LMFDB - Embedded newform 756.2.cf.a.659.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.26
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.994322 - 1.00565i) q^{2} +(-1.27272 + 1.17481i) q^{3} +(-0.0226481 + 1.99987i) q^{4} +(-0.349585 + 0.960476i) q^{5} +(2.44694 + 0.111769i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(2.03368 - 1.96574i) q^{8} +(0.239643 - 2.99041i) q^{9} +(1.31350 - 0.603464i) q^{10} +(-0.828551 + 0.301568i) q^{11} +(-2.32064 - 2.57189i) q^{12} +(4.19087 - 3.51656i) q^{13} +(0.804587 + 1.16303i) q^{14} +(-0.683453 - 1.63311i) q^{15} +(-3.99897 - 0.0905865i) q^{16} +(-0.0129346 + 0.00746778i) q^{17} +(-3.24558 + 2.73244i) q^{18} +(-0.274082 - 0.158241i) q^{19} +(-1.91291 - 0.720878i) q^{20} +(1.45739 - 0.935956i) q^{21} +(1.12712 + 0.533373i) q^{22} +(-0.788442 - 4.47148i) q^{23} +(-0.278942 + 4.89103i) q^{24} +(3.02992 + 2.54240i) q^{25} +(-7.70349 - 0.717942i) q^{26} +(3.20817 + 4.08750i) q^{27} +(0.369578 - 1.96556i) q^{28} +(-4.13426 + 4.92702i) q^{29} +(-0.962764 + 2.31115i) q^{30} +(6.54564 - 1.15417i) q^{31} +(3.88517 + 4.11162i) q^{32} +(0.700230 - 1.35720i) q^{33} +(0.0203711 + 0.00558223i) q^{34} +(0.511059 - 0.885180i) q^{35} +(5.97502 + 0.546983i) q^{36} +(2.31077 + 4.00238i) q^{37} +(0.113391 + 0.432973i) q^{38} +(-1.20253 + 9.39908i) q^{39} +(1.17710 + 2.64050i) q^{40} +(0.483722 + 0.576477i) q^{41} +(-2.39036 - 0.534977i) q^{42} +(3.52530 + 9.68569i) q^{43} +(-0.584332 - 1.66382i) q^{44} +(2.78845 + 1.27557i) q^{45} +(-3.71276 + 5.23898i) q^{46} +(-0.489145 + 2.77408i) q^{47} +(5.19600 - 4.58274i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-0.455956 - 5.57499i) q^{50} +(0.00768890 - 0.0247001i) q^{51} +(6.93775 + 8.46085i) q^{52} -5.23795i q^{53} +(0.920627 - 7.29057i) q^{54} -0.901226i q^{55} +(-2.34413 + 1.58273i) q^{56} +(0.534734 - 0.120597i) q^{57} +(9.06563 - 0.741441i) q^{58} +(4.40483 + 1.60323i) q^{59} +(3.28150 - 1.32983i) q^{60} +(0.347795 - 1.97244i) q^{61} +(-7.66917 - 5.43498i) q^{62} +(-0.755282 + 2.90337i) q^{63} +(0.271731 - 7.99538i) q^{64} +(1.91251 + 5.25457i) q^{65} +(-2.06112 + 0.645312i) q^{66} +(7.70417 + 9.18147i) q^{67} +(-0.0146417 - 0.0260366i) q^{68} +(6.25660 + 4.76468i) q^{69} +(-1.39833 + 0.366209i) q^{70} +(3.54433 + 6.13896i) q^{71} +(-5.39102 - 6.55263i) q^{72} +(3.71226 - 6.42983i) q^{73} +(1.72732 - 6.30347i) q^{74} +(-6.84308 + 0.323805i) q^{75} +(0.322670 - 0.544545i) q^{76} +(0.868330 - 0.153110i) q^{77} +(10.6478 - 8.13639i) q^{78} +(2.61491 - 3.11633i) q^{79} +(1.48499 - 3.80925i) q^{80} +(-8.88514 - 1.43326i) q^{81} +(0.0987568 - 1.05966i) q^{82} +(-2.17499 - 1.82503i) q^{83} +(1.83879 + 2.93579i) q^{84} +(-0.00265090 - 0.0150340i) q^{85} +(6.23509 - 13.1759i) q^{86} +(-0.526548 - 11.1277i) q^{87} +(-1.09221 + 2.24201i) q^{88} +(-5.70033 - 3.29109i) q^{89} +(-1.48984 - 4.07252i) q^{90} +(-4.73785 + 2.73540i) q^{91} +(8.96024 - 1.47551i) q^{92} +(-6.97485 + 9.15883i) q^{93} +(3.27611 - 2.26642i) q^{94} +(0.247802 - 0.207931i) q^{95} +(-9.77512 - 0.668620i) q^{96} +(10.2642 - 3.73585i) q^{97} +(-0.590406 - 1.28508i) q^{98} +(0.703256 + 2.54998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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 $

$2$	−0.994322	−	1.00565i	−0.703092	−	0.711099i
$2$	−0.994322	−	1.00565i	−0.703092	−	0.711099i
$3$	−1.27272	+	1.17481i	−0.734806	+	0.678277i
$3$	−1.27272	+	1.17481i	−0.734806	+	0.678277i
$4$	−0.0226481	+	1.99987i	−0.0113240	+	0.999936i
$5$	−0.349585	+	0.960476i	−0.156339	+	0.429538i	−0.992990	−	0.118198i	$-0.962288\pi$
$5$	−0.349585	+	0.960476i	−0.156339	+	0.429538i	0.836651	+	0.547736i	$0.184510\pi$
$6$	2.44694	+	0.111769i	0.998958	+	0.0456294i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$8$	2.03368	−	1.96574i	0.719015	−	0.694994i
$9$	0.239643	−	2.99041i	0.0798811	−	0.996804i
$10$	1.31350	−	0.603464i	0.415365	−	0.190832i
$11$	−0.828551	+	0.301568i	−0.249817	+	0.0909261i	−0.463894	−	0.885891i	$-0.653548\pi$
$11$	−0.828551	+	0.301568i	−0.249817	+	0.0909261i	0.214076	+	0.976817i	$0.431326\pi$
$12$	−2.32064	−	2.57189i	−0.669912	−	0.742440i
$13$	4.19087	−	3.51656i	1.16234	−	0.975318i	0.162404	−	0.986724i	$-0.448075\pi$
$13$	4.19087	−	3.51656i	1.16234	−	0.975318i	0.999935	+	0.0114065i	$0.00363089\pi$
$14$	0.804587	+	1.16303i	0.215035	+	0.310833i
$15$	−0.683453	−	1.63311i	−0.176467	−	0.421668i
$16$	−3.99897	−	0.0905865i	−0.999744	−	0.0226466i
$17$	−0.0129346	+	0.00746778i	−0.00313710	+	0.00181120i	−0.501568	−	0.865118i	$-0.667243\pi$
$17$	−0.0129346	+	0.00746778i	−0.00313710	+	0.00181120i	0.498431	+	0.866930i	$0.333910\pi$
$18$	−3.24558	+	2.73244i	−0.764990	+	0.644042i
$19$	−0.274082	−	0.158241i	−0.0628788	−	0.0363031i	0.468231	−	0.883606i	$-0.344891\pi$
$19$	−0.274082	−	0.158241i	−0.0628788	−	0.0363031i	−0.531110	+	0.847303i	$0.678225\pi$
$20$	−1.91291	−	0.720878i	−0.427740	−	0.161193i
$21$	1.45739	−	0.935956i	0.318029	−	0.204242i
$22$	1.12712	+	0.533373i	0.240302	+	0.113716i
$23$	−0.788442	−	4.47148i	−0.164402	−	0.932367i	−0.949679	−	0.313224i	$-0.898591\pi$
$23$	−0.788442	−	4.47148i	−0.164402	−	0.932367i	0.785278	−	0.619144i	$-0.212520\pi$
$24$	−0.278942	+	4.89103i	−0.0569387	+	0.998378i
$25$	3.02992	+	2.54240i	0.605983	+	0.508480i
$26$	−7.70349	−	0.717942i	−1.51078	−	0.140800i
$27$	3.20817	+	4.08750i	0.617412	+	0.786640i
$28$	0.369578	−	1.96556i	0.0698437	−	0.371455i
$29$	−4.13426	+	4.92702i	−0.767714	+	0.914926i	−0.998309	−	0.0581241i	$-0.981488\pi$
$29$	−4.13426	+	4.92702i	−0.767714	+	0.914926i	0.230596	+	0.973050i	$0.425933\pi$
$30$	−0.962764	+	2.31115i	−0.175776	+	0.421957i
$31$	6.54564	−	1.15417i	1.17563	−	0.207296i	0.448494	−	0.893786i	$-0.351961\pi$
$31$	6.54564	−	1.15417i	1.17563	−	0.207296i	0.727139	+	0.686490i	$0.240850\pi$
$32$	3.88517	+	4.11162i	0.686807	+	0.726839i
$33$	0.700230	−	1.35720i	0.121894	−	0.236258i
$34$	0.0203711	+	0.00558223i	0.00349361	+	0.000957344i
$35$	0.511059	−	0.885180i	0.0863847	−	0.149623i
$36$	5.97502	+	0.546983i	0.995836	+	0.0911638i
$37$	2.31077	+	4.00238i	0.379889	+	0.657987i	0.991046	−	0.133522i	$-0.0426288\pi$
$37$	2.31077	+	4.00238i	0.379889	+	0.657987i	−0.611157	+	0.791510i	$0.709296\pi$
$38$	0.113391	+	0.432973i	0.0183945	+	0.0702374i
$39$	−1.20253	+	9.39908i	−0.192558	+	1.50506i
$40$	1.17710	+	2.64050i	0.186116	+	0.417499i
$41$	0.483722	+	0.576477i	0.0755446	+	0.0900306i	0.802493	−	0.596662i	$-0.203507\pi$
$41$	0.483722	+	0.576477i	0.0755446	+	0.0900306i	−0.726948	+	0.686692i	$0.759062\pi$
$42$	−2.39036	−	0.534977i	−0.368840	−	0.0825488i
$43$	3.52530	+	9.68569i	0.537604	+	1.47705i	0.849836	+	0.527048i	$0.176701\pi$
$43$	3.52530	+	9.68569i	0.537604	+	1.47705i	−0.312232	+	0.950006i	$0.601077\pi$
$44$	−0.584332	−	1.66382i	−0.0880913	−	0.250831i
$45$	2.78845	+	1.27557i	0.415677	+	0.190151i
$46$	−3.71276	+	5.23898i	−0.547416	+	0.772446i
$47$	−0.489145	+	2.77408i	−0.0713492	+	0.404641i	0.928127	+	0.372265i	$0.121419\pi$
$47$	−0.489145	+	2.77408i	−0.0713492	+	0.404641i	−0.999476	+	0.0323765i	$0.989692\pi$
$48$	5.19600	−	4.58274i	0.749979	−	0.661462i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−0.455956	−	5.57499i	−0.0644819	−	0.788423i
$51$	0.00768890	−	0.0247001i	0.00107666	−	0.00345870i
$52$	6.93775	+	8.46085i	0.962093	+	1.17331i
$53$		−	5.23795i		−	0.719488i	−0.933051	−	0.359744i	$-0.882864\pi$
$53$		−	5.23795i		−	0.719488i	0.933051	−	0.359744i	$-0.117136\pi$
$54$	0.920627	−	7.29057i	0.125281	−	0.992121i
$55$		−	0.901226i		−	0.121521i
$56$	−2.34413	+	1.58273i	−0.313248	+	0.211501i
$57$	0.534734	−	0.120597i	0.0708272	−	0.0159735i
$58$	9.06563	−	0.741441i	1.19038	−	0.0973560i
$59$	4.40483	+	1.60323i	0.573459	+	0.208722i	0.612439	−	0.790518i	$-0.290189\pi$
$59$	4.40483	+	1.60323i	0.573459	+	0.208722i	−0.0389796	+	0.999240i	$0.512411\pi$
$60$	3.28150	−	1.32983i	0.423640	−	0.171680i
$61$	0.347795	−	1.97244i	0.0445306	−	0.252546i	−0.954413	−	0.298488i	$-0.903518\pi$
$61$	0.347795	−	1.97244i	0.0445306	−	0.252546i	0.998944	+	0.0459420i	$0.0146289\pi$
$62$	−7.66917	−	5.43498i	−0.973985	−	0.690243i
$63$	−0.755282	+	2.90337i	−0.0951566	+	0.365790i
$64$	0.271731	−	7.99538i	0.0339663	−	0.999423i
$65$	1.91251	+	5.25457i	0.237217	+	0.651749i
$66$	−2.06112	+	0.645312i	−0.253706	+	0.0794324i
$67$	7.70417	+	9.18147i	0.941214	+	1.12170i	0.992406	+	0.123006i	$0.0392536\pi$
$67$	7.70417	+	9.18147i	0.941214	+	1.12170i	−0.0511918	+	0.998689i	$0.516302\pi$
$68$	−0.0146417	−	0.0260366i	−0.00177556	−	0.00315740i
$69$	6.25660	+	4.76468i	0.753207	+	0.573600i
$70$	−1.39833	+	0.366209i	−0.167133	+	0.0437704i
$71$	3.54433	+	6.13896i	0.420635	+	0.728561i	0.996002	−	0.0893345i	$-0.0284740\pi$
$71$	3.54433	+	6.13896i	0.420635	+	0.728561i	−0.575367	+	0.817895i	$0.695141\pi$
$72$	−5.39102	−	6.55263i	−0.635338	−	0.772235i
$73$	3.71226	−	6.42983i	0.434488	−	0.752555i	−0.562766	−	0.826616i	$-0.690263\pi$
$73$	3.71226	−	6.42983i	0.434488	−	0.752555i	0.997254	+	0.0740616i	$0.0235962\pi$
$74$	1.72732	−	6.30347i	0.200797	−	0.732764i
$75$	−6.84308	+	0.323805i	−0.790171	+	0.0373898i
$76$	0.322670	−	0.544545i	0.0370128	−	0.0624636i
$77$	0.868330	−	0.153110i	0.0989553	−	0.0174485i
$78$	10.6478	−	8.13639i	1.20563	−	0.921265i
$79$	2.61491	−	3.11633i	0.294201	−	0.350615i	−0.598615	−	0.801037i	$-0.704282\pi$
