LMFDB - Embedded newform 72.4.l.b.11.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [72,4,Mod(11,72)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("72.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(72, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.24813752041$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	72.11
Dual form			72.4.l.b.59.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.81730 - 0.250612i) q^{2} +(2.93713 - 4.28640i) q^{3} +(7.87439 + 1.41210i) q^{4} +(3.52304 + 6.10209i) q^{5} +(-9.34902 + 11.3400i) q^{6} +(16.9049 + 9.76005i) q^{7} +(-21.8306 - 5.95172i) q^{8} +(-9.74649 - 25.1795i) q^{9} +(-8.39622 - 18.0744i) q^{10} +(11.8232 + 6.82610i) q^{11} +(29.1810 - 29.6053i) q^{12} +(55.8938 - 32.2703i) q^{13} +(-45.1802 - 31.7336i) q^{14} +(36.5037 + 2.82147i) q^{15} +(60.0120 + 22.2388i) q^{16} -47.8376i q^{17} +(21.1485 + 73.3808i) q^{18} +14.9265 q^{19} +(19.1251 + 53.0251i) q^{20} +(91.4874 - 43.7946i) q^{21} +(-31.5987 - 22.1942i) q^{22} +(-25.1060 - 43.4848i) q^{23} +(-89.6310 + 76.0939i) q^{24} +(37.6763 - 65.2573i) q^{25} +(-165.557 + 76.9075i) q^{26} +(-136.556 - 32.1781i) q^{27} +(119.334 + 100.726i) q^{28} +(-129.302 + 223.957i) q^{29} +(-102.135 - 17.0972i) q^{30} +(-108.559 + 62.6768i) q^{31} +(-163.499 - 77.6932i) q^{32} +(63.9856 - 30.6296i) q^{33} +(-11.9887 + 134.773i) q^{34} +137.540i q^{35} +(-41.1917 - 212.036i) q^{36} +208.987i q^{37} +(-42.0526 - 3.74077i) q^{38} +(25.8441 - 334.365i) q^{39} +(-40.5924 - 154.181i) q^{40} +(411.520 - 237.591i) q^{41} +(-268.723 + 100.455i) q^{42} +(-178.732 + 309.573i) q^{43} +(83.4610 + 70.4468i) q^{44} +(119.310 - 148.182i) q^{45} +(59.8333 + 128.802i) q^{46} +(-156.128 + 270.422i) q^{47} +(271.588 - 191.917i) q^{48} +(19.0170 + 32.9384i) q^{49} +(-122.500 + 174.407i) q^{50} +(-205.051 - 140.506i) q^{51} +(485.698 - 175.181i) q^{52} +476.697 q^{53} +(376.656 + 124.878i) q^{54} +96.1946i q^{55} +(-310.956 - 313.681i) q^{56} +(43.8413 - 63.9812i) q^{57} +(420.409 - 598.551i) q^{58} +(-425.920 + 245.905i) q^{59} +(283.460 + 73.7642i) q^{60} +(-661.465 - 381.897i) q^{61} +(321.552 - 149.373i) q^{62} +(80.9894 - 520.783i) q^{63} +(441.154 + 259.860i) q^{64} +(393.832 + 227.379i) q^{65} +(-187.943 + 70.2574i) q^{66} +(277.112 + 479.972i) q^{67} +(67.5514 - 376.692i) q^{68} +(-260.133 - 20.1064i) q^{69} +(34.4692 - 387.493i) q^{70} -87.1038 q^{71} +(62.9109 + 607.693i) q^{72} -818.083 q^{73} +(52.3747 - 588.780i) q^{74} +(-169.059 - 353.165i) q^{75} +(117.537 + 21.0778i) q^{76} +(133.246 + 230.789i) q^{77} +(-156.606 + 935.531i) q^{78} +(-1030.34 - 594.866i) q^{79} +(75.7214 + 444.547i) q^{80} +(-539.012 + 490.823i) q^{81} +(-1218.92 + 566.235i) q^{82} +(400.564 + 231.266i) q^{83} +(782.250 - 215.667i) q^{84} +(291.910 - 168.534i) q^{85} +(581.125 - 827.369i) q^{86} +(580.194 + 1212.03i) q^{87} +(-217.480 - 219.386i) q^{88} -1047.78i q^{89} +(-373.269 + 387.574i) q^{90} +1259.84 q^{91} +(-136.289 - 377.868i) q^{92} +(-50.1955 + 649.419i) q^{93} +(507.631 - 722.732i) q^{94} +(52.5869 + 91.0831i) q^{95} +(-813.241 + 472.625i) q^{96} +(-562.907 + 974.983i) q^{97} +(-45.3219 - 97.5633i) q^{98} +(56.6434 - 364.231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27}+ \cdots - 2118 q^{99}+O(q^{100}) $ 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.81730	−	0.250612i	−0.996067	−	0.0886047i
$2$	−2.81730	−	0.250612i	−0.996067	−	0.0886047i
$3$	2.93713	−	4.28640i	0.565252	−	0.824919i
$3$	2.93713	−	4.28640i	0.565252	−	0.824919i
$4$	7.87439	+	1.41210i	0.984298	+	0.176512i
$5$	3.52304	+	6.10209i	0.315111	+	0.545788i	0.979461	−	0.201634i	$-0.0646250\pi$
$5$	3.52304	+	6.10209i	0.315111	+	0.545788i	−0.664350	+	0.747421i	$0.731292\pi$
$6$	−9.34902	+	11.3400i	−0.636120	+	0.771590i
$7$	16.9049	+	9.76005i	0.912779	+	0.526993i	0.881324	−	0.472512i	$-0.156653\pi$
$7$	16.9049	+	9.76005i	0.912779	+	0.526993i	0.0314545	+	0.999505i	$0.489986\pi$
$8$	−21.8306	−	5.95172i	−0.964787	−	0.263031i
$9$	−9.74649	−	25.1795i	−0.360981	−	0.932573i
$10$	−8.39622	−	18.0744i	−0.265512	−	0.571561i
$11$	11.8232	+	6.82610i	0.324074	+	0.187104i	0.653207	−	0.757179i	$-0.273423\pi$
$11$	11.8232	+	6.82610i	0.324074	+	0.187104i	−0.329133	+	0.944284i	$0.606756\pi$
$12$	29.1810	−	29.6053i	0.701985	−	0.712192i
$13$	55.8938	−	32.2703i	1.19247	−	0.688474i	0.233606	−	0.972331i	$-0.424947\pi$
$13$	55.8938	−	32.2703i	1.19247	−	0.688474i	0.958867	+	0.283857i	$0.0916141\pi$
$14$	−45.1802	−	31.7336i	−0.862494	−	0.605797i
$15$	36.5037	+	2.82147i	0.628347	+	0.0485668i
$16$	60.0120	+	22.2388i	0.937687	+	0.347482i
$17$		−	47.8376i		−	0.682490i	−0.939974	−	0.341245i	$-0.889151\pi$
$17$		−	47.8376i		−	0.682490i	0.939974	−	0.341245i	$-0.110849\pi$
$18$	21.1485	+	73.3808i	0.276931	+	0.960890i
$19$	14.9265			0.180231			0.0901154	−	0.995931i	$-0.471276\pi$
$19$	14.9265			0.180231			0.0901154	+	0.995931i	$0.471276\pi$
$20$	19.1251	+	53.0251i	0.213825	+	0.592839i
$21$	91.4874	−	43.7946i	0.950676	−	0.455084i
$22$	−31.5987	−	22.1942i	−0.306221	−	0.215083i
$23$	−25.1060	−	43.4848i	−0.227607	−	0.394226i	0.729492	−	0.683990i	$-0.239757\pi$
$23$	−25.1060	−	43.4848i	−0.227607	−	0.394226i	−0.957098	+	0.289763i	$0.906423\pi$
$24$	−89.6310	+	76.0939i	−0.762327	+	0.647192i
$25$	37.6763	−	65.2573i	0.301411	−	0.522058i
$26$	−165.557	+	76.9075i	−1.24878	+	0.580108i
$27$	−136.556	−	32.1781i	−0.973342	−	0.229359i
$28$	119.334	+	100.726i	0.805426	+	0.679835i
$29$	−129.302	+	223.957i	−0.827956	+	1.43406i	0.0716823	+	0.997428i	$0.477163\pi$
$29$	−129.302	+	223.957i	−0.827956	+	1.43406i	−0.899639	+	0.436635i	$0.856170\pi$
$30$	−102.135	−	17.0972i	−0.621572	−	0.104050i
$31$	−108.559	+	62.6768i	−0.628962	+	0.363132i	−0.780350	−	0.625343i	$-0.784959\pi$
$31$	−108.559	+	62.6768i	−0.628962	+	0.363132i	0.151388	+	0.988474i	$0.451626\pi$
$32$	−163.499	−	77.6932i	−0.903210	−	0.429198i
$33$	63.9856	−	30.6296i	0.337529	−	0.161574i
$34$	−11.9887	+	134.773i	−0.0604718	+	0.679806i
$35$			137.540i			0.664244i
$36$	−41.1917	−	212.036i	−0.190702	−	0.981648i
$37$			208.987i			0.928576i	0.885684	+	0.464288i	$0.153690\pi$
$37$			208.987i			0.928576i	−0.885684	+	0.464288i	$0.846310\pi$
$38$	−42.0526	−	3.74077i	−0.179522	−	0.0159693i
$39$	25.8441	−	334.365i	0.106112	−	1.37285i
$40$	−40.5924	−	154.181i	−0.160455	−	0.609453i
$41$	411.520	−	237.591i	1.56753	−	0.905013i	0.571073	−	0.820900i	$-0.306527\pi$
$41$	411.520	−	237.591i	1.56753	−	0.905013i	0.996456	−	0.0841137i	$-0.0268059\pi$
$42$	−268.723	+	100.455i	−0.987259	+	0.369060i
$43$	−178.732	+	309.573i	−0.633870	+	1.09789i	0.352884	+	0.935667i	$0.385201\pi$
$43$	−178.732	+	309.573i	−0.633870	+	1.09789i	−0.986753	+	0.162228i	$0.948132\pi$
$44$	83.4610	+	70.4468i	0.285959	+	0.241369i
$45$	119.310	−	148.182i	0.395238	−	0.490883i
$46$	59.8333	+	128.802i	0.191781	+	0.412843i
$47$	−156.128	+	270.422i	−0.484545	+	0.839256i	−0.999842	−	0.0177550i	$-0.994348\pi$
$47$	−156.128	+	270.422i	−0.484545	+	0.839256i	0.515297	+	0.857011i	$0.327681\pi$
$48$	271.588	−	191.917i	0.816673	−	0.577101i
$49$	19.0170	+	32.9384i	0.0554431	+	0.0960303i
$50$	−122.500	+	174.407i	−0.346482	+	0.493299i
$51$	−205.051	−	140.506i	−0.562999	−	0.385779i
$52$	485.698	−	175.181i	1.29527	−	0.467178i
$53$	476.697			1.23546			0.617729	−	0.786391i	$-0.288053\pi$
$53$	476.697			1.23546			0.617729	+	0.786391i	$0.288053\pi$
$54$	376.656	+	124.878i	0.949191	+	0.314699i
$55$			96.1946i			0.235834i
$56$	−310.956	−	313.681i	−0.742021	−	0.748526i
$57$	43.8413	−	63.9812i	0.101876	−	0.148676i
$58$	420.409	−	598.551i	0.951765	−	1.35506i
$59$	−425.920	+	245.905i	−0.939831	+	0.542612i	−0.889907	−	0.456141i	$-0.849231\pi$
$59$	−425.920	+	245.905i	−0.939831	+	0.542612i	−0.0499237	+	0.998753i	$0.515898\pi$
$60$	283.460	+	73.7642i	0.609908	+	0.158715i
$61$	−661.465	−	381.897i	−1.38839	−	0.801589i	−0.395259	−	0.918570i	$-0.629345\pi$
$61$	−661.465	−	381.897i	−1.38839	−	0.801589i	−0.993134	+	0.116981i	$0.962678\pi$
$62$	321.552	−	149.373i	0.658664	−	0.305974i
$63$	80.9894	−	520.783i	0.161964	−	1.04147i
$64$	441.154	+	259.860i	0.861629	+	0.507539i
$65$	393.832	+	227.379i	0.751521	+	0.433891i
$66$	−187.943	+	70.2574i	−0.350518	+	0.131032i
$67$	277.112	+	479.972i	0.505293	+	0.875193i	0.999981	+	0.00612269i	$0.00194893\pi$
$67$	277.112	+	479.972i	0.505293	+	0.875193i	−0.494688	+	0.869071i	$0.664718\pi$
$68$	67.5514	−	376.692i	0.120468	−	0.671774i
$69$	−260.133	−	20.1064i	−0.453860	−	0.0350801i
$70$	34.4692	−	387.493i	0.0588551	−	0.661632i
$71$	−87.1038			−0.145596			−0.0727980	−	0.997347i	$-0.523193\pi$
$71$	−87.1038			−0.145596			−0.0727980	+	0.997347i	$0.523193\pi$
$72$	62.9109	+	607.693i	0.102974	+	0.994684i
$73$	−818.083			−1.31164			−0.655818	−	0.754919i	$-0.727676\pi$
$73$	−818.083			−1.31164			−0.655818	+	0.754919i	$0.727676\pi$
$74$	52.3747	−	588.780i	0.0822761	−	0.924923i
$75$	−169.059	−	353.165i	−0.260283	−	0.543734i
$76$	117.537	+	21.0778i	0.177401	+	0.0318129i
$77$	133.246	+	230.789i	0.197205	+	0.341569i
$78$	−156.606	+	935.531i	−0.227336	+	1.35805i
