LMFDB - Embedded newform 152.4.t.a.101.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,4,Mod(5,152)] 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("152.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.7
Character	$\chi$	$=$	152.101
Dual form			152.4.t.a.149.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.58074 + 1.15750i) q^{2} +(-2.73201 + 7.50614i) q^{3} +(5.32040 - 5.97439i) q^{4} +(-18.1584 + 3.20182i) q^{5} +(-1.63774 - 22.5337i) q^{6} +(13.1479 - 22.7729i) q^{7} +(-6.81519 + 21.5767i) q^{8} +(-28.1950 - 23.6584i) q^{9} +(43.1560 - 29.2814i) q^{10} +(30.6923 - 17.7202i) q^{11} +(30.3093 + 56.2577i) q^{12} +(-6.32864 - 17.3878i) q^{13} +(-7.57176 + 73.9895i) q^{14} +(25.5757 - 145.047i) q^{15} +(-7.38678 - 63.5723i) q^{16} +(-28.7555 + 24.1287i) q^{17} +(100.149 + 28.4205i) q^{18} +(-56.9239 + 60.1554i) q^{19} +(-77.4812 + 125.521i) q^{20} +(135.016 + 160.906i) q^{21} +(-58.6977 + 81.2576i) q^{22} +(-21.8283 + 123.794i) q^{23} +(-143.338 - 110.103i) q^{24} +(202.016 - 73.5278i) q^{25} +(36.4589 + 37.5479i) q^{26} +(67.8349 - 39.1645i) q^{27} +(-66.1020 - 199.712i) q^{28} +(167.082 - 199.120i) q^{29} +(101.888 + 403.932i) q^{30} +(119.241 - 206.531i) q^{31} +(92.6481 + 155.513i) q^{32} +(49.1587 + 278.793i) q^{33} +(46.2814 - 95.5543i) q^{34} +(-165.831 + 455.617i) q^{35} +(-291.354 + 42.5760i) q^{36} -41.1750i q^{37} +(77.2757 - 221.134i) q^{38} +147.805 q^{39} +(54.6685 - 413.620i) q^{40} +(375.389 + 136.631i) q^{41} +(-534.689 - 258.975i) q^{42} +(136.268 - 24.0276i) q^{43} +(57.4277 - 277.647i) q^{44} +(587.728 + 339.325i) q^{45} +(-86.9587 - 344.747i) q^{46} +(-207.000 - 173.694i) q^{47} +(497.363 + 118.234i) q^{48} +(-174.236 - 301.785i) q^{49} +(-436.241 + 423.589i) q^{50} +(-102.553 - 281.763i) q^{51} +(-137.552 - 54.7002i) q^{52} +(367.123 + 64.7337i) q^{53} +(-129.731 + 179.592i) q^{54} +(-500.588 + 420.043i) q^{55} +(401.757 + 438.890i) q^{56} +(-296.018 - 591.624i) q^{57} +(-200.713 + 707.274i) q^{58} +(-321.396 - 383.025i) q^{59} +(-730.496 - 924.508i) q^{60} +(186.216 + 32.8349i) q^{61} +(-68.6697 + 671.024i) q^{62} +(-909.477 + 331.022i) q^{63} +(-419.106 - 294.098i) q^{64} +(170.591 + 295.472i) q^{65} +(-449.568 - 662.589i) q^{66} +(283.609 - 337.992i) q^{67} +(-8.83610 + 300.171i) q^{68} +(-869.582 - 502.053i) q^{69} +(-99.4098 - 1367.78i) q^{70} +(-143.305 - 812.723i) q^{71} +(702.625 - 447.119i) q^{72} +(-290.644 - 105.786i) q^{73} +(47.6600 + 106.262i) q^{74} +1717.24i q^{75} +(56.5345 + 660.136i) q^{76} -931.937i q^{77} +(-381.446 + 171.084i) q^{78} +(1274.42 + 463.852i) q^{79} +(337.680 + 1130.72i) q^{80} +(-63.9165 - 362.489i) q^{81} +(-1126.93 + 81.9051i) q^{82} +(-135.249 - 78.0860i) q^{83} +(1679.65 + 49.4438i) q^{84} +(444.899 - 530.210i) q^{85} +(-323.859 + 219.738i) q^{86} +(1038.16 + 1798.14i) q^{87} +(173.170 + 783.006i) q^{88} +(-591.251 + 215.198i) q^{89} +(-1909.54 - 195.414i) q^{90} +(-479.178 - 84.4921i) q^{91} +(623.461 + 789.045i) q^{92} +(1224.49 + 1459.28i) q^{93} +(735.263 + 208.656i) q^{94} +(841.042 - 1274.59i) q^{95} +(-1420.42 + 270.566i) q^{96} +(435.962 - 365.816i) q^{97} +(798.972 + 577.150i) q^{98} +(-1284.60 - 226.510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) $ 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−2.58074	+	1.15750i	−0.912428	+	0.409237i
$2$	−2.58074	+	1.15750i	−0.912428	+	0.409237i
$3$	−2.73201	+	7.50614i	−0.525776	+	1.44456i	0.338224	+	0.941065i	$0.390174\pi$
$3$	−2.73201	+	7.50614i	−0.525776	+	1.44456i	−0.864000	+	0.503492i	$0.832049\pi$
$4$	5.32040	−	5.97439i	0.665049	−	0.746799i
$5$	−18.1584	+	3.20182i	−1.62414	+	0.286380i	−0.910307	−	0.413935i	$-0.864154\pi$
$5$	−18.1584	+	3.20182i	−1.62414	+	0.286380i	−0.713834	+	0.700315i	$0.753043\pi$
$6$	−1.63774	−	22.5337i	−0.111434	−	1.53322i
$7$	13.1479	−	22.7729i	0.709921	−	1.22962i	−0.254965	−	0.966950i	$-0.582064\pi$
$7$	13.1479	−	22.7729i	0.709921	−	1.22962i	0.964886	−	0.262669i	$-0.0846027\pi$
$8$	−6.81519	+	21.5767i	−0.301192	+	0.953564i
$9$	−28.1950	−	23.6584i	−1.04426	−	0.876238i
$10$	43.1560	−	29.2814i	1.36471	−	0.925960i
$11$	30.6923	−	17.7202i	0.841281	−	0.485714i	−0.0164186	−	0.999865i	$-0.505226\pi$
$11$	30.6923	−	17.7202i	0.841281	−	0.485714i	0.857699	+	0.514152i	$0.171893\pi$
$12$	30.3093	+	56.2577i	0.729127	+	1.35335i
$13$	−6.32864	−	17.3878i	−0.135019	−	0.370962i	0.853696	−	0.520772i	$-0.174356\pi$
$13$	−6.32864	−	17.3878i	−0.135019	−	0.370962i	−0.988715	+	0.149810i	$0.952134\pi$
$14$	−7.57176	+	73.9895i	−0.144546	+	1.41247i
$15$	25.5757	−	145.047i	0.440242	−	2.49674i
$16$	−7.38678	−	63.5723i	−0.115418	−	0.993317i
$17$	−28.7555	+	24.1287i	−0.410249	+	0.344240i	−0.824439	−	0.565951i	$-0.808509\pi$
$17$	−28.7555	+	24.1287i	−0.410249	+	0.344240i	0.414190	+	0.910190i	$0.364065\pi$
$18$	100.149	+	28.4205i	1.31140	+	0.372154i
$19$	−56.9239	+	60.1554i	−0.687328	+	0.726347i
$19$	−56.9239	+	60.1554i	−0.687328	+	0.726347i
$20$	−77.4812	+	125.521i	−0.866266	+	1.40336i
$21$	135.016	+	160.906i	1.40300	+	1.67203i
$22$	−58.6977	+	81.2576i	−0.568836	+	0.787462i
$23$	−21.8283	+	123.794i	−0.197892	+	1.12230i	0.710348	+	0.703850i	$0.248537\pi$
$23$	−21.8283	+	123.794i	−0.197892	+	1.12230i	−0.908240	+	0.418449i	$0.862574\pi$
$24$	−143.338	−	110.103i	−1.21912	−	0.936449i
$25$	202.016	−	73.5278i	1.61613	−	0.588222i
$26$	36.4589	+	37.5479i	0.275007	+	0.283221i
$27$	67.8349	−	39.1645i	0.483512	−	0.279156i
$28$	−66.1020	−	199.712i	−0.446146	−	1.34793i
$29$	167.082	−	199.120i	1.06987	−	1.27502i	0.110199	−	0.993910i	$-0.464851\pi$
$29$	167.082	−	199.120i	1.06987	−	1.27502i	0.959674	−	0.281115i	$-0.0907043\pi$
$30$	101.888	+	403.932i	0.620069	+	2.45825i
$31$	119.241	−	206.531i	0.690848	−	1.19658i	−0.280712	−	0.959792i	$-0.590570\pi$
$31$	119.241	−	206.531i	0.690848	−	1.19658i	0.971560	−	0.236793i	$-0.0760962\pi$
$32$	92.6481	+	155.513i	0.511813	+	0.859097i
$33$	49.1587	+	278.793i	0.259316	+	1.47065i
$34$	46.2814	−	95.5543i	0.233447	−	0.481983i
$35$	−165.831	+	455.617i	−0.800874	+	2.20038i
$36$	−291.354	+	42.5760i	−1.34886	+	0.197111i
$37$		−	41.1750i		−	0.182950i	−0.995807	−	0.0914748i	$-0.970842\pi$
$37$		−	41.1750i		−	0.182950i	0.995807	−	0.0914748i	$-0.0291581\pi$
$38$	77.2757	−	221.134i	0.329889	−	0.944020i
$39$	147.805			0.606866
$40$	54.6685	−	413.620i	0.216096	−	1.63498i
$41$	375.389	+	136.631i	1.42990	+	0.520442i	0.936903	−	0.349589i	$-0.113679\pi$
$41$	375.389	+	136.631i	1.42990	+	0.520442i	0.492998	+	0.870030i	$0.335901\pi$
$42$	−534.689	−	258.975i	−1.96439	−	0.951444i
$43$	136.268	−	24.0276i	0.483270	−	0.0852135i	0.0732949	−	0.997310i	$-0.476649\pi$
$43$	136.268	−	24.0276i	0.483270	−	0.0852135i	0.409975	+	0.912097i	$0.365537\pi$
$44$	57.4277	−	277.647i	0.196763	−	0.951291i
$45$	587.728	+	339.325i	1.94696	+	1.12408i
$46$	−86.9587	−	344.747i	−0.278725	−	1.10500i
$47$	−207.000	−	173.694i	−0.642428	−	0.539061i	0.262335	−	0.964977i	$-0.415507\pi$
$47$	−207.000	−	173.694i	−0.642428	−	0.539061i	−0.904763	+	0.425916i	$0.859952\pi$
$48$	497.363	+	118.234i	1.49559	+	0.355534i
$49$	−174.236	−	301.785i	−0.507976	−	0.879840i
$50$	−436.241	+	423.589i	−1.23388	+	1.19809i
$51$	−102.553	−	281.763i	−0.281575	−	0.773621i
$52$	−137.552	−	54.7002i	−0.366829	−	0.145876i
$53$	367.123	+	64.7337i	0.951475	+	0.167771i	0.627780	−	0.778391i	$-0.283964\pi$
$53$	367.123	+	64.7337i	0.951475	+	0.167771i	0.323695	+	0.946161i	$0.395075\pi$
$54$	−129.731	+	179.592i	−0.326929	+	0.452581i
$55$	−500.588	+	420.043i	−1.22726	+	1.02979i
$56$	401.757	+	438.890i	0.958698	+	1.04731i
$57$	−296.018	−	591.624i	−0.687869	−	1.37478i
$58$	−200.713	+	707.274i	−0.454394	+	1.60120i
$59$	−321.396	−	383.025i	−0.709190	−	0.845180i	0.284343	−	0.958723i	$-0.408225\pi$
$59$	−321.396	−	383.025i	−0.709190	−	0.845180i	−0.993533	+	0.113543i	$0.963780\pi$
$60$	−730.496	−	924.508i	−1.57178	−	1.98922i
$61$	186.216	+	32.8349i	0.390861	+	0.0689194i	0.365625	−	0.930762i	$-0.380855\pi$
$61$	186.216	+	32.8349i	0.390861	+	0.0689194i	0.0252359	+	0.999682i	$0.491966\pi$
$62$	−68.6697	+	671.024i	−0.140662	+	1.37452i
$63$	−909.477	+	331.022i	−1.81878	+	0.661983i
$64$	−419.106	−	294.098i	−0.818567	−	0.574411i
$65$	170.591	+	295.472i	0.325526	+	0.563828i
$66$	−449.568	−	662.589i	−0.838454	−	1.23574i
$67$	283.609	−	337.992i	0.517139	−	0.616302i	−0.442763	−	0.896639i	$-0.646002\pi$
$67$	283.609	−	337.992i	0.517139	−	0.616302i	0.959902	+	0.280337i	$0.0904461\pi$
$68$	−8.83610	+	300.171i	−0.0157579	+	0.535310i
$69$	−869.582	−	502.053i	−1.51718	−	0.875944i
$70$	−99.4098	−	1367.78i	−0.169739	−	2.33544i
$71$	−143.305	−	812.723i	−0.239538	−	1.35849i	−0.832843	−	0.553509i	$-0.813289\pi$
$71$	−143.305	−	812.723i	−0.239538	−	1.35849i	0.593306	−	0.804977i	$-0.297822\pi$
$72$	702.625	−	447.119i	1.15007	−	0.731853i
$73$	−290.644	−	105.786i	−0.465990	−	0.169606i	0.0983450	−	0.995152i	$-0.468645\pi$
$73$	−290.644	−	105.786i	−0.465990	−	0.169606i	−0.564335	+	0.825546i	$0.690867\pi$
$74$	47.6600	+	106.262i	0.0748698	+	0.166928i
$75$			1717.24i			2.64386i
$76$	56.5345	+	660.136i	0.0853283	+	0.996353i
$77$		−	931.937i		−	1.37927i
