LMFDB - Embedded newform 168.4.ba.c.5.18

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			5.18
Character	$\chi$	$=$	168.5
Dual form			168.4.ba.c.101.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.26030 + 1.70030i) q^{2} +(4.19123 - 3.07141i) q^{3} +(2.21794 - 7.68640i) q^{4} +(-3.83548 - 2.21442i) q^{5} +(-4.25113 + 14.0687i) q^{6} +(-18.2781 - 2.98509i) q^{7} +(8.05600 + 21.1448i) q^{8} +(8.13288 - 25.7460i) q^{9} +(12.4345 - 1.51623i) q^{10} +(-4.57157 - 7.91819i) q^{11} +(-14.3122 - 39.0277i) q^{12} -69.6182 q^{13} +(46.3896 - 24.3311i) q^{14} +(-22.8768 + 2.49920i) q^{15} +(-54.1615 - 34.0959i) q^{16} +(57.1065 + 98.9113i) q^{17} +(25.3932 + 72.0221i) 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} +(98.7088 + 63.8794i) q^{24} +(-52.6927 - 91.2665i) q^{25} +(157.358 - 118.372i) q^{26} +(-44.9897 - 132.887i) q^{27} +(-63.4843 + 133.872i) q^{28} -170.605 q^{29} +(47.4591 - 44.5464i) q^{30} +(-21.2529 + 12.2703i) q^{31} +(180.395 - 15.0238i) q^{32} +(-43.4805 - 19.1458i) q^{33} +(-297.257 - 126.471i) q^{34} +(63.4951 + 51.9246i) q^{35} +(-179.856 - 119.616i) q^{36} +(-128.940 - 74.4434i) q^{37} +(-41.8876 - 343.519i) q^{38} +(-291.786 + 213.826i) q^{39} +(15.9247 - 98.9397i) q^{40} -232.589 q^{41} +(119.699 - 244.459i) q^{42} -330.977i q^{43} +(-71.0019 + 17.5769i) q^{44} +(-88.2059 + 80.7387i) q^{45} +(-56.6238 + 6.90454i) q^{46} +(118.864 - 205.878i) q^{47} +(-331.726 + 23.4482i) q^{48} +(325.178 + 109.124i) q^{49} +(274.282 + 116.696i) q^{50} +(543.144 + 239.163i) q^{51} +(-154.409 + 535.113i) q^{52} +(-165.999 - 287.519i) q^{53} +(327.638 + 223.868i) q^{54} +40.4935i q^{55} +(-84.1293 - 410.534i) q^{56} +(69.0434 + 631.998i) q^{57} +(385.618 - 290.079i) q^{58} +(-378.412 + 218.477i) q^{59} +(-31.5295 + 181.383i) 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} +(130.833 - 30.6547i) q^{66} +(-149.924 + 86.5586i) q^{67} +(886.931 - 219.564i) q^{68} +(104.175 - 11.3807i) q^{69} +(-231.806 - 9.40442i) q^{70} +792.275i q^{71} +(609.911 - 35.4418i) q^{72} +(952.933 - 550.176i) q^{73} +(418.019 - 50.9720i) q^{74} +(-501.164 - 220.678i) q^{75} +(678.764 + 705.234i) q^{76} +(59.9231 + 158.376i) q^{77} +(295.956 - 979.437i) q^{78} +(-517.761 + 896.789i) q^{79} +(132.233 + 250.711i) q^{80} +(-596.713 - 418.778i) q^{81} +(525.721 - 395.471i) q^{82} +364.364i q^{83} +(145.098 + 756.076i) q^{84} -505.830i q^{85} +(562.761 + 748.108i) q^{86} +(-715.043 + 523.996i) q^{87} +(130.600 - 160.454i) q^{88} +(475.732 - 823.992i) q^{89} +(62.0917 - 332.471i) q^{90} +(1272.49 + 207.817i) q^{91} +(116.247 - 111.884i) q^{92} +(-51.3884 + 116.704i) q^{93} +(81.3870 + 667.451i) q^{94} +(469.278 - 270.938i) q^{95} +(709.932 - 617.035i) q^{96} -538.631i q^{97} +(-920.545 + 306.249i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.26030	+	1.70030i	−0.799138	+	0.601148i
$2$	−2.26030	+	1.70030i	−0.799138	+	0.601148i
$3$	4.19123	−	3.07141i	0.806603	−	0.591093i
$3$	4.19123	−	3.07141i	0.806603	−	0.591093i
$4$	2.21794	−	7.68640i	0.277242	−	0.960800i
$5$	−3.83548	−	2.21442i	−0.343056	−	0.198064i	0.318567	−	0.947900i	$-0.396799\pi$
$5$	−3.83548	−	2.21442i	−0.343056	−	0.198064i	−0.661623	+	0.749837i	$0.730132\pi$
$6$	−4.25113	+	14.0687i	−0.289253	+	0.957253i
$7$	−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
$10$	12.4345	−	1.51623i	0.393215	−	0.0479474i
$11$	−4.57157	−	7.91819i	−0.125307	−	0.217039i	0.796546	−	0.604578i	$-0.206658\pi$
$11$	−4.57157	−	7.91819i	−0.125307	−	0.217039i	−0.921853	+	0.387540i	$0.873325\pi$
$12$	−14.3122	−	39.0277i	−0.344298	−	0.938861i
$13$	−69.6182			−1.48528			−0.742639	−	0.669692i	$-0.766426\pi$
$13$	−69.6182			−1.48528			−0.742639	+	0.669692i	$0.766426\pi$
$14$	46.3896	−	24.3311i	0.885582	−	0.464483i
$15$	−22.8768	+	2.49920i	−0.393784	+	0.0430194i
$16$	−54.1615	−	34.0959i	−0.846273	−	0.532749i
$17$	57.1065	+	98.9113i	0.814727	+	1.41115i	0.909524	+	0.415652i	$0.136446\pi$
$17$	57.1065	+	98.9113i	0.814727	+	1.41115i	−0.0947970	+	0.995497i	$0.530220\pi$
$18$	25.3932	+	72.0221i	0.332513	+	0.943099i
$19$	−61.1759	+	105.960i	−0.738669	+	1.27941i	0.214426	+	0.976740i	$0.431212\pi$
$19$	−61.1759	+	105.960i	−0.738669	+	1.27941i	−0.953095	+	0.302672i	$0.902121\pi$
$20$	−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	0.577078	−	0.816689i	$-0.304193\pi$
$23$	17.4658	+	10.0839i	0.158343	+	0.0914191i	−0.418735	+	0.908108i	$0.637526\pi$
$24$	98.7088	+	63.8794i	0.839535	+	0.543305i
$25$	−52.6927	−	91.2665i	−0.421542	−	0.730132i
$26$	157.358	−	118.372i	1.18694	−	0.892872i
$27$	−44.9897	−	132.887i	−0.320677	−	0.947189i
$28$	−63.4843	+	133.872i	−0.428479	+	0.903552i
$29$	−170.605			−1.09243			−0.546215	−	0.837645i	$-0.683932\pi$
$29$	−170.605			−1.09243			−0.546215	+	0.837645i	$0.683932\pi$
$30$	47.4591	−	44.5464i	0.288827	−	0.271101i
$31$	−21.2529	+	12.2703i	−0.123133	+	0.0710909i	−0.560301	−	0.828289i	$-0.689315\pi$
$31$	−21.2529	+	12.2703i	−0.123133	+	0.0710909i	0.437168	+	0.899380i	$0.355981\pi$
$32$	180.395	−	15.0238i	0.996550	−	0.0829957i
$33$	−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
$36$	−179.856	−	119.616i	−0.832666	−	0.553776i
$37$	−128.940	−	74.4434i	−0.572907	−	0.330768i	0.185402	−	0.982663i	$-0.440641\pi$
$37$	−128.940	−	74.4434i	−0.572907	−	0.330768i	−0.758310	+	0.651895i	$0.773974\pi$
$38$	−41.8876	−	343.519i	−0.178818	−	1.46648i
$39$	−291.786	+	213.826i	−1.19803	+	0.877938i
$40$	15.9247	−	98.9397i	0.0629478	−	0.391094i
$41$	−232.589			−0.885957			−0.442978	−	0.896532i	$-0.646078\pi$
$41$	−232.589			−0.885957			−0.442978	+	0.896532i	$0.646078\pi$
$42$	119.699	−	244.459i	0.439761	−	0.898115i
$43$		−	330.977i		−	1.17380i	−0.809659	−	0.586901i	$-0.800348\pi$
$43$		−	330.977i		−	1.17380i	0.809659	−	0.586901i	$-0.199652\pi$
$44$	−71.0019	+	17.5769i	−0.243271	+	0.0602230i
$45$	−88.2059	+	80.7387i	−0.292199	+	0.267463i
$46$	−56.6238	+	6.90454i	−0.181494	+	0.0221308i
$47$	118.864	−	205.878i	0.368895	−	0.638944i	−0.620498	−	0.784208i	$-0.713070\pi$
$47$	118.864	−	205.878i	0.368895	−	0.638944i	0.989393	+	0.145263i	$0.0464029\pi$
$48$	−331.726	+	23.4482i	−0.997511	+	0.0705094i
$49$	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
$52$	−154.409	+	535.113i	−0.411782	+	1.42706i
$53$	−165.999	−	287.519i	−0.430221	−	0.745165i	0.566671	−	0.823944i	$-0.308231\pi$
$53$	−165.999	−	287.519i	−0.430221	−	0.745165i	−0.996892	+	0.0787793i	$0.974898\pi$
$54$	327.638	+	223.868i	0.825665	+	0.564160i
$55$			40.4935i			0.0992752i
$56$	−84.1293	−	410.534i	−0.200755	−	0.979642i
$57$	69.0434	+	631.998i	0.160439	+	1.46860i
$58$	385.618	−	290.079i	0.873002	−	0.656712i
$59$	−378.412	+	218.477i	−0.835002	+	0.482089i	−0.855562	−	0.517700i	$-0.826788\pi$
$59$	−378.412	+	218.477i	−0.835002	+	0.482089i	0.0205604	+	0.999789i	$0.493455\pi$
$60$	−31.5295	+	181.383i	−0.0678406	+	0.390275i
$61$	261.708	−	453.292i	0.549317	−	0.951445i	−0.449005	−	0.893529i	$-0.648221\pi$
$61$	261.708	−	453.292i	0.549317	−	0.951445i	0.998322	−	0.0579152i	$-0.0184453\pi$
$62$	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
$66$	130.833	−	30.6547i	0.244006	−	0.0571718i
$67$	−149.924	+	86.5586i	−0.273375	+	0.157833i	−0.630420	−	0.776254i	$-0.717117\pi$
$67$	−149.924	+	86.5586i	−0.273375	+	0.157833i	0.357045	+	0.934087i	$0.383784\pi$
$68$	886.931	−	219.564i	1.58171	−	0.391560i
$69$	104.175	−	11.3807i	0.181757	−	0.0198562i
$70$	−231.806	−	9.40442i	−0.395801	−	0.0160578i
$71$			792.275i			1.32431i	0.749369	+	0.662153i	$0.230357\pi$
$71$			792.275i			1.32431i	−0.749369	+	0.662153i	$0.769643\pi$
$72$	609.911	−	35.4418i	0.998316	−	0.0580120i
$73$	952.933	−	550.176i	1.52784	−	0.882099i	0.528389	−	0.849003i	$-0.322796\pi$
$73$	952.933	−	550.176i	1.52784	−	0.882099i	0.999452	−	0.0330968i	$-0.0105370\pi$
$74$	418.019	−	50.9720i	0.656672	−	0.0800727i
$75$	−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
$78$	295.956	−	979.437i	0.429621	−	1.42179i
$79$	−517.761	+	896.789i	−0.737376	+	1.27717i	0.216297	+	0.976328i	$0.430602\pi$
