LMFDB - Embedded newform 294.6.e.j.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
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			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.j.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-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} + 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−13.0000	+	22.5167i	−0.232551	+	0.402790i	−0.958558	−	0.284897i	$-0.908041\pi$
$5$	−13.0000	+	22.5167i	−0.232551	+	0.402790i	0.726007	+	0.687687i	$0.241374\pi$
$6$	−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	0.998124	−	0.0612274i	$-0.0195015\pi$
$11$	179.000	+	310.037i	0.446037	+	0.772560i	−0.552086	+	0.833787i	$0.686168\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	332.000			0.544853			0.272427	−	0.962177i	$-0.412174\pi$
$13$	332.000			0.544853			0.272427	+	0.962177i	$0.412174\pi$
$14$		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	$-0.183504\pi$
$17$	−63.0000	−	109.119i	−0.0528711	−	0.0915754i	−0.891250	+	0.453513i	$0.850171\pi$
$18$	162.000	+	280.592i	0.117851	+	0.204124i
$19$	1100.00	−	1905.26i	0.699051	−	1.21079i	−0.269745	−	0.962932i	$-0.586939\pi$
$19$	1100.00	−	1905.26i	0.699051	−	1.21079i	0.968796	−	0.247860i	$-0.0797272\pi$
$20$	416.000			0.232551
$21$		0			0
$22$	1432.00			0.630792
$23$	1071.00	−	1855.03i	0.422153	−	0.731190i	−0.573997	−	0.818858i	$-0.694608\pi$
$23$	1071.00	−	1855.03i	0.422153	−	0.731190i	0.996150	+	0.0876671i	$0.0279412\pi$
$24$	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	−0.999402	−	0.0345917i	$-0.988987\pi$
$31$	−2834.00	−	4908.63i	−0.529658	−	0.917395i	0.469743	−	0.882803i	$-0.344346\pi$
$32$	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	−0.764869	−	0.644186i	$-0.777196\pi$
$37$	1461.00	−	2530.53i	0.175447	−	0.303883i	0.940316	+	0.340303i	$0.110530\pi$
$38$	−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	$-0.531725\pi$
$41$	−2142.00			−0.199003			−0.0995015	+	0.995037i	$0.531725\pi$
$42$		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	$-0.764272\pi$
$47$	3260.00	−	5646.49i	0.215265	−	0.372850i	0.953354	+	0.301853i	$0.0976052\pi$
$48$	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	0.966684	−	0.255971i	$-0.0823952\pi$
$53$	5351.00	+	9268.20i	0.261665	+	0.453217i	−0.705020	+	0.709188i	$0.749062\pi$
$54$	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	−0.922715	−	0.385483i	$-0.874035\pi$
$59$	−21262.0	−	36826.9i	−0.795196	−	1.37732i	0.127519	−	0.991836i	$-0.459299\pi$
$60$	−1872.00	−	3242.40i	−0.0671317	−	0.116276i
$61$	22420.0	−	38832.6i	0.771456	−	1.33620i	−0.165309	−	0.986242i	$-0.552862\pi$
$61$	22420.0	−	38832.6i	0.771456	−	1.33620i	0.936765	−	0.349959i	$-0.113804\pi$
$62$	−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	0.875709	−	0.482839i	$-0.160394\pi$
$67$	724.000	+	1254.00i	0.0197039	+	0.0341281i	−0.856005	+	0.516967i	$0.827061\pi$
$68$	−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	$-0.238945\pi$
$73$	−10250.0	−	17753.5i	−0.225121	−	0.389922i	−0.956356	+	0.292205i	$0.905611\pi$
$74$	−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	0.406475	+	0.913662i	$0.366758\pi$
$79$	−32618.0	+	56496.0i	−0.588017	+	1.01847i	−0.994492	+	0.104813i	$0.966576\pi$
$80$	−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	$-0.805472\pi$
$83$	−102804.			−1.63800			−0.819002	+	0.573791i	$0.805472\pi$
$84$		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	−0.0187543	−	0.999824i	$-0.505970\pi$
$89$	64003.0	−	110856.i	0.856496	−	1.48349i	0.875250	−	0.483670i	$-0.160697\pi$
$90$	−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	$-0.709414\pi$
$97$	−113324.			−1.22290			−0.611452	+	0.791281i	$0.709414\pi$
$98$		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	0.974552	+	0.224163i	$0.0719649\pi$
$101$	69857.0	+	120996.i	0.681407	+	1.18023i	−0.293145	+	0.956068i	$0.594702\pi$
$102$	2268.00	+	3928.29i	0.0215845	+	0.0373855i
$103$	71090.0	−	123131.i	0.660261	−	1.14361i	−0.320286	−	0.947321i	$-0.603779\pi$
$103$	71090.0	−	123131.i	0.660261	−	1.14361i	0.980547	−	0.196284i	$-0.0628875\pi$
$104$	−21248.0			−0.192635
$105$		0			0
$106$	42808.0			0.370050
$107$	99259.0	−	171922.i	0.838128	−	1.45168i	−0.0533296	−	0.998577i	$-0.516983\pi$
