LMFDB - Embedded newform 294.6.e.e.67.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$3$	4.50000	−	7.79423i	0.288675	−	0.500000i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−3.00000	−	5.19615i	−0.0536656	−	0.0929516i	0.837945	−	0.545755i	$-0.183757\pi$
$5$	−3.00000	−	5.19615i	−0.0536656	−	0.0929516i	−0.891610	+	0.452804i	$0.850424\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	−12.0000	+	20.7846i	−0.0379473	+	0.0657267i
$11$	333.000	−	576.773i	0.829779	−	1.43722i	−0.0684322	−	0.997656i	$-0.521800\pi$
$11$	333.000	−	576.773i	0.829779	−	1.43722i	0.898211	−	0.439564i	$-0.144867\pi$
$12$	72.0000	+	124.708i	0.144338	+	0.250000i
$13$	559.000			0.917389			0.458694	−	0.888594i	$-0.348317\pi$
$13$	559.000			0.917389			0.458694	+	0.888594i	$0.348317\pi$
$14$		0			0
$15$	−54.0000			−0.0619677
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−870.000	+	1506.88i	−0.730125	+	1.26461i	0.226705	+	0.973963i	$0.427205\pi$
$17$	−870.000	+	1506.88i	−0.730125	+	1.26461i	−0.956830	+	0.290649i	$0.906129\pi$
$18$	−162.000	+	280.592i	−0.117851	+	0.204124i
$19$	578.500	+	1001.99i	0.367637	+	0.636766i	0.989196	−	0.146602i	$-0.0468335\pi$
$19$	578.500	+	1001.99i	0.367637	+	0.636766i	−0.621558	+	0.783368i	$0.713500\pi$
$20$	96.0000			0.0536656
$21$		0			0
$22$	−2664.00			−1.17348
$23$	1734.00	+	3003.38i	0.683486	+	1.18383i	0.973910	+	0.226934i	$0.0728702\pi$
$23$	1734.00	+	3003.38i	0.683486	+	1.18383i	−0.290424	+	0.956898i	$0.593796\pi$
$24$	288.000	−	498.831i	0.102062	−	0.176777i
$25$	1544.50	−	2675.15i	0.494240	−	0.856049i
$26$	−1118.00	−	1936.43i	−0.324346	−	0.561784i
$27$	−729.000			−0.192450
$28$		0			0
$29$	3372.00			0.744548			0.372274	−	0.928123i	$-0.378578\pi$
$29$	3372.00			0.744548			0.372274	+	0.928123i	$0.378578\pi$
$30$	108.000	+	187.061i	0.0219089	+	0.0379473i
$31$	3146.50	−	5449.90i	0.588063	−	1.01855i	−0.406423	−	0.913685i	$-0.633224\pi$
$31$	3146.50	−	5449.90i	0.588063	−	1.01855i	0.994486	−	0.104869i	$-0.0334424\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	−2997.00	−	5190.96i	−0.479073	−	0.829779i
$34$	6960.00			1.03255
$35$		0			0
$36$	1296.00			0.166667
$37$	−1565.50	−	2711.53i	−0.187996	−	0.325619i	0.756586	−	0.653894i	$-0.226866\pi$
$37$	−1565.50	−	2711.53i	−0.187996	−	0.325619i	−0.944582	+	0.328276i	$0.893533\pi$
$38$	2314.00	−	4007.97i	0.259959	−	0.450262i
$39$	2515.50	−	4356.97i	0.264827	−	0.458694i
$40$	−192.000	−	332.554i	−0.0189737	−	0.0328634i
$41$	4866.00			0.452077			0.226039	−	0.974118i	$-0.427422\pi$
$41$	4866.00			0.452077			0.226039	+	0.974118i	$0.427422\pi$
$42$		0			0
$43$	−11407.0			−0.940806			−0.470403	−	0.882452i	$-0.655892\pi$
$43$	−11407.0			−0.940806			−0.470403	+	0.882452i	$0.655892\pi$
$44$	5328.00	+	9228.37i	0.414890	+	0.718610i
$45$	−243.000	+	420.888i	−0.0178885	+	0.0309839i
$46$	6936.00	−	12013.5i	0.483297	−	0.837096i
$47$	1155.00	+	2000.52i	0.0762671	+	0.132099i	0.901637	−	0.432494i	$-0.142366\pi$
$47$	1155.00	+	2000.52i	0.0762671	+	0.132099i	−0.825369	+	0.564593i	$0.809033\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	−12356.0			−0.698961
$51$	7830.00	+	13562.0i	0.421538	+	0.730125i
$52$	−4472.00	+	7745.73i	−0.229347	+	0.397241i
$53$	14148.0	−	24505.1i	0.691840	−	1.19830i	−0.279395	−	0.960176i	$-0.590134\pi$
$53$	14148.0	−	24505.1i	0.691840	−	1.19830i	0.971235	−	0.238125i	$-0.0765328\pi$
$54$	1458.00	+	2525.33i	0.0680414	+	0.117851i
$55$	−3996.00			−0.178122
$56$		0			0
$57$	10413.0			0.424511
$58$	−6744.00	−	11681.0i	−0.263237	−	0.455941i
$59$	10272.0	−	17791.6i	0.384171	−	0.665404i	−0.607483	−	0.794333i	$-0.707821\pi$
$59$	10272.0	−	17791.6i	0.384171	−	0.665404i	0.991654	+	0.128929i	$0.0411539\pi$
$60$	432.000	−	748.246i	0.0154919	−	0.0268328i
$61$	−2315.00	−	4009.70i	−0.0796575	−	0.137971i	0.823445	−	0.567397i	$-0.192049\pi$
$61$	−2315.00	−	4009.70i	−0.0796575	−	0.137971i	−0.903102	+	0.429426i	$0.858716\pi$
$62$	−25172.0			−0.831646
$63$		0			0
$64$	4096.00			0.125000
$65$	−1677.00	−	2904.65i	−0.0492322	−	0.0852728i
$66$	−11988.0	+	20763.8i	−0.338756	+	0.586742i
$67$	9372.50	−	16233.6i	0.255075	−	0.441803i	−0.709841	−	0.704362i	$-0.751233\pi$
$67$	9372.50	−	16233.6i	0.255075	−	0.441803i	0.964916	+	0.262559i	$0.0845664\pi$
$68$	−13920.0	−	24110.1i	−0.365062	−	0.632306i
$69$	31212.0			0.789221
$70$		0			0
$71$	−38226.0			−0.899939			−0.449969	−	0.893044i	$-0.648565\pi$
$71$	−38226.0			−0.899939			−0.449969	+	0.893044i	$0.648565\pi$
$72$	−2592.00	−	4489.48i	−0.0589256	−	0.102062i
$73$	35294.5	−	61131.9i	0.775175	−	1.34264i	−0.159521	−	0.987195i	$-0.550995\pi$
$73$	35294.5	−	61131.9i	0.775175	−	1.34264i	0.934696	−	0.355448i	$-0.115672\pi$
$74$	−6262.00	+	10846.1i	−0.132933	+	0.230247i
$75$	−13900.5	−	24076.4i	−0.285350	−	0.494240i
$76$	−18512.0			−0.367637
$77$		0			0
$78$	−20124.0			−0.374522
$79$	31146.5	+	53947.3i	0.561489	+	0.972528i	0.997367	+	0.0725221i	$0.0231048\pi$
$79$	31146.5	+	53947.3i	0.561489	+	0.972528i	−0.435877	+	0.900006i	$0.643562\pi$
$80$	−768.000	+	1330.22i	−0.0134164	+	0.0232379i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−9732.00	−	16856.3i	−0.159833	−	0.276840i
$83$	−79818.0			−1.27176			−0.635881	−	0.771787i	$-0.719363\pi$
$83$	−79818.0			−1.27176			−0.635881	+	0.771787i	$0.719363\pi$
$84$		0			0
$85$	10440.0			0.156730
$86$	22814.0	+	39515.0i	0.332625	+	0.576124i
$87$	15174.0	−	26282.1i	0.214932	−	0.372274i
$88$	21312.0	−	36913.5i	0.293371	−	0.508134i
$89$	−9060.00	−	15692.4i	−0.121242	−	0.209997i	0.799016	−	0.601310i	$-0.205354\pi$
$89$	−9060.00	−	15692.4i	−0.121242	−	0.209997i	−0.920258	+	0.391313i	$0.872021\pi$
