LMFDB - Embedded newform 384.2.v.a.181.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			181.19
Character	$\chi$	$=$	384.181
Dual form			384.2.v.a.157.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.393338 - 1.35841i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(-1.69057 - 1.06863i) q^{4} +(0.0758469 + 0.0405410i) q^{5} +(-1.39043 - 0.258296i) q^{6} +(0.343293 - 1.72585i) q^{7} +(-2.11661 + 1.87616i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(0.393338 - 1.35841i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(-1.69057 - 1.06863i) q^{4} +(0.0758469 + 0.0405410i) q^{5} +(-1.39043 - 0.258296i) q^{6} +(0.343293 - 1.72585i) q^{7} +(-2.11661 + 1.87616i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(0.0849049 - 0.0870850i) q^{10} +(-0.408313 - 0.497531i) q^{11} +(-0.897780 + 1.78717i) q^{12} +(-2.79626 - 5.23144i) q^{13} +(-2.20939 - 1.14518i) q^{14} +(0.0329115 - 0.0794554i) q^{15} +(1.71606 + 3.61319i) q^{16} +(-2.17854 - 5.25946i) q^{17} +(-0.120767 + 1.40905i) q^{18} +(-2.13712 + 7.04513i) q^{19} +(-0.0849011 - 0.149590i) q^{20} +(-1.75119 - 0.172477i) q^{21} +(-0.836458 + 0.358960i) q^{22} +(4.54100 + 3.03420i) q^{23} +(2.07459 + 1.92252i) q^{24} +(-2.77374 - 4.15120i) q^{25} +(-8.20633 + 1.74076i) q^{26} +(0.290285 + 0.956940i) q^{27} +(-2.42466 + 2.55082i) q^{28} +(7.83321 + 6.42855i) q^{29} +(-0.0949878 - 0.0759602i) q^{30} +(-2.19208 - 2.19208i) q^{31} +(5.58320 - 0.909908i) q^{32} +(-0.455114 + 0.455114i) q^{33} +(-8.00141 + 0.890610i) q^{34} +(0.0960055 - 0.116983i) q^{35} +(1.86657 + 0.718283i) q^{36} +(0.0550612 - 0.0167026i) q^{37} +(8.72959 + 5.67421i) q^{38} +(-4.93217 + 3.29557i) q^{39} +(-0.236599 + 0.0564915i) q^{40} +(5.89975 - 8.82959i) q^{41} +(-0.923105 + 2.31100i) q^{42} +(1.13140 - 11.4873i) q^{43} +(0.158605 + 1.27745i) q^{44} +(-0.0822987 - 0.0249650i) q^{45} +(5.90784 - 4.97509i) q^{46} +(-2.08506 + 0.863662i) q^{47} +(3.42759 - 2.06195i) q^{48} +(3.60644 + 1.49384i) q^{49} +(-6.73006 + 2.13506i) q^{50} +(-5.02060 + 2.68356i) q^{51} +(-0.863198 + 11.8323i) q^{52} +(2.73594 - 2.24533i) q^{53} +(1.41410 - 0.0179254i) q^{54} +(-0.0107989 - 0.0542896i) q^{55} +(2.51136 + 4.29702i) q^{56} +(7.22068 + 1.43628i) q^{57} +(11.8137 - 8.11214i) q^{58} +(-0.326629 + 0.611080i) q^{59} +(-0.140548 + 0.0991547i) q^{60} +(-5.56994 + 0.548591i) q^{61} +(-3.83997 + 2.11552i) q^{62} +1.75966i q^{63} +(0.960052 - 7.94218i) q^{64} -0.510152i q^{65} +(0.439219 + 0.797246i) q^{66} +(0.335798 - 0.0330732i) q^{67} +(-1.93744 + 11.2195i) q^{68} +(2.57449 - 4.81654i) q^{69} +(-0.121149 - 0.176429i) q^{70} +(1.43346 + 0.285133i) q^{71} +(1.70992 - 2.25304i) q^{72} +(-1.95656 - 9.83631i) q^{73} +(-0.00103141 - 0.0813657i) q^{74} +(-3.85933 + 3.16727i) q^{75} +(11.1416 - 9.62650i) q^{76} +(-0.998836 + 0.533889i) q^{77} +(2.53673 + 7.99619i) q^{78} +(9.00287 + 3.72911i) q^{79} +(-0.0163248 + 0.343620i) q^{80} +(0.923880 - 0.382683i) q^{81} +(-9.67364 - 11.4873i) q^{82} +(8.17302 + 2.47926i) q^{83} +(2.77620 + 2.16296i) q^{84} +(0.0479883 - 0.487233i) q^{85} +(-15.1595 - 6.05532i) q^{86} +(5.62981 - 8.42560i) q^{87} +(1.79769 + 0.287017i) q^{88} +(10.7045 - 7.15255i) q^{89} +(-0.0662840 + 0.101976i) q^{90} +(-9.98863 + 3.03002i) q^{91} +(-4.43444 - 9.98218i) q^{92} +(-1.96666 + 2.39638i) q^{93} +(0.353074 + 3.17209i) q^{94} +(-0.447710 + 0.447710i) q^{95} +(-1.45278 - 5.46712i) q^{96} +(-9.87917 - 9.87917i) q^{97} +(3.44780 - 4.31146i) q^{98} +(0.497531 + 0.408313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{32}\right)$	$1$

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 $

$2$	0.393338	−	1.35841i	0.278132	−	0.960543i
$2$	0.393338	−	1.35841i	0.278132	−	0.960543i
$3$	−0.0980171	−	0.995185i	−0.0565902	−	0.574570i
$3$	−0.0980171	−	0.995185i	−0.0565902	−	0.574570i
$4$	−1.69057	−	1.06863i	−0.845285	−	0.534315i
$5$	0.0758469	+	0.0405410i	0.0339198	+	0.0181305i	0.488269	−	0.872693i	$-0.337628\pi$
$5$	0.0758469	+	0.0405410i	0.0339198	+	0.0181305i	−0.454350	+	0.890823i	$0.650128\pi$
$6$	−1.39043	−	0.258296i	−0.567639	−	0.105449i
$7$	0.343293	−	1.72585i	0.129753	−	0.652311i	−0.860090	−	0.510143i	$-0.829593\pi$
$7$	0.343293	−	1.72585i	0.129753	−	0.652311i	0.989843	−	0.142168i	$-0.0454074\pi$
$8$	−2.11661	+	1.87616i	−0.748334	+	0.663322i
$9$	−0.980785	+	0.195090i	−0.326928	+	0.0650301i
$10$	0.0849049	−	0.0870850i	0.0268493	−	0.0275387i
$11$	−0.408313	−	0.497531i	−0.123111	−	0.150011i	0.707807	−	0.706405i	$-0.249684\pi$
$11$	−0.408313	−	0.497531i	−0.123111	−	0.150011i	−0.830918	+	0.556394i	$0.812184\pi$
$12$	−0.897780	+	1.78717i	−0.259167	+	0.515913i
$13$	−2.79626	−	5.23144i	−0.775544	−	1.45094i	−0.889248	−	0.457426i	$-0.848771\pi$
$13$	−2.79626	−	5.23144i	−0.775544	−	1.45094i	0.113704	−	0.993515i	$-0.463729\pi$
$14$	−2.20939	−	1.14518i	−0.590484	−	0.306061i
$15$	0.0329115	−	0.0794554i	0.00849771	−	0.0205153i
$16$	1.71606	+	3.61319i	0.429014	+	0.903298i
$17$	−2.17854	−	5.25946i	−0.528373	−	1.27561i	−0.932588	−	0.360942i	$-0.882455\pi$
$17$	−2.17854	−	5.25946i	−0.528373	−	1.27561i	0.404215	−	0.914664i	$-0.367545\pi$
$18$	−0.120767	+	1.40905i	−0.0284650	+	0.332116i
$19$	−2.13712	+	7.04513i	−0.490288	+	1.61626i	0.267357	+	0.963598i	$0.413850\pi$
$19$	−2.13712	+	7.04513i	−0.490288	+	1.61626i	−0.757645	+	0.652667i	$0.773650\pi$
$20$	−0.0849011	−	0.149590i	−0.0189845	−	0.0334493i
$21$	−1.75119	−	0.172477i	−0.382141	−	0.0376376i
$22$	−0.836458	+	0.358960i	−0.178333	+	0.0765305i
$23$	4.54100	+	3.03420i	0.946864	+	0.632674i	0.930148	−	0.367186i	$-0.119679\pi$
$23$	4.54100	+	3.03420i	0.946864	+	0.632674i	0.0167164	+	0.999860i	$0.494679\pi$
$24$	2.07459	+	1.92252i	0.423474	+	0.392433i
$25$	−2.77374	−	4.15120i	−0.554748	−	0.830240i
$26$	−8.20633	+	1.74076i	−1.60939	+	0.341390i
$27$	0.290285	+	0.956940i	0.0558653	+	0.184163i
$28$	−2.42466	+	2.55082i	−0.458218	+	0.482060i
$29$	7.83321	+	6.42855i	1.45459	+	1.19375i	0.942223	+	0.334987i	$0.108732\pi$
$29$	7.83321	+	6.42855i	1.45459	+	1.19375i	0.512368	+	0.858766i	$0.328768\pi$
$30$	−0.0949878	−	0.0759602i	−0.0173423	−	0.0138684i
$31$	−2.19208	−	2.19208i	−0.393708	−	0.393708i	0.482298	−	0.876007i	$-0.339802\pi$
$31$	−2.19208	−	2.19208i	−0.393708	−	0.393708i	−0.876007	+	0.482298i	$0.839802\pi$
$32$	5.58320	−	0.909908i	0.986979	−	0.160851i
$33$	−0.455114	+	0.455114i	−0.0792251	+	0.0792251i
$34$	−8.00141	+	0.890610i	−1.37223	+	0.152738i
$35$	0.0960055	−	0.116983i	0.0162279	−	0.0197737i
$36$	1.86657	+	0.718283i	0.311094	+	0.119714i
$37$	0.0550612	−	0.0167026i	0.00905201	−	0.00274590i	−0.285755	−	0.958303i	$-0.592244\pi$
$37$	0.0550612	−	0.0167026i	0.00905201	−	0.00274590i	0.294807	+	0.955557i	$0.404744\pi$
$38$	8.72959	+	5.67421i	1.41613	+	0.920478i
$39$	−4.93217	+	3.29557i	−0.789779	+	0.527713i
$40$	−0.236599	+	0.0564915i	−0.0374097	+	0.00893208i
$41$	5.89975	−	8.82959i	0.921385	−	1.37895i	−0.00402799	−	0.999992i	$-0.501282\pi$
$41$	5.89975	−	8.82959i	0.921385	−	1.37895i	0.925413	−	0.378959i	$-0.123718\pi$
$42$	−0.923105	+	2.31100i	−0.142438	+	0.356595i
$43$	1.13140	−	11.4873i	0.172537	−	1.75180i	−0.386161	−	0.922431i	$-0.626199\pi$
$43$	1.13140	−	11.4873i	0.172537	−	1.75180i	0.558699	−	0.829371i	$-0.311301\pi$
$44$	0.158605	+	1.27745i	0.0239106	+	0.192582i
$45$	−0.0822987	−	0.0249650i	−0.0122684	−	0.00372157i
$46$	5.90784	−	4.97509i	0.871064	−	0.733536i
$47$	−2.08506	+	0.863662i	−0.304138	+	0.125978i	−0.529533	−	0.848289i	$-0.677633\pi$
$47$	−2.08506	+	0.863662i	−0.304138	+	0.125978i	0.225395	+	0.974267i	$0.427633\pi$
$48$	3.42759	−	2.06195i	0.494730	−	0.297617i
$49$	3.60644	+	1.49384i	0.515206	+	0.213405i
$50$	−6.73006	+	2.13506i	−0.951774	+	0.301943i
$51$	−5.02060	+	2.68356i	−0.703024	+	0.375774i
$52$	−0.863198	+	11.8323i	−0.119704	+	1.64084i
$53$	2.73594	−	2.24533i	0.375810	−	0.308419i	−0.427460	−	0.904034i	$-0.640592\pi$
$53$	2.73594	−	2.24533i	0.375810	−	0.308419i	0.803270	+	0.595615i	$0.203092\pi$
$54$	1.41410	−	0.0179254i	0.192435	−	0.00243934i
$55$	−0.0107989	−	0.0542896i	−0.00145612	−	0.00732041i
$56$	2.51136	+	4.29702i	0.335594	+	0.574214i
$57$	7.22068	+	1.43628i	0.956403	+	0.190240i
$58$	11.8137	−	8.11214i	1.55122	−	1.06518i
$59$	−0.326629	+	0.611080i	−0.0425234	+	0.0795558i	−0.902285	−	0.431139i	$-0.858112\pi$
$59$	−0.326629	+	0.611080i	−0.0425234	+	0.0795558i	0.859762	+	0.510695i	$0.170612\pi$
$60$	−0.140548	+	0.0991547i	−0.0181446	+	0.0128008i
$61$	−5.56994	+	0.548591i	−0.713157	+	0.0702399i	−0.448088	−	0.893989i	$-0.647895\pi$
$61$	−5.56994	+	0.548591i	−0.713157	+	0.0702399i	−0.265069	+	0.964229i	$0.585395\pi$
$62$	−3.83997	+	2.11552i	−0.487677	+	0.268671i
$63$			1.75966i			0.221697i
$64$	0.960052	−	7.94218i	0.120007	−	0.992773i
$65$		−	0.510152i		−	0.0632765i
$66$	0.439219	+	0.797246i	0.0540641	+	0.0981341i
$67$	0.335798	−	0.0330732i	0.0410242	−	0.00404053i	−0.0774842	−	0.996994i	$-0.524689\pi$
$67$	0.335798	−	0.0330732i	0.0410242	−	0.00404053i	0.118508	+	0.992953i	$0.462189\pi$
$68$	−1.93744	+	11.2195i	−0.234950	+	1.36057i
$69$	2.57449	−	4.81654i	0.309932	−	0.579843i
$70$	−0.121149	−	0.176429i	−0.0144800	−	0.0210873i
$71$	1.43346	+	0.285133i	0.170121	+	0.0338391i	0.279416	−	0.960170i	$-0.409859\pi$
$71$	1.43346	+	0.285133i	0.170121	+	0.0338391i	−0.109295	+	0.994009i	$0.534859\pi$
$72$	1.70992	−	2.25304i	0.201516	−	0.265523i
$73$	−1.95656	−	9.83631i	−0.228999	−	1.15125i	−0.908599	−	0.417671i	$-0.862847\pi$
$73$	−1.95656	−	9.83631i	−0.228999	−	1.15125i	0.679600	−	0.733583i	$-0.262153\pi$
