LMFDB - Embedded newform 50.4.d.b.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,4,Mod(11,50)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.95009550029$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 135 x^{14} + 7296 x^{12} + 200295 x^{10} + 2912021 x^{8} + 20937420 x^{6} + 57578496 x^{4} + \cdots + 952576 $ x^16 + 135x^14 + 7296x^12 + 200295x^10 + 2912021x^8 + 20937420x^6 + 57578496x^4 + 16724160*x^2 + 952576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.4
Root			$4.04577i$ of defining polynomial
Character	$\chi$	$=$	50.11
Dual form			50.4.d.b.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61803 + 1.17557i) q^{2} +(2.56903 - 7.90665i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-11.1411 + 0.935417i) q^{5} +(5.13805 + 15.8133i) q^{6} -26.4146 q^{7} +(2.47214 + 7.60845i) q^{8} +(-34.0718 - 24.7546i) q^{9} +(16.9271 - 14.6107i) q^{10} +(50.6905 - 36.8288i) q^{11} +(-26.9032 - 19.5463i) q^{12} +(-0.390161 - 0.283469i) q^{13} +(42.7398 - 31.0523i) q^{14} +(-21.2259 + 90.4922i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(-32.7507 - 100.796i) q^{17} +84.2300 q^{18} +(23.4933 + 72.3050i) q^{19} +(-10.2127 + 43.5397i) q^{20} +(-67.8599 + 208.851i) q^{21} +(-38.7241 + 119.180i) q^{22} +(77.3947 - 56.2305i) q^{23} +66.5084 q^{24} +(123.250 - 20.8432i) q^{25} +0.964531 q^{26} +(-101.661 + 73.8608i) q^{27} +(-32.6503 + 100.487i) q^{28} +(1.15369 - 3.55069i) q^{29} +(-72.0358 - 171.372i) q^{30} +(-0.716525 - 2.20524i) q^{31} +32.0000 q^{32} +(-160.967 - 495.406i) q^{33} +(171.485 + 124.591i) q^{34} +(294.289 - 24.7087i) q^{35} +(-136.287 + 99.0184i) q^{36} +(9.60846 + 6.98096i) q^{37} +(-123.013 - 89.3738i) q^{38} +(-3.24362 + 2.35663i) q^{39} +(-34.6595 - 82.4543i) q^{40} +(42.5768 + 30.9339i) q^{41} +(-135.720 - 417.703i) q^{42} -262.484 q^{43} +(-77.4481 - 238.361i) q^{44} +(402.754 + 243.923i) q^{45} +(-59.1243 + 181.966i) q^{46} +(-83.8272 + 257.993i) q^{47} +(-107.613 + 78.1853i) q^{48} +354.734 q^{49} +(-174.920 + 178.614i) q^{50} -881.098 q^{51} +(-1.56064 + 1.13387i) q^{52} +(111.104 - 341.943i) q^{53} +(77.6618 - 239.018i) q^{54} +(-530.299 + 457.731i) q^{55} +(-65.3006 - 200.975i) q^{56} +632.045 q^{57} +(2.30738 + 7.10138i) q^{58} +(-50.2198 - 36.4868i) q^{59} +(318.016 + 192.603i) q^{60} +(295.103 - 214.405i) q^{61} +(3.75177 + 2.72582i) q^{62} +(899.994 + 653.884i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(4.61200 + 2.79320i) q^{65} +(842.835 + 612.355i) q^{66} +(-68.4013 - 210.518i) q^{67} -423.934 q^{68} +(-245.766 - 756.391i) q^{69} +(-447.123 + 385.937i) q^{70} +(220.848 - 679.701i) q^{71} +(104.114 - 320.430i) q^{72} +(-103.747 + 75.3764i) q^{73} -23.7534 q^{74} +(151.832 - 1028.04i) q^{75} +304.104 q^{76} +(-1338.97 + 972.819i) q^{77} +(2.47791 - 7.62621i) q^{78} +(-345.099 + 1062.11i) q^{79} +(153.011 + 92.6693i) q^{80} +(-28.5626 - 87.9065i) q^{81} -105.256 q^{82} +(154.685 + 476.071i) q^{83} +(710.638 + 516.309i) q^{84} +(459.166 + 1092.35i) q^{85} +(424.708 - 308.569i) q^{86} +(-25.1102 - 18.2436i) q^{87} +(405.524 + 294.630i) q^{88} +(920.687 - 668.918i) q^{89} +(-938.419 + 78.7903i) q^{90} +(10.3060 + 7.48772i) q^{91} +(-118.249 - 363.932i) q^{92} -19.2768 q^{93} +(-167.654 - 515.987i) q^{94} +(-329.378 - 783.584i) q^{95} +(82.2089 - 253.013i) q^{96} +(-227.300 + 699.557i) q^{97} +(-573.971 + 417.014i) q^{98} -2638.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 7 q^{3} - 16 q^{4} + 15 q^{5} + 14 q^{6} - 54 q^{7} - 32 q^{8} - 83 q^{9} - 50 q^{10} + 152 q^{11} - 12 q^{12} + 77 q^{13} + 52 q^{14} - 70 q^{15} - 64 q^{16} + 76 q^{17} + 304 q^{18} - 20 q^{19}+ \cdots - 1786 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 7 * q^3 - 16 * q^4 + 15 * q^5 + 14 * q^6 - 54 * q^7 - 32 * q^8 - 83 * q^9 - 50 * q^10 + 152 * q^11 - 12 * q^12 + 77 * q^13 + 52 * q^14 - 70 * q^15 - 64 * q^16 + 76 * q^17 + 304 * q^18 - 20 * q^19 + 20 * q^20 + 257 * q^21 - 226 * q^22 - 383 * q^23 - 64 * q^24 - 215 * q^25 - 716 * q^26 + 415 * q^27 + 4 * q^28 + 105 * q^29 + 140 * q^30 + 177 * q^31 + 512 * q^32 + 64 * q^33 + 342 * q^34 - 210 * q^35 - 332 * q^36 + 446 * q^37 + 90 * q^38 - 146 * q^39 - 40 * q^40 + 462 * q^41 + 514 * q^42 - 1058 * q^43 - 452 * q^44 - 865 * q^45 + 1124 * q^46 - 1114 * q^47 - 48 * q^48 + 1698 * q^49 - 550 * q^50 - 3608 * q^51 + 308 * q^52 + 567 * q^53 + 390 * q^54 - 210 * q^55 + 8 * q^56 - 1520 * q^57 + 210 * q^58 + 1275 * q^59 + 1260 * q^60 + 252 * q^61 - 176 * q^62 + 5402 * q^63 - 256 * q^64 + 2645 * q^65 + 998 * q^66 + 3296 * q^67 - 1976 * q^68 - 5491 * q^69 - 1750 * q^70 + 3712 * q^71 + 56 * q^72 - 1688 * q^73 - 1148 * q^74 - 6315 * q^75 - 200 * q^76 - 5453 * q^77 - 1152 * q^78 + 1750 * q^79 + 160 * q^80 + 4106 * q^81 - 1576 * q^82 - 2153 * q^83 - 612 * q^84 + 5860 * q^85 + 1074 * q^86 - 1255 * q^87 + 1216 * q^88 + 5660 * q^89 + 820 * q^90 - 493 * q^91 + 2248 * q^92 - 256 * q^93 - 2228 * q^94 - 1420 * q^95 + 224 * q^96 - 429 * q^97 - 674 * q^98 - 1786 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$	2.56903	−	7.90665i	0.494409	−	1.52164i	−0.323466	−	0.946240i	$-0.604848\pi$
$3$	2.56903	−	7.90665i	0.494409	−	1.52164i	0.817875	−	0.575396i	$-0.195152\pi$
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	−11.1411	+	0.935417i	−0.996494	+	0.0836663i
$5$	−11.1411	+	0.935417i	−0.996494	+	0.0836663i
$6$	5.13805	+	15.8133i	0.349600	+	1.07596i
$7$	−26.4146			−1.42626			−0.713128	−	0.701033i	$-0.752722\pi$
$7$	−26.4146			−1.42626			−0.713128	+	0.701033i	$0.752722\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$	−34.0718	−	24.7546i	−1.26192	−	0.916837i
$10$	16.9271	−	14.6107i	0.535282	−	0.462032i
$11$	50.6905	−	36.8288i	1.38943	−	1.00948i	0.393504	−	0.919323i	$-0.371263\pi$
$11$	50.6905	−	36.8288i	1.38943	−	1.00948i	0.995927	−	0.0901581i	$-0.0287372\pi$
$12$	−26.9032	−	19.5463i	−0.647190	−	0.470211i
$13$	−0.390161	−	0.283469i	−0.00832394	−	0.00604769i	0.583616	−	0.812030i	$-0.301638\pi$
$13$	−0.390161	−	0.283469i	−0.00832394	−	0.00604769i	−0.591939	+	0.805982i	$0.701638\pi$
$14$	42.7398	−	31.0523i	0.815907	−	0.592791i
$15$	−21.2259	+	90.4922i	−0.365366	+	1.55767i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	−32.7507	−	100.796i	−0.467247	−	1.43804i	−0.856134	−	0.516754i	$-0.827140\pi$
$17$	−32.7507	−	100.796i	−0.467247	−	1.43804i	0.388886	−	0.921286i	$-0.372860\pi$
$18$	84.2300			1.10296
$19$	23.4933	+	72.3050i	0.283670	+	0.873047i	0.986794	+	0.161980i	$0.0517879\pi$
$19$	23.4933	+	72.3050i	0.283670	+	0.873047i	−0.703124	+	0.711067i	$0.748212\pi$
$20$	−10.2127	+	43.5397i	−0.114181	+	0.486788i
$21$	−67.8599	+	208.851i	−0.705155	+	2.17024i
$22$	−38.7241	+	119.180i	−0.375273	+	1.15497i
$23$	77.3947	−	56.2305i	0.701648	−	0.509777i	−0.178820	−	0.983882i	$-0.557228\pi$
$23$	77.3947	−	56.2305i	0.701648	−	0.509777i	0.880469	+	0.474104i	$0.157228\pi$
$24$	66.5084			0.565665
$25$	123.250	−	20.8432i	0.986000	−	0.166746i
$26$	0.964531			0.00727539
$27$	−101.661	+	73.8608i	−0.724615	+	0.526463i
$28$	−32.6503	+	100.487i	−0.220369	+	0.678225i
$29$	1.15369	−	3.55069i	0.00738741	−	0.0227361i	−0.947295	−	0.320363i	$-0.896195\pi$
$29$	1.15369	−	3.55069i	0.00738741	−	0.0227361i	0.954682	+	0.297627i	$0.0961951\pi$
$30$	−72.0358	−	171.372i	−0.438396	−	1.04294i
$31$	−0.716525	−	2.20524i	−0.00415135	−	0.0127765i	0.948959	−	0.315398i	$-0.102138\pi$
$31$	−0.716525	−	2.20524i	−0.00415135	−	0.0127765i	−0.953111	+	0.302622i	$0.902138\pi$
$32$	32.0000			0.176777
$33$	−160.967	−	495.406i	−0.849114	−	2.61331i
$34$	171.485	+	124.591i	0.864982	+	0.628446i
$35$	294.289	−	24.7087i	1.42126	−	0.119330i
$36$	−136.287	+	99.0184i	−0.630959	+	0.458418i
$37$	9.60846	+	6.98096i	0.0426925	+	0.0310179i	0.608927	−	0.793226i	$-0.291600\pi$
$37$	9.60846	+	6.98096i	0.0426925	+	0.0310179i	−0.566234	+	0.824244i	$0.691600\pi$
$38$	−123.013	−	89.3738i	−0.525139	−	0.381536i
$39$	−3.24362	+	2.35663i	−0.0133178	+	0.00967596i
$40$	−34.6595	−	82.4543i	−0.137004	−	0.325929i
$41$	42.5768	+	30.9339i	0.162180	+	0.117831i	0.665915	−	0.746027i	$-0.268041\pi$
$41$	42.5768	+	30.9339i	0.162180	+	0.117831i	−0.503735	+	0.863858i	$0.668041\pi$
$42$	−135.720	−	417.703i	−0.498620	−	1.53459i
$43$	−262.484			−0.930895			−0.465447	−	0.885076i	$-0.654107\pi$
$43$	−262.484			−0.930895			−0.465447	+	0.885076i	$0.654107\pi$
$44$	−77.4481	−	238.361i	−0.265358	−	0.816687i
$45$	402.754	+	243.923i	1.33420	+	0.808042i
$46$	−59.1243	+	181.966i	−0.189509	+	0.583248i
$47$	−83.8272	+	257.993i	−0.260158	+	0.800685i	0.732611	+	0.680648i	$0.238302\pi$
$47$	−83.8272	+	257.993i	−0.260158	+	0.800685i	−0.992769	+	0.120038i	$0.961698\pi$
$48$	−107.613	+	78.1853i	−0.323595	+	0.235106i
$49$	354.734			1.03421
$50$	−174.920	+	178.614i	−0.494748	+	0.505197i
$51$	−881.098			−2.41918
$52$	−1.56064	+	1.13387i	−0.00416197	+	0.00302385i
$53$	111.104	−	341.943i	0.287950	−	0.886218i	−0.697549	−	0.716537i	$-0.745726\pi$
$53$	111.104	−	341.943i	0.287950	−	0.886218i	0.985499	−	0.169681i	$-0.0542737\pi$
$54$	77.6618	−	239.018i	0.195712	−	0.602339i
$55$	−530.299	+	457.731i	−1.30010	+	1.12219i
$56$	−65.3006	−	200.975i	−0.155824	−	0.479578i
$57$	632.045			1.46871
$58$	2.30738	+	7.10138i	0.00522368	+	0.0160768i
$59$	−50.2198	−	36.4868i	−0.110815	−	0.0805115i	0.530998	−	0.847373i	$-0.321817\pi$
