LMFDB - Embedded newform 31.5.f.a.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, 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:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	31.23
Dual form			31.5.f.a.27.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33487 + 4.10831i) q^{2} +(7.83134 - 2.54456i) q^{3} +(-2.15208 - 1.56358i) q^{4} +21.7607 q^{5} +35.5702i q^{6} +(7.98302 + 5.80000i) q^{7} +(-46.6194 + 33.8710i) q^{8} +(-10.6753 + 7.75606i) q^{9} +(-29.0478 + 89.3999i) q^{10} +(-4.48030 + 6.16661i) q^{11} +(-20.8322 - 6.76881i) q^{12} +(116.666 - 37.9069i) q^{13} +(-34.4845 + 25.0545i) q^{14} +(170.416 - 55.3714i) q^{15} +(-90.0740 - 277.219i) q^{16} +(-123.601 - 170.122i) q^{17} +(-17.6142 - 54.2108i) q^{18} +(143.593 - 441.933i) q^{19} +(-46.8308 - 34.0245i) q^{20} +(77.2762 + 25.1085i) q^{21} +(-19.3537 - 26.6381i) q^{22} +(-20.4772 - 28.1844i) q^{23} +(-278.906 + 383.881i) q^{24} -151.471 q^{25} +529.899i q^{26} +(-455.909 + 627.505i) q^{27} +(-8.11133 - 24.9641i) q^{28} +(596.229 + 193.726i) q^{29} +774.034i q^{30} +(-628.777 - 726.747i) q^{31} +337.144 q^{32} +(-19.3955 + 59.6932i) q^{33} +(863.907 - 280.700i) q^{34} +(173.716 + 126.212i) q^{35} +35.1013 q^{36} -1797.91i q^{37} +(1623.92 + 1179.85i) q^{38} +(817.191 - 593.724i) q^{39} +(-1014.47 + 737.057i) q^{40} +(-634.022 + 1951.32i) q^{41} +(-206.307 + 283.958i) q^{42} +(38.7943 + 12.6050i) q^{43} +(19.2839 - 6.26572i) q^{44} +(-232.302 + 168.777i) q^{45} +(143.125 - 46.5041i) q^{46} +(136.154 + 419.040i) q^{47} +(-1410.80 - 1941.80i) q^{48} +(-711.861 - 2190.88i) q^{49} +(202.194 - 622.290i) q^{50} +(-1400.85 - 1017.77i) q^{51} +(-310.344 - 100.837i) q^{52} +(1572.71 + 2164.65i) q^{53} +(-1969.41 - 2710.65i) q^{54} +(-97.4947 + 134.190i) q^{55} -568.616 q^{56} -3826.31i q^{57} +(-1591.78 + 2190.89i) q^{58} +(-143.395 - 441.324i) q^{59} +(-453.325 - 147.294i) q^{60} +4962.02i q^{61} +(3825.04 - 1613.10i) q^{62} -130.206 q^{63} +(991.140 - 3050.41i) q^{64} +(2538.73 - 824.882i) q^{65} +(-219.348 - 159.365i) q^{66} +6406.84 q^{67} +559.375i q^{68} +(-232.081 - 168.616i) q^{69} +(-750.408 + 545.204i) q^{70} +(-4724.23 + 3432.36i) q^{71} +(234.971 - 723.166i) q^{72} +(-5099.73 + 7019.18i) q^{73} +(7386.36 + 2399.97i) q^{74} +(-1186.22 + 385.426i) q^{75} +(-1000.02 + 726.556i) q^{76} +(-71.5327 + 23.2424i) q^{77} +(1348.36 + 4149.82i) q^{78} +(1439.57 + 1981.40i) q^{79} +(-1960.08 - 6032.49i) q^{80} +(-1643.37 + 5057.77i) q^{81} +(-7170.29 - 5209.52i) q^{82} +(7089.31 + 2303.46i) q^{83} +(-127.045 - 174.863i) q^{84} +(-2689.65 - 3701.98i) q^{85} +(-103.571 + 142.553i) q^{86} +5162.21 q^{87} -439.236i q^{88} +(-5884.05 + 8098.69i) q^{89} +(-383.297 - 1179.67i) q^{90} +(1151.20 + 374.049i) q^{91} +92.6727i q^{92} +(-6773.41 - 4091.44i) q^{93} -1903.30 q^{94} +(3124.68 - 9616.78i) q^{95} +(2640.29 - 857.882i) q^{96} +(-5308.52 - 3856.86i) q^{97} +9951.08 q^{98} -100.580i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.33487	+	4.10831i	−0.333718	+	1.02708i	0.633632	+	0.773634i	$0.281563\pi$
$2$	−1.33487	+	4.10831i	−0.333718	+	1.02708i	−0.967350	+	0.253444i	$0.918437\pi$
$3$	7.83134	−	2.54456i	0.870149	−	0.282728i	0.160288	−	0.987070i	$-0.448758\pi$
$3$	7.83134	−	2.54456i	0.870149	−	0.282728i	0.709861	+	0.704342i	$0.248758\pi$
$4$	−2.15208	−	1.56358i	−0.134505	−	0.0977235i
$5$	21.7607			0.870429			0.435215	−	0.900327i	$-0.356673\pi$
$5$	21.7607			0.870429			0.435215	+	0.900327i	$0.356673\pi$
$6$			35.5702i			0.988062i
$7$	7.98302	+	5.80000i	0.162919	+	0.118367i	0.666257	−	0.745722i	$-0.267895\pi$
$7$	7.98302	+	5.80000i	0.162919	+	0.118367i	−0.503339	+	0.864089i	$0.667895\pi$
$8$	−46.6194	+	33.8710i	−0.728429	+	0.529234i
$9$	−10.6753	+	7.75606i	−0.131794	+	0.0957538i
$10$	−29.0478	+	89.3999i	−0.290478	+	0.893999i
$11$	−4.48030	+	6.16661i	−0.0370273	+	0.0509637i	−0.827129	−	0.562012i	$-0.810028\pi$
$11$	−4.48030	+	6.16661i	−0.0370273	+	0.0509637i	0.790102	+	0.612975i	$0.210028\pi$
$12$	−20.8322	−	6.76881i	−0.144668	−	0.0470056i
$13$	116.666	−	37.9069i	0.690329	−	0.224301i	0.0572169	−	0.998362i	$-0.481777\pi$
$13$	116.666	−	37.9069i	0.690329	−	0.224301i	0.633112	+	0.774060i	$0.281777\pi$
$14$	−34.4845	+	25.0545i	−0.175942	+	0.127829i
$15$	170.416	−	55.3714i	0.757403	−	0.246095i
$16$	−90.0740	−	277.219i	−0.351852	−	1.08289i
$17$	−123.601	−	170.122i	−0.427685	−	0.588658i	0.539735	−	0.841835i	$-0.318524\pi$
$17$	−123.601	−	170.122i	−0.427685	−	0.588658i	−0.967420	+	0.253177i	$0.918524\pi$
$18$	−17.6142	−	54.2108i	−0.0543647	−	0.167317i
$19$	143.593	−	441.933i	0.397764	−	1.22419i	−0.529024	−	0.848607i	$-0.677442\pi$
$19$	143.593	−	441.933i	0.397764	−	1.22419i	0.926788	−	0.375585i	$-0.122558\pi$
$20$	−46.8308	−	34.0245i	−0.117077	−	0.0850613i
$21$	77.2762	+	25.1085i	0.175229	+	0.0569355i
$22$	−19.3537	−	26.6381i	−0.0399870	−	0.0550374i
$23$	−20.4772	−	28.1844i	−0.0387092	−	0.0532787i	0.789224	−	0.614106i	$-0.210483\pi$
$23$	−20.4772	−	28.1844i	−0.0387092	−	0.0532787i	−0.827933	+	0.560827i	$0.810483\pi$
$24$	−278.906	+	383.881i	−0.484211	+	0.666460i
$25$	−151.471			−0.242353
$26$			529.899i			0.783875i
$27$	−455.909	+	627.505i	−0.625389	+	0.860774i
$28$	−8.11133	−	24.9641i	−0.0103461	−	0.0318420i
$29$	596.229	+	193.726i	0.708952	+	0.230352i	0.641227	−	0.767352i	$-0.278426\pi$
$29$	596.229	+	193.726i	0.708952	+	0.230352i	0.0677253	+	0.997704i	$0.478426\pi$
$30$			774.034i			0.860038i
$31$	−628.777	−	726.747i	−0.654294	−	0.756240i
$31$	−628.777	−	726.747i	−0.654294	−	0.756240i
$32$	337.144			0.329242
$33$	−19.3955	+	59.6932i	−0.0178104	+	0.0548147i
$34$	863.907	−	280.700i	0.747324	−	0.242820i
$35$	173.716	+	126.212i	0.141809	+	0.103030i
$36$	35.1013			0.0270843
$37$		−	1797.91i		−	1.31330i	−0.754196	−	0.656649i	$-0.771973\pi$
$37$		−	1797.91i		−	1.31330i	0.754196	−	0.656649i	$-0.228027\pi$
$38$	1623.92	+	1179.85i	1.12460	+	0.817069i
$39$	817.191	−	593.724i	0.537272	−	0.390351i
$40$	−1014.47	+	737.057i	−0.634045	+	0.460661i
$41$	−634.022	+	1951.32i	−0.377169	+	1.16081i	0.564834	+	0.825205i	$0.308940\pi$
$41$	−634.022	+	1951.32i	−0.377169	+	1.16081i	−0.942003	+	0.335603i	$0.891060\pi$
$42$	−206.307	+	283.958i	−0.116954	+	0.160974i
$43$	38.7943	+	12.6050i	0.0209813	+	0.00681722i	0.319489	−	0.947590i	$-0.396489\pi$
$43$	38.7943	+	12.6050i	0.0209813	+	0.00681722i	−0.298508	+	0.954407i	$0.596489\pi$
$44$	19.2839	−	6.26572i	0.00996070	−	0.00323643i
$45$	−232.302	+	168.777i	−0.114717	+	0.0833469i
$46$	143.125	−	46.5041i	0.0676393	−	0.0219774i
$47$	136.154	+	419.040i	0.0616362	+	0.189697i	0.977133	−	0.212628i	$-0.0682022\pi$
$47$	136.154	+	419.040i	0.0616362	+	0.189697i	−0.915497	+	0.402325i	$0.868202\pi$
$48$	−1410.80	−	1941.80i	−0.612326	−	0.842795i
$49$	−711.861	−	2190.88i	−0.296485	−	0.912488i
$50$	202.194	−	622.290i	0.0808777	−	0.248916i
$51$	−1400.85	−	1017.77i	−0.538580	−	0.391301i
$52$	−310.344	−	100.837i	−0.114772	−	0.0372917i
$53$	1572.71	+	2164.65i	0.559883	+	0.770613i	0.991312	−	0.131534i	$-0.0419903\pi$
$53$	1572.71	+	2164.65i	0.559883	+	0.770613i	−0.431428	+	0.902147i	$0.641990\pi$
$54$	−1969.41	−	2710.65i	−0.675379	−	0.929579i
$55$	−97.4947	+	134.190i	−0.0322296	+	0.0443603i
$56$	−568.616			−0.181319
$57$		−	3826.31i		−	1.17769i
$58$	−1591.78	+	2190.89i	−0.473180	+	0.651276i
$59$	−143.395	−	441.324i	−0.0411936	−	0.126781i	0.928345	−	0.371720i	$-0.121232\pi$
$59$	−143.395	−	441.324i	−0.0411936	−	0.126781i	−0.969538	+	0.244939i	$0.921232\pi$
$60$	−453.325	−	147.294i	−0.125924	−	0.0409150i
$61$			4962.02i			1.33352i	0.745274	+	0.666758i	$0.232319\pi$
$61$			4962.02i			1.33352i	−0.745274	+	0.666758i	$0.767681\pi$
$62$	3825.04	−	1613.10i	0.995067	−	0.419641i
$63$	−130.206			−0.0328058
$64$	991.140	−	3050.41i	0.241978	−	0.744730i
$65$	2538.73	−	824.882i	0.600882	−	0.195238i
$66$	−219.348	−	159.365i	−0.0503553	−	0.0365853i
$67$	6406.84			1.42723			0.713615	−	0.700538i	$-0.247057\pi$
$67$	6406.84			1.42723			0.713615	+	0.700538i	$0.247057\pi$
$68$			559.375i			0.120972i
$69$	−232.081	−	168.616i	−0.0487462	−	0.0354162i
$70$	−750.408	+	545.204i	−0.153145	+	0.111266i
$71$	−4724.23	+	3432.36i	−0.937162	+	0.680888i	−0.947736	−	0.319056i	$-0.896634\pi$
$71$	−4724.23	+	3432.36i	−0.937162	+	0.680888i	0.0105738	+	0.999944i	$0.496634\pi$
$72$	234.971	−	723.166i	0.0453262	−	0.139500i
$73$	−5099.73	+	7019.18i	−0.956977	+	1.31717i	−0.00861923	+	0.999963i	$0.502744\pi$
$73$	−5099.73	+	7019.18i	−0.956977	+	1.31717i	−0.948358	+	0.317203i	$0.897256\pi$
$74$	7386.36	+	2399.97i	1.34886	+	0.438271i
$75$	−1186.22	+	385.426i	−0.210883	+	0.0685202i
$76$	−1000.02	+	726.556i	−0.173133	+	0.125789i
$77$	−71.5327	+	23.2424i	−0.0120649	+	0.00392012i
$78$	1348.36	+	4149.82i	0.221624	+	0.682088i
