LMFDB - Embedded newform 45.5.i.a.41.4

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			41.4
Character	$\chi$	$=$	45.41
Dual form			45.5.i.a.11.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.37336 + 1.94761i) q^{2} +(8.40237 + 3.22494i) q^{3} +(-0.413632 + 0.716431i) q^{4} +(9.68246 + 5.59017i) q^{5} +(-34.6251 + 5.48565i) q^{6} +(15.5174 + 26.8770i) q^{7} -65.5459i q^{8} +(60.1995 + 54.1943i) q^{9} -43.5499 q^{10} +(-127.765 + 73.7649i) q^{11} +(-5.78593 + 4.68578i) q^{12} +(-159.436 + 276.151i) q^{13} +(-104.692 - 60.4438i) q^{14} +(63.3276 + 78.1960i) q^{15} +(121.040 + 209.647i) q^{16} -295.405i q^{17} +(-308.624 - 65.5715i) q^{18} +492.804 q^{19} +(-8.00994 + 4.62454i) q^{20} +(43.7065 + 275.873i) q^{21} +(287.331 - 497.671i) q^{22} +(-224.940 - 129.869i) q^{23} +(211.382 - 550.741i) q^{24} +(62.5000 + 108.253i) q^{25} -1242.08i q^{26} +(331.045 + 649.500i) q^{27} -25.6740 q^{28} +(1079.30 - 623.132i) q^{29} +(-365.922 - 140.446i) q^{30} +(419.870 - 727.237i) q^{31} +(91.6096 + 52.8908i) q^{32} +(-1311.41 + 207.767i) q^{33} +(575.334 + 996.508i) q^{34} +346.980i q^{35} +(-63.7269 + 20.7123i) q^{36} -32.2394 q^{37} +(-1662.41 + 959.790i) q^{38} +(-2230.21 + 1806.15i) q^{39} +(366.413 - 634.645i) q^{40} +(1330.64 + 768.244i) q^{41} +(-684.731 - 845.496i) q^{42} +(245.177 + 424.659i) q^{43} -122.046i q^{44} +(279.924 + 861.259i) q^{45} +1011.74 q^{46} +(-1529.13 + 882.846i) q^{47} +(340.921 + 2151.88i) q^{48} +(718.919 - 1245.20i) q^{49} +(-421.670 - 243.451i) q^{50} +(952.664 - 2482.10i) q^{51} +(-131.895 - 228.450i) q^{52} -2640.43i q^{53} +(-2381.71 - 1546.25i) q^{54} -1649.43 q^{55} +(1761.68 - 1017.10i) q^{56} +(4140.72 + 1589.26i) q^{57} +(-2427.23 + 4204.09i) q^{58} +(2762.80 + 1595.10i) q^{59} +(-82.2163 + 13.0255i) q^{60} +(796.842 + 1380.17i) q^{61} +3270.97i q^{62} +(-522.436 + 2458.94i) q^{63} -4285.31 q^{64} +(-3087.46 + 1782.55i) q^{65} +(4019.22 - 3254.99i) q^{66} +(2873.92 - 4977.78i) q^{67} +(211.637 + 122.189i) q^{68} +(-1471.21 - 1816.63i) q^{69} +(-675.782 - 1170.49i) q^{70} -1430.34i q^{71} +(3552.21 - 3945.83i) q^{72} -3951.17 q^{73} +(108.755 - 62.7897i) q^{74} +(176.038 + 1111.14i) q^{75} +(-203.839 + 353.060i) q^{76} +(-3965.16 - 2289.28i) q^{77} +(4005.62 - 10436.4i) q^{78} +(712.702 + 1234.44i) q^{79} +2706.53i q^{80} +(686.964 + 6524.94i) q^{81} -5984.96 q^{82} +(3071.50 - 1773.33i) q^{83} +(-215.722 - 82.7971i) q^{84} +(1651.36 - 2860.25i) q^{85} +(-1654.14 - 955.018i) q^{86} +(11078.2 - 1755.12i) q^{87} +(4834.99 + 8374.44i) q^{88} -533.010i q^{89} +(-2621.68 - 2360.15i) q^{90} -9896.14 q^{91} +(186.084 - 107.436i) q^{92} +(5873.20 - 4756.45i) q^{93} +(3438.88 - 5956.31i) q^{94} +(4771.56 + 2754.86i) q^{95} +(599.168 + 739.844i) q^{96} +(-5855.38 - 10141.8i) q^{97} +5600.69i q^{98} +(-11689.0 - 2483.50i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−3.37336	+	1.94761i	−0.843340	+	0.486902i	−0.858398	−	0.512984i	$-0.828540\pi$
$2$	−3.37336	+	1.94761i	−0.843340	+	0.486902i	0.0150583	+	0.999887i	$0.495207\pi$
$3$	8.40237	+	3.22494i	0.933596	+	0.358327i
$3$	8.40237	+	3.22494i	0.933596	+	0.358327i
$4$	−0.413632	+	0.716431i	−0.0258520	+	0.0447769i
$5$	9.68246	+	5.59017i	0.387298	+	0.223607i
$5$	9.68246	+	5.59017i	0.387298	+	0.223607i
$6$	−34.6251	+	5.48565i	−0.961809	+	0.152379i
$7$	15.5174	+	26.8770i	0.316682	+	0.548510i	0.979794	−	0.200011i	$-0.0640978\pi$
$7$	15.5174	+	26.8770i	0.316682	+	0.548510i	−0.663111	+	0.748521i	$0.730764\pi$
$8$		−	65.5459i		−	1.02415i
$9$	60.1995	+	54.1943i	0.743204	+	0.669065i
$10$	−43.5499			−0.435499
$11$	−127.765	+	73.7649i	−1.05591	+	0.609627i	−0.924297	−	0.381674i	$-0.875348\pi$
$11$	−127.765	+	73.7649i	−1.05591	+	0.609627i	−0.131609	+	0.991302i	$0.542014\pi$
$12$	−5.78593	+	4.68578i	−0.0401801	+	0.0325401i
$13$	−159.436	+	276.151i	−0.943407	+	1.63403i	−0.184499	+	0.982833i	$0.559066\pi$
$13$	−159.436	+	276.151i	−0.943407	+	1.63403i	−0.758909	+	0.651197i	$0.774267\pi$
$14$	−104.692	−	60.4438i	−0.534142	−	0.308387i
$15$	63.3276	+	78.1960i	0.281456	+	0.347538i
$16$	121.040	+	209.647i	0.472811	+	0.818933i
$17$		−	295.405i		−	1.02216i	−0.859532	−	0.511082i	$-0.829245\pi$
$17$		−	295.405i		−	1.02216i	0.859532	−	0.511082i	$-0.170755\pi$
$18$	−308.624	−	65.5715i	−0.952543	−	0.202381i
$19$	492.804			1.36511			0.682554	−	0.730835i	$-0.260869\pi$
$19$	492.804			1.36511			0.682554	+	0.730835i	$0.260869\pi$
$20$	−8.00994	+	4.62454i	−0.0200249	+	0.0115614i
$21$	43.7065	+	275.873i	0.0991077	+	0.625562i
$22$	287.331	−	497.671i	0.593658	−	1.02825i
$23$	−224.940	−	129.869i	−0.425217	−	0.245499i	0.272090	−	0.962272i	$-0.412285\pi$
$23$	−224.940	−	129.869i	−0.425217	−	0.245499i	−0.697307	+	0.716773i	$0.745619\pi$
$24$	211.382	−	550.741i	0.366982	−	0.956147i
$25$	62.5000	+	108.253i	0.100000	+	0.173205i
$26$		−	1242.08i		−	1.83739i
$27$	331.045	+	649.500i	0.454109	+	0.890946i
$28$	−25.6740			−0.0327475
$29$	1079.30	−	623.132i	1.28335	−	0.740941i	0.305889	−	0.952067i	$-0.401046\pi$
$29$	1079.30	−	623.132i	1.28335	−	0.740941i	0.977459	+	0.211126i	$0.0677130\pi$
$30$	−365.922	−	140.446i	−0.406580	−	0.156051i
$31$	419.870	−	727.237i	0.436910	−	0.756750i	−0.560540	−	0.828128i	$-0.689406\pi$
$31$	419.870	−	727.237i	0.436910	−	0.756750i	0.997449	+	0.0713776i	$0.0227395\pi$
$32$	91.6096	+	52.8908i	0.0894625	+	0.0516512i
$33$	−1311.41	+	207.767i	−1.20424	+	0.190787i
$34$	575.334	+	996.508i	0.497694	+	0.862031i
$35$			346.980i			0.283249i
$36$	−63.7269	+	20.7123i	−0.0491720	+	0.0159817i
$37$	−32.2394			−0.0235496			−0.0117748	−	0.999931i	$-0.503748\pi$
$37$	−32.2394			−0.0235496			−0.0117748	+	0.999931i	$0.503748\pi$
$38$	−1662.41	+	959.790i	−1.15125	+	0.664675i
$39$	−2230.21	+	1806.15i	−1.46628	+	1.18748i
$40$	366.413	−	634.645i	0.229008	−	0.396653i
$41$	1330.64	+	768.244i	0.791575	+	0.457016i	0.840517	−	0.541786i	$-0.182252\pi$
$41$	1330.64	+	768.244i	0.791575	+	0.457016i	−0.0489419	+	0.998802i	$0.515585\pi$
$42$	−684.731	−	845.496i	−0.388169	−	0.479306i
$43$	245.177	+	424.659i	0.132600	+	0.229669i	0.924678	−	0.380750i	$-0.124334\pi$
$43$	245.177	+	424.659i	0.132600	+	0.229669i	−0.792078	+	0.610420i	$0.791001\pi$
$44$		−	122.046i		−	0.0630403i
$45$	279.924	+	861.259i	0.138234	+	0.425313i
$46$	1011.74			0.478137
$47$	−1529.13	+	882.846i	−0.692229	+	0.399659i	−0.804447	−	0.594025i	$-0.797538\pi$
$47$	−1529.13	+	882.846i	−0.692229	+	0.399659i	0.112217	+	0.993684i	$0.464205\pi$
$48$	340.921	+	2151.88i	0.147969	+	0.933974i
$49$	718.919	−	1245.20i	0.299425	−	0.518619i
$50$	−421.670	−	243.451i	−0.168668	−	0.0973805i
$51$	952.664	−	2482.10i	0.366268	−	0.954288i
$52$	−131.895	−	228.450i	−0.0487779	−	0.0844858i
$53$		−	2640.43i		−	0.939989i	−0.882669	−	0.469994i	$-0.844256\pi$
$53$		−	2640.43i		−	0.939989i	0.882669	−	0.469994i	$-0.155744\pi$
$54$	−2381.71	−	1546.25i	−0.816772	−	0.530264i
$55$	−1649.43			−0.545267
$56$	1761.68	−	1017.10i	0.561759	−	0.324332i
$57$	4140.72	+	1589.26i	1.27446	+	0.489155i
$58$	−2427.23	+	4204.09i	−0.721532	+	1.24973i
$59$	2762.80	+	1595.10i	0.793679	+	0.458231i	0.841256	−	0.540637i	$-0.181817\pi$
$59$	2762.80	+	1595.10i	0.793679	+	0.458231i	−0.0475770	+	0.998868i	$0.515150\pi$
$60$	−82.2163	+	13.0255i	−0.0228379	+	0.00361820i
$61$	796.842	+	1380.17i	0.214147	+	0.370914i	0.953008	−	0.302944i	$-0.0979695\pi$
$61$	796.842	+	1380.17i	0.214147	+	0.370914i	−0.738861	+	0.673858i	$0.764636\pi$
$62$			3270.97i			0.850930i
$63$	−522.436	+	2458.94i	−0.131629	+	0.619536i
$64$	−4285.31			−1.04622
$65$	−3087.46	+	1782.55i	−0.730760	+	0.421905i
$66$	4019.22	−	3254.99i	0.922685	−	0.747243i
$67$	2873.92	−	4977.78i	0.640214	−	1.10888i	−0.345171	−	0.938540i	$-0.612179\pi$
$67$	2873.92	−	4977.78i	0.640214	−	1.10888i	0.985385	−	0.170343i	$-0.0544877\pi$
$68$	211.637	+	122.189i	0.0457693	+	0.0264249i
$69$	−1471.21	−	1816.63i	−0.309012	−	0.381564i
$70$	−675.782	−	1170.49i	−0.137915	−	0.238875i
$71$		−	1430.34i		−	0.283741i	−0.989885	−	0.141870i	$-0.954688\pi$
$71$		−	1430.34i		−	0.283741i	0.989885	−	0.141870i	$-0.0453116\pi$
$72$	3552.21	−	3945.83i	0.685226	−	0.761156i
$73$	−3951.17			−0.741448			−0.370724	−	0.928743i	$-0.620890\pi$
$73$	−3951.17			−0.741448			−0.370724	+	0.928743i	$0.620890\pi$
$74$	108.755	−	62.7897i	0.0198603	−	0.0114663i
$75$	176.038	+	1111.14i	0.0312956	+	0.197536i
$76$	−203.839	+	353.060i	−0.0352908	+	0.0611254i
$77$	−3965.16	−	2289.28i	−0.668773	−	0.386116i
$78$	4005.62	−	10436.4i	0.658386	−	1.71538i
$79$	712.702	+	1234.44i	0.114197	+	0.197795i	0.917458	−	0.397832i	$-0.130237\pi$
$79$	712.702	+	1234.44i	0.114197	+	0.197795i	−0.803262	+	0.595626i	$0.796904\pi$
