LMFDB - Embedded newform 150.6.g.b.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	150.91
Dual form			150.6.g.b.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-8.34027 - 55.2760i) q^{5} +(11.1246 - 34.2380i) q^{6} -188.522 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-8.34027 - 55.2760i) q^{5} +(11.1246 - 34.2380i) q^{6} -188.522 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(-102.972 + 198.486i) q^{10} +(115.116 + 83.6367i) q^{11} +(-116.498 + 84.6411i) q^{12} +(282.422 - 205.191i) q^{13} +(610.070 + 443.242i) q^{14} +(449.940 - 225.120i) q^{15} +(-207.108 + 150.473i) q^{16} +(210.101 - 646.623i) q^{17} +324.000 q^{18} +(-216.073 + 665.003i) q^{19} +(799.894 - 400.213i) q^{20} +(-524.308 - 1613.65i) q^{21} +(-175.882 - 541.308i) q^{22} +(1183.91 + 860.159i) q^{23} +576.000 q^{24} +(-2985.88 + 922.034i) q^{25} -1396.37 q^{26} +(-589.773 - 428.495i) q^{27} +(-932.103 - 2868.72i) q^{28} +(2100.66 + 6465.15i) q^{29} +(-1985.33 - 329.370i) q^{30} +(-676.035 + 2080.62i) q^{31} +1024.00 q^{32} +(-395.734 + 1217.94i) q^{33} +(-2200.20 + 1598.54i) q^{34} +(1572.32 + 10420.7i) q^{35} +(-1048.49 - 761.770i) q^{36} +(1307.25 - 949.774i) q^{37} +(2262.74 - 1643.98i) q^{38} +(2541.79 + 1846.72i) q^{39} +(-3529.47 - 585.547i) q^{40} +(-5088.66 + 3697.13i) q^{41} +(-2097.23 + 6454.62i) q^{42} +23494.6 q^{43} +(-703.526 + 2165.23i) q^{44} +(3178.27 + 3225.17i) q^{45} +(-1808.85 - 5567.07i) q^{46} +(3288.60 + 10121.3i) q^{47} +(-1863.98 - 1354.26i) q^{48} +18733.5 q^{49} +(11830.3 + 4036.46i) q^{50} +6119.10 q^{51} +(4518.74 + 3283.06i) q^{52} +(5489.13 + 16893.8i) q^{53} +(901.094 + 2773.28i) q^{54} +(3663.00 - 7060.71i) q^{55} +(-3728.41 + 11474.9i) q^{56} -6293.03 q^{57} +(8402.62 - 25860.6i) q^{58} +(16419.9 - 11929.7i) q^{59} +(5650.25 + 5733.64i) q^{60} +(9713.46 + 7057.24i) q^{61} +(7079.53 - 5143.58i) q^{62} +(12353.9 - 8975.64i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-13697.6 - 13899.8i) q^{65} +(4144.18 - 3010.92i) q^{66} +(-6054.32 + 18633.3i) q^{67} +10878.4 q^{68} +(-4069.91 + 12525.9i) q^{69} +(19412.5 - 37419.0i) q^{70} +(23916.5 + 73607.5i) q^{71} +(1601.94 + 4930.28i) q^{72} +(-432.726 - 314.394i) q^{73} -6463.41 q^{74} +(-16196.3 - 22993.3i) q^{75} -11187.6 q^{76} +(-21701.9 - 15767.3i) q^{77} +(-3883.52 - 11952.2i) q^{78} +(17562.5 + 54051.8i) q^{79} +(10044.9 + 10193.1i) q^{80} +(2027.46 - 6239.88i) q^{81} +25159.7 q^{82} +(-19926.0 + 61325.8i) q^{83} +(21962.5 - 15956.7i) q^{84} +(-37495.1 - 6220.52i) q^{85} +(-76030.2 - 55239.2i) q^{86} +(-49496.3 + 35961.2i) q^{87} +(7367.42 - 5352.75i) q^{88} +(-41803.1 - 30371.7i) q^{89} +(-2702.25 - 17909.4i) q^{90} +(-53242.6 + 38683.0i) q^{91} +(-7235.40 + 22268.3i) q^{92} -19689.2 q^{93} +(13154.4 - 40485.0i) q^{94} +(38560.8 + 6397.33i) q^{95} +(2847.90 + 8764.94i) q^{96} +(-11436.8 - 35199.0i) q^{97} +(-60622.9 - 44045.1i) q^{98} -11525.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−8.34027	−	55.2760i	−0.149195	−	0.988808i
$5$	−8.34027	−	55.2760i	−0.149195	−	0.988808i
$6$	11.1246	−	34.2380i	0.126156	−	0.388267i
$7$	−188.522			−1.45417			−0.727087	−	0.686545i	$-0.759127\pi$
$7$	−188.522			−1.45417			−0.727087	+	0.686545i	$0.759127\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	−102.972	+	198.486i	−0.325626	+	0.627668i
$11$	115.116	+	83.6367i	0.286849	+	0.208408i	0.721899	−	0.691998i	$-0.243269\pi$
$11$	115.116	+	83.6367i	0.286849	+	0.208408i	−0.435050	+	0.900406i	$0.643269\pi$
$12$	−116.498	+	84.6411i	−0.233543	+	0.169679i
$13$	282.422	−	205.191i	0.463489	−	0.336744i	−0.331409	−	0.943487i	$-0.607524\pi$
$13$	282.422	−	205.191i	0.463489	−	0.336744i	0.794898	+	0.606743i	$0.207524\pi$
$14$	610.070	+	443.242i	0.831877	+	0.604394i
$15$	449.940	−	225.120i	0.516329	−	0.258336i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	210.101	−	646.623i	0.176321	−	0.542662i	−0.823370	−	0.567505i	$-0.807909\pi$
$17$	210.101	−	646.623i	0.176321	−	0.542662i	0.999691	+	0.0248435i	$0.00790874\pi$
$18$	324.000			0.235702
$19$	−216.073	+	665.003i	−0.137314	+	0.422610i	−0.995943	−	0.0899884i	$-0.971317\pi$
$19$	−216.073	+	665.003i	−0.137314	+	0.422610i	0.858628	+	0.512598i	$0.171317\pi$
$20$	799.894	−	400.213i	0.447154	−	0.223726i
$21$	−524.308	−	1613.65i	−0.259441	−	0.798477i
$22$	−175.882	−	541.308i	−0.0774754	−	0.238445i
$23$	1183.91	+	860.159i	0.466657	+	0.339046i	0.796137	−	0.605116i	$-0.206873\pi$
$23$	1183.91	+	860.159i	0.466657	+	0.339046i	−0.329480	+	0.944163i	$0.606873\pi$
$24$	576.000			0.204124
$25$	−2985.88	+	922.034i	−0.955482	+	0.295051i
$26$	−1396.37			−0.405104
$27$	−589.773	−	428.495i	−0.155695	−	0.113119i
$28$	−932.103	−	2868.72i	−0.224682	−	0.691501i
$29$	2100.66	+	6465.15i	0.463831	+	1.42753i	0.860447	+	0.509540i	$0.170185\pi$
$29$	2100.66	+	6465.15i	0.463831	+	1.42753i	−0.396616	+	0.917985i	$0.629815\pi$
$30$	−1985.33	−	329.370i	−0.402743	−	0.0668161i
$31$	−676.035	+	2080.62i	−0.126347	+	0.388856i	−0.994144	−	0.108063i	$-0.965535\pi$
$31$	−676.035	+	2080.62i	−0.126347	+	0.388856i	0.867797	+	0.496919i	$0.165535\pi$
$32$	1024.00			0.176777
$33$	−395.734	+	1217.94i	−0.0632584	+	0.194689i
$34$	−2200.20	+	1598.54i	−0.326411	+	0.237152i
$35$	1572.32	+	10420.7i	0.216956	+	1.43790i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	1307.25	−	949.774i	0.156984	−	0.114055i	−0.506520	−	0.862228i	$-0.669068\pi$
$37$	1307.25	−	949.774i	0.156984	−	0.114055i	0.663504	+	0.748173i	$0.269068\pi$
$38$	2262.74	−	1643.98i	0.254200	−	0.184687i
$39$	2541.79	+	1846.72i	0.267596	+	0.194420i
$40$	−3529.47	−	585.547i	−0.348786	−	0.0578644i
$41$	−5088.66	+	3697.13i	−0.472763	+	0.343483i	−0.798517	−	0.601972i	$-0.794382\pi$
$41$	−5088.66	+	3697.13i	−0.472763	+	0.343483i	0.325754	+	0.945455i	$0.394382\pi$
$42$	−2097.23	+	6454.62i	−0.183452	+	0.564608i
$43$	23494.6			1.93775			0.968875	−	0.247552i	$-0.0796262\pi$
$43$	23494.6			1.93775			0.968875	+	0.247552i	$0.0796262\pi$
$44$	−703.526	+	2165.23i	−0.0547834	+	0.168606i
$45$	3178.27	+	3225.17i	0.233969	+	0.237422i
$46$	−1808.85	−	5567.07i	−0.126040	−	0.387911i
$47$	3288.60	+	10121.3i	0.217153	+	0.668328i	0.998994	+	0.0448501i	$0.0142810\pi$
$47$	3288.60	+	10121.3i	0.217153	+	0.668328i	−0.781841	+	0.623478i	$0.785719\pi$
$48$	−1863.98	−	1354.26i	−0.116772	−	0.0848395i
$49$	18733.5			1.11462
$50$	11830.3	+	4036.46i	0.669225	+	0.228337i
$51$	6119.10			0.329429
$52$	4518.74	+	3283.06i	0.231745	+	0.168372i
$53$	5489.13	+	16893.8i	0.268420	+	0.826111i	0.990886	+	0.134704i	$0.0430085\pi$
$53$	5489.13	+	16893.8i	0.268420	+	0.826111i	−0.722466	+	0.691406i	$0.756992\pi$
$54$	901.094	+	2773.28i	0.0420519	+	0.129422i
$55$	3663.00	−	7060.71i	0.163279	−	0.314732i
$56$	−3728.41	+	11474.9i	−0.158874	+	0.488965i
$57$	−6293.03			−0.256550
$58$	8402.62	−	25860.6i	0.327978	−	1.00941i
$59$	16419.9	−	11929.7i	0.614101	−	0.446170i	−0.236755	−	0.971569i	$-0.576084\pi$
$59$	16419.9	−	11929.7i	0.614101	−	0.446170i	0.850856	+	0.525399i	$0.176084\pi$
$60$	5650.25	+	5733.64i	0.202623	+	0.205614i
$61$	9713.46	+	7057.24i	0.334233	+	0.242835i	0.742225	−	0.670151i	$-0.233771\pi$
$61$	9713.46	+	7057.24i	0.334233	+	0.242835i	−0.407992	+	0.912986i	$0.633771\pi$
$62$	7079.53	−	5143.58i	0.233897	−	0.169936i
$63$	12353.9	−	8975.64i	0.392151	−	0.284914i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−13697.6	−	13899.8i	−0.402126	−	0.408061i
$66$	4144.18	−	3010.92i	0.117106	−	0.0850823i
$67$	−6054.32	+	18633.3i	−0.164770	+	0.507110i	−0.999019	−	0.0442773i	$-0.985901\pi$
$67$	−6054.32	+	18633.3i	−0.164770	+	0.507110i	0.834249	+	0.551388i	$0.185901\pi$
$68$	10878.4			0.285294
$69$	−4069.91	+	12525.9i	−0.102911	+	0.316728i
$70$	19412.5	−	37419.0i	0.473518	−	0.912740i
$71$	23916.5	+	73607.5i	0.563057	+	1.73291i	0.673656	+	0.739045i	$0.264723\pi$
$71$	23916.5	+	73607.5i	0.563057	+	1.73291i	−0.110600	+	0.993865i	$0.535277\pi$
$72$	1601.94	+	4930.28i	0.0364180	+	0.112083i
$73$	−432.726	−	314.394i	−0.00950398	−	0.00690505i	0.583023	−	0.812456i	$-0.301870\pi$
$73$	−432.726	−	314.394i	−0.00950398	−	0.00690505i	−0.592527	+	0.805551i	$0.701870\pi$
$74$	−6463.41			−0.137209
$75$	−16196.3	−	22993.3i	−0.332479	−	0.472008i
$76$	−11187.6			−0.222179
$77$	−21701.9	−	15767.3i	−0.417129	−	0.303062i
$78$	−3883.52	−	11952.2i	−0.0722751	−	0.222440i
$79$	17562.5	+	54051.8i	0.316605	+	0.974411i	0.975089	+	0.221816i	$0.0711983\pi$
$79$	17562.5	+	54051.8i	0.316605	+	0.974411i	−0.658483	+	0.752595i	$0.728802\pi$
$80$	10044.9	+	10193.1i	0.175477	+	0.178067i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	25159.7			0.413210
$83$	−19926.0	+	61325.8i	−0.317486	+	0.977120i	0.657234	+	0.753687i	$0.271726\pi$
$83$	−19926.0	+	61325.8i	−0.317486	+	0.977120i	−0.974719	+	0.223433i	$0.928274\pi$
$84$	21962.5	−	15956.7i	0.339613	−	0.246743i
$85$	−37495.1	−	6220.52i	−0.562894	−	0.0933854i
$86$	−76030.2	−	55239.2i	−1.10851	−	0.805381i
$87$	−49496.3	+	35961.2i	−0.701091	+	0.509373i
$88$	7367.42	−	5352.75i	0.101417	−	0.0736834i