$90$	1944.00			0.0252982
$91$		0			0
$92$	−55488.0			−0.683486
$93$	−28318.5	−	49049.1i	−0.339518	−	0.588063i
$94$	4620.00	−	8002.07i	0.0539290	−	0.0934078i
$95$	3471.00	−	6011.95i	0.0394590	−	0.0683449i
$96$	4608.00	+	7981.29i	0.0510310	+	0.0883883i
$97$	−124754.			−1.34625			−0.673124	−	0.739530i	$-0.735048\pi$
$97$	−124754.			−1.34625			−0.673124	+	0.739530i	$0.735048\pi$
$98$		0			0
$99$	−53946.0			−0.553186
$100$	24712.0	+	42802.4i	0.247120	+	0.428024i
$101$	−46695.0	+	80878.1i	−0.455478	+	0.788910i	−0.998716	−	0.0506685i	$-0.983865\pi$
$101$	−46695.0	+	80878.1i	−0.455478	+	0.788910i	0.543238	+	0.839579i	$0.317198\pi$
$102$	31320.0	−	54247.8i	0.298072	−	0.516276i
$103$	−83865.5	−	145259.i	−0.778915	−	1.34912i	−0.932567	−	0.360996i	$-0.882437\pi$
$103$	−83865.5	−	145259.i	−0.778915	−	1.34912i	0.153652	−	0.988125i	$-0.450897\pi$
$104$	35776.0			0.324346
$105$		0			0
$106$	−113184.			−0.978409
$107$	−34590.0	−	59911.6i	−0.292073	−	0.505885i	0.682227	−	0.731141i	$-0.261012\pi$
$107$	−34590.0	−	59911.6i	−0.292073	−	0.505885i	−0.974300	+	0.225256i	$0.927678\pi$
$108$	5832.00	−	10101.3i	0.0481125	−	0.0833333i
$109$	109779.	−	190144.i	0.885024	−	1.53291i	0.0393377	−	0.999226i	$-0.487475\pi$
$109$	109779.	−	190144.i	0.885024	−	1.53291i	0.845686	−	0.533680i	$-0.179191\pi$
$110$	7992.00	+	13842.6i	0.0629758	+	0.109077i
$111$	−28179.0			−0.217079
$112$		0			0
$113$	−39354.0			−0.289930			−0.144965	−	0.989437i	$-0.546307\pi$
$113$	−39354.0			−0.289930			−0.144965	+	0.989437i	$0.546307\pi$
$114$	−20826.0	−	36071.7i	−0.150087	−	0.259959i
$115$	10404.0	−	18020.3i	0.0733594	−	0.127062i
$116$	−26976.0	+	46723.8i	−0.186137	+	0.322399i
$117$	−22639.5	−	39212.8i	−0.152898	−	0.264827i
$118$	−82176.0			−0.543300
$119$		0			0
$120$	−3456.00			−0.0219089
$121$	−141252.	−	244657.i	−0.877067	−	1.51912i
$122$	−9260.00	+	16038.8i	−0.0563263	+	0.0975601i
$123$	21897.0	−	37926.7i	0.130503	−	0.226039i
$124$	50344.0	+	87198.4i	0.294031	+	0.509277i
$125$	−37284.0			−0.213426
$126$		0			0
$127$	317093.			1.74453			0.872263	−	0.489037i	$-0.162652\pi$
$127$	317093.			1.74453			0.872263	+	0.489037i	$0.162652\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	−51331.5	+	88908.8i	−0.271587	+	0.470403i
$130$	−6708.00	+	11618.6i	−0.0348125	+	0.0602969i
$131$	−77415.0	−	134087.i	−0.394137	−	0.682665i	0.598854	−	0.800858i	$-0.295623\pi$
$131$	−77415.0	−	134087.i	−0.394137	−	0.682665i	−0.992991	+	0.118194i	$0.962290\pi$
$132$	95904.0			0.479073
$133$		0			0
$134$	−74980.0			−0.360731
$135$	2187.00	+	3788.00i	0.0103280	+	0.0178885i
$136$	−55680.0	+	96440.6i	−0.258138	+	0.447108i
$137$	−33666.0	+	58311.2i	−0.153246	+	0.265430i	−0.932419	−	0.361379i	$-0.882306\pi$
$137$	−33666.0	+	58311.2i	−0.153246	+	0.265430i	0.779173	+	0.626809i	$0.215639\pi$
$138$	−62424.0	−	108122.i	−0.279032	−	0.483297i
$139$	365215.			1.60329			0.801644	−	0.597802i	$-0.203959\pi$
$139$	365215.			1.60329			0.801644	+	0.597802i	$0.203959\pi$
$140$		0			0
$141$	20790.0			0.0880657
$142$	76452.0	+	132419.i	0.318176	+	0.551098i
$143$	186147.	−	322416.i	0.761230	−	1.31849i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−10116.0	−	17521.4i	−0.0399566	−	0.0692069i
$146$	−282356.			−1.09626
$147$		0			0
$148$	50096.0			0.187996
$149$	84030.0	+	145544.i	0.310076	+	0.537068i	0.978379	−	0.206822i	$-0.0663120\pi$
$149$	84030.0	+	145544.i	0.310076	+	0.537068i	−0.668302	+	0.743890i	$0.732979\pi$
$150$	−55602.0	+	96305.5i	−0.201773	+	0.349480i
$151$	−76768.0	+	132966.i	−0.273992	+	0.474568i	−0.969880	−	0.243582i	$-0.921678\pi$
$151$	−76768.0	+	132966.i	−0.273992	+	0.474568i	0.695888	+	0.718150i	$0.255011\pi$
$152$	37024.0	+	64127.4i	0.129979	+	0.225131i
$153$	140940.			0.486750
$154$		0			0
$155$	−37758.0			−0.126235
$156$	40248.0	+	69711.6i	0.132414	+	0.229347i
$157$	101209.	−	175299.i	0.327695	−	0.567585i	−0.654359	−	0.756184i	$-0.727061\pi$
$157$	101209.	−	175299.i	0.327695	−	0.567585i	0.982054	+	0.188599i	$0.0603948\pi$
$158$	124586.	−	215789.i	0.397033	−	0.687681i
$159$	−127332.	−	220545.i	−0.399434	−	0.691840i
$160$	6144.00			0.0189737
$161$		0			0
$162$	26244.0			0.0785674
$163$	89882.0	+	155680.i	0.264974	+	0.458949i	0.967557	−	0.252653i	$-0.0813032\pi$
$163$	89882.0	+	155680.i	0.264974	+	0.458949i	−0.702583	+	0.711602i	$0.747970\pi$
$164$	−38928.0	+	67425.3i	−0.113019	+	0.195755i
$165$	−17982.0	+	31145.7i	−0.0514195	+	0.0890612i
$166$	159636.	+	276498.i	0.449636	+	0.778792i
$167$	−217302.			−0.602938			−0.301469	−	0.953476i	$-0.597477\pi$
$167$	−217302.			−0.602938			−0.301469	+	0.953476i	$0.597477\pi$
$168$		0			0
$169$	−58812.0			−0.158398
$170$	−20880.0	−	36165.2i	−0.0554126	−	0.0959774i
$171$	46858.5	−	81161.3i	0.122546	−	0.212255i
$172$	91256.0	−	158060.i	0.235202	−	0.407381i
$173$	−36990.0	−	64068.6i	−0.0939656	−	0.162753i	0.815211	−	0.579164i	$-0.196621\pi$
$173$	−36990.0	−	64068.6i	−0.0939656	−	0.162753i	−0.909176	+	0.416411i	$0.863288\pi$
$174$	−121392.			−0.303960
$175$		0			0
$176$	−170496.			−0.414890
$177$	−92448.0	−	160125.i	−0.221801	−	0.384171i
$178$	−36240.0	+	62769.5i	−0.0857311	+	0.148491i
$179$	−394683.	+	683611.i	−0.920695	+	1.59469i	−0.122353	+	0.992487i	$0.539044\pi$
$179$	−394683.	+	683611.i	−0.920695	+	1.59469i	−0.798342	+	0.602204i	$0.794289\pi$
$180$	−3888.00	−	6734.21i	−0.00894427	−	0.0154919i
$181$	477739.			1.08391			0.541956	−	0.840407i	$-0.317684\pi$
$181$	477739.			1.08391			0.541956	+	0.840407i	$0.317684\pi$
$182$		0			0
$183$	−41670.0			−0.0919805
$184$	110976.	+	192216.i	0.241649	+	0.418548i
$185$	−9393.00	+	16269.2i	−0.0201779	+	0.0349491i
