LMFDB - Embedded newform 5.6.b.a.4.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5,6,Mod(4,5)] 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("5.4"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	5.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:	$0.801919099065$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-11}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 3 $ x^2 - x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.2
Root			$0.500000 - 1.65831i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.6.b.a.4.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+6.63325i q^{2} -19.8997i q^{3} -12.0000 q^{4} +(-45.0000 + 33.1662i) q^{5} +132.000 q^{6} -59.6992i q^{7} +132.665i q^{8} -153.000 q^{9} +(-220.000 - 298.496i) q^{10} +252.000 q^{11} +238.797i q^{12} -119.398i q^{13} +396.000 q^{14} +(660.000 + 895.489i) q^{15} -1264.00 q^{16} -689.858i q^{17} -1014.89i q^{18} -220.000 q^{19} +(540.000 - 397.995i) q^{20} -1188.00 q^{21} +1671.58i q^{22} +2434.40i q^{23} +2640.00 q^{24} +(925.000 - 2984.96i) q^{25} +792.000 q^{26} -1790.98i q^{27} +716.391i q^{28} -6930.00 q^{29} +(-5940.00 + 4377.94i) q^{30} +6752.00 q^{31} -4139.15i q^{32} -5014.74i q^{33} +4576.00 q^{34} +(1980.00 + 2686.47i) q^{35} +1836.00 q^{36} +13969.6i q^{37} -1459.31i q^{38} -2376.00 q^{39} +(-4400.00 - 5969.92i) q^{40} -198.000 q^{41} -7880.30i q^{42} -417.895i q^{43} -3024.00 q^{44} +(6885.00 - 5074.44i) q^{45} -16148.0 q^{46} -10540.2i q^{47} +25153.3i q^{48} +13243.0 q^{49} +(19800.0 + 6135.76i) q^{50} -13728.0 q^{51} +1432.78i q^{52} -5823.99i q^{53} +11880.0 q^{54} +(-11340.0 + 8357.89i) q^{55} +7920.00 q^{56} +4377.94i q^{57} -45968.4i q^{58} -24660.0 q^{59} +(-7920.00 - 10745.9i) q^{60} -5698.00 q^{61} +44787.7i q^{62} +9133.98i q^{63} -12992.0 q^{64} +(3960.00 + 5372.93i) q^{65} +33264.0 q^{66} -43640.1i q^{67} +8278.30i q^{68} +48444.0 q^{69} +(-17820.0 + 13133.8i) q^{70} +53352.0 q^{71} -20297.7i q^{72} +70922.7i q^{73} -92664.0 q^{74} +(-59400.0 - 18407.3i) q^{75} +2640.00 q^{76} -15044.2i q^{77} -15760.6i q^{78} +51920.0 q^{79} +(56880.0 - 41922.1i) q^{80} -72819.0 q^{81} -1313.38i q^{82} -61841.8i q^{83} +14256.0 q^{84} +(22880.0 + 31043.6i) q^{85} +2772.00 q^{86} +137905. i q^{87} +33431.6i q^{88} -9990.00 q^{89} +(33660.0 + 45669.9i) q^{90} -7128.00 q^{91} -29212.8i q^{92} -134363. i q^{93} +69916.0 q^{94} +(9900.00 - 7296.57i) q^{95} -82368.0 q^{96} -101250. i q^{97} +87844.1i q^{98} -38556.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 24 q^{4} - 90 q^{5} + 264 q^{6} - 306 q^{9} - 440 q^{10} + 504 q^{11} + 792 q^{14} + 1320 q^{15} - 2528 q^{16} - 440 q^{19} + 1080 q^{20} - 2376 q^{21} + 5280 q^{24} + 1850 q^{25} + 1584 q^{26} - 13860 q^{29}+ \cdots - 77112 q^{99}+O(q^{100}) $ 2 * q - 24 * q^4 - 90 * q^5 + 264 * q^6 - 306 * q^9 - 440 * q^10 + 504 * q^11 + 792 * q^14 + 1320 * q^15 - 2528 * q^16 - 440 * q^19 + 1080 * q^20 - 2376 * q^21 + 5280 * q^24 + 1850 * q^25 + 1584 * q^26 - 13860 * q^29 - 11880 * q^30 + 13504 * q^31 + 9152 * q^34 + 3960 * q^35 + 3672 * q^36 - 4752 * q^39 - 8800 * q^40 - 396 * q^41 - 6048 * q^44 + 13770 * q^45 - 32296 * q^46 + 26486 * q^49 + 39600 * q^50 - 27456 * q^51 + 23760 * q^54 - 22680 * q^55 + 15840 * q^56 - 49320 * q^59 - 15840 * q^60 - 11396 * q^61 - 25984 * q^64 + 7920 * q^65 + 66528 * q^66 + 96888 * q^69 - 35640 * q^70 + 106704 * q^71 - 185328 * q^74 - 118800 * q^75 + 5280 * q^76 + 103840 * q^79 + 113760 * q^80 - 145638 * q^81 + 28512 * q^84 + 45760 * q^85 + 5544 * q^86 - 19980 * q^89 + 67320 * q^90 - 14256 * q^91 + 139832 * q^94 + 19800 * q^95 - 164736 * q^96 - 77112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			6.63325i			1.17260i	0.810093	+	0.586302i	$0.199417\pi$
$2$			6.63325i			1.17260i	−0.810093	+	0.586302i	$0.800583\pi$
$3$		−	19.8997i		−	1.27657i	−0.769800	−	0.638285i	$-0.779644\pi$
$3$		−	19.8997i		−	1.27657i	0.769800	−	0.638285i	$-0.220356\pi$
$4$	−12.0000			−0.375000
$5$	−45.0000	+	33.1662i	−0.804984	+	0.593296i
$5$	−45.0000	+	33.1662i	−0.804984	+	0.593296i
$6$	132.000			1.49691
$7$		−	59.6992i		−	0.460494i	−0.973132	−	0.230247i	$-0.926047\pi$
$7$		−	59.6992i		−	0.460494i	0.973132	−	0.230247i	$-0.0739534\pi$
$8$			132.665i			0.732877i
$9$	−153.000			−0.629630
$10$	−220.000	−	298.496i	−0.695701	−	0.943928i
$11$	252.000			0.627941			0.313970	−	0.949433i	$-0.398341\pi$
$11$	252.000			0.627941			0.313970	+	0.949433i	$0.398341\pi$
$12$			238.797i			0.478714i
$13$		−	119.398i		−	0.195948i	−0.995189	−	0.0979739i	$-0.968764\pi$
$13$		−	119.398i		−	0.195948i	0.995189	−	0.0979739i	$-0.0312362\pi$
$14$	396.000			0.539977
$15$	660.000	+	895.489i	0.757383	+	1.02762i
$16$	−1264.00			−1.23438
$17$		−	689.858i		−	0.578945i	−0.957186	−	0.289473i	$-0.906520\pi$
$17$		−	689.858i		−	0.578945i	0.957186	−	0.289473i	$-0.0934799\pi$
$18$		−	1014.89i		−	0.738306i
$19$	−220.000			−0.139810			−0.0699051	−	0.997554i	$-0.522270\pi$
$19$	−220.000			−0.139810			−0.0699051	+	0.997554i	$0.522270\pi$
$20$	540.000	−	397.995i	0.301869	−	0.222486i
$21$	−1188.00			−0.587852
$22$			1671.58i			0.736326i
$23$			2434.40i			0.959561i	0.877388	+	0.479781i	$0.159284\pi$
$23$			2434.40i			0.959561i	−0.877388	+	0.479781i	$0.840716\pi$
$24$	2640.00			0.935569
$25$	925.000	−	2984.96i	0.296000	−	0.955188i
$26$	792.000			0.229769
$27$		−	1790.98i		−	0.472804i
$28$			716.391i			0.172685i
$29$	−6930.00			−1.53016			−0.765082	−	0.643932i	$-0.777302\pi$
$29$	−6930.00			−1.53016			−0.765082	+	0.643932i	$0.777302\pi$
$30$	−5940.00	+	4377.94i	−1.20499	+	0.888111i
$31$	6752.00			1.26191			0.630955	−	0.775820i	$-0.282663\pi$
$31$	6752.00			1.26191			0.630955	+	0.775820i	$0.282663\pi$
$32$		−	4139.15i		−	0.714556i
$33$		−	5014.74i		−	0.801610i
$34$	4576.00			0.678873
$35$	1980.00	+	2686.47i	0.273209	+	0.370690i
$36$	1836.00			0.236111
$37$			13969.6i			1.67757i	0.544464	+	0.838785i	$0.316733\pi$
$37$			13969.6i			1.67757i	−0.544464	+	0.838785i	$0.683267\pi$
$38$		−	1459.31i		−	0.163942i
$39$	−2376.00			−0.250141
$40$	−4400.00	−	5969.92i	−0.434813	−	0.589955i
$41$	−198.000			−0.0183952			−0.00919762	−	0.999958i	$-0.502928\pi$
$41$	−198.000			−0.0183952			−0.00919762	+	0.999958i	$0.502928\pi$
$42$		−	7880.30i		−	0.689318i
$43$		−	417.895i		−	0.0344664i	−0.999851	−	0.0172332i	$-0.994514\pi$
$43$		−	417.895i		−	0.0344664i	0.999851	−	0.0172332i	$-0.00548577\pi$
$44$	−3024.00			−0.235478
$45$	6885.00	−	5074.44i	0.506842	−	0.373557i
$46$	−16148.0			−1.12519
$47$		−	10540.2i		−	0.695994i	−0.937496	−	0.347997i	$-0.886862\pi$
$47$		−	10540.2i		−	0.695994i	0.937496	−	0.347997i	$-0.113138\pi$
$48$			25153.3i			1.57577i
$49$	13243.0			0.787945
$50$	19800.0	+	6135.76i	1.12006	+	0.347091i
$51$	−13728.0			−0.739064
$52$			1432.78i			0.0734804i
$53$		−	5823.99i		−	0.284794i	−0.989810	−	0.142397i	$-0.954519\pi$
$53$		−	5823.99i		−	0.284794i	0.989810	−	0.142397i	$-0.0454810\pi$
$54$	11880.0			0.554411
$55$	−11340.0	+	8357.89i	−0.505483	+	0.372555i
$56$	7920.00			0.337485
$57$			4377.94i			0.178477i
$58$		−	45968.4i		−	1.79428i
$59$	−24660.0			−0.922281			−0.461140	−	0.887327i	$-0.652560\pi$
$59$	−24660.0			−0.922281			−0.461140	+	0.887327i	$0.652560\pi$
$60$	−7920.00	−	10745.9i	−0.284019	−	0.385357i
$61$	−5698.00			−0.196064			−0.0980320	−	0.995183i	$-0.531255\pi$
$61$	−5698.00			−0.196064			−0.0980320	+	0.995183i	$0.531255\pi$
$62$			44787.7i			1.47972i