$78$	−381.446	+	171.084i	−0.553721	+	0.248352i
$79$	1274.42	+	463.852i	1.81498	+	0.660600i	0.996259	+	0.0864155i	$0.0275412\pi$
$79$	1274.42	+	463.852i	1.81498	+	0.660600i	0.818726	+	0.574185i	$0.194681\pi$
$80$	337.680	+	1130.72i	0.471922	+	1.58023i
$81$	−63.9165	−	362.489i	−0.0876770	−	0.497241i
$82$	−1126.93	+	81.9051i	−1.51767	+	0.110304i
$83$	−135.249	−	78.0860i	−0.178861	−	0.103266i	0.407896	−	0.913028i	$-0.366263\pi$
$83$	−135.249	−	78.0860i	−0.178861	−	0.103266i	−0.586758	+	0.809763i	$0.699596\pi$
$84$	1679.65	+	49.4438i	2.18173	+	0.0642233i
$85$	444.899	−	530.210i	0.567719	−	0.676581i
$86$	−323.859	+	219.738i	−0.406076	+	0.275523i
$87$	1038.16	+	1798.14i	1.27933	+	2.21587i
$88$	173.170	+	783.006i	0.209772	+	0.948508i
$89$	−591.251	+	215.198i	−0.704185	+	0.256303i	−0.669197	−	0.743085i	$-0.733362\pi$
$89$	−591.251	+	215.198i	−0.704185	+	0.256303i	−0.0349885	+	0.999388i	$0.511139\pi$
$90$	−1909.54	−	195.414i	−2.23648	−	0.228872i
$91$	−479.178	−	84.4921i	−0.551995	−	0.0973316i
$92$	623.461	+	789.045i	0.706525	+	0.894170i
$93$	1224.49	+	1459.28i	1.36530	+	1.62711i
$94$	735.263	+	208.656i	0.806773	+	0.228949i
$95$	841.042	−	1274.59i	0.908306	−	1.37653i
$96$	−1420.42	+	270.566i	−1.51011	+	0.287651i
$97$	435.962	−	365.816i	0.456343	−	0.382917i	−0.385440	−	0.922733i	$-0.625950\pi$
$97$	435.962	−	365.816i	0.456343	−	0.382917i	0.841783	+	0.539816i	$0.181506\pi$
$98$	798.972	+	577.150i	0.823555	+	0.594908i
$99$	−1284.60	−	226.510i	−1.30412	−	0.229951i
$100$	635.521	−	1598.12i	0.635521	−	1.59812i
$101$	−327.006	−	898.442i	−0.322162	−	0.885132i	−0.990031	−	0.140853i	$-0.955016\pi$
$101$	−327.006	−	898.442i	−0.322162	−	0.885132i	0.667869	−	0.744279i	$-0.267207\pi$
$102$	590.803	+	608.450i	0.573511	+	0.590642i
$103$	286.346	+	495.966i	0.273927	+	0.474456i	0.969864	−	0.243647i	$-0.0783439\pi$
$103$	286.346	+	495.966i	0.273927	+	0.474456i	−0.695937	+	0.718103i	$0.745011\pi$
$104$	418.302	−	18.0500i	0.394403	−	0.0170187i
$105$	−2966.87	−	2489.50i	−2.75750	−	2.31382i
$106$	−1022.38	+	257.884i	−0.936811	+	0.236301i
$107$	−805.696	−	465.169i	−0.727940	−	0.420276i	0.0897281	−	0.995966i	$-0.471400\pi$
$107$	−805.696	−	465.169i	−0.727940	−	0.420276i	−0.817668	+	0.575690i	$0.804734\pi$
$108$	126.924	−	613.643i	0.113086	−	0.546739i
$109$	434.260	−	76.5718i	0.381602	−	0.0672867i	0.0204430	−	0.999791i	$-0.493492\pi$
$109$	434.260	−	76.5718i	0.381602	−	0.0672867i	0.361159	+	0.932504i	$0.382381\pi$
$110$	805.686	−	1663.45i	0.698356	−	1.44185i
$111$	309.065	+	112.491i	0.264281	+	0.0961904i
$112$	−1544.84	−	667.625i	−1.30334	−	0.563256i
$113$	2104.25			1.75178			0.875888	−	0.482514i	$-0.160276\pi$
$113$	2104.25			1.75178			0.875888	+	0.482514i	$0.160276\pi$
$114$	1448.75	+	1184.18i	1.19024	+	0.972886i
$115$		−	2317.80i		−	1.87944i
$116$	−300.682	−	2057.61i	−0.240669	−	1.64693i
$117$	−232.932	+	639.975i	−0.184056	+	0.505690i
$118$	1272.79	+	616.471i	0.992964	+	0.480939i
$119$	171.405	+	972.088i	0.132039	+	0.748833i
$120$	2955.33	+	1540.36i	2.24820	+	1.17179i
$121$	−37.4869	+	64.9293i	−0.0281645	+	0.0487823i
$122$	−518.581	+	130.807i	−0.384837	+	0.0970711i
$123$	−2051.14	+	2444.45i	−1.50362	+	1.79194i
$124$	−599.491	−	1811.22i	−0.434160	−	1.31171i
$125$	−1436.84	+	829.559i	−1.02812	+	0.593584i
$126$	1963.96	−	1907.00i	1.38860	−	1.34833i
$127$	733.935	−	267.131i	0.512805	−	0.186646i	−0.0726396	−	0.997358i	$-0.523142\pi$
$127$	733.935	−	267.131i	0.512805	−	0.186646i	0.585444	+	0.810713i	$0.300920\pi$
$128$	1422.02	+	273.875i	0.981954	+	0.189120i
$129$	−191.930	+	1088.49i	−0.130996	+	0.742914i
$130$	−782.259	−	565.077i	−0.527759	−	0.381235i
$131$	−243.404	−	290.078i	−0.162339	−	0.193468i	0.678743	−	0.734376i	$-0.262525\pi$
$131$	−243.404	−	290.078i	−0.162339	−	0.193468i	−0.841082	+	0.540908i	$0.818081\pi$
$132$	1927.16	+	1189.59i	1.27074	+	0.784401i
$133$	621.480	+	2087.24i	0.405182	+	1.36080i
$134$	−340.694	+	1200.54i	−0.219638	+	0.773964i
$135$	−1106.38	+	928.362i	−0.705347	+	0.591857i
$136$	−324.644	−	784.890i	−0.204691	−	0.494881i
$137$	6.57175	−	37.2703i	0.00409827	−	0.0232424i	−0.982690	−	0.185257i	$-0.940688\pi$
$137$	6.57175	−	37.2703i	0.00409827	−	0.0232424i	0.986788	+	0.162015i	$0.0517993\pi$
$138$	2825.29	+	289.128i	1.74279	+	0.178349i
$139$	−541.430	−	1487.57i	−0.330385	−	0.907725i	−0.988011	−	0.154381i	$-0.950662\pi$
$139$	−541.430	−	1487.57i	−0.330385	−	0.907725i	0.657626	−	0.753344i	$-0.271561\pi$
$140$	1839.75	+	3414.80i	1.11062	+	2.06145i
$141$	1869.30	−	1079.24i	1.11648	−	0.644598i
$142$	1310.56	+	1931.55i	0.774504	+	1.14149i
$143$	−502.356	−	421.527i	−0.293770	−	0.246503i
$144$	−1295.75	+	1967.18i	−0.749856	+	1.13842i
$145$	−2396.40	+	4150.68i	−1.37248	+	2.37721i
$146$	872.521	−	63.4147i	0.494592	−	0.0359468i
$147$	2741.25	−	483.357i	1.53806	−	0.271202i
$148$	−245.996	−	219.067i	−0.136627	−	0.121670i
$149$	−57.7230	+	158.593i	−0.0317373	+	0.0871974i	−0.954549	−	0.298053i	$-0.903663\pi$
$149$	−57.7230	+	158.593i	−0.0317373	+	0.0871974i	0.922812	+	0.385251i	$0.125885\pi$
$150$	−1987.70	−	4431.74i	−1.08197	−	2.41233i
$151$	−2783.64			−1.50020			−0.750099	−	0.661326i	$-0.769994\pi$
$151$	−2783.64			−1.50020			−0.750099	+	0.661326i	$0.769994\pi$
$152$	−910.007	−	1638.20i	−0.485601	−	0.874181i
$153$	1381.61			0.730043
$154$	1078.72	+	2405.08i	0.564450	+	1.25849i
$155$	−1503.95	+	4132.08i	−0.779357	+	2.14127i
$156$	786.382	−	883.046i	0.403596	−	0.453207i
$157$	1540.33	−	271.602i	0.783007	−	0.138065i	0.232167	−	0.972676i	$-0.425419\pi$
$157$	1540.33	−	271.602i	0.783007	−	0.138065i	0.550840	+	0.834611i	$0.314307\pi$
$158$	−3825.86	+	278.063i	−1.92639	+	0.140009i
$159$	−1488.88	+	2578.82i	−0.742617	+	1.28625i
$160$	−2180.27	−	2527.23i	−1.07729	−	1.24872i
$161$	2532.15	+	2124.73i	1.23951	+	1.04008i
$162$	584.532	+	861.504i	0.283489	+	0.417816i
$163$	1295.38	−	747.891i	0.622468	−	0.359382i	−0.155361	−	0.987858i	$-0.549654\pi$
$163$	1295.38	−	747.891i	0.622468	−	0.359382i	0.777829	+	0.628475i	$0.216321\pi$
$164$	2813.50	−	1515.80i	1.33962	−	0.721730i
$165$	−1785.29	−	4905.05i	−0.842332	−	2.31429i
$166$	439.426	+	44.9689i	0.205458	+	0.0210257i
$167$	89.1846	−	505.791i	0.0413252	−	0.234367i	−0.957148	−	0.289598i	$-0.906478\pi$
$167$	89.1846	−	505.791i	0.0413252	−	0.234367i	0.998474	+	0.0552309i	$0.0175895\pi$
$168$	−4391.97	+	1816.59i	−2.01695	+	0.834246i
$169$	1420.72	−	1192.12i	0.646662	−	0.542614i
$170$	−534.450	+	1883.30i	−0.241120	+	0.849663i
$171$	3028.15	−	349.353i	1.35420	−	0.156232i
$172$	581.447	−	941.952i	0.257761	−	0.417577i
$173$	−228.420	−	272.220i	−0.100384	−	0.119633i	0.713514	−	0.700641i	$-0.247103\pi$
$173$	−228.420	−	272.220i	−0.100384	−	0.119633i	−0.813897	+	0.581009i	$0.802658\pi$
$174$	−4760.55	−	3438.86i	−2.07412	−	1.49827i
$175$	981.651	−	5567.22i	0.424033	−	2.40481i
$176$	−1353.23	−	1820.29i	−0.579567	−	0.779598i
$177$	3753.10	−	1366.02i	1.59379	−	0.580090i
$178$	1276.77	−	1239.74i	0.537630	−	0.522037i
$179$	−2115.37	+	1221.31i	−0.883296	+	0.509971i	−0.871744	−	0.489962i	$-0.837011\pi$
$179$	−2115.37	+	1221.31i	−0.883296	+	0.509971i	−0.0115523	+	0.999933i	$0.503677\pi$
$180$	5154.21	−	1705.98i	2.13429	−	0.706422i
$181$	−1358.34	+	1618.81i	−0.557815	+	0.664778i	−0.969083	−	0.246736i	$-0.920642\pi$
$181$	−1358.34	+	1618.81i	−0.557815	+	0.664778i	0.411267	+	0.911515i	$0.365086\pi$
$182$	1334.43	−	336.596i	0.543487	−	0.137089i
$183$	−755.208	+	1308.06i	−0.305063	+	0.528385i
$184$	−2522.31	−	1314.66i	−1.01058	−	0.526729i
$185$	131.835	+	747.674i	0.0523931	+	0.297136i
$186$	−4849.19	−	2348.69i	−1.91161	−	0.925883i
$187$	−455.007	+	1250.12i	−0.177933	+	0.488866i
$188$	−2139.04	+	312.581i	−0.829816	+	0.121262i
$189$		−	2059.73i		−	0.792715i
$190$	−695.174	+	4262.88i	−0.265438	+	1.62769i
$191$	−1597.28			−0.605106			−0.302553	−	0.953133i	$-0.597839\pi$
$191$	−1597.28			−0.605106			−0.302553	+	0.953133i	$0.597839\pi$
$192$	3352.55	−	2342.39i	1.26015	−	0.880456i
$193$	−812.789	−	295.831i	−0.303139	−	0.110334i	0.185972	−	0.982555i	$-0.440457\pi$
$193$	−812.789	−	295.831i	−0.303139	−	0.110334i	−0.489111	+	0.872221i	$0.662679\pi$
$194$	−701.672	+	1448.70i	−0.259676	+	0.536137i
$195$	−2683.91	+	473.246i	−0.985635	+	0.173794i
$196$	−2729.99	−	564.663i	−0.994893	−	0.205781i
$197$	−817.644	−	472.067i	−0.295709	−	0.170728i	0.344804	−	0.938675i	$-0.387945\pi$
$197$	−817.644	−	472.067i	−0.295709	−	0.170728i	−0.640514	+	0.767947i	$0.721279\pi$
$198$	3577.41	−	902.364i	1.28402	−	0.323880i
$199$	−3063.04	−	2570.20i	−1.09112	−	0.915560i	−0.0943255	−	0.995541i	$-0.530069\pi$
$199$	−3063.04	−	2570.20i	−1.09112	−	0.915560i	−0.996796	+	0.0799815i	$0.974514\pi$
$200$	209.710	+	4859.94i	0.0741435	+	1.71825i
$201$	1762.19	+	3052.20i	0.618384	+	1.07107i
$202$	1883.86	+	1940.13i	0.656178	+	0.675778i
$203$	−2337.76	−	6422.95i	−0.808270	−	2.22070i
$204$	−2228.98	−	886.395i	−0.765001	−	0.304216i
$205$	−7253.95	−	1279.07i	−2.47141	−	0.435776i
$206$	−1313.06	−	948.512i	−0.444104	−	0.320806i
$207$	3544.23	−	2973.96i	1.19005	−	0.998573i
$208$	−1058.63	+	530.766i	−0.352899	+	0.176933i
$209$	−681.160	+	2855.01i	−0.225439	+	0.944906i