$107$	99259.0	−	171922.i	0.838128	−	1.45168i	0.891458	−	0.453104i	$-0.149683\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	−66269.0	−	114781.i	−0.534250	−	0.925347i	−0.999199	−	0.0400103i	$-0.987261\pi$
$109$	−66269.0	−	114781.i	−0.534250	−	0.925347i	0.464950	−	0.885337i	$-0.346072\pi$
$110$	−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	$-0.717942\pi$
$131$	69654.0	−	120644.i	0.354624	−	0.614226i	0.987053	+	0.160391i	$0.0512756\pi$
$132$	−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	0.944101	+	0.329657i	$0.106933\pi$
$137$	166421.	+	288250.i	0.757542	+	1.31210i	−0.186559	+	0.982444i	$0.559733\pi$
$138$	−38556.0	+	66781.0i	−0.172343	+	0.298507i
$139$	8556.00			0.0375607			0.0187804	−	0.999824i	$-0.494022\pi$
$139$	8556.00			0.0375607			0.0187804	+	0.999824i	$0.494022\pi$
$140$		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	−0.923029	−	0.384729i	$-0.874295\pi$
$149$	−34777.0	+	60235.5i	−0.128329	+	0.222273i	0.794700	+	0.607002i	$0.207628\pi$
$150$	−44082.0	−	76352.3i	−0.159968	−	0.277073i
$151$	−264620.	−	458335.i	−0.944453	−	1.63584i	−0.756843	−	0.653597i	$-0.773259\pi$
$151$	−264620.	−	458335.i	−0.944453	−	1.63584i	−0.187610	−	0.982244i	$-0.560074\pi$
$152$	−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	$-0.173387\pi$
$157$	−6520.00	−	11293.0i	−0.0211105	−	0.0365645i	−0.876388	+	0.481606i	$0.840054\pi$
$158$	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	−0.482056	−	0.876140i	$-0.660110\pi$
$163$	175620.	−	304183.i	0.517732	−	0.896738i	0.999788	−	0.0205976i	$-0.00655687\pi$
$164$	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	$-0.164992\pi$
$167$	626128.			1.73729			0.868644	+	0.495436i	$0.164992\pi$
$168$		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	$-0.757904\pi$
$173$	92413.0	−	160064.i	0.234757	−	0.406610i	0.959202	+	0.282722i	$0.0912374\pi$
$174$	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	0.995637	−	0.0933163i	$-0.0297468\pi$
$179$	178761.	+	309623.i	0.417004	+	0.722272i	−0.578633	+	0.815588i	$0.696413\pi$
$180$	−16848.0	+	29181.6i	−0.0387585	+	0.0671317i
$181$	696508.			1.58026			0.790132	−	0.612937i	$-0.210012\pi$
$181$	696508.			1.58026			0.790132	+	0.612937i	$0.210012\pi$
$182$		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	−0.898065	−	0.439862i	$-0.855027\pi$
$191$	−34335.0	+	59470.0i	−0.0681010	+	0.117954i	0.829964	+	0.557816i	$0.188361\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	−413611.	−	716395.i	−0.799280	−	1.38439i	−0.920086	−	0.391717i	$-0.871881\pi$
$193$	−413611.	−	716395.i	−0.799280	−	1.38439i	0.120806	−	0.992676i	$-0.461452\pi$
$194$	−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	$-0.00525219\pi$
$199$	271300.	+	469905.i	0.485643	+	0.841158i	−0.514221	+	0.857658i	$0.671919\pi$
$200$	−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	$-0.293331\pi$
$223$	897976.			1.20921			0.604606	+	0.796525i	$0.293331\pi$
$224$		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	$-0.0692943\pi$
$227$	233806.	+	404964.i	0.301156	+	0.521617i	−0.675242	+	0.737596i	$0.735961\pi$
$228$	158400.	+	274357.i	0.201799	+	0.349525i
$229$	223070.	−	386369.i	0.281095	−	0.486870i	−0.690560	−	0.723275i	$-0.742636\pi$
$229$	223070.	−	386369.i	0.281095	−	0.486870i	0.971655	+	0.236405i	$0.0759692\pi$
$230$	222768.			0.277673
$231$		0			0
$232$	231040.			0.281817
$233$	−350743.	+	607505.i	−0.423252	+	0.733094i	−0.996255	−	0.0864588i	$-0.972445\pi$
$233$	−350743.	+	607505.i	−0.423252	+	0.733094i	0.573003	+	0.819553i	$0.305778\pi$
$234$	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	0.999432	+	0.0337017i	$0.0107296\pi$
$241$	476890.	+	825998.i	0.528902	+	0.916086i	−0.470529	+	0.882384i	$0.655937\pi$
$242$	−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	$-0.407905\pi$
$251$	569540.			0.570611			0.285305	+	0.958437i	$0.407905\pi$
$252$		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	0.496310	+	0.868146i	$0.334688\pi$
$257$	−533321.	+	923739.i	−0.503681	+	0.872402i	−0.999991	+	0.00425609i	$0.998645\pi$
$258$	−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	0.980412	+	0.196958i	$0.0631064\pi$
$263$	741215.	+	1.28382e6i	0.660777	+	1.14450i	−0.319635	+	0.947541i	$0.603560\pi$
$264$	−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	$-0.137780\pi$