$79$	2.61491	−	3.11633i	0.294201	−	0.350615i	0.892816	+	0.450422i	$0.148726\pi$
$80$	1.48499	−	3.80925i	0.166027	−	0.425887i
$81$	−8.88514	−	1.43326i	−0.987238	−	0.159252i
$82$	0.0987568	−	1.05966i	0.0109059	−	0.117019i
$83$	−2.17499	−	1.82503i	−0.238736	−	0.200323i	0.515568	−	0.856849i	$-0.327581\pi$
$83$	−2.17499	−	1.82503i	−0.238736	−	0.200323i	−0.754304	+	0.656525i	$0.772025\pi$
$84$	1.83879	+	2.93579i	0.200628	+	0.320321i
$85$	−0.00265090	−	0.0150340i	−0.000287530	−	0.00163066i
$86$	6.23509	−	13.1759i	0.672347	−	1.42079i
$87$	−0.526548	−	11.1277i	−0.0564518	−	1.19302i
$88$	−1.09221	+	2.24201i	−0.116429	+	0.238999i
$89$	−5.70033	−	3.29109i	−0.604234	−	0.348854i	0.166472	−	0.986046i	$-0.446763\pi$
$89$	−5.70033	−	3.29109i	−0.604234	−	0.348854i	−0.770705	+	0.637192i	$0.780096\pi$
$90$	−1.48984	−	4.07252i	−0.157042	−	0.429281i
$91$	−4.73785	+	2.73540i	−0.496661	+	0.286748i
$92$	8.96024	−	1.47551i	0.934169	−	0.153833i
$93$	−6.97485	+	9.15883i	−0.723258	+	0.949726i
$94$	3.27611	−	2.26642i	0.337905	−	0.233764i
$95$	0.247802	−	0.207931i	0.0254240	−	0.0213332i
$96$	−9.77512	−	0.668620i	−0.997669	−	0.0682408i
$97$	10.2642	−	3.73585i	1.04217	−	0.379318i	0.236466	−	0.971640i	$-0.424011\pi$
$97$	10.2642	−	3.73585i	1.04217	−	0.379318i	0.805702	+	0.592322i	$0.201789\pi$
$98$	−0.590406	−	1.28508i	−0.0596400	−	0.129812i
$99$	0.703256	+	2.54998i	0.0706799	+	0.256282i
$100$	−5.15310	+	6.00187i	−0.515310	+	0.600187i
$101$	6.47210	+	1.14121i	0.643998	+	0.113554i	0.486103	−	0.873902i	$-0.338418\pi$
$101$	6.47210	+	1.14121i	0.643998	+	0.113554i	0.157895	+	0.987456i	$0.449529\pi$
$102$	−0.0324848	+	0.0168275i	−0.00321647	+	0.00166617i
$103$	−2.37047	+	6.51282i	−0.233569	+	0.641727i	−1.00000		0.000600606i	$-0.999809\pi$
$103$	−2.37047	+	6.51282i	−0.233569	+	0.641727i	0.766430	+	0.642327i	$0.222031\pi$
$104$	1.61026	−	15.3897i	0.157899	−	1.50909i
$105$	0.389482	+	1.72698i	0.0380096	+	0.168536i
$106$	−5.26753	+	5.20821i	−0.511628	+	0.505866i
$107$	19.6413			1.89879			0.949397	−	0.314079i	$-0.101696\pi$
$107$	19.6413			1.89879			0.949397	+	0.314079i	$0.101696\pi$
$108$	−8.24714	+	6.32335i	−0.793581	+	0.608465i
$109$	−4.14089			−0.396625			−0.198312	−	0.980139i	$-0.563546\pi$
$109$	−4.14089			−0.396625			−0.198312	+	0.980139i	$0.563546\pi$
$110$	−0.906315	+	0.896109i	−0.0864137	+	0.0854407i
$111$	−7.64301	−	2.37920i	−0.725442	−	0.225823i
$112$	3.92249	+	0.783625i	0.370641	+	0.0740456i
$113$	1.35342	−	3.71848i	0.127319	−	0.349805i	−0.859613	−	0.510946i	$-0.829295\pi$
$113$	1.35342	−	3.71848i	0.127319	−	0.349805i	0.986931	+	0.161141i	$0.0515174\pi$
$114$	−0.652976	−	0.417841i	−0.0611568	−	0.0391344i
$115$	4.57037	+	0.805880i	0.426190	+	0.0751487i
$116$	−9.75978	−	8.37959i	−0.906173	−	0.778025i
$117$	−9.51165	−	13.3752i	−0.879352	−	1.23653i
$118$	−2.76754	−	6.02382i	−0.254772	−	0.554537i
$119$	0.0140348	−	0.00510826i	0.00128657	−	0.000468274i
$120$	−4.60021	−	1.97775i	−0.419939	−	0.180543i
$121$	−7.83094	+	6.57094i	−0.711903	+	0.597358i
$122$	−2.32940	+	1.61149i	−0.210894	+	0.145897i
$123$	−1.29289	−	0.165414i	−0.116576	−	0.0149149i
$124$	2.15995	+	13.1166i	0.193970	+	1.17790i
$125$	−7.92703	+	4.57667i	−0.709015	+	0.409350i
$126$	3.67075	−	2.12734i	0.327017	−	0.189518i
$127$	11.2420	+	6.49056i	0.997565	+	0.575944i	0.907527	−	0.419994i	$-0.137968\pi$
$127$	11.2420	+	6.49056i	0.997565	+	0.575944i	0.0900379	+	0.995938i	$0.471301\pi$
$128$	−8.31071	+	7.67672i	−0.734570	+	0.678533i
$129$	−15.8656	−	8.18563i	−1.39689	−	0.720705i
$130$	3.38259	−	7.14804i	0.296673	−	0.626924i
$131$	−3.87374	−	21.9691i	−0.338451	−	1.91945i	−0.390078	−	0.920782i	$-0.627552\pi$
$131$	−3.87374	−	21.9691i	−0.338451	−	1.91945i	0.0516273	−	0.998666i	$-0.483559\pi$
$132$	2.69837	+	1.43111i	0.234863	+	0.124562i
$133$	0.242440	+	0.203431i	0.0210222	+	0.0176397i
$134$	1.57289	−	16.8770i	0.135877	−	1.45795i
$135$	−5.04747	+	1.65244i	−0.434417	+	0.142220i
$136$	−0.0116251	+	0.0406131i	−0.000996844	+	0.00348255i
$137$	−13.9492	+	16.6240i	−1.19176	+	1.42028i	−0.308610	+	0.951189i	$0.599864\pi$
$137$	−13.9492	+	16.6240i	−1.19176	+	1.42028i	−0.883149	+	0.469093i	$0.844581\pi$
$138$	−1.42950	−	11.0296i	−0.121687	−	0.938898i
$139$	−5.30651	+	0.935681i	−0.450092	+	0.0793634i	−0.394100	−	0.919068i	$-0.628943\pi$
$139$	−5.30651	+	0.935681i	−0.450092	+	0.0793634i	−0.0559928	+	0.998431i	$0.517832\pi$
$140$	1.75867	+	1.04210i	0.148635	+	0.0880735i
$141$	−2.63647	−	4.10529i	−0.222031	−	0.345728i
$142$	2.64942	−	9.66845i	0.222334	−	0.811358i
$143$	−2.41187	+	4.17748i	−0.201691	+	0.349338i
$144$	−1.22922	+	11.9369i	−0.102435	+	0.994740i
$145$	−3.28701	−	5.69328i	−0.272972	−	0.472801i
$146$	−10.1573	+	2.66010i	−0.840626	+	0.220151i
$147$	−1.59778	+	0.668664i	−0.131782	+	0.0551504i
$148$	−8.05658	+	4.53061i	−0.662247	+	0.372414i
$149$	9.65113	+	11.5018i	0.790651	+	0.942261i	0.999362	−	0.0357160i	$-0.0113712\pi$
$149$	9.65113	+	11.5018i	0.790651	+	0.942261i	−0.208711	+	0.977977i	$0.566927\pi$
$150$	7.12986	+	6.55975i	0.582151	+	0.535602i
$151$	−4.08652	−	11.2276i	−0.332556	−	0.913690i	−0.987445	−	0.157965i	$-0.949507\pi$
$151$	−4.08652	−	11.2276i	−0.332556	−	0.913690i	0.654889	−	0.755725i	$-0.272715\pi$
$152$	−0.868458	+	0.216962i	−0.0704412	+	0.0175979i
$153$	0.0192321	+	0.0404693i	0.00155482	+	0.00327175i
$154$	−1.01737	−	0.720992i	−0.0819823	−	0.0580992i
$155$	−1.17970	+	6.69042i	−0.0947559	+	0.537387i
$156$	−18.7697	−	2.61777i	−1.50278	−	0.209589i
$157$	19.5711	+	7.12330i	1.56194	+	0.568501i	0.971181	−	0.238344i	$-0.0766045\pi$
$157$	19.5711	+	7.12330i	1.56194	+	0.568501i	0.590763	+	0.806845i	$0.298827\pi$
$158$	−5.73399	+	0.468960i	−0.456172	+	0.0373085i
$159$	6.15360	+	6.66646i	0.488012	+	0.528685i
$160$	−5.30731	+	2.29425i	−0.419580	+	0.181376i
$161$			4.54046i			0.357838i
$162$	7.39333	+	10.3604i	0.580875	+	0.813993i
$163$		−	1.88113i		−	0.147342i	−0.997283	−	0.0736709i	$-0.976529\pi$
$163$		−	1.88113i		−	0.147342i	0.997283	−	0.0736709i	$-0.0234714\pi$
$164$	−1.16384	+	0.954325i	−0.0908803	+	0.0745203i
$165$	1.05877	+	1.14701i	0.0824251	+	0.0892947i
$166$	0.327302	+	4.00194i	0.0254036	+	0.310611i
$167$	5.40110	+	1.96584i	0.417949	+	0.152121i	0.542430	−	0.840101i	$-0.317504\pi$
$167$	5.40110	+	1.96584i	0.417949	+	0.152121i	−0.124481	+	0.992222i	$0.539727\pi$
$168$	1.12402	−	4.76829i	0.0867202	−	0.367881i
$169$	2.93979	−	16.6724i	0.226138	−	1.28249i
$170$	−0.0124830	+	0.0176145i	−0.000957403	+	0.00135097i
$171$	−0.538889	+	0.781697i	−0.0412099	+	0.0597779i
$172$	−19.4500	+	6.83079i	−1.48305	+	0.520843i
$173$	3.22757	+	8.86767i	0.245387	+	0.674196i	0.999841	+	0.0178427i	$0.00567979\pi$
$173$	3.22757	+	8.86767i	0.245387	+	0.674196i	−0.754453	+	0.656354i	$0.772098\pi$
$174$	−10.6670	+	11.5940i	−0.808662	+	0.878942i
$175$	−2.54240	−	3.02992i	−0.192188	−	0.229040i
$176$	3.34067	−	1.13091i	0.251812	−	0.0852452i
$177$	−7.48960	+	3.13437i	−0.562953	+	0.235594i
$178$	2.35829	+	9.00491i	0.176762	+	0.674947i
$179$	7.52328	+	13.0307i	0.562316	+	0.973961i	0.997294	+	0.0735192i	$0.0234230\pi$
$179$	7.52328	+	13.0307i	0.562316	+	0.973961i	−0.434977	+	0.900441i	$0.643244\pi$
$180$	−2.61414	+	5.54764i	−0.194846	+	0.413497i
$181$	−2.25687	+	3.90902i	−0.167752	+	0.290555i	−0.937629	−	0.347637i	$-0.886984\pi$
$181$	−2.25687	+	3.90902i	−0.167752	+	0.290555i	0.769877	+	0.638192i	$0.220318\pi$
$182$	7.46179	+	2.04473i	0.553104	+	0.151566i
$183$	1.87460	+	2.91897i	0.138574	+	0.215776i
$184$	−10.3932	−	7.54369i	−0.766197	−	0.556128i
$185$	−4.65200	+	0.820273i	−0.342022	+	0.0603077i
$186$	16.1458	−	2.09259i	1.18387	−	0.153436i
$187$	0.00846491	−	0.0100881i	0.000619015	−	0.000737714i
$188$	−5.53673	−	1.04106i	−0.403807	−	0.0759268i
$189$	−2.44964	−	4.58249i	−0.178185	−	0.333327i
$190$	−0.455500	−	0.0424512i	−0.0330454	−	0.00307973i
$191$	−17.7152	−	14.8648i	−1.28183	−	1.07558i	−0.992989	−	0.118204i	$-0.962286\pi$
$191$	−17.7152	−	14.8648i	−1.28183	−	1.07558i	−0.288839	−	0.957378i	$-0.593269\pi$
$192$	9.04722	+	10.4951i	0.652927	+	0.757421i
$193$	−2.78704	−	15.8061i	−0.200615	−	1.13775i	−0.904192	−	0.427126i	$-0.859526\pi$
$193$	−2.78704	−	15.8061i	−0.200615	−	1.13775i	0.703577	−	0.710619i	$-0.251585\pi$
$194$	−13.9628	−	6.60748i	−1.00247	−	0.474389i
$195$	−8.60721	−	4.44077i	−0.616375	−	0.318010i
$196$	−0.705279	+	1.87152i	−0.0503770	+	0.133680i
$197$	15.1905	+	8.77023i	1.08228	+	0.624853i	0.931510	−	0.363717i	$-0.118492\pi$
$197$	15.1905	+	8.77023i	1.08228	+	0.624853i	0.150767	+	0.988569i	$0.451826\pi$
$198$	1.86511	−	3.24272i	0.132548	−	0.230450i
$199$	8.71014	−	5.02880i	0.617445	−	0.356482i	−0.158428	−	0.987370i	$-0.550643\pi$
$199$	8.71014	−	5.02880i	0.617445	−	0.356482i	0.775874	+	0.630888i	$0.217309\pi$
$200$	11.1596	−	0.785590i	0.789102	−	0.0555496i
$201$	−20.5918	−	2.63453i	−1.45243	−	0.185825i
$202$	−5.28770	−	7.64337i	−0.372041	−	0.537785i
$203$	4.92702	−	4.13426i	0.345809	−	0.290168i
$204$	0.0492228	+	0.0159362i	0.00344629	+	0.00111576i
$205$	−0.722794	+	0.263075i	−0.0504821	+	0.0183740i
$206$	8.90660	−	4.09198i	0.620552	−	0.285102i
$207$	−13.5605	+	1.28621i	−0.942520	+	0.0893977i
$208$	−17.0777	+	13.6830i	−1.18413	+	0.948745i
$209$	0.274811	+	0.0484567i	0.0190091	+	0.00335182i
$210$	1.34946	−	2.10886i	0.0931219	−	0.145525i
$211$	−4.30465	+	11.8269i	−0.296344	+	0.814200i	0.698759	+	0.715358i	$0.253736\pi$
