LMFDB - Embedded newform 294.6.e.q.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:	yes
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.q.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(13.0000 + 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(13.0000 + 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-52.0000 + 90.0666i) q^{10} +(179.000 - 310.037i) q^{11} +(72.0000 + 124.708i) q^{12} -332.000 q^{13} +234.000 q^{15} +(-128.000 - 221.703i) q^{16} +(63.0000 - 109.119i) q^{17} +(162.000 - 280.592i) q^{18} +(-1100.00 - 1905.26i) q^{19} -416.000 q^{20} +1432.00 q^{22} +(1071.00 + 1855.03i) q^{23} +(-288.000 + 498.831i) q^{24} +(1224.50 - 2120.90i) q^{25} +(-664.000 - 1150.08i) q^{26} -729.000 q^{27} -3610.00 q^{29} +(468.000 + 810.600i) q^{30} +(2834.00 - 4908.63i) q^{31} +(512.000 - 886.810i) q^{32} +(-1611.00 - 2790.33i) q^{33} +504.000 q^{34} +1296.00 q^{36} +(1461.00 + 2530.53i) q^{37} +(4400.00 - 7621.02i) q^{38} +(-1494.00 + 2587.68i) q^{39} +(-832.000 - 1441.07i) q^{40} +2142.00 q^{41} +6388.00 q^{43} +(2864.00 + 4960.59i) q^{44} +(1053.00 - 1823.85i) q^{45} +(-4284.00 + 7420.11i) q^{46} +(-3260.00 - 5646.49i) q^{47} -2304.00 q^{48} +9796.00 q^{50} +(-567.000 - 982.073i) q^{51} +(2656.00 - 4600.33i) q^{52} +(5351.00 - 9268.20i) q^{53} +(-1458.00 - 2525.33i) q^{54} +9308.00 q^{55} -19800.0 q^{57} +(-7220.00 - 12505.4i) q^{58} +(21262.0 - 36826.9i) q^{59} +(-1872.00 + 3242.40i) q^{60} +(-22420.0 - 38832.6i) q^{61} +22672.0 q^{62} +4096.00 q^{64} +(-4316.00 - 7475.53i) q^{65} +(6444.00 - 11161.3i) q^{66} +(724.000 - 1254.00i) q^{67} +(1008.00 + 1745.91i) q^{68} +19278.0 q^{69} -4402.00 q^{71} +(2592.00 + 4489.48i) q^{72} +(10250.0 - 17753.5i) q^{73} +(-5844.00 + 10122.1i) q^{74} +(-11020.5 - 19088.1i) q^{75} +35200.0 q^{76} -11952.0 q^{78} +(-32618.0 - 56496.0i) q^{79} +(3328.00 - 5764.27i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(4284.00 + 7420.11i) q^{82} +102804. q^{83} +3276.00 q^{85} +(12776.0 + 22128.7i) q^{86} +(-16245.0 + 28137.2i) q^{87} +(-11456.0 + 19842.4i) q^{88} +(-64003.0 - 110856. i) q^{89} +8424.00 q^{90} -34272.0 q^{92} +(-25506.0 - 44177.7i) q^{93} +(13040.0 - 22585.9i) q^{94} +(28600.0 - 49536.7i) q^{95} +(-4608.00 - 7981.29i) q^{96} +113324. q^{97} -28998.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 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 + 26 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9	\( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} - 104 q^{10} + 358 q^{11} + 144 q^{12} - 664 q^{13} + 468 q^{15} - 256 q^{16} + 126 q^{17} + 324 q^{18} - 2200 q^{19} - 832 q^{20} + 2864 q^{22} + 2142 q^{23} - 576 q^{24} + 2449 q^{25} - 1328 q^{26} - 1458 q^{27} - 7220 q^{29} + 936 q^{30} + 5668 q^{31} + 1024 q^{32} - 3222 q^{33} + 1008 q^{34} + 2592 q^{36} + 2922 q^{37} + 8800 q^{38} - 2988 q^{39} - 1664 q^{40} + 4284 q^{41} + 12776 q^{43} + 5728 q^{44} + 2106 q^{45} - 8568 q^{46} - 6520 q^{47} - 4608 q^{48} + 19592 q^{50} - 1134 q^{51} + 5312 q^{52} + 10702 q^{53} - 2916 q^{54} + 18616 q^{55} - 39600 q^{57} - 14440 q^{58} + 42524 q^{59} - 3744 q^{60} - 44840 q^{61} + 45344 q^{62} + 8192 q^{64} - 8632 q^{65} + 12888 q^{66} + 1448 q^{67} + 2016 q^{68} + 38556 q^{69} - 8804 q^{71} + 5184 q^{72} + 20500 q^{73} - 11688 q^{74} - 22041 q^{75} + 70400 q^{76} - 23904 q^{78} - 65236 q^{79} + 6656 q^{80} - 6561 q^{81} + 8568 q^{82} + 205608 q^{83} + 6552 q^{85} + 25552 q^{86} - 32490 q^{87} - 22912 q^{88} - 128006 q^{89} + 16848 q^{90} - 68544 q^{92} - 51012 q^{93} + 26080 q^{94} + 57200 q^{95} - 9216 q^{96} + 226648 q^{97} - 57996 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 26 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 - 104 * q^10 + 358 * q^11 + 144 * q^12 - 664 * q^13 + 468 * q^15 - 256 * q^16 + 126 * q^17 + 324 * q^18 - 2200 * q^19 - 832 * q^20 + 2864 * q^22 + 2142 * q^23 - 576 * q^24 + 2449 * q^25 - 1328 * q^26 - 1458 * q^27 - 7220 * q^29 + 936 * q^30 + 5668 * q^31 + 1024 * q^32 - 3222 * q^33 + 1008 * q^34 + 2592 * q^36 + 2922 * q^37 + 8800 * q^38 - 2988 * q^39 - 1664 * q^40 + 4284 * q^41 + 12776 * q^43 + 5728 * q^44 + 2106 * q^45 - 8568 * q^46 - 6520 * q^47 - 4608 * q^48 + 19592 * q^50 - 1134 * q^51 + 5312 * q^52 + 10702 * q^53 - 2916 * q^54 + 18616 * q^55 - 39600 * q^57 - 14440 * q^58 + 42524 * q^59 - 3744 * q^60 - 44840 * q^61 + 45344 * q^62 + 8192 * q^64 - 8632 * q^65 + 12888 * q^66 + 1448 * q^67 + 2016 * q^68 + 38556 * q^69 - 8804 * q^71 + 5184 * q^72 + 20500 * q^73 - 11688 * q^74 - 22041 * q^75 + 70400 * q^76 - 23904 * q^78 - 65236 * q^79 + 6656 * q^80 - 6561 * q^81 + 8568 * q^82 + 205608 * q^83 + 6552 * q^85 + 25552 * q^86 - 32490 * q^87 - 22912 * q^88 - 128006 * q^89 + 16848 * q^90 - 68544 * q^92 - 51012 * q^93 + 26080 * q^94 + 57200 * q^95 - 9216 * q^96 + 226648 * q^97 - 57996 * 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
$5$	13.0000	+	22.5167i	0.232551	+	0.402790i	0.958558	−	0.284897i	$-0.0919594\pi$
$5$	13.0000	+	22.5167i	0.232551	+	0.402790i	−0.726007	+	0.687687i	$0.758626\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	−52.0000	+	90.0666i	−0.164438	+	0.284816i
$11$	179.000	−	310.037i	0.446037	−	0.772560i	−0.552086	−	0.833787i	$-0.686168\pi$
$11$	179.000	−	310.037i	0.446037	−	0.772560i	0.998124	+	0.0612274i	$0.0195015\pi$
$12$	72.0000	+	124.708i	0.144338	+	0.250000i
$13$	−332.000			−0.544853			−0.272427	−	0.962177i	$-0.587826\pi$
$13$	−332.000			−0.544853			−0.272427	+	0.962177i	$0.587826\pi$
$14$		0			0
$15$	234.000			0.268527
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	63.0000	−	109.119i	0.0528711	−	0.0915754i	−0.838379	−	0.545088i	$-0.816496\pi$
$17$	63.0000	−	109.119i	0.0528711	−	0.0915754i	0.891250	+	0.453513i	$0.149829\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	−1100.00	−	1905.26i	−0.699051	−	1.21079i	−0.968796	−	0.247860i	$-0.920273\pi$
$19$	−1100.00	−	1905.26i	−0.699051	−	1.21079i	0.269745	−	0.962932i	$-0.413061\pi$
$20$	−416.000			−0.232551
$21$		0			0
$22$	1432.00			0.630792
$23$	1071.00	+	1855.03i	0.422153	+	0.731190i	0.996150	−	0.0876671i	$-0.0279412\pi$
$23$	1071.00	+	1855.03i	0.422153	+	0.731190i	−0.573997	+	0.818858i	$0.694608\pi$
$24$	−288.000	+	498.831i	−0.102062	+	0.176777i
$25$	1224.50	−	2120.90i	0.391840	−	0.678687i
$26$	−664.000	−	1150.08i	−0.192635	−	0.333653i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−3610.00			−0.797099			−0.398549	−	0.917147i	$-0.630486\pi$
$29$	−3610.00			−0.797099			−0.398549	+	0.917147i	$0.630486\pi$
$30$	468.000	+	810.600i	0.0949386	+	0.164438i
$31$	2834.00	−	4908.63i	0.529658	−	0.917395i	−0.469743	−	0.882803i	$-0.655654\pi$
$31$	2834.00	−	4908.63i	0.529658	−	0.917395i	0.999402	−	0.0345917i	$-0.0110131\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−1611.00	−	2790.33i	−0.257520	−	0.446037i