$269$	107555.	+	186291.i	0.0906254	+	0.156968i	−0.817149	+	0.576426i	$0.804447\pi$
$270$	37908.0	+	65658.6i	0.0316462	+	0.0548128i
$271$	−965518.	+	1.67233e6i	−0.798614	+	1.38324i	0.121904	+	0.992542i	$0.461100\pi$
$271$	−965518.	+	1.67233e6i	−0.798614	+	1.38324i	−0.920519	+	0.390699i	$0.872233\pi$
$272$	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	−0.921061	−	0.389419i	$-0.872676\pi$
$277$	−1.01878e6	−	1.76458e6i	−0.797777	−	1.38179i	0.123284	−	0.992371i	$-0.460657\pi$
$278$	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	$-0.171125\pi$
$283$	−18872.0	−	32687.3i	−0.0140072	−	0.0242612i	−0.872944	+	0.487820i	$0.837792\pi$
$284$	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	$-0.715225\pi$
$293$	−1.83921e6			−1.25159			−0.625795	+	0.779987i	$0.715225\pi$
$294$		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	$-0.604481\pi$
$307$	−1.06472e6			−0.644747			−0.322374	+	0.946613i	$0.604481\pi$
$308$		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	$-0.0710383\pi$
$311$	504760.	+	874270.i	0.295927	+	0.512560i	−0.679273	+	0.733885i	$0.737705\pi$
$312$	95616.0	+	165612.i	0.0556089	+	0.0963174i
$313$	724548.	−	1.25495e6i	0.418029	−	0.724047i	−0.577712	−	0.816241i	$-0.696054\pi$
$313$	724548.	−	1.25495e6i	0.418029	−	0.724047i	0.995741	+	0.0921932i	$0.0293877\pi$
$314$	−52160.0			−0.0298548
$315$		0			0
$316$	1.04378e6			0.588017
$317$	−1.36155e6	+	2.35828e6i	−0.761003	+	1.31810i	0.181331	+	0.983422i	$0.441959\pi$
$317$	−1.36155e6	+	2.35828e6i	−0.761003	+	1.31810i	−0.942334	+	0.334674i	$0.891374\pi$
$318$	−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	−0.694366	−	0.719622i	$-0.744315\pi$
$331$	550202.	−	952978.i	0.276027	−	0.478093i	0.970394	+	0.241528i	$0.0776486\pi$
$332$	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	0.632314	−	0.774712i	$-0.282105\pi$
$347$	−795723.	−	1.37823e6i	−0.354763	−	0.614467i	−0.987077	+	0.160244i	$0.948772\pi$
$348$	259920.	−	450195.i	0.115051	−	0.199275i
$349$	−2.33376e6			−1.02563			−0.512817	−	0.858498i	$-0.671398\pi$
$349$	−2.33376e6			−1.02563			−0.512817	+	0.858498i	$0.671398\pi$
$350$		0			0
$351$	242028.			0.104857
$352$	−183296.	+	317478.i	−0.0788490	+	0.136571i
$353$	−1.40541e6	−	2.43424e6i	−0.600296	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$353$	−1.40541e6	−	2.43424e6i	−0.600296	−	1.03974i	0.392480	−	0.919760i	$-0.371617\pi$
$354$	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	−0.946021	−	0.324104i	$-0.894937\pi$
$359$	−469655.	+	813466.i	−0.192328	+	0.333122i	0.753693	+	0.657226i	$0.228270\pi$
$360$	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	−0.992757	−	0.120141i	$-0.961665\pi$
$367$	−1.54926e6	−	2.68339e6i	−0.600424	−	1.03996i	0.392333	−	0.919823i	$-0.371668\pi$
$368$	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	−0.844006	−	0.536334i	$-0.819809\pi$
$373$	114133.	−	197684.i	0.0424756	−	0.0735698i	0.886482	+	0.462764i	$0.153142\pi$
$374$	−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	$-0.821590\pi$
$383$	105888.	−	183403.i	0.0368850	−	0.0638867i	0.883879	+	0.467716i	$0.154923\pi$
$384$	−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	0.723021	−	0.690826i	$-0.242753\pi$
$389$	−706623.	−	1.22391e6i	−0.236763	−	0.410085i	−0.959784	+	0.280741i	$0.909420\pi$
$390$	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	$-0.777793\pi$
$397$	545168.	−	944259.i	0.173602	−	0.300687i	0.939676	+	0.342064i	$0.111126\pi$
$398$	2.17040e6			0.686803
$399$		0			0
$400$	−626944.			−0.195920
$401$	−1.32126e6	+	2.28849e6i	−0.410325	+	0.710704i	−0.994925	−	0.100617i	$-0.967918\pi$
$401$	−1.32126e6	+	2.28849e6i	−0.410325	+	0.710704i	0.584600	+	0.811322i	$0.301252\pi$
$402$	−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	−0.792597	−	0.609746i	$-0.791272\pi$
$409$	−3.12713e6	−	5.41635e6i	−0.924354	−	1.60103i	−0.131757	−	0.991282i	$-0.542062\pi$
$410$	−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	$-0.543266\pi$
$419$	−973924.			−0.271013			−0.135506	+	0.990776i	$0.543266\pi$
$420$		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	0.999576	−	0.0291043i	$-0.00926551\pi$
$431$	1.83023e6	+	3.17005e6i	0.474583	+	0.822002i	−0.524993	+	0.851106i	$0.675932\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	−4.93667e6			−1.26536			−0.632681	−	0.774413i	$-0.718045\pi$
