LMFDB - Embedded newform 294.6.e.s.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not 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:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{9601})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 $ x^4 - x^3 + 2401x^2 + 2400x + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$-24.2462 + 41.9956i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.s.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(44.9847 + 77.9158i) q^{10} +(-170.231 - 294.849i) q^{11} +(-72.0000 + 124.708i) q^{12} +728.416 q^{13} -202.431 q^{15} +(-128.000 + 221.703i) q^{16} +(404.923 + 701.348i) q^{17} +(-162.000 - 280.592i) q^{18} +(513.101 - 888.717i) q^{19} -359.878 q^{20} +1361.85 q^{22} +(-711.015 + 1231.51i) q^{23} +(-288.000 - 498.831i) q^{24} +(1309.55 + 2268.20i) q^{25} +(-1456.83 + 2523.31i) q^{26} +729.000 q^{27} +5218.03 q^{29} +(404.862 - 701.242i) q^{30} +(-3518.87 - 6094.87i) q^{31} +(-512.000 - 886.810i) q^{32} +(-1532.08 + 2653.64i) q^{33} -3239.39 q^{34} +1296.00 q^{36} +(-6396.05 + 11078.3i) q^{37} +(2052.40 + 3554.87i) q^{38} +(-3277.87 - 5677.44i) q^{39} +(719.755 - 1246.65i) q^{40} -1173.51 q^{41} +3664.17 q^{43} +(-2723.69 + 4717.58i) q^{44} +(910.940 + 1577.79i) q^{45} +(-2844.06 - 4926.06i) q^{46} +(4656.60 - 8065.46i) q^{47} +2304.00 q^{48} -10476.4 q^{50} +(3644.31 - 6312.13i) q^{51} +(-5827.33 - 10093.2i) q^{52} +(-17821.4 - 30867.6i) q^{53} +(-1458.00 + 2525.33i) q^{54} -7657.78 q^{55} -9235.81 q^{57} +(-10436.1 + 18075.8i) q^{58} +(-15188.1 - 26306.5i) q^{59} +(1619.45 + 2804.97i) q^{60} +(16093.1 - 27874.1i) q^{61} +28151.0 q^{62} +4096.00 q^{64} +(8191.89 - 14188.8i) q^{65} +(-6128.31 - 10614.5i) q^{66} +(-10675.5 - 18490.6i) q^{67} +(6478.78 - 11221.6i) q^{68} +12798.3 q^{69} +61153.7 q^{71} +(-2592.00 + 4489.48i) q^{72} +(20633.9 + 35739.0i) q^{73} +(-25584.2 - 44313.2i) q^{74} +(11785.9 - 20413.8i) q^{75} -16419.2 q^{76} +26223.0 q^{78} +(17500.2 - 30311.3i) q^{79} +(2879.02 + 4986.61i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(2347.01 - 4065.14i) q^{82} -86193.0 q^{83} +18215.4 q^{85} +(-7328.33 + 12693.0i) q^{86} +(-23481.1 - 40670.5i) q^{87} +(-10894.8 - 18870.3i) q^{88} +(38996.3 - 67543.6i) q^{89} -7287.52 q^{90} +22752.5 q^{92} +(-31669.9 + 54853.8i) q^{93} +(18626.4 + 32261.9i) q^{94} +(-11540.8 - 19989.3i) q^{95} +(-4608.00 + 7981.29i) q^{96} +161765. q^{97} +27577.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 - 53 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} - 212 q^{10} - 191 q^{11} - 288 q^{12} + 758 q^{13} + 954 q^{15} - 512 q^{16} - 340 q^{17} - 648 q^{18} - 1769 q^{19} + 1696 q^{20} + 1528 q^{22} - 3236 q^{23} - 1152 q^{24} + 45 q^{25} - 1516 q^{26} + 2916 q^{27} + 8918 q^{29} - 1908 q^{30} + 1994 q^{31} - 2048 q^{32} - 1719 q^{33} + 2720 q^{34} + 5184 q^{36} - 20587 q^{37} - 7076 q^{38} - 3411 q^{39} - 3392 q^{40} - 17628 q^{41} + 31706 q^{43} - 3056 q^{44} - 4293 q^{45} - 12944 q^{46} + 33912 q^{47} + 9216 q^{48} - 360 q^{50} - 3060 q^{51} - 6064 q^{52} - 49239 q^{53} - 5832 q^{54} - 37882 q^{55} + 31842 q^{57} - 17836 q^{58} - 56735 q^{59} - 7632 q^{60} + 67508 q^{61} - 15952 q^{62} + 16384 q^{64} + 42762 q^{65} - 6876 q^{66} - 75723 q^{67} - 5440 q^{68} + 58248 q^{69} - 17984 q^{71} - 10368 q^{72} - 3201 q^{73} - 82348 q^{74} + 405 q^{75} + 56608 q^{76} + 27288 q^{78} - 26612 q^{79} - 13568 q^{80} - 13122 q^{81} + 35256 q^{82} + 1898 q^{83} + 210040 q^{85} - 63412 q^{86} - 40131 q^{87} - 12224 q^{88} + 176562 q^{89} + 34344 q^{90} + 103552 q^{92} + 17946 q^{93} + 135648 q^{94} - 234098 q^{95} - 18432 q^{96} + 258846 q^{97} + 30942 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 - 53 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 - 212 * q^10 - 191 * q^11 - 288 * q^12 + 758 * q^13 + 954 * q^15 - 512 * q^16 - 340 * q^17 - 648 * q^18 - 1769 * q^19 + 1696 * q^20 + 1528 * q^22 - 3236 * q^23 - 1152 * q^24 + 45 * q^25 - 1516 * q^26 + 2916 * q^27 + 8918 * q^29 - 1908 * q^30 + 1994 * q^31 - 2048 * q^32 - 1719 * q^33 + 2720 * q^34 + 5184 * q^36 - 20587 * q^37 - 7076 * q^38 - 3411 * q^39 - 3392 * q^40 - 17628 * q^41 + 31706 * q^43 - 3056 * q^44 - 4293 * q^45 - 12944 * q^46 + 33912 * q^47 + 9216 * q^48 - 360 * q^50 - 3060 * q^51 - 6064 * q^52 - 49239 * q^53 - 5832 * q^54 - 37882 * q^55 + 31842 * q^57 - 17836 * q^58 - 56735 * q^59 - 7632 * q^60 + 67508 * q^61 - 15952 * q^62 + 16384 * q^64 + 42762 * q^65 - 6876 * q^66 - 75723 * q^67 - 5440 * q^68 + 58248 * q^69 - 17984 * q^71 - 10368 * q^72 - 3201 * q^73 - 82348 * q^74 + 405 * q^75 + 56608 * q^76 + 27288 * q^78 - 26612 * q^79 - 13568 * q^80 - 13122 * q^81 + 35256 * q^82 + 1898 * q^83 + 210040 * q^85 - 63412 * q^86 - 40131 * q^87 - 12224 * q^88 + 176562 * q^89 + 34344 * q^90 + 103552 * q^92 + 17946 * q^93 + 135648 * q^94 - 234098 * q^95 - 18432 * q^96 + 258846 * q^97 + 30942 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	11.2462	−	19.4789i	0.201178	−	0.348450i	−0.747730	−	0.664002i	$-0.768856\pi$
$5$	11.2462	−	19.4789i	0.201178	−	0.348450i	0.948908	+	0.315552i	$0.102190\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	44.9847	+	77.9158i	0.142254	+	0.246391i
$11$	−170.231	−	294.849i	−0.424186	−	0.734712i	0.572158	−	0.820144i	$-0.306106\pi$
$11$	−170.231	−	294.849i	−0.424186	−	0.734712i	−0.996344	+	0.0854314i	$0.972773\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	728.416			1.19542			0.597711	−	0.801712i	$-0.296077\pi$
$13$	728.416			1.19542			0.597711	+	0.801712i	$0.296077\pi$
$14$		0			0
$15$	−202.431			−0.232300
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	404.923	+	701.348i	0.339821	+	0.588588i	0.984399	−	0.175951i	$-0.0563001\pi$
$17$	404.923	+	701.348i	0.339821	+	0.588588i	−0.644578	+	0.764539i	$0.722967\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	513.101	−	888.717i	0.326076	−	0.564780i	−0.655654	−	0.755062i	$-0.727607\pi$
$19$	513.101	−	888.717i	0.326076	−	0.564780i	0.981730	+	0.190282i	$0.0609402\pi$
$20$	−359.878			−0.201178
$21$		0			0
$22$	1361.85			0.599890
$23$	−711.015	+	1231.51i	−0.280259	+	0.485423i	−0.971448	−	0.237251i	$-0.923754\pi$
$23$	−711.015	+	1231.51i	−0.280259	+	0.485423i	0.691190	+	0.722674i	$0.257087\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	1309.55	+	2268.20i	0.419055	+	0.725825i
$26$	−1456.83	+	2523.31i	−0.422645	+	0.732043i
$27$	729.000			0.192450
$28$		0			0
$29$	5218.03			1.15216			0.576079	−	0.817394i	$-0.304582\pi$
$29$	5218.03			1.15216			0.576079	+	0.817394i	$0.304582\pi$
$30$	404.862	−	701.242i	0.0821304	−	0.142254i
$31$	−3518.87	−	6094.87i	−0.657657	−	1.13909i	−0.981221	−	0.192889i	$-0.938214\pi$
