LMFDB - Embedded newform 294.6.e.u.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:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.u.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.4645 - 40.6416i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.4645 - 40.6416i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(93.8579 + 162.567i) q^{10} +(43.7279 + 75.7390i) q^{11} +(-72.0000 + 124.708i) q^{12} -754.566 q^{13} -422.360 q^{15} +(-128.000 + 221.703i) q^{16} +(-724.520 - 1254.90i) q^{17} +(-162.000 - 280.592i) q^{18} +(1270.12 - 2199.91i) q^{19} -750.863 q^{20} -349.823 q^{22} +(456.124 - 790.030i) q^{23} +(-288.000 - 498.831i) q^{24} +(461.338 + 799.060i) q^{25} +(1509.13 - 2613.89i) q^{26} +729.000 q^{27} +173.217 q^{29} +(844.721 - 1463.10i) q^{30} +(2265.57 + 3924.08i) q^{31} +(-512.000 - 886.810i) q^{32} +(393.551 - 681.651i) q^{33} +5796.16 q^{34} +1296.00 q^{36} +(-3414.98 + 5914.92i) q^{37} +(5080.48 + 8799.64i) q^{38} +(3395.55 + 5881.26i) q^{39} +(1501.73 - 2601.07i) q^{40} -13069.3 q^{41} -12277.7 q^{43} +(699.647 - 1211.82i) q^{44} +(1900.62 + 3291.97i) q^{45} +(1824.50 + 3160.12i) q^{46} +(6746.40 - 11685.1i) q^{47} +2304.00 q^{48} -3690.70 q^{50} +(-6520.68 + 11294.1i) q^{51} +(6036.52 + 10455.6i) q^{52} +(4838.85 + 8381.14i) q^{53} +(-1458.00 + 2525.33i) q^{54} +4104.21 q^{55} -22862.1 q^{57} +(-346.434 + 600.041i) q^{58} +(15184.6 + 26300.5i) q^{59} +(3378.88 + 5852.40i) q^{60} +(366.236 - 634.340i) q^{61} -18124.5 q^{62} +4096.00 q^{64} +(-17705.5 + 30666.8i) q^{65} +(1574.21 + 2726.60i) q^{66} +(-23200.0 - 40183.5i) q^{67} +(-11592.3 + 20078.5i) q^{68} -8210.23 q^{69} -3295.39 q^{71} +(-2592.00 + 4489.48i) q^{72} +(5119.09 + 8866.53i) q^{73} +(-13659.9 - 23659.7i) q^{74} +(4152.04 - 7191.54i) q^{75} -40643.8 q^{76} -27164.4 q^{78} +(-49292.0 + 85376.2i) q^{79} +(6006.90 + 10404.3i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(26138.5 - 45273.3i) q^{82} -87792.7 q^{83} -68001.9 q^{85} +(24555.4 - 42531.2i) q^{86} +(-779.476 - 1350.09i) q^{87} +(2798.59 + 4847.29i) q^{88} +(-34549.9 + 59842.2i) q^{89} -15205.0 q^{90} -14596.0 q^{92} +(20390.1 - 35316.7i) q^{93} +(26985.6 + 46740.4i) q^{94} +(-59605.3 - 103239. i) q^{95} +(-4608.00 + 7981.29i) q^{96} +42181.4 q^{97} -7083.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 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 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 1440 q^{13} - 1944 q^{15} - 512 q^{16} + 612 q^{17} - 648 q^{18} + 2088 q^{19} - 3456 q^{20} - 992 q^{22} - 772 q^{23} - 1152 q^{24} + 318 q^{25} + 2880 q^{26} + 2916 q^{27} - 9184 q^{29} + 3888 q^{30} + 9792 q^{31} - 2048 q^{32} + 1116 q^{33} - 4896 q^{34} + 5184 q^{36} + 5992 q^{37} + 8352 q^{38} + 6480 q^{39} + 6912 q^{40} - 40392 q^{41} - 2272 q^{43} + 1984 q^{44} + 8748 q^{45} - 3088 q^{46} + 36936 q^{47} + 9216 q^{48} - 2544 q^{50} + 5508 q^{51} + 11520 q^{52} + 16708 q^{53} - 5832 q^{54} + 12672 q^{55} - 37584 q^{57} + 18368 q^{58} + 74592 q^{59} + 15552 q^{60} - 18648 q^{61} - 78336 q^{62} + 16384 q^{64} - 33300 q^{65} + 4464 q^{66} - 67344 q^{67} + 9792 q^{68} + 13896 q^{69} + 153096 q^{71} - 10368 q^{72} + 47304 q^{73} + 23968 q^{74} + 2862 q^{75} - 66816 q^{76} - 51840 q^{78} - 140656 q^{79} + 27648 q^{80} - 13122 q^{81} + 80784 q^{82} - 188208 q^{83} + 115736 q^{85} + 4544 q^{86} + 41328 q^{87} + 7936 q^{88} - 17604 q^{89} - 69984 q^{90} + 24704 q^{92} + 88128 q^{93} + 147744 q^{94} - 91592 q^{95} - 18432 q^{96} - 170352 q^{97} - 20088 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 1440 * q^13 - 1944 * q^15 - 512 * q^16 + 612 * q^17 - 648 * q^18 + 2088 * q^19 - 3456 * q^20 - 992 * q^22 - 772 * q^23 - 1152 * q^24 + 318 * q^25 + 2880 * q^26 + 2916 * q^27 - 9184 * q^29 + 3888 * q^30 + 9792 * q^31 - 2048 * q^32 + 1116 * q^33 - 4896 * q^34 + 5184 * q^36 + 5992 * q^37 + 8352 * q^38 + 6480 * q^39 + 6912 * q^40 - 40392 * q^41 - 2272 * q^43 + 1984 * q^44 + 8748 * q^45 - 3088 * q^46 + 36936 * q^47 + 9216 * q^48 - 2544 * q^50 + 5508 * q^51 + 11520 * q^52 + 16708 * q^53 - 5832 * q^54 + 12672 * q^55 - 37584 * q^57 + 18368 * q^58 + 74592 * q^59 + 15552 * q^60 - 18648 * q^61 - 78336 * q^62 + 16384 * q^64 - 33300 * q^65 + 4464 * q^66 - 67344 * q^67 + 9792 * q^68 + 13896 * q^69 + 153096 * q^71 - 10368 * q^72 + 47304 * q^73 + 23968 * q^74 + 2862 * q^75 - 66816 * q^76 - 51840 * q^78 - 140656 * q^79 + 27648 * q^80 - 13122 * q^81 + 80784 * q^82 - 188208 * q^83 + 115736 * q^85 + 4544 * q^86 + 41328 * q^87 + 7936 * q^88 - 17604 * q^89 - 69984 * q^90 + 24704 * q^92 + 88128 * q^93 + 147744 * q^94 - 91592 * q^95 - 18432 * q^96 - 170352 * q^97 - 20088 * 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
$5$	23.4645	−	40.6416i	0.419745	−	0.727020i	−0.576168	−	0.817331i	$-0.695453\pi$
$5$	23.4645	−	40.6416i	0.419745	−	0.727020i	0.995914	+	0.0903111i	$0.0287861\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	93.8579	+	162.567i	0.296805	+	0.514081i
$11$	43.7279	+	75.7390i	0.108963	+	0.188729i	0.915350	−	0.402659i	$-0.131914\pi$
$11$	43.7279	+	75.7390i	0.108963	+	0.188729i	−0.806388	+	0.591387i	$0.798580\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	−754.566			−1.23834			−0.619168	−	0.785258i	$-0.712530\pi$
$13$	−754.566			−1.23834			−0.619168	+	0.785258i	$0.712530\pi$
$14$		0			0
$15$	−422.360			−0.484680
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−724.520	−	1254.90i	−0.608034	−	1.05315i	−0.991564	−	0.129617i	$-0.958625\pi$
$17$	−724.520	−	1254.90i	−0.608034	−	1.05315i	0.383530	−	0.923528i	$-0.374708\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	1270.12	−	2199.91i	0.807161	−	1.39804i	−0.107661	−	0.994188i	$-0.534336\pi$
$19$	1270.12	−	2199.91i	0.807161	−	1.39804i	0.914822	−	0.403857i	$-0.132331\pi$
$20$	−750.863			−0.419745
$21$		0			0
$22$	−349.823			−0.154096
$23$	456.124	−	790.030i	0.179789	−	0.311404i	−0.762019	−	0.647555i	$-0.775792\pi$
$23$	456.124	−	790.030i	0.179789	−	0.311404i	0.941808	+	0.336151i	$0.109125\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	461.338	+	799.060i	0.147628	+	0.255699i
$26$	1509.13	−	2613.89i	0.437818	−	0.758323i
$27$	729.000			0.192450
$28$		0			0
$29$	173.217			0.0382468			0.0191234	−	0.999817i	$-0.493912\pi$
$29$	173.217			0.0382468			0.0191234	+	0.999817i	$0.493912\pi$
$30$	844.721	−	1463.10i	0.171360	−	0.296805i
$31$	2265.57	+	3924.08i	0.423421	+	0.733387i	0.996272	−	0.0862730i	$-0.0274957\pi$
$31$	2265.57	+	3924.08i	0.423421	+	0.733387i	−0.572850	+	0.819660i	$0.694162\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	393.551	−	681.651i	0.0629095	−	0.108963i
$34$	5796.16			0.859890
$35$		0			0
$36$	1296.00			0.166667