$89$	−41803.1	−	30371.7i	−0.559414	−	0.406438i	0.271831	−	0.962345i	$-0.412371\pi$
$89$	−41803.1	−	30371.7i	−0.559414	−	0.406438i	−0.831244	+	0.555907i	$0.812371\pi$
$90$	−2702.25	−	17909.4i	−0.0351657	−	0.233064i
$91$	−53242.6	+	38683.0i	−0.673994	+	0.489685i
$92$	−7235.40	+	22268.3i	−0.0891236	+	0.274294i
$93$	−19689.2			−0.236060
$94$	13154.4	−	40485.0i	0.153550	−	0.472580i
$95$	38560.8	+	6397.33i	0.438367	+	0.0727260i
$96$	2847.90	+	8764.94i	0.0315389	+	0.0970668i
$97$	−11436.8	−	35199.0i	−0.123417	−	0.379840i	0.870192	−	0.492713i	$-0.163995\pi$
$97$	−11436.8	−	35199.0i	−0.123417	−	0.379840i	−0.993609	+	0.112873i	$0.963995\pi$
$98$	−60622.9	−	44045.1i	−0.637634	−	0.463268i
$99$	−11525.6			−0.118188
$100$	−28793.5	−	40877.1i	−0.287935	−	0.408771i
$101$	−150067.			−1.46380			−0.731899	−	0.681413i	$-0.761366\pi$
$101$	−150067.			−1.46380			−0.731899	+	0.681413i	$0.761366\pi$
$102$	−19801.8	−	14386.9i	−0.188454	−	0.136920i
$103$	−51501.6	−	158506.i	−0.478330	−	1.47215i	−0.841413	−	0.540393i	$-0.818276\pi$
$103$	−51501.6	−	158506.i	−0.478330	−	1.47215i	0.363083	−	0.931757i	$-0.381724\pi$
$104$	−6904.03	−	21248.4i	−0.0625921	−	0.192639i
$105$	−84823.6	+	42440.0i	−0.750833	+	0.375666i
$106$	21956.5	−	67575.3i	0.189801	−	0.584148i
$107$	111543.			0.941849			0.470924	−	0.882174i	$-0.343920\pi$
$107$	111543.			0.941849			0.470924	+	0.882174i	$0.343920\pi$
$108$	3604.37	−	11093.1i	0.0297352	−	0.0915155i
$109$	123553.	−	89766.4i	0.996062	−	0.723682i	0.0348220	−	0.999394i	$-0.488914\pi$
$109$	123553.	−	89766.4i	0.996062	−	0.723682i	0.961240	+	0.275712i	$0.0889136\pi$
$110$	−28454.4	+	14236.7i	−0.224217	+	0.112183i
$111$	11765.3	+	8547.97i	0.0906347	+	0.0658499i
$112$	39044.5	−	28367.5i	0.294113	−	0.213686i
$113$	89103.8	−	64737.7i	0.656448	−	0.476937i	−0.209014	−	0.977913i	$-0.567025\pi$
$113$	89103.8	−	64737.7i	0.656448	−	0.476937i	0.865461	+	0.500975i	$0.167025\pi$
$114$	20364.7	+	14795.8i	0.146763	+	0.106629i
$115$	37672.1	−	72615.6i	0.265629	−	0.512018i
$116$	−87993.4	+	63930.9i	−0.607163	+	0.441130i
$117$	−8737.91	+	26892.5i	−0.0590124	+	0.181621i
$118$	−81184.3			−0.536744
$119$	−39608.6	+	121903.i	−0.256402	+	0.789125i
$120$	−4804.00	−	31839.0i	−0.0304544	−	0.201840i
$121$	−43510.9	−	133913.i	−0.270168	−	0.831493i
$122$	−14840.8	−	45675.4i	−0.0902733	−	0.277833i
$123$	−45797.9	−	33274.1i	−0.272950	−	0.198310i
$124$	−35003.1			−0.204434
$125$	75869.4	+	157358.i	0.434302	+	0.900767i
$126$	−61081.1			−0.342752
$127$	−202684.	−	147258.i	−1.11509	−	0.810159i	−0.131631	−	0.991299i	$-0.542022\pi$
$127$	−202684.	−	147258.i	−1.11509	−	0.810159i	−0.983457	+	0.181139i	$0.942022\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	65342.2	+	201103.i	0.345716	+	1.06400i
$130$	11646.1	+	77185.7i	0.0604397	+	0.400570i
$131$	−40814.4	+	125614.i	−0.207795	+	0.639527i	0.791792	+	0.610791i	$0.209148\pi$
$131$	−40814.4	+	125614.i	−0.207795	+	0.639527i	−0.999587	+	0.0287361i	$0.990852\pi$
$132$	−20489.9			−0.102354
$133$	40734.4	−	125368.i	0.199679	−	0.614549i
$134$	63401.7	−	46064.0i	0.305027	−	0.221615i
$135$	−18766.7	+	36174.1i	−0.0886242	+	0.170830i
$136$	−35203.2	−	25576.7i	−0.163206	−	0.118576i
$137$	158145.	−	114899.i	0.719871	−	0.523017i	−0.166472	−	0.986046i	$-0.553237\pi$
$137$	158145.	−	114899.i	0.719871	−	0.523017i	0.886343	+	0.463029i	$0.153237\pi$
$138$	42620.7	−	30965.7i	0.190512	−	0.138415i
$139$	232419.	+	168862.i	1.02032	+	0.741303i	0.966348	−	0.257240i	$-0.0828130\pi$
$139$	232419.	+	168862.i	1.02032	+	0.741303i	0.0539682	+	0.998543i	$0.482813\pi$
$140$	−150797.	+	75448.9i	−0.650240	+	0.325336i
$141$	−77486.9	+	56297.5i	−0.328232	+	0.238474i
$142$	95666.1	−	294430.i	0.398141	−	1.22535i
$143$	49672.7			0.203132
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	339848.	−	170037.i	1.34235	−	0.671620i
$146$	661.146	+	2034.80i	0.00256694	+	0.00790022i
$147$	52100.7	+	160350.i	0.198861	+	0.612032i
$148$	20916.0	+	15196.4i	0.0784919	+	0.0570277i
$149$	−241557.			−0.891361			−0.445680	−	0.895192i	$-0.647038\pi$
$149$	−241557.			−0.891361			−0.445680	+	0.895192i	$0.647038\pi$
$150$	−1648.11	+	112488.i	−0.00598080	+	0.408204i
$151$	−480310.			−1.71427			−0.857136	−	0.515091i	$-0.827758\pi$
$151$	−480310.			−1.71427			−0.857136	+	0.515091i	$0.827758\pi$
$152$	36203.9	+	26303.7i	0.127100	+	0.0923437i
$153$	17018.2	+	52376.5i	0.0587738	+	0.180887i
$154$	33157.5	+	102048.i	0.112663	+	0.346740i
$155$	120647.	+	20015.6i	0.403354	+	0.0669174i
$156$	−15534.1	+	47808.9i	−0.0511062	+	0.157289i
$157$	143449.			0.464461			0.232231	−	0.972661i	$-0.425398\pi$
$157$	143449.			0.464461			0.232231	+	0.972661i	$0.425398\pi$
$158$	70249.9	−	216207.i	0.223874	−	0.689013i
$159$	−129337.	+	93968.6i	−0.405722	+	0.294774i
$160$	−8540.44	−	56602.7i	−0.0263743	−	0.174798i
$161$	−223192.	−	162159.i	−0.678601	−	0.493033i
$162$	−21231.8	+	15425.8i	−0.0635624	+	0.0461808i
$163$	282019.	−	204899.i	0.831400	−	0.604047i	−0.0885552	−	0.996071i	$-0.528225\pi$
$163$	282019.	−	204899.i	0.831400	−	0.604047i	0.919955	+	0.392024i	$0.128225\pi$
$164$	−81418.5	−	59154.0i	−0.236382	−	0.171741i
$165$	70623.6	+	11716.6i	0.201948	+	0.0335036i
$166$	208667.	−	151606.i	0.587739	−	0.427017i
$167$	95916.2	−	295200.i	0.266134	−	0.819077i	−0.725296	−	0.688437i	$-0.758297\pi$
$167$	95916.2	−	295200.i	0.266134	−	0.819077i	0.991430	−	0.130639i	$-0.0417030\pi$
$168$	−108589.			−0.296832
$169$	−77077.4	+	237220.i	−0.207592	+	0.638902i
$170$	106711.	+	108286.i	0.283197	+	0.287376i
$171$	−17501.9	−	53865.3i	−0.0457714	−	0.140870i
$172$	116164.	+	357516.i	0.299399	+	0.921454i
$173$	−283985.	−	206327.i	−0.721407	−	0.524133i	0.165426	−	0.986222i	$-0.447100\pi$
$173$	−283985.	−	206327.i	−0.721407	−	0.524133i	−0.886834	+	0.462089i	$0.847100\pi$
$174$	244723.			0.612776
$175$	562904.	−	173824.i	1.38944	−	0.429056i
$176$	−36426.5			−0.0886413
$177$	147779.	+	107368.i	0.354551	+	0.257597i
$178$	63869.4	+	196570.i	0.151092	+	0.465015i
$179$	259700.	+	799275.i	0.605815	+	1.86451i	0.491089	+	0.871109i	$0.336599\pi$
$179$	259700.	+	799275.i	0.605815	+	1.86451i	0.114726	+	0.993397i	$0.463401\pi$
$180$	−33362.9	+	64309.5i	−0.0767508	+	0.147943i
$181$	−156083.	+	480376.i	−0.354128	+	1.08989i	0.602385	+	0.798206i	$0.294217\pi$
$181$	−156083.	+	480376.i	−0.354128	+	1.08989i	−0.956513	+	0.291689i	$0.905783\pi$
$182$	263246.			0.589092
$183$	−33391.9	+	102770.i	−0.0737078	+	0.226849i
$184$	75770.1	−	55050.2i	0.164988	−	0.119871i
$185$	−63402.6	−	64338.3i	−0.136200	−	0.138210i
$186$	63715.7	+	46292.2i	0.135041	+	0.0981127i
$187$	78267.3	−	56864.6i	0.163673	−	0.118915i
$188$	−137755.	+	100085.i	−0.284257	+	0.206525i
$189$	111185.	+	80780.8i	0.226408	+	0.164495i
$190$	−109744.	−	111364.i	−0.220546	−	0.223801i
$191$	367957.	−	267337.i	0.729817	−	0.530243i	−0.159689	−	0.987167i	$-0.551049\pi$
$191$	367957.	−	267337.i	0.729817	−	0.530243i	0.889506	+	0.456924i	$0.151049\pi$
$192$	11391.6	−	35059.7i	0.0223014	−	0.0686366i
$193$	−341145.			−0.659243			−0.329621	−	0.944113i	$-0.606921\pi$
$193$	−341145.			−0.659243			−0.329621	+	0.944113i	$0.606921\pi$
$194$	−45747.4	+	140796.i	−0.0872694	+	0.268587i
$195$	80880.2	−	155902.i	0.152320	−	0.293607i
$196$	92623.5	+	285066.i	0.172219	+	0.530036i
$197$	216601.	+	666630.i	0.397645	+	1.22382i	0.926883	+	0.375351i	$0.122478\pi$
$197$	216601.	+	666630.i	0.397645	+	1.22382i	−0.529238	+	0.848473i	$0.677522\pi$
$198$	37297.6	+	27098.3i	0.0676110	+	0.0491223i
$199$	−664113.			−1.18880			−0.594401	−	0.804169i	$-0.702611\pi$
$199$	−664113.			−1.18880			−0.594401	+	0.804169i	$0.702611\pi$
$200$	−2929.98	+	199979.i	−0.00517952	+	0.353515i
$201$	−176330.			−0.307847
$202$	485626.	+	352828.i	0.837383	+	0.608394i
$203$	−396019.	−	1.21882e6i	−0.674491	−	2.07587i
$204$	30254.5	+	93113.8i	0.0508996	+	0.156653i
$205$	246803.	+	250446.i	0.410172	+	0.416226i
$206$	−206007.	+	634023.i	−0.338231	+	1.04097i
$207$	−118535.			−0.192273
$208$	−27616.1	+	84993.7i	−0.0442593	+	0.136216i
$209$	−80492.1	+	58480.9i	−0.127464	+	0.0926080i
$210$	374277.	+	62093.4i	0.585659	+	0.0971622i
$211$	344298.	+	250147.i	0.532389	+	0.386803i	0.821250	−	0.570568i	$-0.193277\pi$
$211$	344298.	+	250147.i	0.532389	+	0.386803i	−0.288862	+	0.957371i	$0.593277\pi$
$212$	−229932.	+	167055.i	−0.351366	+	0.255282i
$213$	−563528.	+	409427.i	−0.851073	+	0.618341i
$214$	−360959.	−	262252.i	−0.538795	−	0.391458i
$215$	−195952.	−	1.29869e6i	−0.289103	−	1.91606i
$216$	−37745.5	+	27423.7i	−0.0550466	+	0.0399937i
$217$	127447.	−	392242.i	0.183731	−	0.565464i
$218$	−610879.			−0.870590
$219$	1487.58	−	4578.30i	0.00209590	−	0.00645050i
$220$	125553.	+	20829.5i	0.174892	+	0.0290150i
$221$	−73344.5	−	225731.i	−0.101015	−	0.310893i
$222$	−17975.7	−	55323.6i	−0.0244796	−	0.0753404i
$223$	−461186.	−	335071.i	−0.621032	−	0.451206i	0.232250	−	0.972656i	$-0.425391\pi$
$223$	−461186.	−	335071.i	−0.621032	−	0.451206i	−0.853282	+	0.521450i	$0.825391\pi$
$224$	−193046.			−0.257064
$225$	151767.	−	202581.i	0.199858	−	0.266773i
$226$	−440553.			−0.573756
