−0.430606	−	0.902540i
$687$		0			0
$688$	−8.12686	+	13.6528i	−0.309833	+	0.520507i
$689$	−0.862942	+	0.498220i	−0.0328755	+	0.0189807i
$690$		0			0
$691$	12.1180	+	6.99631i	0.460989	+	0.266152i	0.712460	−	0.701713i	$-0.247581\pi$
$691$	12.1180	+	6.99631i	0.460989	+	0.266152i	−0.251471	+	0.967865i	$0.580914\pi$
$692$	−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
$698$	24.9184	+	32.6992i	0.943175	+	1.23768i
$699$		0			0
$700$	15.5655	+	18.1069i	0.588322	+	0.684375i
$701$		−	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
$704$	−19.6107	−	5.67704i	−0.739105	−	0.213962i
$705$		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	−0.0684783	−	0.997653i	$-0.521814\pi$
$709$	22.0939	−	38.2677i	0.829753	−	1.43717i	0.898232	−	0.439522i	$-0.144852\pi$
$710$	0.441343	+	3.44086i	0.0165633	+	0.129133i
$711$		0			0
$712$	−33.2407	−	4.71459i	−1.24575	−	0.176687i
$713$		−	3.78940i		−	0.141914i
$714$		0			0
$715$		−	3.35153i		−	0.125340i
$716$	−25.5278	+	6.65819i	−0.954017	+	0.248828i
$717$		0			0
$718$	−40.7401	+	5.22554i	−1.52041	+	0.195016i
$719$	6.06830	−	10.5106i	0.226309	−	0.391979i	−0.730402	−	0.683017i	$-0.760667\pi$
$719$	6.06830	−	10.5106i	0.226309	−	0.391979i	0.956711	+	0.291038i	$0.0940006\pi$
$720$		0			0
$721$	2.40998	−	35.0411i	0.0897525	−	1.30500i
$722$	−16.8126	+	40.2099i	−0.625701	+	1.49646i
$723$		0			0
$724$	−9.37922	+	34.0936i	−0.348576	+	1.26708i
$725$	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	$0.827542\pi$
$728$	−10.4588	−	9.41940i	−0.387628	−	0.349106i
$729$		0			0
$730$	−2.16041	+	1.64634i	−0.0799605	+	0.0609338i
$731$	7.89114	+	13.6679i	0.291864	+	0.505524i
$732$		0			0
$733$	19.8313	−	34.3488i	0.732486	−	1.26870i	−0.223331	−	0.974743i	$-0.571693\pi$
$733$	19.8313	−	34.3488i	0.732486	−	1.26870i	0.955818	−	0.293961i	$-0.0949734\pi$
$734$	−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	$-0.871756\pi$
$739$	−28.2813	+	16.3282i	−1.04034	+	0.600643i	−0.120414	+	0.992724i	$0.538422\pi$
$740$	2.64329	+	10.1344i	0.0971691	+	0.372550i
$741$		0			0
$742$	−0.116688	−	1.97880i	−0.00428376	−	0.0726439i
$743$	−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
$746$	−18.7890	+	2.40998i	−0.687914	+	0.0882356i
$747$		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	$-0.150618\pi$
$751$	25.7744	+	14.8808i	0.940520	+	0.543010i	0.0503969	+	0.998729i	$0.483951\pi$
$752$	−31.0802	+	17.3962i	−1.13338	+	0.634375i
$753$		0			0
$754$	−3.93686	+	3.00008i	−0.143372	+	0.109257i
$755$	−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	$0.372741\pi$
$758$	14.5731	−	11.1054i	0.529317	−	0.403365i
$759$		0			0
$760$	−10.9735	−	8.59583i	−0.398051	−	0.311803i
$761$	−37.9234	−	21.8951i	−1.37472	−	0.793696i	−0.383203	−	0.923664i	$-0.625179\pi$
$761$	−37.9234	−	21.8951i	−1.37472	−	0.793696i	−0.991518	+	0.129969i	$0.958512\pi$
$762$		0			0
$763$	21.0085	−	31.2235i	0.760560	−	1.13037i
$764$	29.8427	+	30.2430i	1.07967	+	1.09415i
$765$		0			0
$766$	3.55379	−	0.455828i	0.128403	−	0.0164697i
