LMFDB - Embedded newform 168.4.ba.c.101.70

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			101.70
Character	$\chi$	$=$	168.101
Dual form			168.4.ba.c.5.70

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.17768 - 1.80491i) q^{2} +(4.78157 + 2.03385i) q^{3} +(1.48458 - 7.86104i) q^{4} +(11.2278 - 6.48238i) q^{5} +(14.0837 - 4.20125i) q^{6} +(-0.198886 + 18.5192i) q^{7} +(-10.9556 - 19.7984i) q^{8} +(18.7269 + 19.4500i) q^{9} +(12.7505 - 34.3818i) q^{10} +(11.4142 - 19.7700i) q^{11} +(23.0868 - 34.5688i) q^{12} -3.71397 q^{13} +(32.9924 + 40.6878i) q^{14} +(66.8709 - 8.16029i) q^{15} +(-59.5921 - 23.3407i) q^{16} +(-52.8272 + 91.4995i) q^{17} +(75.8868 + 8.55548i) q^{18} +(-58.0142 - 100.484i) q^{19} +(-34.2897 - 97.8860i) q^{20} +(-38.6163 + 88.1464i) q^{21} +(-10.8266 - 63.6542i) q^{22} +(54.0553 - 31.2089i) q^{23} +(-12.1179 - 116.949i) q^{24} +(21.5426 - 37.3129i) q^{25} +(-8.08783 + 6.70339i) q^{26} +(49.9856 + 131.089i) q^{27} +(145.285 + 29.0566i) q^{28} +57.9724 q^{29} +(130.895 - 138.467i) q^{30} +(-10.4280 - 6.02060i) q^{31} +(-171.900 + 56.7299i) q^{32} +(94.7869 - 71.3167i) q^{33} +(50.1077 + 294.605i) q^{34} +(117.815 + 209.219i) q^{35} +(180.699 - 118.338i) q^{36} +(122.443 - 70.6922i) q^{37} +(-307.700 - 114.110i) q^{38} +(-17.7586 - 7.55366i) q^{39} +(-251.348 - 151.274i) q^{40} -417.036 q^{41} +(75.0027 + 261.654i) q^{42} -212.999i q^{43} +(-138.467 - 119.077i) q^{44} +(336.345 + 96.9863i) q^{45} +(61.3859 - 165.528i) q^{46} +(88.0065 + 152.432i) q^{47} +(-237.472 - 232.807i) q^{48} +(-342.921 - 7.36641i) q^{49} +(-20.4336 - 120.138i) q^{50} +(-438.694 + 330.069i) q^{51} +(-5.51368 + 29.1957i) q^{52} +(-201.587 + 349.159i) q^{53} +(345.458 + 195.251i) q^{54} -295.965i q^{55} +(368.829 - 198.951i) q^{56} +(-73.0307 - 598.462i) q^{57} +(126.245 - 104.635i) q^{58} +(-24.0393 - 13.8791i) q^{59} +(35.1266 - 537.789i) q^{60} +(425.644 + 737.237i) q^{61} +(-33.5755 + 5.71067i) q^{62} +(-363.923 + 342.939i) q^{63} +(-271.951 + 433.805i) q^{64} +(-41.6998 + 24.0754i) q^{65} +(77.6951 - 326.387i) q^{66} +(-683.478 - 394.606i) q^{67} +(640.855 + 551.115i) q^{68} +(321.944 - 39.2870i) q^{69} +(634.187 + 242.966i) q^{70} +482.779i q^{71} +(179.915 - 583.848i) q^{72} +(228.529 + 131.942i) q^{73} +(139.047 - 374.943i) q^{74} +(178.897 - 134.600i) q^{75} +(-876.032 + 306.877i) q^{76} +(363.853 + 215.313i) q^{77} +(-52.3063 + 15.6033i) q^{78} +(-71.1227 - 123.188i) q^{79} +(-820.392 + 124.234i) q^{80} +(-27.6063 + 728.477i) q^{81} +(-908.171 + 752.714i) q^{82} +477.893i q^{83} +(635.594 + 434.424i) q^{84} +1369.79i q^{85} +(-384.444 - 463.843i) q^{86} +(277.199 + 117.907i) q^{87} +(-516.462 - 9.39135i) q^{88} +(677.670 + 1173.76i) q^{89} +(907.503 - 395.868i) q^{90} +(0.738656 - 68.7797i) q^{91} +(-165.085 - 471.263i) q^{92} +(-37.6172 - 49.9969i) q^{93} +(466.776 + 173.103i) q^{94} +(-1302.75 - 752.141i) q^{95} +(-937.334 - 78.3611i) q^{96} -1362.01i q^{97} +(-760.068 + 602.901i) q^{98} +(598.278 - 148.224i) 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 $

$2$	2.17768	−	1.80491i	0.769926	−	0.638133i
$2$	2.17768	−	1.80491i	0.769926	−	0.638133i
$3$	4.78157	+	2.03385i	0.920214	+	0.391415i
$3$	4.78157	+	2.03385i	0.920214	+	0.391415i
$4$	1.48458	−	7.86104i	0.185572	−	0.982631i
$5$	11.2278	−	6.48238i	1.00425	−	0.579802i	0.0947447	−	0.995502i	$-0.469797\pi$
$5$	11.2278	−	6.48238i	1.00425	−	0.579802i	0.909502	+	0.415699i	$0.136463\pi$
$6$	14.0837	−	4.20125i	0.958272	−	0.285859i
$7$	−0.198886	+	18.5192i	−0.0107388	+	0.999942i
$7$	−0.198886	+	18.5192i	−0.0107388	+	0.999942i
$8$	−10.9556	−	19.7984i	−0.484172	−	0.874973i
$9$	18.7269	+	19.4500i	0.693589	+	0.720371i
$10$	12.7505	−	34.3818i	0.403205	−	1.08725i
$11$	11.4142	−	19.7700i	0.312864	−	0.541897i	−0.666117	−	0.745847i	$-0.732045\pi$
$11$	11.4142	−	19.7700i	0.312864	−	0.541897i	0.978981	+	0.203951i	$0.0653782\pi$
$12$	23.0868	−	34.5688i	0.555382	−	0.831595i
$13$	−3.71397			−0.0792361			−0.0396181	−	0.999215i	$-0.512614\pi$
$13$	−3.71397			−0.0792361			−0.0396181	+	0.999215i	$0.512614\pi$
$14$	32.9924	+	40.6878i	0.629828	+	0.776734i
$15$	66.8709	−	8.16029i	1.15107	−	0.140465i
$16$	−59.5921	−	23.3407i	−0.931126	−	0.364698i
$17$	−52.8272	+	91.4995i	−0.753676	+	1.30540i	0.192354	+	0.981326i	$0.438388\pi$
$17$	−52.8272	+	91.4995i	−0.753676	+	1.30540i	−0.946030	+	0.324079i	$0.894946\pi$
$18$	75.8868	+	8.55548i	0.993705	+	0.112030i
$19$	−58.0142	−	100.484i	−0.700493	−	1.21329i	−0.968293	−	0.249815i	$-0.919630\pi$
$19$	−58.0142	−	100.484i	−0.700493	−	1.21329i	0.267800	−	0.963474i	$-0.413703\pi$
$20$	−34.2897	−	97.8860i	−0.383371	−	1.09440i
$21$	−38.6163	+	88.1464i	−0.401274	+	0.915958i
$22$	−10.8266	−	63.6542i	−0.104920	−	0.616870i
$23$	54.0553	−	31.2089i	0.490057	−	0.282935i	−0.234541	−	0.972106i	$-0.575359\pi$
$23$	54.0553	−	31.2089i	0.490057	−	0.282935i	0.724598	+	0.689172i	$0.242025\pi$
$24$	−12.1179	−	116.949i	−0.103065	−	0.994675i
$25$	21.5426	−	37.3129i	0.172341	−	0.298503i
$26$	−8.08783	+	6.70339i	−0.0610059	+	0.0505632i
$27$	49.9856	+	131.089i	0.356287	+	0.934377i
$28$	145.285	+	29.0566i	0.980581	+	0.196114i
$29$	57.9724			0.371214			0.185607	−	0.982624i	$-0.440575\pi$
$29$	57.9724			0.371214			0.185607	+	0.982624i	$0.440575\pi$
$30$	130.895	−	138.467i	0.796600	−	0.842681i
$31$	−10.4280	−	6.02060i	−0.0604169	−	0.0348817i	0.469487	−	0.882939i	$-0.344439\pi$
$31$	−10.4280	−	6.02060i	−0.0604169	−	0.0348817i	−0.529904	+	0.848058i	$0.677772\pi$
$32$	−171.900	+	56.7299i	−0.949624	+	0.313392i
$33$	94.7869	−	71.3167i	0.500009	−	0.376202i
$34$	50.1077	+	294.605i	0.252747	+	1.48601i
$35$	117.815	+	209.219i	0.568984	+	1.01042i
$36$	180.699	−	118.338i	0.836570	−	0.547861i
$37$	122.443	−	70.6922i	0.544039	−	0.314101i	−0.202676	−	0.979246i	$-0.564964\pi$
$37$	122.443	−	70.6922i	0.544039	−	0.314101i	0.746714	+	0.665145i	$0.231630\pi$
$38$	−307.700	−	114.110i	−1.31357	−	0.487136i
$39$	−17.7586	−	7.55366i	−0.0729142	−	0.0310142i
$40$	−251.348	−	151.274i	−0.993539	−	0.597965i
$41$	−417.036			−1.58854			−0.794269	−	0.607566i	$-0.792146\pi$
$41$	−417.036			−1.58854			−0.794269	+	0.607566i	$0.792146\pi$
$42$	75.0027	+	261.654i	0.275552	+	0.961286i
$43$		−	212.999i		−	0.755396i	−0.925929	−	0.377698i	$-0.876716\pi$
$43$		−	212.999i		−	0.755396i	0.925929	−	0.377698i	$-0.123284\pi$
$44$	−138.467	−	119.077i	−0.474425	−	0.407991i
$45$	336.345	+	96.9863i	1.11421	+	0.321286i
$46$	61.3859	−	165.528i	0.196758	−	0.530561i
$47$	88.0065	+	152.432i	0.273129	+	0.473074i	0.969661	−	0.244452i	$-0.0786080\pi$
$47$	88.0065	+	152.432i	0.273129	+	0.473074i	−0.696532	+	0.717525i	$0.745275\pi$
$48$	−237.472	−	232.807i	−0.714087	−	0.700057i
$49$	−342.921	−	7.36641i	−0.999769	−	0.0214764i
$50$	−20.4336	−	120.138i	−0.0577951	−	0.339802i
$51$	−438.694	+	330.069i	−1.20450	+	0.906252i
$52$	−5.51368	+	29.1957i	−0.0147040	+	0.0778598i
$53$	−201.587	+	349.159i	−0.522455	+	0.904919i	0.477204	+	0.878793i	$0.341650\pi$
$53$	−201.587	+	349.159i	−0.522455	+	0.904919i	−0.999659	+	0.0261258i	$0.991683\pi$
$54$	345.458	+	195.251i	0.870571	+	0.492043i
$55$		−	295.965i		−	0.725597i
$56$	368.829	−	198.951i	0.880122	−	0.474748i
$57$	−73.0307	−	598.462i	−0.169704	−	1.39067i
$58$	126.245	−	104.635i	0.285807	−	0.236884i
$59$	−24.0393	−	13.8791i	−0.0530449	−	0.0306255i	0.473243	−	0.880932i	$-0.343083\pi$
$59$	−24.0393	−	13.8791i	−0.0530449	−	0.0306255i	−0.526288	+	0.850306i	$0.676417\pi$
$60$	35.1266	−	537.789i	0.0755805	−	1.15714i
$61$	425.644	+	737.237i	0.893412	+	1.54743i	0.835758	+	0.549098i	$0.185029\pi$
$61$	425.644	+	737.237i	0.893412	+	1.54743i	0.0576536	+	0.998337i	$0.481638\pi$
$62$	−33.5755	+	5.71067i	−0.0687757	+	0.0116977i
$63$	−363.923	+	342.939i	−0.727778	+	0.685813i
$64$	−271.951	+	433.805i	−0.531155	+	0.847275i
$65$	−41.6998	+	24.0754i	−0.0795726	+	0.0459413i
$66$	77.6951	−	326.387i	0.144903	−	0.608719i
$67$	−683.478	−	394.606i	−1.24627	−	0.719535i	−0.275908	−	0.961184i	$-0.588978\pi$
$67$	−683.478	−	394.606i	−1.24627	−	0.719535i	−0.970364	+	0.241649i	$0.922312\pi$
$68$	640.855	+	551.115i	1.14287	+	0.982832i
$69$	321.944	−	39.2870i	0.561703	−	0.0685449i
$70$	634.187	+	242.966i	1.08286	+	0.414857i
$71$			482.779i			0.806976i	0.914985	+	0.403488i	$0.132202\pi$
$71$			482.779i			0.806976i	−0.914985	+	0.403488i	$0.867798\pi$
$72$	179.915	−	583.848i	0.294489	−	0.955655i
$73$	228.529	+	131.942i	0.366402	+	0.211542i	0.671885	−	0.740655i	$-0.265485\pi$
$73$	228.529	+	131.942i	0.366402	+	0.211542i	−0.305483	+	0.952197i	$0.598818\pi$
$74$	139.047	−	374.943i	0.218431	−	0.589003i
$75$	178.897	−	134.600i	0.275429	−	0.207230i
$76$	−876.032	+	306.877i	−1.32221	+	0.463173i
$77$	363.853	+	215.313i	0.538506	+	0.318666i
$78$	−52.3063	+	15.6033i	−0.0759297	+	0.0226503i
$79$	−71.1227	−	123.188i	−0.101290	−	0.175440i	0.810926	−	0.585148i	$-0.198964\pi$
$79$	−71.1227	−	123.188i	−0.101290	−	0.175440i	−0.912216	+	0.409709i	$0.865630\pi$
$80$	−820.392	+	124.234i	−1.14653	+	0.173622i
