LMFDB - Embedded newform 693.2.m.b.190.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(64,693)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("693.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(693, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.b.631.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(-0.309017 - 0.224514i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +0.236068 q^{10} +(-0.309017 - 3.30220i) q^{11} +(0.809017 - 0.587785i) q^{13} +(0.190983 + 0.587785i) q^{14} +(-1.50000 - 1.08981i) q^{16} +(-3.42705 - 2.48990i) q^{17} +(0.500000 - 0.363271i) q^{20} +(1.35410 + 1.53884i) q^{22} +3.23607 q^{23} +(-1.50000 - 4.61653i) q^{25} +(-0.190983 + 0.587785i) q^{26} +(1.30902 + 0.951057i) q^{28} +(-2.07295 + 6.37988i) q^{29} +(8.28115 - 6.01661i) q^{31} +5.61803 q^{32} +2.61803 q^{34} +(-0.309017 + 0.224514i) q^{35} +(2.14590 - 6.60440i) q^{37} +(-0.263932 + 0.812299i) q^{40} +(-1.57295 - 4.84104i) q^{41} -1.00000 q^{43} +(5.23607 + 1.17557i) q^{44} +(-1.61803 + 1.17557i) q^{46} +(2.26393 + 6.96767i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(2.42705 + 1.76336i) q^{50} +(0.500000 + 1.53884i) q^{52} +(6.16312 - 4.47777i) q^{53} +(-0.645898 + 1.08981i) q^{55} -2.23607 q^{56} +(-1.28115 - 3.94298i) q^{58} +(1.28115 - 3.94298i) q^{59} +(4.66312 + 3.38795i) q^{61} +(-1.95492 + 6.01661i) q^{62} +(0.190983 - 0.138757i) q^{64} -0.381966 q^{65} -9.23607 q^{67} +(5.54508 - 4.02874i) q^{68} +(0.0729490 - 0.224514i) q^{70} +(-6.04508 - 4.39201i) q^{71} +(3.57295 - 10.9964i) q^{73} +(1.32624 + 4.08174i) q^{74} +(-3.23607 - 0.726543i) q^{77} +(-8.78115 + 6.37988i) q^{79} +(0.218847 + 0.673542i) q^{80} +(2.54508 + 1.84911i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(0.500000 + 1.53884i) q^{85} +(0.500000 - 0.363271i) q^{86} +(-6.80902 + 2.93893i) q^{88} +6.38197 q^{89} +(-0.309017 - 0.951057i) q^{91} +(-1.61803 + 4.97980i) q^{92} +(-3.66312 - 2.66141i) q^{94} +(13.7533 - 9.99235i) q^{97} +0.618034 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} - 5 q^{8} - 8 q^{10} + q^{11} + q^{13} + 3 q^{14} - 6 q^{16} - 7 q^{17} + 2 q^{20} - 8 q^{22} + 4 q^{23} - 6 q^{25} - 3 q^{26} + 3 q^{28} - 15 q^{29} + 13 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 - 5 * q^8 - 8 * q^10 + q^11 + q^13 + 3 * q^14 - 6 * q^16 - 7 * q^17 + 2 * q^20 - 8 * q^22 + 4 * q^23 - 6 * q^25 - 3 * q^26 + 3 * q^28 - 15 * q^29 + 13 * q^31 + 18 * q^32 + 6 * q^34 + q^35 + 22 * q^37 - 10 * q^40 - 13 * q^41 - 4 * q^43 + 12 * q^44 - 2 * q^46 + 18 * q^47 - q^49 + 3 * q^50 + 2 * q^52 + 9 * q^53 - 16 * q^55 + 15 * q^58 - 15 * q^59 + 3 * q^61 - 19 * q^62 + 3 * q^64 - 6 * q^65 - 28 * q^67 + 11 * q^68 + 7 * q^70 - 13 * q^71 + 21 * q^73 - 26 * q^74 - 4 * q^77 - 15 * q^79 + 21 * q^80 - q^82 - 6 * q^83 + 2 * q^85 + 2 * q^86 - 25 * q^88 + 30 * q^89 + q^91 - 2 * q^92 + q^94 + 17 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.500000	+	0.363271i	−0.353553	+	0.256872i	−0.750358	−	0.661031i	$-0.770119\pi$
$2$	−0.500000	+	0.363271i	−0.353553	+	0.256872i	0.396805	+	0.917903i	$0.370119\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	1.53884i	−0.250000	+	0.769421i
$5$	−0.309017	−	0.224514i	−0.138197	−	0.100406i	0.516539	−	0.856264i	$-0.327220\pi$
$5$	−0.309017	−	0.224514i	−0.138197	−	0.100406i	−0.654736	+	0.755858i	$0.727220\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$		0			0
$10$	0.236068			0.0746512
$11$	−0.309017	−	3.30220i	−0.0931721	−	0.995650i
$11$	−0.309017	−	3.30220i	−0.0931721	−	0.995650i
$12$		0			0
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i	−0.469916	−	0.882711i	$-0.655716\pi$
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i	0.694297	+	0.719689i	$0.255716\pi$
$14$	0.190983	+	0.587785i	0.0510424	+	0.157092i
$15$		0			0
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	−3.42705	−	2.48990i	−0.831182	−	0.603889i	0.0887115	−	0.996057i	$-0.471725\pi$
$17$	−3.42705	−	2.48990i	−0.831182	−	0.603889i	−0.919893	+	0.392168i	$0.871725\pi$
$18$		0			0
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	0.500000	−	0.363271i	0.111803	−	0.0812299i
$21$		0			0
$22$	1.35410	+	1.53884i	0.288696	+	0.328082i
$23$	3.23607			0.674767			0.337383	−	0.941367i	$-0.390458\pi$
$23$	3.23607			0.674767			0.337383	+	0.941367i	$0.390458\pi$
$24$		0			0
$25$	−1.50000	−	4.61653i	−0.300000	−	0.923305i
$26$	−0.190983	+	0.587785i	−0.0374548	+	0.115274i
$27$		0			0
$28$	1.30902	+	0.951057i	0.247381	+	0.179733i
$29$	−2.07295	+	6.37988i	−0.384937	+	1.18471i	0.551589	+	0.834116i	$0.314022\pi$
$29$	−2.07295	+	6.37988i	−0.384937	+	1.18471i	−0.936526	+	0.350598i	$0.885978\pi$
$30$		0			0
$31$	8.28115	−	6.01661i	1.48734	−	1.08062i	0.512241	−	0.858842i	$-0.328816\pi$
$31$	8.28115	−	6.01661i	1.48734	−	1.08062i	0.975098	−	0.221773i	$-0.0711844\pi$
$32$	5.61803			0.993137
$33$		0			0
$34$	2.61803			0.448989
$35$	−0.309017	+	0.224514i	−0.0522334	+	0.0379498i
$36$		0			0
$37$	2.14590	−	6.60440i	0.352783	−	1.08576i	−0.604500	−	0.796605i	$-0.706627\pi$
$37$	2.14590	−	6.60440i	0.352783	−	1.08576i	0.957284	−	0.289151i	$-0.0933729\pi$
$38$		0			0
$39$		0			0
$40$	−0.263932	+	0.812299i	−0.0417313	+	0.128436i
$41$	−1.57295	−	4.84104i	−0.245653	−	0.756043i	−0.995528	−	0.0944637i	$-0.969886\pi$
$41$	−1.57295	−	4.84104i	−0.245653	−	0.756043i	0.749875	−	0.661580i	$-0.230114\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	5.23607	+	1.17557i	0.789367	+	0.177224i
$45$		0			0
$46$	−1.61803	+	1.17557i	−0.238566	+	0.173328i
$47$	2.26393	+	6.96767i	0.330228	+	1.01634i	0.969025	+	0.246963i	$0.0794326\pi$
$47$	2.26393	+	6.96767i	0.330228	+	1.01634i	−0.638797	+	0.769376i	$0.720567\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	2.42705	+	1.76336i	0.343237	+	0.249376i
$51$		0			0
$52$	0.500000	+	1.53884i	0.0693375	+	0.213399i
$53$	6.16312	−	4.47777i	0.846569	−	0.615069i	−0.0776285	−	0.996982i	$-0.524735\pi$
$53$	6.16312	−	4.47777i	0.846569	−	0.615069i	0.924198	+	0.381914i	$0.124735\pi$
$54$		0			0
$55$	−0.645898	+	1.08981i	−0.0870929	+	0.146950i
$56$	−2.23607			−0.298807
$57$		0			0
$58$	−1.28115	−	3.94298i	−0.168224	−	0.517739i
$59$	1.28115	−	3.94298i	0.166792	−	0.513333i	−0.832372	−	0.554217i	$-0.813018\pi$
$59$	1.28115	−	3.94298i	0.166792	−	0.513333i	0.999164	+	0.0408847i	$0.0130176\pi$
$60$		0			0
$61$	4.66312	+	3.38795i	0.597051	+	0.433783i	0.844831	−	0.535033i	$-0.179701\pi$
$61$	4.66312	+	3.38795i	0.597051	+	0.433783i	−0.247780	+	0.968816i	$0.579701\pi$
$62$	−1.95492	+	6.01661i	−0.248274	+	0.764110i
$63$		0			0
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	−0.381966			−0.0473771
$66$		0			0
$67$	−9.23607			−1.12837			−0.564183	−	0.825650i	$-0.690809\pi$
$67$	−9.23607			−1.12837			−0.564183	+	0.825650i	$0.690809\pi$
$68$	5.54508	−	4.02874i	0.672440	−	0.488556i
$69$		0			0
$70$	0.0729490	−	0.224514i	0.00871908	−	0.0268346i
$71$	−6.04508	−	4.39201i	−0.717420	−	0.521236i	0.168139	−	0.985763i	$-0.446224\pi$
$71$	−6.04508	−	4.39201i	−0.717420	−	0.521236i	−0.885559	+	0.464527i	$0.846224\pi$
$72$		0			0
$73$	3.57295	−	10.9964i	0.418182	−	1.28703i	−0.491192	−	0.871052i	$-0.663438\pi$
$73$	3.57295	−	10.9964i	0.418182	−	1.28703i	0.909374	−	0.415980i	$-0.136562\pi$
$74$	1.32624	+	4.08174i	0.154172	+	0.474493i
$75$		0			0