$433$	−4.93667e6			−1.26536			−0.632681	+	0.774413i	$0.718045\pi$
$434$		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	$-0.862197\pi$
$439$	−365652.	+	633328.i	−0.0905538	+	0.156844i	0.817190	+	0.576368i	$0.195530\pi$
$440$	595712.			0.146691
$441$		0			0
$442$	−167328.			−0.0407392
$443$	−2.43310e6	+	4.21425e6i	−0.589048	+	1.02026i	0.405310	+	0.914179i	$0.367164\pi$
$443$	−2.43310e6	+	4.21425e6i	−0.589048	+	1.02026i	−0.994357	+	0.106081i	$0.966170\pi$
$444$	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	−0.177063	−	0.984200i	$-0.556660\pi$
$457$	3.41017e6	−	5.90659e6i	0.763811	−	1.32296i	0.940873	−	0.338759i	$-0.110007\pi$
$458$	−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	$-0.804568\pi$
$461$	−7.45934e6			−1.63474			−0.817369	+	0.576115i	$0.804568\pi$
$462$		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	−0.206370	+	0.978474i	$0.566165\pi$
$467$	−4.47997e6	+	7.75954e6i	−0.950568	+	1.64643i	−0.744199	+	0.667958i	$0.767168\pi$
$468$	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	$-0.110803\pi$
$479$	876768.	+	1.51861e6i	0.174601	+	0.302417i	−0.765422	+	0.643528i	$0.777470\pi$
$480$	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	0.818313	−	0.574773i	$-0.194910\pi$
$487$	−463784.	−	803297.i	−0.0886122	−	0.153481i	−0.906925	+	0.421293i	$0.861577\pi$
$488$	−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	−0.919691	−	0.392644i	$-0.871560\pi$
$499$	−666390.	+	1.15422e6i	−0.119806	+	0.207509i	0.799885	+	0.600153i	$0.204894\pi$
$500$	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	$-0.395922\pi$
$503$	3.64494e6			0.642349			0.321174	+	0.947020i	$0.395922\pi$
$504$		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	$-0.743328\pi$
$509$	1.63083e6	−	2.82468e6i	0.279007	−	0.483254i	0.971138	+	0.238518i	$0.0766615\pi$
$510$	−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	$-0.110181\pi$
$521$	1.09370e6	+	1.89435e6i	0.176525	+	0.305750i	−0.764163	+	0.645023i	$0.776848\pi$
$522$	−584820.	−	1.01294e6i	−0.0939390	−	0.162707i
$523$	−5.19451e6	+	8.99716e6i	−0.830406	+	1.43831i	0.0673110	+	0.997732i	$0.478558\pi$
$523$	−5.19451e6	+	8.99716e6i	−0.830406	+	1.43831i	−0.897717	+	0.440573i	$0.854775\pi$
$524$	−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	−0.169091	+	0.985600i	$0.554083\pi$
$541$	−6.38620e6	+	1.10612e7i	−0.938101	+	1.62484i	−0.769009	+	0.639238i	$0.779250\pi$
$542$	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	0.992712	−	0.120507i	$-0.0384520\pi$
$557$	2.87024e6	+	4.97139e6i	0.391994	+	0.678954i	−0.600718	+	0.799461i	$0.705119\pi$
$558$	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	$-0.117707\pi$
$563$	1.15224e6	+	1.99573e6i	0.153204	+	0.265358i	−0.779199	+	0.626776i	$0.784374\pi$
$564$	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	−0.651243	−	0.758869i	$-0.725752\pi$
$569$	2.56075e6	−	4.43535e6i	0.331578	−	0.574311i	0.982822	+	0.184558i	$0.0590855\pi$
$570$	−1.02960e6	−	1.78332e6i	−0.132734	−	0.229902i
$571$	1.19318e6	+	2.06666e6i	0.153150	+	0.265264i	0.932384	−	0.361470i	$-0.117725\pi$
$571$	1.19318e6	+	2.06666e6i	0.153150	+	0.265264i	−0.779234	+	0.626733i	$0.784392\pi$
$572$	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	$-0.0603904\pi$
$577$	2.62076e6	+	4.53928e6i	0.327708	+	0.567607i	−0.654349	+	0.756193i	$0.727057\pi$
$578$	−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	$-0.316168\pi$
$587$	9.11548e6			1.09190			0.545952	+	0.837816i	$0.316168\pi$
$588$		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	$-0.890332\pi$
$593$	−1.52522e6	+	2.64175e6i	−0.178112	+	0.308500i	0.763122	+	0.646255i	$0.223666\pi$
$594$	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	−0.908217	−	0.418499i	$-0.862556\pi$
$599$	−7.17041e6	−	1.24195e7i	−0.816539	−	1.41429i	0.0916783	−	0.995789i	$-0.470777\pi$
$600$	−705312.	+	1.22164e6i	−0.0799840	+	0.138536i
$601$	−3.12662e6			−0.353092			−0.176546	−	0.984292i	$-0.556492\pi$
$601$	−3.12662e6			−0.353092			−0.176546	+	0.984292i	$0.556492\pi$
$602$		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	0.352764	+	0.935712i	$0.385242\pi$
$607$	−5.75492e6	+	9.96782e6i	−0.633969	+	1.09807i	−0.986733	+	0.162354i	$0.948091\pi$