$59$	−50.2198	−	36.4868i	−0.110815	−	0.0805115i	−0.641812	+	0.766862i	$0.721817\pi$
$60$	318.016	+	192.603i	0.684262	+	0.414415i
$61$	295.103	−	214.405i	0.619411	−	0.450028i	−0.233305	−	0.972404i	$-0.574954\pi$
$61$	295.103	−	214.405i	0.619411	−	0.450028i	0.852716	+	0.522375i	$0.174954\pi$
$62$	3.75177	+	2.72582i	0.00768509	+	0.00558355i
$63$	899.994	+	653.884i	1.79982	+	1.30764i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	4.61200	+	2.79320i	0.00880074	+	0.00533006i
$66$	842.835	+	612.355i	1.57191	+	1.14206i
$67$	−68.4013	−	210.518i	−0.124725	−	0.383863i	0.869126	−	0.494590i	$-0.164682\pi$
$67$	−68.4013	−	210.518i	−0.124725	−	0.383863i	−0.993851	+	0.110728i	$0.964682\pi$
$68$	−423.934			−0.756022
$69$	−245.766	−	756.391i	−0.428794	−	1.31969i
$70$	−447.123	+	385.937i	−0.763449	+	0.658976i
$71$	220.848	−	679.701i	0.369153	−	1.13614i	−0.578186	−	0.815905i	$-0.696239\pi$
$71$	220.848	−	679.701i	0.369153	−	1.13614i	0.947339	−	0.320232i	$-0.103761\pi$
$72$	104.114	−	320.430i	0.170416	−	0.524487i
$73$	−103.747	+	75.3764i	−0.166337	+	0.120851i	−0.667840	−	0.744305i	$-0.732781\pi$
$73$	−103.747	+	75.3764i	−0.166337	+	0.120851i	0.501502	+	0.865156i	$0.332781\pi$
$74$	−23.7534			−0.0373146
$75$	151.832	−	1028.04i	0.233761	−	1.58277i
$76$	304.104			0.458988
$77$	−1338.97	+	972.819i	−1.98169	+	1.43978i
$78$	2.47791	−	7.62621i	0.00359702	−	0.0110705i
$79$	−345.099	+	1062.11i	−0.491477	+	1.51261i	0.330898	+	0.943667i	$0.392648\pi$
$79$	−345.099	+	1062.11i	−0.491477	+	1.51261i	−0.822375	+	0.568945i	$0.807352\pi$
$80$	153.011	+	92.6693i	0.213840	+	0.129509i
$81$	−28.5626	−	87.9065i	−0.0391805	−	0.120585i
$82$	−105.256			−0.141750
$83$	154.685	+	476.071i	0.204565	+	0.629585i	0.999731	+	0.0231936i	$0.00738343\pi$
$83$	154.685	+	476.071i	0.204565	+	0.629585i	−0.795166	+	0.606391i	$0.792617\pi$
$84$	710.638	+	516.309i	0.923060	+	0.670642i
$85$	459.166	+	1092.35i	0.585925	+	1.39390i
$86$	424.708	−	308.569i	0.532529	−	0.386905i
$87$	−25.1102	−	18.2436i	−0.0309437	−	0.0224819i
$88$	405.524	+	294.630i	0.491238	+	0.356905i
$89$	920.687	−	668.918i	1.09655	−	0.796688i	0.116054	−	0.993243i	$-0.462975\pi$
$89$	920.687	−	668.918i	1.09655	−	0.796688i	0.980493	+	0.196555i	$0.0629754\pi$
$90$	−938.419	+	78.7903i	−1.09909	+	0.0922802i
$91$	10.3060	+	7.48772i	0.0118721	+	0.00862557i
$92$	−118.249	−	363.932i	−0.134003	−	0.412418i
$93$	−19.2768			−0.0214937
$94$	−167.654	−	515.987i	−0.183960	−	0.566170i
$95$	−329.378	−	783.584i	−0.355720	−	0.846252i
$96$	82.2089	−	253.013i	0.0874001	−	0.268990i
$97$	−227.300	+	699.557i	−0.237926	+	0.732260i	0.758794	+	0.651331i	$0.225789\pi$
$97$	−227.300	+	699.557i	−0.237926	+	0.732260i	−0.996720	+	0.0809295i	$0.974211\pi$
$98$	−573.971	+	417.014i	−0.591631	+	0.429845i
$99$	−2638.79			−2.67888
$100$	73.0530	−	494.634i	0.0730530	−	0.494634i
$101$	−1249.44			−1.23093			−0.615463	−	0.788166i	$-0.711031\pi$
$101$	−1249.44			−1.23093			−0.615463	+	0.788166i	$0.711031\pi$
$102$	1425.65	−	1035.79i	1.38392	−	1.00548i
$103$	102.851	−	316.541i	0.0983899	−	0.302813i	−0.889732	−	0.456483i	$-0.849109\pi$
$103$	102.851	−	316.541i	0.0983899	−	0.302813i	0.988122	+	0.153669i	$0.0491091\pi$
$104$	1.19223	−	3.66929i	0.00112411	−	0.00345965i
$105$	560.674	−	2390.32i	0.521106	−	2.22163i
$106$	222.208	+	683.887i	0.203611	+	0.626651i
$107$	2079.52			1.87883			0.939414	−	0.342786i	$-0.111370\pi$
$107$	2079.52			1.87883			0.939414	+	0.342786i	$0.111370\pi$
$108$	155.324	+	478.037i	0.138389	+	0.425918i
$109$	−570.329	−	414.368i	−0.501170	−	0.364122i	0.308293	−	0.951291i	$-0.400242\pi$
$109$	−570.329	−	414.368i	−0.501170	−	0.364122i	−0.809464	+	0.587170i	$0.800242\pi$
$110$	319.947	−	1364.03i	0.277325	−	1.18232i
$111$	79.8804	−	58.0365i	0.0683055	−	0.0496269i
$112$	341.918	+	248.418i	0.288467	+	0.209583i
$113$	−307.166	−	223.169i	−0.255714	−	0.185787i	0.452541	−	0.891743i	$-0.350518\pi$
$113$	−307.166	−	223.169i	−0.255714	−	0.185787i	−0.708256	+	0.705956i	$0.750518\pi$
$114$	−1022.67	+	743.013i	−0.840192	+	0.610435i
$115$	−809.666	+	698.869i	−0.656537	+	0.566694i
$116$	−12.0816	−	8.77779i	−0.00967024	−	0.00702584i
$117$	6.27633	+	19.3165i	0.00495937	+	0.0152634i
$118$	124.150			0.0968554
$119$	865.098	+	2662.50i	0.666415	+	2.05101i
$120$	−740.979	+	62.2131i	−0.563682	+	0.0473271i
$121$	801.862	−	2467.88i	0.602451	−	1.85415i
$122$	−225.439	+	693.829i	−0.167297	+	0.514888i
$123$	353.964	−	257.170i	0.259479	−	0.188522i
$124$	−9.27490			−0.00671702
$125$	−1353.65	+	347.508i	−0.968592	+	0.248656i
$126$	−2224.91			−1.57310
$127$	1135.05	−	824.664i	0.793068	−	0.576198i	−0.115804	−	0.993272i	$-0.536945\pi$
$127$	1135.05	−	824.664i	0.793068	−	0.576198i	0.908872	+	0.417075i	$0.136945\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$	−674.329	+	2075.37i	−0.460243	+	1.41648i
$130$	−10.7460	+	0.902239i	−0.00724988	+	0.000608705i
$131$	451.412	+	1389.30i	0.301069	+	0.926594i	0.981115	+	0.193425i	$0.0619597\pi$
$131$	451.412	+	1389.30i	0.301069	+	0.926594i	−0.680046	+	0.733169i	$0.738040\pi$
$132$	−2083.60			−1.37390
$133$	−620.567	−	1909.91i	−0.404587	−	1.24519i
$134$	358.154	+	260.214i	0.230894	+	0.167754i
$135$	1063.52	−	917.988i	0.678027	−	0.585243i
$136$	685.939	−	498.364i	0.432491	−	0.314223i
$137$	1202.97	+	874.011i	0.750197	+	0.545050i	0.895888	−	0.444280i	$-0.146541\pi$
$137$	1202.97	+	874.011i	0.750197	+	0.545050i	−0.145691	+	0.989330i	$0.546541\pi$
$138$	1286.85	+	934.950i	0.793796	+	0.576726i
$139$	−104.832	+	76.1650i	−0.0639694	+	0.0464765i	−0.619310	−	0.785146i	$-0.712588\pi$
$139$	−104.832	+	76.1650i	−0.0639694	+	0.0464765i	0.555341	+	0.831623i	$0.312588\pi$
$140$	269.764	−	1150.08i	0.162852	−	0.694285i
$141$	1824.51	+	1325.58i	1.08973	+	0.791733i
$142$	441.697	+	1359.40i	0.261031	+	0.803370i
$143$	−30.2172			−0.0176706
$144$	208.228	+	640.860i	0.120502	+	0.370868i
$145$	−9.53204	+	40.6379i	−0.00545926	+	0.0232745i
$146$	79.2554	−	243.923i	0.0449262	−	0.138269i
$147$	911.320	−	2804.75i	0.511323	−	1.57369i
$148$	38.4339	−	27.9238i	0.0213462	−	0.0155090i
$149$	1055.54			0.580357			0.290179	−	0.956973i	$-0.406285\pi$
$149$	1055.54			0.580357			0.290179	+	0.956973i	$0.406285\pi$
$150$	962.865	+	1841.90i	0.524117	+	1.00260i
$151$	2197.85			1.18449			0.592246	−	0.805757i	$-0.298241\pi$
$151$	2197.85			1.18449			0.592246	+	0.805757i	$0.298241\pi$
$152$	−492.050	+	357.495i	−0.262569	+	0.190768i
$153$	−1379.30	+	4245.04i	−0.728820	+	2.24308i
$154$	1022.88	−	3148.11i	0.535235	−	1.64728i
$155$	10.0457	+	23.8986i	0.00520575	+	0.0123844i
$156$	4.95581	+	15.2524i	0.00254348	+	0.00782802i
$157$	−1392.21			−0.707712			−0.353856	−	0.935300i	$-0.615130\pi$
$157$	−1392.21			−0.707712			−0.353856	+	0.935300i	$0.615130\pi$
$158$	−690.199	−	2124.21i	−0.347527	−	1.06958i
$159$	−2418.20	−	1756.92i	−1.20614	−	0.876309i
$160$	−356.516	+	29.9334i	−0.176157	+	0.0147902i
$161$	−2044.35	+	1485.31i	−1.00073	+	0.727073i
$162$	149.556	+	108.658i	0.0725320	+	0.0526976i
$163$	2827.16	+	2054.05i	1.35853	+	0.987029i	0.998537	+	0.0540743i	$0.0172208\pi$
$163$	2827.16	+	2054.05i	1.35853	+	0.987029i	0.359993	+	0.932955i	$0.382779\pi$
$164$	170.307	−	123.735i	0.0810900	−	0.0589153i
$165$	2256.77	+	5368.81i	1.06478	+	2.53310i
$166$	−809.940	−	588.456i	−0.378696	−	0.275139i
$167$	978.494	+	3011.50i	0.453402	+	1.39543i	0.873001	+	0.487718i	$0.162171\pi$
$167$	978.494	+	3011.50i	0.453402	+	1.39543i	−0.419599	+	0.907710i	$0.637829\pi$
$168$	−1756.79			−0.806784
$169$	−678.838	−	2089.25i	−0.308984	−	0.950956i
$170$	−2027.08	−	1227.68i	−0.914529	−	0.553873i
$171$	989.421	−	3045.13i	0.442473	−	1.36179i
$172$	−324.448	+	998.549i	−0.143831	+	0.442667i
$173$	250.297	−	181.852i	0.109999	−	0.0799186i	−0.531426	−	0.847105i	$-0.678344\pi$
$173$	250.297	−	181.852i	0.109999	−	0.0799186i	0.641425	+	0.767186i	$0.278344\pi$
$174$	62.0759			0.0270457
$175$	−3255.61	+	550.567i	−1.40629	+	0.237822i
$176$	−1002.51			−0.429358
$177$	−417.504	+	303.335i	−0.177297	+	0.128814i
$178$	−703.343	+	2164.67i	−0.296167	+	0.911509i
$179$	1146.86	−	3529.66i	0.478883	−	1.47385i	−0.361764	−	0.932270i	$-0.617826\pi$
$179$	1146.86	−	3529.66i	0.478883	−	1.47385i	0.840648	−	0.541582i	$-0.182174\pi$
$180$	1425.77	−	1230.66i	0.590392	−	0.509601i
$181$	291.607	+	897.473i	0.119751	+	0.368556i	0.992908	−	0.118883i	$-0.0379312\pi$
$181$	291.607	+	897.473i	0.119751	+	0.368556i	−0.873157	+	0.487439i	$0.837931\pi$
$182$	−25.4777			−0.0103766
$183$	−937.097	−	2884.09i	−0.378537	−	1.16502i
$184$	619.158	+	449.844i	0.248070	+	0.180233i
$185$	−113.579	−	68.7879i	−0.0451379	−	0.0273372i
$186$	31.1905	−	22.6613i	0.0122957	−	0.00893335i
$187$	−5372.35	−	3903.24i	−2.10088	−	1.52638i
$188$	877.849	+	637.795i	0.340552	+	0.247425i
$189$	2685.33	−	1951.01i	1.03349	−	0.750872i
$190$	1454.10	+	880.658i	0.555219	+	0.336261i
$191$	−2004.11	−	1456.07i	−0.759227	−	0.551611i	0.139446	−	0.990230i	$-0.455468\pi$
$191$	−2004.11	−	1456.07i	−0.759227	−	0.551611i	−0.898673	+	0.438619i	$0.855468\pi$
$192$	164.418	+	506.026i	0.0618012	+	0.190204i
$193$	−2345.06			−0.874616			−0.437308	−	0.899312i	$-0.644068\pi$
$193$	−2345.06			−0.874616			−0.437308	+	0.899312i	$0.644068\pi$
$194$	−454.600	−	1399.11i	−0.168239	−	0.517786i
$195$	33.9332	−	29.2897i	0.0124616	−	0.0107563i
$196$	438.475	−	1349.49i	0.159794	−	0.491796i