$767$	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	$0.918842\pi$
$770$	5.96023	+	2.98794i	0.214792	+	0.107678i
$771$		0			0
$772$	8.06544	−	2.10364i	0.290281	−	0.0757117i
$773$	−37.6921	+	21.7615i	−1.35569	+	0.782708i	−0.989040	−	0.147650i	$-0.952829\pi$
$773$	−37.6921	+	21.7615i	−1.35569	+	0.782708i	−0.366651	+	0.930359i	$0.619496\pi$
$774$		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
$782$	−17.9957	+	13.7136i	−0.643526	+	0.490398i
$783$		0			0
$784$	26.0753	−	10.2019i	0.931260	−	0.364355i
$785$			1.37897i			0.0492175i
$786$		0			0
$787$	9.79031	−	5.65244i	0.348987	−	0.201488i	−0.315252	−	0.949008i	$-0.602089\pi$
$787$	9.79031	−	5.65244i	0.348987	−	0.201488i	0.664239	+	0.747520i	$0.268756\pi$
$788$	15.5184	+	4.26913i	0.552819	+	0.152082i
$789$		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
$794$	−18.3849	+	2.35815i	−0.652455	+	0.0836874i
$795$		0			0
$796$	0.769091	+	2.94872i	0.0272597	+	0.104515i
$797$			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
$800$	−20.5074	+	15.2000i	−0.725045	+	0.537402i
$801$		0			0
$802$	0.208790	+	1.62780i	0.00737265	+	0.0574796i
$803$	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
$808$	18.4996	−	23.6167i	0.650812	−	0.830832i
$809$	−11.0507	+	6.38012i	−0.388521	+	0.224313i	−0.681519	−	0.731800i	$-0.738680\pi$
$809$	−11.0507	+	6.38012i	−0.388521	+	0.224313i	0.292998	+	0.956113i	$0.405347\pi$
$810$		0			0
$811$			37.2617i			1.30843i	0.756307	+	0.654217i	$0.227002\pi$
$811$			37.2617i			1.30843i	−0.756307	+	0.654217i	$0.772998\pi$
$812$	−1.82545	−	9.67580i	−0.0640608	−	0.339554i
$813$		0			0
$814$	−16.4061	−	21.5289i	−0.575033	−	0.754588i
$815$	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	$-0.0918691\pi$
$821$	34.1392	+	19.7103i	1.19147	+	0.687893i	0.232827	+	0.972518i	$0.425202\pi$
$822$		0			0
$823$	43.1751	−	24.9272i	1.50499	−	0.868907i	0.505007	−	0.863115i	$-0.331490\pi$
$823$	43.1751	−	24.9272i	1.50499	−	0.868907i	0.999983	−	0.00579133i	$-0.00184345\pi$
$824$	37.1769	+	5.27288i	1.29512	+	0.183689i
$825$		0			0
$826$	−49.6805	+	2.92962i	−1.72861	+	0.101935i
$827$	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	0.931097	−	0.364771i	$-0.118853\pi$
$829$	4.30870	+	7.46288i	0.149647	+	0.259197i	−0.781450	+	0.623968i	$0.785520\pi$
$830$	−2.15472	−	16.7989i	−0.0747915	−	0.583100i
$831$		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
$836$	34.7344	+	9.55549i	1.20131	+	0.330484i
$837$		0			0
$838$	−13.8114	−	18.1241i	−0.477107	−	0.626085i
$839$	−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
$842$	4.71440	+	6.18649i	0.162469	+	0.213201i
$843$		0			0
$844$	−37.1938	−	10.2321i	−1.28027	−	0.352204i
$845$	−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
$850$	3.22583	+	25.1497i	0.110645	+	0.862627i
$851$	−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	$0.573491\pi$
$854$	−21.3414	−	32.3969i	−0.730286	−	1.10860i
$855$		0			0
$856$	3.81775	−	26.9174i	0.130488	−	0.920018i