$76$		0			0
$77$	−3.23607	−	0.726543i	−0.368784	−	0.0827972i
$78$		0			0
$79$	−8.78115	+	6.37988i	−0.987957	+	0.717793i	−0.959473	−	0.281802i	$-0.909068\pi$
$79$	−8.78115	+	6.37988i	−0.987957	+	0.717793i	−0.0284842	+	0.999594i	$0.509068\pi$
$80$	0.218847	+	0.673542i	0.0244678	+	0.0753043i
$81$		0			0
$82$	2.54508	+	1.84911i	0.281058	+	0.204200i
$83$	−4.85410	−	3.52671i	−0.532807	−	0.387107i	0.288600	−	0.957450i	$-0.406810\pi$
$83$	−4.85410	−	3.52671i	−0.532807	−	0.387107i	−0.821407	+	0.570343i	$0.806810\pi$
$84$		0			0
$85$	0.500000	+	1.53884i	0.0542326	+	0.166911i
$86$	0.500000	−	0.363271i	0.0539164	−	0.0391725i
$87$		0			0
$88$	−6.80902	+	2.93893i	−0.725844	+	0.313291i
$89$	6.38197			0.676487			0.338244	−	0.941059i	$-0.390167\pi$
$89$	6.38197			0.676487			0.338244	+	0.941059i	$0.390167\pi$
$90$		0			0
$91$	−0.309017	−	0.951057i	−0.0323938	−	0.0996978i
$92$	−1.61803	+	4.97980i	−0.168692	+	0.519180i
$93$		0			0
$94$	−3.66312	−	2.66141i	−0.377822	−	0.274504i
$95$		0			0
$96$		0			0
$97$	13.7533	−	9.99235i	1.39643	−	1.01457i	0.401310	−	0.915942i	$-0.368555\pi$
$97$	13.7533	−	9.99235i	1.39643	−	1.01457i	0.995124	−	0.0986273i	$-0.0314452\pi$
$98$	0.618034			0.0624309
$99$		0			0
$100$	7.85410			0.785410
$101$	−3.38197	+	2.45714i	−0.336518	+	0.244495i	−0.743191	−	0.669079i	$-0.766689\pi$
$101$	−3.38197	+	2.45714i	−0.336518	+	0.244495i	0.406673	+	0.913574i	$0.366689\pi$
$102$		0			0
$103$	−3.92705	+	12.0862i	−0.386944	+	1.19089i	0.548116	+	0.836402i	$0.315345\pi$
$103$	−3.92705	+	12.0862i	−0.386944	+	1.19089i	−0.935060	+	0.354489i	$0.884655\pi$
$104$	−1.80902	−	1.31433i	−0.177389	−	0.128880i
$105$		0			0
$106$	−1.45492	+	4.47777i	−0.141314	+	0.434919i
$107$	−4.87132	−	14.9924i	−0.470929	−	1.44937i	−0.851371	−	0.524564i	$-0.824228\pi$
$107$	−4.87132	−	14.9924i	−0.470929	−	1.44937i	0.380442	−	0.924805i	$-0.375772\pi$
$108$		0			0
$109$	−7.56231			−0.724338			−0.362169	−	0.932113i	$-0.617964\pi$
$109$	−7.56231			−0.724338			−0.362169	+	0.932113i	$0.617964\pi$
$110$	−0.0729490	−	0.779543i	−0.00695542	−	0.0743265i
$111$		0			0
$112$	−1.50000	+	1.08981i	−0.141737	+	0.102978i
$113$	3.60081	+	11.0822i	0.338736	+	1.04252i	0.964852	+	0.262793i	$0.0846435\pi$
$113$	3.60081	+	11.0822i	0.338736	+	1.04252i	−0.626116	+	0.779730i	$0.715357\pi$
$114$		0			0
$115$	−1.00000	−	0.726543i	−0.0932505	−	0.0677504i
$116$	−8.78115	−	6.37988i	−0.815310	−	0.592357i
$117$		0			0
$118$	0.791796	+	2.43690i	0.0728907	+	0.224335i
$119$	−3.42705	+	2.48990i	−0.314157	+	0.228249i
$120$		0			0
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$	−3.56231			−0.322516
$123$		0			0
$124$	5.11803	+	15.7517i	0.459613	+	1.41454i
$125$	−1.16312	+	3.57971i	−0.104033	+	0.320179i
$126$		0			0
$127$	5.92705	+	4.30625i	0.525941	+	0.382118i	0.818837	−	0.574026i	$-0.194619\pi$
$127$	5.92705	+	4.30625i	0.525941	+	0.382118i	−0.292896	+	0.956144i	$0.594619\pi$
$128$	−3.51722	+	10.8249i	−0.310881	+	0.956794i
$129$		0			0
$130$	0.190983	−	0.138757i	0.0167503	−	0.0121698i
$131$	3.32624			0.290615			0.145307	−	0.989387i	$-0.453583\pi$
$131$	3.32624			0.290615			0.145307	+	0.989387i	$0.453583\pi$
$132$		0			0
$133$		0			0
$134$	4.61803	−	3.35520i	0.398937	−	0.289845i
$135$		0			0
$136$	−2.92705	+	9.00854i	−0.250993	+	0.772476i
$137$	−2.47214	−	1.79611i	−0.211209	−	0.153452i	0.477152	−	0.878821i	$-0.341669\pi$
$137$	−2.47214	−	1.79611i	−0.211209	−	0.153452i	−0.688360	+	0.725369i	$0.741669\pi$
$138$		0			0
$139$	−5.42705	+	16.7027i	−0.460316	+	1.41671i	0.404462	+	0.914555i	$0.367459\pi$
$139$	−5.42705	+	16.7027i	−0.460316	+	1.41671i	−0.864778	+	0.502154i	$0.832541\pi$
$140$	−0.190983	−	0.587785i	−0.0161410	−	0.0496769i
$141$		0			0
$142$	4.61803			0.387537
$143$	−2.19098	−	2.48990i	−0.183219	−	0.208216i
$144$		0			0
$145$	2.07295	−	1.50609i	0.172149	−	0.125074i
$146$	2.20820	+	6.79615i	0.182752	+	0.562454i
$147$		0			0
$148$	9.09017	+	6.60440i	0.747207	+	0.542878i
$149$	−10.5902	−	7.69421i	−0.867581	−	0.630334i	0.0623561	−	0.998054i	$-0.480139\pi$
$149$	−10.5902	−	7.69421i	−0.867581	−	0.630334i	−0.929937	+	0.367720i	$0.880139\pi$
$150$		0			0
$151$	−6.51722	−	20.0579i	−0.530364	−	1.63229i	−0.753458	−	0.657495i	$-0.771616\pi$
$151$	−6.51722	−	20.0579i	−0.530364	−	1.63229i	0.223095	−	0.974797i	$-0.428384\pi$
$152$		0			0
$153$		0			0
$154$	1.88197	−	0.812299i	0.151653	−	0.0654569i
$155$	−3.90983			−0.314045
$156$		0			0
$157$	−0.517221	−	1.59184i	−0.0412787	−	0.127043i	0.928293	−	0.371848i	$-0.121276\pi$
$157$	−0.517221	−	1.59184i	−0.0412787	−	0.127043i	−0.969572	+	0.244806i	$0.921276\pi$
$158$	2.07295	−	6.37988i	0.164915	−	0.507556i
$159$		0			0
$160$	−1.73607	−	1.26133i	−0.137248	−	0.0997167i
$161$	1.00000	−	3.07768i	0.0788110	−	0.242555i
$162$		0			0
$163$	−4.88197	+	3.54696i	−0.382385	+	0.277819i	−0.762328	−	0.647191i	$-0.775944\pi$
$163$	−4.88197	+	3.54696i	−0.382385	+	0.277819i	0.379943	+	0.925010i	$0.375944\pi$
$164$	8.23607			0.643129
$165$		0			0
$166$	3.70820			0.287812
$167$	7.59017	−	5.51458i	0.587345	−	0.426731i	−0.254020	−	0.967199i	$-0.581753\pi$
$167$	7.59017	−	5.51458i	0.587345	−	0.426731i	0.841365	+	0.540468i	$0.181753\pi$
$168$		0			0
$169$	−3.70820	+	11.4127i	−0.285246	+	0.877898i
$170$	−0.809017	−	0.587785i	−0.0620488	−	0.0450811i
$171$		0			0
$172$	0.500000	−	1.53884i	0.0381246	−	0.117336i
$173$	4.51722	+	13.9026i	0.343438	+	1.05699i	0.962415	+	0.271584i	$0.0875475\pi$
$173$	4.51722	+	13.9026i	0.343438	+	1.05699i	−0.618977	+	0.785409i	$0.712453\pi$
$174$		0			0
$175$	−4.85410			−0.366936
$176$	−3.13525	+	5.29007i	−0.236329	+	0.398754i
$177$		0			0
$178$	−3.19098	+	2.31838i	−0.239174	+	0.173770i
$179$	0.690983	+	2.12663i	0.0516465	+	0.158952i	0.973553	−	0.228460i	$-0.0733691\pi$
$179$	0.690983	+	2.12663i	0.0516465	+	0.158952i	−0.921907	+	0.387412i	$0.873369\pi$
$180$		0			0
$181$	0.190983	+	0.138757i	0.0141957	+	0.0103137i	0.594860	−	0.803829i	$-0.297207\pi$
$181$	0.190983	+	0.138757i	0.0141957	+	0.0103137i	−0.580665	+	0.814143i	$0.697207\pi$
$182$	0.500000	+	0.363271i	0.0370625	+	0.0269275i
$183$		0			0
$184$	−2.23607	−	6.88191i	−0.164845	−	0.507341i
$185$	−2.14590	+	1.55909i	−0.157770	+	0.114626i
$186$		0			0
$187$	−7.16312	+	12.0862i	−0.523819	+	0.883832i
$188$	−11.8541			−0.864549
$189$		0			0
$190$		0			0
$191$	−3.01722	+	9.28605i	−0.218318	+	0.671915i	0.780583	+	0.625052i	$0.214922\pi$
$191$	−3.01722	+	9.28605i	−0.218318	+	0.671915i	−0.998901	+	0.0468628i	$0.985078\pi$
$192$		0			0
$193$	−4.09017	−	2.97168i	−0.294417	−	0.213906i	0.430764	−	0.902464i	$-0.358244\pi$
$193$	−4.09017	−	2.97168i	−0.294417	−	0.213906i	−0.725181	+	0.688558i	$0.758244\pi$
$194$	−3.24671	+	9.99235i	−0.233100	+	0.717409i
$195$		0			0
$196$	1.30902	−	0.951057i	0.0935012	−	0.0679326i
$197$	9.23607			0.658043			0.329021	−	0.944323i	$-0.393281\pi$
$197$	9.23607			0.658043			0.329021	+	0.944323i	$0.393281\pi$
$198$		0			0
$199$	−7.56231			−0.536078			−0.268039	−	0.963408i	$-0.586376\pi$
$199$	−7.56231			−0.536078			−0.268039	+	0.963408i	$0.586376\pi$
$200$	−8.78115	+	6.37988i	−0.620921	+	0.451126i
$201$		0			0
$202$	0.798374	−	2.45714i	0.0561734	−	0.172884i
$203$	5.42705	+	3.94298i	0.380904	+	0.276743i
$204$		0			0
$205$	−0.600813	+	1.84911i	−0.0419626	+	0.129148i
$206$	−2.42705	−	7.46969i	−0.169101	−	0.520438i