$80$			2706.53i			0.422895i
$81$	686.964	+	6524.94i	0.104704	+	0.994503i
$82$	−5984.96			−0.890089
$83$	3071.50	−	1773.33i	0.445855	−	0.257415i	−0.260223	−	0.965549i	$-0.583796\pi$
$83$	3071.50	−	1773.33i	0.445855	−	0.257415i	0.706078	+	0.708134i	$0.250463\pi$
$84$	−215.722	−	82.7971i	−0.0305729	−	0.0117343i
$85$	1651.36	−	2860.25i	0.228563	−	0.395882i
$86$	−1654.14	−	955.018i	−0.223653	−	0.129126i
$87$	11078.2	−	1755.12i	1.46363	−	0.231882i
$88$	4834.99	+	8374.44i	0.624353	+	1.08141i
$89$		−	533.010i		−	0.0672908i	−0.999434	−	0.0336454i	$-0.989288\pi$
$89$		−	533.010i		−	0.0672908i	0.999434	−	0.0336454i	$-0.0107117\pi$
$90$	−2621.68	−	2360.15i	−0.323664	−	0.291377i
$91$	−9896.14			−1.19504
$92$	186.084	−	107.436i	0.0219854	−	0.0126933i
$93$	5873.20	−	4756.45i	0.679061	−	0.549943i
$94$	3438.88	−	5956.31i	0.389190	−	0.674096i
$95$	4771.56	+	2754.86i	0.528704	+	0.305248i
$96$	599.168	+	739.844i	0.0650139	+	0.0802782i
$97$	−5855.38	−	10141.8i	−0.622317	−	1.07788i	−0.989053	−	0.147560i	$-0.952858\pi$
$97$	−5855.38	−	10141.8i	−0.622317	−	1.07788i	0.366736	−	0.930325i	$-0.380475\pi$
$98$			5600.69i			0.583162i
$99$	−11689.0	−	2483.50i	−1.19263	−	0.253392i
$100$	−103.408			−0.0103408
$101$	−8845.92	+	5107.20i	−0.867163	+	0.500657i	−0.866404	−	0.499343i	$-0.833575\pi$
$101$	−8845.92	+	5107.20i	−0.867163	+	0.500657i	−0.000758245		1.00000i	$0.500241\pi$
$102$	1620.49	+	10228.4i	0.155756	+	0.983126i
$103$	514.018	−	890.305i	0.0484511	−	0.0839197i	−0.840783	−	0.541373i	$-0.817905\pi$
$103$	514.018	−	890.305i	0.0484511	−	0.0839197i	0.889234	+	0.457453i	$0.151238\pi$
$104$	18100.6	+	10450.4i	1.67350	+	0.966195i
$105$	−1118.99	+	2915.46i	−0.101496	+	0.264440i
$106$	5142.52	+	8907.11i	0.457683	+	0.792730i
$107$			12564.7i			1.09745i	0.836003	+	0.548724i	$0.184886\pi$
$107$			12564.7i			1.09745i	−0.836003	+	0.548724i	$0.815114\pi$
$108$	−602.253	−	31.4827i	−0.0516335	−	0.00269914i
$109$	8652.33			0.728250			0.364125	−	0.931350i	$-0.381368\pi$
$109$	8652.33			0.728250			0.364125	+	0.931350i	$0.381368\pi$
$110$	5564.13	−	3212.45i	0.459846	−	0.265492i
$111$	−270.887	−	103.970i	−0.0219858	−	0.00843844i
$112$	−3756.45	+	6506.36i	−0.299462	+	0.518683i
$113$	−18806.0	−	10857.6i	−1.47278	−	0.850312i	−0.473253	−	0.880927i	$-0.656920\pi$
$113$	−18806.0	−	10857.6i	−1.47278	−	0.850312i	−0.999531	+	0.0306144i	$0.990254\pi$
$114$	−17063.4	+	2703.35i	−1.31297	+	0.208014i
$115$	−1451.98	−	2514.90i	−0.109791	−	0.190163i
$116$			1030.99i			0.0766192i
$117$	−24563.8	+	7983.65i	−1.79442	+	0.583216i
$118$	−12426.5			−0.892455
$119$	7939.60	−	4583.93i	0.560667	−	0.323701i
$120$	5125.43	−	4150.86i	0.355932	−	0.288254i
$121$	3562.03	−	6169.61i	0.243291	−	0.421393i
$122$	−5376.07	−	3103.87i	−0.361198	−	0.208538i
$123$	8702.96	+	10746.3i	0.575250	+	0.710311i
$124$	347.343	+	601.616i	0.0225900	+	0.0391270i
$125$			1397.54i			0.0894427i
$126$	−3026.69	−	9312.38i	−0.190645	−	0.586570i
$127$	16093.6			0.997807			0.498903	−	0.866658i	$-0.333736\pi$
$127$	16093.6			0.997807			0.498903	+	0.866658i	$0.333736\pi$
$128$	12990.1	−	7499.87i	0.792856	−	0.457755i
$129$	690.567	+	4358.82i	0.0414979	+	0.261933i
$130$	6943.41	−	12026.3i	0.410853	−	0.711618i
$131$	−12682.7	−	7322.39i	−0.739045	−	0.426688i	0.0826773	−	0.996576i	$-0.473653\pi$
$131$	−12682.7	−	7322.39i	−0.739045	−	0.426688i	−0.821722	+	0.569889i	$0.806986\pi$
$132$	393.591	−	1025.48i	0.0225890	−	0.0588542i
$133$	7647.06	+	13245.1i	0.432306	+	0.748776i
$134$			22389.1i			1.24689i
$135$	−425.484	+	8139.35i	−0.0233462	+	0.446604i
$136$	−19362.6			−1.04685
$137$	−5790.92	+	3343.39i	−0.308537	+	0.178134i	−0.646271	−	0.763108i	$-0.723673\pi$
$137$	−5790.92	+	3343.39i	−0.308537	+	0.178134i	0.337735	+	0.941241i	$0.390339\pi$
$138$	8500.99	+	3262.79i	0.446387	+	0.171329i
$139$	13768.7	−	23848.1i	0.712629	−	1.23431i	−0.251238	−	0.967925i	$-0.580838\pi$
$139$	13768.7	−	23848.1i	0.712629	−	1.23431i	0.963867	−	0.266384i	$-0.0858291\pi$
$140$	−248.587	−	143.522i	−0.0126830	−	0.00732255i
$141$	−15695.5	+	2486.63i	−0.789471	+	0.125076i
$142$	2785.74	+	4825.04i	0.138154	+	0.239290i
$143$		−	47043.1i		−	2.30051i
$144$	−4075.13	+	19180.3i	−0.196524	+	0.924976i
$145$	13933.6			0.662718
$146$	13328.7	−	7695.35i	0.625292	−	0.361013i
$147$	10056.3	−	8144.19i	0.465377	−	0.376889i
$148$	13.3352	−	23.0973i	0.000608803	−	0.00105448i
$149$	−6040.28	−	3487.36i	−0.272073	−	0.157081i	0.357757	−	0.933815i	$-0.383542\pi$
$149$	−6040.28	−	3487.36i	−0.272073	−	0.157081i	−0.629829	+	0.776734i	$0.716875\pi$
$150$	−2757.91	−	3405.43i	−0.122574	−	0.151352i
$151$	17892.3	+	30990.3i	0.784714	+	1.35916i	0.929170	+	0.369653i	$0.120524\pi$
$151$	17892.3	+	30990.3i	0.784714	+	1.35916i	−0.144456	+	0.989511i	$0.546143\pi$
$152$		−	32301.3i		−	1.39808i
$153$	16009.3	−	17783.2i	0.683894	−	0.759676i
$154$	17834.5			0.752004
$155$	8130.75	−	4694.29i	0.338429	−	0.195392i
$156$	−371.497	−	2344.87i	−0.0152653	−	0.0963541i
$157$	−19878.7	+	34431.0i	−0.806472	+	1.39685i	0.108821	+	0.994061i	$0.465293\pi$
$157$	−19878.7	+	34431.0i	−0.806472	+	1.39685i	−0.915293	+	0.402789i	$0.868041\pi$
$158$	−4808.40	−	2776.13i	−0.192613	−	0.111205i
$159$	8515.22	−	22185.8i	0.336823	−	0.877570i
$160$	591.338	+	1024.23i	0.0230991	+	0.0400089i
$161$		−	8060.94i		−	0.310981i
$162$	−15025.4	−	20673.0i	−0.572527	−	0.787724i
$163$	44572.5			1.67761			0.838807	−	0.544429i	$-0.183254\pi$
$163$	44572.5			1.67761			0.838807	+	0.544429i	$0.183254\pi$
$164$	−1100.79	+	635.540i	−0.0409275	+	0.0236295i
$165$	−13859.1	−	5319.33i	−0.509060	−	0.195384i
$166$	−6907.50	+	11964.1i	−0.250672	+	0.434176i
$167$	−3770.19	−	2176.72i	−0.135186	−	0.0780494i	0.430882	−	0.902408i	$-0.358203\pi$
$167$	−3770.19	−	2176.72i	−0.135186	−	0.0780494i	−0.566068	+	0.824359i	$0.691536\pi$
$168$	18082.3	−	2864.78i	0.640673	−	0.101502i
$169$	−36559.1	−	63322.2i	−1.28004	−	2.21709i
$170$			12864.9i			0.445151i
$171$	29666.6	+	26707.2i	1.01455	+	0.913346i
$172$	−405.652			−0.0137119
$173$	−35554.4	+	20527.4i	−1.18796	+	0.685868i	−0.957842	−	0.287295i	$-0.907244\pi$
$173$	−35554.4	+	20527.4i	−1.18796	+	0.685868i	−0.230116	+	0.973163i	$0.573911\pi$
$174$	−33952.5	+	27496.6i	−1.12143	+	0.908199i
$175$	−1939.68	+	3359.62i	−0.0633365	+	0.109702i
$176$	−30929.2	−	17857.0i	−0.998489	−	0.576478i
$177$	18069.9	+	22312.5i	0.576780	+	0.712199i
$178$	1038.10	+	1798.04i	0.0327641	+	0.0567490i
$179$			13299.0i			0.415062i	0.978228	+	0.207531i	$0.0665427\pi$
$179$			13299.0i			0.415062i	−0.978228	+	0.207531i	$0.933457\pi$
$180$	−732.818	−	155.698i	−0.0226179	−	0.00480548i
$181$	−32261.8			−0.984761			−0.492380	−	0.870380i	$-0.663873\pi$
$181$	−32261.8			−0.984761			−0.492380	+	0.870380i	$0.663873\pi$
$182$	33383.2	−	19273.8i	1.00783	−	0.581869i
$183$	2244.39	+	14166.5i	0.0670187	+	0.423018i
$184$	−8512.38	+	14743.9i	−0.251429	+	0.435488i
$185$	−312.156	−	180.223i	−0.00912071	−	0.00526584i
$186$	−10548.7	+	27483.9i	−0.304911	+	0.794425i
$187$	21790.5	+	37742.3i	0.623139	+	1.07931i
$188$		−	1460.69i		−	0.0413279i
$189$	−12319.6	+	18976.1i	−0.344885	+	0.531230i
$190$	−21461.6			−0.594503
$191$	−23925.7	+	13813.5i	−0.655840	+	0.378649i	−0.790690	−	0.612217i	$-0.790278\pi$
$191$	−23925.7	+	13813.5i	−0.655840	+	0.378649i	0.134850	+	0.990866i	$0.456945\pi$
$192$	−36006.8	−	13819.9i	−0.976746	−	0.374888i
$193$	−22835.9	+	39553.0i	−0.613061	+	1.06185i	0.377660	+	0.925944i	$0.376729\pi$
$193$	−22835.9	+	39553.0i	−0.613061	+	1.06185i	−0.990721	+	0.135909i	$0.956605\pi$
$194$	39504.6	+	22808.0i	1.04965	+	0.606015i
$195$	−31690.6	+	5020.73i	−0.833415	+	0.132038i
$196$	594.735	+	1030.11i	0.0154814	+	0.0268146i
$197$			14691.9i			0.378568i	0.981922	+	0.189284i	$0.0606167\pi$
$197$			14691.9i			0.378568i	−0.981922	+	0.189284i	$0.939383\pi$
$198$	44268.1	−	14387.9i	1.12917	−	0.367001i
$199$	25365.3			0.640522			0.320261	−	0.947329i	$-0.396229\pi$
$199$	25365.3			0.640522			0.320261	+	0.947329i	$0.396229\pi$
$200$	7095.55	−	4096.62i	0.177389	−	0.102415i
$201$	40200.8	−	32556.9i	0.995044	−	0.805843i
$202$	19893.7	−	34456.8i	0.487542	−	0.844447i
$203$	33495.8	+	19338.8i	0.812827	+	0.469286i
$204$	1384.20	+	1709.19i	0.0332613	+	0.0410706i
$205$	8589.23	+	14877.0i	0.204384	+	0.354003i
$206$			4004.42i			0.0943638i
$207$	−6503.11	−	20008.5i	−0.151768	−	0.466954i
$208$	−77192.3			−1.78422
$209$	−62962.9	+	36351.7i	−1.44143	+	0.832208i
$210$	−1903.41	−	12014.2i	−0.0431613	−	0.272432i
$211$	19335.9	−	33490.8i	0.434310	−	0.752246i	−0.562929	−	0.826505i	$-0.690326\pi$
$211$	19335.9	−	33490.8i	0.434310	−	0.752246i	0.997239	+	0.0742586i	$0.0236590\pi$
$212$	1891.68	+	1092.16i	0.0420898	+	0.0243006i
