LMFDB - Embedded newform 30.5.b.a.29.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,5,Mod(29,30)] 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("30.29"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	30.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.10109889252$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 80x^{6} + 2612x^{4} + 38240x^{2} + 256036 $ x^8 + 80x^6 + 2612x^4 + 38240*x^2 + 256036
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.8
Root			$1.41421 - 3.69234i$ of defining polynomial
Character	$\chi$	$=$	30.29
Dual form			30.5.b.a.29.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.82843 q^{2} +(7.33029 + 5.22176i) q^{3} +8.00000 q^{4} +(-10.6772 + 22.6053i) q^{5} +(20.7332 + 14.7694i) q^{6} -65.2135i q^{7} +22.6274 q^{8} +(26.4664 + 76.5541i) q^{9} +(-30.1996 + 63.9373i) q^{10} -43.4057i q^{11} +(58.6423 + 41.7741i) q^{12} -156.653i q^{13} -184.452i q^{14} +(-196.306 + 109.950i) q^{15} +64.0000 q^{16} -185.403 q^{17} +(74.8583 + 216.528i) q^{18} -503.597 q^{19} +(-85.4174 + 180.842i) q^{20} +(340.530 - 478.034i) q^{21} -122.770i q^{22} +285.809 q^{23} +(165.866 + 118.155i) q^{24} +(-396.996 - 482.721i) q^{25} -443.081i q^{26} +(-205.741 + 699.365i) q^{27} -521.708i q^{28} +1220.68i q^{29} +(-555.238 + 310.984i) q^{30} +1781.99 q^{31} +181.019 q^{32} +(226.654 - 318.177i) q^{33} -524.399 q^{34} +(1474.17 + 696.296i) q^{35} +(211.731 + 612.433i) q^{36} +663.047i q^{37} -1424.39 q^{38} +(818.004 - 1148.31i) q^{39} +(-241.597 + 511.499i) q^{40} -1331.05i q^{41} +(963.163 - 1352.09i) q^{42} +1701.36i q^{43} -347.246i q^{44} +(-2013.11 - 219.101i) q^{45} +808.391 q^{46} +91.2182 q^{47} +(469.139 + 334.193i) q^{48} -1851.81 q^{49} +(-1122.87 - 1365.34i) q^{50} +(-1359.06 - 968.131i) q^{51} -1253.22i q^{52} -3268.39 q^{53} +(-581.923 + 1978.10i) q^{54} +(981.198 + 463.450i) q^{55} -1475.61i q^{56} +(-3691.51 - 2629.66i) q^{57} +3452.62i q^{58} -1891.53i q^{59} +(-1570.45 + 879.597i) q^{60} +757.194 q^{61} +5040.23 q^{62} +(4992.36 - 1725.97i) q^{63} +512.000 q^{64} +(3541.18 + 1672.61i) q^{65} +(641.075 - 899.939i) q^{66} +3597.91i q^{67} -1483.22 q^{68} +(2095.07 + 1492.43i) q^{69} +(4169.58 + 1969.42i) q^{70} +8210.27i q^{71} +(598.866 + 1732.22i) q^{72} -6988.31i q^{73} +1875.38i q^{74} +(-389.445 - 5611.50i) q^{75} -4028.77 q^{76} -2830.64 q^{77} +(2313.66 - 3247.92i) q^{78} +2211.58 q^{79} +(-683.339 + 1446.74i) q^{80} +(-5160.06 + 4052.22i) q^{81} -3764.77i q^{82} -432.656 q^{83} +(2724.24 - 3824.28i) q^{84} +(1979.58 - 4191.09i) q^{85} +4812.17i q^{86} +(-6374.12 + 8947.97i) q^{87} -982.159i q^{88} -4694.86i q^{89} +(-5693.94 - 619.712i) q^{90} -10215.9 q^{91} +2286.48 q^{92} +(13062.5 + 9305.14i) q^{93} +258.004 q^{94} +(5376.99 - 11383.9i) q^{95} +(1326.92 + 945.240i) q^{96} +3923.02i q^{97} -5237.70 q^{98} +(3322.88 - 1148.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{4} + 32 q^{6} - 56 q^{9} + 160 q^{10} - 760 q^{15} + 512 q^{16} - 816 q^{19} - 1024 q^{21} + 256 q^{24} + 840 q^{25} - 1600 q^{30} + 6224 q^{31} - 3392 q^{34} - 448 q^{36} + 10560 q^{39} + 1280 q^{40}+ \cdots - 22144 q^{99}+O(q^{100}) $ 8 * q + 64 * q^4 + 32 * q^6 - 56 * q^9 + 160 * q^10 - 760 * q^15 + 512 * q^16 - 816 * q^19 - 1024 * q^21 + 256 * q^24 + 840 * q^25 - 1600 * q^30 + 6224 * q^31 - 3392 * q^34 - 448 * q^36 + 10560 * q^39 + 1280 * q^40 - 6080 * q^45 - 2368 * q^46 - 21240 * q^49 - 3376 * q^51 + 5920 * q^54 + 5440 * q^55 - 6080 * q^60 - 368 * q^61 + 4096 * q^64 + 13696 * q^66 + 17296 * q^69 + 14080 * q^70 + 5440 * q^75 - 6528 * q^76 - 1584 * q^79 - 33784 * q^81 - 8192 * q^84 - 3440 * q^85 - 14560 * q^90 + 30720 * q^91 + 6080 * q^94 + 2048 * q^96 - 22144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	2.82843			0.707107
$2$	2.82843			0.707107
$3$	7.33029	+	5.22176i	0.814477	+	0.580196i
$3$	7.33029	+	5.22176i	0.814477	+	0.580196i
$4$	8.00000			0.500000
$5$	−10.6772	+	22.6053i	−0.427087	+	0.904211i
$5$	−10.6772	+	22.6053i	−0.427087	+	0.904211i
$6$	20.7332	+	14.7694i	0.575922	+	0.410260i
$7$		−	65.2135i		−	1.33089i	−0.746447	−	0.665444i	$-0.768242\pi$
$7$		−	65.2135i		−	1.33089i	0.746447	−	0.665444i	$-0.231758\pi$
$8$	22.6274			0.353553
$9$	26.4664	+	76.5541i	0.326746	+	0.945112i
$10$	−30.1996	+	63.9373i	−0.301996	+	0.639373i
$11$		−	43.4057i		−	0.358725i	−0.983783	−	0.179362i	$-0.942597\pi$
$11$		−	43.4057i		−	0.358725i	0.983783	−	0.179362i	$-0.0574035\pi$
$12$	58.6423	+	41.7741i	0.407239	+	0.290098i
$13$		−	156.653i		−	0.926940i	−0.886113	−	0.463470i	$-0.846604\pi$
$13$		−	156.653i		−	0.926940i	0.886113	−	0.463470i	$-0.153396\pi$
$14$		−	184.452i		−	0.941080i
$15$	−196.306	+	109.950i	−0.872472	+	0.488665i
$16$	64.0000			0.250000
$17$	−185.403			−0.641533			−0.320767	−	0.947158i	$-0.603941\pi$
$17$	−185.403			−0.641533			−0.320767	+	0.947158i	$0.603941\pi$
$18$	74.8583	+	216.528i	0.231044	+	0.668295i
$19$	−503.597			−1.39501			−0.697503	−	0.716582i	$-0.745705\pi$
$19$	−503.597			−1.39501			−0.697503	+	0.716582i	$0.745705\pi$
$20$	−85.4174	+	180.842i	−0.213543	+	0.452105i
$21$	340.530	−	478.034i	0.772176	−	1.08398i
$22$		−	122.770i		−	0.253657i
$23$	285.809			0.540283			0.270141	−	0.962821i	$-0.412930\pi$
$23$	285.809			0.540283			0.270141	+	0.962821i	$0.412930\pi$
$24$	165.866	+	118.155i	0.287961	+	0.205130i
$25$	−396.996	−	482.721i	−0.635194	−	0.772353i
$26$		−	443.081i		−	0.655446i
$27$	−205.741	+	699.365i	−0.282223	+	0.959349i
$28$		−	521.708i		−	0.665444i
$29$			1220.68i			1.45147i	0.687976	+	0.725734i	$0.258500\pi$
$29$			1220.68i			1.45147i	−0.687976	+	0.725734i	$0.741500\pi$
$30$	−555.238	+	310.984i	−0.616931	+	0.345538i
$31$	1781.99			1.85431			0.927155	−	0.374678i	$-0.122247\pi$
$31$	1781.99			1.85431			0.927155	+	0.374678i	$0.122247\pi$
$32$	181.019			0.176777
$33$	226.654	−	318.177i	0.208131	−	0.292173i
$34$	−524.399			−0.453633
$35$	1474.17	+	696.296i	1.20340	+	0.568405i
$36$	211.731	+	612.433i	0.163373	+	0.472556i
$37$			663.047i			0.484329i	0.970235	+	0.242165i	$0.0778574\pi$
$37$			663.047i			0.484329i	−0.970235	+	0.242165i	$0.922143\pi$
$38$	−1424.39			−0.986418
$39$	818.004	−	1148.31i	0.537807	−	0.754971i
$40$	−241.597	+	511.499i	−0.150998	+	0.319687i
$41$		−	1331.05i		−	0.791819i	−0.918289	−	0.395910i	$-0.870429\pi$
$41$		−	1331.05i		−	0.791819i	0.918289	−	0.395910i	$-0.129571\pi$
$42$	963.163	−	1352.09i	0.546011	−	0.766488i
$43$			1701.36i			0.920151i	0.887880	+	0.460075i	$0.152178\pi$
$43$			1701.36i			0.920151i	−0.887880	+	0.460075i	$0.847822\pi$
$44$		−	347.246i		−	0.179362i
$45$	−2013.11	−	219.101i	−0.994129	−	0.108198i
$46$	808.391			0.382037
$47$	91.2182			0.0412939			0.0206469	−	0.999787i	$-0.493427\pi$
$47$	91.2182			0.0412939			0.0206469	+	0.999787i	$0.493427\pi$
$48$	469.139	+	334.193i	0.203619	+	0.145049i
$49$	−1851.81			−0.771265
$50$	−1122.87	−	1365.34i	−0.449150	−	0.546136i
$51$	−1359.06	−	968.131i	−0.522514	−	0.372215i
$52$		−	1253.22i		−	0.463470i
$53$	−3268.39			−1.16354			−0.581771	−	0.813353i	$-0.697640\pi$
$53$	−3268.39			−1.16354			−0.581771	+	0.813353i	$0.697640\pi$
$54$	−581.923	+	1978.10i	−0.199562	+	0.678362i
$55$	981.198	+	463.450i	0.324363	+	0.153207i
$56$		−	1475.61i		−	0.470540i
$57$	−3691.51	−	2629.66i	−1.13620	−	0.809376i
$58$			3452.62i			1.02634i
$59$		−	1891.53i		−	0.543388i	−0.962384	−	0.271694i	$-0.912416\pi$
$59$		−	1891.53i		−	0.543388i	0.962384	−	0.271694i	$-0.0875838\pi$
$60$	−1570.45	+	879.597i	−0.436236	+	0.244332i
$61$	757.194			0.203492			0.101746	−	0.994810i	$-0.467557\pi$
$61$	757.194			0.203492			0.101746	+	0.994810i	$0.467557\pi$
$62$	5040.23			1.31120
$63$	4992.36	−	1725.97i	1.25784	−	0.434862i
$64$	512.000			0.125000
$65$	3541.18	+	1672.61i	0.838149	+	0.395884i
$66$	641.075	−	899.939i	0.147171	−	0.206598i
