LMFDB - Embedded newform 147.6.e.j.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.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:	$23.5764215125$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.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)

$f(q)$	$=$	$q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-39.0000 + 67.5500i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-39.0000 + 67.5500i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(234.000 + 405.300i) q^{10} +(-222.000 - 384.515i) q^{11} +(18.0000 - 31.1769i) q^{12} -442.000 q^{13} -702.000 q^{15} +(568.000 - 983.805i) q^{16} +(63.0000 + 109.119i) q^{17} +(243.000 + 420.888i) q^{18} +(-1342.00 + 2324.41i) q^{19} +312.000 q^{20} -2664.00 q^{22} +(-2100.00 + 3637.31i) q^{23} +(756.000 + 1309.43i) q^{24} +(-1479.50 - 2562.57i) q^{25} +(-1326.00 + 2296.70i) q^{26} -729.000 q^{27} -5442.00 q^{29} +(-2106.00 + 3647.70i) q^{30} +(-40.0000 - 69.2820i) q^{31} +(-720.000 - 1247.08i) q^{32} +(1998.00 - 3460.64i) q^{33} +756.000 q^{34} +324.000 q^{36} +(2717.00 - 4705.98i) q^{37} +(8052.00 + 13946.5i) q^{38} +(-1989.00 - 3445.05i) q^{39} +(-6552.00 + 11348.4i) q^{40} +7962.00 q^{41} -11524.0 q^{43} +(-888.000 + 1538.06i) q^{44} +(-3159.00 - 5471.55i) q^{45} +(12600.0 + 21823.8i) q^{46} +(6960.00 - 12055.1i) q^{47} +10224.0 q^{48} -17754.0 q^{50} +(-567.000 + 982.073i) q^{51} +(884.000 + 1531.13i) q^{52} +(4797.00 + 8308.65i) q^{53} +(-2187.00 + 3788.00i) q^{54} +34632.0 q^{55} -24156.0 q^{57} +(-16326.0 + 28277.5i) q^{58} +(-13746.0 - 23808.8i) q^{59} +(1404.00 + 2431.80i) q^{60} +(-24739.0 + 42849.2i) q^{61} -480.000 q^{62} +27712.0 q^{64} +(17238.0 - 29857.1i) q^{65} +(-11988.0 - 20763.8i) q^{66} +(29678.0 + 51403.8i) q^{67} +(252.000 - 436.477i) q^{68} -37800.0 q^{69} +32040.0 q^{71} +(-6804.00 + 11784.9i) q^{72} +(30923.0 + 53560.2i) q^{73} +(-16302.0 - 28235.9i) q^{74} +(13315.5 - 23063.1i) q^{75} +10736.0 q^{76} -23868.0 q^{78} +(32888.0 - 56963.7i) q^{79} +(44304.0 + 76736.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(23886.0 - 41371.8i) q^{82} +40188.0 q^{83} -9828.00 q^{85} +(-34572.0 + 59880.5i) q^{86} +(-24489.0 - 42416.2i) q^{87} +(-37296.0 - 64598.6i) q^{88} +(3987.00 - 6905.69i) q^{89} -37908.0 q^{90} +16800.0 q^{92} +(360.000 - 623.538i) q^{93} +(-41760.0 - 72330.4i) q^{94} +(-104676. - 181304. i) q^{95} +(6480.00 - 11223.7i) q^{96} -143662. q^{97} +35964.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} - 78 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9}+O(q^{10}) $ 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 - 78 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9	\( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} - 78 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9} + 468 q^{10} - 444 q^{11} + 36 q^{12} - 884 q^{13} - 1404 q^{15} + 1136 q^{16} + 126 q^{17} + 486 q^{18} - 2684 q^{19} + 624 q^{20} - 5328 q^{22} - 4200 q^{23} + 1512 q^{24} - 2959 q^{25} - 2652 q^{26} - 1458 q^{27} - 10884 q^{29} - 4212 q^{30} - 80 q^{31} - 1440 q^{32} + 3996 q^{33} + 1512 q^{34} + 648 q^{36} + 5434 q^{37} + 16104 q^{38} - 3978 q^{39} - 13104 q^{40} + 15924 q^{41} - 23048 q^{43} - 1776 q^{44} - 6318 q^{45} + 25200 q^{46} + 13920 q^{47} + 20448 q^{48} - 35508 q^{50} - 1134 q^{51} + 1768 q^{52} + 9594 q^{53} - 4374 q^{54} + 69264 q^{55} - 48312 q^{57} - 32652 q^{58} - 27492 q^{59} + 2808 q^{60} - 49478 q^{61} - 960 q^{62} + 55424 q^{64} + 34476 q^{65} - 23976 q^{66} + 59356 q^{67} + 504 q^{68} - 75600 q^{69} + 64080 q^{71} - 13608 q^{72} + 61846 q^{73} - 32604 q^{74} + 26631 q^{75} + 21472 q^{76} - 47736 q^{78} + 65776 q^{79} + 88608 q^{80} - 6561 q^{81} + 47772 q^{82} + 80376 q^{83} - 19656 q^{85} - 69144 q^{86} - 48978 q^{87} - 74592 q^{88} + 7974 q^{89} - 75816 q^{90} + 33600 q^{92} + 720 q^{93} - 83520 q^{94} - 209352 q^{95} + 12960 q^{96} - 287324 q^{97} + 71928 q^{99}+O(q^{100}) \) 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 - 78 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9 + 468 * q^10 - 444 * q^11 + 36 * q^12 - 884 * q^13 - 1404 * q^15 + 1136 * q^16 + 126 * q^17 + 486 * q^18 - 2684 * q^19 + 624 * q^20 - 5328 * q^22 - 4200 * q^23 + 1512 * q^24 - 2959 * q^25 - 2652 * q^26 - 1458 * q^27 - 10884 * q^29 - 4212 * q^30 - 80 * q^31 - 1440 * q^32 + 3996 * q^33 + 1512 * q^34 + 648 * q^36 + 5434 * q^37 + 16104 * q^38 - 3978 * q^39 - 13104 * q^40 + 15924 * q^41 - 23048 * q^43 - 1776 * q^44 - 6318 * q^45 + 25200 * q^46 + 13920 * q^47 + 20448 * q^48 - 35508 * q^50 - 1134 * q^51 + 1768 * q^52 + 9594 * q^53 - 4374 * q^54 + 69264 * q^55 - 48312 * q^57 - 32652 * q^58 - 27492 * q^59 + 2808 * q^60 - 49478 * q^61 - 960 * q^62 + 55424 * q^64 + 34476 * q^65 - 23976 * q^66 + 59356 * q^67 + 504 * q^68 - 75600 * q^69 + 64080 * q^71 - 13608 * q^72 + 61846 * q^73 - 32604 * q^74 + 26631 * q^75 + 21472 * q^76 - 47736 * q^78 + 65776 * q^79 + 88608 * q^80 - 6561 * q^81 + 47772 * q^82 + 80376 * q^83 - 19656 * q^85 - 69144 * q^86 - 48978 * q^87 - 74592 * q^88 + 7974 * q^89 - 75816 * q^90 + 33600 * q^92 + 720 * q^93 - 83520 * q^94 - 209352 * q^95 + 12960 * q^96 - 287324 * q^97 + 71928 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.00000	−	5.19615i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	3.00000	−	5.19615i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−2.00000	−	3.46410i	−0.0625000	−	0.108253i
$5$	−39.0000	+	67.5500i	−0.697653	+	1.20837i	0.271625	+	0.962403i	$0.412439\pi$
$5$	−39.0000	+	67.5500i	−0.697653	+	1.20837i	−0.969278	+	0.245968i	$0.920894\pi$
$6$	54.0000			0.612372
$7$		0			0
$7$		0			0
$8$	168.000			0.928078
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	234.000	+	405.300i	0.739973	+	1.28167i
$11$	−222.000	−	384.515i	−0.553186	−	0.958146i	−0.998042	−	0.0625444i	$-0.980079\pi$
$11$	−222.000	−	384.515i	−0.553186	−	0.958146i	0.444856	−	0.895602i	$-0.353255\pi$
$12$	18.0000	−	31.1769i	0.0360844	−	0.0625000i
$13$	−442.000			−0.725377			−0.362689	−	0.931910i	$-0.618141\pi$
$13$	−442.000			−0.725377			−0.362689	+	0.931910i	$0.618141\pi$
$14$		0			0
$15$	−702.000			−0.805581
$16$	568.000	−	983.805i	0.554688	−	0.960747i
$17$	63.0000	+	109.119i	0.0528711	+	0.0915754i	0.891250	−	0.453513i	$-0.149829\pi$
$17$	63.0000	+	109.119i	0.0528711	+	0.0915754i	−0.838379	+	0.545088i	$0.816496\pi$
$18$	243.000	+	420.888i	0.176777	+	0.306186i
$19$	−1342.00	+	2324.41i	−0.852842	+	1.47717i	0.0257909	+	0.999667i	$0.491790\pi$
$19$	−1342.00	+	2324.41i	−0.852842	+	1.47717i	−0.878633	+	0.477498i	$0.841544\pi$
$20$	312.000			0.174413
$21$		0			0
$22$	−2664.00			−1.17348
$23$	−2100.00	+	3637.31i	−0.827751	+	1.43371i	0.0720476	+	0.997401i	$0.477047\pi$
$23$	−2100.00	+	3637.31i	−0.827751	+	1.43371i	−0.899799	+	0.436306i	$0.856287\pi$
$24$	756.000	+	1309.43i	0.267913	+	0.464039i
$25$	−1479.50	−	2562.57i	−0.473440	−	0.820022i