$31$	−3518.87	−	6094.87i	−0.657657	−	1.13909i	0.323564	−	0.946206i	$-0.395119\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	−1532.08	+	2653.64i	−0.244904	+	0.424186i
$34$	−3239.39			−0.480580
$35$		0			0
$36$	1296.00			0.166667
$37$	−6396.05	+	11078.3i	−0.768082	+	1.33036i	0.170519	+	0.985354i	$0.445456\pi$
$37$	−6396.05	+	11078.3i	−0.768082	+	1.33036i	−0.938601	+	0.345004i	$0.887878\pi$
$38$	2052.40	+	3554.87i	0.230570	+	0.399360i
$39$	−3277.87	−	5677.44i	−0.345088	−	0.597711i
$40$	719.755	−	1246.65i	0.0711270	−	0.123196i
$41$	−1173.51			−0.109025			−0.0545124	−	0.998513i	$-0.517360\pi$
$41$	−1173.51			−0.109025			−0.0545124	+	0.998513i	$0.517360\pi$
$42$		0			0
$43$	3664.17			0.302207			0.151103	−	0.988518i	$-0.451717\pi$
$43$	3664.17			0.302207			0.151103	+	0.988518i	$0.451717\pi$
$44$	−2723.69	+	4717.58i	−0.212093	+	0.367356i
$45$	910.940	+	1577.79i	0.0670592	+	0.116150i
$46$	−2844.06	−	4926.06i	−0.198173	−	0.343246i
$47$	4656.60	−	8065.46i	0.307485	−	0.532580i	−0.670326	−	0.742066i	$-0.733846\pi$
$47$	4656.60	−	8065.46i	0.307485	−	0.532580i	0.977812	+	0.209487i	$0.0671793\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	−10476.4			−0.592633
$51$	3644.31	−	6312.13i	0.196196	−	0.339821i
$52$	−5827.33	−	10093.2i	−0.298855	−	0.517633i
$53$	−17821.4	−	30867.6i	−0.871469	−	1.50943i	−0.860477	−	0.509489i	$-0.829835\pi$
$53$	−17821.4	−	30867.6i	−0.871469	−	1.50943i	−0.0109916	−	0.999940i	$-0.503499\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	−7657.78			−0.341347
$56$		0			0
$57$	−9235.81			−0.376520
$58$	−10436.1	+	18075.8i	−0.407349	+	0.705549i
$59$	−15188.1	−	26306.5i	−0.568033	−	0.983861i	−0.996760	−	0.0804276i	$-0.974371\pi$
$59$	−15188.1	−	26306.5i	−0.568033	−	0.983861i	0.428728	−	0.903434i	$-0.358962\pi$
$60$	1619.45	+	2804.97i	0.0580750	+	0.100589i
$61$	16093.1	−	27874.1i	0.553753	−	0.959128i	−0.444247	−	0.895904i	$-0.646529\pi$
$61$	16093.1	−	27874.1i	0.553753	−	0.959128i	0.997999	−	0.0632231i	$-0.0201380\pi$
$62$	28151.0			0.930067
$63$		0			0
$64$	4096.00			0.125000
$65$	8191.89	−	14188.8i	0.240492	−	0.416544i
$66$	−6128.31	−	10614.5i	−0.173173	−	0.299945i
$67$	−10675.5	−	18490.6i	−0.290538	−	0.503226i	0.683399	−	0.730045i	$-0.260501\pi$
$67$	−10675.5	−	18490.6i	−0.290538	−	0.503226i	−0.973937	+	0.226819i	$0.927168\pi$
$68$	6478.78	−	11221.6i	0.169911	−	0.294294i
$69$	12798.3			0.323615
$70$		0			0
$71$	61153.7			1.43972			0.719859	−	0.694121i	$-0.244207\pi$
$71$	61153.7			1.43972			0.719859	+	0.694121i	$0.244207\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	20633.9	+	35739.0i	0.453184	+	0.784937i	0.998582	−	0.0532401i	$-0.0169549\pi$
$73$	20633.9	+	35739.0i	0.453184	+	0.784937i	−0.545398	+	0.838177i	$0.683622\pi$
$74$	−25584.2	−	44313.2i	−0.543116	−	0.940705i
$75$	11785.9	−	20413.8i	0.241942	−	0.419055i
$76$	−16419.2			−0.326076
$77$		0			0
$78$	26223.0			0.488029
$79$	17500.2	−	30311.3i	0.315483	−	0.546433i	−0.664057	−	0.747682i	$-0.731167\pi$
$79$	17500.2	−	30311.3i	0.315483	−	0.546433i	0.979540	+	0.201249i	$0.0645001\pi$
$80$	2879.02	+	4986.61i	0.0502944	+	0.0871125i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	2347.01	−	4065.14i	0.0385461	−	0.0667638i
$83$	−86193.0			−1.37334			−0.686668	−	0.726972i	$-0.740927\pi$
$83$	−86193.0			−1.37334			−0.686668	+	0.726972i	$0.740927\pi$
$84$		0			0
$85$	18215.4			0.273458
$86$	−7328.33	+	12693.0i	−0.106846	+	0.185063i
$87$	−23481.1	−	40670.5i	−0.332599	−	0.576079i
$88$	−10894.8	−	18870.3i	−0.149972	−	0.259760i
$89$	38996.3	−	67543.6i	0.521853	−	0.903876i	−0.477824	−	0.878456i	$-0.658574\pi$
$89$	38996.3	−	67543.6i	0.521853	−	0.903876i	0.999677	−	0.0254206i	$-0.00809249\pi$
$90$	−7287.52			−0.0948361
$91$		0			0
$92$	22752.5			0.280259
$93$	−31669.9	+	54853.8i	−0.379698	+	0.657657i
$94$	18626.4	+	32261.9i	0.217425	+	0.376591i
$95$	−11540.8	−	19989.3i	−0.131198	−	0.227242i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	161765.			1.74565			0.872823	−	0.488037i	$-0.162287\pi$
$97$	161765.			1.74565			0.872823	+	0.488037i	$0.162287\pi$
$98$		0			0
$99$	27577.4			0.282791
$100$	20952.8	−	36291.2i	0.209528	−	0.362912i
$101$	−32927.2	−	57031.6i	−0.321182	−	0.556304i	0.659550	−	0.751661i	$-0.270747\pi$
$101$	−32927.2	−	57031.6i	−0.321182	−	0.556304i	−0.980732	+	0.195357i	$0.937414\pi$
$102$	14577.2	+	25248.5i	0.138731	+	0.240290i
$103$	65099.0	−	112755.i	0.604619	−	1.04723i	−0.387493	−	0.921873i	$-0.626659\pi$
$103$	65099.0	−	112755.i	0.604619	−	1.04723i	0.992112	−	0.125358i	$-0.0400078\pi$
$104$	46618.6			0.422645
$105$		0			0
$106$	142571.			1.23244
$107$	−1295.48	+	2243.83i	−0.0109388	+	0.0189466i	−0.871443	−	0.490497i	$-0.836815\pi$
$107$	−1295.48	+	2243.83i	−0.0109388	+	0.0189466i	0.860504	+	0.509443i	$0.170149\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	−55326.9	−	95828.9i	−0.446036	−	0.772557i	0.552088	−	0.833786i	$-0.313831\pi$
$109$	−55326.9	−	95828.9i	−0.446036	−	0.772557i	−0.998124	+	0.0612291i	$0.980498\pi$
$110$	15315.6	−	26527.3i	0.120684	−	0.209032i
$111$	115129.			0.886905
$112$		0			0
$113$	−193910.			−1.42858			−0.714291	−	0.699849i	$-0.753251\pi$
$113$	−193910.			−1.42858			−0.714291	+	0.699849i	$0.753251\pi$
$114$	18471.6	−	31993.8i	0.133120	−	0.230570i
$115$	15992.4	+	27699.7i	0.112764	+	0.195312i
$116$	−41744.3	−	72303.2i	−0.288039	−	0.498899i
$117$	−29500.8	+	51097.0i	−0.199237	+	0.345088i
$118$	121505.			0.803319
$119$		0			0
$120$	−12955.6			−0.0821304
$121$	22568.4	−	39089.6i	0.140132	−	0.242716i
$122$	64372.5	+	111496.i	0.391562	+	0.678206i
$123$	5280.77	+	9146.57i	0.0314728	+	0.0545124i
$124$	−56302.0	+	97517.9i	−0.328828	+	0.569547i
$125$	129198.			0.739573
$126$		0			0
$127$	27429.2			0.150905			0.0754526	−	0.997149i	$-0.475960\pi$
$127$	27429.2			0.150905			0.0754526	+	0.997149i	$0.475960\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	−16488.7	−	28559.3i	−0.0872395	−	0.151103i
$130$	32767.6	+	56755.1i	0.170054	+	0.294541i
$131$	75188.0	−	130229.i	0.382798	−	0.663026i	−0.608663	−	0.793429i	$-0.708294\pi$
$131$	75188.0	−	130229.i	0.382798	−	0.663026i	0.991461	+	0.130403i	$0.0416271\pi$
$132$	49026.5			0.244904
$133$		0			0
$134$	85404.3			0.410883
$135$	8198.46	−	14200.1i	0.0387167	−	0.0670592i
$136$	25915.1	+	44886.3i	0.120145	+	0.208097i
$137$	−48051.0	−	83226.8i	−0.218726	−	0.378845i	0.735693	−	0.677316i	$-0.236857\pi$
$137$	−48051.0	−	83226.8i	−0.218726	−	0.378845i	−0.954419	+	0.298471i	$0.903524\pi$
$138$	−25596.6	+	44334.5i	−0.114415	+	0.198173i
$139$	−100854.			−0.442749			−0.221375	−	0.975189i	$-0.571054\pi$
$139$	−100854.			−0.442749			−0.221375	+	0.975189i	$0.571054\pi$
$140$		0			0
$141$	−83818.7			−0.355053
$142$	−122307.	+	211843.i	−0.509017	+	0.881643i
$143$	−123999.	−	214772.i	−0.507081	−	0.878291i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	58682.9	−	101642.i	0.231788	−	0.401469i