$67$			3597.91i			0.801495i	0.916189	+	0.400747i	$0.131250\pi$
$67$			3597.91i			0.801495i	−0.916189	+	0.400747i	$0.868750\pi$
$68$	−1483.22			−0.320767
$69$	2095.07	+	1492.43i	0.440048	+	0.313470i
$70$	4169.58	+	1969.42i	0.850935	+	0.401923i
$71$			8210.27i			1.62870i	0.580375	+	0.814349i	$0.302906\pi$
$71$			8210.27i			1.62870i	−0.580375	+	0.814349i	$0.697094\pi$
$72$	598.866	+	1732.22i	0.115522	+	0.334148i
$73$		−	6988.31i		−	1.31137i	−0.755033	−	0.655687i	$-0.772379\pi$
$73$		−	6988.31i		−	1.31137i	0.755033	−	0.655687i	$-0.227621\pi$
$74$			1875.38i			0.342473i
$75$	−389.445	−	5611.50i	−0.0692347	−	0.997600i
$76$	−4028.77			−0.697503
$77$	−2830.64			−0.477423
$78$	2313.66	−	3247.92i	0.380287	−	0.533845i
$79$	2211.58			0.354363			0.177182	−	0.984178i	$-0.443302\pi$
$79$	2211.58			0.354363			0.177182	+	0.984178i	$0.443302\pi$
$80$	−683.339	+	1446.74i	−0.106772	+	0.226053i
$81$	−5160.06	+	4052.22i	−0.786475	+	0.617623i
$82$		−	3764.77i		−	0.559901i
$83$	−432.656			−0.0628039			−0.0314020	−	0.999507i	$-0.509997\pi$
$83$	−432.656			−0.0628039			−0.0314020	+	0.999507i	$0.509997\pi$
$84$	2724.24	−	3824.28i	0.386088	−	0.541989i
$85$	1979.58	−	4191.09i	0.273990	−	0.580081i
$86$			4812.17i			0.650645i
$87$	−6374.12	+	8947.97i	−0.842135	+	1.18219i
$88$		−	982.159i		−	0.126828i
$89$		−	4694.86i		−	0.592710i	−0.955078	−	0.296355i	$-0.904229\pi$
$89$		−	4694.86i		−	0.592710i	0.955078	−	0.296355i	$-0.0957712\pi$
$90$	−5693.94	−	619.712i	−0.702956	−	0.0765076i
$91$	−10215.9			−1.23365
$92$	2286.48			0.270141
$93$	13062.5	+	9305.14i	1.51029	+	1.07586i
$94$	258.004			0.0291992
$95$	5376.99	−	11383.9i	0.595788	−	1.26138i
$96$	1326.92	+	945.240i	0.143981	+	0.102565i
$97$			3923.02i			0.416944i	0.978028	+	0.208472i	$0.0668489\pi$
$97$			3923.02i			0.416944i	−0.978028	+	0.208472i	$0.933151\pi$
$98$	−5237.70			−0.545366
$99$	3322.88	−	1148.79i	0.339035	−	0.117212i
$100$	−3175.97	−	3861.76i	−0.317597	−	0.386176i
$101$		−	12399.7i		−	1.21554i	−0.794114	−	0.607768i	$-0.792065\pi$
$101$		−	12399.7i		−	1.21554i	0.794114	−	0.607768i	$-0.207935\pi$
$102$	−3844.00	−	2738.29i	−0.369473	−	0.263196i
$103$		−	3794.25i		−	0.357645i	−0.983881	−	0.178822i	$-0.942771\pi$
$103$		−	3794.25i		−	0.357645i	0.983881	−	0.178822i	$-0.0572287\pi$
$104$		−	3544.65i		−	0.327723i
$105$	7170.20	+	12801.8i	0.650358	+	1.16116i
$106$	−9244.40			−0.822748
$107$	1689.85			0.147598			0.0737990	−	0.997273i	$-0.476488\pi$
$107$	1689.85			0.147598			0.0737990	+	0.997273i	$0.476488\pi$
$108$	−1645.93	+	5594.92i	−0.141112	+	0.479674i
$109$	−703.533			−0.0592150			−0.0296075	−	0.999562i	$-0.509426\pi$
$109$	−703.533			−0.0592150			−0.0296075	+	0.999562i	$0.509426\pi$
$110$	2775.25	+	1310.84i	0.229359	+	0.108333i
$111$	−3462.27	+	4860.33i	−0.281006	+	0.394475i
$112$		−	4173.67i		−	0.332722i
$113$	−23742.7			−1.85940			−0.929700	−	0.368319i	$-0.879933\pi$
$113$	−23742.7			−1.85940			−0.929700	+	0.368319i	$0.879933\pi$
$114$	−10441.2	−	7437.81i	−0.803414	−	0.572315i
$115$	−3051.64	+	6460.80i	−0.230748	+	0.488529i
$116$			9765.47i			0.725734i
$117$	11992.4	−	4146.04i	0.876062	−	0.302874i
$118$		−	5350.06i		−	0.384233i
$119$			12090.8i			0.853809i
$120$	−4441.90	+	2487.87i	−0.308465	+	0.172769i
$121$	12756.9			0.871316
$122$	2141.67			0.143891
$123$	6950.42	−	9756.98i	0.459410	−	0.644919i
$124$	14255.9			0.927155
$125$	15150.8	−	3820.11i	0.969653	−	0.244487i
$126$	14120.5	−	4881.77i	0.889427	−	0.307494i
$127$		−	26178.1i		−	1.62304i	−0.584322	−	0.811522i	$-0.698640\pi$
$127$		−	26178.1i		−	1.62304i	0.584322	−	0.811522i	$-0.301360\pi$
$128$	1448.15			0.0883883
$129$	−8884.09	+	12471.5i	−0.533868	+	0.749442i
$130$	10016.0	+	4730.85i	0.592661	+	0.279932i
$131$			7156.89i			0.417044i	0.978018	+	0.208522i	$0.0668653\pi$
$131$			7156.89i			0.417044i	−0.978018	+	0.208522i	$0.933135\pi$
$132$	1813.23	−	2545.41i	0.104065	−	0.146087i
$133$			32841.3i			1.85660i
$134$			10176.4i			0.566743i
$135$	−13612.6	−	12118.1i	−0.746919	−	0.664915i
$136$	−4195.19			−0.226816
$137$	12209.8			0.650532			0.325266	−	0.945623i	$-0.394546\pi$
$137$	12209.8			0.650532			0.325266	+	0.945623i	$0.394546\pi$
$138$	5925.74	+	4221.23i	0.311161	+	0.221657i
$139$	3973.15			0.205639			0.102819	−	0.994700i	$-0.467214\pi$
$139$	3973.15			0.205639			0.102819	+	0.994700i	$0.467214\pi$
$140$	11793.4	+	5570.37i	0.601702	+	0.284203i
$141$	668.656	+	476.320i	0.0336329	+	0.0239585i
$142$			23222.1i			1.15166i
$143$	−6799.63			−0.332516
$144$	1693.85	+	4899.46i	0.0816864	+	0.236278i
$145$	−27593.9	−	13033.5i	−1.31243	−	0.619903i
$146$		−	19765.9i		−	0.927282i
$147$	−13574.3	−	9669.69i	−0.628177	−	0.447484i
$148$			5304.37i			0.242165i
$149$		−	19199.1i		−	0.864787i	−0.901685	−	0.432393i	$-0.857669\pi$
$149$		−	19199.1i		−	0.864787i	0.901685	−	0.432393i	$-0.142331\pi$
$150$	−1101.52	−	15871.7i	−0.0489563	−	0.705410i
$151$	28956.9			1.26999			0.634993	−	0.772518i	$-0.281003\pi$
$151$	28956.9			1.26999			0.634993	+	0.772518i	$0.281003\pi$
$152$	−11395.1			−0.493209
$153$	−4906.95	−	14193.4i	−0.209618	−	0.606321i
$154$	−8006.26			−0.337589
$155$	−19026.6	+	40282.4i	−0.791951	+	1.67669i
$156$	6544.03	−	9186.49i	0.268903	−	0.377486i
$157$			27194.5i			1.10327i	0.834086	+	0.551635i	$0.185996\pi$
$157$			27194.5i			1.10327i	−0.834086	+	0.551635i	$0.814004\pi$
$158$	6255.30			0.250573
$159$	−23958.2	−	17066.7i	−0.947678	−	0.675082i
$160$	−1932.77	+	4091.99i	−0.0754990	+	0.159843i
$161$		−	18638.6i		−	0.719056i
$162$	−14594.9	+	11461.4i	−0.556121	+	0.436725i
$163$		−	25185.4i		−	0.947923i	−0.880545	−	0.473962i	$-0.842824\pi$
$163$		−	25185.4i		−	0.947923i	0.880545	−	0.473962i	$-0.157176\pi$
$164$		−	10648.4i		−	0.395910i
$165$	4772.44	+	8520.81i	0.175296	+	0.312977i
$166$	−1223.74			−0.0444091
$167$	6741.31			0.241719			0.120860	−	0.992670i	$-0.461435\pi$
$167$	6741.31			0.241719			0.120860	+	0.992670i	$0.461435\pi$
$168$	7705.31	−	10816.7i	0.273005	−	0.383244i
$169$	4020.88			0.140782
$170$	5599.10	−	11854.2i	0.193740	−	0.410179i
$171$	−13328.4	−	38552.4i	−0.455812	−	1.31844i
$172$			13610.9i			0.460075i
$173$	−3467.43			−0.115855			−0.0579276	−	0.998321i	$-0.518449\pi$
$173$	−3467.43			−0.115855			−0.0579276	+	0.998321i	$0.518449\pi$
$174$	−18028.7	+	25308.7i	−0.595480	+	0.835933i
$175$	−31479.9	+	25889.5i	−1.02792	+	0.845372i
$176$		−	2777.97i		−	0.0896812i
$177$	9877.13	−	13865.5i	0.315271	−	0.442577i
$178$		−	13279.1i		−	0.419109i
$179$			13444.5i			0.419603i	0.977744	+	0.209801i	$0.0672817\pi$
$179$			13444.5i			0.419603i	−0.977744	+	0.209801i	$0.932718\pi$
$180$	−16104.9	−	1752.81i	−0.497065	−	0.0540991i
$181$	32861.3			1.00306			0.501530	−	0.865140i	$-0.332771\pi$
$181$	32861.3			1.00306			0.501530	+	0.865140i	$0.332771\pi$
$182$	−28894.9			−0.872325
$183$	5550.45	+	3953.88i	0.165740	+	0.118065i
$184$	6467.13			0.191019
$185$	−14988.3	−	7079.46i	−0.437936	−	0.206851i
$186$	36946.4	+	26318.9i	1.06794	+	0.760750i
$187$			8047.55i			0.230134i
$188$	729.745			0.0206469
$189$	45608.1	+	13417.1i	1.27679	+	0.375608i
$190$	15208.4	−	32198.6i	0.421286	−	0.891929i
$191$			8070.03i			0.221212i	0.993864	+	0.110606i	$0.0352792\pi$
$191$			8070.03i			0.221212i	−0.993864	+	0.110606i	$0.964721\pi$
$192$	3753.11	+	2673.54i	0.101810	+	0.0725245i
$193$			12379.6i			0.332347i	0.986097	+	0.166174i	$0.0531412\pi$
$193$			12379.6i			0.332347i	−0.986097	+	0.166174i	$0.946859\pi$
$194$			11096.0i			0.294824i
$195$	17223.9	+	30751.9i	0.452963	+	0.808729i
$196$	−14814.5			−0.385632
$197$	41058.6			1.05797			0.528983	−	0.848632i	$-0.322573\pi$
$197$	41058.6			1.05797			0.528983	+	0.848632i	$0.322573\pi$
$198$	9398.54	−	3249.28i	0.239734	−	0.0828813i
$199$	−39044.9			−0.985957			−0.492978	−	0.870042i	$-0.664092\pi$
$199$	−39044.9			−0.985957			−0.492978	+	0.870042i	$0.664092\pi$
$200$	−8982.99	−	10922.7i	−0.224575	−	0.273068i
