LMFDB - Embedded newform 168.4.ba.c.101.47

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(5,168)] 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([0, 3, 3, 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("168.5"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [176,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.47
Character	$\chi$	$=$	168.101
Dual form			168.4.ba.c.5.47

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.342354 + 2.80763i) q^{2} +(-4.19123 - 3.07141i) q^{3} +(-7.76559 + 1.92241i) q^{4} +(3.83548 - 2.21442i) q^{5} +(7.18850 - 12.8189i) q^{6} +(-18.2781 + 2.98509i) q^{7} +(-8.05600 - 21.1448i) q^{8} +(8.13288 + 25.7460i) q^{9} +(7.53036 + 10.0105i) q^{10} +(4.57157 - 7.91819i) q^{11} +(38.4519 + 15.7940i) q^{12} +69.6182 q^{13} +(-14.6386 - 50.2962i) q^{14} +(-22.8768 - 2.49920i) q^{15} +(56.6087 - 29.8573i) q^{16} +(57.1065 - 98.9113i) q^{17} +(-69.5009 + 31.6484i) q^{18} +(61.1759 + 105.960i) q^{19} +(-25.5278 + 24.5696i) q^{20} +(85.7763 + 43.6283i) q^{21} +(23.7965 + 10.1245i) q^{22} +(17.4658 - 10.0839i) q^{23} +(-31.1797 + 113.366i) q^{24} +(-52.6927 + 91.2665i) q^{25} +(23.8341 + 195.462i) q^{26} +(44.9897 - 132.887i) q^{27} +(136.202 - 58.3190i) q^{28} +170.605 q^{29} +(-0.815129 - 65.0852i) q^{30} +(-21.2529 - 12.2703i) q^{31} +(103.208 + 148.715i) q^{32} +(-43.4805 + 19.1458i) q^{33} +(297.257 + 126.471i) q^{34} +(-63.4951 + 51.9246i) q^{35} +(-112.651 - 184.298i) q^{36} +(128.940 - 74.4434i) q^{37} +(-276.552 + 208.035i) q^{38} +(-291.786 - 213.826i) q^{39} +(-77.7220 - 63.2610i) q^{40} -232.589 q^{41} +(-93.1264 + 255.764i) q^{42} -330.977i q^{43} +(-20.2789 + 70.2779i) q^{44} +(88.2059 + 80.7387i) q^{45} +(34.2914 + 45.5854i) q^{46} +(118.864 + 205.878i) q^{47} +(-328.964 - 48.7297i) q^{48} +(325.178 - 109.124i) q^{49} +(-274.282 - 116.696i) q^{50} +(-543.144 + 239.163i) q^{51} +(-540.626 + 133.835i) q^{52} +(165.999 - 287.519i) q^{53} +(388.500 + 80.8201i) q^{54} -40.4935i q^{55} +(210.367 + 362.438i) q^{56} +(69.0434 - 631.998i) q^{57} +(58.4072 + 478.995i) q^{58} +(378.412 + 218.477i) q^{59} +(182.456 - 24.5708i) q^{60} +(-261.708 - 453.292i) q^{61} +(27.1746 - 63.8710i) q^{62} +(-225.508 - 446.311i) q^{63} +(-382.202 + 340.684i) q^{64} +(267.019 - 154.164i) q^{65} +(-68.6402 - 115.523i) q^{66} +(149.924 + 86.5586i) q^{67} +(-253.317 + 877.887i) q^{68} +(-104.175 - 11.3807i) q^{69} +(-167.523 - 160.494i) q^{70} -792.275i q^{71} +(478.874 - 379.377i) q^{72} +(952.933 + 550.176i) q^{73} +(253.153 + 336.529i) q^{74} +(501.164 - 220.678i) q^{75} +(-678.764 - 705.234i) q^{76} +(-59.9231 + 158.376i) q^{77} +(500.451 - 892.432i) q^{78} +(-517.761 - 896.789i) q^{79} +(151.005 - 239.872i) q^{80} +(-596.713 + 418.778i) q^{81} +(-79.6277 - 653.023i) q^{82} +364.364i q^{83} +(-749.975 - 173.903i) q^{84} -505.830i q^{85} +(929.261 - 113.311i) q^{86} +(-715.043 - 523.996i) q^{87} +(-204.257 - 32.8758i) q^{88} +(475.732 + 823.992i) q^{89} +(-196.487 + 275.291i) q^{90} +(-1272.49 + 207.817i) q^{91} +(-116.247 + 111.884i) q^{92} +(51.3884 + 116.704i) q^{93} +(-537.336 + 404.209i) q^{94} +(469.278 + 270.938i) q^{95} +(24.1928 - 940.293i) q^{96} +538.631i q^{97} +(417.705 + 875.622i) q^{98} +(241.042 + 53.3019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 30 q^{4} - 76 q^{7} - 110 q^{9} + 330 q^{10} + 162 q^{12} - 332 q^{15} + 374 q^{16} + 18 q^{18} - 212 q^{22} - 84 q^{24} + 1112 q^{25} + 30 q^{28} - 104 q^{30} + 408 q^{31} + 2262 q^{33} + 1372 q^{36}+ \cdots - 1782 q^{96}+O(q^{100}) $ 176 * q + 30 * q^4 - 76 * q^7 - 110 * q^9 + 330 * q^10 + 162 * q^12 - 332 * q^15 + 374 * q^16 + 18 * q^18 - 212 * q^22 - 84 * q^24 + 1112 * q^25 + 30 * q^28 - 104 * q^30 + 408 * q^31 + 2262 * q^33 + 1372 * q^36 - 56 * q^39 - 2274 * q^40 - 1488 * q^42 - 844 * q^46 + 1292 * q^49 - 1632 * q^52 - 480 * q^54 + 100 * q^57 - 574 * q^58 - 524 * q^60 - 3030 * q^63 - 3420 * q^64 + 2376 * q^66 + 2442 * q^70 + 1026 * q^72 - 660 * q^73 - 1316 * q^78 + 3216 * q^79 + 2298 * q^81 - 360 * q^82 - 4164 * q^84 - 6972 * q^87 - 4042 * q^88 + 4476 * q^94 - 1782 * q^96

Character values

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

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

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 $

$2$	0.342354	+	2.80763i	0.121040	+	0.992648i
$2$	0.342354	+	2.80763i	0.121040	+	0.992648i
$3$	−4.19123	−	3.07141i	−0.806603	−	0.591093i
$3$	−4.19123	−	3.07141i	−0.806603	−	0.591093i
$4$	−7.76559	+	1.92241i	−0.970698	+	0.240301i
$5$	3.83548	−	2.21442i	0.343056	−	0.198064i	−0.318567	−	0.947900i	$-0.603201\pi$
$5$	3.83548	−	2.21442i	0.343056	−	0.198064i	0.661623	+	0.749837i	$0.269868\pi$
$6$	7.18850	−	12.8189i	0.489116	−	0.872219i
$7$	−18.2781	+	2.98509i	−0.986925	+	0.161180i
$7$	−18.2781	+	2.98509i	−0.986925	+	0.161180i
$8$	−8.05600	−	21.1448i	−0.356028	−	0.934475i
$9$	8.13288	+	25.7460i	0.301218	+	0.953555i
$10$	7.53036	+	10.0105i	0.238131	+	0.316560i
$11$	4.57157	−	7.91819i	0.125307	−	0.217039i	−0.796546	−	0.604578i	$-0.793342\pi$
$11$	4.57157	−	7.91819i	0.125307	−	0.217039i	0.921853	+	0.387540i	$0.126675\pi$
$12$	38.4519	+	15.7940i	0.925009	+	0.379946i
$13$	69.6182			1.48528			0.742639	−	0.669692i	$-0.233574\pi$
$13$	69.6182			1.48528			0.742639	+	0.669692i	$0.233574\pi$
$14$	−14.6386	−	50.2962i	−0.279453	−	0.960159i
$15$	−22.8768	−	2.49920i	−0.393784	−	0.0430194i
$16$	56.6087	−	29.8573i	0.884511	−	0.466520i
$17$	57.1065	−	98.9113i	0.814727	−	1.41115i	−0.0947970	−	0.995497i	$-0.530220\pi$
$17$	57.1065	−	98.9113i	0.814727	−	1.41115i	0.909524	−	0.415652i	$-0.136446\pi$
$18$	−69.5009	+	31.6484i	−0.910085	+	0.414422i
$19$	61.1759	+	105.960i	0.738669	+	1.27941i	0.953095	+	0.302672i	$0.0978785\pi$
$19$	61.1759	+	105.960i	0.738669	+	1.27941i	−0.214426	+	0.976740i	$0.568788\pi$
$20$	−25.5278	+	24.5696i	−0.285409	+	0.274697i
$21$	85.7763	+	43.6283i	0.891329	+	0.453356i
$22$	23.7965	+	10.1245i	0.230610	+	0.0981156i
$23$	17.4658	−	10.0839i	0.158343	−	0.0914191i	−0.418735	−	0.908108i	$-0.637526\pi$
$23$	17.4658	−	10.0839i	0.158343	−	0.0914191i	0.577078	+	0.816689i	$0.304193\pi$
$24$	−31.1797	+	113.366i	−0.265188	+	0.964197i
$25$	−52.6927	+	91.2665i	−0.421542	+	0.730132i
$26$	23.8341	+	195.462i	0.179779	+	1.47436i
$27$	44.9897	−	132.887i	0.320677	−	0.947189i
$28$	136.202	−	58.3190i	0.919275	−	0.393616i
$29$	170.605			1.09243			0.546215	−	0.837645i	$-0.316068\pi$
$29$	170.605			1.09243			0.546215	+	0.837645i	$0.316068\pi$
$30$	−0.815129	−	65.0852i	−0.00496072	−	0.396096i
$31$	−21.2529	−	12.2703i	−0.123133	−	0.0710909i	0.437168	−	0.899380i	$-0.355981\pi$
$31$	−21.2529	−	12.2703i	−0.123133	−	0.0710909i	−0.560301	+	0.828289i	$0.689315\pi$
$32$	103.208	+	148.715i	0.570151	+	0.821540i
$33$	−43.4805	+	19.1458i	−0.229363	+	0.100996i
$34$	297.257	+	126.471i	1.49939	+	0.637931i
$35$	−63.4951	+	51.9246i	−0.306647	+	0.250768i
$36$	−112.651	−	184.298i	−0.521532	−	0.853232i
$37$	128.940	−	74.4434i	0.572907	−	0.330768i	−0.185402	−	0.982663i	$-0.559359\pi$
$37$	128.940	−	74.4434i	0.572907	−	0.330768i	0.758310	+	0.651895i	$0.226026\pi$
$38$	−276.552	+	208.035i	−1.18060	+	0.888098i
$39$	−291.786	−	213.826i	−1.19803	−	0.877938i
$40$	−77.7220	−	63.2610i	−0.307223	−	0.250061i
$41$	−232.589			−0.885957			−0.442978	−	0.896532i	$-0.646078\pi$
$41$	−232.589			−0.885957			−0.442978	+	0.896532i	$0.646078\pi$
$42$	−93.1264	+	255.764i	−0.342136	+	0.939650i
$43$		−	330.977i		−	1.17380i	−0.809659	−	0.586901i	$-0.800348\pi$
$43$		−	330.977i		−	1.17380i	0.809659	−	0.586901i	$-0.199652\pi$
$44$	−20.2789	+	70.2779i	−0.0694810	+	0.240791i
$45$	88.2059	+	80.7387i	0.292199	+	0.267463i
$46$	34.2914	+	45.5854i	0.109913	+	0.146113i
$47$	118.864	+	205.878i	0.368895	+	0.638944i	0.989393	−	0.145263i	$-0.0464029\pi$
$47$	118.864	+	205.878i	0.368895	+	0.638944i	−0.620498	+	0.784208i	$0.713070\pi$
$48$	−328.964	−	48.7297i	−0.989206	−	0.146532i
$49$	325.178	−	109.124i	0.948042	−	0.318145i
$50$	−274.282	−	116.696i	−0.775787	−	0.330067i
$51$	−543.144	+	239.163i	−1.49128	+	0.656657i
$52$	−540.626	+	133.835i	−1.44176	+	0.356914i
$53$	165.999	−	287.519i	0.430221	−	0.745165i	−0.566671	−	0.823944i	$-0.691769\pi$
$53$	165.999	−	287.519i	0.430221	−	0.745165i	0.996892	+	0.0787793i	$0.0251022\pi$
$54$	388.500	+	80.8201i	0.979039	+	0.203671i
$55$		−	40.4935i		−	0.0992752i
$56$	210.367	+	362.438i	0.501992	+	0.864872i
$57$	69.0434	−	631.998i	0.160439	−	1.46860i
$58$	58.4072	+	478.995i	0.132228	+	1.08440i
$59$	378.412	+	218.477i	0.835002	+	0.482089i	0.855562	−	0.517700i	$-0.173212\pi$
$59$	378.412	+	218.477i	0.835002	+	0.482089i	−0.0205604	+	0.999789i	$0.506545\pi$
$60$	182.456	−	24.5708i	0.392583	−	0.0528679i
$61$	−261.708	−	453.292i	−0.549317	−	0.951445i	−0.998322	−	0.0579152i	$-0.981555\pi$
$61$	−261.708	−	453.292i	−0.549317	−	0.951445i	0.449005	−	0.893529i	$-0.351779\pi$
$62$	27.1746	−	63.8710i	0.0556641	−	0.130833i
$63$	−225.508	−	446.311i	−0.450973	−	0.892537i
$64$	−382.202	+	340.684i	−0.746488	+	0.665399i
$65$	267.019	−	154.164i	0.509534	−	0.294179i
$66$	−68.6402	−	115.523i	−0.128015	−	0.215452i
$67$	149.924	+	86.5586i	0.273375	+	0.157833i	0.630420	−	0.776254i	$-0.282883\pi$