$197$	1175.41	−	3617.54i	0.425099	−	1.30832i	−0.477801	−	0.878468i	$-0.658566\pi$
$197$	1175.41	−	3617.54i	0.425099	−	1.30832i	0.902900	−	0.429852i	$-0.141434\pi$
$198$	4269.66	−	3102.09i	1.53248	−	1.11341i
$199$	2972.61			1.05891			0.529454	−	0.848339i	$-0.322397\pi$
$199$	2972.61			1.05891			0.529454	+	0.848339i	$0.322397\pi$
$200$	463.275	+	886.214i	0.163793	+	0.313324i
$201$	−1840.21			−0.645764
$202$	2021.63	−	1468.80i	0.704165	−	0.511606i
$203$	−30.4743	+	93.7903i	−0.0105363	+	0.0324275i
$204$	−1089.10	+	3351.90i	−0.373785	+	1.15039i
$205$	−503.290	−	304.811i	−0.171470	−	0.103849i
$206$	205.701	+	633.083i	0.0695722	+	0.214121i
$207$	−4028.94			−1.35280
$208$	2.38445	+	7.33859i	0.000794865	+	0.00244634i
$209$	3853.79	+	2799.94i	1.27546	+	0.926679i
$210$	1902.80	+	4526.73i	0.625265	+	1.48750i
$211$	−1663.19	+	1208.38i	−0.542649	+	0.394258i	−0.825068	−	0.565034i	$-0.808863\pi$
$211$	−1663.19	+	1208.38i	−0.542649	+	0.394258i	0.282419	+	0.959291i	$0.408863\pi$
$212$	−1163.50	−	845.331i	−0.376931	−	0.273856i
$213$	−4806.80	−	3492.34i	−1.54627	−	1.12343i
$214$	−3364.73	+	2444.62i	−1.07480	+	0.780891i
$215$	2924.37	−	245.532i	0.927631	−	0.0778845i
$216$	−813.285	−	590.886i	−0.256190	−	0.186133i
$217$	18.9268	+	58.2506i	0.00592089	+	0.0182226i
$218$	1409.93			0.438039
$219$	329.447	+	1013.93i	0.101653	+	0.312855i
$220$	1085.83	+	2583.16i	0.332757	+	0.791622i
$221$	−15.7945	+	48.6105i	−0.00480749	+	0.0147959i
$222$	−61.0232	+	187.810i	−0.0184487	+	0.0567792i
$223$	2551.79	−	1853.99i	0.766281	−	0.556736i	−0.134550	−	0.990907i	$-0.542959\pi$
$223$	2551.79	−	1853.99i	0.766281	−	0.556736i	0.900830	+	0.434171i	$0.142959\pi$
$224$	−845.269			−0.252129
$225$	−4715.31	−	2340.84i	−1.39713	−	0.693581i
$226$	759.355			0.223502
$227$	−3601.86	+	2616.90i	−1.05314	+	0.765154i	−0.972808	−	0.231614i	$-0.925600\pi$
$227$	−3601.86	+	2616.90i	−1.05314	+	0.765154i	−0.0803366	+	0.996768i	$0.525600\pi$
$228$	781.251	−	2404.44i	0.226928	−	0.698413i
$229$	251.451	−	773.885i	0.0725604	−	0.223318i	−0.908199	−	0.418539i	$-0.862542\pi$
$229$	251.451	−	773.885i	0.0725604	−	0.223318i	0.980759	+	0.195221i	$0.0625424\pi$
$230$	488.498	−	2082.61i	0.140046	−	0.597058i
$231$	4251.89	+	13086.0i	1.21106	+	3.72724i
$232$	29.8673			0.00845210
$233$	1582.36	+	4870.00i	0.444909	+	1.36929i	0.882584	+	0.470155i	$0.155802\pi$
$233$	1582.36	+	4870.00i	0.444909	+	1.36929i	−0.437675	+	0.899133i	$0.644198\pi$
$234$	−32.8633	−	23.8766i	−0.00918094	−	0.00667034i
$235$	692.599	−	2952.75i	0.192256	−	0.819645i
$236$	−200.879	+	145.947i	−0.0554073	+	0.0402557i
$237$	7511.14	+	5457.16i	2.05865	+	1.49570i
$238$	−4529.71	−	3291.03i	−1.23369	−	0.896326i
$239$	259.522	−	188.554i	0.0702389	−	0.0510316i	−0.552112	−	0.833770i	$-0.686178\pi$
$239$	259.522	−	188.554i	0.0702389	−	0.0510316i	0.622351	+	0.782739i	$0.286178\pi$
$240$	1125.79	−	971.736i	0.302790	−	0.261355i
$241$	72.4553	+	52.6418i	0.0193662	+	0.0140704i	0.597426	−	0.801924i	$-0.296190\pi$
$241$	72.4553	+	52.6418i	0.0193662	+	0.0140704i	−0.578060	+	0.815994i	$0.696190\pi$
$242$	1603.72	+	4935.75i	0.425997	+	1.31108i
$243$	−4161.23			−1.09853
$244$	−450.877	−	1387.66i	−0.118297	−	0.364081i
$245$	−3952.14	+	331.824i	−1.03058	+	0.0865284i
$246$	−270.405	+	832.220i	−0.0700828	+	0.215693i
$247$	11.3300	−	34.8702i	0.00291867	−	0.00898274i
$248$	15.0071	−	10.9033i	0.00384255	−	0.00279177i
$249$	4161.51			1.05914
$250$	1781.73	−	2153.59i	0.450746	−	0.544819i
$251$	−7071.96			−1.77840			−0.889199	−	0.457520i	$-0.848738\pi$
$251$	−7071.96			−1.77840			−0.889199	+	0.457520i	$0.848738\pi$
$252$	3599.98	−	2615.54i	0.899909	−	0.653822i
$253$	1852.27	−	5700.70i	0.460282	−	1.41660i
$254$	−867.103	+	2668.67i	−0.214200	+	0.659241i
$255$	9816.44	−	824.194i	2.41070	−	0.202404i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	−2518.68			−0.611327			−0.305663	−	0.952140i	$-0.598878\pi$
$257$	−2518.68			−0.611327			−0.305663	+	0.952140i	$0.598878\pi$
$258$	−1348.66	−	4150.74i	−0.325441	−	1.00160i
$259$	−253.804	−	184.400i	−0.0608904	−	0.0442395i
$260$	16.3267	−	14.0925i	0.00389438	−	0.00336146i
$261$	−127.204	+	92.4192i	−0.0301676	+	0.0219180i
$262$	−2363.62	−	1717.27i	−0.557347	−	0.404937i
$263$	6581.43	+	4781.69i	1.54307	+	1.12111i	0.948371	+	0.317164i	$0.102731\pi$
$263$	6581.43	+	4781.69i	1.54307	+	1.12111i	0.594704	+	0.803945i	$0.297269\pi$
$264$	3371.34	−	2449.42i	0.785953	−	0.571028i
$265$	−917.967	+	3913.57i	−0.212793	+	0.907202i
$266$	3249.33	+	2360.78i	0.748983	+	0.544168i
$267$	−2923.63	−	8998.02i	−0.670126	−	2.06243i
$268$	−885.405			−0.201809
$269$	200.838	+	618.115i	0.0455216	+	0.140101i	0.971234	−	0.238127i	$-0.0765335\pi$
$269$	200.838	+	618.115i	0.0455216	+	0.140101i	−0.925712	+	0.378228i	$0.876533\pi$
$270$	−641.659	+	2735.58i	−0.144630	+	0.616601i
$271$	−90.1226	+	277.369i	−0.0202013	+	0.0621733i	−0.960649	−	0.277765i	$-0.910406\pi$
$271$	−90.1226	+	277.369i	−0.0202013	+	0.0621733i	0.940448	+	0.339939i	$0.110406\pi$
$272$	−524.011	+	1612.74i	−0.116812	+	0.359510i
$273$	85.6791	−	62.2495i	0.0189946	−	0.0138004i
$274$	−2973.91			−0.655696
$275$	5479.97	−	5595.70i	1.20165	−	1.22703i
$276$	−3181.26			−0.693803
$277$	2941.19	−	2136.90i	0.637974	−	0.463515i	−0.221179	−	0.975233i	$-0.570991\pi$
$277$	2941.19	−	2136.90i	0.637974	−	0.463515i	0.859154	+	0.511718i	$0.170991\pi$
$278$	80.0847	−	246.475i	0.0172775	−	0.0531748i
$279$	−30.1765	+	92.8736i	−0.00647533	+	0.0199290i
$280$	915.518	+	2178.00i	0.195402	+	0.464859i
$281$	−2598.29	−	7996.72i	−0.551605	−	1.69767i	−0.704745	−	0.709461i	$-0.748938\pi$
$281$	−2598.29	−	7996.72i	−0.551605	−	1.69767i	0.153140	−	0.988205i	$-0.451062\pi$
$282$	−4510.44			−0.952456
$283$	−287.342	−	884.348i	−0.0603559	−	0.185756i	0.916333	−	0.400418i	$-0.131135\pi$
$283$	−287.342	−	884.348i	−0.0603559	−	0.185756i	−0.976688	+	0.214662i	$0.931135\pi$
$284$	−2312.75	−	1680.31i	−0.483228	−	0.351086i
$285$	−7041.70	+	591.226i	−1.46356	+	0.122881i
$286$	48.8925	−	35.5225i	0.0101087	−	0.00734437i
$287$	−1124.65	−	817.107i	−0.231310	−	0.168057i
$288$	−1090.30	−	792.147i	−0.223078	−	0.162075i
$289$	−5112.57	+	3714.50i	−1.04062	+	0.756056i
$290$	−32.3496	−	76.9591i	−0.00655046	−	0.0155834i
$291$	4947.21	+	3594.36i	0.996600	+	0.724072i
$292$	158.511	+	487.846i	0.0317676	+	0.0977707i
$293$	−413.694			−0.0824856			−0.0412428	−	0.999149i	$-0.513132\pi$
$293$	−413.694			−0.0824856			−0.0412428	+	0.999149i	$0.513132\pi$
$294$	1822.64	+	5609.51i	0.361560	+	1.11277i
$295$	593.636	+	359.528i	0.117162	+	0.0709577i
$296$	−29.3609	+	90.3634i	−0.00576542	+	0.0177441i
$297$	−2433.02	+	7488.07i	−0.475348	+	1.46297i
$298$	−1707.90	+	1240.86i	−0.332000	+	0.241212i
$299$	−46.1360			−0.00892345
$300$	−3723.23	−	1848.33i	−0.716535	−	0.355712i
$301$	6933.43			1.32769
$302$	−3556.19	+	2583.72i	−0.677602	+	0.492307i
$303$	−3209.83	+	9878.85i	−0.608581	+	1.87302i
$304$	375.893	−	1156.88i	0.0709176	−	0.218262i
$305$	−3087.23	+	2664.76i	−0.579587	+	0.500274i
$306$	−2758.59	−	8490.07i	−0.515353	−	1.58609i
$307$	5657.76			1.05181			0.525905	−	0.850544i	$-0.323727\pi$
$307$	5657.76			1.05181			0.525905	+	0.850544i	$0.323727\pi$
$308$	2045.76	+	6296.22i	0.378468	+	1.16481i
$309$	−2238.56	−	1626.41i	−0.412126	−	0.299427i
$310$	−44.3488	−	26.8593i	−0.00812530	−	0.00492099i
$311$	1363.27	−	990.474i	0.248566	−	0.180594i	−0.456525	−	0.889711i	$-0.650906\pi$
$311$	1363.27	−	990.474i	0.248566	−	0.180594i	0.705091	+	0.709117i	$0.250906\pi$
$312$	−25.9490	−	18.8530i	−0.00470856	−	0.00342097i
$313$	2957.47	+	2148.73i	0.534078	+	0.388030i	0.821881	−	0.569659i	$-0.192925\pi$
$313$	2957.47	+	2148.73i	0.534078	+	0.388030i	−0.287803	+	0.957690i	$0.592925\pi$
$314$	2252.65	−	1636.64i	0.404854	−	0.294144i
$315$	−10638.6	−	6443.14i	−1.90291	−	1.15248i
$316$	3613.93	+	2625.67i	0.643352	+	0.467423i
$317$	−3169.85	−	9755.79i	−0.561629	−	1.72852i	−0.677761	−	0.735282i	$-0.737050\pi$
$317$	−3169.85	−	9755.79i	−0.561629	−	1.72852i	0.116132	−	0.993234i	$-0.462950\pi$
$318$	5978.11			1.05420
$319$	−72.2865	−	222.475i	−0.0126874	−	0.0390477i
$320$	541.667	−	467.543i	0.0946253	−	0.0816765i
$321$	5342.33	−	16442.0i	0.928910	−	2.85889i
$322$	1561.75	−	4806.56i	0.270288	−	0.831861i
$323$	6518.65	−	4736.07i	1.12293	−	0.815858i
$324$	−369.722			−0.0633953
$325$	−53.9957	−	26.8053i	−0.00921583	−	0.00457504i
$326$	−6989.13			−1.18740
$327$	−4741.45	+	3444.87i	−0.801844	+	0.582574i
$328$	−130.103	+	400.416i	−0.0219017	+	0.0674064i
$329$	2214.27	−	6814.81i	0.371053	−	1.14198i
$330$	−9962.95	−	6033.93i	−1.66195	−	1.00654i
$331$	2508.61	+	7720.70i	0.416573	+	1.28208i	0.910837	+	0.412767i	$0.135438\pi$
$331$	2508.61	+	7720.70i	0.416573	+	1.28208i	−0.494264	+	0.869312i	$0.664562\pi$
$332$	2002.28			0.330992
$333$	−154.567	−	475.707i	−0.0254360	−	0.0782841i
$334$	−5123.46	−	3722.41i	−0.839351	−	0.609824i
$335$	958.990	+	2281.42i	0.156404	+	0.372082i
$336$	2842.55	−	2065.24i	0.461530	−	0.335321i
$337$	1888.55	+	1372.12i	0.305270	+	0.221792i	0.729864	−	0.683592i	$-0.239583\pi$
$337$	1888.55	+	1372.12i	0.305270	+	0.221792i	−0.424594	+	0.905384i	$0.639583\pi$
$338$	3554.44	+	2582.45i	0.572001	+	0.415583i
$339$	−2553.64	+	1855.32i	−0.409128	+	0.297249i
$340$	4723.10	−	396.555i	0.753372	−	0.0632536i
$341$	−117.537	−	85.3958i	−0.0186657	−	0.0135614i