$857$	8.60210	−	4.96642i	0.293842	−	0.169650i	−0.345831	−	0.938297i	$-0.612403\pi$
$857$	8.60210	−	4.96642i	0.293842	−	0.169650i	0.639673	+	0.768647i	$0.279070\pi$
$858$		0			0
$859$	−25.8761	−	14.9395i	−0.882879	−	0.509731i	−0.0112727	−	0.999936i	$-0.503588\pi$
$859$	−25.8761	−	14.9395i	−0.882879	−	0.509731i	−0.871607	+	0.490206i	$0.836922\pi$
$860$	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	−0.894757	−	0.446552i	$-0.852652\pi$
$863$	−1.78179	+	3.08616i	−0.0606530	+	0.105054i	0.834104	+	0.551606i	$0.185985\pi$
$864$		0			0
$865$	1.63397	+	2.83012i	0.0555567	+	0.0962271i
$866$	−27.1554	−	35.6348i	−0.922779	−	1.21092i
$867$		0			0
$868$	−3.77630	+	3.24629i	−0.128176	+	0.110186i
$869$			34.5380i			1.17162i
$870$		0			0
$871$	−4.43546	+	2.56081i	−0.150290	+	0.0867698i
$872$	31.6716	+	24.8092i	1.07254	+	0.840146i
$873$		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	−0.783249	−	0.621708i	$-0.786439\pi$
$877$	4.34706	−	7.52933i	0.146790	−	0.254247i	0.930039	+	0.367460i	$0.119773\pi$
$878$	3.50507	+	27.3267i	0.118290	+	0.922230i
$879$		0			0
$880$	−3.64572	+	6.12464i	−0.122897	+	0.206462i
$881$		−	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	$-0.0354582\pi$
$884$	−3.77216	−	14.4626i	−0.126872	−	0.486430i
$885$		0			0
$886$	−9.65429	+	1.23831i	−0.324342	+	0.0416019i
$887$	−24.0596	+	41.6725i	−0.807844	+	1.39923i	0.106511	+	0.994312i	$0.466032\pi$
$887$	−24.0596	+	41.6725i	−0.807844	+	1.39923i	−0.914354	+	0.404915i	$0.867301\pi$
$888$		0			0
$889$	−1.38460	+	0.677280i	−0.0464380	+	0.0227152i
$890$	−4.52153	+	10.8139i	−0.151562	+	0.362483i
$891$		0			0
$892$	34.9785	+	9.62266i	1.17117	+	0.322191i
$893$	54.4286	−	31.4244i	1.82138	−	1.05158i
$894$		0			0
$895$			9.21040i			0.307870i
$896$	8.86634	+	28.5900i	0.296204	+	0.955125i
$897$		0			0
$898$	21.7379	−	16.5653i	0.725403	−	0.552792i
$899$	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	$-0.709244\pi$
$907$	−6.95656	+	4.01637i	−0.230989	+	0.133361i	0.380039	+	0.924970i	$0.375910\pi$
$908$	18.5362	−	4.83466i	0.615147	−	0.160444i
$909$		0			0
$910$	−4.10358	+	2.70322i	−0.136032	+	0.0896108i
$911$	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
$914$	−6.78495	+	0.870274i	−0.224426	+	0.0287861i
$915$		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	$-0.242390\pi$
$919$	14.7985	+	8.54390i	0.488156	+	0.281837i	−0.235653	+	0.971837i	$0.575723\pi$
$920$	−4.90375	+	6.26016i	−0.161672	+	0.206392i
$921$		0			0
$922$	−29.6383	+	22.5858i	−0.976084	+	0.743823i
$923$	6.60771			0.217495
$924$		0			0
$925$	−33.8431			−1.11275
$926$	42.8589	−	32.6605i	1.40843	−	1.07329i
$927$		0			0
$928$	10.4577	−	1.19997i	0.343291	−	0.0393910i
$929$	24.2444	+	13.9975i	0.795434	+	0.459244i	0.841872	−	0.539677i	$-0.181454\pi$
$929$	24.2444	+	13.9975i	0.795434	+	0.459244i	−0.0464382	+	0.998921i	$0.514787\pi$
$930$		0			0
$931$	−45.7671	+	18.6132i	−1.49996	+	0.610023i
$932$	30.7969	−	30.3893i	1.00879	−	0.995435i
$933$		0			0
$934$	−8.95553	+	1.14868i	−0.293034	+	0.0375861i