$608$	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	0.982022	+	0.188767i	$0.0604492\pi$
$613$	6.08910e6	+	1.05466e7i	0.654488	+	1.13361i	−0.327534	+	0.944840i	$0.606217\pi$
$614$	−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	$-0.0655516\pi$
$619$	2.97758e6	+	5.15732e6i	0.312347	+	0.541001i	−0.666523	+	0.745484i	$0.732218\pi$
$620$	−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	0.999828	+	0.0185398i	$0.00590175\pi$
$641$	5.36747e6	+	9.29673e6i	0.515970	+	0.893686i	−0.483858	+	0.875146i	$0.660765\pi$
$642$	−3.57332e6	+	6.18918e6i	−0.342164	+	0.592646i
$643$	1.62815e7			1.55298			0.776492	−	0.630127i	$-0.216997\pi$
$643$	1.62815e7			1.55298			0.776492	+	0.630127i	$0.216997\pi$
$644$		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	$-0.0453792\pi$
$647$	3.95974e6	+	6.85846e6i	0.371882	+	0.644119i	−0.617973	+	0.786199i	$0.712046\pi$
$648$	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	−0.895229	−	0.445607i	$-0.852988\pi$
$653$	−672391.	+	1.16462e6i	−0.0617076	+	0.106881i	0.833521	+	0.552488i	$0.186321\pi$
$654$	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	$-0.270182\pi$
$661$	−3.58901e6	−	6.21635e6i	−0.319500	−	0.553391i	−0.980384	+	0.197098i	$0.936848\pi$
$662$	−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	$-0.700479\pi$
$677$	4.83408e6	−	8.37287e6i	0.405361	−	0.702106i	0.994363	+	0.106025i	$0.0338125\pi$
$678$	−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	0.857920	−	0.513783i	$-0.171756\pi$
$683$	−194927.	−	337623.i	−0.0159890	−	0.0276937i	−0.873909	+	0.486089i	$0.838423\pi$
$684$	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	$-0.880932\pi$
$691$	−1.86993e6	+	3.23881e6i	−0.148980	+	0.258042i	0.781870	+	0.623441i	$0.214266\pi$
$692$	−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	−0.621739	−	0.783224i	$-0.713574\pi$
$709$	4.91792e6	−	8.51809e6i	0.367423	−	0.636394i	0.989162	+	0.146830i	$0.0469070\pi$
$710$	−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	−0.166717	−	0.986005i	$-0.553317\pi$
$719$	1.06812e7	−	1.85004e7i	0.770546	−	1.33463i	0.937264	−	0.348621i	$-0.113350\pi$
$720$	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	$-0.426415\pi$
$727$	6.53025e6			0.458241			0.229120	+	0.973398i	$0.426415\pi$
$728$		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	−0.423759	−	0.905775i	$-0.639290\pi$
$733$	8.32855e6	−	1.44255e7i	0.572545	−	0.991677i	0.996304	−	0.0859016i	$-0.0273771\pi$
$734$	−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	0.915115	+	0.403192i	$0.132099\pi$
$739$	1.19768e7	+	2.07444e7i	0.806733	+	1.39730i	−0.108383	+	0.994109i	$0.534567\pi$
$740$	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	−0.779557	−	0.626331i	$-0.784556\pi$
$751$	2.35922e6	−	4.08630e6i	0.152640	−	0.264381i	0.932197	+	0.361950i	$0.117889\pi$
$752$	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	$-0.684145\pi$
$761$	7.21654e6	−	1.24994e7i	0.451718	−	0.782398i	0.998493	+	0.0548815i	$0.0174781\pi$
$762$	−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	$-0.584001\pi$
$769$	−8.55510e6			−0.521686			−0.260843	+	0.965381i	$0.584001\pi$
$770$		0			0
$771$	9.59978e6			0.581601
$772$	−6.61778e6	+	1.14623e7i	−0.399640	+	0.692197i
$773$	−9.61358e6	−	1.66512e7i	−0.578677	−	1.00230i	−0.995631	−	0.0933705i	$-0.970236\pi$
$773$	−9.61358e6	−	1.66512e7i	−0.578677	−	1.00230i	0.416954	−	0.908927i	$-0.363097\pi$
$774$	1.03486e6	+	1.79242e6i	0.0620908	+	0.107544i
$775$	6.94047e6	−	1.20212e7i	0.415082	−	0.718944i
$776$	7.25274e6			0.432362
$777$		0			0
$778$	−5.65298e6			−0.334833
$779$	−2.35620e6	+	4.08106e6i	−0.139113	+	0.240951i
$780$	−621504.	−	1.07648e6i	−0.0365769	−	0.0633531i
$781$	−787958.	−	1.36478e6i	−0.0462248	−	0.0800638i
$782$	−539784.	+	934933.i	−0.0315648	+	0.0546718i
$783$	−2.63169e6			−0.153402
$784$		0			0
$785$	339040.			0.0196371
$786$	−2.50754e6	+	4.34319e6i	−0.144775	+	0.250757i
$787$	1.26658e7	+	2.19378e7i	0.728947	+	1.26257i	0.957329	+	0.289002i	$0.0933233\pi$
$787$	1.26658e7	+	2.19378e7i	0.728947	+	1.26257i	−0.228382	+	0.973572i	$0.573343\pi$
$788$	1.14706e6	+	1.98676e6i	0.0658065	+	0.113980i
$789$	6.67094e6	−	1.15544e7i	0.381500	−	0.660777i
$790$	−6.78454e6			−0.386770
$791$		0			0
