LMFDB - Embedded newform 252.2.be.a.179.13

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			179.13
Character	$\chi$	$=$	252.179
Dual form			252.2.be.a.107.13

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

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

Coefficient data

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

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

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

$2$	0.857177	−	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	−0.358655	−	0.933470i	$-0.616764\pi$
$5$	0.604694	−	0.349120i	0.270427	−	0.156131i	0.629082	+	0.777339i	$0.283431\pi$
$6$		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	−0.991731	−	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	$0.416004\pi$
$14$	−1.67683	−	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	0.0208563	−	0.999782i	$-0.493361\pi$
$17$	−3.44095	−	1.98663i	−0.834553	−	0.481829i	−0.855409	+	0.517953i	$0.826694\pi$
$18$		0			0
$19$	6.11257	−	3.52909i	1.40232	−	0.809630i	0.407689	−	0.913121i	$-0.366335\pi$
$19$	6.11257	−	3.52909i	1.40232	−	0.809630i	0.994630	+	0.103491i	$0.0330013\pi$
$20$	−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
$26$	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	$-0.944728\pi$
$29$		−	1.86081i		−	0.345544i	0.984962	−	0.172772i	$-0.0552724\pi$
$30$		0			0
$31$	0.815018	+	0.470551i	0.146382	+	0.0845134i	0.571402	−	0.820670i	$-0.306400\pi$
$31$	0.815018	+	0.470551i	0.146382	+	0.0845134i	−0.425020	+	0.905184i	$0.639733\pi$
$32$	−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	0.990121	+	0.140214i	$0.0447792\pi$
$37$	3.74996	+	6.49512i	0.616490	+	1.06779i	−0.373631	+	0.927577i	$0.621888\pi$
$38$	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	$0.310651\pi$
$41$			10.6065i			1.65646i	−0.560392	+	0.828228i	$0.689349\pi$
$42$		0			0
$43$			3.97212i			0.605743i	0.953031	+	0.302871i	$0.0979452\pi$
$43$			3.97212i			0.605743i	−0.953031	+	0.302871i	$0.902055\pi$
$44$	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	0.983262	+	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
$52$	−0.997797	−	3.62701i	−0.138370	−	0.502976i
$53$	−0.458798	−	0.264887i	−0.0630207	−	0.0363850i	0.468159	−	0.883644i	$-0.344918\pi$
$53$	−0.458798	−	0.264887i	−0.0630207	−	0.0363850i	−0.531179	+	0.847259i	$0.678251\pi$
$54$		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	−0.000442051	−	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	0.348986	−	0.937128i	$-0.386526\pi$
$67$	−2.35819	−	1.36150i	−0.288098	−	0.166334i	−0.637084	+	0.770794i	$0.719860\pi$
$68$	−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	−0.774245	−	0.632886i	$-0.781870\pi$
$73$	1.37535	−	2.38218i	0.160973	−	0.278813i	0.935218	+	0.354073i	$0.115203\pi$
$74$	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	−0.983515	−	0.180827i	$-0.942123\pi$
$79$	−11.7206	+	6.76690i	−1.31867	+	0.761335i	−0.335157	+	0.942162i	$0.608789\pi$
$80$	−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	0.156164	−	0.987731i	$-0.450087\pi$
$89$	10.2797	−	5.93499i	1.08965	−	0.629107i	0.933482	+	0.358624i	$0.116754\pi$
$90$		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	−0.0322775	−	0.999479i	$-0.510276\pi$
$101$	−9.18549	−	5.30325i	−0.913990	−	0.527693i	−0.881713	+	0.471786i	$0.843609\pi$
$102$		0			0
$103$	−11.4970	+	6.63779i	−1.13283	+	0.654041i	−0.944646	−	0.328092i	$-0.893594\pi$
$103$	−11.4970	+	6.63779i	−1.13283	+	0.654041i	−0.188187	+	0.982133i	$0.560261\pi$
$104$	−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	$0.928121\pi$
$110$	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	$-0.807207\pi$