$935$	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	$0.808280\pi$
$938$	−0.599768	−	10.1709i	−0.0195831	−	0.332090i
$939$		0			0
$940$	3.13827	+	12.0323i	0.102359	+	0.392449i
$941$	20.0547	−	11.5786i	0.653765	−	0.377451i	−0.136132	−	0.990691i	$-0.543467\pi$
$941$	20.0547	−	11.5786i	0.653765	−	0.377451i	0.789897	+	0.613239i	$0.210134\pi$
$942$		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	−0.959815	−	0.280633i	$-0.909456\pi$
$947$	−7.28937	+	12.6256i	−0.236873	+	0.410275i	0.722943	+	0.690908i	$0.242789\pi$
$948$		0			0
$949$	2.58687	+	4.48059i	0.0839734	+	0.145446i
$950$	35.8257	−	27.3009i	1.16234	−	0.885758i
$951$		0			0
$952$	29.0827	+	6.18538i	0.942576	+	0.200469i
$953$		−	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
$956$	−10.9043	+	39.6372i	−0.352670	+	1.28196i
$957$		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
$962$	19.7874	−	2.53804i	0.637971	−	0.0818296i
$963$		0			0
$964$	20.8051	−	5.42642i	0.670086	−	0.174773i
$965$		−	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	$-0.116207\pi$
$968$	−1.78233	+	12.5665i	−0.0572861	+	0.403902i
$969$		0			0
$970$	1.36535	+	10.6447i	0.0438386	+	0.341781i
$971$	8.09294	−	14.0174i	0.259715	−	0.449839i	−0.706451	−	0.707762i	$-0.749705\pi$
$971$	8.09294	−	14.0174i	0.259715	−	0.449839i	0.966165	+	0.257923i	$0.0830381\pi$
$972$		0			0
$973$	1.99828	−	0.977461i	0.0640619	−	0.0313360i
$974$	20.5937	+	8.61068i	0.659866	+	0.275904i
$975$		0			0
$976$	36.1898	−	20.2562i	1.15841	−	0.648384i
$977$	−24.7828	+	14.3084i	−0.792873	+	0.457766i	−0.840973	−	0.541077i	$-0.818017\pi$
$977$	−24.7828	+	14.3084i	−0.792873	+	0.457766i	0.0480999	+	0.998843i	$0.484683\pi$
$978$		0			0
$979$		−	30.2920i		−	0.968135i
$980$	−1.14890	−	9.70761i	−0.0367002	−	0.310098i
$981$		0			0
$982$	16.1324	+	21.1698i	0.514805	+	0.675554i
$983$	23.8922	+	41.3824i	0.762041	+	1.31989i	0.941797	+	0.336183i	$0.109136\pi$
$983$	23.8922	+	41.3824i	0.762041	+	1.31989i	−0.179755	+	0.983711i	$0.557531\pi$
$984$		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	$-0.561256\pi$
$991$	17.7282	−	10.2354i	0.563155	−	0.325138i	0.754411	+	0.656403i	$0.227923\pi$
$992$	−3.17006	−	4.27694i	−0.100650	−	0.135793i
$993$		0			0
$994$	−5.89088	+	11.7509i	−0.186847	+	0.372716i
$995$	1.06390			0.0337278
$996$		0			0
$997$	17.1746	+	29.7472i	0.543924	+	0.942104i	0.998674	+	0.0514848i	$0.0163954\pi$
$997$	17.1746	+	29.7472i	0.543924	+	0.942104i	−0.454750	+	0.890619i	$0.650271\pi$
$998$	−1.44996	−	11.3044i	−0.0458977	−	0.357834i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.be.a.107.13	yes	32
3.2	odd	2	inner	252.2.be.a.107.4	yes	32
4.3	odd	2	inner	252.2.be.a.107.15	yes	32
7.2	even	3		1764.2.e.i.1079.9		16
7.4	even	3	inner	252.2.be.a.179.2	yes	32
7.5	odd	6		1764.2.e.h.1079.9		16
12.11	even	2	inner	252.2.be.a.107.2	✓	32
21.2	odd	6		1764.2.e.i.1079.8		16
21.5	even	6		1764.2.e.h.1079.8		16
21.11	odd	6	inner	252.2.be.a.179.15	yes	32
28.11	odd	6	inner	252.2.be.a.179.4	yes	32
