LMFDB - Embedded newform 42.6.e.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,6,Mod(25,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

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("42.25");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	42.e (of order $3$, degree $2$, 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:	$6.73612043215$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	42.37
Dual form			42.6.e.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(3.00000 - 5.19615i) q^{5} +36.0000 q^{6} +(59.5000 + 115.181i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(3.00000 - 5.19615i) q^{5} +36.0000 q^{6} +(59.5000 + 115.181i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(12.0000 + 20.7846i) q^{10} +(333.000 + 576.773i) q^{11} +(-72.0000 + 124.708i) q^{12} -559.000 q^{13} +(-518.000 - 24.2487i) q^{14} -54.0000 q^{15} +(-128.000 + 221.703i) q^{16} +(870.000 + 1506.88i) q^{17} +(-162.000 - 280.592i) q^{18} +(-578.500 + 1001.99i) q^{19} -96.0000 q^{20} +(630.000 - 982.073i) q^{21} -2664.00 q^{22} +(1734.00 - 3003.38i) q^{23} +(-288.000 - 498.831i) q^{24} +(1544.50 + 2675.15i) q^{25} +(1118.00 - 1936.43i) q^{26} +729.000 q^{27} +(1120.00 - 1745.91i) q^{28} +3372.00 q^{29} +(108.000 - 187.061i) q^{30} +(-3146.50 - 5449.90i) q^{31} +(-512.000 - 886.810i) q^{32} +(2997.00 - 5190.96i) q^{33} -6960.00 q^{34} +(777.000 + 36.3731i) q^{35} +1296.00 q^{36} +(-1565.50 + 2711.53i) q^{37} +(-2314.00 - 4007.97i) q^{38} +(2515.50 + 4356.97i) q^{39} +(192.000 - 332.554i) q^{40} -4866.00 q^{41} +(2142.00 + 4146.53i) q^{42} -11407.0 q^{43} +(5328.00 - 9228.37i) q^{44} +(243.000 + 420.888i) q^{45} +(6936.00 + 12013.5i) q^{46} +(-1155.00 + 2000.52i) q^{47} +2304.00 q^{48} +(-9726.50 + 13706.6i) q^{49} -12356.0 q^{50} +(7830.00 - 13562.0i) q^{51} +(4472.00 + 7745.73i) q^{52} +(14148.0 + 24505.1i) q^{53} +(-1458.00 + 2525.33i) q^{54} +3996.00 q^{55} +(3808.00 + 7371.61i) q^{56} +10413.0 q^{57} +(-6744.00 + 11681.0i) q^{58} +(-10272.0 - 17791.6i) q^{59} +(432.000 + 748.246i) q^{60} +(2315.00 - 4009.70i) q^{61} +25172.0 q^{62} +(-10489.5 - 491.036i) q^{63} +4096.00 q^{64} +(-1677.00 + 2904.65i) q^{65} +(11988.0 + 20763.8i) q^{66} +(9372.50 + 16233.6i) q^{67} +(13920.0 - 24110.1i) q^{68} -31212.0 q^{69} +(-1680.00 + 2618.86i) q^{70} -38226.0 q^{71} +(-2592.00 + 4489.48i) q^{72} +(-35294.5 - 61131.9i) q^{73} +(-6262.00 - 10846.1i) q^{74} +(13900.5 - 24076.4i) q^{75} +18512.0 q^{76} +(-46620.0 + 72673.4i) q^{77} -20124.0 q^{78} +(31146.5 - 53947.3i) q^{79} +(768.000 + 1330.22i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(9732.00 - 16856.3i) q^{82} +79818.0 q^{83} +(-18648.0 - 872.954i) q^{84} +10440.0 q^{85} +(22814.0 - 39515.0i) q^{86} +(-15174.0 - 26282.1i) q^{87} +(21312.0 + 36913.5i) q^{88} +(9060.00 - 15692.4i) q^{89} -1944.00 q^{90} +(-33260.5 - 64386.4i) q^{91} -55488.0 q^{92} +(-28318.5 + 49049.1i) q^{93} +(-4620.00 - 8002.07i) q^{94} +(3471.00 + 6011.95i) q^{95} +(-4608.00 + 7981.29i) q^{96} +124754. q^{97} +(-28028.0 - 61106.8i) q^{98} -53946.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} + 6 q^{5} + 72 q^{6} + 119 q^{7} + 128 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 + 6 * q^5 + 72 * q^6 + 119 * q^7 + 128 * q^8 - 81 * q^9	\( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} + 6 q^{5} + 72 q^{6} + 119 q^{7} + 128 q^{8} - 81 q^{9} + 24 q^{10} + 666 q^{11} - 144 q^{12} - 1118 q^{13} - 1036 q^{14} - 108 q^{15} - 256 q^{16} + 1740 q^{17} - 324 q^{18} - 1157 q^{19} - 192 q^{20} + 1260 q^{21} - 5328 q^{22} + 3468 q^{23} - 576 q^{24} + 3089 q^{25} + 2236 q^{26} + 1458 q^{27} + 2240 q^{28} + 6744 q^{29} + 216 q^{30} - 6293 q^{31} - 1024 q^{32} + 5994 q^{33} - 13920 q^{34} + 1554 q^{35} + 2592 q^{36} - 3131 q^{37} - 4628 q^{38} + 5031 q^{39} + 384 q^{40} - 9732 q^{41} + 4284 q^{42} - 22814 q^{43} + 10656 q^{44} + 486 q^{45} + 13872 q^{46} - 2310 q^{47} + 4608 q^{48} - 19453 q^{49} - 24712 q^{50} + 15660 q^{51} + 8944 q^{52} + 28296 q^{53} - 2916 q^{54} + 7992 q^{55} + 7616 q^{56} + 20826 q^{57} - 13488 q^{58} - 20544 q^{59} + 864 q^{60} + 4630 q^{61} + 50344 q^{62} - 20979 q^{63} + 8192 q^{64} - 3354 q^{65} + 23976 q^{66} + 18745 q^{67} + 27840 q^{68} - 62424 q^{69} - 3360 q^{70} - 76452 q^{71} - 5184 q^{72} - 70589 q^{73} - 12524 q^{74} + 27801 q^{75} + 37024 q^{76} - 93240 q^{77} - 40248 q^{78} + 62293 q^{79} + 1536 q^{80} - 6561 q^{81} + 19464 q^{82} + 159636 q^{83} - 37296 q^{84} + 20880 q^{85} + 45628 q^{86} - 30348 q^{87} + 42624 q^{88} + 18120 q^{89} - 3888 q^{90} - 66521 q^{91} - 110976 q^{92} - 56637 q^{93} - 9240 q^{94} + 6942 q^{95} - 9216 q^{96} + 249508 q^{97} - 56056 q^{98} - 107892 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 + 6 * q^5 + 72 * q^6 + 119 * q^7 + 128 * q^8 - 81 * q^9 + 24 * q^10 + 666 * q^11 - 144 * q^12 - 1118 * q^13 - 1036 * q^14 - 108 * q^15 - 256 * q^16 + 1740 * q^17 - 324 * q^18 - 1157 * q^19 - 192 * q^20 + 1260 * q^21 - 5328 * q^22 + 3468 * q^23 - 576 * q^24 + 3089 * q^25 + 2236 * q^26 + 1458 * q^27 + 2240 * q^28 + 6744 * q^29 + 216 * q^30 - 6293 * q^31 - 1024 * q^32 + 5994 * q^33 - 13920 * q^34 + 1554 * q^35 + 2592 * q^36 - 3131 * q^37 - 4628 * q^38 + 5031 * q^39 + 384 * q^40 - 9732 * q^41 + 4284 * q^42 - 22814 * q^43 + 10656 * q^44 + 486 * q^45 + 13872 * q^46 - 2310 * q^47 + 4608 * q^48 - 19453 * q^49 - 24712 * q^50 + 15660 * q^51 + 8944 * q^52 + 28296 * q^53 - 2916 * q^54 + 7992 * q^55 + 7616 * q^56 + 20826 * q^57 - 13488 * q^58 - 20544 * q^59 + 864 * q^60 + 4630 * q^61 + 50344 * q^62 - 20979 * q^63 + 8192 * q^64 - 3354 * q^65 + 23976 * q^66 + 18745 * q^67 + 27840 * q^68 - 62424 * q^69 - 3360 * q^70 - 76452 * q^71 - 5184 * q^72 - 70589 * q^73 - 12524 * q^74 + 27801 * q^75 + 37024 * q^76 - 93240 * q^77 - 40248 * q^78 + 62293 * q^79 + 1536 * q^80 - 6561 * q^81 + 19464 * q^82 + 159636 * q^83 - 37296 * q^84 + 20880 * q^85 + 45628 * q^86 - 30348 * q^87 + 42624 * q^88 + 18120 * q^89 - 3888 * q^90 - 66521 * q^91 - 110976 * q^92 - 56637 * q^93 - 9240 * q^94 + 6942 * q^95 - 9216 * q^96 + 249508 * q^97 - 56056 * q^98 - 107892 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	3.00000	−	5.19615i	0.0536656	−	0.0929516i	−0.837945	−	0.545755i	$-0.816243\pi$
$5$	3.00000	−	5.19615i	0.0536656	−	0.0929516i	0.891610	+	0.452804i	$0.149576\pi$
$6$	36.0000			0.408248
$7$	59.5000	+	115.181i	0.458957	+	0.888459i
$7$	59.5000	+	115.181i	0.458957	+	0.888459i
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	12.0000	+	20.7846i	0.0379473	+	0.0657267i
$11$	333.000	+	576.773i	0.829779	+	1.43722i	0.898211	+	0.439564i	$0.144867\pi$
$11$	333.000	+	576.773i	0.829779	+	1.43722i	−0.0684322	+	0.997656i	$0.521800\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	−559.000			−0.917389			−0.458694	−	0.888594i	$-0.651683\pi$
$13$	−559.000			−0.917389			−0.458694	+	0.888594i	$0.651683\pi$
$14$	−518.000	−	24.2487i	−0.706333	−	0.0330650i
$15$	−54.0000			−0.0619677
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	870.000	+	1506.88i	0.730125	+	1.26461i	0.956830	+	0.290649i	$0.0938713\pi$
$17$	870.000	+	1506.88i	0.730125	+	1.26461i	−0.226705	+	0.973963i	$0.572795\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	−578.500	+	1001.99i	−0.367637	+	0.636766i	−0.989196	−	0.146602i	$-0.953166\pi$
$19$	−578.500	+	1001.99i	−0.367637	+	0.636766i	0.621558	+	0.783368i	$0.286500\pi$
$20$	−96.0000			−0.0536656
$21$	630.000	−	982.073i	0.311740	−	0.485954i
$22$	−2664.00			−1.17348