$207$		0			0
$208$	−1.85410			−0.128559
$209$		0			0
$210$		0			0
$211$	−4.28115	+	3.11044i	−0.294727	+	0.214131i	−0.725315	−	0.688417i	$-0.758306\pi$
$211$	−4.28115	+	3.11044i	−0.294727	+	0.214131i	0.430589	+	0.902548i	$0.358306\pi$
$212$	3.80902	+	11.7229i	0.261604	+	0.805135i
$213$		0			0
$214$	7.88197	+	5.72658i	0.538800	+	0.391461i
$215$	0.309017	+	0.224514i	0.0210748	+	0.0153117i
$216$		0			0
$217$	−3.16312	−	9.73508i	−0.214727	−	0.660860i
$218$	3.78115	−	2.74717i	0.256092	−	0.186062i
$219$		0			0
$220$	−1.35410	−	1.53884i	−0.0912935	−	0.103749i
$221$	−4.23607			−0.284949
$222$		0			0
$223$	−3.92705	−	12.0862i	−0.262975	−	0.809353i	−0.992153	−	0.125029i	$-0.960097\pi$
$223$	−3.92705	−	12.0862i	−0.262975	−	0.809353i	0.729178	−	0.684324i	$-0.239903\pi$
$224$	1.73607	−	5.34307i	0.115996	−	0.356999i
$225$		0			0
$226$	−5.82624	−	4.23301i	−0.387556	−	0.281576i
$227$	−5.86475	+	18.0498i	−0.389257	+	1.19801i	0.544088	+	0.839028i	$0.316876\pi$
$227$	−5.86475	+	18.0498i	−0.389257	+	1.19801i	−0.933345	+	0.358981i	$0.883124\pi$
$228$		0			0
$229$	9.47214	−	6.88191i	0.625936	−	0.454769i	−0.229054	−	0.973414i	$-0.573563\pi$
$229$	9.47214	−	6.88191i	0.625936	−	0.454769i	0.854990	+	0.518644i	$0.173563\pi$
$230$	0.763932			0.0503722
$231$		0			0
$232$	15.0000			0.984798
$233$	5.04508	−	3.66547i	0.330515	−	0.240133i	−0.410134	−	0.912025i	$-0.634518\pi$
$233$	5.04508	−	3.66547i	0.330515	−	0.240133i	0.740649	+	0.671892i	$0.234518\pi$
$234$		0			0
$235$	0.864745	−	2.66141i	0.0564097	−	0.173611i
$236$	5.42705	+	3.94298i	0.353271	+	0.256666i
$237$		0			0
$238$	0.809017	−	2.48990i	0.0524408	−	0.161396i
$239$	−5.91641	−	18.2088i	−0.382701	−	1.17783i	−0.938135	−	0.346271i	$-0.887448\pi$
$239$	−5.91641	−	18.2088i	−0.382701	−	1.17783i	0.555434	−	0.831561i	$-0.312552\pi$
$240$		0			0
$241$	−24.7082			−1.59160			−0.795798	−	0.605563i	$-0.792948\pi$
$241$	−24.7082			−1.59160			−0.795798	+	0.605563i	$0.792948\pi$
$242$	4.66312	−	4.94704i	0.299757	−	0.318008i
$243$		0			0
$244$	−7.54508	+	5.48183i	−0.483025	+	0.350938i
$245$	0.118034	+	0.363271i	0.00754091	+	0.0232085i
$246$		0			0
$247$		0			0
$248$	−18.5172	−	13.4535i	−1.17584	−	0.854301i
$249$		0			0
$250$	−0.718847	−	2.21238i	−0.0454639	−	0.139923i
$251$	21.5172	−	15.6332i	1.35815	−	0.986757i	0.359595	−	0.933108i	$-0.382915\pi$
$251$	21.5172	−	15.6332i	1.35815	−	0.986757i	0.998560	−	0.0536489i	$-0.0170852\pi$
$252$		0			0
$253$	−1.00000	−	10.6861i	−0.0628695	−	0.671832i
$254$	−4.52786			−0.284103
$255$		0			0
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$	−8.32624	+	25.6255i	−0.519376	+	1.59848i	0.255799	+	0.966730i	$0.417662\pi$
$257$	−8.32624	+	25.6255i	−0.519376	+	1.59848i	−0.775175	+	0.631746i	$0.782338\pi$
$258$		0			0
$259$	−5.61803	−	4.08174i	−0.349088	−	0.253627i
$260$	0.190983	−	0.587785i	0.0118443	−	0.0364529i
$261$		0			0
$262$	−1.66312	+	1.20833i	−0.102748	+	0.0746507i
$263$	−0.708204			−0.0436697			−0.0218349	−	0.999762i	$-0.506951\pi$
$263$	−0.708204			−0.0436697			−0.0218349	+	0.999762i	$0.506951\pi$
$264$		0			0
$265$	−2.90983			−0.178749
$266$		0			0
$267$		0			0
$268$	4.61803	−	14.2128i	0.282091	−	0.868188i
$269$	19.3713	+	14.0741i	1.18109	+	0.858112i	0.992294	−	0.123904i	$-0.0395415\pi$
$269$	19.3713	+	14.0741i	1.18109	+	0.858112i	0.188796	+	0.982016i	$0.439541\pi$
$270$		0			0
$271$	−1.98278	+	6.10237i	−0.120445	+	0.370692i	−0.993044	−	0.117746i	$-0.962433\pi$
$271$	−1.98278	+	6.10237i	−0.120445	+	0.370692i	0.872599	+	0.488438i	$0.162433\pi$
$272$	2.42705	+	7.46969i	0.147162	+	0.452917i
$273$		0			0
$274$	1.88854			0.114091
$275$	−14.7812	+	6.37988i	−0.891337	+	0.384721i
$276$		0			0
$277$	20.5623	−	14.9394i	1.23547	−	0.897621i	0.238181	−	0.971221i	$-0.423449\pi$
$277$	20.5623	−	14.9394i	1.23547	−	0.897621i	0.997288	+	0.0735998i	$0.0234487\pi$
$278$	−3.35410	−	10.3229i	−0.201166	−	0.619124i
$279$		0			0
$280$	0.690983	+	0.502029i	0.0412941	+	0.0300019i
$281$	12.6353	+	9.18005i	0.753756	+	0.547636i	0.896989	−	0.442053i	$-0.145750\pi$
$281$	12.6353	+	9.18005i	0.753756	+	0.547636i	−0.143233	+	0.989689i	$0.545750\pi$
$282$		0			0
$283$	2.25329	+	6.93491i	0.133944	+	0.412238i	0.995424	−	0.0955536i	$-0.0304621\pi$
$283$	2.25329	+	6.93491i	0.133944	+	0.412238i	−0.861480	+	0.507791i	$0.830462\pi$
$284$	9.78115	−	7.10642i	0.580405	−	0.421689i
$285$		0			0
$286$	2.00000	+	0.449028i	0.118262	+	0.0265516i
$287$	−5.09017			−0.300463
$288$		0			0
$289$	0.291796	+	0.898056i	0.0171645	+	0.0528268i
$290$	−0.489357	+	1.50609i	−0.0287360	+	0.0884404i
$291$		0			0
$292$	15.1353	+	10.9964i	0.885724	+	0.643516i
$293$	4.09017	−	12.5882i	0.238950	−	0.735413i	−0.757623	−	0.652693i	$-0.773639\pi$
$293$	4.09017	−	12.5882i	0.238950	−	0.735413i	0.996573	−	0.0827204i	$-0.0263608\pi$
$294$		0			0
$295$	−1.28115	+	0.930812i	−0.0745916	+	0.0541940i
$296$	−15.5279			−0.902539
$297$		0			0
$298$	8.09017			0.468651
$299$	2.61803	−	1.90211i	0.151405	−	0.110002i
$300$		0			0
$301$	−0.309017	+	0.951057i	−0.0178114	+	0.0548180i
$302$	10.5451	+	7.66145i	0.606801	+	0.440867i
$303$		0			0
$304$		0			0
$305$	−0.680340	−	2.09387i	−0.0389561	−	0.119895i
$306$		0			0
$307$	19.1803			1.09468			0.547340	−	0.836910i	$-0.315640\pi$
$307$	19.1803			1.09468			0.547340	+	0.836910i	$0.315640\pi$
$308$	2.73607	−	4.61653i	0.155902	−	0.263051i
$309$		0			0
$310$	1.95492	−	1.42033i	0.111032	−	0.0806693i
$311$	−5.19098	−	15.9762i	−0.294354	−	0.905927i	−0.983438	−	0.181246i	$-0.941987\pi$
$311$	−5.19098	−	15.9762i	−0.294354	−	0.905927i	0.689084	−	0.724681i	$-0.258013\pi$
$312$		0			0
$313$	12.7812	+	9.28605i	0.722433	+	0.524879i	0.887161	−	0.461461i	$-0.152674\pi$
$313$	12.7812	+	9.28605i	0.722433	+	0.524879i	−0.164727	+	0.986339i	$0.552674\pi$
$314$	0.836881	+	0.608030i	0.0472279	+	0.0343131i
$315$		0			0
$316$	−5.42705	−	16.7027i	−0.305295	−	0.939603i
$317$	20.5172	−	14.9066i	1.15236	−	0.837240i	0.163569	−	0.986532i	$-0.447699\pi$
$317$	20.5172	−	14.9066i	1.15236	−	0.837240i	0.988793	+	0.149292i	$0.0476994\pi$
$318$		0			0
$319$	21.7082	+	4.87380i	1.21543	+	0.272880i
$320$	−0.0901699			−0.00504065
$321$		0			0
$322$	0.618034	+	1.90211i	0.0344417	+	0.106001i
$323$		0			0
$324$		0			0
$325$	−3.92705	−	2.85317i	−0.217834	−	0.158265i
$326$	1.15248	−	3.54696i	0.0638297	−	0.196448i
$327$		0			0
$328$	−9.20820	+	6.69015i	−0.508438	+	0.369402i
$329$	7.32624			0.403909
$330$		0			0
$331$	−14.7082			−0.808436			−0.404218	−	0.914663i	$-0.632456\pi$
$331$	−14.7082			−0.808436			−0.404218	+	0.914663i	$0.632456\pi$
$332$	7.85410	−	5.70634i	0.431050	−	0.313176i
$333$		0			0
$334$	−1.79180	+	5.51458i	−0.0980427	+	0.301744i
$335$	2.85410	+	2.07363i	0.155936	+	0.113294i
$336$		0			0
$337$	0.399187	−	1.22857i	0.0217451	−	0.0669245i	−0.939595	−	0.342288i	$-0.888798\pi$
$337$	0.399187	−	1.22857i	0.0217451	−	0.0669245i	0.961340	+	0.275363i	$0.0887982\pi$
$338$	−2.29180	−	7.05342i	−0.124657	−	0.383656i
$339$		0			0
$340$	−2.61803			−0.141983
$341$	−22.4271	−	25.4868i	−1.21449	−	1.38019i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.690983	+	2.12663i	0.0372553	+	0.114660i
$345$		0			0
$346$	−7.30902	−	5.31031i	−0.392935	−	0.285484i
$347$	−20.5623	−	14.9394i	−1.10384	−	0.801988i	−0.122159	−	0.992510i	$-0.538982\pi$
