LMFDB - Embedded newform 45.5.h.a.14.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); 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([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (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:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.12
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.316502 + 0.548197i) q^{2} +(4.90909 - 7.54326i) q^{3} +(7.79965 - 13.5094i) q^{4} +(-18.0085 - 17.3406i) q^{5} +(5.68893 + 0.303692i) q^{6} +(-73.2178 + 42.2723i) q^{7} +20.0025 q^{8} +(-32.8017 - 74.0611i) q^{9} +(3.80633 - 15.3605i) q^{10} +(148.474 - 85.7213i) q^{11} +(-63.6157 - 125.154i) q^{12} +(127.218 + 73.4493i) q^{13} +(-46.3471 - 26.7585i) q^{14} +(-219.210 + 50.7162i) q^{15} +(-118.464 - 205.185i) q^{16} +273.459 q^{17} +(30.2183 - 41.4222i) q^{18} +229.656 q^{19} +(-374.720 + 108.033i) q^{20} +(-40.5615 + 759.820i) q^{21} +(93.9843 + 54.2618i) q^{22} +(194.631 - 337.110i) q^{23} +(98.1939 - 150.884i) q^{24} +(23.6096 + 624.554i) q^{25} +92.9873i q^{26} +(-719.689 - 116.141i) q^{27} +1318.84i q^{28} +(306.632 - 177.034i) q^{29} +(-97.1827 - 104.118i) q^{30} +(-310.913 + 538.517i) q^{31} +(235.008 - 407.045i) q^{32} +(82.2521 - 1540.79i) q^{33} +(86.5501 + 149.909i) q^{34} +(2051.57 + 508.379i) q^{35} +(-1256.36 - 134.520i) q^{36} +730.131i q^{37} +(72.6865 + 125.897i) q^{38} +(1178.57 - 599.069i) q^{39} +(-360.214 - 346.854i) q^{40} +(-498.910 - 288.046i) q^{41} +(-429.369 + 218.249i) q^{42} +(-783.565 + 452.392i) q^{43} -2674.39i q^{44} +(-693.554 + 1902.53i) q^{45} +246.404 q^{46} +(396.417 + 686.614i) q^{47} +(-2129.31 - 113.669i) q^{48} +(2373.40 - 4110.85i) q^{49} +(-334.906 + 210.615i) q^{50} +(1342.43 - 2062.77i) q^{51} +(1984.51 - 1145.76i) q^{52} -3467.44 q^{53} +(-164.115 - 431.290i) q^{54} +(-4160.24 - 1030.91i) q^{55} +(-1464.54 + 845.551i) q^{56} +(1127.40 - 1732.36i) q^{57} +(194.099 + 112.063i) q^{58} +(2436.74 + 1406.85i) q^{59} +(-1024.61 + 3356.96i) q^{60} +(2660.83 + 4608.69i) q^{61} -393.618 q^{62} +(5532.41 + 4035.99i) q^{63} -3493.32 q^{64} +(-1017.35 - 3528.74i) q^{65} +(870.688 - 442.572i) q^{66} +(147.934 + 85.4097i) q^{67} +(2132.88 - 3694.26i) q^{68} +(-1587.45 - 3123.05i) q^{69} +(370.633 + 1285.57i) q^{70} +2798.11i q^{71} +(-656.114 - 1481.40i) q^{72} -5866.22i q^{73} +(-400.255 + 231.088i) q^{74} +(4827.08 + 2887.90i) q^{75} +(1791.24 - 3102.52i) q^{76} +(-7247.28 + 12552.7i) q^{77} +(701.428 + 456.483i) q^{78} +(1466.67 + 2540.34i) q^{79} +(-1424.68 + 5749.29i) q^{80} +(-4409.10 + 4858.66i) q^{81} -364.668i q^{82} +(3444.66 + 5966.32i) q^{83} +(9948.35 + 6474.30i) q^{84} +(-4924.57 - 4741.93i) q^{85} +(-495.999 - 286.365i) q^{86} +(169.869 - 3182.08i) q^{87} +(2969.84 - 1714.64i) q^{88} -1031.26i q^{89} +(-1262.47 + 221.949i) q^{90} -12419.5 q^{91} +(-3036.10 - 5258.68i) q^{92} +(2535.88 + 4988.93i) q^{93} +(-250.933 + 434.629i) q^{94} +(-4135.75 - 3982.37i) q^{95} +(-1916.77 - 3770.94i) q^{96} +(12170.7 - 7026.75i) q^{97} +3004.74 q^{98} +(-11218.8 - 8184.32i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * 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 $

$2$	0.316502	+	0.548197i	0.0791254	+	0.137049i	0.902873	−	0.429908i	$-0.141454\pi$
$2$	0.316502	+	0.548197i	0.0791254	+	0.137049i	−0.823747	+	0.566957i	$0.808121\pi$
$3$	4.90909	−	7.54326i	0.545454	−	0.838140i
$3$	4.90909	−	7.54326i	0.545454	−	0.838140i
$4$	7.79965	−	13.5094i	0.487478	−	0.844337i
$5$	−18.0085	−	17.3406i	−0.720339	−	0.693623i
$5$	−18.0085	−	17.3406i	−0.720339	−	0.693623i
$6$	5.68893	+	0.303692i	0.158026	+	0.00843590i
$7$	−73.2178	+	42.2723i	−1.49424	+	0.862701i	−0.999978	−	0.00661118i	$-0.997896\pi$
$7$	−73.2178	+	42.2723i	−1.49424	+	0.862701i	−0.494264	+	0.869312i	$0.664562\pi$
$8$	20.0025			0.312538
$9$	−32.8017	−	74.0611i	−0.404959	−	0.914335i
$10$	3.80633	−	15.3605i	0.0380633	−	0.153605i
$11$	148.474	−	85.7213i	1.22705	−	0.708440i	0.260642	−	0.965436i	$-0.416066\pi$
$11$	148.474	−	85.7213i	1.22705	−	0.708440i	0.966413	+	0.256995i	$0.0827325\pi$
$12$	−63.6157	−	125.154i	−0.441776	−	0.869123i
$13$	127.218	+	73.4493i	0.752769	+	0.434611i	0.826693	−	0.562653i	$-0.190219\pi$
$13$	127.218	+	73.4493i	0.752769	+	0.434611i	−0.0739247	+	0.997264i	$0.523552\pi$
$14$	−46.3471	−	26.7585i	−0.236465	−	0.136523i
$15$	−219.210	+	50.7162i	−0.974265	+	0.225405i
$16$	−118.464	−	205.185i	−0.462749	−	0.801504i
$17$	273.459			0.946224			0.473112	−	0.881002i	$-0.343131\pi$
$17$	273.459			0.946224			0.473112	+	0.881002i	$0.343131\pi$
$18$	30.2183	−	41.4222i	0.0932663	−	0.127846i
$19$	229.656			0.636167			0.318083	−	0.948063i	$-0.396961\pi$
$19$	229.656			0.636167			0.318083	+	0.948063i	$0.396961\pi$
$20$	−374.720	+	108.033i	−0.936801	+	0.270083i
$21$	−40.5615	+	759.820i	−0.0919763	+	1.72295i
$22$	93.9843	+	54.2618i	0.194182	+	0.112111i
$23$	194.631	−	337.110i	0.367922	−	0.637259i	−0.621319	−	0.783558i	$-0.713403\pi$
$23$	194.631	−	337.110i	0.367922	−	0.637259i	0.989240	+	0.146299i	$0.0467361\pi$
$24$	98.1939	−	150.884i	0.170475	−	0.261951i
$25$	23.6096	+	624.554i	0.0377754	+	0.999286i
$26$			92.9873i			0.137555i
$27$	−719.689	−	116.141i	−0.987228	−	0.159316i
$28$			1318.84i			1.68219i
$29$	306.632	−	177.034i	0.364604	−	0.210504i	−0.306494	−	0.951872i	$-0.599156\pi$
$29$	306.632	−	177.034i	0.364604	−	0.210504i	0.671098	+	0.741368i	$0.265823\pi$
$30$	−97.1827	−	104.118i	−0.107981	−	0.115687i
$31$	−310.913	+	538.517i	−0.323531	+	0.560371i	−0.981214	−	0.192923i	$-0.938203\pi$
$31$	−310.913	+	538.517i	−0.323531	+	0.560371i	0.657683	+	0.753295i	$0.271537\pi$
$32$	235.008	−	407.045i	0.229500	−	0.397505i
$33$	82.2521	−	1540.79i	0.0755299	−	1.41487i
$34$	86.5501	+	149.909i	0.0748704	+	0.129679i
$35$	2051.57	+	508.379i	1.67475	+	0.415003i
$36$	−1256.36	−	134.520i	−0.969416	−	0.103797i
$37$			730.131i			0.533332i	0.963789	+	0.266666i	$0.0859220\pi$
$37$			730.131i			0.533332i	−0.963789	+	0.266666i	$0.914078\pi$
$38$	72.6865	+	125.897i	0.0503369	+	0.0871861i
$39$	1178.57	−	599.069i	0.774866	−	0.393865i
$40$	−360.214	−	346.854i	−0.225133	−	0.216784i
$41$	−498.910	−	288.046i	−0.296794	−	0.171354i	0.344208	−	0.938893i	$-0.388148\pi$
$41$	−498.910	−	288.046i	−0.296794	−	0.171354i	−0.641002	+	0.767539i	$0.721481\pi$
$42$	−429.369	+	218.249i	−0.243406	+	0.123724i
$43$	−783.565	+	452.392i	−0.423778	+	0.244668i	−0.696692	−	0.717370i	$-0.745346\pi$
$43$	−783.565	+	452.392i	−0.423778	+	0.244668i	0.272914	+	0.962038i	$0.412012\pi$
$44$		−	2674.39i		−	1.38140i
$45$	−693.554	+	1902.53i	−0.342496	+	0.939519i
$46$	246.404			0.116448
$47$	396.417	+	686.614i	0.179455	+	0.310826i	0.941694	−	0.336470i	$-0.109233\pi$
$47$	396.417	+	686.614i	0.179455	+	0.310826i	−0.762239	+	0.647296i	$0.775900\pi$
$48$	−2129.31	−	113.669i	−0.924181	−	0.0493356i
$49$	2373.40	−	4110.85i	0.988506	−	1.71214i
$50$	−334.906	+	210.615i	−0.133962	+	0.0842460i
$51$	1342.43	−	2062.77i	0.516122	−	0.793069i
$52$	1984.51	−	1145.76i	0.733917	−	0.423727i
$53$	−3467.44			−1.23440			−0.617202	−	0.786805i	$-0.711734\pi$
$53$	−3467.44			−1.23440			−0.617202	+	0.786805i	$0.711734\pi$
$54$	−164.115	−	431.290i	−0.0562807	−	0.147905i
$55$	−4160.24	−	1030.91i	−1.37529	−	0.340796i
$56$	−1464.54	+	845.551i	−0.467008	+	0.269627i
$57$	1127.40	−	1732.36i	0.347000	−	0.533197i
$58$	194.099	+	112.063i	0.0576989	+	0.0333125i
$59$	2436.74	+	1406.85i	0.700013	+	0.404152i	0.807352	−	0.590070i	$-0.200900\pi$
$59$	2436.74	+	1406.85i	0.700013	+	0.404152i	−0.107340	+	0.994222i	$0.534233\pi$
$60$	−1024.61	+	3356.96i	−0.284615	+	0.932489i
$61$	2660.83	+	4608.69i	0.715084	+	1.23856i	0.962927	+	0.269762i	$0.0869450\pi$
$61$	2660.83	+	4608.69i	0.715084	+	1.23856i	−0.247843	+	0.968800i	$0.579722\pi$
$62$	−393.618			−0.102398
$63$	5532.41	+	4035.99i	1.39390	+	1.01688i
$64$	−3493.32			−0.852860
$65$	−1017.35	−	3528.74i	−0.240792	−	0.835205i
$66$	870.688	−	442.572i	0.199883	−	0.101601i
$67$	147.934	+	85.4097i	0.0329548	+	0.0190264i	0.516387	−	0.856355i	$-0.327277\pi$
$67$	147.934	+	85.4097i	0.0329548	+	0.0190264i	−0.483432	+	0.875382i	$0.660610\pi$
$68$	2132.88	−	3694.26i	0.461264	−	0.798932i
$69$	−1587.45	−	3123.05i	−0.333428	−	0.655966i
$70$	370.633	+	1285.57i	0.0756393	+	0.262360i
$71$			2798.11i			0.555071i	0.960715	+	0.277535i	$0.0895176\pi$
$71$			2798.11i			0.555071i	−0.960715	+	0.277535i	$0.910482\pi$
$72$	−656.114	−	1481.40i	−0.126565	−	0.285765i
$73$		−	5866.22i		−	1.10081i	−0.834898	−	0.550405i	$-0.814473\pi$
$73$		−	5866.22i		−	1.10081i	0.834898	−	0.550405i	$-0.185527\pi$
$74$	−400.255	+	231.088i	−0.0730927	+	0.0422001i
$75$	4827.08	+	2887.90i	0.858147	+	0.513404i
$76$	1791.24	−	3102.52i	0.310117	−	0.537139i
$77$	−7247.28	+	12552.7i	−1.22234	+	2.11716i
$78$	701.428	+	456.483i	0.115291	+	0.0750301i
$79$	1466.67	+	2540.34i	0.235005	+	0.407040i	0.959274	−	0.282477i	$-0.0911560\pi$