$113$		−	12.1039i		−	1.13864i	0.822117	−	0.569319i	$-0.192793\pi$
$114$		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	$-0.991771\pi$
$127$		−	0.582584i		−	0.0516960i	0.999666	−	0.0258480i	$-0.00822859\pi$
$128$	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	0.523780	−	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
$136$	6.93006	+	8.84697i	0.594248	+	0.758621i
$137$	−11.5198	−	6.65096i	−0.984203	−	0.568230i	−0.0806665	−	0.996741i	$-0.525705\pi$
$137$	−11.5198	−	6.65096i	−0.984203	−	0.568230i	−0.903536	+	0.428511i	$0.859038\pi$
$138$		0			0
$139$			0.840795i			0.0713153i	0.999364	+	0.0356577i	$0.0113526\pi$
$139$			0.840795i			0.0713153i	−0.999364	+	0.0356577i	$0.988647\pi$
$140$	−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	−0.285722	−	0.958313i	$-0.592233\pi$
$149$	4.89898	−	2.82843i	0.401340	−	0.231714i	0.687062	+	0.726599i	$0.258900\pi$
$150$		0			0
$151$	−14.7077	−	8.49147i	−1.19689	−	0.691026i	−0.237031	−	0.971502i	$-0.576174\pi$
$151$	−14.7077	−	8.49147i	−1.19689	−	0.691026i	−0.959861	+	0.280476i	$0.909508\pi$
$152$	−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	−0.823928	−	0.566695i	$-0.808222\pi$
$157$	0.987461	−	1.71033i	0.0788079	−	0.136499i	0.902736	+	0.430195i	$0.141555\pi$
$158$	−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	−0.401604	−	0.915813i	$-0.631547\pi$
$163$	2.43483	−	1.40575i	0.190711	−	0.110107i	0.592315	+	0.805706i	$0.298214\pi$
$164$	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	−0.337942	−	0.941167i	$-0.609731\pi$
$173$	4.05322	−	2.34013i	0.308161	−	0.177917i	0.646103	+	0.763250i	$0.276398\pi$
$174$		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	−0.507001	−	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	$0.271793\pi$
$182$	−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	0.938332	+	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	$0.214593\pi$
$194$	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	$0.0925510\pi$
$197$			8.04744i			0.573356i	−0.958027	+	0.286678i	$0.907449\pi$
$198$		0			0
$199$	1.31955	+	0.761843i	0.0935405	+	0.0540056i	0.546041	−	0.837759i	$-0.316134\pi$
$199$	1.31955	+	0.761843i	0.0935405	+	0.0540056i	−0.452500	+	0.891764i	$0.649468\pi$
$200$	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	$-0.768894\pi$
$211$		−	19.2878i		−	1.32783i	0.747809	−	0.663914i	$-0.231106\pi$
$212$	−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	$0.207763\pi$
$223$			18.1390i			1.21468i	−0.794443	+	0.607338i	$0.792237\pi$
$224$	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	−0.980042	−	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	−0.966476	−	0.256755i	$-0.917347\pi$
$233$	−18.7348	+	10.8165i	−1.22736	+	0.708615i	−0.260881	+	0.965371i	$0.584013\pi$
$234$		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	−0.985580	−	0.169208i	$-0.945879\pi$
$241$	−5.37528	+	9.31025i	−0.346252	+	0.599726i	0.639328	+	0.768934i	$0.279212\pi$
$242$	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	−0.717063	−	0.697009i	$-0.754514\pi$
$257$	−7.56621	+	4.36835i	−0.471967	+	0.272490i	0.245096	+	0.969499i	$0.421181\pi$
$258$		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	0.304863	+	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
$266$	−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	0.835156	−	0.550014i	$-0.185377\pi$
$269$	12.7340	+	7.35200i	0.776408	+	0.448259i	−0.0587478	+	0.998273i	$0.518711\pi$
$270$		0			0
$271$	4.49275	−	2.59389i	0.272915	−	0.157568i	−0.357296	−	0.933991i	$-0.616301\pi$
$271$	4.49275	−	2.59389i	0.272915	−	0.157568i	0.630212	+	0.776423i	$0.282968\pi$