$347$	−20.5623	−	14.9394i	−1.10384	−	0.801988i	−0.981683	+	0.190522i	$0.938982\pi$
$348$		0			0
$349$	10.7918	+	33.2137i	0.577672	+	1.77789i	0.626896	+	0.779103i	$0.284325\pi$
$349$	10.7918	+	33.2137i	0.577672	+	1.77789i	−0.0492248	+	0.998788i	$0.515675\pi$
$350$	2.42705	−	1.76336i	0.129731	−	0.0942553i
$351$		0			0
$352$	−1.73607	−	18.5519i	−0.0925327	−	0.988817i
$353$	25.4721			1.35574			0.677872	−	0.735179i	$-0.262902\pi$
$353$	25.4721			1.35574			0.677872	+	0.735179i	$0.262902\pi$
$354$		0			0
$355$	0.881966	+	2.71441i	0.0468099	+	0.144066i
$356$	−3.19098	+	9.82084i	−0.169122	+	0.520503i
$357$		0			0
$358$	−1.11803	−	0.812299i	−0.0590899	−	0.0429313i
$359$	10.2639	−	31.5891i	0.541710	−	1.66721i	−0.186978	−	0.982364i	$-0.559869\pi$
$359$	10.2639	−	31.5891i	0.541710	−	1.66721i	0.728687	−	0.684847i	$-0.240131\pi$
$360$		0			0
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$	−0.145898			−0.00766823
$363$		0			0
$364$	1.61803			0.0848080
$365$	−3.57295	+	2.59590i	−0.187017	+	0.135876i
$366$		0			0
$367$	3.48936	−	10.7391i	0.182143	−	0.560578i	−0.817745	−	0.575581i	$-0.804776\pi$
$367$	3.48936	−	10.7391i	0.182143	−	0.560578i	0.999887	+	0.0150030i	$0.00477579\pi$
$368$	−4.85410	−	3.52671i	−0.253038	−	0.183843i
$369$		0			0
$370$	0.506578	−	1.55909i	0.0263357	−	0.0810530i
$371$	−2.35410	−	7.24518i	−0.122219	−	0.376151i
$372$		0			0
$373$	30.1803			1.56268			0.781339	−	0.624106i	$-0.214537\pi$
$373$	30.1803			1.56268			0.781339	+	0.624106i	$0.214537\pi$
$374$	−0.809017	−	8.64527i	−0.0418333	−	0.447036i
$375$		0			0
$376$	13.2533	−	9.62908i	0.683486	−	0.496582i
$377$	2.07295	+	6.37988i	0.106762	+	0.328581i
$378$		0			0
$379$	8.78115	+	6.37988i	0.451058	+	0.327712i	0.790013	−	0.613090i	$-0.210074\pi$
$379$	8.78115	+	6.37988i	0.451058	+	0.327712i	−0.338956	+	0.940802i	$0.610074\pi$
$380$		0			0
$381$		0			0
$382$	−1.86475	−	5.73910i	−0.0954087	−	0.293638i
$383$	−6.39919	+	4.64928i	−0.326983	+	0.237567i	−0.739149	−	0.673541i	$-0.764772\pi$
$383$	−6.39919	+	4.64928i	−0.326983	+	0.237567i	0.412166	+	0.911109i	$0.364772\pi$
$384$		0			0
$385$	0.836881	+	0.951057i	0.0426514	+	0.0484703i
$386$	3.12461			0.159039
$387$		0			0
$388$	8.50000	+	26.1603i	0.431522	+	1.32809i
$389$	−6.38197	+	19.6417i	−0.323579	+	0.995872i	0.648500	+	0.761215i	$0.275397\pi$
$389$	−6.38197	+	19.6417i	−0.323579	+	0.995872i	−0.972078	+	0.234657i	$0.924603\pi$
$390$		0			0
$391$	−11.0902	−	8.05748i	−0.560854	−	0.407484i
$392$	−0.690983	+	2.12663i	−0.0348999	+	0.107411i
$393$		0			0
$394$	−4.61803	+	3.35520i	−0.232653	+	0.169032i
$395$	4.14590			0.208603
$396$		0			0
$397$	25.6869			1.28919			0.644595	−	0.764524i	$-0.277026\pi$
$397$	25.6869			1.28919			0.644595	+	0.764524i	$0.277026\pi$
$398$	3.78115	−	2.74717i	0.189532	−	0.137703i
$399$		0			0
$400$	−2.78115	+	8.55951i	−0.139058	+	0.427975i
$401$	9.44427	+	6.86167i	0.471624	+	0.342655i	0.798074	−	0.602559i	$-0.205852\pi$
$401$	9.44427	+	6.86167i	0.471624	+	0.342655i	−0.326450	+	0.945215i	$0.605852\pi$
$402$		0			0
$403$	3.16312	−	9.73508i	0.157566	−	0.484939i
$404$	−2.09017	−	6.43288i	−0.103990	−	0.320048i
$405$		0			0
$406$	−4.14590			−0.205757
$407$	−22.4721	−	5.04531i	−1.11390	−	0.250087i
$408$		0			0
$409$	21.3435	−	15.5069i	1.05537	−	0.766768i	0.0821406	−	0.996621i	$-0.473824\pi$
$409$	21.3435	−	15.5069i	1.05537	−	0.766768i	0.973226	+	0.229852i	$0.0738243\pi$
$410$	−0.371323	−	1.14281i	−0.0183383	−	0.0564396i
$411$		0			0
$412$	−16.6353	−	12.0862i	−0.819560	−	0.595445i
$413$	−3.35410	−	2.43690i	−0.165045	−	0.119912i
$414$		0			0
$415$	0.708204	+	2.17963i	0.0347644	+	0.106994i
$416$	4.54508	−	3.30220i	0.222841	−	0.161904i
$417$		0			0
$418$		0			0
$419$	15.3262			0.748736			0.374368	−	0.927280i	$-0.377860\pi$
$419$	15.3262			0.748736			0.374368	+	0.927280i	$0.377860\pi$
$420$		0			0
$421$	0.843459	+	2.59590i	0.0411077	+	0.126516i	0.969504	−	0.245074i	$-0.0788124\pi$
$421$	0.843459	+	2.59590i	0.0411077	+	0.126516i	−0.928397	+	0.371591i	$0.878812\pi$
$422$	1.01064	−	3.11044i	0.0491973	−	0.151414i
$423$		0			0
$424$	−13.7812	−	10.0126i	−0.669272	−	0.486255i
$425$	−6.35410	+	19.5559i	−0.308219	+	0.948601i
$426$		0			0
$427$	4.66312	−	3.38795i	0.225664	−	0.163955i
$428$	25.5066			1.23291
$429$		0			0
$430$	−0.236068			−0.0113842
$431$	−30.5795	+	22.2173i	−1.47296	+	1.07017i	−0.493223	+	0.869903i	$0.664181\pi$
$431$	−30.5795	+	22.2173i	−1.47296	+	1.07017i	−0.979741	+	0.200268i	$0.935819\pi$
$432$		0			0
$433$	−0.798374	+	2.45714i	−0.0383674	+	0.118083i	−0.968406	−	0.249380i	$-0.919773\pi$
$433$	−0.798374	+	2.45714i	−0.0383674	+	0.118083i	0.930038	+	0.367462i	$0.119773\pi$
$434$	5.11803	+	3.71847i	0.245673	+	0.178492i
$435$		0			0
$436$	3.78115	−	11.6372i	0.181084	−	0.557320i
$437$		0			0
$438$		0			0
$439$	0.527864			0.0251936			0.0125968	−	0.999921i	$-0.495990\pi$
$439$	0.527864			0.0251936			0.0125968	+	0.999921i	$0.495990\pi$
$440$	2.76393	+	0.620541i	0.131765	+	0.0295832i
$441$		0			0
$442$	2.11803	−	1.53884i	0.100745	−	0.0731952i
$443$	11.3262	+	34.8586i	0.538126	+	1.65618i	0.736796	+	0.676115i	$0.236338\pi$
$443$	11.3262	+	34.8586i	0.538126	+	1.65618i	−0.198671	+	0.980066i	$0.563662\pi$
$444$		0			0
$445$	−1.97214	−	1.43284i	−0.0934882	−	0.0679232i
$446$	6.35410	+	4.61653i	0.300875	+	0.218599i
$447$		0			0
$448$	−0.0729490	−	0.224514i	−0.00344652	−	0.0106073i
$449$	12.6631	−	9.20029i	0.597610	−	0.434189i	−0.247420	−	0.968908i	$-0.579583\pi$
$449$	12.6631	−	9.20029i	0.597610	−	0.434189i	0.845030	+	0.534720i	$0.179583\pi$
$450$		0			0
$451$	−15.5000	+	6.69015i	−0.729866	+	0.315027i
$452$	−18.8541			−0.886822
$453$		0			0
$454$	−3.62461	−	11.1554i	−0.170111	−	0.523549i
$455$	−0.118034	+	0.363271i	−0.00553352	+	0.0170304i
$456$		0			0
$457$	−9.92705	−	7.21242i	−0.464368	−	0.337383i	0.330874	−	0.943675i	$-0.392656\pi$
$457$	−9.92705	−	7.21242i	−0.464368	−	0.337383i	−0.795242	+	0.606292i	$0.792656\pi$
$458$	−2.23607	+	6.88191i	−0.104485	+	0.321571i
$459$		0			0
$460$	1.61803	−	1.17557i	0.0754412	−	0.0548113i
$461$	−23.1803			−1.07962			−0.539808	−	0.841788i	$-0.681503\pi$
$461$	−23.1803			−1.07962			−0.539808	+	0.841788i	$0.681503\pi$
$462$		0			0
$463$	−35.9230			−1.66948			−0.834741	−	0.550642i	$-0.814383\pi$
$463$	−35.9230			−1.66948			−0.834741	+	0.550642i	$0.814383\pi$
$464$	10.0623	−	7.31069i	0.467131	−	0.339390i
$465$		0			0
$466$	−1.19098	+	3.66547i	−0.0551712	+	0.169800i
$467$	25.8435	+	18.7764i	1.19589	+	0.868867i	0.993874	−	0.110515i	$-0.0352500\pi$
$467$	25.8435	+	18.7764i	1.19589	+	0.868867i	0.202018	+	0.979382i	$0.435250\pi$
$468$		0			0
$469$	−2.85410	+	8.78402i	−0.131790	+	0.405608i
$470$	0.534442	+	1.64484i	0.0246520	+	0.0758709i
$471$		0			0
$472$	−9.27051			−0.426710
$473$	0.309017	+	3.30220i	0.0142086	+	0.151835i
$474$		0			0
$475$		0			0
$476$	−2.11803	−	6.51864i	−0.0970799	−	0.298781i
$477$		0			0
$478$	9.57295	+	6.95515i	0.437856	+	0.318121i
$479$	17.3992	+	12.6412i	0.794989	+	0.577593i	0.909440	−	0.415836i	$-0.136511\pi$
$479$	17.3992	+	12.6412i	0.794989	+	0.577593i	−0.114451	+	0.993429i	$0.536511\pi$
$480$		0			0
$481$	−2.14590	−	6.60440i	−0.0978445	−	0.301134i
$482$	12.3541	−	8.97578i	0.562714	−	0.408836i
$483$		0			0
$484$	2.26393	−	17.6538i	0.102906	−	0.802446i