$79$	1439.57	+	1981.40i	0.230664	+	0.317481i	0.908622	−	0.417619i	$-0.137135\pi$
$79$	1439.57	+	1981.40i	0.230664	+	0.317481i	−0.677959	+	0.735100i	$0.737135\pi$
$80$	−1960.08	−	6032.49i	−0.306262	−	0.942577i
$81$	−1643.37	+	5057.77i	−0.250475	+	0.770884i
$82$	−7170.29	−	5209.52i	−1.06637	−	0.774765i
$83$	7089.31	+	2303.46i	1.02908	+	0.334367i	0.774425	−	0.632666i	$-0.218039\pi$
$83$	7089.31	+	2303.46i	1.02908	+	0.334367i	0.254652	+	0.967033i	$0.418039\pi$
$84$	−127.045	−	174.863i	−0.0180053	−	0.0247821i
$85$	−2689.65	−	3701.98i	−0.372270	−	0.512385i
$86$	−103.571	+	142.553i	−0.0140036	+	0.0192744i
$87$	5162.21			0.682021
$88$		−	439.236i		−	0.0567195i
$89$	−5884.05	+	8098.69i	−0.742841	+	1.02243i	0.255609	+	0.966780i	$0.417724\pi$
$89$	−5884.05	+	8098.69i	−0.742841	+	1.02243i	−0.998450	+	0.0556531i	$0.982276\pi$
$90$	−383.297	−	1179.67i	−0.0473206	−	0.145638i
$91$	1151.20	+	374.049i	0.139017	+	0.0451695i
$92$			92.6727i			0.0109490i
$93$	−6773.41	−	4091.44i	−0.783144	−	0.473054i
$94$	−1903.30			−0.215403
$95$	3124.68	−	9616.78i	0.346225	−	1.06557i
$96$	2640.29	−	857.882i	0.286490	−	0.0930862i
$97$	−5308.52	−	3856.86i	−0.564196	−	0.409912i	0.268796	−	0.963197i	$-0.413374\pi$
$97$	−5308.52	−	3856.86i	−0.564196	−	0.409912i	−0.832992	+	0.553285i	$0.813374\pi$
$98$	9951.08			1.03614
$99$		−	100.580i		−	0.0102622i
$100$	325.977	+	236.836i	0.0325977	+	0.0236836i
$101$	−6900.44	+	5013.47i	−0.676448	+	0.491468i	−0.872177	−	0.489190i	$-0.837293\pi$
$101$	−6900.44	+	5013.47i	−0.676448	+	0.491468i	0.195730	+	0.980658i	$0.437293\pi$
$102$	6051.29	−	4396.52i	0.581631	−	0.422579i
$103$	3799.54	−	11693.8i	0.358143	−	1.10225i	−0.596021	−	0.802969i	$-0.703253\pi$
$103$	3799.54	−	11693.8i	0.358143	−	1.10225i	0.954164	−	0.299283i	$-0.0967475\pi$
$104$	−4154.94	+	5718.78i	−0.384147	+	0.528733i
$105$	1681.59	+	546.380i	0.152525	+	0.0495583i
$106$	−10992.4	+	3571.66i	−0.978323	+	0.317876i
$107$	18219.3	−	13237.1i	1.59134	−	1.15618i	0.689350	−	0.724428i	$-0.257896\pi$
$107$	18219.3	−	13237.1i	1.59134	−	1.15618i	0.901993	−	0.431750i	$-0.142104\pi$
$108$	1962.30	−	637.590i	0.168236	−	0.0546631i
$109$	3510.00	+	10802.7i	0.295429	+	0.909238i	0.983077	+	0.183193i	$0.0586434\pi$
$109$	3510.00	+	10802.7i	0.295429	+	0.909238i	−0.687648	+	0.726045i	$0.741357\pi$
$110$	−421.151	−	579.665i	−0.0348059	−	0.0479062i
$111$	−4574.87	−	14080.0i	−0.371307	−	1.14276i
$112$	888.810	−	2735.48i	0.0708554	−	0.218071i
$113$	−18937.8	−	13759.1i	−1.48310	−	1.07754i	−0.976540	−	0.215337i	$-0.930915\pi$
$113$	−18937.8	−	13759.1i	−1.48310	−	1.07754i	−0.506565	−	0.862202i	$-0.669085\pi$
$114$	15719.7	+	5107.63i	1.20958	+	0.393015i
$115$	−445.598	−	613.314i	−0.0336936	−	0.0463753i
$116$	−980.224	−	1349.16i	−0.0728466	−	0.100265i
$117$	−951.431	+	1309.53i	−0.0695033	+	0.0956632i
$118$	2004.51			0.143961
$119$		−	2074.97i		−	0.146527i
$120$	−6069.19	+	8353.53i	−0.421472	+	0.580106i
$121$	4506.36	+	13869.2i	0.307791	+	0.947282i
$122$	−20385.5	−	6623.65i	−1.36963	−	0.445018i
$123$			16894.7i			1.11671i
$124$	216.853	+	2547.15i	0.0141033	+	0.165658i
$125$	−16896.6			−1.08138
$126$	173.809	−	534.928i	0.0109479	−	0.0336941i
$127$	−88.2818	+	28.6845i	−0.00547349	+	0.00177844i	−0.311752	−	0.950163i	$-0.600916\pi$
$127$	−88.2818	+	28.6845i	−0.00547349	+	0.00177844i	0.306279	+	0.951942i	$0.400916\pi$
$128$	15573.1	+	11314.5i	0.950507	+	0.690583i
$129$	335.886			0.0201842
$130$			11531.0i			0.682307i
$131$	13181.4	+	9576.84i	0.768102	+	0.558058i	0.901385	−	0.433020i	$-0.142552\pi$
$131$	13181.4	+	9576.84i	0.768102	+	0.558058i	−0.133283	+	0.991078i	$0.542552\pi$
$132$	135.075	−	98.1380i	0.00775226	−	0.00563235i
$133$	3709.52	−	2695.12i	0.209708	−	0.152361i
$134$	−8552.31	+	26321.3i	−0.476292	+	1.46588i
$135$	−9920.91	+	13655.0i	−0.544357	+	0.749243i
$136$	11524.4	+	3744.51i	0.623076	+	0.202450i
$137$	7503.47	−	2438.02i	0.399780	−	0.129896i	−0.102225	−	0.994761i	$-0.532596\pi$
$137$	7503.47	−	2438.02i	0.399780	−	0.129896i	0.502005	+	0.864865i	$0.332596\pi$
$138$	1002.53	−	728.378i	0.0526426	−	0.0382471i
$139$	20968.5	−	6813.07i	1.08527	−	0.352625i	0.288852	−	0.957374i	$-0.406727\pi$
$139$	20968.5	−	6813.07i	1.08527	−	0.352625i	0.796416	+	0.604749i	$0.206727\pi$
$140$	−176.508	−	543.237i	−0.00900553	−	0.0277162i
$141$	2132.54	+	2935.19i	0.107265	+	0.147638i
$142$	−7794.95	−	23990.4i	−0.386578	−	1.18976i
$143$	−288.940	+	889.265i	−0.0141298	+	0.0434870i
$144$	3111.70	+	2260.78i	0.150063	+	0.109027i
$145$	12974.4	+	4215.63i	0.617092	+	0.200505i
$146$	−22029.5	−	30321.0i	−1.03347	−	1.42245i
$147$	−11149.7	−	15346.2i	−0.515973	−	0.710175i
$148$	−2811.16	+	3869.23i	−0.128340	+	0.176645i
$149$	10548.6			0.475143			0.237571	−	0.971370i	$-0.423649\pi$
$149$	10548.6			0.475143			0.237571	+	0.971370i	$0.423649\pi$
$150$		−	5387.85i		−	0.239460i
$151$	12909.7	−	17768.7i	0.566190	−	0.779293i	−0.425907	−	0.904767i	$-0.640045\pi$
$151$	12909.7	−	17768.7i	0.566190	−	0.779293i	0.992097	+	0.125474i	$0.0400450\pi$
$152$	8274.50	+	25466.3i	0.358141	+	1.10225i
$153$	2638.96	+	857.449i	0.112733	+	0.0366290i
$154$		−	324.904i		−	0.0136998i
$155$	−13682.6	−	15814.5i	−0.569517	−	0.658253i
$156$	−2686.99			−0.110412
$157$	5698.06	−	17536.8i	0.231168	−	0.711462i	−0.766438	−	0.642318i	$-0.777973\pi$
$157$	5698.06	−	17536.8i	0.231168	−	0.711462i	0.997607	−	0.0691447i	$-0.0220270\pi$
$158$	−10061.9	+	3269.30i	−0.403055	+	0.130960i
$159$	17824.5	+	12950.3i	0.705056	+	0.512253i
$160$	7336.50			0.286582
$161$		−	343.765i		−	0.0132620i
$162$	−18585.2	−	13502.9i	−0.708170	−	0.514516i
$163$	19564.5	−	14214.4i	0.736365	−	0.535001i	−0.155206	−	0.987882i	$-0.549604\pi$
$163$	19564.5	−	14214.4i	0.736365	−	0.535001i	0.891571	+	0.452882i	$0.149604\pi$
$164$	4415.50	−	3208.05i	0.164169	−	0.119276i
$165$	−422.060	+	1298.97i	−0.0155027	+	0.0477123i
$166$	−18926.6	+	26050.3i	−0.686843	+	0.945358i
$167$	−47701.9	−	15499.3i	−1.71042	−	0.555750i	−0.720018	−	0.693956i	$-0.755866\pi$
$167$	−47701.9	−	15499.3i	−1.71042	−	0.555750i	−0.990403	+	0.138206i	$0.955866\pi$
$168$	−4453.02	+	1446.87i	−0.157774	+	0.0512640i
$169$	−10932.4	+	7942.87i	−0.382774	+	0.278102i
$170$	18799.2	−	6108.24i	0.650492	−	0.211358i
$171$	1894.76	+	5831.48i	0.0647982	+	0.199428i
$172$	−63.7795	−	87.7849i	−0.00215588	−	0.00296731i
$173$	−6254.36	−	19248.9i	−0.208973	−	0.643153i	−0.999527	−	0.0307604i	$-0.990207\pi$
$173$	−6254.36	−	19248.9i	−0.208973	−	0.643153i	0.790554	−	0.612393i	$-0.209793\pi$
$174$	−6890.89	+	21208.0i	−0.227603	+	0.700488i
$175$	−1209.19	−	878.531i	−0.0394839	−	0.0286867i
$176$	2113.06	+	686.575i	0.0682161	+	0.0221648i
$177$	−2245.95	−	3091.28i	−0.0716891	−	0.0986715i
$178$	−25417.5	−	34984.2i	−0.802220	−	1.10416i
$179$	−20558.6	+	28296.5i	−0.641634	+	0.883134i	−0.998701	−	0.0509448i	$-0.983777\pi$
$179$	−20558.6	+	28296.5i	−0.641634	+	0.883134i	0.357067	+	0.934079i	$0.383777\pi$
$180$	763.829			0.0235750
$181$			2349.68i			0.0717217i	0.999357	+	0.0358609i	$0.0114173\pi$
$181$			2349.68i			0.0717217i	−0.999357	+	0.0358609i	$0.988583\pi$
$182$	−3073.42	+	4230.20i	−0.0927852	+	0.127708i
$183$	12626.1	+	38859.2i	0.377023	+	1.16036i
$184$	1909.27	+	620.359i	0.0563938	+	0.0183235i
$185$		−	39123.7i		−	1.14313i
$186$	25850.5	−	22365.7i	0.747212	−	0.646483i
$187$	1602.85			0.0458362
$188$	362.186	−	1114.69i	0.0102475	−	0.0315384i
$189$	−7279.06	+	2365.11i	−0.203775	+	0.0662106i
$190$	35337.7	+	25674.3i	0.978884	+	0.711201i
$191$	−17984.5			−0.492983			−0.246491	−	0.969145i	$-0.579278\pi$
$191$	−17984.5			−0.492983			−0.246491	+	0.969145i	$0.579278\pi$
$192$		−	26410.8i		−	0.716440i
$193$	47711.5	+	34664.4i	1.28088	+	0.930614i	0.999579	−	0.0290056i	$-0.00923405\pi$
$193$	47711.5	+	34664.4i	1.28088	+	0.930614i	0.281301	+	0.959620i	$0.409234\pi$
$194$	22931.4	−	16660.6i	0.609294	−	0.442678i
$195$	17782.7	−	12919.9i	0.467657	−	0.339773i
$196$	−1893.63	+	5828.00i	−0.0492928	+	0.151708i
$197$	−8644.29	+	11897.8i	−0.222739	+	0.306574i	−0.905732	−	0.423851i	$-0.860678\pi$
$197$	−8644.29	+	11897.8i	−0.222739	+	0.306574i	0.682993	+	0.730425i	$0.260678\pi$
$198$	413.214	+	134.261i	0.0105401	+	0.00342468i
$199$	−43433.4	+	14112.4i	−1.09678	+	0.356364i	−0.800861	−	0.598850i	$-0.795625\pi$
$199$	−43433.4	+	14112.4i	−1.09678	+	0.356364i	−0.295915	+	0.955214i	$0.595625\pi$
$200$	7061.48	−	5130.47i	0.176537	−	0.128262i
$201$	50174.1	−	16302.6i	1.24190	−	0.403519i
$202$	−11385.7	−	35041.5i	−0.279033	−	0.858776i
$203$	3636.09	+	5004.65i	0.0882354	+	0.121446i
$204$	1423.36	+	4380.66i	0.0342023	+	0.105264i
$205$	−13796.8	+	42462.1i	−0.328299	+	1.01040i
$206$	42969.8	+	31219.4i	1.01258	+	0.735682i
$207$	437.200	+	142.055i	0.0102033	+	0.00331525i
$208$	−21017.1	−	28927.5i	−0.485786	−	0.668628i
$209$	2081.89	+	2865.47i	0.0476612	+	0.0656000i