$23$	1734.00	−	3003.38i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$23$	1734.00	−	3003.38i	0.683486	−	1.18383i	0.973910	−	0.226934i	$-0.0728702\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	1544.50	+	2675.15i	0.494240	+	0.856049i
$26$	1118.00	−	1936.43i	0.324346	−	0.561784i
$27$	729.000			0.192450
$28$	1120.00	−	1745.91i	0.269975	−	0.420849i
$29$	3372.00			0.744548			0.372274	−	0.928123i	$-0.378578\pi$
$29$	3372.00			0.744548			0.372274	+	0.928123i	$0.378578\pi$
$30$	108.000	−	187.061i	0.0219089	−	0.0379473i
$31$	−3146.50	−	5449.90i	−0.588063	−	1.01855i	−0.994486	−	0.104869i	$-0.966558\pi$
$31$	−3146.50	−	5449.90i	−0.588063	−	1.01855i	0.406423	−	0.913685i	$-0.366776\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	2997.00	−	5190.96i	0.479073	−	0.829779i
$34$	−6960.00			−1.03255
$35$	777.000	+	36.3731i	0.107214	+	0.00501891i
$36$	1296.00			0.166667
$37$	−1565.50	+	2711.53i	−0.187996	+	0.325619i	−0.944582	−	0.328276i	$-0.893533\pi$
$37$	−1565.50	+	2711.53i	−0.187996	+	0.325619i	0.756586	+	0.653894i	$0.226866\pi$
$38$	−2314.00	−	4007.97i	−0.259959	−	0.450262i
$39$	2515.50	+	4356.97i	0.264827	+	0.458694i
$40$	192.000	−	332.554i	0.0189737	−	0.0328634i
$41$	−4866.00			−0.452077			−0.226039	−	0.974118i	$-0.572578\pi$
$41$	−4866.00			−0.452077			−0.226039	+	0.974118i	$0.572578\pi$
$42$	2142.00	+	4146.53i	0.187368	+	0.362712i
$43$	−11407.0			−0.940806			−0.470403	−	0.882452i	$-0.655892\pi$
$43$	−11407.0			−0.940806			−0.470403	+	0.882452i	$0.655892\pi$
$44$	5328.00	−	9228.37i	0.414890	−	0.718610i
$45$	243.000	+	420.888i	0.0178885	+	0.0309839i
$46$	6936.00	+	12013.5i	0.483297	+	0.837096i
$47$	−1155.00	+	2000.52i	−0.0762671	+	0.132099i	−0.901637	−	0.432494i	$-0.857634\pi$
$47$	−1155.00	+	2000.52i	−0.0762671	+	0.132099i	0.825369	+	0.564593i	$0.190967\pi$
$48$	2304.00			0.144338
$49$	−9726.50	+	13706.6i	−0.578717	+	0.815528i
$50$	−12356.0			−0.698961
$51$	7830.00	−	13562.0i	0.421538	−	0.730125i
$52$	4472.00	+	7745.73i	0.229347	+	0.397241i
$53$	14148.0	+	24505.1i	0.691840	+	1.19830i	0.971235	+	0.238125i	$0.0765328\pi$
$53$	14148.0	+	24505.1i	0.691840	+	1.19830i	−0.279395	+	0.960176i	$0.590134\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	3996.00			0.178122
$56$	3808.00	+	7371.61i	0.162266	+	0.314118i
$57$	10413.0			0.424511
$58$	−6744.00	+	11681.0i	−0.263237	+	0.455941i
$59$	−10272.0	−	17791.6i	−0.384171	−	0.665404i	0.607483	−	0.794333i	$-0.292179\pi$
$59$	−10272.0	−	17791.6i	−0.384171	−	0.665404i	−0.991654	+	0.128929i	$0.958846\pi$
$60$	432.000	+	748.246i	0.0154919	+	0.0268328i
$61$	2315.00	−	4009.70i	0.0796575	−	0.137971i	−0.823445	−	0.567397i	$-0.807951\pi$
$61$	2315.00	−	4009.70i	0.0796575	−	0.137971i	0.903102	+	0.429426i	$0.141284\pi$
$62$	25172.0			0.831646
$63$	−10489.5	−	491.036i	−0.332969	−	0.0155870i
$64$	4096.00			0.125000
$65$	−1677.00	+	2904.65i	−0.0492322	+	0.0852728i
$66$	11988.0	+	20763.8i	0.338756	+	0.586742i
$67$	9372.50	+	16233.6i	0.255075	+	0.441803i	0.964916	−	0.262559i	$-0.0845664\pi$
$67$	9372.50	+	16233.6i	0.255075	+	0.441803i	−0.709841	+	0.704362i	$0.751233\pi$
$68$	13920.0	−	24110.1i	0.365062	−	0.632306i
$69$	−31212.0			−0.789221
$70$	−1680.00	+	2618.86i	−0.0409793	+	0.0638804i
$71$	−38226.0			−0.899939			−0.449969	−	0.893044i	$-0.648565\pi$
$71$	−38226.0			−0.899939			−0.449969	+	0.893044i	$0.648565\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	−35294.5	−	61131.9i	−0.775175	−	1.34264i	−0.934696	−	0.355448i	$-0.884328\pi$
$73$	−35294.5	−	61131.9i	−0.775175	−	1.34264i	0.159521	−	0.987195i	$-0.449005\pi$
$74$	−6262.00	−	10846.1i	−0.132933	−	0.230247i
$75$	13900.5	−	24076.4i	0.285350	−	0.494240i
$76$	18512.0			0.367637
$77$	−46620.0	+	72673.4i	−0.896077	+	1.39685i
$78$	−20124.0			−0.374522
$79$	31146.5	−	53947.3i	0.561489	−	0.972528i	−0.435877	−	0.900006i	$-0.643562\pi$
$79$	31146.5	−	53947.3i	0.561489	−	0.972528i	0.997367	−	0.0725221i	$-0.0231048\pi$
$80$	768.000	+	1330.22i	0.0134164	+	0.0232379i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	9732.00	−	16856.3i	0.159833	−	0.276840i
$83$	79818.0			1.27176			0.635881	−	0.771787i	$-0.280637\pi$
$83$	79818.0			1.27176			0.635881	+	0.771787i	$0.280637\pi$
$84$	−18648.0	−	872.954i	−0.288359	−	0.0134987i
$85$	10440.0			0.156730
$86$	22814.0	−	39515.0i	0.332625	−	0.576124i
$87$	−15174.0	−	26282.1i	−0.214932	−	0.372274i
$88$	21312.0	+	36913.5i	0.293371	+	0.508134i
$89$	9060.00	−	15692.4i	0.121242	−	0.209997i	−0.799016	−	0.601310i	$-0.794646\pi$
$89$	9060.00	−	15692.4i	0.121242	−	0.209997i	0.920258	+	0.391313i	$0.127979\pi$
$90$	−1944.00			−0.0252982
$91$	−33260.5	−	64386.4i	−0.421042	−	0.815062i
$92$	−55488.0			−0.683486
$93$	−28318.5	+	49049.1i	−0.339518	+	0.588063i
$94$	−4620.00	−	8002.07i	−0.0539290	−	0.0934078i
$95$	3471.00	+	6011.95i	0.0394590	+	0.0683449i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	124754.			1.34625			0.673124	−	0.739530i	$-0.264952\pi$
$97$	124754.			1.34625			0.673124	+	0.739530i	$0.264952\pi$
$98$	−28028.0	−	61106.8i	−0.294800	−	0.642723i
$99$	−53946.0			−0.553186
$100$	24712.0	−	42802.4i	0.247120	−	0.428024i
$101$	46695.0	+	80878.1i	0.455478	+	0.788910i	0.998716	−	0.0506685i	$-0.0161352\pi$
$101$	46695.0	+	80878.1i	0.455478	+	0.788910i	−0.543238	+	0.839579i	$0.682802\pi$
$102$	31320.0	+	54247.8i	0.298072	+	0.516276i
$103$	83865.5	−	145259.i	0.778915	−	1.34912i	−0.153652	−	0.988125i	$-0.549103\pi$
$103$	83865.5	−	145259.i	0.778915	−	1.34912i	0.932567	−	0.360996i	$-0.117563\pi$
$104$	−35776.0			−0.324346
$105$	−3213.00	−	6219.79i	−0.0284405	−	0.0550558i
$106$	−113184.			−0.978409
$107$	−34590.0	+	59911.6i	−0.292073	+	0.505885i	−0.974300	−	0.225256i	$-0.927678\pi$
$107$	−34590.0	+	59911.6i	−0.292073	+	0.505885i	0.682227	+	0.731141i	$0.261012\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	109779.	+	190144.i	0.885024	+	1.53291i	0.845686	+	0.533680i	$0.179191\pi$
$109$	109779.	+	190144.i	0.885024	+	1.53291i	0.0393377	+	0.999226i	$0.487475\pi$
$110$	−7992.00	+	13842.6i	−0.0629758	+	0.109077i
$111$	28179.0			0.217079
$112$	−33152.0	−	1551.92i	−0.249727	−	0.0116902i
$113$	−39354.0			−0.289930			−0.144965	−	0.989437i	$-0.546307\pi$
$113$	−39354.0			−0.289930			−0.144965	+	0.989437i	$0.546307\pi$
$114$	−20826.0	+	36071.7i	−0.150087	+	0.259959i
$115$	−10404.0	−	18020.3i	−0.0733594	−	0.127062i
$116$	−26976.0	−	46723.8i	−0.186137	−	0.322399i
$117$	22639.5	−	39212.8i	0.152898	−	0.264827i
$118$	82176.0			0.543300
$119$	−121800.	+	189867.i	−0.788460	+	1.22909i
$120$	−3456.00			−0.0219089
$121$	−141252.	+	244657.i	−0.877067	+	1.51912i
$122$	9260.00	+	16038.8i	0.0563263	+	0.0975601i
$123$	21897.0	+	37926.7i	0.130503	+	0.226039i
$124$	−50344.0	+	87198.4i	−0.294031	+	0.509277i
$125$	37284.0			0.213426
$126$	22680.0	−	35354.6i	0.127267	−	0.198390i
$127$	317093.			1.74453			0.872263	−	0.489037i	$-0.162652\pi$
$127$	317093.			1.74453			0.872263	+	0.489037i	$0.162652\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	51331.5	+	88908.8i	0.271587	+	0.470403i
$130$	−6708.00	−	11618.6i	−0.0348125	−	0.0602969i
$131$	77415.0	−	134087.i	0.394137	−	0.682665i	−0.598854	−	0.800858i	$-0.704377\pi$
$131$	77415.0	−	134087.i	0.394137	−	0.682665i	0.992991	+	0.118194i	$0.0377103\pi$
$132$	−95904.0			−0.479073
$133$	−149832.	−	7013.94i	−0.734470	−	0.0343821i
$134$	−74980.0			−0.360731
$135$	2187.00	−	3788.00i	0.0103280	−	0.0178885i
$136$	55680.0	+	96440.6i	0.258138	+	0.447108i
$137$	−33666.0	−	58311.2i	−0.153246	−	0.265430i	0.779173	−	0.626809i	$-0.215639\pi$