$63$			9133.98i			0.289941i
$64$	−12992.0			−0.396484
$65$	3960.00	+	5372.93i	0.116255	+	0.157735i
$66$	33264.0			0.939971
$67$		−	43640.1i		−	1.18768i	−0.804583	−	0.593840i	$-0.797611\pi$
$67$		−	43640.1i		−	1.18768i	0.804583	−	0.593840i	$-0.202389\pi$
$68$			8278.30i			0.217104i
$69$	48444.0			1.22495
$70$	−17820.0	+	13133.8i	−0.434673	+	0.320366i
$71$	53352.0			1.25604			0.628022	−	0.778196i	$-0.283865\pi$
$71$	53352.0			1.25604			0.628022	+	0.778196i	$0.283865\pi$
$72$		−	20297.7i		−	0.461441i
$73$			70922.7i			1.55768i	0.627223	+	0.778840i	$0.284192\pi$
$73$			70922.7i			1.55768i	−0.627223	+	0.778840i	$0.715808\pi$
$74$	−92664.0			−1.96712
$75$	−59400.0	−	18407.3i	−1.21936	−	0.377865i
$76$	2640.00			0.0524288
$77$		−	15044.2i		−	0.289163i
$78$		−	15760.6i		−	0.293316i
$79$	51920.0			0.935981			0.467990	−	0.883734i	$-0.344978\pi$
$79$	51920.0			0.935981			0.467990	+	0.883734i	$0.344978\pi$
$80$	56880.0	−	41922.1i	0.993653	−	0.732350i
$81$	−72819.0			−1.23320
$82$		−	1313.38i		−	0.0215703i
$83$		−	61841.8i		−	0.985342i	−0.870216	−	0.492671i	$-0.836021\pi$
$83$		−	61841.8i		−	0.985342i	0.870216	−	0.492671i	$-0.163979\pi$
$84$	14256.0			0.220445
$85$	22880.0	+	31043.6i	0.343486	+	0.466042i
$86$	2772.00			0.0404154
$87$			137905.i			1.95336i
$88$			33431.6i			0.460204i
$89$	−9990.00			−0.133687			−0.0668437	−	0.997763i	$-0.521293\pi$
$89$	−9990.00			−0.133687			−0.0668437	+	0.997763i	$0.521293\pi$
$90$	33660.0	+	45669.9i	0.438034	+	0.594325i
$91$	−7128.00			−0.0902328
$92$		−	29212.8i		−	0.359836i
$93$		−	134363.i		−	1.61092i
$94$	69916.0			0.816125
$95$	9900.00	−	7296.57i	0.112545	−	0.0829488i
$96$	−82368.0			−0.912180
$97$		−	101250.i		−	1.09261i	−0.837586	−	0.546305i	$-0.816034\pi$
$97$		−	101250.i		−	1.09261i	0.837586	−	0.546305i	$-0.183966\pi$
$98$			87844.1i			0.923948i
$99$	−38556.0			−0.395370
$100$	−11100.0	+	35819.5i	−0.111000	+	0.358195i
$101$	−109098.			−1.06418			−0.532088	−	0.846689i	$-0.678592\pi$
$101$	−109098.			−1.06418			−0.532088	+	0.846689i	$0.678592\pi$
$102$		−	91061.3i		−	0.866629i
$103$			70624.2i			0.655935i	0.944689	+	0.327967i	$0.106364\pi$
$103$			70624.2i			0.655935i	−0.944689	+	0.327967i	$0.893636\pi$
$104$	15840.0			0.143606
$105$	53460.0	−	39401.5i	0.473212	−	0.348770i
$106$	38632.0			0.333951
$107$			97117.4i			0.820045i	0.912075	+	0.410022i	$0.134479\pi$
$107$			97117.4i			0.820045i	−0.912075	+	0.410022i	$0.865521\pi$
$108$			21491.7i			0.177301i
$109$	−21010.0			−0.169379			−0.0846895	−	0.996407i	$-0.526990\pi$
$109$	−21010.0			−0.169379			−0.0846895	+	0.996407i	$0.526990\pi$
$110$	−55440.0	−	75221.1i	−0.436859	−	0.592731i
$111$	277992.			2.14153
$112$			75459.8i			0.568422i
$113$			105018.i			0.773688i	0.922145	+	0.386844i	$0.126435\pi$
$113$			105018.i			0.773688i	−0.922145	+	0.386844i	$0.873565\pi$
$114$	−29040.0			−0.209283
$115$	−80740.0	−	109548.i	−0.569304	−	0.772432i
$116$	83160.0			0.573812
$117$			18268.0i			0.123375i
$118$		−	163576.i		−	1.08147i
$119$	−41184.0			−0.266601
$120$	−118800.	+	87558.9i	−0.753119	+	0.555069i
$121$	−97547.0			−0.605690
$122$		−	37796.3i		−	0.229905i
$123$			3940.15i			0.0234828i
$124$	−81024.0			−0.473216
$125$	57375.0	+	165002.i	0.328434	+	0.944527i
$126$	−60588.0			−0.339985
$127$		−	87220.6i		−	0.479855i	−0.970791	−	0.239927i	$-0.922876\pi$
$127$		−	87220.6i		−	0.479855i	0.970791	−	0.239927i	$-0.0771236\pi$
$128$		−	218632.i		−	1.17947i
$129$	−8316.00			−0.0439987
$130$	−35640.0	+	26267.7i	−0.184961	+	0.136321i
$131$	192852.			0.981852			0.490926	−	0.871201i	$-0.336659\pi$
$131$	192852.			0.981852			0.490926	+	0.871201i	$0.336659\pi$
$132$			60176.8i			0.300604i
$133$			13133.8i			0.0643817i
$134$	289476.			1.39268
$135$	59400.0	+	80594.0i	0.280512	+	0.380599i
$136$	91520.0			0.424296
$137$		−	143570.i		−	0.653525i	−0.945106	−	0.326763i	$-0.894042\pi$
$137$		−	143570.i		−	0.653525i	0.945106	−	0.326763i	$-0.105958\pi$
$138$			321341.i			1.43638i
$139$	−318340.			−1.39751			−0.698754	−	0.715362i	$-0.746262\pi$
$139$	−318340.			−1.39751			−0.698754	+	0.715362i	$0.746262\pi$
$140$	−23760.0	−	32237.6i	−0.102453	−	0.139009i
$141$	−209748.			−0.888485
$142$			353897.i			1.47284i
$143$		−	30088.4i		−	0.123044i
$144$	193392.			0.777199
$145$	311850.	−	229842.i	1.23176	−	0.907841i
$146$	−470448.			−1.82654
$147$		−	263532.i		−	1.00587i
$148$		−	167635.i		−	0.629088i
$149$	84150.0			0.310519			0.155260	−	0.987874i	$-0.450379\pi$
$149$	84150.0			0.310519			0.155260	+	0.987874i	$0.450379\pi$
$150$	122100.	−	394015.i	0.443085	−	1.42983i
$151$	−155848.			−0.556236			−0.278118	−	0.960547i	$-0.589711\pi$
$151$	−155848.			−0.556236			−0.278118	+	0.960547i	$0.589711\pi$
$152$		−	29186.3i		−	0.102464i
$153$			105548.i			0.364521i
$154$	99792.0			0.339074
$155$	−303840.	+	223939.i	−1.01582	+	0.748686i
$156$	28512.0			0.0938029
$157$			356643.i			1.15474i	0.816482	+	0.577371i	$0.195921\pi$
$157$			356643.i			1.15474i	−0.816482	+	0.577371i	$0.804079\pi$
$158$			344398.i			1.09753i
$159$	−115896.			−0.363560
$160$	137280.	+	186262.i	0.423943	+	0.575206i
$161$	145332.			0.441872
$162$		−	483027.i		−	1.44605i
$163$		−	144890.i		−	0.427139i	−0.976928	−	0.213570i	$-0.931491\pi$
$163$		−	144890.i		−	0.427139i	0.976928	−	0.213570i	$-0.0685090\pi$
$164$	2376.00			0.00689822
$165$	166320.	+	225663.i	0.475592	+	0.645284i
$166$	410212.			1.15542
$167$		−	18102.1i		−	0.0502272i	−0.999685	−	0.0251136i	$-0.992005\pi$
$167$		−	18102.1i		−	0.0502272i	0.999685	−	0.0251136i	$-0.00799474\pi$
$168$		−	157606.i		−	0.430824i
$169$	357037.			0.961604
$170$	−205920.	+	151769.i	−0.546482	+	0.402773i
$171$	33660.0			0.0880286
$172$			5014.74i			0.0129249i
$173$		−	492572.i		−	1.25128i	−0.780112	−	0.625640i	$-0.784838\pi$
$173$		−	492572.i		−	1.25128i	0.780112	−	0.625640i	$-0.215162\pi$
$174$	−914760.			−2.29052
$175$	−178200.	−	55221.8i	−0.439858	−	0.136306i
$176$	−318528.			−0.775115
$177$			490728.i			1.17736i
$178$		−	66266.2i		−	0.156762i
$179$	444420.			1.03672			0.518359	−	0.855163i	$-0.326543\pi$
$179$	444420.			1.03672			0.518359	+	0.855163i	$0.326543\pi$
$180$	−82620.0	+	60893.2i	−0.190066	+	0.140084i
$181$	156902.			0.355985			0.177993	−	0.984032i	$-0.443040\pi$
$181$	156902.			0.355985			0.177993	+	0.984032i	$0.443040\pi$
$182$		−	47281.8i		−	0.105807i
$183$			113389.i			0.250289i
$184$	−322960.			−0.703241
$185$	−463320.	−	628633.i	−0.995295	−	1.35042i
$186$	891264.			1.88897
$187$		−	173844.i		−	0.363543i
$188$			126483.i			0.260998i
$189$	−106920.			−0.217723
$190$	48400.0	+	65669.2i	0.0972661	+	0.131971i
$191$	332352.			0.659196			0.329598	−	0.944121i	$-0.393087\pi$
$191$	332352.			0.659196			0.329598	+	0.944121i	$0.393087\pi$
$192$			258538.i			0.506140i
$193$			786120.i			1.51913i	0.650430	+	0.759566i	$0.274589\pi$
$193$			786120.i			1.51913i	−0.650430	+	0.759566i	$0.725411\pi$
$194$	671616.			1.28120
$195$	106920.	−	78803.0i	0.201360	−	0.148408i
$196$	−158916.			−0.295480
$197$			59606.4i			0.109428i	0.998502	+	0.0547138i	$0.0174247\pi$
$197$			59606.4i			0.109428i	−0.998502	+	0.0547138i	$0.982575\pi$
$198$		−	255752.i		−	0.463613i
$199$	−395800.			−0.708505			−0.354253	−	0.935150i	$-0.615265\pi$
$199$	−395800.			−0.708505			−0.354253	+	0.935150i	$0.615265\pi$
$200$	396000.	+	122715.i	0.700036	+	0.216932i
$201$	−868428.			−1.51616
$202$		−	723674.i		−	1.24786i
$203$			413716.i			0.704631i