$211$	−4.30465	+	11.8269i	−0.296344	+	0.814200i	−0.995103	+	0.0988423i	$0.968486\pi$
$212$	10.4752	+	0.118630i	0.719442	+	0.00814752i
$213$	−11.7231	−	3.64928i	−0.803251	−	0.250044i
$214$	−19.5297	−	19.7522i	−1.33503	−	1.35023i
$215$	−10.5353			−0.718499
$216$	14.5594	+	2.00625i	0.990639	+	0.136508i
$217$	−6.64662			−0.451202
$218$	4.11737	+	4.16427i	0.278864	+	0.282040i
$219$	2.82915	+	12.5446i	0.191176	+	0.847685i
$220$	1.80234	+	0.0204111i	0.121514	+	0.00137611i
$221$	−0.0279463	+	0.0767817i	−0.00187987	+	0.00516490i
$222$	5.20698	+	10.0518i	0.349470	+	0.674636i
$223$	−14.6421	−	2.58180i	−0.980510	−	0.172890i	−0.339653	−	0.940551i	$-0.610310\pi$
$223$	−14.6421	−	2.58180i	−0.980510	−	0.172890i	−0.640857	+	0.767661i	$0.721421\pi$
$224$	−3.11217	−	4.72381i	−0.207941	−	0.315623i
$225$	8.32893	−	8.45144i	0.555262	−	0.563429i
$226$	−5.08520	+	2.33631i	−0.338263	+	0.155409i
$227$	4.10424	−	1.49382i	0.272408	−	0.0991485i	−0.202204	−	0.979343i	$-0.564810\pi$
$227$	4.10424	−	1.49382i	0.272408	−	0.0991485i	0.474612	+	0.880195i	$0.342588\pi$
$228$	0.229068	+	1.07213i	0.0151704	+	0.0710036i
$229$	18.1673	−	15.2442i	1.20053	−	1.00736i	0.200916	−	0.979608i	$-0.435608\pi$
$229$	18.1673	−	15.2442i	1.20053	−	1.00736i	0.999615	−	0.0277565i	$-0.00883629\pi$
$230$	−3.73399	−	5.39748i	−0.246212	−	0.355900i
$231$	−0.925267	+	1.21499i	−0.0608781	+	0.0799404i
$232$	1.27747	+	18.1469i	0.0838699	+	1.19140i
$233$	1.67401	−	0.966493i	0.109668	−	0.0633171i	−0.444163	−	0.895946i	$-0.646499\pi$
$233$	1.67401	−	0.966493i	0.109668	−	0.0633171i	0.553831	+	0.832629i	$0.313165\pi$
$234$	−3.99303	+	22.8646i	−0.261033	+	1.49470i
$235$	−2.49344	−	1.43959i	−0.162654	−	0.0939084i
$236$	−3.30601	+	8.77278i	−0.215203	+	0.571059i
$237$	0.333040	+	7.03825i	0.0216333	+	0.457184i
$238$	−0.0190922	−	0.00903482i	−0.00123757	−	0.000585640i
$239$	−2.67494	−	15.1703i	−0.173027	−	0.981287i	−0.940396	−	0.340081i	$-0.889545\pi$
$239$	−2.67494	−	15.1703i	−0.173027	−	0.981287i	0.767369	−	0.641206i	$-0.221566\pi$
$240$	2.58517	+	6.59270i	0.166872	+	0.425557i
$241$	−14.9046	−	12.5065i	−0.960092	−	0.805613i	0.0208762	−	0.999782i	$-0.493354\pi$
$241$	−14.9046	−	12.5065i	−0.960092	−	0.805613i	−0.980968	+	0.194169i	$0.937799\pi$
$242$	14.3945	+	1.34153i	0.925314	+	0.0862365i
$243$	12.9921	−	8.61421i	0.833446	−	0.552602i
$244$	3.93676	+	0.740218i	0.252025	+	0.0473876i
$245$	−0.657004	+	0.782987i	−0.0419745	+	0.0500232i
$246$	1.11920	+	1.46467i	0.0713579	+	0.0933838i
$247$	−1.70511	+	0.300657i	−0.108493	+	0.0191303i
$248$	11.0430	−	15.2143i	0.701229	−	0.966106i
$249$	4.91222	−	0.232440i	0.311299	−	0.0147303i
$250$	12.4845	+	3.42110i	0.789591	+	0.216369i
$251$	−7.64577	+	13.2429i	−0.482597	+	0.835882i	−0.999800	−	0.0199800i	$-0.993640\pi$
$251$	−7.64577	+	13.2429i	−0.482597	+	0.835882i	0.517203	+	0.855863i	$0.326973\pi$
$252$	−5.78926	−	1.57622i	−0.364689	−	0.0992927i
$253$	2.00172	+	3.46708i	0.125847	+	0.217973i
$254$	−4.65094	−	17.7592i	−0.291826	−	1.11431i
$255$	0.0210359	+	0.0160198i	0.00131732	+	0.00100320i
$256$	15.9836	+	0.724506i	0.998974	+	0.0452816i
$257$	0.439713	+	0.524030i	0.0274286	+	0.0326881i	0.779584	−	0.626297i	$-0.215430\pi$
$257$	0.439713	+	0.524030i	0.0274286	+	0.0326881i	−0.752156	+	0.658985i	$0.770986\pi$
$258$	7.54364	+	24.0943i	0.469647	+	1.50005i
$259$	−1.58066	−	4.34284i	−0.0982176	−	0.269851i
$260$	−10.5518	+	3.70576i	−0.654393	+	0.229822i
$261$	13.7431	+	13.5439i	0.850676	+	0.838346i
$262$	−18.2414	+	25.7400i	−1.12696	+	1.59022i
$263$	0.435362	−	2.46906i	0.0268456	−	0.152249i	−0.968438	−	0.249253i	$-0.919815\pi$
$263$	0.435362	−	2.46906i	0.0268456	−	0.152249i	0.995284	+	0.0970042i	$0.0309260\pi$
$264$	−1.24386	−	4.13659i	−0.0765543	−	0.254589i
$265$	5.03093	+	1.83111i	0.309048	+	0.112484i
$266$	−0.0364835	−	0.446085i	−0.00223695	−	0.0273512i
$267$	11.1213	−	2.50816i	0.680615	−	0.153497i
$268$	−18.5363	+	15.1994i	−1.13228	+	0.928452i
$269$		−	30.6805i		−	1.87062i	−0.353827	−	0.935311i	$-0.615120\pi$
$269$		−	30.6805i		−	1.87062i	0.353827	−	0.935311i	$-0.384880\pi$
$270$	6.68058	+	3.43291i	0.406567	+	0.208920i
$271$			6.28136i			0.381566i	0.981632	+	0.190783i	$0.0611026\pi$
$271$			6.28136i			0.381566i	−0.981632	+	0.190783i	$0.938897\pi$
$272$	0.0524015	−	0.0286918i	0.00317731	−	0.00173969i
$273$	2.81639	−	9.04747i	0.170456	−	0.547578i
$274$	30.5878	−	2.50165i	1.84788	−	0.151130i
$275$	−3.27715	−	1.19278i	−0.197619	−	0.0719276i
$276$	−9.67045	+	12.4045i	−0.582092	+	0.746663i
$277$	3.84781	−	21.8220i	0.231193	−	1.31116i	−0.619293	−	0.785160i	$-0.712581\pi$
$277$	3.84781	−	21.8220i	0.231193	−	1.31116i	0.850485	−	0.525999i	$-0.176308\pi$
$278$	6.21734	+	4.40610i	0.372891	+	0.264261i
$279$	−1.88284	−	19.8508i	−0.112723	−	1.18843i
$280$	−0.700702	−	2.80478i	−0.0418750	−	0.167618i
$281$	8.65451	+	23.7781i	0.516285	+	1.41848i	0.874584	+	0.484874i	$0.161135\pi$
$281$	8.65451	+	23.7781i	0.516285	+	1.41848i	−0.358299	+	0.933607i	$0.616643\pi$
$282$	−1.50696	+	6.73333i	−0.0897384	+	0.400964i
$283$	−7.09245	−	8.45246i	−0.421603	−	0.502446i	0.512877	−	0.858462i	$-0.328580\pi$
$283$	−7.09245	−	8.45246i	−0.421603	−	0.502446i	−0.934480	+	0.356015i	$0.884135\pi$
$284$	−12.3574	+	6.94917i	−0.733278	+	0.412358i
$285$	−0.0711042	+	0.555758i	−0.00421185	+	0.0329203i
$286$	6.59924	−	1.72827i	0.390221	−	0.102195i
$287$	−0.376269	−	0.651716i	−0.0222104	−	0.0384696i
$288$	13.2265	−	10.6329i	0.779380	−	0.626552i
$289$	−8.49989	+	14.7222i	−0.499993	+	0.866014i
$290$	−2.45707	+	8.96652i	−0.144284	+	0.526532i
$291$	−8.67451	+	16.8131i	−0.508509	+	0.985604i
$292$	12.7748	+	7.56967i	0.747586	+	0.442982i
$293$	18.4942	−	3.26102i	1.08044	−	0.190511i	0.395030	−	0.918668i	$-0.370734\pi$
$293$	18.4942	−	3.26102i	1.08044	−	0.190511i	0.685410	+	0.728157i	$0.259623\pi$
$294$	2.26114	+	0.941931i	0.131873	+	0.0549345i
$295$	−3.07972	+	3.67027i	−0.179308	+	0.213691i
$296$	12.5670	+	3.59719i	0.730443	+	0.209082i
$297$	−3.89079	−	2.41922i	−0.225766	−	0.140377i
$298$	1.97038	−	21.1421i	0.114141	−	1.22473i
$299$	−19.0285	−	15.9668i	−1.10044	−	0.923383i
$300$	−0.492586	−	13.6926i	−0.0284395	−	0.790544i
$301$	−1.78984	−	10.1507i	−0.103165	−	0.585077i
$302$	−7.22769	+	15.2734i	−0.415907	+	0.878888i
$303$	−9.57788	+	6.15105i	−0.550235	+	0.353369i
$304$	1.08171	+	0.657631i	0.0620405	+	0.0377177i
$305$	1.77290	+	1.02359i	0.101516	+	0.0586103i
$306$	0.0215750	−	0.0595802i	0.00123336	−	0.00340597i
$307$	20.8273	−	12.0247i	1.18868	−	0.686284i	0.230673	−	0.973031i	$-0.425907\pi$
$307$	20.8273	−	12.0247i	1.18868	−	0.686284i	0.958006	+	0.286747i	$0.0925739\pi$
$308$	0.286534	+	1.74002i	0.0163268	+	0.0991466i
$309$	−4.63437	−	11.0739i	−0.263640	−	0.629970i
$310$	7.90119	−	5.46607i	0.448758	−	0.310452i
$311$	20.0768	−	16.8465i	1.13845	−	0.955276i	0.139067	−	0.990283i	$-0.455590\pi$
$311$	20.0768	−	16.8465i	1.13845	−	0.955276i	0.999387	+	0.0350070i	$0.0111453\pi$
$312$	16.0306	+	21.4786i	0.907554	+	1.21599i
$313$	−4.76677	+	1.73496i	−0.269434	+	0.0980660i	−0.473204	−	0.880953i	$-0.656903\pi$
$313$	−4.76677	+	1.73496i	−0.269434	+	0.0980660i	0.203770	+	0.979019i	$0.434680\pi$
$314$	−12.2965	−	26.7645i	−0.693929	−	1.51041i
$315$	−2.52458	−	1.74040i	−0.142244	−	0.0980607i
$316$	6.17304	+	5.30007i	0.347261	+	0.298152i
$317$	−2.72721	−	0.480882i	−0.153176	−	0.0270090i	0.0965344	−	0.995330i	$-0.469224\pi$
$317$	−2.72721	−	0.480882i	−0.153176	−	0.0270090i	−0.249710	+	0.968321i	$0.580335\pi$
$318$	0.585440	−	12.8170i	0.0328298	−	0.718739i
$319$	1.93962	−	5.32905i	0.108598	−	0.298369i
$320$	7.58438	+	3.05605i	0.423980	+	0.170839i
$321$	−24.9979	+	23.0748i	−1.39525	+	1.28791i
$322$	4.56609	−	4.51468i	0.254458	−	0.251593i
$323$	0.00472685			0.000263009
$324$	3.06758	−	17.7367i	0.170421	−	0.985371i
$325$	21.6385			1.20029
$326$	−1.89175	+	1.87045i	−0.104775	+	0.103595i
$327$	5.27020	−	4.86475i	0.291443	−	0.269022i
$328$	2.11694	+	0.221500i	0.116888	+	0.0122303i
$329$	0.963428	−	2.64700i	0.0531155	−	0.145934i
$330$	0.100729	−	2.20525i	0.00554495	−	0.121395i
$331$	−27.0247	−	4.76518i	−1.48541	−	0.261918i	−0.628674	−	0.777669i	$-0.716402\pi$
$331$	−27.0247	−	4.76518i	−1.48541	−	0.261918i	−0.856738	+	0.515751i	$0.827513\pi$
$332$	3.69909	−	4.30837i	0.203014	−	0.236452i
$333$	12.5225	−	5.95103i	0.686230	−	0.326114i
$334$	−3.39349	−	7.38627i	−0.185684	−	0.404159i
$335$	−11.5118	+	4.18997i	−0.628959	+	0.228922i
$336$	−5.91285	+	3.61084i	−0.322572	+	0.196988i
$337$	−9.65525	+	8.10171i	−0.525955	+	0.441328i	−0.866702	−	0.498827i	$-0.833764\pi$
$337$	−9.65525	+	8.10171i	−0.525955	+	0.441328i	0.340747	+	0.940155i	$0.389320\pi$
$338$	−19.6896	+	13.6213i	−1.07097	+	0.740903i
$339$	2.64598	+	6.32260i	0.143710	+	0.343396i
$340$	0.0301261	−	0.00496096i	0.00163381	−	0.000269046i
$341$	−5.07534	+	2.93025i	−0.274845	+	0.158682i
$342$	1.32194	−	0.235327i	0.0714823	−	0.0127250i
$343$	−0.866025	−	0.500000i	−0.0467610	−	0.0269975i
$344$	26.2089	+	12.7678i	1.41309	+	0.688393i
$345$	−6.76357	+	4.34366i	−0.364139	+	0.233855i
$346$	5.70849	−	12.0631i	0.306891	−	0.648517i
$347$	2.00505	+	11.3712i	0.107637	+	0.610438i	0.990134	+	0.140121i	$0.0447493\pi$
$347$	2.00505	+	11.3712i	0.107637	+	0.610438i	−0.882498	+	0.470317i	$0.844140\pi$
$348$	22.2659	−	0.801007i	1.19358	−	0.0429385i
$349$	−8.55608	−	7.17940i	−0.457997	−	0.384305i	0.384397	−	0.923168i	$-0.374409\pi$
