LMFDB - Embedded newform 384.2.v.a.229.16

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			229.16
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.135367 + 1.40772i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.96335 + 0.381118i) q^{4} +(0.479522 + 0.584299i) q^{5} +(-0.782978 - 1.17769i) q^{6} +(-1.19710 + 0.799874i) q^{7} +(-0.802280 - 2.71226i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(0.135367 + 1.40772i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.96335 + 0.381118i) q^{4} +(0.479522 + 0.584299i) q^{5} +(-0.782978 - 1.17769i) q^{6} +(-1.19710 + 0.799874i) q^{7} +(-0.802280 - 2.71226i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-0.757619 + 0.754128i) q^{10} +(-5.07266 + 1.53878i) q^{11} +(1.55186 - 1.26163i) q^{12} +(-2.10830 - 1.73023i) q^{13} +(-1.28805 - 1.57690i) q^{14} +(-0.698338 - 0.289261i) q^{15} +(3.70950 - 1.49654i) q^{16} +(-1.24782 + 0.516862i) q^{17} +(1.24568 + 0.669534i) q^{18} +(0.153615 + 1.55968i) q^{19} +(-1.16416 - 0.964431i) q^{20} +(0.678687 - 1.26973i) q^{21} +(-2.85284 - 6.93259i) q^{22} +(-0.945999 + 0.188171i) q^{23} +(1.98610 + 2.01381i) q^{24} +(0.863987 - 4.34356i) q^{25} +(2.15029 - 3.20211i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(2.04547 - 2.02667i) q^{28} +(-0.526807 + 1.73665i) q^{29} +(0.312667 - 1.02222i) q^{30} +(-3.31414 - 3.31414i) q^{31} +(2.60885 + 5.01935i) q^{32} +(3.74832 - 3.74832i) q^{33} +(-0.896510 - 1.68661i) q^{34} +(-1.04140 - 0.315905i) q^{35} +(-0.773892 + 1.84420i) q^{36} +(-3.16669 - 0.311892i) q^{37} +(-2.17480 + 0.427377i) q^{38} +(2.67498 + 0.532086i) q^{39} +(1.20006 - 1.76936i) q^{40} +(-0.0889007 - 0.446934i) q^{41} +(1.87930 + 0.783521i) q^{42} +(-3.49287 - 1.86698i) q^{43} +(9.37297 - 4.95444i) q^{44} +(0.752235 - 0.0740887i) q^{45} +(-0.392949 - 1.30623i) q^{46} +(4.80239 + 11.5940i) q^{47} +(-2.56602 + 3.06847i) q^{48} +(-1.88554 + 4.55210i) q^{49} +(6.23147 + 0.628278i) q^{50} +(0.856828 - 1.04405i) q^{51} +(4.79875 + 2.59355i) q^{52} +(2.23575 + 7.37029i) q^{53} +(-1.41421 - 0.00326552i) q^{54} +(-3.33156 - 2.22608i) q^{55} +(3.12987 + 2.60511i) q^{56} +(-0.870705 - 1.30310i) q^{57} +(-2.51603 - 0.506511i) q^{58} +(-9.65297 + 7.92198i) q^{59} +(1.48132 + 0.301772i) q^{60} +(1.18763 + 2.22190i) q^{61} +(4.21676 - 5.11401i) q^{62} +1.43974i q^{63} +(-6.71269 + 4.35198i) q^{64} -2.06156i q^{65} +(5.78398 + 4.76918i) q^{66} +(-1.46613 - 2.74294i) q^{67} +(2.25291 - 1.49035i) q^{68} +(0.745594 - 0.611893i) q^{69} +(0.303735 - 1.50876i) q^{70} +(2.89557 + 4.33353i) q^{71} +(-2.70088 - 0.839779i) q^{72} +(2.34943 + 1.56984i) q^{73} +(0.0103909 - 4.50004i) q^{74} +(1.28557 + 4.23796i) q^{75} +(-0.896023 - 3.00366i) q^{76} +(4.84164 - 5.89955i) q^{77} +(-0.386924 + 3.83765i) q^{78} +(-2.08351 + 5.03003i) q^{79} +(2.65321 + 1.44984i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(0.617124 - 0.185648i) q^{82} +(-8.13622 + 0.801348i) q^{83} +(-0.848582 + 2.75159i) q^{84} +(-0.900357 - 0.481251i) q^{85} +(2.15536 - 5.16971i) q^{86} +(-0.354049 - 1.77992i) q^{87} +(8.24325 + 12.5238i) q^{88} +(13.4032 + 2.66607i) q^{89} +(0.206124 + 1.04891i) q^{90} +(3.90780 + 0.384885i) q^{91} +(1.78561 - 0.729983i) q^{92} +(4.48509 + 1.36054i) q^{93} +(-15.6710 + 8.32986i) q^{94} +(-0.837659 + 0.837659i) q^{95} +(-4.66691 - 3.19687i) q^{96} +(-7.32866 - 7.32866i) q^{97} +(-6.66333 - 2.03811i) q^{98} +(-1.53878 + 5.07266i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	0.135367	+	1.40772i	0.0957189	+	0.995408i
$2$	0.135367	+	1.40772i	0.0957189	+	0.995408i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$4$	−1.96335	+	0.381118i	−0.981676	+	0.190559i
$5$	0.479522	+	0.584299i	0.214449	+	0.261307i	0.869113	−	0.494613i	$-0.164690\pi$
$5$	0.479522	+	0.584299i	0.214449	+	0.261307i	−0.654665	+	0.755919i	$0.727190\pi$
$6$	−0.782978	−	1.17769i	−0.319649	−	0.480789i
$7$	−1.19710	+	0.799874i	−0.452460	+	0.302324i	−0.760840	−	0.648939i	$-0.775213\pi$
$7$	−1.19710	+	0.799874i	−0.452460	+	0.302324i	0.308381	+	0.951263i	$0.400213\pi$
$8$	−0.802280	−	2.71226i	−0.283649	−	0.958928i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−0.757619	+	0.754128i	−0.239580	+	0.238476i
$11$	−5.07266	+	1.53878i	−1.52947	+	0.463958i	−0.939235	−	0.343276i	$-0.888463\pi$
$11$	−5.07266	+	1.53878i	−1.52947	+	0.463958i	−0.590231	+	0.807234i	$0.700963\pi$
$12$	1.55186	−	1.26163i	0.447985	−	0.364202i
$13$	−2.10830	−	1.73023i	−0.584736	−	0.479880i	0.294900	−	0.955528i	$-0.404714\pi$
$13$	−2.10830	−	1.73023i	−0.584736	−	0.479880i	−0.879636	+	0.475648i	$0.842214\pi$
$14$	−1.28805	−	1.57690i	−0.344245	−	0.421444i
$15$	−0.698338	−	0.289261i	−0.180310	−	0.0746868i
$16$	3.70950	−	1.49654i	0.927375	−	0.374134i
$17$	−1.24782	+	0.516862i	−0.302640	+	0.125357i	−0.528835	−	0.848724i	$-0.677371\pi$
$17$	−1.24782	+	0.516862i	−0.302640	+	0.125357i	0.226196	+	0.974082i	$0.427371\pi$
$18$	1.24568	+	0.669534i	0.293610	+	0.157811i
$19$	0.153615	+	1.55968i	0.0352417	+	0.357815i	0.996592	+	0.0824875i	$0.0262865\pi$
$19$	0.153615	+	1.55968i	0.0352417	+	0.357815i	−0.961350	+	0.275328i	$0.911214\pi$
$20$	−1.16416	−	0.964431i	−0.260313	−	0.215653i
$21$	0.678687	−	1.26973i	0.148102	−	0.277078i
$22$	−2.85284	−	6.93259i	−0.608227	−	1.47803i
$23$	−0.945999	+	0.188171i	−0.197255	+	0.0392364i	−0.292729	−	0.956196i	$-0.594563\pi$
$23$	−0.945999	+	0.188171i	−0.197255	+	0.0392364i	0.0954742	+	0.995432i	$0.469563\pi$
$24$	1.98610	+	2.01381i	0.405410	+	0.411066i
$25$	0.863987	−	4.34356i	0.172797	−	0.868711i
$26$	2.15029	−	3.20211i	0.421707	−	0.627985i
$27$	−0.0980171	+	0.995185i	−0.0188634	+	0.191523i
$28$	2.04547	−	2.02667i	0.386558	−	0.383004i
$29$	−0.526807	+	1.73665i	−0.0978256	+	0.322488i	−0.992171	−	0.124890i	$-0.960142\pi$
$29$	−0.526807	+	1.73665i	−0.0978256	+	0.322488i	0.894345	+	0.447378i	$0.147642\pi$
$30$	0.312667	−	1.02222i	0.0570848	−	0.186631i
$31$	−3.31414	−	3.31414i	−0.595237	−	0.595237i	0.343804	−	0.939041i	$-0.388284\pi$
$31$	−3.31414	−	3.31414i	−0.595237	−	0.595237i	−0.939041	+	0.343804i	$0.888284\pi$
$32$	2.60885	+	5.01935i	0.461183	+	0.887305i
$33$	3.74832	−	3.74832i	0.652498	−	0.652498i
$34$	−0.896510	−	1.68661i	−0.153750	−	0.289251i
$35$	−1.04140	−	0.315905i	−0.176029	−	0.0533977i
$36$	−0.773892	+	1.84420i	−0.128982	+	0.307367i
$37$	−3.16669	−	0.311892i	−0.520601	−	0.0512747i	−0.165696	−	0.986177i	$-0.552987\pi$
$37$	−3.16669	−	0.311892i	−0.520601	−	0.0512747i	−0.354905	+	0.934902i	$0.615487\pi$
$38$	−2.17480	+	0.427377i	−0.352799	+	0.0693296i
$39$	2.67498	+	0.532086i	0.428339	+	0.0852019i
$40$	1.20006	−	1.76936i	0.189746	−	0.279760i
$41$	−0.0889007	−	0.446934i	−0.0138840	−	0.0697994i	0.973222	−	0.229866i	$-0.0738289\pi$
$41$	−0.0889007	−	0.446934i	−0.0138840	−	0.0697994i	−0.987106	+	0.160067i	$0.948829\pi$
$42$	1.87930	+	0.783521i	0.289982	+	0.120900i
$43$	−3.49287	−	1.86698i	−0.532658	−	0.284711i	0.183059	−	0.983102i	$-0.441400\pi$
$43$	−3.49287	−	1.86698i	−0.532658	−	0.284711i	−0.715717	+	0.698390i	$0.753900\pi$
$44$	9.37297	−	4.95444i	1.41303	−	0.746910i
$45$	0.752235	−	0.0740887i	0.112137	−	0.0110445i
$46$	−0.392949	−	1.30623i	−0.0579372	−	0.192593i
$47$	4.80239	+	11.5940i	0.700500	+	1.69116i	0.722473	+	0.691399i	$0.243005\pi$
$47$	4.80239	+	11.5940i	0.700500	+	1.69116i	−0.0219728	+	0.999759i	$0.506995\pi$
$48$	−2.56602	+	3.06847i	−0.370374	+	0.442896i
$49$	−1.88554	+	4.55210i	−0.269363	+	0.650301i
$50$	6.23147	+	0.628278i	0.881263	+	0.0888519i
$51$	0.856828	−	1.04405i	0.119980	−	0.146196i
$52$	4.79875	+	2.59355i	0.665466	+	0.359660i
$53$	2.23575	+	7.37029i	0.307104	+	1.01239i	0.965650	+	0.259846i	$0.0836719\pi$
$53$	2.23575	+	7.37029i	0.307104	+	1.01239i	−0.658546	+	0.752541i	$0.728828\pi$
$54$	−1.41421	−	0.00326552i	−0.192450	−	0.000444381i
$55$	−3.33156	−	2.22608i	−0.449227	−	0.300164i
$56$	3.12987	+	2.60511i	0.418247	+	0.348123i
$57$	−0.870705	−	1.30310i	−0.115328	−	0.172600i
$58$	−2.51603	−	0.506511i	−0.330371	−	0.0665082i
$59$	−9.65297	+	7.92198i	−1.25671	+	1.03135i	−0.258852	+	0.965917i	$0.583344\pi$
$59$	−9.65297	+	7.92198i	−1.25671	+	1.03135i	−0.997857	+	0.0654377i	$0.979156\pi$
$60$	1.48132	+	0.301772i	0.191238	+	0.0389586i
$61$	1.18763	+	2.22190i	0.152060	+	0.284485i	0.946405	−	0.322983i	$-0.104686\pi$
$61$	1.18763	+	2.22190i	0.152060	+	0.284485i	−0.794345	+	0.607467i	$0.792186\pi$
$62$	4.21676	−	5.11401i	0.535529	−	0.649480i
$63$			1.43974i			0.181390i
$64$	−6.71269	+	4.35198i	−0.839087	+	0.543998i
$65$		−	2.06156i		−	0.255705i
$66$	5.78398	+	4.76918i	0.711959	+	0.587046i
$67$	−1.46613	−	2.74294i	−0.179116	−	0.335103i	0.776301	−	0.630363i	$-0.217094\pi$
$67$	−1.46613	−	2.74294i	−0.179116	−	0.335103i	−0.955417	+	0.295260i	$0.904594\pi$
$68$	2.25291	−	1.49035i	0.273206	−	0.180731i
$69$	0.745594	−	0.611893i	0.0897590	−	0.0736633i
$70$	0.303735	−	1.50876i	0.0363033	−	0.180332i
$71$	2.89557	+	4.33353i	0.343642	+	0.514296i	0.962527	−	0.271185i	$-0.0874156\pi$
$71$	2.89557	+	4.33353i	0.343642	+	0.514296i	−0.618886	+	0.785481i	$0.712416\pi$
$72$	−2.70088	−	0.839779i	−0.318302	−	0.0989689i
$73$	2.34943	+	1.56984i	0.274980	+	0.183736i	0.685412	−	0.728156i	$-0.259622\pi$
$73$	2.34943	+	1.56984i	0.274980	+	0.183736i	−0.410432	+	0.911891i	$0.634622\pi$
$74$	0.0103909	−	4.50004i	0.00120792	−	0.523119i
$75$	1.28557	+	4.23796i	0.148445	+	0.489357i
$76$	−0.896023	−	3.00366i	−0.102781	−	0.344543i