$81$	−27.6063	+	728.477i	−0.0378688	+	0.999283i
$82$	−908.171	+	752.714i	−1.22306	+	1.01370i
$83$			477.893i			0.631994i	0.948760	+	0.315997i	$0.102339\pi$
$83$			477.893i			0.631994i	−0.948760	+	0.315997i	$0.897661\pi$
$84$	635.594	+	434.424i	0.825583	+	0.564281i
$85$			1369.79i			1.74793i
$86$	−384.444	−	463.843i	−0.482043	−	0.581599i
$87$	277.199	+	117.907i	0.341596	+	0.145299i
$88$	−516.462	−	9.39135i	−0.625625	−	0.0113764i
$89$	677.670	+	1173.76i	0.807111	+	1.39796i	0.914857	+	0.403779i	$0.132304\pi$
$89$	677.670	+	1173.76i	0.807111	+	1.39796i	−0.107745	+	0.994179i	$0.534363\pi$
$90$	907.503	−	395.868i	1.06288	−	0.463646i
$91$	0.738656	−	68.7797i	0.000850903	−	0.0792315i
$92$	−165.085	−	471.263i	−0.187079	−	0.534050i
$93$	−37.6172	−	49.9969i	−0.0419433	−	0.0557467i
$94$	466.776	+	173.103i	0.512173	+	0.189939i
$95$	−1302.75	−	752.141i	−1.40694	−	0.812295i
$96$	−937.334	−	78.3611i	−0.996524	−	0.0833094i
$97$		−	1362.01i		−	1.42569i	−0.701323	−	0.712844i	$-0.747407\pi$
$97$		−	1362.01i		−	1.42569i	0.701323	−	0.712844i	$-0.252593\pi$
$98$	−760.068	+	602.901i	−0.783453	+	0.621451i
$99$	598.278	−	148.224i	0.607366	−	0.150475i
$100$	−261.337	−	224.742i	−0.261337	−	0.224742i
$101$	−960.967	−	554.815i	−0.946731	−	0.546595i	−0.0546669	−	0.998505i	$-0.517410\pi$
$101$	−960.967	−	554.815i	−0.946731	−	0.546595i	−0.892064	+	0.451909i	$0.850743\pi$
$102$	−359.589	+	1510.59i	−0.349065	+	1.46638i
$103$	1462.91	−	844.611i	1.39946	−	0.807981i	0.405127	−	0.914260i	$-0.367227\pi$
$103$	1462.91	−	844.611i	1.39946	−	0.807981i	0.994336	+	0.106280i	$0.0338938\pi$
$104$	40.6886	+	73.5305i	0.0383639	+	0.0693294i
$105$	137.822	+	1240.02i	0.128096	+	1.15251i
$106$	191.210	+	1124.20i	0.175207	+	1.03012i
$107$	−852.137	−	1475.94i	−0.769899	−	1.33350i	−0.937617	−	0.347669i	$-0.886973\pi$
$107$	−852.137	−	1475.94i	−0.769899	−	1.33350i	0.167718	−	0.985835i	$-0.446360\pi$
$108$	1104.71	−	198.327i	0.984264	−	0.176704i
$109$	733.745	+	423.628i	0.644771	+	0.372259i	0.786450	−	0.617654i	$-0.211917\pi$
$109$	733.745	+	423.628i	0.644771	+	0.372259i	−0.141679	+	0.989913i	$0.545250\pi$
$110$	−534.190	−	644.516i	−0.463028	−	0.558656i
$111$	729.245	−	88.9903i	0.623576	−	0.0760953i
$112$	444.102	−	1098.95i	0.374676	−	0.927156i
$113$		−	627.031i		−	0.522001i	−0.965339	−	0.261001i	$-0.915948\pi$
$113$		−	627.031i		−	0.522001i	0.965339	−	0.261001i	$-0.0840525\pi$
$114$	−1239.21	−	1171.44i	−1.01809	−	0.962419i
$115$	404.616	−	700.815i	0.328092	−	0.568272i
$116$	86.0646	−	455.723i	0.0688870	−	0.364766i
$117$	−69.5511	−	72.2367i	−0.0549573	−	0.0570794i
$118$	−77.4004	+	13.1646i	−0.0603838	+	0.0102703i
$119$	−1683.99	−	996.516i	−1.29724	−	0.767651i
$120$	−894.169	−	1234.53i	−0.680217	−	0.939142i
$121$	404.933	+	701.364i	0.304232	+	0.526945i
$122$	2257.56	+	837.216i	1.67533	+	0.621295i
$123$	−1994.09	−	848.189i	−1.46180	−	0.621778i
$124$	−62.8094	+	73.0369i	−0.0454875	+	0.0528944i
$125$			1062.01i			0.759909i
$126$	−173.533	+	1403.66i	−0.122695	+	0.992444i
$127$	−1710.56			−1.19518			−0.597590	−	0.801802i	$-0.703875\pi$
$127$	−1710.56			−1.19518			−0.597590	+	0.801802i	$0.703875\pi$
$128$	190.757	+	1435.54i	0.131724	+	0.991286i
$129$	433.208	−	1018.47i	0.295673	−	0.695126i
$130$	−47.3548	+	127.693i	−0.0319484	+	0.0861493i
$131$	719.105	−	415.175i	0.479607	−	0.276901i	−0.240646	−	0.970613i	$-0.577359\pi$
$131$	719.105	−	415.175i	0.479607	−	0.276901i	0.720253	+	0.693712i	$0.244026\pi$
$132$	−419.905	−	851.000i	−0.276879	−	0.561136i
$133$	1872.41	−	1054.39i	1.22074	−	0.687423i
$134$	−2200.63	+	374.293i	−1.41870	+	0.241298i
$135$	1411.00	+	1147.82i	0.899553	+	0.731769i
$136$	2390.29	+	43.4651i	1.50710	+	0.0274052i
$137$	1636.51	+	944.837i	1.02056	+	0.589218i	0.914265	−	0.405117i	$-0.132769\pi$
$137$	1636.51	+	944.837i	1.02056	+	0.589218i	0.106291	+	0.994335i	$0.466103\pi$
$138$	630.181	−	666.635i	0.388729	−	0.411215i
$139$	−2008.82			−1.22580			−0.612900	−	0.790160i	$-0.709997\pi$
$139$	−2008.82			−1.22580			−0.612900	+	0.790160i	$0.709997\pi$
$140$	1819.59	−	615.550i	1.09845	−	0.371596i
$141$	110.786	+	907.856i	0.0661694	+	0.542236i
$142$	871.374	+	1051.34i	0.514958	+	0.621312i
$143$	−42.3919	+	73.4250i	−0.0247901	+	0.0429378i
$144$	−661.998	−	1596.17i	−0.383101	−	0.923707i
$145$	650.903	−	375.799i	0.372790	−	0.215231i
$146$	735.807	−	125.149i	0.417095	−	0.0709413i
$147$	−1624.72	−	732.673i	−0.911596	−	0.411087i
$148$	−373.939	−	1067.47i	−0.207687	−	0.592877i
$149$	−1426.31	−	2470.43i	−0.784211	−	1.35829i	−0.929469	−	0.368900i	$-0.879734\pi$
$149$	−1426.31	−	2470.43i	−0.784211	−	1.35829i	0.145258	−	0.989394i	$-0.453599\pi$
$150$	146.638	−	616.009i	0.0798197	−	0.335313i
$151$	1309.78	−	2268.60i	0.705882	−	1.22262i	−0.260491	−	0.965476i	$-0.583884\pi$
$151$	1309.78	−	2268.60i	0.705882	−	1.22262i	0.966372	−	0.257147i	$-0.0827824\pi$
$152$	−1353.83	+	2249.44i	−0.722436	+	1.20035i
$153$	−2768.96	+	686.011i	−1.46312	+	0.362488i
$154$	1180.98	−	187.840i	0.617961	−	0.0982894i
$155$	−156.111			−0.0808979
$156$	−85.7437	+	128.387i	−0.0440063	+	0.0658924i
$157$	1685.32	−	2919.06i	0.856708	−	1.48386i	−0.0183426	−	0.999832i	$-0.505839\pi$
$157$	1685.32	−	2919.06i	0.856708	−	1.48386i	0.875051	−	0.484031i	$-0.160828\pi$
$158$	−377.226	−	139.894i	−0.189940	−	0.0704391i
$159$	−1674.04	+	1259.53i	−0.834969	+	0.628222i
$160$	−1562.32	+	1751.28i	−0.771952	+	0.865317i
$161$	567.212	+	1007.27i	0.277656	+	0.493067i
$162$	1254.72	+	1636.22i	0.608519	+	0.793539i
$163$	795.653	−	459.371i	0.382334	−	0.220740i	−0.296499	−	0.955033i	$-0.595819\pi$
$163$	795.653	−	459.371i	0.382334	−	0.220740i	0.678833	+	0.734293i	$0.262486\pi$
$164$	−619.123	+	3278.34i	−0.294789	+	1.56095i
$165$	601.948	−	1415.18i	0.284010	−	0.667705i
$166$	862.555	+	1040.70i	0.403297	+	0.486589i
$167$	3976.72			1.84268			0.921340	−	0.388758i	$-0.127096\pi$
$167$	3976.72			1.84268			0.921340	+	0.388758i	$0.127096\pi$
$168$	2168.22	−	201.154i	0.995724	−	0.0923773i
$169$	−2183.21			−0.993722
$170$	2472.34	+	2982.96i	1.11541	+	1.34578i
$171$	867.980	−	3010.12i	0.388164	−	1.34614i
$172$	−1674.39	−	316.214i	−0.742275	−	0.140181i
$173$	891.820	−	514.892i	0.391930	−	0.226281i	−0.291066	−	0.956703i	$-0.594010\pi$
$173$	891.820	−	514.892i	0.391930	−	0.226281i	0.682996	+	0.730422i	$0.260677\pi$
$174$	816.463	−	243.556i	0.355724	−	0.106115i
$175$	686.721	+	406.373i	0.296635	+	0.175537i
$176$	−1141.64	+	911.717i	−0.488945	+	0.390473i
$177$	−86.7177	−	115.256i	−0.0368254	−	0.0489446i
$178$	3594.28	+	1332.94i	1.51350	+	0.561280i
$179$	1383.73	−	2396.69i	0.577793	−	1.00077i	−0.417939	−	0.908475i	$-0.637247\pi$
$179$	1383.73	−	2396.69i	0.577793	−	1.00077i	0.995732	−	0.0922920i	$-0.0294193\pi$
$180$	1261.74	−	2500.04i	0.522471	−	1.03523i
$181$	482.414			0.198108			0.0990540	−	0.995082i	$-0.468418\pi$
$181$	482.414			0.198108			0.0990540	+	0.995082i	$0.468418\pi$
$182$	−122.533	−	151.113i	−0.0499051	−	0.0615454i
$183$	535.818	+	4390.85i	0.216442	+	1.77367i
$184$	−1210.09	−	728.297i	−0.484832	−	0.291798i
$185$	916.508	−	1587.44i	0.364233	−	0.630869i
$186$	−172.158	−	40.9816i	−0.0678670	−	0.0161554i
$187$	1205.96	+	2088.78i	0.471596	+	0.816829i
$188$	1328.93	−	465.526i	0.515542	−	0.180596i
$189$	−2437.61	+	899.622i	−0.938149	+	0.346232i
$190$	−4194.51	+	713.421i	−1.60159	+	0.272405i
$191$	2001.62	−	1155.64i	0.758284	−	0.437795i	−0.0703955	−	0.997519i	$-0.522426\pi$
$191$	2001.62	−	1155.64i	0.758284	−	0.437795i	0.828679	+	0.559724i	$0.189093\pi$
$192$	−2182.65	+	1521.16i	−0.820412	+	0.571773i
$193$	2051.69	−	3553.63i	0.765202	−	1.32537i	−0.174938	−	0.984579i	$-0.555973\pi$
$193$	2051.69	−	3553.63i	0.765202	−	1.32537i	0.940140	−	0.340789i	$-0.110694\pi$
$194$	−2458.32	−	2966.03i	−0.909778	−	1.09767i
$195$	−248.356	+	30.3071i	−0.0912059	+	0.0111299i
$196$	−567.001	+	2684.78i	−0.206633	+	0.978419i
$197$	2402.75			0.868978			0.434489	−	0.900677i	$-0.356929\pi$
$197$	2402.75			0.868978			0.434489	+	0.900677i	$0.356929\pi$
$198$	1035.33	−	1402.62i	0.371604	−	0.503435i
$199$	−1916.19	−	1106.31i	−0.682589	−	0.394093i	0.118241	−	0.992985i	$-0.462275\pi$
$199$	−1916.19	−	1106.31i	−0.682589	−	0.394093i	−0.800830	+	0.598892i	$0.795608\pi$
$200$	−974.747	−	17.7248i	−0.344625	−	0.00626667i
$201$	−2465.53	−	3276.93i	−0.865200	−	1.14994i
$202$	−3094.07	+	526.253i	−1.07771	+	0.183302i
$203$	−11.5299	+	1073.60i	−0.00398640	+	0.371192i
$204$	1943.41	+	3938.60i	0.666990	+	1.35175i
$205$	−4682.41	+	2703.39i	−1.59528	+	0.921038i
$206$	1661.30	−	4479.72i	0.561884	−	1.51513i
$207$	1619.30	+	466.932i	0.543716	+	0.156783i
$208$	221.323	+	86.6865i	0.0737788	+	0.0288973i
$209$	−2648.74			−0.876637
$210$	2538.26	+	2451.60i	0.834078	+	0.805603i
$211$			588.297i			0.191943i	0.995384	+	0.0959717i	$0.0305958\pi$
$211$			588.297i			0.191943i	−0.995384	+	0.0959717i	$0.969404\pi$
$212$	2445.48	+	2103.04i	0.792247	+	0.681308i
$213$	−981.900	+	2308.44i	−0.315862	+	0.742591i
$214$	−4519.63	−	1676.10i	−1.44372	−	0.535402i
