LMFDB - Embedded newform 168.4.t.a.19.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.t (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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	168.19
Dual form			168.4.t.a.115.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.31785 + 1.62097i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(2.74489 - 7.51436i) q^{4} +(1.39001 - 2.40757i) q^{5} +(3.59050 - 7.68819i) q^{6} +(-15.3983 + 10.2904i) q^{7} +(5.81831 + 21.8666i) q^{8} +(4.50000 - 7.79423i) q^{9} +(0.680764 + 7.83358i) q^{10} +(-24.4292 - 42.3125i) q^{11} +(4.14009 + 23.6402i) q^{12} +34.3223 q^{13} +(19.0106 - 48.8118i) q^{14} +8.34008i q^{15} +(-48.9311 - 41.2522i) q^{16} +(63.6655 - 36.7573i) q^{17} +(2.20389 + 25.3603i) q^{18} +(97.0462 + 56.0297i) q^{19} +(-14.2759 - 17.0536i) q^{20} +(24.5704 - 49.8327i) q^{21} +(125.211 + 58.4753i) q^{22} +(-50.3870 - 29.0910i) q^{23} +(-47.9163 - 48.0836i) q^{24} +(58.6357 + 101.560i) q^{25} +(-79.5540 + 55.6355i) q^{26} +27.0000i q^{27} +(35.0588 + 143.954i) q^{28} +251.752i q^{29} +(-13.5190 - 19.3311i) q^{30} +(15.6722 + 27.1450i) q^{31} +(180.284 + 16.3006i) q^{32} +(126.938 + 73.2875i) q^{33} +(-87.9847 + 188.398i) q^{34} +(3.37098 + 51.3763i) q^{35} +(-46.2166 - 55.2089i) q^{36} +(232.520 + 134.245i) q^{37} +(-315.762 + 27.4407i) q^{38} +(-89.1719 + 51.4834i) q^{39} +(60.7329 + 16.3868i) q^{40} -368.384i q^{41} +(23.8267 + 155.333i) q^{42} +466.118 q^{43} +(-385.007 + 67.4260i) q^{44} +(-12.5101 - 21.6682i) q^{45} +(163.945 - 14.2474i) q^{46} +(-119.025 + 206.158i) q^{47} +(189.005 + 33.7797i) q^{48} +(131.216 - 316.909i) q^{49} +(-300.535 - 140.354i) q^{50} +(-110.272 + 190.996i) q^{51} +(94.2109 - 257.910i) q^{52} +(647.569 - 373.874i) q^{53} +(-43.7663 - 62.5821i) q^{54} -135.827 q^{55} +(-314.608 - 276.836i) q^{56} -336.178 q^{57} +(-408.084 - 583.525i) q^{58} +(160.721 - 92.7921i) q^{59} +(62.6703 + 22.8926i) q^{60} +(-235.308 + 407.566i) q^{61} +(-80.3270 - 37.5139i) q^{62} +(10.9131 + 166.325i) q^{63} +(-444.295 + 254.453i) q^{64} +(47.7084 - 82.6334i) q^{65} +(-413.020 + 35.8928i) q^{66} +(-82.9694 - 143.707i) q^{67} +(-101.452 - 579.300i) q^{68} +174.546 q^{69} +(-91.0931 - 113.619i) q^{70} +218.529i q^{71} +(196.616 + 53.0504i) q^{72} +(538.309 - 310.793i) q^{73} +(-756.556 + 65.7472i) q^{74} +(-304.680 - 175.907i) q^{75} +(687.408 - 575.445i) q^{76} +(811.580 + 400.157i) q^{77} +(123.234 - 263.876i) q^{78} +(-376.553 - 217.403i) q^{79} +(-167.333 + 60.4641i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(597.140 + 853.860i) q^{82} -344.173i q^{83} +(-307.017 - 321.416i) q^{84} -204.372i q^{85} +(-1080.39 + 755.565i) q^{86} +(-377.628 - 654.072i) q^{87} +(783.094 - 780.369i) q^{88} +(-950.113 - 548.548i) q^{89} +(64.1201 + 29.9451i) q^{90} +(-528.505 + 353.189i) q^{91} +(-356.907 + 298.775i) q^{92} +(-81.4349 - 47.0165i) q^{93} +(-58.2930 - 670.780i) q^{94} +(269.791 - 155.764i) q^{95} +(-492.842 + 228.076i) q^{96} +388.550i q^{97} +(209.561 + 947.247i) q^{98} -439.725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) $ 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Character values

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

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$

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 $

$2$	−2.31785	+	1.62097i	−0.819485	+	0.573100i
$2$	−2.31785	+	1.62097i	−0.819485	+	0.573100i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$4$	2.74489	−	7.51436i	0.343112	−	0.939295i
$5$	1.39001	−	2.40757i	0.124327	−	0.215340i	−0.797143	−	0.603791i	$-0.793656\pi$
$5$	1.39001	−	2.40757i	0.124327	−	0.215340i	0.921470	+	0.388451i	$0.126990\pi$
$6$	3.59050	−	7.68819i	0.244303	−	0.523115i
$7$	−15.3983	+	10.2904i	−0.831431	+	0.555628i
$7$	−15.3983	+	10.2904i	−0.831431	+	0.555628i
$8$	5.81831	+	21.8666i	0.257135	+	0.966375i
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$	0.680764	+	7.83358i	0.0215276	+	0.247719i
$11$	−24.4292	−	42.3125i	−0.669606	−	1.15979i	−0.978014	−	0.208538i	$-0.933130\pi$
$11$	−24.4292	−	42.3125i	−0.669606	−	1.15979i	0.308408	−	0.951254i	$-0.400204\pi$
$12$	4.14009	+	23.6402i	0.0995952	+	0.568695i
$13$	34.3223			0.732253			0.366126	−	0.930565i	$-0.380684\pi$
$13$	34.3223			0.732253			0.366126	+	0.930565i	$0.380684\pi$
$14$	19.0106	−	48.8118i	0.362914	−	0.931822i
$15$			8.34008i			0.143560i
$16$	−48.9311	−	41.2522i	−0.764549	−	0.644566i
$17$	63.6655	−	36.7573i	0.908303	−	0.524409i	0.0284180	−	0.999596i	$-0.490953\pi$
$17$	63.6655	−	36.7573i	0.908303	−	0.524409i	0.879885	+	0.475187i	$0.157620\pi$
$18$	2.20389	+	25.3603i	0.0288590	+	0.332082i
$19$	97.0462	+	56.0297i	1.17179	+	0.676531i	0.954100	−	0.299488i	$-0.0968159\pi$
$19$	97.0462	+	56.0297i	1.17179	+	0.676531i	0.217686	+	0.976019i	$0.430149\pi$
$20$	−14.2759	−	17.0536i	−0.159610	−	0.190665i
$21$	24.5704	−	49.8327i	0.255319	−	0.517828i
$22$	125.211	+	58.4753i	1.21341	+	0.566680i
$23$	−50.3870	−	29.0910i	−0.456801	−	0.263734i	0.253897	−	0.967231i	$-0.418288\pi$
$23$	−50.3870	−	29.0910i	−0.456801	−	0.263734i	−0.710698	+	0.703497i	$0.751621\pi$
$24$	−47.9163	−	48.0836i	−0.407536	−	0.408959i
$25$	58.6357	+	101.560i	0.469086	+	0.812480i
$26$	−79.5540	+	55.6355i	−0.600070	+	0.419654i
$27$			27.0000i			0.192450i
$28$	35.0588	+	143.954i	0.236625	+	0.971601i
$29$			251.752i			1.61204i	0.591887	+	0.806021i	$0.298383\pi$
$29$			251.752i			1.61204i	−0.591887	+	0.806021i	$0.701617\pi$
$30$	−13.5190	−	19.3311i	−0.0822743	−	0.117645i
$31$	15.6722	+	27.1450i	0.0908001	+	0.157270i	0.907848	−	0.419299i	$-0.137724\pi$
$31$	15.6722	+	27.1450i	0.0908001	+	0.157270i	−0.817048	+	0.576570i	$0.804391\pi$
$32$	180.284	+	16.3006i	0.995937	+	0.0900489i
$33$	126.938	+	73.2875i	0.669606	+	0.386597i
$34$	−87.9847	+	188.398i	−0.443802	+	0.950294i
$35$	3.37098	+	51.3763i	0.0162800	+	0.248120i
$36$	−46.2166	−	55.2089i	−0.213966	−	0.255597i
$37$	232.520	+	134.245i	1.03314	+	0.596482i	0.917882	−	0.396854i	$-0.129898\pi$
$37$	232.520	+	134.245i	1.03314	+	0.596482i	0.115255	+	0.993336i	$0.463232\pi$
$38$	−315.762	+	27.4407i	−1.34798	+	0.117144i
$39$	−89.1719	+	51.4834i	−0.366126	+	0.211383i
$40$	60.7329	+	16.3868i	0.240068	+	0.0647746i
$41$		−	368.384i		−	1.40322i	−0.712563	−	0.701608i	$-0.752466\pi$
$41$		−	368.384i		−	1.40322i	0.712563	−	0.701608i	$-0.247534\pi$
$42$	23.8267	+	155.333i	0.0875368	+	0.570676i
$43$	466.118			1.65308			0.826539	−	0.562879i	$-0.190306\pi$
$43$	466.118			1.65308			0.826539	+	0.562879i	$0.190306\pi$
$44$	−385.007	+	67.4260i	−1.31914	+	0.231019i
$45$	−12.5101	−	21.6682i	−0.0414422	−	0.0717800i
$46$	163.945	−	14.2474i	0.525488	−	0.0456666i
$47$	−119.025	+	206.158i	−0.369396	+	0.639812i	−0.989471	−	0.144730i	$-0.953769\pi$
$47$	−119.025	+	206.158i	−0.369396	+	0.639812i	0.620075	+	0.784542i	$0.287102\pi$
$48$	189.005	+	33.7797i	0.568345	+	0.101577i
$49$	131.216	−	316.909i	0.382555	−	0.923933i
$50$	−300.535	−	140.354i	−0.850042	−	0.396982i
$51$	−110.272	+	190.996i	−0.302768	+	0.524409i
$52$	94.2109	−	257.910i	0.251244	−	0.687801i
$53$	647.569	−	373.874i	1.67831	−	0.968973i	0.715572	−	0.698539i	$-0.246166\pi$
$53$	647.569	−	373.874i	1.67831	−	0.968973i	0.962738	−	0.270435i	$-0.0871674\pi$
$54$	−43.7663	−	62.5821i	−0.110293	−	0.157710i
$55$	−135.827			−0.332999
$56$	−314.608	−	276.836i	−0.750736	−	0.660603i
$57$	−336.178			−0.781191
$58$	−408.084	−	583.525i	−0.923862	−	1.32104i
$59$	160.721	−	92.7921i	0.354645	−	0.204754i	−0.312084	−	0.950054i	$-0.601027\pi$
$59$	160.721	−	92.7921i	0.354645	−	0.204754i	0.666729	+	0.745300i	$0.267694\pi$
$60$	62.6703	+	22.8926i	0.134845	+	0.0492571i
$61$	−235.308	+	407.566i	−0.493904	+	0.855467i	−0.999975	−	0.00702487i	$-0.997764\pi$
$61$	−235.308	+	407.566i	−0.493904	+	0.855467i	0.506071	+	0.862492i	$0.331097\pi$
$62$	−80.3270	−	37.5139i	−0.164541	−	0.0768431i
$63$	10.9131	+	166.325i	0.0218242	+	0.332618i
$64$	−444.295	+	254.453i	−0.867763	+	0.496978i
$65$	47.7084	−	82.6334i	0.0910384	−	0.157683i
$66$	−413.020	+	35.8928i	−0.770291	+	0.0669409i
$67$	−82.9694	−	143.707i	−0.151288	−	0.262039i	0.780413	−	0.625264i	$-0.215009\pi$
$67$	−82.9694	−	143.707i	−0.151288	−	0.262039i	−0.931701	+	0.363225i	$0.881676\pi$
$68$	−101.452	−	579.300i	−0.180925	−	1.03309i
$69$	174.546			0.304534
$70$	−91.0931	−	113.619i	−0.155539	−	0.194000i
$71$			218.529i			0.365276i	0.983180	+	0.182638i	$0.0584636\pi$
$71$			218.529i			0.365276i	−0.983180	+	0.182638i	$0.941536\pi$
$72$	196.616	+	53.0504i	0.321824	+	0.0868340i
$73$	538.309	−	310.793i	0.863073	−	0.498295i	−0.00196738	−	0.999998i	$-0.500626\pi$
$73$	538.309	−	310.793i	0.863073	−	0.498295i	0.865040	+	0.501703i	$0.167293\pi$
$74$	−756.556	+	65.7472i	−1.18848	+	0.103283i
$75$	−304.680	−	175.907i	−0.469086	−	0.270827i
$76$	687.408	−	575.445i	1.03752	−	0.868527i
$77$	811.580	+	400.157i	1.20114	+	0.592235i