$204$	164736.			0.277149
$205$	8910.00	−	6566.92i	0.0148079	−	0.0109138i
$206$	−468468.			−0.769151
$207$		−	372464.i		−	0.604168i
$208$			150920.i			0.241873i
$209$	−55440.0			−0.0877925
$210$	261360.	+	354614.i	0.408969	+	0.554890i
$211$	−251548.			−0.388969			−0.194484	−	0.980906i	$-0.562303\pi$
$211$	−251548.			−0.388969			−0.194484	+	0.980906i	$0.562303\pi$
$212$			69887.9i			0.106798i
$213$		−	1.06169e6i		−	1.60343i
$214$	−644204.			−0.961588
$215$	13860.0	+	18805.3i	0.0204488	+	0.0277449i
$216$	237600.			0.346507
$217$		−	403089.i		−	0.581101i
$218$		−	139365.i		−	0.198615i
$219$	1.41134e6			1.98849
$220$	136080.	−	100295.i	0.189556	−	0.139708i
$221$	−82368.0			−0.113443
$222$			1.84399e6i			2.51117i
$223$		−	288765.i		−	0.388851i	−0.980917	−	0.194425i	$-0.937716\pi$
$223$		−	288765.i		−	0.388851i	0.980917	−	0.194425i	$-0.0622842\pi$
$224$	−247104.			−0.329048
$225$	−141525.	+	456699.i	−0.186370	+	0.601415i
$226$	−696608.			−0.907230
$227$			1.16414e6i			1.49948i	0.661731	+	0.749741i	$0.269822\pi$
$227$			1.16414e6i			1.49948i	−0.661731	+	0.749741i	$0.730178\pi$
$228$		−	52535.3i		−	0.0669290i
$229$	547670.			0.690129			0.345064	−	0.938579i	$-0.387857\pi$
$229$	547670.			0.690129			0.345064	+	0.938579i	$0.387857\pi$
$230$	726660.	−	535569.i	0.905757	−	0.667568i
$231$	−299376.			−0.369137
$232$		−	919368.i		−	1.12142i
$233$			48104.3i			0.0580489i	0.999579	+	0.0290245i	$0.00924007\pi$
$233$			48104.3i			0.0580489i	−0.999579	+	0.0290245i	$0.990760\pi$
$234$	−121176.			−0.144669
$235$	349580.	+	474311.i	0.412930	+	0.560264i
$236$	295920.			0.345855
$237$		−	1.03319e6i		−	1.19484i
$238$		−	273184.i		−	0.312617i
$239$	−1.00584e6			−1.13903			−0.569514	−	0.821982i	$-0.692868\pi$
$239$	−1.00584e6			−1.13903			−0.569514	+	0.821982i	$0.692868\pi$
$240$	−834240.	−	1.13190e6i	−0.934895	−	1.26847i
$241$	895202.			0.992838			0.496419	−	0.868083i	$-0.334648\pi$
$241$	895202.			0.992838			0.496419	+	0.868083i	$0.334648\pi$
$242$		−	647054.i		−	0.710235i
$243$			1.01387e6i			1.10146i
$244$	68376.0			0.0735240
$245$	−595935.	+	439221.i	−0.634284	+	0.467485i
$246$	−26136.0			−0.0275360
$247$			26267.7i			0.0273955i
$248$			895754.i			0.924825i
$249$	−1.23064e6			−1.25786
$250$	−1.09450e6	+	380583.i	−1.10756	+	0.385123i
$251$	558252.			0.559301			0.279651	−	0.960102i	$-0.409781\pi$
$251$	558252.			0.559301			0.279651	+	0.960102i	$0.409781\pi$
$252$		−	109608.i		−	0.108728i
$253$			613469.i			0.602548i
$254$	578556.			0.562680
$255$	617760.	−	455306.i	0.594935	−	0.438483i
$256$	1.03450e6			0.986572
$257$		−	787924.i		−	0.744135i	−0.928206	−	0.372067i	$-0.878649\pi$
$257$		−	787924.i		−	0.744135i	0.928206	−	0.372067i	$-0.121351\pi$
$258$		−	55162.1i		−	0.0515931i
$259$	833976.			0.772510
$260$	−47520.0	−	64475.2i	−0.0435956	−	0.0591506i
$261$	1.06029e6			0.963437
$262$			1.27924e6i			1.15132i
$263$		−	1.63173e6i		−	1.45465i	−0.686291	−	0.727327i	$-0.740762\pi$
$263$		−	1.63173e6i		−	1.45465i	0.686291	−	0.727327i	$-0.259238\pi$
$264$	665280.			0.587482
$265$	193160.	+	262080.i	0.168967	+	0.229255i
$266$	−87120.0			−0.0754942
$267$			198798.i			0.170661i
$268$			523682.i			0.445380i
$269$	−1.73637e6			−1.46306			−0.731529	−	0.681810i	$-0.761193\pi$
$269$	−1.73637e6			−1.46306			−0.731529	+	0.681810i	$0.761193\pi$
$270$	−534600.	+	394015.i	−0.446292	+	0.328930i
$271$	−1.72005e6			−1.42271			−0.711357	−	0.702831i	$-0.751919\pi$
$271$	−1.72005e6			−1.42271			−0.711357	+	0.702831i	$0.751919\pi$
$272$			871980.i			0.714635i
$273$			141845.i			0.115188i
$274$	952336.			0.766326
$275$	233100.	−	752211.i	0.185871	−	0.599802i
$276$	−581328.			−0.459355
$277$			1.27243e6i			0.996402i	0.867062	+	0.498201i	$0.166006\pi$
$277$			1.27243e6i			0.996402i	−0.867062	+	0.498201i	$0.833994\pi$
$278$		−	2.11163e6i		−	1.63872i
$279$	−1.03306e6			−0.794536
$280$	−356400.	+	262677.i	−0.271671	+	0.200229i
$281$	1.46500e6			1.10681			0.553404	−	0.832913i	$-0.313329\pi$
$281$	1.46500e6			1.10681			0.553404	+	0.832913i	$0.313329\pi$
$282$		−	1.39131e6i		−	1.04184i
$283$		−	1.65051e6i		−	1.22504i	−0.790455	−	0.612521i	$-0.790156\pi$
$283$		−	1.65051e6i		−	1.22504i	0.790455	−	0.612521i	$-0.209844\pi$
$284$	−640224.			−0.471016
$285$	−145200.	−	197008.i	−0.105890	−	0.143672i
$286$	199584.			0.144281
$287$			11820.5i			0.00847089i
$288$			633290.i			0.449905i
$289$	943953.			0.664823
$290$	1.52460e6	+	2.06858e6i	1.06454	+	1.44437i
$291$	−2.01485e6			−1.39479
$292$		−	851072.i		−	0.584130i
$293$			2.38772e6i			1.62485i	0.583064	+	0.812426i	$0.301854\pi$
$293$			2.38772e6i			1.62485i	−0.583064	+	0.812426i	$0.698146\pi$
$294$	1.74808e6			1.17948
$295$	1.10970e6	−	817880.i	0.742422	−	0.547185i
$296$	−1.85328e6			−1.22945
$297$		−	451326.i		−	0.296893i
$298$			558188.i			0.364116i
$299$	290664.			0.188024
$300$	712800.	+	220887.i	0.457261	+	0.141699i
$301$	−24948.0			−0.0158716
$302$		−	1.03378e6i		−	0.652244i
$303$			2.17102e6i			1.35849i
$304$	278080.			0.172578
$305$	256410.	−	188981.i	0.157828	−	0.116324i
$306$	−700128.			−0.427439
$307$			928264.i			0.562115i	0.959691	+	0.281058i	$0.0906852\pi$
$307$			928264.i			0.562115i	−0.959691	+	0.281058i	$0.909315\pi$
$308$			180531.i			0.108436i
$309$	1.40540e6			0.837346
$310$	−1.48544e6	−	2.01545e6i	−0.877912	−	1.19115i
$311$	568152.			0.333092			0.166546	−	0.986034i	$-0.446739\pi$
$311$	568152.			0.333092			0.166546	+	0.986034i	$0.446739\pi$
$312$		−	315212.i		−	0.183323i
$313$		−	1.72244e6i		−	0.993766i	−0.867818	−	0.496883i	$-0.834478\pi$
$313$		−	1.72244e6i		−	0.993766i	0.867818	−	0.496883i	$-0.165522\pi$
$314$	−2.36570e6			−1.35405
$315$	−302940.	−	411029.i	−0.172021	−	0.233398i
$316$	−623040.			−0.350993
$317$			131643.i			0.0735785i	0.999323	+	0.0367893i	$0.0117130\pi$
$317$			131643.i			0.0735785i	−0.999323	+	0.0367893i	$0.988287\pi$
$318$		−	768767.i		−	0.426311i
$319$	−1.74636e6			−0.960853
$320$	584640.	−	430896.i	0.319164	−	0.235233i
$321$	1.93261e6			1.04684
$322$			964023.i			0.518141i
$323$			151769.i			0.0809424i
$324$	873828.			0.462449
$325$	−356400.	−	110444.i	−0.187167	−	0.0580006i
$326$	961092.			0.500865
$327$			418094.i			0.216224i
$328$		−	26267.7i		−	0.0134815i
$329$	−629244.			−0.320501
$330$	−1.49688e6	+	1.10324e6i	−0.756662	+	0.557681i
$331$	−1.58055e6			−0.792935			−0.396468	−	0.918049i	$-0.629764\pi$
$331$	−1.58055e6			−0.792935			−0.396468	+	0.918049i	$0.629764\pi$
$332$			742101.i			0.369503i
$333$		−	2.13735e6i		−	1.05625i
$334$	120076.			0.0588966
$335$	1.44738e6	+	1.96381e6i	0.704645	+	0.956063i
$336$	1.50163e6			0.725630
$337$			1.22885e6i			0.589419i	0.955587	+	0.294709i	$0.0952228\pi$
$337$			1.22885e6i			0.589419i	−0.955587	+	0.294709i	$0.904777\pi$
$338$			2.36832e6i			1.12758i
$339$	2.08982e6			0.987667
$340$	−274560.	−	372523.i	−0.128807	−	0.174766i
$341$	1.70150e6			0.792405
$342$			223275.i			0.103223i
$343$		−	1.79396e6i		−	0.823338i
$344$	55440.0			0.0252596
$345$	−2.17998e6	+	1.60671e6i	−0.986063	+	0.726756i
$346$	3.26735e6			1.46726
$347$		−	3.84224e6i		−	1.71301i	−0.516137	−	0.856506i	$-0.672630\pi$
$347$		−	3.84224e6i		−	1.71301i	0.516137	−	0.856506i	$-0.327370\pi$
$348$		−	1.65486e6i		−	0.732511i
$349$	−1.59445e6			−0.700725			−0.350362	−	0.936614i	$-0.613942\pi$
$349$	−1.59445e6			−0.700725			−0.350362	+	0.936614i	$0.613942\pi$
$350$	366300.	−	1.18205e6i	0.159833	−	0.515779i
$351$	−213840.			−0.0926448