$272$	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	$0.914110\pi$
$278$	0.945754	+	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	$-0.960746\pi$
$281$		−	4.12400i		−	0.246017i	0.992406	−	0.123009i	$-0.0392542\pi$
$282$		0			0
$283$	6.11257	+	3.52909i	0.363355	+	0.209783i	0.670551	−	0.741863i	$-0.266058\pi$
$283$	6.11257	+	3.52909i	0.363355	+	0.209783i	−0.307197	+	0.951646i	$0.599391\pi$
$284$	−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	$-0.845545\pi$
$293$		−	15.9675i		−	0.932830i	0.884566	−	0.466415i	$-0.154455\pi$
$294$		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	$-0.949516\pi$
$307$		−	5.53450i		−	0.315871i	0.987449	−	0.157935i	$-0.0504838\pi$
$308$	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	−0.975536	−	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	−0.713042	−	0.701122i	$-0.752683\pi$
$317$	−8.23233	+	4.75294i	−0.462374	+	0.266952i	0.250668	+	0.968073i	$0.419350\pi$
$318$		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	−0.244374	−	0.969681i	$-0.578583\pi$
$331$	8.60924	−	4.97055i	0.473207	−	0.273206i	0.717581	+	0.696475i	$0.245249\pi$
$332$	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	−0.528416	−	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	$0.216210\pi$
$350$	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	0.217892	−	0.975973i	$-0.430082\pi$
$353$	−9.73945	−	5.62308i	−0.518379	−	0.299286i	−0.736271	+	0.676687i	$0.763415\pi$
$354$		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
$362$	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	−0.155582	−	0.987823i	$-0.549725\pi$
$367$	−20.8594	−	12.0432i	−1.08885	−	0.628649i	−0.933271	+	0.359174i	$0.883059\pi$
$368$	−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	0.638900	−	0.769290i	$-0.279390\pi$
$373$	−6.69734	−	11.6001i	−0.346775	−	0.600632i	−0.985675	+	0.168658i	$0.946057\pi$
$374$	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	$0.107975\pi$
$379$			12.9558i			0.665493i	−0.943016	+	0.332746i	$0.892025\pi$
$380$	−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	0.896573	−	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
$388$	−5.76553	−	20.9578i	−0.292700	−	1.06397i
$389$	13.2543	+	7.65235i	0.672018	+	0.387990i	0.796841	−	0.604189i	$-0.206503\pi$
$389$	13.2543	+	7.65235i	0.672018	+	0.387990i	−0.124823	+	0.992179i	$0.539836\pi$
$390$		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	0.653394	−	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	−0.474697	−	0.880149i	$-0.657442\pi$
$401$	1.00499	−	0.580229i	0.0501866	−	0.0289753i	0.524883	+	0.851174i	$0.324109\pi$
$402$		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	−0.941097	−	0.338136i	$-0.890204\pi$
$409$	−3.59404	+	6.22507i	−0.177714	+	0.307810i	0.763383	+	0.645946i	$0.223537\pi$
$410$	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	−0.658119	−	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	$0.775401\pi$
$434$	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	−0.0400745	−	0.999197i	$-0.512760\pi$
$439$	16.8712	−	9.74059i	0.805218	−	0.464893i	0.845292	+	0.534304i	$0.179426\pi$
$440$	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
$446$	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	$0.150723\pi$
$449$			19.3255i			0.912025i	−0.889973	+	0.456012i	$0.849277\pi$
$450$		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	0.803899	−	0.594766i	$-0.202755\pi$
$457$	−2.41849	−	4.18896i	−0.113132	−	0.195951i	−0.917032	+	0.398814i	$0.869422\pi$
$458$	−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	$-0.789721\pi$
$461$		−	26.3490i		−	1.22720i	0.789618	−	0.613599i	$-0.210279\pi$
$462$		0			0
