LMFDB - Embedded newform 45.5.i.a.11.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] 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("45.11"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, 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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.904609 + 0.522276i) q^{2} +(-2.25893 + 8.71190i) q^{3} +(-7.45446 - 12.9115i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-6.59347 + 6.70108i) q^{6} +(-36.4983 + 63.2168i) q^{7} -32.2860i q^{8} +(-70.7944 - 39.3592i) q^{9} -11.6784 q^{10} +(-122.636 - 70.8041i) q^{11} +(129.323 - 35.7763i) q^{12} +(3.09167 + 5.35493i) q^{13} +(-66.0333 + 38.1243i) q^{14} +(-26.8290 - 96.9804i) q^{15} +(-102.409 + 177.378i) q^{16} +452.463i q^{17} +(-43.4849 - 72.5789i) q^{18} +621.658 q^{19} +(144.355 + 83.3433i) q^{20} +(-468.292 - 460.772i) q^{21} +(-73.9586 - 128.100i) q^{22} +(-28.0293 + 16.1827i) q^{23} +(281.272 + 72.9318i) q^{24} +(62.5000 - 108.253i) q^{25} +6.45882i q^{26} +(502.813 - 527.844i) q^{27} +1088.30 q^{28} +(-869.127 - 501.791i) q^{29} +(26.3808 - 101.741i) q^{30} +(681.173 + 1179.83i) q^{31} +(-632.648 + 365.259i) q^{32} +(893.866 - 908.454i) q^{33} +(-236.311 + 409.302i) q^{34} -816.126i q^{35} +(19.5480 + 1207.46i) q^{36} -711.751 q^{37} +(562.357 + 324.677i) q^{38} +(-53.6355 + 14.8379i) q^{39} +(180.484 + 312.608i) q^{40} +(-917.903 + 529.951i) q^{41} +(-182.971 - 661.396i) q^{42} +(118.544 - 205.324i) q^{43} +2111.23i q^{44} +(905.489 - 14.6592i) q^{45} -33.8073 q^{46} +(-2172.54 - 1254.32i) q^{47} +(-1313.96 - 1292.86i) q^{48} +(-1463.75 - 2535.28i) q^{49} +(113.076 - 65.2845i) q^{50} +(-3941.81 - 1022.08i) q^{51} +(46.0934 - 79.8361i) q^{52} -1128.18i q^{53} +(730.530 - 214.885i) q^{54} +1583.23 q^{55} +(2041.02 + 1178.38i) q^{56} +(-1404.28 + 5415.82i) q^{57} +(-524.147 - 907.849i) q^{58} +(-1601.37 + 924.551i) q^{59} +(-1052.17 + 1069.34i) q^{60} +(-2765.44 + 4789.87i) q^{61} +1423.04i q^{62} +(5072.04 - 3038.86i) q^{63} +2514.03 q^{64} +(-59.8699 - 34.5659i) q^{65} +(1283.06 - 354.951i) q^{66} +(404.470 + 700.562i) q^{67} +(5841.97 - 3372.86i) q^{68} +(-77.6659 - 280.744i) q^{69} +(426.243 - 738.275i) q^{70} -1754.60i q^{71} +(-1270.75 + 2285.67i) q^{72} -1908.13 q^{73} +(-643.856 - 371.731i) q^{74} +(801.908 + 789.030i) q^{75} +(-4634.12 - 8026.53i) q^{76} +(8952.03 - 5168.46i) q^{77} +(-56.2686 - 14.5900i) q^{78} +(1819.34 - 3151.19i) q^{79} -2289.94i q^{80} +(3462.71 + 5572.82i) q^{81} -1107.12 q^{82} +(8463.40 + 4886.35i) q^{83} +(-2458.39 + 9481.15i) q^{84} +(-2529.34 - 4380.95i) q^{85} +(214.472 - 123.825i) q^{86} +(6334.85 - 6438.24i) q^{87} +(-2285.98 + 3959.43i) q^{88} -2458.88i q^{89} +(826.769 + 459.654i) q^{90} -451.362 q^{91} +(417.886 + 241.266i) q^{92} +(-11817.2 + 3269.16i) q^{93} +(-1310.20 - 2269.33i) q^{94} +(-6019.17 + 3475.17i) q^{95} +(-1752.99 - 6336.66i) q^{96} +(-6786.18 + 11754.0i) q^{97} -3057.92i q^{98} +(5895.18 + 9839.41i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.904609	+	0.522276i	0.226152	+	0.130569i	0.608796	−	0.793327i	$-0.291653\pi$
$2$	0.904609	+	0.522276i	0.226152	+	0.130569i	−0.382644	+	0.923896i	$0.624986\pi$
$3$	−2.25893	+	8.71190i	−0.250993	+	0.967989i
$3$	−2.25893	+	8.71190i	−0.250993	+	0.967989i
$4$	−7.45446	−	12.9115i	−0.465903	−	0.806968i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$	−6.59347	+	6.70108i	−0.183152	+	0.186141i
$7$	−36.4983	+	63.2168i	−0.744862	+	1.29014i	0.205397	+	0.978679i	$0.434152\pi$
$7$	−36.4983	+	63.2168i	−0.744862	+	1.29014i	−0.950259	+	0.311461i	$0.899182\pi$
$8$		−	32.2860i		−	0.504468i
$9$	−70.7944	−	39.3592i	−0.874006	−	0.485916i
$10$	−11.6784			−0.116784
$11$	−122.636	−	70.8041i	−1.01352	−	0.585158i	−0.101302	−	0.994856i	$-0.532301\pi$
$11$	−122.636	−	70.8041i	−1.01352	−	0.585158i	−0.912221	+	0.409698i	$0.865634\pi$
$12$	129.323	−	35.7763i	0.898075	−	0.248446i
$13$	3.09167	+	5.35493i	0.0182939	+	0.0316860i	0.875027	−	0.484073i	$-0.160843\pi$
$13$	3.09167	+	5.35493i	0.0182939	+	0.0316860i	−0.856734	+	0.515759i	$0.827510\pi$
$14$	−66.0333	+	38.1243i	−0.336905	+	0.194512i
$15$	−26.8290	−	96.9804i	−0.119240	−	0.431024i
$16$	−102.409	+	177.378i	−0.400036	+	0.692882i
$17$			452.463i			1.56562i	0.622264	+	0.782808i	$0.286213\pi$
$17$			452.463i			1.56562i	−0.622264	+	0.782808i	$0.713787\pi$
$18$	−43.4849	−	72.5789i	−0.134213	−	0.224009i
$19$	621.658			1.72204			0.861022	−	0.508568i	$-0.169825\pi$
$19$	621.658			1.72204			0.861022	+	0.508568i	$0.169825\pi$
$20$	144.355	+	83.3433i	0.360887	+	0.208358i
$21$	−468.292	−	460.772i	−1.06189	−	1.04483i
$22$	−73.9586	−	128.100i	−0.152807	−	0.264670i
$23$	−28.0293	+	16.1827i	−0.0529854	+	0.0305911i	−0.526259	−	0.850325i	$-0.676406\pi$
$23$	−28.0293	+	16.1827i	−0.0529854	+	0.0305911i	0.473273	+	0.880916i	$0.343072\pi$
$24$	281.272	+	72.9318i	0.488320	+	0.126618i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$			6.45882i			0.00955446i
$27$	502.813	−	527.844i	0.689730	−	0.724066i
$28$	1088.30			1.38814
$29$	−869.127	−	501.791i	−1.03344	−	0.596660i	−0.115475	−	0.993310i	$-0.536839\pi$
$29$	−869.127	−	501.791i	−1.03344	−	0.596660i	−0.917970	+	0.396651i	$0.870172\pi$
$30$	26.3808	−	101.741i	0.0293120	−	0.113046i
$31$	681.173	+	1179.83i	0.708816	+	1.22771i	0.965296	+	0.261156i	$0.0841039\pi$
$31$	681.173	+	1179.83i	0.708816	+	1.22771i	−0.256480	+	0.966550i	$0.582563\pi$
$32$	−632.648	+	365.259i	−0.617820	+	0.356699i
$33$	893.866	−	908.454i	0.820814	−	0.834209i
$34$	−236.311	+	409.302i	−0.204421	+	0.354067i
$35$		−	816.126i		−	0.666225i
$36$	19.5480	+	1207.46i	0.0150833	+	0.931685i
$37$	−711.751			−0.519906			−0.259953	−	0.965621i	$-0.583707\pi$
$37$	−711.751			−0.519906			−0.259953	+	0.965621i	$0.583707\pi$
$38$	562.357	+	324.677i	0.389444	+	0.224846i
$39$	−53.6355	+	14.8379i	−0.0352633	+	0.00975535i
$40$	180.484	+	312.608i	0.112803	+	0.195380i
$41$	−917.903	+	529.951i	−0.546046	+	0.315260i	−0.747526	−	0.664233i	$-0.768758\pi$
$41$	−917.903	+	529.951i	−0.546046	+	0.315260i	0.201480	+	0.979493i	$0.435425\pi$
$42$	−182.971	−	661.396i	−0.103725	−	0.374941i
$43$	118.544	−	205.324i	0.0641125	−	0.111046i	−0.832187	−	0.554494i	$-0.812912\pi$
$43$	118.544	−	205.324i	0.0641125	−	0.111046i	0.896300	+	0.443448i	$0.146245\pi$
$44$			2111.23i			1.09051i
$45$	905.489	−	14.6592i	0.447155	−	0.00723913i
$46$	−33.8073			−0.0159770
$47$	−2172.54	−	1254.32i	−0.983496	−	0.567822i	−0.0801724	−	0.996781i	$-0.525547\pi$
$47$	−2172.54	−	1254.32i	−0.983496	−	0.567822i	−0.903324	+	0.428959i	$0.858880\pi$
$48$	−1313.96	−	1292.86i	−0.570296	−	0.561138i
$49$	−1463.75	−	2535.28i	−0.609640	−	1.05593i
$50$	113.076	−	65.2845i	0.0452304	−	0.0261138i
$51$	−3941.81	−	1022.08i	−1.51550	−	0.392958i
$52$	46.0934	−	79.8361i	0.0170464	−	0.0295252i
$53$		−	1128.18i		−	0.401629i	−0.979629	−	0.200815i	$-0.935641\pi$
$53$		−	1128.18i		−	0.401629i	0.979629	−	0.200815i	$-0.0643589\pi$
$54$	730.530	−	214.885i	0.250525	−	0.0736918i
$55$	1583.23			0.523381
$56$	2041.02	+	1178.38i	0.650834	+	0.375759i
$57$	−1404.28	+	5415.82i	−0.432220	+	1.66692i
$58$	−524.147	−	907.849i	−0.155811	−	0.269872i
$59$	−1601.37	+	924.551i	−0.460032	+	0.265599i	−0.712058	−	0.702121i	$-0.752236\pi$
$59$	−1601.37	+	924.551i	−0.460032	+	0.265599i	0.252026	+	0.967720i	$0.418903\pi$
$60$	−1052.17	+	1069.34i	−0.292269	+	0.297039i
$61$	−2765.44	+	4789.87i	−0.743197	+	1.28725i	0.207836	+	0.978164i	$0.433358\pi$
$61$	−2765.44	+	4789.87i	−0.743197	+	1.28725i	−0.951033	+	0.309091i	$0.899975\pi$
$62$			1423.04i			0.370198i
$63$	5072.04	−	3038.86i	1.27791	−	0.765649i
$64$	2514.03			0.613776
$65$	−59.8699	−	34.5659i	−0.0141704	−	0.00818128i
$66$	1283.06	−	354.951i	0.294551	−	0.0814855i
$67$	404.470	+	700.562i	0.0901024	+	0.156062i	0.907554	−	0.419935i	$-0.137947\pi$
$67$	404.470	+	700.562i	0.0901024	+	0.156062i	−0.817452	+	0.575997i	$0.804614\pi$
$68$	5841.97	−	3372.86i	1.26340	−	0.729426i
$69$	−77.6659	−	280.744i	−0.0163129	−	0.0589674i
$70$	426.243	−	738.275i	0.0869884	−	0.150668i
$71$		−	1754.60i		−	0.348066i	−0.984740	−	0.174033i	$-0.944320\pi$
$71$		−	1754.60i		−	0.348066i	0.984740	−	0.174033i	$-0.0556800\pi$
$72$	−1270.75	+	2285.67i	−0.245129	+	0.440908i
$73$	−1908.13			−0.358065			−0.179032	−	0.983843i	$-0.557297\pi$
$73$	−1908.13			−0.358065			−0.179032	+	0.983843i	$0.557297\pi$
$74$	−643.856	−	371.731i	−0.117578	−	0.0678836i
$75$	801.908	+	789.030i	0.142561	+	0.140272i
$76$	−4634.12	−	8026.53i	−0.802306	−	1.38963i
$77$	8952.03	−	5168.46i	1.50987	−	0.871725i
$78$	−56.2686	−	14.5900i	−0.00924862	−	0.00239810i
$79$	1819.34	−	3151.19i	0.291514	−	0.504918i	−0.682654	−	0.730742i	$-0.739174\pi$
