LMFDB - Embedded newform 147.4.e.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,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, 4, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$8.67328077084$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.4.e.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +12.0000 q^{6} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +12.0000 q^{6} +(-4.50000 - 7.79423i) q^{9} +(-36.0000 + 62.3538i) q^{10} +(25.0000 - 43.3013i) q^{11} +(-12.0000 - 20.7846i) q^{12} -36.0000 q^{13} +54.0000 q^{15} +(32.0000 + 55.4256i) q^{16} +(-63.0000 + 109.119i) q^{17} +(-18.0000 + 31.1769i) q^{18} +(36.0000 + 62.3538i) q^{19} +144.000 q^{20} -200.000 q^{22} +(-7.00000 - 12.1244i) q^{23} +(-99.5000 + 172.339i) q^{25} +(72.0000 + 124.708i) q^{26} +27.0000 q^{27} +158.000 q^{29} +(-108.000 - 187.061i) q^{30} +(18.0000 - 31.1769i) q^{31} +(128.000 - 221.703i) q^{32} +(75.0000 + 129.904i) q^{33} +504.000 q^{34} +72.0000 q^{36} +(81.0000 + 140.296i) q^{37} +(144.000 - 249.415i) q^{38} +(54.0000 - 93.5307i) q^{39} -270.000 q^{41} -324.000 q^{43} +(200.000 + 346.410i) q^{44} +(-81.0000 + 140.296i) q^{45} +(-28.0000 + 48.4974i) q^{46} +(36.0000 + 62.3538i) q^{47} -192.000 q^{48} +796.000 q^{50} +(-189.000 - 327.358i) q^{51} +(144.000 - 249.415i) q^{52} +(11.0000 - 19.0526i) q^{53} +(-54.0000 - 93.5307i) q^{54} -900.000 q^{55} -216.000 q^{57} +(-316.000 - 547.328i) q^{58} +(-234.000 + 405.300i) q^{59} +(-216.000 + 374.123i) q^{60} +(-396.000 - 685.892i) q^{61} -144.000 q^{62} -512.000 q^{64} +(324.000 + 561.184i) q^{65} +(300.000 - 519.615i) q^{66} +(-116.000 + 200.918i) q^{67} +(-504.000 - 872.954i) q^{68} +42.0000 q^{69} -734.000 q^{71} +(-90.0000 + 155.885i) q^{73} +(324.000 - 561.184i) q^{74} +(-298.500 - 517.017i) q^{75} -576.000 q^{76} -432.000 q^{78} +(-118.000 - 204.382i) q^{79} +(576.000 - 997.661i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(540.000 + 935.307i) q^{82} +36.0000 q^{83} +2268.00 q^{85} +(648.000 + 1122.37i) q^{86} +(-237.000 + 410.496i) q^{87} +(-117.000 - 202.650i) q^{89} +648.000 q^{90} +112.000 q^{92} +(54.0000 + 93.5307i) q^{93} +(144.000 - 249.415i) q^{94} +(648.000 - 1122.37i) q^{95} +(384.000 + 665.108i) q^{96} +468.000 q^{97} -450.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 3 q^{3} - 8 q^{4} - 18 q^{5} + 24 q^{6} - 9 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 3 * q^3 - 8 * q^4 - 18 * q^5 + 24 * q^6 - 9 * q^9	\( 2 q - 4 q^{2} - 3 q^{3} - 8 q^{4} - 18 q^{5} + 24 q^{6} - 9 q^{9} - 72 q^{10} + 50 q^{11} - 24 q^{12} - 72 q^{13} + 108 q^{15} + 64 q^{16} - 126 q^{17} - 36 q^{18} + 72 q^{19} + 288 q^{20} - 400 q^{22} - 14 q^{23} - 199 q^{25} + 144 q^{26} + 54 q^{27} + 316 q^{29} - 216 q^{30} + 36 q^{31} + 256 q^{32} + 150 q^{33} + 1008 q^{34} + 144 q^{36} + 162 q^{37} + 288 q^{38} + 108 q^{39} - 540 q^{41} - 648 q^{43} + 400 q^{44} - 162 q^{45} - 56 q^{46} + 72 q^{47} - 384 q^{48} + 1592 q^{50} - 378 q^{51} + 288 q^{52} + 22 q^{53} - 108 q^{54} - 1800 q^{55} - 432 q^{57} - 632 q^{58} - 468 q^{59} - 432 q^{60} - 792 q^{61} - 288 q^{62} - 1024 q^{64} + 648 q^{65} + 600 q^{66} - 232 q^{67} - 1008 q^{68} + 84 q^{69} - 1468 q^{71} - 180 q^{73} + 648 q^{74} - 597 q^{75} - 1152 q^{76} - 864 q^{78} - 236 q^{79} + 1152 q^{80} - 81 q^{81} + 1080 q^{82} + 72 q^{83} + 4536 q^{85} + 1296 q^{86} - 474 q^{87} - 234 q^{89} + 1296 q^{90} + 224 q^{92} + 108 q^{93} + 288 q^{94} + 1296 q^{95} + 768 q^{96} + 936 q^{97} - 900 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 3 * q^3 - 8 * q^4 - 18 * q^5 + 24 * q^6 - 9 * q^9 - 72 * q^10 + 50 * q^11 - 24 * q^12 - 72 * q^13 + 108 * q^15 + 64 * q^16 - 126 * q^17 - 36 * q^18 + 72 * q^19 + 288 * q^20 - 400 * q^22 - 14 * q^23 - 199 * q^25 + 144 * q^26 + 54 * q^27 + 316 * q^29 - 216 * q^30 + 36 * q^31 + 256 * q^32 + 150 * q^33 + 1008 * q^34 + 144 * q^36 + 162 * q^37 + 288 * q^38 + 108 * q^39 - 540 * q^41 - 648 * q^43 + 400 * q^44 - 162 * q^45 - 56 * q^46 + 72 * q^47 - 384 * q^48 + 1592 * q^50 - 378 * q^51 + 288 * q^52 + 22 * q^53 - 108 * q^54 - 1800 * q^55 - 432 * q^57 - 632 * q^58 - 468 * q^59 - 432 * q^60 - 792 * q^61 - 288 * q^62 - 1024 * q^64 + 648 * q^65 + 600 * q^66 - 232 * q^67 - 1008 * q^68 + 84 * q^69 - 1468 * q^71 - 180 * q^73 + 648 * q^74 - 597 * q^75 - 1152 * q^76 - 864 * q^78 - 236 * q^79 + 1152 * q^80 - 81 * q^81 + 1080 * q^82 + 72 * q^83 + 4536 * q^85 + 1296 * q^86 - 474 * q^87 - 234 * q^89 + 1296 * q^90 + 224 * q^92 + 108 * q^93 + 288 * q^94 + 1296 * q^95 + 768 * q^96 + 936 * q^97 - 900 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.00000	−	3.46410i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−2.00000	−	3.46410i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−4.00000	+	6.92820i	−0.500000	+	0.866025i
$5$	−9.00000	−	15.5885i	−0.804984	−	1.39427i	−0.916302	−	0.400489i	$-0.868840\pi$
$5$	−9.00000	−	15.5885i	−0.804984	−	1.39427i	0.111317	−	0.993785i	$-0.464493\pi$
$6$	12.0000			0.816497
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−36.0000	+	62.3538i	−1.13842	+	1.97180i
$11$	25.0000	−	43.3013i	0.685253	−	1.18689i	−0.288104	−	0.957599i	$-0.593025\pi$
$11$	25.0000	−	43.3013i	0.685253	−	1.18689i	0.973357	−	0.229294i	$-0.0736417\pi$
$12$	−12.0000	−	20.7846i	−0.288675	−	0.500000i
$13$	−36.0000			−0.768046			−0.384023	−	0.923323i	$-0.625462\pi$
$13$	−36.0000			−0.768046			−0.384023	+	0.923323i	$0.625462\pi$
$14$		0			0
$15$	54.0000			0.929516
$16$	32.0000	+	55.4256i	0.500000	+	0.866025i
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.0697893	+	0.997562i	$0.522233\pi$
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.829019	+	0.559220i	$0.811101\pi$
$18$	−18.0000	+	31.1769i	−0.235702	+	0.408248i
$19$	36.0000	+	62.3538i	0.434682	+	0.752892i	0.997270	−	0.0738459i	$-0.0235273\pi$
$19$	36.0000	+	62.3538i	0.434682	+	0.752892i	−0.562587	+	0.826738i	$0.690194\pi$
$20$	144.000			1.60997
$21$		0			0
$22$	−200.000			−1.93819
$23$	−7.00000	−	12.1244i	−0.0634609	−	0.109918i	0.832549	−	0.553951i	$-0.186880\pi$
$23$	−7.00000	−	12.1244i	−0.0634609	−	0.109918i	−0.896010	+	0.444033i	$0.853547\pi$
$24$		0			0
$25$	−99.5000	+	172.339i	−0.796000	+	1.37871i
$26$	72.0000	+	124.708i	0.543091	+	0.940661i
$27$	27.0000			0.192450
$28$		0			0
$29$	158.000			1.01172			0.505860	−	0.862616i	$-0.331175\pi$
$29$	158.000			1.01172			0.505860	+	0.862616i	$0.331175\pi$
$30$	−108.000	−	187.061i	−0.657267	−	1.13842i
