LMFDB - Embedded newform 294.6.e.s.79.1

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			79.1
Root			$24.7462 - 42.8616i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.s.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-150.985 - 261.513i) q^{10} +(74.7309 + 129.438i) q^{11} +(-72.0000 + 124.708i) q^{12} -349.416 q^{13} +679.431 q^{15} +(-128.000 + 221.703i) q^{16} +(-574.923 - 995.797i) q^{17} +(-162.000 - 280.592i) q^{18} +(-1397.60 + 2420.72i) q^{19} +1207.88 q^{20} -597.847 q^{22} +(-906.985 + 1570.94i) q^{23} +(-288.000 - 498.831i) q^{24} +(-1287.05 - 2229.23i) q^{25} +(698.832 - 1210.41i) q^{26} +729.000 q^{27} -759.033 q^{29} +(-1358.86 + 2353.62i) q^{30} +(4515.87 + 7821.72i) q^{31} +(-512.000 - 886.810i) q^{32} +(672.578 - 1164.94i) q^{33} +4599.39 q^{34} +1296.00 q^{36} +(-3897.45 + 6750.57i) q^{37} +(-5590.40 - 9682.86i) q^{38} +(1572.37 + 2723.43i) q^{39} +(-2415.76 + 4184.21i) q^{40} -7640.49 q^{41} +12188.8 q^{43} +(1195.69 - 2071.00i) q^{44} +(-3057.44 - 5295.64i) q^{45} +(-3627.94 - 6283.77i) q^{46} +(12299.4 - 21303.2i) q^{47} +2304.00 q^{48} +10296.4 q^{50} +(-5174.31 + 8962.17i) q^{51} +(2795.33 + 4841.65i) q^{52} +(-6798.11 - 11774.7i) q^{53} +(-1458.00 + 2525.33i) q^{54} -11283.2 q^{55} +25156.8 q^{57} +(1518.07 - 2629.37i) q^{58} +(-13179.4 - 22827.4i) q^{59} +(-5435.45 - 9414.47i) q^{60} +(17660.9 - 30589.5i) q^{61} -36127.0 q^{62} +4096.00 q^{64} +(13189.1 - 22844.2i) q^{65} +(2690.31 + 4659.76i) q^{66} +(-27186.0 - 47087.5i) q^{67} +(-9198.78 + 15932.7i) q^{68} +16325.7 q^{69} -70145.7 q^{71} +(-2592.00 + 4489.48i) q^{72} +(-22234.4 - 38511.1i) q^{73} +(-15589.8 - 27002.3i) q^{74} +(-11583.4 + 20063.1i) q^{75} +44723.2 q^{76} -12579.0 q^{78} +(-30806.2 + 53357.9i) q^{79} +(-9663.02 - 16736.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(15281.0 - 26467.5i) q^{82} +87142.0 q^{83} +86804.6 q^{85} +(-24377.7 + 42223.4i) q^{86} +(3415.65 + 5916.08i) q^{87} +(4782.78 + 8284.01i) q^{88} +(49284.7 - 85363.6i) q^{89} +24459.5 q^{90} +29023.5 q^{92} +(40642.9 - 70395.5i) q^{93} +(49197.6 + 85212.8i) q^{94} +(-105508. - 182745. i) q^{95} +(-4608.00 + 7981.29i) q^{96} -32342.3 q^{97} -12106.4 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
$5$	−37.7462	+	65.3783i	−0.675224	+	1.16952i	0.301179	+	0.953568i	$0.402620\pi$
$5$	−37.7462	+	65.3783i	−0.675224	+	1.16952i	−0.976403	+	0.215955i	$0.930714\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−150.985	−	261.513i	−0.477456	−	0.826977i
$11$	74.7309	+	129.438i	0.186217	+	0.322537i	0.943986	−	0.329986i	$-0.107044\pi$
$11$	74.7309	+	129.438i	0.186217	+	0.322537i	−0.757769	+	0.652523i	$0.773711\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	−349.416			−0.573435			−0.286717	−	0.958015i	$-0.592564\pi$
$13$	−349.416			−0.573435			−0.286717	+	0.958015i	$0.592564\pi$
$14$		0			0
$15$	679.431			0.779682
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−574.923	−	995.797i	−0.482489	−	0.835696i	0.517309	−	0.855799i	$-0.326934\pi$
$17$	−574.923	−	995.797i	−0.482489	−	0.835696i	−0.999798	+	0.0201029i	$0.993601\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	−1397.60	+	2420.72i	−0.888176	+	1.53837i	−0.0461468	+	0.998935i	$0.514694\pi$
$19$	−1397.60	+	2420.72i	−0.888176	+	1.53837i	−0.842029	+	0.539432i	$0.818639\pi$
$20$	1207.88			0.675224
$21$		0			0
$22$	−597.847			−0.263350
$23$	−906.985	+	1570.94i	−0.357504	+	0.619214i	−0.987543	−	0.157349i	$-0.949705\pi$
$23$	−906.985	+	1570.94i	−0.357504	+	0.619214i	0.630040	+	0.776563i	$0.283039\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	−1287.05	−	2229.23i	−0.411855	−	0.713354i
$26$	698.832	−	1210.41i	0.202740	−	0.351156i
$27$	729.000			0.192450
$28$		0			0
$29$	−759.033			−0.167597			−0.0837984	−	0.996483i	$-0.526705\pi$
$29$	−759.033			−0.167597			−0.0837984	+	0.996483i	$0.526705\pi$
$30$	−1358.86	+	2353.62i	−0.275659	+	0.477456i
$31$	4515.87	+	7821.72i	0.843990	+	1.46183i	0.886495	+	0.462738i	$0.153133\pi$
$31$	4515.87	+	7821.72i	0.843990	+	1.46183i	−0.0425050	+	0.999096i	$0.513534\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	672.578	−	1164.94i	0.107512	−	0.186217i
$34$	4599.39			0.682343
$35$		0			0
$36$	1296.00			0.166667
$37$	−3897.45	+	6750.57i	−0.468032	+	0.810655i	−0.999333	−	0.0365280i	$-0.988370\pi$
$37$	−3897.45	+	6750.57i	−0.468032	+	0.810655i	0.531300	+	0.847183i	$0.321704\pi$
$38$	−5590.40	−	9682.86i	−0.628035	−	1.08779i
$39$	1572.37	+	2723.43i	0.165536	+	0.286717i
$40$	−2415.76	+	4184.21i	−0.238728	+	0.413489i
$41$	−7640.49			−0.709842			−0.354921	−	0.934896i	$-0.615492\pi$
$41$	−7640.49			−0.709842			−0.354921	+	0.934896i	$0.615492\pi$
$42$		0			0
$43$	12188.8			1.00529			0.502645	−	0.864493i	$-0.332360\pi$
$43$	12188.8			1.00529			0.502645	+	0.864493i	$0.332360\pi$
$44$	1195.69	−	2071.00i	0.0931083	−	0.161268i
$45$	−3057.44	−	5295.64i	−0.225075	−	0.389841i
$46$	−3627.94	−	6283.77i	−0.252793	−	0.437851i
$47$	12299.4	−	21303.2i	0.812156	−	1.40670i	−0.0991964	−	0.995068i	$-0.531627\pi$
$47$	12299.4	−	21303.2i	0.812156	−	1.40670i	0.911352	−	0.411627i	$-0.135039\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	10296.4			0.582451
$51$	−5174.31	+	8962.17i	−0.278565	+	0.482489i
$52$	2795.33	+	4841.65i	0.143359	+	0.248305i
$53$	−6798.11	−	11774.7i	−0.332429	−	0.575783i	0.650559	−	0.759456i	$-0.274535\pi$
$53$	−6798.11	−	11774.7i	−0.332429	−	0.575783i	−0.982988	+	0.183672i	$0.941201\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	−11283.2			−0.502952
$56$		0			0
$57$	25156.8			1.02558
$58$	1518.07	−	2629.37i	0.0592544	−	0.102632i
$59$	−13179.4	−	22827.4i	−0.492908	−	0.853742i	0.507059	−	0.861912i	$-0.330733\pi$
$59$	−13179.4	−	22827.4i	−0.492908	−	0.853742i	−0.999967	+	0.00816991i	$0.997399\pi$
$60$	−5435.45	−	9414.47i	−0.194920	−	0.337612i
$61$	17660.9	−	30589.5i	0.607698	−	1.05256i	−0.383921	−	0.923366i	$-0.625427\pi$
$61$	17660.9	−	30589.5i	0.607698	−	1.05256i	0.991619	−	0.129198i	$-0.0412402\pi$
$62$	−36127.0			−1.19358
$63$		0			0
$64$	4096.00			0.125000
$65$	13189.1	−	22844.2i	0.387197	−	0.670645i