$146$	−165071.			−0.640898
$147$		0			0
$148$	204674.			0.768082
$149$	180472.	−	312587.i	0.665954	−	1.15347i	−0.313071	−	0.949730i	$-0.601358\pi$
$149$	180472.	−	312587.i	0.665954	−	1.15347i	0.979026	−	0.203737i	$-0.0653087\pi$
$150$	47143.7	+	81655.3i	0.171079	+	0.296317i
$151$	217028.	+	375903.i	0.774592	+	1.34163i	0.935023	+	0.354586i	$0.115378\pi$
$151$	217028.	+	375903.i	0.774592	+	1.34163i	−0.160431	+	0.987047i	$0.551288\pi$
$152$	32838.4	−	56877.9i	0.115285	−	0.199680i
$153$	−65597.6			−0.226548
$154$		0			0
$155$	−158295.			−0.529223
$156$	−52445.9	+	90839.0i	−0.172544	+	0.298855i
$157$	−255798.	−	443055.i	−0.828225	−	1.43453i	−0.899430	−	0.437066i	$-0.856018\pi$
$157$	−255798.	−	443055.i	−0.828225	−	1.43453i	0.0712046	−	0.997462i	$-0.477316\pi$
$158$	70000.9	+	121245.i	0.223080	+	0.386386i
$159$	−160393.	+	277808.i	−0.503143	+	0.871469i
$160$	−23032.2			−0.0711270
$161$		0			0
$162$	26244.0			0.0785674
$163$	125635.	−	217606.i	0.370374	−	0.641507i	−0.619249	−	0.785195i	$-0.712563\pi$
$163$	125635.	−	217606.i	0.370374	−	0.641507i	0.989623	+	0.143688i	$0.0458962\pi$
$164$	9388.04	+	16260.6i	0.0272562	+	0.0472091i
$165$	34460.0	+	59686.5i	0.0985384	+	0.170674i
$166$	172386.	−	298581.i	0.485547	−	0.840993i
$167$	−419277.			−1.16335			−0.581674	−	0.813422i	$-0.697602\pi$
$167$	−419277.			−1.16335			−0.581674	+	0.813422i	$0.697602\pi$
$168$		0			0
$169$	159297.			0.429032
$170$	−36430.7	+	63099.8i	−0.0966819	+	0.167458i
$171$	41561.2	+	71986.0i	0.108692	+	0.188260i
$172$	−29313.3	−	50772.2i	−0.0755517	−	0.130859i
$173$	−230688.	+	399564.i	−0.586017	+	1.01501i	0.408731	+	0.912655i	$0.365971\pi$
$173$	−230688.	+	399564.i	−0.586017	+	1.01501i	−0.994748	+	0.102356i	$0.967362\pi$
$174$	187849.			0.470366
$175$		0			0
$176$	87158.2			0.212093
$177$	−136693.	+	236759.i	−0.327954	+	0.568033i
$178$	155985.	+	270174.i	0.369006	+	0.639137i
$179$	−370853.	−	642336.i	−0.865105	−	1.49841i	−0.866942	−	0.498408i	$-0.833918\pi$
$179$	−370853.	−	642336.i	−0.865105	−	1.49841i	0.00183697	−	0.999998i	$-0.499415\pi$
$180$	14575.0	−	25244.7i	0.0335296	−	0.0580750i
$181$	−301371.			−0.683762			−0.341881	−	0.939743i	$-0.611064\pi$
$181$	−301371.			−0.683762			−0.341881	+	0.939743i	$0.611064\pi$
$182$		0			0
$183$	−289676.			−0.639418
$184$	−45505.0	+	78816.9i	−0.0990865	+	0.171623i
$185$	143862.	+	249177.i	0.309042	+	0.535277i
$186$	−126679.	−	219415.i	−0.268487	−	0.465034i
$187$	137861.	−	238782.i	0.288295	−	0.499342i
$188$	−149011.			−0.307485
$189$		0			0
$190$	92326.7			0.185542
$191$	−131591.	+	227923.i	−0.261002	+	0.452069i	−0.966508	−	0.256635i	$-0.917386\pi$
$191$	−131591.	+	227923.i	−0.261002	+	0.452069i	0.705507	+	0.708703i	$0.250720\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	415563.	+	719777.i	0.803053	+	1.39093i	0.917598	+	0.397510i	$0.130126\pi$
$193$	415563.	+	719777.i	0.803053	+	1.39093i	−0.114545	+	0.993418i	$0.536541\pi$
$194$	−323531.	+	560372.i	−0.617179	+	1.06899i
$195$	−147454.			−0.277696
$196$		0			0
$197$	−1.05421e6			−1.93536			−0.967681	−	0.252178i	$-0.918853\pi$
$197$	−1.05421e6			−1.93536			−0.967681	+	0.252178i	$0.918853\pi$
$198$	−55154.8	+	95530.9i	−0.0999817	+	0.173173i
$199$	349284.	+	604977.i	0.625239	+	1.08295i	0.988495	+	0.151256i	$0.0483317\pi$
$199$	349284.	+	604977.i	0.625239	+	1.08295i	−0.363256	+	0.931689i	$0.618335\pi$
$200$	83811.0	+	145165.i	0.148158	+	0.256618i
$201$	−96079.9	+	166415.i	−0.167742	+	0.290538i
$202$	263418.			0.454220
$203$		0			0
$204$	−116618.			−0.196196
$205$	−13197.4	+	22858.6i	−0.0219334	+	0.0379897i
$206$	260396.	+	451019.i	0.427530	+	0.740504i
$207$	−57592.2	−	99752.7i	−0.0934196	−	0.161808i
$208$	−93237.2	+	161492.i	−0.149428	+	0.258816i
$209$	−349382.			−0.553268
$210$		0			0
$211$	−99693.6			−0.154156			−0.0770781	−	0.997025i	$-0.524559\pi$
$211$	−99693.6			−0.154156			−0.0770781	+	0.997025i	$0.524559\pi$
$212$	−285142.	+	493881.i	−0.435734	+	0.754714i
$213$	−275192.	−	476646.i	−0.415611	−	0.719859i
$214$	−5181.90	−	8975.32i	−0.00773490	−	0.0133972i
$215$	41207.8	−	71374.1i	0.0607972	−	0.105304i
$216$	46656.0			0.0680414
$217$		0			0
$218$	442615.			0.630790
$219$	185705.	−	321651.i	0.261646	−	0.453184i
$220$	61262.3	+	106109.i	0.0853368	+	0.147808i
$221$	294953.	+	510873.i	0.406230	+	0.703610i
$222$	−230258.	+	398819.i	−0.313568	+	0.543116i
$223$	−526194.			−0.708572			−0.354286	−	0.935137i	$-0.615276\pi$
$223$	−526194.			−0.708572			−0.354286	+	0.935137i	$0.615276\pi$
$224$		0			0
$225$	−212147.			−0.279370
$226$	387821.	−	671725.i	0.505080	−	0.874824i
$227$	−490802.	−	850095.i	−0.632182	−	1.09497i	−0.987105	−	0.160076i	$-0.948826\pi$
$227$	−490802.	−	850095.i	−0.632182	−	1.09497i	0.354923	−	0.934896i	$-0.384507\pi$
$228$	73886.5	+	127975.i	0.0941300	+	0.163038i
$229$	−42540.5	+	73682.3i	−0.0536061	+	0.0928484i	−0.891583	−	0.452857i	$-0.850405\pi$
$229$	−42540.5	+	73682.3i	−0.0536061	+	0.0928484i	0.837977	+	0.545705i	$0.183738\pi$
$230$	−127939.			−0.159472
$231$		0			0
$232$	333954.			0.407349
$233$	−56561.4	+	97967.3i	−0.0682544	+	0.118220i	−0.898133	−	0.439724i	$-0.855076\pi$
$233$	−56561.4	+	97967.3i	−0.0682544	+	0.118220i	0.829879	+	0.557944i	$0.188410\pi$
$234$	−118003.	−	204388.i	−0.140882	−	0.244014i
$235$	−104738.	−	181411.i	−0.123718	−	0.214286i
$236$	−243009.	+	420905.i	−0.284016	+	0.491931i
$237$	−315004.			−0.364288
$238$		0			0
$239$	−895100.			−1.01362			−0.506812	−	0.862057i	$-0.669176\pi$
$239$	−895100.			−1.01362			−0.506812	+	0.862057i	$0.669176\pi$
$240$	25911.2	−	44879.5i	0.0290375	−	0.0502944i
$241$	263857.	+	457014.i	0.292635	+	0.506859i	0.974432	−	0.224683i	$-0.0721345\pi$
$241$	263857.	+	457014.i	0.292635	+	0.506859i	−0.681797	+	0.731542i	$0.738801\pi$
$242$	90273.6	+	156358.i	0.0990883	+	0.171626i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−514980.			−0.553753
$245$		0			0
$246$	−42246.2			−0.0445092
$247$	373751.	−	647355.i	0.389798	−	0.675150i
$248$	−225208.	−	390071.i	−0.232517	−	0.402731i
$249$	387868.	+	671808.i	0.396448	+	0.686668i
$250$	−258396.	+	447556.i	−0.261479	+	0.452894i
$251$	1.19293e6			1.19517			0.597584	−	0.801806i	$-0.296127\pi$
$251$	1.19293e6			1.19517			0.597584	+	0.801806i	$0.296127\pi$
$252$		0			0
$253$	484147.			0.475528
$254$	−54858.5	+	95017.7i	−0.0533531	+	0.0924102i
$255$	−81969.1	−	141975.i	−0.0789405	−	0.136729i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−597462.	+	1.03483e6i	−0.564257	+	0.977322i	0.432861	+	0.901461i	$0.357504\pi$
$257$	−597462.	+	1.03483e6i	−0.564257	+	0.977322i	−0.997118	+	0.0758617i	$0.975829\pi$
$258$	131910.			0.123375
$259$		0			0
$260$	−262140.			−0.240492
$261$	−211330.	+	366035.i	−0.192026	+	0.332599i