$26$	−1326.00	+	2296.70i	−0.384689	+	0.666301i
$27$	−729.000			−0.192450
$28$		0			0
$29$	−5442.00			−1.20161			−0.600805	−	0.799396i	$-0.705153\pi$
$29$	−5442.00			−1.20161			−0.600805	+	0.799396i	$0.705153\pi$
$30$	−2106.00	+	3647.70i	−0.427224	+	0.739973i
$31$	−40.0000	−	69.2820i	−0.00747577	−	0.0129484i	0.862263	−	0.506460i	$-0.169046\pi$
$31$	−40.0000	−	69.2820i	−0.00747577	−	0.0129484i	−0.869739	+	0.493512i	$0.835713\pi$
$32$	−720.000	−	1247.08i	−0.124296	−	0.215287i
$33$	1998.00	−	3460.64i	0.319382	−	0.553186i
$34$	756.000			0.112157
$35$		0			0
$36$	324.000			0.0416667
$37$	2717.00	−	4705.98i	0.326276	−	0.565127i	−0.655494	−	0.755201i	$-0.727539\pi$
$37$	2717.00	−	4705.98i	0.326276	−	0.565127i	0.981770	+	0.190074i	$0.0608727\pi$
$38$	8052.00	+	13946.5i	0.904575	+	1.56677i
$39$	−1989.00	−	3445.05i	−0.209398	−	0.362689i
$40$	−6552.00	+	11348.4i	−0.647476	+	1.12146i
$41$	7962.00			0.739712			0.369856	−	0.929089i	$-0.379407\pi$
$41$	7962.00			0.739712			0.369856	+	0.929089i	$0.379407\pi$
$42$		0			0
$43$	−11524.0			−0.950456			−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−11524.0			−0.950456			−0.475228	+	0.879863i	$0.657634\pi$
$44$	−888.000	+	1538.06i	−0.0691483	+	0.119768i
$45$	−3159.00	−	5471.55i	−0.232551	−	0.402790i
$46$	12600.0	+	21823.8i	0.877962	+	1.52068i
$47$	6960.00	−	12055.1i	0.459584	−	0.796022i	−0.539355	−	0.842078i	$-0.681332\pi$
$47$	6960.00	−	12055.1i	0.459584	−	0.796022i	0.998939	+	0.0460561i	$0.0146653\pi$
$48$	10224.0			0.640498
$49$		0			0
$50$	−17754.0			−1.00432
$51$	−567.000	+	982.073i	−0.0305251	+	0.0528711i
$52$	884.000	+	1531.13i	0.0453361	+	0.0785244i
$53$	4797.00	+	8308.65i	0.234574	+	0.406294i	0.959149	−	0.282902i	$-0.0912971\pi$
$53$	4797.00	+	8308.65i	0.234574	+	0.406294i	−0.724575	+	0.689196i	$0.757964\pi$
$54$	−2187.00	+	3788.00i	−0.102062	+	0.176777i
$55$	34632.0			1.54373
$56$		0			0
$57$	−24156.0			−0.984777
$58$	−16326.0	+	28277.5i	−0.637250	+	1.10375i
$59$	−13746.0	−	23808.8i	−0.514098	−	0.890445i	−0.999866	−	0.0163567i	$-0.994793\pi$
$59$	−13746.0	−	23808.8i	−0.514098	−	0.890445i	0.485768	−	0.874088i	$-0.338540\pi$
$60$	1404.00	+	2431.80i	0.0503488	+	0.0872067i
$61$	−24739.0	+	42849.2i	−0.851251	+	1.47441i	0.0288292	+	0.999584i	$0.490822\pi$
$61$	−24739.0	+	42849.2i	−0.851251	+	1.47441i	−0.880080	+	0.474825i	$0.842511\pi$
$62$	−480.000			−0.0158585
$63$		0			0
$64$	27712.0			0.845703
$65$	17238.0	−	29857.1i	0.506062	−	0.876525i
$66$	−11988.0	−	20763.8i	−0.338756	−	0.586742i
$67$	29678.0	+	51403.8i	0.807695	+	1.39897i	0.914456	+	0.404685i	$0.132619\pi$
$67$	29678.0	+	51403.8i	0.807695	+	1.39897i	−0.106761	+	0.994285i	$0.534048\pi$
$68$	252.000	−	436.477i	0.00660889	−	0.0114469i
$69$	−37800.0			−0.955805
$70$		0			0
$71$	32040.0			0.754304			0.377152	−	0.926151i	$-0.376903\pi$
$71$	32040.0			0.754304			0.377152	+	0.926151i	$0.376903\pi$
$72$	−6804.00	+	11784.9i	−0.154680	+	0.267913i
$73$	30923.0	+	53560.2i	0.679164	+	1.17635i	0.975233	+	0.221180i	$0.0709907\pi$
$73$	30923.0	+	53560.2i	0.679164	+	1.17635i	−0.296069	+	0.955166i	$0.595676\pi$
$74$	−16302.0	−	28235.9i	−0.346068	−	0.599408i
$75$	13315.5	−	23063.1i	0.273341	−	0.473440i
$76$	10736.0			0.213210
$77$		0			0
$78$	−23868.0			−0.444201
$79$	32888.0	−	56963.7i	0.592884	−	1.02691i	−0.400958	−	0.916097i	$-0.631323\pi$
$79$	32888.0	−	56963.7i	0.592884	−	1.02691i	0.993842	−	0.110809i	$-0.0353441\pi$
$80$	44304.0	+	76736.8i	0.773959	+	1.34054i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	23886.0	−	41371.8i	0.392291	−	0.679469i
$83$	40188.0			0.640326			0.320163	−	0.947362i	$-0.396262\pi$
$83$	40188.0			0.640326			0.320163	+	0.947362i	$0.396262\pi$
$84$		0			0
$85$	−9828.00			−0.147543
$86$	−34572.0	+	59880.5i	−0.504056	+	0.873050i
$87$	−24489.0	−	42416.2i	−0.346875	−	0.600805i
$88$	−37296.0	−	64598.6i	−0.513400	−	0.889234i
$89$	3987.00	−	6905.69i	0.0533545	−	0.0924127i	−0.838115	−	0.545494i	$-0.816342\pi$
$89$	3987.00	−	6905.69i	0.0533545	−	0.0924127i	0.891469	+	0.453081i	$0.149675\pi$
$90$	−37908.0			−0.493315
$91$		0			0
$92$	16800.0			0.206938
$93$	360.000	−	623.538i	0.00431614	−	0.00747577i
$94$	−41760.0	−	72330.4i	−0.487462	−	0.844309i
$95$	−104676.	−	181304.i	−1.18998	−	2.06110i
$96$	6480.00	−	11223.7i	0.0717624	−	0.124296i
$97$	−143662.			−1.55029			−0.775144	−	0.631784i	$-0.782323\pi$
$97$	−143662.			−1.55029			−0.775144	+	0.631784i	$0.782323\pi$
$98$		0			0
$99$	35964.0			0.368791
$100$	−5918.00	+	10250.3i	−0.0591800	+	0.102503i
$101$	1353.00	+	2343.46i	0.0131976	+	0.0228589i	0.872549	−	0.488527i	$-0.162466\pi$
$101$	1353.00	+	2343.46i	0.0131976	+	0.0228589i	−0.859351	+	0.511386i	$0.829132\pi$
$102$	3402.00	+	5892.44i	0.0323768	+	0.0560783i
$103$	−65884.0	+	114114.i	−0.611909	+	1.05986i	0.379009	+	0.925393i	$0.376265\pi$
$103$	−65884.0	+	114114.i	−0.611909	+	1.05986i	−0.990918	+	0.134465i	$0.957068\pi$
$104$	−74256.0			−0.673206
$105$		0			0
$106$	57564.0			0.497607
$107$	64458.0	−	111645.i	0.544274	−	0.942710i	−0.454378	−	0.890809i	$-0.650139\pi$
$107$	64458.0	−	111645.i	0.544274	−	0.942710i	0.998652	−	0.0519010i	$-0.0165280\pi$
$108$	1458.00	+	2525.33i	0.0120281	+	0.0208333i
$109$	50489.0	+	87449.5i	0.407034	+	0.705003i	0.994556	−	0.104205i	$-0.0332298\pi$
$109$	50489.0	+	87449.5i	0.407034	+	0.705003i	−0.587522	+	0.809208i	$0.699896\pi$
$110$	103896.	−	179953.i	0.818686	−	1.41800i
$111$	48906.0			0.376751
$112$		0			0
$113$	220146.			1.62186			0.810932	−	0.585140i	$-0.198960\pi$
$113$	220146.			1.62186			0.810932	+	0.585140i	$0.198960\pi$
$114$	−72468.0	+	125518.i	−0.522257	+	0.904575i
$115$	−163800.	−	283710.i	−1.15497	−	2.00046i
$116$	10884.0	+	18851.6i	0.0751006	+	0.130078i
$117$	17901.0	−	31005.4i	0.120896	−	0.209398i
$118$	−164952.			−1.09057
$119$		0			0
$120$	−117936.			−0.747641
$121$	−18042.5	+	31250.5i	−0.112030	+	0.194041i
$122$	148434.	+	257095.i	0.902888	+	1.56385i
$123$	35829.0	+	62057.6i	0.213536	+	0.369856i
$124$	−160.000	+	277.128i	−0.000934471	+	0.00161855i
$125$	−12948.0			−0.0741187
$126$		0			0
$127$	−74320.0			−0.408880			−0.204440	−	0.978879i	$-0.565537\pi$
$127$	−74320.0			−0.408880			−0.204440	+	0.978879i	$0.565537\pi$
$128$	106176.	−	183902.i	0.572798	−	0.992115i
$129$	−51858.0	−	89820.7i	−0.274373	−	0.475228i
$130$	−103428.	−	179143.i	−0.536760	−	0.929695i
$131$	77658.0	−	134508.i	0.395374	−	0.684808i	−0.597775	−	0.801664i	$-0.703948\pi$
$131$	77658.0	−	134508.i	0.395374	−	0.684808i	0.993149	+	0.116856i	$0.0372817\pi$
$132$	−15984.0			−0.0798455
$133$		0			0
$134$	356136.			1.71338
$135$	28431.0	−	49243.9i	0.134263	−	0.232551i
$136$	10584.0	+	18332.0i	0.0490685	+	0.0849891i
$137$	132123.	+	228844.i	0.601419	+	1.04169i	0.992606	+	0.121377i	$0.0387310\pi$
$137$	132123.	+	228844.i	0.601419	+	1.04169i	−0.391188	+	0.920311i	$0.627936\pi$
$138$	−113400.	+	196415.i	−0.506892	+	0.877962i