$79$	−1030.34	−	594.866i	−1.46737	−	0.847186i	−0.468036	−	0.883710i	$-0.655038\pi$
$79$	−1030.34	−	594.866i	−1.46737	−	0.847186i	−0.999333	+	0.0365241i	$0.988371\pi$
$80$	75.7214	+	444.547i	0.105824	+	0.621273i
$81$	−539.012	+	490.823i	−0.739385	+	0.673283i
$82$	−1218.92	+	566.235i	−1.64155	+	0.762563i
$83$	400.564	+	231.266i	0.529730	+	0.305840i	0.740907	−	0.671608i	$-0.234396\pi$
$83$	400.564	+	231.266i	0.529730	+	0.305840i	−0.211176	+	0.977448i	$0.567729\pi$
$84$	782.250	−	215.667i	1.01608	−	0.280133i
$85$	291.910	−	168.534i	0.372495	−	0.215060i
$86$	581.125	−	827.369i	0.728655	−	1.03741i
$87$	580.194	+	1212.03i	0.714981	+	1.49360i
$88$	−217.480	−	219.386i	−0.263448	−	0.265757i
$89$		−	1047.78i		−	1.24791i	−0.781459	−	0.623956i	$-0.785524\pi$
$89$		−	1047.78i		−	1.24791i	0.781459	−	0.623956i	$-0.214476\pi$
$90$	−373.269	+	387.574i	−0.437178	+	0.453932i
$91$	1259.84			1.45128
$92$	−136.289	−	377.868i	−0.154447	−	0.428212i
$93$	−50.1955	+	649.419i	−0.0559680	+	0.724103i
$94$	507.631	−	722.732i	0.557001	−	0.793022i
$95$	52.5869	+	91.0831i	0.0567926	+	0.0983677i
$96$	−813.241	+	472.625i	−0.864595	+	0.502470i
$97$	−562.907	+	974.983i	−0.589222	+	1.02056i	0.405113	+	0.914267i	$0.367232\pi$
$97$	−562.907	+	974.983i	−0.589222	+	1.02056i	−0.994335	+	0.106296i	$0.966101\pi$
$98$	−45.3219	−	97.5633i	−0.0467163	−	0.100565i
$99$	56.6434	−	364.231i	0.0575038	−	0.369764i
$100$	388.828	−	460.659i	0.388828	−	0.460659i
$101$	−312.444	+	541.170i	−0.307816	+	0.533152i	−0.977884	−	0.209147i	$-0.932931\pi$
$101$	−312.444	+	541.170i	−0.307816	+	0.533152i	0.670069	+	0.742299i	$0.266265\pi$
$102$	542.479	+	447.235i	0.526602	+	0.434146i
$103$	135.960	−	78.4965i	0.130063	−	0.0750922i	−0.433557	−	0.901126i	$-0.642742\pi$
$103$	135.960	−	78.4965i	0.130063	−	0.0750922i	0.563620	+	0.826034i	$0.309408\pi$
$104$	−1412.26	+	371.817i	−1.33157	+	0.350573i
$105$	589.553	+	403.974i	0.547947	+	0.375465i
$106$	−1343.00	−	119.466i	−1.23060	−	0.109467i
$107$		−	420.449i		−	0.379872i	−0.981796	−	0.189936i	$-0.939172\pi$
$107$		−	420.449i		−	0.379872i	0.981796	−	0.189936i	$-0.0608280\pi$
$108$	−1029.86	−	446.214i	−0.917574	−	0.397564i
$109$		−	1217.23i		−	1.06963i	−0.844969	−	0.534815i	$-0.820381\pi$
$109$		−	1217.23i		−	1.06963i	0.844969	−	0.534815i	$-0.179619\pi$
$110$	24.1075	−	271.009i	0.0208960	−	0.234907i
$111$	895.803	+	613.824i	0.765999	+	0.524879i
$112$	797.444	+	961.664i	0.672780	+	0.811328i
$113$	303.893	−	175.453i	0.252990	−	0.146064i	−0.368143	−	0.929769i	$-0.620006\pi$
$113$	303.893	−	175.453i	0.252990	−	0.146064i	0.621132	+	0.783706i	$0.286673\pi$
$114$	−139.549	+	169.267i	−0.114648	+	0.139064i
$115$	176.899	−	306.398i	0.143443	−	0.248450i
$116$	−1334.42	+	1580.94i	−1.06809	+	1.26540i
$117$	−1357.32	−	1092.85i	−1.07251	−	0.863542i
$118$	1261.57	−	586.048i	0.984212	−	0.457204i
$119$	466.897	−	808.690i	0.359667	−	0.622962i
$120$	−780.106	−	278.854i	−0.593447	−	0.212132i
$121$	−572.309	−	991.268i	−0.429984	−	0.744754i
$122$	1767.84	+	1241.69i	1.31191	+	0.921454i
$123$	190.278	−	2461.78i	0.139486	−	1.80464i
$124$	−943.344	+	340.245i	−0.683184	+	0.246410i
$125$	1411.70			1.01013
$126$	−358.686	+	1446.91i	−0.253605	+	1.02302i
$127$			2003.55i			1.39989i	0.714195	+	0.699947i	$0.246793\pi$
$127$			2003.55i			1.39989i	−0.714195	+	0.699947i	$0.753207\pi$
$128$	−1177.74	−	842.662i	−0.813270	−	0.581887i
$129$	801.995	+	1675.38i	0.547378	+	1.14348i
$130$	−1052.56	−	739.295i	−0.710121	−	0.498773i
$131$	−967.023	+	558.311i	−0.644956	+	0.372365i	−0.786521	−	0.617564i	$-0.788120\pi$
$131$	−967.023	+	558.311i	−0.644956	+	0.372365i	0.141565	+	0.989929i	$0.454786\pi$
$132$	547.099	−	150.836i	0.360749	−	0.0994587i
$133$	252.332	+	145.684i	0.164511	+	0.0949803i
$134$	−660.422	−	1421.67i	−0.425759	−	0.916522i
$135$	−284.739	−	946.643i	−0.181529	−	0.603511i
$136$	−284.716	+	1044.33i	−0.179516	+	0.658458i
$137$	562.186	+	324.578i	0.350590	+	0.202413i	0.664945	−	0.746892i	$-0.268455\pi$
$137$	562.186	+	324.578i	0.350590	+	0.202413i	−0.314355	+	0.949305i	$0.601788\pi$
$138$	727.834	+	121.838i	0.448966	+	0.0751563i
$139$	−535.022	−	926.685i	−0.326475	−	0.565471i	0.655335	−	0.755338i	$-0.272527\pi$
$139$	−535.022	−	926.685i	−0.326475	−	0.565471i	−0.981810	+	0.189868i	$0.939194\pi$
$140$	−194.220	+	1083.05i	−0.117247	+	0.653815i
$141$	700.567	+	1463.49i	0.418428	+	0.874101i
$142$	245.398	+	21.8292i	0.145023	+	0.0129005i
$143$	881.121			0.515266
$144$	−24.9440	−	1727.82i	−0.0144352	−	0.999896i
$145$	−1822.14			−1.04359
$146$	2304.79	+	205.021i	1.30648	+	0.116217i
$147$	197.043	+	15.2300i	0.110557	+	0.00854523i
$148$	−295.111	+	1645.65i	−0.163905	+	0.913995i
$149$	−296.044	−	512.764i	−0.162771	−	0.281928i	0.773090	−	0.634296i	$-0.218710\pi$
$149$	−296.044	−	512.764i	−0.162771	−	0.281928i	−0.935862	+	0.352368i	$0.885377\pi$
$150$	387.782	+	1037.34i	0.211082	+	0.564657i
$151$	1813.60	+	1047.08i	0.977411	+	0.564308i	0.901487	−	0.432805i	$-0.142476\pi$
$151$	1813.60	+	1047.08i	0.977411	+	0.564308i	0.0759232	+	0.997114i	$0.475810\pi$
$152$	−325.856	−	88.8387i	−0.173884	−	0.0474064i
$153$	−1204.53	+	466.249i	−0.636472	+	0.246366i
$154$	−317.556	−	683.596i	−0.166165	−	0.357699i
$155$	−764.918	−	441.626i	−0.396385	−	0.228853i
$156$	675.663	−	2596.43i	0.346771	−	1.33257i
$157$	122.949	−	70.9848i	0.0624995	−	0.0360841i	−0.468425	−	0.883503i	$-0.655178\pi$
$157$	122.949	−	70.9848i	0.0624995	−	0.0360841i	0.530924	+	0.847419i	$0.321845\pi$
$158$	2753.69	+	1934.13i	1.38653	+	0.973869i
$159$	1400.12	−	2043.31i	0.698345	−	1.01915i
$160$	−101.922	−	1271.40i	−0.0503600	−	0.628206i
$161$		−	980.141i		−	0.479789i
$162$	1641.57	−	1247.71i	0.796133	−	0.605121i
$163$	3642.04			1.75010			0.875051	−	0.484031i	$-0.160828\pi$
$163$	3642.04			1.75010			0.875051	+	0.484031i	$0.160828\pi$
$164$	3575.97	−	1289.78i	1.70266	−	0.614115i
$165$	412.329	+	282.536i	0.194544	+	0.133306i
$166$	−1070.55	−	751.931i	−0.500548	−	0.351573i
$167$	−1424.28	−	2466.93i	−0.659966	−	1.14310i	−0.980624	−	0.195900i	$-0.937237\pi$
$167$	−1424.28	−	2466.93i	−0.659966	−	1.14310i	0.320657	−	0.947195i	$-0.396096\pi$
$168$	−2257.88	+	411.557i	−1.03690	+	0.189002i
$169$	984.242	−	1704.76i	0.447994	−	0.775948i
$170$	−864.634	+	401.655i	−0.390085	+	0.181209i
$171$	−145.481	−	375.843i	−0.0650599	−	0.168078i
$172$	−1844.55	+	2185.31i	−0.817709	+	0.968770i
$173$	11.9219	−	20.6493i	0.00523934	−	0.00907480i	−0.863394	−	0.504531i	$-0.831666\pi$
$173$	11.9219	−	20.6493i	0.00523934	−	0.00907480i	0.868633	+	0.495456i	$0.164999\pi$
$174$	−1330.83	−	3560.06i	−0.579829	−	1.55108i
$175$	1273.83	−	735.445i	0.550242	−	0.317683i
$176$	557.726	+	672.581i	0.238865	+	0.288055i
$177$	−196.936	+	2547.92i	−0.0836306	+	1.08200i
$178$	−262.585	+	2951.91i	−0.110571	+	1.24300i
$179$			1944.64i			0.812009i	0.913871	+	0.406004i	$0.133078\pi$
$179$			1944.64i			0.812009i	−0.913871	+	0.406004i	$0.866922\pi$
$180$	1148.74	−	998.368i	0.475679	−	0.413411i
$181$		−	27.6647i		−	0.0113608i	−0.999984	−	0.00568039i	$-0.998192\pi$
$181$		−	27.6647i		−	0.0113608i	0.999984	−	0.00568039i	$-0.00180813\pi$
$182$	−3549.34	−	315.730i	−1.44558	−	0.128591i
$183$	−3579.78	+	1713.62i	−1.44604	+	0.692211i
$184$	289.270	+	1098.72i	0.115898	+	0.440212i
$185$	−1275.26	+	736.271i	−0.506805	+	0.292604i
$186$	304.168	−	1817.03i	0.119907	−	0.716296i
$187$	326.544	−	565.592i	0.127697	−	0.221177i
$188$	−1611.27	+	1908.94i	−0.625076	+	0.740551i
$189$	−1994.41	−	1876.76i	−0.767575	−	0.722298i
$190$	−125.327	−	269.788i	−0.0478534	−	0.103013i
$191$	−1586.02	+	2747.07i	−0.600840	+	1.04069i	0.391854	+	0.920027i	$0.371834\pi$
$191$	−1586.02	+	2747.07i	−0.600840	+	1.04069i	−0.992694	+	0.120658i	$0.961500\pi$
$192$	2409.59	−	1127.72i	0.905715	−	0.423886i
$193$	221.041	+	382.854i	0.0824398	+	0.142790i	0.904297	−	0.426903i	$-0.140395\pi$
$193$	221.041	+	382.854i	0.0824398	+	0.142790i	−0.821858	+	0.569693i	$0.807062\pi$
$194$	1830.22	−	2605.75i	0.677331	−	0.964341i
$195$	2131.38	−	1020.28i	0.782724	−	0.374686i
$196$	103.235	+	286.224i	0.0376221	+	0.104309i
$197$	−3084.07			−1.11539			−0.557693	−	0.830047i	$-0.688313\pi$
$197$	−3084.07			−1.11539			−0.557693	+	0.830047i	$0.688313\pi$
$198$	−250.862	+	1011.95i	−0.0900404	+	0.363214i
$199$			1784.15i			0.635555i	0.948165	+	0.317777i	$0.102936\pi$
$199$			1784.15i			0.635555i	−0.948165	+	0.317777i	$0.897064\pi$
$200$	−1210.89	+	1200.37i	−0.428115	+	0.424395i
$201$	2871.27	+	221.929i	1.00758	+	0.0778788i
$202$	1015.87	−	1446.34i	0.353845	−	0.503781i
$203$	−4371.67	+	2523.98i	−1.51148	+	0.872654i
$204$	−1416.25	−	1395.95i	−0.486064	−	0.479097i
$205$	2899.61	+	1674.09i	0.987890	+	0.570359i
$206$	−402.712	+	187.075i	−0.136205	+	0.0632726i
$207$	−850.229	+	1055.98i	−0.285483	+	0.354568i
$208$	4071.95	−	693.591i	1.35740	−	0.231211i
$209$	176.479	+	101.890i	0.0584081	+	0.0337219i
$210$	−1559.71	−	1285.87i	−0.512524	−	0.422539i
$211$	734.854	+	1272.80i	0.239760	+	0.415277i	0.960645	−	0.277777i	$-0.0895978\pi$
$211$	734.854	+	1272.80i	0.239760	+	0.415277i	−0.720885	+	0.693055i	$0.756264\pi$