$79$	1466.67	+	2540.34i	0.235005	+	0.407040i	−0.724269	+	0.689517i	$0.757823\pi$
$80$	−1424.68	+	5749.29i	−0.222606	+	0.898327i
$81$	−4409.10	+	4858.66i	−0.672017	+	0.740536i
$82$		−	364.668i		−	0.0542338i
$83$	3444.66	+	5966.32i	0.500023	+	0.866065i	1.00000		2.64929e-5i	$8.43294e-6\pi$
$83$	3444.66	+	5966.32i	0.500023	+	0.866065i	−0.499977	+	0.866039i	$0.666658\pi$
$84$	9948.35	+	6474.30i	1.40991	+	0.917559i
$85$	−4924.57	−	4741.93i	−0.681602	−	0.656323i
$86$	−495.999	−	286.365i	−0.0670632	−	0.0387189i
$87$	169.869	−	3182.08i	0.0224428	−	0.420410i
$88$	2969.84	−	1714.64i	0.383502	−	0.221415i
$89$		−	1031.26i		−	0.130193i	−0.997879	−	0.0650966i	$-0.979264\pi$
$89$		−	1031.26i		−	0.130193i	0.997879	−	0.0650966i	$-0.0207356\pi$
$90$	−1262.47	+	221.949i	−0.155860	+	0.0274011i
$91$	−12419.5			−1.49976
$92$	−3036.10	−	5258.68i	−0.358708	−	0.621300i
$93$	2535.88	+	4988.93i	0.293199	+	0.576821i
$94$	−250.933	+	434.629i	−0.0283990	+	0.0491884i
$95$	−4135.75	−	3982.37i	−0.458255	−	0.441259i
$96$	−1916.77	−	3770.94i	−0.207983	−	0.409174i
$97$	12170.7	−	7026.75i	1.29352	−	0.746811i	0.314240	−	0.949344i	$-0.398250\pi$
$97$	12170.7	−	7026.75i	1.29352	−	0.746811i	0.979276	+	0.202532i	$0.0649171\pi$
$98$	3004.74			0.312864
$99$	−11218.8	−	8184.32i	−1.14466	−	0.835050i
$100$	8621.49	+	4552.35i	0.862149	+	0.455235i
$101$	11797.3	−	6811.17i	1.15648	−	0.667696i	0.206025	−	0.978547i	$-0.433947\pi$
$101$	11797.3	−	6811.17i	1.15648	−	0.667696i	0.950459	+	0.310851i	$0.100614\pi$
$102$	1555.69	+	83.0474i	0.149528	+	0.00798225i
$103$	−14156.3	−	8173.15i	−1.33437	−	0.770397i	−0.348402	−	0.937345i	$-0.613276\pi$
$103$	−14156.3	−	8173.15i	−1.33437	−	0.770397i	−0.985966	+	0.166948i	$0.946609\pi$
$104$	2544.67	+	1469.17i	0.235269	+	0.135833i
$105$	13906.2	−	12979.8i	1.26133	−	1.17731i
$106$	−1097.45	−	1900.84i	−0.0976727	−	0.169174i
$107$	−15293.8			−1.33582			−0.667909	−	0.744243i	$-0.732810\pi$
$107$	−15293.8			−1.33582			−0.667909	+	0.744243i	$0.732810\pi$
$108$	−7182.32	+	8816.70i	−0.615768	+	0.755890i
$109$	−3110.73			−0.261824			−0.130912	−	0.991394i	$-0.541791\pi$
$109$	−3110.73			−0.261824			−0.130912	+	0.991394i	$0.541791\pi$
$110$	−751.581	−	2606.91i	−0.0621142	−	0.215447i
$111$	5507.57	+	3584.28i	0.447007	+	0.290908i
$112$	17347.3	+	10015.5i	1.38292	+	0.798427i
$113$	4020.47	−	6963.67i	0.314862	−	0.545357i	−0.664546	−	0.747247i	$-0.731375\pi$
$113$	4020.47	−	6963.67i	0.314862	−	0.545357i	0.979408	+	0.201890i	$0.0647084\pi$
$114$	1306.50	+	69.7448i	0.100531	+	0.00536664i
$115$	−9350.68	+	2695.83i	−0.707046	+	0.203844i
$116$		−	5523.22i		−	0.410465i
$117$	1266.78	−	11831.2i	0.0925398	−	0.864282i
$118$			1781.09i			0.127915i
$119$	−20022.1	+	11559.7i	−1.41389	+	0.816308i
$120$	−4384.73	+	1014.45i	−0.304495	+	0.0704478i
$121$	7375.77	−	12775.2i	0.503775	−	0.872564i
$122$	−1684.31	+	2917.31i	−0.113163	+	0.196003i
$123$	−4622.00	+	2349.37i	−0.305506	+	0.155289i
$124$	4850.02	+	8400.49i	0.315428	+	0.546338i
$125$	10404.9	−	11656.7i	0.665916	−	0.746026i
$126$	−461.503	+	4310.24i	−0.0290692	+	0.271494i
$127$			8105.72i			0.502555i	0.967915	+	0.251278i	$0.0808507\pi$
$127$			8105.72i			0.502555i	−0.967915	+	0.251278i	$0.919149\pi$
$128$	−4865.76	−	8427.74i	−0.296982	−	0.514389i
$129$	−434.083	+	8131.47i	−0.0260851	+	0.488641i
$130$	1612.45	−	1674.56i	0.0954113	−	0.0990863i
$131$	−5088.68	−	2937.95i	−0.296526	−	0.171199i	0.344355	−	0.938839i	$-0.388098\pi$
$131$	−5088.68	−	2937.95i	−0.296526	−	0.171199i	−0.640881	+	0.767640i	$0.721431\pi$
$132$	−20173.6	−	13128.8i	−1.15780	−	0.753489i
$133$	−16814.9	+	9708.10i	−0.950587	+	0.548821i
$134$			108.129i			0.00602190i
$135$	10946.5	+	14571.3i	0.600633	+	0.799525i
$136$	5469.85			0.295731
$137$	17524.8	+	30353.8i	0.933710	+	1.61723i	0.776918	+	0.629601i	$0.216782\pi$
$137$	17524.8	+	30353.8i	0.933710	+	1.61723i	0.156792	+	0.987632i	$0.449885\pi$
$138$	1209.62	−	1858.69i	0.0635170	−	0.0975996i
$139$	−5993.53	+	10381.1i	−0.310208	+	0.537296i	−0.978407	−	0.206686i	$-0.933732\pi$
$139$	−5993.53	+	10381.1i	−0.310208	+	0.537296i	0.668199	+	0.743982i	$0.267065\pi$
$140$	22869.4	−	23750.3i	1.16681	−	1.21175i
$141$	7125.36	+	380.374i	0.358401	+	0.0191325i
$142$	−1533.92	+	885.606i	−0.0760720	+	0.0439202i
$143$	25184.7			1.23158
$144$	−11310.4	+	15504.0i	−0.545449	+	0.747683i
$145$	−8591.84	−	2129.06i	−0.408649	−	0.101263i
$146$	3215.84	−	1856.67i	0.150865	−	0.0871021i
$147$	−19358.0	−	38083.7i	−0.895831	−	1.76240i
$148$	9863.63	+	5694.77i	0.450312	+	0.259988i
$149$	11303.5	+	6526.09i	0.509145	+	0.293955i	0.732482	−	0.680786i	$-0.238362\pi$
$149$	11303.5	+	6526.09i	0.509145	+	0.293955i	−0.223337	+	0.974741i	$0.571695\pi$
$150$	−55.3589	+	3560.21i	−0.00246039	+	0.158232i
$151$	14442.4	+	25014.9i	0.633409	+	1.09710i	0.986850	+	0.161639i	$0.0516781\pi$
$151$	14442.4	+	25014.9i	0.633409	+	1.09710i	−0.353441	+	0.935457i	$0.614989\pi$
$152$	4593.69			0.198826
$153$	−8969.91	−	20252.7i	−0.383182	−	0.865166i
$154$	−9175.10			−0.386874
$155$	14937.2	−	4306.46i	0.621738	−	0.179249i
$156$	1099.39	−	20594.3i	0.0451754	−	0.846249i
$157$	18003.8	+	10394.5i	0.730405	+	0.421700i	0.818570	−	0.574406i	$-0.194767\pi$
$157$	18003.8	+	10394.5i	0.730405	+	0.421700i	−0.0881652	+	0.996106i	$0.528100\pi$
$158$	−928.404	+	1608.04i	−0.0371897	+	0.0644145i
$159$	−17022.0	+	26155.8i	−0.673311	+	1.03460i
$160$	−11290.5	+	3255.09i	−0.441036	+	0.127152i
$161$			32910.0i			1.26963i
$162$	−4058.99	−	879.282i	−0.154663	−	0.0335041i
$163$			24195.2i			0.910654i	0.890324	+	0.455327i	$0.150478\pi$
$163$			24195.2i			0.910654i	−0.890324	+	0.455327i	$0.849522\pi$
$164$	−7782.66	+	4493.32i	−0.289361	+	0.167063i
$165$	−28199.4	+	26320.9i	−1.03579	+	0.966793i
$166$	−2180.48	+	3776.70i	−0.0791290	+	0.137055i
$167$	−5184.25	+	8979.38i	−0.185889	+	0.321969i	−0.943876	−	0.330301i	$-0.892850\pi$
$167$	−5184.25	+	8979.38i	−0.185889	+	0.321969i	0.757987	+	0.652270i	$0.226183\pi$
$168$	−811.331	+	15198.3i	−0.0287461	+	0.538488i
$169$	−3490.90	−	6046.42i	−0.122226	−	0.211702i
$170$	1040.88	−	4200.46i	0.0360165	−	0.145345i
$171$	−7533.10	−	17008.6i	−0.257621	−	0.581669i
$172$			14114.0i			0.477082i
$173$	−19114.0	−	33106.4i	−0.638644	−	1.10616i	−0.985731	−	0.168331i	$-0.946162\pi$
$173$	−19114.0	−	33106.4i	−0.638644	−	1.10616i	0.347087	−	0.937833i	$-0.387171\pi$
$174$	1798.17	−	914.012i	0.0593926	−	0.0301893i
$175$	−28130.0	−	44730.5i	−0.918531	−	1.46059i
$176$	−35177.5	−	20309.7i	−1.13564	−	0.655660i
$177$	22574.5	−	11474.6i	0.720561	−	0.366262i
$178$	565.334	−	326.396i	0.0178429	−	0.0103016i
$179$		−	29062.0i		−	0.907025i	−0.891250	−	0.453512i	$-0.850171\pi$
$179$		−	29062.0i		−	0.907025i	0.891250	−	0.453512i	$-0.149829\pi$
$180$	20292.5	+	24208.5i	0.626312	+	0.747177i
$181$	23849.6			0.727988			0.363994	−	0.931401i	$-0.381413\pi$
$181$	23849.6			0.727988			0.363994	+	0.931401i	$0.381413\pi$
$182$	−3930.79	−	6808.33i	−0.118669	−	0.205541i
$183$	47826.8	+	2553.14i	1.42813	+	0.0762382i
$184$	3893.09	−	6743.03i	0.114990	−	0.199168i
$185$	12660.9	−	13148.5i	0.369931	−	0.384179i
$186$	−1932.30	+	2969.16i	−0.0558534	+	0.0858238i
$187$	40601.4	−	23441.2i	1.16107	−	0.670343i
$188$	12367.7			0.349923
$189$	57603.6	−	21919.3i	1.61260	−	0.613626i
$190$	874.148	−	3527.63i	0.0242146	−	0.0977183i
$191$	−4976.77	+	2873.34i	−0.136421	+	0.0787626i	−0.566657	−	0.823954i	$-0.691764\pi$
$191$	−4976.77	+	2873.34i	−0.136421	+	0.0787626i	0.430236	+	0.902716i	$0.358430\pi$
$192$	−17149.0	+	26351.0i	−0.465196	+	0.714817i
$193$	5427.21	+	3133.40i	0.145701	+	0.0841204i	0.571078	−	0.820896i	$-0.306525\pi$
$193$	5427.21	+	3133.40i	0.145701	+	0.0841204i	−0.425377	+	0.905016i	$0.639859\pi$
$194$	7704.08	+	4447.95i	0.204700	+	0.118183i
$195$	−31612.5	−	9648.78i	−0.831360	−	0.253748i
$196$	−37023.4	−	64126.5i	−0.963750	−	1.66926i
$197$	−55114.0			−1.42013			−0.710067	−	0.704134i	$-0.751335\pi$
$197$	−55114.0			−1.42013			−0.710067	+	0.704134i	$0.751335\pi$
$198$	935.852	−	8740.46i	0.0238713	−	0.222948i
$199$	10375.3			0.261995			0.130998	−	0.991383i	$-0.458182\pi$
$199$	10375.3			0.261995			0.130998	+	0.991383i	$0.458182\pi$
$200$	472.250	+	12492.6i	0.0118063	+	0.312315i
$201$	1370.49	−	696.621i	0.0339222	−	0.0172427i
$202$	7467.72	+	4311.49i	0.183014	+	0.105663i
$203$	−14967.3	+	25924.1i	−0.363204	+	0.629088i
$204$	−17396.3	−	34224.4i	−0.418019	−	0.822385i
$205$	3989.73	+	13838.7i	0.0949371	+	0.329296i
$206$		−	10347.3i		−	0.243832i
$207$	−31351.0	−	3356.79i	−0.731662	−	0.0783399i
$208$		−	34804.3i		−	0.804463i
$209$	34097.9	−	19686.4i	0.780611	−	0.450686i
$210$	11516.8	+	3515.18i	0.261153	+	0.0797092i
$211$	−25898.6	+	44857.7i	−0.581716	+	1.00756i	0.413560	+	0.910477i	$0.364285\pi$
$211$	−25898.6	+	44857.7i	−0.581716	+	1.00756i	−0.995276	+	0.0970851i	$0.969048\pi$