$227$	696804.	+	506258.i	0.897523	+	0.652089i	0.937829	−	0.347098i	$-0.112833\pi$
$227$	696804.	+	506258.i	0.897523	+	0.652089i	−0.0403052	+	0.999187i	$0.512833\pi$
$228$	−31114.5	−	95760.5i	−0.0396392	−	0.121997i
$229$	−45170.5	−	139020.i	−0.0569201	−	0.175182i	0.918554	−	0.395295i	$-0.129358\pi$
$229$	−45170.5	−	139020.i	−0.0569201	−	0.175182i	−0.975474	+	0.220113i	$0.929358\pi$
$230$	−292639.	+	146417.i	−0.364765	+	0.182504i
$231$	74604.4	−	229609.i	0.0919887	−	0.283112i
$232$	435063.			0.530680
$233$	−257583.	+	792760.i	−0.310834	+	0.956648i	0.666602	+	0.745414i	$0.267748\pi$
$233$	−257583.	+	792760.i	−0.310834	+	0.956648i	−0.977436	+	0.211234i	$0.932252\pi$
$234$	91504.6	−	66482.0i	0.109245	−	0.0793714i
$235$	532035.	−	266195.i	0.628450	−	0.314434i
$236$	262718.	+	190876.i	0.307050	+	0.223085i
$237$	−413813.	+	300652.i	−0.478556	+	0.347691i
$238$	414786.	−	301360.i	0.474659	−	0.344860i
$239$	902503.	+	655707.i	1.02201	+	0.742531i	0.966693	−	0.255938i	$-0.0823842\pi$
$239$	902503.	+	655707.i	1.02201	+	0.742531i	0.0553135	+	0.998469i	$0.482384\pi$
$240$	−59311.9	+	114328.i	−0.0664682	+	0.128122i
$241$	−302581.	+	219838.i	−0.335582	+	0.243815i	−0.742795	−	0.669518i	$-0.766500\pi$
$241$	−302581.	+	219838.i	−0.335582	+	0.243815i	0.407214	+	0.913333i	$0.366500\pi$
$242$	−174044.	+	535651.i	−0.191038	+	0.587954i
$243$	59049.0			0.0641500
$244$	−59363.4	+	182702.i	−0.0638328	+	0.196457i
$245$	−156242.	−	1.03551e6i	−0.166297	−	1.10215i
$246$	69973.0	+	215355.i	0.0737213	+	0.226891i
$247$	75429.3	+	232147.i	0.0786679	+	0.242115i
$248$	113272.	+	82297.2i	0.116949	+	0.0849681i
$249$	−580336.			−0.593172
$250$	124451.	−	687600.i	0.125936	−	0.695802i
$251$	1.60562e6			1.60863			0.804317	−	0.594200i	$-0.202531\pi$
$251$	1.60562e6			1.60863			0.804317	+	0.594200i	$0.202531\pi$
$252$	197663.	+	143610.i	0.196075	+	0.142457i
$253$	64345.8	+	198036.i	0.0632003	+	0.194510i
$254$	309673.	+	953076.i	0.301175	+	0.926922i
$255$	−51035.0	−	338240.i	−0.0491493	−	0.325742i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	176703.			0.166883			0.0834413	−	0.996513i	$-0.473409\pi$
$257$	176703.			0.166883			0.0834413	+	0.996513i	$0.473409\pi$
$258$	261369.	−	804410.i	0.244458	−	0.752364i
$259$	−246446.	+	179053.i	−0.228282	+	0.165857i
$260$	143787.	−	277160.i	0.131913	−	0.254271i
$261$	−445467.	−	323650.i	−0.404775	−	0.294086i
$262$	427413.	−	310534.i	0.384676	−	0.279483i
$263$	961640.	−	698673.i	0.857281	−	0.622851i	−0.0698628	−	0.997557i	$-0.522256\pi$
$263$	961640.	−	698673.i	0.857281	−	0.622851i	0.927144	+	0.374705i	$0.122256\pi$
$264$	66306.8	+	48174.7i	0.0585529	+	0.0425412i
$265$	888042.	−	444317.i	0.776818	−	0.388667i
$266$	−426576.	+	309926.i	−0.369652	+	0.268568i
$267$	143706.	−	442282.i	0.123366	−	0.379683i
$268$	−313475.			−0.266604
$269$	−384780.	+	1.18423e6i	−0.324214	+	0.997828i	0.647580	+	0.761997i	$0.275781\pi$
$269$	−384780.	+	1.18423e6i	−0.324214	+	0.997828i	−0.971794	+	0.235831i	$0.924219\pi$
$270$	145781.	−	72938.8i	0.121700	−	0.0608904i
$271$	39218.8	+	120703.i	0.0324393	+	0.0998379i	0.965965	−	0.258672i	$-0.0832849\pi$
$271$	39218.8	+	120703.i	0.0324393	+	0.0998379i	−0.933526	+	0.358510i	$0.883285\pi$
$272$	53785.8	+	165536.i	0.0440804	+	0.135665i
$273$	−479184.	−	348147.i	−0.389131	−	0.282720i
$274$	−781914.			−0.629191
$275$	−420838.	−	143588.i	−0.335570	−	0.114495i
$276$	−210728.			−0.166514
$277$	−987301.	−	717317.i	−0.773126	−	0.561709i	0.129782	−	0.991543i	$-0.458572\pi$
$277$	−987301.	−	717317.i	−0.773126	−	0.561709i	−0.902908	+	0.429834i	$0.858572\pi$
$278$	−355105.	−	1.09290e6i	−0.275578	−	0.848141i
$279$	−54758.8	−	168530.i	−0.0421156	−	0.129619i
$280$	665382.	+	110388.i	0.507196	+	0.0841450i
$281$	471879.	−	1.45229e6i	0.356505	−	1.09721i	−0.598627	−	0.801028i	$-0.704287\pi$
$281$	471879.	−	1.45229e6i	0.356505	−	1.09721i	0.955132	−	0.296181i	$-0.0957130\pi$
$282$	383116.			0.286885
$283$	−231135.	+	711362.i	−0.171554	+	0.527988i	−0.999459	−	0.0328792i	$-0.989532\pi$
$283$	−231135.	+	711362.i	−0.171554	+	0.527988i	0.827905	+	0.560868i	$0.189532\pi$
$284$	−1.00183e6	+	727871.i	−0.737051	+	0.535499i
$285$	52485.6	+	347854.i	0.0382761	+	0.253679i
$286$	−160744.	−	116788.i	−0.116204	−	0.0844271i
$287$	959324.	−	696989.i	0.687480	−	0.499484i
$288$	−67103.1	+	48753.3i	−0.0476718	+	0.0346356i
$289$	774709.	+	562859.i	0.545625	+	0.396420i
$290$	−1.49955e6	−	248779.i	−1.04705	−	0.173708i
$291$	269478.	−	195787.i	0.186548	−	0.135535i
$292$	2644.58	−	8139.19i	0.00181510	−	0.00558630i
$293$	−386159.			−0.262783			−0.131391	−	0.991331i	$-0.541944\pi$
$293$	−386159.			−0.262783			−0.131391	+	0.991331i	$0.541944\pi$
$294$	208403.	−	641398.i	0.140616	−	0.432772i
$295$	−796374.	−	808128.i	−0.532798	−	0.540661i
$296$	−31956.9	−	98353.1i	−0.0211999	−	0.0652467i
$297$	−32054.4	−	98653.3i	−0.0210861	−	0.0648964i
$298$	781694.	+	567934.i	0.509913	+	0.370473i
$299$	510858.			0.330463
$300$	269808.	−	360144.i	0.173082	−	0.231032i
$301$	−4.42925e6			−2.81783
$302$	1.55432e6	+	1.12928e6i	0.980668	+	0.712497i
$303$	−417359.	−	1.28450e6i	−0.261158	−	0.803761i
$304$	−55314.6	−	170241.i	−0.0343286	−	0.105653i
$305$	309083.	−	595781.i	0.190251	−	0.366722i
$306$	68072.6	−	209506.i	0.0415594	−	0.127907i
$307$	−1.09450e6			−0.662782			−0.331391	−	0.943493i	$-0.607518\pi$
$307$	−1.09450e6			−0.662782			−0.331391	+	0.943493i	$0.607518\pi$
$308$	132630.	−	408193.i	0.0796646	−	0.245182i
$309$	1.21350e6	−	881657.i	0.723007	−	0.525295i
$310$	−343362.	−	348429.i	−0.202931	−	0.205926i
$311$	−1.56304e6	−	1.13561e6i	−0.916366	−	0.665779i	0.0262509	−	0.999655i	$-0.491643\pi$
$311$	−1.56304e6	−	1.13561e6i	−0.916366	−	0.665779i	−0.942617	+	0.333877i	$0.891643\pi$
$312$	162675.	−	118190.i	0.0946093	−	0.0687377i
$313$	−2.54225e6	+	1.84705e6i	−1.46675	+	1.06566i	−0.485215	+	0.874395i	$0.661259\pi$
$313$	−2.54225e6	+	1.84705e6i	−1.46675	+	1.06566i	−0.981539	+	0.191265i	$0.938741\pi$
$314$	−464212.	−	337270.i	−0.265700	−	0.193043i
$315$	−599173.	−	608016.i	−0.340232	−	0.345254i
$316$	−735667.	+	534493.i	−0.414442	+	0.301110i
$317$	−200116.	+	615894.i	−0.111849	+	0.344237i	−0.991277	−	0.131796i	$-0.957926\pi$
$317$	−200116.	+	615894.i	−0.111849	+	0.344237i	0.879427	+	0.476033i	$0.157926\pi$
$318$	639476.			0.354614
$319$	−298905.	+	919934.i	−0.164458	+	0.506151i
$320$	−105443.	+	203250.i	−0.0575631	+	0.110957i
$321$	310217.	+	954749.i	0.168036	+	0.517162i
$322$	341008.	+	1.04951e6i	0.183284	+	0.564090i
$323$	384610.	+	279435.i	0.205123	+	0.149030i
$324$	104976.			0.0555556
$325$	−654083.	+	873079.i	−0.343498	+	0.458506i
$326$	−1.39438e6			−0.726670
$327$	1.11198e6	+	807898.i	0.575077	+	0.417818i
$328$	124396.	+	382853.i	0.0638445	+	0.196493i
$329$	−619972.	−	1.90808e6i	−0.315779	−	0.971866i
$330$	−200995.	−	203962.i	−0.101602	−	0.103101i
$331$	−311887.	+	959889.i	−0.156469	+	0.481561i	−0.998307	−	0.0581694i	$-0.981474\pi$
$331$	−311887.	+	959889.i	−0.156469	+	0.481561i	0.841838	+	0.539730i	$0.181474\pi$
$332$	−1.03171e6			−0.513702
$333$	−40445.4	+	124478.i	−0.0199875	+	0.0615152i
$334$	−1.00445e6	+	729774.i	−0.492675	+	0.357950i
$335$	1.08047e6	+	179252.i	0.526018	+	0.0872675i
$336$	351400.	+	255307.i	0.169806	+	0.123371i
$337$	2.60412e6	−	1.89200e6i	1.24907	−	0.907501i	0.250900	−	0.968013i	$-0.419273\pi$
$337$	2.60412e6	−	1.89200e6i	1.24907	−	0.907501i	0.998167	+	0.0605121i	$0.0192734\pi$
$338$	807165.	−	586439.i	0.384300	−	0.279210i
$339$	801934.	+	582639.i	0.379000	+	0.275360i
$340$	−90728.8	−	601315.i	−0.0425645	−	0.282101i
$341$	−251839.	+	182971.i	−0.117283	+	0.0852113i
$342$	−70007.5	+	215461.i	−0.0323653	+	0.0996101i
$343$	−363187.			−0.166684
$344$	464655.	−	1.43006e6i	0.211707	−	0.651567i
$345$	726326.	+	120499.i	0.328537	+	0.0545050i
$346$	433891.	+	1.33538e6i	0.194845	+	0.599673i
$347$	160649.	+	494428.i	0.0716235	+	0.220434i	0.980460	−	0.196718i	$-0.0630282\pi$
$347$	160649.	+	494428.i	0.0716235	+	0.220434i	−0.908837	+	0.417152i	$0.863028\pi$
$348$	−791941.	−	575378.i	−0.350546	−	0.254686i
$349$	−904609.			−0.397555			−0.198777	−	0.980045i	$-0.563697\pi$
$349$	−904609.			−0.397555			−0.198777	+	0.980045i	$0.563697\pi$
$350$	−2.23028e6	−	760961.i	−0.973171	−	0.332041i
$351$	−254488.			−0.110255
$352$	117879.	+	85643.9i	0.0507083	+	0.0368417i
$353$	313315.	+	964285.i	0.133827	+	0.411878i	0.995406	−	0.0957463i	$-0.0305238\pi$
$353$	313315.	+	964285.i	0.133827	+	0.411878i	−0.861578	+	0.507624i	$0.830524\pi$
$354$	−225786.	−	694898.i	−0.0957610	−	0.294722i
$355$	3.86926e6	−	1.93592e6i	1.62951	−	0.815297i
$356$	255478.	−	786279.i	0.106839	−	0.328815i
$357$	−1.15358e6			−0.479048
$358$	1.03880e6	−	3.19710e6i	0.428376	−	1.31841i
$359$	−1.24178e6	+	902207.i	−0.508521	+	0.369462i	−0.812262	−	0.583292i	$-0.801764\pi$
$359$	−1.24178e6	+	902207.i	−0.508521	+	0.369462i	0.303741	+	0.952755i	$0.401764\pi$
$360$	259166.	−	129669.i	0.105395	−	0.0527327i
$361$	1.60766e6	+	1.16804e6i	0.649273	+	0.471724i
$362$	1.63453e6	−	1.18755e6i	0.655573	−	0.476301i