$201$	−18787.4	+	26373.7i	−0.465024	+	0.652799i
$202$		−	35071.6i		−	0.859514i
$203$	79605.2			1.93174
$204$	−10872.5	−	7745.05i	−0.261257	−	0.186107i
$205$	30088.7	+	14211.8i	0.715972	+	0.338176i
$206$		−	10731.8i		−	0.252893i
$207$	7564.35	+	21879.9i	0.176535	+	0.510628i
$208$		−	10025.8i		−	0.231735i
$209$			21859.0i			0.500423i
$210$	20280.4	+	36209.0i	0.459873	+	0.821066i
$211$	28248.5			0.634498			0.317249	−	0.948342i	$-0.397241\pi$
$211$	28248.5			0.634498			0.317249	+	0.948342i	$0.397241\pi$
$212$	−26147.1			−0.581771
$213$	−42872.1	+	60183.7i	−0.944964	+	1.32654i
$214$	4779.62			0.104368
$215$	−38459.7	−	18165.7i	−0.832010	−	0.392984i
$216$	−4655.38	+	15824.8i	−0.0997810	+	0.339181i
$217$		−	116210.i		−	2.46788i
$218$	−1989.89			−0.0418713
$219$	36491.3	−	51226.4i	0.760854	−	1.06808i
$220$	7849.58	+	3707.60i	0.162181	+	0.0766033i
$221$			29043.9i			0.594663i
$222$	−9792.79	+	13747.1i	−0.198701	+	0.278936i
$223$		−	22828.3i		−	0.459054i	−0.973302	−	0.229527i	$-0.926282\pi$
$223$		−	22828.3i		−	0.459054i	0.973302	−	0.229527i	$-0.0737180\pi$
$224$		−	11804.9i		−	0.235270i
$225$	26447.2	−	43167.5i	0.522413	−	0.852692i
$226$	−67154.4			−1.31479
$227$	2784.73			0.0540420			0.0270210	−	0.999635i	$-0.491398\pi$
$227$	2784.73			0.0540420			0.0270210	+	0.999635i	$0.491398\pi$
$228$	−29532.1	−	21037.3i	−0.568100	−	0.404688i
$229$	−41249.2			−0.786584			−0.393292	−	0.919414i	$-0.628664\pi$
$229$	−41249.2			−0.786584			−0.393292	+	0.919414i	$0.628664\pi$
$230$	−8631.33	+	18273.9i	−0.163163	+	0.345442i
$231$	−20749.4	−	14780.9i	−0.388850	−	0.276999i
$232$			27620.9i			0.513171i
$233$	−79310.6			−1.46090			−0.730448	−	0.682968i	$-0.760689\pi$
$233$	−79310.6			−1.46090			−0.730448	+	0.682968i	$0.760689\pi$
$234$	33919.7	−	11726.8i	0.619470	−	0.214164i
$235$	−973.952	+	2062.01i	−0.0176361	+	0.0373384i
$236$		−	15132.3i		−	0.271694i
$237$	16211.5	+	11548.3i	0.288621	+	0.205600i
$238$			34197.9i			0.603734i
$239$			32220.9i			0.564082i	0.959402	+	0.282041i	$0.0910115\pi$
$239$			32220.9i			0.564082i	−0.959402	+	0.282041i	$0.908989\pi$
$240$	−12563.6	+	7036.77i	−0.218118	+	0.122166i
$241$	−77790.4			−1.33934			−0.669672	−	0.742657i	$-0.733565\pi$
$241$	−77790.4			−1.33934			−0.669672	+	0.742657i	$0.733565\pi$
$242$	36082.1			0.616114
$243$	−58984.5	+	2759.38i	−0.998908	+	0.0467303i
$244$	6057.55			0.101746
$245$	19772.1	−	41860.6i	0.329397	−	0.697386i
$246$	19658.8	−	27596.9i	0.324852	−	0.456026i
$247$			78889.9i			1.29309i
$248$	40321.9			0.655598
$249$	−3171.50	−	2259.23i	−0.0511523	−	0.0364386i
$250$	42853.0	−	10804.9i	0.685648	−	0.172878i
$251$		−	728.156i		−	0.0115578i	−0.999983	−	0.00577892i	$-0.998161\pi$
$251$		−	728.156i		−	0.0115578i	0.999983	−	0.00577892i	$-0.00183950\pi$
$252$	39938.9	−	13807.7i	0.628920	−	0.217431i
$253$		−	12405.8i		−	0.193813i
$254$		−	74042.8i		−	1.14767i
$255$	36395.8	−	20385.0i	0.559720	−	0.313495i
$256$	4096.00			0.0625000
$257$	−90955.1			−1.37708			−0.688542	−	0.725196i	$-0.741749\pi$
$257$	−90955.1			−1.37708			−0.688542	+	0.725196i	$0.741749\pi$
$258$	−25128.0	+	35274.6i	−0.377501	+	0.529935i
$259$	43239.6			0.644588
$260$	28329.4	+	13380.9i	0.419074	+	0.197942i
$261$	−93448.4	+	32307.1i	−1.37180	+	0.474261i
$262$			20242.7i			0.294895i
$263$	131305.			1.89832			0.949160	−	0.314793i	$-0.101935\pi$
$263$	131305.			1.89832			0.949160	+	0.314793i	$0.101935\pi$
$264$	5128.60	−	7199.51i	0.0735853	−	0.103299i
$265$	34897.1	−	73882.8i	0.496933	−	1.05209i
$266$			92889.3i			1.31281i
$267$	24515.4	−	34414.7i	0.343888	−	0.482749i
$268$			28783.3i			0.400747i
$269$		−	80994.3i		−	1.11931i	−0.828726	−	0.559654i	$-0.810934\pi$
$269$		−	80994.3i		−	1.11931i	0.828726	−	0.559654i	$-0.189066\pi$
$270$	−38502.3	−	34275.1i	−0.528152	−	0.470166i
$271$	1408.64			0.0191806			0.00959030	−	0.999954i	$-0.496947\pi$
$271$	1408.64			0.0191806			0.00959030	+	0.999954i	$0.496947\pi$
$272$	−11865.8			−0.160383
$273$	−74885.5	−	53344.9i	−1.00478	−	0.715761i
$274$	34534.6			0.459996
$275$	−20952.8	+	17231.9i	−0.277062	+	0.227860i
$276$	16760.5	+	11939.4i	0.220024	+	0.156735i
$277$			35266.0i			0.459618i	0.973236	+	0.229809i	$0.0738102\pi$
$277$			35266.0i			0.459618i	−0.973236	+	0.229809i	$0.926190\pi$
$278$	11237.8			0.145409
$279$	47162.9	+	136419.i	0.605888	+	1.75253i
$280$	33356.6	+	15755.4i	0.425467	+	0.200962i
$281$			100028.i			1.26680i	0.773824	+	0.633401i	$0.218341\pi$
$281$			100028.i			1.26680i	−0.773824	+	0.633401i	$0.781659\pi$
$282$	1891.24	+	1347.24i	0.0237821	+	0.0169412i
$283$			1114.06i			0.0139102i	0.999976	+	0.00695512i	$0.00221390\pi$
$283$			1114.06i			0.0139102i	−0.999976	+	0.00695512i	$0.997786\pi$
$284$			65682.1i			0.814349i
$285$	98859.1	−	55370.3i	1.21710	−	0.681690i
$286$	−19232.3			−0.235125
$287$	−86802.4			−1.05382
$288$	4790.93	+	13857.8i	0.0577610	+	0.167074i
$289$	−49146.7			−0.588435
$290$	−78047.3	−	36864.2i	−0.928030	−	0.438337i
$291$	−20485.1	+	28756.9i	−0.241909	+	0.339591i
$292$		−	55906.5i		−	0.655687i
$293$	37594.9			0.437919			0.218960	−	0.975734i	$-0.429734\pi$
$293$	37594.9			0.437919			0.218960	+	0.975734i	$0.429734\pi$
$294$	−38393.9	−	27350.0i	−0.444188	−	0.316419i
$295$	42758.6	+	20196.2i	0.491337	+	0.232074i
$296$			15003.0i			0.171236i
$297$	30356.4	+	8930.33i	0.344142	+	0.101241i
$298$		−	54303.4i		−	0.611497i
$299$		−	44772.9i		−	0.500810i
$300$	−3115.56	−	44892.0i	−0.0346174	−	0.498800i
$301$	110952.			1.22462
$302$	81902.6			0.898015
$303$	64748.2	−	90893.4i	0.705249	−	0.990027i
$304$	−32230.2			−0.348751
$305$	−8084.69	+	17116.6i	−0.0869087	+	0.184000i
$306$	−13879.0	−	40144.9i	−0.148222	−	0.428734i
$307$			99842.1i			1.05934i	0.848203	+	0.529672i	$0.177685\pi$
$307$			99842.1i			1.05934i	−0.848203	+	0.529672i	$0.822315\pi$
$308$	−22645.1			−0.238711
$309$	19812.7	−	27813.0i	0.207504	−	0.291293i
$310$	−53815.4	+	113936.i	−0.559994	+	1.18560i
$311$		−	186982.i		−	1.93321i	−0.256273	−	0.966605i	$-0.582495\pi$
$311$		−	186982.i		−	1.93321i	0.256273	−	0.966605i	$-0.417505\pi$
$312$	18509.3	−	25983.3i	0.190143	−	0.266923i
$313$			120168.i			1.22660i	0.789852	+	0.613298i	$0.210158\pi$
$313$			120168.i			1.22660i	−0.789852	+	0.613298i	$0.789842\pi$
$314$			76917.6i			0.780129i
$315$	−14288.4	+	131282.i	−0.144000	+	1.32308i
$316$	17692.6			0.177182
$317$	−5854.85			−0.0582636			−0.0291318	−	0.999576i	$-0.509274\pi$
$317$	−5854.85			−0.0582636			−0.0291318	+	0.999576i	$0.509274\pi$
$318$	−67764.2	−	48272.1i	−0.670110	−	0.477355i
$319$	52984.7			0.520678
$320$	−5466.71	+	11573.9i	−0.0533859	+	0.113026i
$321$	12387.1	+	8823.99i	0.120215	+	0.0856357i
$322$		−	52718.1i		−	0.508449i
$323$	93368.4			0.894942
$324$	−41280.5	+	32417.8i	−0.393237	+	0.308811i
$325$	−75619.6	+	62190.6i	−0.715925	+	0.588786i
$326$		−	71235.0i		−	0.670283i
$327$	−5157.10	−	3673.68i	−0.0482292	−	0.0343563i
$328$		−	30118.2i		−	0.279950i
$329$		−	5948.66i		−	0.0549576i
$330$	13498.5	+	24100.5i	0.123953	+	0.221308i
$331$	−31243.3			−0.285168			−0.142584	−	0.989783i	$-0.545541\pi$
$331$	−31243.3			−0.285168			−0.142584	+	0.989783i	$0.545541\pi$
$332$	−3461.25			−0.0314020
$333$	−50759.0	+	17548.5i	−0.457746	+	0.158253i
$334$	19067.3			0.170921
$335$	−81331.7	−	38415.5i	−0.724720	−	0.342308i
$336$	21793.9	−	30594.2i	0.193044	−	0.270995i
$337$		−	32982.2i		−	0.290416i	−0.989401	−	0.145208i	$-0.953615\pi$
$337$		−	32982.2i		−	0.290416i	0.989401	−	0.145208i	$-0.0463851\pi$
$338$	11372.8			0.0995480
$339$	−174041.	−	123979.i	−1.51444	−	1.07882i
$340$	15836.6	−	33528.7i	0.136995	−	0.290041i
$341$		−	77348.6i		−	0.665187i
$342$	−37698.4	−	109043.i	−0.322308	−	0.932275i
$343$		−	35814.9i		−	0.304421i
$344$			38497.4i			0.325322i
$345$	−56106.1	+	31424.6i	−0.471381	+	0.264017i
$346$	−9807.37			−0.0819220