$349$	−8.55608	−	7.17940i	−0.457997	−	0.384305i	−0.842393	+	0.538863i	$0.818854\pi$
$350$	−0.519058	+	5.56947i	−0.0277448	+	0.297701i
$351$	27.8190	+	5.84848i	1.48487	+	0.312169i
$352$	−4.45899	−	2.23505i	−0.237665	−	0.119128i
$353$	20.3258	−	24.2234i	1.08184	−	1.28928i	0.127079	−	0.991893i	$-0.459440\pi$
$353$	20.3258	−	24.2234i	1.08184	−	1.28928i	0.954756	−	0.297389i	$-0.0961158\pi$
$354$	10.5991	+	4.41532i	0.563338	+	0.234671i
$355$	−7.13537	+	1.25816i	−0.378706	+	0.0667761i
$356$	6.71085	−	11.3254i	0.355674	−	0.600244i
$357$	−0.0118612	+	0.0229897i	−0.000627762	+	0.00121674i
$358$	5.62371	−	20.5225i	0.297223	−	1.08465i
$359$	5.53672	−	9.58988i	0.292217	−	0.506135i	−0.682117	−	0.731243i	$-0.738940\pi$
$359$	5.53672	−	9.58988i	0.292217	−	0.506135i	0.974334	+	0.225109i	$0.0722737\pi$
$360$	8.17826	−	2.88725i	0.431032	−	0.152171i
$361$	−9.44992	−	16.3677i	−0.497364	−	0.861460i
$362$	6.17515	−	1.61721i	0.324559	−	0.0849986i
$363$	2.24700	−	17.5628i	0.117937	−	0.921810i
$364$	−5.36314	−	9.53704i	−0.281105	−	0.499877i
$365$	4.87795	+	5.81331i	0.255323	+	0.304283i
$366$	1.07149	−	4.78758i	0.0560077	−	0.250251i
$367$	−10.1502	−	27.8874i	−0.529835	−	1.45571i	−0.859265	−	0.511530i	$-0.829079\pi$
$367$	−10.1502	−	27.8874i	−0.529835	−	1.45571i	0.329430	−	0.944180i	$-0.393143\pi$
$368$	2.74790	+	17.9527i	0.143244	+	0.935851i
$369$	1.83982	−	1.30838i	0.0957774	−	0.0681115i
$370$	5.45049	+	3.86265i	0.283358	+	0.200810i
$371$	−0.909561	+	5.15838i	−0.0472221	+	0.267810i
$372$	−18.1585	−	14.1562i	−0.941475	−	0.733967i
$373$	29.2697	+	10.6533i	1.51553	+	0.551606i	0.960026	−	0.279911i	$-0.0903050\pi$
$373$	29.2697	+	10.6533i	1.51553	+	0.551606i	0.555499	+	0.831517i	$0.312527\pi$
$374$	−0.0185619	+	0.00151810i	−0.000959812	+	7.84991e-5i
$375$	4.71218	−	15.1376i	0.243336	−	0.781701i
$376$	4.45836	+	6.60313i	0.229922	+	0.340531i
$377$			35.1869i			1.81222i
$378$	−2.17264	+	7.01995i	−0.111748	+	0.361067i
$379$		−	0.759047i		−	0.0389896i	−0.999810	−	0.0194948i	$-0.993794\pi$
$379$		−	0.759047i		−	0.0389896i	0.999810	−	0.0194948i	$-0.00620578\pi$
$380$	0.410222	+	0.500281i	0.0210440	+	0.0256639i
$381$	−21.9331	+	4.94651i	−1.12367	+	0.253417i
$382$	2.66587	+	32.5957i	0.136398	+	1.66774i
$383$	−9.42572	−	3.43068i	−0.481632	−	0.175300i	0.0897825	−	0.995961i	$-0.471383\pi$
$383$	−9.42572	−	3.43068i	−0.481632	−	0.175300i	−0.571414	+	0.820662i	$0.693605\pi$
$384$	1.55854	−	19.5338i	0.0795340	−	0.996832i
$385$	−0.156496	+	0.887535i	−0.00797579	+	0.0452330i
$386$	−13.1241	+	18.5191i	−0.667999	+	0.942597i
$387$	29.8090	−	8.22100i	1.51528	−	0.417897i
$388$	7.23876	+	20.6116i	0.367492	+	1.04640i
$389$	0.533185	+	1.46491i	0.0270336	+	0.0742741i	0.952475	−	0.304616i	$-0.0985281\pi$
$389$	0.533185	+	1.46491i	0.0270336	+	0.0742741i	−0.925442	+	0.378890i	$0.876306\pi$
$390$	4.09249	+	13.0714i	0.207231	+	0.661894i
$391$	0.0435902	+	0.0519487i	0.00220445	+	0.00262716i
$392$	2.58336	−	1.15163i	0.130479	−	0.0581662i
$393$	30.7397	+	23.4096i	1.55061	+	1.18086i
$394$	−6.28448	−	23.9967i	−0.316608	−	1.20893i
$395$	2.07903	+	3.60098i	0.104607	+	0.181185i
$396$	−5.11555	+	1.34867i	−0.257066	+	0.0677732i
$397$	−10.5123	+	18.2078i	−0.527595	+	0.913822i	0.471888	+	0.881659i	$0.343573\pi$
$397$	−10.5123	+	18.2078i	−0.527595	+	0.913822i	−0.999483	+	0.0321628i	$0.989761\pi$
$398$	−13.7179	−	3.75907i	−0.687615	−	0.188425i
$399$	−0.547552	+	0.0259094i	−0.0274119	+	0.00129709i
$400$	−11.8863	−	10.4415i	−0.594313	−	0.522074i
$401$	12.8373	−	2.26357i	0.641065	−	0.113037i	0.156340	−	0.987703i	$-0.450031\pi$
$401$	12.8373	−	2.26357i	0.641065	−	0.113037i	0.484726	+	0.874666i	$0.338919\pi$
$402$	17.8254	+	23.3276i	0.889051	+	1.16347i
$403$	23.3732	−	27.8551i	1.16430	−	1.38756i
$404$	−2.42885	+	12.9175i	−0.120840	+	0.642671i
$405$	4.48273	−	8.03292i	0.222748	−	0.399159i
$406$	−9.05666	−	0.844053i	−0.449474	−	0.0418897i
$407$	−3.12158	−	2.61932i	−0.154731	−	0.129835i
$408$	−0.0329172	−	0.0653465i	−0.00162964	−	0.00323513i
$409$	3.66882	+	20.8069i	0.181412	+	1.02884i	0.930480	+	0.366343i	$0.119390\pi$
$409$	3.66882	+	20.8069i	0.181412	+	1.02884i	−0.749068	+	0.662493i	$0.769498\pi$
$410$	0.983251	+	0.465293i	0.0485593	+	0.0229792i
$411$	−1.77659	−	37.5453i	−0.0876328	−	1.85197i
$412$	−12.9711	−	4.88814i	−0.639041	−	0.240821i
$413$	−4.05951	−	2.34376i	−0.199755	−	0.115329i
$414$	14.7770	+	12.3582i	0.726249	+	0.607371i
$415$	2.51324	−	1.45102i	0.123370	−	0.0712278i
$416$	30.7410	+	3.56886i	1.50720	+	0.174978i
$417$	5.65447	−	7.42500i	0.276900	−	0.363604i
$418$	−0.224521	−	0.324545i	−0.0109817	−	0.0158740i
$419$	−5.78462	+	4.85388i	−0.282597	+	0.237127i	−0.773057	−	0.634337i	$-0.781273\pi$
$419$	−5.78462	+	4.85388i	−0.282597	+	0.237127i	0.490460	+	0.871464i	$0.336829\pi$
$420$	−3.46257	+	0.739801i	−0.168956	+	0.0360986i
$421$	5.79891	−	2.11063i	0.282622	−	0.102866i	−0.196820	−	0.980440i	$-0.563061\pi$
$421$	5.79891	−	2.11063i	0.282622	−	0.102866i	0.479442	+	0.877574i	$0.340839\pi$
$422$	16.1739	−	7.43082i	0.787334	−	0.361727i
$423$	8.17843	+	2.12754i	0.397649	+	0.103444i
$424$	−10.2965	−	10.6523i	−0.500040	−	0.517323i
$425$	−0.0581768	−	0.0102581i	−0.00282199	−	0.000497593i
$426$	7.98662	+	15.4178i	0.386953	+	0.746995i
$427$	−0.685023	+	1.88208i	−0.0331506	+	0.0910805i
$428$	−0.444837	+	39.2800i	−0.0215020	+	1.89867i
$429$	−1.83810	−	8.15026i	−0.0887445	−	0.393498i
$430$	10.4754	+	10.5947i	0.505171	+	0.510924i
$431$	8.77170			0.422518			0.211259	−	0.977430i	$-0.432244\pi$
$431$	8.77170			0.422518			0.211259	+	0.977430i	$0.432244\pi$
$432$	−12.4591	−	16.6364i	−0.599439	−	0.800420i
$433$	−2.14228			−0.102951			−0.0514757	−	0.998674i	$-0.516392\pi$
$433$	−2.14228			−0.102951			−0.0514757	+	0.998674i	$0.516392\pi$
$434$	6.60888	+	6.68415i	0.317236	+	0.320849i
$435$	10.8720	+	3.38434i	0.521271	+	0.162267i
$436$	0.0937831	−	8.28124i	0.00449140	−	0.396600i
$437$	−0.491475	+	1.35032i	−0.0235104	+	0.0645944i
$438$	9.80233	−	15.3185i	0.468374	−	0.731945i
$439$	16.7254	+	2.94913i	0.798258	+	0.140754i	0.557876	−	0.829924i	$-0.311616\pi$
$439$	16.7254	+	2.94913i	0.798258	+	0.140754i	0.240382	+	0.970678i	$0.422727\pi$
$440$	−1.77158	−	1.83281i	−0.0844566	−	0.0873757i
$441$	1.24797	−	2.72811i	0.0594273	−	0.129910i
$442$	0.105003	−	0.0482417i	0.00499447	−	0.00229462i
$443$	4.43342	−	1.61363i	0.210638	−	0.0766659i	−0.234546	−	0.972105i	$-0.575360\pi$
$443$	4.43342	−	1.61363i	0.210638	−	0.0766659i	0.445184	+	0.895439i	$0.353138\pi$
$444$	4.93119	−	15.2312i	0.234024	−	0.722839i
$445$	5.15376	−	4.32452i	0.244312	−	0.205002i
$446$	11.9626	+	17.2919i	0.566446	+	0.818797i
$447$	−25.7956	−	3.30031i	−1.22009	−	0.156099i
$448$	−1.65599	+	7.82673i	−0.0782380	+	0.369778i
$449$	−33.5906	+	19.3935i	−1.58524	+	0.915237i	−0.591160	+	0.806554i	$0.701330\pi$
$449$	−33.5906	+	19.3935i	−1.58524	+	0.915237i	−0.994077	+	0.108682i	$0.965337\pi$
$450$	−16.7808	+	0.0274882i	−0.791054	+	0.00129580i
$451$	−0.574635	−	0.331765i	−0.0270585	−	0.0156222i
$452$	7.40583	+	2.79087i	0.348341	+	0.131272i
$453$	18.3913	+	9.48875i	0.864099	+	0.445820i
$454$	−5.58320	−	2.64208i	−0.262032	−	0.123999i
$455$	−0.971005	−	5.50684i	−0.0455214	−	0.258165i
$456$	0.850417	−	1.29640i	0.0398244	−	0.0607097i
$457$	16.1766	+	13.5737i	0.756708	+	0.634953i	0.937268	−	0.348611i	$-0.113347\pi$
$457$	16.1766	+	13.5737i	0.756708	+	0.634953i	−0.180560	+	0.983564i	$0.557791\pi$
$458$	−33.3944	−	3.11226i	−1.56042	−	0.145426i
$459$	−0.0720208	−	0.0289122i	−0.00336165	−	0.00134951i
$460$	−1.71517	+	9.12191i	−0.0799701	+	0.425311i
$461$	−24.3520	+	29.0216i	−1.13418	+	1.35167i	−0.206437	+	0.978460i	$0.566187\pi$
$461$	−24.3520	+	29.0216i	−1.13418	+	1.35167i	−0.927747	+	0.373209i	$0.878258\pi$
$462$	2.14186	−	0.277598i	0.0996484	−	0.0129150i
$463$	−10.5907	+	1.86743i	−0.492192	+	0.0867867i	−0.414235	−	0.910170i	$-0.635951\pi$
$463$	−10.5907	+	1.86743i	−0.492192	+	0.0867867i	−0.0779570	+	0.996957i	$0.524840\pi$
$464$	16.9791	−	19.3285i	0.788237	−	0.897305i
$465$	−6.35854	−	9.90097i	−0.294870	−	0.459146i
$466$	−2.63646	−	0.722461i	−0.122132	−	0.0334674i
$467$	−5.84673	+	10.1268i	−0.270555	+	0.468614i	−0.969004	−	0.247045i	$-0.920540\pi$
$467$	−5.84673	+	10.1268i	−0.270555	+	0.468614i	0.698449	+	0.715659i	$0.253874\pi$
$468$	26.9640	−	18.7192i	1.24641	−	0.865293i
$469$	−5.99278	−	10.3798i	−0.276721	−	0.479295i
$470$	1.03157	+	3.93893i	0.0475826	+	0.181689i
$471$	−33.2771	+	13.9263i	−1.53333	+	0.641692i
$472$	12.1095	−	5.39829i	0.557387	−	0.248476i
$473$	−5.84178	−	6.96197i	−0.268605	−	0.320112i
$474$	6.74684	−	7.33321i	0.309893	−	0.336825i
$475$	−0.428133	−	1.17629i	−0.0196441	−	0.0539717i
$476$	0.00989801	+	0.0281836i	0.000453674	+	0.00129179i
$477$	−15.6636	−	1.25524i	−0.717189	−	0.0574735i
$478$	−12.5962	+	17.7742i	−0.576138	+	0.812975i
$479$	−6.03555	+	34.2293i	−0.275771	+	1.56398i	0.460729	+	0.887541i	$0.347588\pi$
$479$	−6.03555	+	34.2293i	−0.275771	+	1.56398i	−0.736501	+	0.676437i	$0.763523\pi$
$480$	4.05943	−	9.15503i	0.185287	−	0.417868i
$481$	23.7588	+	8.64748i	1.08331	+	0.394291i
$482$	2.24292	+	27.4242i	0.102162	+	1.24914i
$483$	−5.33417	−	5.77874i	−0.242713	−	0.262942i
$484$	−12.9637	−	15.8097i	−0.589258	−	0.718622i
$485$			11.1645i			0.506953i
$486$	−21.5812	−	4.50019i	−0.978943	−	0.204133i