$66$	2690.31	+	4659.76i	0.0760226	+	0.131675i
$67$	−27186.0	−	47087.5i	−0.739874	−	1.28150i	−0.952552	−	0.304377i	$-0.901552\pi$
$67$	−27186.0	−	47087.5i	−0.739874	−	1.28150i	0.212678	−	0.977122i	$-0.431781\pi$
$68$	−9198.78	+	15932.7i	−0.241245	+	0.417848i
$69$	16325.7			0.412810
$70$		0			0
$71$	−70145.7			−1.65141			−0.825706	−	0.564101i	$-0.809223\pi$
$71$	−70145.7			−1.65141			−0.825706	+	0.564101i	$0.809223\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	−22234.4	−	38511.1i	−0.488335	−	0.845822i	0.511574	−	0.859239i	$-0.329062\pi$
$73$	−22234.4	−	38511.1i	−0.488335	−	0.845822i	−0.999910	+	0.0134170i	$0.995729\pi$
$74$	−15589.8	−	27002.3i	−0.330949	−	0.573220i
$75$	−11583.4	+	20063.1i	−0.237785	+	0.411855i
$76$	44723.2			0.888176
$77$		0			0
$78$	−12579.0			−0.234104
$79$	−30806.2	+	53357.9i	−0.555355	+	0.961903i	0.442521	+	0.896758i	$0.354084\pi$
$79$	−30806.2	+	53357.9i	−0.555355	+	0.961903i	−0.997876	+	0.0651450i	$0.979249\pi$
$80$	−9663.02	−	16736.8i	−0.168806	−	0.292381i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	15281.0	−	26467.5i	0.250967	−	0.434688i
$83$	87142.0			1.38846			0.694228	−	0.719755i	$-0.255746\pi$
$83$	87142.0			1.38846			0.694228	+	0.719755i	$0.255746\pi$
$84$		0			0
$85$	86804.6			1.30315
$86$	−24377.7	+	42223.4i	−0.355423	+	0.615611i
$87$	3415.65	+	5916.08i	0.0483810	+	0.0837984i
$88$	4782.78	+	8284.01i	0.0658375	+	0.114034i
$89$	49284.7	−	85363.6i	0.659534	−	1.14235i	−0.321203	−	0.947010i	$-0.604087\pi$
$89$	49284.7	−	85363.6i	0.659534	−	1.14235i	0.980736	−	0.195336i	$-0.0625796\pi$
$90$	24459.5			0.318304
$91$		0			0
$92$	29023.5			0.357504
$93$	40642.9	−	70395.5i	0.487278	−	0.843990i
$94$	49197.6	+	85212.8i	0.574281	+	0.994684i
$95$	−105508.	−	182745.i	−1.19944	−	2.07748i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	−32342.3			−0.349013			−0.174507	−	0.984656i	$-0.555833\pi$
$97$	−32342.3			−0.349013			−0.174507	+	0.984656i	$0.555833\pi$
$98$		0			0
$99$	−12106.4			−0.124144
$100$	−20592.8	+	35667.7i	−0.205928	+	0.356677i
$101$	15673.2	+	27146.8i	0.152881	+	0.264798i	0.932286	−	0.361723i	$-0.117811\pi$
$101$	15673.2	+	27146.8i	0.152881	+	0.264798i	−0.779404	+	0.626521i	$0.784478\pi$
$102$	−20697.2	−	35848.7i	−0.196975	−	0.341171i
$103$	49666.5	−	86024.8i	0.461286	−	0.798970i	−0.537740	−	0.843111i	$-0.680722\pi$
$103$	49666.5	−	86024.8i	0.461286	−	0.798970i	0.999025	+	0.0441406i	$0.0140549\pi$
$104$	−22362.6			−0.202740
$105$		0			0
$106$	54384.9			0.470125
$107$	72634.0	−	125806.i	0.613310	−	1.06228i	−0.377368	−	0.926063i	$-0.623171\pi$
$107$	72634.0	−	125806.i	0.613310	−	1.06228i	0.990678	−	0.136221i	$-0.0434959\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	90425.4	+	156621.i	0.728994	+	1.26265i	0.957309	+	0.289067i	$0.0933452\pi$
$109$	90425.4	+	156621.i	0.728994	+	1.26265i	−0.228315	+	0.973587i	$0.573321\pi$
$110$	22566.4	−	39086.2i	0.177820	−	0.307994i
$111$	70154.0			0.540437
$112$		0			0
$113$	197832.			1.45748			0.728738	−	0.684793i	$-0.240107\pi$
$113$	197832.			1.45748			0.728738	+	0.684793i	$0.240107\pi$
$114$	−50313.6	+	87145.8i	−0.362596	+	0.628035i
$115$	−68470.4	−	118594.i	−0.482790	−	0.836217i
$116$	6072.27	+	10517.5i	0.0418992	+	0.0725715i
$117$	14151.3	−	24510.8i	0.0955725	−	0.165536i
$118$	105435.			0.697077
$119$		0			0
$120$	43483.6			0.275659
$121$	69356.1	−	120128.i	0.430647	−	0.745902i
$122$	70643.5	+	122358.i	0.429707	+	0.744275i
$123$	34382.2	+	59551.8i	0.204914	+	0.354921i
$124$	72254.0	−	125148.i	0.421995	−	0.730917i
$125$	−41589.2			−0.238070
$126$		0			0
$127$	−33517.2			−0.184399			−0.0921996	−	0.995741i	$-0.529390\pi$
$127$	−33517.2			−0.184399			−0.0921996	+	0.995741i	$0.529390\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	−54849.8	−	95002.6i	−0.290202	−	0.502645i
$130$	52756.4	+	91376.8i	0.273790	+	0.474218i
$131$	−5404.45	+	9360.79i	−0.0275153	+	0.0476578i	−0.879455	−	0.475982i	$-0.842093\pi$
$131$	−5404.45	+	9360.79i	−0.0275153	+	0.0476578i	0.851940	+	0.523640i	$0.175426\pi$
$132$	−21522.5			−0.107512
$133$		0			0
$134$	217488.			1.04634
$135$	−27517.0	+	47660.8i	−0.129947	+	0.225075i
$136$	−36795.1	−	63731.0i	−0.170586	−	0.295463i
$137$	9466.01	+	16395.6i	0.0430889	+	0.0746322i	0.886766	−	0.462220i	$-0.152947\pi$
$137$	9466.01	+	16395.6i	0.0430889	+	0.0746322i	−0.843677	+	0.536852i	$0.819613\pi$
$138$	−32651.4	+	56554.0i	−0.145950	+	0.252793i
$139$	168897.			0.741457			0.370729	−	0.928741i	$-0.379108\pi$
$139$	168897.			0.741457			0.370729	+	0.928741i	$0.379108\pi$
$140$		0			0
$141$	−221389.			−0.937797
$142$	140291.	−	242992.i	0.583862	−	1.01128i
$143$	−26112.1	−	45227.6i	−0.106783	−	0.184954i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	28650.6	−	49624.3i	0.113165	−	0.196008i
$146$	177875.			0.690611
$147$		0			0
$148$	124718.			0.468032
$149$	−132001.	+	228633.i	−0.487093	+	0.843670i	−0.999890	−	0.0148402i	$-0.995276\pi$
$149$	−132001.	+	228633.i	−0.487093	+	0.843670i	0.512797	+	0.858510i	$0.328609\pi$
$150$	−46333.7	−	80252.3i	−0.168139	−	0.291226i
$151$	−139587.	−	241772.i	−0.498200	−	0.862908i	0.501798	−	0.864985i	$-0.332672\pi$
$151$	−139587.	−	241772.i	−0.498200	−	0.862908i	−0.999998	+	0.00207707i	$0.999339\pi$
$152$	−89446.4	+	154926.i	−0.314018	+	0.543895i
$153$	93137.6			0.321660
$154$		0			0
$155$	−681828.			−2.27953
$156$	25157.9	−	43574.8i	0.0827682	−	0.143359i
$157$	94301.2	+	163334.i	0.305329	+	0.528845i	0.977334	−	0.211701i	$-0.0679003\pi$
$157$	94301.2	+	163334.i	0.305329	+	0.528845i	−0.672006	+	0.740546i	$0.734567\pi$
$158$	−123225.	−	213432.i	−0.392695	−	0.680168i
$159$	−61183.0	+	105972.i	−0.191928	+	0.332429i
$160$	77304.2			0.238728
$161$		0			0
$162$	26244.0			0.0785674
$163$	−44858.7	+	77697.5i	−0.132244	+	0.229054i	−0.924541	−	0.381081i	$-0.875552\pi$
$163$	−44858.7	+	77697.5i	−0.132244	+	0.229054i	0.792297	+	0.610136i	$0.208885\pi$
$164$	61124.0	+	105870.i	0.177461	+	0.307371i
$165$	50774.5	+	87944.0i	0.145190	+	0.251476i
$166$	−174284.	+	301869.i	−0.490893	+	0.850252i
$167$	−529411.			−1.46893			−0.734467	−	0.678645i	$-0.762568\pi$
$167$	−529411.			−1.46893			−0.734467	+	0.678645i	$0.762568\pi$