$212$	−27044.8	+	46843.0i	−0.601745	+	1.04225i
$213$	21106.9	+	13736.2i	0.465227	+	0.302766i
$214$	−4840.50	−	8384.00i	−0.105697	−	0.183073i
$215$	21955.5	+	5440.59i	0.474971	+	0.117698i
$216$	−14395.5	−	2323.11i	−0.308547	−	0.0497922i
$217$		−	52572.1i		−	1.11644i
$218$	−984.552	−	1705.29i	−0.0207169	−	0.0358828i
$219$	−44250.4	−	28797.8i	−0.922634	−	0.600442i
$220$	−46375.3	+	48161.6i	−0.958168	+	0.995074i
$221$	34788.9	+	20085.4i	0.712288	+	0.411240i
$222$	−221.735	+	4153.66i	−0.00449913	+	0.0842801i
$223$	−22259.2	+	12851.4i	−0.447611	+	0.258428i	−0.706821	−	0.707393i	$-0.749871\pi$
$223$	−22259.2	+	12851.4i	−0.447611	+	0.258428i	0.259210	+	0.965821i	$0.416538\pi$
$224$			39737.3i			0.791958i
$225$	45480.7	−	22235.0i	0.898385	−	0.439209i
$226$	5089.94			0.0996543
$227$	17114.5	+	29643.2i	0.332133	+	0.575272i	0.982930	−	0.183980i	$-0.0588983\pi$
$227$	17114.5	+	29643.2i	0.332133	+	0.575272i	−0.650797	+	0.759252i	$0.725565\pi$
$228$	−14609.7	−	28742.3i	−0.281043	−	0.552907i
$229$	−2619.98	+	4537.93i	−0.0499605	+	0.0865341i	−0.889924	−	0.456109i	$-0.849243\pi$
$229$	−2619.98	+	4537.93i	−0.0499605	+	0.0865341i	0.839964	+	0.542643i	$0.182576\pi$
$230$	−4437.35	−	4272.78i	−0.0838819	−	0.0807708i
$231$	59110.4	+	116290.i	1.10775	+	2.17931i
$232$	6133.39	−	3541.12i	0.113953	−	0.0657907i
$233$	−44606.8			−0.821654			−0.410827	−	0.911713i	$-0.634760\pi$
$233$	−44606.8			−0.821654			−0.410827	+	0.911713i	$0.634760\pi$
$234$	6886.74	−	3050.14i	0.125771	−	0.0557042i
$235$	4767.42	−	19239.0i	0.0863272	−	0.348374i
$236$	38011.5	−	21946.0i	0.682482	−	0.394031i
$237$	26362.4	+	1407.31i	0.469342	+	0.0250549i
$238$	−12674.0	−	7317.35i	−0.223749	−	0.129181i
$239$	−31245.6	−	18039.7i	−0.547008	−	0.315815i	0.200907	−	0.979610i	$-0.435611\pi$
$239$	−31245.6	−	18039.7i	−0.547008	−	0.315815i	−0.747914	+	0.663795i	$0.768945\pi$
$240$	36374.6	+	38970.5i	0.631503	+	0.676571i
$241$	−17018.3	−	29476.5i	−0.293009	−	0.507507i	0.681511	−	0.731808i	$-0.261323\pi$
$241$	−17018.3	−	29476.5i	−0.293009	−	0.507507i	−0.974520	+	0.224301i	$0.927990\pi$
$242$	9337.78			0.159446
$243$	15005.5	+	57110.6i	0.254119	+	0.967173i
$244$	83014.2			1.39435
$245$	−114026.	+	32874.0i	−1.89964	+	0.547672i
$246$	−2750.79	−	1790.19i	−0.0454555	−	0.0295821i
$247$	29216.4	+	16868.1i	0.478886	+	0.276485i
$248$	−6219.02	+	10771.7i	−0.101116	+	0.175138i
$249$	61915.7	+	3305.25i	0.998624	+	0.0533096i
$250$	9683.32	+	2014.61i	0.154933	+	0.0322337i
$251$			60480.3i			0.959990i	0.877271	+	0.479995i	$0.159361\pi$
$251$			60480.3i			0.959990i	−0.877271	+	0.479995i	$0.840639\pi$
$252$	97674.7	−	43260.1i	1.53809	−	0.681219i
$253$		−	66735.9i		−	1.04260i
$254$	−4443.53	+	2565.47i	−0.0688748	+	0.0397649i
$255$	−59944.8	+	13868.8i	−0.921873	+	0.213284i
$256$	−24866.5	+	43070.0i	−0.379432	+	0.657196i
$257$	7619.79	−	13197.9i	0.115366	−	0.199819i	−0.802560	−	0.596571i	$-0.796529\pi$
$257$	7619.79	−	13197.9i	0.115366	−	0.199819i	0.917926	+	0.396752i	$0.129863\pi$
$258$	−4595.03	+	2335.66i	−0.0690318	+	0.0350889i
$259$	−30864.3	−	53458.6i	−0.460106	−	0.796926i
$260$	−55606.1	−	13779.2i	−0.822575	−	0.203834i
$261$	−23169.4	−	16902.5i	−0.340121	−	0.248125i
$262$		−	3719.46i		−	0.0541848i
$263$	3230.92	+	5596.12i	0.0467106	+	0.0809051i	0.888435	−	0.459002i	$-0.151793\pi$
$263$	3230.92	+	5596.12i	0.0467106	+	0.0809051i	−0.841725	+	0.539907i	$0.818459\pi$
$264$	1645.24	−	30819.6i	0.0236060	−	0.442200i
$265$	62443.3	+	60127.4i	0.889189	+	0.856210i
$266$	−10643.9	−	6145.26i	−0.150431	−	0.0868514i
$267$	−7779.07	−	5062.55i	−0.109120	−	0.0710145i
$268$	2307.67	−	1332.33i	0.0321295	−	0.0185500i
$269$		−	77325.2i		−	1.06860i	−0.845294	−	0.534301i	$-0.820575\pi$
$269$		−	77325.2i		−	1.06860i	0.845294	−	0.534301i	$-0.179425\pi$
$270$	−4523.36	+	10612.7i	−0.0620489	+	0.145579i
$271$	−5856.99			−0.0797510			−0.0398755	−	0.999205i	$-0.512696\pi$
$271$	−5856.99			−0.0797510			−0.0398755	+	0.999205i	$0.512696\pi$
$272$	−32394.9	−	56109.7i	−0.437864	−	0.758403i
$273$	−60968.4	+	93683.5i	−0.818050	+	1.25701i
$274$	−11093.3	+	19214.1i	−0.147760	+	0.255928i
$275$	57043.0	+	90705.9i	0.754287	+	1.19942i
$276$	−54572.2	−	2913.23i	−0.716396	−	0.0382434i
$277$	−45287.4	+	26146.7i	−0.590225	+	0.340767i	−0.765187	−	0.643809i	$-0.777353\pi$
$277$	−45287.4	+	26146.7i	−0.590225	+	0.340767i	0.174961	+	0.984575i	$0.444020\pi$
$278$	−7587.84			−0.0981813
$279$	50081.6	+	5362.30i	0.643384	+	0.0688879i
$280$	41036.4	+	10168.8i	0.523423	+	0.129704i
$281$	9078.13	−	5241.26i	0.114970	−	0.0663779i	−0.441412	−	0.897304i	$-0.645522\pi$
$281$	9078.13	−	5241.26i	0.114970	−	0.0663779i	0.556382	+	0.830927i	$0.312189\pi$
$282$	2046.67	+	4026.49i	0.0257365	+	0.0506324i
$283$	4813.64	+	2779.16i	0.0601036	+	0.0347009i	0.529751	−	0.848153i	$-0.322285\pi$
$283$	4813.64	+	2779.16i	0.0601036	+	0.0347009i	−0.469647	+	0.882854i	$0.655619\pi$
$284$	37800.8	+	21824.3i	0.468667	+	0.270585i
$285$	−50342.8	+	11647.3i	−0.619795	+	0.143395i
$286$	7970.99	+	13806.2i	0.0974496	+	0.168788i
$287$	48705.5			0.591309
$288$	−37854.8	−	4053.17i	−0.456390	−	0.0488663i
$289$	−8741.28			−0.104660
$290$	−1552.19	−	5383.87i	−0.0184564	−	0.0640175i
$291$	6742.37	−	126302.i	0.0796208	−	1.49150i
$292$	−79249.1	−	45754.5i	−0.929455	−	0.536621i
$293$	75376.9	−	130557.i	0.878017	−	1.52077i	0.0245037	−	0.999700i	$-0.492199\pi$
$293$	75376.9	−	130557.i	0.878017	−	1.52077i	0.853514	−	0.521071i	$-0.174467\pi$
$294$	14750.5	−	22665.6i	0.170653	−	0.262224i
$295$	−19486.4	−	67589.8i	−0.223917	−	0.776671i
$296$			14604.4i			0.166687i
$297$	−116811.	+	44448.8i	−1.32425	+	0.503903i
$298$			8262.07i			0.0930371i
$299$	49521.0	−	28591.0i	0.553920	−	0.319806i
$300$	76663.3	−	42686.3i	0.851814	−	0.474292i
$301$	38247.3	−	66246.3i	0.422151	−	0.731187i
$302$	−9142.05	+	15834.5i	−0.100237	+	0.173616i
$303$	6535.51	−	122427.i	0.0711860	−	1.33349i
$304$	−27205.9	−	47122.0i	−0.294385	−	0.509890i
$305$	31999.9	−	129136.i	0.343992	−	1.38818i
$306$	8263.46	−	11327.3i	0.0882509	−	0.120971i
$307$			140225.i			1.48781i	0.668284	+	0.743906i	$0.267029\pi$
$307$			140225.i			1.48781i	−0.668284	+	0.743906i	$0.732971\pi$
$308$	113053.	+	195813.i	1.19173	+	2.06414i
$309$	−131147.	+	66662.0i	−1.37354	+	0.698171i
$310$	7088.45	+	6825.55i	0.0737612	+	0.0710255i
$311$	−165187.	−	95370.9i	−1.70787	−	0.986041i	−0.937187	−	0.348827i	$-0.886580\pi$
$311$	−165187.	−	95370.9i	−1.70787	−	0.986041i	−0.770687	−	0.637214i	$-0.780087\pi$
$312$	23574.3	−	11982.9i	0.242175	−	0.123098i
$313$	29158.8	−	16834.8i	0.297633	−	0.171838i	−0.343746	−	0.939063i	$-0.611696\pi$
$313$	29158.8	−	16834.8i	0.297633	−	0.171838i	0.641379	+	0.767224i	$0.278363\pi$
$314$			13159.5i			0.133469i
$315$	−29643.7	−	168617.i	−0.298753	−	1.69934i
$316$	45757.9			0.458239
$317$	−39248.1	−	67979.6i	−0.390571	−	0.676488i	0.601954	−	0.798531i	$-0.294389\pi$
$317$	−39248.1	−	67979.6i	−0.390571	−	0.676488i	−0.992525	+	0.122042i	$0.961056\pi$
$318$	−19726.0	−	1053.04i	−0.195068	−	0.0104133i
$319$	30351.2	−	52569.8i	0.298259	−	0.516600i
$320$	62909.3	+	60576.1i	0.614348	+	0.591563i
$321$	−75078.5	+	115365.i	−0.728628	+	1.11960i
$322$	−18041.1	+	10416.1i	−0.174001	+	0.100460i
$323$	62801.5			0.601956
$324$	31248.1	+	97460.1i	0.297669	+	0.928404i
$325$	−42869.5	+	81188.6i	−0.405865	+	0.768649i
$326$	−13263.7	+	7657.81i	−0.124804	+	0.0720559i
$327$	−15270.9	+	23465.1i	−0.142813	+	0.219445i
$328$	−9979.44	−	5761.63i	−0.0927595	−	0.0535547i
$329$	−58049.6	−	33515.0i	−0.536300	−	0.309633i
$330$	−23354.2	−	7128.19i	−0.214456	−	0.0654563i
$331$	86246.3	+	149383.i	0.787199	+	1.36347i	0.927677	+	0.373384i	$0.121803\pi$
$331$	86246.3	+	149383.i	0.787199	+	1.36347i	−0.140478	+	0.990084i	$0.544864\pi$
$332$	107469.			0.975001
$333$	54074.3	−	23949.5i	0.487644	−	0.215977i
$334$	−6563.29			−0.0588340
$335$	−1183.01	−	4103.36i	−0.0105414	−	0.0365637i
$336$	160709.	−	81688.5i	1.42351	−	0.723573i
$337$	−27972.6	−	16150.0i	−0.246305	−	0.142204i	0.371766	−	0.928326i	$-0.378752\pi$
$337$	−27972.6	−	16150.0i	−0.246305	−	0.142204i	−0.618071	+	0.786122i	$0.712086\pi$
$338$	2209.75	−	3827.40i	0.0193424	−	0.0335020i
$339$	−32791.9	−	64512.8i	−0.285343	−	0.561366i
$340$	−102471.	+	29542.6i	−0.886424	+	0.255559i
$341$			106607.i			0.916808i
$342$	6939.81	−	9512.87i	0.0593329	−	0.0813316i
$343$			198325.i			1.68574i
$344$	−15673.2	+	9048.94i	−0.132447	+	0.0764682i
$345$	−25568.0	+	83768.7i	−0.214812	+	0.703791i
$346$	12099.2	−	20956.4i	0.101066	−	0.175051i
$347$	116127.	−	201138.i	0.964440	−	1.67046i	0.253329	−	0.967380i	$-0.418474\pi$
$347$	116127.	−	201138.i	0.964440	−	1.67046i	0.711111	−	0.703080i	$-0.248192\pi$
$348$	−41663.1	−	27114.0i	−0.344027	−	0.223890i
$349$	82977.7	+	143722.i	0.681256	+	1.17997i	0.974598	+	0.223963i	$0.0718994\pi$