$67$	149.924	+	86.5586i	0.273375	+	0.157833i	−0.357045	+	0.934087i	$0.616216\pi$
$68$	−253.317	+	877.887i	−0.451754	+	1.56558i
$69$	−104.175	−	11.3807i	−0.181757	−	0.0198562i
$70$	−167.523	−	160.494i	−0.286040	−	0.274039i
$71$		−	792.275i		−	1.32431i	−0.749369	−	0.662153i	$-0.769643\pi$
$71$		−	792.275i		−	1.32431i	0.749369	−	0.662153i	$-0.230357\pi$
$72$	478.874	−	379.377i	0.783832	−	0.620973i
$73$	952.933	+	550.176i	1.52784	+	0.882099i	0.999452	+	0.0330968i	$0.0105370\pi$
$73$	952.933	+	550.176i	1.52784	+	0.882099i	0.528389	+	0.849003i	$0.322796\pi$
$74$	253.153	+	336.529i	0.397681	+	0.528658i
$75$	501.164	−	220.678i	0.771593	−	0.339756i
$76$	−678.764	−	705.234i	−1.02447	−	1.06442i
$77$	−59.9231	+	158.376i	−0.0886867	+	0.234398i
$78$	500.451	−	892.432i	0.726473	−	1.29549i
$79$	−517.761	−	896.789i	−0.737376	−	1.27717i	−0.953673	−	0.300845i	$-0.902731\pi$
$79$	−517.761	−	896.789i	−0.737376	−	1.27717i	0.216297	−	0.976328i	$-0.430602\pi$
$80$	151.005	−	239.872i	0.211036	−	0.335232i
$81$	−596.713	+	418.778i	−0.818536	+	0.574456i
$82$	−79.6277	−	653.023i	−0.107237	−	0.879443i
$83$			364.364i			0.481857i	0.970543	+	0.240928i	$0.0774519\pi$
$83$			364.364i			0.481857i	−0.970543	+	0.240928i	$0.922548\pi$
$84$	−749.975	−	173.903i	−0.974154	−	0.225885i
$85$		−	505.830i		−	0.645471i
$86$	929.261	−	113.311i	1.16517	−	0.142078i
$87$	−715.043	−	523.996i	−0.881158	−	0.645728i
$88$	−204.257	−	32.8758i	−0.247430	−	0.0398247i
$89$	475.732	+	823.992i	0.566601	+	0.981382i	0.996899	+	0.0786949i	$0.0250753\pi$
$89$	475.732	+	823.992i	0.566601	+	0.981382i	−0.430298	+	0.902687i	$0.641591\pi$
$90$	−196.487	+	275.291i	−0.230128	+	0.322425i
$91$	−1272.49	+	207.817i	−1.46586	+	0.239397i
$92$	−116.247	+	111.884i	−0.131735	+	0.126790i
$93$	51.3884	+	116.704i	0.0572982	+	0.130125i
$94$	−537.336	+	404.209i	−0.589595	+	0.443521i
$95$	469.278	+	270.938i	0.506810	+	0.292607i
$96$	24.1928	−	940.293i	0.0257205	−	0.999669i
$97$			538.631i			0.563811i	0.959442	+	0.281906i	$0.0909665\pi$
$97$			538.631i			0.563811i	−0.959442	+	0.281906i	$0.909034\pi$
$98$	417.705	+	875.622i	0.430557	+	0.902563i
$99$	241.042	+	53.3019i	0.244703	+	0.0541116i
$100$	233.738	−	810.035i	0.233738	−	0.810035i
$101$	−1447.64	−	835.793i	−1.42619	−	0.823411i	−0.429372	−	0.903128i	$-0.641265\pi$
$101$	−1447.64	−	835.793i	−1.42619	−	0.823411i	−0.996818	+	0.0797166i	$0.974598\pi$
$102$	−857.429	−	1443.07i	−0.832335	−	1.40083i
$103$	−414.915	+	239.551i	−0.396920	+	0.229162i	−0.685154	−	0.728398i	$-0.740265\pi$
$103$	−414.915	+	239.551i	−0.396920	+	0.229162i	0.288234	+	0.957560i	$0.406932\pi$
$104$	−560.844	−	1472.06i	−0.528801	−	1.38796i
$105$	425.605	−	22.6087i	0.395569	−	0.0210131i
$106$	864.077	+	367.631i	0.791760	+	0.336863i
$107$	21.6556	+	37.5087i	0.0195657	+	0.0338888i	0.875642	−	0.482960i	$-0.160438\pi$
$107$	21.6556	+	37.5087i	0.0195657	+	0.0338888i	−0.856077	+	0.516849i	$0.827105\pi$
$108$	−93.9085	+	1118.43i	−0.0836699	+	0.996494i
$109$	1464.69	+	845.637i	1.28708	+	0.743094i	0.978132	−	0.207985i	$-0.0666906\pi$
$109$	1464.69	+	845.637i	1.28708	+	0.743094i	0.308945	+	0.951080i	$0.400024\pi$
$110$	113.691	−	13.8631i	0.0985453	−	0.0120163i
$111$	−769.063	−	84.0172i	−0.657623	−	0.0718428i
$112$	−945.573	+	714.717i	−0.797752	+	0.602985i
$113$			390.146i			0.324795i	0.986725	+	0.162398i	$0.0519227\pi$
$113$			390.146i			0.324795i	−0.986725	+	0.162398i	$0.948077\pi$
$114$	1798.05	−	22.5189i	1.47722	−	0.0185008i
$115$	44.6600	−	77.3533i	0.0362136	−	0.0627238i
$116$	−1324.84	+	327.972i	−1.06042	+	0.262512i
$117$	566.197	+	1792.39i	0.447392	+	1.41629i
$118$	−483.850	+	1137.24i	−0.377475	+	0.887215i
$119$	−748.539	+	1978.38i	−0.576626	+	1.52402i
$120$	131.450	+	503.858i	0.0999977	+	0.383298i
$121$	623.701	+	1080.28i	0.468596	+	0.811632i
$122$	1183.08	−	889.967i	0.877960	−	0.660441i
$123$	974.833	+	714.375i	0.714616	+	0.523683i
$124$	188.630	+	54.4297i	0.136608	+	0.0394188i
$125$			1020.34i			0.730095i
$126$	1175.87	−	785.939i	0.831389	−	0.555691i
$127$	581.507			0.406302			0.203151	−	0.979147i	$-0.434882\pi$
$127$	581.507			0.406302			0.203151	+	0.979147i	$0.434882\pi$
$128$	−1087.36	−	956.447i	−0.750862	−	0.660459i
$129$	−1016.57	+	1387.20i	−0.693826	+	0.946793i
$130$	524.250	+	696.914i	0.353691	+	0.470180i
$131$	28.9739	−	16.7281i	0.0193242	−	0.0111568i	−0.490307	−	0.871550i	$-0.663115\pi$
$131$	28.9739	−	16.7281i	0.0193242	−	0.0111568i	0.509631	+	0.860393i	$0.329782\pi$
$132$	300.846	−	232.266i	0.198373	−	0.153153i
$133$	−1434.48	−	1754.13i	−0.935226	−	1.14363i
$134$	−191.698	+	450.565i	−0.123583	+	0.290469i
$135$	−121.710	−	609.311i	−0.0775934	−	0.388453i
$136$	−2551.51	−	410.674i	−1.60875	−	0.258934i
$137$	−800.795	−	462.339i	−0.499391	−	0.288324i	0.229071	−	0.973410i	$-0.426431\pi$
$137$	−800.795	−	462.339i	−0.499391	−	0.288324i	−0.728462	+	0.685086i	$0.759765\pi$
$138$	−3.71190	−	296.382i	−0.00228969	−	0.182824i
$139$	534.947			0.326429			0.163214	−	0.986591i	$-0.447814\pi$
$139$	534.947			0.326429			0.163214	+	0.986591i	$0.447814\pi$
$140$	393.257	−	525.289i	0.237402	−	0.317107i
$141$	134.150	−	1227.96i	0.0801240	−	0.733426i
$142$	2224.42	−	271.239i	1.31457	−	0.160295i
$143$	318.265	−	551.250i	0.186116	−	0.322363i
$144$	1229.10	+	1214.62i	0.711283	+	0.702906i
$145$	654.351	−	377.790i	0.374765	−	0.216370i
$146$	−1218.45	+	2863.84i	−0.690683	+	1.62338i
$147$	−1698.06	−	541.394i	−0.952747	−	0.303765i
$148$	−858.182	+	825.972i	−0.476636	+	0.458746i
$149$	−586.155	−	1015.25i	−0.322280	−	0.558205i	0.658678	−	0.752425i	$-0.271116\pi$
$149$	−586.155	−	1015.25i	−0.322280	−	0.558205i	−0.980958	+	0.194220i	$0.937782\pi$
$150$	791.158	+	1331.53i	0.430652	+	0.724795i
$151$	132.573	−	229.623i	0.0714478	−	0.123751i	−0.828088	−	0.560598i	$-0.810571\pi$
$151$	132.573	−	229.623i	0.0714478	−	0.123751i	0.899536	+	0.436847i	$0.143905\pi$
$152$	1747.66	−	2147.16i	0.932592	−	1.14577i
$153$	3011.01	+	665.829i	1.59102	+	0.351824i
$154$	−465.177	−	114.021i	−0.243409	−	0.0596630i
$155$	−108.687			−0.0563221
$156$	2676.95	+	1099.55i	1.37390	+	0.564325i
$157$	139.361	−	241.380i	0.0708420	−	0.122702i	−0.828429	−	0.560095i	$-0.810765\pi$
$157$	139.361	−	241.380i	0.0708420	−	0.122702i	0.899271	+	0.437393i	$0.144098\pi$
$158$	2340.60	−	1760.70i	1.17853	−	0.886544i
$159$	−1578.83	+	695.207i	−0.787480	+	0.346752i
$160$	725.170	+	341.846i	0.358311	+	0.168908i
$161$	−289.141	+	236.452i	−0.141537	+	0.115745i
$162$	−1380.06	−	1531.98i	−0.669308	−	0.742985i
$163$	1401.52	−	809.168i	0.673470	−	0.388828i	−0.123920	−	0.992292i	$-0.539547\pi$
$163$	1401.52	−	809.168i	0.673470	−	0.388828i	0.797390	+	0.603464i	$0.206213\pi$
$164$	1806.19	−	447.130i	0.859997	−	0.212896i
$165$	−124.372	+	169.718i	−0.0586809	+	0.0800757i
$166$	−1023.00	+	124.741i	−0.478314	+	0.0583242i
$167$	3255.34			1.50842			0.754209	−	0.656634i	$-0.228021\pi$
$167$	3255.34			1.50842			0.754209	+	0.656634i	$0.228021\pi$
$168$	231.498	−	2165.19i	0.106312	−	0.994333i
$169$	2649.69			1.20605
$170$	1420.19	−	173.173i	0.640725	−	0.0781281i
$171$	−2230.50	+	2436.79i	−0.997490	+	1.08974i
$172$	636.273	+	2570.23i	0.282066	+	1.13941i
$173$	−909.782	+	525.263i	−0.399823	+	0.230838i	−0.686408	−	0.727217i	$-0.740813\pi$
$173$	−909.782	+	525.263i	−0.399823	+	0.230838i	0.286584	+	0.958055i	$0.407480\pi$
$174$	1226.39	−	2186.97i	0.534324	−	0.952838i
$175$	690.684	−	1825.47i	0.298348	−	0.788529i
$176$	22.3750	−	584.733i	0.00958285	−	0.250431i
$177$	−914.984	−	2077.95i	−0.388556	−	0.882418i
$178$	−2150.60	+	1617.78i	−0.905585	+	0.681222i
$179$	−1140.19	+	1974.88i	−0.476102	+	0.824632i	−0.999625	−	0.0273792i	$-0.991284\pi$
$179$	−1140.19	+	1974.88i	−0.476102	+	0.824632i	0.523524	+	0.852011i	$0.324617\pi$
$180$	−840.183	−	457.416i	−0.347909	−	0.189410i
$181$	3647.62			1.49793			0.748964	−	0.662610i	$-0.230551\pi$
$181$	3647.62			1.49793			0.748964	+	0.662610i	$0.230551\pi$
$182$	−1019.11	−	3501.53i	−0.415065	−	1.42610i
$183$	−295.365	+	2703.67i	−0.119312	+	1.09214i
$184$	−353.927	−	288.075i	−0.141803	−	0.115419i
$185$	329.697	−	571.053i	0.131026	−	0.226944i
$186$	−310.069	+	184.234i	−0.122233	+	0.0726274i
$187$	−522.133	−	904.360i	−0.204183	−	0.353654i
$188$	−1318.83	−	1370.26i	−0.511625	−	0.531577i
$189$	−425.647	+	2563.22i	−0.163816	+	0.986491i
$190$	−600.034	+	1410.32i	−0.229111	+	0.538501i
$191$	−2715.70	+	1567.91i	−1.02880	+	0.593980i	−0.916641	−	0.399710i	$-0.869111\pi$
$191$	−2715.70	+	1567.91i	−1.02880	+	0.593980i	−0.112161	+	0.993690i	$0.535777\pi$
$192$	2648.28	−	253.989i	0.995432	−	0.0954691i
$193$	−1215.31	+	2104.98i	−0.453265	+	0.785078i	−0.998587	−	0.0531487i	$-0.983074\pi$
$193$	−1215.31	+	2104.98i	−0.453265	+	0.785078i	0.545321	+	0.838227i	$0.316408\pi$
$194$	−1512.28	+	184.403i	−0.559666	+	0.0682440i
$195$	−1592.64	−	173.990i	−0.584879	−	0.0638958i
$196$	−2315.42	+	1472.54i	−0.843812	+	0.536638i
$197$	1090.17			0.394272			0.197136	−	0.980376i	$-0.436836\pi$
$197$	1090.17			0.394272			0.197136	+	0.980376i	$0.436836\pi$
$198$	−67.1305	+	695.005i	−0.0240947	+	0.249454i
$199$	1051.02	+	606.809i	0.374398	+	0.216159i	0.675378	−	0.737472i	$-0.263981\pi$
$199$	1051.02	+	606.809i	0.374398	+	0.216159i	−0.300980	+	0.953630i	$0.597314\pi$
$200$	2354.30	+	378.933i	0.832371	+	0.133973i