$262$	300752.	+	520917.i	0.270679	+	0.468830i
$263$	1.06115e6	+	1.83797e6i	0.945993	+	1.63851i	0.753750	+	0.657161i	$0.228243\pi$
$263$	1.06115e6	+	1.83797e6i	0.945993	+	1.63851i	0.192244	+	0.981347i	$0.438424\pi$
$264$	−98053.0	+	169833.i	−0.0865867	+	0.149972i
$265$	−801690.			−0.701280
$266$		0			0
$267$	−701933.			−0.602584
$268$	−170809.	+	295849.i	−0.145269	+	0.251613i
$269$	77488.3	+	134214.i	0.0652913	+	0.113088i	0.896823	−	0.442389i	$-0.145869\pi$
$269$	77488.3	+	134214.i	0.0652913	+	0.113088i	−0.831532	+	0.555477i	$0.812536\pi$
$270$	32793.8	+	56800.6i	0.0273768	+	0.0474180i
$271$	979439.	−	1.69644e6i	0.810129	−	1.40318i	−0.102645	−	0.994718i	$-0.532730\pi$
$271$	979439.	−	1.69644e6i	0.810129	−	1.40318i	0.912773	−	0.408466i	$-0.133936\pi$
$272$	−207321.			−0.169911
$273$		0			0
$274$	384408.			0.309326
$275$	445851.	−	772236.i	0.355515	−	0.615770i
$276$	−102386.	−	177338.i	−0.0809038	−	0.140129i
$277$	874763.	+	1.51513e6i	0.685001	+	1.18646i	0.973437	+	0.228957i	$0.0735315\pi$
$277$	874763.	+	1.51513e6i	0.685001	+	1.18646i	−0.288436	+	0.957499i	$0.593135\pi$
$278$	201709.	−	349370.i	0.156536	−	0.271128i
$279$	570057.			0.438438
$280$		0			0
$281$	1.40665e6			1.06272			0.531361	−	0.847145i	$-0.321681\pi$
$281$	1.40665e6			1.06272			0.531361	+	0.847145i	$0.321681\pi$
$282$	167637.	−	290357.i	0.125530	−	0.217425i
$283$	978536.	+	1.69487e6i	0.726291	+	1.25797i	0.958441	+	0.285292i	$0.0920907\pi$
$283$	978536.	+	1.69487e6i	0.726291	+	1.25797i	−0.232150	+	0.972680i	$0.574576\pi$
$284$	−489230.	−	847371.i	−0.359929	−	0.623416i
$285$	−103868.	+	179904.i	−0.0757474	+	0.131198i
$286$	991991.			0.717121
$287$		0			0
$288$	82944.0			0.0589256
$289$	382002.	−	661648.i	0.269043	−	0.465996i
$290$	234732.	+	406567.i	0.163899	+	0.283882i
$291$	−727944.	−	1.26084e6i	−0.503925	−	0.872823i
$292$	330142.	−	571823.i	0.226592	−	0.392469i
$293$	1.26998e6			0.864229			0.432114	−	0.901819i	$-0.357768\pi$
$293$	1.26998e6			0.864229			0.432114	+	0.901819i	$0.357768\pi$
$294$		0			0
$295$	−683232.			−0.457102
$296$	−409348.	+	709011.i	−0.271558	+	0.470353i
$297$	−124098.	−	214945.i	−0.0816347	−	0.141395i
$298$	721888.	+	1.25035e6i	0.470901	+	0.815624i
$299$	−517915.	+	897055.i	−0.335027	+	0.580285i
$300$	−377150.			−0.241942
$301$		0			0
$302$	−1.73622e6			−1.09544
$303$	−296345.	+	513284.i	−0.185435	+	0.321182i
$304$	131354.	+	227511.i	0.0815190	+	0.141195i
$305$	−361972.	−	626954.i	−0.222805	−	0.385910i
$306$	131195.	−	227237.i	0.0800967	−	0.138731i
$307$	41854.4			0.0253451			0.0126726	−	0.999920i	$-0.495966\pi$
$307$	41854.4			0.0253451			0.0126726	+	0.999920i	$0.495966\pi$
$308$		0			0
$309$	−1.17178e6			−0.698154
$310$	316591.	−	548351.i	0.187109	−	0.324082i
$311$	−1.14595e6	−	1.98484e6i	−0.671837	−	1.16366i	−0.977383	−	0.211478i	$-0.932172\pi$
$311$	−1.14595e6	−	1.98484e6i	−0.671837	−	1.16366i	0.305546	−	0.952177i	$-0.401161\pi$
$312$	−209784.	−	363356.i	−0.122007	−	0.211323i
$313$	1.13575e6	−	1.96717e6i	0.655271	−	1.13496i	−0.326555	−	0.945178i	$-0.605888\pi$
$313$	1.13575e6	−	1.96717e6i	0.655271	−	1.13496i	0.981826	−	0.189785i	$-0.0607790\pi$
$314$	2.04639e6			1.17129
$315$		0			0
$316$	−560007.			−0.315483
$317$	992372.	−	1.71884e6i	0.554659	−	0.960698i	−0.443271	−	0.896388i	$-0.646182\pi$
$317$	992372.	−	1.71884e6i	0.554659	−	0.960698i	0.997930	−	0.0643100i	$-0.0204847\pi$
$318$	−641570.	−	1.11123e6i	−0.355776	−	0.616222i
$319$	−888270.	−	1.53853e6i	−0.488729	−	0.846504i
$320$	46064.3	−	79785.8i	0.0251472	−	0.0435562i
$321$	23318.6			0.0126310
$322$		0			0
$323$	831066.			0.443230
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	953895.	+	1.65219e6i	0.500947	+	0.867666i
$326$	502539.	+	870423.i	0.261894	+	0.453614i
$327$	−497942.	+	862460.i	−0.257519	+	0.446036i
$328$	−75104.3			−0.0385461
$329$		0			0
$330$	−275680.			−0.139354
$331$	−319230.	+	552923.i	−0.160153	+	0.277393i	−0.934923	−	0.354850i	$-0.884532\pi$
$331$	−319230.	+	552923.i	−0.160153	+	0.277393i	0.774771	+	0.632242i	$0.217865\pi$
$332$	689544.	+	1.19432e6i	0.343334	+	0.594672i
$333$	−518080.	−	897342.i	−0.256027	−	0.443453i
$334$	838553.	−	1.45242e6i	0.411305	−	0.712402i
$335$	−480236.			−0.233799
$336$		0			0
$337$	2.72026e6			1.30478			0.652388	−	0.757886i	$-0.273767\pi$
$337$	2.72026e6			1.30478			0.652388	+	0.757886i	$0.273767\pi$
$338$	−318593.	+	551820.i	−0.151686	+	0.262727i
$339$	872597.	+	1.51138e6i	0.412396	+	0.714291i
$340$	−145723.	−	252399.i	−0.0683645	−	0.118411i
$341$	−1.19804e6	+	2.07507e6i	−0.557938	+	0.966377i
$342$	−332489.			−0.153714
$343$		0			0
$344$	234507.			0.106846
$345$	143932.	−	249297.i	0.0651041	−	0.112764i
$346$	−922753.	−	1.59825e6i	−0.414376	−	0.717721i
$347$	−1.31038e6	−	2.26965e6i	−0.584217	−	1.01189i	−0.994973	−	0.100148i	$-0.968068\pi$
$347$	−1.31038e6	−	2.26965e6i	−0.584217	−	1.01189i	0.410755	−	0.911746i	$-0.365265\pi$
$348$	−375698.	+	650729.i	−0.166300	+	0.288039i
$349$	−575592.			−0.252960			−0.126480	−	0.991969i	$-0.540368\pi$
$349$	−575592.			−0.252960			−0.126480	+	0.991969i	$0.540368\pi$
$350$		0			0
$351$	531015.			0.230059
$352$	−174316.	+	301925.i	−0.0749862	+	0.129880i
$353$	−1.29486e6	−	2.24276e6i	−0.553077	−	0.957957i	−0.998050	−	0.0624135i	$-0.980120\pi$
$353$	−1.29486e6	−	2.24276e6i	−0.553077	−	0.957957i	0.444974	−	0.895544i	$-0.353213\pi$
$354$	−546771.	−	947036.i	−0.231898	−	0.401660i
$355$	687746.	−	1.19121e6i	0.289639	−	0.501669i
$356$	−1.24788e6			−0.521853
$357$		0			0
$358$	2.96682e6			1.22344
$359$	−1.43389e6	+	2.48358e6i	−0.587193	+	1.01705i	0.407405	+	0.913248i	$0.366434\pi$
$359$	−1.43389e6	+	2.48358e6i	−0.587193	+	1.01705i	−0.994598	+	0.103801i	$0.966900\pi$
$360$	58300.2	+	100979.i	0.0237090	+	0.0410652i
$361$	711505.	+	1.23236e6i	0.287349	+	0.497703i
$362$	602742.	−	1.04398e6i	0.241746	−	0.418717i
$363$	−406231.			−0.161811
$364$		0			0
$365$	928210.			0.364682
$366$	579352.	−	1.00347e6i	0.226069	−	0.391562i
$367$	−977255.	−	1.69265e6i	−0.378741	−	0.655999i	0.612138	−	0.790751i	$-0.290310\pi$
$367$	−977255.	−	1.69265e6i	−0.378741	−	0.655999i	−0.990879	+	0.134752i	$0.956976\pi$
$368$	−182020.	−	315268.i	−0.0700647	−	0.121356i
$369$	47527.0	−	82319.1i	0.0181708	−	0.0314728i
$370$	−1.15090e6			−0.437052
$371$		0			0
$372$	1.01344e6			0.379698
$373$	−1.10555e6	+	1.91486e6i	−0.411439	+	0.712633i	−0.995047	−	0.0994020i	$-0.968307\pi$
$373$	−1.10555e6	+	1.91486e6i	−0.411439	+	0.712633i	0.583608	+	0.812035i	$0.301640\pi$
$374$	551444.	+	955129.i	0.203855	+	0.353088i
$375$	−581392.	−	1.00700e6i	−0.213496	−	0.369787i
$376$	298022.	−	516190.i	0.108712	−	0.188295i
$377$	3.80090e6			1.37731
$378$		0			0
$379$	3.81232e6			1.36330			0.681649	−	0.731679i	$-0.261263\pi$