$213$	4612.75	−	12018.2i	0.101672	−	0.264899i
$214$	−24471.1	−	42385.2i	−0.534350	−	0.925522i
$215$			5482.32i			0.118601i
$216$	42572.0	−	21698.6i	0.912467	−	0.465077i
$217$	26061.2			0.553446
$218$	−29187.4	+	16851.4i	−0.614162	+	0.354587i
$219$	−33199.2	−	12742.3i	−0.692213	−	0.265680i
$220$	682.258	−	1181.71i	0.0140962	−	0.0244154i
$221$	81576.4	+	47098.2i	1.67024	+	0.964316i
$222$	1116.29	−	176.854i	0.0226502	−	0.00358846i
$223$	−25728.6	−	44563.3i	−0.517376	−	0.896122i	−0.999796	−	0.0201822i	$-0.993575\pi$
$223$	−25728.6	−	44563.3i	−0.517376	−	0.896122i	0.482420	−	0.875940i	$-0.339758\pi$
$224$			3282.92i			0.0654281i
$225$	−2104.23	+	9903.93i	−0.0415651	+	0.195633i
$226$	84585.8			1.65608
$227$	36305.4	−	20960.9i	0.704563	−	0.406779i	−0.104482	−	0.994527i	$-0.533318\pi$
$227$	36305.4	−	20960.9i	0.704563	−	0.406779i	0.809044	+	0.587747i	$0.199985\pi$
$228$	−2851.33	+	2309.17i	−0.0548502	+	0.0444208i
$229$	13130.6	−	22742.9i	0.250389	−	0.433686i	−0.713244	−	0.700916i	$-0.752775\pi$
$229$	13130.6	−	22742.9i	0.250389	−	0.433686i	0.963633	+	0.267230i	$0.0861083\pi$
$230$	9796.10	+	5655.78i	0.185182	+	0.106915i
$231$	−25933.9	−	32022.8i	−0.486008	−	0.600116i
$232$	−40843.7	−	70743.4i	−0.758838	−	1.31435i
$233$			2406.31i			0.0443241i	0.999754	+	0.0221621i	$0.00705498\pi$
$233$			2406.31i			0.0443241i	−0.999754	+	0.0221621i	$0.992945\pi$
$234$	67313.4	−	74772.3i	1.22933	−	1.36556i
$235$	−19741.0			−0.357466
$236$	−2285.56	+	1319.57i	−0.0410364	+	0.0236924i
$237$	2007.40	+	12670.6i	0.0357386	+	0.225580i
$238$	−17855.4	+	30926.5i	−0.315222	+	0.545980i
$239$	59780.1	+	34514.1i	1.04655	+	0.604227i	0.921682	−	0.387946i	$-0.126815\pi$
$239$	59780.1	+	34514.1i	1.04655	+	0.604227i	0.124870	+	0.992173i	$0.460149\pi$
$240$	−8728.40	+	22741.3i	−0.151535	+	0.394814i
$241$	−40913.7	−	70864.6i	−0.704425	−	1.22010i	−0.966899	−	0.255160i	$-0.917872\pi$
$241$	−40913.7	−	70864.6i	−0.704425	−	1.22010i	0.262474	−	0.964939i	$-0.415462\pi$
$242$			27749.8i			0.473837i
$243$	−15270.4	+	57040.3i	−0.258606	+	0.965983i
$244$	−1318.40			−0.0221445
$245$	13921.8	−	8037.75i	0.231933	−	0.133907i
$246$	−50287.8	−	19301.1i	−0.830983	−	0.318943i
$247$	−78570.7	+	136088.i	−1.28785	+	2.23063i
$248$	−47667.4	−	27520.8i	−0.775029	−	0.447463i
$249$	31526.7	−	4994.77i	0.508487	−	0.0805595i
$250$	−2721.87	−	4714.41i	−0.0435499	−	0.0754306i
$251$		−	45043.6i		−	0.714966i	−0.933920	−	0.357483i	$-0.883635\pi$
$251$		−	45043.6i		−	0.714966i	0.933920	−	0.357483i	$-0.116365\pi$
$252$	−1545.56	−	1391.38i	−0.0243380	−	0.0219102i
$253$	38319.1			0.598652
$254$	−54289.6	+	31344.1i	−0.841490	+	0.485834i
$255$	23099.5	−	18707.3i	0.355240	−	0.287694i
$256$	5068.88	−	8779.56i	0.0773450	−	0.133966i
$257$	8849.63	+	5109.34i	0.133986	+	0.0773568i	0.565495	−	0.824752i	$-0.308685\pi$
$257$	8849.63	+	5109.34i	0.133986	+	0.0773568i	−0.431509	+	0.902109i	$0.642019\pi$
$258$	−10818.8	−	13358.9i	−0.162532	−	0.200693i
$259$	−500.272	−	866.497i	−0.00745773	−	0.0129172i
$260$		−	2949.27i		−	0.0436283i
$261$	98743.2	+	20979.4i	1.44953	+	0.307973i
$262$	57044.6			0.831021
$263$	−27122.3	+	15659.0i	−0.392116	+	0.226388i	−0.683076	−	0.730347i	$-0.739358\pi$
$263$	−27122.3	+	15659.0i	−0.392116	+	0.226388i	0.290961	+	0.956735i	$0.406025\pi$
$264$	13618.3	+	85957.7i	0.195395	+	1.23332i
$265$	14760.4	−	25565.8i	0.210188	−	0.364056i
$266$	−51592.5	−	29787.0i	−0.729161	−	0.420981i
$267$	1718.93	−	4478.55i	0.0241121	−	0.0628224i
$268$	2377.49	+	4117.93i	0.0331016	+	0.0573336i
$269$		−	50506.9i		−	0.697985i	−0.937126	−	0.348992i	$-0.886524\pi$
$269$		−	50506.9i		−	0.697985i	0.937126	−	0.348992i	$-0.113476\pi$
$270$	−14417.0	−	28285.6i	−0.197764	−	0.388006i
$271$	−107669.			−1.46606			−0.733028	−	0.680199i	$-0.761893\pi$
$271$	−107669.			−1.46606			−0.733028	+	0.680199i	$0.761893\pi$
$272$	61930.8	−	35755.8i	0.837083	−	0.483290i
$273$	−83151.0	−	31914.5i	−1.11569	−	0.428215i
$274$	13023.2	−	22556.9i	0.173467	−	0.300454i
$275$	−15970.6	−	9220.62i	−0.211181	−	0.121925i
$276$	1910.02	−	302.605i	0.0250738	−	0.00397244i
$277$	−35466.6	−	61429.9i	−0.462232	−	0.800609i	0.536840	−	0.843684i	$-0.319618\pi$
$277$	−35466.6	−	61429.9i	−0.462232	−	0.800609i	−0.999072	+	0.0430750i	$0.986285\pi$
$278$			107264.i			1.38792i
$279$	64688.1	−	21024.7i	0.831028	−	0.270099i
$280$	22743.1			0.290091
$281$	92279.4	−	53277.5i	1.16867	−	0.674732i	0.215304	−	0.976547i	$-0.430926\pi$
$281$	92279.4	−	53277.5i	1.16867	−	0.674732i	0.953367	+	0.301815i	$0.0975924\pi$
$282$	48103.5	−	38957.0i	0.604893	−	0.489877i
$283$	−24519.2	+	42468.4i	−0.306149	+	0.530266i	−0.977516	−	0.210859i	$-0.932374\pi$
$283$	−24519.2	+	42468.4i	−0.306149	+	0.530266i	0.671367	+	0.741125i	$0.265707\pi$
$284$	1024.74	+	591.633i	0.0127050	+	0.00733526i
$285$	31208.1	+	38535.3i	0.384218	+	0.474427i
$286$	91621.6	+	158693.i	1.12012	+	1.94011i
$287$			47684.7i			0.578915i
$288$	2648.47	+	8148.72i	0.0319309	+	0.0982436i
$289$	−3743.20			−0.0448174
$290$	−47003.2	+	27137.3i	−0.558896	+	0.322679i
$291$	−16492.3	−	104099.i	−0.194758	−	1.22930i
$292$	1634.33	−	2830.74i	0.0191679	−	0.0331998i
$293$	−82176.4	−	47444.6i	−0.957220	−	0.552651i	−0.0619037	−	0.998082i	$-0.519717\pi$
$293$	−82176.4	−	47444.6i	−0.957220	−	0.552651i	−0.895316	+	0.445431i	$0.853050\pi$
$294$	−18061.9	+	47059.1i	−0.208963	+	0.544438i
$295$	17833.8	+	30889.0i	0.204927	+	0.354944i
$296$			2113.16i			0.0241184i
$297$	−90206.2	−	58563.6i	−1.02264	−	0.663918i
$298$	27168.1			0.305933
$299$	71727.0	−	41411.6i	0.802306	−	0.463212i
$300$	−868.871	−	333.484i	−0.00965412	−	0.00370538i
$301$	−7609.03	+	13179.2i	−0.0839840	+	0.145464i
$302$	−120714.	−	69694.3i	−1.32356	−	0.764158i
$303$	−90797.1	+	14385.0i	−0.988978	+	0.156684i
$304$	59648.9	+	103315.i	0.645439	+	1.11793i
$305$			17817.9i			0.191539i
$306$	−19370.2	+	91169.1i	−0.206867	+	0.973654i
$307$	82467.3			0.874994			0.437497	−	0.899220i	$-0.355865\pi$
$307$	82467.3			0.874994			0.437497	+	0.899220i	$0.355865\pi$
$308$	3280.23	−	1893.84i	0.0345782	−	0.0199637i
$309$	7190.14	−	5822.99i	0.0753044	−	0.0609858i
$310$	−18285.3	+	31671.1i	−0.190274	+	0.329564i
$311$	31406.8	+	18132.7i	0.324715	+	0.187475i	0.653492	−	0.756933i	$-0.273303\pi$
$311$	31406.8	+	18132.7i	0.324715	+	0.187475i	−0.328777	+	0.944408i	$0.606636\pi$
$312$	118386.	+	146181.i	1.21616	+	1.50170i
$313$	−24030.7	−	41622.4i	−0.245289	−	0.424853i	0.716924	−	0.697152i	$-0.245550\pi$
$313$	−24030.7	−	41622.4i	−0.245289	−	0.424853i	−0.962213	+	0.272298i	$0.912216\pi$
$314$		−	154864.i		−	1.57069i
$315$	−18804.3	+	20888.0i	−0.189512	+	0.210512i
$316$	−1179.18			−0.0118089
$317$	−65088.6	+	37578.9i	−0.647718	+	0.373960i	−0.787582	−	0.616210i	$-0.788667\pi$
$317$	−65088.6	+	37578.9i	−0.647718	+	0.373960i	0.139863	+	0.990171i	$0.455334\pi$
$318$	14484.5	+	91425.2i	0.143235	+	0.904090i
$319$	−91930.5	+	159228.i	−0.903396	+	1.56473i
$320$	−41492.4	−	23955.6i	−0.405199	−	0.233942i
$321$	−40520.4	+	105573.i	−0.393245	+	1.02457i
$322$	15699.6	+	27192.4i	0.151417	+	0.262263i
$323$		−	145577.i		−	1.39536i
$324$	−4958.82	−	2206.76i	−0.0472376	−	0.0210216i
$325$	−39859.0			−0.377363
$326$	−150359.	+	86809.9i	−1.41480	+	0.816834i
$327$	72700.1	+	27903.3i	0.679891	+	0.260951i
$328$	50355.2	−	87217.8i	0.468055	−	0.810695i
$329$	−47456.5	−	27399.0i	−0.438434	−	0.253130i
$330$	57111.9	−	9048.21i	0.524443	−	0.0830874i
$331$	−61336.3	−	106238.i	−0.559837	−	0.969666i	−0.997510	−	0.0705317i	$-0.977530\pi$
$331$	−61336.3	−	106238.i	−0.559837	−	0.969666i	0.437673	−	0.899134i	$-0.355803\pi$
$332$			2934.02i			0.0266187i
$333$	−1940.79	−	1747.19i	−0.0175021	−	0.0157562i
$334$	16957.6			0.152010
$335$	55653.2	−	32131.4i	0.495908	−	0.286312i
$336$	−52545.7	+	42554.5i	−0.465435	+	0.376936i
$337$	58215.7	−	100833.i	0.512602	−	0.887853i	−0.487291	−	0.873240i	$-0.662015\pi$
$337$	58215.7	−	100833.i	0.512602	−	0.887853i	0.999893	−	0.0146132i	$-0.00465169\pi$
$338$	246654.	+	142406.i	2.15901	+	1.24650i
$339$	−122999.	−	151878.i	−1.07030	−	1.32159i
$340$	1366.11	+	2366.18i	0.0118176	+	0.0204687i
$341$			123887.i			1.06541i
$342$	−152091.	−	32313.9i	−1.30032	−	0.276272i
$343$	119138.			1.01265
$344$	27834.6	−	16070.3i	0.235217	−	0.135803i
$345$	−4089.66	−	25813.7i	−0.0343596	−	0.216876i
$346$	79958.5	−	138492.i	0.667902	−	1.15684i
$347$	−94548.8	−	54587.7i	−0.785230	−	0.453353i	0.0530506	−	0.998592i	$-0.483106\pi$
$347$	−94548.8	−	54587.7i	−0.785230	−	0.453353i	−0.838281	+	0.545239i	$0.816439\pi$
$348$	−3324.87	+	8662.74i	−0.0274547	+	0.0715314i
$349$	73600.9	+	127481.i	0.604272	+	1.04663i	0.992166	+	0.124926i	$0.0398693\pi$