$34$	504.000			0.0747710
$35$		0			0
$36$	1296.00			0.166667
$37$	1461.00	+	2530.53i	0.175447	+	0.303883i	0.940316	−	0.340303i	$-0.110530\pi$
$37$	1461.00	+	2530.53i	0.175447	+	0.303883i	−0.764869	+	0.644186i	$0.777196\pi$
$38$	4400.00	−	7621.02i	0.494303	−	0.856159i
$39$	−1494.00	+	2587.68i	−0.157286	+	0.272427i
$40$	−832.000	−	1441.07i	−0.0822192	−	0.142408i
$41$	2142.00			0.199003			0.0995015	−	0.995037i	$-0.468275\pi$
$41$	2142.00			0.199003			0.0995015	+	0.995037i	$0.468275\pi$
$42$		0			0
$43$	6388.00			0.526858			0.263429	−	0.964679i	$-0.415146\pi$
$43$	6388.00			0.526858			0.263429	+	0.964679i	$0.415146\pi$
$44$	2864.00	+	4960.59i	0.223019	+	0.386280i
$45$	1053.00	−	1823.85i	0.0775170	−	0.134263i
$46$	−4284.00	+	7420.11i	−0.298507	+	0.517030i
$47$	−3260.00	−	5646.49i	−0.215265	−	0.372850i	0.738090	−	0.674703i	$-0.235728\pi$
$47$	−3260.00	−	5646.49i	−0.215265	−	0.372850i	−0.953354	+	0.301853i	$0.902395\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	9796.00			0.554145
$51$	−567.000	−	982.073i	−0.0305251	−	0.0528711i
$52$	2656.00	−	4600.33i	0.136213	−	0.235928i
$53$	5351.00	−	9268.20i	0.261665	−	0.453217i	−0.705020	−	0.709188i	$-0.749062\pi$
$53$	5351.00	−	9268.20i	0.261665	−	0.453217i	0.966684	+	0.255971i	$0.0823952\pi$
$54$	−1458.00	−	2525.33i	−0.0680414	−	0.117851i
$55$	9308.00			0.414906
$56$		0			0
$57$	−19800.0			−0.807194
$58$	−7220.00	−	12505.4i	−0.281817	−	0.488121i
$59$	21262.0	−	36826.9i	0.795196	−	1.37732i	−0.127519	−	0.991836i	$-0.540701\pi$
$59$	21262.0	−	36826.9i	0.795196	−	1.37732i	0.922715	−	0.385483i	$-0.125965\pi$
$60$	−1872.00	+	3242.40i	−0.0671317	+	0.116276i
$61$	−22420.0	−	38832.6i	−0.771456	−	1.33620i	−0.936765	−	0.349959i	$-0.886196\pi$
$61$	−22420.0	−	38832.6i	−0.771456	−	1.33620i	0.165309	−	0.986242i	$-0.447138\pi$
$62$	22672.0			0.749050
$63$		0			0
$64$	4096.00			0.125000
$65$	−4316.00	−	7475.53i	−0.126706	−	0.219462i
$66$	6444.00	−	11161.3i	0.182094	−	0.315396i
$67$	724.000	−	1254.00i	0.0197039	−	0.0341281i	−0.856005	−	0.516967i	$-0.827061\pi$
$67$	724.000	−	1254.00i	0.0197039	−	0.0341281i	0.875709	+	0.482839i	$0.160394\pi$
$68$	1008.00	+	1745.91i	0.0264355	+	0.0457877i
$69$	19278.0			0.487460
$70$		0			0
$71$	−4402.00			−0.103634			−0.0518172	−	0.998657i	$-0.516501\pi$
$71$	−4402.00			−0.103634			−0.0518172	+	0.998657i	$0.516501\pi$
$72$	2592.00	+	4489.48i	0.0589256	+	0.102062i
$73$	10250.0	−	17753.5i	0.225121	−	0.389922i	−0.731234	−	0.682126i	$-0.761055\pi$
$73$	10250.0	−	17753.5i	0.225121	−	0.389922i	0.956356	+	0.292205i	$0.0943888\pi$
$74$	−5844.00	+	10122.1i	−0.124060	+	0.214878i
$75$	−11020.5	−	19088.1i	−0.226229	−	0.391840i
$76$	35200.0			0.699051
$77$		0			0
$78$	−11952.0			−0.222435
$79$	−32618.0	−	56496.0i	−0.588017	−	1.01847i	−0.994492	−	0.104813i	$-0.966576\pi$
$79$	−32618.0	−	56496.0i	−0.588017	−	1.01847i	0.406475	−	0.913662i	$-0.366758\pi$
$80$	3328.00	−	5764.27i	0.0581378	−	0.100698i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	4284.00	+	7420.11i	0.0703582	+	0.121864i
$83$	102804.			1.63800			0.819002	−	0.573791i	$-0.194528\pi$
$83$	102804.			1.63800			0.819002	+	0.573791i	$0.194528\pi$
$84$		0			0
$85$	3276.00			0.0491809
$86$	12776.0	+	22128.7i	0.186273	+	0.322633i
$87$	−16245.0	+	28137.2i	−0.230103	+	0.398549i
$88$	−11456.0	+	19842.4i	−0.157698	+	0.273141i
$89$	−64003.0	−	110856.i	−0.856496	−	1.48349i	−0.875250	−	0.483670i	$-0.839303\pi$
$89$	−64003.0	−	110856.i	−0.856496	−	1.48349i	0.0187543	−	0.999824i	$-0.494030\pi$
$90$	8424.00			0.109626
$91$		0			0
$92$	−34272.0			−0.422153
$93$	−25506.0	−	44177.7i	−0.305798	−	0.529658i
$94$	13040.0	−	22585.9i	0.152215	−	0.263644i
$95$	28600.0	−	49536.7i	0.325130	−	0.563142i
$96$	−4608.00	−	7981.29i	−0.0510310	−	0.0883883i
$97$	113324.			1.22290			0.611452	−	0.791281i	$-0.290586\pi$
$97$	113324.			1.22290			0.611452	+	0.791281i	$0.290586\pi$
$98$		0			0
$99$	−28998.0			−0.297358
$100$	19592.0	+	33934.3i	0.195920	+	0.339343i
$101$	−69857.0	+	120996.i	−0.681407	+	1.18023i	0.293145	+	0.956068i	$0.405298\pi$
$101$	−69857.0	+	120996.i	−0.681407	+	1.18023i	−0.974552	+	0.224163i	$0.928035\pi$
$102$	2268.00	−	3928.29i	0.0215845	−	0.0373855i
$103$	−71090.0	−	123131.i	−0.660261	−	1.14361i	−0.980547	−	0.196284i	$-0.937112\pi$
$103$	−71090.0	−	123131.i	−0.660261	−	1.14361i	0.320286	−	0.947321i	$-0.396221\pi$
$104$	21248.0			0.192635
$105$		0			0
$106$	42808.0			0.370050
$107$	99259.0	+	171922.i	0.838128	+	1.45168i	0.891458	+	0.453104i	$0.149683\pi$
$107$	99259.0	+	171922.i	0.838128	+	1.45168i	−0.0533296	+	0.998577i	$0.516983\pi$
$108$	5832.00	−	10101.3i	0.0481125	−	0.0833333i
$109$	−66269.0	+	114781.i	−0.534250	+	0.925347i	0.464950	+	0.885337i	$0.346072\pi$
$109$	−66269.0	+	114781.i	−0.534250	+	0.925347i	−0.999199	+	0.0400103i	$0.987261\pi$
$110$	18616.0	+	32243.9i	0.146691	+	0.254077i
$111$	26298.0			0.202589
$112$		0			0
$113$	47026.0			0.346451			0.173226	−	0.984882i	$-0.444581\pi$
$113$	47026.0			0.346451			0.173226	+	0.984882i	$0.444581\pi$
$114$	−39600.0	−	68589.2i	−0.285386	−	0.494303i
$115$	−27846.0	+	48230.7i	−0.196344	+	0.340078i
$116$	28880.0	−	50021.6i	0.199275	−	0.345154i
$117$	13446.0	+	23289.2i	0.0908089	+	0.157286i
$118$	170096.			1.12458
$119$		0			0
$120$	−14976.0			−0.0949386
$121$	16443.5	+	28481.0i	0.102101	+	0.176844i
$122$	89680.0	−	155330.i	0.545502	−	0.944836i
$123$	9639.00	−	16695.2i	0.0574472	−	0.0995015i
$124$	45344.0	+	78538.1i	0.264829	+	0.458697i
$125$	144924.			0.829593
$126$		0			0
$127$	165548.			0.910782			0.455391	−	0.890291i	$-0.349499\pi$
$127$	165548.			0.910782			0.455391	+	0.890291i	$0.349499\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	28746.0	−	49789.5i	0.152091	−	0.263429i
$130$	17264.0	−	29902.1i	0.0895948	−	0.155183i
$131$	−69654.0	−	120644.i	−0.354624	−	0.614226i	0.632430	−	0.774618i	$-0.282058\pi$
$131$	−69654.0	−	120644.i	−0.354624	−	0.614226i	−0.987053	+	0.160391i	$0.948724\pi$
$132$	51552.0			0.257520
$133$		0			0
$134$	5792.00			0.0278655
$135$	−9477.00	−	16414.6i	−0.0447545	−	0.0775170i
$136$	−4032.00	+	6983.63i	−0.0186928	+	0.0323768i
$137$	166421.	−	288250.i	0.757542	−	1.31210i	−0.186559	−	0.982444i	$-0.559733\pi$
$137$	166421.	−	288250.i	0.757542	−	1.31210i	0.944101	−	0.329657i	$-0.106933\pi$
$138$	38556.0	+	66781.0i	0.172343	+	0.298507i
$139$	−8556.00			−0.0375607			−0.0187804	−	0.999824i	$-0.505978\pi$
$139$	−8556.00			−0.0375607			−0.0187804	+	0.999824i	$0.505978\pi$
$140$		0			0
$141$	−58680.0			−0.248566
$142$	−8804.00	−	15249.0i	−0.0366403	−	0.0634629i
$143$	−59428.0	+	102932.i	−0.243025	+	0.420932i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−46930.0	−	81285.1i	−0.185366	−	0.321064i
$146$	82000.0			0.318370