$201$	−362.509	−	823.265i	−0.127211	−	0.288899i
$202$	1850.99	−	4350.57i	0.644730	−	1.51537i
$203$	−3118.33	+	509.270i	−1.07815	+	0.176078i
$204$	3758.06	−	2901.39i	1.28979	−	0.995773i
$205$	−892.089	+	515.048i	−0.303933	+	0.175476i
$206$	−814.620	−	1082.92i	−0.275521	−	0.366264i
$207$	401.668	+	367.664i	0.134869	+	0.123451i
$208$	3941.00	−	2078.61i	1.31374	−	0.692912i
$209$	1118.68			0.370242
$210$	209.184	+	1187.20i	0.0687385	+	0.390117i
$211$		−	1579.53i		−	0.515353i	−0.966231	−	0.257677i	$-0.917043\pi$
$211$		−	1579.53i		−	0.515353i	0.966231	−	0.257677i	$-0.0829569\pi$
$212$	−736.351	+	2551.87i	−0.238551	+	0.826713i
$213$	−2433.40	+	3320.61i	−0.782788	+	1.06819i
$214$	−97.8966	+	73.6423i	−0.0312714	+	0.0235237i
$215$	−732.921	−	1269.46i	−0.232487	−	0.402680i
$216$	−3172.30	+	119.240i	−0.999294	+	0.0375613i
$217$	425.090	+	160.837i	0.132982	+	0.0503148i
$218$	−1872.79	+	4401.80i	−0.581842	+	1.36756i
$219$	−2304.15	−	5232.77i	−0.710959	−	1.61460i
$220$	77.8450	+	314.456i	0.0238559	+	0.0963663i
$221$	3975.65	−	6886.03i	1.21010	−	2.09595i
$222$	−27.4027	−	2188.01i	−0.00828445	−	0.661484i
$223$		−	686.176i		−	0.206053i	−0.994679	−	0.103026i	$-0.967147\pi$
$223$		−	686.176i		−	0.206053i	0.994679	−	0.103026i	$-0.0328526\pi$
$224$	−2330.38	−	2410.13i	−0.695112	−	0.718901i
$225$	−2778.29	−	614.367i	−0.823197	−	0.182035i
$226$	−1095.39	+	133.568i	−0.322407	+	0.0393134i
$227$	4743.59	+	2738.71i	1.38697	+	0.800769i	0.992973	−	0.118341i	$-0.0377576\pi$
$227$	4743.59	+	2738.71i	1.38697	+	0.800769i	0.394000	+	0.919110i	$0.371091\pi$
$228$	678.796	+	5040.57i	0.197168	+	1.46412i
$229$	−1644.44	−	2848.26i	−0.474532	−	0.821913i	0.525043	−	0.851076i	$-0.324049\pi$
$229$	−1644.44	−	2848.26i	−0.474532	−	0.821913i	−0.999575	+	0.0291627i	$0.990716\pi$
$230$	232.469	+	98.9064i	0.0666459	+	0.0283552i
$231$	737.590	−	479.743i	0.210086	−	0.136644i
$232$	−1374.39	−	3607.39i	−0.388936	−	1.02085i
$233$	−5476.34	+	3161.76i	−1.53977	+	0.888987i	−0.540920	+	0.841074i	$0.681924\pi$
$233$	−5476.34	+	3161.76i	−1.53977	+	0.888987i	−0.998852	+	0.0479130i	$0.984743\pi$
$234$	−4838.53	+	2203.30i	−1.35173	+	0.615532i
$235$	911.800	+	526.428i	0.253103	+	0.146129i
$236$	−3358.60	−	969.135i	−0.926381	−	0.267311i
$237$	−584.348	+	5348.91i	−0.160158	+	1.46603i
$238$	−5810.83	−	1424.31i	−1.58261	−	0.387919i
$239$		−	5332.99i		−	1.44336i	−0.692228	−	0.721679i	$-0.743371\pi$
$239$		−	5332.99i		−	1.44336i	0.692228	−	0.721679i	$-0.256629\pi$
$240$	−1369.64	+	541.562i	−0.368376	+	0.145657i
$241$	−4509.52	−	2603.57i	−1.20533	−	0.695896i	−0.243592	−	0.969878i	$-0.578326\pi$
$241$	−4509.52	−	2603.57i	−1.20533	−	0.695896i	−0.961735	+	0.273982i	$0.911659\pi$
$242$	−2819.51	+	2120.96i	−0.748946	+	0.563391i
$243$	3787.20	+	77.5516i	0.999790	+	0.0204730i
$244$	2903.73	+	3016.97i	0.761854	+	0.791564i
$245$	1005.57	−	1138.62i	0.262219	−	0.296914i
$246$	−1671.96	+	2981.54i	−0.433335	+	0.772748i
$247$	4258.95	+	7376.72i	1.09713	+	1.90028i
$248$	−88.2405	+	548.236i	−0.0225939	+	0.140375i
$249$	1119.11	−	1527.13i	0.284822	−	0.388667i
$250$	−2864.74	+	349.317i	−0.724727	+	0.0883711i
$251$			1845.04i			0.463975i	0.972719	+	0.231987i	$0.0745228\pi$
$251$			1845.04i			0.463975i	−0.972719	+	0.231987i	$0.925477\pi$
$252$	2609.19	+	3032.35i	0.652237	+	0.758015i
$253$		−	184.397i		−	0.0458219i
$254$	199.081	+	1632.66i	0.0491790	+	0.403315i
$255$	−1553.61	+	2120.05i	−0.381533	+	0.520639i
$256$	2313.09	−	3380.36i	0.564719	−	0.825284i
$257$	−1576.56	−	2730.69i	−0.382659	−	0.662785i	0.608782	−	0.793337i	$-0.291658\pi$
$257$	−1576.56	−	2730.69i	−0.382659	−	0.662785i	−0.991441	+	0.130552i	$0.958325\pi$
$258$	−4242.77	−	2379.23i	−1.02381	−	0.574125i
$259$	−2134.55	+	1745.58i	−0.512103	+	0.418784i
$260$	−1777.20	+	1710.49i	−0.423912	+	0.408001i
$261$	1387.51	+	4392.38i	0.329059	+	1.04169i
$262$	56.8857	+	75.6212i	0.0134138	+	0.0178316i
$263$	−921.217	−	531.865i	−0.215987	−	0.124700i	0.388104	−	0.921616i	$-0.373130\pi$
$263$	−921.217	−	531.865i	−0.215987	−	0.124700i	−0.604091	+	0.796915i	$0.706464\pi$
$264$	755.113	+	765.147i	0.176038	+	0.178377i
$265$		−	1470.36i		−	0.340844i
$266$	4433.84	−	4628.02i	1.02202	−	1.06677i
$267$	536.913	−	4914.71i	0.123066	−	1.12650i
$268$	−1330.65	−	383.963i	−0.303292	−	0.0875160i
$269$	−3450.51	−	1992.15i	−0.782087	−	0.451538i	0.0550825	−	0.998482i	$-0.482458\pi$
$269$	−3450.51	−	1992.15i	−0.782087	−	0.451538i	−0.837169	+	0.546944i	$0.815791\pi$
$270$	1669.05	−	550.316i	0.376205	−	0.124041i
$271$	−1098.00	+	633.931i	−0.246121	+	0.142098i	−0.617987	−	0.786188i	$-0.712051\pi$
$271$	−1098.00	+	633.931i	−0.246121	+	0.142098i	0.371866	+	0.928286i	$0.378718\pi$
$272$	279.501	−	7304.28i	0.0623060	−	1.62826i
$273$	5971.59	+	3037.33i	1.32387	+	0.673360i
$274$	1023.92	−	2406.62i	0.225757	−	0.530618i
$275$	481.777	+	834.462i	0.105645	+	0.182982i
$276$	830.860	−	111.889i	0.181203	−	0.0244020i
$277$	−2063.86	−	1191.57i	−0.447672	−	0.258464i	0.259175	−	0.965831i	$-0.416550\pi$
$277$	−2063.86	−	1191.57i	−0.447672	−	0.258464i	−0.706846	+	0.707367i	$0.749883\pi$
$278$	183.141	+	1501.93i	0.0395111	+	0.324029i
$279$	143.065	−	646.969i	0.0306993	−	0.138828i
$280$	1609.45	+	924.285i	0.343511	+	0.197274i
$281$		−	5446.49i		−	1.15626i	−0.815943	−	0.578132i	$-0.803782\pi$
$281$		−	5446.49i		−	1.15626i	0.815943	−	0.578132i	$-0.196218\pi$
$282$	3493.59	−	43.7539i	0.737732	−	0.00923938i
$283$	2102.49	−	3641.62i	0.441626	−	0.764919i	−0.556184	−	0.831059i	$-0.687735\pi$
$283$	2102.49	−	3641.62i	0.441626	−	0.764919i	0.997810	+	0.0661402i	$0.0210684\pi$
$284$	1523.08	+	6152.48i	0.318232	+	1.28550i
$285$	−1134.69	−	2576.91i	−0.235836	−	0.535589i
$286$	1656.67	+	704.847i	0.342520	+	0.145729i
$287$	4251.28	−	694.298i	0.874373	−	0.142798i
$288$	−2989.42	+	3866.68i	−0.611644	+	0.791133i
$289$	−4065.80	−	7042.17i	−0.827560	−	1.43338i
$290$	1284.71	+	1707.84i	0.260141	+	0.345820i
$291$	1654.36	−	2257.53i	0.333265	−	0.454772i
$292$	−8457.75	−	2440.51i	−1.69504	−	0.489111i
$293$			2624.63i			0.523319i	0.965160	+	0.261660i	$0.0842698\pi$
$293$			2624.63i			0.523319i	−0.965160	+	0.261660i	$0.915730\pi$
$294$	938.695	−	4952.88i	0.186210	−	0.982510i
$295$	1935.19			0.381937
$296$	−2612.83	−	2126.68i	−0.513066	−	0.417605i
$297$	−846.551	−	963.739i	−0.165393	−	0.188289i
$298$	2649.78	−	1993.28i	0.515092	−	0.387476i
$299$	1215.94	−	702.023i	0.235183	−	0.135783i
$300$	−3467.60	+	2677.14i	−0.667340	+	0.515215i
$301$	987.996	+	6049.63i	0.189193	+	1.15845i
$302$	690.083	+	293.603i	0.131489	+	0.0559436i
$303$	3500.32	+	7949.29i	0.663657	+	1.50718i
$304$	6626.75	+	4171.70i	1.25023	+	0.787050i
$305$	−2007.56	−	1159.06i	−0.376893	−	0.217599i
$306$	−838.571	+	8681.76i	−0.156660	+	1.62191i
$307$	2803.64			0.521212			0.260606	−	0.965445i	$-0.416078\pi$
$307$	2803.64			0.521212			0.260606	+	0.965445i	$0.416078\pi$
$308$	160.875	−	1345.08i	0.0297619	−	0.248841i
$309$	2474.77	+	270.359i	0.455613	+	0.0497740i
$310$	−37.2093	−	305.152i	−0.00681725	−	0.0559080i
$311$	2351.38	−	4072.72i	0.428729	−	0.742581i	−0.568031	−	0.823007i	$-0.692295\pi$
$311$	2351.38	−	4072.72i	0.428729	−	0.742581i	0.996761	+	0.0804262i	$0.0256281\pi$
$312$	−2170.67	+	7892.33i	−0.393879	+	1.43210i
$313$	6802.88	−	3927.64i	1.22850	−	0.709277i	0.261787	−	0.965126i	$-0.415688\pi$
$313$	6802.88	−	3927.64i	1.22850	−	0.709277i	0.966717	+	0.255849i	$0.0823550\pi$
$314$	725.416	+	308.636i	0.130374	+	0.0554692i
$315$	−1853.25	−	1212.45i	−0.331488	−	0.216869i
$316$	5744.72	+	5968.75i	1.02268	+	1.06256i
$317$	−4755.57	−	8236.90i	−0.842586	−	1.45940i	−0.887701	−	0.460420i	$-0.847699\pi$
$317$	−4755.57	−	8236.90i	−0.842586	−	1.45940i	0.0451156	−	0.998982i	$-0.485634\pi$
$318$	−2492.40	−	4194.76i	−0.439519	−	0.739719i
$319$	779.931	−	1350.88i	0.136889	−	0.237100i
$320$	−711.512	+	2153.04i	−0.124296	+	0.376121i
$321$	24.4406	−	223.721i	0.00424967	−	0.0388999i
$322$	−762.858	−	730.851i	−0.132026	−	0.126487i
$323$	13974.2			2.40725
$324$	3828.76	−	4399.18i	0.656509	−	0.754318i
$325$	−3668.37	+	6353.81i	−0.626107	+	1.08445i
$326$	2751.66	+	3657.93i	0.467486	+	0.621454i
$327$	−3541.54	−	8042.91i	−0.598923	−	1.36017i
$328$	1873.73	+	4918.03i	0.315426	+	0.827905i
$329$	−2787.17	−	3408.24i	−0.467056	−	0.571132i
$330$	−519.084	−	291.087i	−0.0865897	−	0.0485571i
$331$	721.989	−	416.841i	0.119892	−	0.0692194i	−0.438855	−	0.898558i	$-0.644616\pi$
$331$	721.989	−	416.841i	0.119892	−	0.0692194i	0.558747	+	0.829338i	$0.311282\pi$
$332$	−700.456	−	2829.50i	−0.115791	−	0.467738i
$333$	2965.27	+	2714.24i	0.487975	+	0.446665i
$334$	1114.48	+	9139.80i	0.182580	+	1.49733i
$335$	766.707			0.125044
$336$	6158.30	−	91.3015i	0.999890	−	0.0148241i
$337$	−9175.73			−1.48319			−0.741593	−	0.670850i	$-0.765929\pi$
$337$	−9175.73			−1.48319			−0.741593	+	0.670850i	$0.765929\pi$
$338$	907.134	+	7439.37i	0.145981	+	1.19718i
$339$	1198.30	−	1635.19i	0.191984	−	0.261981i
$340$	972.413	+	3928.07i	0.155107	+	0.626557i
$341$	−194.318	+	112.190i	−0.0308590	+	0.0178164i
$342$	−7605.23	−	5428.18i	−1.20247	−	0.858253i
$343$	−5617.90	+	2965.26i	−0.884368	+	0.466790i
$344$	−6998.43	+	2666.35i	−1.09689	+	0.417907i
$345$	−424.764	+	187.037i	−0.0662856	+	0.0291876i
$346$	−1786.21	−	2374.51i	−0.277536	−	0.368943i
