LMFDB - Embedded newform 168.2.bc.a.109.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(37,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.bc (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	168.109
Dual form			168.2.bc.a.37.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31787 + 0.513056i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.47355 - 1.35228i) q^{4} +(-0.0402223 + 0.0232224i) q^{5} +(1.39783 + 0.214614i) q^{6} +(-1.97032 - 1.76574i) q^{7} +(-1.24814 + 2.53814i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.0410933 - 0.0512403i) q^{10} +(-3.11586 - 1.79894i) q^{11} +(-1.95227 + 0.434335i) q^{12} -6.29415i q^{13} +(3.50254 + 1.31613i) q^{14} +0.0464447 q^{15} +(0.342679 - 3.98529i) q^{16} +(0.258110 - 0.447060i) q^{17} +(-1.10325 - 0.884778i) q^{18} +(2.80834 - 1.62140i) q^{19} +(-0.0278663 + 0.0886110i) q^{20} +(0.823477 + 2.51434i) q^{21} +(5.02925 + 0.772156i) q^{22} +(-3.47322 - 6.01578i) q^{23} +(2.34999 - 1.57402i) q^{24} +(-2.49892 + 4.32826i) q^{25} +(3.22925 + 8.29485i) q^{26} -1.00000i q^{27} +(-5.29113 + 0.0625230i) q^{28} +2.29579i q^{29} +(-0.0612079 + 0.0238287i) q^{30} +(-1.05460 + 1.82662i) q^{31} +(1.59308 + 5.42790i) q^{32} +(1.79894 + 3.11586i) q^{33} +(-0.110788 + 0.721591i) q^{34} +(0.120255 + 0.0252667i) q^{35} +(1.90788 + 0.599989i) q^{36} +(1.12720 - 0.650790i) q^{37} +(-2.86915 + 3.57762i) q^{38} +(-3.14708 + 5.45089i) q^{39} +(-0.00873835 - 0.131074i) q^{40} +10.1883 q^{41} +(-2.37523 - 2.89107i) q^{42} +9.12162i q^{43} +(-7.02404 + 1.56269i) q^{44} +(-0.0402223 - 0.0232224i) q^{45} +(7.66367 + 6.14605i) q^{46} +(-2.32465 - 4.02641i) q^{47} +(-2.28942 + 3.28003i) q^{48} +(0.764321 + 6.95815i) q^{49} +(1.07261 - 6.98616i) q^{50} +(-0.447060 + 0.258110i) q^{51} +(-8.51145 - 9.27472i) q^{52} +(-4.91727 - 2.83899i) q^{53} +(0.513056 + 1.31787i) q^{54} +0.167103 q^{55} +(6.94093 - 2.79705i) q^{56} -3.24279 q^{57} +(-1.17787 - 3.02555i) q^{58} +(1.42910 + 0.825090i) q^{59} +(0.0684384 - 0.0628062i) q^{60} +(1.10386 - 0.637312i) q^{61} +(0.452663 - 2.94831i) q^{62} +(0.544016 - 2.58922i) q^{63} +(-4.88428 - 6.33591i) q^{64} +(0.146165 + 0.253165i) q^{65} +(-3.96938 - 3.18333i) q^{66} +(6.72366 + 3.88191i) q^{67} +(-0.224213 - 1.00780i) q^{68} +6.94643i q^{69} +(-0.171444 + 0.0283997i) q^{70} +11.8320 q^{71} +(-2.82216 + 0.188145i) q^{72} +(5.57028 - 9.64802i) q^{73} +(-1.15161 + 1.43597i) q^{74} +(4.32826 - 2.49892i) q^{75} +(1.94564 - 6.18687i) q^{76} +(2.96278 + 9.04630i) q^{77} +(1.35081 - 8.79818i) q^{78} +(-2.75086 - 4.76463i) q^{79} +(0.0787646 + 0.168255i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.4269 + 5.22719i) q^{82} -8.25030i q^{83} +(4.61352 + 2.59142i) q^{84} +0.0239757i q^{85} +(-4.67990 - 12.0211i) q^{86} +(1.14789 - 1.98821i) q^{87} +(8.45501 - 5.66315i) q^{88} +(-7.38218 - 12.7863i) q^{89} +(0.0649220 + 0.00996767i) q^{90} +(-11.1138 + 12.4015i) q^{91} +(-13.2530 - 4.16778i) q^{92} +(1.82662 - 1.05460i) q^{93} +(5.12936 + 4.11360i) q^{94} +(-0.0753053 + 0.130433i) q^{95} +(1.33431 - 5.49724i) q^{96} -6.16464 q^{97} +(-4.57719 - 8.77777i) q^{98} -3.59789i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9} + 6 q^{10} + 22 q^{14} - 10 q^{16} - 2 q^{18} - 40 q^{20} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 16 q^{25} + 6 q^{26} - 26 q^{28} - 8 q^{30} - 24 q^{31} - 8 q^{32}+ \cdots - 64 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 + 16 * q^9 + 6 * q^10 + 22 * q^14 - 10 * q^16 - 2 * q^18 - 40 * q^20 - 12 * q^22 - 8 * q^23 - 6 * q^24 + 16 * q^25 + 6 * q^26 - 26 * q^28 - 8 * q^30 - 24 * q^31 - 8 * q^32 - 24 * q^34 - 4 * q^36 - 26 * q^38 - 6 * q^40 - 4 * q^42 + 20 * q^44 + 16 * q^46 - 24 * q^47 - 16 * q^48 + 8 * q^49 + 52 * q^50 + 44 * q^52 - 64 * q^55 + 40 * q^56 - 16 * q^57 + 34 * q^58 - 22 * q^60 + 100 * q^62 - 20 * q^64 + 12 * q^66 + 16 * q^68 + 38 * q^70 - 80 * q^71 - 8 * q^72 + 8 * q^73 + 10 * q^74 - 32 * q^76 + 12 * q^78 + 8 * q^79 - 56 * q^80 - 16 * q^81 - 16 * q^84 - 22 * q^86 + 24 * q^87 + 50 * q^88 + 12 * q^90 + 64 * q^92 - 48 * q^94 + 24 * q^95 + 10 * q^96 - 48 * q^97 - 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.31787	+	0.513056i	−0.931873	+	0.362786i
$2$	−1.31787	+	0.513056i	−0.931873	+	0.362786i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	1.47355	−	1.35228i	0.736773	−	0.676140i
$5$	−0.0402223	+	0.0232224i	−0.0179880	+	0.0103854i	−0.508967	−	0.860786i	$-0.669972\pi$
$5$	−0.0402223	+	0.0232224i	−0.0179880	+	0.0103854i	0.490979	+	0.871171i	$0.336639\pi$
$6$	1.39783	+	0.214614i	0.570663	+	0.0876157i
$7$	−1.97032	−	1.76574i	−0.744711	−	0.667387i
$7$	−1.97032	−	1.76574i	−0.744711	−	0.667387i
$8$	−1.24814	+	2.53814i	−0.441285	+	0.897367i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.0410933	−	0.0512403i	0.0129948	−	0.0162036i
$11$	−3.11586	−	1.79894i	−0.939468	−	0.542402i	−0.0496743	−	0.998765i	$-0.515818\pi$
$11$	−3.11586	−	1.79894i	−0.939468	−	0.542402i	−0.889793	+	0.456364i	$0.849152\pi$
$12$	−1.95227	+	0.434335i	−0.563571	+	0.125382i
$13$		−	6.29415i		−	1.74568i	−0.488004	−	0.872842i	$-0.662275\pi$
$13$		−	6.29415i		−	1.74568i	0.488004	−	0.872842i	$-0.337725\pi$
$14$	3.50254	+	1.31613i	0.936094	+	0.351749i
$15$	0.0464447			0.0119920
$16$	0.342679	−	3.98529i	0.0856697	−	0.996324i
$17$	0.258110	−	0.447060i	0.0626010	−	0.108428i	−0.833026	−	0.553233i	$-0.813394\pi$
$17$	0.258110	−	0.447060i	0.0626010	−	0.108428i	0.895627	+	0.444805i	$0.146727\pi$
$18$	−1.10325	−	0.884778i	−0.260039	−	0.208544i
$19$	2.80834	−	1.62140i	0.644278	−	0.371974i	−0.141983	−	0.989869i	$-0.545348\pi$
$19$	2.80834	−	1.62140i	0.644278	−	0.371974i	0.786261	+	0.617895i	$0.212014\pi$
$20$	−0.0278663	+	0.0886110i	−0.00623109	+	0.0198140i
$21$	0.823477	+	2.51434i	0.179697	+	0.548673i
$22$	5.02925	+	0.772156i	1.07224	+	0.164624i
$23$	−3.47322	−	6.01578i	−0.724215	−	1.25438i	−0.959296	−	0.282402i	$-0.908869\pi$
$23$	−3.47322	−	6.01578i	−0.724215	−	1.25438i	0.235081	−	0.971976i	$-0.424465\pi$
$24$	2.34999	−	1.57402i	0.479690	−	0.321295i
$25$	−2.49892	+	4.32826i	−0.499784	+	0.865652i
$26$	3.22925	+	8.29485i	0.633309	+	1.62675i
$27$		−	1.00000i		−	0.192450i
$28$	−5.29113	+	0.0625230i	−0.999930	+	0.0118157i
$29$			2.29579i			0.426317i	0.977018	+	0.213159i	$0.0683751\pi$
$29$			2.29579i			0.426317i	−0.977018	+	0.213159i	$0.931625\pi$
$30$	−0.0612079	+	0.0238287i	−0.0111750	+	0.00435051i
$31$	−1.05460	+	1.82662i	−0.189411	+	0.328070i	−0.945054	−	0.326914i	$-0.893991\pi$
$31$	−1.05460	+	1.82662i	−0.189411	+	0.328070i	0.755643	+	0.654984i	$0.227325\pi$
$32$	1.59308	+	5.42790i	0.281619	+	0.959526i
$33$	1.79894	+	3.11586i	0.313156	+	0.542402i
$34$	−0.110788	+	0.721591i	−0.0190000	+	0.123752i
$35$	0.120255	+	0.0252667i	0.0203269	+	0.00427085i
$36$	1.90788	+	0.599989i	0.317980	+	0.0999981i
$37$	1.12720	−	0.650790i	0.185311	−	0.106989i	−0.404475	−	0.914549i	$-0.632546\pi$
$37$	1.12720	−	0.650790i	0.185311	−	0.106989i	0.589785	+	0.807560i	$0.299212\pi$
$38$	−2.86915	+	3.57762i	−0.465438	+	0.580367i
$39$	−3.14708	+	5.45089i	−0.503935	+	0.872842i
$40$	−0.00873835	−	0.131074i	−0.00138165	−	0.0207247i
$41$	10.1883			1.59115			0.795576	−	0.605854i	$-0.207168\pi$
$41$	10.1883			1.59115			0.795576	+	0.605854i	$0.207168\pi$
$42$	−2.37523	−	2.89107i	−0.366506	−	0.446102i
$43$			9.12162i			1.39103i	0.718510	+	0.695517i	$0.244824\pi$
$43$			9.12162i			1.39103i	−0.718510	+	0.695517i	$0.755176\pi$
$44$	−7.02404	+	1.56269i	−1.05891	+	0.235584i
$45$	−0.0402223	−	0.0232224i	−0.00599599	−	0.00346178i
$46$	7.66367	+	6.14605i	1.12995	+	0.906186i
$47$	−2.32465	−	4.02641i	−0.339085	−	0.587313i	0.645176	−	0.764034i	$-0.276784\pi$
$47$	−2.32465	−	4.02641i	−0.339085	−	0.587313i	−0.984261	+	0.176722i	$0.943451\pi$
$48$	−2.28942	+	3.28003i	−0.330449	+	0.473431i
$49$	0.764321	+	6.95815i	0.109189	+	0.994021i
$50$	1.07261	−	6.98616i	0.151689	−	0.987992i
$51$	−0.447060	+	0.258110i	−0.0626010	+	0.0361427i
$52$	−8.51145	−	9.27472i	−1.18033	−	1.28617i
$53$	−4.91727	−	2.83899i	−0.675439	−	0.389965i	0.122696	−	0.992444i	$-0.460846\pi$
$53$	−4.91727	−	2.83899i	−0.675439	−	0.389965i	−0.798134	+	0.602480i	$0.794179\pi$
$54$	0.513056	+	1.31787i	0.0698181	+	0.179339i
$55$	0.167103			0.0225321
$56$	6.94093	−	2.79705i	0.927521	−	0.373771i
$57$	−3.24279			−0.429519
$58$	−1.17787	−	3.02555i	−0.154662	−	0.397274i
$59$	1.42910	+	0.825090i	0.186053	+	0.107418i	0.590133	−	0.807306i	$-0.299075\pi$
$59$	1.42910	+	0.825090i	0.186053	+	0.107418i	−0.404081	+	0.914723i	$0.632409\pi$
$60$	0.0684384	−	0.0628062i	0.00883536	−	0.00810825i
$61$	1.10386	−	0.637312i	0.141334	−	0.0815995i	−0.427665	−	0.903937i	$-0.640664\pi$
$61$	1.10386	−	0.637312i	0.141334	−	0.0815995i	0.569000	+	0.822338i	$0.307331\pi$
$62$	0.452663	−	2.94831i	0.0574882	−	0.374436i
$63$	0.544016	−	2.58922i	0.0685396	−	0.326211i
$64$	−4.88428	−	6.33591i	−0.610535	−	0.791989i
$65$	0.146165	+	0.253165i	0.0181295	+	0.0314013i
$66$	−3.96938	−	3.18333i	−0.488597	−	0.391841i
$67$	6.72366	+	3.88191i	0.821426	+	0.474251i	0.850908	−	0.525315i	$-0.176052\pi$
$67$	6.72366	+	3.88191i	0.821426	+	0.474251i	−0.0294820	+	0.999565i	$0.509386\pi$
$68$	−0.224213	−	1.00780i	−0.0271898	−	0.122214i
$69$			6.94643i			0.836252i
$70$	−0.171444	+	0.0283997i	−0.0204915	+	0.00339441i
$71$	11.8320			1.40420			0.702099	−	0.712080i	$-0.252247\pi$
$71$	11.8320			1.40420			0.702099	+	0.712080i	$0.252247\pi$