$139$	224612.			0.986043			0.493022	−	0.870017i	$-0.335892\pi$
$139$	224612.			0.986043			0.493022	+	0.870017i	$0.335892\pi$
$140$		0			0
$141$	125280.			0.530682
$142$	96120.0	−	166485.i	0.400030	−	0.692873i
$143$	98124.0	+	169956.i	0.401269	+	0.695018i
$144$	46008.0	+	79688.2i	0.184896	+	0.320249i
$145$	212238.	−	367607.i	0.838307	−	1.45199i
$146$	371076.			1.44072
$147$		0			0
$148$	−21736.0			−0.0815690
$149$	41037.0	−	71078.2i	0.151429	−	0.262283i	−0.780324	−	0.625376i	$-0.784946\pi$
$149$	41037.0	−	71078.2i	0.151429	−	0.262283i	0.931753	+	0.363092i	$0.118279\pi$
$150$	−79893.0	−	138379.i	−0.289922	−	0.502159i
$151$	143516.	+	248577.i	0.512222	+	0.887194i	0.999900	+	0.0141703i	$0.00451071\pi$
$151$	143516.	+	248577.i	0.512222	+	0.887194i	−0.487678	+	0.873024i	$0.662156\pi$
$152$	−225456.	+	390501.i	−0.791503	+	1.37092i
$153$	−10206.0			−0.0352474
$154$		0			0
$155$	6240.00			0.0208620
$156$	−7956.00	+	13780.2i	−0.0261748	+	0.0453361i
$157$	−64939.0	−	112478.i	−0.210260	−	0.364181i	0.741536	−	0.670913i	$-0.234098\pi$
$157$	−64939.0	−	112478.i	−0.210260	−	0.364181i	−0.951796	+	0.306732i	$0.900764\pi$
$158$	−197328.	−	341782.i	−0.628848	−	1.08920i
$159$	−43173.0	+	74777.8i	−0.135431	+	0.234574i
$160$	112320.			0.346862
$161$		0			0
$162$	−39366.0			−0.117851
$163$	−277642.	+	480890.i	−0.818495	+	1.41768i	0.0882955	+	0.996094i	$0.471858\pi$
$163$	−277642.	+	480890.i	−0.818495	+	1.41768i	−0.906791	+	0.421581i	$0.861475\pi$
$164$	−15924.0	−	27581.2i	−0.0462320	−	0.0800761i
$165$	155844.	+	269930.i	0.445636	+	0.771864i
$166$	120564.	−	208823.i	0.339584	−	0.588177i
$167$	43512.0			0.120731			0.0603654	−	0.998176i	$-0.480773\pi$
$167$	43512.0			0.120731			0.0603654	+	0.998176i	$0.480773\pi$
$168$		0			0
$169$	−175929.			−0.473828
$170$	−29484.0	+	51067.8i	−0.0782464	+	0.135527i
$171$	−108702.	−	188277.i	−0.284281	−	0.492388i
$172$	23048.0	+	39920.3i	0.0594035	+	0.102890i
$173$	9165.00	−	15874.2i	0.0232818	−	0.0403253i	−0.854150	−	0.520027i	$-0.825922\pi$
$173$	9165.00	−	15874.2i	0.0232818	−	0.0403253i	0.877432	+	0.479702i	$0.159255\pi$
$174$	−293868.			−0.735833
$175$		0			0
$176$	−504384.			−1.22738
$177$	123714.	−	214279.i	0.296815	−	0.514098i
$178$	−23922.0	−	41434.1i	−0.0565910	−	0.0980185i
$179$	76662.0	+	132782.i	0.178833	+	0.309748i	0.941481	−	0.337066i	$-0.109434\pi$
$179$	76662.0	+	132782.i	0.178833	+	0.309748i	−0.762648	+	0.646814i	$0.776101\pi$
$180$	−12636.0	+	21886.2i	−0.0290689	+	0.0503488i
$181$	−382066.			−0.866846			−0.433423	−	0.901191i	$-0.642694\pi$
$181$	−382066.			−0.866846			−0.433423	+	0.901191i	$0.642694\pi$
$182$		0			0
$183$	−445302.			−0.982940
$184$	−352800.	+	611068.i	−0.768217	+	1.33059i
$185$	211926.	+	367067.i	0.455255	+	0.788525i
$186$	−2160.00	−	3741.23i	−0.00457795	−	0.00792925i
$187$	27972.0	−	48448.9i	0.0584951	−	0.101316i
$188$	−55680.0			−0.114896
$189$		0			0
$190$	−1.25611e6			−2.52432
$191$	136704.	−	236778.i	0.271143	−	0.469633i	−0.698012	−	0.716086i	$-0.745932\pi$
$191$	136704.	−	236778.i	0.271143	−	0.469633i	0.969155	+	0.246453i	$0.0792652\pi$
$192$	124704.	+	215994.i	0.244133	+	0.422852i
$193$	−76801.0	−	133023.i	−0.148414	−	0.257060i	0.782228	−	0.622993i	$-0.214083\pi$
$193$	−76801.0	−	133023.i	−0.148414	−	0.257060i	−0.930641	+	0.365933i	$0.880750\pi$
$194$	−430986.	+	746490.i	−0.822165	+	1.42403i
$195$	310284.			0.584350
$196$		0			0
$197$	154422.			0.283494			0.141747	−	0.989903i	$-0.454728\pi$
$197$	154422.			0.283494			0.141747	+	0.989903i	$0.454728\pi$
$198$	107892.	−	186874.i	0.195581	−	0.338756i
$199$	183428.	+	317707.i	0.328347	+	0.568714i	0.982184	−	0.187922i	$-0.0601752\pi$
$199$	183428.	+	317707.i	0.328347	+	0.568714i	−0.653837	+	0.756635i	$0.726842\pi$
$200$	−248556.	−	430512.i	−0.439389	−	0.761044i
$201$	−267102.	+	462634.i	−0.466323	+	0.807695i
$202$	16236.0			0.0279963
$203$		0			0
$204$	4536.00			0.00763128
$205$	−310518.	+	537833.i	−0.516062	+	0.893846i
$206$	395304.	+	684687.i	0.649028	+	1.12415i
$207$	−170100.	−	294622.i	−0.275917	−	0.477902i
$208$	−251056.	+	434842.i	−0.402358	+	0.696904i
$209$	1.19170e6			1.88712
$210$		0			0
$211$	520244.			0.804453			0.402227	−	0.915540i	$-0.368236\pi$
$211$	520244.			0.804453			0.402227	+	0.915540i	$0.368236\pi$
$212$	19188.0	−	33234.6i	0.0293218	−	0.0507868i
$213$	144180.	+	249727.i	0.217749	+	0.377152i
$214$	−386748.	−	669867.i	−0.577289	−	0.999895i
$215$	449436.	−	778446.i	0.663089	−	1.14850i
$216$	−122472.			−0.178609
$217$		0			0
$218$	605868.			0.863449
$219$	−278307.	+	482042.i	−0.392115	+	0.679164i
$220$	−69264.0	−	119969.i	−0.0964830	−	0.167113i
$221$	−27846.0	−	48230.7i	−0.0383515	−	0.0664267i
$222$	146718.	−	254123.i	0.199803	−	0.346068i
$223$	304736.			0.410357			0.205178	−	0.978725i	$-0.434223\pi$
$223$	304736.			0.410357			0.205178	+	0.978725i	$0.434223\pi$
$224$		0			0
$225$	239679.			0.315627
$226$	660438.	−	1.14391e6i	0.860124	−	1.48978i
$227$	−144294.	−	249925.i	−0.185859	−	0.321917i	0.758007	−	0.652247i	$-0.226173\pi$
$227$	−144294.	−	249925.i	−0.185859	−	0.321917i	−0.943866	+	0.330330i	$0.892840\pi$
$228$	48312.0	+	83678.8i	0.0615486	+	0.106605i
$229$	−386095.	+	668736.i	−0.486525	+	0.842687i	−0.999880	−	0.0154899i	$-0.995069\pi$
$229$	−386095.	+	668736.i	−0.486525	+	0.842687i	0.513355	+	0.858177i	$0.328403\pi$
$230$	−1.96560e6			−2.45005
$231$		0			0
$232$	−914256.			−1.11519
$233$	−126117.	+	218441.i	−0.152189	+	0.263599i	−0.932032	−	0.362376i	$-0.881966\pi$
$233$	−126117.	+	218441.i	−0.152189	+	0.263599i	0.779843	+	0.625975i	$0.215299\pi$
$234$	−107406.	−	186033.i	−0.128230	−	0.222100i
$235$	542880.	+	940296.i	0.641260	+	1.11069i
$236$	−54984.0	+	95235.1i	−0.0642623	+	0.111306i
$237$	591984.			0.684603
$238$		0			0
$239$	−1.45114e6			−1.64329			−0.821643	−	0.570002i	$-0.806942\pi$
$239$	−1.45114e6			−1.64329			−0.821643	+	0.570002i	$0.806942\pi$
$240$	−398736.	+	690631.i	−0.446845	+	0.773959i
$241$	73199.0	+	126784.i	0.0811825	+	0.140612i	0.903758	−	0.428043i	$-0.140797\pi$
$241$	73199.0	+	126784.i	0.0811825	+	0.140612i	−0.822576	+	0.568656i	$0.807464\pi$
$242$	108255.	+	187503.i	0.118825	+	0.205812i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	197912.			0.212813
$245$		0			0
$246$	429948.			0.452979
$247$	593164.	−	1.02739e6i	0.618632	−	1.07150i
$248$	−6720.00	−	11639.4i	−0.00693809	−	0.0120171i
$249$	180846.	+	313234.i	0.184846	+	0.320163i
$250$	−38844.0	+	67279.8i	−0.0393074	+	0.0680824i
$251$	607860.			0.609003			0.304501	−	0.952512i	$-0.401510\pi$
$251$	607860.			0.609003			0.304501	+	0.952512i	$0.401510\pi$
$252$		0			0
$253$	1.86480e6			1.83160
$254$	−222960.	+	386178.i	−0.216842	+	0.375581i
$255$	−44226.0	−	76601.7i	−0.0425919	−	0.0737714i
$256$	−193664.	−	335436.i	−0.184692	−	0.319897i
$257$	−47793.0	+	82779.9i	−0.0451369	+	0.0781794i	−0.887711	−	0.460401i	$-0.847706\pi$