$347$	−129786.			−1.07788			−0.538939	−	0.842345i	$-0.681175\pi$
$347$	−129786.			−1.07788			−0.538939	+	0.842345i	$0.681175\pi$
$348$	−50993.0	+	71583.8i	−0.421068	+	0.591094i
$349$	−3795.88			−0.0311646			−0.0155823	−	0.999879i	$-0.504960\pi$
$349$	−3795.88			−0.0311646			−0.0155823	+	0.999879i	$0.504960\pi$
$350$	−89038.7	+	73226.6i	−0.726846	+	0.597768i
$351$	109558.	+	32229.9i	0.889259	+	0.261604i
$352$		−	7857.27i		−	0.0634142i
$353$	16832.0			0.135079			0.0675394	−	0.997717i	$-0.478485\pi$
$353$	16832.0			0.135079			0.0675394	+	0.997717i	$0.478485\pi$
$354$	27936.8	−	39217.5i	0.222930	−	0.312949i
$355$	−185595.	−	87662.4i	−1.47269	−	0.695596i
$356$		−	37558.8i		−	0.296355i
$357$	−63135.3	+	88629.1i	−0.495377	+	0.695408i
$358$			38026.8i			0.296704i
$359$		−	2886.79i		−	0.0223989i	−0.999937	−	0.0111994i	$-0.996435\pi$
$359$		−	2886.79i		−	0.0223989i	0.999937	−	0.0111994i	$-0.00356496\pi$
$360$	−45551.5	−	4957.69i	−0.351478	−	0.0382538i
$361$	123289.			0.946039
$362$	92945.7			0.709271
$363$	93512.1	+	66613.7i	0.709667	+	0.505534i
$364$	−81727.1			−0.616827
$365$	157973.	+	74615.4i	1.18576	+	0.560071i
$366$	15699.0	+	11183.3i	0.117196	+	0.0834847i
$367$		−	99428.8i		−	0.738210i	−0.929388	−	0.369105i	$-0.879664\pi$
$367$		−	99428.8i		−	0.738210i	0.929388	−	0.369105i	$-0.120336\pi$
$368$	18291.8			0.135071
$369$	101897.	−	35228.1i	0.748358	−	0.258724i
$370$	−42393.5	−	20023.7i	−0.309667	−	0.146266i
$371$			213143.i			1.54854i
$372$	104500.	+	74441.1i	0.755147	+	0.537931i
$373$		−	102544.i		−	0.737043i	−0.929619	−	0.368522i	$-0.879864\pi$
$373$		−	102544.i		−	0.737043i	0.929619	−	0.368522i	$-0.120136\pi$
$374$			22761.9i			0.162729i
$375$	131008.	+	51111.5i	0.931610	+	0.363459i
$376$	2064.03			0.0145996
$377$	191224.			1.34542
$378$	128999.	+	37949.3i	0.902824	+	0.265595i
$379$	83600.5			0.582010			0.291005	−	0.956722i	$-0.406010\pi$
$379$	83600.5			0.582010			0.291005	+	0.956722i	$0.406010\pi$
$380$	43015.9	−	91071.5i	0.297894	−	0.630689i
$381$	136696.	−	191893.i	0.941683	−	1.32193i
$382$			22825.5i			0.156420i
$383$	−147151.			−1.00315			−0.501575	−	0.865114i	$-0.667246\pi$
$383$	−147151.			−1.00315			−0.501575	+	0.865114i	$0.667246\pi$
$384$	10615.4	+	7561.92i	0.0719903	+	0.0512825i
$385$	30223.2	−	63987.4i	0.203901	−	0.431691i
$386$			35014.8i			0.235005i
$387$	−130246.	+	45028.8i	−0.869646	+	0.300655i
$388$			31384.2i			0.208472i
$389$			285084.i			1.88397i	0.335656	+	0.941985i	$0.391042\pi$
$389$			285084.i			1.88397i	−0.335656	+	0.941985i	$0.608958\pi$
$390$	48716.6	+	86979.6i	0.320293	+	0.571858i
$391$	−52990.0			−0.346609
$392$	−41901.6			−0.272683
$393$	−37371.6	+	52462.1i	−0.241967	+	0.339673i
$394$	116131.			0.748095
$395$	−23613.4	+	49993.4i	−0.151344	+	0.320419i
$396$	26583.1	−	9190.34i	0.169518	−	0.0586059i
$397$			71798.3i			0.455547i	0.973714	+	0.227773i	$0.0731445\pi$
$397$			71798.3i			0.455547i	−0.973714	+	0.227773i	$0.926855\pi$
$398$	−110436.			−0.697177
$399$	−171490.	+	240737.i	−1.07719	+	1.51216i
$400$	−25407.7	−	30894.1i	−0.158798	−	0.193088i
$401$		−	206979.i		−	1.28717i	−0.765373	−	0.643586i	$-0.777446\pi$
$401$		−	206979.i		−	1.28717i	0.765373	−	0.643586i	$-0.222554\pi$
$402$	−53138.9	+	74596.2i	−0.328822	+	0.461599i
$403$		−	279154.i		−	1.71883i
$404$		−	99197.5i		−	0.607768i
$405$	−36506.7	−	159911.i	−0.222568	−	0.974917i
$406$	225157.			1.36595
$407$	28780.0			0.173741
$408$	−30752.0	−	21906.3i	−0.184737	−	0.131598i
$409$	−106404.			−0.636078			−0.318039	−	0.948078i	$-0.603024\pi$
$409$	−106404.			−0.636078			−0.318039	+	0.948078i	$0.603024\pi$
$410$	85103.7	+	40197.1i	0.506268	+	0.239126i
$411$	89501.7	+	63756.9i	0.529843	+	0.377436i
$412$		−	30354.0i		−	0.178822i
$413$	−123354.			−0.723189
$414$	21395.2	+	61885.7i	0.124829	+	0.361068i
$415$	4619.54	−	9780.31i	0.0268227	−	0.0567880i
$416$		−	28357.2i		−	0.163861i
$417$	29124.3	+	20746.8i	0.167488	+	0.119311i
$418$			61826.5i			0.353853i
$419$		−	226416.i		−	1.28967i	−0.764322	−	0.644835i	$-0.776926\pi$
$419$		−	226416.i		−	1.28967i	0.764322	−	0.644835i	$-0.223074\pi$
$420$	57361.6	+	102415.i	0.325179	+	0.580581i
$421$	−220039.			−1.24147			−0.620734	−	0.784021i	$-0.713165\pi$
$421$	−220039.			−1.24147			−0.620734	+	0.784021i	$0.713165\pi$
$422$	79898.8			0.448658
$423$	2414.22	+	6983.13i	0.0134926	+	0.0390274i
$424$	−73955.2			−0.411374
$425$	73604.3	+	89497.9i	0.407498	+	0.495490i
$426$	−121261.	+	170225.i	−0.668190	+	0.938004i
$427$		−	49379.3i		−	0.270825i
$428$	13518.8			0.0737990
$429$	−49843.3	−	35506.0i	−0.270827	−	0.192925i
$430$	−108780.	−	51380.4i	−0.588320	−	0.277882i
$431$		−	56189.2i		−	0.302481i	−0.988497	−	0.151241i	$-0.951673\pi$
$431$		−	56189.2i		−	0.302481i	0.988497	−	0.151241i	$-0.0483268\pi$
$432$	−13167.4	+	44759.4i	−0.0705558	+	0.239837i
$433$			353092.i			1.88327i	0.336638	+	0.941634i	$0.390710\pi$
$433$			353092.i			1.88327i	−0.336638	+	0.941634i	$0.609290\pi$
$434$		−	328692.i		−	1.74505i
$435$	−134214.	−	239628.i	−0.709281	−	1.26636i
$436$	−5628.26			−0.0296075
$437$	−143933.			−0.753697
$438$	103213.	−	144890.i	0.538005	−	0.755250i
$439$	213.447			0.00110754			0.000553772	−	1.00000i	$-0.499824\pi$
$439$	213.447			0.00110754			0.000553772		1.00000i	$0.499824\pi$
$440$	22202.0	+	10486.7i	0.114680	+	0.0541667i
$441$	−49010.7	−	141763.i	−0.252007	−	0.728932i
$442$			82148.6i			0.420490i
$443$	−148410.			−0.756232			−0.378116	−	0.925758i	$-0.623428\pi$
$443$	−148410.			−0.756232			−0.378116	+	0.925758i	$0.623428\pi$
$444$	−27698.2	+	38882.6i	−0.140503	+	0.197238i
$445$	106128.	+	50127.8i	0.535935	+	0.253139i
$446$		−	64568.2i		−	0.324600i
$447$	100253.	−	140735.i	0.501746	−	0.704349i
$448$		−	33389.3i		−	0.166361i
$449$			116611.i			0.578425i	0.957265	+	0.289212i	$0.0933934\pi$
$449$			116611.i			0.578425i	−0.957265	+	0.289212i	$0.906607\pi$
$450$	74803.9	−	122096.i	0.369402	−	0.602945i
$451$	−57775.1			−0.284045
$452$	−189941.			−0.929700
$453$	212263.	+	151206.i	1.03437	+	0.736840i
$454$	7876.40			0.0382134
$455$	109077.	−	230933.i	0.526877	−	1.11548i
$456$	−83529.4	−	59502.5i	−0.401707	−	0.286158i
$457$		−	59420.0i		−	0.284512i	−0.989830	−	0.142256i	$-0.954564\pi$
$457$		−	59420.0i		−	0.284512i	0.989830	−	0.142256i	$-0.0454356\pi$
$458$	−116670.			−0.556199
$459$	38145.0	−	129664.i	0.181056	−	0.615454i
$460$	−24413.1	+	51686.4i	−0.115374	+	0.244265i
$461$			248043.i			1.16715i	0.812060	+	0.583574i	$0.198346\pi$
$461$			248043.i			1.16715i	−0.812060	+	0.583574i	$0.801654\pi$
$462$	−58688.2	−	41806.8i	−0.274958	−	0.195868i
$463$			68090.6i			0.317633i	0.987308	+	0.158816i	$0.0507678\pi$
$463$			68090.6i			0.317633i	−0.987308	+	0.158816i	$0.949232\pi$
$464$			78123.8i			0.362867i
$465$	−349816.	+	195929.i	−1.61783	+	0.906136i
$466$	−224324.			−1.03301
$467$	288274.			1.32182			0.660908	−	0.750466i	$-0.270171\pi$
$467$	288274.			1.32182			0.660908	+	0.750466i	$0.270171\pi$
$468$	95939.3	−	33168.3i	0.438031	−	0.151437i
$469$	234633.			1.06670
$470$	−2754.75	+	5832.25i	−0.0124706	+	0.0264022i
$471$	−142003.	+	199344.i	−0.640112	+	0.898588i
$472$		−	42800.5i		−	0.192117i
$473$	73848.7			0.330081
$474$	45853.1	+	32663.7i	0.204086	+	0.145381i
$475$	199926.	+	243097.i	0.886098	+	1.07744i
$476$			96726.4i			0.426905i
$477$	−86502.5	−	250209.i	−0.380182	−	1.09968i
$478$			91134.6i			0.398866i
$479$			12102.0i			0.0527455i	0.999652	+	0.0263728i	$0.00839569\pi$
$479$			12102.0i			0.0527455i	−0.999652	+	0.0263728i	$0.991604\pi$
$480$	−35535.2	+	19903.0i	−0.154233	+	0.0863845i
$481$	103868.			0.448944
$482$	−220025.			−0.947059
$483$	97326.6	−	136627.i	0.417193	−	0.585655i
$484$	102056.			0.435658
$485$	−88681.0	−	41886.8i	−0.377005	−	0.178071i
$486$	−166833.	+	7804.71i	−0.706334	+	0.0330433i
$487$			165539.i			0.697979i	0.937127	+	0.348989i	$0.113475\pi$