$352$		−	1.04307e6i		−	0.448699i
$353$		−	295365.i		−	0.126160i	−0.998008	−	0.0630802i	$-0.979908\pi$
$353$		−	295365.i		−	0.126160i	0.998008	−	0.0630802i	$-0.0200924\pi$
$354$	−3.25512e6			−1.38057
$355$	−2.40084e6	+	1.76949e6i	−1.01110	+	0.745206i
$356$	119880.			0.0501328
$357$			819551.i			0.340334i
$358$			2.94795e6i			1.21566i
$359$	1.10484e6			0.452442			0.226221	−	0.974076i	$-0.427363\pi$
$359$	1.10484e6			0.452442			0.226221	+	0.974076i	$0.427363\pi$
$360$	673200.	+	913398.i	0.273771	+	0.371453i
$361$	−2.42770e6			−0.980453
$362$			1.04077e6i			0.417430i
$363$			1.94116e6i			0.773206i
$364$	85536.0			0.0338373
$365$	−2.35224e6	−	3.19152e6i	−0.924165	−	1.25391i
$366$	−752136.			−0.293490
$367$		−	1.83760e6i		−	0.712174i	−0.934453	−	0.356087i	$-0.884111\pi$
$367$		−	1.83760e6i		−	0.712174i	0.934453	−	0.356087i	$-0.115889\pi$
$368$		−	3.07708e6i		−	1.18446i
$369$	30294.0			0.0115822
$370$	4.16988e6	−	3.07332e6i	1.58350	−	1.16709i
$371$	−347688.			−0.131146
$372$			1.61236e6i			0.604093i
$373$			2.93350e6i			1.09173i	0.837874	+	0.545864i	$0.183798\pi$
$373$			2.93350e6i			1.09173i	−0.837874	+	0.545864i	$0.816202\pi$
$374$	1.15315e6			0.426292
$375$	3.28350e6	−	1.14175e6i	1.20575	−	0.419268i
$376$	1.39832e6			0.510078
$377$			827432.i			0.299832i
$378$		−	709227.i		−	0.255303i
$379$	5.09342e6			1.82143			0.910713	−	0.413040i	$-0.135533\pi$
$379$	5.09342e6			1.82143			0.910713	+	0.413040i	$0.135533\pi$
$380$	−118800.	+	87558.9i	−0.0422044	+	0.0311058i
$381$	−1.73567e6			−0.612568
$382$			2.20457e6i			0.772976i
$383$			3.17485e6i			1.10593i	0.833205	+	0.552964i	$0.186503\pi$
$383$			3.17485e6i			1.10593i	−0.833205	+	0.552964i	$0.813497\pi$
$384$	−4.35072e6			−1.50568
$385$	498960.	+	676989.i	0.171559	+	0.232772i
$386$	−5.21453e6			−1.78134
$387$			63937.9i			0.0217011i
$388$			1.21500e6i			0.409729i
$389$	1.79991e6			0.603083			0.301541	−	0.953453i	$-0.402499\pi$
$389$	1.79991e6			0.603083			0.301541	+	0.953453i	$0.402499\pi$
$390$	522720.	+	709227.i	0.174023	+	0.236115i
$391$	1.67939e6			0.555533
$392$			1.75688e6i			0.577467i
$393$		−	3.83771e6i		−	1.25340i
$394$	−395384.			−0.128315
$395$	−2.33640e6	+	1.72199e6i	−0.753450	+	0.555314i
$396$	462672.			0.148264
$397$		−	4.90405e6i		−	1.56163i	−0.624760	−	0.780817i	$-0.714803\pi$
$397$		−	4.90405e6i		−	1.56163i	0.624760	−	0.780817i	$-0.285197\pi$
$398$		−	2.62544e6i		−	0.830796i
$399$	261360.			0.0821877
$400$	−1.16920e6	+	3.77299e6i	−0.365375	+	1.17906i
$401$	−642798.			−0.199624			−0.0998122	−	0.995006i	$-0.531824\pi$
$401$	−642798.			−0.199624			−0.0998122	+	0.995006i	$0.531824\pi$
$402$		−	5.76050e6i		−	1.77785i
$403$		−	806179.i		−	0.247268i
$404$	1.30918e6			0.399066
$405$	3.27686e6	−	2.41513e6i	0.992704	−	0.731650i
$406$	−2.74428e6			−0.826254
$407$			3.52035e6i			1.05341i
$408$		−	1.82123e6i		−	0.541643i
$409$	−2.05711e6			−0.608064			−0.304032	−	0.952662i	$-0.598333\pi$
$409$	−2.05711e6			−0.608064			−0.304032	+	0.952662i	$0.598333\pi$
$410$	43560.0	+	59102.3i	0.0127976	+	0.0173638i
$411$	−2.85701e6			−0.834271
$412$		−	847490.i		−	0.245975i
$413$			1.47218e6i			0.424704i
$414$	2.47064e6			0.708450
$415$	2.05106e6	+	2.78288e6i	0.584599	+	0.793185i
$416$	−494208.			−0.140016
$417$			6.33489e6i			1.78402i
$418$		−	367747.i		−	0.102946i
$419$	−2.93742e6			−0.817393			−0.408697	−	0.912670i	$-0.634017\pi$
$419$	−2.93742e6			−0.817393			−0.408697	+	0.912670i	$0.634017\pi$
$420$	−641520.	+	472818.i	−0.177454	+	0.130789i
$421$	2.71770e6			0.747303			0.373651	−	0.927569i	$-0.378106\pi$
$421$	2.71770e6			0.747303			0.373651	+	0.927569i	$0.378106\pi$
$422$		−	1.66858e6i		−	0.456106i
$423$			1.61266e6i			0.438219i
$424$	772640.			0.208719
$425$	−2.05920e6	−	638119.i	−0.553001	−	0.171368i
$426$	7.04246e6			1.88019
$427$			340166.i			0.0902862i
$428$		−	1.16541e6i		−	0.307517i
$429$	−598752.			−0.157074
$430$	−124740.	+	91936.8i	−0.0325338	+	0.0239783i
$431$	4.99435e6			1.29505			0.647524	−	0.762045i	$-0.275804\pi$
$431$	4.99435e6			1.29505			0.647524	+	0.762045i	$0.275804\pi$
$432$			2.26380e6i			0.583617i
$433$		−	2.08183e6i		−	0.533612i	−0.963750	−	0.266806i	$-0.914032\pi$
$433$		−	2.08183e6i		−	0.533612i	0.963750	−	0.266806i	$-0.0859684\pi$
$434$	2.67379e6			0.681402
$435$	−4.57380e6	−	6.20574e6i	−1.15892	−	1.57243i
$436$	252120.			0.0635172
$437$		−	535569.i		−	0.134156i
$438$			9.36180e6i			2.33171i
$439$	−4.70404e6			−1.16496			−0.582478	−	0.812846i	$-0.697917\pi$
$439$	−4.70404e6			−1.16496			−0.582478	+	0.812846i	$0.697917\pi$
$440$	−1.10880e6	−	1.50442e6i	−0.273037	−	0.370457i
$441$	−2.02618e6			−0.496114
$442$		−	546368.i		−	0.133024i
$443$		−	5.70103e6i		−	1.38021i	−0.723711	−	0.690103i	$-0.757565\pi$
$443$		−	5.70103e6i		−	1.38021i	0.723711	−	0.690103i	$-0.242435\pi$
$444$	−3.33590e6			−0.803075
$445$	449550.	−	331331.i	0.107616	−	0.0793162i
$446$	1.91545e6			0.455968
$447$		−	1.67456e6i		−	0.396399i
$448$			775613.i			0.182579i
$449$	6.20325e6			1.45212			0.726062	−	0.687630i	$-0.241349\pi$
$449$	6.20325e6			1.45212			0.726062	+	0.687630i	$0.241349\pi$
$450$	−3.02940e6	−	938771.i	−0.705221	−	0.218539i
$451$	−49896.0			−0.0115511
$452$		−	1.26021e6i		−	0.290133i
$453$			3.10134e6i			0.710074i
$454$	−7.72204e6			−1.75830
$455$	320760.	−	236409.i	0.0726360	−	0.0535347i
$456$	−580800.			−0.130802
$457$		−	2.15371e6i		−	0.482388i	−0.970477	−	0.241194i	$-0.922461\pi$
$457$		−	2.15371e6i		−	0.482388i	0.970477	−	0.241194i	$-0.0775391\pi$
$458$			3.63283e6i			0.809248i
$459$	−1.23552e6			−0.273727
$460$	968880.	+	1.31458e6i	0.213489	+	0.289662i
$461$	−3.85130e6			−0.844024			−0.422012	−	0.906590i	$-0.638676\pi$
$461$	−3.85130e6			−0.844024			−0.422012	+	0.906590i	$0.638676\pi$
$462$		−	1.98584e6i		−	0.432851i
$463$		−	2.08213e6i		−	0.451394i	−0.974198	−	0.225697i	$-0.927534\pi$
$463$		−	2.08213e6i		−	0.451394i	0.974198	−	0.225697i	$-0.0724659\pi$
$464$	8.75952e6			1.88880
$465$	4.45632e6	+	6.04634e6i	0.955749	+	1.29676i
$466$	−319088.			−0.0680684
$467$			1.30822e6i			0.277579i	0.990322	+	0.138790i	$0.0443212\pi$
$467$			1.30822e6i			0.277579i	−0.990322	+	0.138790i	$0.955679\pi$
$468$		−	219216.i		−	0.0462655i
$469$	−2.60528e6			−0.546919
$470$	−3.14622e6	+	2.31885e6i	−0.656968	+	0.484204i
$471$	7.09711e6			1.47411
$472$		−	3.27152e6i		−	0.675919i
$473$		−	105309.i		−	0.0216429i
$474$	6.85344e6			1.40108
$475$	−203500.	+	656692.i	−0.0413838	+	0.133545i
$476$	494208.			0.0999752
$477$			891071.i			0.179315i
$478$		−	6.67199e6i		−	1.33563i
$479$	−6.76368e6			−1.34693			−0.673464	−	0.739220i	$-0.735194\pi$
$479$	−6.76368e6			−1.34693			−0.673464	+	0.739220i	$0.735194\pi$
$480$	3.70656e6	−	2.73184e6i	0.734291	−	0.541193i
$481$	1.66795e6			0.328716
$482$			5.93810e6i			1.16421i
$483$		−	2.89207e6i		−	0.564080i
$484$	1.17056e6			0.227134
$485$	3.35808e6	+	4.55625e6i	0.648241	+	0.879534i
$486$	−6.72527e6			−1.29157
$487$			6.67193e6i			1.27476i	0.770549	+	0.637381i	$0.219982\pi$
$487$			6.67193e6i			1.27476i	−0.770549	+	0.637381i	$0.780018\pi$
$488$		−	755925.i		−	0.143691i
$489$	−2.88328e6			−0.545273
$490$	−2.91346e6	−	3.95299e6i	−0.548175	−	0.743764i
$491$	−6.87575e6			−1.28711			−0.643556	−	0.765399i	$-0.722542\pi$
$491$	−6.87575e6			−1.28711			−0.643556	+	0.765399i	$0.722542\pi$
$492$		−	47281.8i		−	0.00880605i
$493$			4.78072e6i			0.885881i
$494$	−174240.			−0.0321241
$495$	1.73502e6	−	1.27876e6i	0.318267	−	0.234572i