$137$	−33666.0	−	58311.2i	−0.153246	−	0.265430i	−0.932419	+	0.361379i	$0.882306\pi$
$138$	62424.0	−	108122.i	0.279032	−	0.483297i
$139$	−365215.			−1.60329			−0.801644	−	0.597802i	$-0.796041\pi$
$139$	−365215.			−1.60329			−0.801644	+	0.597802i	$0.796041\pi$
$140$	−5712.00	−	11057.4i	−0.0246302	−	0.0476797i
$141$	20790.0			0.0880657
$142$	76452.0	−	132419.i	0.318176	−	0.551098i
$143$	−186147.	−	322416.i	−0.761230	−	1.31849i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	10116.0	−	17521.4i	0.0399566	−	0.0692069i
$146$	282356.			1.09626
$147$	150602.	+	14130.9i	0.574825	+	0.0539359i
$148$	50096.0			0.187996
$149$	84030.0	−	145544.i	0.310076	−	0.537068i	−0.668302	−	0.743890i	$-0.732979\pi$
$149$	84030.0	−	145544.i	0.310076	−	0.537068i	0.978379	+	0.206822i	$0.0663120\pi$
$150$	55602.0	+	96305.5i	0.201773	+	0.349480i
$151$	−76768.0	−	132966.i	−0.273992	−	0.474568i	0.695888	−	0.718150i	$-0.255011\pi$
$151$	−76768.0	−	132966.i	−0.273992	−	0.474568i	−0.969880	+	0.243582i	$0.921678\pi$
$152$	−37024.0	+	64127.4i	−0.129979	+	0.225131i
$153$	−140940.			−0.486750
$154$	−158508.	−	306843.i	−0.538579	−	1.04259i
$155$	−37758.0			−0.126235
$156$	40248.0	−	69711.6i	0.132414	−	0.229347i
$157$	−101209.	−	175299.i	−0.327695	−	0.567585i	0.654359	−	0.756184i	$-0.272939\pi$
$157$	−101209.	−	175299.i	−0.327695	−	0.567585i	−0.982054	+	0.188599i	$0.939605\pi$
$158$	124586.	+	215789.i	0.397033	+	0.687681i
$159$	127332.	−	220545.i	0.399434	−	0.691840i
$160$	−6144.00			−0.0189737
$161$	449106.	+	21023.6i	1.36548	+	0.0639209i
$162$	26244.0			0.0785674
$163$	89882.0	−	155680.i	0.264974	−	0.458949i	−0.702583	−	0.711602i	$-0.747970\pi$
$163$	89882.0	−	155680.i	0.264974	−	0.458949i	0.967557	+	0.252653i	$0.0813032\pi$
$164$	38928.0	+	67425.3i	0.113019	+	0.195755i
$165$	−17982.0	−	31145.7i	−0.0514195	−	0.0890612i
$166$	−159636.	+	276498.i	−0.449636	+	0.778792i
$167$	217302.			0.602938			0.301469	−	0.953476i	$-0.402523\pi$
$167$	217302.			0.602938			0.301469	+	0.953476i	$0.402523\pi$
$168$	40320.0	−	62852.7i	0.110217	−	0.171811i
$169$	−58812.0			−0.158398
$170$	−20880.0	+	36165.2i	−0.0554126	+	0.0959774i
$171$	−46858.5	−	81161.3i	−0.122546	−	0.212255i
$172$	91256.0	+	158060.i	0.235202	+	0.407381i
$173$	36990.0	−	64068.6i	0.0939656	−	0.162753i	−0.815211	−	0.579164i	$-0.803379\pi$
$173$	36990.0	−	64068.6i	0.0939656	−	0.162753i	0.909176	+	0.416411i	$0.136712\pi$
$174$	121392.			0.303960
$175$	−216230.	+	337069.i	−0.533729	+	0.832001i
$176$	−170496.			−0.414890
$177$	−92448.0	+	160125.i	−0.221801	+	0.384171i
$178$	36240.0	+	62769.5i	0.0857311	+	0.148491i
$179$	−394683.	−	683611.i	−0.920695	−	1.59469i	−0.798342	−	0.602204i	$-0.794289\pi$
$179$	−394683.	−	683611.i	−0.920695	−	1.59469i	−0.122353	−	0.992487i	$-0.539044\pi$
$180$	3888.00	−	6734.21i	0.00894427	−	0.0154919i
$181$	−477739.			−1.08391			−0.541956	−	0.840407i	$-0.682316\pi$
$181$	−477739.			−1.08391			−0.541956	+	0.840407i	$0.682316\pi$
$182$	289562.	+	13555.0i	0.647982	+	0.0303335i
$183$	−41670.0			−0.0919805
$184$	110976.	−	192216.i	0.241649	−	0.418548i
$185$	9393.00	+	16269.2i	0.0201779	+	0.0349491i
$186$	−113274.	−	196196.i	−0.240076	−	0.415823i
$187$	−579420.	+	1.00358e6i	−1.21168	+	2.09870i
$188$	36960.0			0.0762671
$189$	43375.5	+	83967.2i	0.0883263	+	0.170984i
$190$	−27768.0			−0.0558034
$191$	−179487.	+	310881.i	−0.356000	+	0.616609i	−0.987289	−	0.158938i	$-0.949193\pi$
$191$	−179487.	+	310881.i	−0.356000	+	0.616609i	0.631289	+	0.775548i	$0.282526\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	90966.5	+	157559.i	0.175788	+	0.304473i	0.940434	−	0.339978i	$-0.110419\pi$
$193$	90966.5	+	157559.i	0.175788	+	0.304473i	−0.764646	+	0.644451i	$0.777086\pi$
$194$	−249508.	+	432161.i	−0.475971	+	0.824405i
$195$	30186.0			0.0568485
$196$	267736.	+	25121.7i	0.497813	+	0.0467098i
$197$	717924.			1.31799			0.658996	−	0.752146i	$-0.270981\pi$
$197$	717924.			1.31799			0.658996	+	0.752146i	$0.270981\pi$
$198$	107892.	−	186874.i	0.195581	−	0.338756i
$199$	−101548.	−	175886.i	−0.181777	−	0.314847i	0.760709	−	0.649093i	$-0.224852\pi$
$199$	−101548.	−	175886.i	−0.181777	−	0.314847i	−0.942486	+	0.334246i	$0.891518\pi$
$200$	98848.0	+	171210.i	0.174740	+	0.302659i
$201$	84352.5	−	146103.i	0.147268	−	0.255075i
$202$	−373560.			−0.644142
$203$	200634.	+	388392.i	0.341715	+	0.661500i
$204$	−250560.			−0.421538
$205$	−14598.0	+	25284.5i	−0.0242610	+	0.0420213i
$206$	335462.	+	581037.i	0.550776	+	0.953973i
$207$	140454.	+	243273.i	0.227829	+	0.394611i
$208$	71552.0	−	123932.i	0.114674	−	0.198620i
$209$	−770562.			−1.22023
$210$	27972.0	+	1309.43i	0.0437699	+	0.00204896i
$211$	1.17098e6			1.81069			0.905343	−	0.424680i	$-0.139613\pi$
$211$	1.17098e6			1.81069			0.905343	+	0.424680i	$0.139613\pi$
$212$	226368.	−	392081.i	0.345920	−	0.599151i
$213$	172017.	+	297942.i	0.259790	+	0.449969i
$214$	−138360.	−	239647.i	−0.206527	−	0.357715i
$215$	−34221.0	+	59272.5i	−0.0504890	+	0.0874495i
$216$	46656.0			0.0680414
$217$	440510.	−	686687.i	0.635048	−	0.989942i
$218$	−878236.			−1.25161
$219$	−317651.	+	550187.i	−0.447548	+	0.775175i
$220$	−31968.0	−	55370.2i	−0.0445306	−	0.0771293i
$221$	−486330.	−	842348.i	−0.669808	−	1.16014i
$222$	−56358.0	+	97614.9i	−0.0767491	+	0.132933i
$223$	1.24635e6			1.67833			0.839167	−	0.543873i	$-0.183043\pi$
$223$	1.24635e6			1.67833			0.839167	+	0.543873i	$0.183043\pi$
$224$	71680.0	−	111738.i	0.0954504	−	0.148793i
$225$	−250209.			−0.329493
$226$	78708.0	−	136326.i	0.102506	−	0.177545i
$227$	459471.	+	795827.i	0.591825	+	1.02507i	0.993987	+	0.109503i	$0.0349258\pi$
$227$	459471.	+	795827.i	0.591825	+	1.02507i	−0.402161	+	0.915569i	$0.631741\pi$
$228$	−83304.0	−	144287.i	−0.106128	−	0.183819i
$229$	−601874.	+	1.04248e6i	−0.758433	+	1.31364i	0.185216	+	0.982698i	$0.440701\pi$
$229$	−601874.	+	1.04248e6i	−0.758433	+	1.31364i	−0.943649	+	0.330947i	$0.892632\pi$
$230$	83232.0			0.103746
$231$	776223.	+	36336.7i	0.957098	+	0.0448039i
$232$	215808.			0.263237
$233$	459531.	−	795931.i	0.554530	−	0.960474i	−0.443410	−	0.896319i	$-0.646231\pi$
$233$	459531.	−	795931.i	0.554530	−	0.960474i	0.997940	−	0.0641551i	$-0.0204353\pi$
$234$	90558.0	+	156851.i	0.108115	+	0.187261i
$235$	6930.00	+	12003.1i	0.00818585	+	0.0141783i
$236$	−164352.	+	284666.i	−0.192086	+	0.332702i
$237$	−560637.			−0.648352
$238$	−414120.	−	801662.i	−0.473897	−	0.917380i
$239$	−625338.			−0.708142			−0.354071	−	0.935219i	$-0.615203\pi$
$239$	−625338.			−0.708142			−0.354071	+	0.935219i	$0.615203\pi$
$240$	6912.00	−	11971.9i	0.00774597	−	0.0134164i
$241$	−626911.	−	1.08584e6i	−0.695286	−	1.20427i	−0.970084	−	0.242768i	$-0.921945\pi$
$241$	−626911.	−	1.08584e6i	−0.695286	−	1.20427i	0.274799	−	0.961502i	$-0.411389\pi$
$242$	−565010.	−	978626.i	−0.620180	−	1.07418i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−74080.0			−0.0796575
$245$	42042.0	+	91660.1i	0.0447474	+	0.0975585i
$246$	−175176.			−0.184560
$247$	323382.	−	560113.i	0.337266	−	0.584162i
$248$	−201376.	−	348793.i	−0.207911	−	0.360113i
$249$	−359181.	−	622120.i	−0.367126	−	0.635881i
$250$	−74568.0	+	129156.i	−0.0754575	+	0.130696i
$251$	−1.51333e6			−1.51618			−0.758089	−	0.652152i	$-0.773867\pi$
$251$	−1.51333e6			−1.51618			−0.758089	+	0.652152i	$0.773867\pi$
$252$	77112.0	+	149275.i	0.0764928	+	0.148076i
$253$	2.30969e6			2.26857
$254$	−634186.	+	1.09844e6i	−0.616783	+	1.06830i
$255$	−46980.0	−	81371.7i	−0.0452442	−	0.0783652i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	777465.	−	1.34661e6i	0.734257	−	1.27177i	−0.220792	−	0.975321i	$-0.570864\pi$