$487$			165539.i			0.697979i	−0.937127	+	0.348989i	$0.886525\pi$
$488$	17133.3			0.0719453
$489$	131512.	−	184616.i	0.549981	−	0.772062i
$490$	55923.8	−	118400.i	0.232919	−	0.493126i
$491$			313129.i			1.29886i	0.760423	+	0.649428i	$0.224991\pi$
$491$			313129.i			1.29886i	−0.760423	+	0.649428i	$0.775009\pi$
$492$	55603.3	−	78055.8i	0.229705	−	0.322459i
$493$		−	226319.i		−	0.931165i
$494$			223134.i			0.914350i
$495$	−9510.24	+	87380.6i	−0.0388134	+	0.356619i
$496$	114047.			0.463578
$497$	535421.			2.16762
$498$	−8970.35	−	6390.06i	−0.0361702	−	0.0257660i
$499$	156716.			0.629380			0.314690	−	0.949194i	$-0.398099\pi$
$499$	156716.			0.629380			0.314690	+	0.949194i	$0.398099\pi$
$500$	121207.	−	30560.9i	0.484826	−	0.122244i
$501$	49415.8	+	35201.5i	0.196875	+	0.140244i
$502$		−	2059.54i		−	0.00817263i
$503$	−123782.			−0.489239			−0.244620	−	0.969619i	$-0.578663\pi$
$503$	−123782.			−0.489239			−0.244620	+	0.969619i	$0.578663\pi$
$504$	112964.	−	39054.2i	0.444713	−	0.153747i
$505$	280298.	+	132394.i	1.09910	+	0.519140i
$506$		−	35088.8i		−	0.137046i
$507$	29474.2	+	20996.1i	0.114664	+	0.0816812i
$508$		−	209425.i		−	0.811522i
$509$		−	88804.4i		−	0.342767i	−0.985204	−	0.171383i	$-0.945176\pi$
$509$		−	88804.4i		−	0.342767i	0.985204	−	0.171383i	$-0.0548237\pi$
$510$	102943.	−	57657.5i	0.395782	−	0.221674i
$511$	−455733.			−1.74529
$512$	11585.2			0.0441942
$513$	103610.	−	352198.i	0.393703	−	1.33830i
$514$	−257260.			−0.973746
$515$	85770.1	+	40511.9i	0.323386	+	0.152745i
$516$	−71072.7	+	99771.7i	−0.266934	+	0.374721i
$517$		−	3959.39i		−	0.0148131i
$518$	122300.			0.455793
$519$	−25417.3	−	18106.1i	−0.0943614	−	0.0672187i
$520$	80127.7	+	37846.8i	0.296330	+	0.139966i
$521$			165146.i			0.608404i	0.952608	+	0.304202i	$0.0983898\pi$
$521$			165146.i			0.608404i	−0.952608	+	0.304202i	$0.901610\pi$
$522$	−264312.	+	91378.3i	−0.970009	+	0.335353i
$523$			419249.i			1.53274i	0.642400	+	0.766370i	$0.277939\pi$
$523$			419249.i			1.53274i	−0.642400	+	0.766370i	$0.722061\pi$
$524$			57255.1i			0.208522i
$525$	−365946.	+	25397.1i	−1.32770	+	0.0921437i
$526$	371386.			1.34232
$527$	−330387.			−1.18960
$528$	14505.9	−	20363.3i	0.0520327	−	0.0730433i
$529$	−198154.			−0.708095
$530$	98704.0	−	208972.i	0.351385	−	0.743938i
$531$	144805.	−	50062.1i	0.513562	−	0.177550i
$532$			262731.i			0.928298i
$533$	−208513.			−0.733969
$534$	69340.1	−	97339.4i	0.243165	−	0.341355i
$535$	−18042.8	+	38199.5i	−0.0630372	+	0.133460i
$536$			81411.4i			0.283371i
$537$	−70203.9	+	98552.1i	−0.243452	+	0.341757i
$538$		−	229086.i		−	0.791470i
$539$			80379.0i			0.276672i
$540$	−108901.	−	96944.5i	−0.373460	−	0.332457i
$541$	−260252.			−0.889200			−0.444600	−	0.895729i	$-0.646654\pi$
$541$	−260252.			−0.889200			−0.444600	+	0.895729i	$0.646654\pi$
$542$	3984.24			0.0135627
$543$	240883.	+	171594.i	0.816970	+	0.581972i
$544$	−33561.5			−0.113408
$545$	7511.74	−	15903.6i	0.0252899	−	0.0535428i
$546$	−211808.	−	150882.i	−0.710489	−	0.506119i
$547$		−	348245.i		−	1.16388i	−0.813230	−	0.581942i	$-0.802293\pi$
$547$		−	348245.i		−	1.16388i	0.813230	−	0.581942i	$-0.197707\pi$
$548$	97678.7			0.325266
$549$	20040.2	+	57966.3i	0.0664901	+	0.192323i
$550$	−59263.6	+	48739.2i	−0.195913	+	0.161121i
$551$		−	614733.i		−	2.02480i
$552$	47406.0	+	33769.8i	0.155580	+	0.110828i
$553$		−	144225.i		−	0.471618i
$554$			99747.4i			0.324999i
$555$	−72901.7	−	130160.i	−0.236675	−	0.422564i
$556$	31785.2			0.102819
$557$	−238645.			−0.769205			−0.384602	−	0.923082i	$-0.625661\pi$
$557$	−238645.			−0.769205			−0.384602	+	0.923082i	$0.625661\pi$
$558$	133397.	+	385851.i	0.428427	+	1.23923i
$559$	266523.			0.852925
$560$	94346.8	+	44563.0i	0.300851	+	0.142101i
$561$	−42022.4	+	58990.9i	−0.133523	+	0.187439i
$562$			282922.i			0.895764i
$563$	−217039.			−0.684733			−0.342366	−	0.939566i	$-0.611228\pi$
$563$	−217039.			−0.684733			−0.342366	+	0.939566i	$0.611228\pi$
$564$	5349.25	+	3810.56i	0.0168165	+	0.0119793i
$565$	253505.	−	536709.i	0.794125	−	1.68129i
$566$			3151.03i			0.00983603i
$567$	264260.	+	336506.i	0.821987	+	1.04671i
$568$			185777.i			0.575832i
$569$		−	347873.i		−	1.07448i	−0.843431	−	0.537238i	$-0.819468\pi$
$569$		−	347873.i		−	1.07448i	0.843431	−	0.537238i	$-0.180532\pi$
$570$	279616.	−	156611.i	0.860621	−	0.482027i
$571$	−52650.9			−0.161486			−0.0807428	−	0.996735i	$-0.525729\pi$
$571$	−52650.9			−0.161486			−0.0807428	+	0.996735i	$0.525729\pi$
$572$	−54397.0			−0.166258
$573$	−42139.8	+	59155.7i	−0.128346	+	0.180172i
$574$	−245514.			−0.745166
$575$	−113465.	−	137966.i	−0.343184	−	0.417289i
$576$	13550.8	+	39195.7i	0.0408432	+	0.118139i
$577$			41833.2i			0.125652i	0.998024	+	0.0628260i	$0.0200113\pi$
$577$			41833.2i			0.125652i	−0.998024	+	0.0628260i	$0.979989\pi$
$578$	−139008.			−0.416086
$579$	−64643.3	+	90746.1i	−0.192826	+	0.270689i
$580$	−220751.	−	104268.i	−0.656216	−	0.309951i
$581$			28215.0i			0.0835850i
$582$	−57940.6	+	81336.8i	−0.171055	+	0.240127i
$583$			141867.i			0.417391i
$584$		−	158127.i		−	0.463641i
$585$	−34322.8	+	315360.i	−0.100293	+	0.921498i
$586$	106334.			0.309656
$587$	438588.			1.27286			0.636430	−	0.771335i	$-0.280410\pi$
$587$	438588.			1.27286			0.636430	+	0.771335i	$0.280410\pi$
$588$	−108594.	−	77357.5i	−0.314089	−	0.223742i
$589$	−897406.			−2.58677
$590$	120940.	+	57123.5i	0.347428	+	0.164101i
$591$	300972.	+	214398.i	0.861689	+	0.613828i
$592$			42435.0i			0.121082i
$593$	−191930.			−0.545801			−0.272901	−	0.962042i	$-0.587983\pi$
$593$	−191930.			−0.545801			−0.272901	+	0.962042i	$0.587983\pi$
$594$	85861.0	+	25258.8i	0.243345	+	0.0715879i
$595$	−273316.	−	129095.i	−0.772023	−	0.364651i
$596$		−	153593.i		−	0.432393i
$597$	−286210.	−	203883.i	−0.803039	−	0.572048i
$598$		−	126637.i		−	0.354126i
$599$		−	138898.i		−	0.387116i	−0.981089	−	0.193558i	$-0.937997\pi$
$599$		−	138898.i		−	0.387116i	0.981089	−	0.193558i	$-0.0620028\pi$
$600$	−8812.14	−	126974.i	−0.0244782	−	0.352705i
$601$	158349.			0.438396			0.219198	−	0.975680i	$-0.429656\pi$
$601$	158349.			0.438396			0.219198	+	0.975680i	$0.429656\pi$
$602$	313819.			0.865936
$603$	−275435.	+	95223.8i	−0.757503	+	0.261885i
$604$	231656.			0.634993
$605$	−136208.	+	288374.i	−0.372128	+	0.787854i
$606$	183136.	−	257085.i	0.498686	−	0.700055i
$607$		−	527256.i		−	1.43101i	−0.698605	−	0.715507i	$-0.746196\pi$
$607$		−	527256.i		−	1.43101i	0.698605	−	0.715507i	$-0.253804\pi$
$608$	−91160.8			−0.246604
$609$	583529.	+	415679.i	1.57336	+	1.12079i
$610$	−22866.9	+	48412.9i	−0.0614538	+	0.130107i
$611$		−	14289.6i		−	0.0382770i
$612$	−39255.6	−	113547.i	−0.104809	−	0.303160i
$613$		−	662019.i		−	1.76177i	−0.473328	−	0.880886i	$-0.656948\pi$
$613$		−	662019.i		−	1.76177i	0.473328	−	0.880886i	$-0.343052\pi$
$614$			282396.i			0.749069i
$615$	146348.	+	261293.i	0.386934	+	0.690840i
$616$	−64050.1			−0.168794
$617$	−167926.			−0.441111			−0.220556	−	0.975374i	$-0.570787\pi$
$617$	−167926.			−0.441111			−0.220556	+	0.975374i	$0.570787\pi$
$618$	56038.7	−	78667.0i	0.146727	−	0.205976i
$619$	364804.			0.952091			0.476045	−	0.879421i	$-0.342070\pi$
$619$	364804.			0.952091			0.476045	+	0.879421i	$0.342070\pi$
$620$	−152213.	+	322259.i	−0.395976	+	0.838343i
$621$	−58802.7	+	199885.i	−0.152480	+	0.518319i
$622$		−	528865.i		−	1.36699i
$623$	−306168.			−0.788831
$624$	52352.3	−	73491.9i	0.134452	−	0.188743i
$625$	−75413.3	+	383276.i	−0.193058	+	0.981187i
$626$			339888.i			0.867334i
$627$	−114142.	+	160233.i	−0.290343	+	0.407583i
$628$			217556.i			0.551635i
$629$		−	122931.i		−	0.310713i
$630$	−40413.6	+	371322.i	−0.101823	+	0.935556i
$631$	620870.			1.55934			0.779672	−	0.626188i	$-0.215386\pi$
$631$	620870.			1.55934			0.779672	+	0.626188i	$0.215386\pi$
$632$	50042.4			0.125286
$633$	207070.	+	147507.i	0.516784	+	0.368133i