$210$	10538.3	+	2990.60i	3.46292	+	0.982718i
$211$	297.371	+	354.393i	0.0970229	+	0.115627i	0.812371	−	0.583141i	$-0.198176\pi$
$211$	297.371	+	354.393i	0.0970229	+	0.115627i	−0.715348	+	0.698768i	$0.753732\pi$
$212$	2339.98	−	1848.93i	0.758069	−	0.598985i
$213$	6491.92	+	1144.70i	2.08835	+	0.368233i
$214$	2617.72	+	267.886i	0.836186	+	0.0855716i
$215$	−2397.47	+	872.609i	−0.760495	+	0.276797i
$216$	382.732	+	1730.56i	0.120563	+	0.545139i
$217$	−3135.54	−	5430.92i	−0.980896	−	1.69896i
$218$	−1032.08	+	700.267i	−0.320648	+	0.217560i
$219$	1588.08	−	1892.60i	0.490012	−	0.583974i
$220$	−153.823	+	5225.51i	−0.0471396	+	1.60138i
$221$	601.528	+	347.293i	0.183091	+	0.105708i
$222$	−927.824	+	67.4341i	−0.280502	+	0.0203868i
$223$	−27.6585	−	156.859i	−0.00830559	−	0.0471034i	0.980373	−	0.197150i	$-0.0631687\pi$
$223$	−27.6585	−	156.859i	−0.00830559	−	0.0471034i	−0.988679	+	0.150047i	$0.952058\pi$
$224$	4759.61	−	65.1894i	1.41971	−	0.0194449i
$225$	−7435.40	−	2706.26i	−2.20308	−	0.801856i
$226$	−5430.50	+	2435.66i	−1.59837	+	0.716893i
$227$			2234.91i			0.653462i	0.945117	+	0.326731i	$0.105947\pi$
$227$			2234.91i			0.653462i	−0.945117	+	0.326731i	$0.894053\pi$
$228$	−5109.53	−	1379.14i	−1.48415	−	0.400597i
$229$		−	4083.02i		−	1.17822i	−0.808051	−	0.589112i	$-0.799478\pi$
$229$		−	4083.02i		−	1.17822i	0.808051	−	0.589112i	$-0.200522\pi$
$230$	2682.85	+	5981.64i	0.769139	+	1.71486i
$231$	6995.25	+	2546.06i	1.99244	+	0.725189i
$232$	3157.66	+	4962.11i	0.893581	+	1.40422i
$233$	363.304	+	2060.40i	0.102150	+	0.579319i	0.992321	+	0.123692i	$0.0394736\pi$
$233$	363.304	+	2060.40i	0.102150	+	0.579319i	−0.890171	+	0.455626i	$0.849415\pi$
$234$	−139.634	−	1921.22i	−0.0390093	−	0.536728i
$235$	4314.94	+	2491.23i	1.19777	+	0.691532i
$236$	−3998.30	−	117.697i	−1.10283	−	0.0324638i
$237$	−6963.48	+	8298.75i	−1.90855	+	2.27452i
$238$	−1567.54	−	2310.30i	−0.426927	−	0.629221i
$239$	−2173.99	−	3765.46i	−0.588384	−	1.01911i	−0.994444	−	0.105265i	$-0.966431\pi$
$239$	−2173.99	−	3765.46i	−0.588384	−	1.01911i	0.406060	−	0.913846i	$-0.366902\pi$
$240$	−9409.91	−	554.477i	−2.53086	−	0.149131i
$241$	3854.24	−	1402.83i	1.03018	−	0.374955i	0.229031	−	0.973419i	$-0.426444\pi$
$241$	3854.24	−	1402.83i	1.03018	−	0.374955i	0.801150	+	0.598464i	$0.204222\pi$
$242$	21.5884	−	210.956i	0.00573451	−	0.0560363i
$243$	4978.26	+	877.802i	1.31422	+	0.231733i
$244$	1186.91	−	937.834i	0.311411	−	0.246060i
$245$	4130.11	+	4922.08i	1.07699	+	1.28351i
$246$	2464.00	−	8682.66i	0.638612	−	2.25035i
$247$	1406.22	+	609.079i	0.362250	+	0.156902i
$248$	3643.61	+	3980.37i	0.932942	+	1.01917i
$249$	955.625	−	801.865i	0.243214	−	0.204081i
$250$	2747.89	−	3804.01i	0.695167	−	0.962347i
$251$	5590.62	+	985.777i	1.40588	+	0.247895i	0.824559	−	0.565777i	$-0.191424\pi$
$251$	5590.62	+	985.777i	1.40588	+	0.247895i	0.581325	+	0.813672i	$0.302535\pi$
$252$	−2861.12	+	7194.74i	−0.715212	+	1.79852i
$253$	1523.70	+	4186.34i	0.378634	+	1.04029i
$254$	−1584.89	+	1538.92i	−0.391515	+	0.380160i
$255$	2764.36	+	4788.01i	0.678867	+	1.17583i
$256$	−3986.87	+	939.188i	−0.973357	+	0.229294i
$257$	377.004	+	316.344i	0.0915054	+	0.0767821i	0.687393	−	0.726286i	$-0.258755\pi$
$257$	377.004	+	316.344i	0.0915054	+	0.0767821i	−0.595887	+	0.803068i	$0.703200\pi$
$258$	−764.602	−	3031.25i	−0.184504	−	0.731464i
$259$	−937.673	−	541.366i	−0.224958	−	0.129880i
$260$	2672.88	+	552.851i	0.637557	+	0.131871i
$261$	−9421.75	+	1661.31i	−2.23445	+	0.393994i
$262$	963.927	+	466.875i	0.227296	+	0.110090i
$263$	−1594.83	−	580.470i	−0.373922	−	0.136096i	0.148222	−	0.988954i	$-0.452645\pi$
$263$	−1594.83	−	580.470i	−0.373922	−	0.136096i	−0.522143	+	0.852858i	$0.674867\pi$
$264$	−6350.45	−	839.343i	−1.48047	−	0.195674i
$265$	−6873.65			−1.59338
$266$	−4019.85	−	4667.25i	−0.926590	−	1.07582i
$267$		−	5025.94i		−	1.15199i
$268$	−510.385	−	3492.64i	−0.116331	−	0.796070i
$269$	2552.83	−	7013.84i	0.578620	−	1.58975i	−0.211888	−	0.977294i	$-0.567961\pi$
$269$	2552.83	−	7013.84i	0.578620	−	1.58975i	0.790508	−	0.612452i	$-0.209817\pi$
$270$	1780.69	−	3676.49i	0.401369	−	0.828681i
$271$	−476.922	−	2704.76i	−0.106904	−	0.606282i	−0.990443	−	0.137924i	$-0.955957\pi$
$271$	−476.922	−	2704.76i	−0.106904	−	0.606282i	0.883539	−	0.468358i	$-0.155154\pi$
$272$	1746.33	+	1649.82i	0.389289	+	0.367776i
$273$	1943.33	−	3365.95i	0.430827	−	0.746214i
$274$	26.1803	+	103.792i	0.00577230	+	0.0228842i
$275$	4897.41	−	5836.51i	1.07391	−	1.27984i
$276$	−7625.98	+	2524.10i	−1.66315	+	0.550482i
$277$	2347.49	−	1355.32i	0.509194	−	0.293984i	−0.223308	−	0.974748i	$-0.571686\pi$
$277$	2347.49	−	1355.32i	0.509194	−	0.293984i	0.732502	+	0.680764i	$0.238352\pi$
$278$	3119.15	+	3212.31i	0.672928	+	0.693028i
$279$	−8248.21	+	3002.10i	−1.76992	+	0.644198i
$280$	−8700.54	−	6683.20i	−1.85699	−	1.42642i
$281$	35.4019	−	200.774i	0.00751566	−	0.0426234i	−0.980819	−	0.194919i	$-0.937556\pi$
$281$	35.4019	−	200.774i	0.00751566	−	0.0426234i	0.988335	+	0.152296i	$0.0486666\pi$
$282$	−3574.95	+	4948.94i	−0.754911	+	1.04505i
$283$	−1322.22	−	1575.76i	−0.277732	−	0.330988i	0.609089	−	0.793102i	$-0.291535\pi$
$283$	−1322.22	−	1575.76i	−0.277732	−	0.330988i	−0.886820	+	0.462115i	$0.847091\pi$
$284$	−5617.97	−	3467.85i	−1.17382	−	0.724574i
$285$	7269.50	+	9795.17i	1.51091	+	2.03584i
$286$	1784.37	+	506.373i	0.368922	+	0.104694i
$287$	8047.06	−	6752.29i	1.65506	−	1.38876i
$288$	1066.98	−	6576.61i	0.218307	−	1.34559i
$289$	−608.450	+	3450.69i	−0.123845	+	0.702360i
$290$	1380.06	−	13485.6i	0.279448	−	2.73070i
$291$	1554.81	+	4271.81i	0.313212	+	0.860542i
$292$	−2178.34	+	1173.60i	−0.436568	+	0.235204i
$293$	−2261.10	+	1305.45i	−0.450836	+	0.260290i	−0.708183	−	0.706029i	$-0.750485\pi$
$293$	−2261.10	+	1305.45i	−0.450836	+	0.260290i	0.257347	+	0.966319i	$0.417152\pi$
$294$	−6514.97	+	4420.41i	−1.29238	+	0.876884i
$295$	7062.43	+	5926.08i	1.39387	+	1.16959i
$296$	888.420	+	280.615i	0.174454	+	0.0551028i
$297$	1388.01	−	2404.10i	0.271180	−	0.469697i
$298$	−34.6029	−	476.100i	−0.00672648	−	0.0925494i
$299$	2290.65	−	403.904i	0.443050	−	0.0781216i
$300$	10259.5	+	9136.39i	1.97443	+	1.75830i
$301$	1244.46	−	3419.12i	0.238303	−	0.654733i
$302$	7183.85	−	3222.06i	1.36882	−	0.613937i
$303$	7637.21			1.44801
$304$	4244.70	+	3174.43i	0.800823	+	0.598901i
$305$	−3486.53			−0.654551
$306$	−3565.57	+	1599.21i	−0.666111	+	0.298761i
$307$	−3004.51	+	8254.82i	−0.558555	+	1.53462i	0.263180	+	0.964747i	$0.415229\pi$
$307$	−3004.51	+	8254.82i	−0.558555	+	1.53462i	−0.821735	+	0.569870i	$0.806994\pi$
$308$	−5567.76	−	4958.27i	−1.03004	−	0.917285i
$309$	−4505.09	+	794.369i	−0.829403	+	0.146246i
$310$	−901.566	−	12404.6i	−0.165179	−	2.27269i
$311$	−4943.82	+	8562.94i	−0.901409	+	1.56129i	−0.0757426	+	0.997127i	$0.524133\pi$
$311$	−4943.82	+	8562.94i	−0.901409	+	1.56129i	−0.825666	+	0.564159i	$0.809201\pi$
$312$	−1007.32	+	3189.14i	−0.182783	+	0.578685i
$313$	2640.59	+	2215.72i	0.476852	+	0.400127i	0.849287	−	0.527932i	$-0.177032\pi$
$313$	2640.59	+	2215.72i	0.476852	+	0.400127i	−0.372434	+	0.928059i	$0.621477\pi$
$314$	−3660.82	+	2483.87i	−0.657936	+	0.446410i
$315$	15454.8	−	8922.84i	2.76438	−	1.59602i
$316$	9551.67	−	5146.03i	1.70039	−	0.916097i
$317$	233.006	+	640.179i	0.0412837	+	0.113426i	0.958622	−	0.284684i	$-0.0918886\pi$
$317$	233.006	+	640.179i	0.0412837	+	0.113426i	−0.917338	+	0.398110i	$0.869666\pi$
$318$	857.433	−	8378.64i	0.151203	−	1.47752i
$319$	1599.67	−	9072.20i	0.280766	−	1.59231i
$320$	8551.97	+	3998.46i	1.49397	+	0.698502i
$321$	5692.79	−	4776.82i	0.989846	−	0.830580i
$322$	−8994.19	−	2552.40i	−1.55660	−	0.441739i
$323$	185.401	−	3103.30i	0.0319381	−	0.534589i
$324$	−2505.71	−	1546.72i	−0.429649	−	0.265213i
$325$	−2556.97	−	3047.28i	−0.436416	−	0.520101i
$326$	−2477.36	+	3429.51i	−0.420885	+	0.582648i
$327$	−611.645	+	3468.81i	−0.103438	+	0.586623i
$328$	−5506.38	+	7168.49i	−0.926949	+	1.20675i
$329$	−6677.13	+	2430.28i	−1.11891	+	0.407251i
$330$	10284.9	+	10592.2i	1.71566	+	1.76691i
$331$	7245.21	−	4183.02i	1.20312	−	0.694622i	0.241872	−	0.970308i	$-0.422238\pi$
$331$	7245.21	−	4183.02i	1.20312	−	0.694622i	0.961248	+	0.275686i	$0.0889051\pi$
$332$	−1186.09	+	392.582i	−0.196070	+	0.0648968i
$333$	−974.137	+	1160.93i	−0.160307	+	0.191047i
$334$	355.290	+	1408.54i	0.0582055	+	0.230755i
$335$	−4067.70	+	7045.47i	−0.663410	+	1.14906i
$336$	9231.82	−	9771.85i	1.49892	−	1.58660i
$337$	4.64942	+	26.3682i	0.000751543	+	0.00426221i	0.985181	−	0.171517i	$-0.0548667\pi$
$337$	4.64942	+	26.3682i	0.000751543	+	0.00426221i	−0.984430	+	0.175779i	$0.943756\pi$
$338$	−2286.61	+	4721.03i	−0.367974	+	0.759734i
$339$	−5748.82	+	15794.8i	−0.921042	+	2.53054i
$340$	−800.645	−	5478.93i	−0.127709	−	0.873932i
$341$		−	8451.91i		−	1.34222i
$342$	−7410.49	+	4406.67i	−1.17168	+	0.696741i
$343$	−143.876			−0.0226489
$344$	−410.252	+	3103.95i	−0.0643003	+	0.486494i
$345$	17397.7	+	6332.26i	2.71497	+	0.988167i
$346$	904.585	+	438.132i	0.140551	+	0.0680755i
$347$	−9439.63	+	1664.46i	−1.46036	+	0.257501i	−0.846701	−	0.532068i	$-0.821415\pi$
$347$	−9439.63	+	1664.46i	−1.46036	+	0.257501i	−0.613661	+	0.789570i	$0.710304\pi$