$168$		0			0
$169$	−249202.			−0.671172
$170$	−173609.	+	300700.i	−0.460734	+	0.798015i
$171$	−113206.	−	196078.i	−0.296059	−	0.512789i
$172$	−97510.7	−	168893.i	−0.251322	−	0.435303i
$173$	16919.2	−	29304.8i	0.0429797	−	0.0744430i	−0.843735	−	0.536759i	$-0.819648\pi$
$173$	16919.2	−	29304.8i	0.0429797	−	0.0744430i	0.886715	+	0.462316i	$0.152982\pi$
$174$	−27325.2			−0.0684211
$175$		0			0
$176$	−38262.2			−0.0931083
$177$	−118615.	+	205447.i	−0.284581	+	0.492908i
$178$	197139.	+	341454.i	0.466361	+	0.807761i
$179$	123872.	+	214552.i	0.288962	+	0.500496i	0.973562	−	0.228422i	$-0.0733567\pi$
$179$	123872.	+	214552.i	0.288962	+	0.500496i	−0.684601	+	0.728918i	$0.740023\pi$
$180$	−48919.0	+	84730.3i	−0.112537	+	0.194920i
$181$	−369470.			−0.838268			−0.419134	−	0.907924i	$-0.637666\pi$
$181$	−369470.			−0.838268			−0.419134	+	0.907924i	$0.637666\pi$
$182$		0			0
$183$	−317896.			−0.701709
$184$	−58047.0	+	100540.i	−0.126397	+	0.218925i
$185$	−294227.	−	509617.i	−0.632053	−	1.09475i
$186$	162571.	+	281582.i	0.344558	+	0.596791i
$187$	85929.1	−	148833.i	0.179695	−	0.311241i
$188$	−393581.			−0.812156
$189$		0			0
$190$	844065.			1.69626
$191$	242612.	−	420217.i	0.481204	−	0.833470i	−0.518563	−	0.855039i	$-0.673533\pi$
$191$	242612.	−	420217.i	0.481204	−	0.833470i	0.999767	+	0.0215693i	$0.00686625\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	165409.	+	286496.i	0.319643	+	0.553637i	0.980413	−	0.196950i	$-0.0631038\pi$
$193$	165409.	+	286496.i	0.319643	+	0.553637i	−0.660771	+	0.750588i	$0.729770\pi$
$194$	64684.7	−	112037.i	0.123395	−	0.213726i
$195$	−237404.			−0.447097
$196$		0			0
$197$	−161963.			−0.297337			−0.148669	−	0.988887i	$-0.547499\pi$
$197$	−161963.			−0.297337			−0.148669	+	0.988887i	$0.547499\pi$
$198$	24212.8	−	41937.8i	0.0438917	−	0.0760226i
$199$	27698.1	+	47974.5i	0.0495813	+	0.0858773i	0.889751	−	0.456446i	$-0.150878\pi$
$199$	27698.1	+	47974.5i	0.0495813	+	0.0858773i	−0.840170	+	0.542324i	$0.817545\pi$
$200$	−82371.0	−	142671.i	−0.145613	−	0.252209i
$201$	−244674.	+	423787.i	−0.427166	+	0.739874i
$202$	−125386.			−0.216207
$203$		0			0
$204$	165578.			0.278565
$205$	288399.	−	499522.i	0.479303	−	0.830176i
$206$	198666.	+	344099.i	0.326178	+	0.564957i
$207$	−73465.8	−	127246.i	−0.119168	−	0.206405i
$208$	44725.2	−	77466.4i	0.0716794	−	0.124152i
$209$	−417776.			−0.661572
$210$		0			0
$211$	481748.			0.744926			0.372463	−	0.928047i	$-0.378513\pi$
$211$	481748.			0.744926			0.372463	+	0.928047i	$0.378513\pi$
$212$	−108770.	+	188395.i	−0.166214	+	0.287892i
$213$	315656.	+	546732.i	0.476722	+	0.825706i
$214$	290536.	+	503223.i	0.433676	+	0.751149i
$215$	−460082.	+	796885.i	−0.678795	+	1.17571i
$216$	46656.0			0.0680414
$217$		0			0
$218$	−723403.			−1.03095
$219$	−200110.	+	346600.i	−0.281941	+	0.488335i
$220$	90265.7	+	156345.i	0.125738	+	0.217784i
$221$	200887.	+	347947.i	0.276676	+	0.479217i
$222$	−140308.	+	243021.i	−0.191073	+	0.330949i
$223$	−638779.			−0.860178			−0.430089	−	0.902787i	$-0.641518\pi$
$223$	−638779.			−0.860178			−0.430089	+	0.902787i	$0.641518\pi$
$224$		0			0
$225$	208502.			0.274570
$226$	−395665.	+	685312.i	−0.515295	+	0.892518i
$227$	−262841.	−	455254.i	−0.338554	−	0.586394i	0.645607	−	0.763670i	$-0.276605\pi$
$227$	−262841.	−	455254.i	−0.338554	−	0.586394i	−0.984161	+	0.177277i	$0.943271\pi$
$228$	−201255.	−	348583.i	−0.256394	−	0.444088i
$229$	466343.	−	807730.i	0.587647	−	1.01784i	−0.406892	−	0.913476i	$-0.633388\pi$
$229$	466343.	−	807730.i	0.587647	−	1.01784i	0.994540	−	0.104359i	$-0.0332791\pi$
$230$	547763.			0.682768
$231$		0			0
$232$	−48578.1			−0.0592544
$233$	353896.	−	612967.i	0.427058	−	0.739685i	−0.569553	−	0.821955i	$-0.692884\pi$
$233$	353896.	−	612967.i	0.427058	−	0.739685i	0.996610	+	0.0822696i	$0.0262168\pi$
$234$	56605.4	+	98043.4i	0.0675800	+	0.117052i
$235$	928511.	+	1.60823e6i	1.09677	+	1.89967i
$236$	−210871.	+	365238.i	−0.246454	+	0.426871i
$237$	554512.			0.641269
$238$		0			0
$239$	−500614.			−0.566902			−0.283451	−	0.958987i	$-0.591479\pi$
$239$	−500614.			−0.566902			−0.283451	+	0.958987i	$0.591479\pi$
$240$	−86967.2	+	150632.i	−0.0974602	+	0.168806i
$241$	604109.	+	1.04635e6i	0.669997	+	1.16047i	0.977904	+	0.209052i	$0.0670379\pi$
$241$	604109.	+	1.04635e6i	0.669997	+	1.16047i	−0.307907	+	0.951416i	$0.599629\pi$
$242$	277424.	+	480513.i	0.304513	+	0.527432i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−565148.			−0.607698
$245$		0			0
$246$	−275058.			−0.289792
$247$	488344.	−	845836.i	0.509311	−	0.882153i
$248$	289016.	+	500590.i	0.298396	+	0.516836i
$249$	−392139.	−	679204.i	−0.400813	−	0.694228i
$250$	83178.3	−	144069.i	0.0841705	−	0.145788i
$251$	−97826.7			−0.0980106			−0.0490053	−	0.998799i	$-0.515605\pi$
$251$	−97826.7			−0.0980106			−0.0490053	+	0.998799i	$0.515605\pi$
$252$		0			0
$253$	−271119.			−0.266292
$254$	67034.5	−	116107.i	0.0651949	−	0.112921i
$255$	−390621.	−	676575.i	−0.376188	−	0.651577i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−553956.	+	959481.i	−0.523170	+	0.906157i	0.476466	+	0.879193i	$0.341917\pi$
$257$	−553956.	+	959481.i	−0.523170	+	0.906157i	−0.999636	+	0.0269643i	$0.991416\pi$
$258$	438798.			0.410408
$259$		0			0
$260$	−422052.			−0.387197
$261$	30740.8	−	53244.7i	0.0279328	−	0.0483810i
$262$	−21617.8	−	37443.2i	−0.0194562	−	0.0336992i
$263$	−753427.	−	1.30497e6i	−0.671663	−	1.16336i	−0.977432	−	0.211249i	$-0.932247\pi$
$263$	−753427.	−	1.30497e6i	−0.671663	−	1.16336i	0.305769	−	0.952106i	$-0.401087\pi$
$264$	43045.0	−	74556.1i	0.0380113	−	0.0658375i
$265$	1.02641e6			0.897856
$266$		0			0
$267$	−887125.			−0.761564
$268$	−434975.	+	753399.i	−0.369937	+	0.640750i
$269$	−1.06751e6	−	1.84898e6i	−0.899481	−	1.55795i	−0.828159	−	0.560493i	$-0.810612\pi$
$269$	−1.06751e6	−	1.84898e6i	−0.899481	−	1.55795i	−0.0713221	−	0.997453i	$-0.522722\pi$
$270$	−110068.	−	190643.i	−0.0918864	−	0.159152i
$271$	614299.	−	1.06400e6i	0.508108	−	0.880070i	−0.491847	−	0.870681i	$-0.663678\pi$
$271$	614299.	−	1.06400e6i	0.508108	−	0.880070i	0.999956	−	0.00938828i	$-0.00298843\pi$