$496$	−8.53453e6			−1.55767
$497$		−	3.18507e6i		−	0.578400i
$498$		−	8.16312e6i		−	1.47497i
$499$	6.94010e6			1.24771			0.623856	−	0.781539i	$-0.285565\pi$
$499$	6.94010e6			1.24771			0.623856	+	0.781539i	$0.285565\pi$
$500$	−688500.	−	1.98002e6i	−0.123163	−	0.354198i
$501$	−360228.			−0.0641185
$502$			3.70302e6i			0.655839i
$503$			921007.i			0.162309i	0.996702	+	0.0811546i	$0.0258607\pi$
$503$			921007.i			0.162309i	−0.996702	+	0.0811546i	$0.974139\pi$
$504$	−1.21176e6			−0.212491
$505$	4.90941e6	−	3.61837e6i	0.856645	−	0.631371i
$506$	−4.06930e6			−0.706550
$507$		−	7.10495e6i		−	1.22755i
$508$			1.04665e6i			0.179946i
$509$	4.97979e6			0.851955			0.425977	−	0.904734i	$-0.359930\pi$
$509$	4.97979e6			0.851955			0.425977	+	0.904734i	$0.359930\pi$
$510$	3.02016e6	+	4.09776e6i	0.514167	+	0.697623i
$511$	4.23403e6			0.717302
$512$		−	134151.i		−	0.0226161i
$513$			394015.i			0.0661027i
$514$	5.22650e6			0.872575
$515$	−2.34234e6	−	3.17809e6i	−0.389163	−	0.528017i
$516$	99792.0			0.0164995
$517$		−	2.65614e6i		−	0.437043i
$518$			5.53197e6i			0.905848i
$519$	−9.80206e6			−1.59735
$520$	−712800.	+	525353.i	−0.115600	+	0.0852007i
$521$	−147798.			−0.0238547			−0.0119274	−	0.999929i	$-0.503797\pi$
$521$	−147798.			−0.0238547			−0.0119274	+	0.999929i	$0.503797\pi$
$522$			7.03317e6i			1.12973i
$523$			1.23884e7i			1.98043i	0.139543	+	0.990216i	$0.455437\pi$
$523$			1.23884e7i			1.98043i	−0.139543	+	0.990216i	$0.544563\pi$
$524$	−2.31422e6			−0.368194
$525$	−1.09890e6	+	3.54614e6i	−0.174004	+	0.561509i
$526$	1.08237e7			1.70573
$527$		−	4.65792e6i		−	0.730576i
$528$			6.33863e6i			0.989488i
$529$	510027.			0.0792417
$530$	−1.73844e6	+	1.28128e6i	−0.268825	+	0.198132i
$531$	3.77298e6			0.580695
$532$		−	157606.i		−	0.0241431i
$533$			23640.9i			0.00360451i
$534$	−1.31868e6			−0.200118
$535$	−3.22102e6	−	4.37028e6i	−0.486529	−	0.660123i
$536$	5.78952e6			0.870423
$537$		−	8.84385e6i		−	1.32344i
$538$		−	1.15178e7i		−	1.71559i
$539$	3.33724e6			0.494783
$540$	−712800.	−	967128.i	−0.105192	−	0.142725i
$541$	−9.99810e6			−1.46867			−0.734335	−	0.678787i	$-0.762506\pi$
$541$	−9.99810e6			−1.46867			−0.734335	+	0.678787i	$0.762506\pi$
$542$		−	1.14095e7i		−	1.66828i
$543$		−	3.12231e6i		−	0.454440i
$544$	−2.85542e6			−0.413688
$545$	945450.	−	696823.i	0.136348	−	0.100492i
$546$	−940896.			−0.135070
$547$			1.18580e7i			1.69451i	0.531189	+	0.847253i	$0.321745\pi$
$547$			1.18580e7i			1.69451i	−0.531189	+	0.847253i	$0.678255\pi$
$548$			1.72284e6i			0.245072i
$549$	871794.			0.123448
$550$	4.98960e6	+	1.54621e6i	0.703330	+	0.217953i
$551$	1.52460e6			0.213933
$552$			6.42682e6i			0.897736i
$553$		−	3.09958e6i		−	0.431013i
$554$	−8.44034e6			−1.16838
$555$	−1.25096e7	+	9.21995e6i	−1.72390	+	1.27056i
$556$	3.82008e6			0.524065
$557$			904550.i			0.123536i	0.998091	+	0.0617681i	$0.0196739\pi$
$557$			904550.i			0.123536i	−0.998091	+	0.0617681i	$0.980326\pi$
$558$		−	6.85252e6i		−	0.931676i
$559$	−49896.0			−0.00675361
$560$	−2.50272e6	−	3.39569e6i	−0.337242	−	0.457571i
$561$	−3.45946e6			−0.464088
$562$			9.71772e6i			1.29785i
$563$		−	8.68719e6i		−	1.15507i	−0.816366	−	0.577535i	$-0.804015\pi$
$563$		−	8.68719e6i		−	1.15507i	0.816366	−	0.577535i	$-0.195985\pi$
$564$	2.51698e6			0.333182
$565$	−3.48304e6	−	4.72579e6i	−0.459026	−	0.622807i
$566$	1.09482e7			1.43649
$567$			4.34724e6i			0.567879i
$568$			7.07794e6i			0.920526i
$569$	−2.27007e6			−0.293940			−0.146970	−	0.989141i	$-0.546952\pi$
$569$	−2.27007e6			−0.293940			−0.146970	+	0.989141i	$0.546952\pi$
$570$	1.30680e6	−	963148.i	0.168470	−	0.124167i
$571$	1.43807e7			1.84582			0.922908	−	0.385021i	$-0.125806\pi$
$571$	1.43807e7			1.84582			0.922908	+	0.385021i	$0.125806\pi$
$572$			361061.i			0.0461414i
$573$		−	6.61372e6i		−	0.841510i
$574$	−78408.0			−0.00993300
$575$	7.26660e6	+	2.25182e6i	0.916562	+	0.284030i
$576$	1.98778e6			0.249638
$577$			5.63943e6i			0.705173i	0.935779	+	0.352586i	$0.114698\pi$
$577$			5.63943e6i			0.705173i	−0.935779	+	0.352586i	$0.885302\pi$
$578$			6.26148e6i			0.779574i
$579$	1.56436e7			1.93928
$580$	−3.74220e6	+	2.75811e6i	−0.461910	+	0.340440i
$581$	−3.69191e6			−0.453744
$582$		−	1.33650e7i		−	1.63554i
$583$		−	1.46765e6i		−	0.178834i
$584$	−9.40896e6			−1.14159
$585$	−605880.	−	822059.i	−0.0731976	−	0.0993146i
$586$	−1.58383e7			−1.90531
$587$			1.28473e6i			0.153893i	0.997035	+	0.0769464i	$0.0245170\pi$
$587$			1.28473e6i			0.153893i	−0.997035	+	0.0769464i	$0.975483\pi$
$588$			3.16239e6i			0.377200i
$589$	−1.48544e6			−0.176428
$590$	5.42520e6	+	7.36092e6i	0.641632	+	0.870566i
$591$	1.18615e6			0.139692
$592$		−	1.76576e7i		−	2.07075i
$593$			7.00943e6i			0.818552i	0.912411	+	0.409276i	$0.134219\pi$
$593$			7.00943e6i			0.818552i	−0.912411	+	0.409276i	$0.865781\pi$
$594$	2.99376e6			0.348138
$595$	1.85328e6	−	1.36592e6i	0.214609	−	0.158173i
$596$	−1.00980e6			−0.116445
$597$			7.87632e6i			0.904456i
$598$			1.92805e6i			0.220478i
$599$	−8.80020e6			−1.00213			−0.501067	−	0.865409i	$-0.667059\pi$
$599$	−8.80020e6			−1.00213			−0.501067	+	0.865409i	$0.667059\pi$
$600$	2.44200e6	−	7.88030e6i	0.276928	−	0.893644i
$601$	−1.07670e7			−1.21593			−0.607965	−	0.793964i	$-0.708014\pi$
$601$	−1.07670e7			−1.21593			−0.607965	+	0.793964i	$0.708014\pi$
$602$		−	165486.i		−	0.0186110i
$603$			6.67694e6i			0.747798i
$604$	1.87018e6			0.208588
$605$	4.38962e6	−	3.23527e6i	0.487571	−	0.359353i
$606$	−1.44009e7			−1.59298
$607$		−	1.51219e7i		−	1.66584i	−0.553391	−	0.832921i	$-0.686667\pi$
$607$		−	1.51219e7i		−	1.66584i	0.553391	−	0.832921i	$-0.313333\pi$
$608$			910613.i			0.0999021i
$609$	8.23284e6			0.899511
$610$	1.25356e6	+	1.70083e6i	0.136402	+	0.185070i
$611$	−1.25849e6			−0.136379
$612$		−	1.26658e6i		−	0.136695i
$613$		−	8.31622e6i		−	0.893871i	−0.894566	−	0.446936i	$-0.852515\pi$
$613$		−	8.31622e6i		−	0.893871i	0.894566	−	0.446936i	$-0.147485\pi$
$614$	−6.15740e6			−0.659139
$615$	−130680.	−	177307.i	−0.0139323	−	0.0189033i
$616$	1.99584e6			0.211921
$617$			1.21083e7i			1.28047i	0.768178	+	0.640237i	$0.221164\pi$
$617$			1.21083e7i			1.28047i	−0.768178	+	0.640237i	$0.778836\pi$
$618$			9.32240e6i			0.981875i
$619$	9.73238e6			1.02092			0.510461	−	0.859901i	$-0.329475\pi$
$619$	9.73238e6			1.02092			0.510461	+	0.859901i	$0.329475\pi$
$620$	3.64608e6	−	2.68726e6i	0.380932	−	0.280757i
$621$	4.35996e6			0.453684
$622$			3.76869e6i			0.390584i
$623$			596395.i			0.0615622i
$624$	3.00326e6			0.308768
$625$	−8.05437e6	−	5.52218e6i	−0.824768	−	0.565471i
$626$	1.14254e7			1.16529
$627$			1.10324e6i			0.112073i
$628$		−	4.27972e6i		−	0.433028i
$629$	9.63706e6			0.971220
$630$	2.72646e6	−	2.00948e6i	0.273683	−	0.201712i
$631$	−8.60145e6			−0.859999			−0.430000	−	0.902829i	$-0.641486\pi$
$631$	−8.60145e6			−0.859999			−0.430000	+	0.902829i	$0.641486\pi$
$632$			6.88797e6i			0.685959i
$633$			5.00574e6i			0.496546i
$634$	−873224.			−0.0862785
$635$	2.89278e6	+	3.92493e6i	0.284696	+	0.386276i
$636$	1.39075e6			0.136335
$637$		−	1.58119e6i		−	0.154396i
$638$		−	1.15840e7i		−	1.12670i
$639$	−8.16286e6			−0.790842
$640$	7.25120e6	+	9.83844e6i	0.699777	+	0.949459i
$641$	−6.42440e6			−0.617572			−0.308786	−	0.951132i	$-0.599923\pi$
$641$	−6.42440e6			−0.617572			−0.308786	+	0.951132i	$0.599923\pi$
$642$			1.28195e7i			1.22753i
$643$			3.64721e6i			0.347883i	0.984756	+	0.173941i	$0.0556503\pi$