$215$	−1380.74	−	2391.51i	−0.437980	−	0.758604i
$216$	2047.74	−	2425.79i	0.645050	−	0.764140i
$217$	113.571	−	191.921i	0.0355285	−	0.0600388i
$218$	2362.47	−	401.820i	0.733977	−	0.124838i
$219$	824.381	+	1095.68i	0.254368	+	0.338080i
$220$	−2326.59	−	439.383i	−0.712994	−	0.134651i
$221$	196.199	−	339.826i	0.0597183	−	0.103435i
$222$	1427.44	−	1510.02i	0.431548	−	0.456512i
$223$			1897.52i			0.569808i	0.958556	+	0.284904i	$0.0919617\pi$
$223$			1897.52i			0.569808i	−0.958556	+	0.284904i	$0.908038\pi$
$224$	−1016.40	−	3194.74i	−0.303176	−	0.952935i
$225$	1129.16	−	279.751i	0.334567	−	0.0828892i
$226$	−1131.74	−	1365.47i	−0.333106	−	0.401902i
$227$	−443.460	−	256.032i	−0.129663	−	0.0748610i	0.433765	−	0.901026i	$-0.357185\pi$
$227$	−443.460	−	256.032i	−0.129663	−	0.0748610i	−0.563428	+	0.826165i	$0.690518\pi$
$228$	−4812.95	−	314.366i	−1.39801	−	0.0913132i
$229$	−432.514	−	749.136i	−0.124809	−	0.216176i	0.796849	−	0.604178i	$-0.206499\pi$
$229$	−432.514	−	749.136i	−0.124809	−	0.216176i	−0.921658	+	0.388002i	$0.873165\pi$
$230$	−383.787	−	2256.45i	−0.110027	−	0.646894i
$231$	1301.88	+	1769.56i	0.370810	+	0.504020i
$232$	−635.120	−	1147.76i	−0.179731	−	0.324802i
$233$	−1853.37	+	1070.05i	−0.521109	+	0.300863i	−0.737388	−	0.675469i	$-0.763941\pi$
$233$	−1853.37	+	1070.05i	−0.521109	+	0.300863i	0.216279	+	0.976332i	$0.430608\pi$
$234$	−281.841	−	31.7748i	−0.0787373	−	0.00887685i
$235$	1976.24	+	1140.98i	0.548578	+	0.316722i
$236$	−144.792	+	168.369i	−0.0399372	+	0.0464403i
$237$	−89.5322	−	733.686i	−0.0245390	−	0.201089i
$238$	−5465.81	+	869.362i	−1.48864	+	0.236775i
$239$		−	1350.91i		−	0.365619i	−0.983148	−	0.182809i	$-0.941481\pi$
$239$		−	1350.91i		−	0.365619i	0.983148	−	0.182809i	$-0.0585191\pi$
$240$	−4175.44	−	1074.52i	−1.12301	−	0.289001i
$241$	172.940	+	99.8472i	0.0462244	+	0.0266876i	0.522934	−	0.852373i	$-0.324837\pi$
$241$	172.940	+	99.8472i	0.0462244	+	0.0266876i	−0.476710	+	0.879061i	$0.658171\pi$
$242$	2147.71	+	796.478i	0.570497	+	0.211568i
$243$	−1613.62	+	3427.12i	−0.425981	+	0.904732i
$244$	6427.35	−	2251.52i	1.68635	−	0.590733i
$245$	−3898.01	+	2140.24i	−1.01647	+	0.558101i
$246$	−5873.39	+	1752.07i	−1.52225	+	0.454098i
$247$	215.463	+	373.193i	0.0555044	+	0.0961364i
$248$	−4.95363	+	272.416i	−0.00126837	+	0.0697518i
$249$	−971.962	+	2285.08i	−0.247372	+	0.581570i
$250$	1916.83	+	2312.71i	0.484923	+	0.585074i
$251$			7334.11i			1.84432i	0.386806	+	0.922161i	$0.373578\pi$
$251$			7334.11i			1.84432i	−0.386806	+	0.922161i	$0.626422\pi$
$252$	2155.58	+	3369.94i	0.538845	+	0.842405i
$253$		−	1424.90i		−	0.354081i
$254$	−3725.06	+	3087.42i	−0.920201	+	0.762684i
$255$	−2785.94	+	6549.73i	−0.684166	+	1.60847i
$256$	3006.43	+	2781.84i	0.733991	+	0.679160i
$257$	1732.87	+	3001.42i	0.420597	+	0.728495i	0.995998	−	0.0893761i	$-0.0284873\pi$
$257$	1732.87	+	3001.42i	0.420597	+	0.728495i	−0.575401	+	0.817871i	$0.695154\pi$
$258$	−894.861	−	2999.80i	−0.215937	−	0.723875i
$259$	1284.81	+	2281.60i	0.308240	+	0.547380i
$260$	127.351	+	363.545i	0.0303768	+	0.0867159i
$261$	1085.64	+	1127.56i	0.257470	+	0.267412i
$262$	816.625	−	2202.04i	0.192562	−	0.519246i
$263$	−4397.98	−	2539.17i	−1.03114	−	0.595331i	−0.113832	−	0.993500i	$-0.536312\pi$
$263$	−4397.98	−	2539.17i	−1.03114	−	0.595331i	−0.917312	+	0.398169i	$0.869646\pi$
$264$	−2450.40	−	1095.31i	−0.571256	−	0.255348i
$265$			5227.06i			1.21168i
$266$	2174.43	−	5675.67i	0.501214	−	1.30826i
$267$	853.079	+	6990.70i	0.195534	+	1.60234i
$268$	−4116.70	+	4787.03i	−0.938311	+	1.09110i
$269$	3287.27	+	1897.91i	0.745088	+	0.430177i	0.823916	−	0.566712i	$-0.191785\pi$
$269$	3287.27	+	1897.91i	0.745088	+	0.430177i	−0.0788286	+	0.996888i	$0.525118\pi$
$270$	5144.43	−	47.1458i	1.15956	−	0.0106267i
$271$	−2657.85	+	1534.51i	−0.595767	+	0.343966i	−0.767375	−	0.641199i	$-0.778437\pi$
$271$	−2657.85	+	1534.51i	−0.595767	+	0.343966i	0.171607	+	0.985165i	$0.445104\pi$
$272$	5283.74	−	4219.62i	1.17785	−	0.940632i
$273$	143.420	−	327.373i	0.0317954	−	0.0725769i
$274$	5269.13	−	896.198i	1.16175	−	0.197596i
$275$	−491.783	−	851.793i	−0.107839	−	0.186782i
$276$	169.114	−	2589.14i	0.0368821	−	0.564666i
$277$	−6213.21	−	3587.20i	−1.34771	−	0.778100i	−0.359784	−	0.933036i	$-0.617150\pi$
$277$	−6213.21	−	3587.20i	−1.34771	−	0.778100i	−0.987925	+	0.154936i	$0.950483\pi$
$278$	−4374.58	+	3625.75i	−0.943776	+	0.782224i
$279$	−78.1831	−	315.572i	−0.0167767	−	0.0677161i
$280$	2851.47	−	4624.67i	0.608599	−	0.987061i
$281$			3571.40i			0.758191i	0.925357	+	0.379096i	$0.123765\pi$
$281$			3571.40i			0.758191i	−0.925357	+	0.379096i	$0.876235\pi$
$282$	1879.86	+	1777.06i	0.396964	+	0.375257i
$283$	−1218.79	+	2111.01i	−0.256007	+	0.443416i	−0.965168	−	0.261629i	$-0.915740\pi$
$283$	−1218.79	+	2111.01i	−0.256007	+	0.443416i	0.709162	+	0.705046i	$0.249074\pi$
$284$	3795.15	+	716.723i	0.792959	+	0.149752i
$285$	−4699.43	−	6246.01i	−0.976738	−	1.29818i
$286$	40.2096	+	236.410i	0.00831345	+	0.0488783i
$287$	82.9426	−	7723.17i	0.0170590	−	1.58845i
$288$	−4322.56	−	2281.09i	−0.884407	−	0.466717i
$289$	−3124.93	−	5412.54i	−0.636054	−	1.10168i
$290$	739.174	−	1993.19i	0.149675	−	0.403601i
$291$	2770.13	−	6512.57i	0.558035	−	1.31194i
$292$	1376.47	−	1600.60i	0.275862	−	0.320782i
$293$			7890.50i			1.57327i	0.617418	+	0.786635i	$0.288179\pi$
$293$			7890.50i			1.57327i	−0.617418	+	0.786635i	$0.711821\pi$
$294$	−4860.53	+	1336.95i	−0.964190	+	0.265213i
$295$	−359.879			−0.0710269
$296$	−2741.02	−	1649.69i	−0.538238	−	0.323940i
$297$	3162.18	+	508.066i	0.617805	+	0.0992625i
$298$	−7564.95	−	2805.46i	−1.47056	−	0.545355i
$299$	−200.760	+	115.909i	−0.0388302	+	0.0224186i
$300$	−792.511	−	1606.14i	−0.152519	−	0.309102i
$301$	3944.57	+	42.3625i	0.755352	+	0.00811207i
$302$	−1242.35	−	7304.32i	−0.236719	−	1.39178i
$303$	−3466.53	−	4607.35i	−0.657250	−	0.873549i
$304$	1111.83	+	7342.11i	0.209763	+	1.38519i
$305$	9558.11	+	5518.37i	1.79441	+	1.03600i
$306$	−4791.71	+	6491.64i	−0.895176	+	1.21275i
$307$	1122.94			0.208760			0.104380	−	0.994537i	$-0.466714\pi$
$307$	1122.94			0.208760			0.104380	+	0.994537i	$0.466714\pi$
$308$	2232.76	−	2540.62i	0.413062	−	0.470017i
$309$	8712.82	−	1063.23i	1.60406	−	0.195745i
$310$	−339.961	+	281.768i	−0.0622854	+	0.0516236i
$311$	1009.16	−	1747.92i	0.184001	−	0.318700i	−0.759238	−	0.650813i	$-0.774428\pi$
$311$	1009.16	−	1747.92i	0.184001	−	0.318700i	0.943240	+	0.332113i	$0.107762\pi$
$312$	45.0055	+	434.346i	0.00816646	+	0.0788141i
$313$	608.104	−	351.089i	0.109815	−	0.0634016i	−0.444087	−	0.895984i	$-0.646472\pi$
$313$	608.104	−	351.089i	0.109815	−	0.0634016i	0.553901	+	0.832582i	$0.313138\pi$
$314$	−1598.56	−	9398.64i	−0.287300	−	1.68916i
$315$	−1863.00	+	6209.54i	−0.333233	+	1.11069i
$316$	−1073.97	+	376.216i	−0.191189	+	0.0669741i
$317$	−2217.08	−	3840.09i	−0.392819	−	0.680382i	0.600001	−	0.799999i	$-0.295167\pi$
$317$	−2217.08	−	3840.09i	−0.392819	−	0.680382i	−0.992820	+	0.119617i	$0.961833\pi$
$318$	−1372.18	+	5764.36i	−0.241975	+	1.01651i
$319$	661.708	−	1146.11i	0.116140	−	0.201160i
$320$	−241.330	+	6633.57i	−0.0421586	+	1.15884i
$321$	−1072.70	−	8790.46i	−0.186519	−	1.52846i
$322$	3053.24	+	1169.74i	0.528417	+	0.202444i
$323$	12258.9			2.11178
$324$	5685.61	+	1298.50i	0.974898	+	0.222650i
$325$	−80.0086	+	138.579i	−0.0136556	+	0.0236522i
$326$	903.554	−	2436.45i	0.153507	−	0.413934i
$327$	2646.86	+	3517.94i	0.447620	+	0.594931i
$328$	4568.87	+	8256.64i	0.769126	+	1.38993i
$329$	−2840.42	+	1599.49i	−0.475979	+	0.268033i
$330$	−1243.42	−	4168.27i	−0.207418	−	0.695320i
$331$	9094.20	−	5250.54i	1.51016	−	0.871890i	0.510228	−	0.860039i	$-0.329561\pi$
$331$	9094.20	−	5250.54i	1.51016	−	0.871890i	0.999930	−	0.0118508i	$-0.00377232\pi$
$332$	3756.74	+	709.469i	0.621017	+	0.117281i
$333$	3667.93	+	1057.66i	0.603608	+	0.174053i
$334$	8660.01	−	7177.62i	1.41873	−	1.17587i
$335$	−10232.0			−1.66875
$336$	4358.62	−	4351.49i	0.707685	−	0.706528i
$337$	1582.88			0.255861			0.127930	−	0.991783i	$-0.459167\pi$
$337$	1582.88			0.255861			0.127930	+	0.991783i	$0.459167\pi$
$338$	−4754.32	+	3940.50i	−0.765092	+	0.634127i
$339$	1275.29	−	2998.20i	0.204319	−	0.480353i
$340$	10767.9	+	2033.55i	1.71757	+	0.324368i
$341$	−238.054	+	137.441i	−0.0378046	+	0.0218265i
$342$	−3542.83	−	8121.71i	−0.560158	−	1.28413i
$343$	204.622	−	6349.15i	0.0322115	−	0.999481i
$344$	−4217.03	+	2333.52i	−0.660951	+	0.365742i
$345$	3360.05	−	2528.07i	0.524345	−	0.394512i
$346$	1012.76	−	2730.93i	0.157360	−	0.424323i
$347$	−3447.64	+	5971.49i	−0.533369	+	0.923822i	0.465872	+	0.884852i	$0.345741\pi$
$347$	−3447.64	+	5971.49i	−0.533369	+	0.923822i	−0.999240	+	0.0389695i	$0.987592\pi$
$348$	1338.40	−	2004.03i	0.206166	−	0.308700i
$349$	−6864.13			−1.05280			−0.526402	−	0.850236i	$-0.676459\pi$
$349$	−6864.13			−1.05280			−0.526402	+	0.850236i	$0.676459\pi$
$350$	2228.93	−	354.521i	0.340403	−	0.0541426i
$351$	−185.645	−	486.862i	−0.0282308	−	0.0740364i