$349$	73600.9	+	127481.i	0.604272	+	1.04663i	−0.387894	+	0.921704i	$0.626797\pi$
$350$		−	15111.0i		−	0.123355i
$351$	−232141.	−	12135.1i	−1.88424	−	0.0984986i
$352$	−15606.0			−0.125952
$353$	183586.	−	105994.i	1.47330	−	0.850609i	0.473749	−	0.880660i	$-0.342900\pi$
$353$	183586.	−	105994.i	1.47330	−	0.850609i	0.999548	+	0.0300510i	$0.00956697\pi$
$354$	−104412.	−	40074.9i	−0.833193	−	0.319790i
$355$	7995.83	−	13849.2i	0.0634464	−	0.109892i
$356$	381.865	+	220.470i	0.00301308	+	0.00173960i
$357$	81494.3	−	12911.1i	0.639427	−	0.101304i
$358$	−25901.2	−	44862.3i	−0.202095	−	0.350038i
$359$		−	101975.i		−	0.791235i	−0.918415	−	0.395618i	$-0.870531\pi$
$359$		−	101975.i		−	0.791235i	0.918415	−	0.395618i	$-0.129469\pi$
$360$	56452.0	−	18347.9i	0.435586	−	0.141573i
$361$	112535.			0.863522
$362$	108830.	−	62833.3i	0.830488	−	0.479483i
$363$	49826.1	−	40352.0i	0.378132	−	0.306233i
$364$	4093.36	−	7089.90i	0.0308942	−	0.0535103i
$365$	−38257.1	−	22087.7i	−0.287161	−	0.165793i
$366$	−35161.9	−	43417.4i	−0.262488	−	0.324117i
$367$	−63217.5	−	109496.i	−0.469359	−	0.812953i	0.530028	−	0.847980i	$-0.322182\pi$
$367$	−63217.5	−	109496.i	−0.469359	−	0.812953i	−0.999386	+	0.0350273i	$0.988848\pi$
$368$		−	62877.3i		−	0.464299i
$369$	38469.3	+	118361.i	0.282528	+	0.869271i
$370$	1404.02			0.0102558
$371$	70966.7	−	40972.7i	0.515593	−	0.297678i
$372$	978.329	+	6175.16i	0.00706967	+	0.0446234i
$373$	76395.8	−	132321.i	0.549100	−	0.951070i	−0.449236	−	0.893413i	$-0.648304\pi$
$373$	76395.8	−	132321.i	0.549100	−	0.951070i	0.998336	−	0.0576567i	$-0.0183629\pi$
$374$	−147015.	−	84878.9i	−1.05104	−	0.606816i
$375$	−4506.99	+	11742.7i	−0.0320497	+	0.0835034i
$376$	57866.9	+	100228.i	0.409312	+	0.708950i
$377$			397398.i			2.79604i
$378$	4600.56	−	88006.9i	0.0321978	−	0.615933i
$379$	−79468.6			−0.553245			−0.276622	−	0.960979i	$-0.589215\pi$
$379$	−79468.6			−0.553245			−0.276622	+	0.960979i	$0.589215\pi$
$380$	−3947.33	+	2278.99i	−0.0273361	+	0.0157825i
$381$	135225.	+	51901.0i	0.931548	+	0.357541i
$382$	53806.6	−	93195.8i	0.368731	−	0.638660i
$383$	243622.	+	140655.i	1.66081	+	0.958868i	0.972330	+	0.233610i	$0.0750540\pi$
$383$	243622.	+	140655.i	1.66081	+	0.958868i	0.688478	+	0.725258i	$0.258279\pi$
$384$	133335.	−	21124.2i	0.904233	−	0.143257i
$385$	−25595.0	−	44331.8i	−0.172677	−	0.299085i
$386$		−	177902.i		−	1.19400i
$387$	−8254.54	+	38851.4i	−0.0551152	+	0.259409i
$388$	9687.89			0.0643525
$389$	−96819.0	+	55898.5i	−0.639825	+	0.369403i	−0.784547	−	0.620069i	$-0.787105\pi$
$389$	−96819.0	+	55898.5i	−0.639825	+	0.369403i	0.144722	+	0.989472i	$0.453771\pi$
$390$	97125.3	−	78657.7i	0.638562	−	0.517144i
$391$	−38364.0	+	66448.4i	−0.250940	+	0.434641i
$392$	−81618.0	−	47122.2i	−0.531146	−	0.306657i
$393$	−82950.8	−	102426.i	−0.537076	−	0.663173i
$394$	−28614.0	−	49560.9i	−0.184326	−	0.319262i
$395$			15936.5i			0.102141i
$396$	6614.19	−	7347.11i	0.0421781	−	0.0468518i
$397$	−135398.			−0.859077			−0.429539	−	0.903048i	$-0.641324\pi$
$397$	−135398.			−0.859077			−0.429539	+	0.903048i	$0.641324\pi$
$398$	−85566.3	+	49401.7i	−0.540178	+	0.311872i
$399$	21538.7	+	135951.i	0.135293	+	0.853961i
$400$	−15130.0	+	26205.9i	−0.0945623	+	0.163787i
$401$	25179.2	+	14537.2i	0.156586	+	0.0904049i	0.576246	−	0.817277i	$-0.304517\pi$
$401$	25179.2	+	14537.2i	0.156586	+	0.0904049i	−0.419660	+	0.907682i	$0.637851\pi$
$402$	−72203.5	+	188121.i	−0.446793	+	1.16409i
$403$	133885.	+	231895.i	0.824368	+	1.42785i
$404$		−	8449.99i		−	0.0517718i
$405$	−29824.0	+	67017.7i	−0.181826	+	0.408582i
$406$	−150658.			−0.913986
$407$	4119.05	−	2378.13i	0.0248661	−	0.0143565i
$408$	−162692.	−	62443.2i	−0.977338	−	0.375115i
$409$	−150724.	+	261062.i	−0.901024	+	1.56062i	−0.0748560	+	0.997194i	$0.523850\pi$
$409$	−150724.	+	261062.i	−0.901024	+	1.56062i	−0.826168	+	0.563424i	$0.809484\pi$
$410$	−57949.1	−	33456.9i	−0.344730	−	0.199030i
$411$	−59439.7	+	9417.01i	−0.351879	+	0.0557480i
$412$	425.228	+	736.516i	0.00250511	+	0.00433898i
$413$			99007.5i			0.580454i
$414$	60906.1	+	54830.4i	0.355353	+	0.319905i
$415$	39652.8			0.230239
$416$	−29211.7	+	16865.4i	−0.168799	+	0.0974563i
$417$	192598.	−	155977.i	1.10759	−	0.896993i
$418$	141598.	−	245254.i	0.810408	−	1.40367i
$419$	−20808.6	−	12013.9i	−0.118526	−	0.0684313i	0.439565	−	0.898211i	$-0.355133\pi$
$419$	−20808.6	−	12013.9i	−0.118526	−	0.0684313i	−0.558091	+	0.829780i	$0.688466\pi$
$420$	−1625.87	−	2007.60i	−0.00921697	−	0.0113810i
$421$	−57542.4	−	99666.3i	−0.324656	−	0.562321i	0.656787	−	0.754077i	$-0.271915\pi$
$421$	−57542.4	−	99666.3i	−0.324656	−	0.562321i	−0.981443	+	0.191756i	$0.938582\pi$
$422$			150635.i			0.845866i
$423$	−139898.	−	29723.4i	−0.781865	−	0.166118i
$424$	−173069.			−0.962694
$425$	31978.5	−	18462.8i	0.177044	−	0.102216i
$426$	7846.33	+	49525.6i	0.0432362	+	0.272904i
$427$	−24729.9	+	42833.4i	−0.135633	+	0.234924i
$428$	−9001.73	−	5197.15i	−0.0491404	−	0.0283712i
$429$	151711.	−	395273.i	0.824334	−	2.14775i
$430$	−10677.4	−	18493.8i	−0.0577470	−	0.100021i
$431$			203950.i			1.09792i	0.835850	+	0.548958i	$0.184975\pi$
$431$			203950.i			1.09792i	−0.835850	+	0.548958i	$0.815025\pi$
$432$	−96096.1	+	148018.i	−0.514918	+	0.793134i
$433$	−50228.1			−0.267899			−0.133949	−	0.990988i	$-0.542766\pi$
$433$	−50228.1			−0.267899			−0.133949	+	0.990988i	$0.542766\pi$
$434$	−87913.9	+	50757.1i	−0.466743	+	0.269474i
$435$	117076.	+	44935.2i	0.618711	+	0.237470i
$436$	−3578.88	+	6198.80i	−0.0188267	+	0.0326088i
$437$	−110851.	−	64000.0i	−0.580468	−	0.335133i
$438$	136810.	−	21674.8i	0.713131	−	0.112981i
$439$	117902.	+	204212.i	0.611776	+	1.05963i	0.990941	+	0.134298i	$0.0428780\pi$
$439$	117902.	+	204212.i	0.611776	+	1.05963i	−0.379165	+	0.925329i	$0.623789\pi$
$440$			108114.i			0.558438i
$441$	110761.	−	35999.4i	0.569523	−	0.185105i
$442$	−366915.			−1.87811
$443$	−97107.7	+	56065.2i	−0.494819	+	0.285684i	−0.726571	−	0.687091i	$-0.758887\pi$
$443$	−97107.7	+	56065.2i	−0.494819	+	0.285684i	0.231753	+	0.972775i	$0.425554\pi$
$444$	186.535	−	151.067i	0.000946224	−	0.000766306i
$445$	2979.62	−	5160.85i	0.0150467	−	0.0260616i
$446$	173584.	+	100219.i	0.872648	+	0.503824i
$447$	−39506.1	−	48781.6i	−0.197720	−	0.244141i
$448$	−66497.1	−	115176.i	−0.331319	−	0.573861i
$449$		−	170804.i		−	0.847239i	−0.905840	−	0.423620i	$-0.860759\pi$
$449$		−	170804.i		−	0.847239i	0.905840	−	0.423620i	$-0.139241\pi$
$450$	−12190.7	−	37507.7i	−0.0602008	−	0.185223i
$451$	−226678.			−1.11444
$452$	15557.5	−	8982.13i	0.0761488	−	0.0439645i
$453$	50395.4	+	318093.i	0.245581	+	1.55009i
$454$	−81647.4	+	141418.i	−0.396124	+	0.686106i
$455$	−95819.0	−	55321.1i	−0.462838	−	0.267219i
$456$	104170.	−	271407.i	0.500970	−	1.30524i
$457$	98144.5	+	169991.i	0.469930	+	0.813943i	0.999409	−	0.0343802i	$-0.0109457\pi$
$457$	98144.5	+	169991.i	0.469930	+	0.813943i	−0.529478	+	0.848323i	$0.677612\pi$
$458$			102293.i			0.487659i
$459$	191866.	−	97792.4i	0.910693	−	0.464173i
$460$	2402.34			0.0113532
$461$	−59960.0	+	34617.9i	−0.282137	+	0.162892i	−0.634390	−	0.773013i	$-0.718749\pi$
$461$	−59960.0	+	34617.9i	−0.282137	+	0.162892i	0.352254	+	0.935905i	$0.385415\pi$
$462$	149852.	+	57515.3i	0.702068	+	0.269463i
$463$	−15118.5	+	26186.0i	−0.0705256	+	0.122154i	−0.899132	−	0.437678i	$-0.855801\pi$
$463$	−15118.5	+	26186.0i	−0.0705256	+	0.122154i	0.828606	+	0.559832i	$0.189134\pi$
$464$	261275.	+	150847.i	1.21356	+	0.700651i
$465$	83456.4	−	13222.0i	0.385970	−	0.0611491i
$466$	−4686.56	−	8117.36i	−0.0215815	−	0.0373803i
$467$		−	300277.i		−	1.37685i	−0.725305	−	0.688427i	$-0.758301\pi$
$467$		−	300277.i		−	1.37685i	0.725305	−	0.688427i	$-0.241699\pi$
$468$	4440.62	−	20900.5i	0.0202746	−	0.0954258i
$469$	178383.			0.810978
$470$	66593.6	−	38447.8i	0.301465	−	0.174051i
$471$	−278066.	+	225194.i	−1.25345	+	1.01511i
$472$	104552.	−	181090.i	0.469299	−	0.812850i
$473$	−62649.9	−	36170.9i	−0.280026	−	0.161673i
$474$	−31449.1	−	38832.9i	−0.139975	−	0.172839i
$475$	30800.3	+	53347.6i	0.136511	+	0.236444i
$476$			7584.23i			0.0334732i
$477$	143096.	−	158953.i	0.628914	−	0.698603i
$478$	−268880.			−1.17680
$479$	−255838.	+	147708.i	−1.11505	+	0.643773i	−0.940132	−	0.340810i	$-0.889299\pi$
$479$	−255838.	+	147708.i	−1.11505	+	0.643773i	−0.174916	+	0.984583i	$0.555965\pi$
$480$	1665.56	+	10513.0i	0.00722901	+	0.0456291i
$481$	5140.11	−	8902.93i	0.0222168	−	0.0384807i
$482$	276033.	+	159368.i	1.18814	+	0.685972i
$483$	25996.0	−	67731.0i	0.111433	−	0.290331i
$484$	2946.74	+	5103.90i	0.0125791	+	0.0217877i
$485$		−	130930.i		−	0.556617i
$486$	−59579.7	−	222158.i	−0.252247	−	0.940568i