$78$	123.234	−	263.876i	0.178891	−	0.383052i
$79$	−376.553	−	217.403i	−0.536272	−	0.309617i	0.207295	−	0.978279i	$-0.433534\pi$
$79$	−376.553	−	217.403i	−0.536272	−	0.309617i	−0.743567	+	0.668662i	$0.766867\pi$
$80$	−167.333	+	60.4641i	−0.233855	+	0.0845012i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	597.140	+	853.860i	0.804184	+	1.14992i
$83$		−	344.173i		−	0.455155i	−0.973760	−	0.227577i	$-0.926920\pi$
$83$		−	344.173i		−	0.455155i	0.973760	−	0.227577i	$-0.0730805\pi$
$84$	−307.017	−	321.416i	−0.398790	−	0.417493i
$85$		−	204.372i		−	0.260792i
$86$	−1080.39	+	755.565i	−1.35467	+	0.947380i
$87$	−377.628	−	654.072i	−0.465357	−	0.806021i
$88$	783.094	−	780.369i	0.948615	−	0.945314i
$89$	−950.113	−	548.548i	−1.13159	−	0.653326i	−0.187258	−	0.982311i	$-0.559960\pi$
$89$	−950.113	−	548.548i	−1.13159	−	0.653326i	−0.944335	+	0.328985i	$0.893293\pi$
$90$	64.1201	+	29.9451i	0.0750984	+	0.0350721i
$91$	−528.505	+	353.189i	−0.608817	+	0.406860i
$92$	−356.907	+	298.775i	−0.404458	+	0.338580i
$93$	−81.4349	−	47.0165i	−0.0908001	−	0.0524234i
$94$	−58.2930	−	670.780i	−0.0639624	−	0.736017i
$95$	269.791	−	155.764i	0.291368	−	0.168222i
$96$	−492.842	+	228.076i	−0.523964	+	0.242478i
$97$			388.550i			0.406714i	0.979105	+	0.203357i	$0.0651852\pi$
$97$			388.550i			0.406714i	−0.979105	+	0.203357i	$0.934815\pi$
$98$	209.561	+	947.247i	0.216009	+	0.976391i
$99$	−439.725			−0.446404
$100$	924.107	−	161.838i	0.924107	−	0.161838i
$101$	−541.979	−	938.736i	−0.533950	−	0.924828i	−0.999213	−	0.0396562i	$-0.987374\pi$
$101$	−541.979	−	938.736i	−0.533950	−	0.924828i	0.465263	−	0.885172i	$-0.345960\pi$
$102$	−54.0060	−	621.449i	−0.0524254	−	0.603261i
$103$	−505.252	+	875.122i	−0.483339	+	0.837168i	−0.999817	−	0.0191324i	$-0.993910\pi$
$103$	−505.252	+	875.122i	−0.483339	+	0.837168i	0.516478	+	0.856301i	$0.327243\pi$
$104$	199.697	+	750.510i	0.188288	+	0.707631i
$105$	−85.8226	−	128.423i	−0.0797660	−	0.119360i
$106$	−894.931	+	1916.28i	−0.820032	+	1.75590i
$107$	−151.963	+	263.208i	−0.137297	+	0.237806i	−0.926473	−	0.376362i	$-0.877175\pi$
$107$	−151.963	+	263.208i	−0.137297	+	0.237806i	0.789175	+	0.614168i	$0.210508\pi$
$108$	202.888	+	74.1121i	0.180767	+	0.0660319i
$109$	1246.64	−	719.749i	1.09547	−	0.632472i	0.160445	−	0.987045i	$-0.448707\pi$
$109$	1246.64	−	719.749i	1.09547	−	0.632472i	0.935028	+	0.354573i	$0.115374\pi$
$110$	314.828	−	220.173i	0.272888	−	0.190842i
$111$	−805.473			−0.688758
$112$	1177.96	+	131.695i	0.993808	+	0.111107i
$113$	917.615			0.763912			0.381956	−	0.924181i	$-0.375251\pi$
$113$	917.615			0.763912			0.381956	+	0.924181i	$0.375251\pi$
$114$	779.211	−	544.935i	0.640174	−	0.447701i
$115$	−140.077	+	80.8737i	−0.113585	+	0.0655783i
$116$	1891.76	+	691.033i	1.51418	+	0.553111i
$117$	154.450	−	267.516i	0.122042	−	0.211383i
$118$	−222.113	+	475.602i	−0.173281	+	0.371040i
$119$	−602.095	+	1221.14i	−0.463815	+	0.940688i
$120$	−182.369	+	48.5252i	−0.138733	+	0.0369143i
$121$	−528.067	+	914.639i	−0.396745	+	0.687182i
$122$	−115.243	−	1326.11i	−0.0855215	−	0.984099i
$123$	552.576	+	957.089i	0.405074	+	0.701608i
$124$	246.995	−	43.2561i	0.178878	−	0.0313267i
$125$	673.521			0.481932
$126$	−294.903	−	367.826i	−0.208508	−	0.260068i
$127$		−	1302.33i		−	0.909943i	−0.890506	−	0.454972i	$-0.849649\pi$
$127$		−	1302.33i		−	0.909943i	0.890506	−	0.454972i	$-0.150351\pi$
$128$	617.349	−	1309.97i	0.426300	−	0.904582i
$129$	−1211.01	+	699.177i	−0.826539	+	0.477203i
$130$	23.3654	+	268.866i	0.0157637	+	0.181393i
$131$	1361.39	+	786.001i	0.907980	+	0.524223i	0.879781	−	0.475380i	$-0.157689\pi$
$131$	1361.39	+	786.001i	0.907980	+	0.524223i	0.0281997	+	0.999602i	$0.491023\pi$
$132$	899.138	−	752.688i	0.592878	−	0.496311i
$133$	−2070.91	+	135.880i	−1.35016	+	0.0885886i
$134$	425.256	+	198.601i	0.274153	+	0.128034i
$135$	65.0045	+	37.5304i	0.0414422	+	0.0239267i
$136$	1174.18	+	1178.28i	0.740332	+	0.742917i
$137$	−378.721	−	655.963i	−0.236177	−	0.409071i	0.723437	−	0.690390i	$-0.242561\pi$
$137$	−378.721	−	655.963i	−0.236177	−	0.409071i	−0.959614	+	0.281319i	$0.909228\pi$
$138$	−404.572	+	282.934i	−0.249561	+	0.174529i
$139$			742.727i			0.453218i	0.973986	+	0.226609i	$0.0727639\pi$
$139$			742.727i			0.453218i	−0.973986	+	0.226609i	$0.927236\pi$
$140$	395.313	+	115.692i	0.238643	+	0.0698410i
$141$		−	714.151i		−	0.426541i
$142$	−354.229	−	506.517i	−0.209340	−	0.299338i
$143$	−838.464	−	1452.26i	−0.490321	−	0.849260i
$144$	−541.719	+	195.745i	−0.313495	+	0.113279i
$145$	606.112	+	349.939i	0.347137	+	0.200420i
$146$	−743.935	+	1592.96i	−0.421702	+	0.902973i
$147$	134.454	+	1020.18i	0.0754391	+	0.572400i
$148$	1647.01	−	1378.75i	0.914753	−	0.765760i
$149$	2739.87	+	1581.87i	1.50644	+	0.869741i	0.999972	+	0.00748031i	$0.00238108\pi$
$149$	2739.87	+	1581.87i	1.50644	+	0.869741i	0.506464	+	0.862261i	$0.330952\pi$
$150$	991.345	−	86.1512i	0.539620	−	0.0468948i
$151$	1343.45	−	775.642i	0.724030	−	0.418019i	−0.0922041	−	0.995740i	$-0.529391\pi$
$151$	1343.45	−	775.642i	0.724030	−	0.418019i	0.816234	+	0.577721i	$0.196058\pi$
$152$	−660.532	+	2448.07i	−0.352475	+	1.30635i
$153$		−	661.631i		−	0.349606i
$154$	−2529.77	+	388.045i	−1.32373	+	0.203049i
$155$	87.1380			0.0451554
$156$	142.097	+	811.386i	0.0729288	+	0.416428i
$157$	565.944	+	980.243i	0.287689	+	0.498293i	0.973258	−	0.229716i	$-0.0737796\pi$
$157$	565.944	+	980.243i	0.287689	+	0.498293i	−0.685568	+	0.728008i	$0.740446\pi$
$158$	1225.20	−	106.474i	0.616908	−	0.0536114i
$159$	−1121.62	+	1942.71i	−0.559437	+	0.968973i
$160$	289.842	−	411.389i	0.143213	−	0.203270i
$161$	1075.23	−	70.5498i	0.526337	−	0.0345348i
$162$	207.581	+	96.9435i	0.100674	+	0.0470161i
$163$	−677.994	+	1174.32i	−0.325795	+	0.564293i	−0.981673	−	0.190574i	$-0.938965\pi$
$163$	−677.994	+	1174.32i	−0.325795	+	0.564293i	0.655878	+	0.754867i	$0.272299\pi$
$164$	−2768.17	−	1011.17i	−1.31803	−	0.481460i
$165$	352.890	−	203.741i	0.166500	−	0.0961286i
$166$	557.894	+	797.742i	0.260849	+	0.372993i
$167$	−2337.59			−1.08316			−0.541582	−	0.840648i	$-0.682175\pi$
$167$	−2337.59			−1.08316			−0.541582	+	0.840648i	$0.682175\pi$
$168$	1232.63	+	247.329i	0.566067	+	0.113583i
$169$	−1018.98			−0.463806
$170$	331.282	+	473.705i	0.149460	+	0.213715i
$171$	873.416	−	504.267i	0.390595	−	0.225510i
$172$	1279.44	−	3502.58i	0.567190	−	1.55273i
$173$	412.608	−	714.658i	0.181330	−	0.314072i	−0.761004	−	0.648747i	$-0.775293\pi$
$173$	412.608	−	714.658i	0.181330	−	0.314072i	0.942334	+	0.334675i	$0.108627\pi$
$174$	1935.52	+	903.917i	0.843284	+	0.393826i
$175$	−1947.98	−	960.470i	−0.841449	−	0.414884i
$176$	−550.140	+	3078.16i	−0.235616	+	1.31832i
$177$	−278.376	+	482.162i	−0.118215	+	0.204754i
$178$	3091.41	−	268.653i	1.30175	−	0.113126i
$179$	318.142	+	551.039i	0.132844	+	0.230093i	0.924772	−	0.380522i	$-0.124256\pi$
$179$	318.142	+	551.039i	0.132844	+	0.230093i	−0.791928	+	0.610615i	$0.790922\pi$
$180$	−197.161	+	34.5287i	−0.0816418	+	0.0142979i
$181$	−3865.63			−1.58746			−0.793730	−	0.608271i	$-0.791864\pi$
$181$	−3865.63			−1.58746			−0.793730	+	0.608271i	$0.791864\pi$
$182$	652.487	−	1675.33i	0.265745	−	0.682329i
$183$		−	1411.85i		−	0.570311i
$184$	342.953	−	1271.05i	0.137407	−	0.509257i
$185$	646.412	−	373.206i	0.256893	−	0.148317i
$186$	264.967	−	23.0265i	0.104453	−	0.00907733i
$187$	−3110.59	−	1795.90i	−1.21641	−	0.702295i
$188$	1222.43	+	1460.28i	0.474228	+	0.566498i
$189$	−277.840	−	415.755i	−0.106931	−	0.160009i
$190$	−372.847	+	798.362i	−0.142364	+	0.304838i
$191$	2768.25	+	1598.25i	1.04871	+	0.605474i	0.922288	−	0.386503i	$-0.126317\pi$
$191$	2768.25	+	1598.25i	1.04871	+	0.605474i	0.126423	+	0.991976i	$0.459650\pi$
$192$	772.632	−	1327.53i	0.290416	−	0.498991i
$193$	1062.11	+	1839.62i	0.396125	+	0.686109i	0.993244	−	0.116044i	$-0.0370213\pi$
$193$	1062.11	+	1839.62i	0.396125	+	0.686109i	−0.597119	+	0.802153i	$0.703688\pi$
$194$	−629.829	−	900.602i	−0.233088	−	0.333296i
$195$			286.250i			0.105122i
$196$	−2021.19	−	1855.89i	−0.736586	−	0.676344i
$197$			490.260i			0.177307i	0.996063	+	0.0886537i	$0.0282564\pi$
$197$			490.260i			0.177307i	−0.996063	+	0.0886537i	$0.971744\pi$
$198$	1019.22	−	712.782i	0.365821	−	0.255834i
$199$	−1097.83	−	1901.50i	−0.391071	−	0.677354i	0.601520	−	0.798858i	$-0.294562\pi$
$199$	−1097.83	−	1901.50i	−0.391071	−	0.677354i	−0.992591	+	0.121503i	$0.961229\pi$
$200$	−1879.61	+	1873.07i	−0.664543	+	0.662230i
$201$	431.122	+	248.908i	0.151288	+	0.0873464i
$202$	2777.89	+	1297.32i	0.967584	+	0.451876i
$203$	−2590.63	−	3876.56i	−0.895696	−	1.34030i
$204$	1132.53	+	1352.89i	0.388691	+	0.464319i
$205$	−886.911	−	512.058i	−0.302169	−	0.174457i
$206$	−247.449	−	2847.40i	−0.0836922	−	0.963049i
$207$	−453.483	+	261.819i	−0.152267	+	0.0879114i
$208$	−1679.43	−	1415.87i	−0.559843	−	0.471985i
$209$		−	5475.03i		−	1.81204i
$210$	407.095	+	158.550i	0.133772	+	0.0521000i
$211$	172.498			0.0562808			0.0281404	−	0.999604i	$-0.491041\pi$