$257$	777465.	−	1.34661e6i	0.734257	−	1.27177i	0.955049	−	0.296449i	$-0.0958026\pi$
$258$	−410652.			−0.384083
$259$	−405464.	−	18980.7i	−0.375581	−	0.0175818i
$260$	53664.0			0.0492322
$261$	−136566.	+	236539.i	−0.124091	+	0.214932i
$262$	309660.	+	536347.i	0.278697	+	0.482717i
$263$	557658.	+	965892.i	0.497140	+	0.861071i	0.999995	−	0.00329949i	$-0.00105026\pi$
$263$	557658.	+	965892.i	0.497140	+	0.861071i	−0.502855	+	0.864371i	$0.667717\pi$
$264$	191808.	−	332221.i	0.169378	−	0.293371i
$265$	169776.			0.148512
$266$	323960.	−	505004.i	0.280729	−	0.437613i
$267$	−163080.			−0.139998
$268$	149960.	−	259738.i	0.127538	−	0.220902i
$269$	−17835.0	−	30891.1i	−0.0150277	−	0.0260287i	0.858414	−	0.512958i	$-0.171450\pi$
$269$	−17835.0	−	30891.1i	−0.0150277	−	0.0260287i	−0.873441	+	0.486929i	$0.838117\pi$
$270$	8748.00	+	15152.0i	0.00730297	+	0.0126491i
$271$	146384.	−	253545.i	0.121079	−	0.209716i	−0.799114	−	0.601179i	$-0.794698\pi$
$271$	146384.	−	253545.i	0.121079	−	0.209716i	0.920194	+	0.391464i	$0.128031\pi$
$272$	−445440.			−0.365062
$273$	−352170.	+	548979.i	−0.285987	+	0.445809i
$274$	269328.			0.216723
$275$	−1.02864e6	+	1.78165e6i	−0.820220	+	1.42066i
$276$	249696.	+	432486.i	0.197305	+	0.341743i
$277$	−431607.	−	747564.i	−0.337978	−	0.585395i	0.646074	−	0.763275i	$-0.276410\pi$
$277$	−431607.	−	747564.i	−0.337978	−	0.585395i	−0.984052	+	0.177879i	$0.943076\pi$
$278$	730430.	−	1.26514e6i	0.566848	−	0.981810i
$279$	509733.			0.392042
$280$	49728.0	+	2327.88i	0.0379058	+	0.00177445i
$281$	1.47110e6			1.11142			0.555709	−	0.831377i	$-0.312447\pi$
$281$	1.47110e6			1.11142			0.555709	+	0.831377i	$0.312447\pi$
$282$	−41580.0	+	72018.7i	−0.0311359	+	0.0539290i
$283$	−344420.	−	596554.i	−0.255637	−	0.442775i	0.709432	−	0.704774i	$-0.248952\pi$
$283$	−344420.	−	596554.i	−0.255637	−	0.442775i	−0.965068	+	0.261999i	$0.915618\pi$
$284$	305808.	+	529675.i	0.224985	+	0.389685i
$285$	31239.0	−	54107.5i	0.0227816	−	0.0394590i
$286$	1.48918e6			1.07654
$287$	−289527.	−	560473.i	−0.207484	−	0.401652i
$288$	82944.0			0.0589256
$289$	−803872.	+	1.39235e6i	−0.566164	+	0.980624i
$290$	40464.0	+	70085.7i	0.0282536	+	0.0489367i
$291$	−561393.	−	972361.i	−0.388628	−	0.673124i
$292$	−564712.	+	978110.i	−0.387588	+	0.671321i
$293$	722832.			0.491890			0.245945	−	0.969284i	$-0.420902\pi$
$293$	722832.			0.491890			0.245945	+	0.969284i	$0.420902\pi$
$294$	−350154.	+	493437.i	−0.236260	+	0.332938i
$295$	−123264.			−0.0824672
$296$	−100192.	+	173538.i	−0.0664666	+	0.115124i
$297$	242757.	+	420467.i	0.159691	+	0.276593i
$298$	336120.	+	582177.i	0.219257	+	0.379764i
$299$	−969306.	+	1.67889e6i	−0.627022	+	1.08603i
$300$	−444816.			−0.285350
$301$	−678716.	−	1.31387e6i	−0.431790	−	0.835868i
$302$	614144.			0.387483
$303$	420255.	−	727903.i	0.262970	−	0.455478i
$304$	−148096.	−	256510.i	−0.0919093	−	0.159192i
$305$	−13890.0	−	24058.2i	−0.00854973	−	0.0148086i
$306$	281880.	−	488230.i	0.172092	−	0.298072i
$307$	−20125.0			−0.0121868			−0.00609340	−	0.999981i	$-0.501940\pi$
$307$	−20125.0			−0.0121868			−0.00609340	+	0.999981i	$0.501940\pi$
$308$	1.37995e6	+	64598.6i	0.828871	+	0.0388013i
$309$	−1.50958e6			−0.899414
$310$	75516.0	−	130798.i	0.0446308	−	0.0773028i
$311$	871779.	+	1.50997e6i	0.511099	+	0.885250i	0.999917	+	0.0128643i	$0.00409496\pi$
$311$	871779.	+	1.50997e6i	0.511099	+	0.885250i	−0.488818	+	0.872386i	$0.662572\pi$
$312$	160992.	+	278846.i	0.0936306	+	0.162173i
$313$	−904272.	+	1.56624e6i	−0.521721	+	0.903647i	0.477960	+	0.878382i	$0.341376\pi$
$313$	−904272.	+	1.56624e6i	−0.521721	+	0.903647i	−0.999681	+	0.0252651i	$0.991957\pi$
$314$	809672.			0.463431
$315$	−34020.0	+	53031.9i	−0.0193178	+	0.0301135i
$316$	−996688.			−0.561489
$317$	−511776.	+	886422.i	−0.286043	+	0.495442i	−0.972862	−	0.231388i	$-0.925673\pi$
$317$	−511776.	+	886422.i	−0.286043	+	0.495442i	0.686818	+	0.726829i	$0.259007\pi$
$318$	509328.	+	882182.i	0.282442	+	0.489204i
$319$	1.12288e6	+	1.94488e6i	0.617810	+	1.07008i
$320$	12288.0	−	21283.4i	0.00670820	−	0.0116190i
$321$	622620.			0.337257
$322$	−971040.	+	1.51370e6i	−0.521912	+	0.813581i
$323$	−2.01318e6			−1.07368
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	−863376.	−	1.49541e6i	−0.453410	−	0.785330i
$326$	359528.	+	622721.i	0.187365	+	0.324526i
$327$	988016.	−	1.71129e6i	0.510969	−	0.885024i
$328$	−311424.			−0.159833
$329$	−299145.	−	14003.6i	−0.152367	−	0.00713265i
$330$	143856.			0.0727182
$331$	503766.	−	872549.i	0.252731	−	0.437744i	−0.711545	−	0.702640i	$-0.752004\pi$
$331$	503766.	−	872549.i	0.252731	−	0.437744i	0.964277	+	0.264896i	$0.0853378\pi$
$332$	−638544.	−	1.10599e6i	−0.317940	−	0.550689i
$333$	−126806.	−	219634.i	−0.0626654	−	0.108540i
$334$	−434604.	+	752756.i	−0.213171	+	0.369223i
$335$	112470.			0.0547551
$336$	137088.	+	265378.i	0.0662447	+	0.128238i
$337$	−1.56571e6			−0.750993			−0.375496	−	0.926824i	$-0.622528\pi$
$337$	−1.56571e6			−0.750993			−0.375496	+	0.926824i	$0.622528\pi$
$338$	117624.	−	203731.i	0.0560021	−	0.0969985i
$339$	177093.	+	306734.i	0.0836955	+	0.144965i
$340$	−83520.0	−	144661.i	−0.0391826	−	0.0678662i
$341$	2.09557e6	−	3.62963e6i	0.975924	−	1.69035i
$342$	374868.			0.173306
$343$	−2.15747e6	−	304770.i	−0.990169	−	0.139874i
$344$	−730048.			−0.332625
$345$	−93636.0	+	162182.i	−0.0423541	+	0.0733594i
$346$	147960.	+	256274.i	0.0664437	+	0.115084i
$347$	−378642.	−	655827.i	−0.168813	−	0.292392i	0.769190	−	0.639020i	$-0.220660\pi$
$347$	−378642.	−	655827.i	−0.168813	−	0.292392i	−0.938003	+	0.346628i	$0.887327\pi$
$348$	−242784.	+	420514.i	−0.107466	+	0.186137i
$349$	−455638.			−0.200243			−0.100121	−	0.994975i	$-0.531923\pi$
$349$	−455638.			−0.200243			−0.100121	+	0.994975i	$0.531923\pi$
$350$	−735182.	−	1.42318e6i	−0.320793	−	0.620998i
$351$	−407511.			−0.176552
$352$	340992.	−	590615.i	0.146686	−	0.254067i
$353$	1.81569e6	+	3.14487e6i	0.775543	+	1.34328i	0.934489	+	0.355992i	$0.115857\pi$
$353$	1.81569e6	+	3.14487e6i	0.775543	+	1.34328i	−0.158946	+	0.987287i	$0.550810\pi$
$354$	−369792.	−	640499.i	−0.156837	−	0.271650i
$355$	−114678.	+	198628.i	−0.0482958	+	0.0836508i
$356$	−289920.			−0.121242
$357$	2.02797e6	+	94933.7i	0.842153	+	0.0394230i
$358$	3.15746e6			1.30206
$359$	2.01242e6	−	3.48561e6i	0.824104	−	1.42739i	−0.0784980	−	0.996914i	$-0.525012\pi$
$359$	2.01242e6	−	3.48561e6i	0.824104	−	1.42739i	0.902602	−	0.430476i	$-0.141654\pi$
$360$	15552.0	+	26936.9i	0.00632456	+	0.0109545i
$361$	568725.	+	985061.i	0.229686	+	0.397828i
$362$	955478.	−	1.65494e6i	0.383221	−	0.663758i
$363$	2.54254e6			1.01275
$364$	−626080.	+	975962.i	−0.247672	+	0.386082i
$365$	−423534.			−0.166401
$366$	83340.0	−	144349.i	0.0325200	−	0.0563263i
$367$	−1.28894e6	−	2.23251e6i	−0.499536	−	0.865222i	0.500464	−	0.865757i	$-0.333163\pi$
$367$	−1.28894e6	−	2.23251e6i	−0.499536	−	0.865222i	−1.00000		0.000535822i	$0.999829\pi$
$368$	443904.	+	768864.i	0.170871	+	0.295958i
$369$	197073.	−	341340.i	0.0753462	−	0.130503i
$370$	−75144.0			−0.0285358
$371$	−1.98072e6	+	3.08764e6i	−0.747116	+	1.16464i
$372$	906192.			0.339518
$373$	1.26566e6	−	2.19220e6i	0.471028	−	0.815844i	−0.528423	−	0.848981i	$-0.677216\pi$
$373$	1.26566e6	−	2.19220e6i	0.471028	−	0.815844i	0.999451	+	0.0331372i	$0.0105498\pi$
$374$	−2.31768e6	−	4.01434e6i	−0.856790	−	1.48400i
$375$	−167778.	−	290600.i	−0.0616108	−	0.106713i
$376$	−73920.0	+	128033.i	−0.0269645	+	0.0467039i
$377$	−1.88495e6			−0.683040