$79$	−517.761	+	896.789i	−0.737376	+	1.27717i	−0.953673	+	0.300845i	$0.902731\pi$
$80$	132.233	+	250.711i	0.184801	+	0.350379i
$81$	−596.713	−	418.778i	−0.818536	−	0.574456i
$82$	525.721	−	395.471i	0.708002	−	0.532591i
$83$			364.364i			0.481857i	0.970543	+	0.240928i	$0.0774519\pi$
$83$			364.364i			0.481857i	−0.970543	+	0.240928i	$0.922548\pi$
$84$	145.098	+	756.076i	0.188471	+	0.982079i
$85$		−	505.830i		−	0.645471i
$86$	562.761	+	748.108i	0.705629	+	0.938030i
$87$	−715.043	+	523.996i	−0.881158	+	0.645728i
$88$	130.600	−	160.454i	0.158204	−	0.194368i
$89$	475.732	−	823.992i	0.566601	−	0.981382i	−0.430298	−	0.902687i	$-0.641591\pi$
$89$	475.732	−	823.992i	0.566601	−	0.981382i	0.996899	−	0.0786949i	$-0.0250753\pi$
$90$	62.0917	−	332.471i	0.0727227	−	0.389394i
$91$	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
$94$	81.3870	+	667.451i	0.0893024	+	0.732365i
$95$	469.278	−	270.938i	0.506810	−	0.292607i
$96$	709.932	−	617.035i	0.754762	−	0.655998i
$97$		−	538.631i		−	0.563811i	−0.959442	−	0.281906i	$-0.909034\pi$
$97$		−	538.631i		−	0.563811i	0.959442	−	0.281906i	$-0.0909665\pi$
$98$	−920.545	+	306.249i	−0.948868	+	0.315672i
$99$	−241.042	+	53.3019i	−0.244703	+	0.0541116i
$100$	−818.380	+	202.594i	−0.818380	+	0.202594i
$101$	1447.64	−	835.793i	1.42619	−	0.823411i	0.429372	−	0.903128i	$-0.358735\pi$
$101$	1447.64	−	835.793i	1.42619	−	0.823411i	0.996818	+	0.0797166i	$0.0254015\pi$
$102$	−1634.32	+	382.928i	−1.58649	+	0.371721i
$103$	−414.915	−	239.551i	−0.396920	−	0.229162i	0.288234	−	0.957560i	$-0.406932\pi$
$103$	−414.915	−	239.551i	−0.396920	−	0.229162i	−0.685154	+	0.728398i	$0.740265\pi$
$104$	−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	$-0.839562\pi$
$107$	−21.6556	+	37.5087i	−0.0195657	+	0.0338888i	0.856077	+	0.516849i	$0.172895\pi$
$108$	−1121.21	+	51.0739i	−0.998964	+	0.0455055i
$109$	−1464.69	+	845.637i	−1.28708	+	0.743094i	−0.978132	−	0.207985i	$-0.933309\pi$
$109$	−1464.69	+	845.637i	−1.28708	+	0.743094i	−0.308945	+	0.951080i	$0.599976\pi$
$110$	−68.8512	−	91.5275i	−0.0596791	−	0.0793346i
$111$	−769.063	+	84.0172i	−0.657623	+	0.0718428i
$112$	888.190	+	784.886i	0.749340	+	0.662185i
$113$		−	390.146i		−	0.324795i	−0.986725	−	0.162398i	$-0.948077\pi$
$113$		−	390.146i		−	0.324795i	0.986725	−	0.162398i	$-0.0519227\pi$
$114$	−1230.65	−	1311.11i	−1.01106	−	1.07717i
$115$	−44.6600	−	77.3533i	−0.0362136	−	0.0627238i
$116$	−378.390	+	1311.33i	−0.302868	+	1.04961i
$117$	−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
$120$	−237.140	−	463.591i	−0.180399	−	0.352665i
$121$	623.701	−	1080.28i	0.468596	−	0.811632i
$122$	179.194	+	1469.56i	0.132979	+	1.09056i
$123$	−974.833	+	714.375i	−0.714616	+	0.523683i
$124$	47.1772	+	190.573i	0.0341665	+	0.138016i
$125$			1020.34i			0.730095i
$126$	−249.147	−	1392.23i	−0.176157	−	0.984362i
$127$	581.507			0.406302			0.203151	−	0.979147i	$-0.434882\pi$
$127$	581.507			0.406302			0.203151	+	0.979147i	$0.434882\pi$
$128$	284.625	−	1419.91i	0.196544	−	0.980495i
$129$	−1016.57	−	1387.20i	−0.693826	−	0.946793i
$130$	−865.670	+	105.557i	−0.584033	+	0.0712152i
$131$	−28.9739	−	16.7281i	−0.0193242	−	0.0111568i	0.490307	−	0.871550i	$-0.336885\pi$
$131$	−28.9739	−	16.7281i	−0.0193242	−	0.0111568i	−0.509631	+	0.860393i	$0.670218\pi$
$132$	−243.600	+	291.745i	−0.160626	+	0.192372i
$133$	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
$136$	−1631.41	+	2004.33i	−1.02862	+	1.26375i
$137$	−800.795	+	462.339i	−0.499391	+	0.288324i	−0.728462	−	0.685086i	$-0.759765\pi$
$137$	−800.795	+	462.339i	−0.499391	+	0.288324i	0.229071	+	0.973410i	$0.426431\pi$
$138$	−216.117	+	202.853i	−0.133312	+	0.125131i
$139$	−534.947			−0.326429			−0.163214	−	0.986591i	$-0.552186\pi$
$139$	−534.947			−0.326429			−0.163214	+	0.986591i	$0.552186\pi$
$140$	539.942	−	372.883i	0.325953	−	0.225103i
$141$	−134.150	−	1227.96i	−0.0801240	−	0.733426i
$142$	−1347.11	−	1790.78i	−0.796104	−	1.05830i
$143$	318.265	+	551.250i	0.186116	+	0.322363i
$144$	−1318.32	+	1117.14i	−0.762918	+	0.646495i
$145$	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	$-0.728884\pi$
$149$	586.155	−	1015.25i	0.322280	−	0.558205i	0.980958	+	0.194220i	$0.0622175\pi$
$150$	1508.00	−	353.332i	0.820853	−	0.192329i
$151$	132.573	+	229.623i	0.0714478	+	0.123751i	0.899536	−	0.436847i	$-0.143905\pi$
$151$	132.573	+	229.623i	0.0714478	+	0.123751i	−0.828088	+	0.560598i	$0.810571\pi$
$152$	−2733.33	−	439.938i	−1.45857	−	0.234761i
$153$	3011.01	−	665.829i	1.59102	−	0.351824i
$154$	−404.732	−	256.091i	−0.211781	−	0.134002i
$155$	108.687			0.0563221
$156$	996.389	+	2717.04i	0.511378	+	1.39447i
$157$	−139.361	−	241.380i	−0.0708420	−	0.122702i	0.828429	−	0.560095i	$-0.189235\pi$
$157$	−139.361	−	241.380i	−0.0708420	−	0.122702i	−0.899271	+	0.437393i	$0.855902\pi$
$158$	−354.516	−	2907.37i	−0.178505	−	1.46391i
$159$	−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
$162$	2060.80	−	68.0266i	0.999456	−	0.0329918i
$163$	−1401.52	−	809.168i	−0.673470	−	0.388828i	0.123920	−	0.992292i	$-0.460453\pi$
$163$	−1401.52	−	809.168i	−0.673470	−	0.388828i	−0.797390	+	0.603464i	$0.793787\pi$
$164$	−515.867	+	1787.77i	−0.245625	+	0.851227i
$165$	124.372	+	169.718i	0.0586809	+	0.0800757i
$166$	−619.529	−	823.572i	−0.289667	−	0.385070i
$167$	3255.34			1.50842			0.754209	−	0.656634i	$-0.228021\pi$
$167$	3255.34			1.50842			0.754209	+	0.656634i	$0.228021\pi$
$168$	−1613.52	−	1462.25i	−0.740989	−	0.671518i
$169$	2649.69			1.20605
$170$	860.065	+	1143.33i	0.388023	+	0.515820i
$171$	2230.50	+	2436.79i	0.997490	+	1.08974i
$172$	−2544.02	−	734.086i	−1.12779	−	0.325428i
$173$	909.782	+	525.263i	0.399823	+	0.230838i	0.686408	−	0.727217i	$-0.259187\pi$
$173$	909.782	+	525.263i	0.399823	+	0.230838i	−0.286584	+	0.958055i	$0.592520\pi$
$174$	725.262	−	2400.18i	0.315988	−	1.04573i
$175$	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
$178$	325.738	+	2671.36i	0.137163	+	1.12487i
$179$	1140.19	+	1974.88i	0.476102	+	0.824632i	0.999625	−	0.0273792i	$-0.00871615\pi$
$179$	1140.19	+	1974.88i	0.476102	+	0.824632i	−0.523524	+	0.852011i	$0.675383\pi$
$180$	424.955	+	857.059i	0.175968	+	0.354897i
$181$	−3647.62			−1.49793			−0.748964	−	0.662610i	$-0.769449\pi$
$181$	−3647.62			−1.49793			−0.748964	+	0.662610i	$0.769449\pi$
$182$	−3229.56	+	1693.89i	−1.31534	+	0.689887i
$183$	−295.365	−	2703.67i	−0.119312	−	1.09214i
$184$	−72.5171	+	450.547i	−0.0290545	+	0.180515i
$185$	329.697	+	571.053i	0.131026	+	0.226944i
$186$	−82.2789	−	351.163i	−0.0324354	−	0.138433i
$187$	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	−0.112161	−	0.993690i	$-0.535777\pi$
$191$	−2715.70	−	1567.91i	−1.02880	−	0.593980i	−0.916641	+	0.399710i	$0.869111\pi$
$192$	−555.516	+	2601.79i	−0.208807	+	0.977957i
$193$	−1215.31	−	2104.98i	−0.453265	−	0.785078i	0.545321	−	0.838227i	$-0.316408\pi$
$193$	−1215.31	−	2104.98i	−0.453265	−	0.785078i	−0.998587	+	0.0531487i	$0.983074\pi$
$194$	915.836	+	1217.47i	0.338934	+	0.450563i
$195$	1592.64	−	173.990i	0.584879	−	0.0638958i
$196$	1559.99	−	2257.42i	0.568511	−	0.822676i
$197$	−1090.17			−0.394272			−0.197136	−	0.980376i	$-0.563164\pi$
$197$	−1090.17			−0.394272			−0.197136	+	0.980376i	$0.563164\pi$
$198$	454.198	−	530.323i	0.163022	−	0.190345i
$199$	1051.02	−	606.809i	0.374398	−	0.216159i	−0.300980	−	0.953630i	$-0.597314\pi$
$199$	1051.02	−	606.809i	0.374398	−	0.216159i	0.675378	+	0.737472i	$0.263981\pi$
$200$	1505.32	−	1849.42i	0.532209	−	0.653868i
$201$	−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
$204$	3042.96	−	3644.37i	1.04436	−	1.25077i
$205$	892.089	+	515.048i	0.303933	+	0.175476i
$206$	1345.14	−	164.023i	0.454954	−	0.0554758i
$207$	401.668	−	367.664i	0.134869	−	0.123451i
$208$	3770.63	+	2373.70i	1.25695	+	0.791280i
$209$	1118.68			0.370242
$210$	−1000.44	+	672.555i	−0.328746	+	0.221003i
$211$		−	1579.53i		−	0.515353i	−0.966231	−	0.257677i	$-0.917043\pi$