$342$	1978.84	+	6090.25i	0.312876	+	0.962933i
$343$	−309.940			−0.0487906
$344$	−648.897	−	1997.10i	−0.101704	−	0.313013i
$345$	3445.66	+	8197.16i	0.537704	+	1.27919i
$346$	−191.210	+	588.484i	−0.0297096	+	0.0914367i
$347$	−2298.05	+	7072.66i	−0.355520	+	1.09418i	0.600187	+	0.799860i	$0.295093\pi$
$347$	−2298.05	+	7072.66i	−0.355520	+	1.09418i	−0.955707	+	0.294320i	$0.904907\pi$
$348$	−100.441	+	72.9746i	−0.0154718	+	0.0112409i
$349$	−2740.81			−0.420379			−0.210190	−	0.977661i	$-0.567408\pi$
$349$	−2740.81			−0.420379			−0.210190	+	0.977661i	$0.567408\pi$
$350$	4620.45	−	4718.03i	0.705638	−	0.720541i
$351$	60.6012			0.00921554
$352$	1622.09	−	1178.52i	0.245619	−	0.178453i
$353$	−2577.21	+	7931.84i	−0.388587	+	1.19595i	0.545258	+	0.838268i	$0.316432\pi$
$353$	−2577.21	+	7931.84i	−0.388587	+	1.19595i	−0.933845	+	0.357679i	$0.883568\pi$
$354$	318.945	−	981.611i	0.0478862	−	0.147379i
$355$	−1824.70	+	7779.23i	−0.272803	+	1.16304i
$356$	−1406.69	−	4329.33i	−0.209422	−	0.644534i
$357$	23273.9			3.45038
$358$	2293.71	+	7059.33i	0.338622	+	1.04217i
$359$	−1618.26	−	1175.73i	−0.237906	−	0.172849i	0.462444	−	0.886649i	$-0.346973\pi$
$359$	−1618.26	−	1175.73i	−0.237906	−	0.172849i	−0.700350	+	0.713800i	$0.746973\pi$
$360$	−860.213	+	3667.35i	−0.125937	+	0.536906i
$361$	872.975	−	634.254i	0.127274	−	0.0924703i
$362$	−1526.87	−	1109.34i	−0.221687	−	0.161065i
$363$	−17452.6	−	12680.1i	−2.52349	−	1.83342i
$364$	41.2239	−	29.9509i	0.00593604	−	0.00431278i
$365$	1085.35	−	936.826i	0.155643	−	0.134344i
$366$	4906.70	+	3564.93i	0.700758	+	0.509131i
$367$	−1500.47	−	4617.97i	−0.213417	−	0.656829i	−0.999262	−	0.0384063i	$-0.987772\pi$
$367$	−1500.47	−	4617.97i	−0.213417	−	0.656829i	0.785845	−	0.618423i	$-0.212228\pi$
$368$	−1530.64			−0.216821
$369$	−684.912	−	2107.94i	−0.0966263	−	0.297385i
$370$	264.640	−	22.2194i	0.0371838	−	0.00312197i
$371$	−2934.78	+	9032.31i	−0.410690	+	1.26397i
$372$	−23.8275	+	73.3334i	−0.00332096	+	0.0102209i
$373$	−8693.87	+	6316.46i	−1.20684	+	0.876821i	−0.994940	−	0.100471i	$-0.967965\pi$
$373$	−8693.87	+	6316.46i	−1.20684	+	0.876821i	−0.211900	+	0.977291i	$0.567965\pi$
$374$	13281.2			1.83624
$375$	−729.937	+	11595.6i	−0.100517	+	1.59678i
$376$	−2170.16			−0.297653
$377$	−1.45663	+	1.05831i	−0.000198993	+	0.000144577i
$378$	−2051.41	+	6313.59i	−0.279135	+	0.859090i
$379$	−2474.07	+	7614.42i	−0.335316	+	1.03200i	0.631251	+	0.775579i	$0.282542\pi$
$379$	−2474.07	+	7614.42i	−0.335316	+	1.03200i	−0.966566	+	0.256417i	$0.917458\pi$
$380$	−3388.06	+	284.464i	−0.457379	+	0.0384018i
$381$	−3604.35	−	11093.0i	−0.484662	−	1.49164i
$382$	4954.44			0.663589
$383$	48.3925	+	148.937i	0.00645625	+	0.0198703i	0.954233	−	0.299065i	$-0.0966747\pi$
$383$	48.3925	+	148.937i	0.00645625	+	0.0198703i	−0.947776	+	0.318935i	$0.896675\pi$
$384$	−860.902	−	625.482i	−0.114408	−	0.0831224i
$385$	14007.7	−	12090.8i	1.85428	−	1.60053i
$386$	3794.38	−	2756.78i	0.500334	−	0.363514i
$387$	8943.30	+	6497.69i	1.17471	+	0.853478i
$388$	2380.31	+	1729.40i	0.311449	+	0.226281i
$389$	−9192.47	+	6678.72i	−1.19814	+	0.870500i	−0.994101	−	0.108463i	$-0.965407\pi$
$389$	−9192.47	+	6678.72i	−1.19814	+	0.870500i	−0.204040	+	0.978963i	$0.565407\pi$
$390$	−20.4730	+	87.2825i	−0.00265818	+	0.0113326i
$391$	−8202.56	−	5959.51i	−1.06092	−	0.770806i
$392$	876.950	+	2698.97i	0.112991	+	0.347752i
$393$	12144.4			1.55879
$394$	2350.82	+	7235.08i	0.300590	+	0.925122i
$395$	2851.29	−	12155.9i	0.363200	−	1.54843i
$396$	−3261.73	+	10038.6i	−0.413909	+	1.27388i
$397$	194.868	−	599.743i	0.0246352	−	0.0758192i	−0.937983	−	0.346681i	$-0.887309\pi$
$397$	194.868	−	599.743i	0.0246352	−	0.0758192i	0.962618	+	0.270862i	$0.0873086\pi$
$398$	−4809.78	+	3494.51i	−0.605760	+	0.440111i
$399$	−16695.2			−2.09476
$400$	−1791.40	−	889.312i	−0.223925	−	0.111164i
$401$	−2493.80			−0.310560			−0.155280	−	0.987871i	$-0.549628\pi$
$401$	−2493.80			−0.310560			−0.155280	+	0.987871i	$0.549628\pi$
$402$	2977.53	−	2163.30i	0.369417	−	0.268397i
$403$	−0.345555	+	1.06351i	−4.27130e−5	+	0.000131457i
$404$	−1544.39	+	4753.14i	−0.190188	+	0.585340i
$405$	400.449	+	952.661i	0.0491320	+	0.116884i
$406$	−60.9486	−	187.581i	−0.00745032	−	0.0229297i
$407$	744.157			0.0906303
$408$	−2178.19	−	6703.79i	−0.264306	−	0.813449i
$409$	9499.69	+	6901.93i	1.14848	+	0.834422i	0.988278	−	0.152662i	$-0.0487846\pi$
$409$	9499.69	+	6901.93i	1.14848	+	0.834422i	0.160204	+	0.987084i	$0.448785\pi$
$410$	1172.67	−	98.4580i	0.141253	−	0.0118597i
$411$	10001.0	−	7266.13i	1.20027	−	0.872048i
$412$	−1077.06	−	782.533i	−0.128794	−	0.0935744i
$413$	1326.54	+	963.786i	0.158050	+	0.114830i
$414$	6518.96	−	4736.30i	0.773887	−	0.562262i
$415$	−2168.69	−	5159.27i	−0.256522	−	0.610262i
$416$	−12.4852	−	9.07099i	−0.00147148	−	0.00106909i
$417$	332.894	+	1024.54i	0.0390932	+	0.120317i
$418$	−9527.09			−1.11480
$419$	−2334.03	−	7183.41i	−0.272136	−	0.837548i	−0.989963	−	0.141326i	$-0.954863\pi$
$419$	−2334.03	−	7183.41i	−0.272136	−	0.837548i	0.717827	−	0.696221i	$-0.245137\pi$
$420$	−8400.29	−	5087.53i	−0.975933	−	0.591062i
$421$	−3566.94	+	10977.9i	−0.412926	+	1.27086i	0.501167	+	0.865350i	$0.332904\pi$
$421$	−3566.94	+	10977.9i	−0.412926	+	1.27086i	−0.914093	+	0.405505i	$0.867096\pi$
$422$	1270.57	−	3910.40i	0.146564	−	0.451079i
$423$	9242.66	−	6715.19i	1.06240	−	0.771876i
$424$	2876.32			0.329450
$425$	−6137.44	−	11740.5i	−0.700493	−	1.34000i
$426$	11883.1			1.35149
$427$	−7795.04	+	5663.43i	−0.883439	+	0.641856i
$428$	2570.42	−	7910.95i	0.290295	−	0.893435i
$429$	−77.6289	+	238.917i	−0.00873650	+	0.0268882i
$430$	−4443.10	+	3835.09i	−0.498291	+	0.430103i
$431$	−2347.61	−	7225.21i	−0.262368	−	0.807485i	−0.992288	−	0.123953i	$-0.960443\pi$
$431$	−2347.61	−	7225.21i	−0.262368	−	0.807485i	0.729920	−	0.683532i	$-0.239557\pi$
$432$	2010.55			0.223918
$433$	−2685.14	−	8264.01i	−0.298013	−	0.917189i	−0.982193	−	0.187876i	$-0.939840\pi$
$433$	−2685.14	−	8264.01i	−0.298013	−	0.917189i	0.684180	−	0.729313i	$-0.260160\pi$
$434$	−99.1018	−	72.0017i	−0.0109609	−	0.00796357i
$435$	296.822	+	179.766i	0.0327161	+	0.0198141i
$436$	−2281.31	+	1657.47i	−0.250585	+	0.182061i
$437$	5884.00	+	4274.98i	0.644096	+	0.467963i
$438$	−1725.01	−	1253.29i	−0.188183	−	0.136723i
$439$	−12431.6	+	9032.09i	−1.35154	+	0.981954i	−0.352611	+	0.935770i	$0.614706\pi$
$439$	−12431.6	+	9032.09i	−1.35154	+	0.981954i	−0.998933	+	0.0461846i	$0.985294\pi$
$440$	−4793.60	−	2903.18i	−0.519377	−	0.314554i
$441$	−12086.4	−	8781.29i	−1.30509	−	0.948201i
$442$	−31.5890	−	97.2211i	−0.00339941	−	0.0104623i
$443$	2948.65			0.316240			0.158120	−	0.987420i	$-0.449457\pi$
$443$	2948.65			0.316240			0.158120	+	0.987420i	$0.449457\pi$
$444$	−122.046	−	375.620i	−0.0130452	−	0.0401490i
$445$	−9631.79	+	8313.74i	−1.02605	+	0.885639i
$446$	−1949.40	+	5999.62i	−0.206965	+	0.636974i
$447$	2711.71	−	8345.79i	0.286934	−	0.883092i
$448$	1367.67	−	993.673i	0.144233	−	0.104792i
$449$	12471.0			1.31079			0.655394	−	0.755287i	$-0.272503\pi$
$449$	12471.0			1.31079			0.655394	+	0.755287i	$0.272503\pi$
$450$	10381.4	−	1755.63i	1.08751	−	0.183913i
$451$	3297.49			0.344286
$452$	−1228.66	+	892.676i	−0.127857	+	0.0928937i
$453$	5646.33	−	17377.6i	0.585624	−	1.80236i
$454$	2751.58	−	8468.48i	0.284445	−	0.875430i
$455$	−121.824	−	73.7814i	−0.0125521	−	0.00760203i
$456$	1562.50	+	4808.88i	0.160462	+	0.493852i
$457$	−13767.5			−1.40922			−0.704612	−	0.709593i	$-0.748879\pi$
$457$	−13767.5			−1.40922			−0.704612	+	0.709593i	$0.748879\pi$
$458$	502.901	+	1547.77i	0.0513079	+	0.157910i
$459$	10774.3	+	7828.02i	1.09565	+	0.796036i
$460$	1657.85	+	3944.00i	0.168039	+	0.399761i
$461$	−11242.1	+	8167.85i	−1.13578	+	0.825194i	−0.986526	−	0.163604i	$-0.947688\pi$
$461$	−11242.1	+	8167.85i	−1.13578	+	0.825194i	−0.149256	+	0.988799i	$0.547688\pi$
$462$	−22263.2	−	16175.1i	−2.24194	−	1.62887i
$463$	12424.9	+	9027.19i	1.24715	+	0.906110i	0.998053	−	0.0623679i	$-0.0198652\pi$
$463$	12424.9	+	9027.19i	1.24715	+	0.906110i	0.249100	+	0.968478i	$0.419865\pi$
$464$	−48.3264	+	35.1112i	−0.00483512	+	0.00351292i
$465$	214.766	−	18.0319i	0.0214183	−	0.00179830i
$466$	−8285.34	−	6019.65i	−0.823628	−	0.598401i
$467$	−3550.42	−	10927.1i	−0.351807	−	1.08275i	−0.957838	−	0.287309i	$-0.907239\pi$
$467$	−3550.42	−	10927.1i	−0.351807	−	1.08275i	0.606031	−	0.795441i	$-0.292761\pi$
$468$	81.2425			0.00802443
$469$	1806.80	+	5560.75i	0.177889	+	0.547487i
$470$	2350.52	+	5591.86i	0.230684	+	0.548794i
$471$	−3576.63	+	11007.7i	−0.349899	+	1.07688i
$472$	153.458	−	472.295i	0.0149650	−	0.0460575i
$473$	−13305.4	+	9666.97i	−1.29341	+	0.939720i
$474$	−18568.6			−1.79933
$475$	4402.62	+	8421.91i	0.425276	+	0.813524i
$476$	11198.1			1.07828
$477$	−12250.2	+	8900.28i	−1.17589	+	0.854331i
$478$	−198.257	+	610.174i	−0.0189709	+	0.0583864i
$479$	3574.14	−	11000.1i	0.340932	−	1.04928i	−0.622793	−	0.782386i	$-0.714002\pi$
$479$	3574.14	−	11000.1i	0.340932	−	1.04928i	0.963726	−	0.266895i	$-0.0859978\pi$
$480$	−679.228	+	2895.75i	−0.0645883	+	0.275359i
$481$	−1.76997	−	5.44739i	−0.000167783	−	0.000516382i
$482$	−179.119			−0.0169267
$483$	6491.83	+	19979.8i	0.611570	+	1.88222i
$484$	−8397.21	−	6100.93i	−0.788618	−	0.572965i
$485$	1878.00	−	8006.48i	0.175826	−	0.749599i
$486$	6733.01	−	4891.82i	0.628427	−	0.456579i