$463$			38.1024i			1.77077i	0.464858	+	0.885385i	$0.346105\pi$
$463$			38.1024i			1.77077i	−0.464858	+	0.885385i	$0.653895\pi$
$464$	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	0.782666	−	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
$472$	−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	−0.519061	−	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	0.776636	−	0.629949i	$-0.216924\pi$
$487$	13.6690	+	7.89181i	0.619402	+	0.357612i	−0.157234	+	0.987561i	$0.550258\pi$
$488$	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	−0.648014	−	0.761628i	$-0.724400\pi$
$499$	−6.97921	+	4.02945i	−0.312432	+	0.180383i	0.335582	+	0.942011i	$0.391067\pi$
$500$	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	−0.500932	+	0.865487i	$0.667009\pi$
$509$	−33.8626	+	19.5506i	−1.50093	+	0.866563i	−0.999999	+	0.00107666i	$0.999657\pi$
$510$		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	0.509891	−	0.860239i	$-0.329686\pi$
$521$	0.453045	+	0.261566i	0.0198483	+	0.0114594i	−0.490043	+	0.871698i	$0.663019\pi$
$522$		0			0
$523$	−32.5034	+	18.7658i	−1.42127	+	0.820573i	−0.996408	−	0.0846840i	$-0.973012\pi$
$523$	−32.5034	+	18.7658i	−1.42127	+	0.820573i	−0.424865	+	0.905257i	$0.639679\pi$
$524$	−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	0.519212	−	0.854645i	$-0.326225\pi$
$541$	−11.1770	−	19.3592i	−0.480538	−	0.832317i	−0.999751	+	0.0223286i	$0.992892\pi$
$542$	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	$-0.944603\pi$
$547$		−	8.09960i		−	0.346314i	0.984894	−	0.173157i	$-0.0553968\pi$
$548$	−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	0.951130	−	0.308791i	$-0.0999244\pi$
$557$	27.3598	+	15.7962i	1.15927	+	0.669307i	0.208144	+	0.978098i	$0.433258\pi$
$558$		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	−0.940556	−	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	−0.717512	−	0.696546i	$-0.754719\pi$
$569$	−11.2838	+	6.51469i	−0.473041	+	0.273110i	0.244471	+	0.969657i	$0.421386\pi$
$570$		0			0
$571$	12.4590	+	7.19319i	0.521392	+	0.301026i	0.737504	−	0.675343i	$-0.236004\pi$
$571$	12.4590	+	7.19319i	0.521392	+	0.301026i	−0.216112	+	0.976369i	$0.569338\pi$
$572$	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	−0.462868	−	0.886427i	$-0.653180\pi$
$577$	12.8808	−	22.3102i	0.536235	−	0.928786i	0.999102	−	0.0423583i	$-0.0134871\pi$
$578$	−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	0.127989	−	0.991776i	$-0.459148\pi$
$593$	25.5907	−	14.7748i	1.05089	−	0.606729i	0.922897	+	0.385046i	$0.125815\pi$
$594$		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	−0.920777	−	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	$0.535445\pi$
$602$	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	−0.421650	−	0.906759i	$-0.638549\pi$
$607$	3.76460	−	2.17350i	0.152801	−	0.0882195i	0.574451	+	0.818539i	$0.305216\pi$
$608$	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	$0.0689603\pi$
$614$	−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	$-0.857557\pi$
$617$		−	21.4967i		−	0.865425i	0.901532	−	0.432713i	$-0.142443\pi$
$618$		0			0
$619$	12.4590	+	7.19319i	0.500769	+	0.289119i	0.729031	−	0.684481i	$-0.239971\pi$
$619$	12.4590	+	7.19319i	0.500769	+	0.289119i	−0.228262	+	0.973600i	$0.573304\pi$
$620$	−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	$-0.897509\pi$
$631$		−	15.8983i		−	0.632900i	0.948609	−	0.316450i	$-0.102491\pi$
$632$	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	0.526544	−	0.850148i	$-0.323488\pi$
$641$	1.35619	+	0.782995i	0.0535661	+	0.0309264i	−0.472978	+	0.881074i	$0.656821\pi$
$642$		0			0
$643$		−	33.5314i		−	1.32235i	−0.750232	−	0.661174i	$-0.770058\pi$