$349$	82977.7	+	143722.i	0.681256	+	1.17997i	−0.293342	+	0.956008i	$0.594767\pi$
$350$	15617.9	−	29578.0i	0.127493	−	0.241453i
$351$	−83026.9	−	67635.9i	−0.673914	−	0.548988i
$352$		−	80580.6i		−	0.650347i
$353$	−64590.4	−	111874.i	−0.518345	−	0.897800i	−0.999773	−	0.0213140i	$-0.993215\pi$
$353$	−64590.4	−	111874.i	−0.518345	−	0.897800i	0.481428	−	0.876486i	$-0.340118\pi$
$354$	13435.2	+	8743.51i	0.107211	+	0.0697717i
$355$	48520.8	−	50389.7i	0.385010	−	0.399839i
$356$	−13931.7	−	8043.48i	−0.109927	−	0.0634664i
$357$	−11091.9	+	207780.i	−0.0870302	+	1.63030i
$358$	15931.7	−	9198.16i	0.124307	−	0.0717687i
$359$			205368.i			1.59347i	0.604331	+	0.796734i	$0.293441\pi$
$359$			205368.i			1.59347i	−0.604331	+	0.796734i	$0.706559\pi$
$360$	−13872.8	+	38055.2i	−0.107043	+	0.293636i
$361$	−77579.1			−0.595292
$362$	7548.44	+	13074.3i	0.0576023	+	0.0997702i
$363$	−60158.5	−	118352.i	−0.456545	−	0.898179i
$364$	−96867.8	+	167780.i	−0.731100	+	1.26630i
$365$	−101724.	+	105642.i	−0.763547	+	0.792956i
$366$	13737.6	+	27026.6i	0.102553	+	0.201757i
$367$	−89820.1	+	51857.7i	−0.666870	+	0.385018i	−0.794890	−	0.606754i	$-0.792471\pi$
$367$	−89820.1	+	51857.7i	−0.666870	+	0.385018i	0.128019	+	0.991772i	$0.459138\pi$
$368$	−92226.6			−0.681021
$369$	−4967.92	+	46398.3i	−0.0364856	+	0.340760i
$370$	11215.2	+	2779.12i	0.0819224	+	0.0203004i
$371$	253879.	−	146577.i	1.84450	−	1.06492i
$372$	87176.3	+	4653.74i	0.629960	+	0.0336292i
$373$	156191.	+	90176.7i	1.12263	+	0.648152i	0.942071	−	0.335412i	$-0.108876\pi$
$373$	156191.	+	90176.7i	1.12263	+	0.648152i	0.180560	+	0.983564i	$0.442209\pi$
$374$	25700.8	+	14838.4i	0.183740	+	0.106082i
$375$	−36850.5	−	135711.i	−0.262048	−	0.965055i
$376$	7929.31	+	13734.0i	0.0560867	+	0.0971450i
$377$	52012.1			0.365950
$378$	30247.8	+	24640.6i	0.211694	+	0.172452i
$379$	−145168.			−1.01063			−0.505317	−	0.862934i	$-0.668624\pi$
$379$	−145168.			−1.01063			−0.505317	+	0.862934i	$0.668624\pi$
$380$	−86056.8	+	24810.5i	−0.595961	+	0.171818i
$381$	61143.6	+	39791.7i	0.421212	+	0.274121i
$382$	−3150.31	−	1818.83i	−0.0215887	−	0.0124642i
$383$	−56718.9	+	98240.0i	−0.386661	+	0.669716i	−0.991998	−	0.126253i	$-0.959705\pi$
$383$	−56718.9	+	98240.0i	−0.386661	+	0.669716i	0.605337	+	0.795969i	$0.293038\pi$
$384$	−87459.2	−	4668.84i	−0.593120	−	0.0316626i
$385$	348182.	−	100382.i	2.34901	−	0.677228i
$386$			3966.91i			0.0266242i
$387$	59206.9	+	43192.5i	0.395321	+	0.288394i
$388$		−	219225.i		−	1.45622i
$389$	−229341.	+	132410.i	−1.51559	+	0.875026i	−0.515757	+	0.856735i	$0.672489\pi$
$389$	−229341.	+	132410.i	−1.51559	+	0.875026i	−0.999833	+	0.0182911i	$0.994177\pi$
$390$	−4715.96	−	20383.7i	−0.0310057	−	0.134015i
$391$	53223.5	−	92185.7i	0.348137	−	0.602990i
$392$	47473.9	−	82227.2i	0.308946	−	0.535110i
$393$	−47142.5	+	23962.6i	−0.305230	+	0.155149i
$394$	−17443.7	−	30213.3i	−0.112369	−	0.194628i
$395$	17638.5	−	71180.4i	0.113049	−	0.456212i
$396$	−198068.	+	87724.3i	−1.26306	+	0.559409i
$397$		−	82700.5i		−	0.524719i	−0.964970	−	0.262360i	$-0.915499\pi$
$397$		−	82700.5i		−	0.524719i	0.964970	−	0.262360i	$-0.0845007\pi$
$398$	3283.79	+	5687.70i	0.0207305	+	0.0359063i
$399$	−9315.21	+	174497.i	−0.0585122	+	1.09608i
$400$	125352.	−	78831.3i	0.783452	−	0.492695i
$401$	20868.1	+	12048.2i	0.129776	+	0.0749261i	0.563482	−	0.826128i	$-0.309461\pi$
$401$	20868.1	+	12048.2i	0.129776	+	0.0749261i	−0.433707	+	0.901054i	$0.642795\pi$
$402$	815.647	+	530.816i	0.00504720	+	0.00328467i
$403$	−79107.4	+	45672.7i	−0.487087	+	0.281220i
$404$		−	212499.i		−	1.30195i
$405$	163653.	−	11040.7i	0.997732	−	0.0673109i
$406$	−18948.7			−0.114955
$407$	62587.7	+	108405.i	0.377834	+	0.654427i
$408$	26852.0	−	41260.5i	0.161308	−	0.247864i
$409$	83307.9	−	144294.i	0.498012	−	0.862582i	−0.501985	−	0.864876i	$-0.667397\pi$
$409$	83307.9	−	144294.i	0.498012	−	0.862582i	0.999997	+	0.00229409i	$0.000730232\pi$
$410$	−6323.55	+	6567.11i	−0.0376178	+	0.0390667i
$411$	314998.	+	16815.6i	1.86476	+	0.0995469i
$412$	−220829.	+	127495.i	−1.30095	+	0.751104i
$413$	−237884.			−1.39465
$414$	−8082.45	−	18248.9i	−0.0471566	−	0.106472i
$415$	41426.4	−	167177.i	0.240537	−	0.970687i
$416$	59794.3	−	34522.3i	0.345520	−	0.199486i
$417$	48884.6	+	96172.5i	0.281125	+	0.553068i
$418$	21584.1	+	12461.6i	0.123532	+	0.0713214i
$419$	93529.3	+	53999.2i	0.532745	+	0.307581i	0.742134	−	0.670252i	$-0.233814\pi$
$419$	93529.3	+	53999.2i	0.532745	+	0.307581i	−0.209388	+	0.977833i	$0.567147\pi$
$420$	−66886.5	−	289102.i	−0.379175	−	1.63890i
$421$	−129425.	−	224171.i	−0.730222	−	1.26478i	−0.956788	−	0.290785i	$-0.906084\pi$
$421$	−129425.	−	224171.i	−0.730222	−	1.26478i	0.226567	−	0.973996i	$-0.427250\pi$
$422$	−32787.8			−0.184114
$423$	37848.3	−	51881.2i	0.211527	−	0.289954i
$424$	−69357.3			−0.385799
$425$	6456.26	+	170790.i	0.0357440	+	0.945549i
$426$	−849.765	+	15918.3i	−0.00468252	+	0.0877155i
$427$	−389640.	−	224959.i	−2.13702	−	1.23381i
$428$	−119286.	+	206610.i	−0.651182	+	1.12788i
$429$	123634.	−	189975.i	0.671773	−	1.03224i
$430$	3966.45	+	13757.9i	0.0214519	+	0.0744073i
$431$		−	81054.9i		−	0.436340i	−0.975911	−	0.218170i	$-0.929991\pi$
$431$		−	81054.9i		−	0.436340i	0.975911	−	0.218170i	$-0.0700087\pi$
$432$	61426.6	+	161428.i	0.329146	+	0.864990i
$433$			173783.i			0.926897i	0.886124	+	0.463448i	$0.153388\pi$
$433$			173783.i			0.926897i	−0.886124	+	0.463448i	$0.846612\pi$
$434$	28819.8	−	16639.1i	0.153007	−	0.0883388i
$435$	−58238.2	+	54358.8i	−0.307772	+	0.287271i
$436$	−24262.6	+	42024.1i	−0.127634	+	0.221068i
$437$	44698.1	−	77419.4i	0.234060	−	0.405403i
$438$	1781.53	−	33372.5i	0.00928633	−	0.173956i
$439$	129440.	+	224196.i	0.671642	+	1.16332i	0.977438	+	0.211221i	$0.0677441\pi$
$439$	129440.	+	224196.i	0.671642	+	1.16332i	−0.305796	+	0.952097i	$0.598923\pi$
$440$	−83215.0	−	20620.7i	−0.429829	−	0.106512i
$441$	−382306.	−	40934.0i	−1.96578	−	0.210478i
$442$			25428.2i			0.130158i
$443$	−96232.4	−	166679.i	−0.490358	−	0.849326i	0.509580	−	0.860423i	$-0.329801\pi$
$443$	−96232.4	−	166679.i	−0.490358	−	0.849326i	−0.999938	+	0.0110976i	$0.996467\pi$
$444$	91378.6	−	46447.8i	0.463531	−	0.235613i
$445$	−17882.6	+	18571.4i	−0.0903050	+	0.0937832i
$446$	−14090.2	−	8134.96i	−0.0708347	−	0.0408964i
$447$	104718.	−	53228.3i	0.524091	−	0.266396i
$448$	255773.	−	147671.i	1.27438	−	0.735763i
$449$			56772.8i			0.281610i	0.990037	+	0.140805i	$0.0449690\pi$
$449$			56772.8i			0.281610i	−0.990037	+	0.140805i	$0.955031\pi$
$450$	26583.9	+	17895.0i	0.131278	+	0.0883703i
$451$	−98766.7			−0.485576
$452$	−62716.6	−	108628.i	−0.306977	−	0.531700i
$453$	259593.	+	13857.9i	1.26502	+	0.0675304i
$454$	−10833.5	+	18764.2i	−0.0525604	+	0.0910372i
$455$	223656.	+	215361.i	1.08033	+	1.04027i
$456$	22550.8	−	34651.4i	0.108451	−	0.166645i
$457$	271096.	−	156518.i	1.29805	−	0.749429i	0.317983	−	0.948096i	$-0.396995\pi$
$457$	271096.	−	156518.i	1.29805	−	0.749429i	0.980067	+	0.198667i	$0.0636612\pi$
$458$	−3316.91			−0.0158126
$459$	−196805.	−	31759.8i	−0.934139	−	0.150748i
$460$	−36513.0	+	147349.i	−0.172557	+	0.696354i
$461$	53494.0	−	30884.8i	0.251712	−	0.145326i	−0.368836	−	0.929494i	$-0.620244\pi$
$461$	53494.0	−	30884.8i	0.251712	−	0.145326i	0.620548	+	0.784169i	$0.286910\pi$
$462$	−45041.4	+	69210.2i	−0.211022	+	0.324255i
$463$	−146977.	−	84857.4i	−0.685628	−	0.395847i	0.116344	−	0.993209i	$-0.462882\pi$
$463$	−146977.	−	84857.4i	−0.685628	−	0.395847i	−0.801972	+	0.597362i	$0.796216\pi$
$464$	−72649.5	−	41944.2i	−0.337440	−	0.194821i
$465$	40843.6	−	133816.i	0.188894	−	0.618876i
$466$	−14118.1	−	24453.3i	−0.0650137	−	0.112607i
$467$	76633.3			0.351386			0.175693	−	0.984445i	$-0.443783\pi$
$467$	76633.3			0.351386			0.175693	+	0.984445i	$0.443783\pi$
$468$	−149951.	−	109392.i	−0.684635	−	0.499454i
$469$	−14441.9			−0.0656565
$470$	12055.6	−	3475.68i	0.0545751	−	0.0157342i
$471$	166790.	−	84779.7i	0.751846	−	0.382164i
$472$	48740.9	+	28140.5i	0.218781	+	0.126313i
$473$	−77559.2	+	134336.i	−0.346666	+	0.600443i
$474$	7572.27	+	14897.2i	0.0337031	+	0.0663054i
$475$	5422.09	+	143433.i	0.0240314	+	0.635712i
$476$			360648.i			1.59173i
$477$	113738.	+	256803.i	0.499883	+	1.12866i
$478$		−	22838.3i		−	0.0999559i
$479$	−30431.7	+	17569.8i	−0.132634	+	0.0765763i	−0.564849	−	0.825194i	$-0.691066\pi$
$479$	−30431.7	+	17569.8i	−0.132634	+	0.0765763i	0.432215	+	0.901771i	$0.357732\pi$
$480$	−30872.1	+	101147.i	−0.133994	+	0.439006i
$481$	−53627.6	+	92885.7i	−0.231792	+	0.401475i
$482$	10772.6	−	18658.7i	0.0463689	−	0.0803133i
$483$	248249.	+	161558.i	1.06412	+	0.692523i
$484$	−115057.	−	199285.i	−0.491159	−	0.850713i
$485$	−341023.	−	84505.6i	−1.44977	−	0.359254i
$486$	−26558.6	+	26301.5i	−0.112443	+	0.111355i
$487$		−	290883.i		−	1.22648i	−0.789896	−	0.613240i	$-0.789866\pi$
$487$		−	290883.i		−	1.22648i	0.789896	−	0.613240i	$-0.210134\pi$