$379$	3.81232e6			1.36330			0.681649	+	0.731679i	$0.261263\pi$
$380$	−184653.	+	319829.i	−0.0655992	+	0.113621i
$381$	−123432.	−	213790.i	−0.0435626	−	0.0754526i
$382$	−526365.	−	911691.i	−0.184556	−	0.319661i
$383$	1.90303e6	−	3.29614e6i	0.662901	−	1.14818i	−0.316949	−	0.948442i	$-0.602658\pi$
$383$	1.90303e6	−	3.29614e6i	0.662901	−	1.14818i	0.979850	−	0.199735i	$-0.0640082\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	−3.32451e6			−1.13569
$387$	−148399.	+	257034.i	−0.0503678	+	0.0872395i
$388$	−1.29412e6	−	2.24149e6i	−0.436411	−	0.755887i
$389$	−1.53762e6	−	2.66324e6i	−0.515200	−	0.892352i	−0.999844	−	0.0176410i	$-0.994384\pi$
$389$	−1.53762e6	−	2.66324e6i	−0.515200	−	0.892352i	0.484645	−	0.874711i	$-0.338949\pi$
$390$	294908.	−	510796.i	0.0981805	−	0.170054i
$391$	−1.15163e6			−0.380952
$392$		0			0
$393$	−1.35338e6			−0.442017
$394$	2.10842e6	−	3.65190e6i	0.684254	−	1.18516i
$395$	−393621.	−	681772.i	−0.126936	−	0.219860i
$396$	−220619.	−	382124.i	−0.0706977	−	0.122452i
$397$	1.09566e6	−	1.89774e6i	0.348900	−	0.604312i	−0.637154	−	0.770736i	$-0.719889\pi$
$397$	1.09566e6	−	1.89774e6i	0.348900	−	0.604312i	0.986054	+	0.166424i	$0.0532220\pi$
$398$	−2.79427e6			−0.884221
$399$		0			0
$400$	−670488.			−0.209528
$401$	−888340.	+	1.53865e6i	−0.275879	+	0.477836i	−0.970356	−	0.241678i	$-0.922302\pi$
$401$	−888340.	+	1.53865e6i	−0.275879	+	0.477836i	0.694478	+	0.719514i	$0.255635\pi$
$402$	−384319.	−	665661.i	−0.118612	−	0.205441i
$403$	−2.56320e6	−	4.43960e6i	−0.786177	−	1.36170i
$404$	−526835.	+	912505.i	−0.160591	+	0.278152i
$405$	−147572.			−0.0447061
$406$		0			0
$407$	4.35522e6			1.30324
$408$	233236.	−	403976.i	0.0693657	−	0.120145i
$409$	1.18059e6	+	2.04484e6i	0.348973	+	0.604438i	0.986067	−	0.166347i	$-0.0531973\pi$
$409$	1.18059e6	+	2.04484e6i	0.348973	+	0.604438i	−0.637095	+	0.770786i	$0.719864\pi$
$410$	−52789.8	−	91434.6i	−0.0155092	−	0.0268628i
$411$	−432459.	+	749041.i	−0.126282	+	0.218726i
$412$	−2.08317e6			−0.604619
$413$		0			0
$414$	460738.			0.132115
$415$	−969341.	+	1.67895e6i	−0.276284	+	0.478539i
$416$	−372949.	−	645966.i	−0.105661	−	0.183011i
$417$	453845.	+	786082.i	0.127811	+	0.221375i
$418$	698765.	−	1.21030e6i	0.195610	−	0.338806i
$419$	3.23493e6			0.900181			0.450090	−	0.892983i	$-0.351392\pi$
$419$	3.23493e6			0.900181			0.450090	+	0.892983i	$0.351392\pi$
$420$		0			0
$421$	−2.85759e6			−0.785769			−0.392884	−	0.919588i	$-0.628523\pi$
$421$	−2.85759e6			−0.785769			−0.392884	+	0.919588i	$0.628523\pi$
$422$	199387.	−	345349.i	0.0545025	−	0.0944010i
$423$	377184.	+	653302.i	0.102495	+	0.177527i
$424$	−1.14057e6	−	1.97552e6i	−0.308111	−	0.533664i
$425$	−1.06053e6	+	1.83690e6i	−0.284808	+	0.493301i
$426$	2.20153e6			0.587762
$427$		0			0
$428$	41455.2			0.0109388
$429$	−1.11599e6	+	1.93295e6i	−0.292764	+	0.507081i
$430$	164831.	+	285496.i	0.0429901	+	0.0744611i
$431$	44193.1	+	76544.7i	0.0114594	+	0.0198482i	0.871698	−	0.490043i	$-0.163019\pi$
$431$	44193.1	+	76544.7i	0.0114594	+	0.0198482i	−0.860239	+	0.509891i	$0.829686\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	3.09418e6			0.793097			0.396549	−	0.918014i	$-0.370208\pi$
$433$	3.09418e6			0.793097			0.396549	+	0.918014i	$0.370208\pi$
$434$		0			0
$435$	−1.05629e6			−0.267646
$436$	−885230.	+	1.53326e6i	−0.223018	+	0.386278i
$437$	729645.	+	1.26378e6i	0.182771	+	0.316569i
$438$	742820.	+	1.28660e6i	0.185011	+	0.320449i
$439$	242589.	−	420177.i	0.0600773	−	0.104057i	−0.834422	−	0.551125i	$-0.814199\pi$
$439$	242589.	−	420177.i	0.0600773	−	0.104057i	0.894500	+	0.447068i	$0.147532\pi$
$440$	−490098.			−0.120684
$441$		0			0
$442$	−2.35962e6			−0.574495
$443$	−637598.	+	1.10435e6i	−0.154361	+	0.267361i	−0.932826	−	0.360327i	$-0.882665\pi$
$443$	−637598.	+	1.10435e6i	−0.154361	+	0.267361i	0.778465	+	0.627688i	$0.215999\pi$
$444$	−921032.	−	1.59527e6i	−0.221726	−	0.384041i
$445$	−877118.	−	1.51921e6i	−0.209970	−	0.363679i
$446$	1.05239e6	−	1.82279e6i	0.250518	−	0.433910i
$447$	−3.24850e6			−0.768978
$448$		0			0
$449$	−3.79144e6			−0.887541			−0.443770	−	0.896141i	$-0.646359\pi$
$449$	−3.79144e6			−0.887541			−0.443770	+	0.896141i	$0.646359\pi$
$450$	424293.	−	734898.i	0.0987722	−	0.171079i
$451$	199767.	+	346006.i	0.0462468	+	0.0801019i
$452$	1.55128e6	+	2.68690e6i	0.357145	+	0.618594i
$453$	1.95325e6	−	3.38313e6i	0.447211	−	0.774592i
$454$	3.92642e6			0.894040
$455$		0			0
$456$	−591092.			−0.133120
$457$	−851404.	+	1.47467e6i	−0.190698	+	0.330298i	−0.945482	−	0.325675i	$-0.894408\pi$
$457$	−851404.	+	1.47467e6i	−0.190698	+	0.330298i	0.754784	+	0.655973i	$0.227742\pi$
$458$	−170162.	−	294729.i	−0.0379052	−	0.0656537i
$459$	295189.	+	511283.i	0.0653986	+	0.113274i
$460$	255878.	−	443194.i	0.0563818	−	0.0976562i
$461$	−4.55537e6			−0.998323			−0.499161	−	0.866509i	$-0.666358\pi$
$461$	−4.55537e6			−0.998323			−0.499161	+	0.866509i	$0.666358\pi$
$462$		0			0
$463$	5.82647e6			1.26314			0.631572	−	0.775317i	$-0.282410\pi$
$463$	5.82647e6			1.26314			0.631572	+	0.775317i	$0.282410\pi$
$464$	−667908.	+	1.15685e6i	−0.144020	+	0.249449i
$465$	712329.	+	1.23379e6i	0.152774	+	0.264612i
$466$	−226246.	−	391869.i	−0.0482631	−	0.0835942i
$467$	−1.77131e6	+	3.06799e6i	−0.375839	+	0.650972i	−0.990452	−	0.137857i	$-0.955979\pi$
$467$	−1.77131e6	+	3.06799e6i	−0.375839	+	0.650972i	0.614614	+	0.788828i	$0.289312\pi$
$468$	944027.			0.199237
$469$		0			0
$470$	837902.			0.174964
$471$	−2.30218e6	+	3.98750e6i	−0.478176	+	0.828225i
$472$	−972038.	−	1.68362e6i	−0.200830	−	0.347847i
$473$	−623754.	−	1.08037e6i	−0.128192	−	0.222035i
$474$	630008.	−	1.09121e6i	0.128795	−	0.223080i
$475$	2.68772e6			0.546575
$476$		0			0
$477$	2.88707e6			0.580979
$478$	1.79020e6	−	3.10072e6i	0.358370	−	0.620715i
$479$	−2.11771e6	−	3.66798e6i	−0.421723	−	0.730446i	0.574385	−	0.818585i	$-0.305241\pi$
$479$	−2.11771e6	−	3.66798e6i	−0.421723	−	0.730446i	−0.996108	+	0.0881390i	$0.971908\pi$
$480$	103645.	+	179518.i	0.0205326	+	0.0355635i
$481$	−4.65899e6	+	8.06960e6i	−0.918182	+	1.59034i
$482$	−2.11086e6			−0.413849
$483$		0			0
$484$	−722189.			−0.140132
$485$	1.81924e6	−	3.15102e6i	0.351185	−	0.608270i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	2.82740e6	+	4.89719e6i	0.540212	+	0.935675i	0.998891	+	0.0470729i	$0.0149893\pi$
$487$	2.82740e6	+	4.89719e6i	0.540212	+	0.935675i	−0.458679	+	0.888602i	$0.651677\pi$
$488$	1.02996e6	−	1.78394e6i	0.195781	−	0.339103i
$489$	−2.26142e6			−0.427671
$490$		0			0
$491$	8.33183e6			1.55968			0.779842	−	0.625976i	$-0.215299\pi$
$491$	8.33183e6			1.55968			0.779842	+	0.625976i	$0.215299\pi$
$492$	84492.4	−	146345.i	0.0157364	−	0.0272562i
$493$	2.11290e6	+	3.65966e6i	0.391528	+	0.678146i
$494$	1.49500e6	+	2.58942e6i	0.275629	+	0.477403i