$257$	−47793.0	+	82779.9i	−0.0451369	+	0.0781794i	0.842574	+	0.538580i	$0.181039\pi$
$258$	−622296.			−0.582033
$259$		0			0
$260$	−137904.			−0.126515
$261$	220401.	−	381746.i	0.200268	−	0.346875i
$262$	−465948.	−	807046.i	−0.419357	−	0.726348i
$263$	1.10017e6	+	1.90555e6i	0.980779	+	1.69876i	0.659370	+	0.751819i	$0.270823\pi$
$263$	1.10017e6	+	1.90555e6i	0.980779	+	1.69876i	0.321410	+	0.946940i	$0.395843\pi$
$264$	335664.	−	581387.i	0.296411	−	0.513400i
$265$	−748332.			−0.654605
$266$		0			0
$267$	71766.0			0.0616085
$268$	118712.	−	205615.i	0.100962	−	0.174871i
$269$	−885123.	−	1.53308e6i	−0.745801	−	1.29177i	−0.949820	−	0.312798i	$-0.898734\pi$
$269$	−885123.	−	1.53308e6i	−0.745801	−	1.29177i	0.204019	−	0.978967i	$-0.434600\pi$
$270$	−170586.	−	295464.i	−0.142408	−	0.246658i
$271$	111752.	−	193560.i	0.0924341	−	0.160101i	−0.816101	−	0.577910i	$-0.803869\pi$
$271$	111752.	−	193560.i	0.0924341	−	0.160101i	0.908535	+	0.417809i	$0.137202\pi$
$272$	143136.			0.117308
$273$		0			0
$274$	1.58548e6			1.27580
$275$	−656898.	+	1.13778e6i	−0.523801	+	0.907250i
$276$	75600.0	+	130943.i	0.0597378	+	0.103469i
$277$	171389.	+	296854.i	0.134210	+	0.232458i	0.925295	−	0.379248i	$-0.123817\pi$
$277$	171389.	+	296854.i	0.134210	+	0.232458i	−0.791086	+	0.611705i	$0.790484\pi$
$278$	673836.	−	1.16712e6i	0.522928	−	0.905739i
$279$	6480.00			0.00498384
$280$		0			0
$281$	480378.			0.362925			0.181463	−	0.983398i	$-0.441917\pi$
$281$	480378.			0.362925			0.181463	+	0.983398i	$0.441917\pi$
$282$	375840.	−	650974.i	0.281436	−	0.487462i
$283$	14990.0	+	25963.4i	0.0111259	+	0.0192706i	0.871535	−	0.490334i	$-0.163125\pi$
$283$	14990.0	+	25963.4i	0.0111259	+	0.0192706i	−0.860409	+	0.509604i	$0.829792\pi$
$284$	−64080.0	−	110990.i	−0.0471440	−	0.0816558i
$285$	942084.	−	1.63174e6i	0.687033	−	1.18998i
$286$	1.17749e6			0.851219
$287$		0			0
$288$	116640.			0.0828641
$289$	701990.	−	1.21588e6i	0.494409	−	0.856342i
$290$	−1.27343e6	−	2.20564e6i	−0.889159	−	1.54007i
$291$	−646479.	−	1.11973e6i	−0.447530	−	0.775144i
$292$	123692.	−	214241.i	0.0848955	−	0.147043i
$293$	−198066.			−0.134785			−0.0673924	−	0.997727i	$-0.521468\pi$
$293$	−198066.			−0.134785			−0.0673924	+	0.997727i	$0.521468\pi$
$294$		0			0
$295$	2.14438e6			1.43465
$296$	456456.	−	790605.i	0.302810	−	0.524482i
$297$	161838.	+	280312.i	0.106461	+	0.184395i
$298$	−246222.	−	426469.i	−0.160615	−	0.278193i
$299$	928200.	−	1.60769e6i	0.600432	−	1.03998i
$300$	−106524.			−0.0683352
$301$		0			0
$302$	1.72219e6			1.08659
$303$	−12177.0	+	21091.2i	−0.00761963	+	0.0131976i
$304$	1.52451e6	+	2.64053e6i	0.946121	+	1.63873i
$305$	−1.92964e6	−	3.34224e6i	−1.18776	−	2.05725i
$306$	−30618.0	+	53031.9i	−0.0186928	+	0.0323768i
$307$	−1.04564e6			−0.633191			−0.316595	−	0.948561i	$-0.602540\pi$
$307$	−1.04564e6			−0.633191			−0.316595	+	0.948561i	$0.602540\pi$
$308$		0			0
$309$	−1.18591e6			−0.706572
$310$	18720.0	−	32424.0i	0.0110637	−	0.0191629i
$311$	−918588.	−	1.59104e6i	−0.538542	−	0.932783i	−0.998983	−	0.0450920i	$-0.985642\pi$
$311$	−918588.	−	1.59104e6i	−0.538542	−	0.932783i	0.460441	−	0.887691i	$-0.347691\pi$
$312$	−334152.	−	578768.i	−0.194338	−	0.336603i
$313$	182747.	−	316527.i	0.105436	−	0.182621i	−0.808480	−	0.588523i	$-0.799709\pi$
$313$	182747.	−	316527.i	0.105436	−	0.182621i	0.913916	+	0.405903i	$0.133043\pi$
$314$	−779268.			−0.446029
$315$		0			0
$316$	−263104.			−0.148221
$317$	14169.0	−	24541.4i	0.00791938	−	0.0137168i	−0.862039	−	0.506843i	$-0.830812\pi$
$317$	14169.0	−	24541.4i	0.00791938	−	0.0137168i	0.869958	+	0.493126i	$0.164146\pi$
$318$	259038.	+	448667.i	0.143647	+	0.248803i
$319$	1.20812e6	+	2.09253e6i	0.664714	+	1.15132i
$320$	−1.08077e6	+	1.87195e6i	−0.590007	+	1.02192i
$321$	1.16024e6			0.628473
$322$		0			0
$323$	−338184.			−0.180363
$324$	−13122.0	+	22728.0i	−0.00694444	+	0.0120281i
$325$	653939.	+	1.13266e6i	0.343423	+	0.594825i
$326$	1.66585e6	+	2.88534e6i	0.868145	+	1.50367i
$327$	−454401.	+	787046.i	−0.235001	+	0.407034i
$328$	1.33762e6			0.686510
$329$		0			0
$330$	1.87013e6			0.945337
$331$	−966958.	+	1.67482e6i	−0.485107	+	0.840230i	−0.999854	−	0.0171123i	$-0.994553\pi$
$331$	−966958.	+	1.67482e6i	−0.485107	+	0.840230i	0.514746	+	0.857342i	$0.327886\pi$
$332$	−80376.0	−	139215.i	−0.0400204	−	0.0693173i
$333$	220077.	+	381185.i	0.108759	+	0.188376i
$334$	130536.	−	226095.i	0.0640271	−	0.110898i
$335$	−4.62977e6			−2.25397
$336$		0			0
$337$	−1.88817e6			−0.905664			−0.452832	−	0.891596i	$-0.649586\pi$
$337$	−1.88817e6			−0.905664			−0.452832	+	0.891596i	$0.649586\pi$
$338$	−527787.	+	914154.i	−0.251285	+	0.435239i
$339$	990657.	+	1.71587e6i	0.468192	+	0.810932i
$340$	19656.0	+	34045.2i	0.00922142	+	0.0159720i
$341$	−17760.0	+	30761.2i	−0.00827098	+	0.0143258i
$342$	−1.30442e6			−0.603050
$343$		0			0
$344$	−1.93603e6			−0.882097
$345$	1.47420e6	−	2.55339e6i	0.666820	−	1.15497i
$346$	−54990.0	−	95245.5i	−0.0246941	−	0.0427715i
$347$	−1.45969e6	−	2.52825e6i	−0.650782	−	1.12719i	−0.982933	−	0.183962i	$-0.941108\pi$
$347$	−1.45969e6	−	2.52825e6i	−0.650782	−	1.12719i	0.332151	−	0.943226i	$-0.392226\pi$
$348$	−97956.0	+	169665.i	−0.0433594	+	0.0751006i
$349$	−780682.			−0.343092			−0.171546	−	0.985176i	$-0.554876\pi$
$349$	−780682.			−0.343092			−0.171546	+	0.985176i	$0.554876\pi$
$350$		0			0
$351$	322218.			0.139599
$352$	−319680.	+	553702.i	−0.137518	+	0.238188i
$353$	−667185.	−	1.15560e6i	−0.284977	−	0.493594i	0.687627	−	0.726064i	$-0.258653\pi$
$353$	−667185.	−	1.15560e6i	−0.284977	−	0.493594i	−0.972604	+	0.232470i	$0.925319\pi$
$354$	−742284.	−	1.28567e6i	−0.314820	−	0.545284i
$355$	−1.24956e6	+	2.16430e6i	−0.526243	+	0.911479i
$356$	−31896.0			−0.0133386
$357$		0			0
$358$	919944.			0.379362
$359$	−508716.	+	881122.i	−0.208324	+	0.360828i	−0.951187	−	0.308616i	$-0.900134\pi$
$359$	−508716.	+	881122.i	−0.208324	+	0.360828i	0.742863	+	0.669444i	$0.233468\pi$
$360$	−530712.	−	919220.i	−0.215825	−	0.373821i
$361$	−2.36388e6	−	4.09436e6i	−0.954679	−	1.65355i
$362$	−1.14620e6	+	1.98527e6i	−0.459715	+	0.796249i
$363$	−324765.			−0.129361
$364$		0			0
$365$	−4.82399e6			−1.89528
$366$	−1.33591e6	+	2.31386e6i	−0.521283	+	0.902888i
$367$	−418840.	−	725452.i	−0.162324	−	0.281154i	0.773378	−	0.633946i	$-0.218566\pi$
$367$	−418840.	−	725452.i	−0.162324	−	0.281154i	−0.935702	+	0.352792i	$0.885232\pi$
$368$	2.38560e6	+	4.13198e6i	0.918286	+	1.59052i
$369$	−322461.	+	558519.i	−0.123285	+	0.213536i
$370$	2.54311e6			0.965742
$371$		0			0
$372$	−2880.00			−0.00107903
$373$	759965.	−	1.31630e6i	0.282827	−	0.489871i	−0.689253	−	0.724521i	$-0.742061\pi$
$373$	759965.	−	1.31630e6i	0.282827	−	0.489871i	0.972080	+	0.234650i	$0.0753943\pi$
$374$	−167832.	−	290694.i	−0.0620434	−	0.107462i
$375$	−58266.0	−	100920.i	−0.0213962	−	0.0370593i
$376$	1.16928e6	−	2.02525e6i	0.426529	−	0.738770i
$377$	2.40536e6			0.871620