$643$			3.64721e6i			0.347883i	−0.984756	+	0.173941i	$0.944350\pi$
$644$	−1.74398e6			−0.165702
$645$	374220.	−	275811.i	0.0354183	−	0.0261043i
$646$	−1.00672e6			−0.0949134
$647$			3.78036e6i			0.355036i	0.984118	+	0.177518i	$0.0568068\pi$
$647$			3.78036e6i			0.355036i	−0.984118	+	0.177518i	$0.943193\pi$
$648$		−	9.66053e6i		−	0.903782i
$649$	−6.21432e6			−0.579138
$650$	732600.	−	2.36409e6i	0.0680117	−	0.219473i
$651$	−8.02138e6			−0.741816
$652$			1.73868e6i			0.160177i
$653$		−	1.66957e7i		−	1.53223i	−0.642706	−	0.766113i	$-0.722188\pi$
$653$		−	1.66957e7i		−	1.53223i	0.642706	−	0.766113i	$-0.277812\pi$
$654$	−2.77332e6			−0.253545
$655$	−8.67834e6	+	6.39618e6i	−0.790375	+	0.582529i
$656$	250272.			0.0227066
$657$		−	1.08512e7i		−	0.980761i
$658$		−	4.17393e6i		−	0.375821i
$659$	−1.22166e6			−0.109581			−0.0547907	−	0.998498i	$-0.517449\pi$
$659$	−1.22166e6			−0.109581			−0.0547907	+	0.998498i	$0.517449\pi$
$660$	−1.99584e6	−	2.70796e6i	−0.178347	−	0.241981i
$661$	1.62789e7			1.44918			0.724589	−	0.689182i	$-0.242030\pi$
$661$	1.62789e7			1.44918			0.724589	+	0.689182i	$0.242030\pi$
$662$		−	1.04842e7i		−	0.929799i
$663$			1.63910e6i			0.144818i
$664$	8.20424e6			0.722135
$665$	−435600.	−	591023.i	−0.0381974	−	0.0518263i
$666$	1.41776e7			1.23856
$667$		−	1.68704e7i		−	1.46829i
$668$			217226.i			0.0188352i
$669$	−5.74636e6			−0.496395
$670$	−1.30264e7	+	9.60083e6i	−1.12108	+	0.826270i
$671$	−1.43590e6			−0.123117
$672$			4.91731e6i			0.420053i
$673$			1.43928e7i			1.22492i	0.790503	+	0.612459i	$0.209819\pi$
$673$			1.43928e7i			1.22492i	−0.790503	+	0.612459i	$0.790181\pi$
$674$	−8.15126e6			−0.691155
$675$	−5.34600e6	−	1.65665e6i	−0.451616	−	0.139950i
$676$	−4.28444e6			−0.360602
$677$			2.62429e6i			0.220059i	0.993928	+	0.110030i	$0.0350946\pi$
$677$			2.62429e6i			0.220059i	−0.993928	+	0.110030i	$0.964905\pi$
$678$			1.38623e7i			1.15814i
$679$	−6.04454e6			−0.503140
$680$	−4.11840e6	+	3.03538e6i	−0.341552	+	0.251733i
$681$	2.31661e7			1.91419
$682$			1.12865e7i			0.929177i
$683$			1.03039e7i			0.845184i	0.906320	+	0.422592i	$0.138880\pi$
$683$			1.03039e7i			0.845184i	−0.906320	+	0.422592i	$0.861120\pi$
$684$	−403920.			−0.0330107
$685$	4.76168e6	+	6.46065e6i	0.387734	+	0.526078i
$686$	1.18998e7			0.965449
$687$		−	1.08985e7i		−	0.880998i
$688$			528219.i			0.0425444i
$689$	−695376.			−0.0558048
$690$	−1.06577e7	−	1.44604e7i	−0.852197	−	1.15626i
$691$	4.50285e6			0.358751			0.179375	−	0.983781i	$-0.442592\pi$
$691$	4.50285e6			0.358751			0.179375	+	0.983781i	$0.442592\pi$
$692$			5.91086e6i			0.469230i
$693$			2.30176e6i			0.182066i
$694$	2.54865e7			2.00868
$695$	1.43253e7	−	1.05581e7i	1.12497	−	0.829136i
$696$	−1.82952e7			−1.43157
$697$			136592.i			0.0106498i
$698$		−	1.05764e7i		−	0.821672i
$699$	957264.			0.0741035
$700$	2.13840e6	+	662662.i	0.164947	+	0.0511148i
$701$	−4.88090e6			−0.375150			−0.187575	−	0.982250i	$-0.560063\pi$
$701$	−4.88090e6			−0.375150			−0.187575	+	0.982250i	$0.560063\pi$
$702$		−	1.41845e6i		−	0.108636i
$703$		−	3.07332e6i		−	0.234541i
$704$	−3.27398e6			−0.248969
$705$	9.43866e6	−	6.95655e6i	0.715217	−	0.527134i
$706$	1.95923e6			0.147936
$707$			6.51307e6i			0.490046i
$708$		−	5.88873e6i		−	0.441508i
$709$	−9.96961e6			−0.744839			−0.372420	−	0.928064i	$-0.621472\pi$
$709$	−9.96961e6			−0.744839			−0.372420	+	0.928064i	$0.621472\pi$
$710$	−1.17374e7	−	1.59254e7i	−0.873831	−	1.18561i
$711$	−7.94376e6			−0.589321
$712$		−	1.32532e6i		−	0.0979765i
$713$			1.64371e7i			1.21088i
$714$	−5.43629e6			−0.399077
$715$	997920.	+	1.35398e6i	0.0730013	+	0.0990482i
$716$	−5.33304e6			−0.388770
$717$			2.00160e7i			1.45405i
$718$			7.32868e6i			0.530536i
$719$	−1.19167e7			−0.859675			−0.429838	−	0.902906i	$-0.641429\pi$
$719$	−1.19167e7			−0.859675			−0.429838	+	0.902906i	$0.641429\pi$
$720$	−8.70264e6	+	6.41409e6i	−0.625633	+	0.461109i
$721$	4.21621e6			0.302054
$722$		−	1.61035e7i		−	1.14968i
$723$		−	1.78143e7i		−	1.26743i
$724$	−1.88282e6			−0.133494
$725$	−6.41025e6	+	2.06858e7i	−0.452929	+	1.46160i
$726$	−1.28762e7			−0.906664
$727$		−	1.38269e6i		−	0.0970264i	−0.998823	−	0.0485132i	$-0.984552\pi$
$727$		−	1.38269e6i		−	0.0970264i	0.998823	−	0.0485132i	$-0.0154483\pi$
$728$		−	945636.i		−	0.0661296i
$729$	2.48079e6			0.172890
$730$	2.11702e7	−	1.56030e7i	1.47034	−	1.08368i
$731$	−288288.			−0.0199541
$732$		−	1.36067e6i		−	0.0938585i
$733$		−	6.09661e6i		−	0.419110i	−0.977797	−	0.209555i	$-0.932798\pi$
$733$		−	6.09661e6i		−	0.419110i	0.977797	−	0.209555i	$-0.0672016\pi$
$734$	1.21893e7			0.835099
$735$	8.74038e6	+	1.18590e7i	0.596777	+	0.809707i
$736$	1.00764e7			0.685660
$737$		−	1.09973e7i		−	0.745793i
$738$			200948.i			0.0135813i
$739$	6.16946e6			0.415562			0.207781	−	0.978175i	$-0.433376\pi$
$739$	6.16946e6			0.415562			0.207781	+	0.978175i	$0.433376\pi$
$740$	5.55984e6	+	7.54360e6i	0.373236	+	0.506406i
$741$	522720.			0.0349723
$742$		−	2.30630e6i		−	0.153782i
$743$		−	1.57574e7i		−	1.04716i	−0.851978	−	0.523578i	$-0.824597\pi$
$743$		−	1.57574e7i		−	1.04716i	0.851978	−	0.523578i	$-0.175403\pi$
$744$	1.78253e7			1.18060
$745$	−3.78675e6	+	2.79094e6i	−0.249963	+	0.184230i
$746$	−1.94586e7			−1.28016
$747$			9.46179e6i			0.620400i
$748$			2.08613e6i			0.136329i
$749$	5.79784e6			0.377626
$750$	7.57350e6	+	2.17803e7i	0.491636	+	1.41387i
$751$	−1.51816e7			−0.982243			−0.491122	−	0.871091i	$-0.663413\pi$
$751$	−1.51816e7			−0.982243			−0.491122	+	0.871091i	$0.663413\pi$
$752$			1.33229e7i			0.859118i
$753$		−	1.11091e7i		−	0.713987i
$754$	−5.48856e6			−0.351585
$755$	7.01316e6	−	5.16889e6i	0.447761	−	0.330012i
$756$	1.28304e6			0.0816461
$757$		−	652274.i		−	0.0413705i	−0.999786	−	0.0206852i	$-0.993415\pi$
$757$		−	652274.i		−	0.0413705i	0.999786	−	0.0206852i	$-0.00658478\pi$
$758$			3.37859e7i			2.13581i
$759$	1.22079e7			0.769194
$760$	968000.	+	1.31338e6i	0.0607913	+	0.0824817i
$761$	4.51420e6			0.282566			0.141283	−	0.989969i	$-0.454877\pi$
$761$	4.51420e6			0.282566			0.141283	+	0.989969i	$0.454877\pi$
$762$		−	1.15131e7i		−	0.718300i
$763$			1.25428e6i			0.0779980i
$764$	−3.98822e6			−0.247199
$765$	−3.50064e6	−	4.74967e6i	−0.216269	−	0.293434i
$766$	−2.10596e7			−1.29681
$767$			2.94437e6i			0.180719i
$768$		−	2.05862e7i		−	1.25943i
$769$	−1.20799e7			−0.736625			−0.368312	−	0.929702i	$-0.620064\pi$
$769$	−1.20799e7			−0.736625			−0.368312	+	0.929702i	$0.620064\pi$
$770$	−4.49064e6	+	3.30973e6i	−0.272949	+	0.201171i
$771$	−1.56795e7			−0.949939
$772$		−	9.43344e6i		−	0.569674i
$773$		−	1.04245e7i		−	0.627492i	−0.949507	−	0.313746i	$-0.898416\pi$
$773$		−	1.04245e7i		−	0.627492i	0.949507	−	0.313746i	$-0.101584\pi$
$774$	−424116.			−0.0254467
$775$	6.24560e6	−	2.01545e7i	0.373525	−	1.20536i
$776$	1.34323e7			0.800750
$777$		−	1.65959e7i		−	0.986163i
$778$			1.19393e7i			0.707177i
$779$	43560.0			0.00257184
$780$	−1.28304e6	+	945636.i	−0.0755099	+	0.0556529i
$781$	1.34447e7			0.788721
$782$			1.11398e7i			0.651421i
$783$			1.24115e7i			0.723467i
$784$	−1.67392e7			−0.972620
$785$	−1.18285e7	−	1.60489e7i	−0.685104	−	0.929549i
$786$	2.54565e7			1.46974
$787$			3.45366e7i			1.98766i	0.110913	+	0.993830i	$0.464622\pi$
$787$			3.45366e7i			1.98766i	−0.110913	+	0.993830i	$0.535378\pi$
$788$		−	715277.i		−	0.0410354i
$789$	−3.24711e7			−1.85697
$790$	−1.14224e7	−	1.54979e7i	−0.651163	−	0.883498i
$791$	6.26947e6			0.356279