$31$	18.0000	−	31.1769i	0.104287	−	0.180630i	−0.809160	−	0.587589i	$-0.800077\pi$
$31$	18.0000	−	31.1769i	0.104287	−	0.180630i	0.913447	+	0.406958i	$0.133411\pi$
$32$	128.000	−	221.703i	0.707107	−	1.22474i
$33$	75.0000	+	129.904i	0.395631	+	0.685253i
$34$	504.000			2.54221
$35$		0			0
$36$	72.0000			0.333333
$37$	81.0000	+	140.296i	0.359900	+	0.623366i	0.987944	−	0.154812i	$-0.0494773\pi$
$37$	81.0000	+	140.296i	0.359900	+	0.623366i	−0.628043	+	0.778178i	$0.716144\pi$
$38$	144.000	−	249.415i	0.614734	−	1.06475i
$39$	54.0000	−	93.5307i	0.221716	−	0.384023i
$40$		0			0
$41$	−270.000			−1.02846			−0.514231	−	0.857652i	$-0.671922\pi$
$41$	−270.000			−1.02846			−0.514231	+	0.857652i	$0.671922\pi$
$42$		0			0
$43$	−324.000			−1.14906			−0.574529	−	0.818484i	$-0.694815\pi$
$43$	−324.000			−1.14906			−0.574529	+	0.818484i	$0.694815\pi$
$44$	200.000	+	346.410i	0.685253	+	1.18689i
$45$	−81.0000	+	140.296i	−0.268328	+	0.464758i
$46$	−28.0000	+	48.4974i	−0.0897473	+	0.155447i
$47$	36.0000	+	62.3538i	0.111726	+	0.193516i	0.916466	−	0.400112i	$-0.131029\pi$
$47$	36.0000	+	62.3538i	0.111726	+	0.193516i	−0.804740	+	0.593627i	$0.797695\pi$
$48$	−192.000			−0.577350
$49$		0			0
$50$	796.000			2.25143
$51$	−189.000	−	327.358i	−0.518927	−	0.898808i
$52$	144.000	−	249.415i	0.384023	−	0.665148i
$53$	11.0000	−	19.0526i	0.0285088	−	0.0493787i	−0.851419	−	0.524486i	$-0.824257\pi$
$53$	11.0000	−	19.0526i	0.0285088	−	0.0493787i	0.879928	+	0.475107i	$0.157591\pi$
$54$	−54.0000	−	93.5307i	−0.136083	−	0.235702i
$55$	−900.000			−2.20647
$56$		0			0
$57$	−216.000			−0.501928
$58$	−316.000	−	547.328i	−0.715394	−	1.23910i
$59$	−234.000	+	405.300i	−0.516342	+	0.894331i	0.483478	+	0.875357i	$0.339373\pi$
$59$	−234.000	+	405.300i	−0.516342	+	0.894331i	−0.999820	+	0.0189746i	$0.993960\pi$
$60$	−216.000	+	374.123i	−0.464758	+	0.804984i
$61$	−396.000	−	685.892i	−0.831190	−	1.43966i	−0.897095	−	0.441838i	$-0.854327\pi$
$61$	−396.000	−	685.892i	−0.831190	−	1.43966i	0.0659047	−	0.997826i	$-0.479007\pi$
$62$	−144.000			−0.294968
$63$		0			0
$64$	−512.000			−1.00000
$65$	324.000	+	561.184i	0.618265	+	1.07087i
$66$	300.000	−	519.615i	0.559507	−	0.969094i
$67$	−116.000	+	200.918i	−0.211517	+	0.366359i	−0.952190	−	0.305508i	$-0.901174\pi$
$67$	−116.000	+	200.918i	−0.211517	+	0.366359i	0.740672	+	0.671866i	$0.234507\pi$
$68$	−504.000	−	872.954i	−0.898808	−	1.55678i
$69$	42.0000			0.0732783
$70$		0			0
$71$	−734.000			−1.22690			−0.613449	−	0.789734i	$-0.710218\pi$
$71$	−734.000			−1.22690			−0.613449	+	0.789734i	$0.710218\pi$
$72$		0			0
$73$	−90.0000	+	155.885i	−0.144297	+	0.249930i	−0.929111	−	0.369802i	$-0.879425\pi$
$73$	−90.0000	+	155.885i	−0.144297	+	0.249930i	0.784813	+	0.619732i	$0.212759\pi$
$74$	324.000	−	561.184i	0.508976	−	0.881573i
$75$	−298.500	−	517.017i	−0.459571	−	0.796000i
$76$	−576.000			−0.869365
$77$		0			0
$78$	−432.000			−0.627107
$79$	−118.000	−	204.382i	−0.168051	−	0.291073i	0.769683	−	0.638426i	$-0.220414\pi$
$79$	−118.000	−	204.382i	−0.168051	−	0.291073i	−0.937735	+	0.347353i	$0.887081\pi$
$80$	576.000	−	997.661i	0.804984	−	1.39427i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	540.000	+	935.307i	0.727232	+	1.25960i
$83$	36.0000			0.0476086			0.0238043	−	0.999717i	$-0.492422\pi$
$83$	36.0000			0.0476086			0.0238043	+	0.999717i	$0.492422\pi$
$84$		0			0
$85$	2268.00			2.89411
$86$	648.000	+	1122.37i	0.812507	+	1.40730i
$87$	−237.000	+	410.496i	−0.292058	+	0.505860i
$88$		0			0
$89$	−117.000	−	202.650i	−0.139348	−	0.241358i	0.787902	−	0.615801i	$-0.211167\pi$
$89$	−117.000	−	202.650i	−0.139348	−	0.241358i	−0.927250	+	0.374443i	$0.877834\pi$
$90$	648.000			0.758947
$91$		0			0
$92$	112.000			0.126922
$93$	54.0000	+	93.5307i	0.0602101	+	0.104287i
$94$	144.000	−	249.415i	0.158005	−	0.273673i
$95$	648.000	−	1122.37i	0.699825	−	1.21213i
$96$	384.000	+	665.108i	0.408248	+	0.707107i
$97$	468.000			0.489878			0.244939	−	0.969538i	$-0.421232\pi$
$97$	468.000			0.489878			0.244939	+	0.969538i	$0.421232\pi$
$98$		0			0
$99$	−450.000			−0.456835
$100$	−796.000	−	1378.71i	−0.796000	−	1.37871i
$101$	333.000	−	576.773i	0.328067	−	0.568228i	−0.654061	−	0.756441i	$-0.726936\pi$
$101$	333.000	−	576.773i	0.328067	−	0.568228i	0.982128	+	0.188213i	$0.0602696\pi$
$102$	−756.000	+	1309.43i	−0.733874	+	1.27111i
$103$	126.000	+	218.238i	0.120535	+	0.208773i	0.919979	−	0.391968i	$-0.128206\pi$
$103$	126.000	+	218.238i	0.120535	+	0.208773i	−0.799444	+	0.600741i	$0.794872\pi$
$104$		0			0
$105$		0			0
$106$	−88.0000			−0.0806351
$107$	−335.000	−	580.237i	−0.302670	−	0.524240i	0.674070	−	0.738668i	$-0.264545\pi$
$107$	−335.000	−	580.237i	−0.302670	−	0.524240i	−0.976740	+	0.214428i	$0.931211\pi$
$108$	−108.000	+	187.061i	−0.0962250	+	0.166667i
$109$	−81.0000	+	140.296i	−0.0711779	+	0.123284i	−0.899418	−	0.437090i	$-0.856009\pi$
$109$	−81.0000	+	140.296i	−0.0711779	+	0.123284i	0.828240	+	0.560374i	$0.189342\pi$
$110$	1800.00	+	3117.69i	1.56021	+	2.70237i
$111$	−486.000			−0.415577
$112$		0			0
$113$	−1390.00			−1.15717			−0.578585	−	0.815622i	$-0.696395\pi$
$113$	−1390.00			−1.15717			−0.578585	+	0.815622i	$0.696395\pi$
$114$	432.000	+	748.246i	0.354917	+	0.614734i
$115$	−126.000	+	218.238i	−0.102170	+	0.176964i
$116$	−632.000	+	1094.66i	−0.505860	+	0.876175i
$117$	162.000	+	280.592i	0.128008	+	0.221716i
$118$	1872.00			1.46044
$119$		0			0
$120$		0			0
$121$	−584.500	−	1012.38i	−0.439144	−	0.760619i
$122$	−1584.00	+	2743.57i	−1.17548	+	2.03599i
$123$	405.000	−	701.481i	0.296891	−	0.514231i
$124$	144.000	+	249.415i	0.104287	+	0.180630i
$125$	1332.00			0.953102
$126$		0			0
$127$	916.000			0.640015			0.320007	−	0.947415i	$-0.396315\pi$
$127$	916.000			0.640015			0.320007	+	0.947415i	$0.396315\pi$
$128$		0			0
$129$	486.000	−	841.777i	0.331705	−	0.574529i
$130$	1296.00	−	2244.74i	0.874359	−	1.51443i
$131$	−1134.00	−	1964.15i	−0.756321	−	1.30999i	−0.944715	−	0.327893i	$-0.893662\pi$
$131$	−1134.00	−	1964.15i	−0.756321	−	1.30999i	0.188394	−	0.982094i	$-0.439672\pi$
$132$	−1200.00			−0.791262
$133$		0			0
$134$	928.000			0.598261
$135$	−243.000	−	420.888i	−0.154919	−	0.268328i
$136$		0			0
$137$	−403.000	+	698.016i	−0.251318	+	0.435296i	−0.963889	−	0.266304i	$-0.914197\pi$
$137$	−403.000	+	698.016i	−0.251318	+	0.435296i	0.712571	+	0.701600i	$0.247531\pi$
$138$	−84.0000	−	145.492i	−0.0518156	−	0.0897473i
$139$	2628.00			1.60363			0.801813	−	0.597575i	$-0.203869\pi$