$487$		−	8.66789i		−	0.392779i	−0.980526	−	0.196390i	$-0.937078\pi$
$487$		−	8.66789i		−	0.392779i	0.980526	−	0.196390i	$-0.0629218\pi$
$488$	−3.17001	−	4.69500i	−0.143500	−	0.212533i
$489$	2.20997	+	2.39416i	0.0999385	+	0.108268i
$490$	1.44068	−	0.117828i	0.0650834	−	0.00532291i
$491$	21.2299	+	7.72705i	0.958091	+	0.348717i	0.773285	−	0.634058i	$-0.218612\pi$
$491$	21.2299	+	7.72705i	0.958091	+	0.348717i	0.184806	+	0.982775i	$0.440834\pi$
$492$	0.360088	−	2.58188i	0.0162340	−	0.116400i
$493$	0.0166810	−	0.0946027i	0.000751275	−	0.00426069i
$494$	1.99778	+	1.41579i	0.0898844	+	0.0636992i
$495$	−2.69504	−	0.215973i	−0.121133	−	0.00970725i
$496$	−26.2804	+	4.02256i	−1.18003	+	0.180618i
$497$	−2.42447	−	6.66117i	−0.108752	−	0.298794i
$498$	−5.11808	−	4.70884i	−0.229347	−	0.211008i
$499$	−21.1356	−	25.1884i	−0.946160	−	1.12759i	−0.991693	−	0.128626i	$-0.958943\pi$
$499$	−21.1356	−	25.1884i	−0.946160	−	1.12759i	0.0455334	−	0.998963i	$-0.485501\pi$
$500$	−8.97322	−	15.9567i	−0.401295	−	0.713605i
$501$	−9.18358	+	3.84330i	−0.410292	+	0.171706i
$502$	20.9200	−	5.47873i	0.933705	−	0.244528i
$503$	14.3475	+	24.8506i	0.639722	+	1.10803i	0.985494	+	0.169713i	$0.0542840\pi$
$503$	14.3475	+	24.8506i	0.639722	+	1.10803i	−0.345771	+	0.938319i	$0.612383\pi$
$504$	4.17126	+	7.38922i	0.185803	+	0.329142i
$505$	−3.35865	+	5.81735i	−0.149458	+	0.258869i
$506$	1.49630	−	5.46041i	0.0665187	−	0.242745i
$507$	15.8453	+	24.6730i	0.703717	+	1.09577i
$508$	−13.2349	+	22.3355i	−0.587204	+	0.990979i
$509$	4.50348	−	0.794084i	0.199613	−	0.0351972i	−0.0729476	−	0.997336i	$-0.523241\pi$
$509$	4.50348	−	0.794084i	0.199613	−	0.0351972i	0.272561	+	0.962139i	$0.412129\pi$
$510$	−0.00480625	−	0.0370835i	−0.000212824	−	0.00164208i
$511$	−4.77239	+	5.68752i	−0.211118	+	0.251601i
$512$	−15.1642	−	16.7942i	−0.670171	−	0.742207i
$513$	−0.232490	−	1.62798i	−0.0102647	−	0.0718769i
$514$	0.0897721	−	0.963250i	0.00395968	−	0.0424872i
$515$	−5.42672	−	4.55356i	−0.239130	−	0.200654i
$516$	16.7295	−	31.5437i	0.736477	−	1.38864i
$517$	−0.431292	−	2.44598i	−0.0189682	−	0.107574i
$518$	−2.79567	+	5.90776i	−0.122835	+	0.259572i
$519$	−14.5256	−	7.49430i	−0.637604	−	0.328963i
$520$	14.2185	+	6.92663i	0.623524	+	0.303753i
$521$	−24.1730	−	13.9563i	−1.05904	−	0.611435i	−0.133871	−	0.990999i	$-0.542741\pi$
$521$	−24.1730	−	13.9563i	−1.05904	−	0.611435i	−0.925166	+	0.379564i	$0.876074\pi$
$522$	−0.0446992	−	27.2877i	−0.00195643	−	1.19435i
$523$	−23.1614	+	13.3723i	−1.01278	+	0.584728i	−0.912004	−	0.410181i	$-0.865466\pi$
$523$	−23.1614	+	13.3723i	−1.01278	+	0.584728i	−0.100775	+	0.994909i	$0.532132\pi$
$524$	44.0231	−	7.24943i	1.92316	−	0.316693i
$525$	6.79535	+	0.869403i	0.296573	+	0.0379439i
$526$	−2.91589	+	2.01722i	−0.127139	+	0.0879551i
$527$	−0.0760460	+	0.0638102i	−0.00331262	+	0.00277962i
$528$	−2.92314	+	5.36398i	−0.127214	+	0.233437i
$529$	2.24046	−	0.815463i	0.0974115	−	0.0354549i
$530$	−3.16092	−	6.88005i	−0.137301	−	0.298850i
$531$	5.84989	−	12.7880i	0.253864	−	0.554954i
$532$	−0.412327	+	0.480241i	−0.0178766	+	0.0208211i
$533$	4.05443	+	0.714905i	0.175617	+	0.0309660i
$534$	−13.5805	−	8.69020i	−0.587686	−	0.376062i
$535$	−6.86629	+	18.8650i	−0.296856	+	0.815604i
$536$	33.7162	+	3.52780i	1.45632	+	0.152378i
$537$	−24.8836	−	7.74604i	−1.07381	−	0.334266i
$538$	−30.8537	+	30.5063i	−1.33020	+	1.31522i
$539$	−0.881725			−0.0379786
$540$	−3.19036	−	10.1317i	−0.137291	−	0.436000i
$541$	21.0202			0.903727			0.451864	−	0.892087i	$-0.350759\pi$
$541$	21.0202			0.903727			0.451864	+	0.892087i	$0.350759\pi$
$542$	6.31683	−	6.24570i	0.271331	−	0.268276i
$543$	−1.71998	−	7.62650i	−0.0738115	−	0.327284i
$544$	−0.0809577	−	0.0241685i	−0.00347103	−	0.00103622i
$545$	1.44759	−	3.97722i	0.0620080	−	0.170366i
$546$	−11.8990	+	6.16380i	−0.509228	+	0.263786i
$547$	−40.2324	−	7.09406i	−1.72021	−	0.303320i	−0.775532	−	0.631309i	$-0.782518\pi$
$547$	−40.2324	−	7.09406i	−1.72021	−	0.303320i	−0.944682	+	0.327988i	$0.893629\pi$
$548$	−32.9299	−	28.2731i	−1.40670	−	1.20777i
$549$	−5.81508	−	1.51273i	−0.248181	−	0.0645619i
$550$	2.05902	+	4.48166i	0.0877969	+	0.191099i
$551$	1.91279	−	0.696198i	0.0814875	−	0.0296590i
$552$	22.0901	−	2.60901i	0.940216	−	0.111047i
$553$	−3.11633	+	2.61491i	−0.132520	+	0.111197i
$554$	−25.7712	+	17.8286i	−1.09491	+	0.757464i
$555$	4.95704	−	6.50920i	0.210415	−	0.276300i
$556$	−1.75106	−	10.6335i	−0.0742615	−	0.450962i
$557$	26.8048	−	15.4757i	1.13575	−	0.655728i	0.190378	−	0.981711i	$-0.439029\pi$
$557$	26.8048	−	15.4757i	1.13575	−	0.655728i	0.945376	+	0.325983i	$0.105695\pi$
$558$	−18.0907	+	21.6315i	−0.765841	+	0.915735i
$559$	48.8344	+	28.1945i	2.06547	+	1.19250i
$560$	−2.12390	+	3.49352i	−0.0897510	+	0.147628i
$561$	0.00107811	+	0.0227840i	4.55177e−5	+	0.000961941i
$562$	15.3070	−	32.3464i	0.645685	−	1.36445i
$563$	−0.337353	−	1.91322i	−0.0142177	−	0.0806328i	0.976873	−	0.213819i	$-0.0685903\pi$
$563$	−0.337353	−	1.91322i	−0.0142177	−	0.0806328i	−0.991091	+	0.133186i	$0.957479\pi$
$564$	8.26976	−	5.17963i	0.348220	−	0.218102i
$565$	3.09838	+	2.59985i	0.130350	+	0.109376i
$566$	−1.44800	+	15.5370i	−0.0608639	+	0.653067i
$567$	8.50127	+	2.95438i	0.357020	+	0.124072i
$568$	19.2757	+	5.51747i	0.808789	+	0.231508i
$569$	−1.38279	+	1.64795i	−0.0579698	+	0.0690857i	−0.794250	−	0.607591i	$-0.792136\pi$
$569$	−1.38279	+	1.64795i	−0.0579698	+	0.0690857i	0.736280	+	0.676677i	$0.236580\pi$
$570$	0.629596	−	0.481097i	0.0263709	−	0.0201509i
$571$	−30.4775	+	5.37400i	−1.27544	+	0.224895i	−0.770043	−	0.637991i	$-0.779766\pi$
$571$	−30.4775	+	5.37400i	−1.27544	+	0.224895i	−0.505398	+	0.862886i	$0.668654\pi$
$572$	−8.29980	−	4.91804i	−0.347032	−	0.205634i
$573$	40.0099	−	1.89321i	1.67144	−	0.0790901i
$574$	−0.281264	+	1.02641i	−0.0117397	+	0.0428415i
$575$	8.97938	−	15.5527i	0.374466	−	0.648594i
$576$	−23.8444	−	2.72863i	−0.993516	−	0.113693i
$577$	−3.55125	−	6.15094i	−0.147840	−	0.256067i	0.782589	−	0.622539i	$-0.213899\pi$
$577$	−3.55125	−	6.15094i	−0.147840	−	0.256067i	−0.930429	+	0.366472i	$0.880566\pi$
$578$	23.2570	−	6.09076i	0.967363	−	0.253342i
$579$	22.1162	+	16.8425i	0.919120	+	0.699950i
$580$	11.4603	−	6.44466i	0.475862	−	0.267600i
$581$	1.82503	+	2.17499i	0.0757151	+	0.0902337i
$582$	25.5333	−	7.99418i	1.05839	−	0.331369i
$583$	1.57960	+	4.33991i	0.0654203	+	0.179741i
$584$	−5.08981	−	20.3736i	−0.210618	−	0.843065i
$585$	16.1716	−	4.45996i	0.668615	−	0.184397i
$586$	−21.6686	−	15.3561i	−0.895121	−	0.634354i
$587$	−8.38241	+	47.5390i	−0.345979	+	1.96215i	−0.0873000	+	0.996182i	$0.527824\pi$
$587$	−8.38241	+	47.5390i	−0.345979	+	1.96215i	−0.258679	+	0.965963i	$0.583287\pi$
$588$	−1.30105	−	3.21049i	−0.0536546	−	0.132398i
$589$	−1.97668	−	0.719453i	−0.0814478	−	0.0296446i
$590$	6.75322	−	0.552319i	0.278026	−	0.0227386i
$591$	−29.6366	+	6.68386i	−1.21909	+	0.274937i
$592$	−8.87817	−	16.2147i	−0.364890	−	0.666422i
$593$		−	20.5858i		−	0.845359i	−0.906279	−	0.422680i	$-0.861090\pi$
$593$		−	20.5858i		−	0.845359i	0.906279	−	0.422680i	$-0.138910\pi$
$594$	1.43582	+	6.31824i	0.0589122	+	0.259240i
$595$			0.0152659i			0.000625841i
$596$	−23.2206	+	19.0405i	−0.951154	+	0.779930i
$597$	−5.17770	+	16.6330i	−0.211909	+	0.680744i
$598$	2.86349	+	35.0120i	0.117097	+	1.43175i
$599$	−3.51192	−	1.27824i	−0.143493	−	0.0522273i	0.269275	−	0.963063i	$-0.413216\pi$
$599$	−3.51192	−	1.27824i	−0.143493	−	0.0522273i	−0.412768	+	0.910836i	$0.635438\pi$
$600$	−13.2801	+	14.1102i	−0.542159	+	0.576048i
$601$	−4.33097	+	24.5621i	−0.176664	+	1.00191i	0.759542	+	0.650458i	$0.225423\pi$
$601$	−4.33097	+	24.5621i	−0.176664	+	1.00191i	−0.936206	+	0.351452i	$0.885688\pi$
$602$	−8.42834	+	11.8930i	−0.343513	+	0.484723i
$603$	29.3026	−	20.8384i	1.19330	−	0.848604i
$604$	22.5463	−	7.91823i	0.917397	−	0.322188i
$605$	−3.57365	−	9.81853i	−0.145290	−	0.399180i
$606$	15.7093	+	3.51584i	0.638146	+	0.142821i
$607$	8.38769	+	9.99606i	0.340446	+	0.405728i	0.908918	−	0.416975i	$-0.136910\pi$
$607$	8.38769	+	9.99606i	0.340446	+	0.405728i	−0.568472	+	0.822703i	$0.692465\pi$
$608$	−0.414226	−	1.74172i	−0.0167991	−	0.0706360i
$609$	−1.41376	+	11.0501i	−0.0572884	+	0.447772i
$610$	−0.733471	−	2.80069i	−0.0296974	−	0.113396i
$611$	7.70527	+	13.3459i	0.311722	+	0.539918i
$612$	−0.0813690	+	0.0375451i	−0.00328915	+	0.00151767i
$613$	−23.0194	+	39.8707i	−0.929744	+	1.61036i	−0.145995	+	0.989285i	$0.546638\pi$
$613$	−23.0194	+	39.8707i	−0.929744	+	1.61036i	−0.783749	+	0.621078i	$0.786695\pi$
$614$	−32.8017	−	8.98854i	−1.32377	−	0.362748i
$615$	0.610852	−	1.18397i	0.0246319	−	0.0477422i
$616$	1.46493	−	2.01829i	0.0590238	−	0.0813191i
$617$	−25.8760	+	4.56263i	−1.04173	+	0.183685i	−0.668237	−	0.743949i	$-0.732951\pi$
$617$	−25.8760	+	4.56263i	−1.04173	+	0.183685i	−0.373491	+	0.927634i	$0.621839\pi$
$618$	−6.52833	+	15.6715i	−0.262608	+	0.630401i
$619$	−15.4550	+	18.4185i	−0.621188	+	0.740303i	−0.981274	−	0.192616i	$-0.938303\pi$
$619$	−15.4550	+	18.4185i	−0.621188	+	0.740303i	0.360087	+	0.932919i	$0.382747\pi$
$620$	−13.3533	−	2.51078i	−0.536280	−	0.100835i
$621$	15.7477	−	17.5680i	0.631934	−	0.704980i
$622$	−36.9044	−	3.43938i	−1.47973	−	0.137907i
$623$	5.04224	+	4.23094i	0.202013	+	0.169509i
$624$	5.66030	−	37.4777i	0.226593	−	1.50031i
$625$	1.80952	+	10.2623i	0.0723806	+	0.410491i