$79$	1819.34	−	3151.19i	0.291514	−	0.504918i	0.974168	+	0.225824i	$0.0725075\pi$
$80$		−	2289.94i		−	0.357803i
$81$	3462.71	+	5572.82i	0.527771	+	0.849387i
$82$	−1107.12			−0.164653
$83$	8463.40	+	4886.35i	1.22854	+	0.709297i	0.966724	−	0.255821i	$-0.0823459\pi$
$83$	8463.40	+	4886.35i	1.22854	+	0.709297i	0.261814	+	0.965118i	$0.415679\pi$
$84$	−2458.39	+	9481.15i	−0.348412	+	1.34370i
$85$	−2529.34	−	4380.95i	−0.350082	−	0.606360i
$86$	214.472	−	123.825i	0.0289984	−	0.0167422i
$87$	6334.85	−	6438.24i	0.836947	−	0.850606i
$88$	−2285.98	+	3959.43i	−0.295194	+	0.511291i
$89$		−	2458.88i		−	0.310425i	−0.987881	−	0.155213i	$-0.950394\pi$
$89$		−	2458.88i		−	0.310425i	0.987881	−	0.155213i	$-0.0496063\pi$
$90$	826.769	+	459.654i	0.102070	+	0.0567474i
$91$	−451.362			−0.0545057
$92$	417.886	+	241.266i	0.0493721	+	0.0285050i
$93$	−11817.2	+	3269.16i	−1.36631	+	0.377981i
$94$	−1310.20	−	2269.33i	−0.148280	−	0.256828i
$95$	−6019.17	+	3475.17i	−0.666945	+	0.385061i
$96$	−1752.99	−	6336.66i	−0.190212	−	0.687572i
$97$	−6786.18	+	11754.0i	−0.721244	+	1.24923i	0.239258	+	0.970956i	$0.423096\pi$
$97$	−6786.18	+	11754.0i	−0.721244	+	1.24923i	−0.960502	+	0.278274i	$0.910238\pi$
$98$		−	3057.92i		−	0.318400i
$99$	5895.18	+	9839.41i	0.601488	+	1.00392i
$100$	−1863.61			−0.186361
$101$	−495.647	−	286.162i	−0.0485881	−	0.0280523i	0.475509	−	0.879711i	$-0.342264\pi$
$101$	−495.647	−	286.162i	−0.0485881	−	0.0280523i	−0.524097	+	0.851658i	$0.675597\pi$
$102$	−3031.99	−	2983.30i	−0.291425	−	0.286745i
$103$	902.590	+	1563.33i	0.0850778	+	0.147359i	0.905424	−	0.424508i	$-0.139553\pi$
$103$	902.590	+	1563.33i	0.0850778	+	0.147359i	−0.820347	+	0.571867i	$0.806219\pi$
$104$	172.889	−	99.8175i	0.0159846	−	0.00922869i
$105$	7110.01	+	1843.57i	0.644899	+	0.167218i
$106$	589.220	−	1020.56i	0.0524403	−	0.0908293i
$107$		−	2223.92i		−	0.194246i	−0.995272	−	0.0971230i	$-0.969036\pi$
$107$		−	2223.92i		−	0.194246i	0.995272	−	0.0971230i	$-0.0309640\pi$
$108$	−10563.5	−	2557.28i	−0.905647	−	0.219245i
$109$	13838.3			1.16474			0.582370	−	0.812924i	$-0.302126\pi$
$109$	13838.3			1.16474			0.582370	+	0.812924i	$0.302126\pi$
$110$	1432.20	+	826.882i	0.118364	+	0.0683374i
$111$	1607.80	−	6200.71i	0.130492	−	0.503263i
$112$	−7475.51	−	12948.0i	−0.595943	−	1.03220i
$113$	−12739.3	+	7355.03i	−0.997673	+	0.576007i	−0.907559	−	0.419925i	$-0.862057\pi$
$113$	−12739.3	+	7355.03i	−0.997673	+	0.576007i	−0.0901141	+	0.995931i	$0.528723\pi$
$114$	−4098.88	+	4165.77i	−0.315395	+	0.320543i
$115$	180.928	−	313.377i	0.0136808	−	0.0236958i
$116$			14962.3i			1.11194i
$117$	−8.10735	−	500.785i	−0.000592253	−	0.0365830i
$118$	−1931.48			−0.138716
$119$	−28603.3	−	16514.1i	−2.01986	−	1.16617i
$120$	−3131.11	+	866.200i	−0.217438	+	0.0601528i
$121$	2705.95	+	4686.85i	0.184820	+	0.320118i
$122$	−5003.27	+	2888.64i	−0.336151	+	0.194077i
$123$	−2543.40	−	9193.80i	−0.168114	−	0.607694i
$124$	10155.5	−	17589.9i	0.660480	−	1.14398i
$125$			1397.54i			0.0894427i
$126$	6175.33	−	99.9743i	0.388973	−	0.00629720i
$127$	16529.3			1.02482			0.512410	−	0.858741i	$-0.328753\pi$
$127$	16529.3			1.02482			0.512410	+	0.858741i	$0.328753\pi$
$128$	12396.6	+	7157.17i	0.756627	+	0.436839i
$129$	1520.98	+	1496.56i	0.0913997	+	0.0899320i
$130$	−36.1059	−	62.5372i	−0.00213644	−	0.00370043i
$131$	22360.7	−	12910.0i	1.30300	−	0.752286i	0.322080	−	0.946712i	$-0.395618\pi$
$131$	22360.7	−	12910.0i	1.30300	−	0.752286i	0.980917	+	0.194427i	$0.0622846\pi$
$132$	−18392.8	−	4769.12i	−1.05560	−	0.273710i
$133$	−22689.4	+	39299.2i	−1.28269	+	2.22168i
$134$			844.979i			0.0470583i
$135$	−1917.73	+	7921.64i	−0.105225	+	0.434658i
$136$	14608.2			0.789803
$137$	12949.8	+	7476.58i	0.689958	+	0.398347i	0.803596	−	0.595175i	$-0.202917\pi$
$137$	12949.8	+	7476.58i	0.689958	+	0.398347i	−0.113638	+	0.993522i	$0.536250\pi$
$138$	76.3685	−	294.526i	0.00401011	−	0.0154656i
$139$	−3306.67	−	5727.33i	−0.171144	−	0.296430i	0.767676	−	0.640838i	$-0.221413\pi$
$139$	−3306.67	−	5727.33i	−0.171144	−	0.296430i	−0.938820	+	0.344408i	$0.888080\pi$
$140$	−10537.4	+	6083.77i	−0.537623	+	0.310397i
$141$	15835.1	−	16093.6i	0.796495	−	0.809495i
$142$	916.387	−	1587.23i	0.0454467	−	0.0787160i
$143$		−	875.612i		−	0.0428193i
$144$	14231.4	−	8526.62i	0.686316	−	0.411199i
$145$	11220.4			0.533669
$146$	−1726.11	−	996.569i	−0.0809771	−	0.0467521i
$147$	25393.6	−	7024.98i	1.17514	−	0.325095i
$148$	5305.72	+	9189.77i	0.242226	+	0.419548i
$149$	−28399.4	+	16396.4i	−1.27919	+	0.738543i	−0.976700	−	0.214609i	$-0.931152\pi$
$149$	−28399.4	+	16396.4i	−1.27919	+	0.738543i	−0.302493	+	0.953151i	$0.597819\pi$
$150$	313.321	+	1132.58i	0.0139254	+	0.0503369i
$151$	−2334.87	+	4044.11i	−0.102402	+	0.177366i	−0.912674	−	0.408689i	$-0.865986\pi$
$151$	−2334.87	+	4044.11i	−0.102402	+	0.177366i	0.810272	+	0.586054i	$0.199319\pi$
$152$		−	20070.8i		−	0.868716i
$153$	17808.6	−	32031.9i	0.760758	−	1.36836i
$154$	10797.4			0.455281
$155$	−13190.8	−	7615.74i	−0.549047	−	0.316992i
$156$	591.403	+	581.906i	0.0243016	+	0.0239113i
$157$	16316.0	+	28260.2i	0.661934	+	1.14650i	0.980107	+	0.198470i	$0.0635974\pi$
$157$	16316.0	+	28260.2i	0.661934	+	1.14650i	−0.318173	+	0.948033i	$0.603069\pi$
$158$	3291.58	−	1900.40i	0.131853	−	0.0761255i
$159$	9828.57	+	2548.48i	0.388773	+	0.100806i
$160$	4083.72	−	7073.22i	0.159520	−	0.276298i
$161$		−	2362.56i		−	0.0911447i
$162$	221.842	+	6849.71i	0.00845307	+	0.261001i
$163$	−27389.5			−1.03088			−0.515441	−	0.856925i	$-0.672372\pi$
$163$	−27389.5			−1.03088			−0.515441	+	0.856925i	$0.672372\pi$
$164$	13684.9	+	7901.00i	0.508809	+	0.293761i
$165$	−3576.41	+	13792.9i	−0.131365	+	0.506627i
$166$	5104.04	+	8840.46i	0.185224	+	0.320818i
$167$	−26946.8	+	15557.7i	−0.966216	+	0.557845i	−0.898081	−	0.439831i	$-0.855038\pi$
$167$	−26946.8	+	15557.7i	−0.966216	+	0.557845i	−0.0681355	+	0.997676i	$0.521705\pi$
$168$	−14876.5	+	15119.3i	−0.527086	+	0.535688i
$169$	14261.4	−	24701.4i	0.499331	−	0.864866i
$170$		−	5284.06i		−	0.182840i
$171$	−44009.9	−	24467.9i	−1.50508	−	0.836768i
$172$	−3534.73			−0.119481
$173$	5253.14	+	3032.90i	0.175520	+	0.101337i	0.585186	−	0.810899i	$-0.301021\pi$
$173$	5253.14	+	3032.90i	0.175520	+	0.101337i	−0.409666	+	0.912236i	$0.634355\pi$
$174$	9093.10	−	2515.54i	0.300340	−	0.0830871i
$175$	4562.28	+	7902.11i	0.148972	+	0.258028i
$176$	25118.2	−	14502.0i	0.810891	−	0.468168i
$177$	−4437.21	−	16039.5i	−0.141633	−	0.511969i
$178$	1284.21	−	2224.32i	0.0405319	−	0.0702033i
$179$			22086.9i			0.689332i	0.938725	+	0.344666i	$0.112008\pi$
$179$			22086.9i			0.689332i	−0.938725	+	0.344666i	$0.887992\pi$
$180$	−6939.20	−	11581.9i	−0.214173	−	0.357467i
$181$	−13034.4			−0.397864			−0.198932	−	0.980013i	$-0.563747\pi$
$181$	−13034.4			−0.397864			−0.198932	+	0.980013i	$0.563747\pi$
$182$	−408.306	−	235.736i	−0.0123266	−	0.00711676i
$183$	−35482.0	−	34912.2i	−1.05951	−	1.04250i
$184$	522.474	+	904.952i	0.0154322	+	0.0267294i
$185$	6891.50	−	3978.81i	0.201359	−	0.116255i
$186$	−12397.4	−	3214.55i	−0.358347	−	0.0929169i
$187$	32036.2	−	55488.4i	0.916133	−	1.58679i
$188$			37401.0i			1.05820i
$189$	15016.8	+	51051.7i	0.420393	+	1.42918i
$190$	−7260.00			−0.201108
$191$	−14673.0	−	8471.45i	−0.402209	−	0.232215i	0.285228	−	0.958460i	$-0.407931\pi$
$191$	−14673.0	−	8471.45i	−0.402209	−	0.232215i	−0.687437	+	0.726244i	$0.741264\pi$
$192$	−5679.02	+	21901.9i	−0.154053	+	0.594128i
$193$	7094.57	+	12288.2i	0.190463	+	0.329892i	0.945404	−	0.325901i	$-0.105668\pi$
$193$	7094.57	+	12288.2i	0.190463	+	0.329892i	−0.754940	+	0.655793i	$0.772334\pi$
$194$	−12277.7	+	7088.52i	−0.326222	+	0.188344i
$195$	436.377	−	443.499i	0.0114761	−	0.0116633i
$196$	−21822.9	+	37798.3i	−0.568067	+	0.983921i
$197$			4241.79i			0.109299i	0.998506	+	0.0546495i	$0.0174042\pi$
$197$			4241.79i			0.109299i	−0.998506	+	0.0546495i	$0.982596\pi$
$198$	193.943	+	11979.7i	0.00494703	+	0.305574i
$199$	−45721.0			−1.15454			−0.577271	−	0.816553i	$-0.695882\pi$
$199$	−45721.0			−1.15454			−0.577271	+	0.816553i	$0.695882\pi$
$200$	−3495.06	−	2017.87i	−0.0873765	−	0.0504468i
$201$	−7016.90	+	1941.18i	−0.173681	+	0.0480478i
$202$	−298.911	−	517.729i	−0.00732553	−	0.0126882i
$203$	63443.3	−	36629.0i	1.53955	−	0.888859i
$204$	16187.4	+	58513.8i	0.388972	+	1.40604i
$205$	5925.04	−	10262.5i	0.140988	−	0.244199i
$206$			1885.60i			0.0444341i
$207$	2621.25	−	42.4363i	0.0611742	−	0.000990368i
$208$	−1266.46			−0.0292728
$209$	−76237.8	−	44015.9i	−1.74533	−	1.00767i
$210$	5468.92	+	5381.10i	0.124012	+	0.122020i
$211$	2418.45	+	4188.87i	0.0543215	+	0.0940876i	0.891907	−	0.452218i	$-0.149367\pi$