$77$	4.84164	−	5.89955i	0.551756	−	0.672317i
$78$	−0.386924	+	3.83765i	−0.0438106	+	0.434528i
$79$	−2.08351	+	5.03003i	−0.234413	+	0.565922i	−0.996687	−	0.0813316i	$-0.974083\pi$
$79$	−2.08351	+	5.03003i	−0.234413	+	0.565922i	0.762274	+	0.647254i	$0.224083\pi$
$80$	2.65321	+	1.44984i	0.296638	+	0.162097i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	0.617124	−	0.185648i	0.0681499	−	0.0205013i
$83$	−8.13622	+	0.801348i	−0.893067	+	0.0879594i	−0.534130	−	0.845402i	$-0.679361\pi$
$83$	−8.13622	+	0.801348i	−0.893067	+	0.0879594i	−0.358937	+	0.933362i	$0.616861\pi$
$84$	−0.848582	+	2.75159i	−0.0925879	+	0.300223i
$85$	−0.900357	−	0.481251i	−0.0976574	−	0.0521990i
$86$	2.15536	−	5.16971i	0.232419	−	0.557464i
$87$	−0.354049	−	1.77992i	−0.0379580	−	0.190828i
$88$	8.24325	+	12.5238i	0.878734	+	1.33505i
$89$	13.4032	+	2.66607i	1.42074	+	0.282603i	0.844885	−	0.534949i	$-0.179669\pi$
$89$	13.4032	+	2.66607i	1.42074	+	0.282603i	0.575856	+	0.817551i	$0.304669\pi$
$90$	0.206124	+	1.04891i	0.0217274	+	0.110565i
$91$	3.90780	+	0.384885i	0.409649	+	0.0403469i
$92$	1.78561	−	0.729983i	0.186163	−	0.0761060i
$93$	4.48509	+	1.36054i	0.465082	+	0.141081i
$94$	−15.6710	+	8.32986i	−1.61634	+	0.859160i
$95$	−0.837659	+	0.837659i	−0.0859420	+	0.0859420i
$96$	−4.66691	−	3.19687i	−0.476314	−	0.326279i
$97$	−7.32866	−	7.32866i	−0.744113	−	0.744113i	0.229254	−	0.973367i	$-0.426371\pi$
$97$	−7.32866	−	7.32866i	−0.744113	−	0.744113i	−0.973367	+	0.229254i	$0.926371\pi$
$98$	−6.66333	−	2.03811i	−0.673098	−	0.205880i
$99$	−1.53878	+	5.07266i	−0.154653	+	0.509822i
$100$	−0.0409042	+	8.85721i	−0.00409042	+	0.885721i
$101$	−0.0179082	+	0.181825i	−0.00178193	+	0.0180922i	−0.996035	−	0.0889670i	$-0.971643\pi$
$101$	−0.0179082	+	0.181825i	−0.00178193	+	0.0180922i	0.994253	+	0.107059i	$0.0341434\pi$
$102$	1.58571	+	1.06484i	0.157009	+	0.105435i
$103$	3.64549	−	18.3271i	0.359201	−	1.80582i	−0.203401	−	0.979096i	$-0.565200\pi$
$103$	3.64549	−	18.3271i	0.359201	−	1.80582i	0.562602	−	0.826728i	$-0.309800\pi$
$104$	−3.00140	+	7.10637i	−0.294311	+	0.696837i
$105$	1.06735	−	0.212309i	0.104163	−	0.0207192i
$106$	−10.0727	+	4.14501i	−0.978343	+	0.402599i
$107$	−5.00088	+	9.35598i	−0.483453	+	0.904477i	0.515416	+	0.856940i	$0.327637\pi$
$107$	−5.00088	+	9.35598i	−0.483453	+	0.904477i	−0.998869	+	0.0475372i	$0.984863\pi$
$108$	−0.186840	−	1.99125i	−0.0179787	−	0.191608i
$109$	1.71887	+	17.4520i	0.164638	+	1.67160i	0.622533	+	0.782594i	$0.286104\pi$
$109$	1.71887	+	17.4520i	0.164638	+	1.67160i	−0.457895	+	0.889006i	$0.651396\pi$
$110$	2.68271	−	4.99124i	0.255786	−	0.475896i
$111$	2.93980	−	1.21770i	0.279033	−	0.115579i
$112$	−3.24359	+	4.75863i	−0.306490	+	0.449648i
$113$	−18.0574	−	7.47963i	−1.69870	−	0.703624i	−0.698768	−	0.715349i	$-0.746268\pi$
$113$	−18.0574	−	7.47963i	−1.69870	−	0.703624i	−0.999931	+	0.0117244i	$0.996268\pi$
$114$	1.71654	−	1.40211i	0.160769	−	0.131319i
$115$	−0.563576	−	0.462515i	−0.0525537	−	0.0431297i
$116$	0.372439	−	3.61043i	0.0345801	−	0.335220i
$117$	−2.60994	+	0.791717i	−0.241289	+	0.0731943i
$118$	−12.4586	−	12.5163i	−1.14691	−	1.15222i
$119$	1.08033	−	1.61683i	0.0990337	−	0.148214i
$120$	−0.224288	+	2.12614i	−0.0204746	+	0.194089i
$121$	14.2179	−	9.50011i	1.29254	−	0.863646i
$122$	−2.96704	+	1.97262i	−0.268623	+	0.178593i
$123$	0.289087	+	0.352253i	0.0260661	+	0.0317616i
$124$	7.76990	+	5.24375i	0.697758	+	0.470902i
$125$	6.28535	−	3.35959i	0.562179	−	0.300491i
$126$	−2.02674	+	0.194893i	−0.180557	+	0.0173624i
$127$	12.6303			1.12076			0.560379	−	0.828236i	$-0.310655\pi$
$127$	12.6303			1.12076			0.560379	+	0.828236i	$0.310655\pi$
$128$	−7.03505	−	8.86048i	−0.621816	−	0.783163i
$129$	3.96052			0.348705
$130$	2.90210	−	0.279067i	0.254531	−	0.0244758i
$131$	1.47120	−	0.786373i	0.128539	−	0.0687057i	−0.405874	−	0.913929i	$-0.633033\pi$
$131$	1.47120	−	0.786373i	0.128539	−	0.0687057i	0.534413	+	0.845223i	$0.320533\pi$
$132$	−5.93071	+	8.78781i	−0.516202	+	0.764881i
$133$	−1.43144	−	1.74422i	−0.124122	−	0.151243i
$134$	3.66282	−	2.43521i	0.316420	−	0.210370i
$135$	−0.628487	+	0.419942i	−0.0540916	+	0.0361428i
$136$	2.40296	+	2.96973i	0.206052	+	0.254652i
$137$	4.06867	−	6.08919i	0.347610	−	0.520235i	−0.615930	−	0.787801i	$-0.711219\pi$
$137$	4.06867	−	6.08919i	0.347610	−	0.520235i	0.963539	+	0.267566i	$0.0862195\pi$
$138$	0.962303	+	0.966757i	0.0819167	+	0.0822958i
$139$	−5.06219	+	1.53560i	−0.429370	+	0.130248i	−0.497570	−	0.867424i	$-0.665774\pi$
$139$	−5.06219	+	1.53560i	−0.429370	+	0.130248i	0.0682004	+	0.997672i	$0.478274\pi$
$140$	2.16503	+	0.223337i	0.182979	+	0.0188754i
$141$	−9.70070	−	7.96116i	−0.816946	−	0.670450i
$142$	−5.70844	+	4.66278i	−0.479041	+	0.391291i
$143$	13.3571	+	5.53270i	1.11698	+	0.462667i
$144$	0.816563	−	3.91577i	0.0680469	−	0.326314i
$145$	−1.26734	+	0.524949i	−0.105247	+	0.0435946i
$146$	−1.89186	+	3.51984i	−0.156571	+	0.291304i
$147$	−0.482946	−	4.90344i	−0.0398327	−	0.404429i
$148$	6.33620	−	0.594529i	0.520832	−	0.0488700i
$149$	−3.90916	+	7.31352i	−0.320251	+	0.599147i	−0.989608	−	0.143794i	$-0.954070\pi$
$149$	−3.90916	+	7.31352i	−0.320251	+	0.599147i	0.669357	+	0.742941i	$0.266570\pi$
$150$	−5.79183	+	2.38340i	−0.472901	+	0.194604i
$151$	21.7049	−	4.31738i	1.76632	−	0.351344i	0.798311	−	0.602245i	$-0.205727\pi$
$151$	21.7049	−	4.31738i	1.76632	−	0.351344i	0.968013	+	0.250902i	$0.0807271\pi$
$152$	4.10702	−	1.66795i	0.333123	−	0.135288i
$153$	−0.263494	+	1.32467i	−0.0213022	+	0.107094i
$154$	8.96032	+	6.01707i	0.722043	+	0.484869i
$155$	0.347247	−	3.52566i	0.0278915	−	0.283187i
$156$	−5.45471	−	0.0251908i	−0.436726	−	0.00201688i
$157$	1.17425	−	3.87097i	0.0937150	−	0.308937i	−0.897533	−	0.440946i	$-0.854643\pi$
$157$	1.17425	−	3.87097i	0.0937150	−	0.308937i	0.991248	+	0.132009i	$0.0421429\pi$
$158$	−7.36291	−	2.25209i	−0.585762	−	0.179167i
$159$	−5.44609	−	5.44609i	−0.431903	−	0.431903i
$160$	−1.68181	+	3.93124i	−0.132958	+	0.310792i
$161$	0.981939	−	0.981939i	0.0773877	−	0.0773877i
$162$	1.24876	−	0.663774i	0.0981119	−	0.0521510i
$163$	−9.72852	−	2.95111i	−0.761996	−	0.231149i	−0.114713	−	0.993399i	$-0.536595\pi$
$163$	−9.72852	−	2.95111i	−0.761996	−	0.231149i	−0.647283	+	0.762250i	$0.724095\pi$
$164$	0.344878	+	0.843607i	0.0269304	+	0.0658747i
$165$	3.98754	+	0.392738i	0.310430	+	0.0305746i
$166$	−2.22945	−	11.3450i	−0.173039	−	0.880547i
$167$	0.467221	+	0.0929360i	0.0361546	+	0.00719161i	0.213135	−	0.977023i	$-0.431633\pi$
$167$	0.467221	+	0.0929360i	0.0361546	+	0.00719161i	−0.176980	+	0.984214i	$0.556633\pi$
$168$	−3.98834	−	0.822092i	−0.307707	−	0.0634258i
$169$	−1.08497	−	5.45452i	−0.0834594	−	0.419579i
$170$	0.555588	−	1.33260i	0.0426116	−	0.102205i
$171$	1.38217	+	0.738786i	0.105697	+	0.0564964i
$172$	7.56927	+	2.33434i	0.577151	+	0.177992i
$173$	0.549375	−	0.0541087i	0.0417682	−	0.00411381i	−0.0771115	−	0.997022i	$-0.524570\pi$
$173$	0.549375	−	0.0541087i	0.0417682	−	0.00411381i	0.118880	+	0.992909i	$0.462070\pi$
$174$	2.45771	−	0.739344i	0.186318	−	0.0560495i
$175$	2.44002	+	5.89074i	0.184448	+	0.445298i
$176$	−16.5142	+	13.2995i	−1.24481	+	1.00249i
$177$	4.77876	−	11.5369i	0.359193	−	0.867170i
$178$	−1.93872	+	19.2289i	−0.145313	+	1.44127i
$179$	11.5848	−	14.1161i	0.865886	−	1.05508i	−0.132074	−	0.991240i	$-0.542164\pi$
$179$	11.5848	−	14.1161i	0.865886	−	1.05508i	0.997960	−	0.0638450i	$-0.0203363\pi$
$180$	−1.44867	+	0.432152i	−0.107977	+	0.0322107i
$181$	6.17327	+	20.3505i	0.458855	+	1.51264i	0.815697	+	0.578479i	$0.196353\pi$
$181$	6.17327	+	20.3505i	0.458855	+	1.51264i	−0.356842	+	0.934165i	$0.616147\pi$
$182$	−0.0128227	+	5.55319i	−0.000950485	+	0.411630i
$183$	−2.09479	−	1.39969i	−0.154851	−	0.103468i
$184$	1.26932	+	2.41483i	0.0935759	+	0.178024i
$185$	−1.33626	−	1.99986i	−0.0982438	−	0.147032i
$186$	−1.30812	+	6.49792i	−0.0959161	+	0.476451i
$187$	5.53441	−	4.54197i	0.404716	−	0.332142i
$188$	−13.8475	−	20.9328i	−1.00993	−	1.52668i
$189$	−0.678687	−	1.26973i	−0.0493672	−	0.0923595i
$190$	−1.29258	−	1.06580i	−0.0937737	−	0.0773211i
$191$			6.64454i			0.480782i	0.970676	+	0.240391i	$0.0772757\pi$
$191$			6.64454i			0.480782i	−0.970676	+	0.240391i	$0.922724\pi$
$192$	3.86856	−	7.00245i	0.279189	−	0.505358i
$193$		−	5.46747i		−	0.393557i	−0.980448	−	0.196779i	$-0.936952\pi$
$193$		−	5.46747i		−	0.393557i	0.980448	−	0.196779i	$-0.0630480\pi$
$194$	9.32465	−	11.3088i	0.669471	−	0.811922i
$195$	0.971813	+	1.81813i	0.0695930	+	0.130199i
$196$	1.96710	−	9.65600i	0.140507	−	0.689714i
$197$	13.8138	−	11.3367i	0.984190	−	0.807703i	0.00285187	−	0.999996i	$-0.499092\pi$
$197$	13.8138	−	11.3367i	0.984190	−	0.807703i	0.981338	+	0.192292i	$0.0615922\pi$
$198$	−7.34919	−	1.47949i	−0.522284	−	0.105143i
$199$	−11.0141	−	16.4837i	−0.780767	−	1.16850i	−0.981986	−	0.188954i	$-0.939490\pi$
$199$	−11.0141	−	16.4837i	−0.780767	−	1.16850i	0.201219	−	0.979546i	$-0.435510\pi$
$200$	−12.4740	+	1.14139i	−0.882046	+	0.0807086i
$201$	2.58602	+	1.72793i	0.182404	+	0.121879i
$202$	−0.258383		0.000596625i	−0.0181797		4.19784e-5i
$203$	−0.758462	−	2.50031i	−0.0532336	−	0.175488i
$204$	−1.28435	+	2.37638i	−0.0899224	+	0.166380i
$205$	0.218514	−	0.266259i	0.0152616	−	0.0185964i
$206$	26.2929	+	2.65094i	1.83191	+	0.184700i
$207$	−0.369111	+	0.891112i	−0.0256550	+	0.0619366i
$208$	−10.4101	−	3.26316i	−0.721809	−	0.226259i
$209$	−3.17924	−	7.67536i	−0.219913	−	0.530916i