$348$	16266.2	+	3364.46i	2.50563	+	0.518258i
$349$	−6074.85	−	3507.32i	−0.931746	−	0.537944i	−0.0443829	−	0.999015i	$-0.514132\pi$
$349$	−6074.85	−	3507.32i	−0.931746	−	0.537944i	−0.887363	+	0.461071i	$0.847465\pi$
$350$	3910.66	+	15503.8i	0.597239	+	2.36775i
$351$	−1110.29	−	931.641i	−0.168840	−	0.141673i
$352$	5599.32	+	3131.31i	0.847854	+	0.474147i
$353$	−1993.44	−	3452.75i	−0.300568	−	0.520598i	0.675697	−	0.737179i	$-0.263843\pi$
$353$	−1993.44	−	3452.75i	−0.300568	−	0.520598i	−0.976265	+	0.216581i	$0.930509\pi$
$354$	−8104.59	+	7869.53i	−1.21682	+	1.18153i
$355$	5204.39	+	14299.0i	0.778086	+	2.13777i
$356$	−1860.01	+	4677.31i	−0.276912	+	0.696339i
$357$	−7764.91	−	1369.16i	−1.15116	−	0.202980i
$358$	4045.54	−	5600.41i	0.597245	−	0.826790i
$359$	3931.30	−	3298.75i	0.577956	−	0.484962i	−0.306319	−	0.951929i	$-0.599098\pi$
$359$	3931.30	−	3298.75i	0.577956	−	0.484962i	0.884275	+	0.466966i	$0.154653\pi$
$360$	−11327.0	+	10368.7i	−1.65829	+	1.51799i
$361$	−378.343	−	6848.56i	−0.0551601	−	0.998478i
$362$	1631.75	−	5749.99i	0.236914	−	0.834841i
$363$	−384.953	−	458.770i	−0.0556606	−	0.0663338i
$364$	−3054.21	+	2413.27i	−0.439791	+	0.347499i
$365$	5616.34	+	990.313i	0.805405	+	0.142015i
$366$	434.917	−	4249.91i	0.0621133	−	0.606957i
$367$	253.145	−	92.1372i	0.0360056	−	0.0131050i	−0.323955	−	0.946073i	$-0.605012\pi$
$367$	253.145	−	92.1372i	0.0360056	−	0.0131050i	0.359960	+	0.932968i	$0.382790\pi$
$368$	8031.13	+	473.233i	1.13764	+	0.0670352i
$369$	−7351.65	−	12733.4i	−1.03716	−	1.79641i
$370$	−1205.66	−	1776.95i	−0.169404	−	0.249674i
$371$	6301.07	−	7509.33i	0.881767	−	1.05085i
$372$	15233.1	+	448.415i	2.12312	+	0.0624979i
$373$	−1947.46	−	1124.36i	−0.270336	−	0.156079i	0.358704	−	0.933451i	$-0.383219\pi$
$373$	−1947.46	−	1124.36i	−0.270336	−	0.156079i	−0.629041	+	0.777373i	$0.716552\pi$
$374$	−272.760	−	3752.90i	−0.0377115	−	0.518871i
$375$	−2301.33	−	13051.5i	−0.316907	−	1.79727i
$376$	5158.48	−	3282.62i	0.707523	−	0.450235i
$377$	−4519.66	−	1645.02i	−0.617439	−	0.224729i
$378$	2384.13	+	5315.61i	0.324408	+	0.723295i
$379$			8552.38i			1.15912i	0.814930	+	0.579560i	$0.196776\pi$
$379$			8552.38i			1.15912i	−0.814930	+	0.579560i	$0.803224\pi$
$380$	−3140.22	−	11806.0i	−0.423921	−	1.59378i
$381$			6238.82i			0.838910i
$382$	4122.16	−	1848.85i	0.552115	−	0.247632i
$383$	−11309.7	−	4116.39i	−1.50887	−	0.549185i	−0.550532	−	0.834814i	$-0.685575\pi$
$383$	−11309.7	−	4116.39i	−1.50887	−	0.549185i	−0.958340	+	0.285629i	$0.907797\pi$
$384$	−5940.72	+	9925.66i	−0.789482	+	1.31905i
$385$	2983.90	+	16922.5i	0.394996	+	2.24013i
$386$	2440.02	−	177.340i	0.321745	−	0.0233844i
$387$	−4410.52	−	2546.42i	−0.579327	−	0.334475i
$388$	133.964	−	4550.89i	0.0175283	−	0.595455i
$389$	−725.841	+	865.024i	−0.0946057	+	0.112747i	−0.811270	−	0.584671i	$-0.801223\pi$
$389$	−725.841	+	865.024i	−0.0946057	+	0.112747i	0.716665	+	0.697418i	$0.245668\pi$
$390$	6378.68	−	4327.94i	0.828198	−	0.561933i
$391$	−2359.32	−	4086.45i	−0.305155	−	0.528544i
$392$	7698.97	−	1702.71i	0.991981	−	0.219387i
$393$	2842.35	−	1034.53i	0.364828	−	0.132787i
$394$	2656.54	+	271.859i	0.339682	+	0.0347616i
$395$	−24626.7	−	4342.35i	−3.13697	−	0.553133i
$396$	−8187.87	+	6469.61i	−1.03903	+	0.820985i
$397$	6306.71	+	7516.04i	0.797291	+	0.950174i	0.999575	−	0.0291525i	$-0.00928086\pi$
$397$	6306.71	+	7516.04i	0.797291	+	0.950174i	−0.202284	+	0.979327i	$0.564836\pi$
$398$	10879.9	+	3087.53i	1.37025	+	0.388855i
$399$	−17365.0	−	1037.44i	−2.17879	−	0.130168i
$400$	−6166.58	−	12299.5i	−0.770822	−	1.53744i
$401$	−1157.09	+	970.917i	−0.144096	+	0.120911i	−0.711986	−	0.702193i	$-0.752204\pi$
$401$	−1157.09	+	970.917i	−0.144096	+	0.120911i	0.567890	+	0.823104i	$0.307760\pi$
$402$	−8080.66	−	5837.20i	−1.00255	−	0.724211i
$403$	−4345.76	−	766.274i	−0.537165	−	0.0947167i
$404$	−7107.45	−	2826.40i	−0.875269	−	0.348066i
$405$	2321.25	+	6377.58i	0.284800	+	0.782480i
$406$	13467.7	+	13870.0i	1.64628	+	1.69546i
$407$	−729.631	−	1263.76i	−0.0888611	−	0.153912i
$408$	6778.42	−	292.493i	0.822505	−	0.0354916i
$409$	11269.5	+	9456.20i	1.36244	+	1.14322i	0.975220	+	0.221239i	$0.0710100\pi$
$409$	11269.5	+	9456.20i	1.36244	+	1.14322i	0.387223	+	0.921986i	$0.373434\pi$
$410$	20201.1	−	5095.50i	2.43332	−	0.613778i
$411$	261.802	+	151.151i	0.0314203	+	0.0181405i
$412$	4486.57	+	927.991i	0.536499	+	0.110968i
$413$	−12948.3	+	2283.13i	−1.54272	+	0.272023i
$414$	−5704.36	+	11777.4i	−0.677184	+	1.39814i
$415$	2705.93	+	984.877i	0.320069	+	0.116496i
$416$	2117.69	−	2595.13i	0.249588	−	0.305858i
$417$	12645.1			1.48497
$418$	−1546.78	−	8156.48i	−0.180994	−	0.954417i
$419$		−	9827.82i		−	1.14587i	−0.819600	−	0.572936i	$-0.805804\pi$
$419$		−	9827.82i		−	1.14587i	0.819600	−	0.572936i	$-0.194196\pi$
$420$	−30658.2	+	4480.13i	−3.56183	+	0.520496i
$421$	−848.590	+	2331.48i	−0.0982369	+	0.269904i	−0.979070	−	0.203523i	$-0.934761\pi$
$421$	−848.590	+	2331.48i	−0.0982369	+	0.269904i	0.880833	+	0.473427i	$0.156983\pi$
$422$	−1177.64	−	570.388i	−0.135845	−	0.0657963i
$423$	1727.05	+	9794.61i	0.198516	+	1.12584i
$424$	−3898.75	+	7480.12i	−0.446556	+	0.856761i
$425$	−4034.94	+	6988.71i	−0.460525	+	0.797653i
$426$	−18078.9	+	4560.22i	−2.05617	+	0.518646i
$427$	3196.10	−	3808.96i	0.362225	−	0.431683i
$428$	−7065.72	+	2338.66i	−0.797978	+	0.264120i
$429$	4536.48	−	2619.14i	0.510544	−	0.294763i
$430$	5177.20	−	5027.05i	0.580621	−	0.563781i
$431$	10657.1	−	3878.87i	1.19103	−	0.433500i	0.330946	−	0.943650i	$-0.392632\pi$
$431$	10657.1	−	3878.87i	1.19103	−	0.433500i	0.860086	+	0.510149i	$0.170410\pi$
$432$	−2990.86	−	4023.12i	−0.333096	−	0.448061i
$433$	−2007.58	+	11385.5i	−0.222813	+	1.26364i	0.644009	+	0.765018i	$0.277270\pi$
$433$	−2007.58	+	11385.5i	−0.222813	+	1.26364i	−0.866822	+	0.498618i	$0.833841\pi$
$434$	14378.3	+	10386.4i	1.59028	+	1.14876i
$435$	−24608.6	−	29327.4i	−2.71240	−	3.23251i
$436$	1852.97	−	3001.84i	0.203534	−	0.329729i
$437$	−6204.34	−	8359.94i	−0.679163	−	0.915126i
$438$	−1907.74	+	6722.51i	−0.208117	+	0.733366i
$439$	−4929.39	+	4136.25i	−0.535915	+	0.449686i	−0.870138	−	0.492808i	$-0.835971\pi$
$439$	−4929.39	+	4136.25i	−0.535915	+	0.449686i	0.334223	+	0.942494i	$0.391526\pi$
$440$	−5651.54	−	13663.7i	−0.612333	−	1.48044i
$441$	−2227.18	+	12631.0i	−0.240491	+	1.36389i
$442$	−1954.38	−	200.002i	−0.210317	−	0.0215230i
$443$	−2505.99	−	6885.14i	−0.268765	−	0.738427i	−0.998503	−	0.0546993i	$-0.982580\pi$
$443$	−2505.99	−	6885.14i	−0.268765	−	0.738427i	0.729738	−	0.683727i	$-0.239642\pi$
$444$	2316.41	−	1247.98i	0.247595	−	0.133393i
$445$	10047.2	−	5800.74i	1.07030	−	0.617936i
$446$	252.943	+	372.797i	0.0268547	+	0.0395795i
$447$	−1032.72	−	866.554i	−0.109275	−	0.0916926i
$448$	−12207.8	+	5677.48i	−1.28742	+	0.598740i
$449$	3746.63	−	6489.36i	0.393796	−	0.682075i	−0.599150	−	0.800637i	$-0.704495\pi$
$449$	3746.63	−	6489.36i	0.393796	−	0.682075i	0.992947	+	0.118561i	$0.0378282\pi$
$450$	22321.3	−	1622.31i	2.33830	−	0.169947i
$451$	13942.7	−	2458.47i	1.45573	−	0.256685i
$452$	11195.4	−	12571.6i	1.16502	−	1.30823i
$453$	7604.95	−	20894.4i	0.788767	−	2.16712i
$454$	−2586.90	−	5767.70i	−0.267421	−	0.596237i
$455$	8971.66			0.924391
$456$	14782.7	−	2355.06i	1.51812	−	0.241855i
$457$	−15686.6			−1.60566			−0.802832	−	0.596205i	$-0.796674\pi$
$457$	−15686.6			−1.60566			−0.802832	+	0.596205i	$0.796674\pi$
$458$	4726.09	+	10537.2i	0.482174	+	1.07504i
$459$	−1005.64	+	2762.96i	−0.102264	+	0.280967i
$460$	−13847.5	−	12331.6i	−1.40357	−	1.24992i
$461$	16588.3	−	2924.96i	1.67591	−	0.295508i	0.746725	−	0.665132i	$-0.231625\pi$
$461$	16588.3	−	2924.96i	1.67591	−	0.295508i	0.929181	+	0.369625i	$0.120514\pi$
$462$	−20999.9	+	1526.27i	−2.11473	+	0.153698i
$463$	−2587.84	+	4482.27i	−0.259756	+	0.449911i	−0.966176	−	0.257882i	$-0.916976\pi$
$463$	−2587.84	+	4482.27i	−0.259756	+	0.449911i	0.706420	+	0.707793i	$0.250309\pi$
$464$	−13892.7	−	9150.91i	−1.38999	−	0.915562i
$465$	−26907.1	−	22577.8i	−2.68342	−	2.25165i
$466$	−3322.50	−	4896.82i	−0.330283	−	0.486783i
$467$	10958.1	−	6326.63i	1.08582	−	0.626899i	0.153360	−	0.988170i	$-0.450991\pi$
$467$	10958.1	−	6326.63i	1.08582	−	0.626899i	0.932461	+	0.361272i	$0.117657\pi$
$468$	2584.17	+	4796.55i	0.255242	+	0.473762i
$469$	−3968.17	−	10902.5i	−0.390689	−	1.07341i
$470$	−14019.3	−	1434.68i	−1.37588	−	0.140801i
$471$	−2169.52	+	12304.0i	−0.212243	+	1.20369i
$472$	10454.8	−	4324.28i	1.01953	−	0.421697i
$473$	3756.59	−	3152.16i	0.365176	−	0.306419i
$474$	8365.11	−	29477.1i	0.810595	−	2.85639i
$475$	−7076.44	+	16337.8i	−0.683556	+	1.57817i
$476$	6719.58	+	4147.85i	0.647041	+	0.399404i
$477$	−8819.54	−	10510.7i	−0.846581	−	1.00892i
$478$	9969.01	+	7201.27i	0.953916	+	0.689076i
$479$	−829.846	+	4706.29i	−0.0791579	+	0.448927i	0.919307	+	0.393541i	$0.128750\pi$
$479$	−829.846	+	4706.29i	−0.0791579	+	0.448927i	−0.998465	+	0.0553858i	$0.982361\pi$
$480$	24926.3	−	9460.99i	2.37026	−	0.899652i
$481$	−715.943	+	260.582i	−0.0678673	+	0.0247017i
$482$	−8323.01	+	8081.61i	−0.786520	+	0.763708i
$483$	−22866.4	+	13201.9i	−2.15415	+	1.24370i
$484$	188.468	+	569.411i	0.0176998	+	0.0534759i