$211$	2418.45	+	4188.87i	0.0543215	+	0.0940876i	−0.837586	+	0.546306i	$0.816034\pi$
$212$	−14566.5	+	8409.94i	−0.324102	+	0.187121i
$213$	15285.9	+	3963.53i	0.336925	+	0.0873621i
$214$	1161.50	−	2011.78i	0.0253625	−	0.0439292i
$215$			2650.73i			0.0573440i
$216$	−17042.0	−	16233.8i	−0.365269	−	0.347947i
$217$	−99446.4			−2.11188
$218$	12518.2	+	7227.40i	0.263408	+	0.152079i
$219$	4310.33	−	16623.4i	0.0898715	−	0.346603i
$220$	−11802.1	−	20441.8i	−0.243845	−	0.422352i
$221$	−2422.91	+	1398.87i	−0.0496080	+	0.0286412i
$222$	4692.91	−	4769.50i	0.0952217	−	0.0967758i
$223$	19214.1	−	33279.9i	0.386377	−	0.669225i	−0.605582	−	0.795783i	$-0.707060\pi$
$223$	19214.1	−	33279.9i	0.386377	−	0.669225i	0.991959	+	0.126558i	$0.0403930\pi$
$224$		−	53325.3i		−	1.06277i
$225$	−8685.41	+	5203.77i	−0.171564	+	0.102791i
$226$	−15365.4			−0.300835
$227$	85886.5	+	49586.6i	1.66676	+	0.962305i	0.969367	+	0.245617i	$0.0789906\pi$
$227$	85886.5	+	49586.6i	1.66676	+	0.962305i	0.697394	+	0.716688i	$0.254343\pi$
$228$	80394.5	−	22240.6i	1.54652	−	0.427836i
$229$	−10703.8	−	18539.6i	−0.204112	−	0.353533i	0.745737	−	0.666240i	$-0.232097\pi$
$229$	−10703.8	−	18539.6i	−0.204112	−	0.353533i	−0.949849	+	0.312707i	$0.898764\pi$
$230$	327.338	−	188.989i	0.00618787	−	0.00357257i
$231$	24805.0	+	89664.4i	0.464854	+	1.68034i
$232$	−16200.8	+	28060.6i	−0.300996	+	0.521340i
$233$		−	62137.7i		−	1.14457i	−0.820054	−	0.572286i	$-0.806057\pi$
$233$		−	62137.7i		−	1.14457i	0.820054	−	0.572286i	$-0.193943\pi$
$234$	254.214	−	457.248i	0.00464267	−	0.00835065i
$235$	28047.4			0.507875
$236$	23874.7	+	13784.1i	0.428661	+	0.247487i
$237$	23343.1	+	22968.3i	0.415587	+	0.408913i
$238$	−17249.8	−	29877.6i	−0.304531	−	0.527463i
$239$	73441.6	−	42401.5i	1.28572	−	0.742310i	0.307831	−	0.951441i	$-0.400397\pi$
$239$	73441.6	−	42401.5i	1.28572	−	0.742310i	0.977888	+	0.209131i	$0.0670634\pi$
$240$	19949.7	+	5172.81i	0.346349	+	0.0898058i
$241$	6607.02	−	11443.7i	0.113755	−	0.197030i	−0.803526	−	0.595269i	$-0.797045\pi$
$241$	6607.02	−	11443.7i	0.113755	−	0.197030i	0.917281	+	0.398239i	$0.130379\pi$
$242$			5653.02i			0.0965271i
$243$	−56371.9	+	17578.1i	−0.954663	+	0.297687i
$244$	82459.2			1.38503
$245$	28345.3	+	16365.2i	0.472225	+	0.272639i
$246$	2500.92	−	9645.15i	0.0413265	−	0.159382i
$247$	1921.96	+	3328.93i	0.0315029	+	0.0545646i
$248$	38091.8	−	21992.3i	0.619339	−	0.357575i
$249$	−61687.6	+	62694.4i	−0.994946	+	1.01118i
$250$	−729.903	+	1264.23i	−0.0116784	+	0.0202277i
$251$			12222.3i			0.194002i	0.995284	+	0.0970009i	$0.0309250\pi$
$251$			12222.3i			0.194002i	−0.995284	+	0.0970009i	$0.969075\pi$
$252$	−77045.5	−	42834.6i	−1.21324	−	0.674517i
$253$	4583.21			0.0716026
$254$	14952.6	+	8632.86i	0.231765	+	0.133810i
$255$	43880.1	−	12139.1i	0.674818	−	0.186684i
$256$	−12636.2	−	21886.5i	−0.192813	−	0.333961i
$257$	−12206.6	+	7047.50i	−0.184812	+	0.106701i	−0.589551	−	0.807731i	$-0.700695\pi$
$257$	−12206.6	+	7047.50i	−0.184812	+	0.106701i	0.404740	+	0.914432i	$0.367362\pi$
$258$	594.277	+	2148.17i	0.00892791	+	0.0322723i
$259$	25977.7	−	44994.7i	0.387258	−	0.670751i
$260$			1030.68i			0.0152467i
$261$	41779.3	+	69732.1i	0.613310	+	1.02365i
$262$	26970.3			0.392901
$263$	−3595.01	−	2075.58i	−0.0519742	−	0.0300073i	0.473788	−	0.880639i	$-0.342886\pi$
$263$	−3595.01	−	2075.58i	−0.0519742	−	0.0300073i	−0.525762	+	0.850632i	$0.676220\pi$
$264$	−29330.3	−	28859.3i	−0.420832	−	0.414074i
$265$	6306.70	+	10923.5i	0.0898071	+	0.155550i
$266$	−41050.1	+	23700.3i	−0.580164	+	0.334958i
$267$	21421.5	+	5554.44i	0.300488	+	0.0779144i
$268$	6030.20	−	10444.6i	0.0839580	−	0.145420i
$269$			94699.5i			1.30871i	0.756188	+	0.654354i	$0.227060\pi$
$269$			94699.5i			1.30871i	−0.756188	+	0.654354i	$0.772940\pi$
$270$	−5872.08	+	6164.40i	−0.0805498	+	0.0845597i
$271$	−42389.4			−0.577190			−0.288595	−	0.957451i	$-0.593188\pi$
$271$	−42389.4			−0.577190			−0.288595	+	0.957451i	$0.593188\pi$
$272$	−80256.9	−	46336.3i	−1.08479	−	0.626302i
$273$	1019.60	−	3932.22i	0.0136805	−	0.0527610i
$274$	7809.68	+	13526.8i	0.104024	+	0.180174i
$275$	−15329.5	+	8850.52i	−0.202705	+	0.117032i
$276$	−3045.86	+	3095.57i	−0.0399846	+	0.0406371i
$277$	−9035.21	+	15649.4i	−0.117755	+	0.203957i	−0.918878	−	0.394543i	$-0.870903\pi$
$277$	−9035.21	+	15649.4i	−0.117755	+	0.203957i	0.801123	+	0.598500i	$0.204236\pi$
$278$		−	6907.99i		−	0.0893844i
$279$	−1786.25	−	110335.i	−0.0229475	−	1.41745i
$280$	−26349.4			−0.336089
$281$	29059.0	+	16777.2i	0.368017	+	0.212474i	0.672592	−	0.740014i	$-0.265181\pi$
$281$	29059.0	+	16777.2i	0.368017	+	0.212474i	−0.304575	+	0.952488i	$0.598514\pi$
$282$	22729.9	−	6288.07i	0.285824	−	0.0790713i
$283$	46457.3	+	80466.4i	0.580071	+	1.00471i	0.995470	+	0.0950730i	$0.0303085\pi$
$283$	46457.3	+	80466.4i	0.580071	+	1.00471i	−0.415400	+	0.909639i	$0.636358\pi$
$284$	−22654.5	+	13079.6i	−0.280879	+	0.162165i
$285$	−16678.4	−	60288.6i	−0.205336	−	0.742242i
$286$	457.311	−	792.086i	0.00559087	−	0.00968368i
$287$		−	77369.2i		−	0.939300i
$288$	59164.3	−	957.828i	0.713304	−	0.0115479i
$289$	−121202.			−1.45115
$290$	10150.1	+	5860.14i	0.120690	+	0.0696806i
$291$	−87070.2	−	85672.0i	−1.02821	−	1.01170i
$292$	14224.0	+	24636.8i	0.166824	+	0.288947i
$293$	−15030.9	+	8678.09i	−0.175085	+	0.101085i	−0.584981	−	0.811047i	$-0.698898\pi$
$293$	−15030.9	+	8678.09i	−0.175085	+	0.101085i	0.409896	+	0.912132i	$0.365565\pi$
$294$	26640.3	+	6907.63i	0.308208	+	0.0799161i
$295$	10336.8	−	17903.9i	0.118780	−	0.205732i
$296$			22979.6i			0.262276i
$297$	−99036.8	+	29131.7i	−1.12275	+	0.330257i
$298$	−34253.8			−0.385723
$299$	−173.314	−	100.063i	−0.00193862	−	0.00111926i
$300$	4209.78	−	16235.6i	0.0467753	−	0.180396i
$301$	8653.30	+	14988.0i	0.0955100	+	0.165428i
$302$	−4224.29	+	2438.89i	−0.0463169	+	0.0267411i
$303$	3612.65	−	3671.61i	0.0393496	−	0.0399918i
$304$	−63663.4	+	110268.i	−0.688879	+	1.19317i
$305$		−	61837.0i		−	0.664735i
$306$	32839.3	−	19675.3i	0.350712	−	0.210125i
$307$	86351.9			0.916211			0.458105	−	0.888898i	$-0.348528\pi$
$307$	86351.9			0.916211			0.458105	+	0.888898i	$0.348528\pi$
$308$	−133465.	−	77056.0i	−1.40691	−	0.812279i
$309$	−15658.5	+	4331.81i	−0.163996	+	0.0453683i
$310$	−7955.04	−	13778.5i	−0.0827788	−	0.143377i
$311$	−163809.	+	94575.3i	−1.69363	+	0.977815i	−0.742078	+	0.670313i	$0.766160\pi$
$311$	−163809.	+	94575.3i	−1.69363	+	0.977815i	−0.951547	+	0.307502i	$0.900507\pi$
$312$	479.056	+	1731.67i	0.00492127	+	0.0177892i
$313$	52054.5	−	90161.0i	0.531336	−	0.920302i	−0.467995	−	0.883731i	$-0.655023\pi$
$313$	52054.5	−	90161.0i	0.531336	−	0.920302i	0.999331	−	0.0365703i	$-0.0116433\pi$
$314$			34085.8i			0.345712i
$315$	−32122.1	+	57777.2i	−0.323729	+	0.582285i
$316$	−54248.8			−0.543270
$317$	108287.	+	62519.4i	1.07760	+	0.622151i	0.930247	−	0.366933i	$-0.119592\pi$
$317$	108287.	+	62519.4i	1.07760	+	0.622151i	0.147350	+	0.989084i	$0.452925\pi$
$318$	7560.00	+	7438.60i	0.0747597	+	0.0735592i
$319$	71057.7	+	123076.i	0.698281	+	1.20946i
$320$	−24342.0	+	14053.8i	−0.237714	+	0.137244i
$321$	19374.6	+	5023.69i	0.188028	+	0.0487543i
$322$	1233.91	−	2137.19i	0.0119007	−	0.0206126i
$323$			281277.i			2.69606i
$324$	46140.9	−	86251.1i	0.439538	−	0.821627i
$325$	772.917			0.00731756
$326$	−24776.8	−	14304.9i	−0.233136	−	0.134601i
$327$	−31259.7	+	120558.i	−0.292341	+	1.12746i
$328$	17110.0	+	29635.4i	0.159038	+	0.275463i
$329$	158588.	−	91560.9i	1.46514	−	0.845898i
$330$	−10439.0	+	10609.3i	−0.0958583	+	0.0974227i
$331$	87777.3	−	152035.i	0.801172	−	1.38767i	−0.117672	−	0.993052i	$-0.537543\pi$
$331$	87777.3	−	152035.i	0.801172	−	1.38767i	0.918845	−	0.394619i	$-0.129123\pi$
$332$		−	145700.i		−	1.32186i
$333$	50388.0	+	28014.0i	0.454401	+	0.252631i
$334$	−32501.7			−0.291349
$335$	−7832.52	−	4522.11i	−0.0697930	−	0.0402950i
$336$	129688.	−	35877.3i	1.14874	−	0.317791i
$337$	27782.8	+	48121.2i	0.244634	+	0.423718i	0.962029	−	0.272949i	$-0.0879990\pi$
$337$	27782.8	+	48121.2i	0.244634	+	0.423718i	−0.717395	+	0.696667i	$0.754666\pi$
$338$	25801.9	−	14896.8i	0.225849	−	0.130394i
$339$	−35299.1	−	127598.i	−0.307160	−	1.11031i
$340$	−37709.8	+	65315.2i	−0.326209	+	0.565011i
$341$		−	192919.i		−	1.65908i
$342$	−27032.7	−	45119.2i	−0.231120	−	0.385753i
$343$	38432.1			0.326667
$344$	−6629.09	−	3827.31i	−0.0560193	−	0.0323427i
$345$	2321.40	+	2284.12i	0.0195035	+	0.0191903i
$346$	3168.02	+	5487.18i	0.0264628	+	0.0458350i
$347$	−117155.	+	67639.5i	−0.972976	+	0.561748i	−0.900142	−	0.435596i	$-0.856538\pi$
$347$	−117155.	+	67639.5i	−0.972976	+	0.561748i	−0.0728340	+	0.997344i	$0.523204\pi$
$348$	−130350.	−	33798.8i	−1.07635	−	0.279089i