$272$	294361.			0.241245
$273$		0			0
$274$	−75728.1			−0.0609369
$275$	192364.	−	333185.i	0.153388	−	0.265677i
$276$	−130606.	−	226216.i	−0.103202	−	0.178752i
$277$	923412.	+	1.59940e6i	0.723097	+	1.25244i	0.959753	+	0.280847i	$0.0906152\pi$
$277$	923412.	+	1.59940e6i	0.723097	+	1.25244i	−0.236656	+	0.971593i	$0.576051\pi$
$278$	−337795.	+	585078.i	−0.262145	+	0.454048i
$279$	−731571.			−0.562660
$280$		0			0
$281$	−2.28326e6			−1.72500			−0.862500	−	0.506056i	$-0.831103\pi$
$281$	−2.28326e6			−1.72500			−0.862500	+	0.506056i	$0.831103\pi$
$282$	442779.	−	766915.i	0.331561	−	0.574281i
$283$	668463.	+	1.15781e6i	0.496148	+	0.859354i	0.999990	−	0.00444218i	$-0.00141400\pi$
$283$	668463.	+	1.15781e6i	0.496148	+	0.859354i	−0.503842	+	0.863796i	$0.668081\pi$
$284$	561166.	+	971968.i	0.412853	+	0.715082i
$285$	−949573.	+	1.64471e6i	−0.692495	+	1.19944i
$286$	208897.			0.151014
$287$		0			0
$288$	82944.0			0.0589256
$289$	48854.5	−	84618.5i	0.0344081	−	0.0595965i
$290$	114602.	+	198497.i	0.0800200	+	0.138599i
$291$	145541.	+	252084.i	0.100751	+	0.174507i
$292$	−355750.	+	616178.i	−0.244168	+	0.422911i
$293$	2.23033e6			1.51775			0.758875	−	0.651236i	$-0.225749\pi$
$293$	2.23033e6			1.51775			0.758875	+	0.651236i	$0.225749\pi$
$294$		0			0
$295$	1.98989e6			1.33129
$296$	−249436.	+	432037.i	−0.165474	+	0.286610i
$297$	54478.8	+	94360.1i	0.0358374	+	0.0620722i
$298$	−528004.	−	914530.i	−0.344427	−	0.596565i
$299$	316915.	−	548913.i	0.205005	−	0.355079i
$300$	370670.			0.237785
$301$		0			0
$302$	1.11670e6			0.704561
$303$	141059.	−	244321.i	0.0882661	−	0.152881i
$304$	−357786.	−	619703.i	−0.222044	−	0.384592i
$305$	1.33326e6	+	2.30928e6i	0.820664	+	1.42143i
$306$	−186275.	+	322638.i	−0.113724	+	0.196975i
$307$	−1.77782e6			−1.07657			−0.538284	−	0.842763i	$-0.680927\pi$
$307$	−1.77782e6			−1.07657			−0.538284	+	0.842763i	$0.680927\pi$
$308$		0			0
$309$	−893996.			−0.532647
$310$	1.36366e6	−	2.36192e6i	0.805936	−	1.39592i
$311$	701358.	+	1.21479e6i	0.411187	+	0.712196i	0.995020	−	0.0996776i	$-0.0317811\pi$
$311$	701358.	+	1.21479e6i	0.411187	+	0.712196i	−0.583833	+	0.811874i	$0.698448\pi$
$312$	100632.	+	174299.i	0.0585260	+	0.101370i
$313$	609472.	−	1.05564e6i	0.351636	−	0.609051i	−0.634900	−	0.772594i	$-0.718959\pi$
$313$	609472.	−	1.05564e6i	0.351636	−	0.609051i	0.986536	+	0.163543i	$0.0522922\pi$
$314$	−754409.			−0.431800
$315$		0			0
$316$	985799.			0.555355
$317$	−1.34001e6	+	2.32096e6i	−0.748961	+	1.29724i	0.199361	+	0.979926i	$0.436113\pi$
$317$	−1.34001e6	+	2.32096e6i	−0.748961	+	1.29724i	−0.948321	+	0.317312i	$0.897220\pi$
$318$	−244732.	−	423888.i	−0.135713	−	0.235063i
$319$	−56723.2	−	98247.5i	−0.0312093	−	0.0540561i
$320$	−154608.	+	267789.i	−0.0844030	+	0.146190i
$321$	−1.30741e6			−0.708190
$322$		0			0
$323$	3.21405e6			1.71414
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	449715.	+	778929.i	0.236172	+	0.409062i
$326$	−179435.	−	310790.i	−0.0935110	−	0.161966i
$327$	813828.	−	1.40959e6i	0.420885	−	0.728994i
$328$	−488992.			−0.250967
$329$		0			0
$330$	−406196.			−0.205329
$331$	−71280.1	+	123461.i	−0.0357601	+	0.0619383i	−0.883352	−	0.468711i	$-0.844719\pi$
$331$	−71280.1	+	123461.i	−0.0357601	+	0.0619383i	0.847591	+	0.530649i	$0.178052\pi$
$332$	−697136.	−	1.20747e6i	−0.347114	−	0.601219i
$333$	−315693.	−	546796.i	−0.156011	−	0.270218i
$334$	1.05882e6	−	1.83393e6i	0.519346	−	0.899534i
$335$	4.10466e6			1.99832
$336$		0			0
$337$	−1.21206e6			−0.581367			−0.290683	−	0.956819i	$-0.593883\pi$
$337$	−1.21206e6			−0.581367			−0.290683	+	0.956819i	$0.593883\pi$
$338$	498403.	−	863260.i	0.237295	−	0.411007i
$339$	−890246.	−	1.54195e6i	−0.420737	−	0.728738i
$340$	−694437.	−	1.20280e6i	−0.325788	−	0.564282i
$341$	−674950.	+	1.16905e6i	−0.314330	+	0.544435i
$342$	905645.			0.418690
$343$		0			0
$344$	780085.			0.355423
$345$	−616234.	+	1.06735e6i	−0.278739	+	0.482790i
$346$	67676.6	+	117219.i	0.0303912	+	0.0526392i
$347$	−1.73426e6	−	3.00383e6i	−0.773199	−	1.33922i	−0.935801	−	0.352529i	$-0.885322\pi$
$347$	−1.73426e6	−	3.00383e6i	−0.773199	−	1.33922i	0.162602	−	0.986692i	$-0.448011\pi$
$348$	54650.4	−	94657.2i	0.0241905	−	0.0418992i
$349$	−1.01692e6			−0.446911			−0.223456	−	0.974714i	$-0.571734\pi$
$349$	−1.01692e6			−0.446911			−0.223456	+	0.974714i	$0.571734\pi$
$350$		0			0
$351$	−254724.			−0.110358
$352$	76524.4	−	132544.i	0.0329187	−	0.0570169i
$353$	781927.	+	1.35434e6i	0.333987	+	0.578483i	0.983290	−	0.182048i	$-0.0582725\pi$
$353$	781927.	+	1.35434e6i	0.333987	+	0.578483i	−0.649303	+	0.760530i	$0.724939\pi$
$354$	−474459.	−	821786.i	−0.201229	−	0.348539i
$355$	2.64773e6	−	4.58601e6i	1.11507	−	1.93136i
$356$	−1.57711e6			−0.659534
$357$		0			0
$358$	−990975.			−0.408653
$359$	−24776.6	+	42914.3i	−0.0101462	+	0.0175738i	−0.871054	−	0.491187i	$-0.836563\pi$
$359$	−24776.6	+	42914.3i	−0.0101462	+	0.0175738i	0.860908	+	0.508761i	$0.169896\pi$
$360$	−195676.	−	338921.i	−0.0795759	−	0.137830i
$361$	−2.66853e6	−	4.62202e6i	−1.07771	−	1.86666i
$362$	738940.	−	1.27988e6i	0.296373	−	0.513332i
$363$	−1.24841e6			−0.497268
$364$		0			0
$365$	3.35705e6			1.31894
$366$	635792.	−	1.10122e6i	0.248092	−	0.429707i
$367$	1.77416e6	+	3.07293e6i	0.687585	+	1.19093i	0.972617	+	0.232414i	$0.0746626\pi$
$367$	1.77416e6	+	3.07293e6i	0.687585	+	1.19093i	−0.285032	+	0.958518i	$0.592004\pi$
$368$	−232188.	−	402162.i	−0.0893759	−	0.154804i
$369$	309440.	−	535966.i	0.118307	−	0.204914i
$370$	2.35382e6			0.893858
$371$		0			0
$372$	−1.30057e6			−0.487278
$373$	1.12787e6	−	1.95352e6i	0.419745	−	0.727020i	−0.576169	−	0.817331i	$-0.695453\pi$
$373$	1.12787e6	−	1.95352e6i	0.419745	−	0.727020i	0.995914	+	0.0903112i	$0.0287862\pi$
$374$	343716.	+	595334.i	0.127064	+	0.220081i
$375$	187151.	+	324155.i	0.0687250	+	0.119035i
$376$	787162.	−	1.36340e6i	0.287140	−	0.497342i
$377$	265218.			0.0961059
$378$		0			0
$379$	4.39503e6			1.57168			0.785840	−	0.618430i	$-0.212231\pi$
$379$	4.39503e6			1.57168			0.785840	+	0.618430i	$0.212231\pi$
$380$	−1.68813e6	+	2.92393e6i	−0.599718	+	1.03874i
$381$	150828.	+	261241.i	0.0532315	+	0.0921996i