$147$		0			0
$148$	−46752.0			−0.175447
$149$	−34777.0	−	60235.5i	−0.128329	−	0.222273i	0.794700	−	0.607002i	$-0.207628\pi$
$149$	−34777.0	−	60235.5i	−0.128329	−	0.222273i	−0.923029	+	0.384729i	$0.874295\pi$
$150$	44082.0	−	76352.3i	0.159968	−	0.277073i
$151$	−264620.	+	458335.i	−0.944453	+	1.63584i	−0.187610	+	0.982244i	$0.560074\pi$
$151$	−264620.	+	458335.i	−0.944453	+	1.63584i	−0.756843	+	0.653597i	$0.773259\pi$
$152$	70400.0	+	121936.i	0.247152	+	0.428079i
$153$	−10206.0			−0.0352474
$154$		0			0
$155$	147368.			0.492690
$156$	−23904.0	−	41402.9i	−0.0786428	−	0.136213i
$157$	6520.00	−	11293.0i	0.0211105	−	0.0365645i	−0.855277	−	0.518171i	$-0.826613\pi$
$157$	6520.00	−	11293.0i	0.0211105	−	0.0365645i	0.876388	+	0.481606i	$0.159946\pi$
$158$	130472.	−	225984.i	0.415791	−	0.720170i
$159$	−48159.0	−	83413.8i	−0.151072	−	0.261665i
$160$	26624.0			0.0822192
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	175620.	+	304183.i	0.517732	+	0.896738i	0.999788	+	0.0205976i	$0.00655687\pi$
$163$	175620.	+	304183.i	0.517732	+	0.896738i	−0.482056	+	0.876140i	$0.660110\pi$
$164$	−17136.0	+	29680.4i	−0.0497508	+	0.0861709i
$165$	41886.0	−	72548.7i	0.119773	−	0.207453i
$166$	205608.	+	356124.i	0.579122	+	1.00307i
$167$	−626128.			−1.73729			−0.868644	−	0.495436i	$-0.835008\pi$
$167$	−626128.			−1.73729			−0.868644	+	0.495436i	$0.835008\pi$
$168$		0			0
$169$	−261069.			−0.703135
$170$	6552.00	+	11348.4i	0.0173881	+	0.0301170i
$171$	−89100.0	+	154326.i	−0.233017	+	0.403597i
$172$	−51104.0	+	88514.7i	−0.131715	+	0.228136i
$173$	−92413.0	−	160064.i	−0.234757	−	0.406610i	0.724445	−	0.689332i	$-0.242096\pi$
$173$	−92413.0	−	160064.i	−0.234757	−	0.406610i	−0.959202	+	0.282722i	$0.908763\pi$
$174$	−129960.			−0.325414
$175$		0			0
$176$	−91648.0			−0.223019
$177$	−191358.	−	331442.i	−0.459107	−	0.795196i
$178$	256012.	−	443426.i	0.605634	−	1.04899i
$179$	178761.	−	309623.i	0.417004	−	0.722272i	−0.578633	−	0.815588i	$-0.696413\pi$
$179$	178761.	−	309623.i	0.417004	−	0.722272i	0.995637	+	0.0933163i	$0.0297468\pi$
$180$	16848.0	+	29181.6i	0.0387585	+	0.0671317i
$181$	−696508.			−1.58026			−0.790132	−	0.612937i	$-0.789988\pi$
$181$	−696508.			−1.58026			−0.790132	+	0.612937i	$0.789988\pi$
$182$		0			0
$183$	−403560.			−0.890800
$184$	−68544.0	−	118722.i	−0.149254	−	0.258515i
$185$	−37986.0	+	65793.7i	−0.0816008	+	0.141337i
$186$	102024.	−	176711.i	0.216232	−	0.374525i
$187$	−22554.0	−	39064.7i	−0.0471650	−	0.0816921i
$188$	104320.			0.215265
$189$		0			0
$190$	228800.			0.459803
$191$	−34335.0	−	59470.0i	−0.0681010	−	0.117954i	0.829964	−	0.557816i	$-0.188361\pi$
$191$	−34335.0	−	59470.0i	−0.0681010	−	0.117954i	−0.898065	+	0.439862i	$0.855027\pi$
$192$	18432.0	−	31925.2i	0.0360844	−	0.0625000i
$193$	−413611.	+	716395.i	−0.799280	+	1.38439i	0.120806	+	0.992676i	$0.461452\pi$
$193$	−413611.	+	716395.i	−0.799280	+	1.38439i	−0.920086	+	0.391717i	$0.871881\pi$
$194$	226648.	+	392566.i	0.432362	+	0.748873i
$195$	−77688.0			−0.146308
$196$		0			0
$197$	−143382.			−0.263226			−0.131613	−	0.991301i	$-0.542016\pi$
$197$	−143382.			−0.263226			−0.131613	+	0.991301i	$0.542016\pi$
$198$	−57996.0	−	100452.i	−0.105132	−	0.182094i
$199$	−271300.	+	469905.i	−0.485643	+	0.841158i	−0.999864	−	0.0164995i	$-0.994748\pi$
$199$	−271300.	+	469905.i	−0.485643	+	0.841158i	0.514221	+	0.857658i	$0.328081\pi$
$200$	−78368.0	+	135737.i	−0.138536	+	0.239952i
$201$	−6516.00	−	11286.0i	−0.0113760	−	0.0197039i
$202$	−558856.			−0.963655
$203$		0			0
$204$	18144.0			0.0305251
$205$	27846.0	+	48230.7i	0.0462784	+	0.0801565i
$206$	284360.	−	492526.i	0.466875	−	0.808651i
$207$	86751.0	−	150257.i	0.140718	−	0.243730i
$208$	42496.0	+	73605.2i	0.0681067	+	0.117964i
$209$	−787600.			−1.24721
$210$		0			0
$211$	1.12776e6			1.74385			0.871925	−	0.489640i	$-0.162872\pi$
$211$	1.12776e6			1.74385			0.871925	+	0.489640i	$0.162872\pi$
$212$	85616.0	+	148291.i	0.130832	+	0.226608i
$213$	−19809.0	+	34310.2i	−0.0299167	+	0.0518172i
$214$	−397036.	+	687687.i	−0.592646	+	1.02649i
$215$	83044.0	+	143836.i	0.122521	+	0.212213i
$216$	46656.0			0.0680414
$217$		0			0
$218$	−530152.			−0.755543
$219$	−92250.0	−	159782.i	−0.129974	−	0.225121i
$220$	−74464.0	+	128975.i	−0.103726	+	0.179660i
$221$	−20916.0	+	36227.6i	−0.0288070	+	0.0498952i
$222$	52596.0	+	91098.9i	0.0716259	+	0.124060i
$223$	−897976.			−1.20921			−0.604606	−	0.796525i	$-0.706669\pi$
$223$	−897976.			−1.20921			−0.604606	+	0.796525i	$0.706669\pi$
$224$		0			0
$225$	−198369.			−0.261227
$226$	94052.0	+	162903.i	0.122489	+	0.212157i
$227$	−233806.	+	404964.i	−0.301156	+	0.521617i	−0.976398	−	0.215979i	$-0.930706\pi$
$227$	−233806.	+	404964.i	−0.301156	+	0.521617i	0.675242	+	0.737596i	$0.264039\pi$
$228$	158400.	−	274357.i	0.201799	−	0.349525i
$229$	−223070.	−	386369.i	−0.281095	−	0.486870i	0.690560	−	0.723275i	$-0.257364\pi$
$229$	−223070.	−	386369.i	−0.281095	−	0.486870i	−0.971655	+	0.236405i	$0.924031\pi$
$230$	−222768.			−0.277673
$231$		0			0
$232$	231040.			0.281817
$233$	−350743.	−	607505.i	−0.423252	−	0.733094i	0.573003	−	0.819553i	$-0.305778\pi$
$233$	−350743.	−	607505.i	−0.423252	−	0.733094i	−0.996255	+	0.0864588i	$0.972445\pi$
$234$	−53784.0	+	93156.6i	−0.0642116	+	0.111218i
$235$	84760.0	−	146809.i	0.100120	−	0.173413i
$236$	340192.	+	589230.i	0.397598	+	0.688660i
$237$	−587124.			−0.678983
$238$		0			0
$239$	−384198.			−0.435071			−0.217536	−	0.976052i	$-0.569802\pi$
$239$	−384198.			−0.435071			−0.217536	+	0.976052i	$0.569802\pi$
$240$	−29952.0	−	51878.4i	−0.0335659	−	0.0581378i
$241$	−476890.	+	825998.i	−0.528902	+	0.916086i	0.470529	+	0.882384i	$0.344063\pi$
$241$	−476890.	+	825998.i	−0.528902	+	0.916086i	−0.999432	+	0.0337017i	$0.989270\pi$
$242$	−65774.0	+	113924.i	−0.0721964	+	0.125048i
$243$	29524.5	+	51137.9i	0.0320750	+	0.0555556i
$244$	717440.			0.771456
$245$		0			0
$246$	77112.0			0.0812427
$247$	365200.	+	632545.i	0.380880	+	0.659704i
$248$	−181376.	+	314152.i	−0.187262	+	0.324348i
$249$	462618.	−	801278.i	0.472851	−	0.819002i
$250$	289848.	+	502031.i	0.293306	+	0.508020i
$251$	−569540.			−0.570611			−0.285305	−	0.958437i	$-0.592095\pi$
$251$	−569540.			−0.570611			−0.285305	+	0.958437i	$0.592095\pi$
$252$		0			0
$253$	766836.			0.753184
$254$	331096.	+	573475.i	0.322010	+	0.557738i
$255$	14742.0	−	25533.9i	0.0141973	−	0.0245905i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	533321.	+	923739.i	0.503681	+	0.872402i	0.999991	+	0.00425609i	$0.00135476\pi$
$257$	533321.	+	923739.i	0.503681	+	0.872402i	−0.496310	+	0.868146i	$0.665312\pi$
$258$	229968.			0.215089
$259$		0			0
$260$	138112.			0.126706
$261$	146205.	+	253234.i	0.132850	+	0.230103i
$262$	278616.	−	482577.i	0.250757	−	0.434324i