$72$	−2.82216	+	0.188145i	−0.332595	+	0.0221731i
$73$	5.57028	−	9.64802i	0.651953	−	1.12921i	−0.330696	−	0.943737i	$-0.607283\pi$
$73$	5.57028	−	9.64802i	0.651953	−	1.12921i	0.982649	−	0.185478i	$-0.0593832\pi$
$74$	−1.15161	+	1.43597i	−0.133872	+	0.166928i
$75$	4.32826	−	2.49892i	0.499784	−	0.288551i
$76$	1.94564	−	6.18687i	0.223180	−	0.709683i
$77$	2.96278	+	9.04630i	0.337640	+	1.03092i
$78$	1.35081	−	8.79818i	0.152949	−	0.996198i
$79$	−2.75086	−	4.76463i	−0.309496	−	0.536063i	0.668756	−	0.743482i	$-0.266827\pi$
$79$	−2.75086	−	4.76463i	−0.309496	−	0.536063i	−0.978252	+	0.207419i	$0.933494\pi$
$80$	0.0787646	+	0.168255i	0.00880615	+	0.0188115i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−13.4269	+	5.22719i	−1.48275	+	0.577247i
$83$		−	8.25030i		−	0.905588i	−0.891615	−	0.452794i	$-0.850427\pi$
$83$		−	8.25030i		−	0.905588i	0.891615	−	0.452794i	$-0.149573\pi$
$84$	4.61352	+	2.59142i	0.503376	+	0.282747i
$85$			0.0239757i			0.00260053i
$86$	−4.67990	−	12.0211i	−0.504647	−	1.29627i
$87$	1.14789	−	1.98821i	0.123067	−	0.213159i
$88$	8.45501	−	5.66315i	0.901307	−	0.603693i
$89$	−7.38218	−	12.7863i	−0.782510	−	1.35535i	−0.930475	−	0.366354i	$-0.880606\pi$
$89$	−7.38218	−	12.7863i	−0.782510	−	1.35535i	0.147966	−	0.988993i	$-0.452727\pi$
$90$	0.0649220	+	0.00996767i	0.00684338	+	0.00105068i
$91$	−11.1138	+	12.4015i	−1.16505	+	1.30003i
$92$	−13.2530	−	4.16778i	−1.38172	−	0.434521i
$93$	1.82662	−	1.05460i	0.189411	−	0.109357i
$94$	5.12936	+	4.11360i	0.529053	+	0.424285i
$95$	−0.0753053	+	0.130433i	−0.00772616	+	0.0133821i
$96$	1.33431	−	5.49724i	0.136182	−	0.561059i
$97$	−6.16464			−0.625925			−0.312962	−	0.949766i	$-0.601321\pi$
$97$	−6.16464			−0.625925			−0.312962	+	0.949766i	$0.601321\pi$
$98$	−4.57719	−	8.77777i	−0.462366	−	0.886689i
$99$		−	3.59789i		−	0.361601i
$100$	2.17074	+	9.75713i	0.217074	+	0.975713i
$101$	6.93470	+	4.00375i	0.690029	+	0.398388i	0.803623	−	0.595139i	$-0.202903\pi$
$101$	6.93470	+	4.00375i	0.690029	+	0.398388i	−0.113594	+	0.993527i	$0.536236\pi$
$102$	0.456741	−	0.569522i	0.0452241	−	0.0563911i
$103$	6.43821	+	11.1513i	0.634376	+	1.09877i	0.986647	+	0.162873i	$0.0520761\pi$
$103$	6.43821	+	11.1513i	0.634376	+	1.09877i	−0.352271	+	0.935898i	$0.614591\pi$
$104$	15.9754	+	7.85600i	1.56652	+	0.770344i
$105$	−0.0915109	−	0.0820093i	−0.00893055	−	0.00800329i
$106$	7.93686	+	1.21857i	0.770896	+	0.118358i
$107$	−8.84815	+	5.10848i	−0.855383	+	0.493856i	−0.862463	−	0.506119i	$-0.831080\pi$
$107$	−8.84815	+	5.10848i	−0.855383	+	0.493856i	0.00708048	+	0.999975i	$0.497746\pi$
$108$	−1.35228	−	1.47355i	−0.130123	−	0.141792i
$109$	−10.1275	−	5.84714i	−0.970043	−	0.560054i	−0.0707935	−	0.997491i	$-0.522553\pi$
$109$	−10.1275	−	5.84714i	−0.970043	−	0.560054i	−0.899249	+	0.437437i	$0.855886\pi$
$110$	−0.220219	+	0.0857331i	−0.0209971	+	0.00817433i
$111$	−1.30158			−0.123540
$112$	−7.71218	+	7.24722i	−0.728733	+	0.684798i
$113$	−9.08476			−0.854623			−0.427311	−	0.904105i	$-0.640539\pi$
$113$	−9.08476			−0.854623			−0.427311	+	0.904105i	$0.640539\pi$
$114$	4.27357	−	1.66374i	0.400257	−	0.155823i
$115$	0.279401	+	0.161312i	0.0260543	+	0.0150425i
$116$	3.10455	+	3.38295i	0.288250	+	0.314099i
$117$	5.45089	−	3.14708i	0.503935	−	0.290947i
$118$	−2.30668	−	0.354151i	−0.212347	−	0.0326023i
$119$	−1.29795	+	0.425096i	−0.118983	+	0.0389685i
$120$	−0.0579696	+	0.117883i	−0.00529188	+	0.0107612i
$121$	0.972397	+	1.68424i	0.0883997	+	0.153113i
$122$	−1.12776	+	1.40623i	−0.102103	+	0.127314i
$123$	−8.82337	−	5.09417i	−0.795576	−	0.459326i
$124$	0.916099	+	4.11772i	0.0822681	+	0.369782i
$125$		−	0.464347i		−	0.0415324i
$126$	0.611473	+	3.69135i	0.0544744	+	0.328852i
$127$	14.1059			1.25170			0.625849	−	0.779944i	$-0.284753\pi$
$127$	14.1059			1.25170			0.625849	+	0.779944i	$0.284753\pi$
$128$	9.68751	+	5.84398i	0.856263	+	0.516540i
$129$	4.56081	−	7.89955i	0.401557	−	0.695517i
$130$	−0.322514	−	0.258647i	−0.0282863	−	0.0226849i
$131$	14.8183	−	8.55535i	1.29468	−	0.747484i	0.315200	−	0.949025i	$-0.397928\pi$
$131$	14.8183	−	8.55535i	1.29468	−	0.747484i	0.979480	+	0.201541i	$0.0645949\pi$
$132$	6.86434	+	2.15869i	0.597464	+	0.187890i
$133$	−8.39630	−	1.76413i	−0.728052	−	0.152970i
$134$	−10.8525	−	1.66622i	−0.937516	−	0.143940i
$135$	0.0232224	+	0.0402223i	0.00199866	+	0.00346178i
$136$	0.812542	+	1.21311i	0.0696749	+	0.104024i
$137$	2.48594	−	4.30578i	0.212388	−	0.367867i	−0.740073	−	0.672526i	$-0.765209\pi$
$137$	2.48594	−	4.30578i	0.212388	−	0.367867i	0.952462	+	0.304659i	$0.0985425\pi$
$138$	−3.56391	−	9.15447i	−0.303380	−	0.779280i
$139$			5.20468i			0.441455i	0.975335	+	0.220728i	$0.0708432\pi$
$139$			5.20468i			0.441455i	−0.975335	+	0.220728i	$0.929157\pi$
$140$	0.211370	−	0.125387i	0.0178640	−	0.0105972i
$141$			4.64930i			0.391542i
$142$	−15.5930	+	6.07047i	−1.30853	+	0.509422i
$143$	−11.3228	+	19.6117i	−0.946862	+	1.64001i
$144$	3.62271	−	1.69588i	0.301892	−	0.141323i
$145$	−0.0533136	−	0.0923419i	−0.00442746	−	0.00766858i
$146$	−2.39092	+	15.5727i	−0.197874	+	1.28880i
$147$	2.81715	−	6.40809i	0.232355	−	0.528531i
$148$	0.780933	−	2.48326i	0.0641923	−	0.204123i
$149$	0.725874	−	0.419084i	0.0594659	−	0.0343327i	−0.469972	−	0.882681i	$-0.655736\pi$
$149$	0.725874	−	0.419084i	0.0594659	−	0.0343327i	0.529438	+	0.848349i	$0.322403\pi$
$150$	−4.42198	+	5.51389i	−0.361053	+	0.450207i
$151$	−3.21803	+	5.57379i	−0.261879	+	0.453588i	−0.966741	−	0.255756i	$-0.917676\pi$
$151$	−3.21803	+	5.57379i	−0.261879	+	0.453588i	0.704862	+	0.709345i	$0.251009\pi$
$152$	0.610117	+	9.15169i	0.0494870	+	0.742300i
$153$	0.516221			0.0417340
$154$	−8.54581	−	10.4017i	−0.688641	−	0.838197i
$155$		−	0.0979610i		−	0.00786842i
$156$	2.73377	+	12.2879i	0.218877	+	0.983817i
$157$	4.73349	+	2.73288i	0.377774	+	0.218108i	0.676849	−	0.736122i	$-0.263345\pi$
$157$	4.73349	+	2.73288i	0.377774	+	0.218108i	−0.299075	+	0.954229i	$0.596678\pi$
$158$	6.06979	+	4.86780i	0.482887	+	0.387262i
$159$	2.83899	+	4.91727i	0.225146	+	0.389965i
$160$	−0.190126	−	0.181328i	−0.0150308	−	0.0143352i
$161$	−3.77897	+	17.9858i	−0.297825	+	1.41748i
$162$	0.214614	−	1.39783i	0.0168616	−	0.109824i
$163$	13.2105	−	7.62708i	1.03473	−	0.597399i	0.116390	−	0.993204i	$-0.462868\pi$
$163$	13.2105	−	7.62708i	1.03473	−	0.597399i	0.918335	+	0.395805i	$0.129534\pi$
$164$	15.0130	−	13.7775i	1.17232	−	1.07584i
$165$	−0.144715	−	0.0835514i	−0.0112661	−	0.00650447i
$166$	4.23287	+	10.8728i	0.328534	+	0.843893i
$167$	−1.77463			−0.137325			−0.0686625	−	0.997640i	$-0.521873\pi$
$167$	−1.77463			−0.137325			−0.0686625	+	0.997640i	$0.521873\pi$
$168$	−7.40955	−	1.04815i	−0.571659	−	0.0808668i
$169$	−26.6163			−2.04741
$170$	−0.0123009	−	0.0315968i	−0.000943435	−	0.00242336i
$171$	2.80834	+	1.62140i	0.214759	+	0.123991i
$172$	12.3350	+	13.4411i	0.940533	+	1.02488i
$173$	2.23631	−	1.29114i	0.170024	−	0.0981633i	−0.412573	−	0.910924i	$-0.635370\pi$
$173$	2.23631	−	1.29114i	0.170024	−	0.0981633i	0.582597	+	0.812761i	$0.302037\pi$
$174$	−0.492708	+	3.20913i	−0.0373521	+	0.243284i
$175$	12.5663	−	4.11561i	0.949920	−	0.311111i
$176$	−8.23706	+	11.8012i	−0.620892	+	0.889546i
$177$	−0.825090	−	1.42910i	−0.0620175	−	0.107418i
$178$	16.2888	+	13.0632i	1.22090	+	0.979127i
$179$	−17.0438	−	9.84027i	−1.27392	−	0.735496i	−0.298194	−	0.954505i	$-0.596384\pi$
$179$	−17.0438	−	9.84027i	−1.27392	−	0.735496i	−0.975723	+	0.219009i	$0.929718\pi$
$180$	−0.0906725	+	0.0201726i	−0.00675833	+	0.00150358i
$181$		−	25.5613i		−	1.89996i	−0.312315	−	0.949979i	$-0.601104\pi$
$181$		−	25.5613i		−	1.89996i	0.312315	−	0.949979i	$-0.398896\pi$
$182$	8.28390	−	22.0455i	0.614043	−	1.63412i
$183$	−1.27462			−0.0942230
$184$	19.6040	−	1.30694i	1.44522	−	0.0963488i
$185$	−0.0302257	+	0.0523525i	−0.00222224	+	0.00384903i
$186$	−1.86617	+	2.32698i	−0.136834	+	0.170622i
$187$	−1.60847	+	0.928652i	−0.117623	+	0.0679098i
$188$	−8.87032	−	2.78953i	−0.646934	−	0.203447i
$189$	−1.76574	+	1.97032i	−0.128439	+	0.143320i
$190$	0.0323231	−	0.210529i	0.00234496	−	0.0152734i
$191$	6.98804	+	12.1036i	0.505637	+	0.875788i	0.999979	+	0.00652098i	$0.00207571\pi$
$191$	6.98804	+	12.1036i	0.505637	+	0.875788i	−0.494342	+	0.869267i	$0.664591\pi$
$192$	1.06195	+	7.92920i	0.0766399	+	0.572241i
$193$	9.00706	−	15.6007i	0.648342	−	1.12296i	−0.335176	−	0.942155i	$-0.608796\pi$
$193$	9.00706	−	15.6007i	0.648342	−	1.12296i	0.983519	−	0.180806i	$-0.0578707\pi$
$194$	8.12418	−	3.16281i	0.583282	−	0.227076i
$195$		−	0.292330i		−	0.0209342i
$196$	10.5356	+	9.21958i	0.752545	+	0.658541i
$197$		−	3.70082i		−	0.263672i	−0.991272	−	0.131836i	$-0.957913\pi$
$197$		−	3.70082i		−	0.263672i	0.991272	−	0.131836i	$-0.0420873\pi$
$198$	1.84592	+	4.74154i	0.131184	+	0.336966i
$199$	0.882192	−	1.52800i	0.0625369	−	0.108317i	−0.833062	−	0.553180i	$-0.813414\pi$
$199$	0.882192	−	1.52800i	0.0625369	−	0.108317i	0.895599	+	0.444863i	$0.146748\pi$
$200$	−7.86670	−	11.7449i	−0.556260	−	0.830489i
$201$	−3.88191	−	6.72366i	−0.273809	−	0.474251i
$202$	−11.1932	−	1.71852i	−0.787549	−	0.120915i
$203$	4.05377	−	4.52344i	0.284519	−	0.317483i
$204$	−0.309727	+	0.984888i	−0.0216852	+	0.0689560i
$205$	−0.409799	+	0.236597i	−0.0286216	+	0.0165247i
$206$	−14.2060	−	11.3928i	−0.989776	−	0.793772i
$207$	3.47322	−	6.01578i	0.241405	−	0.418126i
$208$	−25.0840	−	2.15687i	−1.73927	−	0.149552i