$487$	7445.44	+	5409.43i	0.692782	+	0.503336i	0.877574	−	0.479442i	$-0.159161\pi$
$487$	7445.44	+	5409.43i	0.692782	+	0.503336i	−0.184791	+	0.982778i	$0.559161\pi$
$488$	2360.82	+	1715.24i	0.218995	+	0.159109i
$489$	23503.7	−	17076.5i	2.17357	−	1.57919i
$490$	6004.61	−	5182.92i	0.553593	−	0.477837i
$491$	−1631.59	−	1185.42i	−0.149965	−	0.108956i	0.510273	−	0.860013i	$-0.329544\pi$
$491$	−1631.59	−	1185.42i	−0.149965	−	0.108956i	−0.660238	+	0.751057i	$0.729544\pi$
$492$	−540.809	−	1664.44i	−0.0495560	−	0.152518i
$493$	−395.680			−0.0361472
$494$	22.6600	+	69.7404i	0.00206381	+	0.00635176i
$495$	29399.2	−	2468.37i	2.66948	−	0.224132i
$496$	−11.4644	+	35.2838i	−0.00103784	+	0.00319413i
$497$	−5833.63	+	17954.1i	−0.526507	+	1.62042i
$498$	−6733.47	+	4892.15i	−0.605892	+	0.440206i
$499$	−1509.37			−0.135408			−0.0677041	−	0.997705i	$-0.521567\pi$
$499$	−1509.37			−0.135408			−0.0677041	+	0.997705i	$0.521567\pi$
$500$	−351.204	+	5579.13i	−0.0314126	+	0.499012i
$501$	26324.6			2.34750
$502$	11442.7	−	8313.59i	1.01735	−	0.739151i
$503$	5014.10	−	15431.8i	0.444469	−	1.36793i	−0.438597	−	0.898684i	$-0.644524\pi$
$503$	5014.10	−	15431.8i	0.444469	−	1.36793i	0.883066	−	0.469250i	$-0.155476\pi$
$504$	−2750.14	+	8464.05i	−0.243057	+	0.748053i
$505$	13920.1	−	1168.74i	1.22661	−	0.102987i
$506$	3704.54	+	11401.4i	0.325468	+	1.00169i
$507$	−18262.9			−1.59977
$508$	−1734.21	−	5337.34i	−0.151462	−	0.466154i
$509$	−10833.8	−	7871.19i	−0.943415	−	0.685431i	0.00582510	−	0.999983i	$-0.498146\pi$
$509$	−10833.8	−	7871.19i	−0.943415	−	0.685431i	−0.949240	+	0.314552i	$0.898146\pi$
$510$	−14914.4	+	12873.5i	−1.29494	+	1.11774i
$511$	2740.43	−	1991.04i	0.237240	−	0.172365i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$	−7728.84	−	5615.33i	−0.665179	−	0.483281i
$514$	4075.31	−	2960.89i	0.349716	−	0.254084i
$515$	−849.774	+	3622.84i	−0.0727097	+	0.309983i
$516$	7061.66	+	5130.60i	0.602466	+	0.437717i
$517$	5252.35	+	16165.1i	0.446804	+	1.37512i
$518$	627.438			0.0532202
$519$	−794.817	−	2446.19i	−0.0672227	−	0.206890i
$520$	−9.85043	+	41.9953i	−0.000830712	+	0.00354157i
$521$	405.387	−	1247.65i	0.0340889	−	0.104915i	−0.932564	−	0.361004i	$-0.882434\pi$
$521$	405.387	−	1247.65i	0.0340889	−	0.104915i	0.966653	+	0.256089i	$0.0824341\pi$
$522$	97.1753	−	299.075i	0.00814799	−	0.0250769i
$523$	5686.64	−	4131.59i	0.475448	−	0.345433i	−0.324113	−	0.946019i	$-0.605066\pi$
$523$	5686.64	−	4131.59i	0.475448	−	0.345433i	0.799561	+	0.600585i	$0.205066\pi$
$524$	5843.19			0.487139
$525$	−4010.60	+	27155.4i	−0.333403	+	2.25744i
$526$	−16270.2			−1.34870
$527$	−198.813	+	144.446i	−0.0164335	+	0.0119396i
$528$	−2575.47	+	7926.49i	−0.212279	+	0.653326i
$529$	−931.744	+	2867.61i	−0.0765796	+	0.235688i
$530$	−3115.37	−	7411.42i	−0.255327	−	0.607418i
$531$	807.861	+	2486.34i	0.0660229	+	0.203198i
$532$	−8032.79			−0.654635
$533$	−7.84303	−	24.1384i	−0.000637372	−	0.00196163i
$534$	15308.4	+	11122.2i	1.24056	+	0.901317i
$535$	−23168.2	+	1945.22i	−1.87224	+	0.157194i
$536$	1432.62	−	1040.86i	0.115447	−	0.0838771i
$537$	−24961.5	−	18135.6i	−2.00590	−	1.45737i
$538$	−1051.60	−	764.033i	−0.0842709	−	0.0612264i
$539$	17981.6	−	13064.4i	1.43696	−	1.04401i
$540$	−2177.65	−	5180.58i	−0.173539	−	0.412846i
$541$	12572.8	+	9134.66i	0.999161	+	0.725933i	0.961908	−	0.273373i	$-0.0881394\pi$
$541$	12572.8	+	9134.66i	0.999161	+	0.725933i	0.0372526	+	0.999306i	$0.488139\pi$
$542$	−180.245	−	554.738i	−0.0142845	−	0.0439631i
$543$	7845.15			0.620014
$544$	−1048.02	−	3225.48i	−0.0825985	−	0.254212i
$545$	6741.72	+	4083.04i	0.529878	+	0.320914i
$546$	−65.4530	+	201.444i	−0.00513027	+	0.0157894i
$547$	3712.57	−	11426.1i	0.290197	−	0.893135i	−0.694595	−	0.719401i	$-0.744417\pi$
$547$	3712.57	−	11426.1i	0.290197	−	0.893135i	0.984793	−	0.173734i	$-0.0555834\pi$
$548$	4811.89	−	3496.04i	0.375098	−	0.272525i
$549$	−15362.2			−1.19425
$550$	−2288.64	+	15496.1i	−0.177432	+	1.20138i
$551$	283.837			0.0219453
$552$	5147.39	−	3739.80i	0.396898	−	0.288363i
$553$	9115.68	−	28055.2i	0.700973	−	2.15737i
$554$	−2246.87	+	6915.15i	−0.172311	+	0.530319i
$555$	−835.670	+	721.314i	−0.0639139	+	0.0551677i
$556$	160.169	+	492.950i	0.0122171	+	0.0376003i
$557$	−2730.35			−0.207700			−0.103850	−	0.994593i	$-0.533116\pi$
$557$	−2730.35			−0.207700			−0.103850	+	0.994593i	$0.533116\pi$
$558$	−60.3529	−	185.747i	−0.00457875	−	0.0140920i
$559$	102.411	+	74.4060i	0.00774871	+	0.00562977i
$560$	−4041.74	−	2447.83i	−0.304990	−	0.184713i
$561$	−44663.3	+	32449.8i	−3.36129	+	2.44212i
$562$	13604.8	+	9884.48i	1.02115	+	0.741907i
$563$	11674.1	+	8481.72i	0.873898	+	0.634924i	0.931630	−	0.363408i	$-0.118387\pi$
$563$	11674.1	+	8481.72i	0.873898	+	0.634924i	−0.0577324	+	0.998332i	$0.518387\pi$
$564$	7298.04	−	5302.34i	0.544863	−	0.395866i
$565$	3630.93	+	2199.03i	0.270362	+	0.163741i
$566$	1504.54	+	1093.11i	0.111733	+	0.0811785i
$567$	754.470	+	2322.02i	0.0558814	+	0.171985i
$568$	5717.44			0.422357
$569$	−177.992	−	547.803i	−0.0131139	−	0.0403604i	0.944285	−	0.329128i	$-0.106755\pi$
$569$	−177.992	−	547.803i	−0.0131139	−	0.0403604i	−0.957399	+	0.288767i	$0.906755\pi$
$570$	10698.7	−	9234.64i	0.786173	−	0.678590i
$571$	1545.12	−	4755.38i	0.113242	−	0.348523i	−0.878334	−	0.478047i	$-0.841345\pi$
$571$	1545.12	−	4755.38i	0.113242	−	0.348523i	0.991576	+	0.129524i	$0.0413450\pi$
$572$	−37.3506	+	114.953i	−0.00273025	+	0.00840286i
$573$	−16661.3	+	12105.1i	−1.21472	+	0.882546i
$574$	2780.29			0.202173
$575$	8366.87	−	8543.57i	0.606822	−	0.619637i
$576$	2695.36			0.194977
$577$	9458.77	−	6872.20i	0.682450	−	0.495829i	−0.191719	−	0.981450i	$-0.561406\pi$
$577$	9458.77	−	6872.20i	0.682450	−	0.495829i	0.874170	+	0.485621i	$0.161406\pi$
$578$	3905.66	−	12020.4i	0.281062	−	0.865020i
$579$	−6024.51	+	18541.5i	−0.432418	+	1.33085i
$580$	142.814	+	86.4933i	0.0102242	+	0.00619213i
$581$	−4085.94	−	12575.2i	−0.291762	−	0.897950i
$582$	−12230.2			−0.871061
$583$	−6961.43	−	21425.1i	−0.494534	−	1.52202i
$584$	−829.974	−	603.011i	−0.0588092	−	0.0427274i
$585$	−87.9945	−	209.337i	−0.00621902	−	0.0147949i
$586$	669.372	−	486.327i	0.0471868	−	0.0342832i
$587$	10587.6	+	7692.37i	0.744462	+	0.540883i	0.894105	−	0.447857i	$-0.147813\pi$
$587$	10587.6	+	7692.37i	0.744462	+	0.540883i	−0.149644	+	0.988740i	$0.547813\pi$
$588$	−9543.47	−	6933.74i	−0.669330	−	0.486297i
$589$	142.616	−	103.617i	0.00997690	−	0.00724864i
$590$	−1383.17	+	116.132i	−0.0965158	+	0.00810353i
$591$	−25583.0	−	18587.1i	−1.78061	−	1.29369i
$592$	−58.7217	−	180.727i	−0.00407677	−	0.0125470i
$593$	−5702.64			−0.394906			−0.197453	−	0.980312i	$-0.563267\pi$
$593$	−5702.64			−0.394906			−0.197453	+	0.980312i	$0.563267\pi$
$594$	−4866.04	−	14976.1i	−0.336121	−	1.03448i
$595$	−12128.7	−	28854.0i	−0.835679	−	1.98807i
$596$	1304.72	−	4015.51i	0.0896701	−	0.275976i
$597$	7636.71	−	23503.4i	0.523534	−	1.61127i
$598$	74.6496	−	54.2361i	0.00510476	−	0.00370883i
$599$	16685.8			1.13817			0.569084	−	0.822279i	$-0.307298\pi$
$599$	16685.8			1.13817			0.569084	+	0.822279i	$0.307298\pi$
$600$	8197.15	−	1386.25i	0.557746	−	0.0943223i
$601$	27123.2			1.84089			0.920446	−	0.390869i	$-0.127826\pi$
$601$	27123.2			1.84089			0.920446	+	0.390869i	$0.127826\pi$
$602$	−11218.5	+	8150.73i	−0.759523	+	0.551826i
$603$	−2880.72	+	8865.95i	−0.194547	+	0.598755i
$604$	2716.69	−	8361.10i	0.183014	−	0.563259i
$605$	−6625.16	+	28245.0i	−0.445208	+	1.89806i
$606$	−6419.67	−	19757.7i	−0.430332	−	1.32443i
$607$	1749.87			0.117010			0.0585050	−	0.998287i	$-0.481367\pi$
$607$	1749.87			0.117010			0.0585050	+	0.998287i	$0.481367\pi$
$608$	751.786	+	2313.76i	0.0501463	+	0.154334i
$609$	663.278	+	481.899i	0.0441336	+	0.0320649i
$610$	1862.62	−	7940.92i	0.123632	−	0.527080i
$611$	105.839	−	76.8966i	0.00700784	−	0.00509150i
$612$	14444.2	+	10494.3i	0.954038	+	0.693149i
$613$	−22624.4	−	16437.6i	−1.49069	−	1.08305i	−0.973912	−	0.226925i	$-0.927133\pi$
$613$	−22624.4	−	16437.6i	−1.49069	−	1.08305i	−0.516774	−	0.856122i	$-0.672867\pi$
$614$	−9154.45	+	6651.09i	−0.601699	+	0.437160i
$615$	−3703.00	+	3196.27i	−0.242796	+	0.209571i
$616$	−10711.8	−	7782.55i	−0.700632	−	0.509039i
$617$	2729.56	+	8400.73i	0.178101	+	0.548137i	0.999761	−	0.0218393i	$-0.00695221\pi$
$617$	2729.56	+	8400.73i	0.178101	+	0.548137i	−0.821661	+	0.569977i	$0.806952\pi$
$618$	5534.02			0.360212
$619$	3093.66	+	9521.32i	0.200880	+	0.618246i	0.999857	+	0.0168844i	$0.00537474\pi$
$619$	3093.66	+	9521.32i	0.200880	+	0.618246i	−0.798977	+	0.601361i	$0.794625\pi$
$620$	103.333	−	8.67590i	0.00669347	−	0.000561988i
$621$	−3714.76	+	11432.9i	−0.240046	+	0.738784i
$622$	−1041.45	+	3205.24i	−0.0671353	+	0.206621i
$623$	−24319.6	+	17669.2i	−1.56396	+	1.13628i
$624$	64.1494			0.00411543
$625$	14756.1	−	5137.86i	0.944392	−	0.328823i
$626$	−7311.28			−0.466801
$627$	32038.6	−	23277.4i	2.04067	−	1.48263i
$628$	−1720.87	+	5296.29i	−0.109347	+	0.336537i
$629$	388.970	−	1197.13i	0.0246570	−	0.0758865i
$630$	24788.0	−	2081.22i	1.56758	−	0.131615i
$631$	−1807.06	−	5561.55i	−0.114006	−	0.350875i	0.877732	−	0.479151i	$-0.159055\pi$
$631$	−1807.06	−	5561.55i	−0.114006	−	0.350875i	−0.991738	+	0.128277i	$0.959055\pi$
$632$	−8934.12			−0.562311
$633$	5281.45	+	16254.6i	0.331626	+	1.02064i