$352$	−840.554	+	4045.99i	−0.127277	+	0.612647i
$353$	1843.40	−	3192.86i	0.277944	−	0.481413i	−0.692930	−	0.721005i	$-0.743680\pi$
$353$	1843.40	−	3192.86i	0.277944	−	0.481413i	0.970874	+	0.239592i	$0.0770137\pi$
$354$	−396.871	−	94.4734i	−0.0595860	−	0.0141842i
$355$	3129.56	+	5420.55i	0.467886	+	0.810403i
$356$	10233.0	−	3584.66i	1.52345	−	0.533670i
$357$	−6025.36	−	8189.90i	−0.893265	−	1.21416i
$358$	−1312.50	−	7716.75i	−0.193765	−	1.13923i
$359$	−4274.90	+	2468.11i	−0.628469	+	0.362847i	−0.780159	−	0.625581i	$-0.784862\pi$
$359$	−4274.90	+	2468.11i	−0.628469	+	0.362847i	0.151690	+	0.988428i	$0.451529\pi$
$360$	−1764.68	−	7721.62i	−0.258352	−	1.13046i
$361$	−3301.79	+	5718.88i	−0.481381	+	0.833777i
$362$	1050.54	−	870.715i	0.152528	−	0.126419i
$363$	509.746	+	4177.20i	0.0737045	+	0.603983i
$364$	−539.584	−	107.915i	−0.0776974	−	0.0155393i
$365$	3421.18			0.490611
$366$	9091.94	+	8594.76i	1.29848	+	1.22747i
$367$	6855.75	+	3958.17i	0.975115	+	0.562983i	0.900792	−	0.434251i	$-0.142987\pi$
$367$	6855.75	+	3958.17i	0.975115	+	0.562983i	0.0743235	+	0.997234i	$0.476320\pi$
$368$	−3949.70	+	598.112i	−0.559491	+	0.0847248i
$369$	−7809.79	−	8111.36i	−1.10179	−	1.14434i
$370$	−869.328	−	5111.15i	−0.122146	−	0.718152i
$371$	−6426.05	−	3802.67i	−0.899256	−	0.532143i
$372$	−448.874	+	221.486i	−0.0625619	+	0.0308697i
$373$	−4997.76	+	2885.46i	−0.693765	+	0.400545i	−0.805021	−	0.593246i	$-0.797846\pi$
$373$	−4997.76	+	2885.46i	−0.693765	+	0.400545i	0.111256	+	0.993792i	$0.464513\pi$
$374$	6396.27	+	2372.05i	0.884340	+	0.327957i
$375$	−2159.96	+	5078.06i	−0.297440	+	0.699280i
$376$	2053.74	−	3412.36i	0.281685	−	0.468030i
$377$	−215.308			−0.0294135
$378$	−3684.60	+	6358.76i	−0.501363	+	0.865237i
$379$		−	11588.5i		−	1.57060i	−0.619113	−	0.785302i	$-0.712508\pi$
$379$		−	11588.5i		−	1.57060i	0.619113	−	0.785302i	$-0.287492\pi$
$380$	−7846.64	+	9124.33i	−1.05927	+	1.23176i
$381$	−8179.18	−	3479.03i	−1.09982	−	0.467811i
$382$	2273.07	−	6129.36i	0.304451	−	0.820956i
$383$	4577.70	+	7928.81i	0.610730	+	1.05782i	0.991118	+	0.132988i	$0.0424572\pi$
$383$	4577.70	+	7928.81i	0.610730	+	1.05782i	−0.380388	+	0.924827i	$0.624209\pi$
$384$	−2007.55	+	7252.09i	−0.266790	+	0.963755i
$385$	5481.03	+	58.8632i	0.725556	+	0.00779207i
$386$	−1946.07	−	11441.8i	−0.256613	−	1.50874i
$387$	4142.83	−	3988.81i	0.544165	−	0.523934i
$388$	−10706.9	−	2022.02i	−1.40092	−	0.264568i
$389$	1178.80	−	2041.75i	0.153644	−	0.266120i	−0.778920	−	0.627123i	$-0.784232\pi$
$389$	1178.80	−	2041.75i	0.153644	−	0.266120i	0.932565	+	0.361003i	$0.117566\pi$
$390$	−486.139	+	514.260i	−0.0631195	+	0.0667707i
$391$			6594.71i			0.852964i
$392$	3611.05	+	6869.98i	0.465269	+	0.885169i
$393$	4282.86	−	522.640i	0.549724	−	0.0670832i
$394$	5232.42	−	4336.75i	0.669049	−	0.554524i
$395$	−1597.11	−	922.089i	−0.203441	−	0.117457i
$396$	−277.003	−	4923.14i	−0.0351513	−	0.624740i
$397$	−6278.72	−	10875.1i	−0.793752	−	1.37482i	−0.923628	−	0.383289i	$-0.874791\pi$
$397$	−6278.72	−	10875.1i	−0.793752	−	1.37482i	0.129876	−	0.991530i	$-0.458542\pi$
$398$	−6169.65	+	1049.36i	−0.777027	+	0.132160i
$399$	11097.6	−	1233.44i	1.39241	−	0.154760i
$400$	−2154.68	+	1720.73i	−0.269335	+	0.215092i
$401$	−70.9500	+	40.9630i	−0.00883560	+	0.00510124i	−0.504411	−	0.863464i	$-0.668290\pi$
$401$	−70.9500	+	40.9630i	−0.00883560	+	0.00510124i	0.495576	+	0.868565i	$0.334957\pi$
$402$	−11283.7	−	2686.04i	−1.39995	−	0.333253i
$403$	38.7292	+	22.3603i	0.00478720	+	0.00276389i
$404$	−5788.05	+	6730.54i	−0.712788	+	0.828854i
$405$	4412.31	+	8358.16i	0.541357	+	1.02548i
$406$	1912.65	+	2358.77i	0.233801	+	0.288335i
$407$		−	3227.58i		−	0.393084i
$408$	11341.0	+	5069.33i	1.37613	+	0.615121i
$409$	4583.49	+	2646.28i	0.554129	+	0.319927i	0.750786	−	0.660546i	$-0.229675\pi$
$409$	4583.49	+	2646.28i	0.554129	+	0.319927i	−0.196656	+	0.980472i	$0.563008\pi$
$410$	−5317.40	+	14338.4i	−0.640507	+	1.72714i
$411$	5903.41	+	7846.21i	0.708501	+	0.941667i
$412$	−4467.72	−	12753.9i	−0.534245	−	1.52509i
$413$	261.811	−	442.428i	0.0311934	−	0.0527130i
$414$	4369.09	−	1905.87i	0.518669	−	0.226252i
$415$	3097.88	+	5365.69i	0.366432	+	0.634678i
$416$	638.432	−	210.693i	0.0752445	−	0.0248319i
$417$	−9605.34	−	4085.65i	−1.12800	−	0.479796i
$418$	−5768.11	+	4780.74i	−0.674946	+	0.559411i
$419$		−	3417.09i		−	0.398415i	−0.979957	−	0.199207i	$-0.936163\pi$
$419$		−	3417.09i		−	0.398415i	0.979957	−	0.199207i	$-0.0638368\pi$
$420$	9952.44	+	757.475i	1.15626	+	0.0880024i
$421$			12653.4i			1.46482i	0.680864	+	0.732410i	$0.261605\pi$
$421$			12653.4i			1.46482i	−0.680864	+	0.732410i	$0.738395\pi$
$422$	1061.83	+	1281.12i	0.122485	+	0.147782i
$423$	−1316.71	+	4566.30i	−0.151349	+	0.524873i
$424$	9121.28	+	165.862i	1.04474	+	0.0189975i
$425$	2276.08	+	3942.28i	0.259778	+	0.449950i
$426$	2028.27	+	6799.29i	0.230681	+	0.773302i
$427$	−13737.7	+	7735.95i	−1.55694	+	0.876743i
$428$	−12867.5	+	4507.53i	−1.45321	+	0.509065i
$429$	−352.036	+	264.868i	−0.0396187	+	0.0298087i
$430$	−7323.28	−	2715.83i	−0.821303	−	0.304579i
$431$	1472.56	+	850.186i	0.164573	+	0.0950163i	0.580024	−	0.814599i	$-0.303043\pi$
$431$	1472.56	+	850.186i	0.164573	+	0.0950163i	−0.415451	+	0.909615i	$0.636376\pi$
$432$	80.9697	−	8978.59i	0.00901772	−	0.999959i
$433$			2777.80i			0.308296i	0.988048	+	0.154148i	$0.0492633\pi$
$433$			2777.80i			0.308296i	−0.988048	+	0.154148i	$0.950737\pi$
$434$	−99.0793	−	622.927i	−0.0109584	−	0.0688973i
$435$	3876.66	−	473.072i	0.427291	−	0.0521426i
$436$	4419.46	−	5139.10i	0.485445	−	0.564491i
$437$	−6271.95	−	3621.11i	−0.686563	−	0.396388i
$438$	3772.85	+	898.111i	0.411584	+	0.0979758i
$439$	−11040.7	+	6374.32i	−1.20032	+	0.693006i	−0.960627	−	0.277842i	$-0.910381\pi$
$439$	−11040.7	+	6374.32i	−1.20032	+	0.693006i	−0.239695	+	0.970848i	$0.577048\pi$
$440$	−5859.62	+	3242.46i	−0.634878	+	0.351314i
$441$	−6278.57	−	6807.77i	−0.677958	−	0.735101i
$442$	−186.099	−	1094.15i	−0.0200267	−	0.117746i
$443$	−6451.54	−	11174.4i	−0.691923	−	1.19845i	−0.971207	−	0.238237i	$-0.923431\pi$
$443$	−6451.54	−	11174.4i	−0.691923	−	1.19845i	0.279284	−	0.960208i	$-0.409903\pi$
$444$	383.066	−	5864.74i	0.0409448	−	0.626866i
$445$	15217.5	+	8785.84i	1.62108	+	0.935930i
$446$	3424.85	+	4132.18i	0.363613	+	0.438710i
$447$	−1795.49	−	14713.5i	−0.189986	−	1.55687i
$448$	−7979.63	−	5122.59i	−0.841522	−	0.540223i
$449$			9435.20i			0.991703i	0.868407	+	0.495852i	$0.165144\pi$
$449$			9435.20i			0.991703i	−0.868407	+	0.495852i	$0.834856\pi$
$450$	1954.03	−	2647.25i	0.204698	−	0.277317i
$451$	−4760.13	+	8244.78i	−0.496997	+	0.860824i
$452$	−4929.12	−	930.877i	−0.512935	−	0.0968690i
$453$	10876.8	−	8183.59i	1.12812	−	0.848783i
$454$	−1427.83	+	242.852i	−0.147602	+	0.0251048i
$455$	−437.563	−	777.034i	−0.0450841	−	0.0800614i
$456$	−11048.5	+	8002.37i	−1.13463	+	0.821810i
$457$	1715.41	+	2971.18i	0.175588	+	0.304127i	0.940365	−	0.340168i	$-0.110484\pi$
$457$	1715.41	+	2971.18i	0.175588	+	0.304127i	−0.764777	+	0.644295i	$0.777151\pi$
$458$	−2294.00	−	850.728i	−0.234043	−	0.0867946i
$459$	−14635.2	−	2351.43i	−1.48826	−	0.239119i
$460$	−4908.45	−	4221.12i	−0.497517	−	0.427849i
$461$		−	3249.61i		−	0.328307i	−0.986435	−	0.164153i	$-0.947511\pi$
$461$		−	3249.61i		−	0.328307i	0.986435	−	0.164153i	$-0.0524892\pi$
$462$	6028.97	+	1503.76i	0.607128	+	0.151432i
$463$	7686.89			0.771577			0.385788	−	0.922587i	$-0.373929\pi$
$463$	7686.89			0.771577			0.385788	+	0.922587i	$0.373929\pi$
$464$	−3454.69	−	1353.11i	−0.345647	−	0.135381i
$465$	−746.459	−	317.507i	−0.0744434	−	0.0316646i
$466$	−2104.71	+	5675.39i	−0.209225	+	0.564179i
$467$	1514.65	−	874.483i	0.150085	−	0.0866515i	−0.423077	−	0.906094i	$-0.639050\pi$
$467$	1514.65	−	874.483i	0.150085	−	0.0866515i	0.573162	+	0.819442i	$0.305717\pi$
$468$	−671.110	+	439.503i	−0.0662865	+	0.0434104i
$469$	7443.73	−	12579.0i	0.732877	−	1.23847i
$470$	6363.00	−	1082.25i	0.624475	−	0.106214i
$471$	13995.4	−	10530.0i	1.36916	−	1.03014i
$472$	−11.4194	+	627.992i	−0.00111361	+	0.0612409i
$473$	−4210.98	−	2431.21i	−0.409347	−	0.236336i
$474$	−1519.21	−	1436.14i	−0.147215	−	0.139164i
$475$	−4999.11			−0.482895
$476$	−10333.7	+	11758.5i	−0.995048	+	1.13225i
$477$	−10566.3	+	2617.79i	−1.01425	+	0.251280i
$478$	−2438.27	−	2941.84i	−0.233313	−	0.281499i
$479$	3453.39	−	5981.45i	0.329415	−	0.570563i	−0.652981	−	0.757374i	$-0.726482\pi$
$479$	3453.39	−	5981.45i	0.329415	−	0.570563i	0.982396	+	0.186811i	$0.0598153\pi$
$480$	−11032.2	+	5196.34i	−1.04906	+	0.494123i
$481$	−454.748	+	262.549i	−0.0431075	+	0.0248881i
$482$	556.824	−	94.7072i	0.0526196	−	0.00894978i
$483$	663.533	+	5969.95i	0.0625089	+	0.562406i
$484$	6114.61	−	2141.96i	0.574249	−	0.201161i
$485$	−8829.10	−	15292.5i	−0.826616	−	1.43174i
$486$	2671.72	+	10375.6i	0.249365	+	0.968410i
$487$	−2097.33	+	3632.69i	−0.195152	+	0.338014i	−0.946950	−	0.321379i	$-0.895854\pi$
$487$	−2097.33	+	3632.69i	−0.195152	+	0.338014i	0.751798	+	0.659393i	$0.229187\pi$