$382$	970449.	+	1.68087e6i	0.340263	+	0.589352i
$383$	−613904.	+	1.06331e6i	−0.213847	+	0.370394i	−0.952915	−	0.303237i	$-0.901933\pi$
$383$	−613904.	+	1.06331e6i	−0.213847	+	0.370394i	0.739068	+	0.673631i	$0.235266\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	−1.32327e6			−0.452043
$387$	−493648.	+	855023.i	−0.167548	+	0.290202i
$388$	258739.	+	448149.i	0.0872533	+	0.151127i
$389$	−1.02712e6	−	1.77903e6i	−0.344150	−	0.596086i	0.641049	−	0.767500i	$-0.278500\pi$
$389$	−1.02712e6	−	1.77903e6i	−0.344150	−	0.596086i	−0.985199	+	0.171415i	$0.945166\pi$
$390$	474808.	−	822391.i	0.158073	−	0.273790i
$391$	2.08579e6			0.689967
$392$		0			0
$393$	97280.2			0.0317719
$394$	323925.	−	561055.i	0.105125	−	0.182081i
$395$	−2.32563e6	−	4.02812e6i	−0.749978	−	1.29900i
$396$	96851.2	+	167751.i	0.0310361	+	0.0537561i
$397$	−1.90184e6	+	3.29408e6i	−0.605615	+	1.04896i	0.386339	+	0.922357i	$0.373740\pi$
$397$	−1.90184e6	+	3.29408e6i	−0.605615	+	1.04896i	−0.991954	+	0.126599i	$0.959594\pi$
$398$	−221585.			−0.0701185
$399$		0			0
$400$	658968.			0.205928
$401$	−592622.	+	1.02645e6i	−0.184042	+	0.318770i	−0.943253	−	0.332074i	$-0.892252\pi$
$401$	−592622.	+	1.02645e6i	−0.184042	+	0.318770i	0.759211	+	0.650844i	$0.225585\pi$
$402$	−978695.	−	1.69515e6i	−0.302052	−	0.523170i
$403$	−1.57792e6	−	2.73303e6i	−0.483974	−	0.838267i
$404$	250771.	−	434349.i	0.0764406	−	0.132399i
$405$	495305.			0.150050
$406$		0			0
$407$	−1.16504e6			−0.348621
$408$	−331156.	+	573579.i	−0.0984877	+	0.170586i
$409$	−2.15197e6	−	3.72731e6i	−0.636102	−	1.10176i	−0.986280	−	0.165079i	$-0.947212\pi$
$409$	−2.15197e6	−	3.72731e6i	−0.636102	−	1.10176i	0.350178	−	0.936683i	$-0.386121\pi$
$410$	1.15360e6	+	1.99809e6i	0.338918	+	0.587023i
$411$	85194.1	−	147560.i	0.0248774	−	0.0430889i
$412$	−1.58933e6			−0.461286
$413$		0			0
$414$	587726.			0.168529
$415$	−3.28928e6	+	5.69719e6i	−0.937519	+	1.62383i
$416$	178901.	+	309865.i	0.0506850	+	0.0877889i
$417$	−760038.	−	1.31643e6i	−0.214040	−	0.370729i
$418$	835551.	−	1.44722e6i	0.233901	−	0.405129i
$419$	113725.			0.0316461			0.0158230	−	0.999875i	$-0.494963\pi$
$419$	113725.			0.0316461			0.0158230	+	0.999875i	$0.494963\pi$
$420$		0			0
$421$	443417.			0.121929			0.0609645	−	0.998140i	$-0.480582\pi$
$421$	443417.			0.121929			0.0609645	+	0.998140i	$0.480582\pi$
$422$	−963495.	+	1.66882e6i	−0.263371	+	0.456172i
$423$	996252.	+	1.72556e6i	0.270719	+	0.468898i
$424$	−435079.	−	753579.i	−0.117531	−	0.203570i
$425$	−1.47991e6	+	2.56327e6i	−0.397431	+	0.688371i
$426$	−2.52525e6			−0.674186
$427$		0			0
$428$	−2.32429e6			−0.613310
$429$	−235009.	+	407048.i	−0.0616512	+	0.106783i
$430$	−1.84033e6	−	3.18754e6i	−0.479981	−	0.831351i
$431$	−2.31655e6	−	4.01239e6i	−0.600688	−	1.04042i	−0.992717	−	0.120469i	$-0.961560\pi$
$431$	−2.31655e6	−	4.01239e6i	−0.600688	−	1.04042i	0.392029	−	0.919953i	$-0.371773\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	−6.57955e6			−1.68646			−0.843231	−	0.537552i	$-0.819349\pi$
$433$	−6.57955e6			−1.68646			−0.843231	+	0.537552i	$0.819349\pi$
$434$		0			0
$435$	−515711.			−0.130672
$436$	1.44681e6	−	2.50594e6i	0.364497	−	0.631327i
$437$	−2.53520e6	−	4.39110e6i	−0.635052	−	1.09994i
$438$	−800438.	−	1.38640e6i	−0.199362	−	0.345305i
$439$	−910348.	+	1.57677e6i	−0.225448	+	0.390487i	−0.956454	−	0.291884i	$-0.905718\pi$
$439$	−910348.	+	1.57677e6i	−0.225448	+	0.390487i	0.731006	+	0.682371i	$0.239051\pi$
$440$	−722126.			−0.177820
$441$		0			0
$442$	−1.60710e6			−0.391279
$443$	1.03495e6	−	1.79259e6i	0.250559	−	0.433982i	−0.713121	−	0.701041i	$-0.752719\pi$
$443$	1.03495e6	−	1.79259e6i	0.250559	−	0.433982i	0.963680	+	0.267060i	$0.0860521\pi$
$444$	−561232.	−	972083.i	−0.135109	−	0.234016i
$445$	3.72062e6	+	6.44430e6i	0.890666	+	1.54268i
$446$	1.27756e6	−	2.21279e6i	0.304119	−	0.526749i
$447$	2.37602e6			0.562447
$448$		0			0
$449$	5.72581e6			1.34036			0.670180	−	0.742199i	$-0.266217\pi$
$449$	5.72581e6			1.34036			0.670180	+	0.742199i	$0.266217\pi$
$450$	−417003.	+	722271.i	−0.0970752	+	0.168139i
$451$	−570981.	−	988968.i	−0.132184	−	0.228950i
$452$	−1.58266e6	−	2.74125e6i	−0.364369	−	0.631105i
$453$	−1.25629e6	+	2.17595e6i	−0.287636	+	0.498200i
$454$	2.10273e6			0.478788
$455$		0			0
$456$	1.61004e6			0.362596
$457$	−159338.	+	275982.i	−0.0356886	+	0.0618144i	−0.883318	−	0.468774i	$-0.844696\pi$
$457$	−159338.	+	275982.i	−0.0356886	+	0.0618144i	0.847629	+	0.530589i	$0.178029\pi$
$458$	1.86537e6	+	3.23092e6i	0.415529	+	0.719718i
$459$	−419119.	−	725936.i	−0.0928551	−	0.160830i
$460$	−1.09553e6	+	1.89751e6i	−0.241395	+	0.418108i
$461$	3.42470e6			0.750535			0.375267	−	0.926917i	$-0.377551\pi$
$461$	3.42470e6			0.750535			0.375267	+	0.926917i	$0.377551\pi$
$462$		0			0
$463$	3.82945e6			0.830201			0.415101	−	0.909775i	$-0.363746\pi$
$463$	3.82945e6			0.830201			0.415101	+	0.909775i	$0.363746\pi$
$464$	97156.2	−	168280.i	0.0209496	−	0.0362858i
$465$	3.06822e6	+	5.31432e6i	0.658044	+	1.13977i
$466$	1.41559e6	+	2.45187e6i	0.301975	+	0.523037i
$467$	1.42231e6	−	2.46351e6i	0.301788	−	0.522712i	−0.674753	−	0.738044i	$-0.735750\pi$
$467$	1.42231e6	−	2.46351e6i	0.301788	−	0.522712i	0.976541	+	0.215332i	$0.0690832\pi$
$468$	−452843.			−0.0955725
$469$		0			0
$470$	−7.42809e6			−1.55107
$471$	848710.	−	1.47001e6i	0.176282	−	0.305329i
$472$	−843482.	−	1.46095e6i	−0.174269	−	0.301843i
$473$	910882.	+	1.57769e6i	0.187202	+	0.324243i
$474$	−1.10902e6	+	1.92089e6i	−0.226723	+	0.392695i
$475$	7.19511e6			1.46320
$476$		0			0
$477$	1.10129e6			0.221619
$478$	1.00123e6	−	1.73418e6i	0.200430	−	0.347155i
$479$	651827.	+	1.12900e6i	0.129806	+	0.224830i	0.923601	−	0.383355i	$-0.125231\pi$
$479$	651827.	+	1.12900e6i	0.129806	+	0.224830i	−0.793796	+	0.608185i	$0.791898\pi$
$480$	−347869.	−	602526.i	−0.0689148	−	0.119364i
$481$	1.36183e6	−	2.35876e6i	0.268386	−	0.464858i
$482$	−4.83287e6			−0.947519
$483$		0			0
$484$	−2.21940e6			−0.430647
$485$	1.22080e6	−	2.11449e6i	0.235662	−	0.408179i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	−3.11812e6	−	5.40074e6i	−0.595759	−	1.03188i	−0.993439	−	0.114360i	$-0.963518\pi$