$139$	2628.00			1.60363			0.801813	+	0.597575i	$0.203869\pi$
$140$		0			0
$141$	−216.000			−0.129011
$142$	1468.00	+	2542.65i	0.867548	+	1.50264i
$143$	−900.000	+	1558.85i	−0.526306	+	0.911589i
$144$	288.000	−	498.831i	0.166667	−	0.288675i
$145$	−1422.00	−	2462.98i	−0.814418	−	1.41061i
$146$	720.000			0.408134
$147$		0			0
$148$	−1296.00			−0.719801
$149$	1195.00	+	2069.80i	0.657035	+	1.13802i	0.981379	+	0.192079i	$0.0615230\pi$
$149$	1195.00	+	2069.80i	0.657035	+	1.13802i	−0.324344	+	0.945939i	$0.605144\pi$
$150$	−1194.00	+	2068.07i	−0.649931	+	1.12571i
$151$	−1620.00	+	2805.92i	−0.873071	+	1.51220i	−0.0142676	+	0.999898i	$0.504542\pi$
$151$	−1620.00	+	2805.92i	−0.873071	+	1.51220i	−0.858803	+	0.512305i	$0.828792\pi$
$152$		0			0
$153$	1134.00			0.599206
$154$		0			0
$155$	−648.000			−0.335798
$156$	432.000	+	748.246i	0.221716	+	0.384023i
$157$	−1512.00	+	2618.86i	−0.768603	+	1.33126i	0.169717	+	0.985493i	$0.445715\pi$
$157$	−1512.00	+	2618.86i	−0.768603	+	1.33126i	−0.938320	+	0.345767i	$0.887619\pi$
$158$	−472.000	+	817.528i	−0.237660	+	0.411639i
$159$	33.0000	+	57.1577i	0.0164596	+	0.0285088i
$160$	−4608.00			−2.27684
$161$		0			0
$162$	324.000			0.157135
$163$	892.000	+	1544.99i	0.428631	+	0.742410i	0.996752	−	0.0805346i	$-0.0256628\pi$
$163$	892.000	+	1544.99i	0.428631	+	0.742410i	−0.568121	+	0.822945i	$0.692329\pi$
$164$	1080.00	−	1870.61i	0.514231	−	0.890674i
$165$	1350.00	−	2338.27i	0.636954	−	1.10324i
$166$	−72.0000	−	124.708i	−0.0336644	−	0.0583084i
$167$	−3024.00			−1.40122			−0.700611	−	0.713543i	$-0.747089\pi$
$167$	−3024.00			−1.40122			−0.700611	+	0.713543i	$0.747089\pi$
$168$		0			0
$169$	−901.000			−0.410105
$170$	−4536.00	−	7856.58i	−2.04644	−	3.54454i
$171$	324.000	−	561.184i	0.144894	−	0.250964i
$172$	1296.00	−	2244.74i	0.574529	−	0.995114i
$173$	−783.000	−	1356.20i	−0.344106	−	0.596010i	0.641085	−	0.767470i	$-0.278485\pi$
$173$	−783.000	−	1356.20i	−0.344106	−	0.596010i	−0.985191	+	0.171461i	$0.945151\pi$
$174$	1896.00			0.826065
$175$		0			0
$176$	3200.00			1.37051
$177$	−702.000	−	1215.90i	−0.298110	−	0.516342i
$178$	−468.000	+	810.600i	−0.197068	+	0.341332i
$179$	−1901.00	+	3292.63i	−0.793784	+	1.37487i	0.129824	+	0.991537i	$0.458559\pi$
$179$	−1901.00	+	3292.63i	−0.793784	+	1.37487i	−0.923608	+	0.383338i	$0.874774\pi$
$180$	−648.000	−	1122.37i	−0.268328	−	0.464758i
$181$	−468.000			−0.192189			−0.0960944	−	0.995372i	$-0.530635\pi$
$181$	−468.000			−0.192189			−0.0960944	+	0.995372i	$0.530635\pi$
$182$		0			0
$183$	2376.00			0.959776
$184$		0			0
$185$	1458.00	−	2525.33i	0.579429	−	1.00360i
$186$	216.000	−	374.123i	0.0851499	−	0.147484i
$187$	3150.00	+	5455.96i	1.23182	+	2.13358i
$188$	−576.000			−0.223453
$189$		0			0
$190$	−5184.00			−1.97940
$191$	−241.000	−	417.424i	−0.0912992	−	0.158135i	0.816759	−	0.576979i	$-0.195769\pi$
$191$	−241.000	−	417.424i	−0.0912992	−	0.158135i	−0.908058	+	0.418844i	$0.862435\pi$
$192$	768.000	−	1330.22i	0.288675	−	0.500000i
$193$	405.000	−	701.481i	0.151049	−	0.261625i	−0.780564	−	0.625076i	$-0.785068\pi$
$193$	405.000	−	701.481i	0.151049	−	0.261625i	0.931614	+	0.363450i	$0.118401\pi$
$194$	−936.000	−	1621.20i	−0.346396	−	0.599976i
$195$	−1944.00			−0.713911
$196$		0			0
$197$	−2462.00			−0.890407			−0.445204	−	0.895429i	$-0.646869\pi$
$197$	−2462.00			−0.890407			−0.445204	+	0.895429i	$0.646869\pi$
$198$	900.000	+	1558.85i	0.323031	+	0.559507i
$199$	2268.00	−	3928.29i	0.807911	−	1.39934i	−0.106397	−	0.994324i	$-0.533932\pi$
$199$	2268.00	−	3928.29i	0.807911	−	1.39934i	0.914308	−	0.405019i	$-0.132735\pi$
$200$		0			0
$201$	−348.000	−	602.754i	−0.122120	−	0.211517i
$202$	−2664.00			−0.927913
$203$		0			0
$204$	3024.00			1.03785
$205$	2430.00	+	4208.88i	0.827895	+	1.43396i
$206$	504.000	−	872.954i	0.170463	−	0.295250i
$207$	−63.0000	+	109.119i	−0.0211536	+	0.0366392i
$208$	−1152.00	−	1995.32i	−0.384023	−	0.665148i
$209$	3600.00			1.19147
$210$		0			0
$211$	2916.00			0.951402			0.475701	−	0.879607i	$-0.342195\pi$
$211$	2916.00			0.951402			0.475701	+	0.879607i	$0.342195\pi$
$212$	88.0000	+	152.420i	0.0285088	+	0.0493787i
$213$	1101.00	−	1906.99i	0.354175	−	0.613449i
$214$	−1340.00	+	2320.95i	−0.428040	+	0.741387i
$215$	2916.00	+	5050.66i	0.924975	+	1.60210i
$216$		0			0
$217$		0			0
$218$	648.000			0.201322
$219$	−270.000	−	467.654i	−0.0833101	−	0.144297i
$220$	3600.00	−	6235.38i	1.10324	−	1.91086i
$221$	2268.00	−	3928.29i	0.690327	−	1.19568i
$222$	972.000	+	1683.55i	0.293858	+	0.508976i
$223$	−1080.00			−0.324315			−0.162157	−	0.986765i	$-0.551845\pi$
$223$	−1080.00			−0.324315			−0.162157	+	0.986765i	$0.551845\pi$
$224$		0			0
$225$	1791.00			0.530667
$226$	2780.00	+	4815.10i	0.818243	+	1.41724i
$227$	666.000	−	1153.55i	0.194731	−	0.337284i	−0.752081	−	0.659070i	$-0.770950\pi$
$227$	666.000	−	1153.55i	0.194731	−	0.337284i	0.946812	+	0.321786i	$0.104283\pi$
$228$	864.000	−	1496.49i	0.250964	−	0.434682i
$229$	−810.000	−	1402.96i	−0.233739	−	0.404848i	0.725166	−	0.688574i	$-0.241763\pi$
$229$	−810.000	−	1402.96i	−0.233739	−	0.404848i	−0.958906	+	0.283725i	$0.908430\pi$
$230$	1008.00			0.288981
$231$		0			0
$232$		0			0
$233$	−3359.00	−	5817.96i	−0.944444	−	1.63582i	−0.756861	−	0.653576i	$-0.773268\pi$
$233$	−3359.00	−	5817.96i	−0.944444	−	1.63582i	−0.187583	−	0.982249i	$-0.560065\pi$
$234$	648.000	−	1122.37i	0.181030	−	0.313554i
$235$	648.000	−	1122.37i	0.179876	−	0.311554i
$236$	−1872.00	−	3242.40i	−0.516342	−	0.894331i
$237$	708.000			0.194049
$238$		0			0
$239$	−3578.00			−0.968375			−0.484187	−	0.874964i	$-0.660885\pi$
$239$	−3578.00			−0.968375			−0.484187	+	0.874964i	$0.660885\pi$
$240$	1728.00	+	2992.98i	0.464758	+	0.804984i
$241$	378.000	−	654.715i	0.101034	−	0.174995i	−0.811077	−	0.584939i	$-0.801118\pi$
$241$	378.000	−	654.715i	0.101034	−	0.174995i	0.912111	+	0.409944i	$0.134452\pi$
$242$	−2338.00	+	4049.53i	−0.621043	+	1.07568i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	6336.00			1.66238
$245$		0			0
$246$	−3240.00			−0.839735
$247$	−1296.00	−	2244.74i	−0.333856	−	0.578256i
$248$		0			0
$249$	−54.0000	+	93.5307i	−0.0137434	+	0.0238043i
$250$	−2664.00	−	4614.18i	−0.673945	−	1.16731i
$251$	−6516.00			−1.63859			−0.819295	−	0.573372i	$-0.805635\pi$
$251$	−6516.00			−1.63859			−0.819295	+	0.573372i	$0.805635\pi$
$252$		0			0
$253$	−700.000			−0.173947
$254$	−1832.00	−	3173.12i	−0.452559	−	0.783855i