$488$	9932.92	−	16503.9i	0.921398	−	1.53094i
$489$	4738.77	−	578.275i	0.438230	−	0.0534775i
$490$	−4625.67	+	11696.3i	−0.426462	+	1.07834i
$491$	−2191.33			−0.201412			−0.100706	−	0.994916i	$-0.532110\pi$
$491$	−2191.33			−0.201412			−0.100706	+	0.994916i	$0.532110\pi$
$492$	−9628.03	+	14416.4i	−0.882247	+	1.32102i
$493$	−3062.52	+	5304.44i	−0.279775	+	0.484584i
$494$	1142.79	+	423.802i	0.104082	+	0.0385987i
$495$	5756.52	−	5542.50i	0.522699	−	0.503266i
$496$	480.900	+	602.177i	0.0435344	+	0.0545132i
$497$	−8940.67	−	96.0179i	−0.806929	−	0.00866597i
$498$	2007.75	+	6730.48i	0.180661	+	0.605622i
$499$	7727.56	−	4461.51i	0.693253	−	0.400250i	−0.111577	−	0.993756i	$-0.535590\pi$
$499$	7727.56	−	4461.51i	0.693253	−	0.400250i	0.804829	+	0.593506i	$0.202257\pi$
$500$	8348.48	+	1576.63i	0.746710	+	0.141018i
$501$	19015.0	+	8088.05i	1.69566	+	0.721252i
$502$	13237.4	+	15971.3i	1.17692	+	1.41999i
$503$	1042.38			0.0924001			0.0462001	−	0.998932i	$-0.485289\pi$
$503$	1042.38			0.0924001			0.0462001	+	0.998932i	$0.485289\pi$
$504$	10776.6	+	3448.00i	0.952437	+	0.304734i
$505$	−14386.1			−1.26767
$506$	−2571.81	−	3102.97i	−0.225951	−	0.272616i
$507$	−10439.2	−	4440.32i	−0.914437	−	0.388957i
$508$	−2539.47	+	13446.8i	−0.221792	+	1.17442i
$509$	291.527	−	168.313i	0.0253865	−	0.0146569i	−0.487253	−	0.873261i	$-0.662001\pi$
$509$	291.527	−	168.313i	0.0253865	−	0.0146569i	0.512640	+	0.858604i	$0.328668\pi$
$510$	5754.81	+	19291.6i	0.499661	+	1.67499i
$511$	−2488.90	+	4205.94i	−0.215465	+	0.364109i
$512$	11568.0	+	631.616i	0.998513	+	0.0545190i
$513$	10272.5	−	12627.8i	0.884093	−	1.08680i
$514$	9190.93	+	3408.45i	0.788706	+	0.292491i
$515$	10950.2	−	18966.3i	0.936938	−	1.62282i
$516$	−7363.11	−	4917.47i	−0.628184	−	0.419534i
$517$	4018.09			0.341809
$518$	6915.99	+	2649.61i	0.586624	+	0.224744i
$519$	5311.52	−	648.168i	0.449229	−	0.0548197i
$520$	933.498	+	561.828i	0.0787242	+	0.0473804i
$521$	−1286.50	+	2228.29i	−0.108182	+	0.187376i	−0.915034	−	0.403377i	$-0.867836\pi$
$521$	−1286.50	+	2228.29i	−0.108182	+	0.187376i	0.806852	+	0.590754i	$0.201170\pi$
$522$	4399.34	+	495.982i	0.368877	+	0.0415872i
$523$	133.339	+	230.950i	0.0111482	+	0.0193093i	0.871546	−	0.490314i	$-0.163118\pi$
$523$	133.339	+	230.950i	0.0111482	+	0.0193093i	−0.860397	+	0.509624i	$0.829785\pi$
$524$	−2196.14	−	6269.27i	−0.183090	−	0.522661i
$525$	2457.10	+	3339.79i	0.204261	+	0.277639i
$526$	−14160.4	+	2408.46i	−1.17380	+	0.199646i
$527$	1101.76	−	636.104i	0.0910694	−	0.0525790i
$528$	−7313.13	+	2037.52i	−0.602771	+	0.167939i
$529$	−4135.51	+	7162.92i	−0.339896	+	0.588717i
$530$	9434.39	+	11382.9i	0.773214	+	0.932906i
$531$	−180.233	−	727.477i	−0.0147296	−	0.0594535i
$532$	−5508.87	−	16284.4i	−0.448947	−	1.32711i
$533$	1548.86			0.125870
$534$	14475.3	+	13683.8i	1.17305	+	1.10890i
$535$	−19135.3	−	11047.8i	−1.54634	−	0.892778i
$536$	−324.674	+	17854.9i	−0.0261638	+	1.43883i
$537$	11490.9	−	8645.67i	0.923409	−	0.694764i
$538$	10584.2	−	1800.21i	0.848172	−	0.144261i
$539$	−4059.80	+	6695.45i	−0.324430	+	0.535053i
$540$	11117.8	−	9387.92i	0.885991	−	0.748133i
$541$	−4708.64	+	2718.54i	−0.374197	+	0.216043i	−0.675290	−	0.737552i	$-0.735982\pi$
$541$	−4708.64	+	2718.54i	−0.374197	+	0.216043i	0.301094	+	0.953595i	$0.402648\pi$
$542$	−3018.29	+	8138.86i	−0.239200	+	0.645007i
$543$	2306.70	+	981.158i	0.182302	+	0.0775424i
$544$	3890.26	−	18725.7i	0.306606	−	1.47584i
$545$	10984.5			0.863346
$546$	−278.558	−	971.773i	−0.0218336	−	0.0761686i
$547$		−	17749.9i		−	1.38744i	−0.720244	−	0.693721i	$-0.755970\pi$
$547$		−	17749.9i		−	1.38744i	0.720244	−	0.693721i	$-0.244030\pi$
$548$	9856.93	−	11462.0i	0.768370	−	0.893486i
$549$	−6368.28	+	22084.9i	−0.495066	+	1.71687i
$550$	−2608.36	−	967.308i	−0.202220	−	0.0749930i
$551$	−3363.22	−	5825.27i	−0.260033	−	0.450390i
$552$	−4304.89	−	5943.55i	−0.331936	−	0.458287i
$553$	2295.49	−	1292.63i	0.176517	−	0.0994004i
$554$	−20004.9	+	3402.53i	−1.53417	+	0.260938i
$555$	7610.97	−	5726.42i	0.582104	−	0.437969i
$556$	−2982.26	+	15791.5i	−0.227475	+	1.20451i
$557$	−3337.54	+	5780.80i	−0.253889	+	0.439749i	−0.964593	−	0.263742i	$-0.915043\pi$
$557$	−3337.54	+	5780.80i	−0.253889	+	0.439749i	0.710704	+	0.703491i	$0.248377\pi$
$558$	−739.838	−	546.101i	−0.0561287	−	0.0414306i
$559$			791.071i			0.0598546i
$560$	−2137.54	−	15217.7i	−0.161299	−	1.14833i
$561$	1518.11	+	12440.4i	0.114251	+	0.936247i
$562$	6446.06	+	7777.36i	0.483827	+	0.583751i
$563$	2223.58	+	1283.79i	0.166453	+	0.0961016i	0.580912	−	0.813966i	$-0.302696\pi$
$563$	2223.58	+	1283.79i	0.166453	+	0.0961016i	−0.414459	+	0.910068i	$0.636029\pi$
$564$	7301.17	+	476.888i	0.545097	+	0.0356039i
$565$	−4064.66	−	7040.20i	−0.302658	−	0.524218i
$566$	1156.05	+	6796.93i	0.0858525	+	0.504764i
$567$	−13485.3	−	656.131i	−0.998818	−	0.0485977i
$568$	9558.23	−	5289.11i	0.706082	−	0.390715i
$569$	−2544.71	+	1469.19i	−0.187486	+	0.108245i	−0.590805	−	0.806814i	$-0.701190\pi$
$569$	−2544.71	+	1469.19i	−0.187486	+	0.108245i	0.403319	+	0.915059i	$0.367857\pi$
$570$	−21507.4	−	5119.74i	−1.58043	−	0.376214i
$571$	−4983.39	−	2877.16i	−0.365233	−	0.210868i	0.306141	−	0.951986i	$-0.400962\pi$
$571$	−4983.39	−	2877.16i	−0.365233	−	0.210868i	−0.671374	+	0.741119i	$0.734296\pi$
$572$	514.263	+	442.250i	0.0375916	+	0.0323276i
$573$	11921.3	−	1454.76i	0.869143	−	0.106062i
$574$	−13759.0	−	16968.3i	−1.00051	−	1.23387i
$575$		−	2689.28i		−	0.195045i
$576$	−13530.3	+	2834.36i	−0.978755	+	0.205032i
$577$	−17569.6	−	10143.8i	−1.26764	−	0.731875i	−0.293103	−	0.956081i	$-0.594688\pi$
$577$	−17569.6	−	10143.8i	−1.26764	−	0.731875i	−0.974542	+	0.224206i	$0.928021\pi$
$578$	−16574.3	−	6146.55i	−1.19273	−	0.442323i
$579$	17037.9	−	12819.1i	1.22292	−	0.920112i
$580$	−1987.86	−	5674.68i	−0.142313	−	0.406256i
$581$	−8850.18	−	95.0461i	−0.631958	−	0.00678688i
$582$	−5722.16	−	19182.2i	−0.407545	−	1.36620i
$583$	4601.91	+	7970.73i	0.326915	+	0.566233i
$584$	108.559	−	5970.01i	0.00769211	−	0.423015i
$585$	−1249.17	−	360.204i	−0.0882854	−	0.0254574i
$586$	14241.7	+	17183.0i	1.00396	+	1.21130i
$587$			19525.2i			1.37290i	0.727178	+	0.686449i	$0.240831\pi$
$587$			19525.2i			1.37290i	−0.727178	+	0.686449i	$0.759169\pi$
$588$	−8171.60	+	11684.3i	−0.573114	+	0.819476i
$589$			1397.12i			0.0977375i
$590$	−783.700	+	649.549i	−0.0546855	+	0.0453246i
$591$	11488.9	+	4886.83i	0.799646	+	0.340131i
$592$	−8946.61	+	1354.80i	−0.621120	+	0.0940576i
$593$	3922.80	+	6794.50i	0.271653	+	0.470517i	0.969285	−	0.245939i	$-0.0790963\pi$
$593$	3922.80	+	6794.50i	0.271653	+	0.470517i	−0.697632	+	0.716456i	$0.745763\pi$
$594$	7803.22	−	4601.05i	0.539007	−	0.317817i
$595$	−25367.3	−	272.431i	−1.74783	−	0.0187707i
$596$	−21537.6	+	7544.70i	−1.48023	+	0.518528i
$597$	−6912.33	−	9187.17i	−0.473874	−	0.629825i
$598$	−227.985	+	614.766i	−0.0155903	+	0.0420395i
$599$	15602.7	+	9008.23i	1.06429	+	0.614468i	0.926616	−	0.376009i	$-0.122704\pi$
$599$	15602.7	+	9008.23i	1.06429	+	0.614468i	0.137674	+	0.990478i	$0.456037\pi$
$600$	−4624.78	−	2067.24i	−0.314676	−	0.140658i
$601$			15679.3i			1.06418i	0.846687	+	0.532091i	$0.178594\pi$
$601$			15679.3i			1.06418i	−0.846687	+	0.532091i	$0.821406\pi$
$602$	8666.47	−	7027.35i	0.586742	−	0.475770i
$603$	−5124.33	−	20683.4i	−0.346068	−	1.39684i
$604$	−15889.1	−	13664.1i	−1.07039	−	0.920506i
$605$	9093.02	+	5249.86i	0.611048	+	0.352789i
$606$	−15864.8	−	3776.56i	−1.06347	−	0.253155i
$607$	11342.4	−	6548.53i	0.758441	−	0.437886i	−0.0702949	−	0.997526i	$-0.522394\pi$
$607$	11342.4	−	6548.53i	0.758441	−	0.437886i	0.828736	+	0.559640i	$0.189061\pi$
$608$	15673.1	+	13982.0i	1.04544	+	0.932640i
$609$	−2238.68	+	5110.06i	−0.148959	+	0.340016i
$610$	30774.7	−	5234.30i	2.04267	−	0.347427i
$611$	−326.853	−	566.127i	−0.0216417	−	0.0374845i
$612$	1282.03	+	22785.3i	0.0846779	+	1.50497i
$613$	18672.8	+	10780.8i	1.23032	+	0.710328i	0.967097	−	0.254406i	$-0.0818801\pi$
$613$	18672.8	+	10780.8i	1.23032	+	0.710328i	0.263226	+	0.964734i	$0.415213\pi$
$614$	2445.40	−	2026.80i	0.160730	−	0.133217i
$615$	−27887.6	+	3403.14i	−1.82851	+	0.223134i
$616$	276.637	−	9562.59i	0.0180942	−	0.625467i
$617$		−	9998.31i		−	0.652377i	−0.945305	−	0.326189i	$-0.894236\pi$
$617$		−	9998.31i		−	0.652377i	0.945305	−	0.326189i	$-0.105764\pi$
$618$	17054.7	−	18041.3i	1.11010	−	1.17431i
$619$	3122.99	−	5409.17i	0.202784	−	0.351233i	−0.746640	−	0.665228i	$-0.768334\pi$
$619$	3122.99	−	5409.17i	0.202784	−	0.351233i	0.949425	+	0.313995i	$0.101668\pi$
$620$	−231.760	+	1227.20i	−0.0150124	+	0.0794928i
$621$	6793.14	+	5526.09i	0.438968	+	0.357092i
$622$	−957.213	−	5627.87i	−0.0617054	−	0.362793i
$623$	−21871.8	+	12316.5i	−1.40654	+	0.792052i
$624$	881.965	+	864.636i	0.0565815	+	0.0554698i
$625$	9577.16	+	16588.1i	0.612938	+	1.06164i
$626$	690.570	−	1862.13i	0.0440906	−	0.118891i
$627$	−12665.1	−	5387.14i	−0.806694	−	0.343129i
$628$	−20444.9	−	17582.0i	−1.29911	−	1.11719i
$629$			14937.9i			0.946921i
$630$	7150.66	+	16885.0i	0.452205	+	1.06780i