$37$	−3414.98	+	5914.92i	−0.410094	+	0.710304i	−0.994900	−	0.100870i	$-0.967838\pi$
$37$	−3414.98	+	5914.92i	−0.410094	+	0.710304i	0.584805	+	0.811174i	$0.301171\pi$
$38$	5080.48	+	8799.64i	0.570749	+	0.988567i
$39$	3395.55	+	5881.26i	0.357477	+	0.619168i
$40$	1501.73	−	2601.07i	0.148402	−	0.257040i
$41$	−13069.3			−1.21420			−0.607102	−	0.794624i	$-0.707668\pi$
$41$	−13069.3			−1.21420			−0.607102	+	0.794624i	$0.707668\pi$
$42$		0			0
$43$	−12277.7			−1.01262			−0.506309	−	0.862352i	$-0.668990\pi$
$43$	−12277.7			−1.01262			−0.506309	+	0.862352i	$0.668990\pi$
$44$	699.647	−	1211.82i	0.0544813	−	0.0943643i
$45$	1900.62	+	3291.97i	0.139915	+	0.242340i
$46$	1824.50	+	3160.12i	0.127130	+	0.220196i
$47$	6746.40	−	11685.1i	0.445479	−	0.771592i	−0.552606	−	0.833442i	$-0.686367\pi$
$47$	6746.40	−	11685.1i	0.445479	−	0.771592i	0.998085	+	0.0618499i	$0.0197000\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	−3690.70			−0.208778
$51$	−6520.68	+	11294.1i	−0.351049	+	0.608034i
$52$	6036.52	+	10455.6i	0.309584	+	0.536215i
$53$	4838.85	+	8381.14i	0.236621	+	0.409839i	0.959742	−	0.280882i	$-0.0906268\pi$
$53$	4838.85	+	8381.14i	0.236621	+	0.409839i	−0.723122	+	0.690721i	$0.757293\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	4104.21			0.182946
$56$		0			0
$57$	−22862.1			−0.932030
$58$	−346.434	+	600.041i	−0.0135223	+	0.0234213i
$59$	15184.6	+	26300.5i	0.567902	+	0.983634i	0.996773	+	0.0802689i	$0.0255779\pi$
$59$	15184.6	+	26300.5i	0.567902	+	0.983634i	−0.428872	+	0.903365i	$0.641089\pi$
$60$	3378.88	+	5852.40i	0.121170	+	0.209873i
$61$	366.236	−	634.340i	0.0126019	−	0.0218272i	−0.859656	−	0.510874i	$-0.829322\pi$
$61$	366.236	−	634.340i	0.0126019	−	0.0218272i	0.872258	+	0.489047i	$0.162655\pi$
$62$	−18124.5			−0.598808
$63$		0			0
$64$	4096.00			0.125000
$65$	−17705.5	+	30666.8i	−0.519786	+	0.900295i
$66$	1574.21	+	2726.60i	0.0444838	+	0.0770481i
$67$	−23200.0	−	40183.5i	−0.631394	−	1.09361i	−0.987267	−	0.159072i	$-0.949150\pi$
$67$	−23200.0	−	40183.5i	−0.631394	−	1.09361i	0.355873	−	0.934534i	$-0.384183\pi$
$68$	−11592.3	+	20078.5i	−0.304017	+	0.526573i
$69$	−8210.23			−0.207603
$70$		0			0
$71$	−3295.39			−0.0775821			−0.0387910	−	0.999247i	$-0.512351\pi$
$71$	−3295.39			−0.0775821			−0.0387910	+	0.999247i	$0.512351\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	5119.09	+	8866.53i	0.112431	+	0.194736i	0.916750	−	0.399462i	$-0.130803\pi$
$73$	5119.09	+	8866.53i	0.112431	+	0.194736i	−0.804319	+	0.594198i	$0.797470\pi$
$74$	−13659.9	−	23659.7i	−0.289980	−	0.502261i
$75$	4152.04	−	7191.54i	0.0852331	−	0.147628i
$76$	−40643.8			−0.807161
$77$		0			0
$78$	−27164.4			−0.505549
$79$	−49292.0	+	85376.2i	−0.888605	+	1.53911i	−0.0470794	+	0.998891i	$0.514991\pi$
$79$	−49292.0	+	85376.2i	−0.888605	+	1.53911i	−0.841525	+	0.540218i	$0.818342\pi$
$80$	6006.90	+	10404.3i	0.104936	+	0.181755i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	26138.5	−	45273.3i	0.429286	−	0.743545i
$83$	−87792.7			−1.39882			−0.699412	−	0.714719i	$-0.746555\pi$
$83$	−87792.7			−1.39882			−0.699412	+	0.714719i	$0.746555\pi$
$84$		0			0
$85$	−68001.9			−1.02088
$86$	24555.4	−	42531.2i	0.358014	−	0.620099i
$87$	−779.476	−	1350.09i	−0.0110409	−	0.0191234i
$88$	2798.59	+	4847.29i	0.0385241	+	0.0667256i
$89$	−34549.9	+	59842.2i	−0.462351	+	0.800816i	−0.999078	−	0.0429406i	$-0.986327\pi$
$89$	−34549.9	+	59842.2i	−0.462351	+	0.800816i	0.536726	+	0.843756i	$0.319661\pi$
$90$	−15205.0			−0.197870
$91$		0			0
$92$	−14596.0			−0.179789
$93$	20390.1	−	35316.7i	0.244462	−	0.423421i
$94$	26985.6	+	46740.4i	0.315001	+	0.545598i
$95$	−59605.3	−	103239.i	−0.677604	−	1.17364i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	42181.4			0.455189			0.227594	−	0.973756i	$-0.426914\pi$
$97$	42181.4			0.455189			0.227594	+	0.973756i	$0.426914\pi$
$98$		0			0
$99$	−7083.92			−0.0726417
$100$	7381.40	−	12785.0i	0.0738140	−	0.127850i
$101$	89237.0	+	154563.i	0.870445	+	1.50766i	0.861537	+	0.507695i	$0.169502\pi$
$101$	89237.0	+	154563.i	0.870445	+	1.50766i	0.00890797	+	0.999960i	$0.497164\pi$
$102$	−26082.7	−	45176.6i	−0.248229	−	0.429945i
$103$	17613.1	−	30506.8i	0.163585	−	0.283337i	−0.772567	−	0.634933i	$-0.781028\pi$
$103$	17613.1	−	30506.8i	0.163585	−	0.283337i	0.936152	+	0.351596i	$0.114361\pi$
$104$	−48292.2			−0.437818
$105$		0			0
$106$	−38710.8			−0.334632
$107$	−44980.4	+	77908.4i	−0.379808	+	0.657847i	−0.991034	−	0.133609i	$-0.957343\pi$
$107$	−44980.4	+	77908.4i	−0.379808	+	0.657847i	0.611226	+	0.791456i	$0.290677\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	−92501.2	−	160217.i	−0.745729	−	1.29164i	−0.949853	−	0.312696i	$-0.898768\pi$
$109$	−92501.2	−	160217.i	−0.745729	−	1.29164i	0.204124	−	0.978945i	$-0.434565\pi$
$110$	−8208.42	+	14217.4i	−0.0646812	+	0.112031i
$111$	61469.6			0.473536
$112$		0			0
$113$	−228275.			−1.68175			−0.840877	−	0.541227i	$-0.817960\pi$
$113$	−228275.			−1.68175			−0.840877	+	0.541227i	$0.817960\pi$
$114$	45724.3	−	79196.8i	0.329522	−	0.570749i
$115$	−21405.4	−	37075.3i	−0.150931	−	0.261421i
$116$	−1385.74	−	2400.16i	−0.00956170	−	0.0165614i
$117$	30559.9	−	52931.3i	0.206389	−	0.357477i
$118$	−121477.			−0.803134
$119$		0			0
$120$	−27031.1			−0.171360
$121$	76701.2	−	132850.i	0.476254	−	0.824897i
$122$	1464.95	+	2537.36i	0.00891091	+	0.0154341i
$123$	58811.7	+	101865.i	0.350510	+	0.607102i
$124$	36249.1	−	62785.2i	0.211711	−	0.366693i
$125$	189953.			1.08735
$126$		0			0
$127$	−343515.			−1.88989			−0.944944	−	0.327232i	$-0.893884\pi$
$127$	−343515.			−1.88989			−0.944944	+	0.327232i	$0.893884\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	55249.6	+	95695.1i	0.292318	+	0.506309i
$130$	−70821.9	−	122667.i	−0.367544	−	0.636605i
$131$	−180636.	+	312871.i	−0.919657	+	1.59289i	−0.119721	+	0.992808i	$0.538200\pi$
$131$	−180636.	+	312871.i	−0.919657	+	1.59289i	−0.799936	+	0.600085i	$0.795133\pi$
$132$	−12593.6			−0.0629095
$133$		0			0
$134$	185600.			0.892926
$135$	17105.6	−	29627.8i	0.0807800	−	0.139915i
$136$	−46369.2	−	80313.9i	−0.214972	−	0.372343i
$137$	152313.	+	263815.i	0.693325	+	1.20087i	0.970742	+	0.240125i	$0.0771883\pi$
$137$	152313.	+	263815.i	0.693325	+	1.20087i	−0.277417	+	0.960750i	$0.589478\pi$
$138$	16420.5	−	28441.1i	0.0733986	−	0.127130i
$139$	−129737.			−0.569543			−0.284772	−	0.958595i	$-0.591918\pi$
$139$	−129737.			−0.569543			−0.284772	+	0.958595i	$0.591918\pi$
$140$		0			0
$141$	−121435.			−0.514395
$142$	6590.79	−	11415.6i	0.0274294	−	0.0475091i
$143$	−32995.6	−	57150.0i	−0.134932	−	0.233710i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	4064.44	−	7039.82i	0.0160539	−	0.0278062i
$146$	−40952.7			−0.159001
$147$		0			0
$148$	109279.			0.410094