$210$	−4489.40	+	6179.13i	−0.101800	+	0.140116i
$211$	−21363.6			−0.479855			−0.239927	−	0.970791i	$-0.577124\pi$
$211$	−21363.6			−0.479855			−0.239927	+	0.970791i	$0.577124\pi$
$212$		−	7117.55i		−	0.158365i
$213$	−28263.2	+	38901.0i	−0.622964	+	0.857436i
$214$	30061.7	+	92520.3i	0.656426	+	2.02027i
$215$	844.193	+	274.295i	0.0182627	+	0.00593391i
$216$		−	44696.0i		−	0.957990i
$217$	−804.405	−	9448.54i	−0.0170826	−	0.200653i
$218$	−49066.1			−1.03245
$219$	−22077.0	+	67946.1i	−0.460312	+	1.41669i
$220$	419.632	−	136.347i	0.00867008	−	0.00281708i
$221$	−20868.8	−	15162.1i	−0.427280	−	0.310437i
$222$	63951.9			1.29762
$223$			29387.0i			0.590944i	0.955351	+	0.295472i	$0.0954768\pi$
$223$			29387.0i			0.590944i	−0.955351	+	0.295472i	$0.904523\pi$
$224$	2691.43	+	1955.44i	0.0536398	+	0.0389716i
$225$	1617.00	−	1174.82i	0.0319407	−	0.0232063i
$226$	81806.1	−	59435.6i	1.60165	−	1.16367i
$227$	−2468.01	+	7595.77i	−0.0478956	+	0.147408i	−0.972144	−	0.234384i	$-0.924693\pi$
$227$	−2468.01	+	7595.77i	−0.0478956	+	0.147408i	0.924248	+	0.381791i	$0.124693\pi$
$228$	−5982.72	+	8234.51i	−0.115088	+	0.158405i
$229$	−69492.7	−	22579.5i	−1.32516	−	0.430570i	−0.440896	−	0.897558i	$-0.645339\pi$
$229$	−69492.7	−	22579.5i	−1.32516	−	0.430570i	−0.884264	+	0.466988i	$0.845339\pi$
$230$	3114.50	−	1011.96i	0.0588752	−	0.0191297i
$231$	−501.055	+	364.038i	−0.00938991	+	0.00682217i
$232$	−34357.5	+	11163.4i	−0.638331	+	0.207406i
$233$	5187.58	+	15965.7i	0.0955549	+	0.294088i	0.987398	−	0.158257i	$-0.0505875\pi$
$233$	5187.58	+	15965.7i	0.0955549	+	0.294088i	−0.891843	+	0.452345i	$0.850588\pi$
$234$	−4109.93	−	5656.84i	−0.0750590	−	0.103310i
$235$	2962.82	+	9118.62i	0.0536500	+	0.165118i
$236$	−381.447	+	1173.97i	−0.00684873	+	0.0210782i
$237$	16315.6	+	11854.0i	0.290473	+	0.211041i
$238$	8524.65	+	2769.83i	0.150495	+	0.0488988i
$239$	−46943.4	−	64612.0i	−0.821824	−	1.13114i	−0.989390	−	0.145282i	$-0.953591\pi$
$239$	−46943.4	−	64612.0i	−0.821824	−	1.13114i	0.167567	−	0.985861i	$-0.446409\pi$
$240$	−30700.0	−	42255.0i	−0.532987	−	0.733593i
$241$	−21965.8	+	30233.3i	−0.378192	+	0.520537i	−0.955104	−	0.296269i	$-0.904257\pi$
$241$	−21965.8	+	30233.3i	−0.378192	+	0.520537i	0.576912	+	0.816806i	$0.304257\pi$
$242$	−62994.3			−1.07565
$243$		−	19036.0i		−	0.322376i
$244$	7758.49	−	10678.6i	0.130316	−	0.179364i
$245$	−15490.6	−	47675.2i	−0.258069	−	0.794256i
$246$	−69408.8	−	22552.3i	−1.14695	−	0.372667i
$247$		−	57001.5i		−	0.934313i
$248$	53928.8	+	12583.2i	0.876835	+	0.204592i
$249$	61380.0			0.989985
$250$	22554.8	−	69416.4i	0.360876	−	1.11066i
$251$	96658.8	−	31406.3i	1.53424	−	0.498505i	0.584461	−	0.811422i	$-0.301306\pi$
$251$	96658.8	−	31406.3i	1.53424	−	0.498505i	0.949781	+	0.312916i	$0.101306\pi$
$252$	280.214	+	203.587i	0.00441254	+	0.00320590i
$253$	265.546			0.00414858
$254$		−	400.980i		−	0.00621520i
$255$	−30483.4	−	22147.5i	−0.468796	−	0.340600i
$256$	−25754.3	+	18711.6i	−0.392979	+	0.285516i
$257$	91744.3	−	66656.2i	1.38903	−	1.00919i	0.393064	−	0.919511i	$-0.371415\pi$
$257$	91744.3	−	66656.2i	1.38903	−	1.00919i	0.995970	−	0.0896816i	$-0.0285849\pi$
$258$	−448.364	+	1379.92i	−0.00673584	+	0.0207308i
$259$	10427.9	−	14352.7i	0.155452	−	0.213961i
$260$	−6753.30	−	2194.28i	−0.0999009	−	0.0324598i
$261$	−7867.47	+	2556.30i	−0.115493	+	0.0375258i
$262$	−56940.1	+	41369.4i	−0.829499	+	0.602666i
$263$	61000.9	−	19820.4i	0.881910	−	0.286550i	0.167160	−	0.985930i	$-0.446540\pi$
$263$	61000.9	−	19820.4i	0.881910	−	0.286550i	0.714750	+	0.699380i	$0.246540\pi$
$264$	−1117.66	−	3439.81i	−0.0160362	−	0.0493544i
$265$	34223.4	+	47104.4i	0.487339	+	0.670764i
$266$	6120.67	+	18837.5i	0.0865040	+	0.266232i
$267$	−25472.4	+	78395.9i	−0.357311	+	1.09969i
$268$	−13788.0	−	10017.6i	−0.191969	−	0.139474i
$269$	34948.0	+	11355.3i	0.482968	+	0.156926i	0.540374	−	0.841425i	$-0.318283\pi$
$269$	34948.0	+	11355.3i	0.482968	+	0.156926i	−0.0574059	+	0.998351i	$0.518283\pi$
$270$	−42855.7	−	58985.8i	−0.587870	−	0.809133i
$271$	62702.0	+	86302.0i	0.853774	+	1.17512i	0.983018	+	0.183507i	$0.0587449\pi$
$271$	62702.0	+	86302.0i	0.853774	+	1.17512i	−0.129244	+	0.991613i	$0.541255\pi$
$272$	−36027.9	+	49588.2i	−0.486969	+	0.670255i
$273$	9967.25			0.133737
$274$			34081.0i			0.453954i
$275$	678.635	−	934.061i	0.00897369	−	0.0123512i
$276$	235.811	+	725.751i	0.00309560	+	0.00952729i
$277$	−103458.	−	33615.6i	−1.34836	−	0.438108i	−0.456218	−	0.889868i	$-0.650796\pi$
$277$	−103458.	−	33615.6i	−1.34836	−	0.438108i	−0.892139	+	0.451760i	$0.850796\pi$
$278$			95239.6i			1.23233i
$279$	12349.1	+	2881.41i	0.158645	+	0.0370166i
$280$	−12373.5			−0.157825
$281$	17.1902	−	52.9060i	0.000217705	−	0.000670027i	−0.950948	−	0.309352i	$-0.899888\pi$
$281$	17.1902	−	52.9060i	0.000217705	−	0.000670027i	0.951165	+	0.308682i	$0.0998879\pi$
$282$	−14905.4	+	4843.05i	−0.187432	+	0.0609004i
$283$	6306.61	+	4582.02i	0.0787450	+	0.0572116i	0.626461	−	0.779453i	$-0.284503\pi$
$283$	6306.61	+	4582.02i	0.0787450	+	0.0572116i	−0.547716	+	0.836664i	$0.684503\pi$
$284$	15533.7			0.192592
$285$		−	83263.2i		−	1.02509i
$286$	−3267.68	−	2374.11i	−0.0399492	−	0.0290248i
$287$	−16379.1	+	11900.1i	−0.198850	+	0.144473i
$288$	−3599.12	+	2614.91i	−0.0433921	+	0.0315262i
$289$	12145.1	−	37378.7i	0.145413	−	0.447536i
$290$	−34638.2	+	47675.4i	−0.411870	+	0.566890i
$291$	−51386.8	−	16696.6i	−0.606828	−	0.197170i
$292$	21950.0	−	7131.99i	0.257436	−	0.0836460i
$293$	−11795.6	+	8569.98i	−0.137399	+	0.0998262i	−0.654362	−	0.756182i	$-0.727063\pi$
$293$	−11795.6	+	8569.98i	−0.137399	+	0.0998262i	0.516963	+	0.856008i	$0.327063\pi$
$294$	77930.2	−	25321.1i	0.901595	−	0.292946i
$295$	−3120.38	−	9603.53i	−0.0358561	−	0.110354i
$296$	60896.8	+	83817.3i	0.695043	+	0.956644i
$297$	−1826.97	−	5622.82i	−0.0207118	−	0.0637443i
$298$	−14081.1	+	43337.1i	−0.158564	+	0.488008i
$299$	−3457.37	−	2511.92i	−0.0386726	−	0.0280973i
$300$	3155.48	+	1025.28i	0.0350609	+	0.0113920i
$301$	236.587	+	325.634i	0.00261130	+	0.00359415i
$302$	55766.5	+	76755.9i	0.611447	+	0.841585i
$303$	−41282.7	+	56820.7i	−0.449658	+	0.618901i
$304$	−135446.			−1.46562
$305$			107977.i			1.16073i
$306$	−7045.33	+	9697.07i	−0.0752417	+	0.103561i
$307$	−9080.33	−	27946.4i	−0.0963440	−	0.296516i	0.891258	−	0.453497i	$-0.149824\pi$
$307$	−9080.33	−	27946.4i	−0.0963440	−	0.296516i	−0.987602	+	0.156981i	$0.949824\pi$
$308$	190.285	+	61.8274i	0.00200587	+	0.000651748i
$309$		−	101246.i		−	1.06038i
$310$	83235.6	−	35102.2i	0.866135	−	0.365267i
$311$	−31421.9			−0.324871			−0.162436	−	0.986719i	$-0.551935\pi$
$311$	−31421.9			−0.324871			−0.162436	+	0.986719i	$0.551935\pi$
$312$	−17986.9	+	55358.1i	−0.184777	+	0.568686i
$313$	113219.	−	36786.9i	1.15566	−	0.375496i	0.332385	−	0.943144i	$-0.392147\pi$
$313$	113219.	−	36786.9i	1.15566	−	0.375496i	0.823271	+	0.567648i	$0.192147\pi$
$314$	64440.6	+	46818.9i	0.653583	+	0.474856i
$315$	−2833.38			−0.0285551
$316$		−	6515.01i		−	0.0652440i
$317$	25676.2	+	18654.8i	0.255512	+	0.185641i	0.708166	−	0.706046i	$-0.249523\pi$
$317$	25676.2	+	18654.8i	0.255512	+	0.185641i	−0.452654	+	0.891686i	$0.649523\pi$
$318$	−76997.2	+	55941.7i	−0.761414	+	0.553199i
$319$	−3865.92	+	2808.76i	−0.0379902	+	0.0276015i
$320$	21567.9	−	66379.2i	0.210624	−	0.648235i
$321$	108999.	−	150024.i	1.05782	−	1.45597i
$322$	1412.29	+	458.882i	0.0136211	+	0.00442577i
$323$	−92930.8	+	30195.1i	−0.890748	+	0.289421i
$324$	11444.9	−	8315.18i	0.109024	−	0.0792103i
$325$	−17671.4	+	5741.80i	−0.167303	+	0.0543602i
$326$	32281.2	+	99351.5i	0.303749	+	0.934844i
$327$	54975.9	+	75667.9i	0.514135	+	0.707646i
$328$	−36535.4	−	112444.i	−0.339598	−	1.04518i
$329$	−1343.51	+	4134.90i	−0.0124122	+	0.0382009i
$330$	−4773.17	−	3467.91i	−0.0438307	−	0.0318449i
$331$	−158087.	−	51365.7i	−1.44292	−	0.468832i	−0.520111	−	0.854099i	$-0.674109\pi$
$331$	−158087.	−	51365.7i	−1.44292	−	0.468832i	−0.922805	+	0.385267i	$0.874109\pi$
$332$	−11655.1	−	16041.9i	−0.105740	−	0.145539i
$333$	13944.7	+	19193.2i	0.125753	+	0.173085i
$334$	127352.	−	175285.i	1.14160	−	1.57127i
$335$	139417.			1.24230
$336$		−	23684.1i		−	0.209787i
$337$	18546.4	−	25527.0i	0.163305	−	0.224770i	−0.719520	−	0.694471i	$-0.755638\pi$
$337$	18546.4	−	25527.0i	0.163305	−	0.224770i	0.882826	+	0.469701i	$0.155638\pi$
$338$	−18038.4	−	55516.5i	−0.157894	−	0.485947i
$339$	−183319.	−	59563.9i	−1.59517	−	0.518303i
$340$			12172.4i			0.105298i
$341$	7298.67	−	621.375i	0.0627676	−	0.00534374i
$342$	−26486.8			−0.226453
$343$	14345.6	−	44151.1i	0.121935	−	0.375278i
$344$	−2235.52	+	726.363i	−0.0188913	+	0.00613814i
$345$	−5050.24	−	3669.22i	−0.0424301	−	0.0308273i
$346$	87429.4			0.730307
$347$		−	160490.i		−	1.33287i	−0.745562	−	0.666436i	$-0.767819\pi$
$347$		−	160490.i		−	1.33287i	0.745562	−	0.666436i	$-0.232181\pi$