$186$	−113274.	+	196196.i	−0.240076	+	0.415823i
$187$	579420.	+	1.00358e6i	1.21168	+	2.09870i
$188$	−36960.0			−0.0762671
$189$		0			0
$190$	−27768.0			−0.0558034
$191$	−179487.	−	310881.i	−0.356000	−	0.616609i	0.631289	−	0.775548i	$-0.282526\pi$
$191$	−179487.	−	310881.i	−0.356000	−	0.616609i	−0.987289	+	0.158938i	$0.949193\pi$
$192$	18432.0	−	31925.2i	0.0360844	−	0.0625000i
$193$	90966.5	−	157559.i	0.175788	−	0.304473i	−0.764646	−	0.644451i	$-0.777086\pi$
$193$	90966.5	−	157559.i	0.175788	−	0.304473i	0.940434	+	0.339978i	$0.110419\pi$
$194$	249508.	+	432161.i	0.475971	+	0.824405i
$195$	−30186.0			−0.0568485
$196$		0			0
$197$	717924.			1.31799			0.658996	−	0.752146i	$-0.270981\pi$
$197$	717924.			1.31799			0.658996	+	0.752146i	$0.270981\pi$
$198$	107892.	+	186874.i	0.195581	+	0.338756i
$199$	101548.	−	175886.i	0.181777	−	0.314847i	−0.760709	−	0.649093i	$-0.775148\pi$
$199$	101548.	−	175886.i	0.181777	−	0.314847i	0.942486	+	0.334246i	$0.108482\pi$
$200$	98848.0	−	171210.i	0.174740	−	0.302659i
$201$	−84352.5	−	146103.i	−0.147268	−	0.255075i
$202$	373560.			0.644142
$203$		0			0
$204$	−250560.			−0.421538
$205$	−14598.0	−	25284.5i	−0.0242610	−	0.0420213i
$206$	−335462.	+	581037.i	−0.550776	+	0.953973i
$207$	140454.	−	243273.i	0.227829	−	0.394611i
$208$	−71552.0	−	123932.i	−0.114674	−	0.198620i
$209$	770562.			1.22023
$210$		0			0
$211$	1.17098e6			1.81069			0.905343	−	0.424680i	$-0.139613\pi$
$211$	1.17098e6			1.81069			0.905343	+	0.424680i	$0.139613\pi$
$212$	226368.	+	392081.i	0.345920	+	0.599151i
$213$	−172017.	+	297942.i	−0.259790	+	0.449969i
$214$	−138360.	+	239647.i	−0.206527	+	0.357715i
$215$	34221.0	+	59272.5i	0.0504890	+	0.0874495i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	−878236.			−1.25161
$219$	−317651.	−	550187.i	−0.447548	−	0.775175i
$220$	31968.0	−	55370.2i	0.0445306	−	0.0771293i
$221$	−486330.	+	842348.i	−0.669808	+	1.16014i
$222$	56358.0	+	97614.9i	0.0767491	+	0.132933i
$223$	−1.24635e6			−1.67833			−0.839167	−	0.543873i	$-0.816957\pi$
$223$	−1.24635e6			−1.67833			−0.839167	+	0.543873i	$0.816957\pi$
$224$		0			0
$225$	−250209.			−0.329493
$226$	78708.0	+	136326.i	0.102506	+	0.177545i
$227$	−459471.	+	795827.i	−0.591825	+	1.02507i	0.402161	+	0.915569i	$0.368259\pi$
$227$	−459471.	+	795827.i	−0.591825	+	1.02507i	−0.993987	+	0.109503i	$0.965074\pi$
$228$	−83304.0	+	144287.i	−0.106128	+	0.183819i
$229$	601874.	+	1.04248e6i	0.758433	+	1.31364i	0.943649	+	0.330947i	$0.107368\pi$
$229$	601874.	+	1.04248e6i	0.758433	+	1.31364i	−0.185216	+	0.982698i	$0.559299\pi$
$230$	−83232.0			−0.103746
$231$		0			0
$232$	215808.			0.263237
$233$	459531.	+	795931.i	0.554530	+	0.960474i	0.997940	+	0.0641551i	$0.0204353\pi$
$233$	459531.	+	795931.i	0.554530	+	0.960474i	−0.443410	+	0.896319i	$0.646231\pi$
$234$	−90558.0	+	156851.i	−0.108115	+	0.187261i
$235$	6930.00	−	12003.1i	0.00818585	−	0.0141783i
$236$	164352.	+	284666.i	0.192086	+	0.332702i
$237$	560637.			0.648352
$238$		0			0
$239$	−625338.			−0.708142			−0.354071	−	0.935219i	$-0.615203\pi$
$239$	−625338.			−0.708142			−0.354071	+	0.935219i	$0.615203\pi$
$240$	6912.00	+	11971.9i	0.00774597	+	0.0134164i
$241$	626911.	−	1.08584e6i	0.695286	−	1.20427i	−0.274799	−	0.961502i	$-0.588611\pi$
$241$	626911.	−	1.08584e6i	0.695286	−	1.20427i	0.970084	−	0.242768i	$-0.0780555\pi$
$242$	−565010.	+	978626.i	−0.620180	+	1.07418i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	74080.0			0.0796575
$245$		0			0
$246$	−175176.			−0.184560
$247$	323382.	+	560113.i	0.337266	+	0.584162i
$248$	201376.	−	348793.i	0.207911	−	0.360113i
$249$	−359181.	+	622120.i	−0.367126	+	0.635881i
$250$	74568.0	+	129156.i	0.0754575	+	0.130696i
$251$	1.51333e6			1.51618			0.758089	−	0.652152i	$-0.226133\pi$
$251$	1.51333e6			1.51618			0.758089	+	0.652152i	$0.226133\pi$
$252$		0			0
$253$	2.30969e6			2.26857
$254$	−634186.	−	1.09844e6i	−0.616783	−	1.06830i
$255$	46980.0	−	81371.7i	0.0452442	−	0.0783652i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−777465.	−	1.34661e6i	−0.734257	−	1.27177i	−0.955049	−	0.296449i	$-0.904197\pi$
$257$	−777465.	−	1.34661e6i	−0.734257	−	1.27177i	0.220792	−	0.975321i	$-0.429136\pi$
$258$	410652.			0.384083
$259$		0			0
$260$	53664.0			0.0492322
$261$	−136566.	−	236539.i	−0.124091	−	0.214932i
$262$	−309660.	+	536347.i	−0.278697	+	0.482717i
$263$	557658.	−	965892.i	0.497140	−	0.861071i	−0.502855	−	0.864371i	$-0.667717\pi$
$263$	557658.	−	965892.i	0.497140	−	0.861071i	0.999995	+	0.00329949i	$0.00105026\pi$
$264$	−191808.	−	332221.i	−0.169378	−	0.293371i
$265$	−169776.			−0.148512
$266$		0			0
$267$	−163080.			−0.139998
$268$	149960.	+	259738.i	0.127538	+	0.220902i
$269$	17835.0	−	30891.1i	0.0150277	−	0.0260287i	−0.858414	−	0.512958i	$-0.828550\pi$
$269$	17835.0	−	30891.1i	0.0150277	−	0.0260287i	0.873441	+	0.486929i	$0.161883\pi$
$270$	8748.00	−	15152.0i	0.00730297	−	0.0126491i
$271$	−146384.	−	253545.i	−0.121079	−	0.209716i	0.799114	−	0.601179i	$-0.205302\pi$
$271$	−146384.	−	253545.i	−0.121079	−	0.209716i	−0.920194	+	0.391464i	$0.871969\pi$
$272$	445440.			0.365062
$273$		0			0
$274$	269328.			0.216723
$275$	−1.02864e6	−	1.78165e6i	−0.820220	−	1.42066i
$276$	−249696.	+	432486.i	−0.197305	+	0.341743i
$277$	−431607.	+	747564.i	−0.337978	+	0.585395i	−0.984052	−	0.177879i	$-0.943076\pi$
$277$	−431607.	+	747564.i	−0.337978	+	0.585395i	0.646074	+	0.763275i	$0.276410\pi$
$278$	−730430.	−	1.26514e6i	−0.566848	−	0.981810i
$279$	−509733.			−0.392042
$280$		0			0
$281$	1.47110e6			1.11142			0.555709	−	0.831377i	$-0.312447\pi$
$281$	1.47110e6			1.11142			0.555709	+	0.831377i	$0.312447\pi$