$263$	741215.	−	1.28382e6i	0.660777	−	1.14450i	−0.319635	−	0.947541i	$-0.603560\pi$
$263$	741215.	−	1.28382e6i	0.660777	−	1.14450i	0.980412	−	0.196958i	$-0.0631064\pi$
$264$	103104.	+	178581.i	0.0910470	+	0.157698i
$265$	278252.			0.243402
$266$		0			0
$267$	−1.15205e6			−0.988996
$268$	11584.0	+	20064.1i	0.00985194	+	0.0170641i
$269$	−107555.	+	186291.i	−0.0906254	+	0.156968i	−0.907774	−	0.419459i	$-0.862220\pi$
$269$	−107555.	+	186291.i	−0.0906254	+	0.156968i	0.817149	+	0.576426i	$0.195553\pi$
$270$	37908.0	−	65658.6i	0.0316462	−	0.0548128i
$271$	965518.	+	1.67233e6i	0.798614	+	1.38324i	0.920519	+	0.390699i	$0.127767\pi$
$271$	965518.	+	1.67233e6i	0.798614	+	1.38324i	−0.121904	+	0.992542i	$0.538900\pi$
$272$	−32256.0			−0.0264355
$273$		0			0
$274$	1.33137e6			1.07133
$275$	−438371.	−	759281.i	−0.349551	−	0.605439i
$276$	−154224.	+	267124.i	−0.121865	+	0.211077i
$277$	−1.01878e6	+	1.76458e6i	−0.797777	+	1.38179i	0.123284	+	0.992371i	$0.460657\pi$
$277$	−1.01878e6	+	1.76458e6i	−0.797777	+	1.38179i	−0.921061	+	0.389419i	$0.872676\pi$
$278$	−17112.0	−	29638.9i	−0.0132797	−	0.0230011i
$279$	−459108.			−0.353105
$280$		0			0
$281$	−639066.			−0.482814			−0.241407	−	0.970424i	$-0.577609\pi$
$281$	−639066.			−0.482814			−0.241407	+	0.970424i	$0.577609\pi$
$282$	−117360.	−	203273.i	−0.0878815	−	0.152215i
$283$	18872.0	−	32687.3i	0.0140072	−	0.0242612i	−0.858937	−	0.512082i	$-0.828875\pi$
$283$	18872.0	−	32687.3i	0.0140072	−	0.0242612i	0.872944	+	0.487820i	$0.162208\pi$
$284$	35216.0	−	60995.9i	0.0259086	−	0.0448750i
$285$	−257400.	−	445830.i	−0.187714	−	0.325130i
$286$	−475424.			−0.343689
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	701990.	+	1.21588e6i	0.494409	+	0.856342i
$290$	187720.	−	325141.i	0.131074	−	0.227026i
$291$	509958.	−	883273.i	0.353022	−	0.611452i
$292$	164000.	+	284056.i	0.112561	+	0.194961i
$293$	1.83921e6			1.25159			0.625795	−	0.779987i	$-0.284775\pi$
$293$	1.83921e6			1.25159			0.625795	+	0.779987i	$0.284775\pi$
$294$		0			0
$295$	1.10562e6			0.739695
$296$	−93504.0	−	161954.i	−0.0620299	−	0.107439i
$297$	−130491.	+	226017.i	−0.0858399	+	0.148679i
$298$	139108.	−	240942.i	0.0907426	−	0.157171i
$299$	−355572.	−	615869.i	−0.230012	−	0.398392i
$300$	352656.			0.226229
$301$		0			0
$302$	−2.11696e6			−1.33566
$303$	628713.	+	1.08896e6i	0.393410	+	0.681407i
$304$	−281600.	+	487746.i	−0.174763	+	0.302698i
$305$	582920.	−	1.00965e6i	0.358806	−	0.621470i
$306$	−20412.0	−	35354.6i	−0.0124618	−	0.0215845i
$307$	1.06472e6			0.644747			0.322374	−	0.946613i	$-0.395519\pi$
$307$	1.06472e6			0.644747			0.322374	+	0.946613i	$0.395519\pi$
$308$		0			0
$309$	−1.27962e6			−0.762403
$310$	294736.	+	510498.i	0.174192	+	0.301710i
$311$	−504760.	+	874270.i	−0.295927	+	0.512560i	−0.975200	−	0.221325i	$-0.928962\pi$
$311$	−504760.	+	874270.i	−0.295927	+	0.512560i	0.679273	+	0.733885i	$0.262295\pi$
$312$	95616.0	−	165612.i	0.0556089	−	0.0963174i
$313$	−724548.	−	1.25495e6i	−0.418029	−	0.724047i	0.577712	−	0.816241i	$-0.303946\pi$
$313$	−724548.	−	1.25495e6i	−0.418029	−	0.724047i	−0.995741	+	0.0921932i	$0.970612\pi$
$314$	52160.0			0.0298548
$315$		0			0
$316$	1.04378e6			0.588017
$317$	−1.36155e6	−	2.35828e6i	−0.761003	−	1.31810i	−0.942334	−	0.334674i	$-0.891374\pi$
$317$	−1.36155e6	−	2.35828e6i	−0.761003	−	1.31810i	0.181331	−	0.983422i	$-0.441959\pi$
$318$	192636.	−	333655.i	0.106824	−	0.185025i
$319$	−646190.	+	1.11923e6i	−0.355536	+	0.615806i
$320$	53248.0	+	92228.2i	0.0290689	+	0.0503488i
$321$	1.78666e6			0.967787
$322$		0			0
$323$	−277200.			−0.147838
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	−406534.	+	704138.i	−0.213495	+	0.369785i
$326$	−702480.	+	1.21673e6i	−0.366092	+	0.634090i
$327$	596421.	+	1.03303e6i	0.308449	+	0.534250i
$328$	−137088.			−0.0703582
$329$		0			0
$330$	335088.			0.169385
$331$	550202.	+	952978.i	0.276027	+	0.478093i	0.970394	−	0.241528i	$-0.0776486\pi$
$331$	550202.	+	952978.i	0.276027	+	0.478093i	−0.694366	+	0.719622i	$0.744315\pi$
$332$	−822432.	+	1.42449e6i	−0.409501	+	0.709276i
$333$	118341.	−	204973.i	0.0584823	−	0.101294i
$334$	−1.25226e6	−	2.16897e6i	−0.614224	−	1.06387i
$335$	37648.0			0.0183286
$336$		0			0
$337$	1.73512e6			0.832251			0.416125	−	0.909307i	$-0.363388\pi$
$337$	1.73512e6			0.832251			0.416125	+	0.909307i	$0.363388\pi$
$338$	−522138.	−	904370.i	−0.248596	−	0.430580i
$339$	211617.	−	366531.i	0.100012	−	0.173226i
$340$	−26208.0	+	45393.6i	−0.0122952	+	0.0212960i
$341$	−1.01457e6	−	1.75729e6i	−0.472495	−	0.818385i
$342$	−712800.			−0.329536
$343$		0			0
$344$	−408832.			−0.186273
$345$	250614.	+	434076.i	0.113359	+	0.196344i
$346$	369652.	−	640256.i	0.165998	−	0.287517i
$347$	−795723.	+	1.37823e6i	−0.354763	+	0.614467i	−0.987077	−	0.160244i	$-0.948772\pi$
$347$	−795723.	+	1.37823e6i	−0.354763	+	0.614467i	0.632314	+	0.774712i	$0.282105\pi$
$348$	−259920.	−	450195.i	−0.115051	−	0.199275i
$349$	2.33376e6			1.02563			0.512817	−	0.858498i	$-0.328602\pi$
$349$	2.33376e6			1.02563			0.512817	+	0.858498i	$0.328602\pi$
$350$		0			0
$351$	242028.			0.104857
$352$	−183296.	−	317478.i	−0.0788490	−	0.136571i
$353$	1.40541e6	−	2.43424e6i	0.600296	−	1.03974i	−0.392480	−	0.919760i	$-0.628383\pi$
$353$	1.40541e6	−	2.43424e6i	0.600296	−	1.03974i	0.992776	−	0.119982i	$-0.0382838\pi$
$354$	765432.	−	1.32577e6i	0.324637	−	0.562288i
$355$	−57226.0	−	99118.3i	−0.0241003	−	0.0417429i
$356$	2.04810e6			0.856496
$357$		0			0
$358$	1.43009e6			0.589733
$359$	−469655.	−	813466.i	−0.192328	−	0.333122i	0.753693	−	0.657226i	$-0.228270\pi$
$359$	−469655.	−	813466.i	−0.192328	−	0.333122i	−0.946021	+	0.324104i	$0.894937\pi$
$360$	−67392.0	+	116726.i	−0.0274064	+	0.0474693i
$361$	−1.18195e6	+	2.04720e6i	−0.477344	+	0.826784i
$362$	−1.39302e6	−	2.41277e6i	−0.558708	−	0.967710i
$363$	295983.			0.117896
$364$		0			0
$365$	533000.			0.209409
$366$	−807120.	−	1.39797e6i	−0.314945	−	0.545502i
$367$	1.54926e6	−	2.68339e6i	0.600424	−	1.03996i	−0.392333	−	0.919823i	$-0.628332\pi$
$367$	1.54926e6	−	2.68339e6i	0.600424	−	1.03996i	0.992757	−	0.120141i	$-0.0383348\pi$
$368$	274176.	−	474887.i	0.105538	−	0.182798i
$369$	−86751.0	−	150257.i	−0.0331672	−	0.0574472i
$370$	−303888.			−0.115401
$371$		0			0
$372$	816192.			0.305798
$373$	114133.	+	197684.i	0.0424756	+	0.0735698i	0.886482	−	0.462764i	$-0.153142\pi$
$373$	114133.	+	197684.i	0.0424756	+	0.0735698i	−0.844006	+	0.536334i	$0.819809\pi$
$374$	90216.0	−	156259.i	0.0333507	−	0.0577651i
$375$	652158.	−	1.12957e6i	0.239483	−	0.414797i
$376$	208640.	+	361375.i	0.0761076	+	0.131822i
$377$	1.19852e6			0.434302
$378$		0			0
$379$	−1.03669e6			−0.370725			−0.185362	−	0.982670i	$-0.559346\pi$
$379$	−1.03669e6			−0.370725			−0.185362	+	0.982670i	$0.559346\pi$
$380$	457600.	+	792586.i	0.162565	+	0.281571i