$149$	−186954.	+	323814.i	−0.689873	+	1.19489i	0.282006	+	0.959413i	$0.409000\pi$
$149$	−186954.	+	323814.i	−0.689873	+	1.19489i	−0.971879	+	0.235482i	$0.924333\pi$
$150$	16608.2	+	28766.2i	0.0602689	+	0.104389i
$151$	43319.9	+	75032.3i	0.154613	+	0.267797i	0.932918	−	0.360089i	$-0.117254\pi$
$151$	43319.9	+	75032.3i	0.154613	+	0.267797i	−0.778305	+	0.627886i	$0.783920\pi$
$152$	81287.6	−	140794.i	0.285375	−	0.494283i
$153$	117372.			0.405356
$154$		0			0
$155$	212641.			0.710916
$156$	54328.7	−	94100.1i	0.178738	−	0.309584i
$157$	−231087.	−	400254.i	−0.748214	−	1.29594i	−0.948678	−	0.316243i	$-0.897579\pi$
$157$	−231087.	−	400254.i	−0.748214	−	1.29594i	0.200465	−	0.979701i	$-0.435755\pi$
$158$	−197168.	−	341505.i	−0.628338	−	1.08831i
$159$	43549.7	−	75430.2i	0.136613	−	0.236621i
$160$	−48055.2			−0.148402
$161$		0			0
$162$	26244.0			0.0785674
$163$	−304516.	+	527437.i	−0.897721	+	1.55490i	−0.0673199	+	0.997731i	$0.521445\pi$
$163$	−304516.	+	527437.i	−0.897721	+	1.55490i	−0.830401	+	0.557166i	$0.811889\pi$
$164$	104554.	+	181093.i	0.303551	+	0.525765i
$165$	−18468.9	−	31989.1i	−0.0528119	−	0.0914730i
$166$	175585.	−	304123.i	0.494559	−	0.856601i
$167$	127786.			0.354562			0.177281	−	0.984160i	$-0.443270\pi$
$167$	127786.			0.354562			0.177281	+	0.984160i	$0.443270\pi$
$168$		0			0
$169$	198076.			0.533477
$170$	136004.	−	235565.i	0.360935	−	0.625157i
$171$	102880.	+	178193.i	0.269054	+	0.466015i
$172$	98221.5	+	170125.i	0.253154	+	0.438476i
$173$	−71269.6	+	123443.i	−0.181046	+	0.313581i	−0.942237	−	0.334947i	$-0.891282\pi$
$173$	−71269.6	+	123443.i	−0.181046	+	0.313581i	0.761191	+	0.648528i	$0.224615\pi$
$174$	6235.81			0.0156142
$175$		0			0
$176$	−22388.7			−0.0544813
$177$	136661.	−	236704.i	0.327878	−	0.567902i
$178$	−138200.	−	239369.i	−0.326932	−	0.566262i
$179$	148317.	+	256893.i	0.345986	+	0.599266i	0.985532	−	0.169487i	$-0.0542110\pi$
$179$	148317.	+	256893.i	0.345986	+	0.599266i	−0.639546	+	0.768753i	$0.720878\pi$
$180$	30409.9	−	52671.6i	0.0699575	−	0.121170i
$181$	277654.			0.629952			0.314976	−	0.949100i	$-0.398004\pi$
$181$	277654.			0.629952			0.314976	+	0.949100i	$0.398004\pi$
$182$		0			0
$183$	−6592.25			−0.0145514
$184$	29191.9	−	50561.9i	0.0635650	−	0.110098i
$185$	160261.	+	277581.i	0.344270	+	0.596293i
$186$	81560.4	+	141267.i	0.172861	+	0.299404i
$187$	63363.5	−	109749.i	0.132506	−	0.229507i
$188$	−215885.			−0.445479
$189$		0			0
$190$	476843.			0.958277
$191$	121292.	−	210084.i	0.240574	−	0.416687i	−0.720304	−	0.693659i	$-0.755998\pi$
$191$	121292.	−	210084.i	0.240574	−	0.416687i	0.960878	+	0.276972i	$0.0893308\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	290762.	+	503615.i	0.561882	+	0.973208i	0.997332	+	0.0729950i	$0.0232557\pi$
$193$	290762.	+	503615.i	0.561882	+	0.973208i	−0.435451	+	0.900213i	$0.643411\pi$
$194$	−84362.8	+	146121.i	−0.160933	+	0.278745i
$195$	318699.			0.600197
$196$		0			0
$197$	748916.			1.37489			0.687444	−	0.726237i	$-0.258733\pi$
$197$	748916.			1.37489			0.687444	+	0.726237i	$0.258733\pi$
$198$	14167.8	−	24539.4i	0.0256827	−	0.0444838i
$199$	−362846.	−	628468.i	−0.649516	−	1.12500i	−0.983239	−	0.182324i	$-0.941638\pi$
$199$	−362846.	−	628468.i	−0.649516	−	1.12500i	0.333722	−	0.942671i	$-0.391695\pi$
$200$	29525.6	+	51139.9i	0.0521944	+	0.0904033i
$201$	−208800.	+	361652.i	−0.364535	+	0.631394i
$202$	−713896.			−1.23100
$203$		0			0
$204$	208662.			0.351049
$205$	−306663.	+	531156.i	−0.509656	+	0.882750i
$206$	70452.3	+	122027.i	0.115672	+	0.200349i
$207$	36946.0	+	63992.4i	0.0599297	+	0.103801i
$208$	96584.4	−	167289.i	0.154792	−	0.268108i
$209$	222159.			0.351801
$210$		0			0
$211$	814718.			1.25980			0.629899	−	0.776677i	$-0.283096\pi$
$211$	814718.			1.25980			0.629899	+	0.776677i	$0.283096\pi$
$212$	77421.6	−	134098.i	0.118310	−	0.204920i
$213$	14829.3	+	25685.1i	0.0223960	+	0.0387910i
$214$	−179922.	−	311634.i	−0.268565	−	0.465168i
$215$	−288089.	+	498985.i	−0.425041	+	0.736193i
$216$	46656.0			0.0680414
$217$		0			0
$218$	740010.			1.05462
$219$	46071.8	−	79798.7i	0.0649120	−	0.112431i
$220$	−32833.7	−	56869.6i	−0.0457365	−	0.0792179i
$221$	546697.	+	946908.i	0.752950	+	1.30415i
$222$	−122939.	+	212937.i	−0.167420	+	0.289980i
$223$	335874.			0.452288			0.226144	−	0.974094i	$-0.427388\pi$
$223$	335874.			0.452288			0.226144	+	0.974094i	$0.427388\pi$
$224$		0			0
$225$	−74736.7			−0.0984187
$226$	456550.	−	790768.i	0.594589	−	1.02986i
$227$	−32360.6	−	56050.2i	−0.0416823	−	0.0721959i	0.844432	−	0.535663i	$-0.179938\pi$
$227$	−32360.6	−	56050.2i	−0.0416823	−	0.0721959i	−0.886114	+	0.463467i	$0.846605\pi$
$228$	182897.	+	316787.i	0.233007	+	0.403581i
$229$	375394.	−	650202.i	0.473041	−	0.819332i	−0.526483	−	0.850186i	$-0.676489\pi$
$229$	375394.	−	650202.i	0.473041	−	0.819332i	0.999524	+	0.0308542i	$0.00982277\pi$
$230$	171243.			0.213449
$231$		0			0
$232$	11085.9			0.0135223
$233$	693589.	−	1.20133e6i	0.836974	−	1.44968i	−0.0554384	−	0.998462i	$-0.517656\pi$
$233$	693589.	−	1.20133e6i	0.836974	−	1.44968i	0.892413	−	0.451220i	$-0.149011\pi$
$234$	122240.	+	211725.i	0.145939	+	0.252774i
$235$	−316601.	−	548369.i	−0.373975	−	0.647744i
$236$	242953.	−	420808.i	0.283951	−	0.491817i
$237$	887256.			1.02607
$238$		0			0
$239$	−160907.			−0.182213			−0.0911064	−	0.995841i	$-0.529040\pi$
$239$	−160907.			−0.182213			−0.0911064	+	0.995841i	$0.529040\pi$
$240$	54062.1	−	93638.4i	0.0605850	−	0.104936i
$241$	−642408.	−	1.11268e6i	−0.712473	−	1.23404i	−0.963926	−	0.266170i	$-0.914242\pi$
$241$	−642408.	−	1.11268e6i	−0.712473	−	1.23404i	0.251453	−	0.967870i	$-0.419092\pi$
$242$	306805.	+	531402.i	0.336763	+	0.583290i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−11719.6			−0.0126019
$245$		0			0
$246$	−470493.			−0.495696
$247$	−958388.	+	1.65998e6i	−0.999537	+	1.73125i
$248$	144996.	+	251141.i	0.149702	+	0.259291i
$249$	395067.	+	684276.i	0.403806	+	0.699412i
$250$	−379906.	+	658017.i	−0.384438	+	0.665866i
$251$	481311.			0.482216			0.241108	−	0.970498i	$-0.422489\pi$
$251$	481311.			0.482216			0.241108	+	0.970498i	$0.422489\pi$
$252$		0			0
$253$	79781.4			0.0783611
$254$	687029.	−	1.18997e6i	0.668176	−	1.15732i
$255$	306008.	+	530022.i	0.294702	+	0.510439i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	16544.3	−	28655.6i	0.0156249	−	0.0270631i	−0.858107	−	0.513470i	$-0.828360\pi$
$257$	16544.3	−	28655.6i	0.0156249	−	0.0270631i	0.873732	+	0.486407i	$0.161693\pi$
$258$	−441997.			−0.413399
$259$		0			0
$260$	566575.			0.519786
$261$	−7015.28	+	12150.8i	−0.00637447	+	0.0110409i
$262$	−722544.	−	1.25148e6i	−0.650296	−	1.12635i
$263$	−223100.	−	386421.i	−0.198889	−	0.344485i	0.749280	−	0.662254i	$-0.230400\pi$