$282$	−41580.0	−	72018.7i	−0.0311359	−	0.0539290i
$283$	344420.	−	596554.i	0.255637	−	0.442775i	−0.709432	−	0.704774i	$-0.751048\pi$
$283$	344420.	−	596554.i	0.255637	−	0.442775i	0.965068	+	0.261999i	$0.0843816\pi$
$284$	305808.	−	529675.i	0.224985	−	0.389685i
$285$	−31239.0	−	54107.5i	−0.0227816	−	0.0394590i
$286$	−1.48918e6			−1.07654
$287$		0			0
$288$	82944.0			0.0589256
$289$	−803872.	−	1.39235e6i	−0.566164	−	0.980624i
$290$	−40464.0	+	70085.7i	−0.0282536	+	0.0489367i
$291$	−561393.	+	972361.i	−0.388628	+	0.673124i
$292$	564712.	+	978110.i	0.387588	+	0.671321i
$293$	−722832.			−0.491890			−0.245945	−	0.969284i	$-0.579098\pi$
$293$	−722832.			−0.491890			−0.245945	+	0.969284i	$0.579098\pi$
$294$		0			0
$295$	−123264.			−0.0824672
$296$	−100192.	−	173538.i	−0.0664666	−	0.115124i
$297$	−242757.	+	420467.i	−0.159691	+	0.276593i
$298$	336120.	−	582177.i	0.219257	−	0.379764i
$299$	969306.	+	1.67889e6i	0.627022	+	1.08603i
$300$	444816.			0.285350
$301$		0			0
$302$	614144.			0.387483
$303$	420255.	+	727903.i	0.262970	+	0.455478i
$304$	148096.	−	256510.i	0.0919093	−	0.159192i
$305$	−13890.0	+	24058.2i	−0.00854973	+	0.0148086i
$306$	−281880.	−	488230.i	−0.172092	−	0.298072i
$307$	20125.0			0.0121868			0.00609340	−	0.999981i	$-0.498060\pi$
$307$	20125.0			0.0121868			0.00609340	+	0.999981i	$0.498060\pi$
$308$		0			0
$309$	−1.50958e6			−0.899414
$310$	75516.0	+	130798.i	0.0446308	+	0.0773028i
$311$	−871779.	+	1.50997e6i	−0.511099	+	0.885250i	0.488818	+	0.872386i	$0.337428\pi$
$311$	−871779.	+	1.50997e6i	−0.511099	+	0.885250i	−0.999917	+	0.0128643i	$0.995905\pi$
$312$	160992.	−	278846.i	0.0936306	−	0.162173i
$313$	904272.	+	1.56624e6i	0.521721	+	0.903647i	0.999681	+	0.0252651i	$0.00804299\pi$
$313$	904272.	+	1.56624e6i	0.521721	+	0.903647i	−0.477960	+	0.878382i	$0.658624\pi$
$314$	−809672.			−0.463431
$315$		0			0
$316$	−996688.			−0.561489
$317$	−511776.	−	886422.i	−0.286043	−	0.495442i	0.686818	−	0.726829i	$-0.259007\pi$
$317$	−511776.	−	886422.i	−0.286043	−	0.495442i	−0.972862	+	0.231388i	$0.925673\pi$
$318$	−509328.	+	882182.i	−0.282442	+	0.489204i
$319$	1.12288e6	−	1.94488e6i	0.617810	−	1.07008i
$320$	−12288.0	−	21283.4i	−0.00670820	−	0.0116190i
$321$	−622620.			−0.337257
$322$		0			0
$323$	−2.01318e6			−1.07368
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	863376.	−	1.49541e6i	0.453410	−	0.785330i
$326$	359528.	−	622721.i	0.187365	−	0.324526i
$327$	−988016.	−	1.71129e6i	−0.510969	−	0.885024i
$328$	311424.			0.159833
$329$		0			0
$330$	143856.			0.0727182
$331$	503766.	+	872549.i	0.252731	+	0.437744i	0.964277	−	0.264896i	$-0.0853378\pi$
$331$	503766.	+	872549.i	0.252731	+	0.437744i	−0.711545	+	0.702640i	$0.752004\pi$
$332$	638544.	−	1.10599e6i	0.317940	−	0.550689i
$333$	−126806.	+	219634.i	−0.0626654	+	0.108540i
$334$	434604.	+	752756.i	0.213171	+	0.369223i
$335$	−112470.			−0.0547551
$336$		0			0
$337$	−1.56571e6			−0.750993			−0.375496	−	0.926824i	$-0.622528\pi$
$337$	−1.56571e6			−0.750993			−0.375496	+	0.926824i	$0.622528\pi$
$338$	117624.	+	203731.i	0.0560021	+	0.0969985i
$339$	−177093.	+	306734.i	−0.0836955	+	0.144965i
$340$	−83520.0	+	144661.i	−0.0391826	+	0.0678662i
$341$	−2.09557e6	−	3.62963e6i	−0.975924	−	1.69035i
$342$	−374868.			−0.173306
$343$		0			0
$344$	−730048.			−0.332625
$345$	−93636.0	−	162182.i	−0.0423541	−	0.0733594i
$346$	−147960.	+	256274.i	−0.0664437	+	0.115084i
$347$	−378642.	+	655827.i	−0.168813	+	0.292392i	−0.938003	−	0.346628i	$-0.887327\pi$
$347$	−378642.	+	655827.i	−0.168813	+	0.292392i	0.769190	+	0.639020i	$0.220660\pi$
$348$	242784.	+	420514.i	0.107466	+	0.186137i
$349$	455638.			0.200243			0.100121	−	0.994975i	$-0.468077\pi$
$349$	455638.			0.200243			0.100121	+	0.994975i	$0.468077\pi$
$350$		0			0
$351$	−407511.			−0.176552
$352$	340992.	+	590615.i	0.146686	+	0.254067i
$353$	−1.81569e6	+	3.14487e6i	−0.775543	+	1.34328i	0.158946	+	0.987287i	$0.449190\pi$
$353$	−1.81569e6	+	3.14487e6i	−0.775543	+	1.34328i	−0.934489	+	0.355992i	$0.884143\pi$
$354$	−369792.	+	640499.i	−0.156837	+	0.271650i
$355$	114678.	+	198628.i	0.0482958	+	0.0836508i
$356$	289920.			0.121242
$357$		0			0
$358$	3.15746e6			1.30206
$359$	2.01242e6	+	3.48561e6i	0.824104	+	1.42739i	0.902602	+	0.430476i	$0.141654\pi$
$359$	2.01242e6	+	3.48561e6i	0.824104	+	1.42739i	−0.0784980	+	0.996914i	$0.525012\pi$
$360$	−15552.0	+	26936.9i	−0.00632456	+	0.0109545i
$361$	568725.	−	985061.i	0.229686	−	0.397828i
$362$	−955478.	−	1.65494e6i	−0.383221	−	0.663758i
$363$	−2.54254e6			−1.01275
$364$		0			0
$365$	−423534.			−0.166401
$366$	83340.0	+	144349.i	0.0325200	+	0.0563263i
$367$	1.28894e6	−	2.23251e6i	0.499536	−	0.865222i	−0.500464	−	0.865757i	$-0.666837\pi$
$367$	1.28894e6	−	2.23251e6i	0.499536	−	0.865222i	1.00000		0.000535822i	$0.000170558\pi$
$368$	443904.	−	768864.i	0.170871	−	0.295958i
$369$	−197073.	−	341340.i	−0.0753462	−	0.130503i
$370$	75144.0			0.0285358
$371$		0			0
$372$	906192.			0.339518
$373$	1.26566e6	+	2.19220e6i	0.471028	+	0.815844i	0.999451	−	0.0331372i	$-0.0105498\pi$
$373$	1.26566e6	+	2.19220e6i	0.471028	+	0.815844i	−0.528423	+	0.848981i	$0.677216\pi$
$374$	2.31768e6	−	4.01434e6i	0.856790	−	1.48400i
$375$	−167778.	+	290600.i	−0.0616108	+	0.106713i
$376$	73920.0	+	128033.i	0.0269645	+	0.0467039i
$377$	1.88495e6			0.683040
$378$		0			0
$379$	−3.06677e6			−1.09669			−0.548344	−	0.836253i	$-0.684742\pi$
$379$	−3.06677e6			−1.09669			−0.548344	+	0.836253i	$0.684742\pi$
$380$	55536.0	+	96191.2i	0.0197295	+	0.0341725i
$381$	1.42692e6	−	2.47150e6i	0.503601	−	0.872263i
$382$	−717948.	+	1.24352e6i	−0.251730	+	0.436009i