$347$	−2267.39	+	3927.23i	−0.350777	+	0.607564i	−0.986386	−	0.164447i	$-0.947416\pi$
$347$	−2267.39	+	3927.23i	−0.350777	+	0.607564i	0.635609	+	0.772012i	$0.280749\pi$
$348$	6560.07	+	2694.53i	1.01051	+	0.415064i
$349$	−5068.91			−0.777457			−0.388729	−	0.921352i	$-0.627086\pi$
$349$	−5068.91			−0.777457			−0.388729	+	0.921352i	$0.627086\pi$
$350$	5361.71	+	1314.23i	0.818844	+	0.200710i
$351$	3132.10	−	9251.35i	0.476294	−	1.40684i
$352$	1649.38	−	137.365i	0.249750	−	0.0207999i
$353$	−5712.39	+	9894.16i	−0.861303	+	1.49182i	0.00936800	+	0.999956i	$0.497018\pi$
$353$	−5712.39	+	9894.16i	−0.861303	+	1.49182i	−0.870671	+	0.491865i	$0.836315\pi$
$354$	5520.86	−	3280.33i	0.828899	−	0.492507i
$355$	−1754.43	−	3038.76i	−0.262297	−	0.454311i
$356$	−5278.39	−	5484.23i	−0.785826	−	0.816471i
$357$	9213.72	−	5992.78i	1.36594	−	0.888436i
$358$	−5935.07	−	2525.14i	−0.876197	−	0.372787i
$359$	−2343.22	+	1352.86i	−0.344486	+	0.198889i	−0.662254	−	0.749279i	$-0.730400\pi$
$359$	−2343.22	+	1352.86i	−0.344486	+	0.198889i	0.317768	+	0.948169i	$0.397067\pi$
$360$	996.615	−	2515.52i	0.145906	−	0.368277i
$361$	−4055.47	+	7024.28i	−0.591263	+	1.02410i
$362$	1248.78	+	10241.2i	0.181310	+	1.48692i
$363$	703.912	−	6443.36i	0.101779	−	0.931649i
$364$	9482.12	−	4060.06i	1.36538	−	0.584630i
$365$	4873.28			0.698847
$366$	−7692.02	+	96.3351i	−1.09855	+	0.0137582i
$367$	4971.62	+	2870.37i	0.707129	+	0.408261i	0.809997	−	0.586434i	$-0.199469\pi$
$367$	4971.62	+	2870.37i	0.707129	+	0.408261i	−0.102868	+	0.994695i	$0.532802\pi$
$368$	687.640	−	1092.32i	0.0974069	−	0.154731i
$369$	−1891.61	−	5988.22i	−0.266866	−	0.844809i
$370$	1716.18	+	730.167i	0.241135	+	0.102593i
$371$	−2175.88	+	5750.82i	−0.304490	+	0.804765i
$372$	−623.414	−	807.486i	−0.0868885	−	0.112544i
$373$	3720.69	−	2148.14i	0.516488	−	0.298195i	−0.219008	−	0.975723i	$-0.570282\pi$
$373$	3720.69	−	2148.14i	0.516488	−	0.298195i	0.735497	+	0.677528i	$0.236949\pi$
$374$	2360.36	−	1775.57i	0.326340	−	0.245488i
$375$	3133.88	−	4276.48i	0.431554	−	0.588897i
$376$	3395.68	−	4171.90i	0.465741	−	0.572205i
$377$	11877.2			1.62256
$378$	−7342.30	−	317.531i	−0.999066	−	0.0432064i
$379$			7102.22i			0.962576i	0.876562	+	0.481288i	$0.159831\pi$
$379$			7102.22i			0.962576i	−0.876562	+	0.481288i	$0.840169\pi$
$380$	−4165.07	−	1201.85i	−0.562273	−	0.162246i
$381$	−2437.23	−	1786.05i	−0.327725	−	0.240162i
$382$	−5331.85	−	7087.91i	−0.714139	−	0.949343i
$383$	4295.05	+	7439.24i	0.573020	+	0.992500i	0.996254	+	0.0864795i	$0.0275617\pi$
$383$	4295.05	+	7439.24i	0.573020	+	0.992500i	−0.423233	+	0.906021i	$0.639105\pi$
$384$	1619.76	+	7348.43i	0.215255	+	0.976558i
$385$	120.877	+	740.144i	0.0160012	+	0.0979772i
$386$	−6326.09	−	2691.50i	−0.834169	−	0.354906i
$387$	8521.33	−	2691.79i	1.11929	−	0.353570i
$388$	−1035.47	−	4182.79i	−0.135484	−	0.547291i
$389$	412.952	−	715.254i	0.0538239	−	0.0932257i	−0.837858	−	0.545888i	$-0.816192\pi$
$389$	412.952	−	715.254i	0.0538239	−	0.0932257i	0.891682	+	0.452662i	$0.149526\pi$
$390$	−56.7478	−	4531.12i	−0.00736805	−	0.588313i
$391$		−	2303.43i		−	0.297926i
$392$	−4927.03	−	5996.72i	−0.634828	−	0.772653i
$393$	−172.815	−	18.8794i	−0.0221816	−	0.00242326i
$394$	373.225	+	3060.80i	0.0477229	+	0.391373i
$395$	−3971.73	−	2293.08i	−0.505923	−	0.292095i
$396$	−1974.30	+	49.4601i	−0.250536	+	0.00627643i
$397$	−1604.37	−	2778.85i	−0.202824	−	0.351301i	0.746614	−	0.665258i	$-0.231678\pi$
$397$	−1604.37	−	2778.85i	−0.202824	−	0.351301i	−0.949437	+	0.313957i	$0.898345\pi$
$398$	−1343.87	+	3158.63i	−0.169252	+	0.397809i
$399$	624.591	+	11757.8i	0.0783675	+	1.47526i
$400$	−257.898	+	6739.73i	−0.0322373	+	0.842467i
$401$	−2653.33	+	1531.90i	−0.330426	+	0.190772i	−0.656030	−	0.754735i	$-0.727766\pi$
$401$	−2653.33	+	1531.90i	−0.330426	+	0.190772i	0.325604	+	0.945506i	$0.394432\pi$
$402$	2187.32	−	1299.64i	0.271377	−	0.161244i
$403$	−1479.59	−	854.239i	−0.182887	−	0.105590i
$404$	12848.5	+	3707.48i	1.58227	+	0.456569i
$405$	−1361.33	+	2927.59i	−0.167025	+	0.359193i
$406$	−2497.42	−	8580.76i	−0.305282	−	1.04891i
$407$		−	1361.29i		−	0.165791i
$408$	9432.61	+	9557.95i	1.14457	+	1.15978i
$409$	−206.447	−	119.192i	−0.0249588	−	0.0144099i	0.487469	−	0.873140i	$-0.337920\pi$
$409$	−206.447	−	119.192i	−0.0249588	−	0.0144099i	−0.512427	+	0.858731i	$0.671254\pi$
$410$	−1751.48	−	2328.33i	−0.210974	−	0.280459i
$411$	1936.29	+	4397.34i	0.232384	+	0.527749i
$412$	2761.54	−	2657.89i	0.330222	−	0.317828i
$413$	−7568.84	−	2863.74i	−0.901787	−	0.341200i
$414$	−894.753	+	1253.61i	−0.106219	+	0.148820i
$415$	806.853	+	1397.51i	0.0954382	+	0.165304i
$416$	7185.19	+	10353.2i	0.846833	+	1.22021i
$417$	−2242.09	−	1643.04i	−0.263299	−	0.192950i
$418$	382.985	+	3140.84i	0.0448143	+	0.367520i
$419$			10250.5i			1.19516i	0.801810	+	0.597579i	$0.203871\pi$
$419$			10250.5i			1.19516i	−0.801810	+	0.597579i	$0.796129\pi$
$420$	−3261.61	+	993.756i	−0.378929	+	0.115453i
$421$			11094.4i			1.28434i	0.766563	+	0.642169i	$0.221965\pi$
$421$			11094.4i			1.28434i	−0.766563	+	0.642169i	$0.778035\pi$
$422$	4434.74	−	540.760i	0.511564	−	0.0623786i
$423$	−4333.83	+	4734.65i	−0.498151	+	0.544223i
$424$	−7416.80	−	1193.76i	−0.849509	−	0.136731i
$425$	6018.19	+	10423.8i	0.686883	+	1.18972i
$426$	−10156.1	−	5695.27i	−1.15509	−	0.647739i
$427$	6136.65	+	7504.10i	0.695488	+	0.850466i
$428$	−240.276	−	249.646i	−0.0271359	−	0.0281941i
$429$	−3027.04	+	1332.90i	−0.340668	+	0.150007i
$430$	3313.25	−	2492.37i	0.371579	−	0.279519i
$431$	2543.69	+	1468.60i	0.284282	+	0.164130i	0.635360	−	0.772216i	$-0.280852\pi$
$431$	2543.69	+	1468.60i	0.284282	+	0.164130i	−0.351079	+	0.936346i	$0.614185\pi$
$432$	−1420.83	−	8865.82i	−0.158240	−	0.987401i
$433$		−	3280.71i		−	0.364113i	−0.983288	−	0.182057i	$-0.941725\pi$
$433$		−	3280.71i		−	0.364113i	0.983288	−	0.182057i	$-0.0582754\pi$
$434$	−306.039	+	1248.56i	−0.0338488	+	0.138094i
$435$	−3902.88	−	426.375i	−0.430182	−	0.0469957i
$436$	−12999.8	−	3751.14i	−1.42793	−	0.412034i
$437$	2136.98	+	1233.78i	0.233925	+	0.135057i
$438$	13902.8	−	8260.66i	1.51667	−	0.901163i
$439$	−11152.1	+	6438.66i	−1.21244	+	0.700001i	−0.963289	−	0.268465i	$-0.913484\pi$
$439$	−11152.1	+	6438.66i	−1.21244	+	0.700001i	−0.249147	+	0.968466i	$0.580150\pi$
$440$	−856.225	+	326.215i	−0.0927703	+	0.0353448i
$441$	5454.14	+	7484.55i	0.588936	+	0.808180i
$442$	20694.5	+	8804.70i	2.22701	+	0.947504i
$443$	−7849.56	−	13595.8i	−0.841860	−	1.45814i	−0.888321	−	0.459223i	$-0.848128\pi$
$443$	−7849.56	−	13595.8i	−0.841860	−	1.45814i	0.0464613	−	0.998920i	$-0.485206\pi$
$444$	6133.74	−	826.011i	0.655618	−	0.0882899i
$445$	3649.32	+	2106.94i	0.388752	+	0.224446i
$446$	1926.53	−	234.915i	0.204538	−	0.0249407i
$447$	−661.537	+	6055.47i	−0.0699992	+	0.640747i
$448$	5968.95	−	7367.97i	0.629479	−	0.777018i
$449$		−	3520.44i		−	0.370022i	−0.982736	−	0.185011i	$-0.940768\pi$
$449$		−	3520.44i		−	0.370022i	0.982736	−	0.185011i	$-0.0592320\pi$
$450$	773.757	−	8010.74i	0.0810562	−	0.839178i
$451$	−1063.30	+	1841.68i	−0.111017	+	0.192287i
$452$	−750.020	−	3029.71i	−0.0780486	−	0.315278i
$453$	−1260.91	+	555.217i	−0.130779	+	0.0575858i
$454$	−6065.30	+	14255.9i	−0.627002	+	1.47370i
$455$	−4420.42	+	3614.90i	−0.455456	+	0.372460i
$456$	−13919.7	+	3631.47i	−1.42949	+	0.372937i
$457$	−3285.51	−	5690.68i	−0.336302	−	0.582492i	0.647432	−	0.762123i	$-0.275843\pi$
$457$	−3285.51	−	5690.68i	−0.336302	−	0.582492i	−0.983734	+	0.179631i	$0.942510\pi$
$458$	7433.87	−	5592.10i	0.758432	−	0.570528i
$459$	−10574.8	−	12038.7i	−1.07536	−	1.22422i
$460$	−198.106	+	686.549i	−0.0200799	+	0.0695880i
$461$			9205.68i			0.930046i	0.885298	+	0.465023i	$0.153954\pi$
$461$			9205.68i			0.930046i	−0.885298	+	0.465023i	$0.846046\pi$
$462$	1599.46	+	1906.64i	0.161068	+	0.192002i
$463$	1257.92			0.126264			0.0631320	−	0.998005i	$-0.479891\pi$
$463$	1257.92			0.126264			0.0631320	+	0.998005i	$0.479891\pi$
$464$	9657.70	−	5093.79i	0.966266	−	0.509640i
$465$	455.531	+	333.821i	0.0454296	+	0.0332916i
$466$	−10751.9	−	14293.1i	−1.06883	−	1.42085i
$467$	−10353.3	+	5977.50i	−1.02590	+	0.592303i	−0.915807	−	0.401618i	$-0.868448\pi$
$467$	−10353.3	+	5977.50i	−1.02590	+	0.592303i	−0.110092	+	0.993921i	$0.535115\pi$
$468$	−7842.55	−	12830.5i	−0.774620	−	1.26729i
$469$	−2998.71	−	1134.59i	−0.295240	−	0.111707i
$470$	−1165.86	+	2740.22i	−0.114419	+	0.268930i
$471$	−1325.47	+	583.645i	−0.129670	+	0.0570975i
$472$	1571.14	−	9761.49i	0.153216	−	0.951926i
$473$	−2620.74	−	1513.08i	−0.254760	−	0.147086i
$474$	−15217.8	+	190.589i	−1.47464	+	0.0184684i
$475$	−12894.1			−1.24552
$476$	2009.59	−	16802.3i	0.193507	−	1.61792i
$477$	8752.51	+	1935.45i	0.840146	+	0.185783i
$478$	14973.1	−	1825.77i	1.43275	−	0.174705i
$479$	−594.250	+	1029.27i	−0.0566847	+	0.0981808i	−0.892975	−	0.450106i	$-0.851386\pi$
$479$	−594.250	+	1029.27i	−0.0566847	+	0.0981808i	0.836291	+	0.548286i	$0.184720\pi$
$480$	−1989.41	−	3660.05i	−0.189174	−	0.348037i
$481$	8976.55	−	5182.62i	0.850926	−	0.491283i
$482$	5766.02	−	13552.4i	0.544886	−	1.28070i
$483$	1938.10	−	102.954i	0.182581	−	0.00969892i
$484$	−6920.15	−	7190.02i	−0.649902	−	0.675246i
$485$	1192.75	+	2065.91i	0.111670	+	0.193419i
$486$	1078.83	+	10659.6i	0.100693	+	0.994918i