$378$		0			0
$379$	2.64465e6			0.945737			0.472869	−	0.881133i	$-0.343219\pi$
$379$	2.64465e6			0.945737			0.472869	+	0.881133i	$0.343219\pi$
$380$	−418704.	+	725217.i	−0.148747	+	0.257637i
$381$	−334440.	−	579267.i	−0.118034	−	0.204440i
$382$	−820224.	−	1.42067e6i	−0.287590	−	0.498121i
$383$	−1.00668e6	+	1.74362e6i	−0.350667	+	0.607373i	−0.986366	−	0.164564i	$-0.947378\pi$
$383$	−1.00668e6	+	1.74362e6i	−0.350667	+	0.607373i	0.635700	+	0.771936i	$0.280712\pi$
$384$	1.91117e6			0.661410
$385$		0			0
$386$	−921612.			−0.314833
$387$	466722.	−	808386.i	0.158409	−	0.274373i
$388$	287324.	+	497660.i	0.0968930	+	0.167824i
$389$	363117.	+	628937.i	0.121667	+	0.210733i	0.920425	−	0.390919i	$-0.127843\pi$
$389$	363117.	+	628937.i	0.121667	+	0.210733i	−0.798758	+	0.601652i	$0.794509\pi$
$390$	930852.	−	1.61228e6i	0.309898	−	0.536760i
$391$	−529200.			−0.175056
$392$		0			0
$393$	1.39784e6			0.456538
$394$	463266.	−	802400.i	0.150345	−	0.260406i
$395$	2.56526e6	+	4.44317e6i	0.827255	+	1.43285i
$396$	−71928.0	−	124583.i	−0.0230494	−	0.0399228i
$397$	−2.28789e6	+	3.96274e6i	−0.728549	+	1.26188i	0.228947	+	0.973439i	$0.426472\pi$
$397$	−2.28789e6	+	3.96274e6i	−0.728549	+	1.26188i	−0.957496	+	0.288446i	$0.906861\pi$
$398$	2.20114e6			0.696529
$399$		0			0
$400$	−3.36142e6			−1.05045
$401$	16935.0	−	29332.3i	0.00525926	−	0.00910930i	−0.863384	−	0.504548i	$-0.831659\pi$
$401$	16935.0	−	29332.3i	0.00525926	−	0.00910930i	0.868643	+	0.495438i	$0.164993\pi$
$402$	1.60261e6	+	2.77581e6i	0.494610	+	0.856690i
$403$	17680.0	+	30622.7i	0.00542275	+	0.00939248i
$404$	5412.00	−	9373.86i	0.00164970	−	0.00285736i
$405$	511758.			0.155034
$406$		0			0
$407$	−2.41270e6			−0.721966
$408$	−95256.0	+	164988.i	−0.0283297	+	0.0490685i
$409$	2.93089e6	+	5.07645e6i	0.866346	+	1.50056i	0.865704	+	0.500556i	$0.166871\pi$
$409$	2.93089e6	+	5.07645e6i	0.866346	+	1.50056i	0.000641640		1.00000i	$0.499796\pi$
$410$	1.86311e6	+	3.22700e6i	0.547367	+	0.948067i
$411$	−1.18911e6	+	2.05959e6i	−0.347229	+	0.601419i
$412$	527072.			0.152977
$413$		0			0
$414$	−2.04120e6			−0.585308
$415$	−1.56733e6	+	2.71470e6i	−0.446726	+	0.773751i
$416$	318240.	+	551208.i	0.0901616	+	0.156164i
$417$	1.01075e6	+	1.75068e6i	0.284646	+	0.493022i
$418$	3.57509e6	−	6.19223e6i	1.00080	−	1.73343i
$419$	302748.			0.0842454			0.0421227	−	0.999112i	$-0.486588\pi$
$419$	302748.			0.0842454			0.0421227	+	0.999112i	$0.486588\pi$
$420$		0			0
$421$	−5.36708e6			−1.47582			−0.737909	−	0.674900i	$-0.764187\pi$
$421$	−5.36708e6			−1.47582			−0.737909	+	0.674900i	$0.764187\pi$
$422$	1.56073e6	−	2.70327e6i	0.426626	−	0.738938i
$423$	563760.	+	976461.i	0.153195	+	0.265341i
$424$	805896.	+	1.39585e6i	0.217703	+	0.377073i
$425$	186417.	−	322884.i	0.0500626	−	0.0867109i
$426$	1.73016e6			0.461915
$427$		0			0
$428$	−515664.			−0.136068
$429$	−883116.	+	1.52960e6i	−0.231673	+	0.401269i
$430$	−2.69662e6	−	4.67068e6i	−0.703312	−	1.21817i
$431$	−588528.	−	1.01936e6i	−0.152607	−	0.264323i	0.779578	−	0.626305i	$-0.215433\pi$
$431$	−588528.	−	1.01936e6i	−0.152607	−	0.264323i	−0.932185	+	0.361982i	$0.882100\pi$
$432$	−414072.	+	717194.i	−0.106750	+	0.184896i
$433$	−3.66249e6			−0.938766			−0.469383	−	0.882995i	$-0.655524\pi$
$433$	−3.66249e6			−0.938766			−0.469383	+	0.882995i	$0.655524\pi$
$434$		0			0
$435$	3.82028e6			0.967994
$436$	201956.	−	349798.i	0.0508792	−	0.0881254i
$437$	−5.63640e6	−	9.76253e6i	−1.41188	−	2.44545i
$438$	1.66984e6	+	2.89225e6i	0.415901	+	0.720362i
$439$	1.26837e6	−	2.19688e6i	0.314113	−	0.544059i	−0.665136	−	0.746722i	$-0.731626\pi$
$439$	1.26837e6	−	2.19688e6i	0.314113	−	0.544059i	0.979248	+	0.202663i	$0.0649597\pi$
$440$	5.81818e6			1.43270
$441$		0			0
$442$	−334152.			−0.0813558
$443$	−3.00752e6	+	5.20917e6i	−0.728113	+	1.26113i	0.229566	+	0.973293i	$0.426269\pi$
$443$	−3.00752e6	+	5.20917e6i	−0.728113	+	1.26113i	−0.957680	+	0.287836i	$0.907064\pi$
$444$	−97812.0	−	169415.i	−0.0235470	−	0.0407845i
$445$	310986.	+	538644.i	0.0744459	+	0.128944i
$446$	914208.	−	1.58345e6i	0.217625	−	0.376937i
$447$	738666.			0.174856
$448$		0			0
$449$	5.65965e6			1.32487			0.662436	−	0.749119i	$-0.269523\pi$
$449$	5.65965e6			1.32487			0.662436	+	0.749119i	$0.269523\pi$
$450$	719037.	−	1.24541e6i	0.167386	−	0.289922i
$451$	−1.76756e6	−	3.06151e6i	−0.409198	−	0.708752i
$452$	−440292.	−	762608.i	−0.101367	−	0.175572i
$453$	−1.29164e6	+	2.23719e6i	−0.295731	+	0.512222i
$454$	−1.73153e6			−0.394267
$455$		0			0
$456$	−4.05821e6			−0.913949
$457$	3.23080e6	−	5.59590e6i	0.723634	−	1.25337i	−0.235900	−	0.971777i	$-0.575804\pi$
$457$	3.23080e6	−	5.59590e6i	0.723634	−	1.25337i	0.959534	−	0.281593i	$-0.0908629\pi$
$458$	2.31657e6	+	4.01242e6i	0.516038	+	0.893804i
$459$	−45927.0	−	79547.9i	−0.0101750	−	0.0176237i
$460$	−655200.	+	1.13484e6i	−0.144371	+	0.250058i
$461$	−3.37353e6			−0.739320			−0.369660	−	0.929167i	$-0.620526\pi$
$461$	−3.37353e6			−0.739320			−0.369660	+	0.929167i	$0.620526\pi$
$462$		0			0
$463$	−4.54974e6			−0.986358			−0.493179	−	0.869928i	$-0.664165\pi$
$463$	−4.54974e6			−0.986358			−0.493179	+	0.869928i	$0.664165\pi$
$464$	−3.09106e6	+	5.35387e6i	−0.666518	+	1.15444i
$465$	28080.0	+	48636.0i	0.00602233	+	0.0104310i
$466$	756702.	+	1.31065e6i	0.161421	+	0.279589i
$467$	−1.00568e6	+	1.74189e6i	−0.213386	+	0.369596i	−0.952772	−	0.303686i	$-0.901783\pi$
$467$	−1.00568e6	+	1.74189e6i	−0.213386	+	0.369596i	0.739386	+	0.673282i	$0.235116\pi$
$468$	−143208.			−0.0302240
$469$		0			0
$470$	6.51456e6			1.36032
$471$	584451.	−	1.01230e6i	0.121394	−	0.210260i
$472$	−2.30933e6	−	3.99987e6i	−0.477123	−	0.826402i
$473$	2.55833e6	+	4.43115e6i	0.525779	+	0.910676i
$474$	1.77595e6	−	3.07604e6i	0.363066	−	0.628848i
$475$	7.94196e6			1.61508
$476$		0			0
$477$	−777114.			−0.156383
$478$	−4.35341e6	+	7.54032e6i	−0.871484	+	1.50946i
$479$	3.80201e6	+	6.58527e6i	0.757137	+	1.31140i	0.944305	+	0.329071i	$0.106736\pi$
$479$	3.80201e6	+	6.58527e6i	0.757137	+	1.31140i	−0.187168	+	0.982328i	$0.559931\pi$
$480$	505440.	+	875448.i	0.100131	+	0.173431i
$481$	−1.20091e6	+	2.08004e6i	−0.236673	+	0.409930i
$482$	878388.			0.172214
$483$		0			0
$484$	144340.			0.0280074
$485$	5.60282e6	−	9.70437e6i	1.08156	−	1.87332i
$486$	−177147.	−	306828.i	−0.0340207	−	0.0589256i
$487$	−336556.	−	582932.i	−0.0643035	−	0.111377i	0.832081	−	0.554654i	$-0.187149\pi$
$487$	−336556.	−	582932.i	−0.0643035	−	0.111377i	−0.896385	+	0.443277i	$0.853816\pi$
$488$	−4.15615e6	+	7.19867e6i	−0.790027	+	1.36837i
$489$	−4.99756e6			−0.945117
$490$		0			0
$491$	−2.47170e6			−0.462692			−0.231346	−	0.972872i	$-0.574313\pi$
$491$	−2.47170e6			−0.462692			−0.231346	+	0.972872i	$0.574313\pi$
$492$	143316.	−	248231.i	0.0266920	−	0.0462320i
$493$	−342846.	−	593827.i	−0.0635304	−	0.110038i
$494$	−3.55898e6	−	6.16434e6i	−0.656158	−	1.13650i
$495$	−1.40260e6	+	2.42937e6i	−0.257288	+	0.445636i