$209$	−11.6672			−0.807038
$210$	0.162675	+	0.0611271i	0.0112256	+	0.00421817i
$211$		−	10.6757i		−	0.734945i	−0.930034	−	0.367473i	$-0.880223\pi$
$211$		−	10.6757i		−	0.734945i	0.930034	−	0.367473i	$-0.119777\pi$
$212$	−11.0849	+	2.46614i	−0.761316	+	0.169375i
$213$	−10.2468	−	5.91599i	−0.702099	−	0.405357i
$214$	9.03975	−	11.2719i	0.617944	−	0.770531i
$215$	−0.211825	−	0.366892i	−0.0144464	−	0.0250218i
$216$	2.53814	+	1.24814i	0.172698	+	0.0849254i
$217$	5.30323	−	1.73688i	0.360007	−	0.117907i
$218$	16.3467	+	2.50975i	1.10714	+	0.169982i
$219$	−9.64802	+	5.57028i	−0.651953	+	0.376405i
$220$	0.246234	−	0.225970i	0.0166011	−	0.0152349i
$221$	−2.81386	−	1.62459i	−0.189281	−	0.109281i
$222$	1.71531	−	0.667784i	0.115124	−	0.0448187i
$223$	−22.2212			−1.48804			−0.744020	−	0.668158i	$-0.767083\pi$
$223$	−22.2212			−1.48804			−0.744020	+	0.668158i	$0.767083\pi$
$224$	6.44540	−	13.5077i	0.430651	−	0.902518i
$225$	−4.99784			−0.333190
$226$	11.9725	−	4.66099i	0.796400	−	0.310045i
$227$	17.0728	+	9.85697i	1.13316	+	0.654230i	0.944728	−	0.327856i	$-0.106326\pi$
$227$	17.0728	+	9.85697i	1.13316	+	0.654230i	0.188432	+	0.982086i	$0.439660\pi$
$228$	−4.77841	+	4.38517i	−0.316458	+	0.290415i
$229$	−6.06806	+	3.50340i	−0.400989	+	0.231511i	−0.686911	−	0.726742i	$-0.741034\pi$
$229$	−6.06806	+	3.50340i	−0.400989	+	0.231511i	0.285922	+	0.958253i	$0.407700\pi$
$230$	−0.450976	−	0.0692397i	−0.0297365	−	0.00456553i
$231$	1.95731	−	9.31571i	0.128781	−	0.612929i
$232$	−5.82703	−	2.86547i	−0.382563	−	0.188128i
$233$	12.3717	+	21.4284i	0.810495	+	1.40382i	0.912518	+	0.409036i	$0.134135\pi$
$233$	12.3717	+	21.4284i	0.810495	+	1.40382i	−0.102023	+	0.994782i	$0.532532\pi$
$234$	−5.56893	+	6.94404i	−0.364052	+	0.453946i
$235$	0.187006	+	0.107968i	0.0121989	+	0.00704303i
$236$	3.22159	−	0.716731i	0.209708	−	0.0466552i
$237$			5.50172i			0.357375i
$238$	1.49243	−	1.22614i	0.0967399	−	0.0794790i
$239$	21.9503			1.41985			0.709924	−	0.704278i	$-0.248729\pi$
$239$	21.9503			1.41985			0.709924	+	0.704278i	$0.248729\pi$
$240$	0.0159156	−	0.185096i	0.00102735	−	0.0119479i
$241$	7.39162	−	12.8027i	0.476136	−	0.824692i	−0.523490	−	0.852032i	$-0.675370\pi$
$241$	7.39162	−	12.8027i	0.476136	−	0.824692i	0.999626	+	0.0273397i	$0.00870359\pi$
$242$	−2.14560	−	1.72071i	−0.137924	−	0.110612i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	0.764761	−	2.43183i	0.0489588	−	0.155682i
$245$	−0.192327	−	0.262123i	−0.0122873	−	0.0167464i
$246$	14.2416	+	2.18656i	0.908013	+	0.139410i
$247$	−10.2053	−	17.6761i	−0.649349	−	1.12471i
$248$	−3.31992	−	4.95660i	−0.210815	−	0.314744i
$249$	−4.12515	+	7.14497i	−0.261421	+	0.452794i
$250$	0.238236	+	0.611947i	0.0150674	+	0.0387029i
$251$			14.4785i			0.913876i	0.889499	+	0.456938i	$0.151054\pi$
$251$			14.4785i			0.913876i	−0.889499	+	0.456938i	$0.848946\pi$
$252$	−2.69971	−	4.55099i	−0.170066	−	0.286686i
$253$			24.9925i			1.57126i
$254$	−18.5897	+	7.23713i	−1.16642	+	0.454098i
$255$	0.0119879	−	0.0207636i	0.000750709	−	0.00130027i
$256$	−15.7651	−	2.73135i	−0.985321	−	0.170710i
$257$	−7.93731	−	13.7478i	−0.495116	−	0.857566i	0.504868	−	0.863196i	$-0.331541\pi$
$257$	−7.93731	−	13.7478i	−0.495116	−	0.857566i	−0.999984	+	0.00563049i	$0.998208\pi$
$258$	−1.95762	+	12.7505i	−0.121876	+	0.793812i
$259$	−3.37007	−	0.708080i	−0.209406	−	0.0439980i
$260$	0.557731	+	0.175395i	0.0345890	+	0.0108775i
$261$	−1.98821	+	1.14789i	−0.123067	+	0.0710529i
$262$	−15.1392	+	18.8774i	−0.935301	+	1.16625i
$263$	−0.162710	+	0.281822i	−0.0100331	+	0.0173779i	−0.870998	−	0.491286i	$-0.836527\pi$
$263$	−0.162710	+	0.281822i	−0.0100331	+	0.0173779i	0.860965	+	0.508664i	$0.169860\pi$
$264$	−10.1538	+	0.676926i	−0.624925	+	0.0416619i
$265$	0.263712			0.0161997
$266$	11.9703	−	1.98288i	0.733947	−	0.121578i
$267$			14.7644i			0.903565i
$268$	15.1571	−	3.37210i	0.925864	−	0.205984i
$269$	−20.3761	−	11.7642i	−1.24235	−	0.717273i	−0.272780	−	0.962076i	$-0.587943\pi$
$269$	−20.3761	−	11.7642i	−1.24235	−	0.717273i	−0.969573	+	0.244803i	$0.921277\pi$
$270$	−0.0512403	−	0.0410933i	−0.00311838	−	0.00250086i
$271$	−0.751567	−	1.30175i	−0.0456544	−	0.0790758i	0.842295	−	0.539017i	$-0.181204\pi$
$271$	−0.751567	−	1.30175i	−0.0456544	−	0.0790758i	−0.887950	+	0.459941i	$0.847871\pi$
$272$	−1.69322	−	1.18184i	−0.102666	−	0.0716598i
$273$	15.8256	−	5.18309i	0.957809	−	0.313695i
$274$	−1.06703	+	6.94987i	−0.0644619	+	0.419857i
$275$	15.5726	−	8.99084i	0.939062	−	0.542168i
$276$	9.39352	+	10.2359i	0.565423	+	0.616128i
$277$	12.6685	+	7.31418i	0.761178	+	0.439466i	0.829719	−	0.558182i	$-0.188501\pi$
$277$	12.6685	+	7.31418i	0.761178	+	0.439466i	−0.0685405	+	0.997648i	$0.521834\pi$
$278$	−2.67030	−	6.85908i	−0.160154	−	0.411380i
$279$	−2.10920			−0.126274
$280$	−0.214226	+	0.273688i	−0.0128025	+	0.0163560i
$281$	21.3285			1.27235			0.636175	−	0.771545i	$-0.280516\pi$
$281$	21.3285			1.27235			0.636175	+	0.771545i	$0.280516\pi$
$282$	−2.38535	−	6.12716i	−0.142046	−	0.364867i
$283$	−15.0068	−	8.66416i	−0.892059	−	0.515031i	−0.0174438	−	0.999848i	$-0.505553\pi$
$283$	−15.0068	−	8.66416i	−0.892059	−	0.515031i	−0.874616	+	0.484817i	$0.838886\pi$
$284$	17.4350	−	16.0001i	1.03457	−	0.949434i
$285$	0.130433	−	0.0753053i	0.00772616	−	0.00446070i
$286$	4.86007	−	31.6549i	0.287382	−	1.87179i
$287$	−20.0743	−	17.9900i	−1.18495	−	1.06191i
$288$	−3.90416	+	4.09359i	−0.230055	+	0.241217i
$289$	8.36676	+	14.4917i	0.492162	+	0.852450i
$290$	0.117637	+	0.0943415i	0.00690787	+	0.00553992i
$291$	5.33874	+	3.08232i	0.312962	+	0.180689i
$292$	−4.83874	−	21.7494i	−0.283166	−	1.27279i
$293$			29.6927i			1.73466i	0.497730	+	0.867332i	$0.334167\pi$
$293$			29.6927i			1.73466i	−0.497730	+	0.867332i	$0.665833\pi$
$294$	−0.424920	+	9.89037i	−0.0247818	+	0.576818i
$295$	−0.0766421			−0.00446228
$296$	0.244886	+	3.67327i	0.0142337	+	0.213504i
$297$	−1.79894	+	3.11586i	−0.104385	+	0.180801i
$298$	−0.741592	+	0.924710i	−0.0429593	+	0.0535670i
$299$	−37.8643	+	21.8609i	−2.18975	+	1.26425i
$300$	2.99865	−	9.53529i	0.173127	−	0.550520i
$301$	16.1064	−	17.9725i	0.928358	−	1.03592i
$302$	1.38127	−	8.99654i	0.0794829	−	0.517693i
$303$	−4.00375	−	6.93470i	−0.230010	−	0.398388i
$304$	−5.49939	−	11.7477i	−0.315411	−	0.673776i
$305$	−0.0295998	+	0.0512683i	−0.00169488	+	0.00293562i
$306$	−0.680310	+	0.264850i	−0.0388907	+	0.0151405i
$307$		−	4.88243i		−	0.278655i	−0.990246	−	0.139327i	$-0.955506\pi$
$307$		−	4.88243i		−	0.278655i	0.990246	−	0.139327i	$-0.0444940\pi$
$308$	16.5989	+	9.32364i	0.945811	+	0.531264i
$309$		−	12.8764i		−	0.732514i
$310$	0.0502595	+	0.129100i	0.00285455	+	0.00733236i
$311$	−9.08277	+	15.7318i	−0.515036	+	0.892069i	0.484811	+	0.874619i	$0.338888\pi$
$311$	−9.08277	+	15.7318i	−0.515036	+	0.892069i	−0.999848	+	0.0174504i	$0.994445\pi$
$312$	−9.90712	−	14.7912i	−0.560880	−	0.837387i
$313$	6.80533	+	11.7872i	0.384660	+	0.666251i	0.991722	−	0.128404i	$-0.0409853\pi$
$313$	6.80533	+	11.7872i	0.384660	+	0.666251i	−0.607062	+	0.794655i	$0.707652\pi$
$314$	−7.64023	−	1.17303i	−0.431163	−	0.0661978i
$315$	0.0382461	+	0.116778i	0.00215493	+	0.00657967i
$316$	−10.4966	−	3.30097i	−0.590482	−	0.185694i
$317$	21.6407	−	12.4943i	1.21546	−	0.701749i	0.251520	−	0.967852i	$-0.419070\pi$
$317$	21.6407	−	12.4943i	1.21546	−	0.701749i	0.963944	+	0.266103i	$0.0857363\pi$
$318$	−6.26424	−	5.02375i	−0.351281	−	0.281718i
$319$	4.13000	−	7.15336i	0.231235	−	0.400511i
$320$	0.343592	+	0.141421i	0.0192074	+	0.00790565i
$321$	10.2170			0.570255
$322$	−4.24756	−	25.6417i	−0.236707	−	1.42896i
$323$		−	1.67400i		−	0.0931437i
$324$	0.434335	+	1.95227i	0.0241297	+	0.108459i
$325$	27.2427	+	15.7286i	1.51115	+	0.872465i
$326$	−13.4965	+	16.8292i	−0.747504	+	0.932083i
$327$	5.84714	+	10.1275i	0.323348	+	0.560054i
$328$	−12.7165	+	25.8594i	−0.702152	+	1.42785i
$329$	−2.52929	+	12.0380i	−0.139445	+	0.663679i
$330$	0.233582	+	0.0358626i	0.0128583	+	0.00197417i
$331$	6.34783	−	3.66492i	0.348908	−	0.201442i	−0.315296	−	0.948993i	$-0.602104\pi$
$331$	6.34783	−	3.66492i	0.348908	−	0.201442i	0.664204	+	0.747551i	$0.268771\pi$
$332$	−11.1567	−	12.1572i	−0.612304	−	0.667213i
$333$	1.12720	+	0.650790i	0.0617702	+	0.0356631i
$334$	2.33873	−	0.910486i	0.127969	−	0.0498196i
$335$	−0.360588			−0.0197010
$336$	10.3026	−	2.42019i	0.562051	−	0.132032i
$337$	1.49107			0.0812237			0.0406118	−	0.999175i	$-0.487069\pi$
$337$	1.49107			0.0812237			0.0406118	+	0.999175i	$0.487069\pi$
$338$	35.0768	−	13.6557i	1.90793	−	0.742771i
$339$	7.86764	+	4.54238i	0.427311	+	0.246708i
$340$	0.0324219	+	0.0353293i	0.00175832	+	0.00191600i
$341$	6.57197	−	3.79433i	0.355892	−	0.205474i
$342$	−4.53289	−	0.695948i	−0.245111	−	0.0376326i
$343$	10.7803	−	15.0594i	0.582083	−	0.813129i
$344$	−23.1519	−	11.3851i	−1.24827	−	0.613842i
$345$	−0.161312	−	0.279401i	−0.00868477	−	0.0150425i
$346$	−2.28474	+	2.84890i	−0.122828	+	0.153158i
$347$	20.6494	+	11.9219i	1.10852	+	0.640003i	0.938445	−	0.345428i	$-0.112266\pi$
$347$	20.6494	+	11.9219i	1.10852	+	0.640003i	0.170073	+	0.985431i	$0.445600\pi$
$348$	−0.997143	−	4.48200i	−0.0534525	−	0.240260i
$349$			11.5733i			0.619504i	0.950817	+	0.309752i	$0.100246\pi$
$349$			11.5733i			0.619504i	−0.950817	+	0.309752i	$0.899754\pi$
$350$	−14.4491	+	11.8710i	−0.772338	+	0.634533i
$351$	−6.29415			−0.335957
$352$	4.80069	−	19.7784i	0.255877	−	1.05419i