$348$	−11109.5	−	8071.51i	−0.0917351	−	0.0666494i
$349$	−26611.1	+	19334.1i	−0.218480	+	0.158735i	−0.691642	−	0.722240i	$-0.743113\pi$
$349$	−26611.1	+	19334.1i	−0.218480	+	0.158735i	0.473162	+	0.880975i	$0.343113\pi$
$350$	5223.40	−	3795.02i	0.0426400	−	0.0309798i
$351$	−29402.1	+	90490.3i	−0.238651	+	0.734493i
$352$	−1510.51	+	2079.04i	−0.0121910	+	0.0167794i
$353$	7409.14	+	2407.38i	0.0594591	+	0.0193194i	0.338596	−	0.940932i	$-0.390048\pi$
$353$	7409.14	+	2407.38i	0.0594591	+	0.0193194i	−0.279136	+	0.960251i	$0.590048\pi$
$354$	15698.0	−	5100.59i	0.125267	−	0.0407018i
$355$	−102803.	+	74690.6i	−0.815733	+	0.592665i
$356$	25325.8	−	8228.86i	0.199831	−	0.0649292i
$357$	−5279.89	−	16249.8i	−0.0414275	−	0.127501i
$358$	−88807.7	−	122233.i	−0.692923	−	0.953726i
$359$	−18809.6	−	57889.9i	−0.145945	−	0.449174i	0.851186	−	0.524864i	$-0.175884\pi$
$359$	−18809.6	−	57889.9i	−0.145945	−	0.449174i	−0.997131	+	0.0756905i	$0.975884\pi$
$360$	5113.14	−	15736.6i	0.0394532	−	0.121425i
$361$	−69254.0	−	50316.0i	−0.531411	−	0.386093i
$362$	−9653.20	−	3136.52i	−0.0736638	−	0.0239348i
$363$	70581.7	+	97147.4i	0.535647	+	0.737255i
$364$	−1892.63	−	2604.98i	−0.0142844	−	0.0196608i
$365$	−110974.	+	152742.i	−0.832980	+	1.14650i
$366$	−176500.			−1.31760
$367$			114347.i			0.848973i	0.905434	+	0.424487i	$0.139545\pi$
$367$			114347.i			0.848973i	−0.905434	+	0.424487i	$0.860455\pi$
$368$	−5968.80	+	8215.35i	−0.0440749	+	0.0606639i
$369$	−8366.17	−	25748.4i	−0.0614432	−	0.189103i
$370$	160732.	+	52225.2i	1.17409	+	0.381484i
$371$			26402.2i			0.191819i
$372$	8179.62	+	19395.8i	0.0591082	+	0.140160i
$373$	72495.9			0.521070			0.260535	−	0.965464i	$-0.416101\pi$
$373$	72495.9			0.521070			0.260535	+	0.965464i	$0.416101\pi$
$374$	−2139.59	+	6585.00i	−0.0152964	+	0.0470774i
$375$	−132323.	+	42994.3i	−0.940962	+	0.305737i
$376$	−20540.8	−	14923.7i	−0.145292	−	0.105561i
$377$	76902.9			0.541078
$378$		−	33061.8i		−	0.231389i
$379$	171947.	+	124927.i	1.19706	+	0.869718i	0.993993	−	0.109446i	$-0.0349077\pi$
$379$	171947.	+	124927.i	1.19706	+	0.869718i	0.203071	+	0.979164i	$0.434908\pi$
$380$	−21761.1	+	15810.4i	−0.150700	+	0.109490i
$381$	−618.376	+	449.276i	−0.00425993	+	0.00309502i
$382$	24007.0	−	73886.0i	0.164517	−	0.506332i
$383$	57091.8	−	78580.1i	0.389203	−	0.535692i	−0.568790	−	0.822482i	$-0.692588\pi$
$383$	57091.8	−	78580.1i	0.389203	−	0.535692i	0.957993	+	0.286791i	$0.0925885\pi$
$384$	150749.	+	48981.2i	1.02233	+	0.332175i
$385$	−1556.60	+	505.771i	−0.0105016	+	0.00341219i
$386$	−206101.	+	149741.i	−1.38327	+	1.00500i
$387$	−511.907	+	166.329i	−0.00341798	+	0.00111057i
$388$	5393.84	+	16600.5i	0.0358290	+	0.110270i
$389$	−117639.	−	161916.i	−0.777415	−	1.07002i	−0.995562	−	0.0941040i	$-0.970001\pi$
$389$	−117639.	−	161916.i	−0.777415	−	1.07002i	0.218147	−	0.975916i	$-0.429999\pi$
$390$	29341.3	+	90303.1i	0.192908	+	0.593709i
$391$	−2263.80	+	6967.25i	−0.0148076	+	0.0455730i
$392$	107394.	+	78026.3i	0.698888	+	0.507772i
$393$	127597.	+	41458.7i	0.826141	+	0.268430i
$394$	−37341.0	−	51395.5i	−0.240544	−	0.331080i
$395$	31326.1	+	43116.7i	0.200776	+	0.276345i
$396$	−157.264	+	216.456i	−0.00100286	+	0.00138032i
$397$	76599.9			0.486012			0.243006	−	0.970025i	$-0.421867\pi$
$397$	76599.9			0.486012			0.243006	+	0.970025i	$0.421867\pi$
$398$		−	197276.i		−	1.24540i
$399$	22192.6	−	30545.5i	0.139400	−	0.191867i
$400$	13643.6	+	41990.6i	0.0852724	+	0.262441i
$401$	118169.	+	38395.5i	0.734879	+	0.238777i	0.652462	−	0.757821i	$-0.273736\pi$
$401$	118169.	+	38395.5i	0.734879	+	0.238777i	0.0824167	+	0.996598i	$0.473736\pi$
$402$			227893.i			1.41019i
$403$	−100905.	−	60951.3i	−0.621304	−	0.375295i
$404$	22689.2			0.139013
$405$	−35760.9	+	110061.i	−0.218021	+	0.671000i
$406$	−25414.4	+	8257.63i	−0.154180	+	0.0500960i
$407$	11087.0	+	8055.16i	0.0669306	+	0.0486279i
$408$	99779.7			0.599407
$409$			221022.i			1.32126i	0.750711	+	0.660631i	$0.229711\pi$
$409$			221022.i			1.32126i	−0.750711	+	0.660631i	$0.770289\pi$
$410$	−156031.	−	113363.i	−0.928201	−	0.674378i
$411$	52558.5	−	38186.0i	0.311142	−	0.226058i
$412$	−26461.0	+	19225.1i	−0.155888	+	0.113259i
$413$	1414.96	−	4354.79i	0.00829551	−	0.0255310i
$414$	−1167.21	+	1606.53i	−0.00681003	+	0.00937321i
$415$	154269.	+	50124.9i	0.895738	+	0.291043i
$416$	39333.1	−	12780.1i	0.227285	−	0.0738495i
$417$	146875.	−	106711.i	0.844647	−	0.613672i
$418$	−14551.3	+	4728.01i	−0.0832817	+	0.0270599i
$419$	−34808.0	−	107128.i	−0.198267	−	0.610203i	−0.999923	−	0.0124173i	$-0.996047\pi$
$419$	−34808.0	−	107128.i	−0.198267	−	0.610203i	0.801656	−	0.597786i	$-0.203953\pi$
$420$	−2764.59	−	3805.14i	−0.0156723	−	0.0215711i
$421$	−7766.45	−	23902.7i	−0.0438186	−	0.134860i	0.926754	−	0.375669i	$-0.122587\pi$
$421$	−7766.45	−	23902.7i	−0.0438186	−	0.134860i	−0.970572	+	0.240809i	$0.922587\pi$
$422$	28517.7	−	87768.4i	0.160136	−	0.492848i
$423$	−4703.59	−	3417.36i	−0.0262875	−	0.0190990i
$424$	−146638.	−	47645.5i	−0.815670	−	0.265027i
$425$	18721.9	+	25768.5i	0.103651	+	0.142663i
$426$	−122090.	−	168042.i	−0.672760	−	0.925974i
$427$	−28779.7	+	39611.9i	−0.157845	+	0.217255i
$428$	−59906.5			−0.327029
$429$			7699.36i			0.0418350i
$430$	−2253.78	+	3102.06i	−0.0121892	+	0.0167770i
$431$	−2859.47	−	8800.53i	−0.0153933	−	0.0473756i	0.943065	−	0.332609i	$-0.107929\pi$
$431$	−2859.47	−	8800.53i	−0.0153933	−	0.0473756i	−0.958458	+	0.285233i	$0.907929\pi$
$432$	215022.	+	69864.9i	1.15217	+	0.374362i
$433$			5059.03i			0.0269831i	0.999909	+	0.0134915i	$0.00429462\pi$
$433$			5059.03i			0.0269831i	−0.999909	+	0.0134915i	$0.995705\pi$
$434$	39891.3	+	9307.84i	0.211787	+	0.0494162i
$435$	112334.			0.593651
$436$	9336.99	−	28736.3i	0.0491172	−	0.151167i
$437$	−15396.0	+	5002.46i	−0.0806204	+	0.0261952i
$438$	−249674.	−	181399.i	−1.30144	−	0.945553i
$439$	−276569.			−1.43508			−0.717538	−	0.696519i	$-0.754731\pi$
$439$	−276569.			−1.43508			−0.717538	+	0.696519i	$0.754731\pi$
$440$		−	9558.10i		−	0.0493703i
$441$	24592.0	+	17867.1i	0.126449	+	0.0918707i
$442$	90147.6	−	65496.1i	0.461434	−	0.335252i
$443$	−216098.	+	157005.i	−1.10114	+	0.800027i	−0.981246	−	0.192759i	$-0.938256\pi$
$443$	−216098.	+	157005.i	−1.10114	+	0.800027i	−0.119897	+	0.992786i	$0.538256\pi$
$444$	−12169.7	+	37454.4i	−0.0617324	+	0.189993i
$445$	−128041.	+	176233.i	−0.646591	+	0.889956i
$446$	−120731.	−	39227.9i	−0.606945	−	0.197208i
$447$	82609.9	−	26841.6i	0.413445	−	0.134336i
$448$	25604.7	−	18602.9i	0.127574	−	0.0926883i
$449$	−325793.	+	105857.i	−1.61603	+	0.525080i	−0.971000	−	0.239078i	$-0.923155\pi$
$449$	−325793.	+	105857.i	−1.61603	+	0.525080i	−0.645029	+	0.764158i	$0.723155\pi$
$450$	2668.03	+	8211.36i	0.0131755	+	0.0405499i
$451$	−9192.41	−	12652.3i	−0.0451935	−	0.0622035i
$452$	19242.1	+	59221.2i	0.0941839	+	0.289868i
$453$	55886.8	−	172002.i	0.272341	−	0.838179i
$454$	−27911.3	−	20278.8i	−0.135416	−	0.0983851i
$455$	25051.0	+	8139.57i	0.121005	+	0.0393169i
$456$	129601.	+	178380.i	0.623273	+	0.857861i
$457$	93717.8	+	128991.i	0.448735	+	0.617630i	0.972125	−	0.234463i	$-0.0753331\pi$
$457$	93717.8	+	128991.i	0.448735	+	0.617630i	−0.523391	+	0.852093i	$0.675333\pi$
$458$	185528.	−	255357.i	0.884459	−	1.21735i
$459$	163103.			0.774172
$460$			2016.62i			0.00953036i
$461$	−110150.	+	151608.i	−0.518300	+	0.713379i	−0.985291	−	0.170883i	$-0.945338\pi$
$461$	−110150.	+	151608.i	−0.518300	+	0.713379i	0.466991	+	0.884262i	$0.345338\pi$
$462$	−826.737	−	2544.44i	−0.00387332	−	0.0119209i
$463$	−76633.9	−	24899.9i	−0.357486	−	0.116154i	0.124767	−	0.992186i	$-0.460182\pi$
$463$	−76633.9	−	24899.9i	−0.357486	−	0.116154i	−0.482253	+	0.876032i	$0.660182\pi$
$464$		−	182736.i		−	0.848765i
$465$	−147394.	−	89032.7i	−0.681671	−	0.411760i
$466$	−72517.0			−0.333940
$467$	63875.8	−	196589.i	0.292889	−	0.901418i	−0.691034	−	0.722822i	$-0.742845\pi$
$467$	63875.8	−	196589.i	0.292889	−	0.901418i	0.983923	−	0.178596i	$-0.0571555\pi$
$468$	4095.11	−	1330.58i	0.0186971	−	0.00607505i
$469$	51145.9	+	37159.7i	0.232523	+	0.168938i
$470$	−41417.1			−0.187493
$471$		−	151836.i		−	0.684436i
$472$	21633.1	+	15717.3i	0.0971033	+	0.0705497i
$473$	−251.541	+	182.755i	−0.00112431	+	0.000816859i
$474$	−70478.9	+	51205.9i	−0.313691	+	0.227910i
$475$	−21750.1	+	66940.0i	−0.0963994	+	0.296687i
$476$	−3244.38	+	4465.51i	−0.0143192	+	0.0197086i
$477$	−33578.3	−	10910.3i	−0.147578	−	0.0479511i
$478$	328110.	−	106609.i	1.43603	−	0.466594i
$479$	295770.	−	214889.i	1.28909	−	0.936577i	0.289301	−	0.957238i	$-0.406577\pi$
$479$	295770.	−	214889.i	1.28909	−	0.936577i	0.999787	+	0.0206611i	$0.00657710\pi$
$480$	57454.6	−	18668.1i	0.249369	−	0.0810249i
$481$	−68153.1	−	209754.i	−0.294575	−	0.906607i
$482$	−94886.3	−	130600.i	−0.408422	−	0.562145i