$485$	−6745.12	+	8038.52i	−0.631505	+	0.752599i
$486$	−13863.6	+	3496.95i	−1.29397	+	0.326389i
$487$	328.495	−	568.970i	0.0305658	−	0.0529415i	−0.850338	−	0.526237i	$-0.823602\pi$
$487$	328.495	−	568.970i	0.0305658	−	0.0529415i	0.880904	+	0.473296i	$0.156936\pi$
$488$	−1977.57	+	3794.15i	−0.183443	+	0.351953i
$489$	2074.77	+	11766.6i	0.191869	+	1.08815i
$490$	−16356.0	−	7921.98i	−1.50794	−	0.730365i
$491$	−6077.70	+	16698.4i	−0.558621	+	1.53480i	0.263019	+	0.964791i	$0.415282\pi$
$491$	−6077.70	+	16698.4i	−0.558621	+	1.53480i	−0.821639	+	0.570008i	$0.806940\pi$
$492$	3691.24	+	25259.7i	0.338240	+	2.31463i
$493$			9757.27i			0.891370i
$494$	−4334.09	+	55.8257i	−0.394737	+	0.00508444i
$495$	24051.7			2.18392
$496$	−14010.5	−	6054.82i	−1.26832	−	0.548124i
$497$	−20392.2	−	7422.15i	−1.84047	−	0.669877i
$498$	−1538.06	+	3175.54i	−0.138398	+	0.285741i
$499$	9397.86	−	1657.10i	0.843099	−	0.148661i	0.264614	−	0.964354i	$-0.414755\pi$
$499$	9397.86	−	1657.10i	0.843099	−	0.148661i	0.578485	+	0.815693i	$0.303644\pi$
$500$	−2688.44	+	12997.8i	−0.240461	+	1.16256i
$501$	3552.89	+	2051.26i	0.316829	+	0.182921i
$502$	−15568.9	+	3927.10i	−1.38421	+	0.349154i
$503$	−16798.4	−	14095.5i	−1.48907	−	1.24948i	−0.895784	−	0.444489i	$-0.853385\pi$
$503$	−16798.4	−	14095.5i	−1.48907	−	1.24948i	−0.593288	−	0.804991i	$-0.702170\pi$
$504$	−944.113	−	21879.5i	−0.0834408	−	1.93371i
$505$	8814.58	+	15267.3i	0.776720	+	1.34532i
$506$	−8777.95	−	9040.15i	−0.771201	−	0.794237i
$507$	5066.82	+	13921.0i	0.443837	+	1.21943i
$508$	2308.88	−	5806.06i	0.201654	−	0.507091i
$509$	8000.16	+	1410.64i	0.696661	+	0.122840i	0.510754	−	0.859727i	$-0.329366\pi$
$509$	8000.16	+	1410.64i	0.696661	+	0.122840i	0.185908	+	0.982567i	$0.440477\pi$
$510$	−12676.2	−	9156.86i	−1.10061	−	0.795044i
$511$	−6230.40	+	5227.93i	−0.539367	+	0.452583i
$512$	9201.95	−	7038.59i	0.794283	−	0.607548i
$513$	−1505.47	+	6310.03i	−0.129567	+	0.543069i
$514$	−1339.12	−	380.019i	−0.114914	−	0.0326107i
$515$	−6787.60	−	8089.14i	−0.580771	−	0.692136i
$516$	5481.91	+	6937.84i	0.467689	+	0.591902i
$517$	−9431.22	−	1662.98i	−0.802291	−	0.141466i
$518$	3046.52	+	311.767i	0.258410	+	0.0264445i
$519$	2667.36	−	970.841i	0.225596	−	0.0821102i
$520$	−7537.92	+	1667.09i	−0.635691	+	0.140590i
$521$	10566.3	+	18301.3i	0.888517	+	1.53896i	0.841629	+	0.540056i	$0.181597\pi$
$521$	10566.3	+	18301.3i	0.888517	+	1.53896i	0.0468876	+	0.998900i	$0.485070\pi$
$522$	22392.1	−	15193.1i	1.87754	−	1.27391i
$523$	−1427.73	+	1701.50i	−0.119370	+	0.142259i	−0.822420	−	0.568881i	$-0.807376\pi$
$523$	−1427.73	+	1701.50i	−0.119370	+	0.142259i	0.703050	+	0.711140i	$0.251821\pi$
$524$	−3028.05	−	89.1363i	−0.252445	−	0.00743118i
$525$	39106.4	+	22578.1i	3.25094	+	1.87693i
$526$	4787.73	−	347.971i	0.396872	−	0.0288446i
$527$	1554.51	+	8816.04i	0.128492	+	0.728715i
$528$	17360.4	−	5184.51i	1.43090	−	0.427324i
$529$	−3415.31	−	1243.07i	−0.280703	−	0.102167i
$530$	17739.1	−	7956.23i	1.45384	−	0.652069i
$531$			18403.1i			1.50401i
$532$	15776.5	+	7391.97i	1.28571	+	0.602411i
$533$		−	7391.88i		−	0.600709i
$534$	5817.51	+	12970.6i	0.471439	+	1.05111i
$535$	16119.6	+	5867.05i	1.30264	+	0.474121i
$536$	5359.89	+	8422.81i	0.431925	+	0.678750i
$537$	−3388.10	−	19214.9i	−0.272267	−	1.54410i
$538$	1530.33	+	21055.8i	0.122634	+	1.68732i
$539$	−10695.4	−	6174.99i	−0.854701	−	0.493462i
$540$	−339.972	+	11549.2i	−0.0270927	+	0.920367i
$541$	6719.85	−	8008.40i	0.534027	−	0.636429i	−0.429810	−	0.902919i	$-0.641420\pi$
$541$	6719.85	−	8008.40i	0.534027	−	0.636429i	0.963838	+	0.266490i	$0.0858640\pi$
$542$	4361.56	+	6428.23i	0.345655	+	0.509440i
$543$	−8439.98	−	14618.5i	−0.667024	−	1.15532i
$544$	−6416.48	−	2236.37i	−0.505706	−	0.176257i
$545$	−7640.32	+	2780.85i	−0.600506	+	0.218566i
$546$	−1119.14	+	10936.0i	−0.0877197	+	0.857177i
$547$	16848.4	+	2970.82i	1.31697	+	0.232218i	0.787608	−	0.616177i	$-0.211319\pi$
$547$	16848.4	+	2970.82i	1.31697	+	0.232218i	0.529364	+	0.848395i	$0.322430\pi$
$548$	−187.703	−	237.555i	−0.0146319	−	0.0185180i
$549$	−4473.55	−	5331.36i	−0.347771	−	0.414457i
$550$	−5883.18	+	20731.2i	−0.456108	+	1.60724i
$551$	2467.22	+	21385.6i	0.190757	+	1.65346i
$552$	16759.0	−	15341.1i	1.29223	−	1.18290i
$553$	27319.3	−	22923.6i	2.10078	−	1.76277i
$554$	−4489.46	+	6214.94i	−0.344294	+	0.476620i
$555$	−5972.32	−	1053.08i	−0.456777	−	0.0805420i
$556$	−11767.9	−	4679.73i	−0.897611	−	0.356951i
$557$	6640.51	+	18244.7i	0.505148	+	1.38788i	0.886188	+	0.463325i	$0.153344\pi$
$557$	6640.51	+	18244.7i	0.505148	+	1.38788i	−0.381040	+	0.924559i	$0.624434\pi$
$558$	17811.5	−	17294.9i	1.35129	−	1.31210i
$559$	−1280.18	−	2217.33i	−0.0968616	−	0.167769i
$560$	30189.6	+	7176.72i	2.27811	+	0.541557i
$561$	−8140.50	−	6830.69i	−0.612642	−	0.514067i
$562$	141.033	+	559.123i	0.0105856	+	0.0419665i
$563$	12872.7	+	7432.07i	0.963624	+	0.556349i	0.897287	−	0.441448i	$-0.145535\pi$
$563$	12872.7	+	7432.07i	0.963624	+	0.556349i	0.0663377	+	0.997797i	$0.478869\pi$
$564$	3497.60	−	16909.9i	0.261127	−	1.26247i
$565$	−38209.8	+	6737.42i	−2.84513	+	0.501674i
$566$	5236.25	+	2536.16i	0.388863	+	0.188344i
$567$	−9095.28	−	3310.41i	−0.673661	−	0.245192i
$568$	18512.5	+	2446.81i	1.36755	+	0.180750i
$569$	1402.74			0.103350			0.0516750	−	0.998664i	$-0.483544\pi$
$569$	1402.74			0.103350			0.0516750	+	0.998664i	$0.483544\pi$
$570$	−30098.6	−	16864.3i	−2.21174	−	1.23924i
$571$		−	14451.9i		−	1.05918i	−0.848253	−	0.529591i	$-0.822345\pi$
$571$		−	14451.9i		−	1.05918i	0.848253	−	0.529591i	$-0.177655\pi$
$572$	−5191.10	+	758.584i	−0.379460	+	0.0554511i
$573$	4363.79	−	11989.4i	0.318150	−	0.874109i
$574$	−12951.6	+	26740.3i	−0.941792	+	1.94446i
$575$	4692.66	+	26613.4i	0.340343	+	1.93018i
$576$	4858.81	+	18207.5i	0.351477	+	1.31709i
$577$	10598.0	−	18356.3i	0.764645	−	1.32440i	−0.175788	−	0.984428i	$-0.556247\pi$
$577$	10598.0	−	18356.3i	0.764645	−	1.32440i	0.940434	−	0.339977i	$-0.110419\pi$
$578$	−2423.92	−	9609.61i	−0.174432	−	0.691535i
$579$	4441.10	−	5292.69i	0.318766	−	0.379891i
$580$	12048.0	+	36400.3i	0.862530	+	2.60593i
$581$	−3556.48	+	2053.34i	−0.253955	+	0.146621i
$582$	−8957.16	−	9224.71i	−0.637949	−	0.657004i
$583$	12415.0	−	4518.67i	0.881946	−	0.321002i
$584$	4263.29	−	5550.18i	0.302083	−	0.393267i
$585$	2180.59	−	12366.8i	0.154114	−	0.874021i
$586$	4324.25	−	5986.24i	0.304835	−	0.421995i
$587$	8869.93	+	10570.8i	0.623682	+	0.743275i	0.981699	−	0.190440i	$-0.0609915\pi$
$587$	8869.93	+	10570.8i	0.623682	+	0.743275i	−0.358017	+	0.933715i	$0.616547\pi$
$588$	11696.8	−	18949.0i	0.820353	−	1.32898i
$589$	5636.32	+	18929.6i	0.394296	+	1.32424i
$590$	−25085.7	−	7118.91i	−1.75044	−	0.496747i
$591$	5777.21	−	4847.66i	0.402103	−	0.337404i
$592$	−2617.59	+	304.151i	−0.181727	+	0.0211157i
$593$	4199.71	−	23817.8i	0.290829	−	1.64937i	−0.392860	−	0.919598i	$-0.628514\pi$
$593$	4199.71	−	23817.8i	0.290829	−	1.64937i	0.683689	−	0.729774i	$-0.260375\pi$
$594$	−799.340	+	7810.96i	−0.0552143	+	0.539541i
$595$	−6224.91	−	17102.8i	−0.428901	−	1.17840i
$596$	640.386	+	1188.64i	0.0440121	+	0.0816920i
$597$	27660.5	−	15969.8i	1.89626	−	1.09481i
$598$	−5444.05	+	3693.80i	−0.372281	+	0.252593i
$599$	−5793.45	−	4861.28i	−0.395182	−	0.331597i	0.423446	−	0.905921i	$-0.360820\pi$
$599$	−5793.45	−	4861.28i	−0.395182	−	0.331597i	−0.818628	+	0.574324i	$0.805265\pi$
$600$	−37052.3	−	11703.3i	−2.52109	−	0.796309i
$601$	−3144.46	+	5446.37i	−0.213420	+	0.369654i	−0.952783	−	0.303653i	$-0.901794\pi$
$601$	−3144.46	+	5446.37i	−0.213420	+	0.369654i	0.739363	+	0.673307i	$0.235127\pi$
$602$	746.007	+	10264.3i	0.0505066	+	0.694919i
$603$	−15992.7	+	2819.95i	−1.08006	+	0.190443i
$604$	−14810.1	+	16630.6i	−0.997705	+	1.12035i
$605$	472.812	−	1299.04i	0.0317728	−	0.0872951i
$606$	−19709.6	+	8840.06i	−1.32120	+	0.592579i
$607$	−16974.8			−1.13507			−0.567533	−	0.823351i	$-0.692102\pi$
$607$	−16974.8			−1.13507			−0.567533	+	0.823351i	$0.692102\pi$
$608$	−14628.8	−	3279.13i	−0.975786	−	0.218727i
$609$	54598.3			3.63290
$610$	8997.81	−	4035.65i	0.597230	−	0.267867i
$611$	−1710.12	+	4698.52i	−0.113231	+	0.311100i
$612$	7350.71	−	8254.28i	0.485515	−	0.545195i
$613$	2142.41	−	377.765i	0.141160	−	0.0248903i	−0.102622	−	0.994720i	$-0.532723\pi$
$613$	2142.41	−	377.765i	0.141160	−	0.0248903i	0.243782	+	0.969830i	$0.421612\pi$
$614$	−1801.10	−	24781.2i	−0.118382	−	1.62881i
$615$	29418.7	−	50954.8i	1.92891	−	3.34097i
$616$	20108.1	+	6351.32i	1.31523	+	0.415425i
$617$	−19343.7	−	16231.3i	−1.26215	−	1.05907i	−0.995449	−	0.0952929i	$-0.969621\pi$
$617$	−19343.7	−	16231.3i	−1.26215	−	1.05907i	−0.266703	−	0.963779i	$-0.585934\pi$
$618$	10707.0	−	7264.69i	0.696921	−	0.472862i
$619$	−3028.79	+	1748.67i	−0.196668	+	0.113546i	−0.595100	−	0.803652i	$-0.702888\pi$
$619$	−3028.79	+	1748.67i	−0.196668	+	0.113546i	0.398433	+	0.917198i	$0.369554\pi$
$620$	16685.0	+	30969.5i	1.08079	+	2.00607i
$621$	3367.62	+	9252.46i	0.217613	+	0.597888i
$622$	2847.10	−	27821.2i	0.183534	−	1.79345i
$623$	−2873.05	+	16293.9i	−0.184761	+	1.04783i
$624$	−1091.80	−	9396.31i	−0.0700434	−	0.602810i