$487$	161215.			0.679746			0.339873	−	0.940471i	$-0.389616\pi$
$487$	161215.			0.679746			0.339873	+	0.940471i	$0.389616\pi$
$488$	90464.5	−	52229.7i	0.379873	−	0.219320i
$489$	374515.	+	143744.i	1.56621	+	0.601134i
$490$	−31308.8	+	54228.5i	−0.130399	+	0.225858i
$491$	63570.0	+	36702.1i	0.263687	+	0.152240i	0.626015	−	0.779811i	$-0.284685\pi$
$491$	63570.0	+	36702.1i	0.263687	+	0.152240i	−0.362328	+	0.932051i	$0.618018\pi$
$492$	−11298.8	+	1790.07i	−0.0466769	+	0.00739501i
$493$	−184076.	−	318829.i	−0.757363	−	1.31179i
$494$		−	612100.i		−	2.50824i
$495$	−99295.1	−	89389.9i	−0.405245	−	0.364819i
$496$	203284.			0.826304
$497$	38443.2	−	22195.2i	0.155635	−	0.0898557i
$498$	−96623.0	+	78250.9i	−0.389603	+	0.315523i
$499$	190524.	−	329997.i	0.765153	−	1.32528i	−0.175013	−	0.984566i	$-0.555997\pi$
$499$	190524.	−	329997.i	0.765153	−	1.32528i	0.940166	−	0.340717i	$-0.110670\pi$
$500$	−1001.24	−	578.068i	−0.00400497	−	0.00231227i
$501$	−24658.7	−	30448.2i	−0.0982415	−	0.121307i
$502$	87727.3	+	151948.i	0.348119	+	0.602960i
$503$			1048.09i			0.00414250i	0.999998	+	0.00207125i	$0.000659300\pi$
$503$			1048.09i			0.00414250i	−0.999998	+	0.00207125i	$0.999341\pi$
$504$	161173.	+	34243.5i	0.634500	+	0.134809i
$505$	−114200.			−0.447801
$506$	−129264.	+	74630.7i	−0.504867	+	0.291485i
$507$	−102973.	−	649957.i	−0.400595	−	2.52853i
$508$	−6656.83	+	11530.0i	−0.0257953	+	0.0446787i
$509$	178632.	+	103133.i	0.689483	+	0.398073i	0.803418	−	0.595415i	$-0.203012\pi$
$509$	178632.	+	103133.i	0.689483	+	0.398073i	−0.113935	+	0.993488i	$0.536346\pi$
$510$	−41488.4	+	108095.i	−0.159509	+	0.415591i
$511$	−61312.1	−	106196.i	−0.234803	−	0.406691i
$512$			279485.i			1.06615i
$513$	163140.	+	320076.i	0.619908	+	1.21624i
$514$	−39804.0			−0.150661
$515$	9953.91	−	5746.89i	0.0375301	−	0.0216680i
$516$	−3408.43	−	1308.20i	−0.0128013	−	0.00491333i
$517$	130246.	−	225593.i	0.487286	−	0.844004i
$518$	3375.19	+	1948.67i	0.0125788	+	0.00726238i
$519$	−364941.	+	57817.4i	−1.35484	+	0.214647i
$520$	116839.	+	202370.i	0.432096	+	0.748411i
$521$			101119.i			0.372526i	0.982500	+	0.186263i	$0.0596376\pi$
$521$			101119.i			0.372526i	−0.982500	+	0.186263i	$0.940362\pi$
$522$	−373956.	+	121542.i	−1.37240	+	0.446053i
$523$	8912.10			0.0325819			0.0162910	−	0.999867i	$-0.494814\pi$
$523$	8912.10			0.0325819			0.0162910	+	0.999867i	$0.494814\pi$
$524$	10492.0	−	6057.54i	0.0382115	−	0.0220614i
$525$	−27132.5	+	21973.4i	−0.0984398	+	0.0797222i
$526$	60995.4	−	105647.i	0.220458	−	0.381844i
$527$	−214829.	−	124032.i	−0.773522	−	0.446593i
$528$	−202291.	−	249786.i	−0.725618	−	0.895982i
$529$	−106189.	−	183924.i	−0.379460	−	0.657244i
$530$			114990.i			0.409364i
$531$	79873.7	+	245752.i	0.283279	+	0.871582i
$532$	−12652.3			−0.0447038
$533$	−424303.	+	244971.i	−1.49356	+	0.862304i
$534$	2923.91	+	18455.6i	0.0102537	+	0.0647209i
$535$	−70238.7	+	121657.i	−0.245397	+	0.425040i
$536$	−326273.	−	188374.i	−1.13567	−	0.655678i
$537$	−42888.5	+	111743.i	−0.148728	+	0.387500i
$538$	98367.7	+	170378.i	0.339850	+	0.588638i
$539$			212124.i			0.730150i
$540$	−5655.29	−	3671.52i	−0.0193940	−	0.0125910i
$541$	424902.			1.45176			0.725879	−	0.687823i	$-0.241433\pi$
$541$	424902.			1.45176			0.725879	+	0.687823i	$0.241433\pi$
$542$	363205.	−	209696.i	1.23638	−	0.713826i
$543$	−271075.	−	104042.i	−0.919369	−	0.352866i
$544$	15624.2	−	27062.0i	0.0527960	−	0.0914453i
$545$	83775.9	+	48368.0i	0.282050	+	0.162842i
$546$	342655.	−	54286.8i	1.14940	−	0.182099i
$547$	110033.	+	190582.i	0.367745	+	0.636953i	0.989213	−	0.146487i	$-0.0467966\pi$
$547$	110033.	+	190582.i	0.367745	+	0.636953i	−0.621468	+	0.783440i	$0.713463\pi$
$548$		−	5531.73i		−	0.0184204i
$549$	−26827.8	+	126270.i	−0.0890104	+	0.418943i
$550$	71832.6			0.237463
$551$	531881.	−	307082.i	1.75191	−	1.01147i
$552$	−119072.	+	96431.6i	−0.390780	+	0.316476i
$553$	−22118.6	+	38310.6i	−0.0723282	+	0.125276i
$554$	239283.	+	138150.i	0.779637	+	0.450124i
$555$	−2041.64	−	2520.99i	−0.00662817	−	0.00818437i
$556$	11390.3	+	19728.7i	0.0368457	+	0.0638187i
$557$		−	335436.i		−	1.08118i	−0.841285	−	0.540592i	$-0.818200\pi$
$557$		−	335436.i		−	1.08118i	0.841285	−	0.540592i	$-0.181800\pi$
$558$	−177268.	+	196911.i	−0.569327	+	0.632414i
$559$	−156360.			−0.500382
$560$	−72743.4	+	41998.4i	−0.231962	+	0.133923i
$561$	61375.3	+	387398.i	0.195015	+	1.23093i
$562$	−207528.	+	359449.i	−0.657058	+	1.13806i
$563$	79111.7	+	45675.2i	0.249588	+	0.144100i	0.619576	−	0.784937i	$-0.287305\pi$
$563$	79111.7	+	45675.2i	0.249588	+	0.144100i	−0.369988	+	0.929037i	$0.620638\pi$
$564$	4710.65	−	12273.3i	0.0148089	−	0.0385836i
$565$	−121392.	−	210257.i	−0.380271	−	0.658649i
$566$		−	191015.i		−	0.596259i
$567$	−164711.	+	119714.i	−0.512337	+	0.372373i
$568$	−93752.7			−0.290594
$569$	−327513.	+	189090.i	−1.01159	+	0.584042i	−0.911657	−	0.410952i	$-0.865196\pi$
$569$	−327513.	+	189090.i	−1.01159	+	0.584042i	−0.0999333	+	0.994994i	$0.531863\pi$
$570$	−180328.	−	69212.3i	−0.555026	−	0.213026i
$571$	−7671.96	+	13288.2i	−0.0235307	+	0.0407563i	−0.877551	−	0.479483i	$-0.840824\pi$
$571$	−7671.96	+	13288.2i	−0.0235307	+	0.0407563i	0.854020	+	0.520240i	$0.174157\pi$
$572$	33703.1	+	19458.5i	0.103010	+	0.0594727i
$573$	−245580.	+	38907.2i	−0.747970	+	0.118501i
$574$	−92871.2	−	160858.i	−0.281875	−	0.488222i
$575$		−	32467.3i		−	0.0981997i
$576$	−257974.	−	232239.i	−0.777554	−	0.699989i
$577$	400796.			1.20385			0.601924	−	0.798553i	$-0.294401\pi$
$577$	400796.			1.20385			0.601924	+	0.798553i	$0.294401\pi$
$578$	12627.2	−	7290.29i	0.0377963	−	0.0218217i
$579$	−319432.	+	258694.i	−0.952842	+	0.771666i
$580$	−5763.40	+	9982.50i	−0.0171326	+	0.0296745i
$581$	95323.4	+	55035.0i	0.282389	+	0.163037i
$582$	258378.	+	319041.i	0.762797	+	0.941891i
$583$	194771.	+	337353.i	0.573043	+	0.992540i
$584$			258983.i			0.759357i
$585$	−282468.	−	60014.3i	−0.825386	−	0.175365i
$586$	369614.			1.07635
$587$	297931.	−	172011.i	0.864650	−	0.499206i	−0.000916938	−	1.00000i	$-0.500292\pi$
$587$	297931.	−	172011.i	0.864650	−	0.499206i	0.865567	+	0.500794i	$0.166959\pi$
$588$	1675.13	+	10573.4i	0.00484501	+	0.0305815i
$589$	206914.	−	358385.i	0.596429	−	1.03305i
$590$	−120319.	−	69466.5i	−0.345646	−	0.199559i
$591$	−47380.4	+	123446.i	−0.135651	+	0.353430i
$592$	−3902.24	−	6758.88i	−0.0111345	−	0.0192855i
$593$			147814.i			0.420347i	0.977664	+	0.210173i	$0.0674028\pi$
$593$			147814.i			0.420347i	−0.977664	+	0.210173i	$0.932597\pi$
$594$	418357.	+	21869.6i	1.18570	+	0.0619823i
$595$	102500.			0.289527
$596$	4996.90	−	2884.96i	0.0140672	−	0.00812172i
$597$	213129.	+	81801.6i	0.597989	+	0.229516i
$598$	−161307.	+	279392.i	−0.451078	+	0.781290i
$599$	−585809.	−	338217.i	−1.63268	−	0.942630i	−0.983261	−	0.182203i	$-0.941677\pi$
$599$	−585809.	−	338217.i	−1.63268	−	0.942630i	−0.649423	−	0.760427i	$-0.724989\pi$
$600$	72830.8	−	11538.6i	0.202308	−	0.0320515i
$601$	−256300.	−	443924.i	−0.709576	−	1.22902i	−0.965015	−	0.262196i	$-0.915553\pi$
$601$	−256300.	−	443924.i	−0.709576	−	1.22902i	0.255439	−	0.966825i	$-0.417780\pi$
$602$		−	59277.7i		−	0.163568i
$603$	442776.	−	143910.i	1.21772	−	0.395782i
$604$	−29603.2			−0.0811456
$605$	68978.4	−	39824.7i	0.188453	−	0.108803i
$606$	278275.	−	225363.i	0.757755	−	0.613673i
$607$	−104809.	+	181535.i	−0.284461	+	0.492701i	−0.972478	−	0.232993i	$-0.925148\pi$
$607$	−104809.	+	181535.i	−0.284461	+	0.492701i	0.688017	+	0.725694i	$0.258481\pi$
$608$	45145.6	+	26064.8i	0.122126	+	0.0705095i
$609$	219077.	+	270514.i	0.590695	+	0.729381i
$610$	−34702.4	−	60106.2i	−0.0932608	−	0.161532i
$611$		−	563029.i		−	1.50816i
$612$	6118.53	+	18825.2i	0.0163359	+	0.0502618i
$613$	288964.			0.768995			0.384497	−	0.923126i	$-0.374375\pi$
$613$	288964.			0.768995			0.384497	+	0.923126i	$0.374375\pi$
$614$	−278192.	+	160614.i	−0.737917	+	0.426037i
$615$	24192.5	+	152702.i	0.0639631	+	0.403732i
$616$	−150053.	+	259900.i	−0.395443	+	0.684927i
$617$	−591955.	−	341765.i	−1.55496	−	0.897755i	−0.997726	−	0.0673964i	$-0.978531\pi$
$617$	−591955.	−	341765.i	−1.55496	−	0.897755i	−0.557230	−	0.830358i	$-0.688136\pi$
$618$	−12914.0	+	33646.6i	−0.0338131	+	0.0880977i
$619$	231616.	+	401170.i	0.604487	+	1.04700i	0.992132	+	0.125193i	$0.0399551\pi$
$619$	231616.	+	401170.i	0.604487	+	1.04700i	−0.387646	+	0.921809i	$0.626712\pi$
$620$			7766.83i			0.0202051i
$621$	9884.72	−	189091.i	0.0256319	−	0.490329i
$622$	−141262.			−0.365127
$623$	14325.7	−	8270.95i	0.0369097	−	0.0213098i
$624$	−648598.	−	248941.i	−1.66574	−	0.639332i
$625$	−7812.50	+	13531.6i	−0.0200000	+	0.0346410i
$626$	162128.	+	93604.9i	0.413724	+	0.238864i