$487$	8212.00	−	14223.6i	0.764110	−	1.32348i	−0.176606	−	0.984282i	$-0.556512\pi$
$487$	8212.00	−	14223.6i	0.764110	−	1.32348i	0.940716	−	0.339195i	$-0.110155\pi$
$488$	−7476.43	+	9185.48i	−0.693529	+	0.852064i
$489$	−8359.39	−	913.231i	−0.773056	−	0.0844534i
$490$	3541.09	+	2433.46i	0.326470	+	0.224352i
$491$	−4192.37			−0.385334			−0.192667	−	0.981264i	$-0.561714\pi$
$491$	−4192.37			−0.385334			−0.192667	+	0.981264i	$0.561714\pi$
$492$	−8943.47	−	3673.51i	−0.819518	−	0.336615i
$493$	9742.63	−	16874.7i	0.890032	−	1.54158i
$494$	−19253.1	+	14483.0i	−1.75351	+	1.31907i
$495$	1042.54	−	329.329i	0.0946644	−	0.0299035i
$496$	−1569.46	−	60.0558i	−0.142078	−	0.00543666i
$497$	2365.01	+	14481.3i	0.213451	+	1.30699i
$498$	4670.76	+	2619.23i	0.420285	+	0.235684i
$499$	−4788.71	+	2764.76i	−0.429603	+	0.248031i	−0.699178	−	0.714948i	$-0.746450\pi$
$499$	−4788.71	+	2764.76i	−0.429603	+	0.248031i	0.269574	+	0.962980i	$0.413117\pi$
$500$	−1961.51	−	7923.53i	−0.175443	−	0.708702i
$501$	−13643.9	−	9998.49i	−1.21669	−	0.891616i
$502$	−5180.18	+	631.656i	−0.460563	+	0.0561597i
$503$	11988.3			1.06268			0.531342	−	0.847157i	$-0.321688\pi$
$503$	11988.3			1.06268			0.531342	+	0.847157i	$0.321688\pi$
$504$	−7620.44	+	8363.79i	−0.673495	+	0.739192i
$505$	−7403.18			−0.652351
$506$	517.719	−	63.1292i	0.0454850	−	0.00554631i
$507$	−11105.5	−	8138.30i	−0.972805	−	0.712889i
$508$	−4515.74	+	1117.89i	−0.394397	+	0.0976349i
$509$	6752.90	−	3898.79i	0.588049	−	0.339510i	−0.176277	−	0.984341i	$-0.556405\pi$
$509$	6752.90	−	3898.79i	0.588049	−	0.339510i	0.764326	+	0.644830i	$0.223072\pi$
$510$	−6484.21	−	3636.16i	−0.562992	−	0.315710i
$511$	−19060.1	−	7211.59i	−1.65004	−	0.624309i
$512$	10282.7	+	5337.02i	0.887570	+	0.460674i
$513$	16832.9	−	3362.37i	1.44872	−	0.289381i
$514$	7127.03	−	5361.28i	0.611595	−	0.460070i
$515$	−1060.93	+	1837.59i	−0.0907773	+	0.157231i
$516$	5227.46	−	12726.7i	0.445981	−	1.08578i
$517$	2173.58			0.184901
$518$	−5631.72	−	5395.43i	−0.477690	−	0.457648i
$519$	5426.41	+	592.814i	0.458946	+	0.0501380i
$520$	−5410.86	−	4404.12i	−0.456312	−	0.371410i
$521$	8827.36	−	15289.4i	0.742291	−	1.28569i	−0.209158	−	0.977882i	$-0.567072\pi$
$521$	8827.36	−	15289.4i	0.742291	−	1.28569i	0.951450	−	0.307805i	$-0.0995944\pi$
$522$	−11857.2	+	5399.36i	−0.994204	+	0.452727i
$523$	3743.99	+	6484.78i	0.313027	+	0.542179i	0.979016	−	0.203782i	$-0.0653235\pi$
$523$	3743.99	+	6484.78i	0.313027	+	0.542179i	−0.665989	+	0.745962i	$0.731990\pi$
$524$	−192.841	+	185.603i	−0.0160769	+	0.0154735i
$525$	−8501.59	+	5529.60i	−0.706742	+	0.459679i
$526$	1177.90	−	2768.52i	0.0976402	−	0.229493i
$527$	−2427.35	+	1401.43i	−0.200640	+	0.115839i
$528$	−1889.73	+	2382.03i	−0.155758	+	0.196334i
$529$	−5880.13	+	10184.7i	−0.483285	+	0.837074i
$530$	4128.24	−	503.386i	0.338338	−	0.0412560i
$531$	−2547.31	+	11519.4i	−0.208181	+	0.941434i
$532$	14511.7	+	10864.2i	1.18264	+	0.885379i
$533$	−16192.4			−1.31589
$534$	13982.5	−	175.117i	1.13311	−	0.0141911i
$535$	166.120	+	95.9092i	0.0134243	+	0.00775050i
$536$	622.474	−	3867.42i	0.0501619	−	0.311655i
$537$	10844.5	−	4775.16i	0.871459	−	0.383731i
$538$	4411.94	−	10369.8i	0.353554	−	0.830991i
$539$	622.514	−	3073.69i	0.0497469	−	0.245628i
$540$	2116.49	+	4497.69i	0.168666	+	0.358425i
$541$	−19644.4	+	11341.7i	−1.56114	+	0.901325i	−0.563999	+	0.825775i	$0.690738\pi$
$541$	−19644.4	+	11341.7i	−1.56114	+	0.901325i	−0.997142	+	0.0755502i	$0.975929\pi$
$542$	−2155.75	−	2865.75i	−0.170844	−	0.227112i
$543$	−15288.0	−	11203.3i	−1.20823	−	0.885415i
$544$	20603.4	−	1715.92i	1.62383	−	0.135238i
$545$	7490.37			0.588720
$546$	−6483.30	+	17805.9i	−0.508167	+	1.39564i
$547$		−	2780.71i		−	0.217357i	−0.994077	−	0.108679i	$-0.965338\pi$
$547$		−	2780.71i		−	0.217357i	0.994077	−	0.108679i	$-0.0346620\pi$
$548$	7107.45	+	2050.88i	0.554043	+	0.159871i
$549$	9542.02	−	10424.5i	0.741791	−	0.810396i
$550$	−2177.92	+	1638.33i	−0.168849	+	0.127016i
$551$	10436.9	+	18077.2i	0.806944	+	1.39767i
$552$	598.592	+	2294.44i	0.0461554	+	0.176917i
$553$	12140.7	+	14846.0i	0.933589	+	1.14162i
$554$	2638.91	−	6202.49i	0.202377	−	0.475665i
$555$	−3135.78	+	1380.78i	−0.239831	+	0.105605i
$556$	−4154.18	+	1028.39i	−0.316864	+	0.0784412i
$557$	−2390.49	+	4140.46i	−0.181846	+	0.314967i	−0.942509	−	0.334180i	$-0.891541\pi$
$557$	−2390.49	+	4140.46i	−0.181846	+	0.314967i	0.760663	+	0.649147i	$0.224874\pi$
$558$	1865.43	+	180.182i	0.141523	+	0.0136697i
$559$		−	23042.0i		−	1.74342i
$560$	−2044.05	+	4835.18i	−0.154244	+	0.364863i
$561$	−589.281	+	5394.07i	−0.0443485	+	0.405950i
$562$	15291.7	−	1864.63i	1.14776	−	0.139955i
$563$	4568.69	+	2637.74i	0.342003	+	0.197455i	0.661157	−	0.750247i	$-0.270066\pi$
$563$	4568.69	+	2637.74i	0.342003	+	0.197455i	−0.319155	+	0.947703i	$0.603399\pi$
$564$	1318.89	+	9793.74i	0.0984668	+	0.731189i
$565$	863.946	+	1496.40i	0.0643301	+	0.111423i
$566$	10944.1	+	4656.30i	0.812749	+	0.345793i
$567$	9656.68	−	9435.71i	0.715243	−	0.698876i
$568$	−16752.5	+	6382.56i	−1.23753	+	0.471490i
$569$	−18776.2	+	10840.4i	−1.38337	+	0.798691i	−0.992557	−	0.121779i	$-0.961140\pi$
$569$	−18776.2	+	10840.4i	−1.38337	+	0.798691i	−0.390815	+	0.920469i	$0.627807\pi$
$570$	6846.54	−	4068.01i	0.503105	−	0.298930i
$571$	−5660.93	−	3268.34i	−0.414891	−	0.239537i	0.277998	−	0.960582i	$-0.410329\pi$
$571$	−5660.93	−	3268.34i	−0.414891	−	0.239537i	−0.692889	+	0.721044i	$0.743662\pi$
$572$	−1411.78	+	4892.62i	−0.103199	+	0.357641i
$573$	16197.8	+	1769.55i	1.18093	+	0.129012i
$574$	3404.78	+	11698.3i	0.247583	+	0.850660i
$575$			2125.39i			0.154148i
$576$	−11879.7	−	7069.42i	−0.859350	−	0.511388i
$577$	14376.6	+	8300.36i	1.03728	+	0.598871i	0.919060	−	0.394117i	$-0.128950\pi$
$577$	14376.6	+	8300.36i	1.03728	+	0.598871i	0.118215	+	0.992988i	$0.462283\pi$
$578$	18379.9	−	13826.2i	1.32267	−	0.994972i
$579$	11558.9	−	5089.76i	0.829660	−	0.365325i
$580$	−4355.15	+	4191.69i	−0.311789	+	0.300087i
$581$	−1087.66	−	6659.88i	−0.0776656	−	0.475556i
$582$	6904.68	+	3871.95i	0.491767	+	0.275769i
$583$	−1517.75	−	2628.83i	−0.107820	−	0.186749i
$584$	3956.52	−	24581.8i	0.280346	−	1.74178i
$585$	6140.74	+	5620.89i	0.433997	+	0.397256i
$586$	−7368.99	+	898.553i	−0.519472	+	0.0633428i
$587$		−	1563.80i		−	0.109957i	−0.998488	−	0.0549785i	$-0.982491\pi$
$587$		−	1563.80i		−	0.109957i	0.998488	−	0.0549785i	$-0.0175090\pi$
$588$	14227.2	+	939.868i	0.997825	+	0.0659175i
$589$		−	3002.60i		−	0.210051i
$590$	662.521	+	5433.31i	0.0462298	+	0.379128i
$591$	−4569.17	−	3348.37i	−0.318021	−	0.233052i
$592$	5076.43	−	8063.93i	0.352433	−	0.559840i
$593$	−5665.14	−	9812.30i	−0.392309	−	0.679499i	0.600445	−	0.799666i	$-0.294990\pi$
$593$	−5665.14	−	9812.30i	−0.392309	−	0.679499i	−0.992754	+	0.120167i	$0.961657\pi$
$594$	2416.00	−	2706.74i	0.166885	−	0.186968i
$595$	1509.95	+	9245.62i	0.104037	+	0.637031i
$596$	6503.56	+	6757.18i	0.446974	+	0.464404i
$597$	−2541.33	−	5771.41i	−0.174221	−	0.395658i
$598$	2387.31	+	3173.57i	0.163251	+	0.217018i
$599$	−14781.1	−	8533.88i	−1.00825	−	0.582112i	−0.0975691	−	0.995229i	$-0.531107\pi$
$599$	−14781.1	−	8533.88i	−1.00825	−	0.582112i	−0.910678	+	0.413117i	$0.864440\pi$
$600$	−8703.56	−	8819.21i	−0.592202	−	0.600072i
$601$			9880.42i			0.670600i	0.942111	+	0.335300i	$0.108838\pi$
$601$			9880.42i			0.670600i	−0.942111	+	0.335300i	$0.891162\pi$
$602$	−16646.9	+	4845.05i	−1.12704	+	0.328022i
$603$	−1009.22	+	4563.91i	−0.0681572	+	0.308220i
$604$	−588.076	+	2038.01i	−0.0396167	+	0.137294i
$605$	4784.39	+	2762.27i	0.321509	+	0.185624i
$606$	−21120.3	+	12549.1i	−1.41577	+	0.841207i
$607$	−15947.1	+	9207.04i	−1.06634	+	0.615654i	−0.927180	−	0.374615i	$-0.877775\pi$
$607$	−15947.1	+	9207.04i	−1.06634	+	0.615654i	−0.139164	+	0.990269i	$0.544442\pi$
$608$	−9443.89	+	20033.7i	−0.629935	+	1.33630i
$609$	14633.8	+	7443.19i	0.973715	+	0.495260i
$610$	2566.93	−	6033.29i	0.170380	−	0.400460i
$611$	8275.08	+	14332.9i	0.547911	+	0.949010i
$612$	−24662.3	+	617.839i	−1.62894	+	0.0408083i
$613$	18953.4	+	10942.7i	1.24881	+	0.720999i	0.970872	−	0.239600i	$-0.0770163\pi$
$613$	18953.4	+	10942.7i	1.24881	+	0.720999i	0.277936	+	0.960600i	$0.410350\pi$
$614$	959.837	+	7871.58i	0.0630877	+	0.517380i
$615$	5320.88	+	581.286i	0.348876	+	0.0381133i
$616$	3831.57	−	8.81752i	0.250614	−	0.000576734i
$617$		−	338.816i		−	0.0221073i	−0.999939	−	0.0110537i	$-0.996481\pi$
$617$		−	338.816i		−	0.0221073i	0.999939	−	0.0110537i	$-0.00351856\pi$
$618$	88.1791	+	7040.79i	0.00573962	+	0.458288i
$619$	5117.86	−	8864.40i	0.332317	−	0.575590i	−0.650649	−	0.759379i	$-0.725503\pi$
$619$	5117.86	−	8864.40i	0.332317	−	0.575590i	0.982966	+	0.183789i	$0.0588363\pi$
$620$	844.016	−	208.940i	0.0546717	−	0.0135343i
$621$	−554.236	−	2774.65i	−0.0358144	−	0.179296i
$622$	12239.7	+	5207.51i	0.789014	+	0.335695i
$623$	−11155.2	−	13640.9i	−0.717372	−	0.877226i
$624$	−22901.9	−	3392.48i	−1.46925	−	0.217641i
$625$	−4327.13	−	7494.81i	−0.276937	−	0.479668i
$626$	13356.4	+	17755.3i	0.852760	+	1.13362i
$627$	−4688.65	−	3435.92i	−0.298639	−	0.218848i
$628$	−618.187	+	2142.36i	−0.0392808	+	0.136130i
$629$		−	17004.8i		−	1.07794i
$630$	2769.64	−	5618.33i	0.175151	−	0.355301i