$487$	−3.11812e6	−	5.40074e6i	−0.595759	−	1.03188i	0.397681	−	0.917524i	$-0.369815\pi$
$488$	1.13030e6	−	1.95773e6i	0.214854	−	0.372137i
$489$	807456.			0.152703
$490$		0			0
$491$	−3.93928e6			−0.737417			−0.368709	−	0.929545i	$-0.620200\pi$
$491$	−3.93928e6			−0.737417			−0.368709	+	0.929545i	$0.620200\pi$
$492$	550116.	−	952828.i	0.102457	−	0.177461i
$493$	436386.	+	755843.i	0.0808637	+	0.140060i
$494$	1.95338e6	+	3.38335e6i	0.360137	+	0.623776i
$495$	456970.	−	791496.i	0.0838253	−	0.145190i
$496$	−2.31213e6			−0.421995
$497$		0			0
$498$	3.13711e6			0.566835
$499$	−3.98785e6	+	6.90717e6i	−0.716948	+	1.24179i	0.245255	+	0.969459i	$0.421128\pi$
$499$	−3.98785e6	+	6.90717e6i	−0.716948	+	1.24179i	−0.962203	+	0.272333i	$0.912205\pi$
$500$	332713.	+	576276.i	0.0595176	+	0.103087i
$501$	2.38235e6	+	4.12635e6i	0.424045	+	0.734467i
$502$	195653.	−	338882.i	0.0346520	−	0.0600190i
$503$	2.70777e6			0.477190			0.238595	−	0.971119i	$-0.423313\pi$
$503$	2.70777e6			0.477190			0.238595	+	0.971119i	$0.423313\pi$
$504$		0			0
$505$	−2.36641e6			−0.412917
$506$	542238.	−	939184.i	0.0941486	−	0.163070i
$507$	1.12141e6	+	1.94233e6i	0.193751	+	0.335586i
$508$	268138.	+	464428.i	0.0460998	+	0.0798472i
$509$	1.95025e6	−	3.37793e6i	0.333653	−	0.577904i	−0.649572	−	0.760300i	$-0.725052\pi$
$509$	1.95025e6	−	3.37793e6i	0.333653	−	0.577904i	0.983225	+	0.182396i	$0.0583852\pi$
$510$	3.12497e6			0.532010
$511$		0			0
$512$	262144.			0.0441942
$513$	−1.01885e6	+	1.76470e6i	−0.170930	+	0.296059i
$514$	−2.21583e6	−	3.83792e6i	−0.369937	−	0.640750i
$515$	3.74944e6	+	6.49422e6i	0.622943	+	1.07897i
$516$	−877596.	+	1.52004e6i	−0.145101	+	0.251322i
$517$	3.67658e6			0.604947
$518$		0			0
$519$	−304545.			−0.0496287
$520$	844103.	−	1.46203e6i	0.136895	−	0.237109i
$521$	3.50032e6	+	6.06273e6i	0.564954	+	0.978529i	0.997054	+	0.0767034i	$0.0244394\pi$
$521$	3.50032e6	+	6.06273e6i	0.564954	+	0.978529i	−0.432100	+	0.901826i	$0.642227\pi$
$522$	122963.	+	212979.i	0.0197515	+	0.0342106i
$523$	−1.05604e6	+	1.82911e6i	−0.168821	+	0.292406i	−0.938005	−	0.346620i	$-0.887329\pi$
$523$	−1.05604e6	+	1.82911e6i	−0.168821	+	0.292406i	0.769185	+	0.639026i	$0.220663\pi$
$524$	172943.			0.0275153
$525$		0			0
$526$	6.02741e6			0.949875
$527$	5.19256e6	−	8.99378e6i	0.814433	−	1.41064i
$528$	172180.	+	298224.i	0.0268780	+	0.0465541i
$529$	1.57293e6	+	2.72439e6i	0.244382	+	0.423283i
$530$	−2.05282e6	+	3.55559e6i	−0.317440	+	0.549822i
$531$	2.13506e6			0.328605
$532$		0			0
$533$	2.66971e6			0.407048
$534$	1.77425e6	−	3.07309e6i	0.269254	−	0.466361i
$535$	5.48331e6	+	9.49737e6i	0.828244	+	1.43456i
$536$	−1.73990e6	−	3.01360e6i	−0.261585	−	0.453078i
$537$	1.11485e6	−	1.93097e6i	0.166832	−	0.288962i
$538$	8.54009e6			1.27206
$539$		0			0
$540$	880543.			0.129947
$541$	−2.85283e6	+	4.94125e6i	−0.419067	+	0.725845i	−0.995846	−	0.0910551i	$-0.970976\pi$
$541$	−2.85283e6	+	4.94125e6i	−0.419067	+	0.725845i	0.576779	+	0.816900i	$0.304309\pi$
$542$	2.45720e6	+	4.25599e6i	0.359287	+	0.622303i
$543$	1.66262e6	+	2.87974e6i	0.241987	+	0.419134i
$544$	−588722.	+	1.01970e6i	−0.0852929	+	0.147732i
$545$	−1.36528e7			−1.96894
$546$		0			0
$547$	2.28054e6			0.325888			0.162944	−	0.986635i	$-0.447901\pi$
$547$	2.28054e6			0.325888			0.162944	+	0.986635i	$0.447901\pi$
$548$	151456.	−	262330.i	0.0215445	−	0.0373161i
$549$	1.43053e6	+	2.47775e6i	0.202566	+	0.350855i
$550$	769457.	+	1.33274e6i	0.108462	+	0.187862i
$551$	1.06083e6	−	1.83740e6i	0.148855	−	0.257825i
$552$	1.04485e6			0.145950
$553$		0			0
$554$	−7.38730e6			−1.02261
$555$	−2.64805e6	+	4.58655e6i	−0.364916	+	0.632053i
$556$	−1.35118e6	−	2.34031e6i	−0.185364	−	0.321060i
$557$	3.36970e6	+	5.83650e6i	0.460208	+	0.797103i	0.998971	−	0.0453541i	$-0.0144416\pi$
$557$	3.36970e6	+	5.83650e6i	0.460208	+	0.797103i	−0.538763	+	0.842457i	$0.681108\pi$
$558$	1.46314e6	−	2.53424e6i	0.198930	−	0.344558i
$559$	−4.25897e6			−0.576468
$560$		0			0
$561$	−1.54672e6			−0.207494
$562$	4.56652e6	−	7.90944e6i	0.609880	−	1.05634i
$563$	−4.83410e6	−	8.37291e6i	−0.642754	−	1.11328i	−0.984815	−	0.173605i	$-0.944458\pi$
$563$	−4.83410e6	−	8.37291e6i	−0.642754	−	1.11328i	0.342061	−	0.939678i	$-0.388875\pi$
$564$	1.77111e6	+	3.06766e6i	0.234449	+	0.406078i
$565$	−7.46742e6	+	1.29339e7i	−0.984123	+	1.70455i
$566$	−5.34770e6			−0.701659
$567$		0			0
$568$	−4.48933e6			−0.583862
$569$	6.97934e6	−	1.20886e7i	0.903719	−	1.56529i	0.0810922	−	0.996707i	$-0.474159\pi$
$569$	6.97934e6	−	1.20886e7i	0.903719	−	1.56529i	0.822627	−	0.568581i	$-0.192507\pi$
$570$	−3.79829e6	−	6.57884e6i	−0.489668	−	0.848129i
$571$	1.17920e6	+	2.04244e6i	0.151355	+	0.262155i	0.931726	−	0.363162i	$-0.118303\pi$
$571$	1.17920e6	+	2.04244e6i	0.151355	+	0.262155i	−0.780371	+	0.625317i	$0.784970\pi$
$572$	−417794.	+	723641.i	−0.0533915	+	0.0924769i
$573$	−4.36702e6			−0.555647
$574$		0			0
$575$	4.66933e6			0.588959
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	2.50549e6	+	4.33963e6i	0.313295	+	0.542642i	0.979074	−	0.203507i	$-0.0652339\pi$
$577$	2.50549e6	+	4.33963e6i	0.313295	+	0.542642i	−0.665779	+	0.746149i	$0.731901\pi$
$578$	195418.	+	338474.i	0.0243302	+	0.0421411i
$579$	1.48868e6	−	2.57846e6i	0.184546	−	0.319643i
$580$	−916819.			−0.113165
$581$		0			0
$582$	−1.16432e6			−0.142484
$583$	1.01606e6	−	1.75986e6i	0.123807	−	0.214441i
$584$	−1.42300e6	−	2.46471e6i	−0.172653	−	0.299043i
$585$	1.06832e6	+	1.85038e6i	0.129066	+	0.223548i
$586$	−4.46066e6	+	7.72609e6i	−0.536606	+	0.929428i
$587$	−3.95106e6			−0.473280			−0.236640	−	0.971597i	$-0.576046\pi$
$587$	−3.95106e6			−0.473280			−0.236640	+	0.971597i	$0.576046\pi$
$588$		0			0
$589$	−2.52455e7			−2.99845
$590$	−3.97978e6	+	6.89318e6i	−0.470683	+	0.815247i
$591$	728832.	+	1.26237e6i	0.0858339	+	0.148669i
$592$	−997746.	−	1.72815e6i	−0.117008	−	0.202664i
$593$	−1.26840e6	+	2.19694e6i	−0.148122	+	0.256555i	−0.930533	−	0.366207i	$-0.880656\pi$
$593$	−1.26840e6	+	2.19694e6i	−0.148122	+	0.256555i	0.782411	+	0.622762i	$0.213990\pi$
$594$	−435830.			−0.0506817
$595$		0			0
$596$	4.22403e6			0.487093