$255$	−3402.00	+	5892.44i	−0.835457	+	1.44705i
$256$	−2048.00	+	3547.24i	−0.500000	+	0.866025i
$257$	3015.00	+	5222.13i	0.731792	+	1.26750i	0.956117	+	0.292986i	$0.0946491\pi$
$257$	3015.00	+	5222.13i	0.731792	+	1.26750i	−0.224325	+	0.974514i	$0.572018\pi$
$258$	−3888.00			−0.938203
$259$		0			0
$260$	−5184.00			−1.23653
$261$	−711.000	−	1231.49i	−0.168620	−	0.292058i
$262$	−4536.00	+	7856.58i	−1.06960	+	1.85260i
$263$	−295.000	+	510.955i	−0.0691653	+	0.119798i	−0.898534	−	0.438904i	$-0.855367\pi$
$263$	−295.000	+	510.955i	−0.0691653	+	0.119798i	0.829369	+	0.558702i	$0.188700\pi$
$264$		0			0
$265$	−396.000			−0.0917966
$266$		0			0
$267$	702.000			0.160905
$268$	−928.000	−	1607.34i	−0.211517	−	0.366359i
$269$	495.000	−	857.365i	0.112196	−	0.194329i	−0.804459	−	0.594008i	$-0.797545\pi$
$269$	495.000	−	857.365i	0.112196	−	0.194329i	0.916655	+	0.399679i	$0.130878\pi$
$270$	−972.000	+	1683.55i	−0.219089	+	0.379473i
$271$	1710.00	+	2961.81i	0.383303	+	0.663900i	0.991532	−	0.129861i	$-0.0414532\pi$
$271$	1710.00	+	2961.81i	0.383303	+	0.663900i	−0.608229	+	0.793761i	$0.708120\pi$
$272$	−8064.00			−1.79762
$273$		0			0
$274$	3224.00			0.710836
$275$	4975.00	+	8616.95i	1.09092	+	1.88953i
$276$	−168.000	+	290.985i	−0.0366392	+	0.0634609i
$277$	1367.00	−	2367.71i	0.296516	−	0.513582i	−0.678820	−	0.734305i	$-0.737508\pi$
$277$	1367.00	−	2367.71i	0.296516	−	0.513582i	0.975337	+	0.220723i	$0.0708417\pi$
$278$	−5256.00	−	9103.66i	−1.13394	−	1.96403i
$279$	−324.000			−0.0695246
$280$		0			0
$281$	598.000			0.126953			0.0634763	−	0.997983i	$-0.479781\pi$
$281$	598.000			0.126953			0.0634763	+	0.997983i	$0.479781\pi$
$282$	432.000	+	748.246i	0.0912242	+	0.158005i
$283$	−1800.00	+	3117.69i	−0.378088	+	0.654868i	−0.990784	−	0.135451i	$-0.956752\pi$
$283$	−1800.00	+	3117.69i	−0.378088	+	0.654868i	0.612696	+	0.790319i	$0.290085\pi$
$284$	2936.00	−	5085.30i	0.613449	−	1.06253i
$285$	1944.00	+	3367.11i	0.404044	+	0.699825i
$286$	7200.00			1.48862
$287$		0			0
$288$	−2304.00			−0.471405
$289$	−5481.50	−	9494.24i	−1.11571	−	1.93247i
$290$	−5688.00	+	9851.90i	−1.15176	+	1.99491i
$291$	−702.000	+	1215.90i	−0.141416	+	0.244939i
$292$	−720.000	−	1247.08i	−0.144297	−	0.249930i
$293$	7902.00			1.57556			0.787781	−	0.615955i	$-0.211230\pi$
$293$	7902.00			1.57556			0.787781	+	0.615955i	$0.211230\pi$
$294$		0			0
$295$	8424.00			1.66259
$296$		0			0
$297$	675.000	−	1169.13i	0.131877	−	0.228418i
$298$	4780.00	−	8279.20i	0.929188	−	1.60940i
$299$	252.000	+	436.477i	0.0487409	+	0.0844218i
$300$	4776.00			0.919142
$301$		0			0
$302$	12960.0			2.46942
$303$	999.000	+	1730.32i	0.189409	+	0.328067i
$304$	−2304.00	+	3990.65i	−0.434682	+	0.752892i
$305$	−7128.00	+	12346.1i	−1.33819	+	2.31781i
$306$	−2268.00	−	3928.29i	−0.423702	−	0.733874i
$307$	−10224.0			−1.90070			−0.950349	−	0.311185i	$-0.899274\pi$
$307$	−10224.0			−1.90070			−0.950349	+	0.311185i	$0.899274\pi$
$308$		0			0
$309$	−756.000			−0.139182
$310$	1296.00	+	2244.74i	0.237445	+	0.411266i
$311$	−1944.00	+	3367.11i	−0.354451	+	0.613926i	−0.987024	−	0.160574i	$-0.948665\pi$
$311$	−1944.00	+	3367.11i	−0.354451	+	0.613926i	0.632573	+	0.774501i	$0.281999\pi$
$312$		0			0
$313$	−2556.00	−	4427.12i	−0.461577	−	0.799475i	0.537463	−	0.843288i	$-0.319383\pi$
$313$	−2556.00	−	4427.12i	−0.461577	−	0.799475i	−0.999040	+	0.0438124i	$0.986050\pi$
$314$	12096.0			2.17394
$315$		0			0
$316$	1888.00			0.336102
$317$	5051.00	+	8748.59i	0.894929	+	1.55006i	0.833893	+	0.551927i	$0.186107\pi$
$317$	5051.00	+	8748.59i	0.894929	+	1.55006i	0.0610361	+	0.998136i	$0.480560\pi$
$318$	132.000	−	228.631i	0.0232773	−	0.0403175i
$319$	3950.00	−	6841.60i	0.693284	−	1.20080i
$320$	4608.00	+	7981.29i	0.804984	+	1.39427i
$321$	2010.00			0.349493
$322$		0			0
$323$	−9072.00			−1.56279
$324$	−324.000	−	561.184i	−0.0555556	−	0.0962250i
$325$	3582.00	−	6204.21i	0.611365	−	1.05892i
$326$	3568.00	−	6179.96i	0.606176	−	1.04993i
$327$	−243.000	−	420.888i	−0.0410946	−	0.0711779i
$328$		0			0
$329$		0			0
$330$	−10800.0			−1.80158
$331$	−2754.00	−	4770.07i	−0.457322	−	0.792105i	0.541497	−	0.840703i	$-0.317858\pi$
$331$	−2754.00	−	4770.07i	−0.457322	−	0.792105i	−0.998818	+	0.0485983i	$0.984525\pi$
$332$	−144.000	+	249.415i	−0.0238043	+	0.0412303i
$333$	729.000	−	1262.67i	0.119967	−	0.207789i
$334$	6048.00	+	10475.4i	0.990814	+	1.71614i
$335$	4176.00			0.681072
$336$		0			0
$337$	−9234.00			−1.49261			−0.746303	−	0.665607i	$-0.768173\pi$
$337$	−9234.00			−1.49261			−0.746303	+	0.665607i	$0.768173\pi$
$338$	1802.00	+	3121.16i	0.289988	+	0.502274i
$339$	2085.00	−	3611.33i	0.334046	−	0.578585i
$340$	−9072.00	+	15713.2i	−1.44705	+	2.50637i
$341$	−900.000	−	1558.85i	−0.142926	−	0.247555i
$342$	−2592.00			−0.409823
$343$		0			0
$344$		0			0
$345$	−378.000	−	654.715i	−0.0589879	−	0.102170i
$346$	−3132.00	+	5424.78i	−0.486640	+	0.842885i
$347$	3247.00	−	5623.97i	0.502329	−	0.870059i	−0.497668	−	0.867368i	$-0.665810\pi$
$347$	3247.00	−	5623.97i	0.502329	−	0.870059i	0.999996	−	0.00269115i	$-0.000856622\pi$
$348$	−1896.00	−	3283.97i	−0.292058	−	0.505860i
$349$	10080.0			1.54605			0.773023	−	0.634378i	$-0.218744\pi$
$349$	10080.0			1.54605			0.773023	+	0.634378i	$0.218744\pi$
$350$		0			0
$351$	−972.000			−0.147811
$352$	−6400.00	−	11085.1i	−0.969094	−	1.67852i
$353$	369.000	−	639.127i	0.0556371	−	0.0963662i	−0.836865	−	0.547409i	$-0.815614\pi$
$353$	369.000	−	639.127i	0.0556371	−	0.0963662i	0.892503	+	0.451042i	$0.148948\pi$
$354$	−2808.00	+	4863.60i	−0.421592	+	0.730219i
$355$	6606.00	+	11441.9i	0.987634	+	1.71063i
$356$	1872.00			0.278696
$357$		0			0
$358$	15208.0			2.24516
$359$	−97.0000	−	168.009i	−0.0142603	−	0.0246996i	0.858807	−	0.512299i	$-0.171206\pi$
$359$	−97.0000	−	168.009i	−0.0142603	−	0.0246996i	−0.873068	+	0.487599i	$0.837873\pi$
$360$		0			0
$361$	837.500	−	1450.59i	0.122102	−	0.211487i
$362$	936.000	+	1621.20i	0.135898	+	0.235382i
$363$	3507.00			0.507079
$364$		0			0
$365$	3240.00			0.464628
$366$	−4752.00	−	8230.71i	−0.678664	−	1.17548i
$367$	2376.00	−	4115.35i	0.337946	−	0.585340i	−0.646100	−	0.763253i	$-0.723601\pi$
$367$	2376.00	−	4115.35i	0.337946	−	0.585340i	0.984046	+	0.177913i	$0.0569345\pi$
$368$	448.000	−	775.959i	0.0634609	−	0.109918i
$369$	1215.00	+	2104.44i	0.171410	+	0.296891i
$370$	−11664.0			−1.63887
$371$		0			0
$372$	−864.000			−0.120420
$373$	1153.00	+	1997.05i	0.160054	+	0.277221i	0.934888	−	0.354943i	$-0.115500\pi$