$495$	310140.	−	537179.i	0.0568912	−	0.0985384i
$496$	1.80166e6			0.328828
$497$		0			0
$498$	−3.10295e6			−0.560662
$499$	3.61884e6	−	6.26802e6i	0.650607	−	1.12688i	−0.332369	−	0.943149i	$-0.607848\pi$
$499$	3.61884e6	−	6.26802e6i	0.650607	−	1.12688i	0.982976	−	0.183734i	$-0.0588187\pi$
$500$	−1.03359e6	−	1.79022e6i	−0.184893	−	0.320245i
$501$	1.88674e6	+	3.26794e6i	0.335829	+	0.581674i
$502$	−2.38585e6	+	4.13242e6i	−0.422556	+	0.731888i
$503$	6.16761e6			1.08692			0.543459	−	0.839436i	$-0.317114\pi$
$503$	6.16761e6			1.08692			0.543459	+	0.839436i	$0.317114\pi$
$504$		0			0
$505$	−1.48122e6			−0.258459
$506$	−968294.	+	1.67713e6i	−0.168124	+	0.291200i
$507$	−716835.	−	1.24159e6i	−0.123851	−	0.214516i
$508$	−219434.	−	380071.i	−0.0377263	−	0.0653439i
$509$	917439.	−	1.58905e6i	0.156958	−	0.271859i	−0.776812	−	0.629732i	$-0.783165\pi$
$509$	917439.	−	1.58905e6i	0.156958	−	0.271859i	0.933770	+	0.357873i	$0.116498\pi$
$510$	655753.			0.111639
$511$		0			0
$512$	262144.			0.0441942
$513$	374050.	−	647874.i	0.0627533	−	0.108692i
$514$	−2.38985e6	−	4.13934e6i	−0.398990	−	0.691071i
$515$	−1.46423e6	−	2.53612e6i	−0.243272	−	0.421359i
$516$	−263820.	+	456950.i	−0.0436198	+	0.0755517i
$517$	−3.17079e6			−0.521724
$518$		0			0
$519$	4.15239e6			0.676674
$520$	524281.	−	908081.i	0.0850268	−	0.147271i
$521$	2.65520e6	+	4.59894e6i	0.428551	+	0.742273i	0.996745	−	0.0806224i	$-0.0256908\pi$
$521$	2.65520e6	+	4.59894e6i	0.428551	+	0.742273i	−0.568193	+	0.822895i	$0.692357\pi$
$522$	−845321.	−	1.46414e6i	−0.135783	−	0.235183i
$523$	−1.49418e6	+	2.58799e6i	−0.238862	+	0.413722i	−0.960388	−	0.278666i	$-0.910108\pi$
$523$	−1.49418e6	+	2.58799e6i	−0.238862	+	0.413722i	0.721526	+	0.692388i	$0.243441\pi$
$524$	−2.40601e6			−0.382798
$525$		0			0
$526$	−8.48921e6			−1.33784
$527$	2.84975e6	−	4.93591e6i	0.446972	−	0.774178i
$528$	−392212.	−	679331.i	−0.0612260	−	0.106047i
$529$	2.20709e6	+	3.82279e6i	0.342910	+	0.593937i
$530$	1.60338e6	−	2.77713e6i	0.247940	−	0.429445i
$531$	2.46047e6			0.378688
$532$		0			0
$533$	−854800.			−0.130331
$534$	1.40387e6	−	2.43157e6i	0.213046	−	0.369006i
$535$	29138.3	+	50469.0i	0.00440128	+	0.00762325i
$536$	−683235.	−	1.18340e6i	−0.102721	−	0.177917i
$537$	−3.33768e6	+	5.78102e6i	−0.499469	+	0.865105i
$538$	−619907.			−0.0923359
$539$		0			0
$540$	−262351.			−0.0387167
$541$	−1.08416e6	+	1.87782e6i	−0.159258	+	0.275843i	−0.934601	−	0.355697i	$-0.884243\pi$
$541$	−1.08416e6	+	1.87782e6i	−0.159258	+	0.275843i	0.775343	+	0.631540i	$0.217577\pi$
$542$	3.91775e6	+	6.78575e6i	0.572848	+	0.992201i
$543$	1.35617e6	+	2.34895e6i	0.197385	+	0.341881i
$544$	414642.	−	718180.i	0.0600725	−	0.104049i
$545$	−2.48886e6			−0.358930
$546$		0			0
$547$	−9.13272e6			−1.30506			−0.652532	−	0.757761i	$-0.726293\pi$
$547$	−9.13272e6			−1.30506			−0.652532	+	0.757761i	$0.726293\pi$
$548$	−768816.	+	1.33163e6i	−0.109363	+	0.189423i
$549$	1.30354e6	+	2.25780e6i	0.184584	+	0.319709i
$550$	1.78340e6	+	3.08894e6i	0.251387	+	0.435415i
$551$	2.67738e6	−	4.63735e6i	0.375691	−	0.650715i
$552$	819090.			0.114415
$553$		0			0
$554$	−6.99810e6			−0.968737
$555$	1.29476e6	−	2.24259e6i	0.178426	−	0.309042i
$556$	806835.	+	1.39748e6i	0.110687	+	0.191716i
$557$	4.61014e6	+	7.98500e6i	0.629617	+	1.09053i	0.987629	+	0.156811i	$0.0501214\pi$
$557$	4.61014e6	+	7.98500e6i	0.629617	+	1.09053i	−0.358012	+	0.933717i	$0.616545\pi$
$558$	−1.14011e6	+	1.97474e6i	−0.155011	+	0.268487i
$559$	2.66904e6			0.361264
$560$		0			0
$561$	−2.48150e6			−0.332894
$562$	−2.81330e6	+	4.87277e6i	−0.375729	+	0.650782i
$563$	4.24638e6	+	7.35495e6i	0.564610	+	0.977933i	0.997086	+	0.0762872i	$0.0243066\pi$
$563$	4.24638e6	+	7.35495e6i	0.564610	+	0.977933i	−0.432476	+	0.901645i	$0.642360\pi$
$564$	670550.	+	1.16143e6i	0.0887633	+	0.153743i
$565$	−2.18075e6	+	3.77717e6i	−0.287399	+	0.497789i
$566$	−7.82828e6			−1.02713
$567$		0			0
$568$	3.91384e6			0.509017
$569$	2.35456e6	−	4.07822e6i	0.304880	−	0.528068i	−0.672355	−	0.740229i	$-0.734717\pi$
$569$	2.35456e6	−	4.07822e6i	0.304880	−	0.528068i	0.977235	+	0.212162i	$0.0680503\pi$
$570$	−415470.	−	719616.i	−0.0535615	−	0.0927712i
$571$	864035.	+	1.49655e6i	0.110902	+	0.192089i	0.916134	−	0.400871i	$-0.131293\pi$
$571$	864035.	+	1.49655e6i	0.110902	+	0.192089i	−0.805232	+	0.592960i	$0.797959\pi$
$572$	−1.98398e6	+	3.43636e6i	−0.253541	+	0.439145i
$573$	2.36864e6			0.301379
$574$		0			0
$575$	−3.72443e6			−0.469776
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	1.19249e6	+	2.06546e6i	0.149113	+	0.258272i	0.930900	−	0.365274i	$-0.119025\pi$
$577$	1.19249e6	+	2.06546e6i	0.149113	+	0.258272i	−0.781787	+	0.623546i	$0.785691\pi$
$578$	1.52801e6	+	2.64659e6i	0.190242	+	0.329509i
$579$	3.74007e6	−	6.47799e6i	0.463643	−	0.803053i
$580$	−1.87785e6			−0.231788
$581$		0			0
$582$	5.82355e6			0.712657
$583$	−6.06750e6	+	1.05092e7i	−0.739330	+	1.28056i
$584$	1.32057e6	+	2.28729e6i	0.160225	+	0.277517i
$585$	663543.	+	1.14929e6i	0.0801640	+	0.138848i
$586$	−2.53997e6	+	4.39935e6i	−0.305551	+	0.529230i
$587$	3.44904e6			0.413145			0.206573	−	0.978431i	$-0.433769\pi$
$587$	3.44904e6			0.413145			0.206573	+	0.978431i	$0.433769\pi$
$588$		0			0
$589$	−7.22214e6			−0.857784
$590$	1.36646e6	−	2.36678e6i	0.161610	−	0.279917i
$591$	4.74395e6	+	8.21676e6i	0.558691	+	0.967681i
$592$	−1.63739e6	−	2.83604e6i	−0.192021	−	0.332589i
$593$	567341.	−	982664.i	0.0662533	−	0.114754i	−0.830996	−	0.556278i	$-0.812229\pi$
$593$	567341.	−	982664.i	0.0662533	−	0.114754i	0.897249	+	0.441524i	$0.145562\pi$
$594$	992786.			0.115449
$595$		0			0
$596$	−5.77511e6			−0.665954
$597$	3.14355e6	−	5.44480e6i	0.360982	−	0.625239i
$598$	−2.07166e6	−	3.58822e6i	−0.236900	−	0.410323i
$599$	−3.80933e6	−	6.59795e6i	−0.433792	−	0.751349i	0.563404	−	0.826181i	$-0.309491\pi$
$599$	−3.80933e6	−	6.59795e6i	−0.433792	−	0.751349i	−0.997196	+	0.0748320i	$0.976158\pi$
$600$	754299.	−	1.30648e6i	0.0855393	−	0.148158i
$601$	−9.78414e6			−1.10493			−0.552467	−	0.833535i	$-0.686314\pi$
$601$	−9.78414e6			−1.10493			−0.552467	+	0.833535i	$0.686314\pi$
$602$		0			0
$603$	1.72944e6			0.193692
$604$	3.47245e6	−	6.01445e6i	0.387296	−	0.670817i
$605$	−507616.	−	879217.i	−0.0563829	−	0.0976580i
$606$	−1.18538e6	−	2.05314e6i	−0.131122	−	0.227110i
$607$	926673.	−	1.60504e6i	0.102083	−	0.176813i	−0.810460	−	0.585795i	$-0.800783\pi$
$607$	926673.	−	1.60504e6i	0.102083	−	0.176813i	0.912543	+	0.408981i	$0.134116\pi$
$608$	−1.05083e6			−0.115285
$609$		0			0
$610$	2.89578e6			0.315094
$611$	3.39194e6	−	5.87501e6i	0.367574	−	0.636657i
$612$	524781.	+	908947.i	0.0566369	+	0.0980980i
$613$	3.56048e6	+	6.16694e6i	0.382699	+	0.662855i	0.991447	−	0.130509i	$-0.0416612\pi$
$613$	3.56048e6	+	6.16694e6i	0.382699	+	0.662855i	−0.608748	+	0.793364i	$0.708328\pi$