$211$	172.498			0.0562808			0.0281404	+	0.999604i	$0.491041\pi$
$212$	−1031.92	−	5892.31i	−0.334303	−	1.90889i
$213$	−327.793	−	567.754i	−0.105446	−	0.182638i
$214$	−74.4244	−	856.405i	−0.0237736	−	0.273564i
$215$	647.910	−	1122.21i	0.205522	−	0.355974i
$216$	−590.398	+	157.094i	−0.185979	+	0.0494857i
$217$	−520.657	−	256.714i	−0.162878	−	0.0803083i
$218$	−1722.84	+	3689.04i	−0.535254	+	1.14612i
$219$	−932.379	+	1614.93i	−0.287691	+	0.498295i
$220$	−372.832	+	1020.66i	−0.114256	+	0.312784i
$221$	2185.14	−	1261.59i	0.665107	−	0.384000i
$222$	1866.97	−	1305.65i	0.564427	−	0.394727i
$223$	5228.62			1.57011			0.785054	−	0.619427i	$-0.212635\pi$
$223$	5228.62			1.57011			0.785054	+	0.619427i	$0.212635\pi$
$224$	−2943.81	+	1604.19i	−0.878087	+	0.478501i
$225$	1055.44			0.312724
$226$	−2126.90	+	1487.43i	−0.626014	+	0.437798i
$227$	1776.90	−	1025.89i	0.519545	−	0.299959i	−0.217204	−	0.976126i	$-0.569694\pi$
$227$	1776.90	−	1025.89i	0.519545	−	0.299959i	0.736748	+	0.676167i	$0.236360\pi$
$228$	−922.773	+	2526.16i	−0.268036	+	0.733768i
$229$	439.472	−	761.188i	0.126817	−	0.219654i	−0.795625	−	0.605790i	$-0.792857\pi$
$229$	439.472	−	761.188i	0.126817	−	0.219654i	0.922442	+	0.386136i	$0.126191\pi$
$230$	193.585	−	414.515i	0.0554982	−	0.118836i
$231$	−2708.78	+	177.733i	−0.771535	+	0.0506231i
$232$	−5504.96	+	1464.77i	−1.55784	+	0.414513i
$233$	−1889.49	+	3272.69i	−0.531264	+	0.920175i	0.468071	+	0.883691i	$0.344949\pi$
$233$	−1889.49	+	3272.69i	−0.531264	+	0.920175i	−0.999334	+	0.0364844i	$0.988384\pi$
$234$	75.6425	+	870.422i	0.0211321	+	0.243168i
$235$	330.893	+	573.124i	0.0918514	+	0.159091i
$236$	−256.112	−	1462.42i	−0.0706418	−	0.403370i
$237$	1304.42			0.357515
$238$	−583.870	−	3806.41i	−0.159020	−	1.03669i
$239$			2779.78i			0.752339i	0.926551	+	0.376169i	$0.122759\pi$
$239$			2779.78i			0.752339i	−0.926551	+	0.376169i	$0.877241\pi$
$240$	344.047	−	408.089i	0.0925339	−	0.109759i
$241$	−6353.88	+	3668.42i	−1.69830	+	0.980512i	−0.750919	+	0.660394i	$0.770389\pi$
$241$	−6353.88	+	3668.42i	−1.69830	+	0.980512i	−0.947378	+	0.320118i	$0.896277\pi$
$242$	−258.623	−	2975.98i	−0.0686979	−	0.790510i
$243$	210.444	+	121.500i	0.0555556	+	0.0320750i
$244$	2416.70	+	2886.92i	0.634071	+	0.757442i
$245$	−580.589	−	756.420i	−0.151398	−	0.197249i
$246$	−2832.21	−	1322.68i	−0.734044	−	0.342810i
$247$	3330.85	+	1923.06i	0.858043	+	0.495391i
$248$	−502.382	+	500.634i	−0.128634	+	0.128187i
$249$	516.259	+	894.186i	0.131392	+	0.227577i
$250$	−1561.12	+	1091.76i	−0.394936	+	0.276196i
$251$			2889.68i			0.726672i	0.931658	+	0.363336i	$0.118362\pi$
$251$			2889.68i			0.726672i	−0.931658	+	0.363336i	$0.881638\pi$
$252$	1279.78	+	374.538i	0.319915	+	0.0936258i
$253$			2842.67i			0.706392i
$254$	2111.04	+	3018.60i	0.521489	+	0.745685i
$255$	306.559	+	530.975i	0.0752841	+	0.130396i
$256$	692.509	+	4037.03i	0.169070	+	0.985604i
$257$	332.025	+	191.695i	0.0805882	+	0.0465276i	0.539753	−	0.841824i	$-0.318518\pi$
$257$	332.025	+	191.695i	0.0805882	+	0.0465276i	−0.459164	+	0.888351i	$0.651851\pi$
$258$	1673.60	−	3583.61i	0.403851	−	0.864750i
$259$	−4961.85	+	325.564i	−1.19040	+	0.0781065i
$260$	−489.982	−	585.318i	−0.116875	−	0.139615i
$261$	1962.21	+	1132.89i	0.465357	+	0.268674i
$262$	−4429.60	+	384.947i	−1.04451	+	0.0907713i
$263$	−83.0238	+	47.9338i	−0.0194656	+	0.0112385i	−0.509701	−	0.860351i	$-0.670244\pi$
$263$	−83.0238	+	47.9338i	−0.0194656	+	0.0112385i	0.490236	+	0.871590i	$0.336911\pi$
$264$	−863.984	+	3202.10i	−0.201419	+	0.746499i
$265$		−	2078.76i		−	0.481876i
$266$	4579.82	−	3671.85i	1.05566	−	0.846374i
$267$	3291.29			0.754395
$268$	−1307.61	+	229.001i	−0.298041	+	0.0521957i
$269$	−856.535	−	1483.56i	−0.194141	−	0.336261i	0.752478	−	0.658618i	$-0.228858\pi$
$269$	−856.535	−	1483.56i	−0.194141	−	0.336261i	−0.946618	+	0.322356i	$0.895525\pi$
$270$	−211.507	+	18.3806i	−0.0476736	+	0.00414300i
$271$	4130.35	−	7153.97i	0.925833	−	1.60359i	0.135617	−	0.990761i	$-0.456698\pi$
$271$	4130.35	−	7153.97i	0.925833	−	1.60359i	0.790216	−	0.612829i	$-0.209968\pi$
$272$	−4631.54	−	827.767i	−1.03246	−	0.184525i
$273$	843.313	−	1710.37i	0.186958	−	0.379180i
$274$	1941.12	+	906.531i	0.427983	+	0.199874i
$275$	2864.84	−	4962.05i	0.628205	−	1.08808i
$276$	479.110	−	1311.60i	0.104489	−	0.286047i
$277$	−5794.37	+	3345.38i	−1.25686	+	0.725648i	−0.972463	−	0.233059i	$-0.925126\pi$
$277$	−5794.37	+	3345.38i	−1.25686	+	0.725648i	−0.284396	+	0.958707i	$0.591793\pi$
$278$	−1203.94	−	1721.53i	−0.259739	−	0.371405i
$279$	282.099			0.0605334
$280$	−1103.81	+	372.635i	−0.235591	+	0.0795329i
$281$	3069.48			0.651636			0.325818	−	0.945432i	$-0.394360\pi$
$281$	3069.48			0.651636			0.325818	+	0.945432i	$0.394360\pi$
$282$	1157.62	+	1655.30i	0.244451	+	0.349544i
$283$	4203.29	−	2426.77i	0.882895	−	0.509740i	0.0112833	−	0.999936i	$-0.496408\pi$
$283$	4203.29	−	2426.77i	0.882895	−	0.509740i	0.871612	+	0.490197i	$0.163075\pi$
$284$	1642.10	+	599.838i	0.343102	+	0.125330i
$285$	−467.292	+	809.373i	−0.0971227	+	0.168222i
$286$	4297.51	+	2007.00i	0.888522	+	0.414953i
$287$	3790.81	+	5672.49i	0.779667	+	1.16668i
$288$	938.328	−	1331.82i	0.191984	−	0.272494i
$289$	245.695	−	425.557i	0.0500092	−	0.0866185i
$290$	−1972.12	+	171.384i	−0.399334	+	0.0347035i
$291$	−582.825	−	1009.48i	−0.117408	−	0.203357i
$292$	−857.808	−	4898.14i	−0.171916	−	0.981650i
$293$	−8373.05			−1.66948			−0.834742	−	0.550641i	$-0.814383\pi$
$293$	−8373.05			−1.66948			−0.834742	+	0.550641i	$0.814383\pi$
$294$	−1965.33	−	2146.68i	−0.389864	−	0.425839i
$295$		−	515.929i		−	0.101826i
$296$	−1582.62	+	5865.50i	−0.310769	+	1.15177i
$297$	1142.44	−	659.587i	0.223202	−	0.128866i
$298$	−8914.78	+	774.724i	−1.73295	+	0.150599i
$299$	−1729.40	−	998.468i	−0.334494	−	0.193120i
$300$	−2158.14	+	1806.63i	−0.415335	+	0.347686i
$301$	−7177.43	+	4796.53i	−1.37442	+	0.918497i
$302$	−1856.63	+	3975.52i	−0.353765	+	0.757502i
$303$	2816.21	+	1625.94i	0.533950	+	0.308276i
$304$	−2437.23	−	6744.97i	−0.459819	−	1.27253i
$305$	654.163	+	1133.04i	0.122811	+	0.212714i
$306$	1072.49	+	1533.56i	0.200359	+	0.286497i
$307$		−	9258.40i		−	1.72119i	−0.509292	−	0.860594i	$-0.670093\pi$
$307$		−	9258.40i		−	1.72119i	0.509292	−	0.860594i	$-0.329907\pi$
$308$	5234.62	−	5000.11i	0.968409	−	0.925026i
$309$		−	3031.51i		−	0.558112i
$310$	−201.973	+	141.248i	−0.0370042	+	0.0258786i
$311$	1104.09	+	1912.35i	0.201310	+	0.348679i	0.948951	−	0.315424i	$-0.102147\pi$
$311$	1104.09	+	1912.35i	0.201310	+	0.348679i	−0.747641	+	0.664104i	$0.768813\pi$
$312$	−1644.59	−	1650.34i	−0.298419	−	0.299461i
$313$	8150.90	+	4705.92i	1.47194	+	0.849823i	0.999502	−	0.0315429i	$-0.0100421\pi$
$313$	8150.90	+	4705.92i	1.47194	+	0.849823i	0.472434	+	0.881366i	$0.343375\pi$
$314$	−2900.72	−	1354.68i	−0.521329	−	0.243468i
$315$	415.608	+	204.919i	0.0743393	+	0.0366536i
$316$	−2667.24	+	2232.80i	−0.474822	+	0.397484i
$317$	4240.07	+	2448.01i	0.751249	+	0.433734i	0.826145	−	0.563457i	$-0.190529\pi$
$317$	4240.07	+	2448.01i	0.751249	+	0.433734i	−0.0748958	+	0.997191i	$0.523862\pi$
$318$	−549.319	−	6321.03i	−0.0968688	−	1.11467i
$319$	10652.3	−	6150.10i	1.86963	−	1.07943i
$320$	−4.96112	+	1423.37i	−0.000866672	+	0.248652i
$321$		−	911.778i		−	0.158537i
$322$	−2377.87	+	1906.45i	−0.411533	+	0.329945i
$323$	8237.99			1.41912
$324$	−638.286	+	111.783i	−0.109445	+	0.0191671i
$325$	2012.51	+	3485.77i	0.343489	+	0.594941i
$326$	−332.050	−	3820.91i	−0.0564127	−	0.649143i
$327$	−2159.25	+	3739.92i	−0.365158	+	0.632472i
$328$	8055.29	−	2143.37i	1.35603	−	0.360817i
$329$	−288.653	−	4399.29i	−0.0483707	−	0.737206i
$330$	−487.688	+	1044.27i	−0.0813526	+	0.174197i
$331$	2411.23	−	4176.37i	0.400402	−	0.693517i	−0.593372	−	0.804928i	$-0.702204\pi$
$331$	2411.23	−	4176.37i	0.400402	−	0.693517i	0.993774	+	0.111411i	$0.0355371\pi$
$332$	−2586.24	−	944.717i	−0.427524	−	0.156169i
$333$	2092.68	−	1208.21i	0.344379	−	0.198827i
$334$	5418.20	−	3789.18i	0.887637	−	0.620762i
$335$	−461.314			−0.0752367
$336$	−3257.97	+	1424.78i	−0.528978	+	0.231334i
$337$	3271.36			0.528791			0.264395	−	0.964414i	$-0.414828\pi$
$337$	3271.36			0.528791			0.264395	+	0.964414i	$0.414828\pi$
$338$	2361.85	−	1651.74i	0.380082	−	0.265808i
$339$	−2384.03	+	1376.42i	−0.381956	+	0.220522i
$340$	−1535.73	−	560.981i	−0.244960	−	0.0894807i
$341$	765.715	−	1326.26i	0.121601	−	0.210618i
$342$	−1207.05	+	2584.60i	−0.190847	+	0.408653i
$343$	1240.60	+	6230.13i	0.195295	+	0.980744i
$344$	2712.02	+	10192.4i	0.425065	+	1.59749i
$345$	242.621	−	420.232i	0.0378617	−	0.0655783i
$346$	202.076	+	2325.30i	0.0313980	+	0.361297i
$347$	1371.94	+	2376.26i	0.212246	+	0.367621i	0.952417	−	0.304798i	$-0.0985888\pi$
$347$	1371.94	+	2376.26i	0.212246	+	0.367621i	−0.740171	+	0.672419i	$0.765255\pi$
$348$	−5951.48	+	1042.28i	−0.916761	+	0.160552i
$349$	−7071.64			−1.08463			−0.542316	−	0.840175i	$-0.682452\pi$