$353$	−5.01488	+	8.68603i	−0.266915	+	0.462311i	−0.968064	−	0.250705i	$-0.919338\pi$
$353$	−5.01488	+	8.68603i	−0.266915	+	0.462311i	0.701148	+	0.713015i	$0.252671\pi$
$354$	1.82057	+	1.46004i	0.0967620	+	0.0776004i
$355$	−0.475909	+	0.274766i	−0.0252586	+	0.0145831i
$356$	−28.1687	−	8.85845i	−1.49294	−	0.469497i
$357$	1.33661	+	0.280832i	0.0707408	+	0.0148632i
$358$	27.5101	+	4.22371i	1.45396	+	0.223230i
$359$	−1.80639	−	3.12876i	−0.0953375	−	0.165129i	0.814412	−	0.580287i	$-0.197060\pi$
$359$	−1.80639	−	3.12876i	−0.0953375	−	0.165129i	−0.909749	+	0.415158i	$0.863726\pi$
$360$	0.109145	−	0.0731049i	0.00575243	−	0.00385297i
$361$	−4.24214	+	7.34760i	−0.223271	+	0.386716i
$362$	13.1144	+	33.6864i	0.689277	+	1.77052i
$363$		−	1.94479i		−	0.102075i
$364$	0.393529	+	33.3032i	0.0206265	+	1.74556i
$365$			0.517420i			0.0270830i
$366$	1.67979	−	0.653954i	0.0878038	−	0.0341827i
$367$	−11.0055	+	19.0620i	−0.574480	+	0.995029i	0.421617	+	0.906774i	$0.361463\pi$
$367$	−11.0055	+	19.0620i	−0.574480	+	0.995029i	−0.996098	+	0.0882554i	$0.971871\pi$
$368$	−25.1649	+	11.7803i	−1.31181	+	0.614091i
$369$	5.09417	+	8.82337i	0.265192	+	0.459326i
$370$	0.0129737	−	0.0845012i	0.000674471	−	0.00439301i
$371$	4.67568	+	14.2763i	0.242749	+	0.741190i
$372$	1.26549	−	4.02410i	0.0656128	−	0.208640i
$373$	−27.9915	+	16.1609i	−1.44934	+	0.836780i	−0.998442	−	0.0557935i	$-0.982231\pi$
$373$	−27.9915	+	16.1609i	−1.44934	+	0.836780i	−0.450903	+	0.892573i	$0.648898\pi$
$374$	1.64330	−	2.04908i	0.0849731	−	0.105955i
$375$	−0.232173	+	0.402136i	−0.0119894	+	0.0207662i
$376$	13.1211	−	0.874744i	0.676668	−	0.0451115i
$377$	14.4500			0.744215
$378$	1.31613	−	3.50254i	0.0676942	−	0.180151i
$379$		−	16.6668i		−	0.856115i	−0.903751	−	0.428058i	$-0.859198\pi$
$379$		−	16.6668i		−	0.856115i	0.903751	−	0.428058i	$-0.140802\pi$
$380$	0.0654155	+	0.294032i	0.00335575	+	0.0150835i
$381$	−12.2161	−	7.05296i	−0.625849	−	0.361334i
$382$	−15.4192	−	12.3657i	−0.788912	−	0.632686i
$383$	−12.1998	−	21.1307i	−0.623383	−	1.07973i	−0.988851	−	0.148907i	$-0.952424\pi$
$383$	−12.1998	−	21.1307i	−0.623383	−	1.07973i	0.365468	−	0.930824i	$-0.380909\pi$
$384$	−5.46764	−	9.90479i	−0.279019	−	0.505452i
$385$	−0.329246	−	0.295060i	−0.0167799	−	0.0150377i
$386$	−3.86608	+	25.1808i	−0.196778	+	1.28167i
$387$	−7.89955	+	4.56081i	−0.401557	+	0.231839i
$388$	−9.08389	+	8.33632i	−0.461164	+	0.423213i
$389$	7.38356	+	4.26290i	0.374362	+	0.216138i	0.675362	−	0.737486i	$-0.263987\pi$
$389$	7.38356	+	4.26290i	0.374362	+	0.216138i	−0.301001	+	0.953624i	$0.597321\pi$
$390$	0.149982	+	0.385252i	0.00759462	+	0.0195080i
$391$	−3.58589			−0.181346
$392$	−18.6147	−	6.74481i	−0.940185	−	0.340664i
$393$	−17.1107			−0.863120
$394$	1.89873	+	4.87719i	0.0956565	+	0.245709i
$395$	0.221292	+	0.127763i	0.0111344	+	0.00642845i
$396$	−4.86535	−	5.30165i	−0.244493	−	0.266418i
$397$	−5.91805	+	3.41679i	−0.297019	+	0.171484i	−0.641103	−	0.767455i	$-0.721523\pi$
$397$	−5.91805	+	3.41679i	−0.297019	+	0.171484i	0.344084	+	0.938939i	$0.388189\pi$
$398$	−0.378661	+	2.46632i	−0.0189806	+	0.123625i
$399$	6.38934	+	5.72593i	0.319867	+	0.286655i
$400$	16.3931	+	11.4421i	0.819653	+	0.572107i
$401$	5.24408	+	9.08301i	0.261877	+	0.453584i	0.966741	−	0.255759i	$-0.0823253\pi$
$401$	5.24408	+	9.08301i	0.261877	+	0.453584i	−0.704864	+	0.709343i	$0.748992\pi$
$402$	8.56545	+	6.86925i	0.427206	+	0.342607i
$403$	11.4970	+	6.63780i	0.572707	+	0.330652i
$404$	15.6328	−	3.47794i	0.777761	−	0.173034i
$405$		−	0.0464447i		−	0.00230786i
$406$	−3.02155	+	8.04110i	−0.149957	+	0.399073i
$407$	−4.68294			−0.232125
$408$	−0.0971245	−	1.45686i	−0.00480838	−	0.0721253i
$409$	−4.01466	+	6.95360i	−0.198512	+	0.343833i	−0.948046	−	0.318133i	$-0.896944\pi$
$409$	−4.01466	+	6.95360i	−0.198512	+	0.343833i	0.749534	+	0.661966i	$0.230278\pi$
$410$	0.418672	−	0.522054i	0.0206768	−	0.0257824i
$411$	−4.30578	+	2.48594i	−0.212388	+	0.122622i
$412$	24.5667	+	7.72571i	1.21031	+	0.380618i
$413$	−1.35888	−	4.14911i	−0.0668663	−	0.204164i
$414$	−1.49080	+	9.70996i	−0.0732688	+	0.477218i
$415$	0.191591	+	0.331846i	0.00940485	+	0.0162897i
$416$	34.1640	−	10.0271i	1.67503	−	0.491617i
$417$	2.60234	−	4.50739i	0.127437	−	0.220728i
$418$	15.3758	−	5.98594i	0.752057	−	0.292782i
$419$		−	16.7264i		−	0.817139i	−0.912727	−	0.408570i	$-0.866028\pi$
$419$		−	16.7264i		−	0.817139i	0.912727	−	0.408570i	$-0.133972\pi$
$420$	−0.245745	+	0.00290386i	−0.0119911	+	0.000141694i
$421$			14.7157i			0.717199i	0.933492	+	0.358599i	$0.116746\pi$
$421$			14.7157i			0.717199i	−0.933492	+	0.358599i	$0.883254\pi$
$422$	5.47723	+	14.0691i	0.266627	+	0.684875i
$423$	2.32465	−	4.02641i	0.113028	−	0.195771i
$424$	13.3432	−	8.93724i	0.648003	−	0.434031i
$425$	1.28999	+	2.23434i	0.0625739	+	0.108381i
$426$	16.5391	+	2.53930i	0.801324	+	0.123030i
$427$	−3.30028	−	0.693416i	−0.159712	−	0.0335568i
$428$	−6.13006	+	19.4928i	−0.296308	+	0.942218i
$429$	19.6117	−	11.3228i	0.946862	−	0.546671i
$430$	0.467394	+	0.374837i	0.0225397	+	0.0180762i
$431$	1.57036	−	2.71995i	0.0756416	−	0.131015i	−0.825723	−	0.564075i	$-0.809233\pi$
$431$	1.57036	−	2.71995i	0.0756416	−	0.131015i	0.901365	+	0.433060i	$0.142566\pi$
$432$	−3.98529	−	0.342679i	−0.191743	−	0.0164871i
$433$	33.6748			1.61831			0.809155	−	0.587595i	$-0.199925\pi$
$433$	33.6748			1.61831			0.809155	+	0.587595i	$0.199925\pi$
$434$	−6.09784	+	5.00983i	−0.292706	+	0.240479i
$435$			0.106627i			0.00511239i
$436$	−22.8304	+	5.07924i	−1.09338	+	0.243251i
$437$	−19.5080	−	11.2629i	−0.933192	−	0.538779i
$438$	9.85693	−	12.2909i	0.470982	−	0.587280i
$439$	3.68016	+	6.37423i	0.175645	+	0.304225i	0.940384	−	0.340114i	$-0.110466\pi$
$439$	3.68016	+	6.37423i	0.175645	+	0.304225i	−0.764740	+	0.644340i	$0.777132\pi$
$440$	−0.208568	+	0.424130i	−0.00994310	+	0.0202196i
$441$	−5.64377	+	4.14100i	−0.268751	+	0.197190i
$442$	4.54180	+	0.697317i	0.216032	+	0.0331680i
$443$	−22.3955	+	12.9300i	−1.06404	+	0.614325i	−0.926547	−	0.376178i	$-0.877238\pi$
$443$	−22.3955	+	12.9300i	−1.06404	+	0.614325i	−0.137494	+	0.990503i	$0.543905\pi$
$444$	−1.91794	+	1.76010i	−0.0910213	+	0.0835307i
$445$	0.593857	+	0.342863i	0.0281515	+	0.0162533i
$446$	29.2845	−	11.4007i	1.38666	−	0.539839i
$447$	−0.838167			−0.0396439
$448$	−1.56399	+	21.1081i	−0.0738914	+	0.997266i
$449$	−19.7508			−0.932096			−0.466048	−	0.884759i	$-0.654323\pi$
$449$	−19.7508			−0.932096			−0.466048	+	0.884759i	$0.654323\pi$
$450$	6.58649	−	2.56417i	0.310490	−	0.120876i
$451$	−31.7455	−	18.3283i	−1.49484	−	0.863044i
$452$	−13.3868	+	12.2851i	−0.629663	+	0.577844i
$453$	5.57379	−	3.21803i	0.261879	−	0.151196i
$454$	−27.5568	−	4.23088i	−1.29331	−	0.198565i
$455$	0.159032	−	0.756906i	0.00745555	−	0.0354843i
$456$	4.04747	−	8.23066i	0.189540	−	0.385436i
$457$	−1.28552	−	2.22658i	−0.0601339	−	0.104155i	0.834391	−	0.551173i	$-0.185819\pi$
$457$	−1.28552	−	2.22658i	−0.0601339	−	0.104155i	−0.894525	+	0.447018i	$0.852486\pi$
$458$	6.19946	−	7.73027i	0.289682	−	0.361212i
$459$	−0.447060	−	0.258110i	−0.0208670	−	0.0120476i
$460$	0.629850	−	0.140127i	0.0293669	−	0.00653347i
$461$		−	30.2081i		−	1.40693i	−0.710728	−	0.703467i	$-0.751634\pi$
$461$		−	30.2081i		−	1.40693i	0.710728	−	0.703467i	$-0.248366\pi$
$462$	2.20001	+	13.2811i	0.102354	+	0.617892i
$463$	−20.1707			−0.937412			−0.468706	−	0.883354i	$-0.655280\pi$
$463$	−20.1707			−0.937412			−0.468706	+	0.883354i	$0.655280\pi$
$464$	9.14940	+	0.786718i	0.424750	+	0.0365225i
$465$	−0.0489805	+	0.0848367i	−0.00227142	+	0.00393421i
$466$	−27.2982	−	21.8924i	−1.26456	−	1.01414i
$467$	7.99333	−	4.61495i	0.369887	−	0.213554i	−0.303522	−	0.952824i	$-0.598163\pi$
$467$	7.99333	−	4.61495i	0.369887	−	0.213554i	0.673409	+	0.739270i	$0.264829\pi$
$468$	3.77642	−	12.0085i	0.174565	−	0.555093i
$469$	−6.39332	−	19.5208i	−0.295216	−	0.901389i
$470$	−0.301842	−	0.0463427i	−0.0139229	−	0.00213763i
$471$	−2.73288	−	4.73349i	−0.125925	−	0.218108i
$472$	−3.87791	+	2.59742i	−0.178495	+	0.119556i
$473$	16.4093	−	28.4217i	0.754499	−	1.30683i
$474$	−2.82269	−	7.25054i	−0.129651	−	0.333028i
$475$			16.2070i			0.743627i
$476$	−1.33774	+	2.38159i	−0.0613154	+	0.109160i
$477$		−	5.67797i		−	0.259976i
$478$	−28.9276	+	11.2617i	−1.32312	+	0.515100i
$479$	19.6055	−	33.9577i	0.895797	−	1.55157i	0.0629820	−	0.998015i	$-0.479939\pi$
$479$	19.6055	−	33.9577i	0.895797	−	1.55157i	0.832815	−	0.553551i	$-0.186728\pi$
$480$	0.0739899	+	0.252097i	0.00337716	+	0.0115066i
$481$	−4.09617	−	7.09477i	−0.186769	−	0.323494i
$482$	−3.17269	+	20.6645i	−0.144512	+	0.941243i
$483$	12.2656	−	13.6867i	0.558104	−	0.622766i
$484$	3.71044	+	1.16685i	0.168656	+	0.0530389i
$485$	0.247956	−	0.143157i	0.0112591	−	0.00650045i
$486$	−0.884778	+	1.10325i	−0.0401344	+	0.0500446i
$487$	−3.06454	+	5.30794i	−0.138868	+	0.240526i	−0.927068	−	0.374893i	$-0.877680\pi$
$487$	−3.06454	+	5.30794i	−0.138868	+	0.240526i	0.788201	+	0.615418i	$0.211013\pi$
$488$	0.239815	+	3.59720i	0.0108559	+	0.162838i
$489$	−15.2542			−0.689817
$490$	0.387946	+	0.246769i	0.0175256	+	0.0111479i
$491$		−	20.5291i		−	0.926463i	−0.886237	−	0.463232i	$-0.846690\pi$
$491$		−	20.5291i		−	0.926463i	0.886237	−	0.463232i	$-0.153310\pi$
$492$	−19.8904	+	4.42516i	−0.896728	+	0.199502i
$493$	1.02636	+	0.592567i	0.0462248	+	0.0266879i
$494$	22.5181	+	18.0589i	1.01314	+	0.812508i
$495$	0.0835514	+	0.144715i	0.00375536	+	0.00650447i