$263$	−223100.	−	386421.i	−0.198889	−	0.344485i	−0.948168	+	0.317768i	$0.897067\pi$
$264$	25187.3	−	43625.7i	0.0222419	−	0.0385241i
$265$	454164.			0.397281
$266$		0			0
$267$	621898.			0.533877
$268$	−371199.	+	642936.i	−0.315697	+	0.546803i
$269$	−974269.	−	1.68748e6i	−0.820915	−	1.42187i	−0.905002	−	0.425407i	$-0.860131\pi$
$269$	−974269.	−	1.68748e6i	−0.820915	−	1.42187i	0.0840873	−	0.996458i	$-0.473203\pi$
$270$	68422.4	+	118511.i	0.0571201	+	0.0989349i
$271$	−48436.5	+	83894.5i	−0.0400636	+	0.0693921i	−0.885362	−	0.464903i	$-0.846089\pi$
$271$	−48436.5	+	83894.5i	−0.0400636	+	0.0693921i	0.845298	+	0.534295i	$0.179423\pi$
$272$	370954.			0.304017
$273$		0			0
$274$	−1.21851e6			−0.980510
$275$	−40346.7	+	69882.5i	−0.0321718	+	0.0557233i
$276$	65681.9	+	113764.i	0.0519006	+	0.0898945i
$277$	−818393.	−	1.41750e6i	−0.640859	−	1.11000i	−0.985241	−	0.171171i	$-0.945245\pi$
$277$	−818393.	−	1.41750e6i	−0.640859	−	1.11000i	0.344382	−	0.938830i	$-0.388088\pi$
$278$	259474.	−	449422.i	0.201364	−	0.348772i
$279$	−367022.			−0.282281
$280$		0			0
$281$	−1.79558e6			−1.35656			−0.678281	−	0.734803i	$-0.737275\pi$
$281$	−1.79558e6			−1.35656			−0.678281	+	0.734803i	$0.737275\pi$
$282$	242870.	−	420664.i	0.181866	−	0.315001i
$283$	−640238.	−	1.10892e6i	−0.475199	−	0.823068i	0.524398	−	0.851473i	$-0.324290\pi$
$283$	−640238.	−	1.10892e6i	−0.475199	−	0.823068i	−0.999596	+	0.0284051i	$0.990957\pi$
$284$	26363.1	+	45662.3i	0.0193955	+	0.0335940i
$285$	−536448.	+	929155.i	−0.391215	+	0.677604i
$286$	263965.			0.190823
$287$		0			0
$288$	82944.0			0.0589256
$289$	−339929.	+	588774.i	−0.239410	+	0.414671i
$290$	16257.8	+	28159.3i	0.0113518	+	0.0196619i
$291$	−189816.	−	328771.i	−0.131402	−	0.227594i
$292$	81905.5	−	141864.i	0.0562155	−	0.0973680i
$293$	330814.			0.225120			0.112560	−	0.993645i	$-0.464095\pi$
$293$	330814.			0.225120			0.112560	+	0.993645i	$0.464095\pi$
$294$		0			0
$295$	1.42519e6			0.953496
$296$	−218559.	+	378555.i	−0.144990	+	0.251130i
$297$	31877.7	+	55213.7i	0.0209698	+	0.0363208i
$298$	−747816.	−	1.29525e6i	−0.487814	−	0.844918i
$299$	−344175.	+	596129.i	−0.222639	+	0.385623i
$300$	−132865.			−0.0852331
$301$		0			0
$302$	−346559.			−0.218655
$303$	803133.	−	1.39107e6i	0.502552	−	0.870445i
$304$	325150.	+	563177.i	0.201790	+	0.349511i
$305$	−17187.1	−	29768.9i	−0.0105792	−	0.0183237i
$306$	−234744.	+	406589.i	−0.143315	+	0.248229i
$307$	−554088.			−0.335531			−0.167766	−	0.985827i	$-0.553655\pi$
$307$	−554088.			−0.335531			−0.167766	+	0.985827i	$0.553655\pi$
$308$		0			0
$309$	−317035.			−0.188891
$310$	−425282.	+	736611.i	−0.251347	+	0.435345i
$311$	879628.	+	1.52356e6i	0.515701	+	0.893221i	0.999834	+	0.0182260i	$0.00580185\pi$
$311$	879628.	+	1.52356e6i	0.515701	+	0.893221i	−0.484133	+	0.874995i	$0.660865\pi$
$312$	217315.	+	376400.i	0.126387	+	0.218909i
$313$	1.16910e6	−	2.02493e6i	0.674512	−	1.16829i	−0.302099	−	0.953276i	$-0.597687\pi$
$313$	1.16910e6	−	2.02493e6i	0.674512	−	1.16829i	0.976611	−	0.215012i	$-0.0689792\pi$
$314$	1.84869e6			1.05813
$315$		0			0
$316$	1.57734e6			0.888605
$317$	483696.	−	837786.i	0.270349	−	0.468258i	−0.698602	−	0.715510i	$-0.746194\pi$
$317$	483696.	−	837786.i	0.270349	−	0.468258i	0.968951	+	0.247252i	$0.0795277\pi$
$318$	174199.	+	301721.i	0.0966000	+	0.167316i
$319$	7574.41	+	13119.3i	0.00416747	+	0.00721827i
$320$	96110.5	−	166468.i	0.0524681	−	0.0908775i
$321$	809648.			0.438565
$322$		0			0
$323$	−3.68090e6			−1.96313
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	−348110.	−	602943.i	−0.182813	−	0.316642i
$326$	−1.21806e6	−	2.10975e6i	−0.634784	−	1.09948i
$327$	−832511.	+	1.44195e6i	−0.430547	+	0.745729i
$328$	−836433.			−0.429286
$329$		0			0
$330$	147752.			0.0746874
$331$	163904.	−	283890.i	0.0822281	−	0.142423i	−0.821979	−	0.569518i	$-0.807130\pi$
$331$	163904.	−	283890.i	0.0822281	−	0.142423i	0.904207	+	0.427095i	$0.140463\pi$
$332$	702341.	+	1.21649e6i	0.349706	+	0.605708i
$333$	−276613.	−	479108.i	−0.136698	−	0.236768i
$334$	−255572.	+	442664.i	−0.125357	+	0.217124i
$335$	−2.17750e6			−1.06010
$336$		0			0
$337$	1.34052e6			0.642983			0.321491	−	0.946913i	$-0.395816\pi$
$337$	1.34052e6			0.642983			0.321491	+	0.946913i	$0.395816\pi$
$338$	−396152.	+	686156.i	−0.188613	+	0.326687i
$339$	1.02724e6	+	1.77923e6i	0.485480	+	0.840877i
$340$	544015.	+	942261.i	0.255219	+	0.442053i
$341$	−198137.	+	343183.i	−0.0922741	+	0.159823i
$342$	−823037.			−0.380500
$343$		0			0
$344$	−785772.			−0.358014
$345$	−192649.	+	333677.i	−0.0871402	+	0.150931i
$346$	−285078.	−	493770.i	−0.128019	−	0.221735i
$347$	1.76687e6	+	3.06031e6i	0.787736	+	1.36440i	0.927351	+	0.374193i	$0.122080\pi$
$347$	1.76687e6	+	3.06031e6i	0.787736	+	1.36440i	−0.139615	+	0.990206i	$0.544586\pi$
$348$	−12471.6	+	21601.5i	−0.00552045	+	0.00956170i
$349$	−3.98108e6			−1.74959			−0.874796	−	0.484491i	$-0.839005\pi$
$349$	−3.98108e6			−1.74959			−0.874796	+	0.484491i	$0.839005\pi$
$350$		0			0
$351$	−550078.			−0.238318
$352$	44777.4	−	77556.7i	0.0192620	−	0.0333628i
$353$	−22139.6	−	38346.8i	−0.00945654	−	0.0163792i	0.861258	−	0.508167i	$-0.169677\pi$
$353$	−22139.6	−	38346.8i	−0.00945654	−	0.0163792i	−0.870715	+	0.491788i	$0.836343\pi$
$354$	546645.	+	946817.i	0.231845	+	0.401567i
$355$	−77324.6	+	133930.i	−0.0325647	+	0.0564037i
$356$	1.10560e6			0.462351
$357$		0			0
$358$	−1.18654e6			−0.489299
$359$	875569.	−	1.51653e6i	0.358554	−	0.621034i	−0.629166	−	0.777271i	$-0.716603\pi$
$359$	875569.	−	1.51653e6i	0.358554	−	0.621034i	0.987719	+	0.156238i	$0.0499366\pi$
$360$	121640.	+	210686.i	0.0494674	+	0.0856801i
$361$	−1.98835e6	−	3.44393e6i	−0.803019	−	1.39087i
$362$	−555308.	+	961821.i	−0.222721	+	0.385765i
$363$	−1.38062e6			−0.549931
$364$		0			0
$365$	480467.			0.188769
$366$	13184.5	−	22836.2i	0.00514471	−	0.00891091i
$367$	1.98557e6	+	3.43911e6i	0.769521	+	1.33285i	0.937823	+	0.347114i	$0.112838\pi$
$367$	1.98557e6	+	3.43911e6i	0.769521	+	1.33285i	−0.168302	+	0.985735i	$0.553828\pi$
$368$	116768.	+	202248.i	0.0449473	+	0.0778510i
$369$	529305.	−	916783.i	0.202367	−	0.350510i
$370$	−1.28209e6			−0.486871
$371$		0			0
$372$	−652483.			−0.244462
$373$	−1.11980e6	+	1.93955e6i	−0.416743	+	0.721820i	−0.995610	−	0.0936023i	$-0.970162\pi$
$373$	−1.11980e6	+	1.93955e6i	−0.416743	+	0.721820i	0.578867	+	0.815422i	$0.303495\pi$
$374$	253454.	+	438995.i	0.0936958	+	0.162286i
$375$	−854789.	−	1.48054e6i	−0.313892	−	0.543677i
$376$	431769.	−	747847.i	0.157501	−	0.272799i
$377$	−130703.			−0.0473624
$378$		0			0
$379$	−4.25421e6			−1.52132			−0.760661	−	0.649149i	$-0.775125\pi$
$379$	−4.25421e6			−1.52132			−0.760661	+	0.649149i	$0.775125\pi$