$614$	−83708.7	+	144988.i	−0.00896086	+	0.0155207i
$615$	237554.			0.0253265
$616$		0			0
$617$	−2.75212e6			−0.291041			−0.145521	−	0.989355i	$-0.546486\pi$
$617$	−2.75212e6			−0.291041			−0.145521	+	0.989355i	$0.546486\pi$
$618$	2.34357e6	−	4.05917e6i	0.246835	−	0.427530i
$619$	−6.51660e6	−	1.12871e7i	−0.683588	−	1.18401i	−0.973878	−	0.227070i	$-0.927085\pi$
$619$	−6.51660e6	−	1.12871e7i	−0.683588	−	1.18401i	0.290291	−	0.956939i	$-0.406248\pi$
$620$	1.26636e6	+	2.19341e6i	0.132306	+	0.229160i
$621$	−518330.	+	897774.i	−0.0539358	+	0.0934196i
$622$	9.16758e6			0.950120
$623$		0			0
$624$	1.67827e6			0.172544
$625$	−2.63935e6	+	4.57149e6i	−0.270269	+	0.468120i
$626$	4.54299e6	+	7.86869e6i	0.463347	+	0.802540i
$627$	1.57222e6	+	2.72317e6i	0.159715	+	0.276634i
$628$	−4.09277e6	+	7.08889e6i	−0.414112	+	0.717264i
$629$	−1.03597e7			−1.04404
$630$		0			0
$631$	−4.40820e6			−0.440745			−0.220373	−	0.975416i	$-0.570727\pi$
$631$	−4.40820e6			−0.440745			−0.220373	+	0.975416i	$0.570727\pi$
$632$	1.12001e6	−	1.93992e6i	0.111540	−	0.193193i
$633$	448621.	+	777035.i	0.0445011	+	0.0770781i
$634$	3.96949e6	+	6.87535e6i	0.392203	+	0.679316i
$635$	308474.	−	534293.i	0.0303588	−	0.0525829i
$636$	5.13256e6			0.503143
$637$		0			0
$638$	7.10616e6			0.691168
$639$	−2.47673e6	+	4.28982e6i	−0.239953	+	0.415611i
$640$	184257.	+	319143.i	0.0177818	+	0.0307989i
$641$	3.99195e6	+	6.91426e6i	0.383742	+	0.664661i	0.991594	−	0.129389i	$-0.0413017\pi$
$641$	3.99195e6	+	6.91426e6i	0.383742	+	0.664661i	−0.607851	+	0.794051i	$0.707968\pi$
$642$	−46637.1	+	80777.8i	−0.00446575	+	0.00773490i
$643$	−1.52102e6			−0.145080			−0.0725398	−	0.997366i	$-0.523110\pi$
$643$	−1.52102e6			−0.145080			−0.0725398	+	0.997366i	$0.523110\pi$
$644$		0			0
$645$	−741741.			−0.0702026
$646$	−1.66213e6	+	2.87890e6i	−0.156706	+	0.271422i
$647$	−6.26247e6	−	1.08469e7i	−0.588146	−	1.01870i	−0.994475	−	0.104972i	$-0.966525\pi$
$647$	−6.26247e6	−	1.08469e7i	−0.588146	−	1.01870i	0.406329	−	0.913727i	$-0.366809\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	−5.17096e6	+	8.95637e6i	−0.481903	+	0.834681i
$650$	−7.63116e6			−0.708447
$651$		0			0
$652$	−4.02031e6			−0.370374
$653$	8.53702e6	−	1.47865e7i	0.783471	−	1.35701i	−0.146436	−	0.989220i	$-0.546780\pi$
$653$	8.53702e6	−	1.47865e7i	0.783471	−	1.35701i	0.929908	−	0.367792i	$-0.119886\pi$
$654$	−1.99177e6	−	3.44984e6i	−0.182093	−	0.315395i
$655$	−1.69115e6	−	2.92916e6i	−0.154021	−	0.266772i
$656$	150209.	−	260169.i	0.0136281	−	0.0236046i
$657$	−3.34269e6			−0.302122
$658$		0			0
$659$	−2.12585e6			−0.190686			−0.0953432	−	0.995444i	$-0.530395\pi$
$659$	−2.12585e6			−0.190686			−0.0953432	+	0.995444i	$0.530395\pi$
$660$	551360.	−	954984.i	0.0492692	−	0.0853368i
$661$	−1.30005e6	−	2.25176e6i	−0.115733	−	0.200456i	0.802339	−	0.596868i	$-0.203588\pi$
$661$	−1.30005e6	−	2.25176e6i	−0.115733	−	0.200456i	−0.918073	+	0.396412i	$0.870255\pi$
$662$	−1.27692e6	−	2.21169e6i	−0.113245	−	0.196146i
$663$	2.65457e6	−	4.59786e6i	0.234537	−	0.406230i
$664$	−5.51635e6			−0.485547
$665$		0			0
$666$	4.14464e6			0.362078
$667$	−3.71010e6	+	6.42608e6i	−0.322902	+	0.559283i
$668$	3.35421e6	+	5.80967e6i	0.290837	+	0.503744i
$669$	2.36787e6	+	4.10128e6i	0.204547	+	0.354286i
$670$	960472.	−	1.66359e6i	0.0826604	−	0.143172i
$671$	−1.09582e7			−0.939577
$672$		0			0
$673$	−1.44746e7			−1.23188			−0.615942	−	0.787792i	$-0.711224\pi$
$673$	−1.44746e7			−1.23188			−0.615942	+	0.787792i	$0.711224\pi$
$674$	−5.44052e6	+	9.42326e6i	−0.461308	+	0.799008i
$675$	954660.	+	1.65352e6i	0.0806472	+	0.139685i
$676$	−1.27437e6	−	2.20728e6i	−0.107258	−	0.185776i
$677$	−1.64423e6	+	2.84788e6i	−0.137876	+	0.238809i	−0.926693	−	0.375820i	$-0.877361\pi$
$677$	−1.64423e6	+	2.84788e6i	−0.137876	+	0.238809i	0.788816	+	0.614629i	$0.210694\pi$
$678$	−6.98077e6			−0.583216
$679$		0			0
$680$	1.16578e6			0.0966819
$681$	−4.41722e6	+	7.65085e6i	−0.364990	+	0.632182i
$682$	−4.79217e6	−	8.30027e6i	−0.394522	−	0.683332i
$683$	−4.40943e6	−	7.63736e6i	−0.361685	−	0.626458i	0.626553	−	0.779379i	$-0.284465\pi$
$683$	−4.40943e6	−	7.63736e6i	−0.361685	−	0.626458i	−0.988238	+	0.152921i	$0.951132\pi$
$684$	664979.	−	1.15178e6i	0.0543460	−	0.0941300i
$685$	−2.16156e6			−0.176011
$686$		0			0
$687$	765729.			0.0618989
$688$	−469013.	+	812355.i	−0.0377758	+	0.0654297i
$689$	−1.29814e7	−	2.24844e7i	−1.04177	−	1.80440i
$690$	575726.	+	997188.i	0.0460356	+	0.0797359i
$691$	−4.29808e6	+	7.44450e6i	−0.342436	+	0.593117i	−0.984885	−	0.173212i	$-0.944585\pi$
$691$	−4.29808e6	+	7.44450e6i	−0.342436	+	0.593117i	0.642448	+	0.766329i	$0.277919\pi$
$692$	7.38202e6			0.586017
$693$		0			0
$694$	1.04831e7			0.826208
$695$	−1.13423e6	+	1.96454e6i	−0.0890713	+	0.154276i
$696$	−1.50279e6	−	2.60291e6i	−0.117592	−	0.203675i
$697$	−475180.	−	823035.i	−0.0370490	−	0.0641707i
$698$	1.15118e6	−	1.99391e6i	0.0894348	−	0.154906i
$699$	1.01811e6			0.0788134
$700$		0			0
$701$	2.06437e7			1.58669			0.793347	−	0.608770i	$-0.208337\pi$
$701$	2.06437e7			1.58669			0.793347	+	0.608770i	$0.208337\pi$
$702$	−1.06203e6	+	1.83949e6i	−0.0813381	+	0.140882i
$703$	6.56364e6	+	1.13686e7i	0.500906	+	0.867595i
$704$	−697266.	−	1.20770e6i	−0.0530233	−	0.0918390i
$705$	−942640.	+	1.63270e6i	−0.0714288	+	0.123718i
$706$	1.03589e7			0.782169
$707$		0			0
$708$	4.37417e6			0.327954
$709$	213441.	−	369691.i	0.0159464	−	0.0276200i	−0.857942	−	0.513746i	$-0.828257\pi$
$709$	213441.	−	369691.i	0.0159464	−	0.0276200i	0.873888	+	0.486126i	$0.161591\pi$
$710$	2.75098e6	+	4.76484e6i	0.204806	+	0.354734i
$711$	1.41752e6	+	2.45521e6i	0.105161	+	0.182144i
$712$	2.49576e6	−	4.32279e6i	0.184503	−	0.319569i
$713$	1.00079e7			0.737257
$714$		0			0
$715$	−5.57805e6			−0.408054
$716$	−5.93365e6	+	1.02774e7i	−0.432553	+	0.749203i
$717$	4.02795e6	+	6.97662e6i	0.292608	+	0.506812i
$718$	−5.73558e6	−	9.93431e6i	−0.415208	−	0.719162i
$719$	1.90362e6	−	3.29716e6i	0.137328	−	0.237858i	−0.789157	−	0.614192i	$-0.789482\pi$
$719$	1.90362e6	−	3.29716e6i	0.137328	−	0.237858i	0.926484	+	0.376334i	$0.122815\pi$
$720$	−466401.			−0.0335296
$721$		0			0
$722$	−5.69204e6			−0.406373
$723$	2.37472e6	−	4.11313e6i	0.168953	−	0.292635i
$724$	2.41097e6	+	4.17592e6i	0.170940	+	0.296077i
$725$	6.83326e6	+	1.18356e7i	0.482817	+	0.836264i
$726$	812463.	−	1.40723e6i	0.0572087	−	0.0990883i
$727$	2.22044e7			1.55813			0.779065	−	0.626943i	$-0.215694\pi$
$727$	2.22044e7			1.55813			0.779065	+	0.626943i	$0.215694\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.85642e6	+	3.21541e6i	−0.128934	+	0.223321i
$731$	1.48371e6	+	2.56986e6i	0.102696	+	0.177875i
$732$	2.31741e6	+	4.01387e6i	0.159855	+	0.276876i