$349$	−7071.64			−1.08463			−0.542316	+	0.840175i	$0.682452\pi$
$350$	6072.04	−	931.398i	0.927326	−	0.142244i
$351$			926.701i			0.140922i
$352$	−3714.46	−	8026.48i	−0.562448	−	1.21538i
$353$	313.901	−	181.231i	0.0473294	−	0.0273256i	−0.476149	−	0.879365i	$-0.657968\pi$
$353$	313.901	−	181.231i	0.0473294	−	0.0273256i	0.523478	+	0.852039i	$0.324634\pi$
$354$	−136.336	−	1568.82i	−0.0204694	−	0.235542i
$355$	526.124	+	303.758i	0.0786585	+	0.0454135i
$356$	−6729.95	+	5633.78i	−1.00193	+	0.838736i
$357$	−267.425	−	4075.76i	−0.0396460	−	0.604236i
$358$	−1630.63	−	761.527i	−0.240730	−	0.112424i
$359$	−5139.46	−	2967.27i	−0.755572	−	0.436230i	0.0721315	−	0.997395i	$-0.477020\pi$
$359$	−5139.46	−	2967.27i	−0.755572	−	0.436230i	−0.827704	+	0.561165i	$0.810353\pi$
$360$	401.021	−	399.626i	0.0587102	−	0.0585059i
$361$	2849.15	+	4934.87i	0.415388	+	0.719473i
$362$	8959.97	−	6266.09i	1.30090	−	0.909774i
$363$		−	3168.40i		−	0.458121i
$364$	1203.30	+	4940.84i	0.173269	+	0.711457i
$365$		−	1728.02i		−	0.247805i
$366$	2288.57	+	3272.46i	0.326846	+	0.467361i
$367$	6453.90	+	11178.5i	0.917959	+	1.58995i	0.802510	+	0.596639i	$0.203498\pi$
$367$	6453.90	+	11178.5i	0.917959	+	1.58995i	0.115449	+	0.993313i	$0.463169\pi$
$368$	1265.43	+	3502.03i	0.179253	+	0.496076i
$369$	−2871.27	−	1657.73i	−0.405074	−	0.233869i
$370$	−893.331	+	1912.85i	−0.125519	+	0.268769i
$371$	−6124.17	+	12420.8i	−0.857011	+	1.73815i
$372$	−576.829	+	482.876i	−0.0803956	+	0.0673009i
$373$	−2609.74	−	1506.74i	−0.362272	−	0.209158i	0.307805	−	0.951449i	$-0.400406\pi$
$373$	−2609.74	−	1506.74i	−0.362272	−	0.209158i	−0.670077	+	0.742292i	$0.733739\pi$
$374$	10121.0	−	879.548i	1.39932	−	0.121605i
$375$	−1749.86	+	1010.28i	−0.240966	+	0.139122i
$376$	−5200.49	−	1403.18i	−0.713283	−	0.192457i
$377$			8640.71i			1.18042i
$378$	1317.92	+	513.287i	0.179329	+	0.0698429i
$379$	3343.65			0.453171			0.226585	−	0.973991i	$-0.427244\pi$
$379$	3343.65			0.453171			0.226585	+	0.973991i	$0.427244\pi$
$380$	−429.918	−	2454.86i	−0.0580377	−	0.331399i
$381$	1953.49	+	3383.54i	0.262678	+	0.454972i
$382$	−9007.13	+	782.750i	−1.20640	+	0.104840i
$383$	553.028	−	957.873i	0.0737818	−	0.127794i	−0.826774	−	0.562534i	$-0.809827\pi$
$383$	553.028	−	957.873i	0.0737818	−	0.127794i	0.900556	+	0.434740i	$0.143160\pi$
$384$	361.043	+	4329.44i	0.0479802	+	0.575353i
$385$	2091.51	−	1397.72i	0.276866	−	0.185024i
$386$	−5443.79	−	2542.33i	−0.717828	−	0.335237i
$387$	2097.53	−	3633.03i	0.275513	−	0.477203i
$388$	2919.70	+	1066.53i	0.382024	+	0.139548i
$389$	−1778.13	+	1026.61i	−0.231761	+	0.133807i	−0.611384	−	0.791334i	$-0.709387\pi$
$389$	−1778.13	+	1026.61i	−0.231761	+	0.133807i	0.379623	+	0.925141i	$0.376054\pi$
$390$	−464.004	−	663.487i	−0.0602455	−	0.0861460i
$391$	−4277.22			−0.553218
$392$	7693.17	+	1025.38i	0.991234	+	0.132116i
$393$	−4716.00			−0.605320
$394$	−794.698	−	1136.35i	−0.101615	−	0.145301i
$395$	−1046.83	+	604.385i	−0.133346	+	0.0769872i
$396$	−1207.00	+	3304.25i	−0.153166	+	0.419305i
$397$	2256.80	−	3908.89i	0.285304	−	0.494160i	−0.687379	−	0.726299i	$-0.741239\pi$
$397$	2256.80	−	3908.89i	0.285304	−	0.494160i	0.972683	+	0.232138i	$0.0745722\pi$
$398$	5626.88	+	2627.84i	0.708669	+	0.330959i
$399$	5176.57	−	3459.40i	0.649506	−	0.434052i
$400$	1320.47	−	7388.30i	0.165058	−	0.923538i
$401$	−7686.86	+	13314.0i	−0.957266	+	1.65803i	−0.228170	+	0.973621i	$0.573274\pi$
$401$	−7686.86	+	13314.0i	−0.957266	+	1.65803i	−0.729096	+	0.684412i	$0.760059\pi$
$402$	−1402.75	+	121.904i	−0.174037	+	0.0151244i
$403$	537.904	+	931.677i	0.0664886	+	0.115162i
$404$	−8541.67	+	1495.90i	−1.05189	+	0.184217i
$405$	−225.182			−0.0276281
$406$	12288.5	+	4785.97i	1.50214	+	0.585033i
$407$		−	13118.0i		−	1.59763i
$408$	−4818.03	−	1299.99i	−0.584628	−	0.157743i
$409$	4088.80	−	2360.67i	0.494323	−	0.285398i	−0.232043	−	0.972706i	$-0.574541\pi$
$409$	4088.80	−	2360.67i	0.494323	−	0.285398i	0.726366	+	0.687308i	$0.241208\pi$
$410$	2885.76	−	250.782i	0.347604	−	0.0302080i
$411$	1967.89	+	1136.16i	0.236177	+	0.136357i
$412$	5189.12	+	6198.76i	0.620508	+	0.741240i
$413$	−1519.96	+	3082.72i	−0.181095	+	0.367290i
$414$	626.707	−	1341.94i	0.0743985	−	0.159306i
$415$	−828.621	−	478.404i	−0.0980130	−	0.0565878i
$416$	6187.75	+	559.473i	0.729278	+	0.0659385i
$417$	−1114.09	−	1929.66i	−0.130833	−	0.226609i
$418$	8874.87	+	12690.3i	1.03848	+	1.48494i
$419$			493.285i			0.0575145i	0.999586	+	0.0287572i	$0.00915497\pi$
$419$			493.285i			0.0575145i	−0.999586	+	0.0287572i	$0.990845\pi$
$420$	−1200.59	+	292.394i	−0.139483	+	0.0339699i
$421$		−	4772.48i		−	0.552485i	−0.961088	−	0.276243i	$-0.910911\pi$
$421$		−	4772.48i		−	0.552485i	0.961088	−	0.276243i	$-0.0890894\pi$
$422$	−399.825	+	279.615i	−0.0461213	+	0.0322546i
$423$	1071.23	+	1855.42i	0.123132	+	0.213271i
$424$	11943.1	+	11984.8i	1.36794	+	1.37272i
$425$	7466.14	+	4310.58i	0.852144	+	0.491985i
$426$	1680.09	+	784.627i	0.191081	+	0.0892378i
$427$	−570.656	−	8697.24i	−0.0646744	−	0.985688i
$428$	1560.71	+	1864.38i	0.176262	+	0.210557i
$429$	4356.79	+	2515.39i	0.490321	+	0.283087i
$430$	317.317	+	3651.37i	0.0355869	+	0.409500i
$431$	−3667.71	+	2117.55i	−0.409901	+	0.236657i	−0.690747	−	0.723096i	$-0.742718\pi$
$431$	−3667.71	+	2117.55i	−0.409901	+	0.236657i	0.280846	+	0.959753i	$0.409385\pi$
$432$	1113.81	−	1321.14i	0.124047	−	0.147137i
$433$		−	12887.5i		−	1.43034i	−0.698953	−	0.715168i	$-0.746350\pi$
$433$		−	12887.5i		−	1.43034i	0.698953	−	0.715168i	$-0.253650\pi$
$434$	1622.93	−	248.944i	0.179501	−	0.0275339i
$435$	−2099.63			−0.231425
$436$	−1986.55	−	11343.3i	−0.218208	−	1.24598i
$437$	−3259.91	−	5646.34i	−0.356849	−	0.618080i
$438$	−456.636	−	5254.53i	−0.0498148	−	0.573221i
$439$	3202.78	−	5547.39i	0.348202	−	0.603103i	−0.637728	−	0.770261i	$-0.720126\pi$
$439$	3202.78	−	5547.39i	0.348202	−	0.603103i	0.985930	+	0.167158i	$0.0534591\pi$
$440$	−790.286	−	2970.08i	−0.0856259	−	0.321802i
$441$	−1879.59	−	2448.82i	−0.202957	−	0.264423i
$442$	−3019.83	+	6466.25i	−0.324975	+	0.695855i
$443$	−5288.60	+	9160.13i	−0.567199	+	0.982417i	0.429643	+	0.902999i	$0.358640\pi$
$443$	−5288.60	+	9160.13i	−0.567199	+	0.982417i	−0.996841	+	0.0794180i	$0.974694\pi$
$444$	−2210.94	+	6052.61i	−0.236321	+	0.646946i
$445$	−2641.34	+	1524.98i	−0.281374	+	0.162451i
$446$	−12119.2	+	8475.45i	−1.28668	+	0.899830i
$447$	−9491.19			−1.00429
$448$	4222.97	−	8490.11i	0.445350	−	0.895357i
$449$	−11890.2			−1.24974			−0.624870	−	0.780729i	$-0.714848\pi$
$449$	−11890.2			−1.24974			−0.624870	+	0.780729i	$0.714848\pi$
$450$	−2446.36	+	1710.84i	−0.256273	+	0.179222i
$451$	−15587.3	+	8999.30i	−1.62744	+	0.939602i
$452$	2518.76	−	6895.29i	0.262107	−	0.717538i
$453$	−2326.93	+	4030.36i	−0.241343	+	0.418019i
$454$	−2455.64	+	5258.16i	−0.253852	+	0.543564i
$455$	115.700	+	1763.35i	0.0119211	+	0.181686i
$456$	−1955.99	−	7351.06i	−0.200872	−	0.754923i
$457$	−4355.44	+	7543.84i	−0.445818	+	0.772180i	−0.998109	−	0.0614719i	$-0.980421\pi$
$457$	−4355.44	+	7543.84i	−0.445818	+	0.772180i	0.552291	+	0.833652i	$0.313754\pi$
$458$	215.233	+	2476.69i	0.0219589	+	0.252682i
$459$	992.447	+	1718.97i	0.100923	+	0.174803i
$460$	223.216	+	1274.58i	0.0226250	+	0.129190i
$461$	−1243.74			−0.125655			−0.0628273	−	0.998024i	$-0.520012\pi$
$461$	−1243.74			−0.125655			−0.0628273	+	0.998024i	$0.520012\pi$
$462$	5990.46	−	4802.82i	0.603250	−	0.483652i
$463$		−	17027.2i		−	1.70911i	−0.519357	−	0.854557i	$-0.673829\pi$
$463$		−	17027.2i		−	1.70911i	0.519357	−	0.854557i	$-0.326171\pi$
$464$	10385.3	−	12318.5i	1.03907	−	1.23248i
$465$	−226.391	+	130.707i	−0.0225777	+	0.0130353i
$466$	−925.383	−	10648.4i	−0.0919904	−	1.05854i
$467$	−7952.67	−	4591.47i	−0.788020	−	0.454964i	0.0512447	−	0.998686i	$-0.483681\pi$
$467$	−7952.67	−	4591.47i	−0.788020	−	0.454964i	−0.839265	+	0.543722i	$0.817014\pi$
$468$	−1586.26	−	1894.90i	−0.156677	−	0.187161i
$469$	2756.39	+	1359.06i	0.271382	+	0.133807i
$470$	−1695.98	−	792.048i	−0.166446	−	0.0777329i
$471$	−2940.73	−	1697.83i	−0.287689	−	0.166098i
$472$	2964.17	+	2974.52i	0.289061	+	0.290070i
$473$	−11386.9	−	19722.6i	−1.10691	−	1.91723i
$474$	−3023.45	+	2114.42i	−0.292978	+	0.204892i
$475$			13141.4i			1.26940i
$476$	7523.41	+	7876.26i	0.724443	+	0.758420i
$477$		−	6729.74i		−	0.645982i
$478$	−4505.95	−	6443.12i	−0.431166	−	0.616530i
$479$	−5874.89	−	10175.6i	−0.560397	−	0.970637i	−0.997462	−	0.0712065i	$-0.977315\pi$
$479$	−5874.89	−	10175.6i	−0.560397	−	0.970637i	0.437064	−	0.899430i	$-0.356018\pi$
$480$	−135.948	+	1503.58i	−0.0129274	+	0.142977i
$481$	7980.61	+	4607.61i	0.756517	+	0.436775i
$482$	8780.97	−	18802.3i	0.829797	−	1.77681i
$483$	−2687.71	+	1796.14i	−0.253199	+	0.169208i
$484$	5423.44	+	6478.67i	0.509338	+	0.608440i
$485$	935.463	+	540.090i	0.0875818	+	0.0505654i
$486$	−684.727	+	59.5051i	−0.0639092	+	0.00555392i