$627$	−646270.	+	102388.i	−1.64391	+	0.260445i
$628$	−16444.9	−	28483.5i	−0.0416978	−	0.0722227i
$629$			9523.67i			0.0240715i
$630$	22752.0	−	107086.i	0.0573244	−	0.269807i
$631$	−1808.96			−0.00454328			−0.00227164	−	0.999997i	$-0.500723\pi$
$631$	−1808.96			−0.00454328			−0.00227164	+	0.999997i	$0.500723\pi$
$632$	80912.2	−	46714.7i	0.202572	−	0.116955i
$633$	270473.	−	219045.i	0.675020	−	0.546670i
$634$	146378.	−	253534.i	0.364164	−	0.630751i
$635$	155826.	+	89966.1i	0.386449	+	0.223116i
$636$	12372.5	+	15277.3i	0.0305874	+	0.0377688i
$637$	229243.	+	397060.i	0.564959	+	0.978538i
$638$		−	716179.i		−	1.75946i
$639$	77516.1	−	86105.6i	0.189841	−	0.210877i
$640$	167702.			0.409429
$641$	−326408.	+	188452.i	−0.794409	+	0.458652i	−0.841513	−	0.540238i	$-0.818334\pi$
$641$	−326408.	+	188452.i	−0.794409	+	0.458652i	0.0471032	+	0.998890i	$0.485001\pi$
$642$	−68925.5	−	435054.i	−0.167228	−	1.05554i
$643$	−84687.9	+	146684.i	−0.204833	+	0.354781i	−0.950079	−	0.312008i	$-0.898998\pi$
$643$	−84687.9	+	146684.i	−0.204833	+	0.354781i	0.745247	+	0.666789i	$0.232332\pi$
$644$	5775.11	+	3334.26i	0.0139248	+	0.00803947i
$645$	−17680.2	+	46064.5i	−0.0424978	+	0.110725i
$646$	283527.	+	491083.i	0.679406	+	1.17677i
$647$			489620.i			1.16964i	0.811165	+	0.584818i	$0.198834\pi$
$647$			489620.i			1.16964i	−0.811165	+	0.584818i	$0.801166\pi$
$648$	427683.	−	45027.7i	1.01853	−	0.107233i
$649$	−470650.			−1.11740
$650$	134459.	−	77629.7i	0.318245	−	0.183739i
$651$	218976.	+	84045.9i	0.516696	+	0.198315i
$652$	−18436.6	+	31933.1i	−0.0433696	+	0.0751184i
$653$	−463912.	−	267840.i	−1.08795	−	0.628129i	−0.154921	−	0.987927i	$-0.549512\pi$
$653$	−463912.	−	267840.i	−1.08795	−	0.628129i	−0.933030	+	0.359798i	$0.882846\pi$
$654$	−299588.	+	47463.7i	−0.700437	+	0.110970i
$655$	−81866.8	−	141797.i	−0.190820	−	0.330511i
$656$			371952.i			0.864329i
$657$	−237859.	−	214131.i	−0.551047	−	0.496077i
$658$	213450.			0.492998
$659$	404395.	−	233478.i	0.931183	−	0.537619i	0.0439978	−	0.999032i	$-0.485991\pi$
$659$	404395.	−	233478.i	0.931183	−	0.537619i	0.887186	+	0.461413i	$0.152657\pi$
$660$	9543.51	−	7728.88i	0.0219089	−	0.0177431i
$661$	−204983.	+	355041.i	−0.469154	+	0.812599i	−0.999378	−	0.0352589i	$-0.988774\pi$
$661$	−204983.	+	355041.i	−0.469154	+	0.812599i	0.530224	+	0.847857i	$0.322108\pi$
$662$	413819.	+	238918.i	0.944266	+	0.545172i
$663$	533546.	+	658815.i	1.21379	+	1.49878i
$664$	−116234.	−	201324.i	−0.263632	−	0.456624i
$665$			170993.i			0.386666i
$666$	9949.84	+	2113.98i	0.0224320	+	0.00476599i
$667$	−323702.			−0.727602
$668$	3118.94	−	1800.72i	0.00698963	−	0.00403546i
$669$	−72467.4	−	457410.i	−0.161916	−	1.02201i
$670$	−125159.	+	216782.i	−0.278812	+	0.482917i
$671$	−203616.	−	117558.i	−0.452238	−	0.261100i
$672$	−10587.2	+	27584.3i	−0.0234446	+	0.0610834i
$673$	−406546.	−	704158.i	−0.897593	−	1.55468i	−0.830563	−	0.556925i	$-0.811981\pi$
$673$	−406546.	−	704158.i	−0.897593	−	1.55468i	−0.0670303	−	0.997751i	$-0.521352\pi$
$674$			453526.i			0.998349i
$675$	−49620.1	+	76430.4i	−0.108906	+	0.167749i
$676$	60488.0			0.132366
$677$	519510.	−	299939.i	1.13349	−	0.654419i	0.188678	−	0.982039i	$-0.439580\pi$
$677$	519510.	−	299939.i	1.13349	−	0.654419i	0.944810	+	0.327620i	$0.106246\pi$
$678$	710721.	+	272784.i	1.54611	+	0.593416i
$679$	181721.	−	314750.i	0.394154	−	0.682694i
$680$	−187477.	−	108240.i	−0.405444	−	0.234083i
$681$	372649.	−	59038.7i	0.803537	−	0.127304i
$682$	−241283.	−	417915.i	−0.518750	−	0.898502i
$683$		−	343871.i		−	0.737147i	−0.929599	−	0.368573i	$-0.879846\pi$
$683$		−	343871.i		−	0.737147i	0.929599	−	0.368573i	$-0.120154\pi$
$684$	−31404.9	+	10207.1i	−0.0671251	+	0.0218168i
$685$	−74760.5			−0.159328
$686$	−401895.	+	232034.i	−0.854012	+	0.493064i
$687$	183673.	−	148749.i	0.389163	−	0.315166i
$688$	−59352.3	+	102801.i	−0.125389	+	0.217181i
$689$	729157.	+	420979.i	1.53597	+	0.886792i
$690$	64070.9	+	79113.8i	0.134574	+	0.166171i
$691$	−428584.	−	742330.i	−0.897594	−	1.55468i	−0.830561	−	0.556928i	$-0.811980\pi$
$691$	−428584.	−	742330.i	−0.897594	−	1.55468i	−0.0670336	−	0.997751i	$-0.521353\pi$
$692$		−	33963.0i		−	0.0709242i
$693$	−114634.	−	352703.i	−0.238698	−	0.734416i
$694$	425263.			0.882954
$695$	266630.	−	153939.i	0.552000	−	0.318697i
$696$	−115041.	−	726130.i	−0.237483	−	1.49898i
$697$	226943.	−	393077.i	0.467145	−	0.809119i
$698$	−496565.	−	286692.i	−1.01921	−	0.588443i
$699$	−7760.22	+	20218.7i	−0.0158825	+	0.0413809i
$700$	−1604.63	−	2779.29i	−0.00327475	−	0.00567203i
$701$		−	96590.5i		−	0.196561i	−0.995159	−	0.0982807i	$-0.968666\pi$
$701$		−	96590.5i		−	0.196561i	0.995159	−	0.0982807i	$-0.0313343\pi$
$702$	806728.	−	411183.i	1.63702	−	0.834374i
$703$	−15887.7			−0.0321477
$704$	547511.	−	316106.i	1.10471	−	0.637804i
$705$	−165871.	−	63663.7i	−0.333729	−	0.128090i
$706$	−412868.	+	715108.i	−0.828327	+	1.43470i
$707$	−274532.	−	158501.i	−0.549230	−	0.317098i
$708$	−23459.7	+	3716.71i	−0.0468010	+	0.00741467i
$709$	−26314.0	−	45577.3i	−0.0523474	−	0.0906684i	0.838664	−	0.544649i	$-0.183337\pi$
$709$	−26314.0	−	45577.3i	−0.0523474	−	0.0906684i	−0.891012	+	0.453980i	$0.850004\pi$
$710$			62291.0i			0.123569i
$711$	−23995.0	+	112937.i	−0.0474660	+	0.223407i
$712$	−34936.6			−0.0689162
$713$	−188891.	+	109056.i	−0.371563	+	0.214522i
$714$	−249764.	+	202273.i	−0.489929	+	0.396772i
$715$	262979.	−	455493.i	0.514409	−	0.890983i
$716$	−9527.81	−	5500.88i	−0.0185852	−	0.0107302i
$717$	390989.	+	482787.i	0.760547	+	0.939112i
$718$	198608.	+	343999.i	0.385254	+	0.667280i
$719$			487471.i			0.942956i	0.881878	+	0.471478i	$0.156279\pi$
$719$			487471.i			0.942956i	−0.881878	+	0.471478i	$0.843721\pi$
$720$	−146678.	+	162932.i	−0.282944	+	0.314297i
$721$	31904.9			0.0613744
$722$	−379621.	+	219174.i	−0.728242	+	0.420451i
$723$	−115238.	−	727374.i	−0.220454	−	1.39149i
$724$	13344.5	−	23113.3i	0.0254580	−	0.0440946i
$725$	134912.	+	77891.4i	0.256670	+	0.148188i
$726$	−89491.4	+	233164.i	−0.169788	+	0.442372i
$727$	−102110.	−	176860.i	−0.193197	−	0.334627i	0.753111	−	0.657894i	$-0.228552\pi$
$727$	−102110.	−	176860.i	−0.193197	−	0.334627i	−0.946308	+	0.323266i	$0.895219\pi$
$728$			648651.i			1.22391i
$729$	−312259.	+	430028.i	−0.587571	+	0.809173i
$730$	172073.			0.322900
$731$	125446.	−	72426.5i	0.234760	−	0.135539i
$732$	−11077.6	−	4251.75i	−0.0206740	−	0.00793497i
$733$	−269729.	+	467184.i	−0.502018	+	0.869520i	0.497980	+	0.867189i	$0.334075\pi$
$733$	−269729.	+	467184.i	−0.502018	+	0.869520i	−0.999997	+	0.00233144i	$0.999258\pi$
$734$	426510.	+	246246.i	0.791658	+	0.457064i
$735$	142897.	−	22639.2i	0.264514	−	0.0419069i
$736$	−13737.8	−	23794.5i	−0.0253607	−	0.0439260i
$737$			847978.i			1.56117i
$738$	−360291.	−	324350.i	−0.661517	−	0.595527i
$739$	581134.			1.06411			0.532057	−	0.846709i	$-0.321419\pi$
$739$	581134.			1.06411			0.532057	+	0.846709i	$0.321419\pi$
$740$	258.235	−	149.092i	0.000471577	−	0.000272265i
$741$	−1.09906e6	+	890079.i	−2.00163	+	1.62103i
$742$	−159598.	+	276431.i	−0.289880	+	0.502087i
$743$	708511.	+	409059.i	1.28342	+	0.740983i	0.977472	−	0.211065i	$-0.0676930\pi$
$743$	708511.	+	409059.i	1.28342	+	0.740983i	0.305949	+	0.952048i	$0.401026\pi$
$744$	−311766.	−	384964.i	−0.563226	−	0.695464i
$745$	−38989.9	−	67532.4i	−0.0702488	−	0.121675i
$746$			595157.i			1.06943i
$747$	281007.	+	59703.9i	0.503588	+	0.106994i
$748$	−36053.0			−0.0644375
$749$	−337701.	+	194972.i	−0.601961	+	0.347542i
$750$	−7666.43	−	48390.1i	−0.0136292	−	0.0860268i
$751$	−207931.	+	360146.i	−0.368671	+	0.638556i	−0.989358	−	0.145502i	$-0.953520\pi$
$751$	−207931.	+	360146.i	−0.368671	+	0.638556i	0.620687	+	0.784058i	$0.286854\pi$
$752$	−370172.	−	213719.i	−0.654588	−	0.377926i
$753$	145263.	−	378473.i	0.256192	−	0.667490i
$754$	−773976.	−	1.34057e6i	−1.36140	−	2.35801i
$755$			400083.i			0.701870i
$756$	−8499.25	−	16675.3i	−0.0148709	−	0.0291762i
$757$	−325017.			−0.567171			−0.283585	−	0.958947i	$-0.591524\pi$
$757$	−325017.			−0.567171			−0.283585	+	0.958947i	$0.591524\pi$
$758$	268076.	−	154774.i	0.466573	−	0.269376i
$759$	321971.	+	123577.i	0.558900	+	0.214513i
$760$	180570.	−	312756.i	0.312621	−	0.541475i
$761$	248820.	+	143657.i	0.429652	+	0.248060i	0.699198	−	0.714928i	$-0.253540\pi$
$761$	248820.	+	143657.i	0.429652	+	0.248060i	−0.269546	+	0.962987i	$0.586874\pi$
$762$	−557244.	+	88284.0i	−0.959699	+	0.152045i
$763$	134262.	+	232549.i	0.230624	+	0.399452i
$764$		−	22854.8i		−	0.0391553i
$765$	254420.	−	82691.0i	0.434739	−	0.141298i
$766$	−1.09577e6			−1.86750
$767$	−880978.	+	508633.i	−1.49753	+	0.864597i
$768$	70904.2	−	57422.3i	0.120212	−	0.0973549i