$485$	−6.49342			−0.294851
$486$		0			0
$487$	5.13525	+	15.8047i	0.232701	+	0.716179i	0.997418	+	0.0718131i	$0.0228785\pi$
$487$	5.13525	+	15.8047i	0.232701	+	0.716179i	−0.764717	+	0.644366i	$0.777121\pi$
$488$	3.98278	−	12.2577i	0.180292	−	0.554882i
$489$		0			0
$490$	−0.190983	−	0.138757i	−0.00862773	−	0.00626841i
$491$	−1.14590	+	3.52671i	−0.0517137	+	0.159158i	−0.973578	−	0.228354i	$-0.926666\pi$
$491$	−1.14590	+	3.52671i	−0.0517137	+	0.159158i	0.921864	+	0.387512i	$0.126666\pi$
$492$		0			0
$493$	22.9894	−	16.7027i	1.03539	−	0.752254i
$494$		0			0
$495$		0			0
$496$	−18.9787			−0.852169
$497$	−6.04508	+	4.39201i	−0.271159	+	0.197009i
$498$		0			0
$499$	−1.54508	+	4.75528i	−0.0691675	+	0.212876i	−0.979665	−	0.200638i	$-0.935699\pi$
$499$	−1.54508	+	4.75528i	−0.0691675	+	0.212876i	0.910498	+	0.413514i	$0.135699\pi$
$500$	−4.92705	−	3.57971i	−0.220344	−	0.160090i
$501$		0			0
$502$	−5.07953	+	15.6332i	−0.226710	+	0.697743i
$503$	9.98278	+	30.7238i	0.445110	+	1.36991i	0.882363	+	0.470569i	$0.155951\pi$
$503$	9.98278	+	30.7238i	0.445110	+	1.36991i	−0.437253	+	0.899339i	$0.644049\pi$
$504$		0			0
$505$	1.59675			0.0710543
$506$	4.38197	+	4.97980i	0.194802	+	0.221379i
$507$		0			0
$508$	−9.59017	+	6.96767i	−0.425495	+	0.309140i
$509$	−12.9271	−	39.7854i	−0.572981	−	1.76346i	−0.642952	−	0.765907i	$-0.722291\pi$
$509$	−12.9271	−	39.7854i	−0.572981	−	1.76346i	0.0699705	−	0.997549i	$-0.477709\pi$
$510$		0			0
$511$	−9.35410	−	6.79615i	−0.413801	−	0.300644i
$512$	−15.1353	−	10.9964i	−0.668890	−	0.485977i
$513$		0			0
$514$	−5.14590	−	15.8374i	−0.226976	−	0.698560i
$515$	3.92705	−	2.85317i	0.173047	−	0.125726i
$516$		0			0
$517$	22.3090	−	9.62908i	0.981149	−	0.423486i
$518$	4.29180			0.188571
$519$		0			0
$520$	0.263932	+	0.812299i	0.0115742	+	0.0356217i
$521$	5.92705	−	18.2416i	0.259669	−	0.799178i	−0.733205	−	0.680008i	$-0.761976\pi$
$521$	5.92705	−	18.2416i	0.259669	−	0.799178i	0.992874	−	0.119171i	$-0.0380236\pi$
$522$		0			0
$523$	−16.4271	−	11.9350i	−0.718305	−	0.521879i	0.167537	−	0.985866i	$-0.446419\pi$
$523$	−16.4271	−	11.9350i	−0.718305	−	0.521879i	−0.885842	+	0.463987i	$0.846419\pi$
$524$	−1.66312	+	5.11855i	−0.0726537	+	0.223605i
$525$		0			0
$526$	0.354102	−	0.257270i	0.0154396	−	0.0112175i
$527$	−43.3607			−1.88882
$528$		0			0
$529$	−12.5279			−0.544690
$530$	1.45492	−	1.05706i	0.0631975	−	0.0459156i
$531$		0			0
$532$		0			0
$533$	−4.11803	−	2.99193i	−0.178372	−	0.129595i
$534$		0			0
$535$	−1.86068	+	5.72658i	−0.0804442	+	0.247582i
$536$	6.38197	+	19.6417i	0.275659	+	0.848391i
$537$		0			0
$538$	−14.7984			−0.638003
$539$	−1.69098	+	2.85317i	−0.0728358	+	0.122895i
$540$		0			0
$541$	−16.2533	+	11.8087i	−0.698783	+	0.507696i	−0.879536	−	0.475833i	$-0.842147\pi$
$541$	−16.2533	+	11.8087i	−0.698783	+	0.507696i	0.180752	+	0.983529i	$0.442147\pi$
$542$	−1.22542	−	3.77147i	−0.0526365	−	0.161999i
$543$		0			0
$544$	−19.2533	−	13.9883i	−0.825478	−	0.599745i
$545$	2.33688	+	1.69784i	0.100101	+	0.0727276i
$546$		0			0
$547$	6.98278	+	21.4908i	0.298562	+	0.918880i	0.982002	+	0.188872i	$0.0604833\pi$
$547$	6.98278	+	21.4908i	0.298562	+	0.918880i	−0.683440	+	0.730007i	$0.739517\pi$
$548$	4.00000	−	2.90617i	0.170872	−	0.124145i
$549$		0			0
$550$	5.07295	−	8.55951i	0.216311	−	0.364979i
$551$		0			0
$552$		0			0
$553$	3.35410	+	10.3229i	0.142631	+	0.438973i
$554$	−4.85410	+	14.9394i	−0.206231	+	0.634714i
$555$		0			0
$556$	−22.9894	−	16.7027i	−0.974966	−	0.708354i
$557$	−0.236068	+	0.726543i	−0.0100025	+	0.0307846i	−0.955933	−	0.293584i	$-0.905152\pi$
$557$	−0.236068	+	0.726543i	−0.0100025	+	0.0307846i	0.945931	+	0.324369i	$0.105152\pi$
$558$		0			0
$559$	−0.809017	+	0.587785i	−0.0342178	+	0.0248607i
$560$	0.708204			0.0299271
$561$		0			0
$562$	−9.65248			−0.407165
$563$	−36.4615	+	26.4908i	−1.53667	+	1.11646i	−0.584287	+	0.811547i	$0.698626\pi$
$563$	−36.4615	+	26.4908i	−1.53667	+	1.11646i	−0.952382	+	0.304908i	$0.901374\pi$
$564$		0			0
$565$	1.37539	−	4.23301i	0.0578630	−	0.178084i
$566$	−3.64590	−	2.64890i	−0.153249	−	0.111342i
$567$		0			0
$568$	−5.16312	+	15.8904i	−0.216640	+	0.666748i
$569$	−12.0729	−	37.1567i	−0.506124	−	1.55769i	−0.798872	−	0.601501i	$-0.794570\pi$
$569$	−12.0729	−	37.1567i	−0.506124	−	1.55769i	0.292748	−	0.956190i	$-0.405430\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$	4.92705	−	2.12663i	0.206010	−	0.0889187i
$573$		0			0
$574$	2.54508	−	1.84911i	0.106230	−	0.0771805i
$575$	−4.85410	−	14.9394i	−0.202430	−	0.623016i
$576$		0			0
$577$	7.63525	+	5.54734i	0.317860	+	0.230939i	0.735262	−	0.677783i	$-0.237059\pi$
$577$	7.63525	+	5.54734i	0.317860	+	0.230939i	−0.417402	+	0.908722i	$0.637059\pi$
$578$	−0.472136	−	0.343027i	−0.0196383	−	0.0142680i
$579$		0			0
$580$	1.28115	+	3.94298i	0.0531970	+	0.163723i
$581$	−4.85410	+	3.52671i	−0.201382	+	0.146313i
$582$		0			0
$583$	−16.6910	−	18.9681i	−0.691270	−	0.785580i
$584$	−25.8541			−1.06985
$585$		0			0
$586$	2.52786	+	7.77997i	0.104425	+	0.321387i
$587$	−11.0902	+	34.1320i	−0.457740	+	1.40878i	0.410147	+	0.912019i	$0.365477\pi$
$587$	−11.0902	+	34.1320i	−0.457740	+	1.40878i	−0.867888	+	0.496761i	$0.834523\pi$
$588$		0			0
$589$		0			0
$590$	0.302439	−	0.930812i	0.0124512	−	0.0383209i
$591$		0			0
$592$	−10.4164	+	7.56796i	−0.428112	+	0.311041i
$593$	23.8885			0.980985			0.490492	−	0.871445i	$-0.336817\pi$
$593$	23.8885			0.980985			0.490492	+	0.871445i	$0.336817\pi$
$594$		0			0
$595$	1.61803			0.0663329
$596$	17.1353	−	12.4495i	0.701887	−	0.509951i
$597$		0			0
$598$	−0.618034	+	1.90211i	−0.0252733	+	0.0777832i
$599$	25.4894	+	18.5191i	1.04147	+	0.756670i	0.970571	−	0.240814i	$-0.0774143\pi$
$599$	25.4894	+	18.5191i	1.04147	+	0.756670i	0.0708955	+	0.997484i	$0.477414\pi$
$600$		0			0
$601$	−4.58359	+	14.1068i	−0.186969	+	0.575430i	−0.999977	−	0.00682211i	$-0.997828\pi$
$601$	−4.58359	+	14.1068i	−0.186969	+	0.575430i	0.813008	+	0.582252i	$0.197828\pi$
$602$	−0.190983	−	0.587785i	−0.00778389	−	0.0239563i
$603$		0			0
$604$	34.1246			1.38851
$605$	3.79837	+	1.79611i	0.154426	+	0.0730223i
$606$		0			0
$607$	13.0623	−	9.49032i	0.530183	−	0.385200i	−0.290243	−	0.956953i	$-0.593736\pi$
$607$	13.0623	−	9.49032i	0.530183	−	0.385200i	0.820426	+	0.571753i	$0.193736\pi$
$608$		0			0
$609$		0			0
$610$	1.10081	+	0.799788i	0.0445706	+	0.0323824i
$611$	5.92705	+	4.30625i	0.239783	+	0.174212i
$612$		0			0
$613$	10.6459	+	32.7647i	0.429984	+	1.32335i	0.898141	+	0.439709i	$0.144918\pi$
$613$	10.6459	+	32.7647i	0.429984	+	1.32335i	−0.468157	+	0.883645i	$0.655082\pi$
$614$	−9.59017	+	6.96767i	−0.387028	+	0.281192i
$615$		0			0
$616$	0.690983	+	7.38394i	0.0278405	+	0.297507i
$617$	10.0902			0.406215			0.203107	−	0.979156i	$-0.434896\pi$
$617$	10.0902			0.406215			0.203107	+	0.979156i	$0.434896\pi$
$618$		0			0
$619$	10.8541	+	33.4055i	0.436263	+	1.34268i	0.891787	+	0.452456i	$0.149452\pi$
$619$	10.8541	+	33.4055i	0.436263	+	1.34268i	−0.455523	+	0.890224i	$0.650548\pi$
$620$	1.95492	−	6.01661i	0.0785113	−	0.241633i
$621$		0			0
$622$	8.39919	+	6.10237i	0.336777	+	0.244683i
$623$	1.97214	−	6.06961i	0.0790120	−	0.243174i
$624$		0			0
$625$	−18.4721	+	13.4208i	−0.738885	+	0.536832i
$626$	−9.76393			−0.390245
$627$		0			0
$628$	2.70820			0.108069
$629$	−23.7984	+	17.2905i	−0.948903	+	0.689419i