$792$		−	5.11503e6i		−	0.289758i
$793$			680333.i			0.0384183i
$794$	3.25298e7			1.83118
$795$	5.21532e6	−	3.84384e6i	0.292660	−	0.215698i
$796$	4.74960e6			0.265689
$797$		−	2.09287e7i		−	1.16707i	−0.812089	−	0.583533i	$-0.801670\pi$
$797$		−	2.09287e7i		−	1.16707i	0.812089	−	0.583533i	$-0.198330\pi$
$798$			1.73367e6i			0.0963736i
$799$	−7.27126e6			−0.402942
$800$	−1.23552e7	−	3.82871e6i	−0.682535	−	0.211508i
$801$	1.52847e6			0.0841735
$802$		−	4.26384e6i		−	0.234080i
$803$			1.78725e7i			0.978131i
$804$	1.04211e7			0.568558
$805$	−6.53994e6	+	4.82012e6i	−0.355700	+	0.262161i
$806$	5.34758e6			0.289948
$807$			3.45533e7i			1.86770i
$808$		−	1.44735e7i		−	0.779910i
$809$	2.48797e7			1.33651			0.668257	−	0.743930i	$-0.267041\pi$
$809$	2.48797e7			1.33651			0.668257	+	0.743930i	$0.267041\pi$
$810$	1.60202e7	+	2.17362e7i	0.857936	+	1.16405i
$811$	−3.95415e6			−0.211106			−0.105553	−	0.994414i	$-0.533661\pi$
$811$	−3.95415e6			−0.211106			−0.105553	+	0.994414i	$0.533661\pi$
$812$		−	4.96459e6i		−	0.264237i
$813$			3.42285e7i			1.81619i
$814$	−2.33513e7			−1.23524
$815$	4.80546e6	+	6.52005e6i	0.253420	+	0.343841i
$816$	1.73522e7			0.912282
$817$			91936.8i			0.00481875i
$818$		−	1.36453e7i		−	0.713018i
$819$	1.09058e6			0.0568132
$820$	−106920.	+	78803.0i	−0.00555296	+	0.00409268i
$821$	−3.43550e6			−0.177882			−0.0889410	−	0.996037i	$-0.528348\pi$
$821$	−3.43550e6			−0.177882			−0.0889410	+	0.996037i	$0.528348\pi$
$822$		−	1.89512e7i		−	0.978269i
$823$		−	3.94833e6i		−	0.203195i	−0.994826	−	0.101598i	$-0.967605\pi$
$823$		−	3.94833e6i		−	0.203195i	0.994826	−	0.101598i	$-0.0323954\pi$
$824$	−9.36936e6			−0.480720
$825$	−1.49688e7	−	4.63863e6i	−0.765688	−	0.237277i
$826$	−9.76536e6			−0.498010
$827$		−	3.38176e7i		−	1.71941i	−0.510791	−	0.859705i	$-0.670647\pi$
$827$		−	3.38176e7i		−	1.71941i	0.510791	−	0.859705i	$-0.329353\pi$
$828$			4.46956e6i			0.226563i
$829$	1.52015e7			0.768244			0.384122	−	0.923282i	$-0.374504\pi$
$829$	1.52015e7			0.768244			0.384122	+	0.923282i	$0.374504\pi$
$830$	−1.84595e7	+	1.36052e7i	−0.930091	+	0.685503i
$831$	2.53210e7			1.27198
$832$			1.55123e6i			0.0776903i
$833$		−	9.13579e6i		−	0.456177i
$834$	−4.20209e7			−2.09194
$835$	600380.	+	814596.i	0.0297996	+	0.0404321i
$836$	665280.			0.0329222
$837$		−	1.20927e7i		−	0.596635i
$838$		−	1.94846e7i		−	0.958478i
$839$	2.89012e7			1.41746			0.708729	−	0.705481i	$-0.249269\pi$
$839$	2.89012e7			1.41746			0.708729	+	0.705481i	$0.249269\pi$
$840$	5.22720e6	+	7.09227e6i	0.255606	+	0.346806i
$841$	2.75138e7			1.34140
$842$			1.80272e7i			0.876290i
$843$		−	2.91532e7i		−	1.41292i
$844$	3.01858e6			0.145863
$845$	−1.60667e7	+	1.18416e7i	−0.774077	+	0.570516i
$846$	−1.06971e7			−0.513857
$847$			5.82348e6i			0.278917i
$848$			7.36153e6i			0.351543i
$849$	−3.28446e7			−1.56385
$850$	4.23280e6	−	1.36592e7i	0.200946	−	0.648452i
$851$	−3.40077e7			−1.60973
$852$			1.27403e7i			0.601285i
$853$		−	2.02107e7i		−	0.951062i	−0.879699	−	0.475531i	$-0.842256\pi$
$853$		−	2.02107e7i		−	0.951062i	0.879699	−	0.475531i	$-0.157744\pi$
$854$	−2.25641e6			−0.105870
$855$	−1.51470e6	+	1.11638e6i	−0.0708617	+	0.0522270i
$856$	−1.28841e7			−0.600992
$857$			1.70522e7i			0.793101i	0.918013	+	0.396550i	$0.129793\pi$
$857$			1.70522e7i			0.793101i	−0.918013	+	0.396550i	$0.870207\pi$
$858$		−	3.97167e6i		−	0.184185i
$859$	1.95505e7			0.904015			0.452008	−	0.892014i	$-0.350708\pi$
$859$	1.95505e7			0.904015			0.452008	+	0.892014i	$0.350708\pi$
$860$	−166320.	−	225663.i	−0.00766829	−	0.0104043i
$861$	235224.			0.0108137
$862$			3.31288e7i			1.51858i
$863$			2.70896e7i			1.23816i	0.785330	+	0.619078i	$0.212493\pi$
$863$			2.70896e7i			1.23816i	−0.785330	+	0.619078i	$0.787507\pi$
$864$	−7.41312e6			−0.337844
$865$	1.63368e7	+	2.21657e7i	0.742379	+	1.00726i
$866$	1.38093e7			0.625716
$867$		−	1.87844e7i		−	0.848692i
$868$			4.83707e6i			0.217913i
$869$	1.30838e7			0.587741
$870$	4.11642e7	−	3.03392e7i	1.84383	−	1.35896i
$871$	−5.21057e6			−0.232723
$872$		−	2.78729e6i		−	0.124134i
$873$			1.54912e7i			0.687940i
$874$	3.55256e6			0.157312
$875$	9.85050e6	−	3.42524e6i	0.434949	−	0.151242i
$876$	−1.69361e7			−0.745682
$877$			1.98285e6i			0.0870545i	0.999052	+	0.0435272i	$0.0138595\pi$
$877$			1.98285e6i			0.0870545i	−0.999052	+	0.0435272i	$0.986140\pi$
$878$		−	3.12031e7i		−	1.36603i
$879$	4.75150e7			2.07424
$880$	1.43338e7	−	1.05644e7i	0.623955	−	0.459872i
$881$	−4.22840e7			−1.83542			−0.917712	−	0.397247i	$-0.869966\pi$
$881$	−4.22840e7			−1.83542			−0.917712	+	0.397247i	$0.869966\pi$
$882$		−	1.34402e7i		−	0.581745i
$883$			134502.i			0.00580535i	0.999996	+	0.00290267i	$0.000923951\pi$
$883$			134502.i			0.00580535i	−0.999996	+	0.00290267i	$0.999076\pi$
$884$	988416.			0.0425411
$885$	−1.62756e7	−	2.20828e7i	−0.698520	−	0.947753i
$886$	3.78164e7			1.61844
$887$			3.87668e6i			0.165444i	0.996573	+	0.0827219i	$0.0263613\pi$
$887$			3.87668e6i			0.165444i	−0.996573	+	0.0827219i	$0.973639\pi$
$888$			3.68798e7i			1.56948i
$889$	−5.20700e6			−0.220970
$890$	2.19780e6	+	2.98198e6i	0.0930065	+	0.126191i
$891$	−1.83504e7			−0.774374
$892$			3.46518e6i			0.145819i
$893$			2.31885e6i			0.0973070i
$894$	1.11078e7			0.464819
$895$	−1.99989e7	+	1.47397e7i	−0.834543	+	0.615081i
$896$	−1.30522e7			−0.543141
$897$		−	5.78414e6i		−	0.240026i
$898$			4.11477e7i			1.70277i
$899$	−4.67914e7			−1.93093
$900$	1.69830e6	−	5.48039e6i	0.0698889	−	0.225530i
$901$	−4.01773e6			−0.164880
$902$		−	330973.i		−	0.0135449i
$903$			496459.i			0.0202611i
$904$	−1.39322e7			−0.567019
$905$	−7.06059e6	+	5.20385e6i	−0.286563	+	0.211205i
$906$	−2.05719e7			−0.832635
$907$		−	2.87363e7i		−	1.15988i	−0.814660	−	0.579939i	$-0.803076\pi$
$907$		−	2.87363e7i		−	1.15988i	0.814660	−	0.579939i	$-0.196924\pi$
$908$		−	1.39697e7i		−	0.562306i
$909$	1.66920e7			0.670037
$910$	1.56816e6	+	2.12768e6i	0.0627750	+	0.0851732i
$911$	1.87675e6			0.0749223			0.0374611	−	0.999298i	$-0.488073\pi$
$911$	1.87675e6			0.0749223			0.0374611	+	0.999298i	$0.488073\pi$
$912$		−	5.53372e6i		−	0.220308i
$913$		−	1.55841e7i		−	0.618736i
$914$	1.42861e7			0.565650
$915$	−3.76068e6	−	5.10249e6i	−0.148496	−	0.201479i
$916$	−6.57204e6			−0.258798
$917$		−	1.15131e7i		−	0.452137i
$918$		−	8.19551e6i		−	0.320974i
$919$	−6.76852e6			−0.264366			−0.132183	−	0.991225i	$-0.542199\pi$
$919$	−6.76852e6			−0.264366			−0.132183	+	0.991225i	$0.542199\pi$
$920$	1.45332e7	−	1.07114e7i	0.566098	−	0.417230i
$921$	1.84722e7			0.717579
$922$		−	2.55466e7i		−	0.989706i
$923$		−	6.37015e6i		−	0.246119i
$924$	3.59251e6			0.138426
$925$	4.16988e7	+	1.29219e7i	1.60239	+	0.496560i
$926$	1.38113e7			0.529306
$927$		−	1.08055e7i		−	0.412996i
$928$			2.86843e7i			1.09339i
$929$	1.15356e7			0.438530			0.219265	−	0.975665i	$-0.429634\pi$
$929$	1.15356e7			0.438530			0.219265	+	0.975665i	$0.429634\pi$
$930$	−4.01069e7	+	2.95599e7i	−1.52059	+	1.12072i
$931$	−2.91346e6			−0.110163
$932$		−	577252.i		−	0.0217684i
$933$		−	1.13061e7i		−	0.425214i
$934$	−8.67772e6			−0.325491
$935$	5.76576e6	+	7.82299e6i	0.215689	+	0.292647i
$936$	−2.42352e6			−0.0904184
$937$			3.92632e7i			1.46096i	0.682936	+	0.730478i	$0.260703\pi$
$937$			3.92632e7i			1.46096i	−0.682936	+	0.730478i	$0.739297\pi$
$938$		−	1.72815e7i		−	0.641319i
$939$	−3.42762e7			−1.26861
$940$	−4.19496e6	−	5.69173e6i	−0.154849	−	0.210099i