$769$	−249463.	+	432082.i	−0.421845	+	0.730657i	−0.996120	−	0.0880054i	$-0.971951\pi$
$769$	−249463.	+	432082.i	−0.421845	+	0.730657i	0.574275	+	0.818663i	$0.305284\pi$
$770$	172682.	+	99698.1i	0.291250	+	0.168153i
$771$	57880.5	+	71470.1i	0.0973697	+	0.120231i
$772$	−18891.3	−	32720.7i	−0.0316977	−	0.0549020i
$773$		−	227257.i		−	0.380328i	−0.981752	−	0.190164i	$-0.939098\pi$
$773$		−	227257.i		−	0.380328i	0.981752	−	0.190164i	$-0.0609020\pi$
$774$	−47821.9	−	147136.i	−0.0798261	−	0.245606i
$775$	104968.			0.174764
$776$	−664755.	+	383796.i	−1.10392	+	0.637349i
$777$	−1409.07	−	8893.97i	−0.00233394	−	0.0147317i
$778$	217737.	−	377131.i	0.359727	−	0.623065i
$779$	655744.	+	378594.i	1.08059	+	0.623876i
$780$	9511.23	−	24780.9i	0.0156332	−	0.0407312i
$781$	105509.	+	182747.i	0.172976	+	0.299604i
$782$		−	298872.i		−	0.488734i
$783$	762019.	+	494718.i	1.24292	+	0.806926i
$784$	348071.			0.566286
$785$	−384950.	+	222251.i	−0.624691	+	0.360665i
$786$	479310.	+	183965.i	0.775838	+	0.297777i
$787$	−44736.4	+	77485.6i	−0.0722289	+	0.125104i	−0.899878	−	0.436142i	$-0.856345\pi$
$787$	−44736.4	+	77485.6i	−0.0722289	+	0.125104i	0.827649	+	0.561246i	$0.189678\pi$
$788$	−10525.7	−	6077.02i	−0.0169511	−	0.00978674i
$789$	−278391.	+	44105.3i	−0.447199	+	0.0708496i
$790$	−31038.1	−	53759.6i	−0.0497326	−	0.0861393i
$791$		−	673931.i		−	1.07712i
$792$	−162783.	+	766166.i	−0.259513	+	1.22144i
$793$	−508180.			−0.808112
$794$	456747.	−	263703.i	0.724494	−	0.418287i
$795$	206471.	−	167212.i	0.326682	−	0.264565i
$796$	−10491.9	+	18172.5i	−0.0165588	+	0.0286806i
$797$	88316.0	+	50989.3i	0.139035	+	0.0802716i	0.567904	−	0.823095i	$-0.307755\pi$
$797$	88316.0	+	50989.3i	0.139035	+	0.0802716i	−0.428869	+	0.903367i	$0.641088\pi$
$798$	−337438.	−	416664.i	−0.529893	−	0.654305i
$799$	260797.	+	451714.i	0.408516	+	0.707571i
$800$			13222.7i			0.0206605i
$801$	28886.1	−	32087.0i	0.0450219	−	0.0500108i
$802$	−113251.			−0.176074
$803$	504820.	−	291458.i	0.782899	−	0.452007i
$804$	6696.45	+	42267.6i	0.0103593	+	0.0653877i
$805$	45062.0	−	78049.7i	0.0695375	−	0.120442i
$806$	−903283.	−	521511.i	−1.39044	−	0.802774i
$807$	162882.	−	424377.i	0.250107	−	0.651636i
$808$	334756.	+	579814.i	0.512750	+	0.888108i
$809$		−	169763.i		−	0.259385i	−0.991554	−	0.129693i	$-0.958601\pi$
$809$		−	169763.i		−	0.259385i	0.991554	−	0.129693i	$-0.0413991\pi$
$810$	−29917.2	−	284160.i	−0.0455985	−	0.433105i
$811$	507416.			0.771476			0.385738	−	0.922608i	$-0.373947\pi$
$811$	507416.			0.771476			0.385738	+	0.922608i	$0.373947\pi$
$812$	−27709.8	+	15998.3i	−0.0420264	+	0.0242639i
$813$	−904671.	−	347225.i	−1.36870	−	0.525327i
$814$	−9263.35	+	16044.6i	−0.0139804	+	0.0242148i
$815$	431572.	+	249168.i	0.649737	+	0.375126i
$816$	635675.	−	100710.i	0.954674	−	0.151249i
$817$	120824.	+	209274.i	0.181013	+	0.313524i
$818$		−	1.17421e6i		−	1.75484i
$819$	−595743.	−	536314.i	−0.888160	−	0.799561i
$820$	−14211.1			−0.0211349
$821$	766188.	−	442359.i	1.13671	−	0.656279i	0.191095	−	0.981572i	$-0.438796\pi$
$821$	766188.	−	442359.i	1.13671	−	0.656279i	0.945613	+	0.325293i	$0.105463\pi$
$822$	182171.	−	147532.i	0.269609	−	0.218345i
$823$	−228795.	+	396285.i	−0.337791	+	0.585071i	−0.984017	−	0.178075i	$-0.943013\pi$
$823$	−228795.	+	396285.i	−0.337791	+	0.585071i	0.646226	+	0.763146i	$0.276346\pi$
$824$	−58355.8	−	33691.7i	−0.0859468	−	0.0496214i
$825$	−104455.	−	128979.i	−0.153469	−	0.189501i
$826$	−192828.	−	333988.i	−0.282625	−	0.489520i
$827$		−	97044.0i		−	0.141892i	−0.997480	−	0.0709459i	$-0.977398\pi$
$827$		−	97044.0i		−	0.141892i	0.997480	−	0.0709459i	$-0.0226018\pi$
$828$	17024.6	+	3617.12i	0.0248323	+	0.00527597i
$829$	195610.			0.284631			0.142315	−	0.989821i	$-0.454545\pi$
$829$	195610.			0.284631			0.142315	+	0.989821i	$0.454545\pi$
$830$	−133763.	+	77228.2i	−0.194169	+	0.112104i
$831$	−99895.4	−	630534.i	−0.144658	−	0.913076i
$832$	683233.	−	1.18339e6i	0.987011	−	1.70955i
$833$	−367840.	−	212372.i	−0.530113	−	0.306061i
$834$	−345921.	+	901274.i	−0.497330	+	1.29576i
$835$	−24336.5	−	42152.0i	−0.0349047	−	0.0604568i
$836$		−	60144.8i		−	0.0860569i
$837$	611336.	+	31957.6i	0.872628	+	0.0456166i
$838$	93593.3			0.133277
$839$	−228146.	+	131720.i	−0.324108	+	0.187124i	−0.653222	−	0.757166i	$-0.726583\pi$
$839$	−228146.	+	131720.i	−0.324108	+	0.187124i	0.329114	+	0.944290i	$0.393250\pi$
$840$	191096.	+	73345.3i	0.270828	+	0.103947i
$841$	422945.	−	732563.i	0.597988	−	1.03575i
$842$	388222.	+	224140.i	0.547591	+	0.316152i
$843$	947182.	−	150062.i	1.33284	−	0.211162i
$844$	15995.9	+	27705.7i	0.0224555	+	0.0388941i
$845$		−	817486.i		−	1.14490i
$846$	529817.	−	172200.i	0.740262	−	0.240598i
$847$	221094.			0.308184
$848$	553558.	−	319597.i	0.769788	−	0.444437i
$849$	−342977.	+	277763.i	−0.475828	+	0.385353i
$850$	−71916.7	+	124563.i	−0.0995387	+	0.172406i
$851$	7251.92	+	4186.90i	0.0100137	+	0.00578140i
$852$	6702.24	+	8275.84i	0.00923296	+	0.0114007i
$853$	99801.6	+	172861.i	0.137164	+	0.237575i	0.926422	−	0.376487i	$-0.122868\pi$
$853$	99801.6	+	172861.i	0.137164	+	0.237575i	−0.789258	+	0.614061i	$0.789535\pi$
$854$		−	192657.i		−	0.264161i
$855$	137948.	+	424432.i	0.188705	+	0.580599i
$856$	823564.			1.12396
$857$	−1.06476e6	+	614737.i	−1.44973	+	0.837004i	−0.998465	−	0.0553838i	$-0.982362\pi$
$857$	−1.06476e6	+	614737.i	−1.44973	+	0.837004i	−0.451269	+	0.892388i	$0.649028\pi$
$858$	258062.	+	1.62887e6i	0.350549	+	2.21265i
$859$	193697.	−	335493.i	0.262504	−	0.454671i	−0.704403	−	0.709801i	$-0.748785\pi$
$859$	193697.	−	335493.i	0.262504	−	0.454671i	0.966907	+	0.255130i	$0.0821183\pi$
$860$	−3927.71	−	2267.66i	−0.00531058	−	0.00306607i
$861$	−153780.	+	400664.i	−0.207441	+	0.540473i
$862$	−397215.	−	687996.i	−0.534578	−	0.925916i
$863$			261691.i			0.351372i	0.984446	+	0.175686i	$0.0562144\pi$
$863$			261691.i			0.351372i	−0.984446	+	0.175686i	$0.943786\pi$
$864$	−4025.68	+	77009.7i	−0.00539276	+	0.103162i
$865$	−459006.			−0.613459
$866$	169437.	−	97824.7i	0.225930	−	0.130441i
$867$	−31451.7	−	12071.6i	−0.0418414	−	0.0160593i
$868$	−10779.8	+	18671.1i	−0.0143077	+	0.0247816i
$869$	−182116.	−	105145.i	−0.241162	−	0.139235i
$870$	−482454.	+	76435.1i	−0.637408	+	0.100984i
$871$	916412.	+	1.58727e6i	1.20797	+	2.09226i
$872$		−	567125.i		−	0.745840i
$873$	197137.	−	927861.i	0.258666	−	1.21746i
$874$	498588.			0.652709
$875$	−37561.7	+	21686.3i	−0.0490602	+	0.0283249i
$876$	22861.2	−	18514.3i	0.0297914	−	0.0241268i
$877$	−579366.	+	1.00349e6i	−0.753276	+	1.30471i	0.192951	+	0.981208i	$0.438194\pi$
$877$	−579366.	+	1.00349e6i	−0.753276	+	1.30471i	−0.946227	+	0.323504i	$0.895139\pi$
$878$	−795452.	−	459255.i	−1.03187	−	0.595751i
$879$	−537470.	−	663660.i	−0.695627	−	0.858951i
$880$	−199647.	−	345799.i	−0.257809	−	0.446538i
$881$		−	389525.i		−	0.501861i	−0.968005	−	0.250930i	$-0.919263\pi$
$881$		−	389525.i		−	0.501861i	0.968005	−	0.250930i	$-0.0807365\pi$
$882$	−303525.	+	337159.i	−0.390174	+	0.433409i
$883$	−176987.			−0.226997			−0.113499	−	0.993538i	$-0.536206\pi$
$883$	−176987.			−0.226997			−0.113499	+	0.993538i	$0.536206\pi$
$884$	−67485.2	+	38962.6i	−0.0863583	+	0.0498590i
$885$	50230.7	+	317054.i	0.0641332	+	0.404805i
$886$	218386.	−	378256.i	0.278200	−	0.481857i
$887$	−101642.	−	58682.8i	−0.129189	−	0.0745871i	0.434013	−	0.900907i	$-0.357097\pi$
$887$	−101642.	−	58682.8i	−0.129189	−	0.0745871i	−0.563202	+	0.826320i	$0.690431\pi$
$888$	−6814.81	+	17755.5i	−0.00864227	+	0.0225168i
$889$	249732.	+	432548.i	0.315988	+	0.547307i
$890$			23212.5i			0.0293051i
$891$	−569081.	−	782982.i	−0.716834	−	0.986271i
$892$	42568.7			0.0535008
$893$	−753564.	+	435070.i	−0.944968	+	0.545578i
$894$	228276.	+	87615.4i	0.285618	+	0.109624i
$895$	−74343.6	+	128767.i	−0.0928106	+	0.160753i
$896$	403148.	+	232757.i	0.502167	+	0.289926i
$897$	736226.	−	116640.i	0.915011	−	0.144965i
$898$	332660.	+	576184.i	0.412523	+	0.714510i
$899$		−	1.04654e6i		−	1.29490i
$900$	−6225.11	−	5604.12i	−0.00768532	−	0.00691866i
$901$	−779996.			−0.960822
$902$	764666.	−	441480.i	0.939850	−	0.542623i
$903$	−106436.	+	86198.0i	−0.130531	+	0.105711i
$904$	−711673.	+	1.23265e6i	−0.870851	+	1.50836i
$905$	−312373.	−	180349.i	−0.381396	−	0.220199i
$906$	−789524.	−	974893.i	−0.961853	−	1.18768i
$907$	259780.	+	449953.i	0.315785	+	0.546956i	0.979604	−	0.200937i	$-0.0643988\pi$
$907$	259780.	+	449953.i	0.315785	+	0.546956i	−0.663819	+	0.747893i	$0.731065\pi$
$908$			34680.4i			0.0420642i
$909$	−809301.	−	171948.i	−0.979450	−	0.208098i
$910$	430976.			0.520439
$911$	82785.8	−	47796.4i	0.0997514	−	0.0575915i	−0.449294	−	0.893384i	$-0.648325\pi$