$496$	6.91822	+	4.82883i	0.310637	+	0.216821i
$497$	−23.3128	−	20.8922i	−1.04572	−	0.937143i
$498$	1.77063	−	11.5326i	0.0793437	−	0.516786i
$499$	9.57940	−	5.53067i	0.428833	−	0.247587i	−0.270016	−	0.962856i	$-0.587029\pi$
$499$	9.57940	−	5.53067i	0.428833	−	0.247587i	0.698849	+	0.715269i	$0.253696\pi$
$500$	−0.627927	−	0.684237i	−0.0280817	−	0.0306000i
$501$	1.53688	+	0.887315i	0.0686625	+	0.0396423i
$502$	−7.42829	−	19.0808i	−0.331541	−	0.851616i
$503$	2.64242			0.117820			0.0589099	−	0.998263i	$-0.481238\pi$
$503$	2.64242			0.117820			0.0589099	+	0.998263i	$0.481238\pi$
$504$	5.89278	+	4.61250i	0.262485	+	0.205457i
$505$	−0.371906			−0.0165496
$506$	−12.8225	−	32.9368i	−0.570032	−	1.46422i
$507$	23.0504	+	13.3082i	1.02371	+	0.591036i
$508$	20.7857	−	19.0751i	0.922218	−	0.846323i
$509$	−28.9903	+	16.7376i	−1.28497	+	0.741880i	−0.977753	−	0.209758i	$-0.932732\pi$
$509$	−28.9903	+	16.7376i	−1.28497	+	0.741880i	−0.307220	+	0.951638i	$0.599399\pi$
$510$	−0.00514552	+	0.0335141i	−0.000227847	+	0.00148403i
$511$	−28.0111	+	9.17400i	−1.23914	+	0.405834i
$512$	22.1777	−	4.48885i	0.980125	−	0.198381i
$513$	−1.62140	−	2.80834i	−0.0715864	−	0.123991i
$514$	17.5137	+	14.0455i	0.772498	+	0.619521i
$515$	−0.517919	−	0.299021i	−0.0228222	−	0.0131764i
$516$	−3.96184	−	17.8078i	−0.174410	−	0.783947i
$517$			16.7277i			0.735682i
$518$	4.80459	−	0.795881i	0.211102	−	0.0349690i
$519$	−2.58227			−0.113349
$520$	−0.825003	+	0.0550005i	−0.0361788	+	0.00241193i
$521$	12.4133	−	21.5005i	0.543837	−	0.941954i	−0.454842	−	0.890572i	$-0.650304\pi$
$521$	12.4133	−	21.5005i	0.543837	−	0.941954i	0.998679	−	0.0513815i	$-0.0163625\pi$
$522$	2.03126	−	2.53284i	0.0889060	−	0.110859i
$523$	4.00205	−	2.31058i	0.174997	−	0.101035i	−0.409943	−	0.912111i	$-0.634451\pi$
$523$	4.00205	−	2.31058i	0.174997	−	0.101035i	0.584940	+	0.811076i	$0.301118\pi$
$524$	10.2662	−	32.6452i	0.448482	−	1.42611i
$525$	−12.9405	−	2.71891i	−0.564770	−	0.118663i
$526$	0.0698396	−	0.454883i	0.00304515	−	0.0198338i
$527$	0.544406	+	0.942938i	0.0237147	+	0.0410750i
$528$	13.0341	−	6.10158i	0.567236	−	0.265537i
$529$	−12.6264	+	21.8696i	−0.548976	+	0.950854i
$530$	−0.347537	+	0.135299i	−0.0150960	+	0.00587701i
$531$			1.65018i			0.0716117i
$532$	−14.7579	+	8.75462i	−0.639838	+	0.379561i
$533$		−	64.1270i		−	2.77765i
$534$	−7.57495	−	19.4575i	−0.327800	−	0.842007i
$535$	0.237262	−	0.410950i	0.0102577	−	0.0177669i
$536$	−18.2449	+	12.2204i	−0.788060	+	0.527841i
$537$	9.84027	+	17.0438i	0.424639	+	0.735496i
$538$	32.8887	+	5.04950i	1.41793	+	0.217699i
$539$	10.1358	−	23.0556i	0.436580	−	0.993075i
$540$	0.0886110	+	0.0278663i	0.00381321	+	0.00119917i
$541$	−21.7241	+	12.5424i	−0.933992	+	0.539241i	−0.888072	−	0.459704i	$-0.847955\pi$
$541$	−21.7241	+	12.5424i	−0.933992	+	0.539241i	−0.0459203	+	0.998945i	$0.514622\pi$
$542$	1.65834	+	1.32994i	0.0712317	+	0.0571258i
$543$	−12.7807	+	22.1367i	−0.548470	+	0.949979i
$544$	2.83779	+	0.688797i	0.121669	+	0.0295319i
$545$	0.543137			0.0232654
$546$	−18.1968	+	14.9500i	−0.778753	+	0.639803i
$547$		−	38.8014i		−	1.65903i	−0.558487	−	0.829514i	$-0.688618\pi$
$547$		−	38.8014i		−	1.65903i	0.558487	−	0.829514i	$-0.311382\pi$
$548$	−2.15947	−	9.70645i	−0.0922478	−	0.414639i
$549$	1.10386	+	0.637312i	0.0471115	+	0.0271998i
$550$	−15.9098	+	19.8383i	−0.678396	+	0.845910i
$551$	3.72239	+	6.44736i	0.158579	+	0.274667i
$552$	−17.6310	−	8.67014i	−0.750425	−	0.369025i
$553$	−2.99303	+	14.2452i	−0.127276	+	0.605766i
$554$	−20.4480	−	3.13945i	−0.868753	−	0.133382i
$555$	0.0523525	−	0.0302257i	0.00222224	−	0.00128301i
$556$	7.03819	+	7.66934i	0.298486	+	0.325253i
$557$	27.2335	+	15.7233i	1.15392	+	0.666217i	0.949840	−	0.312737i	$-0.101246\pi$
$557$	27.2335	+	15.7233i	1.15392	+	0.666217i	0.204082	+	0.978954i	$0.434579\pi$
$558$	2.77964	−	1.08214i	0.117672	−	0.0458105i
$559$	57.4128			2.42830
$560$	0.141904	−	0.470595i	0.00599654	−	0.0198863i
$561$	1.85730			0.0784154
$562$	−28.1081	+	10.9427i	−1.18567	+	0.461590i
$563$	9.22107	+	5.32379i	0.388622	+	0.224371i	0.681563	−	0.731760i	$-0.261301\pi$
$563$	9.22107	+	5.32379i	0.388622	+	0.224371i	−0.292941	+	0.956131i	$0.594634\pi$
$564$	6.28715	+	6.85096i	0.264737	+	0.288477i
$565$	0.365410	−	0.210970i	0.0153729	−	0.00887556i
$566$	24.2221	+	3.71889i	1.01813	+	0.156317i
$567$	2.51434	−	0.823477i	0.105592	−	0.0345828i
$568$	−14.7680	+	30.0312i	−0.619651	+	1.26008i
$569$	−13.1394	−	22.7581i	−0.550832	−	0.954069i	−0.998215	−	0.0597265i	$-0.980977\pi$
$569$	−13.1394	−	22.7581i	−0.550832	−	0.954069i	0.447383	−	0.894343i	$-0.352356\pi$
$570$	−0.133257	+	0.166162i	−0.00558152	+	0.00695975i
$571$	−6.37133	−	3.67849i	−0.266632	−	0.153940i	0.360724	−	0.932673i	$-0.382530\pi$
$571$	−6.37133	−	3.67849i	−0.266632	−	0.153940i	−0.627356	+	0.778733i	$0.715863\pi$
$572$	9.83580	+	44.2104i	0.411256	+	1.84853i
$573$		−	13.9761i		−	0.583859i
$574$	35.6851	+	13.4091i	1.48947	+	0.559687i
$575$	34.7172			1.44781
$576$	3.04492	−	7.39787i	0.126872	−	0.308244i
$577$	6.42935	−	11.1360i	0.267658	−	0.463596i	−0.700599	−	0.713555i	$-0.747084\pi$
$577$	6.42935	−	11.1360i	0.267658	−	0.463596i	0.968256	+	0.249959i	$0.0804171\pi$
$578$	−18.4613	−	14.8054i	−0.767889	−	0.615825i
$579$	−15.6007	+	9.00706i	−0.648342	+	0.374321i
$580$	−0.203432	−	0.0639752i	−0.00844706	−	0.00265642i
$581$	−14.5679	+	16.2557i	−0.604378	+	0.674402i
$582$	−8.61715	−	1.32302i	−0.357192	−	0.0548408i
$583$	10.2144	+	17.6918i	0.423035	+	0.732719i
$584$	17.5355	+	26.1802i	0.725623	+	1.08335i
$585$	−0.146165	+	0.253165i	−0.00604318	+	0.0104671i
$586$	−15.2340	−	39.1310i	−0.629311	−	1.61649i
$587$			7.51402i			0.310137i	0.987904	+	0.155068i	$0.0495598\pi$
$587$			7.51402i			0.310137i	−0.987904	+	0.155068i	$0.950440\pi$
$588$	−4.51433	−	13.2522i	−0.186168	−	0.546512i
$589$			6.83969i			0.281825i
$590$	0.101004	−	0.0393217i	0.00415827	−	0.00161885i
$591$	−1.85041	+	3.20500i	−0.0761157	+	0.131836i
$592$	−2.20732	−	4.71524i	−0.0907204	−	0.193795i
$593$	−9.63761	−	16.6928i	−0.395769	−	0.685492i	0.597430	−	0.801921i	$-0.296189\pi$
$593$	−9.63761	−	16.6928i	−0.395769	−	0.685492i	−0.993199	+	0.116429i	$0.962855\pi$
$594$	0.772156	−	5.02925i	0.0316819	−	0.206353i
$595$	0.0423349	−	0.0472398i	0.00173556	−	0.00193664i
$596$	0.502891	−	1.59912i	0.0205992	−	0.0655027i
$597$	−1.52800	+	0.882192i	−0.0625369	+	0.0361057i
$598$	38.6842	−	48.2363i	1.58191	−	1.97253i
$599$	7.76773	−	13.4541i	0.317381	−	0.549720i	−0.662560	−	0.749009i	$-0.730530\pi$
$599$	7.76773	−	13.4541i	0.317381	−	0.549720i	0.979941	+	0.199289i	$0.0638633\pi$
$600$	0.940321	+	14.1047i	0.0383884	+	0.575823i
$601$	−44.5011			−1.81524			−0.907620	−	0.419793i	$-0.862103\pi$
$601$	−44.5011			−1.81524			−0.907620	+	0.419793i	$0.862103\pi$
$602$	−12.0052	+	31.9489i	−0.489295	+	1.30214i
$603$			7.76382i			0.316167i
$604$	2.79541	+	12.5649i	0.113744	+	0.511259i
$605$	−0.0782241	−	0.0451627i	−0.00318026	−	0.00183612i
$606$	8.83431	+	7.08487i	0.358869	+	0.287803i
$607$	11.9183	+	20.6432i	0.483751	+	0.837881i	0.999826	−	0.0186624i	$-0.00594079\pi$
$607$	11.9183	+	20.6432i	0.483751	+	0.837881i	−0.516075	+	0.856543i	$0.672607\pi$
$608$	13.2747	+	12.6604i	0.538360	+	0.513447i
$609$	−5.77239	+	1.89053i	−0.233909	+	0.0766081i
$610$	0.0127050	−	0.0827512i	0.000514412	−	0.00335050i
$611$	−25.3428	+	14.6317i	−1.02526	+	0.591935i
$612$	0.760675	−	0.698075i	0.0307485	−	0.0282180i
$613$	17.7261	+	10.2342i	0.715950	+	0.413354i	0.813260	−	0.581900i	$-0.197690\pi$
$613$	17.7261	+	10.2342i	0.715950	+	0.413354i	−0.0973099	+	0.995254i	$0.531024\pi$
$614$	2.50496	+	6.43439i	0.101092	+	0.259671i
$615$	0.473195			0.0190811
$616$	−26.6587	−	3.77114i	−1.07411	−	0.151943i
$617$	19.3039			0.777146			0.388573	−	0.921418i	$-0.372968\pi$
$617$	19.3039			0.777146			0.388573	+	0.921418i	$0.372968\pi$
$618$	6.60633	+	16.9694i	0.265746	+	0.682610i
$619$	−21.1475	−	12.2095i	−0.849990	−	0.490742i	0.0106577	−	0.999943i	$-0.496607\pi$
$619$	−21.1475	−	12.2095i	−0.849990	−	0.490742i	−0.860647	+	0.509201i	$0.829941\pi$
$620$	−0.132471	−	0.144350i	−0.00532015	−	0.00579724i
$621$	−6.01578	+	3.47322i	−0.241405	+	0.139375i
$622$	3.89857	−	25.3924i	0.156319	−	1.01814i
$623$	−8.03205	+	38.2282i	−0.321797	+	1.53158i
$624$	20.6450	+	14.4099i	0.826461	+	0.576859i
$625$	−12.4838	−	21.6226i	−0.499353	−	0.864905i
$626$	−15.0160	−	12.0424i	−0.600161	−	0.481312i
$627$	10.1041	+	5.83361i	0.403519	+	0.232972i
$628$	10.6706	−	2.37398i	0.425805	−	0.0947319i
$629$		−	0.671902i		−	0.0267905i
$630$	−0.110317	−	0.134275i	−0.00439513	−	0.00534964i
$631$	−20.7613			−0.826494			−0.413247	−	0.910619i	$-0.635605\pi$
$631$	−20.7613			−0.826494			−0.413247	+	0.910619i	$0.635605\pi$
$632$	15.5268	−	1.03512i	0.617621	−	0.0411750i
$633$	−5.33785	+	9.24542i	−0.212160	+	0.367473i
$634$	−22.1093	+	27.5687i	−0.878074	+	1.09489i
$635$	−0.567372	+	0.327573i	−0.0225155	+	0.0129993i
$636$	10.8329	+	3.40672i	0.429552	+	0.135085i
$637$	43.7956	−	4.81075i	1.73525	−	0.190609i
$638$	−1.77271	+	11.5461i	−0.0701822	+	0.457115i
$639$	5.91599	+	10.2468i	0.234033	+	0.405357i
$640$	−0.525365	−	0.0100916i	−0.0207669	−	0.000398904i
$641$	−11.0483	+	19.1363i	−0.436383	+	0.755838i	−0.997407	−	0.0719616i	$-0.977074\pi$
$641$	−11.0483	+	19.1363i	−0.436383	+	0.755838i	0.561024	+	0.827799i	$0.310407\pi$
$642$	−13.4646	+	5.24188i	−0.531405	+	0.206880i