$210$	0.443356	+	1.47379i	0.0305944	+	0.101701i
$211$	3.86506	−	0.380675i	0.266081	−	0.0262067i	0.0359034	−	0.999355i	$-0.488569\pi$
$211$	3.86506	−	0.380675i	0.266081	−	0.0262067i	0.230178	+	0.973149i	$0.426069\pi$
$212$	−7.19852	−	13.6184i	−0.494396	−	0.935314i
$213$	−4.59648	−	2.45687i	−0.314946	−	0.168342i
$214$	−13.8476	−	5.77334i	−0.946600	−	0.394658i
$215$	−0.584034	−	2.93614i	−0.0398308	−	0.200243i
$216$	2.77784	−	0.532569i	0.189008	−	0.0362367i
$217$	6.61824	+	1.31645i	0.449276	+	0.0893665i
$218$	−24.3349	+	4.78212i	−1.64817	+	0.323886i
$219$	−2.81203	−	0.276960i	−0.190019	−	0.0187152i
$220$	7.38942	+	3.10086i	0.498195	+	0.209060i
$221$	3.52505	+	1.06931i	0.237121	+	0.0719298i
$222$	2.11214	+	3.97358i	0.141757	+	0.266689i
$223$	−3.72634	+	3.72634i	−0.249534	+	0.249534i	−0.820779	−	0.571245i	$-0.806460\pi$
$223$	−3.72634	+	3.72634i	−0.249534	+	0.249534i	0.571245	+	0.820779i	$0.306460\pi$
$224$	−7.13789	−	3.92190i	−0.476921	−	0.262043i
$225$	−3.13153	−	3.13153i	−0.208769	−	0.208769i
$226$	8.08484	−	26.4323i	0.537796	−	1.75825i
$227$	4.73654	−	15.6143i	0.314375	−	1.03636i	−0.647316	−	0.762221i	$-0.724109\pi$
$227$	4.73654	−	15.6143i	0.314375	−	1.03636i	0.961691	−	0.274134i	$-0.0883913\pi$
$228$	2.20614	+	2.22661i	0.146105	+	0.147461i
$229$	−1.18863	+	12.0683i	−0.0785468	+	0.797499i	0.872533	+	0.488555i	$0.162476\pi$
$229$	−1.18863	+	12.0683i	−0.0785468	+	0.797499i	−0.951080	+	0.308944i	$0.900024\pi$
$230$	0.574802	−	0.855966i	0.0379013	−	0.0564407i
$231$	−1.48891	+	7.48528i	−0.0979633	+	0.492495i
$232$	5.13289	+	0.0355572i	0.336991	+	0.00233445i
$233$	−18.5335	+	3.68655i	−1.21417	+	0.241514i	−0.760311	−	0.649559i	$-0.774954\pi$
$233$	−18.5335	+	3.68655i	−1.21417	+	0.241514i	−0.453861	+	0.891073i	$0.649954\pi$
$234$	−1.46782	−	3.56690i	−0.0959542	−	0.233175i
$235$	−4.47151	+	8.36561i	−0.291689	+	0.545712i
$236$	15.9330	−	19.2326i	1.03715	−	1.25193i
$237$	−0.533651	−	5.41825i	−0.0346643	−	0.351953i
$238$	2.42228	+	1.30194i	0.157013	+	0.0843921i
$239$	0.550153	−	0.227881i	0.0355865	−	0.0147404i	−0.364819	−	0.931078i	$-0.618869\pi$
$239$	0.550153	−	0.227881i	0.0355865	−	0.0147404i	0.400406	+	0.916338i	$0.368869\pi$
$240$	−3.02337	−	0.0279255i	−0.195158	−	0.00180259i
$241$	−6.99989	−	2.89945i	−0.450902	−	0.186770i	0.145663	−	0.989334i	$-0.453468\pi$
$241$	−6.99989	−	2.89945i	−0.450902	−	0.186770i	−0.596566	+	0.802564i	$0.703468\pi$
$242$	15.2981	+	18.7289i	0.983401	+	1.20394i
$243$	0.773010	+	0.634393i	0.0495886	+	0.0406963i
$244$	−3.17854	−	3.90974i	−0.203485	−	0.250295i
$245$	−3.56395	+	1.08111i	−0.227693	+	0.0690698i
$246$	−0.456741	+	0.454637i	−0.0291208	+	0.0289866i
$247$	2.37475	−	3.55406i	0.151101	−	0.226139i
$248$	−6.32994	+	11.6477i	−0.401952	+	0.739628i
$249$	6.79776	−	4.54212i	0.430790	−	0.287845i
$250$	5.58019	+	8.39324i	0.352922	+	0.530835i
$251$	−19.0179	−	23.1734i	−1.20040	−	1.46269i	−0.850555	−	0.525886i	$-0.823734\pi$
$251$	−19.0179	−	23.1734i	−1.20040	−	1.46269i	−0.349847	−	0.936807i	$-0.613766\pi$
$252$	−0.548709	−	2.82671i	−0.0345654	−	0.178066i
$253$	4.50918	−	2.41021i	0.283490	−	0.151529i
$254$	1.70973	+	17.7799i	0.107278	+	1.11561i
$255$	1.02090			0.0639315
$256$	11.5208	−	11.1028i	0.720047	−	0.693925i
$257$	−17.0744			−1.06507			−0.532535	−	0.846408i	$-0.678760\pi$
$257$	−17.0744			−1.06507			−0.532535	+	0.846408i	$0.678760\pi$
$258$	0.536124	+	5.57531i	0.0333776	+	0.347104i
$259$	4.04031	−	2.15959i	0.251053	−	0.134190i
$260$	0.785697	+	4.04757i	0.0487269	+	0.251020i
$261$	1.15129	+	1.40285i	0.0712632	+	0.0868345i
$262$	1.30615	+	1.96459i	0.0806939	+	0.121373i
$263$	−22.3146	+	14.9102i	−1.37598	+	0.919399i	−0.999974	−	0.00721841i	$-0.997702\pi$
$263$	−22.3146	+	14.9102i	−1.37598	+	0.919399i	−0.376005	+	0.926618i	$0.622702\pi$
$264$	−13.1736	−	7.15920i	−0.810779	−	0.440619i
$265$	−3.23436	+	4.84057i	−0.198685	+	0.297354i
$266$	2.26160	−	2.25118i	0.138667	−	0.138029i
$267$	−13.0774	+	3.96698i	−0.800322	+	0.242775i
$268$	3.92391	+	4.82658i	0.239691	+	0.294830i
$269$	0.706588	+	0.579882i	0.0430814	+	0.0353560i	0.655688	−	0.755032i	$-0.272379\pi$
$269$	0.706588	+	0.579882i	0.0430814	+	0.0353560i	−0.612606	+	0.790388i	$0.709879\pi$
$270$	−0.676237	−	0.827888i	−0.0411545	−	0.0503836i
$271$	23.4262	+	9.70344i	1.42304	+	0.589442i	0.955622	−	0.294596i	$-0.0951849\pi$
$271$	23.4262	+	9.70344i	1.42304	+	0.589442i	0.467416	+	0.884037i	$0.345185\pi$
$272$	−3.85527	+	3.78470i	−0.233760	+	0.229481i
$273$	−3.62781	+	1.50269i	−0.219565	+	0.0909467i
$274$	9.12264	+	4.90327i	0.551119	+	0.296217i
$275$	2.30104	+	23.3629i	0.138758	+	1.40884i
$276$	−1.23066	+	1.48552i	−0.0740770	+	0.0894178i
$277$	−10.9394	+	20.4662i	−0.657285	+	1.22969i	0.303614	+	0.952795i	$0.401807\pi$
$277$	−10.9394	+	20.4662i	−0.657285	+	1.22969i	−0.960899	+	0.276899i	$0.910693\pi$
$278$	−2.84695	−	6.91828i	−0.170749	−	0.414931i
$279$	−4.59685	+	0.914370i	−0.275206	+	0.0547419i
$280$	−0.0213223	+	3.07799i	−0.00127425	+	0.183945i
$281$	−5.80657	+	29.1916i	−0.346391	+	1.74143i	0.278245	+	0.960510i	$0.410247\pi$
$281$	−5.80657	+	29.1916i	−0.346391	+	1.74143i	−0.624636	+	0.780916i	$0.714753\pi$
$282$	9.89393	−	14.7335i	0.589175	−	0.877370i
$283$	2.45064	−	24.8817i	0.145675	−	1.47907i	−0.593108	−	0.805123i	$-0.702099\pi$
$283$	2.45064	−	24.8817i	0.145675	−	1.47907i	0.738784	−	0.673943i	$-0.235401\pi$
$284$	−7.33662	−	7.40470i	−0.435348	−	0.439388i
$285$	0.343880	−	1.13362i	0.0203697	−	0.0671498i
$286$	−5.98038	+	19.5520i	−0.353627	+	1.15614i
$287$	0.463914	+	0.463914i	0.0273840	+	0.0273840i
$288$	5.62284	+	0.619426i	0.331329	+	0.0365000i
$289$	−10.7309	+	10.7309i	−0.631231	+	0.631231i
$290$	−0.910537	−	1.71300i	−0.0534686	−	0.100591i
$291$	9.91801	+	3.00860i	0.581404	+	0.176367i
$292$	−5.21104	−	2.18673i	−0.304953	−	0.127969i
$293$	−1.24070	−	0.122198i	−0.0724824	−	0.00713890i	0.0617109	−	0.998094i	$-0.480344\pi$
$293$	−1.24070	−	0.122198i	−0.0724824	−	0.00713890i	−0.134193	+	0.990955i	$0.542844\pi$
$294$	6.83729	−	1.34362i	0.398759	−	0.0783613i
$295$	−9.25762	−	1.84146i	−0.539000	−	0.107214i
$296$	1.69464	+	8.83911i	0.0984991	+	0.513763i
$297$	−1.03416	−	5.19906i	−0.0600079	−	0.301680i
$298$	−10.8246	−	4.51299i	−0.627050	−	0.261430i
$299$	2.32003	+	1.24008i	0.134171	+	0.0717157i
$300$	−4.13919	−	7.83064i	−0.238976	−	0.452102i
$301$	5.67465	−	0.558904i	0.327081	−	0.0322147i
$302$	9.01580	+	29.9701i	0.518801	+	1.72458i
$303$	−0.0699180	−	0.168797i	−0.00401669	−	0.00969714i
$304$	2.90396	+	5.55575i	0.166553	+	0.318644i
$305$	−0.728758	+	1.75938i	−0.0417286	+	0.100742i
$306$	−1.90044	−	0.191609i	−0.108641	−	0.0109535i
$307$	15.4160	−	18.7845i	0.879839	−	1.07209i	−0.117039	−	0.993127i	$-0.537340\pi$
$307$	15.4160	−	18.7845i	0.879839	−	1.07209i	0.996878	−	0.0789595i	$-0.0251598\pi$
$308$	−7.25742	+	13.4281i	−0.413530	+	0.765139i
$309$	5.42431	+	17.8815i	0.308578	+	1.01725i
$310$	5.01014	+	0.0115688i	0.284557	+	0.000657064i
$311$	20.8940	+	13.9609i	1.18479	+	0.791650i	0.982241	−	0.187623i	$-0.0600782\pi$
$311$	20.8940	+	13.9609i	1.18479	+	0.791650i	0.202547	+	0.979273i	$0.435078\pi$
$312$	−0.702926	−	7.68211i	−0.0397953	−	0.434914i
$313$	1.99501	+	2.98574i	0.112765	+	0.168764i	0.883559	−	0.468320i	$-0.155140\pi$
$313$	1.99501	+	2.98574i	0.112765	+	0.168764i	−0.770794	+	0.637084i	$0.780140\pi$
$314$	5.60819	+	1.12901i	0.316489	+	0.0637136i
$315$	−0.841236	+	0.690385i	−0.0473983	+	0.0388988i
$316$	2.17362	−	10.6698i	0.122276	−	0.600222i
$317$	−9.88325	−	18.4903i	−0.555098	−	1.03852i	−0.990400	−	0.138231i	$-0.955858\pi$
$317$	−9.88325	−	18.4903i	−0.555098	−	1.03852i	0.435301	−	0.900285i	$-0.356642\pi$
$318$	6.92935	−	8.40379i	0.388579	−	0.471261i
$319$		−	9.62007i		−	0.538621i
$320$	−5.76175	−	1.83535i	−0.322091	−	0.102599i
$321$		−	10.6086i		−	0.592116i
$322$	1.51522	+	1.24937i	0.0844398	+	0.0696249i
$323$	−0.997823	−	1.86680i	−0.0555204	−	0.103871i
$324$	1.10345	+	1.66805i	0.0613027	+	0.0926696i
$325$	−9.33691	+	7.66260i	−0.517918	+	0.425045i
$326$	2.83742	−	14.0945i	0.157150	−	0.780623i
$327$	−9.74273	−	14.5810i	−0.538774	−	0.806333i
$328$	−1.14088	+	0.599688i	−0.0629944	+	0.0331122i
$329$	−15.0227	−	10.0378i	−0.828226	−	0.553403i
$330$	−0.0130844	+	5.66650i	−0.000720272	+	0.311931i
$331$	2.44422	+	8.05751i	0.134346	+	0.442881i	0.998140	−	0.0609654i	$-0.0194179\pi$
$331$	2.44422	+	8.05751i	0.134346	+	0.442881i	−0.863794	+	0.503846i	$0.831918\pi$
$332$	15.6689	−	4.67419i	0.859940	−	0.256529i
$333$	−2.01865	+	2.45973i	−0.110621	+	0.134792i
$334$	−0.0675816	+	0.670297i	−0.00369790	+	0.0366770i
$335$	0.899655	−	2.17196i	0.0491534	−	0.118667i
$336$	0.617385	−	5.72575i	0.0336811	−	0.312365i
$337$	6.09046	+	14.7037i	0.331769	+	0.800960i	0.998452	+	0.0556194i	$0.0177133\pi$
$337$	6.09046	+	14.7037i	0.331769	+	0.800960i	−0.666683	+	0.745341i	$0.732287\pi$
$338$	7.53157	−	2.26570i	0.409664	−	0.123238i
$339$	19.4511	−	1.91577i	1.05644	−	0.104050i
$340$	1.95113	+	0.601723i	0.105815	+	0.0326330i
$341$	21.9112	+	11.7118i	1.18656	+	0.634230i
$342$	−0.852904	+	2.04572i	−0.0461198	+	0.110620i
$343$	−3.35008	−	16.8420i	−0.180887	−	0.909383i
$344$	−2.26147	+	10.9714i	−0.121930	+	0.591539i
$345$	0.715057	+	0.142234i	0.0384974	+	0.00765761i
$346$	0.150537	+	0.766041i	0.00809293	+	0.0411826i
$347$	−4.92957	−	0.485520i	−0.264633	−	0.0260641i	−0.0351697	−	0.999381i	$-0.511197\pi$