$634$	16597.5	+	12058.8i	1.03970	+	0.755389i
$635$	−11874.4	+	10249.4i	−0.742079	+	0.640530i
$636$	−9672.79	+	7027.69i	−0.603068	+	0.438154i
$637$	−138.403	−	100.556i	−0.00860869	−	0.00625458i
$638$	378.497	+	274.994i	0.0234872	+	0.0170645i
$639$	−24350.4	+	17691.6i	−1.50749	+	1.09526i
$640$	−326.805	+	1393.27i	−0.0201846	+	0.0860528i
$641$	2762.44	+	2007.03i	0.170218	+	0.123671i	0.669633	−	0.742692i	$-0.266451\pi$
$641$	2762.44	+	2007.03i	0.170218	+	0.123671i	−0.499414	+	0.866363i	$0.666451\pi$
$642$	10684.7	+	32884.0i	0.656838	+	2.02154i
$643$	−31025.3			−1.90283			−0.951413	−	0.307917i	$-0.900368\pi$
$643$	−31025.3			−1.90283			−0.951413	+	0.307917i	$0.900368\pi$
$644$	3123.49	+	9613.13i	0.191123	+	0.588215i
$645$	5571.45	−	23752.8i	0.340118	−	1.45002i
$646$	−4979.80	+	15326.3i	−0.303294	+	0.933442i
$647$	−3488.60	+	10736.8i	−0.211980	+	0.652408i	0.787374	+	0.616476i	$0.211440\pi$
$647$	−3488.60	+	10736.8i	−0.211980	+	0.652408i	−0.999354	+	0.0359323i	$0.988560\pi$
$648$	598.222	−	434.634i	0.0362660	−	0.0263488i
$649$	−3889.43			−0.235244
$650$	118.878	−	20.1039i	0.00717353	−	0.00121314i
$651$	509.190			0.0306555
$652$	11308.6	−	8216.21i	0.679265	−	0.493515i
$653$	−538.373	+	1656.94i	−0.0322636	+	0.0992973i	−0.965892	−	0.258947i	$-0.916624\pi$
$653$	−538.373	+	1656.94i	−0.0322636	+	0.0992973i	0.933628	+	0.358244i	$0.116624\pi$
$654$	3622.15	−	11147.8i	0.216571	−	0.666536i
$655$	−6328.82	−	15056.1i	−0.377538	−	0.898156i
$656$	−260.206	−	800.832i	−0.0154868	−	0.0476635i
$657$	5400.75			0.320705
$658$	4428.53	+	13629.6i	0.262374	+	0.807504i
$659$	−7571.23	−	5500.82i	−0.447547	−	0.325162i	0.341080	−	0.940034i	$-0.389207\pi$
$659$	−7571.23	−	5500.82i	−0.447547	−	0.325162i	−0.788626	+	0.614873i	$0.789207\pi$
$660$	23213.7	−	1949.04i	1.36908	−	0.114949i
$661$	12990.2	−	9437.92i	0.764387	−	0.555359i	−0.135866	−	0.990727i	$-0.543382\pi$
$661$	12990.2	−	9437.92i	0.764387	−	0.555359i	0.900253	+	0.435368i	$0.143382\pi$
$662$	−13135.2	−	9543.31i	−0.771172	−	0.560289i
$663$	343.770	+	249.764i	0.0201371	+	0.0146305i
$664$	−3239.76	+	2353.82i	−0.189348	+	0.137569i
$665$	8700.39	+	20698.1i	0.507348	+	1.20697i
$666$	809.321	+	588.006i	0.0470879	+	0.0342114i
$667$	−110.368	−	339.677i	−0.00640699	−	0.0197187i
$668$	12665.9			0.733620
$669$	−8103.19	−	24939.1i	−0.468292	−	1.44126i
$670$	−4233.65	−	2564.06i	−0.244120	−	0.147848i
$671$	7062.64	−	21736.6i	0.406334	−	1.25057i
$672$	−2171.52	+	6683.24i	−0.124655	+	0.383648i
$673$	−2206.55	+	1603.15i	−0.126384	+	0.0918232i	−0.649181	−	0.760634i	$-0.724888\pi$
$673$	−2206.55	+	1603.15i	−0.126384	+	0.0918232i	0.522798	+	0.852457i	$0.324888\pi$
$674$	−4668.76			−0.266816
$675$	−10990.2	+	11222.3i	−0.626684	+	0.639919i
$676$	−8787.07			−0.499947
$677$	−10964.2	+	7965.97i	−0.622436	+	0.452226i	−0.853771	−	0.520648i	$-0.825690\pi$
$677$	−10964.2	+	7965.97i	−0.622436	+	0.452226i	0.231336	+	0.972874i	$0.425690\pi$
$678$	1950.80	−	6003.96i	0.110502	−	0.340089i
$679$	6004.04	−	18478.5i	0.339343	−	1.04439i
$680$	−7175.97	+	6193.98i	−0.404685	+	0.349306i
$681$	11437.7	+	35201.5i	0.643601	+	1.98080i
$682$	290.568			0.0163144
$683$	3976.99	+	12239.9i	0.222804	+	0.685720i	0.998507	+	0.0546222i	$0.0173954\pi$
$683$	3976.99	+	12239.9i	0.222804	+	0.685720i	−0.775703	+	0.631098i	$0.782605\pi$
$684$	−10361.4	−	7527.96i	−0.579205	−	0.420817i
$685$	−14220.1	−	8612.20i	−0.793169	−	0.480373i
$686$	501.493	−	364.356i	0.0279112	−	0.0202787i
$687$	−5472.86	−	3976.26i	−0.303934	−	0.220821i
$688$	3397.67	+	2468.55i	0.188277	+	0.136792i
$689$	−140.279	+	101.918i	−0.00775645	+	0.00563539i
$690$	−15211.5	−	9212.67i	−0.839265	−	0.508290i
$691$	−6270.54	−	4555.81i	−0.345213	−	0.250812i	0.401645	−	0.915796i	$-0.368439\pi$
$691$	−6270.54	−	4555.81i	−0.345213	−	0.250812i	−0.746858	+	0.664983i	$0.768439\pi$
$692$	−382.420	−	1176.97i	−0.0210079	−	0.0646555i
$693$	69702.8			3.82077
$694$	−4596.09	−	14145.3i	−0.251391	−	0.773702i
$695$	1096.70	−	946.627i	0.0598566	−	0.0516656i
$696$	76.7300	−	236.151i	0.00417880	−	0.0128610i
$697$	1723.60	−	5304.69i	0.0936670	−	0.288277i
$698$	4434.73	−	3222.02i	0.240483	−	0.174721i
$699$	42570.5			2.30352
$700$	−1929.67	+	13065.6i	−0.104192	+	0.705476i
$701$	18533.5			0.998574			0.499287	−	0.866437i	$-0.333595\pi$
$701$	18533.5			0.998574			0.499287	+	0.866437i	$0.333595\pi$
$702$	−98.0548	+	71.2410i	−0.00527185	+	0.00383022i
$703$	−279.023	+	858.745i	−0.0149695	+	0.0460714i
$704$	−1239.17	+	3813.77i	−0.0663394	+	0.204172i
$705$	−21567.1	−	13061.8i	−1.15215	−	0.697784i
$706$	−5154.42	−	15863.7i	−0.274772	−	0.845662i
$707$	33003.4			1.75562
$708$	637.890	+	1963.22i	0.0338607	+	0.104212i
$709$	10112.5	+	7347.17i	0.535661	+	0.389180i	0.822471	−	0.568807i	$-0.192595\pi$
$709$	10112.5	+	7347.17i	0.535661	+	0.389180i	−0.286810	+	0.957987i	$0.592595\pi$
$710$	−6192.61	−	14732.1i	−0.327331	−	0.778714i
$711$	38050.2	−	27645.1i	2.00702	−	1.45819i
$712$	7365.50	+	5351.35i	0.387688	+	0.281672i
$713$	−179.457	−	130.383i	−0.00942597	−	0.00684837i
$714$	−37657.9	+	27360.1i	−1.97383	+	1.43407i
$715$	336.654	−	28.2657i	0.0176086	−	0.00147843i
$716$	−12010.0	−	8725.81i	−0.626867	−	0.455445i
$717$	−824.111	−	2536.35i	−0.0429247	−	0.132109i
$718$	4000.55			0.207938
$719$	5297.94	+	16305.4i	0.274798	+	0.845742i	0.989273	+	0.146081i	$0.0466659\pi$
$719$	5297.94	+	16305.4i	0.274798	+	0.845742i	−0.714474	+	0.699662i	$0.753334\pi$
$720$	−2919.37	−	6945.13i	−0.151109	−	0.359486i
$721$	−2716.76	+	8361.33i	−0.140329	+	0.431889i
$722$	−666.894	+	2052.49i	−0.0343756	+	0.105797i
$723$	602.360	−	437.640i	0.0309848	−	0.0225118i
$724$	3774.64			0.193761
$725$	68.1843	−	461.669i	0.00349283	−	0.0236496i
$726$	43145.3			2.20561
$727$	−27442.2	+	19938.0i	−1.39997	+	1.01714i	−0.405280	+	0.914193i	$0.632826\pi$
$727$	−27442.2	+	19938.0i	−1.39997	+	1.01714i	−0.994687	+	0.102943i	$0.967174\pi$
$728$	−31.4922	+	96.9231i	−0.00160327	+	0.00493435i
$729$	−9919.12	+	30527.9i	−0.503943	+	1.55098i
$730$	−654.826	+	2791.72i	−0.0332003	+	0.141543i
$731$	8596.54	+	26457.4i	0.434958	+	1.33866i
$732$	−12130.0			−0.612485
$733$	5568.04	+	17136.7i	0.280573	+	0.863515i	0.987691	+	0.156419i	$0.0499951\pi$
$733$	5568.04	+	17136.7i	0.280573	+	0.863515i	−0.707118	+	0.707096i	$0.750005\pi$
$734$	7856.57	+	5708.13i	0.395083	+	0.287045i
$735$	−7529.53	+	32100.6i	−0.377865	+	1.61095i
$736$	2476.63	−	1799.38i	0.124035	−	0.0901167i
$737$	−11220.4	−	8152.09i	−0.560799	−	0.407444i
$738$	3586.25	+	2605.56i	0.178877	+	0.129962i
$739$	−4663.44	+	3388.19i	−0.232135	+	0.168656i	−0.697772	−	0.716320i	$-0.745825\pi$
$739$	−4663.44	+	3388.19i	−0.232135	+	0.168656i	0.465637	+	0.884976i	$0.345825\pi$
$740$	−402.077	+	347.055i	−0.0199738	+	0.0172405i
$741$	−246.599	−	179.165i	−0.0122254	−	0.00888230i
$742$	−5869.55	−	18064.6i	−0.290402	−	0.893765i
$743$	−3472.42			−0.171454			−0.0857272	−	0.996319i	$-0.527321\pi$
$743$	−3472.42			−0.171454			−0.0857272	+	0.996319i	$0.527321\pi$
$744$	−47.6549	−	146.667i	−0.00234827	−	0.00722724i
$745$	−11759.9	+	987.371i	−0.578322	+	0.0485563i
$746$	6641.52	−	20440.5i	0.325956	−	1.00319i
$747$	6514.55	−	20049.7i	0.319083	−	0.982036i
$748$	−21489.4	+	15613.0i	−1.05044	+	0.763190i
$749$	−54929.7			−2.67969
$750$	−12450.4	−	19620.1i	−0.606164	−	0.955235i
$751$	14372.4			0.698344			0.349172	−	0.937059i	$-0.386463\pi$
$751$	14372.4			0.698344			0.349172	+	0.937059i	$0.386463\pi$
$752$	3511.40	−	2551.18i	0.170276	−	0.123713i
$753$	−18168.1	+	55915.5i	−0.879257	+	2.70608i
$754$	1.11277	−	3.42475i	5.37462e−5	−	0.000165414i
$755$	−24486.5	+	2055.90i	−1.18034	+	0.0991020i
$756$	−4102.82	−	12627.2i	−0.197378	−	0.607468i
$757$	−18932.8			−0.909017			−0.454509	−	0.890742i	$-0.650185\pi$
$757$	−18932.8			−0.909017			−0.454509	+	0.890742i	$0.650185\pi$
$758$	−4948.15	−	15228.8i	−0.237104	−	0.729731i
$759$	−40314.9	−	29290.5i	−1.92798	−	1.40076i
$760$	5147.59	−	4443.18i	0.245688	−	0.212067i
$761$	25032.9	−	18187.5i	1.19243	−	0.866354i	0.198915	−	0.980017i	$-0.436258\pi$
$761$	25032.9	−	18187.5i	1.19243	−	0.866354i	0.993519	+	0.113663i	$0.0362583\pi$
$762$	18872.6	+	13711.8i	0.897222	+	0.651870i
$763$	15065.0	+	10945.4i	0.714798	+	0.519331i
$764$	−8016.44	+	5824.29i	−0.379614	+	0.275805i
$765$	11396.0	−	48584.8i	0.538595	−	2.29619i
$766$	−253.386	−	184.096i	−0.0119520	−	0.00868363i
$767$	9.25093	+	28.4714i	0.000435504	+	0.00134034i
$768$	2128.27			0.0999964
$769$	3151.75	+	9700.09i	0.147796	+	0.454869i	0.997360	−	0.0726166i	$-0.0231349\pi$
$769$	3151.75	+	9700.09i	0.147796	+	0.454869i	−0.849564	+	0.527485i	$0.823135\pi$
$770$	−8451.28	+	36030.3i	−0.395536	+	1.68629i
$771$	−6470.56	+	19914.3i	−0.302246	+	0.930216i
$772$	−2898.65	+	8921.12i	−0.135136	+	0.415905i
$773$	13311.4	−	9671.28i	0.619375	−	0.450002i	−0.233328	−	0.972398i	$-0.574962\pi$
$773$	13311.4	−	9671.28i	0.619375	−	0.450002i	0.852703	+	0.522396i	$0.174962\pi$
$774$	−22109.1			−1.02674
$775$	−134.276	−	256.861i	−0.00622366	−	0.0119054i
$776$	−5884.46			−0.272216
$777$	−2110.01	+	1533.01i	−0.0974212	+	0.0707806i
$778$	7022.42	−	21612.8i	0.323607	−	0.995959i
$779$	−1236.40	+	3805.25i	−0.0568661	+	0.175016i
$780$	−69.4808	−	165.294i	−0.00318950	−	0.00758777i
$781$	−13837.7	−	42587.9i	−0.633995	−	1.95124i
$782$	20277.8			0.927281
$783$	144.972	+	446.178i	0.00661670	+	0.0203641i