$74$	−0.00103141	−	0.0813657i	−0.000119899	−	0.00945857i
$75$	−3.85933	+	3.16727i	−0.445638	+	0.365725i
$76$	11.1416	−	9.62650i	1.27803	−	1.10424i
$77$	−0.998836	+	0.533889i	−0.113828	+	0.0608423i
$78$	2.53673	+	7.99619i	0.287229	+	0.905391i
$79$	9.00287	+	3.72911i	1.01290	+	0.419558i	0.826513	−	0.562918i	$-0.190321\pi$
$79$	9.00287	+	3.72911i	1.01290	+	0.419558i	0.186390	+	0.982476i	$0.440321\pi$
$80$	−0.0163248	+	0.343620i	−0.00182517	+	0.0384179i
$81$	0.923880	−	0.382683i	0.102653	−	0.0425204i
$82$	−9.67364	−	11.4873i	−1.06827	−	1.26856i
$83$	8.17302	+	2.47926i	0.897106	+	0.272134i	0.704972	−	0.709235i	$-0.250959\pi$
$83$	8.17302	+	2.47926i	0.897106	+	0.272134i	0.192133	+	0.981369i	$0.438459\pi$
$84$	2.77620	+	2.16296i	0.302908	+	0.235998i
$85$	0.0479883	−	0.487233i	0.00520506	−	0.0528479i
$86$	−15.1595	−	6.05532i	−1.63469	−	0.652962i
$87$	5.62981	−	8.42560i	0.603579	−	0.903320i
$88$	1.79769	+	0.287017i	0.191634	+	0.0305961i
$89$	10.7045	−	7.15255i	1.13468	−	0.758168i	0.161195	−	0.986923i	$-0.448465\pi$
$89$	10.7045	−	7.15255i	1.13468	−	0.758168i	0.973484	+	0.228754i	$0.0734652\pi$
$90$	−0.0662840	+	0.101976i	−0.00698695	+	0.0107492i
$91$	−9.98863	+	3.03002i	−1.04709	+	0.317632i
$92$	−4.43444	−	9.98218i	−0.462322	−	1.04071i
$93$	−1.96666	+	2.39638i	−0.203933	+	0.248493i
$94$	0.353074	+	3.17209i	0.0364168	+	0.327176i
$95$	−0.447710	+	0.447710i	−0.0459341	+	0.0459341i
$96$	−1.45278	−	5.46712i	−0.148273	−	0.557986i
$97$	−9.87917	−	9.87917i	−1.00308	−	1.00308i	−0.999995	−	0.00308208i	$-0.999019\pi$
$97$	−9.87917	−	9.87917i	−1.00308	−	1.00308i	−0.00308208	−	0.999995i	$-0.500981\pi$
$98$	3.44780	−	4.31146i	0.348280	−	0.435523i
$99$	0.497531	+	0.408313i	0.0500037	+	0.0410370i
$100$	0.253108	+	9.98200i	0.0253108	+	0.998200i
$101$	5.11500	+	16.8619i	0.508962	+	1.67782i	0.714875	+	0.699252i	$0.246484\pi$
$101$	5.11500	+	16.8619i	0.508962	+	1.67782i	−0.205913	+	0.978570i	$0.566016\pi$
$102$	1.67060	+	7.87559i	0.165414	+	0.779800i
$103$	4.12740	+	6.17710i	0.406685	+	0.608648i	0.977118	−	0.212697i	$-0.0682246\pi$
$103$	4.12740	+	6.17710i	0.406685	+	0.608648i	−0.570433	+	0.821344i	$0.693225\pi$
$104$	15.7336	+	5.82667i	1.54281	+	0.571352i
$105$	−0.125830	−	0.0840768i	−0.0122797	−	0.00820506i
$106$	−1.97393	−	4.59971i	−0.191725	−	0.446763i
$107$	−10.3515	−	1.01954i	−1.00072	−	0.0985622i	−0.415632	−	0.909533i	$-0.636440\pi$
$107$	−10.3515	−	1.01954i	−1.00072	−	0.0985622i	−0.585087	+	0.810971i	$0.698940\pi$
$108$	0.531869	−	1.92798i	0.0511791	−	0.185520i
$109$	−0.414956	+	1.36792i	−0.0397455	+	0.131023i	−0.974568	−	0.224092i	$-0.928058\pi$
$109$	−0.414956	+	1.36792i	−0.0397455	+	0.131023i	0.934822	+	0.355115i	$0.115558\pi$
$110$	−0.0779953	−	0.00668484i	−0.00743656	−	0.000637374i
$111$	−0.0220192	−	0.0531590i	−0.00208997	−	0.00504563i
$112$	6.82494	−	1.72128i	0.644896	−	0.162645i
$113$	−3.46452	+	8.36410i	−0.325915	+	0.786828i	0.672972	+	0.739668i	$0.265017\pi$
$113$	−3.46452	+	8.36410i	−0.325915	+	0.786828i	−0.998887	+	0.0471607i	$0.984983\pi$
$114$	4.79123	−	9.24372i	0.448740	−	0.865754i
$115$	0.221411	+	0.414231i	0.0206467	+	0.0386273i
$116$	−6.37285	−	19.2387i	−0.591704	−	1.78627i
$117$	3.76314	+	4.58540i	0.347902	+	0.423920i
$118$	0.701623	+	0.684058i	0.0645896	+	0.0629726i
$119$	−9.82492	+	1.95430i	−0.900649	+	0.179150i
$120$	0.0794102	+	0.229923i	0.00724913	+	0.0209890i
$121$	2.06518	−	10.3823i	0.187743	−	0.943849i
$122$	−1.44565	+	7.78205i	−0.130883	+	0.704554i
$123$	−9.36535	−	5.00589i	−0.844445	−	0.451365i
$124$	1.36334	+	6.04838i	0.122431	+	0.543160i
$125$	−0.0842342	−	0.855244i	−0.00753414	−	0.0764954i
$126$	2.39035	+	0.692142i	0.212949	+	0.0616609i
$127$	4.93368			0.437793			0.218897	−	0.975748i	$-0.429754\pi$
$127$	4.93368			0.437793			0.218897	+	0.975748i	$0.429754\pi$
$128$	−10.4111	−	4.42811i	−0.920223	−	0.391393i
$129$	−11.5429			−1.01630
$130$	−0.692997	−	0.200662i	−0.0607798	−	0.0175992i
$131$	0.988706	+	10.0385i	0.0863837	+	0.877068i	0.936545	+	0.350546i	$0.114004\pi$
$131$	0.988706	+	10.0385i	0.0863837	+	0.877068i	−0.850162	+	0.526522i	$0.823496\pi$
$132$	1.25575	−	0.283053i	0.109299	−	0.0246366i
$133$	11.4252	+	6.10689i	0.990690	+	0.529535i
$134$	0.0871549	−	0.469161i	0.00752904	−	0.0405293i
$135$	−0.0167781	+	0.0843494i	−0.00144403	+	0.00725964i
$136$	14.4787	+	7.04492i	1.24154	+	0.604097i
$137$	5.24664	−	1.04362i	0.448251	−	0.0891626i	0.0341972	−	0.999415i	$-0.489113\pi$
$137$	5.24664	−	1.04362i	0.448251	−	0.0891626i	0.414054	+	0.910252i	$0.364113\pi$
$138$	−5.53020	−	5.39175i	−0.470762	−	0.458976i
$139$	7.37910	+	8.99146i	0.625887	+	0.762646i	0.985356	−	0.170511i	$-0.0545419\pi$
$139$	7.37910	+	8.99146i	0.625887	+	0.762646i	−0.359468	+	0.933157i	$0.617042\pi$
$140$	−0.287316	+	0.0951736i	−0.0242826	+	0.00804364i
$141$	1.06388	+	1.99037i	0.0895944	+	0.167619i
$142$	0.951164	−	1.83508i	0.0798199	−	0.153996i
$143$	−1.46105	+	3.52729i	−0.122179	+	0.294967i
$144$	−2.38798	−	3.20898i	−0.198998	−	0.267415i
$145$	0.333505	+	0.805152i	0.0276961	+	0.0668642i
$146$	−14.1314	−	1.21117i	−1.16952	−	0.100237i
$147$	1.13315	−	3.73550i	0.0934607	−	0.308099i
$148$	−0.110934	−	0.0306031i	−0.00911871	−	0.00251556i
$149$	9.26431	+	0.912455i	0.758962	+	0.0747512i	0.470092	−	0.882617i	$-0.344221\pi$
$149$	9.26431	+	0.912455i	0.758962	+	0.0747512i	0.288869	+	0.957368i	$0.406721\pi$
$150$	2.78444	+	6.48838i	0.227349	+	0.529774i
$151$	12.3984	+	8.28436i	1.00897	+	0.674172i	0.946108	−	0.323850i	$-0.104977\pi$
$151$	12.3984	+	8.28436i	1.00897	+	0.674172i	0.0628614	+	0.998022i	$0.479977\pi$
$152$	−8.69435	−	18.9214i	−0.705205	−	1.53472i
$153$	3.16275	+	4.73339i	0.255693	+	0.382672i
$154$	0.332361	+	1.56683i	0.0267824	+	0.126259i
$155$	−0.0773932	−	0.255131i	−0.00621637	−	0.0204926i
$156$	11.8599	−	0.300726i	0.949554	−	0.0240773i
$157$	−5.08205	−	4.17073i	−0.405592	−	0.332861i	0.409377	−	0.912365i	$-0.365746\pi$
$157$	−5.08205	−	4.17073i	−0.405592	−	0.332861i	−0.814969	+	0.579505i	$0.803246\pi$
$158$	8.60685	−	10.7628i	0.684724	−	0.856244i
$159$	−2.50268	−	2.50268i	−0.198476	−	0.198476i
$160$	0.460356	+	0.157335i	0.0363944	+	0.0124384i
$161$	6.79547	−	6.79547i	0.535558	−	0.535558i
$162$	−0.156445	−	1.40553i	−0.0122915	−	0.110429i
$163$	−7.84766	+	9.56240i	−0.614676	+	0.748985i	−0.983578	−	0.180484i	$-0.942234\pi$
$163$	−7.84766	+	9.56240i	−0.614676	+	0.748985i	0.368902	+	0.929468i	$0.379734\pi$
$164$	−19.4095	+	8.62240i	−1.51563	+	0.673296i
$165$	−0.0529697	+	0.0160682i	−0.00412369	+	0.00125091i
$166$	6.58262	−	10.1271i	0.510910	−	0.786019i
$167$	8.83957	−	5.90641i	0.684026	−	0.457052i	−0.164380	−	0.986397i	$-0.552562\pi$
$167$	8.83957	−	5.90641i	0.684026	−	0.457052i	0.848406	+	0.529345i	$0.177562\pi$
$168$	4.03018	−	2.92044i	0.310935	−	0.225317i
$169$	−12.3265	+	18.4479i	−0.948190	+	1.41907i
$170$	−0.642988	−	0.256835i	−0.0493150	−	0.0196984i
$171$	0.721616	−	7.32669i	0.0551834	−	0.560286i
$172$	−14.1884	+	18.2111i	−1.08186	+	1.38858i
$173$	−4.50296	−	1.36596i	−0.342354	−	0.103852i	0.114426	−	0.993432i	$-0.463497\pi$
$173$	−4.50296	−	1.36596i	−0.342354	−	0.103852i	−0.456780	+	0.889580i	$0.650997\pi$
$174$	−9.23103	−	10.9617i	−0.699803	−	0.831005i
$175$	−8.11656	+	3.36199i	−0.613554	+	0.254142i
$176$	1.09699	−	2.32910i	0.0826884	−	0.175563i
$177$	0.640152	+	0.265160i	0.0481168	+	0.0199306i
$178$	−5.50561	−	17.3546i	−0.412663	−	1.30078i
$179$	−14.2415	+	7.61222i	−1.06446	+	0.568964i	−0.908107	−	0.418738i	$-0.862473\pi$
$179$	−14.2415	+	7.61222i	−1.06446	+	0.568964i	−0.156349	+	0.987702i	$0.549973\pi$
$180$	0.112453	+	0.130152i	0.00838177	+	0.00970096i
$181$	−11.5667	+	9.49253i	−0.859745	+	0.705574i	−0.957126	−	0.289673i	$-0.906454\pi$
$181$	−11.5667	+	9.49253i	−0.859745	+	0.705574i	0.0973809	+	0.995247i	$0.468954\pi$
$182$	0.187107	+	14.7605i	0.0138693	+	1.09412i
$183$	1.09190	+	5.48934i	0.0807155	+	0.405784i
$184$	−15.3042	+	2.09743i	−1.12824	+	0.154625i
$185$	0.00485337		0.000965394i	0.000356827		7.09772e-5i
$186$	2.48171	+	3.61412i	0.181968	+	0.265000i
$187$	−1.72722	+	3.23140i	−0.126307	+	0.236303i
$188$	4.44788	+	0.768082i	0.324395	+	0.0560182i
$189$	1.75119	−	0.172477i	0.127380	−	0.0125459i
$190$	0.432074	+	0.784277i	0.0313459	+	0.0568974i
$191$		−	14.7815i		−	1.06955i	−0.844994	−	0.534776i	$-0.820396\pi$
$191$		−	14.7815i		−	1.06955i	0.844994	−	0.534776i	$-0.179604\pi$
$192$	−7.99804	−	0.176959i	−0.577209	−	0.0127709i
$193$			7.97478i			0.574037i	0.957925	+	0.287019i	$0.0926642\pi$
$193$			7.97478i			0.574037i	−0.957925	+	0.287019i	$0.907336\pi$
$194$	−17.3058	+	9.53413i	−1.24249	+	0.684511i
$195$	−0.507695	+	0.0500036i	−0.0363568	+	0.00358083i
$196$	−4.50059	−	6.37939i	−0.321470	−	0.455671i
$197$	−6.19274	+	11.5858i	−0.441214	+	0.825454i	−0.999993	−	0.00386328i	$-0.998770\pi$
$197$	−6.19274	+	11.5858i	−0.441214	+	0.825454i	0.558778	+	0.829317i	$0.311270\pi$
$198$	0.750356	−	0.515247i	0.0533255	−	0.0366170i
$199$	6.13307	+	1.21994i	0.434762	+	0.0864795i	0.407619	−	0.913152i	$-0.366359\pi$
$199$	6.13307	+	1.21994i	0.434762	+	0.0864795i	0.0271428	+	0.999632i	$0.491359\pi$
$200$	13.6592	+	3.58247i	0.965854	+	0.253319i
$201$	−0.0658278	−	0.330939i	−0.00464314	−	0.0233426i
$202$	24.9174	−	0.315857i	1.75318	−	0.0222236i
$203$	13.7838	−	11.3121i	0.967434	−	0.793953i
$204$	11.3554	+	0.828408i	0.795038	+	0.0580002i
$205$	0.805438	−	0.430515i	0.0562542	−	0.0300685i
$206$	10.0145	−	3.17703i	0.697744	−	0.221354i
$207$	−5.04569	−	2.08999i	−0.350700	−	0.145265i