$380$	−953685.	+	1.65183e6i	−0.338802	+	0.586822i
$381$	1.54582e6	+	2.67743e6i	0.545564	+	0.944944i
$382$	485169.	+	840337.i	0.170112	+	0.294642i
$383$	809417.	−	1.40195e6i	0.281952	−	0.488355i	−0.689913	−	0.723892i	$-0.742351\pi$
$383$	809417.	−	1.40195e6i	0.281952	−	0.488355i	0.971865	+	0.235537i	$0.0756848\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	−2.32610e6			−0.794621
$387$	497246.	−	861256.i	0.168770	−	0.292318i
$388$	−337451.	−	584482.i	−0.113797	−	0.197102i
$389$	676577.	+	1.17187e6i	0.226696	+	0.392648i	0.956827	−	0.290659i	$-0.0938744\pi$
$389$	676577.	+	1.17187e6i	0.226696	+	0.392648i	−0.730131	+	0.683307i	$0.760541\pi$
$390$	−637397.	+	1.10400e6i	−0.212202	+	0.367544i
$391$	−1.32188e6			−0.437271
$392$		0			0
$393$	3.25145e6			1.06193
$394$	−1.49783e6	+	2.59432e6i	−0.486097	+	0.841944i
$395$	2.31322e6	+	4.00662e6i	0.745975	+	1.29207i
$396$	56671.4	+	98157.7i	0.0181604	+	0.0314548i
$397$	−214028.	+	370707.i	−0.0681545	+	0.118047i	−0.898089	−	0.439814i	$-0.855044\pi$
$397$	−214028.	+	370707.i	−0.0681545	+	0.118047i	0.829934	+	0.557861i	$0.188378\pi$
$398$	2.90277e6			0.918555
$399$		0			0
$400$	−236205.			−0.0738140
$401$	59114.1	−	102389.i	0.0183582	−	0.0317973i	−0.856700	−	0.515814i	$-0.827489\pi$
$401$	59114.1	−	102389.i	0.0183582	−	0.0317973i	0.875059	+	0.484017i	$0.160823\pi$
$402$	−835199.	−	1.44661e6i	−0.257765	−	0.446463i
$403$	−1.70952e6	−	2.96097e6i	−0.524338	−	0.908180i
$404$	1.42779e6	−	2.47301e6i	0.435223	−	0.753828i
$405$	−307901.			−0.0932767
$406$		0			0
$407$	−597320.			−0.178740
$408$	−417323.	+	722825.i	−0.124114	+	0.214972i
$409$	604871.	+	1.04767e6i	0.178795	+	0.309682i	0.941468	−	0.337102i	$-0.109447\pi$
$409$	604871.	+	1.04767e6i	0.178795	+	0.309682i	−0.762673	+	0.646784i	$0.776114\pi$
$410$	−1.22665e6	−	2.12463e6i	−0.360381	−	0.624199i
$411$	1.37082e6	−	2.37433e6i	0.400291	−	0.693325i
$412$	−563619.			−0.163585
$413$		0			0
$414$	−295568.			−0.0847534
$415$	−2.06001e6	+	3.56804e6i	−0.587149	+	1.01697i
$416$	386338.	+	669156.i	0.109455	+	0.189581i
$417$	583816.	+	1.01120e6i	0.164413	+	0.284772i
$418$	−444317.	+	769580.i	−0.124381	+	0.215433i
$419$	−4.12593e6			−1.14812			−0.574059	−	0.818814i	$-0.694632\pi$
$419$	−4.12593e6			−1.14812			−0.574059	+	0.818814i	$0.694632\pi$
$420$		0			0
$421$	3.12374e6			0.858953			0.429477	−	0.903078i	$-0.358698\pi$
$421$	3.12374e6			0.858953			0.429477	+	0.903078i	$0.358698\pi$
$422$	−1.62944e6	+	2.82227e6i	−0.445406	+	0.771466i
$423$	546458.	+	946493.i	0.148493	+	0.257197i
$424$	309687.	+	536393.i	0.0836580	+	0.144900i
$425$	668496.	−	1.15787e6i	0.179526	−	0.310948i
$426$	−118634.			−0.0316728
$427$		0			0
$428$	1.43937e6			0.379808
$429$	−296960.	+	514350.i	−0.0779032	+	0.134932i
$430$	−1.15236e6	−	1.99594e6i	−0.300550	−	0.520567i
$431$	−557293.	−	965260.i	−0.144507	−	0.250294i	0.784682	−	0.619899i	$-0.212826\pi$
$431$	−557293.	−	965260.i	−0.144507	−	0.250294i	−0.929189	+	0.369605i	$0.879493\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	−266138.			−0.0682161			−0.0341080	−	0.999418i	$-0.510859\pi$
$433$	−266138.			−0.0682161			−0.0341080	+	0.999418i	$0.510859\pi$
$434$		0			0
$435$	−73159.9			−0.0185375
$436$	−1.48002e6	+	2.56347e6i	−0.372865	+	0.645820i
$437$	−1.15866e6	−	2.00686e6i	−0.290238	−	0.502706i
$438$	184287.	+	319195.i	0.0458997	+	0.0795007i
$439$	1.23023e6	−	2.13083e6i	0.304668	−	0.527700i	−0.672519	−	0.740079i	$-0.734788\pi$
$439$	1.23023e6	−	2.13083e6i	0.304668	−	0.527700i	0.977187	+	0.212379i	$0.0681212\pi$
$440$	262669.			0.0646812
$441$		0			0
$442$	−4.37358e6			−1.06483
$443$	605404.	−	1.04859e6i	0.146567	−	0.253861i	−0.783390	−	0.621531i	$-0.786511\pi$
$443$	605404.	−	1.04859e6i	0.146567	−	0.253861i	0.929956	+	0.367670i	$0.119844\pi$
$444$	−491757.	−	851748.i	−0.118384	−	0.205047i
$445$	1.62139e6	+	2.80833e6i	0.388139	+	0.672277i
$446$	−671749.	+	1.16350e6i	−0.159908	+	0.276969i
$447$	3.36517e6			0.796596
$448$		0			0
$449$	−3.66337e6			−0.857561			−0.428781	−	0.903409i	$-0.641057\pi$
$449$	−3.66337e6			−0.857561			−0.428781	+	0.903409i	$0.641057\pi$
$450$	149473.	−	258896.i	0.0347963	−	0.0602689i
$451$	−571492.	−	989853.i	−0.132303	−	0.229155i
$452$	1.82620e6	+	3.16307e6i	0.420438	+	0.728220i
$453$	389879.	−	675291.i	0.0892657	−	0.154613i
$454$	258885.			0.0589477
$455$		0			0
$456$	−1.46318e6			−0.329522
$457$	4.36934e6	−	7.56792e6i	0.978645	−	1.69506i	0.311306	−	0.950310i	$-0.399234\pi$
$457$	4.36934e6	−	7.56792e6i	0.978645	−	1.69506i	0.667340	−	0.744754i	$-0.267433\pi$
$458$	1.50158e6	+	2.60081e6i	0.334491	+	0.579355i
$459$	−528175.	−	914825.i	−0.117016	−	0.202678i
$460$	−342487.	+	593204.i	−0.0754656	+	0.130710i
$461$	−1.23476e6			−0.270602			−0.135301	−	0.990805i	$-0.543200\pi$
$461$	−1.23476e6			−0.270602			−0.135301	+	0.990805i	$0.543200\pi$
$462$		0			0
$463$	−4.07764e6			−0.884008			−0.442004	−	0.897013i	$-0.645732\pi$
$463$	−4.07764e6			−0.884008			−0.442004	+	0.897013i	$0.645732\pi$
$464$	−22171.8	+	38402.6i	−0.00478085	+	0.00828068i
$465$	−956886.	−	1.65737e6i	−0.205224	−	0.355458i
$466$	2.77435e6	+	4.80532e6i	0.591830	+	1.02508i
$467$	2.62510e6	−	4.54681e6i	0.556999	−	0.964750i	−0.440746	−	0.897632i	$-0.645286\pi$
$467$	2.62510e6	−	4.54681e6i	0.556999	−	0.964750i	0.997745	−	0.0671184i	$-0.0213805\pi$
$468$	−977917.			−0.206389
$469$		0			0
$470$	2.53281e6			0.528881
$471$	−2.07978e6	+	3.60228e6i	−0.431981	+	0.748214i
$472$	971814.	+	1.68323e6i	0.200784	+	0.347767i
$473$	−536878.	−	929900.i	−0.110337	−	0.191110i
$474$	−1.77451e6	+	3.07354e6i	−0.362771	+	0.628338i
$475$	2.34381e6			0.476639
$476$		0			0
$477$	−783894.			−0.157747
$478$	321813.	−	557397.i	0.0644220	−	0.111582i
$479$	843534.	+	1.46104e6i	0.167982	+	0.290954i	0.937710	−	0.347418i	$-0.112941\pi$
$479$	843534.	+	1.46104e6i	0.167982	+	0.290954i	−0.769728	+	0.638372i	$0.779608\pi$
$480$	216249.	+	374553.i	0.0428401	+	0.0742012i
$481$	2.57682e6	−	4.46319e6i	0.507834	−	0.879595i
$482$	5.13927e6			1.00759
$483$		0			0
$484$	−2.45444e6			−0.476254
$485$	989763.	−	1.71432e6i	0.191063	−	0.330931i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	−2.19760e6	−	3.80635e6i	−0.419881	−	0.727255i	0.576046	−	0.817417i	$-0.304595\pi$
$487$	−2.19760e6	−	3.80635e6i	−0.419881	−	0.727255i	−0.995927	+	0.0901621i	$0.971261\pi$
$488$	23439.1	−	40597.8i	0.00445545	−	0.00771707i
$489$	5.48129e6			1.03660
$490$		0			0
$491$	2.13582e6			0.399817			0.199909	−	0.979815i	$-0.435935\pi$
$491$	2.13582e6			0.399817			0.199909	+	0.979815i	$0.435935\pi$
$492$	940987.	−	1.62984e6i	0.175255	−	0.303551i
$493$	−125499.	−	217371.i	−0.0232554	−	0.0402795i
$494$	−3.83355e6	−	6.63991e6i	−0.706780	−	1.22418i
$495$	−166220.	+	287902.i	−0.0304910	+	0.0528119i