$383$	−1.96260e6	−	3.39932e6i	−0.683652	−	1.18412i	−0.973859	−	0.227155i	$-0.927057\pi$
$383$	−1.96260e6	−	3.39932e6i	−0.683652	−	1.18412i	0.290207	−	0.956964i	$-0.406276\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	−727732.			−0.248601
$387$	461984.	+	800179.i	0.156801	+	0.271587i
$388$	998032.	−	1.72864e6i	0.336562	−	0.582943i
$389$	2.01334e6	−	3.48722e6i	0.674597	−	1.16844i	−0.301990	−	0.953311i	$-0.597651\pi$
$389$	2.01334e6	−	3.48722e6i	0.674597	−	1.16844i	0.976587	−	0.215125i	$-0.0690158\pi$
$390$	60372.0	+	104567.i	0.0200990	+	0.0348125i
$391$	−6.03432e6			−1.99612
$392$		0			0
$393$	−1.39347e6			−0.455110
$394$	−1.43585e6	−	2.48696e6i	−0.465981	−	0.807102i
$395$	186879.	−	323684.i	0.0602654	−	0.104383i
$396$	431568.	−	747498.i	0.138297	−	0.239537i
$397$	2.28720e6	+	3.96155e6i	0.728329	+	1.26150i	0.957589	+	0.288138i	$0.0930362\pi$
$397$	2.28720e6	+	3.96155e6i	0.728329	+	1.26150i	−0.229260	+	0.973365i	$0.573630\pi$
$398$	−812384.			−0.257071
$399$		0			0
$400$	−790784.			−0.247120
$401$	1.13472e6	+	1.96539e6i	0.352393	+	0.610363i	0.986668	−	0.162744i	$-0.0520346\pi$
$401$	1.13472e6	+	1.96539e6i	0.352393	+	0.610363i	−0.634275	+	0.773108i	$0.718701\pi$
$402$	−337410.	+	584411.i	−0.104134	+	0.180365i
$403$	1.75889e6	−	3.04649e6i	0.539482	−	0.934410i
$404$	−747120.	−	1.29405e6i	−0.227739	−	0.394455i
$405$	39366.0			0.0119257
$406$		0			0
$407$	−2.08525e6			−0.623981
$408$	501120.	+	867965.i	0.149036	+	0.258138i
$409$	−2.02298e6	+	3.50391e6i	−0.597976	+	1.03572i	0.395144	+	0.918619i	$0.370695\pi$
$409$	−2.02298e6	+	3.50391e6i	−0.597976	+	1.03572i	−0.993120	+	0.117105i	$0.962639\pi$
$410$	−58392.0	+	101138.i	−0.0171551	+	0.0297135i
$411$	302994.	+	524801.i	0.0884768	+	0.153246i
$412$	2.68370e6			0.778915
$413$		0			0
$414$	−1.12363e6			−0.322198
$415$	239454.	+	414746.i	0.0682499	+	0.118212i
$416$	−286208.	+	495727.i	−0.0810865	+	0.140446i
$417$	1.64347e6	−	2.84657e6i	0.462829	−	0.801644i
$418$	−1.54112e6	−	2.66931e6i	−0.431417	−	0.747236i
$419$	3.91281e6			1.08881			0.544407	−	0.838821i	$-0.316755\pi$
$419$	3.91281e6			1.08881			0.544407	+	0.838821i	$0.316755\pi$
$420$		0			0
$421$	−2.78086e6			−0.764671			−0.382335	−	0.924024i	$-0.624880\pi$
$421$	−2.78086e6			−0.764671			−0.382335	+	0.924024i	$0.624880\pi$
$422$	−2.34196e6	−	4.05639e6i	−0.640174	−	1.10881i
$423$	93555.0	−	162042.i	0.0254224	−	0.0440328i
$424$	905472.	−	1.56832e6i	0.244602	−	0.423663i
$425$	2.68743e6	+	4.65477e6i	0.721714	+	1.25004i
$426$	1.37614e6			0.367398
$427$		0			0
$428$	1.10688e6			0.292073
$429$	−1.67532e6	−	2.90174e6i	−0.439496	−	0.761230i
$430$	136884.	−	237090.i	0.0357011	−	0.0618361i
$431$	2.19104e6	−	3.79498e6i	0.568141	−	0.984049i	−0.428609	−	0.903490i	$-0.640996\pi$
$431$	2.19104e6	−	3.79498e6i	0.568141	−	0.984049i	0.996750	−	0.0805589i	$-0.0256705\pi$
$432$	93312.0	+	161621.i	0.0240563	+	0.0416667i
$433$	−1.24946e6			−0.320261			−0.160130	−	0.987096i	$-0.551191\pi$
$433$	−1.24946e6			−0.320261			−0.160130	+	0.987096i	$0.551191\pi$
$434$		0			0
$435$	−182088.			−0.0461379
$436$	1.75647e6	+	3.04230e6i	0.442512	+	0.766453i
$437$	−2.00624e6	+	3.47491e6i	−0.502550	+	0.870441i
$438$	−1.27060e6	+	2.20075e6i	−0.316464	+	0.548132i
$439$	−3.37210e6	−	5.84066e6i	−0.835102	−	1.44644i	−0.893947	−	0.448172i	$-0.852075\pi$
$439$	−3.37210e6	−	5.84066e6i	−0.835102	−	1.44644i	0.0588449	−	0.998267i	$-0.481258\pi$
$440$	−255744.			−0.0629758
$441$		0			0
$442$	3.89064e6			0.947252
$443$	−239448.	−	414736.i	−0.0579698	−	0.100407i	0.835584	−	0.549362i	$-0.185129\pi$
$443$	−239448.	−	414736.i	−0.0579698	−	0.100407i	−0.893554	+	0.448956i	$0.851796\pi$
$444$	225432.	−	390460.i	0.0542698	−	0.0939980i
$445$	−54360.0	+	94154.3i	−0.0130131	+	0.0225393i
$446$	2.49270e6	+	4.31749e6i	0.593381	+	1.02777i
$447$	1.51254e6			0.358045
$448$		0			0
$449$	724506.			0.169600			0.0848001	−	0.996398i	$-0.472975\pi$
$449$	724506.			0.169600			0.0848001	+	0.996398i	$0.472975\pi$
$450$	500418.	+	866749.i	0.116493	+	0.201773i
$451$	1.62038e6	−	2.80658e6i	0.375124	−	0.649734i
$452$	314832.	−	545305.i	0.0724824	−	0.125543i
$453$	690912.	+	1.19669e6i	0.158189	+	0.273992i
$454$	3.67577e6			0.836967
$455$		0			0
$456$	666432.			0.150087
$457$	1.16978e6	+	2.02612e6i	0.262008	+	0.453811i	0.966775	−	0.255627i	$-0.0822820\pi$
$457$	1.16978e6	+	2.02612e6i	0.262008	+	0.453811i	−0.704768	+	0.709438i	$0.748949\pi$
$458$	2.40750e6	−	4.16991e6i	0.536293	−	0.928887i
$459$	634230.	−	1.09852e6i	0.140513	−	0.243375i
$460$	166464.	+	288324.i	0.0366797	+	0.0635311i
$461$	−2.98247e6			−0.653617			−0.326809	−	0.945091i	$-0.605973\pi$
$461$	−2.98247e6			−0.653617			−0.326809	+	0.945091i	$0.605973\pi$
$462$		0			0
$463$	4.28423e6			0.928795			0.464398	−	0.885627i	$-0.346271\pi$
$463$	4.28423e6			0.928795			0.464398	+	0.885627i	$0.346271\pi$
$464$	−431616.	−	747581.i	−0.0930685	−	0.161199i
$465$	−169911.	+	294294.i	−0.0364409	+	0.0631175i
$466$	1.83812e6	−	3.18372e6i	0.392112	−	0.679158i
$467$	−2.87018e6	−	4.97129e6i	−0.608998	−	1.05482i	−0.991406	−	0.130822i	$-0.958238\pi$
$467$	−2.87018e6	−	4.97129e6i	−0.608998	−	1.05482i	0.382407	−	0.923994i	$-0.375095\pi$
$468$	724464.			0.152898
$469$		0			0
$470$	−55440.0			−0.0115765
$471$	−910881.	−	1.57769e6i	−0.189195	−	0.327695i
$472$	657408.	−	1.13866e6i	0.135825	−	0.235256i
$473$	−3.79853e6	+	6.57925e6i	−0.780662	+	1.35215i
$474$	−1.12127e6	−	1.94210e6i	−0.229227	−	0.397033i
$475$	3.57397e6			0.726804
$476$		0			0
$477$	−2.29198e6			−0.461226
$478$	1.25068e6	+	2.16623e6i	0.250366	+	0.433646i