$643$		−	33.5314i		−	1.32235i	0.750232	−	0.661174i	$-0.229942\pi$
$644$	−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	−0.984512	−	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	0.0351715	−	0.999381i	$-0.488802\pi$
$653$	23.4648	−	13.5474i	0.918247	−	0.530150i	0.883075	+	0.469231i	$0.155469\pi$
$654$		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	−0.892677	−	0.450697i	$-0.851176\pi$
$661$	−1.44036	+	2.49478i	−0.0560235	+	0.0970355i	0.836654	+	0.547732i	$0.184509\pi$
$662$	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	−0.741612	−	0.670829i	$-0.765938\pi$
$677$	−13.8282	+	7.98374i	−0.531463	+	0.306840i	0.210149	+	0.977669i	$0.432605\pi$
$678$		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	0.0266295	+	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
$686$	−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	−0.251471	−	0.967865i	$-0.580914\pi$
$691$	12.1180	−	6.99631i	0.460989	−	0.266152i	0.712460	+	0.701713i	$0.247581\pi$
$692$	−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	$0.0877022\pi$
$701$			14.4059i			0.544104i	−0.962283	+	0.272052i	$0.912298\pi$
$702$		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	0.898232	+	0.439522i	$0.144852\pi$
$709$	22.0939	+	38.2677i	0.829753	+	1.43717i	−0.0684783	+	0.997653i	$0.521814\pi$
$710$	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	0.956711	−	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
$724$	−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	$-0.827542\pi$
$727$		−	27.8081i		−	1.03134i	0.856786	−	0.515672i	$-0.172458\pi$
$728$	−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	0.955818	+	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	−0.120414	−	0.992724i	$-0.538422\pi$
$739$	−28.2813	−	16.3282i	−1.04034	−	0.600643i	−0.919931	+	0.392080i	$0.871756\pi$
$740$	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	0.0503969	−	0.998729i	$-0.483951\pi$
$751$	25.7744	−	14.8808i	0.940520	−	0.543010i	0.890123	+	0.455720i	$0.150618\pi$
$752$	−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	−0.991518	−	0.129969i	$-0.958512\pi$
$761$	−37.9234	+	21.8951i	−1.37472	+	0.793696i	−0.383203	+	0.923664i	$0.625179\pi$
$762$		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	−0.366651	−	0.930359i	$-0.619496\pi$
$773$	−37.6921	−	21.7615i	−1.35569	−	0.782708i	−0.989040	+	0.147650i	$0.952829\pi$
$774$		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	0.664239	−	0.747520i	$-0.268756\pi$
$787$	9.79031	+	5.65244i	0.348987	+	0.201488i	−0.315252	+	0.949008i	$0.602089\pi$
$788$	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	$-0.626665\pi$
$797$		−	52.0507i		−	1.84373i	0.387511	−	0.921865i	$-0.373335\pi$
$798$		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	0.292998	−	0.956113i	$-0.405347\pi$
$809$	−11.0507	−	6.38012i	−0.388521	−	0.224313i	−0.681519	+	0.731800i	$0.738680\pi$
$810$		0			0
$811$		−	37.2617i		−	1.30843i	−0.756307	−	0.654217i	$-0.772998\pi$
$811$		−	37.2617i		−	1.30843i	0.756307	−	0.654217i	$-0.227002\pi$
$812$	−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	0.232827	−	0.972518i	$-0.425202\pi$
$821$	34.1392	−	19.7103i	1.19147	−	0.687893i	0.958639	+	0.284625i	$0.0918691\pi$
$822$		0			0
$823$	43.1751	+	24.9272i	1.50499	+	0.868907i	0.999983	+	0.00579133i	$0.00184345\pi$
$823$	43.1751	+	24.9272i	1.50499	+	0.868907i	0.505007	+	0.863115i	$0.331490\pi$
$824$	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	−0.781450	−	0.623968i	$-0.785520\pi$
$829$	4.30870	−	7.46288i	0.149647	−	0.259197i	0.931097	+	0.364771i	$0.118853\pi$