$487$	−2474.77	+	1428.81i	−0.230272	+	0.132948i	−0.610698	−	0.791864i	$-0.709111\pi$
$487$	−2474.77	+	1428.81i	−0.230272	+	0.132948i	0.380426	+	0.924812i	$0.375778\pi$
$488$	−10281.2	−	2774.04i	−0.953702	−	0.257326i
$489$		−	4067.96i		−	0.376195i
$490$	2571.86	+	812.152i	0.237112	+	0.0748761i
$491$	288.658			0.0265315			0.0132657	−	0.999912i	$-0.495777\pi$
$491$	288.658			0.0265315			0.0132657	+	0.999912i	$0.495777\pi$
$492$	8708.67	−	1525.14i	0.798002	−	0.139754i
$493$	9253.73	+	16027.9i	0.845369	+	1.46422i
$494$	−10837.7	+	941.828i	−0.987063	+	0.0857790i
$495$	−611.223	+	1058.67i	−0.0554999	+	0.0961286i
$496$	352.934	−	1974.74i	0.0319500	−	0.178767i
$497$	−2248.74	−	3364.97i	−0.202957	−	0.303702i
$498$	−2646.06	−	1235.75i	−0.238098	−	0.111196i
$499$	6943.57	−	12026.6i	0.622920	−	1.07893i	−0.366019	−	0.930607i	$-0.619280\pi$
$499$	6943.57	−	12026.6i	0.622920	−	1.07893i	0.988939	−	0.148322i	$-0.0473871\pi$
$500$	1848.74	−	5061.08i	0.165357	−	0.452677i
$501$	6073.25	−	3506.39i	0.541582	−	0.312683i
$502$	−4684.09	−	6697.85i	−0.416456	−	0.595497i
$503$	−19825.9			−1.75745			−0.878723	−	0.477333i	$-0.841604\pi$
$503$	−19825.9			−1.75745			−0.878723	+	0.477333i	$0.841604\pi$
$504$	−3573.46	+	1206.36i	−0.315822	+	0.106618i
$505$	−3013.43			−0.265537
$506$	−4607.89	−	6588.90i	−0.404834	−	0.578878i
$507$	2647.39	−	1528.47i	0.231903	−	0.133889i
$508$	−9786.15	−	3574.75i	−0.854705	−	0.312212i
$509$	9939.15	−	17215.1i	0.865511	−	1.49911i	−0.00102829	−	0.999999i	$-0.500327\pi$
$509$	9939.15	−	17215.1i	0.865511	−	1.49911i	0.866539	−	0.499109i	$-0.166339\pi$
$510$	−1571.25	−	733.800i	−0.136424	−	0.0637121i
$511$	−5090.88	+	10325.1i	−0.440718	+	0.893846i
$512$	−8149.06	−	8234.72i	−0.703400	−	0.710794i
$513$	−1512.80	+	2620.25i	−0.130198	+	0.225510i
$514$	−1080.32	+	93.8833i	−0.0927059	+	0.00805645i
$515$	1404.61	+	2432.86i	0.120184	+	0.208165i
$516$	1929.77	+	11019.1i	0.164639	+	0.940097i
$517$	11630.7			0.989399
$518$	10973.1	−	8797.64i	0.930755	−	0.746228i
$519$			2475.65i			0.209381i
$520$	2084.49	+	562.433i	0.175790	+	0.0474314i
$521$	−16326.6	+	9426.18i	−1.37290	+	0.792646i	−0.991293	−	0.131678i	$-0.957964\pi$
$521$	−16326.6	+	9426.18i	−1.37290	+	0.792646i	−0.381610	+	0.924323i	$0.624630\pi$
$522$	−6384.50	+	554.835i	−0.535330	+	0.0465219i
$523$	−12338.1	−	7123.38i	−1.03156	−	0.595571i	−0.114128	−	0.993466i	$-0.536407\pi$
$523$	−12338.1	−	7123.38i	−1.03156	−	0.595571i	−0.917431	+	0.397895i	$0.869741\pi$
$524$	9643.17	−	8072.50i	0.803938	−	0.672994i
$525$	6501.71	−	426.600i	0.540491	−	0.0354635i
$526$	114.738	−	245.683i	0.00951102	−	0.0203656i
$527$	1995.55	+	1152.13i	0.164948	+	0.0952327i
$528$	−3187.93	−	8822.49i	−0.262759	−	0.727178i
$529$	−4390.93	−	7605.32i	−0.360889	−	0.625077i
$530$	3369.62	+	4818.26i	0.276164	+	0.394891i
$531$		−	1670.26i		−	0.136503i
$532$	−4663.39	+	15934.6i	−0.380044	+	1.29859i
$533$		−	12643.8i		−	1.02751i
$534$	−7628.73	+	5335.09i	−0.618216	+	0.432344i
$535$	422.461	+	731.724i	0.0341394	+	0.0591312i
$536$	2659.64	−	2650.39i	0.214327	−	0.213581i
$537$	−1653.12	−	954.427i	−0.132844	−	0.0766975i
$538$	4390.13	+	2050.26i	0.351807	+	0.164299i
$539$	−16614.7	+	2189.73i	−1.32773	+	0.174987i
$540$	460.447	−	385.450i	0.0366935	−	0.0307169i
$541$	−6481.90	−	3742.33i	−0.515118	−	0.297403i	0.219817	−	0.975541i	$-0.429454\pi$
$541$	−6481.90	−	3742.33i	−0.515118	−	0.297403i	−0.734935	+	0.678138i	$0.762787\pi$
$542$	2022.85	+	23277.0i	0.160312	+	1.84471i
$543$	10043.2	−	5798.45i	0.793730	−	0.458260i
$544$	12077.0	−	5588.96i	0.951835	−	0.440487i
$545$		−	4001.84i		−	0.314532i
$546$	817.787	+	5331.37i	0.0640990	+	0.417879i
$547$	17567.6			1.37319			0.686597	−	0.727039i	$-0.259104\pi$
$547$	17567.6			1.37319			0.686597	+	0.727039i	$0.259104\pi$
$548$	−5968.69	+	1045.29i	−0.465273	+	0.0814830i
$549$	2117.77	+	3668.09i	0.164635	+	0.285156i
$550$	1403.07	+	16145.1i	0.108776	+	1.25169i
$551$	−14105.6	+	24431.6i	−1.09060	+	1.88897i
$552$	1015.56	+	3816.72i	0.0783064	+	0.294294i
$553$	8035.43	−	527.233i	0.617905	−	0.0405429i
$554$	8007.73	−	17146.6i	0.614108	−	1.31496i
$555$	−1119.62	+	1939.24i	−0.0856309	+	0.148317i
$556$	5581.11	+	2038.71i	0.425705	+	0.155504i
$557$	−10600.4	+	6120.17i	−0.806383	+	0.465566i	−0.845698	−	0.533661i	$-0.820816\pi$
$557$	−10600.4	+	6120.17i	−0.806383	+	0.465566i	0.0393151	+	0.999227i	$0.487482\pi$
$558$	−653.864	+	457.274i	−0.0496062	+	0.0346917i
$559$	15998.2			1.21047
$560$	1954.44	−	2652.96i	0.147483	−	0.200193i
$561$	10775.4			0.810940
$562$	−7114.60	+	4975.54i	−0.534006	+	0.373453i
$563$	6770.14	−	3908.74i	0.506798	−	0.292600i	−0.224718	−	0.974424i	$-0.572146\pi$
$563$	6770.14	−	3908.74i	0.506798	−	0.292600i	0.731516	+	0.681824i	$0.238813\pi$
$564$	−5366.38	−	1960.27i	−0.400648	−	0.146351i
$565$	1275.50	−	2209.23i	0.0949745	−	0.164501i
$566$	−5808.88	+	12438.3i	−0.431387	+	0.923712i
$567$	1345.48	+	663.402i	0.0996560	+	0.0491362i
$568$	−4778.47	+	1271.47i	−0.352993	+	0.0939253i
$569$	3264.04	−	5653.48i	0.240485	−	0.416531i	−0.720368	−	0.693592i	$-0.756027\pi$
$569$	3264.04	−	5653.48i	0.240485	−	0.416531i	0.960852	+	0.277061i	$0.0893603\pi$
$570$	−228.858	−	2633.48i	−0.0168172	−	0.193516i
$571$	10967.3	+	18995.9i	0.803795	+	1.39221i	0.917102	+	0.398654i	$0.130522\pi$
$571$	10967.3	+	18995.9i	0.803795	+	1.39221i	−0.113306	+	0.993560i	$0.536144\pi$
$572$	−13214.3	+	2314.21i	−0.965940	+	0.169164i
$573$	−9589.51			−0.699141
$574$	−17981.5	−	7003.20i	−1.30755	−	0.509248i
$575$		−	6823.08i		−	0.494856i
$576$	−16.0610	+	4607.97i	−0.00116182	+	0.333331i
$577$	−3035.03	+	1752.28i	−0.218977	+	0.126427i	−0.605477	−	0.795863i	$-0.707018\pi$
$577$	−3035.03	+	1752.28i	−0.218977	+	0.126427i	0.386499	+	0.922290i	$0.373684\pi$
$578$	120.330	+	1384.64i	0.00865930	+	0.0996429i
$579$	−5518.87	−	3186.32i	−0.396125	−	0.228703i
$580$	4293.28	−	3594.00i	0.307360	−	0.257298i
$581$	3541.67	+	5299.68i	0.252897	+	0.378430i
$582$	2987.25	+	1395.09i	0.212758	+	0.0993614i
$583$	−31639.1	−	18266.9i	−2.24761	−	1.29766i
$584$	9928.02	+	9962.69i	0.703467	+	0.705923i
$585$	−429.376	−	743.700i	−0.0303461	−	0.0525611i
$586$	19407.5	−	13572.5i	1.36812	−	0.956782i
$587$		−	290.388i		−	0.0204184i	−0.999948	−	0.0102092i	$-0.996750\pi$
$587$		−	290.388i		−	0.0204184i	0.999948	−	0.0102092i	$-0.00324974\pi$
$588$	8035.04	+	1789.95i	0.563537	+	0.125538i
$589$			3512.42i			0.245716i
$590$	836.307	+	1195.85i	0.0583563	+	0.0834446i
$591$	−735.390	−	1273.73i	−0.0511842	−	0.0886537i
$592$	−5839.54	−	16160.7i	−0.405411	−	1.12196i
$593$	19683.6	+	11364.3i	1.36308	+	0.786975i	0.990033	−	0.140837i	$-0.0449794\pi$
$593$	19683.6	+	11364.3i	1.36308	+	0.786975i	0.373048	+	0.927812i	$0.378313\pi$
$594$	−1578.83	+	3380.69i	−0.109058	+	0.233521i
$595$	2103.07	+	3146.99i	0.144903	+	0.216830i
$596$	19407.4	−	16246.3i	1.33382	−	1.11657i
$597$	5704.49	+	3293.49i	0.391071	+	0.225785i
$598$	5626.98	−	489.003i	0.384790	−	0.0334395i
$599$	−14061.2	+	8118.25i	−0.959141	+	0.553761i	−0.895909	−	0.444238i	$-0.853474\pi$
$599$	−14061.2	+	8118.25i	−0.959141	+	0.553761i	−0.0632327	+	0.997999i	$0.520141\pi$
$600$	2073.77	−	7685.80i	0.141102	−	0.522952i
$601$		−	6407.70i		−	0.434901i	−0.976071	−	0.217450i	$-0.930226\pi$
$601$		−	6407.70i		−	0.434901i	0.976071	−	0.217450i	$-0.0697740\pi$
$602$	8861.20	−	22752.1i	0.599926	−	1.54038i
$603$	−1493.45			−0.100859
$604$	−2140.82	−	12224.2i	−0.144220	−	0.823505i
$605$	1468.04	+	2542.72i	0.0986518	+	0.170870i
$606$	−9163.16	+	796.309i	−0.614237	+	0.0533793i
$607$	−9726.37	+	16846.6i	−0.650381	+	1.12649i	0.332649	+	0.943051i	$0.392057\pi$
$607$	−9726.37	+	16846.6i	−0.650381	+	1.12649i	−0.983030	+	0.183443i	$0.941276\pi$
$608$	16582.6	+	11683.2i	1.10610	+	0.779300i
$609$	12545.5	+	6185.66i	0.834760	+	0.411586i
$610$	−3352.89	−	1565.85i	−0.222548	−	0.103933i
$611$	−4085.21	+	7075.79i	−0.270491	+	0.468504i
$612$	−4971.73	−	1816.11i	−0.328383	−	0.119954i
$613$	9778.19	−	5645.44i	0.644270	−	0.371969i	−0.141988	−	0.989868i	$-0.545349\pi$
$613$	9778.19	−	5645.44i	0.644270	−	0.371969i	0.786257	+	0.617899i	$0.212016\pi$
$614$	15007.6	+	21459.6i	0.986414	+	1.41049i
$615$	3072.35			0.201446
$616$	−4028.03	+	20074.7i	−0.263464	+	1.31304i
$617$	19377.1			1.26433			0.632166	−	0.774833i	$-0.282166\pi$
$617$	19377.1			1.26433			0.632166	+	0.774833i	$0.282166\pi$
$618$	4914.00	+	7026.60i	0.319854	+	0.457365i
$619$	4371.17	−	2523.70i	0.283832	−	0.163871i	−0.351325	−	0.936254i	$-0.614269\pi$
$619$	4371.17	−	2523.70i	0.283832	−	0.163871i	0.635157	+	0.772383i	$0.280935\pi$
$620$	239.185	−	654.786i	0.0154934	−	0.0424143i
$621$	785.456	−	1360.45i	0.0507557	−	0.0879114i
$622$	−5659.00	−	2642.84i	−0.364799	−	0.170367i
$623$	20274.9	−	1330.31i	1.30385	−	0.0855500i
$624$	6487.08	+	1159.40i	0.416172	+	0.0743798i
$625$	−6393.26	+	11073.5i	−0.409169	+	0.708701i
$626$	−26520.8	+	2304.74i	−1.69326	+	0.147150i
$627$	8212.54	+	14224.5i	0.523090	+	0.906018i