$488$	53223.1	+	92185.1i	0.223491	+	0.387098i
$489$	182511.	+	118776.i	0.763256	+	0.496720i
$490$	−54110.8	−	52103.9i	−0.225368	−	0.217009i
$491$	−384175.	−	221803.i	−1.59355	−	0.920037i	−0.992691	−	0.120682i	$-0.961492\pi$
$491$	−384175.	−	221803.i	−1.59355	−	0.920037i	−0.600860	−	0.799355i	$-0.705175\pi$
$492$	−4311.47	+	80764.8i	−0.0178113	+	0.333650i
$493$	83851.2	−	48411.5i	0.344997	−	0.199184i
$494$			21355.1i			0.0875080i
$495$	60112.6	+	341927.i	0.245332	+	1.39548i
$496$	147327.			0.598853
$497$	−118283.	−	204872.i	−0.478860	−	0.829410i
$498$	17784.5	+	34988.1i	0.0717105	+	0.141079i
$499$	144661.	−	250561.i	0.580967	−	1.00626i	−0.414398	−	0.910096i	$-0.636008\pi$
$499$	144661.	−	250561.i	0.580967	−	1.00626i	0.995365	−	0.0961687i	$-0.0306588\pi$
$500$	−76319.5	−	231482.i	−0.305278	−	0.925930i
$501$	42283.9	+	83186.8i	0.168461	+	0.331420i
$502$	−33155.1	+	19142.1i	−0.131566	+	0.0759596i
$503$	349897.			1.38294			0.691472	−	0.722403i	$-0.256963\pi$
$503$	349897.			1.38294			0.691472	+	0.722403i	$0.256963\pi$
$504$	110662.	+	80729.8i	0.435649	+	0.317814i
$505$	−330561.	−	81913.0i	−1.29619	−	0.321196i
$506$	36584.4	−	21122.0i	0.142888	−	0.0824963i
$507$	−62746.9	−	3349.62i	−0.244105	−	0.0130311i
$508$	109503.	+	63221.8i	0.424326	+	0.244985i
$509$	406475.	+	234679.i	1.56891	+	0.905812i	0.996296	+	0.0859889i	$0.0274050\pi$
$509$	406475.	+	234679.i	1.56891	+	0.905812i	0.572617	+	0.819823i	$0.305928\pi$
$510$	−26575.5	−	28472.1i	−0.102174	−	0.109466i
$511$	247979.	+	429512.i	0.949670	+	1.64488i
$512$	−187185.			−0.714056
$513$	−165281.	−	26672.5i	−0.628041	−	0.101351i
$514$	9646.70			0.0365134
$515$	113206.	+	392664.i	0.426831	+	1.48049i
$516$	106466.	+	69286.9i	0.399862	+	0.260226i
$517$	117715.	+	67962.7i	0.440403	+	0.254267i
$518$	19537.2	−	33839.5i	0.0728121	−	0.126114i
$519$	−343562.	−	18340.4i	−1.27547	−	0.0680886i
$520$	−20349.4	−	70583.5i	−0.0752568	−	0.261034i
$521$			430054.i			1.58434i	0.610302	+	0.792169i	$0.291048\pi$
$521$			430054.i			1.58434i	−0.610302	+	0.792169i	$0.708952\pi$
$522$	1932.75	−	18051.0i	0.00709307	−	0.0662463i
$523$		−	21279.4i		−	0.0777959i	−0.999243	−	0.0388980i	$-0.987615\pi$
$523$		−	21279.4i		−	0.0777959i	0.999243	−	0.0388980i	$-0.0123847\pi$
$524$	−79379.9	+	45830.0i	−0.289100	+	0.166912i
$525$	−475506.	−	7393.80i	−1.72519	−	0.0268256i
$526$	−2045.18	+	3542.36i	−0.00739198	+	0.0128033i
$527$	−85021.9	+	147262.i	−0.306132	+	0.530237i
$528$	−325891.	+	165651.i	−1.16897	+	0.594190i
$529$	64158.3	+	111125.i	0.229267	+	0.397102i
$530$	−13198.2	+	53261.6i	−0.0469855	+	0.189611i
$531$	24264.0	−	226615.i	0.0860544	−	0.803711i
$532$			302879.i			1.07015i
$533$	−42313.6	−	73289.2i	−0.148945	−	0.257980i
$534$	313.186	−	5866.77i	0.00109830	−	0.0205739i
$535$	275417.	+	265203.i	0.962241	+	0.926553i
$536$	2959.04	+	1708.40i	0.0102996	+	0.00594649i
$537$	−219222.	−	142668.i	−0.760214	−	0.494741i
$538$	42389.4	−	24473.5i	0.146451	−	0.0845536i
$539$		−	813804.i		−	2.80119i
$540$	282229.	−	34229.8i	0.967864	−	0.117386i
$541$	−127926.			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$541$	−127926.			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$542$	−1853.75	−	3210.78i	−0.00631033	−	0.0109298i
$543$	117080.	−	179904.i	0.397084	−	0.610156i
$544$	64264.9	−	111310.i	0.217158	−	0.376129i
$545$	56019.5	+	53941.9i	0.188602	+	0.181607i
$546$	−70653.6	−	3771.71i	−0.237000	−	0.0126518i
$547$	−437484.	+	252582.i	−1.46214	+	0.844165i	−0.999110	−	0.0421802i	$-0.986570\pi$
$547$	−437484.	+	252582.i	−1.46214	+	0.844165i	−0.463026	+	0.886345i	$0.653236\pi$
$548$	546750.			1.82065
$549$	254045.	−	348237.i	0.842881	−	1.15539i
$550$	−31670.5	+	59979.3i	−0.104696	+	0.198279i
$551$	70419.9	−	40657.0i	0.231949	−	0.133916i
$552$	−31752.9	−	62468.8i	−0.104209	−	0.205015i
$553$	−214772.	−	123999.i	−0.702308	−	0.405478i
$554$	−28667.1	−	16550.9i	−0.0934036	−	0.0539266i
$555$	−37029.5	−	160052.i	−0.120216	−	0.519606i
$556$	93494.9	+	161938.i	0.302439	+	0.523840i
$557$	277756.			0.895268			0.447634	−	0.894217i	$-0.352267\pi$
$557$	277756.			0.895268			0.447634	+	0.894217i	$0.352267\pi$
$558$	12911.3	+	29151.8i	0.0414669	+	0.0936260i
$559$	−132911.			−0.425342
$560$	−138724.	−	481175.i	−0.442361	−	1.53436i
$561$	22492.5	−	421342.i	0.0714682	−	1.33878i
$562$	5746.49	+	3317.74i	0.0181941	+	0.0105043i
$563$	80007.5	−	138577.i	0.252414	−	0.437194i	−0.711776	−	0.702407i	$-0.752109\pi$
$563$	80007.5	−	138577.i	0.252414	−	0.437194i	0.964190	+	0.265213i	$0.0854421\pi$
$564$	60714.0	−	93292.5i	0.190867	−	0.293284i
$565$	−193156.	+	55687.6i	−0.605079	+	0.174446i
$566$			3518.43i			0.0109829i
$567$	117438.	−	542123.i	0.365294	−	1.68629i
$568$			55969.1i			0.173481i
$569$	152572.	−	88087.7i	0.471250	−	0.272076i	−0.245513	−	0.969393i	$-0.578956\pi$
$569$	152572.	−	88087.7i	0.471250	−	0.272076i	0.716763	+	0.697317i	$0.245623\pi$
$570$	−22318.6	−	23911.4i	−0.0686937	−	0.0735962i
$571$	227502.	−	394045.i	0.697770	−	1.20857i	−0.271467	−	0.962448i	$-0.587509\pi$
$571$	227502.	−	394045.i	0.697770	−	1.20857i	0.969238	−	0.246126i	$-0.0791577\pi$
$572$	196432.	−	340230.i	0.600371	−	1.03987i
$573$	−2757.05	+	51646.5i	−0.00839722	+	0.157301i
$574$	15415.4	+	26700.2i	0.0467876	+	0.0810384i
$575$	215139.	+	113598.i	0.650703	+	0.343586i
$576$	114587.	+	258719.i	0.345373	+	0.779800i
$577$			356530.i			1.07089i	0.844571	+	0.535444i	$0.179856\pi$
$577$			356530.i			1.07089i	−0.844571	+	0.535444i	$0.820144\pi$
$578$	−2766.63	−	4791.94i	−0.00828124	−	0.0143435i
$579$	50278.8	−	25556.7i	0.149978	−	0.0762339i
$580$	−95775.7	+	99464.7i	−0.284708	+	0.295674i
$581$	−504421.	−	291228.i	−1.49431	−	0.862740i
$582$	71372.1	−	36278.5i	0.210709	−	0.107103i
$583$	−514823.	+	297233.i	−1.51468	+	0.874501i
$584$		−	117339.i		−	0.344046i
$585$	−227972.	+	191094.i	−0.666146	+	0.558388i
$586$	95427.6			0.277894
$587$	253068.	+	438326.i	0.734447	+	1.27210i	0.954965	+	0.296717i	$0.0958919\pi$
$587$	253068.	+	438326.i	0.734447	+	1.27210i	−0.220518	+	0.975383i	$0.570775\pi$
$588$	−665474.	−	35525.1i	−1.92476	−	0.102750i
$589$	−71403.0	+	123674.i	−0.205819	+	0.356489i
$590$	30885.0	−	32074.6i	0.0887246	−	0.0921420i
$591$	−270560.	+	415739.i	−0.774619	+	1.19027i
$592$	149812.	−	86494.0i	0.427467	−	0.246798i
$593$	−412533.			−1.17314			−0.586570	−	0.809899i	$-0.699522\pi$
$593$	−412533.			−1.17314			−0.586570	+	0.809899i	$0.699522\pi$
$594$	−61337.4	−	49967.1i	−0.173841	−	0.141616i
$595$	561019.	+	139021.i	1.58469	+	0.392686i
$596$	176327.	−	101802.i	0.496394	−	0.286593i
$597$	50933.2	−	78263.5i	0.142907	−	0.219589i
$598$	31347.0	+	18098.2i	0.0876583	+	0.0506095i
$599$	−43173.5	−	24926.2i	−0.120327	−	0.0694708i	0.438628	−	0.898668i	$-0.355464\pi$
$599$	−43173.5	−	24926.2i	−0.120327	−	0.0694708i	−0.558956	+	0.829198i	$0.688798\pi$
$600$	96553.4	+	57765.1i	0.268204	+	0.160458i
$601$	−313761.	−	543450.i	−0.868660	−	1.50456i	−0.863367	−	0.504577i	$-0.831648\pi$
$601$	−313761.	−	543450.i	−0.868660	−	1.50456i	−0.00529310	−	0.999986i	$-0.501685\pi$
$602$	48421.3			0.133611
$603$	1473.06	−	13757.7i	0.00405122	−	0.0378366i
$604$	450581.			1.23509
$605$	−354356.	+	102162.i	−0.968119	+	0.279112i
$606$	69182.4	−	35165.5i	0.188387	−	0.0957572i
$607$	281368.	+	162448.i	0.763654	+	0.440896i	0.830606	−	0.556860i	$-0.187994\pi$
$607$	281368.	+	162448.i	0.763654	+	0.440896i	−0.0669521	+	0.997756i	$0.521327\pi$
$608$	53970.9	−	93480.4i	0.146000	−	0.252879i
$609$	122077.	+	240166.i	0.329153	+	0.647555i
$610$	80919.8	−	23329.4i	0.217468	−	0.0626967i
$611$			116466.i			0.311973i
$612$	−343563.	−	36785.8i	−0.917285	−	0.0982148i
$613$		−	53253.9i		−	0.141720i	−0.997486	−	0.0708599i	$-0.977426\pi$
$613$		−	53253.9i		−	0.141720i	0.997486	−	0.0708599i	$-0.0225743\pi$
$614$	−76870.8	+	44381.4i	−0.203903	+	0.117724i
$615$	123975.	+	37839.6i	0.327780	+	0.100045i
$616$	−144963.	+	251084.i	−0.382030	+	0.661695i
$617$	−186658.	+	323301.i	−0.490316	+	0.849252i	−0.999938	−	0.0111464i	$-0.996452\pi$
$617$	−186658.	+	323301.i	−0.490316	+	0.849252i	0.509622	+	0.860398i	$0.329785\pi$
$618$	−78052.1	−	50795.6i	−0.204365	−	0.132999i
$619$	−251035.	−	434806.i	−0.655169	−	1.13479i	−0.981851	−	0.189652i	$-0.939264\pi$
$619$	−251035.	−	434806.i	−0.655169	−	1.13479i	0.326683	−	0.945134i	$-0.394069\pi$
$620$	58327.7	−	235382.i	0.151737	−	0.612336i
$621$	−179226.	+	220010.i	−0.464748	+	0.570504i
$622$		−	120740.i		−	0.312084i
$623$	43593.8	+	75506.7i	0.112318	+	0.194540i
$624$	−262538.	−	170857.i	−0.674253	−	0.438798i
$625$	−389510.	+	29491.0i	−0.997146	+	0.0754969i
$626$	18457.6	+	10656.5i	0.0471006	+	0.0271935i
$627$	18889.7	−	353852.i	0.0480496	−	0.900090i
$628$	280846.	−	162147.i	0.712113	−	0.411139i
$629$			199661.i			0.504651i
$630$	83053.0	−	69618.2i	0.209254	−	0.175405i
$631$	−379130.			−0.952202			−0.476101	−	0.879391i	$-0.657950\pi$