$733$	−1.45286e7	+	2.51643e7i	−0.998766	+	1.72991i	−0.456365	+	0.889793i	$0.650849\pi$
$733$	−1.45286e7	+	2.51643e7i	−0.998766	+	1.72991i	−0.542401	+	0.840120i	$0.682485\pi$
$734$	7.81804e6			0.535621
$735$		0			0
$736$	1.45616e6			0.0990865
$737$	−3.63461e6	+	6.29533e6i	−0.246484	+	0.426923i
$738$	190108.	+	329276.i	0.0128487	+	0.0222546i
$739$	−1.06761e7	−	1.84916e7i	−0.719122	−	1.24556i	−0.961348	−	0.275337i	$-0.911211\pi$
$739$	−1.06761e7	−	1.84916e7i	−0.719122	−	1.24556i	0.242226	−	0.970220i	$-0.422123\pi$
$740$	2.30180e6	−	3.98683e6i	0.154521	−	0.267638i
$741$	−6.72751e6			−0.450100
$742$		0			0
$743$	3.91874e6			0.260420			0.130210	−	0.991486i	$-0.458435\pi$
$743$	3.91874e6			0.260420			0.130210	+	0.991486i	$0.458435\pi$
$744$	−2.02687e6	+	3.51064e6i	−0.134244	+	0.232517i
$745$	−4.05924e6	−	7.03081e6i	−0.267950	−	0.464103i
$746$	−4.42219e6	−	7.65946e6i	−0.290931	−	0.503908i
$747$	3.49081e6	−	6.04627e6i	0.228889	−	0.396448i
$748$	−4.41155e6			−0.288295
$749$		0			0
$750$	4.65113e6			0.301930
$751$	−2.83456e6	+	4.90960e6i	−0.183394	+	0.317648i	−0.943034	−	0.332696i	$-0.892042\pi$
$751$	−2.83456e6	+	4.90960e6i	−0.183394	+	0.317648i	0.759640	+	0.650344i	$0.225375\pi$
$752$	1.19209e6	+	2.06476e6i	0.0768713	+	0.133145i
$753$	−5.36817e6	−	9.29794e6i	−0.345015	−	0.597584i
$754$	−7.60180e6	+	1.31667e7i	−0.486954	+	0.843429i
$755$	9.76293e6			0.623323
$756$		0			0
$757$	−1.91706e7			−1.21590			−0.607949	−	0.793976i	$-0.708007\pi$
$757$	−1.91706e7			−1.21590			−0.607949	+	0.793976i	$0.708007\pi$
$758$	−7.62463e6	+	1.32063e7i	−0.481999	+	0.834846i
$759$	−2.17866e6	−	3.77355e6i	−0.137273	−	0.237764i
$760$	−738614.	−	1.27932e6i	−0.0463856	−	0.0803423i
$761$	7.31680e6	−	1.26731e7i	0.457993	−	0.793268i	−0.540861	−	0.841112i	$-0.681902\pi$
$761$	7.31680e6	−	1.26731e7i	0.457993	−	0.793268i	0.998855	+	0.0478438i	$0.0152350\pi$
$762$	987453.			0.0616068
$763$		0			0
$764$	4.21092e6			0.261002
$765$	−737722.	+	1.27777e6i	−0.0455763	+	0.0789405i
$766$	7.61212e6	+	1.31846e7i	0.468742	+	0.811884i
$767$	−1.10632e7	−	1.91621e7i	−0.679038	−	1.17613i
$768$	−294912.	+	510803.i	−0.0180422	+	0.0312500i
$769$	−1.57337e7

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(11.2462 - 19.4789i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(44.9847 + 77.9158i) q^{10} +(-170.231 - 294.849i) q^{11} +(-72.0000 + 124.708i) q^{12} +728.416 q^{13} -202.431 q^{15} +(-128.000 + 221.703i) q^{16} +(404.923 + 701.348i) q^{17} +(-162.000 - 280.592i) q^{18} +(513.101 - 888.717i) q^{19} -359.878 q^{20} +1361.85 q^{22} +(-711.015 + 1231.51i) q^{23} +(-288.000 - 498.831i) q^{24} +(1309.55 + 2268.20i) q^{25} +(-1456.83 + 2523.31i) q^{26} +729.000 q^{27} +5218.03 q^{29} +(404.862 - 701.242i) q^{30} +(-3518.87 - 6094.87i) q^{31} +(-512.000 - 886.810i) q^{32} +(-1532.08 + 2653.64i) q^{33} -3239.39 q^{34} +1296.00 q^{36} +(-6396.05 + 11078.3i) q^{37} +(2052.40 + 3554.87i) q^{38} +(-3277.87 - 5677.44i) q^{39} +(719.755 - 1246.65i) q^{40} -1173.51 q^{41} +3664.17 q^{43} +(-2723.69 + 4717.58i) q^{44} +(910.940 + 1577.79i) q^{45} +(-2844.06 - 4926.06i) q^{46} +(4656.60 - 8065.46i) q^{47} +2304.00 q^{48} -10476.4 q^{50} +(3644.31 - 6312.13i) q^{51} +(-5827.33 - 10093.2i) q^{52} +(-17821.4 - 30867.6i) q^{53} +(-1458.00 + 2525.33i) q^{54} -7657.78 q^{55} -9235.81 q^{57} +(-10436.1 + 18075.8i) q^{58} +(-15188.1 - 26306.5i) q^{59} +(1619.45 + 2804.97i) q^{60} +(16093.1 - 27874.1i) q^{61} +28151.0 q^{62} +4096.00 q^{64} +(8191.89 - 14188.8i) q^{65} +(-6128.31 - 10614.5i) q^{66} +(-10675.5 - 18490.6i) q^{67} +(6478.78 - 11221.6i) q^{68} +12798.3 q^{69} +61153.7 q^{71} +(-2592.00 + 4489.48i) q^{72} +(20633.9 + 35739.0i) q^{73} +(-25584.2 - 44313.2i) q^{74} +(11785.9 - 20413.8i) q^{75} -16419.2 q^{76} +26223.0 q^{78} +(17500.2 - 30311.3i) q^{79} +(2879.02 + 4986.61i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(2347.01 - 4065.14i) q^{82} -86193.0 q^{83} +18215.4 q^{85} +(-7328.33 + 12693.0i) q^{86} +(-23481.1 - 40670.5i) q^{87} +(-10894.8 - 18870.3i) q^{88} +(38996.3 - 67543.6i) q^{89} -7287.52 q^{90} +22752.5 q^{92} +(-31669.9 + 54853.8i) q^{93} +(18626.4 + 32261.9i) q^{94} +(-11540.8 - 19989.3i) q^{95} +(-4608.00 + 7981.29i) q^{96} +161765. q^{97} +27577.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 - 53 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} - 212 q^{10} - 191 q^{11} - 288 q^{12} + 758 q^{13} + 954 q^{15} - 512 q^{16} - 340 q^{17} - 648 q^{18} - 1769 q^{19} + 1696 q^{20} + 1528 q^{22} - 3236 q^{23} - 1152 q^{24} + 45 q^{25} - 1516 q^{26} + 2916 q^{27} + 8918 q^{29} - 1908 q^{30} + 1994 q^{31} - 2048 q^{32} - 1719 q^{33} + 2720 q^{34} + 5184 q^{36} - 20587 q^{37} - 7076 q^{38} - 3411 q^{39} - 3392 q^{40} - 17628 q^{41} + 31706 q^{43} - 3056 q^{44} - 4293 q^{45} - 12944 q^{46} + 33912 q^{47} + 9216 q^{48} - 360 q^{50} - 3060 q^{51} - 6064 q^{52} - 49239 q^{53} - 5832 q^{54} - 37882 q^{55} + 31842 q^{57} - 17836 q^{58} - 56735 q^{59} - 7632 q^{60} + 67508 q^{61} - 15952 q^{62} + 16384 q^{64} + 42762 q^{65} - 6876 q^{66} - 75723 q^{67} - 5440 q^{68} + 58248 q^{69} - 17984 q^{71} - 10368 q^{72} - 3201 q^{73} - 82348 q^{74} + 405 q^{75} + 56608 q^{76} + 27288 q^{78} - 26612 q^{79} - 13568 q^{80} - 13122 q^{81} + 35256 q^{82} + 1898 q^{83} + 210040 q^{85} - 63412 q^{86} - 40131 q^{87} - 12224 q^{88} + 176562 q^{89} + 34344 q^{90} + 103552 q^{92} + 17946 q^{93} + 135648 q^{94} - 234098 q^{95} - 18432 q^{96} + 258846 q^{97} + 30942 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 - 53 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 - 212 * q^10 - 191 * q^11 - 288 * q^12 + 758 * q^13 + 954 * q^15 - 512 * q^16 - 340 * q^17 - 648 * q^18 - 1769 * q^19 + 1696 * q^20 + 1528 * q^22 - 3236 * q^23 - 1152 * q^24 + 45 * q^25 - 1516 * q^26 + 2916 * q^27 + 8918 * q^29 - 1908 * q^30 + 1994 * q^31 - 2048 * q^32 - 1719 * q^33 + 2720 * q^34 + 5184 * q^36 - 20587 * q^37 - 7076 * q^38 - 3411 * q^39 - 3392 * q^40 - 17628 * q^41 + 31706 * q^43 - 3056 * q^44 - 4293 * q^45 - 12944 * q^46 + 33912 * q^47 + 9216 * q^48 - 360 * q^50 - 3060 * q^51 - 6064 * q^52 - 49239 * q^53 - 5832 * q^54 - 37882 * q^55 + 31842 * q^57 - 17836 * q^58 - 56735 * q^59 - 7632 * q^60 + 67508 * q^61 - 15952 * q^62 + 16384 * q^64 + 42762 * q^65 - 6876 * q^66 - 75723 * q^67 - 5440 * q^68 + 58248 * q^69 - 17984 * q^71 - 10368 * q^72 - 3201 * q^73 - 82348 * q^74 + 405 * q^75 + 56608 * q^76 + 27288 * q^78 - 26612 * q^79 - 13568 * q^80 - 13122 * q^81 + 35256 * q^82 + 1898 * q^83 + 210040 * q^85 - 63412 * q^86 - 40131 * q^87 - 12224 * q^88 + 176562 * q^89 + 34344 * q^90 + 103552 * q^92 + 17946 * q^93 + 135648 * q^94 - 234098 * q^95 - 18432 * q^96 + 258846 * q^97 + 30942 * q^99

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