$625$	2849.04	−	2390.63i	0.182339	−	0.153000i
$626$	−9379.34	−	2661.70i	−0.598840	−	0.169941i
$627$	−19569.2	−	12912.8i	−1.24644	−	0.822469i
$628$	6572.53	−	10647.6i	0.417631	−	0.676569i
$629$	993.501	+	1184.01i	0.0629785	+	0.0750548i
$630$	−29556.6	+	40916.4i	−1.86915	+	2.58754i
$631$	2332.79	−	13229.9i	0.147174	−	0.834666i	−0.818421	−	0.574618i	$-0.805151\pi$
$631$	2332.79	−	13229.9i	0.147174	−	0.834666i	0.965596	−	0.260048i	$-0.0837384\pi$
$632$	−18693.8	+	24336.6i	−1.17658	+	1.53174i
$633$	−3472.54	+	1263.90i	−0.218043	+	0.0793611i
$634$	−1342.33	−	1382.43i	−0.0840866	−	0.0865982i
$635$	−12471.8	+	7200.61i	−0.779416	+	0.449996i
$636$	7485.45	+	22615.5i	0.466694	+	1.41001i
$637$	−4144.70	+	4939.46i	−0.257801	+	0.307235i
$638$	6372.72	+	25264.6i	0.395452	+	1.56776i
$639$	−15187.3	+	26305.1i	−0.940218	+	1.62850i
$640$	−26698.6	−	420.080i	−1.64899	−	0.0259455i
$641$	5147.06	+	29190.4i	0.317155	+	1.79868i	0.559871	+	0.828580i	$0.310851\pi$
$641$	5147.06	+	29190.4i	0.317155	+	1.79868i	−0.242715	+	0.970098i	$0.578038\pi$
$642$	−9162.43	+	18917.1i	−0.563259	+	1.16293i
$643$	−8673.53	+	23830.3i	−0.531960	+	1.46155i	0.324774	+	0.945792i	$0.394712\pi$
$643$	−8673.53	+	23830.3i	−0.531960	+	1.46155i	−0.856735	+	0.515757i	$0.827511\pi$
$644$	26166.0	−	3823.69i	1.60107	−	0.233966i
$645$		−	20379.8i		−	1.24411i
$646$	3113.59	+	8223.40i	0.189632	+	0.500844i
$647$	−470.799			−0.0286074			−0.0143037	−	0.999898i	$-0.504553\pi$
$647$	−470.799			−0.0286074			−0.0143037	+	0.999898i	$0.504553\pi$
$648$	8256.91	+	1091.32i	0.500558	+	0.0661592i
$649$	−16651.7	−	6060.72i	−1.00714	−	0.366570i
$650$	10126.1	+	4904.54i	0.611043	+	0.295956i
$651$	49331.5	−	8698.48i	2.96998	−	0.523687i
$652$	2423.77	−	11718.2i	0.145586	−	0.703866i
$653$	−3893.80	−	2248.09i	−0.233348	−	0.134723i	0.378768	−	0.925492i	$-0.376348\pi$
$653$	−3893.80	−	2248.09i	−0.233348	−	0.134723i	−0.612116	+	0.790768i	$0.709681\pi$
$654$	−2436.65	−	9660.07i	−0.145689	−	0.577582i
$655$	5348.63	+	4488.03i	0.319066	+	0.267728i
$656$	5913.00	−	24873.6i	0.351927	−	1.48041i
$657$	5691.98	+	9858.80i	0.337999	+	0.585432i
$658$	14418.9	−	14000.7i	0.854265	−	0.829488i
$659$	−3848.00	−	10572.3i	−0.227461	−	0.624945i	0.772488	−	0.635030i	$-0.219012\pi$
$659$	−3848.00	−	10572.3i	−0.227461	−	0.624945i	−0.999949	+	0.0100848i	$0.996790\pi$
$660$	−38803.1	−	15430.8i	−2.28850	−	0.910063i
$661$	30188.1	+	5322.97i	1.77637	+	0.313222i	0.963196	−	0.268799i	$-0.0866268\pi$
$661$	30188.1	+	5322.97i	1.77637	+	0.313222i	0.813174	+	0.582021i	$0.197738\pi$
$662$	−13856.1	+	19181.6i	−0.813495	+	1.12615i
$663$	−4250.21	+	3566.35i	−0.248966	+	0.208907i
$664$	2606.58	−	2386.05i	0.152342	−	0.139453i
$665$	−17968.1	−	35911.1i	−1.04778	−	2.09410i
$666$	1170.21	−	4123.62i	0.0680854	−	0.239920i
$667$	21002.9	+	25030.2i	1.21924	+	1.45303i
$668$	−2547.30	−	3223.83i	−0.147542	−	0.186727i
$669$	1252.97	+	220.932i	0.0724104	+	0.0127679i
$670$	2342.55	−	22890.8i	0.135076	−	1.31993i
$671$	6297.25	−	2292.01i	0.362299	−	0.131866i
$672$	−12514.0	+	35904.4i	−0.718359	+	2.06107i
$673$	−1033.95	−	1790.86i	−0.0592213	−	0.102574i	0.834895	−	0.550410i	$-0.185528\pi$
$673$	−1033.95	−	1790.86i	−0.0592213	−	0.102574i	−0.894116	+	0.447835i	$0.852195\pi$
$674$	−42.5200	−	62.6676i	−0.00242999	−	0.00358140i
$675$	10824.0	−	12899.6i	0.617212	−	0.735564i
$676$	436.563	−	14830.5i	0.0248386	−	0.843792i
$677$	637.416	+	368.012i	0.0361859	+	0.0208920i	0.517984	−	0.855390i	$-0.326683\pi$
$677$	637.416	+	368.012i	0.0361859	+	0.0208920i	−0.481798	+	0.876282i	$0.660016\pi$
$678$	−3446.21	−	47416.3i	−0.195208	−	2.68586i
$679$	−2598.68	−	14737.8i	−0.146875	−	0.832969i
$680$	8408.11	+	13212.9i	0.474171	+	0.745136i
$681$	−16775.5	−	6105.79i	−0.943963	−	0.343574i
$682$	9783.07	+	21812.1i	0.549286	+	1.22468i
$683$		−	23710.3i		−	1.32833i	−0.747586	−	0.664165i	$-0.768787\pi$
$683$		−	23710.3i		−	1.32833i	0.747586	−	0.664165i	$-0.231213\pi$
$684$	14023.8	−	19950.1i	0.783938	−	1.11522i
$685$			697.812i			0.0389227i
$686$	371.307	−	166.537i	0.0206655	−	0.00926880i
$687$	30647.7	+	11154.8i	1.70201	+	0.619482i
$688$	−2534.07	−	8485.35i	−0.140422	−	0.470205i
$689$	−1197.81	−	6793.13i	−0.0662308	−	0.375614i
$690$	−52228.6	+	3795.96i	−2.88160	+	0.209435i
$691$	5276.77	+	3046.55i	0.290503	+	0.167722i	0.638169	−	0.769896i	$-0.279692\pi$
$691$	5276.77	+	3046.55i	0.290503	+	0.167722i	−0.347665	+	0.937619i	$0.613025\pi$
$692$	−2841.63	−	83.6487i	−0.156102	−	0.00459516i
$693$	−22048.2	+	26276.0i	−1.20857	+	1.44032i
$694$	22434.6	−	15221.9i	1.22710	−	0.832586i
$695$	14594.5	+	25278.3i	0.796546	+	1.37966i
$696$	−45873.1	+	10145.3i	−2.49830	+	0.552524i
$697$	−14091.2	+	5128.79i	−0.765772	+	0.278718i
$698$	19737.3	+	2019.83i	1.07030	+	0.109530i
$699$	−16458.2	−	2902.02i	−0.890567	−	0.157031i
$700$	−28038.0	−	35484.6i	−1.51391	−	1.91599i
$701$	3578.59	+	4264.80i	0.192812	+	0.229785i	0.853786	−	0.520624i	$-0.174301\pi$
$701$	3578.59	+	4264.80i	0.192812	+	0.229785i	−0.660973	+	0.750409i	$0.729856\pi$
$702$	3943.73	+	1119.16i	0.212032	+	0.0601712i
$703$	2476.90	+	2343.84i	0.132885	+	0.125746i
$704$	−18074.8	−	1599.90i	−0.967644	−	0.0856512i
$705$	−30488.0	+	25582.5i	−1.62872	+	1.36665i
$706$	9141.10	+	6603.22i	0.487295	+	0.352005i
$707$	−24759.6	−	4365.78i	−1.31708	−	0.232238i
$708$	11806.8	−	29690.2i	0.626735	−	1.57603i
$709$	3269.28	+	8982.27i	0.173174	+	0.475791i	0.995668	−	0.0929826i	$-0.0296401\pi$
$709$	3269.28	+	8982.27i	0.173174	+	0.475791i	−0.822494	+	0.568774i	$0.807418\pi$
$710$	−29982.2	−	30877.7i	−1.58480	−	1.63214i
$711$	−24958.4	−	43229.2i	−1.31647	−	2.28020i
$712$	−613.768	−	14223.9i	−0.0323061	−	0.748682i
$713$	22964.6	+	19269.6i	1.20621	+	1.01213i
$714$	21624.0	−	5454.42i	1.13341	−	0.285891i
$715$	10471.7	+	6045.82i	0.547718	+	0.316225i
$716$	−3958.02	+	19135.9i	−0.206589	+	0.998801i
$717$	34203.4	−	6030.99i	1.78152	−	0.314130i
$718$	−6327.35	+	13063.7i	−0.328878	+	0.679014i
$719$	−15614.7	−	5683.30i	−0.809918	−	0.294786i	−0.0963280	−	0.995350i	$-0.530710\pi$
$719$	−15614.7	−	5683.30i	−0.809918	−	0.294786i	−0.713590	+	0.700564i	$0.752932\pi$
$720$	17230.2	−	39869.7i	0.891852	−	2.06369i
$721$	15059.4			0.777867
$722$	8903.60	+	17236.4i	0.458944	+	0.888465i
$723$			32763.0i			1.68530i
$724$	2444.48	+	16727.9i	0.125481	+	0.858687i
$725$	19112.3	−	52510.6i	0.979053	−	2.68993i
$726$	1524.49	+	738.380i	0.0779326	+	0.0377464i
$727$	3761.89	+	21334.7i	0.191913	+	1.08839i	0.916747	+	0.399469i	$0.130805\pi$
$727$	3761.89	+	21334.7i	0.191913	+	1.08839i	−0.724834	+	0.688924i	$0.758084\pi$
$728$	5088.75	−	9763.25i	0.259068	−	0.497047i
$729$	−15220.5	+	26362.7i	−0.773281	+	1.33936i
$730$	−15640.6	+	3945.17i	−0.792992	+	0.200024i
$731$	−3338.68	+	3978.89i	−0.168927	+	0.201319i
$732$	3796.85	+	11471.3i	0.191715	+	0.579223i
$733$	−15198.5	+	8774.88i	−0.765854	+	0.442166i	−0.831393	−	0.555684i	$-0.812456\pi$
$733$	−15198.5	+	8774.88i	−0.765854	+	0.442166i	0.0655399	+	0.997850i	$0.479123\pi$
$734$	−546.652	+	530.797i	−0.0274895	+	0.0266922i
$735$	−48229.3	+	17554.0i	−2.42036	+	0.880939i
$736$	−21274.0	+	8074.73i	−1.06545	+	0.404400i
$737$	2715.32	−	15399.4i	0.135713	−	0.769665i
$738$	33711.6	+	24352.1i	1.68149	+	1.21465i
$739$	−4207.95	−	5014.84i	−0.209461	−	0.249626i	0.651077	−	0.759011i	$-0.274317\pi$
$739$	−4207.95	−	5014.84i	−0.209461	−	0.249626i	−0.860539	+	0.509385i	$0.829873\pi$
$740$	5168.32	+	3190.29i	0.256745	+	0.158483i
$741$	−8413.64	+	8891.27i	−0.417116	+	0.440795i
$742$	−7569.37	+	26673.1i	−0.374502	+	1.31968i
$743$	15953.0	−	13386.2i	0.787699	−	0.660958i	−0.157476	−	0.987523i	$-0.550336\pi$
$743$	15953.0	−	13386.2i	0.787699	−	0.660958i	0.945175	+	0.326565i	$0.105891\pi$
$744$	−39831.6	+	16475.0i	−1.96277	+	0.811833i
$745$	540.374	−	3064.61i	0.0265742	−	0.150710i
$746$	6327.32	+	647.511i	0.310536	+	0.0317789i
$747$	1965.95	+	5401.41i	0.0962925	+	0.264561i
$748$	5047.90	+	9369.53i	0.246751	+	0.458000i
$749$	−21186.5	+	12232.0i	−1.03356	+	0.596726i
$750$	21046.2	+	31018.6i	1.02466	+	1.51019i
$751$	1740.16	+	1460.17i	0.0845531	+	0.0709485i	0.684085	−	0.729403i	$-0.260202\pi$
$751$	1740.16	+	1460.17i	0.0845531	+	0.0709485i	−0.599531	+	0.800351i	$0.704646\pi$
$752$	−9513.05	+	14442.5i	−0.461310	+	0.700352i
$753$	−22673.0	+	39270.8i	−1.09728	+	1.90054i
$754$	13568.2	−	986.132i	0.655336	−	0.0476297i
$755$	50546.7	−	8912.74i	2.43653	−	0.429626i
$756$	−12305.6	−	10958.6i	−0.591999	−	0.527194i
$757$	−5952.60	+	16354.6i	−0.285800	+	0.785230i	0.710842	+	0.703352i	$0.248314\pi$
$757$	−5952.60	+	16354.6i	−0.285800	+	0.785230i	−0.996642	+	0.0818785i	$0.973908\pi$
$758$	−9899.37	−	22071.4i	−0.474355	−	1.05761i
$759$	−35586.0			−1.70183
$760$	21769.5	+	26833.5i	1.03903	+	1.28073i
$761$	4495.10			0.214123			0.107061	−	0.994252i	$-0.465856\pi$
$761$	4495.10			0.214123			0.107061	+	0.994252i	$0.465856\pi$
$762$	−7221.43	−	16100.8i	−0.343313	−	0.765445i
$763$	3965.86	−	10896.1i	0.188170	−	0.516993i
$764$	−8498.16	+	9542.78i	−0.402425	+	0.451892i
$765$	−25087.9	+	4423.67i	−1.18569	+	0.209070i
$766$	33952.0	−	2467.63i	1.60148	−	0.116396i
$767$	−4625.96	+	8012.40i	−0.217775	+	0.377198i