$631$	−1240.36			−0.0782537			−0.0391269	−	0.999234i	$-0.512458\pi$
$631$	−1240.36			−0.0782537			−0.0391269	+	0.999234i	$0.512458\pi$
$632$	−1659.74	+	2757.71i	−0.104463	+	0.173569i
$633$	−1196.51	+	2812.99i	−0.0751295	+	0.176629i
$634$	−11759.1	−	4360.86i	−0.736616	−	0.273173i
$635$	−19205.9	+	11088.5i	−1.20026	+	0.692968i
$636$	7415.99	+	15029.6i	0.462363	+	0.937047i
$637$	1273.60	+	27.3586i	0.0792178	+	0.00170171i
$638$	−627.644	−	3690.19i	−0.0389477	−	0.228991i
$639$	−9390.05	+	9040.95i	−0.581322	+	0.559710i
$640$	11447.5	+	14881.4i	0.707034	+	0.919122i
$641$	−17186.0	−	9922.36i	−1.05898	−	0.611404i	−0.133832	−	0.991004i	$-0.542728\pi$
$641$	−17186.0	−	9922.36i	−1.05898	−	0.611404i	−0.925151	+	0.379600i	$0.876061\pi$
$642$	−18202.0	−	17206.7i	−1.11897	−	1.05778i
$643$	−16526.5			−1.01360			−0.506798	−	0.862065i	$-0.669171\pi$
$643$	−16526.5			−1.01360			−0.506798	+	0.862065i	$0.669171\pi$
$644$	8760.25	−	2963.51i	0.536028	−	0.181333i
$645$	−1738.13	−	14243.4i	−0.106107	−	0.869510i
$646$	26696.0	−	22126.3i	1.62591	−	1.34760i
$647$	8911.89	−	15435.8i	0.541518	−	0.937937i	−0.457299	−	0.889313i	$-0.651183\pi$
$647$	8911.89	−	15435.8i	0.541518	−	0.937937i	0.998817	−	0.0486243i	$-0.0154837\pi$
$648$	14725.1	−	7434.32i	0.892680	−	0.450691i
$649$	−548.778	+	316.837i	−0.0331917	+	0.0191632i
$650$	75.8899	+	446.189i	0.00457946	+	0.0269246i
$651$	933.384	−	686.697i	0.0561939	−	0.0413422i
$652$	−2429.92	−	6936.64i	−0.145956	−	0.416656i
$653$	11568.7	+	20037.6i	0.693291	+	1.20082i	0.970753	+	0.240079i	$0.0771732\pi$
$653$	11568.7	+	20037.6i	0.693291	+	1.20082i	−0.277463	+	0.960736i	$0.589493\pi$
$654$	12113.6	+	2883.59i	0.724279	+	0.172412i
$655$	5382.65	−	9323.03i	0.321096	−	0.556154i
$656$	24852.0	+	9733.90i	1.47913	+	0.579337i
$657$	1713.38	+	6915.76i	0.101743	+	0.410669i
$658$	−3298.57	+	8609.89i	−0.195428	+	0.510104i
$659$	14423.5			0.852597			0.426299	−	0.904583i	$-0.359817\pi$
$659$	14423.5			0.852597			0.426299	+	0.904583i	$0.359817\pi$
$660$	−10231.1	−	6832.88i	−0.603403	−	0.402984i
$661$	8382.41	−	14518.8i	0.493250	−	0.854334i	−0.506720	−	0.862111i	$-0.669142\pi$
$661$	8382.41	−	14518.8i	0.493250	−	0.854334i	0.999970	+	0.00777707i	$0.00247554\pi$
$662$	10327.5	−	27848.2i	0.606328	−	1.63497i
$663$	1629.29	−	1225.86i	0.0954397	−	0.0718079i
$664$	9461.50	−	5235.58i	0.552978	−	0.305994i
$665$	14188.1	−	23976.2i	0.827357	−	1.39813i
$666$	9896.58	−	4317.05i	0.575803	−	0.251175i
$667$	3133.72	−	1809.25i	0.181916	−	0.105029i
$668$	5903.75	−	31261.1i	0.341950	−	1.81067i
$669$	−3859.27	+	9073.12i	−0.223031	+	0.524345i
$670$	−22281.9	+	18467.8i	−1.28482	+	1.06489i
$671$	19433.5			1.11807
$672$	1637.61	−	17343.1i	0.0940061	−	0.995572i
$673$	24785.1			1.41961			0.709803	−	0.704400i	$-0.248784\pi$
$673$	24785.1			1.41961			0.709803	+	0.704400i	$0.248784\pi$
$674$	3447.01	−	2856.96i	0.196994	−	0.163273i
$675$	5968.15	+	958.901i	0.340317	+	0.0546787i
$676$	−3241.14	+	17162.3i	−0.184407	+	0.976461i
$677$	−7591.21	+	4382.79i	−0.430951	+	0.248810i	−0.699752	−	0.714386i	$-0.746706\pi$
$677$	−7591.21	+	4382.79i	−0.430951	+	0.248810i	0.268801	+	0.963196i	$0.413373\pi$
$678$	−2634.32	−	8830.90i	−0.149219	−	0.500219i
$679$	25223.4	+	270.885i	1.42560	+	0.0153102i
$680$	27119.5	−	15006.8i	1.52939	−	0.846300i
$681$	−1599.71	−	2126.17i	−0.0900161	−	0.119640i
$682$	−270.337	+	728.969i	−0.0151785	+	0.0409291i
$683$	−8167.07	+	14145.8i	−0.457546	+	0.792493i	−0.998831	−	0.0483462i	$-0.984605\pi$
$683$	−8167.07	+	14145.8i	−0.457546	+	0.792493i	0.541284	+	0.840840i	$0.317938\pi$
$684$	−22374.1	−	11292.0i	−1.25073	−	0.631228i
$685$	24499.2			1.36652
$686$	−11014.1	−	14195.7i	−0.613001	−	0.790082i
$687$	−544.466	−	4461.72i	−0.0302368	−	0.247780i
$688$	−4971.54	+	12693.0i	−0.275491	+	0.703369i
$689$	748.688	−	1296.77i	0.0413973	−	0.0717022i
$690$	2754.17	−	11569.9i	0.151956	−	0.638348i
$691$	10589.0	+	18340.8i	0.582961	+	1.00972i	0.995126	+	0.0986094i	$0.0314394\pi$
$691$	10589.0	+	18340.8i	0.582961	+	1.00972i	−0.412165	+	0.911109i	$0.635227\pi$
$692$	−2723.62	−	7775.03i	−0.149619	−	0.427113i
$693$	2626.00	+	11109.1i	0.143944	+	0.608947i
$694$	3270.16	+	19226.7i	0.178867	+	1.05163i
$695$	−22554.7	+	13022.0i	−1.23101	+	0.710722i
$696$	−702.504	−	6779.83i	−0.0382591	−	0.369237i
$697$	22030.9	−	38158.6i	1.19724	−	2.07369i
$698$	−14947.9	+	12389.2i	−0.810581	+	0.671829i
$699$	−11038.3	+	1347.02i	−0.597294	+	0.0728882i
$700$	4214.01	−	4795.05i	0.227535	−	0.258908i
$701$	17795.3			0.958802			0.479401	−	0.877596i	$-0.340854\pi$
$701$	17795.3			0.958802			0.479401	+	0.877596i	$0.340854\pi$
$702$	−1283.02	−	725.156i	−0.0689807	−	0.0389875i
$703$	−14206.8	−	8202.31i	−0.762191	−	0.440051i
$704$	5472.20	+	10328.0i	0.292956	+	0.552913i
$705$	7128.96	+	9475.08i	0.380840	+	0.506173i
$706$	−1748.50	−	10280.2i	−0.0932093	−	0.548018i
$707$	10465.8	−	17686.0i	0.556730	−	0.940806i
$708$	−1034.77	+	510.585i	−0.0549282	+	0.0271030i
$709$	−17872.9	+	10318.9i	−0.946731	+	0.546596i	−0.892064	−	0.451909i	$-0.850743\pi$
$709$	−17872.9	+	10318.9i	−0.946731	+	0.546596i	−0.0546672	+	0.998505i	$0.517410\pi$
$710$	16598.8	+	6155.65i	0.877383	+	0.325377i
$711$	1064.10	−	3690.27i	0.0561280	−	0.194650i
$712$	15814.3	−	26276.0i	0.832394	−	1.38305i
$713$	−751.585			−0.0394770
$714$	−27903.3	−	6959.73i	−1.46254	−	0.364792i
$715$			1099.20i			0.0574935i
$716$	−16786.3	−	14435.7i	−0.876162	−	0.753472i
$717$	2747.54	−	6459.46i	0.143108	−	0.336447i
$718$	−4854.63	+	13090.6i	−0.252330	+	0.680412i
$719$	−618.753	−	1071.71i	−0.0320940	−	0.0555885i	0.849532	−	0.527537i	$-0.176884\pi$
$719$	−618.753	−	1071.71i	−0.0320940	−	0.0555885i	−0.881626	+	0.471948i	$0.843551\pi$
$720$	−17779.7	−	13630.1i	−0.920295	−	0.705507i
$721$	15350.6	+	27259.9i	0.792906	+	1.40806i
$722$	3131.82	+	18413.3i	0.161433	+	0.949132i
$723$	623.853	+	829.162i	0.0320904	+	0.0426513i
$724$	716.181	−	3792.28i	0.0367634	−	0.194667i
$725$	1248.88	−	2163.12i	0.0639754	−	0.110809i
$726$	8649.54	+	8176.55i	0.442169	+	0.417989i
$727$			2385.47i			0.121695i	0.998147	+	0.0608475i	$0.0193803\pi$
$727$			2385.47i			0.121695i	−0.998147	+	0.0608475i	$0.980620\pi$
$728$	−1369.82	+	738.896i	−0.0697374	+	0.0376172i
$729$	−14685.9	+	13105.2i	−0.746120	+	0.665812i
$730$	7450.24	−	6174.94i	0.377734	−	0.313075i
$731$	19489.3	+	11252.1i	0.986097	+	0.569324i
$732$	35312.1	+	2306.47i	1.78302	+	0.116461i
$733$	−9688.18	−	16780.4i	−0.488187	−	0.845565i	0.511721	−	0.859152i	$-0.329008\pi$
$733$	−9688.18	−	16780.4i	−0.488187	−	0.845565i	−0.999908	+	0.0135872i	$0.995675\pi$
$734$	22073.8	−	3754.41i	1.11002	−	0.188798i
$735$	−22991.5	+	2305.74i	−1.15382	+	0.115712i
$736$	−7521.65	+	8431.37i	−0.376701	+	0.422261i
$737$	−15602.7	+	9008.22i	−0.779828	+	0.450234i
$738$	−31647.5	−	3567.95i	−1.57854	−	0.177965i
$739$	−1587.59	−	916.595i	−0.0790263	−	0.0456258i	0.459966	−	0.887936i	$-0.347862\pi$
$739$	−1587.59	−	916.595i	−0.0790263	−	0.0456258i	−0.538992	+	0.842311i	$0.681195\pi$
$740$	−11118.3	−	9561.39i	−0.552320	−	0.474978i
$741$	271.234	+	2222.67i	0.0134467	+	0.110191i
$742$	−20857.4	+	3317.46i	−1.03194	+	0.164134i
$743$			24638.6i			1.21656i	0.793722	+	0.608280i	$0.208140\pi$
$743$			24638.6i			1.21656i	−0.793722	+	0.608280i	$0.791860\pi$
$744$	−577.740	+	1292.50i	−0.0284691	+	0.0636902i
$745$	−32028.6	−	18491.7i	−1.57508	−	0.909375i
$746$	−5675.52	+	15304.1i	−0.278546	+	0.751105i
$747$	−9295.02	+	8949.45i	−0.455270	+	0.438344i
$748$	18210.4	−	6379.14i	0.890156	−	0.311824i
$749$	27502.8	−	15487.3i	1.34170	−	0.755534i
$750$	4461.75	+	14956.9i	0.217227	+	0.728200i
$751$	2664.10	+	4614.35i	0.129446	+	0.224208i	0.923462	−	0.383689i	$-0.125347\pi$
$751$	2664.10	+	4614.35i	0.129446	+	0.224208i	−0.794016	+	0.607897i	$0.792013\pi$
$752$	−1686.63	−	11137.9i	−0.0817886	−	0.540101i
$753$	−14916.5	+	35068.6i	−0.721895	+	1.69717i
$754$	−468.871	+	388.611i	−0.0226463	+	0.0187698i
$755$		−	33961.9i		−	1.63709i
$756$	3453.14	+	20497.7i	0.166124	+	0.986105i
$757$			24477.8i			1.17525i	0.809135	+	0.587623i	$0.199936\pi$
$757$			24477.8i			1.17525i	−0.809135	+	0.587623i	$0.800064\pi$
$758$	−20916.2	−	25235.9i	−1.00225	−	1.20925i
$759$	2898.02	−	6813.24i	0.138592	−	0.325830i
$760$	−618.845	+	34032.4i	−0.0295367	+	1.62432i
$761$	11694.8	+	20255.9i	0.557077	+	0.964885i	0.997739	+	0.0672118i	$0.0214103\pi$
$761$	11694.8	+	20255.9i	0.557077	+	0.964885i	−0.440662	+	0.897673i	$0.645256\pi$
$762$	−24091.0	+	7186.50i	−1.14531	+	0.341653i
$763$	−7991.18	+	13504.1i	−0.379161	+	0.640736i
$764$	−6112.95	−	17450.5i	−0.289475	−	0.826355i
$765$	−26642.4	+	25651.8i	−1.25916	+	1.21235i
$766$	24279.6	+	9004.06i	1.14524	+	0.424713i
$767$	89.2812	+	51.5465i	0.00420307	+	0.00242664i
$768$	8717.60	+	19416.2i	0.409596	+	0.912267i
$769$		−	24022.3i		−	1.12648i	−0.826292	−	0.563242i	$-0.809554\pi$
$769$		−	24022.3i		−	1.12648i	0.826292	−	0.563242i	$-0.190446\pi$
$770$	12042.2	−	9764.59i	0.563597	−	0.457002i
$771$	2181.41	+	17875.9i	0.101896	+	0.835000i