$784$	−4591.77	−	3336.12i	−0.209173	−	0.151973i
$785$	15510.8	−	1302.30i	0.705230	−	0.0592116i
$786$	−19650.1	+	14276.6i	−0.891724	+	0.647875i
$787$	6241.03	+	4534.38i	0.282680	+	0.205379i	0.720085	−	0.693886i	$-0.244103\pi$
$787$	6241.03	+	4534.38i	0.282680	+	0.205379i	−0.437406	+	0.899264i	$0.644103\pi$
$788$	−12309.1	−	8943.05i	−0.556462	−	0.404293i
$789$	54715.0	−	39752.8i	2.46883	−	1.79371i
$790$	9676.63	+	23020.5i	0.435796	+	1.03675i
$791$	8113.67	+	5894.93i	0.364714	+	0.264980i
$792$	−6523.46	−	20077.1i	−0.292678	−	0.900770i
$793$	−175.915			−0.00787757
$794$	389.736	+	1199.49i	0.0174197	+	0.0536123i
$795$	28584.9	+	17312.1i	1.27522	+	0.772323i
$796$	3674.35	−	11308.5i	0.163610	−	0.503541i
$797$	7360.39	−	22653.0i	0.327125	−	1.00679i	−0.643348	−	0.765574i	$-0.722455\pi$
$797$	7360.39	−	22653.0i	0.327125	−	1.00679i	0.970472	−	0.241212i	$-0.0775451\pi$
$798$	27013.5	−	19626.4i	1.19833	−	0.870637i
$799$	28750.2			1.27298
$800$	3944.00	−	666.983i	0.174302	−	0.0294768i
$801$	−47928.3			−2.11418
$802$	4035.05	−	2931.64i	0.177659	−	0.129077i
$803$	−2482.95	+	7641.73i	−0.109117	+	0.335829i
$804$	−2274.63	+	7000.59i	−0.0997761	+	0.307079i
$805$	21387.0	−	18460.4i	0.936390	−	0.808252i
$806$	−0.691111	−	2.12702i	−3.02026e−5	−	9.29542e-5i
$807$	5403.18			0.235689
$808$	−3088.77	−	9506.27i	−0.134484	−	0.413898i
$809$	−8259.25	−	6000.70i	−0.358937	−	0.260783i	0.393672	−	0.919251i	$-0.371205\pi$
$809$	−8259.25	−	6000.70i	−0.358937	−	0.260783i	−0.752609	+	0.658468i	$0.771205\pi$
$810$	−1767.86	−	1070.68i	−0.0766867	−	0.0464444i
$811$	−23311.9	+	16937.1i	−1.00936	+	0.733343i	−0.964075	−	0.265631i	$-0.914420\pi$
$811$	−23311.9	+	16937.1i	−1.00936	+	0.733343i	−0.0452857	+	0.998974i	$0.514420\pi$
$812$	319.131	+	231.862i	0.0137922	+	0.0100207i
$813$	1961.53	+	1425.14i	0.0846173	+	0.0614781i
$814$	−1204.07	+	874.810i	−0.0518461	+	0.0376684i
$815$	−33419.2	−	20239.9i	−1.43635	−	0.869906i
$816$	11405.2	+	8286.34i	0.489290	+	0.355490i
$817$	−6166.62	−	18978.9i	−0.264067	−	0.812715i
$818$	−23484.5			−1.00381
$819$	−165.787	−	510.240i	−0.00707334	−	0.0217695i
$820$	−1781.67	+	1537.86i	−0.0758764	+	0.0654933i
$821$	−11760.4	+	36194.8i	−0.499928	+	1.53862i	0.309206	+	0.950995i	$0.399937\pi$
$821$	−11760.4	+	36194.8i	−0.499928	+	1.53862i	−0.809134	+	0.587624i	$0.800063\pi$
$822$	−7640.06	+	23513.7i	−0.324182	+	0.997730i
$823$	26961.0	−	19588.3i	1.14192	−	0.829655i	0.154536	−	0.987987i	$-0.450612\pi$
$823$	26961.0	−	19588.3i	1.14192	−	0.829655i	0.987386	+	0.158332i	$0.0506118\pi$
$824$	2662.65			0.112570
$825$	−30165.1	−	57703.7i	−1.27298	−	2.43513i
$826$	−3279.38			−0.138141
$827$	13786.8	−	10016.7i	0.579702	−	0.421178i	−0.258915	−	0.965900i	$-0.583365\pi$
$827$	13786.8	−	10016.7i	0.579702	−	0.421178i	0.838617	+	0.544722i	$0.183365\pi$
$828$	−4980.04	+	15327.0i	−0.209020	+	0.643297i
$829$	2931.09	−	9020.95i	0.122800	−	0.377938i	−0.870694	−	0.491825i	$-0.836330\pi$
$829$	2931.09	−	9020.95i	0.122800	−	0.377938i	0.993494	+	0.113887i	$0.0363301\pi$
$830$	9574.10	+	5798.44i	0.400388	+	0.242490i
$831$	−9339.72	−	28744.7i	−0.389881	−	1.19993i
$832$	30.8650			0.00128612
$833$	−11617.8	−	35755.8i	−0.483231	−	1.48723i
$834$	−1743.05	−	1266.40i	−0.0723705	−	0.0525803i
$835$	−13718.5	−	32636.2i	−0.568563	−	1.35260i
$836$	15415.2	−	11199.8i	0.637732	−	0.463340i
$837$	235.723	+	171.263i	0.00973450	+	0.00707253i
$838$	12221.1	+	8879.18i	0.503786	+	0.366022i
$839$	12095.2	−	8787.65i	0.497701	−	0.361601i	−0.310437	−	0.950594i	$-0.600475\pi$
$839$	12095.2	−	8787.65i	0.497701	−	0.361601i	0.808138	+	0.588993i	$0.200475\pi$
$840$	19572.7	−	1643.34i	0.803955	−	0.0675006i
$841$	19719.8	+	14327.3i	0.808555	+	0.587449i
$842$	−7133.87	−	21955.8i	−0.291983	−	0.898630i
$843$	−69902.3			−2.85595
$844$	2541.13	+	7820.80i	0.103637	+	0.318961i
$845$	9517.35	+	22641.6i	0.387464	+	0.921770i
$846$	−7060.77	+	21730.8i	−0.286943	+	0.883121i
$847$	−21180.9	+	65188.1i	−0.859250	+	2.64450i
$848$	−4653.99	+	3381.32i	−0.188465	+	0.136928i
$849$	−7730.42			−0.312494
$850$	23732.4	+	11781.5i	0.957663	+	0.475416i
$851$	1136.19			0.0457673
$852$	−19227.2	+	13969.4i	−0.773137	+	0.561717i
$853$	−7339.54	+	22588.8i	−0.294609	+	0.906712i	0.688744	+	0.725005i	$0.258162\pi$
$853$	−7339.54	+	22588.8i	−0.294609	+	0.906712i	−0.983353	+	0.181708i	$0.941838\pi$
$854$	5954.88	−	18327.2i	0.238609	−	0.734362i
$855$	−8174.82	+	34851.7i	−0.326986	+	1.39404i
$856$	5140.85	+	15821.9i	0.205269	+	0.631754i
$857$	37144.3			1.48054			0.740272	−	0.672307i	$-0.234697\pi$
$857$	37144.3			1.48054			0.740272	+	0.672307i	$0.234697\pi$
$858$	−155.258	−	477.834i	−0.00617764	−	0.0190128i
$859$	11378.3	+	8266.79i	0.451946	+	0.328358i	0.790363	−	0.612638i	$-0.209892\pi$
$859$	11378.3	+	8266.79i	0.451946	+	0.328358i	−0.338418	+	0.940996i	$0.609892\pi$
$860$	2680.66	−	11428.5i	0.106291	−	0.453148i
$861$	−9349.84	+	6793.05i	−0.370083	+	0.268881i
$862$	12292.3	+	8930.85i	0.485703	+	0.352884i
$863$	−12985.8	−	9434.75i	−0.512216	−	0.372147i	0.301447	−	0.953483i	$-0.402530\pi$
$863$	−12985.8	−	9434.75i	−0.512216	−	0.372147i	−0.813664	+	0.581336i	$0.802530\pi$
$864$	−3253.14	+	2363.54i	−0.128095	+	0.0930664i
$865$	−2618.49	+	2260.17i	−0.102926	+	0.0888416i
$866$	14059.6	+	10214.9i	0.551690	+	0.400826i
$867$	16234.9	+	49966.0i	0.635948	+	1.95725i
$868$	244.993			0.00958019
$869$	21622.8	+	66548.3i	0.844079	+	2.59781i
$870$	−691.596	+	58.0668i	−0.0269509	+	0.00226282i
$871$	−32.9876	+	101.525i	−0.00128329	+	0.00394955i
$872$	1742.77	−	5363.69i	0.0676808	−	0.208300i
$873$	25061.7	−	18208.4i	0.971605	−	0.705913i
$874$	−14546.1			−0.562961
$875$	35756.1	−	9179.29i	1.38146	−	0.354648i
$876$	4264.45			0.164478
$877$	−3941.73	+	2863.84i	−0.151771	+	0.110268i	−0.661079	−	0.750316i	$-0.729901\pi$
$877$	−3941.73	+	2863.84i	−0.151771	+	0.110268i	0.509308	+	0.860584i	$0.329901\pi$
$878$	9496.90	−	29228.4i	0.365040	−	1.12348i
$879$	−1062.79	+	3270.94i	−0.0407817	+	0.125513i
$880$	11169.1	−	937.765i	0.427853	−	0.0359228i
$881$	−6972.81	−	21460.1i	−0.266652	−	0.820669i	−0.991308	−	0.131559i	$-0.958002\pi$
$881$	−6972.81	−	21460.1i	−0.266652	−	0.820669i	0.724657	−	0.689110i	$-0.241998\pi$
$882$	29879.2			1.14069
$883$	11828.2	+	36403.5i	0.450794	+	1.38740i	0.876003	+	0.482306i	$0.160201\pi$
$883$	11828.2	+	36403.5i	0.450794	+	1.38740i	−0.425209	+	0.905095i	$0.639799\pi$
$884$	165.402	+	120.172i	0.00629308	+	0.00457219i
$885$	4367.73	−	3770.03i	0.165898	−	0.143196i
$886$	−4771.01	+	3466.34i	−0.180909	+	0.131438i
$887$	−16978.7	−	12335.7i	−0.642715	−	0.466960i	0.218067	−	0.975934i	$-0.430025\pi$
$887$	−16978.7	−	12335.7i	−0.642715	−	0.466960i	−0.860782	+	0.508974i	$0.830025\pi$
$888$	639.043	+	464.292i	0.0241496	+	0.0175457i
$889$	−29982.0	+	21783.2i	−1.13112	+	0.821806i
$890$	5811.17	−	24774.8i	0.218866	−	0.933092i
$891$	−4685.34	−	3404.10i	−0.176167	−	0.127993i
$892$	−3898.79	−	11999.2i	−0.146347	−	0.450409i
$893$	−20623.6			−0.772835
$894$	5423.42	+	16691.6i	0.202893	+	0.624440i
$895$	−9475.59	+	40397.3i	−0.353893	+	1.50875i
$896$	−1044.81	+	3215.59i	−0.0389561	+	0.119894i
$897$	−118.525	+	364.781i	−0.00441184	+	0.0135782i
$898$	−20178.5	+	14660.6i	−0.749851	+	0.544799i
$899$	−8.65677			−0.000321156
$900$	−14733.5	+	15044.7i	−0.545686	+	0.557210i
$901$	−38105.3			−1.40896
$902$	−5335.46	+	3876.44i	−0.196953	+	0.143094i
$903$	17812.2	−	54820.2i	0.656425	−	2.02027i
$904$	938.615	−	2888.76i	0.0345330	−	0.106282i
$905$	−4088.34	−	9726.10i	−0.150167	−	0.357245i
$906$	11292.7	+	34755.2i	0.414098	+	1.27446i
$907$	−29670.2			−1.08620			−0.543100	−	0.839668i	$-0.682749\pi$
$907$	−29670.2			−1.08620			−0.543100	+	0.839668i	$0.682749\pi$
$908$	5503.15	+	16937.0i	0.201133	+	0.619023i
$909$	42570.5	+	30929.3i	1.55333	+	1.12856i
$910$	283.851	−	23.8323i	0.0103402	−	0.000868169i
$911$	2609.65	−	1896.02i	0.0949082	−	0.0689549i	−0.539319	−	0.842101i	$-0.681318\pi$
$911$	2609.65	−	1896.02i	0.0949082	−	0.0689549i	0.634227	+	0.773147i	$0.281318\pi$
$912$	−8181.36	−	5944.11i	−0.297053	−	0.215821i
$913$	25374.1	+	18435.4i	0.919782	+	0.668261i
$914$	22276.2	−	16184.6i	0.806162	−	0.585711i
$915$	13138.2	+	31255.5i	0.474682	+	1.12926i
$916$	−2633.23	−	1913.15i	−0.0949828	−	0.0690090i
$917$	−11923.9	−	36697.9i	−0.429401	−	1.32156i
$918$	−26635.6			−0.957633
$919$	−11593.7	−	35681.8i	−0.416149	−	1.28078i	−0.911219	−	0.411922i	$-0.864857\pi$
$919$	−11593.7	−	35681.8i	−0.416149	−	1.28078i	0.495070	−	0.868853i	$-0.335143\pi$
$920$	−7318.91	−	4432.61i	−0.262280	−	0.158846i
$921$	14534.9	−	44733.9i	0.520024	−	1.60047i
$922$	8588.18	−	26431.7i	0.306764	−	0.944124i
$923$	−278.840	+	202.589i	−0.00994382	+	0.00722461i
$924$	55037.6			1.95953
$925$	1329.75	+	660.132i	0.0472669	+	0.0234649i
$926$	−30715.9			−1.09005
$927$	−11340.2	+	8239.10i	−0.401790	+	0.291918i
$928$	36.9181	−	113.622i	0.00130592	−	0.00401921i
$929$	−2141.80	+	6591.78i	−0.0756407	+	0.232798i	−0.981727	−	0.190295i	$-0.939056\pi$
$929$	−2141.80	+	6591.78i	−0.0756407	+	0.232798i	0.906086	+	0.423093i	$0.139056\pi$
$930$	−326.300	+	281.648i	−0.0115052	+	0.00993077i
$931$	8333.87	+	25649.0i	0.293374	+	0.902913i
$932$	20482.5			0.719877
$933$	−4329.05	−	13323.5i	−0.151904	−	0.467514i
$934$	18590.2	+	13506.6i	0.651276	+	0.473179i
$935$	63505.2	+	38461.1i	2.22122	+	1.34526i
