LMFDB - Embedded newform 21.4.e.b.16.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [21,4,Mod(4,21)] 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("21.4"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$21 = 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	21.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [6] 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:	$1.23904011012$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36$ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$3$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$0.124036 - 0.214837i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.4.e.b.4.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.124036 + 0.214837i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.96923 + 6.87491i) q^{4} +(6.21730 - 10.7687i) q^{5} -0.744216 q^{6} +(-18.4385 - 1.73873i) q^{7} -3.95388 q^{8} +(-4.50000 + 7.79423i) q^{9} +(1.54234 + 2.67141i) q^{10} +(-30.1558 - 52.2313i) q^{11} +(-11.9077 + 20.6247i) q^{12} +36.4269 q^{13} +(2.66058 - 3.74559i) q^{14} +37.3038 q^{15} +(-31.2634 + 54.1498i) q^{16} +(24.3731 + 42.2154i) q^{17} +(-1.11632 - 1.93353i) q^{18} +(25.2750 - 43.7776i) q^{19} +98.7116 q^{20} +(-23.1403 - 50.5126i) q^{21} +14.9616 q^{22} +(-69.3962 + 120.198i) q^{23} +(-5.93083 - 10.2725i) q^{24} +(-14.8097 - 25.6511i) q^{25} +(-4.51824 + 7.82583i) q^{26} -27.0000 q^{27} +(-61.2329 - 133.664i) q^{28} -61.1345 q^{29} +(-4.62701 + 8.01422i) q^{30} +(0.584676 + 1.01269i) q^{31} +(-23.5711 - 40.8264i) q^{32} +(90.4673 - 156.694i) q^{33} -12.0925 q^{34} +(-133.361 + 187.748i) q^{35} -71.4461 q^{36} +(-34.7634 + 60.2120i) q^{37} +(6.27001 + 10.8600i) q^{38} +(54.6403 + 94.6398i) q^{39} +(-24.5825 + 42.5781i) q^{40} +308.115 q^{41} +(13.7222 + 1.29399i) q^{42} +174.443 q^{43} +(239.390 - 414.636i) q^{44} +(55.9557 + 96.9181i) q^{45} +(-17.2153 - 29.8177i) q^{46} +(-194.681 + 337.197i) q^{47} -187.581 q^{48} +(336.954 + 64.1190i) q^{49} +7.34774 q^{50} +(-73.1192 + 126.646i) q^{51} +(144.587 + 250.432i) q^{52} +(-157.467 - 272.742i) q^{53} +(3.34897 - 5.80059i) q^{54} -749.950 q^{55} +(72.9035 + 6.87474i) q^{56} +151.650 q^{57} +(7.58287 - 13.1339i) q^{58} +(-422.263 - 731.381i) q^{59} +(148.067 + 256.460i) q^{60} +(169.269 - 293.182i) q^{61} -0.290084 q^{62} +(96.5251 - 135.889i) q^{63} -488.520 q^{64} +(226.477 - 392.270i) q^{65} +(22.4424 + 38.8714i) q^{66} +(485.775 + 841.387i) q^{67} +(-193.485 + 335.125i) q^{68} -416.377 q^{69} +(-23.7935 - 51.9384i) q^{70} -98.4698 q^{71} +(17.7925 - 30.8175i) q^{72} +(-355.117 - 615.082i) q^{73} +(-8.62383 - 14.9369i) q^{74} +(44.4291 - 76.9534i) q^{75} +401.289 q^{76} +(465.210 + 1015.50i) q^{77} -27.1095 q^{78} +(243.442 - 421.654i) q^{79} +(388.748 + 673.332i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-38.2174 + 66.1944i) q^{82} +605.688 q^{83} +(255.420 - 359.584i) q^{84} +606.139 q^{85} +(-21.6372 + 37.4767i) q^{86} +(-91.7017 - 158.832i) q^{87} +(119.232 + 206.517i) q^{88} +(-109.034 + 188.853i) q^{89} -27.7621 q^{90} +(-671.656 - 63.3365i) q^{91} -1101.80 q^{92} +(-1.75403 + 3.03807i) q^{93} +(-48.2949 - 83.6491i) q^{94} +(-314.284 - 544.357i) q^{95} +(70.7133 - 122.479i) q^{96} -782.288 q^{97} +(-55.5695 + 64.4369i) q^{98} +542.804 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - q^{2} + 9 q^{3} - 25 q^{4} - 11 q^{5} - 6 q^{6} - 13 q^{7} + 78 q^{8} - 27 q^{9} + 55 q^{10} - 35 q^{11} + 75 q^{12} + 124 q^{13} - 326 q^{14} - 66 q^{15} - 241 q^{16} - 48 q^{17} - 9 q^{18} + 202 q^{19}+ \cdots + 630 q^{99}+O(q^{100})$ 6 * q - q^2 + 9 * q^3 - 25 * q^4 - 11 * q^5 - 6 * q^6 - 13 * q^7 + 78 * q^8 - 27 * q^9 + 55 * q^10 - 35 * q^11 + 75 * q^12 + 124 * q^13 - 326 * q^14 - 66 * q^15 - 241 * q^16 - 48 * q^17 - 9 * q^18 + 202 * q^19 + 878 * q^20 + 3 * q^21 - 14 * q^22 - 216 * q^23 + 117 * q^24 - 130 * q^25 - 274 * q^26 - 162 * q^27 - 201 * q^28 + 106 * q^29 - 165 * q^30 + 95 * q^31 - 683 * q^32 + 105 * q^33 - 48 * q^34 + 56 * q^35 + 450 * q^36 - 262 * q^37 + 398 * q^38 + 186 * q^39 - 21 * q^40 + 488 * q^41 - 219 * q^42 + 720 * q^43 + 905 * q^44 - 99 * q^45 + 1056 * q^46 + 210 * q^47 - 1446 * q^48 - 303 * q^49 - 2756 * q^50 + 144 * q^51 - 324 * q^52 - 393 * q^53 + 27 * q^54 - 2062 * q^55 + 1299 * q^56 + 1212 * q^57 + 1249 * q^58 - 1143 * q^59 + 1317 * q^60 + 70 * q^61 + 2118 * q^62 + 126 * q^63 - 798 * q^64 + 472 * q^65 - 21 * q^66 + 628 * q^67 - 1944 * q^68 - 1296 * q^69 + 3251 * q^70 + 636 * q^71 - 351 * q^72 - 988 * q^73 - 1002 * q^74 + 390 * q^75 - 4680 * q^76 + 1073 * q^77 - 1644 * q^78 - 861 * q^79 - 175 * q^80 - 243 * q^81 - 124 * q^82 + 1038 * q^83 + 1620 * q^84 + 3600 * q^85 + 3208 * q^86 + 159 * q^87 + 891 * q^88 - 1766 * q^89 - 990 * q^90 - 654 * q^91 - 1344 * q^92 - 285 * q^93 + 3294 * q^94 + 736 * q^95 + 2049 * q^96 + 38 * q^97 - 4267 * q^98 + 630 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$ .

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.124036	+	0.214837i	−0.0438533	+	0.0759562i	−0.887119	−	0.461541i	$-0.847297\pi$
$2$	−0.124036	+	0.214837i	−0.0438533	+	0.0759562i	0.843266	+	0.537497i	$0.180630\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	3.96923	+	6.87491i	0.496154	+	0.859364i
$5$	6.21730	−	10.7687i	0.556092	−	0.963180i	−0.441725	−	0.897150i	$-0.645633\pi$
$5$	6.21730	−	10.7687i	0.556092	−	0.963180i	0.997818	−	0.0660299i	$-0.0210333\pi$
$6$	−0.744216			−0.0506375
$7$	−18.4385	−	1.73873i	−0.995583	−	0.0938826i
$7$	−18.4385	−	1.73873i	−0.995583	−	0.0938826i
$8$	−3.95388			−0.174739
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	1.54234	+	2.67141i	0.0487730	+	0.0844773i
$11$	−30.1558	−	52.2313i	−0.826573	−	1.43167i	−0.900711	−	0.434419i	$-0.856954\pi$
$11$	−30.1558	−	52.2313i	−0.826573	−	1.43167i	0.0741379	−	0.997248i	$-0.476379\pi$
$12$	−11.9077	+	20.6247i	−0.286455	+	0.496154i
$13$	36.4269			0.777154			0.388577	−	0.921416i	$-0.372967\pi$
$13$	36.4269			0.777154			0.388577	+	0.921416i	$0.372967\pi$
$14$	2.66058	−	3.74559i	0.0507906	−	0.0715037i
$15$	37.3038			0.642120
$16$	−31.2634	+	54.1498i	−0.488491	+	0.846091i
$17$	24.3731	+	42.2154i	0.347726	+	0.602279i	0.985845	−	0.167659i	$-0.0536207\pi$
$17$	24.3731	+	42.2154i	0.347726	+	0.602279i	−0.638119	+	0.769937i	$0.720287\pi$
$18$	−1.11632	−	1.93353i	−0.0146178	−	0.0253187i
$19$	25.2750	−	43.7776i	0.305183	−	0.528593i	−0.672119	−	0.740443i	$-0.734616\pi$
$19$	25.2750	−	43.7776i	0.305183	−	0.528593i	0.977302	+	0.211851i	$0.0679490\pi$
$20$	98.7116			1.10363
$21$	−23.1403	−	50.5126i	−0.240459	−	0.524893i
$22$	14.9616			0.144992
$23$	−69.3962	+	120.198i	−0.629135	+	1.08969i	0.358590	+	0.933495i	$0.383257\pi$
$23$	−69.3962	+	120.198i	−0.629135	+	1.08969i	−0.987726	+	0.156199i	$0.950076\pi$
$24$	−5.93083	−	10.2725i	−0.0504427	−	0.0873693i
$25$	−14.8097	−	25.6511i	−0.118478	−	0.205209i
$26$	−4.51824	+	7.82583i	−0.0340808	+	0.0590297i
$27$	−27.0000			−0.192450
$28$	−61.2329	−	133.664i	−0.413283	−	0.902148i
$29$	−61.1345			−0.391462			−0.195731	−	0.980658i	$-0.562708\pi$
$29$	−61.1345			−0.391462			−0.195731	+	0.980658i	$0.562708\pi$
$30$	−4.62701	+	8.01422i	−0.0281591	+	0.0487730i
$31$	0.584676	+	1.01269i	0.00338745	+	0.00586724i	0.867714	−	0.497064i	$-0.165588\pi$
$31$	0.584676	+	1.01269i	0.00338745	+	0.00586724i	−0.864327	+	0.502931i	$0.832255\pi$
$32$	−23.5711	−	40.8264i	−0.130213	−	0.225536i
$33$	90.4673	−	156.694i	0.477222	−	0.826573i
$34$	−12.0925			−0.0609957
$35$	−133.361	+	187.748i	−0.644062	+	0.906719i
$36$	−71.4461			−0.330769
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	−0.932863	−	0.360232i	$-0.882698\pi$
$37$	−34.7634	+	60.2120i	−0.154461	+	0.267535i	0.778401	+	0.627767i	$0.216031\pi$
$38$	6.27001	+	10.8600i	0.0267666	+	0.0463611i
$39$	54.6403	+	94.6398i	0.224345	+	0.388577i
$40$	−24.5825	+	42.5781i	−0.0971708	+	0.168305i
$41$	308.115			1.17365			0.586823	−	0.809715i	$-0.300378\pi$
$41$	308.115			1.17365			0.586823	+	0.809715i	$0.300378\pi$
$42$	13.7222	+	1.29399i	0.0504138	+	0.00475398i
$43$	174.443			0.618657			0.309329	−	0.950955i	$-0.399896\pi$
$43$	174.443			0.618657			0.309329	+	0.950955i	$0.399896\pi$
$44$	239.390	−	414.636i	0.820215	−	1.42065i
$45$	55.9557	+	96.9181i	0.185364	+	0.321060i
$46$	−17.2153	−	29.8177i	−0.0551794	−	0.0955734i
$47$	−194.681	+	337.197i	−0.604194	+	1.04649i	0.387984	+	0.921666i	$0.373172\pi$
$47$	−194.681	+	337.197i	−0.604194	+	1.04649i	−0.992178	+	0.124829i	$0.960162\pi$