$212$	3753.69	+	673.143i	1.21606	+	0.218074i
$213$	−255.835	+	373.362i	−0.0822984	+	0.120105i
$214$	−105.369	+	1184.53i	−0.0336584	+	0.378378i
$215$	−2518.73			−0.798956
$216$	2789.59	+	1515.21i	0.878739	+	0.477302i
$217$	−2446.91			−0.765471
$218$	−305.053	+	3429.31i	−0.0947743	+	1.06542i
$219$	−2402.82	+	3506.63i	−0.741404	+	1.08199i
$220$	−135.836	+	757.474i	−0.0416276	+	0.232131i
$221$	−1543.73	−	2673.83i	−0.469877	−	0.813850i
$222$	−2369.92	−	1953.83i	−0.716480	−	0.590686i
$223$	−1047.05	−	604.513i	−0.314419	−	0.181530i	0.334483	−	0.942402i	$-0.391438\pi$
$223$	−1047.05	−	604.513i	−0.314419	−	0.181530i	−0.648902	+	0.760872i	$0.724772\pi$
$224$	−2005.64	−	2909.15i	−0.598246	−	0.867748i
$225$	−2010.36	−	312.640i	−0.595661	−	0.0926342i
$226$	−900.128	+	418.144i	−0.264937	+	0.123073i
$227$	1946.40	+	1123.76i	0.569107	+	0.328574i	0.756793	−	0.653655i	$-0.226765\pi$
$227$	1946.40	+	1123.76i	0.569107	+	0.328574i	−0.187686	+	0.982229i	$0.560099\pi$
$228$	435.571	−	441.904i	0.126519	−	0.128359i
$229$	663.668	−	383.169i	0.191513	−	0.110570i	−0.401178	−	0.916000i	$-0.631399\pi$
$229$	663.668	−	383.169i	0.191513	−	0.110570i	0.592691	+	0.805430i	$0.298066\pi$
$230$	−575.164	+	818.882i	−0.164892	+	0.234763i
$231$	1380.62	+	106.712i	0.393238	+	0.0303945i
$232$	4155.67	−	4119.56i	1.17601	−	1.16579i
$233$		−	801.184i		−	0.225267i	−0.993637	−	0.112634i	$-0.964071\pi$
$233$		−	801.184i		−	0.225267i	0.993637	−	0.112634i	$-0.0359287\pi$
$234$	3550.09	+	3419.06i	0.991780	+	0.955175i
$235$	−2200.18			−0.610741
$236$	−3701.10	+	1334.91i	−1.02085	+	0.368200i
$237$	−5576.08	+	2669.24i	−1.52829	+	0.731586i
$238$	−1518.06	+	2161.31i	−0.413450	+	0.588644i
$239$	−3032.68	−	5252.75i	−0.820785	−	1.42164i	−0.905098	−	0.425203i	$-0.860203\pi$
$239$	−3032.68	−	5252.75i	−0.820785	−	1.42164i	0.0843128	−	0.996439i	$-0.473130\pi$
$240$	2127.91	+	981.121i	0.572317	+	0.263879i
$241$	2629.87	−	4555.07i	0.702924	−	1.21750i	−0.264511	−	0.964383i	$-0.585211\pi$
$241$	2629.87	−	4555.07i	0.702924	−	1.21750i	0.967435	−	0.253118i	$-0.0814560\pi$
$242$	1363.94	+	2936.13i	0.362304	+	0.779924i
$243$	520.715	+	3752.03i	0.137464	+	0.990507i
$244$	−4669.36	−	3941.26i	−1.22510	−	1.03407i
$245$	−133.995	+	232.087i	−0.0349414	+	0.0605203i
$246$	−1153.02	+	6887.89i	−0.298837	+	1.78519i
$247$	834.301	−	481.684i	0.214920	−	0.124084i
$248$	2742.95	−	722.159i	0.702330	−	0.184908i
$249$	2167.81	−	1037.72i	0.551724	−	0.264108i
$250$	−3977.19	−	353.789i	−1.00616	−	0.0895024i
$251$		−	2860.56i		−	0.719350i	−0.933078	−	0.359675i	$-0.882888\pi$
$251$		−	2860.56i		−	0.719350i	0.933078	−	0.359675i	$-0.117112\pi$
$252$	1373.14	−	3986.48i	0.343252	−	0.996526i
$253$		−	685.503i		−	0.170345i
$254$	502.114	−	5644.61i	0.124037	−	1.39439i
$255$	134.973	−	1746.25i	0.0331463	−	0.428841i
$256$	3106.87	+	2669.19i	0.758513	+	0.651658i
$257$	586.357	−	338.534i	0.142319	−	0.0821679i	−0.427150	−	0.904181i	$-0.640482\pi$
$257$	586.357	−	338.534i	0.142319	−	0.0821679i	0.569469	+	0.822013i	$0.307149\pi$
$258$	−1839.59	−	4921.03i	−0.443907	−	1.18748i
$259$	−2039.73	+	3532.91i	−0.489353	+	0.847584i
$260$	2780.11	+	2346.60i	0.663134	+	0.559731i
$261$	6899.36	+	1072.95i	1.63624	+	0.254460i
$262$	2864.32	−	1330.58i	0.675412	−	0.313755i
$263$	579.488	−	1003.70i	0.135866	−	0.235327i	−0.790062	−	0.613027i	$-0.789952\pi$
$263$	579.488	−	1003.70i	0.135866	−	0.235327i	0.925928	+	0.377700i	$0.123285\pi$
$264$	−1579.15	+	287.840i	−0.368143	+	0.0671035i
$265$	1679.42	+	2908.85i	0.389306	+	0.674298i
$266$	−674.385	−	473.673i	−0.155448	−	0.109183i
$267$	−4491.20	−	3077.46i	−1.02943	−	0.705385i
$268$	1504.32	+	4170.80i	0.342877	+	0.950642i
$269$	7718.35			1.74943			0.874714	−	0.484640i	$-0.161049\pi$
$269$	7718.35			1.74943			0.874714	+	0.484640i	$0.161049\pi$
$270$	564.957	+	2738.34i	0.127341	+	0.617222i
$271$		−	3568.10i		−	0.799804i	−0.916558	−	0.399902i	$-0.869044\pi$
$271$		−	3568.10i		−	0.799804i	0.916558	−	0.399902i	$-0.130956\pi$
$272$	1063.85	−	2870.83i	0.237153	−	0.639962i
$273$	3700.31	−	5400.17i	0.820341	−	1.19719i
$274$	−1502.51	−	1055.33i	−0.331276	−	0.232681i
$275$	890.906	−	514.365i	0.195359	−	0.112790i
$276$	−2020.00	−	525.659i	−0.440541	−	0.114641i
$277$	4007.48	+	2313.72i	0.869265	+	0.501870i	0.867104	−	0.498128i	$-0.165979\pi$
$277$	4007.48	+	2313.72i	0.869265	+	0.501870i	0.00216082	+	0.999998i	$0.499312\pi$
$278$	1275.08	+	2744.84i	0.275087	+	0.592174i
$279$	2636.24	+	2122.59i	0.565690	+	0.455470i
$280$	818.602	−	3002.59i	0.174717	−	0.640854i
$281$	2505.78	+	1446.71i	0.531966	+	0.307131i	0.741817	−	0.670603i	$-0.233964\pi$
$281$	2505.78	+	1446.71i	0.531966	+	0.307131i	−0.209851	+	0.977733i	$0.567298\pi$
$282$	−1606.94	−	4298.67i	−0.339333	−	0.907738i
$283$	−4140.78	−	7172.04i	−0.869766	−	1.50648i	−0.862235	−	0.506508i	$-0.830936\pi$
$283$	−4140.78	−	7172.04i	−0.869766	−	1.50648i	−0.00753096	−	0.999972i	$-0.502397\pi$
$284$	−685.889	−	122.999i	−0.143310	−	0.0256995i
$285$	544.874	+	42.1149i	0.113247	+	0.00875323i
$286$	−2482.38	−	220.819i	−0.513239	−	0.0456550i
$287$	9275.61			1.90774
$288$	−362.737	+	4874.04i	−0.0742170	+	0.997242i
$289$	2624.56			0.534207
$290$	5133.53	+	456.651i	1.03949	+	0.0924671i
$291$	2525.84	+	5276.50i	0.508822	+	1.06293i
$292$	−6441.91	−	1155.21i	−1.29104	−	0.231520i
$293$	1863.44	+	3227.58i	0.371548	+	0.643540i	0.989804	−	0.142437i	$-0.0454937\pi$
$293$	1863.44	+	3227.58i	0.371548	+	0.643540i	−0.618256	+	0.785977i	$0.712160\pi$
$294$	−551.312	−	92.2887i	−0.109365	−	0.0183074i
$295$	−3001.07	−	1732.67i	−0.592301	−	0.341965i
$296$	1243.83	−	4562.33i	0.244245	−	0.895878i
$297$	−1394.87	−	1312.59i	−0.272521	−	0.256446i
$298$	705.542	+	1518.80i	0.137151	+	0.295241i
$299$	−2806.53	−	1620.35i	−0.542830	−	0.313403i
$300$	−832.529	−	3019.69i	−0.160220	−	0.581139i
$301$	−6042.90	+	3488.87i	−1.15717	+	0.668090i
$302$	−4847.06	−	3404.46i	−0.923566	−	0.648692i
$303$	1401.98	+	2928.75i	0.265814	+	0.555288i
$304$	895.771	+	331.949i	0.169000	+	0.0626269i
$305$		−	5381.76i		−	1.01036i
$306$	3510.36	−	1011.70i	0.655798	−	0.189003i
$307$	1481.74			0.275464			0.137732	−	0.990470i	$-0.456019\pi$
$307$	1481.74			0.275464			0.137732	+	0.990470i	$0.456019\pi$
$308$	723.335	+	2005.48i	0.133818	+	0.371015i
$309$	62.8649	−	813.334i	0.0115737	−	0.149738i
$310$	2044.33	+	1435.89i	0.374549	+	0.263075i
$311$	3974.58	+	6884.18i	0.724688	+	1.25520i	0.959102	+	0.283059i	$0.0913492\pi$
$311$	3974.58	+	6884.18i	0.724688	+	1.25520i	−0.234415	+	0.972137i	$0.575317\pi$
$312$	−2554.24	+	7145.59i	−0.463479	+	1.29660i
$313$	1570.79	−	2720.69i	0.283663	−	0.491318i	−0.688621	−	0.725121i	$-0.741784\pi$
$313$	1570.79	−	2720.69i	0.283663	−	0.491318i	0.972284	+	0.233803i	$0.0751170\pi$
$314$	−364.175	+	169.173i	−0.0654509	+	0.0304044i
$315$	3463.19	−	1340.53i	0.619456	−	0.239780i
$316$	−7273.27	−	6139.14i	−1.29479	−	1.09289i
$317$	−954.296	+	1652.89i	−0.169081	+	0.292856i	−0.938097	−	0.346373i	$-0.887413\pi$
$317$	−954.296	+	1652.89i	−0.169081	+	0.292856i	0.769016	+	0.639229i	$0.220747\pi$
$318$	−4456.64	+	5405.75i	−0.785900	+	0.953268i
$319$	−3057.51	+	1765.25i	−0.536638	+	0.309828i
$320$	−31.4839	+	3607.46i	−0.00550001	+	0.630197i
$321$	−1802.21	−	1234.91i	−0.313363	−	0.214723i
$322$	−245.635	+	2761.35i	−0.0425115	+	0.477902i
$323$		−	714.050i		−	0.123006i
$324$	−4937.48	+	3103.79i	−0.846618	+	0.532200i
$325$		−	4863.30i		−	0.830054i
$326$	−10260.7	−	912.738i	−1.74322	−	0.155067i
$327$	−5217.55	−	3575.18i	−0.882358	−	0.604611i
$328$	−10397.8	+	2737.52i	−1.75038	+	0.460836i
$329$	−5278.65	+	3047.63i	−0.884564	+	0.510703i
$330$	−1090.85	−	899.325i	−0.181967	−	0.150019i
$331$	−3378.13	+	5851.10i	−0.560964	+	0.971618i	0.436449	+	0.899729i	$0.356236\pi$
$331$	−3378.13	+	5851.10i	−0.560964	+	0.971618i	−0.997413	+	0.0718887i	$0.977097\pi$
$332$	2827.63	+	2386.71i	0.467428	+	0.394542i
$333$	5262.19	−	2036.89i	0.865965	−	0.335198i
$334$	3394.40	+	7307.04i	0.556087	+	1.19708i
$335$	−1952.56	+	3381.93i	−0.318446	+	0.551565i
$336$	6464.28	−	593.628i	1.04957	−	0.0963842i
$337$	4901.54	+	8489.71i	0.792296	+	1.37230i	0.924542	+	0.381080i	$0.124448\pi$
$337$	4901.54	+	8489.71i	0.792296	+	1.37230i	−0.132246	+	0.991217i	$0.542219\pi$
$338$	−3200.14	+	4556.15i	−0.514984	+	0.733202i
$339$	140.513	−	1817.93i	0.0225122	−	0.291259i
$340$	2536.60	−	914.897i	0.404607	−	0.145933i
$341$	−1711.35			−0.271774
$342$	315.675	+	1095.32i	0.0499115	+	0.173182i
$343$		−	5952.96i		−	0.937113i
$344$	5744.33	−	5694.42i	0.900330	−	0.892507i
$345$	−793.768	−	1658.19i	−0.123870	−	0.258765i
$346$	−38.7626	+	55.1877i	−0.00602280	+	0.00857488i
$347$	10649.2	−	6148.32i	1.64749	−	0.951178i	0.669424	−	0.742881i	$-0.266541\pi$
$347$	10649.2	−	6148.32i	1.64749	−	0.951178i	0.978066	−	0.208297i	$-0.0667922\pi$
$348$	2857.17	+	10363.3i	0.440115	+	1.59635i
$349$	−6231.13	−	3597.55i	−0.955716	−	0.551783i	−0.0608642	−	0.998146i	$-0.519386\pi$
$349$	−6231.13	−	3597.55i	−0.955716	−	0.551783i	−0.894852	+	0.446363i	$0.852719\pi$