$626$	6.48447	+	3.06858i	0.259171	+	0.122645i
$627$	−0.406686	+	0.261179i	−0.0162415	+	0.0104305i
$628$	−14.6889	+	38.9784i	−0.586152	+	1.55541i
$629$	−0.0597778	−	0.0345127i	−0.00238350	−	0.00137611i
$630$	0.760016	+	4.26936i	0.0302798	+	0.170095i
$631$	−7.95830	+	4.59473i	−0.316815	+	0.182913i	−0.649972	−	0.759958i	$-0.725219\pi$
$631$	−7.95830	+	4.59473i	−0.316815	+	0.182913i	0.333157	+	0.942871i	$0.391886\pi$
$632$	−0.807996	−	11.4779i	−0.0321404	−	0.456565i
$633$	−8.41577	−	20.1096i	−0.334497	−	0.799283i
$634$	2.22813	+	3.22076i	0.0884904	+	0.127913i
$635$	−10.1641	+	8.52866i	−0.403348	+	0.338449i
$636$	−13.4714	+	12.1554i	−0.534177	+	0.481994i
$637$	5.14086	−	1.87112i	0.203688	−	0.0741365i
$638$	−7.28774	+	3.34822i	−0.288524	+	0.132557i
$639$	19.2074	−	9.12786i	0.759834	−	0.361092i
$640$	−4.46801	−	10.6659i	−0.176614	−	0.421607i
$641$	16.8296	+	2.96750i	0.664727	+	0.117209i	0.495824	−	0.868423i	$-0.334866\pi$
$641$	16.8296	+	2.96750i	0.664727	+	0.117209i	0.168904	+	0.985633i	$0.445977\pi$
$642$	48.0610	+	2.19528i	1.89682	+	0.0866408i
$643$	13.6386	−	37.4716i	0.537852	−	1.47774i	−0.311673	−	0.950190i	$-0.600889\pi$
$643$	13.6386	−	37.4716i	0.537852	−	1.47774i	0.849525	−	0.527548i	$-0.176889\pi$
$644$	−9.08033	−	0.102833i	−0.357815	−	0.00405217i
$645$	13.4085	−	12.3769i	0.527958	−	0.487341i
$646$	−0.00470001	−	0.00475354i	−0.000184919	−	0.000187025i
$647$	−24.1632			−0.949952			−0.474976	−	0.879999i	$-0.657543\pi$
$647$	−24.1632			−0.949952			−0.474976	+	0.879999i	$0.657543\pi$
$648$	−20.8870	+	14.5511i	−0.820518	+	0.571620i
$649$	−4.13310			−0.162238
$650$	−21.5156	−	21.7607i	−0.843913	−	0.853524i
$651$	8.45930	−	7.80852i	0.331546	−	0.306040i
$652$	3.76203	+	0.0426041i	0.147332	+	0.00166850i
$653$	−1.56669	+	4.30445i	−0.0613094	+	0.168446i	−0.966565	−	0.256421i	$-0.917457\pi$
$653$	−1.56669	+	4.30445i	−0.0613094	+	0.168446i	0.905256	+	0.424867i	$0.139679\pi$
$654$	−10.1325	−	0.462822i	−0.396212	−	0.0180978i
$655$	22.4550	+	3.95942i	0.877389	+	0.154707i
$656$	−1.88217	−	2.34913i	−0.0734863	−	0.0917183i
$657$	−18.3382	−	12.6421i	−0.715442	−	0.493214i
$658$	−3.61990	+	1.66310i	−0.141118	+	0.0648344i
$659$	−8.36618	+	3.04504i	−0.325900	+	0.118618i	−0.499789	−	0.866147i	$-0.666589\pi$
$659$	−8.36618	+	3.04504i	−0.325900	+	0.118618i	0.173889	+	0.984765i	$0.444367\pi$
$660$	−2.31785	+	2.09143i	−0.0902223	+	0.0814087i
$661$	−33.1489	+	27.8152i	−1.28934	+	1.08189i	−0.297460	+	0.954734i	$0.596139\pi$
$661$	−33.1489	+	27.8152i	−1.28934	+	1.08189i	−0.991883	+	0.127153i	$0.959416\pi$
$662$	22.0792	+	31.9154i	0.858131	+	1.24043i
$663$	−0.0546361	−	0.130553i	−0.00212189	−	0.00507027i
$664$	−8.01078	+	0.563926i	−0.310878	+	0.0218846i
$665$	−0.280144	+	0.161741i	−0.0108635	+	0.00627206i
$666$	−18.4361	−	6.67599i	−0.714383	−	0.258690i
$667$	25.2907	+	14.6016i	0.979260	+	0.565376i
$668$	−4.05375	+	10.7570i	−0.156844	+	0.416200i
$669$	21.6685	−	13.9158i	0.837752	−	0.538016i
$670$	15.6601	+	7.41066i	0.605003	+	0.286299i
$671$	0.306660	+	1.73915i	0.0118385	+	0.0671393i
$672$	9.51051	+	2.35589i	0.366876	+	0.0908806i
$673$	−36.5732	−	30.6886i	−1.40979	−	1.18296i	−0.956549	−	0.291571i	$-0.905822\pi$
$673$	−36.5732	−	30.6886i	−1.40979	−	1.18296i	−0.453244	−	0.891386i	$-0.649733\pi$
$674$	17.7479	+	1.65405i	0.683623	+	0.0637116i
$675$	−0.671587	+	20.5412i	−0.0258494	+	0.790633i
$676$	33.2761	+	6.25680i	1.27985	+	0.240646i
$677$	11.4819	−	13.6836i	0.441285	−	0.525902i	−0.498858	−	0.866684i	$-0.666247\pi$
$677$	11.4819	−	13.6836i	0.441285	−	0.525902i	0.940143	+	0.340781i	$0.110692\pi$
$678$	3.72733	−	8.94762i	0.143147	−	0.343631i
$679$	−10.7570	+	1.89674i	−0.412814	+	0.0727902i
$680$	−0.0349440	−	0.0253634i	−0.00134004	−	0.000972640i
$681$	−3.46860	+	6.72293i	−0.132917	+	0.257623i
$682$	7.99331	+	2.19038i	0.306080	+	0.0838741i
$683$	−15.7615	+	27.2998i	−0.603098	+	1.04460i	0.389251	+	0.921132i	$0.372734\pi$
$683$	−15.7615	+	27.2998i	−0.603098	+	1.04460i	−0.992349	+	0.123465i	$0.960599\pi$
$684$	−1.55109	−	1.09541i	−0.0593074	−	0.0418842i
$685$	−11.0905	−	19.2093i	−0.423747	−	0.733951i
$686$	0.358285	+	1.36808i	0.0136794	+	0.0522334i
$687$	−5.21292	+	40.7448i	−0.198885	+	1.55451i
$688$	−13.2202	−	39.0522i	−0.504015	−	1.48885i
$689$	−18.4196	−	21.9516i	−0.701730	−	0.836289i
$690$	11.0934	+	2.48276i	0.422317	+	0.0945172i
$691$	−10.5392	−	28.9562i	−0.400930	−	1.10155i	−0.961826	−	0.273661i	$-0.911766\pi$
$691$	−10.5392	−	28.9562i	−0.400930	−	1.10155i	0.560896	−	0.827886i	$-0.310457\pi$
$692$	−17.8073	+	6.25388i	−0.676932	+	0.237737i
$693$	−0.249773	−	2.63336i	−0.00948808	−	0.100033i
$694$	9.44175	−	13.3230i	0.358404	−	0.505735i
$695$	0.956376	−	5.42388i	0.0362774	−	0.205739i
$696$	−22.9450	−	21.5952i	−0.869729	−	0.818563i
$697$	−0.0105617	−	0.00384416i	−0.000400054	−	0.000145608i
$698$	1.28756	+	15.7430i	0.0487348	+	0.595882i
$699$	−0.995110	+	3.19673i	−0.0376385	+	0.120911i
$700$	6.11703	−	5.01586i	0.231202	−	0.189582i
$701$		−	43.3931i		−	1.63894i	−0.573126	−	0.819468i	$-0.694269\pi$
$701$		−	43.3931i		−	1.63894i	0.573126	−	0.819468i	$-0.305731\pi$
$702$	−21.7795	−	33.7913i	−0.822014	−	1.27537i
$703$		−	1.46264i		−	0.0551645i
$704$	2.18601	+	6.70652i	0.0823882	+	0.252762i
$705$	4.86470	−	1.09712i	0.183215	−	0.0413200i
$706$	−44.5706	+	3.64525i	−1.67744	+	0.137191i
$707$	−6.17560	−	2.24774i	−0.232258	−	0.0845348i
$708$	−6.09872	−	15.0492i	−0.229204	−	0.565585i
$709$	−5.46624	+	31.0006i	−0.205289	+	1.16425i	0.691695	+	0.722190i	$0.256864\pi$
$709$	−5.46624	+	31.0006i	−0.205289	+	1.16425i	−0.896984	+	0.442062i	$0.854247\pi$
$710$	8.36012	+	5.92464i	0.313750	+	0.222348i
$711$	−8.69247	−	8.56648i	−0.325993	−	0.321268i
$712$	−18.0621	+	4.51234i	−0.676905	+	0.169107i
$713$	−10.3217	−	28.3587i	−0.386552	−	1.06204i
$714$	0.0349133	−	0.0109309i	0.00130660	−	0.000409080i
$715$	−3.16922	−	3.77692i	−0.118522	−	0.141249i
$716$	−26.2301	+	14.7505i	−0.980266	+	0.551251i
$717$	21.2267	+	16.1651i	0.792726	+	0.603696i
$718$	−15.1493	+	3.96745i	−0.565367	+	0.148064i
$719$	5.59834	+	9.69662i	0.208783	+	0.361623i	0.951331	−	0.308170i	$-0.0997164\pi$
$719$	5.59834	+	9.69662i	0.208783	+	0.361623i	−0.742548	+	0.669792i	$0.766383\pi$
$720$	−11.0354	−	5.35358i	−0.411264	−	0.199516i
$721$	3.46540	−	6.00224i	0.129058	−	0.223535i
$722$	−7.06389	+	25.7781i	−0.262891	+	0.959361i
$723$	33.6622	−	1.59285i	1.25191	−	0.0592386i
$724$	−7.76643	−	4.60199i	−0.288637	−	0.171032i
$725$	−25.0530	+	4.41751i	−0.930444	+	0.164062i
$726$	−19.8962	+	15.2034i	−0.738419	+	0.564252i
$727$	31.3122	−	37.3164i	1.16130	−	1.38399i	0.252066	−	0.967710i	$-0.418890\pi$
$727$	31.3122	−	37.3164i	1.16130	−	1.38399i	0.909237	−	0.416278i	$-0.136666\pi$
$728$	−4.25820	+	14.8763i	−0.157819	+	0.551353i
$729$	−6.41532	+	26.2268i	−0.237604	+	0.971362i
$730$	0.995884	−	10.6858i	0.0368593	−	0.395499i
$731$	−0.117929	−	0.0989541i	−0.00436176	−	0.00365995i
$732$	−5.88002	+	3.68285i	−0.217332	+	0.136122i
$733$	−6.48970	−	36.8049i	−0.239703	−	1.35942i	−0.832480	−	0.554055i	$-0.813080\pi$
$733$	−6.48970	−	36.8049i	−0.239703	−	1.35942i	0.592778	−	0.805366i	$-0.298031\pi$
$734$	−17.9523	+	37.9365i	−0.662632	+	1.40026i
$735$	−0.0836773	−	1.76838i	−0.00308648	−	0.0652277i
$736$	15.3218	−	20.6142i	0.564769	−	0.759850i
$737$	−9.15213	−	5.28398i	−0.337123	−	0.194638i
$738$	−3.14514	−	0.549263i	−0.115774	−	0.0202187i
$739$	10.5452	−	6.08825i	0.387910	−	0.223960i	−0.293344	−	0.956007i	$-0.594768\pi$
$739$	10.5452	−	6.08825i	0.387910	−	0.223960i	0.681254	+	0.732047i	$0.261435\pi$
$740$	−1.53508	−	9.32198i	−0.0564308	−	0.342683i
$741$	1.81691	−	2.38583i	0.0667460	−	0.0876457i
$742$	6.09190	−	4.21439i	0.223641	−	0.154715i
$743$	16.5647	−	13.8994i	0.607698	−	0.509919i	−0.286211	−	0.958166i	$-0.592396\pi$
$743$	16.5647	−	13.8994i	0.607698	−	0.509919i	0.893910	+	0.448247i	$0.147952\pi$
$744$	3.81925	+	32.3369i	0.140020	+	1.18553i
$745$	−14.4211	+	5.24884i	−0.528347	+	0.192302i
$746$	−18.3900	−	40.0277i	−0.673307	−	1.46552i
$747$	−5.97882	+	6.06676i	−0.218754	+	0.221971i
$748$	0.0199832	+	0.0171572i	0.000730657	+	0.000627330i
$749$	−19.3429	−	3.41067i	−0.706773	−	0.124623i
$750$	−19.9085	+	10.3128i	−0.726955	+	0.376572i
$751$	−4.00293	+	10.9979i	−0.146069	+	0.401321i	−0.991053	−	0.133471i	$-0.957388\pi$
$751$	−4.00293	+	10.9979i	−0.146069	+	0.401321i	0.844984	+	0.534792i	$0.179610\pi$
$752$	2.20737	−	11.0492i	0.0804946	−	0.402922i
$753$	−5.82691	−	25.8368i	−0.212344	−	0.941546i
$754$	35.3856	−	34.9871i	1.28867	−	1.27416i
$755$	12.2124			0.444456
$756$	9.21988	−	4.79518i	0.335324	−	0.174399i
$757$	32.2762			1.17310			0.586549	−	0.809914i	$-0.300486\pi$
$757$	32.2762			1.17310			0.586549	+	0.809914i	$0.300486\pi$
$758$	−0.763332	+	0.754737i	−0.0277255	+	0.0274133i
$759$	−6.62078	−	2.06099i	−0.240319	−	0.0748091i
$760$	0.0952132	−	0.909979i	0.00345374	−	0.0330084i
$761$	15.0556	−	41.3650i	0.545766	−	1.49948i	−0.293609	−	0.955926i	$-0.594856\pi$
$761$	15.0556	−	41.3650i	0.545766	−	1.49948i	0.839375	−	0.543553i	$-0.182921\pi$
$762$	26.7830	+	17.1385i	0.970246	+	0.620863i
$763$	4.07798	+	0.719057i	0.147633	+	0.0260316i
$764$	30.1290	−	35.0915i	1.09003	−	1.26957i
$765$	−0.0455931	+	0.00432448i	−0.00164842	+	0.000156352i
$766$	5.92215	+	12.8901i	0.213976	+	0.465740i
$767$	24.0979	−	8.77092i	0.870124	−	0.316699i