$373$	1153.00	+	1997.05i	0.160054	+	0.277221i	−0.774834	+	0.632165i	$0.782167\pi$
$374$	12600.0	−	21823.8i	1.74206	−	3.01734i
$375$	−1998.00	+	3460.64i	−0.275137	+	0.476551i
$376$		0			0
$377$	−5688.00			−0.777047
$378$		0			0
$379$	−7452.00			−1.00998			−0.504991	−	0.863124i	$-0.668504\pi$
$379$	−7452.00			−1.00998			−0.504991	+	0.863124i	$0.668504\pi$
$380$	5184.00	+	8978.95i	0.699825	+	1.21213i
$381$	−1374.00	+	2379.84i	−0.184756	+	0.320007i
$382$	−964.000	+	1669.70i	−0.129117	+	0.223636i
$383$	576.000	+	997.661i	0.0768465	+	0.133102i	0.901888	−	0.431970i	$-0.142182\pi$
$383$	576.000	+	997.661i	0.0768465	+	0.133102i	−0.825041	+	0.565073i	$0.808848\pi$
$384$		0			0
$385$		0			0
$386$	−3240.00			−0.427232
$387$	1458.00	+	2525.33i	0.191510	+	0.331705i
$388$	−1872.00	+	3242.40i	−0.244939	+	0.424247i
$389$	−947.000	+	1640.25i	−0.123431	+	0.213789i	−0.921119	−	0.389282i	$-0.872723\pi$
$389$	−947.000	+	1640.25i	−0.123431	+	0.213789i	0.797687	+	0.603071i	$0.206057\pi$
$390$	3888.00	+	6734.21i	0.504812	+	0.874359i
$391$	1764.00			0.228157
$392$		0			0
$393$	6804.00			0.873324
$394$	4924.00	+	8528.62i	0.629613	+	1.09052i
$395$	−2124.00	+	3678.88i	−0.270557	+	0.468619i
$396$	1800.00	−	3117.69i	0.228418	−	0.395631i
$397$	−4608.00	−	7981.29i	−0.582541	−	1.00899i	−0.995177	−	0.0980950i	$-0.968725\pi$
$397$	−4608.00	−	7981.29i	−0.582541	−	1.00899i	0.412636	−	0.910896i	$-0.364608\pi$
$398$	−18144.0			−2.28512
$399$		0			0
$400$	−12736.0			−1.59200
$401$	5825.00	+	10089.2i	0.725403	+	1.25643i	0.958808	+	0.284055i	$0.0916799\pi$
$401$	5825.00	+	10089.2i	0.725403	+	1.25643i	−0.233405	+	0.972380i	$0.574987\pi$
$402$	−1392.00	+	2411.01i	−0.172703	+	0.299131i
$403$	−648.000	+	1122.37i	−0.0800972	+	0.138732i
$404$	2664.00	+	4614.18i	0.328067	+	0.568228i
$405$	1458.00			0.178885
$406$		0			0
$407$	8100.00			0.986492
$408$		0			0
$409$	3762.00	−	6515.98i	0.454814	−	0.787761i	−0.543863	−	0.839174i	$-0.683039\pi$
$409$	3762.00	−	6515.98i	0.454814	−	0.787761i	0.998677	+	0.0514127i	$0.0163724\pi$
$410$	9720.00	−	16835.5i	1.17082	−	2.02792i
$411$	−1209.00	−	2094.05i	−0.145099	−	0.251318i
$412$	−2016.00			−0.241071
$413$		0			0
$414$	504.000			0.0598315
$415$	−324.000	−	561.184i	−0.0383242	−	0.0663794i
$416$	−4608.00	+	7981.29i	−0.543091	+	0.940661i
$417$	−3942.00	+	6827.74i	−0.462927	+	0.801813i
$418$	−7200.00	−	12470.8i	−0.842496	−	1.45925i
$419$	−3852.00			−0.449123			−0.224561	−	0.974460i	$-0.572095\pi$
$419$	−3852.00			−0.449123			−0.224561	+	0.974460i	$0.572095\pi$
$420$		0			0
$421$	10402.0			1.20419			0.602093	−	0.798426i	$-0.294334\pi$
$421$	10402.0			1.20419			0.602093	+	0.798426i	$0.294334\pi$
$422$	−5832.00	−	10101.3i	−0.672742	−	1.16522i
$423$	324.000	−	561.184i	0.0372421	−	0.0645053i
$424$		0			0
$425$	−12537.0	−	21714.7i	−1.43090	−	2.47840i
$426$	−8808.00			−1.00176
$427$		0			0
$428$	5360.00			0.605340
$429$	−2700.00	−	4676.54i	−0.303863	−	0.526306i
$430$	11664.0	−	20202.6i	1.30811	−	2.26572i
$431$	5195.00	−	8998.00i	0.580590	−	1.00561i	−0.414819	−	0.909904i	$-0.636155\pi$
$431$	5195.00	−	8998.00i	0.580590	−	1.00561i	0.995409	−	0.0957078i	$-0.0305114\pi$
$432$	864.000	+	1496.49i	0.0962250	+	0.166667i
$433$	11232.0			1.24659			0.623297	−	0.781985i	$-0.285793\pi$
$433$	11232.0			1.24659			0.623297	+	0.781985i	$0.285793\pi$
$434$		0			0
$435$	8532.00			0.940409
$436$	−648.000	−	1122.37i	−0.0711779	−	0.123284i
$437$	504.000	−	872.954i	0.0551707	−	0.0955584i
$438$	−1080.00	+	1870.61i	−0.117818	+	0.204067i
$439$	−7308.00	−	12657.8i	−0.794514	−	1.37614i	−0.923147	−	0.384447i	$-0.874392\pi$
$439$	−7308.00	−	12657.8i	−0.794514	−	1.37614i	0.128633	−	0.991692i	$-0.458941\pi$
$440$		0			0
$441$		0			0
$442$	−18144.0			−1.95254
$443$	−5969.00	−	10338.6i	−0.640171	−	1.10881i	−0.985394	−	0.170288i	$-0.945530\pi$
$443$	−5969.00	−	10338.6i	−0.640171	−	1.10881i	0.345223	−	0.938521i	$-0.387803\pi$
$444$	1944.00	−	3367.11i	0.207789	−	0.359900i
$445$	−2106.00	+	3647.70i	−0.224346	+	0.388579i
$446$	2160.00	+	3741.23i	0.229325	+	0.397203i
$447$	−7170.00			−0.758679
$448$		0			0
$449$	8186.00			0.860404			0.430202	−	0.902733i	$-0.358442\pi$
$449$	8186.00			0.860404			0.430202	+	0.902733i	$0.358442\pi$
$450$	−3582.00	−	6204.21i	−0.375238	−	0.649931i
$451$	−6750.00	+	11691.3i	−0.704756	+	1.22067i
$452$	5560.00	−	9630.20i	0.578585	−	1.00214i
$453$	−4860.00	−	8417.77i	−0.504068	−	0.873071i
$454$	−5328.00			−0.550783
$455$		0			0
$456$		0			0
$457$	−1053.00	−	1823.85i	−0.107784	−	0.186687i	0.807088	−	0.590431i	$-0.201042\pi$
$457$	−1053.00	−	1823.85i	−0.107784	−	0.186687i	−0.914872	+	0.403744i	$0.867709\pi$
$458$	−3240.00	+	5611.84i	−0.330557	+	0.572542i
$459$	−1701.00	+	2946.22i	−0.172976	+	0.299603i
$460$	−1008.00	−	1745.91i	−0.102170	−	0.176964i
$461$	9486.00			0.958367			0.479183	−	0.877715i	$-0.340933\pi$
$461$	9486.00			0.958367			0.479183	+	0.877715i	$0.340933\pi$
$462$		0			0
$463$	−12652.0			−1.26995			−0.634977	−	0.772531i	$-0.718990\pi$
$463$	−12652.0			−1.26995			−0.634977	+	0.772531i	$0.718990\pi$
$464$	5056.00	+	8757.25i	0.505860	+	0.876175i
$465$	972.000	−	1683.55i	0.0969364	−	0.167899i
$466$	−13436.0	+	23271.8i	−1.33565	+	2.31341i
$467$	1854.00	+	3211.22i	0.183711	+	0.318196i	0.943141	−	0.332392i	$-0.107856\pi$
$467$	1854.00	+	3211.22i	0.183711	+	0.318196i	−0.759431	+	0.650588i	$0.774522\pi$
$468$	−2592.00			−0.256015
$469$		0			0
$470$	−5184.00			−0.508766
$471$	−4536.00	−	7856.58i	−0.443753	−	0.768603i
$472$		0			0
$473$	−8100.00	+	14029.6i	−0.787396	+	1.36381i
$474$	−1416.00	−	2452.58i	−0.137213	−	0.237660i
$475$	−14328.0			−1.38403
$476$		0			0
$477$	−198.000			−0.0190059
$478$	7156.00	+	12394.6i	0.684744	+	1.18601i
$479$	4032.00	−	6983.63i	0.384607	−	0.666159i	−0.607108	−	0.794620i	$-0.707670\pi$
$479$	4032.00	−	6983.63i	0.384607	−	0.666159i	0.991715	+	0.128461i	$0.0410036\pi$
$480$	6912.00	−	11971.9i	0.657267	−	1.13842i
$481$	−2916.00	−	5050.66i	−0.276420	−	0.478774i
$482$	−3024.00			−0.285766
$483$		0			0
$484$	9352.00			0.878287
$485$	−4212.00	−	7295.40i	−0.394344	−	0.683025i
$486$	−486.000	+	841.777i	−0.0453609	+	0.0785674i
$487$	5832.00	−	10101.3i	0.542655	−	0.939907i	−0.456095	−	0.889931i	$-0.650752\pi$
$487$	5832.00	−	10101.3i	0.542655	−	0.939907i	0.998750	−	0.0499756i	$-0.0159143\pi$
$488$		0			0
$489$	−5352.00			−0.494940
$490$		0			0
$491$	−9814.00			−0.902036			−0.451018	−	0.892515i	$-0.648939\pi$