$48$	−187.581			−0.564061
$49$	336.954	+	64.1190i	0.982372	+	0.186936i
$50$	7.34774			0.0207825
$51$	−73.1192	+	126.646i	−0.200760	+	0.347726i
$52$	144.587	+	250.432i	0.385588	+	0.667858i
$53$	−157.467	−	272.742i	−0.408110	−	0.706867i	0.586568	−	0.809900i	$-0.300479\pi$
$53$	−157.467	−	272.742i	−0.408110	−	0.706867i	−0.994678	+	0.103033i	$0.967145\pi$
$54$	3.34897	−	5.80059i	0.00843958	−	0.0146178i
$55$	−749.950			−1.83860
$56$	72.9035	+	6.87474i	0.173967	+	0.0164049i
$57$	151.650			0.352395
$58$	7.58287	−	13.1339i	0.0171669	−	0.0297339i
$59$	−422.263	−	731.381i	−0.931762	−	1.61386i	−0.780308	−	0.625396i	$-0.784938\pi$
$59$	−422.263	−	731.381i	−0.931762	−	1.61386i	−0.151455	−	0.988464i	$-0.548396\pi$
$60$	148.067	+	256.460i	0.318590	+	0.551815i
$61$	169.269	−	293.182i	0.355290	−	0.615380i	−0.631878	−	0.775068i	$-0.717716\pi$
$61$	169.269	−	293.182i	0.355290	−	0.615380i	0.987167	+	0.159688i	$0.0510489\pi$
$62$	−0.290084			−0.000594204
$63$	96.5251	−	135.889i	0.193032	−	0.271753i
$64$	−488.520			−0.954141
$65$	226.477	−	392.270i	0.432169	−	0.748539i
$66$	22.4424	+	38.8714i	0.0418556	+	0.0724960i
$67$	485.775	+	841.387i	0.885774	+	1.53421i	0.844824	+	0.535044i	$0.179705\pi$
$67$	485.775	+	841.387i	0.885774	+	1.53421i	0.0409498	+	0.999161i	$0.486962\pi$
$68$	−193.485	+	335.125i	−0.345051	+	0.597646i
$69$	−416.377			−0.726463
$70$	−23.7935	−	51.9384i	−0.0406266	−	0.0886832i
$71$	−98.4698			−0.164595			−0.0822973	−	0.996608i	$-0.526226\pi$
$71$	−98.4698			−0.164595			−0.0822973	+	0.996608i	$0.526226\pi$
$72$	17.7925	−	30.8175i	0.0291231	−	0.0504427i
$73$	−355.117	−	615.082i	−0.569361	−	0.986162i	−0.996629	−	0.0820374i	$-0.973857\pi$
$73$	−355.117	−	615.082i	−0.569361	−	0.986162i	0.427268	−	0.904125i	$-0.359476\pi$
$74$	−8.62383	−	14.9369i	−0.0135473	−	0.0234646i
$75$	44.4291	−	76.9534i	0.0684030	−	0.118478i
$76$	401.289			0.605671
$77$	465.210	+	1015.50i	0.688514	+	1.50294i
$78$	−27.1095			−0.0393531
$79$	243.442	−	421.654i	0.346701	−	0.600504i	−0.638960	−	0.769240i	$-0.720635\pi$
$79$	243.442	−	421.654i	0.346701	−	0.600504i	0.985661	+	0.168736i	$0.0539686\pi$
$80$	388.748	+	673.332i	0.543292	+	0.941010i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−38.2174	+	66.1944i	−0.0514683	+	0.0891458i
$83$	605.688			0.800999			0.400499	−	0.916297i	$-0.368837\pi$
$83$	605.688			0.800999			0.400499	+	0.916297i	$0.368837\pi$
$84$	255.420	−	359.584i	0.331770	−	0.467069i
$85$	606.139			0.773470
$86$	−21.6372	+	37.4767i	−0.0271302	+	0.0469908i
$87$	−91.7017	−	158.832i	−0.113005	−	0.195731i
$88$	119.232	+	206.517i	0.144434	+	0.250168i
$89$	−109.034	+	188.853i	−0.129861	+	0.224925i	−0.923622	−	0.383303i	$-0.874786\pi$
$89$	−109.034	+	188.853i	−0.129861	+	0.224925i	0.793762	+	0.608229i	$0.208120\pi$
$90$	−27.7621			−0.0325153
$91$	−671.656	−	63.3365i	−0.773722	−	0.0729612i
$92$	−1101.80			−1.24859
$93$	−1.75403	+	3.03807i	−0.00195575	+	0.00338745i
$94$	−48.2949	−	83.6491i	−0.0529919	−	0.0917846i
$95$	−314.284	−	544.357i	−0.339420	−	0.587893i
$96$	70.7133	−	122.479i	0.0751787	−	0.130213i
$97$	−782.288			−0.818859			−0.409429	−	0.912342i	$-0.634272\pi$
$97$	−782.288			−0.818859			−0.409429	+	0.912342i	$0.634272\pi$
$98$	−55.5695	+	64.4369i	−0.0572792	+	0.0664195i
$99$	542.804			0.551049
$100$	117.566	−	203.631i	0.117566	−	0.203631i
$101$	155.823	+	269.893i	0.153514	+	0.265895i	0.932517	−	0.361126i	$-0.117608\pi$
$101$	155.823	+	269.893i	0.153514	+	0.265895i	−0.779003	+	0.627021i	$0.784274\pi$
$102$	−18.1388	−	31.4174i	−0.0176079	−	0.0304979i
$103$	74.6289	−	129.261i	0.0713922	−	0.123655i	−0.828119	−	0.560552i	$-0.810589\pi$
$103$	74.6289	−	129.261i	0.0713922	−	0.123655i	0.899512	+	0.436897i	$0.143922\pi$
$104$	−144.028			−0.135799
$105$	−687.825	−	64.8613i	−0.639284	−	0.0602839i
$106$	78.1265			0.0715879
$107$	−425.760	+	737.437i	−0.384670	+	0.666269i	−0.991723	−	0.128393i	$-0.959018\pi$
$107$	−425.760	+	737.437i	−0.384670	+	0.666269i	0.607053	+	0.794661i	$0.292352\pi$
$108$	−107.169	−	185.623i	−0.0954848	−	0.165385i
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	−0.993062	−	0.117592i	$-0.962483\pi$
$109$	−680.939	−	1179.42i	−0.598369	−	1.03640i	0.394694	−	0.918813i	$-0.370851\pi$
$110$	93.0208	−	161.117i	0.0806289	−	0.139653i
$111$	−208.581			−0.178357
$112$	670.601	−	944.081i	0.565767	−	0.796493i
$113$	1048.55			0.872917			0.436459	−	0.899724i	$-0.356233\pi$
$113$	1048.55			0.872917			0.436459	+	0.899724i	$0.356233\pi$
$114$	−18.8100	+	32.5800i	−0.0154537	+	0.0267666i
$115$	862.914	+	1494.61i	0.699715	+	1.21194i
$116$	−242.657	−	420.294i	−0.194225	−	0.336408i
$117$	−163.921	+	283.920i	−0.129526	+	0.224345i
$118$	209.503			0.163444
$119$	−376.001	−	820.765i	−0.289646	−	0.632264i
$120$	−147.495			−0.112203
$121$	−1153.24	+	1997.47i	−0.866446	+	1.50073i
$122$	41.9909	+	72.7303i	0.0311613	+	0.0539729i
$123$	462.173	+	800.507i	0.338803	+	0.586823i
$124$	−4.64143	+	8.03919i	−0.00336139	+	0.00582210i
$125$	1186.02			0.848647
$126$	17.2214	+	37.5923i	0.0121762	+	0.0265793i
$127$	488.408			0.341254			0.170627	−	0.985336i	$-0.445421\pi$
$127$	488.408			0.341254			0.170627	+	0.985336i	$0.445421\pi$
$128$	249.163	−	431.563i	0.172056	−	0.298009i
$129$	261.664	+	453.215i	0.178591	+	0.309329i
$130$	56.1826	+	97.3111i	0.0379041	+	0.0656519i
$131$	927.114	−	1605.81i	0.618338	−	1.07099i	−0.371451	−	0.928453i	$-0.621139\pi$
$131$	927.114	−	1605.81i	0.618338	−	1.07099i	0.989789	−	0.142541i	$-0.0455272\pi$
$132$	1436.34			0.947102
$133$	−542.149	+	763.244i	−0.353461	+	0.497607i
$134$	−241.014			−0.155377
$135$	−167.867	+	290.754i	−0.107020	+	0.185364i
$136$	−96.3683	−	166.915i	−0.0607611	−	0.105241i
$137$	255.558	+	442.639i	0.159370	+	0.276038i	0.934642	−	0.355591i	$-0.115720\pi$
$137$	255.558	+	442.639i	0.159370	+	0.276038i	−0.775271	+	0.631628i	$0.782387\pi$
$138$	51.6458	−	89.4531i	0.0318578	−	0.0551794i
$139$	2266.10			1.38279			0.691397	−	0.722475i	$-0.256995\pi$
$139$	2266.10			1.38279			0.691397	+	0.722475i	$0.256995\pi$
$140$	−1820.09	−	171.633i	−1.09875	−	0.103612i
$141$	−1168.09			−0.697663
$142$	12.2138	−	21.1549i	0.00721802	−	0.0125020i
$143$	−1098.48	−	1902.62i	−0.642375	−	1.11263i
$144$	−281.371	−	487.348i	−0.162830	−	0.282030i
$145$	−380.091	+	658.338i	−0.217689	+	0.377048i
$146$	176.189			0.0998735
$147$	338.844	+	971.610i	0.190118	+	0.545150i
$148$	−551.936			−0.306546
$149$	−753.950	+	1305.88i	−0.414537	+	0.717999i	−0.995380	−	0.0960168i	$-0.969390\pi$
$149$	−753.950	+	1305.88i	−0.414537	+	0.717999i	0.580843	+	0.814016i	$0.302723\pi$
$150$	11.0216	+	19.0900i	0.00599940	+	0.0103913i
$151$	−795.913	−	1378.56i	−0.428943	−	0.742952i	0.567836	−	0.823142i	$-0.307781\pi$
$151$	−795.913	−	1378.56i	−0.428943	−	0.742952i	−0.996780	+	0.0801897i	$0.974447\pi$
$152$	−99.9344	+	173.091i	−0.0533273	+	0.0923656i
$153$	−438.715			−0.231817
$154$	−275.869	−	26.0142i	−0.144352	−	0.0136122i
$155$	14.5404			0.00753494
$156$	−433.760	+	751.295i	−0.222619	+	0.385588i
$157$	−582.080	−	1008.19i	−0.295892	−	0.512500i	0.679300	−	0.733861i	$-0.262283\pi$
$157$	−582.080	−	1008.19i	−0.295892	−	0.512500i	−0.975192	+	0.221361i	$0.928950\pi$
$158$	60.3911	+	104.601i	0.0304080	+	0.0526682i
$159$	472.402	−	818.225i	0.235622	−	0.408110i
$160$	−586.195			−0.289642
$161$	1488.55	−	2095.60i	0.728660	−	1.02582i
$162$	20.0938			0.00974519
$163$	577.940	−	1001.02i	0.277716	−	0.481019i	−0.693101	−	0.720841i	$-0.743756\pi$
$163$	577.940	−	1001.02i	0.277716	−	0.481019i	0.970817	+	0.239822i	$0.0770892\pi$
$164$	1222.98	+	2118.26i	0.582309	+	1.00859i
$165$	−1124.92	−	1948.43i	−0.530759	−	0.919302i
$166$	−75.1271	+	130.124i	−0.0351265	+	0.0608408i
$167$	−2890.61			−1.33941			−0.669707	−	0.742626i	$-0.733580\pi$
$167$	−2890.61			−1.33941			−0.669707	+	0.742626i	$0.733580\pi$
$168$	91.4942	+	199.721i	0.0420175	+	0.0917191i
$169$	−870.082			−0.396032
$170$	−75.1830	+	130.221i	−0.0339193	+	0.0587499i
$171$	227.475	+	393.998i	0.101728	+	0.176198i
$172$	692.403	+	1199.28i	0.306949	+	0.531651i
$173$	−947.468	+	1641.06i	−0.416385	+	0.721200i	−0.995573	−	0.0939940i	$-0.970037\pi$
$173$	−947.468	+	1641.06i	−0.416385	+	0.721200i	0.579188	+	0.815194i	$0.303370\pi$
$174$	45.4972			0.0198226
$175$	228.467	+	498.718i	0.0986887	+	0.215426i
$176$	3771.09			1.61509
$177$	1266.79	−	2194.14i	0.537953	−	0.931762i
$178$	−27.0483	−	46.8491i	−0.0113897	−	0.0197275i
$179$	2144.25	+	3713.94i	0.895355	+	1.55080i	0.833365	+	0.552723i	$0.186411\pi$