$347$	−4.92957	−	0.485520i	−0.264633	−	0.0260641i	−0.229464	+	0.973317i	$0.573697\pi$
$348$	1.37348	+	3.35968i	0.0736264	+	0.180098i
$349$	8.81651	+	2.67446i	0.471937	+	0.143161i	0.517289	−	0.855811i	$-0.326941\pi$
$349$	8.81651	+	2.67446i	0.471937	+	0.143161i	−0.0453525	+	0.998971i	$0.514441\pi$
$350$	−7.96221	+	4.23228i	−0.425598	+	0.226225i
$351$	1.92855	−	1.92855i	0.102938	−	0.102938i
$352$	−20.9575	−	21.4471i	−1.11704	−	1.14313i
$353$	22.5330	+	22.5330i	1.19931	+	1.19931i	0.974373	+	0.224938i	$0.0722178\pi$
$353$	22.5330	+	22.5330i	1.19931	+	1.19931i	0.224938	+	0.974373i	$0.427782\pi$
$354$	16.8877	+	5.16543i	0.897570	+	0.274540i
$355$	−1.14359	+	3.76991i	−0.0606954	+	0.200086i
$356$	−27.3314	−	0.126221i	−1.44856	−	0.00668970i
$357$	−0.190599	+	1.93518i	−0.0100875	+	0.102421i
$358$	21.4397	+	14.3973i	1.13312	+	0.760918i
$359$	−2.54158	+	12.7774i	−0.134139	+	0.674364i	0.853934	+	0.520381i	$0.174210\pi$
$359$	−2.54158	+	12.7774i	−0.134139	+	0.674364i	−0.988073	+	0.153983i	$0.950790\pi$
$360$	−0.804451	−	1.98082i	−0.0423983	−	0.104398i
$361$	16.2259	−	3.22753i	0.853995	−	0.169870i
$362$	−27.8122	+	11.4450i	−1.46178	+	0.601537i
$363$	−8.06077	+	15.0806i	−0.423080	+	0.791528i
$364$	−7.81907	+	0.733668i	−0.409831	+	0.0384546i
$365$	0.209347	+	2.12554i	0.0109577	+	0.111256i
$366$	1.68681	−	3.13835i	0.0881710	−	0.164044i
$367$	9.33088	−	3.86498i	0.487068	−	0.201750i	−0.125615	−	0.992079i	$-0.540090\pi$
$367$	9.33088	−	3.86498i	0.487068	−	0.201750i	0.612683	+	0.790329i	$0.290090\pi$
$368$	−3.22758	+	2.11374i	−0.168249	+	0.110186i
$369$	−0.421003	−	0.174385i	−0.0219165	−	0.00907812i
$370$	2.63435	−	2.15180i	0.136953	−	0.111867i
$371$	−8.57171	−	7.03462i	−0.445021	−	0.365220i
$372$	−9.32433	−	0.961865i	−0.483444	−	0.0498704i
$373$	−29.4645	+	8.93797i	−1.52562	+	0.462791i	−0.938083	−	0.346410i	$-0.887401\pi$
$373$	−29.4645	+	8.93797i	−1.52562	+	0.462791i	−0.587533	+	0.809200i	$0.699901\pi$
$374$	7.14301	+	7.17607i	0.369356	+	0.371066i
$375$	−3.95948	+	5.92579i	−0.204467	+	0.306006i
$376$	27.5930	−	22.3269i	1.42300	−	1.15142i
$377$	4.11547	−	2.74987i	0.211958	−	0.141626i
$378$	1.69556	−	1.12728i	0.0872100	−	0.0579811i
$379$	21.8623	+	26.6393i	1.12299	+	1.36837i	0.921268	+	0.388929i	$0.127155\pi$
$379$	21.8623	+	26.6393i	1.12299	+	1.36837i	0.201726	+	0.979442i	$0.435345\pi$
$380$	1.32537	−	1.96387i	0.0679902	−	0.100744i
$381$	−11.1389	+	5.95389i	−0.570665	+	0.305027i
$382$	−9.35366	+	0.899452i	−0.478575	+	0.0460200i
$383$	3.55374			0.181588			0.0907938	−	0.995870i	$-0.471060\pi$
$383$	3.55374			0.181588			0.0907938	+	0.995870i	$0.471060\pi$
$384$	10.3812	+	4.49795i	0.529761	+	0.229535i
$385$	5.76878			0.294004
$386$	7.69667	−	0.740115i	0.391750	−	0.0376709i
$387$	−3.49287	+	1.86698i	−0.177553	+	0.0949038i
$388$	17.1818	+	11.5957i	0.872275	+	0.588680i
$389$	−6.89272	−	8.39881i	−0.349475	−	0.425836i	0.568372	−	0.822772i	$-0.307574\pi$
$389$	−6.89272	−	8.39881i	−0.349475	−	0.425836i	−0.917846	+	0.396936i	$0.870074\pi$
$390$	−2.42787	+	1.61416i	−0.122940	+	0.0817360i
$391$	1.08317	−	0.723754i	0.0547785	−	0.0366018i
$392$	13.8592	+	1.46202i	0.699996	+	0.0738431i
$393$	−0.926789	+	1.38704i	−0.0467503	+	0.0699668i
$394$	17.8288	+	17.9113i	0.898200	+	0.902358i
$395$	−3.93813	+	1.19462i	−0.198149	+	0.0601078i
$396$	1.08788	−	10.5459i	0.0546678	−	0.529950i
$397$	−22.5098	−	18.4733i	−1.12973	−	0.927149i	−0.131792	−	0.991277i	$-0.542073\pi$
$397$	−22.5098	−	18.4733i	−1.12973	−	0.927149i	−0.997942	+	0.0641286i	$0.979573\pi$
$398$	21.7135	−	17.7361i	1.08840	−	0.889030i
$399$	2.08464	+	0.863485i	0.104362	+	0.0432283i
$400$	−3.29533	−	17.4054i	−0.164767	−	0.870270i
$401$	−14.2036	+	5.88334i	−0.709296	+	0.293800i	−0.708013	−	0.706199i	$-0.750408\pi$
$401$	−14.2036	+	5.88334i	−0.709296	+	0.293800i	−0.00128267	+	0.999999i	$0.500408\pi$
$402$	−2.08237	+	3.87430i	−0.103859	+	0.193233i
$403$	1.25295	+	12.7214i	0.0624139	+	0.633699i
$404$	−0.0341366	−	0.363811i	−0.00169836	−	0.0181003i
$405$	0.356317	−	0.666622i	0.0177055	−	0.0331247i
$406$	3.41707	−	1.40616i	0.169586	−	0.0697867i
$407$	16.5435	−	3.29071i	0.820031	−	0.163114i
$408$	−3.51914	−	1.48632i	−0.174224	−	0.0735838i
$409$	−4.84431	+	24.3540i	−0.239535	+	1.20423i	0.654441	+	0.756113i	$0.272904\pi$
$409$	−4.84431	+	24.3540i	−0.239535	+	1.20423i	−0.893977	+	0.448113i	$0.852096\pi$
$410$	0.404398	+	0.271563i	0.0199718	+	0.0134115i
$411$	−0.717819	+	7.28814i	−0.0354074	+	0.359498i
$412$	−0.172590	+	37.3719i	−0.00850291	+	1.84118i
$413$	5.21894	−	17.2045i	0.256807	−	0.846580i
$414$	−1.30440	−	0.398977i	−0.0641078	−	0.0196087i
$415$	−4.36973	−	4.36973i	−0.214501	−	0.214501i
$416$	3.18443	−	15.0962i	0.156130	−	0.740152i
$417$	3.74058	−	3.74058i	0.183177	−	0.183177i
$418$	10.3744	−	5.51447i	0.507428	−	0.269721i
$419$	−14.5442	−	4.41192i	−0.710529	−	0.215536i	−0.0857254	−	0.996319i	$-0.527321\pi$
$419$	−14.5442	−	4.41192i	−0.710529	−	0.215536i	−0.624803	+	0.780782i	$0.714821\pi$
$420$	−2.01467	+	0.823623i	−0.0983057	+	0.0401887i
$421$	−3.66789	−	0.361256i	−0.178762	−	0.0176065i	0.00824002	−	0.999966i	$-0.497377\pi$
$421$	−3.66789	−	0.361256i	−0.178762	−	0.0176065i	−0.187002	+	0.982360i	$0.559877\pi$
$422$	1.05908	+	5.38939i	0.0515554	+	0.262351i
$423$	12.3081	+	2.44824i	0.598441	+	0.119037i
$424$	18.1964	−	11.9770i	0.883697	−	0.581653i
$425$	1.16692	+	5.86652i	0.0566041	+	0.284568i
$426$	2.83637	−	6.80314i	0.137423	−	0.329613i
$427$	−3.19894	−	1.70987i	−0.154808	−	0.0827464i
$428$	6.25275	−	20.2750i	0.302238	−	0.980029i
$429$	−14.3880	+	1.41710i	−0.694660	+	0.0684180i
$430$	4.05420	−	1.21961i	0.195511	−	0.0588150i
$431$	−5.84580	−	14.1130i	−0.281582	−	0.679800i	0.718291	−	0.695743i	$-0.244925\pi$
$431$	−5.84580	−	14.1130i	−0.281582	−	0.679800i	−0.999873	+	0.0159433i	$0.994925\pi$
$432$	1.12574	+	3.83832i	0.0541620	+	0.184671i
$433$	−14.0563	+	33.9349i	−0.675502	+	1.63081i	0.0966123	+	0.995322i	$0.469199\pi$
$433$	−14.0563	+	33.9349i	−0.675502	+	1.63081i	−0.772114	+	0.635484i	$0.780801\pi$
$434$	−0.957302	+	9.49484i	−0.0459520	+	0.455767i
$435$	0.870234	−	1.06038i	0.0417245	−	0.0508415i
$436$	−10.0260	−	33.6093i	−0.480160	−	1.60960i
$437$	−0.438807	−	1.44655i	−0.0209910	−	0.0691980i
$438$	0.00922716	−	3.99604i	0.000440891	−	0.190938i
$439$	−26.8620	−	17.9486i	−1.28205	−	0.856640i	−0.287190	−	0.957874i	$-0.592721\pi$
$439$	−26.8620	−	17.9486i	−1.28205	−	0.856640i	−0.994863	+	0.101233i	$0.967721\pi$
$440$	−3.36485	+	10.8220i	−0.160413	+	0.515918i
$441$	2.73738	+	4.09679i	0.130352	+	0.195085i
$442$	−1.02812	+	5.10704i	−0.0489026	+	0.242917i
$443$	4.87341	−	3.99951i	0.231543	−	0.190022i	−0.511467	−	0.859303i	$-0.670898\pi$
$443$	4.87341	−	3.99951i	0.231543	−	0.190022i	0.743010	+	0.669281i	$0.233398\pi$
$444$	−5.30777	+	3.51119i	−0.251896	+	0.166634i
$445$	4.86937	+	9.10994i	0.230830	+	0.431853i
$446$	−5.75006	−	4.74122i	−0.272273	−	0.224503i
$447$		−	8.29271i		−	0.392232i
$448$	4.55470	−	10.5791i	0.215189	−	0.499813i
$449$		−	33.5296i		−	1.58236i	−0.611583	−	0.791181i	$-0.709467\pi$
$449$		−	33.5296i		−	1.58236i	0.611583	−	0.791181i	$-0.290533\pi$
$450$	3.98441	−	4.83222i	0.187827	−	0.227793i
$451$	1.13870	+	2.13035i	0.0536191	+	0.100314i
$452$	38.3037	+	7.80314i	1.80165	+	0.367029i
$453$	−17.1069	+	14.0392i	−0.803750	+	0.659621i
$454$	22.6217	+	4.55406i	1.06169	+	0.213733i
$455$	1.64899	+	2.46789i	0.0773058	+	0.115696i
$456$	−2.83580	+	3.40703i	−0.132799	+	0.159549i
$457$	−3.05688	−	2.04254i	−0.142995	−	0.0955462i	0.482015	−	0.876163i	$-0.339905\pi$
$457$	−3.05688	−	2.04254i	−0.142995	−	0.0955462i	−0.625010	+	0.780617i	$0.714905\pi$
$458$	−17.1498	−	0.0396001i	−0.801356	−	0.00185039i
$459$	−0.392066	−	1.29247i	−0.0183001	−	0.0603272i
$460$	1.28277	+	0.693290i	0.0598095	+	0.0323248i
$461$	9.03952	−	11.0147i	0.421012	−	0.513005i	−0.518707	−	0.854952i	$-0.673586\pi$
$461$	9.03952	−	11.0147i	0.421012	−	0.513005i	0.939719	+	0.341947i	$0.111086\pi$
$462$	−10.7387	−	1.08271i	−0.499611	−	0.0503724i
$463$	−10.3307	+	24.9405i	−0.480108	+	1.15908i	0.479449	+	0.877570i	$0.340837\pi$
$463$	−10.3307	+	24.9405i	−0.480108	+	1.15908i	−0.959557	+	0.281514i	$0.909163\pi$
$464$	0.644769	+	7.23048i	0.0299327	+	0.335667i
$465$	1.35574	+	3.27304i	0.0628708	+	0.151784i
$466$	−7.69846	−	25.5910i	−0.356624	−	1.18548i
$467$	27.7745	−	2.73555i	1.28525	−	0.126586i	0.567783	−	0.823178i	$-0.307801\pi$
$467$	27.7745	−	2.73555i	1.28525	−	0.126586i	0.717467	+	0.696592i	$0.245301\pi$
$468$	4.82250	−	2.54911i	0.222920	−	0.117833i
$469$	3.94910	+	2.11084i	0.182353	+	0.0974696i
$470$	−12.3817	−	5.16221i	−0.571127	−	0.238115i
$471$	0.789170	+	3.96743i	0.0363630	+	0.182809i
$472$	29.2309	+	19.8257i	1.34546	+	0.912551i
$473$	20.5910	+	4.09581i	0.946776	+	0.188325i
$474$	7.55514	−	1.48468i	0.347019	−	0.0681937i
$475$	6.90729	+	0.680308i	0.316928	+	0.0312147i
$476$	−1.50487	+	3.58614i	−0.0689754	+	0.164370i
$477$	7.37029	+	2.23575i	0.337462	+	0.102368i
$478$	0.395265	+	0.743614i	0.0180790	+	0.0340121i
$479$	7.94374	−	7.94374i	0.362959	−	0.362959i	−0.501942	−	0.864901i	$-0.667381\pi$
$479$	7.94374	−	7.94374i	0.362959	−	0.362959i	0.864901	+	0.501942i	$0.167381\pi$
$480$	−0.369953	−	4.25984i	−0.0168860	−	0.194434i
$481$	6.13668	+	6.13668i	0.279808	+	0.279808i
$482$	3.13406	−	10.2464i	0.142752	−	0.466709i
$483$	−0.403110	+	1.32888i	−0.0183421	+	0.0604660i
$484$	−24.2941	+	24.0708i	−1.10428	+	1.09413i