$211$		−	1579.53i		−	0.515353i	0.966231	−	0.257677i	$-0.0829569\pi$
$212$	−2578.16	+	638.236i	−0.835230	+	0.206765i
$213$	2433.40	+	3320.61i	0.782788	+	1.06819i
$214$	−14.8278	−	121.602i	−0.00473648	−	0.0388437i
$215$	−732.921	+	1269.46i	−0.232487	+	0.402680i
$216$	2447.42	−	2021.83i	0.770954	−	0.636890i
$217$	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
$220$	311.249	+	89.8120i	0.0953836	+	0.0275233i
$221$	−3975.65	−	6886.03i	−1.21010	−	2.09595i
$222$	1595.46	−	1497.54i	0.482344	−	0.452741i
$223$			686.176i			0.206053i	0.994679	+	0.103026i	$0.0328526\pi$
$223$			686.176i			0.206053i	−0.994679	+	0.103026i	$0.967147\pi$
$224$	−3342.12	−	263.888i	−0.996897	−	0.0787132i
$225$	−2778.29	+	614.367i	−0.823197	+	0.182035i
$226$	663.367	+	881.848i	0.195250	+	0.259556i
$227$	−4743.59	+	2738.71i	−1.38697	+	0.800769i	−0.992973	−	0.118341i	$-0.962242\pi$
$227$	−4743.59	+	2738.71i	−1.38697	+	0.800769i	−0.394000	+	0.919110i	$0.628909\pi$
$228$	5010.92	+	871.038i	1.45551	+	0.253008i
$229$	1644.44	−	2848.26i	0.474532	−	0.821913i	−0.525043	−	0.851076i	$-0.675951\pi$
$229$	1644.44	−	2848.26i	0.474532	−	0.821913i	0.999575	+	0.0291627i	$0.00928409\pi$
$230$	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	−0.998852	−	0.0479130i	$-0.984743\pi$
$233$	−5476.34	−	3161.76i	−1.53977	−	0.888987i	−0.540920	−	0.841074i	$-0.681924\pi$
$234$	−1767.83	−	5014.05i	−0.493875	−	1.40076i
$235$	−911.800	+	526.428i	−0.253103	+	0.146129i
$236$	840.002	+	3393.20i	0.231693	+	0.935925i
$237$	584.348	+	5348.91i	0.160158	+	1.46603i
$238$	5055.77	+	3199.00i	1.37696	+	0.871261i
$239$			5332.99i			1.44336i	0.692228	+	0.721679i	$0.256629\pi$
$239$			5332.99i			1.44336i	−0.692228	+	0.721679i	$0.743371\pi$
$240$	1324.25	+	644.645i	0.356168	+	0.173382i
$241$	−4509.52	+	2603.57i	−1.20533	+	0.695896i	−0.961735	−	0.273982i	$-0.911659\pi$
$241$	−4509.52	+	2603.57i	−1.20533	+	0.695896i	−0.243592	+	0.969878i	$0.578326\pi$
$242$	427.054	+	3502.25i	0.113438	+	0.930302i
$243$	−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
$246$	988.764	−	3272.22i	0.256265	−	0.848085i
$247$	4258.95	−	7376.72i	1.09713	−	1.90028i
$248$	−430.666	−	350.537i	−0.110272	−	0.0897545i
$249$	1119.11	+	1527.13i	0.284822	+	0.388667i
$250$	−1734.89	−	2306.28i	−0.438895	−	0.583447i
$251$			1845.04i			0.463975i	0.972719	+	0.231987i	$0.0745228\pi$
$251$			1845.04i			0.463975i	−0.972719	+	0.231987i	$0.925477\pi$
$252$	2930.36	+	2723.23i	0.732521	+	0.680744i
$253$		−	184.397i		−	0.0458219i
$254$	−1314.38	+	988.738i	−0.324691	+	0.244248i
$255$	−1553.61	−	2120.05i	−0.381533	−	0.520639i
$256$	1770.94	+	3693.37i	0.432357	+	0.901702i
$257$	−1576.56	+	2730.69i	−0.382659	+	0.662785i	−0.991441	−	0.130552i	$-0.958325\pi$
$257$	−1576.56	+	2730.69i	−0.382659	+	0.662785i	0.608782	+	0.793337i	$0.291658\pi$
$258$	4656.41	+	1407.03i	1.12363	+	0.339525i
$259$	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
$262$	93.9327	−	11.4539i	0.0221495	−	0.00270085i
$263$	−921.217	+	531.865i	−0.215987	+	0.124700i	−0.604091	−	0.796915i	$-0.706464\pi$
$263$	−921.217	+	531.865i	−0.215987	+	0.124700i	0.388104	+	0.921616i	$0.373130\pi$
$264$	54.5549	−	1073.62i	0.0127183	−	0.250292i
$265$			1470.36i			0.340844i
$266$	−259.808	+	6403.91i	−0.0598866	+	1.47612i
$267$	−536.913	−	4914.71i	−0.123066	−	1.12650i
$268$	332.802	+	1344.36i	0.0758549	+	0.306417i
$269$	3450.51	−	1992.15i	0.782087	−	0.451538i	−0.0550825	−	0.998482i	$-0.517542\pi$
$269$	3450.51	−	1992.15i	0.782087	−	0.451538i	0.837169	+	0.546944i	$0.184209\pi$
$270$	−760.913	−	1584.17i	−0.171510	−	0.357073i
$271$	−1098.00	−	633.931i	−0.246121	−	0.142098i	0.371866	−	0.928286i	$-0.378718\pi$
$271$	−1098.00	−	633.931i	−0.246121	−	0.142098i	−0.617987	+	0.786188i	$0.712051\pi$
$272$	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
$276$	143.577	−	825.974i	0.0313128	−	0.180137i
$277$	2063.86	−	1191.57i	0.447672	−	0.258464i	−0.259175	−	0.965831i	$-0.583450\pi$
$277$	2063.86	−	1191.57i	0.447672	−	0.258464i	0.706846	+	0.707367i	$0.250117\pi$
$278$	1209.14	−	909.572i	0.260862	−	0.196232i
$279$	143.065	+	646.969i	0.0306993	+	0.138828i
$280$	−586.417	+	1760.89i	−0.125161	+	0.375834i
$281$			5446.49i			1.15626i	0.815943	+	0.578132i	$0.196218\pi$
$281$			5446.49i			1.15626i	−0.815943	+	0.578132i	$0.803782\pi$
$282$	2391.13	+	2547.47i	0.504928	+	0.537942i
$283$	−2102.49	−	3641.62i	−0.441626	−	0.764919i	0.556184	−	0.831059i	$-0.312265\pi$
$283$	−2102.49	−	3641.62i	−0.441626	−	0.764919i	−0.997810	+	0.0661402i	$0.978932\pi$
$284$	6089.74	+	1757.22i	1.27239	+	0.367154i
$285$	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
$288$	1080.33	−	4766.63i	0.221038	−	0.975265i
$289$	−4065.80	+	7042.17i	−0.827560	+	1.43338i
$290$	−2121.39	+	258.676i	−0.429559	+	0.0523792i
$291$	−1654.36	−	2257.53i	−0.333265	−	0.454772i
$292$	−2115.33	−	8544.88i	−0.423939	−	1.71250i
$293$			2624.63i			0.523319i	0.965160	+	0.261660i	$0.0842698\pi$
$293$			2624.63i			0.523319i	−0.965160	+	0.261660i	$0.915730\pi$
$294$	−2917.60	+	4110.93i	−0.578769	+	0.815492i
$295$	1935.19			0.381937
$296$	535.350	−	3326.12i	0.105124	−	0.653130i
$297$	−846.551	+	963.739i	−0.165393	+	0.188289i
$298$	401.345	+	3291.41i	0.0780178	+	0.639820i
$299$	−1215.94	−	702.023i	−0.235183	−	0.135783i
$300$	−2807.77	+	3362.70i	−0.540356	+	0.647152i
$301$	−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
$304$	6926.17	−	3653.09i	1.30672	−	0.689207i
$305$	−2007.56	+	1159.06i	−0.376893	+	0.217599i
$306$	−5673.69	+	6624.61i	−1.05994	+	1.23759i
$307$	−2803.64			−0.521212			−0.260606	−	0.965445i	$-0.583922\pi$
$307$	−2803.64			−0.521212			−0.260606	+	0.965445i	$0.583922\pi$
$308$	1350.25	−	109.325i	0.249797	−	0.0202251i
$309$	−2474.77	+	270.359i	−0.455613	+	0.0497740i
$310$	−245.665	+	184.800i	−0.0450091	+	0.0338579i
$311$	2351.38	+	4072.72i	0.428729	+	0.742581i	0.996761	−	0.0804262i	$-0.0256281\pi$
$311$	2351.38	+	4072.72i	0.428729	+	0.742581i	−0.568031	+	0.823007i	$0.692295\pi$
$312$	−6871.93	−	4447.17i	−1.24694	−	0.806959i
$313$	6802.88	+	3927.64i	1.22850	+	0.709277i	0.966717	−	0.255849i	$-0.0823550\pi$
$313$	6802.88	+	3927.64i	1.22850	+	0.709277i	0.261787	+	0.965126i	$0.415688\pi$
$314$	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	−0.0451156	−	0.998982i	$-0.514366\pi$
$317$	4755.57	−	8236.90i	0.842586	−	1.45940i	0.887701	−	0.460420i	$-0.152301\pi$
$318$	4750.69	−	1113.11i	0.837754	−	0.196289i
$319$	779.931	+	1350.88i	0.136889	+	0.237100i
$320$	2220.35	−	460.334i	0.387878	−	0.0804171i
$321$	24.4406	+	223.721i	0.00424967	+	0.0388999i
$322$	1055.59	+	42.8254i	0.182688	+	0.00741169i
$323$	−13974.2			−2.40725
$324$	−4542.37	+	3657.75i	−0.778870	+	0.627186i
$325$	3668.37	+	6353.81i	0.626107	+	1.08445i
$326$	4543.69	−	554.044i	0.771938	−	0.0941278i
$327$	−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
$330$	−569.690	−	172.143i	−0.0950315	−	0.0287156i
$331$	−721.989	−	416.841i	−0.119892	−	0.0692194i	0.438855	−	0.898558i	$-0.355384\pi$
$331$	−721.989	−	416.841i	−0.119892	−	0.0692194i	−0.558747	+	0.829338i	$0.688718\pi$
$332$	2800.64	+	808.136i	0.462968	+	0.133591i
$333$	−2965.27	+	2714.24i	−0.487975	+	0.446665i
$334$	−7358.06	+	5535.07i	−1.20543	+	0.906782i
$335$	766.707			0.125044
$336$	6133.32	+	561.645i	0.995833	+	0.0911912i
$337$	−9175.73			−1.48319			−0.741593	−	0.670850i	$-0.765929\pi$
$337$	−9175.73			−1.48319			−0.741593	+	0.670850i	$0.765929\pi$
$338$	−5989.11	+	4505.28i	−0.963801	+	0.725015i
$339$	−1198.30	−	1635.19i	−0.191984	−	0.261981i
$340$	−3888.01	−	1121.90i	−0.620168	−	0.178952i
$341$	194.318	+	112.190i	0.0308590	+	0.0178164i
$342$	−9184.89	−	1715.36i	−1.45223	−	0.271216i
$343$	−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
$346$	−2949.49	+	359.652i	−0.458282	+	0.0558815i
$347$	2267.39	+	3927.23i	0.350777	+	0.607564i	0.986386	−	0.164447i	$-0.0525841\pi$
$347$	2267.39	+	3927.23i	0.350777	+	0.607564i	−0.635609	+	0.772012i	$0.719251\pi$
$348$	2441.72	+	6658.30i	0.376121	+	1.02564i