$378$	−377622.	−	17677.3i	−0.135934	−	0.00636336i
$379$	−3.06677e6			−1.09669			−0.548344	−	0.836253i	$-0.684742\pi$
$379$	−3.06677e6			−1.09669			−0.548344	+	0.836253i	$0.684742\pi$
$380$	55536.0	−	96191.2i	0.0197295	−	0.0341725i
$381$	−1.42692e6	−	2.47150e6i	−0.503601	−	0.872263i
$382$	−717948.	−	1.24352e6i	−0.251730	−	0.436009i
$383$	1.96260e6	−	3.39932e6i	0.683652	−	1.18412i	−0.290207	−	0.956964i	$-0.593724\pi$
$383$	1.96260e6	−	3.39932e6i	0.683652	−	1.18412i	0.973859	−	0.227155i	$-0.0729425\pi$
$384$	147456.			0.0510310
$385$	237762.	+	460265.i	0.0817505	+	0.158254i
$386$	−727732.			−0.248601
$387$	461984.	−	800179.i	0.156801	−	0.271587i
$388$	−998032.	−	1.72864e6i	−0.336562	−	0.582943i
$389$	2.01334e6	+	3.48722e6i	0.674597	+	1.16844i	0.976587	+	0.215125i	$0.0690158\pi$
$389$	2.01334e6	+	3.48722e6i	0.674597	+	1.16844i	−0.301990	+	0.953311i	$0.597651\pi$
$390$	−60372.0	+	104567.i	−0.0200990	+	0.0348125i
$391$	6.03432e6			1.99612
$392$	−622496.	+	877221.i	−0.204607	+	0.288333i
$393$	−1.39347e6			−0.455110
$394$	−1.43585e6	+	2.48696e6i	−0.465981	+	0.807102i
$395$	−186879.	−	323684.i	−0.0602654	−	0.104383i
$396$	431568.	+	747498.i	0.138297	+	0.239537i
$397$	−2.28720e6	+	3.96155e6i	−0.728329	+	1.26150i	0.229260	+	0.973365i	$0.426370\pi$
$397$	−2.28720e6	+	3.96155e6i	−0.728329	+	1.26150i	−0.957589	+	0.288138i	$0.906964\pi$
$398$	812384.			0.257071
$399$	619574.	+	1.19938e6i	0.194832	+	0.377160i
$400$	−790784.			−0.247120
$401$	1.13472e6	−	1.96539e6i	0.352393	−	0.610363i	−0.634275	−	0.773108i	$-0.718701\pi$
$401$	1.13472e6	−	1.96539e6i	0.352393	−	0.610363i	0.986668	+	0.162744i	$0.0520346\pi$
$402$	337410.	+	584411.i	0.104134	+	0.180365i
$403$	1.75889e6	+	3.04649e6i	0.539482	+	0.934410i
$404$	747120.	−	1.29405e6i	0.227739	−	0.394455i
$405$	−39366.0			−0.0119257
$406$	−1.74670e6	−	81766.7i	−0.525899	−	0.0246185i
$407$	−2.08525e6			−0.623981
$408$	501120.	−	867965.i	0.149036	−	0.258138i
$409$	2.02298e6	+	3.50391e6i	0.597976	+	1.03572i	0.993120	+	0.117105i	$0.0373615\pi$
$409$	2.02298e6	+	3.50391e6i	0.597976	+	1.03572i	−0.395144	+	0.918619i	$0.629305\pi$
$410$	−58392.0	−	101138.i	−0.0171551	−	0.0297135i
$411$	−302994.	+	524801.i	−0.0884768	+	0.153246i
$412$	−2.68370e6			−0.778915
$413$	1.43808e6	−	2.24174e6i	0.414866	−	0.646712i
$414$	−1.12363e6			−0.322198
$415$	239454.	−	414746.i	0.0682499	−	0.118212i
$416$	286208.	+	495727.i	0.0810865	+	0.140446i
$417$	1.64347e6	+	2.84657e6i	0.462829	+	0.801644i
$418$	1.54112e6	−	2.66931e6i	0.431417	−	0.747236i
$419$	−3.91281e6			−1.08881			−0.544407	−	0.838821i	$-0.683245\pi$
$419$	−3.91281e6			−1.08881			−0.544407	+	0.838821i	$0.683245\pi$
$420$	−60480.0	+	94279.0i	−0.0167297	+	0.0260790i
$421$	−2.78086e6			−0.764671			−0.382335	−	0.924024i	$-0.624880\pi$
$421$	−2.78086e6			−0.764671			−0.382335	+	0.924024i	$0.624880\pi$
$422$	−2.34196e6	+	4.05639e6i	−0.640174	+	1.10881i
$423$	−93555.0	−	162042.i	−0.0254224	−	0.0440328i
$424$	905472.	+	1.56832e6i	0.244602	+	0.423663i
$425$	−2.68743e6	+	4.65477e6i	−0.721714	+	1.25004i
$426$	−1.37614e6			−0.367398
$427$	599585.	+	28067.9i	0.159141	+	0.00744972i
$428$	1.10688e6			0.292073
$429$	−1.67532e6	+	2.90174e6i	−0.439496	+	0.761230i
$430$	−136884.	−	237090.i	−0.0357011	−	0.0618361i
$431$	2.19104e6	+	3.79498e6i	0.568141	+	0.984049i	0.996750	+	0.0805589i	$0.0256705\pi$
$431$	2.19104e6	+	3.79498e6i	0.568141	+	0.984049i	−0.428609	+	0.903490i	$0.640996\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	1.24946e6			0.320261			0.160130	−	0.987096i	$-0.448809\pi$
$433$	1.24946e6			0.320261			0.160130	+	0.987096i	$0.448809\pi$
$434$	1.49773e6	+	2.89935e6i	0.381690	+	0.738883i
$435$	−182088.			−0.0461379
$436$	1.75647e6	−	3.04230e6i	0.442512	−	0.766453i
$437$	2.00624e6	+	3.47491e6i	0.502550	+	0.870441i
$438$	−1.27060e6	−	2.20075e6i	−0.316464	−	0.548132i
$439$	3.37210e6	−	5.84066e6i	0.835102	−	1.44644i	−0.0588449	−	0.998267i	$-0.518742\pi$
$439$	3.37210e6	−	5.84066e6i	0.835102	−	1.44644i	0.893947	−	0.448172i	$-0.147925\pi$
$440$	255744.			0.0629758
$441$	−567567.	−	1.23741e6i	−0.138970	−	0.302983i
$442$	3.89064e6			0.947252
$443$	−239448.	+	414736.i	−0.0579698	+	0.100407i	−0.893554	−	0.448956i	$-0.851796\pi$
$443$	−239448.	+	414736.i	−0.0579698	+	0.100407i	0.835584	+	0.549362i	$0.185129\pi$
$444$	−225432.	−	390460.i	−0.0542698	−	0.0939980i
$445$	−54360.0	−	94154.3i	−0.0130131	−	0.0225393i
$446$	−2.49270e6	+	4.31749e6i	−0.593381	+	1.02777i
$447$	−1.51254e6			−0.358045
$448$	243712.	+	471783.i	0.0573696	+	0.111057i
$449$	724506.			0.169600			0.0848001	−	0.996398i	$-0.472975\pi$
$449$	724506.			0.169600			0.0848001	+	0.996398i	$0.472975\pi$
$450$	500418.	−	866749.i	0.116493	−	0.201773i
$451$	−1.62038e6	−	2.80658e6i	−0.375124	−	0.649734i
$452$	314832.	+	545305.i	0.0724824	+	0.125543i
$453$	−690912.	+	1.19669e6i	−0.158189	+	0.273992i
$454$	−3.67577e6			−0.836967
$455$	−434343.	−	20332.5i	−0.0983568	−	0.00460430i
$456$	666432.			0.150087
$457$	1.16978e6	−	2.02612e6i	0.262008	−	0.453811i	−0.704768	−	0.709438i	$-0.748949\pi$
$457$	1.16978e6	−	2.02612e6i	0.262008	−	0.453811i	0.966775	+	0.255627i	$0.0822820\pi$
$458$	−2.40750e6	−	4.16991e6i	−0.536293	−	0.928887i
$459$	634230.	+	1.09852e6i	0.140513	+	0.243375i
$460$	−166464.	+	288324.i	−0.0366797	+	0.0635311i
$461$	2.98247e6			0.653617			0.326809	−	0.945091i	$-0.394027\pi$
$461$	2.98247e6			0.653617			0.326809	+	0.945091i	$0.394027\pi$
$462$	−1.67832e6	+	2.61624e6i	−0.365822	+	0.570260i
$463$	4.28423e6			0.928795			0.464398	−	0.885627i	$-0.346271\pi$
$463$	4.28423e6			0.928795			0.464398	+	0.885627i	$0.346271\pi$
$464$	−431616.	+	747581.i	−0.0930685	+	0.161199i
$465$	169911.	+	294294.i	0.0364409	+	0.0631175i
$466$	1.83812e6	+	3.18372e6i	0.392112	+	0.679158i
$467$	2.87018e6	−	4.97129e6i	0.608998	−	1.05482i	−0.382407	−	0.923994i	$-0.624905\pi$
$467$	2.87018e6	−	4.97129e6i	0.608998	−	1.05482i	0.991406	−	0.130822i	$-0.0417618\pi$
$468$	−724464.			−0.152898
$469$	−1.31215e6	+	2.04544e6i	−0.275455	+	0.429393i
$470$	−55440.0			−0.0115765
$471$	−910881.	+	1.57769e6i	−0.189195	+	0.327695i
$472$	−657408.	−	1.13866e6i	−0.135825	−	0.235256i
$473$	−3.79853e6	−	6.57925e6i	−0.780662	−	1.35215i
$474$	1.12127e6	−	1.94210e6i	0.229227	−	0.397033i
$475$	−3.57397e6			−0.726804
$476$	3.60528e6	+	168771.i	0.729326	+	0.0341413i
$477$	−2.29198e6			−0.461226
$478$	1.25068e6	−	2.16623e6i	0.250366	−	0.433646i
$479$	−1.32526e6	−	2.29541e6i	−0.263913	−	0.457111i	0.703365	−	0.710829i	$-0.251680\pi$
$479$	−1.32526e6	−	2.29541e6i	−0.263913	−	0.457111i	−0.967278	+	0.253718i	$0.918347\pi$
$480$	27648.0	+	47887.7i	0.00547723	+	0.00948683i
$481$	875114.	−	1.51574e6i	0.172465	−	0.298719i
$482$	5.01529e6			0.983282
$483$	−1.85711e6	−	3.59504e6i	−0.362219	−	0.701191i
$484$	4.52008e6			0.877067
$485$	374262.	−	648241.i	0.0722473	−	0.125136i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	−1.40277e6	−	2.42967e6i	−0.268018	−	0.464221i	0.700332	−	0.713817i	$-0.253035\pi$
$487$	−1.40277e6	−	2.42967e6i	−0.268018	−	0.464221i	−0.968350	+	0.249597i	$0.919702\pi$
$488$	148160.	−	256621.i	0.0281632	−	0.0487800i
$489$	−1.61788e6			−0.305966
$490$	−401604.	−	37682.5i	−0.0755628	−	0.00709005i
$491$	−4.68450e6			−0.876919			−0.438460	−	0.898751i	$-0.644476\pi$
$491$	−4.68450e6			−0.876919			−0.438460	+	0.898751i	$0.644476\pi$
$492$	350352.	−	606827.i	0.0652517	−	0.113019i
$493$	2.93364e6	+	5.08121e6i	0.543613	+	0.941565i
$494$	1.29353e6	+	2.24045e6i	0.238483	+	0.413065i
$495$	−161838.	+	280312.i	−0.0296871	+	0.0514195i