$643$			31.9358i			1.25943i	0.776828	+	0.629713i	$0.216827\pi$
$643$			31.9358i			1.25943i	−0.776828	+	0.629713i	$0.783173\pi$
$644$	18.7534	+	31.6132i	0.738986	+	1.24573i
$645$			0.423651i			0.0166812i
$646$	0.858855	+	2.20611i	0.0337912	+	0.0867981i
$647$	−1.48741	+	2.57626i	−0.0584760	+	0.101283i	−0.893781	−	0.448503i	$-0.851957\pi$
$647$	−1.48741	+	2.57626i	−0.0584760	+	0.101283i	0.835305	+	0.549786i	$0.185291\pi$
$648$	−1.57402	−	2.34999i	−0.0618333	−	0.0923164i
$649$	−2.96858	−	5.14173i	−0.116527	−	0.201831i
$650$	−43.9719	−	6.75114i	−1.72472	−	0.264802i
$651$	−5.46117	−	1.14744i	−0.214040	−	0.0449716i
$652$	9.15232	−	29.1031i	0.358433	−	1.13977i
$653$	−14.9217	+	8.61507i	−0.583933	+	0.337134i	−0.762695	−	0.646758i	$-0.776124\pi$
$653$	−14.9217	+	8.61507i	−0.583933	+	0.337134i	0.178762	+	0.983892i	$0.442791\pi$
$654$	−12.9018	−	10.3468i	−0.504498	−	0.404594i
$655$	−0.397351	+	0.688231i	−0.0155258	+	0.0268914i
$656$	3.49133	−	40.6036i	0.136314	−	1.58530i
$657$	11.1406			0.434635
$658$	−2.84292	−	17.1622i	−0.110829	−	0.669053i
$659$			27.7588i			1.08133i	0.841238	+	0.540665i	$0.181827\pi$
$659$			27.7588i			1.08133i	−0.841238	+	0.540665i	$0.818173\pi$
$660$	−0.326230	+	0.0725787i	−0.0126985	+	0.00282512i
$661$	28.3232	+	16.3524i	1.10164	+	0.636034i	0.936652	−	0.350261i	$-0.113907\pi$
$661$	28.3232	+	16.3524i	1.10164	+	0.636034i	0.164991	+	0.986295i	$0.447241\pi$
$662$	−6.48528	+	8.08667i	−0.252058	+	0.314297i
$663$	1.62459	+	2.81386i	0.0630937	+	0.109281i
$664$	20.9404	+	10.2976i	0.812645	+	0.399623i
$665$	0.378686	−	0.124024i	0.0146848	−	0.00480946i
$666$	−1.81939	−	0.279337i	−0.0705000	−	0.0108241i
$667$	13.8110	−	7.97377i	0.534763	−	0.308746i
$668$	−2.61500	+	2.39980i	−0.101177	+	0.0928510i
$669$	19.2441	+	11.1106i	0.744020	+	0.429560i
$670$	0.475207	−	0.185002i	0.0183589	−	0.00714725i
$671$	−4.58596			−0.177039
$672$	−12.3357	+	8.47528i	−0.475860	+	0.326941i
$673$	12.9387			0.498752			0.249376	−	0.968407i	$-0.419775\pi$
$673$	12.9387			0.498752			0.249376	+	0.968407i	$0.419775\pi$
$674$	−1.96503	+	0.765002i	−0.0756901	+	0.0294668i
$675$	4.32826	+	2.49892i	0.166595	+	0.0961835i
$676$	−39.2204	+	35.9927i	−1.50848	+	1.38434i
$677$	1.12548	−	0.649798i	0.0432558	−	0.0249738i	−0.478216	−	0.878242i	$-0.658716\pi$
$677$	1.12548	−	0.649798i	0.0432558	−	0.0249738i	0.521472	+	0.853268i	$0.325383\pi$
$678$	−12.6990	−	1.94971i	−0.487702	−	0.0748783i
$679$	12.1463	+	10.8852i	0.466133	+	0.417734i
$680$	−0.0608537	−	0.0299251i	−0.00233363	−	0.00114758i
$681$	−9.85697	−	17.0728i	−0.377720	−	0.654230i
$682$	−6.71428	+	8.37221i	−0.257103	+	0.320588i
$683$	16.8225	+	9.71249i	0.643696	+	0.371638i	0.786037	−	0.618179i	$-0.212130\pi$
$683$	16.8225	+	9.71249i	0.643696	+	0.371638i	−0.142341	+	0.989818i	$0.545463\pi$
$684$	6.33081	−	1.40846i	0.242064	−	0.0538538i
$685$			0.230918i			0.00882291i
$686$	−6.48073	+	25.3772i	−0.247435	+	0.968904i
$687$	7.00679			0.267326
$688$	36.3523	+	3.12578i	1.38592	+	0.119169i
$689$	−17.8690	+	30.9500i	−0.680755	+	1.17910i
$690$	0.355937	+	0.285451i	0.0135503	+	0.0108670i
$691$	11.1725	−	6.45042i	0.425020	−	0.245386i	−0.272203	−	0.962240i	$-0.587752\pi$
$691$	11.1725	−	6.45042i	0.425020	−	0.245386i	0.697223	+	0.716854i	$0.254419\pi$
$692$	1.54933	−	4.92667i	0.0588969	−	0.187284i
$693$	−6.35294	+	7.08899i	−0.241328	+	0.269288i
$694$	−33.3298	−	5.11722i	−1.26518	−	0.194247i
$695$	−0.120865	−	0.209344i	−0.00458467	−	0.00794088i
$696$	3.61362	+	5.39509i	0.136974	+	0.204500i
$697$	2.62972	−	4.55480i	0.0996076	−	0.172526i
$698$	−5.93775	−	15.2520i	−0.224747	−	0.577299i
$699$		−	24.7433i		−	0.935879i
$700$	12.9515	−	23.0576i	0.489521	−	0.871497i
$701$			34.3868i			1.29877i	0.760460	+	0.649385i	$0.224974\pi$
$701$			34.3868i			1.29877i	−0.760460	+	0.649385i	$0.775026\pi$
$702$	8.29485	−	3.22925i	0.313069	−	0.121880i
$703$	2.11038	−	3.65528i	0.0795944	−	0.137862i
$704$	3.82079	+	28.5284i	0.144001	+	1.07520i
$705$	−0.107968	−	0.187006i	−0.00406630	−	0.00704303i
$706$	2.15253	−	14.0200i	0.0810114	−	0.527648i
$707$	−6.59400	−	20.1336i	−0.247993	−	0.757201i
$708$	−3.14835	−	0.990089i	−0.118322	−	0.0372098i
$709$	−19.7915	+	11.4266i	−0.743284	+	0.429135i	−0.823262	−	0.567661i	$-0.807848\pi$
$709$	−19.7915	+	11.4266i	−0.743284	+	0.429135i	0.0799779	+	0.996797i	$0.474515\pi$
$710$	0.486214	−	0.606274i	0.0182473	−	0.0227530i
$711$	2.75086	−	4.76463i	0.103165	−	0.178688i
$712$	41.6674	−	2.77785i	1.56155	−	0.104104i
$713$	14.6514			0.548699
$714$	−1.90555	+	0.315655i	−0.0713136	+	0.0118131i
$715$		−	1.05177i		−	0.0393340i
$716$	−38.4217	+	8.54796i	−1.43589	+	0.319452i
$717$	−19.0095	−	10.9752i	−0.709924	−	0.409875i
$718$	3.98581	+	3.19650i	0.148749	+	0.119293i
$719$	5.21620	+	9.03472i	0.194531	+	0.336938i	0.946747	−	0.321979i	$-0.104348\pi$
$719$	5.21620	+	9.03472i	0.194531	+	0.336938i	−0.752215	+	0.658917i	$0.771015\pi$
$720$	−0.106331	+	0.152340i	−0.00396273	+	0.00567737i
$721$	7.00498	−	33.3399i	0.260879	−	1.24164i
$722$	1.82084	−	11.8596i	0.0677648	−	0.441369i
$723$	−12.8027	+	7.39162i	−0.476136	+	0.274897i
$724$	−34.5660	−	37.6658i	−1.28464	−	1.39984i
$725$	−9.93677	−	5.73700i	−0.369042	−	0.213067i
$726$	0.997789	+	2.56298i	0.0370314	+	0.0951211i
$727$	−2.48753			−0.0922572			−0.0461286	−	0.998936i	$-0.514688\pi$
$727$	−2.48753			−0.0922572			−0.0461286	+	0.998936i	$0.514688\pi$
$728$	−17.6050	−	43.6873i	−0.652486	−	1.61916i
$729$	−1.00000			−0.0370370
$730$	−0.265466	−	0.681891i	−0.00982533	−	0.0252379i
$731$	4.07791	+	2.35438i	0.150827	+	0.0870800i
$732$	−1.87822	+	1.72365i	−0.0694210	+	0.0637079i
$733$	−0.674033	+	0.389153i	−0.0248960	+	0.0143737i	−0.512396	−	0.858749i	$-0.671242\pi$
$733$	−0.674033	+	0.389153i	−0.0248960	+	0.0143737i	0.487500	+	0.873123i	$0.337909\pi$
$734$	4.72385	−	30.7676i	0.174360	−	1.13565i
$735$	0.0354987	+	0.323169i	0.00130939	+	0.0119203i
$736$	27.1200	−	28.4359i	0.999656	−	1.04816i
$737$	−13.9667	−	24.1910i	−0.514469	−	0.891086i
$738$	−11.2403	−	9.01443i	−0.413762	−	0.331826i
$739$	22.4331	+	12.9518i	0.825215	+	0.476438i	0.852212	−	0.523197i	$-0.175261\pi$
$739$	22.4331	+	12.9518i	0.825215	+	0.476438i	−0.0269963	+	0.999636i	$0.508594\pi$
$740$	0.0262562	+	0.118018i	0.000965198	+	0.00433841i
$741$			20.4106i			0.749804i
$742$	−13.4865	−	16.4154i	−0.495104	−	0.602629i
$743$	−27.7729			−1.01889			−0.509445	−	0.860503i	$-0.670149\pi$
$743$	−27.7729			−1.01889			−0.509445	+	0.860503i	$0.670149\pi$
$744$	0.396836	+	5.95250i	0.0145487	+	0.218229i
$745$	−0.0194642	+	0.0337130i	−0.000713113	+	0.00123515i
$746$	28.5976	−	35.6591i	1.04703	−	1.30557i
$747$	7.14497	−	4.12515i	0.261421	−	0.150931i
$748$	−1.11436	+	3.54352i	−0.0407451	+	0.129564i
$749$	26.4539	+	5.55819i	0.966606	+	0.203092i
$750$	0.0996552	−	0.649080i	0.00363889	−	0.0237010i
$751$	−10.5549	−	18.2816i	−0.385153	−	0.667105i	0.606637	−	0.794979i	$-0.292518\pi$
$751$	−10.5549	−	18.2816i	−0.385153	−	0.667105i	−0.991790	+	0.127874i	$0.959185\pi$
$752$	−16.8430	+	7.88465i	−0.614203	+	0.287524i
$753$	7.23926	−	12.5388i	0.263813	−	0.456938i
$754$	−19.0432	+	7.41369i	−0.693514	+	0.269991i
$755$		−	0.298921i		−	0.0108788i
$756$	0.0625230	+	5.29113i	0.00227394	+	0.192437i
$757$		−	46.6419i		−	1.69523i	−0.530612	−	0.847615i	$-0.678038\pi$
$757$		−	46.6419i		−	1.69523i	0.530612	−	0.847615i	$-0.321962\pi$
$758$	8.55100	+	21.9646i	0.310586	+	0.797790i
$759$	12.4962	−	21.6441i	0.453585	−	0.785632i
$760$	−0.237064	−	0.353934i	−0.00859922	−	0.0128385i
$761$	12.5114	+	21.6703i	0.453537	+	0.785550i	0.998603	−	0.0528439i	$-0.0168286\pi$
$761$	12.5114	+	21.6703i	0.453537	+	0.785550i	−0.545066	+	0.838393i	$0.683495\pi$
$762$	19.7177	+	3.02732i	0.714298	+	0.109668i
$763$	9.62997	+	29.4034i	0.348628	+	1.06447i
$764$	26.6647	+	8.38549i	0.964695	+	0.303376i
$765$	−0.0207636	+	0.0119879i	−0.000750709	+	0.000433422i
$766$	26.9190	+	21.5883i	0.972624	+	0.780017i
$767$	5.19324	−	8.99495i	0.187517	−	0.324789i
$768$	12.2873	+	10.2480i	0.443381	+	0.369793i
$769$	1.32800			0.0478891			0.0239445	−	0.999713i	$-0.492377\pi$
$769$	1.32800			0.0478891			0.0239445	+	0.999713i	$0.492377\pi$
$770$	0.585285	+	0.219928i	0.0210922	+	0.00792567i
$771$			15.8746i			0.571711i
$772$	−7.82417	−	35.1684i	−0.281598	−	1.26574i
$773$	19.2488	+	11.1133i	0.692332	+	0.399718i	0.804485	−	0.593973i	$-0.202441\pi$
$773$	19.2488	+	11.1133i	0.692332	+	0.399718i	−0.112153	+	0.993691i	$0.535775\pi$
$774$	8.07061	−	10.0635i	0.290092	−	0.361723i
$775$	−5.27072	−	9.12915i	−0.189330	−	0.327929i
$776$	7.69435	−	15.6467i	0.276211	−	0.561684i
$777$	2.56453	+	2.29825i	0.0920020	+	0.0824493i
$778$	−11.9177	−	1.82975i	−0.427269	−	0.0655999i
$779$	28.6124	−	16.5194i	1.02514	−	0.591867i
$780$	−0.395312	−	0.430762i	−0.0141544	−	0.0154237i
$781$	−36.8668	−	21.2851i	−1.31920	−	0.761639i
$782$	4.72573	−	1.83976i	0.168992	−	0.0657898i
$783$	2.29579			0.0820448
$784$	27.9922	−	0.661635i	0.999721	−	0.0236298i
$785$	−0.253856			−0.00906050
$786$	22.5496	−	8.77875i	0.804318	−	0.313128i
$787$	−16.5930	−	9.57996i	−0.591476	−	0.341489i	0.174205	−	0.984709i	$-0.444264\pi$
$787$	−16.5930	−	9.57996i	−0.591476	−	0.341489i	−0.765681	+	0.643221i	$0.777598\pi$
$788$	−5.00454	−	5.45333i	−0.178279	−	0.194267i
$789$	0.281822	−	0.162710i	0.0100331	−	0.00579263i
$790$	−0.357183	−	0.0548394i	−0.0127080	−	0.00195110i
$791$	17.8999	+	16.0413i	0.636447	+	0.570364i