$630$		0			0
$631$	−2.83688	+	8.73102i	−0.112934	+	0.347577i	−0.991511	−	0.130026i	$-0.958494\pi$
$631$	−2.83688	+	8.73102i	−0.112934	+	0.347577i	0.878576	+	0.477602i	$0.158494\pi$
$632$	19.6353	+	14.2658i	0.781049	+	0.567465i
$633$		0			0
$634$	−4.84346	+	14.9066i	−0.192358	+	0.592018i
$635$	−0.864745	−	2.66141i	−0.0343164	−	0.105615i
$636$		0			0
$637$	−1.00000			−0.0396214
$638$	−12.6246	+	5.44907i	−0.499813	+	0.215731i
$639$		0			0
$640$	3.51722	−	2.55541i	0.139030	−	0.101011i
$641$	−8.64590	−	26.6093i	−0.341492	−	1.05101i	−0.963435	−	0.267943i	$-0.913656\pi$
$641$	−8.64590	−	26.6093i	−0.341492	−	1.05101i	0.621942	−	0.783063i	$-0.286344\pi$
$642$		0			0
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	0.813003	−	0.582260i	$-0.197831\pi$
$643$	12.9443	+	9.40456i	0.510472	+	0.370880i	−0.302530	+	0.953140i	$0.597831\pi$
$644$	4.23607	+	3.07768i	0.166924	+	0.121278i
$645$		0			0
$646$		0			0
$647$	1.89919	−	1.37984i	0.0746647	−	0.0542471i	−0.549827	−	0.835279i	$-0.685306\pi$
$647$	1.89919	−	1.37984i	0.0746647	−	0.0542471i	0.624491	+	0.781032i	$0.285306\pi$
$648$		0			0
$649$	−13.4164	−	3.01217i	−0.526640	−	0.118238i
$650$	3.00000			0.117670
$651$		0			0
$652$	−3.01722	−	9.28605i	−0.118163	−	0.363670i
$653$	−0.218847	+	0.673542i	−0.00856415	+	0.0263577i	−0.955247	−	0.295808i	$-0.904411\pi$
$653$	−0.218847	+	0.673542i	−0.00856415	+	0.0263577i	0.946683	+	0.322166i	$0.104411\pi$
$654$		0			0
$655$	−1.02786	−	0.746787i	−0.0401620	−	0.0291794i
$656$	−2.91641	+	8.97578i	−0.113867	+	0.350445i
$657$		0			0
$658$	−3.66312	+	2.66141i	−0.142803	+	0.103753i
$659$	−41.8328			−1.62958			−0.814788	−	0.579760i	$-0.803146\pi$
$659$	−41.8328			−1.62958			−0.814788	+	0.579760i	$0.803146\pi$
$660$		0			0
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$	7.35410	−	5.34307i	0.285825	−	0.207664i
$663$		0			0
$664$	−4.14590	+	12.7598i	−0.160892	+	0.495175i
$665$		0			0
$666$		0			0
$667$	−6.70820	+	20.6457i	−0.259743	+	0.799406i
$668$	4.69098	+	14.4374i	0.181500	+	0.558598i
$669$		0			0
$670$	−2.18034			−0.0842339
$671$	9.74671	−	16.4455i	0.376268	−	0.634871i
$672$		0			0
$673$	6.13525	−	4.45752i	0.236497	−	0.171825i	−0.463224	−	0.886241i	$-0.653308\pi$
$673$	6.13525	−	4.45752i	0.236497	−	0.171825i	0.699721	+	0.714416i	$0.253308\pi$
$674$	0.246711	+	0.759299i	0.00950296	+	0.0292471i
$675$		0			0
$676$	−15.7082	−	11.4127i	−0.604162	−	0.438949i
$677$	18.9721	+	13.7841i	0.729158	+	0.529765i	0.889297	−	0.457330i	$-0.151194\pi$
$677$	18.9721	+	13.7841i	0.729158	+	0.529765i	−0.160139	+	0.987095i	$0.551194\pi$
$678$		0			0
$679$	−5.25329	−	16.1680i	−0.201603	−	0.620469i
$680$	2.92705	−	2.12663i	0.112247	−	0.0815524i
$681$		0			0
$682$	20.4721	+	4.59628i	0.783919	+	0.176001i
$683$	32.3050			1.23611			0.618057	−	0.786133i	$-0.287920\pi$
$683$	32.3050			1.23611			0.618057	+	0.786133i	$0.287920\pi$
$684$		0			0
$685$	0.360680	+	1.11006i	0.0137809	+	0.0424131i
$686$	0.190983	−	0.587785i	0.00729177	−	0.0224417i
$687$		0			0
$688$	1.50000	+	1.08981i	0.0571870	+	0.0415488i
$689$	2.35410	−	7.24518i	0.0896841	−	0.276019i
$690$		0			0
$691$	−11.7812	+	8.55951i	−0.448176	+	0.325619i	−0.788875	−	0.614553i	$-0.789336\pi$
$691$	−11.7812	+	8.55951i	−0.448176	+	0.325619i	0.340699	+	0.940172i	$0.389336\pi$
$692$	−23.6525			−0.899132
$693$		0			0
$694$	15.7082			0.596275
$695$	5.42705	−	3.94298i	0.205860	−	0.149566i
$696$		0			0
$697$	−6.66312	+	20.5070i	−0.252384	+	0.776757i
$698$	−17.4615	−	12.6865i	−0.660927	−	0.480192i
$699$		0			0
$700$	2.42705	−	7.46969i	0.0917339	−	0.282328i
$701$	−8.34346	−	25.6785i	−0.315128	−	0.969865i	−0.975702	−	0.219103i	$-0.929687\pi$
$701$	−8.34346	−	25.6785i	−0.315128	−	0.969865i	0.660574	−	0.750761i	$-0.270313\pi$
$702$		0			0
$703$		0			0
$704$	−0.517221	−	0.587785i	−0.0194935	−	0.0221530i
$705$		0			0
$706$	−12.7361	+	9.25330i	−0.479328	+	0.348252i
$707$	1.29180	+	3.97574i	0.0485830	+	0.149523i
$708$		0			0
$709$	40.9787	+	29.7728i	1.53899	+	1.11814i	0.950966	+	0.309295i	$0.100093\pi$
$709$	40.9787	+	29.7728i	1.53899	+	1.11814i	0.588022	+	0.808845i	$0.299907\pi$
$710$	−1.42705	−	1.03681i	−0.0535563	−	0.0389109i
$711$		0			0
$712$	−4.40983	−	13.5721i	−0.165265	−	0.508635i
$713$	26.7984	−	19.4702i	1.00361	−	0.729163i
$714$		0			0
$715$	0.118034	+	1.26133i	0.00441422	+	0.0471710i
$716$	−3.61803			−0.135212
$717$		0			0
$718$	6.34346	+	19.5232i	0.236736	+	0.728598i
$719$	2.66312	−	8.19624i	0.0993176	−	0.305668i	−0.889037	−	0.457835i	$-0.848625\pi$
$719$	2.66312	−	8.19624i	0.0993176	−	0.305668i	0.988355	+	0.152167i	$0.0486251\pi$
$720$		0			0
$721$	10.2812	+	7.46969i	0.382890	+	0.278186i
$722$	−3.62868	+	11.1679i	−0.135045	+	0.415627i
$723$		0			0
$724$	−0.309017	+	0.224514i	−0.0114845	+	0.00834400i
$725$	32.5623			1.20933
$726$		0			0
$727$	22.1459			0.821346			0.410673	−	0.911783i	$-0.365294\pi$
$727$	22.1459			0.821346			0.410673	+	0.911783i	$0.365294\pi$
$728$	−1.80902	+	1.31433i	−0.0670466	+	0.0487122i
$729$		0			0
$730$	0.843459	−	2.59590i	0.0312178	−	0.0960785i
$731$	3.42705	+	2.48990i	0.126754	+	0.0920922i
$732$		0			0
$733$	1.27458	−	3.92274i	0.0470775	−	0.144890i	−0.924755	−	0.380564i	$-0.875730\pi$
$733$	1.27458	−	3.92274i	0.0470775	−	0.144890i	0.971832	+	0.235674i	$0.0757299\pi$
$734$	2.15654	+	6.63715i	0.0795994	+	0.244982i
$735$		0			0
$736$	18.1803			0.670136
$737$	2.85410	+	30.4993i	0.105132	+	1.12346i
$738$		0			0
$739$	−34.5344	+	25.0907i	−1.27037	+	0.922978i	−0.999217	−	0.0395585i	$-0.987405\pi$
$739$	−34.5344	+	25.0907i	−1.27037	+	0.922978i	−0.271153	+	0.962536i	$0.587405\pi$
$740$	−1.32624	−	4.08174i	−0.0487535	−	0.150048i
$741$		0			0
$742$	3.80902	+	2.76741i	0.139833	+	0.101595i
$743$	20.9615	+	15.2294i	0.769003	+	0.558713i	0.901658	−	0.432449i	$-0.142350\pi$
$743$	20.9615	+	15.2294i	0.769003	+	0.558713i	−0.132656	+	0.991162i	$0.542350\pi$
$744$		0			0
$745$	1.54508	+	4.75528i	0.0566075	+	0.174220i
$746$	−15.0902	+	10.9637i	−0.552490	+	0.401408i
$747$		0			0
$748$	−15.0172	−	17.0660i	−0.549084	−	0.623995i
$749$	−15.7639			−0.576002
$750$		0			0
$751$	−8.91641	−	27.4419i	−0.325364	−	1.00137i	−0.971276	−	0.237956i	$-0.923523\pi$
$751$	−8.91641	−	27.4419i	−0.325364	−	1.00137i	0.645912	−	0.763412i	$-0.276477\pi$
$752$	4.19756	−	12.9188i	0.153069	−	0.471099i
$753$		0			0
$754$	−3.35410	−	2.43690i	−0.122149	−	0.0887466i
$755$	−2.48936	+	7.66145i	−0.0905970	+	0.278829i
$756$		0			0
$757$	−36.5967	+	26.5891i	−1.33013	+	0.966397i	−0.330386	+	0.943846i	$0.607179\pi$
$757$	−36.5967	+	26.5891i	−1.33013	+	0.966397i	−0.999746	+	0.0225510i	$0.992821\pi$
$758$	−6.70820			−0.243653
$759$		0			0
$760$		0			0
$761$	0.0729490	−	0.0530006i	0.00264440	−	0.00192127i	−0.586462	−	0.809977i	$-0.699480\pi$
$761$	0.0729490	−	0.0530006i	0.00264440	−	0.00192127i	0.589107	+	0.808055i	$0.299480\pi$
$762$		0			0
$763$	−2.33688	+	7.19218i	−0.0846008	+	0.260374i
$764$	−12.7812	−	9.28605i	−0.462406	−	0.335958i
$765$		0			0
$766$	1.51064	−	4.64928i	0.0545818	−	0.167985i
$767$	−1.28115	−	3.94298i	−0.0462598	−	0.142373i
$768$		0			0
$769$	44.4721			1.60371			0.801853	−	0.597521i	$-0.203848\pi$
$769$	44.4721			1.60371			0.801853	+	0.597521i	$0.203848\pi$
$770$	−0.763932	−	0.171513i	−0.0275302	−	0.00618091i
$771$		0			0