$381$	744966.	−	1.29032e6i	0.262920	−	0.455391i
$382$	137340.	−	237880.i	0.0481547	−	0.0834064i
$383$	−105888.	−	183403.i	−0.0368850	−	0.0638867i	0.846994	−	0.531603i	$-0.178410\pi$
$383$	−105888.	−	183403.i	−0.0368850	−	0.0638867i	−0.883879	+	0.467716i	$0.845077\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	−3.30889e6			−1.13035
$387$	−258714.	−	448106.i	−0.0878097	−	0.152091i
$388$	−906592.	+	1.57026e6i	−0.305726	+	0.529533i
$389$	−706623.	+	1.22391e6i	−0.236763	+	0.410085i	−0.959784	−	0.280741i	$-0.909420\pi$
$389$	−706623.	+	1.22391e6i	−0.236763	+	0.410085i	0.723021	+	0.690826i	$0.242753\pi$
$390$	−155376.	−	269119.i	−0.0517276	−	0.0895948i
$391$	269892.			0.0892788
$392$		0			0
$393$	−1.25377e6			−0.409484
$394$	−286764.	−	496690.i	−0.0930645	−	0.161192i
$395$	848068.	−	1.46890e6i	0.273488	−	0.473695i
$396$	231984.	−	401808.i	0.0743396	−	0.128760i
$397$	−545168.	−	944259.i	−0.173602	−	0.300687i	0.766075	−	0.642751i	$-0.222207\pi$
$397$	−545168.	−	944259.i	−0.173602	−	0.300687i	−0.939676	+	0.342064i	$0.888874\pi$
$398$	−2.17040e6			−0.686803
$399$		0			0
$400$	−626944.			−0.195920
$401$	−1.32126e6	−	2.28849e6i	−0.410325	−	0.710704i	0.584600	−	0.811322i	$-0.301252\pi$
$401$	−1.32126e6	−	2.28849e6i	−0.410325	−	0.710704i	−0.994925	+	0.100617i	$0.967918\pi$
$402$	26064.0	−	45144.2i	0.00804407	−	0.0139327i
$403$	−940888.	+	1.62967e6i	−0.288586	+	0.499846i
$404$	−1.11771e6	−	1.93593e6i	−0.340703	−	0.590116i
$405$	−170586.			−0.0516780
$406$		0			0
$407$	1.04608e6			0.313024
$408$	36288.0	+	62852.7i	0.0107923	+	0.0186928i
$409$	3.12713e6	−	5.41635e6i	0.924354	−	1.60103i	0.131757	−	0.991282i	$-0.457938\pi$
$409$	3.12713e6	−	5.41635e6i	0.924354	−	1.60103i	0.792597	−	0.609746i	$-0.208728\pi$
$410$	−111384.	+	192923.i	−0.0327238	+	0.0566792i
$411$	−1.49779e6	−	2.59425e6i	−0.437367	−	0.757542i
$412$	2.27488e6			0.660261
$413$		0			0
$414$	694008.			0.199005
$415$	1.33645e6	+	2.31480e6i	0.380919	+	0.659772i
$416$	−169984.	+	294421.i	−0.0481587	+	0.0834133i
$417$	−38502.0	+	66687.4i	−0.0108428	+	0.0187804i
$418$	−1.57520e6	−	2.72833e6i	−0.440956	−	0.763758i
$419$	973924.			0.271013			0.135506	−	0.990776i	$-0.456734\pi$
$419$	973924.			0.271013			0.135506	+	0.990776i	$0.456734\pi$
$420$		0			0
$421$	864618.			0.237749			0.118875	−	0.992909i	$-0.462071\pi$
$421$	864618.			0.237749			0.118875	+	0.992909i	$0.462071\pi$
$422$	2.25551e6	+	3.90666e6i	0.616544	+	1.06789i
$423$	−264060.	+	457365.i	−0.0717549	+	0.124283i
$424$	−342464.	+	593165.i	−0.0925125	+	0.160236i
$425$	−154287.	−	267233.i	−0.0414340	−	0.0717658i
$426$	−158472.			−0.0423086
$427$		0			0
$428$	−3.17629e6			−0.838128
$429$	534852.	+	926391.i	0.140311	+	0.243025i
$430$	−332176.	+	575346.i	−0.0866357	+	0.150058i
$431$	1.83023e6	−	3.17005e6i	0.474583	−	0.822002i	−0.524993	−	0.851106i	$-0.675932\pi$
$431$	1.83023e6	−	3.17005e6i	0.474583	−	0.822002i	0.999576	+	0.0291043i	$0.00926551\pi$
$432$	93312.0	+	161621.i	0.0240563	+	0.0416667i
$433$	4.93667e6			1.26536			0.632681	−	0.774413i	$-0.281955\pi$
$433$	4.93667e6			1.26536			0.632681	+	0.774413i	$0.281955\pi$
$434$		0			0
$435$	−844740.			−0.214042
$436$	−1.06030e6	−	1.83650e6i	−0.267125	−	0.462674i
$437$	2.35620e6	−	4.08106e6i	0.590213	−	1.02228i
$438$	369000.	−	639127.i	0.0919054	−	0.159185i
$439$	365652.	+	633328.i	0.0905538	+	0.156844i	0.907744	−	0.419524i	$-0.137803\pi$
$439$	365652.	+	633328.i	0.0905538	+	0.156844i	−0.817190	+	0.576368i	$0.804470\pi$
$440$	−595712.			−0.146691
$441$		0			0
$442$	−167328.			−0.0407392
$443$	−2.43310e6	−	4.21425e6i	−0.589048	−	1.02026i	−0.994357	−	0.106081i	$-0.966170\pi$
$443$	−2.43310e6	−	4.21425e6i	−0.589048	−	1.02026i	0.405310	−	0.914179i	$-0.367164\pi$
$444$	−210384.	+	364396.i	−0.0506472	+	0.0877235i
$445$	1.66408e6	−	2.88227e6i	0.398358	−	0.689976i
$446$	−1.79595e6	−	3.11068e6i	−0.427521	−	0.740488i
$447$	−625986.			−0.148182
$448$		0			0
$449$	5.71987e6			1.33897			0.669484	−	0.742827i	$-0.266515\pi$
$449$	5.71987e6			1.33897			0.669484	+	0.742827i	$0.266515\pi$
$450$	−396738.	−	687170.i	−0.0923576	−	0.159968i
$451$	383418.	−	664099.i	0.0887628	−	0.153742i
$452$	−376208.	+	651611.i	−0.0866128	+	0.150018i
$453$	2.38158e6	+	4.12502e6i	0.545280	+	0.944453i
$454$	−1.87045e6			−0.425898
$455$		0			0
$456$	1.26720e6			0.285386
$457$	3.41017e6	+	5.90659e6i	0.763811	+	1.32296i	0.940873	+	0.338759i	$0.110007\pi$
$457$	3.41017e6	+	5.90659e6i	0.763811	+	1.32296i	−0.177063	+	0.984200i	$0.556660\pi$
$458$	892280.	−	1.54547e6i	0.198764	−	0.344269i
$459$	−45927.0	+	79547.9i	−0.0101750	+	0.0176237i
$460$	−445536.	−	771691.i	−0.0981721	−	0.170039i
$461$	7.45934e6			1.63474			0.817369	−	0.576115i	$-0.195432\pi$
$461$	7.45934e6			1.63474			0.817369	+	0.576115i	$0.195432\pi$
$462$		0			0
$463$	−5.23848e6			−1.13567			−0.567836	−	0.823142i	$-0.692219\pi$
$463$	−5.23848e6			−1.13567			−0.567836	+	0.823142i	$0.692219\pi$
$464$	462080.	+	800346.i	0.0996374	+	0.172577i
$465$	663156.	−	1.14862e6i	0.142227	−	0.246345i
$466$	1.40297e6	−	2.43002e6i	0.299284	−	0.518376i
$467$	4.47997e6	+	7.75954e6i	0.950568	+	1.64643i	0.744199	+	0.667958i	$0.232832\pi$
$467$	4.47997e6	+	7.75954e6i	0.950568	+	1.64643i	0.206370	+	0.978474i	$0.433835\pi$
$468$	−430272.			−0.0908089
$469$		0			0
$470$	678080.			0.141591
$471$	−58680.0	−	101637.i	−0.0121882	−	0.0211105i
$472$	−1.36077e6	+	2.35692e6i	−0.281144	+	0.486956i
$473$	1.14345e6	−	1.98052e6i	0.234998	−	0.407029i
$474$	−1.17425e6	−	2.03386e6i	−0.240057	−	0.415791i
$475$	−5.38780e6			−1.09566
$476$		0			0
$477$	−866862.			−0.174443
$478$	−768396.	−	1.33090e6i	−0.153821	−	0.266426i
$479$	−876768.	+	1.51861e6i	−0.174601	+	0.302417i	−0.940023	−	0.341111i	$-0.889197\pi$
$479$	−876768.	+	1.51861e6i	−0.174601	+	0.302417i	0.765422	+	0.643528i	$0.222530\pi$
$480$	119808.	−	207514.i	0.0237346	−	0.0411096i
$481$	−485052.	−	840135.i	−0.0955929	−	0.165572i
$482$	−3.81512e6			−0.747981
$483$		0			0
$484$	−526192.			−0.102101
$485$	1.47321e6	+	2.55168e6i	0.284388	+	0.492574i
$486$	−118098.	+	204552.i	−0.0226805	+	0.0392837i
$487$	−463784.	+	803297.i	−0.0886122	+	0.153481i	−0.906925	−	0.421293i	$-0.861577\pi$
$487$	−463784.	+	803297.i	−0.0886122	+	0.153481i	0.818313	+	0.574773i	$0.194910\pi$
$488$	1.43488e6	+	2.48529e6i	0.272751	+	0.472418i
$489$	3.16116e6			0.597825
$490$		0			0
$491$	8.43733e6			1.57943			0.789716	−	0.613472i	$-0.210228\pi$
$491$	8.43733e6			1.57943			0.789716	+	0.613472i	$0.210228\pi$
$492$	154224.	+	267124.i	0.0287236	+	0.0497508i
$493$	−227430.	+	393920.i	−0.0421435	+	0.0729947i
$494$	−1.46080e6	+	2.53018e6i	−0.269323	+	0.466481i
$495$	−376974.	−	652938.i	−0.0691510	−	0.119773i
$496$	−1.45101e6			−0.264829
$497$		0			0
$498$	3.70094e6			0.668712