$363$	1.02522e6	−	744864.i	0.408366	−	0.296695i
$364$	−851882.	−	618929.i	−0.336997	−	0.244843i
$365$	−13769.4	+	26541.5i	−0.00540981	+	0.0104278i
$366$	349685.	−	254061.i	0.136450	−	0.0991368i
$367$	−1.39490e6	+	4.29305e6i	−0.540601	+	1.66380i	0.190624	+	0.981663i	$0.438949\pi$
$367$	−1.39490e6	+	4.29305e6i	−0.540601	+	1.66380i	−0.731225	+	0.682136i	$0.761051\pi$
$368$	−374628.			−0.144205
$369$	157439.	−	484548.i	0.0601932	−	0.185256i
$370$	53906.6	+	357272.i	0.0204709	+	0.135673i
$371$	−1.03482e6	−	3.18485e6i	−0.390329	−	1.20131i
$372$	−97349.0	−	299609.i	−0.0364732	−	0.112253i
$373$	6336.59	+	4603.80i	0.00235822	+	0.00171334i	0.588964	−	0.808159i	$-0.299536\pi$
$373$	6336.59	+	4603.80i	0.00235822	+	0.00171334i	−0.586606	+	0.809873i	$0.699536\pi$
$374$	−386975.			−0.143055
$375$	−1.13590e6	+	1.08704e6i	−0.417121	+	0.399179i
$376$	681096.			0.248450
$377$	1.91986e6	+	1.39486e6i	0.695692	+	0.505450i
$378$	−169876.	−	522824.i	−0.0611508	−	0.188203i
$379$	−529593.	−	1.62992e6i	−0.189384	−	0.582865i	0.810612	−	0.585584i	$-0.199135\pi$
$379$	−529593.	−	1.62992e6i	−0.189384	−	0.582865i	−0.999996	+	0.00271856i	$0.999135\pi$
$380$	93307.7	+	618407.i	0.0331481	+	0.219693i
$381$	696764.	−	2.14442e6i	0.245909	−	0.756829i
$382$	−1.81928e6			−0.637883
$383$	−1.10033e6	+	3.38646e6i	−0.383288	+	1.17964i	0.554427	+	0.832232i	$0.312938\pi$
$383$	−1.10033e6	+	3.38646e6i	−0.383288	+	1.17964i	−0.937715	+	0.347406i	$0.887062\pi$
$384$	−119294.	+	86672.5i	−0.0412850	+	0.0299953i
$385$	−690556.	+	1.33110e6i	−0.237436	+	0.457676i
$386$	1.10397e6	+	802079.i	0.377127	+	0.273999i
$387$	−1.53961e6	+	1.11859e6i	−0.522557	+	0.379660i
$388$	479073.	−	348067.i	0.161556	−	0.117377i
$389$	3.11787e6	+	2.26527e6i	1.04468	+	0.759006i	0.971194	−	0.238290i	$-0.0765868\pi$
$389$	3.11787e6	+	2.26527e6i	1.04468	+	0.759006i	0.0734885	+	0.997296i	$0.476587\pi$
$390$	−628282.	+	314350.i	−0.209167	+	0.104653i
$391$	804938.	−	584822.i	0.266269	−	0.193456i
$392$	370494.	−	1.14026e6i	0.121777	−	0.374792i
$393$	−1.18870e6			−0.388232
$394$	866404.	−	2.66652e6i	0.281177	−	0.865374i
$395$	2.84129e6	−	1.42159e6i	0.916269	−	0.458439i
$396$	−56985.6	−	175384.i	−0.0182611	−	0.0562019i
$397$	262782.	+	808758.i	0.0836794	+	0.257539i	0.984138	−	0.177402i	$-0.0567693\pi$
$397$	262782.	+	808758.i	0.0836794	+	0.257539i	−0.900459	+	0.434941i	$0.856769\pi$
$398$	2.14911e6	+	1.56142e6i	0.680067	+	0.494098i
$399$	1.18637e6			0.373069
$400$	479659.	−	640255.i	0.149894	−	0.200080i
$401$	−393450.			−0.122188			−0.0610939	−	0.998132i	$-0.519459\pi$
$401$	−393450.			−0.122188			−0.0610939	+	0.998132i	$0.519459\pi$
$402$	570615.	+	414576.i	0.176108	+	0.127950i
$403$	235998.	+	726328.i	0.0723847	+	0.222777i
$404$	−741971.	−	2.28355e6i	−0.226169	−	0.696077i
$405$	−361825.	−	60027.7i	−0.109613	−	0.0181850i
$406$	−1.58408e6	+	4.87529e6i	−0.476938	+	1.46786i
$407$	229922.			0.0688008
$408$	121018.	−	372455.i	0.0359915	−	0.110770i
$409$	−3.13146e6	+	2.27514e6i	−0.925632	+	0.672511i	−0.944919	−	0.327303i	$-0.893860\pi$
$409$	−3.13146e6	+	2.27514e6i	−0.925632	+	0.672511i	0.0192873	+	0.999814i	$0.493860\pi$
$410$	−209839.	−	1.39073e6i	−0.0616490	−	0.408585i
$411$	1.42331e6	+	1.03409e6i	0.415618	+	0.301964i
$412$	2.15733e6	−	1.56739e6i	0.626143	−	0.454919i
$413$	−3.09550e6	+	2.24902e6i	−0.893010	+	0.648810i
$414$	383586.	+	278691.i	0.109992	+	0.0799140i
$415$	3.55603e6	+	589954.i	1.01355	+	0.168150i
$416$	289200.	−	210116.i	0.0819341	−	0.0595286i
$417$	−798985.	+	2.45902e6i	−0.225008	+	0.692505i
$418$	397975.			0.111408
$419$	−97833.2	+	301100.i	−0.0272240	+	0.0837867i	−0.963745	−	0.266824i	$-0.914026\pi$
$419$	−97833.2	+	301100.i	−0.0272240	+	0.0837867i	0.936521	+	0.350610i	$0.114026\pi$
$420$	−1.06520e6	−	1.08092e6i	−0.294650	−	0.298999i
$421$	1.26737e6	+	3.90056e6i	0.348496	+	1.07256i	0.959685	+	0.281077i	$0.0906915\pi$
$421$	1.26737e6	+	3.90056e6i	0.348496	+	1.07256i	−0.611189	+	0.791485i	$0.709308\pi$
$422$	−526041.	−	1.61899e6i	−0.143793	−	0.442550i
$423$	−697382.	−	506678.i	−0.189505	−	0.137683i
$424$	1.13685e6			0.307105
$425$	−31126.5	+	2.12446e6i	−0.00835906	+	0.570527i
$426$	2.78624e6			0.743865
$427$	−1.83120e6	−	1.33044e6i	−0.486033	−	0.353124i
$428$	551497.	+	1.69733e6i	0.145524	+	0.447876i
$429$	138147.	+	425174.i	0.0362410	+	0.111538i
$430$	−2.41929e6	+	4.66336e6i	−0.630982	+	1.21626i
$431$	1.90182e6	−	5.85321e6i	0.493148	−	1.51775i	−0.326676	−	0.945136i	$-0.605929\pi$
$431$	1.90182e6	−	5.85321e6i	0.493148	−	1.51775i	0.819824	−	0.572616i	$-0.194071\pi$
$432$	186624.			0.0481125
$433$	−1.30307e6	+	4.01043e6i	−0.334001	+	1.02795i	0.633211	+	0.773979i	$0.281736\pi$
$433$	−1.30307e6	+	4.01043e6i	−0.334001	+	1.02795i	−0.967212	+	0.253970i	$0.918264\pi$
$434$	−1.33465e6	+	969677.i	−0.340127	+	0.247117i
$435$	2.40060e6	+	2.43603e6i	0.608271	+	0.617248i
$436$	1.97685e6	+	1.43626e6i	0.498031	+	0.361841i
$437$	−827818.	+	601445.i	−0.207363	+	0.150658i
$438$	−15578.1	+	11318.2i	−0.00387998	+	0.00281897i
$439$	6.11899e6	+	4.44571e6i	1.51537	+	1.10098i	0.963724	+	0.266901i	$0.0859998\pi$
$439$	6.11899e6	+	4.44571e6i	1.51537	+	1.10098i	0.551645	+	0.834079i	$0.314000\pi$
$440$	−357325.	−	362599.i	−0.0879896	−	0.0892883i
$441$	−1.22761e6	+	891913.i	−0.300583	+	0.218387i
$442$	−293378.	+	902925.i	−0.0714286	+	0.219835i
$443$	5.06633e6			1.22655			0.613274	−	0.789870i	$-0.289852\pi$
$443$	5.06633e6			1.22655			0.613274	+	0.789870i	$0.289852\pi$
$444$	−71902.9	+	221294.i	−0.0173097	+	0.0532737i
$445$	−1.33018e6	+	2.56402e6i	−0.318427	+	0.613791i
$446$	704629.	+	2.16863e6i	0.167735	+	0.516235i
$447$	−671806.	−	2.06761e6i	−0.159029	−	0.489440i
$448$	624711.	+	453879.i	0.147057	+	0.106843i
$449$	4.16986e6			0.976124			0.488062	−	0.872809i	$-0.337704\pi$
$449$	4.16986e6			0.976124			0.488062	+	0.872809i	$0.337704\pi$
$450$	−967425.	+	298739.i	−0.225209	+	0.0695442i
$451$	−895001.			−0.207196
$452$	1.42566e6	+	1.03580e6i	0.328224	+	0.238469i
$453$	−1.33582e6	−	4.11122e6i	−0.305845	−	0.941294i
$454$	−1.06462e6	−	3.27657e6i	−0.242413	−	0.746070i
$455$	2.58230e6	+	2.62041e6i	0.584761	+	0.593392i
$456$	−124458.	+	383042.i	−0.0280292	+	0.0862649i
$457$	−6.22034e6			−1.39323			−0.696617	−	0.717444i	$-0.745312\pi$
$457$	−6.22034e6			−1.39323			−0.696617	+	0.717444i	$0.745312\pi$
$458$	−180682.	+	556082.i	−0.0402486	+	0.123872i
$459$	−400987.	+	291334.i	−0.0888379	+	0.0645445i
$460$	1.29125e6	+	214221.i	0.284521	+	0.0472027i
$461$	−4.01616e6	−	2.91791e6i	−0.880153	−	0.639469i	0.0531386	−	0.998587i	$-0.483077\pi$
$461$	−4.01616e6	−	2.91791e6i	−0.880153	−	0.639469i	−0.933292	+	0.359118i	$0.883077\pi$
$462$	−781268.	+	567624.i	−0.170292	+	0.123725i
$463$	−731762.	+	531656.i	−0.158642	+	0.115260i	−0.664274	−	0.747489i	$-0.731259\pi$
$463$	−731762.	+	531656.i	−0.158642	+	0.115260i	0.505632	+	0.862749i	$0.331259\pi$
$464$	−1.40789e6	−	1.02290e6i	−0.303581	−	0.220565i
$465$	164214.	+	1.08834e6i	0.0352190	+	0.233418i
$466$	2.69745e6	−	1.95981e6i	0.575425	−	0.418071i
$467$	1.58832e6	−	4.88835e6i	0.337013	−	1.03722i	−0.628710	−	0.777640i	$-0.716417\pi$
$467$	1.58832e6	−	4.88835e6i	0.337013	−	1.03722i	0.965722	−	0.259578i	$-0.0835834\pi$
$468$	−452424.			−0.0954840
$469$	1.14137e6	−	3.51278e6i	0.239605	−	0.737427i
$470$	−2.34756e6	−	389466.i	−0.490199	−	0.0813252i
$471$	398955.	+	1.22786e6i	0.0828650	+	0.255032i
$472$	−401397.	−	1.23537e6i	−0.0829315	−	0.255237i
$473$	2.70461e6	+	1.96501e6i	0.555842	+	0.403843i
$474$	2.04600e6			0.418273
$475$	32011.2	−	2.18485e6i	0.00650981	−	0.444311i
$476$	−2.05082e6			−0.414867
$477$	−1.16403e6	−	845717.i	−0.234244	−	0.170188i
$478$	−1.37890e6	−	4.24382e6i	−0.276035	−	0.849547i
$479$	824685.	+	2.53812e6i	0.164229	+	0.505444i	0.998979	−	0.0451851i	$-0.0143878\pi$
$479$	824685.	+	2.53812e6i	0.164229	+	0.505444i	−0.834750	+	0.550629i	$0.814388\pi$
$480$	460739.	−	230523.i	0.0912749	−	0.0456678i
$481$	174311.	−	536473.i	0.0343528	−	0.105727i
$482$	1.49604e6			0.293309
$483$	767267.	−	2.36141e6i	0.149651	−	0.460578i
$484$	1.82261e6	−	1.32420e6i	0.353655	−	0.256945i
$485$	−1.85027e6	+	925752.i	−0.357175	+	0.178707i
$486$	−191087.	−	138833.i	−0.0366978	−	0.0266625i
$487$	4.77182e6	−	3.46693e6i	0.911720	−	0.662403i	−0.0297292	−	0.999558i	$-0.509464\pi$
$487$	4.77182e6	−	3.46693e6i	0.911720	−	0.662403i	0.941449	+	0.337155i	$0.109464\pi$
$488$	621661.	−	451663.i	0.118169	−	0.0858550i
$489$	2.53817e6	+	1.84409e6i	0.480009	+	0.348747i
$490$	−1.92903e6	+	3.71834e6i	−0.362951	+	0.699615i
$491$	5.03503e6	−	3.65816e6i	0.942537	−	0.684793i	−0.00649289	−	0.999979i	$-0.502067\pi$
$491$	5.03503e6	−	3.65816e6i	0.942537	−	0.684793i	0.949030	+	0.315186i	$0.102067\pi$
$492$	279892.	−	861419.i	0.0521288	−	0.160436i
$493$	4.62187e6			0.856446
$494$	301717.	−	928590.i	0.0556266	−	0.171201i
$495$	96126.5	+	637089.i	0.0176332	+	0.116866i
$496$	−173065.	−	532639.i	−0.0315867	−	0.0972140i
$497$	−4.50879e6	−	1.38766e7i	−0.818783	−	2.51995i
$498$	1.87801e6	+	1.36445e6i	0.339331	+	0.246538i