$350$	−3773.07	+	1752.74i	−0.576226	+	0.267679i
$351$	−8671.03	+	2608.15i	−1.31859	+	0.396617i
$352$	−1402.73	−	2034.64i	−0.212402	−	0.308087i
$353$	−2455.03	−	1417.41i	−0.370164	−	0.213714i	0.303366	−	0.952874i	$-0.401889\pi$
$353$	−2455.03	−	1417.41i	−0.370164	−	0.213714i	−0.673530	+	0.739160i	$0.735223\pi$
$354$	1193.37	−	7128.90i	0.179172	−	1.07033i
$355$	−306.870	−	531.515i	−0.0458789	−	0.0794645i
$356$	1479.57	−	8250.61i	0.220272	−	1.22832i
$357$	−2095.03	−	4376.54i	−0.310590	−	0.648827i
$358$	487.351	−	5478.65i	0.0719478	−	0.808815i
$359$	3447.67			0.506856			0.253428	−	0.967354i	$-0.418442\pi$
$359$	3447.67			0.506856			0.253428	+	0.967354i	$0.418442\pi$
$360$	−3486.56	+	2524.82i	−0.510438	+	0.369637i
$361$	−6636.20			−0.967517
$362$	−6.93310	+	77.9398i	−0.00100662	+	0.0113161i
$363$	−5929.92	−	458.341i	−0.857411	−	0.0662718i
$364$	9920.45	+	1779.02i	1.42850	+	0.256170i
$365$	−2882.14	−	4992.02i	−0.413310	−	0.715875i
$366$	10514.8	−	3930.66i	1.50168	−	0.561363i
$367$	4576.87	+	2642.46i	0.650983	+	0.375845i	0.788833	−	0.614608i	$-0.210686\pi$
$367$	4576.87	+	2642.46i	0.650983	+	0.375845i	−0.137850	+	0.990453i	$0.544019\pi$
$368$	−539.607	−	3167.93i	−0.0764374	−	0.448750i
$369$	−9993.31	−	8046.18i	−1.40984	−	1.13514i
$370$	3777.31	−	1754.70i	0.530738	−	0.246548i
$371$	8058.51	+	4652.58i	1.12770	+	0.651078i
$372$	−1312.30	+	5042.90i	−0.182902	+	0.702855i
$373$	−7902.95	+	4562.77i	−1.09705	+	0.633381i	−0.935444	−	0.353474i	$-0.885000\pi$
$373$	−7902.95	+	4562.77i	−1.09705	+	0.633381i	−0.161604	+	0.986856i	$0.551667\pi$
$374$	−1061.72	+	1511.61i	−0.146792	+	0.208993i
$375$	4146.36	−	6051.12i	0.570979	−	0.833277i
$376$	5017.85	−	4974.25i	0.688234	−	0.682253i
$377$			16690.4i			2.28011i
$378$	5148.51	+	5787.23i	0.700557	+	0.787468i
$379$	−1196.44			−0.162156			−0.0810778	−	0.996708i	$-0.525836\pi$
$379$	−1196.44			−0.162156			−0.0810778	+	0.996708i	$0.525836\pi$
$380$	285.471	+	791.482i	0.0385378	+	0.106848i
$381$	8588.03	+	5884.70i	1.15480	+	0.791293i
$382$	5156.75	−	7341.85i	0.690686	−	0.983355i
$383$	2622.07	+	4541.55i	0.349821	+	0.605907i	0.986217	−	0.165455i	$-0.0529092\pi$
$383$	2622.07	+	4541.55i	0.349821	+	0.605907i	−0.636397	+	0.771362i	$0.719576\pi$
$384$	−7071.17	+	2573.26i	−0.939711	+	0.341969i
$385$	−938.864	+	1626.16i	−0.124283	+	0.215264i
$386$	−526.792	−	1134.01i	−0.0694637	−	0.149533i
$387$	9536.90	+	1483.13i	1.25268	+	0.194811i
$388$	−5809.32	+	6882.52i	−0.760112	+	0.900533i
$389$	797.621	−	1381.52i	0.103961	−	0.180067i	−0.809352	−	0.587324i	$-0.800181\pi$
$389$	797.621	−	1381.52i	0.103961	−	0.180067i	0.913313	+	0.407257i	$0.133515\pi$
$390$	−6260.43	+	2340.29i	−0.812844	+	0.303860i
$391$	−2080.21	+	1201.01i	−0.269056	+	0.155339i
$392$	−219.113	−	832.250i	−0.0282318	−	0.107232i
$393$	−447.130	+	5784.88i	−0.0573912	+	0.742516i
$394$	8688.77	+	772.905i	1.11100	+	0.0988284i
$395$		−	8382.96i		−	1.06783i
$396$	960.362	−	2788.11i	0.121869	−	0.353808i
$397$		−	766.199i		−	0.0968625i	−0.998827	−	0.0484313i	$-0.984578\pi$
$397$		−	766.199i		−	0.0968625i	0.998827	−	0.0484313i	$-0.0154222\pi$
$398$	447.130	−	5026.50i	0.0563131	−	0.633055i
$399$	1365.59	−	653.702i	0.171341	−	0.0820202i
$400$	3712.28	−	3078.34i	0.464034	−	0.384793i
$401$	−170.330	+	98.3398i	−0.0212116	+	0.0122465i	−0.510568	−	0.859837i	$-0.670565\pi$
$401$	−170.330	+	98.3398i	−0.0212116	+	0.0122465i	0.489357	+	0.872084i	$0.337232\pi$
$402$	−8033.62	−	1344.81i	−0.996717	−	0.166849i
$403$	−4045.19	+	7006.48i	−0.500013	+	0.866049i
$404$	−3224.49	+	3820.18i	−0.397090	+	0.470448i
$405$	−4894.01	−	1559.91i	−0.600457	−	0.191389i
$406$	12948.8	−	6015.23i	1.58286	−	0.735298i
$407$	−1426.57	+	2470.89i	−0.173740	+	0.300927i
$408$	3640.15	+	4287.73i	0.441702	+	0.520281i
$409$	4719.01	+	8173.56i	0.570513	+	0.988158i	0.996513	+	0.0834349i	$0.0265891\pi$
$409$	4719.01	+	8173.56i	0.570513	+	0.988158i	−0.426000	+	0.904723i	$0.640078\pi$
$410$	−7749.53	−	5443.09i	−0.933468	−	0.655647i
$411$	3042.49	−	1456.43i	0.365146	−	0.174794i
$412$	1181.45	−	426.123i	0.141276	−	0.0509553i
$413$	−9600.17			−1.14381
$414$	2659.99	−	2761.94i	0.315777	−	0.327879i
$415$			3259.04i			0.385494i
$416$	−11645.7	+	933.578i	−1.37255	+	0.110030i
$417$	−5543.58	−	428.479i	−0.651007	−	0.0503183i
$418$	−471.659	−	331.283i	−0.0551905	−	0.0387645i
$419$	10282.4	−	5936.56i	1.19888	−	0.692171i	0.238571	−	0.971125i	$-0.423321\pi$
$419$	10282.4	−	5936.56i	1.19888	−	0.692171i	0.960305	+	0.278954i	$0.0899876\pi$
$420$	4071.92	+	4013.56i	0.473070	+	0.466289i
$421$	−936.025	−	540.414i	−0.108359	−	0.0625610i	0.444841	−	0.895609i	$-0.353260\pi$
$421$	−936.025	−	540.414i	−0.108359	−	0.0625610i	−0.553200	+	0.833048i	$0.686593\pi$
$422$	−1751.33	−	3770.04i	−0.202022	−	0.434888i
$423$	8330.77	+	1295.56i	0.957579	+	0.148918i
$424$	−10406.6	−	2837.17i	−1.19195	−	0.324965i
$425$	−3121.75	−	1802.35i	−0.356300	−	0.205710i
$426$	814.335	−	987.758i	0.0926166	−	0.112340i
$427$	−7454.67	−	12911.9i	−0.844864	−	1.46335i
$428$	593.715	−	3310.78i	0.0670521	−	0.373907i
$429$	2587.97	−	3776.84i	0.291255	−	0.425052i
$430$	7096.01	+	631.222i	0.795814	+	0.0707913i
$431$	−16863.0			−1.88460			−0.942299	−	0.334772i	$-0.891341\pi$
$431$	−16863.0			−1.88460			−0.942299	+	0.334772i	$0.891341\pi$
$432$	−7479.40	−	4967.92i	−0.832992	−	0.553285i
$433$	4717.51			0.523577			0.261789	−	0.965125i	$-0.415688\pi$
$433$	4717.51			0.523577			0.261789	+	0.965125i	$0.415688\pi$
$434$	6893.69	+	613.225i	0.762460	+	0.0678243i
$435$	−5351.88	+	7810.44i	−0.589892	+	0.860878i
$436$	1718.85	−	9584.96i	0.188803	−	1.05284i
$437$	−374.745	−	649.078i	−0.0410217	−	0.0710517i
$438$	7648.28	−	9277.08i	0.834358	−	1.01205i
$439$	−5611.44	−	3239.77i	−0.610068	−	0.352223i	0.162924	−	0.986639i	$-0.447907\pi$
$439$	−5611.44	−	3239.77i	−0.610068	−	0.352223i	−0.772992	+	0.634416i	$0.781241\pi$
$440$	572.524	−	2099.99i	0.0620318	−	0.227530i
$441$	644.023	−	799.872i	0.0695414	−	0.0863699i
$442$	3679.07	+	7919.85i	0.395918	+	0.852283i
$443$	−1696.92	−	979.717i	−0.181993	−	0.105074i	0.406236	−	0.913768i	$-0.366841\pi$
$443$	−1696.92	−	979.717i	−0.181993	−	0.105074i	−0.588229	+	0.808694i	$0.700175\pi$
$444$	6187.12	+	6098.45i	0.661324	+	0.651846i
$445$	6393.63	−	3691.37i	0.681095	−	0.393230i
$446$	2798.35	+	1965.50i	0.297098	+	0.208675i
$447$	−3067.43	−	237.091i	−0.324574	−	0.0250873i
$448$	4921.42	+	8698.59i	0.519007	+	0.917343i
$449$			2566.64i			0.269771i	0.990861	+	0.134885i	$0.0430666\pi$
$449$			2566.64i			0.269771i	−0.990861	+	0.134885i	$0.956933\pi$
$450$	5585.43	+	1384.62i	0.585111	+	0.145048i
$451$	6487.29			0.677327
$452$	2640.73	−	952.455i	0.274799	−	0.0991144i
$453$	9815.02	−	4698.41i	1.01799	−	0.487308i
$454$	−5201.98	−	3653.75i	−0.537756	−	0.377707i
$455$	4438.46	+	7687.64i	0.457315	+	0.792093i
$456$	−1337.88	+	1135.82i	−0.137395	+	0.116644i
$457$	740.460	−	1282.51i	0.0757927	−	0.131277i	−0.825638	−	0.564200i	$-0.809185\pi$
$457$	740.460	−	1282.51i	0.0757927	−	0.131277i	0.901431	+	0.432923i	$0.142518\pi$
$458$	−1965.78	+	913.180i	−0.200557	+	0.0931662i
$459$	−1539.32	+	6532.52i	−0.156535	+	0.664296i
$460$	1825.63	−	2162.90i	0.185045	−	0.219229i
$461$	−6037.19	+	10456.7i	−0.609935	+	1.05644i	0.381316	+	0.924445i	$0.375471\pi$
$461$	−6037.19	+	10456.7i	−0.609935	+	1.05644i	−0.991251	+	0.131993i	$0.957862\pi$
$462$	−3862.87	−	646.638i	−0.388998	−	0.0651176i
$463$	13152.8	−	7593.77i	1.32022	−	0.762230i	0.336457	−	0.941699i	$-0.390771\pi$
$463$	13152.8	−	7593.77i	1.32022	−	0.762230i	0.983764	+	0.179469i	$0.0574379\pi$
$464$	−12740.2	+	10564.6i	−1.27467	+	1.05700i
$465$	−4139.65	+	1981.63i	−0.412843	+	0.197626i
$466$	−200.786	+	2257.18i	−0.0199597	+	0.224381i
$467$		−	46.2660i		−	0.00458445i	−0.999997	−	0.00229222i	$-0.999270\pi$
$467$		−	46.2660i		−	0.00458445i	0.999997	−	0.00229222i	$-0.000729638\pi$
$468$	−9144.82	−	10522.2i	−0.903247	−	1.03929i
$469$			10818.5i			1.06514i
$470$	6198.58	+	551.392i	0.608339	+	0.0541145i
$471$	56.8490	−	735.501i	0.00556150	−	0.0719535i
$472$	10761.7	−	2833.31i	1.04946	−	0.276300i
$473$	−4226.36	+	2440.09i	−0.410842	+	0.237199i
$474$	16378.4	−	6122.63i	1.58710	−	0.593295i
$475$	562.377	−	974.066i	0.0543235	−	0.0940910i
$476$	4818.48	−	5708.63i	0.463981	−	0.549695i
$477$	−4646.12	−	12003.0i	−0.445977	−	1.15216i
$478$	7227.57	+	15558.6i	0.691593	+	1.48878i
$479$	7341.31	−	12715.5i	0.700278	−	1.21292i	−0.268091	−	0.963393i	$-0.586393\pi$
$479$	7341.31	−	12715.5i	0.700278	−	1.21292i	0.968369	−	0.249523i	$-0.0802738\pi$
$480$	−5749.09	−	3297.39i	−0.546685	−	0.313552i
$481$	6744.08	+	11681.1i	0.639300	+	1.10730i
$482$	−8550.69	+	12173.9i	−0.808036	+	1.15043i
$483$	−4201.28	−	2878.81i	−0.395786	−	0.271201i
$484$	−3106.81	−	8613.78i	−0.291774	−	0.808958i
$485$	−7932.58			−0.742680
$486$	−526.707	−	10701.1i	−0.0491603	−	0.998791i
$487$			5556.22i			0.516994i	0.966012	+	0.258497i	$0.0832273\pi$
$487$			5556.22i			0.516994i	−0.966012	+	0.258497i	$0.916773\pi$
$488$	12167.3	+	12273.9i	1.12866	+	1.13855i
$489$	10697.2	−	15611.2i	0.989248	−	1.44369i