$491$	−9814.00			−0.902036			−0.451018	+	0.892515i	$0.648939\pi$
$492$	3240.00	+	5611.84i	0.296891	+	0.514231i
$493$	−9954.00	+	17240.8i	−0.909342	+	1.57503i
$494$	−5184.00	+	8978.95i	−0.472144	+	0.817778i
$495$	4050.00	+	7014.81i	0.367745	+	0.636954i
$496$	2304.00			0.208574
$497$		0			0
$498$	432.000			0.0388723
$499$	7614.00	+	13187.8i	0.683065	+	1.18310i	0.974041	+	0.226373i	$0.0726868\pi$
$499$	7614.00	+	13187.8i	0.683065	+	1.18310i	−0.290976	+	0.956730i	$0.593980\pi$
$500$	−5328.00	+	9228.37i	−0.476551	+	0.825410i
$501$	4536.00	−	7856.58i	0.404498	−	0.700611i
$502$	13032.0	+	22572.1i	1.15866	+	2.00686i
$503$	−11088.0			−0.982882			−0.491441	−	0.870911i	$-0.663530\pi$
$503$	−11088.0			−0.982882			−0.491441	+	0.870911i	$0.663530\pi$
$504$		0			0
$505$	−11988.0			−1.05635
$506$	1400.00	+	2424.87i	0.122999	+	0.213041i
$507$	1351.50	−	2340.87i	0.118387	−	0.205052i
$508$	−3664.00	+	6346.23i	−0.320007	+	0.554269i
$509$	2907.00	+	5035.07i	0.253144	+	0.438459i	0.964390	−	0.264485i	$-0.0852019\pi$
$509$	2907.00	+	5035.07i	0.253144	+	0.438459i	−0.711245	+	0.702944i	$0.751869\pi$
$510$	27216.0			2.36303
$511$		0			0
$512$	16384.0			1.41421
$513$	972.000	+	1683.55i	0.0836547	+	0.144894i
$514$	12060.0	−	20888.5i	1.03491	−	1.79252i
$515$	2268.00	−	3928.29i	0.194058	−	0.336119i
$516$	3888.00	+	6734.21i	0.331705	+	0.574529i
$517$	3600.00			0.306243
$518$		0			0
$519$	4698.00			0.397340
$520$		0			0
$521$	5841.00	−	10116.9i	0.491169	−	0.850729i	−0.508780	−	0.860897i	$-0.669903\pi$
$521$	5841.00	−	10116.9i	0.491169	−	0.850729i	0.999948	+	0.0101677i	$0.00323655\pi$
$522$	−2844.00	+	4925.95i	−0.238465	+	0.413033i
$523$	1494.00	+	2587.68i	0.124910	+	0.216351i	0.921698	−	0.387909i	$-0.126802\pi$
$523$	1494.00	+	2587.68i	0.124910	+	0.216351i	−0.796788	+	0.604259i	$0.793469\pi$
$524$	18144.0			1.51264
$525$		0			0
$526$	2360.00			0.195629
$527$	2268.00	+	3928.29i	0.187468	+	0.324704i
$528$	−4800.00	+	8313.84i	−0.395631	+	0.685253i
$529$	5985.50	−	10367.2i	0.491945	−	0.852074i
$530$	792.000	+	1371.78i	0.0649100	+	0.112427i
$531$	4212.00			0.344228
$532$		0			0
$533$	9720.00			0.789906
$534$	−1404.00	−	2431.80i	−0.113777	−	0.197068i
$535$	−6030.00	+	10444.3i	−0.487289	+	0.844009i
$536$		0			0
$537$	−5703.00	−	9877.89i	−0.458292	−	0.793784i
$538$	−3960.00			−0.317338
$539$		0			0
$540$	3888.00			0.309839
$541$	−3565.00	−	6174.76i	−0.283311	−	0.490709i	0.688887	−	0.724869i	$-0.258100\pi$
$541$	−3565.00	−	6174.76i	−0.283311	−	0.490709i	−0.972198	+	0.234159i	$0.924766\pi$
$542$	6840.00	−	11847.2i	0.542072	−	0.938897i
$543$	702.000	−	1215.90i	0.0554801	−	0.0960944i
$544$	16128.0	+	27934.5i	1.27111	+	2.20162i
$545$	2916.00			0.229188
$546$		0			0
$547$	−5488.00			−0.428976			−0.214488	−	0.976727i	$-0.568808\pi$
$547$	−5488.00			−0.428976			−0.214488	+	0.976727i	$0.568808\pi$
$548$	−3224.00	−	5584.13i	−0.251318	−	0.435296i
$549$	−3564.00	+	6173.03i	−0.277063	+	0.479888i
$550$	19900.0	−	34467.8i	1.54280	−	2.67220i
$551$	5688.00	+	9851.90i	0.439777	+	0.761716i
$552$		0			0
$553$		0			0
$554$	−10936.0			−0.838675
$555$	4374.00	+	7575.99i	0.334533	+	0.579429i
$556$	−10512.0	+	18207.3i	−0.801813	+	1.38878i
$557$	−2873.00	+	4976.18i	−0.218551	+	0.378541i	−0.954365	−	0.298642i	$-0.903466\pi$
$557$	−2873.00	+	4976.18i	−0.218551	+	0.378541i	0.735814	+	0.677183i	$0.236800\pi$
$558$	648.000	+	1122.37i	0.0491613	+	0.0851499i
$559$	11664.0			0.882531
$560$		0			0
$561$	−18900.0			−1.42239
$562$	−1196.00	−	2071.53i	−0.0897691	−	0.155485i
$563$	−6534.00	+	11317.2i	−0.489121	+	0.847183i	−0.999922	−	0.0125165i	$-0.996016\pi$
$563$	−6534.00	+	11317.2i	−0.489121	+	0.847183i	0.510800	+	0.859699i	$0.329349\pi$
$564$	864.000	−	1496.49i	0.0645053	−	0.111726i
$565$	12510.0	+	21668.0i	0.931504	+	1.61341i
$566$	14400.0			1.06939
$567$		0			0
$568$		0			0
$569$	565.000	+	978.609i	0.0416275	+	0.0721009i	0.886088	−	0.463516i	$-0.153412\pi$
$569$	565.000	+	978.609i	0.0416275	+	0.0721009i	−0.844461	+	0.535617i	$0.820079\pi$
$570$	7776.00	−	13468.4i	0.571405	−	0.989702i
$571$	−8432.00	+	14604.7i	−0.617983	+	1.07038i	0.371870	+	0.928285i	$0.378717\pi$
$571$	−8432.00	+	14604.7i	−0.617983	+	1.07038i	−0.989853	+	0.142093i	$0.954617\pi$
$572$	−7200.00	−	12470.8i	−0.526306	−	0.911589i
$573$	1446.00			0.105423
$574$		0			0
$575$	2786.00			0.202060
$576$	2304.00	+	3990.65i	0.166667	+	0.288675i
$577$	1044.00	−	1808.26i	0.0753246	−	0.130466i	−0.825903	−	0.563813i	$-0.809334\pi$
$577$	1044.00	−	1808.26i	0.0753246	−	0.130466i	0.901227	+	0.433347i	$0.142667\pi$
$578$	−21926.0	+	37976.9i	−1.57786	+	2.73293i
$579$	1215.00	+	2104.44i	0.0872084	+	0.151049i
$580$	22752.0			1.62884
$581$		0			0
$582$	5616.00			0.399984
$583$	−550.000	−	952.628i	−0.0390715	−	0.0676738i
$584$		0			0
$585$	2916.00	−	5050.66i	0.206088	−	0.356956i
$586$	−15804.0	−	27373.3i	−1.11409	−	1.92966i
$587$	10260.0			0.721423			0.360712	−	0.932677i	$-0.382534\pi$
$587$	10260.0			0.721423			0.360712	+	0.932677i	$0.382534\pi$
$588$		0			0
$589$	2592.00			0.181327
$590$	−16848.0	−	29181.6i	−1.17563	−	2.03625i
$591$	3693.00	−	6396.46i	0.257038	−	0.445204i
$592$	−5184.00	+	8978.95i	−0.359900	+	0.623366i
$593$	−1791.00	−	3102.10i	−0.124026	−	0.214820i	0.797326	−	0.603549i	$-0.206247\pi$
$593$	−1791.00	−	3102.10i	−0.124026	−	0.214820i	−0.921352	+	0.388730i	$0.872914\pi$
$594$	−5400.00			−0.373005
$595$		0			0
$596$	−19120.0			−1.31407
$597$	6804.00	+	11784.9i	0.466448	+	0.807911i
$598$	1008.00	−	1745.91i	0.0689301	−	0.119390i
$599$	−3517.00	+	6091.62i	−0.239901	+	0.415521i	−0.960686	−	0.277638i	$-0.910448\pi$
$599$	−3517.00	+	6091.62i	−0.239901	+	0.415521i	0.720785	+	0.693159i	$0.243782\pi$
$600$		0			0
$601$	−18072.0			−1.22658			−0.613288	−	0.789859i	$-0.710154\pi$
$601$	−18072.0			−1.22658			−0.613288	+	0.789859i	$0.710154\pi$
$602$		0			0
$603$	2088.00			0.141011
$604$	−12960.0	−	22447.4i	−0.873071	−	1.51220i
$605$	−10521.0	+	18222.9i	−0.707007	+	1.22457i
$606$	3996.00	−	6921.28i	0.267865	−	0.463956i
$607$	−14292.0	−	24754.5i	−0.955674	−	1.65528i	−0.732817	−	0.680426i	$-0.761795\pi$
$607$	−14292.0	−	24754.5i	−0.955674	−	1.65528i	−0.222857	−	0.974851i	$-0.571538\pi$
$608$	18432.0			1.22947
$609$		0			0
$610$	57024.0			3.78497
$611$	−1296.00	−	2244.74i	−0.0858110	−	0.148629i
$612$	−4536.00	+	7856.58i	−0.299603	+	0.518927i
$613$	5455.00	−	9448.34i	0.359421	−	0.622536i	−0.628443	−	0.777856i	$-0.716307\pi$