$208$	14.1036	−	19.0809i	0.977912	−	1.32302i
$209$	4.37779	−	1.81334i	0.302818	−	0.125431i
$210$	−0.163705	+	0.137858i	−0.0112967	+	0.00951313i
$211$	−18.0150	−	5.46478i	−1.24020	−	0.376211i	−0.399009	−	0.916947i	$-0.630646\pi$
$211$	−18.0150	−	5.46478i	−1.24020	−	0.376211i	−0.841192	+	0.540736i	$0.818146\pi$
$212$	−7.02472	+	0.872175i	−0.482460	+	0.0599012i
$213$	0.143257	−	1.45451i	0.00981578	−	0.0996612i
$214$	−5.45659	+	13.6606i	−0.373005	+	0.933820i
$215$	0.551521	−	0.825410i	0.0376134	−	0.0562925i
$216$	−2.40979	−	1.48085i	−0.163966	−	0.100759i
$217$	−4.53572	+	3.03067i	−0.307905	+	0.205735i
$218$	1.69499	+	1.10174i	0.114799	+	0.0746191i
$219$	−9.59717	+	2.91127i	−0.648517	+	0.196725i
$220$	−0.0397593	+	0.103320i	−0.00268057	+	0.00696586i
$221$	−21.4228	+	26.1037i	−1.44105	+	1.75593i
$222$	−0.0808728	+	0.00900167i	−0.00542783	+	0.000604153i
$223$	−15.1087	+	15.1087i	−1.01175	+	1.01175i	−0.0118200	+	0.999930i	$0.503763\pi$
$223$	−15.1087	+	15.1087i	−1.01175	+	1.01175i	−0.999930	+	0.0118200i	$0.996237\pi$
$224$	0.346307	−	9.94813i	0.0231386	−	0.664688i
$225$	3.53030	+	3.53030i	0.235354	+	0.235354i
$226$	9.99917	+	7.99617i	0.665135	+	0.531897i
$227$	−0.0134316	−	0.0110231i	−0.000891490	−	0.000731627i	0.633947	−	0.773376i	$-0.281434\pi$
$227$	−0.0134316	−	0.0110231i	−0.000891490	−	0.000731627i	−0.634839	+	0.772645i	$0.718934\pi$
$228$	−10.6722	−	10.1444i	−0.706785	−	0.671828i
$229$	−5.95402	−	19.6278i	−0.393453	−	1.29704i	−0.900400	−	0.435063i	$-0.856726\pi$
$229$	−5.95402	−	19.6278i	−0.393453	−	1.29704i	0.506947	−	0.861977i	$-0.330774\pi$
$230$	0.649786	−	0.137835i	0.0428456	−	0.00908856i
$231$	0.629221	+	0.941696i	0.0413997	+	0.0619590i
$232$	−28.6408	+	1.08964i	−1.88036	+	0.0715382i
$233$	−0.452237	−	0.302175i	−0.0296270	−	0.0197961i	0.540669	−	0.841236i	$-0.318171\pi$
$233$	−0.452237	−	0.302175i	−0.0296270	−	0.0197961i	−0.570296	+	0.821440i	$0.693171\pi$
$234$	7.70905	−	3.30828i	0.503956	−	0.216269i
$235$	−0.193159	−	0.0190245i	−0.0126003	−	0.00124102i
$236$	1.20521	−	0.684027i	0.0784523	−	0.0445264i
$237$	2.82872	−	9.32504i	0.183745	−	0.605726i
$238$	−1.20977	+	14.1150i	−0.0784178	+	0.914939i
$239$	5.74816	+	13.8773i	0.371817	+	0.897647i	0.993443	+	0.114332i	$0.0364727\pi$
$239$	5.74816	+	13.8773i	0.371817	+	0.897647i	−0.621625	+	0.783315i	$0.713527\pi$
$240$	0.343565	−	0.0174344i	0.0221771	−	0.00112539i
$241$	−1.72048	+	4.15361i	−0.110826	+	0.267557i	−0.969556	−	0.244872i	$-0.921254\pi$
$241$	−1.72048	+	4.15361i	−0.110826	+	0.267557i	0.858730	+	0.512429i	$0.171254\pi$
$242$	−13.2912	−	6.88913i	−0.854390	−	0.442850i
$243$	−0.471397	−	0.881921i	−0.0302401	−	0.0565753i
$244$	10.0026	+	5.02477i	0.640352	+	0.321678i
$245$	0.212976	+	0.259512i	0.0136065	+	0.0165796i
$246$	−10.4838	+	10.7530i	−0.668423	+	0.685587i
$247$	42.8321	−	8.51984i	2.72534	−	0.542105i
$248$	8.75245	+	0.527080i	0.555781	+	0.0334696i
$249$	1.66622	−	8.37668i	0.105593	−	0.530850i
$250$	−1.19491	−	0.221975i	−0.0755726	−	0.0140389i
$251$	−9.93062	−	5.30803i	−0.626815	−	0.335040i	0.127219	−	0.991875i	$-0.459395\pi$
$251$	−9.93062	−	5.30803i	−0.626815	−	0.335040i	−0.754034	+	0.656835i	$0.771895\pi$
$252$	1.88043	−	2.97483i	0.118456	−	0.187397i
$253$	−0.344542	−	3.49819i	−0.0216612	−	0.219929i
$254$	1.94060	−	6.70197i	0.121764	−	0.420519i
$255$	−0.489591			−0.0306594
$256$	−10.1103	+	12.4009i	−0.631894	+	0.775055i
$257$	−22.3343			−1.39318			−0.696589	−	0.717471i	$-0.745300\pi$
$257$	−22.3343			−1.39318			−0.696589	+	0.717471i	$0.745300\pi$
$258$	−4.54027	+	15.6800i	−0.282665	+	0.976197i
$259$	−0.00992414	−	0.100761i	−0.000616656	−	0.00626101i
$260$	−0.545164	+	0.862447i	−0.0338096	+	0.0534867i
$261$	−8.93685	−	4.77685i	−0.553177	−	0.295679i
$262$	14.0253	+	2.60545i	0.866488	+	0.160965i
$263$	−0.830015	+	4.17277i	−0.0511809	+	0.257304i	−0.997901	−	0.0647528i	$-0.979374\pi$
$263$	−0.830015	+	4.17277i	−0.0511809	+	0.257304i	0.946720	+	0.322057i	$0.104374\pi$
$264$	0.109431	−	1.81716i	0.00673502	−	0.111839i
$265$	0.298540	−	0.0593833i	0.0183392	−	0.00364789i
$266$	12.7896	−	13.1181i	0.784184	−	0.804320i
$267$	−8.16733	−	9.95192i	−0.499833	−	0.609048i
$268$	−0.603033	−	0.302931i	−0.0368361	−	0.0185045i
$269$	−5.17501	−	9.68176i	−0.315526	−	0.590307i	0.673302	−	0.739367i	$-0.264875\pi$
$269$	−5.17501	−	9.68176i	−0.315526	−	0.590307i	−0.988828	+	0.149060i	$0.952375\pi$
$270$	0.107982	+	0.0559694i	0.00657156	+	0.00340619i
$271$	6.17003	−	14.8958i	0.374802	−	0.904853i	−0.618119	−	0.786084i	$-0.712105\pi$
$271$	6.17003	−	14.8958i	0.374802	−	0.904853i	0.992922	−	0.118769i	$-0.0378948\pi$
$272$	15.2649	−	16.8970i	0.925572	−	1.02453i
$273$	3.99448	+	9.64354i	0.241757	+	0.583653i
$274$	0.646034	−	7.53760i	0.0390284	−	0.455363i
$275$	−0.932795	+	3.07501i	−0.0562496	+	0.185430i
$276$	−9.49946	+	5.39151i	−0.571800	+	0.324531i
$277$	−3.35823	−	0.330757i	−0.201776	−	0.0198732i	−0.00337606	−	0.999994i	$-0.501075\pi$
$277$	−3.35823	−	0.330757i	−0.201776	−	0.0198732i	−0.198400	+	0.980121i	$0.563575\pi$
$278$	15.1166	−	6.48718i	0.906634	−	0.389075i
$279$	2.57761	+	1.72230i	0.154317	+	0.103112i
$280$	0.0162729	+	0.427729i	0.000972491	+	0.0255617i
$281$	−1.82188	−	2.72664i	−0.108684	−	0.162657i	0.773140	−	0.634235i	$-0.218685\pi$
$281$	−1.82188	−	2.72664i	−0.108684	−	0.162657i	−0.881825	+	0.471577i	$0.843685\pi$
$282$	3.12221	−	0.662293i	0.185925	−	0.0394390i
$283$	2.06616	+	6.81121i	0.122820	+	0.404884i	0.996692	−	0.0812724i	$-0.0258984\pi$
$283$	2.06616	+	6.81121i	0.122820	+	0.404884i	−0.873872	+	0.486157i	$0.838398\pi$
$284$	−2.11867	−	2.01388i	−0.125720	−	0.119502i
$285$	0.489438	+	0.401671i	0.0289918	+	0.0237930i
$286$	4.21683	+	3.37213i	0.249347	+	0.199398i
$287$	−13.2132	−	13.2132i	−0.779952	−	0.779952i
$288$	−5.29840	+	1.98165i	−0.312211	+	0.116770i
$289$	−10.8950	+	10.8950i	−0.640884	+	0.640884i
$290$	1.22491	−	0.136340i	0.0719291	−	0.00800618i
$291$	−8.86327	+	10.7999i	−0.519574	+	0.633103i
$292$	−7.20368	+	18.7198i	−0.421563	+	1.09549i
$293$	26.0396	−	7.89902i	1.52125	−	0.461466i	0.584478	−	0.811410i	$-0.301299\pi$
$293$	26.0396	−	7.89902i	1.52125	−	0.461466i	0.936771	+	0.349944i	$0.113799\pi$
$294$	−4.62864	−	3.00860i	−0.269948	−	0.175465i
$295$	−0.0495475	+	0.0331066i	−0.00288477	+	0.00192754i
$296$	−0.0852062	+	0.138657i	−0.00495251	+	0.00805925i
$297$	0.357580	−	0.535157i	0.0207489	−	0.0310530i
$298$	4.88349	−	12.2259i	0.282893	−	0.708225i
$299$	3.17540	−	32.2404i	0.183638	−	1.86451i
$300$	9.90912	−	1.23030i	0.572104	−	0.0710312i
$301$	−19.4370	−	5.89616i	−1.12033	−	0.339849i
$302$	16.1304	−	13.5836i	0.928198	−	0.781650i
$303$	16.2794	−	6.74313i	0.935224	−	0.387383i
$304$	−29.1228	+	4.36803i	−1.67031	+	0.250524i
$305$	−0.444703	−	0.184202i	−0.0254636	−	0.0105474i
$306$	7.67392	−	2.43450i	0.438689	−	0.139171i
$307$	14.7321	−	7.87447i	0.840805	−	0.449420i	0.00601105	−	0.999982i	$-0.498087\pi$
$307$	14.7321	−	7.87447i	0.840805	−	0.449420i	0.834794	+	0.550562i	$0.185587\pi$
$308$	2.25913	+	0.164810i	0.128726	+	0.00939092i
$309$	5.74280	−	4.71299i	0.326696	−	0.268113i
$310$	−0.377015	+	0.00477911i	−0.0214130	+	0.000271435i
$311$	0.480535	+	2.41581i	0.0272486	+	0.136988i	0.992015	−	0.126120i	$-0.0402524\pi$
$311$	0.480535	+	2.41581i	0.0272486	+	0.136988i	−0.964766	+	0.263108i	$0.915252\pi$
$312$	4.25645	−	16.2290i	0.240974	−	0.918784i
$313$	21.8174	+	4.33975i	1.23319	+	0.245297i	0.768312	−	0.640076i	$-0.221097\pi$
$313$	21.8174	+	4.33975i	1.23319	+	0.245297i	0.464881	+	0.885373i	$0.346097\pi$
$314$	−7.66454	+	5.26302i	−0.432535	+	0.297009i
$315$	−0.0713385	+	0.133465i	−0.00401947	+	0.00751990i
$316$	−11.2349	−	15.9251i	−0.632015	−	0.895856i
$317$	22.8651	−	2.25201i	1.28423	−	0.126486i	0.567230	−	0.823559i	$-0.308015\pi$
$317$	22.8651	−	2.25201i	1.28423	−	0.126486i	0.716999	+	0.697074i	$0.245515\pi$
$318$	−4.38408	+	2.41528i	−0.245847	+	0.135442i
$319$		−	6.52213i		−	0.365169i
$320$	0.394801	−	0.563468i	0.0220701	−	0.0314988i
$321$			10.4016i			0.580561i
$322$	−6.55814	−	11.9040i	−0.365471	−	0.663382i
$323$	41.7094	−	4.10801i	2.32077	−	0.228576i
$324$	−1.97083	−	0.340333i	−0.109491	−	0.0189074i
$325$	−13.9606	+	26.1185i	−0.774397	+	1.44879i
$326$	9.90290	+	14.4216i	0.548471	+	0.798739i
$327$	1.40201	+	0.278877i	0.0775314	+	0.0154219i
$328$	4.07828	+	29.7576i	0.225185	+	1.64309i
$329$	0.774764	+	3.89500i	0.0427141	+	0.214738i
$330$	0.000992228		0.0782749i	5.46204e−5		0.00430889i
$331$	15.2868	−	12.5455i	0.840236	−	0.689564i	−0.112405	−	0.993663i	$-0.535855\pi$
$331$	15.2868	−	12.5455i	0.840236	−	0.689564i	0.952641	+	0.304099i	$0.0983552\pi$
$332$	−11.1677	−	12.9253i	−0.612905	−	0.709368i
$333$	−0.0507447	+	0.0271236i	−0.00278079	+	0.00148637i
$334$	−4.54641	−	14.3310i	−0.248768	−	0.784157i
$335$	0.0268100	+	0.0111051i	0.00146479	+	0.000606735i
$336$	−2.38195	−	6.62336i	−0.129946	−	0.361334i
$337$	2.08553	−	0.863856i	0.113606	−	0.0470572i	−0.325156	−	0.945660i	$-0.605417\pi$
$337$	2.08553	−	0.863856i	0.113606	−	0.0470572i	0.438763	+	0.898603i	$0.355417\pi$
$338$	20.2113	+	24.0007i	1.09935	+	1.30546i
$339$	8.66341	+	2.62802i	0.470532	+	0.142734i
$340$	−0.601800	+	0.772421i	−0.0326372	+	0.0418904i
$341$	−0.195572	+	1.98568i	−0.0105908	+	0.107531i
$342$	−9.66883	−	3.86212i	−0.522831	−	0.208840i
$343$	10.6595	−	15.9531i	0.575560	−	0.861387i
$344$	19.1573	+	26.4369i	1.03289	+	1.42538i
$345$	0.390534	−	0.260947i	0.0210257	−	0.0140489i
$346$	−3.62672	+	5.57960i	−0.194974	+	0.299961i