$499$	−2.42589e6			−0.436134			−0.218067	−	0.975934i	$-0.569975\pi$
$499$	−2.42589e6			−0.436134			−0.218067	+	0.975934i	$0.569975\pi$
$500$	−2.01938e6	+	1.93252e6i	−0.361237	+	0.345699i
$501$	2.79352e6			0.497230
$502$	−5.19588e6	−	3.77503e6i	−0.920238	−	0.668592i
$503$	708836.	+	2.18157e6i	0.124918	+	0.384459i	0.993886	−	0.110409i	$-0.0352162\pi$
$503$	708836.	+	2.18157e6i	0.124918	+	0.384459i	−0.868968	+	0.494869i	$0.835216\pi$
$504$	−302002.	−	929465.i	−0.0529581	−	0.162988i
$505$	1.25160e6	+	8.29510e6i	0.218392	+	1.44742i
$506$	257383.	−	792144.i	0.0446893	−	0.137540i
$507$	−2.24485e6			−0.387853
$508$	1.23869e6	−	3.81230e6i	0.212963	−	0.655433i
$509$	−4.59510e6	+	3.33853e6i	−0.786141	+	0.571165i	−0.906816	−	0.421528i	$-0.861494\pi$
$509$	−4.59510e6	+	3.33853e6i	−0.786141	+	0.571165i	0.120675	+	0.992692i	$0.461494\pi$
$510$	−630096.	+	1.21456e6i	−0.107271	+	0.206772i
$511$	81578.3	+	59270.1i	0.0138205	+	0.0100411i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	412385.	−	299615.i	0.0691846	−	0.0502655i
$514$	−571823.	−	415454.i	−0.0954671	−	0.0693609i
$515$	−8.33203e6	+	4.16879e6i	−1.38431	+	0.692615i
$516$	−2.73709e6	+	1.98861e6i	−0.452548	+	0.328795i
$517$	−467938.	+	1.44017e6i	−0.0769949	+	0.236966i
$518$	1.21849e6			0.199526
$519$	976254.	−	3.00460e6i	0.159091	−	0.489631i
$520$	−1.11695e6	+	558845.i	−0.181144	+	0.0906323i
$521$	786817.	+	2.42157e6i	0.126993	+	0.390844i	0.994259	−	0.107001i	$-0.0341248\pi$
$521$	786817.	+	2.42157e6i	0.126993	+	0.390844i	−0.867266	+	0.497845i	$0.834125\pi$
$522$	680612.	+	2.09471e6i	0.109326	+	0.336471i
$523$	4.39991e6	+	3.19672e6i	0.703379	+	0.511035i	0.881031	−	0.473059i	$-0.156850\pi$
$523$	4.39991e6	+	3.19672e6i	0.703379	+	0.511035i	−0.177652	+	0.984093i	$0.556850\pi$
$524$	−2.11325e6			−0.336219
$525$	3.05337e6	+	4.33475e6i	0.483482	+	0.686382i
$526$	−4.75461e6			−0.749291
$527$	1.20334e6	+	874279.i	0.188739	+	0.137127i
$528$	−101308.	−	311793.i	−0.0158146	−	0.0486723i
$529$	−1.32718e6	−	4.08463e6i	−0.206200	−	0.634620i
$530$	−3.91842e6	−	650074.i	−0.605928	−	0.100525i
$531$	−508018.	+	1.56352e6i	−0.0781885	+	0.240640i
$532$	2.10911e6			0.323087
$533$	−678529.	+	2.08830e6i	−0.103455	+	0.318401i
$534$	−1.50491e6	+	1.09338e6i	−0.228380	+	0.165928i
$535$	−930295.	−	6.16563e6i	−0.140519	−	0.931307i
$536$	1.01443e6	+	737024.i	0.152514	+	0.110808i
$537$	−6.11914e6	+	4.44581e6i	−0.915703	+	0.665297i
$538$	4.02947e6	−	2.92758e6i	0.600194	−	0.436067i
$539$	2.15652e6	+	1.56681e6i	0.319729	+	0.232297i
$540$	−643245.	−	106716.i	−0.0949275	−	0.0157487i
$541$	7.20072e6	−	5.23163e6i	1.05775	−	0.768500i	0.0840783	−	0.996459i	$-0.473205\pi$
$541$	7.20072e6	−	5.23163e6i	1.05775	−	0.768500i	0.973671	+	0.227960i	$0.0732054\pi$
$542$	156875.	−	482813.i	0.0229381	−	0.0705961i
$543$	−4.54587e6			−0.661634
$544$	215143.	−	662142.i	0.0311695	−	0.0959299i
$545$	−5.99239e6	−	6.08084e6i	−0.864190	−	0.876944i
$546$	732128.	+	2.25326e6i	0.105101	+	0.323466i
$547$	−3.82884e6	−	1.17840e7i	−0.547141	−	1.68393i	−0.715844	−	0.698260i	$-0.753958\pi$
$547$	−3.82884e6	−	1.17840e7i	−0.547141	−	1.68393i	0.168703	−	0.985667i	$-0.446042\pi$
$548$	2.53033e6	+	1.83839e6i	0.359936	+	0.261509i
$549$	−972526.			−0.137712
$550$	1.02427e6	+	1.45411e6i	0.144380	+	0.204970i
$551$	−4.75324e6			−0.666977
$552$	681930.	+	495452.i	0.0952560	+	0.0692075i
$553$	−3.31091e6	−	1.01899e7i	−0.460399	−	1.41696i
$554$	1.50846e6	+	4.64257e6i	0.208814	+	0.642664i
$555$	374372.	−	721630.i	0.0515907	−	0.0994448i
$556$	−1.42042e6	+	4.37160e6i	−0.194863	+	0.599727i
$557$	−1.27889e7			−1.74661			−0.873305	−	0.487174i	$-0.838028\pi$
$557$	−1.27889e7			−1.74661			−0.873305	+	0.487174i	$0.838028\pi$
$558$	−219035.	+	674121.i	−0.0297803	+	0.0916542i
$559$	6.63539e6	−	4.82089e6i	0.898125	−	0.652526i
$560$	−1.89368e6	−	1.92163e6i	−0.255174	−	0.258940i
$561$	704406.	+	511781.i	0.0944966	+	0.0686558i
$562$	−4.94158e6	+	3.59027e6i	−0.659972	+	0.479498i
$563$	−4.82420e6	+	3.50499e6i	−0.641437	+	0.466032i	−0.860344	−	0.509714i	$-0.829751\pi$
$563$	−4.82420e6	+	3.50499e6i	−0.641437	+	0.466032i	0.218906	+	0.975746i	$0.429751\pi$
$564$	−1.23979e6	−	900761.i	−0.164116	−	0.119237i
$565$	−4.32159e6	−	4.38538e6i	−0.569538	−	0.577944i
$566$	2.42048e6	−	1.75858e6i	0.317586	−	0.230739i
$567$	−382221.	+	1.17635e6i	−0.0499294	+	0.153667i
$568$	4.95331e6			0.644206
$569$	−486324.	+	1.49675e6i	−0.0629717	+	0.193807i	−0.977593	−	0.210505i	$-0.932489\pi$
$569$	−486324.	+	1.49675e6i	−0.0629717	+	0.193807i	0.914621	+	0.404312i	$0.132489\pi$
$570$	648007.	−	1.24908e6i	0.0835396	−	0.161029i
$571$	−3.06439e6	−	9.43121e6i	−0.393327	−	1.21053i	−0.930257	−	0.366908i	$-0.880416\pi$
$571$	−3.06439e6	−	9.43121e6i	−0.393327	−	1.21053i	0.536931	−	0.843626i	$-0.319584\pi$
$572$	245596.	+	755865.i	0.0313856	+	0.0965949i
$573$	3.31162e6	+	2.40603e6i	0.421360	+	0.306136i
$574$	−4.74316e6			−0.600880
$575$	−4.32810e6	−	1.47673e6i	−0.545918	−	0.186265i
$576$	331776.			0.0416667
$577$	−1.24872e7	−	9.07248e6i	−1.56144	−	1.13445i	−0.934817	−	0.355131i	$-0.884436\pi$
$577$	−1.24872e7	−	9.07248e6i	−1.56144	−	1.13445i	−0.626624	−	0.779322i	$-0.715564\pi$
$578$	−1.18365e6	−	3.64290e6i	−0.147368	−	0.453553i
$579$	−948775.	−	2.92003e6i	−0.117616	−	0.361985i
$580$	4.26774e6	+	4.33072e6i	0.526778	+	0.534553i
$581$	3.75648e6	−	1.15613e7i	0.461680	−	1.42090i
$582$	−1.33237e6			−0.163049
$583$	−781055.	+	2.40384e6i	−0.0951723	+	0.292910i
$584$	−27694.4	+	20121.2i	−0.00336016	+	0.00244130i
$585$	1.55939e6	+	258706.i	0.188393	+	0.0312548i
$586$	1.24964e6	+	907914.i	0.150328	+	0.109220i
$587$	−2.96952e6	+	2.15748e6i	−0.355705	+	0.258435i	−0.751259	−	0.660008i	$-0.770553\pi$
$587$	−2.96952e6	+	2.15748e6i	−0.355705	+	0.258435i	0.395553	+	0.918443i	$0.370553\pi$
$588$	−2.18242e6	+	1.58562e6i	−0.260313	+	0.189128i
$589$	−1.23755e6	−	899130.i	−0.146985	−	0.106791i
$590$	677099.	+	4.48754e6i	0.0800796	+	0.530736i
$591$	−5.10362e6	+	3.70800e6i	−0.601049	+	0.436687i
$592$	−127827.	+	393412.i	−0.0149906	+	0.0461364i
$593$	6.85260e6			0.800237			0.400119	−	0.916463i	$-0.368969\pi$
$593$	6.85260e6			0.800237			0.400119	+	0.916463i	$0.368969\pi$
$594$	−128218.	+	394613.i	−0.0149101	+	0.0458887i
$595$	7.06864e6	+	1.17270e6i	0.818547	+	0.135799i
$596$	−1.19432e6	−	3.67575e6i	−0.137723	−	0.423867i
$597$	−1.84700e6	−	5.68448e6i	−0.212095	−	0.652762i
$598$	−1.65317e6	−	1.20110e6i	−0.189045	−	0.137349i
$599$	−1.58550e7			−1.80551			−0.902753	−	0.430160i	$-0.858457\pi$
$599$	−1.58550e7			−1.80551			−0.902753	+	0.430160i	$0.858457\pi$
$600$	−1.71987e6	+	531092.i	−0.195037	+	0.0602270i
$601$	1.16278e7			1.31314			0.656569	−	0.754266i	$-0.272007\pi$
$601$	1.16278e7			1.31314			0.656569	+	0.754266i	$0.272007\pi$
$602$	1.43334e7	+	1.04138e7i	1.61197	+	1.17116i
$603$	−490400.	−	1.50930e6i	−0.0549234	−	0.169037i
$604$	−2.37478e6	−	7.30884e6i	−0.264869	−	0.815184i
$605$	−7.03927e6	+	3.52198e6i	−0.781879	+	0.391199i
$606$	−1.66944e6	+	5.13799e6i	−0.184666	+	0.568345i
$607$	−6.88417e6			−0.758368			−0.379184	−	0.925321i	$-0.623795\pi$
$607$	−6.88417e6			−0.758368			−0.379184	+	0.925321i	$0.623795\pi$
$608$	−221258.	+	680963.i	−0.0242740	+	0.0747076i
$609$	9.33113e6	−	6.77946e6i	1.01951	−	0.740717i
$610$	−2.40098e6	+	1.20129e6i	−0.261255	+	0.130714i
$611$	3.00556e6	+	2.18367e6i	0.325704	+	0.236638i
$612$	−712866.	+	517927.i	−0.0769359	+	0.0558972i
$613$	−7.98040e6	+	5.79810e6i	−0.857775	+	0.623210i	−0.927279	−	0.374372i	$-0.877858\pi$
$613$	−7.98040e6	+	5.79810e6i	−0.857775	+	0.623210i	0.0695036	+	0.997582i	$0.477858\pi$
$614$	3.54188e6	+	2.57333e6i	0.379152	+	0.275470i
$615$	−1.45730e6	+	2.80904e6i	−0.155367	+	0.299482i
$616$	−1.38892e6	+	1.00911e6i	−0.147477	+	0.107149i
$617$	−1.48505e6	+	4.57050e6i	−0.157046	+	0.483338i	−0.998362	−	0.0572050i	$-0.981781\pi$
$617$	−1.48505e6	+	4.57050e6i	−0.157046	+	0.483338i	0.841316	+	0.540543i	$0.181781\pi$
$618$	−5.99986e6			−0.631931
$619$	5.69241e6	−	1.75194e7i	0.597131	−	1.83778i	0.0533133	−	0.998578i	$-0.483022\pi$
$619$	5.69241e6	−	1.75194e7i	0.597131	−	1.83778i	0.543818	−	0.839203i	$-0.316978\pi$
$620$	291935.	+	1.93483e6i	0.0305005	+	0.202146i
$621$	−329663.	−	1.01460e6i	−0.0343037	−	0.105576i
$622$	2.38811e6	+	7.34985e6i	0.247502	+	0.761733i
$623$	7.88079e6	+	5.72573e6i	0.813485	+	0.591032i
$624$	−804309.			−0.0826916
$625$	8.06533e6	−	5.50617e6i	0.825890	−	0.563831i
$626$	1.25696e7			1.28199
$627$	−724429.	−	526328.i	−0.0735913	−	0.0534672i
$628$	709253.	+	2.18286e6i	0.0717632	+	0.220864i
$629$	−339492.	−	1.04485e6i	−0.0342139	−	0.105300i
$630$	509433.	+	3.37632e6i	0.0511370	+	0.338916i
$631$	460877.	−	1.41844e6i	0.0460800	−	0.141820i	−0.925369	−	0.379067i	$-0.876245\pi$
$631$	460877.	−	1.41844e6i	0.0460800	−	0.141820i	0.971449	+	0.237247i	$0.0762451\pi$
$632$	3.63734e6			0.362235
$633$	−1.18359e6	+	3.64272e6i	−0.117407	+	0.361341i
$634$	2.09564e6	−	1.52257e6i	0.207059	−	0.150437i
$635$	−6.44942e6	+	1.24317e7i	−0.634726	+	1.22348i
$636$	−2.06939e6	−	1.50350e6i	−0.202861	−	0.147387i