$792$	9.13193	+	4.49068i	0.324489	+	0.159569i
$793$	−4.01134	−	6.94784i	−0.142447	−	0.246725i
$794$	6.04620	−	7.53917i	0.214572	−	0.267555i
$795$	−0.228381	−	0.131856i	−0.00809984	−	0.00467645i
$796$	−0.766334	−	3.44455i	−0.0271620	−	0.122089i
$797$			35.9779i			1.27440i	0.770697	+	0.637201i	$0.219908\pi$
$797$			35.9779i			1.27440i	−0.770697	+	0.637201i	$0.780092\pi$
$798$	−11.3580	−	4.26793i	−0.402070	−	0.151083i
$799$	−2.40006			−0.0849082
$800$	−27.4743	−	6.66866i	−0.971364	−	0.235773i
$801$	7.38218	−	12.7863i	0.260837	−	0.451782i
$802$	−11.5711	−	9.27969i	−0.408589	−	0.327677i
$803$	−34.7125	+	20.0413i	−1.22498	+	0.707241i
$804$	−14.8124	−	4.65820i	−0.522395	−	0.164282i
$805$	−0.265674	−	0.811187i	−0.00936378	−	0.0285906i
$806$	−18.5571	−	2.84913i	−0.653646	−	0.100356i
$807$	11.7642	+	20.3761i	0.414118	+	0.717273i
$808$	−18.8176	+	12.6040i	−0.662000	+	0.443406i
$809$	4.56264	−	7.90272i	0.160414	−	0.277845i	−0.774603	−	0.632447i	$-0.782050\pi$
$809$	4.56264	−	7.90272i	0.160414	−	0.277845i	0.935017	+	0.354603i	$0.115384\pi$
$810$	0.0238287	+	0.0612079i	0.000837257	+	0.00215063i
$811$			9.64051i			0.338524i	0.985571	+	0.169262i	$0.0541384\pi$
$811$			9.64051i			0.338524i	−0.985571	+	0.169262i	$0.945862\pi$
$812$	−0.143540	−	12.1473i	−0.00503725	−	0.426288i
$813$			1.50313i			0.0527172i
$814$	6.17149	−	2.40261i	0.216311	−	0.0842115i
$815$	−0.354237	+	0.613557i	−0.0124084	+	0.0214920i
$816$	0.875448	+	1.87012i	0.0306468	+	0.0654671i
$817$	14.7898	+	25.6166i	0.517428	+	0.896212i
$818$	1.72320	−	11.2237i	0.0602504	−	0.392426i
$819$	−16.2969	−	3.42412i	−0.569461	−	0.119648i
$820$	−0.283912	+	0.902800i	−0.00991462	+	0.0315271i
$821$	16.6309	−	9.60187i	0.580423	−	0.335107i	−0.180878	−	0.983505i	$-0.557894\pi$
$821$	16.6309	−	9.60187i	0.580423	−	0.335107i	0.761301	+	0.648398i	$0.224561\pi$
$822$	4.39901	−	5.48525i	0.153433	−	0.191320i
$823$	0.820157	−	1.42055i	0.0285889	−	0.0495174i	−0.851377	−	0.524554i	$-0.824232\pi$
$823$	0.820157	−	1.42055i	0.0285889	−	0.0495174i	0.879966	+	0.475037i	$0.157565\pi$
$824$	−36.3394	+	2.42264i	−1.26594	+	0.0843966i
$825$	−17.9817			−0.626042
$826$	3.91955	+	4.77079i	0.136379	+	0.165997i
$827$			27.3891i			0.952412i	0.879334	+	0.476206i	$0.157988\pi$
$827$			27.3891i			0.952412i	−0.879334	+	0.476206i	$0.842012\pi$
$828$	−3.01708	−	13.5613i	−0.104851	−	0.471288i
$829$	−15.4922	−	8.94441i	−0.538065	−	0.310652i	0.206229	−	0.978504i	$-0.433881\pi$
$829$	−15.4922	−	8.94441i	−0.538065	−	0.310652i	−0.744294	+	0.667852i	$0.767214\pi$
$830$	−0.422748	−	0.339032i	−0.0146738	−	0.0117680i
$831$	−7.31418	−	12.6685i	−0.253726	−	0.439466i
$832$	−39.8792	+	30.7424i	−1.38256	+	1.06580i
$833$	3.30799	+	1.45427i	0.114615	+	0.0503875i
$834$	−1.11700	+	7.27528i	−0.0386784	+	0.251923i
$835$	0.0713797	−	0.0412111i	0.00247020	−	0.00142617i
$836$	−17.1922	+	15.7773i	−0.594604	+	0.545670i
$837$	1.82662	+	1.05460i	0.0631372	+	0.0364523i
$838$	8.58160	+	22.0432i	0.296446	+	0.761470i
$839$	11.0644			0.381986			0.190993	−	0.981591i	$-0.438829\pi$
$839$	11.0644			0.381986			0.190993	+	0.981591i	$0.438829\pi$
$840$	0.322370	−	0.129908i	0.0111228	−	0.00448225i
$841$	23.7294			0.818253
$842$	−7.54997	−	19.3933i	−0.260189	−	0.668338i
$843$	−18.4710	−	10.6642i	−0.636175	−	0.367296i
$844$	−14.4365	−	15.7311i	−0.496926	−	0.541488i
$845$	1.07057	−	0.618094i	0.0368287	−	0.0212631i
$846$	−0.997804	+	6.49895i	−0.0343052	+	0.223439i
$847$	1.05800	−	5.03550i	0.0363533	−	0.173022i
$848$	−12.9992	+	18.6239i	−0.446396	+	0.639547i
$849$	8.66416	+	15.0068i	0.297353	+	0.515031i
$850$	−2.84638	−	2.28272i	−0.0976301	−	0.0782966i
$851$	−7.83002	−	4.52067i	−0.268410	−	0.154966i
$852$	−23.0992	+	5.13905i	−0.791365	+	0.176061i
$853$		−	29.4621i		−	1.00876i	−0.863480	−	0.504382i	$-0.831720\pi$
$853$		−	29.4621i		−	1.00876i	0.863480	−	0.504382i	$-0.168280\pi$
$854$	4.70509	−	0.779399i	0.161005	−	0.0266705i
$855$	−0.150611			−0.00515078
$856$	−1.92227	−	28.8339i	−0.0657020	−	0.985524i
$857$	−8.88103	+	15.3824i	−0.303370	+	0.525453i	−0.976897	−	0.213710i	$-0.931445\pi$
$857$	−8.88103	+	15.3824i	−0.303370	+	0.525453i	0.673527	+	0.739163i	$0.264779\pi$
$858$	−20.0364	+	24.9839i	−0.684030	+	0.852936i
$859$	31.7456	−	18.3283i	1.08314	−	0.625354i	0.151402	−	0.988472i	$-0.451621\pi$
$859$	31.7456	−	18.3283i	1.08314	−	0.625354i	0.931743	+	0.363118i	$0.118288\pi$
$860$	−0.808276	−	0.254186i	−0.0275620	−	0.00866766i
$861$	8.38987	+	25.6169i	0.285926	+	0.873022i
$862$	−0.674042	+	4.39021i	−0.0229580	+	0.149531i
$863$	1.57129	+	2.72156i	0.0534874	+	0.0926429i	0.891529	−	0.452963i	$-0.149633\pi$
$863$	1.57129	+	2.72156i	0.0534874	+	0.0926429i	−0.838042	+	0.545606i	$0.816300\pi$
$864$	5.42790	−	1.59308i	0.184661	−	0.0541975i
$865$	−0.0599664	+	0.103865i	−0.00203892	+	0.00353151i
$866$	−44.3790	+	17.2771i	−1.50806	+	0.587099i
$867$		−	16.7335i		−	0.568300i
$868$	5.46582	−	9.73082i	0.185522	−	0.330285i
$869$			19.7946i			0.671485i
$870$	−0.0547058	−	0.140521i	−0.00185470	−	0.00476409i
$871$	24.4333	−	42.3197i	0.827891	−	1.43395i
$872$	27.4815	−	18.4070i	0.930640	−	0.623341i
$873$	−3.08232	−	5.33874i	−0.104321	−	0.180689i
$874$	31.4874	+	4.83436i	1.06508	+	0.163525i
$875$	−0.819916	+	0.914912i	−0.0277182	+	0.0309297i
$876$	−6.68422	+	21.2549i	−0.225839	+	0.718136i
$877$	12.4428	−	7.18384i	0.420162	−	0.242581i	−0.274984	−	0.961449i	$-0.588673\pi$
$877$	12.4428	−	7.18384i	0.420162	−	0.242581i	0.695147	+	0.718868i	$0.255339\pi$
$878$	−8.12031	−	6.51226i	−0.274047	−	0.219778i
$879$	14.8463	−	25.7146i	0.500754	−	0.867332i
$880$	0.0572626	−	0.665954i	0.00193032	−	0.0224493i
$881$	−21.4314			−0.722043			−0.361022	−	0.932557i	$-0.617572\pi$
$881$	−21.4314			−0.722043			−0.361022	+	0.932557i	$0.617572\pi$
$882$	5.31318	−	8.35285i	0.178904	−	0.281255i
$883$			29.5761i			0.995316i	0.867373	+	0.497658i	$0.165806\pi$
$883$			29.5761i			0.995316i	−0.867373	+	0.497658i	$0.834194\pi$
$884$	−6.34325	+	1.41123i	−0.213347	+	0.0474648i
$885$	0.0663740	+	0.0383210i	0.00223114	+	0.00128815i
$886$	22.8804	−	28.5302i	0.768683	−	0.958491i
$887$	1.90744	+	3.30379i	0.0640456	+	0.110930i	0.896270	−	0.443508i	$-0.146266\pi$
$887$	1.90744	+	3.30379i	0.0640456	+	0.110930i	−0.832225	+	0.554439i	$0.812933\pi$
$888$	1.62456	−	3.30359i	0.0545166	−	0.110861i
$889$	−27.7932	−	24.9074i	−0.932153	−	0.835367i
$890$	−0.958532	−	0.147166i	−0.0321301	−	0.00493303i
$891$	3.11586	−	1.79894i	0.104385	−	0.0602669i
$892$	−32.7439	+	30.0492i	−1.09635	+	1.00612i
$893$	−13.0568	−	7.53836i	−0.436930	−	0.252262i
$894$	1.10459	−	0.430027i	0.0369431	−	0.0143822i
$895$	0.914057			0.0305536
$896$	−8.76854	−	28.6201i	−0.292936	−	0.956132i
$897$	43.7219			1.45983
$898$	26.0289	−	10.1333i	0.868595	−	0.338151i
$899$	−4.19353	−	2.42114i	−0.139862	−	0.0807494i
$900$	−7.36455	+	6.75848i	−0.245485	+	0.225283i
$901$	−2.53840	+	1.46554i	−0.0845662	+	0.0488243i
$902$	51.2397	+	7.86699i	1.70610	+	0.261942i
$903$	−22.9348	+	7.51144i	−0.763223	+	0.249965i
$904$	11.3391	−	23.0584i	0.377132	−	0.766910i
$905$	0.593594	+	1.02813i	0.0197317	+	0.0341763i
$906$	−5.69448	+	7.10060i	−0.189187	+	0.235902i
$907$	−4.23020	−	2.44231i	−0.140462	−	0.0810955i	0.428122	−	0.903721i	$-0.359175\pi$
$907$	−4.23020	−	2.44231i	−0.140462	−	0.0810955i	−0.568584	+	0.822625i	$0.692509\pi$
$908$	38.4869	−	8.56246i	1.27723	−	0.284155i
$909$			8.00751i			0.265592i
$910$	0.178752	+	1.07909i	0.00592557	+	0.0357716i
$911$	−47.3325			−1.56820			−0.784098	−	0.620637i	$-0.786874\pi$
$911$	−47.3325			−1.56820			−0.784098	+	0.620637i	$0.786874\pi$
$912$	−1.11124	+	12.9235i	−0.0367967	+	0.427940i
$913$	−14.8418	+	25.7068i	−0.491193	+	0.850771i
$914$	2.83650	+	2.27479i	0.0938231	+	0.0752435i
$915$	0.0512683	−	0.0295998i	0.00169488	−	0.000978539i
$916$	−4.20400	+	13.3681i	−0.138904	+	0.441696i
$917$	−44.3033	−	9.30849i	−1.46302	−	0.307394i
$918$	0.721591	+	0.110788i	0.0238161	+	0.00365655i
$919$	15.5826	+	26.9898i	0.514022	+	0.890312i	0.999868	+	0.0162672i	$0.00517825\pi$
$919$	15.5826	+	26.9898i	0.514022	+	0.890312i	−0.485846	+	0.874044i	$0.661488\pi$
$920$	−0.758166	+	0.507818i	−0.0249960	+	0.0167423i
$921$	−2.44121	+	4.22831i	−0.0804407	+	0.139327i
$922$	15.4985	+	39.8103i	0.510415	+	1.31108i
$923$		−	74.4722i		−	2.45128i
$924$	−9.71326	−	16.3740i	−0.319543	−	0.538664i
$925$			6.50509i			0.213886i
$926$	26.5823	−	10.3487i	0.873549	−	0.340080i
$927$	−6.43821	+	11.1513i	−0.211459	+	0.366257i
$928$	−12.4613	+	3.65737i	−0.409063	+	0.120059i
$929$	14.3019	+	24.7717i	0.469231	+	0.812733i	0.999381	−	0.0351712i	$-0.0111977\pi$
$929$	14.3019	+	24.7717i	0.469231	+	0.812733i	−0.530150	+	0.847904i	$0.677864\pi$
$930$	0.0210238	−	0.136933i	0.000689397	−	0.00449022i
$931$	13.4284	+	18.3016i	0.440098	+	0.599811i
$932$	47.2074	+	14.8457i	1.54633	+	0.486288i
$933$	15.7318	−	9.08277i	0.515036	−	0.297356i
$934$	−8.16641	+	10.1829i	−0.267213	+	0.333195i
$935$	0.0431310	−	0.0747050i	0.00141053	−	0.00244312i
$936$	1.18421	+	17.7631i	0.0387073	+	0.580606i
$937$	5.62816			0.183864			0.0919320	−	0.995765i	$-0.470696\pi$
$937$	5.62816			0.183864			0.0919320	+	0.995765i	$0.470696\pi$
$938$	18.4408	+	22.4457i	0.602115	+	0.732879i
$939$		−	13.6107i		−	0.444167i
$940$	0.421564	−	0.0937884i	0.0137499	−	0.00305904i
$941$	−29.2442	−	16.8842i	−0.953334	−	0.550408i	−0.0592190	−	0.998245i	$-0.518861\pi$