$631$	−379130.			−0.952202			−0.476101	+	0.879391i	$0.657950\pi$
$632$	29336.9	+	50813.0i	0.0734481	+	0.127216i
$633$	211235.	+	415570.i	0.527179	+	1.03714i
$634$	24844.1	−	43031.3i	0.0618081	−	0.107055i
$635$	140558.	−	145972.i	0.348584	−	0.362010i
$636$	220584.	+	433963.i	0.545330	+	1.07285i
$637$	603879.	−	348649.i	1.48823	−	0.859231i
$638$	38424.8			0.0943996
$639$	207231.	−	91782.7i	0.507520	−	0.224781i
$640$	−58517.0	+	236146.i	−0.142864	+	0.576528i
$641$	325664.	−	188022.i	0.792599	−	0.457607i	−0.0482776	−	0.998834i	$-0.515373\pi$
$641$	325664.	−	188022.i	0.792599	−	0.457607i	0.840877	+	0.541227i	$0.182040\pi$
$642$	−87005.2	−	4644.60i	−0.211094	−	0.0112688i
$643$	−140867.	−	81329.8i	−0.340713	−	0.196711i	0.319874	−	0.947460i	$-0.396359\pi$
$643$	−140867.	−	81329.8i	−0.340713	−	0.196711i	−0.660587	+	0.750749i	$0.729693\pi$
$644$	444594.	+	256686.i	1.07199	+	0.618915i
$645$	148821.	−	138908.i	0.357722	−	0.333894i
$646$	19876.8	+	34427.6i	0.0476300	+	0.0824976i
$647$	−344019.			−0.821814			−0.410907	−	0.911677i	$-0.634788\pi$
$647$	−344019.			−0.821814			−0.410907	+	0.911677i	$0.634788\pi$
$648$	−88192.9	+	97185.1i	−0.210031	+	0.231446i
$649$	482389.			1.14527
$650$	−58075.6	+	2195.39i	−0.137457	+	0.00519620i
$651$	−396565.	−	258081.i	−0.935734	−	0.608967i
$652$	326862.	+	188714.i	0.768899	+	0.443924i
$653$	263282.	−	456018.i	0.617440	−	1.06944i	−0.372511	−	0.928028i	$-0.621503\pi$
$653$	263282.	−	456018.i	0.617440	−	1.06944i	0.989951	−	0.141410i	$-0.0451636\pi$
$654$	−17696.7	−	944.706i	−0.0413750	−	0.00220872i
$655$	40693.6	+	141149.i	0.0948513	+	0.328998i
$656$			136492.i			0.317175i
$657$	−434459.	+	192422.i	−1.00651	+	0.445783i
$658$		−	42430.1i		−	0.0979992i
$659$	−417516.	+	241053.i	−0.961396	+	0.555062i	−0.896602	−	0.442837i	$-0.853972\pi$
$659$	−417516.	+	241053.i	−0.961396	+	0.555062i	−0.0647933	+	0.997899i	$0.520639\pi$
$660$	135635.	+	586251.i	0.311374	+	1.34585i
$661$	−185973.	+	322114.i	−0.425644	+	0.737237i	−0.996480	−	0.0838268i	$-0.973286\pi$
$661$	−185973.	+	322114.i	−0.425644	+	0.737237i	0.570836	+	0.821064i	$0.306619\pi$
$662$	−54594.2	+	94559.9i	−0.124575	+	0.215770i
$663$	322291.	−	163821.i	0.733197	−	0.372685i
$664$	68901.6	+	119341.i	0.156276	+	0.270679i
$665$	471155.	+	116752.i	1.06542	+	0.264011i
$666$	30243.6	+	22063.3i	0.0681845	+	0.0497419i
$667$		−	137825.i		−	0.309796i
$668$	80870.7	+	140072.i	0.181233	+	0.313905i
$669$	−12331.3	+	230996.i	−0.0275521	+	0.516121i
$670$	1875.02	−	1947.24i	0.00417693	−	0.00433781i
$671$	790126.	+	456179.i	1.75489	+	1.01319i
$672$	299749.	+	195074.i	0.663772	+	0.431977i
$673$	−243512.	+	140592.i	−0.537638	+	0.310406i	−0.744121	−	0.668045i	$-0.767132\pi$
$673$	−243512.	+	140592.i	−0.537638	+	0.310406i	0.206483	+	0.978450i	$0.433798\pi$
$674$		−	20446.0i		−	0.0450078i
$675$	55544.8	−	452227.i	0.121909	−	0.992541i
$676$	−108911.			−0.238330
$677$	−134768.	−	233424.i	−0.294041	−	0.509295i	0.680720	−	0.732544i	$-0.261667\pi$
$677$	−134768.	−	233424.i	−0.294041	−	0.509295i	−0.974761	+	0.223249i	$0.928334\pi$
$678$	24987.0	−	38394.8i	0.0543569	−	0.0835243i
$679$	−594074.	+	1.02897e6i	−1.28855	+	2.23183i
$680$	−98503.6	−	94850.3i	−0.213027	−	0.205126i
$681$	307623.	+	16421.9i	0.663322	+	0.0354102i
$682$	−58441.8	+	33741.4i	−0.125648	+	0.0725428i
$683$	−425001.			−0.911063			−0.455531	−	0.890220i	$-0.650551\pi$
$683$	−425001.			−0.911063			−0.455531	+	0.890220i	$0.650551\pi$
$684$	−288531.	−	30893.4i	−0.616710	−	0.0660319i
$685$	210758.	−	850516.i	0.449162	−	1.81260i
$686$	−108721.	+	62770.3i	−0.231029	+	0.133385i
$687$	21369.1	+	42040.3i	0.0452766	+	0.0890743i
$688$	185648.	+	107184.i	0.392205	+	0.226440i
$689$	−441121.	−	254681.i	−0.929221	−	0.536486i
$690$	−54014.0	+	12496.7i	−0.113451	+	0.0262480i
$691$	−204712.	−	354571.i	−0.428732	−	0.742586i	0.568028	−	0.823009i	$-0.307706\pi$
$691$	−204712.	−	354571.i	−0.428732	−	0.742586i	−0.996761	+	0.0804226i	$0.974373\pi$
$692$	−596329.			−1.24530
$693$	1.16739e6	+	124994.i	2.43079	+	0.260268i
$694$	147018.			0.305247
$695$	287948.	−	83016.4i	0.596135	−	0.171868i
$696$	3397.80	−	63649.5i	0.00701423	−	0.131394i
$697$	−136431.	−	78768.7i	−0.280834	−	0.162139i
$698$	−52525.1	+	90976.2i	−0.107809	+	0.186731i
$699$	−218979.	+	336481.i	−0.448175	+	0.688662i
$700$	−823686.	+	31137.3i	−1.68099	+	0.0635455i
$701$		−	590764.i		−	1.20220i	−0.799172	−	0.601102i	$-0.794728\pi$
$701$		−	590764.i		−	1.20220i	0.799172	−	0.601102i	$-0.205272\pi$
$702$	10799.6	−	66921.9i	0.0219147	−	0.135798i
$703$			167679.i			0.339288i
$704$	−518665.	+	299451.i	−1.04651	+	0.604201i
$705$	−121721.	−	130408.i	−0.244899	−	0.262377i
$706$	40885.9	−	70816.5i	0.0820285	−	0.142077i
$707$	−575848.	+	997398.i	−1.15204	+	1.99540i
$708$	21057.8	−	394466.i	0.0420094	−	0.786942i
$709$	−143727.	−	248942.i	−0.285920	−	0.495228i	0.686912	−	0.726741i	$-0.258966\pi$
$709$	−143727.	−	248942.i	−0.285920	−	0.495228i	−0.972832	+	0.231513i	$0.925632\pi$
$710$	42980.4	+	10650.5i	0.0852616	+	0.0211278i
$711$	140031.	−	191950.i	0.277004	−	0.379708i
$712$		−	20627.7i		−	0.0406904i
$713$	121026.	+	209624.i	0.238068	+	0.412346i
$714$	−117415.	+	59682.0i	−0.230317	+	0.117070i
$715$	−453537.	−	436716.i	−0.887158	−	0.854255i
$716$	−392610.	−	226673.i	−0.765835	−	0.442155i
$717$	−289466.	+	147136.i	−0.563065	+	0.286207i
$718$	−112582.	+	64999.2i	−0.218383	+	0.126084i
$719$			645625.i			1.24889i	0.781070	+	0.624443i	$0.214674\pi$
$719$			645625.i			1.24889i	−0.781070	+	0.624443i	$0.785326\pi$
$720$	472531.	−	83073.3i	0.911518	−	0.160249i
$721$	1.38199e6			2.65849
$722$	−24553.9	−	42528.6i	−0.0471027	−	0.0815843i
$723$	−305893.	−	16329.5i	−0.585185	−	0.0312390i
$724$	186019.	−	322194.i	0.354878	−	0.614668i
$725$	117807.	+	187329.i	0.224127	+	0.356392i
$726$	45840.0	−	70437.3i	0.0869703	−	0.133638i
$727$	462909.	−	267261.i	0.875844	−	0.505669i	0.00655839	−	0.999978i	$-0.497912\pi$
$727$	462909.	−	267261.i	0.875844	−	0.505669i	0.869286	+	0.494310i	$0.164579\pi$
$728$	−248420.			−0.468732
$729$	504464.	+	167171.i	0.949237	+	0.314562i
$730$	−90108.0	−	22328.8i	−0.169090	−	0.0419005i
$731$	−214273.	+	123710.i	−0.400989	+	0.231511i
$732$	407524.	−	626198.i	0.760556	−	1.16866i
$733$	163651.	+	94483.8i	0.304586	+	0.175853i	0.644501	−	0.764603i	$-0.277065\pi$
$733$	163651.	+	94483.8i	0.304586	+	0.175853i	−0.339915	+	0.940456i	$0.610398\pi$
$734$	−56856.4	−	32826.1i	−0.105533	−	0.0609294i
$735$	−311786.	+	1.02151e6i	−0.577140	+	1.89089i
$736$	−91479.3	−	158447.i	−0.168876	−	0.292501i
$737$	29285.7			0.0539164
$738$	−27007.7	+	11961.7i	−0.0495879	+	0.0219625i
$739$	−683135.			−1.25089			−0.625443	−	0.780270i	$-0.715082\pi$
$739$	−683135.			−1.25089			−0.625443	+	0.780270i	$0.715082\pi$
$740$	−78878.3	−	273595.i	−0.144044	−	0.499625i
$741$	270666.	−	137580.i	0.492944	−	0.250564i
$742$	160706.	+	92783.6i	0.291893	+	0.168525i
$743$	150819.	−	261226.i	0.273198	−	0.473193i	−0.696481	−	0.717576i	$-0.745252\pi$
$743$	150819.	−	261226.i	0.273198	−	0.473193i	0.969679	+	0.244382i	$0.0785851\pi$
$744$	50723.7	+	99790.8i	0.0916359	+	0.180279i
$745$	−90393.0	−	313534.i	−0.162863	−	0.564901i
$746$			114164.i			0.205141i
$747$	328882.	−	450821.i	0.589385	−	0.807909i
$748$		−	731334.i		−	1.30711i
$749$	1.11978e6	−	646504.i	1.99603	−	1.15241i
$750$	62733.0	−	63154.0i	0.111525	−	0.112274i
$751$	−115004.	+	199192.i	−0.203907	+	0.353177i	−0.949784	−	0.312906i	$-0.898697\pi$
$751$	−115004.	+	199192.i	−0.203907	+	0.353177i	0.745877	+	0.666084i	$0.232031\pi$
$752$	93922.0	−	162678.i	0.166085	−	0.287669i
$753$	456219.	+	296903.i	0.804606	+	0.523631i
$754$	16461.9	+	28512.9i	0.0289559	+	0.0501532i
$755$	173688.	−	700918.i	0.304702	−	1.22963i
$756$	153171.	−	949154.i	0.267999	−	1.66071i
$757$		−	897739.i		−	1.56660i	−0.621644	−	0.783300i	$-0.713535\pi$
$757$		−	897739.i		−	1.56660i	0.621644	−	0.783300i	$-0.286465\pi$
$758$	−45946.1	−	79580.9i	−0.0799668	−	0.138507i
$759$	−503407.	−	327613.i	−0.873847	−	0.568692i
$760$	−82725.3	−	79657.1i	−0.143222	−	0.137911i
$761$	−343014.	−	198039.i	−0.592301	−	0.341965i	0.173706	−	0.984798i	$-0.444426\pi$
$761$	−343014.	−	198039.i	−0.592301	−	0.341965i	−0.766007	+	0.642833i	$0.777759\pi$
$762$	−2461.64	+	46112.8i	−0.00423951	+	0.0794167i
$763$	227761.	−	131498.i	0.391229	−	0.225876i
$764$			89644.1i			0.153580i
$765$	−189658.	+	520263.i	−0.324078	+	0.888996i
$766$	−71806.5			−0.122379
$767$	206665.	+	357954.i	0.351298	+	0.608467i
$768$	202817.	+	399009.i	0.343860	+	0.676488i
$769$	−96241.3	+	166695.i	−0.162745	+	0.281883i	−0.935852	−	0.352392i	$-0.885368\pi$
$769$	−96241.3	+	166695.i	−0.162745	+	0.281883i	0.773107	+	0.634276i	$0.218702\pi$
$770$	165229.	+	159101.i	0.278680	+	0.268344i
$771$	−62148.7	−	122268.i	−0.104550	−	0.205685i
$772$	84660.7	−	48878.9i	0.142052	−	0.0820138i