$936$	−131.453	+	95.5063i	−0.00459047	+	0.00333517i
$937$	22524.3	+	16364.9i	0.785313	+	0.570563i	0.906569	−	0.422058i	$-0.138692\pi$
$937$	22524.3	+	16364.9i	0.785313	+	0.570563i	−0.121256	+	0.992621i	$0.538692\pi$
$938$	−9460.51	−	6873.46i	−0.329314	−	0.239261i
$939$	24587.1	−	17863.6i	0.854494	−	0.620826i
$940$	−10376.8	−	6284.61i	−0.360059	−	0.218065i
$941$	16119.8	+	11711.7i	0.558439	+	0.405729i	0.830887	−	0.556441i	$-0.187833\pi$
$941$	16119.8	+	11711.7i	0.558439	+	0.405729i	−0.272448	+	0.962170i	$0.587833\pi$
$942$	−7153.27	−	22015.5i	−0.247416	−	0.761469i
$943$	5034.65			0.173861
$944$	306.916	+	944.590i	0.0105818	+	0.0325676i
$945$	−28092.6	+	24248.3i	−0.967040	+	0.834707i
$946$	10164.5	−	31283.0i	0.349339	−	1.07516i
$947$	4561.76	−	14039.6i	0.156533	−	0.481760i	−0.841780	−	0.539821i	$-0.818492\pi$
$947$	4561.76	−	14039.6i	0.156533	−	0.481760i	0.998313	+	0.0580610i	$0.0184918\pi$
$948$	30044.6	−	21828.6i	1.02933	−	0.747850i
$949$	61.8448			0.00211545
$950$	−17024.1	−	8451.35i	−0.581406	−	0.288629i
$951$	−85279.0			−2.90785
$952$	−18118.8	+	13164.1i	−0.616843	+	0.448163i
$953$	1258.50	−	3873.26i	0.0427772	−	0.131655i	−0.927387	−	0.374103i	$-0.877951\pi$
$953$	1258.50	−	3873.26i	0.0427772	−	0.131655i	0.970164	+	0.242448i	$0.0779505\pi$
$954$	9358.31	−	28801.9i	0.317596	−	0.977459i
$955$	23690.1	+	14347.6i	0.802716	+	0.486155i
$956$	−396.515	−	1220.35i	−0.0134144	−	0.0412854i
$957$	−1944.74			−0.0656891
$958$	7148.28	+	22000.1i	0.241076	+	0.741954i
$959$	−31776.1	−	23086.7i	−1.06997	−	0.777381i
$960$	−2305.15	−	5483.90i	−0.0774982	−	0.184367i
$961$	24097.1	−	17507.6i	0.808871	−	0.587679i
$962$	9.26766	+	6.73335i	0.000310604	+	0.000225667i
$963$	−70852.8	−	51477.6i	−2.37092	−	1.72258i
$964$	289.821	−	210.567i	0.00968310	−	0.00703519i
$965$	26126.6	−	2193.61i	0.871549	−	0.0731758i
$966$	−33991.7	−	24696.4i	−1.13216	−	0.822560i
$967$	−7809.95	−	24036.5i	−0.259722	−	0.799341i	−0.992863	−	0.119264i	$-0.961946\pi$
$967$	−7809.95	−	24036.5i	−0.259722	−	0.799341i	0.733141	−	0.680077i	$-0.238054\pi$
$968$	20759.0			0.689278
$969$	−20699.9	−	63707.8i	−0.686250	−	2.11206i
$970$	6373.51	+	15162.5i	0.210970	+	0.501895i
$971$	−11621.9	+	35768.6i	−0.384104	+	1.18215i	0.553024	+	0.833165i	$0.313474\pi$
$971$	−11621.9	+	35768.6i	−0.384104	+	1.18215i	−0.937128	+	0.348986i	$0.886526\pi$
$972$	−5143.56	+	15830.3i	−0.169732	+	0.522382i
$973$	2769.10	−	2011.87i	0.0912368	−	0.0662874i
$974$	−18406.1			−0.605514
$975$	−350.656	+	358.062i	−0.0115179	+	0.0117612i
$976$	−5836.28			−0.191409
$977$	10357.5	−	7525.16i	0.339166	−	0.246419i	−0.405144	−	0.914253i	$-0.632779\pi$
$977$	10357.5	−	7525.16i	0.339166	−	0.246419i	0.744310	+	0.667834i	$0.232779\pi$
$978$	−17955.2	+	55260.6i	−0.587061	+	1.80679i
$979$	22034.6	−	67815.6i	0.719335	−	2.21389i
$980$	−3622.78	+	15445.0i	−0.118087	+	0.503441i
$981$	9174.60	+	28236.5i	0.298596	+	0.918983i
$982$	4033.52			0.131074
$983$	−6585.57	−	20268.3i	−0.213680	−	0.657638i	−0.999245	−	0.0388591i	$-0.987628\pi$
$983$	−6585.57	−	20268.3i	−0.213680	−	0.657638i	0.785565	−	0.618779i	$-0.212372\pi$
$984$	2831.71	+	2057.36i	0.0917395	+	0.0666527i
$985$	−9711.50	+	41403.0i	−0.314146	+	1.33930i
$986$	640.224	−	465.150i	0.0206784	−	0.0150237i
$987$	−48193.8	−	35014.8i	−1.55423	−	1.12921i
$988$	−118.649	−	86.2038i	−0.00382059	−	0.00277582i
$989$	−20314.9	+	14759.6i	−0.653161	+	0.474549i
$990$	−44667.1	+	38554.7i	−1.43395	+	1.23773i
$991$	36299.0	+	26372.8i	1.16355	+	0.845368i	0.990223	−	0.139497i	$-0.0445484\pi$
$991$	36299.0	+	26372.8i	1.16355	+	0.845368i	0.173327	+	0.984864i	$0.444548\pi$
$992$	−22.9288	−	70.5676i	−0.000733861	−	0.00225859i
$993$	67489.6			2.15681
$994$	−11667.3	−	35908.1i	−0.372297	−	1.14581i
$995$	−33118.3	+	2780.63i	−1.05520	+	0.0885949i
$996$	5143.91	−	15831.3i	0.163646	−	0.503650i
$997$	−2484.49	+	7646.48i	−0.0789214	+	0.242895i	−0.982731	−	0.185040i	$-0.940759\pi$
$997$	−2484.49	+	7646.48i	−0.0789214	+	0.242895i	0.903810	+	0.427935i	$0.140759\pi$
$998$	2442.21	−	1774.37i	0.0774618	−	0.0562793i
$999$	−1492.42			−0.0472654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.4.d.b.11.4	✓	16
5.2	odd	4		250.4.e.c.199.1		32
5.3	odd	4		250.4.e.c.199.8		32
5.4	even	2		250.4.d.b.51.1		16
25.4	even	10		1250.4.a.g.1.1		8
25.9	even	10		250.4.d.b.201.1		16
25.12	odd	20		250.4.e.c.49.8		32
25.13	odd	20		250.4.e.c.49.1		32
25.16	even	5	inner	50.4.d.b.41.4	yes	16
25.21	even	5		1250.4.a.j.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.d.b.11.4	✓	16	1.1	even	1	trivial
50.4.d.b.41.4	yes	16	25.16	even	5	inner
250.4.d.b.51.1		16	5.4	even	2
250.4.d.b.201.1		16	25.9	even	10
250.4.e.c.49.1		32	25.13	odd	20
250.4.e.c.49.8		32	25.12	odd	20
250.4.e.c.199.1		32	5.2	odd	4
250.4.e.c.199.8		32	5.3	odd	4
1250.4.a.g.1.1		8	25.4	even	10
1250.4.a.j.1.8		8	25.21	even	5

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(2.56903 - 7.90665i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-11.1411 + 0.935417i) q^{5} +(5.13805 + 15.8133i) q^{6} -26.4146 q^{7} +(2.47214 + 7.60845i) q^{8} +(-34.0718 - 24.7546i) q^{9} +(16.9271 - 14.6107i) q^{10} +(50.6905 - 36.8288i) q^{11} +(-26.9032 - 19.5463i) q^{12} +(-0.390161 - 0.283469i) q^{13} +(42.7398 - 31.0523i) q^{14} +(-21.2259 + 90.4922i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(-32.7507 - 100.796i) q^{17} +84.2300 q^{18} +(23.4933 + 72.3050i) q^{19} +(-10.2127 + 43.5397i) q^{20} +(-67.8599 + 208.851i) q^{21} +(-38.7241 + 119.180i) q^{22} +(77.3947 - 56.2305i) q^{23} +66.5084 q^{24} +(123.250 - 20.8432i) q^{25} +0.964531 q^{26} +(-101.661 + 73.8608i) q^{27} +(-32.6503 + 100.487i) q^{28} +(1.15369 - 3.55069i) q^{29} +(-72.0358 - 171.372i) q^{30} +(-0.716525 - 2.20524i) q^{31} +32.0000 q^{32} +(-160.967 - 495.406i) q^{33} +(171.485 + 124.591i) q^{34} +(294.289 - 24.7087i) q^{35} +(-136.287 + 99.0184i) q^{36} +(9.60846 + 6.98096i) q^{37} +(-123.013 - 89.3738i) q^{38} +(-3.24362 + 2.35663i) q^{39} +(-34.6595 - 82.4543i) q^{40} +(42.5768 + 30.9339i) q^{41} +(-135.720 - 417.703i) q^{42} -262.484 q^{43} +(-77.4481 - 238.361i) q^{44} +(402.754 + 243.923i) q^{45} +(-59.1243 + 181.966i) q^{46} +(-83.8272 + 257.993i) q^{47} +(-107.613 + 78.1853i) q^{48} +354.734 q^{49} +(-174.920 + 178.614i) q^{50} -881.098 q^{51} +(-1.56064 + 1.13387i) q^{52} +(111.104 - 341.943i) q^{53} +(77.6618 - 239.018i) q^{54} +(-530.299 + 457.731i) q^{55} +(-65.3006 - 200.975i) q^{56} +632.045 q^{57} +(2.30738 + 7.10138i) q^{58} +(-50.2198 - 36.4868i) q^{59} +(318.016 + 192.603i) q^{60} +(295.103 - 214.405i) q^{61} +(3.75177 + 2.72582i) q^{62} +(899.994 + 653.884i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(4.61200 + 2.79320i) q^{65} +(842.835 + 612.355i) q^{66} +(-68.4013 - 210.518i) q^{67} -423.934 q^{68} +(-245.766 - 756.391i) q^{69} +(-447.123 + 385.937i) q^{70} +(220.848 - 679.701i) q^{71} +(104.114 - 320.430i) q^{72} +(-103.747 + 75.3764i) q^{73} -23.7534 q^{74} +(151.832 - 1028.04i) q^{75} +304.104 q^{76} +(-1338.97 + 972.819i) q^{77} +(2.47791 - 7.62621i) q^{78} +(-345.099 + 1062.11i) q^{79} +(153.011 + 92.6693i) q^{80} +(-28.5626 - 87.9065i) q^{81} -105.256 q^{82} +(154.685 + 476.071i) q^{83} +(710.638 + 516.309i) q^{84} +(459.166 + 1092.35i) q^{85} +(424.708 - 308.569i) q^{86} +(-25.1102 - 18.2436i) q^{87} +(405.524 + 294.630i) q^{88} +(920.687 - 668.918i) q^{89} +(-938.419 + 78.7903i) q^{90} +(10.3060 + 7.48772i) q^{91} +(-118.249 - 363.932i) q^{92} -19.2768 q^{93} +(-167.654 - 515.987i) q^{94} +(-329.378 - 783.584i) q^{95} +(82.2089 - 253.013i) q^{96} +(-227.300 + 699.557i) q^{97} +(-573.971 + 417.014i) q^{98} -2638.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 7 q^{3} - 16 q^{4} + 15 q^{5} + 14 q^{6} - 54 q^{7} - 32 q^{8} - 83 q^{9} - 50 q^{10} + 152 q^{11} - 12 q^{12} + 77 q^{13} + 52 q^{14} - 70 q^{15} - 64 q^{16} + 76 q^{17} + 304 q^{18} - 20 q^{19}+ \cdots - 1786 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 7 * q^3 - 16 * q^4 + 15 * q^5 + 14 * q^6 - 54 * q^7 - 32 * q^8 - 83 * q^9 - 50 * q^10 + 152 * q^11 - 12 * q^12 + 77 * q^13 + 52 * q^14 - 70 * q^15 - 64 * q^16 + 76 * q^17 + 304 * q^18 - 20 * q^19 + 20 * q^20 + 257 * q^21 - 226 * q^22 - 383 * q^23 - 64 * q^24 - 215 * q^25 - 716 * q^26 + 415 * q^27 + 4 * q^28 + 105 * q^29 + 140 * q^30 + 177 * q^31 + 512 * q^32 + 64 * q^33 + 342 * q^34 - 210 * q^35 - 332 * q^36 + 446 * q^37 + 90 * q^38 - 146 * q^39 - 40 * q^40 + 462 * q^41 + 514 * q^42 - 1058 * q^43 - 452 * q^44 - 865 * q^45 + 1124 * q^46 - 1114 * q^47 - 48 * q^48 + 1698 * q^49 - 550 * q^50 - 3608 * q^51 + 308 * q^52 + 567 * q^53 + 390 * q^54 - 210 * q^55 + 8 * q^56 - 1520 * q^57 + 210 * q^58 + 1275 * q^59 + 1260 * q^60 + 252 * q^61 - 176 * q^62 + 5402 * q^63 - 256 * q^64 + 2645 * q^65 + 998 * q^66 + 3296 * q^67 - 1976 * q^68 - 5491 * q^69 - 1750 * q^70 + 3712 * q^71 + 56 * q^72 - 1688 * q^73 - 1148 * q^74 - 6315 * q^75 - 200 * q^76 - 5453 * q^77 - 1152 * q^78 + 1750 * q^79 + 160 * q^80 + 4106 * q^81 - 1576 * q^82 - 2153 * q^83 - 612 * q^84 + 5860 * q^85 + 1074 * q^86 - 1255 * q^87 + 1216 * q^88 + 5660 * q^89 + 820 * q^90 - 493 * q^91 + 2248 * q^92 - 256 * q^93 - 2228 * q^94 - 1420 * q^95 + 224 * q^96 - 429 * q^97 - 674 * q^98 - 1786 * q^99

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