$490$	435.669	−	620.278i	0.0401664	−	0.0571863i
$491$	−7499.65	+	4329.93i	−0.689317	+	0.397977i	−0.803356	−	0.595499i	$-0.796954\pi$
$491$	−7499.65	+	4329.93i	−0.689317	+	0.397977i	0.114039	+	0.993476i	$0.463621\pi$
$492$	4974.60	−	19116.3i	0.455838	−	1.75169i
$493$	10713.6	+	6185.49i	0.978733	+	0.565072i
$494$	−2471.19	+	1147.96i	−0.225069	+	0.104553i
$495$	2422.13	−	937.560i	0.219933	−	0.0851317i
$496$	−7908.71	+	1347.12i	−0.715951	+	0.121951i
$497$	−1472.48	−	850.137i	−0.132897	−	0.0767281i
$498$	−6367.43	+	2380.29i	−0.572955	+	0.214184i
$499$	−1626.32	−	2816.87i	−0.145900	−	0.252707i	0.783808	−	0.621003i	$-0.213274\pi$
$499$	−1626.32	−	2816.87i	−0.145900	−	0.252707i	−0.929708	+	0.368296i	$0.879941\pi$
$500$	11116.3	+	1993.46i	0.994271	+	0.178301i
$501$	−14757.6	−	1140.66i	−1.31601	−	0.101718i
$502$	−716.889	+	8059.06i	−0.0637377	+	0.716520i
$503$	2500.59			0.221662			0.110831	−	0.993839i	$-0.464649\pi$
$503$	2500.59			0.221662			0.110831	+	0.993839i	$0.464649\pi$
$504$	−4867.61	+	10887.0i	−0.430199	+	0.962193i
$505$	−4403.02			−0.387984
$506$	−171.795	+	1931.27i	−0.0150933	+	0.169675i
$507$	−4416.42	−	9225.96i	−0.386865	−	0.808164i
$508$	−2829.21	+	15776.8i	−0.247099	+	1.37791i
$509$	4599.12	+	7965.92i	0.400496	+	0.693680i	0.993786	−	0.111309i	$-0.0355044\pi$
$509$	4599.12	+	7965.92i	0.400496	+	0.693680i	−0.593290	+	0.804989i	$0.702171\pi$
$510$	−817.889	+	4885.89i	−0.0710132	+	0.424217i
$511$	−13829.6	−	7984.53i	−1.19723	−	0.691223i
$512$	−8084.06	−	8298.54i	−0.697790	−	0.716303i
$513$	−2038.31	−	480.308i	−0.175426	−	0.0413375i
$514$	−1736.79	+	806.804i	−0.149040	+	0.0692346i
$515$	957.986	+	553.093i	0.0819687	+	0.0473247i
$516$	3949.42	+	14325.1i	0.336945	+	1.22214i
$517$	−3691.85	+	2131.49i	−0.314057	+	0.181321i
$518$	6631.91	−	9442.09i	0.562528	−	0.800891i
$519$	−53.4952	−	111.752i	−0.00452443	−	0.00945157i
$520$	−7244.32	−	7307.82i	−0.610931	−	0.616286i
$521$			7635.67i			0.642082i	0.947065	+	0.321041i	$0.104033\pi$
$521$			7635.67i			0.642082i	−0.947065	+	0.321041i	$0.895967\pi$
$522$	−19168.7	−	4751.90i	−1.60726	−	0.398438i
$523$	−6152.61			−0.514407			−0.257203	−	0.966357i	$-0.582801\pi$
$523$	−6152.61			−0.514407			−0.257203	+	0.966357i	$0.582801\pi$
$524$	−8403.10	+	3030.83i	−0.700556	+	0.252676i
$525$	588.991	−	7620.24i	0.0489632	−	0.633476i
$526$	−1884.13	+	2682.51i	−0.156183	+	0.222363i
$527$	2998.31	+	5193.22i	0.247834	+	0.429260i
$528$	4521.07	−	415.179i	0.372641	−	0.0342204i
$529$	4822.88	−	8353.48i	0.396390	−	0.686568i
$530$	−4002.45	−	8615.98i	−0.328029	−	0.706140i
$531$	10343.0	+	8327.73i	0.845286	+	0.680589i
$532$	1781.24	+	1503.49i	0.145162	+	0.122527i
$533$	15334.3	−	26559.8i	1.24616	−	2.15841i
$534$	11881.8	+	9795.69i	0.962877	+	0.793822i
$535$	2565.62	−	1481.26i	0.207329	−	0.119702i
$536$	−3192.87	−	12127.4i	−0.257297	−	0.977283i
$537$	8335.53	+	5711.68i	0.669841	+	0.458989i
$538$	−21744.9	−	1934.31i	−1.74255	−	0.155007i
$539$			519.248i			0.0414946i
$540$	−905.395	−	7856.31i	−0.0721519	−	0.626077i
$541$			681.956i			0.0541952i	0.999633	+	0.0270976i	$0.00862649\pi$
$541$			681.956i			0.0541952i	−0.999633	+	0.0270976i	$0.991374\pi$
$542$	−894.209	+	10052.4i	−0.0708664	+	0.796658i
$543$	−118.582	−	81.2549i	−0.00937171	−	0.00642170i
$544$	−3716.66	+	7821.38i	−0.292924	+	0.616432i
$545$	7427.67	−	4288.36i	0.583791	−	0.337052i
$546$	−11778.2	+	14286.6i	−0.923191	+	1.11980i
$547$	2410.39	−	4174.92i	0.188411	−	0.326337i	−0.756310	−	0.654214i	$-0.773000\pi$
$547$	2410.39	−	4174.92i	0.188411	−	0.326337i	0.944721	+	0.327876i	$0.106333\pi$
$548$	3968.54	+	3349.72i	0.309357	+	0.261118i
$549$	−3169.01	+	20377.5i	−0.246357	+	1.58414i
$550$	−2638.86	+	1225.85i	−0.204584	+	0.0950371i
$551$	−1930.03	+	3342.91i	−0.149223	+	0.258462i
$552$	5559.20	+	1987.18i	0.428651	+	0.153224i
$553$	−11611.8	−	20112.3i	−0.892922	−	1.54659i
$554$	−10710.4	−	7522.78i	−0.821378	−	0.576917i
$555$	−589.652	+	7628.80i	−0.0450979	+	0.583468i
$556$	−2904.40	−	8052.58i	−0.221536	−	0.614219i
$557$	5948.96			0.452541			0.226271	−	0.974064i	$-0.427347\pi$
$557$	5948.96			0.452541			0.226271	+	0.974064i	$0.427347\pi$
$558$	−6895.14	−	6640.65i	−0.523109	−	0.503801i
$559$			23071.0i			1.74561i
$560$	−3058.73	+	8254.06i	−0.230813	+	0.622853i
$561$	−1465.25	−	3060.92i	−0.110272	−	0.230360i
$562$	−6696.98	−	4703.81i	−0.502661	−	0.353057i
$563$	1046.18	−	604.012i	0.0783148	−	0.0452151i	−0.460331	−	0.887747i	$-0.652269\pi$
$563$	1046.18	−	604.012i	0.0783148	−	0.0452151i	0.538646	+	0.842532i	$0.318936\pi$
$564$	3449.94	+	12513.4i	0.257569	+	0.934234i
$565$	2141.26	+	1236.25i	0.159439	+	0.0920524i
$566$	9868.43	+	21243.5i	0.732864	+	1.57762i
$567$	−13902.4	+	3036.53i	−1.02971	+	0.224907i
$568$	1901.53	+	518.418i	0.140469	+	0.0382963i
$569$	−2663.36	−	1537.69i	−0.196229	−	0.113293i	0.398667	−	0.917096i	$-0.369473\pi$
$569$	−2663.36	−	1537.69i	−0.196229	−	0.113293i	−0.594895	+	0.803803i	$0.702806\pi$
$570$	−1524.52	−	255.202i	−0.112026	−	0.0187531i
$571$	4651.48	+	8056.60i	0.340908	+	0.590470i	0.984602	−	0.174813i	$-0.0559322\pi$
$571$	4651.48	+	8056.60i	0.340908	+	0.590470i	−0.643694	+	0.765283i	$0.722599\pi$
$572$	6938.29	+	1244.23i	0.507175	+	0.0909508i
$573$	7116.69	+	14866.8i	0.518855	+	1.08389i
$574$	−26132.2	−	2324.58i	−1.90024	−	0.169035i
$575$	−3783.60			−0.274412
$576$	2243.43	−	13640.7i	0.162285	−	0.986744i
$577$	2594.28			0.187178			0.0935888	−	0.995611i	$-0.470166\pi$
$577$	2594.28			0.187178			0.0935888	+	0.995611i	$0.470166\pi$
$578$	−7394.18	−	657.746i	−0.532106	−	0.0473333i
$579$	2290.29	+	177.023i	0.164389	+	0.0127061i
$580$	−14348.3	−	2573.05i	−1.02721	−	0.184207i
$581$	4514.33	+	7819.04i	0.322351	+	0.558328i
$582$	−5793.70	−	15498.5i	−0.412640	−	1.10384i
$583$	5636.06	+	3253.98i	0.400380	+	0.231160i
$584$	17859.3	+	4869.01i	1.26545	+	0.345002i
$585$	1886.81	−	12132.6i	0.133350	−	0.857475i
$586$	−4441.02	−	9560.07i	−0.313066	−	0.673930i
$587$	−11408.0	−	6586.41i	−0.802144	−	0.463118i	0.0420762	−	0.999114i	$-0.486603\pi$
$587$	−11408.0	−	6586.41i	−0.802144	−	0.463118i	−0.844220	+	0.535996i	$0.819936\pi$
$588$	1530.08	+	398.171i	0.107312	+	0.0279256i
$589$	−1620.42	+	935.547i	−0.113358	+	0.0654475i
$590$	8020.69	+	5633.55i	0.559672	+	0.393101i
$591$	−9058.34	+	13219.6i	−0.630474	+	0.920103i
$592$	−4647.63	+	12541.7i	−0.322663	+	0.870713i
$593$		−	20600.6i		−	1.42659i	−0.700865	−	0.713294i	$-0.747202\pi$
$593$		−	20600.6i		−	1.42659i	0.700865	−	0.713294i	$-0.252798\pi$
$594$	3600.83	+	4047.54i	0.248727	+	0.279584i
$595$	6579.60			0.453340
$596$	−1607.10	−	4455.75i	−0.110452	−	0.306232i
$597$	7647.61	+	5240.30i	0.524281	+	0.359248i
$598$	7500.77	+	5268.37i	0.512926	+	0.360267i
$599$	−5529.60	−	9577.55i	−0.377184	−	0.653302i	0.613467	−	0.789720i	$-0.289774\pi$
$599$	−5529.60	−	9577.55i	−0.377184	−	0.653302i	−0.990651	+	0.136418i	$0.956441\pi$
$600$	1588.72	+	8716.02i	0.108099	+	0.593050i
$601$	10115.9	−	17521.2i	0.686581	−	1.18919i	−0.286356	−	0.958123i	$-0.592444\pi$
$601$	10115.9	−	17521.2i	0.686581	−	1.18919i	0.972937	−	0.231070i	$-0.0742227\pi$
$602$	17899.0	−	8314.78i	1.21181	−	0.562932i
$603$	9384.58	−	11655.6i	0.633780	−	0.787151i
$604$	12802.4	+	10806.1i	0.862456	+	0.727973i
$605$	4032.54	−	6984.56i	0.270985	−	0.469360i
$606$	−3215.82	−	8602.53i	−0.215567	−	0.576656i
$607$	24259.0	−	14005.9i	1.62214	−	0.936545i	0.635798	−	0.771856i	$-0.280671\pi$
$607$	24259.0	−	14005.9i	1.62214	−	0.936545i	0.986346	−	0.164689i	$-0.0526621\pi$
$608$	−2440.47	−	1159.69i	−0.162786	−	0.0773547i
$609$	−2021.36	+	26152.0i	−0.134499	+	1.74012i
$610$	−1348.73	+	15162.1i	−0.0895223	+	1.00638i
$611$			20153.2i			1.33439i
$612$	−10143.3	+	1970.51i	−0.669965	+	0.130153i
$613$		−	18577.2i		−	1.22402i	−0.790849	−	0.612012i	$-0.790361\pi$
$613$		−	18577.2i		−	1.22402i	0.790849	−	0.612012i	$-0.209639\pi$
$614$	−4174.52	−	371.342i	−0.274381	−	0.0244074i
$615$	15692.4	−	7511.86i	1.02891	−	0.492533i
$616$	−1535.26	−	5831.32i	−0.100418	−	0.381413i
$617$	1871.75	−	1080.65i	0.122129	−	0.0705114i	−0.437691	−	0.899126i	$-0.644204\pi$
$617$	1871.75	−	1080.65i	0.122129	−	0.0705114i	0.559820	+	0.828614i	$0.310870\pi$
$618$	−380.941	+	2275.65i	−0.0247956	+	0.148123i
$619$	−3435.93	+	5951.20i	−0.223104	+	0.386428i	−0.955749	−	0.294183i	$-0.904952\pi$
$619$	−3435.93	+	5951.20i	−0.223104	+	0.386428i	0.732645	+	0.680611i	$0.238286\pi$
$620$	−5399.65	−	4557.67i	−0.349766	−	0.295227i
$621$	2029.11	+	6745.98i	0.131120	+	0.435921i
$622$	−9472.34	−	20390.9i	−0.610621	−	1.31447i
$623$	10226.4	−	17712.6i	0.657641	−	1.13907i
$624$	8986.84	−	19491.2i	0.576541	−	1.25043i
$625$	263.949	+	457.172i	0.0168927	+	0.0292590i
$626$	−5107.24	+	7271.36i	−0.326080	+	0.464252i
$627$	955.084	−	457.194i	0.0608331	−	0.0291206i
$628$	1068.39	−	385.345i	0.0678874	−	0.0244856i
$629$	9997.45			0.633743
$630$	−10092.8	+	2908.78i	−0.638266	+	0.183950i
$631$		−	14045.7i		−	0.886134i	−0.896488	−	0.443067i	$-0.853890\pi$
$631$		−	14045.7i		−	0.886134i	0.896488	−	0.443067i	$-0.146110\pi$
$632$	18952.5	+	19118.6i	1.19286	+	1.20332i