$911$	82785.8	−	47796.4i	0.0997514	−	0.0575915i	0.549046	+	0.835792i	$0.314991\pi$
$912$	168007.	+	1.06045e6i	0.201994	+	1.27498i
$913$	−261619.	+	453137.i	−0.313854	+	0.543611i
$914$	−662153.	−	382294.i	−0.792622	−	0.457620i
$915$	−57461.7	+	149713.i	−0.0686336	+	0.178820i
$916$	10862.5	+	18814.4i	0.0129461	+	0.0224233i
$917$		−	454498.i		−	0.540498i
$918$	−456770.	+	703568.i	−0.542016	+	0.834874i
$919$	−1.27828e6			−1.51355			−0.756774	−	0.653676i	$-0.773226\pi$
$919$	−1.27828e6			−1.51355			−0.756774	+	0.653676i	$0.773226\pi$
$920$	−164842.	+	95171.3i	−0.194756	+	0.112443i
$921$	692920.	+	265952.i	0.816891	+	0.313534i
$922$	134844.	−	233557.i	0.158625	−	0.274746i
$923$	394989.	+	228047.i	0.463641	+	0.267683i
$924$	33669.2	−	5334.20i	0.0394356	−	0.00624778i
$925$	−2014.96	−	3490.01i	−0.00235496	−	0.00407890i
$926$		−	117780.i		−	0.137356i
$927$	79193.0	−	25739.1i	0.0921568	−	0.0299526i
$928$	131832.			0.153082
$929$	968196.	−	558988.i	1.12184	−	0.647696i	0.179972	−	0.983672i	$-0.442399\pi$
$929$	968196.	−	558988.i	1.12184	−	0.647696i	0.941871	+	0.335976i	$0.109066\pi$
$930$	−255777.	+	207143.i	−0.295730	+	0.239499i
$931$	354286.	−	613642.i	0.408747	−	0.707971i
$932$	−1723.96	−	995.327i	−0.00198470	−	0.00114587i
$933$	205415.	+	253643.i	0.235976	+	0.291380i
$934$	584822.	+	1.01294e6i	0.670394	+	1.16116i
$935$			487251.i			0.557352i
$936$	523295.	+	1.61005e6i	0.597304	+	1.83776i
$937$	690738.			0.786746			0.393373	−	0.919379i	$-0.371308\pi$
$937$	690738.			0.786746			0.393373	+	0.919379i	$0.371308\pi$
$938$	−601752.	+	347421.i	−0.683930	+	0.394867i
$939$	−67685.1	−	427224.i	−0.0767647	−	0.484535i
$940$	8165.52	−	14143.1i	0.00924119	−	0.0160062i
$941$	−255344.	−	147423.i	−0.288367	−	0.166489i	0.348838	−	0.937183i	$-0.386576\pi$
$941$	−255344.	−	147423.i	−0.288367	−	0.166489i	−0.637205	+	0.770694i	$0.719910\pi$
$942$	499427.	−	1.30122e6i	0.562821	−	1.46639i
$943$	−199542.	−	345617.i	−0.224394	−	0.388662i
$944$			772283.i			0.866627i
$945$	−225364.	+	114866.i	−0.252360	+	0.128626i
$946$	281787.			0.314876
$947$	−123956.	+	71565.8i	−0.138218	+	0.0798005i	−0.567515	−	0.823363i	$-0.692095\pi$
$947$	−123956.	+	71565.8i	−0.138218	+	0.0798005i	0.429296	+	0.903164i	$0.358762\pi$
$948$	−9907.94	−	3802.80i	−0.0110247	−	0.00423143i
$949$	629959.	−	1.09112e6i	0.699487	−	1.21155i
$950$	−207801.	−	119974.i	−0.230250	−	0.132935i
$951$	−668088.	+	105845.i	−0.738707	+	0.117033i
$952$	−300458.	−	520408.i	−0.331520	−	0.574209i
$953$			265292.i			0.292104i	0.989277	+	0.146052i	$0.0466567\pi$
$953$			265292.i			0.292104i	−0.989277	+	0.146052i	$0.953343\pi$
$954$	−173137.	+	814899.i	−0.190236	+	0.895380i
$955$	−308879.			−0.338674
$956$	−49453.9	+	28552.2i	−0.0541109	+	0.0312409i
$957$	−1.28594e6	+	1.04142e6i	−1.40409	+	1.13711i
$958$	575355.	−	996545.i	0.626910	−	1.08584i
$959$	−179721.	−	103762.i	−0.195416	−	0.112824i
$960$	−271379.	−	335094.i	−0.294465	−	0.363601i
$961$	109178.	+	189102.i	0.118220	+	0.204762i
$962$			40043.7i			0.0432697i
$963$	−680934.	+	756388.i	−0.734264	+	0.815628i
$964$	67692.8			0.0728431
$965$	−442216.	+	255313.i	−0.474875	+	0.274169i
$966$	44219.5	+	279111.i	0.0473870	+	0.299104i
$967$	481858.	−	834603.i	0.515307	−	0.892538i	−0.484535	−	0.874772i	$-0.661011\pi$
$967$	481858.	−	834603.i	0.515307	−	0.892538i	0.999842	−	0.0177662i	$-0.00565546\pi$
$968$	−404393.	−	233476.i	−0.431572	−	0.249168i
$969$	469477.	−	1.22319e6i	0.499996	−	1.30271i
$970$	255001.	+	441675.i	0.271018	+	0.469418i
$971$			1.21703e6i			1.29081i	0.763839	+	0.645407i	$0.223312\pi$
$971$			1.21703e6i			1.29081i	−0.763839	+	0.645407i	$0.776688\pi$
$972$	−34549.1	−	34533.9i	−0.0365683	−	0.0365521i
$973$	854620.			0.902708
$974$	−543835.	+	313984.i	−0.573257	+	0.330970i
$975$	−334910.	−	128543.i	−0.352305	−	0.135219i
$976$	−192899.	+	334111.i	−0.202502	+	0.350744i
$977$	1.15413e6	+	666337.i	1.20911	+	0.698080i	0.962565	−	0.271052i	$-0.0873715\pi$
$977$	1.15413e6	+	666337.i	1.20911	+	0.698080i	0.246544	+	0.969131i	$0.420705\pi$
$978$	−1.54333e6	+	244509.i	−1.61354	+	0.255633i
$979$	39317.5	+	68099.9i	0.0410223	+	0.0710527i
$980$			13298.7i			0.0138470i
$981$	520866.	+	468907.i	0.541238	+	0.487246i
$982$	−285926.			−0.296504
$983$	30919.6	−	17851.4i	0.0319983	−	0.0184742i	−0.483916	−	0.875115i	$-0.660786\pi$
$983$	30919.6	−	17851.4i	0.0319983	−	0.0184742i	0.515914	+	0.856640i	$0.327452\pi$
$984$	704375.	−	570443.i	0.727468	−	0.589145i
$985$	−82130.0	+	142253.i	−0.0846504	+	0.146619i
$986$	1.24191e6	+	717018.i	1.27743	+	0.737524i
$987$	−310387.	−	383261.i	−0.318617	−	0.393423i
$988$	−64998.6	−	112581.i	−0.0665871	−	0.115332i
$989$		−	127364.i		−	0.130213i
$990$	509055.	+	108156.i	0.519391	+	0.110352i
$991$	−1.30398e6			−1.32777			−0.663884	−	0.747835i	$-0.731093\pi$
$991$	−1.30398e6			−1.32777			−0.663884	+	0.747835i	$0.731093\pi$
$992$	76928.3	−	44414.6i	0.0781741	−	0.0451338i
$993$	−172760.	−	1.09045e6i	−0.175204	−	1.10588i
$994$	−86455.0	+	149745.i	−0.0875019	+	0.151558i
$995$	245599.	+	141796.i	0.248073	+	0.143225i
$996$	−9462.04	+	24652.7i	−0.00953819	+	0.0248511i
$997$	286867.	+	496869.i	0.288596	+	0.499863i	0.973475	−	0.228794i	$-0.0734781\pi$
$997$	286867.	+	496869.i	0.288596	+	0.499863i	−0.684879	+	0.728657i	$0.740145\pi$
$998$			1.48426e6i			1.49022i
$999$	−10672.7	−	20939.5i	−0.0106941	−	0.0209814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.41.4	yes	32
3.2	odd	2		135.5.i.a.71.13		32
9.2	odd	6	inner	45.5.i.a.11.4	✓	32
9.4	even	3		405.5.c.b.161.8		32
9.5	odd	6		405.5.c.b.161.25		32
9.7	even	3		135.5.i.a.116.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.4	✓	32	9.2	odd	6	inner
45.5.i.a.41.4	yes	32	1.1	even	1	trivial
135.5.i.a.71.13		32	3.2	odd	2
135.5.i.a.116.13		32	9.7	even	3
405.5.c.b.161.8		32	9.4	even	3
405.5.c.b.161.25		32	9.5	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+(-3.37336 + 1.94761i) q^{2} +(8.40237 + 3.22494i) q^{3} +(-0.413632 + 0.716431i) q^{4} +(9.68246 + 5.59017i) q^{5} +(-34.6251 + 5.48565i) q^{6} +(15.5174 + 26.8770i) q^{7} -65.5459i q^{8} +(60.1995 + 54.1943i) q^{9} -43.5499 q^{10} +(-127.765 + 73.7649i) q^{11} +(-5.78593 + 4.68578i) q^{12} +(-159.436 + 276.151i) q^{13} +(-104.692 - 60.4438i) q^{14} +(63.3276 + 78.1960i) q^{15} +(121.040 + 209.647i) q^{16} -295.405i q^{17} +(-308.624 - 65.5715i) q^{18} +492.804 q^{19} +(-8.00994 + 4.62454i) q^{20} +(43.7065 + 275.873i) q^{21} +(287.331 - 497.671i) q^{22} +(-224.940 - 129.869i) q^{23} +(211.382 - 550.741i) q^{24} +(62.5000 + 108.253i) q^{25} -1242.08i q^{26} +(331.045 + 649.500i) q^{27} -25.6740 q^{28} +(1079.30 - 623.132i) q^{29} +(-365.922 - 140.446i) q^{30} +(419.870 - 727.237i) q^{31} +(91.6096 + 52.8908i) q^{32} +(-1311.41 + 207.767i) q^{33} +(575.334 + 996.508i) q^{34} +346.980i q^{35} +(-63.7269 + 20.7123i) q^{36} -32.2394 q^{37} +(-1662.41 + 959.790i) q^{38} +(-2230.21 + 1806.15i) q^{39} +(366.413 - 634.645i) q^{40} +(1330.64 + 768.244i) q^{41} +(-684.731 - 845.496i) q^{42} +(245.177 + 424.659i) q^{43} -122.046i q^{44} +(279.924 + 861.259i) q^{45} +1011.74 q^{46} +(-1529.13 + 882.846i) q^{47} +(340.921 + 2151.88i) q^{48} +(718.919 - 1245.20i) q^{49} +(-421.670 - 243.451i) q^{50} +(952.664 - 2482.10i) q^{51} +(-131.895 - 228.450i) q^{52} -2640.43i q^{53} +(-2381.71 - 1546.25i) q^{54} -1649.43 q^{55} +(1761.68 - 1017.10i) q^{56} +(4140.72 + 1589.26i) q^{57} +(-2427.23 + 4204.09i) q^{58} +(2762.80 + 1595.10i) q^{59} +(-82.2163 + 13.0255i) q^{60} +(796.842 + 1380.17i) q^{61} +3270.97i q^{62} +(-522.436 + 2458.94i) q^{63} -4285.31 q^{64} +(-3087.46 + 1782.55i) q^{65} +(4019.22 - 3254.99i) q^{66} +(2873.92 - 4977.78i) q^{67} +(211.637 + 122.189i) q^{68} +(-1471.21 - 1816.63i) q^{69} +(-675.782 - 1170.49i) q^{70} -1430.34i q^{71} +(3552.21 - 3945.83i) q^{72} -3951.17 q^{73} +(108.755 - 62.7897i) q^{74} +(176.038 + 1111.14i) q^{75} +(-203.839 + 353.060i) q^{76} +(-3965.16 - 2289.28i) q^{77} +(4005.62 - 10436.4i) q^{78} +(712.702 + 1234.44i) q^{79} +2706.53i q^{80} +(686.964 + 6524.94i) q^{81} -5984.96 q^{82} +(3071.50 - 1773.33i) q^{83} +(-215.722 - 82.7971i) q^{84} +(1651.36 - 2860.25i) q^{85} +(-1654.14 - 955.018i) q^{86} +(11078.2 - 1755.12i) q^{87} +(4834.99 + 8374.44i) q^{88} -533.010i q^{89} +(-2621.68 - 2360.15i) q^{90} -9896.14 q^{91} +(186.084 - 107.436i) q^{92} +(5873.20 - 4756.45i) q^{93} +(3438.88 - 5956.31i) q^{94} +(4771.56 + 2754.86i) q^{95} +(599.168 + 739.844i) q^{96} +(-5855.38 - 10141.8i) q^{97} +5600.69i q^{98} +(-11689.0 - 2483.50i) 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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