$485$	0.767877	−	7.79639i	0.0348675	−	0.354016i
$486$	−0.788408	+	1.17406i	−0.0357629	+	0.0532564i
$487$	−2.89871	+	14.5728i	−0.131353	+	0.660356i	0.857861	+	0.513881i	$0.171793\pi$
$487$	−2.89871	+	14.5728i	−0.131353	+	0.660356i	−0.989214	+	0.146475i	$0.953207\pi$
$488$	5.07355	−	5.00374i	0.229669	−	0.226509i
$489$	9.97093	−	1.98334i	0.450901	−	0.0896898i
$490$	−2.00435	−	4.87070i	−0.0905471	−	0.220036i
$491$	−12.2843	+	22.9823i	−0.554382	+	1.03718i	0.436148	+	0.899875i	$0.356343\pi$
$491$	−12.2843	+	22.9823i	−0.554382	+	1.03718i	−0.990529	+	0.137300i	$0.956157\pi$
$492$	−0.701829	−	0.581421i	−0.0316409	−	0.0262125i
$493$	−0.240250	−	2.43930i	−0.0108203	−	0.109861i
$494$	5.32458	+	2.86188i	0.239564	+	0.128762i
$495$	−3.70183	+	1.53335i	−0.166385	+	0.0689189i
$496$	−17.2535	−	7.33407i	−0.774707	−	0.329310i
$497$	−6.93256	−	2.87156i	−0.310968	−	0.128807i
$498$	7.31422	+	8.95449i	0.327758	+	0.401260i
$499$	9.26830	+	7.60630i	0.414906	+	0.340505i	0.818574	−	0.574401i	$-0.194765\pi$
$499$	9.26830	+	7.60630i	0.414906	+	0.340505i	−0.403668	+	0.914906i	$0.632265\pi$
$500$	−11.0600	+	8.99151i	−0.494616	+	0.402113i
$501$	−0.455862	+	0.138284i	−0.0203664	+	0.00617808i
$502$	30.0473	−	29.9088i	1.34108	−	1.33490i
$503$	12.6333	−	18.9071i	0.563290	−	0.843024i	−0.435062	−	0.900400i	$-0.643274\pi$
$503$	12.6333	−	18.9071i	0.563290	−	0.843024i	0.998353	+	0.0573767i	$0.0182736\pi$
$504$	3.90493	−	1.15507i	0.173940	−	0.0514509i
$505$	−0.114828	+	0.0767253i	−0.00510976	+	0.00341423i
$506$	4.00329	+	6.02141i	0.177968	+	0.267684i
$507$	3.52811	+	4.29901i	0.156689	+	0.190926i
$508$	−24.7977	+	4.81363i	−1.10022	+	0.213570i
$509$	6.12267	−	3.27264i	0.271383	−	0.145057i	−0.330092	−	0.943949i	$-0.607080\pi$
$509$	6.12267	−	3.27264i	0.271383	−	0.145057i	0.601475	+	0.798892i	$0.294580\pi$
$510$	0.138197	+	1.43715i	0.00611945	+	0.0636380i
$511$	−4.06816			−0.179965
$512$	17.1892	+	14.7151i	0.759661	+	0.650320i
$513$	−1.56723			−0.0691948
$514$	−2.31131	−	24.0359i	−0.101947	−	1.06018i
$515$	12.4566	−	6.65820i	0.548904	−	0.293395i
$516$	−7.77590	+	1.50943i	−0.342315	+	0.0664488i
$517$	−42.2015	−	51.4226i	−1.85602	−	2.26156i
$518$	3.58702	+	5.39529i	0.157605	+	0.237055i
$519$	−0.458999	+	0.306693i	−0.0201478	+	0.0134623i
$520$	−5.59149	+	1.65395i	−0.245203	+	0.0725305i
$521$	−5.40529	+	8.08959i	−0.236810	+	0.354411i	−0.930772	−	0.365601i	$-0.880864\pi$
$521$	−5.40529	+	8.08959i	−0.236810	+	0.354411i	0.693962	+	0.720012i	$0.255864\pi$
$522$	−1.81898	+	1.81060i	−0.0796146	+	0.0792477i
$523$	10.1705	−	3.08519i	0.444725	−	0.134906i	−0.0599766	−	0.998200i	$-0.519103\pi$
$523$	10.1705	−	3.08519i	0.444725	−	0.134906i	0.504701	+	0.863294i	$0.331603\pi$
$524$	−2.58878	+	2.10463i	−0.113092	+	0.0919411i
$525$	−4.92878	−	4.04495i	−0.215110	−	0.176536i
$526$	−24.0100	−	29.3944i	−1.04689	−	1.28166i
$527$	5.84839	+	2.42248i	0.254760	+	0.105525i
$528$	8.29488	−	19.5139i	0.360988	−	0.849232i
$529$	−20.3897	+	8.44570i	−0.886510	+	0.367204i
$530$	−7.25199	−	3.89782i	−0.315006	−	0.169311i
$531$	1.22399	+	12.4274i	0.0531166	+	0.539302i
$532$	3.47517	+	2.87896i	0.150668	+	0.124819i
$533$	−0.585871	+	1.09609i	−0.0253769	+	0.0474769i
$534$	−7.35464	−	17.8723i	−0.318266	−	0.773409i
$535$	−7.86473	+	1.56439i	−0.340022	+	0.0676345i
$536$	−6.26331	+	6.17713i	−0.270534	+	0.266811i
$537$	−3.56258	+	17.9103i	−0.153737	+	0.772886i
$538$	−0.720663	+	1.07317i	−0.0310700	+	0.0462679i
$539$	2.56006	−	25.9927i	0.110270	−	1.11959i
$540$	1.07389	−	1.06402i	0.0462130	−	0.0457882i
$541$	−1.63408	+	5.38685i	−0.0702548	+	0.231599i	−0.985035	−	0.172352i	$-0.944863\pi$
$541$	−1.63408	+	5.38685i	−0.0702548	+	0.231599i	0.914781	+	0.403951i	$0.132363\pi$
$542$	−10.4886	+	34.2910i	−0.450524	+	1.47293i
$543$	−15.0375	−	15.0375i	−0.645322	−	0.645322i
$544$	−5.84967	−	4.91481i	−0.250803	−	0.210721i
$545$	−9.37296	+	9.37296i	−0.401494	+	0.401494i
$546$	−2.60645	−	4.90352i	−0.111546	−	0.209851i
$547$	−25.9372	−	7.86796i	−1.10899	−	0.336410i	−0.317912	−	0.948120i	$-0.602982\pi$
$547$	−25.9372	−	7.86796i	−1.10899	−	0.336410i	−0.791082	+	0.611710i	$0.790482\pi$
$548$	−5.66753	+	13.5059i	−0.242105	+	0.576942i
$549$	2.50725	+	0.246943i	0.107007	+	0.0105393i
$550$	−32.5769	+	6.40179i	−1.38908	+	0.272973i
$551$	−2.78955	−	0.554875i	−0.118839	−	0.0236385i
$552$	−2.25779	−	1.53133i	−0.0960978	−	0.0651779i
$553$	−1.52923	−	7.68797i	−0.0650296	−	0.326926i
$554$	−30.2915	−	12.6292i	−1.28696	−	0.536562i
$555$	2.12120	+	1.13381i	0.0900400	+	0.0481274i
$556$	9.35362	−	4.94421i	0.396682	−	0.209681i
$557$	−17.4005	+	1.71380i	−0.737282	+	0.0726160i	−0.459686	−	0.888082i	$-0.652038\pi$
$557$	−17.4005	+	1.71380i	−0.737282	+	0.0726160i	−0.277597	+	0.960698i	$0.589538\pi$
$558$	−1.90944	−	6.34730i	−0.0808329	−	0.268703i
$559$	4.13369	+	9.97962i	0.174837	+	0.422093i
$560$	−4.33584	+	0.386643i	−0.183222	+	0.0163386i
$561$	−2.73984	+	6.61457i	−0.115676	+	0.279267i
$562$	−41.8796	−	4.22245i	−1.76659	−	0.178113i
$563$	14.9924	−	18.2683i	0.631855	−	0.769918i	−0.354410	−	0.935090i	$-0.615318\pi$
$563$	14.9924	−	18.2683i	0.631855	−	0.769918i	0.986265	+	0.165173i	$0.0528181\pi$
$564$	22.0800	+	11.9334i	0.929737	+	0.502489i
$565$	−4.28859	−	14.1376i	−0.180422	−	0.594773i
$566$	35.3582	+	0.0816449i	1.48622	+	0.00343179i
$567$	1.19710	+	0.799874i	0.0502733	+	0.0335916i
$568$	9.43060	−	11.3303i	0.395699	−	0.475407i
$569$	−2.81203	−	4.20850i	−0.117887	−	0.176430i	0.767834	−	0.640649i	$-0.221335\pi$
$569$	−2.81203	−	4.20850i	−0.117887	−	0.176430i	−0.885720	+	0.464220i	$0.846335\pi$
$570$	1.64237	+	0.330632i	0.0687912	+	0.0138486i
$571$	−3.57679	+	2.93540i	−0.149684	+	0.122843i	−0.706255	−	0.707958i	$-0.749617\pi$
$571$	−3.57679	+	2.93540i	−0.149684	+	0.122843i	0.556571	+	0.830800i	$0.312117\pi$
$572$	−28.3333	−	5.77200i	−1.18468	−	0.241339i
$573$	−3.13222	−	5.85997i	−0.130850	−	0.244804i
$574$	−0.590262	+	0.715859i	−0.0246371	+	0.0298794i
$575$			4.27158i			0.178137i
$576$	−0.110832	+	7.99923i	−0.00461800	+	0.333301i
$577$		−	19.6321i		−	0.817296i	−0.912692	−	0.408648i	$-0.866000\pi$
$577$		−	19.6321i		−	0.817296i	0.912692	−	0.408648i	$-0.134000\pi$
$578$	−16.5587	−	13.6535i	−0.688753	−	0.567911i
$579$	2.57735	+	4.82188i	0.107111	+	0.200390i
$580$	2.28816	−	1.51366i	0.0950108	−	0.0628515i
$581$	9.09887	−	7.46725i	0.377485	−	0.309794i
$582$	−2.89269	+	14.3691i	−0.119906	+	0.595616i
$583$	−22.6824	−	33.9467i	−0.939411	−	1.40593i
$584$	2.37291	−	7.63170i	0.0981915	−	0.315802i
$585$	−1.71413	−	1.14534i	−0.0708703	−	0.0473541i
$586$	0.00407113	−	1.76310i	0.000168177	−	0.0728330i
$587$	−12.2430	−	40.3598i	−0.505323	−	1.66583i	−0.723820	−	0.689989i	$-0.757616\pi$
$587$	−12.2430	−	40.3598i	−0.505323	−	1.66583i	0.218497	−	0.975838i	$-0.429884\pi$
$588$	2.81698	+	9.44311i	0.116170	+	0.389427i
$589$	4.65990	−	5.67811i	0.192008	−	0.233962i
$590$	1.33908	−	13.2814i	0.0551289	−	0.546787i
$591$	−6.83858	+	16.5098i	−0.281302	+	0.679122i
$592$	−12.2136	+	3.58211i	−0.501976	+	0.147224i
$593$	7.65890	+	18.4902i	0.314513	+	0.759302i	0.999526	+	0.0307713i	$0.00979636\pi$
$593$	7.65890	+	18.4902i	0.314513	+	0.759302i	−0.685013	+	0.728531i	$0.740204\pi$
$594$	7.17884	−	2.15959i	0.294551	−	0.0886089i
$595$	1.46275	−	0.144069i	0.0599671	−	0.00590624i
$596$	4.88774	−	15.8489i	0.200209	−	0.649194i
$597$	17.4839	+	9.34535i	0.715569	+	0.382480i
$598$	−1.43163	+	3.43381i	−0.0585437	+	0.140419i
$599$	−2.65541	−	13.3496i	−0.108497	−	0.545452i	−0.996353	−	0.0853297i	$-0.972806\pi$
$599$	−2.65541	−	13.3496i	−0.108497	−	0.545452i	0.887856	−	0.460122i	$-0.152194\pi$
$600$	10.4630	−	6.88683i	0.427152	−	0.281154i
$601$	7.32819	+	1.45767i	0.298923	+	0.0594595i	0.342273	−	0.939600i	$-0.388803\pi$
$601$	7.32819	+	1.45767i	0.298923	+	0.0594595i	−0.0433501	+	0.999060i	$0.513803\pi$
$602$	1.55494	+	7.91266i	0.0633747	+	0.322496i
$603$	−3.09521	−	0.304851i	−0.126047	−	0.0124145i
$604$	−40.9690	+	16.7487i	−1.66701	+	0.681494i
$605$	12.3687	+	3.75201i	0.502860	+	0.152541i
$606$	0.228154	−	0.121275i	0.00926814	−	0.00492644i
$607$	−18.6817	+	18.6817i	−0.758266	+	0.758266i	−0.976007	−	0.217741i	$-0.930131\pi$
$607$	−18.6817	+	18.6817i	−0.758266	+	0.758266i	0.217741	+	0.976007i	$0.430131\pi$
$608$	−7.42784	+	4.84002i	−0.301238	+	0.196289i
$609$	1.84754	+	1.84754i	0.0748663	+	0.0748663i
$610$	−2.57536	−	0.787726i	−0.104273	−	0.0318941i
$611$	9.93546	−	32.7528i	0.401946	−	1.32504i
$612$	0.0124747	−	2.70122i	0.000504261	−	0.109190i
$613$	−1.59760	+	16.2207i	−0.0645265	+	0.655149i	0.907464	+	0.420130i	$0.138015\pi$
$613$	−1.59760	+	16.2207i	−0.0645265	+	0.655149i	−0.971991	+	0.235019i	$0.924485\pi$
$614$	28.5301	+	19.1586i	1.15138	+	0.773180i
$615$	−0.0671979	+	0.337826i	−0.00270968	+	0.0136225i
$616$	−19.8855	−	8.39868i	−0.801208	−	0.338393i
$617$	−38.7599	+	7.70983i	−1.56042	+	0.310386i	−0.898426	−	0.439126i	$-0.855288\pi$
$617$	−38.7599	+	7.70983i	−1.56042	+	0.310386i	−0.661991	+	0.749512i	$0.730288\pi$
$618$	−24.4379	+	10.0565i	−0.983038	+	0.404531i
$619$	−4.71035	+	8.81245i	−0.189325	+	0.354202i	−0.958619	−	0.284693i	$-0.908108\pi$
$619$	−4.71035	+	8.81245i	−0.189325	+	0.354202i	0.769294	+	0.638895i	$0.220608\pi$
$620$	0.661922	+	7.05444i	0.0265834	+	0.283313i
$621$	−0.0945407	−	0.959888i	−0.00379379	−	0.0385190i
$622$	−16.8247	+	31.3027i	−0.674608	+	1.25512i
$623$	−18.1775	+	7.52936i	−0.728265	+	0.301657i
$624$	10.7191	−	2.02943i	0.429108	−	0.0812421i