$633$	7614.12	+	588.517i	0.478095	+	0.0369533i
$634$	3102.77	−	4417.53i	0.194364	−	0.276723i
$635$	−12225.9	+	7058.60i	−0.764045	+	0.441122i
$636$	13910.5	−	14112.7i	0.867273	−	0.879884i
$637$	2125.86	+	1227.37i	0.132229	+	0.0763423i
$638$	9056.32	−	4207.01i	0.561980	−	0.261061i
$639$	848.956	+	2193.23i	0.0525574	+	0.135779i
$640$	992.772	−	10155.4i	0.0613168	−	0.627231i
$641$	−9674.91	−	5585.81i	−0.596156	−	0.344191i	0.171372	−	0.985206i	$-0.445180\pi$
$641$	−9674.91	−	5585.81i	−0.596156	−	0.344191i	−0.767528	+	0.641016i	$0.778513\pi$
$642$	4767.89	+	3930.78i	0.293105	+	0.241644i
$643$	−3853.78	−	6674.94i	−0.236358	−	0.409384i	0.723309	−	0.690525i	$-0.242620\pi$
$643$	−3853.78	−	6674.94i	−0.236358	−	0.409384i	−0.959666	+	0.281141i	$0.909287\pi$
$644$	1384.06	−	7718.01i	0.0846886	−	0.472255i
$645$	−7397.83	+	10796.3i	−0.451611	+	0.659074i
$646$	−178.949	+	2011.70i	−0.0108989	+	0.122522i
$647$	−10087.3			−0.612943			−0.306472	−	0.951880i	$-0.599148\pi$
$647$	−10087.3			−0.612943			−0.306472	+	0.951880i	$0.599148\pi$
$648$	14688.2	−	7506.93i	0.890444	−	0.455093i
$649$	−6714.29			−0.406100
$650$	−1218.80	+	13701.4i	−0.0735466	+	0.826789i
$651$	−7186.91	+	10488.4i	−0.432684	+	0.631451i
$652$	28678.8	+	5142.92i	1.72262	+	0.308915i
$653$	−11606.7	−	20103.4i	−0.695567	−	1.20476i	−0.969989	−	0.243148i	$-0.921820\pi$
$653$	−11606.7	−	20103.4i	−0.695567	−	1.20476i	0.274422	−	0.961609i	$-0.411513\pi$
$654$	13803.4	+	11379.9i	0.825317	+	0.680414i
$655$	−6813.73	−	3933.91i	−0.406465	−	0.234673i
$656$	29979.9	−	5106.60i	1.78433	−	0.303932i
$657$	7973.44	+	20598.9i	0.473476	+	1.22320i
$658$	15635.3	−	7263.21i	0.926336	−	0.430318i
$659$	−23327.3	−	13468.0i	−1.37891	−	0.796115i	−0.386883	−	0.922129i	$-0.626448\pi$
$659$	−23327.3	−	13468.0i	−1.37891	−	0.796115i	−0.992029	+	0.126014i	$0.959782\pi$
$660$	2847.87	+	2807.05i	0.167959	+	0.165552i
$661$	20390.0	−	11772.2i	1.19982	−	0.692715i	0.239304	−	0.970945i	$-0.423081\pi$
$661$	20390.0	−	11772.2i	1.19982	−	0.692715i	0.960515	+	0.278229i	$0.0897475\pi$
$662$	10983.6	−	15637.7i	0.644847	−	0.918092i
$663$	−15995.2	−	1236.32i	−0.936959	−	0.0724203i
$664$	−7368.14	−	7432.72i	−0.430631	−	0.434406i
$665$			2053.00i			0.119717i
$666$	−15335.6	+	4419.77i	−0.892259	+	0.257151i
$667$	12985.0			0.753794
$668$	−7731.81	−	21436.8i	−0.447834	−	1.24164i
$669$	−5666.50	+	2712.53i	−0.327473	+	0.156760i
$670$	6348.49	−	9038.58i	0.366065	−	0.521180i
$671$	−5213.74	−	9030.46i	−0.299961	−	0.519548i
$672$	−18360.6	+	52.4058i	−1.05398	+	0.00300833i
$673$	−11656.7	+	20189.9i	−0.667654	+	1.15641i	0.310905	+	0.950441i	$0.399368\pi$
$673$	−11656.7	+	20189.9i	−0.667654	+	1.15641i	−0.978559	+	0.205969i	$0.933965\pi$
$674$	−11681.5	−	25146.5i	−0.667588	−	1.43710i
$675$	−7244.79	+	7698.93i	−0.413114	+	0.439010i
$676$	10157.6	−	12034.1i	0.577924	−	0.684688i
$677$	−12028.2	+	20833.5i	−0.682840	+	1.18271i	0.291271	+	0.956641i	$0.405922\pi$
$677$	−12028.2	+	20833.5i	−0.682840	+	1.18271i	−0.974110	+	0.226072i	$0.927411\pi$
$678$	−851.465	+	5086.46i	−0.0482305	+	0.288118i
$679$	−19031.8	+	10988.0i	−1.07566	+	0.621032i
$680$	−7375.64	+	1941.84i	−0.415945	+	0.109509i
$681$	10533.7	−	5042.44i	0.592736	−	0.283740i
$682$	4821.39	+	428.885i	0.270705	+	0.0240804i
$683$			18439.7i			1.03305i	0.856272	+	0.516525i	$0.172775\pi$
$683$			18439.7i			1.03305i	−0.856272	+	0.516525i	$0.827225\pi$
$684$	−614.850	−	3164.96i	−0.0343705	−	0.176923i
$685$			4574.02i			0.255130i
$686$	−1491.88	+	16771.3i	−0.0830326	+	0.933428i
$687$	306.866	−	3970.17i	0.0170417	−	0.220482i
$688$	−17610.6	+	14603.3i	−0.975870	+	0.809223i
$689$	26644.4	−	15383.1i	1.47325	−	0.850582i
$690$	1820.72	+	4870.55i	0.100455	+	0.268723i
$691$	−7125.35	+	12341.5i	−0.392274	+	0.679438i	−0.992749	−	0.120205i	$-0.961645\pi$
$691$	−7125.35	+	12341.5i	−0.392274	+	0.679438i	0.600475	+	0.799643i	$0.294978\pi$
$692$	123.037	−	145.766i	0.00675889	−	0.00800750i
$693$	4512.46	−	5604.45i	0.247351	−	0.307208i
$694$	−31542.8	+	14652.9i	−1.72529	+	0.801462i
$695$	3769.81	−	6529.51i	0.205751	−	0.356372i
$696$	−5452.33	−	29912.6i	−0.296940	−	1.62907i
$697$	−11365.8	−	19686.2i	−0.617662	−	1.06982i
$698$	16653.4	+	11697.0i	0.903067	+	0.634294i
$699$	−3434.20	−	2353.19i	−0.185827	−	0.127333i
$700$	11069.1	−	3992.41i	0.597677	−	0.215570i
$701$	−15415.0			−0.830549			−0.415274	−	0.909696i	$-0.636314\pi$
$701$	−15415.0			−0.830549			−0.415274	+	0.909696i	$0.636314\pi$
$702$	25082.6	−	5174.88i	1.34855	−	0.278224i
$703$			3119.46i			0.167358i
$704$	3442.00	+	6083.72i	0.184269	+	0.325695i
$705$	−6462.23	+	9430.87i	−0.345222	+	0.503811i
$706$	6561.33	+	4608.53i	0.349772	+	0.245672i
$707$	−10563.7	+	6098.94i	−0.561935	+	0.324433i
$708$	−5148.66	+	19785.2i	−0.273303	+	1.05025i
$709$	−15877.4	−	9166.80i	−0.841025	−	0.485566i	0.0165875	−	0.999862i	$-0.494720\pi$
$709$	−15877.4	−	9166.80i	−0.841025	−	0.485566i	−0.857613	+	0.514296i	$0.828053\pi$
$710$	731.343	+	1574.34i	0.0386575	+	0.0832170i
$711$	−4936.23	+	31741.2i	−0.260370	+	1.67425i
$712$	−6236.08	+	22873.7i	−0.328240	+	1.20397i
$713$	5450.97	+	3147.12i	0.286312	+	0.165302i
$714$	4805.52	+	12855.1i	0.251880	+	0.673795i
$715$	3104.23	+	5376.68i	0.162366	+	0.281226i
$716$	−2746.03	+	15312.9i	−0.143330	+	0.799259i
$717$	−31422.8	−	2428.76i	−1.63669	−	0.126504i
$718$	−9713.14	−	864.027i	−0.504862	−	0.0449098i
$719$	10428.9			0.540936			0.270468	−	0.962729i	$-0.412822\pi$
$719$	10428.9			0.540936			0.270468	+	0.962729i	$0.412822\pi$
$720$	10455.4	−	6239.40i	0.541182	−	0.322956i
$721$	3064.52			0.158292
$722$	18696.2	+	1663.11i	0.963712	+	0.0857265i
$723$	−11800.6	−	24651.5i	−0.607009	−	1.26805i
$724$	39.0653	−	217.842i	0.00200532	−	0.0111824i
$725$	9743.23	+	16875.8i	0.499110	+	0.864483i
$726$	16591.5	+	2777.39i	0.848166	+	0.141982i
$727$	12935.1	+	7468.08i	0.659884	+	0.380984i	0.792233	−	0.610219i	$-0.208918\pi$
$727$	12935.1	+	7468.08i	0.659884	+	0.380984i	−0.132348	+	0.991203i	$0.542252\pi$
$728$	−27503.1	−	7498.21i	−1.40018	−	0.381733i
$729$	17612.1	+	8788.23i	0.894789	+	0.446489i
$730$	6868.81	+	14786.3i	0.348255	+	0.749680i
$731$	14809.2	+	8550.12i	0.749302	+	0.432610i
$732$	−30608.4	+	8438.74i	−1.54552	+	0.426099i
$733$	−434.025	+	250.584i	−0.0218705	+	0.0126269i	−0.510895	−	0.859643i	$-0.670686\pi$
$733$	−434.025	+	250.584i	−0.0218705	+	0.0126269i	0.489025	+	0.872270i	$0.337353\pi$
$734$	−12232.2	−	8591.63i	−0.615121	−	0.432047i
$735$	601.255	+	1256.03i	0.0301736	+	0.0630331i
$736$	726.315	+	9060.26i	0.0363754	+	0.453758i
$737$			7566.38i			0.378170i
$738$	26137.7	+	25173.0i	1.30372	+	1.25560i
$739$	11047.6			0.549922			0.274961	−	0.961455i	$-0.411335\pi$
$739$	11047.6			0.549922			0.274961	+	0.961455i	$0.411335\pi$
$740$	−11081.6	+	3996.89i	−0.550496	+	0.198552i
$741$	385.763	−	4990.92i	0.0191246	−	0.247430i
$742$	−21537.3	−	15127.3i	−1.06558	−	0.748437i
$743$	−16450.7	−	28493.5i	−0.812272	−	1.40690i	−0.911270	−	0.411808i	$-0.864897\pi$
$743$	−16450.7	−	28493.5i	−0.812272	−	1.40690i	0.0989987	−	0.995088i	$-0.468436\pi$
$744$	4960.96	−	13878.5i	0.244459	−	0.683884i
$745$	2085.95	−	3612.98i	0.102582	−	0.177677i
$746$	23408.5	−	10874.1i	1.14885	−	0.533687i
$747$	1919.06	−	12340.0i	0.0939954	−	0.604414i
$748$	3370.01	−	3992.57i	0.164732	−	0.195164i
$749$	4103.60	−	7107.64i	0.200190	−	0.346739i
$750$	−13198.0	+	16008.7i	−0.642565	+	0.779408i
$751$	−32163.5	+	18569.6i	−1.56280	+	0.902282i	−0.565827	+	0.824524i	$0.691443\pi$
$751$	−32163.5	+	18569.6i	−1.56280	+	0.902282i	−0.996972	+	0.0777583i	$0.975224\pi$
$752$	−15383.4	+	12756.4i	−0.745977	+	0.618589i
$753$	−12261.5	−	8401.84i	−0.593405	−	0.406614i
$754$	4182.82	−	47022.0i	0.202028	−	2.27114i
$755$			14755.7i			0.711278i
$756$	−13054.6	−	17594.6i	−0.628029	−	0.846443i
$757$			7256.87i			0.348422i	0.984708	+	0.174211i	$0.0557375\pi$
$757$			7256.87i			0.348422i	−0.984708	+	0.174211i	$0.944263\pi$
$758$	3370.73	+	299.842i	0.161518	+	0.0143677i
$759$	−2938.34	−	2013.41i	−0.140521	−	0.0962877i
$760$	−605.904	−	2301.39i	−0.0289190	−	0.109842i
$761$	−7953.62	+	4592.02i	−0.378868	+	0.218739i	−0.677326	−	0.735683i	$-0.736861\pi$
$761$	−7953.62	+	4592.02i	−0.378868	+	0.218739i	0.298458	+	0.954423i	$0.403528\pi$
$762$	−22720.3	−	18731.3i	−1.08014	−	0.890501i
$763$	11880.2	−	20577.2i	0.563688	−	0.976336i
$764$	−16368.1	+	19391.9i	−0.775100	+	0.918289i
$765$	−7088.69	−	5707.51i	−0.335023	−	0.269746i
$766$	−6248.99	−	13452.0i	−0.294758	−	0.634520i
$767$	−15870.8	+	27489.1i	−0.747148	+	1.29410i
$768$	20566.5	−	5477.52i	0.966315	−	0.257361i
$769$	17525.0	+	30354.2i	0.821806	+	1.42341i	0.904336	+	0.426821i	$0.140366\pi$
$769$	17525.0	+	30354.2i	0.821806	+	1.42341i	−0.0825304	+	0.996589i	$0.526300\pi$
$770$	3052.60	−	4346.09i	0.142868	−	0.203406i
$771$	271.119	−	3507.68i	0.0126642	−	0.163847i
$772$	1199.93	+	3326.87i	0.0559412	+	0.155100i
$773$	−1390.01			−0.0646768			−0.0323384	−	0.999477i	$-0.510295\pi$
$773$	−1390.01			−0.0646768			−0.0323384	+	0.999477i	$0.510295\pi$
$774$	−26496.7	−	6568.49i	−1.23049	−	0.305038i