$792$	1.85587e6			0.105132
$793$	7.44344e6	−	1.28924e7i	0.420330	−	0.728033i
$794$	−2.18067e6	−	3.77703e6i	−0.122755	−	0.212618i
$795$	1.25213e6	+	2.16876e6i	0.0702640	+	0.121701i
$796$	4.34080e6	−	7.51849e6i	0.242821	−	0.420579i
$797$	−3.13162e7			−1.74632			−0.873158	−	0.487437i	$-0.837932\pi$
$797$	−3.13162e7			−1.74632			−0.873158	+	0.487437i	$0.837932\pi$
$798$		0			0
$799$	−821520.			−0.0455251
$800$	−1.25389e6	+	2.17180e6i	−0.0692682	+	0.119976i
$801$	5.18424e6	+	8.97937e6i	0.285499	+	0.494498i
$802$	5.28505e6	+	9.15398e6i	0.290144	+	0.502544i
$803$	3.66950e6	−	6.35576e6i	0.200825	−	0.347839i
$804$	−208512.			−0.0113760
$805$		0			0
$806$	−7.52710e6			−0.408122
$807$	967995.	−	1.67662e6i	0.0523226	−	0.0906254i
$808$	−4.47085e6	−	7.74374e6i	−0.240914	−	0.417275i
$809$	−242445.	−	419927.i	−0.0130239	−	0.0225581i	0.859440	−	0.511237i	$-0.170812\pi$
$809$	−242445.	−	419927.i	−0.0130239	−	0.0225581i	−0.872464	+	0.488679i	$0.837479\pi$
$810$	341172.	−	590927.i	0.0182709	−	0.0316462i
$811$	−5.32623e6			−0.284359			−0.142180	−	0.989841i	$-0.545411\pi$
$811$	−5.32623e6			−0.284359			−0.142180	+	0.989841i	$0.545411\pi$
$812$		0			0
$813$	1.73793e7			0.922161
$814$	2.09215e6	−	3.62371e6i	0.110671	−	0.191687i
$815$	4.56612e6	+	7.90875e6i	0.240798	+	0.417075i
$816$	−145152.	−	251411.i	−0.00763128	−	0.0132178i
$817$	7.02680e6	−	1.21708e7i	0.368301	−	0.637915i
$818$	−2.50171e7			−1.30723
$819$		0			0
$820$	−891072.			−0.0462784
$821$	−1.60889e7	+	2.78667e7i	−0.833043	+	1.44287i	0.0625713	+	0.998040i	$0.480070\pi$
$821$	−1.60889e7	+	2.78667e7i	−0.833043	+	1.44287i	−0.895614	+	0.444832i	$0.853263\pi$
$822$	−5.99116e6	−	1.03770e7i	−0.309265	−	0.535663i
$823$	4.03704e6	+	6.99235e6i	0.207761	+	0.359852i	0.951009	−	0.309164i	$-0.100049\pi$
$823$	4.03704e6	+	6.99235e6i	0.207761	+	0.359852i	−0.743248	+	0.669016i	$0.766716\pi$
$824$	−4.54976e6	+	7.88042e6i	−0.233437	+	0.404325i
$825$	7.89068e6			0.403626
$826$		0			0
$827$	−8.04922e6			−0.409251			−0.204626	−	0.978840i	$-0.565598\pi$
$827$	−8.04922e6			−0.409251			−0.204626	+	0.978840i	$0.565598\pi$
$828$	1.38802e6	−	2.40411e6i	0.0703588	−	0.121865i
$829$	6.79447e6	+	1.17684e7i	0.343375	+	0.594744i	0.985057	−	0.172227i	$-0.0550963\pi$
$829$	6.79447e6	+	1.17684e7i	0.343375	+	0.594744i	−0.641682	+	0.766971i	$0.721763\pi$
$830$	−5.34581e6	−	9.25921e6i	−0.269351	−	0.466529i
$831$	−9.16903e6	+	1.58812e7i	−0.460597	+	0.797777i
$832$	1.35987e6			0.0681067
$833$		0			0
$834$	−308016.			−0.0153341
$835$	−8.13966e6	+	1.40983e7i	−0.404008	+	0.699763i
$836$	−6.30080e6	−	1.09133e7i	−0.311803	−	0.540058i
$837$	−2.06599e6	−	3.57839e6i	−0.101933	−	0.176553i
$838$	−1.94785e6	+	3.37377e6i	−0.0958175	+	0.165961i
$839$	−3.67721e6			−0.180349			−0.0901744	−	0.995926i	$-0.528742\pi$
$839$	−3.67721e6			−0.180349			−0.0901744	+	0.995926i	$0.528742\pi$
$840$		0			0
$841$	−7.47905e6			−0.364633
$842$	1.72924e6	−	2.99512e6i	0.0840570	−	0.145591i
$843$	2.87580e6	+	4.98103e6i	0.139376	+	0.241407i
$844$	−9.02205e6	−	1.56266e7i	−0.435962	−	0.755109i
$845$	3.39390e6	−	5.87840e6i	0.163515	−	0.283216i
$846$	2.11248e6			0.101477
$847$		0			0
$848$	−2.73971e6			−0.130832
$849$	−169848.	+	294185.i	−0.00808707	+	0.0140072i
$850$	−617148.	−	1.06893e6i	−0.0292983	−	0.0507461i
$851$	−3.12946e6	−	5.42039e6i	−0.148131	−	0.256570i
$852$	316944.	−	548963.i	0.0149583	−	0.0259086i
$853$	−3.25379e7			−1.53115			−0.765573	−	0.643349i	$-0.777544\pi$
$853$	−3.25379e7			−1.53115			−0.765573	+	0.643349i	$0.777544\pi$
$854$		0			0
$855$	−4.63320e6			−0.216753
$856$	−6.35258e6	+	1.10030e7i	−0.296323	+	0.513247i
$857$	−5.63617e6	−	9.76213e6i	−0.262139	−	0.454038i	0.704671	−	0.709534i	$-0.251095\pi$
$857$	−5.63617e6	−	9.76213e6i	−0.262139	−	0.454038i	−0.966810	+	0.255496i	$0.917761\pi$
$858$	−2.13941e6	−	3.70556e6i	−0.0992146	−	0.171845i
$859$	3.84847e6	−	6.66575e6i	0.177953	−	0.308224i	−0.763226	−	0.646131i	$-0.776386\pi$
$859$	3.84847e6	−	6.66575e6i	0.177953	−	0.308224i	0.941179	+	0.337908i	$0.109719\pi$
$860$	2.65741e6			0.122521
$861$		0			0
$862$	1.46418e7			0.671162
$863$	2.29392e6	−	3.97319e6i	0.104846	−	0.181599i	−0.808829	−	0.588044i	$-0.799898\pi$
$863$	2.29392e6	−	3.97319e6i	0.104846	−	0.181599i	0.913675	+	0.406445i	$0.133232\pi$