$597$	249283.	−	431771.i	0.0286258	−	0.0495813i
$598$	1.26766e6	+	2.19565e6i	0.144960	+	0.251079i
$599$	−3.58857e6	−	6.21558e6i	−0.408652	−	0.707807i	0.586087	−	0.810248i	$-0.300668\pi$
$599$	−3.58857e6	−	6.21558e6i	−0.408652	−	0.707807i	−0.994739	+	0.102442i	$0.967335\pi$
$600$	−741339.	+	1.28404e6i	−0.0840696	+	0.145613i
$601$	−1.12527e7			−1.27078			−0.635392	−	0.772190i	$-0.719162\pi$
$601$	−1.12527e7			−1.27078			−0.635392	+	0.772190i	$0.719162\pi$
$602$		0			0
$603$	4.40413e6			0.493249
$604$	−2.23340e6	+	3.86836e6i	−0.249100	+	0.431454i
$605$	5.23585e6	+	9.06877e6i	0.581566	+	1.00730i
$606$	564235.	+	977284.i	0.0624135	+	0.108103i
$607$	−7.01851e6	+	1.21564e7i	−0.773167	+	1.33916i	0.162652	+	0.986684i	$0.447995\pi$
$607$	−7.01851e6	+	1.21564e7i	−0.773167	+	1.33916i	−0.935819	+	0.352481i	$0.885338\pi$
$608$	2.86229e6			0.314018
$609$		0			0
$610$	−1.06661e7			−1.16059
$611$	−4.29761e6	+	7.44367e6i	−0.465719	+	0.806648i
$612$	−745101.	−	1.29055e6i	−0.0804149	−	0.139283i
$613$	3.81436e6	+	6.60667e6i	0.409988	+	0.710119i	0.994888	−	0.100986i	$-0.0321997\pi$
$613$	3.81436e6	+	6.60667e6i	0.409988	+	0.710119i	−0.584900	+	0.811105i	$0.698866\pi$
$614$	3.55564e6	−	6.15855e6i	0.380624	−	0.659261i
$615$	−5.19119e6			−0.553451
$616$		0			0
$617$	−4.41080e6			−0.466450			−0.233225	−	0.972423i	$-0.574928\pi$
$617$	−4.41080e6			−0.466450			−0.233225	+	0.972423i	$0.574928\pi$
$618$	1.78799e6	−	3.09689e6i	0.188319	−	0.326178i
$619$	−4.52178e6	−	7.83195e6i	−0.474332	−	0.821567i	0.525236	−	0.850957i	$-0.323977\pi$
$619$	−4.52178e6	−	7.83195e6i	−0.474332	−	0.821567i	−0.999568	+	0.0293895i	$0.990644\pi$
$620$	5.45462e6	+	9.44768e6i	0.569883	+	0.987065i
$621$	−661192.	+	1.14522e6i	−0.0688016	+	0.119168i
$622$	−5.61087e6			−0.581506
$623$		0			0
$624$	−805054.			−0.0827682
$625$	5.59185e6	−	9.68538e6i	0.572606	−	0.991782i
$626$	2.43789e6	+	4.22255e6i	0.248644	+	0.430664i
$627$	1.87999e6	+	3.25624e6i	0.190980	+	0.330786i
$628$	1.50882e6	−	2.61335e6i	0.152664	−	0.264423i
$629$	8.96293e6			0.903282
$630$		0			0
$631$	−7.33039e6			−0.732916			−0.366458	−	0.930435i	$-0.619430\pi$
$631$	−7.33039e6			−0.732916			−0.366458	+	0.930435i	$0.619430\pi$
$632$	−1.97160e6	+	3.41491e6i	−0.196348	+	0.340084i
$633$	−2.16786e6	−	3.75485e6i	−0.215042	−	0.372463i
$634$	−5.36003e6	−	9.28384e6i	−0.529595	−	0.917286i
$635$	1.26515e6	−	2.19130e6i	0.124511	−	0.215659i
$636$	1.95786e6			0.191928
$637$		0			0
$638$	453786.			0.0441366
$639$	2.84090e6	−	4.92059e6i	0.275235	−	0.476722i
$640$	−618433.	−	1.07116e6i	−0.0596819	−	0.103372i
$641$	−1.84412e6	−	3.19411e6i	−0.177273	−	0.307047i	0.763672	−	0.645604i	$-0.223394\pi$
$641$	−1.84412e6	−	3.19411e6i	−0.177273	−	0.307047i	−0.940946	+	0.338558i	$0.890061\pi$
$642$	2.61482e6	−	4.52901e6i	0.250383	−	0.433676i
$643$	1.17584e7			1.12155			0.560776	−	0.827968i	$-0.310503\pi$
$643$	1.17584e7			1.12155			0.560776	+	0.827968i	$0.310503\pi$
$644$		0			0
$645$	8.28147e6			0.783806
$646$	−6.42811e6	+	1.11338e7i	−0.606041	+	1.04969i
$647$	−4.97025e6	−	8.60873e6i	−0.466786	−	0.808497i	0.532494	−	0.846434i	$-0.321255\pi$
$647$	−4.97025e6	−	8.60873e6i	−0.466786	−	0.808497i	−0.999280	+	0.0379368i	$0.987921\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	1.96982e6	−	3.41182e6i	0.183575	−	0.317962i
$650$	−3.59772e6			−0.333998
$651$		0			0
$652$	1.43548e6			0.132244
$653$	513100.	−	888714.i	0.0470889	−	0.0815604i	−0.841520	−	0.540226i	$-0.818339\pi$
$653$	513100.	−	888714.i	0.0470889	−	0.0815604i	0.888609	+	0.458665i	$0.151672\pi$
$654$	3.25531e6	+	5.63837e6i	0.297611	+	0.515477i
$655$	−407995.	−	706668.i	−0.0371579	−	0.0643594i
$656$	977983.	−	1.69392e6i	0.0887303	−	0.153685i
$657$	3.60197e6			0.325557
$658$		0			0
$659$	1.00207e7			0.898846			0.449423	−	0.893319i	$-0.351630\pi$
$659$	1.00207e7			0.898846			0.449423	+	0.893319i	$0.351630\pi$
$660$	812392.	−	1.40710e6i	0.0725948	−	0.125738i
$661$	1.31413e6	+	2.27614e6i	0.116986	+	0.202626i	0.918572	−	0.395254i	$-0.129343\pi$
$661$	1.31413e6	+	2.27614e6i	0.116986	+	0.202626i	−0.801586	+	0.597880i	$0.796010\pi$
$662$	−285120.	−	493843.i	−0.0252862	−	0.0437970i
$663$	1.80799e6	−	3.13152e6i	0.159739	−	0.276676i
$664$	5.57709e6			0.490893
$665$		0			0
$666$	2.52554e6			0.220632
$667$	688431.	−	1.19240e6i	0.0599165	−	0.103778i
$668$	4.23529e6	+	7.33574e6i	0.367233	+	0.636067i
$669$	2.87450e6	+	4.97879e6i	0.248312	+	0.430089i
$670$	−8.20933e6	+	1.42190e7i	−0.706514	+	1.22372i
$671$	5.27925e6			0.452654
$672$		0			0
$673$	−1.50220e7			−1.27847			−0.639233	−	0.769013i	$-0.720748\pi$
$673$	−1.50220e7			−1.27847			−0.639233	+	0.769013i	$0.720748\pi$
$674$	2.42412e6	−	4.19871e6i	0.205544	−	0.356013i
$675$	−938257.	−	1.62511e6i	−0.0792616	−	0.137285i
$676$	1.99361e6	+	3.45304e6i	0.167793	+	0.290626i
$677$	−3.01655e6	+	5.22482e6i	−0.252953	+	0.438127i	−0.964337	−	0.264676i	$-0.914735\pi$
$677$	−3.01655e6	+	5.22482e6i	−0.252953	+	0.438127i	0.711385	+	0.702803i	$0.248068\pi$
$678$	7.12197e6			0.595012
$679$		0			0
$680$	5.55550e6			0.460734
$681$	−2.36557e6	+	4.09729e6i	−0.195465	+	0.338554i
$682$	−2.69980e6	−	4.67619e6i	−0.222265	−	0.384974i
$683$	−5.53601e6	−	9.58865e6i	−0.454093	−	0.786513i	0.544542	−	0.838734i	$-0.316703\pi$
$683$	−5.53601e6	−	9.58865e6i	−0.454093	−	0.786513i	−0.998636	+	0.0522205i	$0.983370\pi$
$684$	−1.81129e6	+	3.13725e6i	−0.148029	+	0.256394i
$685$	−1.42922e6			−0.116379
$686$		0			0
$687$	−8.39417e6			−0.678557
$688$	−1.56017e6	+	2.70230e6i	−0.125661	+	0.217652i
$689$	2.37537e6	+	4.11426e6i	0.190626	+	0.330174i
$690$	−2.46493e6	−	4.26939e6i	−0.197098	−	0.341384i
$691$	−5.27739e6	+	9.14071e6i	−0.420460	+	0.728257i	−0.995984	−	0.0895269i	$-0.971464\pi$
$691$	−5.27739e6	+	9.14071e6i	−0.420460	+	0.728257i	0.575525	+	0.817784i	$0.304798\pi$
$692$	−541413.			−0.0429797
$693$		0			0
$694$	1.38741e7			1.09347
$695$	−6.37523e6	+	1.10422e7i	−0.500650	+	0.867151i
$696$	218602.	+	378629.i	0.0171053	+	0.0296272i
$697$	4.39270e6	+	7.60838e6i	0.342491	+	0.593212i
$698$	2.03383e6	−	3.52270e6i	0.158007	−	0.273676i
$699$	−6.37014e6			−0.493124
$700$		0			0