$496$	1.61101e6			0.294031
$497$	−2.27445e6	−	4.40292e6i	−0.413033	−	0.799558i
$498$	2.87345e6			0.519194
$499$	−737876.	+	1.27804e6i	−0.132658	+	0.229770i	−0.924700	−	0.380696i	$-0.875684\pi$
$499$	−737876.	+	1.27804e6i	−0.132658	+	0.229770i	0.792043	+	0.610466i	$0.209018\pi$
$500$	−298272.	−	516622.i	−0.0533565	−	0.0924162i
$501$	−977859.	−	1.69370e6i	−0.174053	−	0.301469i
$502$	3.02666e6	−	5.24234e6i	0.536050	−	0.928465i
$503$	63606.0			0.0112093			0.00560465	−	0.999984i	$-0.498216\pi$
$503$	63606.0			0.0112093			0.00560465	+	0.999984i	$0.498216\pi$
$504$	−671328.	−	31426.3i	−0.117722	−	0.00551083i
$505$	560340.			0.0977740
$506$	−4.61938e6	+	8.00099e6i	−0.802060	+	1.38921i
$507$	264654.	+	458394.i	0.0457255	+	0.0791989i
$508$	−2.53674e6	−	4.39377e6i	−0.436131	−	0.755402i
$509$	−3.10578e6	+	5.37937e6i	−0.531345	+	0.920317i	0.467986	+	0.883736i	$0.344980\pi$
$509$	−3.10578e6	+	5.37937e6i	−0.531345	+	0.920317i	−0.999331	+	0.0365806i	$0.988353\pi$
$510$	375840.			0.0639849
$511$	4.94123e6	−	7.70262e6i	0.837111	−	1.30493i
$512$	262144.			0.0441942
$513$	−421726.	+	730452.i	−0.0707518	+	0.122546i
$514$	3.10986e6	+	5.38644e6i	0.519198	+	0.899277i
$515$	−503193.	−	871556.i	−0.0836020	−	0.144803i
$516$	821304.	−	1.42254e6i	0.135794	−	0.235202i
$517$	−1.53846e6			−0.253139
$518$	876680.	−	1.36661e6i	0.143554	−	0.223779i
$519$	−665820.			−0.108502
$520$	−107328.	+	185898.i	−0.0174062	+	0.0301485i
$521$	−706026.	−	1.22287e6i	−0.113953	−	0.197373i	0.803408	−	0.595429i	$-0.203018\pi$
$521$	−706026.	−	1.22287e6i	−0.113953	−	0.197373i	−0.917361	+	0.398057i	$0.869685\pi$
$522$	−546264.	−	946157.i	−0.0877458	−	0.151980i
$523$	−2.61467e6	+	4.52875e6i	−0.417987	+	0.723976i	−0.995737	−	0.0922386i	$-0.970598\pi$
$523$	−2.61467e6	+	4.52875e6i	−0.417987	+	0.723976i	0.577749	+	0.816214i	$0.303931\pi$
$524$	−2.47728e6			−0.394137
$525$	3.60023e6	+	168535.i	0.570075	+	0.0266865i
$526$	−4.46126e6			−0.703062
$527$	5.47491e6	−	9.48282e6i	0.858718	−	1.48734i
$528$	767232.	+	1.32888e6i	0.119768	+	0.207445i
$529$	−2.79534e6	−	4.84167e6i	−0.434306	−	0.752240i
$530$	−339552.	+	588121.i	−0.0525069	+	0.0909447i
$531$	1.66406e6			0.256114
$532$	1.10146e6	+	2.13224e6i	0.168730	+	0.326630i
$533$	2.72009e6			0.414730
$534$	326160.	−	564926.i	0.0494968	−	0.0857311i
$535$	207540.	+	359470.i	0.0313485	+	0.0542973i
$536$	599840.	+	1.03895e6i	0.0901827	+	0.156201i
$537$	−3.55215e6	+	6.15250e6i	−0.531564	+	0.920695i
$538$	142680.			0.0212524
$539$	−1.11445e7	−	1.04569e6i	−1.65230	−	0.155035i
$540$	−69984.0			−0.0103280
$541$	−2.20686e6	+	3.82240e6i	−0.324177	+	0.561491i	−0.981345	−	0.192253i	$-0.938421\pi$
$541$	−2.20686e6	+	3.82240e6i	−0.324177	+	0.561491i	0.657169	+	0.753744i	$0.271754\pi$
$542$	585536.	+	1.01418e6i	0.0856161	+	0.148291i
$543$	2.14983e6	+	3.72361e6i	0.312899	+	0.541956i
$544$	890880.	−	1.54305e6i	0.129069	−	0.223554i
$545$	1.31735e6			0.189981
$546$	−1.19738e6	−	2.31791e6i	−0.171890	−	0.332748i
$547$	−1.19038e7			−1.70105			−0.850523	−	0.525938i	$-0.823714\pi$
$547$	−1.19038e7			−1.70105			−0.850523	+	0.525938i	$0.823714\pi$
$548$	−538656.	+	932980.i	−0.0766232	+	0.132715i
$549$	187515.	+	324786.i	0.0265525	+	0.0459903i
$550$	−4.11455e6	−	7.12661e6i	−0.579983	−	1.00456i
$551$	−1.95070e6	+	3.37871e6i	−0.273723	+	0.474103i
$552$	−1.99757e6			−0.279032
$553$	8.06694e6	+	377631.i	1.12175	+	0.0525116i
$554$	3.45285e6			0.477973
$555$	84537.0	−	146422.i	0.0116497	−	0.0201779i
$556$	2.92172e6	+	5.06057e6i	0.400822	+	0.694244i
$557$	−6.45665e6	−	1.11832e7i	−0.881798	−	1.52732i	−0.849340	−	0.527847i	$-0.823000\pi$
$557$	−6.45665e6	−	1.11832e7i	−0.881798	−	1.52732i	−0.0324587	−	0.999473i	$-0.510334\pi$
$558$	−1.01947e6	+	1.76577e6i	−0.138608	+	0.240076i
$559$	6.37651e6			0.863085
$560$	−107520.	+	167607.i	−0.0144884	+	0.0225851i
$561$	1.04296e7			1.39913
$562$	−2.94221e6	+	5.09605e6i	−0.392946	+	0.680602i
$563$	5.68492e6	+	9.84657e6i	0.755881	+	1.30922i	0.944935	+	0.327257i	$0.106124\pi$
$563$	5.68492e6	+	9.84657e6i	0.755881	+	1.30922i	−0.189055	+	0.981967i	$0.560542\pi$
$564$	−166320.	−	288075.i	−0.0220164	−	0.0381336i
$565$	−118062.	+	204489.i	−0.0155593	+	0.0269494i
$566$	2.75536e6			0.361525
$567$	459270.	−	715931.i	0.0599944	−	0.0935220i
$568$	−2.44646e6			−0.318176
$569$	2.84898e6	−	4.93457e6i	0.368900	−	0.638953i	−0.620494	−	0.784211i	$-0.713068\pi$
$569$	2.84898e6	−	4.93457e6i	0.368900	−	0.638953i	0.989394	+	0.145258i	$0.0464013\pi$
$570$	124956.	+	216430.i	0.0161091	+	0.0279017i
$571$	3.52110e6	+	6.09873e6i	0.451948	+	0.782797i	0.998507	−	0.0546236i	$-0.0173959\pi$
$571$	3.52110e6	+	6.09873e6i	0.451948	+	0.782797i	−0.546559	+	0.837421i	$0.684063\pi$
$572$	−2.97835e6	+	5.15866e6i	−0.380615	+	0.659245i
$573$	3.23077e6			0.411073
$574$	2.52059e6	+	117994.i	0.319317	+	0.0149479i
$575$	1.07127e7			1.35122
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	1.29098e6	+	2.23605e6i	0.161429	+	0.279603i	0.935381	−	0.353641i	$-0.115056\pi$
$577$	1.29098e6	+	2.23605e6i	0.161429	+	0.279603i	−0.773952	+	0.633244i	$0.781723\pi$
$578$	−3.21549e6	−	5.56939e6i	−0.400338	−	0.693406i
$579$	818698.	−	1.41803e6i	0.101491	−	0.175788i
$580$	−323712.			−0.0399566
$581$	4.74917e6	+	9.19355e6i	0.583684	+	1.12991i
$582$	4.49114e6			0.549604
$583$	−9.42257e6	+	1.63204e7i	−1.14815	+	1.98865i
$584$	−2.25885e6	−	3.91244e6i	−0.274066	−	0.474696i
$585$	−135837.	−	235277.i	−0.0164107	−	0.0284243i
$586$	−1.44566e6	+	2.50396e6i	−0.173910	+	0.301220i
$587$	4.69459e6			0.562345			0.281172	−	0.959657i	$-0.409277\pi$
$587$	4.69459e6			0.562345			0.281172	+	0.959657i	$0.409277\pi$
$588$	−1.00901e6	−	2.19984e6i	−0.120351	−	0.262391i
$589$	7.28100e6			0.864774
$590$	246528.	−	426999.i	0.0291566	−	0.0505006i
$591$	−3.23066e6	−	5.59566e6i	−0.380472	−	0.658996i
$592$	−400768.	−	694151.i	−0.0469990	−	0.0814047i
$593$	−6.71175e6	+	1.16251e7i	−0.783789	+	1.35756i	0.145931	+	0.989295i	$0.453382\pi$
$593$	−6.71175e6	+	1.16251e7i	−0.783789	+	1.35756i	−0.929720	+	0.368268i	$0.879951\pi$
$594$	−1.94206e6			−0.225837
$595$	621180.	+	1.20249e6i	0.0719325	+	0.139248i
$596$	−2.68896e6			−0.310076
$597$	−913932.	+	1.58298e6i	−0.104949	+	0.181777i
$598$	−3.87722e6	−	6.71555e6i	−0.443372	−	0.767942i
$599$	−2.52301e6	−	4.36997e6i	−0.287310	−	0.497636i	0.685856	−	0.727737i	$-0.259428\pi$
$599$	−2.52301e6	−	4.36997e6i	−0.287310	−	0.497636i	−0.973167	+	0.230101i	$0.926094\pi$
$600$	889632.	−	1.54089e6i	0.100886	−	0.174740i
$601$	−1.06391e7			−1.20148			−0.600742	−	0.799443i	$-0.705128\pi$
$601$	−1.06391e7			−1.20148			−0.600742	+	0.799443i	$0.705128\pi$
$602$	5.90883e6	+	276605.i	0.664523	+	0.0311078i
$603$	−1.51834e6			−0.170050
$604$	−1.22829e6	+	2.12746e6i	−0.136996	+	0.237284i
$605$	847515.	+	1.46794e6i	0.0941367	+	0.163050i
$606$	1.68102e6	+	2.91161e6i	0.185948	+	0.322071i
$607$	−708041.	+	1.22636e6i	−0.0779986	+	0.135098i	−0.902386	−	0.430928i	$-0.858186\pi$
$607$	−708041.	+	1.22636e6i	−0.0779986	+	0.135098i	0.824388	+	0.566026i	$0.191520\pi$
$608$	1.18477e6			0.129979
$609$	2.12436e6	−	3.31155e6i	0.232105	−	0.361816i
$610$	111120.			0.0120912
$611$	645645.	−	1.11829e6i	0.0699666	−	0.121186i
$612$	1.12752e6	+	1.95292e6i	0.121687	+	0.210769i
$613$	−4.73152e6	−	8.19523e6i	−0.508568	−	0.880866i	−0.999951	−	0.00992215i	$-0.996842\pi$
$613$	−4.73152e6	−	8.19523e6i	−0.508568	−	0.880866i	0.491383	−	0.870944i	$-0.336492\pi$
$614$	40250.0	−	69715.0i	0.00430869	−	0.00746286i
$615$	262764.			0.0280142
$616$	−2.98368e6	+	4.65110e6i	−0.316811	+	0.493860i