$768$	3842.50	−	32491.9i	0.180539	−	1.52663i
$769$	18874.3	+	15837.4i	0.885079	+	0.742669i	0.967217	−	0.253952i	$-0.0817304\pi$
$769$	18874.3	+	15837.4i	0.885079	+	0.742669i	−0.0821381	+	0.996621i	$0.526175\pi$
$770$	−27288.4	−	40218.7i	−1.27715	−	1.88231i
$771$	−3404.50	+	1965.59i	−0.159027	+	0.0918146i
$772$	−6091.77	+	3281.98i	−0.283999	+	0.153007i
$773$	2262.67	+	6216.62i	0.105281	+	0.289258i	0.981137	−	0.193316i	$-0.0619242\pi$
$773$	2262.67	+	6216.62i	0.105281	+	0.289258i	−0.875855	+	0.482574i	$0.839702\pi$
$774$	14329.9	+	1466.46i	0.665473	+	0.0681017i
$775$	8902.77	−	50490.1i	0.412641	−	2.34021i
$776$	4921.93	+	11899.7i	0.227689	+	0.550483i
$777$	6625.30	−	5559.29i	0.305896	−	0.256677i
$778$	871.941	−	3072.56i	0.0401807	−	0.141589i
$779$	−29587.7	+	14804.2i	−1.36083	+	0.680891i
$780$	−11452.1	+	18552.6i	−0.525707	+	0.851653i
$781$	−18800.0	−	22405.0i	−0.861354	−	1.02652i
$782$	10818.8	+	7815.16i	0.494732	+	0.357378i
$783$	3535.53	−	20051.0i	0.161366	−	0.915151i
$784$	−17898.1	+	13305.8i	−0.815330	+	0.606131i
$785$	−27100.5	+	9863.76i	−1.23217	+	0.448475i
$786$	−6137.89	+	5959.87i	−0.278538	+	0.270460i
$787$	10012.1	−	5780.49i	0.453485	−	0.261820i	−0.255816	−	0.966726i	$-0.582344\pi$
$787$	10012.1	−	5780.49i	0.453485	−	0.261820i	0.709301	+	0.704906i	$0.249011\pi$
$788$	−7170.51	+	2373.35i	−0.324161	+	0.107293i
$789$	8714.18	−	10385.2i	0.393198	−	0.468595i
$790$	68581.3	−	17298.9i	3.08863	−	0.779073i
$791$	27666.5	−	47919.7i	1.24362	−	2.15402i
$792$	13642.2	−	26173.8i	0.612062	−	1.17430i
$793$	−607.568	−	3445.69i	−0.0272073	−	0.154300i
$794$	−24975.7	−	12096.9i	−1.11632	−	0.540684i
$795$	18778.9	−	51594.5i	0.837759	−	2.30172i
$796$	−31652.0	+	4625.35i	−1.40939	+	0.205956i
$797$		−	14571.9i		−	0.647634i	−0.946120	−	0.323817i	$-0.895034\pi$
$797$		−	14571.9i		−	0.647634i	0.946120	−	0.323817i	$-0.104966\pi$
$798$	46015.3	−	17422.6i	2.04126	−	0.772873i
$799$	10143.4			0.449121
$800$	30150.9	+	24603.9i	1.33250	+	1.08735i
$801$	21761.6	+	7920.57i	0.959935	+	0.349388i
$802$	1862.32	−	3845.02i	0.0819960	−	0.169292i
$803$	−10795.1	+	1903.46i	−0.474409	+	0.0836510i
$804$	27610.6	+	5710.91i	1.21113	+	0.250508i
$805$	−52783.0	−	30474.3i	−2.31100	−	1.33426i
$806$	12102.2	−	3052.65i	0.528886	−	0.133406i
$807$	45672.5	+	38323.8i	1.99225	+	1.67170i
$808$	21614.0	−	932.658i	0.941062	−	0.0406074i
$809$	16618.1	+	28783.4i	0.722203	+	1.25089i	0.960115	+	0.279606i	$0.0902037\pi$
$809$	16618.1	+	28783.4i	0.722203	+	1.25089i	−0.237912	+	0.971287i	$0.576463\pi$
$810$	−13372.6	−	13772.0i	−0.580079	−	0.597406i
$811$	−3086.16	−	8479.14i	−0.133625	−	0.367131i	0.854777	−	0.518996i	$-0.173694\pi$
$811$	−3086.16	−	8479.14i	−0.133625	−	0.367131i	−0.988401	+	0.151866i	$0.951472\pi$
$812$	−50811.1	−	20205.9i	−2.19596	−	0.873262i
$813$	21605.3	+	3809.59i	0.932016	+	0.164340i
$814$	3345.78	+	2416.88i	0.144066	+	0.104068i
$815$	−21127.6	+	17728.1i	−0.908057	+	0.761950i
$816$	−17154.8	+	8600.86i	−0.735952	+	0.368983i
$817$	−6311.48	+	9564.97i	−0.270270	+	0.409591i
$818$	−40029.0	−	11359.6i	−1.71098	−	0.485548i
$819$	11511.5	+	13718.9i	0.491141	+	0.585319i
$820$	−46235.6	+	36532.8i	−1.96904	+	1.55583i
$821$	−16574.8	−	2922.59i	−0.704586	−	0.124238i	−0.190136	−	0.981758i	$-0.560893\pi$
$821$	−16574.8	−	2922.59i	−0.704586	−	0.124238i	−0.514450	+	0.857520i	$0.672004\pi$
$822$	−850.598	−	87.0466i	−0.0360925	−	0.00369355i
$823$	−12586.8	+	4581.23i	−0.533109	+	0.194036i	−0.594526	−	0.804076i	$-0.702660\pi$
$823$	−12586.8	+	4581.23i	−0.533109	+	0.194036i	0.0614168	+	0.998112i	$0.480438\pi$
$824$	−12652.8	+	2798.30i	−0.534929	+	0.118305i
$825$	30429.9	+	52706.1i	1.28416	+	2.22423i
$826$	30773.3	−	20879.8i	1.29630	−	0.879539i
$827$	15253.2	−	18178.1i	0.641362	−	0.764346i	−0.343222	−	0.939254i	$-0.611518\pi$
$827$	15253.2	−	18178.1i	0.641362	−	0.764346i	0.984585	+	0.174908i	$0.0559629\pi$
$828$	1089.08	−	36997.3i	0.0457105	−	1.55283i
$829$	−35342.9	−	20405.2i	−1.48071	−	0.854888i	−0.480949	−	0.876749i	$-0.659708\pi$
$829$	−35342.9	−	20405.2i	−1.48071	−	0.854888i	−0.999761	+	0.0218603i	$0.993041\pi$
$830$	−8123.28	+	590.398i	−0.339714	+	0.0246904i
$831$	3759.88	+	21323.3i	0.156954	+	0.890130i
$832$	−2461.35	+	9148.58i	−0.102562	+	0.381214i
$833$	12291.9	+	4473.89i	0.511272	+	0.186088i
$834$	−32633.6	+	14636.7i	−1.35493	+	0.607705i
$835$			9469.94i			0.392480i
$836$	13432.9	+	19259.3i	0.555727	+	0.796767i
$837$		−	18680.0i		−	0.771418i
$838$	11375.7	+	25363.0i	0.468934	+	1.04553i
$839$	3866.61	+	1407.33i	0.159106	+	0.0579099i	0.420345	−	0.907364i	$-0.361909\pi$
$839$	3866.61	+	1407.33i	0.159106	+	0.0579099i	−0.261239	+	0.965274i	$0.584131\pi$
$840$	73935.0	−	47048.9i	3.03690	−	1.93255i
$841$	−7497.47	−	42520.3i	−0.307412	−	1.74342i
$842$	−508.699	−	6999.18i	−0.0208206	−	0.286470i
$843$	1410.32	+	814.249i	0.0576204	+	0.0332672i
$844$	3699.41	+	108.899i	0.150876	+	0.00444130i
$845$	−21981.0	+	26196.0i	−0.894876	+	1.06647i
$846$	−15794.3	−	23278.2i	−0.641867	−	0.946007i
$847$	985.750	+	1707.37i	0.0399891	+	0.0692632i
$848$	1403.41	−	23817.0i	0.0568318	−	0.964480i
$849$	15440.2	−	5619.79i	0.624155	−	0.227174i
$850$	2323.68	−	22706.5i	0.0937666	−	0.916265i
$851$	5097.23	+	898.780i	0.205324	+	0.0362042i
$852$	41378.5	−	32695.0i	1.66385	−	1.31469i
$853$	−8057.09	−	9602.07i	−0.323411	−	0.385426i	0.579703	−	0.814828i	$-0.303169\pi$
$853$	−8057.09	−	9602.07i	−0.323411	−	0.385426i	−0.903113	+	0.429402i	$0.858724\pi$
$854$	−3839.42	+	13529.4i	−0.153843	+	0.542116i
$855$	−53868.0	+	16039.3i	−2.15467	+	0.641559i
$856$	15527.8	−	14214.0i	0.620010	−	0.567553i
$857$	16840.5	−	14130.9i	0.671250	−	0.563246i	−0.242185	−	0.970230i	$-0.577864\pi$
$857$	16840.5	−	14130.9i	0.671250	−	0.563246i	0.913435	+	0.406984i	$0.133420\pi$
$858$	−8675.82	+	12010.3i	−0.345207	+	0.477884i
$859$	27676.1	+	4880.04i	1.09930	+	0.193835i	0.693733	−	0.720232i	$-0.255965\pi$
$859$	27676.1	+	4880.04i	1.09930	+	0.193835i	0.405562	+	0.914067i	$0.367076\pi$
$860$	−7542.20	+	18966.1i	−0.299055	+	0.752021i
$861$	28698.9	+	78849.7i	1.13595	+	3.12101i
$862$	−23013.4	+	22345.9i	−0.909326	+	0.882953i
$863$	−5914.29	−	10243.8i	−0.233285	−	0.404061i	0.725488	−	0.688235i	$-0.241614\pi$
$863$	−5914.29	−	10243.8i	−0.233285	−	0.404061i	−0.958773	+	0.284174i	$0.908281\pi$
$864$	12375.4	+	6920.70i	0.487290	+	0.272508i
$865$	5019.34	+	4211.73i	0.197298	+	0.165553i
$866$	−7997.71	−	31706.8i	−0.313826	−	1.24416i
$867$	−24239.1	−	13994.4i	−0.949484	−	0.548185i
$868$	−49128.8	−	10161.7i	−1.92113	−	0.397361i
$869$	47334.6	−	8346.37i	1.84777	−	0.325812i
$870$	97454.7	+	47201.9i	3.79773	+	1.83942i
$871$	−7671.78	−	2792.30i	−0.298448	−	0.108626i
$872$	−1307.40	+	9891.75i	−0.0507731	+	0.384148i
$873$	−20946.6			−0.812067
$874$	25688.4	+	14393.3i	0.994191	+	0.557048i
$875$			43627.9i			1.68559i
$876$	−2857.93	−	19557.2i	−0.110229	−	0.754313i
$877$	2014.64	−	5535.19i	0.0775709	−	0.213124i	−0.894845	−	0.446376i	$-0.852714\pi$
$877$	2014.64	−	5535.19i	0.0775709	−	0.213124i	0.972416	+	0.233252i	$0.0749366\pi$
$878$	7933.75	−	16380.3i	0.304956	−	0.629623i
$879$	−3621.52	−	20538.6i	−0.138966	−	0.788113i
$880$	30400.8	+	28720.8i	1.16456	+	1.10020i
$881$	21221.7	−	36757.1i	0.811554	−	1.40565i	−0.100223	−	0.994965i	$-0.531956\pi$
$881$	21221.7	−	36757.1i	0.811554	−	1.40565i	0.911776	−	0.410687i	$-0.134711\pi$
$882$	−8872.57	−	35175.2i	−0.338724	−	1.34287i
$883$	−12873.6	+	15342.1i	−0.490634	+	0.584715i	−0.953379	−	0.301777i	$-0.902420\pi$
$883$	−12873.6	+	15342.1i	−0.490634	+	0.584715i	0.462745	+	0.886492i	$0.346865\pi$
$884$	5275.23	−	1746.03i	0.200707	−	0.0664315i
$885$	−63776.7	+	36821.5i	−2.42241	+	1.39858i
$886$	14436.8	+	14868.1i	0.547421	+	0.563772i
$887$	−11935.6	+	4344.21i	−0.451814	+	0.164447i	−0.557897	−	0.829910i	$-0.688391\pi$
$887$	−11935.6	+	4344.21i	−0.451814	+	0.164447i	0.106083	+	0.994357i	$0.466169\pi$
$888$	−4533.51	+	5901.96i	−0.171323	+	0.223037i
$889$	3566.39	−	20226.0i	0.134548	−	0.763059i
$890$	−19214.8	+	26599.8i	−0.723686	+	1.00183i
$891$	−8385.13	−	9993.01i	−0.315278	−	0.375733i
$892$	−1084.29	−	669.309i	−0.0407004	−	0.0251235i
$893$	22231.9	−	2564.86i	0.833104	−	0.0961138i
$894$	3668.21	+	1040.98i	0.137230	+	0.0389435i
$895$	34501.4	−	28950.1i	1.28855	−	1.08122i
$896$	24933.5	−	28782.6i	0.929655	−	1.07317i
$897$	−3226.33	+	18297.4i	−0.120094	+	0.681085i
$898$	−2157.65	+	21084.0i	−0.0801801	+	0.783501i
$899$	−21201.6	−	58250.9i	−0.786555	−	2.16104i
$900$	−55727.5	+	30023.6i	−2.06398	+	1.11199i
$901$	−12118.7	+	6996.76i	−0.448095	+	0.258708i
$902$	−33136.8	+	22483.3i	−1.22321	+	0.829948i
$903$	22264.5	+	18682.1i	0.820505	+	0.688485i
$904$	−14340.8	+	45402.6i	−0.527620	+	1.67043i
$905$	19482.2	−	33744.2i	0.715591	−	1.23944i
$906$	4558.89	+	62725.7i	0.167173	+	2.30013i
$907$	−15167.5	+	2674.45i	−0.555270	+	0.0979091i	−0.444240	−	0.895908i	$-0.646526\pi$
$907$	−15167.5	+	2674.45i	−0.555270	+	0.0979091i	−0.111030	+	0.993817i	$0.535415\pi$
$908$	13352.2	+	11890.6i	0.488005	+	0.434585i
$909$	−12035.8	+	33068.1i	−0.439166	+	1.20660i
$910$	−23153.5	+	10384.7i	−0.843441	+	0.378296i