$499$	−666390.	−	1.15422e6i	−0.119806	−	0.207509i	0.799885	−	0.600153i	$-0.204894\pi$
$499$	−666390.	−	1.15422e6i	−0.119806	−	0.207509i	−0.919691	+	0.392644i	$0.871560\pi$
$500$	−1.15939e6	+	2.00813e6i	−0.207398	+	0.359224i
$501$	−2.81758e6	+	4.88018e6i	−0.501512	+	0.868644i
$502$	−1.13908e6	−	1.97294e6i	−0.201741	−	0.349426i
$503$	−3.64494e6			−0.642349			−0.321174	−	0.947020i	$-0.604078\pi$
$503$	−3.64494e6			−0.642349			−0.321174	+	0.947020i	$0.604078\pi$
$504$		0			0
$505$	−3.63256e6			−0.633848
$506$	1.53367e6	+	2.65640e6i	0.266291	+	0.461229i
$507$	−1.17481e6	+	2.03483e6i	−0.202978	+	0.351567i
$508$	−1.32438e6	+	2.29390e6i	−0.227696	+	0.394380i
$509$	−1.63083e6	−	2.82468e6i	−0.279007	−	0.483254i	0.692132	−	0.721771i	$-0.256672\pi$
$509$	−1.63083e6	−	2.82468e6i	−0.279007	−	0.483254i	−0.971138	+	0.238518i	$0.923338\pi$
$510$	117936.			0.0200780
$511$		0			0
$512$	−262144.			−0.0441942
$513$	801900.	+	1.38893e6i	0.134532	+	0.233017i
$514$	−2.13328e6	+	3.69496e6i	−0.356157	+	0.616881i
$515$	1.84834e6	−	3.20142e6i	0.307089	−	0.531893i
$516$	459936.	+	796633.i	0.0760454	+	0.131715i
$517$	−2.33416e6			−0.384065
$518$		0			0
$519$	−1.66343e6			−0.271074
$520$	276224.	+	478434.i	0.0447974	+	0.0775914i
$521$	−1.09370e6	+	1.89435e6i	−0.176525	+	0.305750i	−0.940688	−	0.339273i	$-0.889819\pi$
$521$	−1.09370e6	+	1.89435e6i	−0.176525	+	0.305750i	0.764163	+	0.645023i	$0.223152\pi$
$522$	−584820.	+	1.01294e6i	−0.0939390	+	0.162707i
$523$	5.19451e6	+	8.99716e6i	0.830406	+	1.43831i	0.897717	+	0.440573i	$0.145225\pi$
$523$	5.19451e6	+	8.99716e6i	0.830406	+	1.43831i	−0.0673110	+	0.997732i	$0.521442\pi$
$524$	2.22893e6			0.354624
$525$		0			0
$526$	5.92972e6			0.934480
$527$	−357084.	−	618488.i	−0.0560072	−	0.0970073i
$528$	−412416.	+	714325.i	−0.0643800	+	0.111509i
$529$	924090.	−	1.60057e6i	0.143574	−	0.248677i
$530$	556504.	+	963893.i	0.0860555	+	0.149052i
$531$	−3.44444e6			−0.530131
$532$		0			0
$533$	−711144.			−0.108428
$534$	−2.30411e6	−	3.99083e6i	−0.349663	−	0.605634i
$535$	−2.58073e6	+	4.46996e6i	−0.389815	+	0.675180i
$536$	−46336.0	+	80256.3i	−0.00696637	+	0.0120661i
$537$	−1.60885e6	−	2.78661e6i	−0.240757	−	0.417004i
$538$	−860440.			−0.128164
$539$		0			0
$540$	303264.			0.0447545
$541$	−6.38620e6	−	1.10612e7i	−0.938101	−	1.62484i	−0.769009	−	0.639238i	$-0.779250\pi$
$541$	−6.38620e6	−	1.10612e7i	−0.938101	−	1.62484i	−0.169091	−	0.985600i	$-0.554083\pi$
$542$	−3.86207e6	+	6.68930e6i	−0.564706	+	0.978099i
$543$	−3.13429e6	+	5.42874e6i	−0.456183	+	0.790132i
$544$	−64512.0	−	111738.i	−0.00934638	−	0.0161884i
$545$	−3.44599e6			−0.496961
$546$		0			0
$547$	−5.22238e6			−0.746278			−0.373139	−	0.927776i	$-0.621719\pi$
$547$	−5.22238e6			−0.746278			−0.373139	+	0.927776i	$0.621719\pi$
$548$	2.66274e6	+	4.61199e6i	0.378771	+	0.656051i
$549$	−1.81602e6	+	3.14544e6i	−0.257152	+	0.445400i
$550$	1.75348e6	−	3.03712e6i	0.247170	−	0.428110i
$551$	3.97100e6	+	6.87797e6i	0.557213	+	0.965120i
$552$	−1.23379e6			−0.172343
$553$		0			0
$554$	−8.15025e6			−1.12823
$555$	341874.	+	592143.i	0.0471122	+	0.0816008i
$556$	68448.0	−	118555.i	0.00939018	−	0.0162643i
$557$	2.87024e6	−	4.97139e6i	0.391994	−	0.678954i	−0.600718	−	0.799461i	$-0.705119\pi$
$557$	2.87024e6	−	4.97139e6i	0.391994	−	0.678954i	0.992712	+	0.120507i	$0.0384520\pi$
$558$	−918216.	−	1.59040e6i	−0.124842	−	0.216232i
$559$	−2.12082e6			−0.287061
$560$		0			0
$561$	−405972.			−0.0544614
$562$	−1.27813e6	−	2.21379e6i	−0.170701	−	0.295662i
$563$	−1.15224e6	+	1.99573e6i	−0.153204	+	0.265358i	−0.932404	−	0.361418i	$-0.882293\pi$
$563$	−1.15224e6	+	1.99573e6i	−0.153204	+	0.265358i	0.779199	+	0.626776i	$0.215626\pi$
$564$	469440.	−	813094.i	0.0621416	−	0.107632i
$565$	611338.	+	1.05887e6i	0.0805676	+	0.139547i
$566$	150976.			0.0198092
$567$		0			0
$568$	281728.			0.0366403
$569$	2.56075e6	+	4.43535e6i	0.331578	+	0.574311i	0.982822	−	0.184558i	$-0.0590855\pi$
$569$	2.56075e6	+	4.43535e6i	0.331578	+	0.574311i	−0.651243	+	0.758869i	$0.725752\pi$
$570$	1.02960e6	−	1.78332e6i	0.132734	−	0.229902i
$571$	1.19318e6	−	2.06666e6i	0.153150	−	0.265264i	−0.779234	−	0.626733i	$-0.784392\pi$
$571$	1.19318e6	−	2.06666e6i	0.153150	−	0.265264i	0.932384	+	0.361470i	$0.117725\pi$
$572$	−950848.	−	1.64692e6i	−0.121513	−	0.210466i
$573$	−618030.			−0.0786363
$574$		0			0
$575$	5.24576e6			0.661666
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	−2.62076e6	+	4.53928e6i	−0.327708	+	0.567607i	−0.982057	−	0.188586i	$-0.939610\pi$
$577$	−2.62076e6	+	4.53928e6i	−0.327708	+	0.567607i	0.654349	+	0.756193i	$0.272943\pi$
$578$	−2.80796e6	+	4.86353e6i	−0.349600	+	0.605525i
$579$	3.72250e6	+	6.44756e6i	0.461464	+	0.799280i
$580$	1.50176e6			0.185366
$581$		0			0
$582$	4.07966e6			0.499249
$583$	−1.91566e6	−	3.31802e6i	−0.233425	−	0.404303i
$584$	−656000.	+	1.13623e6i	−0.0795924	+	0.137858i
$585$	−349596.	+	605518.i	−0.0422354	+	0.0731539i
$586$	3.67842e6	+	6.37121e6i	0.442504	+	0.766440i
$587$	−9.11548e6			−1.09190			−0.545952	−	0.837816i	$-0.683832\pi$
$587$	−9.11548e6			−1.09190			−0.545952	+	0.837816i	$0.683832\pi$
$588$		0			0
$589$	−1.24696e7			−1.48103
$590$	2.21125e6	+	3.82999e6i	0.261522	+	0.452969i
$591$	−645219.	+	1.11755e6i	−0.0759869	+	0.131613i
$592$	374016.	−	647815.i	0.0438617	−	0.0759708i
$593$	1.52522e6	+	2.64175e6i	0.178112	+	0.308500i	0.941234	−	0.337755i	$-0.109668\pi$
$593$	1.52522e6	+	2.64175e6i	0.178112	+	0.308500i	−0.763122	+	0.646255i	$0.776334\pi$
$594$	−1.04393e6			−0.121396
$595$		0			0
$596$	1.11286e6			0.128329
$597$	2.44170e6	+	4.22915e6i	0.280386	+	0.485643i
$598$	1.42229e6	−	2.46348e6i	0.162643	−	0.281705i
$599$	−7.17041e6	+	1.24195e7i	−0.816539	+	1.41429i	0.0916783	+	0.995789i	$0.470777\pi$
$599$	−7.17041e6	+	1.24195e7i	−0.816539	+	1.41429i	−0.908217	+	0.418499i	$0.862556\pi$
$600$	705312.	+	1.22164e6i	0.0799840	+	0.138536i
$601$	3.12662e6			0.353092			0.176546	−	0.984292i	$-0.443508\pi$
$601$	3.12662e6			0.353092			0.176546	+	0.984292i	$0.443508\pi$
$602$		0			0
$603$	−117288.			−0.0131359
$604$	−4.23392e6	−	7.33336e6i	−0.472226	−	0.817920i
$605$	−427531.	+	740505.i	−0.0474875	+	0.0822507i
$606$	−2.51485e6	+	4.35585e6i	−0.278183	+	0.481827i
$607$	5.75492e6	+	9.96782e6i	0.633969	+	1.09807i	0.986733	+	0.162354i	$0.0519086\pi$
$607$	5.75492e6	+	9.96782e6i	0.633969	+	1.09807i	−0.352764	+	0.935712i	$0.614758\pi$
$608$	−2.25280e6			−0.247152
$609$		0			0
$610$	4.66336e6			0.507428
$611$	1.08232e6	+	1.87463e6i	0.117288	+	0.203148i
$612$	81648.0	−	141418.i	0.00881185	−	0.0152626i
$613$	6.08910e6	−	1.05466e7i	0.654488	−	1.13361i	−0.327534	−	0.944840i	$-0.606217\pi$
$613$	6.08910e6	−	1.05466e7i	0.654488	−	1.13361i	0.982022	−	0.188767i	$-0.0604492\pi$
$614$	2.12944e6	+	3.68830e6i	0.227953	+	0.394825i
$615$	501228.			0.0534377
$616$		0			0