$179$	2144.25	+	3713.94i	0.895355	+	1.55080i	0.0619893	+	0.998077i	$0.480256\pi$
$180$	−444.202	+	769.381i	−0.183938	+	0.318590i
$181$	383.732			0.157583			0.0787917	−	0.996891i	$-0.474894\pi$
$181$	383.732			0.157583			0.0787917	+	0.996891i	$0.474894\pi$
$182$	96.9165	−	136.440i	0.0394721	−	0.0555694i
$183$	1015.61			0.410253
$184$	274.385	−	475.248i	0.109934	−	0.190412i
$185$	432.269	+	748.712i	0.171790	+	0.297548i
$186$	−0.435125	−	0.753659i	−0.000171532	−	0.000297102i
$187$	1469.98	−	2546.07i	0.574841	−	0.995655i
$188$	−3090.93			−1.19909
$189$	497.838	+	46.9457i	0.191600	+	0.0180677i
$190$	155.930			0.0595388
$191$	−192.655	+	333.689i	−0.0729845	+	0.126413i	−0.900208	−	0.435460i	$-0.856586\pi$
$191$	−192.655	+	333.689i	−0.0729845	+	0.126413i	0.827224	+	0.561873i	$0.189919\pi$
$192$	−732.780	−	1269.21i	−0.275437	−	0.477070i
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	0.801262	−	0.598314i	$-0.204163\pi$
$193$	−315.112	−	545.790i	−0.117525	−	0.203559i	−0.918786	+	0.394756i	$0.870829\pi$
$194$	97.0318	−	168.064i	0.0359097	−	0.0621974i
$195$	1358.86			0.499026
$196$	896.634	+	2571.03i	0.326762	+	0.936964i
$197$	−1250.23			−0.452158			−0.226079	−	0.974109i	$-0.572591\pi$
$197$	−1250.23			−0.452158			−0.226079	+	0.974109i	$0.572591\pi$
$198$	−67.3272	+	116.614i	−0.0241653	+	0.0418556i
$199$	546.122	+	945.912i	0.194541	+	0.336954i	0.946750	−	0.321970i	$-0.104345\pi$
$199$	546.122	+	945.912i	0.194541	+	0.336954i	−0.752209	+	0.658924i	$0.771012\pi$
$200$	58.5558	+	101.422i	0.0207026	+	0.0358580i
$201$	−1457.32	+	2524.16i	−0.511402	+	0.885774i
$202$	−77.3105			−0.0269285
$203$	1127.23	+	106.296i	0.389733	+	0.0367514i
$204$	−1160.91			−0.398430
$205$	1915.65	−	3318.00i	0.652656	−	1.13043i
$206$	18.5133	+	32.0660i	0.00626158	+	0.0108454i
$207$	−624.566	−	1081.78i	−0.209712	−	0.363231i
$208$	−1138.83	+	1972.51i	−0.379633	+	0.657543i
$209$	−3048.75			−1.00902
$210$	99.2496	−	139.725i	0.0326137	−	0.0459139i
$211$	−3620.05			−1.18111			−0.590556	−	0.806997i	$-0.701091\pi$
$211$	−3620.05			−1.18111			−0.590556	+	0.806997i	$0.701091\pi$
$212$	1250.05	−	2165.15i	0.404970	−	0.701429i
$213$	−147.705	−	255.832i	−0.0475143	−	0.0822973i
$214$	−105.619	−	182.937i	−0.0337382	−	0.0584362i
$215$	1084.56	−	1878.52i	0.344030	−	0.595878i
$216$	106.755			0.0336285
$217$	−9.01974	−	19.6890i	−0.00282166	−	0.00615935i
$218$	337.844			0.104962
$219$	1065.35	−	1845.24i	0.328721	−	0.569361i
$220$	−2976.72	−	5155.84i	−0.912230	−	1.58003i
$221$	887.835	+	1537.78i	0.270236	+	0.468063i
$222$	25.8715	−	44.8107i	0.00782153	−	0.0135473i
$223$	−183.844			−0.0552069			−0.0276034	−	0.999619i	$-0.508788\pi$
$223$	−183.844			−0.0552069			−0.0276034	+	0.999619i	$0.508788\pi$
$224$	363.629	+	793.759i	0.108464	+	0.236765i
$225$	266.574			0.0789850
$226$	−130.058	+	225.268i	−0.0382803	+	0.0663035i
$227$	−1139.76	−	1974.12i	−0.333253	−	0.577211i	0.649895	−	0.760024i	$-0.274813\pi$
$227$	−1139.76	−	1974.12i	−0.333253	−	0.577211i	−0.983148	+	0.182813i	$0.941480\pi$
$228$	601.933	+	1042.58i	0.174842	+	0.302836i
$229$	−2706.34	+	4687.51i	−0.780960	+	1.35266i	0.150424	+	0.988622i	$0.451936\pi$
$229$	−2706.34	+	4687.51i	−0.780960	+	1.35266i	−0.931383	+	0.364040i	$0.881397\pi$
$230$	−428.130			−0.122739
$231$	−1940.53	+	2731.90i	−0.552715	+	0.778120i
$232$	241.719			0.0684035
$233$	−569.184	+	985.856i	−0.160036	+	0.277191i	−0.934882	−	0.354960i	$-0.884494\pi$
$233$	−569.184	+	985.856i	−0.160036	+	0.277191i	0.774845	+	0.632151i	$0.217828\pi$
$234$	−40.6642	−	70.4325i	−0.0113603	−	0.0196766i
$235$	2420.78	+	4192.91i	0.671975	+	1.16390i
$236$	3352.12	−	5806.04i	0.924595	−	1.60145i
$237$	1460.65			0.400336
$238$	222.968	+	21.0257i	0.0607263	+	0.00572644i
$239$	−6226.36			−1.68515			−0.842573	−	0.538583i	$-0.818960\pi$
$239$	−6226.36			−1.68515			−0.842573	+	0.538583i	$0.818960\pi$
$240$	−1166.24	+	2020.00i	−0.313670	+	0.543292i
$241$	1598.10	+	2767.99i	0.427147	+	0.739841i	0.996618	−	0.0821704i	$-0.0261852\pi$
$241$	1598.10	+	2767.99i	0.427147	+	0.739841i	−0.569471	+	0.822012i	$0.692852\pi$
$242$	−286.086	−	495.516i	−0.0759931	−	0.131624i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	2687.47			0.705113
$245$	2785.42	−	3229.90i	0.726343	−	0.842248i
$246$	−229.304			−0.0594305
$247$	920.689	−	1594.68i	0.237174	−	0.410798i
$248$	−2.31174	−	4.00406i	−0.000591919	−	0.00102523i
$249$	908.532	+	1573.62i	0.231228	+	0.400499i
$250$	−147.109	+	254.801i	−0.0372160	+	0.0644600i
$251$	239.608			0.0602546			0.0301273	−	0.999546i	$-0.490409\pi$
$251$	239.608			0.0602546			0.0301273	+	0.999546i	$0.490409\pi$
$252$	1317.36	+	124.226i	0.329308	+	0.0310535i
$253$	8370.78			2.08010
$254$	−60.5802	+	104.928i	−0.0149651	+	0.0259203i
$255$	909.208	+	1574.79i	0.223282	+	0.386735i
$256$	−1892.27	−	3277.51i	−0.461980	−	0.800173i
$257$	−349.559	+	605.453i	−0.0848439	+	0.146954i	−0.905325	−	0.424720i	$-0.860372\pi$
$257$	−349.559	+	605.453i	−0.0848439	+	0.146954i	0.820481	+	0.571674i	$0.193706\pi$
$258$	−129.823			−0.0313272
$259$	745.676	−	1049.77i	0.178896	−	0.251852i
$260$	3595.76			0.857690
$261$	275.105	−	476.496i	0.0652436	−	0.113005i
$262$	229.991	+	398.356i	0.0542324	+	0.0939333i
$263$	459.520	+	795.912i	0.107738	+	0.186609i	0.914854	−	0.403785i	$-0.132306\pi$
$263$	459.520	+	795.912i	0.107738	+	0.186609i	−0.807115	+	0.590394i	$0.798972\pi$
$264$	−357.697	+	619.550i	−0.0833892	+	0.144434i
$265$	−3916.09			−0.907787
$266$	−96.7268	−	211.143i	−0.0222959	−	0.0486693i
$267$	−654.206			−0.149950
$268$	−3856.30	+	6679.32i	−0.878960	+	1.52240i
$269$	1389.59	+	2406.84i	0.314961	+	0.545529i	0.979429	−	0.201788i	$-0.0646751\pi$
$269$	1389.59	+	2406.84i	0.314961	+	0.545529i	−0.664468	+	0.747317i	$0.731342\pi$
$270$	−41.6431	−	72.1280i	−0.00938637	−	0.0162577i
$271$	−1113.49	+	1928.62i	−0.249593	+	0.432308i	−0.963413	−	0.268021i	$-0.913630\pi$
$271$	−1113.49	+	1928.62i	−0.249593	+	0.432308i	0.713820	+	0.700329i	$0.246964\pi$
$272$	−3047.94			−0.679443
$273$	−842.931	−	1840.02i	−0.186874	−	0.407923i
$274$	−126.793			−0.0279557
$275$	−893.195	+	1547.06i	−0.195861	+	0.339241i
$276$	−1652.70	−	2862.56i	−0.360437	−	0.624296i
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	−0.924379	−	0.381476i	$-0.875416\pi$
$277$	−3653.85	−	6328.65i	−0.792557	−	1.37275i	0.131821	−	0.991273i	$-0.457917\pi$
$278$	−281.078	+	486.842i	−0.0606402	+	0.105032i
$279$	−10.5242			−0.00225830
$280$	527.295	−	742.333i	0.112543	−	0.158439i
$281$	2730.61			0.579696			0.289848	−	0.957073i	$-0.406395\pi$
$281$	2730.61			0.579696			0.289848	+	0.957073i	$0.406395\pi$
$282$	144.885	−	250.947i	0.0305949	−	0.0529919i
$283$	884.926	+	1532.74i	0.185878	+	0.321950i	0.943872	−	0.330312i	$-0.107154\pi$
$283$	884.926	+	1532.74i	0.185878	+	0.321950i	−0.757994	+	0.652261i	$0.773821\pi$
$284$	−390.849	−	676.971i	−0.0816642	−	0.141447i
$285$	942.853	−	1633.07i	0.195964	−	0.339420i
$286$	545.004			0.112681
$287$	−5681.17	−	535.729i	−1.16846	−	0.110185i
$288$	424.280			0.0868088
$289$	1268.41	−	2196.95i	0.258174	−	0.447170i
$290$	−94.2900	−	163.315i	−0.0190928	−	0.0330696i
$291$	−1173.43	−	2032.44i	−0.236384	−	0.409429i
$292$	2819.09	−	4882.80i	0.564981	−	0.978576i
$293$	8228.81			1.64072			0.820362	−	0.571844i	$-0.193772\pi$
$293$	8228.81			1.64072			0.820362	+	0.571844i	$0.193772\pi$
$294$	−250.766	−	47.7184i	−0.0497448	−	0.00946596i
$295$	−10501.4			−2.07258
$296$	137.451	−	238.071i	0.0269904	−	0.0467487i
$297$	814.206	+	1410.25i	0.159074	+	0.275524i
$298$	−187.034	−	323.952i	−0.0363577	−	0.0629733i
$299$	−2527.89	+	4378.43i	−0.488935	+	0.846860i
$300$	705.397			0.135754
$301$	−3216.45	−	303.309i	−0.615925	−	0.0580811i
$302$	394.887			0.0752424
$303$	−467.468	+	809.679i	−0.0886316	+	0.153514i
$304$	1580.36	+	2737.27i	0.298158	+	0.516425i
$305$	−2104.79	−	3645.61i	−0.395148	−	0.684416i
$306$	54.4165	−	94.2521i	0.0101660	−	0.0176079i
$307$	6019.62			1.11908			0.559541	−	0.828803i	$-0.310977\pi$
$307$	6019.62			1.11908			0.559541	+	0.828803i	$0.310977\pi$
$308$	−5134.93	+	7229.02i	−0.949967	+	1.33738i
$309$	447.773			0.0824366
$310$	−1.80354	+	3.12382i	−0.000330432	+	0.000572326i
$311$	−596.857	−	1033.79i	−0.108825	−	0.188491i	0.806469	−	0.591276i	$-0.201376\pi$
$311$	−596.857	−	1033.79i	−0.108825	−	0.188491i	−0.915295	+	0.402785i	$0.868042\pi$
$312$	−216.042	−	374.195i	−0.0392018	−	0.0678994i
$313$	4423.02	−	7660.89i	0.798734	−	1.38345i	−0.121707	−	0.992566i	$-0.538837\pi$