$349$	−8163.58	+	14139.7i	−0.0670239	+	0.116089i	−0.897590	−	0.440831i	$-0.854684\pi$
$349$	−8163.58	+	14139.7i	−0.0670239	+	0.116089i	0.830566	+	0.556920i	$0.188017\pi$
$350$			9531.08i			0.0778048i
$351$	4381.10	+	1060.61i	0.0355606	+	0.00860876i
$352$	103448.			0.834900
$353$	−140699.	−	81232.4i	−1.12912	−	0.651899i	−0.185408	−	0.982662i	$-0.559361\pi$
$353$	−140699.	−	81232.4i	−1.12912	−	0.651899i	−0.943714	+	0.330763i	$0.892694\pi$
$354$	4363.09	−	16826.9i	0.0348167	−	0.134276i
$355$	9808.53	+	16988.9i	0.0778300	+	0.134806i
$356$	−31747.8	+	18329.6i	−0.250503	+	0.144628i
$357$	208482.	−	211885.i	1.63581	−	1.66251i
$358$	−11535.5	+	19980.0i	−0.0900054	+	0.155894i
$359$			170939.i			1.32633i	0.748472	+	0.663166i	$0.230788\pi$
$359$			170939.i			1.32633i	−0.748472	+	0.663166i	$0.769212\pi$
$360$	−473.288	−	29234.6i	−0.00365191	−	0.225576i
$361$	256137.			1.96543
$362$	−11791.1	−	6807.58i	−0.0899779	−	0.0519488i
$363$	−46943.9	+	12986.7i	−0.356259	+	0.0985567i
$364$	3364.66	+	5827.76i	0.0253944	+	0.0439844i
$365$	18475.4	−	10666.8i	0.138678	−	0.0800657i
$366$	−13863.5	−	50113.3i	−0.103493	−	0.374102i
$367$	15580.1	−	26985.5i	0.115674	−	0.200354i	−0.802375	−	0.596821i	$-0.796430\pi$
$367$	15580.1	−	26985.5i	0.115674	−	0.200354i	0.918049	+	0.396467i	$0.129764\pi$
$368$		−	6629.02i		−	0.0489501i
$369$	85840.9	−	1389.70i	0.630436	−	0.0102063i
$370$	8312.15			0.0607169
$371$	71319.8	+	41176.5i	0.518158	+	0.299159i
$372$	130301.	+	128208.i	0.941589	+	0.926469i
$373$	−108239.	−	187475.i	−0.777974	−	1.34749i	−0.933108	−	0.359596i	$-0.882914\pi$
$373$	−108239.	−	187475.i	−0.777974	−	1.34749i	0.155134	−	0.987893i	$-0.450419\pi$
$374$	57960.5	−	33463.5i	0.414371	−	0.239237i
$375$	−12175.3	−	3156.95i	−0.0865796	−	0.0224495i
$376$	−40496.9	+	70142.7i	−0.286448	+	0.496143i
$377$		−	6205.48i		−	0.0436609i
$378$	−13078.7	+	54024.7i	−0.0915337	+	0.378102i
$379$	60563.5			0.421631			0.210816	−	0.977526i	$-0.432388\pi$
$379$	60563.5			0.421631			0.210816	+	0.977526i	$0.432388\pi$
$380$	89739.3	+	51811.0i	0.621464	+	0.358802i
$381$	−37338.6	+	144002.i	−0.257222	+	0.992014i
$382$	−8848.87	−	15326.7i	−0.0606403	−	0.105032i
$383$	−176171.	+	101712.i	−1.20098	+	0.693388i	−0.960774	−	0.277333i	$-0.910550\pi$
$383$	−176171.	+	101712.i	−1.20098	+	0.693388i	−0.240210	+	0.970721i	$0.577216\pi$
$384$	−90355.5	+	91830.2i	−0.612763	+	0.622763i
$385$	−57785.1	+	100087.i	−0.389847	+	0.675235i
$386$			14821.3i			0.0994745i
$387$	−16473.7	+	9870.02i	−0.109994	+	0.0659016i
$388$	202349.			1.34412
$389$	58699.6	+	33890.2i	0.387914	+	0.223962i	0.681256	−	0.732045i	$-0.261434\pi$
$389$	58699.6	+	33890.2i	0.387914	+	0.223962i	−0.293342	+	0.956008i	$0.594767\pi$
$390$	626.379	−	173.284i	0.00411821	−	0.00113927i
$391$	−7322.07	−	12682.2i	−0.0478939	−	0.0829547i
$392$	−81854.0	+	47258.5i	−0.532682	+	0.307544i
$393$	61959.0	+	223967.i	0.401162	+	1.45011i
$394$	−2215.38	+	3837.16i	−0.0142711	+	0.0247182i
$395$			40681.7i			0.260738i
$396$	83096.1	−	149463.i	0.529896	−	0.953111i
$397$	−279802.			−1.77529			−0.887645	−	0.460529i	$-0.847660\pi$
$397$	−279802.			−1.77529			−0.887645	+	0.460529i	$0.847660\pi$
$398$	−41359.6	−	23879.0i	−0.261102	−	0.150747i
$399$	−291117.	−	286442.i	−1.82861	−	1.79925i
$400$	12801.1	+	22172.2i	0.0800071	+	0.138576i
$401$	259389.	−	149758.i	1.61311	−	0.931328i	0.624463	−	0.781055i	$-0.285318\pi$
$401$	259389.	−	149758.i	1.61311	−	0.931328i	0.988644	−	0.150273i	$-0.0480154\pi$
$402$	−7361.38	−	1908.75i	−0.0455519	−	0.0118113i
$403$	−4211.92	+	7295.26i	−0.0259340	+	0.0449191i
$404$			8532.72i			0.0522787i
$405$	−64680.6	−	34601.5i	−0.394334	−	0.210953i
$406$	76521.8			0.464230
$407$	87286.6	+	50394.9i	0.526937	+	0.304227i
$408$	−32998.9	+	127265.i	−0.198235	+	0.764521i
$409$	−76441.7	−	132401.i	−0.456966	−	0.791488i	0.541833	−	0.840486i	$-0.317730\pi$
$409$	−76441.7	−	132401.i	−0.456966	−	0.791488i	−0.998799	+	0.0489983i	$0.984397\pi$
$410$	10719.7	−	6189.01i	0.0637696	−	0.0368174i
$411$	−94388.0	+	95928.5i	−0.558770	+	0.567890i
$412$	13456.6	−	23307.6i	0.0792760	−	0.137310i
$413$		−	134978.i		−	0.791340i
$414$	2393.37	+	1330.63i	0.0139640	+	0.00776348i
$415$	−109262.			−0.634414
$416$	−3911.87	−	2258.52i	−0.0226047	−	0.0130508i
$417$	57365.5	−	15869.8i	0.329897	−	0.0912638i
$418$	−45976.9	−	79634.4i	−0.263140	−	0.455773i
$419$	113965.	−	65797.5i	0.649145	−	0.374784i	−0.138983	−	0.990295i	$-0.544383\pi$
$419$	113965.	−	65797.5i	0.649145	−	0.374784i	0.788129	+	0.615511i	$0.211050\pi$
$420$	−29198.0	−	105544.i	−0.165521	−	0.598320i
$421$	−58512.2	+	101346.i	−0.330128	+	0.571799i	−0.982537	−	0.186069i	$-0.940425\pi$
$421$	−58512.2	+	101346.i	−0.330128	+	0.571799i	0.652409	+	0.757867i	$0.273759\pi$
$422$			5052.39i			0.0283708i
$423$	104435.	+	174308.i	0.583667	+	0.974176i
$424$	−36424.3			−0.202609
$425$	48980.5	+	28278.9i	0.271173	+	0.156562i
$426$	11757.7	+	11568.9i	0.0647894	+	0.0637490i
$427$	−201867.	−	349644.i	−1.10716	−	1.91766i
$428$	−28714.2	+	16578.1i	−0.156750	+	0.0904999i
$429$	7628.24	+	1977.95i	0.0414486	+	0.0107473i
$430$	−1384.41	+	2397.87i	−0.00748735	+	0.0129685i
$431$		−	141954.i		−	0.764178i	−0.924126	−	0.382089i	$-0.875205\pi$
$431$		−	141954.i		−	0.764178i	0.924126	−	0.382089i	$-0.124795\pi$
$432$	42135.2	+	143244.i	0.225776	+	0.767554i
$433$	−116675.			−0.622305			−0.311152	−	0.950360i	$-0.600715\pi$
$433$	−116675.			−0.622305			−0.311152	+	0.950360i	$0.600715\pi$
$434$	−89960.1	−	51938.5i	−0.477607	−	0.275746i
$435$	−25346.1	+	97750.9i	−0.133947	+	0.516585i
$436$	−103157.	−	178673.i	−0.542656	−	0.939908i
$437$	−17424.6	+	10060.1i	−0.0912431	+	0.0526792i
$438$	12581.2	−	12786.5i	0.0655802	−	0.0666505i
$439$	−189627.	+	328444.i	−0.983947	+	1.70425i	−0.337421	+	0.941354i	$0.609554\pi$
$439$	−189627.	+	328444.i	−0.983947	+	1.70425i	−0.646526	+	0.762892i	$0.723779\pi$
$440$		−	51116.1i		−	0.264029i
$441$	3838.42	+	237096.i	0.0197367	+	1.21912i
$442$	−2922.38			−0.0149586
$443$	−98815.3	−	57051.1i	−0.503520	−	0.290708i	0.226646	−	0.973977i	$-0.427224\pi$
$443$	−98815.3	−	57051.1i	−0.503520	−	0.290708i	−0.730166	+	0.683270i	$0.760557\pi$
$444$	−92045.7	+	25463.8i	−0.466914	+	0.129169i
$445$	13745.5	+	23808.0i	0.0694132	+	0.120227i
$446$	34762.6	−	20070.2i	0.174760	−	0.100898i
$447$	−78691.4	−	284451.i	−0.393833	−	1.42361i
$448$	−91757.6	+	158929.i	−0.457179	+	0.791857i
$449$		−	20644.5i		−	0.102403i	−0.998688	−	0.0512014i	$-0.983695\pi$
$449$		−	20644.5i		−	0.102403i	0.998688	−	0.0512014i	$-0.0163051\pi$
$450$	−10574.7	+	171.197i	−0.0522208	+	0.000845418i
$451$	150091.			0.737907
$452$	189929.	+	109656.i	0.929639	+	0.536727i
$453$	−29957.6	−	29476.5i	−0.145986	−	0.143641i
$454$	51795.8	+	89713.0i	0.251294	+	0.435255i
$455$	4370.29	−	2523.19i	0.0211100	−	0.0121879i
$456$	174855.	+	45338.6i	0.840908	+	0.218041i
$457$	−11854.4	+	20532.4i	−0.0567605	+	0.0983120i	−0.893009	−	0.450038i	$-0.851410\pi$
$457$	−11854.4	+	20532.4i	−0.0567605	+	0.0983120i	0.836249	+	0.548350i	$0.184744\pi$
$458$		−	22361.4i		−	0.106603i
$459$	238830.	+	227504.i	1.13361	+	1.07985i
$460$	−5394.88			−0.0254957
$461$	−321141.	−	185411.i	−1.51110	−	0.872436i	−0.999916	−	0.0129661i	$-0.995873\pi$
$461$	−321141.	−	185411.i	−1.51110	−	0.872436i	−0.511187	−	0.859470i	$-0.670794\pi$
$462$	−24390.7	+	94066.3i	−0.114272	+	0.440707i
$463$	12693.6	+	21986.0i	0.0592140	+	0.102562i	0.894113	−	0.447842i	$-0.147807\pi$
$463$	12693.6	+	21986.0i	0.0592140	+	0.102562i	−0.834899	+	0.550403i	$0.814474\pi$
$464$	178013.	−	102776.i	0.826829	−	0.477370i
$465$	96144.8	−	97713.9i	0.444652	−	0.451909i
$466$	32453.0	−	56210.3i	0.149446	−	0.258847i
$467$		−	199026.i		−	0.912591i	−0.889828	−	0.456296i	$-0.849176\pi$
$467$		−	199026.i		−	0.912591i	0.889828	−	0.456296i	$-0.150824\pi$
$468$	−6405.44	+	3837.76i	−0.0292454	+	0.0175221i
$469$	−59049.8			−0.268456
$470$	25371.9	+	14648.5i	0.114857	+	0.0663128i
$471$	−283056.	+	78305.7i	−1.27594	+	0.352981i
$472$	29850.0	+	51701.8i	0.133986	+	0.232071i
$473$	−29075.6	+	16786.8i	−0.129959	+	0.0750319i
$474$	9120.61	+	32968.8i	0.0405945	+	0.146739i
$475$	38853.6	−	67296.4i	0.172204	−	0.298267i
$476$			492415.i			2.17329i
$477$	−44404.1	+	79868.7i	−0.195158	+	0.351026i
$478$	88581.2			0.387691
$479$	371751.	+	214630.i	1.62025	+	0.935449i	0.986853	+	0.161619i	$0.0516716\pi$
$479$	371751.	+	214630.i	1.62025	+	0.935449i	0.633393	+	0.773830i	$0.281662\pi$
$480$	52396.3	+	51554.9i	0.227415	+	0.223763i
$481$	−2200.50	−	3811.38i	−0.00951111	−	0.0164737i
$482$	11953.5	−	6901.38i	0.0514520	−	0.0297058i
$483$	20582.4	+	5336.87i	0.0882271	+	0.0228766i
$484$	40342.8	−	69875.8i	0.172217	−	0.298288i
$485$		−	151744.i		−	0.645100i