$701$	−7.20675e6			−0.553917			−0.276958	−	0.960882i	$-0.589326\pi$
$701$	−7.20675e6			−0.553917			−0.276958	+	0.960882i	$0.589326\pi$
$702$	509448.	−	882390.i	0.0390173	−	0.0675800i
$703$	−1.08941e7	−	1.88692e7i	−0.831390	−	1.44001i
$704$	306098.	+	530177.i	0.0232771	+	0.0403171i
$705$	8.35660e6	−	1.44741e7i	0.633223	−	1.09677i
$706$	−6.25542e6			−0.472329
$707$		0			0
$708$	3.79567e6			0.284581
$709$	−1.34687e6	+	2.33284e6i	−0.100626	+	0.174289i	−0.911943	−	0.410318i	$-0.865418\pi$
$709$	−1.34687e6	+	2.33284e6i	−0.100626	+	0.174289i	0.811317	+	0.584607i	$0.198751\pi$
$710$	1.05909e7	+	1.83440e7i	0.788476	+	1.36568i
$711$	−2.49530e6	−	4.32199e6i	−0.185118	−	0.320634i
$712$	3.15422e6	−	5.46327e6i	0.233180	−	0.403880i
$713$	−1.63833e7			−1.20692
$714$		0			0
$715$	3.94253e6			0.288410
$716$	1.98195e6	−	3.43284e6i	0.144481	−	0.250248i
$717$	2.25276e6	+	3.90190e6i	0.163651	+	0.283451i
$718$	−99106.3	−	171657.i	−0.00717447	−	0.0124266i
$719$	3.46275e6	−	5.99766e6i	0.249804	−	0.432673i	−0.713667	−	0.700485i	$-0.752967\pi$
$719$	3.46275e6	−	5.99766e6i	0.249804	−	0.432673i	0.963471	+	0.267812i	$0.0863005\pi$
$720$	1.56541e6			0.112537
$721$		0			0
$722$	2.13482e7			1.52412
$723$	5.43698e6	−	9.41713e6i	0.386823	−	0.669997i
$724$	2.95576e6	+	5.11953e6i	0.209567	+	0.362981i
$725$	976911.	+	1.69206e6i	0.0690256	+	0.119556i
$726$	2.49682e6	−	4.32462e6i	0.175811	−	0.304513i
$727$	−4.11366e6			−0.288664			−0.144332	−	0.989529i	$-0.546103\pi$
$727$	−4.11366e6			−0.288664			−0.144332	+	0.989529i	$0.546103\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−6.71411e6	+	1.16292e7i	−0.466317	+	0.807685i
$731$	−7.00765e6	−	1.21376e7i	−0.485041	−	0.840116i
$732$	2.54317e6	+	4.40489e6i	0.175427	+	0.303849i
$733$	3.96019e6	−	6.85925e6i	0.272243	−	0.471538i	−0.697193	−	0.716883i	$-0.745568\pi$
$733$	3.96019e6	−	6.85925e6i	0.272243	−	0.471538i	0.969436	+	0.245345i	$0.0789013\pi$
$734$	−1.41932e7			−0.972392
$735$		0			0
$736$	1.85750e6			0.126397
$737$	4.06326e6	−	7.03777e6i	0.275554	−	0.477273i
$738$	1.23776e6	+	2.14386e6i	0.0836557	+	0.144896i
$739$	−8.02050e6	−	1.38919e7i	−0.540245	−	0.935731i	−0.998890	−	0.0471115i	$-0.984998\pi$
$739$	−8.02050e6	−	1.38919e7i	−0.540245	−	0.935731i	0.458645	−	0.888620i	$-0.348335\pi$
$740$	−4.70764e6	+	8.15387e6i	−0.316027	+	0.547374i
$741$	−8.79019e6			−0.588102
$742$		0			0
$743$	1.53453e7			1.01977			0.509887	−	0.860241i	$-0.329687\pi$
$743$	1.53453e7			1.01977			0.509887	+	0.860241i	$0.329687\pi$
$744$	2.60114e6	−	4.50531e6i	0.172279	−	0.298396i
$745$	−9.96507e6	−	1.72600e7i	−0.657794	−	1.13933i
$746$	4.51147e6	+	7.81409e6i	0.296805	+	0.514081i
$747$	−3.52925e6	+	6.11284e6i	−0.231409	+	0.400813i
$748$	−2.74973e6			−0.179695
$749$		0			0
$750$	−1.49721e6			−0.0971918
$751$	−1.12488e7	+	1.94835e7i	−0.727790	+	1.26057i	0.230025	+	0.973185i	$0.426119\pi$
$751$	−1.12488e7	+	1.94835e7i	−0.727790	+	1.26057i	−0.957815	+	0.287385i	$0.907214\pi$
$752$	3.14865e6	+	5.45362e6i	0.203039	+	0.351674i
$753$	440220.	+	762483.i	0.0282932	+	0.0490053i
$754$	−530436.	+	918743.i	−0.0339786	+	0.0588526i
$755$	2.10756e7			1.34559
$756$		0			0
$757$	2.30349e7			1.46099			0.730494	−	0.682919i	$-0.239290\pi$
$757$	2.30349e7			1.46099			0.730494	+	0.682919i	$0.239290\pi$
$758$	−8.79006e6	+	1.52248e7i	−0.555673	+	0.962453i
$759$	1.22004e6	+	2.11316e6i	0.0768720	+	0.133146i
$760$	−6.75252e6	−	1.16957e7i	−0.424065	−	0.734501i
$761$	2.70368e6	−	4.68290e6i	0.169236	−	0.293126i	−0.768915	−	0.639351i	$-0.779203\pi$
$761$	2.70368e6	−	4.68290e6i	0.169236	−	0.293126i	0.938152	+	0.346225i	$0.112537\pi$
$762$	−1.20662e6			−0.0752806
$763$		0			0
$764$	−7.76359e6			−0.481204
$765$	−3.51559e6	+	6.08918e6i	−0.217192	+	0.376188i
$766$	−2.45562e6	−	4.25325e6i	−0.151213	−	0.261908i
$767$	4.60509e6	+	7.97626e6i	0.282651	+	0.489565i
$768$	−294912.	+	510803.i	−0.0180422	+	0.0312500i
$769$	7.93100e6

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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-37.7462 + 65.3783i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-150.985 - 261.513i) q^{10} +(74.7309 + 129.438i) q^{11} +(-72.0000 + 124.708i) q^{12} -349.416 q^{13} +679.431 q^{15} +(-128.000 + 221.703i) q^{16} +(-574.923 - 995.797i) q^{17} +(-162.000 - 280.592i) q^{18} +(-1397.60 + 2420.72i) q^{19} +1207.88 q^{20} -597.847 q^{22} +(-906.985 + 1570.94i) q^{23} +(-288.000 - 498.831i) q^{24} +(-1287.05 - 2229.23i) q^{25} +(698.832 - 1210.41i) q^{26} +729.000 q^{27} -759.033 q^{29} +(-1358.86 + 2353.62i) q^{30} +(4515.87 + 7821.72i) q^{31} +(-512.000 - 886.810i) q^{32} +(672.578 - 1164.94i) q^{33} +4599.39 q^{34} +1296.00 q^{36} +(-3897.45 + 6750.57i) q^{37} +(-5590.40 - 9682.86i) q^{38} +(1572.37 + 2723.43i) q^{39} +(-2415.76 + 4184.21i) q^{40} -7640.49 q^{41} +12188.8 q^{43} +(1195.69 - 2071.00i) q^{44} +(-3057.44 - 5295.64i) q^{45} +(-3627.94 - 6283.77i) q^{46} +(12299.4 - 21303.2i) q^{47} +2304.00 q^{48} +10296.4 q^{50} +(-5174.31 + 8962.17i) q^{51} +(2795.33 + 4841.65i) q^{52} +(-6798.11 - 11774.7i) q^{53} +(-1458.00 + 2525.33i) q^{54} -11283.2 q^{55} +25156.8 q^{57} +(1518.07 - 2629.37i) q^{58} +(-13179.4 - 22827.4i) q^{59} +(-5435.45 - 9414.47i) q^{60} +(17660.9 - 30589.5i) q^{61} -36127.0 q^{62} +4096.00 q^{64} +(13189.1 - 22844.2i) q^{65} +(2690.31 + 4659.76i) q^{66} +(-27186.0 - 47087.5i) q^{67} +(-9198.78 + 15932.7i) q^{68} +16325.7 q^{69} -70145.7 q^{71} +(-2592.00 + 4489.48i) q^{72} +(-22234.4 - 38511.1i) q^{73} +(-15589.8 - 27002.3i) q^{74} +(-11583.4 + 20063.1i) q^{75} +44723.2 q^{76} -12579.0 q^{78} +(-30806.2 + 53357.9i) q^{79} +(-9663.02 - 16736.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(15281.0 - 26467.5i) q^{82} +87142.0 q^{83} +86804.6 q^{85} +(-24377.7 + 42223.4i) q^{86} +(3415.65 + 5916.08i) q^{87} +(4782.78 + 8284.01i) q^{88} +(49284.7 - 85363.6i) q^{89} +24459.5 q^{90} +29023.5 q^{92} +(40642.9 - 70395.5i) q^{93} +(49197.6 + 85212.8i) q^{94} +(-105508. - 182745. i) q^{95} +(-4608.00 + 7981.29i) q^{96} -32342.3 q^{97} -12106.4 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more