$313$	4423.02	−	7660.89i	0.798734	−	1.38345i	0.920441	−	0.390882i	$-0.127830\pi$
$314$	288.795			0.0519034
$315$	−863.223	−	1884.31i	−0.154403	−	0.337045i
$316$	3865.11			0.688068
$317$	−3040.72	+	5266.68i	−0.538750	+	0.933142i	0.460222	+	0.887804i	$0.347770\pi$
$317$	−3040.72	+	5266.68i	−0.538750	+	0.933142i	−0.998972	+	0.0453380i	$0.985564\pi$
$318$	117.190	+	202.979i	0.0206656	+	0.0357940i
$319$	1843.56	+	3193.13i	0.323572	+	0.560442i
$320$	−3037.28	+	5260.72i	−0.530590	+	0.919009i
$321$	−2554.56			−0.444179
$322$	265.578	+	579.725i	0.0459630	+	0.100332i
$323$	2464.12			0.424480
$324$	321.508	−	556.868i	0.0551282	−	0.0954848i
$325$	−539.471	−	934.391i	−0.0920753	−	0.159479i
$326$	143.371	+	248.325i	0.0243576	+	0.0421885i
$327$	2042.82	−	3538.26i	0.345468	−	0.598369i
$328$	−1218.25			−0.205082
$329$	4175.91	−	5878.90i	0.699773	−	0.985149i
$330$	558.125			0.0931023
$331$	−1526.65	+	2644.23i	−0.253511	+	0.439094i	−0.964490	−	0.264119i	$-0.914919\pi$
$331$	−1526.65	+	2644.23i	−0.253511	+	0.439094i	0.710979	+	0.703213i	$0.248252\pi$
$332$	2404.12	+	4164.05i	0.397419	+	0.688349i
$333$	−312.871	−	541.908i	−0.0514871	−	0.0891783i
$334$	358.539	−	621.009i	0.0587377	−	0.101737i
$335$	12080.8			1.97029
$336$	3458.70	+	326.152i	0.561569	+	0.0529555i
$337$	3865.80			0.624877			0.312438	−	0.949938i	$-0.398854\pi$
$337$	3865.80			0.624877			0.312438	+	0.949938i	$0.398854\pi$
$338$	107.921	−	186.925i	0.0173673	−	0.0300811i
$339$	1572.83	+	2724.22i	0.251989	+	0.436459i
$340$	2405.90	+	4167.15i	0.383760	+	0.664692i
$341$	35.2627	−	61.0768i	0.00559995	−	0.00969940i
$342$	−112.860			−0.0178444
$343$	−6101.42	−	1768.13i	−0.960483	−	0.278338i
$344$	−689.726			−0.108103
$345$	−2588.74	+	4483.83i	−0.403980	+	0.699715i
$346$	−235.040	−	407.101i	−0.0365198	−	0.0632541i
$347$	49.7965	+	86.2501i	0.00770380	+	0.0133434i	0.869852	−	0.493313i	$-0.164214\pi$
$347$	49.7965	+	86.2501i	0.00770380	+	0.0133434i	−0.862148	+	0.506657i	$0.830881\pi$
$348$	727.970	−	1260.88i	0.112136	−	0.194225i
$349$	−3607.34			−0.553285			−0.276643	−	0.960973i	$-0.589222\pi$
$349$	−3607.34			−0.553285			−0.276643	+	0.960973i	$0.589222\pi$
$350$	−135.481	−	12.7757i	−0.0206907	−	0.00195112i
$351$	−983.526			−0.149563
$352$	−1421.61	+	2462.30i	−0.215262	+	0.372844i
$353$	−3565.37	−	6175.40i	−0.537579	−	0.931114i	−0.999034	−	0.0439501i	$-0.986006\pi$
$353$	−3565.37	−	6175.40i	−0.537579	−	0.931114i	0.461455	−	0.887164i	$-0.347328\pi$
$354$	314.255	+	544.306i	0.0471821	+	0.0817218i
$355$	−612.216	+	1060.39i	−0.0915298	+	0.158534i
$356$	−1731.13			−0.257724
$357$	1568.41	−	2208.03i	0.232518	−	0.327342i
$358$	−1063.85			−0.157057
$359$	3250.14	−	5629.41i	0.477816	−	0.827602i	−0.521860	−	0.853031i	$-0.674762\pi$
$359$	3250.14	−	5629.41i	0.477816	−	0.827602i	0.999677	+	0.0254289i	$0.00809514\pi$
$360$	−221.242	−	383.203i	−0.0323903	−	0.0561016i
$361$	2151.85	+	3727.11i	0.313727	+	0.543390i
$362$	−47.5966	+	82.4398i	−0.00691056	+	0.0119694i
$363$	−6919.44			−1.00049
$364$	−2230.52	−	4868.97i	−0.321185	−	0.701108i
$365$	−8831.49			−1.26647
$366$	−125.973	+	218.191i	−0.0179910	+	0.0311613i
$367$	−412.443	−	714.372i	−0.0586631	−	0.101607i	0.835202	−	0.549943i	$-0.185350\pi$
$367$	−412.443	−	714.372i	−0.0586631	−	0.101607i	−0.893866	+	0.448335i	$0.852017\pi$
$368$	−4339.12	−	7515.58i	−0.614654	−	1.06461i
$369$	−1386.52	+	2401.52i	−0.195608	+	0.338803i
$370$	−214.468			−0.0301342
$371$	2429.23	+	5302.73i	0.339945	+	0.742059i
$372$	−27.8486			−0.00388140
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	−0.908596	−	0.417677i	$-0.862845\pi$
$373$	−666.925	+	1155.15i	−0.0925793	+	0.160352i	0.816016	+	0.578029i	$0.196178\pi$
$374$	364.660	+	631.610i	0.0504174	+	0.0873255i
$375$	1779.03	+	3081.37i	0.244983	+	0.424324i
$376$	769.746	−	1333.24i	0.105576	−	0.182863i
$377$	−2226.94			−0.304226
$378$	−71.8355	+	101.131i	−0.00977466	+	0.0137609i
$379$	−1338.29			−0.181380			−0.0906902	−	0.995879i	$-0.528907\pi$
$379$	−1338.29			−0.181380			−0.0906902	+	0.995879i	$0.528907\pi$
$380$	2494.93	−	4321.35i	0.336809	−	0.583370i
$381$	732.612	+	1268.92i	0.0985114	+	0.170627i
$382$	−47.7924	−	82.7788i	−0.00640123	−	0.0110873i
$383$	−176.688	+	306.032i	−0.0235727	+	0.0408290i	−0.877571	−	0.479447i	$-0.840837\pi$
$383$	−176.688	+	306.032i	−0.0235727	+	0.0408290i	0.853998	+	0.520276i	$0.174171\pi$
$384$	1494.98			0.198673
$385$	13827.9	+	1303.96i	1.83048	+	0.172613i
$386$	156.341			0.0206154
$387$	−784.992	+	1359.65i	−0.103110	+	0.178591i
$388$	−3105.08	−	5378.16i	−0.406280	−	0.703697i
$389$	−5868.59	−	10164.7i	−0.764908	−	1.32486i	−0.940295	−	0.340360i	$-0.889451\pi$
$389$	−5868.59	−	10164.7i	−0.764908	−	1.32486i	0.175387	−	0.984500i	$-0.443882\pi$
$390$	−168.548	+	291.933i	−0.0218840	+	0.0379041i
$391$	−6765.59			−0.875066
$392$	−1332.28	−	253.519i	−0.171658	−	0.0326649i
$393$	5562.68			0.713996
$394$	155.073	−	268.595i	0.0198286	−	0.0343442i
$395$	−3027.11	−	5243.10i	−0.385595	−	0.667871i
$396$	2154.51	+	3731.73i	0.273405	+	0.473551i
$397$	−6640.71	+	11502.1i	−0.839516	+	1.45408i	0.0507841	+	0.998710i	$0.483828\pi$
$397$	−6640.71	+	11502.1i	−0.839516	+	1.45408i	−0.890300	+	0.455374i	$0.849505\pi$
$398$	−270.955			−0.0341250
$399$	−2796.19	−	263.678i	−0.350839	−	0.0330838i
$400$	1852.01			0.231501
$401$	3741.18	−	6479.91i	0.465899	−	0.806961i	−0.533343	−	0.845899i	$-0.679064\pi$
$401$	3741.18	−	6479.91i	0.465899	−	0.806961i	0.999242	+	0.0389385i	$0.0123976\pi$
$402$	−361.521	−	626.173i	−0.0448534	−	0.0776883i
$403$	21.2979	+	36.8891i	0.00263257	+	0.00455975i
$404$	−1236.99	+	2142.54i	−0.152333	+	0.263849i
$405$	−1007.20			−0.123576
$406$	−162.653	+	228.985i	−0.0198826	+	0.0279909i
$407$	4193.27			0.510694
$408$	289.105	−	500.744i	0.0350805	−	0.0607611i
$409$	6898.30	+	11948.2i	0.833983	+	1.44450i	0.894856	+	0.446355i	$0.147278\pi$
$409$	6898.30	+	11948.2i	0.833983	+	1.44450i	−0.0608735	+	0.998145i	$0.519389\pi$
$410$	475.218	+	823.102i	0.0572423	+	0.0991466i
$411$	−766.673	+	1327.92i	−0.0920126	+	0.159370i
$412$	1184.88			0.141686
$413$	6514.21	+	14219.7i	0.776134	+	1.69421i
$414$	309.875			0.0367862
$415$	3765.75	−	6522.46i	0.445429	−	0.771506i
$416$	−858.622	−	1487.18i	−0.101196	−	0.175276i
$417$	3399.16	+	5887.51i	0.399179	+	0.691397i
$418$	378.154	−	654.982i	0.0442491	−	0.0766417i
$419$	9497.56			1.10737			0.553683	−	0.832728i	$-0.313222\pi$
$419$	9497.56			1.10737			0.553683	+	0.832728i	$0.313222\pi$
$420$	−2284.22	−	4986.18i	−0.265377	−	0.579288i
$421$	624.367			0.0722797			0.0361399	−	0.999347i	$-0.488494\pi$
$421$	624.367			0.0722797			0.0361399	+	0.999347i	$0.488494\pi$
$422$	449.016	−	777.719i	0.0517957	−	0.0897127i
$423$	−1752.13	−	3034.77i	−0.201398	−	0.348832i
$424$	622.608	+	1078.39i	0.0713126	+	0.123517i
$425$	721.915	−	1250.39i	0.0823954	−	0.142713i
$426$	73.2827			0.00833465
$427$	−3630.82	+	5111.52i	−0.411494	+	0.579306i
$428$	−6759.75			−0.763423
$429$	3295.44	−	5707.87i	0.370875	−	0.642375i
$430$	269.050	+	466.007i	0.0301738	+	0.0522625i
$431$	6698.64	+	11602.4i	0.748636	+	1.29668i	0.948476	+	0.316848i	$0.102624\pi$
$431$	6698.64	+	11602.4i	0.748636	+	1.29668i	−0.199840	+	0.979829i	$0.564042\pi$
$432$	844.112	−	1462.05i	0.0940101	−	0.162830i
$433$	−14057.3			−1.56016			−0.780079	−	0.625681i	$-0.784821\pi$
$433$	−14057.3			−1.56016			−0.780079	+	0.625681i	$0.784821\pi$
$434$	5.34870	+	0.504377i	0.000591580	+	5.57854e-5i
$435$	−2280.55			−0.251365
$436$	5405.61	−	9362.79i	0.593766	−	1.02843i
$437$	3507.98	+	6075.99i	0.384003	+	0.665112i
$438$	264.284	+	457.753i	0.0288310	+	0.0499368i
$439$	8184.42	−	14175.8i	0.889798	−	1.54117i	0.0496832	−	0.998765i	$-0.484179\pi$
$439$	8184.42	−	14175.8i	0.889798	−	1.54117i	0.840114	−	0.542409i	$-0.182488\pi$
$440$	2965.22			0.321275
$441$	−2016.05	+	2337.76i	−0.217692	+	0.252430i
$442$	−440.494			−0.0474031
$443$	589.354	−	1020.79i	0.0632078	−	0.109479i	−0.832690	−	0.553740i	$-0.813200\pi$
$443$	589.354	−	1020.79i	0.0632078	−	0.109479i	0.895898	+	0.444261i	$0.146534\pi$
$444$	−827.904	−	1433.97i	−0.0884923	−	0.153273i
$445$	1355.80	+	2348.31i	0.144429	+	0.250159i
$446$	22.8033	−	39.4965i	0.00242101	−	0.00419331i
$447$	−4523.70			−0.478666
$448$	9007.56	+	849.404i	0.949926	+	0.0895772i
$449$	−12400.9			−1.30342			−0.651709	−	0.758469i	$-0.725948\pi$
$449$	−12400.9			−1.30342			−0.651709	+	0.758469i	$0.725948\pi$
$450$	−33.0648	+	57.2699i	−0.00346376	+	0.00599940i
$451$	−9291.45	−	16093.3i	−0.970105	−	1.68027i