$911$	−45209.2			−1.64418			−0.822091	−	0.569357i	$-0.807192\pi$
$911$	−45209.2			−1.64418			−0.822091	+	0.569357i	$0.807192\pi$
$912$	−35424.3	+	23188.7i	−1.28620	+	0.841947i
$913$	−5534.81			−0.200630
$914$	40483.0	−	18157.2i	1.46505	−	0.657098i
$915$	9525.23	−	26170.4i	0.344147	−	0.945536i
$916$	−24393.6	−	21723.3i	−0.879897	−	0.783578i
$917$	−9806.17	+	1729.09i	−0.353139	+	0.0622679i
$918$	−602.843	−	8294.50i	−0.0216741	−	0.298213i
$919$	−5855.19	+	10141.5i	−0.210169	+	0.364023i	−0.951767	−	0.306821i	$-0.900735\pi$
$919$	−5855.19	+	10141.5i	−0.210169	+	0.364023i	0.741599	+	0.670844i	$0.234068\pi$
$920$	50010.5	+	15796.3i	1.79217	+	0.566073i
$921$	−53753.5	−	45104.5i	−1.92317	−	1.61373i
$922$	−39424.3	+	26749.4i	−1.40821	+	0.955473i
$923$	−13224.5	+	7635.19i	−0.471604	+	0.272281i
$924$	52428.7	−	28246.3i	1.86664	−	1.00567i
$925$	−3027.51	−	8318.01i	−0.107615	−	0.295670i
$926$	1490.31	−	14563.0i	0.0528884	−	0.516813i
$927$	3660.24	−	20758.3i	0.129685	−	0.735481i
$928$	46445.6	+	7535.28i	1.64294	+	0.266549i
$929$	−14815.8	+	12432.0i	−0.523242	+	0.439052i	−0.865760	−	0.500459i	$-0.833165\pi$
$929$	−14815.8	+	12432.0i	−0.523242	+	0.439052i	0.342518	+	0.939511i	$0.388720\pi$
$930$	95573.9	+	27122.3i	3.36988	+	0.956317i
$931$	28072.2	+	6697.56i	0.988215	+	0.235772i
$932$	14242.6	+	8791.62i	0.500569	+	0.308990i
$933$	−50768.1	−	60503.0i	−1.78143	−	2.12302i
$934$	−20956.8	+	29011.3i	−0.734182	+	1.01636i
$935$	4259.55	−	24157.1i	0.148986	−	0.844943i
$936$	−12221.1	−	9387.45i	−0.426771	−	0.327819i
$937$	−14335.7	+	5217.78i	−0.499816	+	0.181918i	−0.579611	−	0.814893i	$-0.696796\pi$
$937$	−14335.7	+	5217.78i	−0.499816	+	0.181918i	0.0797952	+	0.996811i	$0.474573\pi$
$938$	22860.4	+	23543.2i	0.795755	+	0.819525i
$939$	−23845.6	+	13767.3i	−0.828723	+	0.478464i
$940$	37840.8	−	12524.8i	1.31301	−	0.434590i
$941$	17658.9	−	21045.0i	0.611757	−	0.729064i	−0.367873	−	0.929876i	$-0.619914\pi$
$941$	17658.9	−	21045.0i	0.611757	−	0.729064i	0.979630	+	0.200812i	$0.0643582\pi$
$942$	−8642.87	−	34264.5i	−0.298938	−	1.18514i
$943$	−25108.2	+	43488.6i	−0.867057	+	1.50179i
$944$	−21975.7	+	23261.2i	−0.757678	+	0.802000i
$945$	6594.88	+	37401.4i	0.227017	+	1.28748i
$946$	−6046.16	+	12483.1i	−0.207799	+	0.429029i
$947$	−2097.33	+	5762.36i	−0.0719683	+	0.197731i	−0.970461	−	0.241256i	$-0.922441\pi$
$947$	−2097.33	+	5762.36i	−0.0719683	+	0.197731i	0.898493	+	0.438988i	$0.144663\pi$
$948$	12531.5	+	85755.2i	0.429331	+	2.93797i
$949$			5723.13i			0.195765i
$950$	−648.597	−	50354.6i	−0.0221508	−	1.71970i
$951$	−5441.85			−0.185556
$952$	−22142.6	−	2926.60i	−0.753829	−	0.0996341i
$953$	18610.9	+	6773.80i	0.632597	+	0.230247i	0.638361	−	0.769737i	$-0.279613\pi$
$953$	18610.9	+	6773.80i	0.632597	+	0.230247i	−0.00576407	+	0.999983i	$0.501835\pi$
$954$	34927.0	+	16916.8i	1.18533	+	0.574110i
$955$	29004.1	−	5114.21i	0.982777	−	0.173290i
$956$	−34062.8	−	7045.47i	−1.15238	−	0.238354i
$957$	63726.8	+	36792.7i	2.15256	+	1.24278i
$958$	−3305.91	−	13106.2i	−0.111492	−	0.442008i
$959$	−762.346	−	639.684i	−0.0256699	−	0.0215396i
$960$	−53377.1	+	53268.5i	−1.79452	+	1.79087i
$961$	−13541.3	−	23454.2i	−0.454543	−	0.787292i
$962$	1546.04	−	1501.20i	0.0518152	−	0.0503124i
$963$	11711.5	+	32177.0i	0.391897	+	1.07673i
$964$	12125.0	−	30490.4i	0.405105	−	1.01870i
$965$	15706.2	+	2769.42i	0.523938	+	0.0923843i
$966$	43730.9	−	60538.5i	1.45654	−	2.01635i
$967$	788.918	−	661.981i	0.0262357	−	0.0220143i	−0.629576	−	0.776939i	$-0.716771\pi$
$967$	788.918	−	661.981i	0.0262357	−	0.0220143i	0.655811	+	0.754925i	$0.272327\pi$
$968$	−1145.48	−	1251.35i	−0.0380341	−	0.0415494i
$969$	22787.3	+	9869.89i	0.755452	+	0.327210i
$970$	8102.80	−	28552.8i	0.268212	−	0.945128i
$971$	−17037.1	−	20304.0i	−0.563074	−	0.671046i	0.407120	−	0.913375i	$-0.366533\pi$
$971$	−17037.1	−	20304.0i	−0.563074	−	0.671046i	−0.970194	+	0.242329i	$0.922089\pi$
$972$	31730.7	−	25071.9i	1.04708	−	0.827346i
$973$	−40994.9	−	7228.50i	−1.35070	−	0.238166i
$974$	−189.177	+	1848.59i	−0.00622344	+	0.0608140i
$975$	29859.0	−	10867.8i	0.980772	−	0.356972i
$976$	711.855	−	12080.7i	0.0233462	−	0.396204i
$977$	−20954.6	−	36294.4i	−0.686178	−	1.18849i	−0.973065	−	0.230531i	$-0.925954\pi$
$977$	−20954.6	−	36294.4i	−0.686178	−	1.18849i	0.286887	−	0.957964i	$-0.407380\pi$
$978$	−18974.2	−	27964.9i	−0.620377	−	0.914334i
$979$	−14333.5	+	17082.0i	−0.467928	+	0.557655i
$980$	51380.3	+	1512.47i	1.67478	+	0.0493002i
$981$	−14055.6	−	8114.98i	−0.457451	−	0.264109i
$982$	−3643.37	−	50129.0i	−0.118396	−	1.62900i
$983$	−793.718	−	4501.40i	−0.0257535	−	0.146055i	0.969220	−	0.246198i	$-0.0791812\pi$
$983$	−793.718	−	4501.40i	−0.0257535	−	0.146055i	−0.994973	+	0.100142i	$0.968070\pi$
$984$	−38764.2	−	60916.1i	−1.25585	−	1.97351i
$985$	16358.6	+	5954.05i	0.529167	+	0.192601i
$986$	−11294.0	−	25180.9i	−0.364782	−	0.813311i
$987$		−	56759.0i		−	1.83046i
$988$	11120.5	−	5160.77i	0.358088	−	0.166180i
$989$			17393.6i			0.559237i
$990$	−62071.0	+	27839.8i	−1.99267	+	0.893743i
$991$	−5493.54	−	1999.48i	−0.176093	−	0.0640925i	0.252469	−	0.967605i	$-0.418757\pi$
$991$	−5493.54	−	1999.48i	−0.176093	−	0.0640925i	−0.428562	+	0.903512i	$0.640980\pi$
$992$	43165.8	−	591.215i	1.38157	−	0.0189225i
$993$	11604.4	+	65811.6i	0.370849	+	2.10319i
$994$	61218.0	−	4449.32i	1.95344	−	0.141976i
$995$	63849.4	+	36863.5i	2.03433	+	1.17452i
$996$	293.648	−	9975.52i	0.00934197	−	0.317356i
$997$	−15249.4	+	18173.5i	−0.484405	+	0.577292i	−0.951785	−	0.306765i	$-0.900753\pi$
$997$	−15249.4	+	18173.5i	−0.484405	+	0.577292i	0.467380	+	0.884056i	$0.345198\pi$
$998$	−22335.3	+	15154.5i	−0.708429	+	0.480670i
$999$	−1612.60	−	2793.10i	−0.0510714	−	0.0884583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.t.a.101.7	✓	348
8.5	even	2	inner	152.4.t.a.101.20	yes	348
19.16	even	9	inner	152.4.t.a.149.20	yes	348
152.149	even	18	inner	152.4.t.a.149.7	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.t.a.101.7	✓	348	1.1	even	1	trivial
152.4.t.a.101.20	yes	348	8.5	even	2	inner
152.4.t.a.149.7	yes	348	152.149	even	18	inner
152.4.t.a.149.20	yes	348	19.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.58074 + 1.15750i) q^{2} +(-2.73201 + 7.50614i) q^{3} +(5.32040 - 5.97439i) q^{4} +(-18.1584 + 3.20182i) q^{5} +(-1.63774 - 22.5337i) q^{6} +(13.1479 - 22.7729i) q^{7} +(-6.81519 + 21.5767i) q^{8} +(-28.1950 - 23.6584i) q^{9} +(43.1560 - 29.2814i) q^{10} +(30.6923 - 17.7202i) q^{11} +(30.3093 + 56.2577i) q^{12} +(-6.32864 - 17.3878i) q^{13} +(-7.57176 + 73.9895i) q^{14} +(25.5757 - 145.047i) q^{15} +(-7.38678 - 63.5723i) q^{16} +(-28.7555 + 24.1287i) q^{17} +(100.149 + 28.4205i) q^{18} +(-56.9239 + 60.1554i) q^{19} +(-77.4812 + 125.521i) q^{20} +(135.016 + 160.906i) q^{21} +(-58.6977 + 81.2576i) q^{22} +(-21.8283 + 123.794i) q^{23} +(-143.338 - 110.103i) q^{24} +(202.016 - 73.5278i) q^{25} +(36.4589 + 37.5479i) q^{26} +(67.8349 - 39.1645i) q^{27} +(-66.1020 - 199.712i) q^{28} +(167.082 - 199.120i) q^{29} +(101.888 + 403.932i) q^{30} +(119.241 - 206.531i) q^{31} +(92.6481 + 155.513i) q^{32} +(49.1587 + 278.793i) q^{33} +(46.2814 - 95.5543i) q^{34} +(-165.831 + 455.617i) q^{35} +(-291.354 + 42.5760i) q^{36} -41.1750i q^{37} +(77.2757 - 221.134i) q^{38} +147.805 q^{39} +(54.6685 - 413.620i) q^{40} +(375.389 + 136.631i) q^{41} +(-534.689 - 258.975i) q^{42} +(136.268 - 24.0276i) q^{43} +(57.4277 - 277.647i) q^{44} +(587.728 + 339.325i) q^{45} +(-86.9587 - 344.747i) q^{46} +(-207.000 - 173.694i) q^{47} +(497.363 + 118.234i) q^{48} +(-174.236 - 301.785i) q^{49} +(-436.241 + 423.589i) q^{50} +(-102.553 - 281.763i) q^{51} +(-137.552 - 54.7002i) q^{52} +(367.123 + 64.7337i) q^{53} +(-129.731 + 179.592i) q^{54} +(-500.588 + 420.043i) q^{55} +(401.757 + 438.890i) q^{56} +(-296.018 - 591.624i) q^{57} +(-200.713 + 707.274i) q^{58} +(-321.396 - 383.025i) q^{59} +(-730.496 - 924.508i) q^{60} +(186.216 + 32.8349i) q^{61} +(-68.6697 + 671.024i) q^{62} +(-909.477 + 331.022i) q^{63} +(-419.106 - 294.098i) q^{64} +(170.591 + 295.472i) q^{65} +(-449.568 - 662.589i) q^{66} +(283.609 - 337.992i) q^{67} +(-8.83610 + 300.171i) q^{68} +(-869.582 - 502.053i) q^{69} +(-99.4098 - 1367.78i) q^{70} +(-143.305 - 812.723i) q^{71} +(702.625 - 447.119i) q^{72} +(-290.644 - 105.786i) q^{73} +(47.6600 + 106.262i) q^{74} +1717.24i q^{75} +(56.5345 + 660.136i) q^{76} -931.937i q^{77} +(-381.446 + 171.084i) q^{78} +(1274.42 + 463.852i) q^{79} +(337.680 + 1130.72i) q^{80} +(-63.9165 - 362.489i) q^{81} +(-1126.93 + 81.9051i) q^{82} +(-135.249 - 78.0860i) q^{83} +(1679.65 + 49.4438i) q^{84} +(444.899 - 530.210i) q^{85} +(-323.859 + 219.738i) q^{86} +(1038.16 + 1798.14i) q^{87} +(173.170 + 783.006i) q^{88} +(-591.251 + 215.198i) q^{89} +(-1909.54 - 195.414i) q^{90} +(-479.178 - 84.4921i) q^{91} +(623.461 + 789.045i) q^{92} +(1224.49 + 1459.28i) q^{93} +(735.263 + 208.656i) q^{94} +(841.042 - 1274.59i) q^{95} +(-1420.42 + 270.566i) q^{96} +(435.962 - 365.816i) q^{97} +(798.972 + 577.150i) q^{98} +(-1284.60 - 226.510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Introduction

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