$775$			9445.72i			0.437807i
$776$	18091.4	−	17934.2i	0.836914	−	0.829642i
$777$	9152.52	+	19119.7i	0.422580	+	0.882774i
$778$	−2593.37	+	3692.27i	−0.119507	+	0.170147i
$779$	6142.58	−	3546.42i	0.282517	−	0.163111i
$780$	18224.0	−	5024.37i	0.836570	−	0.230643i
$781$	−1029.84	−	594.579i	−0.0471839	−	0.0272416i
$782$	6161.57	−	2862.28i	0.281761	−	0.130889i
$783$	24863.5	−	26422.0i	1.13480	−	1.20593i
$784$	408.736	+	2399.61i	0.0186195	+	0.109312i
$785$	866.311	+	500.165i	0.0393885	+	0.0227410i
$786$	2709.46	−	16185.7i	0.122956	−	0.734510i
$787$	2740.75	+	4747.12i	0.124139	+	0.215015i	0.921396	−	0.388625i	$-0.127050\pi$
$787$	2740.75	+	4747.12i	0.124139	+	0.215015i	−0.797257	+	0.603640i	$0.793717\pi$
$788$	−24285.2	−	4355.02i	−1.09787	−	0.196879i
$789$	−2600.24	−	5431.93i	−0.117327	−	0.245097i
$790$	−2100.87	+	23617.3i	−0.0946146	+	1.06363i
$791$	6849.70			0.307898
$792$	−3404.37	+	7614.28i	−0.152738	+	0.341618i
$793$	−49295.7			−2.20749
$794$	−192.018	+	2158.61i	−0.00858247	+	0.0964815i
$795$	17401.2	+	1344.99i	0.776297	+	0.0600022i
$796$	−2519.40	+	14049.1i	−0.112183	+	0.625575i
$797$	15906.0	+	27550.0i	0.706926	+	1.22443i	0.965992	+	0.258573i	$0.0832521\pi$
$797$	15906.0	+	27550.0i	0.706926	+	1.22443i	−0.259065	+	0.965860i	$0.583415\pi$
$798$	−4011.11	+	1499.44i	−0.177934	+	0.0665160i
$799$	12936.3	+	7468.79i	0.572784	+	0.330697i
$800$	−11230.1	+	7742.28i	−0.496304	+	0.342164i
$801$	−26382.5	+	10212.2i	−1.16377	+	0.450473i
$802$	504.515	−	234.366i	0.0222133	−	0.0103189i
$803$	−9672.33	−	5584.32i	−0.425067	−	0.245413i
$804$	22296.1	+	5802.07i	0.978014	+	0.254506i
$805$	5980.91	−	3453.08i	0.261863	−	0.151186i
$806$	13152.4	−	18725.6i	0.574783	−	0.818339i
$807$	22669.8	−	33084.0i	0.988867	−	1.44314i
$808$	10041.8	−	9954.50i	0.437212	−	0.433413i
$809$			2788.69i			0.121193i	0.998162	+	0.0605966i	$0.0193003\pi$
$809$			2788.69i			0.121193i	−0.998162	+	0.0605966i	$0.980700\pi$
$810$	13397.0	+	5621.23i	0.581138	+	0.243839i
$811$	23968.2			1.03778			0.518889	−	0.854841i	$-0.326346\pi$
$811$	23968.2			1.03778			0.518889	+	0.854841i	$0.326346\pi$
$812$	−37988.3	+	13701.6i	−1.64178	+	0.592157i
$813$	−15294.3	−	10480.0i	−0.659773	−	0.452091i
$814$	4638.31	−	6603.73i	0.199721	−	0.284349i
$815$	12831.1	+	22224.1i	0.551476	+	0.955184i
$816$	−9180.85	−	12992.1i	−0.393865	−	0.557371i
$817$	−2667.85	+	4620.86i	−0.114243	+	0.197874i
$818$	−11246.5	−	24210.0i	−0.480714	−	1.03482i
$819$	−12279.0	−	31722.1i	−0.523886	−	1.35343i
$820$	20468.7	+	17277.0i	0.871703	+	0.735778i
$821$	2750.46	−	4763.94i	0.116921	−	0.202512i	−0.801625	−	0.597827i	$-0.796031\pi$
$821$	2750.46	−	4763.94i	0.116921	−	0.202512i	0.918546	+	0.395314i	$0.129364\pi$
$822$	−8936.61	+	3340.71i	−0.379197	+	0.141753i
$823$	4259.38	−	2459.15i	0.180404	−	0.104156i	−0.407078	−	0.913393i	$-0.633452\pi$
$823$	4259.38	−	2459.15i	0.180404	−	0.104156i	0.587483	+	0.809237i	$0.300119\pi$
$824$	−3435.28	+	904.433i	−0.145235	+	0.0382372i
$825$	411.936	−	5329.54i	0.0173839	−	0.224910i
$826$	27046.6	+	2405.92i	1.13931	+	0.101347i
$827$		−	17035.6i		−	0.716307i	−0.933663	−	0.358153i	$-0.883407\pi$
$827$		−	17035.6i		−	0.716307i	0.933663	−	0.358153i	$-0.116593\pi$
$828$	−8186.18	+	7114.58i	−0.343586	+	0.298610i
$829$			9284.88i			0.388995i	0.980903	+	0.194498i	$0.0623077\pi$
$829$			9284.88i			0.388995i	−0.980903	+	0.194498i	$0.937692\pi$
$830$	816.753	−	9181.69i	0.0341565	−	0.383977i
$831$	21688.1	−	10382.0i	0.905355	−	0.433390i
$832$	33043.5	+	288.386i	1.37690	+	0.0120168i
$833$	1575.69	−	909.728i	0.0655397	−	0.0378394i
$834$	15510.6	+	2596.44i	0.643989	+	0.107803i
$835$	10035.6	−	17382.2i	0.415925	−	0.720403i
$836$	1245.78	+	1051.53i	0.0515387	+	0.0435022i
$837$	16841.3	−	5065.66i	0.695483	−	0.209193i
$838$	−30456.5	+	14148.2i	−1.25549	+	0.583223i
$839$	−4605.12	+	7976.30i	−0.189495	+	0.328215i	−0.945082	−	0.326833i	$-0.894018\pi$
$839$	−4605.12	+	7976.30i	−0.189495	+	0.328215i	0.755587	+	0.655048i	$0.227352\pi$
$840$	−10466.0	−	12327.9i	−0.429894	−	0.506371i
$841$	−21243.4	−	36794.6i	−0.871024	−	1.50866i
$842$	2501.63	+	1757.09i	0.102389	+	0.0719160i
$843$	13561.0	−	6491.60i	0.554053	−	0.265222i
$844$	3989.20	+	11060.2i	0.162694	+	0.451077i
$845$	13870.1			0.564670
$846$	−23145.6	−	5737.77i	−0.940618	−	0.233178i
$847$		−	22343.0i		−	0.906394i
$848$	28607.5	+	10601.2i	1.15847	+	0.429299i
$849$	−42904.3	−	3316.20i	−1.73436	−	0.134054i
$850$	8343.24	+	5860.10i	0.336671	+	0.236470i
$851$	9087.77	−	5246.83i	0.366069	−	0.211350i
$852$	−2541.77	+	2578.73i	−0.102206	+	0.103692i
$853$	−6216.93	−	3589.35i	−0.249547	−	0.144076i	0.370010	−	0.929028i	$-0.379354\pi$
$853$	−6216.93	−	3589.35i	−0.249547	−	0.144076i	−0.619557	+	0.784952i	$0.712688\pi$
$854$	17766.2	+	38244.9i	0.711881	+	1.53245i
$855$	1780.89	−	2211.85i	0.0712340	−	0.0884722i
$856$	−2502.39	+	9178.66i	−0.0999183	+	0.366496i
$857$	13290.3	+	7673.16i	0.529741	+	0.305846i	0.740911	−	0.671603i	$-0.234394\pi$
$857$	13290.3	+	7673.16i	0.529741	+	0.305846i	−0.211170	+	0.977449i	$0.567727\pi$
$858$	−8237.61	+	9991.92i	−0.327771	+	0.397574i
$859$	18277.1	+	31656.9i	0.725969	+	1.25742i	0.958574	+	0.284844i	$0.0919419\pi$
$859$	18277.1	+	31656.9i	0.725969	+	1.25742i	−0.232604	+	0.972571i	$0.574725\pi$
$860$	−19833.4	−	3556.69i	−0.786412	−	0.141026i
$861$	27243.7	−	39759.0i	1.07835	−	1.57373i
$862$	47508.2	+	4226.07i	1.87719	+	0.166984i
$863$	−27501.0			−1.08476			−0.542378	−	0.840135i	$-0.682476\pi$
$863$	−27501.0			−1.08476			−0.542378	+	0.840135i	$0.682476\pi$
$864$	19826.7	+	15870.6i	0.780692	+	0.624916i
$865$	168.006			0.00660388
$866$	−13290.6	−	1182.26i	−0.521518	−	0.0463914i
$867$	7708.69	−	11249.9i	0.301962	−	0.440678i
$868$	−19267.9	−	3455.28i	−0.753452	−	0.135115i
$869$	−8121.23	−	14066.4i	−0.317024	−	0.549102i
$870$	17035.2	−	20663.1i	0.663849	−	0.805225i
$871$	30977.7	+	17885.0i	1.20510	+	0.695763i
$872$	−7244.63	+	26573.0i	−0.281347	+	1.03197i
$873$	30035.9	+	4671.03i	1.16445	+	0.181089i
$874$	893.104	+	1922.56i	0.0345649	+	0.0744070i
$875$	23864.7	+	13778.3i	0.922027	+	0.532332i
$876$	−23872.5	+	24219.6i	−0.920748	+	0.934137i
$877$	4880.15	−	2817.56i	0.187903	−	0.108486i	−0.403098	−	0.915157i	$-0.632066\pi$
$877$	4880.15	−	2817.56i	0.187903	−	0.108486i	0.591000	+	0.806671i	$0.298733\pi$
$878$	14997.2	+	10533.7i	0.576459	+	0.404892i
$879$	19307.9	+	1492.36i	0.740887	+	0.0572653i
$880$	−2139.25	+	5772.83i	−0.0819480	+	0.221139i
$881$		−	51429.9i		−	1.96676i	−0.181554	−	0.983381i	$-0.558113\pi$
$881$		−	51429.9i		−	1.96676i	0.181554	−	0.983381i	$-0.441887\pi$
$882$	−2014.86	+	2092.08i	−0.0769206	+	0.0798685i
$883$	−7015.23			−0.267363			−0.133681	−	0.991024i	$-0.542680\pi$
$883$	−7015.23			−0.267363			−0.133681	+	0.991024i	$0.542680\pi$
$884$	−8380.25	−	23234.6i	−0.318844	−	0.884011i
$885$	−16241.4	+	7774.71i	−0.616893	+	0.295304i
$886$	4535.21	+	3185.43i	0.171968	+	0.120786i
$887$	18173.6	+	31477.6i	0.687948	+	1.19156i	0.972501	+	0.232900i	$0.0748214\pi$
$887$	18173.6	+	31477.6i	0.687948	+	1.19156i	−0.284553	+	0.958660i	$0.591845\pi$
$888$	−15902.7	−	18731.7i	−0.600967	−	0.707878i
$889$	−19554.8	+	33869.9i	−0.737734	+	1.27779i
$890$	−18937.9	+	8797.38i	−0.713258	+	0.331336i
$891$	−9723.23	+	2123.73i	−0.365590	+	0.0798513i
$892$	−7391.22	−	6238.70i	−0.277440	−	0.234178i
$893$	−2330.45	+	4036.46i	−0.0873299	+	0.151260i
$894$	8582.47	+	1436.69i	0.321075	+	0.0537474i
$895$	−11866.4	+	6851.07i	−0.443184	+	0.255873i
$896$	−11685.2	−	25739.9i	−0.435685	−	0.959721i
$897$	−15188.6	+	7270.74i	−0.565367	+	0.270639i
$898$	643.230	−	7230.99i	0.0239030	−	0.268710i
$899$		−	32416.9i		−	1.20263i
$900$	−15388.8	−	5300.67i	−0.569957	−	0.196321i
$901$		−	22804.0i		−	0.843188i
$902$	−18276.7	−	1625.79i	−0.674663	−	0.0600143i
$903$	−2794.10	+	36149.6i	−0.102970	+	1.33221i
$904$	−7678.42	+	2021.56i	−0.282501	+	0.0743761i
$905$	168.812	−	97.4639i	0.00620057	−	0.00357990i
$906$	−28829.4	+	10777.1i	−1.05717	+	0.395192i
$907$	3011.58	−	5216.21i	0.110251	−	0.190961i	−0.805620	−	0.592432i	$-0.798168\pi$
$907$	3011.58	−	5216.21i	0.110251	−	0.190961i	0.915872	+	0.401472i	$0.131501\pi$
$908$	13739.9	+	11597.4i	0.502174	+	0.423869i
$909$	16671.6	+	2592.68i	0.608319	+	0.0946027i
$910$	−10577.9	−	22770.8i	−0.385333	−	0.829498i
$911$	2996.17	−	5189.52i	0.108965	−	0.188734i	−0.806386	−	0.591390i	$-0.798580\pi$
$911$	2996.17	−	5189.52i	0.108965	−	0.188734i	0.915351	+	0.402656i	$0.131913\pi$
$912$	4053.87	−	2864.66i	0.147190	−	0.104011i
$913$	3157.29	+	5468.58i	0.114448	+	0.198230i
$914$	−2407.51	+	3427.66i	−0.0871263	+	0.124045i
$915$	−23068.4	−	15807.0i	−0.833462	−	0.571106i
$916$	5767.05	−	2080.06i	0.208023	−	0.0750295i
$917$	−21796.6			−0.784936
$918$	5973.87	−	18018.3i	0.214779	−	0.647814i
$919$			88.2115i			0.00316630i	0.999999	+	0.00158315i	$0.000503932\pi$
$919$			88.2115i			0.00316630i	−0.999999	+	0.00158315i	$0.999496\pi$
$920$	−5685.41	+	5636.01i	−0.203742	+	0.201971i
$921$	4352.08	−	6351.35i	0.155707	−	0.227236i
$922$	19629.2	−	27946.8i	0.701141	−	0.998240i