$452$	4161.95	+	7208.71i	0.433101	+	0.750153i
$453$	2387.74	−	4135.68i	0.247651	−	0.428943i
$454$	565.484			0.0584570
$455$	−4857.94	+	6839.07i	−0.500535	+	0.704660i
$456$	−599.606			−0.0615771
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	0.491971	+	0.870611i	$0.336277\pi$
$457$	−4962.79	+	8595.81i	−0.507986	+	0.879858i	−0.999957	+	0.00924618i	$0.997057\pi$
$458$	−671.366	−	1162.84i	−0.0684954	−	0.118637i
$459$	−658.073	−	1139.82i	−0.0669198	−	0.115909i
$460$	−6850.21	+	11864.9i	−0.694332	+	1.20262i
$461$	−16010.3			−1.61751			−0.808755	−	0.588146i	$-0.799858\pi$
$461$	−16010.3			−1.61751			−0.808755	+	0.588146i	$0.799858\pi$
$462$	−346.216	−	755.749i	−0.0348646	−	0.0761053i
$463$	17372.4			1.74377			0.871883	−	0.489714i	$-0.162899\pi$
$463$	17372.4			1.74377			0.871883	+	0.489714i	$0.162899\pi$
$464$	1911.27	−	3310.42i	0.191225	−	0.331212i
$465$	21.8107	+	37.7772i	0.00217515	+	0.00376747i
$466$	−141.199	−	244.563i	−0.0140363	−	0.0243115i
$467$	−1054.03	+	1825.64i	−0.104443	+	0.180900i	−0.913510	−	0.406815i	$-0.866639\pi$
$467$	−1054.03	+	1825.64i	−0.104443	+	0.180900i	0.809068	+	0.587716i	$0.199973\pi$
$468$	−2602.56			−0.257059
$469$	−7494.00	−	16358.5i	−0.737826	−	1.61059i
$470$	−1201.05			−0.117873
$471$	1746.24	−	3024.58i	0.170833	−	0.295892i
$472$	1669.58	+	2891.80i	0.162815	+	0.282004i
$473$	−5260.45	−	9111.37i	−0.511365	−	0.885711i
$474$	−181.173	+	313.802i	−0.0175561	+	0.0304080i
$475$	−1497.26			−0.144629
$476$	4150.25	−	5842.77i	0.399635	−	0.562612i
$477$	2834.41			0.272073
$478$	772.293	−	1337.65i	0.0738992	−	0.127997i
$479$	1225.02	+	2121.80i	0.116853	+	0.202395i	0.918519	−	0.395377i	$-0.129386\pi$
$479$	1225.02	+	2121.80i	0.116853	+	0.202395i	−0.801666	+	0.597772i	$0.796053\pi$
$480$	−879.292	−	1522.98i	−0.0836126	−	0.144821i
$481$	−1266.32	+	2193.34i	−0.120040	+	0.207916i
$482$	−792.887			−0.0749274
$483$	7677.35	+	723.967i	0.723254	+	0.0682022i
$484$	−18309.9			−1.71956
$485$	−4863.72	+	8424.21i	−0.455361	+	0.788709i
$486$	30.1407	+	52.2053i	0.00281319	+	0.00487259i
$487$	−322.618	−	558.791i	−0.0300189	−	0.0519943i	0.850626	−	0.525772i	$-0.176223\pi$
$487$	−322.618	−	558.791i	−0.0300189	−	0.0519943i	−0.880645	+	0.473778i	$0.842890\pi$
$488$	−669.270	+	1159.21i	−0.0620828	+	0.107531i
$489$	3467.64			0.320679
$490$	348.408	+	999.034i	0.0321214	+	0.0921056i
$491$	11766.1			1.08146			0.540731	−	0.841196i	$-0.318148\pi$
$491$	11766.1			1.08146			0.540731	+	0.841196i	$0.318148\pi$
$492$	−3668.94	+	6354.79i	−0.336196	+	0.582309i
$493$	−1490.03	−	2580.81i	−0.136121	−	0.235769i
$494$	228.397	+	395.595i	0.0208018	+	0.0360297i
$495$	3374.77	−	5845.28i	0.306434	−	0.530759i
$496$	−73.1159			−0.00661896
$497$	1815.63	+	171.212i	0.163868	+	0.0154526i
$498$	−450.763			−0.0405606
$499$	22.0104	−	38.1232i	0.00197459	−	0.00342010i	−0.865036	−	0.501709i	$-0.832705\pi$
$499$	22.0104	−	38.1232i	0.00197459	−	0.00342010i	0.867011	+	0.498289i	$0.166038\pi$
$500$	4707.59	+	8153.78i	0.421059	+	0.729296i
$501$	−4335.91	−	7510.02i	−0.386655	−	0.669707i
$502$	−29.7200	+	51.4765i	−0.00264236	+	0.00457671i
$503$	8290.27			0.734880			0.367440	−	0.930047i	$-0.380234\pi$
$503$	8290.27			0.734880			0.367440	+	0.930047i	$0.380234\pi$
$504$	−381.649	+	537.291i	−0.0337302	+	0.0474858i
$505$	3875.19			0.341473
$506$	−1038.28	+	1798.35i	−0.0912195	+	0.157997i
$507$	−1305.12	−	2260.54i	−0.114324	−	0.198016i
$508$	1938.60	+	3357.76i	0.169314	+	0.293261i
$509$	−3457.52	+	5988.60i	−0.301084	+	0.521493i	−0.976382	−	0.216052i	$-0.930682\pi$
$509$	−3457.52	+	5988.60i	−0.301084	+	0.521493i	0.675298	+	0.737545i	$0.264015\pi$
$510$	−451.098			−0.0391666
$511$	5478.36	+	11958.6i	0.474263	+	1.03526i
$512$	4925.45			0.425148
$513$	−682.425	+	1181.99i	−0.0587325	+	0.101728i
$514$	−86.7157	−	150.196i	−0.00744137	−	0.0128888i
$515$	−927.980	−	1607.31i	−0.0794014	−	0.137527i
$516$	−2077.21	+	3597.83i	−0.177217	+	0.306949i
$517$	23483.0			1.99764
$518$	133.039	+	290.408i	0.0112845	+	0.0246328i
$519$	−5684.81			−0.480800
$520$	−895.464	+	1550.99i	−0.0755167	+	0.130799i
$521$	−6699.64	−	11604.1i	−0.563371	−	0.975788i	−0.997199	−	0.0747919i	$-0.976171\pi$
$521$	−6699.64	−	11604.1i	−0.563371	−	0.975788i	0.433828	−	0.900996i	$-0.357163\pi$
$522$	68.2458	+	118.205i	0.00572230	+	0.00991131i
$523$	4968.50	−	8605.69i	0.415406	−	0.719504i	−0.580065	−	0.814570i	$-0.696973\pi$
$523$	4968.50	−	8605.69i	0.415406	−	0.719504i	0.995471	+	0.0950662i	$0.0303063\pi$
$524$	14719.7			1.22716
$525$	−953.005	+	1341.65i	−0.0792239	+	0.111532i
$526$	−227.988			−0.0188988
$527$	−28.5007	+	49.3647i	−0.00235581	+	0.00408038i
$528$	5656.63	+	9797.58i	0.466237	+	0.807547i
$529$	−3548.17	−	6145.60i	−0.291622	−	0.505104i
$530$	485.736	−	841.320i	0.0398095	−	0.0689521i
$531$	7600.74			0.621175
$532$	−7399.15	−	697.733i	−0.602996	−	0.0568620i
$533$	11223.7			0.912104
$534$	81.1450	−	140.547i	0.00657582	−	0.0113897i
$535$	5294.15	+	9169.74i	0.427825	+	0.741014i
$536$	−1920.70	−	3326.75i	−0.154779	−	0.268085i
$537$	−6432.74	+	11141.8i	−0.516933	+	0.895355i
$538$	−689.435			−0.0552484
$539$	−6812.07	−	19533.1i	−0.544373	−	1.56095i
$540$	−2665.21			−0.212394
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	−0.989407	−	0.145166i	$-0.953628\pi$
$541$	−4643.08	+	8042.06i	−0.368987	+	0.639103i	0.620421	+	0.784269i	$0.286962\pi$
$542$	−276.226	−	478.437i	−0.0218910	−	0.0379163i
$543$	575.599	+	996.966i	0.0454904	+	0.0787917i
$544$	1149.00	−	1990.13i	0.0905570	−	0.156849i
$545$	−16934.4			−1.33099
$546$	499.857	+	47.1360i	0.0391793	+	0.00369457i
$547$	−16821.6			−1.31488			−0.657438	−	0.753508i	$-0.728360\pi$
$547$	−16821.6			−1.31488			−0.657438	+	0.753508i	$0.728360\pi$
$548$	−2028.73	+	3513.87i	−0.158144	+	0.273914i
$549$	1523.42	+	2638.64i	0.118430	+	0.205127i
$550$	−221.577	−	383.782i	−0.0171783	−	0.0297537i
$551$	−1545.17	+	2676.32i	−0.119467	+	0.206924i
$552$	1646.31			0.126941
$553$	−5221.84	+	7351.37i	−0.401546	+	0.565302i
$554$	1812.83			0.139025
$555$	−1296.81	+	2246.14i	−0.0991828	+	0.171790i
$556$	8994.69	+	15579.3i	0.686079	+	1.18832i
$557$	−902.972	−	1563.99i	−0.0686897	−	0.118974i	0.829635	−	0.558306i	$-0.188549\pi$
$557$	−902.972	−	1563.99i	−0.0686897	−	0.118974i	−0.898325	+	0.439332i	$0.855215\pi$
$558$	1.30538	−	2.26098i	9.90340e−5	−	0.000171532i
$559$	6354.40			0.480792
$560$	−5997.18	−	13091.1i	−0.452548	−	0.987859i
$561$	8819.86			0.663770
$562$	−338.694	+	586.635i	−0.0254216	+	0.0440315i
$563$	−6107.45	−	10578.4i	−0.457190	−	0.791877i	0.541621	−	0.840623i	$-0.317811\pi$
$563$	−6107.45	−	10578.4i	−0.457190	−	0.791877i	−0.998811	+	0.0487460i	$0.984478\pi$
$564$	−4636.40	−	8030.48i	−0.346148	−	0.599546i
$565$	6519.17	−	11291.5i	0.485423	−	0.840776i
$566$	−439.050			−0.0326054
$567$	624.789	+	1363.84i	0.0462763	+	0.101016i
$568$	389.338			0.0287610
$569$	−2141.89	+	3709.86i	−0.157808	+	0.273331i	−0.934078	−	0.357070i	$-0.883776\pi$
$569$	−2141.89	+	3709.86i	−0.157808	+	0.273331i	0.776270	+	0.630400i	$0.217109\pi$
$570$	233.895	+	405.119i	0.0171874	+	0.0297694i
$571$	−3179.97	−	5507.87i	−0.233060	−	0.403673i	0.725647	−	0.688067i	$-0.241541\pi$
$571$	−3179.97	−	5507.87i	−0.233060	−	0.403673i	−0.958707	+	0.284395i	$0.908207\pi$
$572$	8720.25	−	15103.9i	0.637433	−	1.10407i
$573$	−1155.93			−0.0842753
$574$	819.764	−	1154.07i	0.0596103	−	0.0839201i
$575$	4110.95			0.298153
$576$	2198.34	−	3807.64i	0.159023	−	0.275437i
$577$	−7234.36	−	12530.3i	−0.521959	−	0.904059i	−0.999674	−	0.0255444i	$-0.991868\pi$
$577$	−7234.36	−	12530.3i	−0.521959	−	0.904059i	0.477715	−	0.878515i	$-0.341465\pi$
$578$	314.656	+	545.001i	0.0226436	+	0.0392198i
$579$	945.335	−	1637.37i	0.0678528	−	0.117525i
$580$	−6034.68			−0.432028
$581$	−11168.0	−	1053.13i	−0.797461	−	0.0751998i
$582$	582.191			0.0414649
$583$	−9497.10	+	16449.5i	−0.674665	+	1.16855i
$584$	1404.09	+	2431.96i	0.0994894	+	0.172321i
$585$	2038.29	+	3530.43i	0.144056	+	0.249513i
$586$	−1020.67	+	1767.85i	−0.0719513	+	0.124623i
$587$	−11132.6			−0.782777			−0.391388	−	0.920226i	$-0.628005\pi$
$587$	−11132.6			−0.782777			−0.391388	+	0.920226i	$0.628005\pi$
$588$	−5334.78	+	6186.07i	−0.374154	+	0.433859i
$589$	59.1108			0.00413517
$590$	1302.55	−	2256.07i	0.0908897	−	0.157426i
$591$	−1875.34	−	3248.19i	−0.130527	−	0.226079i
$592$	−2173.65	−	3764.87i	−0.150906	−	0.261377i
$593$	9887.81	−	17126.2i	0.684728	−	1.18598i	−0.288794	−	0.957391i	$-0.593254\pi$