$773$	−542226.			−0.907447			−0.453723	−	0.891143i	$-0.649905\pi$
$773$	−542226.			−0.907447			−0.453723	+	0.891143i	$0.649905\pi$
$774$	−4938.93	+	46127.5i	−0.00824425	+	0.0769978i
$775$	−343673.	−	181468.i	−0.572193	−	0.302131i
$776$	243444.	−	140552.i	0.404273	−	0.233407i
$777$	−554768.	−	29615.2i	−0.918903	−	0.0490538i
$778$	−145173.	−	83815.8i	−0.239843	−	0.138474i
$779$	−114578.	−	66151.5i	−0.188810	−	0.109010i
$780$	−376916.	+	351808.i	−0.619519	+	0.578251i
$781$	239858.	+	415446.i	0.393234	+	0.681102i
$782$	67381.2			0.110186
$783$	−241241.	+	91796.9i	−0.393484	+	0.149729i
$784$	−1.12465e6			−1.82972
$785$	−143974.	−	499384.i	−0.233639	−	0.810392i
$786$	−28056.9	−	18259.2i	−0.0454145	−	0.0295554i
$787$	852809.	+	492370.i	1.37690	+	0.794954i	0.991785	−	0.127915i	$-0.0408285\pi$
$787$	852809.	+	492370.i	1.37690	+	0.794954i	0.385115	+	0.922869i	$0.374162\pi$
$788$	−429870.	+	744557.i	−0.692285	+	1.19907i
$789$	58073.9	+	3100.17i	0.0932883	+	0.00498002i
$790$	44603.5	−	12859.3i	0.0714685	−	0.0206046i
$791$			679819.i			1.08653i
$792$	−224404.	−	163707.i	−0.357750	−	0.260985i
$793$			781744.i			1.24313i
$794$	45336.2	−	26174.8i	0.0719124	−	0.0415186i
$795$	760096.	−	175855.i	1.20264	−	0.278241i
$796$	80923.6	−	140164.i	0.127717	−	0.221213i
$797$	−455717.	+	789324.i	−0.717428	+	1.24262i	0.244588	+	0.969627i	$0.421347\pi$
$797$	−455717.	+	789324.i	−0.717428	+	1.24262i	−0.962016	+	0.272994i	$0.911986\pi$
$798$	−98607.2	+	50122.1i	−0.154847	+	0.0787089i
$799$	108404.	+	187761.i	0.169805	+	0.294111i
$800$	259770.	+	137165.i	0.405891	+	0.214320i
$801$	−76376.3	+	33827.1i	−0.119040	+	0.0527229i
$802$			15253.1i			0.0237142i
$803$	−502860.	−	870979.i	−0.779859	−	1.35075i
$804$	1278.41	−	23947.9i	0.00197769	−	0.0370472i
$805$	570678.	−	592658.i	0.880641	−	0.914561i
$806$	−50075.2	−	28910.9i	−0.0770819	−	0.0445033i
$807$	−583284.	−	379596.i	−0.895639	−	0.582874i
$808$	235975.	−	136240.i	0.361446	−	0.208681i
$809$			485562.i			0.741904i	0.928652	+	0.370952i	$0.120969\pi$
$809$			485562.i			0.741904i	−0.928652	+	0.370952i	$0.879031\pi$
$810$	57848.9	+	86219.7i	0.0881708	+	0.131412i
$811$	157252.			0.239087			0.119543	−	0.992829i	$-0.461857\pi$
$811$	157252.			0.239087			0.119543	+	0.992829i	$0.461857\pi$
$812$	233479.	+	404398.i	0.354109	+	0.613334i
$813$	−28752.5	+	44180.9i	−0.0435005	+	0.0668425i
$814$	−39618.2	+	68620.8i	−0.0597924	+	0.103564i
$815$	419558.	−	435718.i	0.631650	−	0.655979i
$816$	−582280.	−	31083.9i	−0.874483	−	0.0466826i
$817$	−179951.	+	103895.i	−0.269593	+	0.155650i
$818$	105468.			0.157622
$819$	407380.	+	919802.i	0.607340	+	1.37128i
$820$	218070.	+	54037.9i	0.324316	+	0.0803657i
$821$	−492419.	+	284298.i	−0.730548	+	0.421782i	−0.818623	−	0.574332i	$-0.805262\pi$
$821$	−492419.	+	284298.i	−0.730548	+	0.421782i	0.0880747	+	0.996114i	$0.471929\pi$
$822$	90479.1	+	178003.i	0.133907	+	0.263441i
$823$	−621801.	−	358997.i	−0.918019	−	0.530018i	−0.0350164	−	0.999387i	$-0.511148\pi$
$823$	−621801.	−	358997.i	−0.918019	−	0.530018i	−0.883002	+	0.469368i	$0.844482\pi$
$824$	−283161.	−	163483.i	−0.417041	−	0.240779i
$825$	964248.	+	14993.4i	1.41671	+	0.0220289i
$826$	−75290.7	−	130407.i	−0.110352	−	0.191136i
$827$	−39891.9			−0.0583275			−0.0291638	−	0.999575i	$-0.509284\pi$
$827$	−39891.9			−0.0583275			−0.0291638	+	0.999575i	$0.509284\pi$
$828$	−289875.	+	397351.i	−0.422815	+	0.579580i
$829$	1.05219e6			1.53103			0.765515	−	0.643418i	$-0.222484\pi$
$829$	1.05219e6			1.53103			0.765515	+	0.643418i	$0.222484\pi$
$830$	104757.	−	30201.8i	0.152064	−	0.0438407i
$831$	−25088.5	+	469971.i	−0.0363306	+	0.680564i
$832$	−444412.	−	256582.i	−0.642007	−	0.370663i
$833$	649028.	−	1.12415e6i	0.935348	−	1.62007i
$834$	−37249.4	+	57237.1i	−0.0535534	+	0.0822897i
$835$	249068.	−	71807.1i	0.357227	−	0.102990i
$836$		−	614189.i		−	0.878799i
$837$	286304.	−	351455.i	0.408674	−	0.501671i
$838$			68363.3i			0.0973498i
$839$	−849479.	+	490447.i	−1.20678	+	0.696736i	−0.962055	−	0.272856i	$-0.912032\pi$
$839$	−849479.	+	490447.i	−1.20678	+	0.696736i	−0.244727	+	0.969592i	$0.578698\pi$
$840$	278157.	−	259629.i	0.394214	−	0.367954i
$841$	−290958.	+	503955.i	−0.411376	+	0.712524i
$842$	81926.5	−	141901.i	0.115558	−	0.200153i
$843$	5029.14	−	94208.6i	0.00707683	−	0.132567i
$844$	404000.	+	699749.i	0.567148	+	0.982329i
$845$	−41982.5	+	169421.i	−0.0587970	+	0.237276i
$846$	40420.1	+	4327.84i	0.0564751	+	0.00604686i
$847$			1.24717e6i			1.73843i
$848$	410766.	+	711467.i	0.571219	+	0.989380i
$849$	44594.5	−	22667.4i	0.0618680	−	0.0314476i
$850$	−91583.0	+	57594.5i	−0.126758	+	0.0797156i
$851$	246135.	+	142106.i	0.339870	+	0.196224i
$852$	350194.	−	178004.i	0.482425	−	0.245217i
$853$	−608193.	+	351140.i	−0.835879	+	0.482595i	−0.855861	−	0.517205i	$-0.826972\pi$
$853$	−608193.	+	351140.i	−0.835879	+	0.482595i	0.0199823	+	0.999800i	$0.493639\pi$
$854$		−	284799.i		−	0.390502i
$855$	−159279.	+	436927.i	−0.217884	+	0.597691i
$856$	−305913.			−0.417494
$857$	−258863.	−	448364.i	−0.352459	−	0.610476i	0.634221	−	0.773152i	$-0.281321\pi$
$857$	−258863.	−	448364.i	−0.352459	−	0.610476i	−0.986680	+	0.162676i	$0.947988\pi$
$858$	143274.	+	7648.39i	0.194622	+	0.0103895i
$859$	324805.	−	562579.i	0.440186	−	0.762425i	−0.557517	−	0.830166i	$-0.688246\pi$
$859$	324805.	−	562579.i	0.440186	−	0.762425i	0.997703	+	0.0677408i	$0.0215791\pi$
$860$	244745.	−	254171.i	0.330915	−	0.343661i
$861$	239100.	−	367399.i	0.322532	−	0.495600i
$862$	44434.0	−	25654.0i	0.0598000	−	0.0345255i
$863$	1.39346e6			1.87100			0.935499	−	0.353329i	$-0.114950\pi$
$863$	1.39346e6			1.87100			0.935499	+	0.353329i	$0.114950\pi$
$864$	−216407.	+	265652.i	−0.289897	+	0.355865i
$865$	−229870.	+	927642.i	−0.307220	+	1.23979i
$866$	−95267.2	+	55002.6i	−0.127030	+	0.0733410i
$867$	−42911.7	+	65937.8i	−0.0570871	+	0.0877195i
$868$	−710217.	−	410044.i	−0.942652	−	0.544240i
$869$	435522.	+	251449.i	0.576728	+	0.332974i
$870$	−48231.8	−	14721.3i	−0.0637228	−	0.0194495i
$871$	12546.6	+	21731.3i	0.0165382	+	0.0286450i
$872$	−62222.3			−0.0818301
$873$	−919628.	−	670886.i	−1.20666	−	0.880278i
$874$	56588.1			0.0740802
$875$	−269073.	+	1.29332e6i	−0.351443	+	1.68923i
$876$	−734179.	+	373184.i	−0.956740	+	0.486312i
$877$	642695.	+	371060.i	0.835614	+	0.482442i	0.855771	−	0.517355i	$-0.173083\pi$
$877$	642695.	+	371060.i	0.835614	+	0.482442i	−0.0201572	+	0.999797i	$0.506417\pi$
$878$	−81935.6	+	141917.i	−0.106288	+	0.184096i
$879$	−614791.	−	1.20950e6i	−0.795701	−	1.56541i
$880$	281310.	+	975744.i	0.363262	+	1.26000i
$881$		−	737962.i		−	0.950784i	−0.879774	−	0.475392i	$-0.842306\pi$
$881$		−	737962.i		−	0.950784i	0.879774	−	0.475392i	$-0.157694\pi$
$882$	−98560.5	−	222535.i	−0.126697	−	0.286062i
$883$			143168.i			0.183622i	0.995776	+	0.0918109i	$0.0292655\pi$
$883$			143168.i			0.183622i	−0.995776	+	0.0918109i	$0.970734\pi$
$884$	542682.	−	313318.i	0.694450	−	0.400941i
$885$	−605508.	−	184814.i	−0.773096	−	0.235965i
$886$	60915.4	−	105509.i	0.0775996	−	0.134406i
$887$	504758.	−	874267.i	0.641559	−	1.11121i	−0.343526	−	0.939143i	$-0.611621\pi$
$887$	504758.	−	874267.i	0.641559	−	1.11121i	0.985085	−	0.172069i	$-0.0550452\pi$
$888$	110165.	+	71694.4i	0.139707	+	0.0909199i
$889$	−342648.	−	593483.i	−0.433555	−	0.750939i
$890$	−15840.7	−	3925.32i	−0.0199983	−	0.00495559i
$891$	−238145.	+	1.09934e6i	−0.299975	+	1.38476i
$892$			400945.i			0.503912i
$893$	91039.6	+	157685.i	0.114164	+	0.197737i
$894$	62323.0	+	40559.2i	0.0779782	+	0.0507475i
$895$	−503951.	+	523362.i	−0.629133	+	0.653365i
$896$	712521.	+	411374.i	0.887527	+	0.512414i
$897$	27433.9	−	513906.i	0.0340959	−	0.638702i
$898$	−31122.7	+	17968.7i	−0.0385944	+	0.0222825i
$899$			220169.i			0.272418i
$900$	54353.0	−	787842.i	0.0671024	−	0.972645i
$901$	−948202.			−1.16802
$902$	−31259.8	−	54143.6i	−0.0384214	−	0.0665478i
$903$	−311954.	−	613719.i	−0.382573	−	0.752651i
$904$	80419.4	−	139290.i	0.0984065	−	0.170445i
$905$	−429495.	−	413566.i	−0.524398	−	0.504949i
$906$	74564.7	+	146694.i	0.0908399	+	0.178713i
$907$	415123.	−	239672.i	0.504618	−	0.291341i	−0.226001	−	0.974127i	$-0.572565\pi$
$907$	415123.	−	239672.i	0.504618	−	0.291341i	0.730618	+	0.682786i	$0.239232\pi$
$908$	533949.			0.647631
$909$	−891414.	−	650303.i	−1.07883	−	0.787024i
$910$	−47272.8	+	190770.i	−0.0570858	+	0.230370i
$911$	755164.	−	435994.i	0.909923	−	0.525344i	0.0295167	−	0.999564i	$-0.490603\pi$
$911$	755164.	−	435994.i	0.909923	−	0.525344i	0.880406	+	0.474220i	$0.157270\pi$
$912$	−489010.	−	26104.9i	−0.587933	−	0.0313857i
$913$	1.02288e6	+	590561.i	1.22711	+	0.708473i
$914$	171605.	+	99076.1i	0.205417	+	0.118598i
$915$	−817015.	−	875322.i	−0.975860	−	1.04550i
$916$	40869.8	+	70788.6i	0.0487093	+	0.0843670i
$917$	496776.			0.590775
$918$	−44878.6	−	117940.i	−0.0532542	−	0.139951i