$637$	5.29074e6	−	3.84395e6i	0.516616	−	0.375344i
$638$	3.13017e6	−	2.27420e6i	0.304450	−	0.221196i
$639$	−5.07175e6	−	3.68484e6i	−0.491367	−	0.356999i
$640$	819091.	−	409818.i	0.0790464	−	0.0395495i
$641$	4.34434e6	−	3.15635e6i	0.417617	−	0.303417i	−0.359061	−	0.933314i	$-0.616903\pi$
$641$	4.34434e6	−	3.15635e6i	0.417617	−	0.303417i	0.776678	+	0.629897i	$0.216903\pi$
$642$	1.24087e6	−	3.81900e6i	0.118820	−	0.365689i
$643$	−4.74659e6			−0.452746			−0.226373	−	0.974041i	$-0.572687\pi$
$643$	−4.74659e6			−0.452746			−0.226373	+	0.974041i	$0.572687\pi$
$644$	1.36403e6	−	4.19805e6i	0.129601	−	0.398872i
$645$	1.05712e7	−	5.28911e6i	1.00052	−	0.500591i
$646$	−587631.	−	1.80854e6i	−0.0554018	−	0.170509i
$647$	5.86793e6	+	1.80596e7i	0.551092	+	1.69609i	0.706046	+	0.708166i	$0.250477\pi$
$647$	5.86793e6	+	1.80596e7i	0.551092	+	1.69609i	−0.154954	+	0.987922i	$0.549523\pi$
$648$	−339709.	−	246813.i	−0.0317812	−	0.0230904i
$649$	2.88795e6			0.269140
$650$	4.16939e6	−	1.28750e6i	0.387070	−	0.119526i
$651$	3.71185e6			0.343272
$652$	4.51231e6	+	3.27838e6i	0.415700	+	0.302024i
$653$	3.30706e6	+	1.01781e7i	0.303501	+	0.934079i	0.980232	+	0.197849i	$0.0633956\pi$
$653$	3.30706e6	+	1.01781e7i	0.303501	+	0.934079i	−0.676732	+	0.736230i	$0.736604\pi$
$654$	−1.69895e6	−	5.22882e6i	−0.155323	−	0.478035i
$655$	7.28383e6	+	1.20840e6i	0.663371	+	0.110055i
$656$	497586.	−	1.53141e6i	0.0451449	−	0.138942i
$657$	43325.2			0.00391586
$658$	−2.47989e6	+	7.63232e6i	−0.223289	+	0.687213i
$659$	928870.	−	674864.i	0.0833185	−	0.0605345i	−0.545346	−	0.838211i	$-0.683602\pi$
$659$	928870.	−	674864.i	0.0833185	−	0.0605345i	0.628665	+	0.777676i	$0.283602\pi$
$660$	170892.	+	1.13260e6i	0.0152708	+	0.101209i
$661$	1.45490e6	+	1.05705e6i	0.129518	+	0.0941004i	0.650658	−	0.759371i	$-0.274493\pi$
$661$	1.45490e6	+	1.05705e6i	0.129518	+	0.0941004i	−0.521140	+	0.853471i	$0.674493\pi$
$662$	3.26612e6	−	2.37298e6i	0.289659	−	0.210450i
$663$	1.72817e6	−	1.25559e6i	0.152687	−	0.110933i
$664$	3.33868e6	+	2.42569e6i	0.293869	+	0.213509i
$665$	−7.26956e6	−	1.20604e6i	−0.637462	−	0.105756i
$666$	423550.	−	307727.i	0.0370015	−	0.0268831i
$667$	−3.07408e6	+	9.46104e6i	−0.267547	+	0.823425i
$668$	4.96626e6			0.430614
$669$	1.58542e6	−	4.87941e6i	0.136955	−	0.421504i
$670$	−3.07502e6	−	3.12041e6i	−0.264644	−	0.268549i
$671$	527930.	+	1.62480e6i	0.0452658	+	0.139314i
$672$	−536892.	−	1.65238e6i	−0.0458631	−	0.141152i
$673$	7.71132e6	+	5.60260e6i	0.656283	+	0.476817i	0.865406	−	0.501072i	$-0.167061\pi$
$673$	7.71132e6	+	5.60260e6i	0.656283	+	0.476817i	−0.209123	+	0.977889i	$0.567061\pi$
$674$	−1.28755e7			−1.09173
$675$	2.15608e6	+	735645.i	0.182140	+	0.0621454i
$676$	−3.99084e6			−0.335891
$677$	−9.71308e6	−	7.05697e6i	−0.814489	−	0.591761i	0.100639	−	0.994923i	$-0.467911\pi$
$677$	−9.71308e6	−	7.05697e6i	−0.814489	−	0.591761i	−0.915129	+	0.403162i	$0.867911\pi$
$678$	−1.22525e6	−	3.77092e6i	−0.102364	−	0.315045i
$679$	2.15609e6	+	6.63578e6i	0.179471	+	0.552354i
$680$	−1.12017e6	+	2.15921e6i	−0.0928992	+	0.179070i
$681$	−2.39540e6	+	7.37228e6i	−0.197929	+	0.609163i
$682$	1.24516e6			0.102509
$683$	−4.09978e6	+	1.26178e7i	−0.336286	+	1.03498i	0.629799	+	0.776758i	$0.283137\pi$
$683$	−4.09978e6	+	1.26178e7i	−0.336286	+	1.03498i	−0.966085	+	0.258224i	$0.916863\pi$
$684$	733129.	−	532649.i	0.0599156	−	0.0435312i
$685$	−7.67015e6	−	7.78336e6i	−0.624565	−	0.633783i
$686$	1.17530e6	+	853904.i	0.0953537	+	0.0692785i
$687$	1.06432e6	−	773274.i	0.0860361	−	0.0625089i
$688$	−4.86593e6	+	3.53531e6i	−0.391918	+	0.284745i
$689$	5.01671e6	+	3.64486e6i	0.402598	+	0.292504i
$690$	−2.06713e6	−	2.09764e6i	−0.165289	−	0.167729i
$691$	7.74123e6	−	5.62433e6i	0.616758	−	0.448101i	−0.235030	−	0.971988i	$-0.575519\pi$
$691$	7.74123e6	−	5.62433e6i	0.616758	−	0.448101i	0.851788	+	0.523887i	$0.175519\pi$
$692$	1.73556e6	−	5.34151e6i	0.137777	−	0.424033i
$693$	2.17282e6			0.171867
$694$	642598.	−	1.97771e6i	0.0506455	−	0.155871i
$695$	7.39560e6	−	1.42556e7i	0.580780	−	1.11950i
$696$	1.20998e6	+	3.72393e6i	0.0946791	+	0.291392i
$697$	1.32152e6	+	4.06721e6i	0.103037	+	0.317114i
$698$	2.92738e6	+	2.12686e6i	0.227426	+	0.165235i
$699$	−7.50202e6			−0.580745
$700$	5.42821e6	+	7.70622e6i	0.418708	+	0.594424i
$701$	1.92810e7			1.48196			0.740978	−	0.671529i	$-0.234362\pi$
$701$	1.92810e7			1.48196			0.740978	+	0.671529i	$0.234362\pi$
$702$	823541.	+	598338.i	0.0630729	+	0.0458251i
$703$	349142.	+	1.07455e6i	0.0266448	+	0.0820044i
$704$	−180103.	−	554299.i	−0.0136958	−	0.0421515i
$705$	3.75817e6	+	3.81363e6i	0.284776	+	0.288979i
$706$	1.25326e6	−	3.85714e6i	0.0946302	−	0.291242i
$707$	2.82909e7			2.12862
$708$	−903144.	+	2.77959e6i	−0.0677132	+	0.208400i
$709$	1.65641e7	−	1.20345e7i	1.23752	−	0.899109i	0.240087	−	0.970751i	$-0.422824\pi$
$709$	1.65641e7	−	1.20345e7i	1.23752	−	0.899109i	0.997430	+	0.0716420i	$0.0228239\pi$
$710$	−1.70728e7	−	2.83242e6i	−1.27104	−	0.210868i
$711$	−3.72431e6	−	2.70587e6i	−0.276294	−	0.200740i
$712$	−2.67540e6	+	1.94379e6i	−0.197783	+	0.143697i
$713$	−2.59003e6	+	1.88176e6i	−0.190801	+	0.138625i
$714$	3.73308e6	+	2.71224e6i	0.274045	+	0.199105i
$715$	−414284.	−	2.74571e6i	−0.0303063	−	0.200858i
$716$	−1.08785e7	+	7.90367e6i	−0.793022	+	0.576164i
$717$	−3.10253e6	+	9.54860e6i	−0.225381	+	0.693652i
$718$	6.13971e6			0.444464
$719$	−7.86527e6	+	2.42068e7i	−0.567403	+	1.74629i	0.0932983	+	0.995638i	$0.470259\pi$
$719$	−7.86527e6	+	2.42068e7i	−0.567403	+	1.74629i	−0.660701	+	0.750649i	$0.729741\pi$
$720$	−1.14355e6	−	189717.i	−0.0822097	−	0.0136388i
$721$	9.70919e6	+	2.98818e7i	0.695576	+	2.14076i
$722$	−2.45629e6	−	7.55969e6i	−0.175363	−	0.539711i
$723$	−2.72323e6	−	1.97854e6i	−0.193748	−	0.140766i
$724$	−8.08155e6			−0.572991
$725$	−1.22334e7	−	1.73673e7i	−0.864375	−	1.22712i
$726$	−5.06895e6			−0.356925
$727$	−3.37573e6	−	2.45261e6i	−0.236882	−	0.172105i	0.463011	−	0.886352i	$-0.346769\pi$
$727$	−3.37573e6	−	2.45261e6i	−0.236882	−	0.172105i	−0.699893	+	0.714248i	$0.746769\pi$
$728$	1.30156e6	+	4.00579e6i	0.0910198	+	0.280130i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	106961.	−	53516.3i	0.00742883	−	0.00371688i
$731$	4.93624e6	−	1.51922e7i	0.341667	−	1.05154i
$732$	−1.72894e6			−0.119262
$733$	8.12034e6	−	2.49918e7i	0.558231	−	1.71806i	−0.129023	−	0.991642i	$-0.541184\pi$
$733$	8.12034e6	−	2.49918e7i	0.558231	−	1.71806i	0.687254	−	0.726417i	$-0.258816\pi$
$734$	1.46076e7	−	1.06130e7i	1.00078	−	0.727107i
$735$	8.42895e6	−	4.21728e6i	0.575513	−	0.287948i
$736$	1.21232e6	+	880803.i	0.0824941	+	0.0599355i
$737$	−2.25538e6	+	1.63863e6i	−0.152950	+	0.111125i
$738$	−1.64873e6	+	1.19787e6i	−0.111431	+	0.0809596i
$739$	4.93869e6	+	3.58817e6i	0.332660	+	0.241692i	0.741559	−	0.670888i	$-0.234087\pi$
$739$	4.93869e6	+	3.58817e6i	0.332660	+	0.241692i	−0.408898	+	0.912580i	$0.634087\pi$
$740$	665551.	−	1.28290e6i	0.0446788	−	0.0861217i
$741$	−1.77729e6	+	1.29128e6i	−0.118908	+	0.0863920i
$742$	−4.13929e6	+	1.27394e7i	−0.276004	+	0.849454i
$743$	1.09977e7			0.730854			0.365427	−	0.930840i	$-0.380923\pi$
$743$	1.09977e7			0.730854			0.365427	+	0.930840i	$0.380923\pi$
$744$	−389396.	+	1.19844e6i	−0.0257905	+	0.0793749i
$745$	2.01465e6	+	1.33523e7i	0.132987	+	0.881384i
$746$	−9681.45	−	29796.4i	−0.000636932	−	0.00196028i
$747$	−1.61400e6	−	4.96739e6i	−0.105829	−	0.325707i
$748$	1.25228e6	+	909833.i	0.0818364	+	0.0594576i
$749$	−2.10282e7			−1.36961
$750$	6.23163e6	−	847079.i	0.404528	−	0.0549883i
$751$	−2.04401e7			−1.32246			−0.661230	−	0.750183i	$-0.729965\pi$
$751$	−2.04401e7			−1.32246			−0.661230	+	0.750183i	$0.729965\pi$
$752$	−2.20407e6	−	1.60135e6i	−0.142129	−	0.103262i
$753$	4.46546e6	+	1.37433e7i	0.286998	+	0.883290i
$754$	−2.93329e6	−	9.02774e6i	−0.187900	−	0.578297i
$755$	4.00592e6	+	2.65496e7i	0.255761	+	1.69508i
$756$	−679503.	+	2.09130e6i	−0.0432401	+	0.133079i
$757$	2.04618e7			1.29779			0.648895	−	0.760878i	$-0.275232\pi$
$757$	2.04618e7			1.29779			0.648895	+	0.760878i	$0.275232\pi$
$758$	−2.11837e6	+	6.51968e6i	−0.133915	+	0.412148i
$759$	−1.51614e6	+	1.10154e6i	−0.0955287	+	0.0694056i
$760$	1.15201e6	−	2.22059e6i	0.0723474	−	0.139455i
$761$	−1.70228e7	−	1.23678e7i	−1.06554	−	0.774160i	−0.0904343	−	0.995902i	$-0.528826\pi$
$761$	−1.70228e7	−	1.23678e7i	−1.06554	−	0.774160i	−0.975105	+	0.221743i	$0.928826\pi$
$762$	−7.29661e6	+	5.30130e6i	−0.455233	+	0.330746i
$763$	−2.32924e7	+	1.69229e7i	−1.44845	+	1.05236i
$764$	5.88732e6	+	4.27739e6i	0.364908	+	0.265122i
$765$	2.75323e6	−	1.37753e6i	0.170094	−	0.0851035i
$766$	1.15228e7	−	8.37179e6i	0.709554	−	0.515521i
$767$	2.18945e6	−	6.73843e6i	0.134384	−	0.413590i
$768$	589824.			0.0360844
$769$	268277.	−	825671.i	0.0163594	−	0.0503490i	−0.942544	−	0.334083i	$-0.891573\pi$
$769$	268277.	−	825671.i	0.0163594	−	0.0503490i	0.958903	+	0.283734i	$0.0915733\pi$
$770$	5.36429e6	−	2.68393e6i	0.326051	−	0.163134i
$771$	491438.	+	1.51249e6i	0.0297737	+	0.0916341i
$772$	−1.68671e6	−	5.19117e6i	−0.101859	−	0.313488i