$830$	−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	0.639673	−	0.768647i	$-0.279070\pi$
$857$	8.60210	+	4.96642i	0.293842	+	0.169650i	−0.345831	+	0.938297i	$0.612403\pi$
$858$		0			0
$859$	−25.8761	+	14.9395i	−0.882879	+	0.509731i	−0.871607	−	0.490206i	$-0.836922\pi$
$859$	−25.8761	+	14.9395i	−0.882879	+	0.509731i	−0.0112727	+	0.999936i	$0.503588\pi$
$860$	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
$866$	−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	0.930039	−	0.367460i	$-0.119773\pi$
$877$	4.34706	+	7.52933i	0.146790	+	0.254247i	−0.783249	+	0.621708i	$0.786439\pi$
$878$	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	$0.301609\pi$
$881$			48.2017i			1.62396i	−0.583688	+	0.811978i	$0.698391\pi$
$882$		0			0
$883$			6.60661i			0.222330i	0.993802	+	0.111165i	$0.0354582\pi$
$883$			6.60661i			0.222330i	−0.993802	+	0.111165i	$0.964542\pi$
$884$	−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	−0.914354	−	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
$892$	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	0.380039	−	0.924970i	$-0.375910\pi$
$907$	−6.95656	−	4.01637i	−0.230989	−	0.133361i	−0.611028	+	0.791609i	$0.709244\pi$
$908$	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	−0.235653	−	0.971837i	$-0.575723\pi$
$919$	14.7985	−	8.54390i	0.488156	−	0.281837i	0.723809	+	0.690000i	$0.242390\pi$
$920$	−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	−0.0464382	−	0.998921i	$-0.514787\pi$
$929$	24.2444	−	13.9975i	0.795434	−	0.459244i	0.841872	+	0.539677i	$0.181454\pi$
$930$		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	0.789897	−	0.613239i	$-0.210134\pi$
$941$	20.0547	+	11.5786i	0.653765	+	0.377451i	−0.136132	+	0.990691i	$0.543467\pi$
$942$		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
$950$	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	$0.149091\pi$
$953$			27.8728i			0.902889i	−0.892299	+	0.451444i	$0.850909\pi$
$954$		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	$0.116207\pi$
$967$			22.2042i			0.714038i	−0.934097	+	0.357019i	$0.883793\pi$
$968$	−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	0.966165	−	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
$976$	36.1898	+	20.2562i	1.15841	+	0.648384i
$977$	−24.7828	−	14.3084i	−0.792873	−	0.457766i	0.0480999	−	0.998843i	$-0.484683\pi$
$977$	−24.7828	−	14.3084i	−0.792873	−	0.457766i	−0.840973	+	0.541077i	$0.818017\pi$
$978$		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	−0.179755	−	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	0.754411	−	0.656403i	$-0.227923\pi$
$991$	17.7282	+	10.2354i	0.563155	+	0.325138i	−0.191256	+	0.981540i	$0.561256\pi$
$992$	−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	−0.454750	−	0.890619i	$-0.650271\pi$
$997$	17.1746	−	29.7472i	0.543924	−	0.942104i	0.998674	−	0.0514848i	$-0.0163954\pi$
$998$	−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.179.13	yes	32
3.2	odd	2	inner	252.2.be.a.179.4	yes	32
4.3	odd	2	inner	252.2.be.a.179.15	yes	32
7.2	even	3	inner	252.2.be.a.107.2	✓	32
7.3	odd	6		1764.2.e.h.1079.10		16
7.4	even	3		1764.2.e.i.1079.10		16
12.11	even	2	inner	252.2.be.a.179.2	yes	32
21.2	odd	6	inner	252.2.be.a.107.15	yes	32
21.11	odd	6		1764.2.e.i.1079.7		16
21.17	even	6		1764.2.e.h.1079.7		16
28.3	even	6		1764.2.e.h.1079.8		16
28.11	odd	6		1764.2.e.i.1079.8		16
28.23	odd	6	inner	252.2.be.a.107.4	yes	32
84.11	even	6		1764.2.e.i.1079.9		16
84.23	even	6	inner	252.2.be.a.107.13	yes	32
84.59	odd	6		1764.2.e.h.1079.9		16

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

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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