$479$	1.32526e6	−	2.29541e6i	0.263913	−	0.457111i	−0.703365	−	0.710829i	$-0.748320\pi$
$479$	1.32526e6	−	2.29541e6i	0.263913	−	0.457111i	0.967278	+	0.253718i	$0.0816534\pi$
$480$	27648.0	−	47887.7i	0.00547723	−	0.00948683i
$481$	−875114.	−	1.51574e6i	−0.172465	−	0.298719i
$482$	−5.01529e6			−0.983282
$483$		0			0
$484$	4.52008e6			0.877067
$485$	374262.	+	648241.i	0.0722473	+	0.125136i
$486$	118098.	−	204552.i	0.0226805	−	0.0392837i
$487$	−1.40277e6	+	2.42967e6i	−0.268018	+	0.464221i	−0.968350	−	0.249597i	$-0.919702\pi$
$487$	−1.40277e6	+	2.42967e6i	−0.268018	+	0.464221i	0.700332	+	0.713817i	$0.253035\pi$
$488$	−148160.	−	256621.i	−0.0281632	−	0.0487800i
$489$	1.61788e6			0.305966
$490$		0			0
$491$	−4.68450e6			−0.876919			−0.438460	−	0.898751i	$-0.644476\pi$
$491$	−4.68450e6			−0.876919			−0.438460	+	0.898751i	$0.644476\pi$
$492$	350352.	+	606827.i	0.0652517	+	0.113019i
$493$	−2.93364e6	+	5.08121e6i	−0.543613	+	0.941565i
$494$	1.29353e6	−	2.24045e6i	0.238483	−	0.413065i
$495$	161838.	+	280312.i	0.0296871	+	0.0514195i
$496$	−1.61101e6			−0.294031
$497$		0			0
$498$	2.87345e6			0.519194
$499$	−737876.	−	1.27804e6i	−0.132658	−	0.229770i	0.792043	−	0.610466i	$-0.209018\pi$
$499$	−737876.	−	1.27804e6i	−0.132658	−	0.229770i	−0.924700	+	0.380696i	$0.875684\pi$
$500$	298272.	−	516622.i	0.0533565	−	0.0924162i
$501$	−977859.	+	1.69370e6i	−0.174053	+	0.301469i
$502$	−3.02666e6	−	5.24234e6i	−0.536050	−	0.928465i
$503$	−63606.0			−0.0112093			−0.00560465	−	0.999984i	$-0.501784\pi$
$503$	−63606.0			−0.0112093			−0.00560465	+	0.999984i	$0.501784\pi$
$504$		0			0
$505$	560340.			0.0977740
$506$	−4.61938e6	−	8.00099e6i	−0.802060	−	1.38921i
$507$	−264654.	+	458394.i	−0.0457255	+	0.0791989i
$508$	−2.53674e6	+	4.39377e6i	−0.436131	+	0.755402i
$509$	3.10578e6	+	5.37937e6i	0.531345	+	0.920317i	0.999331	+	0.0365806i	$0.0116466\pi$
$509$	3.10578e6	+	5.37937e6i	0.531345	+	0.920317i	−0.467986	+	0.883736i	$0.655020\pi$
$510$	−375840.			−0.0639849
$511$		0			0
$512$	262144.			0.0441942
$513$	−421726.	−	730452.i	−0.0707518	−	0.122546i
$514$	−3.10986e6	+	5.38644e6i	−0.519198	+	0.899277i
$515$	−503193.	+	871556.i	−0.0836020	+	0.144803i
$516$	−821304.	−	1.42254e6i	−0.135794	−	0.235202i
$517$	1.53846e6			0.253139
$518$		0			0
$519$	−665820.			−0.108502
$520$	−107328.	−	185898.i	−0.0174062	−	0.0301485i
$521$	706026.	−	1.22287e6i	0.113953	−	0.197373i	−0.803408	−	0.595429i	$-0.796982\pi$
$521$	706026.	−	1.22287e6i	0.113953	−	0.197373i	0.917361	+	0.398057i	$0.130315\pi$
$522$	−546264.	+	946157.i	−0.0877458	+	0.151980i
$523$	2.61467e6	+	4.52875e6i	0.417987	+	0.723976i	0.995737	−	0.0922386i	$-0.0294023\pi$
$523$	2.61467e6	+	4.52875e6i	0.417987	+	0.723976i	−0.577749	+	0.816214i	$0.696069\pi$
$524$	2.47728e6			0.394137
$525$		0			0
$526$	−4.46126e6			−0.703062
$527$	5.47491e6	+	9.48282e6i	0.858718	+	1.48734i
$528$	−767232.	+	1.32888e6i	−0.119768	+	0.207445i
$529$	−2.79534e6	+	4.84167e6i	−0.434306	+	0.752240i
$530$	339552.	+	588121.i	0.0525069	+	0.0909447i
$531$	−1.66406e6			−0.256114
$532$		0			0
$533$	2.72009e6			0.414730
$534$	326160.	+	564926.i	0.0494968	+	0.0857311i
$535$	−207540.	+	359470.i	−0.0313485	+	0.0542973i
$536$	599840.	−	1.03895e6i	0.0901827	−	0.156201i
$537$	3.55215e6	+	6.15250e6i	0.531564	+	0.920695i
$538$	−142680.			−0.0212524
$539$		0			0
$540$	−69984.0			−0.0103280
$541$	−2.20686e6	−	3.82240e6i	−0.324177	−	0.561491i	0.657169	−	0.753744i	$-0.271754\pi$
$541$	−2.20686e6	−	3.82240e6i	−0.324177	−	0.561491i	−0.981345	+	0.192253i	$0.938421\pi$
$542$	−585536.	+	1.01418e6i	−0.0856161	+	0.148291i
$543$	2.14983e6	−	3.72361e6i	0.312899	−	0.541956i
$544$	−890880.	−	1.54305e6i	−0.129069	−	0.223554i
$545$	−1.31735e6			−0.189981
$546$		0			0
$547$	−1.19038e7			−1.70105			−0.850523	−	0.525938i	$-0.823714\pi$
$547$	−1.19038e7			−1.70105			−0.850523	+	0.525938i	$0.823714\pi$
$548$	−538656.	−	932980.i	−0.0766232	−	0.132715i
$549$	−187515.	+	324786.i	−0.0265525	+	0.0459903i
$550$	−4.11455e6	+	7.12661e6i	−0.579983	+	1.00456i
$551$	1.95070e6	+	3.37871e6i	0.273723	+	0.474103i
$552$	1.99757e6			0.279032
$553$		0			0
$554$	3.45285e6			0.477973
$555$	84537.0	+	146422.i	0.0116497	+	0.0201779i
$556$	−2.92172e6	+	5.06057e6i	−0.400822	+	0.694244i
$557$	−6.45665e6	+	1.11832e7i	−0.881798	+	1.52732i	−0.0324587	+	0.999473i	$0.510334\pi$
$557$	−6.45665e6	+	1.11832e7i	−0.881798	+	1.52732i	−0.849340	+	0.527847i	$0.823000\pi$
$558$	1.01947e6	+	1.76577e6i	0.138608	+	0.240076i
$559$	−6.37651e6			−0.863085
$560$		0			0
$561$	1.04296e7			1.39913
$562$	−2.94221e6	−	5.09605e6i	−0.392946	−	0.680602i
$563$	−5.68492e6	+	9.84657e6i	−0.755881	+	1.30922i	0.189055	+	0.981967i	$0.439458\pi$
$563$	−5.68492e6	+	9.84657e6i	−0.755881	+	1.30922i	−0.944935	+	0.327257i	$0.893876\pi$
$564$	−166320.	+	288075.i	−0.0220164	+	0.0381336i
$565$	118062.	+	204489.i	0.0155593	+	0.0269494i
$566$	−2.75536e6			−0.361525
$567$		0			0
$568$	−2.44646e6			−0.318176
$569$	2.84898e6	+	4.93457e6i	0.368900	+	0.638953i	0.989394	−	0.145258i	$-0.0464013\pi$
$569$	2.84898e6	+	4.93457e6i	0.368900	+	0.638953i	−0.620494	+	0.784211i	$0.713068\pi$
$570$	−124956.	+	216430.i	−0.0161091	+	0.0279017i
$571$	3.52110e6	−	6.09873e6i	0.451948	−	0.782797i	−0.546559	−	0.837421i	$-0.684063\pi$
$571$	3.52110e6	−	6.09873e6i	0.451948	−	0.782797i	0.998507	+	0.0546236i	$0.0173959\pi$
$572$	2.97835e6	+	5.15866e6i	0.380615	+	0.659245i
$573$	−3.23077e6			−0.411073
$574$		0			0
$575$	1.07127e7			1.35122
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	−1.29098e6	+	2.23605e6i	−0.161429	+	0.279603i	−0.935381	−	0.353641i	$-0.884944\pi$