$773$	1.27599e7	+	9.27062e6i	0.768067	+	0.558033i	0.901374	−	0.433041i	$-0.142560\pi$
$773$	1.27599e7	+	9.27062e6i	0.768067	+	0.558033i	−0.133307	+	0.991075i	$0.542560\pi$
$774$	7.61226e6			0.456732
$775$	100155.	−	6.83581e6i	0.00598987	−	0.408823i
$776$	−2.36867e6			−0.141205
$777$	−2.21801e6	−	1.61148e6i	−0.131799	−	0.0957573i
$778$	−4.76369e6	−	1.46611e7i	−0.282159	−	0.868396i
$779$	−1.35908e6	−	4.18282e6i	−0.0802420	−	0.246960i
$780$	2.77225e6	+	459922.i	0.163153	+	0.0270675i
$781$	−3.40311e6	+	1.04737e7i	−0.199640	+	0.614430i
$782$	−3.97983e6			−0.232728
$783$	1.53138e6	−	4.71310e6i	0.0892643	−	0.274727i
$784$	−3.87986e6	+	2.81889e6i	−0.225438	+	0.163790i
$785$	−1.19641e6	−	7.92931e6i	−0.0692955	−	0.459263i
$786$	3.84672e6	+	2.79481e6i	0.222093	+	0.161360i
$787$	−6.05873e6	+	4.40193e6i	−0.348694	+	0.253341i	−0.748321	−	0.663337i	$-0.769140\pi$
$787$	−6.05873e6	+	4.40193e6i	−0.348694	+	0.253341i	0.399627	+	0.916678i	$0.369140\pi$
$788$	−9.07310e6	+	6.59200e6i	−0.520523	+	0.378182i
$789$	8.65476e6	+	6.28805e6i	0.494951	+	0.359603i
$790$	−1.25370e7	−	2.07991e6i	−0.714702	−	0.118571i
$791$	−1.67980e7	+	1.22045e7i	−0.954590	+	0.693550i
$792$	−227942.	+	701535.i	−0.0129126	+	0.0397408i
$793$	4.19138e6			0.236687
$794$	1.05113e6	−	3.23503e6i	0.0591703	−	0.182107i
$795$	6.27291e6	+	6.36549e6i	0.352007	+	0.357202i
$796$	−3.28356e6	−	1.01057e7i	−0.183680	−	0.565309i
$797$	−1.78189e6	−	5.48409e6i	−0.0993653	−	0.305815i	0.889001	−	0.457904i	$-0.151400\pi$
$797$	−1.78189e6	−	5.48409e6i	−0.0993653	−	0.305815i	−0.988367	+	0.152090i	$0.951400\pi$
$798$	−3.83919e6	−	2.78933e6i	−0.213419	−	0.155058i
$799$	7.23558e6			0.400965
$800$	−3.05754e6	+	944163.i	−0.168907	+	0.0521581i
$801$	4.18539e6			0.230491
$802$	1.27323e6	+	925055.i	0.0698990	+	0.0507846i
$803$	−23518.8	−	72383.5i	−0.00128714	−	0.00396142i
$804$	−871823.	−	2.68319e6i	−0.0475651	−	0.146390i
$805$	−7.10201e6	+	1.36896e7i	−0.386270	+	0.744564i
$806$	943994.	−	2.90531e6i	0.0511837	−	0.157527i
$807$	−1.12066e7			−0.605743
$808$	−2.96788e6	+	9.13421e6i	−0.159926	+	0.492201i
$809$	−2.03878e7	+	1.48126e7i	−1.09521	+	0.795720i	−0.980272	−	0.197653i	$-0.936668\pi$
$809$	−2.03878e7	+	1.48126e7i	−1.09521	+	0.795720i	−0.114942	+	0.993372i	$0.536668\pi$
$810$	1.02976e6	+	1.04496e6i	0.0551471	+	0.0559610i
$811$	1.10848e6	+	805357.i	0.0591801	+	0.0429968i	0.616982	−	0.786977i	$-0.288355\pi$
$811$	1.10848e6	+	805357.i	0.0591801	+	0.0429968i	−0.557802	+	0.829974i	$0.688355\pi$
$812$	1.65887e7	−	1.20524e7i	0.882921	−	0.641480i
$813$	−924086.	+	671388.i	−0.0490327	+	0.0356244i
$814$	−744042.	−	540578.i	−0.0393583	−	0.0285955i
$815$	−1.36781e7	−	1.38800e7i	−0.721328	−	0.731973i
$816$	−1.26732e6	+	920759.i	−0.0666285	+	0.0484084i
$817$	−5.07655e6	+	1.56240e7i	−0.266081	+	0.818912i
$818$	1.54828e7			0.809032
$819$	1.64729e6	−	5.06983e6i	0.0858143	−	0.264109i
$820$	−2.59075e6	+	4.99385e6i	−0.134552	+	0.259359i
$821$	−7.95996e6	−	2.44982e7i	−0.412148	−	1.26846i	−0.914777	−	0.403959i	$-0.867634\pi$
$821$	−7.95996e6	−	2.44982e7i	−0.412148	−	1.26846i	0.502629	−	0.864502i	$-0.332366\pi$
$822$	−2.17462e6	−	6.69280e6i	−0.112255	−	0.345484i
$823$	−2.51779e7	−	1.82928e7i	−1.29575	−	0.941414i	−0.295841	−	0.955237i	$-0.595600\pi$
$823$	−2.51779e7	−	1.82928e7i	−1.29575	−	0.941414i	−0.999904	+	0.0138234i	$0.995600\pi$
$824$	−1.06664e7			−0.547269
$825$	58628.0	−	4.00151e6i	0.00299896	−	0.204686i
$826$	1.53050e7			0.780519
$827$	1.50005e7	+	1.08985e7i	0.762677	+	0.554118i	0.899730	−	0.436446i	$-0.143763\pi$
$827$	1.50005e7	+	1.08985e7i	0.762677	+	0.554118i	−0.137053	+	0.990564i	$0.543763\pi$
$828$	−586067.	−	1.80373e6i	−0.0297079	−	0.0914314i
$829$	5.47301e6	+	1.68442e7i	0.276592	+	0.851263i	0.988794	+	0.149288i	$0.0476982\pi$
$829$	5.47301e6	+	1.68442e7i	0.276592	+	0.851263i	−0.712201	+	0.701975i	$0.752302\pi$
$830$	−1.01205e7	−	1.02699e7i	−0.509926	−	0.517452i
$831$	3.39404e6	−	1.04458e7i	0.170496	−	0.524733i
$832$	−1.42988e6			−0.0716130
$833$	3.93592e6	−	1.21135e7i	0.196532	−	0.604864i
$834$	8.36708e6	−	6.07904e6i	0.416542	−	0.302636i
$835$	−1.71174e7	−	2.83982e6i	−0.849615	−	0.140953i
$836$	−1.28787e6	−	935695.i	−0.0637320	−	0.0463040i
$837$	1.29024e6	−	937417.i	0.0636587	−	0.0462508i
$838$	1.02452e6	−	744360.i	0.0503978	−	0.0366162i
$839$	−1.76139e7	−	1.27973e7i	−0.863877	−	0.627643i	0.0650602	−	0.997881i	$-0.479276\pi$
$839$	−1.76139e7	−	1.27973e7i	−0.863877	−	0.627643i	−0.928937	+	0.370238i	$0.879276\pi$
$840$	905658.	+	6.00235e6i	0.0442860	+	0.293510i
$841$	−2.07916e7	+	1.51060e7i	−1.01367	+	0.736476i
$842$	5.06948e6	−	1.56023e7i	0.246424	−	0.758415i
$843$	1.37433e7			0.666073
$844$	−2.10416e6	+	6.47595e6i	−0.101677	+	0.312930i
$845$	1.37554e7	+	2.28205e6i	0.662723	+	0.109947i
$846$	1.06551e6	+	3.27929e6i	0.0511835	+	0.157527i
$847$	8.20276e6	+	2.52455e7i	0.392872	+	1.20914i
$848$	−3.67891e6	−	2.67288e6i	−0.175683	−	0.127641i
$849$	−6.73173e6			−0.320522
$850$	5.09563e6	−	6.80171e6i	0.241908	−	0.322902i
$851$	2.36462e6			0.111928
$852$	−9.01645e6	−	6.55084e6i	−0.425536	−	0.309170i
$853$	−1.02409e7	−	3.15183e7i	−0.481911	−	1.48317i	−0.836406	−	0.548111i	$-0.815347\pi$
$853$	−1.02409e7	−	3.15183e7i	−0.481911	−	1.48317i	0.354495	−	0.935058i	$-0.384653\pi$
$854$	2.79782e6	+	8.61082e6i	0.131273	+	0.404017i
$855$	−2.83149e6	+	1.41669e6i	−0.132464	+	0.0662763i
$856$	2.20599e6	−	6.78933e6i	0.102901	−	0.316696i
$857$	2.83979e7			1.32079			0.660397	−	0.750917i	$-0.270388\pi$
$857$	2.83979e7			1.32079			0.660397	+	0.750917i	$0.270388\pi$
$858$	552590.	−	1.70070e6i	0.0256262	−	0.0788694i
$859$	−9.02031e6	+	6.55364e6i	−0.417098	+	0.303040i	−0.776469	−	0.630155i	$-0.782991\pi$
$859$	−9.02031e6	+	6.55364e6i	−0.417098	+	0.303040i	0.359371	+	0.933195i	$0.382991\pi$
$860$	1.87932e7	−	9.40285e6i	0.866472	−	0.433524i
$861$	8.63391e6	+	6.27290e6i	0.396917	+	0.288377i
$862$	−1.99161e7	+	1.44699e7i	−0.912929	+	0.663282i
$863$	−1.45531e7	+	1.05735e7i	−0.665164	+	0.483270i	−0.868403	−	0.495859i	$-0.834853\pi$
$863$	−1.45531e7	+	1.05735e7i	−0.665164	+	0.483270i	0.203239	+	0.979129i	$0.434853\pi$
$864$	−603928.	−	438779.i	−0.0275233	−	0.0199969i
$865$	−9.03644e6	+	1.74184e7i	−0.410636	+	0.791531i
$866$	1.36459e7	−	9.91433e6i	0.618312	−	0.449230i
$867$	−2.66321e6	+	8.19653e6i	−0.120326	+	0.370324i
$868$	6.59885e6			0.297282
$869$	−2.49899e6	+	7.69109e6i	−0.112257	+	0.345492i
$870$	−2.04106e6	−	1.35273e7i	−0.0914233	−	0.605918i
$871$	2.11352e6	+	6.50474e6i	0.0943975	+	0.290526i
$872$	−3.02035e6	−	9.29569e6i	−0.134514	−	0.413990i
$873$	2.42531e6	+	1.76209e6i	0.107704	+	0.0782513i
$874$	4.09296e6			0.181242
$875$	−1.43030e7	−	2.96653e7i	−0.631551	−	1.30987i
$876$	77022.5			0.00339123
$877$	1.34839e7	+	9.79664e6i	0.591994	+	0.430109i	0.843028	−	0.537869i	$-0.180771\pi$
$877$	1.34839e7	+	9.79664e6i	0.591994	+	0.430109i	−0.251034	+	0.967978i	$0.580771\pi$
$878$	−9.34899e6	−	2.87732e7i	−0.409287	−	1.25966i
$879$	−1.07397e6	−	3.30533e6i	−0.0468834	−	0.144292i
$880$	303807.	+	2.01351e6i	0.0132249	+	0.0876492i
$881$	1.72623e6	−	5.31280e6i	0.0749306	−	0.230613i	−0.906575	−	0.422044i	$-0.861313\pi$
$881$	1.72623e6	−	5.31280e6i	0.0749306	−	0.230613i	0.981506	+	0.191431i	$0.0613128\pi$
$882$	6.06965e6			0.262720
$883$	734130.	−	2.25942e6i	0.0316863	−	0.0975203i	−0.933963	−	0.357371i	$-0.883673\pi$
$883$	734130.	−	2.25942e6i	0.0316863	−	0.0975203i	0.965649	+	0.259850i	$0.0836733\pi$
$884$	3.07229e6	−	2.23215e6i	0.132231	−	0.0960712i
$885$	4.70234e6	−	9.06410e6i	0.201816	−	0.389015i
$886$	−1.63950e7	−	1.19117e7i	−0.701661	−	0.509786i
$887$	3.29952e7	−	2.39724e7i	1.40813	−	1.02306i	0.414535	−	0.910033i	$-0.363944\pi$
$887$	3.29952e7	−	2.39724e7i	1.40813	−	1.02306i	0.993592	−	0.113030i	$-0.0360557\pi$
$888$	752977.	−	547070.i	0.0320442	−	0.0232815i
$889$	3.82103e7	+	2.77614e7i	1.62153	+	1.17811i
$890$	1.03329e7	−	5.16989e6i	0.437268	−	0.218779i
$891$	755276.	−	548740.i	0.0318722	−	0.0231565i
$892$	2.81852e6	−	8.67450e6i	0.118607	−	0.365033i
$893$	−7.44125e6			−0.312261
$894$	−2.68722e6	+	8.27043e6i	−0.112450	+	0.346086i
$895$	4.20148e7	−	2.10214e7i	1.75325	−	0.877210i
$896$	−954474.	−	2.93757e6i	−0.0397186	−	0.122241i
$897$	1.42077e6	+	4.37269e6i	0.0589582	+	0.181455i
$898$	−1.34939e7	−	9.80392e6i	−0.558403	−	0.405704i
$899$	−1.48716e7			−0.613705
$900$	3.83303e6	+	1.30781e6i	0.157738	+	0.0538195i
$901$	1.20772e7			0.495627
$902$	2.89628e6	+	2.10427e6i	0.118529	+	0.0861164i
$903$	−1.23184e7	−	3.79122e7i	−0.502731	−	1.54725i
$904$	−2.17822e6	−	6.70386e6i	−0.0886502	−	0.272837i
$905$	2.78550e7	+	4.62121e6i	1.13053	+	0.187558i
$906$	−5.34327e6	+	1.64449e7i	−0.216265	+	0.665595i
$907$	−3.61207e7			−1.45793			−0.728966	−	0.684549i	$-0.759999\pi$
$907$	−3.61207e7			−1.45793			−0.728966	+	0.684549i	$0.759999\pi$
$908$	−4.25849e6	+	1.31063e7i	−0.171412	+	0.527551i
$909$	9.83394e6	−	7.14477e6i	0.394746	−	0.286800i
$910$	−2.19554e6	−	1.45512e7i	−0.0878898	−	0.582499i
$911$	6.21023e6	+	4.51200e6i	0.247920	+	0.180125i	0.704805	−	0.709402i	$-0.251035\pi$