$496$	−90880.0			−0.0165869
$497$		0			0
$498$	2.17015e6			0.392118
$499$	−3.04076e6	+	5.26675e6i	−0.546677	+	0.946873i	0.451822	+	0.892108i	$0.350774\pi$
$499$	−3.04076e6	+	5.26675e6i	−0.546677	+	0.946873i	−0.998499	+	0.0547648i	$0.982559\pi$
$500$	25896.0	+	44853.2i	0.00463242	+	0.00802358i
$501$	195804.	+	339142.i	0.0348520	+	0.0603654i
$502$	1.82358e6	−	3.15853e6i	0.322972	−	0.559405i
$503$	−846216.			−0.149129			−0.0745644	−	0.997216i	$-0.523757\pi$
$503$	−846216.			−0.149129			−0.0745644	+	0.997216i	$0.523757\pi$
$504$		0			0
$505$	−211068.			−0.0368293
$506$	5.59440e6	−	9.68979e6i	0.971353	−	1.68243i
$507$	−791680.	−	1.37123e6i	−0.136782	−	0.236914i
$508$	148640.	+	257452.i	0.0255550	+	0.0442626i
$509$	3.83392e6	−	6.64055e6i	0.655917	−	1.13608i	−0.325746	−	0.945457i	$-0.605615\pi$
$509$	3.83392e6	−	6.64055e6i	0.655917	−	1.13608i	0.981663	−	0.190625i	$-0.0610514\pi$
$510$	−530712.			−0.0903511
$511$		0			0
$512$	4.47130e6			0.753804
$513$	978318.	−	1.69450e6i	0.164129	−	0.284281i
$514$	286758.	+	496679.i	0.0478749	+	0.0829217i
$515$	−5.13895e6	−	8.90093e6i	−0.853801	−	1.47883i
$516$	−207432.	+	359283.i	−0.0342966	+	0.0594035i
$517$	−6.18048e6			−1.01694
$518$		0			0
$519$	164970.			0.0268835
$520$	2.89598e6	−	5.01599e6i	0.469665	−	0.813483i
$521$	4.84469e6	+	8.39125e6i	0.781937	+	1.35435i	0.930812	+	0.365499i	$0.119102\pi$
$521$	4.84469e6	+	8.39125e6i	0.781937	+	1.35435i	−0.148875	+	0.988856i	$0.547565\pi$
$522$	−1.32241e6	−	2.29047e6i	−0.212417	−	0.367916i
$523$	3.75839e6	−	6.50972e6i	0.600824	−	1.04066i	−0.391872	−	0.920020i	$-0.628172\pi$
$523$	3.75839e6	−	6.50972e6i	0.600824	−	1.04066i	0.992696	−	0.120639i	$-0.0384943\pi$
$524$	−621264.			−0.0988435
$525$		0			0
$526$	1.32021e7			2.08055
$527$	5040.00	−	8729.54i	0.000790504	−	0.00136919i
$528$	−2.26973e6	−	3.93128e6i	−0.354315	−	0.613691i
$529$	−5.60183e6	−	9.70265e6i	−0.870343	−	1.50748i
$530$	−2.24500e6	+	3.88845e6i	−0.347157	+	0.601294i
$531$	2.22685e6			0.342732
$532$		0			0
$533$	−3.51920e6			−0.536570
$534$	215298.	−	372907.i	0.0326728	−	0.0565910i
$535$	5.02772e6	+	8.70827e6i	0.759429	+	1.31537i
$536$	4.98590e6	+	8.63584e6i	0.749604	+	1.29835i
$537$	−689958.	+	1.19504e6i	−0.103249	+	0.178833i
$538$	−1.06215e7			−1.58208
$539$		0			0
$540$	−227448.			−0.0335659
$541$	−3.67162e6	+	6.35944e6i	−0.539343	+	0.934169i	0.459597	+	0.888128i	$0.347994\pi$
$541$	−3.67162e6	+	6.35944e6i	−0.539343	+	0.934169i	−0.998940	+	0.0460415i	$0.985339\pi$
$542$	−670512.	−	1.16136e6i	−0.0980411	−	0.169812i
$543$	−1.71930e6	−	2.97791e6i	−0.250237	−	0.433423i
$544$	90720.0	−	157132.i	0.0131433	−	0.0227649i
$545$	−7.87628e6			−1.13587
$546$		0			0
$547$	2.18296e6			0.311945			0.155973	−	0.987761i	$-0.450149\pi$
$547$	2.18296e6			0.311945			0.155973	+	0.987761i	$0.450149\pi$
$548$	528492.	−	915375.i	0.0751774	−	0.130211i
$549$	−2.00386e6	−	3.47079e6i	−0.283750	−	0.491470i
$550$	3.94139e6	+	6.82668e6i	0.555575	+	0.962284i
$551$	7.30316e6	−	1.26495e7i	1.02478	−	1.77498i
$552$	−6.35040e6			−0.887061
$553$		0			0
$554$	2.05667e6			0.284702
$555$	−1.90733e6	+	3.30360e6i	−0.262842	+	0.455255i
$556$	−449224.	−	778079.i	−0.0616277	−	0.106742i
$557$	−6.27328e6	−	1.08656e7i	−0.856755	−	1.48394i	−0.875007	−	0.484110i	$-0.839144\pi$
$557$	−6.27328e6	−	1.08656e7i	−0.856755	−	1.48394i	0.0182524	−	0.999833i	$-0.494190\pi$
$558$	19440.0	−	33671.1i	0.00264308	−	0.00457795i
$559$	5.09361e6			0.689439
$560$		0			0
$561$	503496.			0.0675443
$562$	1.44113e6	−	2.49612e6i	0.192470	−	0.333368i
$563$	−2.57986e6	−	4.46845e6i	−0.343025	−	0.594136i	0.641968	−	0.766731i	$-0.278118\pi$
$563$	−2.57986e6	−	4.46845e6i	−0.343025	−	0.594136i	−0.984993	+	0.172595i	$0.944785\pi$
$564$	−250560.	−	433983.i	−0.0331676	−	0.0574480i
$565$	−8.58569e6	+	1.48709e7i	−1.13150	+	1.95981i
$566$	179880.			0.0236016
$567$		0			0
$568$	5.38272e6			0.700053
$569$	−5.87260e6	+	1.01717e7i	−0.760414	+	1.31708i	0.182223	+	0.983257i	$0.441671\pi$
$569$	−5.87260e6	+	1.01717e7i	−0.760414	+	1.31708i	−0.942637	+	0.333819i	$0.891663\pi$
$570$	−5.65250e6	−	9.79042e6i	−0.728708	−	1.26216i
$571$	3.77364e6	+	6.53614e6i	0.484362	+	0.838940i	0.999839	−	0.0179636i	$-0.00571829\pi$
$571$	3.77364e6	+	6.53614e6i	0.484362	+	0.838940i	−0.515476	+	0.856904i	$0.672385\pi$
$572$	392496.	−	679823.i	0.0501586	−	0.0868772i
$573$	2.46067e6			0.313089
$574$		0			0
$575$	1.24278e7			1.56756
$576$	−1.12234e6	+	1.94394e6i	−0.140951	+	0.244133i
$577$	−4.64242e6	−	8.04090e6i	−0.580503	−	1.00546i	−0.995420	−	0.0956015i	$-0.969523\pi$
$577$	−4.64242e6	−	8.04090e6i	−0.580503	−	1.00546i	0.414916	−	0.909859i	$-0.363811\pi$
$578$	−4.21194e6	−	7.29530e6i	−0.524400	−	0.908288i
$579$	691209.	−	1.19721e6i	0.0856866	−	0.148414i
$580$	−1.69790e6			−0.209577
$581$		0			0
$582$	−7.75775e6			−0.949354
$583$	2.12987e6	−	3.68904e6i	0.259526	−	0.449513i
$584$	5.19506e6	+	8.99811e6i	0.630317	+	1.09174i
$585$	1.39628e6	+	2.41842e6i	0.168687	+	0.292175i
$586$	−594198.	+	1.02918e6i	−0.0714804	+	0.123808i
$587$	1.47623e6			0.176831			0.0884155	−	0.996084i	$-0.471820\pi$
$587$	1.47623e6			0.176831			0.0884155	+	0.996084i	$0.471820\pi$
$588$		0			0
$589$	214720.			0.0255026
$590$	6.43313e6	−	1.11425e7i	0.760838	−	1.31781i
$591$	694899.	+	1.20360e6i	0.0818376	+	0.141747i
$592$	−3.08651e6	−	5.34600e6i	−0.361963	−	0.626938i
$593$	6.20034e6	−	1.07393e7i	0.724067	−	1.25412i	−0.235289	−	0.971925i	$-0.575604\pi$
$593$	6.20034e6	−	1.07393e7i	0.724067	−	1.25412i	0.959357	−	0.282196i	$-0.0910629\pi$
$594$	1.94206e6			0.225837
$595$		0			0
$596$	−328296.			−0.0378573
$597$	−1.65085e6	+	2.85936e6i	−0.189571	+	0.328347i
$598$	−5.56920e6	−	9.64614e6i	−0.636854	−	1.10306i
$599$	1.84564e6	+	3.19674e6i	0.210174	+	0.364032i	0.951769	−	0.306816i	$-0.0992636\pi$
$599$	1.84564e6	+	3.19674e6i	0.210174	+	0.364032i	−0.741595	+	0.670848i	$0.765930\pi$
$600$	2.23700e6	−	3.87460e6i	0.253681	−	0.439389i
$601$	9.12223e6			1.03018			0.515092	−	0.857135i	$-0.327758\pi$
$601$	9.12223e6			1.03018			0.515092	+	0.857135i	$0.327758\pi$
$602$		0			0
$603$	−4.80784e6			−0.538464
$604$	574064.	−	994308.i	0.0640277	−	0.110899i
$605$	−1.40732e6	−	2.43754e6i	−0.156316	−	0.270747i
$606$	73062.0	+	126547.i	0.00808184	+	0.0139981i
$607$	2.83957e6	−	4.91828e6i	0.312810	−	0.541803i	−0.666160	−	0.745809i	$-0.732063\pi$
$607$	2.83957e6	−	4.91828e6i	0.312810	−	0.541803i	0.978970	+	0.204007i	$0.0653964\pi$
$608$	3.86496e6			0.424020
$609$		0			0
$610$	−2.31557e7			−2.51961
$611$	−3.07632e6	+	5.32834e6i	−0.333372	+	0.577416i
$612$	20412.0	+	35354.6i	0.00220296	+	0.00381564i
$613$	7.00529e6	+	1.21335e7i	0.752966	+	1.30417i	0.946379	+	0.323057i	$0.104711\pi$
$613$	7.00529e6	+	1.21335e7i	0.752966	+	1.30417i	−0.193414	+	0.981117i	$0.561956\pi$
$614$	−3.13691e6	+	5.43328e6i	−0.335800	+	0.581623i
$615$	−5.58932e6			−0.595897
$616$		0			0