$625$	−15.4807	−	6.41233i	−0.619229	−	0.256493i
$626$	−3.93303	+	3.21259i	−0.157196	+	0.128401i
$627$	6.42198	+	5.27038i	0.256469	+	0.210479i
$628$	−0.830162	+	8.04760i	−0.0331271	+	0.321134i
$629$	4.11265	−	1.24756i	0.163982	−	0.0497434i
$630$	−1.08574	−	1.09077i	−0.0432571	−	0.0434573i
$631$	−12.4827	+	18.6816i	−0.496927	+	0.743703i	−0.992149	−	0.125063i	$-0.960087\pi$
$631$	−12.4827	+	18.6816i	−0.496927	+	0.743703i	0.495222	+	0.868766i	$0.335087\pi$
$632$	15.3143	+	1.61552i	0.609170	+	0.0642618i
$633$	−3.22923	+	2.15770i	−0.128350	+	0.0857609i
$634$	24.6912	−	16.4158i	0.980614	−	0.651955i
$635$	6.05651	+	7.37988i	0.240345	+	0.292862i
$636$	12.7682	+	8.61699i	0.506292	+	0.341686i
$637$	11.8515	−	6.33475i	0.469573	−	0.250992i
$638$	13.5424	−	1.30224i	0.536148	−	0.0515562i
$639$	5.21190			0.206179
$640$	1.80371	−	8.35937i	0.0712979	−	0.330433i
$641$	25.2508			0.997346			0.498673	−	0.866790i	$-0.333821\pi$
$641$	25.2508			0.997346			0.498673	+	0.866790i	$0.333821\pi$
$642$	14.9340	−	1.43606i	0.589398	−	0.0566767i
$643$	−23.6632	+	12.6482i	−0.933184	+	0.498797i	−0.866611	−	0.498984i	$-0.833707\pi$
$643$	−23.6632	+	12.6482i	−0.933184	+	0.498797i	−0.0665732	+	0.997782i	$0.521207\pi$
$644$	−1.55366	+	2.30213i	−0.0612227	+	0.0907165i
$645$	1.89916	+	2.31413i	0.0747793	+	0.0911188i
$646$	2.49285	−	1.65736i	0.0980800	−	0.0652079i
$647$	−10.6245	+	7.09906i	−0.417692	+	0.279093i	−0.746605	−	0.665267i	$-0.768318\pi$
$647$	−10.6245	+	7.09906i	−0.417692	+	0.279093i	0.328913	+	0.944360i	$0.393318\pi$
$648$	−2.19878	+	1.77915i	−0.0863763	+	0.0698915i
$649$	36.7761	−	55.0393i	1.44359	−	2.16048i
$650$	−12.0507	−	12.1065i	−0.472668	−	0.474856i
$651$	−6.45734	+	1.95881i	−0.253083	+	0.0767719i
$652$	20.2252	+	2.08636i	0.792081	+	0.0817083i
$653$	3.05298	+	2.50551i	0.119472	+	0.0980483i	0.692232	−	0.721675i	$-0.256627\pi$
$653$	3.05298	+	2.50551i	0.119472	+	0.0980483i	−0.572760	+	0.819723i	$0.694127\pi$
$654$	19.2072	−	15.6888i	0.751060	−	0.613482i
$655$	1.16495	+	0.482538i	0.0455184	+	0.0188543i
$656$	−0.998630	−	1.52486i	−0.0389900	−	0.0595357i
$657$	2.61054	−	1.08132i	0.101847	−	0.0421864i
$658$	12.0969	−	22.5065i	0.471585	−	0.877394i
$659$	2.36134	+	23.9750i	0.0919846	+	0.933935i	0.924818	+	0.380411i	$0.124217\pi$
$659$	2.36134	+	23.9750i	0.0919846	+	0.933935i	−0.832833	+	0.553524i	$0.813283\pi$
$660$	−7.97862	+	0.748638i	−0.310567	+	0.0291407i
$661$	18.5569	−	34.7175i	0.721780	−	1.35036i	−0.206490	−	0.978449i	$-0.566204\pi$
$661$	18.5569	−	34.7175i	0.721780	−	1.35036i	0.928270	−	0.371906i	$-0.121296\pi$
$662$	−11.0118	+	4.53149i	−0.427988	+	0.176122i
$663$	−3.61289	+	0.718649i	−0.140313	+	0.0279100i
$664$	8.70099	+	21.4246i	0.337664	+	0.831437i
$665$	0.332737	−	1.67278i	0.0129030	−	0.0648676i
$666$	−3.73587	−	2.50873i	−0.144762	−	0.0972111i
$667$	0.171572	−	1.74200i	0.00664329	−	0.0674505i
$668$	−0.952739	−	0.00439992i	−0.0368626	−	0.000170238i
$669$	1.52975	−	5.04292i	0.0591437	−	0.194971i
$670$	3.17929	+	0.972451i	0.122827	+	0.0375690i
$671$	−9.44344	−	9.44344i	−0.364560	−	0.364560i
$672$	8.14383	+	0.0940277i	0.314155	+	0.00362720i
$673$	6.65881	−	6.65881i	0.256678	−	0.256678i	−0.567023	−	0.823702i	$-0.691905\pi$
$673$	6.65881	−	6.65881i	0.256678	−	0.256678i	0.823702	+	0.567023i	$0.191905\pi$
$674$	−19.8742	+	10.5641i	−0.765526	+	0.406912i
$675$	4.23796	+	1.28557i	0.163119	+	0.0494816i
$676$	4.20900	+	10.2956i	0.161885	+	0.395986i
$677$	40.7816	+	4.01664i	1.56737	+	0.154372i	0.844096	−	0.536193i	$-0.180138\pi$
$677$	40.7816	+	4.01664i	1.56737	+	0.154372i	0.723270	+	0.690565i	$0.242638\pi$
$678$	5.32990	+	27.1224i	0.204693	+	1.04163i
$679$	14.6351	+	2.91111i	0.561645	+	0.111718i
$680$	−0.582938	+	2.82810i	−0.0223547	+	0.108453i
$681$	3.18326	+	16.0034i	0.121983	+	0.613250i
$682$	−13.5209	+	32.4303i	−0.517741	+	1.24182i
$683$	19.9039	+	10.6388i	0.761600	+	0.407084i	0.805989	−	0.591931i	$-0.201634\pi$
$683$	19.9039	+	10.6388i	0.761600	+	0.407084i	−0.0443890	+	0.999014i	$0.514134\pi$
$684$	−2.99525	−	0.923727i	−0.114526	−	0.0353196i
$685$	5.50893	−	0.542582i	0.210485	−	0.0207310i
$686$	23.2553	−	6.99583i	0.887893	−	0.267102i
$687$	−4.64070	−	11.2036i	−0.177054	−	0.427446i
$688$	−15.7508	−	1.69835i	−0.600493	−	0.0647488i
$689$	8.03869	−	19.4071i	0.306250	−	0.739352i
$690$	−0.103430	+	1.02585i	−0.00393752	+	0.0390536i
$691$	12.1161	−	14.7635i	0.460919	−	0.561631i	−0.489741	−	0.871868i	$-0.662908\pi$
$691$	12.1161	−	14.7635i	0.460919	−	0.561631i	0.950659	+	0.310237i	$0.100408\pi$
$692$	−1.05799	+	0.315611i	−0.0402189	+	0.0119977i
$693$	−2.21543	−	7.30329i	−0.0841572	−	0.277429i
$694$	0.0161755	−	7.00518i	0.000614014	−	0.265913i
$695$	−3.32468	−	2.22148i	−0.126112	−	0.0842656i
$696$	−4.54356	+	2.38827i	−0.172223	+	0.0905271i
$697$	0.341935	+	0.511742i	0.0129517	+	0.0193836i
$698$	−2.57142	+	12.7732i	−0.0973299	+	0.483473i
$699$	14.6073	−	11.9879i	0.552498	−	0.453424i
$700$	−7.03569	−	10.6357i	−0.265924	−	0.401990i
$701$	−11.7527	−	21.9877i	−0.443893	−	0.830465i	0.556107	−	0.831111i	$-0.312294\pi$
$701$	−11.7527	−	21.9877i	−0.443893	−	0.830465i	−1.00000		0.000645948i	$0.999794\pi$
$702$	2.97592	+	2.45380i	0.112319	+	0.0926126i
$703$		−	4.98694i		−	0.188086i
$704$	27.3545	−	32.4055i	1.03096	−	1.22133i
$705$		−	9.48566i		−	0.357251i
$706$	−28.6699	+	34.7704i	−1.07901	+	1.30860i
$707$	−0.123999	−	0.231986i	−0.00466347	−	0.00872473i
$708$	−4.98545	+	24.4723i	−0.187365	+	0.919727i
$709$	23.0342	−	18.9037i	0.865067	−	0.709942i	−0.0932517	−	0.995643i	$-0.529726\pi$
$709$	23.0342	−	18.9037i	0.865067	−	0.709942i	0.958319	+	0.285700i	$0.0922261\pi$
$710$	−5.46178	−	1.09953i	−0.204977	−	0.0412647i
$711$	3.02478	+	4.52691i	0.113438	+	0.169772i
$712$	−3.52208	−	38.4920i	−0.131996	−	1.44255i
$713$	3.75880	+	2.51155i	0.140768	+	0.0940583i
$714$	−2.74999	−	0.00634994i	−0.102916	−	0.000237641i
$715$	3.17228	+	10.4576i	0.118637	+	0.391092i
$716$	−17.3651	+	32.1300i	−0.648963	+	1.20075i
$717$	−0.377770	+	0.460314i	−0.0141081	+	0.0171907i
$718$	−18.3310	−	1.84820i	−0.684107	−	0.0689740i
$719$	−4.91757	+	11.8721i	−0.183394	+	0.442753i	−0.988662	−	0.150158i	$-0.952022\pi$
$719$	−4.91757	+	11.8721i	−0.183394	+	0.442753i	0.805268	+	0.592912i	$0.202022\pi$
$720$	2.67954	−	1.40058i	0.0998606	−	0.0521965i
$721$	10.2954	+	24.8552i	0.383420	+	0.925658i
$722$	6.73992	+	22.4046i	0.250834	+	0.833814i
$723$	7.54014	−	0.742639i	0.280421	−	0.0276190i
$724$	−19.8762	−	37.6025i	−0.738695	−	1.39749i
$725$	7.08808	+	3.78866i	0.263245	+	0.140707i
$726$	−22.3205	−	9.30588i	−0.828390	−	0.345374i
$727$	−4.16097	−	20.9186i	−0.154322	−	0.775828i	−0.977973	−	0.208731i	$-0.933067\pi$
$727$	−4.16097	−	20.9186i	−0.154322	−	0.775828i	0.823651	−	0.567096i	$-0.191933\pi$
$728$	−2.09124	−	10.9078i	−0.0775066	−	0.404268i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−2.96383	+	0.582431i	−0.109696	+	0.0215567i
$731$	5.32343	+	0.524312i	0.196894	+	0.0193924i
$732$	4.64625	+	1.94973i	0.171731	+	0.0720640i
$733$	50.6845	+	15.3750i	1.87207	+	0.567887i	0.996379	+	0.0850203i	$0.0270955\pi$
$733$	50.6845	+	15.3750i	1.87207	+	0.567887i	0.875694	+	0.482867i	$0.160404\pi$
$734$	6.70390	+	12.6121i	0.247446	+	0.465520i
$735$	2.63349	−	2.63349i	0.0971378	−	0.0971378i
$736$	−3.41247	−	4.25740i	−0.125785	−	0.156930i
$737$	11.6580	+	11.6580i	0.429426	+	0.429426i
$738$	0.188495	−	0.616260i	0.00693861	−	0.0226848i
$739$	−13.4072	+	44.1976i	−0.493192	+	1.62584i	0.258279	+	0.966070i	$0.416845\pi$
$739$	−13.4072	+	44.1976i	−0.493192	+	1.62584i	−0.751471	+	0.659766i	$0.770655\pi$
$740$	3.38573	+	3.41715i	0.124462	+	0.125617i
$741$	−0.418967	+	4.25385i	−0.0153912	+	0.156269i
$742$	8.74245	−	13.0188i	0.320946	−	0.477936i
$743$	−8.21313	+	41.2902i	−0.301311	+	1.51479i	0.472475	+	0.881344i	$0.343361\pi$
$743$	−8.21313	+	41.2902i	−0.301311	+	1.51479i	−0.773786	+	0.633447i	$0.781639\pi$
$744$	0.0918304	−	13.2562i	0.00336667	−	0.485998i
$745$	−6.14781	+	1.22288i	−0.225238	+	0.0448027i
$746$	−16.5707	−	40.2679i	−0.606696	−	1.47431i
$747$	−3.85395	+	7.21023i	−0.141009	+	0.263808i
$748$	−9.13497	+	11.0268i	−0.334008	+	0.403178i
$749$	−1.49708	−	15.2001i	−0.0547020	−	0.555399i
$750$	−8.87783	−	4.77169i	−0.324173	−	0.174237i
$751$	2.37599	−	0.984168i	0.0867012	−	0.0359128i	−0.338911	−	0.940818i	$-0.610059\pi$
$751$	2.37599	−	0.984168i	0.0867012	−	0.0359128i	0.425613	+	0.904906i	$0.360059\pi$
$752$	35.1653	+	35.8209i	1.28235	+	1.30626i
$753$	27.6962	+	11.4721i	1.00931	+	0.418068i
$754$	4.42815	+	5.42119i	0.161264	+	0.197428i
$755$	12.9306	+	10.6119i	0.470594	+	0.386207i
$756$	1.81642	+	2.23427i	0.0660625	+	0.0812597i
$757$	11.9448	−	3.62341i	0.434140	−	0.131695i	−0.0656477	−	0.997843i	$-0.520911\pi$
$757$	11.9448	−	3.62341i	0.434140	−	0.131695i	0.499788	+	0.866148i	$0.333411\pi$
$758$	−34.5413	+	34.3821i	−1.25460	+	1.24882i
$759$	−2.84058	+	4.25123i	−0.103107	+	0.154310i
$760$	2.94399	+	1.59991i	0.106790	+	0.0580349i
$761$	6.21635	−	4.15363i	0.225342	−	0.150569i	−0.437775	−	0.899085i	$-0.644233\pi$
$761$	6.21635	−	4.15363i	0.225342	−	0.150569i	0.663117	+	0.748516i	$0.269233\pi$
$762$	−9.88925	−	14.8745i	−0.358250	−	0.538848i
$763$	−16.0171	−	19.5169i	−0.579857	−	0.706558i
$764$	−2.53235	−	13.0456i	−0.0916173	−	0.471972i
$765$	−0.900357	+	0.481251i	−0.0325525	+	0.0173997i
$766$	0.481059	+	5.00267i	0.0173814	+	0.180754i
$767$	34.0582			1.22977