$617$	1.77629e6			0.187845			0.0939226	−	0.995580i	$-0.470059\pi$
$617$	1.77629e6			0.187845			0.0939226	+	0.995580i	$0.470059\pi$
$618$	−2.55924e6	−	4.43273e6i	−0.269550	−	0.466875i
$619$	−2.97758e6	+	5.15732e6i	−0.312347	+	0.541001i	−0.978870	−	0.204484i	$-0.934448\pi$
$619$	−2.97758e6	+	5.15732e6i	−0.312347	+	0.541001i	0.666523	+	0.745484i	$0.267782\pi$
$620$	−1.17894e6	+	2.04199e6i	−0.123173	+	0.213341i
$621$	−780759.	−	1.35231e6i	−0.0812434	−	0.140718i
$622$	−4.03808e6			−0.418503
$623$		0			0
$624$	764928.			0.0786428
$625$	−1.94255e6	−	3.36460e6i	−0.198917	−	0.344535i
$626$	2.89819e6	−	5.01982e6i	0.295591	−	0.511979i
$627$	−3.54420e6	+	6.13873e6i	−0.360039	+	0.623606i
$628$	104320.	+	180688.i	0.0105552	+	0.0182822i
$629$	368172.			0.0371043
$630$		0			0
$631$	−1.45351e7			−1.45327			−0.726633	−	0.687026i	$-0.758916\pi$
$631$	−1.45351e7			−1.45327			−0.726633	+	0.687026i	$0.758916\pi$
$632$	2.08755e6	+	3.61575e6i	0.207895	+	0.360085i
$633$	5.07490e6	−	8.78999e6i	0.503406	−	0.871925i
$634$	5.44621e6	−	9.43312e6i	0.538110	−	0.932035i
$635$	2.15212e6	+	3.72759e6i	0.211803	+	0.366854i
$636$	1.54109e6			0.151072
$637$		0			0
$638$	−5.16952e6			−0.502804
$639$	178281.	+	308792.i	0.0172724	+	0.0299167i
$640$	−212992.	+	368913.i	−0.0205548	+	0.0356020i
$641$	5.36747e6	−	9.29673e6i	0.515970	−	0.893686i	−0.483858	−	0.875146i	$-0.660765\pi$
$641$	5.36747e6	−	9.29673e6i	0.515970	−	0.893686i	0.999828	−	0.0185398i	$-0.00590175\pi$
$642$	3.57332e6	+	6.18918e6i	0.342164	+	0.592646i
$643$	−1.62815e7			−1.55298			−0.776492	−	0.630127i	$-0.783003\pi$
$643$	−1.62815e7			−1.55298			−0.776492	+	0.630127i	$0.783003\pi$
$644$		0			0
$645$	1.49479e6			0.141476
$646$	−554400.	−	960249.i	−0.0522687	−	0.0905321i
$647$	−3.95974e6	+	6.85846e6i	−0.371882	+	0.644119i	−0.989855	−	0.142080i	$-0.954621\pi$
$647$	−3.95974e6	+	6.85846e6i	−0.371882	+	0.644119i	0.617973	+	0.786199i	$0.287954\pi$
$648$	209952.	−	363648.i	0.0196419	−	0.0340207i
$649$	−7.61180e6	−	1.31840e7i	−0.709374	−	1.22867i
$650$	−3.25227e6			−0.301928
$651$		0			0
$652$	−5.61984e6			−0.517732
$653$	−672391.	−	1.16462e6i	−0.0617076	−	0.106881i	0.833521	−	0.552488i	$-0.186321\pi$
$653$	−672391.	−	1.16462e6i	−0.0617076	−	0.106881i	−0.895229	+	0.445607i	$0.852988\pi$
$654$	−2.38568e6	+	4.13213e6i	−0.218106	+	0.377771i
$655$	1.81100e6	−	3.13675e6i	0.164936	−	0.285678i
$656$	−274176.	−	474887.i	−0.0248754	−	0.0430854i
$657$	−1.66050e6			−0.150081
$658$		0			0
$659$	2.02235e7			1.81402			0.907010	−	0.421109i	$-0.138359\pi$
$659$	2.02235e7			1.81402			0.907010	+	0.421109i	$0.138359\pi$
$660$	670176.	+	1.16078e6i	0.0598865	+	0.103726i
$661$	3.58901e6	−	6.21635e6i	0.319500	−	0.553391i	−0.660884	−	0.750488i	$-0.729818\pi$
$661$	3.58901e6	−	6.21635e6i	0.319500	−	0.553391i	0.980384	+	0.197098i	$0.0631516\pi$
$662$	−2.20081e6	+	3.81191e6i	−0.195181	+	0.338063i
$663$	188244.	+	326048.i	0.0166317	+	0.0288070i
$664$	−6.57946e6			−0.579122
$665$		0			0
$666$	946728.			0.0827065
$667$	−3.86631e6	−	6.69665e6i	−0.336498	−	0.582831i
$668$	5.00902e6	−	8.67588e6i	0.434322	−	0.752268i
$669$	−4.04089e6	+	6.99903e6i	−0.349070	+	0.604606i
$670$	75296.0	+	130416.i	0.00648015	+	0.0112239i
$671$	−1.60527e7			−1.37639
$672$		0			0
$673$	9.61217e6			0.818057			0.409029	−	0.912522i	$-0.365868\pi$
$673$	9.61217e6			0.818057			0.409029	+	0.912522i	$0.365868\pi$
$674$	3.47024e6	+	6.01063e6i	0.294245	+	0.509647i
$675$	−892660.	+	1.54613e6i	−0.0754096	+	0.130613i
$676$	2.08855e6	−	3.61748e6i	0.175784	−	0.304466i
$677$	−4.83408e6	−	8.37287e6i	−0.405361	−	0.702106i	0.589002	−	0.808131i	$-0.299521\pi$
$677$	−4.83408e6	−	8.37287e6i	−0.405361	−	0.702106i	−0.994363	+	0.106025i	$0.966187\pi$
$678$	1.69294e6			0.141438
$679$		0			0
$680$	−209664.			−0.0173881
$681$	2.10425e6	+	3.64467e6i	0.173872	+	0.301156i
$682$	4.05829e6	−	7.02916e6i	0.334104	−	0.578685i
$683$	−194927.	+	337623.i	−0.0159890	+	0.0276937i	−0.873909	−	0.486089i	$-0.838423\pi$
$683$	−194927.	+	337623.i	−0.0159890	+	0.0276937i	0.857920	+	0.513783i	$0.171756\pi$
$684$	−1.42560e6	−	2.46921e6i	−0.116508	−	0.201799i
$685$	8.65389e6			0.704669
$686$		0			0
$687$	−4.01526e6			−0.324580
$688$	−817664.	−	1.41624e6i	−0.0658573	−	0.114068i
$689$	−1.77653e6	+	3.07704e6i	−0.142569	+	0.246937i
$690$	−1.00246e6	+	1.73630e6i	−0.0801572	+	0.138836i
$691$	1.86993e6	+	3.23881e6i	0.148980	+	0.258042i	0.930851	−	0.365399i	$-0.119068\pi$
$691$	1.86993e6	+	3.23881e6i	0.148980	+	0.258042i	−0.781870	+	0.623441i	$0.785734\pi$
$692$	2.95722e6			0.234757
$693$		0			0
$694$	−6.36578e6			−0.501711
$695$	−111228.	−	192653.i	−0.00873478	−	0.0151291i
$696$	1.03968e6	−	1.80078e6i	0.0813536	−	0.140909i
$697$	134946.	−	233733.i	0.0105215	−	0.0182238i
$698$	4.66752e6	+	8.08438e6i	0.362617	+	0.628070i
$699$	−6.31337e6			−0.488730
$700$		0			0
$701$	2.49886e7			1.92064			0.960322	−	0.278893i	$-0.0899674\pi$
$701$	2.49886e7			1.92064			0.960322	+	0.278893i	$0.0899674\pi$
$702$	484056.	+	838410.i	0.0370726	+	0.0642116i
$703$	3.21420e6	−	5.56716e6i	0.245293	−	0.424859i
$704$	733184.	−	1.26991e6i	0.0557547	−	0.0965699i
$705$	−762840.	−	1.32128e6i	−0.0578044	−	0.100120i
$706$	1.12433e7			0.848947
$707$		0			0
$708$	6.12346e6			0.459107
$709$	4.91792e6	+	8.51809e6i	0.367423	+	0.636394i	0.989162	−	0.146830i	$-0.0469070\pi$
$709$	4.91792e6	+	8.51809e6i	0.367423	+	0.636394i	−0.621739	+	0.783224i	$0.713574\pi$
$710$	228904.	−	396473.i	0.0170415	−	0.0295167i
$711$	−2.64206e6	+	4.57618e6i	−0.196006	+	0.339492i
$712$	4.09619e6	+	7.09481e6i	0.302817	+	0.524495i
$713$	1.21409e7			0.894387
$714$		0			0
$715$	−3.09026e6			−0.226063
$716$	2.86018e6	+	4.95397e6i	0.208502	+	0.361136i
$717$	−1.72889e6	+	2.99453e6i	−0.125594	+	0.217536i
$718$	1.87862e6	−	3.25387e6i	0.135997	−	0.235553i
$719$	−1.06812e7	−	1.85004e7i	−0.770546	−	1.33463i	−0.937264	−	0.348621i	$-0.886650\pi$
$719$	−1.06812e7	−	1.85004e7i	−0.770546	−	1.33463i	0.166717	−	0.986005i	$-0.446683\pi$
$720$	−539136.			−0.0387585
$721$		0			0
$722$	−9.45560e6			−0.675066
$723$	4.29201e6	+	7.43398e6i	0.305362	+	0.528902i
$724$	5.57206e6	−	9.65110e6i	0.395066	−	0.684274i
$725$	−4.42044e6	+	7.65644e6i	−0.312335	+	0.540980i
$726$	591966.	+	1.02532e6i	0.0416826	+	0.0721964i
$727$	−6.53025e6			−0.458241			−0.229120	−	0.973398i	$-0.573585\pi$
$727$	−6.53025e6			−0.458241			−0.229120	+	0.973398i	$0.573585\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	1.06600e6	+	1.84637e6i	0.0740372	+	0.128236i
$731$	402444.	−	697053.i	0.0278556	−	0.0482473i
$732$	3.22848e6	−	5.59189e6i	0.222700	−	0.385728i
$733$	−8.32855e6	−	1.44255e7i	−0.572545	−	0.991677i	−0.996304	−	0.0859016i	$-0.972623\pi$
$733$	−8.32855e6	−	1.44255e7i	−0.572545	−	0.991677i	0.423759	−	0.905775i	$-0.360710\pi$
$734$	1.23940e7			0.849128