$617$	−253686.			−0.0268277			−0.0134139	−	0.999910i	$-0.504270\pi$
$617$	−253686.			−0.0268277			−0.0134139	+	0.999910i	$0.504270\pi$
$618$	−3.55774e6	+	6.16218e6i	−0.374716	+	0.649028i
$619$	−2.15017e6	−	3.72420e6i	−0.225552	−	0.390667i	0.730933	−	0.682449i	$-0.239085\pi$
$619$	−2.15017e6	−	3.72420e6i	−0.225552	−	0.390667i	−0.956485	+	0.291782i	$0.905752\pi$
$620$	−12480.0	−	21616.0i	−0.00130387	−	0.00225837i
$621$	1.53090e6	−	2.65160e6i	0.159301	−	0.275917i
$622$	−1.10231e7			−1.14242
$623$		0			0
$624$	−4.51901e6			−0.464603
$625$	5.12841e6	−	8.88267e6i	0.525149	−	0.909585i
$626$	−1.09648e6	−	1.89916e6i	−0.111832	−	0.193699i
$627$	5.36263e6	+	9.28835e6i	0.544765	+	0.943561i
$628$	−259756.	+	449911.i	−0.0262825	+	0.0455226i
$629$	684684.			0.0690023
$630$		0			0
$631$	1.04150e7			1.04132			0.520662	−	0.853763i	$-0.325685\pi$
$631$	1.04150e7			1.04132			0.520662	+	0.853763i	$0.325685\pi$
$632$	5.52518e6	−	9.56990e6i	0.550242	−	0.953048i
$633$	2.34110e6	+	4.05490e6i	0.232226	+	0.402227i
$634$	−85014.0	−	147249.i	−0.00839977	−	0.0145488i
$635$	2.89848e6	−	5.02031e6i	0.285257	−	0.494079i
$636$	345384.			0.0338579
$637$		0			0
$638$	1.44975e7			1.41007
$639$	−1.29762e6	+	2.24754e6i	−0.125717	+	0.217749i
$640$	8.28173e6	+	1.43444e7i	0.799229	+	1.38430i
$641$	−2.26357e6	−	3.92062e6i	−0.217595	−	0.376885i	0.736477	−	0.676462i	$-0.236488\pi$
$641$	−2.26357e6	−	3.92062e6i	−0.217595	−	0.376885i	−0.954072	+	0.299577i	$0.903154\pi$
$642$	3.48073e6	−	6.02880e6i	0.333298	−	0.577289i
$643$	1.49687e7			1.42776			0.713882	−	0.700266i	$-0.246935\pi$
$643$	1.49687e7			1.42776			0.713882	+	0.700266i	$0.246935\pi$
$644$		0			0
$645$	8.08985e6			0.765669
$646$	−1.01455e6	+	1.75726e6i	−0.0956518	+	0.165674i
$647$	8.65098e6	+	1.49839e7i	0.812465	+	1.40723i	0.911134	+	0.412110i	$0.135208\pi$
$647$	8.65098e6	+	1.49839e7i	0.812465	+	1.40723i	−0.0986691	+	0.995120i	$0.531459\pi$
$648$	−551124.	−	954575.i	−0.0515599	−	0.0893043i
$649$	−6.10322e6	+	1.05711e7i	−0.568784	+	0.985163i
$650$	7.84727e6			0.728509
$651$		0			0
$652$	2.22114e6			0.204624
$653$	−2.03735e6	+	3.52880e6i	−0.186975	+	0.323850i	−0.944240	−	0.329258i	$-0.893202\pi$
$653$	−2.03735e6	+	3.52880e6i	−0.186975	+	0.323850i	0.757265	+	0.653107i	$0.226535\pi$
$654$	2.72641e6	+	4.72227e6i	0.249256	+	0.431725i
$655$	6.05732e6	+	1.04916e7i	0.551668	+	0.955516i
$656$	4.52242e6	−	7.83305e6i	0.410309	−	0.710676i
$657$	−5.00953e6			−0.452776
$658$		0			0
$659$	−3.79475e6			−0.340384			−0.170192	−	0.985411i	$-0.554439\pi$
$659$	−3.79475e6			−0.340384			−0.170192	+	0.985411i	$0.554439\pi$
$660$	623376.	−	1.07972e6i	0.0557045	−	0.0964830i
$661$	−8.21307e6	−	1.42255e7i	−0.731142	−	1.26638i	−0.956395	−	0.292075i	$-0.905654\pi$
$661$	−8.21307e6	−	1.42255e7i	−0.731142	−	1.26638i	0.225253	−	0.974300i	$-0.427679\pi$
$662$	5.80175e6	+	1.00489e7i	0.514534	+	0.891199i
$663$	250614.	−	434076.i	0.0221422	−	0.0383515i
$664$	6.75158e6			0.594272
$665$		0			0
$666$	2.64092e6			0.230712
$667$	1.14282e7	−	1.97942e7i	0.994634	−	1.72276i
$668$	−87024.0	−	150730.i	−0.00754567	−	0.0130695i
$669$	1.37131e6	+	2.37518e6i	0.118460	+	0.205178i
$670$	−1.38893e7	+	2.40570e7i	−1.19535	+	2.07040i
$671$	2.19682e7			1.88360
$672$		0			0
$673$	5.50675e6			0.468660			0.234330	−	0.972157i	$-0.424710\pi$
$673$	5.50675e6			0.468660			0.234330	+	0.972157i	$0.424710\pi$
$674$	−5.66452e6	+	9.81124e6i	−0.480301	+	0.831906i
$675$	1.07856e6	+	1.86811e6i	0.0911136	+	0.157813i
$676$	351858.	+	609436.i	0.0296142	+	0.0512934i
$677$	−9.19787e6	+	1.59312e7i	−0.771286	+	1.33591i	0.165572	+	0.986198i	$0.447053\pi$
$677$	−9.19787e6	+	1.59312e7i	−0.771286	+	1.33591i	−0.936858	+	0.349709i	$0.886280\pi$
$678$	1.18879e7			0.993185
$679$		0			0
$680$	−1.65110e6			−0.136931
$681$	1.29865e6	−	2.24932e6i	0.107306	−	0.185859i
$682$	106560.	+	184567.i	0.00877270	+	0.0151948i
$683$	−879174.	−	1.52277e6i	−0.0721146	−	0.124906i	0.827713	−	0.561151i	$-0.189641\pi$
$683$	−879174.	−	1.52277e6i	−0.0721146	−	0.124906i	−0.899828	+	0.436245i	$0.856308\pi$
$684$	−434808.	+	753110.i	−0.0355351	+	0.0615486i
$685$	−2.06112e7			−1.67833
$686$		0			0
$687$	−6.94971e6			−0.561791
$688$	−6.54563e6	+	1.13374e7i	−0.527206	+	0.913148i
$689$	−2.12027e6	−	3.67242e6i	−0.170155	−	0.294717i
$690$	−8.84520e6	−	1.53203e7i	−0.707270	−	1.22503i
$691$	2.68157e6	−	4.64462e6i	0.213646	−	0.370045i	−0.739207	−	0.673478i	$-0.764800\pi$
$691$	2.68157e6	−	4.64462e6i	0.213646	−	0.370045i	0.952853	+	0.303433i	$0.0981329\pi$
$692$	−73320.0			−0.00582046
$693$		0			0
$694$	−1.75162e7			−1.38052
$695$	−8.75987e6	+	1.51725e7i	−0.687916	+	1.19151i
$696$	−4.11415e6	−	7.12592e6i	−0.321927	−	0.557594i
$697$	501606.	+	868807.i	0.0391094	+	0.0677394i
$698$	−2.34205e6	+	4.05654e6i	−0.181952	+	0.315150i
$699$	−2.27011e6			−0.175733
$700$		0			0
$701$	−2.12606e7			−1.63411			−0.817054	−	0.576561i	$-0.804394\pi$
$701$	−2.12606e7			−1.63411			−0.817054	+	0.576561i	$0.804394\pi$
$702$	966654.	−	1.67429e6i	0.0740335	−	0.128230i
$703$	7.29243e6	+	1.26309e7i	0.556524	+	0.963928i
$704$	−6.15206e6	−	1.06557e7i	−0.467831	−	0.810307i
$705$	−4.88592e6	+	8.46266e6i	−0.370232	+	0.641260i
$706$	−8.00622e6			−0.604527
$707$		0			0
$708$	−989712.			−0.0742037
$709$	−1.03864e6	+	1.79898e6i	−0.0775980	+	0.134404i	−0.902213	−	0.431290i	$-0.858058\pi$
$709$	−1.03864e6	+	1.79898e6i	−0.0775980	+	0.134404i	0.824615	+	0.565694i	$0.191392\pi$
$710$	7.49736e6	+	1.29858e7i	0.558165	+	0.966770i
$711$	2.66393e6	+	4.61406e6i	0.197628	+	0.342302i
$712$	669816.	−	1.16016e6i	0.0495171	−	0.0857662i
$713$	336000.			0.0247523
$714$		0			0
$715$	−1.53073e7			−1.11979
$716$	306648.	−	531130.i	0.0223541	−	0.0387185i
$717$	−6.53011e6	−	1.13105e7i	−0.474376	−	0.821643i
$718$	3.05230e6	+	5.28673e6i	0.220961	+	0.382716i
$719$	−2.11810e6	+	3.66865e6i	−0.152800	+	0.264657i	−0.932256	−	0.361800i	$-0.882162\pi$
$719$	−2.11810e6	+	3.66865e6i	−0.152800	+	0.264657i	0.779456	+	0.626457i	$0.215496\pi$
$720$	−7.17725e6			−0.515973
$721$		0			0
$722$	−2.83665e7			−2.02518
$723$	−658791.	+	1.14106e6i	−0.0468708	+	0.0811825i
$724$	764132.	+	1.32352e6i	0.0541779	+	0.0938388i
$725$	8.05144e6	+	1.39455e7i	0.568890	+	0.985347i
$726$	−974295.	+	1.68753e6i	−0.0686039	+	0.118825i
$727$	2.14524e7			1.50536			0.752678	−	0.658389i	$-0.228762\pi$
$727$	2.14524e7			1.50536			0.752678	+	0.658389i	$0.228762\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.44720e7	+	2.50662e7i	−1.00513	+	1.74093i
$731$	−726012.	−	1.25749e6i	−0.0502517	−	0.0870384i
$732$	890604.	+	1.54257e6i	0.0614337	+	0.106406i
$733$	7.44459e6	−	1.28944e7i	0.511777	−	0.886424i	−0.488130	−	0.872771i	$-0.662321\pi$
$733$	7.44459e6	−	1.28944e7i	0.511777	−	0.886424i	0.999907	−	0.0136528i	$-0.00434594\pi$
$734$	−5.02608e6			−0.344341
$735$		0			0
$736$	6.04800e6			0.411545
$737$	1.31770e7	−	2.28233e7i	0.893612	−	1.54778i