$634$	−16560.0			−0.0411986
$635$	591762.	+	279508.i	1.46757	+	0.693181i
$636$	−191666.	−	136534.i	−0.473839	−	0.337541i
$637$			290091.i			0.714916i
$638$	149863.			0.368175
$639$	−628530.	+	217296.i	−1.53930	+	0.532170i
$640$	−15462.2	+	32735.9i	−0.0377495	+	0.0799217i
$641$		−	194113.i		−	0.472430i	−0.971701	−	0.236215i	$-0.924093\pi$
$641$		−	194113.i		−	0.472430i	0.971701	−	0.236215i	$-0.0759070\pi$
$642$	35036.0	+	24958.0i	0.0850050	+	0.0605536i
$643$			413435.i			0.999966i	0.866035	+	0.499983i	$0.166660\pi$
$643$			413435.i			0.999966i	−0.866035	+	0.499983i	$0.833340\pi$
$644$		−	149109.i		−	0.359528i
$645$	−187064.	−	333987.i	−0.449645	−	0.802805i
$646$	264086.			0.632820
$647$	530520.			1.26734			0.633670	−	0.773604i	$-0.281548\pi$
$647$	530520.			1.26734			0.633670	+	0.773604i	$0.281548\pi$
$648$	−116759.	+	91691.3i	−0.278061	+	0.218363i
$649$	−82103.3			−0.194927
$650$	−213884.	+	175901.i	−0.506235	+	0.416335i
$651$	606821.	−	851854.i	1.43185	−	2.01003i
$652$		−	201483.i		−	0.473962i
$653$	838855.			1.96725			0.983627	−	0.180218i	$-0.0576804\pi$
$653$	838855.			1.96725			0.983627	+	0.180218i	$0.0576804\pi$
$654$	−14586.5	−	10390.7i	−0.0341032	−	0.0242936i
$655$	−161783.	−	76415.4i	−0.377096	−	0.178114i
$656$		−	85187.1i		−	0.197955i
$657$	534984.	−	184956.i	1.23940	−	0.428486i
$658$		−	16825.4i		−	0.0388609i
$659$			633895.i			1.45964i	0.683638	+	0.729821i	$0.260397\pi$
$659$			633895.i			1.45964i	−0.683638	+	0.729821i	$0.739603\pi$
$660$	38179.5	+	68166.5i	0.0876481	+	0.156489i
$661$	315742.			0.722652			0.361326	−	0.932440i	$-0.382324\pi$
$661$	315742.			0.722652			0.361326	+	0.932440i	$0.382324\pi$
$662$	−88369.3			−0.201644
$663$	−151660.	+	212901.i	−0.345021	+	0.484339i
$664$	−9789.89			−0.0222045
$665$	−742387.	−	350653.i	−1.67875	−	0.792928i
$666$	−143568.	+	49634.5i	−0.323675	+	0.111901i
$667$			348883.i			0.784203i
$668$	53930.5			0.120860
$669$	119204.	−	167338.i	0.266341	−	0.373889i
$670$	−230041.	−	108655.i	−0.512455	−	0.242048i
$671$		−	32866.5i		−	0.0729976i
$672$	61642.4	−	86533.5i	0.136503	−	0.191622i
$673$			293889.i			0.648863i	0.945909	+	0.324431i	$0.105173\pi$
$673$			293889.i			0.648863i	−0.945909	+	0.324431i	$0.894827\pi$
$674$		−	93287.8i		−	0.205355i
$675$	419276.	−	178330.i	0.920222	−	0.391396i
$676$	32167.0			0.0703911
$677$	−813804.			−1.77559			−0.887794	−	0.460241i	$-0.847763\pi$
$677$	−813804.			−1.77559			−0.887794	+	0.460241i	$0.847763\pi$
$678$	−492261.	−	350664.i	−1.07087	−	0.762838i
$679$	255834.			0.554905
$680$	44792.8	−	94833.5i	0.0968702	−	0.205090i
$681$	20412.9	+	14541.2i	0.0440159	+	0.0313549i
$682$		−	218775.i		−	0.470358i
$683$	376911.			0.807973			0.403987	−	0.914765i	$-0.367624\pi$
$683$	376911.			0.807973			0.403987	+	0.914765i	$0.367624\pi$
$684$	−106627.	−	308419.i	−0.227906	−	0.659218i
$685$	−130367.	+	276007.i	−0.277834	+	0.588218i
$686$		−	101300.i		−	0.215258i
$687$	−302369.	−	215394.i	−0.640654	−	0.456372i
$688$			108887.i			0.230038i
$689$			512002.i			1.07853i
$690$	−158692.	+	88882.3i	−0.333317	+	0.186688i
$691$	−559158.			−1.17106			−0.585529	−	0.810652i	$-0.699113\pi$
$691$	−559158.			−1.17106			−0.585529	+	0.810652i	$0.699113\pi$
$692$	−27739.4			−0.0579276
$693$	−74916.9	−	216697.i	−0.155996	−	0.451218i
$694$	−367091.			−0.762174
$695$	−42422.0	+	89814.0i	−0.0878256	+	0.185941i
$696$	−144230.	+	202470.i	−0.297740	+	0.417966i
$697$			246781.i			0.507979i
$698$	−10736.4			−0.0220367
$699$	−581370.	−	414141.i	−1.18987	−	0.847606i
$700$	−251839.	+	207116.i	−0.513958	+	0.422686i
$701$		−	441635.i		−	0.898727i	−0.893349	−	0.449363i	$-0.851651\pi$
$701$		−	441635.i		−	0.898727i	0.893349	−	0.449363i	$-0.148349\pi$
$702$	309876.	+	91159.9i	0.628801	+	0.184982i
$703$		−	333908.i		−	0.675642i
$704$		−	22223.7i		−	0.0448406i
$705$	−17906.7	+	10029.4i	−0.0360277	+	0.0201789i
$706$	47608.2			0.0955152
$707$	−808628.			−1.61774
$708$	79017.1	−	110924.i	0.157636	−	0.221288i
$709$	143318.			0.285106			0.142553	−	0.989787i	$-0.454469\pi$
$709$	143318.			0.285106			0.142553	+	0.989787i	$0.454469\pi$
$710$	−524943.	−	247947.i	−1.04135	−	0.491860i
$711$	58532.6	+	169306.i	0.115787	+	0.334913i
$712$		−	106232.i		−	0.209555i
$713$	509310.			1.00185
$714$	−178573.	+	250681.i	−0.350284	+	0.491728i
$715$	72600.8	−	153707.i	0.142013	−	0.300665i
$716$			107556.i			0.209801i
$717$	−168250.	+	236189.i	−0.327278	+	0.459432i
$718$		−	8165.07i		−	0.0158384i
$719$		−	348595.i		−	0.674317i	−0.941448	−	0.337158i	$-0.890534\pi$
$719$		−	348595.i		−	0.674317i	0.941448	−	0.337158i	$-0.109466\pi$
$720$	−128839.	−	14022.5i	−0.248532	−	0.0270495i
$721$	−247437.			−0.475985
$722$	348713.			0.668951
$723$	−570227.	−	406203.i	−1.09086	−	0.777082i
$724$	262890.			0.501530
$725$	589249.	−	484607.i	1.12105	−	0.921963i
$726$	264492.	+	188412.i	0.501811	+	0.357467i
$727$			963450.i			1.82289i	0.411423	+	0.911444i	$0.365032\pi$
$727$			963450.i			1.82289i	−0.411423	+	0.911444i	$0.634968\pi$
$728$	−231159.			−0.436163
$729$	−446782.	−	287776.i	−0.840700	−	0.541501i
$730$	446814.	+	211044.i	0.838458	+	0.396030i
$731$		−	315437.i		−	0.590307i
$732$	44403.6	+	31631.1i	0.0828698	+	0.0590326i
$733$		−	481364.i		−	0.895912i	−0.894056	−	0.447956i	$-0.852152\pi$
$733$		−	481364.i		−	0.895912i	0.894056	−	0.447956i	$-0.147848\pi$
$734$		−	281227.i		−	0.521994i
$735$	363521.	−	203605.i	0.672907	−	0.376890i
$736$	51737.0			0.0955094
$737$	156170.			0.287516
$738$	288209.	−	99640.0i	0.529169	−	0.182945i
$739$	−28527.3			−0.0522363			−0.0261181	−	0.999659i	$-0.508315\pi$
$739$	−28527.3			−0.0522363			−0.0261181	+	0.999659i	$0.508315\pi$
$740$	−119907.	−	56635.7i	−0.218968	−	0.103425i
$741$	−411944.	+	578286.i	−0.750243	+	1.05319i
$742$			602860.i			1.09499i
$743$	246998.			0.447420			0.223710	−	0.974656i	$-0.428183\pi$
$743$	246998.			0.447420			0.223710	+	0.974656i	$0.428183\pi$
$744$	295571.	+	210551.i	0.533969	+	0.380375i
$745$	434002.	+	204992.i	0.781950	+	0.369339i
$746$		−	290038.i		−	0.521168i
$747$	−11450.8	−	33121.6i	−0.0205209	−	0.0593567i
$748$			64380.4i			0.115067i
$749$		−	110201.i		−	0.196437i
$750$	370546.	+	144565.i	0.658748	+	0.257005i
$751$	−3299.61			−0.00585037			−0.00292518	−	0.999996i	$-0.500931\pi$
$751$	−3299.61			−0.00585037			−0.00292518	+	0.999996i	$0.500931\pi$
$752$	5837.96			0.0103235
$753$	3802.26	−	5337.60i	0.00670582	−	0.00941360i
$754$	540862.			0.951358
$755$	−309178.	+	654579.i	−0.542394	+	1.14833i
$756$	364865.	+	107337.i	0.638393	+	0.187804i
$757$			222016.i			0.387429i	0.981058	+	0.193714i	$0.0620535\pi$
$757$			222016.i			0.387429i	−0.981058	+	0.193714i	$0.937946\pi$
$758$	236458.			0.411543
$759$	64779.9	−	90937.9i	0.112449	−	0.157856i
$760$	121667.	−	257589.i	0.210643	−	0.445965i
$761$			749263.i			1.29379i	0.762578	+	0.646896i	$0.223933\pi$
$761$			749263.i			1.29379i	−0.762578	+	0.646896i	$0.776067\pi$
$762$	386634.	−	542755.i	0.665870	−	0.934747i
$763$			45879.9i			0.0788085i
$764$			64560.3i			0.110606i
$765$	373237.	+	40622.0i	0.637767	+	0.0694127i
$766$	−416206.			−0.709334
$767$	−296314.			−0.503688
$768$	30024.9	+	21388.3i	0.0509048	+	0.0362622i
$769$	912266.			1.54265			0.771327	−	0.636439i	$-0.219593\pi$
$769$	912266.			1.54265			0.771327	+	0.636439i	$0.219593\pi$
$770$	85484.2	−	180984.i	0.144180	−	0.305252i
$771$	−666727.	−	474946.i	−1.12160	−	0.798979i
$772$			99036.8i			0.166174i
$773$	820106.			1.37250			0.686248	−	0.727368i	$-0.259257\pi$
$773$	820106.			1.37250			0.686248	+	0.727368i	$0.259257\pi$
$774$	−368391.	+	127361.i	−0.614932	+	0.212595i
$775$	−707444.	−	860204.i	−1.17785	−	1.43218i
$776$			88767.9i			0.147412i
$777$	316959.	+	225787.i	0.525002	+	0.373987i
$778$			806340.i			1.33217i
$779$			670312.i			1.10459i
$780$	137791.	+	246015.i	0.226481	+	0.404364i