$735$		0			0
$736$	2.19341e6			0.149254
$737$	−259192.	−	448934.i	−0.0175773	−	0.0304448i
$738$	347004.	−	601029.i	0.0234527	−	0.0406213i
$739$	1.19768e7	−	2.07444e7i	0.806733	−	1.39730i	−0.108383	−	0.994109i	$-0.534567\pi$
$739$	1.19768e7	−	2.07444e7i	0.806733	−	1.39730i	0.915115	−	0.403192i	$-0.132099\pi$
$740$	−607776.	−	1.05270e6i	−0.0408004	−	0.0706683i
$741$	6.57360e6			0.439803
$742$		0			0
$743$	−7.48982e6			−0.497736			−0.248868	−	0.968537i	$-0.580059\pi$
$743$	−7.48982e6			−0.497736			−0.248868	+	0.968537i	$0.580059\pi$
$744$	1.63238e6	+	2.82737e6i	0.108116	+	0.187262i
$745$	904202.	−	1.56612e6i	0.0596863	−	0.103380i
$746$	−456532.	+	790737.i	−0.0300348	+	0.0520217i
$747$	−4.16356e6	−	7.21150e6i	−0.273001	−	0.472851i
$748$	721728.			0.0471650
$749$		0			0
$750$	5.21726e6			0.338680
$751$	2.35922e6	+	4.08630e6i	0.152640	+	0.264381i	0.932197	−	0.361950i	$-0.117889\pi$
$751$	2.35922e6	+	4.08630e6i	0.152640	+	0.264381i	−0.779557	+	0.626331i	$0.784556\pi$
$752$	−834560.	+	1.44550e6i	−0.0538162	+	0.0932124i
$753$	−2.56293e6	+	4.43912e6i	−0.164721	+	0.285305i
$754$	2.39704e6	+	4.15180e6i	0.153549	+	0.265955i
$755$	−1.37602e7			−0.878534
$756$		0			0
$757$	−2.67397e7			−1.69597			−0.847983	−	0.530024i	$-0.822183\pi$
$757$	−2.67397e7			−1.69597			−0.847983	+	0.530024i	$0.822183\pi$
$758$	−2.07338e6	−	3.59121e6i	−0.131071	−	0.227022i
$759$	3.45076e6	−	5.97690e6i	0.217426	−	0.376592i
$760$	−1.83040e6	+	3.17035e6i	−0.114951	+	0.199101i
$761$	−7.21654e6	−	1.24994e7i	−0.451718	−	0.782398i	0.546775	−	0.837279i	$-0.315855\pi$
$761$	−7.21654e6	−	1.24994e7i	−0.451718	−	0.782398i	−0.998493	+	0.0548815i	$0.982522\pi$
$762$	5.95973e6			0.371825
$763$		0			0
$764$	1.09872e6			0.0681010
$765$	−132678.	−	229805.i	−0.00819682	−	0.0141973i
$766$	423552.	−	733614.i	0.0260816	−	0.0451747i
$767$	−7.05898e6	+	1.22265e7i	−0.433265	+	0.750437i
$768$	294912.	+	510803.i	0.0180422	+	0.0312500i
$769$	8.55510e6			0.521686			0.260843	−	0.965381i	$-0.415999\pi$
$769$	8.55510e6			0.521686			0.260843	+	0.965381i	$0.415999\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(13.0000 + 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(13.0000 + 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-52.0000 + 90.0666i) q^{10} +(179.000 - 310.037i) q^{11} +(72.0000 + 124.708i) q^{12} -332.000 q^{13} +234.000 q^{15} +(-128.000 - 221.703i) q^{16} +(63.0000 - 109.119i) q^{17} +(162.000 - 280.592i) q^{18} +(-1100.00 - 1905.26i) q^{19} -416.000 q^{20} +1432.00 q^{22} +(1071.00 + 1855.03i) q^{23} +(-288.000 + 498.831i) q^{24} +(1224.50 - 2120.90i) q^{25} +(-664.000 - 1150.08i) q^{26} -729.000 q^{27} -3610.00 q^{29} +(468.000 + 810.600i) q^{30} +(2834.00 - 4908.63i) q^{31} +(512.000 - 886.810i) q^{32} +(-1611.00 - 2790.33i) q^{33} +504.000 q^{34} +1296.00 q^{36} +(1461.00 + 2530.53i) q^{37} +(4400.00 - 7621.02i) q^{38} +(-1494.00 + 2587.68i) q^{39} +(-832.000 - 1441.07i) q^{40} +2142.00 q^{41} +6388.00 q^{43} +(2864.00 + 4960.59i) q^{44} +(1053.00 - 1823.85i) q^{45} +(-4284.00 + 7420.11i) q^{46} +(-3260.00 - 5646.49i) q^{47} -2304.00 q^{48} +9796.00 q^{50} +(-567.000 - 982.073i) q^{51} +(2656.00 - 4600.33i) q^{52} +(5351.00 - 9268.20i) q^{53} +(-1458.00 - 2525.33i) q^{54} +9308.00 q^{55} -19800.0 q^{57} +(-7220.00 - 12505.4i) q^{58} +(21262.0 - 36826.9i) q^{59} +(-1872.00 + 3242.40i) q^{60} +(-22420.0 - 38832.6i) q^{61} +22672.0 q^{62} +4096.00 q^{64} +(-4316.00 - 7475.53i) q^{65} +(6444.00 - 11161.3i) q^{66} +(724.000 - 1254.00i) q^{67} +(1008.00 + 1745.91i) q^{68} +19278.0 q^{69} -4402.00 q^{71} +(2592.00 + 4489.48i) q^{72} +(10250.0 - 17753.5i) q^{73} +(-5844.00 + 10122.1i) q^{74} +(-11020.5 - 19088.1i) q^{75} +35200.0 q^{76} -11952.0 q^{78} +(-32618.0 - 56496.0i) q^{79} +(3328.00 - 5764.27i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(4284.00 + 7420.11i) q^{82} +102804. q^{83} +3276.00 q^{85} +(12776.0 + 22128.7i) q^{86} +(-16245.0 + 28137.2i) q^{87} +(-11456.0 + 19842.4i) q^{88} +(-64003.0 - 110856. i) q^{89} +8424.00 q^{90} -34272.0 q^{92} +(-25506.0 - 44177.7i) q^{93} +(13040.0 - 22585.9i) q^{94} +(28600.0 - 49536.7i) q^{95} +(-4608.00 - 7981.29i) q^{96} +113324. q^{97} -28998.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 26 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9	\( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} - 104 q^{10} + 358 q^{11} + 144 q^{12} - 664 q^{13} + 468 q^{15} - 256 q^{16} + 126 q^{17} + 324 q^{18} - 2200 q^{19} - 832 q^{20} + 2864 q^{22} + 2142 q^{23} - 576 q^{24} + 2449 q^{25} - 1328 q^{26} - 1458 q^{27} - 7220 q^{29} + 936 q^{30} + 5668 q^{31} + 1024 q^{32} - 3222 q^{33} + 1008 q^{34} + 2592 q^{36} + 2922 q^{37} + 8800 q^{38} - 2988 q^{39} - 1664 q^{40} + 4284 q^{41} + 12776 q^{43} + 5728 q^{44} + 2106 q^{45} - 8568 q^{46} - 6520 q^{47} - 4608 q^{48} + 19592 q^{50} - 1134 q^{51} + 5312 q^{52} + 10702 q^{53} - 2916 q^{54} + 18616 q^{55} - 39600 q^{57} - 14440 q^{58} + 42524 q^{59} - 3744 q^{60} - 44840 q^{61} + 45344 q^{62} + 8192 q^{64} - 8632 q^{65} + 12888 q^{66} + 1448 q^{67} + 2016 q^{68} + 38556 q^{69} - 8804 q^{71} + 5184 q^{72} + 20500 q^{73} - 11688 q^{74} - 22041 q^{75} + 70400 q^{76} - 23904 q^{78} - 65236 q^{79} + 6656 q^{80} - 6561 q^{81} + 8568 q^{82} + 205608 q^{83} + 6552 q^{85} + 25552 q^{86} - 32490 q^{87} - 22912 q^{88} - 128006 q^{89} + 16848 q^{90} - 68544 q^{92} - 51012 q^{93} + 26080 q^{94} + 57200 q^{95} - 9216 q^{96} + 226648 q^{97} - 57996 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 9 * q^3 - 16 * q^4 + 26 * q^5 + 72 * q^6 - 128 * q^8 - 81 * q^9 - 104 * q^10 + 358 * q^11 + 144 * q^12 - 664 * q^13 + 468 * q^15 - 256 * q^16 + 126 * q^17 + 324 * q^18 - 2200 * q^19 - 832 * q^20 + 2864 * q^22 + 2142 * q^23 - 576 * q^24 + 2449 * q^25 - 1328 * q^26 - 1458 * q^27 - 7220 * q^29 + 936 * q^30 + 5668 * q^31 + 1024 * q^32 - 3222 * q^33 + 1008 * q^34 + 2592 * q^36 + 2922 * q^37 + 8800 * q^38 - 2988 * q^39 - 1664 * q^40 + 4284 * q^41 + 12776 * q^43 + 5728 * q^44 + 2106 * q^45 - 8568 * q^46 - 6520 * q^47 - 4608 * q^48 + 19592 * q^50 - 1134 * q^51 + 5312 * q^52 + 10702 * q^53 - 2916 * q^54 + 18616 * q^55 - 39600 * q^57 - 14440 * q^58 + 42524 * q^59 - 3744 * q^60 - 44840 * q^61 + 45344 * q^62 + 8192 * q^64 - 8632 * q^65 + 12888 * q^66 + 1448 * q^67 + 2016 * q^68 + 38556 * q^69 - 8804 * q^71 + 5184 * q^72 + 20500 * q^73 - 11688 * q^74 - 22041 * q^75 + 70400 * q^76 - 23904 * q^78 - 65236 * q^79 + 6656 * q^80 - 6561 * q^81 + 8568 * q^82 + 205608 * q^83 + 6552 * q^85 + 25552 * q^86 - 32490 * q^87 - 22912 * q^88 - 128006 * q^89 + 16848 * q^90 - 68544 * q^92 - 51012 * q^93 + 26080 * q^94 + 57200 * q^95 - 9216 * q^96 + 226648 * q^97 - 57996 * q^99

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