$919$	411896.			0.487705			0.243852	−	0.969812i	$-0.421589\pi$
$919$	411896.			0.487705			0.243852	+	0.969812i	$0.421589\pi$
$920$	−187037.	+	53923.3i	−0.220979	+	0.0637089i
$921$	1.05775e6	+	688376.i	1.24700	+	0.811533i
$922$	33861.9	+	19550.2i	0.0398336	+	0.0229979i
$923$	−205519.	+	355970.i	−0.241240	+	0.417840i
$924$	2.03205e6	+	108477.i	2.38008	+	0.127056i
$925$	−456006.	+	17238.1i	−0.532951	+	0.0201468i
$926$		−	107430.i		−	0.125286i
$927$	−140962.	+	1.31652e6i	−0.164037	+	1.53204i
$928$		−	166417.i		−	0.193243i
$929$	756603.	−	436825.i	0.876671	−	0.506146i	0.00711192	−	0.999975i	$-0.497736\pi$
$929$	756603.	−	436825.i	0.876671	−	0.506146i	0.869559	+	0.493828i	$0.164403\pi$
$930$	86284.8	−	19962.8i	0.0997627	−	0.0230810i
$931$	545066.	−	944083.i	0.628854	−	1.08921i
$932$	−347918.	+	602611.i	−0.400539	+	0.693753i
$933$	−1.53033e6	+	777867.i	−1.75801	+	0.893597i
$934$	24254.6	+	42010.1i	0.0278035	+	0.0481571i
$935$	−1.13765e6	−	281911.i	−1.30133	−	0.322469i
$936$	25338.7	−	236652.i	0.0289222	−	0.270121i
$937$		−	271368.i		−	0.309086i	−0.987986	−	0.154543i	$-0.950609\pi$
$937$		−	271368.i		−	0.309086i	0.987986	−	0.154543i	$-0.0493906\pi$
$938$	−4570.88	−	7916.99i	−0.00519510	−	0.00899817i
$939$	16153.5	−	302596.i	0.0183204	−	0.343188i
$940$	−222723.	−	214462.i	−0.252063	−	0.242714i
$941$	554563.	+	320177.i	0.626284	+	0.361585i	0.779312	−	0.626636i	$-0.215569\pi$
$941$	554563.	+	320177.i	0.626284	+	0.361585i	−0.153027	+	0.988222i	$0.548902\pi$
$942$	99265.4	+	64601.0i	0.111865	+	0.0728010i
$943$	−194207.	+	112125.i	−0.218394	+	0.126090i
$944$		−	666644.i		−	0.748084i
$945$	−1.41745e6	−	604146.i	−1.58724	−	0.676516i
$946$	−98190.4			−0.109720
$947$	−257159.	−	445412.i	−0.286749	−	0.496663i	0.686283	−	0.727335i	$-0.259241\pi$
$947$	−257159.	−	445412.i	−0.286749	−	0.496663i	−0.973032	+	0.230671i	$0.925908\pi$
$948$	224630.	−	345164.i	0.249949	−	0.384069i
$949$	430870.	−	746288.i	0.478425	−	0.828656i
$950$	−76913.2	+	48369.0i	−0.0852224	+	0.0535945i
$951$	−705460.	−	37659.6i	−0.780031	−	0.0416404i
$952$	−400491.	+	231223.i	−0.441894	+	0.255128i
$953$	926631.			1.02028			0.510142	−	0.860090i	$-0.329593\pi$
$953$	926631.			1.02028			0.510142	+	0.860090i	$0.329593\pi$
$954$	−104780.	+	143629.i	−0.115128	+	0.157814i
$955$	139449.	+	34555.5i	0.152901	+	0.0378888i
$956$	−487410.	+	281406.i	−0.533309	+	0.307906i
$957$	−247551.	−	487017.i	−0.270297	−	0.531765i
$958$	−19263.4	−	11121.7i	−0.0209895	−	0.0121183i
$959$	−2.56626e6	−	1.48163e6i	−2.79038	−	1.61102i
$960$	765768.	−	177168.i	0.830912	−	0.192239i
$961$	268427.	+	464929.i	0.290656	+	0.503431i
$962$	−67892.9			−0.0733625
$963$	501662.	+	1.13267e6i	0.540951	+	1.22138i
$964$	−530946.			−0.571343
$965$	−43400.8	−	150539.i	−0.0466061	−	0.161657i
$966$	−9994.51	+	187222.i	−0.0107104	+	0.200634i
$967$	−236777.	−	136703.i	−0.253213	−	0.146193i	0.368022	−	0.929817i	$-0.380035\pi$
$967$	−236777.	−	136703.i	−0.253213	−	0.146193i	−0.621235	+	0.783625i	$0.713369\pi$
$968$	147534.	−	255536.i	0.157449	−	0.272710i
$969$	308298.	−	473728.i	0.328340	−	0.504524i
$970$	−61608.7	−	213694.i	−0.0654784	−	0.227117i
$971$		−	952676.i		−	1.01043i	−0.862993	−	0.505215i	$-0.831413\pi$
$971$		−	952676.i		−	1.01043i	0.862993	−	0.505215i	$-0.168587\pi$
$972$	888567.	+	242728.i	0.940498	+	0.256914i
$973$		−	1.01344e6i		−	1.07047i
$974$	159461.	−	92065.0i	0.168088	−	0.0970457i
$975$	401977.	+	721938.i	0.422855	+	0.759435i
$976$	630423.	−	1.09192e6i	0.661808	−	1.14629i
$977$	551504.	−	955232.i	0.577776	−	1.00074i	−0.417958	−	0.908466i	$-0.637254\pi$
$977$	551504.	−	955232.i	0.577776	−	1.00074i	0.995734	−	0.0922705i	$-0.0294125\pi$
$978$	−7347.89	+	137645.i	−0.00768219	+	0.143907i
$979$	−88401.0	−	153115.i	−0.0922341	−	0.159754i
$980$	−445254.	+	1.79683e6i	−0.463613	+	1.87091i
$981$	102037.	+	230384.i	0.106028	+	0.239395i
$982$		−	280805.i		−	0.291193i
$983$	−572312.	−	991274.i	−0.592278	−	1.02586i	−0.993925	−	0.110062i	$-0.964895\pi$
$983$	−572312.	−	991274.i	−0.592278	−	1.02586i	0.401646	−	0.915795i	$-0.368438\pi$
$984$	−92451.4	+	46993.2i	−0.0954824	+	0.0485338i
$985$	992518.	+	955708.i	1.02298	+	0.985037i
$986$	53078.1	+	30644.6i	0.0545961	+	0.0315211i
$987$	−537783.	+	273356.i	−0.552043	+	0.280604i
$988$	455755.	−	263130.i	0.466893	−	0.269561i
$989$			352197.i			0.360075i
$990$	−168418.	+	141174.i	−0.171837	+	0.144040i
$991$	−320938.			−0.326794			−0.163397	−	0.986560i	$-0.552245\pi$
$991$	−320938.			−0.326794			−0.163397	+	0.986560i	$0.552245\pi$
$992$	146134.	+	253111.i	0.148500	+	0.257210i
$993$	1.55023e6	+	82755.8i	1.57216	+	0.0839267i
$994$	74873.3	−	129684.i	0.0757800	−	0.131255i
$995$	−186843.	−	179913.i	−0.188725	−	0.181726i
$996$	527573.	−	810664.i	0.531819	−	0.817188i
$997$	−863459.	+	498518.i	−0.868663	+	0.501523i	−0.866904	−	0.498475i	$-0.833893\pi$
$997$	−863459.	+	498518.i	−0.868663	+	0.501523i	−0.00175952	+	0.999998i	$0.500560\pi$
$998$	183142.			0.183877
$999$	84798.2	−	525467.i	0.0849680	−	0.526520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.12	yes	44
3.2	odd	2		135.5.h.a.44.11		44
5.4	even	2	inner	45.5.h.a.14.11	✓	44
9.2	odd	6	inner	45.5.h.a.29.11	yes	44
9.4	even	3		405.5.d.a.404.21		44
9.5	odd	6		405.5.d.a.404.23		44
9.7	even	3		135.5.h.a.89.12		44
15.14	odd	2		135.5.h.a.44.12		44
45.4	even	6		405.5.d.a.404.24		44
45.14	odd	6		405.5.d.a.404.22		44
45.29	odd	6	inner	45.5.h.a.29.12	yes	44
45.34	even	6		135.5.h.a.89.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.11	✓	44	5.4	even	2	inner
45.5.h.a.14.12	yes	44	1.1	even	1	trivial
45.5.h.a.29.11	yes	44	9.2	odd	6	inner
45.5.h.a.29.12	yes	44	45.29	odd	6	inner
135.5.h.a.44.11		44	3.2	odd	2
135.5.h.a.44.12		44	15.14	odd	2
135.5.h.a.89.11		44	45.34	even	6
135.5.h.a.89.12		44	9.7	even	3
405.5.d.a.404.21		44	9.4	even	3
405.5.d.a.404.22		44	45.14	odd	6
405.5.d.a.404.23		44	9.5	odd	6
405.5.d.a.404.24		44	45.4	even	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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.316502 + 0.548197i) q^{2} +(4.90909 - 7.54326i) q^{3} +(7.79965 - 13.5094i) q^{4} +(-18.0085 - 17.3406i) q^{5} +(5.68893 + 0.303692i) q^{6} +(-73.2178 + 42.2723i) q^{7} +20.0025 q^{8} +(-32.8017 - 74.0611i) q^{9} +(3.80633 - 15.3605i) q^{10} +(148.474 - 85.7213i) q^{11} +(-63.6157 - 125.154i) q^{12} +(127.218 + 73.4493i) q^{13} +(-46.3471 - 26.7585i) q^{14} +(-219.210 + 50.7162i) q^{15} +(-118.464 - 205.185i) q^{16} +273.459 q^{17} +(30.2183 - 41.4222i) q^{18} +229.656 q^{19} +(-374.720 + 108.033i) q^{20} +(-40.5615 + 759.820i) q^{21} +(93.9843 + 54.2618i) q^{22} +(194.631 - 337.110i) q^{23} +(98.1939 - 150.884i) q^{24} +(23.6096 + 624.554i) q^{25} +92.9873i q^{26} +(-719.689 - 116.141i) q^{27} +1318.84i q^{28} +(306.632 - 177.034i) q^{29} +(-97.1827 - 104.118i) q^{30} +(-310.913 + 538.517i) q^{31} +(235.008 - 407.045i) q^{32} +(82.2521 - 1540.79i) q^{33} +(86.5501 + 149.909i) q^{34} +(2051.57 + 508.379i) q^{35} +(-1256.36 - 134.520i) q^{36} +730.131i q^{37} +(72.6865 + 125.897i) q^{38} +(1178.57 - 599.069i) q^{39} +(-360.214 - 346.854i) q^{40} +(-498.910 - 288.046i) q^{41} +(-429.369 + 218.249i) q^{42} +(-783.565 + 452.392i) q^{43} -2674.39i q^{44} +(-693.554 + 1902.53i) q^{45} +246.404 q^{46} +(396.417 + 686.614i) q^{47} +(-2129.31 - 113.669i) q^{48} +(2373.40 - 4110.85i) q^{49} +(-334.906 + 210.615i) q^{50} +(1342.43 - 2062.77i) q^{51} +(1984.51 - 1145.76i) q^{52} -3467.44 q^{53} +(-164.115 - 431.290i) q^{54} +(-4160.24 - 1030.91i) q^{55} +(-1464.54 + 845.551i) q^{56} +(1127.40 - 1732.36i) q^{57} +(194.099 + 112.063i) q^{58} +(2436.74 + 1406.85i) q^{59} +(-1024.61 + 3356.96i) q^{60} +(2660.83 + 4608.69i) q^{61} -393.618 q^{62} +(5532.41 + 4035.99i) q^{63} -3493.32 q^{64} +(-1017.35 - 3528.74i) q^{65} +(870.688 - 442.572i) q^{66} +(147.934 + 85.4097i) q^{67} +(2132.88 - 3694.26i) q^{68} +(-1587.45 - 3123.05i) q^{69} +(370.633 + 1285.57i) q^{70} +2798.11i q^{71} +(-656.114 - 1481.40i) q^{72} -5866.22i q^{73} +(-400.255 + 231.088i) q^{74} +(4827.08 + 2887.90i) q^{75} +(1791.24 - 3102.52i) q^{76} +(-7247.28 + 12552.7i) q^{77} +(701.428 + 456.483i) q^{78} +(1466.67 + 2540.34i) q^{79} +(-1424.68 + 5749.29i) q^{80} +(-4409.10 + 4858.66i) q^{81} -364.668i q^{82} +(3444.66 + 5966.32i) q^{83} +(9948.35 + 6474.30i) q^{84} +(-4924.57 - 4741.93i) q^{85} +(-495.999 - 286.365i) q^{86} +(169.869 - 3182.08i) q^{87} +(2969.84 - 1714.64i) q^{88} -1031.26i q^{89} +(-1262.47 + 221.949i) q^{90} -12419.5 q^{91} +(-3036.10 - 5258.68i) q^{92} +(2535.88 + 4988.93i) q^{93} +(-250.933 + 434.629i) q^{94} +(-4135.75 - 3982.37i) q^{95} +(-1916.77 - 3770.94i) q^{96} +(12170.7 - 7026.75i) q^{97} +3004.74 q^{98} +(-11218.8 - 8184.32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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