$496$	−1.15997e6			−0.211711
$497$		0			0
$498$	−3.16054e6			−0.571067
$499$	967196.	−	1.67523e6i	0.173885	−	0.301178i	−0.765890	−	0.642972i	$-0.777701\pi$
$499$	967196.	−	1.67523e6i	0.173885	−	0.301178i	0.939775	+	0.341794i	$0.111034\pi$
$500$	−1.51962e6	−	2.63207e6i	−0.271839	−	0.470838i
$501$	−575037.	−	995993.i	−0.102353	−	0.177281i
$502$	−962622.	+	1.66731e6i	−0.170489	+	0.295296i
$503$	−9.47334e6			−1.66949			−0.834744	−	0.550639i	$-0.814384\pi$
$503$	−9.47334e6			−1.66949			−0.834744	+	0.550639i	$0.814384\pi$
$504$		0			0
$505$	8.37559e6			1.46146
$506$	−159563.	+	276371.i	−0.0277048	+	0.0479862i
$507$	−891343.	−	1.54385e6i	−0.154002	−	0.266738i
$508$	2.74812e6	+	4.75988e6i	0.472472	+	0.818346i
$509$	−5.27947e6	+	9.14431e6i	−0.903225	+	1.56443i	−0.0799428	+	0.996799i	$0.525474\pi$
$509$	−5.27947e6	+	9.14431e6i	−0.903225	+	1.56443i	−0.823282	+	0.567632i	$0.807860\pi$
$510$	−2.44807e6			−0.416771
$511$		0			0
$512$	262144.			0.0441942
$513$	925917.	−	1.60373e6i	0.155338	−	0.269054i
$514$	66177.3	+	114622.i	0.0110484	+	0.0191365i
$515$	−826563.	−	1.43165e6i	−0.137328	−	0.237858i
$516$	883994.	−	1.53112e6i	0.146159	−	0.253154i
$517$	1.18002e6			0.194162
$518$		0			0
$519$	1.28285e6			0.209054
$520$	−1.13315e6	+	1.96267e6i	−0.183772	+	0.318302i
$521$	−3.76595e6	−	6.52282e6i	−0.607827	−	1.05279i	−0.991598	−	0.129359i	$-0.958708\pi$
$521$	−3.76595e6	−	6.52282e6i	−0.607827	−	1.05279i	0.383770	−	0.923429i	$-0.374625\pi$
$522$	−28061.1	−	48603.3i	−0.00450743	−	0.00780710i
$523$	−3.66658e6	+	6.35071e6i	−0.586148	+	1.01524i	0.408583	+	0.912721i	$0.366023\pi$
$523$	−3.66658e6	+	6.35071e6i	−0.586148	+	1.01524i	−0.994731	+	0.102517i	$0.967310\pi$
$524$	5.78035e6			0.919657
$525$		0			0
$526$	1.78480e6			0.281271
$527$	3.28289e6	−	5.68614e6i	0.514909	−	0.891848i
$528$	100749.	+	174503.i	0.0157274	+	0.0272406i
$529$	2.80207e6	+	4.85333e6i	0.435352	+	0.754051i
$530$	−908329.	+	1.57327e6i	−0.140460	+	0.243284i
$531$	−2.45990e6			−0.378601
$532$		0			0
$533$	9.86162e6			1.50359
$534$	−1.24380e6	+	2.15432e6i	−0.188754	+	0.326932i
$535$	2.11088e6	+	3.65616e6i	0.318845	+	0.552256i
$536$	−1.48480e6	−	2.57174e6i	−0.223231	−	0.386648i
$537$	1.33485e6	−	2.31204e6i	0.199755	−	0.345986i
$538$	7.79415e6			1.16095
$539$		0			0
$540$	−547379.			−0.0807800
$541$	6.29893e6	−	1.09101e7i	0.925281	−	1.60263i	0.134173	−	0.990958i	$-0.457162\pi$
$541$	6.29893e6	−	1.09101e7i	0.925281	−	1.60263i	0.791109	−	0.611676i	$-0.209504\pi$
$542$	−193746.	−	335578.i	−0.0283292	−	0.0490676i
$543$	−1.24944e6	−	2.16410e6i	−0.181851	−	0.314976i
$544$	−741908.	+	1.28502e6i	−0.107486	+	0.186172i
$545$	−8.68197e6			−1.25206
$546$		0			0
$547$	−4.21767e6			−0.602704			−0.301352	−	0.953513i	$-0.597438\pi$
$547$	−4.21767e6			−0.602704			−0.301352	+	0.953513i	$0.597438\pi$
$548$	2.43702e6	−	4.22104e6i	0.346663	−	0.600437i
$549$	29665.1	+	51381.5i	0.00420064	+	0.00727572i
$550$	−161387.	−	279530.i	−0.0227489	−	0.0394023i
$551$	220006.	−	381062.i	0.0308713	−	0.0534707i
$552$	−525455.			−0.0733986
$553$		0			0
$554$	6.54715e6			0.906312
$555$	1.44235e6	−	2.49823e6i	0.198764	−	0.344270i
$556$	1.03790e6	+	1.79769e6i	0.142386	+	0.246619i
$557$	4.78265e6	+	8.28379e6i	0.653176	+	1.13133i	0.982348	+	0.187064i	$0.0598972\pi$
$557$	4.78265e6	+	8.28379e6i	0.653176	+	1.13133i	−0.329171	+	0.944270i	$0.606769\pi$
$558$	734044.	−	1.27140e6i	0.0998013	−	0.172861i
$559$	9.26432e6			1.25396
$560$		0			0
$561$	−1.14054e6			−0.153005
$562$	3.59116e6	−	6.22008e6i	0.479617	−	0.830721i
$563$	−4.69593e6	−	8.13359e6i	−0.624382	−	1.08146i	−0.988660	−	0.150172i	$-0.952017\pi$
$563$	−4.69593e6	−	8.13359e6i	−0.624382	−	1.08146i	0.364278	−	0.931290i	$-0.381316\pi$
$564$	971481.	+	1.68266e6i	0.128599	+	0.222740i
$565$	−5.35635e6	+	9.27747e6i	−0.705908	+	1.22267i
$566$	5.12190e6			0.672032
$567$		0			0
$568$	−210905.			−0.0274294
$569$	−5.19337e6	+	8.99517e6i	−0.672463	+	1.16474i	0.304741	+	0.952435i	$0.401430\pi$
$569$	−5.19337e6	+	8.99517e6i	−0.672463	+	1.16474i	−0.977204	+	0.212304i	$0.931903\pi$
$570$	−2.14579e6	−	3.71662e6i	−0.276631	−	0.479138i
$571$	−2.21480e6	−	3.83614e6i	−0.284279	−	0.492385i	0.688155	−	0.725563i	$-0.258421\pi$
$571$	−2.21480e6	−	3.83614e6i	−0.284279	−	0.492385i	−0.972434	+	0.233178i	$0.925087\pi$
$572$	−527929.	+	914400.i	−0.0674661	+	0.116855i
$573$	−2.18326e6			−0.277791
$574$		0			0
$575$	841709.			0.106168
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	−6.00910e6	−	1.04081e7i	−0.751398	−	1.30146i	−0.947145	−	0.320805i	$-0.896047\pi$
$577$	−6.00910e6	−	1.04081e7i	−0.751398	−	1.30146i	0.195747	−	0.980654i	$-0.437287\pi$
$578$	−1.35971e6	−	2.35509e6i	−0.169289	−	0.293217i
$579$	2.61686e6	−	4.53254e6i	0.324403	−	0.561882i
$580$	−130062.			−0.0160539
$581$		0			0
$582$	1.51853e6			0.185830
$583$	−423186.	+	732979.i	−0.0515656	+	0.0893142i
$584$	327622.	+	567458.i	0.0397503	+	0.0688496i
$585$	−1.43414e6	−	2.48401e6i	−0.173262	−	0.300098i
$586$	−661628.	+	1.14597e6i	−0.0795921	+	0.137858i
$587$	−6.97624e6			−0.835653			−0.417826	−	0.908527i	$-0.637208\pi$
$587$	−6.97624e6			−0.835653			−0.417826	+	0.908527i	$0.637208\pi$
$588$		0			0
$589$	1.15102e7			1.36708
$590$	−2.85039e6	+	4.93701e6i	−0.337112	+	0.583894i
$591$	−3.37012e6	−	5.83722e6i	−0.396896	−	0.687444i
$592$	−874234.	−	1.51422e6i	−0.102524	−	0.177576i
$593$	−890739.	+	1.54281e6i	−0.104019	+	0.180167i	−0.913337	−	0.407204i	$-0.866504\pi$
$593$	−890739.	+	1.54281e6i	−0.104019	+	0.180167i	0.809318	+	0.587371i	$0.199837\pi$
$594$	−255021.			−0.0296558
$595$		0			0
$596$	5.98253e6			0.689873
$597$	−3.26562e6	+	5.65622e6i	−0.374998	+	0.649516i
$598$	−1.37670e6	−	2.38452e6i	−0.157430	−	0.272676i
$599$	−801823.	−	1.38880e6i	−0.0913085	−	0.158151i	0.816753	−	0.576987i	$-0.195772\pi$
$599$	−801823.	−	1.38880e6i	−0.0913085	−	0.158151i	−0.908062	+	0.418836i	$0.862438\pi$
$600$	265730.	−	460259.i	0.0301344	−	0.0521944i
$601$	1.51165e7			1.70712			0.853562	−	0.520991i	$-0.174438\pi$
$601$	1.51165e7			1.70712			0.853562	+	0.520991i	$0.174438\pi$
$602$		0			0
$603$	3.75839e6			0.420929
$604$	693119.	−	1.20052e6i	0.0773064	−	0.133899i
$605$	−3.59951e6	−	6.23453e6i	−0.399811	−	0.692493i
$606$	3.21253e6	+	5.56427e6i	0.355358	+	0.615498i
$607$	5.25833e6	−	9.10769e6i	0.579263	−	1.00331i	−0.416301	−	0.909227i	$-0.636674\pi$
$607$	5.25833e6	−	9.10769e6i	0.579263	−	1.00331i	0.995564	−	0.0940863i	$-0.0299930\pi$
$608$	−2.60120e6			−0.285375
$609$		0			0
$610$	137497.			0.0149612
$611$	−5.09060e6	+	8.81718e6i	−0.551653	+	0.955491i
$612$	−938977.	−	1.62636e6i	−0.101339	−	0.175524i
$613$	−1.35649e6	−	2.34951e6i	−0.145802	−	0.252537i	0.783870	−	0.620925i	$-0.213243\pi$