$768$	−21.1938	+	17.8556i	−0.764766	+	0.644308i
$769$	−19.8705	+	16.6733i	−0.716547	+	0.601255i	−0.926428	−	0.376473i	$-0.877137\pi$
$769$	−19.8705	+	16.6733i	−0.716547	+	0.601255i	0.209881	+	0.977727i	$0.432692\pi$
$770$	1.04815	−	0.725115i	0.0377728	−	0.0261313i
$771$	−1.17527	−	0.150365i	−0.0423263	−	0.00541526i
$772$	31.6732	−	5.21574i	1.13994	−	0.187719i
$773$	18.3567	−	10.5982i	0.660244	−	0.381192i	−0.132126	−	0.991233i	$-0.542180\pi$
$773$	18.3567	−	10.5982i	0.660244	−	0.381192i	0.792370	+	0.610041i	$0.208847\pi$
$774$	−37.9072	−	21.8030i	−1.36255	−	0.783693i
$775$	22.7671	+	13.1446i	0.817820	+	0.472168i
$776$	13.5303	−	27.7742i	0.485711	−	0.997036i
$777$	7.11375	+	3.67024i	0.255204	+	0.131669i
$778$	0.943028	−	1.99279i	0.0338092	−	0.0714451i
$779$	−0.0413569	−	0.234547i	−0.00148177	−	0.00840351i
$780$	9.07591	−	17.1127i	0.324970	−	0.612734i
$781$	−4.78797	−	4.01759i	−0.171327	−	0.143761i
$782$	0.00889939	−	0.0954901i	0.000318242	−	0.00341472i
$783$	−33.4026	−	1.09208i	−1.19371	−	0.0390279i
$784$	−3.72682	−	1.45285i	−0.133101	−	0.0518876i
$785$	−13.6835	+	16.3074i	−0.488386	+	0.582035i
$786$	−7.02335	−	54.1900i	−0.250515	−	1.93289i
$787$	−31.0900	+	5.48200i	−1.10824	+	0.195412i	−0.697671	−	0.716418i	$-0.745780\pi$
$787$	−31.0900	+	5.48200i	−1.10824	+	0.195412i	−0.410567	+	0.911831i	$0.634669\pi$
$788$	−17.8834	+	30.1804i	−0.637068	+	1.07513i
$789$	2.34658	+	3.65390i	0.0835406	+	0.130082i
$790$	1.55409	−	5.67130i	0.0552921	−	0.201776i
$791$	−1.97856	+	3.42697i	−0.0703495	+	0.121849i
$792$	6.44279	+	3.80343i	0.228935	+	0.135149i
$793$	−5.47865	−	9.48930i	−0.194553	−	0.336975i
$794$	28.7631	−	7.53277i	1.02077	−	0.267328i
$795$	−8.55418	+	3.57989i	−0.303386	+	0.126966i
$796$	9.85969	+	17.5331i	0.349467	+	0.621443i
$797$	14.6599	+	17.4710i	0.519281	+	0.618855i	0.960411	−	0.278588i	$-0.0898664\pi$
$797$	14.6599	+	17.4710i	0.519281	+	0.618855i	−0.441129	+	0.897444i	$0.645422\pi$
$798$	0.570498	+	0.524881i	0.0201954	+	0.0185806i
$799$	−0.0143893	−	0.0395344i	−0.000509058	−	0.00139863i
$800$	1.31834	+	22.3355i	0.0466102	+	0.789681i
$801$	−11.2078	+	16.2577i	−0.396006	+	0.574436i
$802$	−15.0408	−	10.6591i	−0.531108	−	0.376385i
$803$	−1.13677	+	6.44694i	−0.0401157	+	0.227507i
$804$	5.73508	−	41.1212i	0.202261	−	1.45023i
$805$	−4.36100	−	1.58727i	−0.153705	−	0.0559441i
$806$	−51.2529	+	4.19177i	−1.80531	+	0.147649i
$807$	36.0437	+	39.0477i	1.26880	+	1.37454i
$808$	15.4055	−	10.4016i	0.541964	−	0.365928i
$809$		−	7.37325i		−	0.259230i	−0.991564	−	0.129615i	$-0.958626\pi$
$809$		−	7.37325i		−	0.259230i	0.991564	−	0.129615i	$-0.0413741\pi$
$810$	−12.5355	+	3.47927i	−0.440454	+	0.122249i
$811$			24.5966i			0.863704i	0.901944	+	0.431852i	$0.142140\pi$
$811$			24.5966i			0.863704i	−0.901944	+	0.431852i	$0.857860\pi$
$812$	8.15641	+	9.94705i	0.286234	+	0.349073i
$813$	−7.37941	−	7.99443i	−0.258807	−	0.280377i
$814$	0.469750	+	5.74365i	0.0164647	+	0.201315i
$815$	1.80678	+	0.657616i	0.0632889	+	0.0230353i
$816$	−0.0329852	+	0.0980785i	−0.00115471	+	0.00343343i
$817$	0.566455	−	3.21252i	0.0198177	−	0.112392i
$818$	17.2764	−	24.3783i	0.604056	−	0.852368i
$819$	7.04457	+	14.8236i	0.246157	+	0.517980i
$820$	−0.509747	−	1.45145i	−0.0178011	−	0.0506870i
$821$	−1.24816	−	3.42929i	−0.0435611	−	0.119683i	0.916005	−	0.401168i	$-0.131395\pi$
$821$	−1.24816	−	3.42929i	−0.0435611	−	0.119683i	−0.959566	+	0.281484i	$0.909173\pi$
$822$	−35.9908	+	39.1188i	−1.25532	+	1.36442i
$823$	14.7791	+	17.6130i	0.515166	+	0.613951i	0.959431	−	0.281945i	$-0.0909795\pi$
$823$	14.7791	+	17.6130i	0.515166	+	0.613951i	−0.444265	+	0.895896i	$0.646535\pi$
$824$	7.98172	+	17.9047i	0.278056	+	0.623741i
$825$	5.57219	−	2.33194i	0.193999	−	0.0811878i
$826$	1.67947	+	6.41288i	0.0584361	+	0.223133i
$827$	−15.4297	−	26.7251i	−0.536544	−	0.929321i	−0.999087	−	0.0427245i	$-0.986396\pi$
$827$	−15.4297	−	26.7251i	−0.536544	−	0.929321i	0.462543	−	0.886597i	$-0.346937\pi$
$828$	−2.26513	−	27.1484i	−0.0787188	−	0.943472i
$829$	3.73399	−	6.46746i	0.129687	−	0.224624i	−0.793868	−	0.608090i	$-0.791936\pi$
$829$	3.73399	−	6.46746i	0.129687	−	0.224624i	0.923555	+	0.383465i	$0.125269\pi$
$830$	−3.95819	−	1.08465i	−0.137391	−	0.0376488i
$831$	20.7395	+	32.2938i	0.719447	+	1.12026i
$832$	−26.9774	−	34.4632i	−0.935275	−	1.19480i
$833$	−0.0147087	+	0.00259353i	−0.000509625	+	8.98606e-5i
$834$	−13.0893	+	1.69645i	−0.453245	+	0.0587433i
$835$	−3.77628	+	4.50040i	−0.130684	+	0.155743i
$836$	−0.103131	+	0.548490i	−0.00356686	+	0.0189699i
$837$	25.7172	+	23.0525i	0.888917	+	0.796812i
$838$	10.6331	+	0.990969i	0.367313	+	0.0342325i
$839$	−18.9542	−	15.9045i	−0.654372	−	0.549083i	0.254022	−	0.967198i	$-0.418246\pi$
$839$	−18.9542	−	15.9045i	−0.654372	−	0.549083i	−0.908394	+	0.418115i	$0.862691\pi$
$840$	4.18689	+	2.74652i	0.144461	+	0.0947639i
$841$	−2.14763	−	12.1798i	−0.0740562	−	0.419994i
$842$	−7.88853	−	3.73301i	−0.271857	−	0.128648i
$843$	−38.9495	−	20.0955i	−1.34149	−	0.692125i
$844$	−23.5549	−	8.87661i	−0.810792	−	0.305546i
$845$	14.9857	+	8.65201i	0.515525	+	0.297638i
$846$	−5.99244	−	10.3401i	−0.206024	−	0.355499i
$847$	8.85300	−	5.11128i	0.304193	−	0.175626i
$848$	−0.474488	+	20.9464i	−0.0162940	+	0.719304i
$849$	18.9568	+	2.42534i	0.650594	+	0.0832376i
$850$	0.0475304	+	0.0687052i	0.00163028	+	0.00235657i
$851$	16.0746	−	13.4882i	0.551031	−	0.462370i
$852$	7.56359	−	23.3620i	0.259124	−	0.800368i
$853$	−26.1594	+	9.52125i	−0.895682	+	0.326001i	−0.748521	−	0.663111i	$-0.769236\pi$
$853$	−26.1594	+	9.52125i	−0.895682	+	0.326001i	−0.147161	+	0.989113i	$0.547013\pi$
$854$	2.57384	−	1.18251i	0.0880751	−	0.0404646i
$855$	−0.562414	−	0.790860i	−0.0192342	−	0.0270468i
$856$	39.9441	−	38.6096i	1.36526	−	1.31965i
$857$	9.90846	+	1.74713i	0.338467	+	0.0596808i	0.340298	−	0.940318i	$-0.389472\pi$
$857$	9.90846	+	1.74713i	0.338467	+	0.0596808i	−0.00183176	+	0.999998i	$0.500583\pi$
$858$	−6.36860	+	9.95246i	−0.217421	+	0.339771i
$859$	−17.6714	+	48.5517i	−0.602939	+	1.65656i	0.142346	+	0.989817i	$0.454535\pi$
$859$	−17.6714	+	48.5517i	−0.602939	+	1.65656i	−0.745286	+	0.666745i	$0.767687\pi$
$860$	0.238604	−	21.0692i	0.00813631	−	0.718453i
$861$	1.24453	+	0.387410i	0.0424134	+	0.0132029i
$862$	−8.72189	−	8.82122i	−0.297069	−	0.300452i
$863$	10.1664			0.346068			0.173034	−	0.984916i	$-0.444643\pi$
$863$	10.1664			0.346068			0.173034	+	0.984916i	$0.444643\pi$
$864$	−4.34199	+	29.0714i	−0.147718	+	0.989030i
$865$	−9.64549			−0.327957
$866$	2.13012	+	2.15437i	0.0723843	+	0.0732086i
$867$	−6.47784	−	28.7231i	−0.219999	−	0.975487i
$868$	0.150533	−	13.2924i	0.00510943	−	0.451173i
$869$	−1.22680	+	3.37061i	−0.0416164	+	0.114340i
$870$	−7.40679	−	14.2985i	−0.251114	−	0.484764i
$871$	64.5744	+	11.3862i	2.18802	+	0.385807i
$872$	−8.42125	+	8.13991i	−0.285179	+	0.275652i
$873$	−8.71200	−	31.5894i	−0.294856	−	1.06914i
$874$	1.84662	−	0.848399i	0.0624630	−	0.0286975i
$875$	8.60133	−	3.13063i	0.290778	−	0.105835i
$876$	−25.1516	+	5.37382i	−0.849795	+	0.181565i
$877$	−17.9177	+	15.0347i	−0.605036	+	0.507686i	−0.893060	−	0.449937i	$-0.851446\pi$
$877$	−17.9177	+	15.0347i	−0.605036	+	0.507686i	0.288024	+	0.957623i	$0.407002\pi$
$878$	−13.6646	−	19.7522i	−0.461158	−	0.666604i
$879$	−19.7068	+	25.8775i	−0.664695	+	0.872826i
$880$	−0.0816390	+	3.60398i	−0.00275205	+	0.121490i
$881$	−10.4724	+	6.04623i	−0.352823	+	0.203703i	−0.665928	−	0.746016i	$-0.731964\pi$
$881$	−10.4724	+	6.04623i	−0.352823	+	0.203703i	0.313105	+	0.949719i	$0.398631\pi$
$882$	−3.98440	+	1.45760i	−0.134162	+	0.0490799i
$883$	1.99294	+	1.15062i	0.0670677	+	0.0387215i	0.533159	−	0.846015i	$-0.321005\pi$
$883$	1.99294	+	1.15062i	0.0670677	+	0.0387215i	−0.466091	+	0.884737i	$0.654338\pi$
$884$	−0.152921	−	0.0576279i	−0.00514328	−	0.00193824i
$885$	−0.392239	−	8.28931i	−0.0131850	−	0.278642i
$886$	−6.03098	−	2.85398i	−0.202615	−	0.0958813i
$887$	0.0778886	+	0.441728i	0.00261524	+	0.0148318i	0.986087	−	0.166227i	$-0.0531586\pi$
$887$	0.0778886	+	0.441728i	0.00261524	+	0.0148318i	−0.983472	+	0.181059i	$0.942047\pi$
$888$	−20.2203	+	10.1856i	−0.678550	+	0.341808i
$889$	−9.94412	−	8.34411i	−0.333515	−	0.279852i
$890$	−9.47343	−	0.882895i	−0.317550	−	0.0295947i
$891$	7.79402	−	1.49194i	0.261109	−	0.0499819i
$892$	5.49489	−	29.2239i	0.183983	−	0.978489i
$893$	0.573040	−	0.682923i	0.0191761	−	0.0228531i
$894$	22.3302	+	29.2228i	0.746833	+	0.977357i
$895$	−15.1457	+	2.67060i	−0.506265	+	0.0892682i
$896$	9.51750	−	6.11695i	0.317957	−	0.204353i
$897$	42.9759	−	2.03356i	1.43492	−	0.0678986i
$898$	52.9028	+	14.4968i	1.76539	+	0.483765i
$899$	−21.3748	+	37.0222i	−0.712889	+	1.23476i
$900$	16.7132	+	16.8482i	0.557105	+	0.561607i
$901$	0.0391159	+	0.0677507i	0.00130314	+	0.00225710i
$902$	0.237733	+	0.907761i	0.00791565	+	0.0302251i
$903$	14.2031	+	10.8163i	0.472650	+	0.359944i
$904$	−4.55714	−	10.2227i	−0.151568	−	0.340001i
$905$	−2.96555	−	3.53421i	−0.0985783	−	0.117481i
$906$	−8.74456	−	27.9300i	−0.290518	−	0.927913i
$907$	−11.0631	−	30.3957i	−0.367345	−	1.00927i	−0.976367	−	0.216119i	$-0.930660\pi$
$907$	−11.0631	−	30.3957i	−0.367345	−	1.00927i	0.609022	−	0.793153i	$-0.291562\pi$
$908$	2.89450	+	8.24180i	0.0960574	+	0.273514i
$909$	4.96367	−	19.0808i	0.164635	−	0.632869i
$910$	−4.57244	+	6.45206i	−0.151575	+	0.213884i
$911$	6.92343	−	39.2647i	0.229384	−	1.30090i	−0.624742	−	0.780831i	$-0.714796\pi$