$911$	6.21023e6	+	4.51200e6i	0.247920	+	0.180125i	−0.456884	+	0.889526i	$0.651035\pi$
$912$	1.30334e6	−	946932.i	0.0518884	−	0.0376991i
$913$	−7.42288e6	+	5.39304e6i	−0.294710	+	0.214120i
$914$	2.01294e7	+	1.46249e7i	0.797015	+	0.579065i
$915$	5.95920e6	+	988645.i	0.235307	+	0.0390380i
$916$	1.89213e6	−	1.37471e6i	0.0745094	−	0.0541343i
$917$	7.69440e6	−	2.36809e7i	0.302170	−	0.929984i
$918$	1.98259e6			0.0776472
$919$	−1.05504e7	+	3.24709e7i	−0.412080	+	1.26825i	0.502758	+	0.864427i	$0.332319\pi$
$919$	−1.05504e7	+	3.24709e7i	−0.412080	+	1.26825i	−0.914837	+	0.403823i	$0.867681\pi$
$920$	−3.67490e6	−	3.72913e6i	−0.143145	−	0.145257i
$921$	−3.04398e6	−	9.36840e6i	−0.118248	−	0.363929i
$922$	6.13614e6	+	1.88851e7i	0.237721	+	0.731631i
$923$	2.18581e7	+	1.58809e7i	0.844518	+	0.613579i
$924$	3.86280e6			0.148841
$925$	−3.02757e6	+	4.04124e6i	−0.116343	+	0.155296i
$926$	3.61803e6			0.138658
$927$	1.09215e7	+	7.93492e6i	0.417428	+	0.303279i
$928$	2.15107e6	+	6.62032e6i	0.0819945	+	0.252353i
$929$	−1.55719e7	−	4.79254e7i	−0.591974	−	1.82191i	−0.569248	−	0.822166i	$-0.692766\pi$
$929$	−1.55719e7	−	4.79254e7i	−0.591974	−	1.82191i	−0.0227251	−	0.999742i	$-0.507234\pi$
$930$	2.02744e6	−	3.90804e6i	0.0768672	−	0.148167i
$931$	−4.04780e6	+	1.24578e7i	−0.153054	+	0.471052i
$932$	−1.33369e7			−0.502940
$933$	5.37325e6	−	1.65372e7i	0.202084	−	0.621952i
$934$	−1.66331e7	+	1.20847e7i	−0.623888	+	0.453281i
$935$	−3.79602e6	−	3.85204e6i	−0.142004	−	0.144099i
$936$	1.46407e6	+	1.06371e6i	0.0546227	+	0.0396857i
$937$	−1.23093e7	+	8.94323e6i	−0.458020	+	0.332771i	−0.792754	−	0.609542i	$-0.791353\pi$
$937$	−1.23093e7	+	8.94323e6i	−0.458020	+	0.332771i	0.334734	+	0.942313i	$0.391353\pi$
$938$	−1.19526e7	+	8.68408e6i	−0.443563	+	0.322268i
$939$	−2.28802e7	−	1.66235e7i	−0.846831	−	0.615259i
$940$	6.68119e6	+	6.77979e6i	0.246623	+	0.250263i
$941$	−2.99850e7	+	2.17854e7i	−1.10390	+	0.802030i	−0.981692	−	0.190474i	$-0.938997\pi$
$941$	−2.99850e7	+	2.17854e7i	−1.10390	+	0.802030i	−0.122208	+	0.992505i	$0.538997\pi$
$942$	1.59582e6	−	4.91143e6i	0.0585944	−	0.180335i
$943$	−9.20462e6			−0.337075
$944$	−1.60559e6	+	4.94149e6i	−0.0586414	+	0.180480i
$945$	3.53793e6	−	6.81961e6i	0.128875	−	0.248416i
$946$	−4.13227e6	−	1.27178e7i	−0.150128	−	0.462046i
$947$	3.13534e6	+	9.64957e6i	0.113608	+	0.349650i	0.991654	−	0.128926i	$-0.0411531\pi$
$947$	3.13534e6	+	9.64957e6i	0.113608	+	0.349650i	−0.878046	+	0.478576i	$0.841153\pi$
$948$	−6.62100e6	−	4.81044e6i	−0.239278	−	0.173846i
$949$	−186722.			−0.00673023
$950$	−5.24047e6	+	6.99505e6i	−0.188392	+	0.251467i
$951$	−5.82830e6			−0.208973
$952$	6.63658e6	+	4.82176e6i	0.237330	+	0.172430i
$953$	−3.93482e6	−	1.21101e7i	−0.140344	−	0.431933i	0.856039	−	0.516911i	$-0.172918\pi$
$953$	−3.93482e6	−	1.21101e7i	−0.140344	−	0.431933i	−0.996383	+	0.0849776i	$0.972918\pi$
$954$	1.77848e6	+	5.47360e6i	0.0632671	+	0.194716i
$955$	−1.78462e7	−	1.81096e7i	−0.633194	−	0.642539i
$956$	−5.51561e6	+	1.69753e7i	−0.195186	+	0.600720i
$957$	−8.70548e6			−0.307265
$958$	3.29874e6	−	1.01525e7i	0.116127	−	0.357403i
$959$	−2.98139e7	+	2.16610e7i	−1.04682	+	0.760559i
$960$	−2.03297e6	−	337275.i	−0.0711957	−	0.0118115i
$961$	1.92895e7	+	1.40146e7i	0.673772	+	0.489524i
$962$	−1.82541e6	+	1.32624e6i	−0.0635948	+	0.0462044i
$963$	−7.30943e6	+	5.31061e6i	−0.253991	+	0.184535i
$964$	−4.84129e6	−	3.51740e6i	−0.167791	−	0.121907i
$965$	2.84524e6	+	1.88571e7i	0.0983559	+	0.651864i
$966$	−8.03493e6	+	5.83772e6i	−0.277038	+	0.201280i
$967$	−2.34523e6	+	7.21789e6i	−0.0806529	+	0.248224i	−0.983250	−	0.182262i	$-0.941658\pi$
$967$	−2.34523e6	+	7.21789e6i	−0.0806529	+	0.248224i	0.902597	+	0.430486i	$0.141658\pi$
$968$	−9.01147e6			−0.309106
$969$	−1.32217e6	+	4.06922e6i	−0.0452353	+	0.139220i
$970$	8.16418e6	+	1.35446e6i	0.278602	+	0.0462206i
$971$	−5.43218e6	−	1.67185e7i	−0.184895	−	0.569049i	0.815051	−	0.579389i	$-0.196709\pi$
$971$	−5.43218e6	−	1.67185e7i	−0.184895	−	0.569049i	−0.999947	+	0.0103396i	$0.996709\pi$
$972$	291954.	+	898543.i	0.00991172	+	0.0305052i
$973$	−4.38161e7	−	3.18342e7i	−1.48372	−	1.07798i
$974$	−2.35932e7			−0.796873
$975$	−9.29223e6	−	3.17047e6i	−0.313046	−	0.106810i
$976$	−3.07366e6			−0.103284
$977$	1.53305e7	+	1.11383e7i	0.513831	+	0.373320i	0.814275	−	0.580479i	$-0.197135\pi$
$977$	1.53305e7	+	1.11383e7i	0.513831	+	0.373320i	−0.300444	+	0.953800i	$0.597135\pi$
$978$	−3.87798e6	−	1.19352e7i	−0.129646	−	0.399009i
$979$	−2.27201e6	−	6.99254e6i	−0.0757625	−	0.233173i
$980$	1.49848e7	−	7.49739e6i	0.498409	−	0.249370i
$981$	−3.82263e6	+	1.17649e7i	−0.126821	+	0.390314i
$982$	−2.48946e7			−0.823808
$983$	9.06562e6	−	2.79011e7i	0.299236	−	0.920954i	−0.682530	−	0.730858i	$-0.739120\pi$
$983$	9.06562e6	−	2.79011e7i	0.299236	−	0.920954i	0.981766	−	0.190096i	$-0.0608798\pi$
$984$	−2.93107e6	+	2.12955e6i	−0.0965024	+	0.0701131i
$985$	3.50421e7	−	1.75327e7i	1.15080	−	0.575783i
$986$	−1.49567e7	−	1.08667e7i	−0.489940	−	0.355962i
$987$	1.46080e7	−	1.06133e7i	0.477306	−	0.346783i
$988$	−3.15962e6	+	2.29560e6i	−0.102978	+	0.0748176i
$989$	2.78155e7	+	2.02091e7i	0.904265	+	0.656987i
$990$	1.18681e6	−	2.28767e6i	0.0384853	−	0.0741831i
$991$	−8.60014e6	+	6.24837e6i	−0.278177	+	0.202108i	−0.718122	−	0.695917i	$-0.754998\pi$
$991$	−8.60014e6	+	6.24837e6i	−0.278177	+	0.202108i	0.439945	+	0.898025i	$0.354998\pi$
$992$	−692259.	+	2.13056e6i	−0.0223352	+	0.0687407i
$993$	−9.08358e6			−0.292337
$994$	−1.80351e7	+	5.55065e7i	−0.578967	+	1.78188i
$995$	5.53888e6	+	3.67095e7i	0.177364	+	1.17550i
$996$	−2.86934e6	−	8.83091e6i	−0.0916502	−	0.282070i
$997$	−1.67137e7	−	5.14395e7i	−0.532519	−	1.63893i	−0.748949	−	0.662627i	$-0.769441\pi$
$997$	−1.67137e7	−	5.14395e7i	−0.532519	−	1.63893i	0.216430	−	0.976298i	$-0.430559\pi$
$998$	7.85035e6	+	5.70361e6i	0.249495	+	0.181269i
$999$	−1.17796e6			−0.0373435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.b.91.3	yes	24
25.11	even	5	inner	150.6.g.b.61.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.b.61.3	✓	24	25.11	even	5	inner
150.6.g.b.91.3	yes	24	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-8.34027 - 55.2760i) q^{5} +(11.1246 - 34.2380i) q^{6} -188.522 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-8.34027 - 55.2760i) q^{5} +(11.1246 - 34.2380i) q^{6} -188.522 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(-102.972 + 198.486i) q^{10} +(115.116 + 83.6367i) q^{11} +(-116.498 + 84.6411i) q^{12} +(282.422 - 205.191i) q^{13} +(610.070 + 443.242i) q^{14} +(449.940 - 225.120i) q^{15} +(-207.108 + 150.473i) q^{16} +(210.101 - 646.623i) q^{17} +324.000 q^{18} +(-216.073 + 665.003i) q^{19} +(799.894 - 400.213i) q^{20} +(-524.308 - 1613.65i) q^{21} +(-175.882 - 541.308i) q^{22} +(1183.91 + 860.159i) q^{23} +576.000 q^{24} +(-2985.88 + 922.034i) q^{25} -1396.37 q^{26} +(-589.773 - 428.495i) q^{27} +(-932.103 - 2868.72i) q^{28} +(2100.66 + 6465.15i) q^{29} +(-1985.33 - 329.370i) q^{30} +(-676.035 + 2080.62i) q^{31} +1024.00 q^{32} +(-395.734 + 1217.94i) q^{33} +(-2200.20 + 1598.54i) q^{34} +(1572.32 + 10420.7i) q^{35} +(-1048.49 - 761.770i) q^{36} +(1307.25 - 949.774i) q^{37} +(2262.74 - 1643.98i) q^{38} +(2541.79 + 1846.72i) q^{39} +(-3529.47 - 585.547i) q^{40} +(-5088.66 + 3697.13i) q^{41} +(-2097.23 + 6454.62i) q^{42} +23494.6 q^{43} +(-703.526 + 2165.23i) q^{44} +(3178.27 + 3225.17i) q^{45} +(-1808.85 - 5567.07i) q^{46} +(3288.60 + 10121.3i) q^{47} +(-1863.98 - 1354.26i) q^{48} +18733.5 q^{49} +(11830.3 + 4036.46i) q^{50} +6119.10 q^{51} +(4518.74 + 3283.06i) q^{52} +(5489.13 + 16893.8i) q^{53} +(901.094 + 2773.28i) q^{54} +(3663.00 - 7060.71i) q^{55} +(-3728.41 + 11474.9i) q^{56} -6293.03 q^{57} +(8402.62 - 25860.6i) q^{58} +(16419.9 - 11929.7i) q^{59} +(5650.25 + 5733.64i) q^{60} +(9713.46 + 7057.24i) q^{61} +(7079.53 - 5143.58i) q^{62} +(12353.9 - 8975.64i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-13697.6 - 13899.8i) q^{65} +(4144.18 - 3010.92i) q^{66} +(-6054.32 + 18633.3i) q^{67} +10878.4 q^{68} +(-4069.91 + 12525.9i) q^{69} +(19412.5 - 37419.0i) q^{70} +(23916.5 + 73607.5i) q^{71} +(1601.94 + 4930.28i) q^{72} +(-432.726 - 314.394i) q^{73} -6463.41 q^{74} +(-16196.3 - 22993.3i) q^{75} -11187.6 q^{76} +(-21701.9 - 15767.3i) q^{77} +(-3883.52 - 11952.2i) q^{78} +(17562.5 + 54051.8i) q^{79} +(10044.9 + 10193.1i) q^{80} +(2027.46 - 6239.88i) q^{81} +25159.7 q^{82} +(-19926.0 + 61325.8i) q^{83} +(21962.5 - 15956.7i) q^{84} +(-37495.1 - 6220.52i) q^{85} +(-76030.2 - 55239.2i) q^{86} +(-49496.3 + 35961.2i) q^{87} +(7367.42 - 5352.75i) q^{88} +(-41803.1 - 30371.7i) q^{89} +(-2702.25 - 17909.4i) q^{90} +(-53242.6 + 38683.0i) q^{91} +(-7235.40 + 22268.3i) q^{92} -19689.2 q^{93} +(13154.4 - 40485.0i) q^{94} +(38560.8 + 6397.33i) q^{95} +(2847.90 + 8764.94i) q^{96} +(-11436.8 - 35199.0i) q^{97} +(-60622.9 - 44045.1i) q^{98} -11525.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Introduction

L-functions

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