$781$	356373.			0.584255
$782$	−149878.			−0.245090
$783$	−853704.	−	251145.i	−1.39246	−	0.409638i
$784$	−118516.			−0.192816
$785$	−614739.	−	290360.i	−0.997588	−	0.471192i
$786$	−105703.	+	148385.i	−0.171097	+	0.240185i
$787$		−	742100.i		−	1.19816i	−0.800691	−	0.599078i	$-0.795534\pi$
$787$		−	742100.i		−	1.19816i	0.800691	−	0.599078i	$-0.204466\pi$
$788$	328469.			0.528983
$789$	962504.	+	685643.i	1.54614	+	1.10140i
$790$	−66788.9	+	141403.i	−0.107016	+	0.226570i
$791$			1.54834e6i			2.47465i
$792$	75188.3	−	25994.2i	0.119867	−	0.0414406i
$793$		−	118617.i		−	0.188625i
$794$			203076.i			0.322120i
$795$	641605.	−	359358.i	1.01516	−	0.568582i
$796$	−312359.			−0.492978
$797$	−1.13919e6			−1.79341			−0.896704	−	0.442631i	$-0.854045\pi$
$797$	−1.13919e6			−1.79341			−0.896704	+	0.442631i	$0.854045\pi$
$798$	−485046.	+	680906.i	−0.761688	+	1.06926i
$799$	−16912.1			−0.0264914
$800$	−71864.0	−	87381.8i	−0.112287	−	0.136534i
$801$	359410.	−	124256.i	0.560178	−	0.193665i
$802$		−	585424.i		−	0.910169i
$803$	−303333.			−0.470423
$804$	−150299.	+	210990.i	−0.232512	+	0.326400i
$805$	421332.	+	199008.i	0.650178	+	0.307099i
$806$		−	789567.i		−	1.21540i
$807$	422933.	−	593712.i	0.649418	−	0.911651i
$808$		−	280573.i		−	0.429757i
$809$		−	1.01471e6i		−	1.55040i	−0.631717	−	0.775199i	$-0.717650\pi$
$809$		−	1.01471e6i		−	1.55040i	0.631717	−	0.775199i	$-0.282350\pi$
$810$	−103257.	−	452296.i	−0.157379	−	0.689371i
$811$	−850022.			−1.29237			−0.646187	−	0.763179i	$-0.723637\pi$
$811$	−850022.			−1.29237			−0.646187	+	0.763179i	$0.723637\pi$
$812$	636841.			0.965871
$813$	10325.8	+	7355.59i	0.0156222	+	0.0111285i
$814$	81402.2			0.122853
$815$	569322.	+	268909.i	0.857122	+	0.404846i
$816$	−86979.8	−	61960.4i	−0.130629	−	0.0930537i
$817$		−	856799.i		−	1.28361i
$818$	−300955.			−0.449775
$819$	−270378.	−	782068.i	−0.403091	−	1.16594i
$820$	240710.	+	113695.i	0.357986	+	0.169088i
$821$			376912.i			0.559183i	0.960119	+	0.279591i	$0.0901990\pi$
$821$			376912.i			0.559183i	−0.960119	+	0.279591i	$0.909801\pi$
$822$	253149.	+	180332.i	0.374656	+	0.266888i
$823$			517149.i			0.763512i	0.924263	+	0.381756i	$0.124681\pi$
$823$			517149.i			0.763512i	−0.924263	+	0.381756i	$0.875319\pi$
$824$		−	85854.2i		−	0.126447i
$825$	−243571.	+	16904.1i	−0.357864	+	0.0248362i
$826$	−348897.			−0.511372
$827$	894390.			1.30772			0.653861	−	0.756614i	$-0.273148\pi$
$827$	894390.			1.30772			0.653861	+	0.756614i	$0.273148\pi$
$828$	60514.8	+	175039.i	0.0882675	+	0.255314i
$829$	−485062.			−0.705811			−0.352905	−	0.935659i	$-0.614806\pi$
$829$	−485062.			−0.705811			−0.352905	+	0.935659i	$0.614806\pi$
$830$	13066.0	−	27662.9i	0.0189665	−	0.0401551i
$831$	−184151.	+	258510.i	−0.266668	+	0.374348i
$832$		−	80206.3i		−	0.115868i
$833$	343331.			0.494792
$834$	82376.0	+	58680.9i	0.118432	+	0.0843654i
$835$	−71978.1	+	152389.i	−0.103235	+	0.218565i
$836$			174872.i			0.250212i
$837$	−366628.	+	1.24626e6i	−0.523330	+	1.77893i
$838$		−	640400.i		−	0.911934i
$839$		−	1.15019e6i		−	1.63397i	−0.576658	−	0.816986i	$-0.695643\pi$
$839$		−	1.15019e6i		−	1.63397i	0.576658	−	0.816986i	$-0.304357\pi$
$840$	162243.	+	289672.i	0.229936	+	0.410533i
$841$	−782789.			−1.10676
$842$	−622364.			−0.877850
$843$	−522322.	+	733234.i	−0.734993	+	1.03178i
$844$	225988.			0.317249
$845$	−42931.6	+	90893.1i	−0.0601262	+	0.127297i
$846$	6828.44	+	19751.3i	0.00954071	+	0.0275965i
$847$		−	831926.i		−	1.15963i
$848$	−209177.			−0.290885
$849$	−5817.34	+	8166.37i	−0.00807066	+	0.0113296i
$850$	208184.	+	253138.i	0.288144	+	0.350364i
$851$			189505.i			0.261675i
$852$	−342977.	+	481469.i	−0.472482	+	0.663269i
$853$			791788.i			1.08820i	0.839019	+	0.544102i	$0.183130\pi$
$853$			791788.i			1.08820i	−0.839019	+	0.544102i	$0.816870\pi$
$854$		−	139666.i		−	0.191502i
$855$	1.01380e6	+	110339.i	1.38682	+	0.150937i
$856$	38236.9			0.0521838
$857$	1.35205e6			1.84090			0.920452	−	0.390857i	$-0.127821\pi$
$857$	1.35205e6			1.84090			0.920452	+	0.390857i	$0.127821\pi$
$858$	−140978.	−	100426.i	−0.191504	−	0.136418i
$859$	304256.			0.412338			0.206169	−	0.978516i	$-0.433900\pi$
$859$	304256.			0.412338			0.206169	+	0.978516i	$0.433900\pi$
$860$	−307677.	−	145326.i	−0.416005	−	0.196492i
$861$	−636287.	−	453261.i	−0.858315	−	0.611424i
$862$		−	158927.i		−	0.213886i
$863$	−797071.			−1.07023			−0.535113	−	0.844780i	$-0.679731\pi$
$863$	−797071.			−1.07023			−0.535113	+	0.844780i	$0.679731\pi$
$864$	−37243.1	+	126599.i	−0.0498905	+	0.169590i
$865$	37022.3	−	78382.1i	0.0494802	−	0.104757i
$866$			998695.i			1.33167i
$867$	−360260.	−	256632.i	−0.479267	−	0.341408i
$868$		−	929680.i		−	1.23394i
$869$		−	95995.2i		−	0.127119i
$870$	−379614.	−	677770.i	−0.501537	−	0.895455i
$871$	563623.			0.742938
$872$	−15919.1			−0.0209357
$873$	−300323.	+	103828.i	−0.394059	+	0.136235i
$874$	−407103.			−0.532944
$875$	−249123.	−	988039.i	−0.325385	−	1.29050i
$876$	291930.	−	409811.i	0.380427	−	0.534042i
$877$			1.04303e6i			1.35612i	0.735008	+	0.678058i	$0.237178\pi$
$877$			1.04303e6i			1.35612i	−0.735008	+	0.678058i	$0.762822\pi$
$878$	603.719			0.000783152
$879$	275582.	+	196312.i	0.356675	+	0.254079i
$880$	62796.6	+	29660.8i	0.0810907	+	0.0383017i
$881$		−	1.38766e6i		−	1.78785i	−0.448220	−	0.893923i	$-0.647942\pi$
$881$		−	1.38766e6i		−	1.78785i	0.448220	−	0.893923i	$-0.352058\pi$
$882$	−138623.	−	400967.i	−0.178196	−	0.515433i
$883$		−	594968.i		−	0.763083i	−0.924352	−	0.381542i	$-0.875393\pi$
$883$		−	594968.i		−	0.763083i	0.924352	−	0.381542i	$-0.124607\pi$
$884$			232351.i			0.297331i
$885$	207973.	+	371319.i	0.265534	+	0.474090i
$886$	−419766.			−0.534736
$887$	−736966.			−0.936699			−0.468350	−	0.883543i	$-0.655151\pi$
$887$	−736966.			−0.936699			−0.468350	+	0.883543i	$0.655151\pi$
$888$	−78342.3	+	109977.i	−0.0993506	+	0.139468i
$889$	−1.70716e6			−2.16009
$890$	300177.	+	141783.i	0.378963	+	0.178996i
$891$	175890.	+	223976.i	0.221557	+	0.282128i
$892$		−	182626.i		−	0.229527i
$893$	−45937.2			−0.0576052
$894$	283559.	−	398060.i	0.354788	−	0.498050i
$895$	−303916.	−	143549.i	−0.379409	−	0.179207i
$896$		−	94439.3i		−	0.117635i
$897$	233793.	−	328198.i	0.290568	−	0.407898i
$898$			329826.i			0.409008i
$899$			2.17525e6i			2.69147i
$900$	211577.	−	345340.i	0.261207	−	0.426346i
$901$	605969.			0.746451
$902$	−163413.			−0.200850
$903$	813308.	+	579363.i	0.997423	+	0.710518i
$904$	−537235.			−0.657397
$905$	−350865.	+	742838.i	−0.428394	+	0.906978i
$906$	600370.	+	427676.i	0.731413	+	0.521025i
$907$			767638.i			0.933130i	0.884487	+	0.466565i	$0.154509\pi$
$907$			767638.i			0.933130i	−0.884487	+	0.466565i	$0.845491\pi$
$908$	22277.8			0.0270210
$909$	949247.	−	328175.i	1.14882	−	0.397171i
$910$	308516.	−	653177.i	0.372559	−	0.788766i
$911$		−	450574.i		−	0.542911i	−0.962451	−	0.271456i	$-0.912495\pi$
$911$		−	450574.i		−	0.542911i	0.962451	−	0.271456i	$-0.0875051\pi$
$912$	−236257.	−	168298.i	−0.284050	−	0.202344i
$913$			18779.7i			0.0225293i
$914$		−	168065.i		−	0.201180i
$915$	−148642.	+	83253.1i	−0.177541	+	0.0994394i
$916$	−329994.			−0.393292
$917$	466726.			0.555039
$918$	107890.	−	366747.i	0.128026	−	0.435192i
$919$	1.41858e6			1.67967			0.839835	−	0.542842i	$-0.182652\pi$
$919$	1.41858e6			1.67967			0.839835	+	0.542842i	$0.182652\pi$
$920$	−69050.7	+	146191.i	−0.0815816	+	0.172721i
$921$	−521352.	+	731872.i	−0.614627	+	0.862811i
$922$			701573.i			0.825298i
$923$	1.28616e6			1.50971
$924$	−165995.	−	118247.i	−0.194425	−	0.138499i
$925$	320066.	−	263227.i	0.374073	−	0.307643i
$926$			192589.i			0.224600i
$927$	290466.	−	100420.i	0.338014	−	0.116859i
$928$			220967.i			0.256586i
$929$			260143.i			0.301426i	0.988578	+	0.150713i	$0.0481569\pi$
$929$			260143.i			0.301426i	−0.988578	+	0.150713i	$0.951843\pi$