$593$	9887.81	−	17126.2i	0.684728	−	1.18598i	0.973522	−	0.228592i	$-0.0734123\pi$
$594$	−403.963			−0.0279037
$595$	−11176.3	−	1053.91i	−0.770054	−	0.0726154i
$596$	−11970.4			−0.822696
$597$	−1638.37	+	2837.73i	−0.112318	+	0.194541i
$598$	−627.098	−	1086.17i	−0.0428829	−	0.0742753i
$599$	11945.5	+	20690.2i	0.814825	+	1.41132i	0.909453	+	0.415806i	$0.136500\pi$
$599$	11945.5	+	20690.2i	0.814825	+	1.41132i	−0.0946282	+	0.995513i	$0.530166\pi$
$600$	−175.667	+	304.265i	−0.0119527	+	0.0207026i
$601$	19395.5			1.31641			0.658204	−	0.752840i	$-0.271317\pi$
$601$	19395.5			1.31641			0.658204	+	0.752840i	$0.271317\pi$
$602$	464.118	−	653.391i	0.0314220	−	0.0442362i
$603$	−8743.95			−0.590516
$604$	6318.32	−	10943.7i	0.425644	−	0.737237i
$605$	14340.1	+	24837.8i	0.963648	+	1.66909i
$606$	−115.966	−	200.859i	−0.00777358	−	0.0134642i
$607$	−7298.36	+	12641.1i	−0.488025	+	0.845285i	−0.999905	−	0.0137724i	$-0.995616\pi$
$607$	−7298.36	+	12641.1i	−0.488025	+	0.845285i	0.511880	+	0.859057i	$0.328949\pi$
$608$	−2383.04			−0.158956
$609$	1414.67	+	3088.06i	0.0941304	+	0.205475i
$610$	1044.28			0.0693142
$611$	−7091.62	+	12283.0i	−0.469552	+	0.813288i
$612$	−1741.36	−	3016.13i	−0.115017	−	0.199215i
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	0.831570	−	0.555420i	$-0.187442\pi$
$613$	−989.898	−	1714.55i	−0.0652229	−	0.112969i	−0.896793	+	0.442451i	$0.854109\pi$
$614$	−746.650	+	1293.24i	−0.0490755	+	0.0850012i
$615$	11493.9			0.753622
$616$	−1839.39	−	4015.16i	−0.120310	−	0.262622i
$617$	16262.4			1.06110			0.530551	−	0.847653i	$-0.321985\pi$
$617$	16262.4			1.06110			0.530551	+	0.847653i	$0.321985\pi$
$618$	−55.5400	+	96.1981i	−0.00361512	+	0.00626158i
$619$	6010.49	+	10410.5i	0.390278	+	0.675981i	0.992486	−	0.122358i	$-0.0390457\pi$
$619$	6010.49	+	10410.5i	0.390278	+	0.675981i	−0.602208	+	0.798339i	$0.705712\pi$
$620$	57.7143	+	99.9642i	0.00373849	+	0.00647526i
$621$	1873.70	−	3245.34i	0.121077	−	0.209712i
$622$	296.127			0.0190894
$623$	2338.79	−	3292.58i	0.150404	−	0.211740i
$624$	−6832.97			−0.438362
$625$	9225.06	−	15978.3i	0.590404	−	1.02261i
$626$	1097.23	+	1900.45i	0.0700543	+	0.121338i
$627$	−4573.12	−	7920.87i	−0.291280	−	0.504512i
$628$	4620.82	−	8003.49i	0.293616	−	0.508557i
$629$	−3389.16			−0.214841
$630$	511.890	+	48.2708i	0.0323717	+	0.00305262i
$631$	25347.6			1.59916			0.799582	−	0.600557i	$-0.205055\pi$
$631$	25347.6			1.59916			0.799582	+	0.600557i	$0.205055\pi$
$632$	−962.542	+	1667.17i	−0.0605821	+	0.104931i
$633$	−5430.07	−	9405.16i	−0.340957	−	0.590556i
$634$	−754.317	−	1306.51i	−0.0472519	−	0.0818428i
$635$	3036.58	−	5259.51i	0.189769	−	0.328689i
$636$	7500.29			0.467620
$637$	12274.2	+	2335.66i	0.763454	+	0.145278i
$638$	−914.669			−0.0567588
$639$	443.114	−	767.496i	0.0274324	−	0.0475143i
$640$	−3098.24	−	5366.31i	−0.191358	−	0.331441i
$641$	2555.80	+	4426.78i	0.157485	+	0.272772i	0.933961	−	0.357374i	$-0.116328\pi$
$641$	2555.80	+	4426.78i	0.157485	+	0.272772i	−0.776476	+	0.630147i	$0.782995\pi$
$642$	316.857	−	548.812i	0.0194787	−	0.0337382i
$643$	−10931.3			−0.670435			−0.335217	−	0.942141i	$-0.608810\pi$
$643$	−10931.3			−0.670435			−0.335217	+	0.942141i	$0.608810\pi$
$644$	20315.5	+	1915.73i	1.24308	+	0.117221i
$645$	6507.38			0.397252
$646$	−305.639	+	529.382i	−0.0186149	+	0.0322419i
$647$	9203.06	+	15940.2i	0.559211	+	0.968582i	0.997563	+	0.0697783i	$0.0222292\pi$
$647$	9203.06	+	15940.2i	0.559211	+	0.968582i	−0.438352	+	0.898804i	$0.644437\pi$
$648$	160.132	+	277.357i	0.00970770	+	0.0168142i
$649$	−25467.3	+	44110.7i	−1.54034	+	2.66795i
$650$	267.655			0.0161512
$651$	37.6240	−	52.9675i	0.00226513	−	0.00318888i
$652$	9175.91			0.551160
$653$	−9960.71	+	17252.5i	−0.596926	+	1.03391i	0.396346	+	0.918101i	$0.370278\pi$
$653$	−9960.71	+	17252.5i	−0.596926	+	1.03391i	−0.993272	+	0.115805i	$0.963055\pi$
$654$	506.766	+	877.744i	0.0302999	+	0.0524809i
$655$	−11528.3	−	19967.6i	−0.687707	−	1.19114i
$656$	−9632.74	+	16684.4i	−0.573316	+	0.993012i
$657$	6392.11			0.379574
$658$	745.040	+	1626.33i	0.0441408	+	0.0963542i
$659$	−18858.8			−1.11477			−0.557385	−	0.830254i	$-0.688195\pi$
$659$	−18858.8			−1.11477			−0.557385	+	0.830254i	$0.688195\pi$
$660$	8930.17	−	15467.5i	0.526676	−	0.912230i
$661$	−12916.0	−	22371.2i	−0.760023	−	1.31640i	−0.942838	−	0.333251i	$-0.891854\pi$
$661$	−12916.0	−	22371.2i	−0.760023	−	1.31640i	0.182815	−	0.983147i	$-0.441479\pi$
$662$	−378.718	−	655.960i	−0.0222346	−	0.0385115i
$663$	−2663.50	+	4613.33i	−0.156021	+	0.270236i
$664$	−2394.82			−0.139965
$665$	4848.43	+	10583.6i	0.282728	+	0.617162i
$666$	155.229			0.00903153
$667$	4242.50	−	7348.22i	0.246282	−	0.426573i
$668$	−11473.5	−	19872.7i	−0.664555	−	1.15104i
$669$	−275.767	−	477.642i	−0.0159369	−	0.0276034i
$670$	−1498.46	+	2595.41i	−0.0864037	+	0.149656i
$671$	−20417.7			−1.17469
$672$	−1516.80	+	2135.37i	−0.0870714	+	0.122580i
$673$	−16275.0			−0.932178			−0.466089	−	0.884738i	$-0.654337\pi$
$673$	−16275.0			−0.932178			−0.466089	+	0.884738i	$0.654337\pi$
$674$	−479.498	+	830.515i	−0.0274029	+	0.0474633i
$675$	399.862	+	692.581i	0.0228010	+	0.0394925i
$676$	−3453.55	−	5981.73i	−0.196493	−	0.340335i
$677$	13135.9	−	22752.0i	0.745720	−	1.29163i	−0.204137	−	0.978942i	$-0.565439\pi$
$677$	13135.9	−	22752.0i	0.745720	−	1.29163i	0.949857	−	0.312683i	$-0.101228\pi$
$678$	−780.350			−0.0442023
$679$	14424.2	+	1360.19i	0.815242	+	0.0768766i
$680$	−2396.60			−0.135155
$681$	3419.28	−	5922.36i	0.192404	−	0.333253i
$682$	8.74769	+	15.1514i	0.000491153	+	0.000850702i
$683$	4036.14	+	6990.81i	0.226118	+	0.391648i	0.956654	−	0.291226i	$-0.0940631\pi$
$683$	4036.14	+	6990.81i	0.226118	+	0.391648i	−0.730536	+	0.682874i	$0.760730\pi$
$684$	−1805.80	+	3127.74i	−0.100945	+	0.174842i
$685$	6355.51			0.354499
$686$	1136.65	−	1091.50i	0.0632619	−	0.0607486i
$687$	−16238.0			−0.901774
$688$	−5453.67	+	9446.04i	−0.302208	+	0.523440i
$689$	−5736.05	−	9935.13i	−0.317164	−	0.549344i
$690$	−642.194	−	1112.31i	−0.0354318	−	0.0613696i
$691$	12242.6	−	21204.9i	0.673997	−	1.16740i	−0.302763	−	0.953066i	$-0.597909\pi$
$691$	12242.6	−	21204.9i	0.673997	−	1.16740i	0.976761	−	0.214332i	$-0.0687575\pi$
$692$	−15042.9			−0.826364
$693$	−10008.5	−	943.789i	−0.548615	−	0.0517339i
$694$	−24.7062			−0.00135135
$695$	14089.1	−	24403.0i	0.768962	−	1.33188i
$696$	362.578	+	628.003i	0.0197464	+	0.0342017i
$697$	7509.71	+	13007.2i	0.408107	+	0.706862i
$698$	447.440	−	774.989i	0.0242634	−	0.0420254i
$699$	−3415.10			−0.184794
$700$	−2521.80	+	3550.22i	−0.136164	+	0.191694i
$701$	778.448			0.0419423			0.0209712	−	0.999780i	$-0.493324\pi$
$701$	778.448			0.0419423			0.0209712	+	0.999780i	$0.493324\pi$
$702$	121.993	−	211.297i	0.00655885	−	0.0113603i
$703$	1757.29	+	3043.72i	0.0942780	+	0.163294i
$704$	14731.7	+	25516.0i	0.788667	+	1.36601i
$705$	−7262.34	+	12578.7i	−0.387965	+	0.671975i
$706$	1768.93			0.0942985
$707$	−2403.86	−	5247.35i	−0.127873	−	0.279133i
$708$	20112.7			1.06763
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$709$	12086.0	−	20933.6i	0.640197	−	1.10885i	0.985389	−	0.170322i	$-0.0544806\pi$
$710$	−151.874	−	263.053i	−0.00802777	−	0.0139045i
$711$	2190.98	+	3794.89i	0.115567	+	0.200168i
$712$	431.109	−	746.703i	0.0226917	−	0.0393032i
$713$	−162.297			−0.00852466
$714$	279.826	+	610.826i	0.0146670	+	0.0320162i
$715$	−27318.3			−1.42888
$716$	−17022.0	+	29483.0i	−0.888467	+	1.53887i
$717$	−9339.54	−	16176.6i	−0.486460	−	0.842573i
$718$	806.269	+	1396.50i	0.0419077	+	0.0725862i
$719$	40.9418	−	70.9132i	0.00212360	−	0.00367819i	−0.864962	−	0.501838i	$-0.832657\pi$
$719$	40.9418	−	70.9132i	0.00212360	−	0.00367819i	0.867085	+	0.498160i	$0.165991\pi$
$720$	−6997.47			−0.362195
$721$	−1600.79	+	2253.61i	−0.0826860	+	0.116406i
$722$	−1067.63			−0.0550318
$723$	−4794.29	+	8303.96i	−0.246614	+	0.427147i
$724$	1523.12	+	2638.13i	0.0781856	+	0.135421i
$725$	905.382	+	1568.17i	0.0463794	+	0.0803315i
$726$	858.259	−	1486.55i	0.0438747	−	0.0759931i
$727$	−32542.9			−1.66018			−0.830088	−	0.557632i	$-0.811710\pi$
$727$	−32542.9			−1.66018			−0.830088	+	0.557632i	$0.811710\pi$
$728$	2655.65	+	250.425i	0.135199	+	0.0127491i
$729$	729.000			0.0370370
$730$	1095.42	−	1897.33i	0.0555389	−	0.0961962i
$731$	4251.70	+	7364.16i	0.215123	+	0.372604i
$732$	4031.20	+	6982.25i	0.203549	+	0.352557i
$733$	2534.47	−	4389.83i	0.127712	−	0.221203i	−0.795078	−	0.606507i	$-0.792570\pi$
$733$	2534.47	−	4389.83i	0.127712	−	0.221203i	0.922790	+	0.385304i	$0.125903\pi$