$349$	5068.91			0.777457			0.388729	−	0.921352i	$-0.372914\pi$
$349$	5068.91			0.777457			0.388729	+	0.921352i	$0.372914\pi$
$350$	−4665.01	−	2951.74i	−0.712444	−	0.450792i
$351$	3132.10	+	9251.35i	0.476294	+	1.40684i
$352$	−943.649	−	1359.72i	−0.142888	−	0.205890i
$353$	−5712.39	−	9894.16i	−0.861303	−	1.49182i	−0.870671	−	0.491865i	$-0.836315\pi$
$353$	−5712.39	−	9894.16i	−0.861303	−	1.49182i	0.00936800	−	0.999956i	$-0.497018\pi$
$354$	−1465.00	−	6252.54i	−0.219954	−	0.938753i
$355$	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	0.317768	−	0.948169i	$-0.397067\pi$
$359$	−2343.22	−	1352.86i	−0.344486	−	0.198889i	−0.662254	+	0.749279i	$0.730400\pi$
$360$	−2417.79	−	1214.66i	−0.353968	−	0.177829i
$361$	−4055.47	−	7024.28i	−0.591263	−	1.02410i
$362$	8244.72	−	6202.05i	1.19705	−	0.900477i
$363$	−703.912	−	6443.36i	−0.101779	−	0.931649i
$364$	4419.67	−	9319.94i	0.636410	−	1.34203i
$365$	−4873.28			−0.698847
$366$	5264.67	+	5608.90i	0.751882	+	0.801043i
$367$	4971.62	−	2870.37i	0.707129	−	0.408261i	−0.102868	−	0.994695i	$-0.532802\pi$
$367$	4971.62	−	2870.37i	0.707129	−	0.408261i	0.809997	+	0.586434i	$0.199469\pi$
$368$	−602.156	−	1141.67i	−0.0852977	−	0.161722i
$369$	−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
$372$	783.058	+	653.835i	0.109139	+	0.0911284i
$373$	−3720.69	−	2148.14i	−0.516488	−	0.298195i	0.219008	−	0.975723i	$-0.429718\pi$
$373$	−3720.69	−	2148.14i	−0.516488	−	0.298195i	−0.735497	+	0.677528i	$0.763051\pi$
$374$	357.509	+	2931.91i	0.0494287	+	0.405363i
$375$	3133.88	+	4276.48i	0.431554	+	0.588897i
$376$	5310.81	+	854.792i	0.728415	+	0.117241i
$377$	11877.2			1.62256
$378$	−5320.34	−	5069.92i	−0.723939	−	0.689864i
$379$			7102.22i			0.962576i	0.876562	+	0.481288i	$0.159831\pi$
$379$			7102.22i			0.962576i	−0.876562	+	0.481288i	$0.840169\pi$
$380$	−1041.71	−	4207.98i	−0.140627	−	0.568066i
$381$	2437.23	−	1786.05i	0.327725	−	0.240162i
$382$	8804.24	−	1073.56i	1.17922	−	0.143791i
$383$	4295.05	−	7439.24i	0.573020	−	0.992500i	−0.423233	−	0.906021i	$-0.639105\pi$
$383$	4295.05	−	7439.24i	0.573020	−	0.992500i	0.996254	−	0.0864795i	$-0.0275617\pi$
$384$	−3168.19	−	6825.37i	−0.421031	−	0.907046i
$385$	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
$388$	−4140.13	−	1194.65i	−0.541710	−	0.156312i
$389$	−412.952	−	715.254i	−0.0538239	−	0.0932257i	0.837858	−	0.545888i	$-0.183808\pi$
$389$	−412.952	−	715.254i	−0.0538239	−	0.0932257i	−0.891682	+	0.452662i	$0.850474\pi$
$390$	−3304.02	+	3101.24i	−0.428988	+	0.402660i
$391$			2303.43i			0.297926i
$392$	312.242	+	7754.92i	0.0402312	+	0.999190i
$393$	−172.815	+	18.8794i	−0.0221816	+	0.00242326i
$394$	2464.12	−	1853.62i	0.315078	−	0.237016i
$395$	3971.73	−	2293.08i	0.505923	−	0.292095i
$396$	−124.916	+	1970.96i	−0.0158517	+	0.250113i
$397$	1604.37	−	2778.85i	0.202824	−	0.351301i	−0.746614	−	0.665258i	$-0.768322\pi$
$397$	1604.37	−	2778.85i	0.202824	−	0.351301i	0.949437	+	0.313957i	$0.101655\pi$
$398$	−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	0.325604	−	0.945506i	$-0.394432\pi$
$401$	−2653.33	−	1531.90i	−0.330426	−	0.190772i	−0.656030	+	0.754735i	$0.727766\pi$
$402$	−580.420	−	2477.20i	−0.0720117	−	0.307342i
$403$	1479.59	−	854.239i	0.182887	−	0.105590i
$404$	−3213.47	−	12980.8i	−0.395733	−	1.59857i
$405$	1361.33	+	2927.59i	0.167025	+	0.359193i
$406$	−7914.28	+	4151.00i	−0.967436	+	0.507415i
$407$			1361.29i			0.165791i
$408$	−681.481	+	13411.3i	−0.0826920	+	1.62735i
$409$	−206.447	+	119.192i	−0.0249588	+	0.0144099i	−0.512427	−	0.858731i	$-0.671254\pi$
$409$	−206.447	+	119.192i	−0.0249588	+	0.0144099i	0.487469	+	0.873140i	$0.337920\pi$
$410$	−2892.13	+	352.658i	−0.348371	+	0.0424793i
$411$	−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
$414$	−282.750	+	1513.99i	−0.0335662	+	0.179731i
$415$	806.853	−	1397.51i	0.0954382	−	0.165304i
$416$	−12558.8	+	1045.93i	−1.48015	+	0.123272i
$417$	−2242.09	+	1643.04i	−0.263299	+	0.192950i
$418$	−2528.55	+	1902.09i	−0.295875	+	0.222570i
$419$			10250.5i			1.19516i	0.801810	+	0.597579i	$0.203871\pi$
$419$			10250.5i			1.19516i	−0.801810	+	0.597579i	$0.796129\pi$
$420$	1117.74	−	3221.22i	0.129858	−	0.374237i
$421$			11094.4i			1.28434i	0.766563	+	0.642169i	$0.221965\pi$
$421$			11094.4i			1.28434i	−0.766563	+	0.642169i	$0.778035\pi$
$422$	2685.68	+	3570.22i	0.309803	+	0.411838i
$423$	−4333.83	−	4734.65i	−0.498151	−	0.544223i
$424$	4742.23	−	5826.26i	0.543167	−	0.667331i
$425$	6018.19	−	10423.8i	0.686883	−	1.18972i
$426$	−11146.3	−	3368.06i	−1.26770	−	0.383059i
$427$	−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
$430$	−501.837	−	4115.54i	−0.0562808	−	0.461556i
$431$	2543.69	−	1468.60i	0.284282	−	0.164130i	−0.351079	−	0.936346i	$-0.614185\pi$
$431$	2543.69	−	1468.60i	0.284282	−	0.164130i	0.635360	+	0.772216i	$0.280852\pi$
$432$	−2094.19	+	8731.32i	−0.233233	+	0.972421i
$433$			3280.71i			0.364113i	0.983288	+	0.182057i	$0.0582754\pi$
$433$			3280.71i			0.364113i	−0.983288	+	0.182057i	$0.941725\pi$
$434$	−687.361	+	1086.32i	−0.0760239	+	0.120150i
$435$	3902.88	−	426.375i	0.430182	−	0.0469957i
$436$	3251.32	+	13133.7i	0.357133	+	1.44264i
$437$	−2136.98	+	1233.78i	−0.233925	+	0.135057i
$438$	3689.21	+	15745.4i	0.402460	+	1.71768i
$439$	−11152.1	−	6438.66i	−1.21244	−	0.700001i	−0.249147	−	0.968466i	$-0.580150\pi$
$439$	−11152.1	−	6438.66i	−1.21244	−	0.700001i	−0.963289	+	0.268465i	$0.913484\pi$
$440$	−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	−0.0464613	−	0.998920i	$-0.514794\pi$
$443$	7849.56	−	13595.8i	0.841860	−	1.45814i	0.888321	−	0.459223i	$-0.151872\pi$
$444$	−1059.94	+	6097.67i	−0.113294	+	0.651763i
$445$	−3649.32	+	2106.94i	−0.388752	+	0.224446i
$446$	−1166.71	−	1550.97i	−0.123868	−	0.164664i
$447$	−661.537	−	6055.47i	−0.0699992	−	0.640747i
$448$	8002.90	−	5086.16i	0.843977	−	0.536380i
$449$			3520.44i			0.370022i	0.982736	+	0.185011i	$0.0592320\pi$
$449$			3520.44i			0.370022i	−0.982736	+	0.185011i	$0.940768\pi$
$450$	5235.16	−	6112.59i	0.548418	−	0.640334i
$451$	1063.30	+	1841.68i	0.111017	+	0.192287i
$452$	−2998.82	−	865.320i	−0.312063	−	0.0900470i
$453$	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
$456$	−12807.2	+	6551.28i	−1.31525	+	0.672789i
$457$	−3285.51	+	5690.68i	−0.336302	+	0.582492i	−0.983734	−	0.179631i	$-0.942510\pi$
$457$	−3285.51	+	5690.68i	−0.336302	+	0.582492i	0.647432	+	0.762123i	$0.275843\pi$
$458$	1125.96	+	9233.97i	0.114875	+	0.942085i
$459$	10574.8	−	12038.7i	1.07536	−	1.22422i
$460$	−693.622	+	171.709i	−0.0703049	+	0.0174043i
$461$			9205.68i			0.930046i	0.885298	+	0.465023i	$0.153954\pi$
$461$			9205.68i			0.930046i	−0.885298	+	0.465023i	$0.846046\pi$
$462$	−2482.89	+	169.762i	−0.250031	+	0.0170953i
$463$	1257.92			0.126264			0.0631320	−	0.998005i	$-0.479891\pi$
$463$	1257.92			0.126264			0.0631320	+	0.998005i	$0.479891\pi$
$464$	9240.20	+	5816.92i	0.924494	+	0.581991i
$465$	455.531	−	333.821i	0.0454296	−	0.0332916i
$466$	17754.1	−	2164.89i	1.76490	−	0.215207i
$467$	10353.3	+	5977.50i	1.02590	+	0.592303i	0.915807	−	0.401618i	$-0.131552\pi$
$467$	10353.3	+	5977.50i	1.02590	+	0.592303i	0.110092	+	0.993921i	$0.464885\pi$
$468$	12521.2	+	8327.42i	1.23674	+	0.822511i
$469$	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
$472$	−7668.12	−	6241.39i	−0.747784	−	0.608651i
$473$	−2620.74	+	1513.08i	−0.254760	+	0.147086i
$474$	−10415.6	−	11096.6i	−1.00929	−	1.07528i
$475$	12894.1			1.24552
$476$	−16866.8	+	1365.64i	−1.62414	+	0.131500i
$477$	−8752.51	+	1935.45i	−0.840146	+	0.185783i
$478$	−9067.70	−	12054.2i	−0.867671	−	1.15344i
$479$	−594.250	−	1029.27i	−0.0566847	−	0.0981808i	0.836291	−	0.548286i	$-0.184720\pi$
$479$	−594.250	−	1029.27i	−0.0566847	−	0.0981808i	−0.892975	+	0.450106i	$0.851386\pi$
$480$	−4089.31	+	794.540i	−0.388855	+	0.0755534i
$481$	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
$486$	8428.36	−	6614.68i	0.786663	−	0.617383i
$487$	8212.00	+	14223.6i	0.764110	+	1.32348i	0.940716	+	0.339195i	$0.110155\pi$