$486$	−60175.2	−	13540.4i	−0.254768	−	0.0573269i
$487$	133839.			0.564317			0.282159	−	0.959368i	$-0.408950\pi$
$487$	133839.			0.564317			0.282159	+	0.959368i	$0.408950\pi$
$488$	154646.	+	89284.7i	0.649379	+	0.374919i
$489$	61871.0	−	238615.i	0.258744	−	0.997882i
$490$	17094.3	+	29608.2i	0.0711965	+	0.123316i
$491$	120774.	−	69728.8i	0.500968	−	0.289234i	−0.228145	−	0.973627i	$-0.573266\pi$
$491$	120774.	−	69728.8i	0.500968	−	0.289234i	0.729113	+	0.684393i	$0.239933\pi$
$492$	−99746.0	+	101374.i	−0.412065	+	0.418790i
$493$	227042.	−	393248.i	0.934140	−	1.61798i
$494$			4015.17i			0.0164532i
$495$	−112084.	−	62314.6i	−0.457438	−	0.254319i
$496$	−279033.			−1.13421
$497$	110920.	+	64040.0i	0.449054	+	0.259262i
$498$	−88546.9	+	24495.9i	−0.357038	+	0.0987723i
$499$	−58541.9	−	101398.i	−0.235107	−	0.407217i	0.724197	−	0.689593i	$-0.242211\pi$
$499$	−58541.9	−	101398.i	−0.235107	−	0.407217i	−0.959304	+	0.282376i	$0.908877\pi$
$500$	18044.4	−	10417.9i	0.0721775	−	0.0416717i
$501$	−74666.5	−	269902.i	−0.297475	−	1.07530i
$502$	−6383.42	+	11056.4i	−0.0253306	+	0.0438739i
$503$			150313.i			0.594100i	0.954862	+	0.297050i	$0.0960027\pi$
$503$			150313.i			0.594100i	−0.954862	+	0.297050i	$0.903997\pi$
$504$	−98112.5	−	163756.i	−0.386245	−	0.644667i
$505$	6398.77			0.0250908
$506$	4146.01	+	2393.70i	0.0161931	+	0.00934908i
$507$	182981.	+	180043.i	0.711853	+	0.700422i
$508$	−123217.	−	213418.i	−0.477467	−	0.826997i
$509$	200079.	−	115516.i	0.772264	−	0.445867i	−0.0614179	−	0.998112i	$-0.519562\pi$
$509$	200079.	−	115516.i	0.772264	−	0.445867i	0.833682	+	0.552246i	$0.186229\pi$
$510$	46034.3	+	11936.3i	0.176987	+	0.0458914i
$511$	69643.3	−	120626.i	0.266709	−	0.461953i
$512$		−	255428.i		−	0.974379i
$513$	312578.	−	328139.i	1.18775	−	1.24687i
$514$	−14723.0			−0.0557274
$515$	−17478.6	−	10091.3i	−0.0659010	−	0.0380479i
$516$	7984.71	−	30794.2i	0.0299888	−	0.115656i
$517$	177622.	+	307650.i	0.664531	+	1.15100i
$518$	46999.3	−	27135.0i	0.175159	−	0.101128i
$519$	−38288.8	+	38913.7i	−0.142147	+	0.144467i
$520$	−1115.99	+	1932.96i	−0.00412720	+	0.00714851i
$521$			222624.i			0.820158i	0.912050	+	0.410079i	$0.134499\pi$
$521$			222624.i			0.820158i	−0.912050	+	0.410079i	$0.865501\pi$
$522$	1374.48	+	84900.6i	0.00504427	+	0.311580i
$523$	325020.			1.18825			0.594123	−	0.804374i	$-0.297499\pi$
$523$	325020.			1.18825			0.594123	+	0.804374i	$0.297499\pi$
$524$	−333374.	−	192474.i	−1.21414	−	0.700985i
$525$	−79148.2	+	21895.8i	−0.287159	+	0.0794407i
$526$	−2168.05	−	3755.17i	−0.00783606	−	0.0135724i
$527$	−533827.	+	308205.i	−1.92212	+	1.10973i
$528$	69599.6	+	251586.i	0.249654	+	0.902440i
$529$	−139397.	+	241442.i	−0.498128	+	0.862784i
$530$			13175.4i			0.0469041i
$531$	149758.	−	2424.47i	0.531129	−	0.00859861i
$532$	676549.			2.39043
$533$	−5675.70	−	3276.87i	−0.0199786	−	0.0115347i
$534$	16477.1	+	16212.5i	0.0577829	+	0.0568550i
$535$	12432.1	+	21533.0i	0.0434347	+	0.0752312i
$536$	22618.3	−	13058.7i	0.0787283	−	0.0454538i
$537$	−192419.	−	49892.8i	−0.667266	−	0.173017i
$538$	−49459.3	+	85666.0i	−0.170877	+	0.295967i
$539$			414557.i			1.42694i
$540$	116576.	−	34290.8i	0.399780	−	0.117595i
$541$	−323647.			−1.10580			−0.552900	−	0.833248i	$-0.686479\pi$
$541$	−323647.			−1.10580			−0.552900	+	0.833248i	$0.686479\pi$
$542$	−38345.9	−	22139.0i	−0.130533	−	0.0753632i
$543$	29443.9	−	113555.i	0.0998610	−	0.385128i
$544$	−165266.	−	286250.i	−0.558453	−	0.967269i
$545$	−133988.	+	77358.3i	−0.451102	+	0.260444i
$546$	2976.04	−	3024.61i	0.00998283	−	0.0101458i
$547$	−166370.	+	288162.i	−0.556034	+	0.963079i	0.441788	+	0.897119i	$0.354344\pi$
$547$	−166370.	+	288162.i	−0.556034	+	0.963079i	−0.997822	+	0.0659598i	$0.978989\pi$
$548$		−	222935.i		−	0.742366i
$549$	384303.	−	230251.i	1.27506	−	0.763936i
$550$	−18489.7			−0.0611228
$551$	−540300.	−	311942.i	−1.77964	−	1.02747i
$552$	−9064.08	+	2507.52i	−0.0297472	+	0.00822936i
$553$	132806.	+	230026.i	0.434276	+	0.752189i
$554$	−16346.7	+	9437.75i	−0.0532610	+	0.0307503i
$555$	19095.6	+	69025.9i	0.0619936	+	0.224092i
$556$	−49298.9	+	85388.2i	−0.159473	+	0.276216i
$557$		−	176743.i		−	0.569681i	−0.958575	−	0.284841i	$-0.908059\pi$
$557$		−	176743.i		−	0.569681i	0.958575	−	0.284841i	$-0.0919407\pi$
$558$	56009.7	−	100743.i	0.179885	−	0.323555i
$559$	1466.00			0.00469147
$560$	144763.	+	83578.7i	0.461615	+	0.266514i
$561$	411042.	+	404441.i	1.30605	+	1.28508i
$562$	17524.7	+	30353.6i	0.0554852	+	0.0961031i
$563$	404618.	−	233607.i	1.27652	−	0.737001i	0.300316	−	0.953840i	$-0.402908\pi$
$563$	404618.	−	233607.i	1.27652	−	0.737001i	0.976207	+	0.216839i	$0.0695745\pi$
$564$	−325834.	−	84486.4i	−1.02433	−	0.265600i
$565$	82231.7	−	142430.i	0.257598	−	0.446173i
$566$			97054.1i			0.302957i
$567$	−478679.	+	15503.0i	−1.48894	+	0.0482226i
$568$	−56649.1			−0.175588
$569$	−444829.	−	256822.i	−1.37394	−	0.793246i	−0.382520	−	0.923947i	$-0.624944\pi$
$569$	−444829.	−	256822.i	−1.37394	−	0.793246i	−0.991422	+	0.130702i	$0.958277\pi$
$570$	16399.8	−	63248.4i	0.0504766	−	0.194670i
$571$	232939.	+	403462.i	0.714447	+	1.23746i	0.963172	+	0.268885i	$0.0866550\pi$
$571$	232939.	+	403462.i	0.714447	+	1.23746i	−0.248725	+	0.968574i	$0.580012\pi$
$572$	−11305.5	+	6527.21i	−0.0345538	+	0.0199497i
$573$	106948.	−	108693.i	0.325734	−	0.331050i
$574$	40408.1	−	69988.8i	0.122643	−	0.212425i
$575$			4045.67i			0.0122364i
$576$	−177979.	−	98950.0i	−0.536444	−	0.298244i
$577$	−481977.			−1.44769			−0.723844	−	0.689964i	$-0.757626\pi$
$577$	−481977.			−1.44769			−0.723844	+	0.689964i	$0.757626\pi$
$578$	−109640.	−	63300.8i	−0.328181	−	0.189476i
$579$	−123079.	+	34049.1i	−0.367137	+	0.101566i
$580$	−83641.8	−	144872.i	−0.248638	−	0.430654i
$581$	−617799.	+	356686.i	−1.83018	+	1.05666i
$582$	−34020.0	−	122974.i	−0.100436	−	0.363052i
$583$	−79879.6	+	138356.i	−0.235017	+	0.407061i
$584$			61605.7i			0.180632i
$585$	2877.97	+	4803.51i	0.00840959	+	0.0140361i
$586$	−18129.4			−0.0527945
$587$	192573.	+	111182.i	0.558882	+	0.322671i	0.752697	−	0.658367i	$-0.228753\pi$
$587$	192573.	+	111182.i	0.558882	+	0.322671i	−0.193815	+	0.981038i	$0.562086\pi$
$588$	−279999.	−	275502.i	−0.809844	−	0.796839i
$589$	423456.	+	733448.i	1.22061	+	2.11416i
$590$	18701.5	−	10797.3i	0.0537245	−	0.0310179i
$591$	−36954.0	−	9581.91i	−0.105800	−	0.0274332i
$592$	72889.8	−	126249.i	0.207981	−	0.360233i
$593$		−	149953.i		−	0.426429i	−0.977005	−	0.213214i	$-0.931607\pi$
$593$		−	149953.i		−	0.426429i	0.977005	−	0.213214i	$-0.0683932\pi$
$594$	−104804.	−	25371.8i	−0.297034	−	0.0719081i
$595$	369267.			1.04305
$596$	423404.	+	244452.i	1.19196	+	0.688179i
$597$	103281.	−	398317.i	0.289781	−	1.11758i
$598$	−104.521	−	181.036i	−0.000292282	−	0.000506247i
$599$	−246717.	+	142442.i	−0.687614	+	0.396994i	−0.802718	−	0.596359i	$-0.796613\pi$
$599$	−246717.	+	142442.i	−0.687614	+	0.396994i	0.115104	+	0.993353i	$0.463280\pi$
$600$	25474.6	−	25890.4i	0.0707628	−	0.0719177i
$601$	31474.4	−	54515.3i	0.0871383	−	0.150928i	−0.819162	−	0.573562i	$-0.805561\pi$
$601$	31474.4	−	54515.3i	0.0871383	−	0.150928i	0.906300	+	0.422634i	$0.138894\pi$
$602$			18077.7i			0.0498826i
$603$	−1060.65	−	65515.5i	−0.00291701	−	0.180181i
$604$	69620.7			0.190838
$605$	−52400.5	−	30253.5i	−0.143161	−	0.0826541i
$606$	5185.62	−	1434.57i	0.0141207	−	0.00390639i
$607$	−160289.	−	277629.i	−0.435037	−	0.753506i	0.562262	−	0.826959i	$-0.309931\pi$
$607$	−160289.	−	277629.i	−0.435037	−	0.753506i	−0.997299	+	0.0734533i	$0.976598\pi$
$608$	−393290.	+	227066.i	−1.06391	+	0.614251i
$609$	175794.	+	635454.i	0.473990	+	1.71336i
$610$	32296.0	−	55938.3i	0.0867938	−	0.150331i
$611$		−	15511.7i		−	0.0415507i
$612$	−546333.	+	8844.74i	−1.45866	+	0.0236147i
$613$	−509071.			−1.35474			−0.677372	−	0.735640i	$-0.736881\pi$
$613$	−509071.			−1.35474			−0.677372	+	0.735640i	$0.736881\pi$
$614$	78114.7	+	45099.6i	0.207203	+	0.119629i
$615$	76021.3	+	74800.5i	0.200995	+	0.197767i
$616$	−166869.	−	289025.i	−0.439757	−	0.761682i
$617$	59066.4	−	34102.0i	0.155157	−	0.0895797i	−0.420412	−	0.907334i	$-0.638114\pi$
$617$	59066.4	−	34102.0i	0.155157	−	0.0895797i	0.575568	+	0.817754i	$0.304781\pi$
$618$	−16427.2	−	4259.45i	−0.0430117	−	0.0111526i
$619$	282075.	−	488568.i	0.736178	−	1.27510i	−0.218027	−	0.975943i	$-0.569962\pi$
$619$	282075.	−	488568.i	0.736178	−	1.27510i	0.954205	−	0.299155i	$-0.0967047\pi$
$620$			227085.i			0.590751i
$621$	−5551.54	+	22932.0i	−0.0143956	+	0.0594645i
$622$	−197578.			−0.510690
$623$	155443.	+	89744.8i	0.400492	+	0.231224i
$624$	2860.85	−	11033.3i	0.00734726	−	0.0283358i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	94177.9	−	54373.6i	0.240326	−	0.138752i