$734$	204.631			0.0102903
$735$	12569.7	+	2391.88i	0.630801	+	0.120035i
$736$	6542.98			0.327687
$737$	29297.8	−	50745.3i	1.46431	−	2.53627i
$738$	−343.956	−	595.750i	−0.0171561	−	0.0297153i
$739$	19214.2	+	33280.0i	0.956437	+	1.65660i	0.731045	+	0.682329i	$0.239033\pi$
$739$	19214.2	+	33280.0i	0.956437	+	1.65660i	0.225392	+	0.974268i	$0.427634\pi$
$740$	−3431.55	+	5943.62i	−0.170468	+	0.295259i
$741$	5524.14			0.273865
$742$	−1440.53	−	135.841i	−0.0712717	−	0.00672086i
$743$	21592.9			1.06617			0.533086	−	0.846061i	$-0.321032\pi$
$743$	21592.9			1.06617			0.533086	+	0.846061i	$0.321032\pi$
$744$	6.93523	−	12.0122i	0.000341744	−	0.000591919i
$745$	9375.07	+	16238.1i	0.461042	+	0.798548i
$746$	−165.445	−	286.560i	−0.00811982	−	0.0140639i
$747$	−2725.60	+	4720.87i	−0.133500	+	0.231228i
$748$	23338.7			1.14084
$749$	9132.55	−	12856.9i	0.445522	−	0.627212i
$750$	−882.655			−0.0429733
$751$	−4056.30	+	7025.72i	−0.197093	+	0.341374i	−0.947585	−	0.319505i	$-0.896483\pi$
$751$	−4056.30	+	7025.72i	−0.197093	+	0.341374i	0.750492	+	0.660880i	$0.229817\pi$
$752$	−12172.8	−	21083.9i	−0.590287	−	1.02241i
$753$	359.411	+	622.519i	0.0173940	+	0.0301273i
$754$	276.220	−	478.428i	0.0133413	−	0.0231078i
$755$	−19793.7			−0.954129
$756$	1653.29	+	3608.93i	0.0795364	+	0.173618i
$757$	3108.01			0.149224			0.0746120	−	0.997213i	$-0.476228\pi$
$757$	3108.01			0.149224			0.0746120	+	0.997213i	$0.476228\pi$
$758$	165.996	−	287.513i	0.00795414	−	0.0137770i
$759$	12556.2	+	21747.9i	0.600475	+	1.04005i
$760$	1242.64	+	2152.32i	0.0593098	+	0.102728i
$761$	3605.96	−	6245.71i	0.171769	−	0.297512i	−0.767269	−	0.641325i	$-0.778385\pi$
$761$	3605.96	−	6245.71i	0.171769	−	0.297512i	0.939038	+	0.343812i	$0.111718\pi$
$762$	−363.481			−0.0172802
$763$	10504.8	+	22930.7i	0.498425	+	1.08800i
$764$	−3058.77			−0.144846
$765$	−2727.62	+	4724.38i	−0.128912	+	0.223282i
$766$	−43.8313	−	75.9181i	−0.00206748	−	0.00358098i
$767$	−15381.7	−	26641.9i	−0.724123	−	1.25422i
$768$	5676.81	−	9832.52i	0.266724	−	0.461980i
$769$	−7533.07			−0.353250			−0.176625	−	0.984278i	$-0.556518\pi$
$769$	−7533.07			−0.353250			−0.176625	+	0.984278i	$0.556518\pi$
$770$	−1995.30	+	2809.01i	−0.0933838	+	0.131467i
$771$	−2097.35			−0.0979693
$772$	2501.50	−	4332.73i	0.116621	−	0.201993i
$773$	12416.3	+	21505.7i	0.577728	+	1.00065i	0.995739	+	0.0922122i	$0.0293938\pi$
$773$	12416.3	+	21505.7i	0.577728	+	1.00065i	−0.418012	+	0.908442i	$0.637273\pi$
$774$	−194.734	−	337.290i	−0.00904339	−	0.0156636i
$775$	17.3178	−	29.9952i	0.000802674	−	0.00139027i
$776$	3093.08			0.143086
$777$	3845.90	+	362.665i	0.177569	+	0.0167446i
$778$	2911.66			0.134175
$779$	7787.61	−	13488.5i	0.358177	−	0.620381i
$780$	5393.64	+	9342.05i	0.247594	+	0.428845i
$781$	2969.43	+	5143.20i	0.136049	+	0.235644i
$782$	839.177	−	1453.50i	0.0383746	−	0.0664667i
$783$	1650.63			0.0753368
$784$	−14006.4	+	16241.4i	−0.638045	+	0.739860i
$785$	−14475.9			−0.658173
$786$	−689.973	+	1195.07i	−0.0313111	+	0.0542324i
$787$	−18156.6	−	31448.1i	−0.822378	−	1.42440i	−0.903907	−	0.427730i	$-0.859314\pi$
$787$	−18156.6	−	31448.1i	−0.822378	−	1.42440i	0.0815287	−	0.996671i	$-0.474020\pi$
$788$	−4962.45	−	8595.21i	−0.224340	−	0.388568i
$789$	−1378.56	+	2387.74i	−0.0622028	+	0.107738i
$790$	1501.88			0.0676386
$791$	−19333.7	−	1823.15i	−0.869062	−	0.0819517i
$792$	−2146.18			−0.0962895
$793$	6165.94	−	10679.7i	0.276115	−	0.478245i
$794$	−1647.37	−	2853.34i	−0.0736311	−	0.127533i
$795$	−5874.14	−	10174.3i	−0.262056	−	0.453893i
$796$	−4335.37	+	7509.08i	−0.193044	+	0.334362i
$797$	31665.7			1.40735			0.703675	−	0.710522i	$-0.251541\pi$
$797$	31665.7			1.40735			0.703675	+	0.710522i	$0.251541\pi$
$798$	403.476	−	568.019i	0.0178984	−	0.0251975i
$799$	−18979.9			−0.840375
$800$	−698.162	+	1209.25i	−0.0308547	+	0.0534419i
$801$	−981.308	−	1699.68i	−0.0432869	−	0.0749752i
$802$	928.081	+	1607.48i	0.0408625	+	0.0707759i
$803$	−21417.7	+	37096.5i	−0.941237	+	1.63027i
$804$	−23137.8			−1.01494
$805$	−13312.1	−	29058.7i	−0.582844	−	1.27228i
$806$	−10.5668			−0.000461788
$807$	−4168.76	+	7220.51i	−0.181843	+	0.314961i
$808$	−616.105	−	1067.13i	−0.0268249	−	0.0464621i
$809$	−6192.30	−	10725.4i	−0.269110	−	0.466111i	0.699523	−	0.714610i	$-0.253396\pi$
$809$	−6192.30	−	10725.4i	−0.269110	−	0.466111i	−0.968632	+	0.248499i	$0.920063\pi$
$810$	124.929	−	216.384i	0.00541922	−	0.00938637i
$811$	16742.4			0.724914			0.362457	−	0.932000i	$-0.381938\pi$
$811$	16742.4			0.724914			0.362457	+	0.932000i	$0.381938\pi$
$812$	3743.44	+	8171.49i	0.161784	+	0.353156i
$813$	−6680.94			−0.288205
$814$	−520.116	+	900.868i	−0.0223957	+	0.0387904i
$815$	−7186.45	−	12447.3i	−0.308872	−	0.534982i
$816$	−4571.91	−	7918.78i	−0.196138	−	0.339722i
$817$	4409.04	−	7636.67i	0.188804	−	0.327018i
$818$	−3422.55			−0.146292
$819$	3516.11	−	4950.02i	0.150016	−	0.211194i
$820$	30414.6			1.29527
$821$	−13228.2	+	22911.9i	−0.562322	+	0.973970i	0.434971	+	0.900444i	$0.356759\pi$
$821$	−13228.2	+	22911.9i	−0.562322	+	0.973970i	−0.997293	+	0.0735259i	$0.976575\pi$
$822$	−190.190	−	329.419i	−0.00807012	−	0.0139779i
$823$	−11549.3	−	20003.9i	−0.489164	−	0.847257i	0.510758	−	0.859724i	$-0.329365\pi$
$823$	−11549.3	−	20003.9i	−0.489164	−	0.847257i	−0.999922	+	0.0124673i	$0.996031\pi$
$824$	−295.074	+	511.083i	−0.0124750	+	0.0216073i
$825$	−5359.17			−0.226160
$826$	−3862.92	−	364.270i	−0.162722	−	0.0153445i
$827$	20647.6			0.868183			0.434092	−	0.900869i	$-0.357069\pi$
$827$	20647.6			0.868183			0.434092	+	0.900869i	$0.357069\pi$
$828$	4958.09	−	8587.67i	0.208099	−	0.360437i
$829$	11684.3	+	20237.7i	0.489519	+	0.847871i	0.999927	−	0.0120609i	$-0.00383919\pi$
$829$	11684.3	+	20237.7i	0.489519	+	0.847871i	−0.510409	+	0.859932i	$0.670506\pi$
$830$	934.176	+	1618.04i	0.0390671	+	0.0676662i
$831$	10961.5	−	18985.9i	0.457583	−	0.792557i
$832$	−17795.3			−0.741514
$833$	5505.78	+	15787.4i	0.229009	+	0.656664i
$834$	−1686.47			−0.0700212
$835$	−17971.8	+	31128.0i	−0.744838	+	1.29010i
$836$	−12101.2	−	20959.8i	−0.500631	−	0.867119i
$837$	−15.7863	−	27.3426i	−0.000651915	−	0.00112915i
$838$	−1178.04	+	2040.42i	−0.0485617	+	0.0841113i
$839$	16735.5			0.688645			0.344322	−	0.938851i	$-0.388109\pi$
$839$	16735.5			0.688645			0.344322	+	0.938851i	$0.388109\pi$
$840$	2719.58	+	256.454i	0.111708	+	0.0105339i
$841$	−20651.6			−0.846758
$842$	−77.4439	+	134.137i	−0.00316971	+	0.00549009i
$843$	4095.92	+	7094.34i	0.167344	+	0.289848i
$844$	−14368.8	−	24887.5i	−0.586013	−	1.01500i
$845$	−5409.56	+	9369.63i	−0.220230	+	0.381450i
$846$	869.307			0.0353279
$847$	24737.0	−	34825.1i	1.00351	−	1.41276i
$848$	19691.9			0.797432
$849$	−2654.78	+	4598.21i	−0.107317	+	0.185878i
$850$	179.087	+	310.188i	0.00722662	+	0.0125169i
$851$	−4824.90	−	8356.97i	−0.194354	−	0.336631i
$852$	1172.55	−	2030.91i	0.0471488	−	0.0816642i
$853$	−10294.5			−0.413219			−0.206609	−	0.978424i	$-0.566243\pi$
$853$	−10294.5			−0.413219			−0.206609	+	0.978424i	$0.566243\pi$
$854$	−647.789	−	1414.05i	−0.0259565	−	0.0566600i
$855$	5657.12			0.226280
$856$	1683.40	−	2915.74i	0.0672168	−	0.116423i
$857$	16394.3	+	28395.7i	0.653463	+	1.13183i	0.982277	+	0.187437i	$0.0600180\pi$
$857$	16394.3	+	28395.7i	0.653463	+	1.13183i	−0.328813	+	0.944395i	$0.606649\pi$
$858$	817.507	+	1415.96i	0.0325282	+	0.0563405i
$859$	2454.88	−	4251.98i	0.0975081	−	0.168889i	−0.813145	−	0.582062i	$-0.802246\pi$
$859$	2454.88	−	4251.98i	0.0975081	−	0.168889i	0.910653	+	0.413173i	$0.135579\pi$
$860$	17219.5			0.682768
$861$	−7129.89	−	15563.7i	−0.282214	−	0.616039i
$862$	−3323.49			−0.131321
$863$	−8897.48	+	15410.9i	−0.350954	+	0.607871i	−0.986417	−	0.164261i	$-0.947476\pi$
$863$	−8897.48	+	15410.9i	−0.350954	+	0.607871i	0.635463	+	0.772132i	$0.280809\pi$
$864$	636.420	+	1102.31i	0.0250596	+	0.0434044i
$865$	11781.4	+	20406.0i	0.463097	+	0.802108i
$866$	1743.60	−	3020.01i	0.0684181	−	0.118504i
$867$	7610.44			0.298113
$868$	99.5588	−	140.160i	0.00389314	−	0.00548081i
$869$	−29364.7			−1.14629
$870$	282.870	−	489.945i	0.0110232	−	0.0190928i
$871$	17695.3	+	30649.1i	0.688383	+	1.19231i
$872$	2692.36	+	4663.30i	0.104558	+	0.181100i
$873$	3520.30	−	6097.33i	0.136476	−	0.236384i
$874$	−1740.46			−0.0673592
$875$	−21868.4	−	2062.17i	−0.844899	−	0.0796732i
$876$	16914.5			0.652384
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	0.311099	+	0.950377i	$0.399303\pi$
$877$	−17336.1	+	30027.0i	−0.667501	+	1.15615i	−0.978601	+	0.205769i	$0.934030\pi$