$347$	5.98699	−	1.81613i	0.321398	−	0.0974951i	−0.125463	−	0.992098i	$-0.540042\pi$
$347$	5.98699	−	1.81613i	0.321398	−	0.0974951i	0.446861	+	0.894603i	$0.352542\pi$
$348$	−18.5214	+	8.22789i	−0.992854	+	0.441061i
$349$	−8.37695	+	10.2073i	−0.448408	+	0.546387i	−0.947330	−	0.320260i	$-0.896230\pi$
$349$	−8.37695	+	10.2073i	−0.448408	+	0.546387i	0.498922	+	0.866647i	$0.333730\pi$
$350$	1.37442	+	12.3480i	0.0734657	+	0.660030i
$351$	4.19446	−	4.19446i	0.223884	−	0.223884i
$352$	−2.73240	−	2.40629i	−0.145637	−	0.128255i
$353$	−5.45551	−	5.45551i	−0.290367	−	0.290367i	0.546858	−	0.837225i	$-0.315824\pi$
$353$	−5.45551	−	5.45551i	−0.290367	−	0.290367i	−0.837225	+	0.546858i	$0.815824\pi$
$354$	0.611993	−	0.765294i	0.0325270	−	0.0406749i
$355$	0.0971641	+	0.0797405i	0.00515693	+	0.00423219i
$356$	−25.7402	+	0.652681i	−1.36423	+	0.0345920i
$357$	2.90790	+	9.58605i	0.153902	+	0.507348i
$358$	4.73883	+	22.3400i	0.250455	+	1.18070i
$359$	−8.78377	−	13.1458i	−0.463590	−	0.693811i	0.523849	−	0.851811i	$-0.324495\pi$
$359$	−8.78377	−	13.1458i	−0.463590	−	0.693811i	−0.987439	+	0.158000i	$0.949495\pi$
$360$	0.221032	−	0.101564i	0.0116494	−	0.00535291i
$361$	−29.2687	−	19.5567i	−1.54046	−	1.02930i
$362$	8.34516	+	19.4461i	0.438612	+	1.02206i
$363$	−10.5348	−	1.03758i	−0.552932	−	0.0544591i
$364$	20.1245	+	5.55170i	1.05481	+	0.290988i
$365$	0.250375	−	0.825375i	0.0131052	−	0.0432021i
$366$	7.88628	+	0.675919i	0.412223	+	0.0353309i
$367$	12.2907	+	29.6723i	0.641568	+	1.54888i	0.824564	+	0.565768i	$0.191420\pi$
$367$	12.2907	+	29.6723i	0.641568	+	1.54888i	−0.182996	+	0.983114i	$0.558580\pi$
$368$	−3.17053	+	21.6144i	−0.165275	+	1.12673i
$369$	−4.06382	+	9.81092i	−0.211554	+	0.510736i
$370$	0.00322042	−	0.00621315i	0.000167422	−	0.000323006i
$371$	−2.93587	−	5.49263i	−0.152423	−	0.285163i
$372$	5.88562	−	1.94962i	0.305155	−	0.101083i
$373$	21.1153	+	25.7291i	1.09331	+	1.33220i	0.938898	+	0.344196i	$0.111848\pi$
$373$	21.1153	+	25.7291i	1.09331	+	1.33220i	0.154412	+	0.988006i	$0.450652\pi$
$374$	3.71019	+	3.61730i	0.191849	+	0.187046i
$375$	−0.842870	+	0.167657i	−0.0435256	+	0.00865778i
$376$	2.79289	−	5.73995i	0.144033	−	0.296015i
$377$	11.7269	−	58.9549i	0.603964	−	3.03633i
$378$	0.454514	−	2.44668i	0.0233777	−	0.125844i
$379$	6.89372	+	3.68477i	0.354107	+	0.189274i	0.638853	−	0.769329i	$-0.279409\pi$
$379$	6.89372	+	3.68477i	0.354107	+	0.189274i	−0.284746	+	0.958603i	$0.591909\pi$
$380$	1.23532	−	0.278449i	0.0633707	−	0.0142841i
$381$	−0.483585	−	4.90992i	−0.0247748	−	0.251543i
$382$	−20.0794	−	5.81413i	−1.02735	−	0.297477i
$383$	−38.3004			−1.95706			−0.978529	−	0.206110i	$-0.933920\pi$
$383$	−38.3004			−1.95706			−0.978529	+	0.206110i	$0.933920\pi$
$384$	−3.38632	+	10.7950i	−0.172807	+	0.550882i
$385$	−0.0974030			−0.00496411
$386$	10.8330	+	3.13678i	0.551387	+	0.159658i
$387$	1.13140	+	11.4873i	0.0575125	+	0.583934i
$388$	6.14425	+	27.2586i	0.311927	+	1.38385i
$389$	17.3457	+	9.27146i	0.879461	+	0.470081i	0.848351	−	0.529435i	$-0.177596\pi$
$389$	17.3457	+	9.27146i	0.879461	+	0.470081i	0.0311097	+	0.999516i	$0.490096\pi$
$390$	−0.131770	+	0.709328i	−0.00667245	+	0.0359182i
$391$	6.06550	−	30.4933i	0.306745	−	1.54211i
$392$	−10.4361	+	3.60439i	−0.527103	+	0.182049i
$393$	9.89326	−	1.96789i	0.499049	−	0.0992670i
$394$	13.3025	+	12.9694i	0.670168	+	0.653390i
$395$	0.531658	+	0.647827i	0.0267506	+	0.0325957i
$396$	−0.404775	−	1.22196i	−0.0203407	−	0.0614058i
$397$	−12.7827	−	23.9148i	−0.641547	−	1.20025i	−0.967021	−	0.254698i	$-0.918024\pi$
$397$	−12.7827	−	23.9148i	−0.641547	−	1.20025i	0.325474	−	0.945551i	$-0.394476\pi$
$398$	4.06956	−	7.85139i	0.203988	−	0.393555i
$399$	4.95762	−	11.9688i	0.248192	−	0.599187i
$400$	10.2392	−	17.1458i	0.511959	−	0.857288i
$401$	−1.11978	−	2.70339i	−0.0559191	−	0.135001i	0.893451	−	0.449161i	$-0.148277\pi$
$401$	−1.11978	−	2.70339i	−0.0559191	−	0.135001i	−0.949370	+	0.314160i	$0.898277\pi$
$402$	−0.475444	−	0.0407495i	−0.0237130	−	0.00203240i
$403$	−5.33809	+	17.5973i	−0.265909	+	0.876586i
$404$	9.37188	−	33.9723i	0.466268	−	1.69018i
$405$	0.0855877	+	0.00842966i	0.00425289	+	0.000418873i
$406$	−9.94478	−	23.1736i	−0.493551	−	1.15009i
$407$	−0.0307923	−	0.0205748i	−0.00152632	−	0.00101985i
$408$	5.59184	−	15.0995i	0.276837	−	0.747536i
$409$	6.14341	+	9.19426i	0.303772	+	0.454627i	0.951680	−	0.307092i	$-0.0993558\pi$
$409$	6.14341	+	9.19426i	0.303772	+	0.454627i	−0.647908	+	0.761719i	$0.724356\pi$
$410$	−0.268008	−	1.26346i	−0.0132360	−	0.0623976i
$411$	−1.55286	−	5.11908i	−0.0765968	−	0.252506i
$412$	−0.376632	−	14.8535i	−0.0185553	−	0.731779i
$413$	0.942503	+	0.773492i	0.0463775	+	0.0380611i
$414$	−4.82373	+	6.03205i	−0.237074	+	0.296459i
$415$	0.519386	+	0.519386i	0.0254957	+	0.0254957i
$416$	−20.3722	−	26.6638i	−0.998830	−	1.30730i
$417$	8.22489	−	8.22489i	0.402775	−	0.402775i
$418$	−0.741312	−	6.66009i	−0.0362588	−	0.325756i
$419$	12.1553	−	14.8113i	0.593827	−	0.723580i	−0.386207	−	0.922412i	$-0.626215\pi$
$419$	12.1553	−	14.8113i	0.593827	−	0.723580i	0.980034	+	0.198832i	$0.0637149\pi$
$420$	0.122877	+	0.276603i	0.00599579	+	0.0134969i
$421$	29.7227	−	9.01627i	1.44859	−	0.439426i	0.534583	−	0.845116i	$-0.320469\pi$
$421$	29.7227	−	9.01627i	1.44859	−	0.439426i	0.914011	+	0.405689i	$0.132969\pi$
$422$	−14.5094	+	22.3222i	−0.706306	+	1.08663i
$423$	1.87651	−	1.25384i	0.0912389	−	0.0609639i
$424$	−1.57832	+	9.88553i	−0.0766498	+	0.480084i
$425$	−15.7903	+	23.6319i	−0.765944	+	1.14632i
$426$	−1.91947	−	0.766715i	−0.0929988	−	0.0371475i
$427$	−0.965335	+	9.80121i	−0.0467158	+	0.474314i
$428$	16.4105	+	12.7855i	0.793229	+	0.618012i
$429$	3.65352	+	1.10828i	0.176393	+	0.0535084i
$430$	−0.904313	−	1.07386i	−0.0436099	−	0.0517861i
$431$	−25.7871	+	10.6814i	−1.24212	+	0.514503i	−0.904377	−	0.426735i	$-0.859664\pi$
$431$	−25.7871	+	10.6814i	−1.24212	+	0.514503i	−0.337743	+	0.941238i	$0.609664\pi$
$432$	−2.95946	+	2.69102i	−0.142387	+	0.129472i
$433$	24.3606	+	10.0905i	1.17070	+	0.484919i	0.881423	−	0.472328i	$-0.156586\pi$
$433$	24.3606	+	10.0905i	1.17070	+	0.484919i	0.289274	+	0.957246i	$0.406586\pi$
$434$	2.33283	+	7.35346i	0.111980	+	0.352977i
$435$	0.768586	−	0.410818i	0.0368509	−	0.0196972i
$436$	2.16332	−	1.86914i	0.103604	−	0.0895155i
$437$	−31.0810	+	25.5075i	−1.48681	+	1.22019i
$438$	0.179774	+	14.1820i	0.00858994	+	0.677644i
$439$	−3.65802	−	18.3901i	−0.174588	−	0.877711i	−0.964417	−	0.264385i	$-0.914831\pi$
$439$	−3.65802	−	18.3901i	−0.174588	−	0.877711i	0.789830	−	0.613326i	$-0.210169\pi$
$440$	0.124713	+	0.0946493i	0.00594545	+	0.00451223i
$441$	−3.82858	−	0.761552i	−0.182313	−	0.0362644i
$442$	27.0332	+	39.3685i	1.28584	+	1.87257i
$443$	−4.06900	+	7.61256i	−0.193324	+	0.361684i	−0.959843	−	0.280538i	$-0.909487\pi$
$443$	−4.06900	+	7.61256i	−0.193324	+	0.361684i	0.766519	+	0.642222i	$0.221987\pi$
$444$	−0.0195824	+	0.113399i	−0.000929338	+	0.00538169i
$445$	1.10188	−	0.108525i	0.0522340	−	0.00514460i
$446$	14.5810	+	26.4666i	0.690429	+	1.25323i
$447$		−	9.30913i		−	0.440307i
$448$	−13.3775	−	4.38341i	−0.632025	−	0.207096i
$449$			20.1600i			0.951407i	0.879606	+	0.475704i	$0.157807\pi$
$449$			20.1600i			0.951407i	−0.879606	+	0.475704i	$0.842193\pi$
$450$	6.18421	−	3.40701i	0.291527	−	0.160608i
$451$	−6.80194	+	0.669933i	−0.320291	+	0.0315459i
$452$	14.7952	−	10.4378i	0.695906	−	0.490953i
$453$	7.02921	−	13.1507i	0.330261	−	0.617875i
$454$	−0.0202571	+	0.0139099i	−0.000950711	+	0.000652825i
$455$	−0.880446	−	0.175132i	−0.0412760	−	0.00821030i
$456$	−17.9780	+	10.5071i	−0.841899	+	0.492040i
$457$	3.35927	+	16.8882i	0.157140	+	0.789997i	0.976298	+	0.216429i	$0.0694410\pi$
$457$	3.35927	+	16.8882i	0.157140	+	0.789997i	−0.819158	+	0.573568i	$0.805559\pi$
$458$	−29.0046	+	0.367667i	−1.35529	+	0.0171800i
$459$	4.40059	−	3.61147i	0.205402	−	0.168569i
$460$	0.0683490	−	0.936894i	0.00318679	−	0.0436829i
$461$	−1.89302	+	1.01184i	−0.0881665	+	0.0471260i	−0.514891	−	0.857256i	$-0.672168\pi$
$461$	−1.89302	+	1.01184i	−0.0881665	+	0.0471260i	0.426724	+	0.904382i	$0.359668\pi$
$462$	1.52671	−	0.484337i	0.0710289	−	0.0225334i
$463$	11.3321	+	4.69392i	0.526648	+	0.218145i	0.630135	−	0.776486i	$-0.283000\pi$
$463$	11.3321	+	4.69392i	0.526648	+	0.218145i	−0.103486	+	0.994631i	$0.533000\pi$
$464$	−9.78535	+	39.3347i	−0.454273	+	1.82607i
$465$	−0.246317	+	0.102028i	−0.0114227	+	0.00473142i
$466$	−0.588360	+	0.495467i	−0.0272553	+	0.0229521i
$467$	4.85230	+	1.47193i	0.224538	+	0.0681127i	0.400549	−	0.916275i	$-0.368819\pi$
$467$	4.85230	+	1.47193i	0.224538	+	0.0681127i	−0.176011	+	0.984388i	$0.556319\pi$
$468$	−1.46175	−	11.7733i	−0.0675696	−	0.544223i
$469$	0.0581977	−	0.590891i	0.00268732	−	0.0272848i
$470$	−0.101820	+	0.254907i	−0.00469661	+	0.0117580i
$471$	−3.65252	+	5.46638i	−0.168299	+	0.251878i
$472$	−0.455138	−	1.90622i	−0.0209494	−	0.0877410i
$473$	−6.17727	+	4.12752i	−0.284031	+	0.189784i
$474$	−11.5546	−	7.51046i	−0.530721	−	0.344967i
$475$	35.1736	−	10.6698i	1.61387	−	0.489563i
$476$	18.6981	+	7.19533i	0.857028	+	0.329797i
$477$	−2.24533	+	2.73594i	−0.102806	+	0.125270i
$478$	21.1120	−	2.34991i	0.965643	−	0.107482i
$479$	13.3156	−	13.3156i	0.608403	−	0.608403i	−0.334126	−	0.942529i	$-0.608441\pi$
$479$	13.3156	−	13.3156i	0.608403	−	0.608403i	0.942529	+	0.334126i	$0.108441\pi$
$480$	0.111454	−	0.473561i	0.00508716	−	0.0216150i
$481$	−0.241345	−	0.241345i	−0.0110044	−	0.0110044i
$482$	4.96558	+	3.97089i	0.226176	+	0.180869i
$483$	−7.42882	−	6.09668i	−0.338023	−	0.277408i