$627$	555679.	−	564748.i	1.41348	−	1.43655i
$628$	243254.	−	421328.i	0.616795	−	1.06832i
$629$		−	322041.i		−	0.813973i
$630$	−59233.5	+	35489.2i	−0.149240	+	0.0894159i
$631$	364593.			0.915692			0.457846	−	0.889032i	$-0.348621\pi$
$631$	364593.			0.915692			0.457846	+	0.889032i	$0.348621\pi$
$632$	−101739.	−	58739.2i	−0.254715	−	0.147060i
$633$	−41956.2	+	11606.9i	−0.104710	+	0.0289673i
$634$	65304.7	+	113111.i	0.162467	+	0.281402i
$635$	−160044.	+	92401.6i	−0.396911	+	0.229157i
$636$	−40362.0	−	145899.i	−0.0997834	−	0.360693i
$637$	9050.83	−	15676.5i	0.0223054	−	0.0386341i
$638$			148447.i			0.364695i
$639$	−69059.8	+	124216.i	−0.169131	+	0.304212i
$640$	−160039.			−0.390720
$641$	345891.	+	199700.i	0.841827	+	0.486029i	0.857885	−	0.513842i	$-0.171778\pi$
$641$	345891.	+	199700.i	0.841827	+	0.486029i	−0.0160580	+	0.999871i	$0.505112\pi$
$642$	14902.7	+	14663.4i	0.0361572	+	0.0355765i
$643$	315727.	+	546855.i	0.763641	+	1.32267i	0.940962	+	0.338513i	$0.109924\pi$
$643$	315727.	+	546855.i	0.763641	+	1.32267i	−0.177321	+	0.984153i	$0.556743\pi$
$644$	−30504.2	+	17611.6i	−0.0735509	+	0.0424646i
$645$	−23092.9	−	5987.81i	−0.0555083	−	0.0143929i
$646$	−146904.	+	254446.i	−0.352022	+	0.609719i
$647$			601360.i			1.43657i	0.695751	+	0.718283i	$0.255072\pi$
$647$			601360.i			1.43657i	−0.695751	+	0.718283i	$0.744928\pi$
$648$	179924.	−	111797.i	0.428489	−	0.266244i
$649$	261848.			0.621670
$650$	699.188	+	403.676i	0.00165488	+	0.000955446i
$651$	224643.	−	866368.i	0.530067	−	2.04428i
$652$	204174.	+	353639.i	0.480291	+	0.831889i
$653$	433989.	−	250564.i	1.01778	−	0.587614i	0.104317	−	0.994544i	$-0.466734\pi$
$653$	433989.	−	250564.i	1.01778	−	0.587614i	0.913459	+	0.406930i	$0.133401\pi$
$654$	−91242.2	+	92731.3i	−0.213324	+	0.216806i
$655$	−144338.	+	250001.i	−0.336432	+	0.582718i
$656$		−	217087.i		−	0.504460i
$657$	135085.	+	75102.3i	0.312950	+	0.173989i
$658$	191280.			0.441792
$659$	−392397.	−	226551.i	−0.903556	−	0.521668i	−0.0252038	−	0.999682i	$-0.508023\pi$
$659$	−392397.	−	226551.i	−0.903556	−	0.521668i	−0.878352	+	0.478014i	$0.841357\pi$
$660$	204748.	−	56642.0i	0.470036	−	0.130032i
$661$	270326.	+	468218.i	0.618706	+	1.07163i	0.989722	+	0.143004i	$0.0456763\pi$
$661$	270326.	+	468218.i	0.618706	+	1.07163i	−0.371016	+	0.928627i	$0.620990\pi$
$662$	158808.	−	91687.9i	0.362374	−	0.209217i
$663$	−6713.60	−	24268.1i	−0.0152731	−	0.0552088i
$664$	157760.	−	273249.i	0.357818	−	0.619759i
$665$		−	507351.i		−	1.14727i
$666$	30950.4	+	51658.1i	0.0697780	+	0.116464i
$667$	32481.3			0.0730099
$668$	401747.	+	231949.i	0.900327	+	0.519804i
$669$	246528.	+	242569.i	0.550825	+	0.541979i
$670$	−4723.58	−	8181.48i	−0.0105226	−	0.0182256i
$671$	678286.	−	391608.i	1.50649	−	0.869775i
$672$	464565.	+	120458.i	1.02875	+	0.266746i
$673$	−313471.	+	542948.i	−0.692097	+	1.19875i	0.279052	+	0.960276i	$0.409980\pi$
$673$	−313471.	+	542948.i	−0.692097	+	1.19875i	−0.971149	+	0.238472i	$0.923353\pi$
$674$			58041.1i			0.127766i
$675$	−25715.0	−	87421.4i	−0.0564390	−	0.191871i
$676$	−425243.			−0.930560
$677$	71728.5	+	41412.5i	0.156500	+	0.0903553i	0.576205	−	0.817305i	$-0.304533\pi$
$677$	71728.5	+	41412.5i	0.156500	+	0.0903553i	−0.419705	+	0.907661i	$0.637866\pi$
$678$	34709.5	−	133862.i	0.0755072	−	0.291205i
$679$	−495368.	−	858002.i	−1.07445	−	1.86101i
$680$	−141443.	+	81662.3i	−0.305890	+	0.176605i
$681$	−626006.	+	636222.i	−1.34985	+	1.37188i
$682$	100757.	−	174517.i	0.216624	−	0.375204i
$683$			25277.4i			0.0541866i	0.999633	+	0.0270933i	$0.00862512\pi$
$683$			25277.4i			0.0541866i	−0.999633	+	0.0270933i	$0.991375\pi$
$684$	12152.2	+	750629.i	0.0259741	+	1.60440i
$685$	−167181.			−0.356293
$686$	34766.0	+	20072.2i	0.0738765	+	0.0426526i
$687$	185694.	−	51371.1i	0.393446	−	0.108844i
$688$	24280.0	+	42054.2i	0.0512946	+	0.0888448i
$689$	6041.30	−	3487.95i	0.0127260	−	0.00734737i
$690$	907.017	+	3278.65i	0.00190510	+	0.00688648i
$691$	234367.	−	405935.i	0.490839	−	0.850159i	−0.509105	−	0.860704i	$-0.670023\pi$
$691$	234367.	−	405935.i	0.490839	−	0.850159i	0.999944	+	0.0105455i	$0.00335681\pi$
$692$		−	90434.5i		−	0.188852i
$693$	−837180.	+	13553.4i	−1.74322	+	0.0282215i
$694$	−141306.			−0.293388
$695$	64033.5	+	36969.7i	0.132568	+	0.0765379i
$696$	−207865.	−	204527.i	−0.429104	−	0.422213i
$697$	−239783.	−	415317.i	−0.493575	−	0.854897i
$698$	−14769.7	+	8527.28i	−0.0303152	+	0.0175025i
$699$	541337.	+	140365.i	1.10793	+	0.287279i
$700$	68018.7	−	117812.i	0.138814	−	0.240432i
$701$		−	407194.i		−	0.828640i	−0.910131	−	0.414320i	$-0.864019\pi$
$701$		−	407194.i		−	0.828640i	0.910131	−	0.414320i	$-0.135981\pi$
$702$	3409.25	+	3247.58i	0.00691807	+	0.00659000i
$703$	−442466.			−0.895301
$704$	−308311.	−	178003.i	−0.622076	−	0.359156i
$705$	−63357.2	+	244346.i	−0.127473	+	0.491618i
$706$	−84851.5	−	146967.i	−0.170236	−	0.294857i
$707$	36180.5	−	20888.8i	0.0723828	−	0.0417903i
$708$	−174017.	+	176857.i	−0.347156	+	0.352821i
$709$	132024.	−	228672.i	0.262640	−	0.454905i	−0.704303	−	0.709900i	$-0.748740\pi$
$709$	132024.	−	228672.i	0.262640	−	0.454905i	0.966943	+	0.254994i	$0.0820736\pi$
$710$			20491.0i			0.0406488i
$711$	−252828.	+	151479.i	−0.500133	+	0.299649i
$712$	−79387.3			−0.156600
$713$	−38185.5	−	22046.4i	−0.0751138	−	0.0433670i
$714$	299257.	−	82787.5i	0.587013	−	0.162393i
$715$	4894.82	+	8478.07i	0.00957468	+	0.0165838i
$716$	285175.	−	164646.i	0.556269	−	0.321162i
$717$	203498.	+	735598.i	0.395842	+	1.43088i
$718$	−89277.4	+	154633.i	−0.173178	+	0.299953i
$719$		−	78090.3i		−	0.151056i	−0.997144	−	0.0755282i	$-0.975936\pi$
$719$		−	78090.3i		−	0.151056i	0.997144	−	0.0755282i	$-0.0240643\pi$
$720$	−90130.1	+	162115.i	−0.173862	+	0.312722i
$721$	−131772.			−0.253485
$722$	231704.	+	133774.i	0.444487	+	0.256625i
$723$	84771.5	+	83410.2i	0.162171	+	0.159567i
$724$	97164.6	+	168294.i	0.185366	+	0.321064i
$725$	−108641.	+	62723.8i	−0.206689	+	0.119332i
$726$	−49248.5	−	12769.8i	−0.0934372	−	0.0242276i
$727$	18180.8	−	31490.0i	0.0343988	−	0.0595805i	−0.848313	−	0.529494i	$-0.822382\pi$
$727$	18180.8	−	31490.0i	0.0343988	−	0.0595805i	0.882712	+	0.469914i	$0.155715\pi$
$728$			14572.7i			0.0274964i
$729$	−25798.6	−	530814.i	−0.0485446	−	0.998821i
$730$	22284.0			0.0418164
$731$	92901.6	+	53636.8i	0.173856	+	0.100376i
$732$	−186270.	+	718377.i	−0.347633	+	1.34070i
$733$	−187893.	−	325440.i	−0.349705	−	0.605708i	0.636492	−	0.771284i	$-0.280385\pi$
$733$	−187893.	−	325440.i	−0.349705	−	0.605708i	−0.986197	+	0.165576i	$0.947052\pi$
$734$	28187.8	−	16274.2i	0.0523201	−	0.0302070i
$735$	−206602.	+	209974.i	−0.382437	+	0.388678i
$736$	11821.8	−	20475.9i	0.0218236	−	0.0377996i
$737$		−	114553.i		−	0.210897i
$738$	78378.2	+	43575.5i	0.143907	+	0.0800073i
$739$	−113539.			−0.207901			−0.103950	−	0.994582i	$-0.533148\pi$
$739$	−113539.			−0.207901			−0.103950	+	0.994582i	$0.533148\pi$
$740$	−102745.	−	59319.7i	−0.187627	−	0.108327i
$741$	−33342.9	+	9224.09i	−0.0607249	+	0.0167991i
$742$	43011.0	+	74497.2i	0.0781217	+	0.135311i
$743$	−119266.	+	68858.0i	−0.216042	+	0.124732i	−0.604116	−	0.796896i	$-0.706474\pi$
$743$	−119266.	+	68858.0i	−0.216042	+	0.124732i	0.388074	+	0.921628i	$0.373140\pi$
$744$	105548.	+	381531.i	0.190680	+	0.689262i
$745$	183317.	−	317515.i	0.330286	−	0.572073i
$746$		−	226122.i		−	0.406317i
$747$	−406839.	−	679039.i	−0.729091	−	1.21690i
$748$	−955251.			−1.70732
$749$	140589.	+	81169.3i	0.250605	+	0.144687i
$750$	−9365.04	−	9214.65i	−0.0166490	−	0.0163816i
$751$	−61110.2	−	105846.i	−0.108351	−	0.187670i	0.806751	−	0.590891i	$-0.201224\pi$
$751$	−61110.2	−	105846.i	−0.108351	−	0.187670i	−0.915102	+	0.403221i	$0.867890\pi$
$752$	444976.	−	256907.i	0.786867	−	0.454298i
$753$	−106480.	−	27609.4i	−0.187792	−	0.0486930i
$754$	3240.98	−	5613.53i	0.00570076	−	0.00987401i
$755$		−	52209.3i		−	0.0915912i
$756$	547211.	−	574452.i	0.957439	−	1.00510i
$757$	−216792.			−0.378314			−0.189157	−	0.981947i	$-0.560575\pi$
$757$	−216792.			−0.378314			−0.189157	+	0.981947i	$0.560575\pi$
$758$	54786.3	+	31630.9i	0.0953528	+	0.0550520i
$759$	−10353.2	+	39928.5i	−0.0179717	+	0.0693105i
$760$	112199.	+	194335.i	0.194251	+	0.336452i
$761$	−182037.	+	105099.i	−0.314334	+	0.181481i	−0.648864	−	0.760904i	$-0.724756\pi$
$761$	−182037.	+	105099.i	−0.314334	+	0.181481i	0.334530	+	0.942385i	$0.391422\pi$
$762$	−108985.	+	110764.i	−0.187698	+	0.190761i
$763$	−505073.	+	874812.i	−0.867571	+	1.50268i
$764$			252600.i			0.432760i
$765$	6632.76	+	409700.i	0.0113337	+	0.700073i
$766$	−212488.			−0.362140
$767$	−9901.81	−	5716.81i	−0.0168315	−	0.00971769i