$772$	6.61803	−	4.80828i	0.238188	−	0.173054i
$773$	−3.27051	−	10.0656i	−0.117632	−	0.362034i	0.874855	−	0.484385i	$-0.160957\pi$
$773$	−3.27051	−	10.0656i	−0.117632	−	0.362034i	−0.992487	+	0.122351i	$0.960957\pi$
$774$		0			0
$775$	−40.1976	−	29.2052i	−1.44394	−	1.04908i
$776$	−30.7533	−	22.3436i	−1.10398	−	0.802088i
$777$		0			0
$778$	−3.94427	−	12.1392i	−0.141409	−	0.435212i
$779$		0			0
$780$		0			0
$781$	−12.6353	+	21.3193i	−0.452125	+	0.762863i
$782$	8.47214			0.302963
$783$		0			0
$784$	0.572949	+	1.76336i	0.0204625	+	0.0629770i
$785$	−0.197561	+	0.608030i	−0.00705125	+	0.0217015i
$786$		0			0
$787$	26.5795	+	19.3112i	0.947458	+	0.688368i	0.950204	−	0.311628i	$-0.100874\pi$
$787$	26.5795	+	19.3112i	0.947458	+	0.688368i	−0.00274643	+	0.999996i	$0.500874\pi$
$788$	−4.61803	+	14.2128i	−0.164511	+	0.506312i
$789$		0			0
$790$	−2.07295	+	1.50609i	−0.0737522	+	0.0535841i
$791$	11.6525			0.414314
$792$		0			0
$793$	5.76393			0.204683
$794$	−12.8435	+	9.33132i	−0.455797	+	0.331156i
$795$		0			0
$796$	3.78115	−	11.6372i	0.134019	−	0.412469i
$797$	−26.2533	−	19.0741i	−0.929939	−	0.675640i	0.0160387	−	0.999871i	$-0.494894\pi$
$797$	−26.2533	−	19.0741i	−0.929939	−	0.675640i	−0.945978	+	0.324231i	$0.894894\pi$
$798$		0			0
$799$	9.59017	−	29.5155i	0.339276	−	1.04418i
$800$	−8.42705	−	25.9358i	−0.297941	−	0.916969i
$801$		0			0
$802$	−7.21478			−0.254763
$803$	−37.4164	−	8.40051i	−1.32040	−	0.296447i
$804$		0			0
$805$	−1.00000	+	0.726543i	−0.0352454	+	0.0256073i
$806$	1.95492	+	6.01661i	0.0688589	+	0.211926i
$807$		0			0
$808$	7.56231	+	5.49434i	0.266041	+	0.193290i
$809$	25.0623	+	18.2088i	0.881144	+	0.640188i	0.933554	−	0.358437i	$-0.116690\pi$
$809$	25.0623	+	18.2088i	0.881144	+	0.640188i	−0.0524101	+	0.998626i	$0.516690\pi$
$810$		0			0
$811$	−7.14590	−	21.9928i	−0.250926	−	0.772272i	−0.994605	−	0.103735i	$-0.966921\pi$
$811$	−7.14590	−	21.9928i	−0.250926	−	0.772272i	0.743679	−	0.668537i	$-0.233079\pi$
$812$	−8.78115	+	6.37988i	−0.308158	+	0.223890i
$813$		0			0
$814$	13.0689	−	5.64083i	0.458064	−	0.197711i
$815$	2.30495			0.0807389
$816$		0			0
$817$		0			0
$818$	−5.03851	+	15.5069i	−0.176167	+	0.542187i
$819$		0			0
$820$	−2.54508	−	1.84911i	−0.0888782	−	0.0645738i
$821$	−1.79837	+	5.53483i	−0.0627637	+	0.193167i	−0.977521	−	0.210836i	$-0.932381\pi$
$821$	−1.79837	+	5.53483i	−0.0627637	+	0.193167i	0.914758	+	0.404003i	$0.132381\pi$
$822$		0			0
$823$	21.2361	−	15.4289i	0.740243	−	0.537818i	−0.152544	−	0.988297i	$-0.548747\pi$
$823$	21.2361	−	15.4289i	0.740243	−	0.537818i	0.892787	+	0.450479i	$0.148747\pi$
$824$	28.4164			0.989932
$825$		0			0
$826$	2.56231			0.0891540
$827$	4.13525	−	3.00444i	0.143797	−	0.104475i	−0.513561	−	0.858053i	$-0.671674\pi$
$827$	4.13525	−	3.00444i	0.143797	−	0.104475i	0.657358	+	0.753579i	$0.271674\pi$
$828$		0			0
$829$	11.6459	−	35.8424i	0.404479	−	1.24486i	−0.516851	−	0.856075i	$-0.672896\pi$
$829$	11.6459	−	35.8424i	0.404479	−	1.24486i	0.921330	−	0.388782i	$-0.127104\pi$
$830$	−1.14590	−	0.832544i	−0.0397747	−	0.0288980i
$831$		0			0
$832$	0.0729490	−	0.224514i	0.00252905	−	0.00778362i
$833$	1.30902	+	4.02874i	0.0453548	+	0.139588i
$834$		0			0
$835$	−3.58359			−0.124015
$836$		0			0
$837$		0			0
$838$	−7.66312	+	5.56758i	−0.264718	+	0.192329i
$839$	−8.98278	−	27.6462i	−0.310120	−	0.954451i	−0.977717	−	0.209928i	$-0.932677\pi$
$839$	−8.98278	−	27.6462i	−0.310120	−	0.954451i	0.667597	−	0.744523i	$-0.267323\pi$
$840$		0			0
$841$	−12.9443	−	9.40456i	−0.446354	−	0.324295i
$842$	−1.36475	−	0.991545i	−0.0470322	−	0.0341709i
$843$		0			0
$844$	−2.64590	−	8.14324i	−0.0910756	−	0.280302i
$845$	3.70820	−	2.69417i	0.127566	−	0.0926822i
$846$		0			0
$847$	−1.39919	+	10.9106i	−0.0480766	+	0.374894i
$848$	−14.1246			−0.485041
$849$		0			0
$850$	−3.92705	−	12.0862i	−0.134697	−	0.414554i
$851$	6.94427	−	21.3723i	0.238047	−	0.732632i
$852$		0			0
$853$	−7.44427	−	5.40858i	−0.254887	−	0.185186i	0.453003	−	0.891509i	$-0.350353\pi$
$853$	−7.44427	−	5.40858i	−0.254887	−	0.185186i	−0.707890	+	0.706323i	$0.750353\pi$
$854$	−1.10081	+	3.38795i	−0.0376690	+	0.115933i
$855$		0			0
$856$	−28.5172	+	20.7190i	−0.974699	+	0.708160i
$857$	54.2361			1.85267			0.926334	−	0.376702i	$-0.122942\pi$
$857$	54.2361			1.85267			0.926334	+	0.376702i	$0.122942\pi$
$858$		0			0
$859$	−41.8328			−1.42732			−0.713659	−	0.700494i	$-0.752963\pi$
$859$	−41.8328			−1.42732			−0.713659	+	0.700494i	$0.752963\pi$
$860$	−0.500000	+	0.363271i	−0.0170499	+	0.0123874i
$861$		0			0
$862$	7.21885	−	22.2173i	0.245875	−	0.756725i
$863$	25.3713	+	18.4333i	0.863650	+	0.627478i	0.928875	−	0.370392i	$-0.120777\pi$
$863$	25.3713	+	18.4333i	0.863650	+	0.627478i	−0.0652256	+	0.997871i	$0.520777\pi$
$864$		0			0
$865$	1.72542	−	5.31031i	0.0586662	−	0.180556i
$866$	−0.493422	−	1.51860i	−0.0167672	−	0.0516040i
$867$		0			0
$868$	16.5623			0.562161
$869$	23.7812	+	27.0256i	0.806720	+	0.916781i
$870$		0			0
$871$	−7.47214	+	5.42882i	−0.253184	+	0.183949i
$872$	5.22542	+	16.0822i	0.176955	+	0.544612i
$873$		0			0
$874$		0			0
$875$	3.04508	+	2.21238i	0.102943	+	0.0747922i
$876$		0			0
$877$	12.8992	+	39.6996i	0.435575	+	1.34056i	0.892497	+	0.451054i	$0.148952\pi$
$877$	12.8992	+	39.6996i	0.435575	+	1.34056i	−0.456922	+	0.889507i	$0.651048\pi$
$878$	−0.263932	+	0.191758i	−0.00890727	+	0.00647151i
$879$		0			0
$880$	2.15654	−	0.930812i	0.0726970	−	0.0313777i
$881$	11.9443			0.402413			0.201206	−	0.979549i	$-0.435514\pi$
$881$	11.9443			0.402413			0.201206	+	0.979549i	$0.435514\pi$
$882$		0			0
$883$	−10.2082	−	31.4176i	−0.343533	−	1.05729i	−0.962364	−	0.271763i	$-0.912393\pi$
$883$	−10.2082	−	31.4176i	−0.343533	−	1.05729i	0.618831	−	0.785524i	$-0.287607\pi$
$884$	2.11803	−	6.51864i	0.0712372	−	0.219246i
$885$		0			0
$886$	−18.3262	−	13.3148i	−0.615682	−	0.447319i
$887$	6.63525	−	20.4212i	0.222790	−	0.685677i	−0.775718	−	0.631079i	$-0.782612\pi$
$887$	6.63525	−	20.4212i	0.222790	−	0.685677i	0.998508	−	0.0545980i	$-0.0173877\pi$
$888$		0			0
$889$	5.92705	−	4.30625i	0.198787	−	0.144427i
$890$	1.50658			0.0505006
$891$		0			0
$892$	20.5623			0.688477
$893$		0			0
$894$		0			0
$895$	0.263932	−	0.812299i	0.00882227	−	0.0271522i
$896$	9.20820	+	6.69015i	0.307625	+	0.223502i
$897$		0			0
$898$	−2.98936	+	9.20029i	−0.0997561	+	0.307018i
$899$	21.2188	+	65.3049i	0.707688	+	2.17804i
$900$		0			0
$901$	−32.2705			−1.07509
$902$	5.31966	−	8.97578i	0.177125	−	0.298861i
$903$		0			0
$904$	21.0795	−	15.3152i	0.701095	−	0.509375i
$905$	−0.0278640	−	0.0857567i	−0.000926232	−	0.00285065i
$906$		0			0
$907$	−15.3541	−	11.1554i	−0.509825	−	0.370409i	0.302932	−	0.953012i	$-0.402034\pi$
$907$	−15.3541	−	11.1554i	−0.509825	−	0.370409i	−0.812757	+	0.582603i	$0.802034\pi$
$908$	−24.8435	−	18.0498i	−0.824459	−	0.599005i
$909$		0			0
$910$	−0.0729490	−	0.224514i	−0.00241824	−	0.00744257i
$911$	−26.4336	+	19.2052i	−0.875785	+	0.636295i	−0.932133	−	0.362116i	$-0.882054\pi$
$911$	−26.4336	+	19.2052i	−0.875785	+	0.636295i	0.0563478	+	0.998411i	$0.482054\pi$
$912$		0			0
$913$	−10.1459	+	17.1190i	−0.335780	+	0.566557i
$914$	7.58359			0.250843
$915$		0			0
$916$	5.85410	+	18.0171i	0.193425	+	0.595301i
$917$	1.02786	−	3.16344i	0.0339431	−	0.104466i
$918$		0			0