$484$	−14.5862	+	15.3452i	−0.663010	+	0.697508i
$485$	−0.348793	−	1.14982i	−0.0158379	−	0.0522104i
$486$	−1.38343	+	0.293458i	−0.0627537	+	0.0133115i
$487$	0.752490	+	1.12618i	0.0340986	+	0.0510322i	0.848127	−	0.529792i	$-0.177730\pi$
$487$	0.752490	+	1.12618i	0.0340986	+	0.0510322i	−0.814029	+	0.580825i	$0.802730\pi$
$488$	10.7601	−	11.6112i	0.487088	−	0.525616i
$489$	10.2856	+	6.87259i	0.465129	+	0.310789i
$490$	0.436295	−	0.187233i	0.0197098	−	0.00845833i
$491$	22.0450	+	2.17124i	0.994875	+	0.0979867i	0.582332	−	0.812951i	$-0.302140\pi$
$491$	22.0450	+	2.17124i	0.994875	+	0.0979867i	0.412543	+	0.910938i	$0.364640\pi$
$492$	10.4833	+	18.4709i	0.472626	+	0.832733i
$493$	16.7457	−	55.2033i	0.754190	−	2.48623i
$494$	5.27405	−	61.5349i	0.237291	−	2.76859i
$495$	0.0211827	+	0.0511397i	0.000952094	+	0.00229856i
$496$	4.15866	−	11.6821i	0.186729	−	0.524542i
$497$	0.984196	−	2.37606i	0.0441472	−	0.106581i
$498$	−10.7236	−	5.55829i	−0.480536	−	0.249073i
$499$	−20.4881	−	38.3306i	−0.917175	−	1.71591i	−0.662781	−	0.748813i	$-0.730624\pi$
$499$	−20.4881	−	38.3306i	−0.917175	−	1.71591i	−0.254394	−	0.967101i	$-0.581876\pi$
$500$	−0.771537	+	1.53587i	−0.0345042	+	0.0686860i
$501$	−6.74440	−	8.21807i	−0.301317	−	0.367156i
$502$	−11.1166	+	11.4020i	−0.496157	+	0.508897i
$503$	−12.5652	+	2.49938i	−0.560256	+	0.111442i	−0.467092	−	0.884209i	$-0.654698\pi$
$503$	−12.5652	+	2.49938i	−0.560256	+	0.111442i	−0.0931645	+	0.995651i	$0.529698\pi$
$504$	−3.30141	−	3.72452i	−0.147056	−	0.165903i
$505$	−0.295642	+	1.48629i	−0.0131559	+	0.0661390i
$506$	−4.88751	−	0.907942i	−0.217276	−	0.0403629i
$507$	19.5672	+	10.4589i	0.869012	+	0.464496i
$508$	−8.34073	−	5.27228i	−0.370060	−	0.233920i
$509$	0.572428	+	5.81196i	0.0253724	+	0.257611i	0.999500	+	0.0316126i	$0.0100643\pi$
$509$	0.572428	+	5.81196i	0.0253724	+	0.257611i	−0.974128	+	0.225998i	$0.927436\pi$
$510$	−0.192575	+	0.665067i	−0.00852735	+	0.0294496i
$511$	−17.6477			−0.780688
$512$	12.8688	+	18.6117i	0.568724	+	0.822529i
$513$	−7.36214			−0.325047
$514$	−8.78494	+	30.3392i	−0.387487	+	1.33821i
$515$	0.0626250	+	0.635843i	0.00275959	+	0.0280186i
$516$	19.5141	+	12.3351i	0.859061	+	0.543023i
$517$	1.28106	+	0.684740i	0.0563409	+	0.0301148i
$518$	−0.140779	−	0.0261522i	−0.00618548	−	0.00114906i
$519$	−0.918014	+	4.61517i	−0.0402964	+	0.202583i
$520$	0.957126	+	1.07979i	0.0419727	+	0.0473520i
$521$	−10.8440	+	2.15701i	−0.475084	+	0.0945002i	−0.426824	−	0.904335i	$-0.640368\pi$
$521$	−10.8440	+	2.15701i	−0.475084	+	0.0945002i	−0.0482603	+	0.998835i	$0.515368\pi$
$522$	−10.0041	+	10.2610i	−0.437869	+	0.449112i
$523$	−10.9479	−	13.3401i	−0.478720	−	0.583322i	0.476516	−	0.879166i	$-0.341899\pi$
$523$	−10.9479	−	13.3401i	−0.478720	−	0.583322i	−0.955236	+	0.295843i	$0.904399\pi$
$524$	9.05598	−	18.0274i	0.395612	−	0.787529i
$525$	4.14136	+	7.74794i	0.180744	+	0.338148i
$526$	5.34186	+	2.76881i	0.232916	+	0.120726i
$527$	−6.75361	+	16.3046i	−0.294192	+	0.710242i
$528$	−2.42541	−	0.863412i	−0.105553	−	0.0375752i
$529$	2.61260	+	6.30736i	0.113591	+	0.274233i
$530$	0.0367601	−	0.428898i	0.00159676	−	0.0186302i
$531$	0.201137	−	0.663060i	0.00872860	−	0.0287743i
$532$	−12.7891	−	22.5335i	−0.554477	−	0.976949i
$533$	−62.6887	−	6.17430i	−2.71535	−	0.267439i
$534$	−16.7313	+	7.18014i	−0.724036	+	0.310715i
$535$	−0.743797	−	0.496989i	−0.0321571	−	0.0214867i
$536$	−0.648701	+	0.700013i	−0.0280196	+	0.0302359i
$537$	8.97147	+	13.4268i	0.387148	+	0.579407i
$538$	−15.1873	+	3.22159i	−0.654773	+	0.138893i
$539$	−0.729328	−	2.40427i	−0.0314144	−	0.103559i
$540$	0.118503	−	0.124669i	0.00509955	−	0.00536490i
$541$	−11.5864	−	9.50874i	−0.498140	−	0.408813i	0.351491	−	0.936191i	$-0.385675\pi$
$541$	−11.5864	−	9.50874i	−0.498140	−	0.408813i	−0.849630	+	0.527379i	$0.823175\pi$
$542$	−17.8077	−	14.2405i	−0.764906	−	0.611682i
$543$	10.5806	+	10.5806i	0.454055	+	0.454055i
$544$	−16.9488	−	27.3823i	−0.726675	−	1.17401i
$545$	−0.0869301	+	0.0869301i	−0.00372368	+	0.00372368i
$546$	14.6711	−	1.63299i	0.627865	−	0.0698854i
$547$	9.82766	−	11.9750i	0.420200	−	0.512015i	−0.519287	−	0.854600i	$-0.673802\pi$
$547$	9.82766	−	11.9750i	0.420200	−	0.512015i	0.939487	+	0.342585i	$0.111302\pi$
$548$	−9.98506	−	3.84241i	−0.426541	−	0.164139i
$549$	5.35589	−	1.62469i	0.228584	−	0.0693401i
$550$	3.81023	+	2.47664i	0.162469	+	0.105604i
$551$	−62.0305	+	41.4475i	−2.64259	+	1.76572i
$552$	3.58740	+	15.0249i	0.152690	+	0.639501i
$553$	9.52652	−	14.2574i	0.405109	−	0.606288i
$554$	−1.77022	+	4.43176i	−0.0752096	+	0.188288i
$555$	0.000485033	−	0.00492462i	2.05885e−5	−	0.000209038i
$556$	−2.86634	−	23.0862i	−0.121560	−	0.979075i
$557$	−14.5611	−	4.41705i	−0.616972	−	0.187156i	−0.0336983	−	0.999432i	$-0.510729\pi$
$557$	−14.5611	−	4.41705i	−0.616972	−	0.187156i	−0.583274	+	0.812276i	$0.698229\pi$
$558$	3.35347	−	2.82401i	0.141964	−	0.119550i
$559$	−63.2590	+	26.2027i	−2.67557	+	1.10826i
$560$	0.587433	+	0.146137i	0.0248236	+	0.00617540i
$561$	3.38513	+	1.40217i	0.142920	+	0.0591996i
$562$	−4.42051	+	1.40238i	−0.186468	+	0.0591556i
$563$	−18.8511	+	10.0761i	−0.794479	+	0.424658i	−0.818109	−	0.575063i	$-0.804978\pi$
$563$	−18.8511	+	10.0761i	−0.794479	+	0.424658i	0.0236299	+	0.999721i	$0.492478\pi$
$564$	0.328415	−	4.50175i	0.0138288	−	0.189558i
$565$	−0.601862	+	0.493936i	−0.0253205	+	0.0207800i
$566$	10.0651	−	0.127588i	0.423069	−	0.00536291i
$567$	−0.343293	−	1.72585i	−0.0144170	−	0.0724790i
$568$	−3.56903	+	2.08589i	−0.149753	+	0.0875219i
$569$	19.0560	+	3.79047i	0.798868	+	0.158905i	0.577612	−	0.816311i	$-0.303984\pi$
$569$	19.0560	+	3.79047i	0.798868	+	0.158905i	0.221256	+	0.975216i	$0.428984\pi$
$570$	0.738150	−	0.506866i	0.0309177	−	0.0212303i
$571$	6.66366	−	12.4668i	0.278866	−	0.521721i	−0.703026	−	0.711164i	$-0.748168\pi$
$571$	6.66366	−	12.4668i	0.278866	−	0.521721i	0.981892	+	0.189443i	$0.0606683\pi$
$572$	6.23939	−	4.40181i	0.260882	−	0.184049i
$573$	−14.7103	+	1.44884i	−0.614533	+	0.0605262i
$574$	−23.1463	+	12.7518i	−0.966107	+	0.532248i
$575$		−	27.2667i		−	1.13710i
$576$	0.607838	+	7.97687i	0.0253266	+	0.332370i
$577$		−	8.61588i		−	0.358684i	−0.983787	−	0.179342i	$-0.942603\pi$
$577$		−	8.61588i		−	0.358684i	0.983787	−	0.179342i	$-0.0573968\pi$
$578$	10.5145	+	19.0854i	0.437346	+	0.793847i
$579$	7.93638	−	0.781665i	0.329825	−	0.0324849i
$580$	0.296597	−	1.71756i	0.0123155	−	0.0713178i
$581$	7.08458	−	13.2543i	0.293918	−	0.549881i
$582$	11.1845	+	16.2880i	0.463612	+	0.675159i
$583$	−2.23424	−	0.444418i	−0.0925327	−	0.0184059i
$584$	22.5958	+	17.1488i	0.935020	+	0.709622i
$585$	0.0995257	+	0.500349i	0.00411488	+	0.0206869i
$586$	−0.487773	−	38.4795i	−0.0201497	−	1.58957i
$587$	2.11026	−	1.73185i	0.0870998	−	0.0714809i	−0.589836	−	0.807523i	$-0.700808\pi$
$587$	2.11026	−	1.73185i	0.0870998	−	0.0714809i	0.676936	+	0.736042i	$0.263308\pi$
$588$	−5.90754	+	5.10420i	−0.243623	+	0.210494i
$589$	20.1282	−	10.7587i	0.829368	−	0.443306i
$590$	0.0254835	+	0.0803281i	0.00104914	+	0.00330706i
$591$	12.1370	+	5.02731i	0.499250	+	0.206796i
$592$	0.154838	+	0.170284i	0.00636381	+	0.00699863i
$593$	−21.5439	+	8.92376i	−0.884700	+	0.366455i	−0.778318	−	0.627870i	$-0.783927\pi$
$593$	−21.5439	+	8.92376i	−0.884700	+	0.366455i	−0.106382	+	0.994325i	$0.533927\pi$
$594$	−0.586314	−	0.696239i	−0.0240568	−	0.0285670i
$595$	−0.824418	−	0.250085i	−0.0337979	−	0.0102525i
$596$	−14.6869	−	11.4427i	−0.601598	−	0.468711i
$597$	0.612923	−	6.22311i	0.0250853	−	0.254695i
$598$	−42.5468	−	16.9949i	−1.73987	−	0.694972i
$599$	7.94569	−	11.8916i	0.324652	−	0.485876i	−0.632861	−	0.774265i	$-0.718120\pi$
$599$	7.94569	−	11.8916i	0.324652	−	0.485876i	0.957513	+	0.288389i	$0.0931197\pi$
$600$	2.22638	−	13.9446i	0.0908918	−	0.569286i
$601$	−8.33099	+	5.56659i	−0.339828	+	0.227066i	−0.713760	−	0.700390i	$-0.753009\pi$
$601$	−8.33099	+	5.56659i	−0.339828	+	0.227066i	0.373932	+	0.927456i	$0.378009\pi$
$602$	−15.6547	+	24.0843i	−0.638040	+	0.981604i
$603$	−0.322893	+	0.0979486i	−0.0131492	+	0.00398877i
$604$	−12.1075	−	27.2546i	−0.492647	−	1.10898i
$605$	0.577548	−	0.703744i	0.0234807	−	0.0286113i
$606$	−2.75666	−	24.7664i	−0.111982	−	1.00607i
$607$	4.60901	−	4.60901i	0.187074	−	0.187074i	−0.607356	−	0.794430i	$-0.707770\pi$
$607$	4.60901	−	4.60901i	0.187074	−	0.187074i	0.794430	+	0.607356i	$0.207770\pi$
$608$	−5.52152	+	41.2789i	−0.223927	+	1.67408i
$609$	−12.6087	−	12.6087i	−0.510929	−	0.510929i
$610$	−0.425141	+	0.531636i	−0.0172134	+	0.0215253i
$611$	10.3486	+	8.49286i	0.418659	+	0.343584i
$612$	−0.288605	−	11.3819i	−0.0116662	−	0.460087i
$613$	3.38209	+	11.1493i	0.136601	+	0.450314i	0.998375	−	0.0569781i	$-0.0181465\pi$
$613$	3.38209	+	11.1493i	0.136601	+	0.450314i	−0.861774	+	0.507292i	$0.830647\pi$
$614$	−4.90209	−	23.1096i	−0.197832	−	0.932627i
$615$	−0.507389	−	0.759362i	−0.0204599	−	0.0306204i
$616$	1.11248	−	3.00401i	0.0448232	−	0.121035i
$617$	1.12637	+	0.752615i	0.0453459	+	0.0302991i	0.578037	−	0.816011i	$-0.303819\pi$
$617$	1.12637	+	0.752615i	0.0453459	+	0.0302991i	−0.532691	+	0.846310i	$0.678819\pi$
$618$	−4.14333	−	9.65489i	−0.166669	−	0.388377i
$619$	−21.5238	−	2.11991i	−0.865114	−	0.0852063i	−0.344283	−	0.938866i	$-0.611878\pi$
$619$	−21.5238	−	2.11991i	−0.865114	−	0.0852063i	−0.520831	+	0.853660i	$0.674378\pi$
$620$	−0.141802	+	0.514022i	−0.00569492	+	0.0206436i
$621$	−1.58536	+	5.22625i	−0.0636185	+	0.209722i
$622$	3.47068	+	0.297466i	0.139162	+	0.0119273i
$623$	−8.66944	−	20.9299i	−0.347334	−	0.838538i