$628$	8919.35	−	1562.04i	0.566753	−	0.0992551i
$629$	19738.0			1.25120
$630$	−1295.49	+	198.717i	−0.0819262	+	0.0125668i
$631$			3927.45i			0.247781i	0.992296	+	0.123890i	$0.0395371\pi$
$631$			3927.45i			0.247781i	−0.992296	+	0.123890i	$0.960463\pi$
$632$	2562.96	−	9498.83i	0.161312	−	0.597853i
$633$	−448.163	+	258.747i	−0.0281404	+	0.0162469i
$634$	−13796.0	+	1198.92i	−0.864211	+	0.0751028i
$635$	−3135.45	−	1810.25i	−0.195947	−	0.113130i
$636$	11519.5	+	13760.8i	0.718202	+	0.857942i
$637$	4503.64	−	10877.0i	0.280127	−	0.676552i
$638$	−14721.3	+	31522.1i	−0.913513	+	1.95607i
$639$	1703.26	+	983.379i	0.105446	+	0.0608793i
$640$	−2295.74	−	3307.19i	−0.141792	−	0.204263i
$641$	−760.970	−	1318.04i	−0.0468900	−	0.0812159i	0.841628	−	0.540058i	$-0.181598\pi$
$641$	−760.970	−	1318.04i	−0.0468900	−	0.0812159i	−0.888518	+	0.458842i	$0.848264\pi$
$642$	1477.97	+	2113.37i	0.0908578	+	0.129919i
$643$			3887.71i			0.238439i	0.992868	+	0.119220i	$0.0380393\pi$
$643$			3887.71i			0.238439i	−0.992868	+	0.119220i	$0.961961\pi$
$644$	2421.26	−	8273.33i	0.148154	−	0.506234i
$645$			3887.46i			0.237316i
$646$	−19094.5	+	13353.6i	−1.16294	+	0.813296i
$647$	−4802.49	−	8318.16i	−0.291817	−	0.505441i	0.682423	−	0.730958i	$-0.260926\pi$
$647$	−4802.49	−	8318.16i	−0.291817	−	0.505441i	−0.974239	+	0.225516i	$0.927593\pi$
$648$	1298.26	−	1293.74i	0.0787042	−	0.0784304i
$649$	−7852.54	−	4533.66i	−0.474945	−	0.274209i
$650$	−10315.0	−	4817.28i	−0.622445	−	0.290691i
$651$	1737.78	−	114.022i	0.104622	−	0.00686461i
$652$	6963.23	+	8318.07i	0.418254	+	0.499633i
$653$	15567.5	+	8987.90i	0.932930	+	0.538627i	0.887737	−	0.460351i	$-0.152276\pi$
$653$	15567.5	+	8987.90i	0.932930	+	0.538627i	0.0451931	+	0.998978i	$0.485610\pi$
$654$	−1057.50	−	12168.7i	−0.0632285	−	0.727573i
$655$	3784.71	−	2185.10i	0.225772	−	0.130350i
$656$	−15196.6	+	18025.4i	−0.904466	+	1.07283i
$657$		−	5594.27i		−	0.332197i
$658$	7800.19	+	9729.02i	0.462132	+	0.576408i
$659$	4411.59			0.260776			0.130388	−	0.991463i	$-0.458378\pi$
$659$	4411.59			0.260776			0.130388	+	0.991463i	$0.458378\pi$
$660$	−562.338	−	3210.99i	−0.0331651	−	0.189375i
$661$	1934.89	+	3351.34i	0.113856	+	0.197204i	0.917322	−	0.398147i	$-0.130346\pi$
$661$	1934.89	+	3351.34i	0.113856	+	0.197204i	−0.803466	+	0.595351i	$0.797013\pi$
$662$	1180.91	+	13588.8i	0.0693313	+	0.797798i
$663$	−3784.78	+	6555.43i	−0.221702	+	0.384000i
$664$	7525.88	−	2002.50i	0.439850	−	0.117036i
$665$	−2551.46	+	5174.76i	−0.148784	+	0.301757i
$666$	−2892.05	+	6192.63i	−0.168265	+	0.360300i
$667$	7323.72	−	12685.1i	0.425151	−	0.736383i
$668$	−6416.45	+	17565.5i	−0.371646	+	1.01741i
$669$	−13584.4	+	7842.93i	−0.785054	+	0.453251i
$670$	1069.26	−	747.778i	0.0616553	−	0.0431182i
$671$	22993.5			1.32288
$672$	5241.95	−	8583.51i	0.300912	−	0.492733i
$673$	−12463.8			−0.713885			−0.356942	−	0.934126i	$-0.616181\pi$
$673$	−12463.8			−0.713885			−0.356942	+	0.934126i	$0.616181\pi$
$674$	−7582.54	+	5302.79i	−0.433336	+	0.303050i
$675$	−2742.12	+	1583.16i	−0.156362	+	0.0902756i
$676$	−2797.00	+	7657.00i	−0.159137	+	0.435651i
$677$	−12619.9	+	21858.3i	−0.716428	+	1.24089i	0.245978	+	0.969276i	$0.420891\pi$
$677$	−12619.9	+	21858.3i	−0.716428	+	1.24089i	−0.962406	+	0.271615i	$0.912442\pi$
$678$	3294.70	−	7054.80i	0.186626	−	0.399614i
$679$	−3998.33	−	5983.01i	−0.225982	−	0.338155i
$680$	4468.93	−	1189.10i	0.252023	−	0.0670588i
$681$	−3077.67	+	5330.69i	−0.173182	+	0.299959i
$682$	375.012	+	4315.27i	0.0210556	+	0.242288i
$683$	9011.49	+	15608.4i	0.504854	+	0.874432i	0.999984	+	0.00561378i	$0.00178693\pi$
$683$	9011.49	+	15608.4i	0.504854	+	0.874432i	−0.495130	+	0.868819i	$0.664880\pi$
$684$	−1391.81	−	7947.32i	−0.0778028	−	0.444259i
$685$	−2105.71			−0.117452
$686$	−12974.4	−	12429.5i	−0.722107	−	0.691782i
$687$			2636.83i			0.146436i
$688$	−22807.7	−	19228.4i	−1.26386	−	1.06552i
$689$	22226.0	−	12832.2i	1.22895	−	0.709533i
$690$	118.825	+	1367.32i	0.00655590	+	0.0754390i
$691$	−2586.65	−	1493.40i	−0.142404	−	0.0822167i	0.427105	−	0.904202i	$-0.359533\pi$
$691$	−2586.65	−	1493.40i	−0.142404	−	0.0822167i	−0.569509	+	0.821985i	$0.692867\pi$
$692$	−4237.63	−	5062.15i	−0.232790	−	0.278084i
$693$	6771.02	−	4524.93i	0.371154	−	0.248035i
$694$	−7031.81	−	3283.96i	−0.384616	−	0.179622i
$695$	1788.17	+	1032.40i	0.0975958	+	0.0563470i
$696$	12105.2	−	12063.0i	0.659259	−	0.656966i
$697$	−13540.8	−	23453.3i	−0.735859	−	1.27455i
$698$	16391.0	−	11462.9i	0.888839	−	0.621603i
$699$		−	11336.9i		−	0.613450i
$700$	−12564.3	+	12001.5i	−0.678409	+	0.648017i
$701$		−	11762.1i		−	0.633734i	−0.948470	−	0.316867i	$-0.897369\pi$
$701$		−	11762.1i		−	0.633734i	0.948470	−	0.316867i	$-0.102631\pi$
$702$	−1502.16	−	2147.96i	−0.0807625	−	0.115484i
$703$	15043.5	+	26056.0i	0.807076	+	1.39790i
$704$	21620.3	+	12583.2i	1.15745	+	0.673644i
$705$	−1719.37	−	992.679i	−0.0918514	−	0.0530304i
$706$	−433.807	+	928.892i	−0.0231254	+	0.0495174i
$707$	18005.5	+	8877.77i	0.957803	+	0.472253i
$708$	2859.02	+	3415.30i	0.151764	+	0.181292i
$709$	11823.2	+	6826.12i	0.626276	+	0.361580i	0.779308	−	0.626641i	$-0.215571\pi$
$709$	11823.2	+	6826.12i	0.626276	+	0.361580i	−0.153033	+	0.988221i	$0.548904\pi$
$710$	−1711.86	+	148.766i	−0.0904859	+	0.00786353i
$711$	−3388.97	+	1956.62i	−0.178757	+	0.103206i
$712$	6466.82	−	23967.3i	0.340385	−	1.26154i
$713$		−	1823.67i		−	0.0957883i
$714$	7226.55	+	9013.53i	0.378777	+	0.472441i
$715$	−4661.90			−0.243840
$716$	5013.97	−	878.093i	0.261705	−	0.0458322i
$717$	−4169.67	−	7222.08i	−0.217181	−	0.376169i
$718$	16722.4	−	1453.23i	0.869184	−	0.0755350i
$719$	10277.2	−	17800.6i	0.533066	−	0.923298i	−0.466188	−	0.884686i	$-0.654373\pi$
$719$	10277.2	−	17800.6i	0.533066	−	0.923298i	0.999254	−	0.0386122i	$-0.0122937\pi$
$720$	−281.726	+	1576.32i	−0.0145824	+	0.0815915i
$721$	−1225.31	−	18674.6i	−0.0632911	−	0.964604i
$722$	−14603.2	−	6819.91i	−0.752735	−	0.351539i
$723$	11005.2	−	19061.6i	0.566099	−	0.980512i
$724$	−10610.7	+	29047.7i	−0.544676	+	1.49109i
$725$	−25568.0	+	14761.7i	−1.30975	+	0.756186i
$726$	5135.89	+	7343.89i	0.262549	+	0.375423i
$727$	−37472.8			−1.91168			−0.955838	−	0.293894i	$-0.905049\pi$
$727$	−37472.8			−1.91168			−0.955838	+	0.293894i	$0.905049\pi$
$728$	−10798.0	−	9501.63i	−0.549728	−	0.483728i
$729$	−729.000			−0.0370370
$730$	2801.08	+	4005.31i	0.142017	+	0.203073i
$731$	29675.6	−	17133.2i	1.50150	−	0.866889i
$732$	−10609.1	−	3875.38i	−0.535690	−	0.195680i
$733$	16189.2	−	28040.6i	0.815775	−	1.41296i	−0.0929952	−	0.995667i	$-0.529644\pi$
$733$	16189.2	−	28040.6i	0.815775	−	1.41296i	0.908770	−	0.417297i	$-0.137023\pi$
$734$	−33079.2	−	15448.5i	−1.66346	−	0.776859i
$735$	2643.05	+	1094.35i	0.132640	+	0.0549195i
$736$	−8609.77	−	6065.97i	−0.431196	−	0.303797i
$737$	−4053.74	+	7021.29i	−0.202607	+	0.350926i
$738$	9342.31	−	811.878i	0.465983	−	0.0404954i
$739$	−3854.25	−	6675.77i	−0.191855	−	0.332303i	0.754010	−	0.656863i	$-0.228117\pi$
$739$	−3854.25	−	6675.77i	−0.191855	−	0.332303i	−0.945865	+	0.324560i	$0.894784\pi$
$740$	−1030.07	−	5881.78i	−0.0511705	−	0.292187i
$741$	−11538.4			−0.572029
$742$	−5938.80	−	38716.6i	−0.293828	−	1.91554i
$743$			5207.25i			0.257114i	0.991702	+	0.128557i	$0.0410345\pi$
$743$			5207.25i			0.257114i	−0.991702	+	0.128557i	$0.958966\pi$
$744$	554.276	−	2054.26i	0.0273128	−	0.101227i
$745$	7616.91	−	4397.63i	0.374580	−	0.216264i
$746$	8491.39	−	737.930i	0.416745	−	0.0362165i
$747$	−2682.56	−	1548.78i	−0.131392	−	0.0758591i
$748$	−22033.3	+	18444.5i	−1.07703	+	0.901602i
$749$	−368.532	−	5616.71i	−0.0179785	−	0.274005i
$750$	2418.28	−	5178.16i	0.117737	−	0.252106i
$751$	8043.79	+	4644.09i	0.390842	+	0.225653i	0.682525	−	0.730862i	$-0.260882\pi$
$751$	8043.79	+	4644.09i	0.390842	+	0.225653i	−0.291683	+	0.956515i	$0.594215\pi$
$752$	14328.5	−	5177.47i	0.694822	−	0.251068i
$753$	−4334.51	−	7507.60i	−0.209772	−	0.363336i
$754$	−14006.4	−	20027.9i	−0.676500	−	0.967338i
$755$		−	4312.61i		−	0.207883i
$756$	−3886.77	+	946.589i	−0.186985	+	0.0455385i
$757$			16998.5i			0.816144i	0.912950	+	0.408072i	$0.133799\pi$
$757$			16998.5i			0.816144i	−0.912950	+	0.408072i	$0.866201\pi$
$758$	−7750.09	+	5419.97i	−0.371367	+	0.259712i
$759$	−4264.01	−	7385.48i	−0.203918	−	0.353196i
$760$	4975.75	+	4993.13i	0.237486	+	0.238315i
$761$	9385.74	+	5418.86i	0.447087	+	0.258126i	0.706599	−	0.707614i	$-0.250229\pi$
$761$	9385.74	+	5418.86i	0.447087	+	0.258126i	−0.259512	+	0.965740i	$0.583562\pi$
$762$	−10012.5	−	4676.01i	−0.476005	−	0.222302i
$763$	−11789.7	+	23911.3i	−0.559391	+	1.13453i
$764$	19608.4	−	16414.6i	0.928543	−	0.777304i
$765$	−1592.93	−	919.676i	−0.0752841	−	0.0434653i
$766$	270.847	+	3116.65i	0.0127756	+	0.147009i
$767$	5516.30	−	3184.83i	0.259690	−	0.149932i
$768$	−7854.74	−	9449.76i	−0.369054	−	0.443996i
$769$			2200.25i			0.103177i	0.998668	+	0.0515885i	$0.0164284\pi$
$769$			2200.25i			0.103177i	−0.998668	+	0.0515885i	$0.983572\pi$