$577$	−1.29098e6	+	2.23605e6i	−0.161429	+	0.279603i	0.773952	+	0.633244i	$0.218277\pi$
$578$	−3.21549e6	+	5.56939e6i	−0.400338	+	0.693406i
$579$	−818698.	−	1.41803e6i	−0.101491	−	0.175788i
$580$	323712.			0.0399566
$581$		0			0
$582$	4.49114e6			0.549604
$583$	−9.42257e6	−	1.63204e7i	−1.14815	−	1.98865i
$584$	2.25885e6	−	3.91244e6i	0.274066	−	0.474696i
$585$	−135837.	+	235277.i	−0.0164107	+	0.0284243i
$586$	1.44566e6	+	2.50396e6i	0.173910	+	0.301220i
$587$	−4.69459e6			−0.562345			−0.281172	−	0.959657i	$-0.590723\pi$
$587$	−4.69459e6			−0.562345			−0.281172	+	0.959657i	$0.590723\pi$
$588$		0			0
$589$	7.28100e6			0.864774
$590$	246528.	+	426999.i	0.0291566	+	0.0505006i
$591$	3.23066e6	−	5.59566e6i	0.380472	−	0.658996i
$592$	−400768.	+	694151.i	−0.0469990	+	0.0814047i
$593$	6.71175e6	+	1.16251e7i	0.783789	+	1.35756i	0.929720	+	0.368268i	$0.120049\pi$
$593$	6.71175e6	+	1.16251e7i	0.783789	+	1.35756i	−0.145931	+	0.989295i	$0.546618\pi$
$594$	1.94206e6			0.225837
$595$		0			0
$596$	−2.68896e6			−0.310076
$597$	−913932.	−	1.58298e6i	−0.104949	−	0.181777i
$598$	3.87722e6	−	6.71555e6i	0.443372	−	0.767942i
$599$	−2.52301e6	+	4.36997e6i	−0.287310	+	0.497636i	−0.973167	−	0.230101i	$-0.926094\pi$
$599$	−2.52301e6	+	4.36997e6i	−0.287310	+	0.497636i	0.685856	+	0.727737i	$0.259428\pi$
$600$	−889632.	−	1.54089e6i	−0.100886	−	0.174740i
$601$	1.06391e7			1.20148			0.600742	−	0.799443i	$-0.294872\pi$
$601$	1.06391e7			1.20148			0.600742	+	0.799443i	$0.294872\pi$
$602$		0			0
$603$	−1.51834e6			−0.170050
$604$	−1.22829e6	−	2.12746e6i	−0.136996	−	0.237284i
$605$	−847515.	+	1.46794e6i	−0.0941367	+	0.163050i
$606$	1.68102e6	−	2.91161e6i	0.185948	−	0.322071i
$607$	708041.	+	1.22636e6i	0.0779986	+	0.135098i	0.902386	−	0.430928i	$-0.141814\pi$
$607$	708041.	+	1.22636e6i	0.0779986	+	0.135098i	−0.824388	+	0.566026i	$0.808480\pi$
$608$	−1.18477e6			−0.129979
$609$		0			0
$610$	111120.			0.0120912
$611$	645645.	+	1.11829e6i	0.0699666	+	0.121186i
$612$	−1.12752e6	+	1.95292e6i	−0.121687	+	0.210769i
$613$	−4.73152e6	+	8.19523e6i	−0.508568	+	0.880866i	0.491383	+	0.870944i	$0.336492\pi$
$613$	−4.73152e6	+	8.19523e6i	−0.508568	+	0.880866i	−0.999951	+	0.00992215i	$0.996842\pi$
$614$	−40250.0	−	69715.0i	−0.00430869	−	0.00746286i
$615$	−262764.			−0.0280142
$616$		0			0
$617$	1.29388e7			1.36830			0.684148	−	0.729343i	$-0.260174\pi$
$617$	1.29388e7			1.36830			0.684148	+	0.729343i	$0.260174\pi$
$618$	3.01916e6	+	5.22934e6i	0.317991	+	0.550776i
$619$	−1.90188e6	+	3.29415e6i	−0.199506	+	0.345555i	−0.948368	−	0.317171i	$-0.897267\pi$
$619$	−1.90188e6	+	3.29415e6i	−0.199506	+	0.345555i	0.748862	+	0.662726i	$0.230600\pi$
$620$	302064.	−	523190.i	0.0315587	−	0.0546614i
$621$	−1.26409e6	−	2.18946e6i	−0.131537	−	0.227829i
$622$	6.97423e6			0.722804
$623$		0			0
$624$	−1.28794e6			−0.132414
$625$	−4.71471e6	−	8.16612e6i	−0.482786	−	0.836210i
$626$	3.61709e6	−	6.26498e6i	0.368912	−	0.638975i
$627$	3.46753e6	−	6.00594e6i	0.352250	−	0.610115i
$628$	1.61934e6	+	2.80479e6i	0.163848	+	0.283792i
$629$	5.44794e6			0.549042
$630$		0			0
$631$	−9.17498e6			−0.917343			−0.458671	−	0.888606i	$-0.651674\pi$
$631$	−9.17498e6			−0.917343			−0.458671	+	0.888606i	$0.651674\pi$
$632$	1.99338e6	+	3.45263e6i	0.198516	+	0.343841i
$633$	5.26941e6	−	9.12689e6i	0.522700	−	0.905343i
$634$	−2.04710e6	+	3.54569e6i	−0.202263	+	0.350330i
$635$	−951279.	−	1.64766e6i	−0.0936211	−	0.162156i
$636$	4.07462e6			0.399434
$637$		0			0
$638$	−8.98301e6			−0.873716
$639$	1.54815e6	+	2.68148e6i	0.149990	+	0.259790i
$640$	−49152.0	+	85133.8i	−0.00474342	+	0.00821584i
$641$	−5.12269e6	+	8.87275e6i	−0.492439	+	0.852930i	−0.999962	−	0.00870851i	$-0.997228\pi$
$641$	−5.12269e6	+	8.87275e6i	−0.492439	+	0.852930i	0.507523	+	0.861638i	$0.330561\pi$
$642$	1.24524e6	+	2.15682e6i	0.119238	+	0.206527i
$643$	5.72346e6			0.545922			0.272961	−	0.962025i	$-0.411997\pi$
$643$	5.72346e6			0.545922			0.272961	+	0.962025i	$0.411997\pi$
$644$		0			0
$645$	615978.			0.0582996
$646$	4.02636e6	+	6.97386e6i	0.379604	+	0.657494i
$647$	−4.99397e6	+	8.64981e6i	−0.469013	+	0.812355i	−0.999373	−	0.0354179i	$-0.988724\pi$
$647$	−4.99397e6	+	8.64981e6i	−0.469013	+	0.812355i	0.530359	+	0.847773i	$0.322057\pi$
$648$	−209952.	+	363648.i	−0.0196419	+	0.0340207i
$649$	−6.84115e6	−	1.18492e7i	−0.637555	−	1.10428i
$650$	−6.90700e6			−0.641219
$651$		0			0
$652$	−2.87622e6			−0.264974
$653$	599439.	+	1.03826e6i	0.0550126	+	0.0952846i	0.892220	−	0.451601i	$-0.149147\pi$
$653$	599439.	+	1.03826e6i	0.0550126	+	0.0952846i	−0.837208	+	0.546885i	$0.815813\pi$
$654$	−3.95206e6	+	6.84517e6i	−0.361309	+	0.625806i
$655$	−464490.	+	804520.i	−0.0423032	+	0.0732713i
$656$	−622848.	−	1.07880e6i	−0.0565096	−	0.0978776i
$657$	−5.71771e6			−0.516783
$658$		0			0
$659$	1.18065e7			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$659$	1.18065e7			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$660$	−287712.	−	498332.i	−0.0257098	−	0.0445306i
$661$	2.36020e6	−	4.08798e6i	0.210109	−	0.363919i	−0.741640	−	0.670799i	$-0.765951\pi$
$661$	2.36020e6	−	4.08798e6i	0.210109	−	0.363919i	0.951748	+	0.306879i	$0.0992848\pi$
$662$	2.01507e6	−	3.49020e6i	0.178708	−	0.309532i
$663$	4.37697e6	+	7.58113e6i	0.386714	+	0.669808i
$664$	−5.10835e6			−0.449636
$665$		0			0
$666$	1.01444e6			0.0886222
$667$	5.84705e6	+	1.01274e7i	0.508888	+	0.881420i
$668$	1.73842e6	−	3.01102e6i	0.150734	−	0.261080i
$669$	−5.60858e6	+	9.71435e6i	−0.484493	+	0.839167i
$670$	224940.	+	389608.i	0.0193589	+	0.0335305i
$671$	−3.08358e6			−0.264392
$672$		0			0
$673$	−8.70826e6			−0.741129			−0.370564	−	0.928807i	$-0.620836\pi$