$624$	−20.3714	−	12.1655i	−0.815509	−	0.487009i
$625$	−9.52465	+	22.9945i	−0.380986	+	0.919782i
$626$	14.4768	−	27.9301i	0.578609	−	1.11631i
$627$	−2.23370	−	4.17897i	−0.0892056	−	0.166892i
$628$	4.13459	+	12.4818i	0.164988	+	0.498076i
$629$	−0.207800	−	0.253205i	−0.00828552	−	0.0100959i
$630$	0.153240	+	0.149404i	0.00610524	+	0.00595240i
$631$	−18.5914	+	3.69806i	−0.740112	+	0.147217i	−0.550727	−	0.834685i	$-0.685649\pi$
$631$	−18.5914	+	3.69806i	−0.740112	+	0.147217i	−0.189385	+	0.981903i	$0.560649\pi$
$632$	−26.0520	+	8.99776i	−1.03629	+	0.357912i
$633$	−3.67269	+	18.4639i	−0.145976	+	0.733872i
$634$	5.93453	−	31.9460i	0.235690	−	1.26874i
$635$	0.374204	+	0.200016i	0.0148498	+	0.00793740i
$636$	1.55652	+	6.90541i	0.0617200	+	0.273817i
$637$	−2.26964	−	23.0441i	−0.0899265	−	0.913039i
$638$	−8.85974	−	2.56540i	−0.350761	−	0.101565i
$639$	−1.46155			−0.0578179
$640$	−0.610132	−	0.757936i	−0.0241176	−	0.0299601i
$641$	16.0187			0.632700			0.316350	−	0.948643i	$-0.397543\pi$
$641$	16.0187			0.632700			0.316350	+	0.948643i	$0.397543\pi$
$642$	14.1297	+	4.09134i	0.557653	+	0.161472i
$643$	3.78636	+	38.4435i	0.149319	+	1.51606i	0.719470	+	0.694524i	$0.244385\pi$
$643$	3.78636	+	38.4435i	0.149319	+	1.51606i	−0.570150	+	0.821540i	$0.693115\pi$
$644$	−18.7501	+	4.22637i	−0.738856	+	0.166542i
$645$	−0.875494	−	0.467961i	−0.0344725	−	0.0184260i
$646$	10.8255	−	58.2744i	0.425924	−	2.29277i
$647$	4.71628	−	23.7104i	0.185416	−	0.932150i	−0.770260	−	0.637730i	$-0.779874\pi$
$647$	4.71628	−	23.7104i	0.185416	−	0.932150i	0.955676	−	0.294420i	$-0.0951265\pi$
$648$	−1.23751	+	2.54334i	−0.0486142	+	0.0999117i
$649$	0.437398	−	0.0870038i	0.0171694	−	0.00341520i
$650$	29.9885	+	29.2377i	1.17624	+	1.14680i
$651$	3.46066	+	4.21682i	0.135634	+	0.165270i
$652$	23.4857	−	7.77966i	0.919770	−	0.304675i
$653$	17.5225	+	32.7823i	0.685709	+	1.28287i	0.948119	+	0.317914i	$0.102982\pi$
$653$	17.5225	+	32.7823i	0.685709	+	1.28287i	−0.262411	+	0.964956i	$0.584518\pi$
$654$	0.930295	−	1.79482i	0.0363774	−	0.0701829i
$655$	−0.331981	+	0.801472i	−0.0129716	+	0.0313161i
$656$	42.0273	+	6.16483i	1.64089	+	0.240696i
$657$	3.83794	+	9.26560i	0.149732	+	0.361486i
$658$	5.59576	+	0.479603i	0.218146	+	0.0186969i
$659$	−11.9987	+	39.5544i	−0.467403	+	1.54082i	0.333927	+	0.942599i	$0.391626\pi$
$659$	−11.9987	+	39.5544i	−0.467403	+	1.54082i	−0.801330	+	0.598222i	$0.795874\pi$
$660$	0.106720	+	0.0294407i	0.00415407	+	0.00114598i
$661$	21.6823	+	2.13552i	0.843343	+	0.0830621i	0.510455	−	0.859904i	$-0.329477\pi$
$661$	21.6823	+	2.13552i	0.843343	+	0.0830621i	0.332888	+	0.942966i	$0.391977\pi$
$662$	−11.0291	−	25.7004i	−0.428659	−	0.998872i
$663$	28.0778	+	18.7610i	1.09045	+	0.728617i
$664$	−21.9506	+	10.0863i	−0.851847	+	0.391423i
$665$	0.618986	+	0.926378i	0.0240032	+	0.0359234i
$666$	0.0168852	+	0.0796011i	0.000654290	+	0.00308448i
$667$	16.0651	+	52.9596i	0.622044	+	2.05060i
$668$	−21.2557	+	0.538969i	−0.822407	+	0.0208533i
$669$	16.5168	+	13.5550i	0.638577	+	0.524066i
$670$	0.0256307	−	0.0320510i	0.000990199	−	0.00123824i
$671$	2.54722	+	2.54722i	0.0983343	+	0.0983343i
$672$	−9.93417	+	0.630448i	−0.383219	+	0.0243201i
$673$	21.1933	−	21.1933i	0.816940	−	0.816940i	−0.168723	−	0.985663i	$-0.553964\pi$
$673$	21.1933	−	21.1933i	0.816940	−	0.816940i	0.985663	+	0.168723i	$0.0539644\pi$
$674$	−0.353154	−	3.17280i	−0.0136030	−	0.122212i
$675$	3.16727	−	3.85933i	0.121908	−	0.148546i
$676$	40.5527	−	18.0150i	1.55972	−	0.692884i
$677$	6.94903	−	2.10797i	0.267073	−	0.0810157i	−0.153908	−	0.988085i	$-0.549186\pi$
$677$	6.94903	−	2.10797i	0.267073	−	0.0810157i	0.420981	+	0.907069i	$0.361686\pi$
$678$	6.97758	−	10.7348i	0.267972	−	0.412267i
$679$	−20.4414	+	13.6585i	−0.784470	+	0.524166i
$680$	0.812555	+	1.12132i	0.0311601	+	0.0430005i
$681$	−0.00965346	+	0.0144474i	−0.000369921	+	0.000553626i
$682$	2.62045	+	1.04671i	0.100342	+	0.0400806i
$683$	−0.208383	+	2.11575i	−0.00797355	+	0.0809568i	−0.998348	−	0.0574576i	$-0.981701\pi$
$683$	−0.208383	+	2.11575i	−0.00797355	+	0.0809568i	0.990374	+	0.138414i	$0.0442006\pi$
$684$	−9.04947	+	11.6151i	−0.346015	+	0.444116i
$685$	0.440251	+	0.133549i	0.0168211	+	0.00510263i
$686$	−17.4781	−	20.7550i	−0.667317	−	0.792429i
$687$	−18.9497	+	7.84921i	−0.722975	+	0.299466i
$688$	43.4475	−	15.6249i	1.65642	−	0.595695i
$689$	−19.3967	−	8.03437i	−0.738955	−	0.306085i
$690$	−0.200861	−	0.633147i	−0.00764666	−	0.0241035i
$691$	6.06008	−	3.23918i	0.230536	−	0.123224i	−0.352085	−	0.935968i	$-0.614527\pi$
$691$	6.06008	−	3.23918i	0.230536	−	0.123224i	0.582621	+	0.812744i	$0.302027\pi$
$692$	6.15287	+	7.12126i	0.233897	+	0.270710i
$693$	0.875487	−	0.718494i	0.0332570	−	0.0272933i
$694$	−0.112148	−	8.84715i	−0.00425709	−	0.335833i
$695$	0.195159	+	0.981131i	0.00740280	+	0.0372164i
$696$	3.89168	+	28.3961i	0.147514	+	1.07635i
$697$	−59.2917	−	11.7938i	−2.24583	−	0.446724i
$698$	10.5708	+	15.3943i	0.400111	+	0.582683i
$699$	−0.256393	+	0.479678i	−0.00969768	+	0.0181431i
$700$	17.3143	+	2.98993i	0.654421	+	0.113009i
$701$	−16.7185	+	1.64662i	−0.631448	+	0.0621922i	−0.408678	−	0.912679i	$-0.634010\pi$
$701$	−16.7185	+	1.64662i	−0.631448	+	0.0621922i	−0.222770	+	0.974871i	$0.571510\pi$
$702$	−4.04797	−	7.34766i	−0.152781	−	0.277319i
$703$			0.423609i			0.0159767i
$704$	−4.34349	+	2.76524i	−0.163701	+	0.104219i
$705$			0.194094i			0.00731000i
$706$	−9.55669	+	5.26497i	−0.359671	+	0.198150i
$707$	30.8571	−	3.03916i	1.16050	−	0.114299i
$708$	−0.798865	−	1.13236i	−0.0300232	−	0.0425566i
$709$	−3.63600	+	6.80248i	−0.136553	+	0.255473i	−0.940898	−	0.338690i	$-0.890016\pi$
$709$	−3.63600	+	6.80248i	−0.136553	+	0.255473i	0.804345	+	0.594162i	$0.202516\pi$
$710$	0.146539	−	0.100624i	0.00549950	−	0.00377635i
$711$	−9.55740	−	1.90109i	−0.358431	−	0.0712963i
$712$	−9.23799	+	35.2226i	−0.346208	+	1.32002i
$713$	−3.30302	−	16.6054i	−0.123699	−	0.621877i
$714$	14.1656	−	0.179566i	0.530134	−	0.00672009i
$715$	−0.253816	+	0.208302i	−0.00949219	+	0.00779004i
$716$	32.2108	+	2.34987i	1.20378	+	0.0878187i
$717$	13.2470	−	7.08069i	0.494720	−	0.264433i
$718$	−21.3125	+	6.76123i	−0.795374	+	0.252327i
$719$	23.0861	+	9.56258i	0.860967	+	0.356624i	0.769086	−	0.639146i	$-0.220712\pi$
$719$	23.0861	+	9.56258i	0.860967	+	0.356624i	0.0918813	+	0.995770i	$0.470712\pi$
$720$	−0.0510258	−	0.340202i	−0.00190162	−	0.0126786i
$721$	12.0777	−	5.00273i	0.449796	−	0.186311i
$722$	−38.0786	+	32.0666i	−1.41714	+	1.19339i
$723$	4.30224	+	1.30507i	0.160002	+	0.0485361i
$724$	29.6983	−	3.68728i	1.10373	−	0.137037i
$725$	4.95888	−	50.3484i	0.184168	−	1.86989i
$726$	−5.55319	+	13.9024i	−0.206098	+	0.515968i
$727$	20.8797	−	31.2487i	0.774385	−	1.15895i	−0.209088	−	0.977897i	$-0.567050\pi$
$727$	20.8797	−	31.2487i	0.774385	−	1.15895i	0.983473	−	0.181053i	$-0.0579504\pi$
$728$	15.4572	−	25.1536i	0.572882	−	0.932255i
$729$	−0.831470	+	0.555570i	−0.0307952	+	0.0205767i
$730$	−1.02272	−	0.664763i	−0.0378525	−	0.0246040i
$731$	−62.8819	+	19.0750i	−2.32577	+	0.705515i
$732$	4.02015	−	10.4470i	0.148589	−	0.386131i
$733$	−7.47788	+	9.11183i	−0.276202	+	0.336553i	−0.892573	−	0.450903i	$-0.851102\pi$
$733$	−7.47788	+	9.11183i	−0.276202	+	0.336553i	0.616371	+	0.787456i	$0.288602\pi$
$734$	45.1416	−	5.02456i	1.66621	−	0.185460i
$735$	0.237387	−	0.237387i	0.00875614	−	0.00875614i
$736$	28.1141	+	12.8086i	1.03630	+	0.472132i
$737$	−0.153566	−	0.153566i	−0.00565666	−	0.00565666i
$738$	11.7288	+	9.37935i	0.431744	+	0.345259i
$739$	12.3966	+	10.1736i	0.456016	+	0.374243i	0.834177	−	0.551497i	$-0.185943\pi$
$739$	12.3966	+	10.1736i	0.456016	+	0.374243i	−0.378161	+	0.925740i	$0.623443\pi$
$740$	−0.00717331	−	0.00681852i	−0.000263696	−	0.000250654i
$741$	−12.6771	−	41.7908i	−0.465705	−	1.53522i
$742$	−8.61605	+	1.82767i	−0.316305	+	0.0670957i
$743$	29.1093	+	43.5652i	1.06792	+	1.59825i	0.763608	+	0.645680i	$0.223426\pi$
$743$	29.1093	+	43.5652i	1.06792	+	1.59825i	0.304310	+	0.952573i	$0.401574\pi$
$744$	−0.333348	−	8.76196i	−0.0122211	−	0.321229i
$745$	0.665677	+	0.444791i	0.0243885	+	0.0162959i
$746$	43.2562	−	18.5631i	1.58372	−	0.679643i
$747$	−8.49966	−	0.837143i	−0.310986	−	0.0306295i
$748$	6.37315	−	3.61714i	0.233025	−	0.132256i
$749$	−5.31317	+	17.5152i	−0.194139	+	0.639991i
$750$	−0.103785	+	1.21091i	−0.00378969	+	0.0442162i
$751$	4.93946	+	11.9249i	0.180244	+	0.435147i	0.988017	−	0.154347i	$-0.0493274\pi$
$751$	4.93946	+	11.9249i	0.180244	+	0.435147i	−0.807773	+	0.589494i	$0.799327\pi$
$752$	−6.69866	−	6.05164i	−0.244275	−	0.220681i
$753$	−4.30910	+	10.4031i	−0.157032	+	0.379109i
$754$	−75.4725	−	39.1191i	−2.74855	−	1.42463i
$755$	0.604526	+	1.13099i	0.0220009	+	0.0411609i
$756$	−3.14482	−	1.57979i	−0.114376	−	0.0574564i
$757$	−19.3902	−	23.6270i	−0.704748	−	0.858738i	0.290422	−	0.956899i	$-0.406204\pi$
$757$	−19.3902	−	23.6270i	−0.704748	−	0.858738i	−0.995171	+	0.0981604i	$0.968704\pi$
$758$	7.71700	−	7.91516i	0.280294	−	0.287491i
$759$	−3.44758	+	0.685765i	−0.125139	+	0.0248917i
$760$	0.107651	−	1.78760i	0.00390491	−	0.0648432i
$761$	3.05804	−	15.3738i	0.110854	−	0.557301i	−0.884942	−	0.465701i	$-0.845802\pi$
$761$	3.05804	−	15.3738i	0.110854	−	0.557301i	0.995796	−	0.0915994i	$-0.0291979\pi$
$762$	−6.85991	−	1.27435i	−0.248508	−	0.0461648i
$763$	2.21838	+	1.18575i	0.0803109	+	0.0429271i
$764$	−15.7960	+	24.9892i	−0.571479	+	0.904077i
$765$	0.0479883	+	0.487233i	0.00173502	+	0.0176160i
$766$	−15.0650	+	52.0277i	−0.544320	+	1.87984i