$483$	−874.728	−	2692.14i	−0.00374955	−	0.0115399i
$484$	11987.4	−	36893.5i	0.0511724	−	0.157492i
$485$	−115517.	−	83928.1i	−0.491092	−	0.356799i
$486$	78205.7	+	25410.6i	0.331105	+	0.107583i
$487$	214805.	+	295654.i	0.905704	+	1.24659i	0.968613	+	0.248576i	$0.0799624\pi$
$487$	214805.	+	295654.i	0.905704	+	1.24659i	−0.0629083	+	0.998019i	$0.520038\pi$
$488$	−168068.	−	231326.i	−0.705743	−	0.971372i
$489$	117047.	−	161101.i	0.489487	−	0.673721i
$490$	216543.			0.901885
$491$		−	80671.5i		−	0.334624i	−0.985904	−	0.167312i	$-0.946491\pi$
$491$		−	80671.5i		−	0.334624i	0.985904	−	0.167312i	$-0.0535088\pi$
$492$	26416.2	−	36358.8i	0.109129	−	0.150203i
$493$	−40737.3	−	125376.i	−0.167609	−	0.515849i
$494$	234180.	+	76089.7i	0.959613	+	0.311797i
$495$		−	2188.69i		−	0.00893252i
$496$	−144832.	+	239770.i	−0.588709	+	0.974612i
$497$	−57621.3			−0.233276
$498$	−81934.5	+	252168.i	−0.330376	+	1.01679i
$499$	111277.	−	36156.2i	0.446896	−	0.145205i	−0.0769192	−	0.997037i	$-0.524508\pi$
$499$	111277.	−	36156.2i	0.446896	−	0.145205i	0.523815	+	0.851832i	$0.324508\pi$
$500$	36362.7	+	26419.1i	0.145451	+	0.105676i
$501$	−413009.			−1.64545
$502$			439028.i			1.74215i
$503$	78169.1	+	56793.2i	0.308958	+	0.224471i	0.731449	−	0.681896i	$-0.238844\pi$
$503$	78169.1	+	56793.2i	0.308958	+	0.224471i	−0.422491	+	0.906367i	$0.638844\pi$
$504$	6070.14	−	4410.22i	0.0238967	−	0.0173620i
$505$	−150159.	+	109097.i	−0.588800	+	0.427788i
$506$	−354.470	+	1090.95i	−0.00138445	+	0.00426091i
$507$	−65404.4	+	90021.4i	−0.254443	+	0.350211i
$508$	234.840	+	76.3041i	0.000910006	+	0.000295679i
$509$	−351923.	+	114347.i	−1.35835	+	0.441356i	−0.895493	−	0.445076i	$-0.853177\pi$
$509$	−351923.	+	114347.i	−1.35835	+	0.441356i	−0.462860	+	0.886431i	$0.653177\pi$
$510$	131680.	−	95671.4i	0.506268	−	0.367825i
$511$	−81422.5	+	26455.8i	−0.311819	+	0.101316i
$512$	52680.0	+	162132.i	0.200958	+	0.618486i
$513$	211850.	+	291586.i	0.804995	+	1.10798i
$514$	151377.	+	465892.i	0.572974	+	1.76343i
$515$	82680.8	−	254465.i	0.311738	−	0.959432i
$516$	−722.852	−	525.183i	−0.00271488	−	0.00197247i
$517$	−3194.07	−	1037.82i	−0.0119499	−	0.00388275i
$518$	45045.6	+	61999.9i	0.167878	+	0.231064i
$519$	−97960.0	−	134830.i	−0.363675	−	0.500556i
$520$	−90414.4	+	124445.i	−0.334373	+	0.460225i
$521$	324397.			1.19509			0.597547	−	0.801834i	$-0.296142\pi$
$521$	324397.			1.19509			0.597547	+	0.801834i	$0.296142\pi$
$522$		−	35734.4i		−	0.131143i
$523$	488.749	−	672.706i	0.00178683	−	0.00245936i	−0.808123	−	0.589014i	$-0.799516\pi$
$523$	488.749	−	672.706i	0.00178683	−	0.00245936i	0.809909	+	0.586555i	$0.199516\pi$
$524$	−13393.3	−	41220.2i	−0.0487779	−	0.150123i
$525$	−11705.1	−	3803.21i	−0.0424674	−	0.0137985i
$526$			277068.i			1.00142i
$527$	−45918.3	+	196795.i	−0.165335	+	0.708588i
$528$	18295.1			0.0656247
$529$	86100.6	−	264990.i	0.307677	−	0.946932i
$530$	−239203.	+	77721.9i	−0.851561	+	0.276689i
$531$	4953.72	+	3599.09i	0.0175688	+	0.0127645i
$532$	−12197.2			−0.0430960
$533$			251685.i			0.885939i
$534$	−288072.	−	209297.i	−1.01023	−	0.733973i
$535$	396465.	−	288049.i	1.38515	−	1.00637i
$536$	−298683.	+	217006.i	−1.03964	+	0.755339i
$537$	−88999.4	+	273912.i	−0.308630	+	0.949866i
$538$	−93302.3	+	128420.i	−0.322350	+	0.443677i
$539$	16699.7	+	5426.05i	0.0574818	+	0.0186770i
$540$	42701.1	−	13874.4i	0.146437	−	0.0475803i
$541$	449804.	−	326801.i	1.53684	−	1.11658i	0.584559	−	0.811351i	$-0.301267\pi$
$541$	449804.	−	326801.i	1.53684	−	1.11658i	0.952279	−	0.305228i	$-0.0987326\pi$
$542$	−438255.	+	142398.i	−1.49186	+	0.484734i
$543$	5978.88	+	18401.1i	0.0202778	+	0.0624086i
$544$	−41671.4	−	57355.7i	−0.140812	−	0.193811i
$545$	76380.1	+	235074.i	0.257150	+	0.791427i
$546$	−13305.0	+	40948.6i	−0.0446303	+	0.137358i
$547$	−159094.	−	115588.i	−0.531714	−	0.386313i	0.289284	−	0.957243i	$-0.406583\pi$
$547$	−159094.	−	115588.i	−0.531714	−	0.386313i	−0.820999	+	0.570930i	$0.806583\pi$
$548$	−19960.1	−	6485.42i	−0.0664662	−	0.0215962i
$549$	−38485.7	−	52971.0i	−0.127689	−	0.175749i
$550$	2931.53	+	4034.90i	0.00969099	+	0.0133385i
$551$	171228.	−	235675.i	0.563991	−	0.776267i
$552$	16530.7			0.0542516
$553$			24167.1i			0.0790268i
$554$	276207.	−	380166.i	0.899942	−	1.23866i
$555$	−99552.5	−	306391.i	−0.323196	−	0.994696i
$556$	−55778.5	−	18123.5i	−0.180433	−	0.0586264i
$557$			32389.1i			0.104397i	0.998637	+	0.0521986i	$0.0166229\pi$
$557$			32389.1i			0.104397i	−0.998637	+	0.0521986i	$0.983377\pi$
$558$	−28322.2	+	46887.5i	−0.0909616	+	0.150588i
$559$	5003.78			0.0160131
$560$	19341.2	−	59526.0i	0.0616746	−	0.189815i
$561$	12552.4	−	4078.53i	0.0398843	−	0.0129592i
$562$	194.408	+	141.246i	0.000615518	+	0.000447200i
$563$	−222431.			−0.701743			−0.350872	−	0.936424i	$-0.614115\pi$
$563$	−222431.			−0.701743			−0.350872	+	0.936424i	$0.614115\pi$
$564$		−	9651.15i		−	0.0303404i
$565$	−412099.	−	299408.i	−1.29094	−	0.937921i
$566$	−27242.9	+	19793.1i	−0.0850394	+	0.0617847i
$567$	−42454.1	+	30844.7i	−0.132055	+	0.0959434i
$568$	103984.	−	320029.i	0.322306	−	0.991957i
$569$	93449.2	−	128622.i	0.288637	−	0.397274i	−0.639934	−	0.768430i	$-0.721038\pi$
$569$	93449.2	−	128622.i	0.288637	−	0.397274i	0.928571	+	0.371156i	$0.121038\pi$
$570$	342071.	+	111146.i	1.05285	+	0.342092i
$571$	443406.	−	144071.i	1.35997	−	0.441881i	0.463938	−	0.885868i	$-0.346436\pi$
$571$	443406.	−	144071.i	1.35997	−	0.441881i	0.896034	+	0.443986i	$0.146436\pi$
$572$	2012.25	−	1461.99i	0.00615022	−	0.00446840i
$573$	−140843.	+	45762.6i	−0.428968	+	0.139380i
$574$	−27025.3	−	83175.4i	−0.0820252	−	0.252447i
$575$	3101.70	+	4269.12i	0.00938131	+	0.0129123i
$576$	13078.5	+	40251.4i	0.0394196	+	0.121321i
$577$	106404.	−	327478.i	0.319599	−	0.983626i	−0.654220	−	0.756304i	$-0.727003\pi$
$577$	106404.	−	327478.i	0.319599	−	0.983626i	0.973820	−	0.227322i	$-0.0729969\pi$
$578$	137351.	+	99791.4i	0.411127	+	0.298702i
$579$	461851.	+	150064.i	1.37767	+	0.447631i
$580$	−21330.4	−	29358.8i	−0.0634078	−	0.0872733i
$581$	43234.0	+	59506.6i	0.128078	+	0.176284i
$582$	137190.	−	188825.i	0.405019	−	0.557460i
$583$	−20394.8			−0.0600043
$584$		−	499963.i		−	1.46593i
$585$	−20703.8	+	28496.4i	−0.0604977	+	0.0832680i
$586$	−19462.6	−	59899.7i	−0.0566768	−	0.174433i
$587$	304710.	+	99006.4i	0.884323	+	0.287334i	0.715751	−	0.698355i	$-0.246085\pi$
$587$	304710.	+	99006.4i	0.884323	+	0.287334i	0.168572	+	0.985689i	$0.446085\pi$
$588$			50459.5i			0.145945i
$589$	−411461.	+	173522.i	−1.18604	+	0.500176i
$590$	43619.6			0.125308
$591$	−37421.6	+	115172.i	−0.107139	+	0.329740i
$592$	−498414.	+	161945.i	−1.42215	+	0.462086i
$593$	−293094.	−	212946.i	−0.833485	−	0.605563i	0.0870578	−	0.996203i	$-0.472254\pi$
$593$	−293094.	−	212946.i	−0.833485	−	0.605563i	−0.920543	+	0.390641i	$0.872254\pi$
$594$	25539.1			0.0723823
$595$		−	45153.0i		−	0.127542i
$596$	−22701.5	−	16493.6i	−0.0639090	−	0.0464326i
$597$	−304232.	+	221038.i	−0.853604	+	0.620180i
$598$	14934.9	−	10850.8i	0.0417638	−	0.0303432i
$599$	−32671.7	+	100553.i	−0.0910580	+	0.280248i	−0.986206	−	0.165521i	$-0.947070\pi$
$599$	−32671.7	+	100553.i	−0.0910580	+	0.280248i	0.895148	+	0.445768i	$0.147070\pi$
$600$	42246.1	−	58146.8i	0.117350	−	0.161519i
$601$	277549.	+	90181.2i	0.768406	+	0.249670i	0.666883	−	0.745163i	$-0.267628\pi$
$601$	277549.	+	90181.2i	0.768406	+	0.249670i	0.101524	+	0.994833i	$0.467628\pi$
$602$	−1653.62	+	537.293i	−0.00456291	+	0.00148258i
$603$	−68394.9	+	49691.8i	−0.188100	+	0.136663i
$604$	−55565.3	+	18054.3i	−0.152310	+	0.0494887i
$605$	98061.7	+	301803.i	0.267910	+	0.824542i
$606$	−178330.	−	245450.i	−0.485601	−	0.668372i
$607$	−135841.	−	418077.i	−0.368684	−	1.13469i	−0.947642	−	0.319336i	$-0.896540\pi$
$607$	−135841.	−	418077.i	−0.368684	−	1.13469i	0.578958	−	0.815358i	$-0.303460\pi$
$608$	48411.5	−	148995.i	0.130961	−	0.403056i
$609$	41210.1	+	29940.9i	0.111114	+	0.0807290i
$610$	−443603.	−	144136.i	−1.19216	−	0.387357i
$611$	31769.1	+	43726.4i	0.0850985	+	0.117128i
$612$	−4338.55	−	5971.50i	−0.0115836	−	0.0159434i
$613$	78509.9	−	108060.i	0.208931	−	0.287569i	−0.691672	−	0.722212i	$-0.743125\pi$
$613$	78509.9	−	108060.i	0.208931	−	0.287569i	0.900603	+	0.434643i	$0.143125\pi$
$614$	126933.			0.336697
$615$			367642.i			0.972018i
$616$	2547.57	−	3506.43i	0.00671375	−	0.00924068i
$617$	140511.	+	432447.i	0.369096	+	1.13596i	0.947376	+	0.320122i	$0.103724\pi$
$617$	140511.	+	432447.i	0.369096	+	1.13596i	−0.578281	+	0.815838i	$0.696276\pi$
$618$	415951.	+	135151.i	1.08909	+	0.353868i
$619$		−	135231.i		−	0.352934i	−0.984307	−	0.176467i	$-0.943533\pi$
$619$		−	135231.i		−	0.352934i	0.984307	−	0.176467i	$-0.0564669\pi$
$620$	4718.88	+	55427.9i	0.0122760	+	0.144193i
$621$	27021.6			0.0700693