$770$	−2582.16	+	6629.99i	−0.120850	+	0.310296i
$771$	−1150.17			−0.0537255
$772$	16739.0	−	2931.48i	0.780374	−	0.136666i
$773$	−154.351	−	267.343i	−0.00718189	−	0.0124394i	0.862412	−	0.506207i	$-0.168953\pi$
$773$	−154.351	−	267.343i	−0.00718189	−	0.0124394i	−0.869594	+	0.493767i	$0.835619\pi$
$774$	1027.27	+	11820.9i	0.0477062	+	0.548957i
$775$	−1837.90	+	3183.33i	−0.0851860	+	0.147547i
$776$	−8496.26	+	2260.70i	−0.393039	+	0.104581i
$777$	12402.9	−	8288.62i	0.572654	−	0.382693i
$778$	2457.35	−	5261.83i	0.113240	−	0.242475i
$779$	20640.4	−	35750.3i	0.949319	−	1.64427i
$780$	2150.99	+	785.727i	0.0987407	+	0.0360686i
$781$	9246.50	−	5338.47i	0.423644	−	0.244591i
$782$	9913.97	−	6933.26i	0.453354	−	0.317050i
$783$	−6797.31			−0.310238
$784$	−19493.8	+	10093.8i	−0.888017	+	0.459810i
$785$	3146.68			0.143070
$786$	10931.0	−	7644.51i	0.496051	−	0.346909i
$787$	−26118.6	+	15079.6i	−1.18301	+	0.683009i	−0.956708	−	0.291049i	$-0.905996\pi$
$787$	−26118.6	+	15079.6i	−1.18301	+	0.683009i	−0.226298	+	0.974058i	$0.572662\pi$
$788$	3683.99	+	1345.71i	0.166544	+	0.0608362i
$789$	143.801	−	249.071i	0.00648855	−	0.0112385i
$790$	1446.70	−	3097.75i	0.0651534	−	0.139510i
$791$	−14129.7	+	9442.61i	−0.635140	+	0.424451i
$792$	−2558.45	−	9615.28i	−0.114786	−	0.431394i
$793$	−8076.31	+	13988.6i	−0.361662	+	0.626418i
$794$	1105.28	+	12718.5i	0.0494015	+	0.568465i
$795$	3118.14	+	5400.78i	0.139106	+	0.240938i
$796$	−17302.0	+	3030.08i	−0.770416	+	0.134922i
$797$	19708.1			0.875905			0.437953	−	0.898998i	$-0.355704\pi$
$797$	19708.1			0.875905			0.437953	+	0.898998i	$0.355704\pi$
$798$	−6390.95	+	16409.5i	−0.283505	+	0.727931i
$799$			17500.2i			0.774858i
$800$	8915.59	+	19265.4i	0.394017	+	0.851420i
$801$	−8551.02	+	4936.93i	−0.377198	+	0.217775i
$802$	−3764.67	−	43320.2i	−0.165754	−	1.90734i
$803$	−26300.9	−	15184.8i	−1.15584	−	0.667323i
$804$	3053.77	−	2556.38i	0.133953	−	0.112135i
$805$	1324.73	−	2686.77i	0.0580009	−	0.117635i
$806$	−2757.00	−	1287.56i	−0.120486	−	0.0562686i
$807$	4450.68	+	2569.60i	0.194141	+	0.112087i
$808$	17373.5	−	17313.1i	0.756434	−	0.753802i
$809$	−11522.3	−	19957.2i	−0.500744	−	0.867314i	−1.00000		0.000859083i	$-0.999727\pi$
$809$	−11522.3	−	19957.2i	−0.500744	−	0.867314i	0.499256	−	0.866455i	$-0.333607\pi$
$810$	521.939	−	365.014i	0.0226408	−	0.0158337i
$811$			4808.38i			0.208194i	0.994567	+	0.104097i	$0.0331952\pi$
$811$			4808.38i			0.208194i	−0.994567	+	0.104097i	$0.966805\pi$
$812$	−36240.9	+	8826.14i	−1.56626	+	0.381449i
$813$			24782.1i			1.06906i
$814$	21263.9	+	30405.6i	0.915603	+	1.30923i
$815$	1884.84	+	3264.64i	0.0810099	+	0.140313i
$816$	13274.8	−	4796.71i	0.569497	−	0.205782i
$817$	45235.0	+	26116.4i	1.93705	+	1.11836i
$818$	−5650.66	+	12099.5i	−0.241529	+	0.517176i
$819$	374.564	+	5708.64i	0.0159808	+	0.243560i
$820$	−6282.27	+	5259.02i	−0.267544	+	0.223967i
$821$	21325.6	+	12312.4i	0.906541	+	0.523392i	0.879317	−	0.476238i	$-0.158000\pi$
$821$	21325.6	+	12312.4i	0.906541	+	0.523392i	0.0272244	+	0.999629i	$0.491333\pi$
$822$	−6402.97	+	556.439i	−0.271690	+	0.0236108i
$823$	−606.197	+	349.988i	−0.0256752	+	0.0148236i	−0.512783	−	0.858518i	$-0.671385\pi$
$823$	−606.197	+	349.988i	−0.0256752	+	0.0148236i	0.487107	+	0.873342i	$0.338052\pi$
$824$	−22075.6	−	5956.40i	−0.933302	−	0.251822i
$825$			17189.1i			0.725389i
$826$	−1473.95	−	9609.11i	−0.0620889	−	0.404774i
$827$	−12002.4			−0.504674			−0.252337	−	0.967639i	$-0.581199\pi$
$827$	−12002.4			−0.504674			−0.252337	+	0.967639i	$0.581199\pi$
$828$	722.636	+	4126.30i	0.0303301	+	0.173187i
$829$	−8628.28	−	14944.6i	−0.361487	−	0.626114i	0.626719	−	0.779245i	$-0.284397\pi$
$829$	−8628.28	−	14944.6i	−0.361487	−	0.626114i	−0.988206	+	0.153132i	$0.951064\pi$
$830$	2696.10	−	234.300i	0.112751	−	0.00979841i
$831$	10036.1	−	17383.1i	0.418953	−	0.725648i
$832$	−15249.2	+	8733.40i	−0.635422	+	0.363914i
$833$	−3294.77	−	24999.3i	−0.137043	−	1.03983i
$834$	5710.22	+	2666.76i	0.237085	+	0.110722i
$835$	−3249.29	+	5627.93i	−0.134666	+	0.233249i
$836$	−41141.3	−	15028.4i	−1.70204	−	0.621731i
$837$	−732.914	+	423.148i	−0.0302667	+	0.0174745i
$838$	−799.602	−	1143.36i	−0.0329616	−	0.0471322i
$839$	37200.4			1.53075			0.765375	−	0.643585i	$-0.222554\pi$
$839$	37200.4			1.53075			0.765375	+	0.643585i	$0.222554\pi$
$840$	2308.83	−	2623.85i	0.0948361	−	0.107776i
$841$	−38990.2			−1.59868
$842$	7736.06	+	11061.9i	0.316630	+	0.452754i
$843$	−7974.74	+	4604.22i	−0.325818	+	0.188111i
$844$	473.489	−	1296.21i	0.0193106	−	0.0528643i
$845$	−1416.40	+	2453.28i	−0.0576634	+	0.0998760i
$846$	−5490.53	−	2564.16i	−0.223130	−	0.104205i
$847$	−1280.64	−	19517.9i	−0.0519519	−	0.791787i
$848$	−47109.4	−	8419.58i	−1.90772	−	0.340955i
$849$	−7280.30	+	12609.9i	−0.294298	+	0.509740i
$850$	−24292.8	+	2111.12i	−0.980276	+	0.0851893i
$851$	−7810.66	−	13528.5i	−0.314625	−	0.544947i
$852$	−5166.06	+	904.729i	−0.207731	+	0.0363797i
$853$	−27512.5			−1.10435			−0.552174	−	0.833729i	$-0.686202\pi$
$853$	−27512.5			−1.10435			−0.552174	+	0.833729i	$0.686202\pi$
$854$	15420.7	+	19233.9i	0.617898	+	0.770692i
$855$		−	2803.75i		−	0.112148i
$856$	−6639.62	−	1791.49i	−0.265114	−	0.0715325i
$857$	18504.4	−	10683.5i	0.737571	−	0.425837i	−0.0836142	−	0.996498i	$-0.526646\pi$
$857$	18504.4	−	10683.5i	0.737571	−	0.425837i	0.821186	+	0.570661i	$0.193313\pi$
$858$	−14175.8	+	1231.92i	−0.564048	+	0.0490176i
$859$	−35409.5	−	20443.7i	−1.40647	−	0.812025i	−0.411422	−	0.911445i	$-0.634968\pi$
$859$	−35409.5	−	20443.7i	−1.40647	−	0.812025i	−0.995046	+	0.0994203i	$0.968301\pi$
$860$	−6654.27	−	7948.99i	−0.263847	−	0.315184i
$861$	−18357.5	−	9051.35i	−0.726624	−	0.358268i
$862$	5068.72	−	10853.4i	0.200280	−	0.428851i
$863$	21210.3	+	12245.8i	0.836624	+	0.483025i	0.856115	−	0.516785i	$-0.172871\pi$
$863$	21210.3	+	12245.8i	0.836624	+	0.483025i	−0.0194912	+	0.999810i	$0.506205\pi$
$864$	−440.116	+	4867.67i	−0.0173299	+	0.191668i
$865$	−1147.06	−	1986.77i	−0.0450882	−	0.0780950i
$866$	20890.3	+	29871.4i	0.819726	+	1.17214i
$867$			1474.17i			0.0577457i
$868$	−3358.19	+	3207.75i	−0.131318	+	0.125436i
$869$			21243.9i			0.829285i
$870$	4866.65	−	3403.45i	0.189649	−	0.132630i
$871$	−2847.70	−	4932.36i	−0.110781	−	0.191879i
$872$	22991.8	+	23072.1i	0.892890	+	0.896008i
$873$	3028.45	+	1748.47i	0.117408	+	0.0677857i
$874$	16708.6	+	7803.15i	0.646654	+	0.301997i
$875$	−10371.1	+	6930.79i	−0.400694	+	0.267775i
$876$	9575.86	+	11439.0i	0.369336	+	0.441197i
$877$	−3679.65	−	2124.44i	−0.141679	−	0.0817986i	0.427485	−	0.904023i	$-0.359400\pi$
$877$	−3679.65	−	2124.44i	−0.141679	−	0.0817986i	−0.569164	+	0.822224i	$0.692733\pi$
$878$	1568.58	+	18049.7i	0.0602925	+	0.693789i
$879$	21753.8	−	12559.6i	0.834742	−	0.481939i
$880$	6646.19	+	5603.18i	0.254594	+	0.214640i
$881$			45692.1i			1.74734i	0.486518	+	0.873671i	$0.338267\pi$
$881$			45692.1i			1.74734i	−0.486518	+	0.873671i	$0.661733\pi$
$882$	8326.08	+	2629.24i	0.317861	+	0.100376i
$883$	15047.4			0.573482			0.286741	−	0.958008i	$-0.407428\pi$
$883$	15047.4			0.573482			0.286741	+	0.958008i	$0.407428\pi$
$884$	−3482.08	−	19882.9i	−0.132483	−	0.756486i
$885$	773.894	+	1340.42i	0.0293945	+	0.0509128i
$886$	−2590.11	−	29804.5i	−0.0982128	−	1.13014i
$887$	1111.47	−	1925.12i	0.0420738	−	0.0728739i	−0.844222	−	0.535994i	$-0.819937\pi$
$887$	1111.47	−	1925.12i	0.0420738	−	0.0728739i	0.886295	+	0.463120i	$0.153270\pi$
$888$	−4686.49	−	17612.9i	−0.177104	−	0.665598i
$889$	13401.4	+	20053.6i	0.505590	+	0.756555i
$890$	3650.29	−	7816.22i	0.137481	−	0.294382i
$891$	−1978.76	+	3427.32i	−0.0744007	+	0.128866i
$892$	14352.0	−	39289.7i	0.538723	−	1.47479i
$893$	−23101.9	+	13337.9i	−0.865705	+	0.499815i
$894$	21999.2	−	15385.0i	0.823001	−	0.575560i
$895$	1768.89			0.0660642
$896$	3974.00	+	26524.1i	0.148172	+	0.988962i
$897$	5990.81			0.222996
$898$	27559.7	−	19273.7i	1.02414	−	0.716226i
$899$	−6833.81	+	3945.50i	−0.253526	+	0.146374i
$900$	2897.08	−	7930.98i	0.107299	−	0.293740i
$901$	27485.2	−	47605.8i	1.01628	−	1.76024i
$902$	21541.3	−	46125.6i	0.795175	−	1.70268i
$903$	11452.7	−	23227.9i	0.422063	−	0.856009i
$904$	5338.97	+	20065.1i	0.196429	+	0.738225i
$905$	−5373.28	+	9306.79i	−0.197363	+	0.341843i
$906$	−1139.62	−	13113.7i	−0.0417896	−	0.480874i
$907$	11742.7	+	20339.0i	0.429890	+	0.744592i	0.996863	−	0.0791448i	$-0.0252189\pi$
$907$	11742.7	+	20339.0i	0.429890	+	0.744592i	−0.566973	+	0.823736i	$0.691886\pi$
$908$	−2831.52	−	16168.2i	−0.103488	−	0.590925i
$909$	−9755.63			−0.355967
$910$	−3126.52	−	3899.65i	−0.113894	−	0.142057i
$911$		−	17053.1i		−	0.620190i	−0.950706	−	0.310095i	$-0.899639\pi$
$911$		−	17053.1i		−	0.620190i	0.950706	−	0.310095i	$-0.100361\pi$
$912$	16449.6	+	13868.1i	0.597258	+	0.503529i
$913$	−14562.8	+	8407.84i	−0.527885	+	0.304774i
$914$	−2133.09	−	24545.6i	−0.0771952	−	0.888288i
$915$	−3399.13	−	1962.49i	−0.122811	−	0.0709048i