$767$	4.11017			0.148410
$768$	13.3322	+	8.84612i	0.481083	+	0.319207i
$769$	4.74151			0.170983			0.0854916	−	0.996339i	$-0.472754\pi$
$769$	4.74151			0.170983			0.0854916	+	0.996339i	$0.472754\pi$
$770$	−0.0383123	+	0.132313i	−0.00138068	+	0.00476825i
$771$	2.18915	+	22.2268i	0.0788402	+	0.800478i
$772$	8.52209	−	13.4819i	0.306717	−	0.485225i
$773$	24.2602	+	12.9674i	0.872579	+	0.466403i	0.845963	−	0.533242i	$-0.179027\pi$
$773$	24.2602	+	12.9674i	0.872579	+	0.466403i	0.0266168	+	0.999646i	$0.491527\pi$
$774$	16.0496	+	2.98149i	0.576890	+	0.107168i
$775$	−3.01949	+	15.1800i	−0.108463	+	0.545282i
$776$	39.4452	+	2.37542i	1.41600	+	0.0852728i
$777$	−0.0993035	+	0.0197527i	−0.00356249	+	0.000708624i
$778$	19.4172	−	19.9158i	0.696139	−	0.714015i
$779$	49.5972	+	60.4344i	1.77700	+	2.16529i
$780$	0.911730	+	0.458004i	0.0326452	+	0.0163992i
$781$	−0.443439	−	0.829616i	−0.0158675	−	0.0296860i
$782$	−39.0367	−	20.2336i	−1.39595	−	0.723553i
$783$	−3.87788	+	9.36203i	−0.138584	+	0.334572i
$784$	0.791340	+	15.5943i	0.0282621	+	0.556938i
$785$	−0.216372	−	0.522368i	−0.00772265	−	0.0186441i
$786$	1.21819	−	14.2132i	0.0434512	−	0.506967i
$787$	1.29929	−	4.28320i	0.0463148	−	0.152679i	−0.930733	−	0.365699i	$-0.880830\pi$
$787$	1.29929	−	4.28320i	0.0463148	−	0.152679i	0.977048	+	0.213020i	$0.0683299\pi$
$788$	22.8502	−	12.9689i	0.814005	−	0.461996i
$789$	4.23403	+	0.417015i	0.150735	+	0.0148461i
$790$	1.08914	−	0.467396i	0.0387498	−	0.0166292i
$791$	13.2458	+	8.85059i	0.470968	+	0.314691i
$792$	−1.81914	+	0.0692089i	−0.0646403	+	0.00245923i
$793$	18.4449	+	27.6048i	0.654999	+	0.980275i
$794$	−37.5141	+	7.95762i	−1.33133	+	0.282405i
$795$	−0.0883594	−	0.291282i	−0.00313379	−	0.0103307i
$796$	−9.06472	−	8.61639i	−0.321290	−	0.305400i
$797$	12.1424	+	9.96500i	0.430105	+	0.352978i	0.824402	−	0.566005i	$-0.191512\pi$
$797$	12.1424	+	9.96500i	0.430105	+	0.352978i	−0.394297	+	0.918983i	$0.629012\pi$
$798$	−14.3085	−	11.4423i	−0.506515	−	0.405052i
$799$	9.08478	+	9.08478i	0.321397	+	0.321397i
$800$	−19.2636	−	20.6531i	−0.681069	−	0.730197i
$801$	−9.10346	+	9.10346i	−0.321655	+	0.321655i
$802$	−4.11277	+	0.457778i	−0.145227	+	0.0161647i
$803$	−4.09498	+	4.98975i	−0.144509	+	0.176084i
$804$	−0.242365	+	0.629821i	−0.00854755	+	0.0222121i
$805$	0.790910	−	0.239920i	0.0278759	−	0.00845607i
$806$	21.8048	+	14.1730i	0.768040	+	0.499224i
$807$	−9.12790	+	6.09907i	−0.321317	+	0.214697i
$808$	−42.4621	−	26.0935i	−1.49381	−	0.917965i
$809$	−21.6126	+	32.3455i	−0.759857	+	1.13721i	0.226727	+	0.973958i	$0.427197\pi$
$809$	−21.6126	+	32.3455i	−0.759857	+	1.13721i	−0.986585	+	0.163249i	$0.947803\pi$
$810$	0.0451159	−	0.112948i	0.00158521	−	0.00396858i
$811$	3.56544	−	36.2005i	0.125199	−	1.27117i	−0.703183	−	0.711009i	$-0.748239\pi$
$811$	3.56544	−	36.2005i	0.125199	−	1.27117i	0.828383	−	0.560162i	$-0.189261\pi$
$812$	−35.3910	+	4.39407i	−1.24198	+	0.154202i
$813$	−15.4288	−	4.68028i	−0.541112	−	0.164144i
$814$	−0.0400608	+	0.0337358i	−0.00140413	+	0.00118244i
$815$	−0.982889	+	0.407126i	−0.0344291	+	0.0142610i
$816$	−18.3119	−	13.5352i	−0.641043	−	0.473828i
$817$	78.5118	+	32.5207i	2.74678	+	1.13775i
$818$	14.9060	−	4.72883i	0.521177	−	0.165340i
$819$	9.20557	−	4.92048i	0.321669	−	0.171936i
$820$	−1.82171	−	0.132899i	−0.0636169	−	0.00464103i
$821$	26.9618	−	22.1270i	0.940973	−	0.772237i	−0.0328697	−	0.999460i	$-0.510465\pi$
$821$	26.9618	−	22.1270i	0.940973	−	0.772237i	0.973843	+	0.227223i	$0.0729646\pi$
$822$	−7.56463	+	0.0958907i	−0.263847	+	0.00334457i
$823$	5.15953	+	25.9387i	0.179850	+	0.904166i	0.960304	+	0.278954i	$0.0899877\pi$
$823$	5.15953	+	25.9387i	0.179850	+	0.904166i	−0.780455	+	0.625212i	$0.785012\pi$
$824$	−20.3253	−	5.33082i	−0.708066	−	0.185708i
$825$	3.15163	+	0.626899i	0.109726	+	0.0218258i
$826$	1.42144	−	0.976064i	0.0494584	−	0.0339616i
$827$	20.0707	−	37.5497i	0.697928	−	1.30573i	−0.243953	−	0.969787i	$-0.578444\pi$
$827$	20.0707	−	37.5497i	0.697928	−	1.30573i	0.941882	−	0.335945i	$-0.109056\pi$
$828$	6.29666	+	8.92526i	0.218824	+	0.310174i
$829$	42.0439	−	4.14096i	1.46024	−	0.143822i	0.663517	−	0.748161i	$-0.269063\pi$
$829$	42.0439	−	4.14096i	1.46024	−	0.143822i	0.796727	+	0.604339i	$0.206563\pi$
$830$	0.909836	−	0.501247i	0.0315809	−	0.0173985i
$831$			3.37448i			0.117059i
$832$	−44.2336	+	17.1860i	−1.53353	+	0.595817i
$833$		−	22.2223i		−	0.769957i
$834$	−7.93763	−	14.4080i	−0.274858	−	0.498907i
$835$	0.909905	−	0.0896179i	0.0314886	−	0.00310135i
$836$	−9.33874	−	1.61266i	−0.322987	−	0.0557750i
$837$	1.46136	−	2.73401i	0.0505120	−	0.0945013i
$838$	−15.3387	−	22.3378i	−0.529867	−	0.771647i
$839$	3.74410	+	0.744748i	0.129261	+	0.0257116i	0.259297	−	0.965798i	$-0.416509\pi$
$839$	3.74410	+	0.744748i	0.129261	+	0.0257116i	−0.130036	+	0.991509i	$0.541509\pi$
$840$	0.424074	−	0.0581193i	0.0146319	−	0.00200531i
$841$	14.3753	+	72.2697i	0.495701	+	2.49206i
$842$	−0.556765	−	43.9221i	−0.0191874	−	1.51366i
$843$	−2.53493	+	2.08036i	−0.0873077	+	0.0716515i
$844$	24.6157	+	28.4899i	0.847308	+	0.980664i
$845$	−1.68282	+	0.899486i	−0.0578907	+	0.0309432i
$846$	−0.965134	−	3.04226i	−0.0331820	−	0.104595i
$847$	−17.2094	−	7.12837i	−0.591323	−	0.244934i
$848$	12.8078	+	6.03236i	0.439822	+	0.207152i
$849$	6.57589	−	2.72382i	0.225684	−	0.0934814i
$850$	25.8910	+	30.7451i	0.888052	+	1.05455i
$851$	0.300712	+	0.0912201i	0.0103083	+	0.00312698i
$852$	−1.79652	+	2.30586i	−0.0615477	+	0.0789975i
$853$	1.01208	−	10.2758i	0.0346528	−	0.351836i	−0.962186	−	0.272392i	$-0.912185\pi$
$853$	1.01208	−	10.2758i	0.0346528	−	0.351836i	0.996839	−	0.0794444i	$-0.0253146\pi$
$854$	12.9344	+	5.16651i	0.442606	+	0.176794i
$855$	0.351764	−	0.526452i	0.0120301	−	0.0180043i
$856$	23.8229	−	17.2631i	0.814250	−	0.590042i
$857$	34.5880	−	23.1109i	1.18150	−	0.789455i	0.199793	−	0.979838i	$-0.435973\pi$
$857$	34.5880	−	23.1109i	1.18150	−	0.789455i	0.981710	+	0.190383i	$0.0609731\pi$
$858$	2.94257	−	4.52705i	0.100458	−	0.154551i
$859$	−54.4939	+	16.5305i	−1.85931	+	0.564015i	−0.860827	+	0.508898i	$0.830053\pi$
$859$	−54.4939	+	16.5305i	−1.85931	+	0.564015i	−0.998480	+	0.0551168i	$0.982447\pi$
$860$	−1.81444	+	0.806041i	−0.0618720	+	0.0274858i
$861$	−11.8545	+	14.4447i	−0.404000	+	0.492275i
$862$	4.36665	+	39.2309i	0.148729	+	1.33621i
$863$	−29.3008	+	29.3008i	−0.997411	+	0.997411i	−0.999997	−	0.00258520i	$-0.999177\pi$
$863$	−29.3008	+	29.3008i	−0.997411	+	0.997411i	0.00258520	+	0.999997i	$0.499177\pi$
$864$	2.49144	+	5.07865i	0.0847606	+	0.172779i
$865$	−0.286158	−	0.286158i	−0.00972968	−	0.00972968i
$866$	23.2890	−	29.1228i	0.791394	−	0.989634i
$867$	11.9105	+	9.77467i	0.404501	+	0.331965i
$868$	10.9066	−	0.276553i	0.370195	−	0.00938684i
$869$	−1.82064	−	6.00186i	−0.0617611	−	0.203599i
$870$	−0.255746	−	1.20565i	−0.00867060	−	0.0408753i
$871$	−1.11200	−	1.66422i	−0.0376786	−	0.0563901i
$872$	−1.68815	−	3.67388i	−0.0571679	−	0.124413i
$873$	11.6167	+	7.76201i	0.393165	+	0.262704i
$874$	22.4244	+	52.2539i	0.758516	+	1.76751i
$875$	−1.50494	−	0.148224i	−0.0508763	−	0.00501088i
$876$	19.3358	+	5.33413i	0.653295	+	0.180223i
$877$	3.69610	−	12.1844i	0.124808	−	0.411438i	−0.872162	−	0.489217i	$-0.837283\pi$
$877$	3.69610	−	12.1844i	0.124808	−	0.411438i	0.996971	+	0.0777785i	$0.0247827\pi$
$878$	−26.4202	−	2.26443i	−0.891638	−	0.0764207i
$879$	−10.4133	−	25.1399i	−0.351232	−	0.847949i
$880$	0.177627	−	0.132182i	0.00598781	−	0.00445587i
$881$	−3.54104	+	8.54883i	−0.119301	+	0.288017i	−0.972237	−	0.233997i	$-0.924819\pi$
$881$	−3.54104	+	8.54883i	−0.119301	+	0.288017i	0.852937	+	0.522015i	$0.174819\pi$
$882$	−2.54043	+	4.90124i	−0.0855406	+	0.165033i
$883$	−26.9861	−	50.4874i	−0.908154	−	1.69904i	−0.690938	−	0.722914i	$-0.742802\pi$
$883$	−26.9861	−	50.4874i	−0.908154	−	1.69904i	−0.217217	−	0.976123i	$-0.569698\pi$
$884$	64.1119	−	21.2371i	2.15632	−	0.714282i
$885$	0.0378037	+	0.0460639i	0.00127076	+	0.00154842i
$886$	8.74050	+	8.52169i	0.293643	+	0.286292i
$887$	−37.9759	+	7.55388i	−1.27511	+	0.253634i	−0.785802	−	0.618479i	$-0.787749\pi$
$887$	−37.9759	+	7.55388i	−1.27511	+	0.253634i	−0.489304	+	0.872113i	$0.662749\pi$
$888$	0.146341	+	0.0712052i	0.00491087	+	0.00238949i
$889$	1.69370	−	8.51480i	0.0568048	−	0.285577i
$890$	0.285988	−	1.53949i	0.00958634	−	0.0516039i
$891$	−0.567629	−	0.303404i	−0.0190163	−	0.0101644i
$892$	41.6878	−	9.39667i	1.39581	−	0.314624i
$893$	−1.62858	−	16.5353i	−0.0544985	−	0.553333i
$894$	−12.6456	−	3.66164i	−0.422934	−	0.122463i
$895$	−1.38878			−0.0464217
$896$	−11.2163	+	16.4479i	−0.374711	+	0.549487i
$897$	−32.3964			−1.08168
$898$	27.3855	+	7.92968i	0.913868	+	0.264617i
$899$	−3.07912	−	31.2629i	−0.102695	−	1.04268i
$900$	−2.19564	−	9.74082i	−0.0731879	−	0.324694i
$901$	−17.7695	−	9.49802i	−0.591989	−	0.316425i
$902$	−1.76542	+	9.50335i	−0.0587819	+	0.316427i
$903$	−3.96260	+	19.9214i	−0.131867	+	0.662941i
$904$	−8.35935	−	24.2035i	−0.278028	−	0.804997i
$905$	−1.26213	+	0.251054i	−0.0419547	+	0.00834532i
$906$	−15.0993	−	14.7213i	−0.501640	−	0.489081i
$907$	25.1449	+	30.6391i	0.834922	+	1.01736i	0.999520	+	0.0309945i	$0.00986742\pi$
$907$	25.1449	+	30.6391i	0.834922	+	1.01736i	−0.164598	+	0.986361i	$0.552633\pi$
$908$	0.0109276	+	0.0329887i	0.000362644	+	0.00109477i
$909$	−8.30632	−	15.5400i	−0.275503	−	0.515430i
$910$	−0.584214	+	1.12712i	−0.0193665	+	0.0373638i
$911$	3.71914	−	8.97880i	0.123221	−	0.297481i	−0.850217	−	0.526432i	$-0.823530\pi$