$622$	41944.2	−	129091.i	0.108415	−	0.333668i
$623$	−93944.9	+	30524.6i	−0.242046	+	0.0786454i
$624$	−238199.	−	173062.i	−0.611746	−	0.444460i
$625$	−273012.			−0.698912
$626$			514243.i			1.31226i
$627$	23595.3	+	17143.0i	0.0600193	+	0.0436066i
$628$	−39682.8	+	28831.3i	−0.100620	+	0.0731046i
$629$	−305864.	+	222223.i	−0.773084	+	0.561678i
$630$	3782.20	−	11640.4i	0.00952936	−	0.0293284i
$631$	170906.	−	235232.i	0.429238	−	0.590796i	−0.538540	−	0.842600i	$-0.681024\pi$
$631$	170906.	−	235232.i	0.429238	−	0.590796i	0.967778	+	0.251804i	$0.0810239\pi$
$632$	−134224.	−	43612.1i	−0.336044	−	0.109187i
$633$	−167306.	+	54360.9i	−0.417545	+	0.135669i
$634$	−110914.	+	80584.0i	−0.275937	+	0.200480i
$635$	−1921.08	+	624.196i	−0.00476428	+	0.00154801i
$636$	−18111.0	−	55739.9i	−0.0447743	−	0.137801i
$637$	−166099.	−	228616.i	−0.409345	−	0.563415i
$638$	−6378.74	−	19631.7i	−0.0156709	−	0.0482300i
$639$	23811.1	−	73282.9i	0.0583145	−	0.179474i
$640$	338882.	+	246212.i	0.827348	+	0.601104i
$641$	219463.	+	71307.7i	0.534127	+	0.173548i	0.563647	−	0.826016i	$-0.309398\pi$
$641$	219463.	+	71307.7i	0.534127	+	0.173548i	−0.0295199	+	0.999564i	$0.509398\pi$
$642$	470846.	+	648064.i	1.14238	+	1.57235i
$643$	362172.	+	498487.i	0.875978	+	1.20568i	0.977519	+	0.210849i	$0.0676229\pi$
$643$	362172.	+	498487.i	0.875978	+	1.20568i	−0.101540	+	0.994831i	$0.532377\pi$
$644$	−537.502	+	739.808i	−0.00129601	+	0.00178380i
$645$	7309.12			0.0175689
$646$		−	422095.i		−	1.01145i
$647$	−106594.	+	146714.i	−0.254638	+	0.350479i	−0.917129	−	0.398591i	$-0.869499\pi$
$647$	−106594.	+	146714.i	−0.254638	+	0.350479i	0.662491	+	0.749070i	$0.269499\pi$
$648$	−94698.8	−	291453.i	−0.225525	−	0.694094i
$649$	3363.93	+	1093.01i	0.00798651	+	0.00259497i
$650$		−	80264.3i		−	0.189975i
$651$	−30341.9	−	71947.9i	−0.0715947	−	0.169768i
$652$	−64329.6			−0.151327
$653$	−164610.	+	506619.i	−0.386039	+	1.18811i	0.549685	+	0.835372i	$0.314748\pi$
$653$	−164610.	+	506619.i	−0.386039	+	1.18811i	−0.935724	+	0.352733i	$0.885252\pi$
$654$	−384253.	+	124851.i	−0.898384	+	0.291903i
$655$	286837.	+	208399.i	0.668578	+	0.485750i
$656$	598052.			1.38973
$657$		−	114486.i		−	0.265229i
$658$	−15194.1	−	11039.1i	−0.0350931	−	0.0254966i
$659$	−131510.	+	95547.6i	−0.302822	+	0.220013i	−0.728811	−	0.684715i	$-0.759926\pi$
$659$	−131510.	+	95547.6i	−0.302822	+	0.220013i	0.425988	+	0.904729i	$0.359926\pi$
$660$	2939.34	−	2135.55i	0.00674779	−	0.00490256i
$661$	196341.	−	604275.i	0.449374	−	1.38303i	−0.428241	−	0.903665i	$-0.640867\pi$
$661$	196341.	−	604275.i	0.449374	−	1.38303i	0.877615	−	0.479366i	$-0.159133\pi$
$662$	422052.	−	580905.i	0.963054	−	1.32553i
$663$	−202011.	−	65637.4i	−0.459567	−	0.149322i
$664$	−408520.	+	132736.i	−0.926567	+	0.301060i
$665$	80721.8	−	58647.8i	0.182536	−	0.132620i
$666$	−97465.9	+	31668.6i	−0.219738	+	0.0713971i
$667$	−6749.01	−	20771.3i	−0.0151701	−	0.0466888i
$668$	78423.9	+	107941.i	0.175750	+	0.241899i
$669$	74776.9	+	230140.i	0.167077	+	0.514209i
$670$	−186104.	+	572770.i	−0.414579	+	1.27594i
$671$	−30598.8	−	22231.3i	−0.0679610	−	0.0493765i
$672$	26053.2	+	8465.20i	0.0576929	+	0.0187456i
$673$	3618.40	+	4980.30i	0.00798888	+	0.0109958i	0.812993	−	0.582274i	$-0.197837\pi$
$673$	3618.40	+	4980.30i	0.00798888	+	0.0109958i	−0.805004	+	0.593270i	$0.797837\pi$
$674$	80115.6	+	110270.i	0.176359	+	0.242737i
$675$	69056.9	−	95048.7i	0.151565	−	0.208612i
$676$	35946.7			0.0786621
$677$			481823.i			1.05126i	0.850713	+	0.525630i	$0.176170\pi$
$677$			481823.i			1.05126i	−0.850713	+	0.525630i	$0.823830\pi$
$678$	489414.	−	673621.i	1.06467	−	1.46540i
$679$	−20008.2	−	61578.8i	−0.0433978	−	0.133565i
$680$	250780.	+	81483.2i	0.542343	+	0.176218i
$681$			65765.0i			0.141808i
$682$	−7189.99	+	30814.7i	−0.0154582	+	0.0662505i
$683$	−186901.			−0.400655			−0.200327	−	0.979729i	$-0.564201\pi$
$683$	−186901.			−0.400655			−0.200327	+	0.979729i	$0.564201\pi$
$684$	5040.29	−	15512.4i	0.0107732	−	0.0331564i
$685$	163281.	−	53053.2i	0.347980	−	0.113066i
$686$	162237.	+	117872.i	0.344748	+	0.250474i
$687$	−601675.			−1.27482
$688$		−	11889.9i		−	0.0251190i
$689$	265537.	+	192924.i	0.559353	+	0.406394i
$690$	21815.7	−	15850.0i	0.0458217	−	0.0332914i
$691$	−437161.	+	317616.i	−0.915557	+	0.665191i	−0.942414	−	0.334448i	$-0.891450\pi$
$691$	−437161.	+	317616.i	−0.915557	+	0.665191i	0.0268570	+	0.999639i	$0.491450\pi$
$692$	−16637.3	+	51204.3i	−0.0347433	+	0.106929i
$693$	583.364	−	802.931i	0.00121471	−	0.00167191i
$694$	659342.	+	214233.i	1.36896	+	0.444803i
$695$	456289.	−	148257.i	0.944649	−	0.306935i
$696$	−240659.	+	174849.i	−0.496803	+	0.360949i
$697$	410328.	−	133324.i	0.844629	−	0.274436i
$698$	−43908.2	−	135135.i	−0.0901228	−	0.277369i
$699$	81251.4	+	111833.i	0.166294	+	0.228884i
$700$	1228.63	+	3781.33i	0.00250741	+	0.00771701i
$701$	186972.	−	575441.i	0.380488	−	1.17102i	−0.559213	−	0.829024i	$-0.688897\pi$
$701$	186972.	−	575441.i	0.380488	−	1.17102i	0.939701	−	0.341997i	$-0.111103\pi$
$702$	−332514.	−	241586.i	−0.674739	−	0.490227i
$703$	−794554.	−	258166.i	−1.60773	−	0.522383i
$704$	14370.1	+	19778.8i	0.0289944	+	0.0399074i
$705$	46405.7	+	63871.9i	0.0933669	+	0.128508i
$706$	−19780.5	+	27225.5i	−0.0396851	+	0.0546219i
$707$	−84164.5			−0.168380
$708$			10164.4i			0.0202775i
$709$	−346572.	+	477016.i	−0.689448	+	0.948944i	−0.999999	−	0.00161305i	$-0.999487\pi$
$709$	−346572.	+	477016.i	−0.689448	+	0.948944i	0.310551	+	0.950557i	$0.399487\pi$
$710$	−169624.	−	522048.i	−0.336488	−	1.03560i
$711$	−30735.7	−	9986.65i	−0.0608001	−	0.0197552i
$712$		−	576855.i		−	1.13791i
$713$	−7607.36	+	32603.4i	−0.0149642	+	0.0641334i
$714$	73807.3			0.144778
$715$	−6287.54	+	19351.1i	−0.0122990	+	0.0378523i
$716$	88487.4	−	28751.3i	0.172606	−	0.0560830i
$717$	−532038.	−	386549.i	−1.03491	−	0.751910i
$718$	262938.			0.510041
$719$		−	811683.i		−	1.57011i	−0.619429	−	0.785053i	$-0.712636\pi$
$719$		−	811683.i		−	1.57011i	0.619429	−	0.785053i	$-0.287364\pi$
$720$	67712.8	+	49196.2i	0.130619	+	0.0949001i
$721$	98155.9	−	71314.4i	0.188819	−	0.137185i
$722$	299159.	−	217352.i	0.573889	−	0.416955i
$723$	−95091.1	+	292660.i	−0.181913	+	0.559870i
$724$	3673.90	−	5056.68i	0.00700890	−	0.00964692i
$725$	−90311.2	−	29343.9i	−0.171817	−	0.0558267i
$726$	−493329.	+	160292.i	−0.935974	+	0.304116i
$727$	−689018.	+	500601.i	−1.30365	+	0.947159i	−0.999984	−	0.00561875i	$-0.998211\pi$
$727$	−689018.	+	500601.i	−1.30365	+	0.947159i	−0.303668	+	0.952778i	$0.598211\pi$
$728$	−66337.9	+	21554.5i	−0.125170	+	0.0406701i
$729$	−181551.	−	558756.i	−0.341620	−	1.05140i
$730$	−479378.	−	659807.i	−0.899564	−	1.23814i
$731$	−2650.62	−	8157.77i	−0.00496036	−	0.0152664i
$732$	33586.9	−	103370.i	0.0626827	−	0.192918i
$733$	265777.	+	193098.i	0.494663	+	0.359393i	0.806975	−	0.590586i	$-0.201103\pi$
$733$	265777.	+	193098.i	0.494663	+	0.359393i	−0.312312	+	0.949980i	$0.601103\pi$
$734$	−469775.	−	152639.i	−0.871962	−	0.283318i
$735$	−242624.	−	333944.i	−0.449117	−	0.618157i
$736$	−6903.76	−	9502.22i	−0.0127447	−	0.0175416i
$737$	−28704.6	+	39508.5i	−0.0528465	+	0.0727370i
$738$	116950.			0.214728
$739$			761636.i			1.39463i	0.716765	+	0.697315i	$0.245622\pi$
$739$			761636.i			1.39463i	−0.716765	+	0.697315i	$0.754378\pi$
$740$	−61172.9	+	84197.3i	−0.111711	+	0.153757i
$741$	−145044.	−	446398.i	−0.264157	−	0.812991i
$742$	−108468.	−	35243.5i	−0.197013	−	0.0640135i
$743$			1.00331e6i			1.81743i	0.417413	+	0.908717i	$0.362937\pi$
$743$			1.00331e6i			1.81743i	−0.417413	+	0.908717i	$0.637063\pi$
$744$	454354.	−	38681.6i	0.820820	−	0.0698808i
$745$	229546.			0.413578
$746$	−96772.7	+	297836.i	−0.173890	+	0.535179i
$747$	−93546.3	+	30395.0i	−0.167643	+	0.0544705i
$748$	−3449.45	−	2506.17i	−0.00616519	−	0.00447927i
$749$	222220.			0.396114
$750$		−	601015.i		−	1.06847i
$751$	−131072.	−	95229.5i	−0.232397	−	0.168846i	0.465492	−	0.885052i	$-0.345877\pi$
$751$	−131072.	−	95229.5i	−0.232397	−	0.168846i	−0.697889	+	0.716206i	$0.745877\pi$
$752$	103902.	−	75489.3i	0.183734	−	0.133490i
$753$	677052.	−	491907.i	1.19408	−	0.867548i
$754$	−102656.	+	315941.i	−0.180567	+	0.555730i
$755$	280924.	−	386659.i	0.492828	−	0.678320i
$756$	19363.1	+	6291.46i	0.0338791	+	0.0110080i
$757$	1.05968e6	−	344310.i	1.84919	−	0.600839i	0.852212	−	0.523196i	$-0.175260\pi$
$757$	1.05968e6	−	344310.i	1.84919	−	0.600839i	0.996981	−	0.0776434i	$-0.0247396\pi$
$758$	−742768.	+	539652.i	−1.29275	+	0.939238i
$759$	2079.58	−	675.697i	0.00360988	−	0.00117292i
$760$	180059.	+	554165.i	0.311737	+	0.959427i
$761$	608839.	+	837996.i	1.05132	+	1.44701i	0.887662	+	0.460495i	$0.152328\pi$
$761$	608839.	+	837996.i	1.05132	+	1.44701i	0.163654	+	0.986518i	$0.447672\pi$
$762$	−1020.31	−	3140.21i	−0.00175721	−	0.00540814i