$864$	373248.	+	646484.i	0.0170103	+	0.0294628i
$865$	2.40274e6	+	4.16166e6i	0.109186	+	0.189115i
$866$	−9.87334e6	+	1.71011e7i	−0.447373	+	0.774872i
$867$	−1.26358e7			−0.570895
$868$		0			0
$869$	−2.33545e7			−1.04911
$870$	−1.68948e6	+	2.92627e6i	−0.0756754	+	0.131074i
$871$	240368.	+	416330.i	0.0107357	+	0.0185948i
$872$	4.24122e6	+	7.34600e6i	0.188886	+	0.327160i
$873$	4.58962e6	−	7.94946e6i	0.203817	−	0.353022i
$874$	−1.88496e7			−0.834687
$875$		0			0
$876$	2.95200e6			0.129974
$877$	5.73328e6	−	9.93033e6i	0.251712	−	0.435978i	−0.712285	−	0.701890i	$-0.752340\pi$
$877$	5.73328e6	−	9.93033e6i	0.251712	−	0.435978i	0.963997	+	0.265912i	$0.0856731\pi$
$878$	1.46261e6	+	2.53331e6i	0.0640312	+	0.110905i
$879$	8.27644e6	+	1.43352e7i	0.361303	+	0.625795i
$880$	1.19142e6	−	2.06361e6i	0.0518632	−	0.0898298i
$881$	−3.02550e7			−1.31328			−0.656640	−	0.754204i	$-0.728023\pi$
$881$	−3.02550e7			−1.31328			−0.656640	+	0.754204i	$0.728023\pi$
$882$		0			0
$883$	9.83052e6			0.424302			0.212151	−	0.977237i	$-0.431953\pi$
$883$	9.83052e6			0.424302			0.212151	+	0.977237i	$0.431953\pi$
$884$	−334656.	+	579641.i	−0.0144035	+	0.0249476i
$885$	−4.97531e6	−	8.61749e6i	−0.213531	−	0.369847i
$886$	9.73240e6	+	1.68570e7i	0.416520	+	0.721433i
$887$	−1.16136e7	+	2.01154e7i	−0.495631	+	0.858459i	−0.999987	−	0.00503723i	$-0.998397\pi$
$887$	−1.16136e7	+	2.01154e7i	−0.495631	+	0.858459i	0.504356	+	0.863496i	$0.331730\pi$
$888$	1.68307e6			0.0716259
$889$		0			0
$890$	1.33126e7			0.563363
$891$	1.17442e6	−	2.03415e6i	0.0495597	−	0.0858399i
$892$	−7.18381e6	−	1.24427e7i	−0.302303	−	0.523604i
$893$	−7.17200e6	−	1.24223e7i	−0.300962	−	0.521281i
$894$	1.25197e6	−	2.16848e6i	0.0523903	−	0.0907426i
$895$	−9.29557e6			−0.387899
$896$		0			0
$897$	−6.40030e6			−0.265594
$898$	1.14397e7	−	1.98142e7i	0.473396	−	0.819947i
$899$	1.02307e7	+	1.77202e7i	0.422190	+	0.731254i
$900$	1.58695e6	+	2.74868e6i	0.0653067	+	0.113114i
$901$	674226.	−	1.16779e6i	0.0276690	−	0.0479241i
$902$	−3.06734e6			−0.125530
$903$		0			0
$904$	−3.00966e6			−0.122489
$905$	−9.05460e6	+	1.56830e7i	−0.367492	+	0.636515i
$906$	9.52632e6	+	1.65001e7i	0.385571	+	0.667829i
$907$	−1.52750e7	−	2.64571e7i	−0.616544	−	1.06788i	−0.990112	−	0.140282i	$-0.955199\pi$
$907$	−1.52750e7	−	2.64571e7i	−0.616544	−	1.06788i	0.373568	−	0.927603i	$-0.378134\pi$
$908$	3.74090e6	−	6.47942e6i	0.150578	−	0.260808i
$909$	−1.13168e7			−0.454271
$910$		0			0
$911$	2.21502e7			0.884265			0.442133	−	0.896950i	$-0.354222\pi$
$911$	2.21502e7			0.884265			0.442133	+	0.896950i	$0.354222\pi$
$912$	2.53440e6	−	4.38971e6i	0.100899	−	0.174763i
$913$	−1.84019e7	−	3.18731e7i	−0.730611	−	1.26546i
$914$	−1.36407e7	−	2.36264e7i	−0.540096	−	0.935473i
$915$	5.24628e6	−	9.08682e6i	0.207157	−	0.358806i
$916$	−7.13824e6			−0.281095
$917$		0			0
$918$	−367416.			−0.0143897
$919$	6.33613e6	−	1.09745e7i	0.247477	−	0.428643i	−0.715348	−	0.698769i	$-0.753732\pi$
$919$	6.33613e6	−	1.09745e7i	0.247477	−	0.428643i	0.962825	+	0.270125i	$0.0870651\pi$
$920$	−1.78214e6	−	3.08676e6i	−0.0694182	−	0.120236i
$921$	4.79124e6	+	8.29867e6i	0.186122	+	0.322374i
$922$	−1.49187e7	+	2.58399e7i	−0.577967	+	1.00107i
$923$	−1.46146e6			−0.0564656
$924$		0			0
$925$	7.15598e6			0.274989
$926$	−1.04770e7	+	1.81466e7i	−0.401521	+	0.695455i
$927$	5.75829e6	+	9.97365e6i	0.220087	+	0.381202i
$928$	−1.84832e6	−	3.20138e6i	−0.0704543	−	0.122030i
$929$	2.01420e7	−	3.48870e7i	0.765709	−	1.32625i	−0.174162	−	0.984717i	$-0.555722\pi$
$929$	2.01420e7	−	3.48870e7i	0.765709	−	1.32625i	0.939871	−	0.341530i	$-0.110945\pi$
$930$	−5.30525e6			−0.201140
$931$		0			0
$932$	1.12238e7			0.423252
$933$	4.54284e6	−	7.86843e6i	0.170853	−	0.295927i
$934$	1.79199e7	+	3.10382e7i	0.672153	+	1.16420i
$935$	586404.	+	1.01568e6i	0.0219365	+	0.0379952i
$936$	860544.	−	1.49051e6i	0.0321058	−	0.0556089i
$937$	1.34104e7			0.498992			0.249496	−	0.968376i	$-0.419735\pi$
$937$	1.34104e7			0.498992			0.249496	+	0.968376i	$0.419735\pi$
$938$		0			0
$939$	−1.30419e7			−0.482698
$940$	1.35616e6	−	2.34894e6i	0.0500601	−	0.0867066i
$941$	1.36606e7	+	2.36609e7i	0.502918	+	0.871079i	0.999994	+	0.00337223i	$0.00107342\pi$
$941$	1.36606e7	+	2.36609e7i	0.502918	+	0.871079i	−0.497077	+	0.867707i	$0.665593\pi$