$631$	−11775.5			−0.742906			−0.371453	−	0.928452i	$-0.621140\pi$
$631$	−11775.5			−0.742906			−0.371453	+	0.928452i	$0.621140\pi$
$632$	−14791.3	+	18172.5i	−0.930960	+	1.14377i
$633$	−4851.39	+	6620.19i	−0.304622	+	0.415685i
$634$	21498.1	−	16171.8i	1.34668	−	1.01304i
$635$	2230.36	−	1287.70i	0.139384	−	0.0804736i
$636$	10924.1	−	8433.85i	0.681080	−	0.525824i
$637$	22638.3	−	7596.99i	1.40811	−	0.472534i
$638$	4059.79	+	1727.28i	0.251925	+	0.107184i
$639$	20397.9	−	6443.48i	1.26280	−	0.398905i
$640$	−6288.54	−	1260.56i	−0.388401	−	0.0778562i
$641$	114.122	+	65.8885i	0.00703207	+	0.00405997i	0.503512	−	0.863988i	$-0.332041\pi$
$641$	114.122	+	65.8885i	0.00703207	+	0.00405997i	−0.496480	+	0.868048i	$0.665374\pi$
$642$	636.493	−	7.97146i	0.0391283	−	0.000490044i
$643$	347.865			0.0213351			0.0106676	−	0.999943i	$-0.496604\pi$
$643$	347.865			0.0213351			0.0106676	+	0.999943i	$0.496604\pi$
$644$	1790.79	−	2392.03i	0.109576	−	0.146365i
$645$	−827.178	+	7571.69i	−0.0504963	+	0.462225i
$646$	4784.11	+	39234.3i	0.291375	+	2.38955i
$647$	−1541.84	+	2670.55i	−0.0936880	+	0.162272i	−0.909060	−	0.416665i	$-0.863199\pi$
$647$	−1541.84	+	2670.55i	−0.0936880	+	0.162272i	0.815372	+	0.578937i	$0.196532\pi$
$648$	13662.1	+	9243.67i	0.828236	+	0.560379i
$649$	3459.88	−	1997.56i	0.209264	−	0.120818i
$650$	−19095.0	−	8124.18i	−1.15226	−	0.490241i
$651$	−1287.66	−	1979.73i	−0.0775226	−	0.119189i
$652$	−9328.08	+	8977.96i	−0.560300	+	0.539270i
$653$	−3166.81	−	5485.08i	−0.189781	−	0.328710i	0.755396	−	0.655268i	$-0.227444\pi$
$653$	−3166.81	−	5485.08i	−0.189781	−	0.328710i	−0.945177	+	0.326558i	$0.894111\pi$
$654$	21369.1	−	12696.9i	1.27767	−	0.759154i
$655$	74.0860	−	128.321i	0.00441951	−	0.00765482i
$656$	−13166.5	+	6944.46i	−0.783638	+	0.413316i
$657$	−6414.74	+	29008.7i	−0.380918	+	1.72258i
$658$	8614.88	−	8992.17i	0.510400	−	0.532753i
$659$	17001.3			1.00497			0.502485	−	0.864586i	$-0.332419\pi$
$659$	17001.3			1.00497			0.502485	+	0.864586i	$0.332419\pi$
$660$	639.555	−	1557.05i	0.0377192	−	0.0918305i
$661$	3875.34	−	6712.28i	0.228038	−	0.394974i	−0.729188	−	0.684313i	$-0.760102\pi$
$661$	3875.34	−	6712.28i	0.228038	−	0.394974i	0.957227	+	0.289339i	$0.0934356\pi$
$662$	1417.51	+	1884.37i	0.0832222	+	0.110632i
$663$	−37812.7	+	16650.1i	−2.21497	+	0.975319i
$664$	7704.38	−	2935.31i	0.450283	−	0.171555i
$665$	−9386.29	−	3551.39i	−0.547345	−	0.207093i
$666$	−6605.42	+	9254.62i	−0.384317	+	0.538452i
$667$	2979.75	−	1720.36i	0.172978	−	0.0998690i
$668$	−25279.6	+	6258.10i	−1.46422	+	0.362475i
$669$	−2107.53	+	2875.92i	−0.121796	+	0.166203i
$670$	262.485	+	2152.63i	0.0151354	+	0.124124i
$671$	−4785.67			−0.275334
$672$	2364.66	+	17259.0i	0.135742	+	0.990744i
$673$	13879.3			0.794960			0.397480	−	0.917611i	$-0.369885\pi$
$673$	13879.3			0.794960			0.397480	+	0.917611i	$0.369885\pi$
$674$	−3141.35	−	25762.1i	−0.179526	−	1.47228i
$675$	9757.49	+	11108.2i	0.556394	+	0.633416i
$676$	−20576.4	+	5093.80i	−1.17071	+	0.289815i
$677$	410.740	−	237.141i	0.0233176	−	0.0134624i	−0.488296	−	0.872678i	$-0.662381\pi$
$677$	410.740	−	237.141i	0.0233176	−	0.0134624i	0.511613	+	0.859216i	$0.329048\pi$
$678$	5001.26	+	2804.57i	0.283293	+	0.158862i
$679$	−1607.86	−	9845.15i	−0.0908750	−	0.556439i
$680$	−10695.7	+	4074.97i	−0.603176	+	0.229806i
$681$	−11469.8	−	26048.1i	−0.645408	−	1.46573i
$682$	−381.512	−	507.165i	−0.0214206	−	0.0284756i
$683$	14328.5	−	24817.7i	0.802730	−	1.39037i	−0.115082	−	0.993356i	$-0.536713\pi$
$683$	14328.5	−	24817.7i	0.802730	−	1.39037i	0.917813	−	0.397014i	$-0.129954\pi$
$684$	12636.6	−	23211.1i	0.706395	−	1.29751i
$685$	−4095.25			−0.228425
$686$	−10248.7	−	14757.8i	−0.570403	−	0.821365i
$687$	−1855.92	+	16988.5i	−0.103068	+	0.943450i
$688$	−9882.06	−	18736.2i	−0.547602	−	1.03824i
$689$	11556.6	−	20016.5i	0.638998	−	1.10678i
$690$	−670.550	−	1128.55i	−0.0369962	−	0.0622653i
$691$	16582.2	+	28721.1i	0.912902	+	1.58119i	0.809945	+	0.586506i	$0.199497\pi$
$691$	16582.2	+	28721.1i	0.912902	+	1.58119i	0.102957	+	0.994686i	$0.467170\pi$
$692$	6055.22	−	5827.95i	0.332637	−	0.320152i
$693$	−4564.90	−	254.726i	−0.250225	−	0.0139628i
$694$	−11802.5	−	5021.48i	−0.645555	−	0.274658i
$695$	2051.78	−	1184.60i	0.111983	−	0.0646537i
$696$	−5319.39	+	19340.7i	−0.289700	+	1.05332i
$697$	−13282.3	+	23005.6i	−0.721813	+	1.25022i
$698$	−1735.36	−	14231.6i	−0.0941038	−	0.771741i
$699$	32663.7	+	3568.38i	1.76746	+	0.193088i
$700$	−1854.27	+	15503.6i	−0.100121	+	0.837117i
$701$	20592.3			1.10950			0.554752	−	0.832016i	$-0.312813\pi$
$701$	20592.3			1.10950			0.554752	+	0.832016i	$0.312813\pi$
$702$	27046.7	+	5626.55i	1.45415	+	0.302508i
$703$	15776.0	+	9108.28i	0.846377	+	0.488656i
$704$	950.341	+	4583.81i	0.0508769	+	0.245396i
$705$	−2204.69	−	5006.89i	−0.117778	−	0.267476i
$706$	−29734.8	−	12651.0i	−1.58511	−	0.674400i
$707$	28955.0	+	10955.4i	1.54026	+	0.582772i
$708$	11100.0	+	14377.5i	0.589217	+	0.763191i
$709$	−15935.2	+	9200.17i	−0.844087	+	0.487334i	−0.858651	−	0.512560i	$-0.828697\pi$
$709$	−15935.2	+	9200.17i	−0.844087	+	0.487334i	0.0145643	+	0.999894i	$0.495364\pi$
$710$	7931.07	−	5966.12i	0.419222	−	0.315358i
$711$	18877.8	−	20623.8i	0.995744	−	1.08784i
$712$	13590.6	−	16697.3i	0.715351	−	0.878874i
$713$	−494.932			−0.0259963
$714$	19979.9	+	23817.1i	1.04724	+	1.24836i
$715$		−	2819.08i		−	0.147451i
$716$	5057.76	−	17528.0i	0.263991	−	0.914877i
$717$	−16379.8	+	22351.8i	−0.853159	+	1.16422i
$718$	−4600.54	−	6115.75i	−0.239124	−	0.317880i
$719$	−16112.7	−	27908.0i	−0.835746	−	1.44755i	−0.893422	−	0.449219i	$-0.851702\pi$
$719$	−16112.7	−	27908.0i	−0.835746	−	1.44755i	0.0576763	−	0.998335i	$-0.481631\pi$
$720$	7403.86	+	1936.93i	0.383230	+	0.100257i
$721$	6868.78	−	5617.11i	0.354794	−	0.290141i
$722$	−21110.0	−	8981.48i	−1.08813	−	0.462958i
$723$	10903.8	+	24762.8i	0.560882	+	1.27377i
$724$	−28325.9	+	7012.21i	−1.45404	+	0.359954i
$725$	−8989.62	+	15570.5i	−0.460505	+	0.797618i
$726$	18331.6	−	229.585i	0.937119	−	0.0117365i
$727$		−	2198.99i		−	0.112182i	−0.998426	−	0.0560908i	$-0.982136\pi$
$727$		−	2198.99i		−	0.112182i	0.998426	−	0.0560908i	$-0.0178636\pi$
$728$	14645.4	+	25232.3i	0.745597	+	1.28458i
$729$	−15634.9	−	11957.1i	−0.794333	−	0.607483i
$730$	1668.39	+	13682.4i	0.0845888	+	0.693709i
$731$	−32737.4	−	18900.9i	−1.65641	−	0.956328i
$732$	−2903.87	−	21563.4i	−0.146626	−	1.08881i
$733$	−5132.66	−	8890.04i	−0.258635	−	0.447969i	0.707242	−	0.706972i	$-0.249939\pi$
$733$	−5132.66	−	8890.04i	−0.258635	−	0.447969i	−0.965876	+	0.259003i	$0.916606\pi$
$734$	−6356.88	+	14941.2i	−0.319668	+	0.751346i
$735$	−7711.76	+	1683.71i	−0.387010	+	0.0844962i
$736$	3302.25	+	1556.68i	0.165384	+	0.0779620i
$737$	1370.78	−	791.418i	0.0685118	−	0.0395553i
$738$	16165.1	−	7361.05i	0.806296	−	0.367160i
$739$	−17511.3	−	10110.2i	−0.871670	−	0.503259i	−0.00376726	−	0.999993i	$-0.501199\pi$
$739$	−17511.3	−	10110.2i	−0.871670	−	0.503259i	−0.867903	+	0.496734i	$0.834532\pi$
$740$	−1462.50	+	5068.37i	−0.0726520	+	0.251780i
$741$	4806.67	−	43998.6i	0.238296	−	2.18128i
$742$	−16891.1	−	4140.25i	−0.835704	−	0.204843i
$743$		−	30818.7i		−	1.52171i	−0.648924	−	0.760854i	$-0.724781\pi$
$743$		−	30818.7i		−	1.52171i	0.648924	−	0.760854i	$-0.275219\pi$
$744$	2053.70	−	2026.76i	0.101199	−	0.0998720i
$745$	−4496.37	−	2595.98i	−0.221120	−	0.127664i
$746$	7304.99	+	9710.91i	0.358518	+	0.476597i
$747$	−9380.90	+	2963.33i	−0.459477	+	0.145144i
$748$	5793.22	+	6019.14i	0.283183	+	0.294227i
$749$	−507.791	−	620.943i	−0.0247721	−	0.0302921i
$750$	13079.7	+	7334.71i	0.636803	+	0.357101i
$751$	11160.7	+	19330.8i	0.542288	+	0.939270i	0.998772	+	0.0495383i	$0.0157750\pi$
$751$	11160.7	+	19330.8i	0.542288	+	0.939270i	−0.456485	+	0.889731i	$0.650892\pi$
$752$	12875.7	+	8105.54i	0.624372	+	0.393057i
$753$	5666.86	−	7732.98i	0.274252	−	0.374244i
$754$	4066.20	+	33346.7i	0.196396	+	1.61063i
$755$		−	1174.29i		−	0.0566048i
$756$	−1622.16	−	20723.2i	−0.0780387	−	0.996950i
$757$		−	20252.5i		−	0.972377i	−0.873854	−	0.486189i	$-0.838387\pi$
$757$		−	20252.5i		−	0.972377i	0.873854	−	0.486189i	$-0.161613\pi$
$758$	−19940.4	+	2431.47i	−0.955499	+	0.116511i
$759$	−566.359	+	772.852i	−0.0270850	+	0.0369601i
$760$	1948.41	−	12105.4i	0.0929952	−	0.577777i
$761$	−3413.04	−	5911.55i	−0.162579	−	0.281595i	0.773214	−	0.634145i	$-0.218648\pi$
$761$	−3413.04	−	5911.55i	−0.162579	−	0.281595i	−0.935793	+	0.352550i	$0.885314\pi$
$762$	4180.16	−	7454.31i	0.198729	−	0.354385i
$763$	−29296.0	−	11084.4i	−1.39002	−	0.525928i
$764$	18074.9	−	17396.4i	0.855923	−	0.823798i
$765$	13023.1	−	4113.86i	0.615492	−	0.194427i
$766$	−19416.2	+	14605.8i	−0.915844	+	0.688940i
$767$	26344.4	+	15209.9i	1.24021	+	0.716036i
$768$	−20077.2	+	7063.45i	−0.943323	+	0.331875i
$769$			12470.9i			0.584803i	0.956296	+	0.292402i	$0.0944544\pi$
$769$			12470.9i			0.584803i	−0.956296	+	0.292402i	$0.905546\pi$
$770$	−2036.67	+	592.769i	−0.0953201	+	0.0277427i
$771$	−1779.32	+	16287.2i	−0.0831136	+	0.760792i
$772$	5390.98	−	18682.8i	0.251329	−	0.870994i
$773$	29045.9	+	16769.7i	1.35150	+	0.780289i	0.988460	−	0.151485i	$-0.0484056\pi$
$773$	29045.9	+	16769.7i	1.35150	+	0.780289i	0.363040	+	0.931774i	$0.381739\pi$
$774$	10474.9	+	23003.2i	0.486449	+	1.06826i