$763$	−34635.1	+	106596.i	−0.0594932	+	0.183101i
$764$	38704.0	+	28120.1i	0.0663086	+	0.0481760i
$765$	57425.6	+	18658.7i	0.0981257	+	0.0318830i
$766$	246621.	+	339445.i	0.420313	+	0.578511i
$767$	−33458.5	−	46051.6i	−0.0568742	−	0.0782807i
$768$	−154078.	+	212070.i	−0.261227	+	0.359547i
$769$	−961882.			−1.62656			−0.813278	−	0.581875i	$-0.802319\pi$
$769$	−961882.			−1.62656			−0.813278	+	0.581875i	$0.802319\pi$
$770$		−	7070.15i		−	0.0119247i
$771$	548871.	−	755455.i	0.923339	−	1.27087i
$772$	−48478.4	−	149201.i	−0.0813417	−	0.250344i
$773$	−616248.	−	200231.i	−1.03133	−	0.335099i	−0.256013	−	0.966673i	$-0.582409\pi$
$773$	−616248.	−	200231.i	−1.03133	−	0.335099i	−0.775315	+	0.631575i	$0.782409\pi$
$774$		−	2325.10i		−	0.00388114i
$775$	95241.4	+	110081.i	0.158570	+	0.183277i
$776$	378116.			0.627916
$777$	45142.8	−	138935.i	0.0747733	−	0.230128i
$778$	822237.	−	267161.i	1.35843	−	0.441381i
$779$	771311.	+	560390.i	1.27103	+	0.923455i
$780$	−58470.8			−0.0961059
$781$		−	44510.5i		−	0.0729727i
$782$	−25601.7	−	18600.8i	−0.0418655	−	0.0304171i
$783$	−393390.	+	285815.i	−0.641652	+	0.466188i
$784$	−543235.	+	394683.i	−0.883803	+	0.642121i
$785$	123994.	−	381614.i	0.201215	−	0.619278i
$786$	−340650.	+	468865.i	−0.551396	+	0.758932i
$787$	−442423.	−	143752.i	−0.714312	−	0.232094i	−0.0707569	−	0.997494i	$-0.522541\pi$
$787$	−442423.	−	143752.i	−0.714312	−	0.232094i	−0.643556	+	0.765399i	$0.722541\pi$
$788$	37206.3	−	12089.1i	0.0599190	−	0.0194689i
$789$	427284.	−	310440.i	0.686377	−	0.498682i
$790$	−218953.	+	71142.3i	−0.350831	+	0.113992i
$791$	−71377.8	−	219678.i	−0.114080	−	0.351103i
$792$	3406.74	+	4688.98i	0.00543111	+	0.00747529i
$793$	188095.	+	578896.i	0.299110	+	0.920565i
$794$	−102251.	+	314696.i	−0.162191	+	0.499172i
$795$	387874.	+	281807.i	0.613701	+	0.445880i
$796$	115538.	+	37540.5i	0.182347	+	0.0592481i
$797$	−367709.	−	506108.i	−0.578879	−	0.796759i	0.414693	−	0.909961i	$-0.363889\pi$
$797$	−367709.	−	506108.i	−0.578879	−	0.796759i	−0.993572	+	0.113203i	$0.963889\pi$
$798$	95866.1	+	131948.i	0.150543	+	0.207204i
$799$	54459.2	−	74956.7i	0.0853057	−	0.117413i
$800$	−51067.5			−0.0797930
$801$		−	132093.i		−	0.205880i
$802$	−315482.	+	434223.i	−0.490484	+	0.675094i
$803$	−20436.2	−	62896.1i	−0.0316934	−	0.0975422i
$804$	−133469.	−	43366.6i	−0.206475	−	0.0670878i
$805$		−	7480.57i		−	0.0115436i
$806$	385103.	−	333188.i	0.592798	−	0.512885i
$807$	302584.			0.464621
$808$	151884.	−	467450.i	0.232642	−	0.715999i
$809$	959432.	−	311738.i	1.46594	−	0.476314i	0.536064	−	0.844177i	$-0.319911\pi$
$809$	959432.	−	311738.i	1.46594	−	0.476314i	0.929880	+	0.367863i	$0.119911\pi$
$810$	−404428.	−	293834.i	−0.616412	−	0.447849i
$811$	−389533.			−0.592247			−0.296123	−	0.955150i	$-0.595694\pi$
$811$	−389533.			−0.592247			−0.296123	+	0.955150i	$0.595694\pi$
$812$		−	16455.7i		−	0.0249577i
$813$	710641.	+	516311.i	1.07515	+	0.781142i
$814$	−47892.8	+	34796.2i	−0.0722806	+	0.0525149i
$815$	425737.	−	309316.i	0.640954	−	0.465680i
$816$	−155967.	+	480017.i	−0.234235	+	0.720902i
$817$	11141.2	−	15334.5i	0.0166912	−	0.0229734i
$818$	−908027.	−	295036.i	−1.35704	−	0.440928i
$819$	−15190.6	+	4935.72i	−0.0226468	+	0.00735839i
$820$	96084.4	−	69809.4i	0.142898	−	0.103821i
$821$	−245078.	+	79630.8i	−0.363596	+	0.118139i	−0.485117	−	0.874450i	$-0.661223\pi$
$821$	−245078.	+	79630.8i	−0.363596	+	0.118139i	0.121521	+	0.992589i	$0.461223\pi$
$822$	86721.1	+	266900.i	0.128346	+	0.395007i
$823$	213369.	+	293678.i	0.315016	+	0.433582i	0.936937	−	0.349497i	$-0.113648\pi$
$823$	213369.	+	293678.i	0.315016	+	0.433582i	−0.621921	+	0.783080i	$0.713648\pi$
$824$	218948.	+	673852.i	0.322468	+	0.992453i
$825$	2937.85	−	9041.78i	0.00431640	−	0.0132845i
$826$	16002.0	+	11626.2i	0.0234539	+	0.0170403i
$827$	−339972.	−	110464.i	−0.497087	−	0.161513i	0.0497346	−	0.998762i	$-0.484162\pi$
$827$	−339972.	−	110464.i	−0.497087	−	0.161513i	−0.546822	+	0.837249i	$0.684162\pi$
$828$	−718.775	−	989.309i	−0.00104841	−	0.00144302i
$829$	581030.	+	799719.i	0.845452	+	1.16367i	0.984846	+	0.173428i	$0.0554845\pi$
$829$	581030.	+	799719.i	0.845452	+	1.16367i	−0.139394	+	0.990237i	$0.544515\pi$
$830$	−411857.	+	566873.i	−0.597848	+	0.822867i
$831$	−895752.			−1.29714
$832$		−	393449.i		−	0.568384i
$833$	−284731.	+	391899.i	−0.410341	+	0.564786i
$834$	242342.	+	745853.i	0.348415	+	1.07231i
$835$	−1.03803e6	−	337276.i	−1.48880	−	0.483741i
$836$		−	9421.91i		−	0.0134811i
$837$	742702.	−	63230.2i	1.06014	−	0.0902554i
$838$	486579.			0.692892
$839$	−141232.	+	434667.i	−0.200636	+	0.617493i	0.799229	+	0.601027i	$0.205242\pi$
$839$	−141232.	+	434667.i	−0.200636	+	0.617493i	−0.999864	+	0.0164663i	$0.994758\pi$
$840$	−96901.0	+	31485.0i	−0.137331	+	0.0446216i
$841$	−254244.	−	184719.i	−0.359466	−	0.261168i
$842$	108567.			0.153135
$843$		−	458.066i		−	0.000644575i
$844$	45976.1	+	33403.6i	0.0645428	+	0.0468931i
$845$	−237897.	+	172843.i	−0.333178	+	0.242068i
$846$	20318.3	−	14762.1i	0.0283887	−	0.0206256i
$847$	−44466.8	+	136855.i	−0.0619825	+	0.190762i
$848$	458423.	−	630965.i	0.637492	−	0.877432i
$849$	61048.4	+	19835.8i	0.0846952	+	0.0275191i
$850$	−130857.	+	42517.9i	−0.181116	+	0.0588483i
$851$	−50672.9	+	36816.0i	−0.0699708	+	0.0508368i
$852$	121649.	−	39526.3i	0.167583	−	0.0544511i
$853$	−366692.	−	1.12856e6i	−0.503968	−	1.55106i	−0.802498	−	0.596655i	$-0.796496\pi$
$853$	−366692.	−	1.12856e6i	−0.503968	−	1.55106i	0.298530	−	0.954400i	$-0.403504\pi$
$854$	−124321.	−	171113.i	−0.170462	−	0.234621i
$855$	41231.4	+	126897.i	0.0564022	+	0.173588i
$856$	−401019.	+	1.23421e6i	−0.547290	+	1.68439i
$857$	−1.04294e6	−	757742.i	−1.42003	−	1.03172i	−0.991766	−	0.128064i	$-0.959124\pi$
$857$	−1.04294e6	−	757742.i	−1.42003	−	1.03172i	−0.428269	−	0.903651i	$-0.640876\pi$
$858$	−31631.4	−	10277.7i	−0.0429678	−	0.0139611i
$859$	98505.5	+	135581.i	0.133498	+	0.183744i	0.870533	−	0.492111i	$-0.163775\pi$
$859$	98505.5	+	135581.i	0.133498	+	0.183744i	−0.737035	+	0.675855i	$0.763775\pi$
$860$	−1387.89	−	1910.26i	−0.00187654	−	0.00258283i
$861$	−97989.5	+	134871.i	−0.132182	+	0.181933i
$862$	39972.4			0.0537954
$863$			244058.i			0.327696i	0.986486	+	0.163848i	$0.0523907\pi$
$863$			244058.i			0.327696i	−0.986486	+	0.163848i	$0.947609\pi$
$864$	−153707.	+	211560.i	−0.205905	+	0.283403i
$865$	−136099.	−	418871.i	−0.181896	−	0.559819i
$866$	−20784.1	−	6753.16i	−0.0277137	−	0.00900474i
$867$		−	323629.i		−	0.430535i
$868$	−13042.4	+	21591.7i	−0.0173108	+	0.0286581i
$869$	−18668.3			−0.0247209
$870$	−149951.	+	461501.i	−0.198112	+	0.609726i
$871$	747457.	−	242864.i	0.985258	−	0.320130i
$872$	−529531.	−	384727.i	−0.696399	−	0.505964i
$873$	86584.1			0.113608
$874$		−	69929.2i		−	0.0915453i
$875$	−134886.	−	98000.2i	−0.176177	−	0.128000i
$876$	153750.	−	111706.i	0.200358	−	0.145569i
$877$	1.14729e6	−	833555.i	1.49167	−	1.08377i	0.518121	−	0.855307i	$-0.326632\pi$
$877$	1.14729e6	−	833555.i	1.49167	−	1.08377i	0.973554	−	0.228458i	$-0.0733683\pi$
$878$	369185.	−	1.13623e6i	0.478911	−	1.47394i
$879$	−70568.2	+	97128.9i	−0.0913338	+	0.125710i
$880$	45981.8	+	14940.4i	0.0593773	+	0.0192928i
$881$	−151502.	+	49226.1i	−0.195195	+	0.0634226i	−0.404983	−	0.914324i	$-0.632723\pi$
$881$	−151502.	+	49226.1i	−0.195195	+	0.0634226i	0.209788	+	0.977747i	$0.432723\pi$
$882$	−106231.	+	77181.2i	−0.136557	+	0.0992143i
$883$	827315.	−	268811.i	1.06108	−	0.344767i	0.274075	−	0.961708i	$-0.411628\pi$
$883$	827315.	−	268811.i	1.06108	−	0.344767i	0.787009	+	0.616941i	$0.211628\pi$
$884$	21204.2	+	65259.8i	0.0271342	+	0.0835106i
$885$	−48873.4	−	67268.5i	−0.0624003	−	0.0858866i
$886$	−356560.	−	1.09738e6i	−0.454219	−	1.39794i
$887$	343232.	−	1.05636e6i	0.436255	−	1.34265i	−0.455541	−	0.890215i	$-0.650554\pi$
$887$	343232.	−	1.05636e6i	0.436255	−	1.34265i	0.891795	−	0.452439i	$-0.149446\pi$
$888$	690182.	+	501446.i	0.875261	+	0.635914i
$889$	−871.126	−	283.046i	−0.00110224	−	0.000358141i
$890$	−553104.	−	761282.i	−0.698275	−	0.961093i
$891$	−23826.5	−	32794.4i	−0.0300127	−	0.0413089i
$892$	45948.8	−	63243.2i	0.0577491	−	0.0794848i
$893$	204739.			0.256742
$894$			375218.i			0.469470i
$895$	−447370.	+	615752.i	−0.558497	+	0.768705i
$896$	58696.1	+	180648.i	0.0731128	+	0.225018i
$897$	−33467.5	−	10874.3i	−0.0415948	−	0.0135150i
$898$		−	1.47977e6i		−	1.83502i
$899$	−234105.	−	555118.i	−0.289661	−	0.686856i
$900$	−5316.82			−0.00656397
$901$	173867.	−	535106.i	0.214174	−	0.659159i
$902$	64250.1	−	20876.1i	0.0789698	−	0.0256588i
$903$	2681.38	+	1948.14i	0.00328839	+	0.00238916i
$904$	1.34890e6			1.65061
$905$			51130.6i			0.0624287i
$906$	632036.	+	459201.i	0.769990	+	0.559431i
$907$	368731.	−	267899.i	0.448224	−	0.325654i	−0.340670	−	0.940183i	$-0.610654\pi$
$907$	368731.	−	267899.i	0.448224	−	0.325654i	0.788894	+	0.614529i	$0.210654\pi$