$911$	6.92343	−	39.2647i	0.229384	−	1.30090i	0.854125	−	0.520067i	$-0.174093\pi$
$912$	−2.14931	+	0.433825i	−0.0711708	+	0.0143654i
$913$	2.35246	+	0.856225i	0.0778550	+	0.0283369i
$914$	−2.43432	−	29.7646i	−0.0805203	−	0.984524i
$915$	−3.45893	+	0.780083i	−0.114349	+	0.0257888i
$916$	30.0750	+	36.6776i	0.993705	+	1.21186i
$917$			22.3080i			0.736675i
$918$	0.0425365	+	0.101175i	0.00140391	+	0.00333929i
$919$			49.1239i			1.62045i	0.586121	+	0.810224i	$0.300654\pi$
$919$			49.1239i			1.62045i	−0.586121	+	0.810224i	$0.699346\pi$
$920$	10.8788	−	7.34526i	0.358665	−	0.242166i
$921$	−12.3807	+	39.7722i	−0.407959	+	1.31054i
$922$	53.3991	−	4.36730i	1.75861	−	0.143829i
$923$	36.4419	+	13.2638i	1.19950	+	0.436582i
$924$	−2.40887	−	1.87793i	−0.0792459	−	0.0617795i
$925$	−3.17420	+	18.0018i	−0.104367	+	0.591895i
$926$	12.4085	+	8.79368i	0.407770	+	0.288978i
$927$	18.9079	+	8.64944i	0.621018	+	0.284085i
$928$	−36.3204	+	2.14378i	−1.19228	+	0.0703730i
$929$	−8.24204	−	22.6448i	−0.270413	−	0.742953i	−0.998356	−	0.0573155i	$-0.981746\pi$
$929$	−8.24204	−	22.6448i	−0.270413	−	0.742953i	0.727943	−	0.685637i	$-0.240476\pi$
$930$	−3.63444	+	16.2392i	−0.119178	+	0.532504i
$931$	−0.203431	−	0.242440i	−0.00666719	−	0.00794565i
$932$	1.89495	+	3.36970i	0.0620711	+	0.110378i
$933$	−5.76084	+	45.0274i	−0.188601	+	1.47413i
$934$	15.9975	−	4.18959i	0.523456	−	0.137088i
$935$	0.00673016	+	0.0116570i	0.000220100	+	0.000381224i
$936$	−45.6358	−	8.50339i	−1.49165	−	0.277942i
$937$	6.52740	−	11.3058i	0.213241	−	0.369344i	−0.739486	−	0.673172i	$-0.764931\pi$
$937$	6.52740	−	11.3058i	0.213241	−	0.369344i	0.952727	+	0.303828i	$0.0982648\pi$
$938$	−4.47965	+	16.3475i	−0.146266	+	0.533764i
$939$	4.02853	−	7.80818i	0.131466	−	0.254810i
$940$	2.93546	−	4.95396i	0.0957443	−	0.161580i
$941$	50.7898	−	8.95561i	1.65570	−	0.291944i	0.733797	−	0.679368i	$-0.237746\pi$
$941$	50.7898	−	8.95561i	1.65570	−	0.291944i	0.921902	+	0.387424i	$0.126635\pi$
$942$	47.0931	+	19.6177i	1.53438	+	0.639180i
$943$	2.19632	−	2.61747i	0.0715219	−	0.0852365i
$944$	−17.4696	−	6.81027i	−0.568586	−	0.221656i
$945$	5.25773	−	0.750852i	0.171034	−	0.0244252i
$946$	−1.19266	+	12.7972i	−0.0387768	+	0.416073i
$947$	−24.9458	−	20.9320i	−0.810630	−	0.680199i	0.140128	−	0.990133i	$-0.455249\pi$
$947$	−24.9458	−	20.9320i	−0.810630	−	0.680199i	−0.950758	+	0.309934i	$0.899693\pi$
$948$	−14.0831	+	0.506635i	−0.457399	+	0.0164547i
$949$	−7.05325	−	40.0010i	−0.228958	−	1.29849i
$950$	−0.757225	+	1.60016i	−0.0245676	+	0.0519159i
$951$	4.03593	−	2.59193i	0.130874	−	0.0840491i
$952$	0.0185009	−	0.0379774i	0.000599617	−	0.00123086i
$953$	−2.16048	−	1.24735i	−0.0699848	−	0.0404058i	0.464599	−	0.885521i	$-0.346198\pi$
$953$	−2.16048	−	1.24735i	−0.0699848	−	0.0404058i	−0.534584	+	0.845115i	$0.679532\pi$
$954$	14.3124	+	17.0002i	0.463380	+	0.550402i
$955$	20.4703	−	11.8185i	0.662403	−	0.382439i
$956$	30.3993	−	5.00596i	0.983184	−	0.161904i
$957$	3.79203	+	9.06108i	0.122579	+	0.292903i
$958$	40.4239	−	27.9653i	1.30604	−	0.903519i
$959$	16.6240	−	13.9492i	0.536816	−	0.450442i
$960$	−13.2431	+	5.02070i	−0.427419	+	0.162042i
$961$	12.3829	−	4.50700i	0.399447	−	0.145387i
$962$	−14.9275	−	32.4913i	−0.481284	−	1.04756i
$963$	4.70690	−	58.7355i	0.151678	−	1.89273i
$964$	25.3489	−	29.5241i	0.816433	−	0.950907i
$965$	16.1557	+	2.84868i	0.520069	+	0.0917022i
$966$	−0.507481	+	11.1102i	−0.0163279	+	0.357465i
$967$	−0.263359	+	0.723573i	−0.00846905	+	0.0232685i	−0.943855	−	0.330360i	$-0.892830\pi$
$967$	−0.263359	+	0.723573i	−0.00846905	+	0.0232685i	0.935386	+	0.353628i	$0.115052\pi$
$968$	−3.00889	+	28.7568i	−0.0967093	+	0.924278i
$969$	−0.00601596	+	0.00555315i	−0.000193261	+	0.000178393i
$970$	11.2275	−	11.1011i	0.360494	−	0.356434i
$971$	16.5107			0.529855			0.264927	−	0.964268i	$-0.414652\pi$
$971$	16.5107			0.529855			0.264927	+	0.964268i	$0.414652\pi$
$972$	16.9331	+	26.1777i	0.543128	+	0.839650i
$973$	5.38837			0.172743
$974$	−8.71683	+	8.61867i	−0.279305	+	0.276160i
$975$	−27.5398	+	25.4211i	−0.881979	+	0.814128i
$976$	−1.56950	+	7.85625i	−0.0502385	+	0.251472i
$977$	−15.2249	+	41.8301i	−0.487088	+	1.33826i	0.416217	+	0.909266i	$0.363356\pi$
$977$	−15.2249	+	41.8301i	−0.487088	+	1.33826i	−0.903305	+	0.428999i	$0.858866\pi$
$978$	0.210252	−	4.60302i	0.00672312	−	0.147188i
$979$	5.71550	+	1.00780i	0.182668	+	0.0322093i
$980$	−1.55099	−	1.33166i	−0.0495447	−	0.0425382i
$981$	−0.992335	+	12.3830i	−0.0316828	+	0.395358i
$982$	−13.3387	−	29.0329i	−0.425654	−	0.926478i
$983$	−5.27392	+	1.91955i	−0.168212	+	0.0612242i	−0.424753	−	0.905309i	$-0.639639\pi$
$983$	−5.27392	+	1.91955i	−0.168212	+	0.0612242i	0.256541	+	0.966533i	$0.417417\pi$
$984$	−2.95450	+	2.20509i	−0.0941859	+	0.0702958i
$985$	−13.7340	+	11.5242i	−0.437600	+	0.367190i
$986$	−0.111723	+	0.0772904i	−0.00355799	+	0.00246143i
$987$	1.88354	+	4.50074i	0.0599538	+	0.143260i
$988$	−0.562657	−	3.41681i	−0.0179005	−	0.108703i
$989$	40.5298	−	23.3999i	1.28877	−	0.744074i
$990$	2.46254	+	2.92500i	0.0782648	+	0.0929627i
$991$	1.19076	+	0.687487i	0.0378258	+	0.0218387i	0.518794	−	0.854899i	$-0.326381\pi$
$991$	1.19076	+	0.687487i	0.0378258	+	0.0218387i	−0.480968	+	0.876738i	$0.659715\pi$
$992$	30.1765	+	22.4291i	0.958104	+	0.712124i
$993$	39.9931	−	25.6841i	1.26914	−	0.815061i
$994$	−4.28808	+	9.06150i	−0.136010	+	0.287413i
$995$	1.78511	+	10.1239i	0.0565919	+	0.320948i
$996$	0.353597	+	9.82908i	0.0112041	+	0.311446i
$997$	36.8191	+	30.8949i	1.16607	+	0.978450i	0.999971	−	0.00765857i	$-0.00243782\pi$
$997$	36.8191	+	30.8949i	1.16607	+	0.978450i	0.166101	+	0.986109i	$0.446882\pi$
$998$	−4.31506	+	46.3004i	−0.136591	+	1.46561i
$999$	−8.94637	+	22.2856i	−0.283051	+	0.705085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.26	yes	648
4.3	odd	2	inner	756.2.cf.a.659.87	yes	648
27.5	odd	18	inner	756.2.cf.a.491.87	yes	648
108.59	even	18	inner	756.2.cf.a.491.26	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.26	✓	648	108.59	even	18	inner
756.2.cf.a.491.87	yes	648	27.5	odd	18	inner
756.2.cf.a.659.26	yes	648	1.1	even	1	trivial
756.2.cf.a.659.87	yes	648	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994322 - 1.00565i) q^{2} +(-1.27272 + 1.17481i) q^{3} +(-0.0226481 + 1.99987i) q^{4} +(-0.349585 + 0.960476i) q^{5} +(2.44694 + 0.111769i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(2.03368 - 1.96574i) q^{8} +(0.239643 - 2.99041i) q^{9} +(1.31350 - 0.603464i) q^{10} +(-0.828551 + 0.301568i) q^{11} +(-2.32064 - 2.57189i) q^{12} +(4.19087 - 3.51656i) q^{13} +(0.804587 + 1.16303i) q^{14} +(-0.683453 - 1.63311i) q^{15} +(-3.99897 - 0.0905865i) q^{16} +(-0.0129346 + 0.00746778i) q^{17} +(-3.24558 + 2.73244i) q^{18} +(-0.274082 - 0.158241i) q^{19} +(-1.91291 - 0.720878i) q^{20} +(1.45739 - 0.935956i) q^{21} +(1.12712 + 0.533373i) q^{22} +(-0.788442 - 4.47148i) q^{23} +(-0.278942 + 4.89103i) q^{24} +(3.02992 + 2.54240i) q^{25} +(-7.70349 - 0.717942i) q^{26} +(3.20817 + 4.08750i) q^{27} +(0.369578 - 1.96556i) q^{28} +(-4.13426 + 4.92702i) q^{29} +(-0.962764 + 2.31115i) q^{30} +(6.54564 - 1.15417i) q^{31} +(3.88517 + 4.11162i) q^{32} +(0.700230 - 1.35720i) q^{33} +(0.0203711 + 0.00558223i) q^{34} +(0.511059 - 0.885180i) q^{35} +(5.97502 + 0.546983i) q^{36} +(2.31077 + 4.00238i) q^{37} +(0.113391 + 0.432973i) q^{38} +(-1.20253 + 9.39908i) q^{39} +(1.17710 + 2.64050i) q^{40} +(0.483722 + 0.576477i) q^{41} +(-2.39036 - 0.534977i) q^{42} +(3.52530 + 9.68569i) q^{43} +(-0.584332 - 1.66382i) q^{44} +(2.78845 + 1.27557i) q^{45} +(-3.71276 + 5.23898i) q^{46} +(-0.489145 + 2.77408i) q^{47} +(5.19600 - 4.58274i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-0.455956 - 5.57499i) q^{50} +(0.00768890 - 0.0247001i) q^{51} +(6.93775 + 8.46085i) q^{52} -5.23795i q^{53} +(0.920627 - 7.29057i) q^{54} -0.901226i q^{55} +(-2.34413 + 1.58273i) q^{56} +(0.534734 - 0.120597i) q^{57} +(9.06563 - 0.741441i) q^{58} +(4.40483 + 1.60323i) q^{59} +(3.28150 - 1.32983i) q^{60} +(0.347795 - 1.97244i) q^{61} +(-7.66917 - 5.43498i) q^{62} +(-0.755282 + 2.90337i) q^{63} +(0.271731 - 7.99538i) q^{64} +(1.91251 + 5.25457i) q^{65} +(-2.06112 + 0.645312i) q^{66} +(7.70417 + 9.18147i) q^{67} +(-0.0146417 - 0.0260366i) q^{68} +(6.25660 + 4.76468i) q^{69} +(-1.39833 + 0.366209i) q^{70} +(3.54433 + 6.13896i) q^{71} +(-5.39102 - 6.55263i) q^{72} +(3.71226 - 6.42983i) q^{73} +(1.72732 - 6.30347i) q^{74} +(-6.84308 + 0.323805i) q^{75} +(0.322670 - 0.544545i) q^{76} +(0.868330 - 0.153110i) q^{77} +(10.6478 - 8.13639i) q^{78} +(2.61491 - 3.11633i) q^{79} +(1.48499 - 3.80925i) q^{80} +(-8.88514 - 1.43326i) q^{81} +(0.0987568 - 1.05966i) q^{82} +(-2.17499 - 1.82503i) q^{83} +(1.83879 + 2.93579i) q^{84} +(-0.00265090 - 0.0150340i) q^{85} +(6.23509 - 13.1759i) q^{86} +(-0.526548 - 11.1277i) q^{87} +(-1.09221 + 2.24201i) q^{88} +(-5.70033 - 3.29109i) q^{89} +(-1.48984 - 4.07252i) q^{90} +(-4.73785 + 2.73540i) q^{91} +(8.96024 - 1.47551i) q^{92} +(-6.97485 + 9.15883i) q^{93} +(3.27611 - 2.26642i) q^{94} +(0.247802 - 0.207931i) q^{95} +(-9.77512 - 0.668620i) q^{96} +(10.2642 - 3.73585i) q^{97} +(-0.590406 - 1.28508i) q^{98} +(0.703256 + 2.54998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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