$772$	−24889.4	−	21404.1i	−1.16035	−	0.997862i
$773$	−16368.4	−	9450.27i	−0.761615	−	0.439719i	0.0682601	−	0.997668i	$-0.478255\pi$
$773$	−16368.4	−	9450.27i	−0.761615	−	0.439719i	−0.829875	+	0.557949i	$0.811589\pi$
$774$	1822.31	−	16163.8i	0.0846273	−	0.750641i
$775$	−449.293	+	259.399i	−0.0208246	+	0.0120231i
$776$	−26965.7	+	14921.6i	−1.24744	+	0.690278i
$777$	1502.99	+	13522.7i	0.0693945	+	0.624357i
$778$	−1118.12	−	6573.91i	−0.0515251	−	0.302938i
$779$	24194.0	+	41905.3i	1.11276	+	1.92736i
$780$	−130.459	+	1997.33i	−0.00598870	+	0.0916872i
$781$	9544.51	+	5510.53i	0.437298	+	0.252474i
$782$	11902.9	+	14361.2i	0.544305	+	0.656719i
$783$	2897.79	+	7599.57i	0.132259	+	0.346854i
$784$	20263.4	+	8442.99i	0.923079	+	0.384611i
$785$		−	43699.6i		−	1.98689i
$786$	8383.37	−	8868.33i	0.380439	−	0.402446i
$787$	11764.3	−	20376.4i	0.532849	−	0.922922i	−0.466415	−	0.884566i	$-0.654455\pi$
$787$	11764.3	−	20376.4i	0.532849	−	0.922922i	0.999264	−	0.0383560i	$-0.0122121\pi$
$788$	3567.07	−	18888.1i	0.161258	−	0.853884i
$789$	−15864.9	−	21086.1i	−0.715852	−	0.951437i
$790$	−5142.28	+	874.621i	−0.231587	+	0.0393894i
$791$	11612.1	+	124.708i	0.521971	+	0.00560568i
$792$	−9489.07	−	10221.1i	−0.425731	−	0.458573i
$793$	−1580.83	−	2738.07i	−0.0707905	−	0.122613i
$794$	−33301.6	−	12349.9i	−1.48845	−	0.551990i
$795$	−10631.1	+	24993.6i	−0.474270	+	1.11501i
$796$	−11541.5	+	13420.9i	−0.513917	+	0.597600i
$797$		−	6656.23i		−	0.295829i	−0.989000	−	0.147915i	$-0.952744\pi$
$797$		−	6656.23i		−	0.295829i	0.989000	−	0.147915i	$-0.0472561\pi$
$798$	21940.7	−	22716.2i	0.973297	−	1.00770i
$799$	−18596.6			−0.823403
$800$	−1586.42	+	7636.22i	−0.0701107	+	0.337476i
$801$	−10139.0	+	35161.6i	−0.447245	+	1.55103i
$802$	−80.5718	+	217.263i	−0.00354749	+	0.00956586i
$803$	5216.96	−	3012.01i	0.229268	−	0.132368i
$804$	−29420.4	+	14516.8i	−1.29052	+	0.636776i
$805$	12898.1	+	7632.54i	0.564716	+	0.334176i
$806$	124.698	−	21.2092i	0.00544952	−	0.000926878i
$807$	11858.3	+	15760.8i	0.517263	+	0.687493i
$808$	−456.490	+	25103.9i	−0.0198753	+	1.09301i
$809$	277.317	+	160.109i	0.0120519	+	0.00695814i	0.506014	−	0.862525i	$-0.331118\pi$
$809$	277.317	+	160.109i	0.0120519	+	0.00695814i	−0.493962	+	0.869484i	$0.664452\pi$
$810$	24694.4	+	10237.6i	1.07120	+	0.444088i
$811$	537.182			0.0232590			0.0116295	−	0.999932i	$-0.496298\pi$
$811$	537.182			0.0232590			0.0116295	+	0.999932i	$0.496298\pi$
$812$	8422.51	+	1684.48i	0.364005	+	0.0728002i
$813$	−15829.7	+	1931.70i	−0.682867	+	0.0833307i
$814$	−5825.50	−	7028.63i	−0.250840	−	0.302645i
$815$	5955.64	−	10315.5i	0.255972	−	0.443356i
$816$	33846.7	−	9430.07i	1.45205	−	0.404557i
$817$	−21402.9	+	12357.0i	−0.916514	+	0.529150i
$818$	14757.7	−	2510.05i	0.630794	−	0.107288i
$819$	1351.60	−	1273.66i	0.0576663	−	0.0543412i
$820$	14300.1	+	40822.0i	0.609000	+	1.73849i
$821$	5948.17	+	10302.5i	0.252853	+	0.437955i	0.964310	−	0.264775i	$-0.0852976\pi$
$821$	5948.17	+	10302.5i	0.252853	+	0.437955i	−0.711457	+	0.702730i	$0.751964\pi$
$822$	27017.5	+	6431.39i	1.14640	+	0.272896i
$823$	13650.5	−	23643.4i	0.578162	−	1.00141i	−0.417528	−	0.908664i	$-0.637103\pi$
$823$	13650.5	−	23643.4i	0.578162	−	1.00141i	0.995690	−	0.0927425i	$-0.0295633\pi$
$824$	−32748.9	−	19710.0i	−1.38454	−	0.833291i
$825$	−619.077	−	5073.13i	−0.0261254	−	0.214089i
$826$	−228.404	−	1436.01i	−0.00962130	−	0.0604906i
$827$	−33391.1			−1.40402			−0.702009	−	0.712168i	$-0.747713\pi$
$827$	−33391.1			−1.40402			−0.702009	+	0.712168i	$0.747713\pi$
$828$	6074.55	−	12036.2i	0.254958	−	0.505178i
$829$	−11314.8	+	19597.8i	−0.474040	+	0.821061i	−0.999558	−	0.0297213i	$-0.990538\pi$
$829$	−11314.8	+	19597.8i	−0.474040	+	0.821061i	0.525518	+	0.850782i	$0.323871\pi$
$830$	16430.8	+	6093.35i	0.687135	+	0.254823i
$831$	−22413.1	−	29789.2i	−0.935621	−	1.24353i
$832$	1010.02	−	1611.14i	0.0420866	−	0.0671348i
$833$	18789.6	−	30987.9i	0.781537	−	1.28892i
$834$	−28291.6	+	8439.57i	−1.17465	+	0.350406i
$835$	44649.8	−	25778.6i	1.85050	−	1.06839i
$836$	−3932.26	+	20821.9i	−0.162680	+	0.861411i
$837$	267.988	−	1667.94i	0.0110669	−	0.0688800i
$838$	−6167.55	−	7441.33i	−0.254242	−	0.306750i
$839$	10587.3			0.435653			0.217826	−	0.975988i	$-0.430103\pi$
$839$	10587.3			0.435653			0.217826	+	0.975988i	$0.430103\pi$
$840$	23040.4	−	16313.7i	0.946392	−	0.670093i
$841$	−21028.2			−0.862200
$842$	22838.3	+	27555.1i	0.934750	+	1.12780i
$843$	−7263.69	+	17076.9i	−0.296767	+	0.697699i
$844$	4624.63	+	873.374i	0.188609	+	0.0356194i
$845$	−24512.6	+	14152.4i	−0.997942	+	0.576162i
$846$	5374.40	+	12320.5i	0.218411	+	0.500694i
$847$	−13069.2	+	7359.53i	−0.530182	+	0.298556i
$848$	20162.6	−	16101.9i	0.816493	−	0.652055i
$849$	−10121.2	+	7615.13i	−0.409141	+	0.307833i
$850$	12072.0	+	4476.90i	0.487138	+	0.180655i
$851$	4412.45	−	7642.58i	0.177740	−	0.307855i
$852$	16689.1	+	11145.8i	0.671077	+	0.448180i
$853$	−17268.2			−0.693144			−0.346572	−	0.938023i	$-0.612654\pi$
$853$	−17268.2			−0.693144			−0.346572	+	0.938023i	$0.612654\pi$
$854$	−15953.6	+	41641.8i	−0.639250	+	1.66856i
$855$	−9767.24	−	39423.7i	−0.390682	−	1.57691i
$856$	−19885.7	+	33040.7i	−0.794016	+	1.31929i
$857$	−11518.4	+	19950.4i	−0.459113	+	0.795208i	−0.998914	−	0.0465850i	$-0.985166\pi$
$857$	−11518.4	+	19950.4i	−0.459113	+	0.795208i	0.539801	+	0.841793i	$0.318500\pi$
$858$	−288.557	+	1212.19i	−0.0114816	+	0.0482326i
$859$	17934.9	+	31064.2i	0.712378	+	1.23387i	0.963962	+	0.266039i	$0.0857151\pi$
$859$	17934.9	+	31064.2i	0.712378	+	1.23387i	−0.251584	+	0.967835i	$0.580952\pi$
$860$	−20849.6	+	7303.68i	−0.826704	+	0.289597i
$861$	16104.4	−	36760.2i	0.637440	−	1.45503i
$862$	4741.29	−	806.419i	0.187342	−	0.0318640i
$863$	11853.5	−	6843.62i	0.467553	−	0.269942i	−0.247662	−	0.968846i	$-0.579662\pi$
$863$	11853.5	−	6843.62i	0.467553	−	0.269942i	0.715215	+	0.698905i	$0.246329\pi$
$864$	−16029.2	−	19698.6i	−0.631164	−	0.775649i
$865$	6675.46	−	11562.2i	0.262396	−	0.454483i
$866$	5013.68	+	6049.15i	0.196734	+	0.237365i
$867$	−3933.79	−	32236.1i	−0.154093	−	1.26274i
$868$	−1340.09	−	1177.71i	−0.0524028	−	0.0460529i
$869$	−3247.23			−0.126760
$870$	7588.28	−	8027.24i	0.295709	−	0.312815i
$871$	2538.42	+	1465.56i	0.0987497	+	0.0570132i
$872$	348.552	−	19168.1i	0.0135361	−	0.744395i
$873$	26491.2	−	25506.3i	1.02702	−	0.988841i
$874$	−20194.1	+	3434.70i	−0.781551	+	0.132930i
$875$	−19667.5	−	211.218i	−0.759866	−	0.00816054i
$876$	9837.07	−	4853.87i	0.379411	−	0.187211i
$877$	−28782.3	+	16617.5i	−1.10822	+	0.639831i	−0.938368	−	0.345638i	$-0.887662\pi$
$877$	−28782.3	+	16617.5i	−1.10822	+	0.639831i	−0.169852	+	0.985470i	$0.554329\pi$
$878$	−12537.9	+	33808.6i	−0.481929	+	1.29953i
$879$	−16048.1	+	37729.0i	−0.615801	+	1.44775i
$880$	−6908.02	+	17637.1i	−0.264624	+	0.675623i
$881$	−37284.4			−1.42582			−0.712908	−	0.701257i	$-0.752623\pi$
$881$	−37284.4			−1.42582			−0.712908	+	0.701257i	$0.752623\pi$
$882$	−25960.1	−	3492.87i	−0.991070	−	0.133346i
$883$			11175.4i			0.425916i	0.977061	+	0.212958i	$0.0683097\pi$
$883$			11175.4i			0.425916i	−0.977061	+	0.212958i	$0.931690\pi$
$884$	−2380.12	−	2046.82i	−0.0905565	−	0.0778758i
$885$	−1720.79	−	731.939i	−0.0653600	−	0.0278010i
$886$	−34218.2	−	12689.8i	−1.29750	−	0.481175i
$887$	−7044.36	−	12201.2i	−0.266659	−	0.461867i	0.701338	−	0.712829i	$-0.252586\pi$
$887$	−7044.36	−	12201.2i	−0.266659	−	0.461867i	−0.967997	+	0.250962i	$0.919253\pi$
$888$	−9751.16	−	13462.9i	−0.368499	−	0.508769i
$889$	340.207	−	31678.2i	0.0128348	−	1.19511i
$890$	48996.6	−	8333.55i	1.84536	−	0.313867i
$891$	14086.9	+	8860.75i	0.529660	+	0.333161i
$892$	14916.5	+	2817.01i	0.559910	+	0.105741i
$893$	10211.3	−	17686.4i	0.382650	−	0.662770i
$894$	−30466.5	−	28800.5i	−1.13977	−	1.07744i
$895$		−	35879.5i		−	1.34002i
$896$	−26622.9	+	3247.16i	−0.992644	+	0.121071i
$897$	−1195.69	+	145.911i	−0.0445071	+	0.00543123i
$898$	17029.7	+	20546.8i	0.632839	+	0.763538i
$899$	−604.536	−	349.029i	−0.0224276	−	0.0129486i
$900$	−522.803	−	9291.72i	−0.0193631	−	0.344138i
$901$	−21298.6	−	36890.2i	−0.787523	−	1.36403i
$902$	4515.08	+	26546.1i	0.166669	+	0.979921i
$903$	18775.1	+	8225.22i	0.691911	+	0.303121i
$904$	−12414.2	+	6869.48i	−0.456737	+	0.252739i
$905$	5416.46	−	3127.19i	0.198949	−	0.114863i
$906$	8915.50	−	37452.9i	0.326929	−	1.37339i
$907$	−32502.1	−	18765.1i	−1.18987	−	0.686973i	−0.231594	−	0.972812i	$-0.574394\pi$
$907$	−32502.1	−	18765.1i	−1.18987	−	0.686973i	−0.958277	+	0.285840i	$0.907727\pi$
$908$	−2671.03	+	3105.96i	−0.0976225	+	0.113519i
$909$	−7204.78	−	29080.8i	−0.262891	−	1.06111i
$910$	−2355.35	−	902.369i	−0.0858012	−	0.0328717i
$911$			45690.4i			1.66168i	0.556510	+	0.830841i	$0.312140\pi$
$911$			45690.4i			1.66168i	−0.556510	+	0.830841i	$0.687860\pi$
$912$	−9616.46	+	37368.1i	−0.349159	+	1.35678i
$913$	9447.91	+	5454.76i	0.342476	+	0.197728i
$914$	9098.34	+	3374.11i	0.329263	+	0.122107i
$915$	34479.2	+	45826.3i	1.24574	+	1.65571i