$487$	8212.00	+	14223.6i	0.764110	+	1.32348i	−0.176606	+	0.984282i	$0.556512\pi$
$488$	11693.1	+	1882.04i	1.08467	+	0.174582i
$489$	−8359.39	+	913.231i	−0.773056	+	0.0844534i
$490$	4208.90	+	863.857i	0.388038	+	0.0796430i
$491$	4192.37			0.385334			0.192667	−	0.981264i	$-0.438286\pi$
$491$	4192.37			0.385334			0.192667	+	0.981264i	$0.438286\pi$
$492$	3328.85	+	9077.40i	0.305033	+	0.831790i
$493$	−9742.63	−	16874.7i	−0.890032	−	1.54158i
$494$	2916.14	+	23915.1i	0.265594	+	2.17812i
$495$	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
$498$	−5126.12	−	1548.96i	−0.461259	−	0.139378i
$499$	4788.71	+	2764.76i	0.429603	+	0.248031i	0.699178	−	0.714948i	$-0.253550\pi$
$499$	4788.71	+	2764.76i	0.429603	+	0.248031i	−0.269574	+	0.962980i	$0.586883\pi$
$500$	7842.73	+	2263.05i	0.701475	+	0.202413i
$501$	13643.9	−	9998.49i	1.21669	−	0.891616i
$502$	−3137.12	−	4170.34i	−0.278917	−	0.370780i
$503$	11988.3			1.06268			0.531342	−	0.847157i	$-0.321688\pi$
$503$	11988.3			1.06268			0.531342	+	0.847157i	$0.321688\pi$
$504$	−11253.8	−	1172.83i	−0.994613	−	0.103655i
$505$	−7403.18			−0.652351
$506$	313.531	+	416.794i	0.0275458	+	0.0366180i
$507$	11105.5	−	8138.30i	0.972805	−	0.712889i
$508$	1289.75	−	4469.69i	0.112644	−	0.390375i
$509$	−6752.90	−	3898.79i	−0.588049	−	0.339510i	0.176277	−	0.984341i	$-0.443595\pi$
$509$	−6752.90	−	3898.79i	−0.588049	−	0.339510i	−0.764326	+	0.644830i	$0.776928\pi$
$510$	7116.37	+	2150.35i	0.617879	+	0.186704i
$511$	−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
$514$	−1079.49	−	8852.82i	−0.0926345	−	0.759691i
$515$	1060.93	+	1837.59i	0.0907773	+	0.157231i
$516$	−12917.3	+	4737.00i	−1.10204	+	0.404137i
$517$	−2173.58			−0.184901
$518$	−7792.76	−	316.154i	−0.660992	−	0.0268166i
$519$	5426.41	−	592.814i	0.458946	−	0.0501380i
$520$	−1108.65	+	6888.01i	−0.0934950	+	0.580883i
$521$	8827.36	+	15289.4i	0.742291	+	1.28569i	0.951450	+	0.307805i	$0.0995944\pi$
$521$	8827.36	+	15289.4i	0.742291	+	1.28569i	−0.209158	+	0.977882i	$0.567072\pi$
$522$	−4332.20	−	12287.3i	−0.363248	−	1.03027i
$523$	−3743.99	+	6484.78i	−0.313027	+	0.542179i	−0.979016	−	0.203782i	$-0.934676\pi$
$523$	−3743.99	+	6484.78i	−0.313027	+	0.542179i	0.665989	+	0.745962i	$0.268010\pi$
$524$	−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
$528$	1702.18	+	2519.48i	0.140299	+	0.207663i
$529$	−5880.13	−	10184.7i	−0.483285	−	0.837074i
$530$	−2500.07	−	3323.47i	−0.204898	−	0.272382i
$531$	2547.31	+	11519.4i	0.208181	+	0.941434i
$532$	−10301.3	−	14916.5i	−0.839511	−	1.21563i
$533$	16192.4			1.31589
$534$	9570.09	+	10195.8i	0.775540	+	0.826248i
$535$	166.120	−	95.9092i	0.0134243	−	0.00775050i
$536$	−3038.05	−	2472.79i	−0.244820	−	0.199269i
$537$	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
$540$	4413.47	+	2286.93i	0.351714	+	0.182247i
$541$	19644.4	+	11341.7i	1.56114	+	0.901325i	0.997142	+	0.0755502i	$0.0240713\pi$
$541$	19644.4	+	11341.7i	1.56114	+	0.901325i	0.563999	+	0.825775i	$0.309262\pi$
$542$	3559.69	−	434.058i	0.282107	−	0.0343992i
$543$	−15288.0	+	11203.3i	−1.20823	+	0.885415i
$544$	11787.7	+	16985.1i	0.929035	+	1.33866i
$545$	7490.37			0.588720
$546$	−8333.22	+	17018.8i	−0.653167	+	1.33395i
$547$		−	2780.71i		−	0.217357i	−0.994077	−	0.108679i	$-0.965338\pi$
$547$		−	2780.71i		−	0.217357i	0.994077	−	0.108679i	$-0.0346620\pi$
$548$	1777.61	+	7180.67i	0.138569	+	0.559750i
$549$	−9542.02	−	10424.5i	−0.741791	−	0.810396i
$550$	−329.877	−	2705.30i	−0.0255745	−	0.209736i
$551$	10436.9	−	18077.2i	0.806944	−	1.39767i
$552$	1079.88	+	2111.08i	0.0832657	+	0.162778i
$553$	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
$556$	−1186.48	+	4111.82i	−0.0904999	+	0.313633i
$557$	2390.49	+	4140.46i	0.181846	+	0.314967i	0.942509	−	0.334180i	$-0.108459\pi$
$557$	2390.49	+	4140.46i	0.181846	+	0.314967i	−0.760663	+	0.649147i	$0.775126\pi$
$558$	−1423.41	−	1219.09i	−0.107989	−	0.0924880i
$559$			23042.0i			1.74342i
$560$	−1668.57	−	4977.24i	−0.125911	−	0.375584i
$561$	−589.281	−	5394.07i	−0.0443485	−	0.405950i
$562$	−9260.68	−	12310.7i	−0.695086	−	0.924014i
$563$	−4568.69	+	2637.74i	−0.342003	+	0.197455i	−0.661157	−	0.750247i	$-0.729934\pi$
$563$	−4568.69	+	2637.74i	−0.342003	+	0.197455i	0.319155	+	0.947703i	$0.396601\pi$
$564$	−9736.14	−	1692.41i	−0.726889	−	0.126354i
$565$	−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	−0.390815	−	0.920469i	$-0.627807\pi$
$569$	−18776.2	−	10840.4i	−1.38337	−	0.798691i	−0.992557	+	0.121779i	$0.961140\pi$
$570$	1816.78	+	7753.92i	0.133502	+	0.569782i
$571$	5660.93	−	3268.34i	0.414891	−	0.239537i	−0.277998	−	0.960582i	$-0.589671\pi$
$571$	5660.93	−	3268.34i	0.414891	−	0.239537i	0.692889	+	0.721044i	$0.256338\pi$
$572$	4943.02	−	1223.67i	0.361325	−	0.0894479i
$573$	−16197.8	+	1769.55i	−1.18093	+	0.129012i
$574$	−10789.7	+	5659.14i	−0.784587	+	0.411512i
$575$		−	2125.39i		−	0.154148i
$576$	5662.85	+	12610.9i	0.409639	+	0.912248i
$577$	14376.6	−	8300.36i	1.03728	−	0.598871i	0.118215	−	0.992988i	$-0.462283\pi$
$577$	14376.6	−	8300.36i	1.03728	−	0.598871i	0.919060	+	0.394117i	$0.128950\pi$
$578$	−2783.89	−	22830.5i	−0.200336	−	1.64295i
$579$	−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
$582$	7577.83	+	2289.79i	0.539710	+	0.163084i
$583$	−1517.75	+	2628.83i	−0.107820	+	0.186749i
$584$	19310.2	+	15717.3i	1.36825	+	1.11368i
$585$	6140.74	−	5620.89i	0.433997	−	0.397256i
$586$	−4462.67	−	5932.46i	−0.314592	−	0.418204i
$587$		−	1563.80i		−	0.109957i	−0.998488	−	0.0549785i	$-0.982491\pi$
$587$		−	1563.80i		−	0.109957i	0.998488	−	0.0549785i	$-0.0175090\pi$
$588$	−395.169	−	14252.8i	−0.0277151	−	0.999616i
$589$		−	3002.60i		−	0.210051i
$590$	−4374.12	+	3290.41i	−0.305220	+	0.229600i
$591$	−4569.17	+	3348.37i	−0.318021	+	0.233052i
$592$	4445.35	+	8428.29i	0.308620	+	0.585136i
$593$	−5665.14	+	9812.30i	−0.392309	+	0.679499i	−0.992754	−	0.120167i	$-0.961657\pi$
$593$	−5665.14	+	9812.30i	−0.392309	+	0.679499i	0.600445	+	0.799666i	$0.294990\pi$
$594$	274.812	−	3617.73i	0.0189826	−	0.249895i
$595$	−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
$598$	3942.05	−	480.681i	0.269569	−	0.0328704i
$599$	−14781.1	+	8533.88i	−1.00825	+	0.582112i	−0.910678	−	0.413117i	$-0.864440\pi$
$599$	−14781.1	+	8533.88i	−1.00825	+	0.582112i	−0.0975691	+	0.995229i	$0.531107\pi$
$600$	628.809	−	12374.8i	0.0427850	−	0.841997i
$601$		−	9880.42i		−	0.670600i	−0.942111	−	0.335300i	$-0.891162\pi$
$601$		−	9880.42i		−	0.670600i	0.942111	−	0.335300i	$-0.108838\pi$
$602$	−8053.03	−	15353.9i	−0.545211	−	1.03950i
$603$	1009.22	+	4563.91i	0.0681572	+	0.308220i
$604$	2059.01	−	509.718i	0.138708	−	0.0343380i
$605$	−4784.39	+	2762.27i	−0.321509	+	0.185624i
$606$	5604.42	+	23919.4i	0.375683	+	1.60340i
$607$	−15947.1	−	9207.04i	−1.06634	−	0.615654i	−0.139164	−	0.990269i	$-0.544442\pi$
$607$	−15947.1	−	9207.04i	−1.06634	−	0.615654i	−0.927180	+	0.374615i	$0.877775\pi$
$608$	−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
$612$	1560.41	−	24620.6i	0.103065	−	1.62619i
$613$	−18953.4	+	10942.7i	−1.24881	+	0.720999i	−0.970872	−	0.239600i	$-0.922984\pi$
$613$	−18953.4	+	10942.7i	−1.24881	+	0.720999i	−0.277936	+	0.960600i	$0.589650\pi$
$614$	6337.07	−	4767.03i	0.416520	−	0.313325i
$615$	5320.88	−	581.286i	0.348876	−	0.0381133i
$616$	−2866.09	+	2542.94i	−0.187464	+	0.166328i
$617$			338.816i			0.0221073i	0.999939	+	0.0110537i	$0.00351856\pi$
$617$			338.816i			0.0221073i	−0.999939	+	0.0110537i	$0.996481\pi$
$618$	5134.03	−	4818.95i	0.334176	−	0.313667i
$619$	−5117.86	−	8864.40i	−0.332317	−	0.575590i	0.650649	−	0.759379i	$-0.274497\pi$
$619$	−5117.86	−	8864.40i	−0.332317	−	0.575590i	−0.982966	+	0.183789i	$0.941164\pi$
$620$	241.060	−	835.409i	0.0156149	−	0.0541143i
$621$	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
$624$	23094.2	−	1632.42i	1.48158	−	0.104726i
$625$	−4327.13	+	7494.81i	−0.276937	+	0.479668i
$626$	−22054.8	+	2689.29i	−1.40812	+	0.171702i
$627$	4688.65	−	3435.92i	0.298639	−	0.218848i