$942$	234720.	+	406547.i	0.00861832	+	0.0149274i
$943$	−2.29408e6	+	3.97347e6i	−0.0840098	+	0.145509i
$944$	1.08861e7			0.397598
$945$		0			0
$946$	9.14762e6			0.332338
$947$	−4.35872e6	+	7.54953e6i	−0.157937	+	0.273555i	−0.934125	−	0.356947i	$-0.883818\pi$
$947$	−4.35872e6	+	7.54953e6i	−0.157937	+	0.273555i	0.776187	+	0.630502i	$0.217151\pi$
$948$	−4.69699e6	−	8.13543e6i	−0.169746	−	0.294008i
$949$	−3.40300e6	−	5.89417e6i	−0.122658	−	0.212450i
$950$	1.07756e7	−	1.86639e7i	0.387376	−	0.670955i
$951$	2.45080e7			0.878731
$952$		0			0
$953$	−1.62984e7			−0.581315			−0.290658	−	0.956827i	$-0.593874\pi$
$953$	−1.62984e7			−0.581315			−0.290658	+	0.956827i	$0.593874\pi$
$954$	−1.73372e6	+	3.00290e6i	−0.0616750	+	0.106824i
$955$	−892710.	−	1.54622e6i	−0.0316739	−	0.0548609i
$956$	3.07358e6	+	5.32360e6i	0.108768	+	0.188391i
$957$	−5.81571e6	+	1.00731e7i	−0.205269	+	0.355536i
$958$	7.01414e6			0.246923
$959$		0			0
$960$	958464.			0.0335659
$961$	−1.74854e6	+	3.02855e6i	−0.0610754	+	0.105786i
$962$	−1.94021e6	−	3.36054e6i	−0.0675944	−	0.117077i
$963$	8.03998e6	+	1.39257e7i	0.279376	+	0.483894i
$964$	7.63024e6	−	1.32160e7i	0.264451	−	0.458043i
$965$	2.15078e7			0.743493
$966$		0			0
$967$	−5.49067e6			−0.188825			−0.0944124	−	0.995533i	$-0.530097\pi$
$967$	−5.49067e6			−0.188825			−0.0944124	+	0.995533i	$0.530097\pi$
$968$	−1.05238e6	+	1.82278e6i	−0.0360982	+	0.0625240i
$969$	1.24740e6	+	2.16056e6i	0.0426772	+	0.0739191i
$970$	−5.89285e6	−	1.02067e7i	−0.201093	−	0.348302i
$971$	−2.25838e7	+	3.91162e7i	−0.768685	+	1.33140i	0.169591	+	0.985514i	$0.445755\pi$
$971$	−2.25838e7	+	3.91162e7i	−0.768685	+	1.33140i	−0.938276	+	0.345887i	$0.887578\pi$
$972$	944784.			0.0320750
$973$		0			0
$974$	−3.71027e6			−0.125317
$975$	3.65881e6	−	6.33724e6i	0.123262	−	0.213495i
$976$	5.73952e6	+	9.94114e6i	0.192864	+	0.334050i
$977$	1.19005e7	+	2.06123e7i	0.398868	+	0.690860i	0.993587	−	0.113074i	$-0.0360697\pi$
$977$	1.19005e7	+	2.06123e7i	0.398868	+	0.690860i	−0.594718	+	0.803934i	$0.702736\pi$
$978$	−6.32232e6	+	1.09506e7i	−0.211363	+	0.366092i
$979$	4.58261e7			1.52812
$980$		0			0
$981$	1.07356e7			0.356166
$982$	1.68747e7	−	2.92278e7i	0.558414	−	0.967201i
$983$	−4.68239e6	−	8.11014e6i	−0.154555	−	0.267698i	0.778342	−	0.627841i	$-0.216061\pi$
$983$	−4.68239e6	−	8.11014e6i	−0.154555	−	0.267698i	−0.932897	+	0.360143i	$0.882728\pi$
$984$	−616896.	−	1.06850e6i	−0.0203107	−	0.0351791i
$985$	1.86397e6	−	3.22848e6i	0.0612135	−	0.106025i
$986$	1.81944e6			0.0595999
$987$		0			0
$988$	−1.16864e7			−0.380880
$989$	6.84155e6	−	1.18499e7i	0.222415	−	0.385234i
$990$	−1.50790e6	−	2.61175e6i	−0.0488971	−	0.0846923i
$991$	2.16958e7	+	3.75782e7i	0.701764	+	1.21549i	0.967847	+	0.251541i	$0.0809374\pi$
$991$	2.16958e7	+	3.75782e7i	0.701764	+	1.21549i	−0.266082	+	0.963950i	$0.585729\pi$
$992$	2.90202e6	−	5.02644e6i	0.0936312	−	0.162174i
$993$	−9.90364e6			−0.318729
$994$		0			0
$995$	−1.41076e7			−0.451747
$996$	7.40189e6	−	1.28204e7i	0.236425	−	0.409501i
$997$	−2.17647e6	−	3.76975e6i	−0.0693449	−	0.120109i	0.829268	−	0.558851i	$-0.188758\pi$
$997$	−2.17647e6	−	3.76975e6i	−0.0693449	−	0.120109i	−0.898613	+	0.438742i	$0.855424\pi$
$998$	2.66556e6	+	4.61689e6i	0.0847153	+	0.146731i
$999$	1.06507e6	−	1.84475e6i	0.0337648	−	0.0584823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.e.j.79.1		2
7.2	even	3		294.6.a.g.1.1	yes	1
7.3	odd	6		294.6.e.q.67.1		2
7.4	even	3	inner	294.6.e.j.67.1		2
7.5	odd	6		294.6.a.a.1.1	✓	1
7.6	odd	2		294.6.e.q.79.1		2
21.2	odd	6		882.6.a.p.1.1		1
21.5	even	6		882.6.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.6.a.a.1.1	✓	1	7.5	odd	6
294.6.a.g.1.1	yes	1	7.2	even	3
294.6.e.j.67.1		2	7.4	even	3	inner
294.6.e.j.79.1		2	1.1	even	1	trivial
294.6.e.q.67.1		2	7.3	odd	6
294.6.e.q.79.1		2	7.6	odd	2
882.6.a.p.1.1		1	21.2	odd	6
882.6.a.t.1.1		1	21.5	even	6

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 9 q^{3} - 16 q^{4} - 26 q^{5} - 72 q^{6} - 128 q^{8} - 81 q^{9} + 104 q^{10} + 358 q^{11} - 144 q^{12} + 664 q^{13} + 468 q^{15} - 256 q^{16} - 126 q^{17} + 324 q^{18} + 2200 q^{19} + 832 q^{20}+ \cdots - 57996 q^{99}+O(q^{100}) \) 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

Introduction

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