$617$	1.29388e7			1.36830			0.684148	−	0.729343i	$-0.260174\pi$
$617$	1.29388e7			1.36830			0.684148	+	0.729343i	$0.260174\pi$
$618$	3.01916e6	−	5.22934e6i	0.317991	−	0.550776i
$619$	1.90188e6	+	3.29415e6i	0.199506	+	0.345555i	0.948368	−	0.317171i	$-0.102733\pi$
$619$	1.90188e6	+	3.29415e6i	0.199506	+	0.345555i	−0.748862	+	0.662726i	$0.769400\pi$
$620$	302064.	+	523190.i	0.0315587	+	0.0546614i
$621$	1.26409e6	−	2.18946e6i	0.131537	−	0.227829i
$622$	−6.97423e6			−0.722804
$623$	2.34654e6	+	109847.i	0.242219	+	0.0113388i
$624$	−1.28794e6			−0.132414
$625$	−4.71471e6	+	8.16612e6i	−0.482786	+	0.836210i
$626$	−3.61709e6	−	6.26498e6i	−0.368912	−	0.638975i
$627$	3.46753e6	+	6.00594e6i	0.352250	+	0.610115i
$628$	−1.61934e6	+	2.80479e6i	−0.163848	+	0.283792i
$629$	−5.44794e6			−0.549042
$630$	−115668.	−	223913.i	−0.0116108	−	0.0224764i
$631$	−9.17498e6			−0.917343			−0.458671	−	0.888606i	$-0.651674\pi$
$631$	−9.17498e6			−0.917343			−0.458671	+	0.888606i	$0.651674\pi$
$632$	1.99338e6	−	3.45263e6i	0.198516	−	0.343841i
$633$	−5.26941e6	−	9.12689e6i	−0.522700	−	0.905343i
$634$	−2.04710e6	−	3.54569e6i	−0.202263	−	0.350330i
$635$	951279.	−	1.64766e6i	0.0936211	−	0.162156i
$636$	−4.07462e6			−0.399434
$637$	5.43711e6	−	7.66198e6i	0.530909	−	0.748157i
$638$	−8.98301e6			−0.873716
$639$	1.54815e6	−	2.68148e6i	0.149990	−	0.259790i
$640$	49152.0	+	85133.8i	0.00474342	+	0.00821584i
$641$	−5.12269e6	−	8.87275e6i	−0.492439	−	0.852930i	0.507523	−	0.861638i	$-0.330561\pi$
$641$	−5.12269e6	−	8.87275e6i	−0.492439	−	0.852930i	−0.999962	+	0.00870851i	$0.997228\pi$
$642$	−1.24524e6	+	2.15682e6i	−0.119238	+	0.206527i
$643$	−5.72346e6			−0.545922			−0.272961	−	0.962025i	$-0.588003\pi$
$643$	−5.72346e6			−0.545922			−0.272961	+	0.962025i	$0.588003\pi$
$644$	−3.30154e6	−	6.39118e6i	−0.313691	−	0.607249i
$645$	615978.			0.0582996
$646$	4.02636e6	−	6.97386e6i	0.379604	−	0.657494i
$647$	4.99397e6	+	8.64981e6i	0.469013	+	0.812355i	0.999373	−	0.0354179i	$-0.0112762\pi$
$647$	4.99397e6	+	8.64981e6i	0.469013	+	0.812355i	−0.530359	+	0.847773i	$0.677943\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	6.84115e6	−	1.18492e7i	0.637555	−	1.10428i
$650$	6.90700e6			0.641219
$651$	−7.33449e6	−	343344.i	−0.678293	−	0.0317524i
$652$	−2.87622e6			−0.264974
$653$	599439.	−	1.03826e6i	0.0550126	−	0.0952846i	−0.837208	−	0.546885i	$-0.815813\pi$
$653$	599439.	−	1.03826e6i	0.0550126	−	0.0952846i	0.892220	+	0.451601i	$0.149147\pi$
$654$	3.95206e6	+	6.84517e6i	0.361309	+	0.625806i
$655$	−464490.	−	804520.i	−0.0423032	−	0.0732713i
$656$	622848.	−	1.07880e6i	0.0565096	−	0.0978776i
$657$	5.71771e6			0.516783
$658$	646800.	−	1.00826e6i	0.0582378	−	0.0907838i
$659$	1.18065e7			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$659$	1.18065e7			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$660$	−287712.	+	498332.i	−0.0257098	+	0.0445306i
$661$	−2.36020e6	−	4.08798e6i	−0.210109	−	0.363919i	0.741640	−	0.670799i	$-0.234049\pi$
$661$	−2.36020e6	−	4.08798e6i	−0.210109	−	0.363919i	−0.951748	+	0.306879i	$0.900715\pi$
$662$	2.01507e6	+	3.49020e6i	0.178708	+	0.309532i
$663$	−4.37697e6	+	7.58113e6i	−0.386714	+	0.669808i
$664$	5.10835e6			0.449636
$665$	−485940.	+	757505.i	−0.0426117	+	0.0664250i
$666$	1.01444e6			0.0886222
$667$	5.84705e6	−	1.01274e7i	0.508888	−	0.881420i
$668$	−1.73842e6	−	3.01102e6i	−0.150734	−	0.261080i
$669$	−5.60858e6	−	9.71435e6i	−0.484493	−	0.839167i
$670$	−224940.	+	389608.i	−0.0193589	+	0.0335305i
$671$	3.08358e6			0.264392
$672$	−1.19347e6	−	55869.0i	−0.101950	−	0.00477252i
$673$	−8.70826e6			−0.741129			−0.370564	−	0.928807i	$-0.620836\pi$
$673$	−8.70826e6			−0.741129			−0.370564	+	0.928807i	$0.620836\pi$
$674$	3.13141e6	−	5.42377e6i	0.265516	−	0.459887i
$675$	1.12594e6	+	1.95019e6i	0.0951165	+	0.164747i
$676$	470496.	+	814923.i	0.0395995	+	0.0685883i
$677$	−2.55553e6	+	4.42630e6i	−0.214293	+	0.371167i	−0.953054	−	0.302801i	$-0.902078\pi$
$677$	−2.55553e6	+	4.42630e6i	−0.214293	+	0.371167i	0.738760	+	0.673968i	$0.235412\pi$
$678$	−1.41674e6			−0.118363
$679$	7.42286e6	+	1.43693e7i	0.617870	+	1.19609i
$680$	668160.			0.0554126
$681$	4.13524e6	−	7.16244e6i	0.341690	−	0.591825i
$682$	8.38228e6	+	1.45185e7i	0.690083	+	1.19526i
$683$	8.85989e6	+	1.53458e7i	0.726736	+	1.25874i	0.958256	+	0.285913i	$0.0922968\pi$
$683$	8.85989e6	+	1.53458e7i	0.726736	+	1.25874i	−0.231520	+	0.972830i	$0.574370\pi$
$684$	−749736.	+	1.29858e6i	−0.0612729	+	0.106128i
$685$	−403992.			−0.0328962
$686$	5.37069e6	−	6.86416e6i	0.435733	−	0.556899i
$687$	1.08337e7			0.875763
$688$	1.46010e6	−	2.52896e6i	0.117601	−	0.203691i
$689$	−7.90873e6	−	1.36983e7i	−0.634686	−	1.09931i
$690$	−374544.	−	648729.i	−0.0299488	−	0.0518729i
$691$	1.12997e7	−	1.95716e7i	0.900265	−	1.55931i	0.0731160	−	0.997323i	$-0.476706\pi$
$691$	1.12997e7	−	1.95716e7i	0.900265	−	1.55931i	0.827149	−	0.561982i	$-0.189961\pi$
$692$	−1.18368e6			−0.0939656
$693$	−3.20979e6	−	6.21357e6i	−0.253889	−	0.491483i
$694$	3.02914e6			0.238737
$695$	−1.09564e6	+	1.89771e6i	−0.0860415	+	0.149028i
$696$	−971136.	−	1.68206e6i	−0.0759901	−	0.131619i
$697$	−4.23342e6	−	7.33250e6i	−0.330073	−	0.571702i
$698$	911276.	−	1.57838e6i	0.0707964	−	0.122623i
$699$	−8.27156e6			−0.640316
$700$	6.40041e6	+	299617.i	0.493699	+	0.0231111i
$701$	−818148.			−0.0628835			−0.0314418	−	0.999506i	$-0.510010\pi$
$701$	−818148.			−0.0628835			−0.0314418	+	0.999506i	$0.510010\pi$
$702$	815022.	−	1.41166e6i	0.0624204	−	0.108115i
$703$	−1.81128e6	−	3.13724e6i	−0.138229	−	0.239419i
$704$	1.36397e6	+	2.36246e6i	0.103722	+	0.179652i
$705$	62370.0	−	108028.i	0.00472610	−	0.00818585i
$706$	−1.45255e7			−1.09678
$707$	−6.53730e6	+	1.01906e7i	−0.491869	+	0.766749i
$708$	2.95834e6			0.221801
$709$	2.54591e6	−	4.40965e6i	0.190208	−	0.329449i	−0.755111	−	0.655597i	$-0.772417\pi$
$709$	2.54591e6	−	4.40965e6i	0.190208	−	0.329449i	0.945319	+	0.326147i	$0.105751\pi$
$710$	−458712.	−	794512.i	−0.0341503	−	0.0591500i
$711$	2.52287e6	+	4.36973e6i	0.187163	+	0.324176i
$712$	579840.	−	1.00431e6i	0.0428655	−	0.0742453i
$713$	−2.18241e7			−1.60773
$714$	−4.38480e6	+	6.83523e6i	−0.321888	+	0.501773i
$715$	−2.23376e6			−0.163408
$716$	−6.31493e6	+	1.09378e7i	−0.460348	+	0.797345i
$717$	2.81402e6	+	4.87403e6i	0.204423	+	0.354071i
$718$	8.04967e6	+	1.39424e7i	0.582730	+	1.00932i
$719$	240429.	−	416435.i	0.0173446	−	0.0300418i	−0.857223	−	0.514946i	$-0.827812\pi$
$719$	240429.	−	416435.i	0.0173446	−	0.0300418i	0.874567	+	0.484904i	$0.161145\pi$
$720$	−124416.			−0.00894427
$721$	2.17212e7	+	1.01682e6i	1.55613	+	0.0728457i
$722$	−4.54980e6			−0.324825
$723$	−5.64220e6	+	9.77258e6i	−0.401423	+	0.695286i
$724$	3.82191e6	+	6.61975e6i	0.270978	+	0.469348i
$725$	5.20805e6	+	9.02061e6i	0.367985	+	0.637369i
$726$	−5.08509e6	+	8.80763e6i	−0.358061	+	0.620180i
$727$	−1.40783e7			−0.987905			−0.493952	−	0.869489i	$-0.664448\pi$
$727$	−1.40783e7			−0.987905			−0.493952	+	0.869489i	$0.664448\pi$
$728$	−2.12867e6	−	4.12073e6i	−0.148861	−	0.288168i
$729$	531441.			0.0370370
$730$	847068.	−	1.46716e6i	0.0588317	−	0.101899i
$731$	−9.92409e6	−	1.71890e7i	−0.686906	−	1.18976i
$732$	333360.	+	577396.i	0.0229951	+	0.0398287i
$733$	−1.01966e6	+	1.76610e6i	−0.0700964	+	0.121411i	−0.898943	−	0.438065i	$-0.855664\pi$
$733$	−1.01966e6	+	1.76610e6i	−0.0700964	+	0.121411i	0.828847	+	0.559475i	$0.188997\pi$
$734$	1.03115e7			0.706450
$735$	525231.	−	740156.i	0.0358618	−	0.0505364i
$736$	−3.55123e6			−0.241649