$628$	−2164.43	+	535.816i	−0.137532	+	0.0340468i
$629$		−	17004.8i		−	1.07794i
$630$	−2127.38	+	5891.59i	−0.134534	+	0.372582i
$631$	−11775.5			−0.742906			−0.371453	−	0.928452i	$-0.621140\pi$
$631$	−11775.5			−0.742906			−0.371453	+	0.928452i	$0.621140\pi$
$632$	−23133.5	−	3723.41i	−1.45601	−	0.234350i
$633$	−4851.39	−	6620.19i	−0.304622	−	0.415685i
$634$	3256.18	+	26703.8i	0.203974	+	1.67278i
$635$	−2230.36	−	1287.70i	−0.139384	−	0.0804736i
$636$	−8845.39	+	10593.6i	−0.551482	+	0.660476i
$637$	−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
$640$	−4235.95	+	4815.76i	−0.261626	+	0.297437i
$641$	114.122	−	65.8885i	0.00703207	−	0.00405997i	−0.496480	−	0.868048i	$-0.665374\pi$
$641$	114.122	−	65.8885i	0.00703207	−	0.00405997i	0.503512	+	0.863988i	$0.332041\pi$
$642$	−435.637	−	464.120i	−0.0267807	−	0.0285317i
$643$	−347.865			−0.0213351			−0.0106676	−	0.999943i	$-0.503396\pi$
$643$	−347.865			−0.0213351			−0.0106676	+	0.999943i	$0.503396\pi$
$644$	−2458.76	+	1698.02i	−0.150448	+	0.103900i
$645$	827.178	+	7571.69i	0.0504963	+	0.462225i
$646$	31585.8	−	23760.3i	1.92373	−	1.44712i
$647$	−1541.84	−	2670.55i	−0.0936880	−	0.162272i	0.815372	−	0.578937i	$-0.196532\pi$
$647$	−1541.84	−	2670.55i	−0.0936880	−	0.162272i	−0.909060	+	0.416665i	$0.863199\pi$
$648$	4047.85	−	15991.0i	0.245393	−	0.969424i
$649$	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	$-0.772556\pi$
$653$	3166.81	−	5485.08i	0.189781	−	0.328710i	0.945177	+	0.326558i	$0.105889\pi$
$654$	−5670.43	−	24201.1i	−0.339039	−	1.44700i
$655$	74.0860	+	128.321i	0.00441951	+	0.00765482i
$656$	12597.3	+	7930.32i	0.749762	+	0.471993i
$657$	−6414.74	−	29008.7i	−0.380918	−	1.72258i
$658$	504.803	−	12442.7i	0.0299077	−	0.737183i
$659$	−17001.3			−1.00497			−0.502485	−	0.864586i	$-0.667581\pi$
$659$	−17001.3			−1.00497			−0.502485	+	0.864586i	$0.667581\pi$
$660$	1580.37	−	579.550i	0.0932056	−	0.0341802i
$661$	−3875.34	−	6712.28i	−0.228038	−	0.394974i	0.729188	−	0.684313i	$-0.239898\pi$
$661$	−3875.34	−	6712.28i	−0.228038	−	0.394974i	−0.957227	+	0.289339i	$0.906564\pi$
$662$	2340.67	−	285.414i	0.137421	−	0.0167567i
$663$	−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
$666$	2087.37	−	11176.9i	0.121448	−	0.650293i
$667$	−2979.75	−	1720.36i	−0.172978	−	0.0998690i
$668$	7220.15	−	25021.9i	0.418197	−	1.44929i
$669$	2107.53	+	2875.92i	0.121796	+	0.166203i
$670$	−1732.99	+	1303.63i	−0.0999273	+	0.0751699i
$671$	−4785.67			−0.275334
$672$	−14818.1	+	9159.01i	−0.850627	+	0.525769i
$673$	13879.3			0.794960			0.397480	−	0.917611i	$-0.369885\pi$
$673$	13879.3			0.794960			0.397480	+	0.917611i	$0.369885\pi$
$674$	20739.9	−	15601.5i	1.18527	−	0.891614i
$675$	−9757.49	+	11108.2i	−0.556394	+	0.633416i
$676$	5876.86	−	20366.6i	0.334368	−	1.15877i
$677$	−410.740	−	237.141i	−0.0233176	−	0.0134624i	0.488296	−	0.872678i	$-0.337619\pi$
$677$	−410.740	−	237.141i	−0.0233176	−	0.0134624i	−0.511613	+	0.859216i	$0.670952\pi$
$678$	5488.84	+	1658.56i	0.310911	+	0.0939479i
$679$	−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
$682$	−629.974	+	76.8171i	−0.0353709	+	0.00431302i
$683$	−14328.5	−	24817.7i	−0.802730	−	1.39037i	−0.917813	−	0.397014i	$-0.870046\pi$
$683$	−14328.5	−	24817.7i	−0.802730	−	1.39037i	0.115082	−	0.993356i	$-0.463287\pi$
$684$	23677.3	−	11739.9i	1.32357	−	0.656265i
$685$	4095.25			0.228425
$686$	17740.0	−	2849.75i	0.987342	−	0.158606i
$687$	−1855.92	−	16988.5i	−0.103068	−	0.943450i
$688$	−11285.0	+	17926.2i	−0.625342	+	0.993357i
$689$	11556.6	+	20016.5i	0.638998	+	1.10678i
$690$	1278.11	−	299.468i	0.0705174	−	0.0165225i
$691$	−16582.2	+	28721.1i	−0.912902	+	1.58119i	−0.102957	+	0.994686i	$0.532830\pi$
$691$	−16582.2	+	28721.1i	−0.912902	+	1.58119i	−0.809945	+	0.586506i	$0.800503\pi$
$692$	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
$696$	−16840.2	−	10898.1i	−0.917134	−	0.593523i
$697$	−13282.3	−	23005.6i	−0.721813	−	1.25022i
$698$	−11457.3	+	8618.68i	−0.621295	+	0.467367i
$699$	−32663.7	+	3568.38i	−1.76746	+	0.193088i
$700$	15563.2	−	1260.09i	0.840333	−	0.0680387i
$701$	−20592.3			−1.10950			−0.554752	−	0.832016i	$-0.687187\pi$
$701$	−20592.3			−1.10950			−0.554752	+	0.832016i	$0.687187\pi$
$702$	−22809.6	−	15585.3i	−1.22634	−	0.837935i
$703$	15776.0	−	9108.28i	0.846377	−	0.488656i
$704$	4444.87	+	1468.89i	0.237958	+	0.0786374i
$705$	−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
$708$	13942.5	+	11641.7i	0.740103	+	0.617968i
$709$	15935.2	+	9200.17i	0.844087	+	0.487334i	0.858651	−	0.512560i	$-0.171303\pi$
$709$	15935.2	+	9200.17i	0.844087	+	0.487334i	−0.0145643	+	0.999894i	$0.504636\pi$
$710$	1201.27	+	9851.57i	0.0634970	+	0.520736i
$711$	18877.8	+	20623.8i	0.995744	+	1.08784i
$712$	21255.6	+	3421.16i	1.11880	+	0.180075i
$713$	−494.932			−0.0259963
$714$	31015.3	−	2120.61i	1.62566	−	0.111151i
$715$		−	2819.08i		−	0.147451i
$716$	17708.6	−	4383.84i	0.924302	−	0.228815i
$717$	16379.8	+	22351.8i	0.853159	+	1.16422i
$718$	7596.66	−	926.314i	0.394854	−	0.0481473i
$719$	−16112.7	+	27908.0i	−0.835746	+	1.44755i	0.0576763	+	0.998335i	$0.481631\pi$
$719$	−16112.7	+	27908.0i	−0.835746	+	1.44755i	−0.893422	+	0.449219i	$0.851702\pi$
$720$	7530.23	−	1365.47i	0.389771	−	0.0706778i
$721$	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
$724$	−8090.19	+	28037.0i	−0.415289	+	1.43921i
$725$	8989.62	+	15570.5i	0.460505	+	0.797618i
$726$	12546.7	+	13367.1i	0.641395	+	0.683332i
$727$			2198.99i			0.112182i	0.998426	+	0.0560908i	$0.0178636\pi$
$727$			2198.99i			0.112182i	−0.998426	+	0.0560908i	$0.982136\pi$
$728$	5856.93	+	28580.6i	0.298176	+	1.45504i
$729$	−15634.9	+	11957.1i	−0.794333	+	0.607483i
$730$	11015.1	−	8286.05i	0.558475	−	0.420110i
$731$	32737.4	−	18900.9i	1.65641	−	0.956328i
$732$	−21436.6	−	3726.27i	−1.08240	−	0.188152i
$733$	5132.66	−	8890.04i	0.258635	−	0.447969i	−0.707242	−	0.706972i	$-0.750061\pi$
$733$	5132.66	−	8890.04i	0.258635	−	0.447969i	0.965876	+	0.259003i	$0.0833941\pi$
$734$	−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
$738$	−5906.17	−	16751.5i	−0.294592	−	0.835545i
$739$	17511.3	−	10110.2i	0.871670	−	0.503259i	0.00376726	−	0.999993i	$-0.498801\pi$
$739$	17511.3	−	10110.2i	0.871670	−	0.503259i	0.867903	+	0.496734i	$0.165468\pi$
$740$	5120.59	−	1267.63i	0.254374	−	0.0629715i
$741$	−4806.67	−	43998.6i	−0.238296	−	2.18128i
$742$	−14696.3	−	9298.95i	−0.727113	−	0.460074i
$743$			30818.7i			1.52171i	0.648924	+	0.760854i	$0.275219\pi$
$743$			30818.7i			1.52171i	−0.648924	+	0.760854i	$0.724781\pi$
$744$	−2881.67	−	146.428i	−0.141999	−	0.00721548i
$745$	−4496.37	+	2595.98i	−0.221120	+	0.127664i
$746$	12062.4	−	1470.85i	0.592005	−	0.0721873i
$747$	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
$750$	−14354.8	−	4337.59i	−0.698886	−	0.211182i
$751$	11160.7	−	19330.8i	0.542288	−	0.939270i	−0.456485	−	0.889731i	$-0.650892\pi$
$751$	11160.7	−	19330.8i	0.542288	−	0.939270i	0.998772	−	0.0495383i	$-0.0157750\pi$
$752$	−13457.4	+	7097.89i	−0.652583	+	0.344193i
$753$	5666.86	+	7732.98i	0.274252	+	0.374244i
$754$	−26846.0	+	20194.8i	−1.29665	+	0.975400i
$755$		−	1174.29i		−	0.0566048i
$756$	20646.0	+	2413.37i	0.993237	+	0.116102i
$757$		−	20252.5i		−	0.972377i	−0.873854	−	0.486189i	$-0.838387\pi$
$757$		−	20252.5i		−	0.972377i	0.873854	−	0.486189i	$-0.161613\pi$
$758$	−12075.9	−	16053.2i	−0.578651	−	0.769231i
$759$	−566.359	−	772.852i	−0.0270850	−	0.0369601i
$760$	9509.42	+	7740.10i	0.453872	+	0.369425i
$761$	−3413.04	+	5911.55i	−0.162579	+	0.281595i	−0.935793	−	0.352550i	$-0.885314\pi$
$761$	−3413.04	+	5911.55i	−0.162579	+	0.281595i	0.773214	+	0.634145i	$0.218648\pi$
$762$	−2472.06	+	8181.04i	−0.117524	+	0.388934i
$763$	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
$766$	2940.86	+	24117.8i	0.138717	+	1.13761i
$767$	26344.4	−	15209.9i	1.24021	−	0.716036i
$768$	18766.3	+	10040.5i	0.881731	+	0.471753i
$769$		−	12470.9i		−	0.584803i	−0.956296	−	0.292402i	$-0.905546\pi$