$673$	−8.70826e6			−0.741129			−0.370564	+	0.928807i	$0.620836\pi$
$674$	3.13141e6	+	5.42377e6i	0.265516	+	0.459887i
$675$	−1.12594e6	+	1.95019e6i	−0.0951165	+	0.164747i
$676$	470496.	−	814923.i	0.0395995	−	0.0685883i
$677$	2.55553e6	+	4.42630e6i	0.214293	+	0.371167i	0.953054	−	0.302801i	$-0.0979218\pi$
$677$	2.55553e6	+	4.42630e6i	0.214293	+	0.371167i	−0.738760	+	0.673968i	$0.764588\pi$
$678$	1.41674e6			0.118363
$679$		0			0
$680$	668160.			0.0554126
$681$	4.13524e6	+	7.16244e6i	0.341690	+	0.591825i
$682$	−8.38228e6	+	1.45185e7i	−0.690083	+	1.19526i
$683$	8.85989e6	−	1.53458e7i	0.726736	−	1.25874i	−0.231520	−	0.972830i	$-0.574370\pi$
$683$	8.85989e6	−	1.53458e7i	0.726736	−	1.25874i	0.958256	−	0.285913i	$-0.0922968\pi$
$684$	749736.	+	1.29858e6i	0.0612729	+	0.106128i
$685$	403992.			0.0328962
$686$		0			0
$687$	1.08337e7			0.875763
$688$	1.46010e6	+	2.52896e6i	0.117601	+	0.203691i
$689$	7.90873e6	−	1.36983e7i	0.634686	−	1.09931i
$690$	−374544.	+	648729.i	−0.0299488	+	0.0518729i
$691$	−1.12997e7	−	1.95716e7i	−0.900265	−	1.55931i	−0.827149	−	0.561982i	$-0.810039\pi$
$691$	−1.12997e7	−	1.95716e7i	−0.900265	−	1.55931i	−0.0731160	−	0.997323i	$-0.523294\pi$
$692$	1.18368e6			0.0939656
$693$		0			0
$694$	3.02914e6			0.238737
$695$	−1.09564e6	−	1.89771e6i	−0.0860415	−	0.149028i
$696$	971136.	−	1.68206e6i	0.0759901	−	0.131619i
$697$	−4.23342e6	+	7.33250e6i	−0.330073	+	0.571702i
$698$	−911276.	−	1.57838e6i	−0.0707964	−	0.122623i
$699$	8.27156e6			0.640316
$700$		0			0
$701$	−818148.			−0.0628835			−0.0314418	−	0.999506i	$-0.510010\pi$
$701$	−818148.			−0.0628835			−0.0314418	+	0.999506i	$0.510010\pi$
$702$	815022.	+	1.41166e6i	0.0624204	+	0.108115i
$703$	1.81128e6	−	3.13724e6i	0.138229	−	0.239419i
$704$	1.36397e6	−	2.36246e6i	0.103722	−	0.179652i
$705$	−62370.0	−	108028.i	−0.00472610	−	0.00818585i
$706$	1.45255e7			1.09678
$707$		0			0
$708$	2.95834e6			0.221801
$709$	2.54591e6	+	4.40965e6i	0.190208	+	0.329449i	0.945319	−	0.326147i	$-0.105751\pi$
$709$	2.54591e6	+	4.40965e6i	0.190208	+	0.329449i	−0.755111	+	0.655597i	$0.772417\pi$
$710$	458712.	−	794512.i	0.0341503	−	0.0591500i
$711$	2.52287e6	−	4.36973e6i	0.187163	−	0.324176i
$712$	−579840.	−	1.00431e6i	−0.0428655	−	0.0742453i
$713$	2.18241e7			1.60773
$714$		0			0
$715$	−2.23376e6			−0.163408
$716$	−6.31493e6	−	1.09378e7i	−0.460348	−	0.797345i
$717$	−2.81402e6	+	4.87403e6i	−0.204423	+	0.354071i
$718$	8.04967e6	−	1.39424e7i	0.582730	−	1.00932i
$719$	−240429.	−	416435.i	−0.0173446	−	0.0300418i	0.857223	−	0.514946i	$-0.172188\pi$
$719$	−240429.	−	416435.i	−0.0173446	−	0.0300418i	−0.874567	+	0.484904i	$0.838855\pi$
$720$	124416.			0.00894427
$721$		0			0
$722$	−4.54980e6			−0.324825
$723$	−5.64220e6	−	9.77258e6i	−0.401423	−	0.695286i
$724$	−3.82191e6	+	6.61975e6i	−0.270978	+	0.469348i
$725$	5.20805e6	−	9.02061e6i	0.367985	−	0.637369i
$726$	5.08509e6	+	8.80763e6i	0.358061	+	0.620180i
$727$	1.40783e7			0.987905			0.493952	−	0.869489i	$-0.335552\pi$
$727$	1.40783e7			0.987905			0.493952	+	0.869489i	$0.335552\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	847068.	+	1.46716e6i	0.0588317	+	0.101899i
$731$	9.92409e6	−	1.71890e7i	0.686906	−	1.18976i
$732$	333360.	−	577396.i	0.0229951	−	0.0398287i
$733$	1.01966e6	+	1.76610e6i	0.0700964	+	0.121411i	0.898943	−	0.438065i	$-0.144336\pi$
$733$	1.01966e6	+	1.76610e6i	0.0700964	+	0.121411i	−0.828847	+	0.559475i	$0.811003\pi$
$734$	−1.03115e7			−0.706450
$735$		0			0
$736$	−3.55123e6			−0.241649
$737$	−6.24209e6	−	1.08116e7i	−0.423312	−	0.733199i
$738$	−788292.	+	1.36536e6i	−0.0532778	+	0.0922798i
$739$	8.24785e6	−	1.42857e7i	0.555558	−	0.962255i	−0.442302	−	0.896866i	$-0.645838\pi$
$739$	8.24785e6	−	1.42857e7i	0.555558	−	0.962255i	0.997860	−	0.0653888i	$-0.0208288\pi$
$740$	−150288.	−	260306.i	−0.0100889	−	0.0174745i
$741$	5.82087e6			0.389441
$742$		0			0
$743$	−2.38121e7			−1.58243			−0.791217	−	0.611536i	$-0.790552\pi$
$743$	−2.38121e7			−1.58243			−0.791217	+	0.611536i	$0.790552\pi$
$744$	−1.81238e6	−	3.13914e6i	−0.120038	−	0.207911i
$745$	504180.	−	873265.i	0.0332809	−	0.0576442i
$746$	5.06266e6	−	8.76878e6i	0.333067	−	0.576889i
$747$	3.23263e6	+	5.59908e6i	0.211960	+	0.367126i
$748$	−1.85414e7			−1.21168
$749$		0			0
$750$	1.34222e6			0.0871308
$751$	−962480.	−	1.66707e6i	−0.0622719	−	0.107858i	0.833209	−	0.552959i	$-0.186501\pi$
$751$	−962480.	−	1.66707e6i	−0.0622719	−	0.107858i	−0.895481	+	0.445101i	$0.853168\pi$
$752$	295680.	−	512133.i	0.0190668	−	0.0330246i
$753$	6.80999e6	−	1.17953e7i	0.437683	−	0.758089i
$754$	−3.76990e6	−	6.52965e6i	−0.241491	−	0.418275i
$755$	921216.			0.0588158
$756$		0			0
$757$	8.98092e6			0.569615			0.284807	−	0.958585i	$-0.408070\pi$
$757$	8.98092e6			0.569615			0.284807	+	0.958585i	$0.408070\pi$
$758$	6.13354e6	+	1.06236e7i	0.387738	+	0.671581i
$759$	1.03936e7	−	1.80022e7i	0.654879	−	1.13428i
$760$	222144.	−	384765.i	0.0139508	−	0.0241636i
$761$	7.29955e6	+	1.26432e7i	0.456914	+	0.791398i	0.998796	−	0.0490566i	$-0.0156215\pi$
$761$	7.29955e6	+	1.26432e7i	0.456914	+	0.791398i	−0.541882	+	0.840454i	$0.682288\pi$
$762$	−1.14153e7			−0.712200
$763$		0			0
$764$	5.74358e6			0.356000
$765$	−422820.	−	732346.i	−0.0261217	−	0.0452442i
$766$	−7.85040e6	+	1.35973e7i	−0.483415	+	0.837299i
$767$	5.74205e6	−	9.94552e6i	0.352434	−	0.610434i
$768$	294912.	+	510803.i	0.0180422	+	0.0312500i
$769$	−2.78381e7			−1.69755			−0.848776	−	0.528753i	\(-0.822

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)

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

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