$923$	−4868.56	+	2810.86i	−0.173619	+	0.100239i
$924$	10720.8	+	2789.86i	0.381698	+	0.0993285i
$925$	13637.9	+	7873.87i	0.484771	+	0.279883i
$926$	−38958.5	+	18097.7i	−1.38257	+	0.642254i
$927$	−3301.63	−	2658.33i	−0.116979	−	0.0941868i
$928$	38540.6	−	26570.8i	1.36332	−	0.939903i
$929$	18113.2	+	10457.7i	0.639695	+	0.369328i	0.784497	−	0.620133i	$-0.212921\pi$
$929$	18113.2	+	10457.7i	0.639695	+	0.369328i	−0.144802	+	0.989461i	$0.546255\pi$
$930$	12159.3	−	4545.42i	0.428730	−	0.160269i
$931$	283.858	+	491.657i	0.00999256	+	0.0173076i
$932$	1131.35	−	6308.84i	0.0397625	−	0.221730i
$933$	41182.2	+	3183.09i	1.44507	+	0.111693i
$934$	−11.5948	+	130.345i	−0.000406203	+	0.00456642i
$935$	4601.72			0.160954
$936$	23126.7	+	31936.1i	0.807608	+	1.11524i
$937$	20055.2			0.699227			0.349614	−	0.936894i	$-0.386313\pi$
$937$	20055.2			0.699227			0.349614	+	0.936894i	$0.386313\pi$
$938$	2711.25	−	30479.0i	0.0943767	−	1.06095i
$939$	−7048.36	−	14724.1i	−0.244957	−	0.511717i
$940$	−17325.1	−	3106.88i	−0.601151	−	0.107803i
$941$	1432.61	+	2481.36i	0.0496300	+	0.0859616i	0.889773	−	0.456403i	$-0.150862\pi$
$941$	1432.61	+	2481.36i	0.0496300	+	0.0859616i	−0.840143	+	0.542365i	$0.817529\pi$
$942$	−344.486	+	2057.88i	−0.0119150	+	0.0711778i
$943$	−20663.2	−	11929.9i	−0.713560	−	0.411974i
$944$	−31028.9	+	5285.28i	−1.06981	+	0.182226i
$945$	4425.79	−	18782.0i	0.152350	−	0.646537i
$946$	12518.4	−	5815.29i	0.430243	−	0.199864i
$947$	−7218.72	−	4167.73i	−0.247705	−	0.143013i	0.371008	−	0.928630i	$-0.379012\pi$
$947$	−7218.72	−	4167.73i	−0.247705	−	0.143013i	−0.618713	+	0.785617i	$0.712346\pi$
$948$	−47677.4	+	13144.7i	−1.63343	+	0.450337i
$949$	−45725.8	+	26399.8i	−1.56409	+	0.903028i
$950$	−1828.50	+	2603.30i	−0.0624467	+	0.0889076i
$951$	4282.05	+	8945.25i	0.146010	+	0.305015i
$952$	−15005.8	+	14875.4i	−0.510861	+	0.506422i
$953$			39658.3i			1.34802i	0.738724	+	0.674008i	$0.235429\pi$
$953$			39658.3i			1.34802i	−0.738724	+	0.674008i	$0.764571\pi$
$954$	10081.4	+	34980.4i	0.342137	+	1.18714i
$955$	−22350.5			−0.757324
$956$	−16463.1	−	45644.7i	−0.556960	−	1.54420i
$957$	−1413.73	+	18290.5i	−0.0477526	+	0.617814i
$958$	−23869.3	+	33983.6i	−0.804993	+	1.14610i
$959$	6335.80	+	10973.9i	0.213341	+	0.369517i
$960$	15370.6	+	10730.5i	0.516752	+	0.360757i
$961$	−7038.75	+	12191.5i	−0.236271	+	0.409233i
$962$	−16072.7	−	34599.3i	−0.538674	−	1.15959i
$963$	−10586.7	+	4097.90i	−0.354258	+	0.137127i
$964$	27140.8	−	32154.7i	0.906791	−	1.07431i
$965$	−1557.47	+	2697.62i	−0.0519553	+	0.0899892i
$966$	11114.8	+	9163.36i	0.370200	+	0.305203i
$967$	9529.32	−	5501.75i	0.316900	−	0.182962i	−0.333110	−	0.942888i	$-0.608098\pi$
$967$	9529.32	−	5501.75i	0.316900	−	0.182962i	0.650010	+	0.759926i	$0.274765\pi$
$968$	6594.12	+	25046.2i	0.218949	+	0.831629i
$969$	−3060.71	−	2097.26i	−0.101470	−	0.0695292i
$970$	22348.5	+	1988.00i	0.739759	+	0.0658049i
$971$			18334.6i			0.605958i	0.952997	+	0.302979i	$0.0979813\pi$
$971$			18334.6i			0.605958i	−0.952997	+	0.302979i	$0.902019\pi$
$972$	−1197.93	+	30280.3i	−0.0395306	+	0.999218i
$973$		−	20887.4i		−	0.688199i
$974$	1392.45	−	15653.5i	0.0458081	−	0.514961i
$975$	−20846.1	−	14284.2i	−0.684727	−	0.469189i
$976$	−31202.9	−	37628.6i	−1.02334	−	1.23408i
$977$	32261.5	−	18626.2i	1.05643	−	0.609932i	0.131990	−	0.991251i	$-0.457863\pi$
$977$	32261.5	−	18626.2i	1.05643	−	0.609932i	0.924444	+	0.381319i	$0.124530\pi$
$978$	−34049.5	+	41300.8i	−1.11327	+	1.35036i
$979$	7152.24	−	12388.0i	0.233490	−	0.404416i
$980$	−1382.86	+	1638.33i	−0.0450754	+	0.0534025i
$981$	−30649.3	+	11863.7i	−0.997509	+	0.386117i
$982$	22213.9	−	10319.2i	0.721868	−	0.335335i
$983$	5395.60	−	9345.46i	0.175069	−	0.303229i	−0.765116	−	0.643892i	$-0.777318\pi$
$983$	5395.60	−	9345.46i	0.175069	−	0.303229i	0.940185	+	0.340664i	$0.110652\pi$
$984$	−18805.7	+	52609.7i	−0.609253	+	1.70441i
$985$	−10865.3	−	18819.3i	−0.351470	−	0.608764i
$986$	−28633.2	−	20111.3i	−0.924816	−	0.649570i
$987$	−2440.74	+	31577.7i	−0.0787127	+	1.01837i
$988$	7249.79	−	2614.85i	0.233448	−	0.0841999i
$989$	17949.0			0.577092
$990$	−7058.84	+	2034.38i	−0.226611	+	0.0653098i
$991$		−	12374.8i		−	0.396669i	−0.980134	−	0.198334i	$-0.936447\pi$
$991$		−	12374.8i		−	0.396669i	0.980134	−	0.198334i	$-0.0635532\pi$
$992$	22618.8	−	1813.24i	0.723941	−	0.0580346i
$993$	15158.1	+	31665.5i	0.484420	+	1.01196i
$994$	3935.37	+	2764.11i	0.125576	+	0.0882016i
$995$	−10887.1	+	6285.66i	−0.346878	+	0.200270i
$996$	18535.5	−	5110.25i	0.589679	−	0.162575i
$997$	−4549.81	−	2626.84i	−0.144528	−	0.0834431i	0.425992	−	0.904727i	$-0.359925\pi$
$997$	−4549.81	−	2626.84i	−0.144528	−	0.0834431i	−0.570520	+	0.821284i	$0.693258\pi$
$998$	3875.90	+	8343.56i	0.122935	+	0.264640i
$999$	6724.82	−	28538.5i	0.212977	−	0.903822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.4.l.b.11.1	✓	64
3.2	odd	2		216.4.l.b.35.32		64
4.3	odd	2		288.4.p.b.47.12		64
8.3	odd	2	inner	72.4.l.b.11.10	yes	64
8.5	even	2		288.4.p.b.47.11		64
9.4	even	3		216.4.l.b.179.23		64
9.5	odd	6	inner	72.4.l.b.59.10	yes	64
12.11	even	2		864.4.p.b.143.12		64
24.5	odd	2		864.4.p.b.143.21		64
24.11	even	2		216.4.l.b.35.23		64
36.23	even	6		288.4.p.b.239.11		64
36.31	odd	6		864.4.p.b.719.21		64
72.5	odd	6		288.4.p.b.239.12		64
72.13	even	6		864.4.p.b.719.12		64
72.59	even	6	inner	72.4.l.b.59.1	yes	64
72.67	odd	6		216.4.l.b.179.32		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.1	✓	64	1.1	even	1	trivial
72.4.l.b.11.10	yes	64	8.3	odd	2	inner
72.4.l.b.59.1	yes	64	72.59	even	6	inner
72.4.l.b.59.10	yes	64	9.5	odd	6	inner
216.4.l.b.35.23		64	24.11	even	2
216.4.l.b.35.32		64	3.2	odd	2
216.4.l.b.179.23		64	9.4	even	3
216.4.l.b.179.32		64	72.67	odd	6
288.4.p.b.47.11		64	8.5	even	2
288.4.p.b.47.12		64	4.3	odd	2
288.4.p.b.239.11		64	36.23	even	6
288.4.p.b.239.12		64	72.5	odd	6
864.4.p.b.143.12		64	12.11	even	2
864.4.p.b.143.21		64	24.5	odd	2
864.4.p.b.719.12		64	72.13	even	6
864.4.p.b.719.21		64	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81730 - 0.250612i) q^{2} +(2.93713 - 4.28640i) q^{3} +(7.87439 + 1.41210i) q^{4} +(3.52304 + 6.10209i) q^{5} +(-9.34902 + 11.3400i) q^{6} +(16.9049 + 9.76005i) q^{7} +(-21.8306 - 5.95172i) q^{8} +(-9.74649 - 25.1795i) q^{9} +(-8.39622 - 18.0744i) q^{10} +(11.8232 + 6.82610i) q^{11} +(29.1810 - 29.6053i) q^{12} +(55.8938 - 32.2703i) q^{13} +(-45.1802 - 31.7336i) q^{14} +(36.5037 + 2.82147i) q^{15} +(60.0120 + 22.2388i) q^{16} -47.8376i q^{17} +(21.1485 + 73.3808i) q^{18} +14.9265 q^{19} +(19.1251 + 53.0251i) q^{20} +(91.4874 - 43.7946i) q^{21} +(-31.5987 - 22.1942i) q^{22} +(-25.1060 - 43.4848i) q^{23} +(-89.6310 + 76.0939i) q^{24} +(37.6763 - 65.2573i) q^{25} +(-165.557 + 76.9075i) q^{26} +(-136.556 - 32.1781i) q^{27} +(119.334 + 100.726i) q^{28} +(-129.302 + 223.957i) q^{29} +(-102.135 - 17.0972i) q^{30} +(-108.559 + 62.6768i) q^{31} +(-163.499 - 77.6932i) q^{32} +(63.9856 - 30.6296i) q^{33} +(-11.9887 + 134.773i) q^{34} +137.540i q^{35} +(-41.1917 - 212.036i) q^{36} +208.987i q^{37} +(-42.0526 - 3.74077i) q^{38} +(25.8441 - 334.365i) q^{39} +(-40.5924 - 154.181i) q^{40} +(411.520 - 237.591i) q^{41} +(-268.723 + 100.455i) q^{42} +(-178.732 + 309.573i) q^{43} +(83.4610 + 70.4468i) q^{44} +(119.310 - 148.182i) q^{45} +(59.8333 + 128.802i) q^{46} +(-156.128 + 270.422i) q^{47} +(271.588 - 191.917i) q^{48} +(19.0170 + 32.9384i) q^{49} +(-122.500 + 174.407i) q^{50} +(-205.051 - 140.506i) q^{51} +(485.698 - 175.181i) q^{52} +476.697 q^{53} +(376.656 + 124.878i) q^{54} +96.1946i q^{55} +(-310.956 - 313.681i) q^{56} +(43.8413 - 63.9812i) q^{57} +(420.409 - 598.551i) q^{58} +(-425.920 + 245.905i) q^{59} +(283.460 + 73.7642i) q^{60} +(-661.465 - 381.897i) q^{61} +(321.552 - 149.373i) q^{62} +(80.9894 - 520.783i) q^{63} +(441.154 + 259.860i) q^{64} +(393.832 + 227.379i) q^{65} +(-187.943 + 70.2574i) q^{66} +(277.112 + 479.972i) q^{67} +(67.5514 - 376.692i) q^{68} +(-260.133 - 20.1064i) q^{69} +(34.4692 - 387.493i) q^{70} -87.1038 q^{71} +(62.9109 + 607.693i) q^{72} -818.083 q^{73} +(52.3747 - 588.780i) q^{74} +(-169.059 - 353.165i) q^{75} +(117.537 + 21.0778i) q^{76} +(133.246 + 230.789i) q^{77} +(-156.606 + 935.531i) q^{78} +(-1030.34 - 594.866i) q^{79} +(75.7214 + 444.547i) q^{80} +(-539.012 + 490.823i) q^{81} +(-1218.92 + 566.235i) q^{82} +(400.564 + 231.266i) q^{83} +(782.250 - 215.667i) q^{84} +(291.910 - 168.534i) q^{85} +(581.125 - 827.369i) q^{86} +(580.194 + 1212.03i) q^{87} +(-217.480 - 219.386i) q^{88} -1047.78i q^{89} +(-373.269 + 387.574i) q^{90} +1259.84 q^{91} +(-136.289 - 377.868i) q^{92} +(-50.1955 + 649.419i) q^{93} +(507.631 - 722.732i) q^{94} +(52.5869 + 91.0831i) q^{95} +(-813.241 + 472.625i) q^{96} +(-562.907 + 974.983i) q^{97} +(-45.3219 - 97.5633i) q^{98} +(56.6434 - 364.231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27}+ \cdots - 2118 q^{99}+O(q^{100}) \) 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

Introduction

L-functions

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