$769$		−	12470.9i		−	0.584803i	0.956296	−	0.292402i	$-0.0944544\pi$
$770$	985.251	+	1878.48i	0.0461117	+	0.0879164i
$771$	1779.32	+	16287.2i	0.0831136	+	0.760792i
$772$	−18875.2	+	4672.66i	−0.879967	+	0.217840i
$773$	−29045.9	+	16769.7i	−1.35150	+	0.780289i	−0.988460	−	0.151485i	$-0.951594\pi$
$773$	−29045.9	+	16769.7i	−1.35150	+	0.780289i	−0.363040	+	0.931774i	$0.618261\pi$
$774$	23837.6	−	8404.57i	1.10701	−	0.390305i
$775$	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
$780$	2195.02	−	12627.6i	0.100762	−	0.579666i
$781$	6273.39	−	3621.94i	0.287426	−	0.165945i
$782$	−3916.52	−	5206.44i	−0.179098	−	0.238084i
$783$	7675.45	+	22671.1i	0.350317	+	1.03474i
$784$	−13891.5	−	16997.6i	−0.632811	−	0.774306i
$785$			1234.41i			0.0561248i
$786$	358.514	−	336.512i	0.0162694	−	0.0152710i
$787$	−17244.0	−	29867.5i	−0.781045	−	1.35281i	−0.931334	−	0.364167i	$-0.881354\pi$
$787$	−17244.0	−	29867.5i	−0.781045	−	1.35281i	0.150289	−	0.988642i	$-0.451980\pi$
$788$	−2417.94	+	8379.50i	−0.109309	+	0.378817i
$789$	−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
$792$	−3068.89	−	4667.37i	−0.137687	−	0.209404i
$793$	−18219.7	+	31557.4i	−0.815888	+	1.41316i
$794$	1098.52	+	9008.95i	0.0490997	+	0.402665i
$795$	4516.09	+	6162.64i	0.201471	+	0.274926i
$796$	−2333.07	−	9424.46i	−0.103886	−	0.419650i
$797$			21992.9i			0.977451i	0.872438	+	0.488726i	$0.162538\pi$
$797$			21992.9i			0.977451i	−0.872438	+	0.488726i	$0.837462\pi$
$798$	18580.1	+	27638.2i	0.824221	+	1.22604i
$799$	27151.6			1.20219
$800$	−10876.7	−	15672.3i	−0.480685	−	0.692626i
$801$	−17345.4	−	18949.6i	−0.765132	−	0.835895i
$802$	8602.02	−	1048.90i	0.378738	−	0.0461822i
$803$	−8712.80	−	5030.34i	−0.382899	−	0.221067i
$804$	5523.92	+	4612.34i	0.242306	+	0.202319i
$805$	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
$808$	29334.8	+	23876.8i	1.27722	+	1.03958i
$809$	20132.6	−	11623.6i	0.874939	−	0.505146i	0.00595233	−	0.999982i	$-0.498105\pi$
$809$	20132.6	−	11623.6i	0.874939	−	0.505146i	0.868986	+	0.494836i	$0.164772\pi$
$810$	−8054.81	−	4302.56i	−0.349404	−	0.186638i
$811$	32730.2			1.41715			0.708577	−	0.705634i	$-0.249338\pi$
$811$	32730.2			1.41715			0.708577	+	0.705634i	$0.249338\pi$
$812$	10830.7	−	22839.2i	0.468083	−	0.987067i
$813$	−6549.04	+	715.457i	−0.282515	+	0.0308637i
$814$	−2314.61	−	3076.93i	−0.0996647	−	0.132490i
$815$	3583.67	+	6207.10i	0.154025	+	0.266779i
$816$	−21263.0	−	31472.4i	−0.912198	−	1.35019i
$817$	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	0.375597	+	0.926783i	$0.377438\pi$
$821$	−14463.1	+	25050.9i	−0.614819	+	1.06490i	−0.990416	+	0.138115i	$0.955896\pi$
$822$	−3100.22	−	13231.6i	−0.131548	−	0.561442i
$823$	−1455.37	−	2520.77i	−0.0616415	−	0.106766i	0.833558	−	0.552432i	$-0.186300\pi$
$823$	−1455.37	−	2520.77i	−0.0616415	−	0.106766i	−0.895199	+	0.445666i	$0.852967\pi$
$824$	1722.70	−	10703.1i	0.0728315	−	0.452500i
$825$	543.736	+	4977.16i	0.0229460	+	0.210039i
$826$	−12238.6	+	19342.2i	−0.515541	+	0.814773i
$827$	37411.1			1.57305			0.786524	−	0.617559i	$-0.211878\pi$
$827$	37411.1			1.57305			0.786524	+	0.617559i	$0.211878\pi$
$828$	−1935.14	−	3902.84i	−0.0812207	−	0.163808i
$829$	1963.00	+	3400.01i	0.0822410	+	0.142446i	0.904212	−	0.427083i	$-0.140459\pi$
$829$	1963.00	+	3400.01i	0.0822410	+	0.142446i	−0.821971	+	0.569529i	$0.807126\pi$
$830$	552.459	+	4530.69i	0.0231038	+	0.189473i
$831$	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
$834$	2274.13	−	7526.00i	0.0944205	−	0.312475i
$835$	−12485.8	−	7208.68i	−0.517472	−	0.298763i
$836$	2481.16	−	8598.62i	0.102647	−	0.355729i
$837$	2586.73	+	2272.19i	0.106822	+	0.0938331i
$838$	−17429.0	−	23169.3i	−0.718467	−	0.955096i
$839$	−46725.8			−1.92271			−0.961355	−	0.275313i	$-0.911219\pi$
$839$	−46725.8			−1.92271			−0.961355	+	0.275313i	$0.911219\pi$
$840$	2950.62	+	9181.45i	0.121198	+	0.377131i
$841$	4716.91			0.193403
$842$	−18863.8	−	25076.6i	−0.772078	−	1.02636i
$843$	16728.4	+	22827.5i	0.683460	+	0.932647i
$844$	−12140.9	−	3503.31i	−0.495151	−	0.142878i
$845$	−10162.9	−	5867.53i	−0.413743	−	0.238875i
$846$	17846.1	+	3332.91i	0.725250	+	0.135447i
$847$	−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
$850$	4120.71	+	33793.7i	0.166281	+	1.36366i
$851$	−1501.36	−	2600.43i	−0.0604771	−	0.104749i
$852$	30920.7	−	11339.2i	1.24334	−	0.455956i
$853$	33662.3			1.35120			0.675601	−	0.737268i	$-0.263884\pi$
$853$	33662.3			1.35120			0.675601	+	0.737268i	$0.263884\pi$
$854$	1111.45	−	27395.7i	0.0445352	−	1.09773i
$855$	−3158.98	−	14285.5i	−0.126357	−	0.571409i
$856$	−967.569	−	155.734i	−0.0386342	−	0.00621830i
$857$	−4023.45	−	6968.82i	−0.160372	−	0.277772i	0.774630	−	0.632414i	$-0.217936\pi$
$857$	−4023.45	−	6968.82i	−0.160372	−	0.277772i	−0.935002	+	0.354642i	$0.884603\pi$
$858$	−9108.35	+	2134.13i	−0.362417	+	0.0849160i
$859$	−5884.03	+	10191.4i	−0.233714	+	0.404805i	−0.958898	−	0.283750i	$-0.908421\pi$
$859$	−5884.03	+	10191.4i	−0.233714	+	0.404805i	0.725184	+	0.688555i	$0.241755\pi$
$860$	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	−0.278695	−	0.960380i	$-0.589902\pi$
$863$	−31684.1	−	18292.8i	−1.24976	−	0.721546i	−0.971061	+	0.238833i	$0.923235\pi$
$864$	−10112.4	−	23296.2i	−0.398183	−	0.917306i
$865$	−2326.30	−	4029.27i	−0.0914412	−	0.158381i
$866$	−5578.21	−	7415.41i	−0.218886	−	0.290977i
$867$	4588.68	+	42003.1i	0.179746	+	1.64533i
$868$	−293.433	−	3624.14i	−0.0114744	−	0.141718i
$869$	9467.93			0.369595
$870$	−8096.73	+	7599.82i	−0.315523	+	0.296159i
$871$	10437.4	−	6026.05i	0.406038	−	0.234426i
$872$	−29680.3	−	24158.0i	−1.15264	−	0.938179i
$873$	−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
$876$	−35110.7	−	29316.6i	−1.35420	−	1.13072i
$877$	−6245.25	−	3605.70i	−0.240464	−	0.138832i	0.374926	−	0.927055i	$-0.377668\pi$
$877$	−6245.25	−	3605.70i	−0.240464	−	0.138832i	−0.615390	+	0.788223i	$0.711001\pi$
$878$	36154.7	−	4408.60i	1.38971	−	0.169457i
$879$	8061.32	+	11000.4i	0.309330	+	0.422111i
$880$	1380.66	−	2193.19i	0.0528888	−	0.0840140i
$881$	−31273.8			−1.19596			−0.597980	−	0.801511i	$-0.704030\pi$
$881$	−31273.8			−1.19596			−0.597980	+	0.801511i	$0.704030\pi$
$882$	398.011	+	26191.0i	0.0151947	+	0.999885i
$883$		−	42583.0i		−	1.62291i	−0.584414	−	0.811456i	$-0.698676\pi$
$883$		−	42583.0i		−	1.62291i	0.584414	−	0.811456i	$-0.301324\pi$
$884$	−61746.5	+	15285.7i	−2.34928	+	0.581575i
$885$	8110.85	−	5943.77i	0.308071	−	0.225760i
$886$	5374.66	+	44077.3i	0.203798	+	1.67134i
$887$	18980.1	−	32874.5i	0.718478	−	1.24444i	−0.243125	−	0.969995i	$-0.578173\pi$
$887$	18980.1	−	32874.5i	0.718478	−	1.24444i	0.961603	−	0.274445i	$-0.0884941\pi$
$888$	−7972.09	−	15584.8i	−0.301268	−	0.588955i
$889$	−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
$892$	5274.22	+	1521.90i	0.197975	+	0.0571265i
$893$	14543.2	+	25189.5i	0.544982	+	0.943937i
$894$	11791.4	+	12562.4i	0.441123	+	0.469965i
$895$		−	10099.5i		−	0.377193i
$896$	−9440.97	+	25103.6i	−0.352010	+	0.935996i
$897$	−7252.49	+	792.307i	−0.269959	+	0.0294920i
$898$	−5985.81	−	7957.25i	−0.222438	−	0.295698i
$899$	3625.83	−	2093.38i	0.134514	−	0.0776619i
$900$	−1439.80	+	22717.7i	−0.0533260	+	0.841395i
$901$	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
$906$	−3794.07	+	888.968i	−0.139128	+	0.0325982i
$907$	−41433.3	+	23921.6i	−1.51684	+	0.875746i	−0.517033	+	0.855965i	$0.672964\pi$
$907$	−41433.3	+	23921.6i	−1.51684	+	0.875746i	−0.999804	+	0.0197810i	$0.993703\pi$
$908$	10529.8	+	42535.4i	0.384852	+	1.55461i
$909$	−9744.87	−	44068.2i	−0.355574	−	1.60798i
$910$	16137.9	+	654.718i	0.587875	+	0.0238502i
$911$		−	42439.6i		−	1.54346i	−0.635953	−	0.771728i	$-0.719393\pi$
$911$		−	42439.6i		−	1.54346i	0.635953	−	0.771728i	$-0.280607\pi$
$912$	17809.1	−	36584.1i	0.646620	−	1.32831i
$913$	2885.10	−	1665.71i	0.104582	−	0.0603802i
$914$	−2249.62	−	18449.0i	−0.0814122	−	0.667658i
$915$	−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
$918$	−3432.86	+	45191.5i	−0.123422	+	1.62477i