28.19	even	6		1764.2.e.h.1079.7		16
28.23	odd	6		1764.2.e.i.1079.7		16
84.11	even	6	inner	252.2.be.a.179.13	yes	32
84.23	even	6		1764.2.e.i.1079.10		16
84.47	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	12.11	even	2	inner
252.2.be.a.107.4	yes	32	3.2	odd	2	inner
252.2.be.a.107.13	yes	32	1.1	even	1	trivial
252.2.be.a.107.15	yes	32	4.3	odd	2	inner
252.2.be.a.179.2	yes	32	7.4	even	3	inner
252.2.be.a.179.4	yes	32	28.11	odd	6	inner
252.2.be.a.179.13	yes	32	84.11	even	6	inner
252.2.be.a.179.15	yes	32	21.11	odd	6	inner
1764.2.e.h.1079.7		16	28.19	even	6
1764.2.e.h.1079.8		16	21.5	even	6
1764.2.e.h.1079.9		16	7.5	odd	6
1764.2.e.h.1079.10		16	84.47	odd	6
1764.2.e.i.1079.7		16	28.23	odd	6
1764.2.e.i.1079.8		16	21.2	odd	6
1764.2.e.i.1079.9		16	7.2	even	3
1764.2.e.i.1079.10		16	84.23	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)

\(f(q)\)	\(=\)	\(q+(0.857177 + 1.12483i) q^{2} +(-0.530496 + 1.92836i) q^{4} +(0.604694 + 0.349120i) q^{5} +(1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +O(q^{10})\)	\(q+(0.857177 + 1.12483i) q^{2} +(-0.530496 + 1.92836i) q^{4} +(0.604694 + 0.349120i) q^{5} +(1.16254 + 2.37666i) q^{7} +(-2.62381 + 1.05623i) q^{8} +(0.125628 + 0.979437i) q^{10} +(-1.27599 - 2.21008i) q^{11} +1.88088 q^{13} +(-1.67683 + 3.34488i) q^{14} +(-3.43715 - 2.04597i) q^{16} +(-3.44095 + 1.98663i) q^{17} +(6.11257 + 3.52909i) q^{19} +(-0.994017 + 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} +(2.01328 - 3.48710i) q^{23} +(-2.25623 - 3.90791i) q^{25} +(1.61224 + 2.11567i) q^{26} +(-5.19977 + 0.980998i) q^{28} +1.86081i q^{29} +(0.815018 - 0.470551i) q^{31} +(-0.644865 - 5.61998i) q^{32} +(-5.18413 - 2.16759i) q^{34} +(-0.126755 + 1.84302i) q^{35} +(3.74996 - 6.49512i) q^{37} +(1.26991 + 9.90067i) q^{38} +(-1.95535 - 0.277331i) q^{40} -10.6065i q^{41} -3.97212i q^{43} +(4.93874 - 1.28813i) q^{44} +(5.64814 - 0.724461i) q^{46} +(4.45219 - 7.71142i) q^{47} +(-4.29698 + 5.52593i) q^{49} +(2.46175 - 5.88765i) q^{50} +(-0.997797 + 3.62701i) q^{52} +(-0.458798 + 0.264887i) q^{53} -1.78190i q^{55} +(-5.56058 - 5.00799i) q^{56} +(-2.09310 + 1.59504i) q^{58} +(6.65037 + 11.5188i) q^{59} +(-5.18413 + 8.97918i) q^{61} +(1.22791 + 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} +(1.13735 + 0.656652i) q^{65} +(-2.35819 + 1.36150i) q^{67} +(-2.00553 - 7.68929i) q^{68} +(-2.18174 + 1.43721i) q^{70} +3.51310 q^{71} +(1.37535 + 2.38218i) q^{73} +(10.5203 - 1.34939i) q^{74} +(-10.0481 + 9.91507i) q^{76} +(3.76921 - 5.60191i) q^{77} +(-11.7206 - 6.76690i) q^{79} +(-1.36413 - 2.43717i) q^{80} +(11.9305 - 9.09164i) q^{82} -17.1516 q^{83} -2.77429 q^{85} +(4.46797 - 3.40481i) q^{86} +(5.68231 + 4.45110i) q^{88} +(10.2797 + 5.93499i) q^{89} +(2.18660 + 4.47020i) q^{91} +(5.65635 + 5.73222i) q^{92} +(12.4904 - 1.60208i) q^{94} +(2.46415 + 4.26804i) q^{95} +10.8682 q^{97} +(-9.89902 - 0.0966841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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