$775$	2239.74	−	1293.12i	0.103811	−	0.0599356i
$776$	11389.2	−	4339.21i	0.526868	−	0.200733i
$777$	14307.8	−	760.049i	0.660605	−	0.0350921i
$778$	2149.54	+	914.547i	0.0990552	+	0.0421441i
$779$	−14228.8	−	24645.0i	−0.654429	−	1.13350i
$780$	12702.3	−	1710.57i	0.583095	−	0.0785235i
$781$	−6273.39	−	3621.94i	−0.287426	−	0.165945i
$782$	6467.17	−	788.588i	0.295736	−	0.0360612i
$783$	7675.45	−	22671.1i	0.350317	−	1.03474i
$784$	15149.8	−	15886.3i	0.690133	−	0.723683i
$785$		−	1234.41i		−	0.0561248i
$786$	−6.15763	−	491.665i	−0.000279434	−	0.0223119i
$787$	17244.0	−	29867.5i	0.781045	−	1.35281i	−0.150289	−	0.988642i	$-0.548020\pi$
$787$	17244.0	−	29867.5i	0.781045	−	1.35281i	0.931334	−	0.364167i	$-0.118646\pi$
$788$	−8465.83	+	2095.76i	−0.382719	+	0.0947440i
$789$	2227.46	+	5058.60i	0.100507	+	0.228252i
$790$	5078.38	−	11936.2i	0.228710	−	0.537558i
$791$	−1164.62	−	7131.13i	−0.0523504	−	0.320549i
$792$	−814.776	−	5526.17i	−0.0365553	−	0.247934i
$793$	−18219.7	−	31557.4i	−0.815888	−	1.41316i
$794$	7252.72	−	5455.83i	0.324168	−	0.243854i
$795$	−4516.09	+	6162.64i	−0.201471	+	0.274926i
$796$	−9328.36	−	2691.73i	−0.415370	−	0.119857i
$797$			21992.9i			0.977451i	0.872438	+	0.488726i	$0.162538\pi$
$797$			21992.9i			0.977451i	−0.872438	+	0.488726i	$0.837462\pi$
$798$	−32797.8	+	5778.96i	−1.45493	+	0.256357i
$799$	27151.6			1.20219
$800$	−19011.0	+	1583.29i	−0.840175	+	0.0699723i
$801$	−17345.4	+	18949.6i	−0.765132	+	0.835895i
$802$	−5209.39	−	6925.11i	−0.229364	−	0.304906i
$803$	8712.80	−	5030.34i	0.382899	−	0.221067i
$804$	4397.75	+	5696.25i	0.192906	+	0.249865i
$805$	−585.393	+	1547.19i	−0.0256303	+	0.0677406i
$806$	1891.85	−	4446.58i	0.0826767	−	0.194323i
$807$	8343.18	+	18947.5i	0.363933	+	0.826498i
$808$	−6010.49	+	37343.1i	−0.261694	+	1.62590i
$809$	20132.6	+	11623.6i	0.874939	+	0.505146i	0.868986	−	0.494836i	$-0.164772\pi$
$809$	20132.6	+	11623.6i	0.874939	+	0.505146i	0.00595233	+	0.999982i	$0.498105\pi$
$810$	−8685.64	−	2819.84i	−0.376768	−	0.122320i
$811$	−32730.2			−1.41715			−0.708577	−	0.705634i	$-0.750662\pi$
$811$	−32730.2			−1.41715			−0.708577	+	0.705634i	$0.750662\pi$
$812$	23236.6	−	9949.48i	1.00424	−	0.429998i
$813$	6549.04	+	715.457i	0.282515	+	0.0308637i
$814$	3822.01	−	466.044i	0.164572	−	0.0200674i
$815$	3583.67	−	6207.10i	0.154025	−	0.266779i
$816$	−23605.9	+	29755.5i	−1.01271	+	1.27653i
$817$	35070.2	−	20247.8i	1.50178	−	0.867051i
$818$	263.969	−	620.432i	0.0112830	−	0.0265194i
$819$	−15699.5	−	31071.3i	−0.669821	−	1.32567i
$820$	5937.47	−	5714.61i	0.252860	−	0.243369i
$821$	14463.1	+	25050.9i	0.614819	+	1.06490i	0.990416	+	0.138115i	$0.0441043\pi$
$821$	14463.1	+	25050.9i	0.614819	+	1.06490i	−0.375597	+	0.926783i	$0.622562\pi$
$822$	−11683.2	+	6941.83i	−0.495741	+	0.294555i
$823$	−1455.37	+	2520.77i	−0.0616415	+	0.106766i	−0.895199	−	0.445666i	$-0.852967\pi$
$823$	−1455.37	+	2520.77i	−0.0616415	+	0.106766i	0.833558	+	0.552432i	$0.186300\pi$
$824$	8407.81	+	6843.46i	0.355461	+	0.289324i
$825$	543.736	−	4977.16i	0.0229460	−	0.210039i
$826$	5449.11	−	22230.9i	0.229538	−	0.936456i
$827$	−37411.1			−1.57305			−0.786524	−	0.617559i	$-0.788122\pi$
$827$	−37411.1			−1.57305			−0.786524	+	0.617559i	$0.788122\pi$
$828$	−3825.99	−	2082.96i	−0.160582	−	0.0874249i
$829$	−1963.00	+	3400.01i	−0.0822410	+	0.142446i	−0.904212	−	0.427083i	$-0.859541\pi$
$829$	−1963.00	+	3400.01i	−0.0822410	+	0.142446i	0.821971	+	0.569529i	$0.192874\pi$
$830$	−3647.47	+	2743.79i	−0.152537	+	0.114745i
$831$	4990.31	+	11333.1i	0.208318	+	0.473093i
$832$	−26608.2	+	23717.8i	−1.10874	+	0.988303i
$833$	7776.23	−	38395.5i	0.323446	−	1.59703i
$834$	3845.47	−	6857.46i	0.159661	−	0.284718i
$835$	12485.8	−	7208.68i	0.517472	−	0.298763i
$836$	−8687.20	+	2150.56i	−0.359394	+	0.0889697i
$837$	−2586.73	+	2272.19i	−0.106822	+	0.0938331i
$838$	−28779.7	+	3509.31i	−1.18637	+	0.144663i
$839$	−46725.8			−1.92271			−0.961355	−	0.275313i	$-0.911219\pi$
$839$	−46725.8			−1.92271			−0.961355	+	0.275313i	$0.911219\pi$
$840$	−3906.73	−	8817.18i	−0.160470	−	0.362168i
$841$	4716.91			0.193403
$842$	−31148.9	+	3798.21i	−1.27490	+	0.155457i
$843$	−16728.4	+	22827.5i	−0.683460	+	0.932647i
$844$	3036.51	+	12266.0i	0.123840	+	0.500252i
$845$	10162.9	−	5867.53i	0.413743	−	0.238875i
$846$	−14776.8	−	10546.9i	−0.600518	−	0.428616i
$847$	−14624.8	−	17883.7i	−0.593288	−	0.725492i
$848$	812.463	−	21232.3i	0.0329011	−	0.859813i
$849$	−19997.0	+	8805.28i	−0.808355	+	0.355944i
$850$	−27205.9	+	20465.5i	−1.09783	+	0.825836i
$851$	1501.36	−	2600.43i	0.0604771	−	0.104749i
$852$	12513.2	−	30464.5i	0.503164	−	1.22499i
$853$	−33662.3			−1.35120			−0.675601	−	0.737268i	$-0.736116\pi$
$853$	−33662.3			−1.35120			−0.675601	+	0.737268i	$0.736116\pi$
$854$	−18967.8	+	19798.5i	−0.760030	+	0.793315i
$855$	−3158.98	+	14285.5i	−0.126357	+	0.571409i
$856$	618.654	−	760.073i	0.0247023	−	0.0303490i
$857$	−4023.45	+	6968.82i	−0.160372	+	0.277772i	−0.935002	−	0.354642i	$-0.884603\pi$
$857$	−4023.45	+	6968.82i	−0.160372	+	0.277772i	0.774630	+	0.632414i	$0.217936\pi$
$858$	−4778.61	−	8042.48i	−0.190139	−	0.320007i
$859$	5884.03	+	10191.4i	0.233714	+	0.404805i	0.958898	−	0.283750i	$-0.0915787\pi$
$859$	5884.03	+	10191.4i	0.233714	+	0.404805i	−0.725184	+	0.688555i	$0.758245\pi$
$860$	8131.97	+	8449.10i	0.322440	+	0.335014i
$861$	−19950.6	−	10147.5i	−0.789679	−	0.401654i
$862$	−3252.45	+	7644.53i	−0.128514	+	0.302058i
$863$	−31684.1	+	18292.8i	−1.24976	+	0.721546i	−0.971061	−	0.238833i	$-0.923235\pi$
$863$	−31684.1	+	18292.8i	−1.24976	+	0.721546i	−0.278695	+	0.960380i	$0.589902\pi$
$864$	24405.5	−	7024.42i	0.960987	−	0.276592i
$865$	−2326.30	+	4029.27i	−0.0914412	+	0.158381i
$866$	9211.03	−	1123.17i	0.361436	−	0.0440724i
$867$	−4588.68	+	42003.1i	−0.179746	+	1.64533i
$868$	−3610.27	−	431.796i	−0.141176	−	0.0168849i
$869$	−9467.93			−0.369595
$870$	−139.065	−	11103.8i	−0.00541924	−	0.432707i
$871$	10437.4	+	6026.05i	0.406038	+	0.234426i
$872$	6081.28	−	37782.9i	0.236168	−	1.46730i
$873$	−13867.6	+	4380.62i	−0.537625	+	0.169830i
$874$	−2732.41	+	6422.23i	−0.105749	+	0.248553i
$875$	−3045.81	−	18649.9i	−0.117677	−	0.720549i
$876$	27952.6	+	36206.0i	1.07812	+	1.39645i
$877$	6245.25	−	3605.70i	0.240464	−	0.138832i	−0.374926	−	0.927055i	$-0.622332\pi$
$877$	6245.25	−	3605.70i	0.240464	−	0.138832i	0.615390	+	0.788223i	$0.288999\pi$
$878$	−21895.3	−	29106.6i	−0.841608	−	1.11879i
$879$	8061.32	−	11000.4i	0.309330	−	0.422111i
$880$	−1209.02	−	2292.28i	−0.0463139	−	0.0878100i
$881$	−31273.8			−1.19596			−0.597980	−	0.801511i	$-0.704030\pi$
$881$	−31273.8			−1.19596			−0.597980	+	0.801511i	$0.704030\pi$
$882$	−19146.6	+	17875.6i	−0.730953	+	0.682428i
$883$		−	42583.0i		−	1.62291i	−0.584414	−	0.811456i	$-0.698676\pi$
$883$		−	42583.0i		−	1.62291i	0.584414	−	0.811456i	$-0.301324\pi$
$884$	−17635.5	+	61116.9i	−0.670980	+	2.32532i
$885$	−8110.85	−	5943.77i	−0.308071	−	0.225760i
$886$	35484.8	−	26693.3i	1.34552	−	1.01216i
$887$	18980.1	+	32874.5i	0.718478	+	1.24444i	0.961603	+	0.274445i	$0.0884941\pi$
$887$	18980.1	+	32874.5i	0.718478	+	1.24444i	−0.243125	+	0.969995i	$0.578173\pi$
$888$	4419.04	+	16938.5i	0.166997	+	0.640111i
$889$	−10628.8	+	1735.85i	−0.400990	+	0.0654877i
$890$	−4666.15	+	10967.3i	−0.175741	+	0.413061i
$891$	588.053	+	6639.36i	0.0221106	+	0.249637i
$892$	1319.11	+	5328.56i	0.0495147	+	0.200015i
$893$	−14543.2	+	25189.5i	−0.544982	+	0.943937i
$894$	−17228.0	+	215.764i	−0.644509	+	0.00807185i
$895$			10099.5i			0.377193i
$896$	22730.0	+	14236.2i	0.847497	+	0.530800i
$897$	−7252.49	−	792.307i	−0.269959	−	0.0294920i
$898$	9884.09	−	1205.24i	0.367301	−	0.0447876i
$899$	−3625.83	−	2093.38i	−0.134514	−	0.0776619i
$900$	22756.1	−	570.086i	0.842819	−	0.0211143i
$901$	−18959.2	−	32838.4i	−0.701025	−	1.21421i
$902$	−5534.79	−	2354.83i	−0.204311	−	0.0869261i
$903$	14440.0	−	28390.0i	0.532151	−	1.04624i
$904$	8249.55	−	3143.02i	0.303513	−	0.115636i
$905$	13990.4	−	8077.34i	0.513874	−	0.296685i
$906$	−1990.52	−	3350.09i	−0.0729919	−	0.122847i
$907$	41433.3	+	23921.6i	1.51684	+	0.875746i	0.999804	+	0.0197810i	$0.00629691\pi$
$907$	41433.3	+	23921.6i	1.51684	+	0.875746i	0.517033	+	0.855965i	$0.327036\pi$
$908$	−42101.7	−	12148.6i	−1.53876	−	0.444014i
$909$	9744.87	−	44068.2i	0.355574	−	1.60798i
$910$	−11662.7	−	11173.3i	−0.424850	−	0.407024i
$911$			42439.6i			1.54346i	0.635953	+	0.771728i	$0.280607\pi$
$911$			42439.6i			1.54346i	−0.635953	+	0.771728i	$0.719393\pi$
$912$	−14961.3	−	37838.0i	−0.543221	−	1.37384i
$913$	2885.10	+	1665.71i	0.104582	+	0.0603802i
$914$	14852.5	−	11172.7i	0.537503	−	0.404334i
$915$	4854.18	+	11023.9i	0.175382	+	0.398295i
$916$	18245.6	+	18957.1i	0.658134	+	0.683799i
$917$	−479.654	+	392.248i	−0.0172732	+	0.0141256i
$918$	30179.9	−	33811.7i	1.08506	−	1.21563i
$919$	21528.4	+	37288.2i	0.772748	+	1.33844i	0.936051	+	0.351863i	$0.114452\pi$
$919$	21528.4	+	37288.2i	0.772748	+	1.33844i	−0.163303	+	0.986576i	$0.552215\pi$
$920$	−1995.40	−	321.166i	−0.0715069	−	0.0115093i
$921$	−11750.7	−	8611.12i	−0.420411	−	0.308085i
$922$	−25846.2	+	3151.60i	−0.923208	+	0.112573i
$923$		−	55156.8i		−	1.96696i
$924$	−4805.56	+	5143.44i	−0.171094	+	0.183124i
$925$			15690.5i			0.557730i