$941$	−29.2442	−	16.8842i	−0.953334	−	0.550408i	−0.894115	+	0.447837i	$0.852194\pi$
$942$	6.03012	+	4.83599i	0.196472	+	0.157565i
$943$	−35.3863	−	61.2909i	−1.15234	−	1.99591i
$944$	3.77795	−	5.41263i	0.122962	−	0.176166i
$945$	0.0252667	−	0.120255i	0.000821925	−	0.00391191i
$946$	−7.04331	+	45.8749i	−0.228998	+	1.49152i
$947$	−10.1554	+	5.86321i	−0.330005	+	0.190529i	−0.655843	−	0.754897i	$-0.727687\pi$
$947$	−10.1554	+	5.86321i	−0.330005	+	0.190529i	0.325838	+	0.945426i	$0.394354\pi$
$948$	7.43987	+	8.10705i	0.241636	+	0.263305i
$949$	−60.7261	−	35.0602i	−1.97125	−	1.13810i
$950$	−8.31509	−	21.3586i	−0.269777	−	0.692966i
$951$	−24.9886			−0.810310
$952$	0.541078	−	3.82496i	0.0175364	−	0.123968i
$953$	37.7047			1.22137			0.610687	−	0.791872i	$-0.290893\pi$
$953$	37.7047			1.22137			0.610687	+	0.791872i	$0.290893\pi$
$954$	2.91312	+	7.48281i	0.0943157	+	0.242265i
$955$	−0.562150	−	0.324557i	−0.0181907	−	0.0105024i
$956$	32.3448	−	29.6830i	1.04611	−	0.960016i
$957$	−7.15336	+	4.13000i	−0.231235	+	0.133504i
$958$	−8.41521	+	54.8104i	−0.271883	+	1.77084i
$959$	−12.5010	+	4.09423i	−0.403678	+	0.132210i
$960$	−0.226849	−	0.294270i	−0.00732152	−	0.00949751i
$961$	13.2756	+	22.9941i	0.428247	+	0.741745i
$962$	9.03822	+	7.24840i	0.291404	+	0.233698i
$963$	−8.84815	−	5.10848i	−0.285128	−	0.164619i
$964$	−6.42089	−	28.8609i	−0.206803	−	0.929546i
$965$			0.836660i			0.0269330i
$966$	−9.14238	+	24.3302i	−0.294151	+	0.782811i
$967$	−8.89648			−0.286092			−0.143046	−	0.989716i	$-0.545690\pi$
$967$	−8.89648			−0.286092			−0.143046	+	0.989716i	$0.545690\pi$
$968$	−5.48853	+	0.365904i	−0.176408	+	0.0117606i
$969$	−0.836999	+	1.44972i	−0.0268883	+	0.0465719i
$970$	−0.253325	+	0.315878i	−0.00813378	+	0.0101422i
$971$	52.8744	−	30.5270i	1.69682	−	0.979659i	0.748074	−	0.663615i	$-0.230979\pi$
$971$	52.8744	−	30.5270i	1.69682	−	0.979659i	0.948745	−	0.316044i	$-0.102355\pi$
$972$	0.599989	−	1.90788i	0.0192447	−	0.0611953i
$973$	9.19012	−	10.2549i	0.294622	−	0.328757i
$974$	1.31539	−	8.56744i	0.0421477	−	0.274519i
$975$	−15.7286	−	27.2427i	−0.503718	−	0.872465i
$976$	−2.16161	−	4.61759i	−0.0691914	−	0.147805i
$977$	−23.8132	+	41.2456i	−0.761851	+	1.31956i	0.180045	+	0.983658i	$0.442376\pi$
$977$	−23.8132	+	41.2456i	−0.761851	+	1.31956i	−0.941896	+	0.335906i	$0.890958\pi$
$978$	20.1029	−	7.82624i	0.642821	−	0.250256i
$979$			53.1205i			1.69774i
$980$	−0.637867	−	0.126171i	−0.0203759	−	0.00403037i
$981$		−	11.6943i		−	0.373370i
$982$	10.5326	+	27.0546i	0.336107	+	0.863346i
$983$	−6.89129	+	11.9361i	−0.219798	+	0.380701i	−0.954746	−	0.297422i	$-0.903873\pi$
$983$	−6.89129	+	11.9361i	−0.219798	+	0.380701i	0.734948	+	0.678123i	$0.237207\pi$
$984$	23.9425	−	16.0367i	0.763260	−	0.511230i
$985$	0.0859417	+	0.148855i	0.00273833	+	0.00474293i
$986$	−1.65662	−	0.254346i	−0.0527576	−	0.00810003i
$987$	8.20946	−	9.16061i	0.261310	−	0.291585i
$988$	−38.9411	−	12.2462i	−1.23888	−	0.389602i
$989$	54.8737	−	31.6813i	1.74488	−	1.00741i
$990$	−0.184357	−	0.147849i	−0.00585924	−	0.00469895i
$991$	−4.32034	+	7.48305i	−0.137240	+	0.237707i	−0.926451	−	0.376415i	$-0.877157\pi$
$991$	−4.32034	+	7.48305i	−0.137240	+	0.237707i	0.789211	+	0.614122i	$0.210490\pi$
$992$	−11.5948	−	2.81432i	−0.368134	−	0.0893546i
$993$	−7.32984			−0.232605
$994$	41.4420	+	15.5724i	1.31446	+	0.493926i
$995$			0.0819463i			0.00259787i
$996$	3.58340	+	16.1068i	0.113544	+	0.510364i
$997$	38.0017	+	21.9403i	1.20353	+	0.694856i	0.961337	−	0.275374i	$-0.0888016\pi$
$997$	38.0017	+	21.9403i	1.20353	+	0.694856i	0.242188	+	0.970229i	$0.422135\pi$
$998$	−9.78683	+	12.2035i	−0.309797	+	0.386294i
$999$	−0.650790	−	1.12720i	−0.0205901	−	0.0356631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.bc.a.109.3	yes	32
3.2	odd	2		504.2.cj.e.109.14		32
4.3	odd	2		672.2.bk.a.529.13		32
7.2	even	3	inner	168.2.bc.a.37.14	yes	32
7.3	odd	6		1176.2.c.f.589.9		16
7.4	even	3		1176.2.c.e.589.9		16
8.3	odd	2		672.2.bk.a.529.4		32
8.5	even	2	inner	168.2.bc.a.109.14	yes	32
12.11	even	2		2016.2.cr.e.1873.9		32
21.2	odd	6		504.2.cj.e.37.3		32
24.5	odd	2		504.2.cj.e.109.3		32
24.11	even	2		2016.2.cr.e.1873.8		32
28.3	even	6		4704.2.c.f.2353.12		16
28.11	odd	6		4704.2.c.e.2353.5		16
28.23	odd	6		672.2.bk.a.625.4		32
56.3	even	6		4704.2.c.f.2353.5		16
56.11	odd	6		4704.2.c.e.2353.12		16
56.37	even	6	inner	168.2.bc.a.37.3	✓	32
56.45	odd	6		1176.2.c.f.589.10		16
56.51	odd	6		672.2.bk.a.625.13		32
56.53	even	6		1176.2.c.e.589.10		16
84.23	even	6		2016.2.cr.e.1297.8		32
168.107	even	6		2016.2.cr.e.1297.9		32
168.149	odd	6		504.2.cj.e.37.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.3	✓	32	56.37	even	6	inner
168.2.bc.a.37.14	yes	32	7.2	even	3	inner
168.2.bc.a.109.3	yes	32	1.1	even	1	trivial
168.2.bc.a.109.14	yes	32	8.5	even	2	inner
504.2.cj.e.37.3		32	21.2	odd	6
504.2.cj.e.37.14		32	168.149	odd	6
504.2.cj.e.109.3		32	24.5	odd	2
504.2.cj.e.109.14		32	3.2	odd	2
672.2.bk.a.529.4		32	8.3	odd	2
672.2.bk.a.529.13		32	4.3	odd	2
672.2.bk.a.625.4		32	28.23	odd	6
672.2.bk.a.625.13		32	56.51	odd	6
1176.2.c.e.589.9		16	7.4	even	3
1176.2.c.e.589.10		16	56.53	even	6
1176.2.c.f.589.9		16	7.3	odd	6
1176.2.c.f.589.10		16	56.45	odd	6
2016.2.cr.e.1297.8		32	84.23	even	6
2016.2.cr.e.1297.9		32	168.107	even	6
2016.2.cr.e.1873.8		32	24.11	even	2
2016.2.cr.e.1873.9		32	12.11	even	2
4704.2.c.e.2353.5		16	28.11	odd	6
4704.2.c.e.2353.12		16	56.11	odd	6
4704.2.c.f.2353.5		16	56.3	even	6
4704.2.c.f.2353.12		16	28.3	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31787 + 0.513056i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.47355 - 1.35228i) q^{4} +(-0.0402223 + 0.0232224i) q^{5} +(1.39783 + 0.214614i) q^{6} +(-1.97032 - 1.76574i) q^{7} +(-1.24814 + 2.53814i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.0410933 - 0.0512403i) q^{10} +(-3.11586 - 1.79894i) q^{11} +(-1.95227 + 0.434335i) q^{12} -6.29415i q^{13} +(3.50254 + 1.31613i) q^{14} +0.0464447 q^{15} +(0.342679 - 3.98529i) q^{16} +(0.258110 - 0.447060i) q^{17} +(-1.10325 - 0.884778i) q^{18} +(2.80834 - 1.62140i) q^{19} +(-0.0278663 + 0.0886110i) q^{20} +(0.823477 + 2.51434i) q^{21} +(5.02925 + 0.772156i) q^{22} +(-3.47322 - 6.01578i) q^{23} +(2.34999 - 1.57402i) q^{24} +(-2.49892 + 4.32826i) q^{25} +(3.22925 + 8.29485i) q^{26} -1.00000i q^{27} +(-5.29113 + 0.0625230i) q^{28} +2.29579i q^{29} +(-0.0612079 + 0.0238287i) q^{30} +(-1.05460 + 1.82662i) q^{31} +(1.59308 + 5.42790i) q^{32} +(1.79894 + 3.11586i) q^{33} +(-0.110788 + 0.721591i) q^{34} +(0.120255 + 0.0252667i) q^{35} +(1.90788 + 0.599989i) q^{36} +(1.12720 - 0.650790i) q^{37} +(-2.86915 + 3.57762i) q^{38} +(-3.14708 + 5.45089i) q^{39} +(-0.00873835 - 0.131074i) q^{40} +10.1883 q^{41} +(-2.37523 - 2.89107i) q^{42} +9.12162i q^{43} +(-7.02404 + 1.56269i) q^{44} +(-0.0402223 - 0.0232224i) q^{45} +(7.66367 + 6.14605i) q^{46} +(-2.32465 - 4.02641i) q^{47} +(-2.28942 + 3.28003i) q^{48} +(0.764321 + 6.95815i) q^{49} +(1.07261 - 6.98616i) q^{50} +(-0.447060 + 0.258110i) q^{51} +(-8.51145 - 9.27472i) q^{52} +(-4.91727 - 2.83899i) q^{53} +(0.513056 + 1.31787i) q^{54} +0.167103 q^{55} +(6.94093 - 2.79705i) q^{56} -3.24279 q^{57} +(-1.17787 - 3.02555i) q^{58} +(1.42910 + 0.825090i) q^{59} +(0.0684384 - 0.0628062i) q^{60} +(1.10386 - 0.637312i) q^{61} +(0.452663 - 2.94831i) q^{62} +(0.544016 - 2.58922i) q^{63} +(-4.88428 - 6.33591i) q^{64} +(0.146165 + 0.253165i) q^{65} +(-3.96938 - 3.18333i) q^{66} +(6.72366 + 3.88191i) q^{67} +(-0.224213 - 1.00780i) q^{68} +6.94643i q^{69} +(-0.171444 + 0.0283997i) q^{70} +11.8320 q^{71} +(-2.82216 + 0.188145i) q^{72} +(5.57028 - 9.64802i) q^{73} +(-1.15161 + 1.43597i) q^{74} +(4.32826 - 2.49892i) q^{75} +(1.94564 - 6.18687i) q^{76} +(2.96278 + 9.04630i) q^{77} +(1.35081 - 8.79818i) q^{78} +(-2.75086 - 4.76463i) q^{79} +(0.0787646 + 0.168255i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.4269 + 5.22719i) q^{82} -8.25030i q^{83} +(4.61352 + 2.59142i) q^{84} +0.0239757i q^{85} +(-4.67990 - 12.0211i) q^{86} +(1.14789 - 1.98821i) q^{87} +(8.45501 - 5.66315i) q^{88} +(-7.38218 - 12.7863i) q^{89} +(0.0649220 + 0.00996767i) q^{90} +(-11.1138 + 12.4015i) q^{91} +(-13.2530 - 4.16778i) q^{92} +(1.82662 - 1.05460i) q^{93} +(5.12936 + 4.11360i) q^{94} +(-0.0753053 + 0.130433i) q^{95} +(1.33431 - 5.49724i) q^{96} -6.16464 q^{97} +(-4.57719 - 8.77777i) q^{98} -3.59789i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9} + 6 q^{10} + 22 q^{14} - 10 q^{16} - 2 q^{18} - 40 q^{20} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 16 q^{25} + 6 q^{26} - 26 q^{28} - 8 q^{30} - 24 q^{31} - 8 q^{32}+ \cdots - 64 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 + 16 * q^9 + 6 * q^10 + 22 * q^14 - 10 * q^16 - 2 * q^18 - 40 * q^20 - 12 * q^22 - 8 * q^23 - 6 * q^24 + 16 * q^25 + 6 * q^26 - 26 * q^28 - 8 * q^30 - 24 * q^31 - 8 * q^32 - 24 * q^34 - 4 * q^36 - 26 * q^38 - 6 * q^40 - 4 * q^42 + 20 * q^44 + 16 * q^46 - 24 * q^47 - 16 * q^48 + 8 * q^49 + 52 * q^50 + 44 * q^52 - 64 * q^55 + 40 * q^56 - 16 * q^57 + 34 * q^58 - 22 * q^60 + 100 * q^62 - 20 * q^64 + 12 * q^66 + 16 * q^68 + 38 * q^70 - 80 * q^71 - 8 * q^72 + 8 * q^73 + 10 * q^74 - 32 * q^76 + 12 * q^78 + 8 * q^79 - 56 * q^80 - 16 * q^81 - 16 * q^84 - 22 * q^86 + 24 * q^87 + 50 * q^88 + 12 * q^90 + 64 * q^92 - 48 * q^94 + 24 * q^95 + 10 * q^96 - 48 * q^97 - 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more