$878$	2030.33	+	3516.63i	0.0780412	+	0.135171i
$879$	12343.2	+	21379.1i	0.473636	+	0.820362i
$880$	23446.0	−	40609.7i	0.898141	−	1.55563i
$881$	40848.2			1.56210			0.781051	−	0.624467i	$-0.214684\pi$
$881$	40848.2			1.56210			0.781051	+	0.624467i	$0.214684\pi$
$882$	−252.173	−	723.087i	−0.00962712	−	0.0276050i
$883$	30035.1			1.14469			0.572345	−	0.820013i	$-0.306034\pi$
$883$	30035.1			1.14469			0.572345	+	0.820013i	$0.306034\pi$
$884$	−7048.04	+	12207.6i	−0.268158	+	0.464463i
$885$	−15752.0	−	27283.3i	−0.598304	−	1.03629i
$886$	146.202	+	253.230i	0.00554375	+	0.00960205i
$887$	−16605.4	+	28761.3i	−0.628583	+	1.08874i	0.359253	+	0.933240i	$0.383032\pi$
$887$	−16605.4	+	28761.3i	−0.628583	+	1.08874i	−0.987836	+	0.155498i	$0.950302\pi$
$888$	824.703			0.0311658
$889$	−9005.49	−	849.210i	−0.339746	−	0.0320378i
$890$	−672.671			−0.0253348
$891$	−2442.62	+	4230.74i	−0.0918415	+	0.159074i
$892$	−729.721	−	1263.91i	−0.0273911	−	0.0474428i
$893$	9841.11	+	17045.3i	0.368780	+	0.638745i
$894$	561.102	−	971.856i	0.0209911	−	0.0363577i
$895$	53325.7			1.99160
$896$	−5344.55	+	7524.13i	−0.199273	+	0.280540i
$897$	−15167.3			−0.564573
$898$	1538.16	−	2664.17i	0.0571592	−	0.0990027i
$899$	−35.7439	−	61.9102i	−0.00132606	−	0.00229680i
$900$	1058.10	+	1832.67i	0.0391887	+	0.0678768i
$901$	7675.93	−	13295.1i	0.283820	−	0.491591i
$902$	4609.90			0.170169
$903$	−4036.66	−	8811.55i	−0.148762	−	0.324729i
$904$	−4145.86			−0.152532
$905$	2385.78	−	4132.29i	0.0876310	−	0.151781i
$906$	592.331	+	1025.95i	0.0217206	+	0.0376212i
$907$	−1248.92	−	2163.18i	−0.0457217	−	0.0791923i	0.842259	−	0.539073i	$-0.181225\pi$
$907$	−1248.92	−	2163.18i	−0.0457217	−	0.0791923i	−0.887981	+	0.459881i	$0.847892\pi$
$908$	9047.93	−	15671.5i	0.330690	−	0.572771i
$909$	−2804.81			−0.102343
$910$	−866.723	−	1891.95i	−0.0315732	−	0.0689205i
$911$	−1895.00			−0.0689180			−0.0344590	−	0.999406i	$-0.510971\pi$
$911$	−1895.00			−0.0689180			−0.0344590	+	0.999406i	$0.510971\pi$
$912$	−4741.09	+	8211.82i	−0.172142	+	0.298158i
$913$	−18265.0	−	31635.9i	−0.662084	−	1.14676i
$914$	−1231.13	−	2132.38i	−0.0445538	−	0.0771694i
$915$	6314.38	−	10936.8i	0.228139	−	0.395148i
$916$	−42968.3			−1.54990
$917$	−19886.6	+	27996.6i	−0.716155	+	1.00821i
$918$	326.499			0.0117386
$919$	−3135.36	+	5430.59i	−0.112542	+	0.194928i	−0.916794	−	0.399360i	$-0.869233\pi$
$919$	−3135.36	+	5430.59i	−0.112542	+	0.194928i	0.804253	+	0.594287i	$0.202566\pi$
$920$	−3411.86	−	5909.52i	−0.122267	−	0.211773i
$921$	9029.44	+	15639.4i	0.323051	+	0.559541i
$922$	1985.85	−	3439.59i	0.0709332	−	0.122860i
$923$	−3586.95			−0.127915
$924$	−26483.9	−	2497.41i	−0.942919	−	0.0889164i
$925$	2059.34			0.0732008
$926$	−2154.80	+	3732.23i	−0.0764700	+	0.132450i
$927$	671.660	+	1163.35i	0.0237974	+	0.0412183i
$928$	1441.01	+	2495.90i	0.0509735	+	0.0882887i
$929$	15776.3	−	27325.3i	0.557161	−	0.965032i	−0.440570	−	0.897718i	$-0.645224\pi$
$929$	15776.3	−	27325.3i	0.557161	−	0.965032i	0.997732	−	0.0673138i	$-0.0214429\pi$
$930$	−10.8212			−0.000381550
$931$	11323.5	−	13130.4i	0.398616	−	0.462225i
$932$	−9036.89			−0.317611
$933$	1790.57	−	3101.36i	0.0628303	−	0.108825i
$934$	−261.476	−	452.889i	−0.00916033	−	0.0158662i
$935$	−18278.6	−	31659.4i	−0.639330	−	1.10735i
$936$	648.125	−	1122.59i	0.0226331	−	0.0392018i
$937$	−22030.2			−0.768084			−0.384042	−	0.923316i	$-0.625468\pi$
$937$	−22030.2			−0.768084			−0.384042	+	0.923316i	$0.625468\pi$
$938$	4443.93	+	419.059i	0.154690	+	0.0145872i
$939$	26538.1			0.922299
$940$	−19217.3	+	33285.3i	−0.666806	+	1.15494i
$941$	16269.3	+	28179.3i	0.563618	+	0.976214i	0.997177	+	0.0750892i	$0.0239242\pi$
$941$	16269.3	+	28179.3i	0.563618	+	0.976214i	−0.433559	+	0.901125i	$0.642742\pi$
$942$	433.193	+	750.312i	0.0149832	+	0.0259517i
$943$	−21382.0	+	37034.8i	−0.738383	+	1.27892i
$944$	52805.6			1.82063
$945$	3600.76	−	5069.19i	0.123950	−	0.174498i
$946$	2609.94			0.0897003
$947$	20355.5	−	35256.8i	0.698485	−	1.20981i	−0.270507	−	0.962718i	$-0.587191\pi$
$947$	20355.5	−	35256.8i	0.698485	−	1.20981i	0.968992	−	0.247093i	$-0.0794753\pi$
$948$	5797.67	+	10041.9i	0.198628	+	0.344034i
$949$	−12935.8	−	22405.5i	−0.442481	−	0.766400i
$950$	185.714	−	321.666i	0.00634248	−	0.0109855i
$951$	−18244.3			−0.622095
$952$	1486.66	+	3245.21i	0.0506124	+	0.110481i
$953$	−52516.4			−1.78507			−0.892536	−	0.450976i	$-0.851076\pi$
$953$	−52516.4			−1.78507			−0.892536	+	0.450976i	$0.851076\pi$
$954$	−351.569	+	608.936i	−0.0119313	+	0.0206656i
$955$	2395.59	+	4149.29i	0.0811723	+	0.140595i
$956$	−24713.9	−	42805.7i	−0.836091	−	1.44815i
$957$	−5530.67	+	9579.40i	−0.186814	+	0.323572i
$958$	−607.786			−0.0204976
$959$	−3942.46	−	8605.92i	−0.132751	−	0.289781i
$960$	−18223.7			−0.612673
$961$	14894.8	−	25798.6i	0.499977	−	0.865986i
$962$	−314.139	−	544.105i	−0.0105283	−	0.0182356i
$963$	−3831.84	−	6636.93i	−0.128223	−	0.222090i
$964$	−12686.4	+	21973.6i	−0.423862	+	0.734150i
$965$	−7836.58			−0.261418
$966$	−1107.80	+	1559.58i	−0.0368975	+	0.0519447i
$967$	14721.6			0.489570			0.244785	−	0.969577i	$-0.421283\pi$
$967$	14721.6			0.489570			0.244785	+	0.969577i	$0.421283\pi$
$968$	4559.78	−	7897.77i	0.151402	−	0.262235i
$969$	3696.17	+	6401.96i	0.122537	+	0.212240i
$970$	−1206.55	−	2089.81i	−0.0399382	−	0.0691750i
$971$	−6886.25	+	11927.3i	−0.227590	+	0.394198i	−0.957093	−	0.289779i	$-0.906418\pi$
$971$	−6886.25	+	11927.3i	−0.227590	+	0.394198i	0.729503	+	0.683978i	$0.239751\pi$
$972$	1929.05			0.0636566
$973$	−41783.5	−	3940.14i	−1.37669	−	0.129820i
$974$	160.065			0.00526572
$975$	1618.41	−	2803.17i	0.0531597	−	0.0920753i
$976$	10583.8	+	18331.8i	0.347111	+	0.601215i
$977$	−12391.0	−	21461.9i	−0.405757	−	0.702791i	0.588653	−	0.808386i	$-0.299659\pi$
$977$	−12391.0	−	21461.9i	−0.405757	−	0.702791i	−0.994409	+	0.105595i	$0.966325\pi$
$978$	−430.112	+	744.976i	−0.0140628	+	0.0243576i
$979$	13152.0			0.429358
$980$	33261.2	+	6329.29i	1.08417	+	0.206308i
$981$	12256.9			0.398912
$982$	−1459.42	+	2527.79i	−0.0474257	+	0.0821437i
$983$	−21402.4	−	37070.0i	−0.694435	−	1.20280i	−0.970371	−	0.241620i	$-0.922321\pi$
$983$	−21402.4	−	37070.0i	−0.694435	−	1.20280i	0.275936	−	0.961176i	$-0.411012\pi$
$984$	−1827.38	−	3165.11i	−0.0592019	−	0.102541i
$985$	−7773.05	+	13463.3i	−0.251442	+	0.435510i
$986$	739.271			0.0238775
$987$	21537.7	+	2030.98i	0.694582	+	0.0654984i
$988$	14617.7			0.470700
$989$	−12105.7	+	20967.6i	−0.389219	+	0.674147i
$990$	837.187	+	1450.05i	0.0268763	+	0.0465511i
$991$	−224.931	−	389.592i	−0.00721006	−	0.0124882i	0.862398	−	0.506231i	$-0.168962\pi$
$991$	−224.931	−	389.592i	−0.00721006	−	0.0124882i	−0.869608	+	0.493743i	$0.835628\pi$
$992$	27.5630	−	47.7404i	0.000882182	−	0.00152798i
$993$	−9159.89			−0.292729
$994$	−261.986	+	368.827i	−0.00835986	+	0.0117691i
$995$	13581.6			0.432730
$996$	−7212.35	+	12492.1i	−0.229450	+	0.397419i
$997$	10736.9	+	18596.8i	0.341063	+	0.590739i	0.984630	−	0.174651i	$-0.0558796\pi$
$997$	10736.9	+	18596.8i	0.341063	+	0.590739i	−0.643567	+	0.765390i	$0.722546\pi$
$998$	5.46017	+	9.45729i	0.000173185	+	0.000299965i
$999$	938.612	−	1625.72i	0.0297261	−	0.0514871i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.4.e.b.16.2	yes	6
3.2	odd	2		63.4.e.c.37.2		6
4.3	odd	2		336.4.q.k.289.3		6
7.2	even	3		147.4.a.l.1.2		3
7.3	odd	6		147.4.e.n.67.2		6
7.4	even	3	inner	21.4.e.b.4.2	✓	6
7.5	odd	6		147.4.a.m.1.2		3
7.6	odd	2		147.4.e.n.79.2		6
21.2	odd	6		441.4.a.s.1.2		3
21.5	even	6		441.4.a.t.1.2		3
21.11	odd	6		63.4.e.c.46.2		6
21.17	even	6		441.4.e.w.361.2		6
21.20	even	2		441.4.e.w.226.2		6
28.11	odd	6		336.4.q.k.193.3		6
28.19	even	6		2352.4.a.cg.1.3		3
28.23	odd	6		2352.4.a.ci.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.2	✓	6	7.4	even	3	inner
21.4.e.b.16.2	yes	6	1.1	even	1	trivial
63.4.e.c.37.2		6	3.2	odd	2
63.4.e.c.46.2		6	21.11	odd	6
147.4.a.l.1.2		3	7.2	even	3
147.4.a.m.1.2		3	7.5	odd	6
147.4.e.n.67.2		6	7.3	odd	6
147.4.e.n.79.2		6	7.6	odd	2
336.4.q.k.193.3		6	28.11	odd	6
336.4.q.k.289.3		6	4.3	odd	2
441.4.a.s.1.2		3	21.2	odd	6
441.4.a.t.1.2		3	21.5	even	6
441.4.e.w.226.2		6	21.20	even	2
441.4.e.w.361.2		6	21.17	even	6
2352.4.a.cg.1.3		3	28.19	even	6
2352.4.a.ci.1.1		3	28.23	odd	6

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	21.4.e.b.16.2

Level	$21$
Weight	$4$
Character	21.16
Analytic conductor	$1.239$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$