$613$	5455.00	−	9448.34i	0.359421	−	0.622536i	0.987864	+	0.155320i	$0.0496407\pi$
$614$	20448.0	+	35417.0i	1.34400	+	2.32787i
$615$	−14580.0			−0.955971
$616$		0			0
$617$	−5522.00			−0.360304			−0.180152	−	0.983639i	$-0.557659\pi$
$617$	−5522.00			−0.360304			−0.180152	+	0.983639i	$0.557659\pi$
$618$	1512.00	+	2618.86i	0.0984168	+	0.170463i
$619$	−1206.00	+	2088.85i	−0.0783089	+	0.135635i	−0.902520	−	0.430647i	$-0.858285\pi$
$619$	−1206.00	+	2088.85i	−0.0783089	+	0.135635i	0.824211	+	0.566282i	$0.191619\pi$
$620$	2592.00	−	4489.48i	0.167899	−	0.290809i
$621$	−189.000	−	327.358i	−0.0122131	−	0.0211536i
$622$	15552.0			1.00254
$623$		0			0
$624$	6912.00			0.443432
$625$	449.500	+	778.557i	0.0287680	+	0.0498276i
$626$	−10224.0	+	17708.5i	−0.652769	+	1.13063i
$627$	−5400.00	+	9353.07i	−0.343948	+	0.595735i
$628$	−12096.0	−	20950.9i	−0.768603	−	1.33126i
$629$	−20412.0			−1.29393
$630$		0			0
$631$	24676.0			1.55679			0.778396	−	0.627773i	$-0.216034\pi$
$631$	24676.0			1.55679			0.778396	+	0.627773i	$0.216034\pi$
$632$		0			0
$633$	−4374.00	+	7575.99i	−0.274646	+	0.475701i
$634$	20204.0	−	34994.4i	1.26562	−	2.19212i
$635$	−8244.00	−	14279.0i	−0.515202	−	0.892356i
$636$	−528.000			−0.0329191
$637$		0			0
$638$	−31600.0			−1.96090
$639$	3303.00	+	5720.96i	0.204483	+	0.354175i
$640$		0			0
$641$	13741.0	−	23800.1i	0.846703	−	1.46653i	−0.0374303	−	0.999299i	$-0.511917\pi$
$641$	13741.0	−	23800.1i	0.846703	−	1.46653i	0.884134	−	0.467234i	$-0.154749\pi$
$642$	−4020.00	−	6962.84i	−0.247129	−	0.428040i
$643$	−22752.0			−1.39541			−0.697707	−	0.716383i	$-0.745796\pi$
$643$	−22752.0			−1.39541			−0.697707	+	0.716383i	$0.745796\pi$
$644$		0			0
$645$	−17496.0			−1.06807
$646$	18144.0	+	31426.3i	1.10506	+	1.91401i
$647$	−7416.00	+	12844.9i	−0.450623	+	0.780502i	−0.998425	−	0.0561063i	$-0.982131\pi$
$647$	−7416.00	+	12844.9i	−0.450623	+	0.780502i	0.547802	+	0.836608i	$0.315465\pi$
$648$		0			0
$649$	11700.0	+	20265.0i	0.707650	+	1.22569i
$650$	−28656.0			−1.72920
$651$		0			0
$652$	−14272.0			−0.857262
$653$	−1411.00	−	2443.92i	−0.0845585	−	0.146460i	0.820645	−	0.571439i	$-0.193615\pi$
$653$	−1411.00	−	2443.92i	−0.0845585	−	0.146460i	−0.905203	+	0.424979i	$0.860281\pi$
$654$	−972.000	+	1683.55i	−0.0581165	+	0.100661i
$655$	−20412.0	+	35354.6i	−1.21765	+	2.10904i
$656$	−8640.00	−	14964.9i	−0.514231	−	0.890674i
$657$	1620.00			0.0961982
$658$		0			0
$659$	−15826.0			−0.935498			−0.467749	−	0.883861i	$-0.654935\pi$
$659$	−15826.0			−0.935498			−0.467749	+	0.883861i	$0.654935\pi$
$660$	10800.0	+	18706.1i	0.636954	+	1.10324i
$661$	11916.0	−	20639.1i	0.701178	−	1.21448i	−0.266875	−	0.963731i	$-0.585991\pi$
$661$	11916.0	−	20639.1i	0.701178	−	1.21448i	0.968053	−	0.250745i	$-0.0806755\pi$
$662$	−11016.0	+	19080.3i	−0.646751	+	1.12021i
$663$	6804.00	+	11784.9i	0.398560	+	0.690327i
$664$		0			0
$665$		0			0
$666$	−5832.00			−0.339317
$667$	−1106.00	−	1915.65i	−0.0642046	−	0.111206i
$668$	12096.0	−	20950.9i	0.700611	−	1.21349i
$669$	1620.00	−	2805.92i	0.0936216	−	0.162157i
$670$	−8352.00	−	14466.1i	−0.481591	−	0.834140i
$671$	−39600.0			−2.27830
$672$		0			0
$673$	13770.0			0.788699			0.394350	−	0.918961i	$-0.370970\pi$
$673$	13770.0			0.788699			0.394350	+	0.918961i	$0.370970\pi$
$674$	18468.0	+	31987.5i	1.05543	+	1.82806i
$675$	−2686.50	+	4653.15i	−0.153190	+	0.265333i
$676$	3604.00	−	6242.31i	0.205052	−	0.355161i
$677$	−4167.00	−	7217.46i	−0.236560	−	0.409733i	0.723165	−	0.690675i	$-0.242687\pi$
$677$	−4167.00	−	7217.46i	−0.236560	−	0.409733i	−0.959725	+	0.280942i	$0.909353\pi$
$678$	−16680.0			−0.944825
$679$		0			0
$680$		0			0
$681$	1998.00	+	3460.64i	0.112428	+	0.194731i
$682$	−3600.00	+	6235.38i	−0.202128	+	0.350096i
$683$	9299.00	−	16106.3i	0.520961	−	0.902331i	−0.478742	−	0.877956i	$-0.658907\pi$
$683$	9299.00	−	16106.3i	0.520961	−	0.902331i	0.999703	−	0.0243752i	$-0.00775963\pi$
$684$	2592.00	+	4489.48i	0.144894	+	0.250964i
$685$	14508.0			0.809229
$686$		0			0
$687$	4860.00			0.269899
$688$	−10368.0	−	17957.9i	−0.574529	−	0.995114i
$689$	−396.000	+	685.892i	−0.0218961	+	0.0379251i
$690$	−1512.00	+	2618.86i	−0.0834215	+	0.144490i
$691$	−4482.00	−	7763.05i	−0.246749	−	0.427381i	0.715873	−	0.698230i	$-0.246029\pi$
$691$	−4482.00	−	7763.05i	−0.246749	−	0.427381i	−0.962622	+	0.270849i	$0.912696\pi$
$692$	12528.0			0.688213
$693$		0			0
$694$	−25976.0			−1.42080
$695$	−23652.0	−	40966.5i	−1.29089	−	2.23589i
$696$		0			0
$697$	17010.0	−	29462.2i	0.924390	−	1.60109i
$698$	−20160.0	−	34918.1i	−1.09322	−	1.89351i
$699$	20154.0			1.09055
$700$		0			0
$701$	3542.00			0.190841			0.0954205	−	0.995437i	$-0.469580\pi$
$701$	3542.00			0.190841			0.0954205	+	0.995437i	$0.469580\pi$
$702$	1944.00	+	3367.11i	0.104518	+	0.181030i
$703$	−5832.00	+	10101.3i	−0.312885	+	0.541932i
$704$	−12800.0	+	22170.3i	−0.685253	+	1.18689i
$705$	1944.00	+	3367.11i	0.103851	+	0.179876i
$706$	−2952.00			−0.157365
$707$		0			0
$708$	11232.0			0.596221
$709$	243.000	+	420.888i	0.0128717	+	0.0222945i	0.872390	−	0.488811i	$-0.162569\pi$
$709$	243.000	+	420.888i	0.0128717	+	0.0222945i	−0.859518	+	0.511106i	$0.829236\pi$
$710$	26424.0	−	45767.7i	1.39673	−	2.41920i
$711$	−1062.00	+	1839.44i	−0.0560170	+	0.0970244i
$712$		0			0
$713$	−504.000			−0.0264726
$714$		0			0
$715$	32400.0			1.69467
$716$	−15208.0	−	26341.0i	−0.793784	−	1.37487i
$717$	5367.00	−	9295.92i	0.279546	−	0.484187i
$718$	−388.000	+	672.036i	−0.0201672	+	0.0349306i
$719$	13464.0	+	23320.3i	0.698362	+	1.20960i	0.969034	+	0.246927i	$0.0794209\pi$
$719$	13464.0	+	23320.3i	0.698362	+	1.20960i	−0.270672	+	0.962672i	$0.587246\pi$
$720$	−10368.0			−0.536656
$721$		0			0
$722$	−6700.00			−0.345358
$723$	1134.00	+	1964.15i	0.0583318	+	0.101034i
$724$	1872.00	−	3242.40i	0.0960944	−	0.166440i
$725$	−15721.0	+	27229.6i	−0.805329	+	1.39487i
$726$	−7014.00	−	12148.6i	−0.358559	−	0.621043i
$727$	20628.0			1.05234			0.526169	−	0.850380i	$-0.323628\pi$
$727$	20628.0			1.05234			0.526169	+	0.850380i	$0.323628\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−6480.00	−	11223.7i	−0.328542	−	0.569051i
$731$	20412.0	−	35354.6i	1.03278	−	1.78883i
$732$	−9504.00	+	16461.4i	−0.479888	+	0.831190i
$733$	4878.00	+	8448.94i	0.245802	+	0.425742i	0.962357	−	0.271789i	$-0.0876153\pi$
$733$	4878.00	+	8448.94i	0.245802	+	0.425742i	−0.716555	+	0.697531i	$0.754282\pi$
$734$	−19008.0			−0.955856
$735$		0			0
$736$	−3584.00			−0.179495
$737$	5800.00	+	10045.9i	0.289886	+	0.502097i