$916$	−4513.53	−	5391.73i	−0.162807	−	0.194484i
$917$	−29051.4	+	1906.16i	−1.04620	+	0.0686446i
$918$	−5086.75	−	2375.59i	−0.182884	−	0.0854097i
$919$	−43433.9	−	25076.6i	−1.55903	−	0.900108i	−0.997350	−	0.0727551i	$-0.976821\pi$
$919$	−43433.9	−	25076.6i	−1.55903	−	0.900108i	−0.561683	−	0.827353i	$-0.689846\pi$
$920$	−2583.44	−	2592.46i	−0.0925800	−	0.0929033i
$921$	13887.6	+	24054.0i	0.496864	+	0.860594i
$922$	2882.81	−	2016.07i	0.102972	−	0.0720127i
$923$			7500.40i			0.267474i
$924$	−6099.77	+	20842.6i	−0.217173	+	0.742069i
$925$			31486.3i			1.11920i
$926$	27600.6	+	39466.5i	0.979494	+	1.40059i
$927$	4547.27	+	7876.10i	0.161113	+	0.279056i
$928$	−4103.71	+	45386.9i	−0.145163	+	1.60549i
$929$	−27710.4	−	15998.6i	−0.978630	−	0.565012i	−0.0767740	−	0.997049i	$-0.524462\pi$
$929$	−27710.4	−	15998.6i	−0.978630	−	0.565012i	−0.901856	+	0.432036i	$0.857795\pi$
$930$	312.869	−	669.934i	0.0110316	−	0.0236215i
$931$	30490.3	−	23402.8i	1.07334	−	0.823841i
$932$	19405.7	+	23181.5i	0.682033	+	0.814736i
$933$	−5737.04	−	3312.28i	−0.201310	−	0.116226i
$934$	25875.8	−	2248.69i	0.906511	−	0.0787788i
$935$	−8647.52	+	4992.65i	−0.302464	+	0.174628i
$936$	6748.29	+	1820.81i	0.235657	+	0.0635844i
$937$		−	26286.0i		−	0.916462i	−0.888833	−	0.458231i	$-0.848483\pi$
$937$		−	26286.0i		−	0.916462i	0.888833	−	0.458231i	$-0.151517\pi$
$938$	−8591.91	+	1317.93i	−0.299079	+	0.0458761i
$939$	−28235.5			−0.981291
$940$	5214.92	−	913.285i	0.180949	−	0.0316895i
$941$	−25828.3	−	44735.9i	−0.894770	−	1.54979i	−0.834089	−	0.551631i	$-0.814006\pi$
$941$	−25828.3	−	44735.9i	−0.894770	−	1.54979i	−0.0606818	−	0.998157i	$-0.519327\pi$
$942$	9568.32	−	831.519i	0.330948	−	0.0287605i
$943$	−10716.6	+	18561.8i	−0.370076	+	0.640991i
$944$	−11692.1	−	2089.66i	−0.403121	−	0.0720473i
$945$	−1387.16	+	91.0165i	−0.0477506	+	0.00313309i
$946$	58363.0	+	27256.4i	2.00586	+	0.936767i
$947$	16525.2	−	28622.5i	0.567050	−	0.982159i	−0.429806	−	0.902921i	$-0.641418\pi$
$947$	16525.2	−	28622.5i	0.567050	−	0.982159i	0.996856	−	0.0792378i	$-0.0252486\pi$
$948$	3580.48	−	9801.85i	0.122667	−	0.335811i
$949$	18476.0	−	10667.1i	0.631987	−	0.364878i
$950$	−21301.8	−	30459.8i	−0.727496	−	1.04026i
$951$	−14688.0			−0.500833
$952$	−30205.4	−	6060.77i	−1.02832	−	0.206335i
$953$	−31628.5			−1.07508			−0.537538	−	0.843240i	$-0.680645\pi$
$953$	−31628.5			−1.07508			−0.537538	+	0.843240i	$0.680645\pi$
$954$	10908.7	+	15598.5i	0.370213	+	0.529373i
$955$	7695.82	−	4443.18i	0.260765	−	0.150553i
$956$	20888.2	+	7630.20i	0.706668	+	0.258136i
$957$	−18450.3	+	31956.8i	−0.623211	+	1.07943i
$958$	30111.5	+	14062.5i	1.01551	+	0.474258i
$959$	12581.8	+	6203.55i	0.423656	+	0.208888i
$960$	−2122.16	−	3705.45i	−0.0713462	−	0.124576i
$961$	14404.3	−	24948.9i	0.483511	−	0.837465i
$962$	−25966.7	+	2256.59i	−0.870270	+	0.0756294i
$963$	1367.67	+	2368.87i	0.0457658	+	0.0792686i
$964$	10125.1	+	57814.7i	0.338284	+	1.93163i
$965$	5905.37			0.196996
$966$	3318.22	−	8519.90i	0.110520	−	0.283772i
$967$			43664.8i			1.45208i	0.687651	+	0.726041i	$0.258642\pi$
$967$			43664.8i			1.45208i	−0.687651	+	0.726041i	$0.741358\pi$
$968$	−23072.5	−	6225.37i	−0.766093	−	0.206706i
$969$	−21402.9	+	12357.0i	−0.709558	+	0.409663i
$970$	−3043.74	+	264.511i	−0.100751	+	0.00875560i
$971$	32777.6	+	18924.2i	1.08330	+	0.625444i	0.931785	−	0.363011i	$-0.118251\pi$
$971$	32777.6	+	18924.2i	1.08330	+	0.625444i	0.151516	+	0.988455i	$0.451585\pi$
$972$	1490.64	−	1247.85i	0.0491896	−	0.0411777i
$973$	−7642.94	−	11436.7i	−0.251820	−	0.376819i
$974$	3420.09	−	7323.30i	0.112512	−	0.240918i
$975$	−10457.3	−	6037.53i	−0.343489	−	0.198314i
$976$	28326.9	−	10235.7i	0.929018	−	0.335692i
$977$	−17115.3	−	29644.6i	−0.560458	−	0.970741i	−0.997456	−	0.0712792i	$-0.977292\pi$
$977$	−17115.3	−	29644.6i	−0.560458	−	0.970741i	0.436999	−	0.899462i	$-0.356041\pi$
$978$	6594.06	+	9428.94i	0.215598	+	0.308287i
$979$			53602.3i			1.74988i
$980$	−7277.67	+	2286.46i	−0.237221	+	0.0745290i
$981$		−	12955.5i		−	0.421648i
$982$	−669.067	+	467.907i	−0.0217421	+	0.0152052i
$983$	−19661.5	−	34054.6i	−0.637948	−	1.10496i	−0.985882	−	0.167440i	$-0.946450\pi$
$983$	−19661.5	−	34054.6i	−0.637948	−	1.10496i	0.347934	−	0.937519i	$-0.386883\pi$
$984$	−17713.2	+	17651.6i	−0.573858	+	0.571862i
$985$	1180.34	+	681.468i	0.0381814	+	0.0220440i
$986$	−47429.6	−	22150.4i	−1.53191	−	0.715427i
$987$	7348.88	+	10996.7i	0.236998	+	0.354640i
$988$	23593.4	−	19750.6i	0.759723	−	0.635981i
$989$	−23486.3	−	13559.8i	−0.755128	−	0.435973i
$990$	−299.349	−	3444.62i	−0.00961003	−	0.110583i
$991$	26171.2	−	15109.9i	0.838905	−	0.484342i	−0.0179870	−	0.999838i	$-0.505726\pi$
$991$	26171.2	−	15109.9i	0.838905	−	0.484342i	0.856892	+	0.515496i	$0.172392\pi$
$992$	2382.96	+	5149.27i	0.0762692	+	0.164808i
$993$			14467.4i			0.462345i
$994$	10666.8	+	4154.36i	0.340372	+	0.132564i
$995$	−6103.99			−0.194482
$996$	8136.31	−	1424.91i	0.258844	−	0.0453312i
$997$	−6135.25	−	10626.6i	−0.194890	−	0.337559i	0.751975	−	0.659192i	$-0.229102\pi$
$997$	−6135.25	−	10626.6i	−0.194890	−	0.337559i	−0.946864	+	0.321633i	$0.895768\pi$
$998$	3400.64	+	39131.3i	0.107861	+	1.24116i
$999$	−3624.63	+	6278.04i	−0.114793	+	0.198827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.t.a.19.9	✓	96
4.3	odd	2		672.4.bb.a.271.34		96
7.3	odd	6	inner	168.4.t.a.115.23	yes	96
8.3	odd	2	inner	168.4.t.a.19.23	yes	96
8.5	even	2		672.4.bb.a.271.33		96
28.3	even	6		672.4.bb.a.367.33		96
56.3	even	6	inner	168.4.t.a.115.9	yes	96
56.45	odd	6		672.4.bb.a.367.34		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.9	✓	96	1.1	even	1	trivial
168.4.t.a.19.23	yes	96	8.3	odd	2	inner
168.4.t.a.115.9	yes	96	56.3	even	6	inner
168.4.t.a.115.23	yes	96	7.3	odd	6	inner
672.4.bb.a.271.33		96	8.5	even	2
672.4.bb.a.271.34		96	4.3	odd	2
672.4.bb.a.367.33		96	28.3	even	6
672.4.bb.a.367.34		96	56.45	odd	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.31785 + 1.62097i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(2.74489 - 7.51436i) q^{4} +(1.39001 - 2.40757i) q^{5} +(3.59050 - 7.68819i) q^{6} +(-15.3983 + 10.2904i) q^{7} +(5.81831 + 21.8666i) q^{8} +(4.50000 - 7.79423i) q^{9} +(0.680764 + 7.83358i) q^{10} +(-24.4292 - 42.3125i) q^{11} +(4.14009 + 23.6402i) q^{12} +34.3223 q^{13} +(19.0106 - 48.8118i) q^{14} +8.34008i q^{15} +(-48.9311 - 41.2522i) q^{16} +(63.6655 - 36.7573i) q^{17} +(2.20389 + 25.3603i) q^{18} +(97.0462 + 56.0297i) q^{19} +(-14.2759 - 17.0536i) q^{20} +(24.5704 - 49.8327i) q^{21} +(125.211 + 58.4753i) q^{22} +(-50.3870 - 29.0910i) q^{23} +(-47.9163 - 48.0836i) q^{24} +(58.6357 + 101.560i) q^{25} +(-79.5540 + 55.6355i) q^{26} +27.0000i q^{27} +(35.0588 + 143.954i) q^{28} +251.752i q^{29} +(-13.5190 - 19.3311i) q^{30} +(15.6722 + 27.1450i) q^{31} +(180.284 + 16.3006i) q^{32} +(126.938 + 73.2875i) q^{33} +(-87.9847 + 188.398i) q^{34} +(3.37098 + 51.3763i) q^{35} +(-46.2166 - 55.2089i) q^{36} +(232.520 + 134.245i) q^{37} +(-315.762 + 27.4407i) q^{38} +(-89.1719 + 51.4834i) q^{39} +(60.7329 + 16.3868i) q^{40} -368.384i q^{41} +(23.8267 + 155.333i) q^{42} +466.118 q^{43} +(-385.007 + 67.4260i) q^{44} +(-12.5101 - 21.6682i) q^{45} +(163.945 - 14.2474i) q^{46} +(-119.025 + 206.158i) q^{47} +(189.005 + 33.7797i) q^{48} +(131.216 - 316.909i) q^{49} +(-300.535 - 140.354i) q^{50} +(-110.272 + 190.996i) q^{51} +(94.2109 - 257.910i) q^{52} +(647.569 - 373.874i) q^{53} +(-43.7663 - 62.5821i) q^{54} -135.827 q^{55} +(-314.608 - 276.836i) q^{56} -336.178 q^{57} +(-408.084 - 583.525i) q^{58} +(160.721 - 92.7921i) q^{59} +(62.6703 + 22.8926i) q^{60} +(-235.308 + 407.566i) q^{61} +(-80.3270 - 37.5139i) q^{62} +(10.9131 + 166.325i) q^{63} +(-444.295 + 254.453i) q^{64} +(47.7084 - 82.6334i) q^{65} +(-413.020 + 35.8928i) q^{66} +(-82.9694 - 143.707i) q^{67} +(-101.452 - 579.300i) q^{68} +174.546 q^{69} +(-91.0931 - 113.619i) q^{70} +218.529i q^{71} +(196.616 + 53.0504i) q^{72} +(538.309 - 310.793i) q^{73} +(-756.556 + 65.7472i) q^{74} +(-304.680 - 175.907i) q^{75} +(687.408 - 575.445i) q^{76} +(811.580 + 400.157i) q^{77} +(123.234 - 263.876i) q^{78} +(-376.553 - 217.403i) q^{79} +(-167.333 + 60.4641i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(597.140 + 853.860i) q^{82} -344.173i q^{83} +(-307.017 - 321.416i) q^{84} -204.372i q^{85} +(-1080.39 + 755.565i) q^{86} +(-377.628 - 654.072i) q^{87} +(783.094 - 780.369i) q^{88} +(-950.113 - 548.548i) q^{89} +(64.1201 + 29.9451i) q^{90} +(-528.505 + 353.189i) q^{91} +(-356.907 + 298.775i) q^{92} +(-81.4349 - 47.0165i) q^{93} +(-58.2930 - 670.780i) q^{94} +(269.791 - 155.764i) q^{95} +(-492.842 + 228.076i) q^{96} +388.550i q^{97} +(209.561 + 947.247i) q^{98} -439.725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) \) 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Introduction

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