$613$	−1.35649e6	−	2.34951e6i	−0.145802	−	0.252537i	−0.929672	+	0.368388i	$0.879910\pi$
$614$	1.10818e6	−	1.91942e6i	0.118628	−	0.205470i
$615$	5.51994e6			0.588500
$616$		0			0
$617$	1.14961e7			1.21573			0.607864	−	0.794041i	$-0.292026\pi$
$617$	1.14961e7			1.21573			0.607864	+	0.794041i	$0.292026\pi$
$618$	634071.	−	1.09824e6i	0.0667831	−	0.115672i
$619$	5.49749e6	+	9.52194e6i	0.576684	+	0.998846i	0.995856	+	0.0909396i	$0.0289870\pi$
$619$	5.49749e6	+	9.52194e6i	0.576684	+	0.998846i	−0.419172	+	0.907907i	$0.637680\pi$
$620$	−1.70113e6	−	2.94644e6i	−0.177729	−	0.307836i
$621$	332514.	−	575932.i	0.0346004	−	0.0599297i
$622$	−7.03702e6			−0.729312
$623$		0			0
$624$	−1.73852e6			−0.178738
$625$	3.01547e6	−	5.22294e6i	0.308784	−	0.534829i
$626$	4.67639e6	+	8.09974e6i	0.476952	+	0.826105i
$627$	−999714.	−	1.73156e6i	−0.101556	−	0.175901i
$628$	−3.69739e6	+	6.40406e6i	−0.374107	+	0.647972i
$629$	9.89687e6			0.997405
$630$		0			0
$631$	−4.19503e6			−0.419432			−0.209716	−	0.977762i	$-0.567254\pi$
$631$	−4.19503e6			−0.419432			−0.209716	+	0.977762i	$0.567254\pi$
$632$	−3.15469e6	+	5.46408e6i	−0.314169	+	0.544157i
$633$	−3.66623e6	−	6.35010e6i	−0.363672	−	0.629899i
$634$	1.93478e6	+	3.35114e6i	0.191165	+	0.331108i
$635$	−8.06039e6	+	1.39610e7i	−0.793271	+	1.37399i
$636$	−1.39359e6			−0.136613
$637$		0			0
$638$	−60595.3			−0.00589369
$639$	133463.	−	231165.i	0.0129303	−	0.0223960i
$640$	384442.	+	665873.i	0.0371006	+	0.0642601i
$641$	5.31352e6	+	9.20329e6i	0.510784	+	0.884704i	0.999922	+	0.0124978i	$0.00397826\pi$
$641$	5.31352e6	+	9.20329e6i	0.510784	+	0.884704i	−0.489138	+	0.872207i	$0.662688\pi$
$642$	−1.61930e6	+	2.80470e6i	−0.155056	+	0.268565i
$643$	−1.54228e6			−0.147108			−0.0735538	−	0.997291i	$-0.523434\pi$
$643$	−1.54228e6			−0.147108			−0.0735538	+	0.997291i	$0.523434\pi$
$644$		0			0
$645$	5.18561e6			0.490795
$646$	7.36181e6	−	1.27510e7i	0.694070	−	1.20216i
$647$	−6.40851e6	−	1.10999e7i	−0.601861	−	1.04245i	−0.992539	−	0.121926i	$-0.961093\pi$
$647$	−6.40851e6	−	1.10999e7i	−0.601861	−	1.04245i	0.390678	−	0.920527i	$-0.372241\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	−1.32798e6	+	2.30013e6i	−0.123760	+	0.214359i
$650$	2.78488e6			0.258537
$651$		0			0
$652$	9.74452e6			0.897721
$653$	1.42275e6	−	2.46427e6i	0.130570	−	0.226155i	−0.793326	−	0.608797i	$-0.791652\pi$
$653$	1.42275e6	−	2.46427e6i	0.130570	−	0.226155i	0.923897	+	0.382642i	$0.124986\pi$
$654$	−3.33004e6	−	5.76780e6i	−0.304443	−	0.527310i
$655$	8.47705e6	+	1.46827e7i	0.772043	+	1.33722i
$656$	1.67287e6	−	2.89749e6i	0.151775	−	0.262883i
$657$	−829293.			−0.0749540
$658$		0			0
$659$	−2.04185e7			−1.83151			−0.915755	−	0.401736i	$-0.868407\pi$
$659$	−2.04185e7			−1.83151			−0.915755	+	0.401736i	$0.868407\pi$
$660$	−295503.	+	511826.i	−0.0264060	+	0.0457365i
$661$	1.09464e7	+	1.89597e7i	0.974467	+	1.68783i	0.681681	+	0.731649i	$0.261249\pi$
$661$	1.09464e7	+	1.89597e7i	0.974467	+	1.68783i	0.292786	+	0.956178i	$0.405418\pi$
$662$	655617.	+	1.13556e6i	0.0581440	+	0.100708i
$663$	4.92028e6	−	8.52217e6i	0.434716	−	0.752950i
$664$	−5.61873e6			−0.494559
$665$		0			0
$666$	2.21291e6			0.193320
$667$	79008.4	−	136847.i	0.00687636	−	0.0119102i
$668$	−1.02229e6	−	1.77065e6i	−0.0886405	−	0.153530i
$669$	−1.51143e6	−	2.61788e6i	−0.130564	−	0.226144i
$670$	4.35500e6	−	7.54308e6i	0.374801	−	0.649175i
$671$	64059.0			0.00549255
$672$		0			0
$673$	−992084.			−0.0844327			−0.0422164	−	0.999108i	$-0.513442\pi$
$673$	−992084.			−0.0844327			−0.0422164	+	0.999108i	$0.513442\pi$
$674$	−2.68104e6	+	4.64370e6i	−0.227329	+	0.393745i
$675$	336315.	+	582515.i	0.0284110	+	0.0492094i
$676$	−1.58461e6	−	2.74462e6i	−0.133369	−	0.231002i
$677$	−3.91748e6	+	6.78528e6i	−0.328500	+	0.568979i	−0.982214	−	0.187763i	$-0.939876\pi$
$677$	−3.91748e6	+	6.78528e6i	−0.328500	+	0.568979i	0.653714	+	0.756741i	$0.273210\pi$
$678$	−8.21790e6			−0.686573
$679$		0			0
$680$	−4.35212e6			−0.360935
$681$	−291245.	+	504452.i	−0.0240653	+	0.0416823i
$682$	−792548.	−	1.37273e6i	−0.0652476	−	0.113012i
$683$	3.70591e6	+	6.41883e6i	0.303979	+	0.526507i	0.977033	−	0.213086i	$-0.0683515\pi$
$683$	3.70591e6	+	6.41883e6i	0.303979	+	0.526507i	−0.673055	+	0.739593i	$0.735018\pi$
$684$	1.64607e6	−	2.85108e6i	0.134527	−	0.233007i
$685$	1.42958e7			1.16408
$686$		0			0
$687$	−6.75710e6			−0.546221
$688$	1.57154e6	−	2.72199e6i	0.126577	−	0.219238i
$689$	−3.65123e6	−	6.32412e6i	−0.293016	−	0.507519i
$690$	−770595.	−	1.33471e6i	−0.0616174	−	0.106724i
$691$	5.02584e6	−	8.70502e6i	0.400418	−	0.693545i	−0.593358	−	0.804939i	$-0.702198\pi$
$691$	5.02584e6	−	8.70502e6i	0.400418	−	0.693545i	0.993776	+	0.111394i	$0.0355315\pi$
$692$	2.28063e6			0.181046
$693$		0			0
$694$	−1.41350e7			−1.11403
$695$	−3.04421e6	+	5.27272e6i	−0.239063	+	0.414069i
$696$	−49886.5	−	86405.9i	−0.00390355	−	0.00676114i
$697$	9.46894e6	+	1.64007e7i	0.738277	+	1.27873i
$698$	7.96215e6	−	1.37908e7i	0.618574	−	1.07140i
$699$	−1.24846e7			−0.966455
$700$		0			0
$701$	1.59518e7			1.22607			0.613034	−	0.790057i	$-0.289949\pi$
$701$	1.59518e7			1.22607			0.613034	+	0.790057i	$0.289949\pi$
$702$	1.10016e6	−	1.90553e6i	0.0842581	−	0.145939i
$703$	8.67486e6	+	1.50253e7i	0.662024	+	1.14666i
$704$	179110.	+	310227.i	0.0136203	+	0.0235911i
$705$	−2.84941e6	+	4.93533e6i	−0.215915	+	0.373975i
$706$	177116.			0.0133736
$707$		0			0
$708$	−4.37316e6			−0.327878
$709$	1.91312e6	−	3.31361e6i	0.142931	−	0.247563i	−0.785668	−	0.618648i	$-0.787681\pi$
$709$	1.91312e6	−	3.31361e6i	0.142931	−	0.247563i	0.928599	+	0.371085i	$0.121014\pi$
$710$	−309299.	−	535721.i	−0.0230267	−	0.0398834i
$711$	−3.99265e6	−	6.91548e6i	−0.296202	−	0.513036i
$712$	−2.21119e6	+	3.82990e6i	−0.163466	+	0.283131i
$713$	4.13352e6			0.304506
$714$		0			0
$715$	−3.09690e6			−0.226549
$716$	2.37308e6	−	4.11029e6i	0.172993	−	0.299633i
$717$	724080.	+	1.25414e6i	0.0526003	+	0.0911064i
$718$	3.50228e6	+	6.06612e6i	0.253536	+	0.439137i
$719$	3.96365e6	−	6.86525e6i	0.285939	−	0.495261i	−0.686897	−	0.726754i	$-0.741028\pi$
$719$	3.96365e6	−	6.86525e6i	0.285939	−	0.495261i	0.972836	+	0.231493i	$0.0743612\pi$
$720$	−973118.			−0.0699575
$721$		0			0
$722$	1.59068e7			1.13564
$723$	−5.78167e6	+	1.00142e7i	−0.411347	+	0.712473i
$724$	−2.22123e6	−	3.84728e6i	−0.157488	−	0.272777i
$725$	79911.5	+	138411.i	0.00564630	+	0.00977968i
$726$	2.76124e6	−	4.78262e6i	0.194430	−	0.336763i
$727$	3.24519e6			0.227722			0.113861	−	0.993497i	$-0.463678\pi$
$727$	3.24519e6			0.227722			0.113861	+	0.993497i	$0.463678\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−960934.	+	1.66439e6i	−0.0667400	+	0.115597i
$731$	8.89542e6	+	1.54073e7i	0.615706	+	1.06643i
$732$	52738.0	+	91344.9i	0.00363786	+	0.00630096i