$738$	1.93477e6	+	3.35111e6i	0.130764	+	0.226490i
$739$	−3.49662e6	−	6.05632e6i	−0.235525	−	0.407941i	0.723900	−	0.689905i	$-0.242348\pi$
$739$	−3.49662e6	−	6.05632e6i	−0.235525	−	0.407941i	−0.959425	+	0.281963i	$0.909014\pi$
$740$	847704.	−	1.46827e6i	0.0569069	−	0.0985656i
$741$	1.06770e7			0.714335
$742$		0			0
$743$	1.90428e6			0.126549			0.0632745	−	0.997996i	$-0.479846\pi$
$743$	1.90428e6			0.126549			0.0632745	+	0.997996i	$0.479846\pi$
$744$	60480.0	−	104754.i	0.00400571	−	0.00693809i
$745$	3.20089e6	+	5.54410e6i	0.211290	+	0.365966i
$746$	−4.55979e6	−	7.89779e6i	−0.299984	−	0.519587i
$747$	−1.62761e6	+	2.81911e6i	−0.106721	+	0.184846i
$748$	−223776.			−0.0146238
$749$		0			0
$750$	−699192.			−0.0453882
$751$	−9.76806e6	+	1.69188e7i	−0.631988	+	1.09463i	0.355157	+	0.934807i	$0.384427\pi$
$751$	−9.76806e6	+	1.69188e7i	−0.631988	+	1.09463i	−0.987145	+	0.159828i	$0.948906\pi$
$752$	−7.90656e6	−	1.36946e7i	−0.509851	−	0.883087i
$753$	2.73537e6	+	4.73780e6i	0.175804	+	0.304501i
$754$	7.21609e6	−	1.24986e7i	0.462247	−	0.800635i
$755$	−2.23885e7			−1.42941
$756$		0			0
$757$	1.25183e6			0.0793973			0.0396986	−	0.999212i	$-0.487360\pi$
$757$	1.25183e6			0.0793973			0.0396986	+	0.999212i	$0.487360\pi$
$758$	7.93396e6	−	1.37420e7i	0.501553	−	0.868715i
$759$	8.39160e6	+	1.45347e7i	0.528738	+	0.915801i
$760$	−1.75856e7	−	3.04591e7i	−1.10439	−	1.91286i
$761$	−1.02236e7	+	1.77078e7i	−0.639944	+	1.10841i	0.345501	+	0.938418i	$0.387709\pi$
$761$	−1.02236e7	+	1.77078e7i	−0.639944	+	1.10841i	−0.985445	+	0.169997i	$0.945624\pi$
$762$	−4.01328e6			−0.250387
$763$		0			0
$764$	−1.09363e6			−0.0677857
$765$	398034.	−	689415.i	0.0245905	−	0.0425919i
$766$	6.04008e6	+	1.04617e7i	0.371938	+	0.644216i
$767$	6.07573e6	+	1.05235e7i	0.372915	+	0.645908i
$768$	1.74298e6	−	3.01892e6i	0.106632	−	0.184692i
$769$	2.21064e6			0.134804

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-39.0000 + 67.5500i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(3.00000 - 5.19615i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-39.0000 + 67.5500i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(234.000 + 405.300i) q^{10} +(-222.000 - 384.515i) q^{11} +(18.0000 - 31.1769i) q^{12} -442.000 q^{13} -702.000 q^{15} +(568.000 - 983.805i) q^{16} +(63.0000 + 109.119i) q^{17} +(243.000 + 420.888i) q^{18} +(-1342.00 + 2324.41i) q^{19} +312.000 q^{20} -2664.00 q^{22} +(-2100.00 + 3637.31i) q^{23} +(756.000 + 1309.43i) q^{24} +(-1479.50 - 2562.57i) q^{25} +(-1326.00 + 2296.70i) q^{26} -729.000 q^{27} -5442.00 q^{29} +(-2106.00 + 3647.70i) q^{30} +(-40.0000 - 69.2820i) q^{31} +(-720.000 - 1247.08i) q^{32} +(1998.00 - 3460.64i) q^{33} +756.000 q^{34} +324.000 q^{36} +(2717.00 - 4705.98i) q^{37} +(8052.00 + 13946.5i) q^{38} +(-1989.00 - 3445.05i) q^{39} +(-6552.00 + 11348.4i) q^{40} +7962.00 q^{41} -11524.0 q^{43} +(-888.000 + 1538.06i) q^{44} +(-3159.00 - 5471.55i) q^{45} +(12600.0 + 21823.8i) q^{46} +(6960.00 - 12055.1i) q^{47} +10224.0 q^{48} -17754.0 q^{50} +(-567.000 + 982.073i) q^{51} +(884.000 + 1531.13i) q^{52} +(4797.00 + 8308.65i) q^{53} +(-2187.00 + 3788.00i) q^{54} +34632.0 q^{55} -24156.0 q^{57} +(-16326.0 + 28277.5i) q^{58} +(-13746.0 - 23808.8i) q^{59} +(1404.00 + 2431.80i) q^{60} +(-24739.0 + 42849.2i) q^{61} -480.000 q^{62} +27712.0 q^{64} +(17238.0 - 29857.1i) q^{65} +(-11988.0 - 20763.8i) q^{66} +(29678.0 + 51403.8i) q^{67} +(252.000 - 436.477i) q^{68} -37800.0 q^{69} +32040.0 q^{71} +(-6804.00 + 11784.9i) q^{72} +(30923.0 + 53560.2i) q^{73} +(-16302.0 - 28235.9i) q^{74} +(13315.5 - 23063.1i) q^{75} +10736.0 q^{76} -23868.0 q^{78} +(32888.0 - 56963.7i) q^{79} +(44304.0 + 76736.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(23886.0 - 41371.8i) q^{82} +40188.0 q^{83} -9828.00 q^{85} +(-34572.0 + 59880.5i) q^{86} +(-24489.0 - 42416.2i) q^{87} +(-37296.0 - 64598.6i) q^{88} +(3987.00 - 6905.69i) q^{89} -37908.0 q^{90} +16800.0 q^{92} +(360.000 - 623.538i) q^{93} +(-41760.0 - 72330.4i) q^{94} +(-104676. - 181304. i) q^{95} +(6480.00 - 11223.7i) q^{96} -143662. q^{97} +35964.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} - 78 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9}+O(q^{10}) \) 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 - 78 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9	\( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} - 78 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9} + 468 q^{10} - 444 q^{11} + 36 q^{12} - 884 q^{13} - 1404 q^{15} + 1136 q^{16} + 126 q^{17} + 486 q^{18} - 2684 q^{19} + 624 q^{20} - 5328 q^{22} - 4200 q^{23} + 1512 q^{24} - 2959 q^{25} - 2652 q^{26} - 1458 q^{27} - 10884 q^{29} - 4212 q^{30} - 80 q^{31} - 1440 q^{32} + 3996 q^{33} + 1512 q^{34} + 648 q^{36} + 5434 q^{37} + 16104 q^{38} - 3978 q^{39} - 13104 q^{40} + 15924 q^{41} - 23048 q^{43} - 1776 q^{44} - 6318 q^{45} + 25200 q^{46} + 13920 q^{47} + 20448 q^{48} - 35508 q^{50} - 1134 q^{51} + 1768 q^{52} + 9594 q^{53} - 4374 q^{54} + 69264 q^{55} - 48312 q^{57} - 32652 q^{58} - 27492 q^{59} + 2808 q^{60} - 49478 q^{61} - 960 q^{62} + 55424 q^{64} + 34476 q^{65} - 23976 q^{66} + 59356 q^{67} + 504 q^{68} - 75600 q^{69} + 64080 q^{71} - 13608 q^{72} + 61846 q^{73} - 32604 q^{74} + 26631 q^{75} + 21472 q^{76} - 47736 q^{78} + 65776 q^{79} + 88608 q^{80} - 6561 q^{81} + 47772 q^{82} + 80376 q^{83} - 19656 q^{85} - 69144 q^{86} - 48978 q^{87} - 74592 q^{88} + 7974 q^{89} - 75816 q^{90} + 33600 q^{92} + 720 q^{93} - 83520 q^{94} - 209352 q^{95} + 12960 q^{96} - 287324 q^{97} + 71928 q^{99}+O(q^{100}) \) 2 * q + 6 * q^2 + 9 * q^3 - 4 * q^4 - 78 * q^5 + 108 * q^6 + 336 * q^8 - 81 * q^9 + 468 * q^10 - 444 * q^11 + 36 * q^12 - 884 * q^13 - 1404 * q^15 + 1136 * q^16 + 126 * q^17 + 486 * q^18 - 2684 * q^19 + 624 * q^20 - 5328 * q^22 - 4200 * q^23 + 1512 * q^24 - 2959 * q^25 - 2652 * q^26 - 1458 * q^27 - 10884 * q^29 - 4212 * q^30 - 80 * q^31 - 1440 * q^32 + 3996 * q^33 + 1512 * q^34 + 648 * q^36 + 5434 * q^37 + 16104 * q^38 - 3978 * q^39 - 13104 * q^40 + 15924 * q^41 - 23048 * q^43 - 1776 * q^44 - 6318 * q^45 + 25200 * q^46 + 13920 * q^47 + 20448 * q^48 - 35508 * q^50 - 1134 * q^51 + 1768 * q^52 + 9594 * q^53 - 4374 * q^54 + 69264 * q^55 - 48312 * q^57 - 32652 * q^58 - 27492 * q^59 + 2808 * q^60 - 49478 * q^61 - 960 * q^62 + 55424 * q^64 + 34476 * q^65 - 23976 * q^66 + 59356 * q^67 + 504 * q^68 - 75600 * q^69 + 64080 * q^71 - 13608 * q^72 + 61846 * q^73 - 32604 * q^74 + 26631 * q^75 + 21472 * q^76 - 47736 * q^78 + 65776 * q^79 + 88608 * q^80 - 6561 * q^81 + 47772 * q^82 + 80376 * q^83 - 19656 * q^85 - 69144 * q^86 - 48978 * q^87 - 74592 * q^88 + 7974 * q^89 - 75816 * q^90 + 33600 * q^92 + 720 * q^93 - 83520 * q^94 - 209352 * q^95 + 12960 * q^96 - 287324 * q^97 + 71928 * q^99

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