$738$	4860.00	−	8417.77i	0.242411	−	0.419868i
$739$	−9532.00	+	16509.9i	−0.474479	+	0.821822i	−0.999573	−	0.0292221i	$-0.990697\pi$
$739$	−9532.00	+	16509.9i	−0.474479	+	0.821822i	0.525094	+	0.851045i	$0.324030\pi$
$740$	11664.0	+	20202.6i	0.579429	+	1.00360i
$741$	7776.00			0.385504
$742$		0			0
$743$	−3766.00			−0.185950			−0.0929752	−	0.995668i	$-0.529638\pi$
$743$	−3766.00			−0.185950			−0.0929752	+	0.995668i	$0.529638\pi$
$744$		0			0
$745$	21510.0	−	37256.4i	1.05781	−	1.83217i
$746$	4612.00	−	7988.22i	0.226350	−	0.392050i
$747$	−162.000	−	280.592i	−0.00793477	−	0.0137434i
$748$	−50400.0			−2.46365
$749$		0			0
$750$	15984.0			0.778204
$751$	5832.00	+	10101.3i	0.283372	+	0.490815i	0.972213	−	0.234097i	$-0.0752134\pi$
$751$	5832.00	+	10101.3i	0.283372	+	0.490815i	−0.688841	+	0.724913i	$0.741880\pi$
$752$	−2304.00	+	3990.65i	−0.111726	+	0.193516i
$753$	9774.00	−	16929.1i	0.473020	−	0.819295i
$754$	11376.0	+	19703.8i	0.549456	+	0.951685i
$755$	58320.0			2.81123
$756$		0			0
$757$	−34182.0			−1.64117			−0.820585	−	0.571524i	$-0.806352\pi$
$757$	−34182.0			−1.64117			−0.820585	+	0.571524i	$0.806352\pi$
$758$	14904.0	+	25814.5i	0.714166	+	1.23697i
$759$	1050.00	−	1818.65i	0.0502142	−	0.0869736i
$760$		0			0
$761$	2367.00	+	4099.76i	0.112751	+	0.195291i	0.916879	−	0.399166i	$-0.130700\pi$
$761$	2367.00	+	4099.76i	0.112751	+	0.195291i	−0.804127	+	0.594457i	$0.797367\pi$
$762$	10992.0			0.522570
$763$		0			0
$764$	3856.00			0.182598
$765$	−10206.0	−	17677.3i	−0.482351	−	0.835457i
$766$	2304.00	−	3990.65i	0.108677	−	0.188235i
$767$	8424.00	−	14590.8i	0.396575	−	0.686888i
$768$	−6144.00	−	10641.7i	−0.288675	−	0.500000i
$769$	−30240.0			−1.41805			−0.709026	−	0.705182i	$-0.750865\pi$
$769$	−30240.0			−1.41805			−0.709026	+	0.705182i	$0.750865\pi$
$770$		0			0
$771$	−18090.0			−0.845001
$772$	3240.00	+	5611.84i	0.151049	+	0.261625i
$773$	−13851.0	+	23990.6i	−0.644484	+	1.11628i	0.339937	+	0.940448i	$0.389594\pi$
$773$	−13851.0	+	23990.6i	−0.644484	+	1.11628i	−0.984421	+	0.175830i	$0.943739\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +12.0000 q^{6} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-9.00000 - 15.5885i) q^{5} +12.0000 q^{6} +(-4.50000 - 7.79423i) q^{9} +(-36.0000 + 62.3538i) q^{10} +(25.0000 - 43.3013i) q^{11} +(-12.0000 - 20.7846i) q^{12} -36.0000 q^{13} +54.0000 q^{15} +(32.0000 + 55.4256i) q^{16} +(-63.0000 + 109.119i) q^{17} +(-18.0000 + 31.1769i) q^{18} +(36.0000 + 62.3538i) q^{19} +144.000 q^{20} -200.000 q^{22} +(-7.00000 - 12.1244i) q^{23} +(-99.5000 + 172.339i) q^{25} +(72.0000 + 124.708i) q^{26} +27.0000 q^{27} +158.000 q^{29} +(-108.000 - 187.061i) q^{30} +(18.0000 - 31.1769i) q^{31} +(128.000 - 221.703i) q^{32} +(75.0000 + 129.904i) q^{33} +504.000 q^{34} +72.0000 q^{36} +(81.0000 + 140.296i) q^{37} +(144.000 - 249.415i) q^{38} +(54.0000 - 93.5307i) q^{39} -270.000 q^{41} -324.000 q^{43} +(200.000 + 346.410i) q^{44} +(-81.0000 + 140.296i) q^{45} +(-28.0000 + 48.4974i) q^{46} +(36.0000 + 62.3538i) q^{47} -192.000 q^{48} +796.000 q^{50} +(-189.000 - 327.358i) q^{51} +(144.000 - 249.415i) q^{52} +(11.0000 - 19.0526i) q^{53} +(-54.0000 - 93.5307i) q^{54} -900.000 q^{55} -216.000 q^{57} +(-316.000 - 547.328i) q^{58} +(-234.000 + 405.300i) q^{59} +(-216.000 + 374.123i) q^{60} +(-396.000 - 685.892i) q^{61} -144.000 q^{62} -512.000 q^{64} +(324.000 + 561.184i) q^{65} +(300.000 - 519.615i) q^{66} +(-116.000 + 200.918i) q^{67} +(-504.000 - 872.954i) q^{68} +42.0000 q^{69} -734.000 q^{71} +(-90.0000 + 155.885i) q^{73} +(324.000 - 561.184i) q^{74} +(-298.500 - 517.017i) q^{75} -576.000 q^{76} -432.000 q^{78} +(-118.000 - 204.382i) q^{79} +(576.000 - 997.661i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(540.000 + 935.307i) q^{82} +36.0000 q^{83} +2268.00 q^{85} +(648.000 + 1122.37i) q^{86} +(-237.000 + 410.496i) q^{87} +(-117.000 - 202.650i) q^{89} +648.000 q^{90} +112.000 q^{92} +(54.0000 + 93.5307i) q^{93} +(144.000 - 249.415i) q^{94} +(648.000 - 1122.37i) q^{95} +(384.000 + 665.108i) q^{96} +468.000 q^{97} -450.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 3 q^{3} - 8 q^{4} - 18 q^{5} + 24 q^{6} - 9 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 3 * q^3 - 8 * q^4 - 18 * q^5 + 24 * q^6 - 9 * q^9	\( 2 q - 4 q^{2} - 3 q^{3} - 8 q^{4} - 18 q^{5} + 24 q^{6} - 9 q^{9} - 72 q^{10} + 50 q^{11} - 24 q^{12} - 72 q^{13} + 108 q^{15} + 64 q^{16} - 126 q^{17} - 36 q^{18} + 72 q^{19} + 288 q^{20} - 400 q^{22} - 14 q^{23} - 199 q^{25} + 144 q^{26} + 54 q^{27} + 316 q^{29} - 216 q^{30} + 36 q^{31} + 256 q^{32} + 150 q^{33} + 1008 q^{34} + 144 q^{36} + 162 q^{37} + 288 q^{38} + 108 q^{39} - 540 q^{41} - 648 q^{43} + 400 q^{44} - 162 q^{45} - 56 q^{46} + 72 q^{47} - 384 q^{48} + 1592 q^{50} - 378 q^{51} + 288 q^{52} + 22 q^{53} - 108 q^{54} - 1800 q^{55} - 432 q^{57} - 632 q^{58} - 468 q^{59} - 432 q^{60} - 792 q^{61} - 288 q^{62} - 1024 q^{64} + 648 q^{65} + 600 q^{66} - 232 q^{67} - 1008 q^{68} + 84 q^{69} - 1468 q^{71} - 180 q^{73} + 648 q^{74} - 597 q^{75} - 1152 q^{76} - 864 q^{78} - 236 q^{79} + 1152 q^{80} - 81 q^{81} + 1080 q^{82} + 72 q^{83} + 4536 q^{85} + 1296 q^{86} - 474 q^{87} - 234 q^{89} + 1296 q^{90} + 224 q^{92} + 108 q^{93} + 288 q^{94} + 1296 q^{95} + 768 q^{96} + 936 q^{97} - 900 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 3 * q^3 - 8 * q^4 - 18 * q^5 + 24 * q^6 - 9 * q^9 - 72 * q^10 + 50 * q^11 - 24 * q^12 - 72 * q^13 + 108 * q^15 + 64 * q^16 - 126 * q^17 - 36 * q^18 + 72 * q^19 + 288 * q^20 - 400 * q^22 - 14 * q^23 - 199 * q^25 + 144 * q^26 + 54 * q^27 + 316 * q^29 - 216 * q^30 + 36 * q^31 + 256 * q^32 + 150 * q^33 + 1008 * q^34 + 144 * q^36 + 162 * q^37 + 288 * q^38 + 108 * q^39 - 540 * q^41 - 648 * q^43 + 400 * q^44 - 162 * q^45 - 56 * q^46 + 72 * q^47 - 384 * q^48 + 1592 * q^50 - 378 * q^51 + 288 * q^52 + 22 * q^53 - 108 * q^54 - 1800 * q^55 - 432 * q^57 - 632 * q^58 - 468 * q^59 - 432 * q^60 - 792 * q^61 - 288 * q^62 - 1024 * q^64 + 648 * q^65 + 600 * q^66 - 232 * q^67 - 1008 * q^68 + 84 * q^69 - 1468 * q^71 - 180 * q^73 + 648 * q^74 - 597 * q^75 - 1152 * q^76 - 864 * q^78 - 236 * q^79 + 1152 * q^80 - 81 * q^81 + 1080 * q^82 + 72 * q^83 + 4536 * q^85 + 1296 * q^86 - 474 * q^87 - 234 * q^89 + 1296 * q^90 + 224 * q^92 + 108 * q^93 + 288 * q^94 + 1296 * q^95 + 768 * q^96 + 936 * q^97 - 900 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more