$911$	3.71914	−	8.97880i	0.123221	−	0.297481i	0.973438	+	0.228951i	$0.0735295\pi$
$912$	7.20154	+	28.5544i	0.238467	+	0.945532i
$913$	−2.10364	−	5.07865i	−0.0696205	−	0.168079i
$914$	24.2625	+	2.07949i	0.802531	+	0.0687835i
$915$	−0.139726	+	0.460616i	−0.00461921	+	0.0152275i
$916$	−10.9092	+	39.5448i	−0.360449	+	1.30660i
$917$	17.6644	+	1.73979i	0.583329	+	0.0574529i
$918$	−3.17495	−	7.39834i	−0.104789	−	0.244182i
$919$	−34.8858	−	23.3099i	−1.15078	−	0.768924i	−0.174331	−	0.984687i	$-0.555776\pi$
$919$	−34.8858	−	23.3099i	−1.15078	−	0.768924i	−0.976446	+	0.215763i	$0.930776\pi$
$920$	−1.24580	−	0.461362i	−0.0410729	−	0.0152107i
$921$	−9.28055	−	13.8893i	−0.305805	−	0.457669i
$922$	0.629899	+	2.96949i	0.0207446	+	0.0977950i
$923$	−2.51668	−	8.29638i	−0.0828375	−	0.273079i
$924$	−0.0574174	−	2.26441i	−0.00188889	−	0.0744936i
$925$	−0.222062	−	0.182241i	−0.00730134	−	0.00599206i
$926$	10.8336	−	13.5474i	0.356015	−	0.445195i
$927$	−5.25319	−	5.25319i	−0.172537	−	0.172537i
$928$	49.5838	+	28.7644i	1.62767	+	0.944236i
$929$	26.2463	−	26.2463i	0.861112	−	0.861112i	−0.130356	−	0.991467i	$-0.541612\pi$
$929$	26.2463	−	26.2463i	0.861112	−	0.861112i	0.991467	+	0.130356i	$0.0416119\pi$
$930$	0.0417100	+	0.374731i	0.00136773	+	0.0122879i
$931$	−18.2317	+	22.2154i	−0.597519	+	0.728079i
$932$	0.441625	+	0.994123i	0.0144659	+	0.0325636i
$933$	2.35708	−	0.715012i	0.0771673	−	0.0234085i
$934$	3.90808	−	6.01246i	0.127876	−	0.196734i
$935$	−0.262008	+	0.175068i	−0.00856858	+	0.00572534i
$936$	−16.5680	−	2.64524i	−0.541543	−	0.0864623i
$937$	−5.32753	+	7.97322i	−0.174043	+	0.260474i	−0.908228	−	0.418476i	$-0.862564\pi$
$937$	−5.32753	+	7.97322i	−0.174043	+	0.260474i	0.734185	+	0.678949i	$0.237564\pi$
$938$	−0.779782	−	0.311476i	−0.0254608	−	0.0101701i
$939$	2.18038	−	22.1377i	0.0711539	−	0.722437i
$940$	0.306219	+	0.238578i	0.00998777	+	0.00778157i
$941$	−48.7719	−	14.7948i	−1.58992	−	0.482296i	−0.633364	−	0.773854i	$-0.718326\pi$
$941$	−48.7719	−	14.7948i	−1.58992	−	0.482296i	−0.956553	+	0.291558i	$0.905826\pi$
$942$	5.98893	+	7.11177i	0.195130	+	0.231714i
$943$	53.5815	−	22.1942i	1.74485	−	0.722742i
$944$	−2.76846	−	0.131525i	−0.0901057	−	0.00428078i
$945$	0.139815	+	0.0579131i	0.00454817	+	0.00188391i
$946$	3.17712	+	10.0148i	0.103297	+	0.325609i
$947$	37.7982	−	20.2036i	1.22828	−	0.656528i	0.275823	−	0.961208i	$-0.411050\pi$
$947$	37.7982	−	20.2036i	1.22828	−	0.656528i	0.952455	+	0.304680i	$0.0985496\pi$
$948$	−14.7472	+	12.7418i	−0.478966	+	0.413834i
$949$	−45.9870	+	37.7406i	−1.49280	+	1.22511i
$950$	−0.658871	−	51.9770i	−0.0213766	−	1.68636i
$951$	−4.48233	−	22.5342i	−0.145350	−	0.730722i
$952$	17.1289	−	22.5696i	0.555151	−	0.731485i
$953$	20.2849	+	4.03492i	0.657093	+	0.130704i	0.512365	−	0.858767i	$-0.328769\pi$
$953$	20.2849	+	4.03492i	0.657093	+	0.130704i	0.144728	+	0.989471i	$0.453769\pi$
$954$	2.83336	+	4.12623i	0.0917334	+	0.133592i
$955$	0.599257	−	1.12113i	0.0193915	−	0.0362790i
$956$	5.11202	−	29.6032i	0.165335	−	0.957435i
$957$	−6.49072	+	0.639280i	−0.209815	+	0.0206650i
$958$	−12.8505	−	23.3255i	−0.415181	−	0.753614i
$959$		−	9.41319i		−	0.303968i
$960$	−0.599452	−	0.337670i	−0.0193472	−	0.0108983i
$961$		−	21.3896i		−	0.689987i
$962$	−0.422776	+	0.232916i	−0.0136308	+	0.00750950i
$963$	10.3515	−	1.01954i	0.333573	−	0.0328541i
$964$	7.34726	−	5.18341i	0.236639	−	0.166946i
$965$	−0.323306	+	0.604862i	−0.0104076	+	0.0194712i
$966$	−11.2038	+	7.69335i	−0.360478	+	0.247530i
$967$	−41.6032	−	8.27539i	−1.33787	−	0.266119i	−0.526262	−	0.850322i	$-0.676407\pi$
$967$	−41.6032	−	8.27539i	−1.33787	−	0.266119i	−0.811607	+	0.584204i	$0.801407\pi$
$968$	15.1078	+	25.8499i	0.485582	+	0.830848i
$969$	−8.17646	−	41.1059i	−0.262666	−	1.32051i
$970$	−1.69912	+	0.0215383i	−0.0545554	+	0.000691554i
$971$	10.9353	−	8.97434i	0.350929	−	0.288000i	−0.442369	−	0.896833i	$-0.645862\pi$
$971$	10.9353	−	8.97434i	0.350929	−	0.288000i	0.793299	+	0.608833i	$0.208362\pi$
$972$	−0.145519	+	1.99470i	−0.00466752	+	0.0639800i
$973$	18.0511	−	9.64853i	0.578693	−	0.309318i
$974$	1.82580	−	0.579223i	0.0585025	−	0.0185595i
$975$	27.3611	+	11.3333i	0.876257	+	0.362958i
$976$	−11.5405	−	19.1838i	−0.369402	−	0.614060i
$977$	−10.0726	+	4.17223i	−0.322253	+	0.133481i	−0.537945	−	0.842980i	$-0.680799\pi$
$977$	−10.0726	+	4.17223i	−0.322253	+	0.133481i	0.215692	+	0.976461i	$0.430799\pi$
$978$	13.3815	−	11.2688i	0.427894	−	0.360336i
$979$	−7.92942	−	2.40536i	−0.253425	−	0.0768757i
$980$	−0.0827283	−	0.666315i	−0.00264266	−	0.0212847i
$981$	0.140113	−	1.42259i	0.00447347	−	0.0454199i
$982$	11.6206	−	29.0921i	0.370827	−	0.928367i
$983$	−4.94178	+	7.39589i	−0.157618	+	0.235892i	−0.901871	−	0.432006i	$-0.857806\pi$
$983$	−4.94178	+	7.39589i	−0.157618	+	0.235892i	0.744253	+	0.667898i	$0.232806\pi$
$984$	29.2146	−	6.97540i	0.931328	−	0.222368i
$985$	−0.939399	+	0.627687i	−0.0299318	+	0.0199998i
$986$	−68.4021	−	44.4612i	−2.17837	−	1.41593i
$987$	3.80031	−	1.15281i	0.120965	−	0.0366943i
$988$	−81.5153	−	31.3683i	−2.59335	−	0.997960i
$989$	39.9926	−	48.7311i	1.27169	−	1.54956i
$990$	0.0778008	−	0.00865974i	0.00247267	−	0.000275225i
$991$	−29.2459	+	29.2459i	−0.929026	+	0.929026i	−0.997643	−	0.0686170i	$-0.978141\pi$
$991$	−29.2459	+	29.2459i	−0.929026	+	0.929026i	0.0686170	+	0.997643i	$0.478141\pi$
$992$	−14.2334	−	10.2442i	−0.451910	−	0.325254i
$993$	−13.9835	−	13.9835i	−0.443752	−	0.443752i
$994$	−2.84055	−	2.27154i	−0.0900967	−	0.0720488i
$995$	0.415717	+	0.341170i	0.0131791	+	0.0108158i
$996$	−11.7684	+	12.3808i	−0.372897	+	0.392300i
$997$	6.66202	+	21.9617i	0.210988	+	0.695535i	0.997006	+	0.0773306i	$0.0246397\pi$
$997$	6.66202	+	21.9617i	0.210988	+	0.695535i	−0.786017	+	0.618205i	$0.787860\pi$
$998$	−60.1276	+	12.7545i	−1.90330	+	0.403735i
$999$	0.0319669	+	0.0478418i	0.00101139	+	0.00151365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.181.19	yes	512
128.29	even	32	inner	384.2.v.a.157.19	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.19	✓	512	128.29	even	32	inner
384.2.v.a.181.19	yes	512	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.393338 - 1.35841i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(-1.69057 - 1.06863i) q^{4} +(0.0758469 + 0.0405410i) q^{5} +(-1.39043 - 0.258296i) q^{6} +(0.343293 - 1.72585i) q^{7} +(-2.11661 + 1.87616i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(0.393338 - 1.35841i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(-1.69057 - 1.06863i) q^{4} +(0.0758469 + 0.0405410i) q^{5} +(-1.39043 - 0.258296i) q^{6} +(0.343293 - 1.72585i) q^{7} +(-2.11661 + 1.87616i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(0.0849049 - 0.0870850i) q^{10} +(-0.408313 - 0.497531i) q^{11} +(-0.897780 + 1.78717i) q^{12} +(-2.79626 - 5.23144i) q^{13} +(-2.20939 - 1.14518i) q^{14} +(0.0329115 - 0.0794554i) q^{15} +(1.71606 + 3.61319i) q^{16} +(-2.17854 - 5.25946i) q^{17} +(-0.120767 + 1.40905i) q^{18} +(-2.13712 + 7.04513i) q^{19} +(-0.0849011 - 0.149590i) q^{20} +(-1.75119 - 0.172477i) q^{21} +(-0.836458 + 0.358960i) q^{22} +(4.54100 + 3.03420i) q^{23} +(2.07459 + 1.92252i) q^{24} +(-2.77374 - 4.15120i) q^{25} +(-8.20633 + 1.74076i) q^{26} +(0.290285 + 0.956940i) q^{27} +(-2.42466 + 2.55082i) q^{28} +(7.83321 + 6.42855i) q^{29} +(-0.0949878 - 0.0759602i) q^{30} +(-2.19208 - 2.19208i) q^{31} +(5.58320 - 0.909908i) q^{32} +(-0.455114 + 0.455114i) q^{33} +(-8.00141 + 0.890610i) q^{34} +(0.0960055 - 0.116983i) q^{35} +(1.86657 + 0.718283i) q^{36} +(0.0550612 - 0.0167026i) q^{37} +(8.72959 + 5.67421i) q^{38} +(-4.93217 + 3.29557i) q^{39} +(-0.236599 + 0.0564915i) q^{40} +(5.89975 - 8.82959i) q^{41} +(-0.923105 + 2.31100i) q^{42} +(1.13140 - 11.4873i) q^{43} +(0.158605 + 1.27745i) q^{44} +(-0.0822987 - 0.0249650i) q^{45} +(5.90784 - 4.97509i) q^{46} +(-2.08506 + 0.863662i) q^{47} +(3.42759 - 2.06195i) q^{48} +(3.60644 + 1.49384i) q^{49} +(-6.73006 + 2.13506i) q^{50} +(-5.02060 + 2.68356i) q^{51} +(-0.863198 + 11.8323i) q^{52} +(2.73594 - 2.24533i) q^{53} +(1.41410 - 0.0179254i) q^{54} +(-0.0107989 - 0.0542896i) q^{55} +(2.51136 + 4.29702i) q^{56} +(7.22068 + 1.43628i) q^{57} +(11.8137 - 8.11214i) q^{58} +(-0.326629 + 0.611080i) q^{59} +(-0.140548 + 0.0991547i) q^{60} +(-5.56994 + 0.548591i) q^{61} +(-3.83997 + 2.11552i) q^{62} +1.75966i q^{63} +(0.960052 - 7.94218i) q^{64} -0.510152i q^{65} +(0.439219 + 0.797246i) q^{66} +(0.335798 - 0.0330732i) q^{67} +(-1.93744 + 11.2195i) q^{68} +(2.57449 - 4.81654i) q^{69} +(-0.121149 - 0.176429i) q^{70} +(1.43346 + 0.285133i) q^{71} +(1.70992 - 2.25304i) q^{72} +(-1.95656 - 9.83631i) q^{73} +(-0.00103141 - 0.0813657i) q^{74} +(-3.85933 + 3.16727i) q^{75} +(11.1416 - 9.62650i) q^{76} +(-0.998836 + 0.533889i) q^{77} +(2.53673 + 7.99619i) q^{78} +(9.00287 + 3.72911i) q^{79} +(-0.0163248 + 0.343620i) q^{80} +(0.923880 - 0.382683i) q^{81} +(-9.67364 - 11.4873i) q^{82} +(8.17302 + 2.47926i) q^{83} +(2.77620 + 2.16296i) q^{84} +(0.0479883 - 0.487233i) q^{85} +(-15.1595 - 6.05532i) q^{86} +(5.62981 - 8.42560i) q^{87} +(1.79769 + 0.287017i) q^{88} +(10.7045 - 7.15255i) q^{89} +(-0.0662840 + 0.101976i) q^{90} +(-9.98863 + 3.03002i) q^{91} +(-4.43444 - 9.98218i) q^{92} +(-1.96666 + 2.39638i) q^{93} +(0.353074 + 3.17209i) q^{94} +(-0.447710 + 0.447710i) q^{95} +(-1.45278 - 5.46712i) q^{96} +(-9.87917 - 9.87917i) q^{97} +(3.44780 - 4.31146i) q^{98} +(0.497531 + 0.408313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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