$926$	430.653	+	3531.76i	0.0152831	+	0.125336i
$927$	−9541.94	−	8734.16i	−0.338078	−	0.309458i
$928$	17607.8	+	25371.4i	0.622850	+	0.897474i
$929$	12827.5	+	22217.9i	0.453021	+	0.784655i	0.998572	−	0.0534222i	$-0.0170129\pi$
$929$	12827.5	+	22217.9i	0.453021	+	0.784655i	−0.545551	+	0.838078i	$0.683680\pi$
$930$	−781.294	+	1393.25i	−0.0275480	+	0.0491252i
$931$	31455.8	+	27780.1i	1.10733	+	0.977933i
$932$	36448.8	−	35080.7i	1.28103	−	1.23295i
$933$	−22364.2	+	9847.64i	−0.784749	+	0.345549i
$934$	−20327.1	−	27021.9i	−0.712124	−	0.946664i
$935$	−4005.26	−	2312.44i	−0.140092	−	0.0808822i
$936$	33338.4	−	26411.6i	1.16421	−	0.922318i
$937$		−	23102.8i		−	0.805480i	−0.915315	−	0.402740i	$-0.868058\pi$
$937$		−	23102.8i		−	0.805480i	0.915315	−	0.402740i	$-0.131942\pi$
$938$	2158.89	−	8807.70i	0.0751496	−	0.306590i
$939$	−40575.9	−	4432.76i	−1.41016	−	0.154055i
$940$	−8092.67	−	2335.17i	−0.280802	−	0.0810264i
$941$	11357.7	+	6557.39i	0.393466	+	0.227168i	0.683661	−	0.729800i	$-0.260387\pi$
$941$	11357.7	+	6557.39i	0.393466	+	0.227168i	−0.290195	+	0.956968i	$0.593720\pi$
$942$	−2092.44	−	3521.61i	−0.0723730	−	0.121805i
$943$	−4062.35	+	2345.40i	−0.140285	+	0.0809934i
$944$	27944.5	+	1069.31i	0.963472	+	0.0368676i
$945$	4043.48	+	10773.7i	0.139190	+	0.370868i
$946$	3350.96	−	7876.08i	0.115168	−	0.270691i
$947$	9477.18	+	16415.0i	0.325203	+	0.563267i	0.981553	−	0.191188i	$-0.0612342\pi$
$947$	9477.18	+	16415.0i	0.325203	+	0.563267i	−0.656351	+	0.754456i	$0.727901\pi$
$948$	−5744.99	−	42660.8i	−0.196823	−	1.46156i
$949$	66341.5	+	38302.3i	2.26927	+	1.31016i
$950$	−4414.35	−	36201.8i	−0.150758	−	1.23636i
$951$	−5367.16	+	49129.1i	−0.183010	+	1.67520i
$952$	47862.6	−	110.145i	1.62945	−	0.00374983i
$953$			46313.7i			1.57424i	0.616803	+	0.787118i	$0.288428\pi$
$953$			46313.7i			1.57424i	−0.616803	+	0.787118i	$0.711572\pi$
$954$	−2437.59	+	25236.4i	−0.0827251	+	0.856456i
$955$	−6944.02	+	12027.4i	−0.235291	+	0.407537i
$956$	10252.2	+	41413.8i	0.346840	+	1.40106i
$957$	−7417.98	+	3266.37i	−0.250563	+	0.110331i
$958$	−3093.26	−	1316.06i	−0.104320	−	0.0443841i
$959$	16017.2	+	6060.24i	0.539333	+	0.204062i
$960$	9594.99	−	6838.56i	0.322580	−	0.229910i
$961$	−14594.4	−	25278.2i	−0.489892	−	0.848518i
$962$	17624.0	+	23428.6i	0.590667	+	0.785205i
$963$	−789.575	+	862.599i	−0.0264213	+	0.0288649i
$964$	40024.2	+	11549.1i	1.33723	+	0.385864i
$965$			10764.8i			0.359101i
$966$	952.574	+	5406.22i	0.0317273	+	0.180064i
$967$	49194.0			1.63596			0.817980	−	0.575246i	$-0.195094\pi$
$967$	49194.0			1.63596			0.817980	+	0.575246i	$0.195094\pi$
$968$	17817.8	−	21890.8i	0.591617	−	0.726855i
$969$	−58568.9	−	42920.4i	−1.94170	−	1.42291i
$970$	−5391.97	+	4056.09i	−0.178480	+	0.134261i
$971$	−49420.8	+	28533.1i	−1.63336	+	0.943018i	−0.650307	+	0.759672i	$0.725360\pi$
$971$	−49420.8	+	28533.1i	−1.63336	+	0.943018i	−0.983048	+	0.183346i	$0.941307\pi$
$972$	−29558.9	+	6678.32i	−0.975415	+	0.220378i
$973$	−9777.82	+	1596.87i	−0.322161	+	0.0526138i
$974$	42746.1	+	18186.8i	1.40623	+	0.598297i
$975$	34890.2	−	15363.2i	1.14603	−	0.504632i
$976$	−28349.0	−	17846.4i	−0.929744	−	0.585296i
$977$	45789.7	+	26436.7i	1.49943	+	0.865696i	1.00000		0.000658044i	$-0.000209462\pi$
$977$	45789.7	+	26436.7i	1.49943	+	0.865696i	0.499430	+	0.866354i	$0.333543\pi$
$978$	−297.856	−	23782.7i	−0.00973862	−	0.777595i
$979$	8699.37			0.283997
$980$	−5619.95	+	10775.2i	−0.183186	+	0.351225i
$981$	−9859.64	+	44587.2i	−0.320891	+	1.45113i
$982$	−1435.28	−	11770.6i	−0.0466410	−	0.382501i
$983$	−6384.53	+	11058.3i	−0.207157	+	0.358806i	−0.950818	−	0.309751i	$-0.899754\pi$
$983$	−6384.53	+	11058.3i	−0.207157	+	0.358806i	0.743661	+	0.668557i	$0.233088\pi$
$984$	7252.03	−	26367.6i	0.234946	−	0.854237i
$985$	4181.34	−	2414.10i	0.135257	−	0.0780909i
$986$	50713.4	+	21576.6i	1.63798	+	0.696894i
$987$	1213.57	+	22845.3i	0.0391371	+	0.736751i
$988$	−47254.4	−	49097.1i	−1.52162	−	1.58096i
$989$	−3337.54	−	5780.79i	−0.107308	−	0.185863i
$990$	1281.55	+	2814.33i	0.0411418	+	0.0903489i
$991$	−16360.6	+	28337.4i	−0.524433	+	0.908344i	0.475163	+	0.879898i	$0.342389\pi$
$991$	−16360.6	+	28337.4i	−0.524433	+	0.908344i	−0.999595	+	0.0284459i	$0.990944\pi$
$992$	−368.695	−	4427.01i	−0.0118005	−	0.141691i
$993$	−4306.31	−	470.448i	−0.137620	−	0.0150345i
$994$	−39848.4	+	11597.8i	−1.27155	+	0.370081i
$995$	5374.91			0.171253
$996$	−5754.77	+	14010.5i	−0.183079	+	0.445722i
$997$	4048.90	−	7012.90i	0.128616	−	0.222769i	−0.794525	−	0.607232i	$-0.792280\pi$
$997$	4048.90	−	7012.90i	0.128616	−	0.222769i	0.923141	+	0.384463i	$0.125613\pi$
$998$	−9401.86	−	12498.4i	−0.298207	−	0.396423i
$999$	−4091.59	−	20483.6i	−0.129582	−	0.648721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.ba.c.101.47	yes	176
3.2	odd	2	inner	168.4.ba.c.101.42	yes	176
7.5	odd	6	inner	168.4.ba.c.5.71	yes	176
8.5	even	2	inner	168.4.ba.c.101.18	yes	176
21.5	even	6	inner	168.4.ba.c.5.18	✓	176
24.5	odd	2	inner	168.4.ba.c.101.71	yes	176
56.5	odd	6	inner	168.4.ba.c.5.42	yes	176
168.5	even	6	inner	168.4.ba.c.5.47	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.ba.c.5.18	✓	176	21.5	even	6	inner
168.4.ba.c.5.42	yes	176	56.5	odd	6	inner
168.4.ba.c.5.47	yes	176	168.5	even	6	inner
168.4.ba.c.5.71	yes	176	7.5	odd	6	inner
168.4.ba.c.101.18	yes	176	8.5	even	2	inner
168.4.ba.c.101.42	yes	176	3.2	odd	2	inner
168.4.ba.c.101.47	yes	176	1.1	even	1	trivial
168.4.ba.c.101.71	yes	176	24.5	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342354 + 2.80763i) q^{2} +(-4.19123 - 3.07141i) q^{3} +(-7.76559 + 1.92241i) q^{4} +(3.83548 - 2.21442i) q^{5} +(7.18850 - 12.8189i) q^{6} +(-18.2781 + 2.98509i) q^{7} +(-8.05600 - 21.1448i) q^{8} +(8.13288 + 25.7460i) q^{9} +(7.53036 + 10.0105i) q^{10} +(4.57157 - 7.91819i) q^{11} +(38.4519 + 15.7940i) q^{12} +69.6182 q^{13} +(-14.6386 - 50.2962i) q^{14} +(-22.8768 - 2.49920i) q^{15} +(56.6087 - 29.8573i) q^{16} +(57.1065 - 98.9113i) q^{17} +(-69.5009 + 31.6484i) q^{18} +(61.1759 + 105.960i) q^{19} +(-25.5278 + 24.5696i) q^{20} +(85.7763 + 43.6283i) q^{21} +(23.7965 + 10.1245i) q^{22} +(17.4658 - 10.0839i) q^{23} +(-31.1797 + 113.366i) q^{24} +(-52.6927 + 91.2665i) q^{25} +(23.8341 + 195.462i) q^{26} +(44.9897 - 132.887i) q^{27} +(136.202 - 58.3190i) q^{28} +170.605 q^{29} +(-0.815129 - 65.0852i) q^{30} +(-21.2529 - 12.2703i) q^{31} +(103.208 + 148.715i) q^{32} +(-43.4805 + 19.1458i) q^{33} +(297.257 + 126.471i) q^{34} +(-63.4951 + 51.9246i) q^{35} +(-112.651 - 184.298i) q^{36} +(128.940 - 74.4434i) q^{37} +(-276.552 + 208.035i) q^{38} +(-291.786 - 213.826i) q^{39} +(-77.7220 - 63.2610i) q^{40} -232.589 q^{41} +(-93.1264 + 255.764i) q^{42} -330.977i q^{43} +(-20.2789 + 70.2779i) q^{44} +(88.2059 + 80.7387i) q^{45} +(34.2914 + 45.5854i) q^{46} +(118.864 + 205.878i) q^{47} +(-328.964 - 48.7297i) q^{48} +(325.178 - 109.124i) q^{49} +(-274.282 - 116.696i) q^{50} +(-543.144 + 239.163i) q^{51} +(-540.626 + 133.835i) q^{52} +(165.999 - 287.519i) q^{53} +(388.500 + 80.8201i) q^{54} -40.4935i q^{55} +(210.367 + 362.438i) q^{56} +(69.0434 - 631.998i) q^{57} +(58.4072 + 478.995i) q^{58} +(378.412 + 218.477i) q^{59} +(182.456 - 24.5708i) q^{60} +(-261.708 - 453.292i) q^{61} +(27.1746 - 63.8710i) q^{62} +(-225.508 - 446.311i) q^{63} +(-382.202 + 340.684i) q^{64} +(267.019 - 154.164i) q^{65} +(-68.6402 - 115.523i) q^{66} +(149.924 + 86.5586i) q^{67} +(-253.317 + 877.887i) q^{68} +(-104.175 - 11.3807i) q^{69} +(-167.523 - 160.494i) q^{70} -792.275i q^{71} +(478.874 - 379.377i) q^{72} +(952.933 + 550.176i) q^{73} +(253.153 + 336.529i) q^{74} +(501.164 - 220.678i) q^{75} +(-678.764 - 705.234i) q^{76} +(-59.9231 + 158.376i) q^{77} +(500.451 - 892.432i) q^{78} +(-517.761 - 896.789i) q^{79} +(151.005 - 239.872i) q^{80} +(-596.713 + 418.778i) q^{81} +(-79.6277 - 653.023i) q^{82} +364.364i q^{83} +(-749.975 - 173.903i) q^{84} -505.830i q^{85} +(929.261 - 113.311i) q^{86} +(-715.043 - 523.996i) q^{87} +(-204.257 - 32.8758i) q^{88} +(475.732 + 823.992i) q^{89} +(-196.487 + 275.291i) q^{90} +(-1272.49 + 207.817i) q^{91} +(-116.247 + 111.884i) q^{92} +(51.3884 + 116.704i) q^{93} +(-537.336 + 404.209i) q^{94} +(469.278 + 270.938i) q^{95} +(24.1928 - 940.293i) q^{96} +538.631i q^{97} +(417.705 + 875.622i) q^{98} +(241.042 + 53.3019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 30 q^{4} - 76 q^{7} - 110 q^{9} + 330 q^{10} + 162 q^{12} - 332 q^{15} + 374 q^{16} + 18 q^{18} - 212 q^{22} - 84 q^{24} + 1112 q^{25} + 30 q^{28} - 104 q^{30} + 408 q^{31} + 2262 q^{33} + 1372 q^{36}+ \cdots - 1782 q^{96}+O(q^{100}) \) 176 * q + 30 * q^4 - 76 * q^7 - 110 * q^9 + 330 * q^10 + 162 * q^12 - 332 * q^15 + 374 * q^16 + 18 * q^18 - 212 * q^22 - 84 * q^24 + 1112 * q^25 + 30 * q^28 - 104 * q^30 + 408 * q^31 + 2262 * q^33 + 1372 * q^36 - 56 * q^39 - 2274 * q^40 - 1488 * q^42 - 844 * q^46 + 1292 * q^49 - 1632 * q^52 - 480 * q^54 + 100 * q^57 - 574 * q^58 - 524 * q^60 - 3030 * q^63 - 3420 * q^64 + 2376 * q^66 + 2442 * q^70 + 1026 * q^72 - 660 * q^73 - 1316 * q^78 + 3216 * q^79 + 2298 * q^81 - 360 * q^82 - 4164 * q^84 - 6972 * q^87 - 4042 * q^88 + 4476 * q^94 - 1782 * q^96

Introduction

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