$768$	219217.	−	60645.0i	0.371666	−	0.102819i
$769$	−360591.	−	624561.i	−0.609764	−	1.05614i	−0.991279	−	0.131779i	$-0.957931\pi$
$769$	−360591.	−	624561.i	−0.609764	−	1.05614i	0.381515	−	0.924363i	$-0.375402\pi$
$770$	−104546.	+	60359.5i	−0.176330	+	0.101804i
$771$	−33823.2	−	122263.i	−0.0568991	−	0.205677i
$772$	105772.	−	183203.i	0.177475	−	0.307396i
$773$			767446.i			1.28437i	0.766551	+	0.642183i	$0.221971\pi$
$773$			767446.i			1.28437i	−0.766551	+	0.642183i	$0.778029\pi$
$774$	−20057.1	+	324.710i	−0.0334800	+	0.000542019i
$775$	170293.			0.283527
$776$	379490.	+	219098.i	0.630197	+	0.363844i
$777$	333307.	+	327955.i	0.552081	+	0.543215i
$778$	35400.1	+	61314.8i	0.0584851	+	0.101299i
$779$	−570621.	+	329448.i	−0.940314	+	0.542891i
$780$	−8979.18	−	2328.24i	−0.0147587	−	0.00382682i
$781$	−124233.	+	215178.i	−0.203674	+	0.352774i
$782$		−	15296.6i		−	0.0250139i
$783$	−701876.	+	206457.i	−1.14482	+	0.336749i
$784$	599604.			0.975511
$785$	−315958.	−	182418.i	−0.512732	−	0.296026i
$786$	−60924.1	+	234962.i	−0.0986152	+	0.380324i
$787$	96078.6	+	166413.i	0.155123	+	0.268682i	0.933104	−	0.359607i	$-0.117089\pi$
$787$	96078.6	+	166413.i	0.155123	+	0.268682i	−0.777981	+	0.628288i	$0.783756\pi$
$788$	54767.8	−	31620.2i	0.0882009	−	0.0509228i
$789$	26203.1	−	26630.7i	0.0420919	−	0.0427789i
$790$	−21247.1	+	36801.0i	−0.0340444	+	0.0589666i
$791$		−	1.07378e6i		−	1.71618i
$792$	317675.	−	190332.i	0.506445	−	0.303431i
$793$	−34199.2			−0.0543839
$794$	−253111.	−	146134.i	−0.401486	−	0.231798i
$795$	−109411.	+	30267.8i	−0.173112	+	0.0478903i
$796$	340825.	+	590327.i	0.537905	+	0.931679i
$797$	−159799.	+	92260.1i	−0.251569	+	0.145244i	−0.620483	−	0.784220i	$-0.713063\pi$
$797$	−159799.	+	92260.1i	−0.251569	+	0.145244i	0.368913	+	0.929464i	$0.379730\pi$
$798$	−113745.	−	411162.i	−0.178619	−	0.645665i
$799$	567533.	−	982995.i	0.888991	−	1.53978i
$800$			91314.8i			0.142679i
$801$	−96779.5	+	174075.i	−0.150841	+	0.271313i
$802$	312861.			0.486410
$803$	234006.	+	135103.i	0.362907	+	0.209524i
$804$	77370.6	+	76128.2i	0.119692	+	0.117770i
$805$	13207.1	+	22875.4i	0.0203806	+	0.0353002i
$806$	−7620.28	+	4399.57i	−0.0117301	+	0.00677236i
$807$	−825012.	−	213920.i	−1.26682	−	0.328476i
$808$	−9239.01	+	16002.4i	−0.0141515	+	0.0245111i
$809$			833427.i			1.27342i	0.771104	+	0.636709i	$0.219705\pi$
$809$			833427.i			1.27342i	−0.771104	+	0.636709i	$0.780295\pi$
$810$	−40439.1	−	65081.9i	−0.0616355	−	0.0991952i
$811$	245458.			0.373195			0.186598	−	0.982436i	$-0.440254\pi$
$811$	245458.			0.373195			0.186598	+	0.982436i	$0.440254\pi$
$812$	−945870.	−	546098.i	−1.43456	−	0.828245i
$813$	95754.9	−	369293.i	0.144870	−	0.558714i
$814$	52640.1	+	91175.4i	0.0794453	+	0.137603i
$815$	265198.	−	153112.i	0.399259	−	0.230512i
$816$	584972.	−	594519.i	0.878527	−	0.892865i
$817$	73693.8	−	127641.i	0.110405	−	0.191226i
$818$		−	159695.i		−	0.238662i
$819$	31953.9	+	17765.2i	0.0476383	+	0.0264852i
$820$	−176672.			−0.262748
$821$	707479.	+	408463.i	1.04961	+	0.605992i	0.922540	−	0.385902i	$-0.126110\pi$
$821$	707479.	+	408463.i	1.04961	+	0.605992i	0.127069	+	0.991894i	$0.459443\pi$
$822$	−135485.	+	37481.1i	−0.200516	+	0.0554714i
$823$	−125974.	−	218193.i	−0.185986	−	0.322137i	0.757922	−	0.652345i	$-0.226215\pi$
$823$	−125974.	−	218193.i	−0.185986	−	0.322137i	−0.943908	+	0.330208i	$0.892881\pi$
$824$	50473.7	−	29141.0i	0.0743379	−	0.0429190i
$825$	−42476.4	−	153542.i	−0.0624080	−	0.225590i
$826$	70495.8	−	122102.i	0.103324	−	0.178963i
$827$		−	879008.i		−	1.28523i	−0.766188	−	0.642616i	$-0.777849\pi$
$827$		−	879008.i		−	1.28523i	0.766188	−	0.642616i	$-0.222151\pi$
$828$	−20087.9	−	33528.0i	−0.0293005	−	0.0489042i
$829$	−35645.9			−0.0518682			−0.0259341	−	0.999664i	$-0.508256\pi$
$829$	−35645.9			−0.0518682			−0.0259341	+	0.999664i	$0.508256\pi$
$830$	−98839.4	−	57064.9i	−0.143474	−	0.0828349i
$831$	−115927.	−	114065.i	−0.167873	−	0.165177i
$832$	7772.54	+	13462.4i	0.0112284	+	0.0194481i
$833$	1.14712e6	−	662291.i	1.65318	−	0.954462i
$834$	60181.7	+	15604.7i	0.0865232	+	0.0224348i
$835$	173941.	−	301274.i	0.249476	−	0.432105i
$836$			1.31246e6i			1.87790i
$837$	965267.	+	233679.i	1.37783	+	0.333556i
$838$	137458.			0.195741
$839$	−183283.	−	105818.i	−0.260374	−	0.150327i	0.364131	−	0.931348i	$-0.381366\pi$
$839$	−183283.	−	105818.i	−0.260374	−	0.150327i	−0.624505	+	0.781021i	$0.714699\pi$
$840$	59521.6	−	229554.i	0.0843559	−	0.325331i
$841$	149947.	+	259717.i	0.212005	+	0.367204i
$842$	−105861.	+	61119.1i	−0.149318	+	0.0862090i
$843$	−211804.	+	215260.i	−0.298042	+	0.302907i
$844$	36056.4	−	62451.5i	0.0506171	−	0.0876715i
$845$			318894.i			0.446615i
$846$	3435.77	+	212225.i	0.00480047	+	0.296521i
$847$	−395050.			−0.550662
$848$	200113.	+	115536.i	0.278282	+	0.160666i
$849$	−805959.	+	222963.i	−1.11814	+	0.309327i
$850$	29538.8	+	51162.7i	0.0408842	+	0.0708135i
$851$	19949.9	−	11518.1i	0.0275474	−	0.0159045i
$852$	−62773.2	−	226910.i	−0.0864759	−	0.312590i
$853$	247758.	−	429129.i	0.340510	−	0.589780i	−0.644018	−	0.765011i	$-0.722734\pi$
$853$	247758.	−	429129.i	0.340510	−	0.589780i	0.984527	+	0.175230i	$0.0560670\pi$
$854$		−	421721.i		−	0.578242i
$855$	562904.	−	9113.03i	0.770020	−	0.0124661i
$856$	−71801.5			−0.0979910
$857$	445592.	+	257263.i	0.606703	+	0.350280i	0.771674	−	0.636018i	$-0.219420\pi$
$857$	445592.	+	257263.i	0.606703	+	0.350280i	−0.164971	+	0.986298i	$0.552753\pi$
$858$	5867.54	+	5773.32i	0.00797042	+	0.00784243i
$859$	288030.	+	498882.i	0.390347	+	0.676101i	0.992495	−	0.122283i	$-0.0390217\pi$
$859$	288030.	+	498882.i	0.390347	+	0.676101i	−0.602148	+	0.798384i	$0.705688\pi$
$860$	34224.8	−	19759.7i	0.0462748	−	0.0267168i
$861$	674033.	+	174772.i	0.909232	+	0.235757i
$862$	74139.4	−	128413.i	0.0997779	−	0.172820i
$863$			1.30131e6i			1.74727i	0.486583	+	0.873634i	$0.338243\pi$
$863$			1.30131e6i			1.74727i	−0.486583	+	0.873634i	$0.661757\pi$
$864$	−125304.	+	517597.i	−0.167856	+	0.693369i
$865$	−67817.8			−0.0906382
$866$	−105545.	−	60936.7i	−0.140736	−	0.0812537i
$867$	273786.	−	1.05590e6i	0.364228	−	1.40470i
$868$	741319.	+	1.28400e6i	0.983934	+	1.70422i
$869$	−446235.	+	257634.i	−0.590914	+	0.341164i
$870$	−73981.2	+	75188.6i	−0.0977424	+	0.0993376i
$871$	−2500.97	+	4331.81i	−0.00329665	+	0.00570996i
$872$		−	446782.i		−	0.587574i
$873$	943052.	−	565020.i	1.23739	−	0.741371i
$874$	−21016.6			−0.0275131
$875$	−88348.2	−	51007.9i	−0.115394	−	0.0666225i
$876$	−246764.	+	68265.7i	−0.321569	+	0.0889599i
$877$	314900.	+	545422.i	0.409424	+	0.709143i	0.994825	−	0.101601i	$-0.0323964\pi$
$877$	314900.	+	545422.i	0.409424	+	0.709143i	−0.585401	+	0.810744i	$0.699063\pi$
$878$	−343077.	+	198076.i	−0.445043	+	0.256946i
$879$	−41648.9	−	150551.i	−0.0539046	−	0.194852i
$880$	−162137.	+	280830.i	−0.209371	+	0.362641i
$881$		−	124848.i		−	0.160854i	−0.996761	−	0.0804268i	$-0.974372\pi$
$881$		−	124848.i		−	0.160854i	0.996761	−	0.0804268i	$-0.0256283\pi$
$882$	−120357.	+	216484.i	−0.154716	+	0.278284i
$883$	1.04244e6			1.33699			0.668496	−	0.743716i	$-0.266938\pi$
$883$	1.04244e6			1.33699			0.668496	+	0.743716i	$0.266938\pi$
$884$	36122.9	+	20855.6i	0.0462251	+	0.0266881i
$885$	132627.	+	130497.i	0.169334	+	0.166615i
$886$	−59592.8	−	103218.i	−0.0759148	−	0.131488i
$887$	243676.	−	140687.i	0.309718	−	0.178816i	−0.337083	−	0.941475i	$-0.609440\pi$
$887$	243676.	−	140687.i	0.309718	−	0.178816i	0.646800	+	0.762660i	$0.276107\pi$
$888$	−200196.	−	51909.3i	−0.253880	−	0.0658293i
$889$	−603291.	+	1.04493e6i	−0.763349	+	1.32216i
$890$			28715.9i			0.0362529i
$891$	−30074.8	−	928605.i	−0.0378833	−	1.16970i
$892$	−572924.			−0.720058
$893$	−1.35058e6	−	779757.i	−1.69362	−	0.977814i
$894$	77376.9	−	298415.i	0.0968136	−	0.373376i
$895$	−123470.	−	213855.i	−0.154139	−	0.266977i
$896$	−904907.	+	522448.i	−1.12717	+	0.650770i
$897$	1263.25	−	1283.86i	0.00157001	−	0.00159563i
$898$	10782.1	−	18675.2i	0.0133706	−	0.0231586i
$899$		−	1.36722e6i		−	1.69169i
$900$	131934.	+	73350.3i	0.162881	+	0.0905560i
$901$	510458.			0.628797
$902$	135774.	+	78388.9i	0.166879	+	0.0963478i
$903$	−150121.	+	41529.9i	−0.184105	+	0.0509314i
$904$	237464.	+	411300.i	0.290577	+	0.503294i
$905$	126205.	−	72864.7i	0.154092	−	0.0889652i
$906$	−11705.0	−	42310.9i	−0.0142599	−	0.0515461i
$907$	−725916.	+	1.25732e6i	−0.882413	+	1.52838i	−0.0337618	+	0.999430i	$0.510749\pi$
$907$	−725916.	+	1.25732e6i	−0.882413	+	1.52838i	−0.848651	+	0.528954i	$0.822585\pi$
$908$		−	1.47856e6i		−	1.79336i
$909$	23825.9	+	39766.9i	0.0288352	+	0.0481276i
$910$	5271.21			0.00636543
$911$	−658010.	−	379902.i	−0.792859	−	0.457757i	0.0481091	−	0.998842i	$-0.484680\pi$