$941$	2.94919e7			1.08575			0.542874	−	0.839814i	$-0.317336\pi$
$941$	2.94919e7			1.08575			0.542874	+	0.839814i	$0.317336\pi$
$942$			4.70769e7i			1.72855i
$943$		−	482012.i		−	0.0176514i
$944$	3.11702e7			1.13844
$945$	4.81140e6	−	3.54614e6i	0.175264	−	0.129174i
$946$	698544.			0.0253785
$947$			2.09628e7i			0.759581i	0.925072	+	0.379791i	$0.124004\pi$
$947$			2.09628e7i			0.759581i	−0.925072	+	0.379791i	$0.875996\pi$
$948$			1.23983e7i			0.448067i
$949$	8.46806e6			0.305224
$950$	−4.35600e6	−	1.34987e6i	−0.156595	−	0.0485268i
$951$	2.61967e6			0.0939281
$952$		−	5.46368e6i		−	0.195386i
$953$		−	1.64122e7i		−	0.585375i	−0.956208	−	0.292687i	$-0.905451\pi$
$953$		−	1.64122e7i		−	0.585375i	0.956208	−	0.292687i	$-0.0945495\pi$
$954$	−5.91070e6			−0.210265
$955$	−1.49558e7	+	1.10229e7i	−0.530643	+	0.391099i
$956$	1.20701e7			0.427135
$957$			3.47521e7i			1.22660i
$958$		−	4.48652e7i		−	1.57941i
$959$	−8.57102e6			−0.300944
$960$	−8.57472e6	−	1.16342e7i	−0.300291	−	0.407435i
$961$	1.69604e7			0.592416
$962$			1.10639e7i			0.385454i
$963$		−	1.48590e7i		−	0.516325i
$964$	−1.07424e7			−0.372314
$965$	−2.60726e7	−	3.53754e7i	−0.901295	−	1.22288i
$966$	1.91838e7			0.661443
$967$		−	4.71911e7i		−	1.62291i	−0.584416	−	0.811454i	$-0.698676\pi$
$967$		−	4.71911e7i		−	1.62291i	0.584416	−	0.811454i	$-0.301324\pi$
$968$		−	1.29411e7i		−	0.443897i
$969$	3.02016e6			0.103329
$970$	−3.02227e7	+	2.22750e7i	−1.03135	+	0.760130i
$971$	3.84771e7			1.30965			0.654823	−	0.755783i	$-0.272743\pi$
$971$	3.84771e7			1.30965			0.654823	+	0.755783i	$0.272743\pi$
$972$		−	1.21665e7i		−	0.413046i
$973$			1.90047e7i			0.643544i
$974$	−4.42566e7			−1.49479
$975$	−2.19780e6	+	7.09227e6i	−0.0740417	+	0.238932i
$976$	7.20227e6			0.242016
$977$			2.70184e7i			0.905572i	0.891619	+	0.452786i	$0.149570\pi$
$977$			2.70184e7i			0.905572i	−0.891619	+	0.452786i	$0.850430\pi$
$978$		−	1.91255e7i		−	0.639389i
$979$	−2.51748e6			−0.0839478
$980$	7.15122e6	−	5.27065e6i	0.237856	−	0.175307i
$981$	3.21453e6			0.106646
$982$		−	4.56086e7i		−	1.50927i
$983$			2.88475e7i			0.952192i	0.879393	+	0.476096i	$0.157949\pi$
$983$			2.88475e7i			0.952192i	−0.879393	+	0.476096i	$0.842051\pi$
$984$	−522720.			−0.0172100
$985$	−1.97692e6	−	2.68229e6i	−0.0649230	−	0.0880876i
$986$	−3.17117e7			−1.03879
$987$			1.25218e7i			0.409142i
$988$		−	315212.i		−	0.0102733i
$989$	1.01732e6			0.0330726
$990$	8.48232e6	+	1.15088e7i	0.275060	+	0.373201i
$991$	−5.21596e7			−1.68714			−0.843569	−	0.537021i	$-0.819550\pi$
$991$	−5.21596e7			−1.68714			−0.843569	+	0.537021i	$0.819550\pi$
$992$		−	2.79475e7i		−	0.901704i
$993$			3.14525e7i			1.01224i
$994$	2.11274e7			0.678235
$995$	1.78110e7	−	1.31272e7i	0.570336	−	0.420353i
$996$	1.47676e7			0.471696
$997$		−	9.78148e6i		−	0.311650i	−0.987785	−	0.155825i	$-0.950196\pi$
$997$		−	9.78148e6i		−	0.311650i	0.987785	−	0.155825i	$-0.0498036\pi$
$998$			4.60354e7i			1.46307i
$999$	2.50193e7			0.793161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.6.b.a.4.2	yes	2
3.2	odd	2		45.6.b.b.19.1		2
4.3	odd	2		80.6.c.a.49.2		2
5.2	odd	4		25.6.a.c.1.1		2
5.3	odd	4		25.6.a.c.1.2		2
5.4	even	2	inner	5.6.b.a.4.1	✓	2
7.6	odd	2		245.6.b.a.99.2		2
8.3	odd	2		320.6.c.g.129.1		2
8.5	even	2		320.6.c.f.129.2		2
12.11	even	2		720.6.f.f.289.1		2
15.2	even	4		225.6.a.n.1.2		2
15.8	even	4		225.6.a.n.1.1		2
15.14	odd	2		45.6.b.b.19.2		2
20.3	even	4		400.6.a.t.1.1		2
20.7	even	4		400.6.a.t.1.2		2
20.19	odd	2		80.6.c.a.49.1		2
35.34	odd	2		245.6.b.a.99.1		2
40.19	odd	2		320.6.c.g.129.2		2
40.29	even	2		320.6.c.f.129.1		2
60.59	even	2		720.6.f.f.289.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.6.b.a.4.1	✓	2	5.4	even	2	inner
5.6.b.a.4.2	yes	2	1.1	even	1	trivial
25.6.a.c.1.1		2	5.2	odd	4
25.6.a.c.1.2		2	5.3	odd	4
45.6.b.b.19.1		2	3.2	odd	2
45.6.b.b.19.2		2	15.14	odd	2
80.6.c.a.49.1		2	20.19	odd	2
80.6.c.a.49.2		2	4.3	odd	2
225.6.a.n.1.1		2	15.8	even	4
225.6.a.n.1.2		2	15.2	even	4
245.6.b.a.99.1		2	35.34	odd	2
245.6.b.a.99.2		2	7.6	odd	2
320.6.c.f.129.1		2	40.29	even	2
320.6.c.f.129.2		2	8.5	even	2
320.6.c.g.129.1		2	8.3	odd	2
320.6.c.g.129.2		2	40.19	odd	2
400.6.a.t.1.1		2	20.3	even	4
400.6.a.t.1.2		2	20.7	even	4
720.6.f.f.289.1		2	12.11	even	2
720.6.f.f.289.2		2	60.59	even	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.63325i q^{2} -19.8997i q^{3} -12.0000 q^{4} +(-45.0000 + 33.1662i) q^{5} +132.000 q^{6} -59.6992i q^{7} +132.665i q^{8} -153.000 q^{9} +(-220.000 - 298.496i) q^{10} +252.000 q^{11} +238.797i q^{12} -119.398i q^{13} +396.000 q^{14} +(660.000 + 895.489i) q^{15} -1264.00 q^{16} -689.858i q^{17} -1014.89i q^{18} -220.000 q^{19} +(540.000 - 397.995i) q^{20} -1188.00 q^{21} +1671.58i q^{22} +2434.40i q^{23} +2640.00 q^{24} +(925.000 - 2984.96i) q^{25} +792.000 q^{26} -1790.98i q^{27} +716.391i q^{28} -6930.00 q^{29} +(-5940.00 + 4377.94i) q^{30} +6752.00 q^{31} -4139.15i q^{32} -5014.74i q^{33} +4576.00 q^{34} +(1980.00 + 2686.47i) q^{35} +1836.00 q^{36} +13969.6i q^{37} -1459.31i q^{38} -2376.00 q^{39} +(-4400.00 - 5969.92i) q^{40} -198.000 q^{41} -7880.30i q^{42} -417.895i q^{43} -3024.00 q^{44} +(6885.00 - 5074.44i) q^{45} -16148.0 q^{46} -10540.2i q^{47} +25153.3i q^{48} +13243.0 q^{49} +(19800.0 + 6135.76i) q^{50} -13728.0 q^{51} +1432.78i q^{52} -5823.99i q^{53} +11880.0 q^{54} +(-11340.0 + 8357.89i) q^{55} +7920.00 q^{56} +4377.94i q^{57} -45968.4i q^{58} -24660.0 q^{59} +(-7920.00 - 10745.9i) q^{60} -5698.00 q^{61} +44787.7i q^{62} +9133.98i q^{63} -12992.0 q^{64} +(3960.00 + 5372.93i) q^{65} +33264.0 q^{66} -43640.1i q^{67} +8278.30i q^{68} +48444.0 q^{69} +(-17820.0 + 13133.8i) q^{70} +53352.0 q^{71} -20297.7i q^{72} +70922.7i q^{73} -92664.0 q^{74} +(-59400.0 - 18407.3i) q^{75} +2640.00 q^{76} -15044.2i q^{77} -15760.6i q^{78} +51920.0 q^{79} +(56880.0 - 41922.1i) q^{80} -72819.0 q^{81} -1313.38i q^{82} -61841.8i q^{83} +14256.0 q^{84} +(22880.0 + 31043.6i) q^{85} +2772.00 q^{86} +137905. i q^{87} +33431.6i q^{88} -9990.00 q^{89} +(33660.0 + 45669.9i) q^{90} -7128.00 q^{91} -29212.8i q^{92} -134363. i q^{93} +69916.0 q^{94} +(9900.00 - 7296.57i) q^{95} -82368.0 q^{96} -101250. i q^{97} +87844.1i q^{98} -38556.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 24 q^{4} - 90 q^{5} + 264 q^{6} - 306 q^{9} - 440 q^{10} + 504 q^{11} + 792 q^{14} + 1320 q^{15} - 2528 q^{16} - 440 q^{19} + 1080 q^{20} - 2376 q^{21} + 5280 q^{24} + 1850 q^{25} + 1584 q^{26} - 13860 q^{29}+ \cdots - 77112 q^{99}+O(q^{100}) \) 2 * q - 24 * q^4 - 90 * q^5 + 264 * q^6 - 306 * q^9 - 440 * q^10 + 504 * q^11 + 792 * q^14 + 1320 * q^15 - 2528 * q^16 - 440 * q^19 + 1080 * q^20 - 2376 * q^21 + 5280 * q^24 + 1850 * q^25 + 1584 * q^26 - 13860 * q^29 - 11880 * q^30 + 13504 * q^31 + 9152 * q^34 + 3960 * q^35 + 3672 * q^36 - 4752 * q^39 - 8800 * q^40 - 396 * q^41 - 6048 * q^44 + 13770 * q^45 - 32296 * q^46 + 26486 * q^49 + 39600 * q^50 - 27456 * q^51 + 23760 * q^54 - 22680 * q^55 + 15840 * q^56 - 49320 * q^59 - 15840 * q^60 - 11396 * q^61 - 25984 * q^64 + 7920 * q^65 + 66528 * q^66 + 96888 * q^69 - 35640 * q^70 + 106704 * q^71 - 185328 * q^74 - 118800 * q^75 + 5280 * q^76 + 103840 * q^79 + 113760 * q^80 - 145638 * q^81 + 28512 * q^84 + 45760 * q^85 + 5544 * q^86 - 19980 * q^89 + 67320 * q^90 - 14256 * q^91 + 139832 * q^94 + 19800 * q^95 - 164736 * q^96 - 77112 * q^99

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