$768$	−4.92658	+	15.2226i	−0.177773	+	0.549300i
$769$	24.1534			0.870994			0.435497	−	0.900190i	$-0.356573\pi$
$769$	24.1534			0.870994			0.435497	+	0.900190i	$0.356573\pi$
$770$	0.780902	+	8.12083i	0.0281418	+	0.292654i
$771$	15.0582	−	8.04880i	0.542309	−	0.289870i
$772$	2.08375	+	10.7346i	0.0749958	+	0.386346i
$773$	−7.05268	−	8.59372i	−0.253667	−	0.309095i	0.630570	−	0.776132i	$-0.282821\pi$
$773$	−7.05268	−	8.59372i	−0.253667	−	0.309095i	−0.884237	+	0.467038i	$0.845321\pi$
$774$	−3.10100	−	4.66426i	−0.111463	−	0.167653i
$775$	−17.2585	+	11.5318i	−0.619945	+	0.414234i
$776$	−13.9976	+	25.7569i	−0.502484	+	0.924618i
$777$	−2.54521	+	3.80918i	−0.0913089	+	0.136653i
$778$	10.8901	−	10.8399i	0.390430	−	0.388631i
$779$	0.683419	−	0.207313i	0.0244860	−	0.00742775i
$780$	−2.60093	−	3.19926i	−0.0931284	−	0.114552i
$781$	−21.3566	−	17.5269i	−0.764200	−	0.627163i
$782$	1.16547	+	1.42683i	0.0416771	+	0.0510235i
$783$	−1.67665	−	0.694491i	−0.0599186	−	0.0248191i
$784$	−0.182032	+	19.7078i	−0.00650115	+	0.703850i
$785$	2.82488	−	1.17010i	0.100824	−	0.0417628i
$786$	−2.07802	−	1.11690i	−0.0741205	−	0.0398385i
$787$	1.14736	+	11.6494i	0.0408991	+	0.415255i	0.993734	+	0.111767i	$0.0356511\pi$
$787$	1.14736	+	11.6494i	0.0408991	+	0.415255i	−0.952835	+	0.303488i	$0.901849\pi$
$788$	−22.8007	+	27.5225i	−0.812240	+	0.980449i
$789$	12.6511	−	23.6686i	0.450393	−	0.842625i
$790$	−2.21478	−	5.38207i	−0.0787984	−	0.191486i
$791$	27.5992	−	5.48983i	0.981316	−	0.195196i
$792$	14.9929	+	0.103861i	0.532750	+	0.00369053i
$793$	1.34053	−	6.73929i	0.0476035	−	0.239319i
$794$	22.9582	−	34.1882i	0.814755	−	1.21329i
$795$	0.570626	−	5.79367i	0.0202380	−	0.205480i
$796$	27.9067	+	28.1657i	0.989128	+	0.998307i
$797$	14.5557	−	47.9836i	0.515588	−	1.69966i	−0.182115	−	0.983277i	$-0.558294\pi$
$797$	14.5557	−	47.9836i	0.515588	−	1.69966i	0.697702	−	0.716388i	$-0.254206\pi$
$798$	−0.933354	+	3.05147i	−0.0330404	+	0.108021i
$799$	−11.9850	−	11.9850i	−0.423998	−	0.423998i
$800$	24.0559	−	6.99502i	0.850503	−	0.247311i
$801$	9.66320	−	9.66320i	0.341432	−	0.341432i
$802$	−10.2048	−	19.1983i	−0.360344	−	0.677917i
$803$	−14.3335	−	4.34801i	−0.505818	−	0.153438i
$804$	−5.73582	−	2.40695i	−0.202287	−	0.0848865i
$805$	1.04461	+	0.102885i	0.0368176	+	0.00362622i
$806$	−17.7386	+	3.48587i	−0.624816	+	0.122784i
$807$	−0.896509	−	0.178327i	−0.0315586	−	0.00627740i
$808$	0.507523	−	0.0973028i	0.0178546	−	0.00342310i
$809$	4.75272	+	23.8935i	0.167097	+	0.840051i	0.969843	+	0.243731i	$0.0783713\pi$
$809$	4.75272	+	23.8935i	0.167097	+	0.840051i	−0.802746	+	0.596321i	$0.796629\pi$
$810$	0.986651	+	0.411356i	0.0346674	+	0.0144536i
$811$	33.5150	+	17.9141i	1.17687	+	0.629051i	0.939561	−	0.342383i	$-0.111234\pi$
$811$	33.5150	+	17.9141i	1.17687	+	0.629051i	0.237311	+	0.971434i	$0.423734\pi$
$812$	2.44204	+	4.61993i	0.0856989	+	0.162128i
$813$	−25.2342	+	2.48535i	−0.885002	+	0.0871651i
$814$	6.87184	+	22.8432i	0.240858	+	0.800652i
$815$	−2.94071	−	7.09949i	−0.103008	−	0.248684i
$816$	1.61595	−	5.15517i	0.0565694	−	0.180467i
$817$	2.37533	−	5.73456i	0.0831024	−	0.200627i
$818$	−34.9393	−	3.52270i	−1.22162	−	0.123168i
$819$	2.49108	−	3.03539i	0.0870453	−	0.106065i
$820$	−0.327543	+	0.606040i	−0.0114383	+	0.0211638i
$821$	12.7299	+	41.9650i	0.444278	+	1.46459i	0.838159	+	0.545426i	$0.183632\pi$
$821$	12.7299	+	41.9650i	0.444278	+	1.46459i	−0.393881	+	0.919161i	$0.628868\pi$
$822$	−10.3568	−	0.0239147i	−0.361236	−	0.000834122i
$823$	1.85409	+	1.23886i	0.0646295	+	0.0431840i	0.587465	−	0.809249i	$-0.300126\pi$
$823$	1.85409	+	1.23886i	0.0646295	+	0.0431840i	−0.522836	+	0.852433i	$0.675126\pi$
$824$	−52.6326	+	4.81597i	−1.83354	+	0.167772i
$825$	−13.0425	−	19.5195i	−0.454083	−	0.679583i
$826$	24.9256	+	5.01788i	0.867274	+	0.174594i
$827$	−26.2537	+	21.5459i	−0.912932	+	0.749224i	−0.968443	−	0.249234i	$-0.919821\pi$
$827$	−26.2537	+	21.5459i	−0.912932	+	0.749224i	0.0555115	+	0.998458i	$0.482321\pi$
$828$	0.385075	−	1.89024i	0.0133823	−	0.0656904i
$829$	6.57930	+	12.3090i	0.228509	+	0.427509i	0.969879	−	0.243586i	$-0.0783239\pi$
$829$	6.57930	+	12.3090i	0.228509	+	0.427509i	−0.741371	+	0.671096i	$0.765824\pi$
$830$	5.55984	−	6.74287i	0.192985	−	0.234048i
$831$		−	23.2064i		−	0.805020i
$832$	21.6823	+	2.43926i	0.751698	+	0.0845662i
$833$		−	6.65475i		−	0.230573i
$834$	5.77204	+	4.75934i	0.199869	+	0.164802i
$835$	0.169740	+	0.317562i	0.00587411	+	0.0109897i
$836$	9.16718	+	13.8578i	0.317054	+	0.479281i
$837$	3.62303	−	2.97334i	0.125230	−	0.102774i
$838$	4.24195	−	21.0713i	0.146536	−	0.727897i
$839$	−27.2559	−	40.7913i	−0.940978	−	1.40827i	−0.912681	−	0.408673i	$-0.865992\pi$
$839$	−27.2559	−	40.7913i	−0.940978	−	1.40827i	−0.0282967	−	0.999600i	$-0.509008\pi$
$840$	−1.43215	−	2.72460i	−0.0494139	−	0.0940075i
$841$	21.3742	+	14.2818i	0.737041	+	0.492475i
$842$	0.0120355	−	5.21226i	0.000414771	−	0.179626i
$843$	−8.63989	−	28.4819i	−0.297574	−	0.980969i
$844$	−7.44338	+	2.22044i	−0.256212	+	0.0764307i
$845$	2.66681	−	3.24951i	0.0917410	−	0.111787i
$846$	−1.78032	+	17.6578i	−0.0612086	+	0.607087i
$847$	−9.42133	+	22.7451i	−0.323721	+	0.781531i
$848$	19.3234	+	23.9942i	0.663569	+	0.823964i
$849$	9.56790	+	23.0990i	0.328369	+	0.792754i
$850$	−8.10045	+	2.43683i	−0.277843	+	0.0835827i
$851$	3.05438	−	0.300830i	0.104703	−	0.0103123i
$852$	9.96087	+	3.07190i	0.341254	+	0.105242i
$853$	−37.6179	−	20.1072i	−1.28801	−	0.688456i	−0.321947	−	0.946758i	$-0.604337\pi$
$853$	−37.6179	−	20.1072i	−1.28801	−	0.688456i	−0.966064	+	0.258302i	$0.916837\pi$
$854$	1.97399	−	4.73467i	0.0675484	−	0.162017i
$855$	0.231110	+	1.16187i	0.00790378	+	0.0397350i
$856$	29.3879	+	6.05755i	1.00446	+	0.207043i
$857$	23.2316	+	4.62106i	0.793577	+	0.157852i	0.575201	−	0.818012i	$-0.304924\pi$
$857$	23.2316	+	4.62106i	0.793577	+	0.157852i	0.218376	+	0.975865i	$0.429924\pi$
$858$	−3.94254	−	20.0625i	−0.134596	−	0.684922i
$859$	21.1125	+	2.07940i	0.720349	+	0.0709482i	0.451547	−	0.892247i	$-0.350872\pi$
$859$	21.1125	+	2.07940i	0.720349	+	0.0709482i	0.268802	+	0.963195i	$0.413372\pi$
$860$	2.26568	+	5.54209i	0.0772590	+	0.188984i
$861$	−0.627823	−	0.190448i	−0.0213961	−	0.00649045i
$862$	19.0758	−	10.1397i	0.649726	−	0.345359i
$863$	−21.0642	+	21.0642i	−0.717032	+	0.717032i	−0.967996	−	0.250964i	$-0.919252\pi$
$863$	−21.0642	+	21.0642i	−0.717032	+	0.717032i	0.250964	+	0.967996i	$0.419252\pi$
$864$	−5.25090	+	2.10430i	−0.178639	+	0.0715898i
$865$	0.295053	+	0.295053i	0.0100321	+	0.0100321i
$866$	−49.6736	−	15.1937i	−1.68798	−	0.516301i
$867$	4.40531	−	14.5223i	0.149612	−	0.493205i
$868$	−13.4957	−	0.0623254i	−0.458073	−	0.00211546i
$869$	2.82884	−	28.7217i	0.0959618	−	0.974317i
$870$	1.61052	+	1.08150i	0.0546018	+	0.0366664i
$871$	−1.65489	+	8.31967i	−0.0560737	+	0.281901i
$872$	45.9554	−	18.6634i	1.55624	−	0.632024i
$873$	−10.1651	+	2.02197i	−0.344038	+	0.0684334i
$874$	1.97694	−	0.813532i	0.0668710	−	0.0275181i
$875$	−4.83692	+	9.04924i	−0.163518	+	0.305920i
$876$	5.62655	−	0.527942i	0.190103	−	0.0178375i
$877$	3.46715	+	35.2026i	0.117077	+	1.18871i	0.856747	+	0.515736i	$0.172482\pi$
$877$	3.46715	+	35.2026i	0.117077	+	1.18871i	−0.739670	+	0.672970i	$0.765018\pi$
$878$	21.6304	−	40.2438i	0.729990	−	1.35816i
$879$	1.15180	−	0.477092i	0.0388494	−	0.0160919i
$880$	−15.6898	−	3.27183i	−0.528904	−	0.110293i
$881$	−9.69121	−	4.01423i	−0.326505	−	0.135243i	0.213409	−	0.976963i	$-0.431543\pi$
$881$	−9.69121	−	4.01423i	−0.326505	−	0.135243i	−0.539914	+	0.841720i	$0.681543\pi$
$882$	−5.39658	+	4.40804i	−0.181712	+	0.148426i
$883$	15.9437	+	13.0846i	0.536547	+	0.440333i	0.863237	−	0.504799i	$-0.168433\pi$
$883$	15.9437	+	13.0846i	0.536547	+	0.440333i	−0.326690	+	0.945132i	$0.605933\pi$
$884$	−7.32846	−	0.755978i	−0.246483	−	0.0254263i
$885$	9.03255	−	2.73999i	0.303626	−	0.0921039i
$886$	6.28988	+	6.31900i	0.211313	+	0.212291i
$887$	−15.3263	+	22.9374i	−0.514606	+	0.770162i	−0.994225	−	0.107315i	$-0.965775\pi$
$887$	−15.3263	+	22.9374i	−0.514606	+	0.770162i	0.479619	+	0.877477i	$0.340775\pi$
$888$	−5.66127	−	6.99655i	−0.189980	−	0.234789i
$889$	−15.1197	+	10.1027i	−0.507098	+	0.338832i
$890$	−12.1651	+	8.08789i	−0.407775	+	0.271107i
$891$	3.36287	+	4.09767i	0.112660	+	0.137277i
$892$	5.89594	−	8.73629i	0.197411	−	0.292512i
$893$	−17.3452	+	9.27121i	−0.580436	+	0.310249i
$894$	11.6738	−	1.12256i	0.390431	−	0.0375440i
$895$	13.8032			0.461389
$896$	15.5089	+	4.97969i	0.518116	+	0.166360i
$897$	−2.63065			−0.0878348
$898$	47.2003	−	4.53881i	1.57510	−	0.151462i
$899$	7.50141	−	4.00959i	0.250186	−	0.133727i
$900$	7.34178	+	4.95481i	0.244726	+	0.165160i
$901$	−6.59923	−	8.04118i	−0.219852	−	0.267891i
$902$	−2.84479	+	1.89134i	−0.0947212	+	0.0629748i
$903$	−4.74113	+	3.16792i	−0.157775	+	0.105422i
$904$	−5.79958	+	54.9771i	−0.192891	+	1.82851i
$905$	−8.93059	+	13.3656i	−0.296863	+	0.444287i
$906$	−22.0790	−	22.1812i	−0.733526	−	0.736921i
$907$	32.8648	−	9.96944i	1.09126	−	0.331030i	0.307155	−	0.951659i	$-0.400623\pi$
$907$	32.8648	−	9.96944i	1.09126	−	0.331030i	0.784104	+	0.620630i	$0.213123\pi$
$908$	−3.34861	+	32.4615i	−0.111128	+	1.07727i
$909$	0.141233	+	0.115907i	0.00468439	+	0.00384438i
$910$	−3.25087	+	2.65539i	−0.107765	+	0.0880252i
$911$	−18.2635	−	7.56498i	−0.605096	−	0.250639i	0.0590343	−	0.998256i	$-0.481198\pi$
$911$	−18.2635	−	7.56498i	−0.605096	−	0.250639i	−0.664130	+	0.747617i	$0.731198\pi$