$919$	13.4164	+	9.74759i	0.442566	+	0.321543i	0.786654	−	0.617394i	$-0.211812\pi$
$919$	13.4164	+	9.74759i	0.442566	+	0.321543i	−0.344087	+	0.938938i	$0.611812\pi$
$920$	−0.854102	+	2.62866i	−0.0281589	+	0.0866642i
$921$		0			0
$922$	11.5902	−	8.42075i	0.381702	−	0.277323i
$923$	−7.47214			−0.245948
$924$		0			0
$925$	−33.7082			−1.10832
$926$	17.9615	−	13.0498i	0.590251	−	0.428843i
$927$		0			0
$928$	−11.6459	+	35.8424i	−0.382295	+	1.17658i
$929$	−12.7639	−	9.27354i	−0.418771	−	0.304255i	0.358372	−	0.933579i	$-0.383332\pi$
$929$	−12.7639	−	9.27354i	−0.418771	−	0.304255i	−0.777143	+	0.629324i	$0.783332\pi$
$930$		0			0
$931$		0			0
$932$	3.11803	+	9.59632i	0.102135	+	0.314338i
$933$		0			0
$934$	−19.7426			−0.645999
$935$	4.92705	−	2.12663i	0.161132	−	0.0695481i
$936$		0			0
$937$	5.66312	−	4.11450i	0.185006	−	0.134415i	−0.491427	−	0.870919i	$-0.663525\pi$
$937$	5.66312	−	4.11450i	0.185006	−	0.134415i	0.676433	+	0.736504i	$0.263525\pi$
$938$	−1.76393	−	5.42882i	−0.0575944	−	0.177257i
$939$		0			0
$940$	3.66312	+	2.66141i	0.119478	+	0.0868057i
$941$	−43.8328	−	31.8464i	−1.42891	−	1.03816i	−0.990219	−	0.139525i	$-0.955442\pi$
$941$	−43.8328	−	31.8464i	−1.42891	−	1.03816i	−0.438690	−	0.898638i	$-0.644558\pi$
$942$		0			0
$943$	−5.09017	−	15.6659i	−0.165759	−	0.510153i
$944$	−6.21885	+	4.51826i	−0.202406	+	0.147057i
$945$		0			0
$946$	−1.35410	−	1.53884i	−0.0440257	−	0.0500321i
$947$	0.618034			0.0200834			0.0100417	−	0.999950i	$-0.496804\pi$
$947$	0.618034			0.0200834			0.0100417	+	0.999950i	$0.496804\pi$
$948$		0			0
$949$	−3.57295	−	10.9964i	−0.115983	−	0.356958i
$950$		0			0
$951$		0			0
$952$	7.66312	+	5.56758i	0.248363	+	0.180446i
$953$	−5.93363	+	18.2618i	−0.192209	+	0.591559i	0.807789	+	0.589472i	$0.200664\pi$
$953$	−5.93363	+	18.2618i	−0.192209	+	0.591559i	−0.999998	+	0.00208665i	$0.999336\pi$
$954$		0			0
$955$	3.01722	−	2.19214i	0.0976350	−	0.0709360i
$956$	30.9787			1.00192
$957$		0			0
$958$	−13.2918			−0.429438
$959$	−2.47214	+	1.79611i	−0.0798294	+	0.0579995i
$960$		0			0
$961$	22.7984	−	70.1662i	0.735431	−	2.26343i
$962$	3.47214	+	2.52265i	0.111946	+	0.0813336i
$963$		0			0
$964$	12.3541	−	38.0220i	0.397899	−	1.22461i
$965$	0.596748	+	1.83660i	0.0192100	+	0.0591223i
$966$		0			0
$967$	36.2918			1.16707			0.583533	−	0.812090i	$-0.301670\pi$
$967$	36.2918			1.16707			0.583533	+	0.812090i	$0.301670\pi$
$968$	11.8090	+	21.5765i	0.379556	+	0.693496i
$969$		0			0
$970$	3.24671	−	2.35887i	0.104246	−	0.0757389i
$971$	7.63525	+	23.4989i	0.245027	+	0.754116i	0.995632	+	0.0933644i	$0.0297621\pi$
$971$	7.63525	+	23.4989i	0.245027	+	0.754116i	−0.750605	+	0.660751i	$0.770238\pi$
$972$		0			0
$973$	14.2082	+	10.3229i	0.455494	+	0.330936i
$974$	−8.30902	−	6.03685i	−0.266238	−	0.193433i
$975$		0			0
$976$	−3.30244	−	10.1639i	−0.105709	−	0.325337i
$977$	26.6976	−	19.3969i	0.854131	−	0.620562i	−0.0721512	−	0.997394i	$-0.522986\pi$
$977$	26.6976	−	19.3969i	0.854131	−	0.620562i	0.926282	+	0.376831i	$0.122986\pi$
$978$		0			0
$979$	−1.97214	−	21.0745i	−0.0630297	−	0.673544i
$980$	−0.618034			−0.0197424
$981$		0			0
$982$	−0.708204	−	2.17963i	−0.0225997	−	0.0695547i
$983$	9.25329	−	28.4787i	0.295134	−	0.908329i	−0.688042	−	0.725671i	$-0.741530\pi$
$983$	9.25329	−	28.4787i	0.295134	−	0.908329i	0.983176	−	0.182659i	$-0.0584703\pi$
$984$		0			0
$985$	−2.85410	−	2.07363i	−0.0909393	−	0.0660712i
$986$	−5.42705	+	16.7027i	−0.172833	+	0.531924i
$987$		0			0
$988$		0			0
$989$	−3.23607			−0.102901
$990$		0			0
$991$	33.6312			1.06833			0.534165	−	0.845380i	$-0.320626\pi$
$991$	33.6312			1.06833			0.534165	+	0.845380i	$0.320626\pi$
$992$	46.5238	−	33.8015i	1.47713	−	1.07320i
$993$		0			0
$994$	1.42705	−	4.39201i	0.0452633	−	0.139306i
$995$	2.33688	+	1.69784i	0.0740841	+	0.0538253i
$996$		0			0
$997$	0.437694	−	1.34708i	0.0138619	−	0.0426626i	−0.943886	−	0.330271i	$-0.892860\pi$
$997$	0.437694	−	1.34708i	0.0138619	−	0.0426626i	0.957748	+	0.287608i	$0.0928600\pi$
$998$	−0.954915	−	2.93893i	−0.0302273	−	0.0930301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.b.190.1		4
3.2	odd	2		231.2.j.d.190.1	yes	4
11.2	odd	10		7623.2.a.bp.1.1		2
11.4	even	5	inner	693.2.m.b.631.1		4
11.9	even	5		7623.2.a.ba.1.2		2
33.2	even	10		2541.2.a.s.1.2		2
33.20	odd	10		2541.2.a.bb.1.1		2
33.26	odd	10		231.2.j.d.169.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.d.169.1	✓	4	33.26	odd	10
231.2.j.d.190.1	yes	4	3.2	odd	2
693.2.m.b.190.1		4	1.1	even	1	trivial
693.2.m.b.631.1		4	11.4	even	5	inner
2541.2.a.s.1.2		2	33.2	even	10
2541.2.a.bb.1.1		2	33.20	odd	10
7623.2.a.ba.1.2		2	11.9	even	5
7623.2.a.bp.1.1		2	11.2	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(-0.309017 - 0.224514i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +0.236068 q^{10} +(-0.309017 - 3.30220i) q^{11} +(0.809017 - 0.587785i) q^{13} +(0.190983 + 0.587785i) q^{14} +(-1.50000 - 1.08981i) q^{16} +(-3.42705 - 2.48990i) q^{17} +(0.500000 - 0.363271i) q^{20} +(1.35410 + 1.53884i) q^{22} +3.23607 q^{23} +(-1.50000 - 4.61653i) q^{25} +(-0.190983 + 0.587785i) q^{26} +(1.30902 + 0.951057i) q^{28} +(-2.07295 + 6.37988i) q^{29} +(8.28115 - 6.01661i) q^{31} +5.61803 q^{32} +2.61803 q^{34} +(-0.309017 + 0.224514i) q^{35} +(2.14590 - 6.60440i) q^{37} +(-0.263932 + 0.812299i) q^{40} +(-1.57295 - 4.84104i) q^{41} -1.00000 q^{43} +(5.23607 + 1.17557i) q^{44} +(-1.61803 + 1.17557i) q^{46} +(2.26393 + 6.96767i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(2.42705 + 1.76336i) q^{50} +(0.500000 + 1.53884i) q^{52} +(6.16312 - 4.47777i) q^{53} +(-0.645898 + 1.08981i) q^{55} -2.23607 q^{56} +(-1.28115 - 3.94298i) q^{58} +(1.28115 - 3.94298i) q^{59} +(4.66312 + 3.38795i) q^{61} +(-1.95492 + 6.01661i) q^{62} +(0.190983 - 0.138757i) q^{64} -0.381966 q^{65} -9.23607 q^{67} +(5.54508 - 4.02874i) q^{68} +(0.0729490 - 0.224514i) q^{70} +(-6.04508 - 4.39201i) q^{71} +(3.57295 - 10.9964i) q^{73} +(1.32624 + 4.08174i) q^{74} +(-3.23607 - 0.726543i) q^{77} +(-8.78115 + 6.37988i) q^{79} +(0.218847 + 0.673542i) q^{80} +(2.54508 + 1.84911i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(0.500000 + 1.53884i) q^{85} +(0.500000 - 0.363271i) q^{86} +(-6.80902 + 2.93893i) q^{88} +6.38197 q^{89} +(-0.309017 - 0.951057i) q^{91} +(-1.61803 + 4.97980i) q^{92} +(-3.66312 - 2.66141i) q^{94} +(13.7533 - 9.99235i) q^{97} +0.618034 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} - 5 q^{8} - 8 q^{10} + q^{11} + q^{13} + 3 q^{14} - 6 q^{16} - 7 q^{17} + 2 q^{20} - 8 q^{22} + 4 q^{23} - 6 q^{25} - 3 q^{26} + 3 q^{28} - 15 q^{29} + 13 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 - 5 * q^8 - 8 * q^10 + q^11 + q^13 + 3 * q^14 - 6 * q^16 - 7 * q^17 + 2 * q^20 - 8 * q^22 + 4 * q^23 - 6 * q^25 - 3 * q^26 + 3 * q^28 - 15 * q^29 + 13 * q^31 + 18 * q^32 + 6 * q^34 + q^35 + 22 * q^37 - 10 * q^40 - 13 * q^41 - 4 * q^43 + 12 * q^44 - 2 * q^46 + 18 * q^47 - q^49 + 3 * q^50 + 2 * q^52 + 9 * q^53 - 16 * q^55 + 15 * q^58 - 15 * q^59 + 3 * q^61 - 19 * q^62 + 3 * q^64 - 6 * q^65 - 28 * q^67 + 11 * q^68 + 7 * q^70 - 13 * q^71 + 21 * q^73 - 26 * q^74 - 4 * q^77 - 15 * q^79 + 21 * q^80 - q^82 - 6 * q^83 + 2 * q^85 + 2 * q^86 - 25 * q^88 + 30 * q^89 + q^91 - 2 * q^92 + q^94 + 17 * q^97 - 2 * q^98

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