$930$	−989429.	+	554172.i	−1.14398	+	0.640735i
$931$	932564.			1.07592
$932$	−634485.			−0.730448
$933$	976375.	−	1.37063e6i	1.12164	−	1.57455i
$934$	815361.			0.934666
$935$	−181917.	−	85925.1i	−0.208090	−	0.0982872i
$936$	271357.	−	93814.1i	0.309735	−	0.107082i
$937$		−	1.27182e6i		−	1.44860i	−0.689486	−	0.724299i	$-0.742164\pi$
$937$		−	1.27182e6i		−	1.44860i	0.689486	−	0.724299i	$-0.257836\pi$
$938$	663641.			0.754271
$939$	−627491.	+	880870.i	−0.711666	+	0.999034i
$940$	−7791.62	+	16496.1i	−0.00881804	+	0.0186692i
$941$		−	1.06149e6i		−	1.19877i	−0.800461	−	0.599385i	$-0.795412\pi$
$941$		−	1.06149e6i		−	1.19877i	0.800461	−	0.599385i	$-0.204588\pi$
$942$	−401646.	+	563829.i	−0.452628	+	0.635398i
$943$		−	380426.i		−	0.427806i
$944$		−	121058.i		−	0.135847i
$945$	−790262.	+	887726.i	−0.884927	+	0.994067i
$946$	208876.			0.233402
$947$	213920.			0.238535			0.119267	−	0.992862i	$-0.461945\pi$
$947$	213920.			0.238535			0.119267	+	0.992862i	$0.461945\pi$
$948$	129692.	+	92386.8i	0.144310	+	0.102800i
$949$	−1.09474e6			−1.21557
$950$	565476.	+	687581.i	0.626566	+	0.761862i
$951$	−42917.7	−	30572.6i	−0.0474543	−	0.0338043i
$952$			273583.i			0.301867i
$953$	−1.50019e6			−1.65182			−0.825908	−	0.563804i	$-0.809337\pi$
$953$	−1.50019e6			−1.65182			−0.825908	+	0.563804i	$0.809337\pi$
$954$	−244666.	−	707697.i	−0.268829	−	0.777589i
$955$	−182425.	−	86165.1i	−0.200022	−	0.0944767i
$956$			257768.i			0.282041i
$957$	388393.	+	276673.i	0.424080	+	0.302095i
$958$			34229.6i			0.0372967i
$959$		−	796247.i		−	0.865786i
$960$	−100509.	+	56294.2i	−0.109059	+	0.0610831i
$961$	2.25197e6			2.43847
$962$	293784.			0.317452
$963$	44724.2	+	129365.i	0.0482270	+	0.139497i
$964$	−622323.			−0.669672
$965$	−279844.	−	132179.i	−0.300512	−	0.141941i
$966$	275281.	−	386439.i	0.295000	−	0.414120i
$967$			821125.i			0.878125i	0.898457	+	0.439062i	$0.144689\pi$
$967$			821125.i			0.878125i	−0.898457	+	0.439062i	$0.855311\pi$
$968$	288657.			0.308057
$969$	684418.	+	487548.i	0.728910	+	0.519242i
$970$	−250828.	−	118474.i	−0.266583	−	0.125915i
$971$			190589.i			0.202144i	0.994879	+	0.101072i	$0.0322272\pi$
$971$			190589.i			0.202144i	−0.994879	+	0.101072i	$0.967773\pi$
$972$	−471876.	+	22075.0i	−0.499454	+	0.0233652i
$973$		−	259103.i		−	0.273682i
$974$			468215.i			0.493545i
$975$	−879058.	+	61007.7i	−0.924716	+	0.0641764i
$976$	48460.4			0.0508730
$977$	−1.03085e6			−1.07996			−0.539978	−	0.841679i	$-0.681567\pi$
$977$	−1.03085e6			−1.07996			−0.539978	+	0.841679i	$0.681567\pi$
$978$	371972.	−	522173.i	0.388895	−	0.545930i
$979$	−203784.			−0.212620
$980$	158176.	−	334885.i	0.164698	−	0.348693i
$981$	−18620.0	−	53858.3i	−0.0193482	−	0.0559648i
$982$			885663.i			0.918429i
$983$	−314101.			−0.325059			−0.162529	−	0.986704i	$-0.551965\pi$
$983$	−314101.			−0.325059			−0.162529	+	0.986704i	$0.551965\pi$
$984$	157270.	−	220775.i	0.162426	−	0.228013i
$985$	−438390.	+	928141.i	−0.451843	+	0.956624i
$986$		−	640126.i		−	0.658433i
$987$	31062.5	−	43605.4i	0.0318861	−	0.0447617i
$988$			631119.i			0.646543i
$989$			486264.i			0.497141i
$990$	−26899.0	+	247150.i	−0.0274452	+	0.252168i
$991$	−1.07730e6			−1.09695			−0.548476	−	0.836166i	$-0.684792\pi$
$991$	−1.07730e6			−1.09695			−0.548476	+	0.836166i	$0.684792\pi$
$992$	322575.			0.327799
$993$	−229022.	−	163145.i	−0.232263	−	0.165453i
$994$	1.51440e6			1.53274
$995$	416889.	−	882620.i	0.421089	−	0.891512i
$996$	−25372.0	−	18073.8i	−0.0255762	−	0.0182193i
$997$			146638.i			0.147522i	0.997276	+	0.0737608i	$0.0235001\pi$
$997$			146638.i			0.147522i	−0.997276	+	0.0737608i	$0.976500\pi$
$998$	443261.			0.445039
$999$	−463712.	−	136416.i	−0.464641	−	0.136689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.5.b.a.29.8	yes	8
3.2	odd	2	inner	30.5.b.a.29.2	yes	8
4.3	odd	2		240.5.c.d.209.1		8
5.2	odd	4		150.5.d.e.101.7		8
5.3	odd	4		150.5.d.e.101.2		8
5.4	even	2	inner	30.5.b.a.29.1	✓	8
12.11	even	2		240.5.c.d.209.7		8
15.2	even	4		150.5.d.e.101.3		8
15.8	even	4		150.5.d.e.101.6		8
15.14	odd	2	inner	30.5.b.a.29.7	yes	8
20.19	odd	2		240.5.c.d.209.8		8
60.59	even	2		240.5.c.d.209.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.5.b.a.29.1	✓	8	5.4	even	2	inner
30.5.b.a.29.2	yes	8	3.2	odd	2	inner
30.5.b.a.29.7	yes	8	15.14	odd	2	inner
30.5.b.a.29.8	yes	8	1.1	even	1	trivial
150.5.d.e.101.2		8	5.3	odd	4
150.5.d.e.101.3		8	15.2	even	4
150.5.d.e.101.6		8	15.8	even	4
150.5.d.e.101.7		8	5.2	odd	4
240.5.c.d.209.1		8	4.3	odd	2
240.5.c.d.209.2		8	60.59	even	2
240.5.c.d.209.7		8	12.11	even	2
240.5.c.d.209.8		8	20.19	odd	2

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	30.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} +(7.33029 + 5.22176i) q^{3} +8.00000 q^{4} +(-10.6772 + 22.6053i) q^{5} +(20.7332 + 14.7694i) q^{6} -65.2135i q^{7} +22.6274 q^{8} +(26.4664 + 76.5541i) q^{9} +(-30.1996 + 63.9373i) q^{10} -43.4057i q^{11} +(58.6423 + 41.7741i) q^{12} -156.653i q^{13} -184.452i q^{14} +(-196.306 + 109.950i) q^{15} +64.0000 q^{16} -185.403 q^{17} +(74.8583 + 216.528i) q^{18} -503.597 q^{19} +(-85.4174 + 180.842i) q^{20} +(340.530 - 478.034i) q^{21} -122.770i q^{22} +285.809 q^{23} +(165.866 + 118.155i) q^{24} +(-396.996 - 482.721i) q^{25} -443.081i q^{26} +(-205.741 + 699.365i) q^{27} -521.708i q^{28} +1220.68i q^{29} +(-555.238 + 310.984i) q^{30} +1781.99 q^{31} +181.019 q^{32} +(226.654 - 318.177i) q^{33} -524.399 q^{34} +(1474.17 + 696.296i) q^{35} +(211.731 + 612.433i) q^{36} +663.047i q^{37} -1424.39 q^{38} +(818.004 - 1148.31i) q^{39} +(-241.597 + 511.499i) q^{40} -1331.05i q^{41} +(963.163 - 1352.09i) q^{42} +1701.36i q^{43} -347.246i q^{44} +(-2013.11 - 219.101i) q^{45} +808.391 q^{46} +91.2182 q^{47} +(469.139 + 334.193i) q^{48} -1851.81 q^{49} +(-1122.87 - 1365.34i) q^{50} +(-1359.06 - 968.131i) q^{51} -1253.22i q^{52} -3268.39 q^{53} +(-581.923 + 1978.10i) q^{54} +(981.198 + 463.450i) q^{55} -1475.61i q^{56} +(-3691.51 - 2629.66i) q^{57} +3452.62i q^{58} -1891.53i q^{59} +(-1570.45 + 879.597i) q^{60} +757.194 q^{61} +5040.23 q^{62} +(4992.36 - 1725.97i) q^{63} +512.000 q^{64} +(3541.18 + 1672.61i) q^{65} +(641.075 - 899.939i) q^{66} +3597.91i q^{67} -1483.22 q^{68} +(2095.07 + 1492.43i) q^{69} +(4169.58 + 1969.42i) q^{70} +8210.27i q^{71} +(598.866 + 1732.22i) q^{72} -6988.31i q^{73} +1875.38i q^{74} +(-389.445 - 5611.50i) q^{75} -4028.77 q^{76} -2830.64 q^{77} +(2313.66 - 3247.92i) q^{78} +2211.58 q^{79} +(-683.339 + 1446.74i) q^{80} +(-5160.06 + 4052.22i) q^{81} -3764.77i q^{82} -432.656 q^{83} +(2724.24 - 3824.28i) q^{84} +(1979.58 - 4191.09i) q^{85} +4812.17i q^{86} +(-6374.12 + 8947.97i) q^{87} -982.159i q^{88} -4694.86i q^{89} +(-5693.94 - 619.712i) q^{90} -10215.9 q^{91} +2286.48 q^{92} +(13062.5 + 9305.14i) q^{93} +258.004 q^{94} +(5376.99 - 11383.9i) q^{95} +(1326.92 + 945.240i) q^{96} +3923.02i q^{97} -5237.70 q^{98} +(3322.88 - 1148.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{4} + 32 q^{6} - 56 q^{9} + 160 q^{10} - 760 q^{15} + 512 q^{16} - 816 q^{19} - 1024 q^{21} + 256 q^{24} + 840 q^{25} - 1600 q^{30} + 6224 q^{31} - 3392 q^{34} - 448 q^{36} + 10560 q^{39} + 1280 q^{40}+ \cdots - 22144 q^{99}+O(q^{100}) \) 8 * q + 64 * q^4 + 32 * q^6 - 56 * q^9 + 160 * q^10 - 760 * q^15 + 512 * q^16 - 816 * q^19 - 1024 * q^21 + 256 * q^24 + 840 * q^25 - 1600 * q^30 + 6224 * q^31 - 3392 * q^34 - 448 * q^36 + 10560 * q^39 + 1280 * q^40 - 6080 * q^45 - 2368 * q^46 - 21240 * q^49 - 3376 * q^51 + 5920 * q^54 + 5440 * q^55 - 6080 * q^60 - 368 * q^61 + 4096 * q^64 + 13696 * q^66 + 17296 * q^69 + 14080 * q^70 + 5440 * q^75 - 6528 * q^76 - 1584 * q^79 - 33784 * q^81 - 8192 * q^84 - 3440 * q^85 - 14560 * q^90 + 30720 * q^91 + 6080 * q^94 + 2048 * q^96 - 22144 * q^99

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