$916$	−6531.09	+	2287.86i	−0.235582	+	0.0825251i
$917$	7545.69	+	13399.8i	0.271735	+	0.482553i
$918$	−36114.9	+	21294.6i	−1.29844	+	0.765607i
$919$	−8003.35	−	13862.2i	−0.287276	−	0.497576i	0.685883	−	0.727712i	$-0.259416\pi$
$919$	−8003.35	−	13862.2i	−0.287276	−	0.497576i	−0.973158	+	0.230136i	$0.926083\pi$
$920$	−18307.8	−	332.909i	−0.656076	−	0.0119301i
$921$	5369.40	+	2283.89i	0.192104	+	0.0817118i
$922$	−5865.27	−	7076.61i	−0.209504	−	0.252772i
$923$		−	1793.02i		−	0.0639416i
$924$	15843.3	−	7607.06i	0.564077	−	0.270837i
$925$		−	6091.59i		−	0.216530i
$926$	16739.6	−	13874.2i	0.594057	−	0.492369i
$927$	43823.5	+	12636.7i	1.55270	+	0.447727i
$928$	−9965.47	+	3288.77i	−0.352514	+	0.116335i
$929$	−6989.54	−	12106.2i	−0.246845	−	0.427549i	0.715803	−	0.698302i	$-0.246061\pi$
$929$	−6989.54	−	12106.2i	−0.246845	−	0.427549i	−0.962649	+	0.270753i	$0.912727\pi$
$930$	−2198.62	+	655.863i	−0.0775222	+	0.0231254i
$931$	19154.1	+	34885.3i	0.674274	+	1.22805i
$932$	5660.20	+	16158.0i	0.198933	+	0.567890i
$933$	8380.41	−	6305.33i	0.294064	−	0.221251i
$934$	1720.06	−	4638.16i	0.0602590	−	0.162489i
$935$	27080.6	+	15635.0i	0.947198	+	0.546865i
$936$	−668.198	+	2168.39i	−0.0233341	+	0.0757224i
$937$			18184.3i			0.633996i	0.948426	+	0.316998i	$0.102675\pi$
$937$			18184.3i			0.633996i	−0.948426	+	0.316998i	$0.897325\pi$
$938$	−6493.92	−	40828.3i	−0.226049	−	1.42121i
$939$	3621.75	−	441.965i	0.125870	−	0.0153599i
$940$	11903.2	−	13841.5i	0.413021	−	0.480275i
$941$	6499.38	+	3752.42i	0.225158	+	0.129995i	0.608336	−	0.793679i	$-0.291837\pi$
$941$	6499.38	+	3752.42i	0.225158	+	0.129995i	−0.383178	+	0.923674i	$0.625171\pi$
$942$	11471.8	−	48191.5i	0.396784	−	1.66684i
$943$	−22543.0	+	13015.2i	−0.778475	+	0.449453i
$944$	1108.60	+	1388.18i	0.0382224	+	0.0478616i
$945$	−21537.4	+	25902.3i	−0.741387	+	0.891643i
$946$	−13558.3	+	2306.05i	−0.465981	+	0.0792561i
$947$	−12640.2	−	21893.4i	−0.433739	−	0.751257i	0.563453	−	0.826148i	$-0.309473\pi$
$947$	−12640.2	−	21893.4i	−0.433739	−	0.751257i	−0.997192	+	0.0748906i	$0.976139\pi$
$948$	−5900.46	−	385.398i	−0.202150	−	0.0132038i
$949$	−848.751	−	490.027i	−0.0290323	−	0.0167618i
$950$	−10886.5	+	9022.96i	−0.371793	+	0.308151i
$951$	−2790.95	−	22870.9i	−0.0951659	−	0.779852i
$952$	−1280.33	+	44257.6i	−0.0435881	+	1.50672i
$953$		−	42226.4i		−	1.43531i	−0.696401	−	0.717653i	$-0.745216\pi$
$953$		−	42226.4i		−	1.43531i	0.696401	−	0.717653i	$-0.254784\pi$
$954$	−18285.0	+	24771.9i	−0.620544	+	0.840691i
$955$	14982.6	−	25950.6i	0.507669	−	0.879309i
$956$	−10619.5	−	2005.53i	−0.359268	−	0.0678487i
$957$	5495.02	−	4134.40i	0.185610	−	0.139651i
$958$	−3275.62	−	19258.8i	−0.110470	−	0.649501i
$959$	−17823.1	+	30118.8i	−0.600144	+	1.01417i
$960$	−14645.6	+	31228.1i	−0.492381	+	1.04988i
$961$	−14823.0	−	25674.2i	−0.497567	−	0.861811i
$962$	−516.417	+	1392.53i	−0.0173077	+	0.0466703i
$963$	12749.3	−	44213.9i	0.426624	−	1.47952i
$964$	1041.65	−	1211.26i	0.0348021	−	0.0404690i
$965$		−	53199.4i		−	1.77466i
$966$	12220.2	+	11803.0i	0.407017	+	0.393122i
$967$	39321.9			1.30766			0.653830	−	0.756641i	$-0.273161\pi$
$967$	39321.9			1.30766			0.653830	+	0.756641i	$0.273161\pi$
$968$	9449.60	−	15700.8i	0.313762	−	0.521327i
$969$	58616.9	+	24932.8i	1.94329	+	0.826581i
$970$	−46828.5	−	17366.3i	−1.55008	−	0.574844i
$971$	−36638.2	+	21153.1i	−1.21089	+	0.699109i	−0.962954	−	0.269667i	$-0.913086\pi$
$971$	−36638.2	+	21153.1i	−1.21089	+	0.699109i	−0.247938	+	0.968776i	$0.579753\pi$
$972$	24545.2	+	17772.5i	0.809967	+	0.586476i
$973$	399.527	−	37201.8i	0.0131637	−	1.22573i
$974$	1989.37	+	11696.3i	0.0654449	+	0.384779i
$975$	−664.416	+	499.900i	−0.0218239	+	0.0164201i
$976$	−8157.39	−	53868.3i	−0.267532	−	1.76668i
$977$	1911.51	+	1103.61i	0.0625941	+	0.0361387i	0.530970	−	0.847390i	$-0.321828\pi$
$977$	1911.51	+	1103.61i	0.0625941	+	0.0361387i	−0.468376	+	0.883529i	$0.655161\pi$
$978$	9275.78	−	9812.36i	0.303279	−	0.320823i
$979$	30940.2			1.01007
$980$	11037.6	+	33819.7i	0.359779	+	1.10238i
$981$	5501.20	+	22204.6i	0.179042	+	0.722669i
$982$	−4772.02	+	3955.17i	−0.155073	+	0.128528i
$983$	−11382.6	+	19715.3i	−0.369328	+	0.639694i	−0.989461	−	0.144803i	$-0.953745\pi$
$983$	−11382.6	+	19715.3i	−0.369328	+	0.639694i	0.620133	+	0.784497i	$0.287079\pi$
$984$	5053.60	+	48772.1i	0.163723	+	1.58008i
$985$	26977.6	−	15575.5i	0.872668	−	0.503835i
$986$	2904.87	+	17079.0i	0.0938233	+	0.551628i
$987$	−16834.8	+	1871.11i	−0.542915	+	0.0603426i
$988$	3253.56	−	1139.73i	0.104767	−	0.0367000i
$989$	−6647.45	−	11513.7i	−0.213728	−	0.370187i
$990$	2532.12	−	22459.8i	0.0812890	−	0.721030i
$991$	−7588.23	+	13143.2i	−0.243237	+	0.421299i	−0.961635	−	0.274334i	$-0.911543\pi$
$991$	−7588.23	+	13143.2i	−0.243237	+	0.421299i	0.718397	+	0.695633i	$0.244876\pi$
$992$	2134.12	+	443.364i	0.0683049	+	0.0141904i
$993$	54163.4	−	6609.59i	1.73094	−	0.211228i
$994$	−19643.2	+	15928.0i	−0.626806	+	0.508256i
$995$	−28686.2			−0.913984
$996$	16520.2	+	11033.0i	0.525563	+	0.350999i
$997$	20870.9	−	36149.4i	0.662976	−	1.14831i	−0.316853	−	0.948475i	$-0.602626\pi$
$997$	20870.9	−	36149.4i	0.662976	−	1.14831i	0.979830	−	0.199834i	$-0.0640403\pi$
$998$	8775.51	−	23663.3i	0.278341	−	0.750550i
$999$	15387.4	+	12517.3i	0.487322	+	0.396427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.ba.c.101.70	yes	176
3.2	odd	2	inner	168.4.ba.c.101.19	yes	176
7.5	odd	6	inner	168.4.ba.c.5.13	✓	176
8.5	even	2	inner	168.4.ba.c.101.76	yes	176
21.5	even	6	inner	168.4.ba.c.5.76	yes	176
24.5	odd	2	inner	168.4.ba.c.101.13	yes	176
56.5	odd	6	inner	168.4.ba.c.5.19	yes	176
168.5	even	6	inner	168.4.ba.c.5.70	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.ba.c.5.13	✓	176	7.5	odd	6	inner
168.4.ba.c.5.19	yes	176	56.5	odd	6	inner
168.4.ba.c.5.70	yes	176	168.5	even	6	inner
168.4.ba.c.5.76	yes	176	21.5	even	6	inner
168.4.ba.c.101.13	yes	176	24.5	odd	2	inner
168.4.ba.c.101.19	yes	176	3.2	odd	2	inner
168.4.ba.c.101.70	yes	176	1.1	even	1	trivial
168.4.ba.c.101.76	yes	176	8.5	even	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+(2.17768 - 1.80491i) q^{2} +(4.78157 + 2.03385i) q^{3} +(1.48458 - 7.86104i) q^{4} +(11.2278 - 6.48238i) q^{5} +(14.0837 - 4.20125i) q^{6} +(-0.198886 + 18.5192i) q^{7} +(-10.9556 - 19.7984i) q^{8} +(18.7269 + 19.4500i) q^{9} +(12.7505 - 34.3818i) q^{10} +(11.4142 - 19.7700i) q^{11} +(23.0868 - 34.5688i) q^{12} -3.71397 q^{13} +(32.9924 + 40.6878i) q^{14} +(66.8709 - 8.16029i) q^{15} +(-59.5921 - 23.3407i) q^{16} +(-52.8272 + 91.4995i) q^{17} +(75.8868 + 8.55548i) q^{18} +(-58.0142 - 100.484i) q^{19} +(-34.2897 - 97.8860i) q^{20} +(-38.6163 + 88.1464i) q^{21} +(-10.8266 - 63.6542i) q^{22} +(54.0553 - 31.2089i) q^{23} +(-12.1179 - 116.949i) q^{24} +(21.5426 - 37.3129i) q^{25} +(-8.08783 + 6.70339i) q^{26} +(49.9856 + 131.089i) q^{27} +(145.285 + 29.0566i) q^{28} +57.9724 q^{29} +(130.895 - 138.467i) q^{30} +(-10.4280 - 6.02060i) q^{31} +(-171.900 + 56.7299i) q^{32} +(94.7869 - 71.3167i) q^{33} +(50.1077 + 294.605i) q^{34} +(117.815 + 209.219i) q^{35} +(180.699 - 118.338i) q^{36} +(122.443 - 70.6922i) q^{37} +(-307.700 - 114.110i) q^{38} +(-17.7586 - 7.55366i) q^{39} +(-251.348 - 151.274i) q^{40} -417.036 q^{41} +(75.0027 + 261.654i) q^{42} -212.999i q^{43} +(-138.467 - 119.077i) q^{44} +(336.345 + 96.9863i) q^{45} +(61.3859 - 165.528i) q^{46} +(88.0065 + 152.432i) q^{47} +(-237.472 - 232.807i) q^{48} +(-342.921 - 7.36641i) q^{49} +(-20.4336 - 120.138i) q^{50} +(-438.694 + 330.069i) q^{51} +(-5.51368 + 29.1957i) q^{52} +(-201.587 + 349.159i) q^{53} +(345.458 + 195.251i) q^{54} -295.965i q^{55} +(368.829 - 198.951i) q^{56} +(-73.0307 - 598.462i) q^{57} +(126.245 - 104.635i) q^{58} +(-24.0393 - 13.8791i) q^{59} +(35.1266 - 537.789i) q^{60} +(425.644 + 737.237i) q^{61} +(-33.5755 + 5.71067i) q^{62} +(-363.923 + 342.939i) q^{63} +(-271.951 + 433.805i) q^{64} +(-41.6998 + 24.0754i) q^{65} +(77.6951 - 326.387i) q^{66} +(-683.478 - 394.606i) q^{67} +(640.855 + 551.115i) q^{68} +(321.944 - 39.2870i) q^{69} +(634.187 + 242.966i) q^{70} +482.779i q^{71} +(179.915 - 583.848i) q^{72} +(228.529 + 131.942i) q^{73} +(139.047 - 374.943i) q^{74} +(178.897 - 134.600i) q^{75} +(-876.032 + 306.877i) q^{76} +(363.853 + 215.313i) q^{77} +(-52.3063 + 15.6033i) q^{78} +(-71.1227 - 123.188i) q^{79} +(-820.392 + 124.234i) q^{80} +(-27.6063 + 728.477i) q^{81} +(-908.171 + 752.714i) q^{82} +477.893i q^{83} +(635.594 + 434.424i) q^{84} +1369.79i q^{85} +(-384.444 - 463.843i) q^{86} +(277.199 + 117.907i) q^{87} +(-516.462 - 9.39135i) q^{88} +(677.670 + 1173.76i) q^{89} +(907.503 - 395.868i) q^{90} +(0.738656 - 68.7797i) q^{91} +(-165.085 - 471.263i) q^{92} +(-37.6172 - 49.9969i) q^{93} +(466.776 + 173.103i) q^{94} +(-1302.75 - 752.141i) q^{95} +(-937.334 - 78.3611i) q^{96} -1362.01i q^{97} +(-760.068 + 602.901i) q^{98} +(598.278 - 148.224i) 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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