$912$	−5.18002	−	3.53082i	−0.171528	−	0.116917i
$913$	40.0392	−	16.5848i	1.32511	−	0.548877i
$914$	2.46153	−	4.57973i	0.0814201	−	0.151484i
$915$	−0.186658	−	1.89517i	−0.00617071	−	0.0626523i
$916$	−2.26577	−	24.1474i	−0.0748630	−	0.797853i
$917$	−1.13217	+	2.11814i	−0.0373875	+	0.0699471i
$918$	1.76636	−	0.726876i	0.0582986	−	0.0239905i
$919$	6.43859	−	1.28071i	0.212389	−	0.0422469i	−0.0877487	−	0.996143i	$-0.527967\pi$
$919$	6.43859	−	1.28071i	0.212389	−	0.0422469i	0.300138	+	0.953896i	$0.402967\pi$
$920$	−0.802314	+	1.89963i	−0.0264515	+	0.0626289i
$921$	−4.74078	+	23.8335i	−0.156214	+	0.785340i
$922$	16.7292	+	11.2341i	0.550948	+	0.369975i
$923$	1.39330	−	14.1464i	0.0458609	−	0.465634i
$924$	0.0704904	−	15.2637i	0.00231896	−	0.502138i
$925$	−4.09070	+	13.4852i	−0.134501	+	0.443392i
$926$	−36.5077	−	11.1666i	−1.19972	−	0.366957i
$927$	−13.2131	−	13.2131i	−0.433975	−	0.433975i
$928$	−10.0912	+	1.88642i	−0.331260	+	0.0619249i
$929$	−17.1701	+	17.1701i	−0.563334	+	0.563334i	−0.930253	−	0.366919i	$-0.880413\pi$
$929$	−17.1701	+	17.1701i	−0.563334	+	0.563334i	0.366919	+	0.930253i	$0.380413\pi$
$930$	−4.42400	+	2.35156i	−0.145069	+	0.0771107i
$931$	−7.38948	−	2.24157i	−0.242180	−	0.0734646i
$932$	34.9828	−	14.3014i	1.14590	−	0.468460i
$933$	−25.0080	−	2.46307i	−0.818724	−	0.0806372i
$934$	7.61064	+	38.7284i	0.249028	+	1.26723i
$935$	5.30775	+	1.05578i	0.173582	+	0.0345276i
$936$	4.24125	+	6.44366i	0.138629	+	0.210618i
$937$	−8.67618	−	43.6181i	−0.283439	−	1.42494i	−0.815756	−	0.578397i	$-0.803679\pi$
$937$	−8.67618	−	43.6181i	−0.283439	−	1.42494i	0.532317	−	0.846545i	$-0.321321\pi$
$938$	−2.43689	+	5.84497i	−0.0795674	+	0.190845i
$939$	−3.16691	−	1.69275i	−0.103348	−	0.0552408i
$940$	5.59087	−	18.1288i	0.182354	−	0.591296i
$941$	−31.3744	+	3.09010i	−1.02277	+	0.100735i	−0.595474	−	0.803375i	$-0.703036\pi$
$941$	−31.3744	+	3.09010i	−1.02277	+	0.100735i	−0.427301	+	0.904109i	$0.640536\pi$
$942$	−5.47820	+	1.64799i	−0.178489	+	0.0536944i
$943$	0.168200	+	0.406071i	0.00547735	+	0.0132235i
$944$	−23.9521	+	43.8326i	−0.779575	+	1.42663i
$945$	0.416459	−	1.00542i	0.0135474	−	0.0327064i
$946$	−2.97841	+	29.5408i	−0.0968364	+	0.960455i
$947$	−30.7982	+	37.5277i	−1.00081	+	1.21949i	−0.0252620	+	0.999681i	$0.508042\pi$
$947$	−30.7982	+	37.5277i	−1.00081	+	1.21949i	−0.975544	+	0.219805i	$0.929458\pi$
$948$	3.11273	+	10.4345i	0.101097	+	0.338898i
$949$	−2.23710	−	7.37474i	−0.0726194	−	0.239394i
$950$	−0.0226650	+	9.81562i	−0.000735350	+	0.318461i
$951$	17.4325	+	11.6480i	0.565287	+	0.377713i
$952$	−5.25198	−	1.63299i	−0.170218	−	0.0529254i
$953$	6.83960	+	10.2362i	0.221557	+	0.331583i	0.925551	−	0.378622i	$-0.123602\pi$
$953$	6.83960	+	10.2362i	0.221557	+	0.331583i	−0.703995	+	0.710205i	$0.748602\pi$
$954$	−2.14962	+	10.6780i	−0.0695965	+	0.345711i
$955$	−3.88240	+	3.18621i	−0.125632	+	0.103103i
$956$	−0.993295	+	0.657084i	−0.0321255	+	0.0212516i
$957$	4.53487	+	8.48415i	0.146592	+	0.274254i
$958$	12.2579	+	10.1072i	0.396034	+	0.326550i
$959$			10.5438i			0.340476i
$960$	5.94658	−	1.09743i	0.191925	−	0.0354195i
$961$		−	9.03293i		−	0.291385i
$962$	−7.80802	+	9.46942i	−0.251741	+	0.305307i
$963$	5.00088	+	9.35598i	0.161151	+	0.301492i
$964$	14.8483	+	3.02486i	0.478231	+	0.0974240i
$965$	3.19464	−	2.62177i	0.102839	−	0.0843979i
$966$	−1.92525	−	0.387580i	−0.0619440	−	0.0124702i
$967$	33.6115	+	50.3032i	1.08087	+	1.61764i	0.733180	+	0.680035i	$0.238035\pi$
$967$	33.6115	+	50.3032i	1.08087	+	1.61764i	0.347694	+	0.937608i	$0.386965\pi$
$968$	−37.1735	−	30.9409i	−1.19480	−	0.994479i
$969$	1.76000	+	1.17600i	0.0565395	+	0.0377785i
$970$	11.0791	+	0.0255825i	0.355728	+	0.000821403i
$971$	11.0326	+	36.3697i	0.354054	+	1.16716i	0.935426	+	0.353521i	$0.115016\pi$
$971$	11.0326	+	36.3697i	0.354054	+	1.16716i	−0.581373	+	0.813637i	$0.697484\pi$
$972$	−1.75947	−	0.950929i	−0.0564350	−	0.0305011i
$973$	4.83165	−	5.88738i	0.154895	−	0.188741i
$974$	−20.9068	−	2.10790i	−0.669897	−	0.0675413i
$975$	4.62229	−	11.1592i	0.148032	−	0.357380i
$976$	7.73065	+	6.46479i	0.247452	+	0.206933i
$977$	0.862992	+	2.08345i	0.0276096	+	0.0666554i	0.937083	−	0.349107i	$-0.113515\pi$
$977$	0.862992	+	2.08345i	0.0276096	+	0.0666554i	−0.909473	+	0.415762i	$0.863515\pi$
$978$	4.14173	+	13.7678i	0.132438	+	0.440246i
$979$	−72.0926	+	7.10050i	−2.30409	+	0.226933i
$980$	6.58526	−	3.48089i	0.210358	−	0.111193i
$981$	15.4658	+	8.26663i	0.493784	+	0.263933i
$982$	−34.0155	−	14.1818i	−1.08548	−	0.452559i
$983$	4.57143	+	22.9821i	0.145806	+	0.733016i	0.982635	+	0.185551i	$0.0594070\pi$
$983$	4.57143	+	22.9821i	0.145806	+	0.733016i	−0.836829	+	0.547465i	$0.815593\pi$
$984$	0.723473	−	1.06668i	0.0230635	−	0.0340046i
$985$	13.2480	+	2.63519i	0.422117	+	0.0839642i
$986$	3.40133	−	0.668407i	0.108321	−	0.0212864i
$987$	17.9806	+	1.77093i	0.572329	+	0.0563694i
$988$	−3.30795	+	7.88293i	−0.105240	+	0.250789i
$989$	3.65556	+	1.10890i	0.116240	+	0.0352611i
$990$	−2.65963	−	5.00358i	−0.0845286	−	0.159024i
$991$	−37.2788	+	37.2788i	−1.18420	+	1.18420i	−0.205553	+	0.978646i	$0.565899\pi$
$991$	−37.2788	+	37.2788i	−1.18420	+	1.18420i	−0.978646	+	0.205553i	$0.934101\pi$
$992$	7.98876	−	25.2809i	0.253643	−	0.802671i
$993$	−5.95389	−	5.95389i	−0.188941	−	0.188941i
$994$	3.10391	−	10.1478i	0.0984502	−	0.321869i
$995$	4.34994	−	14.3398i	0.137902	−	0.454603i
$996$	−11.6153	+	11.5085i	−0.368045	+	0.364661i
$997$	1.44313	−	14.6524i	0.0457045	−	0.464046i	−0.944907	−	0.327339i	$-0.893848\pi$
$997$	1.44313	−	14.6524i	0.0457045	−	0.464046i	0.990612	−	0.136707i	$-0.0436519\pi$
$998$	−9.45291	+	14.0768i	−0.299227	+	0.445594i
$999$	0.620780	−	3.12087i	0.0196406	−	0.0987400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.16	yes	512
128.109	even	32	inner	384.2.v.a.109.16	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.16	✓	512	128.109	even	32	inner
384.2.v.a.229.16	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)

\(f(q)\)	\(=\)	\(q+(0.135367 + 1.40772i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.96335 + 0.381118i) q^{4} +(0.479522 + 0.584299i) q^{5} +(-0.782978 - 1.17769i) q^{6} +(-1.19710 + 0.799874i) q^{7} +(-0.802280 - 2.71226i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.135367 + 1.40772i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.96335 + 0.381118i) q^{4} +(0.479522 + 0.584299i) q^{5} +(-0.782978 - 1.17769i) q^{6} +(-1.19710 + 0.799874i) q^{7} +(-0.802280 - 2.71226i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-0.757619 + 0.754128i) q^{10} +(-5.07266 + 1.53878i) q^{11} +(1.55186 - 1.26163i) q^{12} +(-2.10830 - 1.73023i) q^{13} +(-1.28805 - 1.57690i) q^{14} +(-0.698338 - 0.289261i) q^{15} +(3.70950 - 1.49654i) q^{16} +(-1.24782 + 0.516862i) q^{17} +(1.24568 + 0.669534i) q^{18} +(0.153615 + 1.55968i) q^{19} +(-1.16416 - 0.964431i) q^{20} +(0.678687 - 1.26973i) q^{21} +(-2.85284 - 6.93259i) q^{22} +(-0.945999 + 0.188171i) q^{23} +(1.98610 + 2.01381i) q^{24} +(0.863987 - 4.34356i) q^{25} +(2.15029 - 3.20211i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(2.04547 - 2.02667i) q^{28} +(-0.526807 + 1.73665i) q^{29} +(0.312667 - 1.02222i) q^{30} +(-3.31414 - 3.31414i) q^{31} +(2.60885 + 5.01935i) q^{32} +(3.74832 - 3.74832i) q^{33} +(-0.896510 - 1.68661i) q^{34} +(-1.04140 - 0.315905i) q^{35} +(-0.773892 + 1.84420i) q^{36} +(-3.16669 - 0.311892i) q^{37} +(-2.17480 + 0.427377i) q^{38} +(2.67498 + 0.532086i) q^{39} +(1.20006 - 1.76936i) q^{40} +(-0.0889007 - 0.446934i) q^{41} +(1.87930 + 0.783521i) q^{42} +(-3.49287 - 1.86698i) q^{43} +(9.37297 - 4.95444i) q^{44} +(0.752235 - 0.0740887i) q^{45} +(-0.392949 - 1.30623i) q^{46} +(4.80239 + 11.5940i) q^{47} +(-2.56602 + 3.06847i) q^{48} +(-1.88554 + 4.55210i) q^{49} +(6.23147 + 0.628278i) q^{50} +(0.856828 - 1.04405i) q^{51} +(4.79875 + 2.59355i) q^{52} +(2.23575 + 7.37029i) q^{53} +(-1.41421 - 0.00326552i) q^{54} +(-3.33156 - 2.22608i) q^{55} +(3.12987 + 2.60511i) q^{56} +(-0.870705 - 1.30310i) q^{57} +(-2.51603 - 0.506511i) q^{58} +(-9.65297 + 7.92198i) q^{59} +(1.48132 + 0.301772i) q^{60} +(1.18763 + 2.22190i) q^{61} +(4.21676 - 5.11401i) q^{62} +1.43974i q^{63} +(-6.71269 + 4.35198i) q^{64} -2.06156i q^{65} +(5.78398 + 4.76918i) q^{66} +(-1.46613 - 2.74294i) q^{67} +(2.25291 - 1.49035i) q^{68} +(0.745594 - 0.611893i) q^{69} +(0.303735 - 1.50876i) q^{70} +(2.89557 + 4.33353i) q^{71} +(-2.70088 - 0.839779i) q^{72} +(2.34943 + 1.56984i) q^{73} +(0.0103909 - 4.50004i) q^{74} +(1.28557 + 4.23796i) q^{75} +(-0.896023 - 3.00366i) q^{76} +(4.84164 - 5.89955i) q^{77} +(-0.386924 + 3.83765i) q^{78} +(-2.08351 + 5.03003i) q^{79} +(2.65321 + 1.44984i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(0.617124 - 0.185648i) q^{82} +(-8.13622 + 0.801348i) q^{83} +(-0.848582 + 2.75159i) q^{84} +(-0.900357 - 0.481251i) q^{85} +(2.15536 - 5.16971i) q^{86} +(-0.354049 - 1.77992i) q^{87} +(8.24325 + 12.5238i) q^{88} +(13.4032 + 2.66607i) q^{89} +(0.206124 + 1.04891i) q^{90} +(3.90780 + 0.384885i) q^{91} +(1.78561 - 0.729983i) q^{92} +(4.48509 + 1.36054i) q^{93} +(-15.6710 + 8.32986i) q^{94} +(-0.837659 + 0.837659i) q^{95} +(-4.66691 - 3.19687i) q^{96} +(-7.32866 - 7.32866i) q^{97} +(-6.66333 - 2.03811i) q^{98} +(-1.53878 + 5.07266i) 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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