$737$	−6.24209e6	+	1.08116e7i	−0.423312	+	0.733199i
$738$	788292.	+	1.36536e6i	0.0532778	+	0.0922798i
$739$	8.24785e6	+	1.42857e7i	0.555558	+	0.962255i	0.997860	+	0.0653888i	$0.0208288\pi$
$739$	8.24785e6	+	1.42857e7i	0.555558	+	0.962255i	−0.442302	+	0.896866i	$0.645838\pi$
$740$	150288.	−	260306.i	0.0100889	−	0.0174745i
$741$	−5.82087e6			−0.389441
$742$	−6.73445e6	−	1.30367e7i	−0.449047	−	0.869276i
$743$	−2.38121e7			−1.58243			−0.791217	−	0.611536i	$-0.790552\pi$
$743$	−2.38121e7			−1.58243			−0.791217	+	0.611536i	$0.790552\pi$
$744$	−1.81238e6	+	3.13914e6i	−0.120038	+	0.207911i
$745$	−504180.	−	873265.i	−0.0332809	−	0.0576442i
$746$	5.06266e6	+	8.76878e6i	0.333067	+	0.576889i
$747$	−3.23263e6	+	5.59908e6i	−0.211960	+	0.367126i
$748$	1.85414e7			1.21168
$749$	−8.95881e6	−	419381.i	−0.583507	−	0.0273152i
$750$	1.34222e6			0.0871308
$751$	−962480.	+	1.66707e6i	−0.0622719	+	0.107858i	−0.895481	−	0.445101i	$-0.853168\pi$
$751$	−962480.	+	1.66707e6i	−0.0622719	+	0.107858i	0.833209	+	0.552959i	$0.186501\pi$
$752$	−295680.	−	512133.i	−0.0190668	−	0.0330246i
$753$	6.80999e6	+	1.17953e7i	0.437683	+	0.758089i
$754$	3.76990e6	−	6.52965e6i	0.241491	−	0.418275i
$755$	−921216.			−0.0588158
$756$	816480.	−	1.27277e6i	0.0519566	−	0.0809924i
$757$	8.98092e6			0.569615			0.284807	−	0.958585i	$-0.408070\pi$
$757$	8.98092e6			0.569615			0.284807	+	0.958585i	$0.408070\pi$
$758$	6.13354e6	−	1.06236e7i	0.387738	−	0.671581i
$759$	−1.03936e7	−	1.80022e7i	−0.654879	−	1.13428i
$760$	222144.	+	384765.i	0.0139508	+	0.0241636i
$761$	−7.29955e6	+	1.26432e7i	−0.456914	+	0.791398i	−0.998796	−	0.0490566i	$-0.984379\pi$
$761$	−7.29955e6	+	1.26432e7i	−0.456914	+	0.791398i	0.541882	+	0.840454i	$0.317712\pi$

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(3.00000 - 5.19615i) q^{5} +36.0000 q^{6} +(59.5000 + 115.181i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(3.00000 - 5.19615i) q^{5} +36.0000 q^{6} +(59.5000 + 115.181i) q^{7} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(12.0000 + 20.7846i) q^{10} +(333.000 + 576.773i) q^{11} +(-72.0000 + 124.708i) q^{12} -559.000 q^{13} +(-518.000 - 24.2487i) q^{14} -54.0000 q^{15} +(-128.000 + 221.703i) q^{16} +(870.000 + 1506.88i) q^{17} +(-162.000 - 280.592i) q^{18} +(-578.500 + 1001.99i) q^{19} -96.0000 q^{20} +(630.000 - 982.073i) q^{21} -2664.00 q^{22} +(1734.00 - 3003.38i) q^{23} +(-288.000 - 498.831i) q^{24} +(1544.50 + 2675.15i) q^{25} +(1118.00 - 1936.43i) q^{26} +729.000 q^{27} +(1120.00 - 1745.91i) q^{28} +3372.00 q^{29} +(108.000 - 187.061i) q^{30} +(-3146.50 - 5449.90i) q^{31} +(-512.000 - 886.810i) q^{32} +(2997.00 - 5190.96i) q^{33} -6960.00 q^{34} +(777.000 + 36.3731i) q^{35} +1296.00 q^{36} +(-1565.50 + 2711.53i) q^{37} +(-2314.00 - 4007.97i) q^{38} +(2515.50 + 4356.97i) q^{39} +(192.000 - 332.554i) q^{40} -4866.00 q^{41} +(2142.00 + 4146.53i) q^{42} -11407.0 q^{43} +(5328.00 - 9228.37i) q^{44} +(243.000 + 420.888i) q^{45} +(6936.00 + 12013.5i) q^{46} +(-1155.00 + 2000.52i) q^{47} +2304.00 q^{48} +(-9726.50 + 13706.6i) q^{49} -12356.0 q^{50} +(7830.00 - 13562.0i) q^{51} +(4472.00 + 7745.73i) q^{52} +(14148.0 + 24505.1i) q^{53} +(-1458.00 + 2525.33i) q^{54} +3996.00 q^{55} +(3808.00 + 7371.61i) q^{56} +10413.0 q^{57} +(-6744.00 + 11681.0i) q^{58} +(-10272.0 - 17791.6i) q^{59} +(432.000 + 748.246i) q^{60} +(2315.00 - 4009.70i) q^{61} +25172.0 q^{62} +(-10489.5 - 491.036i) q^{63} +4096.00 q^{64} +(-1677.00 + 2904.65i) q^{65} +(11988.0 + 20763.8i) q^{66} +(9372.50 + 16233.6i) q^{67} +(13920.0 - 24110.1i) q^{68} -31212.0 q^{69} +(-1680.00 + 2618.86i) q^{70} -38226.0 q^{71} +(-2592.00 + 4489.48i) q^{72} +(-35294.5 - 61131.9i) q^{73} +(-6262.00 - 10846.1i) q^{74} +(13900.5 - 24076.4i) q^{75} +18512.0 q^{76} +(-46620.0 + 72673.4i) q^{77} -20124.0 q^{78} +(31146.5 - 53947.3i) q^{79} +(768.000 + 1330.22i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(9732.00 - 16856.3i) q^{82} +79818.0 q^{83} +(-18648.0 - 872.954i) q^{84} +10440.0 q^{85} +(22814.0 - 39515.0i) q^{86} +(-15174.0 - 26282.1i) q^{87} +(21312.0 + 36913.5i) q^{88} +(9060.00 - 15692.4i) q^{89} -1944.00 q^{90} +(-33260.5 - 64386.4i) q^{91} -55488.0 q^{92} +(-28318.5 + 49049.1i) q^{93} +(-4620.00 - 8002.07i) q^{94} +(3471.00 + 6011.95i) q^{95} +(-4608.00 + 7981.29i) q^{96} +124754. q^{97} +(-28028.0 - 61106.8i) q^{98} -53946.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} + 6 q^{5} + 72 q^{6} + 119 q^{7} + 128 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 + 6 * q^5 + 72 * q^6 + 119 * q^7 + 128 * q^8 - 81 * q^9	\( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} + 6 q^{5} + 72 q^{6} + 119 q^{7} + 128 q^{8} - 81 q^{9} + 24 q^{10} + 666 q^{11} - 144 q^{12} - 1118 q^{13} - 1036 q^{14} - 108 q^{15} - 256 q^{16} + 1740 q^{17} - 324 q^{18} - 1157 q^{19} - 192 q^{20} + 1260 q^{21} - 5328 q^{22} + 3468 q^{23} - 576 q^{24} + 3089 q^{25} + 2236 q^{26} + 1458 q^{27} + 2240 q^{28} + 6744 q^{29} + 216 q^{30} - 6293 q^{31} - 1024 q^{32} + 5994 q^{33} - 13920 q^{34} + 1554 q^{35} + 2592 q^{36} - 3131 q^{37} - 4628 q^{38} + 5031 q^{39} + 384 q^{40} - 9732 q^{41} + 4284 q^{42} - 22814 q^{43} + 10656 q^{44} + 486 q^{45} + 13872 q^{46} - 2310 q^{47} + 4608 q^{48} - 19453 q^{49} - 24712 q^{50} + 15660 q^{51} + 8944 q^{52} + 28296 q^{53} - 2916 q^{54} + 7992 q^{55} + 7616 q^{56} + 20826 q^{57} - 13488 q^{58} - 20544 q^{59} + 864 q^{60} + 4630 q^{61} + 50344 q^{62} - 20979 q^{63} + 8192 q^{64} - 3354 q^{65} + 23976 q^{66} + 18745 q^{67} + 27840 q^{68} - 62424 q^{69} - 3360 q^{70} - 76452 q^{71} - 5184 q^{72} - 70589 q^{73} - 12524 q^{74} + 27801 q^{75} + 37024 q^{76} - 93240 q^{77} - 40248 q^{78} + 62293 q^{79} + 1536 q^{80} - 6561 q^{81} + 19464 q^{82} + 159636 q^{83} - 37296 q^{84} + 20880 q^{85} + 45628 q^{86} - 30348 q^{87} + 42624 q^{88} + 18120 q^{89} - 3888 q^{90} - 66521 q^{91} - 110976 q^{92} - 56637 q^{93} - 9240 q^{94} + 6942 q^{95} - 9216 q^{96} + 249508 q^{97} - 56056 q^{98} - 107892 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 9 * q^3 - 16 * q^4 + 6 * q^5 + 72 * q^6 + 119 * q^7 + 128 * q^8 - 81 * q^9 + 24 * q^10 + 666 * q^11 - 144 * q^12 - 1118 * q^13 - 1036 * q^14 - 108 * q^15 - 256 * q^16 + 1740 * q^17 - 324 * q^18 - 1157 * q^19 - 192 * q^20 + 1260 * q^21 - 5328 * q^22 + 3468 * q^23 - 576 * q^24 + 3089 * q^25 + 2236 * q^26 + 1458 * q^27 + 2240 * q^28 + 6744 * q^29 + 216 * q^30 - 6293 * q^31 - 1024 * q^32 + 5994 * q^33 - 13920 * q^34 + 1554 * q^35 + 2592 * q^36 - 3131 * q^37 - 4628 * q^38 + 5031 * q^39 + 384 * q^40 - 9732 * q^41 + 4284 * q^42 - 22814 * q^43 + 10656 * q^44 + 486 * q^45 + 13872 * q^46 - 2310 * q^47 + 4608 * q^48 - 19453 * q^49 - 24712 * q^50 + 15660 * q^51 + 8944 * q^52 + 28296 * q^53 - 2916 * q^54 + 7992 * q^55 + 7616 * q^56 + 20826 * q^57 - 13488 * q^58 - 20544 * q^59 + 864 * q^60 + 4630 * q^61 + 50344 * q^62 - 20979 * q^63 + 8192 * q^64 - 3354 * q^65 + 23976 * q^66 + 18745 * q^67 + 27840 * q^68 - 62424 * q^69 - 3360 * q^70 - 76452 * q^71 - 5184 * q^72 - 70589 * q^73 - 12524 * q^74 + 27801 * q^75 + 37024 * q^76 - 93240 * q^77 - 40248 * q^78 + 62293 * q^79 + 1536 * q^80 - 6561 * q^81 + 19464 * q^82 + 159636 * q^83 - 37296 * q^84 + 20880 * q^85 + 45628 * q^86 - 30348 * q^87 + 42624 * q^88 + 18120 * q^89 - 3888 * q^90 - 66521 * q^91 - 110976 * q^92 - 56637 * q^93 - 9240 * q^94 + 6942 * q^95 - 9216 * q^96 + 249508 * q^97 - 56056 * q^98 - 107892 * q^99

Introduction

L-functions

Modular forms

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