$733$	−2.98840e6	+	5.17605e6i	−0.205437	+	0.355827i	−0.950272	−	0.311422i	$-0.899195\pi$
$733$	−2.98840e6	+	5.17605e6i	−0.205437	+	0.355827i	0.744835	+	0.667249i	$0.232528\pi$
$734$	−1.58846e7			−1.08827
$735$		0			0
$736$	−934142.			−0.0635650
$737$	2.02897e6	−	3.51428e6i	0.137596	−	0.238324i
$738$	2.11722e6	+	3.66713e6i	0.143095	+	0.247848i
$739$	1.30032e6	+	2.25222e6i	0.0875870	+	0.151705i	0.906491	−	0.422226i	$-0.138751\pi$
$739$	1.30032e6	+	2.25222e6i	0.0875870	+	0.151705i	−0.818904	+	0.573931i	$0.805418\pi$
$740$	2.56418e6	−	4.44129e6i	0.172135	−	0.298147i
$741$	1.72510e7			1.15417
$742$		0			0
$743$	−2.29585e7			−1.52571			−0.762854	−	0.646571i	$-0.776203\pi$
$743$	−2.29585e7			−1.52571			−0.762854	+	0.646571i	$0.776203\pi$
$744$	1.30497e6	−	2.26027e6i	0.0864305	−	0.149702i
$745$	8.77355e6	+	1.51962e7i	0.579141	+	1.00310i
$746$	−4.47920e6	−	7.75820e6i	−0.294682	−	0.510404i
$747$	3.55560e6	−	6.15848e6i	0.233137	−	0.403806i
$748$	−2.02763e6			−0.132506
$749$		0			0
$750$	6.83831e6			0.443911
$751$	−2.30159e6	+	3.98647e6i	−0.148911	+	0.257922i	−0.930825	−	0.365464i	$-0.880910\pi$
$751$	−2.30159e6	+	3.98647e6i	−0.148911	+	0.257922i	0.781914	+	0.623386i	$0.214244\pi$
$752$	1.72708e6	+	2.99139e6i	0.111370	+	0.192898i
$753$	−2.16590e6	−	3.75145e6i	−0.139204	−	0.241108i
$754$	261407.	−	452770.i	0.0167451	−	0.0290034i
$755$	4.06591e6			0.259592
$756$		0			0
$757$	4.78695e6			0.303612			0.151806	−	0.988410i	$-0.451491\pi$
$757$	4.78695e6			0.303612			0.151806	+	0.988410i	$0.451491\pi$
$758$	8.50843e6	−	1.47370e7i	0.537869	−	0.931616i
$759$	−359016.	−	621835.i	−0.0226209	−	0.0391805i
$760$	−3.81474e6	−	6.60733e6i	−0.239569	−	0.414946i
$761$	1.14221e7	−	1.97836e7i	0.714962	−	1.23835i	−0.248013	−	0.968757i	$-0.579777\pi$
$761$	1.14221e7	−	1.97836e7i	0.714962	−	1.23835i	0.962974	−	0.269593i	$-0.0868892\pi$
$762$	−1.23665e7			−0.771544
$763$		0			0
$764$	−3.88135e6			−0.240574
$765$	2.75408e6	−	4.77020e6i	0.170146	−	0.294702i
$766$	3.23767e6	+	5.60780e6i	0.199370	+	0.345319i
$767$	−1.14578e7	−	1.98454e7i	−0.703253	−	1.21807i
$768$	−294912.	+	510803.i	−0.0180422	+	0.0312500i
$769$

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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.4645 - 40.6416i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(23.4645 - 40.6416i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(93.8579 + 162.567i) q^{10} +(43.7279 + 75.7390i) q^{11} +(-72.0000 + 124.708i) q^{12} -754.566 q^{13} -422.360 q^{15} +(-128.000 + 221.703i) q^{16} +(-724.520 - 1254.90i) q^{17} +(-162.000 - 280.592i) q^{18} +(1270.12 - 2199.91i) q^{19} -750.863 q^{20} -349.823 q^{22} +(456.124 - 790.030i) q^{23} +(-288.000 - 498.831i) q^{24} +(461.338 + 799.060i) q^{25} +(1509.13 - 2613.89i) q^{26} +729.000 q^{27} +173.217 q^{29} +(844.721 - 1463.10i) q^{30} +(2265.57 + 3924.08i) q^{31} +(-512.000 - 886.810i) q^{32} +(393.551 - 681.651i) q^{33} +5796.16 q^{34} +1296.00 q^{36} +(-3414.98 + 5914.92i) q^{37} +(5080.48 + 8799.64i) q^{38} +(3395.55 + 5881.26i) q^{39} +(1501.73 - 2601.07i) q^{40} -13069.3 q^{41} -12277.7 q^{43} +(699.647 - 1211.82i) q^{44} +(1900.62 + 3291.97i) q^{45} +(1824.50 + 3160.12i) q^{46} +(6746.40 - 11685.1i) q^{47} +2304.00 q^{48} -3690.70 q^{50} +(-6520.68 + 11294.1i) q^{51} +(6036.52 + 10455.6i) q^{52} +(4838.85 + 8381.14i) q^{53} +(-1458.00 + 2525.33i) q^{54} +4104.21 q^{55} -22862.1 q^{57} +(-346.434 + 600.041i) q^{58} +(15184.6 + 26300.5i) q^{59} +(3378.88 + 5852.40i) q^{60} +(366.236 - 634.340i) q^{61} -18124.5 q^{62} +4096.00 q^{64} +(-17705.5 + 30666.8i) q^{65} +(1574.21 + 2726.60i) q^{66} +(-23200.0 - 40183.5i) q^{67} +(-11592.3 + 20078.5i) q^{68} -8210.23 q^{69} -3295.39 q^{71} +(-2592.00 + 4489.48i) q^{72} +(5119.09 + 8866.53i) q^{73} +(-13659.9 - 23659.7i) q^{74} +(4152.04 - 7191.54i) q^{75} -40643.8 q^{76} -27164.4 q^{78} +(-49292.0 + 85376.2i) q^{79} +(6006.90 + 10404.3i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(26138.5 - 45273.3i) q^{82} -87792.7 q^{83} -68001.9 q^{85} +(24555.4 - 42531.2i) q^{86} +(-779.476 - 1350.09i) q^{87} +(2798.59 + 4847.29i) q^{88} +(-34549.9 + 59842.2i) q^{89} -15205.0 q^{90} -14596.0 q^{92} +(20390.1 - 35316.7i) q^{93} +(26985.6 + 46740.4i) q^{94} +(-59605.3 - 103239. i) q^{95} +(-4608.00 + 7981.29i) q^{96} +42181.4 q^{97} -7083.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 1440 q^{13} - 1944 q^{15} - 512 q^{16} + 612 q^{17} - 648 q^{18} + 2088 q^{19} - 3456 q^{20} - 992 q^{22} - 772 q^{23} - 1152 q^{24} + 318 q^{25} + 2880 q^{26} + 2916 q^{27} - 9184 q^{29} + 3888 q^{30} + 9792 q^{31} - 2048 q^{32} + 1116 q^{33} - 4896 q^{34} + 5184 q^{36} + 5992 q^{37} + 8352 q^{38} + 6480 q^{39} + 6912 q^{40} - 40392 q^{41} - 2272 q^{43} + 1984 q^{44} + 8748 q^{45} - 3088 q^{46} + 36936 q^{47} + 9216 q^{48} - 2544 q^{50} + 5508 q^{51} + 11520 q^{52} + 16708 q^{53} - 5832 q^{54} + 12672 q^{55} - 37584 q^{57} + 18368 q^{58} + 74592 q^{59} + 15552 q^{60} - 18648 q^{61} - 78336 q^{62} + 16384 q^{64} - 33300 q^{65} + 4464 q^{66} - 67344 q^{67} + 9792 q^{68} + 13896 q^{69} + 153096 q^{71} - 10368 q^{72} + 47304 q^{73} + 23968 q^{74} + 2862 q^{75} - 66816 q^{76} - 51840 q^{78} - 140656 q^{79} + 27648 q^{80} - 13122 q^{81} + 80784 q^{82} - 188208 q^{83} + 115736 q^{85} + 4544 q^{86} + 41328 q^{87} + 7936 q^{88} - 17604 q^{89} - 69984 q^{90} + 24704 q^{92} + 88128 q^{93} + 147744 q^{94} - 91592 q^{95} - 18432 q^{96} - 170352 q^{97} - 20088 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 1440 * q^13 - 1944 * q^15 - 512 * q^16 + 612 * q^17 - 648 * q^18 + 2088 * q^19 - 3456 * q^20 - 992 * q^22 - 772 * q^23 - 1152 * q^24 + 318 * q^25 + 2880 * q^26 + 2916 * q^27 - 9184 * q^29 + 3888 * q^30 + 9792 * q^31 - 2048 * q^32 + 1116 * q^33 - 4896 * q^34 + 5184 * q^36 + 5992 * q^37 + 8352 * q^38 + 6480 * q^39 + 6912 * q^40 - 40392 * q^41 - 2272 * q^43 + 1984 * q^44 + 8748 * q^45 - 3088 * q^46 + 36936 * q^47 + 9216 * q^48 - 2544 * q^50 + 5508 * q^51 + 11520 * q^52 + 16708 * q^53 - 5832 * q^54 + 12672 * q^55 - 37584 * q^57 + 18368 * q^58 + 74592 * q^59 + 15552 * q^60 - 18648 * q^61 - 78336 * q^62 + 16384 * q^64 - 33300 * q^65 + 4464 * q^66 - 67344 * q^67 + 9792 * q^68 + 13896 * q^69 + 153096 * q^71 - 10368 * q^72 + 47304 * q^73 + 23968 * q^74 + 2862 * q^75 - 66816 * q^76 - 51840 * q^78 - 140656 * q^79 + 27648 * q^80 - 13122 * q^81 + 80784 * q^82 - 188208 * q^83 + 115736 * q^85 + 4544 * q^86 + 41328 * q^87 + 7936 * q^88 - 17604 * q^89 - 69984 * q^90 + 24704 * q^92 + 88128 * q^93 + 147744 * q^94 - 91592 * q^95 - 18432 * q^96 - 170352 * q^97 - 20088 * q^99

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