$908$	17187.9	−	12487.8i	0.0208474	−	0.0151465i
$909$	34779.6	−	107041.i	0.0420917	−	0.129545i
$910$	−66879.8	+	92052.2i	−0.0807630	+	0.111161i
$911$	−930462.	−	302326.i	−1.12115	−	0.364282i	−0.310941	−	0.950429i	$-0.600644\pi$
$911$	−930462.	−	302326.i	−1.12115	−	0.364282i	−0.810205	+	0.586147i	$0.800644\pi$
$912$	−1.06073e6	+	344651.i	−1.27530	+	0.414371i
$913$	−45966.8	+	33396.8i	−0.0551445	+	0.0400648i
$914$	−655038.	+	212835.i	−0.784105	+	0.254771i
$915$	274754.	+	845605.i	0.328172	+	1.01001i
$916$	114249.	+	157250.i	0.136163	+	0.187413i
$917$	49681.6	+	152904.i	0.0590822	+	0.181836i
$918$	−217722.	+	670079.i	−0.258355	+	0.795135i
$919$	771130.	+	560259.i	0.913054	+	0.663373i	0.941785	−	0.336215i	$-0.109147\pi$
$919$	771130.	+	560259.i	0.913054	+	0.663373i	−0.0287313	+	0.999587i	$0.509147\pi$
$920$	41547.1	+	13499.5i	0.0490868	+	0.0159493i
$921$	−142222.	−	195752.i	−0.167667	−	0.230774i
$922$	−475818.	−	654907.i	−0.559730	−	0.770402i
$923$	−421045.	+	579519.i	−0.494226	+	0.680243i
$924$	1647.51			0.00192967
$925$			272330.i			0.318282i
$926$	204593.	−	281598.i	0.238599	−	0.328403i
$927$	50136.5	+	154304.i	0.0583438	+	0.179564i
$928$	201015.	+	65313.7i	0.233417	+	0.0758418i
$929$			429079.i			0.497172i	0.968610	+	0.248586i	$0.0799658\pi$
$929$			429079.i			0.497172i	−0.968610	+	0.248586i	$0.920034\pi$
$930$	562527.	−	486695.i	0.650395	−	0.562718i
$931$	−1.07044e6			−1.23499
$932$	13799.6	−	42470.7i	0.0158867	−	0.0488942i
$933$	−246075.	+	79954.7i	−0.282686	+	0.0918503i
$934$	722385.	+	524843.i	0.828085	+	0.601639i
$935$	34879.1			0.0398972
$936$		−	93275.6i		−	0.106467i
$937$	−1.36253e6	−	989933.i	−1.55191	−	1.12753i	−0.942275	−	0.334841i	$-0.891317\pi$
$937$	−1.36253e6	−	989933.i	−1.55191	−	1.12753i	−0.609632	−	0.792685i	$-0.708683\pi$
$938$	−220937.	+	160520.i	−0.251109	+	0.182441i
$939$	793046.	−	576182.i	0.899430	−	0.653474i
$940$	7881.44	−	24256.6i	0.00891969	−	0.0274520i
$941$	−757454.	+	1.04255e6i	−0.855415	+	1.17738i	0.127228	+	0.991873i	$0.459392\pi$
$941$	−757454.	+	1.04255e6i	−0.855415	+	1.17738i	−0.982643	+	0.185504i	$0.940608\pi$
$942$	623789.	+	202681.i	0.702969	+	0.228408i
$943$	67979.8	−	22088.0i	0.0764463	−	0.0248389i
$944$	−109427.	+	79503.6i	−0.122795	+	0.0892161i
$945$	−158398.	+	51466.5i	−0.177372	+	0.0576316i
$946$	−415.040	−	1277.36i	−0.000463776	−	0.00142736i
$947$	160268.	+	220591.i	0.178710	+	0.245973i	0.888969	−	0.457967i	$-0.151422\pi$
$947$	160268.	+	220591.i	0.178710	+	0.245973i	−0.710259	+	0.703940i	$0.751422\pi$
$948$	−16577.8	−	51021.2i	−0.0184463	−	0.0567720i
$949$	−328887.	+	1.01221e6i	−0.365187	+	1.12393i
$950$	−245977.	−	178713.i	−0.272550	−	0.198019i
$951$	248547.	+	80757.9i	0.274820	+	0.0892943i
$952$	70281.5	+	96734.1i	0.0775473	+	0.106735i
$953$	−173989.	−	239476.i	−0.191574	−	0.263679i	0.702415	−	0.711767i	$-0.252105\pi$
$953$	−173989.	−	239476.i	−0.191574	−	0.263679i	−0.893989	+	0.448088i	$0.852105\pi$
$954$	89645.6	−	123387.i	0.0984991	−	0.135572i
$955$	−391356.			−0.429107
$956$			212450.i			0.232456i
$957$	−23128.3	+	31833.4i	−0.0252534	+	0.0347583i
$958$	488017.	+	1.50196e6i	0.531746	+	1.63655i
$959$	74040.9	+	24057.3i	0.0805071	+	0.0261584i
$960$		−	574719.i		−	0.623610i
$961$	−132800.	+	913923.i	−0.143798	+	0.989607i
$962$	952709.			1.02946
$963$	−91828.7	+	282620.i	−0.0990207	+	0.304754i
$964$	94544.1	−	30719.2i	0.101737	−	0.0330565i
$965$	1.03824e6	+	754323.i	1.11492	+	0.810033i
$966$	12227.8			0.0131037
$967$			544231.i			0.582010i	0.956722	+	0.291005i	$0.0939896\pi$
$967$			544231.i			0.582010i	−0.956722	+	0.291005i	$0.906010\pi$
$968$	−679846.	−	493937.i	−0.725538	−	0.527134i
$969$	−650940.	+	472935.i	−0.693255	+	0.503679i
$970$	499004.	−	362547.i	0.530347	−	0.385320i
$971$	−406752.	+	1.25185e6i	−0.431411	+	1.32775i	0.465308	+	0.885149i	$0.345943\pi$
$971$	−406752.	+	1.25185e6i	−0.431411	+	1.32775i	−0.896720	+	0.442599i	$0.854057\pi$
$972$	−29764.2	+	40966.8i	−0.0315037	+	0.0433611i
$973$	206907.	+	67228.3i	0.218550	+	0.0710111i
$974$	−1.50137e6	+	487826.i	−1.58260	+	0.514218i
$975$	−123781.	+	89931.9i	−0.130210	+	0.0946029i
$976$	1.37557e6	−	446949.i	1.44405	−	0.469200i
$977$	167114.	+	514325.i	0.175075	+	0.538826i	0.999637	−	0.0269458i	$-0.00857814\pi$
$977$	167114.	+	514325.i	0.175075	+	0.538826i	−0.824562	+	0.565772i	$0.808578\pi$
$978$	505611.	+	695913.i	0.528614	+	0.727574i
$979$	−23579.2	−	72569.2i	−0.0246016	−	0.0757159i
$980$	−41206.8	+	126821.i	−0.0429059	+	0.132051i
$981$	−121256.	−	88097.9i	−0.125999	−	0.0915435i
$982$	331424.	+	107686.i	0.343685	+	0.111670i
$983$	−944073.	−	1.29941e6i	−0.977009	−	1.34474i	−0.938425	−	0.345483i	$-0.887715\pi$
$983$	−944073.	−	1.29941e6i	−0.977009	−	1.34474i	−0.0385842	−	0.999255i	$-0.512285\pi$
$984$	−572241.	−	787623.i	−0.591002	−	0.813445i
$985$	−188106.	+	258906.i	−0.193879	+	0.266851i
$986$	569465.			0.585751
$987$			35800.5i			0.0367497i
$988$	−89126.2	+	122672.i	−0.0913043	+	0.125670i
$989$	−439.133	−	1351.51i	−0.000448956	−	0.00138174i
$990$	8991.83	+	2921.62i	0.00917440	+	0.00298094i
$991$			363136.i			0.369761i	0.982761	+	0.184881i	$0.0591899\pi$
$991$			363136.i			0.369761i	−0.982761	+	0.184881i	$0.940810\pi$
$992$	−211988.	−	245018.i	−0.215421	−	0.248986i
$993$	−1.36874e6			−1.38810
$994$	76917.1	−	236726.i	0.0778485	−	0.239593i
$995$	−945143.	+	307096.i	−0.954666	+	0.310190i
$996$	−132095.	−	95972.3i	−0.133158	−	0.0967447i
$997$	939524.			0.945187			0.472594	−	0.881281i	$-0.343318\pi$
$997$	939524.			0.945187			0.472594	+	0.881281i	$0.343318\pi$
$998$			505427.i			0.507454i
$999$	1.12819e6	+	819681.i	1.13045	+	0.821323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.23.3	✓	36
31.27	odd	10	inner	31.5.f.a.27.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.23.3	✓	36	1.1	even	1	trivial
31.5.f.a.27.3	yes	36	31.27	odd	10	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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33487 + 4.10831i) q^{2} +(7.83134 - 2.54456i) q^{3} +(-2.15208 - 1.56358i) q^{4} +21.7607 q^{5} +35.5702i q^{6} +(7.98302 + 5.80000i) q^{7} +(-46.6194 + 33.8710i) q^{8} +(-10.6753 + 7.75606i) q^{9} +(-29.0478 + 89.3999i) q^{10} +(-4.48030 + 6.16661i) q^{11} +(-20.8322 - 6.76881i) q^{12} +(116.666 - 37.9069i) q^{13} +(-34.4845 + 25.0545i) q^{14} +(170.416 - 55.3714i) q^{15} +(-90.0740 - 277.219i) q^{16} +(-123.601 - 170.122i) q^{17} +(-17.6142 - 54.2108i) q^{18} +(143.593 - 441.933i) q^{19} +(-46.8308 - 34.0245i) q^{20} +(77.2762 + 25.1085i) q^{21} +(-19.3537 - 26.6381i) q^{22} +(-20.4772 - 28.1844i) q^{23} +(-278.906 + 383.881i) q^{24} -151.471 q^{25} +529.899i q^{26} +(-455.909 + 627.505i) q^{27} +(-8.11133 - 24.9641i) q^{28} +(596.229 + 193.726i) q^{29} +774.034i q^{30} +(-628.777 - 726.747i) q^{31} +337.144 q^{32} +(-19.3955 + 59.6932i) q^{33} +(863.907 - 280.700i) q^{34} +(173.716 + 126.212i) q^{35} +35.1013 q^{36} -1797.91i q^{37} +(1623.92 + 1179.85i) q^{38} +(817.191 - 593.724i) q^{39} +(-1014.47 + 737.057i) q^{40} +(-634.022 + 1951.32i) q^{41} +(-206.307 + 283.958i) q^{42} +(38.7943 + 12.6050i) q^{43} +(19.2839 - 6.26572i) q^{44} +(-232.302 + 168.777i) q^{45} +(143.125 - 46.5041i) q^{46} +(136.154 + 419.040i) q^{47} +(-1410.80 - 1941.80i) q^{48} +(-711.861 - 2190.88i) q^{49} +(202.194 - 622.290i) q^{50} +(-1400.85 - 1017.77i) q^{51} +(-310.344 - 100.837i) q^{52} +(1572.71 + 2164.65i) q^{53} +(-1969.41 - 2710.65i) q^{54} +(-97.4947 + 134.190i) q^{55} -568.616 q^{56} -3826.31i q^{57} +(-1591.78 + 2190.89i) q^{58} +(-143.395 - 441.324i) q^{59} +(-453.325 - 147.294i) q^{60} +4962.02i q^{61} +(3825.04 - 1613.10i) q^{62} -130.206 q^{63} +(991.140 - 3050.41i) q^{64} +(2538.73 - 824.882i) q^{65} +(-219.348 - 159.365i) q^{66} +6406.84 q^{67} +559.375i q^{68} +(-232.081 - 168.616i) q^{69} +(-750.408 + 545.204i) q^{70} +(-4724.23 + 3432.36i) q^{71} +(234.971 - 723.166i) q^{72} +(-5099.73 + 7019.18i) q^{73} +(7386.36 + 2399.97i) q^{74} +(-1186.22 + 385.426i) q^{75} +(-1000.02 + 726.556i) q^{76} +(-71.5327 + 23.2424i) q^{77} +(1348.36 + 4149.82i) q^{78} +(1439.57 + 1981.40i) q^{79} +(-1960.08 - 6032.49i) q^{80} +(-1643.37 + 5057.77i) q^{81} +(-7170.29 - 5209.52i) q^{82} +(7089.31 + 2303.46i) q^{83} +(-127.045 - 174.863i) q^{84} +(-2689.65 - 3701.98i) q^{85} +(-103.571 + 142.553i) q^{86} +5162.21 q^{87} -439.236i q^{88} +(-5884.05 + 8098.69i) q^{89} +(-383.297 - 1179.67i) q^{90} +(1151.20 + 374.049i) q^{91} +92.6727i q^{92} +(-6773.41 - 4091.44i) q^{93} -1903.30 q^{94} +(3124.68 - 9616.78i) q^{95} +(2640.29 - 857.882i) q^{96} +(-5308.52 - 3856.86i) q^{97} +9951.08 q^{98} -100.580i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Introduction

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