$911$	−658010.	−	379902.i	−0.792859	−	0.457757i	−0.840968	+	0.541085i	$0.818014\pi$
$912$	−816835.	−	803718.i	−0.982075	−	0.966304i
$913$	−691947.	−	1.19849e6i	−0.830102	−	1.43778i
$914$	−21447.1	+	12382.5i	−0.0256730	+	0.0148223i
$915$	538718.	+	139686.i	0.643457	+	0.166844i
$916$	−159583.	+	276405.i	−0.190193	+	0.329424i
$917$			1.88477e6i			2.24140i
$918$	97227.7	+	330538.i	0.115373	+	0.392225i
$919$	916419.			1.08508			0.542541	−	0.840029i	$-0.317462\pi$
$919$	916419.			1.08508			0.542541	+	0.840029i	$0.317462\pi$
$920$	−10117.7	−	5841.44i	−0.0119538	−	0.00690151i
$921$	−195063.	+	752290.i	−0.229962	+	0.886882i
$922$	−193671.	−	335449.i	−0.227826	−	0.394606i
$923$	9395.77	−	5424.65i	0.0110288	−	0.00636749i
$924$	972793.	−	988669.i	1.13940	−	1.15800i
$925$	−44484.5	+	77049.3i	−0.0519906	+	0.0900504i
$926$			26518.3i			0.0309260i
$927$	−2366.88	−	146200.i	−0.00275434	−	0.170133i
$928$	733135.			0.851311
$929$	495736.	+	286213.i	0.574406	+	0.331633i	0.758907	−	0.651199i	$-0.225734\pi$
$929$	495736.	+	286213.i	0.574406	+	0.331633i	−0.184501	+	0.982832i	$0.559067\pi$
$930$	138007.	−	38178.7i	0.159564	−	0.0441424i
$931$	−909949.	−	1.57608e6i	−1.04983	−	1.81835i
$932$	−802290.	+	463202.i	−0.923633	+	0.533260i
$933$	−453897.	−	1.64073e6i	−0.521427	−	1.88484i
$934$	103947.	−	180041.i	0.119156	−	0.206385i
$935$			716352.i			0.819414i
$936$	−16168.3	+	261.754i	−0.0184550	+	0.000298773i
$937$	1.28619e6			1.46496			0.732481	−	0.680788i	$-0.238362\pi$
$937$	1.28619e6			1.46496			0.732481	+	0.680788i	$0.238362\pi$
$938$	−53416.9	−	30840.3i	−0.0607118	−	0.0350520i
$939$	667886.	+	657161.i	0.757480	+	0.745317i
$940$	−209078.	−	362134.i	−0.236621	−	0.409839i
$941$	−799776.	+	461751.i	−0.903211	+	0.521469i	−0.878240	−	0.478219i	$-0.841282\pi$
$941$	−799776.	+	461751.i	−0.903211	+	0.521469i	−0.0249702	+	0.999688i	$0.507949\pi$
$942$	−296952.	−	76997.6i	−0.334646	−	0.0867712i
$943$	17152.1	−	29708.3i	0.0192883	−	0.0334083i
$944$		−	378730.i		−	0.424997i
$945$	−430788.	−	410359.i	−0.482391	−	0.459516i
$946$	−35069.4			−0.0391874
$947$	1.35775e6	+	783896.i	1.51398	+	0.874095i	0.999866	+	0.0163718i	$0.00521153\pi$
$947$	1.35775e6	+	783896.i	1.51398	+	0.874095i	0.514111	+	0.857723i	$0.328122\pi$
$948$	122544.	−	472610.i	0.136357	−	0.525880i
$949$	−5899.29	−	10217.9i	−0.00655040	−	0.0113456i
$950$	70294.6	−	40584.6i	0.0778888	−	0.0449691i
$951$	−789275.	+	802156.i	−0.872705	+	0.886948i
$952$	−533174.	+	923485.i	−0.588295	+	1.01896i
$953$			84474.3i			0.0930120i	0.998918	+	0.0465060i	$0.0148087\pi$
$953$			84474.3i			0.0930120i	−0.998918	+	0.0465060i	$0.985191\pi$
$954$	−81881.9	+	49058.7i	−0.0899686	+	0.0539037i
$955$	189427.			0.207700
$956$	−1.09493e6	−	632160.i	−1.19804	−	0.691690i
$957$	−1.23274e6	+	341028.i	−1.34600	+	0.372363i
$958$	224193.	+	388313.i	0.244281	+	0.423108i
$959$	−945292.	+	545765.i	−1.02785	+	0.593428i
$960$	−67448.8	−	243811.i	−0.0731866	−	0.264552i
$961$	−466232.	+	807537.i	−0.504841	+	0.874411i
$962$		−	4597.07i		−	0.00496742i
$963$	−87531.8	+	157441.i	−0.0943873	+	0.169772i
$964$	−197007.			−0.211996
$965$	−137386.	−	79319.7i	−0.147532	−	0.0851778i
$966$	15831.7	+	15577.5i	0.0169658	+	0.0166933i
$967$	−104516.	−	181027.i	−0.111771	−	0.193594i	0.804713	−	0.593664i	$-0.202319\pi$
$967$	−104516.	−	181027.i	−0.111771	−	0.193594i	−0.916485	+	0.400070i	$0.868986\pi$
$968$	151319.	−	87364.3i	0.161489	−	0.0932359i
$969$	−2.45046e6	−	635386.i	−2.60975	−	0.676690i
$970$	79252.0	−	137269.i	0.0842300	−	0.145891i
$971$			1.76359e6i			1.87050i	0.353984	+	0.935252i	$0.384827\pi$
$971$			1.76359e6i			1.87050i	−0.353984	+	0.935252i	$0.615173\pi$
$972$	647182.	+	596810.i	0.685005	+	0.631690i
$973$	482751.			0.509915
$974$	121072.	+	69900.7i	0.127622	+	0.0736824i
$975$	−1745.97	+	6733.58i	−0.00183665	+	0.00708332i
$976$	−566411.	−	981053.i	−0.594610	−	1.02990i
$977$	314138.	−	181367.i	0.329102	−	0.190007i	−0.326340	−	0.945252i	$-0.605815\pi$
$977$	314138.	−	181367.i	0.329102	−	0.190007i	0.655442	+	0.755245i	$0.272482\pi$
$978$	180592.	−	183539.i	0.188808	−	0.191889i
$979$	−174099.	+	301548.i	−0.181648	+	0.314623i
$980$		−	487974.i		−	0.508094i
$981$	−979673.	−	544663.i	−1.01799	−	0.565966i
$982$	145671.			0.151060
$983$	885055.	+	510986.i	0.915931	+	0.528813i	0.882335	−	0.470622i	$-0.155971\pi$
$983$	885055.	+	510986.i	0.915931	+	0.528813i	0.0335966	+	0.999435i	$0.489304\pi$
$984$	−296831.	+	82116.2i	−0.306562	+	0.0848084i
$985$	−23712.3	−	41070.9i	−0.0244400	−	0.0423313i
$986$	410768.	−	237157.i	0.422515	−	0.243939i
$987$	439430.	+	1.58843e6i	0.451081	+	1.63055i
$988$	28654.3	−	49630.7i	0.0293546	−	0.0508437i
$989$			7673.45i			0.00784509i
$990$	−68846.5	−	114909.i	−0.0702444	−	0.117242i
$991$	610666.			0.621808			0.310904	−	0.950441i	$-0.399368\pi$
$991$	610666.			0.621808			0.310904	+	0.950441i	$0.399368\pi$
$992$	−861885.	−	497609.i	−0.875842	−	0.505668i
$993$	1.12623e6	+	1.10814e6i	1.14216	+	1.12382i
$994$	66893.1	+	115862.i	0.0677031	+	0.117265i
$995$	442692.	−	255588.i	0.447152	−	0.258163i
$996$	1.26933e6	+	329127.i	1.27954	+	0.331776i
$997$	676803.	−	1.17226e6i	0.680882	−	1.17932i	−0.293830	−	0.955858i	$-0.594930\pi$
$997$	676803.	−	1.17226e6i	0.680882	−	1.17932i	0.974712	−	0.223465i	$-0.0717367\pi$
$998$		−	122300.i		−	0.122791i
$999$	−357878.	+	375694.i	−0.358595	+	0.376446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.10	✓	32
3.2	odd	2		135.5.i.a.116.7		32
9.2	odd	6		405.5.c.b.161.18		32
9.4	even	3		135.5.i.a.71.7		32
9.5	odd	6	inner	45.5.i.a.41.10	yes	32
9.7	even	3		405.5.c.b.161.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.10	✓	32	1.1	even	1	trivial
45.5.i.a.41.10	yes	32	9.5	odd	6	inner
135.5.i.a.71.7		32	9.4	even	3
135.5.i.a.116.7		32	3.2	odd	2
405.5.c.b.161.15		32	9.7	even	3
405.5.c.b.161.18		32	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.904609 + 0.522276i) q^{2} +(-2.25893 + 8.71190i) q^{3} +(-7.45446 - 12.9115i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-6.59347 + 6.70108i) q^{6} +(-36.4983 + 63.2168i) q^{7} -32.2860i q^{8} +(-70.7944 - 39.3592i) q^{9} -11.6784 q^{10} +(-122.636 - 70.8041i) q^{11} +(129.323 - 35.7763i) q^{12} +(3.09167 + 5.35493i) q^{13} +(-66.0333 + 38.1243i) q^{14} +(-26.8290 - 96.9804i) q^{15} +(-102.409 + 177.378i) q^{16} +452.463i q^{17} +(-43.4849 - 72.5789i) q^{18} +621.658 q^{19} +(144.355 + 83.3433i) q^{20} +(-468.292 - 460.772i) q^{21} +(-73.9586 - 128.100i) q^{22} +(-28.0293 + 16.1827i) q^{23} +(281.272 + 72.9318i) q^{24} +(62.5000 - 108.253i) q^{25} +6.45882i q^{26} +(502.813 - 527.844i) q^{27} +1088.30 q^{28} +(-869.127 - 501.791i) q^{29} +(26.3808 - 101.741i) q^{30} +(681.173 + 1179.83i) q^{31} +(-632.648 + 365.259i) q^{32} +(893.866 - 908.454i) q^{33} +(-236.311 + 409.302i) q^{34} -816.126i q^{35} +(19.5480 + 1207.46i) q^{36} -711.751 q^{37} +(562.357 + 324.677i) q^{38} +(-53.6355 + 14.8379i) q^{39} +(180.484 + 312.608i) q^{40} +(-917.903 + 529.951i) q^{41} +(-182.971 - 661.396i) q^{42} +(118.544 - 205.324i) q^{43} +2111.23i q^{44} +(905.489 - 14.6592i) q^{45} -33.8073 q^{46} +(-2172.54 - 1254.32i) q^{47} +(-1313.96 - 1292.86i) q^{48} +(-1463.75 - 2535.28i) q^{49} +(113.076 - 65.2845i) q^{50} +(-3941.81 - 1022.08i) q^{51} +(46.0934 - 79.8361i) q^{52} -1128.18i q^{53} +(730.530 - 214.885i) q^{54} +1583.23 q^{55} +(2041.02 + 1178.38i) q^{56} +(-1404.28 + 5415.82i) q^{57} +(-524.147 - 907.849i) q^{58} +(-1601.37 + 924.551i) q^{59} +(-1052.17 + 1069.34i) q^{60} +(-2765.44 + 4789.87i) q^{61} +1423.04i q^{62} +(5072.04 - 3038.86i) q^{63} +2514.03 q^{64} +(-59.8699 - 34.5659i) q^{65} +(1283.06 - 354.951i) q^{66} +(404.470 + 700.562i) q^{67} +(5841.97 - 3372.86i) q^{68} +(-77.6659 - 280.744i) q^{69} +(426.243 - 738.275i) q^{70} -1754.60i q^{71} +(-1270.75 + 2285.67i) q^{72} -1908.13 q^{73} +(-643.856 - 371.731i) q^{74} +(801.908 + 789.030i) q^{75} +(-4634.12 - 8026.53i) q^{76} +(8952.03 - 5168.46i) q^{77} +(-56.2686 - 14.5900i) q^{78} +(1819.34 - 3151.19i) q^{79} -2289.94i q^{80} +(3462.71 + 5572.82i) q^{81} -1107.12 q^{82} +(8463.40 + 4886.35i) q^{83} +(-2458.39 + 9481.15i) q^{84} +(-2529.34 - 4380.95i) q^{85} +(214.472 - 123.825i) q^{86} +(6334.85 - 6438.24i) q^{87} +(-2285.98 + 3959.43i) q^{88} -2458.88i q^{89} +(826.769 + 459.654i) q^{90} -451.362 q^{91} +(417.886 + 241.266i) q^{92} +(-11817.2 + 3269.16i) q^{93} +(-1310.20 - 2269.33i) q^{94} +(-6019.17 + 3475.17i) q^{95} +(-1752.99 - 6336.66i) q^{96} +(-6786.18 + 11754.0i) q^{97} -3057.92i q^{98} +(5895.18 + 9839.41i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

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