$919$	21528.4	−	37288.2i	0.772748	−	1.33844i	−0.163303	−	0.986576i	$-0.552215\pi$
$919$	21528.4	−	37288.2i	0.772748	−	1.33844i	0.936051	−	0.351863i	$-0.114452\pi$
$920$	1275.84	−	1567.48i	0.0457208	−	0.0561721i
$921$	−11750.7	+	8611.12i	−0.420411	+	0.308085i
$922$	−15652.5	−	20807.6i	−0.559095	−	0.743235i
$923$		−	55156.8i		−	1.96696i
$924$	5323.43	−	4605.37i	0.189532	−	0.163967i
$925$			15690.5i			0.557730i
$926$	−2843.27	+	2138.84i	−0.100902	+	0.0759034i
$927$	−9541.94	+	8734.16i	−0.338078	+	0.309458i
$928$	−30776.2	+	2563.13i	−1.08866	+	0.0906670i
$929$	12827.5	−	22217.9i	0.453021	−	0.784655i	−0.545551	−	0.838078i	$-0.683680\pi$
$929$	12827.5	−	22217.9i	0.453021	−	0.784655i	0.998572	+	0.0534222i	$0.0170129\pi$
$930$	−462.041	+	1529.08i	−0.0162913	+	0.0539145i
$931$	−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
$934$	−33565.2	+	4092.84i	−1.17590	+	0.143385i
$935$	−4005.26	+	2312.44i	−0.140092	+	0.0808822i
$936$	−42460.9	+	2467.40i	−1.48278	+	0.0861639i
$937$			23102.8i			0.805480i	0.915315	+	0.402740i	$0.131942\pi$
$937$			23102.8i			0.805480i	−0.915315	+	0.402740i	$0.868058\pi$
$938$	−4848.85	+	7663.23i	−0.168785	+	0.266752i
$939$	40575.9	−	4432.76i	1.41016	−	0.154055i
$940$	2024.02	+	8176.04i	0.0702300	+	0.283695i
$941$	−11357.7	+	6557.39i	−0.393466	+	0.227168i	−0.683661	−	0.729800i	$-0.739613\pi$
$941$	−11357.7	+	6557.39i	−0.393466	+	0.227168i	0.290195	+	0.956968i	$0.406280\pi$
$942$	3988.33	−	934.484i	0.137948	−	0.0323218i
$943$	−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	$-0.938766\pi$
$947$	−9477.18	+	16415.0i	−0.325203	+	0.563267i	0.656351	+	0.754456i	$0.272099\pi$
$948$	42409.9	+	7372.02i	1.45296	+	0.252566i
$949$	−66341.5	+	38302.3i	−2.26927	+	1.31016i
$950$	−29144.5	+	21923.9i	−0.995341	+	0.748741i
$951$	−5367.16	−	49129.1i	−0.183010	−	1.67520i
$952$	35802.1	−	31765.5i	1.21886	−	1.08143i
$953$		−	46313.7i		−	1.57424i	−0.616803	−	0.787118i	$-0.711572\pi$
$953$		−	46313.7i		−	1.57424i	0.616803	−	0.787118i	$-0.288428\pi$
$954$	16492.5	−	19256.6i	0.559710	−	0.653518i
$955$	6944.02	+	12027.4i	0.235291	+	0.407537i
$956$	40991.5	+	11828.2i	1.38678	+	0.400160i
$957$	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
$960$	7892.11	−	8748.96i	0.265330	−	0.294137i
$961$	−14594.4	+	25278.2i	−0.489892	+	0.848518i
$962$	−29101.7	+	3548.58i	−0.975341	+	0.118930i
$963$	789.575	+	862.599i	0.0264213	+	0.0288649i
$964$	10010.3	+	40436.6i	0.334449	+	1.35101i
$965$			10764.8i			0.359101i
$966$	4555.74	−	3062.65i	0.151738	−	0.102007i
$967$	49194.0			1.63596			0.817980	−	0.575246i	$-0.195094\pi$
$967$	49194.0			1.63596			0.817980	+	0.575246i	$0.195094\pi$
$968$	27866.9	+	4485.26i	0.925284	+	0.148928i
$969$	−58568.9	+	42920.4i	−1.94170	+	1.42291i
$970$	−816.688	−	6697.62i	−0.0270333	−	0.221699i
$971$	49420.8	+	28533.1i	1.63336	+	0.943018i	0.983048	+	0.183346i	$0.0586930\pi$
$971$	49420.8	+	28533.1i	1.63336	+	0.943018i	0.650307	+	0.759672i	$0.274640\pi$
$972$	−7803.69	+	29281.9i	−0.257514	+	0.966275i
$973$	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
$976$	−29629.9	+	15627.8i	−0.971753	+	0.512534i
$977$	45789.7	−	26436.7i	1.49943	−	0.865696i	0.499430	−	0.866354i	$-0.333543\pi$
$977$	45789.7	−	26436.7i	1.49943	−	0.865696i	1.00000		0.000658044i	$0.000209462\pi$
$978$	17342.0	−	16277.7i	0.567009	−	0.532211i
$979$	−8699.37			−0.283997
$980$	−10982.2	+	5203.83i	−0.357973	+	0.169623i
$981$	9859.64	+	44587.2i	0.320891	+	1.45113i
$982$	−9476.03	+	7128.30i	−0.307935	+	0.231643i
$983$	−6384.53	−	11058.3i	−0.207157	−	0.358806i	0.743661	−	0.668557i	$-0.233088\pi$
$983$	−6384.53	−	11058.3i	−0.207157	−	0.358806i	−0.950818	+	0.309751i	$0.899754\pi$
$984$	−22958.5	−	14857.6i	−0.743792	−	0.481345i
$985$	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
$990$	−2916.42	+	1028.26i	−0.0936263	+	0.0330103i
$991$	−16360.6	−	28337.4i	−0.524433	−	0.908344i	−0.999595	−	0.0284459i	$-0.990944\pi$
$991$	−16360.6	−	28337.4i	−0.524433	−	0.908344i	0.475163	−	0.879898i	$-0.342389\pi$
$992$	−3649.56	+	2532.81i	−0.116808	+	0.0810652i
$993$	−4306.31	+	470.448i	−0.137620	+	0.0150345i
$994$	19276.9	+	36753.3i	0.615118	+	1.17278i
$995$	−5374.91			−0.171253
$996$	14220.3	−	5214.84i	0.452396	−	0.165902i
$997$	−4048.90	−	7012.90i	−0.128616	−	0.222769i	0.794525	−	0.607232i	$-0.207720\pi$
$997$	−4048.90	−	7012.90i	−0.128616	−	0.222769i	−0.923141	+	0.384463i	$0.874387\pi$
$998$	−15524.9	+	1893.06i	−0.492416	+	0.0600437i
$999$	−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.5.18	✓	176
3.2	odd	2	inner	168.4.ba.c.5.71	yes	176
7.3	odd	6	inner	168.4.ba.c.101.42	yes	176
8.5	even	2	inner	168.4.ba.c.5.47	yes	176
21.17	even	6	inner	168.4.ba.c.101.47	yes	176
24.5	odd	2	inner	168.4.ba.c.5.42	yes	176
56.45	odd	6	inner	168.4.ba.c.101.71	yes	176
168.101	even	6	inner	168.4.ba.c.101.18	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.ba.c.5.18	✓	176	1.1	even	1	trivial
168.4.ba.c.5.42	yes	176	24.5	odd	2	inner
168.4.ba.c.5.47	yes	176	8.5	even	2	inner
168.4.ba.c.5.71	yes	176	3.2	odd	2	inner
168.4.ba.c.101.18	yes	176	168.101	even	6	inner
168.4.ba.c.101.42	yes	176	7.3	odd	6	inner
168.4.ba.c.101.47	yes	176	21.17	even	6	inner
168.4.ba.c.101.71	yes	176	56.45	odd	6	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+(-2.26030 + 1.70030i) q^{2} +(4.19123 - 3.07141i) q^{3} +(2.21794 - 7.68640i) q^{4} +(-3.83548 - 2.21442i) q^{5} +(-4.25113 + 14.0687i) q^{6} +(-18.2781 - 2.98509i) q^{7} +(8.05600 + 21.1448i) q^{8} +(8.13288 - 25.7460i) q^{9} +(12.4345 - 1.51623i) q^{10} +(-4.57157 - 7.91819i) q^{11} +(-14.3122 - 39.0277i) q^{12} -69.6182 q^{13} +(46.3896 - 24.3311i) q^{14} +(-22.8768 + 2.49920i) q^{15} +(-54.1615 - 34.0959i) q^{16} +(57.1065 + 98.9113i) q^{17} +(25.3932 + 72.0221i) 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} +(98.7088 + 63.8794i) q^{24} +(-52.6927 - 91.2665i) q^{25} +(157.358 - 118.372i) q^{26} +(-44.9897 - 132.887i) q^{27} +(-63.4843 + 133.872i) q^{28} -170.605 q^{29} +(47.4591 - 44.5464i) q^{30} +(-21.2529 + 12.2703i) q^{31} +(180.395 - 15.0238i) q^{32} +(-43.4805 - 19.1458i) q^{33} +(-297.257 - 126.471i) q^{34} +(63.4951 + 51.9246i) q^{35} +(-179.856 - 119.616i) q^{36} +(-128.940 - 74.4434i) q^{37} +(-41.8876 - 343.519i) q^{38} +(-291.786 + 213.826i) q^{39} +(15.9247 - 98.9397i) q^{40} -232.589 q^{41} +(119.699 - 244.459i) q^{42} -330.977i q^{43} +(-71.0019 + 17.5769i) q^{44} +(-88.2059 + 80.7387i) q^{45} +(-56.6238 + 6.90454i) q^{46} +(118.864 - 205.878i) q^{47} +(-331.726 + 23.4482i) q^{48} +(325.178 + 109.124i) q^{49} +(274.282 + 116.696i) q^{50} +(543.144 + 239.163i) q^{51} +(-154.409 + 535.113i) q^{52} +(-165.999 - 287.519i) q^{53} +(327.638 + 223.868i) q^{54} +40.4935i q^{55} +(-84.1293 - 410.534i) q^{56} +(69.0434 + 631.998i) q^{57} +(385.618 - 290.079i) q^{58} +(-378.412 + 218.477i) q^{59} +(-31.5295 + 181.383i) 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} +(130.833 - 30.6547i) q^{66} +(-149.924 + 86.5586i) q^{67} +(886.931 - 219.564i) q^{68} +(104.175 - 11.3807i) q^{69} +(-231.806 - 9.40442i) q^{70} +792.275i q^{71} +(609.911 - 35.4418i) q^{72} +(952.933 - 550.176i) q^{73} +(418.019 - 50.9720i) q^{74} +(-501.164 - 220.678i) q^{75} +(678.764 + 705.234i) q^{76} +(59.9231 + 158.376i) q^{77} +(295.956 - 979.437i) q^{78} +(-517.761 + 896.789i) q^{79} +(132.233 + 250.711i) q^{80} +(-596.713 - 418.778i) q^{81} +(525.721 - 395.471i) q^{82} +364.364i q^{83} +(145.098 + 756.076i) q^{84} -505.830i q^{85} +(562.761 + 748.108i) q^{86} +(-715.043 + 523.996i) q^{87} +(130.600 - 160.454i) q^{88} +(475.732 - 823.992i) q^{89} +(62.0917 - 332.471i) q^{90} +(1272.49 + 207.817i) q^{91} +(116.247 - 111.884i) q^{92} +(-51.3884 + 116.704i) q^{93} +(81.3870 + 667.451i) q^{94} +(469.278 - 270.938i) q^{95} +(709.932 - 617.035i) q^{96} -538.631i q^{97} +(-920.545 + 306.249i) 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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